# Properties

 Label 1.12.a.a.1.1 Level $1$ Weight $12$ Character 1.1 Self dual yes Analytic conductor $0.768$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,12,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1$$ Weight: $$k$$ $$=$$ $$12$$ Character orbit: $$[\chi]$$ $$=$$ 1.a (trivial)

## 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: yes Analytic conductor: $$0.768343180560$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-24.0000 q^{2} +252.000 q^{3} -1472.00 q^{4} +4830.00 q^{5} -6048.00 q^{6} -16744.0 q^{7} +84480.0 q^{8} -113643. q^{9} +O(q^{10})$$ $$q-24.0000 q^{2} +252.000 q^{3} -1472.00 q^{4} +4830.00 q^{5} -6048.00 q^{6} -16744.0 q^{7} +84480.0 q^{8} -113643. q^{9} -115920. q^{10} +534612. q^{11} -370944. q^{12} -577738. q^{13} +401856. q^{14} +1.21716e6 q^{15} +987136. q^{16} -6.90593e6 q^{17} +2.72743e6 q^{18} +1.06614e7 q^{19} -7.10976e6 q^{20} -4.21949e6 q^{21} -1.28307e7 q^{22} +1.86433e7 q^{23} +2.12890e7 q^{24} -2.54992e7 q^{25} +1.38657e7 q^{26} -7.32791e7 q^{27} +2.46472e7 q^{28} +1.28407e8 q^{29} -2.92118e7 q^{30} -5.28432e7 q^{31} -1.96706e8 q^{32} +1.34722e8 q^{33} +1.65742e8 q^{34} -8.08735e7 q^{35} +1.67282e8 q^{36} -1.82213e8 q^{37} -2.55874e8 q^{38} -1.45590e8 q^{39} +4.08038e8 q^{40} +3.08120e8 q^{41} +1.01268e8 q^{42} -1.71257e7 q^{43} -7.86949e8 q^{44} -5.48896e8 q^{45} -4.47439e8 q^{46} +2.68735e9 q^{47} +2.48758e8 q^{48} -1.69697e9 q^{49} +6.11981e8 q^{50} -1.74030e9 q^{51} +8.50430e8 q^{52} -1.59606e9 q^{53} +1.75870e9 q^{54} +2.58218e9 q^{55} -1.41453e9 q^{56} +2.68668e9 q^{57} -3.08176e9 q^{58} -5.18920e9 q^{59} -1.79166e9 q^{60} +6.95648e9 q^{61} +1.26824e9 q^{62} +1.90284e9 q^{63} +2.69930e9 q^{64} -2.79047e9 q^{65} -3.23333e9 q^{66} -1.54818e10 q^{67} +1.01655e10 q^{68} +4.69810e9 q^{69} +1.94096e9 q^{70} +9.79149e9 q^{71} -9.60056e9 q^{72} +1.46379e9 q^{73} +4.37312e9 q^{74} -6.42580e9 q^{75} -1.56936e10 q^{76} -8.95154e9 q^{77} +3.49416e9 q^{78} +3.81168e10 q^{79} +4.76787e9 q^{80} +1.66519e9 q^{81} -7.39489e9 q^{82} -2.93351e10 q^{83} +6.21109e9 q^{84} -3.33557e10 q^{85} +4.11017e8 q^{86} +3.23585e10 q^{87} +4.51640e10 q^{88} -2.49929e10 q^{89} +1.31735e10 q^{90} +9.67365e9 q^{91} -2.74429e10 q^{92} -1.33165e10 q^{93} -6.44964e10 q^{94} +5.14947e10 q^{95} -4.95700e10 q^{96} +7.50136e10 q^{97} +4.07272e10 q^{98} -6.07549e10 q^{99} +O(q^{100})$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −24.0000 −0.530330 −0.265165 0.964203i $$-0.585426\pi$$
−0.265165 + 0.964203i $$0.585426\pi$$
$$3$$ 252.000 0.598734 0.299367 0.954138i $$-0.403225\pi$$
0.299367 + 0.954138i $$0.403225\pi$$
$$4$$ −1472.00 −0.718750
$$5$$ 4830.00 0.691213 0.345607 0.938379i $$-0.387673\pi$$
0.345607 + 0.938379i $$0.387673\pi$$
$$6$$ −6048.00 −0.317526
$$7$$ −16744.0 −0.376548 −0.188274 0.982117i $$-0.560289\pi$$
−0.188274 + 0.982117i $$0.560289\pi$$
$$8$$ 84480.0 0.911505
$$9$$ −113643. −0.641518
$$10$$ −115920. −0.366571
$$11$$ 534612. 1.00087 0.500436 0.865773i $$-0.333173\pi$$
0.500436 + 0.865773i $$0.333173\pi$$
$$12$$ −370944. −0.430340
$$13$$ −577738. −0.431561 −0.215781 0.976442i $$-0.569230\pi$$
−0.215781 + 0.976442i $$0.569230\pi$$
$$14$$ 401856. 0.199695
$$15$$ 1.21716e6 0.413853
$$16$$ 987136. 0.235352
$$17$$ −6.90593e6 −1.17965 −0.589825 0.807531i $$-0.700803\pi$$
−0.589825 + 0.807531i $$0.700803\pi$$
$$18$$ 2.72743e6 0.340216
$$19$$ 1.06614e7 0.987803 0.493901 0.869518i $$-0.335570\pi$$
0.493901 + 0.869518i $$0.335570\pi$$
$$20$$ −7.10976e6 −0.496810
$$21$$ −4.21949e6 −0.225452
$$22$$ −1.28307e7 −0.530793
$$23$$ 1.86433e7 0.603975 0.301988 0.953312i $$-0.402350\pi$$
0.301988 + 0.953312i $$0.402350\pi$$
$$24$$ 2.12890e7 0.545749
$$25$$ −2.54992e7 −0.522224
$$26$$ 1.38657e7 0.228870
$$27$$ −7.32791e7 −0.982832
$$28$$ 2.46472e7 0.270644
$$29$$ 1.28407e8 1.16251 0.581257 0.813720i $$-0.302561\pi$$
0.581257 + 0.813720i $$0.302561\pi$$
$$30$$ −2.92118e7 −0.219479
$$31$$ −5.28432e7 −0.331512 −0.165756 0.986167i $$-0.553006\pi$$
−0.165756 + 0.986167i $$0.553006\pi$$
$$32$$ −1.96706e8 −1.03632
$$33$$ 1.34722e8 0.599256
$$34$$ 1.65742e8 0.625604
$$35$$ −8.08735e7 −0.260275
$$36$$ 1.67282e8 0.461091
$$37$$ −1.82213e8 −0.431987 −0.215993 0.976395i $$-0.569299\pi$$
−0.215993 + 0.976395i $$0.569299\pi$$
$$38$$ −2.55874e8 −0.523862
$$39$$ −1.45590e8 −0.258390
$$40$$ 4.08038e8 0.630044
$$41$$ 3.08120e8 0.415345 0.207673 0.978198i $$-0.433411\pi$$
0.207673 + 0.978198i $$0.433411\pi$$
$$42$$ 1.01268e8 0.119564
$$43$$ −1.71257e7 −0.0177653 −0.00888264 0.999961i $$-0.502827\pi$$
−0.00888264 + 0.999961i $$0.502827\pi$$
$$44$$ −7.86949e8 −0.719377
$$45$$ −5.48896e8 −0.443426
$$46$$ −4.47439e8 −0.320306
$$47$$ 2.68735e9 1.70917 0.854586 0.519310i $$-0.173811\pi$$
0.854586 + 0.519310i $$0.173811\pi$$
$$48$$ 2.48758e8 0.140913
$$49$$ −1.69697e9 −0.858212
$$50$$ 6.11981e8 0.276951
$$51$$ −1.74030e9 −0.706296
$$52$$ 8.50430e8 0.310185
$$53$$ −1.59606e9 −0.524241 −0.262120 0.965035i $$-0.584422\pi$$
−0.262120 + 0.965035i $$0.584422\pi$$
$$54$$ 1.75870e9 0.521225
$$55$$ 2.58218e9 0.691817
$$56$$ −1.41453e9 −0.343225
$$57$$ 2.68668e9 0.591431
$$58$$ −3.08176e9 −0.616517
$$59$$ −5.18920e9 −0.944963 −0.472481 0.881341i $$-0.656642\pi$$
−0.472481 + 0.881341i $$0.656642\pi$$
$$60$$ −1.79166e9 −0.297457
$$61$$ 6.95648e9 1.05457 0.527285 0.849689i $$-0.323210\pi$$
0.527285 + 0.849689i $$0.323210\pi$$
$$62$$ 1.26824e9 0.175811
$$63$$ 1.90284e9 0.241562
$$64$$ 2.69930e9 0.314240
$$65$$ −2.79047e9 −0.298301
$$66$$ −3.23333e9 −0.317804
$$67$$ −1.54818e10 −1.40091 −0.700456 0.713696i $$-0.747020\pi$$
−0.700456 + 0.713696i $$0.747020\pi$$
$$68$$ 1.01655e10 0.847874
$$69$$ 4.69810e9 0.361620
$$70$$ 1.94096e9 0.138032
