LMFDB - Embedded newform 630.2.g.c.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(379,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("630.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	630.379
Dual form			630.2.g.c.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +(2.00000 + 1.00000i) q^{10} -2.00000 q^{11} -6.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} +6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} +2.00000i q^{22} -8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -6.00000 q^{26} +1.00000i q^{28} +6.00000 q^{29} -2.00000 q^{31} -1.00000i q^{32} -4.00000 q^{34} +(2.00000 + 1.00000i) q^{35} +4.00000i q^{37} -6.00000i q^{38} +(-2.00000 - 1.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +2.00000 q^{44} -8.00000 q^{46} -8.00000i q^{47} -1.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000i q^{52} +6.00000i q^{53} +(2.00000 - 4.00000i) q^{55} +1.00000 q^{56} -6.00000i q^{58} -8.00000 q^{59} -10.0000 q^{61} +2.00000i q^{62} -1.00000 q^{64} +(12.0000 + 6.00000i) q^{65} +8.00000i q^{67} +4.00000i q^{68} +(1.00000 - 2.00000i) q^{70} +6.00000 q^{71} +14.0000i q^{73} +4.00000 q^{74} -6.00000 q^{76} +2.00000i q^{77} +12.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +2.00000i q^{82} -8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} -4.00000 q^{86} -2.00000i q^{88} -10.0000 q^{89} -6.00000 q^{91} +8.00000i q^{92} -8.00000 q^{94} +(-6.00000 + 12.0000i) q^{95} -10.0000i q^{97} +1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{5}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^5	$ 2 q - 2 q^{4} - 2 q^{5} + 4 q^{10} - 4 q^{11} - 2 q^{14} + 2 q^{16} + 12 q^{19} + 2 q^{20} - 6 q^{25} - 12 q^{26} + 12 q^{29} - 4 q^{31} - 8 q^{34} + 4 q^{35} - 4 q^{40} - 4 q^{41} + 4 q^{44} - 16 q^{46} - 2 q^{49} - 8 q^{50} + 4 q^{55} + 2 q^{56} - 16 q^{59} - 20 q^{61} - 2 q^{64} + 24 q^{65} + 2 q^{70} + 12 q^{71} + 8 q^{74} - 12 q^{76} + 24 q^{79} - 2 q^{80} + 16 q^{85} - 8 q^{86} - 20 q^{89} - 12 q^{91} - 16 q^{94} - 12 q^{95}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^5 + 4 * q^10 - 4 * q^11 - 2 * q^14 + 2 * q^16 + 12 * q^19 + 2 * q^20 - 6 * q^25 - 12 * q^26 + 12 * q^29 - 4 * q^31 - 8 * q^34 + 4 * q^35 - 4 * q^40 - 4 * q^41 + 4 * q^44 - 16 * q^46 - 2 * q^49 - 8 * q^50 + 4 * q^55 + 2 * q^56 - 16 * q^59 - 20 * q^61 - 2 * q^64 + 24 * q^65 + 2 * q^70 + 12 * q^71 + 8 * q^74 - 12 * q^76 + 24 * q^79 - 2 * q^80 + 16 * q^85 - 8 * q^86 - 20 * q^89 - 12 * q^91 - 16 * q^94 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		0			0
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$		0			0
$22$			2.00000i			0.426401i
$23$		−	8.00000i		−	1.66812i	−0.551677	−	0.834058i	$-0.686012\pi$
$23$		−	8.00000i		−	1.66812i	0.551677	−	0.834058i	$-0.313988\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−6.00000			−1.17670
$27$		0			0
$28$			1.00000i			0.188982i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−4.00000			−0.685994
$35$	2.00000	+	1.00000i	0.338062	+	0.169031i
$36$		0			0
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$		−	6.00000i		−	0.973329i
$39$		0			0
$40$	−2.00000	−	1.00000i	−0.316228	−	0.158114i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	−8.00000			−1.17954
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$			6.00000i			0.832050i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$	2.00000	−	4.00000i	0.269680	−	0.539360i
$56$	1.00000			0.133631
$57$		0			0
$58$		−	6.00000i		−	0.787839i
$59$	−8.00000			−1.04151			−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000			−1.04151			−0.520756	+	0.853706i	$0.674350\pi$
$60$		0			0
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$			2.00000i			0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	12.0000	+	6.00000i	1.48842	+	0.744208i
$66$		0			0
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$			4.00000i			0.485071i
$69$		0			0
$70$	1.00000	−	2.00000i	0.119523	−	0.239046i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$			14.0000i			1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$			14.0000i			1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$	4.00000			0.464991
$75$		0			0
$76$	−6.00000			−0.688247
$77$			2.00000i			0.227921i
$78$		0			0
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$		0			0
$82$			2.00000i			0.220863i
$83$		−	8.00000i		−	0.878114i	−0.898459	−	0.439057i	$-0.855313\pi$
$83$		−	8.00000i		−	0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$		0			0
$85$	8.00000	+	4.00000i	0.867722	+	0.433861i
$86$	−4.00000			−0.431331
$87$		0			0
$88$		−	2.00000i		−	0.213201i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$			8.00000i			0.834058i
$93$		0			0
$94$	−8.00000			−0.825137
$95$	−6.00000	+	12.0000i	−0.615587	+	1.23117i
$96$		0			0
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$			1.00000i			0.101015i
$99$		0			0
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$		0			0
