LMFDB - Embedded newform 960.3.c.k.449.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(449,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, 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("960.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.c (of order $2$, degree $1$, 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:	$26.1581053786$
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:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.7
Root			$-0.723561i$ of defining polynomial
Character	$\chi$	$=$	960.449
Dual form			960.3.c.k.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.938195 - 2.84952i) q^{3} +(-4.88807 + 1.05205i) q^{5} +6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} +O(q^{10})$	\(q+(0.938195 - 2.84952i) q^{3} +(-4.88807 + 1.05205i) q^{5} +6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} -7.52980i q^{11} -16.2362i q^{13} +(-1.58813 + 14.9157i) q^{15} +4.11928 q^{17} -7.86469 q^{19} +(19.4115 + 6.39117i) q^{21} -19.5246 q^{23} +(22.7864 - 10.2850i) q^{25} +(-22.0280 + 15.6130i) q^{27} +55.8878i q^{29} +43.4375 q^{31} +(-21.4563 - 7.06442i) q^{33} +(-7.16675 - 33.2984i) q^{35} +31.5824i q^{37} +(-46.2655 - 15.2328i) q^{39} +51.3487i q^{41} +51.2914i q^{43} +(41.0127 + 18.5192i) q^{45} -61.7596 q^{47} +2.59407 q^{49} +(3.86469 - 11.7380i) q^{51} -82.7111 q^{53} +(7.92170 + 36.8061i) q^{55} +(-7.37861 + 22.4106i) q^{57} +97.6026i q^{59} -4.13531 q^{61} +(36.4236 - 49.3174i) q^{63} +(17.0813 + 79.3638i) q^{65} -63.1940i q^{67} +(-18.3179 + 55.6358i) q^{69} -40.3087i q^{71} +78.5111i q^{73} +(-7.92915 - 74.5797i) q^{75} +51.2944 q^{77} -51.0103 q^{79} +(23.8230 + 77.4175i) q^{81} -2.72011 q^{83} +(-20.1353 + 4.33368i) q^{85} +(159.254 + 52.4337i) q^{87} +70.4279i q^{89} +110.604 q^{91} +(40.7528 - 123.776i) q^{93} +(38.4431 - 8.27403i) q^{95} +3.44364i q^{97} +(-40.2605 + 54.5126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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	$0.161758\pi$
$7$			6.81219i			0.973170i	−0.873633	+	0.486585i	$0.838242\pi$
$8$		0			0
$9$	−7.23958	−	5.34682i	−0.804398	−	0.594091i
$10$		0			0
$11$		−	7.52980i		−	0.684527i	−0.939604	−	0.342263i	$-0.888806\pi$
$11$		−	7.52980i		−	0.684527i	0.939604	−	0.342263i	$-0.111194\pi$
$12$		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
$15$	−1.58813	+	14.9157i	−0.105875	+	0.994379i
$16$		0			0
$17$	4.11928			0.242311			0.121155	−	0.992634i	$-0.461340\pi$
$17$	4.11928			0.242311			0.121155	+	0.992634i	$0.461340\pi$
$18$		0			0
$19$	−7.86469			−0.413931			−0.206965	−	0.978348i	$-0.566359\pi$
$19$	−7.86469			−0.413931			−0.206965	+	0.978348i	$0.566359\pi$
$20$		0			0
$21$	19.4115	+	6.39117i	0.924357	+	0.304341i
$22$		0			0
$23$	−19.5246			−0.848895			−0.424447	−	0.905453i	$-0.639532\pi$
$23$	−19.5246			−0.848895			−0.424447	+	0.905453i	$0.639532\pi$
$24$		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	$0.413833\pi$
$29$			55.8878i			1.92717i	−0.267408	+	0.963583i	$0.586167\pi$
$30$		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
