LMFDB - Embedded newform 1224.2.bq.c.937.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(145,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("1224.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.bq (of order $8$, degree $4$, 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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
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} + 28x^{10} + 258x^{8} + 880x^{6} + 1033x^{4} + 132x^{2} + 4 $ x^12 + 28x^10 + 258x^8 + 880x^6 + 1033x^4 + 132*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			937.2
Root			$-3.49562i$ of defining polynomial
Character	$\chi$	$=$	1224.937
Dual form			1224.2.bq.c.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.392531 + 0.947653i) q^{5} +(-0.893542 + 2.15720i) q^{7} +(4.81196 + 1.99318i) q^{11} +4.35777i q^{13} +(-3.77648 - 1.65476i) q^{17} +(-1.89281 - 1.89281i) q^{19} +(-3.79373 - 1.57141i) q^{23} +(2.79157 - 2.79157i) q^{25} +(1.46962 + 3.54797i) q^{29} +(-10.1411 + 4.20057i) q^{31} -2.39502 q^{35} +(1.02168 - 0.423195i) q^{37} +(1.00448 - 2.42504i) q^{41} +(-2.86647 + 2.86647i) q^{43} +10.4047i q^{47} +(1.09465 + 1.09465i) q^{49} +(5.49867 + 5.49867i) q^{53} +5.34245i q^{55} +(-7.69489 + 7.69489i) q^{59} +(3.04576 - 7.35311i) q^{61} +(-4.12965 + 1.71056i) q^{65} +6.44882 q^{67} +(-1.73561 + 0.718913i) q^{71} +(5.05217 + 12.1970i) q^{73} +(-8.59937 + 8.59937i) q^{77} +(2.31129 + 0.957366i) q^{79} +(-0.0232879 - 0.0232879i) q^{83} +(0.0857556 - 4.22833i) q^{85} -7.34936i q^{89} +(-9.40057 - 3.89384i) q^{91} +(1.05074 - 2.53671i) q^{95} +(-6.98779 - 16.8700i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} + 12 q^{11} - 4 q^{17} - 4 q^{19} + 8 q^{23} - 16 q^{25} - 8 q^{29} - 32 q^{31} + 32 q^{35} + 4 q^{37} - 16 q^{41} + 8 q^{43} + 44 q^{49} + 8 q^{53} - 16 q^{59} + 44 q^{61} + 20 q^{65} - 40 q^{67}+ \cdots - 16 q^{97}+O(q^{100}) $ 12 * q - 4 * q^5 + 12 * q^11 - 4 * q^17 - 4 * q^19 + 8 * q^23 - 16 * q^25 - 8 * q^29 - 32 * q^31 + 32 * q^35 + 4 * q^37 - 16 * q^41 + 8 * q^43 + 44 * q^49 + 8 * q^53 - 16 * q^59 + 44 * q^61 + 20 * q^65 - 40 * q^67 - 32 * q^71 + 8 * q^73 + 12 * q^77 - 8 * q^79 - 40 * q^83 + 40 * q^85 - 40 * q^91 - 28 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	0.392531	+	0.947653i	0.175545	+	0.423803i	0.987023	−	0.160580i	$-0.0513364\pi$
$5$	0.392531	+	0.947653i	0.175545	+	0.423803i	−0.811478	+	0.584383i	$0.801336\pi$
$6$		0			0
$7$	−0.893542	+	2.15720i	−0.337727	+	0.815345i	0.660206	+	0.751084i	$0.270469\pi$
$7$	−0.893542	+	2.15720i	−0.337727	+	0.815345i	−0.997933	+	0.0642606i	$0.979531\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.81196	+	1.99318i	1.45086	+	0.600966i	0.962404	−	0.271622i	$-0.0875601\pi$
$11$	4.81196	+	1.99318i	1.45086	+	0.600966i	0.488457	+	0.872588i	$0.337560\pi$
$12$		0			0
$13$			4.35777i			1.20863i	0.796747	+	0.604313i	$0.206552\pi$
$13$			4.35777i			1.20863i	−0.796747	+	0.604313i	$0.793448\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.77648	−	1.65476i	−0.915930	−	0.401338i
$17$	−3.77648	−	1.65476i	−0.915930	−	0.401338i
$18$		0			0
$19$	−1.89281	−	1.89281i	−0.434240	−	0.434240i	0.455828	−	0.890068i	$-0.349343\pi$
$19$	−1.89281	−	1.89281i	−0.434240	−	0.434240i	−0.890068	+	0.455828i	$0.849343\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.79373	−	1.57141i	−0.791047	−	0.327662i	−0.0496826	−	0.998765i	$-0.515821\pi$
$23$	−3.79373	−	1.57141i	−0.791047	−	0.327662i	−0.741364	+	0.671103i	$0.765821\pi$
$24$		0			0
$25$	2.79157	−	2.79157i	0.558314	−	0.558314i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.46962	+	3.54797i	0.272901	+	0.658841i	0.999605	−	0.0281099i	$-0.00894885\pi$
$29$	1.46962	+	3.54797i	0.272901	+	0.658841i	−0.726704	+	0.686951i	$0.758949\pi$
$30$		0			0
$31$	−10.1411	+	4.20057i	−1.82139	+	0.754444i	−0.846272	+	0.532751i	$0.821158\pi$
$31$	−10.1411	+	4.20057i	−1.82139	+	0.754444i	−0.975117	+	0.221693i	$0.928842\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.39502			−0.404832
$36$		0			0
$37$	1.02168	−	0.423195i	0.167964	−	0.0695728i	−0.297117	−	0.954841i	$-0.596025\pi$
$37$	1.02168	−	0.423195i	0.167964	−	0.0695728i	0.465081	+	0.885268i	$0.346025\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.00448	−	2.42504i	0.156874	−	0.378728i	−0.825828	−	0.563923i	$-0.809292\pi$
$41$	1.00448	−	2.42504i	0.156874	−	0.378728i	0.982702	+	0.185195i	$0.0592916\pi$
$42$		0			0
$43$	−2.86647	+	2.86647i	−0.437132	+	0.437132i	−0.891046	−	0.453914i	$-0.850027\pi$
$43$	−2.86647	+	2.86647i	−0.437132	+	0.437132i	0.453914	+	0.891046i	$0.350027\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			10.4047i			1.51768i	0.651280	+	0.758838i	$0.274233\pi$
$47$			10.4047i			1.51768i	−0.651280	+	0.758838i	$0.725767\pi$
$48$		0			0
$49$	1.09465	+	1.09465i	0.156379	+	0.156379i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.49867	+	5.49867i	0.755301	+	0.755301i	0.975463	−	0.220162i	$-0.0706587\pi$
$53$	5.49867	+	5.49867i	0.755301	+	0.755301i	−0.220162	+	0.975463i	$0.570659\pi$
$54$		0			0
$55$			5.34245i			0.720376i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.69489	+	7.69489i	−1.00179	+	1.00179i	−0.00179152	+	0.999998i	$0.500570\pi$
$59$	−7.69489	+	7.69489i	−1.00179	+	1.00179i	−0.999998	+	0.00179152i	$0.999430\pi$
$60$		0			0
$61$	3.04576	−	7.35311i	0.389969	−	0.941469i	−0.599976	−	0.800018i	$-0.704823\pi$
$61$	3.04576	−	7.35311i	0.389969	−	0.941469i	0.989945	−	0.141451i	$-0.0451767\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.12965	+	1.71056i	−0.512220	+	0.212169i
$66$		0			0
$67$	6.44882			0.787848			0.393924	−	0.919143i	$-0.371117\pi$
$67$	6.44882			0.787848			0.393924	+	0.919143i	$0.371117\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.73561	+	0.718913i	−0.205979	+	0.0853193i	−0.483288	−	0.875462i	$-0.660558\pi$
$71$	−1.73561	+	0.718913i	−0.205979	+	0.0853193i	0.277309	+	0.960781i	$0.410558\pi$
$72$		0			0
$73$	5.05217	+	12.1970i	0.591312	+	1.42755i	0.882236	+	0.470807i	$0.156037\pi$
