Properties

Label 1050.3.c.a.449.6
Level $1050$
Weight $3$
Character 1050.449
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,3,Mod(449,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.449");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.c (of order \(2\), degree \(1\), 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: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.157351936.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + x^{4} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5^{4} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.6
Root \(-1.28897 - 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 1050.449
Dual form 1050.3.c.a.449.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421 q^{2} +(-1.41421 - 2.64575i) q^{3} +2.00000 q^{4} +(-2.00000 - 3.74166i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-5.00000 + 7.48331i) q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +(-1.41421 - 2.64575i) q^{3} +2.00000 q^{4} +(-2.00000 - 3.74166i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-5.00000 + 7.48331i) q^{9} +14.5544i q^{11} +(-2.82843 - 5.29150i) q^{12} +0.583005i q^{13} -3.74166i q^{14} +4.00000 q^{16} -21.5367 q^{17} +(-7.07107 + 10.5830i) q^{18} +16.0000 q^{19} +(-7.00000 + 3.74166i) q^{21} +20.5830i q^{22} -38.8308 q^{23} +(-4.00000 - 7.48331i) q^{24} +0.824494i q^{26} +(26.8701 + 2.64575i) q^{27} -5.29150i q^{28} +35.7676i q^{29} -58.4575 q^{31} +5.65685 q^{32} +(38.5073 - 20.5830i) q^{33} -30.4575 q^{34} +(-10.0000 + 14.9666i) q^{36} +20.0000i q^{37} +22.6274 q^{38} +(1.54249 - 0.824494i) q^{39} +8.75149i q^{41} +(-9.89949 + 5.29150i) q^{42} +11.7490i q^{43} +29.1088i q^{44} -54.9150 q^{46} -8.48528 q^{47} +(-5.65685 - 10.5830i) q^{48} -7.00000 q^{49} +(30.4575 + 56.9808i) q^{51} +1.16601i q^{52} +50.9117 q^{53} +(38.0000 + 3.74166i) q^{54} -7.48331i q^{56} +(-22.6274 - 42.3320i) q^{57} +50.5830i q^{58} +58.2175i q^{59} +38.9150 q^{61} -82.6714 q^{62} +(19.7990 + 13.2288i) q^{63} +8.00000 q^{64} +(54.4575 - 29.1088i) q^{66} +70.5830i q^{67} -43.0734 q^{68} +(54.9150 + 102.737i) q^{69} +17.0279i q^{71} +(-14.1421 + 21.1660i) q^{72} -72.3320i q^{73} +28.2843i q^{74} +32.0000 q^{76} +38.5073 q^{77} +(2.18141 - 1.16601i) q^{78} -20.9150 q^{79} +(-31.0000 - 74.8331i) q^{81} +12.3765i q^{82} +145.544 q^{83} +(-14.0000 + 7.48331i) q^{84} +16.6156i q^{86} +(94.6321 - 50.5830i) q^{87} +41.1660i q^{88} +53.6514i q^{89} +1.54249 q^{91} -77.6616 q^{92} +(82.6714 + 154.664i) q^{93} -12.0000 q^{94} +(-8.00000 - 14.9666i) q^{96} -111.166i q^{97} -9.89949 q^{98} +(-108.915 - 72.7719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{4} - 16 q^{6} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{4} - 16 q^{6} - 40 q^{9} + 32 q^{16} + 128 q^{19} - 56 q^{21} - 32 q^{24} - 256 q^{31} - 32 q^{34} - 80 q^{36} + 224 q^{39} - 16 q^{46} - 56 q^{49} + 32 q^{51} + 304 q^{54} - 112 q^{61} + 64 q^{64} + 224 q^{66} + 16 q^{69} + 256 q^{76} + 256 q^{79} - 248 q^{81} - 112 q^{84} + 224 q^{91} - 96 q^{94} - 64 q^{96} - 448 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) −1.41421 2.64575i −0.471405 0.881917i
\(4\) 2.00000 0.500000
\(5\) 0 0
\(6\) −2.00000 3.74166i −0.333333 0.623610i
\(7\) 2.64575i 0.377964i
\(8\) 2.82843 0.353553
\(9\) −5.00000 + 7.48331i −0.555556 + 0.831479i
\(10\) 0 0
\(11\) 14.5544i 1.32313i 0.749890 + 0.661563i \(0.230107\pi\)
−0.749890 + 0.661563i \(0.769893\pi\)
\(12\) −2.82843 5.29150i −0.235702 0.440959i
\(13\) 0.583005i 0.0448466i 0.999749 + 0.0224233i \(0.00713815\pi\)
−0.999749 + 0.0224233i \(0.992862\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) −21.5367 −1.26687 −0.633433 0.773798i \(-0.718355\pi\)
−0.633433 + 0.773798i \(0.718355\pi\)
\(18\) −7.07107 + 10.5830i −0.392837 + 0.587945i
\(19\) 16.0000 0.842105 0.421053 0.907036i \(-0.361661\pi\)
0.421053 + 0.907036i \(0.361661\pi\)
\(20\) 0 0
\(21\) −7.00000 + 3.74166i −0.333333 + 0.178174i
\(22\) 20.5830i 0.935591i
\(23\) −38.8308 −1.68830 −0.844148 0.536111i \(-0.819893\pi\)
−0.844148 + 0.536111i \(0.819893\pi\)
\(24\) −4.00000 7.48331i −0.166667 0.311805i
\(25\) 0 0
\(26\) 0.824494i 0.0317113i
\(27\) 26.8701 + 2.64575i 0.995187 + 0.0979908i
\(28\) 5.29150i 0.188982i
\(29\) 35.7676i 1.23337i 0.787212 + 0.616683i \(0.211524\pi\)
−0.787212 + 0.616683i \(0.788476\pi\)
\(30\) 0 0
\(31\) −58.4575 −1.88573 −0.942863 0.333180i \(-0.891878\pi\)
−0.942863 + 0.333180i \(0.891878\pi\)
\(32\) 5.65685 0.176777
\(33\) 38.5073 20.5830i 1.16689 0.623727i
\(34\) −30.4575 −0.895809
\(35\) 0 0
\(36\) −10.0000 + 14.9666i −0.277778 + 0.415740i
\(37\) 20.0000i 0.540541i 0.962784 + 0.270270i \(0.0871131\pi\)
−0.962784 + 0.270270i \(0.912887\pi\)
\(38\) 22.6274 0.595458
\(39\) 1.54249 0.824494i 0.0395509 0.0211409i
\(40\) 0 0
\(41\) 8.75149i 0.213451i 0.994289 + 0.106725i \(0.0340366\pi\)
−0.994289 + 0.106725i \(0.965963\pi\)
\(42\) −9.89949 + 5.29150i −0.235702 + 0.125988i
\(43\) 11.7490i 0.273233i 0.990624 + 0.136616i \(0.0436228\pi\)
−0.990624 + 0.136616i \(0.956377\pi\)
\(44\) 29.1088i 0.661563i
\(45\) 0 0
\(46\) −54.9150 −1.19380
\(47\) −8.48528 −0.180538 −0.0902690 0.995917i \(-0.528773\pi\)
−0.0902690 + 0.995917i \(0.528773\pi\)
\(48\) −5.65685 10.5830i −0.117851 0.220479i
\(49\) −7.00000 −0.142857
\(50\) 0 0
\(51\) 30.4575 + 56.9808i 0.597206 + 1.11727i
\(52\) 1.16601i 0.0224233i
\(53\) 50.9117 0.960598 0.480299 0.877105i \(-0.340528\pi\)
0.480299 + 0.877105i \(0.340528\pi\)
\(54\) 38.0000 + 3.74166i 0.703704 + 0.0692900i
\(55\) 0 0
\(56\) 7.48331i 0.133631i
\(57\) −22.6274 42.3320i −0.396972 0.742667i
\(58\) 50.5830i 0.872121i
\(59\) 58.2175i 0.986738i 0.869820 + 0.493369i \(0.164235\pi\)
−0.869820 + 0.493369i \(0.835765\pi\)
\(60\) 0 0
\(61\) 38.9150 0.637951 0.318976 0.947763i \(-0.396661\pi\)
0.318976 + 0.947763i \(0.396661\pi\)
