LMFDB - Embedded newform 840.2.cc.c.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(289,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, 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("840.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	840.289
Dual form			840.2.cc.c.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.17066 - 0.536884i) q^{5} +(-0.933675 + 2.47553i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.87680 - 4.98276i) q^{11} +4.56531i q^{13} +(2.14829 - 0.620374i) q^{15} +(4.23940 - 2.44762i) q^{17} +(2.68072 - 4.64314i) q^{19} +(-0.429179 - 2.61071i) q^{21} +(0.775297 + 0.447618i) q^{23} +(4.42351 + 2.33078i) q^{25} +1.00000i q^{27} +4.20085 q^{29} +(1.74075 + 3.01506i) q^{31} +(4.98276 + 2.87680i) q^{33} +(3.35576 - 4.87226i) q^{35} +(-3.89750 - 2.25022i) q^{37} +(-2.28265 - 3.95367i) q^{39} +8.67682 q^{41} -8.57420i q^{43} +(-1.55028 + 1.61140i) q^{45} +(-3.14064 - 1.81325i) q^{47} +(-5.25650 - 4.62268i) q^{49} +(-2.44762 + 4.23940i) q^{51} +(11.9248 - 6.88476i) q^{53} +(3.56938 + 12.3604i) q^{55} +5.36144i q^{57} +(3.50176 + 6.06523i) q^{59} +(3.04955 - 5.28198i) q^{61} +(1.67704 + 2.04635i) q^{63} +(2.45104 - 9.90972i) q^{65} +(-7.75980 + 4.48012i) q^{67} -0.895236 q^{69} -5.38928 q^{71} +(7.10518 - 4.10218i) q^{73} +(-4.99626 + 0.193239i) q^{75} +(15.0210 - 2.46932i) q^{77} +(6.64226 - 11.5047i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.44085i q^{83} +(-10.5164 + 3.03688i) q^{85} +(-3.63804 + 2.10042i) q^{87} +(-1.88139 + 3.25866i) q^{89} +(-11.3016 - 4.26251i) q^{91} +(-3.01506 - 1.74075i) q^{93} +(-8.31175 + 8.63944i) q^{95} +4.32089i q^{97} -5.75359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$	$1$

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	−0.864657	−	0.502362i	$-0.832464\pi$
$11$	−2.87680	−	4.98276i	−0.867387	−	1.50236i	−0.00272961	−	0.999996i	$-0.500869\pi$
$12$		0			0
$13$			4.56531i			1.26619i	0.774075	+	0.633094i	$0.218216\pi$
$13$			4.56531i			1.26619i	−0.774075	+	0.633094i	$0.781784\pi$
$14$		0			0
$15$	2.14829	−	0.620374i	0.554685	−	0.160180i
$16$		0			0
$17$	4.23940	−	2.44762i	1.02821	−	0.593635i	0.111735	−	0.993738i	$-0.464359\pi$
$17$	4.23940	−	2.44762i	1.02821	−	0.593635i	0.916470	+	0.400104i	$0.131026\pi$
$18$		0			0
$19$	2.68072	−	4.64314i	0.614999	−	1.06521i	−0.375386	−	0.926869i	$-0.622490\pi$
$19$	2.68072	−	4.64314i	0.614999	−	1.06521i	0.990385	−	0.138341i	$-0.0441770\pi$
$20$		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	$-0.303581\pi$
$23$	0.775297	+	0.447618i	0.161661	+	0.0933348i	−0.416987	+	0.908912i	$0.636914\pi$
$24$		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	$-0.0654508\pi$
$31$	1.74075	+	3.01506i	0.312648	+	0.541521i	−0.666287	+	0.745695i	$0.732117\pi$
$32$		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	0.144156	−	0.989555i	$-0.453953\pi$
$37$	−3.89750	−	2.25022i	−0.640745	−	0.369934i	−0.784901	+	0.619621i	$0.787286\pi$
$38$		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	$-0.418537\pi$
$47$	−3.14064	−	1.81325i	−0.458110	−	0.264490i	−0.711249	+	0.702940i	$0.751870\pi$
$48$		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	0.656467	−	0.754355i	$-0.272050\pi$
$53$	11.9248	−	6.88476i	1.63799	−	0.945694i	0.981524	−	0.191340i	$-0.0612832\pi$
