Properties

Label 525.3.f.a.449.7
Level $525$
Weight $3$
Character 525.449
Analytic conductor $14.305$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,3,Mod(449,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, 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("525.449");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.f (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: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4337012736.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 8x^{6} + 4x^{5} + 12x^{4} - 40x^{3} + 72x^{2} + 24x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.7
Root \(2.25296 + 2.25296i\) of defining polynomial
Character \(\chi\) \(=\) 525.449
Dual form 525.3.f.a.449.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.50592 q^{2} +(2.88494 - 0.822876i) q^{3} +8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} +2.64575i q^{7} +15.0457 q^{8} +(7.64575 - 4.74789i) q^{9} +O(q^{10})\) \(q+3.50592 q^{2} +(2.88494 - 0.822876i) q^{3} +8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} +2.64575i q^{7} +15.0457 q^{8} +(7.64575 - 4.74789i) q^{9} -7.01185i q^{11} +(23.9205 - 6.82288i) q^{12} +11.6458i q^{13} +9.27580i q^{14} +19.5830 q^{16} -4.52791 q^{17} +(26.8054 - 16.6458i) q^{18} -16.2288 q^{19} +(2.17712 + 7.63283i) q^{21} -24.5830i q^{22} -25.5635 q^{23} +(43.4059 - 12.3807i) q^{24} +40.8291i q^{26} +(18.1506 - 19.9889i) q^{27} +21.9373i q^{28} -9.49579i q^{29} +28.7085 q^{31} +8.47380 q^{32} +(-5.76988 - 20.2288i) q^{33} -15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} -33.0405i q^{37} -56.8968 q^{38} +(9.58301 + 33.5973i) q^{39} +67.1946i q^{41} +(7.63283 + 26.7601i) q^{42} +24.1255i q^{43} -58.1388i q^{44} -89.6235 q^{46} +33.0153 q^{47} +(56.4958 - 16.1144i) q^{48} -7.00000 q^{49} +(-13.0627 + 3.72591i) q^{51} +96.5608i q^{52} -15.1877 q^{53} +(63.6346 - 70.0795i) q^{54} +39.8071i q^{56} +(-46.8190 + 13.3542i) q^{57} -33.2915i q^{58} -92.3960i q^{59} -57.5203 q^{61} +100.650 q^{62} +(12.5617 + 20.2288i) q^{63} -48.6235 q^{64} +(-20.2288 - 70.9205i) q^{66} +15.1660i q^{67} -37.5432 q^{68} +(-73.7490 + 21.0355i) q^{69} -70.5584i q^{71} +(115.036 - 71.4353i) q^{72} +76.7895i q^{73} -115.838i q^{74} -134.561 q^{76} +18.5516 q^{77} +(33.5973 + 117.790i) q^{78} -127.247 q^{79} +(35.9150 - 72.6024i) q^{81} +235.579i q^{82} +74.2844 q^{83} +(18.0516 + 63.2876i) q^{84} +84.5821i q^{86} +(-7.81385 - 27.3948i) q^{87} -105.498i q^{88} +127.377i q^{89} -30.8118 q^{91} -211.959 q^{92} +(82.8223 - 23.6235i) q^{93} +115.749 q^{94} +(24.4464 - 6.97288i) q^{96} -23.1660i q^{97} -24.5415 q^{98} +(-33.2915 - 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9} + 72 q^{16} - 24 q^{19} + 28 q^{21} + 252 q^{24} + 272 q^{31} + 232 q^{36} - 8 q^{39} - 336 q^{46} - 56 q^{49} - 168 q^{51} + 308 q^{54} - 312 q^{61} - 8 q^{64} - 56 q^{66} - 336 q^{69} - 632 q^{76} - 256 q^{79} - 136 q^{81} + 28 q^{84} - 56 q^{91} + 672 q^{94} - 196 q^{96} - 224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.50592 1.75296 0.876481 0.481436i \(-0.159885\pi\)
0.876481 + 0.481436i \(0.159885\pi\)
\(3\) 2.88494 0.822876i 0.961646 0.274292i
\(4\) 8.29150 2.07288
\(5\) 0 0
\(6\) 10.1144 2.88494i 1.68573 0.480823i
\(7\) 2.64575i 0.377964i
\(8\) 15.0457 1.88071
\(9\) 7.64575 4.74789i 0.849528 0.527544i
\(10\) 0 0
\(11\) 7.01185i 0.637441i −0.947849 0.318720i \(-0.896747\pi\)
0.947849 0.318720i \(-0.103253\pi\)
\(12\) 23.9205 6.82288i 1.99337 0.568573i
\(13\) 11.6458i 0.895827i 0.894077 + 0.447914i \(0.147833\pi\)
−0.894077 + 0.447914i \(0.852167\pi\)
\(14\) 9.27580i 0.662557i
\(15\) 0 0
\(16\) 19.5830 1.22394
\(17\) −4.52791 −0.266348 −0.133174 0.991093i \(-0.542517\pi\)
−0.133174 + 0.991093i \(0.542517\pi\)
\(18\) 26.8054 16.6458i 1.48919 0.924764i
\(19\) −16.2288 −0.854145 −0.427073 0.904217i \(-0.640455\pi\)
−0.427073 + 0.904217i \(0.640455\pi\)
\(20\) 0 0
\(21\) 2.17712 + 7.63283i 0.103673 + 0.363468i
\(22\) 24.5830i 1.11741i
\(23\) −25.5635 −1.11145 −0.555727 0.831365i \(-0.687560\pi\)
−0.555727 + 0.831365i \(0.687560\pi\)
\(24\) 43.4059 12.3807i 1.80858 0.515864i
\(25\) 0 0
\(26\) 40.8291i 1.57035i
\(27\) 18.1506 19.9889i 0.672245 0.740329i
\(28\) 21.9373i 0.783473i
\(29\) 9.49579i 0.327441i −0.986507 0.163720i \(-0.947650\pi\)
0.986507 0.163720i \(-0.0523495\pi\)
\(30\) 0 0
\(31\) 28.7085 0.926081 0.463040 0.886337i \(-0.346759\pi\)
0.463040 + 0.886337i \(0.346759\pi\)
\(32\) 8.47380 0.264806
\(33\) −5.76988 20.2288i −0.174845 0.612993i
\(34\) −15.8745 −0.466897
\(35\) 0 0
\(36\) 63.3948 39.3672i 1.76097 1.09353i
\(37\) 33.0405i 0.892987i −0.894787 0.446493i \(-0.852673\pi\)
0.894787 0.446493i \(-0.147327\pi\)
\(38\) −56.8968 −1.49728
\(39\) 9.58301 + 33.5973i 0.245718 + 0.861469i
\(40\) 0 0
\(41\) 67.1946i 1.63889i 0.573156 + 0.819446i \(0.305719\pi\)
−0.573156 + 0.819446i \(0.694281\pi\)
\(42\) 7.63283 + 26.7601i 0.181734 + 0.637146i
\(43\) 24.1255i 0.561058i 0.959846 + 0.280529i \(0.0905099\pi\)
−0.959846 + 0.280529i \(0.909490\pi\)
\(44\) 58.1388i 1.32134i
\(45\) 0 0
\(46\) −89.6235 −1.94834
\(47\) 33.0153 0.702452 0.351226 0.936291i \(-0.385765\pi\)
0.351226 + 0.936291i \(0.385765\pi\)
\(48\) 56.4958 16.1144i 1.17700 0.335716i
\(49\) −7.00000 −0.142857
\(50\) 0 0
\(51\) −13.0627 + 3.72591i −0.256132 + 0.0730570i
\(52\) 96.5608i 1.85694i
\(53\) −15.1877 −0.286561 −0.143281 0.989682i \(-0.545765\pi\)
−0.143281 + 0.989682i \(0.545765\pi\)
\(54\) 63.6346 70.0795i 1.17842 1.29777i
\(55\) 0 0
\(56\) 39.8071i 0.710842i
\(57\) −46.8190 + 13.3542i −0.821386 + 0.234285i
\(58\) 33.2915i 0.573991i
\(59\) 92.3960i 1.56603i −0.622000 0.783017i \(-0.713680\pi\)
0.622000 0.783017i \(-0.286320\pi\)
\(60\) 0 0
\(61\) −57.5203 −0.942955 −0.471478 0.881878i \(-0.656279\pi\)
−0.471478 + 0.881878i \(0.656279\pi\)
