LMFDB - Embedded newform 630.2.ce.c.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("630.53");

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.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	630.107
Dual form			630.2.ce.c.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.24269 + 1.85895i) q^{5} +(-1.31709 - 2.29462i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.24269 + 1.85895i) q^{5} +(-1.31709 - 2.29462i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.11725 + 0.719217i) q^{10} +(1.05318 - 0.608054i) q^{11} +(2.42429 - 2.42429i) q^{13} +(-1.87554 + 1.86610i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.34437 + 0.896120i) q^{17} +(-7.32453 - 4.22882i) q^{19} +(0.146727 - 2.23125i) q^{20} +(-0.859918 - 0.859918i) q^{22} +(-7.15780 + 1.91793i) q^{23} +(-1.91143 - 4.62022i) q^{25} +(-2.96914 - 1.71423i) q^{26} +(2.28794 + 1.32865i) q^{28} -7.86256 q^{29} +(-3.47398 - 6.01711i) q^{31} +(-0.965926 - 0.258819i) q^{32} -3.46234i q^{34} +(5.90233 + 0.403088i) q^{35} +(4.19017 - 1.12275i) q^{37} +(-2.18900 + 8.16945i) q^{38} +(-2.19320 + 0.435763i) q^{40} -5.75220i q^{41} +(1.25749 - 1.25749i) q^{43} +(-0.608054 + 1.05318i) q^{44} +(3.70515 + 6.41751i) q^{46} +(-1.94967 - 7.27627i) q^{47} +(-3.53053 + 6.04445i) q^{49} +(-3.96808 + 3.04210i) q^{50} +(-0.887352 + 3.31164i) q^{52} +(2.15260 - 8.03362i) q^{53} +(-0.178435 + 2.71344i) q^{55} +(0.691214 - 2.55386i) q^{56} +(2.03498 + 7.59465i) q^{58} +(0.0764567 + 0.132427i) q^{59} +(6.62709 - 11.4785i) q^{61} +(-4.91295 + 4.91295i) q^{62} +1.00000i q^{64} +(1.49400 + 7.51930i) q^{65} +(-3.50886 + 13.0952i) q^{67} +(-3.34437 + 0.896120i) q^{68} +(-1.13828 - 5.80554i) q^{70} +11.6129i q^{71} +(7.69391 + 2.06158i) q^{73} +(-2.16899 - 3.75681i) q^{74} +8.45764 q^{76} +(-2.78239 - 1.61578i) q^{77} +(-1.09930 - 0.634683i) q^{79} +(0.988555 + 2.00568i) q^{80} +(-5.55620 + 1.48878i) q^{82} +(3.08077 + 3.08077i) q^{83} +(-5.82187 + 5.10342i) q^{85} +(-1.54011 - 0.889183i) q^{86} +(1.17467 + 0.314752i) q^{88} +(-1.92654 + 3.33687i) q^{89} +(-8.75584 - 2.36980i) q^{91} +(5.23987 - 5.23987i) q^{92} +(-6.52373 + 3.76648i) q^{94} +(16.9633 - 8.36084i) q^{95} +(3.22607 + 3.22607i) q^{97} +(6.75226 + 1.84581i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{7}+O(q^{10}) $ 32 * q - 12 * q^7	$ 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) $ 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.24269	+	1.85895i	−0.555749	+	0.831350i
$5$	−1.24269	+	1.85895i	−0.555749	+	0.831350i
$6$		0			0
$7$	−1.31709	−	2.29462i	−0.497814	−	0.867284i
$7$	−1.31709	−	2.29462i	−0.497814	−	0.867284i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.11725	+	0.719217i	0.669532	+	0.227436i
$11$	1.05318	−	0.608054i	0.317546	−	0.183335i	−0.332752	−	0.943014i	$-0.607977\pi$
$11$	1.05318	−	0.608054i	0.317546	−	0.183335i	0.650298	+	0.759679i	$0.274644\pi$
$12$		0			0
$13$	2.42429	−	2.42429i	0.672377	−	0.672377i	−0.285886	−	0.958264i	$-0.592288\pi$
$13$	2.42429	−	2.42429i	0.672377	−	0.672377i	0.958264	+	0.285886i	$0.0922879\pi$
$14$	−1.87554	+	1.86610i	−0.501259	+	0.498737i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.34437	+	0.896120i	0.811128	+	0.217341i	0.640464	−	0.767988i	$-0.278742\pi$
$17$	3.34437	+	0.896120i	0.811128	+	0.217341i	0.170664	+	0.985329i	$0.445409\pi$
$18$		0			0
$19$	−7.32453	−	4.22882i	−1.68036	−	0.970158i	−0.961419	−	0.275089i	$-0.911293\pi$
$19$	−7.32453	−	4.22882i	−1.68036	−	0.970158i	−0.718943	−	0.695069i	$-0.755374\pi$
$20$	0.146727	−	2.23125i	0.0328091	−	0.498922i
$21$		0			0
$22$	−0.859918	−	0.859918i	−0.183335	−	0.183335i
$23$	−7.15780	+	1.91793i	−1.49250	+	0.399915i	−0.910582	−	0.413329i	$-0.864366\pi$
$23$	−7.15780	+	1.91793i	−1.49250	+	0.399915i	−0.581923	+	0.813244i	$0.697699\pi$
$24$		0			0
$25$	−1.91143	−	4.62022i	−0.382285	−	0.924044i
$26$	−2.96914	−	1.71423i	−0.582296	−	0.336189i
$27$		0			0
$28$	2.28794	+	1.32865i	0.432381	+	0.251091i
$29$	−7.86256			−1.46004			−0.730020	−	0.683425i	$-0.760489\pi$
$29$	−7.86256			−1.46004			−0.730020	+	0.683425i	$0.760489\pi$
$30$		0			0
$31$	−3.47398	−	6.01711i	−0.623945	−	1.08070i	−0.988744	−	0.149618i	$-0.952196\pi$
$31$	−3.47398	−	6.01711i	−0.623945	−	1.08070i	0.364799	−	0.931086i	$-0.381138\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$		−	3.46234i		−	0.593787i
$35$	5.90233	+	0.403088i	0.997676	+	0.0681344i
$36$		0			0
$37$	4.19017	−	1.12275i	0.688860	−	0.184580i	0.102625	−	0.994720i	$-0.467276\pi$
$37$	4.19017	−	1.12275i	0.688860	−	0.184580i	0.586236	+	0.810141i	$0.300609\pi$
$38$	−2.18900	+	8.16945i	−0.355102	+	1.32526i
$39$		0			0
$40$	−2.19320	+	0.435763i	−0.346775	+	0.0689001i
$41$		−	5.75220i		−	0.898343i	−0.893446	−	0.449171i	$-0.851719\pi$
$41$		−	5.75220i		−	0.898343i	0.893446	−	0.449171i	$-0.148281\pi$
$42$		0			0
$43$	1.25749	−	1.25749i	0.191766	−	0.191766i	−0.604693	−	0.796459i	$-0.706704\pi$
$43$	1.25749	−	1.25749i	0.191766	−	0.191766i	0.796459	+	0.604693i	$0.206704\pi$
$44$	−0.608054	+	1.05318i	−0.0916676	+	0.158773i
$45$		0			0
$46$	3.70515	+	6.41751i	0.546295	+	0.946210i
$47$	−1.94967	−	7.27627i	−0.284389	−	1.06135i	−0.949285	−	0.314418i	$-0.898191\pi$
$47$	−1.94967	−	7.27627i	−0.284389	−	1.06135i	0.664896	−	0.746936i	$-0.268476\pi$
$48$		0			0
$49$	−3.53053	+	6.04445i	−0.504362	+	0.863493i
$50$	−3.96808	+	3.04210i	−0.561171	+	0.430218i
$51$		0			0
$52$	−0.887352	+	3.31164i	−0.123054	+	0.459242i
$53$	2.15260	−	8.03362i	0.295683	−	1.10350i	−0.644991	−	0.764190i	$-0.723139\pi$
$53$	2.15260	−	8.03362i	0.295683	−	1.10350i	0.940674	−	0.339313i	$-0.110195\pi$
$54$		0			0
$55$	−0.178435	+	2.71344i	−0.0240602	+	0.365880i
$56$	0.691214	−	2.55386i	0.0923673	−	0.341274i
$57$		0			0
$58$	2.03498	+	7.59465i	0.267206	+	0.997226i
$59$	0.0764567	+	0.132427i	0.00995381	+	0.0172405i	0.870959	−	0.491355i	$-0.163498\pi$
$59$	0.0764567	+	0.132427i	0.00995381	+	0.0172405i	−0.861006	+	0.508595i	$0.830165\pi$
$60$		0			0
$61$	6.62709	−	11.4785i	0.848512	−	1.46967i	−0.0340241	−	0.999421i	$-0.510832\pi$
$61$	6.62709	−	11.4785i	0.848512	−	1.46967i	0.882536	−	0.470245i	$-0.155834\pi$
$62$	−4.91295	+	4.91295i	−0.623945	+	0.623945i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.49400	+	7.51930i	0.185308	+	0.932654i
$66$		0			0
$67$	−3.50886	+	13.0952i	−0.428676	+	1.59984i	0.327088	+	0.944994i	$0.393933\pi$
$67$	−3.50886	+	13.0952i	−0.428676	+	1.59984i	−0.755763	+	0.654845i	$0.772734\pi$
$68$	−3.34437	+	0.896120i	−0.405564	+	0.108671i
$69$		0			0
$70$	−1.13828	−	5.80554i	−0.136051	−	0.693895i
$71$			11.6129i			1.37820i	0.724668	+	0.689098i	$0.241993\pi$
$71$			11.6129i			1.37820i	−0.724668	+	0.689098i	$0.758007\pi$
$72$		0			0
$73$	7.69391	+	2.06158i	0.900504	+	0.241289i	0.679233	−	0.733923i	$-0.262313\pi$
$73$	7.69391	+	2.06158i	0.900504	+	0.241289i	0.221271	+	0.975212i	$0.428979\pi$
$74$	−2.16899	−	3.75681i	−0.252140	−	0.436720i
$75$		0			0
$76$	8.45764			0.970158
$77$	−2.78239	−	1.61578i	−0.317082	−	0.184135i
$78$		0			0
$79$	−1.09930	−	0.634683i	−0.123681	−	0.0714074i	0.436883	−	0.899518i	$-0.356082\pi$
$79$	−1.09930	−	0.634683i	−0.123681	−	0.0714074i	−0.560564	+	0.828111i	$0.689416\pi$
$80$	0.988555	+	2.00568i	0.110524	+	0.224242i
$81$		0			0
$82$	−5.55620	+	1.48878i	−0.613580	+	0.164408i
$83$	3.08077	+	3.08077i	0.338159	+	0.338159i	0.855674	−	0.517515i	$-0.173143\pi$
$83$	3.08077	+	3.08077i	0.338159	+	0.338159i	−0.517515	+	0.855674i	$0.673143\pi$
$84$		0			0