$54$		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	$-0.0159875\pi$
$59$	3.50176	+	6.06523i	0.455891	+	0.789626i	−0.542848	+	0.839831i	$0.682654\pi$
$60$		0			0
$61$	3.04955	−	5.28198i	0.390455	−	0.676288i	−0.602054	−	0.798455i	$-0.705651\pi$
$61$	3.04955	−	5.28198i	0.390455	−	0.676288i	0.992510	+	0.122167i	$0.0389843\pi$
$62$		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	$-0.851024\pi$
$67$	−7.75980	+	4.48012i	−0.948010	+	0.547334i	−0.0555479	+	0.998456i	$0.517691\pi$
$68$		0			0
$69$	−0.895236			−0.107774
$70$		0			0
$71$	−5.38928			−0.639589			−0.319795	−	0.947487i	$-0.603614\pi$
$71$	−5.38928			−0.639589			−0.319795	+	0.947487i	$0.603614\pi$
$72$		0			0
$73$	7.10518	−	4.10218i	0.831598	−	0.480123i	−0.0228013	−	0.999740i	$-0.507259\pi$
$73$	7.10518	−	4.10218i	0.831598	−	0.480123i	0.854400	+	0.519617i	$0.173925\pi$
$74$		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	−0.201795	−	0.979428i	$-0.564677\pi$
$79$	6.64226	−	11.5047i	0.747312	−	1.29438i	0.949107	−	0.314955i	$-0.101989\pi$
$80$		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	−0.948343	−	0.317248i	$-0.897241\pi$
$89$	−1.88139	+	3.25866i	−0.199427	+	0.345417i	0.748916	+	0.662665i	$0.230575\pi$
$90$		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	$0.0703969\pi$
$97$			4.32089i			0.438720i	−0.975644	+	0.219360i	$0.929603\pi$
$98$		0			0
$99$	−5.75359			−0.578258
$100$		0			0
$101$	0.497171	+	0.861126i	0.0494704	+	0.0856852i	0.889700	−	0.456545i	$-0.150913\pi$
$101$	0.497171	+	0.861126i	0.0494704	+	0.0856852i	−0.840230	+	0.542230i	$0.817580\pi$
$102$		0			0
$103$	11.3609	+	6.55920i	1.11942	+	0.646297i	0.941253	−	0.337703i	$-0.109650\pi$
$103$	11.3609	+	6.55920i	1.11942	+	0.646297i	0.178167	+	0.984000i	$0.442983\pi$
$104$		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	$-0.594886\pi$
$107$	−13.1202	−	7.57495i	−1.26838	−	0.732298i	−0.974681	+	0.223600i	$0.928219\pi$
$108$		0			0
$109$	6.74295	+	11.6791i	0.645857	+	1.11866i	0.984103	+	0.177600i	$0.0568333\pi$
$109$	6.74295	+	11.6791i	0.645857	+	1.11866i	−0.338245	+	0.941058i	$0.609833\pi$
$110$		0			0
$111$	4.50044			0.427163
$112$		0			0
$113$		−	12.1854i		−	1.14631i	−0.819448	−	0.573153i	$-0.805720\pi$
$113$		−	12.1854i		−	1.14631i	0.819448	−	0.573153i	$-0.194280\pi$
$114$		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	$-0.831181\pi$
$131$	0.0773948	−	0.134052i	0.00676201	−	0.0117121i	0.869387	+	0.494132i	$0.164514\pi$
$132$		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	−0.628951	+	0.777445i	$0.716515\pi$
$137$	−18.9231	+	10.9253i	−1.61671	+	0.933410i	−0.987763	+	0.155965i	$0.950151\pi$
$138$		0			0
$139$	6.93562			0.588271			0.294136	−	0.955764i	$-0.404968\pi$
$139$	6.93562			0.588271			0.294136	+	0.955764i	$0.404968\pi$
$140$		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	−0.684639	−	0.728882i	$-0.740040\pi$
$149$	3.52660	−	6.10826i	0.288911	−	0.500408i	0.973550	+	0.228474i	$0.0733736\pi$
$150$		0			0
$151$	−9.57640	−	16.5868i	−0.779316	−	1.34982i	−0.932336	−	0.361592i	$-0.882233\pi$
$151$	−9.57640	−	16.5868i	−0.779316	−	1.34982i	0.153020	−	0.988223i	$-0.451100\pi$
$152$		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	−0.324760	−	0.945796i	$-0.605284\pi$
$157$	4.15924	−	2.40134i	0.331943	−	0.191648i	0.656704	+	0.754149i	$0.271950\pi$
