LMFDB - Embedded newform 420.2.bb.a.109.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [420,2,Mod(109,420)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("420.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(420, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.81284711803392324796416.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 20 x^{13} - 12 x^{12} + 124 x^{11} - 24 x^{10} + 328 x^{9} + 1132 x^{8} + \cdots + 16 $ x^16 - 2x^15 + 2x^14 - 20x^13 - 12x^12 + 124x^11 - 24x^10 + 328x^9 + 1132x^8 - 760x^7 + 96x^6 - 640x^5 + 96x^4 + 224x^3 + 32x^2 + 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.7
Root			$0.521577 - 1.94655i$ of defining polynomial
Character	$\chi$	$=$	420.109
Dual form			420.2.bb.a.289.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{3} +(0.779855 - 2.09567i) q^{5} +(-1.29633 - 2.30641i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.07409 - 1.86038i) q^{11} -3.20929i q^{13} +(1.72321 - 1.42497i) q^{15} +(-3.12880 - 1.80641i) q^{17} +(2.65730 + 4.60257i) q^{19} +(0.0305535 - 2.64557i) q^{21} +(1.91330 - 1.10465i) q^{23} +(-3.78365 - 3.26863i) q^{25} +1.00000i q^{27} +9.12035 q^{29} +(-3.70929 + 6.42468i) q^{31} +(1.86038 - 1.07409i) q^{33} +(-5.84442 + 0.918007i) q^{35} +(-2.20985 + 1.27586i) q^{37} +(1.60465 - 2.77933i) q^{39} +6.14818 q^{41} +5.44455i q^{43} +(2.20483 - 0.372460i) q^{45} +(9.13644 - 5.27492i) q^{47} +(-3.63907 + 5.97973i) q^{49} +(-1.80641 - 3.12880i) q^{51} +(4.67960 + 2.70177i) q^{53} +(-3.06111 - 3.70177i) q^{55} +5.31459i q^{57} +(-4.43796 + 7.68677i) q^{59} +(-6.90194 - 11.9545i) q^{61} +(1.34925 - 2.27586i) q^{63} +(-6.72561 - 2.50278i) q^{65} +(0.0141657 + 0.00817856i) q^{67} +2.20929 q^{69} -5.63105 q^{71} +(-9.91127 - 5.72227i) q^{73} +(-1.64242 - 4.72255i) q^{75} +(-5.68318 - 0.0656346i) q^{77} +(7.65543 + 13.2596i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.0314i q^{83} +(-6.22565 + 5.14818i) q^{85} +(7.89845 + 4.56017i) q^{87} +(-1.96879 - 3.41005i) q^{89} +(-7.40194 + 4.16029i) q^{91} +(-6.42468 + 3.70929i) q^{93} +(11.7178 - 1.97947i) q^{95} +5.16454i q^{97} +2.14818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) $ 16 * q + 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 + 8 * q^19 - 4 * q^21 + 12 * q^25 + 24 * q^29 + 10 * q^35 - 4 * q^39 + 48 * q^41 - 2 * q^45 + 8 * q^49 + 4 * q^51 - 40 * q^55 - 28 * q^59 - 32 * q^61 - 26 * q^65 - 24 * q^69 - 56 * q^71 - 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 - 16 * q^89 - 40 * q^91 + 22 * q^95 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	0.779855	−	2.09567i	0.348762	−	0.937211i
$5$	0.779855	−	2.09567i	0.348762	−	0.937211i
$6$		0			0
$7$	−1.29633	−	2.30641i	−0.489966	−	0.871742i
$7$	−1.29633	−	2.30641i	−0.489966	−	0.871742i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	1.07409	−	1.86038i	0.323851	−	0.560926i	−0.657428	−	0.753517i	$-0.728356\pi$
$11$	1.07409	−	1.86038i	0.323851	−	0.560926i	0.981279	+	0.192591i	$0.0616891\pi$
$12$		0			0
$13$		−	3.20929i		−	0.890097i	−0.895506	−	0.445048i	$-0.853186\pi$
$13$		−	3.20929i		−	0.890097i	0.895506	−	0.445048i	$-0.146814\pi$
$14$		0			0
$15$	1.72321	−	1.42497i	0.444930	−	0.367927i
$16$		0			0
$17$	−3.12880	−	1.80641i	−0.758845	−	0.438119i	0.0700361	−	0.997544i	$-0.477689\pi$
$17$	−3.12880	−	1.80641i	−0.758845	−	0.438119i	−0.828881	+	0.559425i	$0.811022\pi$
$18$		0			0
$19$	2.65730	+	4.60257i	0.609625	+	1.05590i	0.991302	+	0.131606i	$0.0420134\pi$
$19$	2.65730	+	4.60257i	0.609625	+	1.05590i	−0.381677	+	0.924296i	$0.624653\pi$
$20$		0			0
$21$	0.0305535	−	2.64557i	0.00666733	−	0.577312i
$22$		0			0
$23$	1.91330	−	1.10465i	0.398951	−	0.230334i	−0.287080	−	0.957907i	$-0.592685\pi$
$23$	1.91330	−	1.10465i	0.398951	−	0.230334i	0.686031	+	0.727572i	$0.259351\pi$
$24$		0			0
$25$	−3.78365	−	3.26863i	−0.756731	−	0.653727i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	9.12035			1.69361			0.846803	−	0.531907i	$-0.178524\pi$
$29$	9.12035			1.69361			0.846803	+	0.531907i	$0.178524\pi$
$30$		0			0
$31$	−3.70929	+	6.42468i	−0.666208	+	1.15391i	0.312748	+	0.949836i	$0.398750\pi$
$31$	−3.70929	+	6.42468i	−0.666208	+	1.15391i	−0.978956	+	0.204070i	$0.934583\pi$
$32$		0			0
$33$	1.86038	−	1.07409i	0.323851	−	0.186975i
$34$		0			0
$35$	−5.84442	+	0.918007i	−0.987888	+	0.155171i
$36$		0			0
$37$	−2.20985	+	1.27586i	−0.363297	+	0.209750i	−0.670526	−	0.741886i	$-0.733932\pi$
$37$	−2.20985	+	1.27586i	−0.363297	+	0.209750i	0.307229	+	0.951636i	$0.400598\pi$
$38$		0			0
$39$	1.60465	−	2.77933i	0.256949	−	0.445048i
$40$		0			0
$41$	6.14818			0.960185			0.480092	−	0.877218i	$-0.340603\pi$
$41$	6.14818			0.960185			0.480092	+	0.877218i	$0.340603\pi$
$42$		0			0
$43$			5.44455i			0.830286i	0.909756	+	0.415143i	$0.136268\pi$
$43$			5.44455i			0.830286i	−0.909756	+	0.415143i	$0.863732\pi$
$44$		0			0
$45$	2.20483	−	0.372460i	0.328677	−	0.0555231i
$46$		0			0
$47$	9.13644	−	5.27492i	1.33269	−	0.769427i	0.346976	−	0.937874i	$-0.387209\pi$
$47$	9.13644	−	5.27492i	1.33269	−	0.769427i	0.985711	+	0.168447i	$0.0538753\pi$
$48$		0			0
$49$	−3.63907	+	5.97973i	−0.519867	+	0.854247i
$50$		0			0
$51$	−1.80641	−	3.12880i	−0.252948	−	0.438119i
$52$		0			0
$53$	4.67960	+	2.70177i	0.642792	+	0.371116i	0.785689	−	0.618621i	$-0.212308\pi$
$53$	4.67960	+	2.70177i	0.642792	+	0.371116i	−0.142897	+	0.989738i	$0.545642\pi$
$54$		0			0
$55$	−3.06111	−	3.70177i	−0.412760	−	0.499146i
$56$		0			0
$57$			5.31459i			0.703935i
$58$		0			0
$59$	−4.43796	+	7.68677i	−0.577773	+	1.00073i	0.417961	+	0.908465i	$0.362745\pi$
$59$	−4.43796	+	7.68677i	−0.577773	+	1.00073i	−0.995734	+	0.0922675i	$0.970589\pi$
$60$		0			0
$61$	−6.90194	−	11.9545i	−0.883703	−	1.53062i	−0.847192	−	0.531286i	$-0.821709\pi$
$61$	−6.90194	−	11.9545i	−0.883703	−	1.53062i	−0.0365110	−	0.999333i	$-0.511624\pi$
$62$		0			0
$63$	1.34925	−	2.27586i	0.169989	−	0.286731i
$64$		0			0
$65$	−6.72561	−	2.50278i	−0.834209	−	0.310432i
$66$		0			0
$67$	0.0141657	+	0.00817856i	0.00173061	+	0.000999170i	0.500865	−	0.865525i	$-0.333015\pi$
$67$	0.0141657	+	0.00817856i	0.00173061	+	0.000999170i	−0.499134	+	0.866525i	$0.666349\pi$
$68$		0			0
$69$	2.20929			0.265967
$70$		0			0
$71$	−5.63105			−0.668282			−0.334141	−	0.942523i	$-0.608446\pi$
$71$	−5.63105			−0.668282			−0.334141	+	0.942523i	$0.608446\pi$
$72$		0			0
$73$	−9.91127	−	5.72227i	−1.16003	−	0.669742i	−0.208716	−	0.977976i	$-0.566928\pi$
$73$	−9.91127	−	5.72227i	−1.16003	−	0.669742i	−0.951310	+	0.308235i	$0.900262\pi$
$74$		0			0
$75$	−1.64242	−	4.72255i	−0.189651	−	0.545313i
$76$		0			0
$77$	−5.68318	−	0.0656346i	−0.647658	−	0.00747976i
$78$		0			0