$85$	−5.82187	+	5.10342i	−0.631470	+	0.553544i
$86$	−1.54011	−	0.889183i	−0.166074	−	0.0958830i
$87$		0			0
$88$	1.17467	+	0.314752i	0.125220	+	0.0335527i
$89$	−1.92654	+	3.33687i	−0.204213	+	0.353707i	−0.949882	−	0.312610i	$-0.898797\pi$
$89$	−1.92654	+	3.33687i	−0.204213	+	0.353707i	0.745669	+	0.666317i	$0.232130\pi$
$90$		0			0
$91$	−8.75584	−	2.36980i	−0.917861	−	0.248423i
$92$	5.23987	−	5.23987i	0.546295	−	0.546295i
$93$		0			0
$94$	−6.52373	+	3.76648i	−0.672871	+	0.388482i
$95$	16.9633	−	8.36084i	1.74040	−	0.857804i
$96$		0			0
$97$	3.22607	+	3.22607i	0.327558	+	0.327558i	0.851657	−	0.524099i	$-0.175598\pi$
$97$	3.22607	+	3.22607i	0.327558	+	0.327558i	−0.524099	+	0.851657i	$0.675598\pi$
$98$	6.75226	+	1.84581i	0.682081	+	0.186455i
$99$		0			0
$100$	3.96545	+	3.04552i	0.396545	+	0.304552i
$101$	−1.50414	+	0.868415i	−0.149667	+	0.0864105i	−0.572963	−	0.819581i	$-0.694206\pi$
$101$	−1.50414	+	0.868415i	−0.149667	+	0.0864105i	0.423296	+	0.905991i	$0.360873\pi$
$102$		0			0
$103$	1.08337	+	4.04320i	0.106748	+	0.398389i	0.998538	−	0.0540614i	$-0.0172167\pi$
$103$	1.08337	+	4.04320i	0.106748	+	0.398389i	−0.891790	+	0.452450i	$0.850550\pi$
$104$	3.42847			0.336189
$105$		0			0
$106$	−8.31702			−0.807820
$107$	−2.09384	−	7.81431i	−0.202419	−	0.755438i	−0.990221	−	0.139509i	$-0.955448\pi$
$107$	−2.09384	−	7.81431i	−0.202419	−	0.755438i	0.787802	−	0.615929i	$-0.211219\pi$
$108$		0			0
$109$	−1.23624	+	0.713741i	−0.118410	+	0.0683640i	−0.558035	−	0.829817i	$-0.688445\pi$
$109$	−1.23624	+	0.713741i	−0.118410	+	0.0683640i	0.439625	+	0.898181i	$0.355111\pi$
$110$	2.66716	−	0.529934i	0.254304	−	0.0505273i
$111$		0			0
$112$	−2.64574	−	0.00667224i	−0.249999	−	0.000630468i
$113$	7.18817	+	7.18817i	0.676206	+	0.676206i	0.959139	−	0.282934i	$-0.0913076\pi$
$113$	7.18817	+	7.18817i	0.676206	+	0.676206i	−0.282934	+	0.959139i	$0.591308\pi$
$114$		0			0
$115$	5.32961	−	15.6894i	0.496989	−	1.46305i
$116$	6.80918	−	3.93128i	0.632216	−	0.365010i
$117$		0			0
$118$	0.108126	−	0.108126i	0.00995381	−	0.00995381i
$119$	−2.34859	−	8.85431i	−0.215295	−	0.811673i
$120$		0			0
$121$	−4.76054	+	8.24550i	−0.432776	+	0.749591i
$122$	−12.8026	−	3.43043i	−1.15909	−	0.310577i
$123$		0			0
$124$	6.01711	+	3.47398i	0.540352	+	0.311973i
$125$	10.9641	+	2.18826i	0.980659	+	0.195724i
$126$		0			0
$127$	0.268829	+	0.268829i	0.0238547	+	0.0238547i	0.718934	−	0.695079i	$-0.244631\pi$
$127$	0.268829	+	0.268829i	0.0238547	+	0.0238547i	−0.695079	+	0.718934i	$0.744631\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	6.87641	−	3.38923i	0.603101	−	0.297255i
$131$	−1.27630	−	0.736873i	−0.111511	−	0.0643809i	0.443207	−	0.896419i	$-0.353841\pi$
$131$	−1.27630	−	0.736873i	−0.111511	−	0.0643809i	−0.554718	+	0.832038i	$0.687174\pi$
$132$		0			0
$133$	−0.0564314	+	22.3767i	−0.00489322	+	1.94031i
$134$	13.5572			1.17116
$135$		0			0
$136$	1.73117	+	2.99848i	0.148447	+	0.257117i
$137$	1.70107	+	0.455800i	0.145332	+	0.0389417i	0.330752	−	0.943718i	$-0.392698\pi$
$137$	1.70107	+	0.455800i	0.145332	+	0.0389417i	−0.185419	+	0.982659i	$0.559364\pi$
$138$		0			0
$139$		−	18.3644i		−	1.55764i	−0.627245	−	0.778822i	$-0.715817\pi$
$139$		−	18.3644i		−	1.55764i	0.627245	−	0.778822i	$-0.284183\pi$
$140$	−5.31311	+	2.60208i	−0.449040	+	0.219916i
$141$		0			0
$142$	11.2172	−	3.00564i	0.941325	−	0.252227i
$143$	1.07912	−	4.02731i	0.0902402	−	0.336781i
$144$		0			0
$145$	9.77075	−	14.6161i	0.811417	−	1.21380i
$146$		−	7.96532i		−	0.659214i
$147$		0			0
$148$	−3.06742	+	3.06742i	−0.252140	+	0.252140i
$149$	6.01294	−	10.4147i	0.492599	−	0.853207i	−0.507364	−	0.861732i	$-0.669380\pi$
$149$	6.01294	−	10.4147i	0.492599	−	0.853207i	0.999964	+	0.00852452i	$0.00271347\pi$
$150$		0			0
$151$	−1.31381	−	2.27559i	−0.106917	−	0.185185i	0.807603	−	0.589726i	$-0.200764\pi$
$151$	−1.31381	−	2.27559i	−0.106917	−	0.185185i	−0.914520	+	0.404541i	$0.867431\pi$
$152$	−2.18900	−	8.16945i	−0.177551	−	0.662630i
$153$		0			0
$154$	−0.840590	+	3.10577i	−0.0677367	+	0.250270i
$155$	15.5026	+	1.01945i	1.24520	+	0.0818842i
$156$		0			0
$157$	−0.957870	+	3.57482i	−0.0764464	+	0.285302i	−0.993557	−	0.113330i	$-0.963848\pi$
$157$	−0.957870	+	3.57482i	−0.0764464	+	0.285302i	0.917111	+	0.398632i	$0.130515\pi$
$158$	−0.328536	+	1.22611i	−0.0261369	+	0.0975443i
$159$		0			0
$160$	1.68148	−	1.47398i	0.132933	−	0.116528i
$161$	13.8284	+	13.8983i	1.08983	+	1.09534i
$162$		0			0
$163$	0.317179	+	1.18373i	0.0248434	+	0.0927167i	0.977234	−	0.212162i	$-0.0680506\pi$
$163$	0.317179	+	1.18373i	0.0248434	+	0.0927167i	−0.952391	+	0.304879i	$0.901384\pi$
$164$	2.87610	+	4.98155i	0.224586	+	0.388994i
$165$		0			0
$166$	2.17844	−	3.77316i	0.169079	−	0.292854i
$167$	6.03137	−	6.03137i	0.466721	−	0.466721i	−0.434129	−	0.900851i	$-0.642944\pi$
$167$	6.03137	−	6.03137i	0.466721	−	0.466721i	0.900851	+	0.434129i	$0.142944\pi$
$168$		0			0
$169$			1.24562i			0.0958171i
$170$	6.43634	+	4.30263i	0.493645	+	0.329997i
$171$		0			0
$172$	−0.460275	+	1.71777i	−0.0350956	+	0.130979i
$173$	−13.6944	+	3.66940i	−1.04117	+	0.278979i	−0.738596	−	0.674148i	$-0.764511\pi$
$173$	−13.6944	+	3.66940i	−1.04117	+	0.278979i	−0.302569	+	0.953128i	$0.597844\pi$
$174$		0			0
$175$	−8.08411	+	10.4713i	−0.611101	+	0.791552i
$176$		−	1.21611i		−	0.0916676i
$177$		0			0
$178$	3.72179	+	0.997251i	0.278960	+	0.0747471i
$179$	−8.15708	−	14.1285i	−0.609689	−	1.05601i	−0.991292	−	0.131686i	$-0.957961\pi$
$179$	−8.15708	−	14.1285i	−0.609689	−	1.05601i	0.381603	−	0.924327i	$-0.375372\pi$
$180$		0			0
$181$	−12.5911			−0.935888			−0.467944	−	0.883758i	$-0.655005\pi$
$181$	−12.5911			−0.935888			−0.467944	+	0.883758i	$0.655005\pi$
$182$	−0.0228756	+	9.07084i	−0.00169565	+	0.672375i
$183$		0			0
$184$	−6.41751	−	3.70515i	−0.473105	−	0.273147i
$185$	−3.11995	+	9.18458i	−0.229384	+	0.675264i
$186$		0			0
$187$	4.06711	−	1.08978i	0.297416	−	0.0796925i
$188$	5.32660	+	5.32660i	0.388482	+	0.388482i
$189$		0			0
$190$	−12.4664	−	14.2214i	−0.904407	−	1.03173i
$191$	−7.69330	−	4.44173i	−0.556668	−	0.321392i	0.195139	−	0.980776i	$-0.437484\pi$
$191$	−7.69330	−	4.44173i	−0.556668	−	0.321392i	−0.751807	+	0.659383i	$0.770817\pi$
$192$		0			0
$193$	22.4807	+	6.02367i	1.61819	+	0.433593i	0.950470	−	0.310817i	$-0.100603\pi$
$193$	22.4807	+	6.02367i	1.61819	+	0.433593i	0.667723	+	0.744410i	$0.267269\pi$
$194$	2.28118	−	3.95112i	0.163779	−	0.283674i
$195$		0			0
$196$	0.0353061	−	6.99991i	0.00252186	−	0.499994i
$197$	−12.5439	+	12.5439i	−0.893718	+	0.893718i	−0.994871	−	0.101153i	$-0.967747\pi$
$197$	−12.5439	+	12.5439i	−0.893718	+	0.893718i	0.101153	+	0.994871i	$0.467747\pi$
$198$		0			0
$199$	−14.3683	+	8.29554i	−1.01854	+	0.588056i	−0.913681	−	0.406431i	$-0.866773\pi$
$199$	−14.3683	+	8.29554i	−1.01854	+	0.588056i	−0.104861	+	0.994487i	$0.533440\pi$
$200$	1.91541	−	4.61857i	0.135440	−	0.326582i
$201$		0			0
$202$	1.22812	+	1.22812i	0.0864105	+	0.0864105i
$203$	10.3557	+	18.0416i	0.726829	+	1.26627i
$204$		0			0
$205$	10.6931	+	7.14822i	0.746837	+	0.499254i
$206$	3.62504	−	2.09292i	0.252568	−	0.145820i
$207$		0			0
$208$	−0.887352	−	3.31164i	−0.0615268	−	0.229621i
$209$	−10.2854			−0.711456
$210$		0			0
$211$	9.26908			0.638110			0.319055	−	0.947736i	$-0.396635\pi$
$211$	9.26908			0.638110			0.319055	+	0.947736i	$0.396635\pi$
$212$	2.15260	+	8.03362i	0.147841	+	0.551752i
$213$		0			0
$214$	−7.00612	+	4.04498i	−0.478928	+	0.276509i
$215$	0.774945	+	3.90030i	0.0528508	+	0.265999i
$216$		0			0
