LMFDB - Embedded newform 420.2.bb.a.289.1

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			289.1
Root			$-1.94655 + 0.521577i$ of defining polynomial
Character	$\chi$	$=$	420.289
Dual form			420.2.bb.a.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.20483 + 0.372460i) q^{5} +(1.29633 - 2.30641i) q^{7} +(0.500000 - 0.866025i) q^{9} +(1.07409 + 1.86038i) q^{11} -3.20929i q^{13} +(1.72321 - 1.42497i) q^{15} +(3.12880 - 1.80641i) q^{17} +(2.65730 - 4.60257i) q^{19} +(0.0305535 + 2.64557i) q^{21} +(-1.91330 - 1.10465i) q^{23} +(4.72255 - 1.64242i) q^{25} +1.00000i q^{27} +9.12035 q^{29} +(-3.70929 - 6.42468i) q^{31} +(-1.86038 - 1.07409i) q^{33} +(-1.99913 + 5.56808i) q^{35} +(2.20985 + 1.27586i) q^{37} +(1.60465 + 2.77933i) q^{39} +6.14818 q^{41} +5.44455i q^{43} +(-0.779855 + 2.09567i) q^{45} +(-9.13644 - 5.27492i) q^{47} +(-3.63907 - 5.97973i) q^{49} +(-1.80641 + 3.12880i) q^{51} +(-4.67960 + 2.70177i) q^{53} +(-3.06111 - 3.70177i) q^{55} +5.31459i q^{57} +(-4.43796 - 7.68677i) q^{59} +(-6.90194 + 11.9545i) q^{61} +(-1.34925 - 2.27586i) q^{63} +(1.19533 + 7.07594i) q^{65} +(-0.0141657 + 0.00817856i) q^{67} +2.20929 q^{69} -5.63105 q^{71} +(9.91127 - 5.72227i) q^{73} +(-3.26863 + 3.78365i) q^{75} +(5.68318 - 0.0656346i) q^{77} +(7.65543 - 13.2596i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.0314i q^{83} +(-6.22565 + 5.14818i) q^{85} +(-7.89845 + 4.56017i) q^{87} +(-1.96879 + 3.41005i) q^{89} +(-7.40194 - 4.16029i) q^{91} +(6.42468 + 3.70929i) q^{93} +(-4.14461 + 11.1376i) q^{95} +5.16454i q^{97} +2.14818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

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

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
$5$	−2.20483	+	0.372460i	−0.986030	+	0.166569i
$5$	−2.20483	+	0.372460i	−0.986030	+	0.166569i
$6$		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	0.981279	−	0.192591i	$-0.0616891\pi$
$11$	1.07409	+	1.86038i	0.323851	+	0.560926i	−0.657428	+	0.753517i	$0.728356\pi$
$12$		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	$-0.522311\pi$
$17$	3.12880	−	1.80641i	0.758845	−	0.438119i	0.828881	+	0.559425i	$0.188978\pi$
$18$		0			0
$19$	2.65730	−	4.60257i	0.609625	−	1.05590i	−0.381677	−	0.924296i	$-0.624653\pi$
$19$	2.65730	−	4.60257i	0.609625	−	1.05590i	0.991302	−	0.131606i	$-0.0420134\pi$
$20$		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	$-0.407315\pi$
$23$	−1.91330	−	1.10465i	−0.398951	−	0.230334i	−0.686031	+	0.727572i	$0.740649\pi$
$24$		0			0
$25$	4.72255	−	1.64242i	0.944509	−	0.328485i
$26$		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	−0.978956	−	0.204070i	$-0.934583\pi$
$31$	−3.70929	−	6.42468i	−0.666208	−	1.15391i	0.312748	−	0.949836i	$-0.398750\pi$
$32$		0			0
$33$	−1.86038	−	1.07409i	−0.323851	−	0.186975i
$34$		0			0
$35$	−1.99913	+	5.56808i	−0.337915	+	0.941177i
$36$		0			0
$37$	2.20985	+	1.27586i	0.363297	+	0.209750i	0.670526	−	0.741886i	$-0.266068\pi$
$37$	2.20985	+	1.27586i	0.363297	+	0.209750i	−0.307229	+	0.951636i	$0.599402\pi$
$38$		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
$45$	−0.779855	+	2.09567i	−0.116254	+	0.312404i
$46$		0			0
$47$	−9.13644	−	5.27492i	−1.33269	−	0.769427i	−0.346976	−	0.937874i	$-0.612791\pi$
$47$	−9.13644	−	5.27492i	−1.33269	−	0.769427i	−0.985711	+	0.168447i	$0.946125\pi$
$48$		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	$-0.787692\pi$
$53$	−4.67960	+	2.70177i	−0.642792	+	0.371116i	0.142897	+	0.989738i	$0.454358\pi$
$54$		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	−0.995734	−	0.0922675i	$-0.970589\pi$
$59$	−4.43796	−	7.68677i	−0.577773	−	1.00073i	0.417961	−	0.908465i	$-0.362745\pi$
$60$		0			0
$61$	−6.90194	+	11.9545i	−0.883703	+	1.53062i	−0.0365110	+	0.999333i	$0.511624\pi$
$61$	−6.90194	+	11.9545i	−0.883703	+	1.53062i	−0.847192	+	0.531286i	$0.821709\pi$
$62$		0			0
$63$	−1.34925	−	2.27586i	−0.169989	−	0.286731i
$64$		0			0
$65$	1.19533	+	7.07594i	0.148263	+	0.877662i
$66$		0			0