\(62\) 100.650 1.62338
\(63\) 12.5617 + 20.2288i 0.199393 + 0.321091i
\(64\) −48.6235 −0.759743
\(65\) 0 0
\(66\) −20.2288 70.9205i −0.306496 1.07455i
\(67\) 15.1660i 0.226358i 0.993575 + 0.113179i \(0.0361034\pi\)
−0.993575 + 0.113179i \(0.963897\pi\)
\(68\) −37.5432 −0.552106
\(69\) −73.7490 + 21.0355i −1.06883 + 0.304863i
\(70\) 0 0
\(71\) 70.5584i 0.993781i −0.867813 0.496890i \(-0.834475\pi\)
0.867813 0.496890i \(-0.165525\pi\)
\(72\) 115.036 71.4353i 1.59772 0.992157i
\(73\) 76.7895i 1.05191i 0.850512 + 0.525956i \(0.176292\pi\)
−0.850512 + 0.525956i \(0.823708\pi\)
\(74\) 115.838i 1.56537i
\(75\) 0 0
\(76\) −134.561 −1.77054
\(77\) 18.5516 0.240930
\(78\) 33.5973 + 117.790i 0.430734 + 1.51012i
\(79\) −127.247 −1.61072 −0.805361 0.592785i \(-0.798029\pi\)
−0.805361 + 0.592785i \(0.798029\pi\)
\(80\) 0 0
\(81\) 35.9150 72.6024i 0.443395 0.896326i
\(82\) 235.579i 2.87292i
\(83\) 74.2844 0.894992 0.447496 0.894286i \(-0.352316\pi\)
0.447496 + 0.894286i \(0.352316\pi\)
\(84\) 18.0516 + 63.2876i 0.214900 + 0.753424i
\(85\) 0 0
\(86\) 84.5821i 0.983513i
\(87\) −7.81385 27.3948i −0.0898144 0.314882i
\(88\) 105.498i 1.19884i
\(89\) 127.377i 1.43121i 0.698507 + 0.715603i \(0.253848\pi\)
−0.698507 + 0.715603i \(0.746152\pi\)
\(90\) 0 0
\(91\) −30.8118 −0.338591
\(92\) −211.959 −2.30391
\(93\) 82.8223 23.6235i 0.890562 0.254016i
\(94\) 115.749 1.23137
\(95\) 0 0
\(96\) 24.4464 6.97288i 0.254650 0.0726342i
\(97\) 23.1660i 0.238825i −0.992845 0.119412i \(-0.961899\pi\)
0.992845 0.119412i \(-0.0381011\pi\)
\(98\) −24.5415 −0.250423
\(99\) −33.2915 53.6108i −0.336278 0.541524i
\(100\) 0 0
\(101\) 134.907i 1.33571i −0.744290 0.667857i \(-0.767212\pi\)
0.744290 0.667857i \(-0.232788\pi\)
\(102\) −45.7970 + 13.0627i −0.448990 + 0.128066i
\(103\) 119.749i 1.16261i 0.813685 + 0.581306i \(0.197458\pi\)
−0.813685 + 0.581306i \(0.802542\pi\)
\(104\) 175.218i 1.68479i
\(105\) 0 0
\(106\) −53.2470 −0.502331
\(107\) 77.8544 0.727611 0.363806 0.931475i \(-0.381477\pi\)
0.363806 + 0.931475i \(0.381477\pi\)
\(108\) 150.496 165.738i 1.39348 1.53461i
\(109\) 36.5385 0.335216 0.167608 0.985854i \(-0.446396\pi\)
0.167608 + 0.985854i \(0.446396\pi\)
\(110\) 0 0
\(111\) −27.1882 95.3199i −0.244939 0.858738i
\(112\) 51.8118i 0.462605i
\(113\) 21.7596 0.192563 0.0962815 0.995354i \(-0.469305\pi\)
0.0962815 + 0.995354i \(0.469305\pi\)
\(114\) −164.144 + 46.8190i −1.43986 + 0.410693i
\(115\) 0 0
\(116\) 78.7343i 0.678744i
\(117\) 55.2928 + 89.0405i 0.472588 + 0.761030i
\(118\) 323.933i 2.74520i
\(119\) 11.9797i 0.100670i
\(120\) 0 0
\(121\) 71.8340 0.593669
\(122\) −201.662 −1.65296
\(123\) 55.2928 + 193.852i 0.449535 + 1.57603i
\(124\) 238.037 1.91965
\(125\) 0 0
\(126\) 44.0405 + 70.9205i 0.349528 + 0.562861i
\(127\) 15.4170i 0.121394i −0.998156 0.0606968i \(-0.980668\pi\)
0.998156 0.0606968i \(-0.0193323\pi\)
\(128\) −204.366 −1.59661
\(129\) 19.8523 + 69.6006i 0.153894 + 0.539539i
\(130\) 0 0
\(131\) 183.110i 1.39779i 0.715226 + 0.698893i \(0.246324\pi\)
−0.715226 + 0.698893i \(0.753676\pi\)
\(132\) −47.8410 167.727i −0.362432 1.27066i
\(133\) 42.9373i 0.322836i
\(134\) 53.1709i 0.396798i
\(135\) 0 0
\(136\) −68.1255 −0.500923
\(137\) −33.0153 −0.240987 −0.120494 0.992714i \(-0.538448\pi\)
−0.120494 + 0.992714i \(0.538448\pi\)
\(138\) −258.558 + 73.7490i −1.87361 + 0.534413i
\(139\) −64.6418 −0.465049 −0.232525 0.972591i \(-0.574699\pi\)
−0.232525 + 0.972591i \(0.574699\pi\)
\(140\) 0 0
\(141\) 95.2470 27.1675i 0.675511 0.192677i
\(142\) 247.373i 1.74206i
\(143\) 81.6582 0.571037
\(144\) 149.727 92.9780i 1.03977 0.645681i
\(145\) 0 0
\(146\) 269.218i 1.84396i
\(147\) −20.1946 + 5.76013i −0.137378 + 0.0391846i
\(148\) 273.956i 1.85105i
\(149\) 195.736i 1.31366i −0.754037 0.656832i \(-0.771896\pi\)
0.754037 0.656832i \(-0.228104\pi\)
\(150\) 0 0
\(151\) 102.251 0.677159 0.338579 0.940938i \(-0.390054\pi\)
0.338579 + 0.940938i \(0.390054\pi\)
\(152\) −244.173 −1.60640
\(153\) −34.6193 + 21.4980i −0.226270 + 0.140510i
\(154\) 65.0405 0.422341
\(155\) 0 0
\(156\) 79.4575 + 278.572i 0.509343 + 1.78572i
\(157\) 104.723i 0.667025i 0.942746 + 0.333512i \(0.108234\pi\)
−0.942746 + 0.333512i \(0.891766\pi\)
\(158\) −446.118 −2.82353
\(159\) −43.8157 + 12.4976i −0.275570 + 0.0786014i
\(160\) 0 0
\(161\) 67.6345i 0.420090i
\(162\) 125.915 254.539i 0.777255 1.57123i
\(163\) 70.9595i 0.435334i 0.976023 + 0.217667i \(0.0698447\pi\)
−0.976023 + 0.217667i \(0.930155\pi\)
\(164\) 557.144i 3.39722i
\(165\) 0 0
\(166\) 260.435 1.56889
\(167\) 206.992 1.23947 0.619735 0.784811i \(-0.287240\pi\)
0.619735 + 0.784811i \(0.287240\pi\)
\(168\) 32.7563 + 114.841i 0.194978 + 0.683578i
\(169\) 33.3765 0.197494
\(170\) 0 0
\(171\) −124.081 + 77.0524i −0.725620 + 0.450599i
\(172\) 200.037i 1.16300i
\(173\) 108.464 0.626958 0.313479 0.949595i \(-0.398506\pi\)
0.313479 + 0.949595i \(0.398506\pi\)
\(174\) −27.3948 96.0440i −0.157441 0.551977i
\(175\) 0 0
\(176\) 137.313i 0.780188i
\(177\) −76.0304 266.557i −0.429550 1.50597i
\(178\) 446.575i 2.50885i
\(179\) 159.357i 0.890261i −0.895466 0.445131i \(-0.853157\pi\)
0.895466 0.445131i \(-0.146843\pi\)
\(180\) 0 0
\(181\) −233.889 −1.29220 −0.646102 0.763251i \(-0.723602\pi\)
−0.646102 + 0.763251i \(0.723602\pi\)
\(182\) −108.024 −0.593537
\(183\) −165.942 + 47.3320i −0.906789 + 0.258645i
\(184\) −384.620 −2.09032
\(185\) 0 0
\(186\) 290.369 82.8223i 1.56112 0.445281i
\(187\) 31.7490i 0.169781i
\(188\) 273.746 1.45610
\(189\) 52.8856 + 48.0220i 0.279818 + 0.254085i
\(190\) 0 0
\(191\) 288.210i 1.50895i −0.656328 0.754476i \(-0.727891\pi\)
0.656328 0.754476i \(-0.272109\pi\)
\(192\) −140.276 + 40.0111i −0.730604 + 0.208391i
\(193\) 77.1216i 0.399594i −0.979837 0.199797i \(-0.935972\pi\)
0.979837 0.199797i \(-0.0640282\pi\)
