LMFDB - Embedded newform 1920.2.bh.g.1087.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(703,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("1920.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bh (of order $4$, degree $2$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1087.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1920.1087
Dual form			1920.2.bh.g.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{3} +(2.00000 - 1.00000i) q^{5} +(-2.82843 + 2.82843i) q^{7} -1.00000i q^{9} -5.65685 q^{11} +(-3.00000 - 3.00000i) q^{13} +(0.707107 - 2.12132i) q^{15} +(5.00000 + 5.00000i) q^{17} +4.00000i q^{21} +(-2.82843 - 2.82843i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-0.707107 - 0.707107i) q^{27} -6.00000 q^{29} +5.65685i q^{31} +(-4.00000 + 4.00000i) q^{33} +(-2.82843 + 8.48528i) q^{35} +(-3.00000 + 3.00000i) q^{37} -4.24264 q^{39} -8.00000 q^{41} +(2.82843 - 2.82843i) q^{43} +(-1.00000 - 2.00000i) q^{45} +(-8.48528 + 8.48528i) q^{47} -9.00000i q^{49} +7.07107 q^{51} +(-5.00000 - 5.00000i) q^{53} +(-11.3137 + 5.65685i) q^{55} +10.0000i q^{61} +(2.82843 + 2.82843i) q^{63} +(-9.00000 - 3.00000i) q^{65} +(-2.82843 - 2.82843i) q^{67} -4.00000 q^{69} +5.65685i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-0.707107 - 4.94975i) q^{75} +(16.0000 - 16.0000i) q^{77} -1.00000 q^{81} +(8.48528 - 8.48528i) q^{83} +(15.0000 + 5.00000i) q^{85} +(-4.24264 + 4.24264i) q^{87} +16.9706 q^{91} +(4.00000 + 4.00000i) q^{93} +(3.00000 + 3.00000i) q^{97} +5.65685i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{5} - 12 q^{13} + 20 q^{17} + 12 q^{25} - 24 q^{29} - 16 q^{33} - 12 q^{37} - 32 q^{41} - 4 q^{45} - 20 q^{53} - 36 q^{65} - 16 q^{69} - 20 q^{73} + 64 q^{77} - 4 q^{81} + 60 q^{85} + 16 q^{93}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q + 8 * q^5 - 12 * q^13 + 20 * q^17 + 12 * q^25 - 24 * q^29 - 16 * q^33 - 12 * q^37 - 32 * q^41 - 4 * q^45 - 20 * q^53 - 36 * q^65 - 16 * q^69 - 20 * q^73 + 64 * q^77 - 4 * q^81 + 60 * q^85 + 16 * q^93 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$		0			0
$7$	−2.82843	+	2.82843i	−1.06904	+	1.06904i	−0.0716124	+	0.997433i	$0.522814\pi$
$7$	−2.82843	+	2.82843i	−1.06904	+	1.06904i	−0.997433	+	0.0716124i	$0.977186\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−5.65685			−1.70561			−0.852803	−	0.522233i	$-0.825099\pi$
$11$	−5.65685			−1.70561			−0.852803	+	0.522233i	$0.825099\pi$
$12$		0			0
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$		0			0
$15$	0.707107	−	2.12132i	0.182574	−	0.547723i
$16$		0			0
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$			4.00000i			0.872872i
$22$		0			0
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	0.347801	−	0.937568i	$-0.386929\pi$
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	−0.937568	+	0.347801i	$0.886929\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$			5.65685i			1.01600i	0.861357	+	0.508001i	$0.169615\pi$
$31$			5.65685i			1.01600i	−0.861357	+	0.508001i	$0.830385\pi$
$32$		0			0
$33$	−4.00000	+	4.00000i	−0.696311	+	0.696311i
$34$		0			0
$35$	−2.82843	+	8.48528i	−0.478091	+	1.43427i
$36$		0			0
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$		0			0
$39$	−4.24264			−0.679366
$40$		0			0
$41$	−8.00000			−1.24939			−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000			−1.24939			−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	2.82843	−	2.82843i	0.431331	−	0.431331i	−0.457750	−	0.889081i	$-0.651344\pi$
$43$	2.82843	−	2.82843i	0.431331	−	0.431331i	0.889081	+	0.457750i	$0.151344\pi$
$44$		0			0
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$		0			0
$47$	−8.48528	+	8.48528i	−1.23771	+	1.23771i	−0.276769	+	0.960936i	$0.589264\pi$
$47$	−8.48528	+	8.48528i	−1.23771	+	1.23771i	−0.960936	+	0.276769i	$0.910736\pi$
$48$		0			0
$49$		−	9.00000i		−	1.28571i
$50$		0			0
$51$	7.07107			0.990148
$52$		0			0
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	0.274721	−	0.961524i	$-0.411414\pi$
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	−0.961524	+	0.274721i	$0.911414\pi$
$54$		0			0
$55$	−11.3137	+	5.65685i	−1.52554	+	0.762770i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$			10.0000i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$			10.0000i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$	2.82843	+	2.82843i	0.356348	+	0.356348i
$64$		0			0
$65$	−9.00000	−	3.00000i	−1.11631	−	0.372104i
$66$		0			0
$67$	−2.82843	−	2.82843i	−0.345547	−	0.345547i	0.512901	−	0.858448i	$-0.328571\pi$
$67$	−2.82843	−	2.82843i	−0.345547	−	0.345547i	−0.858448	+	0.512901i	$0.828571\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$		0			0
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$		0			0
$75$	−0.707107	−	4.94975i	−0.0816497	−	0.571548i
$76$		0			0
$77$	16.0000	−	16.0000i	1.82337	−	1.82337i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	−0.0664117	−	0.997792i	$-0.521155\pi$
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	0.997792	+	0.0664117i	$0.0211551\pi$
$84$		0			0
$85$	15.0000	+	5.00000i	1.62698	+	0.542326i
$86$		0			0
$87$	−4.24264	+	4.24264i	−0.454859	+	0.454859i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$	16.9706			1.77900
$92$		0			0
$93$	4.00000	+	4.00000i	0.414781	+	0.414781i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$		0			0
$99$			5.65685i			0.568535i
$100$		0			0
$101$		−	4.00000i		−	0.398015i	−0.979998	−	0.199007i	$-0.936228\pi$
$101$		−	4.00000i		−	0.398015i	0.979998	−	0.199007i	$-0.0637718\pi$
$102$		0			0
$103$	−14.1421	−	14.1421i	−1.39347	−	1.39347i	−0.817411	−	0.576055i	$-0.804591\pi$