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	6.00000			0.582772
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	−4.00000	−	2.00000i	−0.381385	−	0.190693i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	16.0000	+	8.00000i	1.49201	+	0.746004i
$116$	−6.00000			−0.557086
$117$		0			0
$118$			8.00000i			0.736460i
$119$	−4.00000			−0.366679
$120$		0			0
$121$	−7.00000			−0.636364
$122$			10.0000i			0.905357i
$123$		0			0
$124$	2.00000			0.179605
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	6.00000	−	12.0000i	0.526235	−	1.05247i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		−	6.00000i		−	0.520266i
$134$	8.00000			0.691095
$135$		0			0
$136$	4.00000			0.342997
$137$			6.00000i			0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	−2.00000	−	1.00000i	−0.169031	−	0.0845154i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$			12.0000i			1.00349i
$144$		0			0
$145$	−6.00000	+	12.0000i	−0.498273	+	0.996546i
$146$	14.0000			1.15865
$147$		0			0
$148$		−	4.00000i		−	0.328798i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$			6.00000i			0.486664i
$153$		0			0
$154$	2.00000			0.161165
$155$	2.00000	−	4.00000i	0.160644	−	0.321288i
$156$		0			0
$157$		−	22.0000i		−	1.75579i	−0.478852	−	0.877896i	$-0.658947\pi$
$157$		−	22.0000i		−	1.75579i	0.478852	−	0.877896i	$-0.341053\pi$
$158$		−	12.0000i		−	0.954669i
$159$		0			0
$160$	2.00000	+	1.00000i	0.158114	+	0.0790569i
$161$	−8.00000			−0.630488
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	−8.00000			−0.620920
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$	4.00000	−	8.00000i	0.306786	−	0.613572i
$171$		0			0
$172$			4.00000i			0.304997i
$173$			8.00000i			0.608229i	0.952636	+	0.304114i	$0.0983605\pi$
$173$			8.00000i			0.608229i	−0.952636	+	0.304114i	$0.901639\pi$
$174$		0			0
$175$	−4.00000	+	3.00000i	−0.302372	+	0.226779i
$176$	−2.00000			−0.150756
$177$		0			0
$178$			10.0000i			0.749532i
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$			6.00000i			0.444750i
$183$		0			0
$184$	8.00000			0.589768
$185$	−8.00000	−	4.00000i	−0.588172	−	0.294086i
$186$		0			0
$187$			8.00000i			0.585018i
$188$			8.00000i			0.583460i
$189$		0			0
$190$	12.0000	+	6.00000i	0.870572	+	0.435286i
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$		0			0
$193$			8.00000i			0.575853i	0.957653	+	0.287926i	$0.0929658\pi$
$193$			8.00000i			0.575853i	−0.957653	+	0.287926i	$0.907034\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	1.00000			0.0714286
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		0			0
$199$	−6.00000			−0.425329			−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000			−0.425329			−0.212664	+	0.977125i	$0.568214\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$			10.0000i			0.703598i
$203$		−	6.00000i		−	0.421117i
$204$		0			0
$205$	2.00000	−	4.00000i	0.139686	−	0.279372i
$206$	−8.00000			−0.557386
$207$		0			0
$208$		−	6.00000i		−	0.416025i
$209$	−12.0000			−0.830057
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$		−	6.00000i		−	0.412082i
$213$		0			0
$214$	−12.0000			−0.820303
$215$	8.00000	+	4.00000i	0.545595	+	0.272798i
$216$		0			0
$217$			2.00000i			0.135769i
$218$		−	14.0000i		−	0.948200i
$219$		0			0
$220$	−2.00000	+	4.00000i	−0.134840	+	0.269680i
$221$	−24.0000			−1.61441
$222$		0			0
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	6.00000			0.399114
$227$			8.00000i			0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$227$			8.00000i			0.530979i	−0.964114	+	0.265489i	$0.914466\pi$
$228$		0			0
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	8.00000	−	16.0000i	0.527504	−	1.05501i
$231$		0			0
$232$			6.00000i			0.393919i
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$		0			0
$235$	16.0000	+	8.00000i	1.04372	+	0.521862i
$236$	8.00000			0.520756
$237$		0			0
$238$			4.00000i			0.259281i
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$		0			0
$241$	−26.0000			−1.67481			−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000			−1.67481			−0.837404	+	0.546585i	$0.815928\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	10.0000			0.640184
$245$	1.00000	−	2.00000i	0.0638877	−	0.127775i
$246$		0			0
$247$		−	36.0000i		−	2.29063i
$248$		−	2.00000i		−	0.127000i
$249$		0			0
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$			16.0000i			1.00591i
$254$	4.00000			0.250982
$255$		0			0
$256$	1.00000			0.0625000
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$	−12.0000	−	6.00000i	−0.744208	−	0.372104i
$261$		0			0
$262$		−	12.0000i		−	0.741362i
$263$			16.0000i			0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$			16.0000i			0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$		0			0
$265$	−12.0000	−	6.00000i	−0.737154	−	0.368577i
$266$	−6.00000			−0.367884
$267$		0			0
$268$		−	8.00000i		−	0.488678i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$	10.0000			0.607457			0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000			0.607457			0.303728	+	0.952759i	$0.401768\pi$