$67$	−0.0141657	+	0.00817856i	−0.00173061	+	0.000999170i	−0.500865	−	0.865525i	$-0.666985\pi$
$67$	−0.0141657	+	0.00817856i	−0.00173061	+	0.000999170i	0.499134	+	0.866525i	$0.333651\pi$
$68$		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	$-0.433072\pi$
$73$	9.91127	−	5.72227i	1.16003	−	0.669742i	0.951310	+	0.308235i	$0.0997382\pi$
$74$		0			0
$75$	−3.26863	+	3.78365i	−0.377429	+	0.436899i
$76$		0			0
$77$	5.68318	−	0.0656346i	0.647658	−	0.00747976i
$78$		0			0
$79$	7.65543	−	13.2596i	0.861303	−	1.49182i	−0.00936887	−	0.999956i	$-0.502982\pi$
$79$	7.65543	−	13.2596i	0.861303	−	1.49182i	0.870672	−	0.491864i	$-0.163684\pi$
$80$		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	−0.951303	−	0.308259i	$-0.900254\pi$
$89$	−1.96879	+	3.41005i	−0.208691	+	0.361464i	0.742611	+	0.669723i	$0.233587\pi$
$90$		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
$95$	−4.14461	+	11.1376i	−0.425228	+	1.14270i
$96$		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	0.903743	−	0.428075i	$-0.140808\pi$
$101$	0.815524	+	1.41253i	0.0811477	+	0.140552i	−0.822595	+	0.568627i	$0.807475\pi$
$102$		0			0
$103$	1.77081	+	1.02237i	0.174483	+	0.100738i	0.584698	−	0.811251i	$-0.301213\pi$
$103$	1.77081	+	1.02237i	0.174483	+	0.100738i	−0.410215	+	0.911989i	$0.634546\pi$
$104$		0			0
$105$	−1.05274	−	5.82166i	−0.102737	−	0.568136i
$106$		0			0
$107$	−5.23442	−	3.02210i	−0.506031	−	0.292157i	0.225170	−	0.974320i	$-0.427706\pi$
$107$	−5.23442	−	3.02210i	−0.506031	−	0.292157i	−0.731201	+	0.682162i	$0.761040\pi$
$108$		0			0
$109$	−1.59619	−	2.76468i	−0.152887	−	0.264808i	0.779401	−	0.626526i	$-0.215524\pi$
$109$	−1.59619	−	2.76468i	−0.152887	−	0.264808i	−0.932288	+	0.361718i	$0.882190\pi$
$110$		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
$115$	4.62994	+	1.72293i	0.431744	+	0.160664i
$116$		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	0.318507	+	0.947921i	$0.396819\pi$
$131$	−7.57316	+	13.1171i	−0.661670	+	1.14605i	−0.980177	+	0.198125i	$0.936515\pi$
$132$		0			0
$133$	−7.17070	−	12.0953i	−0.621778	−	1.04879i
$134$		0			0
$135$	−0.372460	−	2.20483i	−0.0320563	−	0.189762i
$136$		0			0
$137$	6.66160	−	3.84608i	0.569139	−	0.328593i	−0.187666	−	0.982233i	$-0.560092\pi$
$137$	6.66160	−	3.84608i	0.569139	−	0.328593i	0.756805	+	0.653640i	$0.226759\pi$
$138$		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
$145$	−20.1088	+	3.39697i	−1.66995	+	0.282103i
$146$		0			0
$147$	6.14139	+	3.35906i	0.506534	+	0.277051i
$148$		0			0
$149$	4.48608	−	7.77012i	0.367514	−	0.636553i	−0.621662	−	0.783286i	$-0.713542\pi$
$149$	4.48608	−	7.77012i	0.367514	−	0.636553i	0.989176	+	0.146732i	$0.0468756\pi$
$150$		0			0
$151$	1.84084	+	3.18842i	0.149805	+	0.259470i	0.931155	−	0.364623i	$-0.118802\pi$
$151$	1.84084	+	3.18842i	0.149805	+	0.259470i	−0.781350	+	0.624093i	$0.785469\pi$
$152$		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	$-0.548825\pi$
$157$	7.85224	−	4.53349i	0.626677	−	0.361812i	0.779464	+	0.626447i	$0.215492\pi$
$158$		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	$-0.271497\pi$
$163$	4.26888	+	2.46464i	0.334365	+	0.193046i	−0.323413	+	0.946258i	$0.604830\pi$
$164$		0			0
$165$	4.50188	+	1.67527i	0.350471	+	0.130420i
$166$		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	$-0.274264\pi$
$173$	4.20341	+	2.42684i	0.319580	+	0.184509i	−0.331626	+	0.943411i	$0.607597\pi$
$174$		0			0
$175$	2.33386	−	13.0213i	0.176423	−	0.984314i
$176$		0			0
$177$	7.68677	+	4.43796i	0.577773	+	0.333577i
$178$		0			0
$179$	2.89470	+	5.01377i	0.216360	+	0.374747i	0.953692	−	0.300784i	$-0.0972482\pi$
$179$	2.89470	+	5.01377i	0.216360	+	0.374747i	−0.737332	+	0.675530i	$0.763915\pi$
$180$		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
$185$	−5.34755	−	1.98997i	−0.393160	−	0.146305i
$186$		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	−0.767954	−	0.640504i	$-0.778725\pi$
$191$	2.35934	−	4.08650i	0.170716	−	0.295689i	0.938670	+	0.344816i	$0.112059\pi$
