Properties

Label 1350.2.q.f.1043.1
Level $1350$
Weight $2$
Character 1350.1043
Analytic conductor $10.780$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(143,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.q (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 450)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1043.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1350.1043
Dual form 1350.2.q.f.1007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(3.34607 + 0.896575i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(3.34607 + 0.896575i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.50000 - 0.866025i) q^{11} +(3.34607 - 0.896575i) q^{13} +(-1.73205 + 3.00000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.12132 - 2.12132i) q^{17} +7.00000i q^{19} +(0.448288 + 1.67303i) q^{22} +(-1.55291 - 5.79555i) q^{23} +3.46410i q^{26} +(-2.44949 - 2.44949i) q^{28} +(-1.73205 - 3.00000i) q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.59808 - 1.50000i) q^{34} +(4.89898 - 4.89898i) q^{37} +(-6.76148 - 1.81173i) q^{38} +(10.5000 + 6.06218i) q^{41} +(-1.34486 + 5.01910i) q^{43} -1.73205 q^{44} +6.00000 q^{46} +(1.55291 - 5.79555i) q^{47} +(4.33013 + 2.50000i) q^{49} +(-3.34607 - 0.896575i) q^{52} +(3.00000 - 1.73205i) q^{56} +(3.34607 - 0.896575i) q^{58} +(-6.06218 + 10.5000i) q^{59} +(2.00000 + 3.46410i) q^{61} +(5.65685 + 5.65685i) q^{62} -1.00000i q^{64} +(0.448288 + 1.67303i) q^{67} +(0.776457 + 2.89778i) q^{68} +13.8564i q^{71} +(-6.12372 - 6.12372i) q^{73} +(3.46410 + 6.00000i) q^{74} +(3.50000 - 6.06218i) q^{76} +(5.79555 - 1.55291i) q^{77} +(-3.46410 + 2.00000i) q^{79} +(-8.57321 + 8.57321i) q^{82} +(11.5911 + 3.10583i) q^{83} +(-4.50000 - 2.59808i) q^{86} +(0.448288 - 1.67303i) q^{88} +6.92820 q^{89} +12.0000 q^{91} +(-1.55291 + 5.79555i) q^{92} +(5.19615 + 3.00000i) q^{94} +(-8.36516 - 2.24144i) q^{97} +(-3.53553 + 3.53553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{11} + 4 q^{16} + 32 q^{31} + 84 q^{41} + 48 q^{46} + 24 q^{56} + 16 q^{61} + 28 q^{76} - 36 q^{86} + 96 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.183013 + 0.683013i
\(3\) 0 0
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 0 0
\(6\) 0 0
\(7\) 3.34607 + 0.896575i 1.26469 + 0.338874i 0.827996 0.560734i \(-0.189481\pi\)
0.436698 + 0.899608i \(0.356148\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 0.866025i 0.452267 0.261116i −0.256520 0.966539i \(-0.582576\pi\)
0.708787 + 0.705422i \(0.249243\pi\)
\(12\) 0 0
\(13\) 3.34607 0.896575i 0.928032 0.248665i 0.237016 0.971506i \(-0.423830\pi\)
0.691015 + 0.722840i \(0.257164\pi\)
\(14\) −1.73205 + 3.00000i −0.462910 + 0.801784i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −2.12132 2.12132i −0.514496 0.514496i 0.401405 0.915901i \(-0.368522\pi\)
−0.915901 + 0.401405i \(0.868522\pi\)
\(18\) 0 0
\(19\) 7.00000i 1.60591i 0.596040 + 0.802955i \(0.296740\pi\)
−0.596040 + 0.802955i \(0.703260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.448288 + 1.67303i 0.0955753 + 0.356692i
\(23\) −1.55291 5.79555i −0.323805 1.20846i −0.915508 0.402300i \(-0.868211\pi\)
0.591703 0.806156i \(-0.298456\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.46410i 0.679366i
\(27\) 0 0
\(28\) −2.44949 2.44949i −0.462910 0.462910i
\(29\) −1.73205 3.00000i −0.321634 0.557086i 0.659192 0.751975i \(-0.270899\pi\)
−0.980825 + 0.194889i \(0.937565\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) −0.965926 + 0.258819i −0.170753 + 0.0457532i
\(33\) 0 0
\(34\) 2.59808 1.50000i 0.445566 0.257248i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.89898 4.89898i 0.805387 0.805387i −0.178545 0.983932i \(-0.557139\pi\)
0.983932 + 0.178545i \(0.0571389\pi\)
\(38\) −6.76148 1.81173i −1.09686 0.293902i
\(39\) 0 0
\(40\) 0 0
\(41\) 10.5000 + 6.06218i 1.63982 + 0.946753i 0.980892 + 0.194551i \(0.0623249\pi\)
0.658932 + 0.752202i \(0.271008\pi\)
\(42\) 0 0
\(43\) −1.34486 + 5.01910i −0.205090 + 0.765405i 0.784332 + 0.620341i \(0.213006\pi\)
−0.989422 + 0.145065i \(0.953661\pi\)
\(44\) −1.73205 −0.261116
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 1.55291 5.79555i 0.226516 0.845369i −0.755276 0.655407i \(-0.772497\pi\)
0.981792 0.189961i \(-0.0608363\pi\)
\(48\) 0 0
\(49\) 4.33013 + 2.50000i 0.618590 + 0.357143i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.34607 0.896575i −0.464016 0.124333i
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 3.00000 1.73205i 0.400892 0.231455i
\(57\) 0 0
\(58\) 3.34607 0.896575i 0.439360 0.117726i
\(59\) −6.06218 + 10.5000i −0.789228 + 1.36698i 0.137212 + 0.990542i \(0.456186\pi\)
−0.926440 + 0.376442i \(0.877147\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) 5.65685 + 5.65685i 0.718421 + 0.718421i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.448288 + 1.67303i 0.0547671 + 0.204393i 0.987888 0.155170i \(-0.0495924\pi\)
−0.933121 + 0.359563i \(0.882926\pi\)
\(68\) 0.776457 + 2.89778i 0.0941593 + 0.351407i
\(69\) 0 0
\(70\) 0 0
\(71\) 13.8564i 1.64445i 0.569160 + 0.822226i \(0.307268\pi\)
−0.569160 + 0.822226i \(0.692732\pi\)
\(72\) 0 0
\(73\) −6.12372 6.12372i −0.716728 0.716728i 0.251206 0.967934i \(-0.419173\pi\)
−0.967934 + 0.251206i \(0.919173\pi\)
\(74\) 3.46410 + 6.00000i 0.402694 + 0.697486i
\(75\) 0 0
\(76\) 3.50000 6.06218i 0.401478 0.695379i
\(77\) 5.79555 1.55291i 0.660465 0.176971i
\(78\) 0 0
\(79\) −3.46410 + 2.00000i −0.389742 + 0.225018i −0.682048 0.731307i \(-0.738911\pi\)
