Properties

Label 525.3.f.a.449.3
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 449.3
Root \(-0.153548 + 0.153548i\) of defining polynomial
Character \(\chi\) \(=\) 525.449
Dual form 525.3.f.a.449.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.30710 q^{2} +(2.38267 - 1.82288i) q^{3} -2.29150 q^{4} +(-3.11438 + 2.38267i) q^{6} +2.64575i q^{7} +8.22359 q^{8} +(2.35425 - 8.68663i) q^{9} +O(q^{10})\) \(q-1.30710 q^{2} +(2.38267 - 1.82288i) q^{3} -2.29150 q^{4} +(-3.11438 + 2.38267i) q^{6} +2.64575i q^{7} +8.22359 q^{8} +(2.35425 - 8.68663i) q^{9} -2.61419i q^{11} +(-5.45990 + 4.17712i) q^{12} -6.35425i q^{13} -3.45825i q^{14} -1.58301 q^{16} -12.1449 q^{17} +(-3.07723 + 11.3542i) q^{18} +10.2288 q^{19} +(4.82288 + 6.30396i) q^{21} +3.41699i q^{22} -4.30231 q^{23} +(19.5941 - 14.9906i) q^{24} +8.30561i q^{26} +(-10.2252 - 24.9889i) q^{27} -6.06275i q^{28} -17.3733i q^{29} +39.2915 q^{31} -30.8252 q^{32} +(-4.76534 - 6.22876i) q^{33} +15.8745 q^{34} +(-5.39477 + 19.9054i) q^{36} -41.0405i q^{37} -13.3700 q^{38} +(-11.5830 - 15.1401i) q^{39} -30.2802i q^{41} +(-6.30396 - 8.23987i) q^{42} -55.8745i q^{43} +5.99042i q^{44} +5.62352 q^{46} -39.9749 q^{47} +(-3.77178 + 2.88562i) q^{48} -7.00000 q^{49} +(-28.9373 + 22.1386i) q^{51} +14.5608i q^{52} -105.002 q^{53} +(13.3654 + 32.6628i) q^{54} +21.7576i q^{56} +(24.3718 - 18.6458i) q^{57} +22.7085i q^{58} -41.3640i q^{59} -20.4797 q^{61} -51.3577 q^{62} +(22.9827 + 6.22876i) q^{63} +46.6235 q^{64} +(6.22876 + 8.14158i) q^{66} +27.1660i q^{67} +27.8300 q^{68} +(-10.2510 + 7.84257i) q^{69} -67.8049i q^{71} +(19.3604 - 71.4353i) q^{72} +60.7895i q^{73} +53.6439i q^{74} -23.4392 q^{76} +6.91650 q^{77} +(15.1401 + 19.7895i) q^{78} +63.2470 q^{79} +(-69.9150 - 40.9010i) q^{81} +39.5791i q^{82} -89.9435 q^{83} +(-11.0516 - 14.4455i) q^{84} +73.0333i q^{86} +(-31.6693 - 41.3948i) q^{87} -21.4980i q^{88} -63.1745i q^{89} +16.8118 q^{91} +9.85875 q^{92} +(93.6188 - 71.6235i) q^{93} +52.2510 q^{94} +(-73.4464 + 56.1906i) q^{96} -19.1660i q^{97} +9.14967 q^{98} +(-22.7085 - 6.15445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30710 −0.653548 −0.326774 0.945103i \(-0.605962\pi\)
−0.326774 + 0.945103i \(0.605962\pi\)
\(3\) 2.38267 1.82288i 0.794224 0.607625i
\(4\) −2.29150 −0.572876
\(5\) 0 0
\(6\) −3.11438 + 2.38267i −0.519063 + 0.397112i
\(7\) 2.64575i 0.377964i
\(8\) 8.22359 1.02795
\(9\) 2.35425 8.68663i 0.261583 0.965181i
\(10\) 0 0
\(11\) 2.61419i 0.237654i −0.992915 0.118827i \(-0.962087\pi\)
0.992915 0.118827i \(-0.0379133\pi\)
\(12\) −5.45990 + 4.17712i −0.454992 + 0.348094i
\(13\) 6.35425i 0.488788i −0.969676 0.244394i \(-0.921411\pi\)
0.969676 0.244394i \(-0.0785891\pi\)
\(14\) 3.45825i 0.247018i
\(15\) 0 0
\(16\) −1.58301 −0.0989378
\(17\) −12.1449 −0.714405 −0.357202 0.934027i \(-0.616269\pi\)
−0.357202 + 0.934027i \(0.616269\pi\)
\(18\) −3.07723 + 11.3542i −0.170957 + 0.630792i
\(19\) 10.2288 0.538356 0.269178 0.963090i \(-0.413248\pi\)
0.269178 + 0.963090i \(0.413248\pi\)
\(20\) 0 0
\(21\) 4.82288 + 6.30396i 0.229661 + 0.300188i
\(22\) 3.41699i 0.155318i
\(23\) −4.30231 −0.187057 −0.0935284 0.995617i \(-0.529815\pi\)
−0.0935284 + 0.995617i \(0.529815\pi\)
\(24\) 19.5941 14.9906i 0.816422 0.624608i
\(25\) 0 0
\(26\) 8.30561i 0.319446i
\(27\) −10.2252 24.9889i −0.378713 0.925514i
\(28\) 6.06275i 0.216527i
\(29\) 17.3733i 0.599078i −0.954084 0.299539i \(-0.903167\pi\)
0.954084 0.299539i \(-0.0968328\pi\)
\(30\) 0 0
\(31\) 39.2915 1.26747 0.633734 0.773551i \(-0.281521\pi\)
0.633734 + 0.773551i \(0.281521\pi\)
\(32\) −30.8252 −0.963288
\(33\) −4.76534 6.22876i −0.144404 0.188750i
\(34\) 15.8745 0.466897
\(35\) 0 0
\(36\) −5.39477 + 19.9054i −0.149855 + 0.552929i
\(37\) 41.0405i 1.10920i −0.832116 0.554602i \(-0.812871\pi\)
0.832116 0.554602i \(-0.187129\pi\)
\(38\) −13.3700 −0.351841
\(39\) −11.5830 15.1401i −0.297000 0.388207i
\(40\) 0 0
\(41\) 30.2802i 0.738541i −0.929322 0.369270i \(-0.879608\pi\)
0.929322 0.369270i \(-0.120392\pi\)
\(42\) −6.30396 8.23987i −0.150094 0.196187i
\(43\) 55.8745i 1.29941i −0.760188 0.649704i \(-0.774893\pi\)
0.760188 0.649704i \(-0.225107\pi\)
\(44\) 5.99042i 0.136146i
\(45\) 0 0
\(46\) 5.62352 0.122251
\(47\) −39.9749 −0.850530 −0.425265 0.905069i \(-0.639819\pi\)
−0.425265 + 0.905069i \(0.639819\pi\)
\(48\) −3.77178 + 2.88562i −0.0785788 + 0.0601171i
\(49\) −7.00000 −0.142857
\(50\) 0 0
\(51\) −28.9373 + 22.1386i −0.567397 + 0.434090i
\(52\) 14.5608i 0.280015i
\(53\) −105.002 −1.98116 −0.990581 0.136928i \(-0.956277\pi\)
−0.990581 + 0.136928i \(0.956277\pi\)
\(54\) 13.3654 + 32.6628i 0.247507 + 0.604868i
\(55\) 0 0
\(56\) 21.7576i 0.388528i
\(57\) 24.3718 18.6458i 0.427575 0.327118i
\(58\) 22.7085i 0.391526i
\(59\) 41.3640i 0.701085i −0.936547 0.350542i \(-0.885997\pi\)
0.936547 0.350542i \(-0.114003\pi\)
\(60\) 0 0
\(61\) −20.4797 −0.335733 −0.167867 0.985810i \(-0.553688\pi\)
−0.167867 + 0.985810i \(0.553688\pi\)
\(62\) −51.3577 −0.828350
\(63\) 22.9827 + 6.22876i 0.364804 + 0.0988692i
\(64\) 46.6235 0.728493
\(65\) 0 0
\(66\) 6.22876 + 8.14158i 0.0943751 + 0.123357i
\(67\) 27.1660i 0.405463i 0.979234 + 0.202731i \(0.0649818\pi\)
−0.979234 + 0.202731i \(0.935018\pi\)
\(68\) 27.8300 0.409265
\(69\) −10.2510 + 7.84257i −0.148565 + 0.113660i
\(70\) 0 0
\(71\) 67.8049i 0.954999i −0.878632 0.477499i \(-0.841543\pi\)
0.878632 0.477499i \(-0.158457\pi\)
\(72\) 19.3604 71.4353i 0.268894 0.992157i
\(73\) 60.7895i 0.832733i 0.909197 + 0.416367i \(0.136697\pi\)
−0.909197 + 0.416367i \(0.863303\pi\)
\(74\) 53.6439i 0.724917i
\(75\) 0 0
\(76\) −23.4392 −0.308411
\(77\) 6.91650 0.0898246
\(78\) 15.1401 + 19.7895i 0.194104 + 0.253712i
