LMFDB - Embedded newform 120.3.c.a.89.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,3,Mod(89,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("120.89");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	120.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.26976317232$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 $ x^12 + 34x^10 + 305x^8 + 616x^6 + 305x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			89.7
Root			$-1.38205i$ of defining polynomial
Character	$\chi$	$=$	120.89
Dual form			120.3.c.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.938195 - 2.84952i) q^{3} +(-4.88807 - 1.05205i) q^{5} -6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} +O(q^{10})$	\(q+(0.938195 - 2.84952i) q^{3} +(-4.88807 - 1.05205i) q^{5} -6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} +7.52980i q^{11} -16.2362i q^{13} +(-7.58380 + 12.9416i) q^{15} -4.11928 q^{17} +7.86469 q^{19} +(-19.4115 - 6.39117i) q^{21} +19.5246 q^{23} +(22.7864 + 10.2850i) q^{25} +(-22.0280 + 15.6130i) q^{27} -55.8878i q^{29} +43.4375 q^{31} +(21.4563 + 7.06442i) q^{33} +(-7.16675 + 33.2984i) q^{35} +31.5824i q^{37} +(-46.2655 - 15.2328i) q^{39} +51.3487i q^{41} +51.2914i q^{43} +(29.7624 + 33.7520i) q^{45} +61.7596 q^{47} +2.59407 q^{49} +(-3.86469 + 11.7380i) q^{51} -82.7111 q^{53} +(7.92170 - 36.8061i) q^{55} +(7.37861 - 22.4106i) q^{57} -97.6026i q^{59} +4.13531 q^{61} +(-36.4236 + 49.3174i) q^{63} +(-17.0813 + 79.3638i) q^{65} -63.1940i q^{67} +(18.3179 - 55.6358i) q^{69} -40.3087i q^{71} -78.5111i q^{73} +(50.6853 - 55.2811i) q^{75} +51.2944 q^{77} -51.0103 q^{79} +(23.8230 + 77.4175i) q^{81} -2.72011 q^{83} +(20.1353 + 4.33368i) q^{85} +(-159.254 - 52.4337i) q^{87} +70.4279i q^{89} -110.604 q^{91} +(40.7528 - 123.776i) q^{93} +(-38.4431 - 8.27403i) q^{95} -3.44364i q^{97} +(40.2605 - 54.5126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{9}+O(q^{10}) $ 12 * q + 8 * q^9	$ 12 q + 8 q^{9} + 16 q^{15} + 4 q^{21} + 36 q^{25} - 48 q^{31} - 128 q^{39} - 68 q^{45} - 252 q^{49} + 48 q^{51} - 48 q^{55} + 144 q^{61} + 268 q^{69} + 304 q^{75} + 432 q^{79} - 188 q^{81} + 336 q^{85} - 560 q^{99}+O(q^{100}) $ 12 * q + 8 * q^9 + 16 * q^15 + 4 * q^21 + 36 * q^25 - 48 * q^31 - 128 * q^39 - 68 * q^45 - 252 * q^49 + 48 * q^51 - 48 * q^55 + 144 * q^61 + 268 * q^69 + 304 * q^75 + 432 * q^79 - 188 * q^81 + 336 * q^85 - 560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.938195	−	2.84952i	0.312732	−	0.949841i
$3$	0.938195	−	2.84952i	0.312732	−	0.949841i
$4$		0			0
$5$	−4.88807	−	1.05205i	−0.977613	−	0.210409i
$5$	−4.88807	−	1.05205i	−0.977613	−	0.210409i
$6$		0			0
$7$		−	6.81219i		−	0.973170i	−0.873633	−	0.486585i	$-0.838242\pi$
$7$		−	6.81219i		−	0.973170i	0.873633	−	0.486585i	$-0.161758\pi$
$8$		0			0
$9$	−7.23958	−	5.34682i	−0.804398	−	0.594091i
$10$		0			0
$11$			7.52980i			0.684527i	0.939604	+	0.342263i	$0.111194\pi$
$11$			7.52980i			0.684527i	−0.939604	+	0.342263i	$0.888806\pi$
$12$		0			0
$13$		−	16.2362i		−	1.24894i	−0.781048	−	0.624471i	$-0.785315\pi$
$13$		−	16.2362i		−	1.24894i	0.781048	−	0.624471i	$-0.214685\pi$
$14$		0			0
$15$	−7.58380	+	12.9416i	−0.505586	+	0.862776i
$16$		0			0
$17$	−4.11928			−0.242311			−0.121155	−	0.992634i	$-0.538660\pi$
$17$	−4.11928			−0.242311			−0.121155	+	0.992634i	$0.538660\pi$
$18$		0			0
$19$	7.86469			0.413931			0.206965	−	0.978348i	$-0.433641\pi$
$19$	7.86469			0.413931			0.206965	+	0.978348i	$0.433641\pi$
$20$		0			0
$21$	−19.4115	−	6.39117i	−0.924357	−	0.304341i
$22$		0			0
$23$	19.5246			0.848895			0.424447	−	0.905453i	$-0.360468\pi$
$23$	19.5246			0.848895			0.424447	+	0.905453i	$0.360468\pi$
$24$		0			0
$25$	22.7864	+	10.2850i	0.911456	+	0.411398i
$26$		0			0
$27$	−22.0280	+	15.6130i	−0.815853	+	0.578259i
$28$		0			0
$29$		−	55.8878i		−	1.92717i	−0.267408	−	0.963583i	$-0.586167\pi$
$29$		−	55.8878i		−	1.92717i	0.267408	−	0.963583i	$-0.413833\pi$
$30$		0			0
$31$	43.4375			1.40121			0.700604	−	0.713550i	$-0.252914\pi$
$31$	43.4375			1.40121			0.700604	+	0.713550i	$0.252914\pi$
$32$		0			0
$33$	21.4563	+	7.06442i	0.650192	+	0.214073i
$34$		0			0
$35$	−7.16675	+	33.2984i	−0.204764	+	0.951384i
$36$		0			0
$37$			31.5824i			0.853579i	0.904351	+	0.426790i	$0.140356\pi$
$37$			31.5824i			0.853579i	−0.904351	+	0.426790i	$0.859644\pi$
$38$		0			0
$39$	−46.2655	−	15.2328i	−1.18630	−	0.390584i
$40$		0			0
$41$			51.3487i			1.25241i	0.779659	+	0.626204i	$0.215392\pi$
$41$			51.3487i			1.25241i	−0.779659	+	0.626204i	$0.784608\pi$
$42$		0			0
$43$			51.2914i			1.19282i	0.802678	+	0.596412i	$0.203408\pi$
$43$			51.2914i			1.19282i	−0.802678	+	0.596412i	$0.796592\pi$
$44$		0			0
$45$	29.7624	+	33.7520i	0.661387	+	0.750044i
$46$		0			0
$47$	61.7596			1.31403			0.657017	−	0.753875i	$-0.271818\pi$
$47$	61.7596			1.31403			0.657017	+	0.753875i	$0.271818\pi$
$48$		0			0
$49$	2.59407			0.0529401
$50$		0			0
$51$	−3.86469	+	11.7380i	−0.0757782	+	0.230157i
$52$		0			0
$53$	−82.7111			−1.56059			−0.780293	−	0.625414i	$-0.784930\pi$
$53$	−82.7111			−1.56059			−0.780293	+	0.625414i	$0.784930\pi$
$54$		0			0
$55$	7.92170	−	36.8061i	0.144031	−	0.669203i
$56$		0			0
$57$	7.37861	−	22.4106i	0.129449	−	0.393169i
$58$		0			0
$59$		−	97.6026i		−	1.65428i	−0.561994	−	0.827141i	$-0.689966\pi$
$59$		−	97.6026i		−	1.65428i	0.561994	−	0.827141i	$-0.310034\pi$
$60$		0			0
$61$	4.13531			0.0677920			0.0338960	−	0.999425i	$-0.489209\pi$
$61$	4.13531			0.0677920			0.0338960	+	0.999425i	$0.489209\pi$
$62$		0			0
$63$	−36.4236	+	49.3174i	−0.578152	+	0.782816i
$64$		0			0
$65$	−17.0813	+	79.3638i	−0.262789	+	1.22098i
$66$		0			0
$67$		−	63.1940i		−	0.943194i	−0.881814	−	0.471597i	$-0.843678\pi$
$67$		−	63.1940i		−	0.943194i	0.881814	−	0.471597i	$-0.156322\pi$
$68$		0			0
$69$	18.3179	−	55.6358i	0.265476	−	0.806316i
$70$		0			0
$71$		−	40.3087i		−	0.567729i	−0.958864	−	0.283864i	$-0.908383\pi$
$71$		−	40.3087i		−	0.567729i	0.958864	−	0.283864i	$-0.0916165\pi$
$72$		0			0
$73$		−	78.5111i		−	1.07549i	−0.843106	−	0.537747i	$-0.819276\pi$
