Properties

Label 684.2.f.b.379.6
Level $684$
Weight $2$
Character 684.379
Analytic conductor $5.462$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(379,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.f (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: \(5.46176749826\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.14453810176.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.6
Root \(0.331077 + 1.37491i\) of defining polynomial
Character \(\chi\) \(=\) 684.379
Dual form 684.2.f.b.379.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.331077 + 1.37491i) q^{2} +(-1.78078 + 0.910404i) q^{4} +2.56155 q^{5} -4.15286i q^{7} +(-1.84130 - 2.14700i) q^{8} +O(q^{10})\) \(q+(0.331077 + 1.37491i) q^{2} +(-1.78078 + 0.910404i) q^{4} +2.56155 q^{5} -4.15286i q^{7} +(-1.84130 - 2.14700i) q^{8} +(0.848071 + 3.52191i) q^{10} -2.33205i q^{11} -4.29400i q^{13} +(5.70982 - 1.37491i) q^{14} +(2.34233 - 3.24245i) q^{16} +1.00000 q^{17} +(-3.68260 - 2.33205i) q^{19} +(-4.56155 + 2.33205i) q^{20} +(3.20636 - 0.772087i) q^{22} -1.82081i q^{23} +1.56155 q^{25} +(5.90388 - 1.42164i) q^{26} +(3.78078 + 7.39531i) q^{28} +1.20565i q^{29} +1.32431 q^{31} +(5.23358 + 2.14700i) q^{32} +(0.331077 + 1.37491i) q^{34} -10.6378i q^{35} +5.49966i q^{37} +(1.98714 - 5.83535i) q^{38} +(-4.71659 - 5.49966i) q^{40} +5.49966i q^{41} -1.30957i q^{43} +(2.12311 + 4.15286i) q^{44} +(2.50345 - 0.602827i) q^{46} +6.99614i q^{47} -10.2462 q^{49} +(0.516994 + 2.14700i) q^{50} +(3.90928 + 7.64666i) q^{52} +9.79366i q^{53} -5.97366i q^{55} +(-8.91618 + 7.64666i) q^{56} +(-1.65767 + 0.399164i) q^{58} +6.33122 q^{59} +11.6847 q^{61} +(0.438447 + 1.82081i) q^{62} +(-1.21922 + 7.90655i) q^{64} -10.9993i q^{65} +0.290319 q^{67} +(-1.78078 + 0.910404i) q^{68} +(14.6260 - 3.52191i) q^{70} +2.06798 q^{71} -0.123106 q^{73} +(-7.56155 + 1.82081i) q^{74} +(8.68100 + 0.800201i) q^{76} -9.68466 q^{77} +13.4061 q^{79} +(6.00000 - 8.30571i) q^{80} +(-7.56155 + 1.82081i) q^{82} +11.9473i q^{83} +2.56155 q^{85} +(1.80054 - 0.433567i) q^{86} +(-5.00691 + 4.29400i) q^{88} -14.0877i q^{89} -17.8324 q^{91} +(1.65767 + 3.24245i) q^{92} +(-9.61909 + 2.31626i) q^{94} +(-9.43318 - 5.97366i) q^{95} +2.41131i q^{97} +(-3.39228 - 14.0877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{4} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{4} + 4 q^{5} - 6 q^{16} + 8 q^{17} - 20 q^{20} - 4 q^{25} + 6 q^{26} + 22 q^{28} - 18 q^{38} - 16 q^{44} - 16 q^{49} - 38 q^{58} + 44 q^{61} + 20 q^{62} - 18 q^{64} - 6 q^{68} + 32 q^{73} - 44 q^{74} - 16 q^{76} - 28 q^{77} + 48 q^{80} - 44 q^{82} + 4 q^{85} + 38 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.331077 + 1.37491i 0.234107 + 0.972211i
\(3\) 0 0
\(4\) −1.78078 + 0.910404i −0.890388 + 0.455202i
\(5\) 2.56155 1.14556 0.572781 0.819709i \(-0.305865\pi\)
0.572781 + 0.819709i \(0.305865\pi\)
\(6\) 0 0
\(7\) 4.15286i 1.56963i −0.619729 0.784816i \(-0.712757\pi\)
0.619729 0.784816i \(-0.287243\pi\)
\(8\) −1.84130 2.14700i −0.650998 0.759079i
\(9\) 0 0
\(10\) 0.848071 + 3.52191i 0.268183 + 1.11373i
\(11\) 2.33205i 0.703139i −0.936162 0.351569i \(-0.885648\pi\)
0.936162 0.351569i \(-0.114352\pi\)
\(12\) 0 0
\(13\) 4.29400i 1.19094i −0.803377 0.595471i \(-0.796966\pi\)
0.803377 0.595471i \(-0.203034\pi\)
\(14\) 5.70982 1.37491i 1.52601 0.367461i
\(15\) 0 0
\(16\) 2.34233 3.24245i 0.585582 0.810613i
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) −3.68260 2.33205i −0.844847 0.535008i
\(20\) −4.56155 + 2.33205i −1.01999 + 0.521462i
\(21\) 0 0
\(22\) 3.20636 0.772087i 0.683599 0.164609i
\(23\) 1.82081i 0.379665i −0.981817 0.189832i \(-0.939206\pi\)
0.981817 0.189832i \(-0.0607944\pi\)
\(24\) 0 0
\(25\) 1.56155 0.312311
\(26\) 5.90388 1.42164i 1.15785 0.278807i
\(27\) 0 0
\(28\) 3.78078 + 7.39531i 0.714500 + 1.39758i
\(29\) 1.20565i 0.223884i 0.993715 + 0.111942i \(0.0357071\pi\)
−0.993715 + 0.111942i \(0.964293\pi\)
\(30\) 0 0
\(31\) 1.32431 0.237853 0.118926 0.992903i \(-0.462055\pi\)
0.118926 + 0.992903i \(0.462055\pi\)
\(32\) 5.23358 + 2.14700i 0.925175 + 0.379540i
\(33\) 0 0
\(34\) 0.331077 + 1.37491i 0.0567792 + 0.235796i
\(35\) 10.6378i 1.79811i
\(36\) 0 0
\(37\) 5.49966i 0.904138i 0.891983 + 0.452069i \(0.149314\pi\)
−0.891983 + 0.452069i \(0.850686\pi\)
\(38\) 1.98714 5.83535i 0.322357 0.946618i
\(39\) 0 0
\(40\) −4.71659 5.49966i −0.745758 0.869572i
\(41\) 5.49966i 0.858902i 0.903090 + 0.429451i \(0.141293\pi\)
−0.903090 + 0.429451i \(0.858707\pi\)
\(42\) 0 0
\(43\) 1.30957i 0.199707i −0.995002 0.0998536i \(-0.968163\pi\)
0.995002 0.0998536i \(-0.0318375\pi\)
\(44\) 2.12311 + 4.15286i 0.320070 + 0.626067i
\(45\) 0 0
\(46\) 2.50345 0.602827i 0.369114 0.0888820i
\(47\) 6.99614i 1.02049i 0.860028 + 0.510246i \(0.170446\pi\)
−0.860028 + 0.510246i \(0.829554\pi\)
\(48\) 0 0
\(49\) −10.2462 −1.46374
\(50\) 0.516994 + 2.14700i 0.0731140 + 0.303632i
\(51\) 0 0
\(52\) 3.90928 + 7.64666i 0.542119 + 1.06040i
\(53\) 9.79366i 1.34526i 0.739978 + 0.672631i \(0.234836\pi\)
−0.739978 + 0.672631i \(0.765164\pi\)
\(54\) 0 0
\(55\) 5.97366i 0.805489i
\(56\) −8.91618 + 7.64666i −1.19148 + 1.02183i
\(57\) 0 0
\(58\) −1.65767 + 0.399164i −0.217663 + 0.0524128i
\(59\) 6.33122 0.824254 0.412127 0.911126i \(-0.364786\pi\)
0.412127 + 0.911126i \(0.364786\pi\)
\(60\) 0 0
\(61\) 11.6847 1.49607 0.748034 0.663661i \(-0.230998\pi\)
0.748034 + 0.663661i \(0.230998\pi\)
\(62\) 0.438447 + 1.82081i 0.0556828 + 0.231243i
\(63\) 0 0
\(64\) −1.21922 + 7.90655i −0.152403 + 0.988318i
\(65\) 10.9993i 1.36430i
\(66\) 0 0
\(67\) 0.290319 0.0354681 0.0177341 0.999843i \(-0.494355\pi\)
