LMFDB - Embedded newform 912.2.q.l.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(49,912)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("912.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	912.49
Dual form			912.2.q.l.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-1.66044 + 2.87597i) q^{5} -2.32088 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-1.66044 + 2.87597i) q^{5} -2.32088 q^{7} +(-0.500000 - 0.866025i) q^{9} +1.70739 q^{11} +(-2.01414 - 3.48859i) q^{13} +(1.66044 + 2.87597i) q^{15} +(-0.193252 - 4.35461i) q^{19} +(-1.16044 + 2.00994i) q^{21} +(-1.17458 - 2.03443i) q^{23} +(-3.01414 - 5.22064i) q^{25} -1.00000 q^{27} +(-3.32088 - 5.75194i) q^{29} -6.70739 q^{31} +(0.853695 - 1.47864i) q^{33} +(3.85369 - 6.67479i) q^{35} -1.00000 q^{37} -4.02827 q^{39} +(3.32088 - 5.75194i) q^{41} +(0.353695 - 0.612617i) q^{43} +3.32088 q^{45} +(-3.00000 - 5.19615i) q^{47} -1.61350 q^{49} +(4.98133 + 8.62791i) q^{53} +(-2.83502 + 4.91040i) q^{55} +(-3.86783 - 2.00994i) q^{57} +(0.853695 - 1.47864i) q^{59} +(-1.69325 - 2.93280i) q^{61} +(1.16044 + 2.00994i) q^{63} +13.3774 q^{65} +(-4.18872 - 7.25507i) q^{67} -2.34916 q^{69} +(-4.70739 + 8.15344i) q^{71} +(-5.82088 + 10.0821i) q^{73} -6.02827 q^{75} -3.96265 q^{77} +(-1.67458 + 2.90046i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0565 q^{83} -6.64177 q^{87} +(1.33956 + 2.32018i) q^{89} +(4.67458 + 8.09661i) q^{91} +(-3.35369 + 5.80877i) q^{93} +(12.8446 + 6.67479i) q^{95} +(-8.86330 + 15.3517i) q^{97} +(-0.853695 - 1.47864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9 + q^13 + 2 * q^15 - 4 * q^19 + q^21 + 14 * q^23 - 5 * q^25 - 6 * q^27 - 4 * q^29 - 30 * q^31 + 18 * q^35 - 6 * q^37 + 2 * q^39 + 4 * q^41 - 3 * q^43 + 4 * q^45 - 18 * q^47 - 4 * q^49 + 6 * q^53 + 12 * q^55 - 5 * q^57 - 13 * q^61 - q^63 + 12 * q^65 + 9 * q^67 + 28 * q^69 - 18 * q^71 - 19 * q^73 - 10 * q^75 + 24 * q^77 + 11 * q^79 - 3 * q^81 + 8 * q^83 - 8 * q^87 + 16 * q^89 + 7 * q^91 - 15 * q^93 - 2 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−1.66044	+	2.87597i	−0.742572	+	1.28617i	0.208748	+	0.977969i	$0.433061\pi$
$5$	−1.66044	+	2.87597i	−0.742572	+	1.28617i	−0.951320	+	0.308204i	$0.900272\pi$
$6$		0			0
$7$	−2.32088			−0.877212			−0.438606	−	0.898679i	$-0.644528\pi$
$7$	−2.32088			−0.877212			−0.438606	+	0.898679i	$0.644528\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.70739			0.514797			0.257399	−	0.966305i	$-0.417135\pi$
$11$	1.70739			0.514797			0.257399	+	0.966305i	$0.417135\pi$
$12$		0			0
$13$	−2.01414	−	3.48859i	−0.558621	−	0.967560i	−0.997612	−	0.0690685i	$-0.977997\pi$
$13$	−2.01414	−	3.48859i	−0.558621	−	0.967560i	0.438991	−	0.898492i	$-0.355336\pi$
$14$		0			0
$15$	1.66044	+	2.87597i	0.428724	+	0.742572i
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−0.193252	−	4.35461i	−0.0443351	−	0.999017i
$19$	−0.193252	−	4.35461i	−0.0443351	−	0.999017i
$20$		0			0
$21$	−1.16044	+	2.00994i	−0.253229	+	0.438606i
$22$		0			0
$23$	−1.17458	−	2.03443i	−0.244917	−	0.424208i	0.717191	−	0.696876i	$-0.245427\pi$
$23$	−1.17458	−	2.03443i	−0.244917	−	0.424208i	−0.962108	+	0.272668i	$0.912094\pi$
$24$		0			0
$25$	−3.01414	−	5.22064i	−0.602827	−	1.04413i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.32088	−	5.75194i	−0.616673	−	1.06811i	−0.990089	−	0.140444i	$-0.955147\pi$
$29$	−3.32088	−	5.75194i	−0.616673	−	1.06811i	0.373416	−	0.927664i	$-0.378186\pi$
$30$		0			0
$31$	−6.70739			−1.20468			−0.602341	−	0.798239i	$-0.705765\pi$
$31$	−6.70739			−1.20468			−0.602341	+	0.798239i	$0.705765\pi$
$32$		0			0
$33$	0.853695	−	1.47864i	0.148609	−	0.257399i
$34$		0			0
$35$	3.85369	−	6.67479i	0.651393	−	1.12825i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$	−4.02827			−0.645040
$40$		0			0
$41$	3.32088	−	5.75194i	0.518635	−	0.898302i	−0.481131	−	0.876649i	$-0.659774\pi$
$41$	3.32088	−	5.75194i	0.518635	−	0.898302i	0.999766	−	0.0216532i	$-0.00689298\pi$
$42$		0			0
$43$	0.353695	−	0.612617i	0.0539379	−	0.0934232i	−0.837796	−	0.545984i	$-0.816156\pi$
$43$	0.353695	−	0.612617i	0.0539379	−	0.0934232i	0.891734	+	0.452561i	$0.149489\pi$
$44$		0			0
$45$	3.32088			0.495048
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−1.61350			−0.230499
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.98133	+	8.62791i	0.684238	+	1.18513i	0.973676	+	0.227938i	$0.0731983\pi$
$53$	4.98133	+	8.62791i	0.684238	+	1.18513i	−0.289438	+	0.957197i	$0.593468\pi$
$54$		0			0
$55$	−2.83502	+	4.91040i	−0.382274	+	0.662118i
$56$		0			0
$57$	−3.86783	−	2.00994i	−0.512307	−	0.266224i
$58$		0			0
$59$	0.853695	−	1.47864i	0.111142	−	0.192503i	−0.805089	−	0.593154i	$-0.797883\pi$
$59$	0.853695	−	1.47864i	0.111142	−	0.192503i	0.916231	+	0.400651i	$0.131216\pi$
$60$		0			0
$61$	−1.69325	−	2.93280i	−0.216799	−	0.375506i	0.737029	−	0.675861i	$-0.236228\pi$
$61$	−1.69325	−	2.93280i	−0.216799	−	0.375506i	−0.953828	+	0.300355i	$0.902895\pi$
$62$		0			0
$63$	1.16044	+	2.00994i	0.146202	+	0.253229i
$64$		0			0
$65$	13.3774			1.65927
$66$		0			0
$67$	−4.18872	−	7.25507i	−0.511733	−	0.886348i	−0.999907	−	0.0136016i	$-0.995670\pi$
$67$	−4.18872	−	7.25507i	−0.511733	−	0.886348i	0.488174	−	0.872746i	$-0.337663\pi$
$68$		0			0
$69$	−2.34916			−0.282805
$70$		0			0
$71$	−4.70739	+	8.15344i	−0.558664	+	0.967635i	0.438944	+	0.898514i	$0.355353\pi$
$71$	−4.70739	+	8.15344i	−0.558664	+	0.967635i	−0.997608	+	0.0691206i	$0.977981\pi$
$72$		0			0
$73$	−5.82088	+	10.0821i	−0.681283	+	1.18002i	0.293307	+	0.956018i	$0.405244\pi$
$73$	−5.82088	+	10.0821i	−0.681283	+	1.18002i	−0.974590	+	0.223998i	$0.928089\pi$
$74$		0			0
$75$	−6.02827			−0.696085
$76$		0			0
$77$	−3.96265			−0.451586
$78$		0			0
$79$	−1.67458	+	2.90046i	−0.188405	+	0.326327i	−0.944719	−	0.327882i	$-0.893665\pi$
$79$	−1.67458	+	2.90046i	−0.188405	+	0.326327i	0.756314	+	0.654209i	$0.226998\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	10.0565			1.10385			0.551925	−	0.833894i	$-0.313894\pi$
$83$	10.0565			1.10385			0.551925	+	0.833894i	$0.313894\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.64177			−0.712072
$88$		0			0
$89$	1.33956	+	2.32018i	0.141993	+	0.245939i	0.928247	−	0.371964i	$-0.121316\pi$