$217$	−9.23140	+	15.8965i	−0.626669	+	1.07913i
$218$	1.00938	+	1.00938i	0.0683640	+	0.0683640i
$219$		0			0
$220$	−1.20219	−	2.43912i	−0.0810516	−	0.164446i
$221$	10.2802	−	5.93526i	0.691519	−	0.399249i
$222$		0			0
$223$	13.3315	−	13.3315i	0.892746	−	0.892746i	−0.102035	−	0.994781i	$-0.532535\pi$
$223$	13.3315	−	13.3315i	0.892746	−	0.892746i	0.994781	+	0.102035i	$0.0325352\pi$
$224$	0.678324	+	2.55732i	0.0453224	+	0.170868i
$225$		0			0
$226$	5.08280	−	8.80367i	0.338103	−	0.585611i
$227$	4.51783	+	1.21055i	0.299859	+	0.0803470i	0.405612	−	0.914045i	$-0.367059\pi$
$227$	4.51783	+	1.21055i	0.299859	+	0.0803470i	−0.105753	+	0.994392i	$0.533725\pi$
$228$		0			0
$229$	19.0096	+	10.9752i	1.25619	+	0.725262i	0.972332	−	0.233604i	$-0.0750518\pi$
$229$	19.0096	+	10.9752i	1.25619	+	0.725262i	0.283859	+	0.958866i	$0.408385\pi$
$230$	−16.5342	−	1.08729i	−1.09023	−	0.0716937i
$231$		0			0
$232$	−5.55967	−	5.55967i	−0.365010	−	0.365010i
$233$	−28.5061	+	7.63818i	−1.86750	+	0.500394i	−0.867500	+	0.497437i	$0.834275\pi$
$233$	−28.5061	+	7.63818i	−1.86750	+	0.500394i	−0.999996	+	0.00295737i	$0.999059\pi$
$234$		0			0
$235$	15.9491	+	5.41783i	1.04041	+	0.353420i
$236$	−0.132427	−	0.0764567i	−0.00862025	−	0.00497690i
$237$		0			0
$238$	−7.94475	+	4.56023i	−0.514981	+	0.295596i
$239$	18.2869			1.18288			0.591440	−	0.806349i	$-0.298560\pi$
$239$	18.2869			1.18288			0.591440	+	0.806349i	$0.298560\pi$
$240$		0			0
$241$	−8.64147	−	14.9675i	−0.556646	−	0.964139i	−0.997773	−	0.0666949i	$-0.978755\pi$
$241$	−8.64147	−	14.9675i	−0.556646	−	0.964139i	0.441127	−	0.897445i	$-0.354579\pi$
$242$	9.19666	+	2.46424i	0.591184	+	0.158407i
$243$		0			0
$244$			13.2542i			0.848512i
$245$	−6.84899	−	14.0745i	−0.437566	−	0.899186i
$246$		0			0
$247$	−28.0087	+	7.50490i	−1.78215	+	0.477526i
$248$	1.79826	−	6.71121i	0.114190	−	0.426162i
$249$		0			0
$250$	−0.724017	−	11.1569i	−0.0457909	−	0.705623i
$251$		−	14.5725i		−	0.919806i	−0.887969	−	0.459903i	$-0.847884\pi$
$251$		−	14.5725i		−	0.919806i	0.887969	−	0.459903i	$-0.152116\pi$
$252$		0			0
$253$	−6.37225	+	6.37225i	−0.400620	+	0.400620i
$254$	0.190091	−	0.329247i	0.0119274	−	0.0206588i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.84310	−	14.3426i	−0.239726	−	0.894669i	−0.975961	−	0.217943i	$-0.930065\pi$
$257$	−3.84310	−	14.3426i	−0.239726	−	0.894669i	0.736236	−	0.676725i	$-0.236601\pi$
$258$		0			0
$259$	−8.09514	−	8.13607i	−0.503008	−	0.505551i
$260$	−5.05349	−	5.76491i	−0.313404	−	0.357524i
$261$		0			0
$262$	−0.381433	+	1.42353i	−0.0235650	+	0.0879459i
$263$	3.13486	−	11.6995i	0.193304	−	0.721420i	−0.799396	−	0.600805i	$-0.794847\pi$
$263$	3.13486	−	11.6995i	0.193304	−	0.721420i	0.992699	−	0.120615i	$-0.0384865\pi$
$264$		0			0
$265$	12.2591	+	13.9849i	0.753072	+	0.859087i
$266$	21.6289	−	5.73702i	1.32615	−	0.351759i
$267$		0			0
$268$	−3.50886	−	13.0952i	−0.214338	−	0.799919i
$269$	−4.33223	−	7.50364i	−0.264141	−	0.457505i	0.703197	−	0.710995i	$-0.251755\pi$
$269$	−4.33223	−	7.50364i	−0.264141	−	0.457505i	−0.967338	+	0.253490i	$0.918422\pi$
$270$		0			0
$271$	−2.44256	+	4.23064i	−0.148375	+	0.256993i	−0.930627	−	0.365969i	$-0.880738\pi$
$271$	−2.44256	+	4.23064i	−0.148375	+	0.256993i	0.782252	+	0.622962i	$0.214071\pi$
$272$	2.44825	−	2.44825i	0.148447	−	0.148447i
$273$		0			0
$274$		−	1.76108i		−	0.106391i
$275$	−4.82242	−	3.70368i	−0.290803	−	0.223340i
$276$		0			0
$277$	5.18252	−	19.3414i	0.311387	−	1.16211i	−0.615919	−	0.787810i	$-0.711215\pi$
$277$	5.18252	−	19.3414i	0.311387	−	1.16211i	0.927306	−	0.374304i	$-0.122118\pi$
$278$	−17.7386	+	4.75304i	−1.06389	+	0.285069i
$279$		0			0
$280$	3.88855	+	4.45861i	0.232385	+	0.266453i
$281$			30.9645i			1.84719i	0.383375	+	0.923593i	$0.374762\pi$
$281$			30.9645i			1.84719i	−0.383375	+	0.923593i	$0.625238\pi$
$282$		0			0
$283$	14.8694	+	3.98423i	0.883891	+	0.236838i	0.672085	−	0.740474i	$-0.265399\pi$
$283$	14.8694	+	3.98423i	0.883891	+	0.236838i	0.211806	+	0.977312i	$0.432066\pi$
$284$	−5.80644	−	10.0571i	−0.344549	−	0.596776i
$285$		0			0
$286$	−4.16938			−0.246541
$287$	−13.1991	+	7.57619i	−0.779118	+	0.447208i
$288$		0			0
$289$	−4.34068	−	2.50609i	−0.255334	−	0.147417i
$290$	−16.6470	−	5.65488i	−0.977544	−	0.332066i
$291$		0			0
$292$	−7.69391	+	2.06158i	−0.450252	+	0.120645i
$293$	−9.12076	−	9.12076i	−0.532840	−	0.532840i	0.388576	−	0.921417i	$-0.372967\pi$
$293$	−9.12076	−	9.12076i	−0.532840	−	0.532840i	−0.921417	+	0.388576i	$0.872967\pi$
$294$		0			0
$295$	−0.341188	−	0.0224365i	−0.0198647	−	0.00130630i
$296$	3.75681	+	2.16899i	0.218360	+	0.126070i
$297$		0			0
$298$	−11.6161	−	3.11253i	−0.672903	−	0.180304i
$299$	−12.7030	+	22.0022i	−0.734632	+	1.27242i
$300$		0			0
$301$	−4.54170	−	1.22923i	−0.261779	−	0.0708516i
$302$	−1.85801	+	1.85801i	−0.106917	+	0.106917i
$303$		0			0
$304$	−7.32453	+	4.22882i	−0.420091	+	0.242539i
$305$	13.1025	+	26.5837i	0.750246	+	1.52218i
$306$		0			0
$307$	2.98143	+	2.98143i	0.170159	+	0.170159i	0.787049	−	0.616890i	$-0.211608\pi$
$307$	2.98143	+	2.98143i	0.170159	+	0.170159i	−0.616890	+	0.787049i	$0.711608\pi$
$308$	3.21751	+	0.00811416i	0.183335	+	0.000462347i
$309$		0			0
$310$	−3.02766	−	15.2382i	−0.171960	−	0.865474i
$311$	−27.6208	+	15.9469i	−1.56623	+	0.904265i	−0.569631	+	0.821900i	$0.692914\pi$
$311$	−27.6208	+	15.9469i	−1.56623	+	0.904265i	−0.996602	+	0.0823648i	$0.973753\pi$
$312$		0			0
$313$	−4.38354	−	16.3596i	−0.247773	−	0.924700i	−0.971970	−	0.235107i	$-0.924456\pi$
$313$	−4.38354	−	16.3596i	−0.247773	−	0.924700i	0.724197	−	0.689593i	$-0.242211\pi$
$314$	3.70093			0.208855
$315$		0			0
$316$	1.26937			0.0714074
$317$	1.53993	+	5.74708i	0.0864909	+	0.322788i	0.995592	−	0.0937864i	$-0.0298971\pi$
$317$	1.53993	+	5.74708i	0.0864909	+	0.322788i	−0.909101	+	0.416575i	$0.863230\pi$
$318$		0			0
$319$	−8.28069	+	4.78086i	−0.463630	+	0.267677i
$320$	−1.85895	−	1.24269i	−0.103919	−	0.0694687i
$321$		0			0
$322$	9.84570	−	16.9544i	0.548679	−	0.944829i
$323$	−20.7064	−	20.7064i	−1.15213	−	1.15213i
$324$		0			0
$325$	−15.8346	−	6.56691i	−0.878347	−	0.364267i
$326$	1.06130	−	0.612743i	0.0587800	−	0.0339367i
$327$		0			0
$328$	4.06742	−	4.06742i	0.224586	−	0.224586i
$329$	−14.1284	+	14.0573i	−0.778922	+	0.775003i
$330$		0			0
$331$	0.330850	−	0.573050i	0.0181852	−	0.0314977i	−0.856790	−	0.515666i	$-0.827544\pi$
$331$	0.330850	−	0.573050i	0.0181852	−	0.0314977i	0.874975	+	0.484168i	$0.160878\pi$
$332$	−4.20841	−	1.12764i	−0.230967	−	0.0618873i
$333$		0			0
$334$	−7.38689	−	4.26482i	−0.404192	−	0.233361i
$335$	−19.9830	−	22.7962i	−1.09179	−	1.24549i
$336$		0			0
$337$	23.0409	+	23.0409i	1.25512	+	1.25512i	0.953396	+	0.301722i	$0.0975614\pi$
$337$	23.0409	+	23.0409i	1.25512	+	1.25512i	0.301722	+	0.953396i	$0.402439\pi$
$338$	1.20318	−	0.322391i	0.0654443	−	0.0175357i
$339$		0			0
$340$	2.49017	−	7.33063i	0.135049	−	0.397559i
$341$	−7.31745	−	4.22473i	−0.396262	−	0.228782i
$342$		0			0
$343$	18.5197	+	0.140116i	0.999971	+	0.00756555i
$344$	1.77837			0.0958830
$345$		0			0
$346$	7.08874	+	12.2781i	0.381093	+	0.660072i
$347$	11.8037	+	3.16280i	0.633657	+	0.169788i	0.561328	−	0.827593i	$-0.310290\pi$
$347$	11.8037	+	3.16280i	0.633657	+	0.169788i	0.0723282	+	0.997381i	$0.476957\pi$
$348$		0			0
$349$		−	11.3328i		−	0.606631i	−0.952890	−	0.303316i	$-0.901906\pi$
$349$		−	11.3328i		−	0.606631i	0.952890	−	0.303316i	$-0.0980937\pi$
$350$	12.2068	+	5.09849i	0.652480	+	0.272526i
$351$		0			0
$352$	−1.17467	+	0.314752i	−0.0626101	+	0.0167763i
