LMFDB - Embedded newform 1728.3.o.f.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1728.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-1.07834i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.f.1279.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.01729 - 5.22611i) q^{5} +(10.2332 + 5.90815i) q^{7} +O(q^{10})$	$q+(-3.01729 - 5.22611i) q^{5} +(10.2332 + 5.90815i) q^{7} +(5.28454 + 3.05103i) q^{11} +(-7.44868 - 12.9015i) q^{13} -26.6919 q^{17} +9.45610i q^{19} +(17.2673 - 9.96931i) q^{23} +(-5.70813 + 9.88677i) q^{25} +(22.3114 - 38.6445i) q^{29} +(5.42359 - 3.13131i) q^{31} -71.3065i q^{35} +6.65707 q^{37} +(-8.82853 - 15.2915i) q^{41} +(-20.2696 - 11.7027i) q^{43} +(36.4261 + 21.0306i) q^{47} +(45.3125 + 78.4835i) q^{49} -51.6192 q^{53} -36.8234i q^{55} +(-32.9024 + 18.9962i) q^{59} +(45.3815 - 78.6031i) q^{61} +(-44.9497 + 77.8552i) q^{65} +(-53.4577 + 30.8638i) q^{67} -39.5232i q^{71} +35.0355 q^{73} +(36.0519 + 62.4437i) q^{77} +(-77.9605 - 45.0105i) q^{79} +(102.357 + 59.0957i) q^{83} +(80.5372 + 139.494i) q^{85} +14.4499 q^{89} -176.032i q^{91} +(49.4186 - 28.5318i) q^{95} +(67.5561 - 117.011i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} + 3 q^{7}+O(q^{10}) $ 8 * q + 3 * q^5 + 3 * q^7	$ 8 q + 3 q^{5} + 3 q^{7} + 18 q^{11} - 5 q^{13} - 6 q^{17} + 81 q^{23} - 23 q^{25} + 69 q^{29} + 45 q^{31} + 20 q^{37} - 54 q^{41} - 207 q^{47} + 41 q^{49} - 252 q^{53} - 306 q^{59} - 7 q^{61} - 93 q^{65} - 12 q^{67} + 74 q^{73} + 207 q^{77} + 33 q^{79} + 549 q^{83} + 30 q^{85} + 168 q^{89} + 684 q^{95} - 10 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 + 3 * q^7 + 18 * q^11 - 5 * q^13 - 6 * q^17 + 81 * q^23 - 23 * q^25 + 69 * q^29 + 45 * q^31 + 20 * q^37 - 54 * q^41 - 207 * q^47 + 41 * q^49 - 252 * q^53 - 306 * q^59 - 7 * q^61 - 93 * q^65 - 12 * q^67 + 74 * q^73 + 207 * q^77 + 33 * q^79 + 549 * q^83 + 30 * q^85 + 168 * q^89 + 684 * q^95 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.01729	−	5.22611i	−0.603459	−	1.04522i	−0.992293	−	0.123914i	$-0.960455\pi$
$5$	−3.01729	−	5.22611i	−0.603459	−	1.04522i	0.388834	−	0.921308i	$-0.372878\pi$
$6$		0			0
$7$	10.2332	+	5.90815i	1.46189	+	0.844021i	0.999099	−	0.0424471i	$-0.0135154\pi$
$7$	10.2332	+	5.90815i	1.46189	+	0.844021i	0.462789	+	0.886468i	$0.346849\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.28454	+	3.05103i	0.480413	+	0.277366i	0.720588	−	0.693363i	$-0.243872\pi$
$11$	5.28454	+	3.05103i	0.480413	+	0.277366i	−0.240176	+	0.970729i	$0.577205\pi$
$12$		0			0
$13$	−7.44868	−	12.9015i	−0.572975	−	0.992422i	−0.996258	−	0.0864245i	$-0.972456\pi$
$13$	−7.44868	−	12.9015i	−0.572975	−	0.992422i	0.423283	−	0.905997i	$-0.360877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−26.6919			−1.57011			−0.785055	−	0.619427i	$-0.787365\pi$
$17$	−26.6919			−1.57011			−0.785055	+	0.619427i	$0.787365\pi$
$18$		0			0
$19$			9.45610i			0.497689i	0.968543	+	0.248845i	$0.0800509\pi$
$19$			9.45610i			0.497689i	−0.968543	+	0.248845i	$0.919949\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	17.2673	−	9.96931i	0.750754	−	0.433448i	−0.0752122	−	0.997168i	$-0.523963\pi$
$23$	17.2673	−	9.96931i	0.750754	−	0.433448i	0.825966	+	0.563719i	$0.190630\pi$
$24$		0			0
$25$	−5.70813	+	9.88677i	−0.228325	+	0.395471i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	22.3114	−	38.6445i	0.769360	−	1.33257i	−0.168551	−	0.985693i	$-0.553909\pi$
$29$	22.3114	−	38.6445i	0.769360	−	1.33257i	0.937910	−	0.346877i	$-0.112758\pi$
$30$		0			0
$31$	5.42359	−	3.13131i	0.174955	−	0.101010i	−0.409965	−	0.912101i	$-0.634459\pi$
$31$	5.42359	−	3.13131i	0.174955	−	0.101010i	0.584920	+	0.811091i	$0.301126\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	71.3065i		−	2.03733i
$36$		0			0
$37$	6.65707			0.179921			0.0899604	−	0.995945i	$-0.471326\pi$
$37$	6.65707			0.179921			0.0899604	+	0.995945i	$0.471326\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.82853	−	15.2915i	−0.215330	−	0.372963i	0.738045	−	0.674752i	$-0.235749\pi$
$41$	−8.82853	−	15.2915i	−0.215330	−	0.372963i	−0.953375	+	0.301789i	$0.902416\pi$
$42$		0			0
$43$	−20.2696	−	11.7027i	−0.471386	−	0.272155i	0.245433	−	0.969413i	$-0.421070\pi$
$43$	−20.2696	−	11.7027i	−0.471386	−	0.272155i	−0.716820	+	0.697258i	$0.754403\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	36.4261	+	21.0306i	0.775023	+	0.447460i	0.834664	−	0.550760i	$-0.185662\pi$
$47$	36.4261	+	21.0306i	0.775023	+	0.447460i	−0.0596404	+	0.998220i	$0.518995\pi$
$48$		0			0
$49$	45.3125	+	78.4835i	0.924744	+	1.60170i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−51.6192			−0.973948			−0.486974	−	0.873416i	$-0.661899\pi$
$53$	−51.6192			−0.973948			−0.486974	+	0.873416i	$0.661899\pi$
$54$		0			0
$55$		−	36.8234i		−	0.669517i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−32.9024	+	18.9962i	−0.557668	+	0.321970i	−0.752209	−	0.658925i	$-0.771012\pi$
$59$	−32.9024	+	18.9962i	−0.557668	+	0.321970i	0.194541	+	0.980894i	$0.437678\pi$
$60$		0			0
$61$	45.3815	−	78.6031i	0.743960	−	1.28858i	−0.206720	−	0.978400i	$-0.566279\pi$
$61$	45.3815	−	78.6031i	0.743960	−	1.28858i	0.950679	−	0.310176i	$-0.100388\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−44.9497	+	77.8552i	−0.691534	+	1.19777i
$66$		0			0
$67$	−53.4577	+	30.8638i	−0.797876	+	0.460654i	−0.842728	−	0.538340i	$-0.819052\pi$
$67$	−53.4577	+	30.8638i	−0.797876	+	0.460654i	0.0448520	+	0.998994i	$0.485718\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	39.5232i		−	0.556665i	−0.960485	−	0.278333i	$-0.910218\pi$
$71$		−	39.5232i		−	0.556665i	0.960485	−	0.278333i	$-0.0897817\pi$
$72$		0			0
$73$	35.0355			0.479938			0.239969	−	0.970780i	$-0.422863\pi$
$73$	35.0355			0.479938			0.239969	+	0.970780i	$0.422863\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	36.0519	+	62.4437i	0.468206	+	0.810957i
$78$		0			0
$79$	−77.9605	−	45.0105i	−0.986842	−	0.569753i	−0.0825131	−	0.996590i	$-0.526295\pi$
