Properties

Label 1350.2.q.f.143.2
Level $1350$
Weight $2$
Character 1350.143
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 143.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1350.143
Dual form 1350.2.q.f.557.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(0.896575 + 3.34607i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(0.896575 + 3.34607i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.50000 + 0.866025i) q^{11} +(0.896575 - 3.34607i) q^{13} +(1.73205 + 3.00000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.12132 - 2.12132i) q^{17} +7.00000i q^{19} +(1.67303 + 0.448288i) q^{22} +(5.79555 + 1.55291i) q^{23} -3.46410i q^{26} +(2.44949 + 2.44949i) q^{28} +(1.73205 - 3.00000i) q^{29} +(4.00000 + 6.92820i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.59808 - 1.50000i) q^{34} +(-4.89898 + 4.89898i) q^{37} +(1.81173 + 6.76148i) q^{38} +(10.5000 - 6.06218i) q^{41} +(-5.01910 + 1.34486i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(-5.79555 + 1.55291i) q^{47} +(-4.33013 + 2.50000i) q^{49} +(-0.896575 - 3.34607i) q^{52} +(3.00000 + 1.73205i) q^{56} +(0.896575 - 3.34607i) q^{58} +(6.06218 + 10.5000i) q^{59} +(2.00000 - 3.46410i) q^{61} +(5.65685 + 5.65685i) q^{62} -1.00000i q^{64} +(1.67303 + 0.448288i) q^{67} +(-2.89778 - 0.776457i) q^{68} -13.8564i q^{71} +(6.12372 + 6.12372i) q^{73} +(-3.46410 + 6.00000i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-1.55291 + 5.79555i) q^{77} +(3.46410 + 2.00000i) q^{79} +(8.57321 - 8.57321i) q^{82} +(-3.10583 - 11.5911i) q^{83} +(-4.50000 + 2.59808i) q^{86} +(1.67303 - 0.448288i) q^{88} -6.92820 q^{89} +12.0000 q^{91} +(5.79555 - 1.55291i) q^{92} +(-5.19615 + 3.00000i) q^{94} +(-2.24144 - 8.36516i) q^{97} +(-3.53553 + 3.53553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0 0
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.896575 + 3.34607i 0.338874 + 1.26469i 0.899608 + 0.436698i \(0.143852\pi\)
−0.560734 + 0.827996i \(0.689481\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 + 0.866025i 0.452267 + 0.261116i 0.708787 0.705422i \(-0.249243\pi\)
−0.256520 + 0.966539i \(0.582576\pi\)
\(12\) 0 0
\(13\) 0.896575 3.34607i 0.248665 0.928032i −0.722840 0.691015i \(-0.757164\pi\)
0.971506 0.237016i \(-0.0761695\pi\)
\(14\) 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
\(22\) 1.67303 + 0.448288i 0.356692 + 0.0955753i
\(23\) 5.79555 + 1.55291i 1.20846 + 0.323805i 0.806156 0.591703i \(-0.201544\pi\)
0.402300 + 0.915508i \(0.368211\pi\)
\(24\) 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 \(-0.729101\pi\)
0.980825 + 0.194889i \(0.0624347\pi\)
\(30\) 0 0
\(31\) 4.00000 + 6.92820i 0.718421 + 1.24434i 0.961625 + 0.274367i \(0.0884683\pi\)
−0.243204 + 0.969975i \(0.578198\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 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 −0.983932 0.178545i \(-0.942861\pi\)
0.178545 + 0.983932i \(0.442861\pi\)
\(38\) 1.81173 + 6.76148i 0.293902 + 1.09686i
\(39\) 0 0
\(40\) 0 0
\(41\) 10.5000 6.06218i 1.63982 0.946753i 0.658932 0.752202i \(-0.271008\pi\)
0.980892 0.194551i \(-0.0623249\pi\)
\(42\) 0 0
\(43\) −5.01910 + 1.34486i −0.765405 + 0.205090i −0.620341 0.784332i \(-0.713006\pi\)
−0.145065 + 0.989422i \(0.546339\pi\)
\(44\) 1.73205 0.261116
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) −5.79555 + 1.55291i −0.845369 + 0.226516i −0.655407 0.755276i \(-0.727503\pi\)
−0.189961 + 0.981792i \(0.560836\pi\)
\(48\) 0 0
\(49\) −4.33013 + 2.50000i −0.618590 + 0.357143i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.896575 3.34607i −0.124333 0.464016i
\(53\) 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
\(58\) 0.896575 3.34607i 0.117726 0.439360i
\(59\) 6.06218 + 10.5000i 0.789228 + 1.36698i 0.926440 + 0.376442i \(0.122853\pi\)
−0.137212 + 0.990542i \(0.543814\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 5.65685 + 5.65685i 0.718421 + 0.718421i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.67303 + 0.448288i 0.204393 + 0.0547671i 0.359563 0.933121i \(-0.382926\pi\)
−0.155170 + 0.987888i \(0.549592\pi\)
\(68\) −2.89778 0.776457i −0.351407 0.0941593i
\(69\) 0 0
\(70\) 0 0
\(71\) 13.8564i 1.64445i −0.569160 0.822226i \(-0.692732\pi\)
0.569160 0.822226i \(-0.307268\pi\)
\(72\) 0 0
\(73\) 6.12372 + 6.12372i 0.716728 + 0.716728i 0.967934 0.251206i \(-0.0808271\pi\)
−0.251206 + 0.967934i \(0.580827\pi\)