$79$	7.65543	+	13.2596i	0.861303	+	1.49182i	0.870672	+	0.491864i	$0.163684\pi$
$79$	7.65543	+	13.2596i	0.861303	+	1.49182i	−0.00936887	+	0.999956i	$0.502982\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			14.0314i			1.54015i	0.637955	+	0.770073i	$0.279780\pi$
$83$			14.0314i			1.54015i	−0.637955	+	0.770073i	$0.720220\pi$
$84$		0			0
$85$	−6.22565	+	5.14818i	−0.675266	+	0.558399i
$86$		0			0
$87$	7.89845	+	4.56017i	0.846803	+	0.488902i
$88$		0			0
$89$	−1.96879	−	3.41005i	−0.208691	−	0.361464i	0.742611	−	0.669723i	$-0.233587\pi$
$89$	−1.96879	−	3.41005i	−0.208691	−	0.361464i	−0.951303	+	0.308259i	$0.900254\pi$
$90$		0			0
$91$	−7.40194	+	4.16029i	−0.775935	+	0.436117i
$92$		0			0
$93$	−6.42468	+	3.70929i	−0.666208	+	0.384635i
$94$		0			0
$95$	11.7178	−	1.97947i	1.20222	−	0.203090i
$96$		0			0
$97$			5.16454i			0.524380i	0.965016	+	0.262190i	$0.0844447\pi$
$97$			5.16454i			0.524380i	−0.965016	+	0.262190i	$0.915555\pi$
$98$		0			0
$99$	2.14818			0.215901
$100$		0			0
$101$	0.815524	−	1.41253i	0.0811477	−	0.140552i	−0.822595	−	0.568627i	$-0.807475\pi$
$101$	0.815524	−	1.41253i	0.0811477	−	0.140552i	0.903743	+	0.428075i	$0.140808\pi$
$102$		0			0
$103$	−1.77081	+	1.02237i	−0.174483	+	0.100738i	−0.584698	−	0.811251i	$-0.698787\pi$
$103$	−1.77081	+	1.02237i	−0.174483	+	0.100738i	0.410215	+	0.911989i	$0.365454\pi$
$104$		0			0
$105$	−5.52042	−	2.12719i	−0.538738	−	0.207593i
$106$		0			0
$107$	5.23442	−	3.02210i	0.506031	−	0.292157i	−0.225170	−	0.974320i	$-0.572294\pi$
$107$	5.23442	−	3.02210i	0.506031	−	0.292157i	0.731201	+	0.682162i	$0.238960\pi$
$108$		0			0
$109$	−1.59619	+	2.76468i	−0.152887	+	0.264808i	−0.932288	−	0.361718i	$-0.882190\pi$
$109$	−1.59619	+	2.76468i	−0.152887	+	0.264808i	0.779401	+	0.626526i	$0.215524\pi$
$110$		0			0
$111$	−2.55172			−0.242198
$112$		0			0
$113$			1.10343i			0.103802i	0.998652	+	0.0519011i	$0.0165281\pi$
$113$			1.10343i			0.103802i	−0.998652	+	0.0519011i	$0.983472\pi$
$114$		0			0
$115$	−0.822873	−	4.87111i	−0.0767333	−	0.454233i
$116$		0			0
$117$	2.77933	−	1.60465i	0.256949	−	0.148349i
$118$		0			0
$119$	−0.110385	+	9.55800i	−0.0101189	+	0.876180i
$120$		0			0
$121$	3.19265	+	5.52984i	0.290241	+	0.502713i
$122$		0			0
$123$	5.32448	+	3.07409i	0.480092	+	0.277182i
$124$		0			0
$125$	−9.80067	+	5.38022i	−0.876599	+	0.481222i
$126$		0			0
$127$			19.6798i			1.74630i	0.487451	+	0.873150i	$0.337927\pi$
$127$			19.6798i			1.74630i	−0.487451	+	0.873150i	$0.662073\pi$
$128$		0			0
$129$	−2.72227	+	4.71512i	−0.239683	+	0.415143i
$130$		0			0
$131$	−7.57316	−	13.1171i	−0.661670	−	1.14605i	−0.980177	−	0.198125i	$-0.936515\pi$
$131$	−7.57316	−	13.1171i	−0.661670	−	1.14605i	0.318507	−	0.947921i	$-0.396819\pi$
$132$		0			0
$133$	7.17070	−	12.0953i	0.621778	−	1.04879i
$134$		0			0
$135$	2.09567	+	0.779855i	0.180366	+	0.0671192i
$136$		0			0
$137$	−6.66160	−	3.84608i	−0.569139	−	0.328593i	0.187666	−	0.982233i	$-0.439908\pi$
$137$	−6.66160	−	3.84608i	−0.569139	−	0.328593i	−0.756805	+	0.653640i	$0.773241\pi$
$138$		0			0
$139$	4.84034			0.410552			0.205276	−	0.978704i	$-0.434191\pi$
$139$	4.84034			0.410552			0.205276	+	0.978704i	$0.434191\pi$
$140$		0			0
$141$	10.5498			0.888458
$142$		0			0
$143$	−5.97050	−	3.44707i	−0.499279	−	0.288259i
$144$		0			0
$145$	7.11254	−	19.1132i	0.590665	−	1.58727i
$146$		0			0
$147$	−6.14139	+	3.35906i	−0.506534	+	0.277051i
$148$		0			0
$149$	4.48608	+	7.77012i	0.367514	+	0.636553i	0.989176	−	0.146732i	$-0.0468756\pi$
$149$	4.48608	+	7.77012i	0.367514	+	0.636553i	−0.621662	+	0.783286i	$0.713542\pi$
$150$		0			0
$151$	1.84084	−	3.18842i	0.149805	−	0.259470i	−0.781350	−	0.624093i	$-0.785469\pi$
$151$	1.84084	−	3.18842i	0.149805	−	0.259470i	0.931155	+	0.364623i	$0.118802\pi$
$152$		0			0
$153$		−	3.61282i		−	0.292079i
$154$		0			0
$155$	10.5713	+	12.7838i	0.849107	+	1.02682i
$156$		0			0
$157$	−7.85224	−	4.53349i	−0.626677	−	0.361812i	0.152787	−	0.988259i	$-0.451175\pi$
$157$	−7.85224	−	4.53349i	−0.626677	−	0.361812i	−0.779464	+	0.626447i	$0.784508\pi$
$158$		0			0
$159$	2.70177	+	4.67960i	0.214264	+	0.371116i
$160$		0			0
$161$	−5.02803	−	2.98088i	−0.396264	−	0.234926i
$162$		0			0
$163$	−4.26888	+	2.46464i	−0.334365	+	0.193046i	−0.657777	−	0.753213i	$-0.728503\pi$
$163$	−4.26888	+	2.46464i	−0.334365	+	0.193046i	0.323413	+	0.946258i	$0.395170\pi$
$164$		0			0
$165$	−0.800113	−	4.73638i	−0.0622887	−	0.368726i
$166$		0			0
$167$		−	17.0920i		−	1.32262i	−0.750115	−	0.661308i	$-0.770002\pi$
$167$		−	17.0920i		−	1.32262i	0.750115	−	0.661308i	$-0.229998\pi$
$168$		0			0
$169$	2.70046			0.207727
$170$		0			0
$171$	−2.65730	+	4.60257i	−0.203208	+	0.351967i
$172$		0			0
$173$	−4.20341	+	2.42684i	−0.319580	+	0.184509i	−0.651205	−	0.758902i	$-0.725736\pi$
$173$	−4.20341	+	2.42684i	−0.319580	+	0.184509i	0.331626	+	0.943411i	$0.392403\pi$
$174$		0			0
$175$	−2.63396	+	12.9639i	−0.199109	+	0.979977i
$176$		0			0
$177$	−7.68677	+	4.43796i	−0.577773	+	0.333577i
$178$		0			0
$179$	2.89470	−	5.01377i	0.216360	−	0.374747i	−0.737332	−	0.675530i	$-0.763915\pi$
$179$	2.89470	−	5.01377i	0.216360	−	0.374747i	0.953692	+	0.300784i	$0.0972482\pi$
$180$		0			0
$181$	18.6817			1.38860			0.694299	−	0.719687i	$-0.255715\pi$
$181$	18.6817			1.38860			0.694299	+	0.719687i	$0.255715\pi$
$182$		0			0
$183$		−	13.8039i		−	1.02041i
$184$		0			0
$185$	0.950413	+	5.62610i	0.0698758	+	0.413639i
$186$		0			0
$187$	−6.72123	+	3.88050i	−0.491505	+	0.283771i
$188$		0			0
$189$	2.30641	−	1.29633i	0.167767	−	0.0942939i
$190$		0			0
$191$	2.35934	+	4.08650i	0.170716	+	0.295689i	0.938670	−	0.344816i	$-0.112059\pi$
$191$	2.35934	+	4.08650i	0.170716	+	0.295689i	−0.767954	+	0.640504i	$0.778725\pi$
$192$		0			0
$193$	15.3673	+	8.87232i	1.10616	+	0.638644i	0.937833	−	0.347087i	$-0.112829\pi$
$193$	15.3673	+	8.87232i	1.10616	+	0.638644i	0.168331	+	0.985731i	$0.446162\pi$
$194$		0			0
$195$	−4.57316	−	5.53028i	−0.327491	−	0.396031i
$196$		0			0
$197$		−	24.5813i		−	1.75134i	−0.482908	−	0.875671i	$-0.660420\pi$
$197$		−	24.5813i		−	1.75134i	0.482908	−	0.875671i	$-0.339580\pi$
$198$		0			0
$199$	6.15543	−	10.6615i	0.436347	−	0.755775i	−0.561058	−	0.827777i	$-0.689605\pi$
$199$	6.15543	−	10.6615i	0.436347	−	0.755775i	0.997404	+	0.0720019i	$0.0229388\pi$
$200$		0			0
$201$	0.00817856	+	0.0141657i	0.000576871	+	0.000999170i
$202$		0			0
$203$	−11.8230	−	21.0353i	−0.829809	−	1.47639i
$204$		0			0
$205$	4.79469	−	12.8846i	0.334876	−	0.899896i
$206$		0			0
$207$	1.91330	+	1.10465i	0.132984	+	0.0767781i
$208$		0			0
$209$	11.4167			0.789711
$210$		0			0
$211$	−2.99944			−0.206490			−0.103245	−	0.994656i	$-0.532923\pi$
$211$	−2.99944			−0.206490			−0.103245	+	0.994656i	$0.532923\pi$
