Properties

Label 90.5.g.b.37.1
Level $90$
Weight $5$
Character 90.37
Analytic conductor $9.303$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [90,5,Mod(37,90)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(90, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("90.37");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 90.g (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: \(9.30329667755\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 90.37
Dual form 90.5.g.b.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(15.0000 - 20.0000i) q^{5} +(29.0000 + 29.0000i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(70.0000 - 10.0000i) q^{10} +118.000 q^{11} +(69.0000 - 69.0000i) q^{13} +116.000i q^{14} -64.0000 q^{16} +(271.000 + 271.000i) q^{17} +280.000i q^{19} +(160.000 + 120.000i) q^{20} +(236.000 + 236.000i) q^{22} +(-269.000 + 269.000i) q^{23} +(-175.000 - 600.000i) q^{25} +276.000 q^{26} +(-232.000 + 232.000i) q^{28} -680.000i q^{29} +202.000 q^{31} +(-128.000 - 128.000i) q^{32} +1084.00i q^{34} +(1015.00 - 145.000i) q^{35} +(-651.000 - 651.000i) q^{37} +(-560.000 + 560.000i) q^{38} +(80.0000 + 560.000i) q^{40} -1682.00 q^{41} +(1089.00 - 1089.00i) q^{43} +944.000i q^{44} -1076.00 q^{46} +(-1269.00 - 1269.00i) q^{47} -719.000i q^{49} +(850.000 - 1550.00i) q^{50} +(552.000 + 552.000i) q^{52} +(611.000 - 611.000i) q^{53} +(1770.00 - 2360.00i) q^{55} -928.000 q^{56} +(1360.00 - 1360.00i) q^{58} -1160.00i q^{59} -5598.00 q^{61} +(404.000 + 404.000i) q^{62} -512.000i q^{64} +(-345.000 - 2415.00i) q^{65} +(-751.000 - 751.000i) q^{67} +(-2168.00 + 2168.00i) q^{68} +(2320.00 + 1740.00i) q^{70} -6442.00 q^{71} +(-2951.00 + 2951.00i) q^{73} -2604.00i q^{74} -2240.00 q^{76} +(3422.00 + 3422.00i) q^{77} +10560.0i q^{79} +(-960.000 + 1280.00i) q^{80} +(-3364.00 - 3364.00i) q^{82} +(6231.00 - 6231.00i) q^{83} +(9485.00 - 1355.00i) q^{85} +4356.00 q^{86} +(-1888.00 + 1888.00i) q^{88} +14480.0i q^{89} +4002.00 q^{91} +(-2152.00 - 2152.00i) q^{92} -5076.00i q^{94} +(5600.00 + 4200.00i) q^{95} +(-7311.00 - 7311.00i) q^{97} +(1438.00 - 1438.00i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 30 q^{5} + 58 q^{7} - 32 q^{8} + 140 q^{10} + 236 q^{11} + 138 q^{13} - 128 q^{16} + 542 q^{17} + 320 q^{20} + 472 q^{22} - 538 q^{23} - 350 q^{25} + 552 q^{26} - 464 q^{28} + 404 q^{31}+ \cdots + 2876 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 2.00000i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 8.00000i 0.500000i
\(5\) 15.0000 20.0000i 0.600000 0.800000i
\(6\) 0 0
\(7\) 29.0000 + 29.0000i 0.591837 + 0.591837i 0.938127 0.346291i \(-0.112559\pi\)
−0.346291 + 0.938127i \(0.612559\pi\)
\(8\) −16.0000 + 16.0000i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 70.0000 10.0000i 0.700000 0.100000i
\(11\) 118.000 0.975207 0.487603 0.873065i \(-0.337871\pi\)
0.487603 + 0.873065i \(0.337871\pi\)
\(12\) 0 0
\(13\) 69.0000 69.0000i 0.408284 0.408284i −0.472856 0.881140i \(-0.656777\pi\)
0.881140 + 0.472856i \(0.156777\pi\)
\(14\) 116.000i 0.591837i
\(15\) 0 0
\(16\) −64.0000 −0.250000
\(17\) 271.000 + 271.000i 0.937716 + 0.937716i 0.998171 0.0604547i \(-0.0192551\pi\)
−0.0604547 + 0.998171i \(0.519255\pi\)
\(18\) 0 0
\(19\) 280.000i 0.775623i 0.921739 + 0.387812i \(0.126769\pi\)
−0.921739 + 0.387812i \(0.873231\pi\)
\(20\) 160.000 + 120.000i 0.400000 + 0.300000i
\(21\) 0 0
\(22\) 236.000 + 236.000i 0.487603 + 0.487603i
\(23\) −269.000 + 269.000i −0.508507 + 0.508507i −0.914068 0.405561i \(-0.867076\pi\)
0.405561 + 0.914068i \(0.367076\pi\)
\(24\) 0 0
\(25\) −175.000 600.000i −0.280000 0.960000i
\(26\) 276.000 0.408284
\(27\) 0 0
\(28\) −232.000 + 232.000i −0.295918 + 0.295918i
\(29\) 680.000i 0.808561i −0.914635 0.404281i \(-0.867522\pi\)
0.914635 0.404281i \(-0.132478\pi\)
\(30\) 0 0
\(31\) 202.000 0.210198 0.105099 0.994462i \(-0.466484\pi\)
0.105099 + 0.994462i \(0.466484\pi\)
\(32\) −128.000 128.000i −0.125000 0.125000i
\(33\) 0 0
\(34\) 1084.00i 0.937716i
\(35\) 1015.00 145.000i 0.828571 0.118367i
\(36\) 0 0
\(37\) −651.000 651.000i −0.475530 0.475530i 0.428169 0.903699i \(-0.359159\pi\)
−0.903699 + 0.428169i \(0.859159\pi\)
\(38\) −560.000 + 560.000i −0.387812 + 0.387812i
\(39\) 0 0
\(40\) 80.0000 + 560.000i 0.0500000 + 0.350000i
\(41\) −1682.00 −1.00059 −0.500297 0.865854i \(-0.666776\pi\)
−0.500297 + 0.865854i \(0.666776\pi\)
\(42\) 0 0
\(43\) 1089.00 1089.00i 0.588967 0.588967i −0.348385 0.937352i \(-0.613270\pi\)
0.937352 + 0.348385i \(0.113270\pi\)
\(44\) 944.000i 0.487603i
\(45\) 0 0
\(46\) −1076.00 −0.508507
\(47\) −1269.00 1269.00i −0.574468 0.574468i 0.358906 0.933374i \(-0.383150\pi\)
−0.933374 + 0.358906i \(0.883150\pi\)
\(48\) 0 0
\(49\) 719.000i 0.299459i
\(50\) 850.000 1550.00i 0.340000 0.620000i
\(51\) 0 0
\(52\) 552.000 + 552.000i 0.204142 + 0.204142i
\(53\) 611.000 611.000i 0.217515 0.217515i −0.589935 0.807450i \(-0.700847\pi\)
0.807450 + 0.589935i \(0.200847\pi\)
\(54\) 0 0
\(55\) 1770.00 2360.00i 0.585124 0.780165i
\(56\) −928.000 −0.295918
\(57\) 0 0
\(58\) 1360.00 1360.00i 0.404281 0.404281i
\(59\) 1160.00i 0.333238i −0.986021 0.166619i \(-0.946715\pi\)
0.986021 0.166619i \(-0.0532849\pi\)
\(60\) 0 0
\(61\) −5598.00 −1.50443 −0.752217 0.658915i \(-0.771016\pi\)
−0.752217 + 0.658915i \(0.771016\pi\)
\(62\) 404.000 + 404.000i 0.105099 + 0.105099i
\(63\) 0 0
\(64\) 512.000i 0.125000i
\(65\) −345.000 2415.00i −0.0816568 0.571598i
\(66\) 0 0
\(67\) −751.000 751.000i −0.167298 0.167298i 0.618493 0.785791i \(-0.287744\pi\)
−0.785791 + 0.618493i \(0.787744\pi\)
\(68\) −2168.00 + 2168.00i −0.468858 + 0.468858i
\(69\) 0 0
\(70\) 2320.00 + 1740.00i 0.473469 + 0.355102i
\(71\) −6442.00 −1.27792 −0.638961 0.769240i \(-0.720635\pi\)