$158$		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	$-0.386982\pi$
$163$	−3.70943	−	2.14164i	−0.290545	−	0.167746i	−0.638188	+	0.769881i	$0.720316\pi$
$164$		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	0.138104	−	0.990418i	$-0.455899\pi$
$173$	−8.55693	−	4.94034i	−0.650571	−	0.375607i	−0.788675	+	0.614810i	$0.789233\pi$
$174$		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	$-0.0982894\pi$
$179$	2.85195	+	4.93973i	0.213165	+	0.369213i	−0.739538	+	0.673114i	$0.764956\pi$
$180$		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	$-0.812986\pi$
$191$	0.882834	−	1.52911i	0.0638796	−	0.110643i	0.896196	+	0.443657i	$0.146319\pi$
$192$		0			0
$193$	10.3958	−	6.00200i	0.748304	−	0.432034i	−0.0767766	−	0.997048i	$-0.524463\pi$
$193$	10.3958	−	6.00200i	0.748304	−	0.432034i	0.825081	+	0.565015i	$0.191130\pi$
$194$		0			0
$195$	2.83220	+	9.80759i	0.202818	+	0.702336i
$196$		0			0
$197$		−	9.65235i		−	0.687702i	−0.939024	−	0.343851i	$-0.888269\pi$
$197$		−	9.65235i		−	0.687702i	0.939024	−	0.343851i	$-0.111731\pi$
$198$		0			0
$199$	3.09283	+	5.35695i	0.219245	+	0.379744i	0.954577	−	0.297963i	$-0.0963072\pi$
$199$	3.09283	+	5.35695i	0.219245	+	0.379744i	−0.735332	+	0.677707i	$0.762974\pi$
$200$		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	$-0.233170\pi$
$211$	21.5996			1.48698			0.743488	+	0.668749i	$0.233170\pi$
$212$		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	$-0.497185\pi$
$227$	13.2474	−	7.64837i	0.879258	−	0.507640i	0.870414	+	0.492321i	$0.163851\pi$
$228$		0			0
$229$	1.86287	−	3.22659i	0.123102	−	0.213219i	−0.797887	−	0.602807i	$-0.794049\pi$
$229$	1.86287	−	3.22659i	0.123102	−	0.213219i	0.920990	+	0.389587i	$0.127382\pi$
$230$		0			0
$231$	−11.7739	+	9.64898i	−0.774664	+	0.634856i
$232$		0			0
$233$	4.99613	+	2.88452i	0.327308	+	0.188971i	0.654645	−	0.755936i	$-0.272818\pi$
$233$	4.99613	+	2.88452i	0.327308	+	0.188971i	−0.327338	+	0.944907i	$0.606151\pi$
$234$		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	$-0.669406\pi$
$239$	−15.6895			−1.01487			−0.507435	+	0.861690i	$0.669406\pi$
$240$		0			0
$241$	8.63222	+	14.9515i	0.556050	+	0.963108i	0.997821	+	0.0659796i	$0.0210172\pi$
$241$	8.63222	+	14.9515i	0.556050	+	0.963108i	−0.441770	+	0.897128i	$0.645649\pi$
$242$		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	$-0.700985\pi$
$251$	−18.7038			−1.18057			−0.590286	+	0.807194i	$0.700985\pi$
$252$		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	0.660711	−	0.750640i	$-0.270255\pi$
$257$	5.46653	+	3.15610i	0.340993	+	0.196872i	−0.319718	+	0.947513i	$0.603588\pi$
$258$		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	$-0.444584\pi$
$263$	18.0459	−	10.4188i	1.11276	−	0.642451i	0.939542	+	0.342433i	$0.111251\pi$
$264$		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	−0.891050	−	0.453904i	$-0.850031\pi$
$269$	−13.7544	−	23.8232i	−0.838618	−	1.45253i	0.0524327	−	0.998624i	$-0.483302\pi$
$270$		0			0
$271$	−13.8331	+	23.9596i	−0.840299	+	1.45544i	0.0493424	+	0.998782i	$0.484287\pi$
$271$	−13.8331	+	23.9596i	−0.840299	+	1.45544i	−0.889642	+	0.456659i	$0.849046\pi$
$272$		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	−0.624573	−	0.780966i	$-0.714727\pi$
