LMFDB - Embedded newform 840.2.cc.c.289.11

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			289.11
Character	$\chi$	$=$	840.289
Dual form			840.2.cc.c.529.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +(1.55028 + 1.61140i) q^{5} +(0.933675 - 2.47553i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.87680 - 4.98276i) q^{11} -4.56531i q^{13} +(2.14829 + 0.620374i) q^{15} +(-4.23940 + 2.44762i) q^{17} +(2.68072 - 4.64314i) q^{19} +(-0.429179 - 2.61071i) q^{21} +(-0.775297 - 0.447618i) q^{23} +(-0.193239 + 4.99626i) q^{25} -1.00000i q^{27} +4.20085 q^{29} +(1.74075 + 3.01506i) q^{31} +(-4.98276 - 2.87680i) q^{33} +(5.43654 - 2.33325i) q^{35} +(3.89750 + 2.25022i) q^{37} +(-2.28265 - 3.95367i) q^{39} +8.67682 q^{41} +8.57420i q^{43} +(2.17066 - 0.536884i) q^{45} +(3.14064 + 1.81325i) q^{47} +(-5.25650 - 4.62268i) q^{49} +(-2.44762 + 4.23940i) q^{51} +(-11.9248 + 6.88476i) q^{53} +(3.56938 - 12.3604i) q^{55} -5.36144i q^{57} +(3.50176 + 6.06523i) q^{59} +(3.04955 - 5.28198i) q^{61} +(-1.67704 - 2.04635i) q^{63} +(7.35655 - 7.07752i) q^{65} +(7.75980 - 4.48012i) q^{67} -0.895236 q^{69} -5.38928 q^{71} +(-7.10518 + 4.10218i) q^{73} +(2.33078 + 4.42351i) q^{75} +(-15.0210 + 2.46932i) q^{77} +(6.64226 - 11.5047i) q^{79} +(-0.500000 - 0.866025i) q^{81} +3.44085i q^{83} +(-10.5164 - 3.03688i) q^{85} +(3.63804 - 2.10042i) q^{87} +(-1.88139 + 3.25866i) q^{89} +(-11.3016 - 4.26251i) q^{91} +(3.01506 + 1.74075i) q^{93} +(11.6378 - 2.87847i) q^{95} -4.32089i q^{97} -5.75359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.55028	+	1.61140i	0.693308	+	0.720641i
$5$	1.55028	+	1.61140i	0.693308	+	0.720641i
$6$		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	$-0.781784\pi$
$13$		−	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	$-0.868974\pi$
$17$	−4.23940	+	2.44762i	−1.02821	+	0.593635i	−0.111735	+	0.993738i	$0.535641\pi$
$18$		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	0.416987	−	0.908912i	$-0.363086\pi$
$23$	−0.775297	−	0.447618i	−0.161661	−	0.0933348i	−0.578648	+	0.815578i	$0.696419\pi$
$24$		0			0
$25$	−0.193239	+	4.99626i	−0.0386479	+	0.999253i
$26$		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
$35$	5.43654	−	2.33325i	0.918943	−	0.394391i
$36$		0			0
$37$	3.89750	+	2.25022i	0.640745	+	0.369934i	0.784901	−	0.619621i	$-0.212714\pi$
$37$	3.89750	+	2.25022i	0.640745	+	0.369934i	−0.144156	+	0.989555i	$0.546047\pi$
$38$		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	$0.226816\pi$
$43$			8.57420i			1.30755i	−0.756688	+	0.653777i	$0.773184\pi$
$44$		0			0
$45$	2.17066	−	0.536884i	0.323583	−	0.0800339i
$46$		0			0
$47$	3.14064	+	1.81325i	0.458110	+	0.264490i	0.711249	−	0.702940i	$-0.248130\pi$
$47$	3.14064	+	1.81325i	0.458110	+	0.264490i	−0.253139	+	0.967430i	$0.581463\pi$
$48$		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	$0.727950\pi$
$53$	−11.9248	+	6.88476i	−1.63799	+	0.945694i	−0.981524	+	0.191340i	$0.938717\pi$
$54$		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
$65$	7.35655	−	7.07752i	0.912468	−	0.877859i
$66$		0			0
$67$	7.75980	−	4.48012i	0.948010	−	0.547334i	0.0555479	−	0.998456i	$-0.482309\pi$
$67$	7.75980	−	4.48012i	0.948010	−	0.547334i	0.892462	+	0.451122i	$0.148976\pi$
$68$		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	−0.854400	−	0.519617i	$-0.826075\pi$
