LMFDB - Embedded newform 722.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.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:	$5.76519902594$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.90211$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.442463 q^{3} +1.00000 q^{4} -0.891491 q^{5} +0.442463 q^{6} +2.52015 q^{7} -1.00000 q^{8} -2.80423 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.442463 q^{3} +1.00000 q^{4} -0.891491 q^{5} +0.442463 q^{6} +2.52015 q^{7} -1.00000 q^{8} -2.80423 q^{9} +0.891491 q^{10} +1.95199 q^{11} -0.442463 q^{12} -6.45965 q^{13} -2.52015 q^{14} +0.394452 q^{15} +1.00000 q^{16} -3.42226 q^{17} +2.80423 q^{18} -0.891491 q^{20} -1.11507 q^{21} -1.95199 q^{22} +8.18504 q^{23} +0.442463 q^{24} -4.20524 q^{25} +6.45965 q^{26} +2.56816 q^{27} +2.52015 q^{28} +4.58064 q^{29} -0.394452 q^{30} -8.79360 q^{31} -1.00000 q^{32} -0.863684 q^{33} +3.42226 q^{34} -2.24669 q^{35} -2.80423 q^{36} -5.97980 q^{37} +2.85816 q^{39} +0.891491 q^{40} -3.48932 q^{41} +1.11507 q^{42} -6.24669 q^{43} +1.95199 q^{44} +2.49994 q^{45} -8.18504 q^{46} -10.5498 q^{47} -0.442463 q^{48} -0.648859 q^{49} +4.20524 q^{50} +1.51423 q^{51} -6.45965 q^{52} +3.76278 q^{53} -2.56816 q^{54} -1.74018 q^{55} -2.52015 q^{56} -4.58064 q^{58} +2.84162 q^{59} +0.394452 q^{60} -2.45495 q^{61} +8.79360 q^{62} -7.06706 q^{63} +1.00000 q^{64} +5.75872 q^{65} +0.863684 q^{66} -2.67261 q^{67} -3.42226 q^{68} -3.62158 q^{69} +2.24669 q^{70} +0.0564404 q^{71} +2.80423 q^{72} -6.96917 q^{73} +5.97980 q^{74} +1.86067 q^{75} +4.91930 q^{77} -2.85816 q^{78} -9.13162 q^{79} -0.891491 q^{80} +7.27636 q^{81} +3.48932 q^{82} -14.1239 q^{83} -1.11507 q^{84} +3.05092 q^{85} +6.24669 q^{86} -2.02677 q^{87} -1.95199 q^{88} +1.86774 q^{89} -2.49994 q^{90} -16.2793 q^{91} +8.18504 q^{92} +3.89085 q^{93} +10.5498 q^{94} +0.442463 q^{96} +7.82432 q^{97} +0.648859 q^{98} -5.47382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} + 4 q^{16} + 6 q^{17} - 4 q^{18} - 2 q^{20} - 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} + 4 q^{27} - 2 q^{28} + 2 q^{29} + 4 q^{30} - 26 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} + 6 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{39} + 2 q^{40} + 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} + 10 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} - 6 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} - 4 q^{54} - 26 q^{55} + 2 q^{56} - 2 q^{58} + 8 q^{59} - 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} + 4 q^{65} + 16 q^{66} - 10 q^{67} + 6 q^{68} + 20 q^{69} - 6 q^{70} - 4 q^{72} - 14 q^{73} + 4 q^{74} - 8 q^{75} + 4 q^{77} + 6 q^{78} - 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} - 4 q^{84} - 18 q^{85} + 10 q^{86} - 26 q^{87} - 2 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} - 10 q^{92} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 28 q^{97} + 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 + 4 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 18 * q^13 + 2 * q^14 - 4 * q^15 + 4 * q^16 + 6 * q^17 - 4 * q^18 - 2 * q^20 - 4 * q^21 - 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 + 4 * q^27 - 2 * q^28 + 2 * q^29 + 4 * q^30 - 26 * q^31 - 4 * q^32 - 16 * q^33 - 6 * q^34 + 6 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^39 + 2 * q^40 + 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 + 10 * q^46 - 12 * q^47 - 2 * q^48 - 12 * q^49 - 6 * q^50 + 2 * q^51 - 18 * q^52 - 8 * q^53 - 4 * q^54 - 26 * q^55 + 2 * q^56 - 2 * q^58 + 8 * q^59 - 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 + 4 * q^65 + 16 * q^66 - 10 * q^67 + 6 * q^68 + 20 * q^69 - 6 * q^70 - 4 * q^72 - 14 * q^73 + 4 * q^74 - 8 * q^75 + 4 * q^77 + 6 * q^78 - 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 - 4 * q^84 - 18 * q^85 + 10 * q^86 - 26 * q^87 - 2 * q^88 + 16 * q^89 + 22 * q^90 + 4 * q^91 - 10 * q^92 + 8 * q^93 + 12 * q^94 + 2 * q^96 - 28 * q^97 + 12 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

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 $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.442463	−0.255456	−0.127728	−	0.991809i	$-0.540769\pi$
$3$	−0.442463	−0.255456	−0.127728	+	0.991809i	$0.540769\pi$
$4$	1.00000	0.500000
$5$	−0.891491	−0.398687	−0.199344	−	0.979930i	$-0.563881\pi$
$5$	−0.891491	−0.398687	−0.199344	+	0.979930i	$0.563881\pi$
$6$	0.442463	0.180635
$7$	2.52015	0.952526	0.476263	−	0.879303i	$-0.341991\pi$
$7$	2.52015	0.952526	0.476263	+	0.879303i	$0.341991\pi$
$8$	−1.00000	−0.353553
$9$	−2.80423	−0.934742
$10$	0.891491	0.281914
$11$	1.95199	0.588547	0.294273	−	0.955721i	$-0.404922\pi$
$11$	1.95199	0.588547	0.294273	+	0.955721i	$0.404922\pi$
$12$	−0.442463	−0.127728
$13$	−6.45965	−1.79158	−0.895792	−	0.444473i	$-0.853391\pi$
$13$	−6.45965	−1.79158	−0.895792	+	0.444473i	$0.853391\pi$
$14$	−2.52015	−0.673538
$15$	0.394452	0.101847
$16$	1.00000	0.250000
$17$	−3.42226	−0.830020	−0.415010	−	0.909817i	$-0.636222\pi$
$17$	−3.42226	−0.830020	−0.415010	+	0.909817i	$0.636222\pi$
$18$	2.80423	0.660962
$19$	0	0
$19$	0	0
$20$	−0.891491	−0.199344
$21$	−1.11507	−0.243329
$22$	−1.95199	−0.416165
$23$	8.18504	1.70670	0.853349	−	0.521339i	$-0.174567\pi$
$23$	8.18504	1.70670	0.853349	+	0.521339i	$0.174567\pi$
$24$	0.442463	0.0903175
$25$	−4.20524	−0.841049
$26$	6.45965	1.26684
$27$	2.56816	0.494242
$28$	2.52015	0.476263
$29$	4.58064	0.850604	0.425302	−	0.905051i	$-0.360168\pi$
$29$	4.58064	0.850604	0.425302	+	0.905051i	$0.360168\pi$
$30$	−0.394452	−0.0720168
$31$	−8.79360	−1.57938	−0.789689	−	0.613507i	$-0.789758\pi$
$31$	−8.79360	−1.57938	−0.789689	+	0.613507i	$0.789758\pi$
$32$	−1.00000	−0.176777
$33$	−0.863684	−0.150348
$34$	3.42226	0.586913
$35$	−2.24669	−0.379760
$36$	−2.80423	−0.467371
$37$	−5.97980	−0.983073	−0.491536	−	0.870857i	$-0.663564\pi$
$37$	−5.97980	−0.983073	−0.491536	+	0.870857i	$0.663564\pi$
$38$	0	0
$39$	2.85816	0.457672
$40$	0.891491	0.140957
$41$	−3.48932	−0.544941	−0.272470	−	0.962164i	$-0.587841\pi$
$41$	−3.48932	−0.544941	−0.272470	+	0.962164i	$0.587841\pi$
$42$	1.11507	0.172060
$43$	−6.24669	−0.952611	−0.476306	−	0.879280i	$-0.658024\pi$