\(74\) −3.46410 + 6.00000i −0.402694 + 0.697486i
\(75\) 0 0
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) −1.55291 + 5.79555i −0.176971 + 0.660465i
\(78\) 0 0
\(79\) 3.46410 + 2.00000i 0.389742 + 0.225018i 0.682048 0.731307i \(-0.261089\pi\)
−0.292306 + 0.956325i \(0.594423\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 8.57321 8.57321i 0.946753 0.946753i
\(83\) −3.10583 11.5911i −0.340909 1.27229i −0.897319 0.441382i \(-0.854488\pi\)
0.556410 0.830908i \(-0.312178\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.50000 + 2.59808i −0.485247 + 0.280158i
\(87\) 0 0
\(88\) 1.67303 0.448288i 0.178346 0.0477876i
\(89\) −6.92820 −0.734388 −0.367194 0.930144i \(-0.619682\pi\)
−0.367194 + 0.930144i \(0.619682\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) 5.79555 1.55291i 0.604228 0.161903i
\(93\) 0 0
\(94\) −5.19615 + 3.00000i −0.535942 + 0.309426i
\(95\) 0 0
\(96\) 0 0
\(97\) −2.24144 8.36516i −0.227584 0.849354i −0.981353 0.192215i \(-0.938433\pi\)
0.753769 0.657139i \(-0.228234\pi\)
\(98\) −3.53553 + 3.53553i −0.357143 + 0.357143i
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 + 3.46410i 0.597022 + 0.344691i 0.767869 0.640607i \(-0.221317\pi\)
−0.170847 + 0.985298i \(0.554650\pi\)
\(102\) 0 0
\(103\) 4.48288 16.7303i 0.441711 1.64849i −0.282766 0.959189i \(-0.591252\pi\)
0.724477 0.689299i \(-0.242081\pi\)
\(104\) −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
\(112\) 3.34607 + 0.896575i 0.316173 + 0.0847184i
\(113\) −17.3867 4.65874i −1.63560 0.438258i −0.680069 0.733148i \(-0.738050\pi\)
−0.955531 + 0.294891i \(0.904717\pi\)
\(114\) 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
\(122\) 1.03528 3.86370i 0.0937295 0.349803i
\(123\) 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 −0.953491 0.301420i \(-0.902539\pi\)
0.301420 + 0.953491i \(0.402539\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 1.73205i −0.262111 + 0.151330i −0.625297 0.780387i \(-0.715022\pi\)
0.363186 + 0.931717i \(0.381689\pi\)
\(132\) 0 0
\(133\) −23.4225 + 6.27603i −2.03098 + 0.544201i
\(134\) 1.73205 0.149626
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) −2.89778 + 0.776457i −0.247574 + 0.0663372i −0.380472 0.924793i \(-0.624238\pi\)
0.132898 + 0.991130i \(0.457572\pi\)
\(138\) 0 0
\(139\) −4.33013 + 2.50000i −0.367277 + 0.212047i −0.672268 0.740308i \(-0.734680\pi\)
0.304991 + 0.952355i \(0.401346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.58630 13.3843i −0.300956 1.12318i
\(143\) 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
\(148\) −1.79315 + 6.69213i −0.147396 + 0.550090i
\(149\) 5.19615 + 9.00000i 0.425685 + 0.737309i 0.996484 0.0837813i \(-0.0266997\pi\)
−0.570799 + 0.821090i \(0.693366\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) 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 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(158\) 3.86370 + 1.03528i 0.307380 + 0.0823622i
\(159\) 0 0
\(160\) 0 0
\(161\) 20.7846i 1.63806i
\(162\) 0 0
\(163\) −2.44949 2.44949i −0.191859 0.191859i 0.604640 0.796499i \(-0.293317\pi\)
−0.796499 + 0.604640i \(0.793317\pi\)
\(164\) 6.06218 10.5000i 0.473377 0.819912i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(168\) 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
\(173\) 1.55291 + 5.79555i 0.118066 + 0.440628i 0.999498 0.0316829i \(-0.0100867\pi\)
−0.881432 + 0.472311i \(0.843420\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.50000 0.866025i 0.113067 0.0652791i
\(177\) 0 0
\(178\) −6.69213 + 1.79315i −0.501596 + 0.134402i
\(179\) −3.46410 −0.258919 −0.129460 0.991585i \(-0.541324\pi\)
−0.129460 + 0.991585i \(0.541324\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 11.5911 3.10583i 0.859190 0.230219i
\(183\) 0 0
\(184\) 5.19615 3.00000i 0.383065 0.221163i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.34486 5.01910i −0.0983461 0.367033i
\(188\) −4.24264 + 4.24264i −0.309426 + 0.309426i
\(189\) 0 0
\(190\) 0 0
\(191\) −21.0000 12.1244i −1.51951 0.877288i −0.999736 0.0229818i \(-0.992684\pi\)
−0.519771 0.854306i \(-0.673983\pi\)
\(192\) 0 0
\(193\) −2.24144 + 8.36516i −0.161342 + 0.602138i 0.837136 + 0.546995i \(0.184228\pi\)
−0.998478 + 0.0551431i \(0.982439\pi\)
\(194\) −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
\(202\) 6.69213 + 1.79315i 0.470857 + 0.126166i
\(203\) 11.5911 + 3.10583i 0.813536 + 0.217986i