$73$	5.05217	+	12.1970i	0.591312	+	1.42755i	−0.290924	+	0.956746i	$0.593963\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.59937	+	8.59937i	−0.979989	+	0.979989i
$78$		0			0
$79$	2.31129	+	0.957366i	0.260040	+	0.107712i	0.508895	−	0.860829i	$-0.330054\pi$
$79$	2.31129	+	0.957366i	0.260040	+	0.107712i	−0.248855	+	0.968541i	$0.580054\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.0232879	−	0.0232879i	−0.00255618	−	0.00255618i	0.705828	−	0.708384i	$-0.250575\pi$
$83$	−0.0232879	−	0.0232879i	−0.00255618	−	0.00255618i	−0.708384	+	0.705828i	$0.750575\pi$
$84$		0			0
$85$	0.0857556	−	4.22833i	0.00930150	−	0.458627i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	7.34936i		−	0.779030i	−0.921020	−	0.389515i	$-0.872643\pi$
$89$		−	7.34936i		−	0.779030i	0.921020	−	0.389515i	$-0.127357\pi$
$90$		0			0
$91$	−9.40057	−	3.89384i	−0.985448	−	0.408186i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.05074	−	2.53671i	0.107804	−	0.260261i
$96$		0			0
$97$	−6.98779	−	16.8700i	−0.709502	−	1.71289i	−0.701241	−	0.712924i	$-0.747370\pi$
$97$	−6.98779	−	16.8700i	−0.709502	−	1.71289i	−0.00826130	−	0.999966i	$-0.502630\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.20094			−0.915528			−0.457764	−	0.889074i	$-0.651350\pi$
$101$	−9.20094			−0.915528			−0.457764	+	0.889074i	$0.651350\pi$
$102$		0			0
$103$	7.88599			0.777029			0.388515	−	0.921443i	$-0.372988\pi$
$103$	7.88599			0.777029			0.388515	+	0.921443i	$0.372988\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.67810	+	4.05130i	0.162228	+	0.391654i	0.984001	−	0.178161i	$-0.0570149\pi$
$107$	1.67810	+	4.05130i	0.162228	+	0.391654i	−0.821773	+	0.569815i	$0.807015\pi$
$108$		0			0
$109$	2.32974	−	5.62449i	0.223149	−	0.538729i	−0.772166	−	0.635421i	$-0.780826\pi$
$109$	2.32974	−	5.62449i	0.223149	−	0.538729i	0.995314	+	0.0966928i	$0.0308264\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	16.8902	+	6.99617i	1.58890	+	0.658144i	0.989791	−	0.142523i	$-0.0455216\pi$
$113$	16.8902	+	6.99617i	1.58890	+	0.658144i	0.599109	+	0.800667i	$0.295522\pi$
$114$		0			0
$115$		−	4.21197i		−	0.392768i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.94409	−	6.66802i	0.636563	−	0.611256i
$120$		0			0
$121$	11.4040	+	11.4040i	1.03673	+	1.03673i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.47948	+	3.51232i	0.758428	+	0.314151i
$126$		0			0
$127$	−6.83989	+	6.83989i	−0.606942	+	0.606942i	−0.942146	−	0.335203i	$-0.891195\pi$
$127$	−6.83989	+	6.83989i	−0.606942	+	0.606942i	0.335203	+	0.942146i	$0.391195\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.79494	−	9.16179i	−0.331565	−	0.800469i	−0.998468	−	0.0553249i	$-0.982381\pi$
$131$	−3.79494	−	9.16179i	−0.331565	−	0.800469i	0.666903	−	0.745144i	$-0.267619\pi$
$132$		0			0
$133$	5.77448	−	2.39187i	0.500711	−	0.207401i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.40322			−0.205321			−0.102661	−	0.994716i	$-0.532736\pi$
$137$	−2.40322			−0.205321			−0.102661	+	0.994716i	$0.532736\pi$
$138$		0			0
$139$	−8.03405	+	3.32781i	−0.681439	+	0.282261i	−0.696428	−	0.717626i	$-0.745229\pi$
$139$	−8.03405	+	3.32781i	−0.681439	+	0.282261i	0.0149893	+	0.999888i	$0.495229\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.68581	+	20.9694i	−0.726344	+	1.75355i
$144$		0			0
$145$	−2.78537	+	2.78537i	−0.231313	+	0.231313i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	3.90029i		−	0.319524i	−0.987156	−	0.159762i	$-0.948927\pi$
$149$		−	3.90029i		−	0.319524i	0.987156	−	0.159762i	$-0.0510727\pi$
$150$		0			0
$151$	2.53060	+	2.53060i	0.205938	+	0.205938i	0.802538	−	0.596601i	$-0.203482\pi$
$151$	2.53060	+	2.53060i	0.205938	+	0.205938i	−0.596601	+	0.802538i	$0.703482\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.96136	−	7.96136i	−0.639472	−	0.639472i
$156$		0			0
$157$			13.5186i			1.07890i	0.842018	+	0.539449i	$0.181367\pi$
$157$			13.5186i			1.07890i	−0.842018	+	0.539449i	$0.818633\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.77971	−	6.77971i	0.534316	−	0.534316i
$162$		0			0
$163$	0.517312	−	1.24890i	0.0405190	−	0.0978216i	−0.902324	−	0.431058i	$-0.858141\pi$
$163$	0.517312	−	1.24890i	0.0405190	−	0.0978216i	0.942843	+	0.333236i	$0.108141\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.52757	+	1.04696i	−0.195589	+	0.0810158i	−0.478328	−	0.878181i	$-0.658757\pi$
$167$	−2.52757	+	1.04696i	−0.195589	+	0.0810158i	0.282739	+	0.959197i	$0.408757\pi$
$168$		0			0
$169$	−5.99012			−0.460778
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.58906	−	1.48664i	0.272871	−	0.113027i	−0.242052	−	0.970263i	$-0.577820\pi$
$173$	3.58906	−	1.48664i	0.272871	−	0.113027i	0.514923	+	0.857236i	$0.327820\pi$
$174$		0			0
$175$	3.52759	+	8.51635i	0.266661	+	0.643776i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.91821	−	5.91821i	0.442348	−	0.442348i	−0.450452	−	0.892800i	$-0.648737\pi$
$179$	5.91821	−	5.91821i	0.442348	−	0.442348i	0.892800	+	0.450452i	$0.148737\pi$
$180$		0			0
$181$	−6.48711	−	2.68705i	−0.482183	−	0.199727i	0.128332	−	0.991731i	$-0.459038\pi$
$181$	−6.48711	−	2.68705i	−0.482183	−	0.199727i	−0.610515	+	0.792004i	$0.709038\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.802084	+	0.802084i	0.0589704	+	0.0589704i
$186$		0			0
$187$	−14.8740	−	15.4898i	−1.08770	−	1.13273i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	12.6238i		−	0.913427i	−0.889614	−	0.456713i	$-0.849027\pi$
$191$		−	12.6238i		−	0.913427i	0.889614	−	0.456713i	$-0.150973\pi$
$192$		0			0
$193$	17.3393	+	7.18217i	1.24811	+	0.516984i	0.906240	−	0.422764i	$-0.138940\pi$
$193$	17.3393	+	7.18217i	1.24811	+	0.516984i	0.341869	+	0.939748i	$0.388940\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.51876	−	13.3235i	0.393196	−	0.949258i	−0.596044	−	0.802952i	$-0.703261\pi$
$197$	5.51876	−	13.3235i	0.393196	−	0.949258i	0.989239	−	0.146306i	$-0.0467385\pi$
$198$		0			0
$199$	−3.66350	−	8.84447i	−0.259699	−	0.626968i	0.739220	−	0.673464i	$-0.235194\pi$
$199$	−3.66350	−	8.84447i	−0.259699	−	0.626968i	−0.998918	+	0.0464963i	$0.985194\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.96683			−0.629348