$79$	−77.9605	−	45.0105i	−0.986842	−	0.569753i	−0.904329	+	0.426837i	$0.859628\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	102.357	+	59.0957i	1.23321	+	0.711996i	0.967698	−	0.252111i	$-0.0811247\pi$
$83$	102.357	+	59.0957i	1.23321	+	0.711996i	0.265515	+	0.964107i	$0.414458\pi$
$84$		0			0
$85$	80.5372	+	139.494i	0.947496	+	1.64111i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	14.4499			0.162359			0.0811794	−	0.996700i	$-0.474131\pi$
$89$	14.4499			0.162359			0.0811794	+	0.996700i	$0.474131\pi$
$90$		0			0
$91$		−	176.032i		−	1.93441i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	49.4186	−	28.5318i	0.520196	−	0.300335i
$96$		0			0
$97$	67.5561	−	117.011i	0.696455	−	1.20629i	−0.273233	−	0.961948i	$-0.588093\pi$
$97$	67.5561	−	117.011i	0.696455	−	1.20629i	0.969688	−	0.244347i	$-0.0785736\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.7439	+	20.3411i	−0.116277	+	0.201397i	−0.918289	−	0.395910i	$-0.870429\pi$
$101$	−11.7439	+	20.3411i	−0.116277	+	0.201397i	0.802013	+	0.597307i	$0.203763\pi$
$102$		0			0
$103$	−27.2852	+	15.7531i	−0.264905	+	0.152943i	−0.626570	−	0.779365i	$-0.715542\pi$
$103$	−27.2852	+	15.7531i	−0.264905	+	0.152943i	0.361665	+	0.932308i	$0.382208\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	208.386i		−	1.94753i	−0.227558	−	0.973765i	$-0.573074\pi$
$107$		−	208.386i		−	1.94753i	0.227558	−	0.973765i	$-0.426926\pi$
$108$		0			0
$109$	−64.5228			−0.591952			−0.295976	−	0.955195i	$-0.595645\pi$
$109$	−64.5228			−0.591952			−0.295976	+	0.955195i	$0.595645\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.79115	−	3.10236i	−0.0158509	−	0.0274545i	0.857991	−	0.513664i	$-0.171712\pi$
$113$	−1.79115	−	3.10236i	−0.0158509	−	0.0274545i	−0.873842	+	0.486210i	$0.838379\pi$
$114$		0			0
$115$	−104.201	−	60.1607i	−0.906098	−	0.523136i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−273.143	−	157.699i	−2.29532	−	1.32521i
$120$		0			0
$121$	−41.8824	−	72.5425i	−0.346136	−	0.599525i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−81.9723			−0.655778
$126$		0			0
$127$		−	92.5083i		−	0.728412i	−0.931319	−	0.364206i	$-0.881340\pi$
$127$		−	92.5083i		−	0.728412i	0.931319	−	0.364206i	$-0.118660\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−105.265	+	60.7749i	−0.803552	+	0.463931i	−0.844712	−	0.535222i	$-0.820228\pi$
$131$	−105.265	+	60.7749i	−0.803552	+	0.463931i	0.0411598	+	0.999153i	$0.486895\pi$
$132$		0			0
$133$	−55.8680	+	96.7663i	−0.420060	+	0.727566i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	128.420	−	222.430i	0.937372	−	1.62358i	0.167024	−	0.985953i	$-0.446584\pi$
$137$	128.420	−	222.430i	0.937372	−	1.62358i	0.770348	−	0.637623i	$-0.220082\pi$
$138$		0			0
$139$	111.156	−	64.1761i	0.799685	−	0.461698i	−0.0436761	−	0.999046i	$-0.513907\pi$
$139$	111.156	−	64.1761i	0.799685	−	0.461698i	0.843361	+	0.537348i	$0.180574\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	90.9045i		−	0.635696i
$144$		0			0
$145$	−269.281			−1.85711
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.8586	+	18.8076i	0.0728762	+	0.126225i	0.900161	−	0.435558i	$-0.143449\pi$
$149$	10.8586	+	18.8076i	0.0728762	+	0.126225i	−0.827285	+	0.561783i	$0.810116\pi$
$150$		0			0
$151$	−242.937	−	140.260i	−1.60886	−	0.928874i	−0.989626	−	0.143665i	$-0.954111\pi$
$151$	−242.937	−	140.260i	−1.60886	−	0.928874i	−0.619230	−	0.785209i	$-0.712555\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−32.7291	−	18.8962i	−0.211156	−	0.121911i
$156$		0			0
$157$	−52.5346	−	90.9926i	−0.334615	−	0.579571i	0.648796	−	0.760963i	$-0.275273\pi$
$157$	−52.5346	−	90.9926i	−0.334615	−	0.579571i	−0.983411	+	0.181392i	$0.941940\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	235.601			1.46336
$162$		0			0
$163$			145.690i			0.893804i	0.894583	+	0.446902i	$0.147473\pi$
$163$			145.690i			0.893804i	−0.894583	+	0.446902i	$0.852527\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	212.778	−	122.847i	1.27412	−	0.735613i	0.298359	−	0.954454i	$-0.403561\pi$
$167$	212.778	−	122.847i	1.27412	−	0.735613i	0.975761	+	0.218840i	$0.0702274\pi$
$168$		0			0
$169$	−26.4655	+	45.8396i	−0.156601	+	0.271241i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	21.9101	−	37.9494i	0.126648	−	0.219361i	−0.795728	−	0.605654i	$-0.792911\pi$
$173$	21.9101	−	37.9494i	0.126648	−	0.219361i	0.922376	+	0.386294i	$0.126245\pi$
$174$		0			0
$175$	−116.825	+	67.4490i	−0.667572	+	0.385423i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	57.0637i		−	0.318791i	−0.987215	−	0.159396i	$-0.949045\pi$
$179$		−	57.0637i		−	0.318791i	0.987215	−	0.159396i	$-0.0509546\pi$
$180$		0			0
$181$	−92.7281			−0.512310			−0.256155	−	0.966636i	$-0.582456\pi$
$181$	−92.7281			−0.512310			−0.256155	+	0.966636i	$0.582456\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−20.0863	−	34.7905i	−0.108575	−	0.188057i
$186$		0			0
$187$	−141.054	−	81.4377i	−0.754300	−	0.435495i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	77.4667	+	44.7254i	0.405585	+	0.234164i	0.688891	−	0.724865i	$-0.258098\pi$
$191$	77.4667	+	44.7254i	0.405585	+	0.234164i	−0.283306	+	0.959030i	$0.591431\pi$
$192$		0			0
$193$	−115.213	−	199.555i	−0.596959	−	1.03396i	−0.993267	−	0.115846i	$-0.963042\pi$
$193$	−115.213	−	199.555i	−0.596959	−	1.03396i	0.396308	−	0.918118i	$-0.370291\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−95.9308			−0.486958			−0.243479	−	0.969906i	$-0.578289\pi$
$197$	−95.9308			−0.486958			−0.243479	+	0.969906i	$0.578289\pi$
$198$		0			0
$199$		−	50.1566i		−	0.252043i	−0.992028	−	0.126021i	$-0.959779\pi$
$199$		−	50.1566i		−	0.252043i	0.992028	−	0.126021i	$-0.0402208\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	456.635	−	263.639i	2.24944	−	1.29871i
$204$		0			0
$205$	−53.2766	+	92.2777i	−0.259886	+	0.450135i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−28.8508	+	49.9711i	−0.138042	+	0.239096i
$210$		0			0
