Properties

Label 315.3.o.b.253.2
Level $315$
Weight $3$
Character 315.253
Analytic conductor $8.583$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,3,Mod(127,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 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("315.127");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.o (of order \(4\), degree \(2\), 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: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.2
Character \(\chi\) \(=\) 315.253
Dual form 315.3.o.b.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.41688 + 2.41688i) q^{2} -7.68258i q^{4} +(-4.18124 - 2.74175i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(8.90034 + 8.90034i) q^{8} +O(q^{10})\) \(q+(-2.41688 + 2.41688i) q^{2} -7.68258i q^{4} +(-4.18124 - 2.74175i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(8.90034 + 8.90034i) q^{8} +(16.7320 - 3.47908i) q^{10} +20.9312 q^{11} +(-9.34319 - 9.34319i) q^{13} -9.04312i q^{14} -12.2917 q^{16} +(-7.08868 + 7.08868i) q^{17} +14.9507i q^{19} +(-21.0637 + 32.1228i) q^{20} +(-50.5882 + 50.5882i) q^{22} +(-12.9691 - 12.9691i) q^{23} +(9.96562 + 22.9279i) q^{25} +45.1627 q^{26} +(14.3728 + 14.3728i) q^{28} +39.6296i q^{29} +12.8776 q^{31} +(-5.89378 + 5.89378i) q^{32} -34.2649i q^{34} +(12.9517 - 2.69305i) q^{35} +(-31.7205 + 31.7205i) q^{37} +(-36.1341 - 36.1341i) q^{38} +(-12.8120 - 61.6170i) q^{40} -69.4519 q^{41} +(4.46880 + 4.46880i) q^{43} -160.806i q^{44} +62.6895 q^{46} +(4.41044 - 4.41044i) q^{47} -7.00000i q^{49} +(-79.4994 - 31.3281i) q^{50} +(-71.7798 + 71.7798i) q^{52} +(48.5314 + 48.5314i) q^{53} +(-87.5186 - 57.3882i) q^{55} -33.3020 q^{56} +(-95.7797 - 95.7797i) q^{58} +29.4254i q^{59} +7.09295 q^{61} +(-31.1235 + 31.1235i) q^{62} -77.6560i q^{64} +(13.4495 + 64.6829i) q^{65} +(-1.39800 + 1.39800i) q^{67} +(54.4593 + 54.4593i) q^{68} +(-24.7940 + 37.8115i) q^{70} +15.9437 q^{71} +(32.4160 + 32.4160i) q^{73} -153.329i q^{74} +114.860 q^{76} +(-39.1588 + 39.1588i) q^{77} +66.1155i q^{79} +(51.3947 + 33.7009i) q^{80} +(167.857 - 167.857i) q^{82} +(83.6744 + 83.6744i) q^{83} +(49.0749 - 10.2041i) q^{85} -21.6011 q^{86} +(186.295 + 186.295i) q^{88} +62.7487i q^{89} +34.9590 q^{91} +(-99.6363 + 99.6363i) q^{92} +21.3190i q^{94} +(40.9912 - 62.5127i) q^{95} +(-85.4547 + 85.4547i) q^{97} +(16.9181 + 16.9181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41688 + 2.41688i −1.20844 + 1.20844i −0.236905 + 0.971533i \(0.576133\pi\)
−0.971533 + 0.236905i \(0.923867\pi\)
\(3\) 0 0
\(4\) 7.68258i 1.92065i
\(5\) −4.18124 2.74175i −0.836249 0.548350i
\(6\) 0 0
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) 8.90034 + 8.90034i 1.11254 + 1.11254i
\(9\) 0 0
\(10\) 16.7320 3.47908i 1.67320 0.347908i
\(11\) 20.9312 1.90284 0.951420 0.307897i \(-0.0996252\pi\)
0.951420 + 0.307897i \(0.0996252\pi\)
\(12\) 0 0
\(13\) −9.34319 9.34319i −0.718707 0.718707i 0.249633 0.968340i \(-0.419690\pi\)
−0.968340 + 0.249633i \(0.919690\pi\)
\(14\) 9.04312i 0.645937i
\(15\) 0 0
\(16\) −12.2917 −0.768233
\(17\) −7.08868 + 7.08868i −0.416981 + 0.416981i −0.884162 0.467181i \(-0.845270\pi\)
0.467181 + 0.884162i \(0.345270\pi\)
\(18\) 0 0
\(19\) 14.9507i 0.786881i 0.919350 + 0.393440i \(0.128715\pi\)
−0.919350 + 0.393440i \(0.871285\pi\)
\(20\) −21.0637 + 32.1228i −1.05319 + 1.60614i
\(21\) 0 0
\(22\) −50.5882 + 50.5882i −2.29946 + 2.29946i
\(23\) −12.9691 12.9691i −0.563874 0.563874i 0.366531 0.930406i \(-0.380545\pi\)
−0.930406 + 0.366531i \(0.880545\pi\)
\(24\) 0 0
\(25\) 9.96562 + 22.9279i 0.398625 + 0.917114i
\(26\) 45.1627 1.73703
\(27\) 0 0
\(28\) 14.3728 + 14.3728i 0.513314 + 0.513314i
\(29\) 39.6296i 1.36654i 0.730168 + 0.683268i \(0.239442\pi\)
−0.730168 + 0.683268i \(0.760558\pi\)
\(30\) 0 0
\(31\) 12.8776 0.415405 0.207703 0.978192i \(-0.433401\pi\)
0.207703 + 0.978192i \(0.433401\pi\)
\(32\) −5.89378 + 5.89378i −0.184181 + 0.184181i
\(33\) 0 0
\(34\) 34.2649i 1.00779i
\(35\) 12.9517 2.69305i 0.370050 0.0769443i
\(36\) 0 0
\(37\) −31.7205 + 31.7205i −0.857312 + 0.857312i −0.991021 0.133709i \(-0.957311\pi\)
0.133709 + 0.991021i \(0.457311\pi\)
\(38\) −36.1341 36.1341i −0.950897 0.950897i
\(39\) 0 0
\(40\) −12.8120 61.6170i −0.320300 1.54043i
\(41\) −69.4519 −1.69395 −0.846974 0.531634i \(-0.821578\pi\)
−0.846974 + 0.531634i \(0.821578\pi\)
\(42\) 0 0
\(43\) 4.46880 + 4.46880i 0.103926 + 0.103926i 0.757158 0.653232i \(-0.226587\pi\)
−0.653232 + 0.757158i \(0.726587\pi\)
\(44\) 160.806i 3.65468i
\(45\) 0 0
\(46\) 62.6895 1.36281
\(47\) 4.41044 4.41044i 0.0938392 0.0938392i −0.658629 0.752468i \(-0.728863\pi\)
0.752468 + 0.658629i \(0.228863\pi\)
\(48\) 0 0
\(49\) 7.00000i 0.142857i
\(50\) −79.4994 31.3281i −1.58999 0.626562i
\(51\) 0 0
\(52\) −71.7798 + 71.7798i −1.38038 + 1.38038i
\(53\) 48.5314 + 48.5314i 0.915687 + 0.915687i 0.996712 0.0810246i \(-0.0258192\pi\)
−0.0810246 + 0.996712i \(0.525819\pi\)
\(54\) 0 0
\(55\) −87.5186 57.3882i −1.59125 1.04342i
\(56\) −33.3020 −0.594679
\(57\) 0 0
\(58\) −95.7797 95.7797i −1.65137 1.65137i
\(59\) 29.4254i 0.498736i 0.968409 + 0.249368i \(0.0802229\pi\)
−0.968409 + 0.249368i \(0.919777\pi\)
\(60\) 0 0
\(61\) 7.09295 0.116278 0.0581389 0.998309i \(-0.481483\pi\)
0.0581389 + 0.998309i \(0.481483\pi\)
\(62\) −31.1235 + 31.1235i −0.501992 + 0.501992i
\(63\) 0 0
\(64\) 77.6560i 1.21338i
\(65\) 13.4495 + 64.6829i 0.206915 + 0.995121i
\(66\) 0 0
\(67\) −1.39800 + 1.39800i −0.0208657 + 0.0208657i −0.717463 0.696597i \(-0.754697\pi\)
0.696597 + 0.717463i \(0.254697\pi\)
\(68\) 54.4593 + 54.4593i 0.800873 + 0.800873i
\(69\) 0 0
\(70\) −24.7940 + 37.8115i −0.354200 + 0.540164i