\(204\) 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 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) 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
\(218\) −1.03528 3.86370i −0.0701178 0.261683i
\(219\) 0 0
\(220\) 0 0
\(221\) −9.00000 + 5.19615i −0.605406 + 0.349531i
\(222\) 0 0
\(223\) −10.0382 + 2.68973i −0.672207 + 0.180117i −0.578749 0.815506i \(-0.696459\pi\)
−0.0934584 + 0.995623i \(0.529792\pi\)
\(224\) 3.46410 0.231455
\(225\) 0 0
\(226\) −18.0000 −1.19734
\(227\) −2.89778 + 0.776457i −0.192332 + 0.0515353i −0.353699 0.935359i \(-0.615076\pi\)
0.161367 + 0.986894i \(0.448410\pi\)
\(228\) 0 0
\(229\) 19.0526 11.0000i 1.25903 0.726900i 0.286143 0.958187i \(-0.407627\pi\)
0.972886 + 0.231287i \(0.0742935\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.896575 3.34607i −0.0588631 0.219680i
\(233\) 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
\(238\) 2.68973 10.0382i 0.174349 0.650680i
\(239\) −5.19615 9.00000i −0.336111 0.582162i 0.647586 0.761992i \(-0.275778\pi\)
−0.983698 + 0.179830i \(0.942445\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) −5.65685 5.65685i −0.363636 0.363636i
\(243\) 0 0
\(244\) 4.00000i 0.256074i
\(245\) 0 0
\(246\) 0 0
\(247\) 23.4225 + 6.27603i 1.49034 + 0.399334i
\(248\) 7.72741 + 2.07055i 0.490691 + 0.131480i
\(249\) 0 0
\(250\) 0 0
\(251\) 25.9808i 1.63989i 0.572441 + 0.819946i \(0.305996\pi\)
−0.572441 + 0.819946i \(0.694004\pi\)
\(252\) 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
\(257\) 6.98811 26.0800i 0.435907 1.62683i −0.302981 0.952997i \(-0.597982\pi\)
0.738887 0.673829i \(-0.235352\pi\)
\(258\) 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
\(263\) −1.55291 5.79555i −0.0957568 0.357369i 0.901376 0.433037i \(-0.142558\pi\)
−0.997133 + 0.0756674i \(0.975891\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −21.0000 + 12.1244i −1.28759 + 0.743392i
\(267\) 0 0
\(268\) 1.67303 0.448288i 0.102197 0.0273835i
\(269\) −6.92820 −0.422420 −0.211210 0.977441i \(-0.567740\pi\)
−0.211210 + 0.977441i \(0.567740\pi\)
\(270\) 0 0
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −2.89778 + 0.776457i −0.175704 + 0.0470796i
\(273\) 0 0
\(274\) −2.59808 + 1.50000i −0.156956 + 0.0906183i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.68973 + 10.0382i 0.161610 + 0.603137i 0.998448 + 0.0556866i \(0.0177348\pi\)
−0.836838 + 0.547450i \(0.815599\pi\)
\(278\) −3.53553 + 3.53553i −0.212047 + 0.212047i
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 10.3923i −1.07379 0.619953i −0.144575 0.989494i \(-0.546182\pi\)
−0.929214 + 0.369541i \(0.879515\pi\)
\(282\) 0 0
\(283\) 8.06918 30.1146i 0.479663 1.79013i −0.123314 0.992368i \(-0.539352\pi\)
0.602977 0.797759i \(-0.293981\pi\)
\(284\) −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
\(292\) 8.36516 + 2.24144i 0.489534 + 0.131170i
\(293\) −5.79555 1.55291i −0.338580 0.0907222i 0.0855230 0.996336i \(-0.472744\pi\)
−0.424103 + 0.905614i \(0.639411\pi\)
\(294\) 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
\(302\) −2.58819 + 9.65926i −0.148934 + 0.555828i
\(303\) 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 −0.594440 0.804140i \(-0.702626\pi\)
0.804140 + 0.594440i \(0.202626\pi\)
\(308\) 1.55291 + 5.79555i 0.0884855 + 0.330232i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.00000 1.73205i 0.170114 0.0982156i −0.412525 0.910946i \(-0.635353\pi\)
0.582640 + 0.812731i \(0.302020\pi\)
\(312\) 0 0
\(313\) 8.36516 2.24144i 0.472827 0.126694i −0.0145337 0.999894i \(-0.504626\pi\)
0.487361 + 0.873201i \(0.337960\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) −5.79555 + 1.55291i −0.325511 + 0.0872204i −0.417874 0.908505i \(-0.637225\pi\)
0.0923631 + 0.995725i \(0.470558\pi\)
\(318\) 0 0
\(319\) 5.19615 3.00000i 0.290929 0.167968i
\(320\) 0 0
\(321\) 0 0
\(322\) 5.37945 + 20.0764i 0.299785 + 1.11881i
\(323\) 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
\(328\) 3.13801 11.7112i 0.173268 0.646644i
\(329\) −10.3923 18.0000i −0.572946 0.992372i
\(330\) 0 0
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) −8.48528 8.48528i −0.465690 0.465690i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.7112 3.13801i −0.637951 0.170939i −0.0746760 0.997208i \(-0.523792\pi\)
−0.563275 + 0.826269i \(0.690459\pi\)
\(338\) 0.965926 + 0.258819i 0.0525394 + 0.0140779i
