Properties

Label 72.4.d.d.37.4
Level $72$
Weight $4$
Character 72.37
Analytic conductor $4.248$
Analytic rank $0$
Dimension $6$
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] = [72,4,Mod(37,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 72.d (of order \(2\), degree \(1\), 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: \(4.24813752041\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.8248384.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 24)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.4
Root \(-0.641412 - 1.89436i\) of defining polynomial
Character \(\chi\) \(=\) 72.37
Dual form 72.4.d.d.37.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25295 + 2.53577i) q^{2} +(-4.86025 - 6.35436i) q^{4} -9.15486i q^{5} +27.4175 q^{7} +(22.2028 - 4.36281i) q^{8} +O(q^{10})\) \(q+(-1.25295 + 2.53577i) q^{2} +(-4.86025 - 6.35436i) q^{4} -9.15486i q^{5} +27.4175 q^{7} +(22.2028 - 4.36281i) q^{8} +(23.2146 + 11.4705i) q^{10} -20.5252i q^{11} +32.0471i q^{13} +(-34.3526 + 69.5243i) q^{14} +(-16.7559 + 61.7676i) q^{16} +111.764 q^{17} -129.764i q^{19} +(-58.1733 + 44.4950i) q^{20} +(52.0471 + 25.7169i) q^{22} -9.16510 q^{23} +41.1885 q^{25} +(-81.2641 - 40.1533i) q^{26} +(-133.256 - 174.220i) q^{28} -41.0606i q^{29} -187.606 q^{31} +(-135.634 - 119.880i) q^{32} +(-140.034 + 283.408i) q^{34} -251.003i q^{35} +114.127i q^{37} +(329.052 + 162.587i) q^{38} +(-39.9409 - 203.264i) q^{40} -282.915 q^{41} -89.3870i q^{43} +(-130.424 + 99.7576i) q^{44} +(11.4834 - 23.2406i) q^{46} +54.6464 q^{47} +408.717 q^{49} +(-51.6070 + 104.445i) q^{50} +(203.639 - 155.757i) q^{52} +726.878i q^{53} -187.905 q^{55} +(608.745 - 119.617i) q^{56} +(104.120 + 51.4467i) q^{58} +216.579i q^{59} +754.222i q^{61} +(235.060 - 475.726i) q^{62} +(473.932 - 193.734i) q^{64} +293.387 q^{65} -379.433i q^{67} +(-543.202 - 710.189i) q^{68} +(636.486 + 314.493i) q^{70} -302.080 q^{71} -504.396 q^{73} +(-289.401 - 142.995i) q^{74} +(-824.568 + 630.686i) q^{76} -562.748i q^{77} +301.780 q^{79} +(565.474 + 153.398i) q^{80} +(354.477 - 717.408i) q^{82} +599.003i q^{83} -1023.18i q^{85} +(226.665 + 111.997i) q^{86} +(-89.5475 - 455.717i) q^{88} +277.528 q^{89} +878.651i q^{91} +(44.5447 + 58.2383i) q^{92} +(-68.4689 + 138.571i) q^{94} -1187.97 q^{95} -765.905 q^{97} +(-512.100 + 1036.41i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8} + 60 q^{10} + 100 q^{14} + 56 q^{16} - 52 q^{17} - 56 q^{20} + 224 q^{22} - 328 q^{23} - 106 q^{25} - 56 q^{26} - 352 q^{28} - 636 q^{31} + 248 q^{32} - 548 q^{34} + 776 q^{38} + 232 q^{40} - 236 q^{41} - 1152 q^{44} + 328 q^{46} + 408 q^{47} + 654 q^{49} - 1970 q^{50} - 368 q^{52} + 1024 q^{55} + 1864 q^{56} + 140 q^{58} + 2108 q^{62} + 832 q^{64} + 1744 q^{65} - 2976 q^{68} + 1352 q^{70} + 1704 q^{71} + 956 q^{73} - 1568 q^{74} - 1744 q^{76} - 44 q^{79} + 2112 q^{80} - 2236 q^{82} + 760 q^{86} + 1856 q^{88} + 220 q^{89} - 1728 q^{92} + 2088 q^{94} - 5104 q^{95} - 2444 q^{97} - 3354 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25295 + 2.53577i −0.442983 + 0.896530i
\(3\) 0 0
\(4\) −4.86025 6.35436i −0.607532 0.794295i
\(5\) 9.15486i 0.818836i −0.912347 0.409418i \(-0.865732\pi\)
0.912347 0.409418i \(-0.134268\pi\)
\(6\) 0 0
\(7\) 27.4175 1.48040 0.740202 0.672385i \(-0.234730\pi\)
0.740202 + 0.672385i \(0.234730\pi\)
\(8\) 22.2028 4.36281i 0.981236 0.192811i
\(9\) 0 0
\(10\) 23.2146 + 11.4705i 0.734111 + 0.362730i
\(11\) 20.5252i 0.562598i −0.959620 0.281299i \(-0.909235\pi\)
0.959620 0.281299i \(-0.0907652\pi\)
\(12\) 0 0
\(13\) 32.0471i 0.683713i 0.939752 + 0.341857i \(0.111056\pi\)
−0.939752 + 0.341857i \(0.888944\pi\)
\(14\) −34.3526 + 69.5243i −0.655794 + 1.32723i
\(15\) 0 0
\(16\) −16.7559 + 61.7676i −0.261810 + 0.965119i
\(17\) 111.764 1.59452 0.797258 0.603639i \(-0.206283\pi\)
0.797258 + 0.603639i \(0.206283\pi\)
\(18\) 0 0
\(19\) 129.764i 1.56684i −0.621494 0.783419i \(-0.713474\pi\)
0.621494 0.783419i \(-0.286526\pi\)
\(20\) −58.1733 + 44.4950i −0.650397 + 0.497469i
\(21\) 0 0
\(22\) 52.0471 + 25.7169i 0.504386 + 0.249221i
\(23\) −9.16510 −0.0830893 −0.0415447 0.999137i \(-0.513228\pi\)
−0.0415447 + 0.999137i \(0.513228\pi\)
\(24\) 0 0
\(25\) 41.1885 0.329508
\(26\) −81.2641 40.1533i −0.612970 0.302874i
\(27\) 0 0
\(28\) −133.256 174.220i −0.899392 1.17588i
\(29\) 41.0606i 0.262923i −0.991321 0.131461i \(-0.958033\pi\)
0.991321 0.131461i \(-0.0419669\pi\)
\(30\) 0 0
\(31\) −187.606 −1.08694 −0.543468 0.839430i \(-0.682889\pi\)
−0.543468 + 0.839430i \(0.682889\pi\)
\(32\) −135.634 119.880i −0.749281 0.662252i
\(33\) 0 0
\(34\) −140.034 + 283.408i −0.706344 + 1.42953i
\(35\) 251.003i 1.21221i
\(36\) 0 0
\(37\) 114.127i 0.507093i 0.967323 + 0.253546i \(0.0815970\pi\)
−0.967323 + 0.253546i \(0.918403\pi\)
\(38\) 329.052 + 162.587i 1.40472 + 0.694083i
\(39\) 0 0
\(40\) −39.9409 203.264i −0.157880 0.803471i
\(41\) −282.915 −1.07766 −0.538828 0.842416i \(-0.681133\pi\)
−0.538828 + 0.842416i \(0.681133\pi\)
\(42\) 0 0
\(43\) 89.3870i 0.317009i −0.987358 0.158505i \(-0.949333\pi\)
0.987358 0.158505i \(-0.0506673\pi\)
\(44\) −130.424 + 99.7576i −0.446869 + 0.341796i
\(45\) 0 0
\(46\) 11.4834 23.2406i 0.0368072 0.0744921i
\(47\) 54.6464 0.169596 0.0847978 0.996398i \(-0.472976\pi\)
0.0847978 + 0.996398i \(0.472976\pi\)
\(48\) 0 0
\(49\) 408.717 1.19159
\(50\) −51.6070 + 104.445i −0.145967 + 0.295414i
\(51\) 0 0
\(52\) 203.639 155.757i 0.543070 0.415378i
\(53\) 726.878i 1.88386i 0.335815 + 0.941928i \(0.390988\pi\)
−0.335815 + 0.941928i \(0.609012\pi\)
\(54\) 0 0
\(55\) −187.905 −0.460675
\(56\) 608.745 119.617i 1.45262 0.285438i
\(57\) 0 0