$43$	−6.24669	−0.952611	−0.476306	+	0.879280i	$0.658024\pi$
$44$	1.95199	0.294273
$45$	2.49994	0.372670
$46$	−8.18504	−1.20682
$47$	−10.5498	−1.53885	−0.769425	−	0.638738i	$-0.779457\pi$
$47$	−10.5498	−1.53885	−0.769425	+	0.638738i	$0.779457\pi$
$48$	−0.442463	−0.0638641
$49$	−0.648859	−0.0926941
$50$	4.20524	0.594711
$51$	1.51423	0.212034
$52$	−6.45965	−0.895792
$53$	3.76278	0.516858	0.258429	−	0.966030i	$-0.416795\pi$
$53$	3.76278	0.516858	0.258429	+	0.966030i	$0.416795\pi$
$54$	−2.56816	−0.349482
$55$	−1.74018	−0.234646
$56$	−2.52015	−0.336769
$57$	0	0
$58$	−4.58064	−0.601468
$59$	2.84162	0.369947	0.184973	−	0.982744i	$-0.440780\pi$
$59$	2.84162	0.369947	0.184973	+	0.982744i	$0.440780\pi$
$60$	0.394452	0.0509236
$61$	−2.45495	−0.314324	−0.157162	−	0.987573i	$-0.550235\pi$
$61$	−2.45495	−0.314324	−0.157162	+	0.987573i	$0.550235\pi$
$62$	8.79360	1.11679
$63$	−7.06706	−0.890366
$64$	1.00000	0.125000
$65$	5.75872	0.714282
$66$	0.863684	0.106312
$67$	−2.67261	−0.326511	−0.163256	−	0.986584i	$-0.552200\pi$
$67$	−2.67261	−0.326511	−0.163256	+	0.986584i	$0.552200\pi$
$68$	−3.42226	−0.415010
$69$	−3.62158	−0.435987
$70$	2.24669	0.268531
$71$	0.0564404	0.00669824	0.00334912	−	0.999994i	$-0.498934\pi$
$71$	0.0564404	0.00669824	0.00334912	+	0.999994i	$0.498934\pi$
$72$	2.80423	0.330481
$73$	−6.96917	−0.815680	−0.407840	−	0.913053i	$-0.633718\pi$
$73$	−6.96917	−0.815680	−0.407840	+	0.913053i	$0.633718\pi$
$74$	5.97980	0.695137
$75$	1.86067	0.214851
$76$	0	0
$77$	4.91930	0.560606
$78$	−2.85816	−0.323623
$79$	−9.13162	−1.02739	−0.513694	−	0.857974i	$-0.671723\pi$
$79$	−9.13162	−1.02739	−0.513694	+	0.857974i	$0.671723\pi$
$80$	−0.891491	−0.0996718
$81$	7.27636	0.808485
$82$	3.48932	0.385331
$83$	−14.1239	−1.55030	−0.775150	−	0.631778i	$-0.782326\pi$
$83$	−14.1239	−1.55030	−0.775150	+	0.631778i	$0.782326\pi$
$84$	−1.11507	−0.121664
$85$	3.05092	0.330918
$86$	6.24669	0.673598
$87$	−2.02677	−0.217292
$88$	−1.95199	−0.208083
$89$	1.86774	0.197980	0.0989901	−	0.995088i	$-0.468439\pi$
$89$	1.86774	0.197980	0.0989901	+	0.995088i	$0.468439\pi$
$90$	−2.49994	−0.263517
$91$	−16.2793	−1.70653
$92$	8.18504	0.853349
$93$	3.89085	0.403462
$94$	10.5498	1.08813
$95$	0	0
$96$	0.442463	0.0451587
$97$	7.82432	0.794439	0.397219	−	0.917724i	$-0.369975\pi$
$97$	7.82432	0.794439	0.397219	+	0.917724i	$0.369975\pi$
$98$	0.648859	0.0655447
$99$	−5.47382	−0.550139
$100$	−4.20524	−0.420524
$101$	−5.38487	−0.535815	−0.267907	−	0.963445i	$-0.586332\pi$
$101$	−5.38487	−0.535815	−0.267907	+	0.963445i	$0.586332\pi$
$102$	−1.51423	−0.149931
$103$	−4.69468	−0.462580	−0.231290	−	0.972885i	$-0.574295\pi$
$103$	−4.69468	−0.462580	−0.231290	+	0.972885i	$0.574295\pi$
$104$	6.45965	0.633421
$105$	0.994078	0.0970121
$106$	−3.76278	−0.365473
$107$	16.0373	1.55038	0.775191	−	0.631727i	$-0.217654\pi$
$107$	16.0373	1.55038	0.775191	+	0.631727i	$0.217654\pi$
$108$	2.56816	0.247121
$109$	14.1008	1.35061	0.675305	−	0.737538i	$-0.264012\pi$
$109$	14.1008	1.35061	0.675305	+	0.737538i	$0.264012\pi$
$110$	1.74018	0.165920
$111$	2.64584	0.251132
$112$	2.52015	0.238132
$113$	−12.7224	−1.19682	−0.598410	−	0.801190i	$-0.704201\pi$
$113$	−12.7224	−1.19682	−0.598410	+	0.801190i	$0.704201\pi$
$114$	0	0
$115$	−7.29689	−0.680439
$116$	4.58064	0.425302
$117$	18.1143	1.67467
$118$	−2.84162	−0.261592
$119$	−8.62460	−0.790616
$120$	−0.394452	−0.0360084
$121$	−7.18974	−0.653613
$122$	2.45495	0.222261
$123$	1.54390	0.139209
$124$	−8.79360	−0.789689
$125$	8.20640	0.734002
$126$	7.06706	0.629584
$127$	7.17442	0.636627	0.318313	−	0.947986i	$-0.396884\pi$
$127$	7.17442	0.636627	0.318313	+	0.947986i	$0.396884\pi$
$128$	−1.00000	−0.0883883
$129$	2.76393	0.243351
$130$	−5.75872	−0.505073
$131$	−3.52265	−0.307776	−0.153888	−	0.988088i	$-0.549179\pi$
$131$	−3.52265	−0.307776	−0.153888	+	0.988088i	$0.549179\pi$
$132$	−0.863684	−0.0751740
$133$	0	0
$134$	2.67261	0.230878
$135$	−2.28949	−0.197048
$136$	3.42226	0.293456
$137$	−11.0035	−0.940096	−0.470048	−	0.882641i	$-0.655763\pi$
$137$	−11.0035	−0.940096	−0.470048	+	0.882641i	$0.655763\pi$
$138$	3.62158	0.308289
$139$	21.7586	1.84554	0.922771	−	0.385350i	$-0.125919\pi$
$139$	21.7586	1.84554	0.922771	+	0.385350i	$0.125919\pi$
$140$	−2.24669	−0.189880
$141$	4.66791	0.393109
$142$	−0.0564404	−0.00473637
$143$	−12.6092	−1.05443
$144$	−2.80423	−0.233686
$145$	−4.08361	−0.339125
$146$	6.96917	0.576773
$147$	0.287096	0.0236793
$148$	−5.97980	−0.491536
$149$	14.3896	1.17884	0.589420	−	0.807827i	$-0.299356\pi$
$149$	14.3896	1.17884	0.589420	+	0.807827i	$0.299356\pi$
$150$	−1.86067	−0.151923
$151$	12.4068	1.00965	0.504824	−	0.863222i	$-0.331557\pi$
$151$	12.4068	1.00965	0.504824	+	0.863222i	$0.331557\pi$
$152$	0	0
$153$	9.59679	0.775855
$154$	−4.91930	−0.396408
$155$	7.83942	0.629678
$156$	2.85816	0.228836
$157$	−0.451220	−0.0360113	−0.0180056	−	0.999838i	$-0.505732\pi$
$157$	−0.451220	−0.0360113	−0.0180056	+	0.999838i	$0.505732\pi$
$158$	9.13162	0.726472
$159$	−1.66489	−0.132035
$160$	0.891491	0.0704786
$161$	20.6275	1.62567
$162$	−7.27636	−0.571685
$163$	−0.0692542	−0.00542441	−0.00271220	−	0.999996i	$-0.500863\pi$
$163$	−0.0692542	−0.00542441	−0.00271220	+	0.999996i	$0.500863\pi$
$164$	−3.48932	−0.272470
$165$	0.769967	0.0599418
$166$	14.1239	1.09623
$167$	2.17371	0.168206	0.0841032	−	0.996457i	$-0.473197\pi$
$167$	2.17371	0.168206	0.0841032	+	0.996457i	$0.473197\pi$
$168$	1.11507	0.0860298
$169$	28.7271	2.20977
$170$	−3.05092	−0.233995
$171$	0	0
$172$	−6.24669	−0.476306
$173$	−16.8493	−1.28103	−0.640514	−	0.767947i	$-0.721279\pi$
$173$	−16.8493	−1.28103	−0.640514	+	0.767947i	$0.721279\pi$
$174$	2.02677	0.153649
$175$	−10.5978	−0.801121
$176$	1.95199	0.147137
$177$	−1.25731	−0.0945053
$178$	−1.86774	−0.139993
$179$	18.9655	1.41755	0.708775	−	0.705435i	$-0.249248\pi$
$179$	18.9655	1.41755	0.708775	+	0.705435i	$0.249248\pi$
$180$	2.49994	0.186335
$181$	−1.98687	−0.147683	−0.0738415	−	0.997270i	$-0.523526\pi$
$181$	−1.98687	−0.147683	−0.0738415	+	0.997270i	$0.523526\pi$
$182$	16.2793	1.20670
$183$	1.08623	0.0802961
$184$	−8.18504	−0.603409
$185$	5.33094	0.391938
$186$	−3.89085	−0.285291