$$71$$ 9.79149e9 0.644062 0.322031 0.946729i $$-0.395634\pi$$
0.322031 + 0.946729i $$0.395634\pi$$
$$72$$ −9.60056e9 −0.584747
$$73$$ 1.46379e9 0.0826425 0.0413212 0.999146i $$-0.486843\pi$$
0.0413212 + 0.999146i $$0.486843\pi$$
$$74$$ 4.37312e9 0.229096
$$75$$ −6.42580e9 −0.312673
$$76$$ −1.56936e10 −0.709983
$$77$$ −8.95154e9 −0.376876
$$78$$ 3.49416e9 0.137032
$$79$$ 3.81168e10 1.39370 0.696848 0.717219i $$-0.254585\pi$$
0.696848 + 0.717219i $$0.254585\pi$$
$$80$$ 4.76787e9 0.162678
$$81$$ 1.66519e9 0.0530635
$$82$$ −7.39489e9 −0.220270
$$83$$ −2.93351e10 −0.817444 −0.408722 0.912659i $$-0.634025\pi$$
−0.408722 + 0.912659i $$0.634025\pi$$
$$84$$ 6.21109e9 0.162043
$$85$$ −3.33557e10 −0.815390
$$86$$ 4.11017e8 0.00942146
$$87$$ 3.23585e10 0.696037
$$88$$ 4.51640e10 0.912300
$$89$$ −2.49929e10 −0.474430 −0.237215 0.971457i $$-0.576235\pi$$
−0.237215 + 0.971457i $$0.576235\pi$$
$$90$$ 1.31735e10 0.235162
$$91$$ 9.67365e9 0.162503
$$92$$ −2.74429e10 −0.434107
$$93$$ −1.33165e10 −0.198488
$$94$$ −6.44964e10 −0.906425
$$95$$ 5.14947e10 0.682782
$$96$$ −4.95700e10 −0.620479
$$97$$ 7.50136e10 0.886942 0.443471 0.896289i $$-0.353747\pi$$
0.443471 + 0.896289i $$0.353747\pi$$
$$98$$ 4.07272e10 0.455136
$$99$$ −6.07549e10 −0.642078
$$100$$ 3.75349e10 0.375349
$$101$$ 8.17430e10 0.773896 0.386948 0.922101i $$-0.373529\pi$$
0.386948 + 0.922101i $$0.373529\pi$$
$$102$$ 4.17671e10 0.374570
$$103$$ −2.25755e11 −1.91881 −0.959407 0.282025i $$-0.908994\pi$$
−0.959407 + 0.282025i $$0.908994\pi$$
$$104$$ −4.88073e10 −0.393370
$$105$$ −2.03801e10 −0.155835
$$106$$ 3.83053e10 0.278021
$$107$$ 9.02413e10 0.622006 0.311003 0.950409i $$-0.399335\pi$$
0.311003 + 0.950409i $$0.399335\pi$$
$$108$$ 1.07867e11 0.706411
$$109$$ 7.34827e10 0.457445 0.228723 0.973492i $$-0.426545\pi$$
0.228723 + 0.973492i $$0.426545\pi$$
$$110$$ −6.19722e10 −0.366891
$$111$$ −4.59178e10 −0.258645
$$112$$ −1.65286e10 −0.0886211
$$113$$ −8.51469e10 −0.434748 −0.217374 0.976088i $$-0.569749\pi$$
−0.217374 + 0.976088i $$0.569749\pi$$
$$114$$ −6.44803e10 −0.313654
$$115$$ 9.00470e10 0.417476
$$116$$ −1.89015e11 −0.835557
$$117$$ 6.56559e10 0.276854
$$118$$ 1.24541e11 0.501142
$$119$$ 1.15633e11 0.444195
$$120$$ 1.02826e11 0.377229
$$121$$ 4.98320e8 0.00174658
$$122$$ −1.66955e11 −0.559270
$$123$$ 7.76464e10 0.248681
$$124$$ 7.77851e10 0.238274
$$125$$ −3.59001e11 −1.05218
$$126$$ −4.56681e10 −0.128108
$$127$$ −2.62717e11 −0.705615 −0.352808 0.935696i $$-0.614773\pi$$
−0.352808 + 0.935696i $$0.614773\pi$$
$$128$$ 3.38071e11 0.869668
$$129$$ −4.31568e9 −0.0106367
$$130$$ 6.69714e10 0.158198
$$131$$ 6.31529e11 1.43021 0.715107 0.699015i $$-0.246378\pi$$
0.715107 + 0.699015i $$0.246378\pi$$
$$132$$ −1.98311e11 −0.430715
$$133$$ −1.78515e11 −0.371955
$$134$$ 3.71564e11 0.742946
$$135$$ −3.53938e11 −0.679347
$$136$$ −5.83413e11 −1.07526
$$137$$ −2.97199e11 −0.526119 −0.263059 0.964780i $$-0.584732\pi$$
−0.263059 + 0.964780i $$0.584732\pi$$
$$138$$ −1.12755e11 −0.191778
$$139$$ 5.96794e11 0.975535 0.487767 0.872974i $$-0.337811\pi$$
0.487767 + 0.872974i $$0.337811\pi$$
$$140$$ 1.19046e11 0.187073
$$141$$ 6.77212e11 1.02334
$$142$$ −2.34996e11 −0.341565
$$143$$ −3.08866e11 −0.431938
$$144$$ −1.12181e11 −0.150982
$$145$$ 6.20204e11 0.803546
$$146$$ −3.51310e10 −0.0438278
$$147$$ −4.27635e11 −0.513840
$$148$$ 2.68218e11 0.310491
$$149$$ −1.11543e12 −1.24428 −0.622142 0.782905i $$-0.713737\pi$$
−0.622142 + 0.782905i $$0.713737\pi$$
$$150$$ 1.54219e11 0.165820
$$151$$ −8.24447e11 −0.854653 −0.427326 0.904097i $$-0.640544\pi$$
−0.427326 + 0.904097i $$0.640544\pi$$
$$152$$ 9.00677e11 0.900387
$$153$$ 7.84811e11 0.756767
$$154$$ 2.14837e11 0.199869
$$155$$ −2.55233e11 −0.229146
$$156$$ 2.14308e11 0.185718
$$157$$ 1.31512e12 1.10031 0.550156 0.835062i $$-0.314568\pi$$
0.550156 + 0.835062i $$0.314568\pi$$
$$158$$ −9.14804e11 −0.739119
$$159$$ −4.02206e11 −0.313881
$$160$$ −9.50091e11 −0.716317
$$161$$ −3.12163e11 −0.227425
$$162$$ −3.99645e10 −0.0281412
$$163$$ −3.57833e11 −0.243584 −0.121792 0.992556i $$-0.538864\pi$$
−0.121792 + 0.992556i $$0.538864\pi$$
$$164$$ −4.53553e11 −0.298529
$$165$$ 6.50708e11 0.414214
$$166$$ 7.04042e11 0.433515
$$167$$ 2.75483e12 1.64117 0.820587 0.571521i $$-0.193646\pi$$
0.820587 + 0.571521i $$0.193646\pi$$
$$168$$ −3.56462e11 −0.205500
$$169$$ −1.45838e12 −0.813755
$$170$$ 8.00536e11 0.432426
$$171$$ −1.21160e12 −0.633693
$$172$$ 2.52090e10 0.0127688
$$173$$ −9.50387e11 −0.466280 −0.233140 0.972443i $$-0.574900\pi$$
−0.233140 + 0.972443i $$0.574900\pi$$
$$174$$ −7.76603e11 −0.369129
$$175$$ 4.26959e11 0.196642
$$176$$ 5.27735e11 0.235557
$$177$$ −1.30768e12 −0.565781
$$178$$ 5.99830e11 0.251604
$$179$$ 1.68138e12 0.683873 0.341936 0.939723i $$-0.388917\pi$$
0.341936 + 0.939723i $$0.388917\pi$$
$$180$$ 8.07974e11 0.318712
$$181$$ −9.96774e11 −0.381386 −0.190693 0.981650i $$-0.561073\pi$$
−0.190693 + 0.981650i $$0.561073\pi$$
$$182$$ −2.32167e11 −0.0861804
$$183$$ 1.75303e12 0.631406
$$184$$ 1.57498e12 0.550526
$$185$$ −8.80090e11 −0.298595
$$186$$ 3.19595e11 0.105264
$$187$$ −3.69200e12 −1.18068
$$188$$ −3.95578e12 −1.22847
$$189$$ 1.22698e12 0.370083
$$190$$ −1.23587e12 −0.362100
$$191$$ 2.76240e12 0.786328 0.393164 0.919468i $$-0.371381\pi$$
0.393164 + 0.919468i $$0.371381\pi$$
$$192$$ 6.80223e11 0.188146
$$193$$ 5.44239e12 1.46293 0.731466 0.681878i $$-0.238836\pi$$
0.731466 + 0.681878i $$0.238836\pi$$
$$194$$ −1.80033e12 −0.470372
$$195$$ −7.03200e11 −0.178603
$$196$$ 2.49793e12 0.616840
$$197$$ −2.87609e12 −0.690619 −0.345309 0.938489i $$-0.612226\pi$$
−0.345309 + 0.938489i $$0.612226\pi$$
$$198$$ 1.45812e12 0.340513
$$199$$ 7.28391e11 0.165452 0.0827262 0.996572i $$-0.473637\pi$$
0.0827262 + 0.996572i $$0.473637\pi$$