\(194\) 81.2183i 0.418651i
\(195\) 0 0
\(196\) −58.0405 −0.296125
\(197\) 136.433 0.692554 0.346277 0.938132i \(-0.387446\pi\)
0.346277 + 0.938132i \(0.387446\pi\)
\(198\) −116.717 187.956i −0.589482 0.949270i
\(199\) −86.5830 −0.435090 −0.217545 0.976050i \(-0.569805\pi\)
−0.217545 + 0.976050i \(0.569805\pi\)
\(200\) 0 0
\(201\) 12.4797 + 43.7530i 0.0620883 + 0.217677i
\(202\) 472.974i 2.34145i
\(203\) 25.1235 0.123761
\(204\) −108.310 + 30.8934i −0.530930 + 0.151438i
\(205\) 0 0
\(206\) 419.831i 2.03801i
\(207\) −195.452 + 121.373i −0.944212 + 0.586341i
\(208\) 228.059i 1.09644i
\(209\) 113.794i 0.544467i
\(210\) 0 0
\(211\) 19.4170 0.0920237 0.0460118 0.998941i \(-0.485349\pi\)
0.0460118 + 0.998941i \(0.485349\pi\)
\(212\) −125.929 −0.594005
\(213\) −58.0608 203.557i −0.272586 0.955666i
\(214\) 272.952 1.27547
\(215\) 0 0
\(216\) 273.088 300.746i 1.26430 1.39234i
\(217\) 75.9555i 0.350026i
\(218\) 128.101 0.587621
\(219\) 63.1882 + 221.533i 0.288531 + 1.01157i
\(220\) 0 0
\(221\) 52.7309i 0.238601i
\(222\) −95.3199 334.184i −0.429369 1.50533i
\(223\) 175.041i 0.784935i −0.919766 0.392468i \(-0.871622\pi\)
0.919766 0.392468i \(-0.128378\pi\)
\(224\) 22.4196i 0.100087i
\(225\) 0 0
\(226\) 76.2876 0.337556
\(227\) 177.574 0.782264 0.391132 0.920335i \(-0.372084\pi\)
0.391132 + 0.920335i \(0.372084\pi\)
\(228\) −388.200 + 110.727i −1.70263 + 0.485644i
\(229\) −40.8118 −0.178217 −0.0891087 0.996022i \(-0.528402\pi\)
−0.0891087 + 0.996022i \(0.528402\pi\)
\(230\) 0 0
\(231\) 53.5203 15.2657i 0.231689 0.0660851i
\(232\) 142.871i 0.615821i
\(233\) 387.696 1.66393 0.831965 0.554828i \(-0.187216\pi\)
0.831965 + 0.554828i \(0.187216\pi\)
\(234\) 193.852 + 312.169i 0.828429 + 1.33406i
\(235\) 0 0
\(236\) 766.102i 3.24619i
\(237\) −367.100 + 104.708i −1.54895 + 0.441808i
\(238\) 42.0000i 0.176471i
\(239\) 49.5229i 0.207209i 0.994619 + 0.103604i \(0.0330376\pi\)
−0.994619 + 0.103604i \(0.966962\pi\)
\(240\) 0 0
\(241\) 325.247 1.34957 0.674786 0.738013i \(-0.264236\pi\)
0.674786 + 0.738013i \(0.264236\pi\)
\(242\) 251.845 1.04068
\(243\) 43.8699 239.007i 0.180535 0.983569i
\(244\) −476.929 −1.95463
\(245\) 0 0
\(246\) 193.852 + 679.631i 0.788017 + 2.76273i
\(247\) 188.996i 0.765166i
\(248\) 431.939 1.74169
\(249\) 214.306 61.1268i 0.860666 0.245489i
\(250\) 0 0
\(251\) 263.732i 1.05073i −0.850878 0.525364i \(-0.823929\pi\)
0.850878 0.525364i \(-0.176071\pi\)
\(252\) 104.156 + 167.727i 0.413316 + 0.665582i
\(253\) 179.247i 0.708486i
\(254\) 54.0508i 0.212798i
\(255\) 0 0
\(256\) −521.996 −2.03905
\(257\) 151.181 0.588252 0.294126 0.955767i \(-0.404971\pi\)
0.294126 + 0.955767i \(0.404971\pi\)
\(258\) 69.6006 + 244.014i 0.269770 + 0.945792i
\(259\) 87.4170 0.337517
\(260\) 0 0
\(261\) −45.0850 72.6024i −0.172739 0.278170i
\(262\) 641.970i 2.45027i
\(263\) 114.389 0.434941 0.217470 0.976067i \(-0.430219\pi\)
0.217470 + 0.976067i \(0.430219\pi\)
\(264\) −86.8118 304.355i −0.328832 1.15286i
\(265\) 0 0
\(266\) 150.535i 0.565920i
\(267\) 104.816 + 367.476i 0.392568 + 1.37631i
\(268\) 125.749i 0.469213i
\(269\) 4.76170i 0.0177015i −0.999961 0.00885074i \(-0.997183\pi\)
0.999961 0.00885074i \(-0.00281731\pi\)
\(270\) 0 0
\(271\) −518.701 −1.91402 −0.957012 0.290048i \(-0.906329\pi\)
−0.957012 + 0.290048i \(0.906329\pi\)
\(272\) −88.6701 −0.325993
\(273\) −88.8901 + 25.3542i −0.325605 + 0.0928727i
\(274\) −115.749 −0.422442
\(275\) 0 0
\(276\) −611.490 + 174.416i −2.21554 + 0.631943i
\(277\) 121.085i 0.437130i −0.975822 0.218565i \(-0.929862\pi\)
0.975822 0.218565i \(-0.0701375\pi\)
\(278\) −226.629 −0.815213
\(279\) 219.498 136.305i 0.786731 0.488548i
\(280\) 0 0
\(281\) 407.255i 1.44931i 0.689113 + 0.724654i \(0.258000\pi\)
−0.689113 + 0.724654i \(0.742000\pi\)
\(282\) 333.929 95.2470i 1.18415 0.337755i
\(283\) 398.634i 1.40860i 0.709902 + 0.704300i \(0.248739\pi\)
−0.709902 + 0.704300i \(0.751261\pi\)
\(284\) 585.036i 2.05998i
\(285\) 0 0
\(286\) 286.288 1.00101
\(287\) −177.780 −0.619443
\(288\) 64.7886 40.2327i 0.224960 0.139697i
\(289\) −268.498 −0.929059
\(290\) 0 0
\(291\) −19.0627 66.8325i −0.0655077 0.229665i
\(292\) 636.701i 2.18048i
\(293\) 2.53426 0.00864935 0.00432468 0.999991i \(-0.498623\pi\)
0.00432468 + 0.999991i \(0.498623\pi\)
\(294\) −70.8006 + 20.1946i −0.240819 + 0.0686890i
\(295\) 0 0
\(296\) 497.117i 1.67945i
\(297\) −140.159 127.269i −0.471916 0.428516i
\(298\) 686.235i 2.30280i
\(299\) 297.706i 0.995671i
\(300\) 0 0
\(301\) −63.8301 −0.212060
\(302\) 358.484 1.18703
\(303\) −111.012 389.199i −0.366375 1.28448i
\(304\) −317.808 −1.04542
\(305\) 0 0
\(306\) −121.373 + 75.3705i −0.396642 + 0.246309i
\(307\) 86.2366i 0.280901i 0.990088 + 0.140451i \(0.0448551\pi\)
−0.990088 + 0.140451i \(0.955145\pi\)
\(308\) 153.821 0.499418
\(309\) 98.5385 + 345.469i 0.318895 + 1.11802i
\(310\) 0 0
\(311\) 151.777i 0.488028i 0.969772 + 0.244014i \(0.0784643\pi\)
−0.969772 + 0.244014i \(0.921536\pi\)
\(312\) 144.183 + 505.494i 0.462125 + 1.62017i
\(313\) 318.118i 1.01635i −0.861254 0.508175i \(-0.830320\pi\)
0.861254 0.508175i \(-0.169680\pi\)
\(314\) 367.150i 1.16927i
\(315\) 0 0
\(316\) −1055.07 −3.33883
\(317\) −364.020 −1.14833 −0.574164 0.818740i \(-0.694673\pi\)
−0.574164 + 0.818740i \(0.694673\pi\)
\(318\) −153.615 + 43.8157i −0.483064 + 0.137785i
\(319\) −66.5830 −0.208724
\(320\) 0 0
\(321\) 224.605 64.0645i 0.699705 0.199578i
\(322\) 237.122i 0.736402i
\(323\) 73.4823 0.227500
\(324\) 297.790 601.983i 0.919104 1.85797i
\(325\) 0 0
\(326\) 248.779i 0.763124i
\(327\) 105.412 30.0667i 0.322359 0.0919470i
\(328\) 1010.99i 3.08228i
\(329\) 87.3502i 0.265502i
\(330\) 0 0
\(331\) 154.369 0.466370 0.233185 0.972432i \(-0.425085\pi\)
0.233185 + 0.972432i \(0.425085\pi\)
\(332\) 615.929 1.85521