$103$	−14.1421	−	14.1421i	−1.39347	−	1.39347i	−0.576055	−	0.817411i	$-0.695409\pi$
$104$		0			0
$105$	4.00000	+	8.00000i	0.390360	+	0.780720i
$106$		0			0
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	0.557047	−	0.830481i	$-0.311934\pi$
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	−0.830481	+	0.557047i	$0.811934\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$			4.24264i			0.402694i
$112$		0			0
$113$	7.00000	−	7.00000i	0.658505	−	0.658505i	−0.296522	−	0.955026i	$-0.595827\pi$
$113$	7.00000	−	7.00000i	0.658505	−	0.658505i	0.955026	+	0.296522i	$0.0958267\pi$
$114$		0			0
$115$	−8.48528	−	2.82843i	−0.791257	−	0.263752i
$116$		0			0
$117$	−3.00000	+	3.00000i	−0.277350	+	0.277350i
$118$		0			0
$119$	−28.2843			−2.59281
$120$		0			0
$121$	21.0000			1.90909
$122$		0			0
$123$	−5.65685	+	5.65685i	−0.510061	+	0.510061i
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$	8.48528	−	8.48528i	0.752947	−	0.752947i	−0.222081	−	0.975028i	$-0.571285\pi$
$127$	8.48528	−	8.48528i	0.752947	−	0.752947i	0.975028	+	0.222081i	$0.0712850\pi$
$128$		0			0
$129$		−	4.00000i		−	0.352180i
$130$		0			0
$131$	5.65685			0.494242			0.247121	−	0.968985i	$-0.420516\pi$
$131$	5.65685			0.494242			0.247121	+	0.968985i	$0.420516\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.12132	−	0.707107i	−0.182574	−	0.0608581i
$136$		0			0
$137$	1.00000	+	1.00000i	0.0854358	+	0.0854358i	0.748533	−	0.663097i	$-0.230758\pi$
$137$	1.00000	+	1.00000i	0.0854358	+	0.0854358i	−0.663097	+	0.748533i	$0.730758\pi$
$138$		0			0
$139$			22.6274i			1.91923i	0.281312	+	0.959616i	$0.409230\pi$
$139$			22.6274i			1.91923i	−0.281312	+	0.959616i	$0.590770\pi$
$140$		0			0
$141$			12.0000i			1.01058i
$142$		0			0
$143$	16.9706	+	16.9706i	1.41915	+	1.41915i
$144$		0			0
$145$	−12.0000	+	6.00000i	−0.996546	+	0.498273i
$146$		0			0
$147$	−6.36396	−	6.36396i	−0.524891	−	0.524891i
$148$		0			0
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$		0			0
$151$			5.65685i			0.460348i	0.973149	+	0.230174i	$0.0739296\pi$
$151$			5.65685i			0.460348i	−0.973149	+	0.230174i	$0.926070\pi$
$152$		0			0
$153$	5.00000	−	5.00000i	0.404226	−	0.404226i
$154$		0			0
$155$	5.65685	+	11.3137i	0.454369	+	0.908739i
$156$		0			0
$157$	−13.0000	+	13.0000i	−1.03751	+	1.03751i	−0.0382445	+	0.999268i	$0.512177\pi$
$157$	−13.0000	+	13.0000i	−1.03751	+	1.03751i	−0.999268	+	0.0382445i	$0.987823\pi$
$158$		0			0
$159$	−7.07107			−0.560772
$160$		0			0
$161$	16.0000			1.26098
$162$		0			0
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	−0.956465	−	0.291847i	$-0.905730\pi$
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	0.291847	+	0.956465i	$0.405730\pi$
$164$		0			0
$165$	−4.00000	+	12.0000i	−0.311400	+	0.934199i
$166$		0			0
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	−0.954577	−	0.297966i	$-0.903692\pi$
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	0.297966	+	0.954577i	$0.403692\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.00000	+	1.00000i	0.0760286	+	0.0760286i	0.744099	−	0.668070i	$-0.232879\pi$
$173$	1.00000	+	1.00000i	0.0760286	+	0.0760286i	−0.668070	+	0.744099i	$0.732879\pi$
$174$		0			0
$175$	2.82843	+	19.7990i	0.213809	+	1.49666i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	11.3137i		−	0.845626i	−0.906217	−	0.422813i	$-0.861043\pi$
$179$		−	11.3137i		−	0.845626i	0.906217	−	0.422813i	$-0.138957\pi$
$180$		0			0
$181$		−	12.0000i		−	0.891953i	−0.895045	−	0.445976i	$-0.852856\pi$
$181$		−	12.0000i		−	0.891953i	0.895045	−	0.445976i	$-0.147144\pi$
$182$		0			0
$183$	7.07107	+	7.07107i	0.522708	+	0.522708i
$184$		0			0
$185$	−3.00000	+	9.00000i	−0.220564	+	0.661693i
$186$		0			0
$187$	−28.2843	−	28.2843i	−2.06835	−	2.06835i
$188$		0			0
$189$	4.00000			0.290957
$190$		0			0
$191$		−	16.9706i		−	1.22795i	−0.789327	−	0.613973i	$-0.789570\pi$
$191$		−	16.9706i		−	1.22795i	0.789327	−	0.613973i	$-0.210430\pi$
$192$		0			0
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	−0.806787	−	0.590842i	$-0.798796\pi$
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	0.590842	+	0.806787i	$0.298796\pi$
$194$		0			0
$195$	−8.48528	+	4.24264i	−0.607644	+	0.303822i
$196$		0			0
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	−0.741832	−	0.670585i	$-0.766043\pi$
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	0.670585	+	0.741832i	$0.266043\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	−4.00000			−0.282138
$202$		0			0
$203$	16.9706	−	16.9706i	1.19110	−	1.19110i
$204$		0			0
$205$	−16.0000	+	8.00000i	−1.11749	+	0.558744i
$206$		0			0
$207$	−2.82843	+	2.82843i	−0.196589	+	0.196589i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	5.65685			0.389434			0.194717	−	0.980859i	$-0.437621\pi$
$211$	5.65685			0.389434			0.194717	+	0.980859i	$0.437621\pi$
$212$		0			0
$213$	4.00000	+	4.00000i	0.274075	+	0.274075i
$214$		0			0
$215$	2.82843	−	8.48528i	0.192897	−	0.578691i
$216$		0			0
$217$	−16.0000	−	16.0000i	−1.08615	−	1.08615i
$218$		0			0
$219$			7.07107i			0.477818i
$220$		0			0
$221$		−	30.0000i		−	2.01802i
$222$		0			0
$223$	−8.48528	−	8.48528i	−0.568216	−	0.568216i	0.363412	−	0.931629i	$-0.381612\pi$
$223$	−8.48528	−	8.48528i	−0.568216	−	0.568216i	−0.931629	+	0.363412i	$0.881612\pi$
$224$		0			0
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$		0			0
$227$	−8.48528	−	8.48528i	−0.563188	−	0.563188i	0.367024	−	0.930212i	$-0.380377\pi$
$227$	−8.48528	−	8.48528i	−0.563188	−	0.563188i	−0.930212	+	0.367024i	$0.880377\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$		−	22.6274i		−	1.48877i
$232$		0			0
$233$	−3.00000	+	3.00000i	−0.196537	+	0.196537i	−0.798513	−	0.601977i	$-0.794380\pi$
