LMFDB - Embedded newform 1680.2.di.g.529.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(289,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.di (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,2,0,0,0,12,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.9
Character	$\chi$	$=$	1680.529
Dual form			1680.2.di.g.289.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{3} +(-2.17066 + 0.536884i) q^{5} +(0.933675 + 2.47553i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.87680 - 4.98276i) q^{11} -4.56531i q^{13} +(-2.14829 - 0.620374i) q^{15} +(4.23940 + 2.44762i) q^{17} +(-2.68072 - 4.64314i) q^{19} +(-0.429179 + 2.61071i) q^{21} +(-0.775297 + 0.447618i) q^{23} +(4.42351 - 2.33078i) q^{25} +1.00000i q^{27} +4.20085 q^{29} +(-1.74075 + 3.01506i) q^{31} +(4.98276 - 2.87680i) q^{33} +(-3.35576 - 4.87226i) q^{35} +(-3.89750 + 2.25022i) q^{37} +(2.28265 - 3.95367i) q^{39} +8.67682 q^{41} -8.57420i q^{43} +(-1.55028 - 1.61140i) q^{45} +(3.14064 - 1.81325i) q^{47} +(-5.25650 + 4.62268i) q^{49} +(2.44762 + 4.23940i) q^{51} +(11.9248 + 6.88476i) q^{53} +(-3.56938 + 12.3604i) q^{55} -5.36144i q^{57} +(-3.50176 + 6.06523i) q^{59} +(3.04955 + 5.28198i) q^{61} +(-1.67704 + 2.04635i) q^{63} +(2.45104 + 9.90972i) q^{65} +(7.75980 + 4.48012i) q^{67} -0.895236 q^{69} +5.38928 q^{71} +(7.10518 + 4.10218i) q^{73} +(4.99626 + 0.193239i) q^{75} +(15.0210 + 2.46932i) q^{77} +(-6.64226 - 11.5047i) q^{79} +(-0.500000 + 0.866025i) q^{81} -3.44085i q^{83} +(-10.5164 - 3.03688i) q^{85} +(3.63804 + 2.10042i) q^{87} +(-1.88139 - 3.25866i) q^{89} +(11.3016 - 4.26251i) q^{91} +(-3.01506 + 1.74075i) q^{93} +(8.31175 + 8.63944i) q^{95} -4.32089i q^{97} +5.75359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5} + 12 q^{9} + 8 q^{11} - 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} - 4 q^{31} - 30 q^{35} - 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} + 20 q^{51} - 12 q^{55} + 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots + 16 q^{99}+O(q^{100}) $ 24 * q + 2 * q^5 + 12 * q^9 + 8 * q^11 - 8 * q^19 + 12 * q^21 + 2 * q^25 - 24 * q^29 - 4 * q^31 - 30 * q^35 - 4 * q^39 + 32 * q^41 - 2 * q^45 - 12 * q^49 + 20 * q^51 - 12 * q^55 + 4 * q^59 + 32 * q^61 + 22 * q^65 + 56 * q^69 - 72 * q^71 + 16 * q^75 - 20 * q^79 - 12 * q^81 + 8 * q^85 + 24 * q^89 - 8 * q^91 + 18 * q^95 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		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
$5$	−2.17066	+	0.536884i	−0.970748	+	0.240102i
$5$	−2.17066	+	0.536884i	−0.970748	+	0.240102i
$6$		0			0
$7$	0.933675	+	2.47553i	0.352896	+	0.935663i
$7$	0.933675	+	2.47553i	0.352896	+	0.935663i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.87680	−	4.98276i	0.867387	−	1.50236i	0.00272961	−	0.999996i	$-0.499131\pi$
$11$	2.87680	−	4.98276i	0.867387	−	1.50236i	0.864657	−	0.502362i	$-0.167536\pi$
$12$		0			0
$13$		−	4.56531i		−	1.26619i	−0.774075	−	0.633094i	$-0.781784\pi$
$13$		−	4.56531i		−	1.26619i	0.774075	−	0.633094i	$-0.218216\pi$
$14$		0			0
$15$	−2.14829	−	0.620374i	−0.554685	−	0.160180i
$16$		0			0
$17$	4.23940	+	2.44762i	1.02821	+	0.593635i	0.916470	−	0.400104i	$-0.131026\pi$
$17$	4.23940	+	2.44762i	1.02821	+	0.593635i	0.111735	+	0.993738i	$0.464359\pi$
$18$		0			0
$19$	−2.68072	−	4.64314i	−0.614999	−	1.06521i	−0.990385	−	0.138341i	$-0.955823\pi$
$19$	−2.68072	−	4.64314i	−0.614999	−	1.06521i	0.375386	−	0.926869i	$-0.377510\pi$
$20$		0			0
$21$	−0.429179	+	2.61071i	−0.0936546	+	0.569704i
$22$		0			0
$23$	−0.775297	+	0.447618i	−0.161661	+	0.0933348i	−0.578648	−	0.815578i	$-0.696419\pi$
$23$	−0.775297	+	0.447618i	−0.161661	+	0.0933348i	0.416987	+	0.908912i	$0.363086\pi$
$24$		0			0
$25$	4.42351	−	2.33078i	0.884702	−	0.466156i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	4.20085			0.780078			0.390039	−	0.920798i	$-0.372462\pi$
$29$	4.20085			0.780078			0.390039	+	0.920798i	$0.372462\pi$
$30$		0			0
$31$	−1.74075	+	3.01506i	−0.312648	+	0.541521i	−0.978935	−	0.204174i	$-0.934549\pi$
$31$	−1.74075	+	3.01506i	−0.312648	+	0.541521i	0.666287	+	0.745695i	$0.267883\pi$
$32$		0			0
$33$	4.98276	−	2.87680i	0.867387	−	0.500786i
$34$		0			0
$35$	−3.35576	−	4.87226i	−0.567227	−	0.823561i
$36$		0			0
$37$	−3.89750	+	2.25022i	−0.640745	+	0.369934i	−0.784901	−	0.619621i	$-0.787286\pi$
$37$	−3.89750	+	2.25022i	−0.640745	+	0.369934i	0.144156	+	0.989555i	$0.453953\pi$
$38$		0			0
$39$	2.28265	−	3.95367i	0.365517	−	0.633094i
$40$		0			0
$41$	8.67682			1.35509			0.677546	−	0.735481i	$-0.263044\pi$
$41$	8.67682			1.35509			0.677546	+	0.735481i	$0.263044\pi$
$42$		0			0
$43$		−	8.57420i		−	1.30755i	−0.756688	−	0.653777i	$-0.773184\pi$
$43$		−	8.57420i		−	1.30755i	0.756688	−	0.653777i	$-0.226816\pi$
$44$		0			0
$45$	−1.55028	−	1.61140i	−0.231103	−	0.240214i
$46$		0			0
$47$	3.14064	−	1.81325i	0.458110	−	0.264490i	−0.253139	−	0.967430i	$-0.581463\pi$
$47$	3.14064	−	1.81325i	0.458110	−	0.264490i	0.711249	+	0.702940i	$0.248130\pi$
$48$		0			0
$49$	−5.25650	+	4.62268i	−0.750929	+	0.660383i
$50$		0			0
$51$	2.44762	+	4.23940i	0.342735	+	0.593635i
$52$		0			0
$53$	11.9248	+	6.88476i	1.63799	+	0.945694i	0.981524	+	0.191340i	$0.0612832\pi$
$53$	11.9248	+	6.88476i	1.63799	+	0.945694i	0.656467	+	0.754355i	$0.272050\pi$
$54$		0			0
$55$	−3.56938	+	12.3604i	−0.481295	+	1.66667i
$56$		0			0
$57$		−	5.36144i		−	0.710140i
$58$		0			0
$59$	−3.50176	+	6.06523i	−0.455891	+	0.789626i	−0.998739	−	0.0502051i	$-0.984012\pi$
$59$	−3.50176	+	6.06523i	−0.455891	+	0.789626i	0.542848	+	0.839831i	$0.317346\pi$
$60$		0			0
$61$	3.04955	+	5.28198i	0.390455	+	0.676288i	0.992510	−	0.122167i	$-0.0389843\pi$
$61$	3.04955	+	5.28198i	0.390455	+	0.676288i	−0.602054	+	0.798455i	$0.705651\pi$
$62$		0			0
$63$	−1.67704	+	2.04635i	−0.211287	+	0.257816i
$64$		0			0
$65$	2.45104	+	9.90972i	0.304014	+	1.22915i
$66$		0			0
$67$	7.75980	+	4.48012i	0.948010	+	0.547334i	0.892462	−	0.451122i	$-0.148976\pi$
$67$	7.75980	+	4.48012i	0.948010	+	0.547334i	0.0555479	+	0.998456i	$0.482309\pi$
$68$		0			0
$69$	−0.895236			−0.107774
$70$		0			0
$71$	5.38928			0.639589			0.319795	−	0.947487i	$-0.396386\pi$
$71$	5.38928			0.639589			0.319795	+	0.947487i	$0.396386\pi$
$72$		0			0
$73$	7.10518	+	4.10218i	0.831598	+	0.480123i	0.854400	−	0.519617i	$-0.173925\pi$
$73$	7.10518	+	4.10218i	0.831598	+	0.480123i	−0.0228013	+	0.999740i	$0.507259\pi$
$74$		0			0
$75$	4.99626	+	0.193239i	0.576919	+	0.0223134i
$76$		0			0
$77$	15.0210	+	2.46932i	1.71180	+	0.281406i
$78$		0			0