$73$		−	78.5111i		−	1.07549i	0.843106	−	0.537747i	$-0.180724\pi$
$74$		0			0
$75$	50.6853	−	55.2811i	0.675804	−	0.737081i
$76$		0			0
$77$	51.2944			0.666161
$78$		0			0
$79$	−51.0103			−0.645699			−0.322850	−	0.946450i	$-0.604641\pi$
$79$	−51.0103			−0.645699			−0.322850	+	0.946450i	$0.604641\pi$
$80$		0			0
$81$	23.8230	+	77.4175i	0.294111	+	0.955771i
$82$		0			0
$83$	−2.72011			−0.0327725			−0.0163862	−	0.999866i	$-0.505216\pi$
$83$	−2.72011			−0.0327725			−0.0163862	+	0.999866i	$0.505216\pi$
$84$		0			0
$85$	20.1353	+	4.33368i	0.236886	+	0.0509844i
$86$		0			0
$87$	−159.254	−	52.4337i	−1.83050	−	0.602686i
$88$		0			0
$89$			70.4279i			0.791325i	0.918396	+	0.395662i	$0.129485\pi$
$89$			70.4279i			0.791325i	−0.918396	+	0.395662i	$0.870515\pi$
$90$		0			0
$91$	−110.604			−1.21543
$92$		0			0
$93$	40.7528	−	123.776i	0.438203	−	1.33093i
$94$		0			0
$95$	−38.4431	−	8.27403i	−0.404664	−	0.0870950i
$96$		0			0
$97$		−	3.44364i		−	0.0355015i	−0.999842	−	0.0177507i	$-0.994349\pi$
$97$		−	3.44364i		−	0.0355015i	0.999842	−	0.0177507i	$-0.00565053\pi$
$98$		0			0
$99$	40.2605	−	54.5126i	0.406671	−	0.550632i
$100$		0			0
$101$		−	49.2446i		−	0.487570i	−0.969829	−	0.243785i	$-0.921611\pi$
$101$		−	49.2446i		−	0.487570i	0.969829	−	0.243785i	$-0.0783892\pi$
$102$		0			0
$103$			90.5470i			0.879097i	0.898219	+	0.439548i	$0.144862\pi$
$103$			90.5470i			0.879097i	−0.898219	+	0.439548i	$0.855138\pi$
$104$		0			0
$105$	88.1609	+	51.6623i	0.839628	+	0.492022i
$106$		0			0
$107$	65.3836			0.611062			0.305531	−	0.952182i	$-0.401166\pi$
$107$	65.3836			0.611062			0.305531	+	0.952182i	$0.401166\pi$
$108$		0			0
$109$	−170.469			−1.56394			−0.781968	−	0.623319i	$-0.785784\pi$
$109$	−170.469			−1.56394			−0.781968	+	0.623319i	$0.785784\pi$
$110$		0			0
$111$	89.9949	+	29.6305i	0.810765	+	0.266941i
$112$		0			0
$113$	−55.4137			−0.490387			−0.245193	−	0.969474i	$-0.578851\pi$
$113$	−55.4137			−0.490387			−0.245193	+	0.969474i	$0.578851\pi$
$114$		0			0
$115$	−95.4375	−	20.5408i	−0.829891	−	0.178616i
$116$		0			0
$117$	−86.8123	+	117.544i	−0.741985	+	1.00465i
$118$		0			0
$119$			28.0613i			0.235809i
$120$		0			0
$121$	64.3022			0.531423
$122$		0			0
$123$	146.319	+	48.1751i	1.18959	+	0.391668i
$124$		0			0
$125$	−100.561	−	74.2459i	−0.804489	−	0.593967i
$126$		0			0
$127$			74.9923i			0.590491i	0.955421	+	0.295245i	$0.0954014\pi$
$127$			74.9923i			0.590491i	−0.955421	+	0.295245i	$0.904599\pi$
$128$		0			0
$129$	146.156	+	48.1214i	1.13299	+	0.373034i
$130$		0			0
$131$			101.149i			0.772130i	0.922472	+	0.386065i	$0.126166\pi$
$131$			101.149i			0.772130i	−0.922472	+	0.386065i	$0.873834\pi$
$132$		0			0
$133$		−	53.5758i		−	0.402825i
$134$		0			0
$135$	124.100	−	53.1428i	0.919260	−	0.393650i
$136$		0			0
$137$	114.292			0.834248			0.417124	−	0.908850i	$-0.363038\pi$
$137$	114.292			0.834248			0.417124	+	0.908850i	$0.363038\pi$
$138$		0			0
$139$	230.156			1.65580			0.827899	−	0.560878i	$-0.189536\pi$
$139$	230.156			1.65580			0.827899	+	0.560878i	$0.189536\pi$
$140$		0			0
$141$	57.9426	−	175.986i	0.410940	−	1.24812i
$142$		0			0
$143$	122.256			0.854934
$144$		0			0
$145$	−58.7966	+	273.183i	−0.405494	+	1.88402i
$146$		0			0
$147$	2.43374	−	7.39185i	0.0165561	−	0.0502847i
$148$		0			0
$149$			9.12446i			0.0612380i	0.999531	+	0.0306190i	$0.00974785\pi$
$149$			9.12446i			0.0612380i	−0.999531	+	0.0306190i	$0.990252\pi$
$150$		0			0
$151$	−163.010			−1.07954			−0.539769	−	0.841813i	$-0.681488\pi$
$151$	−163.010			−1.07954			−0.539769	+	0.841813i	$0.681488\pi$
$152$		0			0
$153$	29.8218	+	22.0250i	0.194914	+	0.143955i
$154$		0			0
$155$	−212.325	−	45.6983i	−1.36984	−	0.294828i
$156$		0			0
$157$			122.529i			0.780442i	0.920721	+	0.390221i	$0.127601\pi$
$157$			122.529i			0.780442i	−0.920721	+	0.390221i	$0.872399\pi$
$158$		0			0
$159$	−77.5991	+	235.687i	−0.488045	+	1.48231i
$160$		0			0
$161$		−	133.005i		−	0.826119i
$162$		0			0
$163$			66.6959i			0.409177i	0.978848	+	0.204589i	$0.0655857\pi$
$163$			66.6959i			0.409177i	−0.978848	+	0.204589i	$0.934414\pi$
$164$		0			0
$165$	−97.4479	−	57.1044i	−0.590593	−	0.346088i
$166$		0			0
$167$	163.583			0.979539			0.489769	−	0.871852i	$-0.337081\pi$
$167$	163.583			0.979539			0.489769	+	0.871852i	$0.337081\pi$
$168$		0			0
$169$	−94.6153			−0.559854
$170$		0			0
$171$	−56.9370	−	42.0511i	−0.332965	−	0.245913i
$172$		0			0
$173$	34.7133			0.200655			0.100327	−	0.994954i	$-0.468011\pi$
$173$	34.7133			0.200655			0.100327	+	0.994954i	$0.468011\pi$
$174$		0			0
$175$	70.0631	−	155.225i	0.400360	−	0.887001i
$176$		0			0
$177$	−278.121	−	91.5704i	−1.57131	−	0.517347i
$178$		0			0
$179$			273.448i			1.52764i	0.645429	+	0.763820i	$0.276679\pi$
$179$			273.448i			1.52764i	−0.645429	+	0.763820i	$0.723321\pi$
$180$		0			0
$181$	−40.8749			−0.225828			−0.112914	−	0.993605i	$-0.536019\pi$
$181$	−40.8749			−0.225828			−0.112914	+	0.993605i	$0.536019\pi$
$182$		0			0
$183$	3.87973	−	11.7837i	0.0212007	−	0.0643916i
$184$		0			0
$185$	33.2262	−	154.377i	0.179601	−	0.834471i
$186$		0			0
$187$		−	31.0173i		−	0.165868i
$188$		0			0
$189$	106.359	+	150.059i	0.562744	+	0.793964i
$190$		0			0
$191$			40.5934i			0.212531i	0.994338	+	0.106266i	$0.0338894\pi$
$191$			40.5934i			0.212531i	−0.994338	+	0.106266i	$0.966111\pi$
$192$		0			0
$193$		−	141.259i		−	0.731912i	−0.930632	−	0.365956i	$-0.880742\pi$
$193$		−	141.259i		−	0.731912i	0.930632	−	0.365956i	$-0.119258\pi$
$194$		0			0
$195$	210.124	+	123.132i	1.07756	+	0.631448i
$196$		0			0
$197$	232.643			1.18093			0.590464	−	0.807064i	$-0.298945\pi$
$197$	232.643			1.18093			0.590464	+	0.807064i	$0.298945\pi$
$198$		0			0
$199$	85.3744			0.429017			0.214509	−	0.976722i	$-0.431185\pi$
$199$	85.3744			0.429017			0.214509	+	0.976722i	$0.431185\pi$
$200$		0			0
$201$	−180.073	−	59.2883i	−0.895885	−	0.294967i
$202$		0			0
$203$	−380.719			−1.87546
$204$		0			0
$205$	54.0213	−	250.996i	0.263518	−	1.22437i
$206$		0			0
$207$	−141.350	−	104.394i	−0.682849	−	0.504321i
$208$		0			0
$209$			59.2195i			0.283347i
$210$		0			0