\(71\) 15.9437 0.224559 0.112279 0.993677i \(-0.464185\pi\)
0.112279 + 0.993677i \(0.464185\pi\)
\(72\) 0 0
\(73\) 32.4160 + 32.4160i 0.444055 + 0.444055i 0.893372 0.449317i \(-0.148333\pi\)
−0.449317 + 0.893372i \(0.648333\pi\)
\(74\) 153.329i 2.07202i
\(75\) 0 0
\(76\) 114.860 1.51132
\(77\) −39.1588 + 39.1588i −0.508555 + 0.508555i
\(78\) 0 0
\(79\) 66.1155i 0.836905i 0.908239 + 0.418453i \(0.137427\pi\)
−0.908239 + 0.418453i \(0.862573\pi\)
\(80\) 51.3947 + 33.7009i 0.642434 + 0.421261i
\(81\) 0 0
\(82\) 167.857 167.857i 2.04703 2.04703i
\(83\) 83.6744 + 83.6744i 1.00812 + 1.00812i 0.999967 + 0.00815803i \(0.00259681\pi\)
0.00815803 + 0.999967i \(0.497403\pi\)
\(84\) 0 0
\(85\) 49.0749 10.2041i 0.577352 0.120048i
\(86\) −21.6011 −0.251175
\(87\) 0 0
\(88\) 186.295 + 186.295i 2.11699 + 2.11699i
\(89\) 62.7487i 0.705042i 0.935804 + 0.352521i \(0.114675\pi\)
−0.935804 + 0.352521i \(0.885325\pi\)
\(90\) 0 0
\(91\) 34.9590 0.384165
\(92\) −99.6363 + 99.6363i −1.08300 + 1.08300i
\(93\) 0 0
\(94\) 21.3190i 0.226798i
\(95\) 40.9912 62.5127i 0.431486 0.658028i
\(96\) 0 0
\(97\) −85.4547 + 85.4547i −0.880976 + 0.880976i −0.993634 0.112658i \(-0.964064\pi\)
0.112658 + 0.993634i \(0.464064\pi\)
\(98\) 16.9181 + 16.9181i 0.172634 + 0.172634i
\(99\) 0 0
\(100\) 176.145 76.5617i 1.76145 0.765617i
\(101\) −145.641 −1.44199 −0.720997 0.692938i \(-0.756316\pi\)
−0.720997 + 0.692938i \(0.756316\pi\)
\(102\) 0 0
\(103\) 62.2547 + 62.2547i 0.604414 + 0.604414i 0.941481 0.337067i \(-0.109435\pi\)
−0.337067 + 0.941481i \(0.609435\pi\)
\(104\) 166.315i 1.59918i
\(105\) 0 0
\(106\) −234.589 −2.21310
\(107\) 4.15809 4.15809i 0.0388607 0.0388607i −0.687409 0.726270i \(-0.741252\pi\)
0.726270 + 0.687409i \(0.241252\pi\)
\(108\) 0 0
\(109\) 78.6347i 0.721419i −0.932678 0.360710i \(-0.882535\pi\)
0.932678 0.360710i \(-0.117465\pi\)
\(110\) 350.222 72.8215i 3.18383 0.662013i
\(111\) 0 0
\(112\) 22.9957 22.9957i 0.205319 0.205319i
\(113\) 107.343 + 107.343i 0.949938 + 0.949938i 0.998805 0.0488672i \(-0.0155611\pi\)
−0.0488672 + 0.998805i \(0.515561\pi\)
\(114\) 0 0
\(115\) 18.6690 + 89.7851i 0.162339 + 0.780740i
\(116\) 304.457 2.62463
\(117\) 0 0
\(118\) −71.1176 71.1176i −0.602692 0.602692i
\(119\) 26.5234i 0.222886i
\(120\) 0 0
\(121\) 317.117 2.62080
\(122\) −17.1428 + 17.1428i −0.140515 + 0.140515i
\(123\) 0 0
\(124\) 98.9329i 0.797846i
\(125\) 21.1937 123.190i 0.169550 0.985522i
\(126\) 0 0
\(127\) −116.651 + 116.651i −0.918514 + 0.918514i −0.996921 0.0784074i \(-0.975017\pi\)
0.0784074 + 0.996921i \(0.475017\pi\)
\(128\) 164.110 + 164.110i 1.28211 + 1.28211i
\(129\) 0 0
\(130\) −188.836 123.825i −1.45259 0.952498i
\(131\) −139.820 −1.06733 −0.533664 0.845697i \(-0.679185\pi\)
−0.533664 + 0.845697i \(0.679185\pi\)
\(132\) 0 0
\(133\) −27.9703 27.9703i −0.210303 0.210303i
\(134\) 6.75760i 0.0504298i
\(135\) 0 0
\(136\) −126.183 −0.927819
\(137\) 161.119 161.119i 1.17605 1.17605i 0.195313 0.980741i \(-0.437428\pi\)
0.980741 0.195313i \(-0.0625723\pi\)
\(138\) 0 0
\(139\) 201.129i 1.44697i 0.690340 + 0.723485i \(0.257461\pi\)
−0.690340 + 0.723485i \(0.742539\pi\)
\(140\) −20.6896 99.5028i −0.147783 0.710734i
\(141\) 0 0
\(142\) −38.5339 + 38.5339i −0.271365 + 0.271365i
\(143\) −195.565 195.565i −1.36758 1.36758i
\(144\) 0 0
\(145\) 108.654 165.701i 0.749340 1.14276i
\(146\) −156.691 −1.07323
\(147\) 0 0
\(148\) 243.696 + 243.696i 1.64659 + 1.64659i
\(149\) 23.2371i 0.155954i 0.996955 + 0.0779768i \(0.0248460\pi\)
−0.996955 + 0.0779768i \(0.975154\pi\)
\(150\) 0 0
\(151\) −39.3517 −0.260607 −0.130304 0.991474i \(-0.541595\pi\)
−0.130304 + 0.991474i \(0.541595\pi\)
\(152\) −133.067 + 133.067i −0.875439 + 0.875439i
\(153\) 0 0
\(154\) 189.284i 1.22912i
\(155\) −53.8443 35.3071i −0.347382 0.227787i
\(156\) 0 0
\(157\) 51.1623 51.1623i 0.325874 0.325874i −0.525141 0.851015i \(-0.675987\pi\)
0.851015 + 0.525141i \(0.175987\pi\)
\(158\) −159.793 159.793i −1.01135 1.01135i
\(159\) 0 0
\(160\) 40.8026 8.48407i 0.255016 0.0530254i
\(161\) 48.5260 0.301404
\(162\) 0 0
\(163\) −40.2804 40.2804i −0.247119 0.247119i 0.572668 0.819787i \(-0.305908\pi\)
−0.819787 + 0.572668i \(0.805908\pi\)
\(164\) 533.570i 3.25347i
\(165\) 0 0
\(166\) −404.461 −2.43651
\(167\) 66.9974 66.9974i 0.401182 0.401182i −0.477467 0.878649i \(-0.658445\pi\)
0.878649 + 0.477467i \(0.158445\pi\)
\(168\) 0 0
\(169\) 5.59045i 0.0330796i
\(170\) −93.9458 + 143.270i −0.552622 + 0.842765i
\(171\) 0 0
\(172\) 34.3319 34.3319i 0.199604 0.199604i
\(173\) −221.843 221.843i −1.28233 1.28233i −0.939339 0.342991i \(-0.888560\pi\)
−0.342991 0.939339i \(-0.611440\pi\)
\(174\) 0 0
\(175\) −61.5380 24.2501i −0.351646 0.138572i
\(176\) −257.281 −1.46182
\(177\) 0 0
\(178\) −151.656 151.656i −0.851999 0.851999i
\(179\) 129.207i 0.721827i 0.932599 + 0.360914i \(0.117535\pi\)
−0.932599 + 0.360914i \(0.882465\pi\)
\(180\) 0 0
\(181\) 28.8400 0.159337 0.0796685 0.996821i \(-0.474614\pi\)
0.0796685 + 0.996821i \(0.474614\pi\)
\(182\) −84.4916 + 84.4916i −0.464240 + 0.464240i
\(183\) 0 0
\(184\) 230.859i 1.25467i
\(185\) 219.601 45.6616i 1.18703 0.246819i
\(186\) 0 0
\(187\) −148.375 + 148.375i −0.793448 + 0.793448i
\(188\) −33.8836 33.8836i −0.180232 0.180232i
\(189\) 0 0
\(190\) 52.0148 + 250.156i 0.273762 + 1.31661i
\(191\) −29.9221 −0.156660 −0.0783302 0.996927i \(-0.524959\pi\)
−0.0783302 + 0.996927i \(0.524959\pi\)
\(192\) 0 0
\(193\) −42.5417 42.5417i −0.220423 0.220423i 0.588253 0.808677i \(-0.299816\pi\)
−0.808677 + 0.588253i \(0.799816\pi\)
\(194\) 413.067i 2.12921i
\(195\) 0 0
\(196\) −53.7781 −0.274378
\(197\) −249.093 + 249.093i −1.26443 + 1.26443i −0.315509 + 0.948922i \(0.602175\pi\)