\(62\) −82.6714 −1.33341
\(63\) 19.7990 + 13.2288i 0.314270 + 0.209980i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 54.4575 29.1088i 0.825114 0.441042i
\(67\) 70.5830i 1.05348i 0.850027 + 0.526739i \(0.176585\pi\)
−0.850027 + 0.526739i \(0.823415\pi\)
\(68\) −43.0734 −0.633433
\(69\) 54.9150 + 102.737i 0.795870 + 1.48894i
\(70\) 0 0
\(71\) 17.0279i 0.239829i 0.992784 + 0.119915i \(0.0382621\pi\)
−0.992784 + 0.119915i \(0.961738\pi\)
\(72\) −14.1421 + 21.1660i −0.196419 + 0.293972i
\(73\) 72.3320i 0.990850i −0.868651 0.495425i \(-0.835012\pi\)
0.868651 0.495425i \(-0.164988\pi\)
\(74\) 28.2843i 0.382220i
\(75\) 0 0
\(76\) 32.0000 0.421053
\(77\) 38.5073 0.500095
\(78\) 2.18141 1.16601i 0.0279667 0.0149489i
\(79\) −20.9150 −0.264747 −0.132374 0.991200i \(-0.542260\pi\)
−0.132374 + 0.991200i \(0.542260\pi\)
\(80\) 0 0
\(81\) −31.0000 74.8331i −0.382716 0.923866i
\(82\) 12.3765i 0.150933i
\(83\) 145.544 1.75354 0.876770 0.480910i \(-0.159694\pi\)
0.876770 + 0.480910i \(0.159694\pi\)
\(84\) −14.0000 + 7.48331i −0.166667 + 0.0890871i
\(85\) 0 0
\(86\) 16.6156i 0.193205i
\(87\) 94.6321 50.5830i 1.08773 0.581414i
\(88\) 41.1660i 0.467796i
\(89\) 53.6514i 0.602824i 0.953494 + 0.301412i \(0.0974580\pi\)
−0.953494 + 0.301412i \(0.902542\pi\)
\(90\) 0 0
\(91\) 1.54249 0.0169504
\(92\) −77.6616 −0.844148
\(93\) 82.6714 + 154.664i 0.888940 + 1.66305i
\(94\) −12.0000 −0.127660
\(95\) 0 0
\(96\) −8.00000 14.9666i −0.0833333 0.155902i
\(97\) 111.166i 1.14604i −0.819541 0.573021i \(-0.805771\pi\)
0.819541 0.573021i \(-0.194229\pi\)
\(98\) −9.89949 −0.101015
\(99\) −108.915 72.7719i −1.10015 0.735070i
\(100\) 0 0
\(101\) 57.8367i 0.572641i 0.958134 + 0.286320i \(0.0924322\pi\)
−0.958134 + 0.286320i \(0.907568\pi\)
\(102\) 43.0734 + 80.5830i 0.422289 + 0.790029i
\(103\) 119.373i 1.15896i 0.814988 + 0.579478i \(0.196744\pi\)
−0.814988 + 0.579478i \(0.803256\pi\)
\(104\) 1.64899i 0.0158557i
\(105\) 0 0
\(106\) 72.0000 0.679245
\(107\) −116.492 −1.08871 −0.544357 0.838854i \(-0.683226\pi\)
−0.544357 + 0.838854i \(0.683226\pi\)
\(108\) 53.7401 + 5.29150i 0.497594 + 0.0489954i
\(109\) −87.8301 −0.805780 −0.402890 0.915248i \(-0.631994\pi\)
−0.402890 + 0.915248i \(0.631994\pi\)
\(110\) 0 0
\(111\) 52.9150 28.2843i 0.476712 0.254813i
\(112\) 10.5830i 0.0944911i
\(113\) −69.1763 −0.612180 −0.306090 0.952003i \(-0.599021\pi\)
−0.306090 + 0.952003i \(0.599021\pi\)
\(114\) −32.0000 59.8665i −0.280702 0.525145i
\(115\) 0 0
\(116\) 71.5352i 0.616683i
\(117\) −4.36281 2.91503i −0.0372890 0.0249148i
\(118\) 82.3320i 0.697729i
\(119\) 56.9808i 0.478830i
\(120\) 0 0
\(121\) −90.8301 −0.750662
\(122\) 55.0342 0.451100
\(123\) 23.1543 12.3765i 0.188246 0.100622i
\(124\) −116.915 −0.942863
\(125\) 0 0
\(126\) 28.0000 + 18.7083i 0.222222 + 0.148478i
\(127\) 27.0850i 0.213268i −0.994298 0.106634i \(-0.965993\pi\)
0.994298 0.106634i \(-0.0340072\pi\)
\(128\) 11.3137 0.0883883
\(129\) 31.0850 16.6156i 0.240969 0.128803i
\(130\) 0 0
\(131\) 145.544i 1.11102i −0.831509 0.555511i \(-0.812523\pi\)
0.831509 0.555511i \(-0.187477\pi\)
\(132\) 77.0146 41.1660i 0.583444 0.311864i
\(133\) 42.3320i 0.318286i
\(134\) 99.8194i 0.744921i
\(135\) 0 0
\(136\) −60.9150 −0.447905
\(137\) 24.8088 0.181086 0.0905431 0.995893i \(-0.471140\pi\)
0.0905431 + 0.995893i \(0.471140\pi\)
\(138\) 77.6616 + 145.292i 0.562765 + 1.05284i
\(139\) −146.458 −1.05365 −0.526826 0.849973i \(-0.676618\pi\)
−0.526826 + 0.849973i \(0.676618\pi\)
\(140\) 0 0
\(141\) 12.0000 + 22.4499i 0.0851064 + 0.159219i
\(142\) 24.0810i 0.169585i
\(143\) −8.48528 −0.0593376
\(144\) −20.0000 + 29.9333i −0.138889 + 0.207870i
\(145\) 0 0
\(146\) 102.293i 0.700636i
\(147\) 9.89949 + 18.5203i 0.0673435 + 0.125988i
\(148\) 40.0000i 0.270270i
\(149\) 219.552i 1.47351i 0.676162 + 0.736753i \(0.263642\pi\)
−0.676162 + 0.736753i \(0.736358\pi\)
\(150\) 0 0
\(151\) −211.660 −1.40172 −0.700861 0.713298i \(-0.747201\pi\)
−0.700861 + 0.713298i \(0.747201\pi\)
\(152\) 45.2548 0.297729
\(153\) 107.684 161.166i 0.703814 1.05337i
\(154\) 54.4575 0.353620
\(155\) 0 0
\(156\) 3.08497 1.64899i 0.0197755 0.0105704i
\(157\) 208.745i 1.32959i 0.747027 + 0.664793i \(0.231480\pi\)
−0.747027 + 0.664793i \(0.768520\pi\)
\(158\) −29.5783 −0.187205
\(159\) −72.0000 134.700i −0.452830 0.847168i
\(160\) 0 0
\(161\) 102.737i 0.638116i
\(162\) −43.8406 105.830i −0.270621 0.653272i
\(163\) 266.996i 1.63801i −0.573784 0.819006i \(-0.694525\pi\)
0.573784 0.819006i \(-0.305475\pi\)
\(164\) 17.5030i 0.106725i
\(165\) 0 0
\(166\) 205.830 1.23994
\(167\) −7.19124 −0.0430613 −0.0215307 0.999768i \(-0.506854\pi\)
−0.0215307 + 0.999768i \(0.506854\pi\)
\(168\) −19.7990 + 10.5830i −0.117851 + 0.0629941i
\(169\) 168.660 0.997989
\(170\) 0 0
\(171\) −80.0000 + 119.733i −0.467836 + 0.700193i
\(172\) 23.4980i 0.136616i
\(173\) 192.536 1.11293 0.556464 0.830872i \(-0.312158\pi\)
0.556464 + 0.830872i \(0.312158\pi\)
\(174\) 133.830 71.5352i 0.769138 0.411122i
\(175\) 0 0
\(176\) 58.2175i 0.330781i
\(177\) 154.029 82.3320i 0.870221 0.465153i
\(178\) 75.8745i 0.426261i
\(179\) 43.6631i 0.243928i −0.992535 0.121964i \(-0.961081\pi\)
0.992535 0.121964i \(-0.0389193\pi\)
\(180\) 0 0
\(181\) −81.0850 −0.447983 −0.223992 0.974591i \(-0.571909\pi\)
−0.223992 + 0.974591i \(0.571909\pi\)
\(182\) 2.18141 0.0119857
\(183\) −55.0342 102.959i −0.300733 0.562620i
\(184\) −109.830 −0.596902
\(185\) 0 0
\(186\) 116.915 + 218.728i 0.628575 + 1.17596i
\(187\) 313.454i 1.67622i
\(188\) −16.9706 −0.0902690
\(189\) 7.00000 71.0915i 0.0370370 0.376145i
\(190\) 0 0
\(191\) 53.5571i 0.280404i −0.990123 0.140202i \(-0.955225\pi\)
0.990123 0.140202i \(-0.0447751\pi\)
\(192\) −11.3137 21.1660i −0.0589256 0.110240i
\(193\) 110.494i 0.572508i 0.958154 + 0.286254i \(0.0924102\pi\)
−0.958154 + 0.286254i \(0.907590\pi\)