$277$	−4.33597	+	2.50337i	−0.260523	+	0.150413i	0.364050	+	0.931379i	$0.381394\pi$
$278$		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	$-0.434737\pi$
$283$	19.4012	−	11.2013i	1.15328	−	0.665847i	0.949685	+	0.313208i	$0.101404\pi$
$284$		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	$0.207189\pi$
$293$			20.7429i			1.21181i	−0.795536	+	0.605906i	$0.792811\pi$
$294$		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	$-0.293029\pi$
$311$	−6.81835	−	11.8097i	−0.386633	−	0.669668i	−0.991994	+	0.126283i	$0.959695\pi$
$312$		0			0
$313$	−8.05335	−	4.64960i	−0.455202	−	0.262811i	0.254823	−	0.966988i	$-0.417983\pi$
$313$	−8.05335	−	4.64960i	−0.455202	−	0.262811i	−0.710025	+	0.704177i	$0.751316\pi$
$314$		0			0
$315$	−2.54162	−	5.34230i	−0.143204	−	0.301005i
$316$		0			0
$317$	−14.9071	−	8.60662i	−0.837266	−	0.483396i	0.0190676	−	0.999818i	$-0.493930\pi$
$317$	−14.9071	−	8.60662i	−0.837266	−	0.483396i	−0.856334	+	0.516422i	$0.827264\pi$
$318$		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	$-0.855237\pi$
$331$	−1.25092	+	2.16666i	−0.0687569	+	0.119090i	0.829597	+	0.558362i	$0.188570\pi$
$332$		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	$0.0583276\pi$
$337$			6.69015i			0.364436i	−0.983258	+	0.182218i	$0.941672\pi$
$338$		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	$-0.643272\pi$
$347$	2.36917	−	1.36784i	0.127184	−	0.0734296i	0.562242	+	0.826973i	$0.309939\pi$
$348$		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	−0.249894	−	0.968273i	$-0.580396\pi$
$353$	8.71230	−	5.03005i	0.463709	−	0.267722i	0.713602	+	0.700551i	$0.247062\pi$
$354$		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	$-0.731207\pi$
$359$	5.97529	−	10.3495i	0.315364	−	0.546226i	0.979515	+	0.201373i	$0.0645402\pi$
$360$		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	0.516067	−	0.856548i	$-0.327395\pi$
$367$	29.0403	−	16.7664i	1.51589	−	0.875201i	0.999826	−	0.0186533i	$-0.00593788\pi$
$368$		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	0.0149049	−	0.999889i	$-0.495255\pi$
$373$	−16.2921	−	9.40624i	−0.843572	−	0.487036i	−0.858477	+	0.512852i	$0.828589\pi$
$374$		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	$-0.316463\pi$
$379$	21.2269			1.09035			0.545176	+	0.838322i	$0.316463\pi$
$380$		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	$-0.256110\pi$
$383$	8.14310	+	4.70142i	0.416093	+	0.240232i	−0.277311	+	0.960780i	$0.589443\pi$
$384$		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	0.988863	−	0.148828i	$-0.0475501\pi$
$389$	7.20963	+	12.4874i	0.365543	+	0.633139i	−0.623320	+	0.781967i	$0.714217\pi$
$390$		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	0.538276	−	0.842769i	$-0.319076\pi$
$397$	1.54528	+	0.892166i	0.0775552	+	0.0447765i	−0.460721	+	0.887545i	$0.652409\pi$
$398$		0			0
$399$	−13.2724	−	5.00584i	−0.664451	−	0.250605i
$400$		0			0
$401$	18.9425	−	32.8094i	0.945944	−	1.63842i	0.192095	−	0.981376i	$-0.438472\pi$
$401$	18.9425	−	32.8094i	0.945944	−	1.63842i	0.753849	−	0.657048i	$-0.228195\pi$
$402$		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	0.824920	−	0.565250i	$-0.191220\pi$
$409$	−1.55846	−	2.69933i	−0.0770609	−	0.133473i	−0.901981	+	0.431777i	$0.857887\pi$
$410$		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	$-0.429398\pi$