−0.948922 + 0.315509i \(0.897825\pi\)
\(198\) 0 0
\(199\) 16.7548i 0.0841949i −0.999114 0.0420974i \(-0.986596\pi\)
0.999114 0.0420974i \(-0.0134040\pi\)
\(200\) −115.368 + 292.763i −0.576842 + 1.46382i
\(201\) 0 0
\(202\) 351.997 351.997i 1.74256 1.74256i
\(203\) −74.1401 74.1401i −0.365222 0.365222i
\(204\) 0 0
\(205\) 290.395 + 190.420i 1.41656 + 0.928876i
\(206\) −300.924 −1.46079
\(207\) 0 0
\(208\) 114.844 + 114.844i 0.552135 + 0.552135i
\(209\) 312.937i 1.49731i
\(210\) 0 0
\(211\) 77.0276 0.365060 0.182530 0.983200i \(-0.441571\pi\)
0.182530 + 0.983200i \(0.441571\pi\)
\(212\) 372.847 372.847i 1.75871 1.75871i
\(213\) 0 0
\(214\) 20.0992i 0.0939214i
\(215\) −6.43281 30.9375i −0.0299201 0.143895i
\(216\) 0 0
\(217\) −24.0917 + 24.0917i −0.111022 + 0.111022i
\(218\) 190.050 + 190.050i 0.871791 + 0.871791i
\(219\) 0 0
\(220\) −440.890 + 672.369i −2.00404 + 3.05622i
\(221\) 132.462 0.599374
\(222\) 0 0
\(223\) −44.1625 44.1625i −0.198038 0.198038i 0.601120 0.799158i \(-0.294721\pi\)
−0.799158 + 0.601120i \(0.794721\pi\)
\(224\) 22.0525i 0.0984487i
\(225\) 0 0
\(226\) −518.869 −2.29588
\(227\) 176.500 176.500i 0.777533 0.777533i −0.201878 0.979411i \(-0.564704\pi\)
0.979411 + 0.201878i \(0.0647044\pi\)
\(228\) 0 0
\(229\) 296.743i 1.29582i −0.761716 0.647911i \(-0.775643\pi\)
0.761716 0.647911i \(-0.224357\pi\)
\(230\) −262.120 171.879i −1.13965 0.747299i
\(231\) 0 0
\(232\) −352.717 + 352.717i −1.52033 + 1.52033i
\(233\) 88.1651 + 88.1651i 0.378391 + 0.378391i 0.870521 0.492131i \(-0.163782\pi\)
−0.492131 + 0.870521i \(0.663782\pi\)
\(234\) 0 0
\(235\) −30.5335 + 6.34881i −0.129930 + 0.0270162i
\(236\) 226.063 0.957895
\(237\) 0 0
\(238\) 64.1038 + 64.1038i 0.269344 + 0.269344i
\(239\) 370.319i 1.54945i −0.632297 0.774726i \(-0.717888\pi\)
0.632297 0.774726i \(-0.282112\pi\)
\(240\) 0 0
\(241\) −202.313 −0.839471 −0.419736 0.907646i \(-0.637877\pi\)
−0.419736 + 0.907646i \(0.637877\pi\)
\(242\) −766.431 + 766.431i −3.16707 + 3.16707i
\(243\) 0 0
\(244\) 54.4921i 0.223328i
\(245\) −19.1922 + 29.2687i −0.0783357 + 0.119464i
\(246\) 0 0
\(247\) 139.688 139.688i 0.565537 0.565537i
\(248\) 114.615 + 114.615i 0.462156 + 0.462156i
\(249\) 0 0
\(250\) 246.513 + 348.958i 0.986051 + 1.39583i
\(251\) 358.910 1.42992 0.714960 0.699165i \(-0.246445\pi\)
0.714960 + 0.699165i \(0.246445\pi\)
\(252\) 0 0
\(253\) −271.459 271.459i −1.07296 1.07296i
\(254\) 563.863i 2.21993i
\(255\) 0 0
\(256\) −482.642 −1.88532
\(257\) 157.946 157.946i 0.614576 0.614576i −0.329559 0.944135i \(-0.606900\pi\)
0.944135 + 0.329559i \(0.106900\pi\)
\(258\) 0 0
\(259\) 118.687i 0.458252i
\(260\) 496.931 103.327i 1.91127 0.397410i
\(261\) 0 0
\(262\) 337.927 337.927i 1.28980 1.28980i
\(263\) −9.79809 9.79809i −0.0372551 0.0372551i 0.688234 0.725489i \(-0.258386\pi\)
−0.725489 + 0.688234i \(0.758386\pi\)
\(264\) 0 0
\(265\) −69.8608 335.983i −0.263626 1.26786i
\(266\) 135.201 0.508276
\(267\) 0 0
\(268\) 10.7403 + 10.7403i 0.0400756 + 0.0400756i
\(269\) 143.504i 0.533473i −0.963770 0.266736i \(-0.914055\pi\)
0.963770 0.266736i \(-0.0859453\pi\)
\(270\) 0 0
\(271\) −29.4732 −0.108757 −0.0543785 0.998520i \(-0.517318\pi\)
−0.0543785 + 0.998520i \(0.517318\pi\)
\(272\) 87.1321 87.1321i 0.320339 0.320339i
\(273\) 0 0
\(274\) 778.811i 2.84238i
\(275\) 208.593 + 479.908i 0.758519 + 1.74512i
\(276\) 0 0
\(277\) 189.827 189.827i 0.685295 0.685295i −0.275894 0.961188i \(-0.588974\pi\)
0.961188 + 0.275894i \(0.0889738\pi\)
\(278\) −486.103 486.103i −1.74857 1.74857i
\(279\) 0 0
\(280\) 139.244 + 91.3058i 0.497300 + 0.326092i
\(281\) 61.2502 0.217972 0.108986 0.994043i \(-0.465240\pi\)
0.108986 + 0.994043i \(0.465240\pi\)
\(282\) 0 0
\(283\) −176.415 176.415i −0.623375 0.623375i 0.323018 0.946393i \(-0.395303\pi\)
−0.946393 + 0.323018i \(0.895303\pi\)
\(284\) 122.489i 0.431298i
\(285\) 0 0
\(286\) 945.310 3.30528
\(287\) 129.933 129.933i 0.452727 0.452727i
\(288\) 0 0
\(289\) 188.501i 0.652254i
\(290\) 137.874 + 663.083i 0.475429 + 2.28649i
\(291\) 0 0
\(292\) 249.039 249.039i 0.852873 0.852873i
\(293\) 92.7415 + 92.7415i 0.316524 + 0.316524i 0.847430 0.530907i \(-0.178148\pi\)
−0.530907 + 0.847430i \(0.678148\pi\)
\(294\) 0 0
\(295\) 80.6772 123.035i 0.273482 0.417068i
\(296\) −564.647 −1.90759
\(297\) 0 0
\(298\) −56.1612 56.1612i −0.188460 0.188460i
\(299\) 242.346i 0.810521i
\(300\) 0 0
\(301\) −16.7207 −0.0555505
\(302\) 95.1081 95.1081i 0.314927 0.314927i
\(303\) 0 0
\(304\) 183.770i 0.604508i
\(305\) −29.6573 19.4471i −0.0972372 0.0637609i
\(306\) 0 0
\(307\) −228.867 + 228.867i −0.745494 + 0.745494i −0.973629 0.228135i \(-0.926737\pi\)
0.228135 + 0.973629i \(0.426737\pi\)
\(308\) 300.840 + 300.840i 0.976754 + 0.976754i
\(309\) 0 0
\(310\) 215.468 44.8021i 0.695057 0.144523i
\(311\) −291.118 −0.936070 −0.468035 0.883710i \(-0.655038\pi\)
−0.468035 + 0.883710i \(0.655038\pi\)
\(312\) 0 0
\(313\) 251.667 + 251.667i 0.804049 + 0.804049i 0.983726 0.179677i \(-0.0575052\pi\)
−0.179677 + 0.983726i \(0.557505\pi\)
\(314\) 247.306i 0.787598i
\(315\) 0 0
\(316\) 507.938 1.60740
\(317\) −30.4080 + 30.4080i −0.0959244 + 0.0959244i −0.753440 0.657516i \(-0.771607\pi\)
0.657516 + 0.753440i \(0.271607\pi\)
\(318\) 0 0
\(319\) 829.495i 2.60030i
\(320\) −212.913 + 324.699i −0.665354 + 1.01468i
\(321\) 0 0
\(322\) −117.281 + 117.281i −0.364228 + 0.364228i
\(323\) −105.981 105.981i −0.328114 0.328114i
\(324\) 0 0
\(325\) 121.109 307.330i 0.372642 0.945631i
\(326\) 194.705 0.597255
\(327\) 0 0
\(328\) −618.146 618.146i −1.88459 1.88459i
\(329\) 16.5024i 0.0501592i
\(330\) 0 0
\(331\) −600.898 −1.81540 −0.907701 0.419617i \(-0.862164\pi\)