\(194\) 157.212i 0.810374i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) −86.1469 −0.437294 −0.218647 0.975804i \(-0.570164\pi\)
−0.218647 + 0.975804i \(0.570164\pi\)
\(198\) −154.029 102.915i −0.777925 0.519773i
\(199\) 88.0000 0.442211 0.221106 0.975250i \(-0.429033\pi\)
0.221106 + 0.975250i \(0.429033\pi\)
\(200\) 0 0
\(201\) 186.745 99.8194i 0.929080 0.496614i
\(202\) 81.7935i 0.404918i
\(203\) 94.6321 0.466168
\(204\) 60.9150 + 113.962i 0.298603 + 0.558635i
\(205\) 0 0
\(206\) 168.818i 0.819506i
\(207\) 194.154 290.583i 0.937942 1.40378i
\(208\) 2.33202i 0.0112116i
\(209\) 232.870i 1.11421i
\(210\) 0 0
\(211\) −61.2549 −0.290308 −0.145154 0.989409i \(-0.546368\pi\)
−0.145154 + 0.989409i \(0.546368\pi\)
\(212\) 101.823 0.480299
\(213\) 45.0515 24.0810i 0.211509 0.113057i
\(214\) −164.745 −0.769837
\(215\) 0 0
\(216\) 76.0000 + 7.48331i 0.351852 + 0.0346450i
\(217\) 154.664i 0.712738i
\(218\) −124.210 −0.569773
\(219\) −191.373 + 102.293i −0.873847 + 0.467091i
\(220\) 0 0
\(221\) 12.5560i 0.0568146i
\(222\) 74.8331 40.0000i 0.337086 0.180180i
\(223\) 150.494i 0.674861i −0.941350 0.337431i \(-0.890442\pi\)
0.941350 0.337431i \(-0.109558\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −97.8301 −0.432876
\(227\) −190.558 −0.839464 −0.419732 0.907648i \(-0.637876\pi\)
−0.419732 + 0.907648i \(0.637876\pi\)
\(228\) −45.2548 84.6640i −0.198486 0.371334i
\(229\) 142.915 0.624083 0.312042 0.950068i \(-0.398987\pi\)
0.312042 + 0.950068i \(0.398987\pi\)
\(230\) 0 0
\(231\) −54.4575 101.881i −0.235747 0.441042i
\(232\) 101.166i 0.436060i
\(233\) 7.83826 0.0336406 0.0168203 0.999859i \(-0.494646\pi\)
0.0168203 + 0.999859i \(0.494646\pi\)
\(234\) −6.16995 4.12247i −0.0263673 0.0176174i
\(235\) 0 0
\(236\) 116.435i 0.493369i
\(237\) 29.5783 + 55.3360i 0.124803 + 0.233485i
\(238\) 80.5830i 0.338584i
\(239\) 213.369i 0.892756i −0.894844 0.446378i \(-0.852714\pi\)
0.894844 0.446378i \(-0.147286\pi\)
\(240\) 0 0
\(241\) −130.000 −0.539419 −0.269710 0.962942i \(-0.586928\pi\)
−0.269710 + 0.962942i \(0.586928\pi\)
\(242\) −128.453 −0.530798
\(243\) −154.149 + 187.848i −0.634359 + 0.773038i
\(244\) 77.8301 0.318976
\(245\) 0 0
\(246\) 32.7451 17.5030i 0.133110 0.0711503i
\(247\) 9.32808i 0.0377655i
\(248\) −165.343 −0.666705
\(249\) −205.830 385.073i −0.826627 1.54648i
\(250\) 0 0
\(251\) 389.258i 1.55083i −0.631453 0.775415i \(-0.717541\pi\)
0.631453 0.775415i \(-0.282459\pi\)
\(252\) 39.5980 + 26.4575i 0.157135 + 0.104990i
\(253\) 565.158i 2.23383i
\(254\) 38.3039i 0.150803i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) −336.139 −1.30793 −0.653967 0.756523i \(-0.726897\pi\)
−0.653967 + 0.756523i \(0.726897\pi\)
\(258\) 43.9608 23.4980i 0.170391 0.0910776i
\(259\) 52.9150 0.204305
\(260\) 0 0
\(261\) −267.660 178.838i −1.02552 0.685203i
\(262\) 205.830i 0.785611i
\(263\) −438.933 −1.66895 −0.834473 0.551048i \(-0.814228\pi\)
−0.834473 + 0.551048i \(0.814228\pi\)
\(264\) 108.915 58.2175i 0.412557 0.220521i
\(265\) 0 0
\(266\) 59.8665i 0.225062i
\(267\) 141.948 75.8745i 0.531641 0.284174i
\(268\) 141.166i 0.526739i
\(269\) 14.4601i 0.0537549i 0.999639 + 0.0268775i \(0.00855639\pi\)
−0.999639 + 0.0268775i \(0.991444\pi\)
\(270\) 0 0
\(271\) 61.5425 0.227094 0.113547 0.993533i \(-0.463779\pi\)
0.113547 + 0.993533i \(0.463779\pi\)
\(272\) −86.1469 −0.316716
\(273\) −2.18141 4.08104i −0.00799050 0.0149489i
\(274\) 35.0850 0.128047
\(275\) 0 0
\(276\) 109.830 + 205.473i 0.397935 + 0.744468i
\(277\) 150.494i 0.543300i 0.962396 + 0.271650i \(0.0875693\pi\)
−0.962396 + 0.271650i \(0.912431\pi\)
\(278\) −207.122 −0.745044
\(279\) 292.288 437.456i 1.04763 1.56794i
\(280\) 0 0
\(281\) 300.220i 1.06840i 0.845359 + 0.534199i \(0.179387\pi\)
−0.845359 + 0.534199i \(0.820613\pi\)
\(282\) 16.9706 + 31.7490i 0.0601793 + 0.112585i
\(283\) 98.8340i 0.349237i −0.984636 0.174618i \(-0.944131\pi\)
0.984636 0.174618i \(-0.0558692\pi\)
\(284\) 34.0557i 0.119915i
\(285\) 0 0
\(286\) −12.0000 −0.0419580
\(287\) 23.1543 0.0806769
\(288\) −28.2843 + 42.3320i −0.0982093 + 0.146986i
\(289\) 174.830 0.604948
\(290\) 0 0
\(291\) −294.118 + 157.212i −1.01071 + 0.540249i
\(292\) 144.664i 0.495425i
\(293\) 7.15424 0.0244172 0.0122086 0.999925i \(-0.496114\pi\)
0.0122086 + 0.999925i \(0.496114\pi\)
\(294\) 14.0000 + 26.1916i 0.0476190 + 0.0890871i
\(295\) 0 0
\(296\) 56.5685i 0.191110i
\(297\) −38.5073 + 391.077i −0.129654 + 1.31676i
\(298\) 310.494i 1.04193i
\(299\) 22.6386i 0.0757142i
\(300\) 0 0
\(301\) 31.0850 0.103272
\(302\) −299.333 −0.991168
\(303\) 153.022 81.7935i 0.505022 0.269945i
\(304\) 64.0000 0.210526
\(305\) 0 0
\(306\) 152.288 227.923i 0.497672 0.744847i
\(307\) 105.830i 0.344723i 0.985034 + 0.172362i \(0.0551398\pi\)
−0.985034 + 0.172362i \(0.944860\pi\)
\(308\) 77.0146 0.250047
\(309\) 315.830 168.818i 1.02210 0.546337i
\(310\) 0 0
\(311\) 265.403i 0.853385i −0.904397 0.426692i \(-0.859679\pi\)
0.904397 0.426692i \(-0.140321\pi\)
\(312\) 4.36281 2.33202i 0.0139834 0.00747443i
\(313\) 259.328i 0.828524i −0.910158 0.414262i \(-0.864040\pi\)
0.910158 0.414262i \(-0.135960\pi\)
\(314\) 295.210i 0.940160i
\(315\) 0 0
\(316\) −41.8301 −0.132374
\(317\) −37.8233 −0.119316 −0.0596581 0.998219i \(-0.519001\pi\)
−0.0596581 + 0.998219i \(0.519001\pi\)
\(318\) −101.823 190.494i −0.320199 0.599038i
\(319\) −520.575 −1.63190
\(320\) 0 0
\(321\) 164.745 + 308.210i 0.513225 + 0.960155i
\(322\) 145.292i 0.451216i
\(323\) −344.587 −1.06683
\(324\) −62.0000 149.666i −0.191358 0.461933i
\(325\) 0 0
\(326\) 377.589i 1.15825i
\(327\) 124.210 + 232.376i 0.379848 + 0.710631i
\(328\) 24.7530i 0.0754663i
\(329\) 22.4499i 0.0682369i
\(330\) 0 0
\(331\) 145.490 0.439547 0.219774 0.975551i \(-0.429468\pi\)
0.219774 + 0.975551i \(0.429468\pi\)
\(332\) 291.088 0.876770
\(333\) −149.666 100.000i −0.449448 0.300300i