$272$		−	4.00000i		−	0.242536i
$273$		0			0
$274$	6.00000			0.362473
$275$	6.00000	+	8.00000i	0.361814	+	0.482418i
$276$		0			0
$277$			28.0000i			1.68236i	0.540758	+	0.841178i	$0.318138\pi$
$277$			28.0000i			1.68236i	−0.540758	+	0.841178i	$0.681862\pi$
$278$		−	14.0000i		−	0.839664i
$279$		0			0
$280$	−1.00000	+	2.00000i	−0.0597614	+	0.119523i
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$		−	20.0000i		−	1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$		−	20.0000i		−	1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	12.0000			0.709575
$287$			2.00000i			0.118056i
$288$		0			0
$289$	1.00000			0.0588235
$290$	12.0000	+	6.00000i	0.704664	+	0.352332i
$291$		0			0
$292$		−	14.0000i		−	0.819288i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$	8.00000	−	16.0000i	0.465778	−	0.931556i
$296$	−4.00000			−0.232495
$297$		0			0
$298$		−	10.0000i		−	0.579284i
$299$	−48.0000			−2.77591
$300$		0			0
$301$	−4.00000			−0.230556
$302$			8.00000i			0.460348i
$303$		0			0
$304$	6.00000			0.344124
$305$	10.0000	−	20.0000i	0.572598	−	1.14520i
$306$		0			0
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		−	2.00000i		−	0.113961i
$309$		0			0
$310$	−4.00000	−	2.00000i	−0.227185	−	0.113592i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$			2.00000i			0.113047i	0.998401	+	0.0565233i	$0.0180015\pi$
$313$			2.00000i			0.113047i	−0.998401	+	0.0565233i	$0.981998\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−12.0000			−0.675053
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	−12.0000			−0.671871
$320$	1.00000	−	2.00000i	0.0559017	−	0.111803i
$321$		0			0
$322$			8.00000i			0.445823i
$323$		−	24.0000i		−	1.33540i
$324$		0			0
$325$	−24.0000	+	18.0000i	−1.33128	+	0.998460i
$326$	4.00000			0.221540
$327$		0			0
$328$		−	2.00000i		−	0.110432i
$329$	−8.00000			−0.441054
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$			8.00000i			0.439057i
$333$		0			0
$334$	12.0000			0.656611
$335$	−16.0000	−	8.00000i	−0.874173	−	0.437087i
$336$		0			0
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$			23.0000i			1.25104i
$339$		0			0
$340$	−8.00000	−	4.00000i	−0.433861	−	0.216930i
$341$	4.00000			0.216612
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	4.00000			0.215666
$345$		0			0
$346$	8.00000			0.430083
$347$		−	36.0000i		−	1.93258i	−0.257454	−	0.966291i	$-0.582883\pi$
$347$		−	36.0000i		−	1.93258i	0.257454	−	0.966291i	$-0.417117\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	3.00000	+	4.00000i	0.160357	+	0.213809i
$351$		0			0
$352$			2.00000i			0.106600i
$353$			20.0000i			1.06449i	0.846590	+	0.532246i	$0.178652\pi$
$353$			20.0000i			1.06449i	−0.846590	+	0.532246i	$0.821348\pi$
$354$		0			0
$355$	−6.00000	+	12.0000i	−0.318447	+	0.636894i
$356$	10.0000			0.529999
$357$		0			0
$358$		−	10.0000i		−	0.528516i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$		−	2.00000i		−	0.105118i
$363$		0			0
$364$	6.00000			0.314485
$365$	−28.0000	−	14.0000i	−1.46559	−	0.732793i
$366$		0			0
$367$		−	32.0000i		−	1.67039i	−0.549957	−	0.835193i	$-0.685356\pi$
$367$		−	32.0000i		−	1.67039i	0.549957	−	0.835193i	$-0.314644\pi$
$368$		−	8.00000i		−	0.417029i
$369$		0			0
$370$	−4.00000	+	8.00000i	−0.207950	+	0.415900i
$371$	6.00000			0.311504
$372$		0			0
$373$			24.0000i			1.24267i	0.783544	+	0.621336i	$0.213410\pi$
$373$			24.0000i			1.24267i	−0.783544	+	0.621336i	$0.786590\pi$
$374$	8.00000			0.413670
$375$		0			0
$376$	8.00000			0.412568
$377$		−	36.0000i		−	1.85409i
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	6.00000	−	12.0000i	0.307794	−	0.615587i
$381$		0			0
$382$		−	18.0000i		−	0.920960i
$383$			20.0000i			1.02195i	0.859595	+	0.510976i	$0.170716\pi$
$383$			20.0000i			1.02195i	−0.859595	+	0.510976i	$0.829284\pi$
$384$		0			0
$385$	−4.00000	−	2.00000i	−0.203859	−	0.101929i
$386$	8.00000			0.407189
$387$		0			0
$388$			10.0000i			0.507673i
$389$	2.00000			0.101404			0.0507020	−	0.998714i	$-0.483854\pi$
$389$	2.00000			0.101404			0.0507020	+	0.998714i	$0.483854\pi$
$390$		0			0
$391$	−32.0000			−1.61831
$392$		−	1.00000i		−	0.0505076i
$393$		0			0
$394$	−2.00000			−0.100759
$395$	−12.0000	+	24.0000i	−0.603786	+	1.20757i
$396$		0			0
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$			6.00000i			0.300753i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	14.0000			0.699127			0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000			0.699127			0.349563	+	0.936913i	$0.386330\pi$
$402$		0			0
$403$			12.0000i			0.597763i
$404$	10.0000			0.497519
$405$		0			0
$406$	−6.00000			−0.297775
$407$		−	8.00000i		−	0.396545i
$408$		0			0
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$	−4.00000	−	2.00000i	−0.197546	−	0.0987730i
$411$		0			0
$412$			8.00000i			0.394132i
$413$			8.00000i			0.393654i
$414$		0			0