$79$	−6.64226	−	11.5047i	−0.747312	−	1.29438i	−0.949107	−	0.314955i	$-0.898011\pi$
$79$	−6.64226	−	11.5047i	−0.747312	−	1.29438i	0.201795	−	0.979428i	$-0.435323\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	3.44085i		−	0.377682i	−0.982008	−	0.188841i	$-0.939527\pi$
$83$		−	3.44085i		−	0.377682i	0.982008	−	0.188841i	$-0.0604731\pi$
$84$		0			0
$85$	−10.5164	−	3.03688i	−1.14066	−	0.329396i
$86$		0			0
$87$	3.63804	+	2.10042i	0.390039	+	0.225189i
$88$		0			0
$89$	−1.88139	−	3.25866i	−0.199427	−	0.345417i	0.748916	−	0.662665i	$-0.230575\pi$
$89$	−1.88139	−	3.25866i	−0.199427	−	0.345417i	−0.948343	+	0.317248i	$0.897241\pi$
$90$		0			0
$91$	11.3016	−	4.26251i	1.18473	−	0.446833i
$92$		0			0
$93$	−3.01506	+	1.74075i	−0.312648	+	0.180507i
$94$		0			0
$95$	8.31175	+	8.63944i	0.852768	+	0.886388i
$96$		0			0
$97$		−	4.32089i		−	0.438720i	−0.975644	−	0.219360i	$-0.929603\pi$
$97$		−	4.32089i		−	0.438720i	0.975644	−	0.219360i	$-0.0703969\pi$
$98$		0			0
$99$	5.75359			0.578258
$100$		0			0
$101$	0.497171	−	0.861126i	0.0494704	−	0.0856852i	−0.840230	−	0.542230i	$-0.817580\pi$
$101$	0.497171	−	0.861126i	0.0494704	−	0.0856852i	0.889700	+	0.456545i	$0.150913\pi$
$102$		0			0
$103$	−11.3609	+	6.55920i	−1.11942	+	0.646297i	−0.941253	−	0.337703i	$-0.890350\pi$
$103$	−11.3609	+	6.55920i	−1.11942	+	0.646297i	−0.178167	+	0.984000i	$0.557017\pi$
$104$		0			0
$105$	−0.470046	−	5.89738i	−0.0458718	−	0.575525i
$106$		0			0
$107$	13.1202	−	7.57495i	1.26838	−	0.732298i	0.293697	−	0.955899i	$-0.405114\pi$
$107$	13.1202	−	7.57495i	1.26838	−	0.732298i	0.974681	+	0.223600i	$0.0717810\pi$
$108$		0			0
$109$	6.74295	−	11.6791i	0.645857	−	1.11866i	−0.338245	−	0.941058i	$-0.609833\pi$
$109$	6.74295	−	11.6791i	0.645857	−	1.11866i	0.984103	−	0.177600i	$-0.0568333\pi$
$110$		0			0
$111$	−4.50044			−0.427163
$112$		0			0
$113$			12.1854i			1.14631i	0.819448	+	0.573153i	$0.194280\pi$
$113$			12.1854i			1.14631i	−0.819448	+	0.573153i	$0.805720\pi$
$114$		0			0
$115$	1.44259	−	1.38787i	0.134522	−	0.129419i
$116$		0			0
$117$	3.95367	−	2.28265i	0.365517	−	0.211031i
$118$		0			0
$119$	−2.10093	+	12.7800i	−0.192592	+	1.17154i
$120$		0			0
$121$	−11.0519	−	19.1425i	−1.00472	−	1.74023i
$122$		0			0
$123$	7.51434	+	4.33841i	0.677546	+	0.391181i
$124$		0			0
$125$	−8.35057	+	7.43424i	−0.746898	+	0.664939i
$126$		0			0
$127$			2.35791i			0.209231i	0.994513	+	0.104616i	$0.0333612\pi$
$127$			2.35791i			0.209231i	−0.994513	+	0.104616i	$0.966639\pi$
$128$		0			0
$129$	4.28710	−	7.42547i	0.377458	−	0.653777i
$130$		0			0
$131$	−0.0773948	−	0.134052i	−0.00676201	−	0.0117121i	0.862625	−	0.505845i	$-0.168819\pi$
$131$	−0.0773948	−	0.134052i	−0.00676201	−	0.0117121i	−0.869387	+	0.494132i	$0.835486\pi$
$132$		0			0
$133$	8.99132	−	10.9714i	0.779646	−	0.951340i
$134$		0			0
$135$	−0.536884	−	2.17066i	−0.0462076	−	0.186820i
$136$		0			0
$137$	−18.9231	−	10.9253i	−1.61671	−	0.933410i	−0.987763	−	0.155965i	$-0.950151\pi$
$137$	−18.9231	−	10.9253i	−1.61671	−	0.933410i	−0.628951	−	0.777445i	$-0.716515\pi$
$138$		0			0
$139$	−6.93562			−0.588271			−0.294136	−	0.955764i	$-0.595032\pi$
$139$	−6.93562			−0.588271			−0.294136	+	0.955764i	$0.595032\pi$
$140$		0			0
$141$	3.62650			0.305406
$142$		0			0
$143$	−22.7478	−	13.1335i	−1.90227	−	1.09828i
$144$		0			0
$145$	−9.11860	+	2.25537i	−0.757259	+	0.187298i
$146$		0			0
$147$	−6.86361	+	1.37511i	−0.566101	+	0.113417i
$148$		0			0
$149$	3.52660	+	6.10826i	0.288911	+	0.500408i	0.973550	−	0.228474i	$-0.0733736\pi$
$149$	3.52660	+	6.10826i	0.288911	+	0.500408i	−0.684639	+	0.728882i	$0.740040\pi$
$150$		0			0
$151$	9.57640	−	16.5868i	0.779316	−	1.34982i	−0.153020	−	0.988223i	$-0.548900\pi$
$151$	9.57640	−	16.5868i	0.779316	−	1.34982i	0.932336	−	0.361592i	$-0.117767\pi$
$152$		0			0
$153$			4.89524i			0.395756i
$154$		0			0
$155$	2.15983	−	7.47925i	0.173482	−	0.600748i
$156$		0			0
$157$	4.15924	+	2.40134i	0.331943	+	0.191648i	0.656704	−	0.754149i	$-0.271950\pi$
$157$	4.15924	+	2.40134i	0.331943	+	0.191648i	−0.324760	+	0.945796i	$0.605284\pi$
$158$		0			0
$159$	6.88476	+	11.9248i	0.545997	+	0.945694i
$160$		0			0
$161$	−1.83197	−	1.50134i	−0.144379	−	0.118322i
$162$		0			0
$163$	3.70943	−	2.14164i	0.290545	−	0.167746i	−0.347643	−	0.937627i	$-0.613018\pi$
$163$	3.70943	−	2.14164i	0.290545	−	0.167746i	0.638188	+	0.769881i	$0.279684\pi$
$164$		0			0
$165$	−9.27136	+	8.91970i	−0.721774	+	0.694398i
$166$		0			0
$167$		−	8.70217i		−	0.673394i	−0.941613	−	0.336697i	$-0.890690\pi$
$167$		−	8.70217i		−	0.673394i	0.941613	−	0.336697i	$-0.109310\pi$
$168$		0			0
$169$	−7.84204			−0.603234
$170$		0			0
$171$	2.68072	−	4.64314i	0.205000	−	0.355070i
$172$		0			0
$173$	−8.55693	+	4.94034i	−0.650571	+	0.375607i	−0.788675	−	0.614810i	$-0.789233\pi$
$173$	−8.55693	+	4.94034i	−0.650571	+	0.375607i	0.138104	+	0.990418i	$0.455899\pi$
$174$		0			0
$175$	9.90004	+	8.77435i	0.748373	+	0.663278i
$176$		0			0
$177$	−6.06523	+	3.50176i	−0.455891	+	0.263209i
$178$		0			0
$179$	−2.85195	+	4.93973i	−0.213165	+	0.369213i	−0.952703	−	0.303902i	$-0.901711\pi$
$179$	−2.85195	+	4.93973i	−0.213165	+	0.369213i	0.739538	+	0.673114i	$0.235044\pi$
$180$		0			0
$181$	−14.7881			−1.09919			−0.549597	−	0.835430i	$-0.685219\pi$
$181$	−14.7881			−1.09919			−0.549597	+	0.835430i	$0.685219\pi$
$182$		0			0
$183$			6.09911i			0.450859i
$184$		0			0
$185$	7.25203	−	6.97697i	0.533180	−	0.512957i
$186$		0			0
$187$	24.3918	−	14.0826i	1.78370	−	1.02982i
$188$		0			0
$189$	−2.47553	+	0.933675i	−0.180068	+	0.0679148i
$190$		0			0
$191$	−0.882834	−	1.52911i	−0.0638796	−	0.110643i	0.832317	−	0.554300i	$-0.187014\pi$
$191$	−0.882834	−	1.52911i	−0.0638796	−	0.110643i	−0.896196	+	0.443657i	$0.853681\pi$
$192$		0			0
$193$	10.3958	+	6.00200i	0.748304	+	0.432034i	0.825081	−	0.565015i	$-0.191130\pi$
$193$	10.3958	+	6.00200i	0.748304	+	0.432034i	−0.0767766	+	0.997048i	$0.524463\pi$
$194$		0			0
$195$	−2.83220	+	9.80759i	−0.202818	+	0.702336i
$196$		0			0
$197$			9.65235i			0.687702i	0.939024	+	0.343851i	$0.111731\pi$
$197$			9.65235i			0.687702i	−0.939024	+	0.343851i	$0.888269\pi$
$198$		0			0
$199$	−3.09283	+	5.35695i	−0.219245	+	0.379744i	−0.954577	−	0.297963i	$-0.903693\pi$
$199$	−3.09283	+	5.35695i	−0.219245	+	0.379744i	0.735332	+	0.677707i	$0.237026\pi$
$200$		0			0
$201$	4.48012	+	7.75980i	0.316003	+	0.547334i
$202$		0			0
$203$	3.92222	+	10.3993i	0.275286	+	0.729890i
$204$		0			0
$205$	−18.8344	+	4.65844i	−1.31545	+	0.325360i
$206$		0			0
$207$	−0.775297	−	0.447618i	−0.0538869	−	0.0311116i
$208$		0			0