−0.638961 + 0.769240i \(0.720635\pi\)
\(72\) 0 0
\(73\) −2951.00 + 2951.00i −0.553762 + 0.553762i −0.927525 0.373762i \(-0.878068\pi\)
0.373762 + 0.927525i \(0.378068\pi\)
\(74\) 2604.00i 0.475530i
\(75\) 0 0
\(76\) −2240.00 −0.387812
\(77\) 3422.00 + 3422.00i 0.577163 + 0.577163i
\(78\) 0 0
\(79\) 10560.0i 1.69204i 0.533154 + 0.846018i \(0.321007\pi\)
−0.533154 + 0.846018i \(0.678993\pi\)
\(80\) −960.000 + 1280.00i −0.150000 + 0.200000i
\(81\) 0 0
\(82\) −3364.00 3364.00i −0.500297 0.500297i
\(83\) 6231.00 6231.00i 0.904485 0.904485i −0.0913348 0.995820i \(-0.529113\pi\)
0.995820 + 0.0913348i \(0.0291134\pi\)
\(84\) 0 0
\(85\) 9485.00 1355.00i 1.31280 0.187543i
\(86\) 4356.00 0.588967
\(87\) 0 0
\(88\) −1888.00 + 1888.00i −0.243802 + 0.243802i
\(89\) 14480.0i 1.82805i 0.405656 + 0.914026i \(0.367043\pi\)
−0.405656 + 0.914026i \(0.632957\pi\)
\(90\) 0 0
\(91\) 4002.00 0.483275
\(92\) −2152.00 2152.00i −0.254253 0.254253i
\(93\) 0 0
\(94\) 5076.00i 0.574468i
\(95\) 5600.00 + 4200.00i 0.620499 + 0.465374i
\(96\) 0 0
\(97\) −7311.00 7311.00i −0.777022 0.777022i 0.202301 0.979323i \(-0.435158\pi\)
−0.979323 + 0.202301i \(0.935158\pi\)
\(98\) 1438.00 1438.00i 0.149729 0.149729i
\(99\) 0 0
\(100\) 4800.00 1400.00i 0.480000 0.140000i
\(101\) 878.000 0.0860700 0.0430350 0.999074i \(-0.486297\pi\)
0.0430350 + 0.999074i \(0.486297\pi\)
\(102\) 0 0
\(103\) 10429.0 10429.0i 0.983033 0.983033i −0.0168252 0.999858i \(-0.505356\pi\)
0.999858 + 0.0168252i \(0.00535587\pi\)
\(104\) 2208.00i 0.204142i
\(105\) 0 0
\(106\) 2444.00 0.217515
\(107\) 4711.00 + 4711.00i 0.411477 + 0.411477i 0.882253 0.470776i \(-0.156026\pi\)
−0.470776 + 0.882253i \(0.656026\pi\)
\(108\) 0 0
\(109\) 22040.0i 1.85506i 0.373745 + 0.927531i \(0.378073\pi\)
−0.373745 + 0.927531i \(0.621927\pi\)
\(110\) 8260.00 1180.00i 0.682645 0.0975207i
\(111\) 0 0
\(112\) −1856.00 1856.00i −0.147959 0.147959i
\(113\) 2111.00 2111.00i 0.165322 0.165322i −0.619597 0.784920i \(-0.712704\pi\)
0.784920 + 0.619597i \(0.212704\pi\)
\(114\) 0 0
\(115\) 1345.00 + 9415.00i 0.101701 + 0.711909i
\(116\) 5440.00 0.404281
\(117\) 0 0
\(118\) 2320.00 2320.00i 0.166619 0.166619i
\(119\) 15718.0i 1.10995i
\(120\) 0 0
\(121\) −717.000 −0.0489721
\(122\) −11196.0 11196.0i −0.752217 0.752217i
\(123\) 0 0
\(124\) 1616.00i 0.105099i
\(125\) −14625.0 5500.00i −0.936000 0.352000i
\(126\) 0 0
\(127\) 5909.00 + 5909.00i 0.366359 + 0.366359i 0.866147 0.499789i \(-0.166589\pi\)
−0.499789 + 0.866147i \(0.666589\pi\)
\(128\) 1024.00 1024.00i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 4140.00 5520.00i 0.244970 0.326627i
\(131\) 6358.00 0.370491 0.185246 0.982692i \(-0.440692\pi\)
0.185246 + 0.982692i \(0.440692\pi\)
\(132\) 0 0
\(133\) −8120.00 + 8120.00i −0.459042 + 0.459042i
\(134\) 3004.00i 0.167298i
\(135\) 0 0
\(136\) −8672.00 −0.468858
\(137\) −20409.0 20409.0i −1.08738 1.08738i −0.995798 0.0915804i \(-0.970808\pi\)
−0.0915804 0.995798i \(-0.529192\pi\)
\(138\) 0 0
\(139\) 9400.00i 0.486517i −0.969961 0.243259i \(-0.921784\pi\)
0.969961 0.243259i \(-0.0782164\pi\)
\(140\) 1160.00 + 8120.00i 0.0591837 + 0.414286i
\(141\) 0 0
\(142\) −12884.0 12884.0i −0.638961 0.638961i
\(143\) 8142.00 8142.00i 0.398161 0.398161i
\(144\) 0 0
\(145\) −13600.0 10200.0i −0.646849 0.485137i
\(146\) −11804.0 −0.553762
\(147\) 0 0
\(148\) 5208.00 5208.00i 0.237765 0.237765i
\(149\) 13800.0i 0.621594i −0.950476 0.310797i \(-0.899404\pi\)
0.950476 0.310797i \(-0.100596\pi\)
\(150\) 0 0
\(151\) −18998.0 −0.833209 −0.416605 0.909088i \(-0.636780\pi\)
−0.416605 + 0.909088i \(0.636780\pi\)
\(152\) −4480.00 4480.00i −0.193906 0.193906i
\(153\) 0 0
\(154\) 13688.0i 0.577163i
\(155\) 3030.00 4040.00i 0.126119 0.168158i
\(156\) 0 0
\(157\) −16371.0 16371.0i −0.664165 0.664165i 0.292194 0.956359i \(-0.405615\pi\)
−0.956359 + 0.292194i \(0.905615\pi\)
\(158\) −21120.0 + 21120.0i −0.846018 + 0.846018i
\(159\) 0 0
\(160\) −4480.00 + 640.000i −0.175000 + 0.0250000i
\(161\) −15602.0 −0.601906
\(162\) 0 0
\(163\) 20009.0 20009.0i 0.753096 0.753096i −0.221960 0.975056i \(-0.571245\pi\)
0.975056 + 0.221960i \(0.0712455\pi\)
\(164\) 13456.0i 0.500297i
\(165\) 0 0
\(166\) 24924.0 0.904485
\(167\) −1549.00 1549.00i −0.0555416 0.0555416i 0.678790 0.734332i \(-0.262504\pi\)
−0.734332 + 0.678790i \(0.762504\pi\)
\(168\) 0 0
\(169\) 19039.0i 0.666608i
\(170\) 21680.0 + 16260.0i 0.750173 + 0.562630i
\(171\) 0 0
\(172\) 8712.00 + 8712.00i 0.294484 + 0.294484i
\(173\) −2789.00 + 2789.00i −0.0931872 + 0.0931872i −0.752164 0.658976i \(-0.770990\pi\)
0.658976 + 0.752164i \(0.270990\pi\)
\(174\) 0 0
\(175\) 12325.0 22475.0i 0.402449 0.733878i
\(176\) −7552.00 −0.243802
\(177\) 0 0
\(178\) −28960.0 + 28960.0i −0.914026 + 0.914026i
\(179\) 2600.00i 0.0811460i 0.999177 + 0.0405730i \(0.0129183\pi\)
−0.999177 + 0.0405730i \(0.987082\pi\)
\(180\) 0 0
\(181\) −44398.0 −1.35521 −0.677604 0.735427i \(-0.736982\pi\)
−0.677604 + 0.735427i \(0.736982\pi\)
\(182\) 8004.00 + 8004.00i 0.241637 + 0.241637i
\(183\) 0 0
\(184\) 8608.00i 0.254253i
\(185\) −22785.0 + 3255.00i −0.665741 + 0.0951059i
\(186\) 0 0
\(187\) 31978.0 + 31978.0i 0.914467 + 0.914467i
\(188\) 10152.0 10152.0i 0.287234 0.287234i
\(189\) 0 0
\(190\) 2800.00 + 19600.0i 0.0775623 + 0.542936i
\(191\) 14678.0 0.402346 0.201173 0.979556i \(-0.435525\pi\)
0.201173 + 0.979556i \(0.435525\pi\)
\(192\) 0 0
\(193\) 42849.0 42849.0i 1.15034 1.15034i 0.163855 0.986484i \(-0.447607\pi\)
0.986484 0.163855i \(-0.0523930\pi\)
\(194\) 29244.0i 0.777022i
\(195\) 0 0
\(196\) 5752.00 0.149729
\(197\) 10971.0 + 10971.0i 0.282692 + 0.282692i 0.834182 0.551490i \(-0.185940\pi\)
−0.551490 + 0.834182i \(0.685940\pi\)
\(198\) 0 0
\(199\) 38160.0i 0.963612i −0.876278 0.481806i \(-0.839981\pi\)