$45$	41.0127	+	18.5192i	0.911392	+	0.411539i
$46$		0			0
$47$	−61.7596			−1.31403			−0.657017	−	0.753875i	$-0.728182\pi$
$47$	−61.7596			−1.31403			−0.657017	+	0.753875i	$0.728182\pi$
$48$		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	$0.310034\pi$
$59$			97.6026i			1.65428i	−0.561994	+	0.827141i	$0.689966\pi$
$60$		0			0
$61$	−4.13531			−0.0677920			−0.0338960	−	0.999425i	$-0.510791\pi$
$61$	−4.13531			−0.0677920			−0.0338960	+	0.999425i	$0.510791\pi$
$62$		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	$0.180724\pi$
$73$			78.5111i			1.07549i	−0.843106	+	0.537747i	$0.819276\pi$
$74$		0			0
$75$	−7.92915	−	74.5797i	−0.105722	−	0.994396i
$76$		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	$0.00565053\pi$
$97$			3.44364i			0.0355015i	−0.999842	+	0.0177507i	$0.994349\pi$
$98$		0			0
$99$	−40.2605	+	54.5126i	−0.406671	+	0.550632i
$100$		0			0
$101$			49.2446i			0.487570i	0.969829	+	0.243785i	$0.0783892\pi$
$101$			49.2446i			0.487570i	−0.969829	+	0.243785i	$0.921611\pi$
$102$		0			0
$103$		−	90.5470i		−	0.879097i	−0.898219	−	0.439548i	$-0.855138\pi$
$103$		−	90.5470i		−	0.879097i	0.898219	−	0.439548i	$-0.144862\pi$
$104$		0			0
$105$	−101.609	−	10.8186i	−0.967700	−	0.103034i
$106$		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	$-0.214216\pi$
$109$	170.469			1.56394			0.781968	+	0.623319i	$0.214216\pi$
$110$		0			0
$111$	89.9949	+	29.6305i	0.810765	+	0.266941i
$112$		0			0
$113$	55.4137			0.490387			0.245193	−	0.969474i	$-0.421149\pi$
$113$	55.4137			0.490387			0.245193	+	0.969474i	$0.421149\pi$
$114$		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	$-0.904599\pi$
$127$		−	74.9923i		−	0.590491i	0.955421	−	0.295245i	$-0.0954014\pi$
$128$		0			0
$129$	146.156	+	48.1214i	1.13299	+	0.373034i
$130$		0			0
$131$		−	101.149i		−	0.772130i	−0.922472	−	0.386065i	$-0.873834\pi$
$131$		−	101.149i		−	0.772130i	0.922472	−	0.386065i	$-0.126166\pi$
$132$		0			0
$133$		−	53.5758i		−	0.402825i
$134$		0			0
$135$	91.2489	−	99.4919i	0.675918	−	0.736977i
$136$		0			0
$137$	−114.292			−0.834248			−0.417124	−	0.908850i	$-0.636962\pi$
$137$	−114.292			−0.834248			−0.417124	+	0.908850i	$0.636962\pi$
$138$		0			0
$139$	−230.156			−1.65580			−0.827899	−	0.560878i	$-0.810464\pi$
$139$	−230.156			−1.65580			−0.827899	+	0.560878i	$0.810464\pi$
$140$		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	$-0.990252\pi$
$149$		−	9.12446i		−	0.0612380i	0.999531	−	0.0306190i	$-0.00974785\pi$
$150$		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
$165$	112.312	+	11.9583i	0.680680	+	0.0724744i
$166$		0			0
$167$	−163.583			−0.979539			−0.489769	−	0.871852i	$-0.662919\pi$
$167$	−163.583			−0.979539			−0.489769	+	0.871852i	$0.662919\pi$
$168$		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	$-0.723321\pi$
$179$		−	273.448i		−	1.52764i	0.645429	−	0.763820i	$-0.276679\pi$
$180$		0			0
$181$	40.8749			0.225828			0.112914	−	0.993605i	$-0.463981\pi$
$181$	40.8749			0.225828			0.112914	+	0.993605i	$0.463981\pi$