\(58\) 104.120 + 51.4467i 0.235718 + 0.116470i
\(59\) 216.579i 0.477900i 0.971032 + 0.238950i \(0.0768033\pi\)
−0.971032 + 0.238950i \(0.923197\pi\)
\(60\) 0 0
\(61\) 754.222i 1.58309i 0.611114 + 0.791543i \(0.290722\pi\)
−0.611114 + 0.791543i \(0.709278\pi\)
\(62\) 235.060 475.726i 0.481495 0.974471i
\(63\) 0 0
\(64\) 473.932 193.734i 0.925648 0.378386i
\(65\) 293.387 0.559849
\(66\) 0 0
\(67\) 379.433i 0.691868i −0.938259 0.345934i \(-0.887562\pi\)
0.938259 0.345934i \(-0.112438\pi\)
\(68\) −543.202 710.189i −0.968719 1.26652i
\(69\) 0 0
\(70\) 636.486 + 314.493i 1.08678 + 0.536987i
\(71\) −302.080 −0.504933 −0.252467 0.967606i \(-0.581242\pi\)
−0.252467 + 0.967606i \(0.581242\pi\)
\(72\) 0 0
\(73\) −504.396 −0.808700 −0.404350 0.914604i \(-0.632502\pi\)
−0.404350 + 0.914604i \(0.632502\pi\)
\(74\) −289.401 142.995i −0.454624 0.224634i
\(75\) 0 0
\(76\) −824.568 + 630.686i −1.24453 + 0.951904i
\(77\) 562.748i 0.832872i
\(78\) 0 0
\(79\) 301.780 0.429784 0.214892 0.976638i \(-0.431060\pi\)
0.214892 + 0.976638i \(0.431060\pi\)
\(80\) 565.474 + 153.398i 0.790274 + 0.214380i
\(81\) 0 0
\(82\) 354.477 717.408i 0.477384 0.966151i
\(83\) 599.003i 0.792158i 0.918216 + 0.396079i \(0.129629\pi\)
−0.918216 + 0.396079i \(0.870371\pi\)
\(84\) 0 0
\(85\) 1023.18i 1.30565i
\(86\) 226.665 + 111.997i 0.284208 + 0.140430i
\(87\) 0 0
\(88\) −89.5475 455.717i −0.108475 0.552041i
\(89\) 277.528 0.330538 0.165269 0.986248i \(-0.447151\pi\)
0.165269 + 0.986248i \(0.447151\pi\)
\(90\) 0 0
\(91\) 878.651i 1.01217i
\(92\) 44.5447 + 58.2383i 0.0504794 + 0.0659975i
\(93\) 0 0
\(94\) −68.4689 + 138.571i −0.0751280 + 0.152048i
\(95\) −1187.97 −1.28298
\(96\) 0 0
\(97\) −765.905 −0.801710 −0.400855 0.916141i \(-0.631287\pi\)
−0.400855 + 0.916141i \(0.631287\pi\)
\(98\) −512.100 + 1036.41i −0.527856 + 1.06830i
\(99\) 0 0
\(100\) −200.187 261.727i −0.200187 0.261727i
\(101\) 201.253i 0.198272i −0.995074 0.0991360i \(-0.968392\pi\)
0.995074 0.0991360i \(-0.0316079\pi\)
\(102\) 0 0
\(103\) 682.440 0.652843 0.326421 0.945224i \(-0.394157\pi\)
0.326421 + 0.945224i \(0.394157\pi\)
\(104\) 139.816 + 711.537i 0.131827 + 0.670884i
\(105\) 0 0
\(106\) −1843.20 910.739i −1.68893 0.834517i
\(107\) 457.252i 0.413123i −0.978434 0.206562i \(-0.933773\pi\)
0.978434 0.206562i \(-0.0662274\pi\)
\(108\) 0 0
\(109\) 625.812i 0.549926i 0.961455 + 0.274963i \(0.0886655\pi\)
−0.961455 + 0.274963i \(0.911334\pi\)
\(110\) 235.435 476.484i 0.204071 0.413009i
\(111\) 0 0
\(112\) −459.403 + 1693.51i −0.387585 + 1.42877i
\(113\) −981.151 −0.816805 −0.408402 0.912802i \(-0.633914\pi\)
−0.408402 + 0.912802i \(0.633914\pi\)
\(114\) 0 0
\(115\) 83.9052i 0.0680365i
\(116\) −260.914 + 199.565i −0.208838 + 0.159734i
\(117\) 0 0
\(118\) −549.193 271.361i −0.428452 0.211702i
\(119\) 3064.29 2.36053
\(120\) 0 0
\(121\) 909.717 0.683484
\(122\) −1912.53 944.999i −1.41928 0.701280i
\(123\) 0 0
\(124\) 911.813 + 1192.12i 0.660348 + 0.863349i
\(125\) 1521.43i 1.08865i
\(126\) 0 0
\(127\) −808.055 −0.564593 −0.282296 0.959327i \(-0.591096\pi\)
−0.282296 + 0.959327i \(0.591096\pi\)
\(128\) −102.547 + 1444.52i −0.0708121 + 0.997490i
\(129\) 0 0
\(130\) −367.598 + 743.962i −0.248004 + 0.501921i
\(131\) 1110.85i 0.740884i −0.928856 0.370442i \(-0.879206\pi\)
0.928856 0.370442i \(-0.120794\pi\)
\(132\) 0 0
\(133\) 3557.80i 2.31955i
\(134\) 962.155 + 475.409i 0.620280 + 0.306486i
\(135\) 0 0
\(136\) 2481.48 487.606i 1.56460 0.307440i
\(137\) 466.765 0.291084 0.145542 0.989352i \(-0.453507\pi\)
0.145542 + 0.989352i \(0.453507\pi\)
\(138\) 0 0
\(139\) 351.773i 0.214654i 0.994224 + 0.107327i \(0.0342292\pi\)
−0.994224 + 0.107327i \(0.965771\pi\)
\(140\) −1594.96 + 1219.94i −0.962850 + 0.736454i
\(141\) 0 0
\(142\) 378.489 766.005i 0.223677 0.452688i
\(143\) 657.773 0.384656
\(144\) 0 0
\(145\) −375.904 −0.215291
\(146\) 631.981 1279.03i 0.358240 0.725023i
\(147\) 0 0
\(148\) 725.207 554.688i 0.402781 0.308075i
\(149\) 1290.49i 0.709540i 0.934954 + 0.354770i \(0.115441\pi\)
−0.934954 + 0.354770i \(0.884559\pi\)
\(150\) 0 0
\(151\) 1175.51 0.633521 0.316761 0.948505i \(-0.397405\pi\)
0.316761 + 0.948505i \(0.397405\pi\)
\(152\) −566.136 2881.13i −0.302103 1.53744i
\(153\) 0 0
\(154\) 1427.00 + 705.093i 0.746694 + 0.368948i
\(155\) 1717.51i 0.890022i
\(156\) 0 0
\(157\) 1092.09i 0.555148i −0.960704 0.277574i \(-0.910470\pi\)
0.960704 0.277574i \(-0.0895303\pi\)
\(158\) −378.115 + 765.246i −0.190387 + 0.385314i
\(159\) 0 0
\(160\) −1097.49 + 1241.71i −0.542276 + 0.613538i
\(161\) −251.284 −0.123006
\(162\) 0 0
\(163\) 3626.97i 1.74286i 0.490519 + 0.871430i \(0.336807\pi\)
−0.490519 + 0.871430i \(0.663193\pi\)
\(164\) 1375.04 + 1797.75i 0.654711 + 0.855978i
\(165\) 0 0
\(166\) −1518.93 750.518i −0.710193 0.350913i
\(167\) −45.8012 −0.0212228 −0.0106114 0.999944i \(-0.503378\pi\)
−0.0106114 + 0.999944i \(0.503378\pi\)
\(168\) 0 0
\(169\) 1169.98 0.532536
\(170\) 2594.56 + 1281.99i 1.17055 + 0.578379i
\(171\) 0 0
\(172\) −567.998 + 434.444i −0.251799 + 0.192593i
\(173\) 2455.02i 1.07891i −0.842014 0.539455i \(-0.818630\pi\)
0.842014 0.539455i \(-0.181370\pi\)
\(174\) 0 0
\(175\) 1129.28 0.487805
\(176\) 1267.79 + 343.917i 0.542974 + 0.147294i
\(177\) 0 0
\(178\) −347.728 + 703.747i −0.146423 + 0.296338i
\(179\) 1026.28i 0.428533i 0.976775 + 0.214267i \(0.0687362\pi\)
−0.976775 + 0.214267i \(0.931264\pi\)
\(180\) 0 0
\(181\) 3699.05i 1.51905i 0.650477 + 0.759526i \(0.274569\pi\)
−0.650477 + 0.759526i \(0.725431\pi\)
\(182\) −2228.06 1100.90i −0.907442 0.448375i
\(183\) 0 0
\(184\) −203.491 + 39.9856i −0.0815302 + 0.0160205i
\(185\) 1044.82 0.415226
\(186\) 0 0
\(187\) 2293.98i 0.897071i