$204$		0			0
$205$	2.69239			0.188045
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.33542	−	12.8808i	−0.369059	−	0.890986i
$210$		0			0
$211$	0.615646	−	1.48630i	0.0423828	−	0.102321i	−0.901270	−	0.433257i	$-0.857364\pi$
$211$	0.615646	−	1.48630i	0.0423828	−	0.102321i	0.943653	+	0.330936i	$0.107364\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.84159	−	1.59124i	−0.261995	−	0.108522i
$216$		0			0
$217$		−	25.6297i		−	1.73986i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.21106	−	16.4570i	0.485068	−	1.10702i
$222$		0			0
$223$	6.70407	+	6.70407i	0.448937	+	0.448937i	0.895001	−	0.446064i	$-0.147175\pi$
$223$	6.70407	+	6.70407i	0.448937	+	0.448937i	−0.446064	+	0.895001i	$0.647175\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.41865	−	1.00184i	−0.160531	−	0.0664943i	0.300971	−	0.953633i	$-0.402689\pi$
$227$	−2.41865	−	1.00184i	−0.160531	−	0.0664943i	−0.461502	+	0.887139i	$0.652689\pi$
$228$		0			0
$229$	3.48993	−	3.48993i	0.230621	−	0.230621i	−0.582331	−	0.812952i	$-0.697859\pi$
$229$	3.48993	−	3.48993i	0.230621	−	0.230621i	0.812952	+	0.582331i	$0.197859\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.873453	+	2.10870i	0.0572218	+	0.138146i	0.949905	−	0.312540i	$-0.101180\pi$
$233$	0.873453	+	2.10870i	0.0572218	+	0.138146i	−0.892683	+	0.450685i	$0.851180\pi$
$234$		0			0
$235$	−9.86001	+	4.08415i	−0.643196	+	0.266421i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.1821			0.787995			0.393997	−	0.919112i	$-0.371092\pi$
$239$	12.1821			0.787995			0.393997	+	0.919112i	$0.371092\pi$
$240$		0			0
$241$	−13.3105	+	5.51338i	−0.857404	+	0.355148i	−0.767692	−	0.640820i	$-0.778595\pi$
$241$	−13.3105	+	5.51338i	−0.857404	+	0.355148i	−0.0897121	+	0.995968i	$0.528595\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.607666	+	1.46704i	−0.0388223	+	0.0937254i
$246$		0			0
$247$	8.24842	−	8.24842i	0.524835	−	0.524835i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	17.8445i		−	1.12634i	−0.826342	−	0.563168i	$-0.809582\pi$
$251$		−	17.8445i		−	1.12634i	0.826342	−	0.563168i	$-0.190418\pi$
$252$		0			0
$253$	−15.1232	−	15.1232i	−0.950785	−	0.950785i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.82080	+	3.82080i	0.238335	+	0.238335i	0.816160	−	0.577825i	$-0.196099\pi$
$257$	3.82080	+	3.82080i	0.238335	+	0.238335i	−0.577825	+	0.816160i	$0.696099\pi$
$258$		0			0
$259$			2.58212i			0.160445i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.98795	+	6.98795i	−0.430896	+	0.430896i	−0.888933	−	0.458037i	$-0.848553\pi$
$263$	−6.98795	+	6.98795i	−0.430896	+	0.430896i	0.458037	+	0.888933i	$0.348553\pi$
$264$		0			0
$265$	−3.05244	+	7.36924i	−0.187510	+	0.452689i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	24.7296	−	10.2433i	1.50779	−	0.624546i	0.532688	−	0.846312i	$-0.321182\pi$
$269$	24.7296	−	10.2433i	1.50779	−	0.624546i	0.975100	+	0.221765i	$0.0711819\pi$
$270$		0			0
$271$	26.6483			1.61877			0.809384	−	0.587280i	$-0.199801\pi$
$271$	26.6483			1.61877			0.809384	+	0.587280i	$0.199801\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	18.9970	−	7.86882i	1.14556	−	0.474508i
$276$		0			0
$277$	−10.7366	−	25.9204i	−0.645097	−	1.55740i	−0.819718	−	0.572767i	$-0.805870\pi$
$277$	−10.7366	−	25.9204i	−0.645097	−	1.55740i	0.174621	−	0.984636i	$-0.444130\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.9649	−	14.9649i	0.892731	−	0.892731i	−0.102049	−	0.994779i	$-0.532540\pi$
$281$	14.9649	−	14.9649i	0.892731	−	0.892731i	0.994779	+	0.102049i	$0.0325397\pi$
$282$		0			0
$283$	4.05293	+	1.67878i	0.240922	+	0.0997931i	0.499877	−	0.866096i	$-0.333378\pi$
$283$	4.05293	+	1.67878i	0.240922	+	0.0997931i	−0.258956	+	0.965889i	$0.583378\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.33375	+	4.33375i	0.255813	+	0.255813i
$288$		0			0
$289$	11.5235	+	12.4983i	0.677855	+	0.735195i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			11.8892i			0.694573i	0.937759	+	0.347286i	$0.112897\pi$
$293$			11.8892i			0.694573i	−0.937759	+	0.347286i	$0.887103\pi$
$294$		0			0
$295$	−10.3126	−	4.27161i	−0.600421	−	0.248703i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.84785	−	16.5322i	0.396022	−	0.956080i
$300$		0			0
$301$	−3.62224	−	8.74485i	−0.208782	−	0.504045i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.16375			0.467455
$306$		0			0
$307$	20.9185			1.19388			0.596941	−	0.802285i	$-0.296383\pi$
$307$	20.9185			1.19388			0.596941	+	0.802285i	$0.296383\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.34082	−	5.65124i	−0.132736	−	0.320453i	0.843512	−	0.537111i	$-0.180484\pi$
$311$	−2.34082	−	5.65124i	−0.132736	−	0.320453i	−0.976248	+	0.216658i	$0.930484\pi$
$312$		0			0
$313$	−10.9736	+	26.4926i	−0.620264	+	1.49745i	0.231130	+	0.972923i	$0.425758\pi$
$313$	−10.9736	+	26.4926i	−0.620264	+	1.49745i	−0.851394	+	0.524527i	$0.824242\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.79187	−	2.39907i	−0.325304	−	0.134745i	0.214054	−	0.976822i	$-0.431333\pi$
$317$	−5.79187	−	2.39907i	−0.325304	−	0.134745i	−0.539358	+	0.842077i	$0.681333\pi$
$318$		0			0
$319$			20.0019i			1.11989i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.01601	+	10.2803i	0.223457	+	0.572011i
$324$		0			0
$325$	12.1650	+	12.1650i	0.674793	+	0.674793i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−22.4449	−	9.29700i	−1.23743	−	0.512560i
$330$		0			0
$331$	6.76610	−	6.76610i	0.371899	−	0.371899i	−0.496270	−	0.868168i	$-0.665297\pi$
$331$	6.76610	−	6.76610i	0.371899	−	0.371899i	0.868168	+	0.496270i	$0.165297\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.53136	+	6.11124i	0.138303	+	0.333893i
$336$		0			0
$337$	−2.11552	+	0.876277i	−0.115240	+	0.0477339i	−0.439558	−	0.898214i	$-0.644865\pi$
$337$	−2.11552	+	0.876277i	−0.115240	+	0.0477339i	0.324319	+	0.945948i	$0.394865\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−57.1709			−3.09598
$342$		0			0
$343$	−18.4399	+	7.63806i	−0.995661	+	0.412416i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.53048	−	3.69490i	0.0821603	−	0.198353i	−0.877461	−	0.479648i	$-0.840764\pi$