$73$	−7.10518	+	4.10218i	−0.831598	+	0.480123i	0.0228013	+	0.999740i	$0.492741\pi$
$74$		0			0
$75$	2.33078	+	4.42351i	0.269136	+	0.510783i
$76$		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	$0.0604731\pi$
$83$			3.44085i			0.377682i	−0.982008	+	0.188841i	$0.939527\pi$
$84$		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
$95$	11.6378	−	2.87847i	1.19402	−	0.295325i
$96$		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	0.889700	−	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	−0.178167	−	0.984000i	$-0.557017\pi$
$103$	−11.3609	−	6.55920i	−1.11942	−	0.646297i	−0.941253	+	0.337703i	$0.890350\pi$
$104$		0			0
$105$	3.54156	−	4.73892i	0.345620	−	0.462471i
$106$		0			0
$107$	13.1202	+	7.57495i	1.26838	+	0.732298i	0.974681	−	0.223600i	$-0.0717810\pi$
$107$	13.1202	+	7.57495i	1.26838	+	0.732298i	0.293697	+	0.955899i	$0.405114\pi$
$108$		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	$0.194280\pi$
$113$			12.1854i			1.14631i	−0.819448	+	0.573153i	$0.805720\pi$
$114$		0			0
$115$	−0.480637	−	1.94325i	−0.0448197	−	0.181209i
$116$		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	$-0.966639\pi$
$127$		−	2.35791i		−	0.209231i	0.994513	−	0.104616i	$-0.0333612\pi$
$128$		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
$135$	1.61140	−	1.55028i	0.138687	−	0.133427i
$136$		0			0
$137$	18.9231	−	10.9253i	1.61671	−	0.933410i	0.628951	−	0.777445i	$-0.283485\pi$
$137$	18.9231	−	10.9253i	1.61671	−	0.933410i	0.987763	−	0.155965i	$-0.0498487\pi$
$138$		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
$145$	6.51251	+	6.76926i	0.540834	+	0.562156i
$146$		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	−0.656704	−	0.754149i	$-0.728050\pi$
$157$	−4.15924	+	2.40134i	−0.331943	+	0.191648i	0.324760	+	0.945796i	$0.394716\pi$
$158$		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	0.638188	−	0.769881i	$-0.279684\pi$
$163$	3.70943	+	2.14164i	0.290545	+	0.167746i	−0.347643	+	0.937627i	$0.613018\pi$
$164$		0			0
$165$	−3.08901	−	12.4891i	−0.240479	−	0.972274i
$166$		0			0
$167$			8.70217i			0.673394i	0.941613	+	0.336697i	$0.109310\pi$
$167$			8.70217i			0.673394i	−0.941613	+	0.336697i	$0.890690\pi$
$168$		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	$-0.210767\pi$
$173$	8.55693	+	4.94034i	0.650571	+	0.375607i	−0.138104	+	0.990418i	$0.544101\pi$
$174$		0			0
$175$	12.1880	+	5.14326i	0.921325	+	0.388794i
$176$		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
$185$	2.41622	+	9.76893i	0.177644	+	0.718226i
$186$		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	−0.825081	−	0.565015i	$-0.808870\pi$
$193$	−10.3958	+	6.00200i	−0.748304	+	0.432034i	0.0767766	+	0.997048i	$0.475537\pi$
$194$		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	$-0.0963072\pi$
$199$	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
$205$	13.4515	+	13.9818i	0.939496	+	0.976535i
$206$		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
$215$	−13.8165	+	13.2924i	−0.942277	+	0.906537i
$216$		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	$-0.759496\pi$
$223$		−	20.4794i		−	1.37140i	0.727884	−	0.685700i	$-0.240504\pi$
$224$		0			0
$225$	4.23027	+	2.66548i	0.282018	+	0.177699i
$226$		0			0
$227$	−13.2474	+	7.64837i	−0.879258	+	0.507640i	−0.870414	−	0.492321i	$-0.836149\pi$
$227$	−13.2474	+	7.64837i	−0.879258	+	0.507640i	−0.00884444	+	0.999961i	$0.502815\pi$