\(79\) 63.2470 0.800596 0.400298 0.916385i \(-0.368907\pi\)
0.400298 + 0.916385i \(0.368907\pi\)
\(80\) 0 0
\(81\) −69.9150 40.9010i −0.863148 0.504950i
\(82\) 39.5791i 0.482672i
\(83\) −89.9435 −1.08366 −0.541828 0.840489i \(-0.682268\pi\)
−0.541828 + 0.840489i \(0.682268\pi\)
\(84\) −11.0516 14.4455i −0.131567 0.171971i
\(85\) 0 0
\(86\) 73.0333i 0.849224i
\(87\) −31.6693 41.3948i −0.364015 0.475802i
\(88\) 21.4980i 0.244296i
\(89\) 63.1745i 0.709826i −0.934899 0.354913i \(-0.884510\pi\)
0.934899 0.354913i \(-0.115490\pi\)
\(90\) 0 0
\(91\) 16.8118 0.184745
\(92\) 9.85875 0.107160
\(93\) 93.6188 71.6235i 1.00665 0.770145i
\(94\) 52.2510 0.555862
\(95\) 0 0
\(96\) −73.4464 + 56.1906i −0.765067 + 0.585318i
\(97\) 19.1660i 0.197588i −0.995108 0.0987939i \(-0.968502\pi\)
0.995108 0.0987939i \(-0.0314984\pi\)
\(98\) 9.14967 0.0933639
\(99\) −22.7085 6.15445i −0.229379 0.0621662i
\(100\) 0 0
\(101\) 98.7122i 0.977348i −0.872466 0.488674i \(-0.837481\pi\)
0.872466 0.488674i \(-0.162519\pi\)
\(102\) 37.8237 28.9373i 0.370821 0.283699i
\(103\) 56.2510i 0.546126i −0.961996 0.273063i \(-0.911963\pi\)
0.961996 0.273063i \(-0.0880368\pi\)
\(104\) 52.2547i 0.502449i
\(105\) 0 0
\(106\) 137.247 1.29478
\(107\) 123.137 1.15081 0.575406 0.817868i \(-0.304844\pi\)
0.575406 + 0.817868i \(0.304844\pi\)
\(108\) 23.4312 + 57.2621i 0.216955 + 0.530205i
\(109\) −164.539 −1.50953 −0.754764 0.655996i \(-0.772249\pi\)
−0.754764 + 0.655996i \(0.772249\pi\)
\(110\) 0 0
\(111\) −74.8118 97.7861i −0.673980 0.880956i
\(112\) 4.18824i 0.0373950i
\(113\) 144.050 1.27478 0.637391 0.770540i \(-0.280014\pi\)
0.637391 + 0.770540i \(0.280014\pi\)
\(114\) −31.8562 + 24.3718i −0.279441 + 0.213787i
\(115\) 0 0
\(116\) 39.8109i 0.343197i
\(117\) −55.1970 14.9595i −0.471769 0.127859i
\(118\) 54.0667i 0.458192i
\(119\) 32.1323i 0.270020i
\(120\) 0 0
\(121\) 114.166 0.943521
\(122\) 26.7690 0.219418
\(123\) −55.1970 72.1477i −0.448756 0.586567i
\(124\) −90.0366 −0.726101
\(125\) 0 0
\(126\) −30.0405 8.14158i −0.238417 0.0646157i
\(127\) 36.5830i 0.288055i 0.989574 + 0.144028i \(0.0460054\pi\)
−0.989574 + 0.144028i \(0.953995\pi\)
\(128\) 62.3595 0.487184
\(129\) −101.852 133.131i −0.789553 1.03202i
\(130\) 0 0
\(131\) 33.6855i 0.257141i 0.991700 + 0.128570i \(0.0410389\pi\)
−0.991700 + 0.128570i \(0.958961\pi\)
\(132\) 10.9198 + 14.2732i 0.0827257 + 0.108130i
\(133\) 27.0627i 0.203479i
\(134\) 35.5086i 0.264989i
\(135\) 0 0
\(136\) −99.8745 −0.734371
\(137\) 39.9749 0.291788 0.145894 0.989300i \(-0.453394\pi\)
0.145894 + 0.989300i \(0.453394\pi\)
\(138\) 13.3990 10.2510i 0.0970943 0.0742825i
\(139\) 194.642 1.40030 0.700150 0.713995i \(-0.253116\pi\)
0.700150 + 0.713995i \(0.253116\pi\)
\(140\) 0 0
\(141\) −95.2470 + 72.8693i −0.675511 + 0.516803i
\(142\) 88.6275i 0.624137i
\(143\) −16.6112 −0.116162
\(144\) −3.72679 + 13.7510i −0.0258805 + 0.0954929i
\(145\) 0 0
\(146\) 79.4577i 0.544231i
\(147\) −16.6787 + 12.7601i −0.113461 + 0.0868036i
\(148\) 94.0445i 0.635436i
\(149\) 203.685i 1.36701i 0.729945 + 0.683506i \(0.239546\pi\)
−0.729945 + 0.683506i \(0.760454\pi\)
\(150\) 0 0
\(151\) 165.749 1.09768 0.548838 0.835929i \(-0.315070\pi\)
0.548838 + 0.835929i \(0.315070\pi\)
\(152\) 84.1171 0.553402
\(153\) −28.5921 + 105.498i −0.186876 + 0.689530i
\(154\) −9.04052 −0.0587047
\(155\) 0 0
\(156\) 26.5425 + 34.6936i 0.170144 + 0.222395i
\(157\) 302.723i 1.92817i 0.265592 + 0.964086i \(0.414433\pi\)
−0.265592 + 0.964086i \(0.585567\pi\)
\(158\) −82.6699 −0.523227
\(159\) −250.184 + 191.405i −1.57349 + 1.20380i
\(160\) 0 0
\(161\) 11.3828i 0.0707008i
\(162\) 91.3856 + 53.4615i 0.564109 + 0.330009i
\(163\) 145.041i 0.889819i −0.895576 0.444910i \(-0.853236\pi\)
0.895576 0.444910i \(-0.146764\pi\)
\(164\) 69.3871i 0.423092i
\(165\) 0 0
\(166\) 117.565 0.708221
\(167\) 19.6594 0.117721 0.0588604 0.998266i \(-0.481253\pi\)
0.0588604 + 0.998266i \(0.481253\pi\)
\(168\) 39.6614 + 51.8412i 0.236080 + 0.308578i
\(169\) 128.624 0.761086
\(170\) 0 0
\(171\) 24.0810 88.8534i 0.140825 0.519611i
\(172\) 128.037i 0.744399i
\(173\) −19.6884 −0.113806 −0.0569030 0.998380i \(-0.518123\pi\)
−0.0569030 + 0.998380i \(0.518123\pi\)
\(174\) 41.3948 + 54.1069i 0.237901 + 0.310959i
\(175\) 0 0
\(176\) 4.13828i 0.0235129i
\(177\) −75.4014 98.5568i −0.425997 0.556818i
\(178\) 82.5751i 0.463905i
\(179\) 341.745i 1.90919i 0.297910 + 0.954594i \(0.403711\pi\)
−0.297910 + 0.954594i \(0.596289\pi\)
\(180\) 0 0
\(181\) 215.889 1.19276 0.596378 0.802704i \(-0.296606\pi\)
0.596378 + 0.802704i \(0.296606\pi\)
\(182\) −21.9746 −0.120739
\(183\) −48.7965 + 37.3320i −0.266648 + 0.204000i
\(184\) −35.3804 −0.192285
\(185\) 0 0
\(186\) −122.369 + 93.6188i −0.657896 + 0.503327i
\(187\) 31.7490i 0.169781i
\(188\) 91.6026 0.487248
\(189\) 66.1144 27.0534i 0.349812 0.143140i
\(190\) 0 0
\(191\) 44.7112i 0.234090i 0.993127 + 0.117045i \(0.0373422\pi\)
−0.993127 + 0.117045i \(0.962658\pi\)
\(192\) 111.089 84.9889i 0.578586 0.442650i
\(193\) 145.122i 0.751925i −0.926635 0.375963i \(-0.877312\pi\)
0.926635 0.375963i \(-0.122688\pi\)
\(194\) 25.0518i 0.129133i
\(195\) 0 0
\(196\) 16.0405 0.0818394
\(197\) 87.4643 0.443981 0.221991 0.975049i \(-0.428745\pi\)
0.221991 + 0.975049i \(0.428745\pi\)
\(198\) 29.6822 + 8.04446i 0.149910 + 0.0406286i
\(199\) −65.4170 −0.328729 −0.164364 0.986400i \(-0.552557\pi\)
−0.164364 + 0.986400i \(0.552557\pi\)
\(200\) 0 0
\(201\) 49.5203 + 64.7277i 0.246369 + 0.322028i
\(202\) 129.026i 0.638743i
\(203\) 45.9653 0.226430
\(204\) 66.3098 50.7307i 0.325048 0.248680i
\(205\) 0 0
\(206\) 73.5254i 0.356919i
\(207\) −10.1287 + 37.3725i −0.0489309 + 0.180544i
\(208\) 10.0588i 0.0483597i
\(209\) 26.7399i 0.127942i
\(210\) 0 0