0.876278 0.481806i \(-0.160019\pi\)
\(200\) 12400.0 + 6800.00i 0.310000 + 0.170000i
\(201\) 0 0
\(202\) 1756.00 + 1756.00i 0.0430350 + 0.0430350i
\(203\) 19720.0 19720.0i 0.478536 0.478536i
\(204\) 0 0
\(205\) −25230.0 + 33640.0i −0.600357 + 0.800476i
\(206\) 41716.0 0.983033
\(207\) 0 0
\(208\) −4416.00 + 4416.00i −0.102071 + 0.102071i
\(209\) 33040.0i 0.756393i
\(210\) 0 0
\(211\) 72842.0 1.63613 0.818063 0.575128i \(-0.195048\pi\)
0.818063 + 0.575128i \(0.195048\pi\)
\(212\) 4888.00 + 4888.00i 0.108758 + 0.108758i
\(213\) 0 0
\(214\) 18844.0i 0.411477i
\(215\) −5445.00 38115.0i −0.117793 0.824554i
\(216\) 0 0
\(217\) 5858.00 + 5858.00i 0.124403 + 0.124403i
\(218\) −44080.0 + 44080.0i −0.927531 + 0.927531i
\(219\) 0 0
\(220\) 18880.0 + 14160.0i 0.390083 + 0.292562i
\(221\) 37398.0 0.765709
\(222\) 0 0
\(223\) −30891.0 + 30891.0i −0.621187 + 0.621187i −0.945835 0.324648i \(-0.894754\pi\)
0.324648 + 0.945835i \(0.394754\pi\)
\(224\) 7424.00i 0.147959i
\(225\) 0 0
\(226\) 8444.00 0.165322
\(227\) 54911.0 + 54911.0i 1.06563 + 1.06563i 0.997689 + 0.0679438i \(0.0216439\pi\)
0.0679438 + 0.997689i \(0.478356\pi\)
\(228\) 0 0
\(229\) 50280.0i 0.958792i −0.877599 0.479396i \(-0.840856\pi\)
0.877599 0.479396i \(-0.159144\pi\)
\(230\) −16140.0 + 21520.0i −0.305104 + 0.406805i
\(231\) 0 0
\(232\) 10880.0 + 10880.0i 0.202140 + 0.202140i
\(233\) 2391.00 2391.00i 0.0440421 0.0440421i −0.684743 0.728785i \(-0.740085\pi\)
0.728785 + 0.684743i \(0.240085\pi\)
\(234\) 0 0
\(235\) −44415.0 + 6345.00i −0.804255 + 0.114894i
\(236\) 9280.00 0.166619
\(237\) 0 0
\(238\) −31436.0 + 31436.0i −0.554975 + 0.554975i
\(239\) 17760.0i 0.310919i 0.987842 + 0.155459i \(0.0496858\pi\)
−0.987842 + 0.155459i \(0.950314\pi\)
\(240\) 0 0
\(241\) −28238.0 −0.486183 −0.243092 0.970003i \(-0.578162\pi\)
−0.243092 + 0.970003i \(0.578162\pi\)
\(242\) −1434.00 1434.00i −0.0244860 0.0244860i
\(243\) 0 0
\(244\) 44784.0i 0.752217i
\(245\) −14380.0 10785.0i −0.239567 0.179675i
\(246\) 0 0
\(247\) 19320.0 + 19320.0i 0.316675 + 0.316675i
\(248\) −3232.00 + 3232.00i −0.0525494 + 0.0525494i
\(249\) 0 0
\(250\) −18250.0 40250.0i −0.292000 0.644000i
\(251\) −121002. −1.92064 −0.960318 0.278907i \(-0.910028\pi\)
−0.960318 + 0.278907i \(0.910028\pi\)
\(252\) 0 0
\(253\) −31742.0 + 31742.0i −0.495899 + 0.495899i
\(254\) 23636.0i 0.366359i
\(255\) 0 0
\(256\) 4096.00 0.0625000
\(257\) 72431.0 + 72431.0i 1.09663 + 1.09663i 0.994803 + 0.101823i \(0.0324674\pi\)
0.101823 + 0.994803i \(0.467533\pi\)
\(258\) 0 0
\(259\) 37758.0i 0.562872i
\(260\) 19320.0 2760.00i 0.285799 0.0408284i
\(261\) 0 0
\(262\) 12716.0 + 12716.0i 0.185246 + 0.185246i
\(263\) 14771.0 14771.0i 0.213549 0.213549i −0.592224 0.805773i \(-0.701750\pi\)
0.805773 + 0.592224i \(0.201750\pi\)
\(264\) 0 0
\(265\) −3055.00 21385.0i −0.0435030 0.304521i
\(266\) −32480.0 −0.459042
\(267\) 0 0
\(268\) 6008.00 6008.00i 0.0836489 0.0836489i
\(269\) 89720.0i 1.23989i −0.784644 0.619947i \(-0.787154\pi\)
0.784644 0.619947i \(-0.212846\pi\)
\(270\) 0 0
\(271\) 68202.0 0.928664 0.464332 0.885661i \(-0.346294\pi\)
0.464332 + 0.885661i \(0.346294\pi\)
\(272\) −17344.0 17344.0i −0.234429 0.234429i
\(273\) 0 0
\(274\) 81636.0i 1.08738i
\(275\) −20650.0 70800.0i −0.273058 0.936198i
\(276\) 0 0
\(277\) 18549.0 + 18549.0i 0.241747 + 0.241747i 0.817573 0.575826i \(-0.195319\pi\)
−0.575826 + 0.817573i \(0.695319\pi\)
\(278\) 18800.0 18800.0i 0.243259 0.243259i
\(279\) 0 0
\(280\) −13920.0 + 18560.0i −0.177551 + 0.236735i
\(281\) −2322.00 −0.0294069 −0.0147035 0.999892i \(-0.504680\pi\)
−0.0147035 + 0.999892i \(0.504680\pi\)
\(282\) 0 0
\(283\) −91711.0 + 91711.0i −1.14511 + 1.14511i −0.157613 + 0.987501i \(0.550380\pi\)
−0.987501 + 0.157613i \(0.949620\pi\)
\(284\) 51536.0i 0.638961i
\(285\) 0 0
\(286\) 32568.0 0.398161
\(287\) −48778.0 48778.0i −0.592189 0.592189i
\(288\) 0 0
\(289\) 63361.0i 0.758624i
\(290\) −6800.00 47600.0i −0.0808561 0.565993i
\(291\) 0 0
\(292\) −23608.0 23608.0i −0.276881 0.276881i
\(293\) 4851.00 4851.00i 0.0565062 0.0565062i −0.678289 0.734795i \(-0.737278\pi\)
0.734795 + 0.678289i \(0.237278\pi\)
\(294\) 0 0
\(295\) −23200.0 17400.0i −0.266590 0.199943i
\(296\) 20832.0 0.237765
\(297\) 0 0
\(298\) 27600.0 27600.0i 0.310797 0.310797i
\(299\) 37122.0i 0.415230i
\(300\) 0 0
\(301\) 63162.0 0.697145
\(302\) −37996.0 37996.0i −0.416605 0.416605i
\(303\) 0 0
\(304\) 17920.0i 0.193906i
\(305\) −83970.0 + 111960.i −0.902661 + 1.20355i
\(306\) 0 0
\(307\) 42849.0 + 42849.0i 0.454636 + 0.454636i 0.896890 0.442254i \(-0.145821\pi\)
−0.442254 + 0.896890i \(0.645821\pi\)
\(308\) −27376.0 + 27376.0i −0.288582 + 0.288582i
\(309\) 0 0
\(310\) 14140.0 2020.00i 0.147138 0.0210198i
\(311\) 72278.0 0.747283 0.373642 0.927573i \(-0.378109\pi\)
0.373642 + 0.927573i \(0.378109\pi\)
\(312\) 0 0
\(313\) 18249.0 18249.0i 0.186273 0.186273i −0.607810 0.794083i \(-0.707952\pi\)
0.794083 + 0.607810i \(0.207952\pi\)
\(314\) 65484.0i 0.664165i
\(315\) 0 0
\(316\) −84480.0 −0.846018
\(317\) −25149.0 25149.0i −0.250266 0.250266i 0.570814 0.821080i \(-0.306628\pi\)
−0.821080 + 0.570814i \(0.806628\pi\)
\(318\) 0 0
\(319\) 80240.0i 0.788514i
\(320\) −10240.0 7680.00i −0.100000 0.0750000i
\(321\) 0 0
\(322\) −31204.0 31204.0i −0.300953 0.300953i
\(323\) −75880.0 + 75880.0i −0.727315 + 0.727315i
\(324\) 0 0
\(325\) −53475.0 29325.0i −0.506272 0.277633i
\(326\) 80036.0 0.753096
\(327\) 0 0
\(328\) 26912.0 26912.0i 0.250149 0.250149i
\(329\) 73602.0i 0.679983i
\(330\) 0 0
\(331\) −54038.0 −0.493223 −0.246611 0.969114i \(-0.579317\pi\)
−0.246611 + 0.969114i \(0.579317\pi\)
\(332\) 49848.0 + 49848.0i 0.452243 + 0.452243i
\(333\) 0 0
\(334\) 6196.00i 0.0555416i
\(335\) −26285.0 + 3755.00i −0.234217 + 0.0334596i
\(336\) 0 0