\(339\) 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
\(347\) −3.88229 + 14.4889i −0.208412 + 0.777804i 0.779970 + 0.625816i \(0.215234\pi\)
−0.988382 + 0.151988i \(0.951433\pi\)
\(348\) 0 0
\(349\) 6.92820 + 4.00000i 0.370858 + 0.214115i 0.673833 0.738883i \(-0.264647\pi\)
−0.302975 + 0.952998i \(0.597980\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.22474 1.22474i 0.0652791 0.0652791i
\(353\) 5.43520 + 20.2844i 0.289287 + 1.07963i 0.945650 + 0.325187i \(0.105427\pi\)
−0.656363 + 0.754445i \(0.727906\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 + 3.46410i −0.317999 + 0.183597i
\(357\) 0 0
\(358\) −3.34607 + 0.896575i −0.176845 + 0.0473855i
\(359\) −24.2487 −1.27980 −0.639899 0.768459i \(-0.721024\pi\)
−0.639899 + 0.768459i \(0.721024\pi\)
\(360\) 0 0
\(361\) −30.0000 −1.57895
\(362\) −1.93185 + 0.517638i −0.101536 + 0.0272065i
\(363\) 0 0
\(364\) 10.3923 6.00000i 0.544705 0.314485i
\(365\) 0 0
\(366\) 0 0
\(367\) −3.58630 13.3843i −0.187203 0.698653i −0.994148 0.108026i \(-0.965547\pi\)
0.806945 0.590627i \(-0.201120\pi\)
\(368\) 4.24264 4.24264i 0.221163 0.221163i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4.48288 + 16.7303i −0.232115 + 0.866263i 0.747314 + 0.664471i \(0.231343\pi\)
−0.979428 + 0.201792i \(0.935323\pi\)
\(374\) −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
\(382\) −23.4225 6.27603i −1.19840 0.321110i
\(383\) 11.5911 + 3.10583i 0.592278 + 0.158700i 0.542494 0.840060i \(-0.317480\pi\)
0.0497839 + 0.998760i \(0.484147\pi\)
\(384\) 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 \(-0.918196\pi\)
0.703702 + 0.710495i \(0.251529\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) −1.29410 + 4.82963i −0.0653617 + 0.243933i
\(393\) 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 −0.234498 0.972117i \(-0.575345\pi\)
0.972117 + 0.234498i \(0.0753447\pi\)
\(398\) −2.58819 9.65926i −0.129734 0.484175i
\(399\) 0 0
\(400\) 0 0
\(401\) 4.50000 2.59808i 0.224719 0.129742i −0.383414 0.923576i \(-0.625252\pi\)
0.608134 + 0.793835i \(0.291919\pi\)
\(402\) 0 0
\(403\) 26.7685 7.17260i 1.33344 0.357293i
\(404\) 6.92820 0.344691
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) −11.5911 + 3.10583i −0.574550 + 0.153950i
\(408\) 0 0
\(409\) 6.06218 3.50000i 0.299755 0.173064i −0.342578 0.939490i \(-0.611300\pi\)
0.642333 + 0.766426i \(0.277967\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.48288 16.7303i −0.220856 0.824244i
\(413\) −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
\(418\) −3.13801 + 11.7112i −0.153485 + 0.572815i
\(419\) 5.19615 + 9.00000i 0.253849 + 0.439679i 0.964582 0.263783i \(-0.0849701\pi\)
−0.710734 + 0.703461i \(0.751637\pi\)
\(420\) 0 0
\(421\) −14.0000 + 24.2487i −0.682318 + 1.18181i 0.291953 + 0.956433i \(0.405695\pi\)
−0.974272 + 0.225377i \(0.927639\pi\)
\(422\) 2.82843 + 2.82843i 0.137686 + 0.137686i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 13.3843 + 3.58630i 0.647710 + 0.173553i
\(428\) −2.89778 0.776457i −0.140069 0.0375315i
\(429\) 0 0
\(430\) 0 0
\(431\) 3.46410i 0.166860i −0.996514 0.0834300i \(-0.973413\pi\)
0.996514 0.0834300i \(-0.0265875\pi\)
\(432\) 0 0
\(433\) 18.3712 + 18.3712i 0.882862 + 0.882862i 0.993825 0.110962i \(-0.0353933\pi\)
−0.110962 + 0.993825i \(0.535393\pi\)
\(434\) −13.8564 + 24.0000i −0.665129 + 1.15204i
\(435\) 0 0
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) −10.8704 + 40.5689i −0.520002 + 1.94067i
\(438\) 0 0
\(439\) 13.8564 + 8.00000i 0.661330 + 0.381819i 0.792784 0.609503i \(-0.208631\pi\)
−0.131453 + 0.991322i \(0.541964\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −7.34847 + 7.34847i −0.349531 + 0.349531i
\(443\) 6.98811 + 26.0800i 0.332015 + 1.23910i 0.907069 + 0.420982i \(0.138315\pi\)
−0.575054 + 0.818116i \(0.695019\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −9.00000 + 5.19615i −0.426162 + 0.246045i
\(447\) 0 0
\(448\) 3.34607 0.896575i 0.158087 0.0423592i
\(449\) 39.8372 1.88003 0.940016 0.341130i \(-0.110810\pi\)
0.940016 + 0.341130i \(0.110810\pi\)
\(450\) 0 0
\(451\) 21.0000 0.988851
\(452\) −17.3867 + 4.65874i −0.817800 + 0.219129i
\(453\) 0 0
\(454\) −2.59808 + 1.50000i −0.121934 + 0.0703985i
\(455\) 0 0
\(456\) 0 0
\(457\) −6.72432 25.0955i −0.314550 1.17392i −0.924408 0.381406i \(-0.875440\pi\)
0.609857 0.792511i \(-0.291227\pi\)