$211$	284.532			1.34849			0.674247	−	0.738506i	$-0.264468\pi$
$211$	284.532			1.34849			0.674247	+	0.738506i	$0.264468\pi$
$212$		0			0
$213$	−114.861	−	37.8175i	−0.539252	−	0.177547i
$214$		0			0
$215$	53.9610	−	250.716i	0.250982	−	1.16612i
$216$		0			0
$217$		−	295.904i		−	1.36361i
$218$		0			0
$219$	−223.719	−	73.6587i	−1.02155	−	0.336341i
$220$		0			0
$221$			66.8816i			0.302632i
$222$		0			0
$223$		−	30.2924i		−	0.135840i	−0.997691	−	0.0679201i	$-0.978364\pi$
$223$		−	30.2924i		−	0.135840i	0.997691	−	0.0679201i	$-0.0216363\pi$
$224$		0			0
$225$	−109.972	−	196.294i	−0.488765	−	0.872416i
$226$		0			0
$227$	−239.380			−1.05454			−0.527269	−	0.849698i	$-0.676784\pi$
$227$	−239.380			−1.05454			−0.527269	+	0.849698i	$0.676784\pi$
$228$		0			0
$229$	284.959			1.24436			0.622180	−	0.782874i	$-0.286247\pi$
$229$	284.959			1.24436			0.622180	+	0.782874i	$0.286247\pi$
$230$		0			0
$231$	48.1242	−	146.165i	0.208330	−	0.632747i
$232$		0			0
$233$	−93.8635			−0.402848			−0.201424	−	0.979504i	$-0.564557\pi$
$233$	−93.8635			−0.402848			−0.201424	+	0.979504i	$0.564557\pi$
$234$		0			0
$235$	−301.885	−	64.9741i	−1.28462	−	0.276485i
$236$		0			0
$237$	−47.8576	+	145.355i	−0.201931	+	0.613312i
$238$		0			0
$239$			238.326i			0.997181i	0.866838	+	0.498590i	$0.166149\pi$
$239$			238.326i			0.997181i	−0.866838	+	0.498590i	$0.833851\pi$
$240$		0			0
$241$	44.2919			0.183784			0.0918919	−	0.995769i	$-0.470709\pi$
$241$	44.2919			0.183784			0.0918919	+	0.995769i	$0.470709\pi$
$242$		0			0
$243$	242.954	+	4.74848i	0.999809	+	0.0195411i
$244$		0			0
$245$	−12.6800	−	2.72908i	−0.0517550	−	0.0111391i
$246$		0			0
$247$		−	127.693i		−	0.516975i
$248$		0			0
$249$	−2.55200	+	7.75103i	−0.0102490	+	0.0311286i
$250$		0			0
$251$		−	293.093i		−	1.16770i	−0.811862	−	0.583850i	$-0.801546\pi$
$251$		−	293.093i		−	1.16770i	0.811862	−	0.583850i	$-0.198454\pi$
$252$		0			0
$253$			147.016i			0.581092i
$254$		0			0
$255$	31.2398	−	53.3102i	0.122509	−	0.209060i
$256$		0			0
$257$	169.330			0.658870			0.329435	−	0.944178i	$-0.393142\pi$
$257$	169.330			0.658870			0.329435	+	0.944178i	$0.393142\pi$
$258$		0			0
$259$	215.146			0.830678
$260$		0			0
$261$	−298.822	+	404.604i	−1.14491	+	1.55021i
$262$		0			0
$263$	−91.1958			−0.346752			−0.173376	−	0.984856i	$-0.555468\pi$
$263$	−91.1958			−0.346752			−0.173376	+	0.984856i	$0.555468\pi$
$264$		0			0
$265$	404.297	+	87.0160i	1.52565	+	0.328362i
$266$		0			0
$267$	200.686	+	66.0751i	0.751633	+	0.247472i
$268$		0			0
$269$			325.164i			1.20879i	0.796686	+	0.604393i	$0.206584\pi$
$269$			325.164i			1.20879i	−0.796686	+	0.604393i	$0.793416\pi$
$270$		0			0
$271$	−132.719			−0.489738			−0.244869	−	0.969556i	$-0.578745\pi$
$271$	−132.719			−0.489738			−0.244869	+	0.969556i	$0.578745\pi$
$272$		0			0
$273$	−103.768	+	315.170i	−0.380104	+	1.15447i
$274$		0			0
$275$	−77.4436	+	171.577i	−0.281613	+	0.623916i
$276$		0			0
$277$			254.199i			0.917687i	0.888517	+	0.458844i	$0.151736\pi$
$277$			254.199i			0.917687i	−0.888517	+	0.458844i	$0.848264\pi$
$278$		0			0
$279$	−314.469	−	232.252i	−1.12713	−	0.832446i
$280$		0			0
$281$			19.5488i			0.0695687i	0.999395	+	0.0347843i	$0.0110744\pi$
$281$			19.5488i			0.0695687i	−0.999395	+	0.0347843i	$0.988926\pi$
$282$		0			0
$283$		−	109.674i		−	0.387541i	−0.981047	−	0.193770i	$-0.937928\pi$
$283$		−	109.674i		−	0.387541i	0.981047	−	0.193770i	$-0.0620717\pi$
$284$		0			0
$285$	−59.6442	+	101.782i	−0.209278	+	0.357130i
$286$		0			0
$287$	349.797			1.21881
$288$		0			0
$289$	−272.032			−0.941286
$290$		0			0
$291$	−9.81275	−	3.23081i	−0.0337208	−	0.0111024i
$292$		0			0
$293$	178.388			0.608832			0.304416	−	0.952539i	$-0.401539\pi$
$293$	178.388			0.608832			0.304416	+	0.952539i	$0.401539\pi$
$294$		0			0
$295$	−102.683	+	477.088i	−0.348077	+	1.61725i
$296$		0			0
$297$	−117.563	−	165.867i	−0.395834	−	0.558474i
$298$		0			0
$299$		−	317.006i		−	1.06022i
$300$		0			0
$301$	349.407			1.16082
$302$		0			0
$303$	−140.324	−	46.2011i	−0.463115	−	0.152479i
$304$		0			0
$305$	−20.2137	−	4.35054i	−0.0662744	−	0.0142641i
$306$		0			0
$307$			289.046i			0.941518i	0.882262	+	0.470759i	$0.156020\pi$
$307$			289.046i			0.941518i	−0.882262	+	0.470759i	$0.843980\pi$
$308$		0			0
$309$	258.016	+	84.9508i	0.835003	+	0.274922i
$310$		0			0
$311$		−	336.061i		−	1.08058i	−0.841478	−	0.540291i	$-0.818314\pi$
$311$		−	336.061i		−	1.08058i	0.841478	−	0.540291i	$-0.181686\pi$
$312$		0			0
$313$			563.702i			1.80096i	0.434894	+	0.900482i	$0.356786\pi$
$313$			563.702i			1.80096i	−0.434894	+	0.900482i	$0.643214\pi$
$314$		0			0
$315$	229.925	−	202.747i	0.729921	−	0.643642i
$316$		0			0
$317$	139.938			0.441445			0.220722	−	0.975337i	$-0.429158\pi$
$317$	139.938			0.441445			0.220722	+	0.975337i	$0.429158\pi$
$318$		0			0
$319$	420.824			1.31920
$320$		0			0
$321$	61.3426	−	186.312i	0.191098	−	0.580412i
$322$		0			0
$323$	−32.3968			−0.100300
$324$		0			0
$325$	166.989	−	369.965i	0.513812	−	1.13835i
$326$		0			0
$327$	−159.933	+	485.756i	−0.489092	+	1.48549i
$328$		0			0
$329$		−	420.718i		−	1.27878i
$330$		0			0
$331$	−14.5116			−0.0438416			−0.0219208	−	0.999760i	$-0.506978\pi$
$331$	−14.5116			−0.0438416			−0.0219208	+	0.999760i	$0.506978\pi$
$332$		0			0
$333$	168.866	−	228.644i	0.507104	−	0.686617i
$334$		0			0
$335$	−66.4831	+	308.896i	−0.198457	+	0.922079i
$336$		0			0
$337$		−	347.492i		−	1.03113i	−0.856850	−	0.515566i	$-0.827582\pi$
$337$		−	347.492i		−	1.03113i	0.856850	−	0.515566i	$-0.172418\pi$
$338$		0			0
$339$	−51.9889	+	157.903i	−0.153359	+	0.465790i
$340$		0			0
$341$			327.075i			0.959165i
$342$		0			0
$343$		−	351.469i		−	1.02469i
$344$		0			0
$345$	−148.070	+	252.680i	−0.429190	+	0.732406i
$346$		0			0
$347$	−273.321			−0.787670			−0.393835	−	0.919181i	$-0.628852\pi$
$347$	−273.321			−0.787670			−0.393835	+	0.919181i	$0.628852\pi$
$348$		0			0
$349$	−550.853			−1.57838			−0.789188	−	0.614152i	$-0.789498\pi$
$349$	−550.853			−1.57838			−0.789188	+	0.614152i	$0.789498\pi$
$350$		0			0
$351$	253.496	+	357.652i	0.722212	+	1.01895i