\(333\) −156.873 252.620i −0.471090 0.758617i
\(334\) 725.697 2.17274
\(335\) 0 0
\(336\) 42.6346 + 149.474i 0.126889 + 0.444862i
\(337\) 403.041i 1.19597i 0.801509 + 0.597983i \(0.204031\pi\)
−0.801509 + 0.597983i \(0.795969\pi\)
\(338\) 117.015 0.346199
\(339\) 62.7752 17.9055i 0.185178 0.0528185i
\(340\) 0 0
\(341\) 201.300i 0.590321i
\(342\) −435.019 + 270.140i −1.27198 + 0.789883i
\(343\) 18.5203i 0.0539949i
\(344\) 362.984i 1.05519i
\(345\) 0 0
\(346\) 380.265 1.09903
\(347\) 471.242 1.35805 0.679023 0.734117i \(-0.262404\pi\)
0.679023 + 0.734117i \(0.262404\pi\)
\(348\) −64.7886 227.144i −0.186174 0.652712i
\(349\) 364.516 1.04446 0.522230 0.852805i \(-0.325100\pi\)
0.522230 + 0.852805i \(0.325100\pi\)
\(350\) 0 0
\(351\) 232.786 + 211.377i 0.663207 + 0.602215i
\(352\) 59.4170i 0.168798i
\(353\) −86.3420 −0.244595 −0.122297 0.992493i \(-0.539026\pi\)
−0.122297 + 0.992493i \(0.539026\pi\)
\(354\) −266.557 934.528i −0.752985 2.63991i
\(355\) 0 0
\(356\) 1056.15i 2.96671i
\(357\) −9.85782 34.5608i −0.0276129 0.0968089i
\(358\) 558.693i 1.56059i
\(359\) 372.068i 1.03640i −0.855259 0.518200i \(-0.826602\pi\)
0.855259 0.518200i \(-0.173398\pi\)
\(360\) 0 0
\(361\) −97.6275 −0.270436
\(362\) −819.997 −2.26518
\(363\) 207.237 59.1104i 0.570900 0.162839i
\(364\) −255.476 −0.701857
\(365\) 0 0
\(366\) −581.782 + 165.942i −1.58957 + 0.453395i
\(367\) 161.786i 0.440833i −0.975406 0.220416i \(-0.929258\pi\)
0.975406 0.220416i \(-0.0707416\pi\)
\(368\) −500.609 −1.36035
\(369\) 319.033 + 513.753i 0.864587 + 1.39228i
\(370\) 0 0
\(371\) 40.1830i 0.108310i
\(372\) 686.721 195.875i 1.84602 0.526544i
\(373\) 378.251i 1.01408i −0.861923 0.507039i \(-0.830740\pi\)
0.861923 0.507039i \(-0.169260\pi\)
\(374\) 111.310i 0.297619i
\(375\) 0 0
\(376\) 496.737 1.32111
\(377\) 110.586 0.293330
\(378\) 185.413 + 168.361i 0.490510 + 0.445401i
\(379\) 50.7974 0.134030 0.0670151 0.997752i \(-0.478652\pi\)
0.0670151 + 0.997752i \(0.478652\pi\)
\(380\) 0 0
\(381\) −12.6863 44.4771i −0.0332973 0.116738i
\(382\) 1010.44i 2.64514i
\(383\) 113.381 0.296034 0.148017 0.988985i \(-0.452711\pi\)
0.148017 + 0.988985i \(0.452711\pi\)
\(384\) −589.582 + 168.167i −1.53537 + 0.437936i
\(385\) 0 0
\(386\) 270.382i 0.700472i
\(387\) 114.545 + 184.458i 0.295983 + 0.476634i
\(388\) 192.081i 0.495054i
\(389\) 725.584i 1.86526i 0.360841 + 0.932628i \(0.382490\pi\)
−0.360841 + 0.932628i \(0.617510\pi\)
\(390\) 0 0
\(391\) 115.749 0.296033
\(392\) −105.320 −0.268673
\(393\) 150.677 + 528.261i 0.383402 + 1.34418i
\(394\) 478.324 1.21402
\(395\) 0 0
\(396\) −276.037 444.514i −0.697062 1.12251i
\(397\) 94.3464i 0.237648i −0.992915 0.118824i \(-0.962088\pi\)
0.992915 0.118824i \(-0.0379125\pi\)
\(398\) −303.553 −0.762697
\(399\) −35.3320 123.871i −0.0885514 0.310455i
\(400\) 0 0
\(401\) 677.665i 1.68994i −0.534815 0.844969i \(-0.679619\pi\)
0.534815 0.844969i \(-0.320381\pi\)
\(402\) 43.7530 + 153.395i 0.108838 + 0.381579i
\(403\) 334.332i 0.829608i
\(404\) 1118.58i 2.76877i
\(405\) 0 0
\(406\) 88.0810 0.216948
\(407\) −231.675 −0.569226
\(408\) −196.538 + 56.0588i −0.481711 + 0.137399i
\(409\) −17.3647 −0.0424564 −0.0212282 0.999775i \(-0.506758\pi\)
−0.0212282 + 0.999775i \(0.506758\pi\)
\(410\) 0 0
\(411\) −95.2470 + 27.1675i −0.231745 + 0.0661009i
\(412\) 992.899i 2.40995i
\(413\) 244.457 0.591905
\(414\) −685.239 + 425.523i −1.65517 + 1.02783i
\(415\) 0 0
\(416\) 98.6838i 0.237221i
\(417\) −186.488 + 53.1922i −0.447213 + 0.127559i
\(418\) 398.952i 0.954430i
\(419\) 136.071i 0.324752i −0.986729 0.162376i \(-0.948084\pi\)
0.986729 0.162376i \(-0.0519157\pi\)
\(420\) 0 0
\(421\) 423.992 1.00711 0.503554 0.863964i \(-0.332026\pi\)
0.503554 + 0.863964i \(0.332026\pi\)
\(422\) 68.0745 0.161314
\(423\) 252.427 156.753i 0.596753 0.370574i
\(424\) −228.510 −0.538938
\(425\) 0 0
\(426\) −203.557 713.655i −0.477833 1.67525i
\(427\) 152.184i 0.356404i
\(428\) 645.530 1.50825
\(429\) 235.579 67.1946i 0.549135 0.156631i
\(430\) 0 0
\(431\) 340.244i 0.789430i 0.918804 + 0.394715i \(0.129157\pi\)
−0.918804 + 0.394715i \(0.870843\pi\)
\(432\) 355.443 391.442i 0.822786 0.906117i
\(433\) 159.166i 0.367589i −0.982965 0.183794i \(-0.941162\pi\)
0.982965 0.183794i \(-0.0588381\pi\)
\(434\) 266.294i 0.613581i
\(435\) 0 0
\(436\) 302.959 0.694861
\(437\) 414.863 0.949343
\(438\) 221.533 + 776.678i 0.505783 + 1.77324i
\(439\) −128.073 −0.291738 −0.145869 0.989304i \(-0.546598\pi\)
−0.145869 + 0.989304i \(0.546598\pi\)
\(440\) 0 0
\(441\) −53.5203 + 33.2353i −0.121361 + 0.0753634i
\(442\) 184.871i 0.418259i
\(443\) −197.340 −0.445463 −0.222731 0.974880i \(-0.571497\pi\)
−0.222731 + 0.974880i \(0.571497\pi\)
\(444\) −225.431 790.345i −0.507728 1.78006i
\(445\) 0 0
\(446\) 613.679i 1.37596i
\(447\) −161.066 564.686i −0.360327 1.26328i
\(448\) 128.646i 0.287156i
\(449\) 148.101i 0.329847i −0.986306 0.164923i \(-0.947262\pi\)
0.986306 0.164923i \(-0.0527377\pi\)
\(450\) 0 0
\(451\) 471.158 1.04470
\(452\) 180.420 0.399159
\(453\) 294.988 84.1398i 0.651187 0.185739i
\(454\) 622.561 1.37128
\(455\) 0 0
\(456\) −704.423 + 200.924i −1.54479 + 0.440622i
\(457\) 122.214i 0.267428i −0.991020 0.133714i \(-0.957310\pi\)
0.991020 0.133714i \(-0.0426903\pi\)
\(458\) −143.083 −0.312408
\(459\) −82.1843 + 90.5079i −0.179051 + 0.197185i
\(460\) 0 0
\(461\) 602.089i 1.30605i 0.757337 + 0.653025i \(0.226500\pi\)
−0.757337 + 0.653025i \(0.773500\pi\)
\(462\) 187.638 53.5203i 0.406143 0.115845i
\(463\) 637.061i 1.37594i 0.725738 + 0.687971i \(0.241498\pi\)
−0.725738 + 0.687971i \(0.758502\pi\)
\(464\) 185.956i 0.400767i
\(465\) 0 0
\(466\) 1359.23 2.91681
\(467\) 767.706 1.64391 0.821955 0.569553i \(-0.192884\pi\)
0.821955 + 0.569553i \(0.192884\pi\)
\(468\) 458.460 + 738.280i 0.979616 + 1.57752i
\(469\) −40.1255 −0.0855554