\(458\) 15.5563 15.5563i 0.726900 0.726900i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 8.66025i −0.698620 0.403348i 0.108213 0.994128i \(-0.465487\pi\)
−0.806833 + 0.590779i \(0.798820\pi\)
\(462\) 0 0
\(463\) 3.58630 13.3843i 0.166670 0.622019i −0.831152 0.556046i \(-0.812318\pi\)
0.997821 0.0659737i \(-0.0210154\pi\)
\(464\) −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
\(472\) 11.7112 + 3.13801i 0.539053 + 0.144439i
\(473\) −8.69333 2.32937i −0.399720 0.107105i
\(474\) 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 \(-0.703836\pi\)
0.993190 + 0.116507i \(0.0371697\pi\)
\(480\) 0 0
\(481\) 12.0000 + 20.7846i 0.547153 + 0.947697i
\(482\) 0.258819 0.965926i 0.0117889 0.0439967i
\(483\) 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 −0.202337 0.979316i \(-0.564854\pi\)
0.979316 + 0.202337i \(0.0648537\pi\)
\(488\) −1.03528 3.86370i −0.0468648 0.174902i
\(489\) 0 0
\(490\) 0 0
\(491\) 19.5000 11.2583i 0.880023 0.508081i 0.00935679 0.999956i \(-0.497022\pi\)
0.870666 + 0.491875i \(0.163688\pi\)
\(492\) 0 0
\(493\) −10.0382 + 2.68973i −0.452098 + 0.121139i
\(494\) 24.2487 1.09100
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 46.3644 12.4233i 2.07973 0.557262i
\(498\) 0 0
\(499\) −16.4545 + 9.50000i −0.736604 + 0.425278i −0.820833 0.571168i \(-0.806490\pi\)
0.0842294 + 0.996446i \(0.473157\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 6.72432 + 25.0955i 0.300121 + 1.12007i
\(503\) 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
\(508\) −2.68973 + 10.0382i −0.119337 + 0.445373i
\(509\) −10.3923 18.0000i −0.460631 0.797836i 0.538362 0.842714i \(-0.319043\pi\)
−0.998992 + 0.0448779i \(0.985710\pi\)
\(510\) 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
\(517\) −10.0382 2.68973i −0.441479 0.118294i
\(518\) −23.1822 6.21166i −1.01857 0.272925i
\(519\) 0 0
\(520\) 0 0
\(521\) 5.19615i 0.227648i 0.993501 + 0.113824i \(0.0363099\pi\)
−0.993501 + 0.113824i \(0.963690\pi\)
\(522\) 0 0
\(523\) −12.2474 12.2474i −0.535544 0.535544i 0.386673 0.922217i \(-0.373624\pi\)
−0.922217 + 0.386673i \(0.873624\pi\)
\(524\) −1.73205 + 3.00000i −0.0756650 + 0.131056i
\(525\) 0 0
\(526\) −3.00000 5.19615i −0.130806 0.226563i
\(527\) 6.21166 23.1822i 0.270584 1.00983i
\(528\) 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
\(533\) −10.8704 40.5689i −0.470849 1.75723i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.50000 0.866025i 0.0647901 0.0374066i
\(537\) 0 0
\(538\) −6.69213 + 1.79315i −0.288518 + 0.0773082i
\(539\) −8.66025 −0.373024
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −27.0459 + 7.24693i −1.16172 + 0.311282i
\(543\) 0 0
\(544\) −2.59808 + 1.50000i −0.111392 + 0.0643120i
\(545\) 0 0
\(546\) 0 0
\(547\) 5.82774 + 21.7494i 0.249176 + 0.929938i 0.971238 + 0.238110i \(0.0765278\pi\)
−0.722062 + 0.691828i \(0.756805\pi\)
\(548\) −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
\(553\) −3.58630 + 13.3843i −0.152505 + 0.569157i
\(554\) 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
\(562\) −20.0764 5.37945i −0.846871 0.226919i
\(563\) 14.4889 + 3.88229i 0.610634 + 0.163619i 0.550866 0.834593i \(-0.314297\pi\)
0.0597675 + 0.998212i \(0.480964\pi\)
\(564\) 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 \(-0.964102\pi\)
0.594285 + 0.804255i \(0.297435\pi\)
\(570\) 0 0
\(571\) −2.50000 4.33013i −0.104622 0.181210i 0.808962 0.587861i \(-0.200030\pi\)
−0.913584 + 0.406651i \(0.866697\pi\)
\(572\) 1.55291 5.79555i 0.0649306 0.242324i
\(573\) 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 −0.0307771 0.999526i \(-0.509798\pi\)
0.999526 + 0.0307771i \(0.00979822\pi\)
\(578\) −2.07055 7.72741i −0.0861236 0.321418i
\(579\) 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
\(587\) 31.8756 8.54103i 1.31564 0.352526i 0.468300 0.883569i \(-0.344867\pi\)
0.847345 + 0.531043i \(0.178200\pi\)
\(588\) 0 0
\(589\) −48.4974 + 28.0000i −1.99830 + 1.15372i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.79315 + 6.69213i 0.0736980 + 0.275045i
\(593\) −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
\(598\) 5.37945 20.0764i 0.219982 0.820985i
\(599\) 6.92820 + 12.0000i 0.283079 + 0.490307i 0.972141 0.234395i \(-0.0753109\pi\)
−0.689063 + 0.724702i \(0.741978\pi\)
\(600\) 0 0
\(601\) 14.5000 25.1147i 0.591467 1.02445i −0.402568 0.915390i \(-0.631882\pi\)
0.994035 0.109061i \(-0.0347845\pi\)
\(602\) −12.7279 12.7279i −0.518751 0.518751i
\(603\) 0 0
\(604\) 10.0000i 0.406894i