$211$	2.28029	−	1.31653i	0.0108071	−	0.00623946i	−0.494587	−	0.869128i	$-0.664681\pi$
$211$	2.28029	−	1.31653i	0.0108071	−	0.00623946i	0.505394	+	0.862889i	$0.331347\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			141.242i			0.656938i
$216$		0			0
$217$	74.0010			0.341019
$218$		0			0
$219$		0			0
$220$		0			0
$221$	198.819	+	344.365i	0.899633	+	1.55821i
$222$		0			0
$223$	152.757	+	88.1940i	0.685007	+	0.395489i	0.801739	−	0.597675i	$-0.203909\pi$
$223$	152.757	+	88.1940i	0.685007	+	0.395489i	−0.116732	+	0.993163i	$0.537242\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.85772	−	1.07256i	−0.00818380	−	0.00472492i	0.495903	−	0.868378i	$-0.334837\pi$
$227$	−1.85772	−	1.07256i	−0.00818380	−	0.00472492i	−0.504086	+	0.863653i	$0.668171\pi$
$228$		0			0
$229$	−63.6447	−	110.236i	−0.277925	−	0.481379i	0.692944	−	0.720991i	$-0.256313\pi$
$229$	−63.6447	−	110.236i	−0.277925	−	0.481379i	−0.970869	+	0.239612i	$0.922980\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−262.526			−1.12672			−0.563360	−	0.826211i	$-0.690492\pi$
$233$	−262.526			−1.12672			−0.563360	+	0.826211i	$0.690492\pi$
$234$		0			0
$235$		−	253.822i		−	1.08009i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	270.558	−	156.207i	1.13204	−	0.653584i	0.187594	−	0.982247i	$-0.439931\pi$
$239$	270.558	−	156.207i	1.13204	−	0.653584i	0.944447	+	0.328662i	$0.106598\pi$
$240$		0			0
$241$	−14.7110	+	25.4801i	−0.0610413	+	0.105727i	−0.894931	−	0.446204i	$-0.852775\pi$
$241$	−14.7110	+	25.4801i	−0.0610413	+	0.105727i	0.833890	+	0.551931i	$0.186109\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	273.442	−	473.616i	1.11609	−	1.93312i
$246$		0			0
$247$	121.998	−	70.4354i	0.493918	−	0.285164i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			195.326i			0.778192i	0.921197	+	0.389096i	$0.127213\pi$
$251$			195.326i			0.778192i	−0.921197	+	0.389096i	$0.872787\pi$
$252$		0			0
$253$	121.667			0.480896
$254$		0			0
$255$		0			0
$256$		0			0
$257$	218.673	+	378.753i	0.850867	+	1.47375i	0.880427	+	0.474182i	$0.157256\pi$
$257$	218.673	+	378.753i	0.850867	+	1.47375i	−0.0295596	+	0.999563i	$0.509410\pi$
$258$		0			0
$259$	68.1232	+	39.3310i	0.263024	+	0.151857i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−64.8138	−	37.4203i	−0.246440	−	0.142282i	0.371693	−	0.928356i	$-0.378777\pi$
$263$	−64.8138	−	37.4203i	−0.246440	−	0.142282i	−0.618133	+	0.786073i	$0.712111\pi$
$264$		0			0
$265$	155.750	+	269.768i	0.587738	+	1.01799i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	40.6759			0.151212			0.0756058	−	0.997138i	$-0.475911\pi$
$269$	40.6759			0.151212			0.0756058	+	0.997138i	$0.475911\pi$
$270$		0			0
$271$		−	130.442i		−	0.481337i	−0.970607	−	0.240668i	$-0.922633\pi$
$271$		−	130.442i		−	0.481337i	0.970607	−	0.240668i	$-0.0773666\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−60.3297	+	34.8314i	−0.219381	+	0.126659i
$276$		0			0
$277$	114.408	−	198.160i	0.413025	−	0.715379i	−0.582194	−	0.813050i	$-0.697806\pi$
$277$	114.408	−	198.160i	0.413025	−	0.715379i	0.995219	+	0.0976702i	$0.0311390\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−23.9532	+	41.4882i	−0.0852429	+	0.147645i	−0.905495	−	0.424358i	$-0.860500\pi$
$281$	−23.9532	+	41.4882i	−0.0852429	+	0.147645i	0.820252	+	0.572003i	$0.193833\pi$
$282$		0			0
$283$	−307.250	+	177.391i	−1.08569	+	0.626824i	−0.932426	−	0.361361i	$-0.882312\pi$
$283$	−307.250	+	177.391i	−1.08569	+	0.626824i	−0.153265	+	0.988185i	$0.548979\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	208.641i		−	0.726973i
$288$		0			0
$289$	423.455			1.46524
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−27.9478	−	48.4071i	−0.0953851	−	0.165212i	0.814384	−	0.580326i	$-0.197075\pi$
$293$	−27.9478	−	48.4071i	−0.0953851	−	0.165212i	−0.909769	+	0.415114i	$0.863742\pi$
$294$		0			0
$295$	198.552	+	114.634i	0.673059	+	0.388591i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−257.238	−	148.516i	−0.860327	−	0.496710i
$300$		0			0
$301$	−138.282	−	239.512i	−0.459409	−	0.795720i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−547.718			−1.79580
$306$		0			0
$307$		−	57.3939i		−	0.186951i	−0.995622	−	0.0934754i	$-0.970202\pi$
$307$		−	57.3939i		−	0.186951i	0.995622	−	0.0934754i	$-0.0297976\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−215.498	+	124.418i	−0.692920	+	0.400058i	−0.804705	−	0.593675i	$-0.797677\pi$
$311$	−215.498	+	124.418i	−0.692920	+	0.400058i	0.111785	+	0.993732i	$0.464343\pi$
$312$		0			0
$313$	−307.856	+	533.222i	−0.983565	+	1.70358i	−0.335417	+	0.942070i	$0.608877\pi$
$313$	−307.856	+	533.222i	−0.983565	+	1.70358i	−0.648147	+	0.761515i	$0.724456\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−128.314	+	222.246i	−0.404775	+	0.701090i	−0.994295	−	0.106663i	$-0.965983\pi$
$317$	−128.314	+	222.246i	−0.404775	+	0.701090i	0.589521	+	0.807753i	$0.299317\pi$
$318$		0			0
$319$	235.811	−	136.146i	0.739220	−	0.426789i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	252.401i		−	0.781427i
$324$		0			0
$325$	170.072			0.523299
$326$		0			0
$327$		0			0
$328$		0			0
$329$	248.504	+	430.422i	0.755331	+	1.30827i
$330$		0			0
$331$	125.743	+	72.5978i	0.379889	+	0.219329i	0.677770	−	0.735274i	$-0.262947\pi$
$331$	125.743	+	72.5978i	0.379889	+	0.219329i	−0.297881	+	0.954603i	$0.596280\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	322.595	+	186.250i	0.962971	+	0.555971i
$336$		0			0
$337$	21.8136	+	37.7823i	0.0647288	+	0.112114i	0.896574	−	0.442895i	$-0.146048\pi$
$337$	21.8136	+	37.7823i	0.0647288	+	0.112114i	−0.831845	+	0.555008i	$0.812715\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	38.2149			0.112067
$342$		0			0
$343$			491.852i			1.43397i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	156.116	−	90.1337i	0.449902	−	0.259751i	−0.257887	−	0.966175i	$-0.583026\pi$
$347$	156.116	−	90.1337i	0.449902	−	0.259751i	0.707789	+	0.706424i	$0.249693\pi$
$348$		0			0
$349$	−46.5629	+	80.6493i	−0.133418	+	0.231087i	−0.924992	−	0.379987i	$-0.875929\pi$