$352$		0			0
$353$	643.177			1.82203			0.911015	−	0.412373i	$-0.135300\pi$
$353$	643.177			1.82203			0.911015	+	0.412373i	$0.135300\pi$
$354$		0			0
$355$	−42.4067	+	197.032i	−0.119455	+	0.555019i
$356$		0			0
$357$	79.9614	+	26.3270i	0.223982	+	0.0737451i
$358$		0			0
$359$		−	465.873i		−	1.29770i	−0.760918	−	0.648849i	$-0.775251\pi$
$359$		−	465.873i		−	1.29770i	0.760918	−	0.648849i	$-0.224749\pi$
$360$		0			0
$361$	−299.147			−0.828661
$362$		0			0
$363$	60.3280	−	183.231i	0.166193	−	0.504767i
$364$		0			0
$365$	−82.5974	+	383.767i	−0.226294	+	1.05142i
$366$		0			0
$367$		−	44.7168i		−	0.121844i	−0.998143	−	0.0609221i	$-0.980596\pi$
$367$		−	44.7168i		−	0.121844i	0.998143	−	0.0609221i	$-0.0194041\pi$
$368$		0			0
$369$	274.552	−	371.743i	0.744044	−	1.00743i
$370$		0			0
$371$			563.443i			1.51872i
$372$		0			0
$373$		−	275.158i		−	0.737688i	−0.929491	−	0.368844i	$-0.879754\pi$
$373$		−	275.158i		−	0.737688i	0.929491	−	0.368844i	$-0.120246\pi$
$374$		0			0
$375$	−305.912	+	216.894i	−0.815764	+	0.578385i
$376$		0			0
$377$	−907.408			−2.40692
$378$		0			0
$379$	−505.072			−1.33264			−0.666322	−	0.745664i	$-0.732132\pi$
$379$	−505.072			−1.33264			−0.666322	+	0.745664i	$0.732132\pi$
$380$		0			0
$381$	213.692	+	70.3575i	0.560873	+	0.184665i
$382$		0			0
$383$	193.577			0.505422			0.252711	−	0.967542i	$-0.418678\pi$
$383$	193.577			0.505422			0.252711	+	0.967542i	$0.418678\pi$
$384$		0			0
$385$	−250.730	−	53.9642i	−0.651248	−	0.140167i
$386$		0			0
$387$	274.246	−	371.328i	0.708646	−	0.959505i
$388$		0			0
$389$		−	280.077i		−	0.719993i	−0.932954	−	0.359996i	$-0.882778\pi$
$389$		−	280.077i		−	0.719993i	0.932954	−	0.359996i	$-0.117222\pi$
$390$		0			0
$391$	−80.4272			−0.205696
$392$		0			0
$393$	288.226	+	94.8975i	0.733401	+	0.241469i
$394$		0			0
$395$	249.342	+	53.6652i	0.631244	+	0.135861i
$396$		0			0
$397$			468.421i			1.17990i	0.807439	+	0.589951i	$0.200853\pi$
$397$			468.421i			1.17990i	−0.807439	+	0.589951i	$0.799147\pi$
$398$		0			0
$399$	−152.665	−	50.2645i	−0.382620	−	0.125976i
$400$		0			0
$401$		−	274.969i		−	0.685707i	−0.939389	−	0.342854i	$-0.888606\pi$
$401$		−	274.969i		−	0.685707i	0.939389	−	0.342854i	$-0.111394\pi$
$402$		0			0
$403$		−	705.261i		−	1.75003i
$404$		0			0
$405$	−35.0016	−	403.485i	−0.0864237	−	0.996258i
$406$		0			0
$407$	−237.809			−0.584298
$408$		0			0
$409$	−202.697			−0.495592			−0.247796	−	0.968812i	$-0.579706\pi$
$409$	−202.697			−0.495592			−0.247796	+	0.968812i	$0.579706\pi$
$410$		0			0
$411$	107.228	−	325.678i	0.260896	−	0.792403i
$412$		0			0
$413$	−664.888			−1.60990
$414$		0			0
$415$	13.2961	+	2.86169i	0.0320388	+	0.00689564i
$416$		0			0
$417$	215.931	−	655.835i	0.517820	−	1.57274i
$418$		0			0
$419$			76.6340i			0.182897i	0.995810	+	0.0914487i	$0.0291497\pi$
$419$			76.6340i			0.182897i	−0.995810	+	0.0914487i	$0.970850\pi$
$420$		0			0
$421$	−183.991			−0.437033			−0.218516	−	0.975833i	$-0.570122\pi$
$421$	−183.991			−0.437033			−0.218516	+	0.975833i	$0.570122\pi$
$422$		0			0
$423$	−447.114	−	330.218i	−1.05701	−	0.780657i
$424$		0			0
$425$	−93.8635	−	42.3666i	−0.220855	−	0.0996861i
$426$		0			0
$427$		−	28.1705i		−	0.0659731i
$428$		0			0
$429$	114.700	−	348.370i	0.267365	−	0.812052i
$430$		0			0
$431$			671.408i			1.55779i	0.627153	+	0.778896i	$0.284220\pi$
$431$			671.408i			1.55779i	−0.627153	+	0.778896i	$0.715780\pi$
$432$		0			0
$433$			399.351i			0.922288i	0.887325	+	0.461144i	$0.152561\pi$
$433$			399.351i			0.922288i	−0.887325	+	0.461144i	$0.847439\pi$
$434$		0			0
$435$	723.280	+	423.842i	1.66271	+	0.974349i
$436$		0			0
$437$	153.555			0.351384
$438$		0			0
$439$	140.833			0.320804			0.160402	−	0.987052i	$-0.448721\pi$
$439$	140.833			0.320804			0.160402	+	0.987052i	$0.448721\pi$
$440$		0			0
$441$	−18.7799	−	13.8700i	−0.0425849	−	0.0314513i
$442$		0			0
$443$	211.416			0.477237			0.238618	−	0.971113i	$-0.423306\pi$
$443$	211.416			0.477237			0.238618	+	0.971113i	$0.423306\pi$
$444$		0			0
$445$	74.0935	−	344.256i	0.166502	−	0.773610i
$446$		0			0
$447$	26.0004	+	8.56052i	0.0581664	+	0.0191511i
$448$		0			0
$449$		−	455.166i		−	1.01373i	−0.862025	−	0.506866i	$-0.830804\pi$
$449$		−	455.166i		−	1.01373i	0.862025	−	0.506866i	$-0.169196\pi$
$450$		0			0
$451$	−386.645			−0.857307
$452$		0			0
$453$	−152.935	+	464.502i	−0.337606	+	1.02539i
$454$		0			0
$455$	540.641	+	116.361i	1.18822	+	0.255738i
$456$		0			0
$457$		−	555.776i		−	1.21614i	−0.793883	−	0.608070i	$-0.791944\pi$
$457$		−	555.776i		−	1.21614i	0.793883	−	0.608070i	$-0.208056\pi$
$458$		0			0
$459$	90.7396	−	64.3143i	0.197690	−	0.140118i
$460$		0			0
$461$		−	369.227i		−	0.800927i	−0.916313	−	0.400463i	$-0.868849\pi$
$461$		−	369.227i		−	0.800927i	0.916313	−	0.400463i	$-0.131151\pi$
$462$		0			0
$463$			360.832i			0.779336i	0.920955	+	0.389668i	$0.127410\pi$
$463$			360.832i			0.779336i	−0.920955	+	0.389668i	$0.872590\pi$
$464$		0			0
$465$	−329.421	+	562.152i	−0.708432	+	1.20893i
$466$		0			0
$467$	496.306			1.06275			0.531377	−	0.847135i	$-0.321675\pi$
$467$	496.306			1.06275			0.531377	+	0.847135i	$0.321675\pi$
$468$		0			0
$469$	−430.490			−0.917888
$470$		0			0
$471$	349.151	+	114.957i	0.741296	+	0.244069i
$472$		0			0
$473$	−386.214			−0.816520
$474$		0			0
$475$	179.208	+	80.8880i	0.377280	+	0.170290i
$476$		0			0
$477$	598.793	+	442.241i	1.25533	+	0.927131i
$478$		0			0
$479$		−	286.032i		−	0.597145i	−0.954387	−	0.298572i	$-0.903490\pi$
$479$		−	286.032i		−	0.597145i	0.954387	−	0.298572i	$-0.0965105\pi$
$480$		0			0
$481$	512.780			1.06607
$482$		0			0
$483$	−379.002	−	124.785i	−0.784682	−	0.258354i
$484$		0			0
$485$	−3.62288	+	16.8328i	−0.00746985	+	0.0347067i
$486$		0			0
$487$		−	34.3276i		−	0.0704880i	−0.999379	−	0.0352440i	$-0.988779\pi$
$487$		−	34.3276i		−	0.0704880i	0.999379	−	0.0352440i	$-0.0112208\pi$
$488$		0			0
$489$	190.052	+	62.5738i	0.388653	+	0.127963i
$490$		0			0
$491$			26.4204i			0.0538094i	0.999638	+	0.0269047i	$0.00856507\pi$
$491$			26.4204i			0.0538094i	−0.999638	+	0.0269047i	$0.991435\pi$
$492$		0			0