$228$		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	0.327338	−	0.944907i	$-0.393849\pi$
$233$	−4.99613	−	2.88452i	−0.327308	−	0.188971i	−0.654645	+	0.755936i	$0.727182\pi$
$234$		0			0
$235$	1.94701	+	7.87189i	0.127009	+	0.513506i
$236$		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
$245$	−0.700072	−	15.6368i	−0.0447260	−	0.998999i
$246$		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
$255$	−10.6259	+	2.62817i	−0.665419	+	0.164583i
$256$		0			0
$257$	−5.46653	−	3.15610i	−0.340993	−	0.196872i	0.319718	−	0.947513i	$-0.396412\pi$
$257$	−5.46653	−	3.15610i	−0.340993	−	0.196872i	−0.660711	+	0.750640i	$0.729745\pi$
$258$		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	−0.939542	−	0.342433i	$-0.888749\pi$
$263$	−18.0459	+	10.4188i	−1.11276	+	0.642451i	−0.173215	+	0.984884i	$0.555416\pi$
$264$		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
$275$	25.4511	−	13.4104i	1.53476	−	0.808676i
$276$		0			0
$277$	4.33597	−	2.50337i	0.260523	−	0.150413i	−0.364050	−	0.931379i	$-0.618606\pi$
$277$	4.33597	−	2.50337i	0.260523	−	0.150413i	0.624573	+	0.780966i	$0.285273\pi$
$278$		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	−0.949685	−	0.313208i	$-0.898596\pi$
$283$	−19.4012	+	11.2013i	−1.15328	+	0.665847i	−0.203597	+	0.979055i	$0.565263\pi$
$284$		0			0
$285$	8.63944	−	8.31175i	0.511756	−	0.492346i
$286$		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
$305$	13.2391	−	3.27451i	0.758067	−	0.187498i
$306$		0			0
$307$		−	8.12145i		−	0.463516i	−0.972774	−	0.231758i	$-0.925552\pi$
$307$		−	8.12145i		−	0.463516i	0.972774	−	0.231758i	$-0.0744477\pi$
$308$		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	0.710025	−	0.704177i	$-0.248684\pi$
$313$	8.05335	+	4.64960i	0.455202	+	0.262811i	−0.254823	+	0.966988i	$0.582017\pi$
$314$		0			0
$315$	0.697616	−	5.87480i	0.0393062	−	0.331008i
$316$		0			0
$317$	14.9071	+	8.60662i	0.837266	+	0.483396i	0.856334	−	0.516422i	$-0.172736\pi$
$317$	14.9071	+	8.60662i	0.837266	+	0.483396i	−0.0190676	+	0.999818i	$0.506070\pi$
$318$		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
$325$	22.8095	+	0.882198i	1.26524	+	0.0489355i
$326$		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	$-0.941672\pi$
$337$		−	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
$345$	−1.38787	−	1.44259i	−0.0747204	−	0.0776662i
$346$		0			0
$347$	−2.36917	+	1.36784i	−0.127184	+	0.0734296i	−0.562242	−	0.826973i	$-0.690061\pi$
$347$	−2.36917	+	1.36784i	−0.127184	+	0.0734296i	0.435058	+	0.900402i	$0.356728\pi$
$348$		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	$-0.752938\pi$
$353$	−8.71230	+	5.03005i	−0.463709	+	0.267722i	0.249894	+	0.968273i	$0.419604\pi$
$354$		0			0
$355$	−8.35491	−	8.68430i	−0.443432	−	0.460915i
$356$		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	$0.672605\pi$
$367$	−29.0403	+	16.7664i	−1.51589	+	0.875201i	−0.999826	+	0.0186533i	$0.994062\pi$
$368$		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	$-0.171411\pi$
$373$	16.2921	+	9.40624i	0.843572	+	0.487036i	−0.0149049	+	0.999889i	$0.504745\pi$
$374$		0			0
$375$	−3.51469	+	10.6135i	−0.181498	+	0.548080i
$376$		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	0.277311	−	0.960780i	$-0.410557\pi$
$383$	−8.14310	−	4.70142i	−0.416093	−	0.240232i	−0.693404	+	0.720549i	$0.743890\pi$
$384$		0			0