0.0177341 + 0.999843i \(0.494355\pi\)
\(68\) −1.78078 + 0.910404i −0.215951 + 0.110403i
\(69\) 0 0
\(70\) 14.6260 3.52191i 1.74814 0.420949i
\(71\) 2.06798 0.245423 0.122712 0.992442i \(-0.460841\pi\)
0.122712 + 0.992442i \(0.460841\pi\)
\(72\) 0 0
\(73\) −0.123106 −0.0144084 −0.00720421 0.999974i \(-0.502293\pi\)
−0.00720421 + 0.999974i \(0.502293\pi\)
\(74\) −7.56155 + 1.82081i −0.879013 + 0.211665i
\(75\) 0 0
\(76\) 8.68100 + 0.800201i 0.995778 + 0.0917893i
\(77\) −9.68466 −1.10367
\(78\) 0 0
\(79\) 13.4061 1.50830 0.754152 0.656700i \(-0.228048\pi\)
0.754152 + 0.656700i \(0.228048\pi\)
\(80\) 6.00000 8.30571i 0.670820 0.928607i
\(81\) 0 0
\(82\) −7.56155 + 1.82081i −0.835034 + 0.201075i
\(83\) 11.9473i 1.31139i 0.755026 + 0.655695i \(0.227624\pi\)
−0.755026 + 0.655695i \(0.772376\pi\)
\(84\) 0 0
\(85\) 2.56155 0.277839
\(86\) 1.80054 0.433567i 0.194158 0.0467528i
\(87\) 0 0
\(88\) −5.00691 + 4.29400i −0.533738 + 0.457742i
\(89\) 14.0877i 1.49329i −0.665223 0.746644i \(-0.731664\pi\)
0.665223 0.746644i \(-0.268336\pi\)
\(90\) 0 0
\(91\) −17.8324 −1.86934
\(92\) 1.65767 + 3.24245i 0.172824 + 0.338049i
\(93\) 0 0
\(94\) −9.61909 + 2.31626i −0.992134 + 0.238904i
\(95\) −9.43318 5.97366i −0.967824 0.612885i
\(96\) 0 0
\(97\) 2.41131i 0.244831i 0.992479 + 0.122416i \(0.0390641\pi\)
−0.992479 + 0.122416i \(0.960936\pi\)
\(98\) −3.39228 14.0877i −0.342672 1.42307i
\(99\) 0 0
\(100\) −2.78078 + 1.42164i −0.278078 + 0.142164i
\(101\) 8.24621 0.820529 0.410264 0.911967i \(-0.365436\pi\)
0.410264 + 0.911967i \(0.365436\pi\)
\(102\) 0 0
\(103\) −12.0818 −1.19045 −0.595227 0.803557i \(-0.702938\pi\)
−0.595227 + 0.803557i \(0.702938\pi\)
\(104\) −9.21922 + 7.90655i −0.904019 + 0.775301i
\(105\) 0 0
\(106\) −13.4654 + 3.24245i −1.30788 + 0.314935i
\(107\) −5.75058 −0.555929 −0.277965 0.960591i \(-0.589660\pi\)
−0.277965 + 0.960591i \(0.589660\pi\)
\(108\) 0 0
\(109\) 12.2050i 1.16902i −0.811385 0.584512i \(-0.801286\pi\)
0.811385 0.584512i \(-0.198714\pi\)
\(110\) 8.21327 1.97774i 0.783105 0.188570i
\(111\) 0 0
\(112\) −13.4654 9.72736i −1.27236 0.919149i
\(113\) 5.49966i 0.517364i −0.965963 0.258682i \(-0.916712\pi\)
0.965963 0.258682i \(-0.0832882\pi\)
\(114\) 0 0
\(115\) 4.66410i 0.434929i
\(116\) −1.09763 2.14700i −0.101913 0.199344i
\(117\) 0 0
\(118\) 2.09612 + 8.70488i 0.192963 + 0.801349i
\(119\) 4.15286i 0.380692i
\(120\) 0 0
\(121\) 5.56155 0.505596
\(122\) 3.86852 + 16.0654i 0.350239 + 1.45449i
\(123\) 0 0
\(124\) −2.35829 + 1.20565i −0.211781 + 0.108271i
\(125\) −8.80776 −0.787790
\(126\) 0 0
\(127\) −6.04090 −0.536043 −0.268021 0.963413i \(-0.586370\pi\)
−0.268021 + 0.963413i \(0.586370\pi\)
\(128\) −11.2745 + 0.941346i −0.996533 + 0.0832041i
\(129\) 0 0
\(130\) 15.1231 3.64162i 1.32638 0.319391i
\(131\) 5.97366i 0.521921i −0.965349 0.260961i \(-0.915961\pi\)
0.965349 0.260961i \(-0.0840393\pi\)
\(132\) 0 0
\(133\) −9.68466 + 15.2933i −0.839766 + 1.32610i
\(134\) 0.0961180 + 0.399164i 0.00830333 + 0.0344825i
\(135\) 0 0
\(136\) −1.84130 2.14700i −0.157890 0.184104i
\(137\) 12.1231 1.03575 0.517873 0.855457i \(-0.326724\pi\)
0.517873 + 0.855457i \(0.326724\pi\)
\(138\) 0 0
\(139\) 18.9435i 1.60676i 0.595464 + 0.803382i \(0.296968\pi\)
−0.595464 + 0.803382i \(0.703032\pi\)
\(140\) 9.68466 + 18.9435i 0.818503 + 1.60102i
\(141\) 0 0
\(142\) 0.684658 + 2.84329i 0.0574553 + 0.238603i
\(143\) −10.0138 −0.837397
\(144\) 0 0
\(145\) 3.08835i 0.256473i
\(146\) −0.0407574 0.169260i −0.00337311 0.0140080i
\(147\) 0 0
\(148\) −5.00691 9.79366i −0.411565 0.805034i
\(149\) −2.80776 −0.230021 −0.115010 0.993364i \(-0.536690\pi\)
−0.115010 + 0.993364i \(0.536690\pi\)
\(150\) 0 0
\(151\) 8.85254 0.720409 0.360205 0.932873i \(-0.382707\pi\)
0.360205 + 0.932873i \(0.382707\pi\)
\(152\) 1.77387 + 12.2005i 0.143880 + 0.989595i
\(153\) 0 0
\(154\) −3.20636 13.3156i −0.258376 1.07300i
\(155\) 3.39228 0.272475
\(156\) 0 0
\(157\) 6.00000 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) 4.43845 + 18.4322i 0.353104 + 1.46639i
\(159\) 0 0
\(160\) 13.4061 + 5.49966i 1.05985 + 0.434786i
\(161\) −7.56155 −0.595934
\(162\) 0 0
\(163\) 17.6339i 1.38119i −0.723240 0.690597i \(-0.757348\pi\)
0.723240 0.690597i \(-0.242652\pi\)
\(164\) −5.00691 9.79366i −0.390974 0.764756i
\(165\) 0 0
\(166\) −16.4265 + 3.95548i −1.27495 + 0.307005i
\(167\) −10.7575 −0.832439 −0.416220 0.909264i \(-0.636645\pi\)
−0.416220 + 0.909264i \(0.636645\pi\)
\(168\) 0 0
\(169\) −5.43845 −0.418342
\(170\) 0.848071 + 3.52191i 0.0650440 + 0.270119i
\(171\) 0 0
\(172\) 1.19224 + 2.33205i 0.0909071 + 0.177817i
\(173\) 2.41131i 0.183328i −0.995790 0.0916642i \(-0.970781\pi\)
0.995790 0.0916642i \(-0.0292186\pi\)
\(174\) 0 0
\(175\) 6.48490i 0.490213i
\(176\) −7.56155 5.46242i −0.569973 0.411746i
\(177\) 0 0
\(178\) 19.3693 4.66410i 1.45179 0.349589i
\(179\) −8.10887 −0.606085 −0.303043 0.952977i \(-0.598002\pi\)
−0.303043 + 0.952977i \(0.598002\pi\)
\(180\) 0 0
\(181\) 19.5873i 1.45591i −0.685623 0.727957i \(-0.740470\pi\)
0.685623 0.727957i \(-0.259530\pi\)
\(182\) −5.90388 24.5180i −0.437625 1.81739i
\(183\) 0 0
\(184\) −3.90928 + 3.35265i −0.288196 + 0.247161i
\(185\) 14.0877i 1.03575i
\(186\) 0 0
\(187\) 2.33205i 0.170536i
\(188\) −6.36932 12.4586i −0.464530 0.908634i
\(189\) 0 0
\(190\) 5.09017 14.9475i 0.369280 1.08441i
\(191\) 7.79447i 0.563988i 0.959416 + 0.281994i \(0.0909959\pi\)
−0.959416 + 0.281994i \(0.909004\pi\)
\(192\) 0 0
\(193\) 5.49966i 0.395874i −0.980215 0.197937i \(-0.936576\pi\)
0.980215 0.197937i \(-0.0634241\pi\)
\(194\) −3.31534 + 0.798328i −0.238028 + 0.0573166i