$$200$$ −2.15417e12 −0.476010
$$201$$ −3.90142e12 −0.838773
$$202$$ −1.96183e12 −0.410421
$$203$$ −2.15004e12 −0.437742
$$204$$ 2.56171e12 0.507651
$$205$$ 1.48822e12 0.287092
$$206$$ 5.41812e12 1.01760
$$207$$ −2.11868e12 −0.387461
$$208$$ −5.70306e11 −0.101569
$$209$$ 5.69972e12 0.988665
$$210$$ 4.89123e11 0.0826441
$$211$$ −6.79317e12 −1.11820 −0.559099 0.829101i $$-0.688853\pi$$
−0.559099 + 0.829101i $$0.688853\pi$$
$$212$$ 2.34939e12 0.376798
$$213$$ 2.46745e12 0.385622
$$214$$ −2.16579e12 −0.329868
$$215$$ −8.27172e10 −0.0122796
$$216$$ −6.19062e12 −0.895856
$$217$$ 8.84806e11 0.124830
$$218$$ −1.76358e12 −0.242597
$$219$$ 3.68875e11 0.0494808
$$220$$ −3.80096e12 −0.497243
$$221$$ 3.98982e12 0.509092
$$222$$ 1.10203e12 0.137167
$$223$$ 7.33486e12 0.890667 0.445333 0.895365i $$-0.353085\pi$$
0.445333 + 0.895365i $$0.353085\pi$$
$$224$$ 3.29365e12 0.390223
$$225$$ 2.89781e12 0.335016
$$226$$ 2.04352e12 0.230560
$$227$$ −1.35984e12 −0.149743 −0.0748713 0.997193i $$-0.523855\pi$$
−0.0748713 + 0.997193i $$0.523855\pi$$
$$228$$ −3.95479e12 −0.425091
$$229$$ −1.18244e13 −1.24075 −0.620375 0.784305i $$-0.713020\pi$$
−0.620375 + 0.784305i $$0.713020\pi$$
$$230$$ −2.16113e12 −0.221400
$$231$$ −2.25579e12 −0.225649
$$232$$ 1.08478e13 1.05964
$$233$$ −1.75634e13 −1.67552 −0.837761 0.546038i $$-0.816135\pi$$
−0.837761 + 0.546038i $$0.816135\pi$$
$$234$$ −1.57574e12 −0.146824
$$235$$ 1.29799e13 1.18140
$$236$$ 7.63851e12 0.679192
$$237$$ 9.60545e12 0.834452
$$238$$ −2.77519e12 −0.235570
$$239$$ −7.13958e12 −0.592221 −0.296111 0.955154i $$-0.595690\pi$$
−0.296111 + 0.955154i $$0.595690\pi$$
$$240$$ 1.20150e12 0.0974009
$$241$$ −2.31307e11 −0.0183271 −0.00916357 0.999958i $$-0.502917\pi$$
−0.00916357 + 0.999958i $$0.502917\pi$$
$$242$$ −1.19597e10 −0.000926264 0
$$243$$ 1.34008e13 1.01460
$$244$$ −1.02399e13 −0.757972
$$245$$ −8.19634e12 −0.593207
$$246$$ −1.86351e12 −0.131883
$$247$$ −6.15951e12 −0.426297
$$248$$ −4.46419e12 −0.302175
$$249$$ −7.39245e12 −0.489431
$$250$$ 8.61603e12 0.558004
$$251$$ 1.29831e13 0.822567 0.411284 0.911507i $$-0.365081\pi$$
0.411284 + 0.911507i $$0.365081\pi$$
$$252$$ −2.80098e12 −0.173623
$$253$$ 9.96692e12 0.604502
$$254$$ 6.30521e12 0.374209
$$255$$ −8.40563e12 −0.488201
$$256$$ −1.36419e13 −0.775451
$$257$$ 2.39612e13 1.33314 0.666571 0.745442i $$-0.267761\pi$$
0.666571 + 0.745442i $$0.267761\pi$$
$$258$$ 1.03576e11 0.00564095
$$259$$ 3.05098e12 0.162664
$$260$$ 4.10758e12 0.214404
$$261$$ −1.45925e13 −0.745774
$$262$$ −1.51567e13 −0.758485
$$263$$ −2.42737e13 −1.18954 −0.594771 0.803895i $$-0.702757\pi$$
−0.594771 + 0.803895i $$0.702757\pi$$
$$264$$ 1.13813e13 0.546225
$$265$$ −7.70895e12 −0.362362
$$266$$ 4.28436e12 0.197259
$$267$$ −6.29822e12 −0.284057
$$268$$ 2.27892e13 1.00691
$$269$$ 2.58377e13 1.11845 0.559225 0.829016i $$-0.311099\pi$$
0.559225 + 0.829016i $$0.311099\pi$$
$$270$$ 8.49451e12 0.360278
$$271$$ −3.76793e12 −0.156593 −0.0782964 0.996930i $$-0.524948\pi$$
−0.0782964 + 0.996930i $$0.524948\pi$$
$$272$$ −6.81710e12 −0.277633
$$273$$ 2.43776e12 0.0972963
$$274$$ 7.13277e12 0.279017
$$275$$ −1.36322e13 −0.522680
$$276$$ −6.91561e12 −0.259915
$$277$$ −1.64189e13 −0.604931 −0.302466 0.953160i $$-0.597810\pi$$
−0.302466 + 0.953160i $$0.597810\pi$$
$$278$$ −1.43230e13 −0.517355
$$279$$ 6.00526e12 0.212671
$$280$$ −6.83219e12 −0.237242
$$281$$ 2.10357e13 0.716263 0.358132 0.933671i $$-0.383414\pi$$
0.358132 + 0.933671i $$0.383414\pi$$
$$282$$ −1.62531e13 −0.542707
$$283$$ 1.67132e13 0.547310 0.273655 0.961828i $$-0.411767\pi$$
0.273655 + 0.961828i $$0.411767\pi$$
$$284$$ −1.44131e13 −0.462920
$$285$$ 1.29767e13 0.408805
$$286$$ 7.41278e12 0.229070
$$287$$ −5.15917e12 −0.156397
$$288$$ 2.23543e13 0.664817
$$289$$ 1.34200e13 0.391575
$$290$$ −1.48849e13 −0.426144
$$291$$ 1.89034e13 0.531042
$$292$$ −2.15470e12 −0.0593993
$$293$$ −2.39269e13 −0.647312 −0.323656 0.946175i $$-0.604912\pi$$
−0.323656 + 0.946175i $$0.604912\pi$$
$$294$$ 1.02632e13 0.272505
$$295$$ −2.50639e13 −0.653171
$$296$$ −1.53934e13 −0.393758
$$297$$ −3.91759e13 −0.983690
$$298$$ 2.67704e13 0.659881
$$299$$ −1.07709e13 −0.260652
$$300$$ 9.45878e12 0.224734
$$301$$ 2.86753e11 0.00668947
$$302$$ 1.97867e13 0.453248
$$303$$ 2.05992e13 0.463358
$$304$$ 1.05243e13 0.232481
$$305$$ 3.35998e13 0.728933
$$306$$ −1.88355e13 −0.401336
$$307$$ 1.53111e13 0.320439 0.160219 0.987081i $$-0.448780\pi$$
0.160219 + 0.987081i $$0.448780\pi$$
$$308$$ 1.31767e13 0.270880
$$309$$ −5.68903e13 −1.14886
$$310$$ 6.12558e12 0.121523
$$311$$ 4.98752e13 0.972080 0.486040 0.873936i $$-0.338441\pi$$
0.486040 + 0.873936i $$0.338441\pi$$
$$312$$ −1.22994e13 −0.235524
$$313$$ −9.94808e13 −1.87174 −0.935870 0.352345i $$-0.885384\pi$$
−0.935870 + 0.352345i $$0.885384\pi$$
$$314$$ −3.15628e13 −0.583529
$$315$$ 9.19071e12 0.166971
$$316$$ −5.61080e13 −1.00172
$$317$$ 8.33692e13 1.46278 0.731392 0.681958i $$-0.238871\pi$$
0.731392 + 0.681958i $$0.238871\pi$$
$$318$$ 9.65294e12 0.166460
$$319$$ 6.86477e13 1.16353
$$320$$ 1.30376e13 0.217207
$$321$$ 2.27408e13 0.372416
$$322$$ 7.49191e12 0.120611
$$323$$ −7.36271e13 −1.16526
$$324$$ −2.45116e12 −0.0381394
$$325$$ 1.47319e13 0.225372
$$326$$ 8.58799e12 0.129180
$$327$$ 1.85176e13 0.273888
$$328$$ 2.60300e13 0.378589
$$329$$ −4.49970e13 −0.643585
$$330$$ −1.56170e13 −0.219670
$$331$$ −6.35840e13 −0.879618 −0.439809 0.898091i $$-0.644954\pi$$
−0.439809 + 0.898091i $$0.644954\pi$$
$$332$$ 4.31813e13 0.587538
$$333$$ 2.07073e13 0.277127
$$334$$ −6.61160e13 −0.870364
$$335$$ −7.47772e13 −0.968329
$$336$$ −4.16521e12 −0.0530604
$$337$$ 1.21001e14 1.51644 0.758221 0.651997i $$-0.226069\pi$$
0.758221 + 0.651997i $$0.226069\pi$$