$192$		0			0
$193$	−15.3673	+	8.87232i	−1.10616	+	0.638644i	−0.937833	−	0.347087i	$-0.887171\pi$
$193$	−15.3673	+	8.87232i	−1.10616	+	0.638644i	−0.168331	+	0.985731i	$0.553838\pi$
$194$		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	0.997404	−	0.0720019i	$-0.0229388\pi$
$199$	6.15543	+	10.6615i	0.436347	+	0.755775i	−0.561058	+	0.827777i	$0.689605\pi$
$200$		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
$205$	−13.5557	+	2.28995i	−0.946771	+	0.159937i
$206$		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
$215$	−2.02788	−	12.0043i	−0.138300	−	0.818687i
$216$		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	$-0.601665\pi$
$227$	5.29205	−	3.05537i	0.351246	−	0.202792i	0.665234	+	0.746635i	$0.268332\pi$
$228$		0			0
$229$	−9.55737	+	16.5539i	−0.631569	+	1.09391i	0.355662	+	0.934615i	$0.384255\pi$
$229$	−9.55737	+	16.5539i	−0.631569	+	1.09391i	−0.987231	+	0.159295i	$0.949078\pi$
$230$		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	$-0.239149\pi$
$233$	7.70926	+	4.45094i	0.505050	+	0.291591i	−0.225746	+	0.974186i	$0.572482\pi$
$234$		0			0
$235$	22.1090	+	8.22735i	1.44223	+	0.536693i
$236$		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	0.994499	+	0.104743i	$0.0334021\pi$
$241$	9.12759	+	15.8095i	0.587960	+	1.01838i	−0.406539	+	0.913633i	$0.633265\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	10.2507	+	11.8289i	0.654896	+	0.755719i
$246$		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
$255$	2.81748	−	7.57128i	0.176437	−	0.474132i
$256$		0			0
$257$	−14.0455	−	8.10917i	−0.876134	−	0.505836i	−0.00675233	−	0.999977i	$-0.502149\pi$
$257$	−14.0455	−	8.10917i	−0.876134	−	0.505836i	−0.869382	+	0.494141i	$0.835483\pi$
$258$		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	$-0.958506\pi$
$263$	−22.2939	+	12.8714i	−1.37470	+	0.793684i	−0.383185	+	0.923671i	$0.625173\pi$
$264$		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	−0.933286	−	0.359134i	$-0.883072\pi$
$269$	−12.7546	−	22.0916i	−0.777662	−	1.34695i	0.155623	−	0.987816i	$-0.450261\pi$
$270$		0			0
$271$	−2.03508	+	3.52486i	−0.123622	+	0.214120i	−0.921194	−	0.389105i	$-0.872784\pi$
$271$	−2.03508	+	3.52486i	−0.123622	+	0.214120i	0.797571	+	0.603225i	$0.206118\pi$
$272$		0			0
$273$	8.49042	−	0.0980552i	0.513863	−	0.00593457i
$274$		0			0
$275$	8.12798	+	7.02162i	0.490136	+	0.423420i
$276$		0			0
$277$	−11.3384	+	6.54626i	−0.681261	+	0.393326i	−0.800330	−	0.599560i	$-0.795342\pi$
$277$	−11.3384	+	6.54626i	−0.681261	+	0.393326i	0.119069	+	0.992886i	$0.462009\pi$
$278$		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	$-0.566006\pi$
$283$	9.06151	−	5.23167i	0.538651	−	0.310990i	0.744532	+	0.667587i	$0.232673\pi$
$284$		0			0
$285$	−1.97947	−	11.7178i	−0.117254	−	0.694101i
$286$		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
$305$	10.7650	−	28.9284i	0.616404	−	1.65643i
$306$		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	0.617093	−	0.786891i	$-0.288310\pi$
$311$	−6.57653	−	11.3909i	−0.372921	−	0.645918i	−0.990013	+	0.140973i	$0.954977\pi$
$312$		0			0
$313$	13.8952	+	8.02237i	0.785401	+	0.453451i	0.838341	−	0.545146i	$-0.183526\pi$
$313$	13.8952	+	8.02237i	0.785401	+	0.453451i	−0.0529400	+	0.998598i	$0.516859\pi$
$314$		0			0
$315$	3.82253	+	4.51534i	0.215375	+	0.254410i
$316$		0			0
$317$	17.2712	+	9.97151i	0.970045	+	0.560056i	0.899250	−	0.437435i	$-0.144113\pi$
$317$	17.2712	+	9.97151i	0.970045	+	0.560056i	0.0707950	+	0.997491i	$0.477446\pi$
$318$		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
$325$	−5.27101	−	15.1560i	−0.292383	−	0.840705i
$326$		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	−0.792125	−	0.610359i	$-0.791025\pi$
$331$	2.41106	−	4.17607i	0.132524	−	0.229538i	0.924649	+	0.380821i	$0.124359\pi$
$332$		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
$345$	−4.87111	+	0.822873i	−0.262252	+	0.0443020i
$346$		0			0
$347$	14.3247	−	8.27040i	0.768993	−	0.443978i	−0.0635224	−	0.997980i	$-0.520233\pi$