$493$			230.218i			0.466973i
$494$		0			0
$495$	−254.146	+	224.105i	−0.513426	+	0.452738i
$496$		0			0
$497$	−274.591			−0.552496
$498$		0			0
$499$	−72.9046			−0.146101			−0.0730507	−	0.997328i	$-0.523273\pi$
$499$	−72.9046			−0.146101			−0.0730507	+	0.997328i	$0.523273\pi$
$500$		0			0
$501$	153.473	−	466.134i	0.306333	−	0.930407i
$502$		0			0
$503$	228.404			0.454083			0.227041	−	0.973885i	$-0.427095\pi$
$503$	228.404			0.454083			0.227041	+	0.973885i	$0.427095\pi$
$504$		0			0
$505$	−51.8077	+	240.711i	−0.102589	+	0.476655i
$506$		0			0
$507$	−88.7677	+	269.609i	−0.175084	+	0.531773i
$508$		0			0
$509$			99.1735i			0.194840i	0.995243	+	0.0974199i	$0.0310590\pi$
$509$			99.1735i			0.194840i	−0.995243	+	0.0974199i	$0.968941\pi$
$510$		0			0
$511$	−534.832			−1.04664
$512$		0			0
$513$	−173.244	+	122.791i	−0.337707	+	0.239359i
$514$		0			0
$515$	95.2597	−	442.600i	0.184970	−	0.859417i
$516$		0			0
$517$			465.037i			0.899492i
$518$		0			0
$519$	32.5678	−	98.9163i	0.0627511	−	0.190590i
$520$		0			0
$521$			691.462i			1.32718i	0.748095	+	0.663592i	$0.230969\pi$
$521$			691.462i			1.32718i	−0.748095	+	0.663592i	$0.769031\pi$
$522$		0			0
$523$			821.405i			1.57056i	0.619138	+	0.785282i	$0.287482\pi$
$523$			821.405i			1.57056i	−0.619138	+	0.785282i	$0.712518\pi$
$524$		0			0
$525$	−376.585	−	345.278i	−0.717305	−	0.657672i
$526$		0			0
$527$	−178.931			−0.339528
$528$		0			0
$529$	−147.791			−0.279377
$530$		0			0
$531$	−521.864	+	706.602i	−0.982795	+	1.33070i
$532$		0			0
$533$	833.710			1.56418
$534$		0			0
$535$	−319.599	−	68.7866i	−0.597382	−	0.128573i
$536$		0			0
$537$	779.196	+	256.547i	1.45102	+	0.477742i
$538$		0			0
$539$			19.5328i			0.0362389i
$540$		0			0
$541$	446.354			0.825054			0.412527	−	0.910945i	$-0.364646\pi$
$541$	446.354			0.825054			0.412527	+	0.910945i	$0.364646\pi$
$542$		0			0
$543$	−38.3487	+	116.474i	−0.0706237	+	0.214501i
$544$		0			0
$545$	833.264	+	179.341i	1.52892	+	0.329067i
$546$		0			0
$547$			485.492i			0.887553i	0.896137	+	0.443777i	$0.146362\pi$
$547$			485.492i			0.887553i	−0.896137	+	0.443777i	$0.853638\pi$
$548$		0			0
$549$	−29.9379	−	22.1108i	−0.0545317	−	0.0402746i
$550$		0			0
$551$		−	439.540i		−	0.797714i
$552$		0			0
$553$			347.492i			0.628375i
$554$		0			0
$555$	−408.729	−	239.515i	−0.736448	−	0.431558i
$556$		0			0
$557$	−995.191			−1.78670			−0.893349	−	0.449363i	$-0.851651\pi$
$557$	−995.191			−1.78670			−0.893349	+	0.449363i	$0.851651\pi$
$558$		0			0
$559$	832.780			1.48977
$560$		0			0
$561$	−88.3847	−	29.1003i	−0.157548	−	0.0518722i
$562$		0			0
$563$	−486.571			−0.864248			−0.432124	−	0.901814i	$-0.642236\pi$
$563$	−486.571			−0.864248			−0.432124	+	0.901814i	$0.642236\pi$
$564$		0			0
$565$	270.866	+	58.2978i	0.479408	+	0.103182i
$566$		0			0
$567$	527.383	−	162.287i	0.930128	−	0.286220i
$568$		0			0
$569$			737.704i			1.29649i	0.761431	+	0.648246i	$0.224497\pi$
$569$			737.704i			1.29649i	−0.761431	+	0.648246i	$0.775503\pi$
$570$		0			0
$571$	805.843			1.41128			0.705642	−	0.708569i	$-0.250659\pi$
$571$	805.843			1.41128			0.705642	+	0.708569i	$0.250659\pi$
$572$		0			0
$573$	115.672	+	38.0846i	0.201871	+	0.0664652i
$574$		0			0
$575$	444.895	+	200.810i	0.773730	+	0.349234i
$576$		0			0
$577$		−	690.512i		−	1.19673i	−0.801225	−	0.598364i	$-0.795818\pi$
$577$		−	690.512i		−	1.19673i	0.801225	−	0.598364i	$-0.204182\pi$
$578$		0			0
$579$	−402.521	−	132.529i	−0.695201	−	0.228892i
$580$		0			0
$581$			18.5299i			0.0318932i
$582$		0			0
$583$		−	622.798i		−	1.06826i
$584$		0			0
$585$	548.005	−	483.230i	0.936761	−	0.826034i
$586$		0			0
$587$	−670.611			−1.14244			−0.571219	−	0.820798i	$-0.693529\pi$
$587$	−670.611			−1.14244			−0.571219	+	0.820798i	$0.693529\pi$
$588$		0			0
$589$	341.622			0.580004
$590$		0			0
$591$	218.265	−	662.922i	0.369314	−	1.12170i
$592$		0			0
$593$	−214.249			−0.361296			−0.180648	−	0.983548i	$-0.557819\pi$
$593$	−214.249			−0.361296			−0.180648	+	0.983548i	$0.557819\pi$
$594$		0			0
$595$	29.5218	−	137.166i	0.0496165	−	0.230530i
$596$		0			0
$597$	80.0979	−	243.276i	0.134167	−	0.407498i
$598$		0			0
$599$		−	303.315i		−	0.506368i	−0.967418	−	0.253184i	$-0.918522\pi$
$599$		−	303.315i		−	0.506368i	0.967418	−	0.253184i	$-0.0814779\pi$
$600$		0			0
$601$	66.0555			0.109909			0.0549546	−	0.998489i	$-0.482499\pi$
$601$	66.0555			0.109909			0.0549546	+	0.998489i	$0.482499\pi$
$602$		0			0
$603$	−337.887	+	457.498i	−0.560343	+	0.758703i
$604$		0			0
$605$	−314.313	−	67.6489i	−0.519526	−	0.111816i
$606$		0			0
$607$			178.972i			0.294847i	0.989073	+	0.147423i	$0.0470980\pi$
$607$			178.972i			0.294847i	−0.989073	+	0.147423i	$0.952902\pi$
$608$		0			0
$609$	−357.188	+	1084.87i	−0.586516	+	1.78139i
$610$		0			0
$611$		−	1002.74i		−	1.64115i
$612$		0			0
$613$		−	728.201i		−	1.18793i	−0.804491	−	0.593965i	$-0.797562\pi$
$613$		−	728.201i		−	1.18793i	0.804491	−	0.593965i	$-0.202438\pi$
$614$		0			0
$615$	−664.537	−	389.418i	−1.08055	−	0.633200i
$616$		0			0
$617$	−198.426			−0.321598			−0.160799	−	0.986987i	$-0.551407\pi$
$617$	−198.426			−0.321598			−0.160799	+	0.986987i	$0.551407\pi$
$618$		0			0
$619$	17.1752			0.0277468			0.0138734	−	0.999904i	$-0.495584\pi$
$619$	17.1752			0.0277468			0.0138734	+	0.999904i	$0.495584\pi$
$620$		0			0
$621$	−430.088	+	304.837i	−0.692574	+	0.490881i
$622$		0			0
$623$	479.768			0.770094
$624$		0			0
$625$	413.439	+	468.714i	0.661503	+	0.749943i
$626$		0			0
$627$	168.747	+	55.5595i	0.269135	+	0.0886116i
$628$		0			0
$629$		−	130.097i		−	0.206831i
$630$		0			0
$631$	−388.876			−0.616285			−0.308142	−	0.951340i	$-0.599707\pi$
$631$	−388.876			−0.616285			−0.308142	+	0.951340i	$0.599707\pi$
$632$		0			0
$633$	266.947	−	810.781i	0.421717	−	1.28085i
$634$		0			0
$635$	78.8955	−	366.568i	0.124245	−	0.577272i
$636$		0			0
$637$		−	42.1179i		−	0.0661191i
$638$		0			0
$639$	−215.524	+	291.818i	−0.337283	+	0.456680i
$640$		0			0
$641$			180.547i			0.281664i	0.990034	+	0.140832i	$0.0449778\pi$
$641$			180.547i			0.281664i	−0.990034	+	0.140832i	$0.955022\pi$