\(195\) 0 0
\(196\) 18.2462 9.32819i 1.30330 0.666299i
\(197\) 22.4924 1.60252 0.801259 0.598317i \(-0.204164\pi\)
0.801259 + 0.598317i \(0.204164\pi\)
\(198\) 0 0
\(199\) 5.17534i 0.366870i 0.983032 + 0.183435i \(0.0587217\pi\)
−0.983032 + 0.183435i \(0.941278\pi\)
\(200\) −2.87529 3.35265i −0.203314 0.237069i
\(201\) 0 0
\(202\) 2.73013 + 11.3378i 0.192091 + 0.797727i
\(203\) 5.00691 0.351416
\(204\) 0 0
\(205\) 14.0877i 0.983925i
\(206\) −4.00000 16.6114i −0.278693 1.15737i
\(207\) 0 0
\(208\) −13.9231 10.0580i −0.965393 0.697394i
\(209\) −5.43845 + 8.58800i −0.376185 + 0.594045i
\(210\) 0 0
\(211\) 25.1976 1.73467 0.867336 0.497723i \(-0.165830\pi\)
0.867336 + 0.497723i \(0.165830\pi\)
\(212\) −8.91618 17.4403i −0.612366 1.19781i
\(213\) 0 0
\(214\) −1.90388 7.90655i −0.130147 0.540480i
\(215\) 3.35453i 0.228777i
\(216\) 0 0
\(217\) 5.49966i 0.373341i
\(218\) 16.7808 4.04078i 1.13654 0.273676i
\(219\) 0 0
\(220\) 5.43845 + 10.6378i 0.366660 + 0.717198i
\(221\) 4.29400i 0.288846i
\(222\) 0 0
\(223\) −22.2586 −1.49055 −0.745274 0.666758i \(-0.767681\pi\)
−0.745274 + 0.666758i \(0.767681\pi\)
\(224\) 8.91618 21.7343i 0.595738 1.45218i
\(225\) 0 0
\(226\) 7.56155 1.82081i 0.502987 0.121118i
\(227\) 24.6169 1.63388 0.816942 0.576720i \(-0.195668\pi\)
0.816942 + 0.576720i \(0.195668\pi\)
\(228\) 0 0
\(229\) −6.56155 −0.433600 −0.216800 0.976216i \(-0.569562\pi\)
−0.216800 + 0.976216i \(0.569562\pi\)
\(230\) 6.41273 1.54417i 0.422843 0.101820i
\(231\) 0 0
\(232\) 2.58854 2.21997i 0.169946 0.145748i
\(233\) −10.8078 −0.708040 −0.354020 0.935238i \(-0.615186\pi\)
−0.354020 + 0.935238i \(0.615186\pi\)
\(234\) 0 0
\(235\) 17.9210i 1.16904i
\(236\) −11.2745 + 5.76396i −0.733906 + 0.375202i
\(237\) 0 0
\(238\) 5.70982 1.37491i 0.370113 0.0891224i
\(239\) 9.83943i 0.636460i 0.948014 + 0.318230i \(0.103088\pi\)
−0.948014 + 0.318230i \(0.896912\pi\)
\(240\) 0 0
\(241\) 22.6757i 1.46067i −0.683090 0.730334i \(-0.739365\pi\)
0.683090 0.730334i \(-0.260635\pi\)
\(242\) 1.84130 + 7.64666i 0.118363 + 0.491546i
\(243\) 0 0
\(244\) −20.8078 + 10.6378i −1.33208 + 0.681013i
\(245\) −26.2462 −1.67681
\(246\) 0 0
\(247\) −10.0138 + 15.8131i −0.637164 + 1.00616i
\(248\) −2.43845 2.84329i −0.154842 0.180549i
\(249\) 0 0
\(250\) −2.91605 12.1099i −0.184427 0.765898i
\(251\) 21.5626i 1.36102i 0.732739 + 0.680510i \(0.238242\pi\)
−0.732739 + 0.680510i \(0.761758\pi\)
\(252\) 0 0
\(253\) −4.24621 −0.266957
\(254\) −2.00000 8.30571i −0.125491 0.521147i
\(255\) 0 0
\(256\) −5.02699 15.1898i −0.314187 0.949361i
\(257\) 17.1760i 1.07141i −0.844405 0.535705i \(-0.820046\pi\)
0.844405 0.535705i \(-0.179954\pi\)
\(258\) 0 0
\(259\) 22.8393 1.41916
\(260\) 10.0138 + 19.5873i 0.621031 + 1.21475i
\(261\) 0 0
\(262\) 8.21327 1.97774i 0.507418 0.122185i
\(263\) 14.2794i 0.880504i 0.897874 + 0.440252i \(0.145111\pi\)
−0.897874 + 0.440252i \(0.854889\pi\)
\(264\) 0 0
\(265\) 25.0870i 1.54108i
\(266\) −24.2334 8.25231i −1.48584 0.505982i
\(267\) 0 0
\(268\) −0.516994 + 0.264308i −0.0315804 + 0.0161452i
\(269\) 5.49966i 0.335320i 0.985845 + 0.167660i \(0.0536211\pi\)
−0.985845 + 0.167660i \(0.946379\pi\)
\(270\) 0 0
\(271\) 22.0738i 1.34089i 0.741959 + 0.670445i \(0.233897\pi\)
−0.741959 + 0.670445i \(0.766103\pi\)
\(272\) 2.34233 3.24245i 0.142025 0.196603i
\(273\) 0 0
\(274\) 4.01368 + 16.6682i 0.242475 + 1.00696i
\(275\) 3.64162i 0.219598i
\(276\) 0 0
\(277\) 13.0540 0.784337 0.392169 0.919893i \(-0.371725\pi\)
0.392169 + 0.919893i \(0.371725\pi\)
\(278\) −26.0456 + 6.27174i −1.56211 + 0.376154i
\(279\) 0 0
\(280\) −22.8393 + 19.5873i −1.36491 + 1.17057i
\(281\) 28.1753i 1.68080i 0.541968 + 0.840399i \(0.317679\pi\)
−0.541968 + 0.840399i \(0.682321\pi\)
\(282\) 0 0
\(283\) 5.97366i 0.355097i 0.984112 + 0.177549i \(0.0568167\pi\)
−0.984112 + 0.177549i \(0.943183\pi\)
\(284\) −3.68260 + 1.88269i −0.218522 + 0.111717i
\(285\) 0 0
\(286\) −3.31534 13.7681i −0.196040 0.814127i
\(287\) 22.8393 1.34816
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) −4.24621 + 1.02248i −0.249346 + 0.0600421i
\(291\) 0 0
\(292\) 0.219224 0.112076i 0.0128291 0.00655874i
\(293\) 4.29400i 0.250858i −0.992103 0.125429i \(-0.959969\pi\)
0.992103 0.125429i \(-0.0400308\pi\)
\(294\) 0 0
\(295\) 16.2177 0.944233
\(296\) 11.8078 10.1265i 0.686312 0.588592i
\(297\) 0 0
\(298\) −0.929585 3.86043i −0.0538494 0.223629i
\(299\) −7.81855 −0.452159
\(300\) 0 0
\(301\) −5.43845 −0.313467
\(302\) 2.93087 + 12.1715i 0.168653 + 0.700390i
\(303\) 0 0
\(304\) −16.1874 + 6.47823i −0.928412 + 0.371552i
\(305\) 29.9309 1.71384
\(306\) 0 0
\(307\) 13.4061 0.765126 0.382563 0.923929i \(-0.375041\pi\)
0.382563 + 0.923929i \(0.375041\pi\)
\(308\) 17.2462 8.81695i 0.982694 0.502392i
\(309\) 0 0
\(310\) 1.12311 + 4.66410i 0.0637881 + 0.264903i
\(311\) 4.15286i 0.235487i 0.993044 + 0.117743i \(0.0375660\pi\)
−0.993044 + 0.117743i \(0.962434\pi\)
\(312\) 0 0
\(313\) −0.438447 −0.0247825 −0.0123913 0.999923i \(-0.503944\pi\)
−0.0123913 + 0.999923i \(0.503944\pi\)
\(314\) 1.98646 + 8.24948i 0.112102 + 0.465545i
\(315\) 0 0
\(316\) −23.8733 + 12.2050i −1.34298 + 0.686583i
\(317\) 4.29400i 0.241175i 0.992703 + 0.120588i \(0.0384779\pi\)
−0.992703 + 0.120588i \(0.961522\pi\)
\(318\) 0 0
\(319\) 2.81164 0.157422
\(320\) −3.12311 + 20.2530i −0.174587 + 1.13218i
\(321\) 0 0
\(322\) −2.50345 10.3965i −0.139512 0.579373i
\(323\) −3.68260 2.33205i −0.204905 0.129759i
\(324\) 0 0
\(325\) 6.70531i 0.371944i
\(326\) 24.2451 5.83817i 1.34281 0.323347i
\(327\) 0 0
\(328\) 11.8078 10.1265i 0.651975 0.559144i