$347$	14.3247	−	8.27040i	0.768993	−	0.443978i	0.832515	+	0.554002i	$0.186900\pi$
$348$		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	$-0.962428\pi$
$353$	−26.0702	+	15.0516i	−1.38758	+	0.801118i	−0.394535	+	0.918881i	$0.629094\pi$
$354$		0			0
$355$	12.4155	−	2.09734i	0.658946	−	0.111315i
$356$		0			0
$357$	4.87459	+	8.22227i	0.257991	+	0.435169i
$358$		0			0
$359$	−14.5305	+	25.1675i	−0.766889	+	1.32829i	0.172353	+	0.985035i	$0.444863\pi$
$359$	−14.5305	+	25.1675i	−0.766889	+	1.32829i	−0.939242	+	0.343255i	$0.888470\pi$
$360$		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	$-0.676002\pi$
$367$	−0.973001	+	0.561762i	−0.0507902	+	0.0293237i	0.474390	+	0.880315i	$0.342669\pi$
$368$		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	$-0.553202\pi$
$373$	−21.3121	−	12.3045i	−1.10350	−	0.637105i	−0.937138	+	0.348960i	$0.886535\pi$
$374$		0			0
$375$	5.79752	−	9.55975i	0.299383	−	0.493663i
$376$		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	$-0.0700970\pi$
$383$	24.9444	+	14.4017i	1.27460	+	0.735891i	0.298750	+	0.954331i	$0.403430\pi$
$384$		0			0
$385$	−12.5060	+	2.26147i	−0.637365	+	0.115255i
$386$		0			0
$387$	4.71512	+	2.72227i	0.239683	+	0.138381i
$388$		0			0
$389$	7.06901	+	12.2439i	0.358413	+	0.620789i	0.987696	−	0.156387i	$-0.0499847\pi$
$389$	7.06901	+	12.2439i	0.358413	+	0.620789i	−0.629283	+	0.777176i	$0.716651\pi$
$390$		0			0
$391$	−7.98178			−0.403656
$392$		0			0
$393$		−	15.1463i		−	0.764031i
$394$		0			0
$395$	−11.9402	+	32.0865i	−0.600779	+	1.61445i
$396$		0			0
$397$	−12.2230	−	7.05696i	−0.613455	−	0.354178i	0.160861	−	0.986977i	$-0.448573\pi$
$397$	−12.2230	−	7.05696i	−0.613455	−	0.354178i	−0.774316	+	0.632799i	$0.781906\pi$
$398$		0			0
$399$	12.2576	+	6.88945i	0.613649	+	0.344904i
$400$		0			0
$401$	0.727736	−	1.26048i	0.0363414	−	0.0629451i	−0.847283	−	0.531142i	$-0.821763\pi$
$401$	0.727736	−	1.26048i	0.0363414	−	0.0629451i	0.883624	+	0.468197i	$0.155096\pi$
$402$		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	0.827704	+	0.561164i	$0.189646\pi$
$409$	18.1980	+	31.5199i	0.899835	+	1.55856i	0.0721304	+	0.997395i	$0.477020\pi$
$410$		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
$415$	−5.22614	−	30.9369i	−0.256541	−	1.51863i
$416$		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
$425$	11.8090	−	13.6697i	0.572820	−	0.663077i
$426$		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	0.594193	−	0.804322i	$-0.297471\pi$
$431$	−8.29315	−	14.3642i	−0.399467	−	0.691897i	−0.993660	+	0.112425i	$0.964138\pi$
$432$		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	−0.687564	−	0.726124i	$-0.741320\pi$
$439$	5.97266	−	10.3450i	0.285060	−	0.493738i	0.972624	+	0.232386i	$0.0746532\pi$
$440$		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	$-0.00952616\pi$
$443$	31.0118	+	17.9047i	1.47341	+	0.850676i	0.473862	+	0.880599i	$0.342859\pi$
$444$		0			0
$445$	3.07074	−	8.25187i	0.145567	−	0.391176i
$446$		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
$455$	17.8696	+	6.41580i	0.837738	+	0.300777i
$456$		0			0
$457$	3.11577	+	1.79889i	0.145749	+	0.0841484i	0.571101	−	0.820880i	$-0.306516\pi$
$457$	3.11577	+	1.79889i	0.145749	+	0.0841484i	−0.425352	+	0.905028i	$0.639850\pi$
$458$		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
$465$	−15.5469	−	5.78541i	−0.720970	−	0.268292i
$466$		0			0
$467$	−3.72400	−	2.15005i	−0.172326	−	0.0994925i	0.411356	−	0.911475i	$-0.365055\pi$
$467$	−3.72400	−	2.15005i	−0.172326	−	0.0994925i	−0.583682	+	0.811982i	$0.698389\pi$
$468$		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	0.998492	−	0.0549041i	$-0.0174853\pi$
$479$	9.88588	+	17.1228i	0.451697	+	0.782363i	−0.546794	+	0.837267i	$0.684152\pi$
$480$		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
$485$	−1.92359	−	11.3869i	−0.0873456	−	0.517054i
$486$		0			0
$487$	37.7796	−	21.8121i	1.71196	−	0.988399i	0.780039	−	0.625730i	$-0.215199\pi$
$487$	37.7796	−	21.8121i	1.71196	−	0.988399i	0.931918	−	0.362669i	$-0.118134\pi$