$233$	−3.00000	+	3.00000i	−0.196537	+	0.196537i	0.601977	+	0.798513i	$0.294380\pi$
$234$		0			0
$235$	−8.48528	+	25.4558i	−0.553519	+	1.66056i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	22.6274			1.46365			0.731823	−	0.681495i	$-0.238670\pi$
$239$	22.6274			1.46365			0.731823	+	0.681495i	$0.238670\pi$
$240$		0			0
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−9.00000	−	18.0000i	−0.574989	−	1.14998i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		−	12.0000i		−	0.760469i
$250$		0			0
$251$	5.65685			0.357057			0.178529	−	0.983935i	$-0.442866\pi$
$251$	5.65685			0.357057			0.178529	+	0.983935i	$0.442866\pi$
$252$		0			0
$253$	16.0000	+	16.0000i	1.00591	+	1.00591i
$254$		0			0
$255$	14.1421	−	7.07107i	0.885615	−	0.442807i
$256$		0			0
$257$	−9.00000	−	9.00000i	−0.561405	−	0.561405i	0.368302	−	0.929706i	$-0.379939\pi$
$257$	−9.00000	−	9.00000i	−0.561405	−	0.561405i	−0.929706	+	0.368302i	$0.879939\pi$
$258$		0			0
$259$		−	16.9706i		−	1.05450i
$260$		0			0
$261$			6.00000i			0.371391i
$262$		0			0
$263$	−8.48528	−	8.48528i	−0.523225	−	0.523225i	0.395319	−	0.918544i	$-0.370634\pi$
$263$	−8.48528	−	8.48528i	−0.523225	−	0.523225i	−0.918544	+	0.395319i	$0.870634\pi$
$264$		0			0
$265$	−15.0000	−	5.00000i	−0.921443	−	0.307148i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	20.0000			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$269$	20.0000			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$270$		0			0
$271$			16.9706i			1.03089i	0.856923	+	0.515444i	$0.172373\pi$
$271$			16.9706i			1.03089i	−0.856923	+	0.515444i	$0.827627\pi$
$272$		0			0
$273$	12.0000	−	12.0000i	0.726273	−	0.726273i
$274$		0			0
$275$	−16.9706	+	22.6274i	−1.02336	+	1.36448i
$276$		0			0
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	−0.611213	−	0.791466i	$-0.709318\pi$
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	0.791466	+	0.611213i	$0.209318\pi$
$278$		0			0
$279$	5.65685			0.338667
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	19.7990	−	19.7990i	1.17693	−	1.17693i	0.196405	−	0.980523i	$-0.437073\pi$
$283$	19.7990	−	19.7990i	1.17693	−	1.17693i	0.980523	−	0.196405i	$-0.0629267\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	22.6274	−	22.6274i	1.33565	−	1.33565i
$288$		0			0
$289$			33.0000i			1.94118i
$290$		0			0
$291$	4.24264			0.248708
$292$		0			0
$293$	−17.0000	−	17.0000i	−0.993151	−	0.993151i	0.00682610	−	0.999977i	$-0.497827\pi$
$293$	−17.0000	−	17.0000i	−0.993151	−	0.993151i	−0.999977	+	0.00682610i	$0.997827\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.00000	+	4.00000i	0.232104	+	0.232104i
$298$		0			0
$299$			16.9706i			0.981433i
$300$		0			0
$301$			16.0000i			0.922225i
$302$		0			0
$303$	−2.82843	−	2.82843i	−0.162489	−	0.162489i
$304$		0			0
$305$	10.0000	+	20.0000i	0.572598	+	1.14520i
$306$		0			0
$307$	19.7990	+	19.7990i	1.12999	+	1.12999i	0.990178	+	0.139810i	$0.0446491\pi$
$307$	19.7990	+	19.7990i	1.12999	+	1.12999i	0.139810	+	0.990178i	$0.455351\pi$
$308$		0			0
$309$	−20.0000			−1.13776
$310$		0			0
$311$			5.65685i			0.320771i	0.987054	+	0.160385i	$0.0512737\pi$
$311$			5.65685i			0.320771i	−0.987054	+	0.160385i	$0.948726\pi$
$312$		0			0
$313$	−17.0000	+	17.0000i	−0.960897	+	0.960897i	−0.999264	−	0.0383669i	$-0.987784\pi$
$313$	−17.0000	+	17.0000i	−0.960897	+	0.960897i	0.0383669	+	0.999264i	$0.487784\pi$
$314$		0			0
$315$	8.48528	+	2.82843i	0.478091	+	0.159364i
$316$		0			0
$317$	9.00000	−	9.00000i	0.505490	−	0.505490i	−0.407649	−	0.913139i	$-0.633651\pi$
$317$	9.00000	−	9.00000i	0.505490	−	0.505490i	0.913139	+	0.407649i	$0.133651\pi$
$318$		0			0
$319$	33.9411			1.90034
$320$		0			0
$321$	−4.00000			−0.223258
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−21.0000	+	3.00000i	−1.16487	+	0.166410i
$326$		0			0
$327$	−2.82843	+	2.82843i	−0.156412	+	0.156412i
$328$		0			0
$329$		−	48.0000i		−	2.64633i
$330$		0			0
$331$	−5.65685			−0.310929			−0.155464	−	0.987841i	$-0.549687\pi$
$331$	−5.65685			−0.310929			−0.155464	+	0.987841i	$0.549687\pi$
$332$		0			0
$333$	3.00000	+	3.00000i	0.164399	+	0.164399i
$334$		0			0
$335$	−8.48528	−	2.82843i	−0.463600	−	0.154533i
$336$		0			0
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$		0			0
$339$		−	9.89949i		−	0.537667i
$340$		0			0
$341$		−	32.0000i		−	1.73290i
$342$		0			0
$343$	5.65685	+	5.65685i	0.305441	+	0.305441i
$344$		0			0
$345$	−8.00000	+	4.00000i	−0.430706	+	0.215353i
$346$		0			0
$347$	−19.7990	−	19.7990i	−1.06287	−	1.06287i	−0.997887	−	0.0649788i	$-0.979302\pi$
$347$	−19.7990	−	19.7990i	−1.06287	−	1.06287i	−0.0649788	−	0.997887i	$-0.520698\pi$
$348$		0			0
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$			4.24264i			0.226455i
$352$		0			0
$353$	1.00000	−	1.00000i	0.0532246	−	0.0532246i	−0.679994	−	0.733218i	$-0.738017\pi$
$353$	1.00000	−	1.00000i	0.0532246	−	0.0532246i	0.733218	+	0.679994i	$0.238017\pi$
$354$		0			0
$355$	5.65685	+	11.3137i	0.300235	+	0.600469i
$356$		0			0
$357$	−20.0000	+	20.0000i	−1.05851	+	1.05851i
$358$		0			0
$359$	11.3137			0.597115			0.298557	−	0.954392i	$-0.403495\pi$
$359$	11.3137			0.597115			0.298557	+	0.954392i	$0.403495\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	14.8492	−	14.8492i	0.779383	−	0.779383i
$364$		0			0
$365$	−5.00000	+	15.0000i	−0.261712	+	0.785136i
$366$		0			0
$367$	8.48528	−	8.48528i	0.442928	−	0.442928i	−0.450067	−	0.892995i	$-0.648600\pi$
$367$	8.48528	−	8.48528i	0.442928	−	0.442928i	0.892995	+	0.450067i	$0.148600\pi$
$368$		0			0
$369$			8.00000i			0.416463i
$370$		0			0
$371$	28.2843			1.46845
$372$		0			0