\(470\) 0 0
\(471\) 86.1739 + 302.119i 0.182959 + 0.641442i
\(472\) 1390.16i 2.94526i
\(473\) 169.164 0.357641
\(474\) −1287.02 + 367.100i −2.71524 + 0.774473i
\(475\) 0 0
\(476\) 99.3299i 0.208676i
\(477\) −116.122 + 72.1097i −0.243442 + 0.151173i
\(478\) 173.624i 0.363229i
\(479\) 393.855i 0.822245i −0.911580 0.411122i \(-0.865137\pi\)
0.911580 0.411122i \(-0.134863\pi\)
\(480\) 0 0
\(481\) 384.782 0.799962
\(482\) 1140.29 2.36575
\(483\) −55.6548 195.122i −0.115227 0.403978i
\(484\) 595.612 1.23060
\(485\) 0 0
\(486\) 153.805 837.941i 0.316470 1.72416i
\(487\) 573.409i 1.17743i 0.808340 + 0.588716i \(0.200366\pi\)
−0.808340 + 0.588716i \(0.799634\pi\)
\(488\) −865.432 −1.77343
\(489\) 58.3908 + 204.714i 0.119409 + 0.418638i
\(490\) 0 0
\(491\) 170.796i 0.347853i −0.984759 0.173927i \(-0.944354\pi\)
0.984759 0.173927i \(-0.0556455\pi\)
\(492\) 458.460 + 1607.33i 0.931830 + 3.26692i
\(493\) 42.9961i 0.0872131i
\(494\) 662.606i 1.34131i
\(495\) 0 0
\(496\) 562.199 1.13347
\(497\) 186.680 0.375614
\(498\) 751.340 214.306i 1.50871 0.430333i
\(499\) 847.814 1.69903 0.849513 0.527567i \(-0.176896\pi\)
0.849513 + 0.527567i \(0.176896\pi\)
\(500\) 0 0
\(501\) 597.158 170.328i 1.19193 0.339977i
\(502\) 924.626i 1.84188i
\(503\) 197.624 0.392891 0.196445 0.980515i \(-0.437060\pi\)
0.196445 + 0.980515i \(0.437060\pi\)
\(504\) 189.000 + 304.355i 0.375000 + 0.603880i
\(505\) 0 0
\(506\) 628.427i 1.24195i
\(507\) 96.2891 27.4647i 0.189919 0.0541710i
\(508\) 127.830i 0.251634i
\(509\) 491.448i 0.965516i −0.875754 0.482758i \(-0.839635\pi\)
0.875754 0.482758i \(-0.160365\pi\)
\(510\) 0 0
\(511\) −203.166 −0.397585
\(512\) −1012.62 −1.97777
\(513\) −294.562 + 324.395i −0.574194 + 0.632348i
\(514\) 530.029 1.03118
\(515\) 0 0
\(516\) 164.605 + 577.093i 0.319002 + 1.11840i
\(517\) 231.498i 0.447772i
\(518\) 306.477 0.591655
\(519\) 312.911 89.2521i 0.602912 0.171969i
\(520\) 0 0
\(521\) 870.010i 1.66988i 0.550338 + 0.834942i \(0.314499\pi\)
−0.550338 + 0.834942i \(0.685501\pi\)
\(522\) −158.064 254.539i −0.302806 0.487622i
\(523\) 798.707i 1.52716i −0.645710 0.763582i \(-0.723439\pi\)
0.645710 0.763582i \(-0.276561\pi\)
\(524\) 1518.26i 2.89744i
\(525\) 0 0
\(526\) 401.041 0.762434
\(527\) −129.989 −0.246659
\(528\) −112.992 396.140i −0.213999 0.750265i
\(529\) 124.490 0.235331
\(530\) 0 0
\(531\) −438.686 706.437i −0.826151 1.33039i
\(532\) 356.014i 0.669200i
\(533\) −782.531 −1.46816
\(534\) 367.476 + 1288.34i 0.688157 + 2.41263i
\(535\) 0 0
\(536\) 228.183i 0.425714i
\(537\) −131.131 459.735i −0.244191 0.856117i
\(538\) 16.6941i 0.0310300i
\(539\) 49.0829i 0.0910630i
\(540\) 0 0
\(541\) −736.243 −1.36089 −0.680446 0.732798i \(-0.738214\pi\)
−0.680446 + 0.732798i \(0.738214\pi\)
\(542\) −1818.52 −3.35521
\(543\) −674.755 + 192.461i −1.24264 + 0.354441i
\(544\) −38.3686 −0.0705305
\(545\) 0 0
\(546\) −311.642 + 88.8901i −0.570773 + 0.162802i
\(547\) 228.952i 0.418559i −0.977856 0.209279i \(-0.932888\pi\)
0.977856 0.209279i \(-0.0671118\pi\)
\(548\) −273.746 −0.499537
\(549\) −439.786 + 273.100i −0.801067 + 0.497450i
\(550\) 0 0
\(551\) 154.105i 0.279682i
\(552\) −1109.60 + 316.494i −2.01015 + 0.573359i
\(553\) 336.664i 0.608796i
\(554\) 424.515i 0.766272i
\(555\) 0 0
\(556\) −535.978 −0.963989
\(557\) −906.288 −1.62709 −0.813544 0.581503i \(-0.802465\pi\)
−0.813544 + 0.581503i \(0.802465\pi\)
\(558\) 769.543 477.875i 1.37911 0.856406i
\(559\) −280.959 −0.502611
\(560\) 0 0
\(561\) 26.1255 + 91.5940i 0.0465695 + 0.163269i
\(562\) 1427.81i 2.54058i
\(563\) −458.616 −0.814593 −0.407297 0.913296i \(-0.633529\pi\)
−0.407297 + 0.913296i \(0.633529\pi\)
\(564\) 789.741 225.259i 1.40025 0.399396i
\(565\) 0 0
\(566\) 1397.58i 2.46922i
\(567\) 192.088 + 95.0222i 0.338779 + 0.167588i
\(568\) 1061.60i 1.86901i
\(569\) 577.428i 1.01481i 0.861707 + 0.507406i \(0.169395\pi\)
−0.861707 + 0.507406i \(0.830605\pi\)
\(570\) 0 0
\(571\) −103.122 −0.180598 −0.0902991 0.995915i \(-0.528782\pi\)
−0.0902991 + 0.995915i \(0.528782\pi\)
\(572\) 677.069 1.18369
\(573\) −237.161 831.468i −0.413893 1.45108i
\(574\) −623.284 −1.08586
\(575\) 0 0
\(576\) −371.763 + 230.859i −0.645423 + 0.400797i
\(577\) 676.583i 1.17259i −0.810099 0.586294i \(-0.800586\pi\)
0.810099 0.586294i \(-0.199414\pi\)
\(578\) −941.334 −1.62860
\(579\) −63.4615 222.491i −0.109605 0.384268i
\(580\) 0 0
\(581\) 196.538i 0.338275i
\(582\) −66.8325 234.310i −0.114833 0.402594i
\(583\) 106.494i 0.182666i
\(584\) 1155.35i 1.97834i
\(585\) 0 0
\(586\) 8.88492 0.0151620
\(587\) −158.683 −0.270329 −0.135164 0.990823i \(-0.543156\pi\)
−0.135164 + 0.990823i \(0.543156\pi\)
\(588\) −167.443 + 47.7601i −0.284768 + 0.0812247i
\(589\) −465.903 −0.791007
\(590\) 0 0
\(591\) 393.601 112.267i 0.665992 0.189962i
\(592\) 647.033i 1.09296i
\(593\) −935.371 −1.57735 −0.788677 0.614807i \(-0.789234\pi\)
−0.788677 + 0.614807i \(0.789234\pi\)
\(594\) −491.387 446.196i −0.827251 0.751172i
\(595\) 0 0
\(596\) 1622.94i 2.72306i
\(597\) −249.787 + 71.2470i −0.418403 + 0.119342i
\(598\) 1043.73i 1.74537i
\(599\) 73.7665i 0.123149i −0.998102 0.0615747i \(-0.980388\pi\)
0.998102 0.0615747i \(-0.0196122\pi\)
\(600\) 0 0
\(601\) −934.280 −1.55454 −0.777271 0.629166i \(-0.783397\pi\)
−0.777271 + 0.629166i \(0.783397\pi\)
\(602\) −223.783 −0.371733
\(603\) 72.0066 + 115.956i 0.119414 + 0.192298i
\(604\) 847.814 1.40367
\(605\) 0 0
\(606\) −389.199 1364.50i −0.642242 2.25165i
\(607\) 181.608i 0.299189i −0.988747 0.149595i \(-0.952203\pi\)
0.988747 0.149595i \(-0.0477968\pi\)
\(608\) −137.519 −0.226183
\(609\) 72.4797 20.6735i 0.119014 0.0339466i
\(610\) 0 0
\(611\) 384.488i 0.629276i
\(612\) −287.046 + 178.251i −0.469029 + 0.291260i
\(613\) 897.940i 1.46483i 0.680859 + 0.732414i \(0.261606\pi\)
−0.680859 + 0.732414i \(0.738394\pi\)