$488$		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
$495$	−4.73638	+	0.800113i	−0.212884	+	0.0359624i
$496$		0			0
$497$	−7.29968	+	12.9875i	−0.327435	+	0.582570i
$498$		0			0
$499$	−13.7353	+	23.7902i	−0.614875	+	1.06499i	0.375532	+	0.926809i	$0.377460\pi$
$499$	−13.7353	+	23.7902i	−0.614875	+	1.06499i	−0.990406	+	0.138185i	$0.955873\pi$
$500$		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	−0.993692	−	0.112145i	$-0.964228\pi$
$509$	−9.01822	+	15.6200i	−0.399726	+	0.692345i	0.593966	+	0.804490i	$0.297561\pi$
$510$		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
$515$	−4.28512	−	1.59461i	−0.188825	−	0.0702668i
$516$		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	0.856681	−	0.515847i	$-0.172523\pi$
$521$	−0.419891	−	0.727272i	−0.0183957	−	0.0318624i	−0.875077	+	0.483984i	$0.839189\pi$
$522$		0			0
$523$	34.9852	+	20.1987i	1.52979	+	0.883227i	0.999370	+	0.0354945i	$0.0113006\pi$
$523$	34.9852	+	20.1987i	1.52979	+	0.883227i	0.530424	+	0.847732i	$0.322033\pi$
$524$		0			0
$525$	4.48944	+	12.4437i	0.195935	+	0.543086i
$526$		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
$535$	12.6666	+	4.71359i	0.547626	+	0.203786i
$536$		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	−0.496595	−	0.867983i	$-0.665416\pi$
$541$	11.7087	−	20.2801i	0.503398	−	0.871911i	0.999992	−	0.00392786i	$-0.00125028\pi$
$542$		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
$555$	5.62610	−	0.950413i	0.238815	−	0.0403428i
$556$		0			0
$557$	21.2576	−	12.2731i	0.900712	−	0.520026i	0.0232807	−	0.999729i	$-0.492589\pi$
$557$	21.2576	−	12.2731i	0.900712	−	0.520026i	0.877431	+	0.479703i	$0.159256\pi$
$558$		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	$-0.635541\pi$
$563$	4.01222	−	2.31646i	0.169095	−	0.0976270i	0.582159	+	0.813075i	$0.302208\pi$
$564$		0			0
$565$	−0.410985	−	2.43288i	−0.0172903	−	0.102352i
$566$		0			0
$567$	−2.64557	+	0.0305535i	−0.111104	+	0.00128313i
$568$		0			0
$569$	5.47818	−	9.48849i	0.229657	−	0.397778i	−0.728049	−	0.685525i	$-0.759573\pi$
$569$	5.47818	−	9.48849i	0.229657	−	0.397778i	0.957707	+	0.287747i	$0.0929061\pi$
$570$		0			0
$571$	4.07044	+	7.05021i	0.170343	+	0.295042i	0.938540	−	0.345171i	$-0.112179\pi$
$571$	4.07044	+	7.05021i	0.170343	+	0.295042i	−0.768197	+	0.640213i	$0.778846\pi$
$572$		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	$-0.669324\pi$
$577$	−0.347371	+	0.200555i	−0.0144612	+	0.00834921i	0.492752	+	0.870170i	$0.335991\pi$
$578$		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
$585$	6.72561	+	2.50278i	0.278070	+	0.103477i
$586$		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	$-0.225271\pi$
$593$	14.0455	+	8.10917i	0.576780	+	0.333004i	−0.183073	+	0.983099i	$0.558604\pi$
$594$		0			0
$595$	3.80335	+	21.0326i	0.155922	+	0.862254i
$596$		0			0
$597$	−10.6615	−	6.15543i	−0.436347	−	0.251925i
$598$		0			0
$599$	8.30276	+	14.3808i	0.339242	+	0.587584i	0.984290	−	0.176558i	$-0.0564962\pi$
$599$	8.30276	+	14.3808i	0.339242	+	0.587584i	−0.645049	+	0.764141i	$0.723163\pi$
$600$		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
$605$	−4.97961	+	13.3815i	−0.202450	+	0.544035i
$606$		0			0
$607$	8.90178	+	5.13945i	0.361312	+	0.208604i	0.669656	−	0.742671i	$-0.266441\pi$
$607$	8.90178	+	5.13945i	0.361312	+	0.208604i	−0.308344	+	0.951275i	$0.599775\pi$
$608$		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	$-0.470720\pi$
$613$	24.7625	−	14.2967i	1.00015	−	0.577437i	0.908293	+	0.418336i	$0.137386\pi$
$614$		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	0.761611	−	0.648035i	$-0.224409\pi$
$619$	−4.48852	−	7.77435i	−0.180409	−	0.312477i	−0.942020	+	0.335557i	$0.891075\pi$
$620$		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
$625$	19.6049	−	15.5128i	0.784196	−	0.620514i
$626$		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
$635$	−7.32995	−	43.3906i	−0.290880	−	1.72190i
$636$		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	0.957142	−	0.289620i	$-0.0935288\pi$