\(334\) −10.1699 −0.0304489
\(335\) 0 0
\(336\) −28.0000 + 14.9666i −0.0833333 + 0.0445435i
\(337\) 600.316i 1.78135i −0.454637 0.890677i \(-0.650231\pi\)
0.454637 0.890677i \(-0.349769\pi\)
\(338\) 238.521 0.705685
\(339\) 97.8301 + 183.023i 0.288584 + 0.539892i
\(340\) 0 0
\(341\) 850.813i 2.49505i
\(342\) −113.137 + 169.328i −0.330810 + 0.495111i
\(343\) 18.5203i 0.0539949i
\(344\) 33.2312i 0.0966024i
\(345\) 0 0
\(346\) 272.288 0.786958
\(347\) −31.6395 −0.0911803 −0.0455901 0.998960i \(-0.514517\pi\)
−0.0455901 + 0.998960i \(0.514517\pi\)
\(348\) 189.264 101.166i 0.543863 0.290707i
\(349\) 592.405 1.69744 0.848718 0.528846i \(-0.177375\pi\)
0.848718 + 0.528846i \(0.177375\pi\)
\(350\) 0 0
\(351\) −1.54249 + 15.6654i −0.00439455 + 0.0446307i
\(352\) 82.3320i 0.233898i
\(353\) −621.977 −1.76197 −0.880987 0.473141i \(-0.843120\pi\)
−0.880987 + 0.473141i \(0.843120\pi\)
\(354\) 217.830 116.435i 0.615339 0.328913i
\(355\) 0 0
\(356\) 107.303i 0.301412i
\(357\) 150.757 80.5830i 0.422289 0.225723i
\(358\) 61.7490i 0.172483i
\(359\) 499.509i 1.39139i −0.718337 0.695696i \(-0.755096\pi\)
0.718337 0.695696i \(-0.244904\pi\)
\(360\) 0 0
\(361\) −105.000 −0.290859
\(362\) −114.671 −0.316772
\(363\) 128.453 + 240.314i 0.353865 + 0.662021i
\(364\) 3.08497 0.00847520
\(365\) 0 0
\(366\) −77.8301 145.607i −0.212650 0.397833i
\(367\) 73.0039i 0.198921i 0.995042 + 0.0994604i \(0.0317117\pi\)
−0.995042 + 0.0994604i \(0.968288\pi\)
\(368\) −155.323 −0.422074
\(369\) −65.4902 43.7575i −0.177480 0.118584i
\(370\) 0 0
\(371\) 134.700i 0.363072i
\(372\) 165.343 + 309.328i 0.444470 + 0.831527i
\(373\) 474.664i 1.27256i 0.771459 + 0.636279i \(0.219527\pi\)
−0.771459 + 0.636279i \(0.780473\pi\)
\(374\) 443.290i 1.18527i
\(375\) 0 0
\(376\) −24.0000 −0.0638298
\(377\) −20.8527 −0.0553122
\(378\) 9.89949 100.539i 0.0261891 0.265975i
\(379\) 223.660 0.590132 0.295066 0.955477i \(-0.404658\pi\)
0.295066 + 0.955477i \(0.404658\pi\)
\(380\) 0 0
\(381\) −71.6601 + 38.3039i −0.188084 + 0.100535i
\(382\) 75.7411i 0.198275i
\(383\) 518.175 1.35294 0.676469 0.736471i \(-0.263509\pi\)
0.676469 + 0.736471i \(0.263509\pi\)
\(384\) −16.0000 29.9333i −0.0416667 0.0779512i
\(385\) 0 0
\(386\) 156.262i 0.404824i
\(387\) −87.9216 58.7451i −0.227188 0.151796i
\(388\) 222.332i 0.573021i
\(389\) 44.1383i 0.113466i −0.998389 0.0567330i \(-0.981932\pi\)
0.998389 0.0567330i \(-0.0180684\pi\)
\(390\) 0 0
\(391\) 836.288 2.13884
\(392\) −19.7990 −0.0505076
\(393\) −385.073 + 205.830i −0.979829 + 0.523741i
\(394\) −121.830 −0.309213
\(395\) 0 0
\(396\) −217.830 145.544i −0.550076 0.367535i
\(397\) 299.417i 0.754199i 0.926173 + 0.377099i \(0.123079\pi\)
−0.926173 + 0.377099i \(0.876921\pi\)
\(398\) 124.451 0.312690
\(399\) −112.000 + 59.8665i −0.280702 + 0.150041i
\(400\) 0 0
\(401\) 277.008i 0.690794i 0.938457 + 0.345397i \(0.112256\pi\)
−0.938457 + 0.345397i \(0.887744\pi\)
\(402\) 264.097 141.166i 0.656959 0.351159i
\(403\) 34.0810i 0.0845683i
\(404\) 115.673i 0.286320i
\(405\) 0 0
\(406\) 133.830 0.329631
\(407\) −291.088 −0.715203
\(408\) 86.1469 + 161.166i 0.211144 + 0.395015i
\(409\) 740.980 1.81169 0.905844 0.423612i \(-0.139238\pi\)
0.905844 + 0.423612i \(0.139238\pi\)
\(410\) 0 0
\(411\) −35.0850 65.6380i −0.0853649 0.159703i
\(412\) 238.745i 0.579478i
\(413\) 154.029 0.372952
\(414\) 274.575 410.946i 0.663225 0.992624i
\(415\) 0 0
\(416\) 3.29798i 0.00792783i
\(417\) 207.122 + 387.490i 0.496696 + 0.929233i
\(418\) 329.328i 0.787866i
\(419\) 89.7998i 0.214319i −0.994242 0.107160i \(-0.965824\pi\)
0.994242 0.107160i \(-0.0341756\pi\)
\(420\) 0 0
\(421\) 281.150 0.667815 0.333908 0.942606i \(-0.391633\pi\)
0.333908 + 0.942606i \(0.391633\pi\)
\(422\) −86.6275 −0.205279
\(423\) 42.4264 63.4980i 0.100299 0.150114i
\(424\) 144.000 0.339623
\(425\) 0 0
\(426\) 63.7124 34.0557i 0.149560 0.0799430i
\(427\) 102.959i 0.241123i
\(428\) −232.985 −0.544357
\(429\) 12.0000 + 22.4499i 0.0279720 + 0.0523309i
\(430\) 0 0
\(431\) 560.200i 1.29977i 0.760033 + 0.649885i \(0.225183\pi\)
−0.760033 + 0.649885i \(0.774817\pi\)
\(432\) 107.480 + 10.5830i 0.248797 + 0.0244977i
\(433\) 543.004i 1.25405i 0.778999 + 0.627025i \(0.215728\pi\)
−0.778999 + 0.627025i \(0.784272\pi\)
\(434\) 218.728i 0.503982i
\(435\) 0 0
\(436\) −175.660 −0.402890
\(437\) −621.293 −1.42172
\(438\) −270.642 + 144.664i −0.617903 + 0.330283i
\(439\) −342.170 −0.779430 −0.389715 0.920935i \(-0.627427\pi\)
−0.389715 + 0.920935i \(0.627427\pi\)
\(440\) 0 0
\(441\) 35.0000 52.3832i 0.0793651 0.118783i
\(442\) 17.7569i 0.0401740i
\(443\) −399.816 −0.902519 −0.451259 0.892393i \(-0.649025\pi\)
−0.451259 + 0.892393i \(0.649025\pi\)
\(444\) 105.830 56.5685i 0.238356 0.127407i
\(445\) 0 0
\(446\) 212.831i 0.477199i
\(447\) 580.881 310.494i 1.29951 0.694618i
\(448\) 21.1660i 0.0472456i
\(449\) 737.040i 1.64151i 0.571277 + 0.820757i \(0.306448\pi\)
−0.571277 + 0.820757i \(0.693552\pi\)
\(450\) 0 0
\(451\) −127.373 −0.282422
\(452\) −138.353 −0.306090
\(453\) 299.333 + 560.000i 0.660778 + 1.23620i
\(454\) −269.490 −0.593591
\(455\) 0 0
\(456\) −64.0000 119.733i −0.140351 0.262572i
\(457\) 665.336i 1.45588i 0.685642 + 0.727939i \(0.259521\pi\)
−0.685642 + 0.727939i \(0.740479\pi\)
\(458\) 202.112 0.441293
\(459\) −578.693 56.9808i −1.26077 0.124141i
\(460\) 0 0
\(461\) 318.865i 0.691682i −0.938293 0.345841i \(-0.887594\pi\)
0.938293 0.345841i \(-0.112406\pi\)
\(462\) −77.0146 144.081i −0.166698 0.311864i
\(463\) 402.332i 0.868968i −0.900680 0.434484i \(-0.856931\pi\)
0.900680 0.434484i \(-0.143069\pi\)
\(464\) 143.070i 0.308341i
\(465\) 0 0
\(466\) 11.0850 0.0237875
\(467\) 697.087 1.49269 0.746346 0.665558i \(-0.231806\pi\)
0.746346 + 0.665558i \(0.231806\pi\)
\(468\) −8.72562 5.83005i −0.0186445 0.0124574i
\(469\) 186.745 0.398177
\(470\) 0 0