$182$		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	$0.119258\pi$
$193$			141.259i			0.731912i	−0.930632	+	0.365956i	$0.880742\pi$
$194$		0			0
$195$	242.175	+	25.7852i	1.24192	+	0.132232i
$196$		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	$-0.735532\pi$
$211$	−284.532			−1.34849			−0.674247	+	0.738506i	$0.735532\pi$
$212$		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	$0.0216363\pi$
$223$			30.2924i			0.135840i	−0.997691	+	0.0679201i	$0.978364\pi$
$224$		0			0
$225$	−219.956	−	47.3760i	−0.977581	−	0.210560i
$226$		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	$-0.713753\pi$
$229$	−284.959			−1.24436			−0.622180	+	0.782874i	$0.713753\pi$
$230$		0			0
$231$	48.1242	−	146.165i	0.208330	−	0.632747i
$232$		0			0
$233$	93.8635			0.402848			0.201424	−	0.979504i	$-0.435443\pi$
$233$	93.8635			0.402848			0.201424	+	0.979504i	$0.435443\pi$
$234$		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	$0.198454\pi$
$251$			293.093i			1.16770i	−0.811862	+	0.583850i	$0.801546\pi$
$252$		0			0
$253$			147.016i			0.581092i
$254$		0			0
$255$	−6.54194	+	61.4419i	−0.0256547	+	0.240949i
$256$		0			0
$257$	−169.330			−0.658870			−0.329435	−	0.944178i	$-0.606858\pi$
$257$	−169.330			−0.658870			−0.329435	+	0.944178i	$0.606858\pi$
$258$		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	$-0.444532\pi$
$263$	91.1958			0.346752			0.173376	+	0.984856i	$0.444532\pi$
$264$		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	$-0.793416\pi$
$269$		−	325.164i		−	1.20879i	0.796686	−	0.604393i	$-0.206584\pi$
$270$		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
$285$	12.4901	−	117.307i	0.0438250	−	0.411604i
$286$		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	$-0.643214\pi$
$313$		−	563.702i		−	1.80096i	0.434894	−	0.900482i	$-0.356786\pi$
$314$		0			0
$315$	−126.157	+	279.386i	−0.400497	+	0.886940i
$316$		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	$-0.493022\pi$
$331$	14.5116			0.0438416			0.0219208	+	0.999760i	$0.493022\pi$
$332$		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	$0.172418\pi$
$337$			347.492i			1.03113i	−0.856850	+	0.515566i	$0.827582\pi$
$338$		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
$345$	31.0075	−	291.223i	0.0898769	−	0.844124i
$346$		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	$-0.210502\pi$
$349$	550.853			1.57838			0.789188	+	0.614152i	$0.210502\pi$
$350$		0			0
$351$	253.496	+	357.652i	0.722212	+	1.01895i
$352$		0			0
$353$	−643.177			−1.82203			−0.911015	−	0.412373i	$-0.864700\pi$
$353$	−643.177			−1.82203			−0.911015	+	0.412373i	$0.864700\pi$
$354$		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	$0.0194041\pi$
$367$			44.7168i			0.121844i	−0.998143	+	0.0609221i	$0.980596\pi$
$368$		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
$375$	117.220	+	356.209i	0.312585	+	0.949890i
$376$		0			0
$377$	907.408			2.40692
$378$		0			0
$379$	505.072			1.33264			0.666322	−	0.745664i	$-0.267868\pi$
$379$	505.072			1.33264			0.666322	+	0.745664i	$0.267868\pi$
$380$		0			0
$381$	−213.692	−	70.3575i	−0.560873	−	0.184665i