$347$	1.53048	−	3.69490i	0.0821603	−	0.198353i	0.959621	+	0.281296i	$0.0907642\pi$
$348$		0			0
$349$	18.7738	−	18.7738i	1.00494	−	1.00494i	0.00495064	−	0.999988i	$-0.498424\pi$
$349$	18.7738	−	18.7738i	1.00494	−	1.00494i	0.999988	−	0.00495064i	$-0.00157584\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			1.75320i			0.0933134i	0.998911	+	0.0466567i	$0.0148567\pi$
$353$			1.75320i			0.0933134i	−0.998911	+	0.0466567i	$0.985143\pi$
$354$		0			0
$355$	−1.36256	−	1.36256i	−0.0723172	−	0.0723172i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.0466	+	14.0466i	0.741353	+	0.741353i	0.972838	−	0.231486i	$-0.0743586\pi$
$359$	14.0466	+	14.0466i	0.741353	+	0.741353i	−0.231486	+	0.972838i	$0.574359\pi$
$360$		0			0
$361$		−	11.8345i		−	0.622870i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.57541	+	9.57541i	−0.501200	+	0.501200i
$366$		0			0
$367$	6.63148	−	16.0098i	0.346160	−	0.835705i	−0.650906	−	0.759159i	$-0.725611\pi$
$367$	6.63148	−	16.0098i	0.346160	−	0.835705i	0.997066	−	0.0765462i	$-0.0243893\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.7750	+	6.94845i	−0.870916	+	0.360745i
$372$		0			0
$373$	0.854460			0.0442423			0.0221211	−	0.999755i	$-0.492958\pi$
$373$	0.854460			0.0442423			0.0221211	+	0.999755i	$0.492958\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.4612	+	6.40424i	−0.796292	+	0.329835i
$378$		0			0
$379$	−11.4441	−	27.6284i	−0.587843	−	1.41918i	−0.885561	−	0.464524i	$-0.846226\pi$
$379$	−11.4441	−	27.6284i	−0.587843	−	1.41918i	0.297718	−	0.954654i	$-0.403774\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	19.5522	−	19.5522i	0.999073	−	0.999073i	−0.000926910	−	1.00000i	$-0.500295\pi$
$383$	19.5522	−	19.5522i	0.999073	−	0.999073i	1.00000		0.000926910i	$0.000295045\pi$
$384$		0			0
$385$	−11.5247	−	4.77370i	−0.587355	−	0.243291i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	20.7260	+	20.7260i	1.05085	+	1.05085i	0.998636	+	0.0522161i	$0.0166285\pi$
$389$	20.7260	+	20.7260i	1.05085	+	1.05085i	0.0522161	+	0.998636i	$0.483372\pi$
$390$		0			0
$391$	11.7266	+	12.2121i	0.593040	+	0.617593i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			2.56609i			0.129114i
$396$		0			0
$397$	17.1844	+	7.11800i	0.862458	+	0.357242i	0.769668	−	0.638444i	$-0.220422\pi$
$397$	17.1844	+	7.11800i	0.862458	+	0.357242i	0.0927899	+	0.995686i	$0.470422\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.03684	+	7.33159i	−0.151653	+	0.366122i	−0.981388	−	0.192035i	$-0.938491\pi$
$401$	−3.03684	+	7.33159i	−0.151653	+	0.366122i	0.829735	+	0.558157i	$0.188491\pi$
$402$		0			0
$403$	−18.3051	−	44.1924i	−0.911841	−	2.20138i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.75980			0.285503
$408$		0			0
$409$	−6.93345			−0.342837			−0.171418	−	0.985198i	$-0.554835\pi$
$409$	−6.93345			−0.342837			−0.171418	+	0.985198i	$0.554835\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.72372	−	23.4751i	−0.478473	−	1.15514i
$414$		0			0
$415$	0.0129276	−	0.0312100i	0.000634592	−	0.00153204i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−23.6912	−	9.81323i	−1.15739	−	0.479407i	−0.280386	−	0.959887i	$-0.590463\pi$
$419$	−23.6912	−	9.81323i	−1.15739	−	0.479407i	−0.877006	+	0.480480i	$0.840463\pi$
$420$		0			0
$421$			34.5518i			1.68395i	0.539513	+	0.841977i	$0.318608\pi$
$421$			34.5518i			1.68395i	−0.539513	+	0.841977i	$0.681392\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.1617	+	5.92291i	−0.735449	+	0.287303i
$426$		0			0
$427$	13.1406	+	13.1406i	0.635919	+	0.635919i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.65090	+	1.09804i	0.127689	+	0.0528907i	0.445613	−	0.895226i	$-0.352986\pi$
$431$	2.65090	+	1.09804i	0.127689	+	0.0528907i	−0.317924	+	0.948116i	$0.602986\pi$
$432$		0			0
$433$	11.9564	−	11.9564i	0.574586	−	0.574586i	−0.358820	−	0.933407i	$-0.616821\pi$
$433$	11.9564	−	11.9564i	0.574586	−	0.574586i	0.933407	+	0.358820i	$0.116821\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.20642	+	10.1552i	0.201220	+	0.485789i
$438$		0			0
$439$	19.2330	−	7.96657i	0.917941	−	0.380223i	0.126850	−	0.991922i	$-0.459513\pi$
$439$	19.2330	−	7.96657i	0.917941	−	0.380223i	0.791091	+	0.611698i	$0.209513\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	23.5157			1.11726			0.558632	−	0.829416i	$-0.311327\pi$
$443$	23.5157			1.11726			0.558632	+	0.829416i	$0.311327\pi$
$444$		0			0
$445$	6.96464	−	2.88485i	0.330156	−	0.136755i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.67748	+	8.87821i	−0.173551	+	0.418989i	−0.986590	−	0.163221i	$-0.947812\pi$
$449$	−3.67748	+	8.87821i	−0.173551	+	0.418989i	0.813039	+	0.582210i	$0.197812\pi$
$450$		0			0
$451$	9.66708	−	9.66708i	0.455205	−	0.455205i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	10.4369i		−	0.489291i
$456$		0			0
$457$	−12.1391	−	12.1391i	−0.567843	−	0.567843i	0.363681	−	0.931524i	$-0.381520\pi$
$457$	−12.1391	−	12.1391i	−0.567843	−	0.567843i	−0.931524	+	0.363681i	$0.881520\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	21.3878	+	21.3878i	0.996131	+	0.996131i	0.999993	−	0.00386124i	$-0.00122907\pi$
$461$	21.3878	+	21.3878i	0.996131	+	0.996131i	−0.00386124	+	0.999993i	$0.501229\pi$
$462$		0			0
$463$			33.1695i			1.54152i	0.637128	+	0.770758i	$0.280122\pi$
$463$			33.1695i			1.54152i	−0.637128	+	0.770758i	$0.719878\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.94231	+	3.94231i	−0.182428	+	0.182428i	−0.792413	−	0.609985i	$-0.791176\pi$
$467$	−3.94231	+	3.94231i	−0.182428	+	0.182428i	0.609985	+	0.792413i	$0.291176\pi$
$468$		0			0
$469$	−5.76229	+	13.9114i	−0.266078	+	0.642368i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−19.5067	+	8.07994i	−0.896919	+	0.371516i
$474$		0			0
$475$	−10.5678			−0.484885
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−21.3489	+	8.84301i	−0.975457	+	0.404047i	−0.812741	−	0.582626i	$-0.802025\pi$
$479$	−21.3489	+	8.84301i	−0.975457	+	0.404047i	−0.162716	+	0.986673i	$0.552025\pi$