$89$	1.33956	+	2.32018i	0.141993	+	0.245939i	−0.786254	+	0.617903i	$0.787982\pi$
$90$		0			0
$91$	4.67458	+	8.09661i	0.490029	+	0.848755i
$92$		0			0
$93$	−3.35369	+	5.80877i	−0.347762	+	0.602341i
$94$		0			0
$95$	12.8446	+	6.67479i	1.31783	+	0.684820i
$96$		0			0
$97$	−8.86330	+	15.3517i	−0.899931	+	1.55873i	−0.0723511	+	0.997379i	$0.523050\pi$
$97$	−8.86330	+	15.3517i	−0.899931	+	1.55873i	−0.827580	+	0.561347i	$0.810283\pi$
$98$		0			0
$99$	−0.853695	−	1.47864i	−0.0857995	−	0.148609i
$100$		0			0
$101$	−8.02827	−	13.9054i	−0.798843	−	1.38364i	−0.920370	−	0.391049i	$-0.872112\pi$
$101$	−8.02827	−	13.9054i	−0.798843	−	1.38364i	0.121527	−	0.992588i	$-0.461221\pi$
$102$		0			0
$103$	7.54787			0.743714			0.371857	−	0.928290i	$-0.378721\pi$
$103$	7.54787			0.743714			0.371857	+	0.928290i	$0.378721\pi$
$104$		0			0
$105$	−3.85369	−	6.67479i	−0.376082	−	0.651393i
$106$		0			0
$107$	−7.28354			−0.704126			−0.352063	−	0.935976i	$-0.614520\pi$
$107$	−7.28354			−0.704126			−0.352063	+	0.935976i	$0.614520\pi$
$108$		0			0
$109$	6.12763	−	10.6134i	0.586921	−	1.01658i	−0.407712	−	0.913110i	$-0.633673\pi$
$109$	6.12763	−	10.6134i	0.586921	−	1.01658i	0.994633	−	0.103466i	$-0.0329933\pi$
$110$		0			0
$111$	−0.500000	+	0.866025i	−0.0474579	+	0.0821995i
$112$		0			0
$113$	7.37743			0.694010			0.347005	−	0.937863i	$-0.387199\pi$
$113$	7.37743			0.694010			0.347005	+	0.937863i	$0.387199\pi$
$114$		0			0
$115$	7.80128			0.727473
$116$		0			0
$117$	−2.01414	+	3.48859i	−0.186207	+	0.322520i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−8.08482			−0.734984
$122$		0			0
$123$	−3.32088	−	5.75194i	−0.299434	−	0.518635i
$124$		0			0
$125$	3.41478			0.305427
$126$		0			0
$127$	7.32088	+	12.6801i	0.649623	+	1.12518i	0.983213	+	0.182462i	$0.0584068\pi$
$127$	7.32088	+	12.6801i	0.649623	+	1.12518i	−0.333589	+	0.942718i	$0.608260\pi$
$128$		0			0
$129$	−0.353695	−	0.612617i	−0.0311411	−	0.0539379i
$130$		0			0
$131$	0.320884	−	0.555788i	0.0280358	−	0.0485594i	−0.851667	−	0.524083i	$-0.824408\pi$
$131$	0.320884	−	0.555788i	0.0280358	−	0.0485594i	0.879703	+	0.475524i	$0.157741\pi$
$132$		0			0
$133$	0.448517	+	10.1066i	0.0388913	+	0.876349i
$134$		0			0
$135$	1.66044	−	2.87597i	0.142908	−	0.247524i
$136$		0			0
$137$	−1.29261	−	2.23887i	−0.110435	−	0.191279i	0.805511	−	0.592581i	$-0.201891\pi$
$137$	−1.29261	−	2.23887i	−0.110435	−	0.191279i	−0.915946	+	0.401302i	$0.868558\pi$
$138$		0			0
$139$	−9.28807	−	16.0874i	−0.787804	−	1.36452i	−0.927309	−	0.374296i	$-0.877885\pi$
$139$	−9.28807	−	16.0874i	−0.787804	−	1.36452i	0.139505	−	0.990221i	$-0.455449\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−3.43892	−	5.95638i	−0.287577	−	0.498097i
$144$		0			0
$145$	22.0565			1.83170
$146$		0			0
$147$	−0.806748	+	1.39733i	−0.0665394	+	0.115250i
$148$		0			0
$149$	1.98133	−	3.43176i	0.162317	−	0.281141i	−0.773382	−	0.633940i	$-0.781437\pi$
$149$	1.98133	−	3.43176i	0.162317	−	0.281141i	0.935699	+	0.352799i	$0.114770\pi$
$150$		0			0
$151$	8.69832			0.707859			0.353929	−	0.935272i	$-0.384845\pi$
$151$	8.69832			0.707859			0.353929	+	0.935272i	$0.384845\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.1372	−	19.2903i	0.894564	−	1.54943i
$156$		0			0
$157$	2.84916	−	4.93489i	0.227388	−	0.393847i	−0.729645	−	0.683826i	$-0.760315\pi$
$157$	2.84916	−	4.93489i	0.227388	−	0.393847i	0.957033	+	0.289979i	$0.0936482\pi$
$158$		0			0
$159$	9.96265			0.790090
$160$		0			0
$161$	2.72606	+	4.72168i	0.214844	+	0.372120i
$162$		0			0
$163$	−18.3774			−1.43943			−0.719716	−	0.694269i	$-0.755728\pi$
$163$	−18.3774			−1.43943			−0.719716	+	0.694269i	$0.755728\pi$
$164$		0			0
$165$	2.83502	+	4.91040i	0.220706	+	0.382274i
$166$		0			0
$167$	10.8163	+	18.7345i	0.836994	+	1.44972i	0.892396	+	0.451252i	$0.149023\pi$
$167$	10.8163	+	18.7345i	0.836994	+	1.44972i	−0.0554023	+	0.998464i	$0.517644\pi$
$168$		0			0
$169$	−1.61350	+	2.79466i	−0.124115	+	0.214974i
$170$		0			0
$171$	−3.67458	+	2.34467i	−0.281002	+	0.179301i
$172$		0			0
$173$	2.34916	−	4.06886i	0.178603	−	0.309350i	−0.762799	−	0.646636i	$-0.776175\pi$
$173$	2.34916	−	4.06886i	0.178603	−	0.309350i	0.941402	+	0.337286i	$0.109509\pi$
$174$		0			0
$175$	6.99546	+	12.1165i	0.528807	+	0.915921i
$176$		0			0
$177$	−0.853695	−	1.47864i	−0.0641676	−	0.111142i
$178$		0			0
$179$	1.06562			0.0796482			0.0398241	−	0.999207i	$-0.487320\pi$
$179$	1.06562			0.0796482			0.0398241	+	0.999207i	$0.487320\pi$
$180$		0			0
$181$	1.83502	+	3.17835i	0.136396	+	0.236245i	0.926130	−	0.377205i	$-0.123115\pi$
$181$	1.83502	+	3.17835i	0.136396	+	0.236245i	−0.789734	+	0.613450i	$0.789781\pi$
$182$		0			0
$183$	−3.38650			−0.250338
$184$		0			0
$185$	1.66044	−	2.87597i	0.122078	−	0.211446i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.32088			0.168820
$190$		0			0
$191$	0.877832			0.0635177			0.0317588	−	0.999496i	$-0.489889\pi$
$191$	0.877832			0.0635177			0.0317588	+	0.999496i	$0.489889\pi$
$192$		0			0
$193$	4.30675	−	7.45951i	0.310006	−	0.536947i	−0.668357	−	0.743841i	$-0.733002\pi$
$193$	4.30675	−	7.45951i	0.310006	−	0.536947i	0.978363	+	0.206894i	$0.0663354\pi$
$194$		0			0
$195$	6.68872	−	11.5852i	0.478989	−	0.829633i
$196$		0			0
$197$	24.7357			1.76234			0.881172	−	0.472797i	$-0.156756\pi$
$197$	24.7357			1.76234			0.881172	+	0.472797i	$0.156756\pi$
$198$		0			0
$199$	−10.9955	−	19.0447i	−0.779448	−	1.35004i	−0.932260	−	0.361788i	$-0.882166\pi$
$199$	−10.9955	−	19.0447i	−0.779448	−	1.35004i	0.152813	−	0.988255i	$-0.451167\pi$
$200$		0			0
$201$	−8.37743			−0.590899
$202$		0			0
$203$	7.70739	+	13.3496i	0.540953	+	0.936958i
$204$		0			0
$205$	11.0283	+	19.1015i	0.770248	+	1.33411i
$206$		0			0
$207$	−1.17458	+	2.03443i	−0.0816389	+	0.141403i
$208$		0			0
$209$	−0.329957	−	7.43502i	−0.0228236	−	0.514291i
$210$		0			0
$211$	−6.60896	+	11.4471i	−0.454979	+	0.788048i	−0.998687	−	0.0512272i	$-0.983687\pi$
$211$	−6.60896	+	11.4471i	−0.454979	+	0.788048i	0.543708	+	0.839275i	$0.317020\pi$
$212$		0			0
$213$	4.70739	+	8.15344i	0.322545	+	0.558664i
$214$		0			0
$215$	1.17458	+	2.03443i	0.0801056	+	0.138747i
$216$		0			0
$217$	15.5671			1.05676
$218$		0			0