\(471\) 552.288 295.210i 1.17259 0.626773i
\(472\) 164.664i 0.348864i
\(473\) −171.000 −0.361522
\(474\) 41.8301 + 78.2569i 0.0882491 + 0.165099i
\(475\) 0 0
\(476\) 113.962i 0.239415i
\(477\) −254.558 + 380.988i −0.533665 + 0.798717i
\(478\) 301.749i 0.631274i
\(479\) 163.808i 0.341980i 0.985273 + 0.170990i \(0.0546966\pi\)
−0.985273 + 0.170990i \(0.945303\pi\)
\(480\) 0 0
\(481\) −11.6601 −0.0242414
\(482\) −183.848 −0.381427
\(483\) 271.816 145.292i 0.562765 0.300811i
\(484\) −181.660 −0.375331
\(485\) 0 0
\(486\) −218.000 + 265.658i −0.448560 + 0.546621i
\(487\) 103.498i 0.212522i −0.994338 0.106261i \(-0.966112\pi\)
0.994338 0.106261i \(-0.0338878\pi\)
\(488\) 110.068 0.225550
\(489\) −706.405 + 377.589i −1.44459 + 0.772167i
\(490\) 0 0
\(491\) 570.094i 1.16109i 0.814229 + 0.580544i \(0.197160\pi\)
−0.814229 + 0.580544i \(0.802840\pi\)
\(492\) 46.3085 24.7530i 0.0941230 0.0503109i
\(493\) 770.316i 1.56251i
\(494\) 13.1919i 0.0267043i
\(495\) 0 0
\(496\) −233.830 −0.471432
\(497\) 45.0515 0.0906469
\(498\) −291.088 544.575i −0.584513 1.09352i
\(499\) 487.660 0.977275 0.488637 0.872487i \(-0.337494\pi\)
0.488637 + 0.872487i \(0.337494\pi\)
\(500\) 0 0
\(501\) 10.1699 + 19.0262i 0.0202993 + 0.0379765i
\(502\) 550.494i 1.09660i
\(503\) 97.9412 0.194714 0.0973571 0.995250i \(-0.468961\pi\)
0.0973571 + 0.995250i \(0.468961\pi\)
\(504\) 56.0000 + 37.4166i 0.111111 + 0.0742392i
\(505\) 0 0
\(506\) 799.254i 1.57955i
\(507\) −238.521 446.233i −0.470456 0.880143i
\(508\) 54.1699i 0.106634i
\(509\) 318.104i 0.624958i −0.949925 0.312479i \(-0.898841\pi\)
0.949925 0.312479i \(-0.101159\pi\)
\(510\) 0 0
\(511\) −191.373 −0.374506
\(512\) 22.6274 0.0441942
\(513\) 429.921 + 42.3320i 0.838052 + 0.0825186i
\(514\) −475.373 −0.924849
\(515\) 0 0
\(516\) 62.1699 33.2312i 0.120484 0.0644016i
\(517\) 123.498i 0.238874i
\(518\) 74.8331 0.144466
\(519\) −272.288 509.403i −0.524639 0.981509i
\(520\) 0 0
\(521\) 727.150i 1.39568i 0.716253 + 0.697840i \(0.245856\pi\)
−0.716253 + 0.697840i \(0.754144\pi\)
\(522\) −378.529 252.915i −0.725150 0.484512i
\(523\) 207.624i 0.396986i 0.980102 + 0.198493i \(0.0636047\pi\)
−0.980102 + 0.198493i \(0.936395\pi\)
\(524\) 291.088i 0.555511i
\(525\) 0 0
\(526\) −620.745 −1.18012
\(527\) 1258.98 2.38896
\(528\) 154.029 82.3320i 0.291722 0.155932i
\(529\) 978.830 1.85034
\(530\) 0 0
\(531\) −435.660 291.088i −0.820452 0.548188i
\(532\) 84.6640i 0.159143i
\(533\) −5.10216 −0.00957254
\(534\) 200.745 107.303i 0.375927 0.200941i
\(535\) 0 0
\(536\) 199.639i 0.372461i
\(537\) −115.522 + 61.7490i −0.215124 + 0.114989i
\(538\) 20.4496i 0.0380105i
\(539\) 101.881i 0.189018i
\(540\) 0 0
\(541\) 1025.15 1.89492 0.947459 0.319878i \(-0.103642\pi\)
0.947459 + 0.319878i \(0.103642\pi\)
\(542\) 87.0342 0.160580
\(543\) 114.671 + 214.531i 0.211181 + 0.395084i
\(544\) −121.830 −0.223952
\(545\) 0 0
\(546\) −3.08497 5.77146i −0.00565014 0.0105704i
\(547\) 560.089i 1.02393i −0.859007 0.511964i \(-0.828918\pi\)
0.859007 0.511964i \(-0.171082\pi\)
\(548\) 49.6176 0.0905431
\(549\) −194.575 + 291.213i −0.354417 + 0.530443i
\(550\) 0 0
\(551\) 572.281i 1.03862i
\(552\) 155.323 + 290.583i 0.281383 + 0.526418i
\(553\) 55.3360i 0.100065i
\(554\) 212.831i 0.384171i
\(555\) 0 0
\(556\) −292.915 −0.526826
\(557\) −575.705 −1.03358 −0.516791 0.856112i \(-0.672874\pi\)
−0.516791 + 0.856112i \(0.672874\pi\)
\(558\) 413.357 618.656i 0.740783 1.10870i
\(559\) −6.84974 −0.0122536
\(560\) 0 0
\(561\) −829.320 + 443.290i −1.47829 + 0.790179i
\(562\) 424.575i 0.755472i
\(563\) −468.558 −0.832251 −0.416126 0.909307i \(-0.636612\pi\)
−0.416126 + 0.909307i \(0.636612\pi\)
\(564\) 24.0000 + 44.8999i 0.0425532 + 0.0796097i
\(565\) 0 0
\(566\) 139.772i 0.246948i
\(567\) −197.990 + 82.0183i −0.349189 + 0.144653i
\(568\) 48.1621i 0.0847924i
\(569\) 506.455i 0.890079i 0.895511 + 0.445039i \(0.146810\pi\)
−0.895511 + 0.445039i \(0.853190\pi\)
\(570\) 0 0
\(571\) 32.9150 0.0576445 0.0288223 0.999585i \(-0.490824\pi\)
0.0288223 + 0.999585i \(0.490824\pi\)
\(572\) −16.9706 −0.0296688
\(573\) −141.699 + 75.7411i −0.247293 + 0.132183i
\(574\) 32.7451 0.0570472
\(575\) 0 0
\(576\) −40.0000 + 59.8665i −0.0694444 + 0.103935i
\(577\) 252.154i 0.437009i −0.975836 0.218505i \(-0.929882\pi\)
0.975836 0.218505i \(-0.0701178\pi\)
\(578\) 247.247 0.427763
\(579\) 292.340 156.262i 0.504905 0.269883i
\(580\) 0 0
\(581\) 385.073i 0.662776i
\(582\) −415.945 + 222.332i −0.714682 + 0.382014i
\(583\) 740.988i 1.27099i
\(584\) 204.586i 0.350318i
\(585\) 0 0
\(586\) 10.1176 0.0172656
\(587\) −366.882 −0.625012 −0.312506 0.949916i \(-0.601168\pi\)
−0.312506 + 0.949916i \(0.601168\pi\)
\(588\) 19.7990 + 37.0405i 0.0336718 + 0.0629941i
\(589\) −935.320 −1.58798
\(590\) 0 0
\(591\) 121.830 + 227.923i 0.206142 + 0.385657i
\(592\) 80.0000i 0.135135i
\(593\) −620.757 −1.04681 −0.523404 0.852085i \(-0.675338\pi\)
−0.523404 + 0.852085i \(0.675338\pi\)
\(594\) −54.4575 + 553.067i −0.0916793 + 0.931088i
\(595\) 0 0
\(596\) 439.105i 0.736753i
\(597\) −124.451 232.826i −0.208460 0.389993i
\(598\) 32.0157i 0.0535380i
\(599\) 26.3488i 0.0439879i 0.999758 + 0.0219940i \(0.00700146\pi\)
−0.999758 + 0.0219940i \(0.992999\pi\)
\(600\) 0 0
\(601\) 930.470 1.54820 0.774102 0.633061i \(-0.218202\pi\)
0.774102 + 0.633061i \(0.218202\pi\)
\(602\) 43.9608 0.0730246
\(603\) −528.195 352.915i −0.875945 0.585265i
\(604\) −423.320 −0.700861
\(605\) 0 0
\(606\) 216.405 115.673i 0.357104 0.190880i
\(607\) 216.146i 0.356089i 0.984022 + 0.178045i \(0.0569772\pi\)
−0.984022 + 0.178045i \(0.943023\pi\)
\(608\) 90.5097 0.148865
\(609\) −133.830 250.373i −0.219754 0.411122i
\(610\) 0 0
\(611\) 4.94696i 0.00809650i
\(612\) 215.367 322.332i 0.351907 0.526686i
\(613\) 268.834i 0.438555i 0.975663 + 0.219277i \(0.0703699\pi\)
−0.975663 + 0.219277i \(0.929630\pi\)