$419$	9.00616			0.439980			0.219990	+	0.975502i	$0.429398\pi$
$420$		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	$-0.132409\pi$
$431$	2.23003	+	3.86253i	0.107417	+	0.186051i	−0.807306	+	0.590133i	$0.799075\pi$
$432$		0			0
$433$		−	37.1411i		−	1.78489i	−0.451159	−	0.892444i	$-0.648989\pi$
$433$		−	37.1411i		−	1.78489i	0.451159	−	0.892444i	$-0.351011\pi$
$434$		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	0.147360	−	0.989083i	$-0.452922\pi$
$439$	19.4909	−	33.7593i	0.930251	−	1.61124i	0.782891	−	0.622159i	$-0.213744\pi$
$440$		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	$-0.0393376\pi$
$443$	29.0837	+	16.7915i	1.38181	+	0.797786i	0.389433	+	0.921055i	$0.372671\pi$
$444$		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	−0.0505802	−	0.998720i	$-0.516107\pi$
$457$	−20.1117	−	11.6115i	−0.940787	−	0.543164i	−0.890207	+	0.455556i	$0.849440\pi$
$458$		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	$-0.516813\pi$
$467$	−20.4002	−	11.7781i	−0.944009	−	0.545024i	−0.891215	+	0.453581i	$0.850146\pi$
$468$		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	$-0.247932\pi$
$479$	−5.52709	−	9.57320i	−0.252539	−	0.437410i	−0.964224	+	0.265088i	$0.914599\pi$
$480$		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	$-0.580813\pi$
$487$	10.1849	−	5.88025i	0.461521	−	0.266460i	0.712684	+	0.701485i	$0.247479\pi$
$488$		0			0
$489$	4.28328			0.193697
$490$		0			0
$491$	−17.8544			−0.805759			−0.402880	−	0.915253i	$-0.631991\pi$
$491$	−17.8544			−0.805759			−0.402880	+	0.915253i	$0.631991\pi$
$492$		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	$-0.772208\pi$
$499$	4.26332	−	7.38429i	0.190853	−	0.330566i	0.945533	+	0.325526i	$0.105541\pi$
$500$		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	0.0245493	+	0.999699i	$0.492185\pi$
$509$	−19.2556	+	33.3517i	−0.853490	+	1.47829i	−0.878039	+	0.478589i	$0.841148\pi$
$510$		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	−0.982721	−	0.185091i	$-0.940742\pi$
$521$	−14.8743	−	25.7630i	−0.651654	−	1.12870i	0.331067	−	0.943607i	$-0.392591\pi$
$522$		0			0
$523$	−1.81046	−	1.04527i	−0.0791659	−	0.0457064i	0.459895	−	0.887974i	$-0.347887\pi$
$523$	−1.81046	−	1.04527i	−0.0791659	−	0.0457064i	−0.539060	+	0.842267i	$0.681221\pi$
$524$		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	0.387453	+	0.921889i	$0.373355\pi$
$541$	−14.0639	+	24.3593i	−0.604653	+	1.04729i	−0.992106	+	0.125400i	$0.959979\pi$
$542$		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	−0.594104	−	0.804388i	$-0.702493\pi$
$557$	−4.59121	+	2.65073i	−0.194536	+	0.112315i	0.399568	+	0.916703i	$0.369160\pi$
$558$		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	$-0.808149\pi$
$563$	−17.6714	+	10.2026i	−0.744760	+	0.429987i	0.0790375	+	0.996872i	$0.474815\pi$
$564$		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	0.482401	+	0.875950i	$0.339765\pi$
$569$	−12.3418	+	21.3766i	−0.517395	+	0.896154i	−0.999796	+	0.0202035i	$0.993569\pi$
$570$		0			0
$571$	−10.2615	−	17.7734i	−0.429429	−	0.743793i	0.567394	−	0.823447i	$-0.307952\pi$
$571$	−10.2615	−	17.7734i	−0.429429	−	0.743793i	−0.996823	+	0.0796540i	$0.974618\pi$
$572$		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	−0.615125	−	0.788430i	$-0.710894\pi$