$353$	−0.684730	+	2.55545i	−0.0364445	+	0.136013i	−0.981751	−	0.190170i	$-0.939096\pi$
$353$	−0.684730	+	2.55545i	−0.0364445	+	0.136013i	0.945307	+	0.326183i	$0.105763\pi$
$354$		0			0
$355$	−21.5878	−	14.4313i	−1.14576	−	0.765931i
$356$		−	3.85308i		−	0.204213i
$357$		0			0
$358$	−11.5359	+	11.5359i	−0.609689	+	0.609689i
$359$	6.02101	−	10.4287i	0.317777	−	0.550405i	−0.662247	−	0.749285i	$-0.730397\pi$
$359$	6.02101	−	10.4287i	0.317777	−	0.550405i	0.980024	+	0.198880i	$0.0637305\pi$
$360$		0			0
$361$	26.2658	+	45.4937i	1.38241	+	2.39441i
$362$	3.25881	+	12.1621i	0.171279	+	0.639224i
$363$		0			0
$364$	8.76768	−	2.32561i	0.459551	−	0.121895i
$365$	−13.3935	+	11.7407i	−0.701050	+	0.614537i
$366$		0			0
$367$	3.98231	−	14.8622i	0.207875	−	0.775800i	−0.780679	−	0.624932i	$-0.785127\pi$
$367$	3.98231	−	14.8622i	0.207875	−	0.775800i	0.988554	−	0.150868i	$-0.0482068\pi$
$368$	−1.91793	+	7.15780i	−0.0999789	+	0.373126i
$369$		0			0
$370$	9.67913	+	0.636498i	0.503194	+	0.0330900i
$371$	−21.2693	+	5.64163i	−1.10425	+	0.292899i
$372$		0			0
$373$	−6.09031	−	22.7293i	−0.315344	−	1.17688i	−0.923669	−	0.383192i	$-0.874825\pi$
$373$	−6.09031	−	22.7293i	−0.315344	−	1.17688i	0.608324	−	0.793688i	$-0.291842\pi$
$374$	−2.10529	−	3.64647i	−0.108862	−	0.188554i
$375$		0			0
$376$	3.76648	−	6.52373i	0.194241	−	0.336436i
$377$	−19.0611	+	19.0611i	−0.981698	+	0.981698i
$378$		0			0
$379$			4.21063i			0.216285i	0.994135	+	0.108143i	$0.0344903\pi$
$379$			4.21063i			0.216285i	−0.994135	+	0.108143i	$0.965510\pi$
$380$	−10.5103	+	15.7224i	−0.539164	+	0.806540i
$381$		0			0
$382$	−2.29921	+	8.58076i	−0.117638	+	0.439030i
$383$	−15.7218	+	4.21264i	−0.803345	+	0.215256i	−0.637052	−	0.770821i	$-0.719846\pi$
$383$	−15.7218	+	4.21264i	−0.803345	+	0.215256i	−0.166293	+	0.986076i	$0.553180\pi$
$384$		0			0
$385$	6.46132	−	3.16441i	0.329299	−	0.161273i
$386$		−	23.2737i		−	1.18460i
$387$		0			0
$388$	−4.40690	−	1.18083i	−0.223726	−	0.0599473i
$389$	−8.09315	−	14.0178i	−0.410339	−	0.710728i	0.584587	−	0.811331i	$-0.301256\pi$
$389$	−8.09315	−	14.0178i	−0.410339	−	0.710728i	−0.994927	+	0.100602i	$0.967923\pi$
$390$		0			0
$391$	−25.6570			−1.29753
$392$	−6.77053	+	1.77761i	−0.341964	+	0.0897827i
$393$		0			0
$394$	15.3631	+	8.86990i	0.773983	+	0.446859i
$395$	2.54594	−	1.25484i	0.128100	−	0.0631378i
$396$		0			0
$397$	−9.07468	+	2.43155i	−0.455445	+	0.122036i	−0.479246	−	0.877681i	$-0.659090\pi$
$397$	−9.07468	+	2.43155i	−0.455445	+	0.122036i	0.0238009	+	0.999717i	$0.492423\pi$
$398$	11.7317	+	11.7317i	0.588056	+	0.588056i
$399$		0			0
$400$	−4.95694	−	0.654767i	−0.247847	−	0.0327384i
$401$	14.4737	+	8.35638i	0.722780	+	0.417297i	0.815775	−	0.578369i	$-0.196311\pi$
$401$	14.4737	+	8.35638i	0.722780	+	0.417297i	−0.0929947	+	0.995667i	$0.529644\pi$
$402$		0			0
$403$	−23.0092	−	6.16529i	−1.14617	−	0.307115i
$404$	0.868415	−	1.50414i	0.0432052	−	0.0748337i
$405$		0			0
$406$	14.7466	−	14.6724i	0.731859	−	0.728177i
$407$	3.73031	−	3.73031i	0.184905	−	0.184905i
$408$		0			0
$409$	13.1057	−	7.56660i	0.648037	−	0.374144i	−0.139667	−	0.990199i	$-0.544603\pi$
$409$	13.1057	−	7.56660i	0.648037	−	0.374144i	0.787704	+	0.616054i	$0.211270\pi$
$410$	4.13708	−	12.1788i	0.204316	−	0.601469i
$411$		0			0
$412$	−2.95983	−	2.95983i	−0.145820	−	0.145820i
$413$	0.203168	−	0.349857i	0.00999726	−	0.0172153i
$414$		0			0
$415$	−9.55547	+	1.89856i	−0.469060	+	0.0931967i
$416$	−2.96914	+	1.71423i	−0.145574	+	0.0840472i
$417$		0			0
$418$	2.66206	+	9.93493i	0.130205	+	0.485933i
$419$	12.8495			0.627741			0.313870	−	0.949466i	$-0.398374\pi$
$419$	12.8495			0.627741			0.313870	+	0.949466i	$0.398374\pi$
$420$		0			0
$421$	−3.39419			−0.165423			−0.0827114	−	0.996574i	$-0.526358\pi$
$421$	−3.39419			−0.165423			−0.0827114	+	0.996574i	$0.526358\pi$
$422$	−2.39901	−	8.95324i	−0.116782	−	0.435837i
$423$		0			0
$424$	7.20275	−	4.15851i	0.349796	−	0.201955i
$425$	−2.25223	−	17.1646i	−0.109249	−	0.832604i
$426$		0			0
$427$	−35.0672	−	0.0884351i	−1.69702	−	0.00427967i
$428$	5.72047	+	5.72047i	0.276509	+	0.276509i
$429$		0			0
$430$	3.56683	−	1.75801i	0.172008	−	0.0847789i
$431$	−5.42180	+	3.13027i	−0.261159	+	0.150780i	−0.624863	−	0.780734i	$-0.714845\pi$
$431$	−5.42180	+	3.13027i	−0.261159	+	0.150780i	0.363704	+	0.931514i	$0.381512\pi$
$432$		0			0
$433$	3.42688	−	3.42688i	0.164685	−	0.164685i	−0.619953	−	0.784639i	$-0.712849\pi$
$433$	3.42688	−	3.42688i	0.164685	−	0.164685i	0.784639	+	0.619953i	$0.212849\pi$
$434$	17.7441	+	4.80252i	0.851746	+	0.230529i
$435$		0			0
$436$	0.713741	−	1.23624i	0.0341820	−	0.0592050i
$437$	60.5381	+	16.2211i	2.89593	+	0.775962i
$438$		0			0
$439$	16.2016	+	9.35398i	0.773259	+	0.446441i	0.834036	−	0.551710i	$-0.186025\pi$
$439$	16.2016	+	9.35398i	0.773259	+	0.446441i	−0.0607771	+	0.998151i	$0.519358\pi$
$440$	−2.04486	+	1.79252i	−0.0974851	+	0.0854549i
$441$		0			0
$442$	−8.39373	−	8.39373i	−0.399249	−	0.399249i
$443$	34.3615	−	9.20714i	1.63257	−	0.437444i	0.677907	−	0.735148i	$-0.262887\pi$
$443$	34.3615	−	9.20714i	1.63257	−	0.437444i	0.954658	+	0.297703i	$0.0962207\pi$
$444$		0			0
$445$	−3.80898	−	7.72805i	−0.180563	−	0.366345i
$446$	−16.3277	−	9.42683i	−0.773141	−	0.446373i
$447$		0			0
$448$	2.29462	−	1.31709i	0.108410	−	0.0622268i
$449$	−5.42293			−0.255924			−0.127962	−	0.991779i	$-0.540844\pi$
$449$	−5.42293			−0.255924			−0.127962	+	0.991779i	$0.540844\pi$
$450$		0			0
$451$	−3.49765	−	6.05810i	−0.164698	−	0.285265i
$452$	−9.81922	−	2.63105i	−0.461857	−	0.123754i
$453$		0			0
$454$		−	4.67720i		−	0.219512i
$455$	15.2862	−	13.3318i	0.716627	−	0.625003i
$456$		0			0
$457$	17.6042	−	4.71703i	0.823490	−	0.220653i	0.177618	−	0.984099i	$-0.443161\pi$
$457$	17.6042	−	4.71703i	0.823490	−	0.220653i	0.645872	+	0.763446i	$0.276494\pi$
$458$	5.68119	−	21.2025i	0.265464	−	0.990727i
$459$		0			0
$460$	3.22913	+	16.2522i	0.150559	+	0.757765i
$461$		−	9.21273i		−	0.429080i	−0.976715	−	0.214540i	$-0.931175\pi$
$461$		−	9.21273i		−	0.429080i	0.976715	−	0.214540i	$-0.0688252\pi$
$462$		0			0
$463$	12.6873	−	12.6873i	0.589628	−	0.589628i	−0.347903	−	0.937531i	$-0.613106\pi$
$463$	12.6873	−	12.6873i	0.589628	−	0.589628i	0.937531	+	0.347903i	$0.113106\pi$
$464$	−3.93128	+	6.80918i	−0.182505	+	0.316108i
$465$		0			0
$466$	14.7558	+	25.5579i	0.683551	+	1.18394i
$467$	−3.94598	−	14.7266i	−0.182598	−	0.681465i	−0.995132	−	0.0985514i	$-0.968579\pi$
$467$	−3.94598	−	14.7266i	−0.182598	−	0.681465i	0.812534	−	0.582914i	$-0.198088\pi$
$468$		0			0
$469$	34.6701	−	9.19617i	1.60091	−	0.424640i
$470$	1.10528	−	16.8079i	0.0509830	−	0.775290i
$471$		0			0
$472$	−0.0395769	+	0.147703i	−0.00182167	+	0.00679858i
$473$	0.559744	−	2.08899i	0.0257370	−	0.0960519i
$474$		0			0
$475$	−5.53778	+	41.9240i	−0.254091	+	1.92361i
$476$	6.46109	+	6.49376i	0.296144	+	0.297641i
$477$		0			0
$478$	−4.73299	−	17.6638i	−0.216482	−	0.807922i
$479$	13.5727	+	23.5086i	0.620151	+	1.07413i	0.989457	+	0.144825i	$0.0462621\pi$
$479$	13.5727	+	23.5086i	0.620151	+	1.07413i	−0.369306	+	0.929308i	$0.620405\pi$
$480$		0			0
$481$	7.43632	−	12.8801i	0.339067	−	0.587281i
$482$	−12.2209	+	12.2209i	−0.556646	+	0.556646i
$483$		0			0
$484$		−	9.52108i		−	0.432776i
$485$	−10.0061	+	1.98811i	−0.454356	+	0.0902752i
$486$		0			0
$487$	5.23690	−	19.5444i	0.237307	−	0.885641i	−0.739789	−	0.672839i	$-0.765075\pi$
$487$	5.23690	−	19.5444i	0.237307	−	0.885641i	0.977095	−	0.212802i	$-0.0682588\pi$
$488$	12.8026	−	3.43043i	0.579544	−	0.155288i