$209$	−30.8475			−2.13377
$210$		0			0
$211$	−21.5996			−1.48698			−0.743488	−	0.668749i	$-0.766830\pi$
$211$	−21.5996			−1.48698			−0.743488	+	0.668749i	$0.766830\pi$
$212$		0			0
$213$	4.66725	+	2.69464i	0.319795	+	0.184634i
$214$		0			0
$215$	4.60335	+	18.6117i	0.313946	+	1.26930i
$216$		0			0
$217$	−9.08918	−	1.49419i	−0.617013	−	0.101432i
$218$		0			0
$219$	4.10218	+	7.10518i	0.277199	+	0.480123i
$220$		0			0
$221$	11.1741	−	19.3542i	0.751653	−	1.30190i
$222$		0			0
$223$			20.4794i			1.37140i	0.727884	+	0.685700i	$0.240504\pi$
$223$			20.4794i			1.37140i	−0.727884	+	0.685700i	$0.759496\pi$
$224$		0			0
$225$	4.23027	+	2.66548i	0.282018	+	0.177699i
$226$		0			0
$227$	−13.2474	−	7.64837i	−0.879258	−	0.507640i	−0.00884444	−	0.999961i	$-0.502815\pi$
$227$	−13.2474	−	7.64837i	−0.879258	−	0.507640i	−0.870414	+	0.492321i	$0.836149\pi$
$228$		0			0
$229$	1.86287	+	3.22659i	0.123102	+	0.213219i	0.920990	−	0.389587i	$-0.127382\pi$
$229$	1.86287	+	3.22659i	0.123102	+	0.213219i	−0.797887	+	0.602807i	$0.794049\pi$
$230$		0			0
$231$	11.7739	+	9.64898i	0.774664	+	0.634856i
$232$		0			0
$233$	4.99613	−	2.88452i	0.327308	−	0.188971i	−0.327338	−	0.944907i	$-0.606151\pi$
$233$	4.99613	−	2.88452i	0.327308	−	0.188971i	0.654645	+	0.755936i	$0.272818\pi$
$234$		0			0
$235$	−5.84375	+	5.62211i	−0.381204	+	0.366746i
$236$		0			0
$237$		−	13.2845i		−	0.862922i
$238$		0			0
$239$	15.6895			1.01487			0.507435	−	0.861690i	$-0.330594\pi$
$239$	15.6895			1.01487			0.507435	+	0.861690i	$0.330594\pi$
$240$		0			0
$241$	8.63222	−	14.9515i	0.556050	−	0.963108i	−0.441770	−	0.897128i	$-0.645649\pi$
$241$	8.63222	−	14.9515i	0.556050	−	0.963108i	0.997821	−	0.0659796i	$-0.0210172\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	8.92823	−	12.8564i	0.570404	−	0.821365i
$246$		0			0
$247$	−21.1974	+	12.2383i	−1.34876	+	0.778705i
$248$		0			0
$249$	1.72042	−	2.97986i	0.109027	−	0.188841i
$250$		0			0
$251$	18.7038			1.18057			0.590286	−	0.807194i	$-0.299015\pi$
$251$	18.7038			1.18057			0.590286	+	0.807194i	$0.299015\pi$
$252$		0			0
$253$			5.15082i			0.323829i
$254$		0			0
$255$	−7.58901	−	7.88820i	−0.475242	−	0.493978i
$256$		0			0
$257$	5.46653	−	3.15610i	0.340993	−	0.196872i	−0.319718	−	0.947513i	$-0.603588\pi$
$257$	5.46653	−	3.15610i	0.340993	−	0.196872i	0.660711	+	0.750640i	$0.270255\pi$
$258$		0			0
$259$	−9.20949	−	7.54740i	−0.572250	−	0.468973i
$260$		0			0
$261$	2.10042	+	3.63804i	0.130013	+	0.225189i
$262$		0			0
$263$	−18.0459	−	10.4188i	−1.11276	−	0.642451i	−0.173215	−	0.984884i	$-0.555416\pi$
$263$	−18.0459	−	10.4188i	−1.11276	−	0.642451i	−0.939542	+	0.342433i	$0.888749\pi$
$264$		0			0
$265$	−29.5809	−	8.54225i	−1.81714	−	0.524746i
$266$		0			0
$267$		−	3.76278i		−	0.230278i
$268$		0			0
$269$	−13.7544	+	23.8232i	−0.838618	+	1.45253i	0.0524327	+	0.998624i	$0.483302\pi$
$269$	−13.7544	+	23.8232i	−0.838618	+	1.45253i	−0.891050	+	0.453904i	$0.850031\pi$
$270$		0			0
$271$	13.8331	+	23.9596i	0.840299	+	1.45544i	0.889642	+	0.456659i	$0.150954\pi$
$271$	13.8331	+	23.9596i	0.840299	+	1.45544i	−0.0493424	+	0.998782i	$0.515713\pi$
$272$		0			0
$273$	11.9187	+	1.95934i	0.721352	+	0.118584i
$274$		0			0
$275$	1.11182	−	28.7465i	0.0670454	−	1.73348i
$276$		0			0
$277$	−4.33597	−	2.50337i	−0.260523	−	0.150413i	0.364050	−	0.931379i	$-0.381394\pi$
$277$	−4.33597	−	2.50337i	−0.260523	−	0.150413i	−0.624573	+	0.780966i	$0.714727\pi$
$278$		0			0
$279$	−3.48150			−0.208432
$280$		0			0
$281$	30.4051			1.81381			0.906907	−	0.421332i	$-0.138437\pi$
$281$	30.4051			1.81381			0.906907	+	0.421332i	$0.138437\pi$
$282$		0			0
$283$	−19.4012	−	11.2013i	−1.15328	−	0.665847i	−0.203597	−	0.979055i	$-0.565263\pi$
$283$	−19.4012	−	11.2013i	−1.15328	−	0.665847i	−0.949685	+	0.313208i	$0.898596\pi$
$284$		0			0
$285$	2.87847	+	11.6378i	0.170506	+	0.689367i
$286$		0			0
$287$	8.10132	+	21.4797i	0.478206	+	1.26791i
$288$		0			0
$289$	3.48167	+	6.03042i	0.204804	+	0.354731i
$290$		0			0
$291$	2.16044	−	3.74200i	0.126647	−	0.219360i
$292$		0			0
$293$		−	20.7429i		−	1.21181i	−0.795536	−	0.605906i	$-0.792811\pi$
$293$		−	20.7429i		−	1.21181i	0.795536	−	0.605906i	$-0.207189\pi$
$294$		0			0
$295$	4.34480	−	15.0456i	0.252964	−	0.875987i
$296$		0			0
$297$	4.98276	+	2.87680i	0.289129	+	0.166929i
$298$		0			0
$299$	2.04351	+	3.53947i	0.118179	+	0.204693i
$300$		0			0
$301$	21.2257	−	8.00551i	1.22343	−	0.461430i
$302$		0			0
$303$	0.861126	−	0.497171i	0.0494704	−	0.0285617i
$304$		0			0
$305$	−9.45535	−	9.82812i	−0.541412	−	0.562756i
$306$		0			0
$307$			8.12145i			0.463516i	0.972774	+	0.231758i	$0.0744477\pi$
$307$			8.12145i			0.463516i	−0.972774	+	0.231758i	$0.925552\pi$
$308$		0			0
$309$	−13.1184			−0.746279
$310$		0			0
$311$	6.81835	−	11.8097i	0.386633	−	0.669668i	−0.605361	−	0.795951i	$-0.706971\pi$
$311$	6.81835	−	11.8097i	0.386633	−	0.669668i	0.991994	+	0.126283i	$0.0403046\pi$
$312$		0			0
$313$	−8.05335	+	4.64960i	−0.455202	+	0.262811i	−0.710025	−	0.704177i	$-0.751316\pi$
$313$	−8.05335	+	4.64960i	−0.455202	+	0.262811i	0.254823	+	0.966988i	$0.417983\pi$
$314$		0			0
$315$	2.54162	−	5.34230i	0.143204	−	0.301005i
$316$		0			0
$317$	−14.9071	+	8.60662i	−0.837266	+	0.483396i	−0.856334	−	0.516422i	$-0.827264\pi$
$317$	−14.9071	+	8.60662i	−0.837266	+	0.483396i	0.0190676	+	0.999818i	$0.493930\pi$
$318$		0			0
$319$	12.0850	−	20.9318i	0.676629	−	1.17196i
$320$		0			0
$321$	15.1499			0.845585
$322$		0			0
$323$		−	26.2455i		−	1.46034i
$324$		0			0
$325$	−10.6407	−	20.1947i	−0.590242	−	1.12020i
$326$		0			0
$327$	11.6791	−	6.74295i	0.645857	−	0.372886i
$328$		0			0
$329$	7.42109	+	6.08177i	0.409138	+	0.335299i
$330$		0			0
$331$	1.25092	+	2.16666i	0.0687569	+	0.119090i	0.898354	−	0.439272i	$-0.144763\pi$
$331$	1.25092	+	2.16666i	0.0687569	+	0.119090i	−0.829597	+	0.558362i	$0.811430\pi$
$332$		0			0
$333$	−3.89750	−	2.25022i	−0.213582	−	0.123311i
$334$		0			0
$335$	−19.2492	−	5.55870i	−1.05169	−	0.303704i
$336$		0			0
$337$		−	6.69015i		−	0.364436i	−0.983258	−	0.182218i	$-0.941672\pi$
$337$		−	6.69015i		−	0.364436i	0.983258	−	0.182218i	$-0.0583276\pi$
$338$		0			0
$339$	−6.09270	+	10.5529i	−0.330910	+	0.573153i
$340$		0			0
$341$	10.0156	+	17.3475i	0.542373	+	0.939417i
$342$		0			0
$343$	−16.3514	−	8.69656i	−0.882895	−	0.469570i
$344$		0			0
$345$	1.94325	−	0.480637i	0.104621	−	0.0258767i
$346$		0			0
$347$	−2.36917	−	1.36784i	−0.127184	−	0.0734296i	0.435058	−	0.900402i	$-0.356728\pi$
$347$	−2.36917	−	1.36784i	−0.127184	−	0.0734296i	−0.562242	+	0.826973i	$0.690061\pi$