$212$		0			0
$213$	−4.87663	−	2.81552i	−0.334141	−	0.192917i
$214$		0			0
$215$	11.4100	+	4.24596i	0.778154	+	0.289572i
$216$		0			0
$217$	19.6264	+	0.226664i	1.33233	+	0.0153869i
$218$		0			0
$219$	−5.72227	−	9.91127i	−0.386675	−	0.669742i
$220$		0			0
$221$	−5.79730	+	10.0412i	−0.389969	+	0.675445i
$222$		0			0
$223$		−	6.11848i		−	0.409724i	−0.978791	−	0.204862i	$-0.934325\pi$
$223$		−	6.11848i		−	0.409724i	0.978791	−	0.204862i	$-0.0656745\pi$
$224$		0			0
$225$	0.938893	−	4.91106i	0.0625929	−	0.327404i
$226$		0			0
$227$	−5.29205	−	3.05537i	−0.351246	−	0.202792i	0.313988	−	0.949427i	$-0.398335\pi$
$227$	−5.29205	−	3.05537i	−0.351246	−	0.202792i	−0.665234	+	0.746635i	$0.731668\pi$
$228$		0			0
$229$	−9.55737	−	16.5539i	−0.631569	−	1.09391i	−0.987231	−	0.159295i	$-0.949078\pi$
$229$	−9.55737	−	16.5539i	−0.631569	−	1.09391i	0.355662	−	0.934615i	$-0.384255\pi$
$230$		0			0
$231$	−4.88896	−	2.89843i	−0.321670	−	0.190703i
$232$		0			0
$233$	−7.70926	+	4.45094i	−0.505050	+	0.291591i	−0.730797	−	0.682595i	$-0.760851\pi$
$233$	−7.70926	+	4.45094i	−0.505050	+	0.291591i	0.225746	+	0.974186i	$0.427518\pi$
$234$		0			0
$235$	−3.92940	−	23.2606i	−0.256326	−	1.51736i
$236$		0			0
$237$			15.3109i			0.994547i
$238$		0			0
$239$	20.4276			1.32135			0.660677	−	0.750670i	$-0.270269\pi$
$239$	20.4276			1.32135			0.660677	+	0.750670i	$0.270269\pi$
$240$		0			0
$241$	9.12759	−	15.8095i	0.587960	−	1.01838i	−0.406539	−	0.913633i	$-0.633265\pi$
$241$	9.12759	−	15.8095i	0.587960	−	1.01838i	0.994499	−	0.104743i	$-0.0334021\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	9.69358	+	12.2896i	0.619300	+	0.785154i
$246$		0			0
$247$	14.7710	−	8.52803i	0.939855	−	0.542626i
$248$		0			0
$249$	−7.01570	+	12.1516i	−0.444602	+	0.770073i
$250$		0			0
$251$	−14.5630			−0.919210			−0.459605	−	0.888123i	$-0.652009\pi$
$251$	−14.5630			−0.919210			−0.459605	+	0.888123i	$0.652009\pi$
$252$		0			0
$253$		−	4.74596i		−	0.298376i
$254$		0			0
$255$	−7.96566	+	1.34563i	−0.498829	+	0.0842669i
$256$		0			0
$257$	14.0455	−	8.10917i	0.876134	−	0.505836i	0.00675233	−	0.999977i	$-0.497851\pi$
$257$	14.0455	−	8.10917i	0.876134	−	0.505836i	0.869382	+	0.494141i	$0.164517\pi$
$258$		0			0
$259$	5.80735	+	3.44290i	0.360851	+	0.213931i
$260$		0			0
$261$	4.56017	+	7.89845i	0.282268	+	0.488902i
$262$		0			0
$263$	22.2939	+	12.8714i	1.37470	+	0.793684i	0.991516	−	0.129987i	$-0.0414937\pi$
$263$	22.2939	+	12.8714i	1.37470	+	0.793684i	0.383185	+	0.923671i	$0.374827\pi$
$264$		0			0
$265$	9.31141	−	7.69990i	0.571996	−	0.473001i
$266$		0			0
$267$		−	3.93758i		−	0.240976i
$268$		0			0
$269$	−12.7546	+	22.0916i	−0.777662	+	1.34695i	0.155623	+	0.987816i	$0.450261\pi$
$269$	−12.7546	+	22.0916i	−0.777662	+	1.34695i	−0.933286	+	0.359134i	$0.883072\pi$
$270$		0			0
$271$	−2.03508	−	3.52486i	−0.123622	−	0.214120i	0.797571	−	0.603225i	$-0.206118\pi$
$271$	−2.03508	−	3.52486i	−0.123622	−	0.214120i	−0.921194	+	0.389105i	$0.872784\pi$
$272$		0			0
$273$	−8.49042	−	0.0980552i	−0.513863	−	0.00593457i
$274$		0			0
$275$	−10.1449	+	3.52823i	−0.611760	+	0.212760i
$276$		0			0
$277$	11.3384	+	6.54626i	0.681261	+	0.393326i	0.800330	−	0.599560i	$-0.204658\pi$
$277$	11.3384	+	6.54626i	0.681261	+	0.393326i	−0.119069	+	0.992886i	$0.537991\pi$
$278$		0			0
$279$	−7.41858			−0.444139
$280$		0			0
$281$	19.5976			1.16910			0.584548	−	0.811359i	$-0.301272\pi$
$281$	19.5976			1.16910			0.584548	+	0.811359i	$0.301272\pi$
$282$		0			0
$283$	−9.06151	−	5.23167i	−0.538651	−	0.310990i	0.205881	−	0.978577i	$-0.433994\pi$
$283$	−9.06151	−	5.23167i	−0.538651	−	0.310990i	−0.744532	+	0.667587i	$0.767327\pi$
$284$		0			0
$285$	11.1376	+	4.14461i	0.659736	+	0.245505i
$286$		0			0
$287$	−7.97006	−	14.1802i	−0.470458	−	0.837033i
$288$		0			0
$289$	−1.97375	−	3.41864i	−0.116103	−	0.201096i
$290$		0			0
$291$	−2.58227	+	4.47262i	−0.151375	+	0.262190i
$292$		0			0
$293$			24.7240i			1.44439i	0.691689	+	0.722196i	$0.256867\pi$
$293$			24.7240i			1.44439i	−0.691689	+	0.722196i	$0.743133\pi$
$294$		0			0
$295$	12.6480	+	15.2951i	0.736393	+	0.890513i
$296$		0			0
$297$	1.86038	+	1.07409i	0.107950	+	0.0623251i
$298$		0			0
$299$	−3.54513	−	6.14034i	−0.205020	−	0.355105i
$300$		0			0
$301$	12.5574	−	7.05792i	0.723795	−	0.406812i
$302$		0			0
$303$	1.41253	−	0.815524i	0.0811477	−	0.0468506i
$304$		0			0
$305$	−30.4352	+	5.14140i	−1.74272	+	0.294396i
$306$		0			0
$307$			3.24574i			0.185244i	0.995701	+	0.0926220i	$0.0295248\pi$
$307$			3.24574i			0.185244i	−0.995701	+	0.0926220i	$0.970475\pi$
$308$		0			0
$309$	−2.04475			−0.116322
$310$		0			0
$311$	−6.57653	+	11.3909i	−0.372921	+	0.645918i	−0.990013	−	0.140973i	$-0.954977\pi$
$311$	−6.57653	+	11.3909i	−0.372921	+	0.645918i	0.617093	+	0.786891i	$0.288310\pi$
$312$		0			0
$313$	−13.8952	+	8.02237i	−0.785401	+	0.453451i	−0.838341	−	0.545146i	$-0.816474\pi$
$313$	−13.8952	+	8.02237i	−0.785401	+	0.453451i	0.0529400	+	0.998598i	$0.483141\pi$
$314$		0			0
$315$	−3.71723	−	4.60241i	−0.209442	−	0.259317i
$316$		0			0
$317$	−17.2712	+	9.97151i	−0.970045	+	0.560056i	−0.899250	−	0.437435i	$-0.855887\pi$
$317$	−17.2712	+	9.97151i	−0.970045	+	0.560056i	−0.0707950	+	0.997491i	$0.522554\pi$
$318$		0			0
$319$	9.79609	−	16.9673i	0.548476	−	0.949988i
$320$		0			0
$321$	6.04419			0.337354
$322$		0			0
$323$		−	19.2007i		−	1.06835i
$324$		0			0
$325$	−10.4900	+	12.1428i	−0.581880	+	0.673564i
$326$		0			0
$327$	−2.76468	+	1.59619i	−0.152887	+	0.0882694i
$328$		0			0
$329$	−24.0100	−	14.2344i	−1.32371	−	0.784766i
$330$		0			0
$331$	2.41106	+	4.17607i	0.132524	+	0.229538i	0.924649	−	0.380821i	$-0.124359\pi$
$331$	2.41106	+	4.17607i	0.132524	+	0.229538i	−0.792125	+	0.610359i	$0.791025\pi$
$332$		0			0
$333$	−2.20985	−	1.27586i	−0.121099	−	0.0699166i
$334$		0			0
$335$	0.0281867	−	0.0233085i	0.00154001	−	0.00127348i
$336$		0			0
$337$			33.7464i			1.83828i	0.393930	+	0.919140i	$0.371115\pi$
$337$			33.7464i			1.83828i	−0.393930	+	0.919140i	$0.628885\pi$
$338$		0			0
$339$	−0.551717	+	0.955601i	−0.0299651	+	0.0519011i
$340$		0			0
$341$	7.96823	+	13.8014i	0.431504	+	0.747387i
$342$		0			0
$343$	18.5091	+	0.641510i	0.999400	+	0.0346383i
$344$		0			0
$345$	1.72293	−	4.62994i	0.0927592	−	0.249268i
$346$		0			0
$347$	−14.3247	−	8.27040i	−0.768993	−	0.443978i	0.0635224	−	0.997980i	$-0.479767\pi$
$347$	−14.3247	−	8.27040i	−0.768993	−	0.443978i	−0.832515	+	0.554002i	$0.813100\pi$
$348$		0			0
$349$	−21.0842			−1.12861			−0.564306	−	0.825566i	$-0.690856\pi$
$349$	−21.0842			−1.12861			−0.564306	+	0.825566i	$0.690856\pi$
$350$		0			0
$351$	3.20929			0.171299
$352$		0			0