\(211\) 40.5830 0.192337 0.0961683 0.995365i \(-0.469341\pi\)
0.0961683 + 0.995365i \(0.469341\pi\)
\(212\) 240.611 1.13496
\(213\) −123.600 161.557i −0.580281 0.758483i
\(214\) −160.952 −0.752110
\(215\) 0 0
\(216\) −84.0882 205.498i −0.389297 0.951381i
\(217\) 103.956i 0.479058i
\(218\) 215.068 0.986548
\(219\) 110.812 + 144.842i 0.505990 + 0.661377i
\(220\) 0 0
\(221\) 77.1716i 0.349193i
\(222\) 97.7861 + 127.816i 0.440478 + 0.575746i
\(223\) 100.959i 0.452733i 0.974042 + 0.226367i \(0.0726847\pi\)
−0.974042 + 0.226367i \(0.927315\pi\)
\(224\) 81.5559i 0.364089i
\(225\) 0 0
\(226\) −188.288 −0.833131
\(227\) −391.279 −1.72370 −0.861849 0.507166i \(-0.830693\pi\)
−0.861849 + 0.507166i \(0.830693\pi\)
\(228\) −55.8480 + 42.7268i −0.244947 + 0.187398i
\(229\) 6.81176 0.0297457 0.0148728 0.999889i \(-0.495266\pi\)
0.0148728 + 0.999889i \(0.495266\pi\)
\(230\) 0 0
\(231\) 16.4797 12.6079i 0.0713409 0.0545797i
\(232\) 142.871i 0.615821i
\(233\) −116.877 −0.501616 −0.250808 0.968037i \(-0.580696\pi\)
−0.250808 + 0.968037i \(0.580696\pi\)
\(234\) 72.1477 + 19.5535i 0.308324 + 0.0835618i
\(235\) 0 0
\(236\) 94.7857i 0.401634i
\(237\) 150.697 115.292i 0.635852 0.486462i
\(238\) 42.0000i 0.176471i
\(239\) 59.9623i 0.250888i 0.992101 + 0.125444i \(0.0400356\pi\)
−0.992101 + 0.125444i \(0.959964\pi\)
\(240\) 0 0
\(241\) 134.753 0.559141 0.279570 0.960125i \(-0.409808\pi\)
0.279570 + 0.960125i \(0.409808\pi\)
\(242\) −149.226 −0.616636
\(243\) −241.142 + 29.9928i −0.992354 + 0.123427i
\(244\) 46.9294 0.192334
\(245\) 0 0
\(246\) 72.1477 + 94.3039i 0.293283 + 0.383349i
\(247\) 64.9961i 0.263142i
\(248\) 323.117 1.30289
\(249\) −214.306 + 163.956i −0.860666 + 0.658457i
\(250\) 0 0
\(251\) 268.248i 1.06872i 0.845257 + 0.534359i \(0.179447\pi\)
−0.845257 + 0.534359i \(0.820553\pi\)
\(252\) −52.6648 14.2732i −0.208987 0.0566397i
\(253\) 11.2470i 0.0444547i
\(254\) 47.8175i 0.188258i
\(255\) 0 0
\(256\) −268.004 −1.04689
\(257\) 234.129 0.911007 0.455504 0.890234i \(-0.349459\pi\)
0.455504 + 0.890234i \(0.349459\pi\)
\(258\) 133.131 + 174.014i 0.516010 + 0.674474i
\(259\) 108.583 0.419239
\(260\) 0 0
\(261\) −150.915 40.9010i −0.578218 0.156709i
\(262\) 44.0301i 0.168054i
\(263\) −250.142 −0.951111 −0.475555 0.879686i \(-0.657753\pi\)
−0.475555 + 0.879686i \(0.657753\pi\)
\(264\) −39.1882 51.2228i −0.148440 0.194026i
\(265\) 0 0
\(266\) 35.3736i 0.132983i
\(267\) −115.159 150.524i −0.431308 0.563761i
\(268\) 62.2510i 0.232280i
\(269\) 340.684i 1.26648i −0.773955 0.633241i \(-0.781724\pi\)
0.773955 0.633241i \(-0.218276\pi\)
\(270\) 0 0
\(271\) −21.2994 −0.0785955 −0.0392977 0.999228i \(-0.512512\pi\)
−0.0392977 + 0.999228i \(0.512512\pi\)
\(272\) 19.2254 0.0706816
\(273\) 40.0569 30.6458i 0.146729 0.112255i
\(274\) −52.2510 −0.190697
\(275\) 0 0
\(276\) 23.4902 17.9713i 0.0851093 0.0651133i
\(277\) 226.915i 0.819188i 0.912268 + 0.409594i \(0.134330\pi\)
−0.912268 + 0.409594i \(0.865670\pi\)
\(278\) −254.415 −0.915163
\(279\) 92.5020 341.311i 0.331548 1.22334i
\(280\) 0 0
\(281\) 235.489i 0.838039i −0.907977 0.419019i \(-0.862374\pi\)
0.907977 0.419019i \(-0.137626\pi\)
\(282\) 124.497 95.2470i 0.441479 0.337755i
\(283\) 368.634i 1.30259i 0.758823 + 0.651297i \(0.225775\pi\)
−0.758823 + 0.651297i \(0.774225\pi\)
\(284\) 155.375i 0.547096i
\(285\) 0 0
\(286\) 21.7124 0.0759176
\(287\) 80.1138 0.279142
\(288\) −72.5703 + 267.767i −0.251980 + 0.929748i
\(289\) −141.502 −0.489626
\(290\) 0 0
\(291\) −34.9373 45.6663i −0.120059 0.156929i
\(292\) 139.299i 0.477053i
\(293\) 531.625 1.81442 0.907211 0.420677i \(-0.138207\pi\)
0.907211 + 0.420677i \(0.138207\pi\)
\(294\) 21.8006 16.6787i 0.0741519 0.0567303i
\(295\) 0 0
\(296\) 337.500i 1.14020i
\(297\) −65.3257 + 26.7307i −0.219952 + 0.0900024i
\(298\) 266.235i 0.893407i
\(299\) 27.3379i 0.0914312i
\(300\) 0 0
\(301\) 147.830 0.491130
\(302\) −216.650 −0.717383
\(303\) −179.940 235.199i −0.593861 0.776233i
\(304\) −16.1922 −0.0532637
\(305\) 0 0
\(306\) 37.3725 137.896i 0.122132 0.450640i
\(307\) 567.763i 1.84939i −0.380706 0.924696i \(-0.624319\pi\)
0.380706 0.924696i \(-0.375681\pi\)
\(308\) −15.8492 −0.0514583
\(309\) −102.539 134.028i −0.331840 0.433746i
\(310\) 0 0
\(311\) 42.7531i 0.137470i 0.997635 + 0.0687349i \(0.0218963\pi\)
−0.997635 + 0.0687349i \(0.978104\pi\)
\(312\) −95.2539 124.506i −0.305301 0.399057i
\(313\) 158.118i 0.505168i −0.967575 0.252584i \(-0.918720\pi\)
0.967575 0.252584i \(-0.0812804\pi\)
\(314\) 395.688i 1.26015i
\(315\) 0 0
\(316\) −144.931 −0.458642
\(317\) −140.944 −0.444619 −0.222309 0.974976i \(-0.571359\pi\)
−0.222309 + 0.974976i \(0.571359\pi\)
\(318\) 327.015 250.184i 1.02835 0.786743i
\(319\) −45.4170 −0.142373
\(320\) 0 0
\(321\) 293.395 224.463i 0.914002 0.699262i
\(322\) 14.8784i 0.0462064i
\(323\) −124.227 −0.384604
\(324\) 160.210 + 93.7247i 0.494477 + 0.289274i
\(325\) 0 0
\(326\) 189.582i 0.581539i
\(327\) −392.041 + 299.933i −1.19890 + 0.917227i
\(328\) 249.012i 0.759182i
\(329\) 105.764i 0.321470i
\(330\) 0 0
\(331\) −258.369 −0.780570 −0.390285 0.920694i \(-0.627623\pi\)
−0.390285 + 0.920694i \(0.627623\pi\)
\(332\) 206.106 0.620801
\(333\) −356.504 96.6196i −1.07058 0.290149i
\(334\) −25.6967 −0.0769362
\(335\) 0 0
\(336\) −7.63464 9.97920i −0.0227221 0.0297000i
\(337\) 328.959i 0.976141i −0.872804 0.488070i \(-0.837701\pi\)
0.872804 0.488070i \(-0.162299\pi\)
\(338\) −168.123 −0.497406
\(339\) 343.225 262.586i 1.01246 0.774590i
\(340\) 0 0
\(341\) 102.715i 0.301218i
\(342\) −31.4762 + 116.140i −0.0920357 + 0.339590i
\(343\) 18.5203i 0.0539949i
\(344\) 459.489i 1.33572i
\(345\) 0 0
\(346\) 25.7347 0.0743776
\(347\) 128.635 0.370707 0.185353 0.982672i \(-0.440657\pi\)