$480$		0			0
$481$	1.84418	+	4.45225i	0.0840875	+	0.203005i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.2440	−	13.2440i	0.601379	−	0.601379i
$486$		0			0
$487$	13.6778	+	5.66554i	0.619801	+	0.256730i	0.670413	−	0.741988i	$-0.266117\pi$
$487$	13.6778	+	5.66554i	0.619801	+	0.256730i	−0.0506118	+	0.998718i	$0.516117\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.370833	+	0.370833i	0.0167355	+	0.0167355i	0.715425	−	0.698690i	$-0.246233\pi$
$491$	0.370833	+	0.370833i	0.0167355	+	0.0167355i	−0.698690	+	0.715425i	$0.746233\pi$
$492$		0			0
$493$	0.321065	−	15.8307i	0.0144600	−	0.712977i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	4.38644i		−	0.196759i
$498$		0			0
$499$	14.9111	+	6.17637i	0.667512	+	0.276492i	0.690596	−	0.723241i	$-0.257348\pi$
$499$	14.9111	+	6.17637i	0.667512	+	0.276492i	−0.0230839	+	0.999734i	$0.507348\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.92666	+	11.8940i	−0.219669	+	0.530328i	−0.994844	−	0.101419i	$-0.967662\pi$
$503$	−4.92666	+	11.8940i	−0.219669	+	0.530328i	0.775175	+	0.631747i	$0.217662\pi$
$504$		0			0
$505$	−3.61165	−	8.71931i	−0.160717	−	0.388004i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.684018			−0.0303185			−0.0151593	−	0.999885i	$-0.504826\pi$
$509$	−0.684018			−0.0303185			−0.0151593	+	0.999885i	$0.504826\pi$
$510$		0			0
$511$	−30.8257			−1.36365
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.09549	+	7.47318i	0.136404	+	0.329308i
$516$		0			0
$517$	−20.7384	+	50.0668i	−0.912072	+	2.20194i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.38938	+	1.81814i	0.192302	+	0.0796543i	0.476757	−	0.879035i	$-0.341812\pi$
$521$	4.38938	+	1.81814i	0.192302	+	0.0796543i	−0.284454	+	0.958690i	$0.591812\pi$
$522$		0			0
$523$		−	40.6707i		−	1.77840i	−0.457515	−	0.889202i	$-0.651260\pi$
$523$		−	40.6707i		−	1.77840i	0.457515	−	0.889202i	$-0.348740\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	45.2484	+	0.917691i	1.97105	+	0.0399753i
$528$		0			0
$529$	−4.34042	−	4.34042i	−0.188714	−	0.188714i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.5678	+	4.37731i	0.457740	+	0.189602i
$534$		0			0
$535$	−3.18052	+	3.18052i	−0.137506	+	0.137506i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.08558	+	7.44926i	0.132906	+	0.320862i
$540$		0			0
$541$	−31.9376	+	13.2290i	−1.37310	+	0.568759i	−0.942629	−	0.333843i	$-0.891654\pi$
$541$	−31.9376	+	13.2290i	−1.37310	+	0.568759i	−0.430476	+	0.902602i	$0.641654\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.24456			0.267488
$546$		0			0
$547$	−24.4795	+	10.1397i	−1.04667	+	0.433544i	−0.838701	−	0.544592i	$-0.816685\pi$
$547$	−24.4795	+	10.1397i	−1.04667	+	0.433544i	−0.207967	+	0.978136i	$0.566685\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.93392	−	9.49733i	0.167591	−	0.404600i
$552$		0			0
$553$	−4.13046	+	4.13046i	−0.175645	+	0.175645i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	24.1708i		−	1.02415i	−0.858941	−	0.512075i	$-0.828877\pi$
$557$		−	24.1708i		−	1.02415i	0.858941	−	0.512075i	$-0.171123\pi$
$558$		0			0
$559$	−12.4914	−	12.4914i	−0.528330	−	0.528330i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.50308	−	2.50308i	−0.105492	−	0.105492i	0.652391	−	0.757883i	$-0.273766\pi$
$563$	−2.50308	−	2.50308i	−0.105492	−	0.105492i	−0.757883	+	0.652391i	$0.773766\pi$
$564$		0			0
$565$			18.7523i			0.788916i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.2348	+	11.2348i	−0.470987	+	0.470987i	−0.902234	−	0.431247i	$-0.858074\pi$
$569$	−11.2348	+	11.2348i	−0.470987	+	0.470987i	0.431247	+	0.902234i	$0.358074\pi$
$570$		0			0
$571$	−6.56569	+	15.8510i	−0.274765	+	0.663342i	−0.999675	−	0.0255019i	$-0.991882\pi$
$571$	−6.56569	+	15.8510i	−0.274765	+	0.663342i	0.724909	+	0.688844i	$0.241882\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−14.9772	+	6.20374i	−0.624591	+	0.258714i
$576$		0			0
$577$	39.0319			1.62492			0.812460	−	0.583017i	$-0.198128\pi$
$577$	39.0319			1.62492			0.812460	+	0.583017i	$0.198128\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.0710453	−	0.0294279i	0.00294745	−	0.00122088i
$582$		0			0
$583$	15.4996	+	37.4192i	0.641926	+	1.54975i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.2227	−	11.2227i	0.463212	−	0.463212i	−0.436495	−	0.899707i	$-0.643780\pi$
$587$	11.2227	−	11.2227i	0.463212	−	0.463212i	0.899707	+	0.436495i	$0.143780\pi$
$588$		0			0
$589$	27.1460	+	11.2442i	1.11853	+	0.463311i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.35714	−	7.35714i	−0.302121	−	0.302121i	0.539722	−	0.841843i	$-0.318529\pi$
$593$	−7.35714	−	7.35714i	−0.302121	−	0.302121i	−0.841843	+	0.539722i	$0.818529\pi$
$594$		0			0
$595$	9.04474	+	3.96318i	0.370798	+	0.162475i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			35.7297i			1.45988i	0.683513	+	0.729938i	$0.260451\pi$
$599$			35.7297i			1.45988i	−0.683513	+	0.729938i	$0.739549\pi$
$600$		0			0
$601$	−25.7150	−	10.6515i	−1.04894	−	0.434484i	−0.209425	−	0.977825i	$-0.567159\pi$
$601$	−25.7150	−	10.6515i	−1.04894	−	0.434484i	−0.839512	+	0.543341i	$0.817159\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.33063	+	15.2835i	−0.257377	+	0.621362i
$606$		0			0
$607$	6.58165	+	15.8895i	0.267141	+	0.644935i	0.999346	−	0.0361486i	$-0.0115090\pi$
$607$	6.58165	+	15.8895i	0.267141	+	0.644935i	−0.732206	+	0.681084i	$0.761509\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−45.3411			−1.83430
$612$		0			0
$613$	−44.0031			−1.77727			−0.888634	−	0.458618i	$-0.848345\pi$
$613$	−44.0031			−1.77727			−0.888634	+	0.458618i	$0.848345\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.3310	+	27.3555i	0.456169	+	1.10129i	0.969936	+	0.243360i	$0.0782497\pi$
$617$	11.3310	+	27.3555i	0.456169	+	1.10129i	−0.513767	+	0.857930i	$0.671750\pi$
$618$		0			0
$619$	10.0162	−	24.1812i	0.402584	−	0.971923i	−0.584453	−	0.811428i	$-0.698691\pi$
$619$	10.0162	−	24.1812i	0.402584	−	0.971923i	0.987037	−	0.160495i	$-0.0513091\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	15.8540	+	6.56695i	0.635178	+	0.263099i