\(614\) 149.666i 0.243756i
\(615\) 0 0
\(616\) 108.915 0.176810
\(617\) 531.338 0.861163 0.430582 0.902552i \(-0.358308\pi\)
0.430582 + 0.902552i \(0.358308\pi\)
\(618\) 446.651 238.745i 0.722736 0.386319i
\(619\) −425.203 −0.686919 −0.343459 0.939168i \(-0.611599\pi\)
−0.343459 + 0.939168i \(0.611599\pi\)
\(620\) 0 0
\(621\) −1043.39 102.737i −1.68017 0.165437i
\(622\) 375.336i 0.603434i
\(623\) 141.948 0.227846
\(624\) 6.16995 3.29798i 0.00988774 0.00528522i
\(625\) 0 0
\(626\) 366.745i 0.585855i
\(627\) 616.116 329.328i 0.982642 0.525244i
\(628\) 417.490i 0.664793i
\(629\) 430.734i 0.684792i
\(630\) 0 0
\(631\) −453.490 −0.718685 −0.359342 0.933206i \(-0.616999\pi\)
−0.359342 + 0.933206i \(0.616999\pi\)
\(632\) −59.1566 −0.0936023
\(633\) 86.6275 + 162.065i 0.136852 + 0.256027i
\(634\) −53.4902 −0.0843693
\(635\) 0 0
\(636\) −144.000 269.399i −0.226415 0.423584i
\(637\) 4.08104i 0.00640665i
\(638\) −736.204 −1.15393
\(639\) −127.425 85.1393i −0.199413 0.133238i
\(640\) 0 0
\(641\) 463.455i 0.723019i −0.932368 0.361510i \(-0.882261\pi\)
0.932368 0.361510i \(-0.117739\pi\)
\(642\) 232.985 + 435.875i 0.362905 + 0.678932i
\(643\) 820.988i 1.27681i −0.769701 0.638405i \(-0.779595\pi\)
0.769701 0.638405i \(-0.220405\pi\)
\(644\) 205.473i 0.319058i
\(645\) 0 0
\(646\) −487.320 −0.754366
\(647\) −996.660 −1.54043 −0.770216 0.637783i \(-0.779852\pi\)
−0.770216 + 0.637783i \(0.779852\pi\)
\(648\) −87.6812 211.660i −0.135311 0.326636i
\(649\) −847.320 −1.30558
\(650\) 0 0
\(651\) 409.203 218.728i 0.628575 0.335988i
\(652\) 533.992i 0.819006i
\(653\) 357.602 0.547629 0.273815 0.961782i \(-0.411715\pi\)
0.273815 + 0.961782i \(0.411715\pi\)
\(654\) 175.660 + 328.630i 0.268593 + 0.502492i
\(655\) 0 0
\(656\) 35.0060i 0.0533627i
\(657\) 541.283 + 361.660i 0.823871 + 0.550472i
\(658\) 31.7490i 0.0482508i
\(659\) 131.562i 0.199640i −0.995006 0.0998198i \(-0.968173\pi\)
0.995006 0.0998198i \(-0.0318266\pi\)
\(660\) 0 0
\(661\) −250.915 −0.379599 −0.189800 0.981823i \(-0.560784\pi\)
−0.189800 + 0.981823i \(0.560784\pi\)
\(662\) 205.754 0.310807
\(663\) −33.2201 + 17.7569i −0.0501057 + 0.0267826i
\(664\) 411.660 0.619970
\(665\) 0 0
\(666\) −211.660 141.421i −0.317808 0.212344i
\(667\) 1388.88i 2.08228i
\(668\) −14.3825 −0.0215307
\(669\) −398.170 + 212.831i −0.595172 + 0.318133i
\(670\) 0 0
\(671\) 566.384i 0.844090i
\(672\) −39.5980 + 21.1660i −0.0589256 + 0.0314970i
\(673\) 196.502i 0.291979i −0.989286 0.145990i \(-0.953363\pi\)
0.989286 0.145990i \(-0.0466366\pi\)
\(674\) 848.975i 1.25961i
\(675\) 0 0
\(676\) 337.320 0.498994
\(677\) 54.1838 0.0800352 0.0400176 0.999199i \(-0.487259\pi\)
0.0400176 + 0.999199i \(0.487259\pi\)
\(678\) 138.353 + 258.834i 0.204060 + 0.381761i
\(679\) −294.118 −0.433163
\(680\) 0 0
\(681\) 269.490 + 504.170i 0.395727 + 0.740338i
\(682\) 1203.23i 1.76427i
\(683\) 749.006 1.09664 0.548321 0.836268i \(-0.315267\pi\)
0.548321 + 0.836268i \(0.315267\pi\)
\(684\) −160.000 + 239.466i −0.233918 + 0.350097i
\(685\) 0 0
\(686\) 26.1916i 0.0381802i
\(687\) −202.112 378.118i −0.294196 0.550390i
\(688\) 46.9961i 0.0683082i
\(689\) 29.6818i 0.0430795i
\(690\) 0 0
\(691\) 475.137 0.687608 0.343804 0.939041i \(-0.388284\pi\)
0.343804 + 0.939041i \(0.388284\pi\)
\(692\) 385.073 0.556464
\(693\) −192.536 + 288.162i −0.277830 + 0.415818i
\(694\) −44.7451 −0.0644742
\(695\) 0 0
\(696\) 267.660 143.070i 0.384569 0.205561i
\(697\) 188.478i 0.270414i
\(698\) 837.787 1.20027
\(699\) −11.0850 20.7381i −0.0158583 0.0296682i
\(700\) 0 0
\(701\) 1251.49i 1.78529i 0.450760 + 0.892645i \(0.351153\pi\)
−0.450760 + 0.892645i \(0.648847\pi\)
\(702\) −2.18141 + 22.1542i −0.00310742 + 0.0315587i
\(703\) 320.000i 0.455192i
\(704\) 116.435i 0.165391i
\(705\) 0 0
\(706\) −879.608 −1.24590
\(707\) 153.022 0.216438
\(708\) 308.058 164.664i 0.435110 0.232576i
\(709\) 16.5098 0.0232861 0.0116430 0.999932i \(-0.496294\pi\)
0.0116430 + 0.999932i \(0.496294\pi\)
\(710\) 0 0
\(711\) 104.575 156.514i 0.147082 0.220132i
\(712\) 151.749i 0.213131i
\(713\) 2269.95 3.18366
\(714\) 213.203 113.962i 0.298603 0.159610i
\(715\) 0 0
\(716\) 87.3263i 0.121964i
\(717\) −564.521 + 301.749i −0.787337 + 0.420849i
\(718\) 706.413i 0.983862i
\(719\) 1327.59i 1.84643i 0.384279 + 0.923217i \(0.374450\pi\)
−0.384279 + 0.923217i \(0.625550\pi\)
\(720\) 0 0
\(721\) 315.830 0.438044
\(722\) −148.492 −0.205668
\(723\) 183.848 + 343.948i 0.254285 + 0.475723i
\(724\) −162.170 −0.223992
\(725\) 0 0
\(726\) 181.660 + 339.855i 0.250221 + 0.468120i
\(727\) 202.782i 0.278929i −0.990227 0.139465i \(-0.955462\pi\)
0.990227 0.139465i \(-0.0445382\pi\)
\(728\) 4.36281 0.00599287
\(729\) 715.000 + 142.183i 0.980796 + 0.195038i
\(730\) 0 0
\(731\) 253.035i 0.346149i
\(732\) −110.068 205.919i −0.150367 0.281310i
\(733\) 582.559i 0.794760i 0.917654 + 0.397380i \(0.130081\pi\)
−0.917654 + 0.397380i \(0.869919\pi\)
\(734\) 103.243i 0.140658i
\(735\) 0 0
\(736\) −219.660 −0.298451
\(737\) −1027.29 −1.39388
\(738\) −92.6171 61.8824i −0.125497 0.0838515i
\(739\) 256.810 0.347511 0.173755 0.984789i \(-0.444410\pi\)
0.173755 + 0.984789i \(0.444410\pi\)
\(740\) 0 0
\(741\) 24.6798 13.1919i 0.0333061 0.0178028i
\(742\) 190.494i 0.256731i
\(743\) −573.256 −0.771542 −0.385771 0.922595i \(-0.626064\pi\)
−0.385771 + 0.922595i \(0.626064\pi\)
\(744\) 233.830 + 437.456i 0.314288 + 0.587978i
\(745\) 0 0
\(746\) 671.276i 0.899834i
\(747\) −727.719 + 1089.15i −0.974189 + 1.45803i
\(748\) 626.907i 0.838111i
\(749\) 308.210i 0.411495i
\(750\) 0 0
\(751\) −579.085 −0.771085 −0.385543 0.922690i \(-0.625986\pi\)
−0.385543 + 0.922690i \(0.625986\pi\)
\(752\) −33.9411 −0.0451345
\(753\) −1029.88 + 550.494i −1.36770 + 0.731068i
\(754\) −29.4902 −0.0391116
\(755\) 0 0
\(756\) 14.0000 142.183i 0.0185185 0.188073i
\(757\) 1167.13i 1.54179i 0.636963 + 0.770895i \(0.280191\pi\)