$187$	−6.68021	−0.488506
$188$	−10.5498	−0.769425
$189$	6.47214	0.470779
$190$	0	0
$191$	−20.9259	−1.51415	−0.757074	−	0.653329i	$-0.773372\pi$
$191$	−20.9259	−1.51415	−0.757074	+	0.653329i	$0.773372\pi$
$192$	−0.442463	−0.0319321
$193$	7.78879	0.560650	0.280325	−	0.959905i	$-0.409558\pi$
$193$	7.78879	0.560650	0.280325	+	0.959905i	$0.409558\pi$
$194$	−7.82432	−0.561753
$195$	−2.54802	−0.182468
$196$	−0.648859	−0.0463471
$197$	1.82514	0.130036	0.0650180	−	0.997884i	$-0.479290\pi$
$197$	1.82514	0.130036	0.0650180	+	0.997884i	$0.479290\pi$
$198$	5.47382	0.389007
$199$	2.35926	0.167243	0.0836216	−	0.996498i	$-0.473351\pi$
$199$	2.35926	0.167243	0.0836216	+	0.996498i	$0.473351\pi$
$200$	4.20524	0.297356
$201$	1.18253	0.0834094
$202$	5.38487	0.378878
$203$	11.5439	0.810223
$204$	1.51423	0.106017
$205$	3.11070	0.217261
$206$	4.69468	0.327094
$207$	−22.9527	−1.59532
$208$	−6.45965	−0.447896
$209$	0	0
$210$	−0.994078	−0.0685979
$211$	−0.361050	−0.0248557	−0.0124279	−	0.999923i	$-0.503956\pi$
$211$	−0.361050	−0.0248557	−0.0124279	+	0.999923i	$0.503956\pi$
$212$	3.76278	0.258429
$213$	−0.0249728	−0.00171111
$214$	−16.0373	−1.09629
$215$	5.56887	0.379794
$216$	−2.56816	−0.174741
$217$	−22.1612	−1.50440
$218$	−14.1008	−0.955026
$219$	3.08361	0.208371
$220$	−1.74018	−0.117323
$221$	22.1066	1.48705
$222$	−2.64584	−0.177577
$223$	18.0486	1.20862	0.604312	−	0.796748i	$-0.293448\pi$
$223$	18.0486	1.20862	0.604312	+	0.796748i	$0.293448\pi$
$224$	−2.52015	−0.168384
$225$	11.7925	0.786163
$226$	12.7224	0.846280
$227$	12.2845	0.815349	0.407675	−	0.913127i	$-0.366340\pi$
$227$	12.2845	0.815349	0.407675	+	0.913127i	$0.366340\pi$
$228$	0	0
$229$	6.79174	0.448811	0.224405	−	0.974496i	$-0.427956\pi$
$229$	6.79174	0.448811	0.224405	+	0.974496i	$0.427956\pi$
$230$	7.29689	0.481143
$231$	−2.17661	−0.143210
$232$	−4.58064	−0.300734
$233$	21.4294	1.40388	0.701942	−	0.712234i	$-0.252317\pi$
$233$	21.4294	1.40388	0.701942	+	0.712234i	$0.252317\pi$
$234$	−18.1143	−1.18417
$235$	9.40507	0.613519
$236$	2.84162	0.184973
$237$	4.04041	0.262453
$238$	8.62460	0.559050
$239$	−11.8376	−0.765713	−0.382856	−	0.923808i	$-0.625060\pi$
$239$	−11.8376	−0.765713	−0.382856	+	0.923808i	$0.625060\pi$
$240$	0.394452	0.0254618
$241$	−21.7463	−1.40080	−0.700401	−	0.713749i	$-0.746996\pi$
$241$	−21.7463	−1.40080	−0.700401	+	0.713749i	$0.746996\pi$
$242$	7.18974	0.462174
$243$	−10.9240	−0.700775
$244$	−2.45495	−0.157162
$245$	0.578452	0.0369560
$246$	−1.54390	−0.0984353
$247$	0	0
$248$	8.79360	0.558394
$249$	6.24931	0.396034
$250$	−8.20640	−0.519018
$251$	23.6410	1.49221	0.746104	−	0.665829i	$-0.231922\pi$
$251$	23.6410	1.49221	0.746104	+	0.665829i	$0.231922\pi$
$252$	−7.06706	−0.445183
$253$	15.9771	1.00447
$254$	−7.17442	−0.450163
$255$	−1.34992	−0.0845352
$256$	1.00000	0.0625000
$257$	−0.923469	−0.0576044	−0.0288022	−	0.999585i	$-0.509169\pi$
$257$	−0.923469	−0.0576044	−0.0288022	+	0.999585i	$0.509169\pi$
$258$	−2.76393	−0.172075
$259$	−15.0700	−0.936402
$260$	5.75872	0.357141
$261$	−12.8452	−0.795096
$262$	3.52265	0.217630
$263$	4.31967	0.266362	0.133181	−	0.991092i	$-0.457481\pi$
$263$	4.31967	0.266362	0.133181	+	0.991092i	$0.457481\pi$
$264$	0.863684	0.0531561
$265$	−3.35449	−0.206064
$266$	0	0
$267$	−0.826407	−0.0505753
$268$	−2.67261	−0.163256
$269$	−10.7954	−0.658205	−0.329102	−	0.944294i	$-0.606746\pi$
$269$	−10.7954	−0.658205	−0.329102	+	0.944294i	$0.606746\pi$
$270$	2.28949	0.139334
$271$	0.807243	0.0490365	0.0245183	−	0.999699i	$-0.492195\pi$
$271$	0.807243	0.0490365	0.0245183	+	0.999699i	$0.492195\pi$
$272$	−3.42226	−0.207505
$273$	7.20298	0.435944
$274$	11.0035	0.664749
$275$	−8.20859	−0.494996
$276$	−3.62158	−0.217994
$277$	−9.14869	−0.549691	−0.274846	−	0.961488i	$-0.588627\pi$
$277$	−9.14869	−0.549691	−0.274846	+	0.961488i	$0.588627\pi$
$278$	−21.7586	−1.30499
$279$	24.6593	1.47631
$280$	2.24669	0.134265
$281$	21.2158	1.26563	0.632813	−	0.774305i	$-0.281900\pi$
$281$	21.2158	1.26563	0.632813	+	0.774305i	$0.281900\pi$
$282$	−4.66791	−0.277970
$283$	5.18985	0.308505	0.154252	−	0.988031i	$-0.450703\pi$
$283$	5.18985	0.308505	0.154252	+	0.988031i	$0.450703\pi$
$284$	0.0564404	0.00334912
$285$	0	0
$286$	12.6092	0.745596
$287$	−8.79360	−0.519070
$288$	2.80423	0.165241
$289$	−5.28814	−0.311067
$290$	4.08361	0.239798
$291$	−3.46197	−0.202945
$292$	−6.96917	−0.407840
$293$	−17.5660	−1.02621	−0.513107	−	0.858324i	$-0.671506\pi$
$293$	−17.5660	−1.02621	−0.513107	+	0.858324i	$0.671506\pi$
$294$	−0.287096	−0.0167438
$295$	−2.53328	−0.147493
$296$	5.97980	0.347569
$297$	5.01302	0.290885
$298$	−14.3896	−0.833565
$299$	−52.8725	−3.05769
$300$	1.86067	0.107426
$301$	−15.7426	−0.907387
$302$	−12.4068	−0.713929
$303$	2.38261	0.136877
$304$	0	0
$305$	2.18857	0.125317
$306$	−9.59679	−0.548612
$307$	−21.5684	−1.23097	−0.615486	−	0.788148i	$-0.711040\pi$
$307$	−21.5684	−1.23097	−0.615486	+	0.788148i	$0.711040\pi$
$308$	4.91930	0.280303
$309$	2.07722	0.118169
$310$	−7.83942	−0.445249
$311$	−2.57368	−0.145940	−0.0729701	−	0.997334i	$-0.523248\pi$
$311$	−2.57368	−0.145940	−0.0729701	+	0.997334i	$0.523248\pi$
$312$	−2.85816	−0.161811
$313$	−5.18389	−0.293011	−0.146505	−	0.989210i	$-0.546803\pi$
$313$	−5.18389	−0.293011	−0.146505	+	0.989210i	$0.546803\pi$
$314$	0.451220	0.0254638
$315$	6.30023	0.354977
$316$	−9.13162	−0.513694
$317$	−20.2562	−1.13770	−0.568850	−	0.822442i	$-0.692611\pi$
$317$	−20.2562	−1.13770	−0.568850	+	0.822442i	$0.692611\pi$
$318$	1.66489	0.0933625
$319$	8.94137	0.500620
$320$	−0.891491	−0.0498359
$321$	−7.09591	−0.396055
$322$	−20.6275	−1.14953
$323$	0	0
$324$	7.27636	0.404242
$325$	27.1644	1.50681
$326$	0.0692542	0.00383564
$327$	−6.23909	−0.345022
$328$	3.48932	0.192666
$329$	−26.5871	−1.46579
$330$	−0.769967	−0.0423853
$331$	−21.3280	−1.17229	−0.586146	−	0.810205i	$-0.699356\pi$
$331$	−21.3280	−1.17229	−0.586146	+	0.810205i	$0.699356\pi$
$332$	−14.1239	−0.775150
$333$	16.7687	0.918919
$334$	−2.17371	−0.118940
$335$	2.38261	0.130176
$336$	−1.11507	−0.0608322
$337$	−22.7275	−1.23804	−0.619022	−	0.785374i	$-0.712471\pi$
$337$	−22.7275	−1.23804	−0.619022	+	0.785374i	$0.712471\pi$
$338$	−28.7271	−1.56255