$624$		0			0
$625$		−	10.3251i		−	0.413003i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.55865	−	0.0924547i	−0.181765	−	0.00368641i
$630$		0			0
$631$	28.4881	+	28.4881i	1.13409	+	1.13409i	0.989490	+	0.144604i	$0.0461908\pi$
$631$	28.4881	+	28.4881i	1.13409	+	1.13409i	0.144604	+	0.989490i	$0.453809\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.16672	−	3.79698i	−0.363770	−	0.150678i
$636$		0			0
$637$	−4.77024	+	4.77024i	−0.189004	+	0.189004i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.02621	−	7.30593i	−0.119528	−	0.288567i	0.852779	−	0.522271i	$-0.174915\pi$
$641$	−3.02621	−	7.30593i	−0.119528	−	0.288567i	−0.972308	+	0.233705i	$0.924915\pi$
$642$		0			0
$643$	−5.12127	+	2.12130i	−0.201963	+	0.0836559i	−0.481372	−	0.876516i	$-0.659861\pi$
$643$	−5.12127	+	2.12130i	−0.201963	+	0.0836559i	0.279409	+	0.960172i	$0.409861\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.3835			−0.722731			−0.361366	−	0.932424i	$-0.617689\pi$
$647$	−18.3835			−0.722731			−0.361366	+	0.932424i	$0.617689\pi$
$648$		0			0
$649$	−52.3648	+	21.6902i	−2.05550	+	0.851416i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.5240	+	32.6499i	−0.529236	+	1.27769i	0.402789	+	0.915293i	$0.368041\pi$
$653$	−13.5240	+	32.6499i	−0.529236	+	1.27769i	−0.932024	+	0.362395i	$0.881959\pi$
$654$		0			0
$655$	7.19257	−	7.19257i	0.281037	−	0.281037i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			0.950773i			0.0370369i	0.999829	+	0.0185184i	$0.00589494\pi$
$659$			0.950773i			0.0370369i	−0.999829	+	0.0185184i	$0.994105\pi$
$660$		0			0
$661$	−8.16636	−	8.16636i	−0.317635	−	0.317635i	0.530223	−	0.847858i	$-0.322108\pi$
$661$	−8.16636	−	8.16636i	−0.317635	−	0.317635i	−0.847858	+	0.530223i	$0.822108\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.53332	+	4.53332i	0.175795	+	0.175795i
$666$		0			0
$667$		−	15.7694i		−	0.610593i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	29.3121	−	29.3121i	1.13158	−	1.13158i
$672$		0			0
$673$	4.59155	−	11.0850i	0.176991	−	0.427295i	−0.810341	−	0.585958i	$-0.800718\pi$
$673$	4.59155	−	11.0850i	0.176991	−	0.427295i	0.987333	+	0.158663i	$0.0507183\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.5010	+	15.9476i	−1.47971	+	0.612917i	−0.969050	−	0.246864i	$-0.920600\pi$
$677$	−38.5010	+	15.9476i	−1.47971	+	0.612917i	−0.510663	+	0.859781i	$0.670600\pi$
$678$		0			0
$679$	42.6359			1.63621
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.4611	+	4.33312i	−0.400282	+	0.165802i	−0.573737	−	0.819039i	$-0.694507\pi$
$683$	−10.4611	+	4.33312i	−0.400282	+	0.165802i	0.173455	+	0.984842i	$0.444507\pi$
$684$		0			0
$685$	−0.943339	−	2.27742i	−0.0360431	−	0.0870158i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−23.9619	+	23.9619i	−0.912877	+	0.912877i
$690$		0			0
$691$	22.8129	+	9.44941i	0.867843	+	0.359472i	0.771770	−	0.635902i	$-0.219372\pi$
$691$	22.8129	+	9.44941i	0.867843	+	0.359472i	0.0960732	+	0.995374i	$0.469372\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.30722	−	6.30722i	−0.239247	−	0.239247i
$696$		0			0
$697$	−7.80627	+	7.49592i	−0.295684	+	0.283928i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	38.0011i		−	1.43528i	−0.696413	−	0.717642i	$-0.745222\pi$
$701$		−	38.0011i		−	1.43528i	0.696413	−	0.717642i	$-0.254778\pi$
$702$		0			0
$703$	−2.73488	−	1.13282i	−0.103148	−	0.0427253i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.22143	−	19.8483i	0.309199	−	0.746471i
$708$		0			0
$709$	−7.48697	−	18.0752i	−0.281179	−	0.678827i	0.718685	−	0.695336i	$-0.244745\pi$
$709$	−7.48697	−	18.0752i	−0.281179	−	0.678827i	−0.999864	+	0.0165097i	$0.994745\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	45.0733			1.68801
$714$		0			0
$715$	−23.2812			−0.870666
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.0002	+	36.2137i	0.559414	+	1.35054i	0.910231	+	0.414100i	$0.135904\pi$
$719$	15.0002	+	36.2137i	0.559414	+	1.35054i	−0.350818	+	0.936444i	$0.614096\pi$
$720$		0			0
$721$	−7.04646	+	17.0116i	−0.262424	+	0.633547i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.0069	+	5.80186i	0.520204	+	0.215475i
$726$		0			0
$727$		−	49.8981i		−	1.85062i	−0.379212	−	0.925310i	$-0.623805\pi$
$727$		−	49.8981i		−	1.85062i	0.379212	−	0.925310i	$-0.376195\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.5685	−	6.08183i	0.575820	−	0.224945i
$732$		0			0
$733$	19.7537	+	19.7537i	0.729620	+	0.729620i	0.970544	−	0.240924i	$-0.0774505\pi$
$733$	19.7537	+	19.7537i	0.729620	+	0.729620i	−0.240924	+	0.970544i	$0.577451\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	31.0315	+	12.8536i	1.14306	+	0.473470i
$738$		0			0
$739$	−21.3501	+	21.3501i	−0.785375	+	0.785375i	−0.980732	−	0.195357i	$-0.937413\pi$
$739$	−21.3501	+	21.3501i	−0.785375	+	0.785375i	0.195357	+	0.980732i	$0.437413\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.00765	+	4.84689i	0.0736534	+	0.177815i	0.956418	−	0.292000i	$-0.0943207\pi$
$743$	2.00765	+	4.84689i	0.0736534	+	0.177815i	−0.882765	+	0.469815i	$0.844321\pi$
$744$		0			0
$745$	3.69612	−	1.53098i	0.135415	−	0.0560909i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.2389			−0.374122
$750$		0			0
$751$	13.3168	−	5.51601i	0.485938	−	0.201282i	−0.126244	−	0.991999i	$-0.540292\pi$
$751$	13.3168	−	5.51601i	0.485938	−	0.201282i	0.612182	+	0.790717i	$0.290292\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.40480	+	3.39148i	−0.0511257	+	0.123428i
$756$		0			0
$757$	−4.45055	+	4.45055i	−0.161758	+	0.161758i	−0.783345	−	0.621587i	$-0.786488\pi$
$757$	−4.45055	+	4.45055i	−0.161758	+	0.161758i	0.621587	+	0.783345i	$0.286488\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			6.45544i			0.234010i	0.993131	+	0.117005i	$0.0373293\pi$
$761$			6.45544i			0.234010i	−0.993131	+	0.117005i	$0.962671\pi$
$762$		0			0
$763$	10.0514	+	10.0514i	0.363886	+	0.363886i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−33.5325	−	33.5325i	−1.21079	−	1.21079i
$768$		0			0
$769$		−	0.665285i		−	0.0239908i	−0.999928	−	0.0119954i	$-0.996182\pi$