$353$	26.0702	+	15.0516i	1.38758	+	0.801118i	0.993042	−	0.117763i	$-0.0375724\pi$
$353$	26.0702	+	15.0516i	1.38758	+	0.801118i	0.394535	+	0.918881i	$0.370906\pi$
$354$		0			0
$355$	−4.39140	+	11.8008i	−0.233071	+	0.626322i
$356$		0			0
$357$	−4.87459	+	8.22227i	−0.257991	+	0.435169i
$358$		0			0
$359$	−14.5305	−	25.1675i	−0.766889	−	1.32829i	−0.939242	−	0.343255i	$-0.888470\pi$
$359$	−14.5305	−	25.1675i	−0.766889	−	1.32829i	0.172353	−	0.985035i	$-0.444863\pi$
$360$		0			0
$361$	−4.62244	+	8.00629i	−0.243286	+	0.421384i
$362$		0			0
$363$			6.38531i			0.335142i
$364$		0			0
$365$	−19.7213	+	16.3082i	−1.03226	+	0.853610i
$366$		0			0
$367$	0.973001	+	0.561762i	0.0507902	+	0.0293237i	0.525180	−	0.850991i	$-0.323998\pi$
$367$	0.973001	+	0.561762i	0.0507902	+	0.0293237i	−0.474390	+	0.880315i	$0.657331\pi$
$368$		0			0
$369$	3.07409	+	5.32448i	0.160031	+	0.277182i
$370$		0			0
$371$	0.165097	−	14.2955i	0.00857141	−	0.742183i
$372$		0			0
$373$	21.3121	−	12.3045i	1.10350	−	0.637105i	0.166361	−	0.986065i	$-0.446798\pi$
$373$	21.3121	−	12.3045i	1.10350	−	0.637105i	0.937138	+	0.348960i	$0.113465\pi$
$374$		0			0
$375$	−11.1777	−	0.240925i	−0.577216	−	0.0124413i
$376$		0			0
$377$		−	29.2698i		−	1.50747i
$378$		0			0
$379$	−28.0997			−1.44338			−0.721692	−	0.692214i	$-0.756635\pi$
$379$	−28.0997			−1.44338			−0.721692	+	0.692214i	$0.756635\pi$
$380$		0			0
$381$	−9.83990	+	17.0432i	−0.504114	+	0.873150i
$382$		0			0
$383$	−24.9444	+	14.4017i	−1.27460	+	0.735891i	−0.975850	−	0.218441i	$-0.929903\pi$
$383$	−24.9444	+	14.4017i	−1.27460	+	0.735891i	−0.298750	+	0.954331i	$0.596570\pi$
$384$		0			0
$385$	−4.56960	+	11.8589i	−0.232888	+	0.604384i
$386$		0			0
$387$	−4.71512	+	2.72227i	−0.239683	+	0.138381i
$388$		0			0
$389$	7.06901	−	12.2439i	0.358413	−	0.620789i	−0.629283	−	0.777176i	$-0.716651\pi$
$389$	7.06901	−	12.2439i	0.358413	−	0.620789i	0.987696	+	0.156387i	$0.0499847\pi$
$390$		0			0
$391$	−7.98178			−0.403656
$392$		0			0
$393$		−	15.1463i		−	0.764031i
$394$		0			0
$395$	33.7578	−	5.70269i	1.69854	−	0.286933i
$396$		0			0
$397$	12.2230	−	7.05696i	0.613455	−	0.354178i	−0.160861	−	0.986977i	$-0.551427\pi$
$397$	12.2230	−	7.05696i	0.613455	−	0.354178i	0.774316	+	0.632799i	$0.218094\pi$
$398$		0			0
$399$	12.2576	−	6.88945i	0.613649	−	0.344904i
$400$		0			0
$401$	0.727736	+	1.26048i	0.0363414	+	0.0629451i	0.883624	−	0.468197i	$-0.155096\pi$
$401$	0.727736	+	1.26048i	0.0363414	+	0.0629451i	−0.847283	+	0.531142i	$0.821763\pi$
$402$		0			0
$403$	20.6187	+	11.9042i	1.02709	+	0.592990i
$404$		0			0
$405$	1.42497	+	1.72321i	0.0708076	+	0.0856269i
$406$		0			0
$407$			5.48155i			0.271711i
$408$		0			0
$409$	18.1980	−	31.5199i	0.899835	−	1.55856i	0.0721304	−	0.997395i	$-0.477020\pi$
$409$	18.1980	−	31.5199i	0.899835	−	1.55856i	0.827704	−	0.561164i	$-0.189646\pi$
$410$		0			0
$411$	−3.84608	−	6.66160i	−0.189713	−	0.328593i
$412$		0			0
$413$	23.4819	+	0.271191i	1.15547	+	0.0133444i
$414$		0			0
$415$	29.4052	+	10.9425i	1.44344	+	0.537144i
$416$		0			0
$417$	4.19186	+	2.42017i	0.205276	+	0.118516i
$418$		0			0
$419$	−31.9369			−1.56022			−0.780109	−	0.625644i	$-0.784836\pi$
$419$	−31.9369			−1.56022			−0.780109	+	0.625644i	$0.784836\pi$
$420$		0			0
$421$	−35.5151			−1.73090			−0.865450	−	0.500995i	$-0.832967\pi$
$421$	−35.5151			−1.73090			−0.865450	+	0.500995i	$0.832967\pi$
$422$		0			0
$423$	9.13644	+	5.27492i	0.444229	+	0.256476i
$424$		0			0
$425$	5.93379	+	17.0617i	0.287831	+	0.827615i
$426$		0			0
$427$	−18.6249	+	31.4157i	−0.901320	+	1.52031i
$428$		0			0
$429$	−3.44707	−	5.97050i	−0.166426	−	0.288259i
$430$		0			0
$431$	−8.29315	+	14.3642i	−0.399467	+	0.691897i	−0.993660	−	0.112425i	$-0.964138\pi$
$431$	−8.29315	+	14.3642i	−0.399467	+	0.691897i	0.594193	+	0.804322i	$0.297471\pi$
$432$		0			0
$433$			38.2014i			1.83584i	0.396764	+	0.917921i	$0.370133\pi$
$433$			38.2014i			1.83584i	−0.396764	+	0.917921i	$0.629867\pi$
$434$		0			0
$435$	15.7163	−	12.9963i	0.753537	−	0.623123i
$436$		0			0
$437$	10.1684	+	5.87074i	0.486421	+	0.280835i
$438$		0			0
$439$	5.97266	+	10.3450i	0.285060	+	0.493738i	0.972624	−	0.232386i	$-0.0746532\pi$
$439$	5.97266	+	10.3450i	0.285060	+	0.493738i	−0.687564	+	0.726124i	$0.741320\pi$
$440$		0			0
$441$	−6.99813	−	0.161663i	−0.333244	−	0.00769825i
$442$		0			0
$443$	−31.0118	+	17.9047i	−1.47341	+	0.850676i	−0.999552	−	0.0299229i	$-0.990474\pi$
$443$	−31.0118	+	17.9047i	−1.47341	+	0.850676i	−0.473862	+	0.880599i	$0.657141\pi$
$444$		0			0
$445$	−8.68170	+	1.46659i	−0.411552	+	0.0695232i
$446$		0			0
$447$			8.97216i			0.424369i
$448$		0			0
$449$	−25.5848			−1.20742			−0.603711	−	0.797203i	$-0.706312\pi$
$449$	−25.5848			−1.20742			−0.603711	+	0.797203i	$0.706312\pi$
$450$		0			0
$451$	6.60371	−	11.4380i	0.310957	−	0.538593i
$452$		0			0
$453$	3.18842	−	1.84084i	0.149805	−	0.0864901i
$454$		0			0
$455$	2.94615	+	18.7564i	0.138118	+	0.879316i
$456$		0			0
$457$	−3.11577	+	1.79889i	−0.145749	+	0.0841484i	−0.571101	−	0.820880i	$-0.693484\pi$
$457$	−3.11577	+	1.79889i	−0.145749	+	0.0841484i	0.425352	+	0.905028i	$0.360150\pi$
$458$		0			0
$459$	1.80641	−	3.12880i	0.0843161	−	0.146040i
$460$		0			0
$461$	32.8037			1.52782			0.763911	−	0.645322i	$-0.223277\pi$
$461$	32.8037			1.52782			0.763911	+	0.645322i	$0.223277\pi$
$462$		0			0
$463$		−	9.28219i		−	0.431380i	−0.976462	−	0.215690i	$-0.930800\pi$
$463$		−	9.28219i		−	0.431380i	0.976462	−	0.215690i	$-0.0692000\pi$
$464$		0			0
$465$	2.76313	+	16.3567i	0.128137	+	0.758524i
$466$		0			0
$467$	3.72400	−	2.15005i	0.172326	−	0.0994925i	−0.411356	−	0.911475i	$-0.634945\pi$
$467$	3.72400	−	2.15005i	0.172326	−	0.0994925i	0.583682	+	0.811982i	$0.301611\pi$
$468$		0			0
$469$	0.000499768	−	0.0432740i	2.30771e−5	−	0.00199821i
$470$		0			0
$471$	−4.53349	−	7.85224i	−0.208892	−	0.361812i
$472$		0			0
$473$	10.1289	+	5.84794i	0.465729	+	0.268889i
$474$		0			0
$475$	4.98983	−	26.1003i	0.228949	−	1.19756i
$476$		0			0
$477$			5.40353i			0.247411i
$478$		0			0
$479$	9.88588	−	17.1228i	0.451697	−	0.782363i	−0.546794	−	0.837267i	$-0.684152\pi$
$479$	9.88588	−	17.1228i	0.451697	−	0.782363i	0.998492	+	0.0549041i	$0.0174853\pi$
$480$		0			0
$481$	4.09460	+	7.09205i	0.186698	+	0.323370i
$482$		0			0
$483$	−2.86396	−	5.09553i	−0.130315	−	0.231855i
$484$		0			0
$485$	10.8232	+	4.02759i	0.491455	+	0.182883i
$486$		0			0
$487$	−37.7796	−	21.8121i	−1.71196	−	0.988399i	−0.931918	−	0.362669i	$-0.881866\pi$
$487$	−37.7796	−	21.8121i	−1.71196	−	0.988399i	−0.780039	−	0.625730i	$-0.784801\pi$
$488$		0			0
$489$	−4.92928			−0.222910
$490$		0			0
$491$	−3.23582			−0.146030			−0.0730152	−	0.997331i	$-0.523262\pi$
$491$	−3.23582			−0.146030			−0.0730152	+	0.997331i	$0.523262\pi$