$385$	−27.2658	−	20.3767i	−1.38960	−	1.03849i
$386$		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
$395$	28.8361	−	7.13224i	1.45090	−	0.358862i
$396$		0			0
$397$	−1.54528	−	0.892166i	−0.0775552	−	0.0447765i	0.460721	−	0.887545i	$-0.347591\pi$
$397$	−1.54528	−	0.892166i	−0.0775552	−	0.0447765i	−0.538276	+	0.842769i	$0.680924\pi$
$398$		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
$415$	−5.54459	+	5.33429i	−0.272173	+	0.261850i
$416$		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
$425$	−11.4097	−	21.6541i	−0.553453	−	1.05038i
$426$		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	$0.351011\pi$
$433$			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	0.147360	−	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	−0.389433	−	0.921055i	$-0.627329\pi$
$443$	−29.0837	−	16.7915i	−1.38181	−	0.797786i	−0.992373	+	0.123268i	$0.960662\pi$
$444$		0			0
$445$	−8.16770	+	2.02017i	−0.387186	+	0.0957654i
$446$		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
$455$	−10.6520	−	24.8195i	−0.499374	−	1.16355i
$456$		0			0
$457$	20.1117	+	11.6115i	0.940787	+	0.543164i	0.890207	−	0.455556i	$-0.150560\pi$
$457$	20.1117	+	11.6115i	0.940787	+	0.543164i	0.0505802	+	0.998720i	$0.483893\pi$
$458$		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	$-0.867115\pi$
$463$		−	17.4485i		−	0.810901i	0.914117	−	0.405450i	$-0.132885\pi$
$464$		0			0
$465$	1.86916	+	7.55714i	0.0866802	+	0.350454i
$466$		0			0
$467$	20.4002	+	11.7781i	0.944009	+	0.545024i	0.891215	−	0.453581i	$-0.149854\pi$
$467$	20.4002	+	11.7781i	0.944009	+	0.545024i	0.0527945	+	0.998605i	$0.483187\pi$
$468$		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
$485$	6.96269	−	6.69860i	0.316160	−	0.304168i
$486$		0			0
$487$	−10.1849	+	5.88025i	−0.461521	+	0.266460i	−0.712684	−	0.701485i	$-0.752521\pi$
$487$	−10.1849	+	5.88025i	−0.461521	+	0.266460i	0.251162	+	0.967945i	$0.419187\pi$
$488$		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
$495$	−8.91970	−	9.27136i	−0.400911	−	0.416717i
$496$		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	$-0.740485\pi$
$503$		−	32.6513i		−	1.45585i	0.685657	−	0.727925i	$-0.259515\pi$
$504$		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
$515$	−7.04305	−	28.4755i	−0.310354	−	1.25478i
$516$		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	0.539060	−	0.842267i	$-0.318779\pi$
$523$	1.81046	+	1.04527i	0.0791659	+	0.0457064i	−0.459895	+	0.887974i	$0.652113\pi$
$524$		0			0
$525$	13.1267	−	1.63980i	0.572897	−	0.0715668i
$526$		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
$535$	8.13374	+	32.8853i	0.351652	+	1.42175i
$536$		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	$0.221475\pi$
$547$			29.9829i			1.28198i	−0.767550	+	0.640989i	$0.778525\pi$
$548$		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
$555$	6.97697	+	7.25203i	0.296156	+	0.307832i
$556$		0			0
$557$	4.59121	−	2.65073i	0.194536	−	0.112315i	−0.399568	−	0.916703i	$-0.630840\pi$
$557$	4.59121	−	2.65073i	0.194536	−	0.112315i	0.594104	+	0.804388i	$0.297507\pi$
$558$		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	−0.0790375	−	0.996872i	$-0.525185\pi$
$563$	17.6714	−	10.2026i	0.744760	−	0.429987i	0.823797	+	0.566884i	$0.191851\pi$
$564$		0			0
$565$	−19.6356	+	18.8908i	−0.826076	+	0.794744i
$566$		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	−0.375238	−	0.926929i	$-0.622439\pi$