$$338$$ 3.50011e13 0.431559
$$339$$ −2.14570e13 −0.260298
$$340$$ 4.90995e13 0.586062
$$341$$ −2.82506e13 −0.331802
$$342$$ 2.90783e13 0.336067
$$343$$ 6.15223e13 0.699705
$$344$$ −1.44678e12 −0.0161931
$$345$$ 2.26918e13 0.249957
$$346$$ 2.28093e13 0.247283
$$347$$ −1.55662e14 −1.66100 −0.830499 0.557020i $$-0.811945\pi$$
−0.830499 + 0.557020i $$0.811945\pi$$
$$348$$ −4.76317e13 −0.500276
$$349$$ −2.56430e13 −0.265112 −0.132556 0.991176i $$-0.542318\pi$$
−0.132556 + 0.991176i $$0.542318\pi$$
$$350$$ −1.02470e13 −0.104285
$$351$$ 4.23361e13 0.424152
$$352$$ −1.05162e14 −1.03722
$$353$$ 2.49098e13 0.241885 0.120943 0.992659i $$-0.461408\pi$$
0.120943 + 0.992659i $$0.461408\pi$$
$$354$$ 3.13843e13 0.300051
$$355$$ 4.72929e13 0.445184
$$356$$ 3.67896e13 0.340996
$$357$$ 2.91395e13 0.265954
$$358$$ −4.03532e13 −0.362678
$$359$$ 1.57584e14 1.39474 0.697370 0.716712i $$-0.254354\pi$$
0.697370 + 0.716712i $$0.254354\pi$$
$$360$$ −4.63707e13 −0.404185
$$361$$ −2.82438e12 −0.0242457
$$362$$ 2.39226e13 0.202260
$$363$$ 1.25577e11 0.00104574
$$364$$ −1.42396e13 −0.116799
$$365$$ 7.07011e12 0.0571236
$$366$$ −4.20728e13 −0.334854
$$367$$ −1.77901e14 −1.39481 −0.697406 0.716676i $$-0.745662\pi$$
−0.697406 + 0.716676i $$0.745662\pi$$
$$368$$ 1.84034e13 0.142146
$$369$$ −3.50157e13 −0.266452
$$370$$ 2.11222e13 0.158354
$$371$$ 2.67244e13 0.197402
$$372$$ 1.96019e13 0.142663
$$373$$ −5.51617e13 −0.395585 −0.197792 0.980244i $$-0.563377\pi$$
−0.197792 + 0.980244i $$0.563377\pi$$
$$374$$ 8.86079e13 0.626150
$$375$$ −9.04683e13 −0.629976
$$376$$ 2.27027e14 1.55792
$$377$$ −7.41854e13 −0.501696
$$378$$ −2.94476e13 −0.196266
$$379$$ 1.46463e14 0.962083 0.481042 0.876698i $$-0.340259\pi$$
0.481042 + 0.876698i $$0.340259\pi$$
$$380$$ −7.58001e13 −0.490750
$$381$$ −6.62047e13 −0.422476
$$382$$ −6.62977e13 −0.417013
$$383$$ 2.31450e14 1.43504 0.717519 0.696539i $$-0.245278\pi$$
0.717519 + 0.696539i $$0.245278\pi$$
$$384$$ 8.51940e13 0.520700
$$385$$ −4.32360e13 −0.260502
$$386$$ −1.30617e14 −0.775837
$$387$$ 1.94622e12 0.0113967
$$388$$ −1.10420e14 −0.637490
$$389$$ −1.49872e14 −0.853093 −0.426547 0.904466i $$-0.640270\pi$$
−0.426547 + 0.904466i $$0.640270\pi$$
$$390$$ 1.68768e13 0.0947184
$$391$$ −1.28749e14 −0.712480
$$392$$ −1.43360e14 −0.782264
$$393$$ 1.59145e14 0.856317
$$394$$ 6.90262e13 0.366256
$$395$$ 1.84104e14 0.963341
$$396$$ 8.94312e13 0.461494
$$397$$ 2.08111e14 1.05912 0.529562 0.848271i $$-0.322356\pi$$
0.529562 + 0.848271i $$0.322356\pi$$
$$398$$ −1.74814e13 −0.0877443
$$399$$ −4.49857e13 −0.222702
$$400$$ −2.51712e13 −0.122906
$$401$$ −1.33408e14 −0.642521 −0.321261 0.946991i $$-0.604107\pi$$
−0.321261 + 0.946991i $$0.604107\pi$$
$$402$$ 9.36341e13 0.444827
$$403$$ 3.05295e13 0.143068
$$404$$ −1.20326e14 −0.556238
$$405$$ 8.04286e12 0.0366782
$$406$$ 5.16010e13 0.232148
$$407$$ −9.74134e13 −0.432364
$$408$$ −1.47020e14 −0.643793
$$409$$ −2.06168e14 −0.890722 −0.445361 0.895351i $$-0.646925\pi$$
−0.445361 + 0.895351i $$0.646925\pi$$
$$410$$ −3.57173e13 −0.152254
$$411$$ −7.48941e13 −0.315005
$$412$$ 3.32312e14 1.37915
$$413$$ 8.68880e13 0.355824
$$414$$ 5.08483e13 0.205482
$$415$$ −1.41689e14 −0.565028
$$416$$ 1.13645e14 0.447235
$$417$$ 1.50392e14 0.584085
$$418$$ −1.36793e14 −0.524319
$$419$$ 7.34035e13 0.277677 0.138838 0.990315i $$-0.455663\pi$$
0.138838 + 0.990315i $$0.455663\pi$$
$$420$$ 2.99995e13 0.112007
$$421$$ 1.71112e14 0.630563 0.315282 0.948998i $$-0.397901\pi$$
0.315282 + 0.948998i $$0.397901\pi$$
$$422$$ 1.63036e14 0.593014
$$423$$ −3.05398e14 −1.09646
$$424$$ −1.34835e14 −0.477848
$$425$$ 1.76096e14 0.616042
$$426$$ −5.92189e13 −0.204507
$$427$$ −1.16479e14 −0.397096
$$428$$ −1.32835e14 −0.447067
$$429$$ −7.78341e13 −0.258616
$$430$$ 1.98521e12 0.00651224
$$431$$ −7.17758e13 −0.232463 −0.116231 0.993222i $$-0.537081\pi$$
−0.116231 + 0.993222i $$0.537081\pi$$
$$432$$ −7.23364e13 −0.231311
$$433$$ 9.98812e13 0.315356 0.157678 0.987491i $$-0.449599\pi$$
0.157678 + 0.987491i $$0.449599\pi$$
$$434$$ −2.12353e13 −0.0662012
$$435$$ 1.56291e14 0.481110
$$436$$ −1.08166e14 −0.328789
$$437$$ 1.98764e14 0.596608
$$438$$ −8.85301e12 −0.0262412
$$439$$ −2.90312e13 −0.0849788 −0.0424894 0.999097i $$-0.513529\pi$$
−0.0424894 + 0.999097i $$0.513529\pi$$
$$440$$ 2.18142e14 0.630594
$$441$$ 1.92848e14 0.550558
$$442$$ −9.57557e13 −0.269987
$$443$$ 3.28370e14 0.914414 0.457207 0.889360i $$-0.348850\pi$$
0.457207 + 0.889360i $$0.348850\pi$$
$$444$$ 6.75909e13 0.185901
$$445$$ −1.20716e14 −0.327932
$$446$$ −1.76037e14 −0.472347
$$447$$ −2.81089e14 −0.744994
$$448$$ −4.51970e13 −0.118326
$$449$$ −6.12368e14 −1.58364 −0.791822 0.610752i $$-0.790867\pi$$
−0.791822 + 0.610752i $$0.790867\pi$$
$$450$$ −6.95474e13 −0.177669
$$451$$ 1.64725e14 0.415708
$$452$$ 1.25336e14 0.312475
$$453$$ −2.07761e14 −0.511709
$$454$$ 3.26361e13 0.0794130
$$455$$ 4.67237e13 0.112325
$$456$$ 2.26971e14 0.539092
$$457$$ 3.03483e14 0.712189 0.356095 0.934450i $$-0.384108\pi$$
0.356095 + 0.934450i $$0.384108\pi$$
$$458$$ 2.83786e14 0.658007
$$459$$ 5.06060e14 1.15940
$$460$$ −1.32549e14 −0.300061
$$461$$ −7.29308e14 −1.63138 −0.815691 0.578487i $$-0.803643\pi$$
−0.815691 + 0.578487i $$0.803643\pi$$
$$462$$ 5.41389e13 0.119668
$$463$$ 1.22188e14 0.266891 0.133445 0.991056i $$-0.457396\pi$$
0.133445 + 0.991056i $$0.457396\pi$$
$$464$$ 1.26755e14 0.273600
$$465$$ −6.43186e13 −0.137197
$$466$$ 4.21520e14 0.888579
$$467$$ −6.17381e14 −1.28621 −0.643103 0.765780i $$-0.722353\pi$$
−0.643103 + 0.765780i $$0.722353\pi$$
$$468$$ −9.66455e13 −0.198989
$$469$$ 2.59228e14 0.527510
$$470$$ −3.11517e14 −0.626533
$$471$$ 3.31409e14 0.658794
$$472$$ −4.38384e14 −0.861338
$$473$$ −9.15561e12 −0.0177808