\(329\) 29.0540 1.60180
\(330\) 0 0
\(331\) 23.8733 1.31219 0.656097 0.754677i \(-0.272206\pi\)
0.656097 + 0.754677i \(0.272206\pi\)
\(332\) −10.8769 21.2755i −0.596947 1.16765i
\(333\) 0 0
\(334\) −3.56155 14.7906i −0.194879 0.809306i
\(335\) 0.743668 0.0406309
\(336\) 0 0
\(337\) 6.17669i 0.336466i 0.985747 + 0.168233i \(0.0538061\pi\)
−0.985747 + 0.168233i \(0.946194\pi\)
\(338\) −1.80054 7.47740i −0.0979366 0.406717i
\(339\) 0 0
\(340\) −4.56155 + 2.33205i −0.247385 + 0.126473i
\(341\) 3.08835i 0.167243i
\(342\) 0 0
\(343\) 13.4810i 0.727908i
\(344\) −2.81164 + 2.41131i −0.151594 + 0.130009i
\(345\) 0 0
\(346\) 3.31534 0.798328i 0.178234 0.0429184i
\(347\) 29.8683i 1.60342i −0.597716 0.801708i \(-0.703925\pi\)
0.597716 0.801708i \(-0.296075\pi\)
\(348\) 0 0
\(349\) 9.05398 0.484648 0.242324 0.970195i \(-0.422090\pi\)
0.242324 + 0.970195i \(0.422090\pi\)
\(350\) 8.91618 2.14700i 0.476590 0.114762i
\(351\) 0 0
\(352\) 5.00691 12.2050i 0.266869 0.650527i
\(353\) −18.6847 −0.994484 −0.497242 0.867612i \(-0.665654\pi\)
−0.497242 + 0.867612i \(0.665654\pi\)
\(354\) 0 0
\(355\) 5.29723 0.281148
\(356\) 12.8255 + 25.0870i 0.679748 + 1.32961i
\(357\) 0 0
\(358\) −2.68466 11.1490i −0.141889 0.589243i
\(359\) 6.19782i 0.327108i 0.986534 + 0.163554i \(0.0522958\pi\)
−0.986534 + 0.163554i \(0.947704\pi\)
\(360\) 0 0
\(361\) 8.12311 + 17.1760i 0.427532 + 0.904000i
\(362\) 26.9309 6.48490i 1.41546 0.340839i
\(363\) 0 0
\(364\) 31.7555 16.2347i 1.66444 0.850927i
\(365\) −0.315342 −0.0165057
\(366\) 0 0
\(367\) 1.02248i 0.0533730i −0.999644 0.0266865i \(-0.991504\pi\)
0.999644 0.0266865i \(-0.00849559\pi\)
\(368\) −5.90388 4.26493i −0.307761 0.222325i
\(369\) 0 0
\(370\) −19.3693 + 4.66410i −1.00696 + 0.242475i
\(371\) 40.6716 2.11157
\(372\) 0 0
\(373\) 6.70531i 0.347188i −0.984817 0.173594i \(-0.944462\pi\)
0.984817 0.173594i \(-0.0555380\pi\)
\(374\) 3.20636 0.772087i 0.165797 0.0399237i
\(375\) 0 0
\(376\) 15.0207 12.8820i 0.774635 0.664339i
\(377\) 5.17708 0.266633
\(378\) 0 0
\(379\) −15.7644 −0.809762 −0.404881 0.914369i \(-0.632687\pi\)
−0.404881 + 0.914369i \(0.632687\pi\)
\(380\) 22.2368 + 2.04976i 1.14073 + 0.105150i
\(381\) 0 0
\(382\) −10.7167 + 2.58057i −0.548315 + 0.132033i
\(383\) −22.2586 −1.13736 −0.568682 0.822558i \(-0.692546\pi\)
−0.568682 + 0.822558i \(0.692546\pi\)
\(384\) 0 0
\(385\) −24.8078 −1.26432
\(386\) 7.56155 1.82081i 0.384873 0.0926767i
\(387\) 0 0
\(388\) −2.19526 4.29400i −0.111448 0.217995i
\(389\) −14.8078 −0.750783 −0.375392 0.926866i \(-0.622492\pi\)
−0.375392 + 0.926866i \(0.622492\pi\)
\(390\) 0 0
\(391\) 1.82081i 0.0920822i
\(392\) 18.8664 + 21.9986i 0.952895 + 1.11110i
\(393\) 0 0
\(394\) 7.44672 + 30.9251i 0.375160 + 1.55799i
\(395\) 34.3404 1.72785
\(396\) 0 0
\(397\) −3.93087 −0.197285 −0.0986423 0.995123i \(-0.531450\pi\)
−0.0986423 + 0.995123i \(0.531450\pi\)
\(398\) −7.11564 + 1.71343i −0.356675 + 0.0858866i
\(399\) 0 0
\(400\) 3.65767 5.06326i 0.182884 0.253163i
\(401\) 7.91096i 0.395055i 0.980297 + 0.197527i \(0.0632911\pi\)
−0.980297 + 0.197527i \(0.936709\pi\)
\(402\) 0 0
\(403\) 5.68658i 0.283269i
\(404\) −14.6847 + 7.50738i −0.730589 + 0.373506i
\(405\) 0 0
\(406\) 1.65767 + 6.88407i 0.0822688 + 0.341651i
\(407\) 12.8255 0.635734
\(408\) 0 0
\(409\) 27.4983i 1.35970i 0.733350 + 0.679851i \(0.237956\pi\)
−0.733350 + 0.679851i \(0.762044\pi\)
\(410\) −19.3693 + 4.66410i −0.956582 + 0.230343i
\(411\) 0 0
\(412\) 21.5150 10.9993i 1.05997 0.541897i
\(413\) 26.2926i 1.29378i
\(414\) 0 0
\(415\) 30.6037i 1.50228i
\(416\) 9.21922 22.4730i 0.452010 1.10183i
\(417\) 0 0
\(418\) −13.6083 4.63411i −0.665604 0.226662i
\(419\) 39.9319i 1.95080i −0.220440 0.975401i \(-0.570749\pi\)
0.220440 0.975401i \(-0.429251\pi\)
\(420\) 0 0
\(421\) 23.2043i 1.13091i 0.824780 + 0.565454i \(0.191299\pi\)
−0.824780 + 0.565454i \(0.808701\pi\)
\(422\) 8.34233 + 34.6445i 0.406098 + 1.68647i
\(423\) 0 0
\(424\) 21.0270 18.0331i 1.02116 0.875763i
\(425\) 1.56155 0.0757464
\(426\) 0 0
\(427\) 48.5247i 2.34827i
\(428\) 10.2405 5.23535i 0.494993 0.253060i
\(429\) 0 0
\(430\) 4.61219 1.11061i 0.222419 0.0535582i
\(431\) −5.29723 −0.255158 −0.127579 0.991828i \(-0.540721\pi\)
−0.127579 + 0.991828i \(0.540721\pi\)
\(432\) 0 0
\(433\) 18.9103i 0.908770i 0.890805 + 0.454385i \(0.150141\pi\)
−0.890805 + 0.454385i \(0.849859\pi\)
\(434\) 7.56155 1.82081i 0.362966 0.0874016i
\(435\) 0 0
\(436\) 11.1114 + 21.7343i 0.532142 + 1.04088i
\(437\) −4.24621 + 6.70531i −0.203124 + 0.320758i
\(438\) 0 0
\(439\) −19.6100 −0.935935 −0.467968 0.883746i \(-0.655014\pi\)
−0.467968 + 0.883746i \(0.655014\pi\)
\(440\) −12.8255 + 10.9993i −0.611430 + 0.524372i
\(441\) 0 0
\(442\) 5.90388 1.42164i 0.280819 0.0676207i
\(443\) 12.2344i 0.581275i 0.956833 + 0.290637i \(0.0938673\pi\)
−0.956833 + 0.290637i \(0.906133\pi\)
\(444\) 0 0
\(445\) 36.0863i 1.71065i
\(446\) −7.36932 30.6037i −0.348947 1.44913i
\(447\) 0 0
\(448\) 32.8348 + 5.06326i 1.55130 + 0.239217i
\(449\) 14.7647i 0.696789i 0.937348 + 0.348395i \(0.113273\pi\)
−0.937348 + 0.348395i \(0.886727\pi\)
\(450\) 0 0
\(451\) 12.8255 0.603927
\(452\) 5.00691 + 9.79366i 0.235505 + 0.460655i
\(453\) 0 0
\(454\) 8.15009 + 33.8462i 0.382503 + 1.58848i
\(455\) −45.6786 −2.14144
\(456\) 0 0
\(457\) 3.87689 0.181353 0.0906767 0.995880i \(-0.471097\pi\)
0.0906767 + 0.995880i \(0.471097\pi\)
\(458\) −2.17238 9.02157i −0.101509 0.421550i
\(459\) 0 0
\(460\) 4.24621 + 8.30571i 0.197981 + 0.387256i
\(461\) −31.6847 −1.47570 −0.737851 0.674964i \(-0.764159\pi\)
−0.737851 + 0.674964i \(0.764159\pi\)
\(462\) 0 0