$577$	5.76228	−	3.32685i	0.239887	−	0.138499i	0.615125	+	0.788430i	$0.289106\pi$
$578$		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
$585$	−2.45104	−	9.90972i	−0.101338	−	0.409717i
$586$		0			0
$587$		−	11.7672i		−	0.485683i	−0.970066	−	0.242842i	$-0.921920\pi$
$587$		−	11.7672i		−	0.485683i	0.970066	−	0.242842i	$-0.0780796\pi$
$588$		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	$-0.314132\pi$
$593$	2.54283	+	1.46810i	0.104421	+	0.0602877i	−0.446880	+	0.894594i	$0.647465\pi$
$594$		0			0
$595$	−17.3367	+	23.1981i	−0.710737	+	0.951031i
$596$		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
$605$	−47.9799	+	11.8672i	−1.95066	+	0.482470i
$606$		0			0
$607$	−23.5128	−	13.5751i	−0.954355	−	0.550997i	−0.0599239	−	0.998203i	$-0.519086\pi$
$607$	−23.5128	−	13.5751i	−0.954355	−	0.550997i	−0.894431	+	0.447206i	$0.852419\pi$
$608$		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	$-0.484245\pi$
$613$	23.2529	−	13.4251i	0.939177	−	0.542234i	0.889702	+	0.456541i	$0.150912\pi$
$614$		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	0.924838	+	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
$625$	−24.9253	−	1.93095i	−0.997013	−	0.0772380i
$626$		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
$635$	3.79955	−	3.65544i	0.150781	−	0.145062i
$636$		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	$-0.925549\pi$
$643$		−	11.7541i		−	0.463537i	0.972771	−	0.231769i	$-0.0744512\pi$
$644$		0			0
$645$	−5.31921	+	18.4198i	−0.209444	+	0.725280i
$646$		0			0
$647$	9.60514	−	5.54553i	0.377617	−	0.218017i	−0.299164	−	0.954202i	$-0.596708\pi$
$647$	9.60514	−	5.54553i	0.377617	−	0.218017i	0.676781	+	0.736184i	$0.263374\pi$
$648$		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	$-0.282329\pi$
$653$	7.06171	+	4.07708i	0.276346	+	0.159549i	−0.355422	+	0.934706i	$0.615663\pi$
$654$		0			0
$655$	0.335995	−	0.0831040i	0.0131284	−	0.00324714i
$656$		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
$665$	3.74023	−	31.4974i	0.145040	−	1.22142i
$666$		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
$675$	4.99626	+	0.193239i	0.192306	+	0.00743779i
$676$		0			0
$677$	14.2448	+	8.22425i	0.547473	+	0.316084i	0.748102	−	0.663584i	$-0.230965\pi$
$677$	14.2448	+	8.22425i	0.547473	+	0.316084i	−0.200629	+	0.979667i	$0.564299\pi$
$678$		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	−0.979413	−	0.201866i	$-0.935300\pi$
$683$	−33.8256	+	19.5292i	−1.29430	+	0.747264i	−0.314886	+	0.949130i	$0.601966\pi$
$684$		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
$695$	10.7522	+	11.1761i	0.407853	+	0.423933i
$696$		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
$705$	5.62211	+	5.84375i	0.211741	+	0.220088i
$706$		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
$725$	−0.811770	+	20.9885i	−0.0301484	+	0.779495i
$726$		0			0
$727$			7.81682i			0.289910i	0.989438	+	0.144955i	$0.0463037\pi$
$727$			7.81682i			0.289910i	−0.989438	+	0.144955i	$0.953696\pi$
$728$		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	$-0.480579\pi$
$733$	−20.9269	−	12.0822i	−0.772954	−	0.446265i	−0.833927	+	0.551874i	$0.813913\pi$
$734$		0			0
$735$	−8.42469	−	13.1918i	−0.310749	−	0.486588i
$736$		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	$0.0190223\pi$