$339$	5.62919	0.305735
$340$	3.05092	0.165459
$341$	−17.1650	−0.929538
$342$	0	0
$343$	−19.2762	−1.04082
$344$	6.24669	0.336799
$345$	3.22861	0.173822
$346$	16.8493	0.905823
$347$	−4.92855	−0.264579	−0.132289	−	0.991211i	$-0.542233\pi$
$347$	−4.92855	−0.264579	−0.132289	+	0.991211i	$0.542233\pi$
$348$	−2.02677	−0.108646
$349$	26.1615	1.40039	0.700197	−	0.713950i	$-0.253096\pi$
$349$	26.1615	1.40039	0.700197	+	0.713950i	$0.253096\pi$
$350$	10.5978	0.566478
$351$	−16.5894	−0.885477
$352$	−1.95199	−0.104041
$353$	2.70813	0.144139	0.0720697	−	0.997400i	$-0.477040\pi$
$353$	2.70813	0.144139	0.0720697	+	0.997400i	$0.477040\pi$
$354$	1.25731	0.0668253
$355$	−0.0503161	−0.00267050
$356$	1.86774	0.0989901
$357$	3.81607	0.201968
$358$	−18.9655	−1.00236
$359$	−9.31002	−0.491364	−0.245682	−	0.969350i	$-0.579012\pi$
$359$	−9.31002	−0.491364	−0.245682	+	0.969350i	$0.579012\pi$
$360$	−2.49994	−0.131759
$361$	0	0
$362$	1.98687	0.104428
$363$	3.18120	0.166970
$364$	−16.2793	−0.853265
$365$	6.21296	0.325201
$366$	−1.08623	−0.0567779
$367$	7.75442	0.404777	0.202389	−	0.979305i	$-0.435130\pi$
$367$	7.75442	0.404777	0.202389	+	0.979305i	$0.435130\pi$
$368$	8.18504	0.426675
$369$	9.78485	0.509379
$370$	−5.33094	−0.277142
$371$	9.48276	0.492320
$372$	3.89085	0.201731
$373$	−25.0124	−1.29509	−0.647546	−	0.762027i	$-0.724205\pi$
$373$	−25.0124	−1.29509	−0.647546	+	0.762027i	$0.724205\pi$
$374$	6.68021	0.345426
$375$	−3.63103	−0.187506
$376$	10.5498	0.544065
$377$	−29.5894	−1.52393
$378$	−6.47214	−0.332891
$379$	19.1802	0.985222	0.492611	−	0.870250i	$-0.336043\pi$
$379$	19.1802	0.985222	0.492611	+	0.870250i	$0.336043\pi$
$380$	0	0
$381$	−3.17442	−0.162630
$382$	20.9259	1.07066
$383$	−4.83319	−0.246964	−0.123482	−	0.992347i	$-0.539406\pi$
$383$	−4.83319	−0.246964	−0.123482	+	0.992347i	$0.539406\pi$
$384$	0.442463	0.0225794
$385$	−4.38551	−0.223506
$386$	−7.78879	−0.396439
$387$	17.5171	0.890446
$388$	7.82432	0.397219
$389$	21.7291	1.10171	0.550855	−	0.834601i	$-0.314302\pi$
$389$	21.7291	1.10171	0.550855	+	0.834601i	$0.314302\pi$
$390$	2.54802	0.129024
$391$	−28.0113	−1.41659
$392$	0.648859	0.0327723
$393$	1.55865	0.0786233
$394$	−1.82514	−0.0919493
$395$	8.14076	0.409606
$396$	−5.47382	−0.275070
$397$	11.7140	0.587909	0.293955	−	0.955819i	$-0.405029\pi$
$397$	11.7140	0.587909	0.293955	+	0.955819i	$0.405029\pi$
$398$	−2.35926	−0.118259
$399$	0	0
$400$	−4.20524	−0.210262
$401$	−11.8123	−0.589880	−0.294940	−	0.955516i	$-0.595300\pi$
$401$	−11.8123	−0.589880	−0.294940	+	0.955516i	$0.595300\pi$
$402$	−1.18253	−0.0589793
$403$	56.8036	2.82959
$404$	−5.38487	−0.267907
$405$	−6.48681	−0.322332
$406$	−11.5439	−0.572914
$407$	−11.6725	−0.578584
$408$	−1.51423	−0.0749653
$409$	25.2663	1.24934	0.624668	−	0.780890i	$-0.285234\pi$
$409$	25.2663	1.24934	0.624668	+	0.780890i	$0.285234\pi$
$410$	−3.11070	−0.153627
$411$	4.86867	0.240154
$412$	−4.69468	−0.231290
$413$	7.16129	0.352384
$414$	22.9527	1.12806
$415$	12.5913	0.618084
$416$	6.45965	0.316710
$417$	−9.62739	−0.471455
$418$	0	0
$419$	31.6143	1.54446	0.772229	−	0.635344i	$-0.219142\pi$
$419$	31.6143	1.54446	0.772229	+	0.635344i	$0.219142\pi$
$420$	0.994078	0.0485060
$421$	−2.18972	−0.106720	−0.0533602	−	0.998575i	$-0.516993\pi$
$421$	−2.18972	−0.106720	−0.0533602	+	0.998575i	$0.516993\pi$
$422$	0.361050	0.0175757
$423$	29.5841	1.43843
$424$	−3.76278	−0.182737
$425$	14.3914	0.698087
$426$	0.0249728	0.00120994
$427$	−6.18683	−0.299402
$428$	16.0373	0.775191
$429$	5.57909	0.269361
$430$	−5.56887	−0.268555
$431$	−1.80372	−0.0868819	−0.0434410	−	0.999056i	$-0.513832\pi$
$431$	−1.80372	−0.0868819	−0.0434410	+	0.999056i	$0.513832\pi$
$432$	2.56816	0.123561
$433$	−6.57233	−0.315846	−0.157923	−	0.987451i	$-0.550480\pi$
$433$	−6.57233	−0.315846	−0.157923	+	0.987451i	$0.550480\pi$
$434$	22.1612	1.06377
$435$	1.80685	0.0866316
$436$	14.1008	0.675305
$437$	0	0
$438$	−3.08361	−0.147340
$439$	−9.13060	−0.435780	−0.217890	−	0.975973i	$-0.569917\pi$
$439$	−9.13060	−0.435780	−0.217890	+	0.975973i	$0.569917\pi$
$440$	1.74018	0.0829599
$441$	1.81955	0.0866451
$442$	−22.1066	−1.05150
$443$	−27.4686	−1.30507	−0.652536	−	0.757757i	$-0.726295\pi$
$443$	−27.4686	−1.30507	−0.652536	+	0.757757i	$0.726295\pi$
$444$	2.64584	0.125566
$445$	−1.66508	−0.0789321
$446$	−18.0486	−0.854626
$447$	−6.36686	−0.301142
$448$	2.52015	0.119066
$449$	−7.57293	−0.357389	−0.178694	−	0.983905i	$-0.557187\pi$
$449$	−7.57293	−0.357389	−0.178694	+	0.983905i	$0.557187\pi$
$450$	−11.7925	−0.555902
$451$	−6.81112	−0.320723
$452$	−12.7224	−0.598410
$453$	−5.48954	−0.257921
$454$	−12.2845	−0.576539
$455$	14.5128	0.680372
$456$	0	0
$457$	−21.7675	−1.01824	−0.509120	−	0.860696i	$-0.670029\pi$
$457$	−21.7675	−1.01824	−0.509120	+	0.860696i	$0.670029\pi$
$458$	−6.79174	−0.317357
$459$	−8.78890	−0.410231
$460$	−7.29689	−0.340219
$461$	11.9444	0.556305	0.278153	−	0.960537i	$-0.410278\pi$
$461$	11.9444	0.556305	0.278153	+	0.960537i	$0.410278\pi$
$462$	2.17661	0.101265
$463$	−8.75371	−0.406819	−0.203410	−	0.979094i	$-0.565202\pi$
$463$	−8.75371	−0.406819	−0.203410	+	0.979094i	$0.565202\pi$
$464$	4.58064	0.212651
$465$	−3.46866	−0.160855
$466$	−21.4294	−0.992696
$467$	29.3568	1.35847	0.679236	−	0.733920i	$-0.262311\pi$
$467$	29.3568	1.35847	0.679236	+	0.733920i	$0.262311\pi$
$468$	18.1143	0.837335
$469$	−6.73537	−0.311010
$470$	−9.40507	−0.433824
$471$	0.199648	0.00919932
$472$	−2.84162	−0.130796
$473$	−12.1935	−0.560656
$474$	−4.04041	−0.185582
$475$	0	0
$476$	−8.62460	−0.395308
$477$	−10.5517	−0.483128
$478$	11.8376	0.541441
$479$	−24.8705	−1.13636	−0.568180	−	0.822904i	$-0.692352\pi$
$479$	−24.8705	−1.13636	−0.568180	+	0.822904i	$0.692352\pi$
$480$	−0.394452	−0.0180042
$481$	38.6274	1.76126
$482$	21.7463	0.990517
$483$	−9.12692	−0.415289
$484$	−7.18974	−0.326806
$485$	−6.97531	−0.316733
$486$	10.9240	0.495523
$487$	−8.53766	−0.386878	−0.193439	−	0.981112i	$-0.561964\pi$
$487$	−8.53766	−0.386878	−0.193439	+	0.981112i	$0.561964\pi$
$488$	2.45495	0.111130
$489$	0.0306425	0.00138570
$490$	−0.578452	−0.0261318
$491$	−11.5397	−0.520780	−0.260390	−	0.965504i	$-0.583851\pi$
$491$	−11.5397	−0.520780	−0.260390	+	0.965504i	$0.583851\pi$