0.292306 + 0.956325i \(0.405577\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −8.57321 + 8.57321i −0.946753 + 0.946753i
\(83\) 11.5911 + 3.10583i 1.27229 + 0.340909i 0.830908 0.556410i \(-0.187822\pi\)
0.441382 + 0.897319i \(0.354488\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.50000 2.59808i −0.485247 0.280158i
\(87\) 0 0
\(88\) 0.448288 1.67303i 0.0477876 0.178346i
\(89\) 6.92820 0.734388 0.367194 0.930144i \(-0.380318\pi\)
0.367194 + 0.930144i \(0.380318\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) −1.55291 + 5.79555i −0.161903 + 0.604228i
\(93\) 0 0
\(94\) 5.19615 + 3.00000i 0.535942 + 0.309426i
\(95\) 0 0
\(96\) 0 0
\(97\) −8.36516 2.24144i −0.849354 0.227584i −0.192215 0.981353i \(-0.561567\pi\)
−0.657139 + 0.753769i \(0.728234\pi\)
\(98\) −3.53553 + 3.53553i −0.357143 + 0.357143i
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 3.46410i 0.597022 0.344691i −0.170847 0.985298i \(-0.554650\pi\)
0.767869 + 0.640607i \(0.221317\pi\)
\(102\) 0 0
\(103\) 16.7303 4.48288i 1.64849 0.441711i 0.689299 0.724477i \(-0.257919\pi\)
0.959189 + 0.282766i \(0.0912520\pi\)
\(104\) 1.73205 3.00000i 0.169842 0.294174i
\(105\) 0 0
\(106\) 0 0
\(107\) −2.12132 2.12132i −0.205076 0.205076i 0.597095 0.802171i \(-0.296322\pi\)
−0.802171 + 0.597095i \(0.796322\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.896575 + 3.34607i 0.0847184 + 0.316173i
\(113\) 4.65874 + 17.3867i 0.438258 + 1.63560i 0.733148 + 0.680069i \(0.238050\pi\)
−0.294891 + 0.955531i \(0.595283\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.46410i 0.321634i
\(117\) 0 0
\(118\) −8.57321 8.57321i −0.789228 0.789228i
\(119\) −5.19615 9.00000i −0.476331 0.825029i
\(120\) 0 0
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) −3.86370 + 1.03528i −0.349803 + 0.0937295i
\(123\) 0 0
\(124\) −6.92820 + 4.00000i −0.622171 + 0.359211i
\(125\) 0 0
\(126\) 0 0
\(127\) 7.34847 7.34847i 0.652071 0.652071i −0.301420 0.953491i \(-0.597461\pi\)
0.953491 + 0.301420i \(0.0974607\pi\)
\(128\) 0.965926 + 0.258819i 0.0853766 + 0.0228766i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 1.73205i −0.262111 0.151330i 0.363186 0.931717i \(-0.381689\pi\)
−0.625297 + 0.780387i \(0.715022\pi\)
\(132\) 0 0
\(133\) −6.27603 + 23.4225i −0.544201 + 2.03098i
\(134\) −1.73205 −0.149626
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 0.776457 2.89778i 0.0663372 0.247574i −0.924793 0.380472i \(-0.875762\pi\)
0.991130 + 0.132898i \(0.0424283\pi\)
\(138\) 0 0
\(139\) 4.33013 + 2.50000i 0.367277 + 0.212047i 0.672268 0.740308i \(-0.265320\pi\)
−0.304991 + 0.952355i \(0.598654\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −13.3843 3.58630i −1.12318 0.300956i
\(143\) 4.24264 4.24264i 0.354787 0.354787i
\(144\) 0 0
\(145\) 0 0
\(146\) 7.50000 4.33013i 0.620704 0.358364i
\(147\) 0 0
\(148\) −6.69213 + 1.79315i −0.550090 + 0.147396i
\(149\) −5.19615 + 9.00000i −0.425685 + 0.737309i −0.996484 0.0837813i \(-0.973300\pi\)
0.570799 + 0.821090i \(0.306634\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 4.94975 + 4.94975i 0.401478 + 0.401478i
\(153\) 0 0
\(154\) 6.00000i 0.483494i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(158\) −1.03528 3.86370i −0.0823622 0.307380i
\(159\) 0 0
\(160\) 0 0
\(161\) 20.7846i 1.63806i
\(162\) 0 0
\(163\) 2.44949 + 2.44949i 0.191859 + 0.191859i 0.796499 0.604640i \(-0.206683\pi\)
−0.604640 + 0.796499i \(0.706683\pi\)
\(164\) −6.06218 10.5000i −0.473377 0.819912i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(168\) 0 0
\(169\) −0.866025 + 0.500000i −0.0666173 + 0.0384615i
\(170\) 0 0
\(171\) 0 0
\(172\) 3.67423 3.67423i 0.280158 0.280158i
\(173\) −5.79555 1.55291i −0.440628 0.118066i 0.0316829 0.999498i \(-0.489913\pi\)
−0.472311 + 0.881432i \(0.656580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.50000 + 0.866025i 0.113067 + 0.0652791i
\(177\) 0 0
\(178\) −1.79315 + 6.69213i −0.134402 + 0.501596i
\(179\) 3.46410 0.258919 0.129460 0.991585i \(-0.458676\pi\)
0.129460 + 0.991585i \(0.458676\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −3.10583 + 11.5911i −0.230219 + 0.859190i
\(183\) 0 0
\(184\) −5.19615 3.00000i −0.383065 0.221163i
\(185\) 0 0
\(186\) 0 0
\(187\) −5.01910 1.34486i −0.367033 0.0983461i
\(188\) −4.24264 + 4.24264i −0.309426 + 0.309426i
\(189\) 0 0
\(190\) 0 0
\(191\) −21.0000 + 12.1244i −1.51951 + 0.877288i −0.519771 + 0.854306i \(0.673983\pi\)
−0.999736 + 0.0229818i \(0.992684\pi\)
\(192\) 0 0
\(193\) −8.36516 + 2.24144i −0.602138 + 0.161342i −0.546995 0.837136i \(-0.684228\pi\)
−0.0551431 + 0.998478i \(0.517561\pi\)
\(194\) 4.33013 7.50000i 0.310885 0.538469i
\(195\) 0 0
\(196\) −2.50000 4.33013i −0.178571 0.309295i
\(197\) −16.9706 16.9706i −1.20910 1.20910i −0.971318 0.237785i \(-0.923579\pi\)
−0.237785 0.971318i \(-0.576421\pi\)
\(198\) 0 0
\(199\) 10.0000i 0.708881i −0.935079 0.354441i \(-0.884671\pi\)
0.935079 0.354441i \(-0.115329\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1.79315 + 6.69213i 0.126166 + 0.470857i
\(203\) −3.10583 11.5911i −0.217986 0.813536i
\(204\) 0 0
\(205\) 0 0
\(206\) 17.3205i 1.20678i
\(207\) 0 0
\(208\) 2.44949 + 2.44949i 0.169842 + 0.169842i
\(209\) 6.06218 + 10.5000i 0.419330 + 0.726300i
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 2.59808 1.50000i 0.177601 0.102538i
\(215\) 0 0
\(216\) 0 0
\(217\) 19.5959 19.5959i 1.33026 1.33026i
\(218\) 3.86370 + 1.03528i 0.261683 + 0.0701178i
\(219\) 0 0
\(220\) 0 0