$219$	5.82088	+	10.0821i	0.393339	+	0.681283i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−2.74020	+	4.74616i	−0.183497	+	0.317827i	−0.943069	−	0.332597i	$-0.892075\pi$
$223$	−2.74020	+	4.74616i	−0.183497	+	0.317827i	0.759572	+	0.650423i	$0.225409\pi$
$224$		0			0
$225$	−3.01414	+	5.22064i	−0.200942	+	0.348043i
$226$		0			0
$227$	−7.70739			−0.511557			−0.255779	−	0.966735i	$-0.582332\pi$
$227$	−7.70739			−0.511557			−0.255779	+	0.966735i	$0.582332\pi$
$228$		0			0
$229$	4.02827			0.266196			0.133098	−	0.991103i	$-0.457508\pi$
$229$	4.02827			0.266196			0.133098	+	0.991103i	$0.457508\pi$
$230$		0			0
$231$	−1.98133	+	3.43176i	−0.130362	+	0.225793i
$232$		0			0
$233$	−13.0565	+	22.6146i	−0.855363	+	1.48153i	0.0209451	+	0.999781i	$0.493332\pi$
$233$	−13.0565	+	22.6146i	−0.855363	+	1.48153i	−0.876308	+	0.481751i	$0.840001\pi$
$234$		0			0
$235$	19.9253			1.29978
$236$		0			0
$237$	1.67458	+	2.90046i	0.108776	+	0.188405i
$238$		0			0
$239$	7.70739			0.498550			0.249275	−	0.968433i	$-0.419808\pi$
$239$	7.70739			0.498550			0.249275	+	0.968433i	$0.419808\pi$
$240$		0			0
$241$	−10.8492	−	18.7913i	−0.698856	−	1.21045i	−0.968863	−	0.247595i	$-0.920360\pi$
$241$	−10.8492	−	18.7913i	−0.698856	−	1.21045i	0.270008	−	0.962858i	$-0.412974\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	2.67912	−	4.64036i	0.171162	−	0.296462i
$246$		0			0
$247$	−14.8022	+	9.44496i	−0.941842	+	0.600969i
$248$		0			0
$249$	5.02827	−	8.70923i	0.318654	−	0.551925i
$250$		0			0
$251$	4.70739	+	8.15344i	0.297128	+	0.514640i	0.975478	−	0.220099i	$-0.0706379\pi$
$251$	4.70739	+	8.15344i	0.297128	+	0.514640i	−0.678350	+	0.734739i	$0.737305\pi$
$252$		0			0
$253$	−2.00546	−	3.47357i	−0.126082	−	0.218381i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.07522	+	8.79054i	0.316584	+	0.548339i	0.979773	−	0.200113i	$-0.0641309\pi$
$257$	5.07522	+	8.79054i	0.316584	+	0.548339i	−0.663189	+	0.748452i	$0.730798\pi$
$258$		0			0
$259$	2.32088			0.144213
$260$		0			0
$261$	−3.32088	+	5.75194i	−0.205558	+	0.356036i
$262$		0			0
$263$	1.29261	−	2.23887i	0.0797058	−	0.138054i	−0.823417	−	0.567436i	$-0.807935\pi$
$263$	1.29261	−	2.23887i	0.0797058	−	0.138054i	0.903123	+	0.429382i	$0.141269\pi$
$264$		0			0
$265$	−33.0848			−2.03238
$266$		0			0
$267$	2.67912			0.163959
$268$		0			0
$269$	−0.273937	+	0.474473i	−0.0167023	+	0.0289292i	−0.874256	−	0.485466i	$-0.838650\pi$
$269$	−0.273937	+	0.474473i	−0.0167023	+	0.0289292i	0.857553	+	0.514395i	$0.171983\pi$
$270$		0			0
$271$	−10.4431	+	18.0879i	−0.634370	+	1.09876i	0.352278	+	0.935895i	$0.385407\pi$
$271$	−10.4431	+	18.0879i	−0.634370	+	1.09876i	−0.986648	+	0.162866i	$0.947926\pi$
$272$		0			0
$273$	9.34916			0.565837
$274$		0			0
$275$	−5.14631	−	8.91366i	−0.310334	−	0.537514i
$276$		0			0
$277$	−23.7831			−1.42899			−0.714495	−	0.699640i	$-0.753344\pi$
$277$	−23.7831			−1.42899			−0.714495	+	0.699640i	$0.753344\pi$
$278$		0			0
$279$	3.35369	+	5.80877i	0.200780	+	0.347762i
$280$		0			0
$281$	5.95305	+	10.3110i	0.355129	+	0.615102i	0.987140	−	0.159858i	$-0.0511035\pi$
$281$	5.95305	+	10.3110i	0.355129	+	0.615102i	−0.632011	+	0.774960i	$0.717770\pi$
$282$		0			0
$283$	9.02827	−	15.6374i	0.536675	−	0.929549i	−0.462405	−	0.886669i	$-0.653013\pi$
$283$	9.02827	−	15.6374i	0.536675	−	0.929549i	0.999080	−	0.0428799i	$-0.0136533\pi$
$284$		0			0
$285$	12.2029	−	7.78637i	0.722835	−	0.461225i
$286$		0			0
$287$	−7.70739	+	13.3496i	−0.454953	+	0.788001i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	8.86330	+	15.3517i	0.519576	+	0.899931i
$292$		0			0
$293$	−27.3966			−1.60053			−0.800264	−	0.599648i	$-0.795307\pi$
$293$	−27.3966			−1.60053			−0.800264	+	0.599648i	$0.795307\pi$
$294$		0			0
$295$	2.83502	+	4.91040i	0.165061	+	0.285895i
$296$		0			0
$297$	−1.70739			−0.0990728
$298$		0			0
$299$	−4.73153	+	8.19524i	−0.273631	+	0.473943i
$300$		0			0
$301$	−0.820884	+	1.42181i	−0.0473150	+	0.0819520i
$302$		0			0
$303$	−16.0565			−0.922425
$304$		0			0
$305$	11.2462			0.643955
$306$		0			0
$307$	1.80675	−	3.12938i	0.103117	−	0.178603i	−0.809851	−	0.586636i	$-0.800452\pi$
$307$	1.80675	−	3.12938i	0.103117	−	0.178603i	0.912967	+	0.408033i	$0.133785\pi$
$308$		0			0
$309$	3.77394	−	6.53665i	0.214692	−	0.371857i
$310$		0			0
$311$	−18.4057			−1.04369			−0.521846	−	0.853040i	$-0.674756\pi$
$311$	−18.4057			−1.04369			−0.521846	+	0.853040i	$0.674756\pi$
$312$		0			0
$313$	−11.5424	−	19.9920i	−0.652416	−	1.13002i	−0.982535	−	0.186078i	$-0.940422\pi$
$313$	−11.5424	−	19.9920i	−0.652416	−	1.13002i	0.330119	−	0.943939i	$-0.392911\pi$
$314$		0			0
$315$	−7.70739			−0.434262
$316$		0			0
$317$	12.6887	+	21.9775i	0.712669	+	1.23438i	0.963852	+	0.266440i	$0.0858473\pi$
$317$	12.6887	+	21.9775i	0.712669	+	1.23438i	−0.251182	+	0.967940i	$0.580819\pi$
$318$		0			0
$319$	−5.67004	−	9.82080i	−0.317461	−	0.549859i
$320$		0			0
$321$	−3.64177	+	6.30773i	−0.203264	+	0.352063i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−12.1418	+	21.0302i	−0.673504	+	1.16654i
$326$		0			0
$327$	−6.12763	−	10.6134i	−0.338859	−	0.586921i
$328$		0			0
$329$	6.96265	+	12.0597i	0.383864	+	0.664871i
$330$		0			0
$331$	21.3492			1.17346			0.586728	−	0.809784i	$-0.300416\pi$
$331$	21.3492			1.17346			0.586728	+	0.809784i	$0.300416\pi$
$332$		0			0
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$		0			0
$335$	27.8205			1.52000
$336$		0			0
$337$	2.04241	−	3.53756i	0.111257	−	0.192703i	−0.805020	−	0.593247i	$-0.797846\pi$
$337$	2.04241	−	3.53756i	0.111257	−	0.192703i	0.916277	+	0.400544i	$0.131179\pi$
$338$		0			0
$339$	3.68872	−	6.38904i	0.200344	−	0.347005i
$340$		0			0
$341$	−11.4521			−0.620167
$342$		0			0
$343$	19.9909			1.07941
$344$		0			0
$345$	3.90064	−	6.75611i	0.210003	−	0.363737i
$346$		0			0
$347$	9.85369	−	17.0671i	0.528974	−	0.916210i	−0.470455	−	0.882424i	$-0.655910\pi$
$347$	9.85369	−	17.0671i	0.528974	−	0.916210i	0.999429	−	0.0337860i	$-0.0107565\pi$
$348$		0			0
$349$	23.3118			1.24785			0.623926	−	0.781483i	$-0.285537\pi$
$349$	23.3118			1.24785			0.623926	+	0.781483i	$0.285537\pi$
$350$		0			0
$351$	2.01414	+	3.48859i	0.107507	+	0.186207i
$352$		0			0