$349$	−46.5629	+	80.6493i	−0.133418	+	0.231087i	0.791574	+	0.611073i	$0.209262\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	215.455	−	373.178i	0.610353	−	1.05716i	−0.380828	−	0.924646i	$-0.624361\pi$
$353$	215.455	−	373.178i	0.610353	−	1.05716i	0.991181	−	0.132516i	$-0.0423057\pi$
$354$		0			0
$355$	−206.553	+	119.253i	−0.581838	+	0.335925i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			316.054i			0.880374i	0.897906	+	0.440187i	$0.145088\pi$
$359$			316.054i			0.880374i	−0.897906	+	0.440187i	$0.854912\pi$
$360$		0			0
$361$	271.582			0.752305
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−105.712	−	183.099i	−0.289623	−	0.501642i
$366$		0			0
$367$	−453.751	−	261.973i	−1.23638	−	0.713824i	−0.268027	−	0.963411i	$-0.586372\pi$
$367$	−453.751	−	261.973i	−1.23638	−	0.713824i	−0.968352	+	0.249588i	$0.919705\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−528.231	−	304.974i	−1.42380	−	0.822033i
$372$		0			0
$373$	163.567	+	283.306i	0.438518	+	0.759535i	0.997575	−	0.0695940i	$-0.0221704\pi$
$373$	163.567	+	283.306i	0.438518	+	0.759535i	−0.559058	+	0.829129i	$0.688837\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−664.763			−1.76330
$378$		0			0
$379$			443.580i			1.17040i	0.810890	+	0.585198i	$0.198983\pi$
$379$			443.580i			1.17040i	−0.810890	+	0.585198i	$0.801017\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−393.008	+	226.903i	−1.02613	+	0.592436i	−0.915873	−	0.401467i	$-0.868500\pi$
$383$	−393.008	+	226.903i	−1.02613	+	0.592436i	−0.110256	+	0.993903i	$0.535167\pi$
$384$		0			0
$385$	217.558	−	376.822i	0.565086	−	0.978758i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	82.4361	−	142.783i	0.211918	−	0.367053i	−0.740397	−	0.672170i	$-0.765362\pi$
$389$	82.4361	−	142.783i	0.211918	−	0.367053i	0.952315	+	0.305117i	$0.0986957\pi$
$390$		0			0
$391$	−460.897	+	266.099i	−1.17877	+	0.680561i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			543.240i			1.37529i
$396$		0			0
$397$	395.775			0.996914			0.498457	−	0.866915i	$-0.333900\pi$
$397$	395.775			0.996914			0.498457	+	0.866915i	$0.333900\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−173.838	−	301.097i	−0.433512	−	0.750864i	0.563661	−	0.826006i	$-0.309392\pi$
$401$	−173.838	−	301.097i	−0.433512	−	0.750864i	−0.997173	+	0.0751418i	$0.976059\pi$
$402$		0			0
$403$	−80.7971	−	46.6483i	−0.200489	−	0.115752i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	35.1795	+	20.3109i	0.0864362	+	0.0499040i
$408$		0			0
$409$	−32.7989	−	56.8094i	−0.0801930	−	0.138898i	0.823140	−	0.567839i	$-0.192220\pi$
$409$	−32.7989	−	56.8094i	−0.0801930	−	0.138898i	−0.903333	+	0.428941i	$0.858887\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−448.930			−1.08700
$414$		0			0
$415$		−	713.236i		−	1.71864i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−595.923	+	344.056i	−1.42225	+	0.821137i	−0.996491	−	0.0836989i	$-0.973327\pi$
$419$	−595.923	+	344.056i	−1.42225	+	0.821137i	−0.425760	+	0.904836i	$0.639993\pi$
$420$		0			0
$421$	146.855	−	254.360i	0.348823	−	0.604180i	−0.637217	−	0.770684i	$-0.719915\pi$
$421$	146.855	−	254.360i	0.348823	−	0.604180i	0.986041	+	0.166504i	$0.0532480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	152.361	−	263.896i	0.358496	−	0.620932i
$426$		0			0
$427$	928.798	−	536.242i	2.17517	−	1.25584i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	555.264i		−	1.28832i	−0.764893	−	0.644158i	$-0.777208\pi$
$431$		−	555.264i		−	1.28832i	0.764893	−	0.644158i	$-0.222792\pi$
$432$		0			0
$433$	−559.107			−1.29124			−0.645620	−	0.763659i	$-0.723401\pi$
$433$	−559.107			−1.29124			−0.645620	+	0.763659i	$0.723401\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	94.2707	+	163.282i	0.215722	+	0.373642i
$438$		0			0
$439$	518.563	+	299.393i	1.18124	+	0.681988i	0.956301	−	0.292385i	$-0.0944490\pi$
$439$	518.563	+	299.393i	1.18124	+	0.681988i	0.224937	+	0.974373i	$0.427782\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	528.448	+	305.100i	1.19289	+	0.688713i	0.958960	−	0.283542i	$-0.0915094\pi$
$443$	528.448	+	305.100i	1.19289	+	0.688713i	0.233926	+	0.972254i	$0.424843\pi$
$444$		0			0
$445$	−43.5997	−	75.5169i	−0.0979768	−	0.169701i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	342.989			0.763896			0.381948	−	0.924184i	$-0.375253\pi$
$449$	342.989			0.763896			0.381948	+	0.924184i	$0.375253\pi$
$450$		0			0
$451$		−	107.744i		−	0.238901i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−919.960	+	531.139i	−2.02189	+	1.16734i
$456$		0			0
$457$	140.770	−	243.821i	0.308030	−	0.533524i	−0.669901	−	0.742450i	$-0.733663\pi$
$457$	140.770	−	243.821i	0.308030	−	0.533524i	0.977931	+	0.208926i	$0.0669968\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	49.0643	−	84.9819i	0.106430	−	0.184343i	−0.807891	−	0.589331i	$-0.799391\pi$
$461$	49.0643	−	84.9819i	0.106430	−	0.184343i	0.914322	+	0.404989i	$0.132725\pi$
$462$		0			0
$463$	625.293	−	361.013i	1.35052	−	0.779726i	0.362202	−	0.932100i	$-0.382025\pi$
$463$	625.293	−	361.013i	1.35052	−	0.779726i	0.988323	+	0.152374i	$0.0486918\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			723.722i			1.54972i	0.632130	+	0.774862i	$0.282181\pi$
$467$			723.722i			1.54972i	−0.632130	+	0.774862i	$0.717819\pi$
$468$		0			0
$469$	−729.392			−1.55521
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−71.4104	−	123.686i	−0.150973	−	0.261494i
$474$		0			0
$475$	−93.4903	−	53.9766i	−0.196822	−	0.113635i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	303.671	+	175.325i	0.633969	+	0.366022i	0.782288	−	0.622917i	$-0.214053\pi$
$479$	303.671	+	175.325i	0.633969	+	0.366022i	−0.148318	+	0.988940i	$0.547386\pi$
$480$		0			0
$481$	−49.5863	−	85.8861i	−0.103090	−	0.178557i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−815.347			−1.68113
$486$		0			0
$487$			693.565i			1.42416i	0.702099	+	0.712079i	$0.252246\pi$