\(463\) 16.3243i 0.758656i −0.925262 0.379328i \(-0.876155\pi\)
0.925262 0.379328i \(-0.123845\pi\)
\(464\) 3.90928 + 2.82404i 0.181484 + 0.131103i
\(465\) 0 0
\(466\) −3.57820 14.8597i −0.165757 0.688364i
\(467\) 2.33205i 0.107914i −0.998543 0.0539572i \(-0.982817\pi\)
0.998543 0.0539572i \(-0.0171834\pi\)
\(468\) 0 0
\(469\) 1.20565i 0.0556719i
\(470\) −24.6398 + 5.93322i −1.13655 + 0.273679i
\(471\) 0 0
\(472\) −11.6577 13.5931i −0.536588 0.625674i
\(473\) −3.05398 −0.140422
\(474\) 0 0
\(475\) −5.75058 3.64162i −0.263855 0.167089i
\(476\) 3.78078 + 7.39531i 0.173292 + 0.338963i
\(477\) 0 0
\(478\) −13.5284 + 3.25761i −0.618773 + 0.148999i
\(479\) 41.5286i 1.89749i 0.316045 + 0.948744i \(0.397645\pi\)
−0.316045 + 0.948744i \(0.602355\pi\)
\(480\) 0 0
\(481\) 23.6155 1.07678
\(482\) 31.1771 7.50738i 1.42008 0.341952i
\(483\) 0 0
\(484\) −9.90388 + 5.06326i −0.450176 + 0.230148i
\(485\) 6.17669i 0.280469i
\(486\) 0 0
\(487\) −18.8664 −0.854916 −0.427458 0.904035i \(-0.640591\pi\)
−0.427458 + 0.904035i \(0.640591\pi\)
\(488\) −21.5150 25.0870i −0.973937 1.13563i
\(489\) 0 0
\(490\) −8.68951 36.0863i −0.392552 1.63021i
\(491\) 21.2755i 0.960151i −0.877227 0.480075i \(-0.840609\pi\)
0.877227 0.480075i \(-0.159391\pi\)
\(492\) 0 0
\(493\) 1.20565i 0.0542999i
\(494\) −25.0570 8.53279i −1.12737 0.383908i
\(495\) 0 0
\(496\) 3.10196 4.29400i 0.139282 0.192806i
\(497\) 8.58800i 0.385225i
\(498\) 0 0
\(499\) 1.30957i 0.0586243i −0.999570 0.0293122i \(-0.990668\pi\)
0.999570 0.0293122i \(-0.00933169\pi\)
\(500\) 15.6847 8.01862i 0.701439 0.358604i
\(501\) 0 0
\(502\) −29.6467 + 7.13888i −1.32320 + 0.318624i
\(503\) 16.3873i 0.730672i −0.930876 0.365336i \(-0.880954\pi\)
0.930876 0.365336i \(-0.119046\pi\)
\(504\) 0 0
\(505\) 21.1231 0.939966
\(506\) −1.40582 5.83817i −0.0624964 0.259539i
\(507\) 0 0
\(508\) 10.7575 5.49966i 0.477286 0.244008i
\(509\) 8.58800i 0.380657i −0.981721 0.190328i \(-0.939045\pi\)
0.981721 0.190328i \(-0.0609552\pi\)
\(510\) 0 0
\(511\) 0.511240i 0.0226159i
\(512\) 19.2203 11.9407i 0.849426 0.527707i
\(513\) 0 0
\(514\) 23.6155 5.68658i 1.04164 0.250824i
\(515\) −30.9481 −1.36374
\(516\) 0 0
\(517\) 16.3153 0.717548
\(518\) 7.56155 + 31.4020i 0.332236 + 1.37973i
\(519\) 0 0
\(520\) −23.6155 + 20.2530i −1.03561 + 0.888155i
\(521\) 22.6757i 0.993439i −0.867911 0.496719i \(-0.834538\pi\)
0.867911 0.496719i \(-0.165462\pi\)
\(522\) 0 0
\(523\) −2.19526 −0.0959922 −0.0479961 0.998848i \(-0.515284\pi\)
−0.0479961 + 0.998848i \(0.515284\pi\)
\(524\) 5.43845 + 10.6378i 0.237580 + 0.464713i
\(525\) 0 0
\(526\) −19.6329 + 4.72757i −0.856036 + 0.206132i
\(527\) 1.32431 0.0576877
\(528\) 0 0
\(529\) 19.6847 0.855855
\(530\) −34.4924 + 8.30571i −1.49826 + 0.360777i
\(531\) 0 0
\(532\) 3.32312 36.0509i 0.144075 1.56301i
\(533\) 23.6155 1.02290
\(534\) 0 0
\(535\) −14.7304 −0.636851
\(536\) −0.534565 0.623316i −0.0230897 0.0269231i
\(537\) 0 0
\(538\) −7.56155 + 1.82081i −0.326002 + 0.0785006i
\(539\) 23.8947i 1.02922i
\(540\) 0 0
\(541\) −32.8078 −1.41052 −0.705258 0.708951i \(-0.749169\pi\)
−0.705258 + 0.708951i \(0.749169\pi\)
\(542\) −30.3496 + 7.30814i −1.30363 + 0.313911i
\(543\) 0 0
\(544\) 5.23358 + 2.14700i 0.224388 + 0.0920519i
\(545\) 31.2637i 1.33919i
\(546\) 0 0
\(547\) −0.580639 −0.0248263 −0.0124132 0.999923i \(-0.503951\pi\)
−0.0124132 + 0.999923i \(0.503951\pi\)
\(548\) −21.5885 + 11.0369i −0.922217 + 0.471474i
\(549\) 0 0
\(550\) 5.00691 1.20565i 0.213495 0.0514093i
\(551\) 2.81164 4.43994i 0.119780 0.189148i
\(552\) 0 0
\(553\) 55.6736i 2.36748i
\(554\) 4.32187 + 17.9481i 0.183619 + 0.762541i
\(555\) 0 0
\(556\) −17.2462 33.7341i −0.731402 1.43064i
\(557\) −9.93087 −0.420784 −0.210392 0.977617i \(-0.567474\pi\)
−0.210392 + 0.977617i \(0.567474\pi\)
\(558\) 0 0
\(559\) −5.62329 −0.237840
\(560\) −34.4924 24.9171i −1.45757 1.05294i
\(561\) 0 0
\(562\) −38.7386 + 9.32819i −1.63409 + 0.393486i
\(563\) 21.3519 0.899877 0.449938 0.893060i \(-0.351446\pi\)
0.449938 + 0.893060i \(0.351446\pi\)
\(564\) 0 0
\(565\) 14.0877i 0.592672i
\(566\) −8.21327 + 1.97774i −0.345230 + 0.0831307i
\(567\) 0 0
\(568\) −3.80776 4.43994i −0.159770 0.186296i
\(569\) 41.5859i 1.74337i 0.490064 + 0.871687i \(0.336973\pi\)
−0.490064 + 0.871687i \(0.663027\pi\)
\(570\) 0 0
\(571\) 15.5889i 0.652377i 0.945305 + 0.326188i \(0.105764\pi\)
−0.945305 + 0.326188i \(0.894236\pi\)
\(572\) 17.8324 9.11662i 0.745609 0.381185i
\(573\) 0 0
\(574\) 7.56155 + 31.4020i 0.315613 + 1.31070i
\(575\) 2.84329i 0.118573i
\(576\) 0 0
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) −5.29723 21.9986i −0.220336 0.915022i
\(579\) 0 0
\(580\) −2.81164 5.49966i −0.116747 0.228361i
\(581\) 49.6155 2.05840
\(582\) 0 0
\(583\) 22.8393 0.945906
\(584\) 0.226674 + 0.264308i 0.00937986 + 0.0109371i
\(585\) 0 0
\(586\) 5.90388 1.42164i 0.243887 0.0587276i
\(587\) 5.97366i 0.246559i −0.992372 0.123280i \(-0.960659\pi\)
0.992372 0.123280i \(-0.0393412\pi\)
\(588\) 0 0
\(589\) −4.87689 3.08835i −0.200949 0.127253i
\(590\) 5.36932 + 22.2980i 0.221051 + 0.917994i
\(591\) 0 0
\(592\) 17.8324 + 12.8820i 0.732906 + 0.529447i
\(593\) −12.7386 −0.523113 −0.261556 0.965188i \(-0.584236\pi\)
−0.261556 + 0.965188i \(0.584236\pi\)
\(594\) 0 0
\(595\) 10.6378i 0.436106i
\(596\) 5.00000 2.55620i 0.204808 0.104706i
\(597\) 0 0
\(598\) −2.58854 10.7498i −0.105853 0.439593i
\(599\) −24.9073 −1.01768 −0.508841 0.860860i \(-0.669926\pi\)
−0.508841 + 0.860860i \(0.669926\pi\)
\(600\) 0 0
\(601\) 35.4092i 1.44437i −0.691698 0.722187i \(-0.743137\pi\)
0.691698 0.722187i \(-0.256863\pi\)