$489$		0			0
$490$	−11.8223	+	10.2584i	−0.534076	+	0.463425i
$491$			22.6077i			1.02027i	0.860094	+	0.510136i	$0.170405\pi$
$491$			22.6077i			1.02027i	−0.860094	+	0.510136i	$0.829595\pi$
$492$		0			0
$493$	−26.2953	−	7.04580i	−1.18428	−	0.317327i
$494$	14.4984	+	25.1119i	0.652312	+	1.12984i
$495$		0			0
$496$	−6.94796			−0.311973
$497$	26.6471	−	15.2952i	1.19529	−	0.686086i
$498$		0			0
$499$	−5.87570	−	3.39234i	−0.263032	−	0.151862i	0.362685	−	0.931912i	$-0.381860\pi$
$499$	−5.87570	−	3.39234i	−0.263032	−	0.151862i	−0.625717	+	0.780050i	$0.715194\pi$
$500$	−10.5893	+	3.58696i	−0.473569	+	0.160414i
$501$		0			0
$502$	−14.0759	+	3.77163i	−0.628239	+	0.168336i
$503$	7.43812	+	7.43812i	0.331649	+	0.331649i	0.853213	−	0.521563i	$-0.174651\pi$
$503$	7.43812	+	7.43812i	0.331649	+	0.331649i	−0.521563	+	0.853213i	$0.674651\pi$
$504$		0			0
$505$	0.254839	−	3.87530i	0.0113402	−	0.172449i
$506$	7.80438	+	4.50586i	0.346947	+	0.200310i
$507$		0			0
$508$	−0.367227	−	0.0983983i	−0.0162931	−	0.00436572i
$509$	8.08054	−	13.9959i	0.358164	−	0.620358i	−0.629490	−	0.777008i	$-0.716736\pi$
$509$	8.08054	−	13.9959i	0.358164	−	0.620358i	0.987654	+	0.156651i	$0.0500697\pi$
$510$		0			0
$511$	−5.40306	−	20.3699i	−0.239018	−	0.901109i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−12.8592	+	7.42429i	−0.567197	+	0.327471i
$515$	−8.86244	−	3.01052i	−0.390526	−	0.132659i
$516$		0			0
$517$	−6.47772	−	6.47772i	−0.284890	−	0.284890i
$518$	−5.76367	+	9.92508i	−0.253241	+	0.436083i
$519$		0			0
$520$	−4.26053	+	6.37336i	−0.186837	+	0.279490i
$521$	11.9092	−	6.87577i	0.521751	−	0.301233i	−0.215900	−	0.976416i	$-0.569268\pi$
$521$	11.9092	−	6.87577i	0.521751	−	0.301233i	0.737651	+	0.675182i	$0.235935\pi$
$522$		0			0
$523$	4.79259	+	17.8862i	0.209565	+	0.782108i	0.988009	+	0.154394i	$0.0493426\pi$
$523$	4.79259	+	17.8862i	0.209565	+	0.782108i	−0.778444	+	0.627714i	$0.783991\pi$
$524$	1.47375			0.0643809
$525$		0			0
$526$	−12.1122			−0.528116
$527$	−6.22621	−	23.2365i	−0.271218	−	1.01220i
$528$		0			0
$529$	27.6371	−	15.9563i	1.20161	−	0.693751i
$530$	10.3355	−	15.4610i	0.448946	−	0.671581i
$531$		0			0
$532$	−11.1395	−	19.4070i	−0.482958	−	0.841402i
$533$	−13.9450	−	13.9450i	−0.604026	−	0.604026i
$534$		0			0
$535$	17.1284	+	5.81844i	0.740527	+	0.251553i
$536$	−11.7409	+	6.77860i	−0.507129	+	0.292791i
$537$		0			0
$538$	−6.12670	+	6.12670i	−0.264141	+	0.264141i
$539$	−0.0429360	+	8.51264i	−0.00184938	+	0.366666i
$540$		0			0
$541$	−15.2348	+	26.3874i	−0.654993	+	1.13448i	0.326902	+	0.945058i	$0.393995\pi$
$541$	−15.2348	+	26.3874i	−0.654993	+	1.13448i	−0.981895	+	0.189423i	$0.939338\pi$
$542$	4.71866	+	1.26436i	0.202684	+	0.0543090i
$543$		0			0
$544$	−2.99848	−	1.73117i	−0.128559	−	0.0742233i
$545$	0.209450	−	3.18507i	0.00897184	−	0.136433i
$546$		0			0
$547$	−4.16892	−	4.16892i	−0.178250	−	0.178250i	0.612343	−	0.790593i	$-0.290227\pi$
$547$	−4.16892	−	4.16892i	−0.178250	−	0.178250i	−0.790593	+	0.612343i	$0.790227\pi$
$548$	−1.70107	+	0.455800i	−0.0726661	+	0.0194708i
$549$		0			0
$550$	−2.32934	+	5.61668i	−0.0993235	+	0.239496i
$551$	57.5895	+	33.2493i	2.45340	+	1.41647i
$552$		0			0
$553$	−0.00846951	+	3.35842i	−0.000360160	+	0.142814i
$554$	−20.0237			−0.850726
$555$		0			0
$556$	9.18218	+	15.9040i	0.389411	+	0.674480i
$557$	−8.58871	−	2.30134i	−0.363915	−	0.0975108i	0.0722278	−	0.997388i	$-0.476989\pi$
$557$	−8.58871	−	2.30134i	−0.363915	−	0.0975108i	−0.436143	+	0.899877i	$0.643656\pi$
$558$		0			0
$559$		−	6.09706i		−	0.257878i
$560$	3.30025	−	4.91003i	0.139461	−	0.207486i
$561$		0			0
$562$	29.9094	−	8.01420i	1.26165	−	0.338058i
$563$	6.20457	−	23.1558i	0.261492	−	0.975900i	−0.702871	−	0.711317i	$-0.748099\pi$
$563$	6.20457	−	23.1558i	0.261492	−	0.975900i	0.964363	−	0.264583i	$-0.0852342\pi$
$564$		0			0
$565$	−22.2952	+	4.42979i	−0.937965	+	0.186363i
$566$		−	15.3939i		−	0.647053i
$567$		0			0
$568$	−8.21155	+	8.21155i	−0.344549	+	0.344549i
$569$	19.5755	−	33.9058i	0.820648	−	1.42140i	−0.0845518	−	0.996419i	$-0.526946\pi$
$569$	19.5755	−	33.9058i	0.820648	−	1.42140i	0.905200	−	0.424986i	$-0.139721\pi$
$570$		0			0
$571$	−0.922634	−	1.59805i	−0.0386111	−	0.0668763i	0.846074	−	0.533065i	$-0.178960\pi$
$571$	−0.922634	−	1.59805i	−0.0386111	−	0.0668763i	−0.884685	+	0.466189i	$0.845627\pi$
$572$	1.07912	+	4.02731i	0.0451201	+	0.168390i
$573$		0			0
$574$	10.7342	+	10.7885i	0.448037	+	0.450303i
$575$	22.5429	+	29.4047i	0.940102	+	1.22626i
$576$		0			0
$577$	−1.70494	+	6.36291i	−0.0709774	+	0.264891i	−0.992291	−	0.123929i	$-0.960451\pi$
$577$	−1.70494	+	6.36291i	−0.0709774	+	0.264891i	0.921314	+	0.388820i	$0.127117\pi$
$578$	−1.29725	+	4.84140i	−0.0539585	+	0.201376i
$579$		0			0
$580$	−1.15365	+	17.5433i	−0.0479026	+	0.728447i
$581$	3.01153	−	11.1269i	0.124939	−	0.461620i
$582$		0			0
$583$	−2.61780	−	9.76975i	−0.108418	−	0.404622i
$584$	3.98266	+	6.89817i	0.164804	+	0.285448i
$585$		0			0
$586$	−6.44935	+	11.1706i	−0.266420	+	0.461453i
$587$	−9.68417	+	9.68417i	−0.399709	+	0.399709i	−0.878130	−	0.478422i	$-0.841209\pi$
$587$	−9.68417	+	9.68417i	−0.399709	+	0.399709i	0.478422	+	0.878130i	$0.341209\pi$
$588$		0			0
$589$			58.7633i			2.42130i
$590$	0.0666339	+	0.335369i	0.00274327	+	0.0138069i
$591$		0			0
$592$	1.12275	−	4.19017i	0.0461449	−	0.172215i
$593$	22.2249	−	5.95514i	0.912666	−	0.244548i	0.228218	−	0.973610i	$-0.426710\pi$
$593$	22.2249	−	5.95514i	0.912666	−	0.244548i	0.684448	+	0.729062i	$0.260043\pi$
$594$		0			0
$595$	19.3783	+	6.63727i	0.794434	+	0.272102i
$596$			12.0259i			0.492599i
$597$		0			0
$598$	24.5403	+	6.57555i	1.00353	+	0.268894i
$599$	12.8665	+	22.2855i	0.525713	+	0.910561i	0.999551	+	0.0299496i	$0.00953469\pi$
$599$	12.8665	+	22.2855i	0.525713	+	0.910561i	−0.473839	+	0.880612i	$0.657132\pi$
$600$		0			0
$601$	0.224810			0.00917019			0.00458509	−	0.999989i	$-0.498541\pi$
$601$	0.224810			0.00917019			0.00458509	+	0.999989i	$0.498541\pi$
$602$	−0.0118657	+	4.70510i	−0.000483609	+	0.191765i
$603$		0			0
$604$	2.27559	+	1.31381i	0.0925925	+	0.0534583i
$605$	−9.41212	−	19.0963i	−0.382657	−	0.776373i
$606$		0			0
$607$	42.8638	−	11.4853i	1.73979	−	0.466175i	0.757388	−	0.652965i	$-0.226475\pi$
$607$	42.8638	−	11.4853i	1.73979	−	0.466175i	0.982400	+	0.186791i	$0.0598086\pi$
$608$	5.98045	+	5.98045i	0.242539	+	0.242539i
$609$		0			0
$610$	22.2867	−	19.5364i	0.902361	−	0.791005i
$611$	−22.3664	−	12.9132i	−0.904847	−	0.522414i
$612$		0			0
$613$	−41.7479	−	11.1863i	−1.68618	−	0.451811i	−0.716782	−	0.697297i	$-0.754386\pi$
$613$	−41.7479	−	11.1863i	−1.68618	−	0.451811i	−0.969400	+	0.245486i	$0.921053\pi$
$614$	2.10819	−	3.65149i	0.0850796	−	0.147362i
$615$		0			0
$616$	−0.824915	−	3.10997i	−0.0332368	−	0.125304i
$617$	−0.221996	+	0.221996i	−0.00893723	+	0.00893723i	−0.711561	−	0.702624i	$-0.752012\pi$
$617$	−0.221996	+	0.221996i	−0.00893723	+	0.00893723i	0.702624	+	0.711561i	$0.252012\pi$
$618$		0			0
$619$	−9.04155	+	5.22014i	−0.363410	+	0.209815i	−0.670576	−	0.741841i	$-0.733953\pi$
$619$	−9.04155	+	5.22014i	−0.363410	+	0.209815i	0.307165	+	0.951656i	$0.400620\pi$
$620$	−13.9354	+	6.86844i	−0.559659	+	0.275843i
$621$		0			0
$622$	22.5523	+	22.5523i	0.904265	+	0.904265i
$623$	10.1943	+	0.0257087i	0.408425	+	0.00103000i
$624$		0			0
$625$	−17.6929	+	17.6624i	−0.707716	+	0.706497i
$626$	−14.6676	+	8.46836i	−0.586236	+	0.338464i
$627$		0			0
$628$	−0.957870	−	3.57482i	−0.0382232	−	0.142651i
$629$	15.0196			0.598871