$353$	25.1896			1.34071			0.670355	−	0.742041i	$-0.266142\pi$
$353$	25.1896			1.34071			0.670355	+	0.742041i	$0.266142\pi$
$354$		0			0
$355$	−15.6327	−	27.0766i	−0.829697	−	1.43708i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.61350	+	2.79466i	−0.0851570	+	0.147496i	−0.905458	−	0.424436i	$-0.860473\pi$
$359$	−1.61350	+	2.79466i	−0.0851570	+	0.147496i	0.820301	+	0.571932i	$0.193806\pi$
$360$		0			0
$361$	−18.9253	+	1.68308i	−0.996069	+	0.0885831i
$362$		0			0
$363$	−4.04241	+	7.00166i	−0.212172	+	0.367492i
$364$		0			0
$365$	−19.3305	−	33.4814i	−1.01180	−	1.75250i
$366$		0			0
$367$	−14.7311	−	25.5151i	−0.768959	−	1.33188i	−0.938128	−	0.346288i	$-0.887442\pi$
$367$	−14.7311	−	25.5151i	−0.768959	−	1.33188i	0.169170	−	0.985587i	$-0.445891\pi$
$368$		0			0
$369$	−6.64177			−0.345757
$370$		0			0
$371$	−11.5611	−	20.0244i	−0.600222	−	1.03961i
$372$		0			0
$373$	19.6700			1.01848			0.509238	−	0.860626i	$-0.329927\pi$
$373$	19.6700			1.01848			0.509238	+	0.860626i	$0.329927\pi$
$374$		0			0
$375$	1.70739	−	2.95729i	0.0881692	−	0.152714i
$376$		0			0
$377$	−13.3774	+	23.1704i	−0.688973	+	1.19334i
$378$		0			0
$379$	0.763937			0.0392408			0.0196204	−	0.999808i	$-0.493754\pi$
$379$	0.763937			0.0392408			0.0196204	+	0.999808i	$0.493754\pi$
$380$		0			0
$381$	14.6418			0.750121
$382$		0			0
$383$	1.91932	−	3.32435i	0.0980724	−	0.169866i	−0.812814	−	0.582523i	$-0.802066\pi$
$383$	1.91932	−	3.32435i	0.0980724	−	0.169866i	0.910887	+	0.412656i	$0.135399\pi$
$384$		0			0
$385$	6.57976	−	11.3965i	0.335335	−	0.580818i
$386$		0			0
$387$	−0.707389			−0.0359586
$388$		0			0
$389$	−16.1035	−	27.8921i	−0.816480	−	1.41418i	−0.908261	−	0.418405i	$-0.862589\pi$
$389$	−16.1035	−	27.8921i	−0.816480	−	1.41418i	0.0917810	−	0.995779i	$-0.470744\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−0.320884	−	0.555788i	−0.0161865	−	0.0280358i
$394$		0			0
$395$	−5.56108	−	9.63208i	−0.279809	−	0.484643i
$396$		0			0
$397$	13.2977	−	23.0322i	0.667391	−	1.15596i	−0.311240	−	0.950331i	$-0.600744\pi$
$397$	13.2977	−	23.0322i	0.667391	−	1.15596i	0.978631	−	0.205624i	$-0.0659224\pi$
$398$		0			0
$399$	8.97679	+	4.66485i	0.449402	+	0.233535i
$400$		0			0
$401$	4.66044	−	8.07212i	0.232731	−	0.403103i	−0.725880	−	0.687822i	$-0.758567\pi$
$401$	4.66044	−	8.07212i	0.232731	−	0.403103i	0.958611	+	0.284719i	$0.0919004\pi$
$402$		0			0
$403$	13.5096	+	23.3993i	0.672961	+	1.16560i
$404$		0			0
$405$	−1.66044	−	2.87597i	−0.0825080	−	0.142908i
$406$		0			0
$407$	−1.70739			−0.0846321
$408$		0			0
$409$	−10.9006	−	18.8805i	−0.539002	−	0.933579i	−0.998958	−	0.0456372i	$-0.985468\pi$
$409$	−10.9006	−	18.8805i	−0.539002	−	0.933579i	0.459956	−	0.887942i	$-0.347865\pi$
$410$		0			0
$411$	−2.58522			−0.127520
$412$		0			0
$413$	−1.98133	+	3.43176i	−0.0974947	+	0.168866i
$414$		0			0
$415$	−16.6983	+	28.9223i	−0.819688	+	1.41974i
$416$		0			0
$417$	−18.5761			−0.909678
$418$		0			0
$419$	−4.93438			−0.241060			−0.120530	−	0.992710i	$-0.538459\pi$
$419$	−4.93438			−0.241060			−0.120530	+	0.992710i	$0.538459\pi$
$420$		0			0
$421$	−2.12763	+	3.68517i	−0.103694	+	0.179604i	−0.913204	−	0.407503i	$-0.866400\pi$
$421$	−2.12763	+	3.68517i	−0.103694	+	0.179604i	0.809510	+	0.587107i	$0.199733\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.92984	+	6.80669i	0.190178	+	0.329399i
$428$		0			0
$429$	−6.87783			−0.332065
$430$		0			0
$431$	−0.414779	−	0.718418i	−0.0199792	−	0.0346050i	0.855863	−	0.517203i	$-0.173027\pi$
$431$	−0.414779	−	0.718418i	−0.0199792	−	0.0346050i	−0.875842	+	0.482598i	$0.839693\pi$
$432$		0			0
$433$	−8.24113	−	14.2741i	−0.396043	−	0.685967i	0.597190	−	0.802099i	$-0.296284\pi$
$433$	−8.24113	−	14.2741i	−0.396043	−	0.685967i	−0.993234	+	0.116132i	$0.962950\pi$
$434$		0			0
$435$	11.0283	−	19.1015i	0.528765	−	0.915848i
$436$		0			0
$437$	−8.63217	+	5.50800i	−0.412933	+	0.263483i
$438$		0			0
$439$	14.2170	−	24.6245i	0.678540	−	1.17527i	−0.296881	−	0.954915i	$-0.595946\pi$
$439$	14.2170	−	24.6245i	0.678540	−	1.17527i	0.975421	−	0.220351i	$-0.0707203\pi$
$440$		0			0
$441$	0.806748	+	1.39733i	0.0384166	+	0.0665394i
$442$		0			0
$443$	−7.70739	−	13.3496i	−0.366189	−	0.634258i	0.622777	−	0.782399i	$-0.286004\pi$
$443$	−7.70739	−	13.3496i	−0.366189	−	0.634258i	−0.988966	+	0.148141i	$0.952671\pi$
$444$		0			0
$445$	−8.89703			−0.421760
$446$		0			0
$447$	−1.98133	−	3.43176i	−0.0937135	−	0.162317i
$448$		0			0
$449$	−23.1523			−1.09262			−0.546312	−	0.837582i	$-0.683969\pi$
$449$	−23.1523			−1.09262			−0.546312	+	0.837582i	$0.683969\pi$
$450$		0			0
$451$	5.67004	−	9.82080i	0.266992	−	0.462444i
$452$		0			0
$453$	4.34916	−	7.53296i	0.204341	−	0.353929i
$454$		0			0
$455$	−31.0475			−1.45553
$456$		0			0
$457$	4.68819			0.219304			0.109652	−	0.993970i	$-0.465026\pi$
$457$	4.68819			0.219304			0.109652	+	0.993970i	$0.465026\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.27394	+	10.8668i	−0.292206	+	0.506116i	−0.974331	−	0.225119i	$-0.927723\pi$
$461$	−6.27394	+	10.8668i	−0.292206	+	0.506116i	0.682125	+	0.731236i	$0.261056\pi$
$462$		0			0
$463$	−22.8880			−1.06369			−0.531847	−	0.846841i	$-0.678502\pi$
$463$	−22.8880			−1.06369			−0.531847	+	0.846841i	$0.678502\pi$
$464$		0			0
$465$	−11.1372	−	19.2903i	−0.516477	−	0.894564i
$466$		0			0
$467$	11.8122			0.546604			0.273302	−	0.961928i	$-0.411884\pi$
$467$	11.8122			0.546604			0.273302	+	0.961928i	$0.411884\pi$
$468$		0			0
$469$	9.72153	+	16.8382i	0.448898	+	0.777515i
$470$		0			0
$471$	−2.84916	−	4.93489i	−0.131282	−	0.227388i
$472$		0			0
$473$	0.603895	−	1.04598i	0.0277671	−	0.0480940i
$474$		0			0
$475$	−22.1514	+	14.1343i	−1.01637	+	0.648526i
$476$		0			0
$477$	4.98133	−	8.62791i	0.228079	−	0.395045i
$478$		0			0
$479$	−17.0192	−	29.4781i	−0.777627	−	1.34689i	−0.933306	−	0.359082i	$-0.883090\pi$
$479$	−17.0192	−	29.4781i	−0.777627	−	1.34689i	0.155679	−	0.987808i	$-0.450244\pi$
$480$		0			0
$481$	2.01414	+	3.48859i	0.0918367	+	0.159066i
$482$		0			0
$483$	5.45213			0.248080
$484$		0			0
$485$	−29.4340	−	50.9811i	−1.33653	−	2.31493i
$486$		0			0
$487$	7.41478			0.335996			0.167998	−	0.985787i	$-0.446270\pi$
$487$	7.41478			0.335996			0.167998	+	0.985787i	$0.446270\pi$