$769$		−	0.665285i		−	0.0239908i	0.999928	−	0.0119954i	$-0.00381835\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.09332	+	3.09332i	−0.111259	+	0.111259i	−0.760545	−	0.649286i	$-0.775068\pi$
$773$	−3.09332	+	3.09332i	−0.111259	+	0.111259i	0.649286	+	0.760545i	$0.275068\pi$
$774$		0			0
$775$	−16.5833	+	40.0356i	−0.595690	+	1.43812i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.49144	+	2.68884i	−0.232580	+	0.0963378i
$780$		0			0
$781$	−9.78461			−0.350121
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.8109	+	5.30645i	−0.457241	+	0.189395i
$786$		0			0
$787$	−2.82833	−	6.82819i	−0.100819	−	0.243399i	0.865419	−	0.501048i	$-0.167052\pi$
$787$	−2.82833	−	6.82819i	−0.100819	−	0.243399i	−0.966238	+	0.257649i	$0.917052\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−30.1843	+	30.1843i	−1.07323	+	1.07323i
$792$		0			0
$793$	32.0431	+	13.2727i	1.13788	+	0.471327i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.9635	−	15.9635i	−0.565458	−	0.565458i	0.365395	−	0.930853i	$-0.380934\pi$
$797$	−15.9635	−	15.9635i	−0.565458	−	0.565458i	−0.930853	+	0.365395i	$0.880934\pi$
$798$		0			0
$799$	17.2172	−	39.2930i	0.609101	−	1.39008i
$800$		0			0
$801$		0			0
$802$		0			0
$803$			68.7615i			2.42654i
$804$		0			0
$805$	9.08606	+	3.76357i	0.320241	+	0.132648i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.68152	+	4.05955i	−0.0591191	+	0.142726i	−0.950679	−	0.310177i	$-0.899612\pi$
$809$	−1.68152	+	4.05955i	−0.0591191	+	0.142726i	0.891560	+	0.452903i	$0.149612\pi$
$810$		0			0
$811$	4.35027	+	10.5025i	0.152759	+	0.368792i	0.981670	−	0.190588i	$-0.0610394\pi$
$811$	4.35027	+	10.5025i	0.152759	+	0.368792i	−0.828912	+	0.559380i	$0.811039\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.38659			0.0485700
$816$		0			0
$817$	10.8514			0.379641
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.2551	−	41.6575i	−0.602207	−	1.45386i	−0.871304	−	0.490743i	$-0.836725\pi$
$821$	−17.2551	−	41.6575i	−0.602207	−	1.45386i	0.269097	−	0.963113i	$-0.413275\pi$
$822$		0			0
$823$	4.09403	−	9.88385i	0.142709	−	0.344529i	−0.836323	−	0.548237i	$-0.815299\pi$
$823$	4.09403	−	9.88385i	0.142709	−	0.344529i	0.979032	+	0.203708i	$0.0652992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	46.9906	+	19.4641i	1.63402	+	0.676834i	0.995674	−	0.0929138i	$-0.0296181\pi$
$827$	46.9906	+	19.4641i	1.63402	+	0.676834i	0.638348	+	0.769748i	$0.279618\pi$
$828$		0			0
$829$			6.52156i			0.226503i	0.993566	+	0.113252i	$0.0361266\pi$
$829$			6.52156i			0.226503i	−0.993566	+	0.113252i	$0.963873\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.32254	−	5.94531i	−0.0804712	−	0.205993i
$834$		0			0
$835$	−1.98430	−	1.98430i	−0.0686696	−	0.0686696i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.72808	−	3.20108i	−0.266803	−	0.110513i	0.245272	−	0.969454i	$-0.421123\pi$
$839$	−7.72808	−	3.20108i	−0.266803	−	0.110513i	−0.512075	+	0.858941i	$0.671123\pi$
$840$		0			0
$841$	10.0778	−	10.0778i	0.347511	−	0.347511i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.35131	−	5.67656i	−0.0808874	−	0.195279i
$846$		0			0
$847$	−34.7907	+	14.4108i	−1.19542	+	0.495161i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.54100			−0.155663
$852$		0			0
$853$	−2.86110	+	1.18511i	−0.0979622	+	0.0405773i	−0.431126	−	0.902292i	$-0.641884\pi$
$853$	−2.86110	+	1.18511i	−0.0979622	+	0.0405773i	0.333164	+	0.942869i	$0.391884\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.14145	+	7.58414i	−0.107310	+	0.259069i	−0.968409	−	0.249369i	$-0.919777\pi$
$857$	−3.14145	+	7.58414i	−0.107310	+	0.259069i	0.861099	+	0.508438i	$0.169777\pi$
$858$		0			0
$859$	−7.93014	+	7.93014i	−0.270573	+	0.270573i	−0.829331	−	0.558758i	$-0.811278\pi$
$859$	−7.93014	+	7.93014i	−0.270573	+	0.270573i	0.558758	+	0.829331i	$0.311278\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			34.8722i			1.18706i	0.804811	+	0.593532i	$0.202267\pi$
$863$			34.8722i			1.18706i	−0.804811	+	0.593532i	$0.797733\pi$
$864$		0			0
$865$	2.81763	+	2.81763i	0.0958024	+	0.0958024i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.21361	+	9.21361i	0.312550	+	0.312550i
$870$		0			0
$871$			28.1024i			0.952215i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.1535	+	15.1535i	−0.512283	+	0.512283i
$876$		0			0
$877$	4.71367	−	11.3798i	0.159169	−	0.384269i	−0.824095	−	0.566451i	$-0.808316\pi$
$877$	4.71367	−	11.3798i	0.159169	−	0.384269i	0.983265	+	0.182182i	$0.0583160\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	38.7338	−	16.0441i	1.30498	−	0.540538i	0.381561	−	0.924344i	$-0.375387\pi$
$881$	38.7338	−	16.0441i	1.30498	−	0.540538i	0.923414	+	0.383805i	$0.125387\pi$
$882$		0			0
$883$	14.6148			0.491828			0.245914	−	0.969292i	$-0.420912\pi$
$883$	14.6148			0.491828			0.245914	+	0.969292i	$0.420912\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.37765	−	2.22750i	0.180564	−	0.0747920i	−0.290570	−	0.956854i	$-0.593845\pi$
$887$	5.37765	−	2.22750i	0.180564	−	0.0747920i	0.471134	+	0.882062i	$0.343845\pi$
$888$		0			0
$889$	−8.64329	−	20.8667i	−0.289887	−	0.699848i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	19.6941	−	19.6941i	0.659036	−	0.659036i
$894$		0			0
$895$	7.93150	+	3.28533i	0.265121	+	0.109817i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−29.8069	−	29.8069i	−0.994117	−	0.994117i
$900$		0			0
$901$	−11.6666	−	29.8646i	−0.388672	−	0.994934i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	7.20228i		−	0.239412i
$906$		0			0
$907$	−2.22827	−	0.922978i	−0.0739884	−	0.0306470i	0.345382	−	0.938462i	$-0.387749\pi$
$907$	−2.22827	−	0.922978i	−0.0739884	−	0.0306470i	−0.419371	+	0.907815i	$0.637749\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.59570	−	18.3377i	0.251657	−	0.607553i	−0.746681	−	0.665182i	$-0.768354\pi$
$911$	7.59570	−	18.3377i	0.251657	−	0.607553i	0.998338	+	0.0576286i	$0.0183539\pi$
$912$		0			0
$913$	−0.0656434	−	0.158477i	−0.00217248	−	0.00524483i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23.1547			0.764637
$918$		0			0