0.185353 + 0.982672i \(0.440657\pi\)
\(348\) 72.5703 + 94.8562i 0.208535 + 0.272575i
\(349\) 73.4837 0.210555 0.105277 0.994443i \(-0.466427\pi\)
0.105277 + 0.994443i \(0.466427\pi\)
\(350\) 0 0
\(351\) −158.786 + 64.9737i −0.452381 + 0.185110i
\(352\) 80.5830i 0.228929i
\(353\) 239.685 0.678995 0.339498 0.940607i \(-0.389743\pi\)
0.339498 + 0.940607i \(0.389743\pi\)
\(354\) 98.5568 + 128.823i 0.278409 + 0.363907i
\(355\) 0 0
\(356\) 144.765i 0.406642i
\(357\) −58.5732 76.5608i −0.164071 0.214456i
\(358\) 446.693i 1.24775i
\(359\) 180.215i 0.501992i −0.967988 0.250996i \(-0.919242\pi\)
0.967988 0.250996i \(-0.0807581\pi\)
\(360\) 0 0
\(361\) −256.373 −0.710173
\(362\) −282.187 −0.779523
\(363\) 272.020 208.110i 0.749367 0.573307i
\(364\) −38.5242 −0.105836
\(365\) 0 0
\(366\) 63.7817 48.7965i 0.174267 0.133324i
\(367\) 229.786i 0.626119i −0.949734 0.313059i \(-0.898646\pi\)
0.949734 0.313059i \(-0.101354\pi\)
\(368\) 6.81057 0.0185070
\(369\) −263.033 71.2871i −0.712826 0.193190i
\(370\) 0 0
\(371\) 277.808i 0.748809i
\(372\) −214.528 + 164.125i −0.576687 + 0.441198i
\(373\) 441.749i 1.18431i 0.805823 + 0.592157i \(0.201723\pi\)
−0.805823 + 0.592157i \(0.798277\pi\)
\(374\) 41.4990i 0.110960i
\(375\) 0 0
\(376\) −328.737 −0.874301
\(377\) −110.394 −0.292822
\(378\) −86.4178 + 35.3614i −0.228618 + 0.0935487i
\(379\) 421.203 1.11135 0.555676 0.831399i \(-0.312459\pi\)
0.555676 + 0.831399i \(0.312459\pi\)
\(380\) 0 0
\(381\) 66.6863 + 87.1653i 0.175030 + 0.228780i
\(382\) 58.4418i 0.152989i
\(383\) −595.591 −1.55507 −0.777534 0.628841i \(-0.783530\pi\)
−0.777534 + 0.628841i \(0.783530\pi\)
\(384\) 148.582 113.674i 0.386933 0.296025i
\(385\) 0 0
\(386\) 189.688i 0.491419i
\(387\) −485.361 131.542i −1.25416 0.339903i
\(388\) 43.9190i 0.113193i
\(389\) 367.347i 0.944336i 0.881509 + 0.472168i \(0.156528\pi\)
−0.881509 + 0.472168i \(0.843472\pi\)
\(390\) 0 0
\(391\) 52.2510 0.133634
\(392\) −57.5651 −0.146850
\(393\) 61.4044 + 80.2614i 0.156245 + 0.204227i
\(394\) −114.324 −0.290163
\(395\) 0 0
\(396\) 52.0366 + 14.1029i 0.131406 + 0.0356135i
\(397\) 408.346i 1.02858i −0.857616 0.514290i \(-0.828055\pi\)
0.857616 0.514290i \(-0.171945\pi\)
\(398\) 85.5062 0.214840
\(399\) 49.3320 + 64.4816i 0.123639 + 0.161608i
\(400\) 0 0
\(401\) 238.817i 0.595555i −0.954635 0.297777i \(-0.903755\pi\)
0.954635 0.297777i \(-0.0962453\pi\)
\(402\) −64.7277 84.6052i −0.161014 0.210461i
\(403\) 249.668i 0.619524i
\(404\) 226.199i 0.559899i
\(405\) 0 0
\(406\) −60.0810 −0.147983
\(407\) −107.288 −0.263606
\(408\) −237.968 + 182.059i −0.583255 + 0.446223i
\(409\) 649.365 1.58769 0.793844 0.608121i \(-0.208076\pi\)
0.793844 + 0.608121i \(0.208076\pi\)
\(410\) 0 0
\(411\) 95.2470 72.8693i 0.231745 0.177297i
\(412\) 128.899i 0.312862i
\(413\) 109.439 0.264985
\(414\) 13.2392 48.8495i 0.0319787 0.117994i
\(415\) 0 0
\(416\) 195.871i 0.470844i
\(417\) 463.768 354.808i 1.11215 0.850858i
\(418\) 34.9516i 0.0836163i
\(419\) 11.5178i 0.0274888i 0.999906 + 0.0137444i \(0.00437512\pi\)
−0.999906 + 0.0137444i \(0.995625\pi\)
\(420\) 0 0
\(421\) −83.9921 −0.199506 −0.0997531 0.995012i \(-0.531805\pi\)
−0.0997531 + 0.995012i \(0.531805\pi\)
\(422\) −53.0458 −0.125701
\(423\) −94.1108 + 347.247i −0.222484 + 0.820915i
\(424\) −863.490 −2.03653
\(425\) 0 0
\(426\) 161.557 + 211.170i 0.379241 + 0.495705i
\(427\) 54.1843i 0.126895i
\(428\) −282.168 −0.659272
\(429\) −39.5791 + 30.2802i −0.0922589 + 0.0705832i
\(430\) 0 0
\(431\) 694.004i 1.61022i 0.593127 + 0.805109i \(0.297893\pi\)
−0.593127 + 0.805109i \(0.702107\pi\)
\(432\) 16.1866 + 39.5575i 0.0374690 + 0.0915684i
\(433\) 116.834i 0.269824i 0.990858 + 0.134912i \(0.0430752\pi\)
−0.990858 + 0.134912i \(0.956925\pi\)
\(434\) 135.880i 0.313087i
\(435\) 0 0
\(436\) 377.041 0.864772
\(437\) −44.0072 −0.100703
\(438\) −144.842 189.322i −0.330688 0.432241i
\(439\) 528.073 1.20290 0.601450 0.798910i \(-0.294590\pi\)
0.601450 + 0.798910i \(0.294590\pi\)
\(440\) 0 0
\(441\) −16.4797 + 60.8064i −0.0373690 + 0.137883i
\(442\) 100.871i 0.228214i
\(443\) −272.252 −0.614564 −0.307282 0.951619i \(-0.599419\pi\)
−0.307282 + 0.951619i \(0.599419\pi\)
\(444\) 171.431 + 224.077i 0.386107 + 0.504678i
\(445\) 0 0
\(446\) 131.964i 0.295883i
\(447\) 371.292 + 485.314i 0.830631 + 1.08571i
\(448\) 123.354i 0.275344i
\(449\) 525.770i 1.17098i 0.810680 + 0.585490i \(0.199098\pi\)
−0.810680 + 0.585490i \(0.800902\pi\)
\(450\) 0 0
\(451\) −79.1581 −0.175517
\(452\) −330.092 −0.730292
\(453\) 394.925 302.140i 0.871800 0.666975i
\(454\) 511.439 1.12652
\(455\) 0 0
\(456\) 200.423 153.335i 0.439525 0.336261i
\(457\) 513.786i 1.12426i 0.827050 + 0.562129i \(0.190017\pi\)
−0.827050 + 0.562129i \(0.809983\pi\)
\(458\) −8.90362 −0.0194402
\(459\) 124.184 + 303.487i 0.270554 + 0.661192i
\(460\) 0 0
\(461\) 687.879i 1.49214i 0.665865 + 0.746072i \(0.268063\pi\)
−0.665865 + 0.746072i \(0.731937\pi\)
\(462\) −21.5406 + 16.4797i −0.0466246 + 0.0356704i
\(463\) 781.061i 1.68696i 0.537162 + 0.843479i \(0.319496\pi\)
−0.537162 + 0.843479i \(0.680504\pi\)
\(464\) 27.5020i 0.0592715i
\(465\) 0 0
\(466\) 152.769 0.327830
\(467\) 163.353 0.349792 0.174896 0.984587i \(-0.444041\pi\)
0.174896 + 0.984587i \(0.444041\pi\)
\(468\) 126.484 + 34.2797i 0.270265 + 0.0732472i
\(469\) −71.8745 −0.153251
\(470\) 0 0
\(471\) 551.826 + 721.289i 1.17161 + 1.53140i
\(472\) 340.161i 0.720679i
\(473\) −146.067 −0.308809
\(474\) −196.975 + 150.697i −0.415560 + 0.317926i
\(475\) 0 0
\(476\) 73.6313i 0.154688i
\(477\) −247.200 + 912.110i −0.518239 + 1.91218i
\(478\) 78.3765i 0.163968i
\(479\) 700.159i 1.46171i −0.682533 0.730855i \(-0.739122\pi\)
0.682533 0.730855i \(-0.260878\pi\)
\(480\) 0 0
\(481\) −260.782 −0.542166