$348$		0			0
$349$	17.7486			0.950059			0.475030	−	0.879970i	$-0.342437\pi$
$349$	17.7486			0.950059			0.475030	+	0.879970i	$0.342437\pi$
$350$		0			0
$351$	4.56531			0.243678
$352$		0			0
$353$	8.71230	+	5.03005i	0.463709	+	0.267722i	0.713602	−	0.700551i	$-0.247062\pi$
$353$	8.71230	+	5.03005i	0.463709	+	0.267722i	−0.249894	+	0.968273i	$0.580396\pi$
$354$		0			0
$355$	−11.6983	+	2.89341i	−0.620880	+	0.153567i
$356$		0			0
$357$	−8.20948	+	10.0174i	−0.434492	+	0.530176i
$358$		0			0
$359$	−5.97529	−	10.3495i	−0.315364	−	0.546226i	0.664151	−	0.747598i	$-0.268793\pi$
$359$	−5.97529	−	10.3495i	−0.315364	−	0.546226i	−0.979515	+	0.201373i	$0.935460\pi$
$360$		0			0
$361$	−4.87251	+	8.43943i	−0.256448	+	0.444181i
$362$		0			0
$363$		−	22.1038i		−	1.16015i
$364$		0			0
$365$	−17.6253	−	5.08977i	−0.922551	−	0.266411i
$366$		0			0
$367$	−29.0403	−	16.7664i	−1.51589	−	0.875201i	−0.999826	−	0.0186533i	$-0.994062\pi$
$367$	−29.0403	−	16.7664i	−1.51589	−	0.875201i	−0.516067	−	0.856548i	$-0.672605\pi$
$368$		0			0
$369$	4.33841	+	7.51434i	0.225849	+	0.391181i
$370$		0			0
$371$	−5.90959	+	35.9482i	−0.306811	+	1.86634i
$372$		0			0
$373$	−16.2921	+	9.40624i	−0.843572	+	0.487036i	−0.858477	−	0.512852i	$-0.828589\pi$
$373$	−16.2921	+	9.40624i	−0.843572	+	0.487036i	0.0149049	+	0.999889i	$0.495255\pi$
$374$		0			0
$375$	−10.9489	+	2.26296i	−0.565400	+	0.116859i
$376$		0			0
$377$		−	19.1782i		−	0.987726i
$378$		0			0
$379$	−21.2269			−1.09035			−0.545176	−	0.838322i	$-0.683537\pi$
$379$	−21.2269			−1.09035			−0.545176	+	0.838322i	$0.683537\pi$
$380$		0			0
$381$	−1.17896	+	2.04201i	−0.0603998	+	0.104616i
$382$		0			0
$383$	−8.14310	+	4.70142i	−0.416093	+	0.240232i	−0.693404	−	0.720549i	$-0.743890\pi$
$383$	−8.14310	+	4.70142i	−0.416093	+	0.240232i	0.277311	+	0.960780i	$0.410557\pi$
$384$		0			0
$385$	−33.9311	+	2.70445i	−1.72929	+	0.137832i
$386$		0			0
$387$	7.42547	−	4.28710i	0.377458	−	0.217926i
$388$		0			0
$389$	7.20963	−	12.4874i	0.365543	−	0.633139i	−0.623320	−	0.781967i	$-0.714217\pi$
$389$	7.20963	−	12.4874i	0.365543	−	0.633139i	0.988863	+	0.148828i	$0.0475501\pi$
$390$		0			0
$391$	−4.38239			−0.221627
$392$		0			0
$393$		−	0.154790i		−	0.00780810i
$394$		0			0
$395$	20.5948	+	21.4067i	1.03624	+	1.07709i
$396$		0			0
$397$	1.54528	−	0.892166i	0.0775552	−	0.0447765i	−0.460721	−	0.887545i	$-0.652409\pi$
$397$	1.54528	−	0.892166i	0.0775552	−	0.0447765i	0.538276	+	0.842769i	$0.319076\pi$
$398$		0			0
$399$	13.2724	−	5.00584i	0.664451	−	0.250605i
$400$		0			0
$401$	18.9425	+	32.8094i	0.945944	+	1.63842i	0.753849	+	0.657048i	$0.228195\pi$
$401$	18.9425	+	32.8094i	0.945944	+	1.63842i	0.192095	+	0.981376i	$0.438472\pi$
$402$		0			0
$403$	13.7647	+	7.94705i	0.685668	+	0.395871i
$404$		0			0
$405$	0.620374	−	2.14829i	0.0308266	−	0.106749i
$406$		0			0
$407$			25.8937i			1.28350i
$408$		0			0
$409$	−1.55846	+	2.69933i	−0.0770609	+	0.133473i	−0.901981	−	0.431777i	$-0.857887\pi$
$409$	−1.55846	+	2.69933i	−0.0770609	+	0.133473i	0.824920	+	0.565250i	$0.191220\pi$
$410$		0			0
$411$	−10.9253	−	18.9231i	−0.538904	−	0.933410i
$412$		0			0
$413$	−18.2842	−	3.00577i	−0.899705	−	0.147904i
$414$		0			0
$415$	1.84734	+	7.46891i	0.0906822	+	0.366634i
$416$		0			0
$417$	−6.00642	−	3.46781i	−0.294136	−	0.169819i
$418$		0			0
$419$	−9.00616			−0.439980			−0.219990	−	0.975502i	$-0.570602\pi$
$419$	−9.00616			−0.439980			−0.219990	+	0.975502i	$0.570602\pi$
$420$		0			0
$421$	33.2819			1.62206			0.811031	−	0.585003i	$-0.198907\pi$
$421$	33.2819			1.62206			0.811031	+	0.585003i	$0.198907\pi$
$422$		0			0
$423$	3.14064	+	1.81325i	0.152703	+	0.0881632i
$424$		0			0
$425$	24.4579	+	0.945953i	1.18638	+	0.0458854i
$426$		0			0
$427$	−10.2284	+	12.4809i	−0.494988	+	0.603994i
$428$		0			0
$429$	−13.1335	−	22.7478i	−0.634090	−	1.09828i
$430$		0			0
$431$	−2.23003	+	3.86253i	−0.107417	+	0.186051i	−0.914723	−	0.404081i	$-0.867591\pi$
$431$	−2.23003	+	3.86253i	−0.107417	+	0.186051i	0.807306	+	0.590133i	$0.200925\pi$
$432$		0			0
$433$			37.1411i			1.78489i	0.451159	+	0.892444i	$0.351011\pi$
$433$			37.1411i			1.78489i	−0.451159	+	0.892444i	$0.648989\pi$
$434$		0			0
$435$	−9.02463	−	2.60610i	−0.432698	−	0.124953i
$436$		0			0
$437$	4.15671	+	2.39987i	0.198842	+	0.114802i
$438$		0			0
$439$	−19.4909	−	33.7593i	−0.930251	−	1.61124i	−0.782891	−	0.622159i	$-0.786256\pi$
$439$	−19.4909	−	33.7593i	−0.930251	−	1.61124i	−0.147360	−	0.989083i	$-0.547078\pi$
$440$		0			0
$441$	−6.63161	−	2.24093i	−0.315791	−	0.106711i
$442$		0			0
$443$	−29.0837	+	16.7915i	−1.38181	+	0.797786i	−0.992373	−	0.123268i	$-0.960662\pi$
$443$	−29.0837	+	16.7915i	−1.38181	+	0.797786i	−0.389433	+	0.921055i	$0.627329\pi$
$444$		0			0
$445$	5.83337	+	6.06335i	0.276528	+	0.287430i
$446$		0			0
$447$			7.05321i			0.333605i
$448$		0			0
$449$	13.7170			0.647347			0.323674	−	0.946169i	$-0.395082\pi$
$449$	13.7170			0.647347			0.323674	+	0.946169i	$0.395082\pi$
$450$		0			0
$451$	24.9614	−	43.2345i	1.17539	−	2.03583i
$452$		0			0
$453$	16.5868	−	9.57640i	0.779316	−	0.449938i
$454$		0			0
$455$	−22.2434	+	15.3201i	−1.04278	+	0.718217i
$456$		0			0
$457$	−20.1117	+	11.6115i	−0.940787	+	0.543164i	−0.890207	−	0.455556i	$-0.849440\pi$
$457$	−20.1117	+	11.6115i	−0.940787	+	0.543164i	−0.0505802	+	0.998720i	$0.516107\pi$
$458$		0			0
$459$	−2.44762	+	4.23940i	−0.114245	+	0.197878i
$460$		0			0
$461$	−28.2837			−1.31730			−0.658651	−	0.752449i	$-0.728873\pi$
$461$	−28.2837			−1.31730			−0.658651	+	0.752449i	$0.728873\pi$
$462$		0			0
$463$			17.4485i			0.810901i	0.914117	+	0.405450i	$0.132885\pi$
$463$			17.4485i			0.810901i	−0.914117	+	0.405450i	$0.867115\pi$
$464$		0			0
$465$	5.61009	−	5.39731i	0.260162	−	0.250294i
$466$		0			0
$467$	20.4002	−	11.7781i	0.944009	−	0.545024i	0.0527945	−	0.998605i	$-0.483187\pi$
$467$	20.4002	−	11.7781i	0.944009	−	0.545024i	0.891215	+	0.453581i	$0.149854\pi$
$468$		0			0
$469$	−3.84555	+	23.3926i	−0.177571	+	1.08017i
$470$		0			0
$471$	2.40134	+	4.15924i	0.110648	+	0.191648i
$472$		0			0
$473$	−42.7232	−	24.6662i	−1.96441	−	1.13415i
$474$		0			0
$475$	−22.6803	−	14.2908i	−1.04065	−	0.655708i
$476$		0			0
$477$			13.7695i			0.630463i
$478$		0			0
$479$	5.52709	−	9.57320i	0.252539	−	0.437410i	−0.711685	−	0.702499i	$-0.752068\pi$
$479$	5.52709	−	9.57320i	0.252539	−	0.437410i	0.964224	+	0.265088i	$0.0854010\pi$
$480$		0			0
$481$	10.2730	+	17.7933i	0.468407	+	0.811304i
$482$		0			0
$483$	−0.835859	−	2.21618i	−0.0380329	−	0.100840i
$484$		0			0
$485$	2.31981	+	9.37917i	0.105337	+	0.425886i