\(221\) −9.00000 5.19615i −0.605406 0.349531i
\(222\) 0 0
\(223\) −2.68973 + 10.0382i −0.180117 + 0.672207i 0.815506 + 0.578749i \(0.196459\pi\)
−0.995623 + 0.0934584i \(0.970208\pi\)
\(224\) −3.46410 −0.231455
\(225\) 0 0
\(226\) −18.0000 −1.19734
\(227\) 0.776457 2.89778i 0.0515353 0.192332i −0.935359 0.353699i \(-0.884924\pi\)
0.986894 + 0.161367i \(0.0515903\pi\)
\(228\) 0 0
\(229\) −19.0526 11.0000i −1.25903 0.726900i −0.286143 0.958187i \(-0.592373\pi\)
−0.972886 + 0.231287i \(0.925707\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.34607 0.896575i −0.219680 0.0588631i
\(233\) 2.12132 2.12132i 0.138972 0.138972i −0.634198 0.773171i \(-0.718670\pi\)
0.773171 + 0.634198i \(0.218670\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 10.5000 6.06218i 0.683492 0.394614i
\(237\) 0 0
\(238\) 10.0382 2.68973i 0.650680 0.174349i
\(239\) 5.19615 9.00000i 0.336111 0.582162i −0.647586 0.761992i \(-0.724222\pi\)
0.983698 + 0.179830i \(0.0575549\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) −5.65685 5.65685i −0.363636 0.363636i
\(243\) 0 0
\(244\) 4.00000i 0.256074i
\(245\) 0 0
\(246\) 0 0
\(247\) 6.27603 + 23.4225i 0.399334 + 1.49034i
\(248\) −2.07055 7.72741i −0.131480 0.490691i
\(249\) 0 0
\(250\) 0 0
\(251\) 25.9808i 1.63989i −0.572441 0.819946i \(-0.694004\pi\)
0.572441 0.819946i \(-0.305996\pi\)
\(252\) 0 0
\(253\) −7.34847 7.34847i −0.461994 0.461994i
\(254\) 5.19615 + 9.00000i 0.326036 + 0.564710i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −26.0800 + 6.98811i −1.62683 + 0.435907i −0.952997 0.302981i \(-0.902018\pi\)
−0.673829 + 0.738887i \(0.735352\pi\)
\(258\) 0 0
\(259\) 20.7846 12.0000i 1.29149 0.745644i
\(260\) 0 0
\(261\) 0 0
\(262\) 2.44949 2.44949i 0.151330 0.151330i
\(263\) 5.79555 + 1.55291i 0.357369 + 0.0957568i 0.433037 0.901376i \(-0.357442\pi\)
−0.0756674 + 0.997133i \(0.524109\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −21.0000 12.1244i −1.28759 0.743392i
\(267\) 0 0
\(268\) 0.448288 1.67303i 0.0273835 0.102197i
\(269\) 6.92820 0.422420 0.211210 0.977441i \(-0.432260\pi\)
0.211210 + 0.977441i \(0.432260\pi\)
\(270\) 0 0
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0.776457 2.89778i 0.0470796 0.175704i
\(273\) 0 0
\(274\) 2.59808 + 1.50000i 0.156956 + 0.0906183i
\(275\) 0 0
\(276\) 0 0
\(277\) 10.0382 + 2.68973i 0.603137 + 0.161610i 0.547450 0.836838i \(-0.315599\pi\)
0.0556866 + 0.998448i \(0.482265\pi\)
\(278\) −3.53553 + 3.53553i −0.212047 + 0.212047i
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 + 10.3923i −1.07379 + 0.619953i −0.929214 0.369541i \(-0.879515\pi\)
−0.144575 + 0.989494i \(0.546182\pi\)
\(282\) 0 0
\(283\) 30.1146 8.06918i 1.79013 0.479663i 0.797759 0.602977i \(-0.206019\pi\)
0.992368 + 0.123314i \(0.0393522\pi\)
\(284\) 6.92820 12.0000i 0.411113 0.712069i
\(285\) 0 0
\(286\) 3.00000 + 5.19615i 0.177394 + 0.307255i
\(287\) 29.6985 + 29.6985i 1.75305 + 1.75305i
\(288\) 0 0
\(289\) 8.00000i 0.470588i
\(290\) 0 0
\(291\) 0 0
\(292\) 2.24144 + 8.36516i 0.131170 + 0.489534i
\(293\) 1.55291 + 5.79555i 0.0907222 + 0.338580i 0.996336 0.0855230i \(-0.0272561\pi\)
−0.905614 + 0.424103i \(0.860589\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6.92820i 0.402694i
\(297\) 0 0
\(298\) −7.34847 7.34847i −0.425685 0.425685i
\(299\) −10.3923 18.0000i −0.601003 1.04097i
\(300\) 0 0
\(301\) −9.00000 + 15.5885i −0.518751 + 0.898504i
\(302\) 9.65926 2.58819i 0.555828 0.148934i
\(303\) 0 0
\(304\) −6.06218 + 3.50000i −0.347690 + 0.200739i
\(305\) 0 0
\(306\) 0 0
\(307\) −3.67423 + 3.67423i −0.209700 + 0.209700i −0.804140 0.594440i \(-0.797374\pi\)
0.594440 + 0.804140i \(0.297374\pi\)
\(308\) −5.79555 1.55291i −0.330232 0.0884855i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.00000 + 1.73205i 0.170114 + 0.0982156i 0.582640 0.812731i \(-0.302020\pi\)
−0.412525 + 0.910946i \(0.635353\pi\)
\(312\) 0 0
\(313\) 2.24144 8.36516i 0.126694 0.472827i −0.873201 0.487361i \(-0.837960\pi\)
0.999894 + 0.0145337i \(0.00462638\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 1.55291 5.79555i 0.0872204 0.325511i −0.908505 0.417874i \(-0.862775\pi\)
0.995725 + 0.0923631i \(0.0294421\pi\)
\(318\) 0 0
\(319\) −5.19615 3.00000i −0.290929 0.167968i
\(320\) 0 0
\(321\) 0 0
\(322\) 20.0764 + 5.37945i 1.11881 + 0.299785i
\(323\) 14.8492 14.8492i 0.826234 0.826234i
\(324\) 0 0
\(325\) 0 0
\(326\) −3.00000 + 1.73205i −0.166155 + 0.0959294i
\(327\) 0 0
\(328\) 11.7112 3.13801i 0.646644 0.173268i
\(329\) 10.3923 18.0000i 0.572946 0.992372i
\(330\) 0 0
\(331\) 14.0000 + 24.2487i 0.769510 + 1.33283i 0.937829 + 0.347097i \(0.112833\pi\)
−0.168320 + 0.985732i \(0.553834\pi\)
\(332\) −8.48528 8.48528i −0.465690 0.465690i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.13801 11.7112i −0.170939 0.637951i −0.997208 0.0746760i \(-0.976208\pi\)
0.826269 0.563275i \(-0.190459\pi\)
\(338\) −0.258819 0.965926i −0.0140779 0.0525394i
\(339\) 0 0
\(340\) 0 0
\(341\) 13.8564i 0.750366i
\(342\) 0 0
\(343\) −4.89898 4.89898i −0.264520 0.264520i
\(344\) 2.59808 + 4.50000i 0.140079 + 0.242624i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 14.4889 3.88229i 0.777804 0.208412i 0.151988 0.988382i \(-0.451433\pi\)
0.625816 + 0.779970i \(0.284766\pi\)
\(348\) 0 0
\(349\) −6.92820 + 4.00000i −0.370858 + 0.214115i −0.673833 0.738883i \(-0.735353\pi\)
0.302975 + 0.952998i \(0.402020\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.22474 + 1.22474i −0.0652791 + 0.0652791i