$373$	17.0000	+	17.0000i	0.880227	+	0.880227i	0.993557	−	0.113331i	$-0.0361520\pi$
$373$	17.0000	+	17.0000i	0.880227	+	0.880227i	−0.113331	+	0.993557i	$0.536152\pi$
$374$		0			0
$375$	−6.36396	−	9.19239i	−0.328634	−	0.474693i
$376$		0			0
$377$	18.0000	+	18.0000i	0.927047	+	0.927047i
$378$		0			0
$379$			11.3137i			0.581146i	0.956853	+	0.290573i	$0.0938459\pi$
$379$			11.3137i			0.581146i	−0.956853	+	0.290573i	$0.906154\pi$
$380$		0			0
$381$		−	12.0000i		−	0.614779i
$382$		0			0
$383$	2.82843	+	2.82843i	0.144526	+	0.144526i	0.775668	−	0.631142i	$-0.217413\pi$
$383$	2.82843	+	2.82843i	0.144526	+	0.144526i	−0.631142	+	0.775668i	$0.717413\pi$
$384$		0			0
$385$	16.0000	−	48.0000i	0.815436	−	2.44631i
$386$		0			0
$387$	−2.82843	−	2.82843i	−0.143777	−	0.143777i
$388$		0			0
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$		−	28.2843i		−	1.43040i
$392$		0			0
$393$	4.00000	−	4.00000i	0.201773	−	0.201773i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.0000	+	17.0000i	−0.853206	+	0.853206i	−0.990527	−	0.137321i	$-0.956151\pi$
$397$	−17.0000	+	17.0000i	−0.853206	+	0.853206i	0.137321	+	0.990527i	$0.456151\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−34.0000			−1.69788			−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000			−1.69788			−0.848939	+	0.528490i	$0.822758\pi$
$402$		0			0
$403$	16.9706	−	16.9706i	0.845364	−	0.845364i
$404$		0			0
$405$	−2.00000	+	1.00000i	−0.0993808	+	0.0496904i
$406$		0			0
$407$	16.9706	−	16.9706i	0.841200	−	0.841200i
$408$		0			0
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$		0			0
$411$	1.41421			0.0697580
$412$		0			0
$413$		0			0
$414$		0			0
$415$	8.48528	−	25.4558i	0.416526	−	1.24958i
$416$		0			0
$417$	16.0000	+	16.0000i	0.783523	+	0.783523i
$418$		0			0
$419$			22.6274i			1.10542i	0.833373	+	0.552711i	$0.186407\pi$
$419$			22.6274i			1.10542i	−0.833373	+	0.552711i	$0.813593\pi$
$420$		0			0
$421$			2.00000i			0.0974740i	0.998812	+	0.0487370i	$0.0155196\pi$
$421$			2.00000i			0.0974740i	−0.998812	+	0.0487370i	$0.984480\pi$
$422$		0			0
$423$	8.48528	+	8.48528i	0.412568	+	0.412568i
$424$		0			0
$425$	35.0000	−	5.00000i	1.69775	−	0.242536i
$426$		0			0
$427$	−28.2843	−	28.2843i	−1.36877	−	1.36877i
$428$		0			0
$429$	24.0000			1.15873
$430$		0			0
$431$			5.65685i			0.272481i	0.990676	+	0.136241i	$0.0435020\pi$
$431$			5.65685i			0.272481i	−0.990676	+	0.136241i	$0.956498\pi$
$432$		0			0
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	−0.631337	−	0.775508i	$-0.717494\pi$
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	0.775508	+	0.631337i	$0.217494\pi$
$434$		0			0
$435$	−4.24264	+	12.7279i	−0.203419	+	0.610257i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	22.6274			1.07995			0.539974	−	0.841682i	$-0.318434\pi$
$439$	22.6274			1.07995			0.539974	+	0.841682i	$0.318434\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−14.1421	+	14.1421i	−0.671913	+	0.671913i	−0.958157	−	0.286244i	$-0.907593\pi$
$443$	−14.1421	+	14.1421i	−0.671913	+	0.671913i	0.286244	+	0.958157i	$0.407593\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.48528	−	8.48528i	0.401340	−	0.401340i
$448$		0			0
$449$			2.00000i			0.0943858i	0.998886	+	0.0471929i	$0.0150276\pi$
$449$			2.00000i			0.0943858i	−0.998886	+	0.0471929i	$0.984972\pi$
$450$		0			0
$451$	45.2548			2.13097
$452$		0			0
$453$	4.00000	+	4.00000i	0.187936	+	0.187936i
$454$		0			0
$455$	33.9411	−	16.9706i	1.59118	−	0.795592i
$456$		0			0
$457$	15.0000	+	15.0000i	0.701670	+	0.701670i	0.964769	−	0.263099i	$-0.0847444\pi$
$457$	15.0000	+	15.0000i	0.701670	+	0.701670i	−0.263099	+	0.964769i	$0.584744\pi$
$458$		0			0
$459$		−	7.07107i		−	0.330049i
$460$		0			0
$461$		−	28.0000i		−	1.30409i	−0.758180	−	0.652045i	$-0.773911\pi$
$461$		−	28.0000i		−	1.30409i	0.758180	−	0.652045i	$-0.226089\pi$
$462$		0			0
$463$	−2.82843	−	2.82843i	−0.131448	−	0.131448i	0.638322	−	0.769770i	$-0.279629\pi$
$463$	−2.82843	−	2.82843i	−0.131448	−	0.131448i	−0.769770	+	0.638322i	$0.779629\pi$
$464$		0			0
$465$	12.0000	+	4.00000i	0.556487	+	0.185496i
$466$		0			0
$467$	−19.7990	−	19.7990i	−0.916188	−	0.916188i	0.0805616	−	0.996750i	$-0.474329\pi$
$467$	−19.7990	−	19.7990i	−0.916188	−	0.916188i	−0.996750	+	0.0805616i	$0.974329\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$		0			0
$471$			18.3848i			0.847126i
$472$		0			0
$473$	−16.0000	+	16.0000i	−0.735681	+	0.735681i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$		0			0
$479$	11.3137			0.516937			0.258468	−	0.966020i	$-0.416782\pi$
$479$	11.3137			0.516937			0.258468	+	0.966020i	$0.416782\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$	11.3137	−	11.3137i	0.514792	−	0.514792i
$484$		0			0
$485$	9.00000	+	3.00000i	0.408669	+	0.136223i
$486$		0			0
$487$	19.7990	−	19.7990i	0.897178	−	0.897178i	−0.0980078	−	0.995186i	$-0.531247\pi$
$487$	19.7990	−	19.7990i	0.897178	−	0.897178i	0.995186	+	0.0980078i	$0.0312470\pi$
$488$		0			0
$489$			12.0000i			0.542659i
$490$		0			0
$491$	5.65685			0.255290			0.127645	−	0.991820i	$-0.459258\pi$
$491$	5.65685			0.255290			0.127645	+	0.991820i	$0.459258\pi$
$492$		0			0
$493$	−30.0000	−	30.0000i	−1.35113	−	1.35113i
$494$		0			0
$495$	5.65685	+	11.3137i	0.254257	+	0.508513i
$496$		0			0
$497$	−16.0000	−	16.0000i	−0.717698	−	0.717698i
$498$		0			0
$499$			11.3137i			0.506471i	0.967405	+	0.253236i	$0.0814948\pi$
$499$			11.3137i			0.506471i	−0.967405	+	0.253236i	$0.918505\pi$
$500$		0			0
$501$			12.0000i			0.536120i
$502$		0			0
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	0.870503	−	0.492163i	$-0.163794\pi$
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	−0.492163	+	0.870503i	$0.663794\pi$