\(337\) 8529.00 + 8529.00i 0.0750997 + 0.0750997i 0.743659 0.668559i \(-0.233089\pi\)
−0.668559 + 0.743659i \(0.733089\pi\)
\(338\) −38078.0 + 38078.0i −0.333304 + 0.333304i
\(339\) 0 0
\(340\) 10840.0 + 75880.0i 0.0937716 + 0.656401i
\(341\) 23836.0 0.204986
\(342\) 0 0
\(343\) 90480.0 90480.0i 0.769067 0.769067i
\(344\) 34848.0i 0.294484i
\(345\) 0 0
\(346\) −11156.0 −0.0931872
\(347\) 56551.0 + 56551.0i 0.469658 + 0.469658i 0.901804 0.432146i \(-0.142244\pi\)
−0.432146 + 0.901804i \(0.642244\pi\)
\(348\) 0 0
\(349\) 22520.0i 0.184892i −0.995718 0.0924459i \(-0.970531\pi\)
0.995718 0.0924459i \(-0.0294685\pi\)
\(350\) 69600.0 20300.0i 0.568163 0.165714i
\(351\) 0 0
\(352\) −15104.0 15104.0i −0.121901 0.121901i
\(353\) 44511.0 44511.0i 0.357205 0.357205i −0.505576 0.862782i \(-0.668720\pi\)
0.862782 + 0.505576i \(0.168720\pi\)
\(354\) 0 0
\(355\) −96630.0 + 128840.i −0.766753 + 1.02234i
\(356\) −115840. −0.914026
\(357\) 0 0
\(358\) −5200.00 + 5200.00i −0.0405730 + 0.0405730i
\(359\) 9680.00i 0.0751080i 0.999295 + 0.0375540i \(0.0119566\pi\)
−0.999295 + 0.0375540i \(0.988043\pi\)
\(360\) 0 0
\(361\) 51921.0 0.398409
\(362\) −88796.0 88796.0i −0.677604 0.677604i
\(363\) 0 0
\(364\) 32016.0i 0.241637i
\(365\) 14755.0 + 103285.i 0.110752 + 0.775267i
\(366\) 0 0
\(367\) −14971.0 14971.0i −0.111152 0.111152i 0.649343 0.760496i \(-0.275044\pi\)
−0.760496 + 0.649343i \(0.775044\pi\)
\(368\) 17216.0 17216.0i 0.127127 0.127127i
\(369\) 0 0
\(370\) −52080.0 39060.0i −0.380424 0.285318i
\(371\) 35438.0 0.257467
\(372\) 0 0
\(373\) −13811.0 + 13811.0i −0.0992676 + 0.0992676i −0.754996 0.655729i \(-0.772361\pi\)
0.655729 + 0.754996i \(0.272361\pi\)
\(374\) 127912.i 0.914467i
\(375\) 0 0
\(376\) 40608.0 0.287234
\(377\) −46920.0 46920.0i −0.330123 0.330123i
\(378\) 0 0
\(379\) 251080.i 1.74797i 0.485954 + 0.873984i \(0.338472\pi\)
−0.485954 + 0.873984i \(0.661528\pi\)
\(380\) −33600.0 + 44800.0i −0.232687 + 0.310249i
\(381\) 0 0
\(382\) 29356.0 + 29356.0i 0.201173 + 0.201173i
\(383\) 86091.0 86091.0i 0.586895 0.586895i −0.349894 0.936789i \(-0.613783\pi\)
0.936789 + 0.349894i \(0.113783\pi\)
\(384\) 0 0
\(385\) 119770. 17110.0i 0.808028 0.115433i
\(386\) 171396. 1.15034
\(387\) 0 0
\(388\) 58488.0 58488.0i 0.388511 0.388511i
\(389\) 75000.0i 0.495635i 0.968807 + 0.247818i \(0.0797134\pi\)
−0.968807 + 0.247818i \(0.920287\pi\)
\(390\) 0 0
\(391\) −145798. −0.953670
\(392\) 11504.0 + 11504.0i 0.0748646 + 0.0748646i
\(393\) 0 0
\(394\) 43884.0i 0.282692i
\(395\) 211200. + 158400.i 1.35363 + 1.01522i
\(396\) 0 0
\(397\) 29149.0 + 29149.0i 0.184945 + 0.184945i 0.793507 0.608562i \(-0.208253\pi\)
−0.608562 + 0.793507i \(0.708253\pi\)
\(398\) 76320.0 76320.0i 0.481806 0.481806i
\(399\) 0 0
\(400\) 11200.0 + 38400.0i 0.0700000 + 0.240000i
\(401\) 45918.0 0.285558 0.142779 0.989755i \(-0.454396\pi\)
0.142779 + 0.989755i \(0.454396\pi\)
\(402\) 0 0
\(403\) 13938.0 13938.0i 0.0858204 0.0858204i
\(404\) 7024.00i 0.0430350i
\(405\) 0 0
\(406\) 78880.0 0.478536
\(407\) −76818.0 76818.0i −0.463740 0.463740i
\(408\) 0 0
\(409\) 78720.0i 0.470585i 0.971925 + 0.235293i \(0.0756049\pi\)
−0.971925 + 0.235293i \(0.924395\pi\)
\(410\) −117740. + 16820.0i −0.700416 + 0.100059i
\(411\) 0 0
\(412\) 83432.0 + 83432.0i 0.491517 + 0.491517i
\(413\) 33640.0 33640.0i 0.197222 0.197222i
\(414\) 0 0
\(415\) −31155.0 218085.i −0.180897 1.26628i
\(416\) −17664.0 −0.102071
\(417\) 0 0
\(418\) −66080.0 + 66080.0i −0.378196 + 0.378196i
\(419\) 14760.0i 0.0840733i 0.999116 + 0.0420367i \(0.0133846\pi\)
−0.999116 + 0.0420367i \(0.986615\pi\)
\(420\) 0 0
\(421\) 221282. 1.24848 0.624240 0.781232i \(-0.285409\pi\)
0.624240 + 0.781232i \(0.285409\pi\)
\(422\) 145684. + 145684.i 0.818063 + 0.818063i
\(423\) 0 0
\(424\) 19552.0i 0.108758i
\(425\) 115175. 210025.i 0.637647 1.16277i
\(426\) 0 0
\(427\) −162342. 162342.i −0.890379 0.890379i
\(428\) −37688.0 + 37688.0i −0.205738 + 0.205738i
\(429\) 0 0
\(430\) 65340.0 87120.0i 0.353380 0.471174i
\(431\) −212522. −1.14406 −0.572031 0.820232i \(-0.693844\pi\)
−0.572031 + 0.820232i \(0.693844\pi\)
\(432\) 0 0
\(433\) 145409. 145409.i 0.775560 0.775560i −0.203512 0.979072i \(-0.565236\pi\)
0.979072 + 0.203512i \(0.0652357\pi\)
\(434\) 23432.0i 0.124403i
\(435\) 0 0
\(436\) −176320. −0.927531
\(437\) −75320.0 75320.0i −0.394410 0.394410i
\(438\) 0 0
\(439\) 299440.i 1.55375i −0.629656 0.776874i \(-0.716804\pi\)
0.629656 0.776874i \(-0.283196\pi\)
\(440\) 9440.00 + 66080.0i 0.0487603 + 0.341322i
\(441\) 0 0
\(442\) 74796.0 + 74796.0i 0.382855 + 0.382855i
\(443\) −240609. + 240609.i −1.22604 + 1.22604i −0.260590 + 0.965450i \(0.583917\pi\)
−0.965450 + 0.260590i \(0.916083\pi\)
\(444\) 0 0
\(445\) 289600. + 217200.i 1.46244 + 1.09683i
\(446\) −123564. −0.621187
\(447\) 0 0
\(448\) 14848.0 14848.0i 0.0739796 0.0739796i
\(449\) 82480.0i 0.409125i 0.978854 + 0.204562i \(0.0655772\pi\)
−0.978854 + 0.204562i \(0.934423\pi\)
\(450\) 0 0
\(451\) −198476. −0.975787
\(452\) 16888.0 + 16888.0i 0.0826611 + 0.0826611i
\(453\) 0 0
\(454\) 219644.i 1.06563i
\(455\) 60030.0 80040.0i 0.289965 0.386620i
\(456\) 0 0
\(457\) −188151. 188151.i −0.900895 0.900895i 0.0946187 0.995514i \(-0.469837\pi\)
−0.995514 + 0.0946187i \(0.969837\pi\)
\(458\) 100560. 100560.i 0.479396 0.479396i
\(459\) 0 0
\(460\) −75320.0 + 10760.0i −0.355955 + 0.0508507i
\(461\) 326158. 1.53471 0.767355 0.641223i \(-0.221573\pi\)
0.767355 + 0.641223i \(0.221573\pi\)
\(462\) 0 0
\(463\) −218731. + 218731.i −1.02035 + 1.02035i −0.0205595 + 0.999789i \(0.506545\pi\)
−0.999789 + 0.0205595i \(0.993455\pi\)
\(464\) 43520.0i 0.202140i
\(465\) 0 0
\(466\) 9564.00 0.0440421
\(467\) −59249.0 59249.0i −0.271673 0.271673i 0.558100 0.829774i \(-0.311530\pi\)