\(605\) 0 0
\(606\) 0 0
\(607\) −13.3843 3.58630i −0.543250 0.145564i −0.0232502 0.999730i \(-0.507401\pi\)
−0.520000 + 0.854166i \(0.674068\pi\)
\(608\) 6.76148 + 1.81173i 0.274214 + 0.0734755i
\(609\) 0 0
\(610\) 0 0
\(611\) 20.7846i 0.840855i
\(612\) 0 0
\(613\) 4.89898 + 4.89898i 0.197868 + 0.197868i 0.799085 0.601218i \(-0.205317\pi\)
−0.601218 + 0.799085i \(0.705317\pi\)
\(614\) 2.59808 4.50000i 0.104850 0.181605i
\(615\) 0 0
\(616\) 3.00000 + 5.19615i 0.120873 + 0.209359i
\(617\) 11.6469 43.4667i 0.468885 1.74990i −0.174793 0.984605i \(-0.555926\pi\)
0.643678 0.765297i \(-0.277408\pi\)
\(618\) 0 0
\(619\) 11.2583 + 6.50000i 0.452510 + 0.261257i 0.708890 0.705319i \(-0.249196\pi\)
−0.256379 + 0.966576i \(0.582530\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 2.44949 2.44949i 0.0982156 0.0982156i
\(623\) −6.21166 23.1822i −0.248865 0.928776i
\(624\) 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 \(0.369672\pi\)
\(632\) 3.86370 1.03528i 0.153690 0.0411811i
\(633\) 0 0
\(634\) −5.19615 + 3.00000i −0.206366 + 0.119145i
\(635\) 0 0
\(636\) 0 0
\(637\) 4.48288 + 16.7303i 0.177618 + 0.662880i
\(638\) 4.24264 4.24264i 0.167968 0.167968i
\(639\) 0 0
\(640\) 0 0
\(641\) −19.5000 11.2583i −0.770204 0.444677i 0.0627436 0.998030i \(-0.480015\pi\)
−0.832947 + 0.553352i \(0.813348\pi\)
\(642\) 0 0
\(643\) −9.41404 + 35.1337i −0.371254 + 1.38554i 0.487489 + 0.873129i \(0.337913\pi\)
−0.858742 + 0.512408i \(0.828754\pi\)
\(644\) 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
\(652\) −3.34607 0.896575i −0.131042 0.0351126i
\(653\) −17.3867 4.65874i −0.680393 0.182311i −0.0979610 0.995190i \(-0.531232\pi\)
−0.582432 + 0.812880i \(0.697899\pi\)
\(654\) 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 \(-0.898212\pi\)
0.746892 + 0.664945i \(0.231545\pi\)
\(660\) 0 0
\(661\) 16.0000 + 27.7128i 0.622328 + 1.07790i 0.989051 + 0.147573i \(0.0471463\pi\)
−0.366723 + 0.930330i \(0.619520\pi\)
\(662\) 7.24693 27.0459i 0.281660 1.05117i
\(663\) 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
\(673\) 6.69213 1.79315i 0.257963 0.0691209i −0.127520 0.991836i \(-0.540702\pi\)
0.385483 + 0.922715i \(0.374035\pi\)
\(674\) −12.1244 −0.467013
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) −11.5911 + 3.10583i −0.445483 + 0.119367i −0.474585 0.880210i \(-0.657402\pi\)
0.0291023 + 0.999576i \(0.490735\pi\)
\(678\) 0 0
\(679\) 25.9808 15.0000i 0.997050 0.575647i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.58630 + 13.3843i 0.137327 + 0.512510i
\(683\) 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
\(688\) −1.34486 + 5.01910i −0.0512724 + 0.191351i
\(689\) 0 0
\(690\) 0 0
\(691\) 4.00000 6.92820i 0.152167 0.263561i −0.779857 0.625958i \(-0.784708\pi\)
0.932024 + 0.362397i \(0.118041\pi\)
\(692\) 4.24264 + 4.24264i 0.161281 + 0.161281i
\(693\) 0 0
\(694\) 15.0000i 0.569392i
\(695\) 0 0
\(696\) 0 0
\(697\) −35.1337 9.41404i −1.33078 0.356582i
\(698\) 7.72741 + 2.07055i 0.292487 + 0.0783716i
\(699\) 0 0
\(700\) 0 0
\(701\) 17.3205i 0.654187i −0.944992 0.327093i \(-0.893931\pi\)
0.944992 0.327093i \(-0.106069\pi\)
\(702\) 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
\(707\) −6.21166 + 23.1822i −0.233613 + 0.871857i
\(708\) 0 0
\(709\) −34.6410 20.0000i −1.30097 0.751116i −0.320400 0.947282i \(-0.603817\pi\)
−0.980571 + 0.196167i \(0.937151\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −4.89898 + 4.89898i −0.183597 + 0.183597i
\(713\) 12.4233 + 46.3644i 0.465257 + 1.73636i
\(714\) 0 0
\(715\) 0 0
\(716\) −3.00000 + 1.73205i −0.112115 + 0.0647298i
\(717\) 0 0
\(718\) −23.4225 + 6.27603i −0.874118 + 0.234219i
\(719\) −27.7128 −1.03351 −0.516757 0.856132i \(-0.672861\pi\)
−0.516757 + 0.856132i \(0.672861\pi\)
\(720\) 0 0
\(721\) 60.0000 2.23452
\(722\) −28.9778 + 7.76457i −1.07844 + 0.288967i
\(723\) 0 0
\(724\) −1.73205 + 1.00000i −0.0643712 + 0.0371647i
\(725\) 0 0
\(726\) 0 0
\(727\) 2.68973 + 10.0382i 0.0997564 + 0.372296i 0.997698 0.0678194i \(-0.0216042\pi\)
−0.897941 + 0.440115i \(0.854938\pi\)
\(728\) 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
\(733\) −13.4486 + 50.1910i −0.496737 + 1.85385i 0.0233418 + 0.999728i \(0.492569\pi\)
−0.520078 + 0.854119i \(0.674097\pi\)
\(734\) −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
\(743\) 17.3867 + 4.65874i 0.637855 + 0.170913i 0.563232 0.826299i \(-0.309558\pi\)