$492$		0			0
$493$	−28.5357	−	16.4751i	−1.28518	−	0.742001i
$494$		0			0
$495$	1.67527	−	4.50188i	0.0752978	−	0.202344i
$496$		0			0
$497$	7.29968	+	12.9875i	0.327435	+	0.582570i
$498$		0			0
$499$	−13.7353	−	23.7902i	−0.614875	−	1.06499i	−0.990406	−	0.138185i	$-0.955873\pi$
$499$	−13.7353	−	23.7902i	−0.614875	−	1.06499i	0.375532	−	0.926809i	$-0.377460\pi$
$500$		0			0
$501$	8.54598	−	14.8021i	0.381806	−	0.661308i
$502$		0			0
$503$		−	25.2182i		−	1.12442i	−0.826993	−	0.562212i	$-0.809951\pi$
$503$		−	25.2182i		−	1.12442i	0.826993	−	0.562212i	$-0.190049\pi$
$504$		0			0
$505$	−2.32420	−	2.81063i	−0.103426	−	0.125072i
$506$		0			0
$507$	2.33866	+	1.35023i	0.103864	+	0.0599657i
$508$		0			0
$509$	−9.01822	−	15.6200i	−0.399726	−	0.692345i	0.593966	−	0.804490i	$-0.297561\pi$
$509$	−9.01822	−	15.6200i	−0.399726	−	0.692345i	−0.993692	+	0.112145i	$0.964228\pi$
$510$		0			0
$511$	−0.349671	+	30.2774i	−0.0154686	+	1.33939i
$512$		0			0
$513$	−4.60257	+	2.65730i	−0.203208	+	0.117322i
$514$		0			0
$515$	0.761588	+	4.50833i	0.0335596	+	0.198661i
$516$		0			0
$517$		−	22.6630i		−	0.996718i
$518$		0			0
$519$	−4.85368			−0.213053
$520$		0			0
$521$	−0.419891	+	0.727272i	−0.0183957	+	0.0318624i	−0.875077	−	0.483984i	$-0.839189\pi$
$521$	−0.419891	+	0.727272i	−0.0183957	+	0.0318624i	0.856681	+	0.515847i	$0.172523\pi$
$522$		0			0
$523$	−34.9852	+	20.1987i	−1.52979	+	0.883227i	−0.530424	+	0.847732i	$0.677967\pi$
$523$	−34.9852	+	20.1987i	−1.52979	+	0.883227i	−0.999370	+	0.0354945i	$0.988699\pi$
$524$		0			0
$525$	−8.76302	+	9.91007i	−0.382450	+	0.432511i
$526$		0			0
$527$	23.2112	−	13.4010i	1.01110	−	0.583757i
$528$		0			0
$529$	−9.05952	+	15.6915i	−0.393892	+	0.682241i
$530$		0			0
$531$	−8.87592			−0.385182
$532$		0			0
$533$		−	19.7313i		−	0.854658i
$534$		0			0
$535$	−2.25122	−	13.3264i	−0.0973288	−	0.576151i
$536$		0			0
$537$	5.01377	−	2.89470i	0.216360	−	0.124916i
$538$		0			0
$539$	7.21588	+	13.1928i	0.310810	+	0.568256i
$540$		0			0
$541$	11.7087	+	20.2801i	0.503398	+	0.871911i	0.999992	+	0.00392786i	$0.00125028\pi$
$541$	11.7087	+	20.2801i	0.503398	+	0.871911i	−0.496595	+	0.867983i	$0.665416\pi$
$542$		0			0
$543$	16.1788	+	9.34084i	0.694299	+	0.400854i
$544$		0			0
$545$	4.54906	+	5.50113i	0.194860	+	0.235642i
$546$		0			0
$547$			7.66719i			0.327825i	0.986475	+	0.163913i	$0.0524115\pi$
$547$			7.66719i			0.327825i	−0.986475	+	0.163913i	$0.947588\pi$
$548$		0			0
$549$	6.90194	−	11.9545i	0.294568	−	0.510206i
$550$		0			0
$551$	24.2355	+	41.9770i	1.03247	+	1.78828i
$552$		0			0
$553$	20.6581	−	34.8453i	0.878473	−	1.48177i
$554$		0			0
$555$	−1.98997	+	5.34755i	−0.0844694	+	0.226991i
$556$		0			0
$557$	−21.2576	−	12.2731i	−0.900712	−	0.520026i	−0.0232807	−	0.999729i	$-0.507411\pi$
$557$	−21.2576	−	12.2731i	−0.900712	−	0.520026i	−0.877431	+	0.479703i	$0.840744\pi$
$558$		0			0
$559$	17.4731			0.739035
$560$		0			0
$561$	−7.76101			−0.327670
$562$		0			0
$563$	−4.01222	−	2.31646i	−0.169095	−	0.0976270i	0.413064	−	0.910702i	$-0.364459\pi$
$563$	−4.01222	−	2.31646i	−0.169095	−	0.0976270i	−0.582159	+	0.813075i	$0.697792\pi$
$564$		0			0
$565$	2.31243	+	0.860517i	0.0972847	+	0.0362022i
$566$		0			0
$567$	2.64557	+	0.0305535i	0.111104	+	0.00128313i
$568$		0			0
$569$	5.47818	+	9.48849i	0.229657	+	0.397778i	0.957707	−	0.287747i	$-0.0929061\pi$
$569$	5.47818	+	9.48849i	0.229657	+	0.397778i	−0.728049	+	0.685525i	$0.759573\pi$
$570$		0			0
$571$	4.07044	−	7.05021i	0.170343	−	0.295042i	−0.768197	−	0.640213i	$-0.778846\pi$
$571$	4.07044	−	7.05021i	0.170343	−	0.295042i	0.938540	+	0.345171i	$0.112179\pi$
$572$		0			0
$573$			4.71868i			0.197126i
$574$		0			0
$575$	−10.8499	−	2.07429i	−0.452474	−	0.0865037i
$576$		0			0
$577$	0.347371	+	0.200555i	0.0144612	+	0.00834921i	0.507213	−	0.861821i	$-0.330676\pi$
$577$	0.347371	+	0.200555i	0.0144612	+	0.00834921i	−0.492752	+	0.870170i	$0.664009\pi$
$578$		0			0
$579$	8.87232	+	15.3673i	0.368721	+	0.638644i
$580$		0			0
$581$	32.3622	−	18.1893i	1.34261	−	0.754619i
$582$		0			0
$583$	10.0526	−	5.80389i	0.416337	−	0.240373i
$584$		0			0
$585$	−1.19533	−	7.07594i	−0.0494210	−	0.292554i
$586$		0			0
$587$			8.46651i			0.349450i	0.984617	+	0.174725i	$0.0559037\pi$
$587$			8.46651i			0.349450i	−0.984617	+	0.174725i	$0.944096\pi$
$588$		0			0
$589$	−39.4267			−1.62455
$590$		0			0
$591$	12.2906	−	21.2880i	0.505569	−	0.875671i
$592$		0			0
$593$	−14.0455	+	8.10917i	−0.576780	+	0.333004i	−0.759852	−	0.650096i	$-0.774729\pi$
$593$	−14.0455	+	8.10917i	−0.576780	+	0.333004i	0.183073	+	0.983099i	$0.441396\pi$
$594$		0			0
$595$	19.9443	+	7.68518i	0.817637	+	0.315062i
$596$		0			0
$597$	10.6615	−	6.15543i	0.436347	−	0.251925i
$598$		0			0
$599$	8.30276	−	14.3808i	0.339242	−	0.587584i	−0.645049	−	0.764141i	$-0.723163\pi$
$599$	8.30276	−	14.3808i	0.339242	−	0.587584i	0.984290	+	0.176558i	$0.0564962\pi$
$600$		0			0
$601$	29.7659			1.21418			0.607088	−	0.794635i	$-0.292338\pi$
$601$	29.7659			1.21418			0.607088	+	0.794635i	$0.292338\pi$
$602$		0			0
$603$			0.0163571i			0.000666114i
$604$		0			0
$605$	14.0785	−	2.37827i	0.572373	−	0.0966906i
$606$		0			0
$607$	−8.90178	+	5.13945i	−0.361312	+	0.208604i	−0.669656	−	0.742671i	$-0.733559\pi$
$607$	−8.90178	+	5.13945i	−0.361312	+	0.208604i	0.308344	+	0.951275i	$0.400225\pi$
$608$		0			0
$609$	0.278659	−	24.1286i	0.0112918	−	0.977739i
$610$		0			0
$611$	−16.9288	−	29.3215i	−0.684864	−	1.18622i
$612$		0			0
$613$	−24.7625	−	14.2967i	−1.00015	−	0.577437i	−0.0918571	−	0.995772i	$-0.529280\pi$
$613$	−24.7625	−	14.2967i	−1.00015	−	0.577437i	−0.908293	+	0.418336i	$0.862614\pi$
$614$		0			0
$615$	10.5946	−	8.76101i	0.427215	−	0.353278i
$616$		0			0
$617$		−	31.1625i		−	1.25456i	−0.778796	−	0.627278i	$-0.784169\pi$
$617$		−	31.1625i		−	1.25456i	0.778796	−	0.627278i	$-0.215831\pi$
$618$		0			0
$619$	−4.48852	+	7.77435i	−0.180409	+	0.312477i	−0.942020	−	0.335557i	$-0.891075\pi$
$619$	−4.48852	+	7.77435i	−0.180409	+	0.312477i	0.761611	+	0.648035i	$0.224409\pi$
$620$		0			0
$621$	1.10465	+	1.91330i	0.0443279	+	0.0767781i
$622$		0			0
$623$	−5.31277	+	8.96138i	−0.212852	+	0.359030i
$624$		0			0
$625$	3.63207	+	24.7348i	0.145283	+	0.989390i
$626$		0			0
$627$	9.88716	+	5.70836i	0.394855	+	0.227970i
$628$		0			0
$629$	9.21890			0.367582
$630$		0			0
$631$	−23.3961			−0.931383			−0.465691	−	0.884947i	$-0.654194\pi$
$631$	−23.3961			−0.931383			−0.465691	+	0.884947i	$0.654194\pi$
$632$		0			0
$633$	−2.59759	−	1.49972i	−0.103245	−	0.0596086i
$634$		0			0
$635$	41.2424	+	15.3474i	1.63665	+	0.609043i
$636$		0			0
$637$	19.1907	+	11.6788i	0.760363	+	0.462732i
$638$		0			0