$488$		0			0
$489$	−9.18872	+	15.9153i	−0.415528	+	0.719716i
$490$		0			0
$491$	1.93438	−	3.35044i	0.0872973	−	0.151203i	−0.819071	−	0.573693i	$-0.805510\pi$
$491$	1.93438	−	3.35044i	0.0872973	−	0.151203i	0.906368	+	0.422489i	$0.138844\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	5.67004			0.254849
$496$		0			0
$497$	10.9253	−	18.9232i	0.490067	−	0.848821i
$498$		0			0
$499$	−17.7931	+	30.8186i	−0.796530	+	1.37963i	0.125333	+	0.992115i	$0.460000\pi$
$499$	−17.7931	+	30.8186i	−0.796530	+	1.37963i	−0.921863	+	0.387516i	$0.873333\pi$
$500$		0			0
$501$	21.6327			0.966478
$502$		0			0
$503$	4.29261	+	7.43502i	0.191398	+	0.331511i	0.945714	−	0.325001i	$-0.105365\pi$
$503$	4.29261	+	7.43502i	0.191398	+	0.331511i	−0.754316	+	0.656512i	$0.772031\pi$
$504$		0			0
$505$	53.3219			2.37280
$506$		0			0
$507$	1.61350	+	2.79466i	0.0716578	+	0.124115i
$508$		0			0
$509$	3.97173	+	6.87923i	0.176044	+	0.304917i	0.940522	−	0.339733i	$-0.110337\pi$
$509$	3.97173	+	6.87923i	0.176044	+	0.304917i	−0.764478	+	0.644649i	$0.777003\pi$
$510$		0			0
$511$	13.5096	−	23.3993i	0.597630	−	1.03512i
$512$		0			0
$513$	0.193252	+	4.35461i	0.00853230	+	0.192261i
$514$		0			0
$515$	−12.5328	+	21.7075i	−0.552262	+	0.956545i
$516$		0			0
$517$	−5.12217	−	8.87186i	−0.225273	−	0.390184i
$518$		0			0
$519$	−2.34916	−	4.06886i	−0.103117	−	0.178603i
$520$		0			0
$521$	−0.0757489			−0.00331862			−0.00165931	−	0.999999i	$-0.500528\pi$
$521$	−0.0757489			−0.00331862			−0.00165931	+	0.999999i	$0.500528\pi$
$522$		0			0
$523$	10.1514	+	17.5827i	0.443888	+	0.768837i	0.997974	−	0.0636224i	$-0.0202653\pi$
$523$	10.1514	+	17.5827i	0.443888	+	0.768837i	−0.554086	+	0.832460i	$0.686932\pi$
$524$		0			0
$525$	13.9909			0.610614
$526$		0			0
$527$		0			0
$528$		0			0
$529$	8.74073	−	15.1394i	0.380032	−	0.658234i
$530$		0			0
$531$	−1.70739			−0.0740944
$532$		0			0
$533$	−26.7549			−1.15888
$534$		0			0
$535$	12.0939	−	20.9472i	0.522865	−	0.905628i
$536$		0			0
$537$	0.532810	−	0.922854i	0.0229925	−	0.0398241i
$538$		0			0
$539$	−2.75486			−0.118660
$540$		0			0
$541$	16.5475	+	28.6611i	0.711432	+	1.23224i	0.964320	+	0.264740i	$0.0852862\pi$
$541$	16.5475	+	28.6611i	0.711432	+	1.23224i	−0.252888	+	0.967495i	$0.581381\pi$
$542$		0			0
$543$	3.67004			0.157497
$544$		0			0
$545$	20.3492	+	35.2458i	0.871662	+	1.50976i
$546$		0			0
$547$	−17.9581	−	31.1044i	−0.767834	−	1.32993i	−0.938735	−	0.344639i	$-0.888001\pi$
$547$	−17.9581	−	31.1044i	−0.767834	−	1.32993i	0.170902	−	0.985288i	$-0.445332\pi$
$548$		0			0
$549$	−1.69325	+	2.93280i	−0.0722663	+	0.125169i
$550$		0			0
$551$	−24.4057	+	15.5727i	−1.03972	+	0.663421i
$552$		0			0
$553$	3.88650	−	6.73162i	0.165271	−	0.286258i
$554$		0			0
$555$	−1.66044	−	2.87597i	−0.0704818	−	0.122078i
$556$		0			0
$557$	0.962653	+	1.66736i	0.0407889	+	0.0706485i	0.885699	−	0.464260i	$-0.153680\pi$
$557$	0.962653	+	1.66736i	0.0407889	+	0.0706485i	−0.844910	+	0.534908i	$0.820346\pi$
$558$		0			0
$559$	−2.84956			−0.120523
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.8861			−0.458795			−0.229397	−	0.973333i	$-0.573676\pi$
$563$	−10.8861			−0.458795			−0.229397	+	0.973333i	$0.573676\pi$
$564$		0			0
$565$	−12.2498	+	21.2173i	−0.515353	+	0.892618i
$566$		0			0
$567$	1.16044	−	2.00994i	0.0487340	−	0.0844098i
$568$		0			0
$569$	−36.4358			−1.52747			−0.763735	−	0.645530i	$-0.776636\pi$
$569$	−36.4358			−1.52747			−0.763735	+	0.645530i	$0.776636\pi$
$570$		0			0
$571$	7.54787			0.315869			0.157934	−	0.987450i	$-0.449517\pi$
$571$	7.54787			0.315869			0.157934	+	0.987450i	$0.449517\pi$
$572$		0			0
$573$	0.438916	−	0.760225i	0.0183360	−	0.0317588i
$574$		0			0
$575$	−7.08068	+	12.2641i	−0.295285	+	0.511449i
$576$		0			0
$577$	−15.4823			−0.644535			−0.322267	−	0.946649i	$-0.604445\pi$
$577$	−15.4823			−0.644535			−0.322267	+	0.946649i	$0.604445\pi$
$578$		0			0
$579$	−4.30675	−	7.45951i	−0.178982	−	0.310006i
$580$		0			0
$581$	−23.3401			−0.968310
$582$		0			0
$583$	8.50506	+	14.7312i	0.352244	+	0.610104i
$584$		0			0
$585$	−6.68872	−	11.5852i	−0.276544	−	0.478989i
$586$		0			0
$587$	−14.8729	+	25.7606i	−0.613870	+	1.06325i	0.376712	+	0.926331i	$0.377055\pi$
$587$	−14.8729	+	25.7606i	−0.613870	+	1.06325i	−0.990582	+	0.136924i	$0.956279\pi$
$588$		0			0
$589$	1.29622	+	29.2081i	0.0534098	+	1.20350i
$590$		0			0
$591$	12.3678	−	21.4217i	0.508745	−	0.881172i
$592$		0			0
$593$	0.273937	+	0.474473i	0.0112493	+	0.0194843i	0.871595	−	0.490226i	$-0.163086\pi$
$593$	0.273937	+	0.474473i	0.0112493	+	0.0194843i	−0.860346	+	0.509711i	$0.829753\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−21.9909			−0.900029
$598$		0			0
$599$	−22.8163	−	39.5191i	−0.932251	−	1.61471i	−0.779465	−	0.626446i	$-0.784509\pi$
$599$	−22.8163	−	39.5191i	−0.932251	−	1.61471i	−0.152786	−	0.988259i	$-0.548825\pi$
$600$		0			0
$601$	−6.85783			−0.279737			−0.139868	−	0.990170i	$-0.544668\pi$
$601$	−6.85783			−0.279737			−0.139868	+	0.990170i	$0.544668\pi$
$602$		0			0
$603$	−4.18872	+	7.25507i	−0.170578	+	0.295449i
$604$		0			0
$605$	13.4244	−	23.2517i	0.545779	−	0.945316i
$606$		0			0
$607$	6.76394			0.274540			0.137270	−	0.990534i	$-0.456167\pi$
$607$	6.76394			0.274540			0.137270	+	0.990534i	$0.456167\pi$
$608$		0			0
$609$	15.4148			0.624638
$610$		0			0
$611$	−12.0848	+	20.9315i	−0.488900	+	0.846799i
$612$		0			0
$613$	−2.22153	+	3.84780i	−0.0897266	+	0.155411i	−0.907396	−	0.420278i	$-0.861933\pi$
$613$	−2.22153	+	3.84780i	−0.0897266	+	0.155411i	0.817669	+	0.575689i	$0.195266\pi$
$614$		0			0
$615$	22.0565			0.889406
$616$		0			0
$617$	16.0005	+	27.7137i	0.644157	+	1.11571i	0.984496	+	0.175410i	$0.0561250\pi$
$617$	16.0005	+	27.7137i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$618$		0			0
$619$	14.3774			0.577878			0.288939	−	0.957348i	$-0.406698\pi$
$619$	14.3774			0.577878			0.288939	+	0.957348i	$0.406698\pi$
$620$		0			0
$621$	1.17458	+	2.03443i	0.0471342	+	0.0816389i
$622$		0			0
$623$	−3.10896	−	5.38487i	−0.124558	−	0.215740i
$624$		0			0
$625$	9.40064	−	16.2824i	0.376026	−	0.651296i
$626$		0			0
$627$	−6.60389	−	3.43176i	−0.263734	−	0.137051i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	5.54695	+	9.60759i	0.220820	+	0.382472i	0.955057	−	0.296421i	$-0.0957932\pi$