$415$	16.0000	+	8.00000i	0.785409	+	0.392705i
$416$	−6.00000			−0.294174
$417$		0			0
$418$			12.0000i			0.586939i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$		0			0
$424$	−6.00000			−0.291386
$425$	−16.0000	+	12.0000i	−0.776114	+	0.582086i
$426$		0			0
$427$			10.0000i			0.483934i
$428$			12.0000i			0.580042i
$429$		0			0
$430$	4.00000	−	8.00000i	0.192897	−	0.385794i
$431$	−2.00000			−0.0963366			−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000			−0.0963366			−0.0481683	+	0.998839i	$0.515338\pi$
$432$		0			0
$433$			26.0000i			1.24948i	0.780833	+	0.624740i	$0.214795\pi$
$433$			26.0000i			1.24948i	−0.780833	+	0.624740i	$0.785205\pi$
$434$	2.00000			0.0960031
$435$		0			0
$436$	−14.0000			−0.670478
$437$		−	48.0000i		−	2.29615i
$438$		0			0
$439$	18.0000			0.859093			0.429547	−	0.903045i	$-0.358673\pi$
$439$	18.0000			0.859093			0.429547	+	0.903045i	$0.358673\pi$
$440$	4.00000	+	2.00000i	0.190693	+	0.0953463i
$441$		0			0
$442$			24.0000i			1.14156i
$443$		−	12.0000i		−	0.570137i	−0.958507	−	0.285069i	$-0.907984\pi$
$443$		−	12.0000i		−	0.570137i	0.958507	−	0.285069i	$-0.0920164\pi$
$444$		0			0
$445$	10.0000	−	20.0000i	0.474045	−	0.948091i
$446$	8.00000			0.378811
$447$		0			0
$448$			1.00000i			0.0472456i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$		−	6.00000i		−	0.282216i
$453$		0			0
$454$	8.00000			0.375459
$455$	6.00000	−	12.0000i	0.281284	−	0.562569i
$456$		0			0
$457$			28.0000i			1.30978i	0.755722	+	0.654892i	$0.227286\pi$
$457$			28.0000i			1.30978i	−0.755722	+	0.654892i	$0.772714\pi$
$458$			14.0000i			0.654177i
$459$		0			0
$460$	−16.0000	−	8.00000i	−0.746004	−	0.373002i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$		−	36.0000i		−	1.67306i	−0.547920	−	0.836531i	$-0.684580\pi$
$463$		−	36.0000i		−	1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	−10.0000			−0.463241
$467$			24.0000i			1.11059i	0.831654	+	0.555294i	$0.187394\pi$
$467$			24.0000i			1.11059i	−0.831654	+	0.555294i	$0.812606\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$	8.00000	−	16.0000i	0.369012	−	0.738025i
$471$		0			0
$472$		−	8.00000i		−	0.368230i
$473$			8.00000i			0.367840i
$474$		0			0
$475$	−18.0000	−	24.0000i	−0.825897	−	1.10120i
$476$	4.00000			0.183340
$477$		0			0
$478$		−	26.0000i		−	1.18921i
$479$	8.00000			0.365529			0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000			0.365529			0.182765	+	0.983157i	$0.441495\pi$
$480$		0			0
$481$	24.0000			1.09431
$482$			26.0000i			1.18427i
$483$		0			0
$484$	7.00000			0.318182
$485$	20.0000	+	10.0000i	0.908153	+	0.454077i
$486$		0			0
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$		−	10.0000i		−	0.452679i
$489$		0			0
$490$	−2.00000	−	1.00000i	−0.0903508	−	0.0451754i
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$		0			0
$493$		−	24.0000i		−	1.08091i
$494$	−36.0000			−1.61972
$495$		0			0
$496$	−2.00000			−0.0898027
$497$		−	6.00000i		−	0.269137i
$498$		0			0
$499$	12.0000			0.537194			0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000			0.537194			0.268597	+	0.963253i	$0.413440\pi$
$500$	−11.0000	+	2.00000i	−0.491935	+	0.0894427i
$501$		0			0
$502$		0			0
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$		0			0
$505$	10.0000	−	20.0000i	0.444994	−	0.889988i
$506$	16.0000			0.711287
$507$		0			0
$508$		−	4.00000i		−	0.177471i
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		0			0
$515$	16.0000	+	8.00000i	0.705044	+	0.352522i
$516$		0			0
$517$			16.0000i			0.703679i
$518$		−	4.00000i		−	0.175750i
$519$		0			0
$520$	−6.00000	+	12.0000i	−0.263117	+	0.526235i
$521$	26.0000			1.13908			0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000			1.13908			0.569540	+	0.821963i	$0.307121\pi$
$522$		0			0
$523$			28.0000i			1.22435i	0.790721	+	0.612177i	$0.209706\pi$
$523$			28.0000i			1.22435i	−0.790721	+	0.612177i	$0.790294\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	16.0000			0.697633
$527$			8.00000i			0.348485i
$528$		0			0
$529$	−41.0000			−1.78261
$530$	−6.00000	+	12.0000i	−0.260623	+	0.521247i
$531$		0			0
$532$			6.00000i			0.260133i
$533$			12.0000i			0.519778i
$534$		0			0
$535$	24.0000	+	12.0000i	1.03761	+	0.518805i
$536$	−8.00000			−0.345547
$537$		0			0
$538$		−	18.0000i		−	0.776035i
$539$	2.00000			0.0861461
$540$		0			0
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$		−	10.0000i		−	0.429537i
$543$		0			0
$544$	−4.00000			−0.171499
$545$	−14.0000	+	28.0000i	−0.599694	+	1.19939i
$546$		0			0
$547$			40.0000i			1.71028i	0.518400	+	0.855138i	$0.326528\pi$
$547$			40.0000i			1.71028i	−0.518400	+	0.855138i	$0.673472\pi$
$548$		−	6.00000i		−	0.256307i
$549$		0			0
$550$	8.00000	−	6.00000i	0.341121	−	0.255841i
$551$	36.0000			1.53365
$552$		0			0
$553$		−	12.0000i		−	0.510292i
$554$	28.0000			1.18961
$555$		0			0
$556$	−14.0000			−0.593732
$557$			42.0000i			1.77960i	0.456354	+	0.889799i	$0.349155\pi$