$642$		0			0
$643$		−	701.008i		−	1.09021i	−0.838367	−	0.545107i	$-0.816489\pi$
$643$		−	701.008i		−	1.09021i	0.838367	−	0.545107i	$-0.183511\pi$
$644$		0			0
$645$	−663.795	−	388.984i	−1.02914	−	0.603076i
$646$		0			0
$647$	−114.266			−0.176609			−0.0883046	−	0.996094i	$-0.528145\pi$
$647$	−114.266			−0.176609			−0.0883046	+	0.996094i	$0.528145\pi$
$648$		0			0
$649$	734.928			1.13240
$650$		0			0
$651$	−843.187	−	277.616i	−1.29522	−	0.426446i
$652$		0			0
$653$	−240.882			−0.368884			−0.184442	−	0.982843i	$-0.559048\pi$
$653$	−240.882			−0.368884			−0.184442	+	0.982843i	$0.559048\pi$
$654$		0			0
$655$	106.414	−	494.423i	0.162463	−	0.754844i
$656$		0			0
$657$	−419.785	+	568.387i	−0.638942	+	0.865125i
$658$		0			0
$659$			1218.15i			1.84848i	0.381807	+	0.924242i	$0.375302\pi$
$659$			1218.15i			1.84848i	−0.381807	+	0.924242i	$0.624698\pi$
$660$		0			0
$661$	−1075.32			−1.62681			−0.813404	−	0.581699i	$-0.802388\pi$
$661$	−1075.32			−1.62681			−0.813404	+	0.581699i	$0.802388\pi$
$662$		0			0
$663$	190.581	+	62.7480i	0.287452	+	0.0946425i
$664$		0			0
$665$	−56.3642	+	261.882i	−0.0847583	+	0.393807i
$666$		0			0
$667$		−	1091.19i		−	1.63596i
$668$		0			0
$669$	−86.3189	−	28.4202i	−0.129027	−	0.0424816i
$670$		0			0
$671$			31.1381i			0.0464054i
$672$		0			0
$673$		−	356.367i		−	0.529521i	−0.964314	−	0.264760i	$-0.914707\pi$
$673$		−	356.367i		−	0.529521i	0.964314	−	0.264760i	$-0.0852928\pi$
$674$		0			0
$675$	−662.518	+	129.206i	−0.981509	+	0.191417i
$676$		0			0
$677$	79.8649			0.117969			0.0589844	−	0.998259i	$-0.481214\pi$
$677$	79.8649			0.117969			0.0589844	+	0.998259i	$0.481214\pi$
$678$		0			0
$679$	−23.4588			−0.0345490
$680$		0			0
$681$	−224.585	+	682.120i	−0.329788	+	1.00164i
$682$		0			0
$683$	1270.41			1.86004			0.930021	−	0.367507i	$-0.119789\pi$
$683$	1270.41			1.86004			0.930021	+	0.367507i	$0.119789\pi$
$684$		0			0
$685$	−558.667	−	120.241i	−0.815572	−	0.175534i
$686$		0			0
$687$	267.347	−	811.996i	0.389151	−	1.18195i
$688$		0			0
$689$			1342.92i			1.94908i
$690$		0			0
$691$	1244.39			1.80085			0.900424	−	0.435013i	$-0.143256\pi$
$691$	1244.39			1.80085			0.900424	+	0.435013i	$0.143256\pi$
$692$		0			0
$693$	−371.350	−	274.262i	−0.535858	−	0.395760i
$694$		0			0
$695$	−1125.02	−	242.135i	−1.61873	−	0.348395i
$696$		0			0
$697$		−	211.520i		−	0.303472i
$698$		0			0
$699$	−88.0623	+	267.466i	−0.125983	+	0.382641i
$700$		0			0
$701$		−	1034.47i		−	1.47570i	−0.674965	−	0.737850i	$-0.735841\pi$
$701$		−	1034.47i		−	1.47570i	0.674965	−	0.737850i	$-0.264159\pi$
$702$		0			0
$703$			248.386i			0.353323i
$704$		0			0
$705$	−468.372	+	799.271i	−0.664358	+	1.13372i
$706$		0			0
$707$	−335.464			−0.474489
$708$		0			0
$709$	659.081			0.929592			0.464796	−	0.885418i	$-0.346128\pi$
$709$	659.081			0.929592			0.464796	+	0.885418i	$0.346128\pi$
$710$		0			0
$711$	369.293	+	272.743i	0.519399	+	0.383604i
$712$		0			0
$713$	848.099			1.18948
$714$		0			0
$715$	−597.593	−	128.619i	−0.835795	−	0.179886i
$716$		0			0
$717$	679.116	+	223.597i	0.947164	+	0.311850i
$718$		0			0
$719$			471.213i			0.655373i	0.944787	+	0.327686i	$0.106269\pi$
$719$			471.213i			0.655373i	−0.944787	+	0.327686i	$0.893731\pi$
$720$		0			0
$721$	616.823			0.855511
$722$		0			0
$723$	41.5545	−	126.211i	0.0574750	−	0.174566i
$724$		0			0
$725$	574.804	−	1273.48i	0.792833	−	1.75653i
$726$		0			0
$727$			640.411i			0.880895i	0.897778	+	0.440447i	$0.145180\pi$
$727$			640.411i			0.880895i	−0.897778	+	0.440447i	$0.854820\pi$
$728$		0			0
$729$	241.469	−	687.847i	0.331233	−	0.943549i
$730$		0			0
$731$		−	211.284i		−	0.289034i
$732$		0			0
$733$		−	619.831i		−	0.845608i	−0.906221	−	0.422804i	$-0.861046\pi$
$733$		−	619.831i		−	0.845608i	0.906221	−	0.422804i	$-0.138954\pi$
$734$		0			0
$735$	−19.6729	+	33.5715i	−0.0267658	+	0.0456755i
$736$		0			0
$737$	475.838			0.645642
$738$		0			0
$739$	−135.992			−0.184022			−0.0920111	−	0.995758i	$-0.529330\pi$
$739$	−135.992			−0.184022			−0.0920111	+	0.995758i	$0.529330\pi$
$740$		0			0
$741$	−363.864	−	119.801i	−0.491045	−	0.161675i
$742$		0			0
$743$	−986.468			−1.32768			−0.663841	−	0.747874i	$-0.731075\pi$
$743$	−986.468			−1.32768			−0.663841	+	0.747874i	$0.731075\pi$
$744$		0			0
$745$	9.59936	−	44.6010i	0.0128851	−	0.0598671i
$746$		0			0
$747$	19.6925	+	14.5440i	0.0263621	+	0.0194698i
$748$		0			0
$749$		−	445.405i		−	0.594667i
$750$		0			0
$751$	−551.977			−0.734990			−0.367495	−	0.930026i	$-0.619784\pi$
$751$	−551.977			−0.734990			−0.367495	+	0.930026i	$0.619784\pi$
$752$		0			0
$753$	−835.175	−	274.978i	−1.10913	−	0.365177i
$754$		0			0
$755$	796.805	+	171.495i	1.05537	+	0.227145i
$756$		0			0
$757$			1143.91i			1.51111i	0.655084	+	0.755556i	$0.272633\pi$
$757$			1143.91i			1.51111i	−0.655084	+	0.755556i	$0.727367\pi$
$758$		0			0
$759$	418.926	+	137.930i	0.551945	+	0.181726i
$760$		0			0
$761$		−	29.3201i		−	0.0385284i	−0.999814	−	0.0192642i	$-0.993868\pi$
$761$		−	29.3201i		−	0.0385284i	0.999814	−	0.0192642i	$-0.00613236\pi$
$762$		0			0
$763$			1161.27i			1.52198i
$764$		0			0
$765$	−122.600	−	139.034i	−0.160261	−	0.181744i
$766$		0			0
$767$	−1584.70			−2.06610
$768$		0			0
$769$	−61.7841			−0.0803434			−0.0401717	−	0.999193i	$-0.512790\pi$
$769$	−61.7841			−0.0803434			−0.0401717	+	0.999193i	$0.512790\pi$
$770$		0			0
$771$	158.864	−	482.509i	0.206050	−	0.625822i
$772$		0			0
$773$	−444.408			−0.574913			−0.287457	−	0.957794i	$-0.592810\pi$
$773$	−444.408			−0.574913			−0.287457	+	0.957794i	$0.592810\pi$
$774$		0			0
$775$	989.783	+	446.753i	1.27714	+	0.576455i
$776$		0			0
$777$	201.849	−	613.063i	0.259779	−	0.789012i
$778$		0			0
$779$			403.842i			0.518410i
$780$		0			0
$781$	303.517			0.388626
$782$		0			0
$783$	872.576	+	1231.10i	1.11440	+	1.57229i
$784$		0			0
$785$	128.907	−	598.932i	0.164212	−	0.762971i
$786$		0			0
$787$			206.738i			0.262691i	0.991337	+	0.131346i	$0.0419298\pi$
$787$			206.738i			0.262691i	−0.991337	+	0.131346i	$0.958070\pi$
$788$		0			0
$789$	−85.5595	+	259.865i	−0.108440	+	0.329360i
$790$		0			0