$492$	1.54390	0.0696043
$493$	−15.6762	−0.706019
$494$	0	0
$495$	4.87986	0.219333
$496$	−8.79360	−0.394844
$497$	0.142238	0.00638025
$498$	−6.24931	−0.280038
$499$	−29.6091	−1.32548	−0.662742	−	0.748848i	$-0.730607\pi$
$499$	−29.6091	−1.32548	−0.662742	+	0.748848i	$0.730607\pi$
$500$	8.20640	0.367001
$501$	−0.961785	−0.0429694
$502$	−23.6410	−1.05515
$503$	5.86827	0.261653	0.130827	−	0.991405i	$-0.458237\pi$
$503$	5.86827	0.261653	0.130827	+	0.991405i	$0.458237\pi$
$504$	7.06706	0.314792
$505$	4.80057	0.213622
$506$	−15.9771	−0.710269
$507$	−12.7107	−0.564501
$508$	7.17442	0.318313
$509$	25.5687	1.13331	0.566656	−	0.823954i	$-0.308237\pi$
$509$	25.5687	1.13331	0.566656	+	0.823954i	$0.308237\pi$
$510$	1.34992	0.0597754
$511$	−17.5633	−0.776957
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	0.923469	0.0407325
$515$	4.18527	0.184425
$516$	2.76393	0.121675
$517$	−20.5931	−0.905685
$518$	15.0700	0.662136
$519$	7.45520	0.327247
$520$	−5.75872	−0.252537
$521$	14.0332	0.614807	0.307403	−	0.951579i	$-0.400540\pi$
$521$	14.0332	0.614807	0.307403	+	0.951579i	$0.400540\pi$
$522$	12.8452	0.562217
$523$	−31.0784	−1.35896	−0.679482	−	0.733692i	$-0.737795\pi$
$523$	−31.0784	−1.35896	−0.679482	+	0.733692i	$0.737795\pi$
$524$	−3.52265	−0.153888
$525$	4.68915	0.204651
$526$	−4.31967	−0.188347
$527$	30.0940	1.31092
$528$	−0.863684	−0.0375870
$529$	43.9949	1.91282
$530$	3.35449	0.145710
$531$	−7.96853	−0.345805
$532$	0	0
$533$	22.5398	0.976307
$534$	0.826407	0.0357621
$535$	−14.2971	−0.618117
$536$	2.67261	0.115439
$537$	−8.39155	−0.362122
$538$	10.7954	0.465421
$539$	−1.26657	−0.0545548
$540$	−2.28949	−0.0985240
$541$	2.89608	0.124512	0.0622561	−	0.998060i	$-0.480170\pi$
$541$	2.89608	0.124512	0.0622561	+	0.998060i	$0.480170\pi$
$542$	−0.807243	−0.0346741
$543$	0.879118	0.0377266
$544$	3.42226	0.146728
$545$	−12.5707	−0.538471
$546$	−7.20298	−0.308259
$547$	−30.3861	−1.29922	−0.649608	−	0.760269i	$-0.725067\pi$
$547$	−30.3861	−1.29922	−0.649608	+	0.760269i	$0.725067\pi$
$548$	−11.0035	−0.470048
$549$	6.88423	0.293812
$550$	8.20859	0.350015
$551$	0	0
$552$	3.62158	0.154145
$553$	−23.0130	−0.978613
$554$	9.14869	0.388691
$555$	−2.35875	−0.100123
$556$	21.7586	0.922771
$557$	−6.13412	−0.259911	−0.129956	−	0.991520i	$-0.541483\pi$
$557$	−6.13412	−0.259911	−0.129956	+	0.991520i	$0.541483\pi$
$558$	−24.6593	−1.04391
$559$	40.3514	1.70668
$560$	−2.24669	−0.0949400
$561$	2.95575	0.124792
$562$	−21.2158	−0.894932
$563$	28.1917	1.18814	0.594069	−	0.804414i	$-0.297521\pi$
$563$	28.1917	1.18814	0.594069	+	0.804414i	$0.297521\pi$
$564$	4.66791	0.196554
$565$	11.3419	0.477157
$566$	−5.18985	−0.218146
$567$	18.3375	0.770103
$568$	−0.0564404	−0.00236819
$569$	42.1145	1.76553	0.882766	−	0.469812i	$-0.155678\pi$
$569$	42.1145	1.76553	0.882766	+	0.469812i	$0.155678\pi$
$570$	0	0
$571$	0.166927	0.00698566	0.00349283	−	0.999994i	$-0.498888\pi$
$571$	0.166927	0.00698566	0.00349283	+	0.999994i	$0.498888\pi$
$572$	−12.6092	−0.527216
$573$	9.25896	0.386799
$574$	8.79360	0.367038
$575$	−34.4201	−1.43542
$576$	−2.80423	−0.116843
$577$	−19.9631	−0.831076	−0.415538	−	0.909576i	$-0.636407\pi$
$577$	−19.9631	−0.831076	−0.415538	+	0.909576i	$0.636407\pi$
$578$	5.28814	0.219957
$579$	−3.44626	−0.143222
$580$	−4.08361	−0.169562
$581$	−35.5943	−1.47670
$582$	3.46197	0.143503
$583$	7.34490	0.304195
$584$	6.96917	0.288387
$585$	−16.1488	−0.667669
$586$	17.5660	0.725643
$587$	10.1440	0.418689	0.209345	−	0.977842i	$-0.432867\pi$
$587$	10.1440	0.418689	0.209345	+	0.977842i	$0.432867\pi$
$588$	0.287096	0.0118397
$589$	0	0
$590$	2.53328	0.104293
$591$	−0.807559	−0.0332185
$592$	−5.97980	−0.245768
$593$	7.45315	0.306064	0.153032	−	0.988221i	$-0.451096\pi$
$593$	7.45315	0.306064	0.153032	+	0.988221i	$0.451096\pi$
$594$	−5.01302	−0.205687
$595$	7.68876	0.315208
$596$	14.3896	0.589420
$597$	−1.04388	−0.0427233
$598$	52.8725	2.16212
$599$	6.37141	0.260329	0.130164	−	0.991492i	$-0.458449\pi$
$599$	6.37141	0.260329	0.130164	+	0.991492i	$0.458449\pi$
$600$	−1.86067	−0.0759614
$601$	−1.74631	−0.0712333	−0.0356166	−	0.999366i	$-0.511340\pi$
$601$	−1.74631	−0.0712333	−0.0356166	+	0.999366i	$0.511340\pi$
$602$	15.7426	0.641620
$603$	7.49460	0.305204
$604$	12.4068	0.504824
$605$	6.40959	0.260587
$606$	−2.38261	−0.0967869
$607$	−32.1612	−1.30538	−0.652691	−	0.757624i	$-0.726360\pi$
$607$	−32.1612	−1.30538	−0.652691	+	0.757624i	$0.726360\pi$
$608$	0	0
$609$	−5.10775	−0.206977
$610$	−2.18857	−0.0886125
$611$	68.1481	2.75698
$612$	9.59679	0.387927
$613$	12.7645	0.515552	0.257776	−	0.966205i	$-0.417010\pi$
$613$	12.7645	0.515552	0.257776	+	0.966205i	$0.417010\pi$
$614$	21.5684	0.870428
$615$	−1.37637	−0.0555007
$616$	−4.91930	−0.198204
$617$	−1.68323	−0.0677643	−0.0338822	−	0.999426i	$-0.510787\pi$
$617$	−1.68323	−0.0677643	−0.0338822	+	0.999426i	$0.510787\pi$
$618$	−2.07722	−0.0835582
$619$	31.5285	1.26724	0.633618	−	0.773646i	$-0.281569\pi$
$619$	31.5285	1.26724	0.633618	+	0.773646i	$0.281569\pi$
$620$	7.83942	0.314839
$621$	21.0205	0.843523
$622$	2.57368	0.103195
$623$	4.70698	0.188581
$624$	2.85816	0.114418
$625$	13.7103	0.548411
$626$	5.18389	0.207190
$627$	0	0
$628$	−0.451220	−0.0180056
$629$	20.4644	0.815970
$630$	−6.30023	−0.251007
$631$	−31.7662	−1.26459	−0.632297	−	0.774726i	$-0.717888\pi$
$631$	−31.7662	−1.26459	−0.632297	+	0.774726i	$0.717888\pi$
$632$	9.13162	0.363236
$633$	0.159752	0.00634955
$634$	20.2562	0.804475
$635$	−6.39593	−0.253815
$636$	−1.66489	−0.0660173
$637$	4.19140	0.166069
$638$	−8.94137	−0.353992
$639$	−0.158272	−0.00626113
$640$	0.891491	0.0352393
$641$	40.4437	1.59743	0.798715	−	0.601709i	$-0.205513\pi$
$641$	40.4437	1.59743	0.798715	+	0.601709i	$0.205513\pi$
$642$	7.09591	0.280053
$643$	−26.1033	−1.02941	−0.514706	−	0.857367i	$-0.672099\pi$
$643$	−26.1033	−1.02941	−0.514706	+	0.857367i	$0.672099\pi$
$644$	20.6275	0.812837
$645$	−2.46402	−0.0970208
$646$	0	0
$647$	−48.7713	−1.91740	−0.958699	−	0.284423i	$-0.908198\pi$
$647$	−48.7713	−1.91740	−0.958699	+	0.284423i	$0.908198\pi$
$648$	−7.27636	−0.285842
$649$	5.54680	0.217731
$650$	−27.1644	−1.06548
$651$	9.80551	0.384308