−0.907701 + 0.419617i \(0.862164\pi\)
\(332\) 642.835 642.835i 1.93625 1.93625i
\(333\) 0 0
\(334\) 323.849i 0.969607i
\(335\) 9.67836 2.01242i 0.0288906 0.00600722i
\(336\) 0 0
\(337\) −18.3744 + 18.3744i −0.0545235 + 0.0545235i −0.733843 0.679319i \(-0.762275\pi\)
0.679319 + 0.733843i \(0.262275\pi\)
\(338\) −13.5114 13.5114i −0.0399746 0.0399746i
\(339\) 0 0
\(340\) −78.3940 377.022i −0.230570 1.10889i
\(341\) 269.543 0.790450
\(342\) 0 0
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 79.5477i 0.231243i
\(345\) 0 0
\(346\) 1072.33 3.09923
\(347\) −274.252 + 274.252i −0.790351 + 0.790351i −0.981551 0.191200i \(-0.938762\pi\)
0.191200 + 0.981551i \(0.438762\pi\)
\(348\) 0 0
\(349\) 218.995i 0.627494i 0.949507 + 0.313747i \(0.101584\pi\)
−0.949507 + 0.313747i \(0.898416\pi\)
\(350\) 207.339 90.1203i 0.592398 0.257487i
\(351\) 0 0
\(352\) −123.364 + 123.364i −0.350466 + 0.350466i
\(353\) −77.0417 77.0417i −0.218248 0.218248i 0.589512 0.807760i \(-0.299320\pi\)
−0.807760 + 0.589512i \(0.799320\pi\)
\(354\) 0 0
\(355\) −66.6644 43.7136i −0.187787 0.123137i
\(356\) 482.072 1.35413
\(357\) 0 0
\(358\) −312.277 312.277i −0.872283 0.872283i
\(359\) 532.713i 1.48388i 0.670466 + 0.741940i \(0.266094\pi\)
−0.670466 + 0.741940i \(0.733906\pi\)
\(360\) 0 0
\(361\) 137.476 0.380819
\(362\) −69.7027 + 69.7027i −0.192549 + 0.192549i
\(363\) 0 0
\(364\) 268.576i 0.737845i
\(365\) −46.6627 224.416i −0.127843 0.614838i
\(366\) 0 0
\(367\) 367.459 367.459i 1.00125 1.00125i 0.00125078 0.999999i \(-0.499602\pi\)
0.999999 0.00125078i \(-0.000398137\pi\)
\(368\) 159.413 + 159.413i 0.433187 + 0.433187i
\(369\) 0 0
\(370\) −420.390 + 641.107i −1.13619 + 1.73272i
\(371\) −181.588 −0.489456
\(372\) 0 0
\(373\) 30.1723 + 30.1723i 0.0808908 + 0.0808908i 0.746395 0.665504i \(-0.231783\pi\)
−0.665504 + 0.746395i \(0.731783\pi\)
\(374\) 717.207i 1.91767i
\(375\) 0 0
\(376\) 78.5089 0.208800
\(377\) 370.267 370.267i 0.982139 0.982139i
\(378\) 0 0
\(379\) 254.898i 0.672555i −0.941763 0.336277i \(-0.890832\pi\)
0.941763 0.336277i \(-0.109168\pi\)
\(380\) −480.259 314.918i −1.26384 0.828732i
\(381\) 0 0
\(382\) 72.3181 72.3181i 0.189314 0.189314i
\(383\) −104.737 104.737i −0.273465 0.273465i 0.557028 0.830493i \(-0.311941\pi\)
−0.830493 + 0.557028i \(0.811941\pi\)
\(384\) 0 0
\(385\) 271.096 56.3688i 0.704145 0.146413i
\(386\) 205.636 0.532736
\(387\) 0 0
\(388\) 656.512 + 656.512i 1.69204 + 1.69204i
\(389\) 667.039i 1.71475i −0.514689 0.857377i \(-0.672092\pi\)
0.514689 0.857377i \(-0.327908\pi\)
\(390\) 0 0
\(391\) 183.868 0.470250
\(392\) 62.3024 62.3024i 0.158935 0.158935i
\(393\) 0 0
\(394\) 1204.05i 3.05598i
\(395\) 181.272 276.445i 0.458917 0.699861i
\(396\) 0 0
\(397\) −171.665 + 171.665i −0.432406 + 0.432406i −0.889446 0.457040i \(-0.848910\pi\)
0.457040 + 0.889446i \(0.348910\pi\)
\(398\) 40.4942 + 40.4942i 0.101744 + 0.101744i
\(399\) 0 0
\(400\) −122.495 281.823i −0.306237 0.704558i
\(401\) −686.098 −1.71097 −0.855484 0.517829i \(-0.826740\pi\)
−0.855484 + 0.517829i \(0.826740\pi\)
\(402\) 0 0
\(403\) −120.318 120.318i −0.298555 0.298555i
\(404\) 1118.90i 2.76956i
\(405\) 0 0
\(406\) 358.375 0.882697
\(407\) −663.950 + 663.950i −1.63133 + 1.63133i
\(408\) 0 0
\(409\) 556.252i 1.36003i 0.733198 + 0.680015i \(0.238027\pi\)
−0.733198 + 0.680015i \(0.761973\pi\)
\(410\) −1162.07 + 241.629i −2.83432 + 0.589339i
\(411\) 0 0
\(412\) 478.277 478.277i 1.16087 1.16087i
\(413\) −55.0499 55.0499i −0.133293 0.133293i
\(414\) 0 0
\(415\) −120.449 579.277i −0.290238 1.39585i
\(416\) 110.133 0.264744
\(417\) 0 0
\(418\) −756.331 756.331i −1.80940 1.80940i
\(419\) 143.631i 0.342794i 0.985202 + 0.171397i \(0.0548280\pi\)
−0.985202 + 0.171397i \(0.945172\pi\)
\(420\) 0 0
\(421\) 110.369 0.262159 0.131080 0.991372i \(-0.458156\pi\)
0.131080 + 0.991372i \(0.458156\pi\)
\(422\) −186.166 + 186.166i −0.441152 + 0.441152i
\(423\) 0 0
\(424\) 863.893i 2.03748i
\(425\) −233.171 91.8851i −0.548638 0.216200i
\(426\) 0 0
\(427\) −13.2697 + 13.2697i −0.0310766 + 0.0310766i
\(428\) −31.9449 31.9449i −0.0746376 0.0746376i
\(429\) 0 0
\(430\) 90.3193 + 59.2247i 0.210045 + 0.137732i
\(431\) −439.840 −1.02051 −0.510255 0.860023i \(-0.670449\pi\)
−0.510255 + 0.860023i \(0.670449\pi\)
\(432\) 0 0
\(433\) −118.543 118.543i −0.273770 0.273770i 0.556846 0.830616i \(-0.312011\pi\)
−0.830616 + 0.556846i \(0.812011\pi\)
\(434\) 116.453i 0.268326i
\(435\) 0 0
\(436\) −604.118 −1.38559
\(437\) 193.898 193.898i 0.443702 0.443702i
\(438\) 0 0
\(439\) 351.519i 0.800727i −0.916356 0.400363i \(-0.868884\pi\)
0.916356 0.400363i \(-0.131116\pi\)
\(440\) −268.171 1289.72i −0.609480 2.93118i
\(441\) 0 0
\(442\) −320.144 + 320.144i −0.724307 + 0.724307i
\(443\) 41.1332 + 41.1332i 0.0928514 + 0.0928514i 0.752007 0.659155i \(-0.229086\pi\)
−0.659155 + 0.752007i \(0.729086\pi\)
\(444\) 0 0
\(445\) 172.041 262.368i 0.386610 0.589590i
\(446\) 213.470 0.478633
\(447\) 0 0
\(448\) 145.281 + 145.281i 0.324288 + 0.324288i
\(449\) 209.909i 0.467503i 0.972296 + 0.233751i \(0.0751002\pi\)
−0.972296 + 0.233751i \(0.924900\pi\)
\(450\) 0 0
\(451\) −1453.71 −3.22331
\(452\) 824.671 824.671i 1.82449 1.82449i
\(453\) 0 0
\(454\) 853.157i 1.87920i
\(455\) −146.172 95.8489i −0.321258 0.210657i
\(456\) 0 0
\(457\) −156.842 + 156.842i −0.343199 + 0.343199i −0.857568 0.514370i \(-0.828026\pi\)
0.514370 + 0.857568i \(0.328026\pi\)
\(458\) 717.192 + 717.192i 1.56592 + 1.56592i
\(459\) 0 0
\(460\) 689.781 143.426i 1.49952 0.311795i
\(461\) −274.147 −0.594680 −0.297340 0.954772i \(-0.596099\pi\)
−0.297340 + 0.954772i \(0.596099\pi\)
\(462\) 0 0