−0.829774 + 0.558100i \(0.811530\pi\)
\(468\) 0 0
\(469\) 43558.0i 0.198026i
\(470\) −101520. 76140.0i −0.459574 0.344681i
\(471\) 0 0
\(472\) 18560.0 + 18560.0i 0.0833094 + 0.0833094i
\(473\) 128502. 128502.i 0.574365 0.574365i
\(474\) 0 0
\(475\) 168000. 49000.0i 0.744598 0.217175i
\(476\) −125744. −0.554975
\(477\) 0 0
\(478\) −35520.0 + 35520.0i −0.155459 + 0.155459i
\(479\) 273440.i 1.19177i −0.803071 0.595883i \(-0.796802\pi\)
0.803071 0.595883i \(-0.203198\pi\)
\(480\) 0 0
\(481\) −89838.0 −0.388302
\(482\) −56476.0 56476.0i −0.243092 0.243092i
\(483\) 0 0
\(484\) 5736.00i 0.0244860i
\(485\) −255885. + 36555.0i −1.08783 + 0.155404i
\(486\) 0 0
\(487\) −123651. 123651.i −0.521362 0.521362i 0.396620 0.917983i \(-0.370183\pi\)
−0.917983 + 0.396620i \(0.870183\pi\)
\(488\) 89568.0 89568.0i 0.376109 0.376109i
\(489\) 0 0
\(490\) −7190.00 50330.0i −0.0299459 0.209621i
\(491\) −198442. −0.823134 −0.411567 0.911379i \(-0.635018\pi\)
−0.411567 + 0.911379i \(0.635018\pi\)
\(492\) 0 0
\(493\) 184280. 184280.i 0.758201 0.758201i
\(494\) 77280.0i 0.316675i
\(495\) 0 0
\(496\) −12928.0 −0.0525494
\(497\) −186818. 186818.i −0.756321 0.756321i
\(498\) 0 0
\(499\) 269240.i 1.08128i 0.841254 + 0.540640i \(0.181818\pi\)
−0.841254 + 0.540640i \(0.818182\pi\)
\(500\) 44000.0 117000.i 0.176000 0.468000i
\(501\) 0 0
\(502\) −242004. 242004.i −0.960318 0.960318i
\(503\) −109869. + 109869.i −0.434249 + 0.434249i −0.890071 0.455822i \(-0.849345\pi\)
0.455822 + 0.890071i \(0.349345\pi\)
\(504\) 0 0
\(505\) 13170.0 17560.0i 0.0516420 0.0688560i
\(506\) −126968. −0.495899
\(507\) 0 0
\(508\) −47272.0 + 47272.0i −0.183179 + 0.183179i
\(509\) 211000.i 0.814417i 0.913335 + 0.407209i \(0.133498\pi\)
−0.913335 + 0.407209i \(0.866502\pi\)
\(510\) 0 0
\(511\) −171158. −0.655474
\(512\) 8192.00 + 8192.00i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 289724.i 1.09663i
\(515\) −52145.0 365015.i −0.196607 1.37625i
\(516\) 0 0
\(517\) −149742. 149742.i −0.560225 0.560225i
\(518\) 75516.0 75516.0i 0.281436 0.281436i
\(519\) 0 0
\(520\) 44160.0 + 33120.0i 0.163314 + 0.122485i
\(521\) −297282. −1.09520 −0.547600 0.836740i \(-0.684458\pi\)
−0.547600 + 0.836740i \(0.684458\pi\)
\(522\) 0 0
\(523\) −25071.0 + 25071.0i −0.0916576 + 0.0916576i −0.751449 0.659791i \(-0.770645\pi\)
0.659791 + 0.751449i \(0.270645\pi\)
\(524\) 50864.0i 0.185246i
\(525\) 0 0
\(526\) 59084.0 0.213549
\(527\) 54742.0 + 54742.0i 0.197106 + 0.197106i
\(528\) 0 0
\(529\) 135119.i 0.482842i
\(530\) 36660.0 48880.0i 0.130509 0.174012i
\(531\) 0 0
\(532\) −64960.0 64960.0i −0.229521 0.229521i
\(533\) −116058. + 116058.i −0.408527 + 0.408527i
\(534\) 0 0
\(535\) 164885. 23555.0i 0.576068 0.0822954i
\(536\) 24032.0 0.0836489
\(537\) 0 0
\(538\) 179440. 179440.i 0.619947 0.619947i
\(539\) 84842.0i 0.292034i
\(540\) 0 0
\(541\) −142478. −0.486803 −0.243402 0.969926i \(-0.578263\pi\)
−0.243402 + 0.969926i \(0.578263\pi\)
\(542\) 136404. + 136404.i 0.464332 + 0.464332i
\(543\) 0 0
\(544\) 69376.0i 0.234429i
\(545\) 440800. + 330600.i 1.48405 + 1.11304i
\(546\) 0 0
\(547\) 291009. + 291009.i 0.972594 + 0.972594i 0.999634 0.0270399i \(-0.00860813\pi\)
−0.0270399 + 0.999634i \(0.508608\pi\)
\(548\) 163272. 163272.i 0.543689 0.543689i
\(549\) 0 0
\(550\) 100300. 182900.i 0.331570 0.604628i
\(551\) 190400. 0.627139
\(552\) 0 0
\(553\) −306240. + 306240.i −1.00141 + 1.00141i
\(554\) 74196.0i 0.241747i
\(555\) 0 0
\(556\) 75200.0 0.243259
\(557\) 83091.0 + 83091.0i 0.267820 + 0.267820i 0.828221 0.560401i \(-0.189353\pi\)
−0.560401 + 0.828221i \(0.689353\pi\)
\(558\) 0 0
\(559\) 150282.i 0.480932i
\(560\) −64960.0 + 9280.00i −0.207143 + 0.0295918i
\(561\) 0 0
\(562\) −4644.00 4644.00i −0.0147035 0.0147035i
\(563\) −43449.0 + 43449.0i −0.137076 + 0.137076i −0.772316 0.635239i \(-0.780902\pi\)
0.635239 + 0.772316i \(0.280902\pi\)
\(564\) 0 0
\(565\) −10555.0 73885.0i −0.0330645 0.231451i
\(566\) −366844. −1.14511
\(567\) 0 0
\(568\) 103072. 103072.i 0.319480 0.319480i
\(569\) 270560.i 0.835678i 0.908521 + 0.417839i \(0.137212\pi\)
−0.908521 + 0.417839i \(0.862788\pi\)
\(570\) 0 0
\(571\) 57482.0 0.176303 0.0881515 0.996107i \(-0.471904\pi\)
0.0881515 + 0.996107i \(0.471904\pi\)
\(572\) 65136.0 + 65136.0i 0.199081 + 0.199081i
\(573\) 0 0
\(574\) 195112.i 0.592189i
\(575\) 208475. + 114325.i 0.630548 + 0.345784i
\(576\) 0 0
\(577\) 195889. + 195889.i 0.588381 + 0.588381i 0.937193 0.348812i \(-0.113415\pi\)
−0.348812 + 0.937193i \(0.613415\pi\)
\(578\) −126722. + 126722.i −0.379312 + 0.379312i
\(579\) 0 0
\(580\) 81600.0 108800.i 0.242568 0.323424i
\(581\) 361398. 1.07062
\(582\) 0 0
\(583\) 72098.0 72098.0i 0.212122 0.212122i
\(584\) 94432.0i 0.276881i
\(585\) 0 0
\(586\) 19404.0 0.0565062
\(587\) 404631. + 404631.i 1.17431 + 1.17431i 0.981171 + 0.193139i \(0.0618669\pi\)
0.193139 + 0.981171i \(0.438133\pi\)
\(588\) 0 0
\(589\) 56560.0i 0.163034i
\(590\) −11600.0 81200.0i −0.0333238 0.233266i
\(591\) 0 0
\(592\) 41664.0 + 41664.0i 0.118882 + 0.118882i
\(593\) 210991. 210991.i 0.600005 0.600005i −0.340309 0.940314i \(-0.610532\pi\)
0.940314 + 0.340309i \(0.110532\pi\)
\(594\) 0 0
\(595\) 314360. + 235770.i 0.887960 + 0.665970i
\(596\) 110400. 0.310797
\(597\) 0 0
\(598\) −74244.0 + 74244.0i −0.207615 + 0.207615i
\(599\) 300560.i 0.837679i −0.908060 0.418839i \(-0.862437\pi\)
0.908060 0.418839i \(-0.137563\pi\)
\(600\) 0 0
\(601\) 367442. 1.01728 0.508639 0.860980i \(-0.330149\pi\)
0.508639 + 0.860980i \(0.330149\pi\)
\(602\) 126324. + 126324.i 0.348572 + 0.348572i
\(603\) 0 0
\(604\) 151984.i 0.416605i
\(605\) −10755.0 + 14340.0i −0.0293832 + 0.0391777i
\(606\) 0 0
\(607\) 146469. + 146469.i 0.397529 + 0.397529i 0.877360 0.479832i \(-0.159302\pi\)
−0.479832 + 0.877360i \(0.659302\pi\)