$631$	5.54695	+	9.60759i	0.220820	+	0.382472i	−0.734237	+	0.678893i	$0.762460\pi$
$632$		0			0
$633$	6.60896	+	11.4471i	0.262683	+	0.454979i
$634$		0			0
$635$	−48.6236			−1.92957
$636$		0			0
$637$	3.24980	+	5.62882i	0.128762	+	0.223022i
$638$		0			0
$639$	9.41478			0.372443
$640$		0			0
$641$	−21.7357	+	37.6473i	−0.858507	+	1.48698i	0.0148458	+	0.999890i	$0.495274\pi$
$641$	−21.7357	+	37.6473i	−0.858507	+	1.48698i	−0.873353	+	0.487088i	$0.838059\pi$
$642$		0			0
$643$	−11.8113	+	20.4577i	−0.465792	+	0.806775i	−0.999237	−	0.0390599i	$-0.987564\pi$
$643$	−11.8113	+	20.4577i	−0.465792	+	0.806775i	0.533445	+	0.845835i	$0.320897\pi$
$644$		0			0
$645$	2.34916			0.0924980
$646$		0			0
$647$	19.9253			0.783345			0.391672	−	0.920105i	$-0.371897\pi$
$647$	19.9253			0.783345			0.391672	+	0.920105i	$0.371897\pi$
$648$		0			0
$649$	1.45759	−	2.52462i	0.0572154	−	0.0990999i
$650$		0			0
$651$	7.78354	−	13.4815i	0.305061	−	0.528381i
$652$		0			0
$653$	−2.11310			−0.0826918			−0.0413459	−	0.999145i	$-0.513165\pi$
$653$	−2.11310			−0.0826918			−0.0413459	+	0.999145i	$0.513165\pi$
$654$		0			0
$655$	1.06562	+	1.84571i	0.0416372	+	0.0721178i
$656$		0			0
$657$	11.6418			0.454189
$658$		0			0
$659$	21.7507	+	37.6734i	0.847288	+	1.46755i	0.883619	+	0.468206i	$0.155100\pi$
$659$	21.7507	+	37.6734i	0.847288	+	1.46755i	−0.0363312	+	0.999340i	$0.511567\pi$
$660$		0			0
$661$	−11.0565	−	19.1505i	−0.430050	−	0.744868i	0.566827	−	0.823837i	$-0.308171\pi$
$661$	−11.0565	−	19.1505i	−0.430050	−	0.744868i	−0.996877	+	0.0789685i	$0.974837\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−29.8109	−	15.4914i	−1.15602	−	0.600732i
$666$		0			0
$667$	−7.80128	+	13.5122i	−0.302067	+	0.523195i
$668$		0			0
$669$	2.74020	+	4.74616i	0.105942	+	0.183497i
$670$		0			0
$671$	−2.89104	−	5.00743i	−0.111607	−	0.193310i
$672$		0			0
$673$	12.5953			0.485515			0.242758	−	0.970087i	$-0.421948\pi$
$673$	12.5953			0.485515			0.242758	+	0.970087i	$0.421948\pi$
$674$		0			0
$675$	3.01414	+	5.22064i	0.116014	+	0.200942i
$676$		0			0
$677$	−32.9427			−1.26609			−0.633045	−	0.774115i	$-0.718195\pi$
$677$	−32.9427			−1.26609			−0.633045	+	0.774115i	$0.718195\pi$
$678$		0			0
$679$	20.5707	−	35.6295i	0.789430	−	1.36733i
$680$		0			0
$681$	−3.85369	+	6.67479i	−0.147674	+	0.255779i
$682$		0			0
$683$	18.3876			0.703580			0.351790	−	0.936079i	$-0.385573\pi$
$683$	18.3876			0.703580			0.351790	+	0.936079i	$0.385573\pi$
$684$		0			0
$685$	8.58522			0.328024
$686$		0			0
$687$	2.01414	−	3.48859i	0.0768441	−	0.133098i
$688$		0			0
$689$	20.0661	−	34.7556i	0.764459	−	1.32408i
$690$		0			0
$691$	16.6599			0.633773			0.316887	−	0.948463i	$-0.397363\pi$
$691$	16.6599			0.633773			0.316887	+	0.948463i	$0.397363\pi$
$692$		0			0
$693$	1.98133	+	3.43176i	0.0752644	+	0.130362i
$694$		0			0
$695$	61.6892			2.34001
$696$		0			0
$697$		0			0
$698$		0			0
$699$	13.0565	+	22.6146i	0.493844	+	0.855363i
$700$		0			0
$701$	24.3588	−	42.1906i	0.920018	−	1.59352i	0.120633	−	0.992697i	$-0.461507\pi$
$701$	24.3588	−	42.1906i	0.920018	−	1.59352i	0.799384	−	0.600820i	$-0.205159\pi$
$702$		0			0
$703$	0.193252	+	4.35461i	0.00728865	+	0.164237i
$704$		0			0
$705$	9.96265	−	17.2558i	0.375215	−	0.649892i
$706$		0			0
$707$	18.6327	+	32.2728i	0.700755	+	1.21374i
$708$		0			0
$709$	−14.7498	−	25.5474i	−0.553940	−	0.959453i	−0.997985	−	0.0634483i	$-0.979790\pi$
$709$	−14.7498	−	25.5474i	−0.553940	−	0.959453i	0.444045	−	0.896005i	$-0.353543\pi$
$710$		0			0
$711$	3.34916			0.125603
$712$		0			0
$713$	7.87836	+	13.6457i	0.295047	+	0.511036i
$714$		0			0
$715$	22.8405			0.854186
$716$		0			0
$717$	3.85369	−	6.67479i	0.143919	−	0.249275i
$718$		0			0
$719$	11.3250	−	19.6155i	0.422352	−	0.731535i	−0.573817	−	0.818984i	$-0.694538\pi$
$719$	11.3250	−	19.6155i	0.422352	−	0.731535i	0.996169	+	0.0874484i	$0.0278713\pi$
$720$		0			0
$721$	−17.5177			−0.652395
$722$		0			0
$723$	−21.6983			−0.806969
$724$		0			0
$725$	−20.0192	+	34.6743i	−0.743494	+	1.28777i
$726$		0			0
$727$	26.3638	−	45.6635i	0.977780	−	1.69356i	0.307342	−	0.951599i	$-0.400560\pi$
$727$	26.3638	−	45.6635i	0.977780	−	1.69356i	0.670438	−	0.741966i	$-0.266106\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	5.72659			0.211516			0.105758	−	0.994392i	$-0.466273\pi$
$733$	5.72659			0.211516			0.105758	+	0.994392i	$0.466273\pi$
$734$		0			0
$735$	−2.67912	−	4.64036i	−0.0988207	−	0.171162i
$736$		0			0
$737$	−7.15177	−	12.3872i	−0.263439	−	0.456289i
$738$		0			0
$739$	16.7083	−	28.9397i	0.614625	−	1.06456i	−0.375825	−	0.926691i	$-0.622641\pi$
$739$	16.7083	−	28.9397i	0.614625	−	1.06456i	0.990450	−	0.137872i	$-0.0440261\pi$
$740$		0			0
$741$	0.778474	+	17.5416i	0.0285979	+	0.644406i
$742$		0			0
$743$	−17.9759	+	31.1351i	−0.659470	+	1.14224i	0.321282	+	0.946983i	$0.395886\pi$
$743$	−17.9759	+	31.1351i	−0.659470	+	1.14224i	−0.980753	+	0.195253i	$0.937447\pi$
$744$		0			0
$745$	6.57976	+	11.3965i	0.241064	+	0.417534i
$746$		0			0
$747$	−5.02827	−	8.70923i	−0.183975	−	0.318654i
$748$		0			0
$749$	16.9043			0.617668
$750$		0			0
$751$	−11.5752	−	20.0489i	−0.422386	−	0.731594i	0.573787	−	0.819005i	$-0.305474\pi$
$751$	−11.5752	−	20.0489i	−0.422386	−	0.731594i	−0.996172	+	0.0874112i	$0.972141\pi$
$752$		0			0
$753$	9.41478			0.343094
$754$		0			0
$755$	−14.4431	+	25.0161i	−0.525637	+	0.910429i
$756$		0			0
$757$	−6.49454	+	11.2489i	−0.236048	+	0.408847i	−0.959577	−	0.281447i	$-0.909186\pi$
$757$	−6.49454	+	11.2489i	−0.236048	+	0.408847i	0.723529	+	0.690294i	$0.242519\pi$
$758$		0			0
$759$	−4.01093			−0.145587
$760$		0			0
$761$	13.3593			0.484274			0.242137	−	0.970242i	$-0.422152\pi$
$761$	13.3593			0.484274			0.242137	+	0.970242i	$0.422152\pi$
$762$		0			0
$763$	−14.2215	+	24.6324i	−0.514854	+	0.891753i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.87783			−0.248344
$768$		0			0
$769$	−5.81181	−	10.0664i	−0.209579	−	0.363002i	0.742003	−	0.670397i	$-0.233876\pi$
$769$	−5.81181	−	10.0664i	−0.209579	−	0.363002i	−0.951582	+	0.307395i	$0.900543\pi$
$770$		0			0
$771$	10.1504			0.365559
$772$		0			0