$641$	5.76625	+	9.98743i	0.227753	+	0.394480i	−0.729389	+	0.684099i	$0.760195\pi$
$642$		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	$-0.829973\pi$
$647$	−21.6244	+	12.4849i	−0.850144	+	0.490831i	0.0105554	+	0.999944i	$0.496640\pi$
$648$		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	$-0.516280\pi$
$653$	−24.0610	−	13.8916i	−0.941579	−	0.543621i	−0.890455	+	0.455071i	$0.849614\pi$
$654$		0			0
$655$	11.8119	−	31.7417i	0.461530	−	1.24025i
$656$		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	0.693136	−	0.720807i	$-0.256229\pi$
$661$	−7.13885	−	12.3649i	−0.277669	−	0.480937i	−0.970805	+	0.239870i	$0.922895\pi$
$662$		0			0
$663$	10.0412	+	5.79730i	0.389969	+	0.225148i
$664$		0			0
$665$	20.3152	+	23.9972i	0.787789	+	0.930570i
$666$		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
$675$	1.64242	+	4.72255i	0.0632169	+	0.181771i
$676$		0			0
$677$	−0.121354	−	0.0700638i	−0.00466402	−	0.00269277i	0.497666	−	0.867369i	$-0.334190\pi$
$677$	−0.121354	−	0.0700638i	−0.00466402	−	0.00269277i	−0.502330	+	0.864676i	$0.667524\pi$
$678$		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	$-0.820866\pi$
$683$	−21.0805	+	12.1708i	−0.806623	+	0.465704i	0.0391587	+	0.999233i	$0.487532\pi$
$684$		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	−0.807294	−	0.590150i	$-0.799069\pi$
$691$	2.82420	−	4.89166i	0.107438	−	0.186088i	0.914732	+	0.404062i	$0.132402\pi$
$692$		0			0
$693$	2.78475	−	4.95459i	0.105784	−	0.188209i
$694$		0			0
$695$	−10.6721	+	1.80283i	−0.404817	+	0.0683854i
$696$		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
$705$	−23.2606	+	3.92940i	−0.876046	+	0.147990i
$706$		0			0
$707$	4.31506	−	0.0498343i	0.162285	−	0.00187421i
$708$		0			0
$709$	7.42900	−	12.8674i	0.279002	−	0.483246i	−0.692135	−	0.721768i	$-0.743330\pi$
$709$	7.42900	−	12.8674i	0.279002	−	0.483246i	0.971137	+	0.238522i	$0.0766630\pi$
$710$		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	−0.0191777	+	0.999816i	$0.506105\pi$
$719$	−23.4746	+	40.6592i	−0.875455	+	1.51633i	−0.856277	+	0.516516i	$0.827229\pi$
$720$		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
$725$	43.0713	−	14.9795i	1.59963	−	0.556324i
$726$		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	0.990784	+	0.135449i	$0.0432477\pi$
$733$	43.4125	+	25.0642i	1.60348	+	0.925769i	0.612694	+	0.790320i	$0.290086\pi$
$734$		0			0
$735$	−14.7918	−	5.11873i	−0.545605	−	0.188807i
$736$		0			0
$737$	−0.0304305	−	0.0175690i	−0.00112092	−	0.000647164i
$738$		0			0
$739$	−9.99972	−	17.3200i	−0.367846	−	0.637127i	0.621383	−	0.783507i	$-0.286571\pi$
$739$	−9.99972	−	17.3200i	−0.367846	−	0.637127i	−0.989228	+	0.146380i	$0.953238\pi$
$740$		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
$745$	−6.99698	+	18.8027i	−0.256350	+	0.688877i
$746$		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	−0.857600	−	0.514318i	$-0.828045\pi$
$751$	0.455250	−	0.788516i	0.0166123	−	0.0287734i	0.874212	+	0.485544i	$0.161379\pi$
$752$		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	−0.737817	−	0.675001i	$-0.764143\pi$
$761$	5.94922	−	10.3043i	0.215659	−	0.373532i	0.953476	+	0.301468i	$0.0974767\pi$
$762$		0			0
$763$	−8.44567	+	0.0975384i	−0.305754	+	0.00353113i
$764$		0			0
$765$	1.34563	+	7.96566i	0.0486515	+	0.287999i
$766$		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	$-0.467485\pi$
$773$	28.2051	−	16.2842i	1.01447	−	0.585703i	0.912497	+	0.409084i	$0.134152\pi$
$774$		0			0
$775$	−28.0693	−	24.2486i	−1.00828	−	0.871036i
$776$		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	$-0.773869\pi$
$787$	−16.0568	+	9.27040i	−0.572363	+	0.330454i	0.185730	+	0.982601i	$0.440535\pi$
$788$		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
$795$	−4.21397	+	11.3240i	−0.149454	+	0.401621i
$796$		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
$805$	9.97569	−	8.44507i	0.351597	−	0.297650i
$806$		0			0
$807$	22.0916	+	12.7546i	0.777662	+	0.448984i