$486$		0			0
$487$	−10.1849	−	5.88025i	−0.461521	−	0.266460i	0.251162	−	0.967945i	$-0.419187\pi$
$487$	−10.1849	−	5.88025i	−0.461521	−	0.266460i	−0.712684	+	0.701485i	$0.752521\pi$
$488$		0			0
$489$	4.28328			0.193697
$490$		0			0
$491$	17.8544			0.805759			0.402880	−	0.915253i	$-0.368009\pi$
$491$	17.8544			0.805759			0.402880	+	0.915253i	$0.368009\pi$
$492$		0			0
$493$	17.8091	+	10.2821i	0.802080	+	0.463081i
$494$		0			0
$495$	−12.4891	+	3.08901i	−0.561343	+	0.138841i
$496$		0			0
$497$	5.03183	+	13.3413i	0.225708	+	0.598440i
$498$		0			0
$499$	−4.26332	−	7.38429i	−0.190853	−	0.330566i	0.754680	−	0.656093i	$-0.227792\pi$
$499$	−4.26332	−	7.38429i	−0.190853	−	0.330566i	−0.945533	+	0.325526i	$0.894459\pi$
$500$		0			0
$501$	4.35109	−	7.53630i	0.194392	−	0.336697i
$502$		0			0
$503$			32.6513i			1.45585i	0.685657	+	0.727925i	$0.259515\pi$
$503$			32.6513i			1.45585i	−0.685657	+	0.727925i	$0.740485\pi$
$504$		0			0
$505$	−0.616864	+	2.13613i	−0.0274501	+	0.0950566i
$506$		0			0
$507$	−6.79141	−	3.92102i	−0.301617	−	0.174139i
$508$		0			0
$509$	−19.2556	−	33.3517i	−0.853490	−	1.47829i	−0.878039	−	0.478589i	$-0.841148\pi$
$509$	−19.2556	−	33.3517i	−0.853490	−	1.47829i	0.0245493	−	0.999699i	$-0.492185\pi$
$510$		0			0
$511$	−3.52114	+	21.4192i	−0.155766	+	0.947529i
$512$		0			0
$513$	4.64314	−	2.68072i	0.205000	−	0.118357i
$514$		0			0
$515$	21.1390	−	20.3372i	0.931497	−	0.896166i
$516$		0			0
$517$		−	20.8654i		−	0.917660i
$518$		0			0
$519$	−9.88069			−0.433714
$520$		0			0
$521$	−14.8743	+	25.7630i	−0.651654	+	1.12870i	0.331067	+	0.943607i	$0.392591\pi$
$521$	−14.8743	+	25.7630i	−0.651654	+	1.12870i	−0.982721	+	0.185091i	$0.940742\pi$
$522$		0			0
$523$	1.81046	−	1.04527i	0.0791659	−	0.0457064i	−0.459895	−	0.887974i	$-0.652113\pi$
$523$	1.81046	−	1.04527i	0.0791659	−	0.0457064i	0.539060	+	0.842267i	$0.318779\pi$
$524$		0			0
$525$	4.18652	+	12.5488i	0.182714	+	0.547676i
$526$		0			0
$527$	−14.7594	+	8.52137i	−0.642932	+	0.371197i
$528$		0			0
$529$	−11.0993	+	19.2245i	−0.482577	+	0.835848i
$530$		0			0
$531$	−7.00352			−0.303927
$532$		0			0
$533$		−	39.6123i		−	1.71580i
$534$		0			0
$535$	−24.4126	+	23.4867i	−1.05545	+	1.01542i
$536$		0			0
$537$	−4.93973	+	2.85195i	−0.213165	+	0.123071i
$538$		0			0
$539$	7.91181	+	39.4904i	0.340786	+	1.70097i
$540$		0			0
$541$	−14.0639	−	24.3593i	−0.604653	−	1.04729i	−0.992106	−	0.125400i	$-0.959979\pi$
$541$	−14.0639	−	24.3593i	−0.604653	−	1.04729i	0.387453	−	0.921889i	$-0.373355\pi$
$542$		0			0
$543$	−12.8069	−	7.39407i	−0.549597	−	0.317310i
$544$		0			0
$545$	−8.36630	+	28.9716i	−0.358373	+	1.24101i
$546$		0			0
$547$		−	29.9829i		−	1.28198i	−0.767550	−	0.640989i	$-0.778525\pi$
$547$		−	29.9829i		−	1.28198i	0.767550	−	0.640989i	$-0.221475\pi$
$548$		0			0
$549$	−3.04955	+	5.28198i	−0.130152	+	0.225429i
$550$		0			0
$551$	−11.2613	−	19.5051i	−0.479747	−	0.830946i
$552$		0			0
$553$	22.2786	−	27.1848i	0.947382	−	1.15601i
$554$		0			0
$555$	9.76893	−	2.41622i	0.414668	−	0.102563i
$556$		0			0
$557$	−4.59121	−	2.65073i	−0.194536	−	0.112315i	0.399568	−	0.916703i	$-0.369160\pi$
$557$	−4.59121	−	2.65073i	−0.194536	−	0.112315i	−0.594104	+	0.804388i	$0.702493\pi$
$558$		0			0
$559$	−39.1439			−1.65561
$560$		0			0
$561$	28.1652			1.18914
$562$		0			0
$563$	17.6714	+	10.2026i	0.744760	+	0.429987i	0.823797	−	0.566884i	$-0.191851\pi$
$563$	17.6714	+	10.2026i	0.744760	+	0.429987i	−0.0790375	+	0.996872i	$0.525185\pi$
$564$		0			0
$565$	−6.54215	−	26.4503i	−0.275230	−	1.11277i
$566$		0			0
$567$	−2.61071	−	0.429179i	−0.109640	−	0.0180238i
$568$		0			0
$569$	−12.3418	−	21.3766i	−0.517395	−	0.896154i	−0.999796	−	0.0202035i	$-0.993569\pi$
$569$	−12.3418	−	21.3766i	−0.517395	−	0.896154i	0.482401	−	0.875950i	$-0.339765\pi$
$570$		0			0
$571$	10.2615	−	17.7734i	0.429429	−	0.743793i	−0.567394	−	0.823447i	$-0.692048\pi$
$571$	10.2615	−	17.7734i	0.429429	−	0.743793i	0.996823	+	0.0796540i	$0.0253815\pi$
$572$		0			0
$573$		−	1.76567i		−	0.0737618i
$574$		0			0
$575$	−2.38623	+	3.78709i	−0.0995129	+	0.157933i
$576$		0			0
$577$	−5.76228	−	3.32685i	−0.239887	−	0.138499i	0.375238	−	0.926929i	$-0.377561\pi$
$577$	−5.76228	−	3.32685i	−0.239887	−	0.138499i	−0.615125	+	0.788430i	$0.710894\pi$
$578$		0			0
$579$	6.00200	+	10.3958i	0.249435	+	0.432034i
$580$		0			0
$581$	8.51793	−	3.21263i	0.353383	−	0.133282i
$582$		0			0
$583$	68.6102	−	39.6121i	2.84154	−	1.64057i
$584$		0			0
$585$	−7.35655	+	7.07752i	−0.304156	+	0.292620i
$586$		0			0
$587$			11.7672i			0.485683i	0.970066	+	0.242842i	$0.0780796\pi$
$587$			11.7672i			0.485683i	−0.970066	+	0.242842i	$0.921920\pi$
$588$		0			0
$589$	18.6658			0.769112
$590$		0			0
$591$	−4.82618	+	8.35918i	−0.198522	+	0.343851i
$592$		0			0
$593$	−2.54283	+	1.46810i	−0.104421	+	0.0602877i	−0.551301	−	0.834306i	$-0.685868\pi$
$593$	−2.54283	+	1.46810i	−0.104421	+	0.0602877i	0.446880	+	0.894594i	$0.352535\pi$
$594$		0			0
$595$	−2.30099	−	28.8691i	−0.0943312	−	1.18352i
$596$		0			0
$597$	−5.35695	+	3.09283i	−0.219245	+	0.126581i
$598$		0			0
$599$	−0.668246	+	1.15744i	−0.0273038	+	0.0472915i	−0.879354	−	0.476168i	$-0.842025\pi$
$599$	−0.668246	+	1.15744i	−0.0273038	+	0.0472915i	0.852051	+	0.523459i	$0.175359\pi$
$600$		0			0
$601$	−32.1493			−1.31140			−0.655699	−	0.755023i	$-0.727626\pi$
$601$	−32.1493			−1.31140			−0.655699	+	0.755023i	$0.727626\pi$
$602$		0			0
$603$			8.96024i			0.364889i
$604$		0			0
$605$	34.2672	+	35.6182i	1.39316	+	1.44809i
$606$		0			0
$607$	−23.5128	+	13.5751i	−0.954355	+	0.550997i	−0.894431	−	0.447206i	$-0.852419\pi$
$607$	−23.5128	+	13.5751i	−0.954355	+	0.550997i	−0.0599239	+	0.998203i	$0.519086\pi$
$608$		0			0
$609$	−1.80292	+	10.9672i	−0.0730579	+	0.444413i
$610$		0			0
$611$	−8.27805	−	14.3380i	−0.334894	−	0.580053i
$612$		0			0
$613$	−23.2529	−	13.4251i	−0.939177	−	0.542234i	−0.0494749	−	0.998775i	$-0.515755\pi$
$613$	−23.2529	−	13.4251i	−0.939177	−	0.542234i	−0.889702	+	0.456541i	$0.849088\pi$
$614$		0			0
$615$	−18.6403	−	5.38287i	−0.751649	−	0.217058i
$616$		0			0
$617$		−	7.17896i		−	0.289014i	−0.989504	−	0.144507i	$-0.953840\pi$
$617$		−	7.17896i		−	0.289014i	0.989504	−	0.144507i	$-0.0461596\pi$
$618$		0			0
$619$	−19.7003	+	34.1219i	−0.791821	+	1.37147i	0.133017	+	0.991114i	$0.457534\pi$
$619$	−19.7003	+	34.1219i	−0.791821	+	1.37147i	−0.924838	+	0.380361i	$0.875800\pi$
$620$		0			0
$621$	−0.447618	−	0.775297i	−0.0179623	−	0.0311116i
$622$		0			0
$623$	6.31031	−	7.69996i	0.252817	−	0.308492i
$624$		0			0