$639$	−2.81552	−	4.87663i	−0.111380	−	0.192917i
$640$		0			0
$641$	5.76625	−	9.98743i	0.227753	−	0.394480i	−0.729389	−	0.684099i	$-0.760195\pi$
$641$	5.76625	−	9.98743i	0.227753	−	0.394480i	0.957142	+	0.289620i	$0.0935288\pi$
$642$		0			0
$643$		−	34.3755i		−	1.35564i	−0.735229	−	0.677819i	$-0.762925\pi$
$643$		−	34.3755i		−	1.35564i	0.735229	−	0.677819i	$-0.237075\pi$
$644$		0			0
$645$	7.75835	+	9.38209i	0.305485	+	0.369420i
$646$		0			0
$647$	21.6244	+	12.4849i	0.850144	+	0.490831i	0.860699	−	0.509113i	$-0.170027\pi$
$647$	21.6244	+	12.4849i	0.850144	+	0.490831i	−0.0105554	+	0.999944i	$0.503360\pi$
$648$		0			0
$649$	9.53355	+	16.5126i	0.374225	+	0.648176i
$650$		0			0
$651$	16.8836	+	10.0095i	0.661722	+	0.392303i
$652$		0			0
$653$	24.0610	−	13.8916i	0.941579	−	0.543621i	0.0511243	−	0.998692i	$-0.483720\pi$
$653$	24.0610	−	13.8916i	0.941579	−	0.543621i	0.890455	+	0.455071i	$0.150386\pi$
$654$		0			0
$655$	−33.3950	+	5.64140i	−1.30485	+	0.220428i
$656$		0			0
$657$		−	11.4445i		−	0.446494i
$658$		0			0
$659$	39.1662			1.52570			0.762850	−	0.646575i	$-0.223799\pi$
$659$	39.1662			1.52570			0.762850	+	0.646575i	$0.223799\pi$
$660$		0			0
$661$	−7.13885	+	12.3649i	−0.277669	+	0.480937i	−0.970805	−	0.239870i	$-0.922895\pi$
$661$	−7.13885	+	12.3649i	−0.277669	+	0.480937i	0.693136	+	0.720807i	$0.256229\pi$
$662$		0			0
$663$	−10.0412	+	5.79730i	−0.389969	+	0.225148i
$664$		0			0
$665$	−19.7555	−	24.4599i	−0.766087	−	0.948516i
$666$		0			0
$667$	17.4500	−	10.0747i	0.675666	−	0.390096i
$668$		0			0
$669$	3.05924	−	5.29876i	0.118277	−	0.204862i
$670$		0			0
$671$	−29.6533			−1.14475
$672$		0			0
$673$		−	19.5978i		−	0.755439i	−0.925920	−	0.377719i	$-0.876708\pi$
$673$		−	19.5978i		−	0.755439i	0.925920	−	0.377719i	$-0.123292\pi$
$674$		0			0
$675$	3.26863	−	3.78365i	0.125810	−	0.145633i
$676$		0			0
$677$	0.121354	−	0.0700638i	0.00466402	−	0.00269277i	−0.497666	−	0.867369i	$-0.665810\pi$
$677$	0.121354	−	0.0700638i	0.00466402	−	0.00269277i	0.502330	+	0.864676i	$0.332476\pi$
$678$		0			0
$679$	11.9116	−	6.69493i	0.457124	−	0.256928i
$680$		0			0
$681$	−3.05537	−	5.29205i	−0.117082	−	0.202792i
$682$		0			0
$683$	21.0805	+	12.1708i	0.806623	+	0.465704i	0.845782	−	0.533529i	$-0.179134\pi$
$683$	21.0805	+	12.1708i	0.806623	+	0.465704i	−0.0391587	+	0.999233i	$0.512468\pi$
$684$		0			0
$685$	−13.2552	+	10.9611i	−0.506455	+	0.418803i
$686$		0			0
$687$		−	19.1147i		−	0.729273i
$688$		0			0
$689$	8.67075	−	15.0182i	0.330329	−	0.572147i
$690$		0			0
$691$	2.82420	+	4.89166i	0.107438	+	0.186088i	0.914732	−	0.404062i	$-0.132402\pi$
$691$	2.82420	+	4.89166i	0.107438	+	0.186088i	−0.807294	+	0.590150i	$0.799069\pi$
$692$		0			0
$693$	−2.78475	−	4.95459i	−0.105784	−	0.188209i
$694$		0			0
$695$	3.77476	−	10.1437i	0.143185	−	0.384774i
$696$		0			0
$697$	−19.2364	−	11.1062i	−0.728631	−	0.420675i
$698$		0			0
$699$	−8.90189			−0.336700
$700$		0			0
$701$	−13.4269			−0.507126			−0.253563	−	0.967319i	$-0.581603\pi$
$701$	−13.4269			−0.507126			−0.253563	+	0.967319i	$0.581603\pi$
$702$		0			0
$703$	−11.7445	−	6.78066i	−0.442951	−	0.255738i
$704$		0			0
$705$	8.22735	−	22.1090i	0.309860	−	0.832673i
$706$		0			0
$707$	−4.31506	−	0.0498343i	−0.162285	−	0.00187421i
$708$		0			0
$709$	7.42900	+	12.8674i	0.279002	+	0.483246i	0.971137	−	0.238522i	$-0.0766630\pi$
$709$	7.42900	+	12.8674i	0.279002	+	0.483246i	−0.692135	+	0.721768i	$0.743330\pi$
$710$		0			0
$711$	−7.65543	+	13.2596i	−0.287101	+	0.497273i
$712$		0			0
$713$			16.3898i			0.613803i
$714$		0			0
$715$	−11.8800	+	9.82398i	−0.444288	+	0.367396i
$716$		0			0
$717$	17.6909	+	10.2138i	0.660677	+	0.381442i
$718$		0			0
$719$	−23.4746	−	40.6592i	−0.875455	−	1.51633i	−0.856277	−	0.516516i	$-0.827229\pi$
$719$	−23.4746	−	40.6592i	−0.875455	−	1.51633i	−0.0191777	−	0.999816i	$-0.506105\pi$
$720$		0			0
$721$	4.65356	+	2.75887i	0.173308	+	0.102746i
$722$		0			0
$723$	15.8095	−	9.12759i	0.587960	−	0.339459i
$724$		0			0
$725$	−34.5082	−	29.8111i	−1.28160	−	1.10716i
$726$		0			0
$727$		−	15.3550i		−	0.569487i	−0.958604	−	0.284744i	$-0.908092\pi$
$727$		−	15.3550i		−	0.569487i	0.958604	−	0.284744i	$-0.0919085\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	9.83510	−	17.0349i	0.363764	−	0.630058i
$732$		0			0
$733$	−43.4125	+	25.0642i	−1.60348	+	0.925769i	−0.612694	+	0.790320i	$0.709914\pi$
$733$	−43.4125	+	25.0642i	−1.60348	+	0.925769i	−0.990784	+	0.135449i	$0.956752\pi$
$734$		0			0
$735$	2.25009	+	15.4899i	0.0829957	+	0.571354i
$736$		0			0
$737$	0.0304305	−	0.0175690i	0.00112092	−	0.000647164i
$738$		0			0
$739$	−9.99972	+	17.3200i	−0.367846	+	0.637127i	−0.989228	−	0.146380i	$-0.953238\pi$
$739$	−9.99972	+	17.3200i	−0.367846	+	0.637127i	0.621383	+	0.783507i	$0.286571\pi$
$740$		0			0
$741$	17.0561			0.626570
$742$		0			0
$743$		−	28.2183i		−	1.03523i	−0.855613	−	0.517615i	$-0.826820\pi$
$743$		−	28.2183i		−	1.03523i	0.855613	−	0.517615i	$-0.173180\pi$
$744$		0			0
$745$	19.7821	−	3.34178i	0.724760	−	0.122433i
$746$		0			0
$747$	−12.1516	+	7.01570i	−0.444602	+	0.256691i
$748$		0			0
$749$	−13.7557	−	8.15511i	−0.502623	−	0.297981i
$750$		0			0
$751$	0.455250	+	0.788516i	0.0166123	+	0.0287734i	0.874212	−	0.485544i	$-0.161379\pi$
$751$	0.455250	+	0.788516i	0.0166123	+	0.0287734i	−0.857600	+	0.514318i	$0.828045\pi$
$752$		0			0
$753$	−12.6120	−	7.28151i	−0.459605	−	0.265353i
$754$		0			0
$755$	−5.24630	−	6.34429i	−0.190932	−	0.230892i
$756$		0			0
$757$		−	27.3441i		−	0.993839i	−0.867797	−	0.496920i	$-0.834464\pi$
$757$		−	27.3441i		−	0.993839i	0.867797	−	0.496920i	$-0.165536\pi$
$758$		0			0
$759$	2.37298	−	4.11012i	0.0861337	−	0.149188i
$760$		0			0
$761$	5.94922	+	10.3043i	0.215659	+	0.373532i	0.953476	−	0.301468i	$-0.0974767\pi$
$761$	5.94922	+	10.3043i	0.215659	+	0.373532i	−0.737817	+	0.675001i	$0.764143\pi$
$762$		0			0
$763$	8.44567	+	0.0975384i	0.305754	+	0.00353113i
$764$		0			0
$765$	−7.57128	−	2.81748i	−0.273740	−	0.101866i
$766$		0			0
$767$	24.6691	+	14.2427i	0.890749	+	0.514274i
$768$		0			0
$769$	1.97760			0.0713140			0.0356570	−	0.999364i	$-0.488648\pi$
$769$	1.97760			0.0713140			0.0356570	+	0.999364i	$0.488648\pi$
$770$		0			0
$771$	16.2183			0.584089
$772$		0			0
$773$	−28.2051	−	16.2842i	−1.01447	−	0.585703i	−0.101971	−	0.994787i	$-0.532515\pi$
$773$	−28.2051	−	16.2842i	−1.01447	−	0.585703i	−0.912497	+	0.409084i	$0.865848\pi$
$774$		0			0
$775$	35.0346	−	12.1844i	1.25848	−	0.437678i
$776$		0			0
$777$	3.30786	+	5.88531i	0.118669	+	0.211134i
$778$		0			0
$779$	16.3375	+	28.2974i	0.585353	+	1.01386i
$780$		0			0
$781$	−6.04826	+	10.4759i	−0.216424	+	0.374857i
$782$		0			0
$783$			9.12035i			0.325935i
$784$		0			0