\(188\) −265.595 347.243i −0.103035 0.134709i
\(189\) 0 0
\(190\) 1488.46 3012.42i 0.568340 1.15023i
\(191\) −5108.93 −1.93544 −0.967721 0.252023i \(-0.918904\pi\)
−0.967721 + 0.252023i \(0.918904\pi\)
\(192\) 0 0
\(193\) −1414.13 −0.527417 −0.263709 0.964602i \(-0.584946\pi\)
−0.263709 + 0.964602i \(0.584946\pi\)
\(194\) 959.638 1942.16i 0.355144 0.718757i
\(195\) 0 0
\(196\) −1986.47 2597.13i −0.723931 0.946477i
\(197\) 2816.66i 1.01867i 0.860567 + 0.509337i \(0.170109\pi\)
−0.860567 + 0.509337i \(0.829891\pi\)
\(198\) 0 0
\(199\) −948.556 −0.337896 −0.168948 0.985625i \(-0.554037\pi\)
−0.168948 + 0.985625i \(0.554037\pi\)
\(200\) 914.502 179.698i 0.323325 0.0635328i
\(201\) 0 0
\(202\) 510.332 + 252.160i 0.177757 + 0.0878311i
\(203\) 1125.78i 0.389232i
\(204\) 0 0
\(205\) 2590.05i 0.882424i
\(206\) −855.060 + 1730.51i −0.289198 + 0.585293i
\(207\) 0 0
\(208\) −1979.48 536.977i −0.659865 0.179003i
\(209\) −2663.43 −0.881499
\(210\) 0 0
\(211\) 4487.28i 1.46406i −0.681271 0.732032i \(-0.738572\pi\)
0.681271 0.732032i \(-0.261428\pi\)
\(212\) 4618.85 3532.81i 1.49634 1.14450i
\(213\) 0 0
\(214\) 1159.49 + 572.912i 0.370377 + 0.183007i
\(215\) −818.326 −0.259578
\(216\) 0 0
\(217\) −5143.68 −1.60910
\(218\) −1586.91 784.108i −0.493025 0.243608i
\(219\) 0 0
\(220\) 913.267 + 1194.02i 0.279875 + 0.365912i
\(221\) 3581.72i 1.09019i
\(222\) 0 0
\(223\) −4590.98 −1.37863 −0.689315 0.724462i \(-0.742088\pi\)
−0.689315 + 0.724462i \(0.742088\pi\)
\(224\) −3718.75 3286.82i −1.10924 0.980401i
\(225\) 0 0
\(226\) 1229.33 2487.97i 0.361831 0.732290i
\(227\) 2897.47i 0.847189i 0.905852 + 0.423594i \(0.139232\pi\)
−0.905852 + 0.423594i \(0.860768\pi\)
\(228\) 0 0
\(229\) 34.6293i 0.00999288i −0.999988 0.00499644i \(-0.998410\pi\)
0.999988 0.00499644i \(-0.00159042\pi\)
\(230\) −212.764 105.129i −0.0609968 0.0301390i
\(231\) 0 0
\(232\) −179.140 911.662i −0.0506944 0.257989i
\(233\) 1054.02 0.296355 0.148178 0.988961i \(-0.452659\pi\)
0.148178 + 0.988961i \(0.452659\pi\)
\(234\) 0 0
\(235\) 500.280i 0.138871i
\(236\) 1376.22 1052.63i 0.379594 0.290340i
\(237\) 0 0
\(238\) −3839.38 + 7770.32i −1.04567 + 2.11628i
\(239\) 654.700 0.177192 0.0885962 0.996068i \(-0.471762\pi\)
0.0885962 + 0.996068i \(0.471762\pi\)
\(240\) 0 0
\(241\) 3194.00 0.853707 0.426854 0.904321i \(-0.359622\pi\)
0.426854 + 0.904321i \(0.359622\pi\)
\(242\) −1139.83 + 2306.83i −0.302772 + 0.612764i
\(243\) 0 0
\(244\) 4792.60 3665.71i 1.25744 0.961774i
\(245\) 3741.74i 0.975719i
\(246\) 0 0
\(247\) 4158.57 1.07127
\(248\) −4165.38 + 818.490i −1.06654 + 0.209573i
\(249\) 0 0
\(250\) 3858.00 + 1906.27i 0.976006 + 0.482253i
\(251\) 5042.90i 1.26815i −0.773273 0.634074i \(-0.781382\pi\)
0.773273 0.634074i \(-0.218618\pi\)
\(252\) 0 0
\(253\) 188.115i 0.0467459i
\(254\) 1012.45 2049.04i 0.250105 0.506174i
\(255\) 0 0
\(256\) −3534.48 2069.94i −0.862911 0.505356i
\(257\) 5166.64 1.25403 0.627016 0.779007i \(-0.284276\pi\)
0.627016 + 0.779007i \(0.284276\pi\)
\(258\) 0 0
\(259\) 3129.08i 0.750702i
\(260\) −1425.94 1864.29i −0.340126 0.444685i
\(261\) 0 0
\(262\) 2816.87 + 1391.84i 0.664225 + 0.328199i
\(263\) 7366.11 1.72705 0.863524 0.504308i \(-0.168252\pi\)
0.863524 + 0.504308i \(0.168252\pi\)
\(264\) 0 0
\(265\) 6654.47 1.54257
\(266\) 9021.76 + 4457.73i 2.07955 + 1.02752i
\(267\) 0 0
\(268\) −2411.06 + 1844.14i −0.549548 + 0.420332i
\(269\) 7877.80i 1.78557i 0.450484 + 0.892784i \(0.351251\pi\)
−0.450484 + 0.892784i \(0.648749\pi\)
\(270\) 0 0
\(271\) −5399.92 −1.21041 −0.605206 0.796069i \(-0.706909\pi\)
−0.605206 + 0.796069i \(0.706909\pi\)
\(272\) −1872.70 + 6903.40i −0.417461 + 1.53890i
\(273\) 0 0
\(274\) −584.832 + 1183.61i −0.128945 + 0.260965i
\(275\) 845.402i 0.185381i
\(276\) 0 0
\(277\) 4416.07i 0.957892i 0.877844 + 0.478946i \(0.158981\pi\)
−0.877844 + 0.478946i \(0.841019\pi\)
\(278\) −892.014 440.752i −0.192444 0.0950883i
\(279\) 0 0
\(280\) −1095.08 5572.98i −0.233727 1.18946i
\(281\) −8068.94 −1.71300 −0.856499 0.516148i \(-0.827365\pi\)
−0.856499 + 0.516148i \(0.827365\pi\)
\(282\) 0 0
\(283\) 5241.13i 1.10089i −0.834870 0.550447i \(-0.814457\pi\)
0.834870 0.550447i \(-0.185543\pi\)
\(284\) 1468.18 + 1919.52i 0.306763 + 0.401066i
\(285\) 0 0
\(286\) −824.154 + 1667.96i −0.170396 + 0.344855i
\(287\) −7756.81 −1.59537
\(288\) 0 0
\(289\) 7578.21 1.54248
\(290\) 470.987 953.206i 0.0953701 0.193014i
\(291\) 0 0
\(292\) 2451.49 + 3205.11i 0.491311 + 0.642346i
\(293\) 6372.75i 1.27065i −0.772246 0.635324i \(-0.780867\pi\)
0.772246 0.635324i \(-0.219133\pi\)
\(294\) 0 0
\(295\) 1982.75 0.391322
\(296\) 497.916 + 2533.95i 0.0977730 + 0.497577i
\(297\) 0 0
\(298\) −3272.40 1616.92i −0.636124 0.314314i
\(299\) 293.715i 0.0568093i
\(300\) 0 0
\(301\) 2450.76i 0.469301i
\(302\) −1472.85 + 2980.83i −0.280639 + 0.567971i
\(303\) 0 0
\(304\) 8015.22 + 2174.31i 1.51219 + 0.410214i
\(305\) 6904.79 1.29629
\(306\) 0 0
\(307\) 3810.22i 0.708342i −0.935181 0.354171i \(-0.884763\pi\)
0.935181 0.354171i \(-0.115237\pi\)
\(308\) −3575.91 + 2735.10i −0.661546 + 0.505996i
\(309\) 0 0
\(310\) −4355.20 2151.94i −0.797932 0.394265i
\(311\) 8106.73 1.47810 0.739052 0.673648i \(-0.235274\pi\)
0.739052 + 0.673648i \(0.235274\pi\)
\(312\) 0 0
\(313\) −559.983 −0.101125 −0.0505625 0.998721i \(-0.516101\pi\)
−0.0505625 + 0.998721i \(0.516101\pi\)
\(314\) 2769.29 + 1368.33i 0.497707 + 0.245921i
\(315\) 0 0
\(316\) −1466.73 1917.62i −0.261108 0.341376i
\(317\) 5828.98i 1.03277i −0.856357 0.516385i \(-0.827277\pi\)
0.856357 0.516385i \(-0.172723\pi\)
\(318\) 0 0
\(319\) −842.776 −0.147920
\(320\) −1773.60 4338.78i −0.309836 0.757953i