$487$			693.565i			1.42416i	−0.702099	+	0.712079i	$0.747754\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	450.850	−	260.298i	0.918228	−	0.530139i	0.0351585	−	0.999382i	$-0.488806\pi$
$491$	450.850	−	260.298i	0.918228	−	0.530139i	0.883069	+	0.469243i	$0.155473\pi$
$492$		0			0
$493$	−595.534	+	1031.49i	−1.20798	+	2.09228i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	233.509	−	404.450i	0.469837	−	0.813782i
$498$		0			0
$499$	−359.858	+	207.764i	−0.721158	+	0.416361i	−0.815179	−	0.579209i	$-0.803361\pi$
$499$	−359.858	+	207.764i	−0.721158	+	0.416361i	0.0940208	+	0.995570i	$0.470028\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	153.470i		−	0.305109i	−0.988295	−	0.152555i	$-0.951250\pi$
$503$		−	153.470i		−	0.305109i	0.988295	−	0.152555i	$-0.0487500\pi$
$504$		0			0
$505$	141.740			0.280673
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−290.604	−	503.341i	−0.570932	−	0.988883i	−0.996471	−	0.0839427i	$-0.973249\pi$
$509$	−290.604	−	503.341i	−0.570932	−	0.988883i	0.425539	−	0.904940i	$-0.360085\pi$
$510$		0			0
$511$	358.526	+	206.995i	0.701616	+	0.405078i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	164.655	+	95.0635i	0.319718	+	0.184589i
$516$		0			0
$517$	128.330	+	222.274i	0.248221	+	0.429931i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	119.457			0.229284			0.114642	−	0.993407i	$-0.463428\pi$
$521$	119.457			0.229284			0.114642	+	0.993407i	$0.463428\pi$
$522$		0			0
$523$		−	291.527i		−	0.557413i	−0.960376	−	0.278706i	$-0.910094\pi$
$523$		−	291.527i		−	0.557413i	0.960376	−	0.278706i	$-0.0899056\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−144.766	+	83.5805i	−0.274698	+	0.158597i
$528$		0			0
$529$	−65.7259	+	113.841i	−0.124246	+	0.215200i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−131.522	+	227.802i	−0.246758	+	0.427397i
$534$		0			0
$535$	−1089.05	+	628.761i	−2.03560	+	1.17525i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			552.999i			1.02597i
$540$		0			0
$541$	918.712			1.69817			0.849087	−	0.528254i	$-0.177153\pi$
$541$	918.712			1.69817			0.849087	+	0.528254i	$0.177153\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	194.684	+	337.203i	0.357219	+	0.618721i
$546$		0			0
$547$	865.726	+	499.827i	1.58268	+	0.913761i	0.994466	+	0.105056i	$0.0335022\pi$
$547$	865.726	+	499.827i	1.58268	+	0.913761i	0.588214	+	0.808705i	$0.299831\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	365.427	+	210.979i	0.663206	+	0.382902i
$552$		0			0
$553$	−531.858	−	921.205i	−0.961768	−	1.66583i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	730.122			1.31081			0.655406	−	0.755277i	$-0.272497\pi$
$557$	730.122			1.31081			0.655406	+	0.755277i	$0.272497\pi$
$558$		0			0
$559$			348.678i			0.623752i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−335.889	+	193.926i	−0.596606	+	0.344451i	−0.767705	−	0.640803i	$-0.778601\pi$
$563$	−335.889	+	193.926i	−0.596606	+	0.344451i	0.171099	+	0.985254i	$0.445268\pi$
$564$		0			0
$565$	−10.8088	+	18.7215i	−0.0191307	+	0.0331353i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	278.389	−	482.184i	0.489260	−	0.847423i	−0.510664	−	0.859780i	$-0.670600\pi$
$569$	278.389	−	482.184i	0.489260	−	0.847423i	0.999924	+	0.0123576i	$0.00393366\pi$
$570$		0			0
$571$	−28.0470	+	16.1930i	−0.0491191	+	0.0283589i	−0.524358	−	0.851498i	$-0.675695\pi$
$571$	−28.0470	+	16.1930i	−0.0491191	+	0.0283589i	0.475239	+	0.879857i	$0.342361\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			227.624i			0.395869i
$576$		0			0
$577$	221.536			0.383945			0.191972	−	0.981400i	$-0.438512\pi$
$577$	221.536			0.383945			0.191972	+	0.981400i	$0.438512\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	698.292	+	1209.48i	1.20188	+	2.08172i
$582$		0			0
$583$	−272.784	−	157.492i	−0.467897	−	0.270140i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	653.747	+	377.441i	1.11371	+	0.643000i	0.939787	−	0.341759i	$-0.111023\pi$
$587$	653.747	+	377.441i	1.11371	+	0.643000i	0.173921	+	0.984760i	$0.444356\pi$
$588$		0			0
$589$	29.6100	+	51.2860i	0.0502716	+	0.0870730i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−697.420			−1.17609			−0.588044	−	0.808829i	$-0.700102\pi$
$593$	−697.420			−1.17609			−0.588044	+	0.808829i	$0.700102\pi$
$594$		0			0
$595$			1903.30i			3.19883i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−80.7777	+	46.6370i	−0.134854	+	0.0778581i	−0.565909	−	0.824467i	$-0.691475\pi$
$599$	−80.7777	+	46.6370i	−0.134854	+	0.0778581i	0.431055	+	0.902326i	$0.358141\pi$
$600$		0			0
$601$	215.014	−	372.414i	0.357760	−	0.619658i	−0.629827	−	0.776736i	$-0.716874\pi$
$601$	215.014	−	372.414i	0.357760	−	0.619658i	0.987586	+	0.157078i	$0.0502074\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−252.743	+	437.764i	−0.417757	+	0.723577i
$606$		0			0
$607$	474.182	−	273.769i	0.781189	−	0.451019i	−0.0556627	−	0.998450i	$-0.517727\pi$
$607$	474.182	−	273.769i	0.781189	−	0.451019i	0.836851	+	0.547430i	$0.184394\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	626.601i		−	1.02553i
$612$		0			0
$613$	6.42863			0.0104872			0.00524358	−	0.999986i	$-0.498331\pi$
$613$	6.42863			0.0104872			0.00524358	+	0.999986i	$0.498331\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	517.155	+	895.739i	0.838177	+	1.45177i	0.891417	+	0.453184i	$0.149712\pi$
$617$	517.155	+	895.739i	0.838177	+	1.45177i	−0.0532398	+	0.998582i	$0.516955\pi$
$618$		0			0
$619$	641.544	+	370.395i	1.03642	+	0.598377i	0.918817	−	0.394684i	$-0.129146\pi$
$619$	641.544	+	370.395i	1.03642	+	0.598377i	0.117602	+	0.993061i	$0.462479\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	147.869	+	85.3724i	0.237350	+	0.137034i
$624$		0			0
$625$	390.038	+	675.565i	0.624060	+	1.08090i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−177.689			−0.282495
$630$		0			0
$631$			693.165i			1.09852i	0.835652	+	0.549259i	$0.185090\pi$
$631$			693.165i			1.09852i	−0.835652	+	0.549259i	$0.814910\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−483.458	+	279.125i	−0.761351	+	0.439566i