$773$	3.87783	+	6.71660i	0.139476	+	0.241579i	0.927298	−	0.374323i	$-0.122125\pi$
$773$	3.87783	+	6.71660i	0.139476	+	0.241579i	−0.787822	+	0.615902i	$0.788792\pi$
$774$		0			0
$775$	20.2170	+	35.0169i	0.726216	+	1.25784i
$776$		0			0
$777$	1.16044	−	2.00994i	0.0416306	−	0.0721064i
$778$		0			0
$779$	−25.6892	−	13.3496i	−0.920413	−	0.478299i
$780$		0			0
$781$	−8.03735	+	13.9211i	−0.287599	+	0.498136i
$782$		0			0
$783$	3.32088	+	5.75194i	0.118679	+	0.205558i
$784$		0			0
$785$	9.46173	+	16.3882i	0.337703	+	0.584920i
$786$		0			0
$787$	18.8880			0.673283			0.336642	−	0.941633i	$-0.390709\pi$
$787$	18.8880			0.673283			0.336642	+	0.941633i	$0.390709\pi$
$788$		0			0
$789$	−1.29261	−	2.23887i	−0.0460182	−	0.0797058i
$790$		0			0
$791$	−17.1222			−0.608794
$792$		0			0
$793$	−6.82088	+	11.8141i	−0.242217	+	0.419532i
$794$		0			0
$795$	−16.5424	+	28.6523i	−0.586699	+	1.01619i
$796$		0			0
$797$	34.5105			1.22243			0.611213	−	0.791466i	$-0.290682\pi$
$797$	34.5105			1.22243			0.611213	+	0.791466i	$0.290682\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	1.33956	−	2.32018i	0.0473309	−	0.0819796i
$802$		0			0
$803$	−9.93852	+	17.2140i	−0.350723	+	0.607469i
$804$		0			0
$805$	−18.1059			−0.638148
$806$		0			0
$807$	0.273937	+	0.474473i	0.00964305	+	0.0167023i
$808$		0			0
$809$	40.6044			1.42758			0.713788	−	0.700362i	$-0.246978\pi$
$809$	40.6044			1.42758			0.713788	+	0.700362i	$0.246978\pi$
$810$		0			0
$811$	−8.54787	−	14.8054i	−0.300156	−	0.519886i	0.676015	−	0.736888i	$-0.263706\pi$
$811$	−8.54787	−	14.8054i	−0.300156	−	0.519886i	−0.976171	+	0.217002i	$0.930372\pi$
$812$		0			0
$813$	10.4431	+	18.0879i	0.366254	+	0.634370i
$814$		0			0
$815$	30.5147	−	52.8529i	1.06888	−	1.85136i
$816$		0			0
$817$	−2.73606	−	1.42181i	−0.0957227	−	0.0497430i
$818$		0			0
$819$	4.67458	−	8.09661i	0.163343	−	0.282918i
$820$		0			0
$821$	19.0475	+	32.9912i	0.664761	+	1.15140i	0.979350	+	0.202172i	$0.0648002\pi$
$821$	19.0475	+	32.9912i	0.664761	+	1.15140i	−0.314588	+	0.949228i	$0.601867\pi$
$822$		0			0
$823$	−6.60442	−	11.4392i	−0.230216	−	0.398745i	0.727656	−	0.685942i	$-0.240610\pi$
$823$	−6.60442	−	11.4392i	−0.230216	−	0.398745i	−0.957871	+	0.287197i	$0.907277\pi$
$824$		0			0
$825$	−10.2926			−0.358343
$826$		0			0
$827$	−16.9344	−	29.3312i	−0.588866	−	1.01995i	−0.994381	−	0.105858i	$-0.966241\pi$
$827$	−16.9344	−	29.3312i	−0.588866	−	1.01995i	0.405515	−	0.914088i	$-0.367092\pi$
$828$		0			0
$829$	16.8397			0.584866			0.292433	−	0.956286i	$-0.405535\pi$
$829$	16.8397			0.584866			0.292433	+	0.956286i	$0.405535\pi$
$830$		0			0
$831$	−11.8916	+	20.5968i	−0.412514	+	0.714495i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−71.8397			−2.48611
$836$		0			0
$837$	6.70739			0.231841
$838$		0			0
$839$	−1.26847	+	2.19706i	−0.0437926	+	0.0758509i	−0.887091	−	0.461595i	$-0.847277\pi$
$839$	−1.26847	+	2.19706i	−0.0437926	+	0.0758509i	0.843298	+	0.537446i	$0.180611\pi$
$840$		0			0
$841$	−7.55655	+	13.0883i	−0.260571	+	0.451322i
$842$		0			0
$843$	11.9061			0.410068
$844$		0			0
$845$	−5.35823	−	9.28073i	−0.184329	−	0.319267i
$846$		0			0
$847$	18.7639			0.644737
$848$		0			0
$849$	−9.02827	−	15.6374i	−0.309850	−	0.536675i
$850$		0			0
$851$	1.17458	+	2.03443i	0.0402641	+	0.0697394i
$852$		0			0
$853$	0.312212	−	0.540766i	0.0106899	−	0.0185155i	−0.860631	−	0.509229i	$-0.829931\pi$
$853$	0.312212	−	0.540766i	0.0106899	−	0.0185155i	0.871321	+	0.490714i	$0.163264\pi$
$854$		0			0
$855$	−0.641769	−	14.4612i	−0.0219480	−	0.494561i
$856$		0			0
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$		0			0
$859$	−13.6035	−	23.5619i	−0.464145	−	0.803923i	0.535017	−	0.844841i	$-0.320305\pi$
$859$	−13.6035	−	23.5619i	−0.464145	−	0.803923i	−0.999163	+	0.0409180i	$0.986972\pi$
$860$		0			0
$861$	7.70739	+	13.3496i	0.262667	+	0.454953i
$862$		0			0
$863$	26.1131			0.888900			0.444450	−	0.895804i	$-0.353399\pi$
$863$	26.1131			0.888900			0.444450	+	0.895804i	$0.353399\pi$
$864$		0			0
$865$	7.80128	+	13.5122i	0.265252	+	0.459429i
$866$		0			0
$867$	17.0000			0.577350
$868$		0			0
$869$	−2.85916	+	4.95221i	−0.0969903	+	0.167992i
$870$		0			0
$871$	−16.8733	+	29.2254i	−0.571730	+	0.990265i
$872$		0			0
$873$	17.7266			0.599954
$874$		0			0
$875$	−7.92531			−0.267924
$876$		0			0
$877$	13.3296	−	23.0875i	0.450107	−	0.779608i	−0.548285	−	0.836292i	$-0.684719\pi$
$877$	13.3296	−	23.0875i	0.450107	−	0.779608i	0.998392	+	0.0566830i	$0.0180524\pi$
$878$		0			0
$879$	−13.6983	+	23.7262i	−0.462033	+	0.800264i
$880$		0			0
$881$	6.73566			0.226930			0.113465	−	0.993542i	$-0.463805\pi$
$881$	6.73566			0.226930			0.113465	+	0.993542i	$0.463805\pi$
$882$		0			0
$883$	16.0803	+	27.8519i	0.541145	+	0.937290i	0.998839	+	0.0481803i	$0.0153422\pi$
$883$	16.0803	+	27.8519i	0.541145	+	0.937290i	−0.457694	+	0.889110i	$0.651324\pi$
$884$		0			0
$885$	5.67004			0.190596
$886$		0			0
$887$	1.91932	+	3.32435i	0.0644443	+	0.111621i	0.896447	−	0.443150i	$-0.146139\pi$
$887$	1.91932	+	3.32435i	0.0644443	+	0.111621i	−0.832003	+	0.554771i	$0.812806\pi$
$888$		0			0
$889$	−16.9909	−	29.4291i	−0.569857	−	0.987022i
$890$		0			0
$891$	−0.853695	+	1.47864i	−0.0285998	+	0.0495364i
$892$		0			0
$893$	−22.0475	+	14.0680i	−0.737791	+	0.470768i
$894$		0			0
$895$	−1.76940	+	3.06469i	−0.0591446	+	0.102441i
$896$		0			0
$897$	4.73153	+	8.19524i	0.157981	+	0.273631i
$898$		0			0
$899$	22.2745	+	38.5805i	0.742895	+	1.28673i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	0.820884	+	1.42181i	0.0273173	+	0.0473150i
$904$		0			0
$905$	−12.1878			−0.405136
$906$		0			0
$907$	−19.9819	+	34.6096i	−0.663487	+	1.14919i	0.316207	+	0.948690i	$0.397591\pi$
$907$	−19.9819	+	34.6096i	−0.663487	+	1.14919i	−0.979693	+	0.200502i	$0.935743\pi$
$908$		0			0
$909$	−8.02827	+	13.9054i	−0.266281	+	0.461212i
$910$		0			0
$911$	−29.3219			−0.971479			−0.485740	−	0.874104i	$-0.661450\pi$
$911$	−29.3219			−0.971479			−0.485740	+	0.874104i	$0.661450\pi$
$912$		0			0
$913$	17.1704			0.568259
$914$		0			0
$915$	5.62310	−	9.73949i	0.185894	−	0.321978i
$916$		0			0
$917$	−0.744736	+	1.28992i	−0.0245933	+	0.0425969i
$918$		0			0
$919$	30.6218			1.01012			0.505059	−	0.863085i	$-0.331471\pi$