$504$		0			0
$505$	−4.00000	−	8.00000i	−0.177998	−	0.355995i
$506$		0			0
$507$	3.53553	+	3.53553i	0.157019	+	0.157019i
$508$		0			0
$509$	6.00000			0.265945			0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000			0.265945			0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$		−	28.2843i		−	1.25122i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−42.4264	−	14.1421i	−1.86953	−	0.623177i
$516$		0			0
$517$	48.0000	−	48.0000i	2.11104	−	2.11104i
$518$		0			0
$519$	1.41421			0.0620771
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	8.48528	−	8.48528i	0.371035	−	0.371035i	−0.496819	−	0.867854i	$-0.665499\pi$
$523$	8.48528	−	8.48528i	0.371035	−	0.371035i	0.867854	+	0.496819i	$0.165499\pi$
$524$		0			0
$525$	16.0000	+	12.0000i	0.698297	+	0.523723i
$526$		0			0
$527$	−28.2843	+	28.2843i	−1.23208	+	1.23208i
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.0000	+	24.0000i	1.03956	+	1.03956i
$534$		0			0
$535$	−8.48528	−	2.82843i	−0.366851	−	0.122284i
$536$		0			0
$537$	−8.00000	−	8.00000i	−0.345225	−	0.345225i
$538$		0			0
$539$			50.9117i			2.19292i
$540$		0			0
$541$			20.0000i			0.859867i	0.902861	+	0.429934i	$0.141463\pi$
$541$			20.0000i			0.859867i	−0.902861	+	0.429934i	$0.858537\pi$
$542$		0			0
$543$	−8.48528	−	8.48528i	−0.364138	−	0.364138i
$544$		0			0
$545$	−8.00000	+	4.00000i	−0.342682	+	0.171341i
$546$		0			0
$547$	−19.7990	−	19.7990i	−0.846544	−	0.846544i	0.143156	−	0.989700i	$-0.454275\pi$
$547$	−19.7990	−	19.7990i	−0.846544	−	0.846544i	−0.989700	+	0.143156i	$0.954275\pi$
$548$		0			0
$549$	10.0000			0.426790
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.24264	+	8.48528i	0.180090	+	0.360180i
$556$		0			0
$557$	5.00000	−	5.00000i	0.211857	−	0.211857i	−0.593199	−	0.805056i	$-0.702135\pi$
$557$	5.00000	−	5.00000i	0.211857	−	0.211857i	0.805056	+	0.593199i	$0.202135\pi$
$558$		0			0
$559$	−16.9706			−0.717778
$560$		0			0
$561$	−40.0000			−1.68880
$562$		0			0
$563$	−19.7990	+	19.7990i	−0.834428	+	0.834428i	−0.988119	−	0.153691i	$-0.950884\pi$
$563$	−19.7990	+	19.7990i	−0.834428	+	0.834428i	0.153691	+	0.988119i	$0.450884\pi$
$564$		0			0
$565$	7.00000	−	21.0000i	0.294492	−	0.883477i
$566$		0			0
$567$	2.82843	−	2.82843i	0.118783	−	0.118783i
$568$		0			0
$569$			22.0000i			0.922288i	0.887325	+	0.461144i	$0.152561\pi$
$569$			22.0000i			0.922288i	−0.887325	+	0.461144i	$0.847439\pi$
$570$		0			0
$571$	−16.9706			−0.710196			−0.355098	−	0.934829i	$-0.615552\pi$
$571$	−16.9706			−0.710196			−0.355098	+	0.934829i	$0.615552\pi$
$572$		0			0
$573$	−12.0000	−	12.0000i	−0.501307	−	0.501307i
$574$		0			0
$575$	−19.7990	+	2.82843i	−0.825675	+	0.117954i
$576$		0			0
$577$	−25.0000	−	25.0000i	−1.04076	−	1.04076i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$	−25.0000	−	25.0000i	−1.04076	−	1.04076i	−0.0416305	−	0.999133i	$-0.513255\pi$
$578$		0			0
$579$			4.24264i			0.176318i
$580$		0			0
$581$			48.0000i			1.99138i
$582$		0			0
$583$	28.2843	+	28.2843i	1.17141	+	1.17141i
$584$		0			0
$585$	−3.00000	+	9.00000i	−0.124035	+	0.372104i
$586$		0			0
$587$	−19.7990	−	19.7990i	−0.817192	−	0.817192i	0.168508	−	0.985700i	$-0.446105\pi$
$587$	−19.7990	−	19.7990i	−0.817192	−	0.817192i	−0.985700	+	0.168508i	$0.946105\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$			1.41421i			0.0581730i
$592$		0			0
$593$	9.00000	−	9.00000i	0.369586	−	0.369586i	−0.497740	−	0.867326i	$-0.665837\pi$
$593$	9.00000	−	9.00000i	0.369586	−	0.369586i	0.867326	+	0.497740i	$0.165837\pi$
$594$		0			0
$595$	−56.5685	+	28.2843i	−2.31908	+	1.15954i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.3137			0.462266			0.231133	−	0.972922i	$-0.425757\pi$
$599$	11.3137			0.462266			0.231133	+	0.972922i	$0.425757\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$	−2.82843	+	2.82843i	−0.115182	+	0.115182i
$604$		0			0
$605$	42.0000	−	21.0000i	1.70754	−	0.853771i
$606$		0			0
$607$	2.82843	−	2.82843i	0.114802	−	0.114802i	−0.647372	−	0.762174i	$-0.724132\pi$
$607$	2.82843	−	2.82843i	0.114802	−	0.114802i	0.762174	+	0.647372i	$0.224132\pi$
$608$		0			0
$609$		−	24.0000i		−	0.972529i
$610$		0			0
$611$	50.9117			2.05967
$612$		0			0
$613$	5.00000	+	5.00000i	0.201948	+	0.201948i	0.800834	−	0.598886i	$-0.204390\pi$
$613$	5.00000	+	5.00000i	0.201948	+	0.201948i	−0.598886	+	0.800834i	$0.704390\pi$
$614$		0			0
$615$	−5.65685	+	16.9706i	−0.228106	+	0.684319i
$616$		0			0
$617$	5.00000	+	5.00000i	0.201292	+	0.201292i	0.800554	−	0.599261i	$-0.204539\pi$
$617$	5.00000	+	5.00000i	0.201292	+	0.201292i	−0.599261	+	0.800554i	$0.704539\pi$
$618$		0			0
$619$			11.3137i			0.454736i	0.973809	+	0.227368i	$0.0730121\pi$
$619$			11.3137i			0.454736i	−0.973809	+	0.227368i	$0.926988\pi$
$620$		0			0
$621$			4.00000i			0.160514i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−30.0000			−1.19618
$630$		0			0
$631$		−	5.65685i		−	0.225196i	−0.993641	−	0.112598i	$-0.964083\pi$
$631$		−	5.65685i		−	0.225196i	0.993641	−	0.112598i	$-0.0359172\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	8.48528	−	25.4558i	0.336728	−	1.01018i
$636$		0			0
$637$	−27.0000	+	27.0000i	−1.06978	+	1.06978i
$638$		0			0
$639$	5.65685			0.223782
$640$		0			0
$641$	−24.0000			−0.947943			−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000			−0.947943			−0.473972	+	0.880540i	$0.657180\pi$
$642$		0			0
$643$	−2.82843	+	2.82843i	−0.111542	+	0.111542i	−0.760675	−	0.649133i	$-0.775132\pi$
$643$	−2.82843	+	2.82843i	−0.111542	+	0.111542i	0.649133	+	0.760675i	$0.275132\pi$
$644$		0			0
$645$	−4.00000	−	8.00000i	−0.157500	−	0.315000i
$646$		0			0
$647$	19.7990	−	19.7990i	0.778379	−	0.778379i	−0.201176	−	0.979555i	$-0.564476\pi$