$$474$$ −2.30531e14 −0.442535
$$475$$ −2.71858e14 −0.515854
$$476$$ −1.70212e14 −0.319265
$$477$$ 1.81381e14 0.336310
$$478$$ 1.71350e14 0.314073
$$479$$ 1.05084e15 1.90410 0.952052 0.305938i $$-0.0989700\pi$$
0.952052 + 0.305938i $$0.0989700\pi$$
$$480$$ −2.39423e14 −0.428883
$$481$$ 1.05272e14 0.186429
$$482$$ 5.55137e12 0.00971944
$$483$$ −7.86651e13 −0.136167
$$484$$ −7.33527e11 −0.00125536
$$485$$ 3.62316e14 0.613066
$$486$$ −3.21619e14 −0.538074
$$487$$ −2.19910e14 −0.363777 −0.181889 0.983319i $$-0.558221\pi$$
−0.181889 + 0.983319i $$0.558221\pi$$
$$488$$ 5.87683e14 0.961246
$$489$$ −9.01739e13 −0.145842
$$490$$ 1.96712e14 0.314596
$$491$$ −4.83863e14 −0.765199 −0.382599 0.923914i $$-0.624971\pi$$
−0.382599 + 0.923914i $$0.624971\pi$$
$$492$$ −1.14295e14 −0.178740
$$493$$ −8.86768e14 −1.37136
$$494$$ 1.47828e14 0.226078
$$495$$ −2.93446e14 −0.443813
$$496$$ −5.21634e13 −0.0780219
$$497$$ −1.63949e14 −0.242520
$$498$$ 1.77419e14 0.259560
$$499$$ −1.08878e14 −0.157538 −0.0787691 0.996893i $$-0.525099\pi$$
−0.0787691 + 0.996893i $$0.525099\pi$$
$$500$$ 5.28450e14 0.756256
$$501$$ 6.94218e14 0.982626
$$502$$ −3.11593e14 −0.436232
$$503$$ 5.06588e14 0.701506 0.350753 0.936468i $$-0.385926\pi$$
0.350753 + 0.936468i $$0.385926\pi$$
$$504$$ 1.60752e14 0.220185
$$505$$ 3.94818e14 0.534927
$$506$$ −2.39206e14 −0.320586
$$507$$ −3.67512e14 −0.487222
$$508$$ 3.86720e14 0.507161
$$509$$ 8.57534e13 0.111251 0.0556254 0.998452i $$-0.482285\pi$$
0.0556254 + 0.998452i $$0.482285\pi$$
$$510$$ 2.01735e14 0.258908
$$511$$ −2.45097e13 −0.0311188
$$512$$ −3.64965e14 −0.458423
$$513$$ −7.81259e14 −0.970844
$$514$$ −5.75069e14 −0.707005
$$515$$ −1.09040e15 −1.32631
$$516$$ 6.35268e12 0.00764511
$$517$$ 1.43669e15 1.71066
$$518$$ −7.32235e13 −0.0862654
$$519$$ −2.39498e14 −0.279178
$$520$$ −2.35739e14 −0.271903
$$521$$ 9.27575e14 1.05862 0.529312 0.848428i $$-0.322450\pi$$
0.529312 + 0.848428i $$0.322450\pi$$
$$522$$ 3.50220e14 0.395506
$$523$$ −2.18187e13 −0.0243820 −0.0121910 0.999926i $$-0.503881\pi$$
−0.0121910 + 0.999926i $$0.503881\pi$$
$$524$$ −9.29610e14 −1.02797
$$525$$ 1.07594e14 0.117736
$$526$$ 5.82569e14 0.630850
$$527$$ 3.64931e14 0.391069
$$528$$ 1.32989e14 0.141036
$$529$$ −6.05238e14 −0.635214
$$530$$ 1.85015e14 0.192172
$$531$$ 5.89717e14 0.606211
$$532$$ 2.62774e14 0.267343
$$533$$ −1.78013e14 −0.179247
$$534$$ 1.51157e14 0.150644
$$535$$ 4.35865e14 0.429939
$$536$$ −1.30790e15 −1.27694
$$537$$ 4.23709e14 0.409458
$$538$$ −6.20105e14 −0.593147
$$539$$ −9.07218e14 −0.858961
$$540$$ 5.20997e14 0.488280
$$541$$ −1.69527e15 −1.57273 −0.786363 0.617765i $$-0.788038\pi$$
−0.786363 + 0.617765i $$0.788038\pi$$
$$542$$ 9.04304e13 0.0830459
$$543$$ −2.51187e14 −0.228349
$$544$$ 1.35844e15 1.22249
$$545$$ 3.54921e14 0.316192
$$546$$ −5.85062e13 −0.0515991
$$547$$ 7.52145e14 0.656706 0.328353 0.944555i $$-0.393506\pi$$
0.328353 + 0.944555i $$0.393506\pi$$
$$548$$ 4.37477e14 0.378148
$$549$$ −7.90555e14 −0.676526
$$550$$ 3.27173e14 0.277193
$$551$$ 1.36900e15 1.14834
$$552$$ 3.96896e14 0.329619
$$553$$ −6.38228e14 −0.524793
$$554$$ 3.94054e14 0.320813
$$555$$ −2.21783e14 −0.178779
$$556$$ −8.78480e14 −0.701166
$$557$$ 1.87489e14 0.148174 0.0740870 0.997252i $$-0.476396\pi$$
0.0740870 + 0.997252i $$0.476396\pi$$
$$558$$ −1.44126e14 −0.112786
$$559$$ 9.89417e12 0.00766681
$$560$$ −7.98332e13 −0.0612561
$$561$$ −9.30383e14 −0.706913
$$562$$ −5.04857e14 −0.379856
$$563$$ 2.44971e14 0.182524 0.0912618 0.995827i $$-0.470910\pi$$
0.0912618 + 0.995827i $$0.470910\pi$$
$$564$$ −9.96856e14 −0.735525
$$565$$ −4.11259e14 −0.300503
$$566$$ −4.01116e14 −0.290255
$$567$$ −2.78819e13 −0.0199809
$$568$$ 8.27185e14 0.587066
$$569$$ 1.35243e15 0.950596 0.475298 0.879825i $$-0.342340\pi$$
0.475298 + 0.879825i $$0.342340\pi$$
$$570$$ −3.11440e14 −0.216801
$$571$$ 1.43223e15 0.987447 0.493723 0.869619i $$-0.335636\pi$$
0.493723 + 0.869619i $$0.335636\pi$$
$$572$$ 4.54650e14 0.310455
$$573$$ 6.96126e14 0.470801
$$574$$ 1.23820e14 0.0829422
$$575$$ −4.75389e14 −0.315410
$$576$$ −3.06756e14 −0.201590
$$577$$ −8.77659e14 −0.571293 −0.285647 0.958335i $$-0.592208\pi$$
−0.285647 + 0.958335i $$0.592208\pi$$
$$578$$ −3.22081e14 −0.207664
$$579$$ 1.37148e15 0.875907
$$580$$ −9.12940e14 −0.577548
$$581$$ 4.91187e14 0.307807
$$582$$ −4.53682e14 −0.281628
$$583$$ −8.53271e14 −0.524698
$$584$$ 1.23661e14 0.0753290
$$585$$ 3.17118e14 0.191365
$$586$$ 5.74245e14 0.343289
$$587$$ −2.43425e15 −1.44164 −0.720818 0.693124i $$-0.756234\pi$$
−0.720818 + 0.693124i $$0.756234\pi$$
$$588$$ 6.29479e14 0.369323
$$589$$ −5.63383e14 −0.327469
$$590$$ 6.01532e14 0.346396
$$591$$ −7.24775e14 −0.413497
$$592$$ −1.79869e14 −0.101669
$$593$$ −3.03318e14 −0.169863 −0.0849313 0.996387i $$-0.527067\pi$$
−0.0849313 + 0.996387i $$0.527067\pi$$
$$594$$ 9.40221e14 0.521680
$$595$$ 5.58507e14 0.307033
$$596$$ 1.64192e15 0.894329
$$597$$ 1.83555e14 0.0990619
$$598$$ 2.58502e14 0.138232
$$599$$ −1.70198e15 −0.901795 −0.450898 0.892576i $$-0.648896\pi$$
−0.450898 + 0.892576i $$0.648896\pi$$
$$600$$ −5.42852e14 −0.285003
$$601$$ 2.33922e15 1.21692 0.608458 0.793586i $$-0.291788\pi$$
0.608458 + 0.793586i $$0.291788\pi$$
$$602$$ −6.88207e12 −0.00354763
$$603$$ 1.75940e15 0.898710
$$604$$ 1.21359e15 0.614282
$$605$$ 2.40689e12 0.00120726
$$606$$ −4.94381e14 −0.245733
$$607$$ −2.49607e15 −1.22947 −0.614737 0.788732i $$-0.710738\pi$$
−0.614737 + 0.788732i $$0.710738\pi$$
$$608$$ −2.09717e15 −1.02368
$$609$$ −5.41810e14 −0.262091
$$610$$ −8.06395e14 −0.386575
$$611$$ −1.55258e15 −0.737612
$$612$$ −1.15524e15 −0.543926
$$613$$ 2.47301e15 1.15397 0.576983 0.816756i $$-0.304230\pi$$
0.576983 + 0.816756i $$0.304230\pi$$
$$614$$ −3.67466e14 −0.169938