\(463\) 483.190 + 483.190i 1.04361 + 1.04361i 0.999005 + 0.0446032i \(0.0142023\pi\)
0.0446032 + 0.999005i \(0.485798\pi\)
\(464\) 487.116i 1.04982i
\(465\) 0 0
\(466\) −426.168 −0.914524
\(467\) −8.70901 + 8.70901i −0.0186489 + 0.0186489i −0.716370 0.697721i \(-0.754198\pi\)
0.697721 + 0.716370i \(0.254198\pi\)
\(468\) 0 0
\(469\) 5.23085i 0.0111532i
\(470\) 58.4513 89.1399i 0.124365 0.189659i
\(471\) 0 0
\(472\) −261.896 + 261.896i −0.554865 + 0.554865i
\(473\) 93.5374 + 93.5374i 0.197754 + 0.197754i
\(474\) 0 0
\(475\) −342.788 + 148.993i −0.721659 + 0.313670i
\(476\) −203.768 −0.428084
\(477\) 0 0
\(478\) 895.015 + 895.015i 1.87242 + 1.87242i
\(479\) 806.280i 1.68326i 0.540056 + 0.841629i \(0.318403\pi\)
−0.540056 + 0.841629i \(0.681597\pi\)
\(480\) 0 0
\(481\) 592.742 1.23231
\(482\) 488.965 488.965i 1.01445 1.01445i
\(483\) 0 0
\(484\) 2436.27i 5.03362i
\(485\) 591.602 123.012i 1.21980 0.253632i
\(486\) 0 0
\(487\) −153.496 + 153.496i −0.315186 + 0.315186i −0.846915 0.531729i \(-0.821543\pi\)
0.531729 + 0.846915i \(0.321543\pi\)
\(488\) 63.1297 + 63.1297i 0.129364 + 0.129364i
\(489\) 0 0
\(490\) −24.3536 117.124i −0.0497012 0.239029i
\(491\) 180.954 0.368543 0.184271 0.982875i \(-0.441007\pi\)
0.184271 + 0.982875i \(0.441007\pi\)
\(492\) 0 0
\(493\) −280.921 280.921i −0.569820 0.569820i
\(494\) 675.215i 1.36683i
\(495\) 0 0
\(496\) −158.288 −0.319128
\(497\) −29.8279 + 29.8279i −0.0600159 + 0.0600159i
\(498\) 0 0
\(499\) 13.9603i 0.0279765i −0.999902 0.0139883i \(-0.995547\pi\)
0.999902 0.0139883i \(-0.00445275\pi\)
\(500\) −946.419 162.823i −1.89284 0.325645i
\(501\) 0 0
\(502\) −867.441 + 867.441i −1.72797 + 1.72797i
\(503\) −358.510 358.510i −0.712743 0.712743i 0.254365 0.967108i \(-0.418134\pi\)
−0.967108 + 0.254365i \(0.918134\pi\)
\(504\) 0 0
\(505\) 608.962 + 399.312i 1.20587 + 0.790717i
\(506\) 1312.17 2.59322
\(507\) 0 0
\(508\) 896.183 + 896.183i 1.76414 + 1.76414i
\(509\) 446.506i 0.877223i −0.898677 0.438611i \(-0.855470\pi\)
0.898677 0.438611i \(-0.144530\pi\)
\(510\) 0 0
\(511\) −121.290 −0.237357
\(512\) 510.047 510.047i 0.996186 0.996186i
\(513\) 0 0
\(514\) 763.472i 1.48535i
\(515\) −89.6153 430.989i −0.174010 0.836871i
\(516\) 0 0
\(517\) 92.3160 92.3160i 0.178561 0.178561i
\(518\) 286.853 + 286.853i 0.553770 + 0.553770i
\(519\) 0 0
\(520\) −455.995 + 695.405i −0.876913 + 1.33732i
\(521\) 682.112 1.30924 0.654618 0.755960i \(-0.272829\pi\)
0.654618 + 0.755960i \(0.272829\pi\)
\(522\) 0 0
\(523\) −252.224 252.224i −0.482263 0.482263i 0.423591 0.905854i \(-0.360769\pi\)
−0.905854 + 0.423591i \(0.860769\pi\)
\(524\) 1074.18i 2.04996i
\(525\) 0 0
\(526\) 47.3615 0.0900410
\(527\) −91.2849 + 91.2849i −0.173216 + 0.173216i
\(528\) 0 0
\(529\) 192.604i 0.364091i
\(530\) 980.874 + 643.184i 1.85071 + 1.21356i
\(531\) 0 0
\(532\) −214.884 + 214.884i −0.403917 + 0.403917i
\(533\) 648.902 + 648.902i 1.21745 + 1.21745i
\(534\) 0 0
\(535\) −28.7864 + 5.98555i −0.0538064 + 0.0111879i
\(536\) −24.8854 −0.0464280
\(537\) 0 0
\(538\) 346.832 + 346.832i 0.644669 + 0.644669i
\(539\) 146.519i 0.271834i
\(540\) 0 0
\(541\) 225.356 0.416554 0.208277 0.978070i \(-0.433214\pi\)
0.208277 + 0.978070i \(0.433214\pi\)
\(542\) 71.2330 71.2330i 0.131426 0.131426i
\(543\) 0 0
\(544\) 83.5582i 0.153600i
\(545\) −215.597 + 328.791i −0.395590 + 0.603286i
\(546\) 0 0
\(547\) 211.802 211.802i 0.387207 0.387207i −0.486483 0.873690i \(-0.661720\pi\)
0.873690 + 0.486483i \(0.161720\pi\)
\(548\) −1237.81 1237.81i −2.25878 2.25878i
\(549\) 0 0
\(550\) −1664.02 655.736i −3.02549 1.19225i
\(551\) −592.491 −1.07530
\(552\) 0 0
\(553\) −123.691 123.691i −0.223672 0.223672i
\(554\) 917.575i 1.65627i
\(555\) 0 0
\(556\) 1545.19 2.77912
\(557\) 74.4003 74.4003i 0.133573 0.133573i −0.637159 0.770732i \(-0.719891\pi\)
0.770732 + 0.637159i \(0.219891\pi\)
\(558\) 0 0
\(559\) 83.5057i 0.149384i
\(560\) −159.199 + 33.1022i −0.284284 + 0.0591111i
\(561\) 0 0
\(562\) −148.034 + 148.034i −0.263406 + 0.263406i
\(563\) 340.172 + 340.172i 0.604214 + 0.604214i 0.941428 0.337214i \(-0.109485\pi\)
−0.337214 + 0.941428i \(0.609485\pi\)
\(564\) 0 0
\(565\) −154.520 743.135i −0.273486 1.31528i
\(566\) 852.747 1.50662
\(567\) 0 0
\(568\) 141.904 + 141.904i 0.249831 + 0.249831i
\(569\) 672.360i 1.18165i 0.806799 + 0.590826i \(0.201198\pi\)
−0.806799 + 0.590826i \(0.798802\pi\)
\(570\) 0 0
\(571\) 613.562 1.07454 0.537269 0.843411i \(-0.319456\pi\)
0.537269 + 0.843411i \(0.319456\pi\)
\(572\) −1502.44 + 1502.44i −2.62664 + 2.62664i
\(573\) 0 0
\(574\) 628.062i 1.09418i
\(575\) 168.109 426.599i 0.292363 0.741911i
\(576\) 0 0
\(577\) −81.3337 + 81.3337i −0.140960 + 0.140960i −0.774065 0.633106i \(-0.781780\pi\)
0.633106 + 0.774065i \(0.281780\pi\)
\(578\) −455.584 455.584i −0.788208 0.788208i
\(579\) 0 0
\(580\) −1273.01 834.746i −2.19485 1.43922i
\(581\) −313.081 −0.538865
\(582\) 0 0
\(583\) 1015.82 + 1015.82i 1.74241 + 1.74241i
\(584\) 577.028i 0.988061i
\(585\) 0 0
\(586\) −448.289 −0.764999
\(587\) −819.321 + 819.321i −1.39578 + 1.39578i −0.584082 + 0.811694i \(0.698546\pi\)
−0.811694 + 0.584082i \(0.801454\pi\)
\(588\) 0 0
\(589\) 192.529i 0.326874i
\(590\) 102.373 + 492.347i 0.173514 + 0.834486i
\(591\) 0 0
\(592\) 389.900 389.900i 0.658615 0.658615i
\(593\) 308.110 + 308.110i 0.519578 + 0.519578i 0.917444 0.397865i \(-0.130249\pi\)
−0.397865 + 0.917444i \(0.630249\pi\)
\(594\) 0 0
\(595\) −72.7205 + 110.901i −0.122219 + 0.186388i
\(596\) 178.521 0.299532
\(597\) 0 0
\(598\) −585.720 585.720i −0.979464 0.979464i
\(599\) 458.753i 0.765864i 0.923776 + 0.382932i \(0.125086\pi\)
−0.923776 + 0.382932i \(0.874914\pi\)
\(600\) 0 0