$577$	−5.76228	+	3.32685i	−0.239887	+	0.138499i	0.375238	+	0.926929i	$0.377561\pi$
$578$		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	0.446880	−	0.894594i	$-0.352535\pi$
$593$	−2.54283	−	1.46810i	−0.104421	−	0.0602877i	−0.551301	+	0.834306i	$0.685868\pi$
$594$		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	$-0.157975\pi$
$599$	0.668246	+	1.15744i	0.0273038	+	0.0472915i	−0.852051	+	0.523459i	$0.824641\pi$
$600$		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	$-0.147581\pi$
$607$	23.5128	+	13.5751i	0.954355	+	0.550997i	0.0599239	+	0.998203i	$0.480914\pi$
$608$		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	−0.889702	−	0.456541i	$-0.849088\pi$
$613$	−23.2529	+	13.4251i	−0.939177	+	0.542234i	−0.0494749	+	0.998775i	$0.515755\pi$
$614$		0			0
$615$	18.6403	−	5.38287i	0.751649	−	0.217058i
$616$		0			0
$617$			7.17896i			0.289014i	0.989504	+	0.144507i	$0.0461596\pi$
$617$			7.17896i			0.289014i	−0.989504	+	0.144507i	$0.953840\pi$
$618$		0			0
$619$	19.7003	+	34.1219i	0.791821	+	1.37147i	0.924838	+	0.380361i	$0.124200\pi$
$619$	19.7003	+	34.1219i	0.791821	+	1.37147i	−0.133017	+	0.991114i	$0.542466\pi$
$620$		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	$-0.535060\pi$
$631$	−5.52238			−0.219842			−0.109921	+	0.993940i	$0.535060\pi$
$632$		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	0.992955	−	0.118490i	$-0.0378054\pi$
$641$	9.97180	+	17.2717i	0.393862	+	0.682189i	−0.599093	+	0.800679i	$0.704472\pi$
$642$		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	$-0.736626\pi$
$647$	−9.60514	+	5.54553i	−0.377617	+	0.218017i	0.299164	+	0.954202i	$0.403292\pi$
$648$		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	0.355422	−	0.934706i	$-0.384337\pi$
$653$	−7.06171	−	4.07708i	−0.276346	−	0.159549i	−0.631768	+	0.775157i	$0.717671\pi$
$654$		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	$-0.608411\pi$
$659$	−17.1502			−0.668075			−0.334038	+	0.942560i	$0.608411\pi$
$660$		0			0
$661$	7.58270	+	13.1336i	0.294933	+	0.510839i	0.974969	−	0.222340i	$-0.0713694\pi$
$661$	7.58270	+	13.1336i	0.294933	+	0.510839i	−0.680036	+	0.733178i	$0.738036\pi$
$662$		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	$-0.841212\pi$
$673$		−	24.8223i		−	0.956830i	0.878134	−	0.478415i	$-0.158788\pi$
$674$		0			0
$675$	−2.33078	+	4.42351i	−0.0897118	+	0.170261i
$676$		0			0
$677$	−14.2448	−	8.22425i	−0.547473	−	0.316084i	0.200629	−	0.979667i	$-0.435701\pi$
$677$	−14.2448	−	8.22425i	−0.547473	−	0.316084i	−0.748102	+	0.663584i	$0.769035\pi$
$678$		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	$-0.398034\pi$
$683$	33.8256	−	19.5292i	1.29430	−	0.747264i	0.979413	+	0.201866i	$0.0647004\pi$
$684$		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	0.264200	+	0.964468i	$0.414892\pi$
$691$	−18.4837	+	32.0147i	−0.703154	+	1.21790i	−0.967354	+	0.253430i	$0.918441\pi$
$692$		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	−0.879096	−	0.476644i	$-0.841853\pi$
$709$	−0.712591	+	1.23424i	−0.0267619	+	0.0463530i	0.852334	+	0.522997i	$0.175186\pi$
$710$		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	0.465409	+	0.885096i	$0.345907\pi$
$719$	−14.3137	+	24.7920i	−0.533811	+	0.924587i	−0.999220	+	0.0394917i	$0.987426\pi$
$720$		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	0.833927	−	0.551874i	$-0.186087\pi$