$652$	−0.0692542	−0.00271220
$653$	−43.1831	−1.68988	−0.844942	−	0.534858i	$-0.820365\pi$
$653$	−43.1831	−1.68988	−0.844942	+	0.534858i	$0.820365\pi$
$654$	6.23909	0.243968
$655$	3.14042	0.122706
$656$	−3.48932	−0.136235
$657$	19.5431	0.762451
$658$	26.5871	1.03647
$659$	14.2769	0.556148	0.278074	−	0.960560i	$-0.410304\pi$
$659$	14.2769	0.556148	0.278074	+	0.960560i	$0.410304\pi$
$660$	0.769967	0.0299709
$661$	−35.7497	−1.39050	−0.695251	−	0.718768i	$-0.744707\pi$
$661$	−35.7497	−1.39050	−0.695251	+	0.718768i	$0.744707\pi$
$662$	21.3280	0.828936
$663$	−9.78136	−0.379877
$664$	14.1239	0.548114
$665$	0	0
$666$	−16.7687	−0.649774
$667$	37.4928	1.45173
$668$	2.17371	0.0841032
$669$	−7.98585	−0.308751
$670$	−2.38261	−0.0920482
$671$	−4.79204	−0.184994
$672$	1.11507	0.0430149
$673$	−10.3574	−0.399248	−0.199624	−	0.979873i	$-0.563972\pi$
$673$	−10.3574	−0.399248	−0.199624	+	0.979873i	$0.563972\pi$
$674$	22.7275	0.875429
$675$	−10.7997	−0.415682
$676$	28.7271	1.10489
$677$	10.7171	0.411891	0.205945	−	0.978564i	$-0.433973\pi$
$677$	10.7171	0.411891	0.205945	+	0.978564i	$0.433973\pi$
$678$	−5.62919	−0.216188
$679$	19.7184	0.756724
$680$	−3.05092	−0.116997
$681$	−5.43543	−0.208286
$682$	17.1650	0.657283
$683$	−0.122930	−0.00470377	−0.00235188	−	0.999997i	$-0.500749\pi$
$683$	−0.122930	−0.00470377	−0.00235188	+	0.999997i	$0.500749\pi$
$684$	0	0
$685$	9.80957	0.374804
$686$	19.2762	0.735971
$687$	−3.00510	−0.114652
$688$	−6.24669	−0.238153
$689$	−24.3062	−0.925994
$690$	−3.22861	−0.122911
$691$	−25.2815	−0.961752	−0.480876	−	0.876789i	$-0.659681\pi$
$691$	−25.2815	−0.961752	−0.480876	+	0.876789i	$0.659681\pi$
$692$	−16.8493	−0.640514
$693$	−13.7948	−0.524022
$694$	4.92855	0.187085
$695$	−19.3976	−0.735793
$696$	2.02677	0.0768244
$697$	11.9414	0.452312
$698$	−26.1615	−0.990228
$699$	−9.48171	−0.358631
$700$	−10.5978	−0.400560
$701$	−5.17287	−0.195377	−0.0976883	−	0.995217i	$-0.531145\pi$
$701$	−5.17287	−0.195377	−0.0976883	+	0.995217i	$0.531145\pi$
$702$	16.5894	0.626127
$703$	0	0
$704$	1.95199	0.0735684
$705$	−4.16140	−0.156727
$706$	−2.70813	−0.101922
$707$	−13.5707	−0.510377
$708$	−1.25731	−0.0472526
$709$	−29.9907	−1.12632	−0.563162	−	0.826346i	$-0.690415\pi$
$709$	−29.9907	−1.12632	−0.563162	+	0.826346i	$0.690415\pi$
$710$	0.0503161	0.00188833
$711$	25.6071	0.960342
$712$	−1.86774	−0.0699965
$713$	−71.9760	−2.69552
$714$	−3.81607	−0.142813
$715$	11.2410	0.420388
$716$	18.9655	0.708775
$717$	5.23772	0.195606
$718$	9.31002	0.347447
$719$	−22.7033	−0.846688	−0.423344	−	0.905969i	$-0.639144\pi$
$719$	−22.7033	−0.846688	−0.423344	+	0.905969i	$0.639144\pi$
$720$	2.49994	0.0931674
$721$	−11.8313	−0.440620
$722$	0	0
$723$	9.62195	0.357844
$724$	−1.98687	−0.0738415
$725$	−19.2627	−0.715400
$726$	−3.18120	−0.118065
$727$	36.5937	1.35719	0.678593	−	0.734514i	$-0.262590\pi$
$727$	36.5937	1.35719	0.678593	+	0.734514i	$0.262590\pi$
$728$	16.2793	0.603350
$729$	−16.9956	−0.629467
$730$	−6.21296	−0.229952
$731$	21.3778	0.790686
$732$	1.08623	0.0401481
$733$	21.1522	0.781275	0.390637	−	0.920545i	$-0.372255\pi$
$733$	21.1522	0.781275	0.390637	+	0.920545i	$0.372255\pi$
$734$	−7.75442	−0.286221
$735$	−0.255944	−0.00944064
$736$	−8.18504	−0.301705
$737$	−5.21690	−0.192167
$738$	−9.78485	−0.360185
$739$	48.3066	1.77699	0.888494	−	0.458888i	$-0.151752\pi$
$739$	48.3066	1.77699	0.888494	+	0.458888i	$0.151752\pi$
$740$	5.33094	0.195969
$741$	0	0
$742$	−9.48276	−0.348123
$743$	−31.8598	−1.16882	−0.584412	−	0.811457i	$-0.698675\pi$
$743$	−31.8598	−1.16882	−0.584412	+	0.811457i	$0.698675\pi$
$744$	−3.89085	−0.142645
$745$	−12.8282	−0.469988
$746$	25.0124	0.915768
$747$	39.6066	1.44913
$748$	−6.68021	−0.244253
$749$	40.4163	1.47678
$750$	3.63103	0.132586
$751$	40.9962	1.49597	0.747987	−	0.663713i	$-0.231020\pi$
$751$	40.9962	1.49597	0.747987	+	0.663713i	$0.231020\pi$
$752$	−10.5498	−0.384712
$753$	−10.4603	−0.381194
$754$	29.5894	1.07758
$755$	−11.0605	−0.402533
$756$	6.47214	0.235389
$757$	−12.8215	−0.466006	−0.233003	−	0.972476i	$-0.574855\pi$
$757$	−12.8215	−0.466006	−0.233003	+	0.972476i	$0.574855\pi$
$758$	−19.1802	−0.696657
$759$	−7.06929	−0.256599
$760$	0	0
$761$	35.6382	1.29188	0.645942	−	0.763386i	$-0.276465\pi$
$761$	35.6382	1.29188	0.645942	+	0.763386i	$0.276465\pi$
$762$	3.17442	0.114997
$763$	35.5361	1.28649
$764$	−20.9259	−0.757074
$765$	−8.55546	−0.309323
$766$	4.83319	0.174630
$767$	−18.3558	−0.662791
$768$	−0.442463	−0.0159660
$769$	−5.57401	−0.201004	−0.100502	−	0.994937i	$-0.532045\pi$
$769$	−5.57401	−0.201004	−0.100502	+	0.994937i	$0.532045\pi$
$770$	4.38551	0.158043
$771$	0.408601	0.0147154
$772$	7.78879	0.280325
$773$	36.4119	1.30965	0.654823	−	0.755782i	$-0.272743\pi$
$773$	36.4119	1.30965	0.654823	+	0.755782i	$0.272743\pi$
$774$	−17.5171	−0.629640
$775$	36.9792	1.32833
$776$	−7.82432	−0.280877
$777$	6.66791	0.239210
$778$	−21.7291	−0.779027
$779$	0	0
$780$	−2.54802	−0.0912339
$781$	0.110171	0.00394223
$782$	28.0113	1.00168
$783$	11.7638	0.420405
$784$	−0.648859	−0.0231735
$785$	0.402259	0.0143572
$786$	−1.55865	−0.0555951
$787$	31.9046	1.13728	0.568638	−	0.822588i	$-0.307471\pi$
$787$	31.9046	1.13728	0.568638	+	0.822588i	$0.307471\pi$
$788$	1.82514	0.0650180
$789$	−1.91130	−0.0680440
$790$	−8.14076	−0.289635
$791$	−32.0622	−1.14000
$792$	5.47382	0.194504
$793$	15.8581	0.563138
$794$	−11.7140	−0.415715
$795$	1.48424	0.0526405
$796$	2.35926	0.0836216
$797$	−2.09165	−0.0740900	−0.0370450	−	0.999314i	$-0.511794\pi$
$797$	−2.09165	−0.0740900	−0.0370450	+	0.999314i	$0.511794\pi$
$798$	0	0
$799$	36.1042	1.27728
$800$	4.20524	0.148678
$801$	−5.23757	−0.185060
$802$	11.8123	0.417108
$803$	−13.6038	−0.480066
$804$	1.18253	0.0417047
$805$	−18.3892	−0.648136
$806$	−56.8036	−2.00082
$807$	4.77655	0.168143
$808$	5.38487	0.189439
$809$	−30.0719	−1.05727	−0.528636	−	0.848849i	$-0.677296\pi$
$809$	−30.0719	−1.05727	−0.528636	+	0.848849i	$0.677296\pi$
$810$	6.48681	0.227923
$811$	0.823592	0.0289202	0.0144601	−	0.999895i	$-0.495397\pi$
$811$	0.823592	0.0289202	0.0144601	+	0.999895i	$0.495397\pi$
$812$	11.5439	0.405111
$813$	−0.357176	−0.0125267
$814$	11.6725	0.409121
$815$	0.0617395	0.00216264