\(601\) 829.765 1.38064 0.690320 0.723504i \(-0.257470\pi\)
0.690320 + 0.723504i \(0.257470\pi\)
\(602\) 40.4119 40.4119i 0.0671294 0.0671294i
\(603\) 0 0
\(604\) 302.322i 0.500534i
\(605\) −1325.94 869.454i −2.19164 1.43711i
\(606\) 0 0
\(607\) −249.775 + 249.775i −0.411490 + 0.411490i −0.882258 0.470767i \(-0.843977\pi\)
0.470767 + 0.882258i \(0.343977\pi\)
\(608\) −88.1163 88.1163i −0.144928 0.144928i
\(609\) 0 0
\(610\) 118.679 24.6769i 0.194556 0.0404540i
\(611\) −82.4152 −0.134886
\(612\) 0 0
\(613\) 90.9769 + 90.9769i 0.148413 + 0.148413i 0.777409 0.628996i \(-0.216534\pi\)
−0.628996 + 0.777409i \(0.716534\pi\)
\(614\) 1106.29i 1.80177i
\(615\) 0 0
\(616\) −697.053 −1.13158
\(617\) 445.593 445.593i 0.722193 0.722193i −0.246858 0.969052i \(-0.579398\pi\)
0.969052 + 0.246858i \(0.0793983\pi\)
\(618\) 0 0
\(619\) 943.969i 1.52499i −0.646994 0.762495i \(-0.723974\pi\)
0.646994 0.762495i \(-0.276026\pi\)
\(620\) −271.249 + 413.663i −0.437499 + 0.667198i
\(621\) 0 0
\(622\) 703.595 703.595i 1.13118 1.13118i
\(623\) −117.392 117.392i −0.188430 0.188430i
\(624\) 0 0
\(625\) −426.373 + 456.980i −0.682197 + 0.731169i
\(626\) −1216.50 −1.94329
\(627\) 0 0
\(628\) −393.058 393.058i −0.625889 0.625889i
\(629\) 449.713i 0.714965i
\(630\) 0 0
\(631\) −1001.49 −1.58714 −0.793570 0.608478i \(-0.791780\pi\)
−0.793570 + 0.608478i \(0.791780\pi\)
\(632\) −588.451 + 588.451i −0.931093 + 0.931093i
\(633\) 0 0
\(634\) 146.985i 0.231837i
\(635\) 807.576 167.919i 1.27177 0.264439i
\(636\) 0 0
\(637\) −65.4023 + 65.4023i −0.102672 + 0.102672i
\(638\) −2004.79 2004.79i −3.14230 3.14230i
\(639\) 0 0
\(640\) −236.235 1136.13i −0.369118 1.77521i
\(641\) 878.051 1.36981 0.684907 0.728630i \(-0.259843\pi\)
0.684907 + 0.728630i \(0.259843\pi\)
\(642\) 0 0
\(643\) −551.380 551.380i −0.857511 0.857511i 0.133533 0.991044i \(-0.457368\pi\)
−0.991044 + 0.133533i \(0.957368\pi\)
\(644\) 372.805i 0.578889i
\(645\) 0 0
\(646\) 512.286 0.793012
\(647\) −315.391 + 315.391i −0.487466 + 0.487466i −0.907506 0.420039i \(-0.862016\pi\)
0.420039 + 0.907506i \(0.362016\pi\)
\(648\) 0 0
\(649\) 615.911i 0.949015i
\(650\) 450.074 + 1035.48i 0.692421 + 1.59305i
\(651\) 0 0
\(652\) −309.457 + 309.457i −0.474628 + 0.474628i
\(653\) 825.176 + 825.176i 1.26367 + 1.26367i 0.949301 + 0.314368i \(0.101793\pi\)
0.314368 + 0.949301i \(0.398207\pi\)
\(654\) 0 0
\(655\) 584.621 + 383.351i 0.892552 + 0.585269i
\(656\) 853.684 1.30135
\(657\) 0 0
\(658\) −39.8842 39.8842i −0.0606143 0.0606143i
\(659\) 956.471i 1.45140i −0.688012 0.725699i \(-0.741517\pi\)
0.688012 0.725699i \(-0.258483\pi\)
\(660\) 0 0
\(661\) 18.2815 0.0276573 0.0138286 0.999904i \(-0.495598\pi\)
0.0138286 + 0.999904i \(0.495598\pi\)
\(662\) 1452.30 1452.30i 2.19380 2.19380i
\(663\) 0 0
\(664\) 1489.46i 2.24316i
\(665\) 40.2631 + 193.638i 0.0605460 + 0.291185i
\(666\) 0 0
\(667\) 513.960 513.960i 0.770555 0.770555i
\(668\) −514.713 514.713i −0.770528 0.770528i
\(669\) 0 0
\(670\) −18.5276 + 28.2552i −0.0276532 + 0.0421719i
\(671\) 148.464 0.221258
\(672\) 0 0
\(673\) −829.059 829.059i −1.23189 1.23189i −0.963239 0.268647i \(-0.913424\pi\)
−0.268647 0.963239i \(-0.586576\pi\)
\(674\) 88.8173i 0.131776i
\(675\) 0 0
\(676\) 42.9491 0.0635342
\(677\) 421.712 421.712i 0.622913 0.622913i −0.323362 0.946275i \(-0.604813\pi\)
0.946275 + 0.323362i \(0.104813\pi\)
\(678\) 0 0
\(679\) 319.742i 0.470901i
\(680\) 527.603 + 345.963i 0.775887 + 0.508769i
\(681\) 0 0
\(682\) −651.453 + 651.453i −0.955209 + 0.955209i
\(683\) 40.2821 + 40.2821i 0.0589782 + 0.0589782i 0.735981 0.677003i \(-0.236721\pi\)
−0.677003 + 0.735981i \(0.736721\pi\)
\(684\) 0 0
\(685\) −1115.43 + 231.931i −1.62836 + 0.338585i
\(686\) −63.3019 −0.0922768
\(687\) 0 0
\(688\) −54.9293 54.9293i −0.0798390 0.0798390i
\(689\) 906.877i 1.31622i
\(690\) 0 0
\(691\) 499.429 0.722763 0.361381 0.932418i \(-0.382305\pi\)
0.361381 + 0.932418i \(0.382305\pi\)
\(692\) −1704.33 + 1704.33i −2.46290 + 2.46290i
\(693\) 0 0
\(694\) 1325.67i 1.91018i
\(695\) 551.445 840.969i 0.793446 1.21003i
\(696\) 0 0
\(697\) 492.322 492.322i 0.706344 0.706344i
\(698\) −529.285 529.285i −0.758287 0.758287i
\(699\) 0 0
\(700\) −186.304 + 472.771i −0.266148 + 0.675387i
\(701\) −29.9935 −0.0427867 −0.0213934 0.999771i \(-0.506810\pi\)
−0.0213934 + 0.999771i \(0.506810\pi\)
\(702\) 0 0
\(703\) −474.245 474.245i −0.674602 0.674602i
\(704\) 1625.44i 2.30886i
\(705\) 0 0
\(706\) 372.401 0.527480
\(707\) 272.470 272.470i 0.385389 0.385389i
\(708\) 0 0
\(709\) 983.508i 1.38718i 0.720372 + 0.693588i \(0.243971\pi\)
−0.720372 + 0.693588i \(0.756029\pi\)
\(710\) 266.770 55.4694i 0.375732 0.0781259i
\(711\) 0 0
\(712\) −558.485 + 558.485i −0.784389 + 0.784389i
\(713\) −167.011 167.011i −0.234236 0.234236i
\(714\) 0 0
\(715\) 281.514 + 1353.89i 0.393726 + 1.89356i
\(716\) 992.644 1.38637
\(717\) 0 0
\(718\) −1287.50 1287.50i −1.79318 1.79318i
\(719\) 59.3020i 0.0824784i 0.999149 + 0.0412392i \(0.0131306\pi\)
−0.999149 + 0.0412392i \(0.986869\pi\)
\(720\) 0 0
\(721\) −232.936 −0.323073
\(722\) −332.261 + 332.261i −0.460196 + 0.460196i
\(723\) 0 0
\(724\) 221.566i 0.306030i
\(725\) −908.621 + 394.933i −1.25327 + 0.544735i
\(726\) 0 0
\(727\) −25.0937 + 25.0937i −0.0345168 + 0.0345168i −0.724155 0.689638i \(-0.757770\pi\)
0.689638 + 0.724155i \(0.257770\pi\)
\(728\) 311.147 + 311.147i 0.427400 + 0.427400i
\(729\) 0 0
\(730\) 655.164 + 429.608i 0.897485 + 0.588504i
\(731\) −63.3557 −0.0866699
\(732\) 0 0
\(733\) 611.839 + 611.839i 0.834706 + 0.834706i 0.988156 0.153451i \(-0.0490386\pi\)
−0.153451 + 0.988156i \(0.549039\pi\)
\(734\) 1776.20i 2.41990i
\(735\) 0 0