0.0746233 + 0.997212i \(0.476225\pi\)
\(744\) 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 0.988761 0.149505i \(-0.0477681\pi\)
−0.623856 + 0.781540i \(0.714435\pi\)
\(752\) −1.55291 + 5.79555i −0.0566290 + 0.211342i
\(753\) 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 −0.999790 0.0204799i \(-0.993481\pi\)
0.0204799 + 0.999790i \(0.493481\pi\)
\(758\) 0.258819 + 0.965926i 0.00940073 + 0.0350840i
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000 17.3205i 1.08750 0.627868i 0.154590 0.987979i \(-0.450594\pi\)
0.932910 + 0.360111i \(0.117261\pi\)
\(762\) 0 0
\(763\) 13.3843 3.58630i 0.484543 0.129833i
\(764\) −24.2487 −0.877288
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) 40.5689 10.8704i 1.46486 0.392507i
\(768\) 0 0
\(769\) 12.1244 7.00000i 0.437215 0.252426i −0.265200 0.964193i \(-0.585438\pi\)
0.702416 + 0.711767i \(0.252105\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.24144 + 8.36516i 0.0806711 + 0.301069i
\(773\) −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
\(778\) −2.68973 + 10.0382i −0.0964314 + 0.359887i
\(779\) 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
\(787\) 16.7303 + 4.48288i 0.596372 + 0.159797i 0.544364 0.838849i \(-0.316771\pi\)
0.0520081 + 0.998647i \(0.483438\pi\)
\(788\) −23.1822 6.21166i −0.825832 0.221281i
\(789\) 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
\(797\) 6.21166 23.1822i 0.220028 0.821156i −0.764308 0.644852i \(-0.776919\pi\)
0.984336 0.176304i \(-0.0564143\pi\)
\(798\) 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
\(803\) 3.88229 + 14.4889i 0.137003 + 0.511302i
\(804\) 0 0
\(805\) 0 0
\(806\) 24.0000 13.8564i 0.845364 0.488071i
\(807\) 0 0
\(808\) 6.69213 1.79315i 0.235428 0.0630828i
\(809\) 12.1244 0.426270 0.213135 0.977023i \(-0.431633\pi\)
0.213135 + 0.977023i \(0.431633\pi\)
\(810\) 0 0
\(811\) −41.0000 −1.43970 −0.719852 0.694127i \(-0.755791\pi\)
−0.719852 + 0.694127i \(0.755791\pi\)
\(812\) 11.5911 3.10583i 0.406768 0.108993i
\(813\) 0 0
\(814\) −10.3923 + 6.00000i −0.364250 + 0.210300i
\(815\) 0 0
\(816\) 0 0
\(817\) −9.41404 35.1337i −0.329356 1.22917i
\(818\) 4.94975 4.94975i 0.173064 0.173064i
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 8.66025i −0.523504 0.302245i 0.214863 0.976644i \(-0.431069\pi\)
−0.738367 + 0.674399i \(0.764403\pi\)
\(822\) 0 0
\(823\) −3.58630 + 13.3843i −0.125011 + 0.466546i −0.999840 0.0178851i \(-0.994307\pi\)
0.874829 + 0.484431i \(0.160973\pi\)
\(824\) −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
\(832\) −3.34607 0.896575i −0.116004 0.0310832i
\(833\) 14.4889 + 3.88229i 0.502010 + 0.134513i
\(834\) 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 0.395150 + 0.918617i \(0.370693\pi\)
−0.993120 + 0.117098i \(0.962641\pi\)
\(840\) 0 0
\(841\) 8.50000 + 14.7224i 0.293103 + 0.507670i
\(842\) −7.24693 + 27.0459i −0.249746 + 0.932064i
\(843\) 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
\(853\) 36.8067 9.86233i 1.26024 0.337680i 0.433955 0.900935i \(-0.357118\pi\)
0.826283 + 0.563255i \(0.190451\pi\)
\(854\) 13.8564 0.474156
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) −40.5689 + 10.8704i −1.38581 + 0.371326i −0.873227 0.487314i \(-0.837977\pi\)
−0.512580 + 0.858640i \(0.671310\pi\)
\(858\) 0 0
\(859\) −11.2583 + 6.50000i −0.384129 + 0.221777i −0.679613 0.733571i \(-0.737852\pi\)
0.295484 + 0.955348i \(0.404519\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.896575 3.34607i −0.0305375 0.113967i
\(863\) 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
\(868\) −7.17260 + 26.7685i −0.243454 + 0.908583i
\(869\) 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
\(877\) 26.7685 + 7.17260i 0.903909 + 0.242202i 0.680694 0.732568i \(-0.261678\pi\)
0.223215 + 0.974769i \(0.428345\pi\)
\(878\) 15.4548 + 4.14110i 0.521575 + 0.139756i
\(879\) 0 0
\(880\) 0 0
\(881\) 6.92820i 0.233417i −0.993166 0.116709i \(-0.962766\pi\)
0.993166 0.116709i \(-0.0372343\pi\)
\(882\) 0 0
\(883\) −8.57321 8.57321i −0.288512 0.288512i 0.547980 0.836492i \(-0.315397\pi\)
−0.836492 + 0.547980i \(0.815397\pi\)
\(884\) −5.19615 + 9.00000i −0.174766 + 0.302703i
\(885\) 0 0
\(886\) 13.5000 + 23.3827i 0.453541 + 0.785557i
\(887\) −12.4233 + 46.3644i −0.417134 + 1.55677i 0.363388 + 0.931638i \(0.381620\pi\)
−0.780522 + 0.625128i \(0.785047\pi\)
\(888\) 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