$816$	1.51423	0.0530085
$817$	0	0
$818$	−25.2663	−0.883414
$819$	45.6507	1.59517
$820$	3.11070	0.108630
$821$	7.71124	0.269124	0.134562	−	0.990905i	$-0.457037\pi$
$821$	7.71124	0.269124	0.134562	+	0.990905i	$0.457037\pi$
$822$	−4.86867	−0.169814
$823$	−24.8120	−0.864893	−0.432447	−	0.901660i	$-0.642350\pi$
$823$	−24.8120	−0.864893	−0.432447	+	0.901660i	$0.642350\pi$
$824$	4.69468	0.163547
$825$	3.63200	0.126450
$826$	−7.16129	−0.249173
$827$	10.6285	0.369588	0.184794	−	0.982777i	$-0.440838\pi$
$827$	10.6285	0.369588	0.184794	+	0.982777i	$0.440838\pi$
$828$	−22.9527	−0.797662
$829$	21.4710	0.745718	0.372859	−	0.927888i	$-0.378377\pi$
$829$	21.4710	0.745718	0.372859	+	0.927888i	$0.378377\pi$
$830$	−12.5913	−0.437052
$831$	4.04796	0.140422
$832$	−6.45965	−0.223948
$833$	2.22056	0.0769380
$834$	9.62739	0.333369
$835$	−1.93784	−0.0670617
$836$	0	0
$837$	−22.5834	−0.780595
$838$	−31.6143	−1.09210
$839$	−48.8239	−1.68559	−0.842794	−	0.538237i	$-0.819091\pi$
$839$	−48.8239	−1.68559	−0.842794	+	0.538237i	$0.819091\pi$
$840$	−0.994078	−0.0342990
$841$	−8.01770	−0.276472
$842$	2.18972	0.0754627
$843$	−9.38720	−0.323312
$844$	−0.361050	−0.0124279
$845$	−25.6099	−0.881009
$846$	−29.5841	−1.01712
$847$	−18.1192	−0.622583
$848$	3.76278	0.129214
$849$	−2.29632	−0.0788095
$850$	−14.3914	−0.493622
$851$	−48.9449	−1.67781
$852$	−0.0249728	−0.000855554 0
$853$	−21.0110	−0.719404	−0.359702	−	0.933067i	$-0.617122\pi$
$853$	−21.0110	−0.719404	−0.359702	+	0.933067i	$0.617122\pi$
$854$	6.18683	0.211709
$855$	0	0
$856$	−16.0373	−0.548143
$857$	32.2392	1.10127	0.550635	−	0.834746i	$-0.314386\pi$
$857$	32.2392	1.10127	0.550635	+	0.834746i	$0.314386\pi$
$858$	−5.57909	−0.190467
$859$	−41.2274	−1.40666	−0.703331	−	0.710863i	$-0.748305\pi$
$859$	−41.2274	−1.40666	−0.703331	+	0.710863i	$0.748305\pi$
$860$	5.56887	0.189897
$861$	3.89085	0.132600
$862$	1.80372	0.0614348
$863$	−42.0649	−1.43191	−0.715953	−	0.698148i	$-0.754008\pi$
$863$	−42.0649	−1.43191	−0.715953	+	0.698148i	$0.754008\pi$
$864$	−2.56816	−0.0873705
$865$	15.0210	0.510729
$866$	6.57233	0.223337
$867$	2.33981	0.0794640
$868$	−22.1612	−0.752199
$869$	−17.8248	−0.604665
$870$	−1.80685	−0.0612578
$871$	17.2641	0.584972
$872$	−14.1008	−0.477513
$873$	−21.9412	−0.742596
$874$	0	0
$875$	20.6813	0.699156
$876$	3.08361	0.104185
$877$	−2.35551	−0.0795400	−0.0397700	−	0.999209i	$-0.512663\pi$
$877$	−2.35551	−0.0795400	−0.0397700	+	0.999209i	$0.512663\pi$
$878$	9.13060	0.308143
$879$	7.77230	0.262153
$880$	−1.74018	−0.0586615
$881$	23.1354	0.779450	0.389725	−	0.920931i	$-0.372570\pi$
$881$	23.1354	0.779450	0.389725	+	0.920931i	$0.372570\pi$
$882$	−1.81955	−0.0612673
$883$	7.01191	0.235969	0.117985	−	0.993015i	$-0.462357\pi$
$883$	7.01191	0.235969	0.117985	+	0.993015i	$0.462357\pi$
$884$	22.1066	0.743525
$885$	1.12088	0.0376780
$886$	27.4686	0.922826
$887$	−48.9293	−1.64289	−0.821443	−	0.570291i	$-0.806830\pi$
$887$	−48.9293	−1.64289	−0.821443	+	0.570291i	$0.806830\pi$
$888$	−2.64584	−0.0887886
$889$	18.0806	0.606403
$890$	1.66508	0.0558134
$891$	14.2034	0.475831
$892$	18.0486	0.604312
$893$	0	0
$894$	6.36686	0.212940
$895$	−16.9076	−0.565159
$896$	−2.52015	−0.0841922
$897$	23.3941	0.781108
$898$	7.57293	0.252712
$899$	−40.2804	−1.34343
$900$	11.7925	0.393082
$901$	−12.8772	−0.429002
$902$	6.81112	0.226785
$903$	6.96552	0.231798
$904$	12.7224	0.423140
$905$	1.77128	0.0588793
$906$	5.48954	0.182378
$907$	1.19304	0.0396143	0.0198071	−	0.999804i	$-0.493695\pi$
$907$	1.19304	0.0396143	0.0198071	+	0.999804i	$0.493695\pi$
$908$	12.2845	0.407675
$909$	15.1004	0.500848
$910$	−14.5128	−0.481096
$911$	−37.6344	−1.24688	−0.623442	−	0.781870i	$-0.714266\pi$
$911$	−37.6344	−1.24688	−0.623442	+	0.781870i	$0.714266\pi$
$912$	0	0
$913$	−27.5697	−0.912424
$914$	21.7675	0.720004
$915$	−0.968361	−0.0320130
$916$	6.79174	0.224405
$917$	−8.87761	−0.293164
$918$	8.78890	0.290077
$919$	26.9476	0.888921	0.444460	−	0.895799i	$-0.353395\pi$
$919$	26.9476	0.888921	0.444460	+	0.895799i	$0.353395\pi$
$920$	7.29689	0.240571
$921$	9.54321	0.314460
$922$	−11.9444	−0.393367
$923$	−0.364585	−0.0120005
$924$	−2.17661	−0.0716052
$925$	25.1465	0.826812
$926$	8.75371	0.287665
$927$	13.1649	0.432393
$928$	−4.58064	−0.150367
$929$	−17.8550	−0.585804	−0.292902	−	0.956142i	$-0.594621\pi$
$929$	−17.8550	−0.585804	−0.292902	+	0.956142i	$0.594621\pi$
$930$	3.46866	0.113742
$931$	0	0
$932$	21.4294	0.701942
$933$	1.13876	0.0372814
$934$	−29.3568	−0.960585
$935$	5.95535	0.194761
$936$	−18.1143	−0.592085
$937$	−23.8326	−0.778576	−0.389288	−	0.921116i	$-0.627279\pi$
$937$	−23.8326	−0.778576	−0.389288	+	0.921116i	$0.627279\pi$
$938$	6.73537	0.219918
$939$	2.29368	0.0748514
$940$	9.40507	0.306760
$941$	−20.3651	−0.663882	−0.331941	−	0.943300i	$-0.607704\pi$
$941$	−20.3651	−0.663882	−0.331941	+	0.943300i	$0.607704\pi$
$942$	−0.199648	−0.00650490
$943$	−28.5602	−0.930049
$944$	2.84162	0.0924867
$945$	−5.76985	−0.187693
$946$	12.1935	0.396444
$947$	−3.41590	−0.111002	−0.0555009	−	0.998459i	$-0.517676\pi$
$947$	−3.41590	−0.111002	−0.0555009	+	0.998459i	$0.517676\pi$
$948$	4.04041	0.131226
$949$	45.0184	1.46136
$950$	0	0
$951$	8.96261	0.290633
$952$	8.62460	0.279525
$953$	17.7393	0.574634	0.287317	−	0.957836i	$-0.407237\pi$
$953$	17.7393	0.574634	0.287317	+	0.957836i	$0.407237\pi$
$954$	10.5517	0.341623
$955$	18.6553	0.603671
$956$	−11.8376	−0.382856
$957$	−3.95623	−0.127887
$958$	24.8705	0.803528
$959$	−27.7306	−0.895466
$960$	0.394452	0.0127309
$961$	46.3275	1.49443
$962$	−38.6274	−1.24540
$963$	−44.9721	−1.44921
$964$	−21.7463	−0.700401
$965$	−6.94364	−0.223524
$966$	9.12692	0.293654
$967$	−42.7551	−1.37491	−0.687456	−	0.726226i	$-0.741273\pi$
$967$	−42.7551	−1.37491	−0.687456	+	0.726226i	$0.741273\pi$
$968$	7.18974	0.231087
$969$	0	0
$970$	6.97531	0.223964
$971$	−53.0487	−1.70241	−0.851207	−	0.524830i	$-0.824129\pi$
$971$	−53.0487	−1.70241	−0.851207	+	0.524830i	$0.824129\pi$
$972$	−10.9240	−0.350387
$973$	54.8349	1.75793
$974$	8.53766	0.273564
$975$	−12.0193	−0.384924
$976$	−2.45495	−0.0785810
$977$	12.3264	0.394356	0.197178	−	0.980368i	$-0.436822\pi$
$977$	12.3264	0.394356	0.197178	+	0.980368i	$0.436822\pi$