\(736\) 152.874 0.207709
\(737\) −29.2619 + 29.2619i −0.0397041 + 0.0397041i
\(738\) 0 0
\(739\) 566.278i 0.766277i −0.923691 0.383138i \(-0.874843\pi\)
0.923691 0.383138i \(-0.125157\pi\)
\(740\) −350.799 1687.10i −0.474052 2.27987i
\(741\) 0 0
\(742\) 438.876 438.876i 0.591477 0.591477i
\(743\) −65.5539 65.5539i −0.0882287 0.0882287i 0.661615 0.749844i \(-0.269871\pi\)
−0.749844 + 0.661615i \(0.769871\pi\)
\(744\) 0 0
\(745\) 63.7103 97.1600i 0.0855172 0.130416i
\(746\) −145.845 −0.195503
\(747\) 0 0
\(748\) 1139.90 + 1139.90i 1.52393 + 1.52393i
\(749\) 15.5582i 0.0207719i
\(750\) 0 0
\(751\) −99.3347 −0.132270 −0.0661350 0.997811i \(-0.521067\pi\)
−0.0661350 + 0.997811i \(0.521067\pi\)
\(752\) −54.2120 + 54.2120i −0.0720904 + 0.0720904i
\(753\) 0 0
\(754\) 1789.78i 2.37371i
\(755\) 164.539 + 107.892i 0.217932 + 0.142904i
\(756\) 0 0
\(757\) 605.866 605.866i 0.800351 0.800351i −0.182799 0.983150i \(-0.558516\pi\)
0.983150 + 0.182799i \(0.0585159\pi\)
\(758\) 616.058 + 616.058i 0.812741 + 0.812741i
\(759\) 0 0
\(760\) 921.220 191.549i 1.21213 0.252038i
\(761\) −126.096 −0.165698 −0.0828489 0.996562i \(-0.526402\pi\)
−0.0828489 + 0.996562i \(0.526402\pi\)
\(762\) 0 0
\(763\) 147.112 + 147.112i 0.192807 + 0.192807i
\(764\) 229.879i 0.300889i
\(765\) 0 0
\(766\) 506.273 0.660931
\(767\) 274.927 274.927i 0.358445 0.358445i
\(768\) 0 0
\(769\) 115.901i 0.150716i −0.997157 0.0753582i \(-0.975990\pi\)
0.997157 0.0753582i \(-0.0240100\pi\)
\(770\) −518.969 + 791.442i −0.673985 + 1.02785i
\(771\) 0 0
\(772\) −326.830 + 326.830i −0.423355 + 0.423355i
\(773\) −325.618 325.618i −0.421240 0.421240i 0.464391 0.885630i \(-0.346273\pi\)
−0.885630 + 0.464391i \(0.846273\pi\)
\(774\) 0 0
\(775\) 128.333 + 295.255i 0.165591 + 0.380974i
\(776\) −1521.15 −1.96025
\(777\) 0 0
\(778\) 1612.15 + 1612.15i 2.07217 + 2.07217i
\(779\) 1038.36i 1.33294i
\(780\) 0 0
\(781\) 333.721 0.427299
\(782\) −444.385 + 444.385i −0.568268 + 0.568268i
\(783\) 0 0
\(784\) 86.0421i 0.109748i
\(785\) −354.196 + 73.6478i −0.451205 + 0.0938189i
\(786\) 0 0
\(787\) −140.660 + 140.660i −0.178730 + 0.178730i −0.790802 0.612072i \(-0.790336\pi\)
0.612072 + 0.790802i \(0.290336\pi\)
\(788\) 1913.68 + 1913.68i 2.42852 + 2.42852i
\(789\) 0 0
\(790\) 230.021 + 1106.25i 0.291166 + 1.40031i
\(791\) −401.641 −0.507763
\(792\) 0 0
\(793\) −66.2708 66.2708i −0.0835697 0.0835697i
\(794\) 829.788i 1.04507i
\(795\) 0 0
\(796\) −128.720 −0.161709
\(797\) 533.305 533.305i 0.669141 0.669141i −0.288376 0.957517i \(-0.593115\pi\)
0.957517 + 0.288376i \(0.0931154\pi\)
\(798\) 0 0
\(799\) 62.5284i 0.0782584i
\(800\) −193.867 76.3966i −0.242334 0.0954957i
\(801\) 0 0
\(802\) 1658.21 1658.21i 2.06760 2.06760i
\(803\) 678.507 + 678.507i 0.844966 + 0.844966i
\(804\) 0 0
\(805\) −202.899 133.046i −0.252048 0.165275i
\(806\) 581.585 0.721570
\(807\) 0 0
\(808\) −1296.26 1296.26i −1.60428 1.60428i
\(809\) 651.161i 0.804896i 0.915443 + 0.402448i \(0.131841\pi\)
−0.915443 + 0.402448i \(0.868159\pi\)
\(810\) 0 0
\(811\) 94.9703 0.117103 0.0585513 0.998284i \(-0.481352\pi\)
0.0585513 + 0.998284i \(0.481352\pi\)
\(812\) −569.587 + 569.587i −0.701462 + 0.701462i
\(813\) 0 0
\(814\) 3209.37i 3.94271i
\(815\) 57.9834 + 278.861i 0.0711453 + 0.342160i
\(816\) 0 0
\(817\) −66.8118 + 66.8118i −0.0817770 + 0.0817770i
\(818\) −1344.39 1344.39i −1.64351 1.64351i
\(819\) 0 0
\(820\) 1462.91 2230.99i 1.78404 2.72071i
\(821\) 368.589 0.448952 0.224476 0.974480i \(-0.427933\pi\)
0.224476 + 0.974480i \(0.427933\pi\)
\(822\) 0 0
\(823\) 494.462 + 494.462i 0.600804 + 0.600804i 0.940526 0.339722i \(-0.110333\pi\)
−0.339722 + 0.940526i \(0.610333\pi\)
\(824\) 1108.18i 1.34487i
\(825\) 0 0
\(826\) 266.098 0.322152
\(827\) 191.666 191.666i 0.231761 0.231761i −0.581666 0.813427i \(-0.697599\pi\)
0.813427 + 0.581666i \(0.197599\pi\)
\(828\) 0 0
\(829\) 110.729i 0.133569i −0.997767 0.0667847i \(-0.978726\pi\)
0.997767 0.0667847i \(-0.0212741\pi\)
\(830\) 1691.15 + 1108.93i 2.03753 + 1.33606i
\(831\) 0 0
\(832\) −725.555 + 725.555i −0.872061 + 0.872061i
\(833\) 49.6207 + 49.6207i 0.0595687 + 0.0595687i
\(834\) 0 0
\(835\) −463.823 + 96.4424i −0.555476 + 0.115500i
\(836\) 2404.17 2.87580
\(837\) 0 0
\(838\) −347.137 347.137i −0.414245 0.414245i
\(839\) 184.793i 0.220254i 0.993918 + 0.110127i \(0.0351258\pi\)
−0.993918 + 0.110127i \(0.964874\pi\)
\(840\) 0 0
\(841\) −729.502 −0.867422
\(842\) −266.748 + 266.748i −0.316803 + 0.316803i
\(843\) 0 0
\(844\) 591.771i 0.701150i
\(845\) 15.3276 23.3750i 0.0181392 0.0276628i
\(846\) 0 0
\(847\) −593.271 + 593.271i −0.700438 + 0.700438i
\(848\) −596.535 596.535i −0.703462 0.703462i
\(849\) 0 0
\(850\) 785.621 341.471i 0.924260 0.401731i
\(851\) 822.774 0.966832
\(852\) 0 0
\(853\) 3.11065 + 3.11065i 0.00364672 + 0.00364672i 0.708928 0.705281i \(-0.249179\pi\)
−0.705281 + 0.708928i \(0.749179\pi\)
\(854\) 64.1424i 0.0751082i
\(855\) 0 0
\(856\) 74.0169 0.0864683
\(857\) −141.310 + 141.310i −0.164889 + 0.164889i −0.784729 0.619840i \(-0.787198\pi\)
0.619840 + 0.784729i \(0.287198\pi\)
\(858\) 0 0
\(859\) 1054.78i 1.22792i −0.789338 0.613959i \(-0.789576\pi\)
0.789338 0.613959i \(-0.210424\pi\)
\(860\) −237.680 + 49.4206i −0.276372 + 0.0574658i
\(861\) 0 0
\(862\) 1063.04 1063.04i 1.23322 1.23322i
\(863\) 227.600 + 227.600i 0.263732 + 0.263732i 0.826568 0.562837i \(-0.190290\pi\)
−0.562837 + 0.826568i \(0.690290\pi\)
\(864\) 0 0
\(865\) 319.342 + 1535.82i 0.369181 + 1.77551i
\(866\) 573.005 0.661669
\(867\) 0 0
\(868\) 185.087 + 185.087i 0.213233 + 0.213233i
\(869\) 1383.88i 1.59250i
\(870\) 0 0
\(871\) 26.1236 0.0299927
\(872\) 699.876 699.876i 0.802610 0.802610i