\(482\) −176.135 −0.365425
\(483\) −20.7495 27.1216i −0.0429596 0.0561523i
\(484\) −261.612 −0.540520
\(485\) 0 0
\(486\) 315.195 39.2035i 0.648550 0.0806656i
\(487\) 86.5909i 0.177805i −0.996040 0.0889023i \(-0.971664\pi\)
0.996040 0.0889023i \(-0.0283359\pi\)
\(488\) −168.417 −0.345117
\(489\) −264.391 345.584i −0.540677 0.706716i
\(490\) 0 0
\(491\) 741.494i 1.51017i −0.655627 0.755085i \(-0.727596\pi\)
0.655627 0.755085i \(-0.272404\pi\)
\(492\) 126.484 + 165.327i 0.257081 + 0.336030i
\(493\) 210.996i 0.427984i
\(494\) 84.9560i 0.171976i
\(495\) 0 0
\(496\) −62.1987 −0.125401
\(497\) 179.395 0.360956
\(498\) 280.118 214.306i 0.562486 0.430333i
\(499\) −379.814 −0.761151 −0.380575 0.924750i \(-0.624274\pi\)
−0.380575 + 0.924750i \(0.624274\pi\)
\(500\) 0 0
\(501\) 46.8419 35.8366i 0.0934967 0.0715302i
\(502\) 350.626i 0.698458i
\(503\) 465.808 0.926059 0.463029 0.886343i \(-0.346762\pi\)
0.463029 + 0.886343i \(0.346762\pi\)
\(504\) 189.000 + 51.2228i 0.375000 + 0.101632i
\(505\) 0 0
\(506\) 14.7010i 0.0290533i
\(507\) 306.468 234.465i 0.604473 0.462455i
\(508\) 83.8301i 0.165020i
\(509\) 750.503i 1.47447i 0.675639 + 0.737233i \(0.263868\pi\)
−0.675639 + 0.737233i \(0.736132\pi\)
\(510\) 0 0
\(511\) −160.834 −0.314744
\(512\) 100.868 0.197009
\(513\) −104.592 255.605i −0.203882 0.498256i
\(514\) −306.029 −0.595387
\(515\) 0 0
\(516\) 233.395 + 305.069i 0.452315 + 0.591219i
\(517\) 104.502i 0.202131i
\(518\) −141.928 −0.273993
\(519\) −46.9111 + 35.8896i −0.0903875 + 0.0691514i
\(520\) 0 0
\(521\) 726.946i 1.39529i −0.716443 0.697645i \(-0.754231\pi\)
0.716443 0.697645i \(-0.245769\pi\)
\(522\) 197.260 + 53.4615i 0.377893 + 0.102417i
\(523\) 624.707i 1.19447i −0.802067 0.597234i \(-0.796266\pi\)
0.802067 0.597234i \(-0.203734\pi\)
\(524\) 77.1903i 0.147310i
\(525\) 0 0
\(526\) 326.959 0.621596
\(527\) −477.190 −0.905485
\(528\) 7.54356 + 9.86015i 0.0142871 + 0.0186745i
\(529\) −510.490 −0.965010
\(530\) 0 0
\(531\) −359.314 97.3812i −0.676674 0.183392i
\(532\) 62.0144i 0.116568i
\(533\) −192.408 −0.360990
\(534\) 150.524 + 196.749i 0.281881 + 0.368445i
\(535\) 0 0
\(536\) 223.402i 0.416795i
\(537\) 622.958 + 814.265i 1.16007 + 1.51632i
\(538\) 445.306i 0.827706i
\(539\) 18.2993i 0.0339505i
\(540\) 0 0
\(541\) −291.757 −0.539292 −0.269646 0.962960i \(-0.586907\pi\)
−0.269646 + 0.962960i \(0.586907\pi\)
\(542\) 27.8403 0.0513659
\(543\) 514.392 393.539i 0.947315 0.724749i
\(544\) 374.369 0.688178
\(545\) 0 0
\(546\) −52.3582 + 40.0569i −0.0958941 + 0.0733643i
\(547\) 204.952i 0.374683i −0.982295 0.187342i \(-0.940013\pi\)
0.982295 0.187342i \(-0.0599871\pi\)
\(548\) −91.6026 −0.167158
\(549\) −48.2144 + 177.900i −0.0878222 + 0.324044i
\(550\) 0 0
\(551\) 177.707i 0.322517i
\(552\) −84.2999 + 64.4941i −0.152717 + 0.116837i
\(553\) 167.336i 0.302597i
\(554\) 296.599i 0.535378i
\(555\) 0 0
\(556\) −446.022 −0.802198
\(557\) 503.883 0.904637 0.452318 0.891857i \(-0.350597\pi\)
0.452318 + 0.891857i \(0.350597\pi\)
\(558\) −120.909 + 446.125i −0.216683 + 0.799508i
\(559\) −355.041 −0.635135
\(560\) 0 0
\(561\) 57.8745 + 75.6475i 0.103163 + 0.134844i
\(562\) 307.806i 0.547698i
\(563\) 108.735 0.193135 0.0965674 0.995326i \(-0.469214\pi\)
0.0965674 + 0.995326i \(0.469214\pi\)
\(564\) 218.259 166.980i 0.386984 0.296064i
\(565\) 0 0
\(566\) 481.840i 0.851307i
\(567\) 108.214 184.978i 0.190853 0.326239i
\(568\) 557.600i 0.981690i
\(569\) 434.871i 0.764273i −0.924106 0.382136i \(-0.875188\pi\)
0.924106 0.382136i \(-0.124812\pi\)
\(570\) 0 0
\(571\) 119.122 0.208619 0.104310 0.994545i \(-0.466737\pi\)
0.104310 + 0.994545i \(0.466737\pi\)
\(572\) 38.0646 0.0665466
\(573\) 81.5029 + 106.532i 0.142239 + 0.185920i
\(574\) −104.716 −0.182433
\(575\) 0 0
\(576\) 109.763 405.001i 0.190561 0.703127i
\(577\) 655.417i 1.13590i 0.823061 + 0.567952i \(0.192264\pi\)
−0.823061 + 0.567952i \(0.807736\pi\)
\(578\) 184.957 0.319994
\(579\) −264.539 345.777i −0.456889 0.597197i
\(580\) 0 0
\(581\) 237.968i 0.409584i
\(582\) 45.6663 + 59.6902i 0.0784645 + 0.102560i
\(583\) 274.494i 0.470830i
\(584\) 499.908i 0.856007i
\(585\) 0 0
\(586\) −694.885 −1.18581
\(587\) −736.236 −1.25424 −0.627118 0.778925i \(-0.715765\pi\)
−0.627118 + 0.778925i \(0.715765\pi\)
\(588\) 38.2193 29.2399i 0.0649988 0.0497277i
\(589\) 401.903 0.682348
\(590\) 0 0
\(591\) 208.399 159.437i 0.352620 0.269774i
\(592\) 64.9674i 0.109742i
\(593\) 832.884 1.40453 0.702263 0.711917i \(-0.252173\pi\)
0.702263 + 0.711917i \(0.252173\pi\)
\(594\) 85.3869 34.9396i 0.143749 0.0588209i
\(595\) 0 0
\(596\) 466.744i 0.783127i
\(597\) −155.867 + 119.247i −0.261084 + 0.199744i
\(598\) 35.7333i 0.0597546i
\(599\) 69.3290i 0.115741i 0.998324 + 0.0578706i \(0.0184311\pi\)
−0.998324 + 0.0578706i \(0.981569\pi\)
\(600\) 0 0
\(601\) −161.720 −0.269085 −0.134543 0.990908i \(-0.542957\pi\)
−0.134543 + 0.990908i \(0.542957\pi\)
\(602\) −193.228 −0.320977
\(603\) 235.981 + 63.9555i 0.391345 + 0.106062i
\(604\) −379.814 −0.628832
\(605\) 0 0
\(606\) 235.199 + 307.427i 0.388117 + 0.507305i
\(607\) 929.608i 1.53148i −0.643151 0.765740i \(-0.722373\pi\)
0.643151 0.765740i \(-0.277627\pi\)
\(608\) −315.304 −0.518592
\(609\) 109.520 83.7891i 0.179836 0.137585i
\(610\) 0 0
\(611\) 254.010i 0.415729i
\(612\) 65.5188 241.749i 0.107057 0.395015i
\(613\) 297.940i 0.486036i 0.970022 + 0.243018i \(0.0781373\pi\)
−0.970022 + 0.243018i \(0.921863\pi\)
\(614\) 742.121i 1.20867i
\(615\) 0 0
\(616\) 56.8784 0.0923351
\(617\) 975.575 1.58116 0.790579 0.612360i \(-0.209780\pi\)
0.790579 + 0.612360i \(0.209780\pi\)
\(618\) 134.028 + 175.187i 0.216873 + 0.283474i
\(619\) −357.034 −0.576792 −0.288396 0.957511i \(-0.593122\pi\)
−0.288396 + 0.957511i \(0.593122\pi\)