\(608\) 35840.0 35840.0i 0.0969529 0.0969529i
\(609\) 0 0
\(610\) −391860. + 55980.0i −1.05310 + 0.150443i
\(611\) −175122. −0.469092
\(612\) 0 0
\(613\) 160989. 160989.i 0.428425 0.428425i −0.459666 0.888092i \(-0.652031\pi\)
0.888092 + 0.459666i \(0.152031\pi\)
\(614\) 171396.i 0.454636i
\(615\) 0 0
\(616\) −109504. −0.288582
\(617\) −320409. 320409.i −0.841656 0.841656i 0.147419 0.989074i \(-0.452904\pi\)
−0.989074 + 0.147419i \(0.952904\pi\)
\(618\) 0 0
\(619\) 341160.i 0.890383i 0.895435 + 0.445191i \(0.146864\pi\)
−0.895435 + 0.445191i \(0.853136\pi\)
\(620\) 32320.0 + 24240.0i 0.0840791 + 0.0630593i
\(621\) 0 0
\(622\) 144556. + 144556.i 0.373642 + 0.373642i
\(623\) −419920. + 419920.i −1.08191 + 1.08191i
\(624\) 0 0
\(625\) −329375. + 210000.i −0.843200 + 0.537600i
\(626\) 72996.0 0.186273
\(627\) 0 0
\(628\) 130968. 130968.i 0.332082 0.332082i
\(629\) 352842.i 0.891824i
\(630\) 0 0
\(631\) −390998. −0.982010 −0.491005 0.871157i \(-0.663370\pi\)
−0.491005 + 0.871157i \(0.663370\pi\)
\(632\) −168960. 168960.i −0.423009 0.423009i
\(633\) 0 0
\(634\) 100596.i 0.250266i
\(635\) 206815. 29545.0i 0.512902 0.0732717i
\(636\) 0 0
\(637\) −49611.0 49611.0i −0.122264 0.122264i
\(638\) 160480. 160480.i 0.394257 0.394257i
\(639\) 0 0
\(640\) −5120.00 35840.0i −0.0125000 0.0875000i
\(641\) 585038. 1.42386 0.711931 0.702249i \(-0.247821\pi\)
0.711931 + 0.702249i \(0.247821\pi\)
\(642\) 0 0
\(643\) −31911.0 + 31911.0i −0.0771824 + 0.0771824i −0.744644 0.667462i \(-0.767381\pi\)
0.667462 + 0.744644i \(0.267381\pi\)
\(644\) 124816.i 0.300953i
\(645\) 0 0
\(646\) −303520. −0.727315
\(647\) 280931. + 280931.i 0.671106 + 0.671106i 0.957971 0.286865i \(-0.0926131\pi\)
−0.286865 + 0.957971i \(0.592613\pi\)
\(648\) 0 0
\(649\) 136880.i 0.324975i
\(650\) −48300.0 165600.i −0.114320 0.391953i
\(651\) 0 0
\(652\) 160072. + 160072.i 0.376548 + 0.376548i
\(653\) −523989. + 523989.i −1.22884 + 1.22884i −0.264439 + 0.964402i \(0.585187\pi\)
−0.964402 + 0.264439i \(0.914813\pi\)
\(654\) 0 0
\(655\) 95370.0 127160.i 0.222295 0.296393i
\(656\) 107648. 0.250149
\(657\) 0 0
\(658\) 147204. 147204.i 0.339991 0.339991i
\(659\) 404360.i 0.931102i 0.885021 + 0.465551i \(0.154144\pi\)
−0.885021 + 0.465551i \(0.845856\pi\)
\(660\) 0 0
\(661\) −5278.00 −0.0120800 −0.00603999 0.999982i \(-0.501923\pi\)
−0.00603999 + 0.999982i \(0.501923\pi\)
\(662\) −108076. 108076.i −0.246611 0.246611i
\(663\) 0 0
\(664\) 199392.i 0.452243i
\(665\) 40600.0 + 284200.i 0.0918085 + 0.642659i
\(666\) 0 0
\(667\) 182920. + 182920.i 0.411159 + 0.411159i
\(668\) 12392.0 12392.0i 0.0277708 0.0277708i
\(669\) 0 0
\(670\) −60080.0 45060.0i −0.133838 0.100379i
\(671\) −660564. −1.46713
\(672\) 0 0
\(673\) −332111. + 332111.i −0.733252 + 0.733252i −0.971263 0.238011i \(-0.923505\pi\)
0.238011 + 0.971263i \(0.423505\pi\)
\(674\) 34116.0i 0.0750997i
\(675\) 0 0
\(676\) −152312. −0.333304
\(677\) −578309. 578309.i −1.26178 1.26178i −0.950231 0.311546i \(-0.899153\pi\)
−0.311546 0.950231i \(-0.600847\pi\)
\(678\) 0 0
\(679\) 424038.i 0.919740i
\(680\) −130080. + 173440.i −0.281315 + 0.375087i
\(681\) 0 0
\(682\) 47672.0 + 47672.0i 0.102493 + 0.102493i
\(683\) 349311. 349311.i 0.748809 0.748809i −0.225447 0.974255i \(-0.572384\pi\)
0.974255 + 0.225447i \(0.0723842\pi\)
\(684\) 0 0
\(685\) −714315. + 102045.i −1.52233 + 0.217476i
\(686\) 361920. 0.769067
\(687\) 0 0
\(688\) −69696.0 + 69696.0i −0.147242 + 0.147242i
\(689\) 84318.0i 0.177616i
\(690\) 0 0
\(691\) 282762. 0.592195 0.296098 0.955158i \(-0.404315\pi\)
0.296098 + 0.955158i \(0.404315\pi\)
\(692\) −22312.0 22312.0i −0.0465936 0.0465936i
\(693\) 0 0
\(694\) 226204.i 0.469658i
\(695\) −188000. 141000.i −0.389214 0.291910i
\(696\) 0 0
\(697\) −455822. 455822.i −0.938274 0.938274i
\(698\) 45040.0 45040.0i 0.0924459 0.0924459i
\(699\) 0 0
\(700\) 179800. + 98600.0i 0.366939 + 0.201224i
\(701\) −270242. −0.549942 −0.274971 0.961453i \(-0.588668\pi\)
−0.274971 + 0.961453i \(0.588668\pi\)
\(702\) 0 0
\(703\) 182280. 182280.i 0.368832 0.368832i
\(704\) 60416.0i 0.121901i
\(705\) 0 0
\(706\) 178044. 0.357205
\(707\) 25462.0 + 25462.0i 0.0509394 + 0.0509394i
\(708\) 0 0
\(709\) 297800.i 0.592423i −0.955122 0.296212i \(-0.904277\pi\)
0.955122 0.296212i \(-0.0957234\pi\)
\(710\) −450940. + 64420.0i −0.894545 + 0.127792i
\(711\) 0 0
\(712\) −231680. 231680.i −0.457013 0.457013i
\(713\) −54338.0 + 54338.0i −0.106887 + 0.106887i
\(714\) 0 0
\(715\) −40710.0 284970.i −0.0796323 0.557426i
\(716\) −20800.0 −0.0405730
\(717\) 0 0
\(718\) −19360.0 + 19360.0i −0.0375540 + 0.0375540i
\(719\) 913760.i 1.76756i −0.467902 0.883780i \(-0.654990\pi\)
0.467902 0.883780i \(-0.345010\pi\)
\(720\) 0 0
\(721\) 604882. 1.16359
\(722\) 103842. + 103842.i 0.199204 + 0.199204i
\(723\) 0 0
\(724\) 355184.i 0.677604i
\(725\) −408000. + 119000.i −0.776219 + 0.226397i
\(726\) 0 0
\(727\) −417651. 417651.i −0.790214 0.790214i 0.191315 0.981529i \(-0.438725\pi\)
−0.981529 + 0.191315i \(0.938725\pi\)
\(728\) −64032.0 + 64032.0i −0.120819 + 0.120819i
\(729\) 0 0
\(730\) −177060. + 236080.i −0.332257 + 0.443010i
\(731\) 590238. 1.10457
\(732\) 0 0
\(733\) 394549. 394549.i 0.734333 0.734333i −0.237142 0.971475i \(-0.576211\pi\)
0.971475 + 0.237142i \(0.0762107\pi\)
\(734\) 59884.0i 0.111152i
\(735\) 0 0
\(736\) 68864.0 0.127127
\(737\) −88618.0 88618.0i −0.163150 0.163150i
\(738\) 0 0
\(739\) 109880.i 0.201201i 0.994927 + 0.100600i \(0.0320764\pi\)
−0.994927 + 0.100600i \(0.967924\pi\)
\(740\) −26040.0 182280.i −0.0475530 0.332871i
\(741\) 0 0
\(742\) 70876.0 + 70876.0i 0.128733 + 0.128733i
\(743\) 466451. 466451.i 0.844945 0.844945i −0.144552 0.989497i \(-0.546174\pi\)
0.989497 + 0.144552i \(0.0461742\pi\)
\(744\) 0 0