$630$		0			0
$631$	26.1673			1.04170			0.520851	−	0.853647i	$-0.325615\pi$
$631$	26.1673			1.04170			0.520851	+	0.853647i	$0.325615\pi$
$632$	−0.328536	−	1.22611i	−0.0130685	−	0.0487722i
$633$		0			0
$634$	5.15269	−	2.97491i	0.204640	−	0.118149i
$635$	−0.833813	+	0.165669i	−0.0330889	+	0.00657437i
$636$		0			0
$637$	6.09447	+	23.2125i	0.241472	+	0.919714i
$638$	6.76116	+	6.76116i	0.267677	+	0.267677i
$639$		0			0
$640$	−0.719217	+	2.11725i	−0.0284295	+	0.0836915i
$641$	−42.7331	+	24.6720i	−1.68785	+	0.974484i	−0.731698	+	0.681629i	$0.761272\pi$
$641$	−42.7331	+	24.6720i	−1.68785	+	0.974484i	−0.956157	+	0.292855i	$0.905395\pi$
$642$		0			0
$643$	−27.7760	+	27.7760i	−1.09538	+	1.09538i	−0.100437	+	0.994943i	$0.532024\pi$
$643$	−27.7760	+	27.7760i	−1.09538	+	1.09538i	−0.994943	+	0.100437i	$0.967976\pi$
$644$	−18.9249	−	5.12210i	−0.745746	−	0.201839i
$645$		0			0
$646$	−14.6416	+	25.3600i	−0.576067	+	0.997777i
$647$	−12.7135	−	3.40657i	−0.499819	−	0.133926i	9.71178e−5	−	1.00000i	$-0.499969\pi$
$647$	−12.7135	−	3.40657i	−0.499819	−	0.133926i	−0.499916	+	0.866074i	$0.666636\pi$
$648$		0			0
$649$	0.161045	+	0.0929795i	0.00632158	+	0.00364977i
$650$	−2.24485	+	16.9947i	−0.0880501	+	0.666587i
$651$		0			0
$652$	−0.866549	−	0.866549i	−0.0339367	−	0.0339367i
$653$	25.4252	−	6.81266i	0.994964	−	0.266600i	0.275630	−	0.961264i	$-0.411114\pi$
$653$	25.4252	−	6.81266i	0.994964	−	0.266600i	0.719334	+	0.694664i	$0.244447\pi$
$654$		0			0
$655$	2.95586	−	1.45688i	0.115495	−	0.0569250i
$656$	−4.98155	−	2.87610i	−0.194497	−	0.112293i
$657$		0			0
$658$	17.2350	+	10.0087i	0.671889	+	0.390178i
$659$	−10.4789			−0.408200			−0.204100	−	0.978950i	$-0.565427\pi$
$659$	−10.4789			−0.408200			−0.204100	+	0.978950i	$0.565427\pi$
$660$		0			0
$661$	−14.3731	−	24.8949i	−0.559049	−	0.968301i	−0.997576	−	0.0695833i	$-0.977833\pi$
$661$	−14.3731	−	24.8949i	−0.559049	−	0.968301i	0.438527	−	0.898718i	$-0.355500\pi$
$662$	−0.639154	−	0.171261i	−0.0248414	−	0.00665624i
$663$		0			0
$664$			4.35687i			0.169079i
$665$	−41.5272	−	27.9123i	−1.61036	−	1.08239i
$666$		0			0
$667$	56.2786	−	15.0798i	2.17912	−	0.583893i
$668$	−2.20763	+	8.23900i	−0.0854159	+	0.318776i
$669$		0			0
$670$	−16.8474	+	25.2022i	−0.650873	+	0.973646i
$671$		−	16.1185i		−	0.622248i
$672$		0			0
$673$	0.998735	−	0.998735i	0.0384984	−	0.0384984i	−0.687596	−	0.726094i	$-0.741334\pi$
$673$	0.998735	−	0.998735i	0.0384984	−	0.0384984i	0.726094	+	0.687596i	$0.241334\pi$
$674$	16.2924	−	28.2192i	0.627559	−	1.08696i
$675$		0			0
$676$	−0.622811	−	1.07874i	−0.0239543	−	0.0414900i
$677$	8.12350	+	30.3173i	0.312211	+	1.16519i	0.926558	+	0.376152i	$0.122753\pi$
$677$	8.12350	+	30.3173i	0.312211	+	1.16519i	−0.614347	+	0.789036i	$0.710580\pi$
$678$		0			0
$679$	3.15356	−	11.6516i	0.121023	−	0.447149i
$680$	−7.72535	−	0.508018i	−0.296254	−	0.0194816i
$681$		0			0
$682$	−2.18688	+	8.16156i	−0.0837401	+	0.312522i
$683$	12.9666	−	48.3920i	0.496154	−	1.85167i	−0.0273177	−	0.999627i	$-0.508697\pi$
$683$	12.9666	−	48.3920i	0.496154	−	1.85167i	0.523471	−	0.852043i	$-0.324637\pi$
$684$		0			0
$685$	−2.96122	+	2.59579i	−0.113142	+	0.0991802i
$686$	−4.65792	−	17.9249i	−0.177840	−	0.684378i
$687$		0			0
$688$	−0.460275	−	1.71777i	−0.0175478	−	0.0654893i
$689$	−14.2573	−	24.6944i	−0.543160	−	0.940781i
$690$		0			0
$691$	−2.15341	+	3.72982i	−0.0819197	+	0.141889i	−0.904074	−	0.427375i	$-0.859438\pi$
$691$	−2.15341	+	3.72982i	−0.0819197	+	0.141889i	0.822155	+	0.569264i	$0.192772\pi$
$692$	10.0250	−	10.0250i	0.381093	−	0.381093i
$693$		0			0
$694$		−	12.2201i		−	0.463869i
$695$	34.1385	+	22.8213i	1.29495	+	0.865660i
$696$		0			0
$697$	5.15466	−	19.2375i	0.195247	−	0.728671i
$698$	−10.9467	+	2.93315i	−0.414337	+	0.111021i
$699$		0			0
$700$	1.76542	−	13.1104i	0.0667266	−	0.495528i
$701$		−	51.8332i		−	1.95771i	−0.204545	−	0.978857i	$-0.565571\pi$
$701$		−	51.8332i		−	1.95771i	0.204545	−	0.978857i	$-0.434429\pi$
$702$		0			0
$703$	−35.4390	−	9.49585i	−1.33661	−	0.358143i
$704$	0.608054	+	1.05318i	0.0229169	+	0.0396932i
$705$		0			0
$706$	2.64559			0.0995682
$707$	3.97377	+	2.30764i	0.149449	+	0.0867877i
$708$		0			0
$709$	−14.8304	−	8.56232i	−0.556967	−	0.321565i	0.194960	−	0.980811i	$-0.437542\pi$
$709$	−14.8304	−	8.56232i	−0.556967	−	0.321565i	−0.751927	+	0.659246i	$0.770875\pi$
$710$	−8.35218	+	24.5873i	−0.313452	+	0.922746i
$711$		0			0
$712$	−3.72179	+	0.997251i	−0.139480	+	0.0373736i
$713$	36.4064	+	36.4064i	1.36343	+	1.36343i
$714$		0			0
$715$	6.14559	+	7.01075i	0.229832	+	0.262187i
$716$	14.1285	+	8.15708i	0.528006	+	0.304844i
$717$		0			0
$718$	−11.6317	−	3.11670i	−0.434091	−	0.116314i
$719$	−17.1714	+	29.7417i	−0.640385	+	1.10918i	0.344962	+	0.938617i	$0.387892\pi$
$719$	−17.1714	+	29.7417i	−0.640385	+	1.10918i	−0.985347	+	0.170563i	$0.945442\pi$
$720$		0			0
$721$	7.85070	−	7.81120i	0.292375	−	0.290904i
$722$	37.1455	−	37.1455i	1.38241	−	1.38241i
$723$		0			0
$724$	10.9042	−	6.29554i	0.405252	−	0.233972i
$725$	15.0287	+	36.3268i	0.558152	+	1.34914i
$726$		0			0
$727$	10.4410	+	10.4410i	0.387235	+	0.387235i	0.873700	−	0.486465i	$-0.161714\pi$
$727$	10.4410	+	10.4410i	0.387235	+	0.387235i	−0.486465	+	0.873700i	$0.661714\pi$
$728$	−4.51561	−	7.86701i	−0.167360	−	0.291571i
$729$		0			0
$730$	14.8072	+	9.89845i	0.548038	+	0.366358i
$731$	5.33238	−	3.07865i	0.197225	−	0.113868i
$732$		0			0
$733$	4.61601	+	17.2272i	0.170496	+	0.636301i	0.997275	+	0.0737734i	$0.0235042\pi$
$733$	4.61601	+	17.2272i	0.170496	+	0.636301i	−0.826779	+	0.562527i	$0.809829\pi$
$734$	−15.3865			−0.567925
$735$		0			0
$736$	7.41030			0.273147
$737$	4.26715	+	15.9252i	0.157183	+	0.586613i
$738$		0			0
$739$	−37.8189	+	21.8348i	−1.39119	+	0.803204i	−0.993447	−	0.114292i	$-0.963540\pi$
$739$	−37.8189	+	21.8348i	−1.39119	+	0.803204i	−0.397744	+	0.917497i	$0.630207\pi$
$740$	−1.89033	−	9.51406i	−0.0694900	−	0.349744i
$741$		0			0
$742$	10.9543	+	19.0844i	0.402145	+	0.700609i
$743$	−13.7573	−	13.7573i	−0.504707	−	0.504707i	0.408190	−	0.912897i	$-0.366160\pi$
$743$	−13.7573	−	13.7573i	−0.504707	−	0.504707i	−0.912897	+	0.408190i	$0.866160\pi$
$744$		0			0
$745$	11.8883	+	24.1201i	0.435552	+	0.883692i
$746$	−20.3786	+	11.7656i	−0.746112	+	0.430768i
$747$		0			0
$748$	−2.97733	+	2.97733i	−0.108862	+	0.108862i
$749$	−15.1731	+	15.0967i	−0.554412	+	0.551622i
$750$		0			0
$751$	−3.63361	+	6.29360i	−0.132592	+	0.229657i	−0.924675	−	0.380757i	$-0.875663\pi$
$751$	−3.63361	+	6.29360i	−0.132592	+	0.229657i	0.792083	+	0.610414i	$0.208997\pi$
$752$	−7.27627	−	1.94967i	−0.265338	−	0.0710972i
$753$		0			0
$754$	23.3450	+	13.4783i	0.850176	+	0.490849i
$755$	5.86289	+	0.385543i	0.213372	+	0.0140313i
$756$		0			0
$757$	−32.4397	−	32.4397i	−1.17904	−	1.17904i	−0.979989	−	0.199051i	$-0.936214\pi$
$757$	−32.4397	−	32.4397i	−1.17904	−	1.17904i	−0.199051	−	0.979989i	$-0.563786\pi$
$758$	4.06715	−	1.08979i	0.147726	−	0.0395830i
$759$		0			0
$760$	17.9069	+	6.08287i	0.649551	+	0.220649i
$761$	35.4954	+	20.4933i	1.28671	+	0.742882i	0.978066	−	0.208296i	$-0.0667918\pi$
$761$	35.4954	+	20.4933i	1.28671	+	0.742882i	0.308643	+	0.951178i	$0.400125\pi$
$762$		0			0
$763$	3.26600	+	1.89662i	0.118237	+	0.0686624i
$764$	8.88346			0.321392
$765$		0			0
$766$	8.13819	+	14.0958i	0.294045	+	0.509301i
$767$	0.506394	+	0.135688i	0.0182848	+	0.00489941i
$768$		0			0
$769$		−	46.8719i		−	1.69025i	−0.534573	−	0.845123i	$-0.679527\pi$
$769$		−	46.8719i		−	1.69025i	0.534573	−	0.845123i	$-0.320473\pi$