$382$		0			0
$383$	−193.577			−0.505422			−0.252711	−	0.967542i	$-0.581322\pi$
$383$	−193.577			−0.505422			−0.252711	+	0.967542i	$0.581322\pi$
$384$		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	$0.117222\pi$
$389$			280.077i			0.719993i	−0.932954	+	0.359996i	$0.882778\pi$
$390$		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
$405$	−197.895	−	353.359i	−0.488630	−	0.872491i
$406$		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	$-0.970850\pi$
$419$		−	76.6340i		−	0.182897i	0.995810	−	0.0914487i	$-0.0291497\pi$
$420$		0			0
$421$	183.991			0.437033			0.218516	−	0.975833i	$-0.429878\pi$
$421$	183.991			0.437033			0.218516	+	0.975833i	$0.429878\pi$
$422$		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	$-0.847439\pi$
$433$		−	399.351i		−	0.922288i	0.887325	−	0.461144i	$-0.152561\pi$
$434$		0			0
$435$	−833.606	−	88.7570i	−1.91633	−	0.204039i
$436$		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	$0.208056\pi$
$457$			555.776i			1.21614i	−0.793883	+	0.608070i	$0.791944\pi$
$458$		0			0
$459$	−90.7396	+	64.3143i	−0.197690	+	0.140118i
$460$		0			0
$461$			369.227i			0.800927i	0.916313	+	0.400463i	$0.131151\pi$
$461$			369.227i			0.800927i	−0.916313	+	0.400463i	$0.868849\pi$
$462$		0			0
$463$		−	360.832i		−	0.779336i	−0.920955	−	0.389668i	$-0.872590\pi$
$463$		−	360.832i		−	0.779336i	0.920955	−	0.389668i	$-0.127410\pi$
$464$		0			0
$465$	−68.9842	+	647.900i	−0.148353	+	1.39333i
$466$		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	$0.0112208\pi$
$487$			34.3276i			0.0704880i	−0.999379	+	0.0352440i	$0.988779\pi$
$488$		0			0
$489$	190.052	+	62.5738i	0.388653	+	0.127963i
$490$		0			0
$491$		−	26.4204i		−	0.0538094i	−0.999638	−	0.0269047i	$-0.991435\pi$
$491$		−	26.4204i		−	0.0538094i	0.999638	−	0.0269047i	$-0.00856507\pi$
$492$		0			0
$493$			230.218i			0.466973i
$494$		0			0
$495$	139.446	−	308.817i	0.281709	−	0.623873i
$496$		0			0
$497$	274.591			0.552496
$498$		0			0
$499$	72.9046			0.146101			0.0730507	−	0.997328i	$-0.476727\pi$
$499$	72.9046			0.146101			0.0730507	+	0.997328i	$0.476727\pi$
$500$		0			0
$501$	−153.473	+	466.134i	−0.306333	+	0.930407i
$502$		0			0
$503$	−228.404			−0.454083			−0.227041	−	0.973885i	$-0.572905\pi$
$503$	−228.404			−0.454083			−0.227041	+	0.973885i	$0.572905\pi$
$504$		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	$-0.968941\pi$
$509$		−	99.1735i		−	0.194840i	0.995243	−	0.0974199i	$-0.0310590\pi$
$510$		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
$525$	508.051	−	54.0149i	0.967716	−	0.102885i
$526$		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	$-0.635354\pi$
$541$	−446.354			−0.825054			−0.412527	+	0.910945i	$0.635354\pi$
$542$		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
$555$	−471.074	−	50.1569i	−0.848782	−	0.0903728i
$556$		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	$-0.749341\pi$
$571$	−805.843			−1.41128			−0.705642	+	0.708569i	$0.749341\pi$
$572$		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	$0.204182\pi$