\(353\) −20.2844 5.43520i −1.07963 0.289287i −0.325187 0.945650i \(-0.605427\pi\)
−0.754445 + 0.656363i \(0.772094\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 3.46410i −0.317999 0.183597i
\(357\) 0 0
\(358\) −0.896575 + 3.34607i −0.0473855 + 0.176845i
\(359\) 24.2487 1.27980 0.639899 0.768459i \(-0.278976\pi\)
0.639899 + 0.768459i \(0.278976\pi\)
\(360\) 0 0
\(361\) −30.0000 −1.57895
\(362\) 0.517638 1.93185i 0.0272065 0.101536i
\(363\) 0 0
\(364\) −10.3923 6.00000i −0.544705 0.314485i
\(365\) 0 0
\(366\) 0 0
\(367\) −13.3843 3.58630i −0.698653 0.187203i −0.108026 0.994148i \(-0.534453\pi\)
−0.590627 + 0.806945i \(0.701120\pi\)
\(368\) 4.24264 4.24264i 0.221163 0.221163i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −16.7303 + 4.48288i −0.866263 + 0.232115i −0.664471 0.747314i \(-0.731343\pi\)
−0.201792 + 0.979428i \(0.564677\pi\)
\(374\) 2.59808 4.50000i 0.134343 0.232689i
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) −8.48528 8.48528i −0.437014 0.437014i
\(378\) 0 0
\(379\) 1.00000i 0.0513665i 0.999670 + 0.0256833i \(0.00817614\pi\)
−0.999670 + 0.0256833i \(0.991824\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −6.27603 23.4225i −0.321110 1.19840i
\(383\) −3.10583 11.5911i −0.158700 0.592278i −0.998760 0.0497839i \(-0.984147\pi\)
0.840060 0.542494i \(-0.182520\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.66025i 0.440795i
\(387\) 0 0
\(388\) 6.12372 + 6.12372i 0.310885 + 0.310885i
\(389\) 5.19615 + 9.00000i 0.263455 + 0.456318i 0.967158 0.254177i \(-0.0818045\pi\)
−0.703702 + 0.710495i \(0.748471\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) 4.82963 1.29410i 0.243933 0.0653617i
\(393\) 0 0
\(394\) 20.7846 12.0000i 1.04711 0.604551i
\(395\) 0 0
\(396\) 0 0
\(397\) −14.6969 + 14.6969i −0.737618 + 0.737618i −0.972117 0.234498i \(-0.924655\pi\)
0.234498 + 0.972117i \(0.424655\pi\)
\(398\) 9.65926 + 2.58819i 0.484175 + 0.129734i
\(399\) 0 0
\(400\) 0 0
\(401\) 4.50000 + 2.59808i 0.224719 + 0.129742i 0.608134 0.793835i \(-0.291919\pi\)
−0.383414 + 0.923576i \(0.625252\pi\)
\(402\) 0 0
\(403\) 7.17260 26.7685i 0.357293 1.33344i
\(404\) −6.92820 −0.344691
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) 3.10583 11.5911i 0.153950 0.574550i
\(408\) 0 0
\(409\) −6.06218 3.50000i −0.299755 0.173064i 0.342578 0.939490i \(-0.388700\pi\)
−0.642333 + 0.766426i \(0.722033\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −16.7303 4.48288i −0.824244 0.220856i
\(413\) −29.6985 + 29.6985i −1.46137 + 1.46137i
\(414\) 0 0
\(415\) 0 0
\(416\) −3.00000 + 1.73205i −0.147087 + 0.0849208i
\(417\) 0 0
\(418\) −11.7112 + 3.13801i −0.572815 + 0.153485i
\(419\) −5.19615 + 9.00000i −0.253849 + 0.439679i −0.964582 0.263783i \(-0.915030\pi\)
0.710734 + 0.703461i \(0.248363\pi\)
\(420\) 0 0
\(421\) −14.0000 24.2487i −0.682318 1.18181i −0.974272 0.225377i \(-0.927639\pi\)
0.291953 0.956433i \(-0.405695\pi\)
\(422\) 2.82843 + 2.82843i 0.137686 + 0.137686i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.58630 + 13.3843i 0.173553 + 0.647710i
\(428\) 0.776457 + 2.89778i 0.0375315 + 0.140069i
\(429\) 0 0
\(430\) 0 0
\(431\) 3.46410i 0.166860i 0.996514 + 0.0834300i \(0.0265875\pi\)
−0.996514 + 0.0834300i \(0.973413\pi\)
\(432\) 0 0
\(433\) −18.3712 18.3712i −0.882862 0.882862i 0.110962 0.993825i \(-0.464607\pi\)
−0.993825 + 0.110962i \(0.964607\pi\)
\(434\) 13.8564 + 24.0000i 0.665129 + 1.15204i
\(435\) 0 0
\(436\) −2.00000 + 3.46410i −0.0957826 + 0.165900i
\(437\) 40.5689 10.8704i 1.94067 0.520002i
\(438\) 0 0
\(439\) −13.8564 + 8.00000i −0.661330 + 0.381819i −0.792784 0.609503i \(-0.791369\pi\)
0.131453 + 0.991322i \(0.458036\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 7.34847 7.34847i 0.349531 0.349531i
\(443\) −26.0800 6.98811i −1.23910 0.332015i −0.420982 0.907069i \(-0.638315\pi\)
−0.818116 + 0.575054i \(0.804981\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −9.00000 5.19615i −0.426162 0.246045i
\(447\) 0 0
\(448\) 0.896575 3.34607i 0.0423592 0.158087i
\(449\) −39.8372 −1.88003 −0.940016 0.341130i \(-0.889190\pi\)
−0.940016 + 0.341130i \(0.889190\pi\)
\(450\) 0 0
\(451\) 21.0000 0.988851
\(452\) 4.65874 17.3867i 0.219129 0.817800i
\(453\) 0 0
\(454\) 2.59808 + 1.50000i 0.121934 + 0.0703985i
\(455\) 0 0
\(456\) 0 0
\(457\) −25.0955 6.72432i −1.17392 0.314550i −0.381406 0.924408i \(-0.624560\pi\)
−0.792511 + 0.609857i \(0.791227\pi\)
\(458\) 15.5563 15.5563i 0.726900 0.726900i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 + 8.66025i −0.698620 + 0.403348i −0.806833 0.590779i \(-0.798820\pi\)
0.108213 + 0.994128i \(0.465487\pi\)
\(462\) 0 0
\(463\) 13.3843 3.58630i 0.622019 0.166670i 0.0659737 0.997821i \(-0.478985\pi\)
0.556046 + 0.831152i \(0.312318\pi\)
\(464\) 1.73205 3.00000i 0.0804084 0.139272i
\(465\) 0 0
\(466\) 1.50000 + 2.59808i 0.0694862 + 0.120354i
\(467\) 6.36396 + 6.36396i 0.294489 + 0.294489i 0.838851 0.544362i \(-0.183228\pi\)
−0.544362 + 0.838851i \(0.683228\pi\)
\(468\) 0 0
\(469\) 6.00000i 0.277054i
\(470\) 0 0
\(471\) 0 0
\(472\) 3.13801 + 11.7112i 0.144439 + 0.539053i
\(473\) 2.32937 + 8.69333i 0.107105 + 0.399720i
\(474\) 0 0
\(475\) 0 0
\(476\) 10.3923i 0.476331i
\(477\) 0 0
\(478\) 7.34847 + 7.34847i 0.336111 + 0.336111i
\(479\) −8.66025 15.0000i −0.395697 0.685367i 0.597493 0.801874i \(-0.296164\pi\)
−0.993190 + 0.116507i \(0.962830\pi\)
\(480\) 0 0
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) −0.965926 + 0.258819i −0.0439967 + 0.0117889i