$791$			377.489i			0.477230i
$792$		0			0
$793$		−	67.1419i		−	0.0846682i
$794$		0			0
$795$	627.264	−	1070.42i	0.789011	−	1.34644i
$796$		0			0
$797$	235.281			0.295208			0.147604	−	0.989047i	$-0.452844\pi$
$797$	235.281			0.295208			0.147604	+	0.989047i	$0.452844\pi$
$798$		0			0
$799$	−254.405			−0.318404
$800$		0			0
$801$	376.565	−	509.868i	0.470119	−	0.636540i
$802$		0			0
$803$	591.172			0.736205
$804$		0			0
$805$	−139.928	+	650.138i	−0.173823	+	0.807625i
$806$		0			0
$807$	926.561	+	305.067i	1.14816	+	0.378026i
$808$		0			0
$809$		−	56.7919i		−	0.0702001i	−0.999384	−	0.0351000i	$-0.988825\pi$
$809$		−	56.7919i		−	0.0702001i	0.999384	−	0.0351000i	$-0.0111750\pi$
$810$		0			0
$811$	743.889			0.917249			0.458625	−	0.888630i	$-0.348342\pi$
$811$	743.889			0.917249			0.458625	+	0.888630i	$0.348342\pi$
$812$		0			0
$813$	−124.516	+	378.186i	−0.153157	+	0.465174i
$814$		0			0
$815$	70.1672	−	326.014i	0.0860948	−	0.400017i
$816$		0			0
$817$			403.391i			0.493747i
$818$		0			0
$819$	800.729	+	591.382i	0.977691	+	0.722078i
$820$		0			0
$821$			314.095i			0.382576i	0.981534	+	0.191288i	$0.0612665\pi$
$821$			314.095i			0.382576i	−0.981534	+	0.191288i	$0.938733\pi$
$822$		0			0
$823$			1059.68i			1.28758i	0.765203	+	0.643789i	$0.222639\pi$
$823$			1059.68i			1.28758i	−0.765203	+	0.643789i	$0.777361\pi$
$824$		0			0
$825$	416.255	+	381.650i	0.504552	+	0.462606i
$826$		0			0
$827$	834.408			1.00896			0.504479	−	0.863424i	$-0.331685\pi$
$827$	834.408			1.00896			0.504479	+	0.863424i	$0.331685\pi$
$828$		0			0
$829$	19.3660			0.0233607			0.0116803	−	0.999932i	$-0.496282\pi$
$829$	19.3660			0.0233607			0.0116803	+	0.999932i	$0.496282\pi$
$830$		0			0
$831$	724.347	+	238.489i	0.871658	+	0.286990i
$832$		0			0
$833$	−10.6857			−0.0128279
$834$		0			0
$835$	−799.605	−	172.097i	−0.957610	−	0.206104i
$836$		0			0
$837$	−956.842	+	678.189i	−1.14318	+	0.810262i
$838$		0			0
$839$			1565.62i			1.86605i	0.359808	+	0.933026i	$0.382842\pi$
$839$			1565.62i			1.86605i	−0.359808	+	0.933026i	$0.617158\pi$
$840$		0			0
$841$	−2282.45			−2.71397
$842$		0			0
$843$	55.7048	+	18.3406i	0.0660792	+	0.0217563i
$844$		0			0
$845$	462.486	+	99.5398i	0.547321	+	0.117799i
$846$		0			0
$847$		−	438.039i		−	0.517165i
$848$		0			0
$849$	−312.519	−	102.896i	−0.368102	−	0.121196i
$850$		0			0
$851$			616.634i			0.724599i
$852$		0			0
$853$		−	20.9266i		−	0.0245329i	−0.999925	−	0.0122665i	$-0.996095\pi$
$853$		−	20.9266i		−	0.0245329i	0.999925	−	0.0122665i	$-0.00390463\pi$
$854$		0			0
$855$	234.072	+	265.449i	0.273769	+	0.310467i
$856$		0			0
$857$	−236.110			−0.275508			−0.137754	−	0.990466i	$-0.543988\pi$
$857$	−236.110			−0.275508			−0.137754	+	0.990466i	$0.543988\pi$
$858$		0			0
$859$	−997.970			−1.16178			−0.580891	−	0.813982i	$-0.697296\pi$
$859$	−997.970			−1.16178			−0.580891	+	0.813982i	$0.697296\pi$
$860$		0			0
$861$	328.178	−	996.756i	0.381159	−	1.15767i
$862$		0			0
$863$	−1147.63			−1.32982			−0.664909	−	0.746924i	$-0.731530\pi$
$863$	−1147.63			−1.32982			−0.664909	+	0.746924i	$0.731530\pi$
$864$		0			0
$865$	−169.681	−	36.5200i	−0.196163	−	0.0422197i
$866$		0			0
$867$	−255.219	+	775.161i	−0.294370	+	0.894072i
$868$		0			0
$869$		−	384.097i		−	0.441999i
$870$		0			0
$871$	−1026.03			−1.17799
$872$		0			0
$873$	−18.4125	+	24.9305i	−0.0210911	+	0.0285573i
$874$		0			0
$875$	−505.777	+	685.042i	−0.578031	+	0.782905i
$876$		0			0
$877$		−	166.283i		−	0.189604i	−0.995496	−	0.0948022i	$-0.969778\pi$
$877$		−	166.283i		−	0.189604i	0.995496	−	0.0948022i	$-0.0302219\pi$
$878$		0			0
$879$	167.363	−	508.321i	0.190401	−	0.578294i
$880$		0			0
$881$		−	275.137i		−	0.312301i	−0.987733	−	0.156150i	$-0.950092\pi$
$881$		−	275.137i		−	0.312301i	0.987733	−	0.156150i	$-0.0499085\pi$
$882$		0			0
$883$			262.830i			0.297656i	0.988863	+	0.148828i	$0.0475501\pi$
$883$			262.830i			0.297656i	−0.988863	+	0.148828i	$0.952450\pi$
$884$		0			0
$885$	1263.14	+	740.199i	1.42727	+	0.836383i
$886$		0			0
$887$	406.164			0.457908			0.228954	−	0.973437i	$-0.426469\pi$
$887$	406.164			0.457908			0.228954	+	0.973437i	$0.426469\pi$
$888$		0			0
$889$	510.862			0.574648
$890$		0			0
$891$	−582.938	+	179.382i	−0.654251	+	0.201327i
$892$		0			0
$893$	485.720			0.543920
$894$		0			0
$895$	287.680	−	1336.63i	0.321430	−	1.49344i
$896$		0			0
$897$	−903.316	−	297.413i	−1.00704	−	0.331564i
$898$		0			0
$899$		−	2427.63i		−	2.70036i
$900$		0			0
$901$	340.710			0.378146
$902$		0			0
$903$	327.812	−	995.644i	0.363026	−	1.10260i
$904$		0			0
$905$	199.799	+	43.0024i	0.220773	+	0.0475164i
$906$		0			0
$907$		−	1284.19i		−	1.41587i	−0.706278	−	0.707934i	$-0.749627\pi$
$907$		−	1284.19i		−	1.41587i	0.706278	−	0.707934i	$-0.250373\pi$
$908$		0			0
$909$	−263.302	+	356.510i	−0.289661	+	0.392201i
$910$		0			0
$911$		−	353.054i		−	0.387546i	−0.981046	−	0.193773i	$-0.937928\pi$
$911$		−	353.054i		−	0.387546i	0.981046	−	0.193773i	$-0.0620725\pi$
$912$		0			0
$913$		−	20.4819i		−	0.0224336i
$914$		0			0
$915$	−31.3614	+	53.5177i	−0.0342747	+	0.0584893i
$916$		0			0
$917$	689.046			0.751413
$918$		0			0
$919$	210.284			0.228818			0.114409	−	0.993434i	$-0.463503\pi$
$919$	210.284			0.228818			0.114409	+	0.993434i	$0.463503\pi$
$920$		0			0
$921$	823.644	+	271.182i	0.894293	+	0.294443i
$922$		0			0
$923$	−654.462			−0.709060
$924$		0			0
$925$	−324.824	+	719.650i	−0.351161	+	0.778000i
$926$		0			0
$927$	484.139	−	655.522i	0.522264	−	0.707143i
$928$		0			0
$929$		−	1095.27i		−	1.17898i	−0.807777	−	0.589488i	$-0.799330\pi$
$929$		−	1095.27i		−	1.17898i	0.807777	−	0.589488i	$-0.200670\pi$
$930$		0			0
$931$	20.4015			0.0219136
$932$		0			0
$933$	−957.614	−	315.291i	−1.02638	−	0.337932i
$934$		0			0
$935$	−32.6317	+	151.615i	−0.0349002	+	0.162155i
$936$		0			0
$937$			567.824i			0.606002i	0.952990	+	0.303001i	$0.0979885\pi$
$937$			567.824i			0.606002i	−0.952990	+	0.303001i	$0.902011\pi$
$938$		0			0
$939$	1606.28	+	528.862i	1.71063	+	0.563219i
$940$		0			0
$941$			726.052i			0.771575i	0.922588	+	0.385787i	$0.126070\pi$