$$615$$ 3.75032e14 0.171892
$$616$$ −7.56226e14 −0.343525
$$617$$ 2.43368e13 0.0109571 0.00547854 0.999985i $$-0.498256\pi$$
0.00547854 + 0.999985i $$0.498256\pi$$
$$618$$ 1.36537e15 0.609274
$$619$$ 4.22545e15 1.86885 0.934425 0.356160i $$-0.115914\pi$$
0.934425 + 0.356160i $$0.115914\pi$$
$$620$$ 3.75702e14 0.164698
$$621$$ −1.36616e15 −0.593606
$$622$$ −1.19700e15 −0.515523
$$623$$ 4.18481e14 0.178645
$$624$$ −1.43717e14 −0.0608126
$$625$$ −4.88896e14 −0.205058
$$626$$ 2.38754e15 0.992640
$$627$$ 1.43633e15 0.591947
$$628$$ −1.93585e15 −0.790850
$$629$$ 1.25835e15 0.509594
$$630$$ −2.20577e14 −0.0885497
$$631$$ −4.26326e15 −1.69660 −0.848302 0.529513i $$-0.822375\pi$$
−0.848302 + 0.529513i $$0.822375\pi$$
$$632$$ 3.22011e15 1.27036
$$633$$ −1.71188e15 −0.669503
$$634$$ −2.00086e15 −0.775758
$$635$$ −1.26892e15 −0.487731
$$636$$ 5.92047e14 0.225602
$$637$$ 9.80401e14 0.370371
$$638$$ −1.64755e15 −0.617055
$$639$$ −1.11273e15 −0.413177
$$640$$ 1.63288e15 0.601126
$$641$$ 1.00830e15 0.368018 0.184009 0.982925i $$-0.441092\pi$$
0.184009 + 0.982925i $$0.441092\pi$$
$$642$$ −5.45779e14 −0.197503
$$643$$ 3.03982e14 0.109066 0.0545328 0.998512i $$-0.482633\pi$$
0.0545328 + 0.998512i $$0.482633\pi$$
$$644$$ 4.59504e14 0.163462
$$645$$ −2.08447e13 −0.00735221
$$646$$ 1.76705e15 0.617974
$$647$$ 3.43583e15 1.19140 0.595700 0.803207i $$-0.296875\pi$$
0.595700 + 0.803207i $$0.296875\pi$$
$$648$$ 1.40675e14 0.0483676
$$649$$ −2.77421e15 −0.945788
$$650$$ −3.53565e14 −0.119521
$$651$$ 2.22971e14 0.0747400
$$652$$ 5.26730e14 0.175076
$$653$$ −1.18539e15 −0.390695 −0.195347 0.980734i $$-0.562583\pi$$
−0.195347 + 0.980734i $$0.562583\pi$$
$$654$$ −4.44423e14 −0.145251
$$655$$ 3.05028e15 0.988583
$$656$$ 3.04157e14 0.0977522
$$657$$ −1.66350e14 −0.0530167
$$658$$ 1.07993e15 0.341312
$$659$$ −2.26510e15 −0.709934 −0.354967 0.934879i $$-0.615508\pi$$
−0.354967 + 0.934879i $$0.615508\pi$$
$$660$$ −9.57843e14 −0.297716
$$661$$ −5.33012e15 −1.64297 −0.821484 0.570232i $$-0.806853\pi$$
−0.821484 + 0.570232i $$0.806853\pi$$
$$662$$ 1.52602e15 0.466488
$$663$$ 1.00543e15 0.304810
$$664$$ −2.47823e15 −0.745104
$$665$$ −8.62227e14 −0.257100
$$666$$ −4.96974e14 −0.146969
$$667$$ 2.39392e15 0.702130
$$668$$ −4.05512e15 −1.17959
$$669$$ 1.84839e15 0.533272
$$670$$ 1.79465e15 0.513534
$$671$$ 3.71902e15 1.05549
$$672$$ 8.30000e14 0.233640
$$673$$ 4.74120e15 1.32375 0.661874 0.749615i $$-0.269761\pi$$
0.661874 + 0.749615i $$0.269761\pi$$
$$674$$ −2.90403e15 −0.804215
$$675$$ 1.86856e15 0.513259
$$676$$ 2.14673e15 0.584886
$$677$$ −1.41307e15 −0.381880 −0.190940 0.981602i $$-0.561154\pi$$
−0.190940 + 0.981602i $$0.561154\pi$$
$$678$$ 5.14968e14 0.138044
$$679$$ −1.25603e15 −0.333976
$$680$$ −2.81789e15 −0.743232
$$681$$ −3.42680e14 −0.0896559
$$682$$ 6.78014e14 0.175964
$$683$$ −3.03116e15 −0.780359 −0.390180 0.920739i $$-0.627587\pi$$
−0.390180 + 0.920739i $$0.627587\pi$$
$$684$$ 1.78347e15 0.455467
$$685$$ −1.43547e15 −0.363660
$$686$$ −1.47654e15 −0.371075
$$687$$ −2.97975e15 −0.742879
$$688$$ −1.69054e13 −0.00418109
$$689$$ 9.22102e14 0.226242
$$690$$ −5.44604e14 −0.132560
$$691$$ −2.74731e15 −0.663405 −0.331703 0.943384i $$-0.607623\pi$$
−0.331703 + 0.943384i $$0.607623\pi$$
$$692$$ 1.39897e15 0.335139
$$693$$ 1.01728e15 0.241773
$$694$$ 3.73588e15 0.880878
$$695$$ 2.88251e15 0.674303
$$696$$ 2.73364e15 0.634441
$$697$$ −2.12786e15 −0.489962
$$698$$ 6.15433e14 0.140597
$$699$$ −4.42597e15 −1.00319
$$700$$ −6.28484e14 −0.141337
$$701$$ 5.72747e15 1.27795 0.638974 0.769228i $$-0.279359\pi$$
0.638974 + 0.769228i $$0.279359\pi$$
$$702$$ −1.01607e15 −0.224941
$$703$$ −1.94265e15 −0.426718
$$704$$ 1.44308e15 0.314514
$$705$$ 3.27093e15 0.707345
$$706$$ −5.97836e14 −0.128279
$$707$$ −1.36870e15 −0.291409
$$708$$ 1.92490e15 0.406655
$$709$$ 6.98326e14 0.146388 0.0731938 0.997318i $$-0.476681\pi$$
0.0731938 + 0.997318i $$0.476681\pi$$
$$710$$ −1.13503e15 −0.236095
$$711$$ −4.33171e15 −0.894081
$$712$$ −2.11140e15 −0.432445
$$713$$ −9.85170e14 −0.200225
$$714$$ −6.99348e14 −0.141044
$$715$$ −1.49182e15 −0.298561
$$716$$ −2.47500e15 −0.491534
$$717$$ −1.79917e15 −0.354583
$$718$$ −3.78202e15 −0.739672
$$719$$ 9.70979e15 1.88452 0.942260 0.334882i $$-0.108696\pi$$
0.942260 + 0.334882i $$0.108696\pi$$
$$720$$ −5.41835e14 −0.104361
$$721$$ 3.78004e15 0.722525
$$722$$ 6.77852e13 0.0128582
$$723$$ −5.82893e13 −0.0109731
$$724$$ 1.46725e15 0.274121
$$725$$ −3.27427e15 −0.607093
$$726$$ −3.01384e12 −0.000554586 0
$$727$$ 2.46469e15 0.450114 0.225057 0.974346i $$-0.427743\pi$$
0.225057 + 0.974346i $$0.427743\pi$$
$$728$$ 8.17230e14 0.148123
$$729$$ 3.08202e15 0.554413
$$730$$ −1.69683e14 −0.0302944
$$731$$ 1.18269e14 0.0209568
$$732$$ −2.58046e15 −0.453823
$$733$$ 7.91285e15 1.38121 0.690607 0.723230i $$-0.257343\pi$$
0.690607 + 0.723230i $$0.257343\pi$$
$$734$$ 4.26963e15 0.739711
$$735$$ −2.06548e15 −0.355173
$$736$$ −3.66725e15 −0.625911
$$737$$ −8.27677e15 −1.40213
$$738$$ 8.40378e14 0.141307
$$739$$ −8.40694e15 −1.40312 −0.701558 0.712613i $$-0.747512\pi$$
−0.701558 + 0.712613i $$0.747512\pi$$
$$740$$ 1.29549e15 0.214615
$$741$$ −1.55220e15 −0.255239
$$742$$ −6.41385e14 −0.104688
$$743$$ 1.36287e15 0.220809 0.110404 0.993887i $$-0.464785\pi$$
0.110404 + 0.993887i $$0.464785\pi$$
$$744$$ −1.12498e15 −0.180922
$$745$$ −5.38754e15 −0.860065
$$746$$ 1.32388e15 0.209790
$$747$$ 3.33373e15 0.524405
$$748$$ 5.43462e15 0.848614
$$749$$ −1.51100e15 −0.234215
$$750$$ 2.17124e15 0.334095
$$751$$ 6.81722e15 1.04133 0.520664 0.853762i $$-0.325684\pi$$
0.520664 + 0.853762i $$0.325684\pi$$
$$752$$ 2.65278e15 0.402256
$$753$$ 3.27173e15 0.492499
$$754$$ 1.78045e15 0.266065
$$755$$ −3.98208e15 −0.590747