$625$	14.1349	−	20.6205i	0.565396	−	0.824819i
$626$		0			0
$627$	−26.7148	−	15.4238i	−1.06688	−	0.615966i
$628$		0			0
$629$	−22.0307			−0.878423
$630$		0			0
$631$	5.52238			0.219842			0.109921	−	0.993940i	$-0.464940\pi$
$631$	5.52238			0.219842			0.109921	+	0.993940i	$0.464940\pi$
$632$		0			0
$633$	−18.7058	−	10.7998i	−0.743488	−	0.429253i
$634$		0			0
$635$	−1.26593	−	5.11822i	−0.0502367	−	0.203111i
$636$		0			0
$637$	21.1040	+	23.9976i	0.836169	+	0.950818i
$638$		0			0
$639$	2.69464	+	4.66725i	0.106598	+	0.184634i
$640$		0			0
$641$	9.97180	−	17.2717i	0.393862	−	0.682189i	−0.599093	−	0.800679i	$-0.704472\pi$
$641$	9.97180	−	17.2717i	0.393862	−	0.682189i	0.992955	+	0.118490i	$0.0378054\pi$
$642$		0			0
$643$			11.7541i			0.463537i	0.972771	+	0.231769i	$0.0744512\pi$
$643$			11.7541i			0.463537i	−0.972771	+	0.231769i	$0.925549\pi$
$644$		0			0
$645$	−5.31921	+	18.4198i	−0.209444	+	0.725280i
$646$		0			0
$647$	9.60514	+	5.54553i	0.377617	+	0.218017i	0.676781	−	0.736184i	$-0.263374\pi$
$647$	9.60514	+	5.54553i	0.377617	+	0.218017i	−0.299164	+	0.954202i	$0.596708\pi$
$648$		0			0
$649$	20.1477	+	34.8969i	0.790867	+	1.36982i
$650$		0			0
$651$	−7.12436	−	5.83859i	−0.279226	−	0.228832i
$652$		0			0
$653$	−7.06171	+	4.07708i	−0.276346	+	0.159549i	−0.631768	−	0.775157i	$-0.717671\pi$
$653$	−7.06171	+	4.07708i	−0.276346	+	0.159549i	0.355422	+	0.934706i	$0.384337\pi$
$654$		0			0
$655$	0.239968	+	0.249428i	0.00937632	+	0.00974597i
$656$		0			0
$657$			8.20435i			0.320082i
$658$		0			0
$659$	17.1502			0.668075			0.334038	−	0.942560i	$-0.391589\pi$
$659$	17.1502			0.668075			0.334038	+	0.942560i	$0.391589\pi$
$660$		0			0
$661$	7.58270	−	13.1336i	0.294933	−	0.510839i	−0.680036	−	0.733178i	$-0.738036\pi$
$661$	7.58270	−	13.1336i	0.294933	−	0.510839i	0.974969	+	0.222340i	$0.0713694\pi$
$662$		0			0
$663$	19.3542	−	11.1741i	0.751653	−	0.433967i
$664$		0			0
$665$	−13.6267	+	28.6424i	−0.528422	+	1.11071i
$666$		0			0
$667$	−3.25690	+	1.88037i	−0.126108	+	0.0728084i
$668$		0			0
$669$	−10.2397	+	17.7356i	−0.395889	+	0.685700i
$670$		0			0
$671$	35.0918			1.35470
$672$		0			0
$673$			24.8223i			0.956830i	0.878134	+	0.478415i	$0.158788\pi$
$673$			24.8223i			0.956830i	−0.878134	+	0.478415i	$0.841212\pi$
$674$		0			0
$675$	2.33078	+	4.42351i	0.0897118	+	0.170261i
$676$		0			0
$677$	−14.2448	+	8.22425i	−0.547473	+	0.316084i	−0.748102	−	0.663584i	$-0.769035\pi$
$677$	−14.2448	+	8.22425i	−0.547473	+	0.316084i	0.200629	+	0.979667i	$0.435701\pi$
$678$		0			0
$679$	10.6965	−	4.03430i	0.410494	−	0.154822i
$680$		0			0
$681$	−7.64837	−	13.2474i	−0.293086	−	0.507640i
$682$		0			0
$683$	−33.8256	−	19.5292i	−1.29430	−	0.747264i	−0.314886	−	0.949130i	$-0.601966\pi$
$683$	−33.8256	−	19.5292i	−1.29430	−	0.747264i	−0.979413	+	0.201866i	$0.935300\pi$
$684$		0			0
$685$	46.9413	+	13.5555i	1.79353	+	0.517930i
$686$		0			0
$687$			3.72575i			0.142146i
$688$		0			0
$689$	31.4311	−	54.4402i	1.19743	−	2.07401i
$690$		0			0
$691$	18.4837	+	32.0147i	0.703154	+	1.21790i	0.967354	+	0.253430i	$0.0815588\pi$
$691$	18.4837	+	32.0147i	0.703154	+	1.21790i	−0.264200	+	0.964468i	$0.585108\pi$
$692$		0			0
$693$	5.37198	+	14.2432i	0.204065	+	0.541054i
$694$		0			0
$695$	15.0549	−	3.72362i	0.571063	−	0.141245i
$696$		0			0
$697$	36.7845	+	21.2375i	1.39331	+	0.804429i
$698$		0			0
$699$	5.76904			0.218205
$700$		0			0
$701$	23.1619			0.874814			0.437407	−	0.899264i	$-0.355897\pi$
$701$	23.1619			0.874814			0.437407	+	0.899264i	$0.355897\pi$
$702$		0			0
$703$	20.8962	+	12.0644i	0.788115	+	0.455018i
$704$		0			0
$705$	−7.87189	+	1.94701i	−0.296473	+	0.0733286i
$706$		0			0
$707$	2.59594	+	0.426751i	0.0976303	+	0.0160496i
$708$		0			0
$709$	−0.712591	−	1.23424i	−0.0267619	−	0.0463530i	0.852334	−	0.522997i	$-0.175186\pi$
$709$	−0.712591	−	1.23424i	−0.0267619	−	0.0463530i	−0.879096	+	0.476644i	$0.841853\pi$
$710$		0			0
$711$	6.64226	−	11.5047i	0.249104	−	0.431461i
$712$		0			0
$713$		−	3.11676i		−	0.116724i
$714$		0			0
$715$	56.4289	+	16.2953i	2.11032	+	0.609411i
$716$		0			0
$717$	13.5875	+	7.84476i	0.507435	+	0.292968i
$718$		0			0
$719$	14.3137	+	24.7920i	0.533811	+	0.924587i	0.999220	+	0.0394917i	$0.0125739\pi$
$719$	14.3137	+	24.7920i	0.533811	+	0.924587i	−0.465409	+	0.885096i	$0.654093\pi$
$720$		0			0
$721$	−26.8448	−	22.0000i	−0.999754	−	0.819323i
$722$		0			0
$723$	14.9515	−	8.63222i	0.556050	−	0.321036i
$724$		0			0
$725$	18.5825	−	9.79126i	0.690137	−	0.363638i
$726$		0			0
$727$		−	7.81682i		−	0.289910i	−0.989438	−	0.144955i	$-0.953696\pi$
$727$		−	7.81682i		−	0.289910i	0.989438	−	0.144955i	$-0.0463037\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	20.9864	−	36.3494i	0.776209	−	1.34443i
$732$		0			0
$733$	20.9269	−	12.0822i	0.772954	−	0.446265i	−0.0609737	−	0.998139i	$-0.519421\pi$
$733$	20.9269	−	12.0822i	0.772954	−	0.446265i	0.833927	+	0.551874i	$0.186087\pi$
$734$		0			0
$735$	14.1603	−	6.66984i	0.522309	−	0.246021i
$736$		0			0
$737$	44.6467	−	25.7768i	1.64458	−	0.949501i
$738$		0			0
$739$	5.90892	−	10.2346i	0.217363	−	0.376484i	−0.736638	−	0.676287i	$-0.763588\pi$
$739$	5.90892	−	10.2346i	0.217363	−	0.376484i	0.954001	+	0.299803i	$0.0969211\pi$
$740$		0			0
$741$	−24.4766			−0.899171
$742$		0			0
$743$		−	3.25596i		−	0.119450i	−0.998215	−	0.0597248i	$-0.980978\pi$
$743$		−	3.25596i		−	0.119450i	0.998215	−	0.0597248i	$-0.0190223\pi$
$744$		0			0
$745$	−10.9345	−	11.3656i	−0.400608	−	0.416402i
$746$		0			0
$747$	2.97986	−	1.72042i	0.109027	−	0.0629470i
$748$		0			0
$749$	31.0020	+	25.4069i	1.13279	+	0.928349i
$750$		0			0
$751$	23.3000	+	40.3568i	0.850229	+	1.47264i	0.881002	+	0.473113i	$0.156870\pi$
$751$	23.3000	+	40.3568i	0.850229	+	1.47264i	−0.0307729	+	0.999526i	$0.509797\pi$
$752$		0			0
$753$	16.1979	+	9.35189i	0.590286	+	0.340802i
$754$		0			0
$755$	−11.8819	+	41.1457i	−0.432427	+	1.49745i
$756$		0			0
$757$		−	29.9847i		−	1.08981i	−0.838497	−	0.544906i	$-0.816565\pi$
$757$		−	29.9847i		−	1.08981i	0.838497	−	0.544906i	$-0.183435\pi$
$758$		0			0
$759$	−2.57541	+	4.46074i	−0.0934815	+	0.161915i
$760$		0			0
$761$	−21.3504	−	36.9799i	−0.773950	−	1.34052i	−0.935383	−	0.353638i	$-0.884945\pi$
$761$	−21.3504	−	36.9799i	−0.773950	−	1.34052i	0.161432	−	0.986884i	$-0.448389\pi$
$762$		0			0
$763$	35.2078	+	5.78787i	1.27461	+	0.209535i
$764$		0			0
$765$	−2.62817	−	10.6259i	−0.0950218	−	0.384180i
$766$		0			0
$767$	27.6896	+	15.9866i	0.999815	+	0.577244i
$768$		0			0
$769$	10.8840			0.392488			0.196244	−	0.980555i	$-0.437126\pi$