$733$	20.9269	+	12.0822i	0.772954	+	0.446265i	−0.0609737	+	0.998139i	$0.519421\pi$
$734$		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	$-0.236412\pi$
$739$	−5.90892	−	10.2346i	−0.217363	−	0.376484i	−0.954001	+	0.299803i	$0.903079\pi$
$740$		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	0.0307729	+	0.999526i	$0.490203\pi$
$751$	−23.3000	+	40.3568i	−0.850229	+	1.47264i	−0.881002	+	0.473113i	$0.843130\pi$
$752$		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	$0.183435\pi$
$757$			29.9847i			1.08981i	−0.838497	+	0.544906i	$0.816565\pi$
$758$		0			0
$759$	2.57541	+	4.46074i	0.0934815	+	0.161915i
$760$		0			0
$761$	−21.3504	+	36.9799i	−0.773950	+	1.34052i	0.161432	+	0.986884i	$0.448389\pi$
$761$	−21.3504	+	36.9799i	−0.773950	+	1.34052i	−0.935383	+	0.353638i	$0.884945\pi$
$762$		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	−0.965460	−	0.260550i	$-0.916096\pi$
$773$	−33.9903	+	19.6243i	−1.22255	+	0.705838i	−0.257087	+	0.966388i	$0.582763\pi$
$774$		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	$-0.814506\pi$
$787$	−21.7650	+	12.5661i	−0.775840	+	0.447931i	0.0591139	+	0.998251i	$0.481172\pi$
$788$		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	$-0.978466\pi$
$797$		−	3.81681i		−	0.135198i	0.997713	−	0.0675991i	$-0.0215339\pi$
$798$		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	0.977382	−	0.211480i	$-0.0678284\pi$
$809$	8.69056	+	15.0525i	0.305544	+	0.529217i	−0.671839	+	0.740698i	$0.734495\pi$
$810$		0			0
$811$	13.8289			0.485599			0.242799	−	0.970076i	$-0.421934\pi$
$811$	13.8289			0.485599			0.242799	+	0.970076i	$0.421934\pi$
$812$		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	−0.997416	−	0.0718362i	$-0.977114\pi$
$821$	−12.5070	+	21.6627i	−0.436496	+	0.756034i	0.560920	+	0.827870i	$0.310447\pi$
$822$		0			0
$823$	−12.0736	+	6.97068i	−0.420859	+	0.242983i	−0.695445	−	0.718580i	$-0.744793\pi$
$823$	−12.0736	+	6.97068i	−0.420859	+	0.242983i	0.274586	+	0.961563i	$0.411459\pi$
$824$		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	0.643324	−	0.765594i	$-0.277555\pi$
$829$	−9.82862	−	17.0237i	−0.341362	−	0.591256i	−0.984686	+	0.174338i	$0.944222\pi$
$830$		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	$-0.802611\pi$
$839$	−47.1449			−1.62762			−0.813811	+	0.581129i	$0.802611\pi$
$840$		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	$-0.915409\pi$
$853$		−	15.3410i		−	0.525266i	0.964896	−	0.262633i	$-0.0845909\pi$
$854$		0			0
$855$	3.32610	+	11.5179i	0.113750	+	0.393904i
$856$		0			0
$857$	9.02603	−	5.21118i	0.308323	−	0.178011i	−0.337853	−	0.941199i	$-0.609701\pi$
$857$	9.02603	−	5.21118i	0.308323	−	0.178011i	0.646176	+	0.763188i	$0.276367\pi$
$858$		0			0
$859$	−25.8513	+	44.7758i	−0.882036	+	1.52773i	−0.0329624	+	0.999457i	$0.510494\pi$
$859$	−25.8513	+	44.7758i	−0.882036	+	1.52773i	−0.849074	+	0.528275i	$0.822839\pi$
$860$		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	$-0.346367\pi$
$863$	−2.08282	−	1.20251i	−0.0708999	−	0.0409341i	−0.535031	+	0.844833i	$0.679700\pi$
$864$		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	0.400698	−	0.916210i	$-0.368768\pi$
$877$	−5.69818	−	3.28985i	−0.192414	−	0.111090i	−0.593112	+	0.805120i	$0.702101\pi$