$919$	16.7830			0.553619			0.276810	−	0.960925i	$-0.410723\pi$
$919$	16.7830			0.553619			0.276810	+	0.960925i	$0.410723\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.13286	−	7.56338i	−0.103119	−	0.248952i
$924$		0			0
$925$	1.67072	−	4.03347i	0.0549329	−	0.132620i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.5034	+	8.90700i	0.705504	+	0.292229i	0.706443	−	0.707770i	$-0.250299\pi$
$929$	21.5034	+	8.90700i	0.705504	+	0.292229i	−0.000938752		1.00000i	$0.500299\pi$
$930$		0			0
$931$		−	4.14394i		−	0.135812i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.84048	−	20.1756i	0.289115	−	0.659814i
$936$		0			0
$937$	−28.1329	−	28.1329i	−0.919062	−	0.919062i	0.0778997	−	0.996961i	$-0.475179\pi$
$937$	−28.1329	−	28.1329i	−0.919062	−	0.919062i	−0.996961	+	0.0778997i	$0.975179\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−26.4136	−	10.9409i	−0.861059	−	0.356662i	−0.0919374	−	0.995765i	$-0.529306\pi$
$941$	−26.4136	−	10.9409i	−0.861059	−	0.356662i	−0.769122	+	0.639102i	$0.779306\pi$
$942$		0			0
$943$	−7.62148	+	7.62148i	−0.248190	+	0.248190i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.3787	−	39.5418i	−0.532238	−	1.28494i	−0.930038	−	0.367463i	$-0.880226\pi$
$947$	−16.3787	−	39.5418i	−0.532238	−	1.28494i	0.397801	−	0.917472i	$-0.369774\pi$
$948$		0			0
$949$	−53.1517	+	22.0162i	−1.72538	+	0.714675i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	41.2093			1.33490			0.667451	−	0.744654i	$-0.267386\pi$
$953$	41.2093			1.33490			0.667451	+	0.744654i	$0.267386\pi$
$954$		0			0
$955$	11.9630	−	4.95523i	0.387113	−	0.160348i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.14738	−	5.18423i	0.0693425	−	0.167408i
$960$		0			0
$961$	63.2761	−	63.2761i	2.04116	−	2.04116i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			19.2509i			0.619707i
$966$		0			0
$967$	−21.3856	−	21.3856i	−0.687714	−	0.687714i	0.274013	−	0.961726i	$-0.411649\pi$
$967$	−21.3856	−	21.3856i	−0.687714	−	0.687714i	−0.961726	+	0.274013i	$0.911649\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	26.4835	+	26.4835i	0.849896	+	0.849896i	0.990120	−	0.140224i	$-0.0447822\pi$
$971$	26.4835	+	26.4835i	0.849896	+	0.849896i	−0.140224	+	0.990120i	$0.544782\pi$
$972$		0			0
$973$		−	20.3046i		−	0.650935i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.9082	+	26.9082i	−0.860868	+	0.860868i	−0.991439	−	0.130571i	$-0.958319\pi$
$977$	−26.9082	+	26.9082i	−0.860868	+	0.860868i	0.130571	+	0.991439i	$0.458319\pi$
$978$		0			0
$979$	14.6486	−	35.3648i	0.468171	−	1.13026i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−45.3329	+	18.7775i	−1.44590	+	0.598909i	−0.961219	−	0.275785i	$-0.911062\pi$
$983$	−45.3329	+	18.7775i	−1.44590	+	0.598909i	−0.484676	+	0.874694i	$0.661062\pi$
$984$		0			0
$985$	14.7923			0.471323
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.3790	−	6.37019i	0.489024	−	0.202560i
$990$		0			0
$991$	−12.8773	−	31.0886i	−0.409062	−	0.987563i	−0.985385	−	0.170341i	$-0.945513\pi$
$991$	−12.8773	−	31.0886i	−0.409062	−	0.987563i	0.576323	−	0.817222i	$-0.304487\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.94345	−	6.94345i	0.220122	−	0.220122i
$996$		0			0
$997$	35.8385	+	14.8448i	1.13502	+	0.470139i	0.869483	−	0.493963i	$-0.164452\pi$
$997$	35.8385	+	14.8448i	1.13502	+	0.470139i	0.265533	+	0.964102i	$0.414452\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.bq.c.937.2		12
3.2	odd	2		136.2.n.c.121.3	yes	12
12.11	even	2		272.2.v.f.257.1		12
17.9	even	8	inner	1224.2.bq.c.145.2		12
51.5	even	16		2312.2.b.n.577.10		12
51.14	even	16		2312.2.a.w.1.3		12
51.20	even	16		2312.2.a.w.1.10		12
51.26	odd	8		136.2.n.c.9.3	✓	12
51.29	even	16		2312.2.b.n.577.3		12
204.71	odd	16		4624.2.a.bt.1.3		12
204.167	odd	16		4624.2.a.bt.1.10		12
204.179	even	8		272.2.v.f.145.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.c.9.3	✓	12	51.26	odd	8
136.2.n.c.121.3	yes	12	3.2	odd	2
272.2.v.f.145.1		12	204.179	even	8
272.2.v.f.257.1		12	12.11	even	2
1224.2.bq.c.145.2		12	17.9	even	8	inner
1224.2.bq.c.937.2		12	1.1	even	1	trivial
2312.2.a.w.1.3		12	51.14	even	16
2312.2.a.w.1.10		12	51.20	even	16
2312.2.b.n.577.3		12	51.29	even	16
2312.2.b.n.577.10		12	51.5	even	16
4624.2.a.bt.1.3		12	204.71	odd	16
4624.2.a.bt.1.10		12	204.167	odd	16

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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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.bq (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.392531 + 0.947653i) q^{5} +(-0.893542 + 2.15720i) q^{7} +(4.81196 + 1.99318i) q^{11} +4.35777i q^{13} +(-3.77648 - 1.65476i) q^{17} +(-1.89281 - 1.89281i) q^{19} +(-3.79373 - 1.57141i) q^{23} +(2.79157 - 2.79157i) q^{25} +(1.46962 + 3.54797i) q^{29} +(-10.1411 + 4.20057i) q^{31} -2.39502 q^{35} +(1.02168 - 0.423195i) q^{37} +(1.00448 - 2.42504i) q^{41} +(-2.86647 + 2.86647i) q^{43} +10.4047i q^{47} +(1.09465 + 1.09465i) q^{49} +(5.49867 + 5.49867i) q^{53} +5.34245i q^{55} +(-7.69489 + 7.69489i) q^{59} +(3.04576 - 7.35311i) q^{61} +(-4.12965 + 1.71056i) q^{65} +6.44882 q^{67} +(-1.73561 + 0.718913i) q^{71} +(5.05217 + 12.1970i) q^{73} +(-8.59937 + 8.59937i) q^{77} +(2.31129 + 0.957366i) q^{79} +(-0.0232879 - 0.0232879i) q^{83} +(0.0857556 - 4.22833i) q^{85} -7.34936i q^{89} +(-9.40057 - 3.89384i) q^{91} +(1.05074 - 2.53671i) q^{95} +(-6.98779 - 16.8700i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} + 12 q^{11} - 4 q^{17} - 4 q^{19} + 8 q^{23} - 16 q^{25} - 8 q^{29} - 32 q^{31} + 32 q^{35} + 4 q^{37} - 16 q^{41} + 8 q^{43} + 44 q^{49} + 8 q^{53} - 16 q^{59} + 44 q^{61} + 20 q^{65} - 40 q^{67}+ \cdots - 16 q^{97}+O(q^{100}) \) 12 * q - 4 * q^5 + 12 * q^11 - 4 * q^17 - 4 * q^19 + 8 * q^23 - 16 * q^25 - 8 * q^29 - 32 * q^31 + 32 * q^35 + 4 * q^37 - 16 * q^41 + 8 * q^43 + 44 * q^49 + 8 * q^53 - 16 * q^59 + 44 * q^61 + 20 * q^65 - 40 * q^67 - 32 * q^71 + 8 * q^73 + 12 * q^77 - 8 * q^79 - 40 * q^83 + 40 * q^85 - 40 * q^91 - 28 * q^95 - 16 * q^97

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