\(602\) −1.80054 7.47740i −0.0733847 0.304756i
\(603\) 0 0
\(604\) −15.7644 + 8.05939i −0.641444 + 0.327932i
\(605\) 14.2462 0.579191
\(606\) 0 0
\(607\) −31.5288 −1.27971 −0.639857 0.768494i \(-0.721006\pi\)
−0.639857 + 0.768494i \(0.721006\pi\)
\(608\) −14.2663 20.1115i −0.578574 0.815630i
\(609\) 0 0
\(610\) 9.90941 + 41.1524i 0.401220 + 1.66621i
\(611\) 30.0414 1.21535
\(612\) 0 0
\(613\) −29.3002 −1.18342 −0.591712 0.806150i \(-0.701548\pi\)
−0.591712 + 0.806150i \(0.701548\pi\)
\(614\) 4.43845 + 18.4322i 0.179121 + 0.743864i
\(615\) 0 0
\(616\) 17.8324 + 20.7930i 0.718487 + 0.837773i
\(617\) −41.5464 −1.67259 −0.836297 0.548276i \(-0.815284\pi\)
−0.836297 + 0.548276i \(0.815284\pi\)
\(618\) 0 0
\(619\) 6.70906i 0.269660i 0.990869 + 0.134830i \(0.0430488\pi\)
−0.990869 + 0.134830i \(0.956951\pi\)
\(620\) −6.04090 + 3.08835i −0.242608 + 0.124031i
\(621\) 0 0
\(622\) −5.70982 + 1.37491i −0.228943 + 0.0551290i
\(623\) −58.5040 −2.34391
\(624\) 0 0
\(625\) −30.3693 −1.21477
\(626\) −0.145160 0.602827i −0.00580175 0.0240938i
\(627\) 0 0
\(628\) −10.6847 + 5.46242i −0.426364 + 0.217974i
\(629\) 5.49966i 0.219286i
\(630\) 0 0
\(631\) 9.61528i 0.382778i 0.981514 + 0.191389i \(0.0612992\pi\)
−0.981514 + 0.191389i \(0.938701\pi\)
\(632\) −24.6847 28.7829i −0.981903 1.14492i
\(633\) 0 0
\(634\) −5.90388 + 1.42164i −0.234473 + 0.0564607i
\(635\) −15.4741 −0.614070
\(636\) 0 0
\(637\) 43.9972i 1.74323i
\(638\) 0.930870 + 3.86577i 0.0368535 + 0.153047i
\(639\) 0 0
\(640\) −28.8802 + 2.41131i −1.14159 + 0.0953153i
\(641\) 26.8212i 1.05938i −0.848193 0.529688i \(-0.822309\pi\)
0.848193 0.529688i \(-0.177691\pi\)
\(642\) 0 0
\(643\) 14.2794i 0.563124i −0.959543 0.281562i \(-0.909148\pi\)
0.959543 0.281562i \(-0.0908524\pi\)
\(644\) 13.4654 6.88407i 0.530612 0.271270i
\(645\) 0 0
\(646\) 1.98714 5.83535i 0.0781830 0.229589i
\(647\) 32.1374i 1.26345i 0.775191 + 0.631726i \(0.217653\pi\)
−0.775191 + 0.631726i \(0.782347\pi\)
\(648\) 0 0
\(649\) 14.7647i 0.579565i
\(650\) 9.21922 2.21997i 0.361608 0.0870745i
\(651\) 0 0
\(652\) 16.0540 + 31.4020i 0.628722 + 1.22980i
\(653\) 25.1922 0.985848 0.492924 0.870072i \(-0.335928\pi\)
0.492924 + 0.870072i \(0.335928\pi\)
\(654\) 0 0
\(655\) 15.3019i 0.597893i
\(656\) 17.8324 + 12.8820i 0.696237 + 0.502958i
\(657\) 0 0
\(658\) 9.61909 + 39.9467i 0.374991 + 1.55729i
\(659\) 41.9960 1.63593 0.817965 0.575268i \(-0.195102\pi\)
0.817965 + 0.575268i \(0.195102\pi\)
\(660\) 0 0
\(661\) 37.2919i 1.45049i 0.688492 + 0.725244i \(0.258273\pi\)
−0.688492 + 0.725244i \(0.741727\pi\)
\(662\) 7.90388 + 32.8237i 0.307193 + 1.27573i
\(663\) 0 0
\(664\) 25.6509 21.9986i 0.995449 0.853712i
\(665\) −24.8078 + 39.1746i −0.962004 + 1.51913i
\(666\) 0 0
\(667\) 2.19526 0.0850010
\(668\) 19.1567 9.79366i 0.741194 0.378928i
\(669\) 0 0
\(670\) 0.246211 + 1.02248i 0.00951197 + 0.0395018i
\(671\) 27.2492i 1.05194i
\(672\) 0 0
\(673\) 24.4099i 0.940934i −0.882418 0.470467i \(-0.844086\pi\)
0.882418 0.470467i \(-0.155914\pi\)
\(674\) −8.49242 + 2.04496i −0.327116 + 0.0787689i
\(675\) 0 0
\(676\) 9.68466 4.95118i 0.372487 0.190430i
\(677\) 40.3803i 1.55194i −0.630770 0.775970i \(-0.717261\pi\)
0.630770 0.775970i \(-0.282739\pi\)
\(678\) 0 0
\(679\) 10.0138 0.384295
\(680\) −4.71659 5.49966i −0.180873 0.210902i
\(681\) 0 0
\(682\) 4.24621 1.02248i 0.162596 0.0391528i
\(683\) −31.5288 −1.20642 −0.603208 0.797584i \(-0.706111\pi\)
−0.603208 + 0.797584i \(0.706111\pi\)
\(684\) 0 0
\(685\) 31.0540 1.18651
\(686\) −18.5353 + 4.46326i −0.707680 + 0.170408i
\(687\) 0 0
\(688\) −4.24621 3.06744i −0.161885 0.116945i
\(689\) 42.0540 1.60213
\(690\) 0 0
\(691\) 8.01862i 0.305043i 0.988300 + 0.152521i \(0.0487393\pi\)
−0.988300 + 0.152521i \(0.951261\pi\)
\(692\) 2.19526 + 4.29400i 0.0834514 + 0.163233i
\(693\) 0 0
\(694\) 41.0664 9.88871i 1.55886 0.375370i
\(695\) 48.5247i 1.84065i
\(696\) 0 0
\(697\) 5.49966i 0.208314i
\(698\) 2.99756 + 12.4484i 0.113459 + 0.471180i
\(699\) 0 0
\(700\) 5.90388 + 11.5482i 0.223146 + 0.436480i
\(701\) −4.63068 −0.174898 −0.0874492 0.996169i \(-0.527872\pi\)
−0.0874492 + 0.996169i \(0.527872\pi\)
\(702\) 0 0
\(703\) 12.8255 20.2530i 0.483721 0.763858i
\(704\) 18.4384 + 2.84329i 0.694925 + 0.107160i
\(705\) 0 0
\(706\) −6.18606 25.6898i −0.232815 0.966848i
\(707\) 34.2453i 1.28793i
\(708\) 0 0
\(709\) 12.6307 0.474355 0.237178 0.971466i \(-0.423778\pi\)
0.237178 + 0.971466i \(0.423778\pi\)
\(710\) 1.75379 + 7.28323i 0.0658185 + 0.273335i
\(711\) 0 0
\(712\) −30.2462 + 25.9396i −1.13352 + 0.972128i
\(713\) 2.41131i 0.0903042i
\(714\) 0 0
\(715\) −25.6509 −0.959290
\(716\) 14.4401 7.38235i 0.539651 0.275891i
\(717\) 0 0
\(718\) −8.52146 + 2.05195i −0.318018 + 0.0765782i
\(719\) 26.4509i 0.986450i 0.869902 + 0.493225i \(0.164182\pi\)
−0.869902 + 0.493225i \(0.835818\pi\)
\(720\) 0 0
\(721\) 50.1739i 1.86858i
\(722\) −20.9262 + 16.8551i −0.778791 + 0.627284i
\(723\) 0 0
\(724\) 17.8324 + 34.8806i 0.662735 + 1.29633i
\(725\) 1.88269i 0.0699215i
\(726\) 0 0
\(727\) 44.6589i 1.65631i −0.560500 0.828154i \(-0.689391\pi\)
0.560500 0.828154i \(-0.310609\pi\)
\(728\) 32.8348 + 38.2861i 1.21694 + 1.41898i
\(729\) 0 0
\(730\) −0.104402 0.433567i −0.00386410 0.0160471i
\(731\) 1.30957i 0.0484361i
\(732\) 0 0
\(733\) −5.12311 −0.189226 −0.0946131 0.995514i \(-0.530161\pi\)
−0.0946131 + 0.995514i \(0.530161\pi\)
\(734\) 1.40582 0.338519i 0.0518898 0.0124950i
\(735\) 0 0
\(736\) 3.90928 9.52935i 0.144098 0.351256i
\(737\) 0.677039i 0.0249390i
\(738\) 0 0
\(739\) 25.2042i 0.927152i −0.886057 0.463576i \(-0.846566\pi\)
0.886057 0.463576i \(-0.153434\pi\)