\(614\) 302.339i 0.492409i
\(615\) 0 0
\(616\) 279.122 0.453119
\(617\) −1169.69 −1.89576 −0.947882 0.318622i \(-0.896780\pi\)
−0.947882 + 0.318622i \(0.896780\pi\)
\(618\) 345.469 + 1211.19i 0.559011 + 1.95985i
\(619\) −1208.97 −1.95310 −0.976548 0.215301i \(-0.930927\pi\)
−0.976548 + 0.215301i \(0.930927\pi\)
\(620\) 0 0
\(621\) −463.992 + 510.985i −0.747169 + 0.822842i
\(622\) 532.118i 0.855495i
\(623\) −337.009 −0.540945
\(624\) 187.664 + 657.936i 0.300744 + 1.05438i
\(625\) 0 0
\(626\) 1115.30i 1.78162i
\(627\) 93.6380 + 328.288i 0.149343 + 0.523585i
\(628\) 868.310i 1.38266i
\(629\) 149.604i 0.237845i
\(630\) 0 0
\(631\) 901.223 1.42825 0.714123 0.700020i \(-0.246826\pi\)
0.714123 + 0.700020i \(0.246826\pi\)
\(632\) −1914.52 −3.02930
\(633\) 56.0169 15.9778i 0.0884942 0.0252413i
\(634\) −1276.23 −2.01298
\(635\) 0 0
\(636\) −363.298 + 103.624i −0.571223 + 0.162931i
\(637\) 81.5203i 0.127975i
\(638\) −233.435 −0.365886
\(639\) −335.004 539.472i −0.524263 0.844245i
\(640\) 0 0
\(641\) 528.629i 0.824694i 0.911027 + 0.412347i \(0.135291\pi\)
−0.911027 + 0.412347i \(0.864709\pi\)
\(642\) 787.449 224.605i 1.22656 0.349852i
\(643\) 33.4392i 0.0520050i −0.999662 0.0260025i \(-0.991722\pi\)
0.999662 0.0260025i \(-0.00827779\pi\)
\(644\) 560.792i 0.870795i
\(645\) 0 0
\(646\) 257.624 0.398798
\(647\) 786.308 1.21531 0.607657 0.794200i \(-0.292110\pi\)
0.607657 + 0.794200i \(0.292110\pi\)
\(648\) 540.366 1092.35i 0.833898 1.68573i
\(649\) −647.867 −0.998254
\(650\) 0 0
\(651\) 62.5020 + 219.127i 0.0960092 + 0.336601i
\(652\) 588.361i 0.902394i
\(653\) −385.807 −0.590823 −0.295412 0.955370i \(-0.595457\pi\)
−0.295412 + 0.955370i \(0.595457\pi\)
\(654\) 369.565 105.412i 0.565084 0.161180i
\(655\) 0 0
\(656\) 1315.87i 2.00590i
\(657\) 364.588 + 587.114i 0.554929 + 0.893628i
\(658\) 306.243i 0.465415i
\(659\) 97.2583i 0.147585i 0.997274 + 0.0737924i \(0.0235102\pi\)
−0.997274 + 0.0737924i \(0.976490\pi\)
\(660\) 0 0
\(661\) −961.505 −1.45462 −0.727311 0.686309i \(-0.759230\pi\)
−0.727311 + 0.686309i \(0.759230\pi\)
\(662\) 541.205 0.817530
\(663\) −43.3910 152.125i −0.0654464 0.229450i
\(664\) 1117.66 1.68322
\(665\) 0 0
\(666\) −549.984 885.665i −0.825802 1.32983i
\(667\) 242.745i 0.363936i
\(668\) 1716.27 2.56927
\(669\) −144.037 504.981i −0.215301 0.754830i
\(670\) 0 0
\(671\) 403.323i 0.601078i
\(672\) 18.4485 + 64.6791i 0.0274531 + 0.0962487i
\(673\) 1089.81i 1.61933i 0.586895 + 0.809663i \(0.300350\pi\)
−0.586895 + 0.809663i \(0.699650\pi\)
\(674\) 1413.03i 2.09648i
\(675\) 0 0
\(676\) 276.741 0.409380
\(677\) −1252.56 −1.85016 −0.925080 0.379771i \(-0.876003\pi\)
−0.925080 + 0.379771i \(0.876003\pi\)
\(678\) 220.085 62.7752i 0.324609 0.0925888i
\(679\) 61.2915 0.0902673
\(680\) 0 0
\(681\) 512.290 146.121i 0.752262 0.214569i
\(682\) 705.741i 1.03481i
\(683\) 341.097 0.499409 0.249705 0.968322i \(-0.419666\pi\)
0.249705 + 0.968322i \(0.419666\pi\)
\(684\) −1028.82 + 638.880i −1.50412 + 0.934035i
\(685\) 0 0
\(686\) 64.9306i 0.0946510i
\(687\) −117.739 + 33.5830i −0.171382 + 0.0488836i
\(688\) 472.450i 0.686700i
\(689\) 176.873i 0.256709i
\(690\) 0 0
\(691\) −783.667 −1.13411 −0.567053 0.823682i \(-0.691916\pi\)
−0.567053 + 0.823682i \(0.691916\pi\)
\(692\) 899.327 1.29961
\(693\) 141.841 88.0810i 0.204677 0.127101i
\(694\) 1652.14 2.38060
\(695\) 0 0
\(696\) −117.565 412.173i −0.168915 0.592203i
\(697\) 304.251i 0.436515i
\(698\) 1277.97 1.83090
\(699\) 1118.48 319.025i 1.60011 0.456402i
\(700\) 0 0
\(701\) 1331.76i 1.89979i −0.312562 0.949897i \(-0.601187\pi\)
0.312562 0.949897i \(-0.398813\pi\)
\(702\) 816.129 + 741.073i 1.16258 + 1.05566i
\(703\) 536.207i 0.762740i
\(704\) 340.941i 0.484291i
\(705\) 0 0
\(706\) −302.708 −0.428766
\(707\) 356.930 0.504852
\(708\) −630.406 2210.16i −0.890404 3.12169i
\(709\) −763.963 −1.07752 −0.538761 0.842459i \(-0.681107\pi\)
−0.538761 + 0.842459i \(0.681107\pi\)
\(710\) 0 0
\(711\) −972.899 + 604.155i −1.36835 + 0.849726i
\(712\) 1916.48i 2.69168i
\(713\) −733.888 −1.02930
\(714\) −34.5608 121.167i −0.0484045 0.169702i
\(715\) 0 0
\(716\) 1321.31i 1.84540i
\(717\) 40.7512 + 142.871i 0.0568357 + 0.199262i
\(718\) 1304.44i 1.81677i
\(719\) 623.715i 0.867476i 0.901039 + 0.433738i \(0.142806\pi\)
−0.901039 + 0.433738i \(0.857194\pi\)
\(720\) 0 0
\(721\) −316.826 −0.439426
\(722\) −342.274 −0.474064
\(723\) 938.318 267.638i 1.29781 0.370177i
\(724\) −1939.29 −2.67858
\(725\) 0 0
\(726\) 726.556 207.237i 1.00077 0.285450i
\(727\) 678.494i 0.933279i 0.884448 + 0.466640i \(0.154536\pi\)
−0.884448 + 0.466640i \(0.845464\pi\)
\(728\) −463.584 −0.636791
\(729\) −70.1111 725.621i −0.0961744 0.995364i
\(730\) 0 0
\(731\) 109.238i 0.149436i
\(732\) −1375.91 + 392.454i −1.87966 + 0.536139i
\(733\) 394.966i 0.538835i 0.963023 + 0.269417i \(0.0868311\pi\)
−0.963023 + 0.269417i \(0.913169\pi\)
\(734\) 567.208i 0.772763i
\(735\) 0 0
\(736\) −216.620 −0.294320
\(737\) 106.342 0.144290
\(738\) 1118.50 + 1801.18i 1.51559 + 2.44062i
\(739\) −292.199 −0.395397 −0.197699 0.980263i \(-0.563347\pi\)
−0.197699 + 0.980263i \(0.563347\pi\)
\(740\) 0 0
\(741\) −155.520 545.242i −0.209879 0.735819i
\(742\) 140.878i 0.189863i
\(743\) 383.452 0.516086 0.258043 0.966133i \(-0.416922\pi\)
0.258043 + 0.966133i \(0.416922\pi\)
\(744\) 1246.12 355.432i 1.67489 0.477731i
\(745\) 0 0
\(746\) 1326.12i 1.77764i
\(747\) 567.960 352.694i 0.760321 0.472147i
\(748\) 263.247i 0.351935i
\(749\) 205.983i 0.275011i
\(750\) 0 0
\(751\) −696.332 −0.927206 −0.463603 0.886043i \(-0.653444\pi\)
−0.463603 + 0.886043i \(0.653444\pi\)
\(752\) 646.538 0.859758
\(753\) −217.019 760.852i −0.288206 1.01043i
\(754\) 387.705 0.514197
\(755\) 0 0
\(756\) 438.501 + 398.174i 0.580028 + 0.526686i
\(757\) 967.357i 1.27788i 0.769256 + 0.638941i \(0.220627\pi\)