−0.636963 + 0.770895i \(0.719809\pi\)
\(758\) 316.303 0.417286
\(759\) −1495.27 + 799.254i −1.97005 + 1.05304i
\(760\) 0 0
\(761\) 800.970i 1.05252i −0.850323 0.526261i \(-0.823593\pi\)
0.850323 0.526261i \(-0.176407\pi\)
\(762\) −101.343 + 54.1699i −0.132996 + 0.0710892i
\(763\) 232.376i 0.304556i
\(764\) 107.114i 0.140202i
\(765\) 0 0
\(766\) 732.810 0.956671
\(767\) −33.9411 −0.0442518
\(768\) −22.6274 42.3320i −0.0294628 0.0551198i
\(769\) 242.680 0.315578 0.157789 0.987473i \(-0.449563\pi\)
0.157789 + 0.987473i \(0.449563\pi\)
\(770\) 0 0
\(771\) 475.373 + 889.341i 0.616566 + 1.15349i
\(772\) 220.988i 0.286254i
\(773\) −1262.83 −1.63367 −0.816836 0.576870i \(-0.804274\pi\)
−0.816836 + 0.576870i \(0.804274\pi\)
\(774\) −124.340 83.0781i −0.160646 0.107336i
\(775\) 0 0
\(776\) 314.425i 0.405187i
\(777\) −74.8331 140.000i −0.0963104 0.180180i
\(778\) 62.4209i 0.0802326i
\(779\) 140.024i 0.179748i
\(780\) 0 0
\(781\) −247.830 −0.317324
\(782\) 1182.69 1.51239
\(783\) −94.6321 + 961.077i −0.120858 + 1.22743i
\(784\) −28.0000 −0.0357143
\(785\) 0 0
\(786\) −544.575 + 291.088i −0.692844 + 0.370341i
\(787\) 1347.00i 1.71156i 0.517336 + 0.855782i \(0.326924\pi\)
−0.517336 + 0.855782i \(0.673076\pi\)
\(788\) −172.294 −0.218647
\(789\) 620.745 + 1161.31i 0.786749 + 1.47187i
\(790\) 0 0
\(791\) 183.023i 0.231382i
\(792\) −308.058 205.830i −0.388962 0.259886i
\(793\) 22.6877i 0.0286099i
\(794\) 423.440i 0.533299i
\(795\) 0 0
\(796\) 176.000 0.221106
\(797\) 1210.62 1.51897 0.759487 0.650523i \(-0.225450\pi\)
0.759487 + 0.650523i \(0.225450\pi\)
\(798\) −158.392 + 84.6640i −0.198486 + 0.106095i
\(799\) 182.745 0.228717
\(800\) 0 0
\(801\) −401.490 268.257i −0.501236 0.334902i
\(802\) 391.749i 0.488465i
\(803\) 1052.75 1.31102
\(804\) 373.490 199.639i 0.464540 0.248307i
\(805\) 0 0
\(806\) 48.1979i 0.0597988i
\(807\) 38.2578 20.4496i 0.0474074 0.0253403i
\(808\) 163.587i 0.202459i
\(809\) 310.876i 0.384271i −0.981368 0.192136i \(-0.938459\pi\)
0.981368 0.192136i \(-0.0615414\pi\)
\(810\) 0 0
\(811\) −65.7777 −0.0811069 −0.0405535 0.999177i \(-0.512912\pi\)
−0.0405535 + 0.999177i \(0.512912\pi\)
\(812\) 189.264 0.233084
\(813\) −87.0342 162.826i −0.107053 0.200278i
\(814\) −411.660 −0.505725
\(815\) 0 0
\(816\) 121.830 + 227.923i 0.149302 + 0.279318i
\(817\) 187.984i 0.230091i
\(818\) 1047.90 1.28106
\(819\) −7.71243 + 11.5429i −0.00941689 + 0.0140939i
\(820\) 0 0
\(821\) 370.994i 0.451880i −0.974141 0.225940i \(-0.927455\pi\)
0.974141 0.225940i \(-0.0725453\pi\)
\(822\) −49.6176 92.8261i −0.0603621 0.112927i
\(823\) 441.077i 0.535938i −0.963428 0.267969i \(-0.913647\pi\)
0.963428 0.267969i \(-0.0863525\pi\)
\(824\) 337.637i 0.409753i
\(825\) 0 0
\(826\) 217.830 0.263717
\(827\) 116.492 0.140861 0.0704307 0.997517i \(-0.477563\pi\)
0.0704307 + 0.997517i \(0.477563\pi\)
\(828\) 388.308 581.166i 0.468971 0.701891i
\(829\) 881.425 1.06324 0.531619 0.846983i \(-0.321584\pi\)
0.531619 + 0.846983i \(0.321584\pi\)
\(830\) 0 0
\(831\) 398.170 212.831i 0.479146 0.256114i
\(832\) 4.66404i 0.00560582i
\(833\) 150.757 0.180981
\(834\) 292.915 + 547.994i 0.351217 + 0.657067i
\(835\) 0 0
\(836\) 465.740i 0.557106i
\(837\) −1570.76 154.664i −1.87665 0.184784i
\(838\) 126.996i 0.151547i
\(839\) 1346.42i 1.60480i 0.596789 + 0.802398i \(0.296443\pi\)
−0.596789 + 0.802398i \(0.703557\pi\)
\(840\) 0 0
\(841\) −438.320 −0.521189
\(842\) 397.607 0.472217
\(843\) 794.307 424.575i 0.942239 0.503648i
\(844\) −122.510 −0.145154
\(845\) 0 0
\(846\) 60.0000 89.7998i 0.0709220 0.106146i
\(847\) 240.314i 0.283723i
\(848\) 203.647 0.240149
\(849\) −261.490 + 139.772i −0.307998 + 0.164632i
\(850\) 0 0
\(851\) 776.616i 0.912592i
\(852\) 90.1030 48.1621i 0.105755 0.0565283i
\(853\) 966.235i 1.13275i 0.824148 + 0.566375i \(0.191654\pi\)
−0.824148 + 0.566375i \(0.808346\pi\)
\(854\) 145.607i 0.170500i
\(855\) 0 0
\(856\) −329.490 −0.384918
\(857\) 982.241 1.14614 0.573069 0.819507i \(-0.305753\pi\)
0.573069 + 0.819507i \(0.305753\pi\)
\(858\) 16.9706 + 31.7490i 0.0197792 + 0.0370035i
\(859\) −1309.49 −1.52444 −0.762218 0.647321i \(-0.775889\pi\)
−0.762218 + 0.647321i \(0.775889\pi\)
\(860\) 0 0
\(861\) −32.7451 61.2604i −0.0380315 0.0711503i
\(862\) 792.243i 0.919076i
\(863\) 1001.55 1.16054 0.580272 0.814423i \(-0.302946\pi\)
0.580272 + 0.814423i \(0.302946\pi\)
\(864\) 152.000 + 14.9666i 0.175926 + 0.0173225i
\(865\) 0 0
\(866\) 767.924i 0.886748i
\(867\) −247.247 462.557i −0.285175 0.533514i
\(868\) 309.328i 0.356369i
\(869\) 304.405i 0.350294i
\(870\) 0 0
\(871\) −41.1503 −0.0472448
\(872\) −248.421 −0.284886
\(873\) 831.890 + 555.830i 0.952910 + 0.636690i
\(874\) −878.640 −1.00531
\(875\) 0 0
\(876\) −382.745 + 204.586i −0.436924 + 0.233545i
\(877\) 33.1424i 0.0377906i −0.999821 0.0188953i \(-0.993985\pi\)
0.999821 0.0188953i \(-0.00601492\pi\)
\(878\) −483.901 −0.551141
\(879\) −10.1176 18.9283i −0.0115104 0.0215339i
\(880\) 0 0
\(881\) 944.040i 1.07156i −0.844359 0.535778i \(-0.820019\pi\)
0.844359 0.535778i \(-0.179981\pi\)
\(882\) 49.4975 74.0810i 0.0561196 0.0839921i
\(883\) 55.5138i 0.0628695i −0.999506 0.0314348i \(-0.989992\pi\)
0.999506 0.0314348i \(-0.0100076\pi\)
\(884\) 25.1120i 0.0284073i
\(885\) 0 0
\(886\) −565.425 −0.638177
\(887\) 20.1317 0.0226964 0.0113482 0.999936i \(-0.496388\pi\)
0.0113482 + 0.999936i \(0.496388\pi\)
\(888\) 149.666 80.0000i 0.168543 0.0900901i
\(889\) −71.6601 −0.0806075
\(890\) 0 0
\(891\) 1089.15 451.186i 1.22239 0.506381i
\(892\) 300.988i 0.337431i
\(893\) −135.765 −0.152032
\(894\) 821.490 439.105i 0.918893 0.491169i
\(895\) 0 0
\(896\) 29.9333i 0.0334077i
\(897\) −59.8960 + 32.0157i −0.0667737 + 0.0356920i
\(898\) 1042.33i 1.16073i
\(899\) 2090.88i 2.32579i
\(900\) 0 0
\(901\) −1096.47 −1.21695
\(902\) −180.132 −0.199703