$557$			42.0000i			1.77960i	−0.456354	+	0.889799i	$0.650845\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$	2.00000	+	1.00000i	0.0845154	+	0.0422577i
$561$		0			0
$562$			30.0000i			1.26547i
$563$		−	4.00000i		−	0.168580i	−0.996441	−	0.0842900i	$-0.973138\pi$
$563$		−	4.00000i		−	0.168580i	0.996441	−	0.0842900i	$-0.0268622\pi$
$564$		0			0
$565$	−12.0000	−	6.00000i	−0.504844	−	0.252422i
$566$	−20.0000			−0.840663
$567$		0			0
$568$			6.00000i			0.251754i
$569$	−46.0000			−1.92842			−0.964210	−	0.265139i	$-0.914582\pi$
$569$	−46.0000			−1.92842			−0.964210	+	0.265139i	$0.914582\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$		−	12.0000i		−	0.501745i
$573$		0			0
$574$	2.00000			0.0834784
$575$	−32.0000	+	24.0000i	−1.33449	+	1.00087i
$576$		0			0
$577$		−	26.0000i		−	1.08239i	−0.840896	−	0.541197i	$-0.817971\pi$
$577$		−	26.0000i		−	1.08239i	0.840896	−	0.541197i	$-0.182029\pi$
$578$		−	1.00000i		−	0.0415945i
$579$		0			0
$580$	6.00000	−	12.0000i	0.249136	−	0.498273i
$581$	−8.00000			−0.331896
$582$		0			0
$583$		−	12.0000i		−	0.496989i
$584$	−14.0000			−0.579324
$585$		0			0
$586$		0			0
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$	−16.0000	−	8.00000i	−0.658710	−	0.329355i
$591$		0			0
$592$			4.00000i			0.164399i
$593$			12.0000i			0.492781i	0.969171	+	0.246390i	$0.0792446\pi$
$593$			12.0000i			0.492781i	−0.969171	+	0.246390i	$0.920755\pi$
$594$		0			0
$595$	4.00000	−	8.00000i	0.163984	−	0.327968i
$596$	−10.0000			−0.409616
$597$		0			0
$598$			48.0000i			1.96287i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$			4.00000i			0.163028i
$603$		0			0
$604$	8.00000			0.325515
$605$	7.00000	−	14.0000i	0.284590	−	0.569181i
$606$		0			0
$607$			8.00000i			0.324710i	0.986732	+	0.162355i	$0.0519090\pi$
$607$			8.00000i			0.324710i	−0.986732	+	0.162355i	$0.948091\pi$
$608$		−	6.00000i		−	0.243332i
$609$		0			0
$610$	−20.0000	−	10.0000i	−0.809776	−	0.404888i
$611$	−48.0000			−1.94187
$612$		0			0
$613$		−	28.0000i		−	1.13091i	−0.824779	−	0.565455i	$-0.808701\pi$
$613$		−	28.0000i		−	1.13091i	0.824779	−	0.565455i	$-0.191299\pi$
$614$	−12.0000			−0.484281
$615$		0			0
$616$	−2.00000			−0.0805823
$617$			26.0000i			1.04672i	0.852111	+	0.523360i	$0.175322\pi$
$617$			26.0000i			1.04672i	−0.852111	+	0.523360i	$0.824678\pi$
$618$		0			0
$619$	22.0000			0.884255			0.442127	−	0.896952i	$-0.354224\pi$
$619$	22.0000			0.884255			0.442127	+	0.896952i	$0.354224\pi$
$620$	−2.00000	+	4.00000i	−0.0803219	+	0.160644i
$621$		0			0
$622$			24.0000i			0.962312i
$623$			10.0000i			0.400642i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	2.00000			0.0799361
$627$		0			0
$628$			22.0000i			0.877896i
$629$	16.0000			0.637962
$630$		0			0
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$			12.0000i			0.477334i
$633$		0			0
$634$	2.00000			0.0794301
$635$	−8.00000	−	4.00000i	−0.317470	−	0.158735i
$636$		0			0
$637$			6.00000i			0.237729i
$638$			12.0000i			0.475085i
$639$		0			0
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	−14.0000			−0.552967			−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000			−0.552967			−0.276483	+	0.961019i	$0.589169\pi$
$642$		0			0
$643$		−	12.0000i		−	0.473234i	−0.971603	−	0.236617i	$-0.923961\pi$
$643$		−	12.0000i		−	0.473234i	0.971603	−	0.236617i	$-0.0760386\pi$
$644$	8.00000			0.315244
$645$		0			0
$646$	−24.0000			−0.944267
$647$		−	36.0000i		−	1.41531i	−0.706560	−	0.707653i	$-0.749754\pi$
$647$		−	36.0000i		−	1.41531i	0.706560	−	0.707653i	$-0.250246\pi$
$648$		0			0
$649$	16.0000			0.628055
$650$	18.0000	+	24.0000i	0.706018	+	0.941357i
$651$		0			0
$652$		−	4.00000i		−	0.156652i
$653$			34.0000i			1.33052i	0.746611	+	0.665261i	$0.231680\pi$
$653$			34.0000i			1.33052i	−0.746611	+	0.665261i	$0.768320\pi$
$654$		0			0
$655$	−12.0000	+	24.0000i	−0.468879	+	0.937758i
$656$	−2.00000			−0.0780869
$657$		0			0
$658$			8.00000i			0.311872i
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$		0			0
$661$	38.0000			1.47803			0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000			1.47803			0.739014	+	0.673690i	$0.235292\pi$
$662$			8.00000i			0.310929i
$663$		0			0
$664$	8.00000			0.310460
$665$	12.0000	+	6.00000i	0.465340	+	0.232670i
$666$		0			0
$667$		−	48.0000i		−	1.85857i
$668$		−	12.0000i		−	0.464294i
$669$		0			0
$670$	−8.00000	+	16.0000i	−0.309067	+	0.618134i
$671$	20.0000			0.772091
$672$		0			0
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$	−8.00000			−0.308148
$675$		0			0
$676$	23.0000			0.884615
$677$		−	40.0000i		−	1.53732i	−0.639655	−	0.768662i	$-0.720923\pi$
$677$		−	40.0000i		−	1.53732i	0.639655	−	0.768662i	$-0.279077\pi$
$678$		0			0
$679$	−10.0000			−0.383765
$680$	−4.00000	+	8.00000i	−0.153393	+	0.306786i
$681$		0			0
$682$		−	4.00000i		−	0.153168i
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	−12.0000	−	6.00000i	−0.458496	−	0.229248i
$686$	1.00000			0.0381802
$687$		0			0
$688$		−	4.00000i		−	0.152499i
$689$	36.0000			1.37149