$808$		0			0
$809$	−14.2270	−	24.6419i	−0.500195	−	0.866362i	−1.00000		0.000224716i	$-0.999928\pi$
$809$	−14.2270	−	24.6419i	−0.500195	−	0.866362i	0.499805	−	0.866138i	$-0.333405\pi$
$810$		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
$815$	−10.3301	−	3.84412i	−0.361849	−	0.134654i
$816$		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	0.379546	+	0.925173i	$0.376080\pi$
$821$	−17.5200	+	30.3454i	−0.611451	+	1.05906i	−0.990996	+	0.133890i	$0.957253\pi$
$822$		0			0
$823$	−48.0872	+	27.7632i	−1.67622	+	0.967763i	−0.712177	+	0.702000i	$0.752290\pi$
$823$	−48.0872	+	27.7632i	−1.67622	+	0.967763i	−0.964038	+	0.265763i	$0.914376\pi$
$824$		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	0.883920	−	0.467638i	$-0.154895\pi$
$829$	1.06456	+	1.84388i	0.0369738	+	0.0640405i	−0.846946	+	0.531678i	$0.821562\pi$
$830$		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
$835$	6.36608	+	37.6848i	0.220307	+	1.30414i
$836$		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
$845$	−5.95405	+	1.00581i	−0.204825	+	0.0346010i
$846$		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	$-0.679395\pi$
$857$	−2.02698	+	1.17028i	−0.0692404	+	0.0399760i	0.464980	+	0.885321i	$0.346061\pi$
$858$		0			0
$859$	27.7053	−	47.9869i	0.945292	−	1.63729i	0.190126	−	0.981760i	$-0.439110\pi$
$859$	27.7053	−	47.9869i	0.945292	−	1.63729i	0.755166	−	0.655534i	$-0.227556\pi$
$860$		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	$-0.277512\pi$
$863$	8.87751	+	5.12543i	0.302194	+	0.174472i	−0.341234	+	0.939978i	$0.610845\pi$
$864$		0			0
$865$	−10.1717	−	3.78517i	−0.345849	−	0.128700i
$866$		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
$875$	−0.295865	+	29.5789i	−0.0100021	+	0.999950i
$876$		0			0
$877$	7.18810	+	4.15005i	0.242725	+	0.140137i	0.616428	−	0.787411i	$-0.288579\pi$
$877$	7.18810	+	4.15005i	0.242725	+	0.140137i	−0.373704	+	0.927548i	$0.621912\pi$
$878$		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
$885$	−18.6010	−	6.92193i	−0.625265	−	0.232678i
$886$		0			0
$887$	41.3356	+	23.8651i	1.38791	+	0.801313i	0.993080	−	0.117439i	$-0.0374686\pi$
$887$	41.3356	+	23.8651i	1.38791	+	0.801313i	0.394834	+	0.918752i	$0.370802\pi$
$888$		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
$905$	−41.1899	+	6.95818i	−1.36920	+	0.231298i
$906$		0			0
$907$	10.1451	−	5.85728i	0.336863	−	0.194488i	−0.322021	−	0.946732i	$-0.604362\pi$
$907$	10.1451	−	5.85728i	0.336863	−	0.194488i	0.658884	+	0.752245i	$0.271029\pi$
$908$		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
$915$	5.14140	+	30.4352i	0.169970	+	1.00616i
$916$		0			0
$917$	20.4361	+	34.4709i	0.674860	+	1.13833i
$918$		0			0
$919$	−12.5925	+	21.8109i	−0.415389	+	0.719474i	−0.995469	−	0.0950849i	$-0.969688\pi$
$919$	−12.5925	+	21.8109i	−0.415389	+	0.719474i	0.580081	+	0.814559i	$0.303021\pi$
$920$		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	−0.866031	−	0.499990i	$-0.833337\pi$
$929$	−0.000361436	0	0.000626026i	−1.18583e−5	0	2.05392e-5i	0.866019	+	0.500010i	$0.166670\pi$
$930$		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
$935$	−16.2645	−	6.05246i	−0.531906	−	0.197937i
$936$		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	0.911379	−	0.411568i	$-0.135019\pi$
$941$	3.04491	+	5.27393i	0.0992611	+	0.171925i	−0.812118	+	0.583493i	$0.801685\pi$
$942$		0			0
$943$	−11.7633	−	6.79156i	−0.383067	−	0.221164i
$944$		0			0
$945$	−5.56808	−	1.99913i	−0.181130	−	0.0650318i
$946$		0			0
$947$	−11.1422	−	6.43293i	−0.362072	−	0.209042i	0.307917	−	0.951413i	$-0.400368\pi$
$947$	−11.1422	−	6.43293i	−0.362072	−	0.209042i	−0.669989	+	0.742371i	$0.733701\pi$
$948$		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
$955$	−3.67988	+	9.88879i	−0.119078	+	0.319994i
$956$		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	−0.771989	−	0.635636i	$-0.780738\pi$
$971$	5.12543	−	8.87751i	0.164483	−	0.284893i	0.936472	+	0.350744i	$0.114071\pi$
$972$		0			0
$973$	6.27466	−	11.1638i	0.201156	−	0.357895i