\(620\) 0 0
\(621\) 43.9921 + 107.510i 0.0708408 + 0.173124i
\(622\) 55.8824i 0.0898431i
\(623\) 167.144 0.268289
\(624\) 18.3360 + 23.9668i 0.0293845 + 0.0384084i
\(625\) 0 0
\(626\) 206.675i 0.330151i
\(627\) −48.7435 63.7124i −0.0777409 0.101615i
\(628\) 693.690i 1.10460i
\(629\) 498.432i 0.792420i
\(630\) 0 0
\(631\) −813.223 −1.28879 −0.644393 0.764695i \(-0.722890\pi\)
−0.644393 + 0.764695i \(0.722890\pi\)
\(632\) 520.118 0.822971
\(633\) 96.6960 73.9778i 0.152758 0.116869i
\(634\) 184.227 0.290579
\(635\) 0 0
\(636\) 573.298 438.605i 0.901412 0.689630i
\(637\) 44.4797i 0.0698269i
\(638\) 59.3643 0.0930475
\(639\) −588.996 159.630i −0.921747 0.249812i
\(640\) 0 0
\(641\) 646.727i 1.00893i −0.863431 0.504467i \(-0.831689\pi\)
0.863431 0.504467i \(-0.168311\pi\)
\(642\) −383.495 + 293.395i −0.597344 + 0.457001i
\(643\) 144.561i 0.224822i 0.993662 + 0.112411i \(0.0358574\pi\)
−0.993662 + 0.112411i \(0.964143\pi\)
\(644\) 26.0838i 0.0405028i
\(645\) 0 0
\(646\) 162.376 0.251357
\(647\) 716.654 1.10766 0.553828 0.832631i \(-0.313166\pi\)
0.553828 + 0.832631i \(0.313166\pi\)
\(648\) −574.953 336.353i −0.887273 0.519063i
\(649\) −108.133 −0.166615
\(650\) 0 0
\(651\) 189.498 + 247.692i 0.291088 + 0.380479i
\(652\) 332.361i 0.509756i
\(653\) 378.999 0.580397 0.290199 0.956966i \(-0.406279\pi\)
0.290199 + 0.956966i \(0.406279\pi\)
\(654\) 512.435 392.041i 0.783540 0.599452i
\(655\) 0 0
\(656\) 47.9337i 0.0730696i
\(657\) 528.056 + 143.114i 0.803738 + 0.217829i
\(658\) 138.243i 0.210096i
\(659\) 710.721i 1.07848i −0.842151 0.539242i \(-0.818711\pi\)
0.842151 0.539242i \(-0.181289\pi\)
\(660\) 0 0
\(661\) 91.5045 0.138433 0.0692167 0.997602i \(-0.477950\pi\)
0.0692167 + 0.997602i \(0.477950\pi\)
\(662\) 337.712 0.510139
\(663\) 140.674 + 183.875i 0.212178 + 0.277337i
\(664\) −739.659 −1.11394
\(665\) 0 0
\(666\) 465.984 + 126.291i 0.699676 + 0.189626i
\(667\) 74.7451i 0.112062i
\(668\) −45.0495 −0.0674394
\(669\) 184.037 + 240.553i 0.275092 + 0.359571i
\(670\) 0 0
\(671\) 53.5379i 0.0797883i
\(672\) −148.666 194.321i −0.221230 0.289168i
\(673\) 645.806i 0.959594i 0.877380 + 0.479797i \(0.159290\pi\)
−0.877380 + 0.479797i \(0.840710\pi\)
\(674\) 429.981i 0.637954i
\(675\) 0 0
\(676\) −294.741 −0.436008
\(677\) 335.571 0.495674 0.247837 0.968802i \(-0.420280\pi\)
0.247837 + 0.968802i \(0.420280\pi\)
\(678\) −448.627 + 343.225i −0.661692 + 0.506231i
\(679\) 50.7085 0.0746811
\(680\) 0 0
\(681\) −932.290 + 713.254i −1.36900 + 1.04736i
\(682\) 134.259i 0.196860i
\(683\) −113.336 −0.165939 −0.0829694 0.996552i \(-0.526440\pi\)
−0.0829694 + 0.996552i \(0.526440\pi\)
\(684\) −55.1818 + 203.608i −0.0806751 + 0.297672i
\(685\) 0 0
\(686\) 24.2077i 0.0352882i
\(687\) 16.2302 12.4170i 0.0236247 0.0180742i
\(688\) 88.4496i 0.128561i
\(689\) 667.206i 0.968369i
\(690\) 0 0
\(691\) 565.667 0.818620 0.409310 0.912395i \(-0.365769\pi\)
0.409310 + 0.912395i \(0.365769\pi\)
\(692\) 45.1161 0.0651967
\(693\) 16.2832 60.0810i 0.0234966 0.0866970i
\(694\) −168.138 −0.242274
\(695\) 0 0
\(696\) −260.435 340.414i −0.374189 0.489100i
\(697\) 367.749i 0.527617i
\(698\) −96.0501 −0.137608
\(699\) −278.478 + 213.051i −0.398395 + 0.304794i
\(700\) 0 0
\(701\) 872.955i 1.24530i 0.782501 + 0.622650i \(0.213944\pi\)
−0.782501 + 0.622650i \(0.786056\pi\)
\(702\) 207.548 84.9268i 0.295652 0.120978i
\(703\) 419.793i 0.597146i
\(704\) 121.883i 0.173129i
\(705\) 0 0
\(706\) −313.292 −0.443756
\(707\) 261.168 0.369403
\(708\) 172.783 + 225.843i 0.244043 + 0.318988i
\(709\) −1092.04 −1.54025 −0.770125 0.637894i \(-0.779806\pi\)
−0.770125 + 0.637894i \(0.779806\pi\)
\(710\) 0 0
\(711\) 148.899 549.404i 0.209422 0.772720i
\(712\) 519.522i 0.729665i
\(713\) −169.044 −0.237088
\(714\) 76.5608 + 100.072i 0.107228 + 0.140157i
\(715\) 0 0
\(716\) 783.109i 1.09373i
\(717\) 109.304 + 142.871i 0.152446 + 0.199262i
\(718\) 235.558i 0.328076i
\(719\) 901.769i 1.25420i −0.778939 0.627099i \(-0.784242\pi\)
0.778939 0.627099i \(-0.215758\pi\)
\(720\) 0 0
\(721\) 148.826 0.206416
\(722\) 335.103 0.464132
\(723\) 321.072 245.638i 0.444083 0.339748i
\(724\) −494.710 −0.683301
\(725\) 0 0
\(726\) −355.556 + 272.020i −0.489747 + 0.374683i
\(727\) 297.506i 0.409224i −0.978843 0.204612i \(-0.934407\pi\)
0.978843 0.204612i \(-0.0655933\pi\)
\(728\) 138.253 0.189908
\(729\) −519.889 + 511.035i −0.713153 + 0.701008i
\(730\) 0 0
\(731\) 678.589i 0.928302i
\(732\) 111.817 85.5464i 0.152756 0.116867i
\(733\) 456.966i 0.623419i 0.950177 + 0.311709i \(0.100902\pi\)
−0.950177 + 0.311709i \(0.899098\pi\)
\(734\) 300.352i 0.409198i
\(735\) 0 0
\(736\) 132.620 0.180190
\(737\) 71.0171 0.0963597
\(738\) 343.809 + 93.1790i 0.465865 + 0.126259i
\(739\) 332.199 0.449525 0.224762 0.974414i \(-0.427839\pi\)
0.224762 + 0.974414i \(0.427839\pi\)
\(740\) 0 0
\(741\) −118.480 154.864i −0.159892 0.208994i
\(742\) 363.122i 0.489382i
\(743\) 64.5346 0.0868568 0.0434284 0.999057i \(-0.486172\pi\)
0.0434284 + 0.999057i \(0.486172\pi\)
\(744\) 769.882 589.003i 1.03479 0.791670i
\(745\) 0 0
\(746\) 577.408i 0.774005i
\(747\) −211.749 + 781.306i −0.283466 + 1.04592i
\(748\) 72.7530i 0.0972633i
\(749\) 325.790i 0.434966i
\(750\) 0 0
\(751\) −611.668 −0.814471 −0.407236 0.913323i \(-0.633507\pi\)
−0.407236 + 0.913323i \(0.633507\pi\)
\(752\) 63.2805 0.0841496
\(753\) 488.983 + 639.148i 0.649380 + 0.848802i
\(754\) 144.295 0.191373
\(755\) 0 0
\(756\) −151.501 + 61.9930i −0.200399 + 0.0820014i
\(757\) 207.357i 0.273919i 0.990577 + 0.136960i \(0.0437330\pi\)
−0.990577 + 0.136960i \(0.956267\pi\)
\(758\) −550.552 −0.726322
\(759\) 20.5020 + 26.7980i 0.0270118 + 0.0353070i
\(760\) 0 0
\(761\) 337.770i 0.443851i 0.975064 + 0.221925i \(0.0712341\pi\)