$785$	−15.6243	+	12.9202i	−0.557655	+	0.461143i
$786$		0			0
$787$	16.0568	+	9.27040i	0.572363	+	0.330454i	0.758093	−	0.652147i	$-0.226131\pi$
$787$	16.0568	+	9.27040i	0.572363	+	0.330454i	−0.185730	+	0.982601i	$0.559465\pi$
$788$		0			0
$789$	12.8714	+	22.2939i	0.458234	+	0.793684i
$790$		0			0
$791$	2.54497	−	1.43041i	0.0904888	−	0.0508595i
$792$		0			0
$793$	−38.3655	+	22.1503i	−1.36240	+	0.786582i
$794$		0			0
$795$	11.9139	−	2.01260i	0.422541	−	0.0713796i
$796$		0			0
$797$			40.8182i			1.44586i	0.690924	+	0.722928i	$0.257204\pi$
$797$			40.8182i			1.44586i	−0.690924	+	0.722928i	$0.742796\pi$
$798$		0			0
$799$	−38.1147			−1.34840
$800$		0			0
$801$	1.96879	−	3.41005i	0.0695638	−	0.120488i
$802$		0			0
$803$	−21.2912	+	12.2925i	−0.751351	+	0.433793i
$804$		0			0
$805$	−10.1681	+	8.21243i	−0.358377	+	0.289450i
$806$		0			0
$807$	−22.0916	+	12.7546i	−0.777662	+	0.448984i
$808$		0			0
$809$	−14.2270	+	24.6419i	−0.500195	+	0.866362i	0.499805	+	0.866138i	$0.333405\pi$
$809$	−14.2270	+	24.6419i	−0.500195	+	0.866362i	−1.00000		0.000224716i	$0.999928\pi$
$810$		0			0
$811$	−39.2740			−1.37910			−0.689548	−	0.724240i	$-0.742191\pi$
$811$	−39.2740			−1.37910			−0.689548	+	0.724240i	$0.742191\pi$
$812$		0			0
$813$		−	4.07016i		−	0.142747i
$814$		0			0
$815$	1.83596	+	10.8682i	0.0643109	+	0.380697i
$816$		0			0
$817$	−25.0589	+	14.4678i	−0.876701	+	0.506163i
$818$		0			0
$819$	−7.30389	−	4.33013i	−0.255219	−	0.151307i
$820$		0			0
$821$	−17.5200	−	30.3454i	−0.611451	−	1.05906i	−0.990996	−	0.133890i	$-0.957253\pi$
$821$	−17.5200	−	30.3454i	−0.611451	−	1.05906i	0.379546	−	0.925173i	$-0.376080\pi$
$822$		0			0
$823$	48.0872	+	27.7632i	1.67622	+	0.967763i	0.964038	+	0.265763i	$0.0856238\pi$
$823$	48.0872	+	27.7632i	1.67622	+	0.967763i	0.712177	+	0.702000i	$0.247710\pi$
$824$		0			0
$825$	−10.5498	−	2.01691i	−0.367299	−	0.0702199i
$826$		0			0
$827$			6.07933i			0.211399i	0.994398	+	0.105700i	$0.0337082\pi$
$827$			6.07933i			0.211399i	−0.994398	+	0.105700i	$0.966292\pi$
$828$		0			0
$829$	1.06456	−	1.84388i	0.0369738	−	0.0640405i	−0.846946	−	0.531678i	$-0.821562\pi$
$829$	1.06456	−	1.84388i	0.0369738	−	0.0640405i	0.883920	+	0.467638i	$0.154895\pi$
$830$		0			0
$831$	6.54626	+	11.3384i	0.227087	+	0.393326i
$832$		0			0
$833$	22.1878	−	12.1357i	0.768761	−	0.420477i
$834$		0			0
$835$	−35.8191	−	13.3292i	−1.23957	−	0.461277i
$836$		0			0
$837$	−6.42468	−	3.70929i	−0.222069	−	0.128212i
$838$		0			0
$839$	33.0636			1.14148			0.570740	−	0.821131i	$-0.306656\pi$
$839$	33.0636			1.14148			0.570740	+	0.821131i	$0.306656\pi$
$840$		0			0
$841$	54.1807			1.86830
$842$		0			0
$843$	16.9720	+	9.79881i	0.584548	+	0.337489i
$844$		0			0
$845$	2.10596	−	5.65926i	0.0724473	−	0.194685i
$846$		0			0
$847$	8.61536	−	14.5321i	0.296027	−	0.499327i
$848$		0			0
$849$	−5.23167	−	9.06151i	−0.179550	−	0.310990i
$850$		0			0
$851$	−2.81874	+	4.88220i	−0.0966252	+	0.167360i
$852$		0			0
$853$			15.3223i			0.524627i	0.964983	+	0.262313i	$0.0844854\pi$
$853$			15.3223i			0.524627i	−0.964983	+	0.262313i	$0.915515\pi$
$854$		0			0
$855$	7.57316	+	9.15815i	0.258997	+	0.313202i
$856$		0			0
$857$	2.02698	+	1.17028i	0.0692404	+	0.0399760i	0.534221	−	0.845345i	$-0.320605\pi$
$857$	2.02698	+	1.17028i	0.0692404	+	0.0399760i	−0.464980	+	0.885321i	$0.653939\pi$
$858$		0			0
$859$	27.7053	+	47.9869i	0.945292	+	1.63729i	0.755166	+	0.655534i	$0.227556\pi$
$859$	27.7053	+	47.9869i	0.945292	+	1.63729i	0.190126	+	0.981760i	$0.439110\pi$
$860$		0			0
$861$	0.187849	−	16.2655i	0.00640187	−	0.554326i
$862$		0			0
$863$	−8.87751	+	5.12543i	−0.302194	+	0.174472i	−0.643428	−	0.765507i	$-0.722488\pi$
$863$	−8.87751	+	5.12543i	−0.302194	+	0.174472i	0.341234	+	0.939978i	$0.389155\pi$
$864$		0			0
$865$	1.80781	+	10.7015i	0.0614672	+	0.363863i
$866$		0			0
$867$		−	3.94751i		−	0.134064i
$868$		0			0
$869$	32.8905			1.11573
$870$		0			0
$871$	0.0262474	−	0.0454618i	0.000889359	−	0.00154041i
$872$		0			0
$873$	−4.47262	+	2.58227i	−0.151375	+	0.0873966i
$874$		0			0
$875$	25.1139	+	15.6299i	0.849005	+	0.528386i
$876$		0			0
$877$	−7.18810	+	4.15005i	−0.242725	+	0.140137i	−0.616428	−	0.787411i	$-0.711421\pi$
$877$	−7.18810	+	4.15005i	−0.242725	+	0.140137i	0.373704	+	0.927548i	$0.378088\pi$
$878$		0			0
$879$	−12.3620	+	21.4116i	−0.416960	+	0.722196i
$880$		0			0
$881$	−58.0463			−1.95563			−0.977815	−	0.209473i	$-0.932825\pi$
$881$	−58.0463			−1.95563			−0.977815	+	0.209473i	$0.932825\pi$
$882$		0			0
$883$			13.8439i			0.465885i	0.972491	+	0.232942i	$0.0748353\pi$
$883$			13.8439i			0.465885i	−0.972491	+	0.232942i	$0.925165\pi$
$884$		0			0
$885$	3.30593	+	19.5699i	0.111128	+	0.657835i
$886$		0			0
$887$	−41.3356	+	23.8651i	−1.38791	+	0.801313i	−0.993080	−	0.117439i	$-0.962531\pi$
$887$	−41.3356	+	23.8651i	−1.38791	+	0.801313i	−0.394834	+	0.918752i	$0.629198\pi$
$888$		0			0
$889$	45.3897	−	25.5115i	1.52232	−	0.855627i
$890$		0			0
$891$	1.07409	+	1.86038i	0.0359834	+	0.0623251i
$892$		0			0
$893$	48.5564	+	28.0341i	1.62488	+	0.938124i
$894$		0			0
$895$	−8.24975	−	9.97634i	−0.275759	−	0.333472i
$896$		0			0
$897$		−	7.09025i		−	0.236737i
$898$		0			0
$899$	−33.8300	+	58.5953i	−1.12829	+	1.95426i
$900$		0			0
$901$	−9.76101	−	16.9066i	−0.325186	−	0.563239i
$902$		0			0
$903$	14.4040	+	0.166350i	0.479334	+	0.00553579i
$904$		0			0
$905$	14.5690	−	39.1506i	0.484290	−	1.30141i
$906$		0			0
$907$	−10.1451	−	5.85728i	−0.336863	−	0.194488i	0.322021	−	0.946732i	$-0.395638\pi$
$907$	−10.1451	−	5.85728i	−0.336863	−	0.194488i	−0.658884	+	0.752245i	$0.728971\pi$
$908$		0			0
$909$	1.63105			0.0540984
$910$		0			0
$911$	−28.6551			−0.949387			−0.474694	−	0.880151i	$-0.657441\pi$
$911$	−28.6551			−0.949387			−0.474694	+	0.880151i	$0.657441\pi$
$912$		0			0
$913$	26.1038	+	15.0710i	0.863908	+	0.498778i
$914$		0			0
$915$	−28.9284	−	10.7650i	−0.956343	−	0.355881i
$916$		0			0
$917$	−20.4361	+	34.4709i	−0.674860	+	1.13833i
$918$		0			0
$919$	−12.5925	−	21.8109i	−0.415389	−	0.719474i	0.580081	−	0.814559i	$-0.303021\pi$
$919$	−12.5925	−	21.8109i	−0.415389	−	0.719474i	−0.995469	+	0.0950849i	$0.969688\pi$
$920$		0			0
$921$	−1.62287	+	2.81089i	−0.0534754	+	0.0926220i
$922$		0			0
$923$			18.0717i			0.594836i
$924$		0			0
$925$	12.5316	+	2.39579i	0.412037	+	0.0787730i
$926$		0			0
$927$	−1.77081	−	1.02237i	−0.0581609	−	0.0335792i
$928$		0			0
$929$	−0.000361436	0	0.000626026i	−1.18583e−5	0	2.05392e-5i	0.866019	−	0.500010i	$-0.166670\pi$
$929$	−0.000361436	0	0.000626026i	−1.18583e−5	0	2.05392e-5i	−0.866031	+	0.499990i	$0.833337\pi$
$930$		0			0
$931$	−37.1922	−	0.859174i	−1.21893	−	0.0281583i
$932$		0			0
$933$	−11.3909	+	6.57653i	−0.372921	+	0.215306i