\(483\) 0 0
\(484\) 6.92820 4.00000i 0.314918 0.181818i
\(485\) 0 0
\(486\) 0 0
\(487\) −17.1464 + 17.1464i −0.776979 + 0.776979i −0.979316 0.202337i \(-0.935146\pi\)
0.202337 + 0.979316i \(0.435146\pi\)
\(488\) 3.86370 + 1.03528i 0.174902 + 0.0468648i
\(489\) 0 0
\(490\) 0 0
\(491\) 19.5000 + 11.2583i 0.880023 + 0.508081i 0.870666 0.491875i \(-0.163688\pi\)
0.00935679 + 0.999956i \(0.497022\pi\)
\(492\) 0 0
\(493\) −2.68973 + 10.0382i −0.121139 + 0.452098i
\(494\) −24.2487 −1.09100
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) −12.4233 + 46.3644i −0.557262 + 2.07973i
\(498\) 0 0
\(499\) 16.4545 + 9.50000i 0.736604 + 0.425278i 0.820833 0.571168i \(-0.193510\pi\)
−0.0842294 + 0.996446i \(0.526843\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 25.0955 + 6.72432i 1.12007 + 0.300121i
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 9.00000 5.19615i 0.400099 0.230997i
\(507\) 0 0
\(508\) −10.0382 + 2.68973i −0.445373 + 0.119337i
\(509\) 10.3923 18.0000i 0.460631 0.797836i −0.538362 0.842714i \(-0.680957\pi\)
0.998992 + 0.0448779i \(0.0142899\pi\)
\(510\) 0 0
\(511\) −15.0000 25.9808i −0.663561 1.14932i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 27.0000i 1.19092i
\(515\) 0 0
\(516\) 0 0
\(517\) −2.68973 10.0382i −0.118294 0.441479i
\(518\) 6.21166 + 23.1822i 0.272925 + 1.01857i
\(519\) 0 0
\(520\) 0 0
\(521\) 5.19615i 0.227648i −0.993501 0.113824i \(-0.963690\pi\)
0.993501 0.113824i \(-0.0363099\pi\)
\(522\) 0 0
\(523\) 12.2474 + 12.2474i 0.535544 + 0.535544i 0.922217 0.386673i \(-0.126376\pi\)
−0.386673 + 0.922217i \(0.626376\pi\)
\(524\) 1.73205 + 3.00000i 0.0756650 + 0.131056i
\(525\) 0 0
\(526\) −3.00000 + 5.19615i −0.130806 + 0.226563i
\(527\) −23.1822 + 6.21166i −1.00983 + 0.270584i
\(528\) 0 0
\(529\) −11.2583 + 6.50000i −0.489493 + 0.282609i
\(530\) 0 0
\(531\) 0 0
\(532\) 17.1464 17.1464i 0.743392 0.743392i
\(533\) 40.5689 + 10.8704i 1.75723 + 0.470849i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.50000 + 0.866025i 0.0647901 + 0.0374066i
\(537\) 0 0
\(538\) −1.79315 + 6.69213i −0.0773082 + 0.288518i
\(539\) 8.66025 0.373024
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 7.24693 27.0459i 0.311282 1.16172i
\(543\) 0 0
\(544\) 2.59808 + 1.50000i 0.111392 + 0.0643120i
\(545\) 0 0
\(546\) 0 0
\(547\) 21.7494 + 5.82774i 0.929938 + 0.249176i 0.691828 0.722062i \(-0.256805\pi\)
0.238110 + 0.971238i \(0.423472\pi\)
\(548\) −2.12132 + 2.12132i −0.0906183 + 0.0906183i
\(549\) 0 0
\(550\) 0 0
\(551\) 21.0000 12.1244i 0.894630 0.516515i
\(552\) 0 0
\(553\) −13.3843 + 3.58630i −0.569157 + 0.152505i
\(554\) −5.19615 + 9.00000i −0.220763 + 0.382373i
\(555\) 0 0
\(556\) −2.50000 4.33013i −0.106024 0.183638i
\(557\) 12.7279 + 12.7279i 0.539299 + 0.539299i 0.923323 0.384024i \(-0.125462\pi\)
−0.384024 + 0.923323i \(0.625462\pi\)
\(558\) 0 0
\(559\) 18.0000i 0.761319i
\(560\) 0 0
\(561\) 0 0
\(562\) −5.37945 20.0764i −0.226919 0.846871i
\(563\) −3.88229 14.4889i −0.163619 0.610634i −0.998212 0.0597675i \(-0.980964\pi\)
0.834593 0.550866i \(-0.185703\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 31.1769i 1.31046i
\(567\) 0 0
\(568\) 9.79796 + 9.79796i 0.411113 + 0.411113i
\(569\) 9.52628 + 16.5000i 0.399362 + 0.691716i 0.993647 0.112539i \(-0.0358982\pi\)
−0.594285 + 0.804255i \(0.702565\pi\)
\(570\) 0 0
\(571\) −2.50000 + 4.33013i −0.104622 + 0.181210i −0.913584 0.406651i \(-0.866697\pi\)
0.808962 + 0.587861i \(0.200030\pi\)
\(572\) −5.79555 + 1.55291i −0.242324 + 0.0649306i
\(573\) 0 0
\(574\) −36.3731 + 21.0000i −1.51818 + 0.876523i
\(575\) 0 0
\(576\) 0 0
\(577\) −23.2702 + 23.2702i −0.968749 + 0.968749i −0.999526 0.0307771i \(-0.990202\pi\)
0.0307771 + 0.999526i \(0.490202\pi\)
\(578\) 7.72741 + 2.07055i 0.321418 + 0.0861236i
\(579\) 0 0
\(580\) 0 0
\(581\) 36.0000 + 20.7846i 1.49353 + 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) −8.66025 −0.358364
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −8.54103 + 31.8756i −0.352526 + 1.31564i 0.531043 + 0.847345i \(0.321800\pi\)
−0.883569 + 0.468300i \(0.844867\pi\)
\(588\) 0 0
\(589\) 48.4974 + 28.0000i 1.99830 + 1.15372i
\(590\) 0 0
\(591\) 0 0
\(592\) 6.69213 + 1.79315i 0.275045 + 0.0736980i
\(593\) −12.7279 + 12.7279i −0.522673 + 0.522673i −0.918378 0.395705i \(-0.870500\pi\)
0.395705 + 0.918378i \(0.370500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.00000 5.19615i 0.368654 0.212843i
\(597\) 0 0
\(598\) 20.0764 5.37945i 0.820985 0.219982i
\(599\) −6.92820 + 12.0000i −0.283079 + 0.490307i −0.972141 0.234395i \(-0.924689\pi\)
0.689063 + 0.724702i \(0.258022\pi\)
\(600\) 0 0
\(601\) 14.5000 + 25.1147i 0.591467 + 1.02445i 0.994035 + 0.109061i \(0.0347845\pi\)
−0.402568 + 0.915390i \(0.631882\pi\)
\(602\) −12.7279 12.7279i −0.518751 0.518751i
\(603\) 0 0
\(604\) 10.0000i 0.406894i
\(605\) 0 0
\(606\) 0 0
\(607\) −3.58630 13.3843i −0.145564 0.543250i −0.999730 0.0232502i \(-0.992599\pi\)
0.854166 0.520000i \(-0.174068\pi\)
\(608\) −1.81173 6.76148i −0.0734755 0.274214i
\(609\) 0 0
\(610\) 0 0
\(611\) 20.7846i 0.840855i
\(612\) 0 0
\(613\) −4.89898 4.89898i −0.197868 0.197868i 0.601218 0.799085i \(-0.294683\pi\)
−0.799085 + 0.601218i \(0.794683\pi\)
\(614\) −2.59808 4.50000i −0.104850 0.181605i
\(615\) 0 0
\(616\) 3.00000 5.19615i 0.120873 0.209359i
\(617\) −43.4667 + 11.6469i −1.74990 + 0.468885i −0.984605 0.174793i \(-0.944074\pi\)
−0.765297 + 0.643678i \(0.777408\pi\)