−0.975064 + 0.221925i \(0.928766\pi\)
\(762\) −87.1653 113.933i −0.114390 0.149519i
\(763\) 435.328i 0.570548i
\(764\) 102.456i 0.134104i
\(765\) 0 0
\(766\) 778.494 1.01631
\(767\) −262.837 −0.342682
\(768\) −638.565 + 488.538i −0.831465 + 0.636117i
\(769\) 1042.22 1.35529 0.677646 0.735388i \(-0.263000\pi\)
0.677646 + 0.735388i \(0.263000\pi\)
\(770\) 0 0
\(771\) 557.852 426.788i 0.723544 0.553551i
\(772\) 332.546i 0.430760i
\(773\) −291.448 −0.377035 −0.188517 0.982070i \(-0.560368\pi\)
−0.188517 + 0.982070i \(0.560368\pi\)
\(774\) 634.413 + 171.939i 0.819655 + 0.222143i
\(775\) 0 0
\(776\) 157.613i 0.203110i
\(777\) 258.718 197.933i 0.332970 0.254740i
\(778\) 480.157i 0.617168i
\(779\) 309.729i 0.397598i
\(780\) 0 0
\(781\) −177.255 −0.226959
\(782\) −68.2970 −0.0873363
\(783\) −434.138 + 177.646i −0.554455 + 0.226878i
\(784\) 11.0810 0.0141340
\(785\) 0 0
\(786\) −80.2614 104.909i −0.102114 0.133472i
\(787\) 293.889i 0.373429i −0.982414 0.186715i \(-0.940216\pi\)
0.982414 0.186715i \(-0.0597840\pi\)
\(788\) −200.425 −0.254346
\(789\) −596.006 + 455.978i −0.755395 + 0.577919i
\(790\) 0 0
\(791\) 381.122i 0.481822i
\(792\) −186.745 50.6117i −0.235790 0.0639037i
\(793\) 130.133i 0.164103i
\(794\) 533.748i 0.672226i
\(795\) 0 0
\(796\) 149.903 0.188321
\(797\) −568.764 −0.713631 −0.356816 0.934175i \(-0.616138\pi\)
−0.356816 + 0.934175i \(0.616138\pi\)
\(798\) −64.4816 84.2836i −0.0808041 0.105619i
\(799\) 485.490 0.607622
\(800\) 0 0
\(801\) −548.774 148.729i −0.685111 0.185679i
\(802\) 312.157i 0.389223i
\(803\) 158.915 0.197902
\(804\) −113.476 148.324i −0.141139 0.184482i
\(805\) 0 0
\(806\) 326.340i 0.404888i
\(807\) −621.024 811.737i −0.769546 1.00587i
\(808\) 811.768i 1.00466i
\(809\) 183.697i 0.227067i 0.993534 + 0.113534i \(0.0362169\pi\)
−0.993534 + 0.113534i \(0.963783\pi\)
\(810\) 0 0
\(811\) −544.663 −0.671594 −0.335797 0.941934i \(-0.609006\pi\)
−0.335797 + 0.941934i \(0.609006\pi\)
\(812\) −105.330 −0.129716
\(813\) −50.7494 + 38.8261i −0.0624224 + 0.0477566i
\(814\) 140.235 0.172279
\(815\) 0 0
\(816\) 45.8078 35.0455i 0.0561370 0.0429479i
\(817\) 571.527i 0.699543i
\(818\) −848.781 −1.03763
\(819\) 39.5791 146.038i 0.0483261 0.178312i
\(820\) 0 0
\(821\) 1188.78i 1.44797i 0.689818 + 0.723983i \(0.257691\pi\)
−0.689818 + 0.723983i \(0.742309\pi\)
\(822\) −124.497 + 95.2470i −0.151456 + 0.115872i
\(823\) 1265.15i 1.53724i 0.639704 + 0.768621i \(0.279057\pi\)
−0.639704 + 0.768621i \(0.720943\pi\)
\(824\) 462.585i 0.561390i
\(825\) 0 0
\(826\) −143.047 −0.173180
\(827\) −790.941 −0.956398 −0.478199 0.878252i \(-0.658710\pi\)
−0.478199 + 0.878252i \(0.658710\pi\)
\(828\) 23.2099 85.6393i 0.0280313 0.103429i
\(829\) −99.1961 −0.119658 −0.0598288 0.998209i \(-0.519055\pi\)
−0.0598288 + 0.998209i \(0.519055\pi\)
\(830\) 0 0
\(831\) 413.638 + 540.664i 0.497759 + 0.650619i
\(832\) 296.257i 0.356079i
\(833\) 85.0141 0.102058
\(834\) −606.188 + 463.768i −0.726844 + 0.556076i
\(835\) 0 0
\(836\) 61.2746i 0.0732950i
\(837\) −401.765 981.851i −0.480006 1.17306i
\(838\) 15.0549i 0.0179652i
\(839\) 243.824i 0.290612i −0.989387 0.145306i \(-0.953583\pi\)
0.989387 0.145306i \(-0.0464167\pi\)
\(840\) 0 0
\(841\) 539.170 0.641106
\(842\) 109.786 0.130387
\(843\) −429.267 561.093i −0.509214 0.665591i
\(844\) −92.9961 −0.110185
\(845\) 0 0
\(846\) 123.012 453.885i 0.145404 0.536507i
\(847\) 302.055i 0.356617i
\(848\) 166.218 0.196012
\(849\) 671.974 + 878.334i 0.791489 + 1.03455i
\(850\) 0 0
\(851\) 176.569i 0.207484i
\(852\) 283.230 + 370.208i 0.332429 + 0.434516i
\(853\) 1122.06i 1.31543i −0.753268 0.657713i \(-0.771524\pi\)
0.753268 0.657713i \(-0.228476\pi\)
\(854\) 70.8240i 0.0829321i
\(855\) 0 0
\(856\) 1012.63 1.18298
\(857\) −871.489 −1.01691 −0.508453 0.861090i \(-0.669783\pi\)
−0.508453 + 0.861090i \(0.669783\pi\)
\(858\) 51.7336 39.5791i 0.0602956 0.0461295i
\(859\) 1674.92 1.94985 0.974925 0.222533i \(-0.0714324\pi\)
0.974925 + 0.222533i \(0.0714324\pi\)
\(860\) 0 0
\(861\) 190.885 146.038i 0.221701 0.169614i
\(862\) 907.129i 1.05235i
\(863\) 1320.74 1.53041 0.765205 0.643787i \(-0.222638\pi\)
0.765205 + 0.643787i \(0.222638\pi\)
\(864\) 315.195 + 770.288i 0.364810 + 0.891537i
\(865\) 0 0
\(866\) 152.713i 0.176343i
\(867\) −337.153 + 257.940i −0.388873 + 0.297509i
\(868\) 238.214i 0.274441i
\(869\) 165.340i 0.190264i
\(870\) 0 0
\(871\) 172.620 0.198186
\(872\) −1353.10 −1.55172
\(873\) −166.488 45.1216i −0.190708 0.0516856i
\(874\) 57.5217 0.0658142
\(875\) 0 0
\(876\) −253.925 331.905i −0.289869 0.378887i
\(877\) 344.790i 0.393147i 0.980489 + 0.196573i \(0.0629814\pi\)
−0.980489 + 0.196573i \(0.937019\pi\)
\(878\) −690.242 −0.786152
\(879\) 1266.69 969.087i 1.44106 1.10249i
\(880\) 0 0
\(881\) 518.737i 0.588805i 0.955682 + 0.294403i \(0.0951206\pi\)
−0.955682 + 0.294403i \(0.904879\pi\)
\(882\) 21.5406 79.4797i 0.0244224 0.0901131i
\(883\) 584.008i 0.661391i −0.943738 0.330695i \(-0.892717\pi\)
0.943738 0.330695i \(-0.107283\pi\)
\(884\) 176.839i 0.200044i
\(885\) 0 0
\(886\) 355.859 0.401646
\(887\) 263.213 0.296745 0.148373 0.988932i \(-0.452597\pi\)
0.148373 + 0.988932i \(0.452597\pi\)
\(888\) −615.221 804.153i −0.692817 0.905577i
\(889\) −96.7895 −0.108875
\(890\) 0 0
\(891\) −106.923 + 182.771i −0.120003 + 0.205130i
\(892\) 231.349i 0.259360i
\(893\) −408.893 −0.457887
\(894\) −485.314 634.351i −0.542857 0.709565i
\(895\) 0 0
\(896\) 164.988i 0.184138i
\(897\) 49.8336 + 65.1373i 0.0555559 + 0.0726168i
\(898\) 687.231i 0.765291i
\(899\) 682.621i 0.759312i
\(900\) 0 0
\(901\) 1275.23 1.41535
\(902\) 103.467 0.114709
\(903\) 352.230 269.476i 0.390067 0.298423i
\(904\) 1184.61 1.31041
\(905\) 0 0