$934$		0			0
$935$	2.89067	+	17.1117i	0.0945349	+	0.559612i
$936$		0			0
$937$			1.23395i			0.0403114i	0.999797	+	0.0201557i	$0.00641619\pi$
$937$			1.23395i			0.0403114i	−0.999797	+	0.0201557i	$0.993584\pi$
$938$		0			0
$939$	−16.0447			−0.523601
$940$		0			0
$941$	3.04491	−	5.27393i	0.0992611	−	0.171925i	−0.812118	−	0.583493i	$-0.801685\pi$
$941$	3.04491	−	5.27393i	0.0992611	−	0.171925i	0.911379	+	0.411568i	$0.135019\pi$
$942$		0			0
$943$	11.7633	−	6.79156i	0.383067	−	0.221164i
$944$		0			0
$945$	−0.918007	−	5.84442i	−0.0298628	−	0.190119i
$946$		0			0
$947$	11.1422	−	6.43293i	0.362072	−	0.209042i	−0.307917	−	0.951413i	$-0.599632\pi$
$947$	11.1422	−	6.43293i	0.362072	−	0.209042i	0.669989	+	0.742371i	$0.266299\pi$
$948$		0			0
$949$	−18.3644	+	31.8081i	−0.596135	+	1.03254i
$950$		0			0
$951$	−19.9430			−0.646697
$952$		0			0
$953$		−	8.72241i		−	0.282547i	−0.989971	−	0.141273i	$-0.954880\pi$
$953$		−	8.72241i		−	0.282547i	0.989971	−	0.141273i	$-0.0451197\pi$
$954$		0			0
$955$	10.4039	−	1.75752i	0.336662	−	0.0568721i
$956$		0			0
$957$	16.9673	−	9.79609i	0.548476	−	0.316663i
$958$		0			0
$959$	−0.235023	+	20.3502i	−0.00758927	+	0.657141i
$960$		0			0
$961$	−12.0177	−	20.8152i	−0.387667	−	0.671458i
$962$		0			0
$963$	5.23442	+	3.02210i	0.168677	+	0.0973857i
$964$		0			0
$965$	30.5777	−	25.2857i	0.984332	−	0.813975i
$966$		0			0
$967$			29.6333i			0.952943i	0.879190	+	0.476471i	$0.158084\pi$
$967$			29.6333i			0.952943i	−0.879190	+	0.476471i	$0.841916\pi$
$968$		0			0
$969$	9.60034	−	16.6283i	0.308407	−	0.534177i
$970$		0			0
$971$	5.12543	+	8.87751i	0.164483	+	0.284893i	0.936472	−	0.350744i	$-0.114071\pi$
$971$	5.12543	+	8.87751i	0.164483	+	0.284893i	−0.771989	+	0.635636i	$0.780738\pi$
$972$		0			0
$973$	−6.27466	−	11.1638i	−0.201156	−	0.357895i
$974$		0			0
$975$	−15.1560	+	5.27101i	−0.485381	+	0.168808i
$976$		0			0
$977$	−20.6396	−	11.9163i	−0.660319	−	0.381236i	0.132079	−	0.991239i	$-0.457835\pi$
$977$	−20.6396	−	11.9163i	−0.660319	−	0.381236i	−0.792399	+	0.610004i	$0.791168\pi$
$978$		0			0
$979$	−8.45865			−0.270340
$980$		0			0
$981$	−3.19238			−0.101925
$982$		0			0
$983$	−40.9314	−	23.6317i	−1.30551	−	0.753736i	−0.324165	−	0.946000i	$-0.605083\pi$
$983$	−40.9314	−	23.6317i	−1.30551	−	0.753736i	−0.981343	+	0.192265i	$0.938417\pi$
$984$		0			0
$985$	−51.5142	−	19.1698i	−1.64138	−	0.610801i
$986$		0			0
$987$	−13.6761	−	24.3323i	−0.435314	−	0.774506i
$988$		0			0
$989$	6.01429	+	10.4171i	0.191243	+	0.331243i
$990$		0			0
$991$	21.2833	−	36.8638i	0.676086	−	1.17102i	−0.300064	−	0.953919i	$-0.597008\pi$
$991$	21.2833	−	36.8638i	0.676086	−	1.17102i	0.976150	−	0.217097i	$-0.0696587\pi$
$992$		0			0
$993$			4.82211i			0.153025i
$994$		0			0
$995$	−17.5427	−	21.2142i	−0.556140	−	0.672534i
$996$		0			0
$997$	−27.9851	−	16.1572i	−0.886297	−	0.511704i	−0.0135678	−	0.999908i	$-0.504319\pi$
$997$	−27.9851	−	16.1572i	−0.886297	−	0.511704i	−0.872730	+	0.488204i	$0.837652\pi$
$998$		0			0
$999$	−1.27586	−	2.20985i	−0.0403664	−	0.0699166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bb.a.109.7	yes	16
3.2	odd	2		1260.2.bm.c.109.4		16
4.3	odd	2		1680.2.di.e.529.3		16
5.2	odd	4		2100.2.q.m.1201.4		8
5.3	odd	4		2100.2.q.l.1201.1		8
5.4	even	2	inner	420.2.bb.a.109.1	✓	16
7.2	even	3	inner	420.2.bb.a.289.1	yes	16
7.3	odd	6		2940.2.k.g.589.5		8
7.4	even	3		2940.2.k.f.589.4		8
7.5	odd	6		2940.2.bb.i.1549.8		16
7.6	odd	2		2940.2.bb.i.949.2		16
15.14	odd	2		1260.2.bm.c.109.8		16
20.19	odd	2		1680.2.di.e.529.5		16
21.2	odd	6		1260.2.bm.c.289.8		16
28.23	odd	6		1680.2.di.e.289.5		16
35.2	odd	12		2100.2.q.m.1801.4		8
35.4	even	6		2940.2.k.f.589.8		8
35.9	even	6	inner	420.2.bb.a.289.7	yes	16
35.19	odd	6		2940.2.bb.i.1549.2		16
35.23	odd	12		2100.2.q.l.1801.1		8
35.24	odd	6		2940.2.k.g.589.1		8
35.34	odd	2		2940.2.bb.i.949.8		16
105.44	odd	6		1260.2.bm.c.289.4		16
140.79	odd	6		1680.2.di.e.289.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.1	✓	16	5.4	even	2	inner
420.2.bb.a.109.7	yes	16	1.1	even	1	trivial
420.2.bb.a.289.1	yes	16	7.2	even	3	inner
420.2.bb.a.289.7	yes	16	35.9	even	6	inner
1260.2.bm.c.109.4		16	3.2	odd	2
1260.2.bm.c.109.8		16	15.14	odd	2
1260.2.bm.c.289.4		16	105.44	odd	6
1260.2.bm.c.289.8		16	21.2	odd	6
1680.2.di.e.289.3		16	140.79	odd	6
1680.2.di.e.289.5		16	28.23	odd	6
1680.2.di.e.529.3		16	4.3	odd	2
1680.2.di.e.529.5		16	20.19	odd	2
2100.2.q.l.1201.1		8	5.3	odd	4
2100.2.q.l.1801.1		8	35.23	odd	12
2100.2.q.m.1201.4		8	5.2	odd	4
2100.2.q.m.1801.4		8	35.2	odd	12
2940.2.k.f.589.4		8	7.4	even	3
2940.2.k.f.589.8		8	35.4	even	6
2940.2.k.g.589.1		8	35.24	odd	6
2940.2.k.g.589.5		8	7.3	odd	6
2940.2.bb.i.949.2		16	7.6	odd	2
2940.2.bb.i.949.8		16	35.34	odd	2
2940.2.bb.i.1549.2		16	35.19	odd	6
2940.2.bb.i.1549.8		16	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(0.779855 - 2.09567i) q^{5} +(-1.29633 - 2.30641i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.07409 - 1.86038i) q^{11} -3.20929i q^{13} +(1.72321 - 1.42497i) q^{15} +(-3.12880 - 1.80641i) q^{17} +(2.65730 + 4.60257i) q^{19} +(0.0305535 - 2.64557i) q^{21} +(1.91330 - 1.10465i) q^{23} +(-3.78365 - 3.26863i) q^{25} +1.00000i q^{27} +9.12035 q^{29} +(-3.70929 + 6.42468i) q^{31} +(1.86038 - 1.07409i) q^{33} +(-5.84442 + 0.918007i) q^{35} +(-2.20985 + 1.27586i) q^{37} +(1.60465 - 2.77933i) q^{39} +6.14818 q^{41} +5.44455i q^{43} +(2.20483 - 0.372460i) q^{45} +(9.13644 - 5.27492i) q^{47} +(-3.63907 + 5.97973i) q^{49} +(-1.80641 - 3.12880i) q^{51} +(4.67960 + 2.70177i) q^{53} +(-3.06111 - 3.70177i) q^{55} +5.31459i q^{57} +(-4.43796 + 7.68677i) q^{59} +(-6.90194 - 11.9545i) q^{61} +(1.34925 - 2.27586i) q^{63} +(-6.72561 - 2.50278i) q^{65} +(0.0141657 + 0.00817856i) q^{67} +2.20929 q^{69} -5.63105 q^{71} +(-9.91127 - 5.72227i) q^{73} +(-1.64242 - 4.72255i) q^{75} +(-5.68318 - 0.0656346i) q^{77} +(7.65543 + 13.2596i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.0314i q^{83} +(-6.22565 + 5.14818i) q^{85} +(7.89845 + 4.56017i) q^{87} +(-1.96879 - 3.41005i) q^{89} +(-7.40194 + 4.16029i) q^{91} +(-6.42468 + 3.70929i) q^{93} +(11.7178 - 1.97947i) q^{95} +5.16454i q^{97} +2.14818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) \) 16 * q + 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 + 8 * q^19 - 4 * q^21 + 12 * q^25 + 24 * q^29 + 10 * q^35 - 4 * q^39 + 48 * q^41 - 2 * q^45 + 8 * q^49 + 4 * q^51 - 40 * q^55 - 28 * q^59 - 32 * q^61 - 26 * q^65 - 24 * q^69 - 56 * q^71 - 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 - 16 * q^89 - 40 * q^91 + 22 * q^95 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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