\(321\) 0 0
\(322\) 314.845 637.197i 0.0544895 0.110278i
\(323\) 14503.0i 2.49835i
\(324\) 0 0
\(325\) 1319.97i 0.225289i
\(326\) −9197.16 4544.40i −1.56253 0.772058i
\(327\) 0 0
\(328\) −6281.52 + 1234.31i −1.05744 + 0.207784i
\(329\) 1498.26 0.251070
\(330\) 0 0
\(331\) 2847.98i 0.472928i 0.971640 + 0.236464i \(0.0759885\pi\)
−0.971640 + 0.236464i \(0.924011\pi\)
\(332\) 3806.28 2911.31i 0.629207 0.481261i
\(333\) 0 0
\(334\) 57.3864 116.141i 0.00940133 0.0190269i
\(335\) −3473.66 −0.566526
\(336\) 0 0
\(337\) −10127.8 −1.63707 −0.818537 0.574454i \(-0.805214\pi\)
−0.818537 + 0.574454i \(0.805214\pi\)
\(338\) −1465.92 + 2966.80i −0.235904 + 0.477434i
\(339\) 0 0
\(340\) −6501.69 + 4972.94i −1.03707 + 0.793222i
\(341\) 3850.65i 0.611508i
\(342\) 0 0
\(343\) 1801.78 0.283636
\(344\) −389.979 1984.65i −0.0611228 0.311061i
\(345\) 0 0
\(346\) 6225.36 + 3076.00i 0.967276 + 0.477939i
\(347\) 10148.2i 1.56999i 0.619505 + 0.784993i \(0.287333\pi\)
−0.619505 + 0.784993i \(0.712667\pi\)
\(348\) 0 0
\(349\) 9515.96i 1.45954i −0.683695 0.729768i \(-0.739628\pi\)
0.683695 0.729768i \(-0.260372\pi\)
\(350\) −1414.93 + 2863.60i −0.216089 + 0.437332i
\(351\) 0 0
\(352\) −2460.57 + 2783.92i −0.372582 + 0.421544i
\(353\) −2813.56 −0.424223 −0.212111 0.977245i \(-0.568034\pi\)
−0.212111 + 0.977245i \(0.568034\pi\)
\(354\) 0 0
\(355\) 2765.50i 0.413457i
\(356\) −1348.86 1763.51i −0.200813 0.262545i
\(357\) 0 0
\(358\) −2602.40 1285.87i −0.384193 0.189833i
\(359\) 2427.25 0.356839 0.178419 0.983955i \(-0.442902\pi\)
0.178419 + 0.983955i \(0.442902\pi\)
\(360\) 0 0
\(361\) −9979.71 −1.45498
\(362\) −9379.95 4634.71i −1.36188 0.672915i
\(363\) 0 0
\(364\) 5583.27 4270.47i 0.803963 0.614926i
\(365\) 4617.67i 0.662192i
\(366\) 0 0
\(367\) 5021.46 0.714219 0.357109 0.934063i \(-0.383762\pi\)
0.357109 + 0.934063i \(0.383762\pi\)
\(368\) 153.569 566.106i 0.0217536 0.0801911i
\(369\) 0 0
\(370\) −1309.10 + 2649.42i −0.183938 + 0.372262i
\(371\) 19929.1i 2.78887i
\(372\) 0 0
\(373\) 3182.40i 0.441765i 0.975300 + 0.220882i \(0.0708937\pi\)
−0.975300 + 0.220882i \(0.929106\pi\)
\(374\) 5817.00 + 2874.23i 0.804251 + 0.397387i
\(375\) 0 0
\(376\) 1213.30 238.412i 0.166413 0.0326999i
\(377\) 1315.87 0.179764
\(378\) 0 0
\(379\) 5868.93i 0.795426i 0.917510 + 0.397713i \(0.130196\pi\)
−0.917510 + 0.397713i \(0.869804\pi\)
\(380\) 5773.85 + 7548.81i 0.779453 + 1.01907i
\(381\) 0 0
\(382\) 6401.22 12955.1i 0.857368 1.73518i
\(383\) −7350.18 −0.980618 −0.490309 0.871549i \(-0.663116\pi\)
−0.490309 + 0.871549i \(0.663116\pi\)
\(384\) 0 0
\(385\) −5151.88 −0.681985
\(386\) 1771.83 3585.92i 0.233637 0.472846i
\(387\) 0 0
\(388\) 3722.49 + 4866.84i 0.487064 + 0.636795i
\(389\) 13009.1i 1.69560i −0.530317 0.847800i \(-0.677927\pi\)
0.530317 0.847800i \(-0.322073\pi\)
\(390\) 0 0
\(391\) −1024.33 −0.132487
\(392\) 9074.67 1783.15i 1.16923 0.229752i
\(393\) 0 0
\(394\) −7142.41 3529.13i −0.913272 0.451256i
\(395\) 2762.76i 0.351923i
\(396\) 0 0
\(397\) 4877.88i 0.616659i −0.951280 0.308330i \(-0.900230\pi\)
0.951280 0.308330i \(-0.0997700\pi\)
\(398\) 1188.49 2405.32i 0.149682 0.302934i
\(399\) 0 0
\(400\) −690.149 + 2544.12i −0.0862686 + 0.318015i
\(401\) −5552.33 −0.691446 −0.345723 0.938337i \(-0.612366\pi\)
−0.345723 + 0.938337i \(0.612366\pi\)
\(402\) 0 0
\(403\) 6012.23i 0.743153i
\(404\) −1278.84 + 978.143i −0.157486 + 0.120456i
\(405\) 0 0
\(406\) 2854.71 + 1410.54i 0.348958 + 0.172423i
\(407\) 2342.49 0.285289
\(408\) 0 0
\(409\) 6989.27 0.844981 0.422491 0.906367i \(-0.361156\pi\)
0.422491 + 0.906367i \(0.361156\pi\)
\(410\) −6567.77 3245.19i −0.791119 0.390899i
\(411\) 0 0
\(412\) −3316.83 4336.47i −0.396623 0.518550i
\(413\) 5938.03i 0.707485i
\(414\) 0 0
\(415\) 5483.79 0.648647
\(416\) 3841.83 4346.69i 0.452791 0.512293i
\(417\) 0 0
\(418\) 3337.13 6753.85i 0.390489 0.790291i
\(419\) 10461.0i 1.21970i −0.792518 0.609849i \(-0.791230\pi\)
0.792518 0.609849i \(-0.208770\pi\)
\(420\) 0 0
\(421\) 4648.55i 0.538139i 0.963121 + 0.269070i \(0.0867162\pi\)
−0.963121 + 0.269070i \(0.913284\pi\)
\(422\) 11378.7 + 5622.32i 1.31258 + 0.648555i
\(423\) 0 0
\(424\) 3171.23 + 16138.8i 0.363228 + 1.84851i
\(425\) 4603.40 0.525406
\(426\) 0 0
\(427\) 20678.8i 2.34360i
\(428\) −2905.54 + 2222.36i −0.328142 + 0.250986i
\(429\) 0 0
\(430\) 1025.32 2075.09i 0.114989 0.232720i
\(431\) −12490.7 −1.39595 −0.697975 0.716122i \(-0.745915\pi\)
−0.697975 + 0.716122i \(0.745915\pi\)
\(432\) 0 0
\(433\) 9446.37 1.04842 0.524208 0.851590i \(-0.324362\pi\)
0.524208 + 0.851590i \(0.324362\pi\)
\(434\) 6444.75 13043.2i 0.712806 1.44261i
\(435\) 0 0
\(436\) 3976.64 3041.60i 0.436803 0.334097i
\(437\) 1189.30i 0.130188i
\(438\) 0 0
\(439\) 2793.60 0.303716 0.151858 0.988402i \(-0.451474\pi\)
0.151858 + 0.988402i \(0.451474\pi\)
\(440\) −4172.03 + 819.795i −0.452031 + 0.0888232i
\(441\) 0 0
\(442\) −9082.41 4487.70i −0.977390 0.482937i
\(443\) 7601.37i 0.815241i 0.913151 + 0.407621i \(0.133641\pi\)
−0.913151 + 0.407621i \(0.866359\pi\)
\(444\) 0 0
\(445\) 2540.73i 0.270657i
\(446\) 5752.25 11641.7i 0.610710 1.23598i
\(447\) 0 0
\(448\) 12994.0 5311.68i 1.37033 0.560164i
\(449\) −10708.8 −1.12557 −0.562785 0.826603i \(-0.690270\pi\)
−0.562785 + 0.826603i \(0.690270\pi\)
\(450\) 0 0
\(451\) 5806.89i 0.606287i
\(452\) 4768.64 + 6234.59i 0.496235 + 0.648784i
\(453\) 0 0
\(454\) −7347.32 3630.37i −0.759530 0.375290i
\(455\) 8043.92 0.828802
\(456\) 0 0
\(457\) 233.840 0.0239356 0.0119678 0.999928i \(-0.496190\pi\)
0.0119678 + 0.999928i \(0.496190\pi\)
\(458\) 87.8120 + 43.3887i 0.00895892 + 0.00442668i
\(459\) 0 0
\(460\) 533.164 407.801i 0.0540411 0.0413343i