$743$			3.25596i			0.119450i	−0.998215	+	0.0597248i	$0.980978\pi$
$744$		0			0
$745$	15.3101	−	3.78675i	0.560919	−	0.138736i
$746$		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	$-0.816565\pi$
$757$		−	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	0.161432	+	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
$765$	−7.88820	+	7.58901i	−0.285198	+	0.274381i
$766$		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	$-0.417237\pi$
$773$	33.9903	−	19.6243i	1.22255	−	0.705838i	0.965460	+	0.260550i	$0.0839040\pi$
$774$		0			0
$775$	−15.4004	+	8.11461i	−0.553200	+	0.291485i
$776$		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	−0.0591139	−	0.998251i	$-0.518828\pi$
$787$	21.7650	−	12.5661i	0.775840	−	0.447931i	0.834954	+	0.550320i	$0.185494\pi$
$788$		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
$795$	−29.8889	+	7.39263i	−1.06005	+	0.262190i
$796$		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
$805$	−5.25933	−	0.624531i	−0.185367	−	0.0220118i
$806$		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
$815$	2.29962	+	9.29754i	0.0805523	+	0.325679i
$816$		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	−0.274586	−	0.961563i	$-0.588541\pi$
$823$	12.0736	−	6.97068i	0.420859	−	0.242983i	0.695445	+	0.718580i	$0.255207\pi$
$824$		0			0
$825$	15.3361	−	24.3393i	0.533935	−	0.847385i
$826$		0			0
$827$		−	16.1987i		−	0.563284i	−0.959520	−	0.281642i	$-0.909121\pi$
$827$		−	16.1987i		−	0.563284i	0.959520	−	0.281642i	$-0.0908790\pi$
$828$		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
$835$	−14.0227	+	13.4908i	−0.485276	+	0.466870i
$836$		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
$845$	−12.1574	−	12.6367i	−0.418227	−	0.434715i
$846$		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	$-0.723633\pi$
$857$	−9.02603	+	5.21118i	−0.308323	+	0.178011i	0.337853	+	0.941199i	$0.390299\pi$
$858$		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	0.535031	−	0.844833i	$-0.320300\pi$
$863$	2.08282	+	1.20251i	0.0708999	+	0.0409341i	−0.464131	+	0.885767i	$0.653633\pi$
$864$		0			0
$865$	5.30478	+	21.4476i	0.180368	+	0.729240i
$866$		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
$875$	10.6070	+	27.6133i	0.358581	+	0.933499i
$876$		0			0
$877$	5.69818	+	3.28985i	0.192414	+	0.111090i	0.593112	−	0.805120i	$-0.297899\pi$
$877$	5.69818	+	3.28985i	0.192414	+	0.111090i	−0.400698	+	0.916210i	$0.631232\pi$
$878$		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	$0.0710870\pi$
$883$			13.1624i			0.442949i	−0.975166	+	0.221475i	$0.928913\pi$
$884$		0			0
$885$	3.76008	+	15.2023i	0.126394	+	0.511018i
$886$		0			0
$887$	5.72166	+	3.30340i	0.192115	+	0.110917i	0.592972	−	0.805223i	$-0.297954\pi$
$887$	5.72166	+	3.30340i	0.192115	+	0.110917i	−0.400858	+	0.916140i	$0.631288\pi$
$888$		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
$905$	−22.9258	−	23.8297i	−0.762080	−	0.792125i
$906$		0			0
$907$	48.3941	−	27.9403i	1.60690	−	0.927743i	0.616840	−	0.787088i	$-0.288413\pi$
$907$	48.3941	−	27.9403i	1.60690	−	0.927743i	0.990059	−	0.140655i	$-0.0449208\pi$
$908$		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
$915$	9.82812	−	9.45535i	0.324908	−	0.312584i
$916$		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
$935$	15.1214	+	61.1370i	0.494524	+	1.99939i
$936$		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	−0.904341	−	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