$690$		0			0
$691$	−2.00000			−0.0760836			−0.0380418	−	0.999276i	$-0.512112\pi$
$691$	−2.00000			−0.0760836			−0.0380418	+	0.999276i	$0.512112\pi$
$692$		−	8.00000i		−	0.304114i
$693$		0			0
$694$	−36.0000			−1.36654
$695$	−14.0000	+	28.0000i	−0.531050	+	1.06210i
$696$		0			0
$697$			8.00000i			0.303022i
$698$		−	26.0000i		−	0.984115i
$699$		0			0
$700$	4.00000	−	3.00000i	0.151186	−	0.113389i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$			24.0000i			0.905177i
$704$	2.00000			0.0753778
$705$		0			0
$706$	20.0000			0.752710
$707$			10.0000i			0.376089i
$708$		0			0
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	12.0000	+	6.00000i	0.450352	+	0.225176i
$711$		0			0
$712$		−	10.0000i		−	0.374766i
$713$			16.0000i			0.599205i
$714$		0			0
$715$	−24.0000	−	12.0000i	−0.897549	−	0.448775i
$716$	−10.0000			−0.373718
$717$		0			0
$718$		−	6.00000i		−	0.223918i
$719$	−4.00000			−0.149175			−0.0745874	−	0.997214i	$-0.523764\pi$
$719$	−4.00000			−0.149175			−0.0745874	+	0.997214i	$0.523764\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		−	17.0000i		−	0.632674i
$723$		0			0
$724$	−2.00000			−0.0743294
$725$	−18.0000	−	24.0000i	−0.668503	−	0.891338i
$726$		0			0
$727$			24.0000i			0.890111i	0.895503	+	0.445055i	$0.146816\pi$
$727$			24.0000i			0.890111i	−0.895503	+	0.445055i	$0.853184\pi$
$728$		−	6.00000i		−	0.222375i
$729$		0			0
$730$	−14.0000	+	28.0000i	−0.518163	+	1.03633i
$731$	−16.0000			−0.591781
$732$		0			0
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−8.00000			−0.294884
$737$		−	16.0000i		−	0.589368i
$738$		0			0
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	8.00000	+	4.00000i	0.294086	+	0.147043i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$		−	48.0000i		−	1.76095i	−0.474093	−	0.880475i	$-0.657224\pi$
$743$		−	48.0000i		−	1.76095i	0.474093	−	0.880475i	$-0.342776\pi$
$744$		0			0
$745$	−10.0000	+	20.0000i	−0.366372	+	0.732743i
$746$	24.0000			0.878702
$747$		0			0
$748$		−	8.00000i		−	0.292509i
$749$	−12.0000			−0.438470
$750$		0			0
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$	−36.0000			−1.31104
$755$	8.00000	−	16.0000i	0.291150	−	0.582300i
$756$		0			0
$757$		−	32.0000i		−	1.16306i	−0.813525	−	0.581530i	$-0.802454\pi$
$757$		−	32.0000i		−	1.16306i	0.813525	−	0.581530i	$-0.197546\pi$
$758$			20.0000i			0.726433i
$759$		0			0
$760$	−12.0000	−	6.00000i	−0.435286	−	0.217643i
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$		−	14.0000i		−	0.506834i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	20.0000			0.722629
$767$			48.0000i			1.73318i
$768$		0			0
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$	−2.00000	+	4.00000i	−0.0720750	+	0.144150i
$771$		0			0
$772$		−	8.00000i		−	0.287926i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	6.00000	+	8.00000i	0.215526	+	0.287368i
$776$	10.0000			0.358979
$777$		0			0
$778$		−	2.00000i		−	0.0717035i
$779$	−12.0000			−0.429945
$780$		0			0
$781$	−12.0000			−0.429394
$782$			32.0000i			1.14432i
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	44.0000	+	22.0000i	1.57043	+	0.785214i
$786$		0			0
$787$			28.0000i			0.998092i	0.866575	+	0.499046i	$0.166316\pi$
$787$			28.0000i			0.998092i	−0.866575	+	0.499046i	$0.833684\pi$
$788$			2.00000i			0.0712470i
$789$		0			0
$790$	24.0000	+	12.0000i	0.853882	+	0.426941i
$791$	6.00000			0.213335
$792$		0			0
$793$			60.0000i			2.13066i
$794$	−2.00000			−0.0709773
$795$		0			0
$796$	6.00000			0.212664
$797$			8.00000i			0.283375i	0.989911	+	0.141687i	$0.0452527\pi$
$797$			8.00000i			0.283375i	−0.989911	+	0.141687i	$0.954747\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$		0			0
$802$		−	14.0000i		−	0.494357i
$803$		−	28.0000i		−	0.988099i
$804$		0			0
$805$	8.00000	−	16.0000i	0.281963	−	0.563926i
$806$	12.0000			0.422682
$807$		0			0
$808$		−	10.0000i		−	0.351799i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$			6.00000i			0.210559i
$813$		0			0
$814$	−8.00000			−0.280400
$815$	−8.00000	−	4.00000i	−0.280228	−	0.140114i
$816$		0			0
$817$		−	24.0000i		−	0.839654i
$818$			26.0000i			0.909069i
$819$		0			0
$820$	−2.00000	+	4.00000i	−0.0698430	+	0.139686i
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$		0			0
$823$		−	12.0000i		−	0.418294i	−0.977884	−	0.209147i	$-0.932931\pi$
$823$		−	12.0000i		−	0.418294i	0.977884	−	0.209147i	$-0.0670687\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	8.00000			0.278356
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$		0			0
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$	8.00000	−	16.0000i	0.277684	−	0.555368i
$831$		0			0
$832$			6.00000i			0.208013i
$833$			4.00000i			0.138592i
$834$		0			0
$835$	−24.0000	−	12.0000i	−0.830554	−	0.415277i
$836$	12.0000			0.415029
$837$		0			0
$838$		−	20.0000i		−	0.690889i
$839$	−20.0000			−0.690477			−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		−	34.0000i		−	1.17172i
$843$		0			0