\(461\) 981.307i 0.0991410i 0.998771 + 0.0495705i \(0.0157853\pi\)
−0.998771 + 0.0495705i \(0.984215\pi\)
\(462\) 0 0
\(463\) −14082.7 −1.41356 −0.706782 0.707431i \(-0.749854\pi\)
−0.706782 + 0.707431i \(0.749854\pi\)
\(464\) 2536.22 + 688.006i 0.253752 + 0.0688359i
\(465\) 0 0
\(466\) −1320.62 + 2672.74i −0.131280 + 0.265692i
\(467\) 9286.49i 0.920188i 0.887870 + 0.460094i \(0.152184\pi\)
−0.887870 + 0.460094i \(0.847816\pi\)
\(468\) 0 0
\(469\) 10403.1i 1.02424i
\(470\) 1268.59 + 626.824i 0.124502 + 0.0615175i
\(471\) 0 0
\(472\) 944.892 + 4808.66i 0.0921444 + 0.468933i
\(473\) −1834.68 −0.178349
\(474\) 0 0
\(475\) 5344.79i 0.516286i
\(476\) −14893.2 19471.6i −1.43409 1.87496i
\(477\) 0 0
\(478\) −820.303 + 1660.17i −0.0784933 + 0.158858i
\(479\) 19409.3 1.85143 0.925715 0.378222i \(-0.123464\pi\)
0.925715 + 0.378222i \(0.123464\pi\)
\(480\) 0 0
\(481\) −3657.46 −0.346706
\(482\) −4001.90 + 8099.24i −0.378178 + 0.765374i
\(483\) 0 0
\(484\) −4421.46 5780.67i −0.415238 0.542888i
\(485\) 7011.76i 0.656469i
\(486\) 0 0
\(487\) 12124.8 1.12818 0.564091 0.825712i \(-0.309227\pi\)
0.564091 + 0.825712i \(0.309227\pi\)
\(488\) 3290.53 + 16745.9i 0.305236 + 1.55338i
\(489\) 0 0
\(490\) 9488.20 + 4688.20i 0.874762 + 0.432227i
\(491\) 5100.69i 0.468820i −0.972138 0.234410i \(-0.924684\pi\)
0.972138 0.234410i \(-0.0753159\pi\)
\(492\) 0 0
\(493\) 4589.10i 0.419235i
\(494\) −5210.46 + 10545.2i −0.474554 + 0.960424i
\(495\) 0 0
\(496\) 3143.50 11588.0i 0.284571 1.04902i
\(497\) −8282.26 −0.747505
\(498\) 0 0
\(499\) 85.2797i 0.00765058i 0.999993 + 0.00382529i \(0.00121763\pi\)
−0.999993 + 0.00382529i \(0.998782\pi\)
\(500\) −9667.74 + 7394.55i −0.864709 + 0.661389i
\(501\) 0 0
\(502\) 12787.6 + 6318.48i 1.13693 + 0.561768i
\(503\) 12287.2 1.08918 0.544592 0.838701i \(-0.316684\pi\)
0.544592 + 0.838701i \(0.316684\pi\)
\(504\) 0 0
\(505\) −1842.45 −0.162352
\(506\) −477.017 235.698i −0.0419091 0.0207076i
\(507\) 0 0
\(508\) 3927.35 + 5134.67i 0.343008 + 0.448453i
\(509\) 450.441i 0.0392248i −0.999808 0.0196124i \(-0.993757\pi\)
0.999808 0.0196124i \(-0.00624322\pi\)
\(510\) 0 0
\(511\) −13829.2 −1.19720
\(512\) 9677.40 6369.11i 0.835322 0.549761i
\(513\) 0 0
\(514\) −6473.52 + 13101.4i −0.555515 + 1.12428i
\(515\) 6247.64i 0.534571i
\(516\) 0 0
\(517\) 1121.63i 0.0954141i
\(518\) −7934.63 3920.57i −0.673026 0.332548i
\(519\) 0 0
\(520\) 6514.02 1279.99i 0.549344 0.107945i
\(521\) 15088.1 1.26876 0.634378 0.773023i \(-0.281256\pi\)
0.634378 + 0.773023i \(0.281256\pi\)
\(522\) 0 0
\(523\) 17719.4i 1.48149i −0.671789 0.740743i \(-0.734474\pi\)
0.671789 0.740743i \(-0.265526\pi\)
\(524\) −7058.77 + 5399.04i −0.588481 + 0.450111i
\(525\) 0 0
\(526\) −9229.33 + 18678.7i −0.765053 + 1.54835i
\(527\) −20967.6 −1.73314
\(528\) 0 0
\(529\) −12083.0 −0.993096
\(530\) −8337.69 + 16874.2i −0.683332 + 1.38296i
\(531\) 0 0
\(532\) −22607.6 + 17291.8i −1.84241 + 1.40920i
\(533\) 9066.62i 0.736808i
\(534\) 0 0
\(535\) −4186.08 −0.338280
\(536\) −1655.40 8424.50i −0.133400 0.678886i
\(537\) 0 0
\(538\) −19976.3 9870.46i −1.60082 0.790977i
\(539\) 8388.98i 0.670388i
\(540\) 0 0
\(541\) 12244.5i 0.973074i 0.873660 + 0.486537i \(0.161740\pi\)
−0.873660 + 0.486537i \(0.838260\pi\)
\(542\) 6765.80 13692.9i 0.536192 1.08517i
\(543\) 0 0
\(544\) −15159.0 13398.3i −1.19474 1.05597i
\(545\) 5729.22 0.450299
\(546\) 0 0
\(547\) 7822.46i 0.611452i 0.952119 + 0.305726i \(0.0988992\pi\)
−0.952119 + 0.305726i \(0.901101\pi\)
\(548\) −2268.60 2966.00i −0.176843 0.231206i
\(549\) 0 0
\(550\) 2143.74 + 1059.24i 0.166199 + 0.0821205i
\(551\) −5328.19 −0.411957
\(552\) 0 0
\(553\) 8274.05 0.636254
\(554\) −11198.1 5533.10i −0.858779 0.424330i
\(555\) 0 0
\(556\) 2235.29 1709.70i 0.170499 0.130409i
\(557\) 16555.5i 1.25938i −0.776845 0.629692i \(-0.783181\pi\)
0.776845 0.629692i \(-0.216819\pi\)
\(558\) 0 0
\(559\) 2864.60 0.216743
\(560\) 15503.9 + 4205.77i 1.16992 + 0.317368i
\(561\) 0 0
\(562\) 10109.9 20461.0i 0.758830 1.53575i
\(563\) 12580.7i 0.941766i −0.882196 0.470883i \(-0.843935\pi\)
0.882196 0.470883i \(-0.156065\pi\)
\(564\) 0 0
\(565\) 8982.30i 0.668829i
\(566\) 13290.3 + 6566.86i 0.986985 + 0.487678i
\(567\) 0 0
\(568\) −6707.03 + 1317.92i −0.495459 + 0.0973567i
\(569\) −2657.93 −0.195828 −0.0979141 0.995195i \(-0.531217\pi\)
−0.0979141 + 0.995195i \(0.531217\pi\)
\(570\) 0 0
\(571\) 17669.0i 1.29496i −0.762081 0.647481i \(-0.775822\pi\)
0.762081 0.647481i \(-0.224178\pi\)
\(572\) −3196.94 4179.73i −0.233691 0.305530i
\(573\) 0 0
\(574\) 9718.86 19669.5i 0.706721 1.43029i
\(575\) −377.497 −0.0273786
\(576\) 0 0
\(577\) 14617.7 1.05467 0.527334 0.849658i \(-0.323192\pi\)
0.527334 + 0.849658i \(0.323192\pi\)
\(578\) −9495.08 + 19216.6i −0.683293 + 1.38288i
\(579\) 0 0
\(580\) 1826.99 + 2388.63i 0.130796 + 0.171004i
\(581\) 16423.1i 1.17271i
\(582\) 0 0
\(583\) 14919.3 1.05985
\(584\) −11199.0 + 2200.59i −0.793525 + 0.155926i
\(585\) 0 0
\(586\) 16159.8 + 7984.70i 1.13917 + 0.562876i
\(587\) 4096.53i 0.288044i −0.989574 0.144022i \(-0.953996\pi\)
0.989574 0.144022i \(-0.0460036\pi\)
\(588\) 0 0
\(589\) 24344.5i 1.70305i
\(590\) −2484.27 + 5027.79i −0.173349 + 0.350832i
\(591\) 0 0
\(592\) −7049.38 1912.30i −0.489405 0.132762i
\(593\) 21988.3 1.52269 0.761343 0.648349i \(-0.224540\pi\)
0.761343 + 0.648349i \(0.224540\pi\)
\(594\) 0 0
\(595\) 28053.1i 1.93288i
\(596\) 8200.27 6272.13i 0.563584 0.431068i
\(597\) 0 0
\(598\) 744.794 + 368.009i 0.0509312 + 0.0251656i
\(599\) −20767.7 −1.41660 −0.708302 0.705909i \(-0.750539\pi\)
−0.708302 + 0.705909i \(0.750539\pi\)
\(600\) 0 0
\(601\) 5382.61 0.365326 0.182663 0.983176i \(-0.441528\pi\)