\(906\) −516.205 + 394.925i −0.569763 + 0.435900i
\(907\) 1501.72i 1.65570i 0.560951 + 0.827849i \(0.310435\pi\)
−0.560951 + 0.827849i \(0.689565\pi\)
\(908\) 896.618 0.987464
\(909\) −857.476 232.393i −0.943318 0.255658i
\(910\) 0 0
\(911\) 879.178i 0.965069i 0.875877 + 0.482534i \(0.160284\pi\)
−0.875877 + 0.482534i \(0.839716\pi\)
\(912\) −38.5806 + 29.5163i −0.0423033 + 0.0323644i
\(913\) 235.129i 0.257535i
\(914\) 671.567i 0.734756i
\(915\) 0 0
\(916\) −15.6092 −0.0170406
\(917\) −89.1234 −0.0971901
\(918\) −162.321 396.686i −0.176820 0.432120i
\(919\) −76.9882 −0.0837739 −0.0418869 0.999122i \(-0.513337\pi\)
−0.0418869 + 0.999122i \(0.513337\pi\)
\(920\) 0 0
\(921\) −1034.96 1352.79i −1.12374 1.46883i
\(922\) 899.123i 0.975188i
\(923\) −430.849 −0.466792
\(924\) −37.7634 + 28.8911i −0.0408694 + 0.0312674i
\(925\) 0 0
\(926\) 1020.92i 1.10251i
\(927\) −488.631 132.429i −0.527110 0.142857i
\(928\) 535.535i 0.577085i
\(929\) 1629.76i 1.75431i −0.480204 0.877157i \(-0.659437\pi\)
0.480204 0.877157i \(-0.340563\pi\)
\(930\) 0 0
\(931\) −71.6013 −0.0769079
\(932\) 267.823 0.287364
\(933\) 77.9336 + 101.867i 0.0835301 + 0.109182i
\(934\) −213.517 −0.228605
\(935\) 0 0
\(936\) −453.918 123.021i −0.484955 0.131432i
\(937\) 497.720i 0.531185i 0.964085 + 0.265592i \(0.0855676\pi\)
−0.964085 + 0.265592i \(0.914432\pi\)
\(938\) 93.9468 0.100157
\(939\) −288.229 376.742i −0.306953 0.401217i
\(940\) 0 0
\(941\) 238.894i 0.253873i −0.991911 0.126936i \(-0.959486\pi\)
0.991911 0.126936i \(-0.0405144\pi\)
\(942\) −721.289 942.793i −0.765700 1.00084i
\(943\) 130.275i 0.138149i
\(944\) 65.4794i 0.0693638i
\(945\) 0 0
\(946\) 190.923 0.201821
\(947\) −667.910 −0.705291 −0.352645 0.935757i \(-0.614718\pi\)
−0.352645 + 0.935757i \(0.614718\pi\)
\(948\) −345.322 + 264.191i −0.364264 + 0.278682i
\(949\) 386.272 0.407030
\(950\) 0 0
\(951\) −335.824 + 256.924i −0.353127 + 0.270162i
\(952\) 264.243i 0.277566i
\(953\) 11.3247 0.0118832 0.00594162 0.999982i \(-0.498109\pi\)
0.00594162 + 0.999982i \(0.498109\pi\)
\(954\) 323.114 1192.21i 0.338694 1.24970i
\(955\) 0 0
\(956\) 137.404i 0.143728i
\(957\) −108.214 + 82.7895i −0.113076 + 0.0865094i
\(958\) 915.174i 0.955296i
\(959\) 105.764i 0.110285i
\(960\) 0 0
\(961\) 582.822 0.606475
\(962\) 340.866 0.354331
\(963\) 289.895 1069.64i 0.301033 1.11074i
\(964\) −308.787 −0.320318
\(965\) 0 0
\(966\) 27.1216 + 35.4504i 0.0280761 + 0.0366982i
\(967\) 830.324i 0.858660i −0.903148 0.429330i \(-0.858750\pi\)
0.903148 0.429330i \(-0.141250\pi\)
\(968\) 938.855 0.969891
\(969\) −295.992 + 226.450i −0.305461 + 0.233695i
\(970\) 0 0
\(971\) 1217.58i 1.25394i −0.779044 0.626970i \(-0.784295\pi\)
0.779044 0.626970i \(-0.215705\pi\)
\(972\) 552.577 68.7286i 0.568495 0.0707085i
\(973\) 514.974i 0.529264i
\(974\) 113.183i 0.116204i
\(975\) 0 0
\(976\) 32.4195 0.0332167
\(977\) 424.579 0.434574 0.217287 0.976108i \(-0.430279\pi\)
0.217287 + 0.976108i \(0.430279\pi\)
\(978\) 345.584 + 451.711i 0.353358 + 0.461872i
\(979\) −165.150 −0.168693
\(980\) 0 0
\(981\) −387.365 + 1429.29i −0.394867 + 1.45697i
\(982\) 969.203i 0.986968i
\(983\) −76.7273 −0.0780542 −0.0390271 0.999238i \(-0.512426\pi\)
−0.0390271 + 0.999238i \(0.512426\pi\)
\(984\) −453.918 593.313i −0.461298 0.602961i
\(985\) 0 0
\(986\) 275.792i 0.279708i
\(987\) −192.794 252.000i −0.195333 0.255319i
\(988\) 148.939i 0.150748i
\(989\) 240.389i 0.243063i
\(990\) 0 0
\(991\) 181.271 0.182917 0.0914585 0.995809i \(-0.470847\pi\)
0.0914585 + 0.995809i \(0.470847\pi\)
\(992\) −1211.17 −1.22094
\(993\) −615.608 + 470.974i −0.619947 + 0.474294i
\(994\) −234.486 −0.235902
\(995\) 0 0
\(996\) 491.082 375.705i 0.493055 0.377214i
\(997\) 1184.43i 1.18800i 0.804466 + 0.593998i \(0.202451\pi\)
−0.804466 + 0.593998i \(0.797549\pi\)
\(998\) 496.453 0.497448
\(999\) −1025.56 + 419.649i −1.02658 + 0.420069i
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.449.3 8
3.2 odd 2 inner 525.3.f.a.449.5 8
5.2 odd 4 21.3.b.a.8.2 4
5.3 odd 4 525.3.c.a.176.3 4
5.4 even 2 inner 525.3.f.a.449.6 8
15.2 even 4 21.3.b.a.8.3 yes 4
15.8 even 4 525.3.c.a.176.2 4
15.14 odd 2 inner 525.3.f.a.449.4 8
20.7 even 4 336.3.d.c.113.4 4
35.2 odd 12 147.3.h.e.116.2 8
35.12 even 12 147.3.h.c.116.2 8
35.17 even 12 147.3.h.c.128.3 8
35.27 even 4 147.3.b.f.50.2 4
35.32 odd 12 147.3.h.e.128.3 8
40.27 even 4 1344.3.d.b.449.1 4
40.37 odd 4 1344.3.d.f.449.4 4
45.2 even 12 567.3.r.c.134.3 8
45.7 odd 12 567.3.r.c.134.2 8
45.22 odd 12 567.3.r.c.512.3 8
45.32 even 12 567.3.r.c.512.2 8
60.47 odd 4 336.3.d.c.113.3 4
105.2 even 12 147.3.h.e.116.3 8
105.17 odd 12 147.3.h.c.128.2 8
105.32 even 12 147.3.h.e.128.2 8
105.47 odd 12 147.3.h.c.116.3 8
105.62 odd 4 147.3.b.f.50.3 4
120.77 even 4 1344.3.d.f.449.3 4
120.107 odd 4 1344.3.d.b.449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.b.a.8.2 4 5.2 odd 4
21.3.b.a.8.3 yes 4 15.2 even 4
147.3.b.f.50.2 4 35.27 even 4
147.3.b.f.50.3 4 105.62 odd 4
147.3.h.c.116.2 8 35.12 even 12
147.3.h.c.116.3 8 105.47 odd 12
147.3.h.c.128.2 8 105.17 odd 12
147.3.h.c.128.3 8 35.17 even 12
147.3.h.e.116.2 8 35.2 odd 12
147.3.h.e.116.3 8 105.2 even 12
147.3.h.e.128.2 8 105.32 even 12
147.3.h.e.128.3 8 35.32 odd 12
336.3.d.c.113.3 4 60.47 odd 4
336.3.d.c.113.4 4 20.7 even 4
525.3.c.a.176.2 4 15.8 even 4
525.3.c.a.176.3 4 5.3 odd 4
525.3.f.a.449.3 8 1.1 even 1 trivial
525.3.f.a.449.4 8 15.14 odd 2 inner
525.3.f.a.449.5 8 3.2 odd 2 inner
525.3.f.a.449.6 8 5.4 even 2 inner
567.3.r.c.134.2 8 45.7 odd 12
567.3.r.c.134.3 8 45.2 even 12
567.3.r.c.512.2 8 45.32 even 12
567.3.r.c.512.3 8 45.22 odd 12
1344.3.d.b.449.1 4 40.27 even 4
1344.3.d.b.449.2 4 120.107 odd 4
1344.3.d.f.449.3 4 120.77 even 4
1344.3.d.f.449.4 4 40.37 odd 4