\(745\) −276000. 207000.i −0.497275 0.372956i
\(746\) −55244.0 −0.0992676
\(747\) 0 0
\(748\) −255824. + 255824.i −0.457234 + 0.457234i
\(749\) 273238.i 0.487054i
\(750\) 0 0
\(751\) 1.01092e6 1.79241 0.896206 0.443638i \(-0.146313\pi\)
0.896206 + 0.443638i \(0.146313\pi\)
\(752\) 81216.0 + 81216.0i 0.143617 + 0.143617i
\(753\) 0 0
\(754\) 187680.i 0.330123i
\(755\) −284970. + 379960.i −0.499925 + 0.666567i
\(756\) 0 0
\(757\) 313269. + 313269.i 0.546671 + 0.546671i 0.925476 0.378806i \(-0.123665\pi\)
−0.378806 + 0.925476i \(0.623665\pi\)
\(758\) −502160. + 502160.i −0.873984 + 0.873984i
\(759\) 0 0
\(760\) −156800. + 22400.0i −0.271468 + 0.0387812i
\(761\) −142082. −0.245341 −0.122670 0.992447i \(-0.539146\pi\)
−0.122670 + 0.992447i \(0.539146\pi\)
\(762\) 0 0
\(763\) −639160. + 639160.i −1.09789 + 1.09789i
\(764\) 117424.i 0.201173i
\(765\) 0 0
\(766\) 344364. 0.586895
\(767\) −80040.0 80040.0i −0.136056 0.136056i
\(768\) 0 0
\(769\) 13280.0i 0.0224567i 0.999937 + 0.0112283i \(0.00357417\pi\)
−0.999937 + 0.0112283i \(0.996426\pi\)
\(770\) 273760. + 205320.i 0.461730 + 0.346298i
\(771\) 0 0
\(772\) 342792. + 342792.i 0.575170 + 0.575170i
\(773\) 782211. 782211.i 1.30908 1.30908i 0.386994 0.922082i \(-0.373513\pi\)
0.922082 0.386994i \(-0.126487\pi\)
\(774\) 0 0
\(775\) −35350.0 121200.i −0.0588554 0.201790i
\(776\) 233952. 0.388511
\(777\) 0 0
\(778\) −150000. + 150000.i −0.247818 + 0.247818i
\(779\) 470960.i 0.776085i
\(780\) 0 0
\(781\) −760156. −1.24624
\(782\) −291596. 291596.i −0.476835 0.476835i
\(783\) 0 0
\(784\) 46016.0i 0.0748646i
\(785\) −572985. + 81855.0i −0.929831 + 0.132833i
\(786\) 0 0
\(787\) 201409. + 201409.i 0.325184 + 0.325184i 0.850752 0.525568i \(-0.176147\pi\)
−0.525568 + 0.850752i \(0.676147\pi\)
\(788\) −87768.0 + 87768.0i −0.141346 + 0.141346i
\(789\) 0 0
\(790\) 105600. + 739200.i 0.169204 + 1.18443i
\(791\) 122438. 0.195688
\(792\) 0 0
\(793\) −386262. + 386262.i −0.614236 + 0.614236i
\(794\) 116596.i 0.184945i
\(795\) 0 0
\(796\) 305280. 0.481806
\(797\) 36291.0 + 36291.0i 0.0571324 + 0.0571324i 0.735096 0.677963i \(-0.237137\pi\)
−0.677963 + 0.735096i \(0.737137\pi\)
\(798\) 0 0
\(799\) 687798.i 1.07738i
\(800\) −54400.0 + 99200.0i −0.0850000 + 0.155000i
\(801\) 0 0
\(802\) 91836.0 + 91836.0i 0.142779 + 0.142779i
\(803\) −348218. + 348218.i −0.540033 + 0.540033i
\(804\) 0 0
\(805\) −234030. + 312040.i −0.361143 + 0.481525i
\(806\) 55752.0 0.0858204
\(807\) 0 0
\(808\) −14048.0 + 14048.0i −0.0215175 + 0.0215175i
\(809\) 71600.0i 0.109400i 0.998503 + 0.0546998i \(0.0174202\pi\)
−0.998503 + 0.0546998i \(0.982580\pi\)
\(810\) 0 0
\(811\) −103318. −0.157085 −0.0785424 0.996911i \(-0.525027\pi\)
−0.0785424 + 0.996911i \(0.525027\pi\)
\(812\) 157760. + 157760.i 0.239268 + 0.239268i
\(813\) 0 0
\(814\) 307272.i 0.463740i
\(815\) −100045. 700315.i −0.150619 1.05433i
\(816\) 0 0
\(817\) 304920. + 304920.i 0.456817 + 0.456817i
\(818\) −157440. + 157440.i −0.235293 + 0.235293i
\(819\) 0 0
\(820\) −269120. 201840.i −0.400238 0.300178i
\(821\) 157438. 0.233573 0.116787 0.993157i \(-0.462741\pi\)
0.116787 + 0.993157i \(0.462741\pi\)
\(822\) 0 0
\(823\) 791309. 791309.i 1.16828 1.16828i 0.185666 0.982613i \(-0.440556\pi\)
0.982613 0.185666i \(-0.0594441\pi\)
\(824\) 333728.i 0.491517i
\(825\) 0 0
\(826\) 134560. 0.197222
\(827\) 889671. + 889671.i 1.30082 + 1.30082i 0.927837 + 0.372987i \(0.121666\pi\)
0.372987 + 0.927837i \(0.378334\pi\)
\(828\) 0 0
\(829\) 618280.i 0.899655i −0.893115 0.449828i \(-0.851485\pi\)
0.893115 0.449828i \(-0.148515\pi\)
\(830\) 373860. 498480.i 0.542691 0.723588i
\(831\) 0 0
\(832\) −35328.0 35328.0i −0.0510355 0.0510355i
\(833\) 194849. 194849.i 0.280807 0.280807i
\(834\) 0 0
\(835\) −54215.0 + 7745.00i −0.0777583 + 0.0111083i
\(836\) −264320. −0.378196
\(837\) 0 0
\(838\) −29520.0 + 29520.0i −0.0420367 + 0.0420367i
\(839\) 821360.i 1.16684i 0.812172 + 0.583418i \(0.198285\pi\)
−0.812172 + 0.583418i \(0.801715\pi\)
\(840\) 0 0
\(841\) 244881. 0.346229
\(842\) 442564. + 442564.i 0.624240 + 0.624240i
\(843\) 0 0
\(844\) 582736.i 0.818063i
\(845\) 380780. + 285585.i 0.533287 + 0.399965i
\(846\) 0 0
\(847\) −20793.0 20793.0i −0.0289835 0.0289835i
\(848\) −39104.0 + 39104.0i −0.0543788 + 0.0543788i
\(849\) 0 0
\(850\) 650400. 189700.i 0.900208 0.262561i
\(851\) 350238. 0.483620
\(852\) 0 0
\(853\) −698291. + 698291.i −0.959706 + 0.959706i −0.999219 0.0395127i \(-0.987419\pi\)
0.0395127 + 0.999219i \(0.487419\pi\)
\(854\) 649368.i 0.890379i
\(855\) 0 0
\(856\) −150752. −0.205738
\(857\) −144489. 144489.i −0.196731 0.196731i 0.601866 0.798597i \(-0.294424\pi\)
−0.798597 + 0.601866i \(0.794424\pi\)
\(858\) 0 0
\(859\) 943480.i 1.27863i −0.768943 0.639317i \(-0.779217\pi\)
0.768943 0.639317i \(-0.220783\pi\)
\(860\) 304920. 43560.0i 0.412277 0.0588967i
\(861\) 0 0
\(862\) −425044. 425044.i −0.572031 0.572031i
\(863\) −438149. + 438149.i −0.588302 + 0.588302i −0.937171 0.348869i \(-0.886566\pi\)
0.348869 + 0.937171i \(0.386566\pi\)
\(864\) 0 0
\(865\) 13945.0 + 97615.0i 0.0186374 + 0.130462i
\(866\) 581636. 0.775560
\(867\) 0 0
\(868\) −46864.0 + 46864.0i −0.0622014 + 0.0622014i
\(869\) 1.24608e6i 1.65009i
\(870\) 0 0
\(871\) −103638. −0.136610
\(872\) −352640. 352640.i −0.463766 0.463766i
\(873\) 0 0
\(874\) 301280.i 0.394410i
\(875\) −264625. 583625.i −0.345633 0.762286i
\(876\) 0 0
\(877\) 281469. + 281469.i 0.365958 + 0.365958i 0.866001 0.500043i \(-0.166682\pi\)
−0.500043 + 0.866001i \(0.666682\pi\)
\(878\) 598880. 598880.i 0.776874 0.776874i
\(879\) 0 0
\(880\) −113280. + 151040.i −0.146281 + 0.195041i
\(881\) −876722. −1.12956 −0.564781 0.825241i \(-0.691039\pi\)
−0.564781 + 0.825241i \(0.691039\pi\)
\(882\) 0 0