0.182663 + 0.983176i \(0.441528\pi\)
\(602\) 6214.57 + 3070.67i 0.420743 + 0.207893i
\(603\) 0 0
\(604\) −5713.28 7469.62i −0.384884 0.503203i
\(605\) 8328.33i 0.559661i
\(606\) 0 0
\(607\) 11165.4 0.746607 0.373304 0.927709i \(-0.378225\pi\)
0.373304 + 0.927709i \(0.378225\pi\)
\(608\) −15556.2 + 17600.5i −1.03764 + 1.17400i
\(609\) 0 0
\(610\) −8651.33 + 17509.0i −0.574233 + 1.16216i
\(611\) 1751.26i 0.115955i
\(612\) 0 0
\(613\) 16413.5i 1.08146i −0.841195 0.540731i \(-0.818148\pi\)
0.841195 0.540731i \(-0.181852\pi\)
\(614\) 9661.85 + 4774.00i 0.635050 + 0.313784i
\(615\) 0 0
\(616\) −2455.17 12494.6i −0.160587 0.817243i
\(617\) 51.5882 0.00336607 0.00168303 0.999999i \(-0.499464\pi\)
0.00168303 + 0.999999i \(0.499464\pi\)
\(618\) 0 0
\(619\) 6349.55i 0.412294i 0.978521 + 0.206147i \(0.0660925\pi\)
−0.978521 + 0.206147i \(0.933907\pi\)
\(620\) 10913.7 8347.52i 0.706941 0.540717i
\(621\) 0 0
\(622\) −10157.3 + 20556.8i −0.654775 + 1.32516i
\(623\) 7609.11 0.489330
\(624\) 0 0
\(625\) −8779.94 −0.561916
\(626\) 701.629 1419.99i 0.0447967 0.0906616i
\(627\) 0 0
\(628\) −6939.53 + 5307.83i −0.440951 + 0.337270i
\(629\) 12755.3i 0.808567i
\(630\) 0 0
\(631\) −13379.1 −0.844078 −0.422039 0.906578i \(-0.638685\pi\)
−0.422039 + 0.906578i \(0.638685\pi\)
\(632\) 6700.38 1316.61i 0.421720 0.0828671i
\(633\) 0 0
\(634\) 14780.9 + 7303.39i 0.925909 + 0.457500i
\(635\) 7397.63i 0.462309i
\(636\) 0 0
\(637\) 13098.2i 0.814709i
\(638\) 1055.95 2137.09i 0.0655260 0.132615i
\(639\) 0 0
\(640\) 13224.4 + 938.802i 0.816780 + 0.0579835i
\(641\) 20406.3 1.25741 0.628705 0.777644i \(-0.283585\pi\)
0.628705 + 0.777644i \(0.283585\pi\)
\(642\) 0 0
\(643\) 19415.1i 1.19076i 0.803446 + 0.595378i \(0.202998\pi\)
−0.803446 + 0.595378i \(0.797002\pi\)
\(644\) 1221.30 + 1596.75i 0.0747299 + 0.0977029i
\(645\) 0 0
\(646\) 36776.2 + 18171.4i 2.23984 + 1.10673i
\(647\) 8167.12 0.496264 0.248132 0.968726i \(-0.420183\pi\)
0.248132 + 0.968726i \(0.420183\pi\)
\(648\) 0 0
\(649\) 4445.31 0.268866
\(650\) −3347.15 1653.86i −0.201978 0.0997993i
\(651\) 0 0
\(652\) 23047.1 17628.0i 1.38435 1.05884i
\(653\) 7444.93i 0.446160i −0.974800 0.223080i \(-0.928389\pi\)
0.974800 0.223080i \(-0.0716111\pi\)
\(654\) 0 0
\(655\) −10169.7 −0.606662
\(656\) 4740.49 17475.0i 0.282142 1.04007i
\(657\) 0 0
\(658\) −1877.24 + 3799.25i −0.111220 + 0.225092i
\(659\) 23780.4i 1.40569i 0.711342 + 0.702846i \(0.248088\pi\)
−0.711342 + 0.702846i \(0.751912\pi\)
\(660\) 0 0
\(661\) 2528.90i 0.148809i 0.997228 + 0.0744046i \(0.0237056\pi\)
−0.997228 + 0.0744046i \(0.976294\pi\)
\(662\) −7221.82 3568.36i −0.423994 0.209499i
\(663\) 0 0
\(664\) 2613.34 + 13299.6i 0.152737 + 0.777294i
\(665\) −32571.2 −1.89933
\(666\) 0 0
\(667\) 376.324i 0.0218461i
\(668\) 222.605 + 291.037i 0.0128935 + 0.0168571i
\(669\) 0 0
\(670\) 4352.31 8808.40i 0.250962 0.507908i
\(671\) 15480.5 0.890640
\(672\) 0 0
\(673\) 16733.7 0.958447 0.479224 0.877693i \(-0.340918\pi\)
0.479224 + 0.877693i \(0.340918\pi\)
\(674\) 12689.5 25681.6i 0.725196 1.46769i
\(675\) 0 0
\(676\) −5686.41 7434.49i −0.323532 0.422991i
\(677\) 24191.5i 1.37335i 0.726966 + 0.686673i \(0.240930\pi\)
−0.726966 + 0.686673i \(0.759070\pi\)
\(678\) 0 0
\(679\) −20999.2 −1.18685
\(680\) −4463.96 22717.6i −0.251743 1.28115i
\(681\) 0 0
\(682\) −9764.35 4824.65i −0.548235 0.270888i
\(683\) 13965.2i 0.782376i −0.920311 0.391188i \(-0.872064\pi\)
0.920311 0.391188i \(-0.127936\pi\)
\(684\) 0 0
\(685\) 4273.17i 0.238350i
\(686\) −2257.54 + 4568.91i −0.125646 + 0.254288i
\(687\) 0 0
\(688\) 5521.23 + 1497.76i 0.305952 + 0.0829962i
\(689\) −23294.4 −1.28802
\(690\) 0 0
\(691\) 8685.63i 0.478172i −0.970998 0.239086i \(-0.923152\pi\)
0.970998 0.239086i \(-0.0768479\pi\)
\(692\) −15600.1 + 11932.0i −0.856974 + 0.655472i
\(693\) 0 0
\(694\) −25733.5 12715.2i −1.40754 0.695477i
\(695\) 3220.43 0.175767
\(696\) 0 0
\(697\) −31619.7 −1.71834
\(698\) 24130.3 + 11923.0i 1.30852 + 0.646550i
\(699\) 0 0
\(700\) −5488.61 7175.88i −0.296357 0.387461i
\(701\) 25942.2i 1.39775i 0.715243 + 0.698876i \(0.246316\pi\)
−0.715243 + 0.698876i \(0.753684\pi\)
\(702\) 0 0
\(703\) 14809.6 0.794532
\(704\) −3976.42 9727.53i −0.212879 0.520767i
\(705\) 0 0
\(706\) 3525.24 7134.54i 0.187924 0.380329i
\(707\) 5517.86i 0.293522i
\(708\) 0 0
\(709\) 5487.75i 0.290687i −0.989381 0.145343i \(-0.953571\pi\)
0.989381 0.145343i \(-0.0464287\pi\)
\(710\) −7012.66 3465.02i −0.370677 0.183155i
\(711\) 0 0
\(712\) 6161.91 1210.80i 0.324336 0.0637314i
\(713\) 1719.43 0.0903128
\(714\) 0 0
\(715\) 6021.82i 0.314970i
\(716\) 6521.33 4987.96i 0.340382 0.260348i
\(717\) 0 0
\(718\) −3041.21 + 6154.94i −0.158074 + 0.319917i
\(719\) −17141.2 −0.889094 −0.444547 0.895756i \(-0.646635\pi\)
−0.444547 + 0.895756i \(0.646635\pi\)
\(720\) 0 0
\(721\) 18710.8 0.966470
\(722\) 12504.0 25306.3i 0.644532 1.30443i
\(723\) 0 0
\(724\) 23505.1 17978.3i 1.20658 0.922873i
\(725\) 1691.23i 0.0866352i
\(726\) 0 0
\(727\) −15946.4 −0.813508 −0.406754 0.913538i \(-0.633339\pi\)
−0.406754 + 0.913538i \(0.633339\pi\)
\(728\) 3833.39 + 19508.5i 0.195158 + 0.993179i
\(729\) 0 0
\(730\) −11709.4 5785.69i −0.593675 0.293340i
\(731\) 9990.26i 0.505476i
\(732\) 0 0
\(733\) 15914.2i 0.801917i 0.916096 + 0.400958i \(0.131323\pi\)
−0.916096 + 0.400958i \(0.868677\pi\)
\(734\) −6291.62 + 12733.3i −0.316387 + 0.640318i
\(735\) 0 0
\(736\) 1243.10 + 1098.72i 0.0622572 + 0.0550261i
\(737\) −7787.94 −0.389243
\(738\) 0 0
\(739\) 13555.4i 0.674755i 0.941369 + 0.337377i \(0.109540\pi\)
−0.941369 + 0.337377i \(0.890460\pi\)
\(740\) −5078.09 6639.17i −0.252263 0.329812i