$647$	19.7990	−	19.7990i	0.778379	−	0.778379i	0.979555	+	0.201176i	$0.0644765\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−22.6274			−0.886838
$652$		0			0
$653$	−29.0000	−	29.0000i	−1.13486	−	1.13486i	−0.989358	−	0.145499i	$-0.953521\pi$
$653$	−29.0000	−	29.0000i	−1.13486	−	1.13486i	−0.145499	−	0.989358i	$-0.546479\pi$
$654$		0			0
$655$	11.3137	−	5.65685i	0.442063	−	0.221032i
$656$		0			0
$657$	5.00000	+	5.00000i	0.195069	+	0.195069i
$658$		0			0
$659$		−	22.6274i		−	0.881439i	−0.897645	−	0.440720i	$-0.854723\pi$
$659$		−	22.6274i		−	0.881439i	0.897645	−	0.440720i	$-0.145277\pi$
$660$		0			0
$661$			46.0000i			1.78919i	0.446875	+	0.894596i	$0.352537\pi$
$661$			46.0000i			1.78919i	−0.446875	+	0.894596i	$0.647463\pi$
$662$		0			0
$663$	−21.2132	−	21.2132i	−0.823853	−	0.823853i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.9706	+	16.9706i	0.657103	+	0.657103i
$668$		0			0
$669$	−12.0000			−0.463947
$670$		0			0
$671$		−	56.5685i		−	2.18380i
$672$		0			0
$673$	−21.0000	+	21.0000i	−0.809491	+	0.809491i	−0.984557	−	0.175066i	$-0.943986\pi$
$673$	−21.0000	+	21.0000i	−0.809491	+	0.809491i	0.175066	+	0.984557i	$0.443986\pi$
$674$		0			0
$675$	−4.94975	+	0.707107i	−0.190516	+	0.0272166i
$676$		0			0
$677$	7.00000	−	7.00000i	0.269032	−	0.269032i	−0.559678	−	0.828710i	$-0.689075\pi$
$677$	7.00000	−	7.00000i	0.269032	−	0.269032i	0.828710	+	0.559678i	$0.189075\pi$
$678$		0			0
$679$	−16.9706			−0.651270
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	25.4558	−	25.4558i	0.974041	−	0.974041i	−0.0256307	−	0.999671i	$-0.508159\pi$
$683$	25.4558	−	25.4558i	0.974041	−	0.974041i	0.999671	+	0.0256307i	$0.00815939\pi$
$684$		0			0
$685$	3.00000	+	1.00000i	0.114624	+	0.0382080i
$686$		0			0
$687$	9.89949	−	9.89949i	0.377689	−	0.377689i
$688$		0			0
$689$			30.0000i			1.14291i
$690$		0			0
$691$	−16.9706			−0.645591			−0.322795	−	0.946469i	$-0.604623\pi$
$691$	−16.9706			−0.645591			−0.322795	+	0.946469i	$0.604623\pi$
$692$		0			0
$693$	−16.0000	−	16.0000i	−0.607790	−	0.607790i
$694$		0			0
$695$	22.6274	+	45.2548i	0.858307	+	1.71661i
$696$		0			0
$697$	−40.0000	−	40.0000i	−1.51511	−	1.51511i
$698$		0			0
$699$			4.24264i			0.160471i
$700$		0			0
$701$			22.0000i			0.830929i	0.909610	+	0.415464i	$0.136381\pi$
$701$			22.0000i			0.830929i	−0.909610	+	0.415464i	$0.863619\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	12.0000	+	24.0000i	0.451946	+	0.903892i
$706$		0			0
$707$	11.3137	+	11.3137i	0.425496	+	0.425496i
$708$		0			0
$709$	−14.0000			−0.525781			−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000			−0.525781			−0.262891	+	0.964826i	$0.584676\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.0000	−	16.0000i	0.599205	−	0.599205i
$714$		0			0
$715$	50.9117	+	16.9706i	1.90399	+	0.634663i
$716$		0			0
$717$	16.0000	−	16.0000i	0.597531	−	0.597531i
$718$		0			0
$719$	−45.2548			−1.68772			−0.843860	−	0.536563i	$-0.819722\pi$
$719$	−45.2548			−1.68772			−0.843860	+	0.536563i	$0.819722\pi$
$720$		0			0
$721$	80.0000			2.97936
$722$		0			0
$723$	−5.65685	+	5.65685i	−0.210381	+	0.210381i
$724$		0			0
$725$	−18.0000	+	24.0000i	−0.668503	+	0.891338i
$726$		0			0
$727$	−25.4558	+	25.4558i	−0.944105	+	0.944105i	−0.998518	−	0.0544135i	$-0.982671\pi$
$727$	−25.4558	+	25.4558i	−0.944105	+	0.944105i	0.0544135	+	0.998518i	$0.482671\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	28.2843			1.04613
$732$		0			0
$733$	33.0000	+	33.0000i	1.21888	+	1.21888i	0.968024	+	0.250859i	$0.0807131\pi$
$733$	33.0000	+	33.0000i	1.21888	+	1.21888i	0.250859	+	0.968024i	$0.419287\pi$
$734$		0			0
$735$	−19.0919	−	6.36396i	−0.704215	−	0.234738i
$736$		0			0
$737$	16.0000	+	16.0000i	0.589368	+	0.589368i
$738$		0			0
$739$		−	45.2548i		−	1.66473i	−0.554231	−	0.832363i	$-0.686988\pi$
$739$		−	45.2548i		−	1.66473i	0.554231	−	0.832363i	$-0.313012\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−31.1127	−	31.1127i	−1.14141	−	1.14141i	−0.988192	−	0.153222i	$-0.951035\pi$
$743$	−31.1127	−	31.1127i	−1.14141	−	1.14141i	−0.153222	−	0.988192i	$-0.548965\pi$
$744$		0			0
$745$	24.0000	−	12.0000i	0.879292	−	0.439646i
$746$		0			0
$747$	−8.48528	−	8.48528i	−0.310460	−	0.310460i
$748$		0			0
$749$	16.0000			0.584627
$750$		0			0
$751$			39.5980i			1.44495i	0.691397	+	0.722475i	$0.256996\pi$
$751$			39.5980i			1.44495i	−0.691397	+	0.722475i	$0.743004\pi$
$752$		0			0
$753$	4.00000	−	4.00000i	0.145768	−	0.145768i
$754$		0			0
$755$	5.65685	+	11.3137i	0.205874	+	0.411748i
$756$		0			0
$757$	11.0000	−	11.0000i	0.399802	−	0.399802i	−0.478361	−	0.878163i	$-0.658769\pi$
$757$	11.0000	−	11.0000i	0.399802	−	0.399802i	0.878163	+	0.478361i	$0.158769\pi$
$758$		0			0
$759$	22.6274			0.821323
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	11.3137	−	11.3137i	0.409584	−	0.409584i
$764$		0			0
$765$	5.00000	−	15.0000i	0.180775	−	0.542326i
$766$		0			0
$767$		0			0
$768$		0			0
$769$			40.0000i			1.44244i	0.692708	+	0.721218i	$0.256418\pi$
$769$			40.0000i			1.44244i	−0.692708	+	0.721218i	$0.743582\pi$
$770$		0			0
$771$	−12.7279			−0.458385
$772$		0			0
$773$	−11.0000	−	11.0000i	−0.395643	−	0.395643i	0.481050	−	0.876693i	$-0.340255\pi$
$773$	−11.0000	−	11.0000i	−0.395643	−	0.395643i	−0.876693	+	0.481050i	$0.840255\pi$
$774$		0			0
$775$	22.6274	+	16.9706i	0.812801	+	0.609601i
$776$		0			0
$777$	−12.0000	−	12.0000i	−0.430498	−	0.430498i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		−	32.0000i		−	1.14505i
$782$		0			0
$783$	4.24264	+	4.24264i	0.151620	+	0.151620i
$784$		0			0
$785$	−13.0000	+	39.0000i	−0.463990	+	1.39197i