$636$		0			0
$637$	675.036	−	1169.20i	1.05971	−	1.83547i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−115.145	+	199.438i	−0.179634	+	0.311135i	−0.941755	−	0.336299i	$-0.890825\pi$
$641$	−115.145	+	199.438i	−0.179634	+	0.311135i	0.762121	+	0.647434i	$0.224158\pi$
$642$		0			0
$643$	662.916	−	382.735i	1.03097	−	0.595233i	0.113710	−	0.993514i	$-0.463726\pi$
$643$	662.916	−	382.735i	1.03097	−	0.595233i	0.917263	+	0.398281i	$0.130393\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			339.078i			0.524078i	0.965057	+	0.262039i	$0.0843949\pi$
$647$			339.078i			0.524078i	−0.965057	+	0.262039i	$0.915605\pi$
$648$		0			0
$649$	−231.832			−0.357214
$650$		0			0
$651$		0			0
$652$		0			0
$653$	73.8243	+	127.867i	0.113054	+	0.195815i	0.917000	−	0.398887i	$-0.130603\pi$
$653$	73.8243	+	127.867i	0.113054	+	0.195815i	−0.803946	+	0.594702i	$0.797270\pi$
$654$		0			0
$655$	635.233	+	366.752i	0.969821	+	0.559926i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−795.428	−	459.241i	−1.20702	−	0.696875i	−0.244915	−	0.969544i	$-0.578760\pi$
$659$	−795.428	−	459.241i	−1.20702	−	0.696875i	−0.962108	+	0.272669i	$0.912094\pi$
$660$		0			0
$661$	103.150	+	178.662i	0.156052	+	0.270290i	0.933442	−	0.358729i	$-0.116790\pi$
$661$	103.150	+	178.662i	0.156052	+	0.270290i	−0.777389	+	0.629020i	$0.783457\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	674.281			1.01396
$666$		0			0
$667$		−	889.718i		−	1.33391i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	479.641	−	276.921i	0.714815	−	0.412699i
$672$		0			0
$673$	−333.272	+	577.245i	−0.495204	+	0.857719i	−0.999985	−	0.00552878i	$-0.998240\pi$
$673$	−333.272	+	577.245i	−0.495204	+	0.857719i	0.504780	+	0.863248i	$0.331573\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	235.497	−	407.893i	0.347854	−	0.602500i	−0.638014	−	0.770025i	$-0.720244\pi$
$677$	235.497	−	407.893i	0.347854	−	0.602500i	0.985868	+	0.167524i	$0.0535773\pi$
$678$		0			0
$679$	1382.63	−	798.263i	2.03628	−	1.17565i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	909.494i		−	1.33162i	−0.746123	−	0.665808i	$-0.768087\pi$
$683$		−	909.494i		−	1.33162i	0.746123	−	0.665808i	$-0.231913\pi$
$684$		0			0
$685$	−1549.92			−2.26266
$686$		0			0
$687$		0			0
$688$		0			0
$689$	384.495	+	665.965i	0.558048	+	0.966567i
$690$		0			0
$691$	366.787	+	211.764i	0.530805	+	0.306461i	0.741344	−	0.671125i	$-0.234189\pi$
$691$	366.787	+	211.764i	0.530805	+	0.306461i	−0.210539	+	0.977585i	$0.567522\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−670.782	−	387.276i	−0.965154	−	0.557232i
$696$		0			0
$697$	235.650	+	408.158i	0.338092	+	0.585592i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−66.5738			−0.0949697			−0.0474849	−	0.998872i	$-0.515121\pi$
$701$	−66.5738			−0.0949697			−0.0474849	+	0.998872i	$0.515121\pi$
$702$		0			0
$703$			62.9499i			0.0895446i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−240.356	+	138.770i	−0.339967	+	0.196280i
$708$		0			0
$709$	48.3932	−	83.8194i	0.0682555	−	0.118222i	−0.829878	−	0.557945i	$-0.811590\pi$
$709$	48.3932	−	83.8194i	0.0682555	−	0.118222i	0.898133	+	0.439723i	$0.144923\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	62.4340	−	108.139i	0.0875652	−	0.151667i
$714$		0			0
$715$	−475.077	+	274.286i	−0.664443	+	0.383616i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			1184.39i			1.64727i	0.567120	+	0.823635i	$0.308058\pi$
$719$			1184.39i			1.64727i	−0.567120	+	0.823635i	$0.691942\pi$
$720$		0			0
$721$	−372.287			−0.516348
$722$		0			0
$723$		0			0
$724$		0			0
$725$	254.713	+	441.176i	0.351329	+	0.608519i
$726$		0			0
$727$	687.700	+	397.044i	0.945942	+	0.546140i	0.891818	−	0.452394i	$-0.149430\pi$
$727$	687.700	+	397.044i	0.945942	+	0.546140i	0.0541243	+	0.998534i	$0.482763\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	541.034	+	312.366i	0.740128	+	0.427313i
$732$		0			0
$733$	64.4932	+	111.706i	0.0879853	+	0.152395i	0.906659	−	0.421863i	$-0.138624\pi$
$733$	64.4932	+	111.706i	0.0879853	+	0.152395i	−0.818674	+	0.574258i	$0.805290\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−376.666			−0.511080
$738$		0			0
$739$			17.7228i			0.0239822i	0.999928	+	0.0119911i	$0.00381697\pi$
$739$			17.7228i			0.0239822i	−0.999928	+	0.0119911i	$0.996183\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−39.9367	+	23.0575i	−0.0537507	+	0.0310330i	−0.526635	−	0.850092i	$-0.676546\pi$
$743$	−39.9367	+	23.0575i	−0.0537507	+	0.0310330i	0.472884	+	0.881125i	$0.343213\pi$
$744$		0			0
$745$	65.5269	−	113.496i	0.0879556	−	0.152343i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1231.17	−	2132.45i	1.64376	−	2.84707i
$750$		0			0
$751$	−205.122	+	118.427i	−0.273132	+	0.157693i	−0.630310	−	0.776343i	$-0.717072\pi$
$751$	−205.122	+	118.427i	−0.273132	+	0.157693i	0.357178	+	0.934036i	$0.383739\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1692.82i			2.24215i
$756$		0			0
$757$	−193.736			−0.255925			−0.127963	−	0.991779i	$-0.540844\pi$
$757$	−193.736			−0.255925			−0.127963	+	0.991779i	$0.540844\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	41.0648	+	71.1263i	0.0539616	+	0.0934642i	0.891744	−	0.452539i	$-0.149482\pi$
$761$	41.0648	+	71.1263i	0.0539616	+	0.0934642i	−0.837783	+	0.546004i	$0.816148\pi$
$762$		0			0
$763$	−660.276	−	381.210i	−0.865368	−	0.499620i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	490.159	+	282.993i	0.639060	+	0.368961i
$768$		0			0
$769$	659.227	+	1141.82i	0.857253	+	1.48481i	0.874539	+	0.484955i	$0.161164\pi$
$769$	659.227	+	1141.82i	0.857253	+	1.48481i	−0.0172867	+	0.999851i	$0.505503\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.74554			−0.00225814			−0.00112907	−	0.999999i	$-0.500359\pi$
$773$	−1.74554			−0.00225814			−0.00112907	+	0.999999i	$0.500359\pi$
$774$		0			0
$775$			71.4958i			0.0922526i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	144.598	−	83.4835i	0.185620	−	0.107167i