$$756$$ −1.80612e15 −0.265997
$$757$$ −6.67049e14 −0.0975282 −0.0487641 0.998810i $$-0.515528\pi$$
−0.0487641 + 0.998810i $$0.515528\pi$$
$$758$$ −3.51511e15 −0.510222
$$759$$ 2.51166e15 0.361936
$$760$$ 4.35027e15 0.622360
$$761$$ −7.74408e15 −1.09990 −0.549951 0.835197i $$-0.685354\pi$$
−0.549951 + 0.835197i $$0.685354\pi$$
$$762$$ 1.58891e15 0.224052
$$763$$ −1.23039e15 −0.172250
$$764$$ −4.06626e15 −0.565173
$$765$$ 3.79064e15 0.523088
$$766$$ −5.55479e15 −0.761043
$$767$$ 2.99800e15 0.407809
$$768$$ −3.43775e15 −0.464288
$$769$$ 2.52411e15 0.338465 0.169232 0.985576i $$-0.445871\pi$$
0.169232 + 0.985576i $$0.445871\pi$$
$$770$$ 1.03766e15 0.138152
$$771$$ 6.03822e15 0.798197
$$772$$ −8.01119e15 −1.05148
$$773$$ −1.11453e16 −1.45246 −0.726229 0.687453i $$-0.758729\pi$$
−0.726229 + 0.687453i $$0.758729\pi$$
$$774$$ −4.67092e13 −0.00604404
$$775$$ 1.34746e15 0.173124
$$776$$ 6.33715e15 0.808452
$$777$$ 7.68847e14 0.0973922
$$778$$ 3.59692e15 0.452421
$$779$$ 3.28500e15 0.410279
$$780$$ 1.03511e15 0.128371
$$781$$ 5.23465e15 0.644624
$$782$$ 3.08998e15 0.377849
$$783$$ −9.40952e15 −1.14256
$$784$$ −1.67514e15 −0.201981
$$785$$ 6.35201e15 0.760551
$$786$$ −3.81949e15 −0.454131
$$787$$ 1.32271e16 1.56172 0.780861 0.624705i $$-0.214781\pi$$
0.780861 + 0.624705i $$0.214781\pi$$
$$788$$ 4.23361e15 0.496382
$$789$$ −6.11698e15 −0.712219
$$790$$ −4.41850e15 −0.510889
$$791$$ 1.42570e15 0.163703
$$792$$ −5.13257e15 −0.585257
$$793$$ −4.01902e15 −0.455112
$$794$$ −4.99466e15 −0.561685
$$795$$ −1.94266e15 −0.216958
$$796$$ −1.07219e15 −0.118919
$$797$$ 2.30248e15 0.253615 0.126807 0.991927i $$-0.459527\pi$$
0.126807 + 0.991927i $$0.459527\pi$$
$$798$$ 1.07966e15 0.118106
$$799$$ −1.85587e16 −2.01623
$$800$$ 5.01586e15 0.541191
$$801$$ 2.84027e15 0.304355
$$802$$ 3.20179e15 0.340748
$$803$$ 7.82560e14 0.0827146
$$804$$ 5.74289e15 0.602868
$$805$$ −1.50775e15 −0.157199
$$806$$ −7.32708e14 −0.0758732
$$807$$ 6.51110e15 0.669653
$$808$$ 6.90565e15 0.705410
$$809$$ 5.60472e15 0.568639 0.284320 0.958730i $$-0.408232\pi$$
0.284320 + 0.958730i $$0.408232\pi$$
$$810$$ −1.93029e14 −0.0194515
$$811$$ −5.08516e15 −0.508968 −0.254484 0.967077i $$-0.581906\pi$$
−0.254484 + 0.967077i $$0.581906\pi$$
$$812$$ 3.16486e15 0.314627
$$813$$ −9.49519e14 −0.0937574
$$814$$ 2.33792e15 0.229296
$$815$$ −1.72833e15 −0.168368
$$816$$ −1.71791e15 −0.166228
$$817$$ −1.82584e14 −0.0175486
$$818$$ 4.94802e15 0.472377
$$819$$ −1.09934e15 −0.104249
$$820$$ −2.19066e15 −0.206348
$$821$$ 2.79111e14 0.0261150 0.0130575 0.999915i $$-0.495844\pi$$
0.0130575 + 0.999915i $$0.495844\pi$$
$$822$$ 1.79746e15 0.167057
$$823$$ −1.35265e16 −1.24878 −0.624391 0.781112i $$-0.714653\pi$$
−0.624391 + 0.781112i $$0.714653\pi$$
$$824$$ −1.90718e16 −1.74901
$$825$$ −3.43531e15 −0.312946
$$826$$ −2.08531e15 −0.188704
$$827$$ 2.72544e14 0.0244994 0.0122497 0.999925i $$-0.496101\pi$$
0.0122497 + 0.999925i $$0.496101\pi$$
$$828$$ 3.11869e15 0.278488
$$829$$ 1.80459e16 1.60077 0.800385 0.599486i $$-0.204628\pi$$
0.800385 + 0.599486i $$0.204628\pi$$
$$830$$ 3.40052e15 0.299651
$$831$$ −4.13757e15 −0.362193
$$832$$ −1.55949e15 −0.135614
$$833$$ 1.17191e16 1.01239
$$834$$ −3.60941e15 −0.309758
$$835$$ 1.33058e16 1.13440
$$836$$ −8.38999e15 −0.710603
$$837$$ 3.87230e15 0.325821
$$838$$ −1.76168e15 −0.147260
$$839$$ −7.96183e15 −0.661184 −0.330592 0.943774i $$-0.607248\pi$$
−0.330592 + 0.943774i $$0.607248\pi$$
$$840$$ −1.72171e15 −0.142045
$$841$$ 4.28775e15 0.351440
$$842$$ −4.10669e15 −0.334407
$$843$$ 5.30100e15 0.428851
$$844$$ 9.99954e15 0.803705
$$845$$ −7.04397e15 −0.562478
$$846$$ 7.32956e15 0.581488
$$847$$ −8.34387e12 −0.000657671 0
$$848$$ −1.57552e15 −0.123381
$$849$$ 4.21172e15 0.327693
$$850$$ −4.22630e15 −0.326706
$$851$$ −3.39705e15 −0.260909
$$852$$ −3.63209e15 −0.277165
$$853$$ −1.49826e16 −1.13598 −0.567988 0.823037i $$-0.692278\pi$$
−0.567988 + 0.823037i $$0.692278\pi$$
$$854$$ 2.79550e15 0.210592
$$855$$ −5.85201e15 −0.438017
$$856$$ 7.62358e15 0.566961
$$857$$ −2.22561e16 −1.64458 −0.822290 0.569068i $$-0.807304\pi$$
−0.822290 + 0.569068i $$0.807304\pi$$
$$858$$ 1.86802e15 0.137152
$$859$$ 5.44237e15 0.397032 0.198516 0.980098i $$-0.436388\pi$$
0.198516 + 0.980098i $$0.436388\pi$$
$$860$$ 1.21760e14 0.00882596
$$861$$ −1.30011e15 −0.0936403
$$862$$ 1.72262e15 0.123282
$$863$$ 1.08110e16 0.768787 0.384393 0.923169i $$-0.374411\pi$$
0.384393 + 0.923169i $$0.374411\pi$$
$$864$$ 1.44145e16 1.01853
$$865$$ −4.59037e15 −0.322299
$$866$$ −2.39715e15 −0.167243
$$867$$ 3.38185e15 0.234449
$$868$$ −1.30243e15 −0.0897217
$$869$$ 2.03777e16 1.39491
$$870$$ −3.75099e15 −0.255147
$$871$$ 8.94444e15 0.604579
$$872$$ 6.20782e15 0.416964
$$873$$ −8.52477e15 −0.568989
$$874$$ −4.77033e15 −0.316399
$$875$$ 6.01111e15 0.396197
$$876$$ −5.42985e14 −0.0355644
$$877$$ −2.81024e16 −1.82914 −0.914568 0.404431i $$-0.867470\pi$$
−0.914568 + 0.404431i $$0.867470\pi$$
$$878$$ 6.96749e14 0.0450668
$$879$$ −6.02957e15 −0.387568
$$880$$ 2.54896e15 0.162820
$$881$$ 4.22209e15 0.268016 0.134008 0.990980i $$-0.457215\pi$$
0.134008 + 0.990980i $$0.457215\pi$$
$$882$$ −4.62836e15 −0.291978
$$883$$ 5.16092e14 0.0323551 0.0161776 0.999869i $$-0.494850\pi$$
0.0161776 + 0.999869i $$0.494850\pi$$
$$884$$ −5.87302e15 −0.365910
$$885$$ −6.31609e15 −0.391075
$$886$$ −7.88088e15 −0.484941
$$887$$ 5.71906e15 0.349740 0.174870 0.984592i $$-0.444050\pi$$
0.174870 + 0.984592i $$0.444050\pi$$
$$888$$ −3.87913e15 −0.235756
$$889$$ 4.39894e15 0.265698
$$890$$ 2.89718e15 0.173912
$$891$$ 8.90230e14 0.0531098
$$892$$ −1.07969e16 −0.640167
$$893$$ 2.86510e16 1.68832
$$894$$ 6.74614e15 0.395093
$$895$$ 8.12109e15 0.472702
$$896$$ −5.66067e15 −0.327472