\(618\) 0 0
\(619\) −11.2583 + 6.50000i −0.452510 + 0.261257i −0.708890 0.705319i \(-0.750804\pi\)
0.256379 + 0.966576i \(0.417470\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −2.44949 + 2.44949i −0.0982156 + 0.0982156i
\(623\) 23.1822 + 6.21166i 0.928776 + 0.248865i
\(624\) 0 0
\(625\) 0 0
\(626\) 7.50000 + 4.33013i 0.299760 + 0.173067i
\(627\) 0 0
\(628\) 0 0
\(629\) −20.7846 −0.828737
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −1.03528 + 3.86370i −0.0411811 + 0.153690i
\(633\) 0 0
\(634\) 5.19615 + 3.00000i 0.206366 + 0.119145i
\(635\) 0 0
\(636\) 0 0
\(637\) 16.7303 + 4.48288i 0.662880 + 0.177618i
\(638\) 4.24264 4.24264i 0.167968 0.167968i
\(639\) 0 0
\(640\) 0 0
\(641\) −19.5000 + 11.2583i −0.770204 + 0.444677i −0.832947 0.553352i \(-0.813348\pi\)
0.0627436 + 0.998030i \(0.480015\pi\)
\(642\) 0 0
\(643\) −35.1337 + 9.41404i −1.38554 + 0.371254i −0.873129 0.487489i \(-0.837913\pi\)
−0.512408 + 0.858742i \(0.671246\pi\)
\(644\) −10.3923 + 18.0000i −0.409514 + 0.709299i
\(645\) 0 0
\(646\) 10.5000 + 18.1865i 0.413117 + 0.715540i
\(647\) −21.2132 21.2132i −0.833977 0.833977i 0.154081 0.988058i \(-0.450758\pi\)
−0.988058 + 0.154081i \(0.950758\pi\)
\(648\) 0 0
\(649\) 21.0000i 0.824322i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.896575 3.34607i −0.0351126 0.131042i
\(653\) 4.65874 + 17.3867i 0.182311 + 0.680393i 0.995190 + 0.0979610i \(0.0312320\pi\)
−0.812880 + 0.582432i \(0.802101\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 12.1244i 0.473377i
\(657\) 0 0
\(658\) 14.6969 + 14.6969i 0.572946 + 0.572946i
\(659\) 5.19615 + 9.00000i 0.202413 + 0.350590i 0.949306 0.314355i \(-0.101788\pi\)
−0.746892 + 0.664945i \(0.768455\pi\)
\(660\) 0 0
\(661\) 16.0000 27.7128i 0.622328 1.07790i −0.366723 0.930330i \(-0.619520\pi\)
0.989051 0.147573i \(-0.0471463\pi\)
\(662\) −27.0459 + 7.24693i −1.05117 + 0.281660i
\(663\) 0 0
\(664\) 10.3923 6.00000i 0.403300 0.232845i
\(665\) 0 0
\(666\) 0 0
\(667\) −14.6969 + 14.6969i −0.569068 + 0.569068i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.00000 + 3.46410i 0.231627 + 0.133730i
\(672\) 0 0
\(673\) 1.79315 6.69213i 0.0691209 0.257963i −0.922715 0.385483i \(-0.874035\pi\)
0.991836 + 0.127520i \(0.0407017\pi\)
\(674\) 12.1244 0.467013
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 3.10583 11.5911i 0.119367 0.445483i −0.880210 0.474585i \(-0.842598\pi\)
0.999576 + 0.0291023i \(0.00926487\pi\)
\(678\) 0 0
\(679\) −25.9808 15.0000i −0.997050 0.575647i
\(680\) 0 0
\(681\) 0 0
\(682\) 13.3843 + 3.58630i 0.512510 + 0.137327i
\(683\) 23.3345 23.3345i 0.892871 0.892871i −0.101922 0.994792i \(-0.532499\pi\)
0.994792 + 0.101922i \(0.0324991\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 6.00000 3.46410i 0.229081 0.132260i
\(687\) 0 0
\(688\) −5.01910 + 1.34486i −0.191351 + 0.0512724i
\(689\) 0 0
\(690\) 0 0
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 4.24264 + 4.24264i 0.161281 + 0.161281i
\(693\) 0 0
\(694\) 15.0000i 0.569392i
\(695\) 0 0
\(696\) 0 0
\(697\) −9.41404 35.1337i −0.356582 1.33078i
\(698\) −2.07055 7.72741i −0.0783716 0.292487i
\(699\) 0 0
\(700\) 0 0
\(701\) 17.3205i 0.654187i 0.944992 + 0.327093i \(0.106069\pi\)
−0.944992 + 0.327093i \(0.893931\pi\)
\(702\) 0 0
\(703\) 34.2929 + 34.2929i 1.29338 + 1.29338i
\(704\) −0.866025 1.50000i −0.0326396 0.0565334i
\(705\) 0 0
\(706\) 10.5000 18.1865i 0.395173 0.684459i
\(707\) 23.1822 6.21166i 0.871857 0.233613i
\(708\) 0 0
\(709\) 34.6410 20.0000i 1.30097 0.751116i 0.320400 0.947282i \(-0.396183\pi\)
0.980571 + 0.196167i \(0.0628493\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.89898 4.89898i 0.183597 0.183597i
\(713\) −46.3644 12.4233i −1.73636 0.465257i
\(714\) 0 0
\(715\) 0 0
\(716\) −3.00000 1.73205i −0.112115 0.0647298i
\(717\) 0 0
\(718\) −6.27603 + 23.4225i −0.234219 + 0.874118i
\(719\) 27.7128 1.03351 0.516757 0.856132i \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(720\) 0 0
\(721\) 60.0000 2.23452
\(722\) 7.76457 28.9778i 0.288967 1.07844i
\(723\) 0 0
\(724\) 1.73205 + 1.00000i 0.0643712 + 0.0371647i
\(725\) 0 0
\(726\) 0 0
\(727\) 10.0382 + 2.68973i 0.372296 + 0.0997564i 0.440115 0.897941i \(-0.354938\pi\)
−0.0678194 + 0.997698i \(0.521604\pi\)
\(728\) 8.48528 8.48528i 0.314485 0.314485i
\(729\) 0 0
\(730\) 0 0
\(731\) 13.5000 7.79423i 0.499316 0.288280i
\(732\) 0 0
\(733\) −50.1910 + 13.4486i −1.85385 + 0.496737i −0.999728 0.0233418i \(-0.992569\pi\)
−0.854119 + 0.520078i \(0.825903\pi\)
\(734\) 6.92820 12.0000i 0.255725 0.442928i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 2.12132 + 2.12132i 0.0781398 + 0.0781398i
\(738\) 0 0
\(739\) 41.0000i 1.50821i −0.656754 0.754105i \(-0.728071\pi\)
0.656754 0.754105i \(-0.271929\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.65874 17.3867i −0.170913 0.637855i −0.997212 0.0746233i \(-0.976225\pi\)
0.826299 0.563232i \(-0.190442\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 17.3205i 0.634149i
\(747\) 0 0
\(748\) 3.67423 + 3.67423i 0.134343 + 0.134343i
\(749\) −5.19615 9.00000i −0.189863 0.328853i
\(750\) 0 0
\(751\) 10.0000 17.3205i 0.364905 0.632034i −0.623856 0.781540i \(-0.714435\pi\)
0.988761 + 0.149505i \(0.0477681\pi\)
\(752\) 5.79555 1.55291i 0.211342 0.0566290i
\(753\) 0 0
\(754\) 10.3923 6.00000i 0.378465 0.218507i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.9444 26.9444i 0.979310 0.979310i −0.0204799 0.999790i \(-0.506519\pi\)
0.999790 + 0.0204799i \(0.00651940\pi\)