$941$			726.052i			0.771575i	−0.922588	+	0.385787i	$0.873930\pi$
$942$		0			0
$943$			1002.56i			1.06316i
$944$		0			0
$945$	−362.019	−	845.394i	−0.383089	−	0.894596i
$946$		0			0
$947$	568.400			0.600211			0.300105	−	0.953906i	$-0.402978\pi$
$947$	568.400			0.600211			0.300105	+	0.953906i	$0.402978\pi$
$948$		0			0
$949$	−1274.72			−1.34323
$950$		0			0
$951$	131.289	−	398.757i	0.138054	−	0.419303i
$952$		0			0
$953$	−1118.37			−1.17353			−0.586765	−	0.809758i	$-0.699599\pi$
$953$	−1118.37			−1.17353			−0.586765	+	0.809758i	$0.699599\pi$
$954$		0			0
$955$	42.7062	−	198.423i	0.0447186	−	0.207773i
$956$		0			0
$957$	394.815	−	1199.15i	0.412555	−	1.25303i
$958$		0			0
$959$		−	778.578i		−	0.811865i
$960$		0			0
$961$	925.814			0.963386
$962$		0			0
$963$	−473.350	−	349.594i	−0.491537	−	0.363026i
$964$		0			0
$965$	−148.611	+	690.484i	−0.154001	+	0.715527i
$966$		0			0
$967$		−	759.775i		−	0.785704i	−0.919602	−	0.392852i	$-0.871489\pi$
$967$		−	759.775i		−	0.785704i	0.919602	−	0.392852i	$-0.128511\pi$
$968$		0			0
$969$	−30.3946	+	92.3156i	−0.0313669	+	0.0952689i
$970$		0			0
$971$			1342.50i			1.38259i	0.722570	+	0.691297i	$0.242960\pi$
$971$			1342.50i			1.38259i	−0.722570	+	0.691297i	$0.757040\pi$
$972$		0			0
$973$		−	1567.87i		−	1.61137i
$974$		0			0
$975$	−897.557	−	822.939i	−0.920571	−	0.844040i
$976$		0			0
$977$	897.030			0.918147			0.459074	−	0.888398i	$-0.348181\pi$
$977$	897.030			0.918147			0.459074	+	0.888398i	$0.348181\pi$
$978$		0			0
$979$	−530.308			−0.541683
$980$		0			0
$981$	1234.12	+	911.467i	1.25803	+	0.929121i
$982$		0			0
$983$	377.542			0.384071			0.192035	−	0.981388i	$-0.438491\pi$
$983$	377.542			0.384071			0.192035	+	0.981388i	$0.438491\pi$
$984$		0			0
$985$	−1137.17	−	244.751i	−1.15449	−	0.248479i
$986$		0			0
$987$	−1198.85	−	394.716i	−1.21464	−	0.399915i
$988$		0			0
$989$			1001.44i			1.01258i
$990$		0			0
$991$	−224.222			−0.226258			−0.113129	−	0.993580i	$-0.536087\pi$
$991$	−224.222			−0.226258			−0.113129	+	0.993580i	$0.536087\pi$
$992$		0			0
$993$	−13.6147	+	41.3511i	−0.0137107	+	0.0416426i
$994$		0			0
$995$	−417.316	−	89.8179i	−0.419413	−	0.0902693i
$996$		0			0
$997$		−	1018.21i		−	1.02127i	−0.859797	−	0.510635i	$-0.829410\pi$
$997$		−	1018.21i		−	1.02127i	0.859797	−	0.510635i	$-0.170590\pi$
$998$		0			0
$999$	−493.096	−	695.699i	−0.493590	−	0.696396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.3.c.a.89.7	yes	12
3.2	odd	2	inner	120.3.c.a.89.5	✓	12
4.3	odd	2		240.3.c.e.209.6		12
5.2	odd	4		600.3.l.g.401.1		12
5.3	odd	4		600.3.l.g.401.12		12
5.4	even	2	inner	120.3.c.a.89.6	yes	12
8.3	odd	2		960.3.c.j.449.7		12
8.5	even	2		960.3.c.k.449.6		12
12.11	even	2		240.3.c.e.209.8		12
15.2	even	4		600.3.l.g.401.2		12
15.8	even	4		600.3.l.g.401.11		12
15.14	odd	2	inner	120.3.c.a.89.8	yes	12
20.3	even	4		1200.3.l.y.401.1		12
20.7	even	4		1200.3.l.y.401.12		12
20.19	odd	2		240.3.c.e.209.7		12
24.5	odd	2		960.3.c.k.449.8		12
24.11	even	2		960.3.c.j.449.5		12
40.19	odd	2		960.3.c.j.449.6		12
40.29	even	2		960.3.c.k.449.7		12
60.23	odd	4		1200.3.l.y.401.2		12
60.47	odd	4		1200.3.l.y.401.11		12
60.59	even	2		240.3.c.e.209.5		12
120.29	odd	2		960.3.c.k.449.5		12
120.59	even	2		960.3.c.j.449.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.c.a.89.5	✓	12	3.2	odd	2	inner
120.3.c.a.89.6	yes	12	5.4	even	2	inner
120.3.c.a.89.7	yes	12	1.1	even	1	trivial
120.3.c.a.89.8	yes	12	15.14	odd	2	inner
240.3.c.e.209.5		12	60.59	even	2
240.3.c.e.209.6		12	4.3	odd	2
240.3.c.e.209.7		12	20.19	odd	2
240.3.c.e.209.8		12	12.11	even	2
600.3.l.g.401.1		12	5.2	odd	4
600.3.l.g.401.2		12	15.2	even	4
600.3.l.g.401.11		12	15.8	even	4
600.3.l.g.401.12		12	5.3	odd	4
960.3.c.j.449.5		12	24.11	even	2
960.3.c.j.449.6		12	40.19	odd	2
960.3.c.j.449.7		12	8.3	odd	2
960.3.c.j.449.8		12	120.59	even	2
960.3.c.k.449.5		12	120.29	odd	2
960.3.c.k.449.6		12	8.5	even	2
960.3.c.k.449.7		12	40.29	even	2
960.3.c.k.449.8		12	24.5	odd	2
1200.3.l.y.401.1		12	20.3	even	4
1200.3.l.y.401.2		12	60.23	odd	4
1200.3.l.y.401.11		12	60.47	odd	4
1200.3.l.y.401.12		12	20.7	even	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	120.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.938195 - 2.84952i) q^{3} +(-4.88807 - 1.05205i) q^{5} -6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} +O(q^{10})\)	\(q+(0.938195 - 2.84952i) q^{3} +(-4.88807 - 1.05205i) q^{5} -6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} +7.52980i q^{11} -16.2362i q^{13} +(-7.58380 + 12.9416i) q^{15} -4.11928 q^{17} +7.86469 q^{19} +(-19.4115 - 6.39117i) q^{21} +19.5246 q^{23} +(22.7864 + 10.2850i) q^{25} +(-22.0280 + 15.6130i) q^{27} -55.8878i q^{29} +43.4375 q^{31} +(21.4563 + 7.06442i) q^{33} +(-7.16675 + 33.2984i) q^{35} +31.5824i q^{37} +(-46.2655 - 15.2328i) q^{39} +51.3487i q^{41} +51.2914i q^{43} +(29.7624 + 33.7520i) q^{45} +61.7596 q^{47} +2.59407 q^{49} +(-3.86469 + 11.7380i) q^{51} -82.7111 q^{53} +(7.92170 - 36.8061i) q^{55} +(7.37861 - 22.4106i) q^{57} -97.6026i q^{59} +4.13531 q^{61} +(-36.4236 + 49.3174i) q^{63} +(-17.0813 + 79.3638i) q^{65} -63.1940i q^{67} +(18.3179 - 55.6358i) q^{69} -40.3087i q^{71} -78.5111i q^{73} +(50.6853 - 55.2811i) q^{75} +51.2944 q^{77} -51.0103 q^{79} +(23.8230 + 77.4175i) q^{81} -2.72011 q^{83} +(20.1353 + 4.33368i) q^{85} +(-159.254 - 52.4337i) q^{87} +70.4279i q^{89} -110.604 q^{91} +(40.7528 - 123.776i) q^{93} +(-38.4431 - 8.27403i) q^{95} -3.44364i q^{97} +(40.2605 - 54.5126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{9}+O(q^{10}) \) 12 * q + 8 * q^9	\( 12 q + 8 q^{9} + 16 q^{15} + 4 q^{21} + 36 q^{25} - 48 q^{31} - 128 q^{39} - 68 q^{45} - 252 q^{49} + 48 q^{51} - 48 q^{55} + 144 q^{61} + 268 q^{69} + 304 q^{75} + 432 q^{79} - 188 q^{81} + 336 q^{85} - 560 q^{99}+O(q^{100}) \) 12 * q + 8 * q^9 + 16 * q^15 + 4 * q^21 + 36 * q^25 - 48 * q^31 - 128 * q^39 - 68 * q^45 - 252 * q^49 + 48 * q^51 - 48 * q^55 + 144 * q^61 + 268 * q^69 + 304 * q^75 + 432 * q^79 - 188 * q^81 + 336 * q^85 - 560 * q^99

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