$978$	−0.0306425	−0.000979838 0
$979$	3.64581	0.116521
$980$	0.578452	0.0184780
$981$	−39.5418	−1.26247
$982$	11.5397	0.368247
$983$	32.2554	1.02879	0.514394	−	0.857554i	$-0.328017\pi$
$983$	32.2554	1.02879	0.514394	+	0.857554i	$0.328017\pi$
$984$	−1.54390	−0.0492177
$985$	−1.62710	−0.0518437
$986$	15.6762	0.499231
$987$	11.7638	0.374446
$988$	0	0
$989$	−51.1294	−1.62582
$990$	−4.87986	−0.155092
$991$	−27.8366	−0.884258	−0.442129	−	0.896951i	$-0.645777\pi$
$991$	−27.8366	−0.884258	−0.442129	+	0.896951i	$0.645777\pi$
$992$	8.79360	0.279197
$993$	9.43686	0.299470
$994$	−0.142238	−0.00451152
$995$	−2.10326	−0.0666777
$996$	6.24931	0.198017
$997$	−43.3313	−1.37232	−0.686159	−	0.727452i	$-0.740704\pi$
$997$	−43.3313	−1.37232	−0.686159	+	0.727452i	$0.740704\pi$
$998$	29.6091	0.937258
$999$	−15.3571	−0.485876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.m.1.3	✓	4
3.2	odd	2		6498.2.a.ca.1.2		4
4.3	odd	2		5776.2.a.bv.1.2		4
19.2	odd	18		722.2.e.r.99.2		24
19.3	odd	18		722.2.e.r.389.2		24
19.4	even	9		722.2.e.s.415.2		24
19.5	even	9		722.2.e.s.595.2		24
19.6	even	9		722.2.e.s.245.3		24
19.7	even	3		722.2.c.n.429.2		8
19.8	odd	6		722.2.c.m.653.3		8
19.9	even	9		722.2.e.s.423.3		24
19.10	odd	18		722.2.e.r.423.2		24
19.11	even	3		722.2.c.n.653.2		8
19.12	odd	6		722.2.c.m.429.3		8
19.13	odd	18		722.2.e.r.245.2		24
19.14	odd	18		722.2.e.r.595.3		24
19.15	odd	18		722.2.e.r.415.3		24
19.16	even	9		722.2.e.s.389.3		24
19.17	even	9		722.2.e.s.99.3		24
19.18	odd	2		722.2.a.n.1.2	yes	4
57.56	even	2		6498.2.a.bx.1.2		4
76.75	even	2		5776.2.a.bt.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.3	✓	4	1.1	even	1	trivial
722.2.a.n.1.2	yes	4	19.18	odd	2
722.2.c.m.429.3		8	19.12	odd	6
722.2.c.m.653.3		8	19.8	odd	6
722.2.c.n.429.2		8	19.7	even	3
722.2.c.n.653.2		8	19.11	even	3
722.2.e.r.99.2		24	19.2	odd	18
722.2.e.r.245.2		24	19.13	odd	18
722.2.e.r.389.2		24	19.3	odd	18
722.2.e.r.415.3		24	19.15	odd	18
722.2.e.r.423.2		24	19.10	odd	18
722.2.e.r.595.3		24	19.14	odd	18
722.2.e.s.99.3		24	19.17	even	9
722.2.e.s.245.3		24	19.6	even	9
722.2.e.s.389.3		24	19.16	even	9
722.2.e.s.415.2		24	19.4	even	9
722.2.e.s.423.3		24	19.9	even	9
722.2.e.s.595.2		24	19.5	even	9
5776.2.a.bt.1.3		4	76.75	even	2
5776.2.a.bv.1.2		4	4.3	odd	2
6498.2.a.bx.1.2		4	57.56	even	2
6498.2.a.ca.1.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.442463 q^{3} +1.00000 q^{4} -0.891491 q^{5} +0.442463 q^{6} +2.52015 q^{7} -1.00000 q^{8} -2.80423 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.442463 q^{3} +1.00000 q^{4} -0.891491 q^{5} +0.442463 q^{6} +2.52015 q^{7} -1.00000 q^{8} -2.80423 q^{9} +0.891491 q^{10} +1.95199 q^{11} -0.442463 q^{12} -6.45965 q^{13} -2.52015 q^{14} +0.394452 q^{15} +1.00000 q^{16} -3.42226 q^{17} +2.80423 q^{18} -0.891491 q^{20} -1.11507 q^{21} -1.95199 q^{22} +8.18504 q^{23} +0.442463 q^{24} -4.20524 q^{25} +6.45965 q^{26} +2.56816 q^{27} +2.52015 q^{28} +4.58064 q^{29} -0.394452 q^{30} -8.79360 q^{31} -1.00000 q^{32} -0.863684 q^{33} +3.42226 q^{34} -2.24669 q^{35} -2.80423 q^{36} -5.97980 q^{37} +2.85816 q^{39} +0.891491 q^{40} -3.48932 q^{41} +1.11507 q^{42} -6.24669 q^{43} +1.95199 q^{44} +2.49994 q^{45} -8.18504 q^{46} -10.5498 q^{47} -0.442463 q^{48} -0.648859 q^{49} +4.20524 q^{50} +1.51423 q^{51} -6.45965 q^{52} +3.76278 q^{53} -2.56816 q^{54} -1.74018 q^{55} -2.52015 q^{56} -4.58064 q^{58} +2.84162 q^{59} +0.394452 q^{60} -2.45495 q^{61} +8.79360 q^{62} -7.06706 q^{63} +1.00000 q^{64} +5.75872 q^{65} +0.863684 q^{66} -2.67261 q^{67} -3.42226 q^{68} -3.62158 q^{69} +2.24669 q^{70} +0.0564404 q^{71} +2.80423 q^{72} -6.96917 q^{73} +5.97980 q^{74} +1.86067 q^{75} +4.91930 q^{77} -2.85816 q^{78} -9.13162 q^{79} -0.891491 q^{80} +7.27636 q^{81} +3.48932 q^{82} -14.1239 q^{83} -1.11507 q^{84} +3.05092 q^{85} +6.24669 q^{86} -2.02677 q^{87} -1.95199 q^{88} +1.86774 q^{89} -2.49994 q^{90} -16.2793 q^{91} +8.18504 q^{92} +3.89085 q^{93} +10.5498 q^{94} +0.442463 q^{96} +7.82432 q^{97} +0.648859 q^{98} -5.47382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} + 4 q^{16} + 6 q^{17} - 4 q^{18} - 2 q^{20} - 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} + 4 q^{27} - 2 q^{28} + 2 q^{29} + 4 q^{30} - 26 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} + 6 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{39} + 2 q^{40} + 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} + 10 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} - 6 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} - 4 q^{54} - 26 q^{55} + 2 q^{56} - 2 q^{58} + 8 q^{59} - 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} + 4 q^{65} + 16 q^{66} - 10 q^{67} + 6 q^{68} + 20 q^{69} - 6 q^{70} - 4 q^{72} - 14 q^{73} + 4 q^{74} - 8 q^{75} + 4 q^{77} + 6 q^{78} - 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} - 4 q^{84} - 18 q^{85} + 10 q^{86} - 26 q^{87} - 2 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} - 10 q^{92} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 28 q^{97} + 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 + 4 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 18 * q^13 + 2 * q^14 - 4 * q^15 + 4 * q^16 + 6 * q^17 - 4 * q^18 - 2 * q^20 - 4 * q^21 - 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 + 4 * q^27 - 2 * q^28 + 2 * q^29 + 4 * q^30 - 26 * q^31 - 4 * q^32 - 16 * q^33 - 6 * q^34 + 6 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^39 + 2 * q^40 + 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 + 10 * q^46 - 12 * q^47 - 2 * q^48 - 12 * q^49 - 6 * q^50 + 2 * q^51 - 18 * q^52 - 8 * q^53 - 4 * q^54 - 26 * q^55 + 2 * q^56 - 2 * q^58 + 8 * q^59 - 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 + 4 * q^65 + 16 * q^66 - 10 * q^67 + 6 * q^68 + 20 * q^69 - 6 * q^70 - 4 * q^72 - 14 * q^73 + 4 * q^74 - 8 * q^75 + 4 * q^77 + 6 * q^78 - 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 - 4 * q^84 - 18 * q^85 + 10 * q^86 - 26 * q^87 - 2 * q^88 + 16 * q^89 + 22 * q^90 + 4 * q^91 - 10 * q^92 + 8 * q^93 + 12 * q^94 + 2 * q^96 - 28 * q^97 + 12 * q^98 + 22 * q^99

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