$844$		0			0
$845$	23.0000	−	46.0000i	0.791224	−	1.58245i
$846$		0			0
$847$			7.00000i			0.240523i
$848$			6.00000i			0.206041i
$849$		0			0
$850$	12.0000	+	16.0000i	0.411597	+	0.548795i
$851$	32.0000			1.09695
$852$		0			0
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$	10.0000			0.342193
$855$		0			0
$856$	12.0000			0.410152
$857$		−	24.0000i		−	0.819824i	−0.912125	−	0.409912i	$-0.865559\pi$
$857$		−	24.0000i		−	0.819824i	0.912125	−	0.409912i	$-0.134441\pi$
$858$		0			0
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	−8.00000	−	4.00000i	−0.272798	−	0.136399i
$861$		0			0
$862$			2.00000i			0.0681203i
$863$		−	48.0000i		−	1.63394i	−0.576681	−	0.816970i	$-0.695652\pi$
$863$		−	48.0000i		−	1.63394i	0.576681	−	0.816970i	$-0.304348\pi$
$864$		0			0
$865$	−16.0000	−	8.00000i	−0.544016	−	0.272008i
$866$	26.0000			0.883516
$867$		0			0
$868$		−	2.00000i		−	0.0678844i
$869$	−24.0000			−0.814144
$870$		0			0
$871$	48.0000			1.62642
$872$			14.0000i			0.474100i
$873$		0			0
$874$	−48.0000			−1.62362
$875$	−2.00000	−	11.0000i	−0.0676123	−	0.371868i
$876$		0			0
$877$		−	28.0000i		−	0.945493i	−0.881199	−	0.472746i	$-0.843263\pi$
$877$		−	28.0000i		−	0.945493i	0.881199	−	0.472746i	$-0.156737\pi$
$878$		−	18.0000i		−	0.607471i
$879$		0			0
$880$	2.00000	−	4.00000i	0.0674200	−	0.134840i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$		−	24.0000i		−	0.807664i	−0.914833	−	0.403832i	$-0.867678\pi$
$883$		−	24.0000i		−	0.807664i	0.914833	−	0.403832i	$-0.132322\pi$
$884$	24.0000			0.807207
$885$		0			0
$886$	−12.0000			−0.403148
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		0			0
$889$	4.00000			0.134156
$890$	−20.0000	−	10.0000i	−0.670402	−	0.335201i
$891$		0			0
$892$		−	8.00000i		−	0.267860i
$893$		−	48.0000i		−	1.60626i
$894$		0			0
$895$	−10.0000	+	20.0000i	−0.334263	+	0.668526i
$896$	1.00000			0.0334077
$897$		0			0
$898$			6.00000i			0.200223i
$899$	−12.0000			−0.400222
$900$		0			0
$901$	24.0000			0.799556
$902$		−	4.00000i		−	0.133185i
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−2.00000	+	4.00000i	−0.0664822	+	0.132964i
$906$		0			0
$907$			24.0000i			0.796907i	0.917189	+	0.398453i	$0.130453\pi$
$907$			24.0000i			0.796907i	−0.917189	+	0.398453i	$0.869547\pi$
$908$		−	8.00000i		−	0.265489i
$909$		0			0
$910$	−12.0000	−	6.00000i	−0.397796	−	0.198898i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$			16.0000i			0.529523i
$914$	28.0000			0.926158
$915$		0			0
$916$	14.0000			0.462573
$917$		−	12.0000i		−	0.396275i
$918$		0			0
$919$	−60.0000			−1.97922			−0.989609	−	0.143787i	$-0.954072\pi$
$919$	−60.0000			−1.97922			−0.989609	+	0.143787i	$0.954072\pi$
$920$	−8.00000	+	16.0000i	−0.263752	+	0.527504i
$921$		0			0
$922$		−	18.0000i		−	0.592798i
$923$		−	36.0000i		−	1.18495i
$924$		0			0
$925$	16.0000	−	12.0000i	0.526077	−	0.394558i
$926$	−36.0000			−1.18303
$927$		0			0
$928$		−	6.00000i		−	0.196960i
$929$	−30.0000			−0.984268			−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000			−0.984268			−0.492134	+	0.870519i	$0.663783\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$			10.0000i			0.327561i
$933$		0			0
$934$	24.0000			0.785304
$935$	−16.0000	−	8.00000i	−0.523256	−	0.261628i
$936$		0			0
$937$			26.0000i			0.849383i	0.905338	+	0.424691i	$0.139617\pi$
$937$			26.0000i			0.849383i	−0.905338	+	0.424691i	$0.860383\pi$
$938$		−	8.00000i		−	0.261209i
$939$		0			0
$940$	−16.0000	−	8.00000i	−0.521862	−	0.260931i
$941$	10.0000			0.325991			0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000			0.325991			0.162995	+	0.986627i	$0.447884\pi$
$942$		0			0
$943$			16.0000i			0.521032i
$944$	−8.00000			−0.260378
$945$		0			0
$946$	8.00000			0.260102
$947$			12.0000i			0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$			12.0000i			0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$		0			0
$949$	84.0000			2.72676
$950$	−24.0000	+	18.0000i	−0.778663	+	0.583997i
$951$		0			0
$952$		−	4.00000i		−	0.129641i
$953$		−	10.0000i		−	0.323932i	−0.986796	−	0.161966i	$-0.948217\pi$
$953$		−	10.0000i		−	0.323932i	0.986796	−	0.161966i	$-0.0517835\pi$
$954$		0			0
$955$	−18.0000	+	36.0000i	−0.582466	+	1.16493i
$956$	−26.0000			−0.840900
$957$		0			0
$958$		−	8.00000i		−	0.258468i
$959$	6.00000			0.193750
$960$		0			0
$961$	−27.0000			−0.870968
$962$		−	24.0000i		−	0.773791i
$963$		0			0
$964$	26.0000			0.837404
$965$	−16.0000	−	8.00000i	−0.515058	−	0.257529i
$966$		0			0
$967$			56.0000i			1.80084i	0.435023	+	0.900419i	$0.356740\pi$
$967$			56.0000i			1.80084i	−0.435023	+	0.900419i	$0.643260\pi$
$968$		−	7.00000i		−	0.224989i
$969$		0			0
$970$	10.0000	−	20.0000i	0.321081	−	0.642161i
$971$	24.0000			0.770197			0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000			0.770197			0.385098	+	0.922876i	$0.374168\pi$
$972$		0			0
$973$		−	14.0000i		−	0.448819i
$974$	12.0000			0.384505
$975$		0			0
$976$	−10.0000			−0.320092