$780$		0			0
$781$	120.587	−	208.862i	0.154400	−	0.267429i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−317.025	+	549.103i	−0.403853	+	0.699494i
$786$		0			0
$787$	−1026.21	+	592.484i	−1.30395	+	0.752838i	−0.981080	−	0.193603i	$-0.937983\pi$
$787$	−1026.21	+	592.484i	−1.30395	+	0.752838i	−0.322875	+	0.946442i	$0.604649\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	42.3295i		−	0.0535139i
$792$		0			0
$793$	−1352.13			−1.70508
$794$		0			0
$795$		0			0
$796$		0			0
$797$	243.421	+	421.617i	0.305421	+	0.529005i	0.977355	−	0.211606i	$-0.0678695\pi$
$797$	243.421	+	421.617i	0.305421	+	0.529005i	−0.671934	+	0.740611i	$0.734536\pi$
$798$		0			0
$799$	−972.280	−	561.346i	−1.21687	−	0.702561i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	185.147	+	106.894i	0.230569	+	0.133119i
$804$		0			0
$805$	−710.876	−	1231.27i	−0.883076	−	1.52953i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1104.99			−1.36587			−0.682936	−	0.730478i	$-0.739297\pi$
$809$	−1104.99			−1.36587			−0.682936	+	0.730478i	$0.739297\pi$
$810$		0			0
$811$			321.548i			0.396483i	0.980153	+	0.198241i	$0.0635230\pi$
$811$			321.548i			0.396483i	−0.980153	+	0.198241i	$0.936477\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	761.392	−	439.590i	0.934224	−	0.539374i
$816$		0			0
$817$	110.662	−	191.671i	0.135449	−	0.234604i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	397.311	−	688.163i	0.483936	−	0.838201i	−0.515894	−	0.856652i	$-0.672540\pi$
$821$	397.311	−	688.163i	0.483936	−	0.838201i	0.999830	+	0.0184511i	$0.00587351\pi$
$822$		0			0
$823$	−1020.29	+	589.063i	−1.23972	+	0.715750i	−0.969036	−	0.246919i	$-0.920582\pi$
$823$	−1020.29	+	589.063i	−1.23972	+	0.715750i	−0.270680	+	0.962669i	$0.587249\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	722.570i		−	0.873725i	−0.899528	−	0.436862i	$-0.856090\pi$
$827$		−	722.570i		−	0.873725i	0.899528	−	0.436862i	$-0.143910\pi$
$828$		0			0
$829$	−1435.00			−1.73100			−0.865501	−	0.500906i	$-0.833000\pi$
$829$	−1435.00			−1.73100			−0.865501	+	0.500906i	$0.833000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1209.47	−	2094.87i	−1.45195	−	2.51485i
$834$		0			0
$835$	−1284.03	−	741.334i	−1.53776	−	0.887825i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−510.234	−	294.584i	−0.608145	−	0.351113i	0.164094	−	0.986445i	$-0.447530\pi$
$839$	−510.234	−	294.584i	−0.608145	−	0.351113i	−0.772239	+	0.635332i	$0.780863\pi$
$840$		0			0
$841$	−575.101	−	996.103i	−0.683829	−	1.18443i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	319.417			0.378009
$846$		0			0
$847$		−	989.791i		−	1.16858i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	114.950	−	66.3663i	0.135076	−	0.0779863i
$852$		0			0
$853$	158.954	−	275.316i	0.186347	−	0.322762i	−0.757683	−	0.652623i	$-0.773669\pi$
$853$	158.954	−	275.316i	0.186347	−	0.322762i	0.944029	+	0.329861i	$0.107002\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−270.238	+	468.066i	−0.315330	+	0.546168i	−0.979508	−	0.201407i	$-0.935449\pi$
$857$	−270.238	+	468.066i	−0.315330	+	0.546168i	0.664177	+	0.747575i	$0.268782\pi$
$858$		0			0
$859$	878.889	−	507.427i	1.02315	−	0.590718i	0.108138	−	0.994136i	$-0.465511\pi$
$859$	878.889	−	507.427i	1.02315	−	0.590718i	0.915016	+	0.403418i	$0.132178\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			894.091i			1.03603i	0.855373	+	0.518013i	$0.173328\pi$
$863$			894.091i			1.03603i	−0.855373	+	0.518013i	$0.826672\pi$
$864$		0			0
$865$	−264.437			−0.305707
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−274.657	−	475.720i	−0.316061	−	0.547434i
$870$		0			0
$871$	796.378	+	459.789i	0.914326	+	0.527886i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−838.840	−	484.304i	−0.958674	−	0.553491i
$876$		0			0
$877$	354.879	+	614.669i	0.404652	+	0.700877i	0.994281	−	0.106797i	$-0.0340595\pi$
$877$	354.879	+	614.669i	0.404652	+	0.700877i	−0.589629	+	0.807674i	$0.700726\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1318.63			1.49674			0.748371	−	0.663281i	$-0.230837\pi$
$881$	1318.63			1.49674			0.748371	+	0.663281i	$0.230837\pi$
$882$		0			0
$883$		−	1035.56i		−	1.17277i	−0.810032	−	0.586386i	$-0.800550\pi$
$883$		−	1035.56i		−	1.17277i	0.810032	−	0.586386i	$-0.199450\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−721.263	+	416.421i	−0.813149	+	0.469472i	−0.848048	−	0.529919i	$-0.822222\pi$
$887$	−721.263	+	416.421i	−0.813149	+	0.469472i	0.0348996	+	0.999391i	$0.488889\pi$
$888$		0			0
$889$	546.553	−	946.657i	0.614795	−	1.06486i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−198.868	+	344.449i	−0.222696	+	0.385721i
$894$		0			0
$895$	−298.221	+	172.178i	−0.333208	+	0.192377i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	279.456i		−	0.310852i
$900$		0			0
$901$	1377.81			1.52920
$902$		0			0
$903$		0			0
$904$		0			0
$905$	279.788	+	484.607i	0.309158	+	0.535477i
$906$		0			0
$907$	−8.59611	−	4.96297i	−0.00947752	−	0.00547185i	0.495254	−	0.868748i	$-0.335075\pi$
$907$	−8.59611	−	4.96297i	−0.00947752	−	0.00547185i	−0.504731	+	0.863277i	$0.668408\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1444.63	−	834.057i	−1.58576	−	0.915540i	−0.993994	−	0.109431i	$-0.965097\pi$
$911$	−1444.63	−	834.057i	−1.58576	−	0.915540i	−0.591767	−	0.806109i	$-0.701569\pi$
$912$		0			0
$913$	360.605	+	624.587i	0.394968	+	0.684104i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1436.27			−1.56627
$918$		0			0
$919$		−	1787.42i		−	1.94496i	−0.232988	−	0.972480i	$-0.574850\pi$
$919$		−	1787.42i		−	1.94496i	0.232988	−	0.972480i	$-0.425150\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−509.908	+	294.396i	−0.552447	+	0.318955i
$924$		0			0
$925$	−37.9994	+	65.8169i	−0.0410804	+	0.0711534i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−359.857	+	623.291i	−0.387360	+	0.670926i	−0.992093	−	0.125501i	$-0.959946\pi$
$929$	−359.857	+	623.291i	−0.387360	+	0.670926i	0.604734	+	0.796428i	$0.293279\pi$