$577$			690.512i			1.19673i	−0.801225	+	0.598364i	$0.795818\pi$
$578$		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
$585$	300.683	−	665.891i	0.513988	−	1.13828i
$586$		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	$-0.442181\pi$
$593$	214.249			0.361296			0.180648	+	0.983548i	$0.442181\pi$
$594$		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	$-0.952902\pi$
$607$		−	178.972i		−	0.294847i	0.989073	−	0.147423i	$-0.0470980\pi$
$608$		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
$615$	−765.902	−	81.5483i	−1.24537	−	0.132599i
$616$		0			0
$617$	198.426			0.321598			0.160799	−	0.986987i	$-0.448593\pi$
$617$	198.426			0.321598			0.160799	+	0.986987i	$0.448593\pi$
$618$		0			0
$619$	−17.1752			−0.0277468			−0.0138734	−	0.999904i	$-0.504416\pi$
$619$	−17.1752			−0.0277468			−0.0138734	+	0.999904i	$0.504416\pi$
$620$		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
$645$	−765.047	−	81.4573i	−1.18612	−	0.126290i
$646$		0			0
$647$	114.266			0.176609			0.0883046	−	0.996094i	$-0.471855\pi$
$647$	114.266			0.176609			0.0883046	+	0.996094i	$0.471855\pi$
$648$		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	$-0.624698\pi$
$659$		−	1218.15i		−	1.84848i	0.381807	−	0.924242i	$-0.375302\pi$
$660$		0			0
$661$	1075.32			1.62681			0.813404	−	0.581699i	$-0.197612\pi$
$661$	1075.32			1.62681			0.813404	+	0.581699i	$0.197612\pi$
$662$		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	$0.0852928\pi$
$673$			356.367i			0.529521i	−0.964314	+	0.264760i	$0.914707\pi$
$674$		0			0
$675$	−341.361	+	582.321i	−0.505719	+	0.862698i
$676$		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	$-0.856744\pi$
$691$	−1244.39			−1.80085			−0.900424	+	0.435013i	$0.856744\pi$
$692$		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	$0.264159\pi$
$701$			1034.47i			1.47570i	−0.674965	+	0.737850i	$0.735841\pi$
$702$		0			0
$703$		−	248.386i		−	0.353323i
$704$		0			0
$705$	98.0821	−	921.188i	0.139124	−	1.30665i
$706$		0			0
$707$	−335.464			−0.474489
$708$		0			0
$709$	−659.081			−0.929592			−0.464796	−	0.885418i	$-0.653872\pi$
$709$	−659.081			−0.929592			−0.464796	+	0.885418i	$0.653872\pi$
$710$		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	$-0.854820\pi$
$727$		−	640.411i		−	0.880895i	0.897778	−	0.440447i	$-0.145180\pi$
$728$		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
$735$	−4.11971	+	38.6923i	−0.00560504	+	0.0526426i
$736$		0			0
$737$	−475.838			−0.645642
$738$		0			0
$739$	135.992			0.184022			0.0920111	−	0.995758i	$-0.470670\pi$
$739$	135.992			0.184022			0.0920111	+	0.995758i	$0.470670\pi$
$740$		0			0
$741$	363.864	+	119.801i	0.491045	+	0.161675i
$742$		0			0
$743$	986.468			1.32768			0.663841	−	0.747874i	$-0.268925\pi$
$743$	986.468			1.32768			0.663841	+	0.747874i	$0.268925\pi$
$744$		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
$765$	168.943	+	76.2859i	0.220840	+	0.0997201i
$766$		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
$795$	131.356	−	1233.69i	0.165227	−	1.55181i
$796$		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	$-0.651658\pi$