$786$		0			0
$787$	−14.1421	−	14.1421i	−0.504113	−	0.504113i	0.408601	−	0.912713i	$-0.366017\pi$
$787$	−14.1421	−	14.1421i	−0.504113	−	0.504113i	−0.912713	+	0.408601i	$0.866017\pi$
$788$		0			0
$789$	−12.0000			−0.427211
$790$		0			0
$791$			39.5980i			1.40794i
$792$		0			0
$793$	30.0000	−	30.0000i	1.06533	−	1.06533i
$794$		0			0
$795$	−14.1421	+	7.07107i	−0.501570	+	0.250785i
$796$		0			0
$797$	−15.0000	+	15.0000i	−0.531327	+	0.531327i	−0.920967	−	0.389640i	$-0.872599\pi$
$797$	−15.0000	+	15.0000i	−0.531327	+	0.531327i	0.389640	+	0.920967i	$0.372599\pi$
$798$		0			0
$799$	−84.8528			−3.00188
$800$		0			0
$801$		0			0
$802$		0			0
$803$	28.2843	−	28.2843i	0.998130	−	0.998130i
$804$		0			0
$805$	32.0000	−	16.0000i	1.12785	−	0.563926i
$806$		0			0
$807$	14.1421	−	14.1421i	0.497827	−	0.497827i
$808$		0			0
$809$			24.0000i			0.843795i	0.906644	+	0.421898i	$0.138636\pi$
$809$			24.0000i			0.843795i	−0.906644	+	0.421898i	$0.861364\pi$
$810$		0			0
$811$	−5.65685			−0.198639			−0.0993195	−	0.995056i	$-0.531667\pi$
$811$	−5.65685			−0.198639			−0.0993195	+	0.995056i	$0.531667\pi$
$812$		0			0
$813$	12.0000	+	12.0000i	0.420858	+	0.420858i
$814$		0			0
$815$	−8.48528	+	25.4558i	−0.297226	+	0.891679i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		−	16.9706i		−	0.592999i
$820$		0			0
$821$			18.0000i			0.628204i	0.949389	+	0.314102i	$0.101703\pi$
$821$			18.0000i			0.628204i	−0.949389	+	0.314102i	$0.898297\pi$
$822$		0			0
$823$	19.7990	+	19.7990i	0.690149	+	0.690149i	0.962265	−	0.272115i	$-0.0877232\pi$
$823$	19.7990	+	19.7990i	0.690149	+	0.690149i	−0.272115	+	0.962265i	$0.587723\pi$
$824$		0			0
$825$	4.00000	+	28.0000i	0.139262	+	0.974835i
$826$		0			0
$827$	−19.7990	−	19.7990i	−0.688478	−	0.688478i	0.273417	−	0.961896i	$-0.411846\pi$
$827$	−19.7990	−	19.7990i	−0.688478	−	0.688478i	−0.961896	+	0.273417i	$0.911846\pi$
$828$		0			0
$829$	−28.0000			−0.972480			−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000			−0.972480			−0.486240	+	0.873825i	$0.661632\pi$
$830$		0			0
$831$		−	4.24264i		−	0.147176i
$832$		0			0
$833$	45.0000	−	45.0000i	1.55916	−	1.55916i
$834$		0			0
$835$	−8.48528	+	25.4558i	−0.293645	+	0.880936i
$836$		0			0
$837$	4.00000	−	4.00000i	0.138260	−	0.138260i
$838$		0			0
$839$	45.2548			1.56237			0.781185	−	0.624299i	$-0.214615\pi$
$839$	45.2548			1.56237			0.781185	+	0.624299i	$0.214615\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.00000	+	10.0000i	0.172005	+	0.344010i
$846$		0			0
$847$	−59.3970	+	59.3970i	−2.04090	+	2.04090i
$848$		0			0
$849$		−	28.0000i		−	0.960958i
$850$		0			0
$851$	16.9706			0.581743
$852$		0			0
$853$	−19.0000	−	19.0000i	−0.650548	−	0.650548i	0.302577	−	0.953125i	$-0.402153\pi$
$853$	−19.0000	−	19.0000i	−0.650548	−	0.650548i	−0.953125	+	0.302577i	$0.902153\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.00000	−	7.00000i	−0.239115	−	0.239115i	0.577368	−	0.816484i	$-0.304080\pi$
$857$	−7.00000	−	7.00000i	−0.239115	−	0.239115i	−0.816484	+	0.577368i	$0.804080\pi$
$858$		0			0
$859$			56.5685i			1.93009i	0.262077	+	0.965047i	$0.415592\pi$
$859$			56.5685i			1.93009i	−0.262077	+	0.965047i	$0.584408\pi$
$860$		0			0
$861$		−	32.0000i		−	1.09056i
$862$		0			0
$863$	−25.4558	−	25.4558i	−0.866527	−	0.866527i	0.125559	−	0.992086i	$-0.459928\pi$
$863$	−25.4558	−	25.4558i	−0.866527	−	0.866527i	−0.992086	+	0.125559i	$0.959928\pi$
$864$		0			0
$865$	3.00000	+	1.00000i	0.102003	+	0.0340010i
$866$		0			0
$867$	23.3345	+	23.3345i	0.792482	+	0.792482i
$868$		0			0
$869$		0			0
$870$		0			0
$871$			16.9706i			0.575026i
$872$		0			0
$873$	3.00000	−	3.00000i	0.101535	−	0.101535i
$874$		0			0
$875$	25.4558	+	36.7696i	0.860565	+	1.24304i
$876$		0			0
$877$	27.0000	−	27.0000i	0.911725	−	0.911725i	−0.0846827	−	0.996408i	$-0.526988\pi$
$877$	27.0000	−	27.0000i	0.911725	−	0.911725i	0.996408	+	0.0846827i	$0.0269877\pi$
$878$		0			0
$879$	−24.0416			−0.810904
$880$		0			0
$881$	32.0000			1.07811			0.539054	−	0.842271i	$-0.318782\pi$
$881$	32.0000			1.07811			0.539054	+	0.842271i	$0.318782\pi$
$882$		0			0
$883$	2.82843	−	2.82843i	0.0951842	−	0.0951842i	−0.657911	−	0.753095i	$-0.728560\pi$
$883$	2.82843	−	2.82843i	0.0951842	−	0.0951842i	0.753095	+	0.657911i	$0.228560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.1421	+	14.1421i	−0.474846	+	0.474846i	−0.903479	−	0.428632i	$-0.858996\pi$
$887$	−14.1421	+	14.1421i	−0.474846	+	0.474846i	0.428632	+	0.903479i	$0.358996\pi$
$888$		0			0
$889$			48.0000i			1.60987i
$890$		0			0
$891$	5.65685			0.189512
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−11.3137	−	22.6274i	−0.378176	−	0.756351i
$896$		0			0
$897$	12.0000	+	12.0000i	0.400668	+	0.400668i
$898$		0			0
$899$		−	33.9411i		−	1.13200i
$900$		0			0
$901$		−	50.0000i		−	1.66574i
$902$		0			0
$903$	11.3137	+	11.3137i	0.376497	+	0.376497i
$904$		0			0
$905$	−12.0000	−	24.0000i	−0.398893	−	0.797787i
$906$		0			0
$907$	8.48528	+	8.48528i	0.281749	+	0.281749i	0.833806	−	0.552057i	$-0.186157\pi$
$907$	8.48528	+	8.48528i	0.281749	+	0.281749i	−0.552057	+	0.833806i	$0.686157\pi$
$908$		0			0
$909$	−4.00000			−0.132672
$910$		0			0
$911$			39.5980i			1.31194i	0.754787	+	0.655970i	$0.227740\pi$
$911$			39.5980i			1.31194i	−0.754787	+	0.655970i	$0.772260\pi$
$912$		0			0
$913$	−48.0000	+	48.0000i	−1.58857	+	1.58857i
$914$		0			0
$915$	21.2132	+	7.07107i	0.701287	+	0.233762i
$916$		0			0
$917$	−16.0000	+	16.0000i	−0.528367	+	0.528367i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$	28.0000			0.922631
$922$		0			0
$923$	16.9706	−	16.9706i	0.558593	−	0.558593i
$924$		0			0
$925$	3.00000	+	21.0000i	0.0986394	+	0.690476i