\(893\) −10.8704 40.5689i −0.363764 1.35759i
\(894\) 0 0
\(895\) 0 0
\(896\) 3.00000 1.73205i 0.100223 0.0578638i
\(897\) 0 0
\(898\) 38.4797 10.3106i 1.28409 0.344070i
\(899\) 27.7128 0.924274
\(900\) 0 0
\(901\) 0 0
\(902\) 20.2844 5.43520i 0.675398 0.180972i
\(903\) 0 0
\(904\) −15.5885 + 9.00000i −0.518464 + 0.299336i
\(905\) 0 0
\(906\) 0 0
\(907\) 2.24144 + 8.36516i 0.0744257 + 0.277761i 0.993102 0.117250i \(-0.0374077\pi\)
−0.918677 + 0.395010i \(0.870741\pi\)
\(908\) −2.12132 + 2.12132i −0.0703985 + 0.0703985i
\(909\) 0 0
\(910\) 0 0
\(911\) 30.0000 + 17.3205i 0.993944 + 0.573854i 0.906451 0.422311i \(-0.138781\pi\)
0.0874934 + 0.996165i \(0.472114\pi\)
\(912\) 0 0
\(913\) 5.37945 20.0764i 0.178034 0.664432i
\(914\) −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
\(922\) −16.7303 4.48288i −0.550984 0.147636i
\(923\) −46.3644 12.4233i −1.52610 0.408918i
\(924\) 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 −0.428470 0.903556i \(-0.640947\pi\)
0.996737 0.0807121i \(-0.0257194\pi\)
\(930\) 0 0
\(931\) −17.5000 30.3109i −0.573539 0.993399i
\(932\) 0.776457 2.89778i 0.0254337 0.0949199i
\(933\) 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 −0.182915 0.983129i \(-0.558553\pi\)
0.983129 + 0.182915i \(0.0585534\pi\)
\(938\) 1.55291 + 5.79555i 0.0507044 + 0.189232i
\(939\) 0 0
\(940\) 0 0
\(941\) 18.0000 10.3923i 0.586783 0.338779i −0.177041 0.984203i \(-0.556653\pi\)
0.763825 + 0.645424i \(0.223319\pi\)
\(942\) 0 0
\(943\) 70.2674 18.8281i 2.28822 0.613127i
\(944\) 12.1244 0.394614
\(945\) 0 0
\(946\) −9.00000 −0.292615
\(947\) −26.0800 + 6.98811i −0.847486 + 0.227083i −0.656328 0.754476i \(-0.727891\pi\)
−0.191158 + 0.981559i \(0.561224\pi\)
\(948\) 0 0
\(949\) 25.9808 15.0000i 0.843371 0.486921i
\(950\) 0 0
\(951\) 0 0
\(952\) −2.68973 10.0382i −0.0871745 0.325340i
\(953\) 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
\(958\) 4.48288 16.7303i 0.144835 0.540532i
\(959\) −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
\(967\) −3.34607 0.896575i −0.107602 0.0288319i 0.204616 0.978842i \(-0.434405\pi\)
−0.312218 + 0.950010i \(0.601072\pi\)
\(968\) −7.72741 2.07055i −0.248368 0.0665501i
\(969\) 0 0
\(970\) 0 0
\(971\) 3.46410i 0.111168i 0.998454 + 0.0555842i \(0.0177021\pi\)
−0.998454 + 0.0555842i \(0.982298\pi\)
\(972\) 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
\(977\) 0.776457 2.89778i 0.0248411 0.0927081i −0.952392 0.304875i \(-0.901385\pi\)
0.977233 + 0.212167i \(0.0680520\pi\)
\(978\) 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
\(983\) 9.31749 + 34.7733i 0.297182 + 1.10910i 0.939469 + 0.342633i \(0.111319\pi\)
−0.642288 + 0.766464i \(0.722015\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −9.00000 + 5.19615i −0.286618 + 0.165479i
\(987\) 0 0
\(988\) 23.4225 6.27603i 0.745168 0.199667i
\(989\) −31.1769 −0.991368
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) 7.72741 2.07055i 0.245345 0.0657401i
\(993\) 0 0
\(994\) 41.5692 24.0000i 1.31850 0.761234i
\(995\) 0 0
\(996\) 0 0
\(997\) 10.7589 + 40.1528i 0.340738 + 1.27165i 0.897513 + 0.440988i \(0.145372\pi\)
−0.556775 + 0.830663i \(0.687961\pi\)
\(998\) −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.143.2 8
3.2 odd 2 450.2.p.f.443.1 yes 8
5.2 odd 4 inner 1350.2.q.f.1007.2 8
5.3 odd 4 inner 1350.2.q.f.1007.1 8
5.4 even 2 inner 1350.2.q.f.143.1 8
9.4 even 3 450.2.p.f.293.1 yes 8
9.5 odd 6 inner 1350.2.q.f.1043.2 8
15.2 even 4 450.2.p.f.407.1 yes 8
15.8 even 4 450.2.p.f.407.2 yes 8
15.14 odd 2 450.2.p.f.443.2 yes 8
45.4 even 6 450.2.p.f.293.2 yes 8
45.13 odd 12 450.2.p.f.257.2 yes 8
45.14 odd 6 inner 1350.2.q.f.1043.1 8
45.22 odd 12 450.2.p.f.257.1 8
45.23 even 12 inner 1350.2.q.f.557.1 8
45.32 even 12 inner 1350.2.q.f.557.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.p.f.257.1 8 45.22 odd 12
450.2.p.f.257.2 yes 8 45.13 odd 12
450.2.p.f.293.1 yes 8 9.4 even 3
450.2.p.f.293.2 yes 8 45.4 even 6
450.2.p.f.407.1 yes 8 15.2 even 4
450.2.p.f.407.2 yes 8 15.8 even 4
450.2.p.f.443.1 yes 8 3.2 odd 2
450.2.p.f.443.2 yes 8 15.14 odd 2
1350.2.q.f.143.1 8 5.4 even 2 inner
1350.2.q.f.143.2 8 1.1 even 1 trivial
1350.2.q.f.557.1 8 45.23 even 12 inner
1350.2.q.f.557.2 8 45.32 even 12 inner
1350.2.q.f.1007.1 8 5.3 odd 4 inner
1350.2.q.f.1007.2 8 5.2 odd 4 inner
1350.2.q.f.1043.1 8 45.14 odd 6 inner
1350.2.q.f.1043.2 8 9.5 odd 6 inner