$878$		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	$-0.368712\pi$
$887$	−5.72166	−	3.30340i	−0.192115	−	0.110917i	−0.592972	+	0.805223i	$0.702046\pi$
$888$		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	−0.616840	+	0.787088i	$0.711587\pi$
$907$	−48.3941	+	27.9403i	−1.60690	+	0.927743i	−0.990059	+	0.140655i	$0.955079\pi$
$908$		0			0
$909$	0.994342			0.0329803
$910$		0			0
$911$	26.7182			0.885214			0.442607	−	0.896716i	$-0.354054\pi$
$911$	26.7182			0.885214			0.442607	+	0.896716i	$0.354054\pi$
$912$		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	−0.443915	−	0.896069i	$-0.646411\pi$
$919$	16.7964	−	29.0922i	0.554061	−	0.959662i	0.997976	−	0.0635928i	$-0.0202559\pi$
$920$		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	−0.442646	−	0.896697i	$-0.645960\pi$
$929$	16.9234	−	29.3122i	0.555239	−	0.961702i	0.997885	−	0.0650058i	$-0.0207066\pi$
$930$		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	$-0.680449\pi$
$937$		−	51.6442i		−	1.68714i	0.537017	−	0.843571i	$-0.319551\pi$
$938$		0			0
$939$	9.29921			0.303468
$940$		0			0
$941$	−25.2093	−	43.6638i	−0.821800	−	1.42340i	−0.904341	−	0.426812i	$-0.859637\pi$
$941$	−25.2093	−	43.6638i	−0.821800	−	1.42340i	0.0825405	−	0.996588i	$-0.473697\pi$
$942$		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	$-0.124391\pi$
$947$	32.5284	+	18.7803i	1.05703	+	0.610277i	0.132421	+	0.991194i	$0.457725\pi$
$948$		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	$-0.906018\pi$
$953$		−	17.9656i		−	0.581964i	0.956729	−	0.290982i	$-0.0939820\pi$
$954$		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	$-0.869232\pi$
$971$	−3.50688	+	6.07410i	−0.112541	+	0.194927i	0.804253	+	0.594287i	$0.202566\pi$
$972$		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	0.510613	−	0.859810i	$-0.329418\pi$
$977$	47.2149	−	27.2595i	1.51054	−	0.872109i	0.999924	−	0.0122990i	$-0.00391500\pi$
$978$		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	$-0.895876\pi$
$983$	−35.8110	+	20.6755i	−1.14219	+	0.659446i	−0.195221	+	0.980759i	$0.562542\pi$
$984$		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	$-0.0267854\pi$
$991$	13.3930	+	23.1973i	0.425442	+	0.736887i	−0.571020	+	0.820936i	$0.693452\pi$
$992$		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	−0.945250	−	0.326347i	$-0.894182\pi$
$997$	−35.8459	+	20.6956i	−1.13525	+	0.655437i	−0.190000	+	0.981784i	$0.560849\pi$
$998$		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	840.2.cc.c.289.1	✓	24
4.3	odd	2		1680.2.di.g.289.9		24
5.4	even	2	inner	840.2.cc.c.289.11	yes	24
7.4	even	3	inner	840.2.cc.c.529.11	yes	24
20.19	odd	2		1680.2.di.g.289.6		24
28.11	odd	6		1680.2.di.g.529.6		24
35.4	even	6	inner	840.2.cc.c.529.1	yes	24
140.39	odd	6		1680.2.di.g.529.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cc.c.289.1	✓	24	1.1	even	1	trivial
840.2.cc.c.289.11	yes	24	5.4	even	2	inner
840.2.cc.c.529.1	yes	24	35.4	even	6	inner
840.2.cc.c.529.11	yes	24	7.4	even	3	inner
1680.2.di.g.289.6		24	20.19	odd	2
1680.2.di.g.289.9		24	4.3	odd	2
1680.2.di.g.529.6		24	28.11	odd	6
1680.2.di.g.529.9		24	140.39	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cc (of order \(6\), degree \(2\), 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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