$811$	−743.889			−0.917249			−0.458625	+	0.888630i	$0.651658\pi$
$812$		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	$-0.938733\pi$
$821$		−	314.095i		−	0.382576i	0.981534	−	0.191288i	$-0.0612665\pi$
$822$		0			0
$823$		−	1059.68i		−	1.28758i	−0.765203	−	0.643789i	$-0.777361\pi$
$823$		−	1059.68i		−	1.28758i	0.765203	−	0.643789i	$-0.222639\pi$
$824$		0			0
$825$	−561.570	+	59.7049i	−0.680691	+	0.0723695i
$826$		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	$-0.503718\pi$
$829$	−19.3660			−0.0233607			−0.0116803	+	0.999932i	$0.503718\pi$
$830$		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
$855$	−322.552	−	145.648i	−0.377254	−	0.170349i
$856$		0			0
$857$	236.110			0.275508			0.137754	−	0.990466i	$-0.456012\pi$
$857$	236.110			0.275508			0.137754	+	0.990466i	$0.456012\pi$
$858$		0			0
$859$	997.970			1.16178			0.580891	−	0.813982i	$-0.302704\pi$
$859$	997.970			1.16178			0.580891	+	0.813982i	$0.302704\pi$
$860$		0			0
$861$	−328.178	+	996.756i	−0.381159	+	1.15767i
$862$		0			0
$863$	1147.63			1.32982			0.664909	−	0.746924i	$-0.268470\pi$
$863$	1147.63			1.32982			0.664909	+	0.746924i	$0.268470\pi$
$864$		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
$885$	−1455.81	−	155.005i	−1.64498	−	0.175147i
$886$		0			0
$887$	−406.164			−0.457908			−0.228954	−	0.973437i	$-0.573531\pi$
$887$	−406.164			−0.457908			−0.228954	+	0.973437i	$0.573531\pi$
$888$		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
$915$	6.56740	−	61.6810i	0.00717748	−	0.0674110i
$916$		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	$-0.902011\pi$
$937$		−	567.824i		−	0.606002i	0.952990	−	0.303001i	$-0.0979885\pi$
$938$		0			0
$939$	−1606.28	−	528.862i	−1.71063	−	0.563219i
$940$		0			0
$941$		−	726.052i		−	0.771575i	−0.922588	−	0.385787i	$-0.873930\pi$
$941$		−	726.052i		−	0.771575i	0.922588	−	0.385787i	$-0.126070\pi$
$942$		0			0
$943$		−	1002.56i		−	1.06316i
$944$		0			0
$945$	677.758	+	621.605i	0.717204	+	0.657783i
$946$		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	$-0.300401\pi$
$953$	1118.37			1.17353			0.586765	+	0.809758i	$0.300401\pi$
$954$		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	$0.128511\pi$
$967$			759.775i			0.785704i	−0.919602	+	0.392852i	$0.871489\pi$
$968$		0			0
$969$	−30.3946	+	92.3156i	−0.0313669	+	0.0952689i
$970$		0			0
$971$		−	1342.50i		−	1.38259i	−0.722570	−	0.691297i	$-0.757040\pi$
$971$		−	1342.50i		−	1.38259i	0.722570	−	0.691297i	$-0.242960\pi$
$972$		0			0
$973$		−	1567.87i		−	1.61137i
$974$		0			0
$975$	−1210.89	+	128.739i	−1.24194	+	0.132041i
$976$		0			0
$977$	−897.030			−0.918147			−0.459074	−	0.888398i	$-0.651819\pi$
$977$	−897.030			−0.918147			−0.459074	+	0.888398i	$0.651819\pi$
$978$		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	$-0.561509\pi$
$983$	−377.542			−0.384071			−0.192035	+	0.981388i	$0.561509\pi$
$984$		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	960.3.c.k.449.7		12
3.2	odd	2	inner	960.3.c.k.449.5		12
4.3	odd	2		960.3.c.j.449.6		12
5.4	even	2	inner	960.3.c.k.449.6		12