$930$		0			0
$931$	−742.147	+	428.479i	−0.797151	+	0.460235i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			982.886i			1.05121i
$936$		0			0
$937$	1352.51			1.44345			0.721724	−	0.692181i	$-0.243350\pi$
$937$	1352.51			1.44345			0.721724	+	0.692181i	$0.243350\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−755.908	−	1309.27i	−0.803303	−	1.39136i	−0.917431	−	0.397896i	$-0.869741\pi$
$941$	−755.908	−	1309.27i	−0.803303	−	1.39136i	0.114127	−	0.993466i	$-0.463593\pi$
$942$		0			0
$943$	−304.891	−	176.029i	−0.323320	−	0.186669i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−733.423	−	423.442i	−0.774470	−	0.447140i	0.0599968	−	0.998199i	$-0.480891\pi$
$947$	−733.423	−	423.442i	−0.774470	−	0.447140i	−0.834467	+	0.551058i	$0.814224\pi$
$948$		0			0
$949$	−260.968	−	452.010i	−0.274993	−	0.476301i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	198.475			0.208263			0.104131	−	0.994564i	$-0.466794\pi$
$953$	198.475			0.208263			0.104131	+	0.994564i	$0.466794\pi$
$954$		0			0
$955$		−	539.799i		−	0.565234i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2628.30	−	1517.45i	2.74067	−	1.58232i
$960$		0			0
$961$	−460.890	+	798.284i	−0.479594	+	0.830681i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−695.264	+	1204.23i	−0.720481	+	1.24791i
$966$		0			0
$967$	178.365	−	102.979i	0.184452	−	0.106493i	−0.404931	−	0.914347i	$-0.632704\pi$
$967$	178.365	−	102.979i	0.184452	−	0.106493i	0.589383	+	0.807854i	$0.299371\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1364.48i		−	1.40523i	−0.711568	−	0.702617i	$-0.752015\pi$
$971$		−	1364.48i		−	1.40523i	0.711568	−	0.702617i	$-0.247985\pi$
$972$		0			0
$973$	1516.65			1.55873
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−472.081	−	817.668i	−0.483194	−	0.836917i	0.516620	−	0.856215i	$-0.327190\pi$
$977$	−472.081	−	817.668i	−0.483194	−	0.836917i	−0.999814	+	0.0192983i	$0.993857\pi$
$978$		0			0
$979$	76.3612	+	44.0872i	0.0779992	+	0.0450329i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1322.14	−	763.336i	−1.34500	−	0.776537i	−0.357465	−	0.933927i	$-0.616359\pi$
$983$	−1322.14	−	763.336i	−1.34500	−	0.776537i	−0.987537	+	0.157390i	$0.949692\pi$
$984$		0			0
$985$	289.452	+	501.345i	0.293859	+	0.508979i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−466.670			−0.471860
$990$		0			0
$991$			599.630i			0.605075i	0.953137	+	0.302538i	$0.0978338\pi$
$991$			599.630i			0.605075i	−0.953137	+	0.302538i	$0.902166\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−262.124	+	151.337i	−0.263441	+	0.152098i
$996$		0			0
$997$	−297.117	+	514.622i	−0.298011	+	0.516170i	−0.975681	−	0.219196i	$-0.929657\pi$
$997$	−297.117	+	514.622i	−0.298011	+	0.516170i	0.677670	+	0.735366i	$0.262990\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.f.127.1		8
3.2	odd	2		576.3.o.f.511.4		8
4.3	odd	2		1728.3.o.e.127.1		8
8.3	odd	2		432.3.o.a.127.4		8
8.5	even	2		432.3.o.b.127.4		8
9.4	even	3		1728.3.o.e.1279.1		8
9.5	odd	6		576.3.o.d.319.1		8
12.11	even	2		576.3.o.d.511.1		8
24.5	odd	2		144.3.o.a.79.1	yes	8
24.11	even	2		144.3.o.c.79.4	yes	8
36.23	even	6		576.3.o.f.319.4		8
36.31	odd	6	inner	1728.3.o.f.1279.1		8
72.5	odd	6		144.3.o.c.31.4	yes	8
72.11	even	6		1296.3.g.j.1135.8		8
72.13	even	6		432.3.o.a.415.4		8
72.29	odd	6		1296.3.g.j.1135.7		8
72.43	odd	6		1296.3.g.k.1135.2		8
72.59	even	6		144.3.o.a.31.1	✓	8
72.61	even	6		1296.3.g.k.1135.1		8
72.67	odd	6		432.3.o.b.415.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.1	✓	8	72.59	even	6
144.3.o.a.79.1	yes	8	24.5	odd	2
144.3.o.c.31.4	yes	8	72.5	odd	6
144.3.o.c.79.4	yes	8	24.11	even	2
432.3.o.a.127.4		8	8.3	odd	2
432.3.o.a.415.4		8	72.13	even	6
432.3.o.b.127.4		8	8.5	even	2
432.3.o.b.415.4		8	72.67	odd	6
576.3.o.d.319.1		8	9.5	odd	6
576.3.o.d.511.1		8	12.11	even	2
576.3.o.f.319.4		8	36.23	even	6
576.3.o.f.511.4		8	3.2	odd	2
1296.3.g.j.1135.7		8	72.29	odd	6
1296.3.g.j.1135.8		8	72.11	even	6
1296.3.g.k.1135.1		8	72.61	even	6
1296.3.g.k.1135.2		8	72.43	odd	6
1728.3.o.e.127.1		8	4.3	odd	2
1728.3.o.e.1279.1		8	9.4	even	3
1728.3.o.f.127.1		8	1.1	even	1	trivial
1728.3.o.f.1279.1		8	36.31	odd	6	inner

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.01729 - 5.22611i) q^{5} +(10.2332 + 5.90815i) q^{7} +O(q^{10})\)	\(q+(-3.01729 - 5.22611i) q^{5} +(10.2332 + 5.90815i) q^{7} +(5.28454 + 3.05103i) q^{11} +(-7.44868 - 12.9015i) q^{13} -26.6919 q^{17} +9.45610i q^{19} +(17.2673 - 9.96931i) q^{23} +(-5.70813 + 9.88677i) q^{25} +(22.3114 - 38.6445i) q^{29} +(5.42359 - 3.13131i) q^{31} -71.3065i q^{35} +6.65707 q^{37} +(-8.82853 - 15.2915i) q^{41} +(-20.2696 - 11.7027i) q^{43} +(36.4261 + 21.0306i) q^{47} +(45.3125 + 78.4835i) q^{49} -51.6192 q^{53} -36.8234i q^{55} +(-32.9024 + 18.9962i) q^{59} +(45.3815 - 78.6031i) q^{61} +(-44.9497 + 77.8552i) q^{65} +(-53.4577 + 30.8638i) q^{67} -39.5232i q^{71} +35.0355 q^{73} +(36.0519 + 62.4437i) q^{77} +(-77.9605 - 45.0105i) q^{79} +(102.357 + 59.0957i) q^{83} +(80.5372 + 139.494i) q^{85} +14.4499 q^{89} -176.032i q^{91} +(49.4186 - 28.5318i) q^{95} +(67.5561 - 117.011i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} + 3 q^{7}+O(q^{10}) \) 8 * q + 3 * q^5 + 3 * q^7	\( 8 q + 3 q^{5} + 3 q^{7} + 18 q^{11} - 5 q^{13} - 6 q^{17} + 81 q^{23} - 23 q^{25} + 69 q^{29} + 45 q^{31} + 20 q^{37} - 54 q^{41} - 207 q^{47} + 41 q^{49} - 252 q^{53} - 306 q^{59} - 7 q^{61} - 93 q^{65} - 12 q^{67} + 74 q^{73} + 207 q^{77} + 33 q^{79} + 549 q^{83} + 30 q^{85} + 168 q^{89} + 684 q^{95} - 10 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 + 3 * q^7 + 18 * q^11 - 5 * q^13 - 6 * q^17 + 81 * q^23 - 23 * q^25 + 69 * q^29 + 45 * q^31 + 20 * q^37 - 54 * q^41 - 207 * q^47 + 41 * q^49 - 252 * q^53 - 306 * q^59 - 7 * q^61 - 93 * q^65 - 12 * q^67 + 74 * q^73 + 207 * q^77 + 33 * q^79 + 549 * q^83 + 30 * q^85 + 168 * q^89 + 684 * q^95 - 10 * q^97

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