$919$	30.6218			1.01012			0.505059	+	0.863085i	$0.331471\pi$
$920$		0			0
$921$	−1.80675	−	3.12938i	−0.0595344	−	0.103117i
$922$		0			0
$923$	37.9253			1.24833
$924$		0			0
$925$	3.01414	+	5.22064i	0.0991042	+	0.171654i
$926$		0			0
$927$	−3.77394	−	6.53665i	−0.123952	−	0.214692i
$928$		0			0
$929$	2.96213	−	5.13055i	0.0971842	−	0.168328i	−0.813334	−	0.581797i	$-0.802350\pi$
$929$	2.96213	−	5.13055i	0.0971842	−	0.168328i	0.910518	+	0.413469i	$0.135683\pi$
$930$		0			0
$931$	0.311812	+	7.02615i	0.0102192	+	0.230273i
$932$		0			0
$933$	−9.20285	+	15.9398i	−0.301288	+	0.521846i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.50546	+	4.33959i	0.0818499	+	0.141768i	0.904045	−	0.427438i	$-0.140584\pi$
$937$	2.50546	+	4.33959i	0.0818499	+	0.141768i	−0.822195	+	0.569206i	$0.807251\pi$
$938$		0			0
$939$	−23.0848			−0.753345
$940$		0			0
$941$	−4.19872	−	7.27239i	−0.136874	−	0.237073i	0.789438	−	0.613831i	$-0.210372\pi$
$941$	−4.19872	−	7.27239i	−0.136874	−	0.237073i	−0.926312	+	0.376758i	$0.877039\pi$
$942$		0			0
$943$	−15.6026			−0.508089
$944$		0			0
$945$	−3.85369	+	6.67479i	−0.125361	+	0.217131i
$946$		0			0
$947$	−9.73566	+	16.8627i	−0.316367	+	0.547963i	−0.979727	−	0.200337i	$-0.935796\pi$
$947$	−9.73566	+	16.8627i	−0.316367	+	0.547963i	0.663360	+	0.748300i	$0.269130\pi$
$948$		0			0
$949$	46.8962			1.52232
$950$		0			0
$951$	25.3774			0.822920
$952$		0			0
$953$	−10.7543	+	18.6271i	−0.348367	+	0.603390i	−0.985960	−	0.166984i	$-0.946597\pi$
$953$	−10.7543	+	18.6271i	−0.348367	+	0.603390i	0.637592	+	0.770374i	$0.279930\pi$
$954$		0			0
$955$	−1.45759	+	2.52462i	−0.0471665	+	0.0816947i
$956$		0			0
$957$	−11.3401			−0.366573
$958$		0			0
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	13.9891			0.451260
$962$		0			0
$963$	3.64177	+	6.30773i	0.117354	+	0.203264i
$964$		0			0
$965$	14.3022	+	24.7722i	0.460404	+	0.797444i
$966$		0			0
$967$	−5.41024	+	9.37081i	−0.173982	+	0.301345i	−0.939808	−	0.341702i	$-0.888997\pi$
$967$	−5.41024	+	9.37081i	−0.173982	+	0.301345i	0.765827	+	0.643047i	$0.222330\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.4996	−	26.8461i	0.497406	−	0.861532i	−0.502590	−	0.864525i	$-0.667619\pi$
$971$	15.4996	−	26.8461i	0.497406	−	0.861532i	0.999996	+	0.00299289i	$0.000952667\pi$
$972$		0			0
$973$	21.5565	+	37.3370i	0.691071	+	1.19697i
$974$		0			0
$975$	12.1418	+	21.0302i	0.388848	+	0.673504i
$976$		0			0
$977$	56.0950			1.79464			0.897318	−	0.441384i	$-0.145512\pi$
$977$	56.0950			1.79464			0.897318	+	0.441384i	$0.145512\pi$
$978$		0			0
$979$	2.28715	+	3.96145i	0.0730975	+	0.126609i
$980$		0			0
$981$	−12.2553			−0.391280
$982$		0			0
$983$	−16.7225	+	28.9641i	−0.533363	+	0.923813i	0.465877	+	0.884849i	$0.345739\pi$
$983$	−16.7225	+	28.9641i	−0.533363	+	0.923813i	−0.999241	+	0.0389632i	$0.987594\pi$
$984$		0			0
$985$	−41.0721	+	71.1390i	−1.30867	+	2.26668i
$986$		0			0
$987$	13.9253			0.443247
$988$		0			0
$989$	−1.66177			−0.0528412
$990$		0			0
$991$	4.22245	−	7.31350i	0.134131	−	0.232321i	−0.791134	−	0.611642i	$-0.790509\pi$
$991$	4.22245	−	7.31350i	0.134131	−	0.232321i	0.925265	+	0.379321i	$0.123842\pi$
$992$		0			0
$993$	10.6746	−	18.4889i	0.338748	−	0.586728i
$994$		0			0
$995$	73.0293			2.31519
$996$		0			0
$997$	−25.2074	−	43.6605i	−0.798326	−	1.38274i	−0.920706	−	0.390258i	$-0.872386\pi$
$997$	−25.2074	−	43.6605i	−0.798326	−	1.38274i	0.122380	−	0.992483i	$-0.460947\pi$
$998$		0			0
$999$	1.00000			0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.q.l.49.1		6
3.2	odd	2		2736.2.s.z.1873.3		6
4.3	odd	2		57.2.e.b.49.3	yes	6
12.11	even	2		171.2.f.b.163.1		6
19.7	even	3	inner	912.2.q.l.577.1		6
57.26	odd	6		2736.2.s.z.577.3		6
76.7	odd	6		57.2.e.b.7.3	✓	6
76.11	odd	6		1083.2.a.l.1.1		3
76.27	even	6		1083.2.a.o.1.3		3
228.11	even	6		3249.2.a.y.1.3		3
228.83	even	6		171.2.f.b.64.1		6
228.179	odd	6		3249.2.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.b.7.3	✓	6	76.7	odd	6
57.2.e.b.49.3	yes	6	4.3	odd	2
171.2.f.b.64.1		6	228.83	even	6
171.2.f.b.163.1		6	12.11	even	2
912.2.q.l.49.1		6	1.1	even	1	trivial
912.2.q.l.577.1		6	19.7	even	3	inner
1083.2.a.l.1.1		3	76.11	odd	6
1083.2.a.o.1.3		3	76.27	even	6
2736.2.s.z.577.3		6	57.26	odd	6
2736.2.s.z.1873.3		6	3.2	odd	2
3249.2.a.t.1.1		3	228.179	odd	6
3249.2.a.y.1.3		3	228.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.66044 + 2.87597i) q^{5} -2.32088 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.66044 + 2.87597i) q^{5} -2.32088 q^{7} +(-0.500000 - 0.866025i) q^{9} +1.70739 q^{11} +(-2.01414 - 3.48859i) q^{13} +(1.66044 + 2.87597i) q^{15} +(-0.193252 - 4.35461i) q^{19} +(-1.16044 + 2.00994i) q^{21} +(-1.17458 - 2.03443i) q^{23} +(-3.01414 - 5.22064i) q^{25} -1.00000 q^{27} +(-3.32088 - 5.75194i) q^{29} -6.70739 q^{31} +(0.853695 - 1.47864i) q^{33} +(3.85369 - 6.67479i) q^{35} -1.00000 q^{37} -4.02827 q^{39} +(3.32088 - 5.75194i) q^{41} +(0.353695 - 0.612617i) q^{43} +3.32088 q^{45} +(-3.00000 - 5.19615i) q^{47} -1.61350 q^{49} +(4.98133 + 8.62791i) q^{53} +(-2.83502 + 4.91040i) q^{55} +(-3.86783 - 2.00994i) q^{57} +(0.853695 - 1.47864i) q^{59} +(-1.69325 - 2.93280i) q^{61} +(1.16044 + 2.00994i) q^{63} +13.3774 q^{65} +(-4.18872 - 7.25507i) q^{67} -2.34916 q^{69} +(-4.70739 + 8.15344i) q^{71} +(-5.82088 + 10.0821i) q^{73} -6.02827 q^{75} -3.96265 q^{77} +(-1.67458 + 2.90046i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0565 q^{83} -6.64177 q^{87} +(1.33956 + 2.32018i) q^{89} +(4.67458 + 8.09661i) q^{91} +(-3.35369 + 5.80877i) q^{93} +(12.8446 + 6.67479i) q^{95} +(-8.86330 + 15.3517i) q^{97} +(-0.853695 - 1.47864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9 + q^13 + 2 * q^15 - 4 * q^19 + q^21 + 14 * q^23 - 5 * q^25 - 6 * q^27 - 4 * q^29 - 30 * q^31 + 18 * q^35 - 6 * q^37 + 2 * q^39 + 4 * q^41 - 3 * q^43 + 4 * q^45 - 18 * q^47 - 4 * q^49 + 6 * q^53 + 12 * q^55 - 5 * q^57 - 13 * q^61 - q^63 + 12 * q^65 + 9 * q^67 + 28 * q^69 - 18 * q^71 - 19 * q^73 - 10 * q^75 + 24 * q^77 + 11 * q^79 - 3 * q^81 + 8 * q^83 - 8 * q^87 + 16 * q^89 + 7 * q^91 - 15 * q^93 - 2 * q^95 + 2 * q^97

Introduction

L-functions

Modular forms

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