$769$	10.8840			0.392488			0.196244	+	0.980555i	$0.437126\pi$
$770$		0			0
$771$	6.31221			0.227329
$772$		0			0
$773$	−33.9903	−	19.6243i	−1.22255	−	0.705838i	−0.257087	−	0.966388i	$-0.582763\pi$
$773$	−33.9903	−	19.6243i	−1.22255	−	0.705838i	−0.965460	+	0.260550i	$0.916096\pi$
$774$		0			0
$775$	−0.672762	+	17.3945i	−0.0241663	+	0.624828i
$776$		0			0
$777$	−4.20195	−	11.1410i	−0.150744	−	0.399681i
$778$		0			0
$779$	−23.2601	−	40.2877i	−0.833380	−	1.44346i
$780$		0			0
$781$	15.5039	−	26.8535i	0.554772	−	0.960892i
$782$		0			0
$783$			4.20085i			0.150126i
$784$		0			0
$785$	−10.3175	−	2.97946i	−0.368248	−	0.106341i
$786$		0			0
$787$	21.7650	+	12.5661i	0.775840	+	0.447931i	0.834954	−	0.550320i	$-0.185494\pi$
$787$	21.7650	+	12.5661i	0.775840	+	0.447931i	−0.0591139	+	0.998251i	$0.518828\pi$
$788$		0			0
$789$	−10.4188	−	18.0459i	−0.370919	−	0.642451i
$790$		0			0
$791$	−30.1653	+	11.3772i	−1.07256	+	0.404527i
$792$		0			0
$793$	24.1139	−	13.9222i	0.856309	−	0.494390i
$794$		0			0
$795$	−21.3467	−	22.1882i	−0.757088	−	0.786936i
$796$		0			0
$797$			3.81681i			0.135198i	0.997713	+	0.0675991i	$0.0215339\pi$
$797$			3.81681i			0.135198i	−0.997713	+	0.0675991i	$0.978466\pi$
$798$		0			0
$799$	17.7526			0.628041
$800$		0			0
$801$	1.88139	−	3.25866i	0.0664756	−	0.115139i
$802$		0			0
$803$	40.8803	−	23.6023i	1.44264	−	0.832906i
$804$		0			0
$805$	4.78262	+	2.27535i	0.168565	+	0.0801954i
$806$		0			0
$807$	−23.8232	+	13.7544i	−0.838618	+	0.484176i
$808$		0			0
$809$	8.69056	−	15.0525i	0.305544	−	0.529217i	−0.671839	−	0.740698i	$-0.734495\pi$
$809$	8.69056	−	15.0525i	0.305544	−	0.529217i	0.977382	+	0.211480i	$0.0678284\pi$
$810$		0			0
$811$	−13.8289			−0.485599			−0.242799	−	0.970076i	$-0.578066\pi$
$811$	−13.8289			−0.485599			−0.242799	+	0.970076i	$0.578066\pi$
$812$		0			0
$813$			27.6661i			0.970294i
$814$		0			0
$815$	−6.90209	+	6.64030i	−0.241770	+	0.232600i
$816$		0			0
$817$	−39.8112	+	22.9850i	−1.39282	+	0.804144i
$818$		0			0
$819$	9.34223	+	7.65618i	0.326444	+	0.267529i
$820$		0			0
$821$	−12.5070	−	21.6627i	−0.436496	−	0.756034i	0.560920	−	0.827870i	$-0.310447\pi$
$821$	−12.5070	−	21.6627i	−0.436496	−	0.756034i	−0.997416	+	0.0718362i	$0.977114\pi$
$822$		0			0
$823$	12.0736	+	6.97068i	0.420859	+	0.242983i	0.695445	−	0.718580i	$-0.255207\pi$
$823$	12.0736	+	6.97068i	0.420859	+	0.242983i	−0.274586	+	0.961563i	$0.588541\pi$
$824$		0			0
$825$	15.3361	−	24.3393i	0.533935	−	0.847385i
$826$		0			0
$827$			16.1987i			0.563284i	0.959520	+	0.281642i	$0.0908790\pi$
$827$			16.1987i			0.563284i	−0.959520	+	0.281642i	$0.909121\pi$
$828$		0			0
$829$	−9.82862	+	17.0237i	−0.341362	+	0.591256i	−0.984686	−	0.174338i	$-0.944222\pi$
$829$	−9.82862	+	17.0237i	−0.341362	+	0.591256i	0.643324	+	0.765594i	$0.277555\pi$
$830$		0			0
$831$	−2.50337	−	4.33597i	−0.0868410	−	0.150413i
$832$		0			0
$833$	−33.5990	+	6.73147i	−1.16414	+	0.233232i
$834$		0			0
$835$	4.67205	+	18.8894i	0.161683	+	0.653696i
$836$		0			0
$837$	−3.01506	−	1.74075i	−0.104216	−	0.0601691i
$838$		0			0
$839$	47.1449			1.62762			0.813811	−	0.581129i	$-0.197389\pi$
$839$	47.1449			1.62762			0.813811	+	0.581129i	$0.197389\pi$
$840$		0			0
$841$	−11.3529			−0.391479
$842$		0			0
$843$	26.3315	+	15.2025i	0.906907	+	0.523603i
$844$		0			0
$845$	17.0224	−	4.21027i	0.585588	−	0.144838i
$846$		0			0
$847$	37.0689	−	45.2322i	1.27370	−	1.55420i
$848$		0			0
$849$	−11.2013	−	19.4012i	−0.384427	−	0.665847i
$850$		0			0
$851$	2.01448	−	3.48918i	0.0690555	−	0.119608i
$852$		0			0
$853$			15.3410i			0.525266i	0.964896	+	0.262633i	$0.0845909\pi$
$853$			15.3410i			0.525266i	−0.964896	+	0.262633i	$0.915409\pi$
$854$		0			0
$855$	−3.32610	+	11.5179i	−0.113750	+	0.393904i
$856$		0			0
$857$	9.02603	+	5.21118i	0.308323	+	0.178011i	0.646176	−	0.763188i	$-0.276367\pi$
$857$	9.02603	+	5.21118i	0.308323	+	0.178011i	−0.337853	+	0.941199i	$0.609701\pi$
$858$		0			0
$859$	25.8513	+	44.7758i	0.882036	+	1.52773i	0.849074	+	0.528275i	$0.177161\pi$
$859$	25.8513	+	44.7758i	0.882036	+	1.52773i	0.0329624	+	0.999457i	$0.489506\pi$
$860$		0			0
$861$	−3.72391	+	22.6527i	−0.126911	+	0.772000i
$862$		0			0
$863$	2.08282	−	1.20251i	0.0708999	−	0.0409341i	−0.464131	−	0.885767i	$-0.653633\pi$
$863$	2.08282	−	1.20251i	0.0708999	−	0.0409341i	0.535031	+	0.844833i	$0.320300\pi$
$864$		0			0
$865$	15.9218	−	15.3179i	0.541356	−	0.520823i
$866$		0			0
$867$			6.96333i			0.236487i
$868$		0			0
$869$	−76.4337			−2.59284
$870$		0			0
$871$	20.4531	−	35.4259i	0.693028	−	1.20036i
$872$		0			0
$873$	3.74200	−	2.16044i	0.126647	−	0.0731200i
$874$		0			0
$875$	−26.2004	−	13.7309i	−0.885736	−	0.464190i
$876$		0			0
$877$	−5.69818	+	3.28985i	−0.192414	+	0.111090i	−0.593112	−	0.805120i	$-0.702101\pi$
$877$	−5.69818	+	3.28985i	−0.192414	+	0.111090i	0.400698	+	0.916210i	$0.368768\pi$
$878$		0			0
$879$	10.3714	−	17.9639i	0.349820	−	0.605906i
$880$		0			0
$881$	−30.3674			−1.02311			−0.511553	−	0.859252i	$-0.670929\pi$
$881$	−30.3674			−1.02311			−0.511553	+	0.859252i	$0.670929\pi$
$882$		0			0
$883$		−	13.1624i		−	0.442949i	−0.975166	−	0.221475i	$-0.928913\pi$
$883$		−	13.1624i		−	0.442949i	0.975166	−	0.221475i	$-0.0710870\pi$
$884$		0			0
$885$	11.2855	−	10.8575i	0.379358	−	0.364969i
$886$		0			0
$887$	5.72166	−	3.30340i	0.192115	−	0.110917i	−0.400858	−	0.916140i	$-0.631288\pi$
$887$	5.72166	−	3.30340i	0.192115	−	0.110917i	0.592972	+	0.805223i	$0.297954\pi$
$888$		0			0
$889$	−5.83709	+	2.20152i	−0.195770	+	0.0738368i
$890$		0			0
$891$	2.87680	+	4.98276i	0.0963763	+	0.166929i
$892$		0			0
$893$	−16.8384	−	9.72163i	−0.563474	−	0.325322i
$894$		0			0
$895$	3.53856	−	12.2536i	0.118281	−	0.409594i
$896$		0			0
$897$			4.08703i			0.136462i
$898$		0			0
$899$	−7.31262	+	12.6658i	−0.243889	+	0.422429i
$900$		0			0
$901$	33.7025	+	58.3745i	1.12279	+	1.94474i
$902$		0			0
$903$	22.3847	+	3.67987i	0.744918	+	0.122458i
$904$		0			0
$905$	32.1000	−	7.93952i	1.06704	−	0.263918i
$906$		0			0
$907$	48.3941	+	27.9403i	1.60690	+	0.927743i	0.990059	+	0.140655i	$0.0449208\pi$
$907$	48.3941	+	27.9403i	1.60690	+	0.927743i	0.616840	+	0.787088i	$0.288413\pi$
$908$		0			0
$909$	0.994342			0.0329803
$910$		0			0
$911$	−26.7182			−0.885214			−0.442607	−	0.896716i	$-0.645946\pi$
$911$	−26.7182			−0.885214			−0.442607	+	0.896716i	$0.645946\pi$
$912$		0			0
$913$	−17.1449	−	9.89863i	−0.567414	−	0.327597i
$914$		0			0
$915$	−3.27451	−	13.2391i	−0.108252	−	0.437670i
$916$		0			0
$917$	0.259587	−	0.316754i	0.00857233	−	0.0104601i
$918$		0			0