−0.769256 + 0.638941i \(0.779373\pi\)
\(758\) 178.092 0.234950
\(759\) 147.498 + 517.117i 0.194332 + 0.681313i
\(760\) 0 0
\(761\) 89.7059i 0.117879i 0.998262 + 0.0589395i \(0.0187719\pi\)
−0.998262 + 0.0589395i \(0.981228\pi\)
\(762\) −44.4771 155.933i −0.0583689 0.204637i
\(763\) 96.6719i 0.126700i
\(764\) 2389.69i 3.12787i
\(765\) 0 0
\(766\) 397.506 0.518937
\(767\) 1076.02 1.40290
\(768\) −1505.93 + 429.538i −1.96084 + 0.559294i
\(769\) −926.219 −1.20445 −0.602223 0.798328i \(-0.705718\pi\)
−0.602223 + 0.798328i \(0.705718\pi\)
\(770\) 0 0
\(771\) 436.148 124.403i 0.565691 0.161353i
\(772\) 639.454i 0.828308i
\(773\) −424.125 −0.548674 −0.274337 0.961634i \(-0.588458\pi\)
−0.274337 + 0.961634i \(0.588458\pi\)
\(774\) 401.587 + 646.694i 0.518846 + 0.835522i
\(775\) 0 0
\(776\) 348.548i 0.449160i
\(777\) 252.193 71.9333i 0.324572 0.0925783i
\(778\) 2543.84i 3.26972i
\(779\) 1090.48i 1.39985i
\(780\) 0 0
\(781\) −494.745 −0.633476
\(782\) 405.807 0.518935
\(783\) −189.810 172.354i −0.242414 0.220120i
\(784\) −137.081 −0.174848
\(785\) 0 0
\(786\) 528.261 + 1852.04i 0.672088 + 2.35629i
\(787\) 155.889i 0.198080i −0.995083 0.0990399i \(-0.968423\pi\)
0.995083 0.0990399i \(-0.0315772\pi\)
\(788\) 1131.24 1.43558
\(789\) 330.006 94.1282i 0.418259 0.119301i
\(790\) 0 0
\(791\) 57.5705i 0.0727820i
\(792\) −500.893 806.612i −0.632441 1.01845i
\(793\) 669.867i 0.844725i
\(794\) 330.771i 0.416588i
\(795\) 0 0
\(796\) −717.903 −0.901888
\(797\) −719.191 −0.902373 −0.451186 0.892430i \(-0.648999\pi\)
−0.451186 + 0.892430i \(0.648999\pi\)
\(798\) −123.871 434.284i −0.155227 0.544215i
\(799\) −149.490 −0.187097
\(800\) 0 0
\(801\) 604.774 + 973.895i 0.755023 + 1.21585i
\(802\) 2375.84i 2.96240i
\(803\) 538.437 0.670531
\(804\) 103.476 + 362.778i 0.128701 + 0.451217i
\(805\) 0 0
\(806\) 1172.14i 1.45427i
\(807\) −3.91828 13.7372i −0.00485537 0.0170226i
\(808\) 2029.77i 2.51209i
\(809\) 212.244i 0.262353i −0.991359 0.131176i \(-0.958125\pi\)
0.991359 0.131176i \(-0.0418755\pi\)
\(810\) 0 0
\(811\) 1058.66 1.30538 0.652690 0.757625i \(-0.273641\pi\)
0.652690 + 0.757625i \(0.273641\pi\)
\(812\) 208.311 0.256541
\(813\) −1496.42 + 426.826i −1.84061 + 0.525001i
\(814\) −812.235 −0.997832
\(815\) 0 0
\(816\) −255.808 + 72.9645i −0.313490 + 0.0894172i
\(817\) 391.527i 0.479225i
\(818\) −60.8792 −0.0744244
\(819\) −235.579 + 146.291i −0.287642 + 0.178621i
\(820\) 0 0
\(821\) 818.571i 0.997042i −0.866878 0.498521i \(-0.833877\pi\)
0.866878 0.498521i \(-0.166123\pi\)
\(822\) −333.929 + 95.2470i −0.406240 + 0.115872i
\(823\) 206.850i 0.251336i −0.992072 0.125668i \(-0.959893\pi\)
0.992072 0.125668i \(-0.0401074\pi\)
\(824\) 1801.71i 2.18654i
\(825\) 0 0
\(826\) 857.047 1.03759
\(827\) −438.639 −0.530398 −0.265199 0.964194i \(-0.585438\pi\)
−0.265199 + 0.964194i \(0.585438\pi\)
\(828\) −1620.59 + 1006.36i −1.95723 + 1.21541i
\(829\) −654.804 −0.789872 −0.394936 0.918709i \(-0.629233\pi\)
−0.394936 + 0.918709i \(0.629233\pi\)
\(830\) 0 0
\(831\) −99.6379 349.323i −0.119901 0.420364i
\(832\) 566.257i 0.680598i
\(833\) 31.6954 0.0380497
\(834\) −653.812 + 186.488i −0.783947 + 0.223606i
\(835\) 0 0
\(836\) 943.520i 1.12861i
\(837\) 521.077 573.851i 0.622553 0.685604i
\(838\) 477.055i 0.569278i
\(839\) 50.9710i 0.0607521i 0.999539 + 0.0303761i \(0.00967049\pi\)
−0.999539 + 0.0303761i \(0.990330\pi\)
\(840\) 0 0
\(841\) 750.830 0.892782
\(842\) 1486.48 1.76542
\(843\) 335.121 + 1174.91i 0.397533 + 1.39372i
\(844\) 160.996 0.190754
\(845\) 0 0
\(846\) 884.988 549.564i 1.04609 0.649603i
\(847\) 190.055i 0.224386i
\(848\) −297.422 −0.350733
\(849\) 328.026 + 1150.03i 0.386368 + 1.35458i
\(850\) 0 0
\(851\) 844.630i 0.992514i
\(852\) −481.411 1687.79i −0.565037 1.98098i
\(853\) 883.941i 1.03627i 0.855298 + 0.518137i \(0.173374\pi\)
−0.855298 + 0.518137i \(0.826626\pi\)
\(854\) 533.547i 0.624762i
\(855\) 0 0
\(856\) 1171.37 1.36843
\(857\) −556.521 −0.649382 −0.324691 0.945820i \(-0.605260\pi\)
−0.324691 + 0.945820i \(0.605260\pi\)
\(858\) 825.922 235.579i 0.962613 0.274568i
\(859\) 643.078 0.748636 0.374318 0.927300i \(-0.377877\pi\)
0.374318 + 0.927300i \(0.377877\pi\)
\(860\) 0 0
\(861\) −512.885 + 146.291i −0.595685 + 0.169908i
\(862\) 1192.87i 1.38384i
\(863\) 204.892 0.237419 0.118709 0.992929i \(-0.462124\pi\)
0.118709 + 0.992929i \(0.462124\pi\)
\(864\) 153.805 169.382i 0.178015 0.196044i
\(865\) 0 0
\(866\) 558.024i 0.644369i
\(867\) −774.601 + 220.940i −0.893426 + 0.254833i
\(868\) 629.786i 0.725559i
\(869\) 892.237i 1.02674i
\(870\) 0 0
\(871\) −176.620 −0.202778
\(872\) 549.747 0.630444
\(873\) −109.990 177.122i −0.125991 0.202888i
\(874\) 1454.48 1.66416
\(875\) 0 0
\(876\) 523.925 + 1836.84i 0.598088 + 2.09685i
\(877\) 207.210i 0.236272i −0.992997 0.118136i \(-0.962308\pi\)
0.992997 0.118136i \(-0.0376919\pi\)
\(878\) −449.015 −0.511406
\(879\) 7.31119 2.08538i 0.00831762 0.00237245i
\(880\) 0 0
\(881\) 1391.37i 1.57931i −0.613552 0.789654i \(-0.710260\pi\)
0.613552 0.789654i \(-0.289740\pi\)
\(882\) −187.638 + 116.520i −0.212741 + 0.132109i
\(883\) 1091.99i 1.23668i 0.785909 + 0.618342i \(0.212195\pi\)
−0.785909 + 0.618342i \(0.787805\pi\)
\(884\) 437.219i 0.494591i
\(885\) 0 0
\(886\) −691.859 −0.780879
\(887\) −149.449 −0.168488 −0.0842439 0.996445i \(-0.526847\pi\)
−0.0842439 + 0.996445i \(0.526847\pi\)
\(888\) −409.066 1434.15i −0.460659 1.61504i
\(889\) 40.7895 0.0458825
\(890\) 0 0
\(891\) −509.077 251.831i −0.571355 0.282638i
\(892\) 1451.35i 1.62707i
\(893\) −535.797 −0.599996
\(894\) −564.686 1979.75i −0.631640 2.21448i
\(895\) 0 0
\(896\) 540.700i 0.603460i
\(897\) −244.975 858.863i −0.273104 0.957483i
\(898\) 519.231i 0.578209i
\(899\) 272.610i 0.303237i
\(900\) 0 0
\(901\) 68.7687 0.0763249