$770$	−4.72890	−	5.42214i	−0.170418	−	0.195400i
$771$		0			0
$772$	−22.4807	+	6.02367i	−0.809096	+	0.216797i
$773$	11.7154	−	43.7224i	0.421373	−	1.57258i	−0.350346	−	0.936620i	$-0.613936\pi$
$773$	11.7154	−	43.7224i	0.421373	−	1.57258i	0.771719	−	0.635964i	$-0.219397\pi$
$774$		0			0
$775$	−21.1601	+	27.5518i	−0.760094	+	0.989691i
$776$			4.56236i			0.163779i
$777$		0			0
$778$	−11.4454	+	11.4454i	−0.410339	+	0.410339i
$779$	−24.3250	+	42.1322i	−0.871534	+	1.50954i
$780$		0			0
$781$	7.06126	+	12.2305i	0.252672	+	0.437640i
$782$	6.64052	+	24.7828i	0.237464	+	0.886230i
$783$		0			0
$784$	3.46938	+	6.07975i	0.123906	+	0.217134i
$785$	−5.45509	−	6.22304i	−0.194701	−	0.222110i
$786$		0			0
$787$	7.27006	−	27.1322i	0.259150	−	0.967159i	−0.706585	−	0.707628i	$-0.749765\pi$
$787$	7.27006	−	27.1322i	0.259150	−	0.967159i	0.965735	−	0.259531i	$-0.0835680\pi$
$788$	4.59140	−	17.1353i	0.163562	−	0.610421i
$789$		0			0
$790$	−1.87102	−	2.13442i	−0.0665679	−	0.0759391i
$791$	7.02660	−	25.9616i	0.249837	−	0.923087i
$792$		0			0
$793$	−11.7611	−	43.8931i	−0.417650	−	1.55869i
$794$	4.69740	+	8.13614i	0.166705	+	0.288741i
$795$		0			0
$796$	8.29554	−	14.3683i	0.294028	−	0.509271i
$797$	22.4695	−	22.4695i	0.795910	−	0.795910i	−0.186538	−	0.982448i	$-0.559727\pi$
$797$	22.4695	−	22.4695i	0.795910	−	0.795910i	0.982448	+	0.186538i	$0.0597267\pi$
$798$		0			0
$799$		−	26.0817i		−	0.922703i
$800$	0.650495	+	4.95751i	0.0229985	+	0.175274i
$801$		0			0
$802$	4.32558	−	16.1433i	0.152741	−	0.570039i
$803$	9.35662	−	2.50710i	0.330188	−	0.0884736i
$804$		0			0
$805$	−43.0208	+	8.43502i	−1.51628	+	0.297295i
$806$			23.8208i			0.839053i
$807$		0			0
$808$	−1.67765	−	0.449524i	−0.0590195	−	0.0158142i
$809$	3.54696	+	6.14352i	0.124705	+	0.215995i	0.921617	−	0.388100i	$-0.126868\pi$
$809$	3.54696	+	6.14352i	0.124705	+	0.215995i	−0.796913	+	0.604094i	$0.793535\pi$
$810$		0			0
$811$	−45.3597			−1.59279			−0.796396	−	0.604775i	$-0.793263\pi$
$811$	−45.3597			−1.59279			−0.796396	+	0.604775i	$0.793263\pi$
$812$	−17.9891	−	10.4466i	−0.631294	−	0.366603i
$813$		0			0
$814$	−4.56868	−	2.63773i	−0.160132	−	0.0924524i
$815$	−2.59465	−	0.881389i	−0.0908867	−	0.0308737i
$816$		0			0
$817$	−14.5283	+	3.89284i	−0.508280	+	0.136193i
$818$	−10.7008	−	10.7008i	−0.374144	−	0.374144i
$819$		0			0
$820$	−12.8346	−	0.844001i	−0.448203	−	0.0294738i
$821$	−28.0252	−	16.1803i	−0.978086	−	0.564698i	−0.0763940	−	0.997078i	$-0.524341\pi$
$821$	−28.0252	−	16.1803i	−0.978086	−	0.564698i	−0.901692	+	0.432380i	$0.857674\pi$
$822$		0			0
$823$	−50.1497	−	13.4376i	−1.74811	−	0.468404i	−0.763888	−	0.645349i	$-0.776712\pi$
$823$	−50.1497	−	13.4376i	−1.74811	−	0.468404i	−0.984221	+	0.176944i	$0.943379\pi$
$824$	−2.09292	+	3.62504i	−0.0729102	+	0.126284i
$825$		0			0
$826$	−0.390520	−	0.105696i	−0.0135879	−	0.00367763i
$827$	−20.0870	+	20.0870i	−0.698493	+	0.698493i	−0.964085	−	0.265593i	$-0.914432\pi$
$827$	−20.0870	+	20.0870i	−0.698493	+	0.698493i	0.265593	+	0.964085i	$0.414432\pi$
$828$		0			0
$829$	11.4368	−	6.60303i	0.397216	−	0.229333i	−0.288066	−	0.957611i	$-0.593012\pi$
$829$	11.4368	−	6.60303i	0.397216	−	0.229333i	0.685282	+	0.728278i	$0.259679\pi$
$830$	4.30701	+	8.73849i	0.149498	+	0.303318i
$831$		0			0
$832$	2.42429	+	2.42429i	0.0840472	+	0.0840472i
$833$	−17.2239	+	17.0511i	−0.596774	+	0.590784i
$834$		0			0
$835$	3.71690	+	18.7072i	0.128629	+	0.647389i
$836$	8.90742	−	5.14270i	0.308069	−	0.177864i
$837$		0			0
$838$	−3.32570	−	12.4117i	−0.114885	−	0.428755i
$839$	−30.5399			−1.05435			−0.527177	−	0.849756i	$-0.676749\pi$
$839$	−30.5399			−1.05435			−0.527177	+	0.849756i	$0.676749\pi$
$840$		0			0
$841$	32.8198			1.13172
$842$	0.878482	+	3.27854i	0.0302745	+	0.112986i
$843$		0			0
$844$	−8.02726	+	4.63454i	−0.276310	+	0.159527i
$845$	−2.31556	−	1.54793i	−0.0796575	−	0.0532503i
$846$		0			0
$847$	25.1903	+	0.0635270i	0.865550	+	0.00218281i
$848$	−5.88102	−	5.88102i	−0.201955	−	0.201955i
$849$		0			0
$850$	−15.9968	+	6.61801i	−0.548685	+	0.226996i
$851$	−27.8391	+	16.0729i	−0.954311	+	0.550972i
$852$		0			0
$853$	19.7166	−	19.7166i	0.675085	−	0.675085i	−0.283799	−	0.958884i	$-0.591595\pi$
$853$	19.7166	−	19.7166i	0.675085	−	0.675085i	0.958884	+	0.283799i	$0.0915948\pi$
$854$	8.99063	+	33.8952i	0.307653	+	1.15987i
$855$		0			0
$856$	4.04498	−	7.00612i	0.138255	−	0.239464i
$857$	−3.42197	−	0.916913i	−0.116892	−	0.0313211i	0.199899	−	0.979817i	$-0.435939\pi$
$857$	−3.42197	−	0.916913i	−0.116892	−	0.0313211i	−0.316791	+	0.948495i	$0.602605\pi$
$858$		0			0
$859$	26.5474	+	15.3272i	0.905786	+	0.522956i	0.879073	−	0.476687i	$-0.158163\pi$
$859$	26.5474	+	15.3272i	0.905786	+	0.522956i	0.0267132	+	0.999643i	$0.491496\pi$
$860$	−2.62127	−	2.99029i	−0.0893847	−	0.101968i
$861$		0			0
$862$	4.42688	+	4.42688i	0.150780	+	0.150780i
$863$	−34.2710	+	9.18288i	−1.16660	+	0.312589i	−0.789598	−	0.613625i	$-0.789711\pi$
$863$	−34.2710	+	9.18288i	−1.16660	+	0.312589i	−0.376999	+	0.926214i	$0.623044\pi$
$864$		0			0
$865$	10.1967	−	30.0172i	0.346697	−	1.02062i
$866$	−4.19705	−	2.42317i	−0.142622	−	0.0823426i
$867$		0			0
$868$	0.0463585	−	18.3825i	0.00157351	−	0.623943i
$869$	−1.54369			−0.0523659
$870$		0			0
$871$	23.2402	+	40.2532i	0.787464	+	1.36393i
$872$	−1.37884	−	0.369460i	−0.0466935	−	0.0125115i
$873$		0			0
$874$		−	62.6736i		−	2.11997i
$875$	−9.41951	−	28.0406i	−0.318438	−	0.947944i
$876$		0			0
$877$	−45.4980	+	12.1912i	−1.53636	+	0.411666i	−0.925088	−	0.379754i	$-0.876009\pi$
$877$	−45.4980	+	12.1912i	−1.53636	+	0.411666i	−0.611272	+	0.791420i	$0.709342\pi$
$878$	4.84198	−	18.0705i	0.163409	−	0.609850i
$879$		0			0
$880$	2.26069	+	1.51125i	0.0762078	+	0.0509442i
$881$		−	9.98426i		−	0.336378i	−0.985755	−	0.168189i	$-0.946208\pi$
$881$		−	9.98426i		−	0.336378i	0.985755	−	0.168189i	$-0.0537919\pi$
$882$		0			0
$883$	36.5377	−	36.5377i	1.22959	−	1.22959i	0.265475	−	0.964118i	$-0.414471\pi$
$883$	36.5377	−	36.5377i	1.22959	−	1.22959i	0.964118	−	0.265475i	$-0.0855287\pi$
$884$	−5.93526	+	10.2802i	−0.199624	+	0.345760i
$885$		0			0
$886$	−17.7868	−	30.8077i	−0.597560	−	1.03500i
$887$	−8.81052	−	32.8813i	−0.295828	−	1.10405i	−0.940557	−	0.339635i	$-0.889696\pi$
$887$	−8.81052	−	32.8813i	−0.295828	−	1.10405i	0.644729	−	0.764411i	$-0.276970\pi$
$888$		0			0
$889$	0.262787	−	0.970933i	0.00881358	−	0.0325640i
$890$	−6.47889	+	5.67936i	−0.217173	+	0.190373i
$891$		0			0
$892$	−4.87968	+	18.2112i	−0.163384	+	0.609757i
$893$	−16.4896	+	61.5401i	−0.551804	+	2.05936i
$894$		0			0
$895$	36.4010	+	2.39372i	1.21675	+	0.0800133i
$896$	−1.86610	−	1.87554i	−0.0623422	−	0.0626574i
$897$		0			0
$898$	1.40356	+	5.23815i	0.0468374	+	0.174799i
$899$	27.3144	+	47.3099i	0.910985	+	1.57787i
$900$		0			0
$901$	14.3982	−	24.9384i	0.479673	−	0.830818i
$902$	−4.94642	+	4.94642i	−0.164698	+	0.164698i
$903$		0			0
$904$			10.1656i			0.338103i
$905$	15.6469	−	23.4063i	0.520119	−	0.778051i
$906$		0			0
$907$	7.57647	−	28.2758i	0.251573	−	0.938882i	−0.718392	−	0.695638i	$-0.755122\pi$
$907$	7.57647	−	28.2758i	0.251573	−	0.938882i	0.969965	−	0.243244i	$-0.0782116\pi$
$908$	−4.51783	+	1.21055i	−0.149930	+	0.0401735i
$909$		0			0
$910$	−16.8339	−	11.3148i	−0.558037	−	0.375082i
$911$		−	35.9935i		−	1.19252i	−0.802792	−	0.596259i	$-0.796653\pi$
$911$		−	35.9935i		−	1.19252i	0.802792	−	0.596259i	$-0.203347\pi$
$912$		0			0
$913$	5.11788	+	1.37133i	0.169377	+	0.0453845i
$914$	−9.11261	−	15.7835i	−0.301418	−	0.522072i