$$897$$ −2.71427e15 −0.156061
$$898$$ 1.46968e16 0.839854
$$899$$ −6.78541e15 −0.385388
$$900$$ −4.26557e15 −0.240793
$$901$$ 1.10223e16 0.618421
$$902$$ −3.95340e15 −0.220462
$$903$$ 7.22617e13 0.00400521
$$904$$ −7.19321e15 −0.396275
$$905$$ −4.81442e15 −0.263619
$$906$$ 4.98626e15 0.271375
$$907$$ −8.43778e13 −0.00456445 −0.00228222 0.999997i $$-0.500726\pi$$
−0.00228222 + 0.999997i $$0.500726\pi$$
$$908$$ 2.00168e15 0.107628
$$909$$ −9.28952e15 −0.496468
$$910$$ −1.12137e15 −0.0595691
$$911$$ −1.10091e16 −0.581298 −0.290649 0.956830i $$-0.593871\pi$$
−0.290649 + 0.956830i $$0.593871\pi$$
$$912$$ 2.65212e15 0.139194
$$913$$ −1.56829e16 −0.818158
$$914$$ −7.28359e15 −0.377695
$$915$$ 8.46715e15 0.436437
$$916$$ 1.74055e16 0.891789
$$917$$ −1.05743e16 −0.538544
$$918$$ −1.21455e16 −0.614864
$$919$$ −4.86351e15 −0.244746 −0.122373 0.992484i $$-0.539050\pi$$
−0.122373 + 0.992484i $$0.539050\pi$$
$$920$$ 7.60717e15 0.380531
$$921$$ 3.85840e15 0.191857
$$922$$ 1.75034e16 0.865171
$$923$$ −5.65691e15 −0.277952
$$924$$ 3.32052e15 0.162185
$$925$$ 4.64630e15 0.225594
$$926$$ −2.93252e15 −0.141540
$$927$$ 2.56555e16 1.23095
$$928$$ −2.52584e16 −1.20474
$$929$$ 3.57534e15 0.169524 0.0847620 0.996401i $$-0.472987\pi$$
0.0847620 + 0.996401i $$0.472987\pi$$
$$930$$ 1.54365e15 0.0727598
$$931$$ −1.80921e16 −0.847744
$$932$$ 2.58533e16 1.20428
$$933$$ 1.25685e16 0.582017
$$934$$ 1.48171e16 0.682113
$$935$$ −1.78323e16 −0.816102
$$936$$ 5.54661e15 0.252354
$$937$$ 3.86373e16 1.74759 0.873795 0.486295i $$-0.161652\pi$$
0.873795 + 0.486295i $$0.161652\pi$$
$$938$$ −6.22147e15 −0.279754
$$939$$ −2.50692e16 −1.12067
$$940$$ −1.91064e16 −0.849133
$$941$$ −3.48997e16 −1.54198 −0.770991 0.636846i $$-0.780239\pi$$
−0.770991 + 0.636846i $$0.780239\pi$$
$$942$$ −7.95383e15 −0.349378
$$943$$ 5.74437e15 0.250858
$$944$$ −5.12245e15 −0.222398
$$945$$ 5.92634e15 0.255806
$$946$$ 2.19735e14 0.00942969
$$947$$ −2.85123e16 −1.21649 −0.608243 0.793751i $$-0.708125\pi$$
−0.608243 + 0.793751i $$0.708125\pi$$
$$948$$ −1.41392e16 −0.599763
$$949$$ −8.45688e14 −0.0356653
$$950$$ 6.52459e15 0.273573
$$951$$ 2.10091e16 0.875817
$$952$$ 9.76867e15 0.404886
$$953$$ 4.00334e16 1.64973 0.824863 0.565332i $$-0.191252\pi$$
0.824863 + 0.565332i $$0.191252\pi$$
$$954$$ −4.35313e15 −0.178355
$$955$$ 1.33424e16 0.543520
$$956$$ 1.05095e16 0.425659
$$957$$ 1.72992e16 0.696644
$$958$$ −2.52201e16 −1.00980
$$959$$ 4.97630e15 0.198109
$$960$$ 3.28548e15 0.130049
$$961$$ −2.26161e16 −0.890100
$$962$$ −2.52652e15 −0.0988688
$$963$$ −1.02553e16 −0.399028
$$964$$ 3.40484e14 0.0131726
$$965$$ 2.62867e16 1.01120
$$966$$ 1.88796e15 0.0722136
$$967$$ 1.84953e16 0.703422 0.351711 0.936109i $$-0.385600\pi$$
0.351711 + 0.936109i $$0.385600\pi$$
$$968$$ 4.20981e13 0.00159202
$$969$$ −1.85540e16 −0.697682
$$970$$ −8.69557e15 −0.325127
$$971$$ −2.14877e16 −0.798884 −0.399442 0.916759i $$-0.630796\pi$$
−0.399442 + 0.916759i $$0.630796\pi$$
$$972$$ −1.97260e16 −0.729246
$$973$$ −9.99271e15 −0.367335
$$974$$ 5.27784e15 0.192922
$$975$$ 3.71243e15 0.134938
$$976$$ 6.86699e15 0.248195
$$977$$ −8.73880e15 −0.314074 −0.157037 0.987593i $$-0.550194\pi$$
−0.157037 + 0.987593i $$0.550194\pi$$
$$978$$ 2.16417e15 0.0773443
$$979$$ −1.33615e16 −0.474844
$$980$$ 1.20650e16 0.426368
$$981$$ −8.35079e15 −0.293459
$$982$$ 1.16127e16 0.405808
$$983$$ 1.18924e16 0.413263 0.206631 0.978419i $$-0.433750\pi$$
0.206631 + 0.978419i $$0.433750\pi$$
$$984$$ 6.55956e15 0.226674
$$985$$ −1.38915e16 −0.477365
$$986$$ 2.12824e16 0.727274
$$987$$ −1.13392e16 −0.385336
$$988$$ 9.06679e15 0.306401
$$989$$ −3.19279e14 −0.0107298
$$990$$ 7.04271e15 0.235367
$$991$$ 2.34409e16 0.779056 0.389528 0.921015i $$-0.372638\pi$$
0.389528 + 0.921015i $$0.372638\pi$$
$$992$$ 1.03946e16 0.343552
$$993$$ −1.60232e16 −0.526657
$$994$$ 3.93477e15 0.128616
$$995$$ 3.51813e15 0.114363
$$996$$ 1.08817e16 0.351779
$$997$$ −2.14004e16 −0.688016 −0.344008 0.938967i $$-0.611785\pi$$
−0.344008 + 0.938967i $$0.611785\pi$$
$$998$$ 2.61307e15 0.0835473
$$999$$ 1.33524e16 0.424571
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.12.a.a.1.1 1
3.2 odd 2 9.12.a.b.1.1 1
4.3 odd 2 16.12.a.a.1.1 1
5.2 odd 4 25.12.b.b.24.1 2
5.3 odd 4 25.12.b.b.24.2 2
5.4 even 2 25.12.a.b.1.1 1
7.2 even 3 49.12.c.b.18.1 2
7.3 odd 6 49.12.c.c.30.1 2
7.4 even 3 49.12.c.b.30.1 2
7.5 odd 6 49.12.c.c.18.1 2
7.6 odd 2 49.12.a.a.1.1 1
8.3 odd 2 64.12.a.f.1.1 1
8.5 even 2 64.12.a.b.1.1 1
9.2 odd 6 81.12.c.b.28.1 2
9.4 even 3 81.12.c.d.55.1 2
9.5 odd 6 81.12.c.b.55.1 2
9.7 even 3 81.12.c.d.28.1 2
11.10 odd 2 121.12.a.b.1.1 1
12.11 even 2 144.12.a.d.1.1 1
13.12 even 2 169.12.a.a.1.1 1
15.2 even 4 225.12.b.d.199.2 2
15.8 even 4 225.12.b.d.199.1 2
15.14 odd 2 225.12.a.b.1.1 1
16.3 odd 4 256.12.b.c.129.1 2
16.5 even 4 256.12.b.e.129.1 2
16.11 odd 4 256.12.b.c.129.2 2
16.13 even 4 256.12.b.e.129.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1.12.a.a.1.1 1 1.1 even 1 trivial
9.12.a.b.1.1 1 3.2 odd 2
16.12.a.a.1.1 1 4.3 odd 2
25.12.a.b.1.1 1 5.4 even 2
25.12.b.b.24.1 2 5.2 odd 4
25.12.b.b.24.2 2 5.3 odd 4
49.12.a.a.1.1 1 7.6 odd 2
49.12.c.b.18.1 2 7.2 even 3
49.12.c.b.30.1 2 7.4 even 3
49.12.c.c.18.1 2 7.5 odd 6
49.12.c.c.30.1 2 7.3 odd 6
64.12.a.b.1.1 1 8.5 even 2
64.12.a.f.1.1 1 8.3 odd 2
81.12.c.b.28.1 2 9.2 odd 6
81.12.c.b.55.1 2 9.5 odd 6
81.12.c.d.28.1 2 9.7 even 3
81.12.c.d.55.1 2 9.4 even 3
121.12.a.b.1.1 1 11.10 odd 2
144.12.a.d.1.1 1 12.11 even 2
169.12.a.a.1.1 1 13.12 even 2
225.12.a.b.1.1 1 15.14 odd 2
225.12.b.d.199.1 2 15.8 even 4
225.12.b.d.199.2 2 15.2 even 4
256.12.b.c.129.1 2 16.3 odd 4
256.12.b.c.129.2 2 16.11 odd 4
256.12.b.e.129.1 2 16.5 even 4
256.12.b.e.129.2 2 16.13 even 4