\(902\) 1651.84 1.83131
\(903\) −184.146 + 52.5242i −0.203927 + 0.0581663i
\(904\) 327.388 0.362155
\(905\) 0 0
\(906\) 1034.21 294.988i 1.14151 0.325594i
\(907\) 593.718i 0.654595i 0.944921 + 0.327297i \(0.106138\pi\)
−0.944921 + 0.327297i \(0.893862\pi\)
\(908\) 1472.35 1.62154
\(909\) −640.524 1031.47i −0.704647 1.13473i
\(910\) 0 0
\(911\) 1133.75i 1.24451i 0.782815 + 0.622254i \(0.213783\pi\)
−0.782815 + 0.622254i \(0.786217\pi\)
\(912\) −916.856 + 261.516i −1.00532 + 0.286750i
\(913\) 520.871i 0.570504i
\(914\) 428.474i 0.468790i
\(915\) 0 0
\(916\) −338.391 −0.369422
\(917\) −484.464 −0.528314
\(918\) −288.132 + 317.314i −0.313869 + 0.345658i
\(919\) 684.988 0.745363 0.372681 0.927959i \(-0.378438\pi\)
0.372681 + 0.927959i \(0.378438\pi\)
\(920\) 0 0
\(921\) 70.9620 + 248.787i 0.0770489 + 0.270128i
\(922\) 2110.88i 2.28945i
\(923\) 821.706 0.890256
\(924\) 443.763 126.575i 0.480263 0.136986i
\(925\) 0 0
\(926\) 2233.49i 2.41197i
\(927\) 568.556 + 915.571i 0.613328 + 0.987671i
\(928\) 80.4654i 0.0867084i
\(929\) 192.317i 0.207015i 0.994629 + 0.103507i \(0.0330066\pi\)
−0.994629 + 0.103507i \(0.966993\pi\)
\(930\) 0 0
\(931\) 113.601 0.122021
\(932\) 3214.58 3.44912
\(933\) 124.893 + 437.867i 0.133862 + 0.469310i
\(934\) 2691.52 2.88171
\(935\) 0 0
\(936\) 831.918 + 1339.68i 0.888801 + 1.43128i
\(937\) 1270.28i 1.35569i −0.735206 0.677844i \(-0.762914\pi\)
0.735206 0.677844i \(-0.237086\pi\)
\(938\) −140.677 −0.149975
\(939\) −261.771 917.750i −0.278777 0.977370i
\(940\) 0 0
\(941\) 156.951i 0.166791i 0.996517 + 0.0833957i \(0.0265766\pi\)
−0.996517 + 0.0833957i \(0.973423\pi\)
\(942\) 302.119 + 1059.21i 0.320721 + 1.12442i
\(943\) 1717.73i 1.82155i
\(944\) 1809.39i 1.91673i
\(945\) 0 0
\(946\) 593.077 0.626931
\(947\) −879.945 −0.929193 −0.464596 0.885523i \(-0.653801\pi\)
−0.464596 + 0.885523i \(0.653801\pi\)
\(948\) −3043.81 + 868.191i −3.21077 + 0.915813i
\(949\) −894.272 −0.942331
\(950\) 0 0
\(951\) −1050.18 + 299.543i −1.10429 + 0.314977i
\(952\) 180.243i 0.189331i
\(953\) 563.276 0.591056 0.295528 0.955334i \(-0.404505\pi\)
0.295528 + 0.955334i \(0.404505\pi\)
\(954\) −407.114 + 252.811i −0.426744 + 0.265001i
\(955\) 0 0
\(956\) 410.619i 0.429518i
\(957\) −192.088 + 54.7895i −0.200719 + 0.0572513i
\(958\) 1380.83i 1.44136i
\(959\) 87.3502i 0.0910847i
\(960\) 0 0
\(961\) −136.822 −0.142375
\(962\) 1349.02 1.40230
\(963\) 595.255 369.644i 0.618126 0.383847i
\(964\) 2696.79 2.79750
\(965\) 0 0
\(966\) −195.122 684.081i −0.201989 0.708159i
\(967\) 237.676i 0.245787i 0.992420 + 0.122893i \(0.0392173\pi\)
−0.992420 + 0.122893i \(0.960783\pi\)
\(968\) 1080.79 1.11652
\(969\) 211.992 60.4668i 0.218774 0.0624013i
\(970\) 0 0
\(971\) 1355.00i 1.39546i −0.716359 0.697732i \(-0.754192\pi\)
0.716359 0.697732i \(-0.245808\pi\)
\(972\) 363.748 1981.73i 0.374226 2.03882i
\(973\) 171.026i 0.175772i
\(974\) 2010.33i 2.06399i
\(975\) 0 0
\(976\) −1126.42 −1.15412
\(977\) 493.726 0.505349 0.252674 0.967551i \(-0.418690\pi\)
0.252674 + 0.967551i \(0.418690\pi\)
\(978\) 204.714 + 717.711i 0.209319 + 0.733856i
\(979\) 893.150 0.912309
\(980\) 0 0
\(981\) 279.365 173.481i 0.284775 0.176841i
\(982\) 598.797i 0.609773i
\(983\) −1538.05 −1.56465 −0.782325 0.622870i \(-0.785966\pi\)
−0.782325 + 0.622870i \(0.785966\pi\)
\(984\) 831.918 + 2916.64i 0.845445 + 2.96406i
\(985\) 0 0
\(986\) 150.741i 0.152881i
\(987\) 71.8783 + 252.000i 0.0728251 + 0.255319i
\(988\) 1567.06i 1.58609i
\(989\) 616.731i 0.623590i
\(990\) 0 0
\(991\) 1514.73 1.52849 0.764243 0.644929i \(-0.223113\pi\)
0.764243 + 0.644929i \(0.223113\pi\)
\(992\) 243.270 0.245232
\(993\) 445.344 127.026i 0.448483 0.127922i
\(994\) 654.486 0.658437
\(995\) 0 0
\(996\) 1776.92 506.833i 1.78405 0.508868i
\(997\) 1826.43i 1.83193i 0.401260 + 0.915964i \(0.368572\pi\)
−0.401260 + 0.915964i \(0.631428\pi\)
\(998\) 2972.37 2.97833
\(999\) −660.443 599.705i −0.661104 0.600306i
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 525.3.f.a.449.7 8
3.2 odd 2 inner 525.3.f.a.449.1 8
5.2 odd 4 525.3.c.a.176.4 4
5.3 odd 4 21.3.b.a.8.1 4
5.4 even 2 inner 525.3.f.a.449.2 8
15.2 even 4 525.3.c.a.176.1 4
15.8 even 4 21.3.b.a.8.4 yes 4
15.14 odd 2 inner 525.3.f.a.449.8 8
20.3 even 4 336.3.d.c.113.1 4
35.3 even 12 147.3.h.c.128.4 8
35.13 even 4 147.3.b.f.50.1 4
35.18 odd 12 147.3.h.e.128.4 8
35.23 odd 12 147.3.h.e.116.1 8
35.33 even 12 147.3.h.c.116.1 8
40.3 even 4 1344.3.d.b.449.4 4
40.13 odd 4 1344.3.d.f.449.1 4
45.13 odd 12 567.3.r.c.512.4 8
45.23 even 12 567.3.r.c.512.1 8
45.38 even 12 567.3.r.c.134.4 8
45.43 odd 12 567.3.r.c.134.1 8
60.23 odd 4 336.3.d.c.113.2 4
105.23 even 12 147.3.h.e.116.4 8
105.38 odd 12 147.3.h.c.128.1 8
105.53 even 12 147.3.h.e.128.1 8
105.68 odd 12 147.3.h.c.116.4 8
105.83 odd 4 147.3.b.f.50.4 4
120.53 even 4 1344.3.d.f.449.2 4
120.83 odd 4 1344.3.d.b.449.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.b.a.8.1 4 5.3 odd 4
21.3.b.a.8.4 yes 4 15.8 even 4
147.3.b.f.50.1 4 35.13 even 4
147.3.b.f.50.4 4 105.83 odd 4
147.3.h.c.116.1 8 35.33 even 12
147.3.h.c.116.4 8 105.68 odd 12
147.3.h.c.128.1 8 105.38 odd 12
147.3.h.c.128.4 8 35.3 even 12
147.3.h.e.116.1 8 35.23 odd 12
147.3.h.e.116.4 8 105.23 even 12
147.3.h.e.128.1 8 105.53 even 12
147.3.h.e.128.4 8 35.18 odd 12
336.3.d.c.113.1 4 20.3 even 4
336.3.d.c.113.2 4 60.23 odd 4
525.3.c.a.176.1 4 15.2 even 4
525.3.c.a.176.4 4 5.2 odd 4
525.3.f.a.449.1 8 3.2 odd 2 inner
525.3.f.a.449.2 8 5.4 even 2 inner
525.3.f.a.449.7 8 1.1 even 1 trivial
525.3.f.a.449.8 8 15.14 odd 2 inner
567.3.r.c.134.1 8 45.43 odd 12
567.3.r.c.134.4 8 45.38 even 12
567.3.r.c.512.1 8 45.23 even 12
567.3.r.c.512.4 8 45.13 odd 12
1344.3.d.b.449.3 4 120.83 odd 4
1344.3.d.b.449.4 4 40.3 even 4
1344.3.d.f.449.1 4 40.13 odd 4
1344.3.d.f.449.2 4 120.53 even 4