\(740\) −12.8255 25.0870i −0.471473 0.922215i
\(741\) 0 0
\(742\) 13.4654 + 55.9200i 0.494332 + 2.05289i
\(743\) −11.9188 −0.437257 −0.218628 0.975808i \(-0.570158\pi\)
−0.218628 + 0.975808i \(0.570158\pi\)
\(744\) 0 0
\(745\) −7.19224 −0.263503
\(746\) 9.21922 2.21997i 0.337540 0.0812789i
\(747\) 0 0
\(748\) 2.12311 + 4.15286i 0.0776284 + 0.151843i
\(749\) 23.8813i 0.872604i
\(750\) 0 0
\(751\) −35.6647 −1.30142 −0.650712 0.759324i \(-0.725530\pi\)
−0.650712 + 0.759324i \(0.725530\pi\)
\(752\) 22.6847 + 16.3873i 0.827224 + 0.597582i
\(753\) 0 0
\(754\) 1.71401 + 7.11804i 0.0624206 + 0.259224i
\(755\) 22.6762 0.825273
\(756\) 0 0
\(757\) −44.8078 −1.62857 −0.814283 0.580468i \(-0.802870\pi\)
−0.814283 + 0.580468i \(0.802870\pi\)
\(758\) −5.21922 21.6747i −0.189571 0.787260i
\(759\) 0 0
\(760\) 4.54386 + 31.2524i 0.164823 + 1.13364i
\(761\) −30.6155 −1.10981 −0.554906 0.831913i \(-0.687246\pi\)
−0.554906 + 0.831913i \(0.687246\pi\)
\(762\) 0 0
\(763\) −50.6855 −1.83494
\(764\) −7.09612 13.8802i −0.256729 0.502168i
\(765\) 0 0
\(766\) −7.36932 30.6037i −0.266264 1.10576i
\(767\) 27.1862i 0.981638i
\(768\) 0 0
\(769\) −28.2311 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(770\) −8.21327 34.1085i −0.295986 1.22919i
\(771\) 0 0
\(772\) 5.00691 + 9.79366i 0.180203 + 0.352481i
\(773\) 41.0573i 1.47673i 0.674402 + 0.738365i \(0.264402\pi\)
−0.674402 + 0.738365i \(0.735598\pi\)
\(774\) 0 0
\(775\) 2.06798 0.0742839
\(776\) 5.17708 4.43994i 0.185846 0.159385i
\(777\) 0 0
\(778\) −4.90251 20.3594i −0.175763 0.729920i
\(779\) 12.8255 20.2530i 0.459520 0.725640i
\(780\) 0 0
\(781\) 4.82262i 0.172567i
\(782\) 2.50345 0.602827i 0.0895233 0.0215571i
\(783\) 0 0
\(784\) −24.0000 + 33.2228i −0.857143 + 1.18653i
\(785\) 15.3693 0.548554
\(786\) 0 0
\(787\) 26.3588 0.939591 0.469796 0.882775i \(-0.344328\pi\)
0.469796 + 0.882775i \(0.344328\pi\)
\(788\) −40.0540 + 20.4772i −1.42686 + 0.729470i
\(789\) 0 0
\(790\) 11.3693 + 47.2151i 0.404502 + 1.67984i
\(791\) −22.8393 −0.812071
\(792\) 0 0
\(793\) 50.1739i 1.78173i
\(794\) −1.30142 5.40461i −0.0461856 0.191802i
\(795\) 0 0
\(796\) −4.71165 9.21612i −0.167000 0.326657i
\(797\) 23.2043i 0.821938i 0.911649 + 0.410969i \(0.134809\pi\)
−0.911649 + 0.410969i \(0.865191\pi\)
\(798\) 0 0
\(799\) 6.99614i 0.247506i
\(800\) 8.17252 + 3.35265i 0.288942 + 0.118534i
\(801\) 0 0
\(802\) −10.8769 + 2.61914i −0.384076 + 0.0924849i
\(803\) 0.287088i 0.0101311i
\(804\) 0 0
\(805\) −19.3693 −0.682679
\(806\) 7.81855 1.88269i 0.275397 0.0663150i
\(807\) 0 0
\(808\) −15.1838 17.7046i −0.534163 0.622846i
\(809\) −44.3693 −1.55994 −0.779971 0.625816i \(-0.784766\pi\)
−0.779971 + 0.625816i \(0.784766\pi\)
\(810\) 0 0
\(811\) 29.9142 1.05043 0.525214 0.850970i \(-0.323985\pi\)
0.525214 + 0.850970i \(0.323985\pi\)
\(812\) −8.91618 + 4.55831i −0.312897 + 0.159965i
\(813\) 0 0
\(814\) 4.24621 + 17.6339i 0.148830 + 0.618068i
\(815\) 45.1702i 1.58224i
\(816\) 0 0
\(817\) −3.05398 + 4.82262i −0.106845 + 0.168722i
\(818\) −37.8078 + 9.10404i −1.32192 + 0.318315i
\(819\) 0 0
\(820\) −12.8255 25.0870i −0.447884 0.876075i
\(821\) 28.4233 0.991980 0.495990 0.868328i \(-0.334805\pi\)
0.495990 + 0.868328i \(0.334805\pi\)
\(822\) 0 0
\(823\) 31.1150i 1.08460i 0.840185 + 0.542299i \(0.182446\pi\)
−0.840185 + 0.542299i \(0.817554\pi\)
\(824\) 22.2462 + 25.9396i 0.774983 + 0.903649i
\(825\) 0 0
\(826\) 36.1501 8.70488i 1.25782 0.302881i
\(827\) −49.5242 −1.72212 −0.861062 0.508499i \(-0.830200\pi\)
−0.861062 + 0.508499i \(0.830200\pi\)
\(828\) 0 0
\(829\) 43.4686i 1.50973i −0.655881 0.754864i \(-0.727703\pi\)
0.655881 0.754864i \(-0.272297\pi\)
\(830\) −42.0775 + 10.1322i −1.46053 + 0.351693i
\(831\) 0 0
\(832\) 33.9507 + 5.23535i 1.17703 + 0.181503i
\(833\) −10.2462 −0.355010
\(834\) 0 0
\(835\) −27.5559 −0.953610
\(836\) 1.86611 20.2445i 0.0645407 0.700171i
\(837\) 0 0
\(838\) 54.9029 13.2205i 1.89659 0.456695i
\(839\) −15.8917 −0.548642 −0.274321 0.961638i \(-0.588453\pi\)
−0.274321 + 0.961638i \(0.588453\pi\)
\(840\) 0 0
\(841\) 27.5464 0.949876
\(842\) −31.9039 + 7.68240i −1.09948 + 0.264753i
\(843\) 0 0
\(844\) −44.8712 + 22.9400i −1.54453 + 0.789626i
\(845\) −13.9309 −0.479236
\(846\) 0 0
\(847\) 23.0963i 0.793599i
\(848\) 31.7555 + 22.9400i 1.09049 + 0.787762i
\(849\) 0 0
\(850\) 0.516994 + 2.14700i 0.0177327 + 0.0736415i
\(851\) 10.0138 0.343269
\(852\) 0 0
\(853\) 31.3693 1.07406 0.537032 0.843562i \(-0.319545\pi\)
0.537032 + 0.843562i \(0.319545\pi\)
\(854\) 66.7173 16.0654i 2.28302 0.549747i
\(855\) 0 0
\(856\) 10.5885 + 12.3465i 0.361909 + 0.421994i
\(857\) 39.1746i 1.33818i −0.743181 0.669090i \(-0.766684\pi\)
0.743181 0.669090i \(-0.233316\pi\)
\(858\) 0 0
\(859\) 45.9056i 1.56628i −0.621847 0.783139i \(-0.713617\pi\)
0.621847 0.783139i \(-0.286383\pi\)
\(860\) 3.05398 + 5.97366i 0.104140 + 0.203700i
\(861\) 0 0
\(862\) −1.75379 7.28323i −0.0597343 0.248068i
\(863\) 23.4199 0.797223 0.398612 0.917120i \(-0.369492\pi\)
0.398612 + 0.917120i \(0.369492\pi\)
\(864\) 0 0
\(865\) 6.17669i 0.210014i
\(866\) −26.0000 + 6.26075i −0.883516 + 0.212749i
\(867\) 0 0
\(868\) 5.00691 + 9.79366i 0.169946 + 0.332418i
\(869\) 31.2637i 1.06055i
\(870\) 0 0
\(871\) 1.24663i 0.0422405i
\(872\) −26.2041 + 22.4730i −0.887382 + 0.761032i
\(873\) 0 0
\(874\) −10.6250 3.61820i −0.359398 0.122388i
\(875\) 36.5774i 1.23654i
\(876\) 0 0
\(877\) 12.8820i 0.434994i 0.976061 + 0.217497i \(0.0697893\pi\)
−0.976061 + 0.217497i \(0.930211\pi\)
\(878\) −6.49242 26.9621i −0.219109 0.909927i
\(879\) 0 0
\(880\) −19.3693 13.9923i −0.652940 0.471680i