$977$			18.0000i			0.575871i	0.957650	+	0.287936i	$0.0929689\pi$
$977$			18.0000i			0.575871i	−0.957650	+	0.287936i	$0.907031\pi$
$978$		0			0
$979$	20.0000			0.639203
$980$	−1.00000	+	2.00000i	−0.0319438	+	0.0638877i
$981$		0			0
$982$		−	30.0000i		−	0.957338i
$983$		−	16.0000i		−	0.510321i	−0.966899	−	0.255160i	$-0.917872\pi$
$983$		−	16.0000i		−	0.510321i	0.966899	−	0.255160i	$-0.0821283\pi$
$984$		0			0
$985$	4.00000	+	2.00000i	0.127451	+	0.0637253i
$986$	−24.0000			−0.764316
$987$		0			0
$988$			36.0000i			1.14531i
$989$	−32.0000			−1.01754
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$			2.00000i			0.0635001i
$993$		0			0
$994$	−6.00000			−0.190308
$995$	6.00000	−	12.0000i	0.190213	−	0.380426i
$996$		0			0
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$		−	12.0000i		−	0.379853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.g.c.379.1		2
3.2	odd	2		210.2.g.b.169.2	yes	2
4.3	odd	2		5040.2.t.h.1009.2		2
5.2	odd	4		3150.2.a.bk.1.1		1
5.3	odd	4		3150.2.a.d.1.1		1
5.4	even	2	inner	630.2.g.c.379.2		2
12.11	even	2		1680.2.t.e.1009.2		2
15.2	even	4		1050.2.a.d.1.1		1
15.8	even	4		1050.2.a.p.1.1		1
15.14	odd	2		210.2.g.b.169.1	✓	2
20.19	odd	2		5040.2.t.h.1009.1		2
21.2	odd	6		1470.2.n.b.949.2		4
21.5	even	6		1470.2.n.f.949.2		4
21.11	odd	6		1470.2.n.b.79.1		4
21.17	even	6		1470.2.n.f.79.1		4
21.20	even	2		1470.2.g.b.589.2		2
60.23	odd	4		8400.2.a.w.1.1		1
60.47	odd	4		8400.2.a.bp.1.1		1
60.59	even	2		1680.2.t.e.1009.1		2
105.44	odd	6		1470.2.n.b.949.1		4
105.59	even	6		1470.2.n.f.79.2		4
105.62	odd	4		7350.2.a.bk.1.1		1
105.74	odd	6		1470.2.n.b.79.2		4
105.83	odd	4		7350.2.a.bz.1.1		1
105.89	even	6		1470.2.n.f.949.1		4
105.104	even	2		1470.2.g.b.589.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.g.b.169.1	✓	2	15.14	odd	2
210.2.g.b.169.2	yes	2	3.2	odd	2
630.2.g.c.379.1		2	1.1	even	1	trivial
630.2.g.c.379.2		2	5.4	even	2	inner
1050.2.a.d.1.1		1	15.2	even	4
1050.2.a.p.1.1		1	15.8	even	4
1470.2.g.b.589.1		2	105.104	even	2
1470.2.g.b.589.2		2	21.20	even	2
1470.2.n.b.79.1		4	21.11	odd	6
1470.2.n.b.79.2		4	105.74	odd	6
1470.2.n.b.949.1		4	105.44	odd	6
1470.2.n.b.949.2		4	21.2	odd	6
1470.2.n.f.79.1		4	21.17	even	6
1470.2.n.f.79.2		4	105.59	even	6
1470.2.n.f.949.1		4	105.89	even	6
1470.2.n.f.949.2		4	21.5	even	6
1680.2.t.e.1009.1		2	60.59	even	2
1680.2.t.e.1009.2		2	12.11	even	2
3150.2.a.d.1.1		1	5.3	odd	4
3150.2.a.bk.1.1		1	5.2	odd	4
5040.2.t.h.1009.1		2	20.19	odd	2
5040.2.t.h.1009.2		2	4.3	odd	2
7350.2.a.bk.1.1		1	105.62	odd	4
7350.2.a.bz.1.1		1	105.83	odd	4
8400.2.a.w.1.1		1	60.23	odd	4
8400.2.a.bp.1.1		1	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +(2.00000 + 1.00000i) q^{10} -2.00000 q^{11} -6.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} +6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} +2.00000i q^{22} -8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -6.00000 q^{26} +1.00000i q^{28} +6.00000 q^{29} -2.00000 q^{31} -1.00000i q^{32} -4.00000 q^{34} +(2.00000 + 1.00000i) q^{35} +4.00000i q^{37} -6.00000i q^{38} +(-2.00000 - 1.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +2.00000 q^{44} -8.00000 q^{46} -8.00000i q^{47} -1.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000i q^{52} +6.00000i q^{53} +(2.00000 - 4.00000i) q^{55} +1.00000 q^{56} -6.00000i q^{58} -8.00000 q^{59} -10.0000 q^{61} +2.00000i q^{62} -1.00000 q^{64} +(12.0000 + 6.00000i) q^{65} +8.00000i q^{67} +4.00000i q^{68} +(1.00000 - 2.00000i) q^{70} +6.00000 q^{71} +14.0000i q^{73} +4.00000 q^{74} -6.00000 q^{76} +2.00000i q^{77} +12.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +2.00000i q^{82} -8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} -4.00000 q^{86} -2.00000i q^{88} -10.0000 q^{89} -6.00000 q^{91} +8.00000i q^{92} -8.00000 q^{94} +(-6.00000 + 12.0000i) q^{95} -10.0000i q^{97} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{5}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^5	\( 2 q - 2 q^{4} - 2 q^{5} + 4 q^{10} - 4 q^{11} - 2 q^{14} + 2 q^{16} + 12 q^{19} + 2 q^{20} - 6 q^{25} - 12 q^{26} + 12 q^{29} - 4 q^{31} - 8 q^{34} + 4 q^{35} - 4 q^{40} - 4 q^{41} + 4 q^{44} - 16 q^{46} - 2 q^{49} - 8 q^{50} + 4 q^{55} + 2 q^{56} - 16 q^{59} - 20 q^{61} - 2 q^{64} + 24 q^{65} + 2 q^{70} + 12 q^{71} + 8 q^{74} - 12 q^{76} + 24 q^{79} - 2 q^{80} + 16 q^{85} - 8 q^{86} - 20 q^{89} - 12 q^{91} - 16 q^{94} - 12 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^5 + 4 * q^10 - 4 * q^11 - 2 * q^14 + 2 * q^16 + 12 * q^19 + 2 * q^20 - 6 * q^25 - 12 * q^26 + 12 * q^29 - 4 * q^31 - 8 * q^34 + 4 * q^35 - 4 * q^40 - 4 * q^41 + 4 * q^44 - 16 * q^46 - 2 * q^49 - 8 * q^50 + 4 * q^55 + 2 * q^56 - 16 * q^59 - 20 * q^61 - 2 * q^64 + 24 * q^65 + 2 * q^70 + 12 * q^71 + 8 * q^74 - 12 * q^76 + 24 * q^79 - 2 * q^80 + 16 * q^85 - 8 * q^86 - 20 * q^89 - 12 * q^91 - 16 * q^94 - 12 * q^95

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