\(903\) −43.9608 82.2431i −0.0486830 0.0910776i
\(904\) −195.660 −0.216438
\(905\) 0 0
\(906\) 423.320 + 791.960i 0.467241 + 0.874128i
\(907\) 219.644i 0.242166i 0.992642 + 0.121083i \(0.0386367\pi\)
−0.992642 + 0.121083i \(0.961363\pi\)
\(908\) −381.117 −0.419732
\(909\) −432.810 289.184i −0.476139 0.318134i
\(910\) 0 0
\(911\) 827.126i 0.907932i 0.891019 + 0.453966i \(0.149991\pi\)
−0.891019 + 0.453966i \(0.850009\pi\)
\(912\) −90.5097 169.328i −0.0992431 0.185667i
\(913\) 2118.30i 2.32015i
\(914\) 940.927i 1.02946i
\(915\) 0 0
\(916\) 285.830 0.312042
\(917\) −385.073 −0.419927
\(918\) −818.395 80.5830i −0.891498 0.0877811i
\(919\) 1029.39 1.12011 0.560057 0.828454i \(-0.310779\pi\)
0.560057 + 0.828454i \(0.310779\pi\)
\(920\) 0 0
\(921\) 280.000 149.666i 0.304017 0.162504i
\(922\) 450.944i 0.489093i
\(923\) −9.92733 −0.0107555
\(924\) −108.915 203.761i −0.117873 0.220521i
\(925\) 0 0
\(926\) 568.983i 0.614453i
\(927\) −893.302 596.863i −0.963649 0.643865i
\(928\) 202.332i 0.218030i
\(929\) 1440.98i 1.55111i −0.631282 0.775553i \(-0.717471\pi\)
0.631282 0.775553i \(-0.282529\pi\)
\(930\) 0 0
\(931\) −112.000 −0.120301
\(932\) 15.6765 0.0168203
\(933\) −702.189 + 375.336i −0.752614 + 0.402289i
\(934\) 985.830 1.05549
\(935\) 0 0
\(936\) −12.3399 8.24494i −0.0131836 0.00880870i
\(937\) 1010.00i 1.07791i 0.842335 + 0.538954i \(0.181180\pi\)
−0.842335 + 0.538954i \(0.818820\pi\)
\(938\) 264.097 0.281554
\(939\) −686.118 + 366.745i −0.730690 + 0.390570i
\(940\) 0 0
\(941\) 191.775i 0.203799i −0.994795 0.101899i \(-0.967508\pi\)
0.994795 0.101899i \(-0.0324920\pi\)
\(942\) 781.053 417.490i 0.829143 0.443195i
\(943\) 339.827i 0.360368i
\(944\) 232.870i 0.246684i
\(945\) 0 0
\(946\) −241.830 −0.255634
\(947\) 893.108 0.943092 0.471546 0.881841i \(-0.343696\pi\)
0.471546 + 0.881841i \(0.343696\pi\)
\(948\) 59.1566 + 110.672i 0.0624015 + 0.116743i
\(949\) 42.1699 0.0444362
\(950\) 0 0
\(951\) 53.4902 + 100.071i 0.0562462 + 0.105227i
\(952\) 161.166i 0.169292i
\(953\) −1300.12 −1.36423 −0.682117 0.731243i \(-0.738941\pi\)
−0.682117 + 0.731243i \(0.738941\pi\)
\(954\) −360.000 + 538.799i −0.377358 + 0.564778i
\(955\) 0 0
\(956\) 426.738i 0.446378i
\(957\) 736.204 + 1377.31i 0.769284 + 1.43920i
\(958\) 231.660i 0.241816i
\(959\) 65.6380i 0.0684442i
\(960\) 0 0
\(961\) 2456.28 2.55596
\(962\) −16.4899 −0.0171412
\(963\) 582.462 871.749i 0.604841 0.905243i
\(964\) −260.000 −0.269710
\(965\) 0 0
\(966\) 384.405 205.473i 0.397935 0.212705i
\(967\) 375.247i 0.388053i −0.980996 0.194026i \(-0.937845\pi\)
0.980996 0.194026i \(-0.0621547\pi\)
\(968\) −256.906 −0.265399
\(969\) 487.320 + 911.693i 0.502910 + 0.940859i
\(970\) 0 0
\(971\) 1045.06i 1.07628i 0.842856 + 0.538138i \(0.180872\pi\)
−0.842856 + 0.538138i \(0.819128\pi\)
\(972\) −308.299 + 375.697i −0.317180 + 0.386519i
\(973\) 387.490i 0.398243i
\(974\) 146.368i 0.150275i
\(975\) 0 0
\(976\) 155.660 0.159488
\(977\) −459.425 −0.470241 −0.235120 0.971966i \(-0.575548\pi\)
−0.235120 + 0.971966i \(0.575548\pi\)
\(978\) −999.008 + 533.992i −1.02148 + 0.546004i
\(979\) −780.863 −0.797613
\(980\) 0 0
\(981\) 439.150 657.260i 0.447656 0.669990i
\(982\) 806.235i 0.821013i
\(983\) −103.265 −0.105051 −0.0525257 0.998620i \(-0.516727\pi\)
−0.0525257 + 0.998620i \(0.516727\pi\)
\(984\) 65.4902 35.0060i 0.0665550 0.0355752i
\(985\) 0 0
\(986\) 1089.39i 1.10486i
\(987\) 59.3970 31.7490i 0.0601793 0.0321672i
\(988\) 18.6562i 0.0188828i
\(989\) 456.224i 0.461298i
\(990\) 0 0
\(991\) 1329.73 1.34180 0.670901 0.741547i \(-0.265908\pi\)
0.670901 + 0.741547i \(0.265908\pi\)
\(992\) −330.686 −0.333352
\(993\) −205.754 384.931i −0.207205 0.387644i
\(994\) 63.7124 0.0640970
\(995\) 0 0
\(996\) −411.660 770.146i −0.413313 0.773238i
\(997\) 664.259i 0.666258i 0.942881 + 0.333129i \(0.108104\pi\)
−0.942881 + 0.333129i \(0.891896\pi\)
\(998\) 689.656 0.691038
\(999\) −52.9150 + 537.401i −0.0529680 + 0.537939i
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 1050.3.c.a.449.6 8
3.2 odd 2 inner 1050.3.c.a.449.1 8
5.2 odd 4 1050.3.e.a.701.3 4
5.3 odd 4 42.3.b.a.29.2 4
5.4 even 2 inner 1050.3.c.a.449.4 8
15.2 even 4 1050.3.e.a.701.1 4
15.8 even 4 42.3.b.a.29.4 yes 4
15.14 odd 2 inner 1050.3.c.a.449.7 8
20.3 even 4 336.3.d.b.113.2 4
35.3 even 12 294.3.h.g.275.4 8
35.13 even 4 294.3.b.h.197.1 4
35.18 odd 12 294.3.h.d.275.3 8
35.23 odd 12 294.3.h.d.263.1 8
35.33 even 12 294.3.h.g.263.2 8
40.3 even 4 1344.3.d.e.449.3 4
40.13 odd 4 1344.3.d.c.449.2 4
45.13 odd 12 1134.3.q.a.1079.4 8
45.23 even 12 1134.3.q.a.1079.1 8
45.38 even 12 1134.3.q.a.701.4 8
45.43 odd 12 1134.3.q.a.701.1 8
60.23 odd 4 336.3.d.b.113.1 4
105.23 even 12 294.3.h.d.263.3 8
105.38 odd 12 294.3.h.g.275.2 8
105.53 even 12 294.3.h.d.275.1 8
105.68 odd 12 294.3.h.g.263.4 8
105.83 odd 4 294.3.b.h.197.3 4
120.53 even 4 1344.3.d.c.449.1 4
120.83 odd 4 1344.3.d.e.449.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.3.b.a.29.2 4 5.3 odd 4
42.3.b.a.29.4 yes 4 15.8 even 4
294.3.b.h.197.1 4 35.13 even 4
294.3.b.h.197.3 4 105.83 odd 4
294.3.h.d.263.1 8 35.23 odd 12
294.3.h.d.263.3 8 105.23 even 12
294.3.h.d.275.1 8 105.53 even 12
294.3.h.d.275.3 8 35.18 odd 12
294.3.h.g.263.2 8 35.33 even 12
294.3.h.g.263.4 8 105.68 odd 12
294.3.h.g.275.2 8 105.38 odd 12
294.3.h.g.275.4 8 35.3 even 12
336.3.d.b.113.1 4 60.23 odd 4
336.3.d.b.113.2 4 20.3 even 4
1050.3.c.a.449.1 8 3.2 odd 2 inner
1050.3.c.a.449.4 8 5.4 even 2 inner
1050.3.c.a.449.6 8 1.1 even 1 trivial
1050.3.c.a.449.7 8 15.14 odd 2 inner
1050.3.e.a.701.1 4 15.2 even 4
1050.3.e.a.701.3 4 5.2 odd 4
1134.3.q.a.701.1 8 45.43 odd 12
1134.3.q.a.701.4 8 45.38 even 12
1134.3.q.a.1079.1 8 45.23 even 12
1134.3.q.a.1079.4 8 45.13 odd 12
1344.3.d.c.449.1 4 120.53 even 4
1344.3.d.c.449.2 4 40.13 odd 4
1344.3.d.e.449.3 4 40.3 even 4
1344.3.d.e.449.4 4 120.83 odd 4