\(881\) 10.1771 0.342875 0.171437 0.985195i \(-0.445159\pi\)
0.171437 + 0.985195i \(0.445159\pi\)
\(882\) 0 0
\(883\) 48.5247i 1.63299i 0.577355 + 0.816493i \(0.304085\pi\)
−0.577355 + 0.816493i \(0.695915\pi\)
\(884\) 3.90928 + 7.64666i 0.131483 + 0.257185i
\(885\) 0 0
\(886\) −16.8213 + 4.05053i −0.565122 + 0.136080i
\(887\) −23.0023 −0.772342 −0.386171 0.922427i \(-0.626203\pi\)
−0.386171 + 0.922427i \(0.626203\pi\)
\(888\) 0 0
\(889\) 25.0870i 0.841390i
\(890\) 49.6155 11.9473i 1.66312 0.400475i
\(891\) 0 0
\(892\) 39.6377 20.2644i 1.32717 0.678501i
\(893\) 16.3153 25.7640i 0.545972 0.862160i
\(894\) 0 0
\(895\) −20.7713 −0.694308
\(896\) 3.90928 + 46.8213i 0.130600 + 1.56419i
\(897\) 0 0
\(898\) −20.3002 + 4.88825i −0.677426 + 0.163123i
\(899\) 1.59666i 0.0532515i
\(900\) 0 0
\(901\) 9.79366i 0.326274i
\(902\) 4.24621 + 17.6339i 0.141383 + 0.587145i
\(903\) 0 0
\(904\) −11.8078 + 10.1265i −0.392720 + 0.336803i
\(905\) 50.1739i 1.66784i
\(906\) 0 0
\(907\) 25.0345 0.831258 0.415629 0.909534i \(-0.363561\pi\)
0.415629 + 0.909534i \(0.363561\pi\)
\(908\) −43.8373 + 22.4114i −1.45479 + 0.743747i
\(909\) 0 0
\(910\) −15.1231 62.8041i −0.501326 2.08193i
\(911\) 40.3813 1.33789 0.668946 0.743311i \(-0.266746\pi\)
0.668946 + 0.743311i \(0.266746\pi\)
\(912\) 0 0
\(913\) 27.8617 0.922089
\(914\) 1.28355 + 5.33040i 0.0424560 + 0.176314i
\(915\) 0 0
\(916\) 11.6847 5.97366i 0.386072 0.197375i
\(917\) −24.8078 −0.819225
\(918\) 0 0
\(919\) 24.1188i 0.795606i −0.917471 0.397803i \(-0.869773\pi\)
0.917471 0.397803i \(-0.130227\pi\)
\(920\) −10.0138 + 8.58800i −0.330146 + 0.283138i
\(921\) 0 0
\(922\) −10.4901 43.5637i −0.345471 1.43469i
\(923\) 8.87989i 0.292285i
\(924\) 0 0
\(925\) 8.58800i 0.282372i
\(926\) 22.4446 5.40461i 0.737574 0.177606i
\(927\) 0 0
\(928\) −2.58854 + 6.30989i −0.0849730 + 0.207132i
\(929\) 13.3153 0.436862 0.218431 0.975852i \(-0.429906\pi\)
0.218431 + 0.975852i \(0.429906\pi\)
\(930\) 0 0
\(931\) 37.7327 + 23.8947i 1.23664 + 0.783116i
\(932\) 19.2462 9.83943i 0.630431 0.322301i
\(933\) 0 0
\(934\) 3.20636 0.772087i 0.104915 0.0252635i
\(935\) 5.97366i 0.195360i
\(936\) 0 0
\(937\) −13.8769 −0.453338 −0.226669 0.973972i \(-0.572784\pi\)
−0.226669 + 0.973972i \(0.572784\pi\)
\(938\) 1.65767 0.399164i 0.0541249 0.0130332i
\(939\) 0 0
\(940\) −16.3153 31.9133i −0.532148 1.04090i
\(941\) 48.2912i 1.57425i 0.616794 + 0.787125i \(0.288431\pi\)
−0.616794 + 0.787125i \(0.711569\pi\)
\(942\) 0 0
\(943\) 10.0138 0.326095
\(944\) 14.8298 20.5287i 0.482669 0.668151i
\(945\) 0 0
\(946\) −1.01110 4.19895i −0.0328737 0.136520i
\(947\) 21.2755i 0.691361i −0.938352 0.345681i \(-0.887648\pi\)
0.938352 0.345681i \(-0.112352\pi\)
\(948\) 0 0
\(949\) 0.528616i 0.0171596i
\(950\) 3.10303 9.11220i 0.100675 0.295639i
\(951\) 0 0
\(952\) −8.91618 + 7.64666i −0.288975 + 0.247830i
\(953\) 31.2637i 1.01273i −0.862319 0.506365i \(-0.830989\pi\)
0.862319 0.506365i \(-0.169011\pi\)
\(954\) 0 0
\(955\) 19.9660i 0.646083i
\(956\) −8.95786 17.5218i −0.289718 0.566696i
\(957\) 0 0
\(958\) −57.0982 + 13.7491i −1.84476 + 0.444215i
\(959\) 50.3455i 1.62574i
\(960\) 0 0
\(961\) −29.2462 −0.943426
\(962\) 7.81855 + 32.4693i 0.252080 + 1.04685i
\(963\) 0 0
\(964\) 20.6440 + 40.3803i 0.664899 + 1.30056i
\(965\) 14.0877i 0.453498i
\(966\) 0 0
\(967\) 10.3507i 0.332855i 0.986054 + 0.166428i \(0.0532232\pi\)
−0.986054 + 0.166428i \(0.946777\pi\)
\(968\) −10.2405 11.9407i −0.329142 0.383787i
\(969\) 0 0
\(970\) −8.49242 + 2.04496i −0.272675 + 0.0656597i
\(971\) −0.580639 −0.0186336 −0.00931679 0.999957i \(-0.502966\pi\)
−0.00931679 + 0.999957i \(0.502966\pi\)
\(972\) 0 0
\(973\) 78.6695 2.52203
\(974\) −6.24621 25.9396i −0.200142 0.831159i
\(975\) 0 0
\(976\) 27.3693 37.8869i 0.876070 1.21273i
\(977\) 50.8510i 1.62687i 0.581658 + 0.813433i \(0.302404\pi\)
−0.581658 + 0.813433i \(0.697596\pi\)
\(978\) 0 0
\(979\) −32.8531 −1.04999
\(980\) 46.7386 23.8947i 1.49301 0.763287i
\(981\) 0 0
\(982\) 29.2520 7.04383i 0.933469 0.224778i
\(983\) −6.78456 −0.216394 −0.108197 0.994129i \(-0.534508\pi\)
−0.108197 + 0.994129i \(0.534508\pi\)
\(984\) 0 0
\(985\) 57.6155 1.83578
\(986\) −1.65767 + 0.399164i −0.0527910 + 0.0127120i
\(987\) 0 0
\(988\) 3.43606 37.2762i 0.109316 1.18591i
\(989\) −2.38447 −0.0758218
\(990\) 0 0
\(991\) −0.417609 −0.0132658 −0.00663289 0.999978i \(-0.502111\pi\)
−0.00663289 + 0.999978i \(0.502111\pi\)
\(992\) 6.93087 + 2.84329i 0.220055 + 0.0902745i
\(993\) 0 0
\(994\) 11.8078 2.84329i 0.374520 0.0901836i
\(995\) 13.2569i 0.420272i
\(996\) 0 0
\(997\) 41.5464 1.31579 0.657894 0.753111i \(-0.271448\pi\)
0.657894 + 0.753111i \(0.271448\pi\)
\(998\) 1.80054 0.433567i 0.0569952 0.0137243i
\(999\) 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 684.2.f.b.379.6 8
3.2 odd 2 76.2.d.a.75.3 8
4.3 odd 2 inner 684.2.f.b.379.4 8
12.11 even 2 76.2.d.a.75.5 yes 8
19.18 odd 2 inner 684.2.f.b.379.3 8
24.5 odd 2 1216.2.h.d.1215.7 8
24.11 even 2 1216.2.h.d.1215.2 8
57.56 even 2 76.2.d.a.75.6 yes 8
76.75 even 2 inner 684.2.f.b.379.5 8
228.227 odd 2 76.2.d.a.75.4 yes 8
456.227 odd 2 1216.2.h.d.1215.8 8
456.341 even 2 1216.2.h.d.1215.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.2.d.a.75.3 8 3.2 odd 2
76.2.d.a.75.4 yes 8 228.227 odd 2
76.2.d.a.75.5 yes 8 12.11 even 2
76.2.d.a.75.6 yes 8 57.56 even 2
684.2.f.b.379.3 8 19.18 odd 2 inner
684.2.f.b.379.4 8 4.3 odd 2 inner
684.2.f.b.379.5 8 76.75 even 2 inner
684.2.f.b.379.6 8 1.1 even 1 trivial
1216.2.h.d.1215.1 8 456.341 even 2
1216.2.h.d.1215.2 8 24.11 even 2
1216.2.h.d.1215.7 8 24.5 odd 2
1216.2.h.d.1215.8 8 456.227 odd 2