$915$		0			0
$916$	−21.9504			−0.725262
$917$	−0.00983319	+	3.89915i	−0.000324720	+	0.128761i
$918$		0			0
$919$	10.3314	+	5.96485i	0.340802	+	0.196762i	0.660627	−	0.750714i	$-0.270291\pi$
$919$	10.3314	+	5.96485i	0.340802	+	0.196762i	−0.319824	+	0.947477i	$0.603624\pi$
$920$	14.8627	−	7.32549i	0.490009	−	0.241514i
$921$		0			0
$922$	−8.89881	+	2.38443i	−0.293067	+	0.0785270i
$923$	28.1530	+	28.1530i	0.926668	+	0.926668i
$924$		0			0
$925$	−13.1966	−	17.2135i	−0.433901	−	0.565976i
$926$	−15.5387	−	8.97126i	−0.510633	−	0.294814i
$927$		0			0
$928$	7.59465	+	2.03498i	0.249307	+	0.0668015i
$929$	4.36844	−	7.56637i	0.143324	−	0.248244i	−0.785422	−	0.618960i	$-0.787554\pi$
$929$	4.36844	−	7.56637i	0.143324	−	0.248244i	0.928746	+	0.370716i	$0.120888\pi$
$930$		0			0
$931$	51.4204	−	29.3428i	1.68523	−	0.961670i
$932$	20.8679	−	20.8679i	0.683551	−	0.683551i
$933$		0			0
$934$	−13.2035	+	7.62304i	−0.432032	+	0.249434i
$935$	−3.02832	+	8.91483i	−0.0990366	+	0.291546i
$936$		0			0
$937$	2.98130	+	2.98130i	0.0973949	+	0.0973949i	0.754125	−	0.656730i	$-0.228061\pi$
$937$	2.98130	+	2.98130i	0.0973949	+	0.0973949i	−0.656730	+	0.754125i	$0.728061\pi$
$938$	−17.8561	−	31.1086i	−0.583022	−	1.01573i
$939$		0			0
$940$	−16.5212	+	3.28258i	−0.538864	+	0.107066i
$941$	−13.6741	+	7.89476i	−0.445764	+	0.257362i	−0.706039	−	0.708173i	$-0.749520\pi$
$941$	−13.6741	+	7.89476i	−0.445764	+	0.257362i	0.260276	+	0.965534i	$0.416187\pi$
$942$		0			0
$943$	11.0323	+	41.1731i	0.359261	+	1.34078i
$944$	0.152913			0.00497690
$945$		0			0
$946$	−2.16268			−0.0703149
$947$	5.18506	+	19.3509i	0.168492	+	0.628820i	0.997569	+	0.0696859i	$0.0221997\pi$
$947$	5.18506	+	19.3509i	0.168492	+	0.628820i	−0.829077	+	0.559134i	$0.811134\pi$
$948$		0			0
$949$	23.6501	−	13.6544i	0.767716	−	0.443241i
$950$	41.9288	−	5.50165i	1.36035	−	0.178497i
$951$		0			0
$952$	4.60024	−	7.92165i	0.149095	−	0.256742i
$953$	−10.2016	−	10.2016i	−0.330461	−	0.330461i	0.522300	−	0.852762i	$-0.325074\pi$
$953$	−10.2016	−	10.2016i	−0.330461	−	0.330461i	−0.852762	+	0.522300i	$0.825074\pi$
$954$		0			0
$955$	17.8174	−	8.78179i	0.576557	−	0.284172i
$956$	−15.8369	+	9.14344i	−0.512202	+	0.295720i
$957$		0			0
$958$	19.1947	−	19.1947i	0.620151	−	0.620151i
$959$	−1.19458	−	4.50364i	−0.0385750	−	0.145430i
$960$		0			0
$961$	−8.63707	+	14.9598i	−0.278615	+	0.482576i
$962$	−14.3659	−	3.84932i	−0.463174	−	0.124107i
$963$		0			0
$964$	14.9675	+	8.64147i	0.482070	+	0.278323i
$965$	−39.1343	+	34.3049i	−1.25978	+	1.10432i
$966$		0			0
$967$	13.0589	+	13.0589i	0.419945	+	0.419945i	0.885185	−	0.465240i	$-0.154032\pi$
$967$	13.0589	+	13.0589i	0.419945	+	0.419945i	−0.465240	+	0.885185i	$0.654032\pi$
$968$	−9.19666	+	2.46424i	−0.295592	+	0.0792036i
$969$		0			0
$970$	4.51014	+	9.15064i	0.144812	+	0.293809i
$971$	−17.0295	−	9.83200i	−0.546503	−	0.315524i	0.201207	−	0.979549i	$-0.435514\pi$
$971$	−17.0295	−	9.83200i	−0.546503	−	0.315524i	−0.747710	+	0.664025i	$0.768847\pi$
$972$		0			0
$973$	−42.1392	+	24.1876i	−1.35092	+	0.775418i
$974$	−20.2338			−0.648334
$975$		0			0
$976$	−6.62709	−	11.4785i	−0.212128	−	0.367416i
$977$	12.1866	+	3.26540i	0.389885	+	0.104469i	0.448436	−	0.893815i	$-0.351981\pi$
$977$	12.1866	+	3.26540i	0.389885	+	0.104469i	−0.0585507	+	0.998284i	$0.518648\pi$
$978$		0			0
$979$			4.68576i			0.149758i
$980$	12.9686	+	8.76438i	0.414268	+	0.279968i
$981$		0			0
$982$	21.8374	−	5.85131i	0.696859	−	0.186723i
$983$	7.23418	−	26.9983i	0.230735	−	0.861113i	−0.749291	−	0.662241i	$-0.769605\pi$
$983$	7.23418	−	26.9983i	0.230735	−	0.861113i	0.980025	−	0.198872i	$-0.0637279\pi$
$984$		0			0
$985$	−7.73034	−	38.9069i	−0.246309	−	1.23968i
$986$			27.2229i			0.866953i
$987$		0			0
$988$	20.5038	−	20.5038i	0.652312	−	0.652312i
$989$	−6.58911	+	11.4127i	−0.209522	+	0.362902i
$990$		0			0
$991$	−4.37792	−	7.58278i	−0.139069	−	0.240875i	0.788075	−	0.615579i	$-0.211078\pi$
$991$	−4.37792	−	7.58278i	−0.139069	−	0.240875i	−0.927145	+	0.374704i	$0.877744\pi$
$992$	1.79826	+	6.71121i	0.0570949	+	0.213081i
$993$		0			0
$994$	−21.6709	−	21.7804i	−0.687358	−	0.690833i
$995$	2.43435	−	37.0188i	0.0771742	−	1.17358i
$996$		0			0
$997$	−11.3759	+	42.4554i	−0.360278	+	1.34458i	0.513433	+	0.858130i	$0.328373\pi$
$997$	−11.3759	+	42.4554i	−0.360278	+	1.34458i	−0.873711	+	0.486445i	$0.838293\pi$
$998$	−1.75600	+	6.55349i	−0.0555853	+	0.207447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.c.107.2	yes	32
3.2	odd	2	inner	630.2.ce.c.107.7	yes	32
5.3	odd	4	inner	630.2.ce.c.233.4	yes	32
7.4	even	3	inner	630.2.ce.c.557.5	yes	32
15.8	even	4	inner	630.2.ce.c.233.5	yes	32
21.11	odd	6	inner	630.2.ce.c.557.4	yes	32
35.18	odd	12	inner	630.2.ce.c.53.7	yes	32
105.53	even	12	inner	630.2.ce.c.53.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.c.53.2	✓	32	105.53	even	12	inner
630.2.ce.c.53.7	yes	32	35.18	odd	12	inner
630.2.ce.c.107.2	yes	32	1.1	even	1	trivial
630.2.ce.c.107.7	yes	32	3.2	odd	2	inner
630.2.ce.c.233.4	yes	32	5.3	odd	4	inner
630.2.ce.c.233.5	yes	32	15.8	even	4	inner
630.2.ce.c.557.4	yes	32	21.11	odd	6	inner
630.2.ce.c.557.5	yes	32	7.4	even	3	inner

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.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.24269 + 1.85895i) q^{5} +(-1.31709 - 2.29462i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.24269 + 1.85895i) q^{5} +(-1.31709 - 2.29462i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.11725 + 0.719217i) q^{10} +(1.05318 - 0.608054i) q^{11} +(2.42429 - 2.42429i) q^{13} +(-1.87554 + 1.86610i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.34437 + 0.896120i) q^{17} +(-7.32453 - 4.22882i) q^{19} +(0.146727 - 2.23125i) q^{20} +(-0.859918 - 0.859918i) q^{22} +(-7.15780 + 1.91793i) q^{23} +(-1.91143 - 4.62022i) q^{25} +(-2.96914 - 1.71423i) q^{26} +(2.28794 + 1.32865i) q^{28} -7.86256 q^{29} +(-3.47398 - 6.01711i) q^{31} +(-0.965926 - 0.258819i) q^{32} -3.46234i q^{34} +(5.90233 + 0.403088i) q^{35} +(4.19017 - 1.12275i) q^{37} +(-2.18900 + 8.16945i) q^{38} +(-2.19320 + 0.435763i) q^{40} -5.75220i q^{41} +(1.25749 - 1.25749i) q^{43} +(-0.608054 + 1.05318i) q^{44} +(3.70515 + 6.41751i) q^{46} +(-1.94967 - 7.27627i) q^{47} +(-3.53053 + 6.04445i) q^{49} +(-3.96808 + 3.04210i) q^{50} +(-0.887352 + 3.31164i) q^{52} +(2.15260 - 8.03362i) q^{53} +(-0.178435 + 2.71344i) q^{55} +(0.691214 - 2.55386i) q^{56} +(2.03498 + 7.59465i) q^{58} +(0.0764567 + 0.132427i) q^{59} +(6.62709 - 11.4785i) q^{61} +(-4.91295 + 4.91295i) q^{62} +1.00000i q^{64} +(1.49400 + 7.51930i) q^{65} +(-3.50886 + 13.0952i) q^{67} +(-3.34437 + 0.896120i) q^{68} +(-1.13828 - 5.80554i) q^{70} +11.6129i q^{71} +(7.69391 + 2.06158i) q^{73} +(-2.16899 - 3.75681i) q^{74} +8.45764 q^{76} +(-2.78239 - 1.61578i) q^{77} +(-1.09930 - 0.634683i) q^{79} +(0.988555 + 2.00568i) q^{80} +(-5.55620 + 1.48878i) q^{82} +(3.08077 + 3.08077i) q^{83} +(-5.82187 + 5.10342i) q^{85} +(-1.54011 - 0.889183i) q^{86} +(1.17467 + 0.314752i) q^{88} +(-1.92654 + 3.33687i) q^{89} +(-8.75584 - 2.36980i) q^{91} +(5.23987 - 5.23987i) q^{92} +(-6.52373 + 3.76648i) q^{94} +(16.9633 - 8.36084i) q^{95} +(3.22607 + 3.22607i) q^{97} +(6.75226 + 1.84581i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{7}+O(q^{10}) \) 32 * q - 12 * q^7	\( 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) \) 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Introduction

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