\(741\) 0 0
\(742\) −50535.7 24970.1i −2.50030 1.23542i
\(743\) 1772.73 0.0875303 0.0437652 0.999042i \(-0.486065\pi\)
0.0437652 + 0.999042i \(0.486065\pi\)
\(744\) 0 0
\(745\) 11814.3 0.580997
\(746\) −8069.82 3987.37i −0.396055 0.195694i
\(747\) 0 0
\(748\) −14576.8 + 11149.3i −0.712539 + 0.544999i
\(749\) 12536.7i 0.611589i
\(750\) 0 0
\(751\) −1006.65 −0.0489124 −0.0244562 0.999701i \(-0.507785\pi\)
−0.0244562 + 0.999701i \(0.507785\pi\)
\(752\) −915.647 + 3375.38i −0.0444019 + 0.163680i
\(753\) 0 0
\(754\) −1648.72 + 3336.75i −0.0796324 + 0.161164i
\(755\) 10761.6i 0.518750i
\(756\) 0 0
\(757\) 28774.0i 1.38152i −0.723086 0.690758i \(-0.757277\pi\)
0.723086 0.690758i \(-0.242723\pi\)
\(758\) −14882.2 7353.45i −0.713123 0.352360i
\(759\) 0 0
\(760\) −26376.3 + 5182.90i −1.25891 + 0.247373i
\(761\) −18393.5 −0.876166 −0.438083 0.898934i \(-0.644342\pi\)
−0.438083 + 0.898934i \(0.644342\pi\)
\(762\) 0 0
\(763\) 17158.2i 0.814112i
\(764\) 24830.7 + 32464.0i 1.17584 + 1.53731i
\(765\) 0 0
\(766\) 9209.38 18638.4i 0.434397 0.879153i
\(767\) −6940.72 −0.326747
\(768\) 0 0
\(769\) −14672.2 −0.688027 −0.344014 0.938965i \(-0.611787\pi\)
−0.344014 + 0.938965i \(0.611787\pi\)
\(770\) 6455.03 13064.0i 0.302108 0.611420i
\(771\) 0 0
\(772\) 6873.05 + 8985.92i 0.320423 + 0.418925i
\(773\) 16256.4i 0.756405i −0.925723 0.378202i \(-0.876542\pi\)
0.925723 0.378202i \(-0.123458\pi\)
\(774\) 0 0
\(775\) −7727.21 −0.358154
\(776\) −17005.3 + 3341.50i −0.786667 + 0.154578i
\(777\) 0 0
\(778\) 32988.1 + 16299.7i 1.52016 + 0.751122i
\(779\) 36712.2i 1.68851i
\(780\) 0 0
\(781\) 6200.24i 0.284074i
\(782\) 1283.43 2597.46i 0.0586896 0.118779i
\(783\) 0 0
\(784\) −6848.40 + 25245.5i −0.311971 + 1.15003i
\(785\) −9997.92 −0.454575
\(786\) 0 0
\(787\) 23988.3i 1.08652i 0.839565 + 0.543259i \(0.182810\pi\)
−0.839565 + 0.543259i \(0.817190\pi\)
\(788\) 17898.1 13689.7i 0.809129 0.618877i
\(789\) 0 0
\(790\) 7005.72 + 3461.59i 0.315509 + 0.155896i
\(791\) −26900.7 −1.20920
\(792\) 0 0
\(793\) −24170.6 −1.08238
\(794\) 12369.2 + 6111.72i 0.552853 + 0.273170i
\(795\) 0 0
\(796\) 4610.22 + 6027.47i 0.205283 + 0.268389i
\(797\) 32966.9i 1.46518i −0.680672 0.732589i \(-0.738312\pi\)
0.680672 0.732589i \(-0.261688\pi\)
\(798\) 0 0
\(799\) 6107.50 0.270423
\(800\) −5586.58 4937.70i −0.246894 0.218218i
\(801\) 0 0
\(802\) 6956.76 14079.4i 0.306299 0.619902i
\(803\) 10352.8i 0.454973i
\(804\) 0 0
\(805\) 2300.47i 0.100721i
\(806\) 15245.6 + 7533.00i 0.666259 + 0.329204i
\(807\) 0 0
\(808\) −878.031 4468.40i −0.0382290 0.194552i
\(809\) 41700.3 1.81224 0.906122 0.423017i \(-0.139029\pi\)
0.906122 + 0.423017i \(0.139029\pi\)
\(810\) 0 0
\(811\) 5981.80i 0.259000i −0.991579 0.129500i \(-0.958663\pi\)
0.991579 0.129500i \(-0.0413373\pi\)
\(812\) −7153.60 + 5471.56i −0.309165 + 0.236471i
\(813\) 0 0
\(814\) −2935.01 + 5940.00i −0.126378 + 0.255770i
\(815\) 33204.4 1.42712
\(816\) 0 0
\(817\) −11599.2 −0.496702
\(818\) −8757.18 + 17723.2i −0.374312 + 0.757551i
\(819\) 0 0
\(820\) 16458.1 12588.3i 0.700905 0.536100i
\(821\) 9846.06i 0.418550i 0.977857 + 0.209275i \(0.0671104\pi\)
−0.977857 + 0.209275i \(0.932890\pi\)
\(822\) 0 0
\(823\) 47001.9 1.99074 0.995372 0.0960935i \(-0.0306348\pi\)
0.995372 + 0.0960935i \(0.0306348\pi\)
\(824\) 15152.1 2977.36i 0.640593 0.125875i
\(825\) 0 0
\(826\) −15057.5 7440.03i −0.634282 0.313404i
\(827\) 21727.4i 0.913587i 0.889573 + 0.456794i \(0.151002\pi\)
−0.889573 + 0.456794i \(0.848998\pi\)
\(828\) 0 0
\(829\) 22772.3i 0.954058i −0.878888 0.477029i \(-0.841714\pi\)
0.878888 0.477029i \(-0.158286\pi\)
\(830\) −6870.89 + 13905.6i −0.287340 + 0.581532i
\(831\) 0 0
\(832\) 6208.61 + 15188.2i 0.258708 + 0.632878i
\(833\) 45679.8 1.90002
\(834\) 0 0
\(835\) 419.304i 0.0173780i
\(836\) 12945.0 + 16924.4i 0.535539 + 0.700171i
\(837\) 0 0
\(838\) 26526.7 + 13107.1i 1.09350 + 0.540306i
\(839\) −11010.4 −0.453064 −0.226532 0.974004i \(-0.572739\pi\)
−0.226532 + 0.974004i \(0.572739\pi\)
\(840\) 0 0
\(841\) 22703.0 0.930872
\(842\) −11787.7 5824.39i −0.482458 0.238387i
\(843\) 0 0
\(844\) −28513.8 + 21809.3i −1.16290 + 0.889465i
\(845\) 10711.0i 0.436059i
\(846\) 0 0
\(847\) 24942.1 1.01183
\(848\) −44897.5 12179.5i −1.81815 0.493213i
\(849\) 0 0
\(850\) −5767.81 + 11673.2i −0.232746 + 0.471042i
\(851\) 1045.99i 0.0421340i
\(852\) 0 0
\(853\) 38177.4i 1.53244i −0.642579 0.766219i \(-0.722136\pi\)
0.642579 0.766219i \(-0.277864\pi\)
\(854\) −52436.8 25909.5i −2.10111 1.03818i
\(855\) 0 0
\(856\) −1994.90 10152.3i −0.0796547 0.405372i
\(857\) −8848.01 −0.352675 −0.176337 0.984330i \(-0.556425\pi\)
−0.176337 + 0.984330i \(0.556425\pi\)
\(858\) 0 0
\(859\) 4347.66i 0.172690i −0.996265 0.0863448i \(-0.972481\pi\)
0.996265 0.0863448i \(-0.0275187\pi\)
\(860\) 3977.27 + 5199.94i 0.157702 + 0.206182i
\(861\) 0 0
\(862\) 15650.1 31673.5i 0.618382 1.25151i
\(863\) 33669.9 1.32808 0.664042 0.747695i \(-0.268839\pi\)
0.664042 + 0.747695i \(0.268839\pi\)
\(864\) 0 0
\(865\) −22475.3 −0.883450
\(866\) −11835.8 + 23953.8i −0.464430 + 0.939936i
\(867\) 0 0
\(868\) 24999.6 + 32684.8i 0.977582 + 1.27810i
\(869\) 6194.10i 0.241796i
\(870\) 0 0
\(871\) 12159.7 0.473039
\(872\) 2730.30 + 13894.8i 0.106032 + 0.539607i
\(873\) 0 0
\(874\) −3015.79 1490.13i −0.116717 0.0576709i
\(875\) 41713.8i 1.61164i
\(876\) 0 0
\(877\) 50102.0i 1.92910i −0.263892 0.964552i \(-0.585006\pi\)
0.263892 0.964552i \(-0.414994\pi\)
\(878\) −3500.23 + 7083.93i −0.134541 + 0.272291i
\(879\) 0 0
\(880\) 3148.51 11606.5i 0.120609 0.444606i
\(881\) −18716.9 −0.715766 −0.357883 0.933766i \(-0.616501\pi\)
−0.357883 + 0.933766i \(0.616501\pi\)