\(758\) −0.965926 0.258819i −0.0350840 0.00940073i
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000 + 17.3205i 1.08750 + 0.627868i 0.932910 0.360111i \(-0.117261\pi\)
0.154590 + 0.987979i \(0.450594\pi\)
\(762\) 0 0
\(763\) 3.58630 13.3843i 0.129833 0.484543i
\(764\) 24.2487 0.877288
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) −10.8704 + 40.5689i −0.392507 + 1.46486i
\(768\) 0 0
\(769\) −12.1244 7.00000i −0.437215 0.252426i 0.265200 0.964193i \(-0.414562\pi\)
−0.702416 + 0.711767i \(0.747895\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.36516 + 2.24144i 0.301069 + 0.0806711i
\(773\) −38.1838 + 38.1838i −1.37337 + 1.37337i −0.517985 + 0.855390i \(0.673318\pi\)
−0.855390 + 0.517985i \(0.826682\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −7.50000 + 4.33013i −0.269234 + 0.155443i
\(777\) 0 0
\(778\) −10.0382 + 2.68973i −0.359887 + 0.0964314i
\(779\) −42.4352 + 73.5000i −1.52040 + 2.63341i
\(780\) 0 0
\(781\) 12.0000 + 20.7846i 0.429394 + 0.743732i
\(782\) −12.7279 12.7279i −0.455150 0.455150i
\(783\) 0 0
\(784\) 5.00000i 0.178571i
\(785\) 0 0
\(786\) 0 0
\(787\) 4.48288 + 16.7303i 0.159797 + 0.596372i 0.998647 + 0.0520081i \(0.0165622\pi\)
−0.838849 + 0.544364i \(0.816771\pi\)
\(788\) 6.21166 + 23.1822i 0.221281 + 0.825832i
\(789\) 0 0
\(790\) 0 0
\(791\) 62.3538i 2.21705i
\(792\) 0 0
\(793\) 9.79796 + 9.79796i 0.347936 + 0.347936i
\(794\) −10.3923 18.0000i −0.368809 0.638796i
\(795\) 0 0
\(796\) −5.00000 + 8.66025i −0.177220 + 0.306955i
\(797\) −23.1822 + 6.21166i −0.821156 + 0.220028i −0.644852 0.764308i \(-0.723081\pi\)
−0.176304 + 0.984336i \(0.556414\pi\)
\(798\) 0 0
\(799\) −15.5885 + 9.00000i −0.551480 + 0.318397i
\(800\) 0 0
\(801\) 0 0
\(802\) −3.67423 + 3.67423i −0.129742 + 0.129742i
\(803\) −14.4889 3.88229i −0.511302 0.137003i
\(804\) 0 0
\(805\) 0 0
\(806\) 24.0000 + 13.8564i 0.845364 + 0.488071i
\(807\) 0 0
\(808\) 1.79315 6.69213i 0.0630828 0.235428i
\(809\) −12.1244 −0.426270 −0.213135 0.977023i \(-0.568367\pi\)
−0.213135 + 0.977023i \(0.568367\pi\)
\(810\) 0 0
\(811\) −41.0000 −1.43970 −0.719852 0.694127i \(-0.755791\pi\)
−0.719852 + 0.694127i \(0.755791\pi\)
\(812\) −3.10583 + 11.5911i −0.108993 + 0.406768i
\(813\) 0 0
\(814\) 10.3923 + 6.00000i 0.364250 + 0.210300i
\(815\) 0 0
\(816\) 0 0
\(817\) −35.1337 9.41404i −1.22917 0.329356i
\(818\) 4.94975 4.94975i 0.173064 0.173064i
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 + 8.66025i −0.523504 + 0.302245i −0.738367 0.674399i \(-0.764403\pi\)
0.214863 + 0.976644i \(0.431069\pi\)
\(822\) 0 0
\(823\) −13.3843 + 3.58630i −0.466546 + 0.125011i −0.484431 0.874829i \(-0.660973\pi\)
0.0178851 + 0.999840i \(0.494307\pi\)
\(824\) 8.66025 15.0000i 0.301694 0.522550i
\(825\) 0 0
\(826\) −21.0000 36.3731i −0.730683 1.26558i
\(827\) 25.4558 + 25.4558i 0.885186 + 0.885186i 0.994056 0.108870i \(-0.0347231\pi\)
−0.108870 + 0.994056i \(0.534723\pi\)
\(828\) 0 0
\(829\) 34.0000i 1.18087i 0.807086 + 0.590434i \(0.201044\pi\)
−0.807086 + 0.590434i \(0.798956\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −0.896575 3.34607i −0.0310832 0.116004i
\(833\) −3.88229 14.4889i −0.134513 0.502010i
\(834\) 0 0
\(835\) 0 0
\(836\) 12.1244i 0.419330i
\(837\) 0 0
\(838\) −7.34847 7.34847i −0.253849 0.253849i
\(839\) 17.3205 + 30.0000i 0.597970 + 1.03572i 0.993120 + 0.117098i \(0.0373593\pi\)
−0.395150 + 0.918617i \(0.629307\pi\)
\(840\) 0 0
\(841\) 8.50000 14.7224i 0.293103 0.507670i
\(842\) 27.0459 7.24693i 0.932064 0.249746i
\(843\) 0 0
\(844\) −3.46410 + 2.00000i −0.119239 + 0.0688428i
\(845\) 0 0
\(846\) 0 0
\(847\) −19.5959 + 19.5959i −0.673324 + 0.673324i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −36.0000 20.7846i −1.23406 0.712487i
\(852\) 0 0
\(853\) 9.86233 36.8067i 0.337680 1.26024i −0.563255 0.826283i \(-0.690451\pi\)
0.900935 0.433955i \(-0.142882\pi\)
\(854\) −13.8564 −0.474156
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) 10.8704 40.5689i 0.371326 1.38581i −0.487314 0.873227i \(-0.662023\pi\)
0.858640 0.512580i \(-0.171310\pi\)
\(858\) 0 0
\(859\) 11.2583 + 6.50000i 0.384129 + 0.221777i 0.679613 0.733571i \(-0.262148\pi\)
−0.295484 + 0.955348i \(0.595481\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −3.34607 0.896575i −0.113967 0.0305375i
\(863\) 16.9706 16.9706i 0.577685 0.577685i −0.356580 0.934265i \(-0.616057\pi\)
0.934265 + 0.356580i \(0.116057\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 22.5000 12.9904i 0.764581 0.441431i
\(867\) 0 0
\(868\) −26.7685 + 7.17260i −0.908583 + 0.243454i
\(869\) −3.46410 + 6.00000i −0.117512 + 0.203536i
\(870\) 0 0
\(871\) 3.00000 + 5.19615i 0.101651 + 0.176065i
\(872\) −2.82843 2.82843i −0.0957826 0.0957826i
\(873\) 0 0
\(874\) 42.0000i 1.42067i
\(875\) 0 0
\(876\) 0 0
\(877\) 7.17260 + 26.7685i 0.242202 + 0.903909i 0.974769 + 0.223215i \(0.0716551\pi\)
−0.732568 + 0.680694i \(0.761678\pi\)
\(878\) −4.14110 15.4548i −0.139756 0.521575i
\(879\) 0 0
\(880\) 0 0
\(881\) 6.92820i 0.233417i 0.993166 + 0.116709i \(0.0372343\pi\)
−0.993166 + 0.116709i \(0.962766\pi\)
\(882\) 0 0
\(883\) 8.57321 + 8.57321i 0.288512 + 0.288512i 0.836492 0.547980i \(-0.184603\pi\)
−0.547980 + 0.836492i \(0.684603\pi\)
\(884\) 5.19615 + 9.00000i 0.174766 + 0.302703i
\(885\) 0 0
\(886\) 13.5000 23.3827i 0.453541 0.785557i
\(887\) 46.3644 12.4233i 1.55677 0.417134i 0.625128 0.780522i \(-0.285047\pi\)
0.931638 + 0.363388i \(0.118380\pi\)
\(888\) 0 0