\(873\) 0 0
\(874\) 937.254i 1.07237i
\(875\) 190.818 + 270.118i 0.218078 + 0.308706i
\(876\) 0 0
\(877\) −71.4976 + 71.4976i −0.0815252 + 0.0815252i −0.746693 0.665168i \(-0.768360\pi\)
0.665168 + 0.746693i \(0.268360\pi\)
\(878\) 849.578 + 849.578i 0.967629 + 0.967629i
\(879\) 0 0
\(880\) 1075.76 + 705.400i 1.22245 + 0.801591i
\(881\) −932.073 −1.05797 −0.528986 0.848631i \(-0.677428\pi\)
−0.528986 + 0.848631i \(0.677428\pi\)
\(882\) 0 0
\(883\) −616.640 616.640i −0.698346 0.698346i 0.265708 0.964054i \(-0.414394\pi\)
−0.964054 + 0.265708i \(0.914394\pi\)
\(884\) 1017.65i 1.15119i
\(885\) 0 0
\(886\) −198.828 −0.224410
\(887\) 990.320 990.320i 1.11648 1.11648i 0.124229 0.992254i \(-0.460354\pi\)
0.992254 0.124229i \(-0.0396459\pi\)
\(888\) 0 0
\(889\) 436.469i 0.490966i
\(890\) 218.308 + 1049.91i 0.245290 + 1.17968i
\(891\) 0 0
\(892\) −339.282 + 339.282i −0.380361 + 0.380361i
\(893\) 65.9394 + 65.9394i 0.0738403 + 0.0738403i
\(894\) 0 0
\(895\) 354.253 540.246i 0.395814 0.603627i
\(896\) −614.043 −0.685316
\(897\) 0 0
\(898\) −507.323 507.323i −0.564948 0.564948i
\(899\) 510.332i 0.567666i
\(900\) 0 0
\(901\) −688.047 −0.763649
\(902\) 3513.45 3513.45i 3.89517 3.89517i
\(903\) 0 0
\(904\) 1910.78i 2.11369i
\(905\) −120.587 79.0721i −0.133245 0.0873725i
\(906\) 0 0
\(907\) −449.584 + 449.584i −0.495682 + 0.495682i −0.910091 0.414409i \(-0.863988\pi\)
0.414409 + 0.910091i \(0.363988\pi\)
\(908\) −1355.98 1355.98i −1.49336 1.49336i
\(909\) 0 0
\(910\) 584.935 121.625i 0.642786 0.133654i
\(911\) −1065.29 −1.16936 −0.584680 0.811264i \(-0.698780\pi\)
−0.584680 + 0.811264i \(0.698780\pi\)
\(912\) 0 0
\(913\) 1751.41 + 1751.41i 1.91830 + 1.91830i
\(914\) 758.134i 0.829468i
\(915\) 0 0
\(916\) −2279.75 −2.48881
\(917\) 261.579 261.579i 0.285255 0.285255i
\(918\) 0 0
\(919\) 1080.05i 1.17525i −0.809135 0.587623i \(-0.800064\pi\)
0.809135 0.587623i \(-0.199936\pi\)
\(920\) −632.958 + 965.278i −0.687998 + 1.04922i
\(921\) 0 0
\(922\) 662.580 662.580i 0.718634 0.718634i
\(923\) −148.965 148.965i −0.161392 0.161392i
\(924\) 0 0
\(925\) −1043.40 411.169i −1.12800 0.444507i
\(926\) −2335.62 −2.52227
\(927\) 0 0
\(928\) −233.568 233.568i −0.251690 0.251690i
\(929\) 1513.19i 1.62884i 0.580278 + 0.814419i \(0.302944\pi\)
−0.580278 + 0.814419i \(0.697056\pi\)
\(930\) 0 0
\(931\) 104.655 0.112412
\(932\) 677.335 677.335i 0.726755 0.726755i
\(933\) 0 0
\(934\) 42.0972i 0.0450720i
\(935\) 1027.20 213.585i 1.09861 0.228433i
\(936\) 0 0
\(937\) 754.545 754.545i 0.805278 0.805278i −0.178637 0.983915i \(-0.557169\pi\)
0.983915 + 0.178637i \(0.0571688\pi\)
\(938\) 12.6423 + 12.6423i 0.0134779 + 0.0134779i
\(939\) 0 0
\(940\) 48.7753 + 234.576i 0.0518886 + 0.249549i
\(941\) −1377.61 −1.46399 −0.731993 0.681312i \(-0.761410\pi\)
−0.731993 + 0.681312i \(0.761410\pi\)
\(942\) 0 0
\(943\) 900.729 + 900.729i 0.955174 + 0.955174i
\(944\) 361.690i 0.383146i
\(945\) 0 0
\(946\) −452.137 −0.477946
\(947\) −133.593 + 133.593i −0.141070 + 0.141070i −0.774115 0.633045i \(-0.781805\pi\)
0.633045 + 0.774115i \(0.281805\pi\)
\(948\) 0 0
\(949\) 605.738i 0.638291i
\(950\) 468.378 1188.58i 0.493030 1.25113i
\(951\) 0 0
\(952\) 236.067 236.067i 0.247970 0.247970i
\(953\) 498.927 + 498.927i 0.523533 + 0.523533i 0.918636 0.395104i \(-0.129291\pi\)
−0.395104 + 0.918636i \(0.629291\pi\)
\(954\) 0 0
\(955\) 125.112 + 82.0390i 0.131007 + 0.0859047i
\(956\) −2845.01 −2.97595
\(957\) 0 0
\(958\) −1948.68 1948.68i −2.03411 2.03411i
\(959\) 602.854i 0.628627i
\(960\) 0 0
\(961\) −795.168 −0.827438
\(962\) −1432.58 + 1432.58i −1.48917 + 1.48917i
\(963\) 0 0
\(964\) 1554.28i 1.61233i
\(965\) 61.2386 + 294.516i 0.0634597 + 0.305198i
\(966\) 0 0
\(967\) 506.991 506.991i 0.524293 0.524293i −0.394572 0.918865i \(-0.629107\pi\)
0.918865 + 0.394572i \(0.129107\pi\)
\(968\) 2822.45 + 2822.45i 2.91575 + 2.91575i
\(969\) 0 0
\(970\) −1132.53 + 1727.13i −1.16755 + 1.78055i
\(971\) 74.6256 0.0768543 0.0384272 0.999261i \(-0.487765\pi\)
0.0384272 + 0.999261i \(0.487765\pi\)
\(972\) 0 0
\(973\) −376.277 376.277i −0.386719 0.386719i
\(974\) 741.960i 0.761766i
\(975\) 0 0
\(976\) −87.1846 −0.0893285
\(977\) 291.427 291.427i 0.298288 0.298288i −0.542055 0.840343i \(-0.682354\pi\)
0.840343 + 0.542055i \(0.182354\pi\)
\(978\) 0 0
\(979\) 1313.41i 1.34158i
\(980\) 224.859 + 147.446i 0.229448 + 0.150455i
\(981\) 0 0
\(982\) −437.345 + 437.345i −0.445361 + 0.445361i
\(983\) 932.709 + 932.709i 0.948839 + 0.948839i 0.998754 0.0499141i \(-0.0158948\pi\)
−0.0499141 + 0.998754i \(0.515895\pi\)
\(984\) 0 0
\(985\) 1724.47 358.568i 1.75073 0.364029i
\(986\) 1357.90 1.37718
\(987\) 0 0
\(988\) −1073.16 1073.16i −1.08620 1.08620i
\(989\) 115.913i 0.117202i
\(990\) 0 0
\(991\) 294.340 0.297013 0.148507 0.988911i \(-0.452553\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(992\) −75.8975 + 75.8975i −0.0765096 + 0.0765096i
\(993\) 0 0
\(994\) 144.181i 0.145051i
\(995\) −45.9374 + 70.0559i −0.0461683 + 0.0704079i
\(996\) 0 0
\(997\) 678.292 678.292i 0.680333 0.680333i −0.279742 0.960075i \(-0.590249\pi\)
0.960075 + 0.279742i \(0.0902489\pi\)
\(998\) 33.7403 + 33.7403i 0.0338079 + 0.0338079i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 315.3.o.b.253.2 24
3.2 odd 2 105.3.l.a.43.11 yes 24
5.2 odd 4 inner 315.3.o.b.127.2 24
15.2 even 4 105.3.l.a.22.11 24
15.8 even 4 525.3.l.e.232.2 24
15.14 odd 2 525.3.l.e.43.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.l.a.22.11 24 15.2 even 4
105.3.l.a.43.11 yes 24 3.2 odd 2
315.3.o.b.127.2 24 5.2 odd 4 inner
315.3.o.b.253.2 24 1.1 even 1 trivial
525.3.l.e.43.2 24 15.14 odd 2
525.3.l.e.232.2 24 15.8 even 4