\(882\) 0 0
\(883\) 7514.19i 0.286379i 0.989695 + 0.143189i \(0.0457358\pi\)
−0.989695 + 0.143189i \(0.954264\pi\)
\(884\) 22759.5 17408.1i 0.865934 0.662326i
\(885\) 0 0
\(886\) −19275.3 9524.10i −0.730888 0.361138i
\(887\) 15544.6 0.588429 0.294215 0.955739i \(-0.404942\pi\)
0.294215 + 0.955739i \(0.404942\pi\)
\(888\) 0 0
\(889\) −22154.8 −0.835825
\(890\) 6442.71 + 3183.40i 0.242652 + 0.119896i
\(891\) 0 0
\(892\) 22313.3 + 29172.7i 0.837562 + 1.09504i
\(893\) 7091.14i 0.265729i
\(894\) 0 0
\(895\) 9395.42 0.350898
\(896\) −2811.57 + 39605.0i −0.104830 + 1.47669i
\(897\) 0 0
\(898\) 13417.6 27155.1i 0.498609 1.00911i
\(899\) 7703.21i 0.285780i
\(900\) 0 0
\(901\) 81238.8i 3.00384i
\(902\) −14724.9 7275.71i −0.543555 0.268575i
\(903\) 0 0
\(904\) −21784.3 + 4280.58i −0.801478 + 0.157489i
\(905\) 33864.3 1.24385
\(906\) 0 0
\(907\) 8713.10i 0.318979i 0.987200 + 0.159489i \(0.0509848\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(908\) 18411.6 14082.4i 0.672918 0.514694i
\(909\) 0 0
\(910\) −10078.6 + 20397.5i −0.367145 + 0.743046i
\(911\) −1975.97 −0.0718627 −0.0359313 0.999354i \(-0.511440\pi\)
−0.0359313 + 0.999354i \(0.511440\pi\)
\(912\) 0 0
\(913\) 12294.6 0.445666
\(914\) −292.988 + 592.964i −0.0106031 + 0.0214590i
\(915\) 0 0
\(916\) −220.047 + 168.307i −0.00793730 + 0.00607099i
\(917\) 30456.8i 1.09681i
\(918\) 0 0
\(919\) −18430.5 −0.661552 −0.330776 0.943709i \(-0.607311\pi\)
−0.330776 + 0.943709i \(0.607311\pi\)
\(920\) 366.063 + 1862.93i 0.0131182 + 0.0667599i
\(921\) 0 0
\(922\) −2488.37 1229.52i −0.0888829 0.0439178i
\(923\) 9680.79i 0.345230i
\(924\) 0 0
\(925\) 4700.74i 0.167091i
\(926\) 17644.9 35710.6i 0.626185 1.26730i
\(927\) 0 0
\(928\) −4922.36 + 5569.23i −0.174121 + 0.197003i
\(929\) −12506.8 −0.441697 −0.220848 0.975308i \(-0.570883\pi\)
−0.220848 + 0.975308i \(0.570883\pi\)
\(930\) 0 0
\(931\) 53036.7i 1.86703i
\(932\) −5122.78 6697.59i −0.180045 0.235394i
\(933\) 0 0
\(934\) −23548.4 11635.5i −0.824976 0.407628i
\(935\) −21001.0 −0.734554
\(936\) 0 0
\(937\) 39267.5 1.36906 0.684532 0.728982i \(-0.260006\pi\)
0.684532 + 0.728982i \(0.260006\pi\)
\(938\) 26379.9 + 13034.5i 0.918265 + 0.453723i
\(939\) 0 0
\(940\) −3178.96 + 2431.49i −0.110305 + 0.0843685i
\(941\) 23727.2i 0.821981i 0.911640 + 0.410991i \(0.134817\pi\)
−0.911640 + 0.410991i \(0.865183\pi\)
\(942\) 0 0
\(943\) 2592.94 0.0895418
\(944\) −13377.5 3628.96i −0.461231 0.125119i
\(945\) 0 0
\(946\) 2298.76 4652.34i 0.0790054 0.159895i
\(947\) 23399.8i 0.802948i −0.915870 0.401474i \(-0.868498\pi\)
0.915870 0.401474i \(-0.131502\pi\)
\(948\) 0 0
\(949\) 16164.4i 0.552919i
\(950\) 13553.2 + 6696.73i 0.462866 + 0.228706i
\(951\) 0 0
\(952\) 68035.8 13368.9i 2.31623 0.455135i
\(953\) −41497.1 −1.41052 −0.705258 0.708950i \(-0.749169\pi\)
−0.705258 + 0.708950i \(0.749169\pi\)
\(954\) 0 0
\(955\) 46771.6i 1.58481i
\(956\) −3182.01 4160.20i −0.107650 0.140743i
\(957\) 0 0
\(958\) −24318.8 + 49217.6i −0.820152 + 1.65986i
\(959\) 12797.5 0.430921
\(960\) 0 0
\(961\) 5405.00 0.181431
\(962\) 4582.59 9274.46i 0.153585 0.310832i
\(963\) 0 0
\(964\) −15523.6 20295.8i −0.518654 0.678096i
\(965\) 12946.2i 0.431868i
\(966\) 0 0
\(967\) −49123.6 −1.63362 −0.816808 0.576909i \(-0.804259\pi\)
−0.816808 + 0.576909i \(0.804259\pi\)
\(968\) 20198.3 3968.92i 0.670659 0.131783i
\(969\) 0 0
\(970\) −17780.2 8785.35i −0.588544 0.290805i
\(971\) 20346.8i 0.672462i 0.941780 + 0.336231i \(0.109152\pi\)
−0.941780 + 0.336231i \(0.890848\pi\)
\(972\) 0 0
\(973\) 9644.71i 0.317775i
\(974\) −15191.7 + 30745.6i −0.499766 + 1.01145i
\(975\) 0 0
\(976\) −46586.5 12637.6i −1.52787 0.414468i
\(977\) −40602.1 −1.32955 −0.664777 0.747042i \(-0.731474\pi\)
−0.664777 + 0.747042i \(0.731474\pi\)
\(978\) 0 0
\(979\) 5696.32i 0.185960i
\(980\) −23776.4 + 18185.8i −0.775009 + 0.592781i
\(981\) 0 0
\(982\) 12934.2 + 6390.89i 0.420312 + 0.207680i
\(983\) −50425.9 −1.63615 −0.818075 0.575112i \(-0.804959\pi\)
−0.818075 + 0.575112i \(0.804959\pi\)
\(984\) 0 0
\(985\) 25786.2 0.834127
\(986\) 11636.9 + 5749.89i 0.375856 + 0.185714i
\(987\) 0 0
\(988\) −20211.7 26425.0i −0.650829 0.850903i
\(989\) 819.241i 0.0263401i
\(990\) 0 0
\(991\) −8511.62 −0.272836 −0.136418 0.990651i \(-0.543559\pi\)
−0.136418 + 0.990651i \(0.543559\pi\)
\(992\) 25445.8 + 22490.3i 0.814421 + 0.719826i
\(993\) 0 0
\(994\) 10377.2 21001.9i 0.331132 0.670161i
\(995\) 8683.90i 0.276681i
\(996\) 0 0
\(997\) 25302.1i 0.803738i −0.915697 0.401869i \(-0.868361\pi\)
0.915697 0.401869i \(-0.131639\pi\)
\(998\) −216.250 106.851i −0.00685898 0.00338908i
\(999\) 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 72.4.d.d.37.4 6
3.2 odd 2 24.4.d.a.13.3 6
4.3 odd 2 288.4.d.d.145.2 6
8.3 odd 2 288.4.d.d.145.5 6
8.5 even 2 inner 72.4.d.d.37.3 6
12.11 even 2 96.4.d.a.49.6 6
16.3 odd 4 2304.4.a.bw.1.1 3
16.5 even 4 2304.4.a.bt.1.3 3
16.11 odd 4 2304.4.a.bu.1.3 3
16.13 even 4 2304.4.a.bv.1.1 3
24.5 odd 2 24.4.d.a.13.4 yes 6
24.11 even 2 96.4.d.a.49.1 6
48.5 odd 4 768.4.a.r.1.1 3
48.11 even 4 768.4.a.t.1.1 3
48.29 odd 4 768.4.a.s.1.3 3
48.35 even 4 768.4.a.q.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.4.d.a.13.3 6 3.2 odd 2
24.4.d.a.13.4 yes 6 24.5 odd 2
72.4.d.d.37.3 6 8.5 even 2 inner
72.4.d.d.37.4 6 1.1 even 1 trivial
96.4.d.a.49.1 6 24.11 even 2
96.4.d.a.49.6 6 12.11 even 2
288.4.d.d.145.2 6 4.3 odd 2
288.4.d.d.145.5 6 8.3 odd 2
768.4.a.q.1.3 3 48.35 even 4
768.4.a.r.1.1 3 48.5 odd 4
768.4.a.s.1.3 3 48.29 odd 4
768.4.a.t.1.1 3 48.11 even 4
2304.4.a.bt.1.3 3 16.5 even 4
2304.4.a.bu.1.3 3 16.11 odd 4
2304.4.a.bv.1.1 3 16.13 even 4
2304.4.a.bw.1.1 3 16.3 odd 4