8.3	odd	2		240.3.c.e.209.7		12
8.5	even	2		120.3.c.a.89.6	yes	12
12.11	even	2		960.3.c.j.449.8		12
15.14	odd	2	inner	960.3.c.k.449.8		12
20.19	odd	2		960.3.c.j.449.7		12
24.5	odd	2		120.3.c.a.89.8	yes	12
24.11	even	2		240.3.c.e.209.5		12
40.3	even	4		1200.3.l.y.401.12		12
40.13	odd	4		600.3.l.g.401.1		12
40.19	odd	2		240.3.c.e.209.6		12
40.27	even	4		1200.3.l.y.401.1		12
40.29	even	2		120.3.c.a.89.7	yes	12
40.37	odd	4		600.3.l.g.401.12		12
60.59	even	2		960.3.c.j.449.5		12
120.29	odd	2		120.3.c.a.89.5	✓	12
120.53	even	4		600.3.l.g.401.2		12
120.59	even	2		240.3.c.e.209.8		12
120.77	even	4		600.3.l.g.401.11		12
120.83	odd	4		1200.3.l.y.401.11		12
120.107	odd	4		1200.3.l.y.401.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.c.a.89.5	✓	12	120.29	odd	2
120.3.c.a.89.6	yes	12	8.5	even	2
120.3.c.a.89.7	yes	12	40.29	even	2
120.3.c.a.89.8	yes	12	24.5	odd	2
240.3.c.e.209.5		12	24.11	even	2
240.3.c.e.209.6		12	40.19	odd	2
240.3.c.e.209.7		12	8.3	odd	2
240.3.c.e.209.8		12	120.59	even	2
600.3.l.g.401.1		12	40.13	odd	4
600.3.l.g.401.2		12	120.53	even	4
600.3.l.g.401.11		12	120.77	even	4
600.3.l.g.401.12		12	40.37	odd	4
960.3.c.j.449.5		12	60.59	even	2
960.3.c.j.449.6		12	4.3	odd	2
960.3.c.j.449.7		12	20.19	odd	2
960.3.c.j.449.8		12	12.11	even	2
960.3.c.k.449.5		12	3.2	odd	2	inner
960.3.c.k.449.6		12	5.4	even	2	inner
960.3.c.k.449.7		12	1.1	even	1	trivial
960.3.c.k.449.8		12	15.14	odd	2	inner
1200.3.l.y.401.1		12	40.27	even	4
1200.3.l.y.401.2		12	120.107	odd	4
1200.3.l.y.401.11		12	120.83	odd	4
1200.3.l.y.401.12		12	40.3	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.938195 - 2.84952i) q^{3} +(-4.88807 + 1.05205i) q^{5} +6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} +O(q^{10})\)	\(q+(0.938195 - 2.84952i) q^{3} +(-4.88807 + 1.05205i) q^{5} +6.81219i q^{7} +(-7.23958 - 5.34682i) q^{9} -7.52980i q^{11} -16.2362i q^{13} +(-1.58813 + 14.9157i) q^{15} +4.11928 q^{17} -7.86469 q^{19} +(19.4115 + 6.39117i) q^{21} -19.5246 q^{23} +(22.7864 - 10.2850i) q^{25} +(-22.0280 + 15.6130i) q^{27} +55.8878i q^{29} +43.4375 q^{31} +(-21.4563 - 7.06442i) q^{33} +(-7.16675 - 33.2984i) q^{35} +31.5824i q^{37} +(-46.2655 - 15.2328i) q^{39} +51.3487i q^{41} +51.2914i q^{43} +(41.0127 + 18.5192i) q^{45} -61.7596 q^{47} +2.59407 q^{49} +(3.86469 - 11.7380i) q^{51} -82.7111 q^{53} +(7.92170 + 36.8061i) q^{55} +(-7.37861 + 22.4106i) q^{57} +97.6026i q^{59} -4.13531 q^{61} +(36.4236 - 49.3174i) q^{63} +(17.0813 + 79.3638i) q^{65} -63.1940i q^{67} +(-18.3179 + 55.6358i) q^{69} -40.3087i q^{71} +78.5111i q^{73} +(-7.92915 - 74.5797i) q^{75} +51.2944 q^{77} -51.0103 q^{79} +(23.8230 + 77.4175i) q^{81} -2.72011 q^{83} +(-20.1353 + 4.33368i) q^{85} +(159.254 + 52.4337i) q^{87} +70.4279i q^{89} +110.604 q^{91} +(40.7528 - 123.776i) q^{93} +(38.4431 - 8.27403i) q^{95} +3.44364i q^{97} +(-40.2605 + 54.5126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{9}+O(q^{10}) \) 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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