$919$	−16.7964	−	29.0922i	−0.554061	−	0.959662i	−0.997976	−	0.0635928i	$-0.979744\pi$
$919$	−16.7964	−	29.0922i	−0.554061	−	0.959662i	0.443915	−	0.896069i	$-0.353589\pi$
$920$		0			0
$921$	−4.06072	+	7.03338i	−0.133805	+	0.231758i
$922$		0			0
$923$		−	24.6037i		−	0.809841i
$924$		0			0
$925$	−11.9959	+	19.0381i	−0.394421	+	0.625969i
$926$		0			0
$927$	−11.3609	−	6.55920i	−0.373140	−	0.215432i
$928$		0			0
$929$	16.9234	+	29.3122i	0.555239	+	0.961702i	0.997885	+	0.0650058i	$0.0207066\pi$
$929$	16.9234	+	29.3122i	0.555239	+	0.961702i	−0.442646	+	0.896697i	$0.645960\pi$
$930$		0			0
$931$	35.5550	+	12.0146i	1.16527	+	0.393762i
$932$		0			0
$933$	11.8097	−	6.81835i	0.386633	−	0.223223i
$934$		0			0
$935$	−45.3855	+	43.6641i	−1.48426	+	1.42797i
$936$		0			0
$937$			51.6442i			1.68714i	0.537017	+	0.843571i	$0.319551\pi$
$937$			51.6442i			1.68714i	−0.537017	+	0.843571i	$0.680449\pi$
$938$		0			0
$939$	−9.29921			−0.303468
$940$		0			0
$941$	−25.2093	+	43.6638i	−0.821800	+	1.42340i	0.0825405	+	0.996588i	$0.473697\pi$
$941$	−25.2093	+	43.6638i	−0.821800	+	1.42340i	−0.904341	+	0.426812i	$0.859637\pi$
$942$		0			0
$943$	−6.72711	+	3.88390i	−0.219065	+	0.126477i
$944$		0			0
$945$	4.87226	−	3.35576i	0.158494	−	0.109163i
$946$		0			0
$947$	−32.5284	+	18.7803i	−1.05703	+	0.610277i	−0.924609	−	0.380916i	$-0.875609\pi$
$947$	−32.5284	+	18.7803i	−1.05703	+	0.610277i	−0.132421	+	0.991194i	$0.542275\pi$
$948$		0			0
$949$	18.7277	−	32.4373i	0.607927	−	1.05296i
$950$		0			0
$951$	−17.2132			−0.558178
$952$		0			0
$953$			17.9656i			0.581964i	0.956729	+	0.290982i	$0.0939820\pi$
$953$			17.9656i			0.581964i	−0.956729	+	0.290982i	$0.906018\pi$
$954$		0			0
$955$	2.73729	+	2.84520i	0.0885765	+	0.0920686i
$956$		0			0
$957$	20.9318	−	12.0850i	0.676629	−	0.390652i
$958$		0			0
$959$	9.37781	−	57.0455i	0.302825	−	1.84209i
$960$		0			0
$961$	9.43959	+	16.3499i	0.304503	+	0.527415i
$962$		0			0
$963$	13.1202	+	7.57495i	0.422793	+	0.244099i
$964$		0			0
$965$	−25.7880	−	7.44697i	−0.830147	−	0.239727i
$966$		0			0
$967$			5.45276i			0.175349i	0.996149	+	0.0876745i	$0.0279435\pi$
$967$			5.45276i			0.175349i	−0.996149	+	0.0876745i	$0.972056\pi$
$968$		0			0
$969$	13.1228	−	22.7293i	0.421563	−	0.730169i
$970$		0			0
$971$	3.50688	+	6.07410i	0.112541	+	0.194927i	0.916794	−	0.399360i	$-0.130768\pi$
$971$	3.50688	+	6.07410i	0.112541	+	0.194927i	−0.804253	+	0.594287i	$0.797434\pi$
$972$		0			0
$973$	−6.47561	−	17.1693i	−0.207599	−	0.550424i
$974$		0			0
$975$	0.882198	−	22.8095i	0.0282529	−	0.730488i
$976$		0			0
$977$	47.2149	+	27.2595i	1.51054	+	0.872109i	0.999924	+	0.0122990i	$0.00391500\pi$
$977$	47.2149	+	27.2595i	1.51054	+	0.872109i	0.510613	+	0.859810i	$0.329418\pi$
$978$		0			0
$979$	−21.6495			−0.691921
$980$		0			0
$981$	13.4859			0.430572
$982$		0			0
$983$	35.8110	+	20.6755i	1.14219	+	0.659446i	0.946973	−	0.321313i	$-0.104124\pi$
$983$	35.8110	+	20.6755i	1.14219	+	0.659446i	0.195221	+	0.980759i	$0.437458\pi$
$984$		0			0
$985$	−5.18219	−	20.9520i	−0.165118	−	0.667585i
$986$		0			0
$987$	3.38597	+	8.97751i	0.107777	+	0.285757i
$988$		0			0
$989$	3.83796	+	6.64755i	0.122040	+	0.211380i
$990$		0			0
$991$	−13.3930	+	23.1973i	−0.425442	+	0.736887i	−0.996462	−	0.0840496i	$-0.973215\pi$
$991$	−13.3930	+	23.1973i	−0.425442	+	0.736887i	0.571020	+	0.820936i	$0.306548\pi$
$992$		0			0
$993$			2.50184i			0.0793936i
$994$		0			0
$995$	3.83743	−	13.2886i	0.121655	−	0.421277i
$996$		0			0
$997$	−35.8459	−	20.6956i	−1.13525	−	0.655437i	−0.190000	−	0.981784i	$-0.560849\pi$
$997$	−35.8459	−	20.6956i	−1.13525	−	0.655437i	−0.945250	+	0.326347i	$0.894182\pi$
$998$		0			0
$999$	−2.25022	−	3.89750i	−0.0711939	−	0.123311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.di.g.529.9		24
4.3	odd	2		840.2.cc.c.529.1	yes	24
5.4	even	2	inner	1680.2.di.g.529.6		24
7.2	even	3	inner	1680.2.di.g.289.6		24
20.19	odd	2		840.2.cc.c.529.11	yes	24
28.23	odd	6		840.2.cc.c.289.11	yes	24
35.9	even	6	inner	1680.2.di.g.289.9		24
140.79	odd	6		840.2.cc.c.289.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cc.c.289.1	✓	24	140.79	odd	6
840.2.cc.c.289.11	yes	24	28.23	odd	6
840.2.cc.c.529.1	yes	24	4.3	odd	2
840.2.cc.c.529.11	yes	24	20.19	odd	2
1680.2.di.g.289.6		24	7.2	even	3	inner
1680.2.di.g.289.9		24	35.9	even	6	inner
1680.2.di.g.529.6		24	5.4	even	2	inner
1680.2.di.g.529.9		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.di (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-2.17066 + 0.536884i) q^{5} +(0.933675 + 2.47553i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.87680 - 4.98276i) q^{11} -4.56531i q^{13} +(-2.14829 - 0.620374i) q^{15} +(4.23940 + 2.44762i) q^{17} +(-2.68072 - 4.64314i) q^{19} +(-0.429179 + 2.61071i) q^{21} +(-0.775297 + 0.447618i) q^{23} +(4.42351 - 2.33078i) q^{25} +1.00000i q^{27} +4.20085 q^{29} +(-1.74075 + 3.01506i) q^{31} +(4.98276 - 2.87680i) q^{33} +(-3.35576 - 4.87226i) q^{35} +(-3.89750 + 2.25022i) q^{37} +(2.28265 - 3.95367i) q^{39} +8.67682 q^{41} -8.57420i q^{43} +(-1.55028 - 1.61140i) q^{45} +(3.14064 - 1.81325i) q^{47} +(-5.25650 + 4.62268i) q^{49} +(2.44762 + 4.23940i) q^{51} +(11.9248 + 6.88476i) q^{53} +(-3.56938 + 12.3604i) q^{55} -5.36144i q^{57} +(-3.50176 + 6.06523i) q^{59} +(3.04955 + 5.28198i) q^{61} +(-1.67704 + 2.04635i) q^{63} +(2.45104 + 9.90972i) q^{65} +(7.75980 + 4.48012i) q^{67} -0.895236 q^{69} +5.38928 q^{71} +(7.10518 + 4.10218i) q^{73} +(4.99626 + 0.193239i) q^{75} +(15.0210 + 2.46932i) q^{77} +(-6.64226 - 11.5047i) q^{79} +(-0.500000 + 0.866025i) q^{81} -3.44085i q^{83} +(-10.5164 - 3.03688i) q^{85} +(3.63804 + 2.10042i) q^{87} +(-1.88139 - 3.25866i) q^{89} +(11.3016 - 4.26251i) q^{91} +(-3.01506 + 1.74075i) q^{93} +(8.31175 + 8.63944i) q^{95} -4.32089i q^{97} +5.75359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5} + 12 q^{9} + 8 q^{11} - 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} - 4 q^{31} - 30 q^{35} - 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} + 20 q^{51} - 12 q^{55} + 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots + 16 q^{99}+O(q^{100}) \) 24 * q + 2 * q^5 + 12 * q^9 + 8 * q^11 - 8 * q^19 + 12 * q^21 + 2 * q^25 - 24 * q^29 - 4 * q^31 - 30 * q^35 - 4 * q^39 + 32 * q^41 - 2 * q^45 - 12 * q^49 + 20 * q^51 - 12 * q^55 + 4 * q^59 + 32 * q^61 + 22 * q^65 + 56 * q^69 - 72 * q^71 + 16 * q^75 - 20 * q^79 - 12 * q^81 + 8 * q^85 + 24 * q^89 - 8 * q^91 + 18 * q^95 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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