$926$		0			0
$927$	−14.1421	+	14.1421i	−0.464489	+	0.464489i
$928$		0			0
$929$		−	34.0000i		−	1.11550i	−0.830008	−	0.557752i	$-0.811664\pi$
$929$		−	34.0000i		−	1.11550i	0.830008	−	0.557752i	$-0.188336\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	4.00000	+	4.00000i	0.130954	+	0.130954i
$934$		0			0
$935$	−84.8528	−	28.2843i	−2.77498	−	0.924995i
$936$		0			0
$937$	−27.0000	−	27.0000i	−0.882052	−	0.882052i	0.111691	−	0.993743i	$-0.464373\pi$
$937$	−27.0000	−	27.0000i	−0.882052	−	0.882052i	−0.993743	+	0.111691i	$0.964373\pi$
$938$		0			0
$939$			24.0416i			0.784569i
$940$		0			0
$941$			60.0000i			1.95594i	0.208736	+	0.977972i	$0.433065\pi$
$941$			60.0000i			1.95594i	−0.208736	+	0.977972i	$0.566935\pi$
$942$		0			0
$943$	22.6274	+	22.6274i	0.736850	+	0.736850i
$944$		0			0
$945$	8.00000	−	4.00000i	0.260240	−	0.130120i
$946$		0			0
$947$	31.1127	+	31.1127i	1.01103	+	1.01103i	0.999939	+	0.0110883i	$0.00352960\pi$
$947$	31.1127	+	31.1127i	1.01103	+	1.01103i	0.0110883	+	0.999939i	$0.496470\pi$
$948$		0			0
$949$	30.0000			0.973841
$950$		0			0
$951$		−	12.7279i		−	0.412731i
$952$		0			0
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.00419731	−	0.999991i	$-0.498664\pi$
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.999991	−	0.00419731i	$-0.00133605\pi$
$954$		0			0
$955$	−16.9706	−	33.9411i	−0.549155	−	1.09831i
$956$		0			0
$957$	24.0000	−	24.0000i	0.775810	−	0.775810i
$958$		0			0
$959$	−5.65685			−0.182669
$960$		0			0
$961$	−1.00000			−0.0322581
$962$		0			0
$963$	−2.82843	+	2.82843i	−0.0911448	+	0.0911448i
$964$		0			0
$965$	−3.00000	+	9.00000i	−0.0965734	+	0.289720i
$966$		0			0
$967$	2.82843	−	2.82843i	0.0909561	−	0.0909561i	−0.660165	−	0.751121i	$-0.729514\pi$
$967$	2.82843	−	2.82843i	0.0909561	−	0.0909561i	0.751121	+	0.660165i	$0.229514\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−50.9117			−1.63383			−0.816917	−	0.576755i	$-0.804319\pi$
$971$	−50.9117			−1.63383			−0.816917	+	0.576755i	$0.804319\pi$
$972$		0			0
$973$	−64.0000	−	64.0000i	−2.05175	−	2.05175i
$974$		0			0
$975$	−12.7279	+	16.9706i	−0.407620	+	0.543493i
$976$		0			0
$977$	−29.0000	−	29.0000i	−0.927792	−	0.927792i	0.0697708	−	0.997563i	$-0.477773\pi$
$977$	−29.0000	−	29.0000i	−0.927792	−	0.927792i	−0.997563	+	0.0697708i	$0.977773\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$			4.00000i			0.127710i
$982$		0			0
$983$	25.4558	+	25.4558i	0.811915	+	0.811915i	0.984921	−	0.173006i	$-0.0553478\pi$
$983$	25.4558	+	25.4558i	0.811915	+	0.811915i	−0.173006	+	0.984921i	$0.555348\pi$
$984$		0			0
$985$	−1.00000	+	3.00000i	−0.0318626	+	0.0955879i
$986$		0			0
$987$	−33.9411	−	33.9411i	−1.08036	−	1.08036i
$988$		0			0
$989$	−16.0000			−0.508770
$990$		0			0
$991$		−	39.5980i		−	1.25787i	−0.777457	−	0.628936i	$-0.783491\pi$
$991$		−	39.5980i		−	1.25787i	0.777457	−	0.628936i	$-0.216509\pi$
$992$		0			0
$993$	−4.00000	+	4.00000i	−0.126936	+	0.126936i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−31.0000	+	31.0000i	−0.981780	+	0.981780i	−0.999837	−	0.0180571i	$-0.994252\pi$
$997$	−31.0000	+	31.0000i	−0.981780	+	0.981780i	0.0180571	+	0.999837i	$0.494252\pi$
$998$		0			0
$999$	4.24264			0.134231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bh.g.1087.2	yes	4
4.3	odd	2	inner	1920.2.bh.g.1087.1	yes	4
5.3	odd	4		1920.2.bh.b.703.2	yes	4
8.3	odd	2		1920.2.bh.b.1087.2	yes	4
8.5	even	2		1920.2.bh.b.1087.1	yes	4
20.3	even	4		1920.2.bh.b.703.1	✓	4
40.3	even	4	inner	1920.2.bh.g.703.2	yes	4
40.13	odd	4	inner	1920.2.bh.g.703.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.bh.b.703.1	✓	4	20.3	even	4
1920.2.bh.b.703.2	yes	4	5.3	odd	4
1920.2.bh.b.1087.1	yes	4	8.5	even	2
1920.2.bh.b.1087.2	yes	4	8.3	odd	2
1920.2.bh.g.703.1	yes	4	40.13	odd	4	inner
1920.2.bh.g.703.2	yes	4	40.3	even	4	inner
1920.2.bh.g.1087.1	yes	4	4.3	odd	2	inner
1920.2.bh.g.1087.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bh (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(2.00000 - 1.00000i) q^{5} +(-2.82843 + 2.82843i) q^{7} -1.00000i q^{9} -5.65685 q^{11} +(-3.00000 - 3.00000i) q^{13} +(0.707107 - 2.12132i) q^{15} +(5.00000 + 5.00000i) q^{17} +4.00000i q^{21} +(-2.82843 - 2.82843i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-0.707107 - 0.707107i) q^{27} -6.00000 q^{29} +5.65685i q^{31} +(-4.00000 + 4.00000i) q^{33} +(-2.82843 + 8.48528i) q^{35} +(-3.00000 + 3.00000i) q^{37} -4.24264 q^{39} -8.00000 q^{41} +(2.82843 - 2.82843i) q^{43} +(-1.00000 - 2.00000i) q^{45} +(-8.48528 + 8.48528i) q^{47} -9.00000i q^{49} +7.07107 q^{51} +(-5.00000 - 5.00000i) q^{53} +(-11.3137 + 5.65685i) q^{55} +10.0000i q^{61} +(2.82843 + 2.82843i) q^{63} +(-9.00000 - 3.00000i) q^{65} +(-2.82843 - 2.82843i) q^{67} -4.00000 q^{69} +5.65685i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-0.707107 - 4.94975i) q^{75} +(16.0000 - 16.0000i) q^{77} -1.00000 q^{81} +(8.48528 - 8.48528i) q^{83} +(15.0000 + 5.00000i) q^{85} +(-4.24264 + 4.24264i) q^{87} +16.9706 q^{91} +(4.00000 + 4.00000i) q^{93} +(3.00000 + 3.00000i) q^{97} +5.65685i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{5} - 12 q^{13} + 20 q^{17} + 12 q^{25} - 24 q^{29} - 16 q^{33} - 12 q^{37} - 32 q^{41} - 4 q^{45} - 20 q^{53} - 36 q^{65} - 16 q^{69} - 20 q^{73} + 64 q^{77} - 4 q^{81} + 60 q^{85} + 16 q^{93}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q + 8 * q^5 - 12 * q^13 + 20 * q^17 + 12 * q^25 - 24 * q^29 - 16 * q^33 - 12 * q^37 - 32 * q^41 - 4 * q^45 - 20 * q^53 - 36 * q^65 - 16 * q^69 - 20 * q^73 + 64 * q^77 - 4 * q^81 + 60 * q^85 + 16 * q^93 + 12 * q^97

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