\(889\) 31.1769 18.0000i 1.04564 0.603701i
\(890\) 0 0
\(891\) 0 0
\(892\) 7.34847 7.34847i 0.246045 0.246045i
\(893\) 40.5689 + 10.8704i 1.35759 + 0.363764i
\(894\) 0 0
\(895\) 0 0
\(896\) 3.00000 + 1.73205i 0.100223 + 0.0578638i
\(897\) 0 0
\(898\) 10.3106 38.4797i 0.344070 1.28409i
\(899\) −27.7128 −0.924274
\(900\) 0 0
\(901\) 0 0
\(902\) −5.43520 + 20.2844i −0.180972 + 0.675398i
\(903\) 0 0
\(904\) 15.5885 + 9.00000i 0.518464 + 0.299336i
\(905\) 0 0
\(906\) 0 0
\(907\) 8.36516 + 2.24144i 0.277761 + 0.0744257i 0.395010 0.918677i \(-0.370741\pi\)
−0.117250 + 0.993102i \(0.537408\pi\)
\(908\) −2.12132 + 2.12132i −0.0703985 + 0.0703985i
\(909\) 0 0
\(910\) 0 0
\(911\) 30.0000 17.3205i 0.993944 0.573854i 0.0874934 0.996165i \(-0.472114\pi\)
0.906451 + 0.422311i \(0.138781\pi\)
\(912\) 0 0
\(913\) 20.0764 5.37945i 0.664432 0.178034i
\(914\) 12.9904 22.5000i 0.429684 0.744234i
\(915\) 0 0
\(916\) 11.0000 + 19.0526i 0.363450 + 0.629514i
\(917\) −8.48528 8.48528i −0.280209 0.280209i
\(918\) 0 0
\(919\) 22.0000i 0.725713i 0.931845 + 0.362857i \(0.118198\pi\)
−0.931845 + 0.362857i \(0.881802\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −4.48288 16.7303i −0.147636 0.550984i
\(923\) 12.4233 + 46.3644i 0.408918 + 1.52610i
\(924\) 0 0
\(925\) 0 0
\(926\) 13.8564i 0.455350i
\(927\) 0 0
\(928\) 2.44949 + 2.44949i 0.0804084 + 0.0804084i
\(929\) −17.3205 30.0000i −0.568267 0.984268i −0.996737 0.0807121i \(-0.974281\pi\)
0.428470 0.903556i \(-0.359053\pi\)
\(930\) 0 0
\(931\) −17.5000 + 30.3109i −0.573539 + 0.993399i
\(932\) −2.89778 + 0.776457i −0.0949199 + 0.0254337i
\(933\) 0 0
\(934\) −7.79423 + 4.50000i −0.255035 + 0.147244i
\(935\) 0 0
\(936\) 0 0
\(937\) −24.4949 + 24.4949i −0.800213 + 0.800213i −0.983129 0.182915i \(-0.941447\pi\)
0.182915 + 0.983129i \(0.441447\pi\)
\(938\) −5.79555 1.55291i −0.189232 0.0507044i
\(939\) 0 0
\(940\) 0 0
\(941\) 18.0000 + 10.3923i 0.586783 + 0.338779i 0.763825 0.645424i \(-0.223319\pi\)
−0.177041 + 0.984203i \(0.556653\pi\)
\(942\) 0 0
\(943\) 18.8281 70.2674i 0.613127 2.28822i
\(944\) −12.1244 −0.394614
\(945\) 0 0
\(946\) −9.00000 −0.292615
\(947\) 6.98811 26.0800i 0.227083 0.847486i −0.754476 0.656328i \(-0.772109\pi\)
0.981559 0.191158i \(-0.0612244\pi\)
\(948\) 0 0
\(949\) −25.9808 15.0000i −0.843371 0.486921i
\(950\) 0 0
\(951\) 0 0
\(952\) −10.0382 2.68973i −0.325340 0.0871745i
\(953\) 23.3345 23.3345i 0.755879 0.755879i −0.219690 0.975570i \(-0.570505\pi\)
0.975570 + 0.219690i \(0.0705047\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −9.00000 + 5.19615i −0.291081 + 0.168056i
\(957\) 0 0
\(958\) 16.7303 4.48288i 0.540532 0.144835i
\(959\) 5.19615 9.00000i 0.167793 0.290625i
\(960\) 0 0
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) 16.9706 + 16.9706i 0.547153 + 0.547153i
\(963\) 0 0
\(964\) 1.00000i 0.0322078i
\(965\) 0 0
\(966\) 0 0
\(967\) −0.896575 3.34607i −0.0288319 0.107602i 0.950010 0.312218i \(-0.101072\pi\)
−0.978842 + 0.204616i \(0.934405\pi\)
\(968\) 2.07055 + 7.72741i 0.0665501 + 0.248368i
\(969\) 0 0
\(970\) 0 0
\(971\) 3.46410i 0.111168i −0.998454 0.0555842i \(-0.982298\pi\)
0.998454 0.0555842i \(-0.0177021\pi\)
\(972\) 0 0
\(973\) 12.2474 + 12.2474i 0.392635 + 0.392635i
\(974\) −12.1244 21.0000i −0.388489 0.672883i
\(975\) 0 0
\(976\) −2.00000 + 3.46410i −0.0640184 + 0.110883i
\(977\) −2.89778 + 0.776457i −0.0927081 + 0.0248411i −0.304875 0.952392i \(-0.598615\pi\)
0.212167 + 0.977233i \(0.431948\pi\)
\(978\) 0 0
\(979\) 10.3923 6.00000i 0.332140 0.191761i
\(980\) 0 0
\(981\) 0 0
\(982\) −15.9217 + 15.9217i −0.508081 + 0.508081i
\(983\) −34.7733 9.31749i −1.10910 0.297182i −0.342633 0.939469i \(-0.611319\pi\)
−0.766464 + 0.642288i \(0.777985\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −9.00000 5.19615i −0.286618 0.165479i
\(987\) 0 0
\(988\) 6.27603 23.4225i 0.199667 0.745168i
\(989\) 31.1769 0.991368
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) −2.07055 + 7.72741i −0.0657401 + 0.245345i
\(993\) 0 0
\(994\) −41.5692 24.0000i −1.31850 0.761234i
\(995\) 0 0
\(996\) 0 0
\(997\) 40.1528 + 10.7589i 1.27165 + 0.340738i 0.830663 0.556775i \(-0.187961\pi\)
0.440988 + 0.897513i \(0.354628\pi\)
\(998\) −13.4350 + 13.4350i −0.425278 + 0.425278i
\(999\) 0 0
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 1350.2.q.f.1043.1 8
3.2 odd 2 450.2.p.f.293.2 yes 8
5.2 odd 4 inner 1350.2.q.f.557.1 8
5.3 odd 4 inner 1350.2.q.f.557.2 8
5.4 even 2 inner 1350.2.q.f.1043.2 8
9.2 odd 6 inner 1350.2.q.f.143.1 8
9.7 even 3 450.2.p.f.443.2 yes 8
15.2 even 4 450.2.p.f.257.2 yes 8
15.8 even 4 450.2.p.f.257.1 8
15.14 odd 2 450.2.p.f.293.1 yes 8
45.2 even 12 inner 1350.2.q.f.1007.1 8
45.7 odd 12 450.2.p.f.407.2 yes 8
45.29 odd 6 inner 1350.2.q.f.143.2 8
45.34 even 6 450.2.p.f.443.1 yes 8
45.38 even 12 inner 1350.2.q.f.1007.2 8
45.43 odd 12 450.2.p.f.407.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.p.f.257.1 8 15.8 even 4
450.2.p.f.257.2 yes 8 15.2 even 4
450.2.p.f.293.1 yes 8 15.14 odd 2
450.2.p.f.293.2 yes 8 3.2 odd 2
450.2.p.f.407.1 yes 8 45.43 odd 12
450.2.p.f.407.2 yes 8 45.7 odd 12
450.2.p.f.443.1 yes 8 45.34 even 6
450.2.p.f.443.2 yes 8 9.7 even 3
1350.2.q.f.143.1 8 9.2 odd 6 inner
1350.2.q.f.143.2 8 45.29 odd 6 inner
1350.2.q.f.557.1 8 5.2 odd 4 inner
1350.2.q.f.557.2 8 5.3 odd 4 inner
1350.2.q.f.1007.1 8 45.2 even 12 inner
1350.2.q.f.1007.2 8 45.38 even 12 inner
1350.2.q.f.1043.1 8 1.1 even 1 trivial
1350.2.q.f.1043.2 8 5.4 even 2 inner