$974$		0			0
$975$	12.1428	+	10.4900i	0.388882	+	0.335949i
$976$		0			0
$977$	20.6396	−	11.9163i	0.660319	−	0.381236i	−0.132079	−	0.991239i	$-0.542165\pi$
$977$	20.6396	−	11.9163i	0.660319	−	0.381236i	0.792399	+	0.610004i	$0.208832\pi$
$978$		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	$-0.394917\pi$
$983$	40.9314	−	23.6317i	1.30551	−	0.753736i	0.981343	+	0.192265i	$0.0615833\pi$
$984$		0			0
$985$	9.15554	+	54.1975i	0.291720	+	1.72688i
$986$		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	0.976150	+	0.217097i	$0.0696587\pi$
$991$	21.2833	+	36.8638i	0.676086	+	1.17102i	−0.300064	+	0.953919i	$0.597008\pi$
$992$		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	$-0.495681\pi$
$997$	27.9851	−	16.1572i	0.886297	−	0.511704i	0.872730	+	0.488204i	$0.162348\pi$
$998$		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.289.1	yes	16
3.2	odd	2		1260.2.bm.c.289.8		16
4.3	odd	2		1680.2.di.e.289.5		16
5.2	odd	4		2100.2.q.m.1801.4		8
5.3	odd	4		2100.2.q.l.1801.1		8
5.4	even	2	inner	420.2.bb.a.289.7	yes	16
7.2	even	3		2940.2.k.f.589.4		8
7.3	odd	6		2940.2.bb.i.949.2		16
7.4	even	3	inner	420.2.bb.a.109.7	yes	16
7.5	odd	6		2940.2.k.g.589.5		8
7.6	odd	2		2940.2.bb.i.1549.8		16
15.14	odd	2		1260.2.bm.c.289.4		16
20.19	odd	2		1680.2.di.e.289.3		16
21.11	odd	6		1260.2.bm.c.109.4		16
28.11	odd	6		1680.2.di.e.529.3		16
35.4	even	6	inner	420.2.bb.a.109.1	✓	16
35.9	even	6		2940.2.k.f.589.8		8
35.18	odd	12		2100.2.q.l.1201.1		8
35.19	odd	6		2940.2.k.g.589.1		8
35.24	odd	6		2940.2.bb.i.949.8		16
35.32	odd	12		2100.2.q.m.1201.4		8
35.34	odd	2		2940.2.bb.i.1549.2		16
105.74	odd	6		1260.2.bm.c.109.8		16
140.39	odd	6		1680.2.di.e.529.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.1	✓	16	35.4	even	6	inner
420.2.bb.a.109.7	yes	16	7.4	even	3	inner
420.2.bb.a.289.1	yes	16	1.1	even	1	trivial
420.2.bb.a.289.7	yes	16	5.4	even	2	inner
1260.2.bm.c.109.4		16	21.11	odd	6
1260.2.bm.c.109.8		16	105.74	odd	6
1260.2.bm.c.289.4		16	15.14	odd	2
1260.2.bm.c.289.8		16	3.2	odd	2
1680.2.di.e.289.3		16	20.19	odd	2
1680.2.di.e.289.5		16	4.3	odd	2
1680.2.di.e.529.3		16	28.11	odd	6
1680.2.di.e.529.5		16	140.39	odd	6
2100.2.q.l.1201.1		8	35.18	odd	12
2100.2.q.l.1801.1		8	5.3	odd	4
2100.2.q.m.1201.4		8	35.32	odd	12
2100.2.q.m.1801.4		8	5.2	odd	4
2940.2.k.f.589.4		8	7.2	even	3
2940.2.k.f.589.8		8	35.9	even	6
2940.2.k.g.589.1		8	35.19	odd	6
2940.2.k.g.589.5		8	7.5	odd	6
2940.2.bb.i.949.2		16	7.3	odd	6
2940.2.bb.i.949.8		16	35.24	odd	6
2940.2.bb.i.1549.2		16	35.34	odd	2
2940.2.bb.i.1549.8		16	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.20483 + 0.372460i) q^{5} +(1.29633 - 2.30641i) q^{7} +(0.500000 - 0.866025i) q^{9} +(1.07409 + 1.86038i) q^{11} -3.20929i q^{13} +(1.72321 - 1.42497i) q^{15} +(3.12880 - 1.80641i) q^{17} +(2.65730 - 4.60257i) q^{19} +(0.0305535 + 2.64557i) q^{21} +(-1.91330 - 1.10465i) q^{23} +(4.72255 - 1.64242i) q^{25} +1.00000i q^{27} +9.12035 q^{29} +(-3.70929 - 6.42468i) q^{31} +(-1.86038 - 1.07409i) q^{33} +(-1.99913 + 5.56808i) q^{35} +(2.20985 + 1.27586i) q^{37} +(1.60465 + 2.77933i) q^{39} +6.14818 q^{41} +5.44455i q^{43} +(-0.779855 + 2.09567i) q^{45} +(-9.13644 - 5.27492i) q^{47} +(-3.63907 - 5.97973i) q^{49} +(-1.80641 + 3.12880i) q^{51} +(-4.67960 + 2.70177i) q^{53} +(-3.06111 - 3.70177i) q^{55} +5.31459i q^{57} +(-4.43796 - 7.68677i) q^{59} +(-6.90194 + 11.9545i) q^{61} +(-1.34925 - 2.27586i) q^{63} +(1.19533 + 7.07594i) q^{65} +(-0.0141657 + 0.00817856i) q^{67} +2.20929 q^{69} -5.63105 q^{71} +(9.91127 - 5.72227i) q^{73} +(-3.26863 + 3.78365i) q^{75} +(5.68318 - 0.0656346i) q^{77} +(7.65543 - 13.2596i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.0314i q^{83} +(-6.22565 + 5.14818i) q^{85} +(-7.89845 + 4.56017i) q^{87} +(-1.96879 + 3.41005i) q^{89} +(-7.40194 - 4.16029i) q^{91} +(6.42468 + 3.70929i) q^{93} +(-4.14461 + 11.1376i) q^{95} +5.16454i q^{97} +2.14818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more