$945$	−2.33325	−	5.43654i	−0.0759006	−	0.176851i
$946$		0			0
$947$	−32.5284	−	18.7803i	−1.05703	−	0.610277i	−0.132421	−	0.991194i	$-0.542275\pi$
$947$	−32.5284	−	18.7803i	−1.05703	−	0.610277i	−0.924609	+	0.380916i	$0.875609\pi$
$948$		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
$955$	3.83266	−	0.947958i	0.124022	−	0.0306752i
$956$		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	$-0.972056\pi$
$967$		−	5.45276i		−	0.175349i	0.996149	−	0.0876745i	$-0.0279435\pi$
$968$		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
$975$	20.1947	−	10.6407i	0.646748	−	0.340776i
$976$		0			0
$977$	−47.2149	+	27.2595i	−1.51054	+	0.872109i	−0.510613	+	0.859810i	$0.670582\pi$
$977$	−47.2149	+	27.2595i	−1.51054	+	0.872109i	−0.999924	+	0.0122990i	$0.996085\pi$
$978$		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	0.195221	−	0.980759i	$-0.437458\pi$
$983$	35.8110	−	20.6755i	1.14219	−	0.659446i	0.946973	+	0.321313i	$0.104124\pi$
$984$		0			0
$985$	−15.5538	+	14.9639i	−0.495586	+	0.476789i
$986$		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	0.190000	−	0.981784i	$-0.439151\pi$
$997$	35.8459	−	20.6956i	1.13525	−	0.655437i	0.945250	+	0.326347i	$0.105818\pi$
$998$		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.289.11	yes	24
4.3	odd	2		1680.2.di.g.289.6		24
5.4	even	2	inner	840.2.cc.c.289.1	✓	24
7.4	even	3	inner	840.2.cc.c.529.1	yes	24
20.19	odd	2		1680.2.di.g.289.9		24
28.11	odd	6		1680.2.di.g.529.9		24
35.4	even	6	inner	840.2.cc.c.529.11	yes	24
140.39	odd	6		1680.2.di.g.529.6		24

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.55028 + 1.61140i) q^{5} +(0.933675 - 2.47553i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.87680 - 4.98276i) q^{11} -4.56531i q^{13} +(2.14829 + 0.620374i) q^{15} +(-4.23940 + 2.44762i) q^{17} +(2.68072 - 4.64314i) q^{19} +(-0.429179 - 2.61071i) q^{21} +(-0.775297 - 0.447618i) q^{23} +(-0.193239 + 4.99626i) q^{25} -1.00000i q^{27} +4.20085 q^{29} +(1.74075 + 3.01506i) q^{31} +(-4.98276 - 2.87680i) q^{33} +(5.43654 - 2.33325i) q^{35} +(3.89750 + 2.25022i) q^{37} +(-2.28265 - 3.95367i) q^{39} +8.67682 q^{41} +8.57420i q^{43} +(2.17066 - 0.536884i) q^{45} +(3.14064 + 1.81325i) q^{47} +(-5.25650 - 4.62268i) q^{49} +(-2.44762 + 4.23940i) q^{51} +(-11.9248 + 6.88476i) q^{53} +(3.56938 - 12.3604i) q^{55} -5.36144i q^{57} +(3.50176 + 6.06523i) q^{59} +(3.04955 - 5.28198i) q^{61} +(-1.67704 - 2.04635i) q^{63} +(7.35655 - 7.07752i) q^{65} +(7.75980 - 4.48012i) q^{67} -0.895236 q^{69} -5.38928 q^{71} +(-7.10518 + 4.10218i) q^{73} +(2.33078 + 4.42351i) q^{75} +(-15.0210 + 2.46932i) q^{77} +(6.64226 - 11.5047i) q^{79} +(-0.500000 - 0.866025i) q^{81} +3.44085i q^{83} +(-10.5164 - 3.03688i) q^{85} +(3.63804 - 2.10042i) q^{87} +(-1.88139 + 3.25866i) q^{89} +(-11.3016 - 4.26251i) q^{91} +(3.01506 + 1.74075i) q^{93} +(11.6378 - 2.87847i) q^{95} -4.32089i q^{97} -5.75359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5} + 12 q^{9} - 8 q^{11} + 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} + 4 q^{31} + 30 q^{35} + 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} - 20 q^{51} + 12 q^{55} - 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) \) 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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