\(883\) −327431. + 327431.i −0.419951 + 0.419951i −0.885187 0.465236i \(-0.845969\pi\)
0.465236 + 0.885187i \(0.345969\pi\)
\(884\) 299184.i 0.382855i
\(885\) 0 0
\(886\) −962436. −1.22604
\(887\) 477171. + 477171.i 0.606494 + 0.606494i 0.942028 0.335534i \(-0.108917\pi\)
−0.335534 + 0.942028i \(0.608917\pi\)
\(888\) 0 0
\(889\) 342722.i 0.433649i
\(890\) 144800. + 1.01360e6i 0.182805 + 1.27964i
\(891\) 0 0
\(892\) −247128. 247128.i −0.310593 0.310593i
\(893\) 355320. 355320.i 0.445571 0.445571i
\(894\) 0 0
\(895\) 52000.0 + 39000.0i 0.0649168 + 0.0486876i
\(896\) 59392.0 0.0739796
\(897\) 0 0
\(898\) −164960. + 164960.i −0.204562 + 0.204562i
\(899\) 137360.i 0.169958i
\(900\) 0 0
\(901\) 331162. 0.407935
\(902\) −396952. 396952.i −0.487893 0.487893i
\(903\) 0 0
\(904\) 67552.0i 0.0826611i
\(905\) −665970. + 887960.i −0.813125 + 1.08417i
\(906\) 0 0
\(907\) 1.11209e6 + 1.11209e6i 1.35184 + 1.35184i 0.883604 + 0.468235i \(0.155110\pi\)
0.468235 + 0.883604i \(0.344890\pi\)
\(908\) −439288. + 439288.i −0.532816 + 0.532816i
\(909\) 0 0
\(910\) 280140. 40020.0i 0.338292 0.0483275i
\(911\) 883958. 1.06511 0.532556 0.846395i \(-0.321232\pi\)
0.532556 + 0.846395i \(0.321232\pi\)
\(912\) 0 0
\(913\) 735258. 735258.i 0.882060 0.882060i
\(914\) 752604.i 0.900895i
\(915\) 0 0
\(916\) 402240. 0.479396
\(917\) 184382. + 184382.i 0.219270 + 0.219270i
\(918\) 0 0
\(919\) 1.24040e6i 1.46869i 0.678775 + 0.734346i \(0.262511\pi\)
−0.678775 + 0.734346i \(0.737489\pi\)
\(920\) −172160. 129120.i −0.203403 0.152552i
\(921\) 0 0
\(922\) 652316. + 652316.i 0.767355 + 0.767355i
\(923\) −444498. + 444498.i −0.521755 + 0.521755i
\(924\) 0 0
\(925\) −276675. + 504525.i −0.323360 + 0.589657i
\(926\) −874924. −1.02035
\(927\) 0 0
\(928\) −87040.0 + 87040.0i −0.101070 + 0.101070i
\(929\) 1.22744e6i 1.42223i −0.703077 0.711113i \(-0.748191\pi\)
0.703077 0.711113i \(-0.251809\pi\)
\(930\) 0 0
\(931\) 201320. 0.232267
\(932\) 19128.0 + 19128.0i 0.0220210 + 0.0220210i
\(933\) 0 0
\(934\) 236996.i 0.271673i
\(935\) 1.11923e6 159890.i 1.28025 0.182893i
\(936\) 0 0
\(937\) −1.07047e6 1.07047e6i −1.21926 1.21926i −0.967892 0.251366i \(-0.919120\pi\)
−0.251366 0.967892i \(-0.580880\pi\)
\(938\) 87116.0 87116.0i 0.0990130 0.0990130i
\(939\) 0 0
\(940\) −50760.0 355320.i −0.0574468 0.402128i
\(941\) −558642. −0.630891 −0.315446 0.948944i \(-0.602154\pi\)
−0.315446 + 0.948944i \(0.602154\pi\)
\(942\) 0 0
\(943\) 452458. 452458.i 0.508809 0.508809i
\(944\) 74240.0i 0.0833094i
\(945\) 0 0
\(946\) 514008. 0.574365
\(947\) 191711. + 191711.i 0.213770 + 0.213770i 0.805867 0.592097i \(-0.201700\pi\)
−0.592097 + 0.805867i \(0.701700\pi\)
\(948\) 0 0
\(949\) 407238.i 0.452185i
\(950\) 434000. + 238000.i 0.480886 + 0.263712i
\(951\) 0 0
\(952\) −251488. 251488.i −0.277487 0.277487i
\(953\) 630231. 630231.i 0.693927 0.693927i −0.269166 0.963094i \(-0.586748\pi\)
0.963094 + 0.269166i \(0.0867482\pi\)
\(954\) 0 0
\(955\) 220170. 293560.i 0.241408 0.321877i
\(956\) −142080. −0.155459
\(957\) 0 0
\(958\) 546880. 546880.i 0.595883 0.595883i
\(959\) 1.18372e6i 1.28710i
\(960\) 0 0
\(961\) −882717. −0.955817
\(962\) −179676. 179676.i −0.194151 0.194151i
\(963\) 0 0
\(964\) 225904.i 0.243092i
\(965\) −214245. 1.49972e6i −0.230068 1.61048i
\(966\) 0 0
\(967\) −345491. 345491.i −0.369474 0.369474i 0.497811 0.867285i \(-0.334137\pi\)
−0.867285 + 0.497811i \(0.834137\pi\)
\(968\) 11472.0 11472.0i 0.0122430 0.0122430i
\(969\) 0 0
\(970\) −584880. 438660.i −0.621618 0.466213i
\(971\) −1.08308e6 −1.14874 −0.574372 0.818595i \(-0.694753\pi\)
−0.574372 + 0.818595i \(0.694753\pi\)
\(972\) 0 0
\(973\) 272600. 272600.i 0.287939 0.287939i
\(974\) 494604.i 0.521362i
\(975\) 0 0
\(976\) 358272. 0.376109
\(977\) 146751. + 146751.i 0.153742 + 0.153742i 0.779787 0.626045i \(-0.215327\pi\)
−0.626045 + 0.779787i \(0.715327\pi\)
\(978\) 0 0
\(979\) 1.70864e6i 1.78273i
\(980\) 86280.0 115040.i 0.0898376 0.119783i
\(981\) 0 0
\(982\) −396884. 396884.i −0.411567 0.411567i
\(983\) −466909. + 466909.i −0.483198 + 0.483198i −0.906151 0.422953i \(-0.860993\pi\)
0.422953 + 0.906151i \(0.360993\pi\)
\(984\) 0 0
\(985\) 383985. 54855.0i 0.395769 0.0565384i
\(986\) 737120. 0.758201
\(987\) 0 0
\(988\) −154560. + 154560.i −0.158337 + 0.158337i
\(989\) 585882.i 0.598987i
\(990\) 0 0
\(991\) −901238. −0.917682 −0.458841 0.888518i \(-0.651735\pi\)
−0.458841 + 0.888518i \(0.651735\pi\)
\(992\) −25856.0 25856.0i −0.0262747 0.0262747i
\(993\) 0 0
\(994\) 747272.i 0.756321i
\(995\) −763200. 572400.i −0.770890 0.578167i
\(996\) 0 0
\(997\) 152149. + 152149.i 0.153066 + 0.153066i 0.779486 0.626420i \(-0.215480\pi\)
−0.626420 + 0.779486i \(0.715480\pi\)
\(998\) −538480. + 538480.i −0.540640 + 0.540640i
\(999\) 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 90.5.g.b.37.1 2
3.2 odd 2 10.5.c.a.7.1 yes 2
5.2 odd 4 450.5.g.a.343.1 2
5.3 odd 4 inner 90.5.g.b.73.1 2
5.4 even 2 450.5.g.a.307.1 2
12.11 even 2 80.5.p.b.17.1 2
15.2 even 4 50.5.c.b.43.1 2
15.8 even 4 10.5.c.a.3.1 2
15.14 odd 2 50.5.c.b.7.1 2
24.5 odd 2 320.5.p.b.257.1 2
24.11 even 2 320.5.p.i.257.1 2
60.23 odd 4 80.5.p.b.33.1 2
60.47 odd 4 400.5.p.c.193.1 2
60.59 even 2 400.5.p.c.257.1 2
120.53 even 4 320.5.p.b.193.1 2
120.83 odd 4 320.5.p.i.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.5.c.a.3.1 2 15.8 even 4
10.5.c.a.7.1 yes 2 3.2 odd 2
50.5.c.b.7.1 2 15.14 odd 2
50.5.c.b.43.1 2 15.2 even 4
80.5.p.b.17.1 2 12.11 even 2
80.5.p.b.33.1 2 60.23 odd 4
90.5.g.b.37.1 2 1.1 even 1 trivial
90.5.g.b.73.1 2 5.3 odd 4 inner
320.5.p.b.193.1 2 120.53 even 4
320.5.p.b.257.1 2 24.5 odd 2
320.5.p.i.193.1 2 120.83 odd 4
320.5.p.i.257.1 2 24.11 even 2
400.5.p.c.193.1 2 60.47 odd 4
400.5.p.c.257.1 2 60.59 even 2
450.5.g.a.307.1 2 5.4 even 2
450.5.g.a.343.1 2 5.2 odd 4