LMFDB - Embedded newform 912.2.bn.h.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.h.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.724745 - 1.57313i) q^{3} +(1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(0.724745 - 1.57313i) q^{3} +(1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.94949 - 2.28024i) q^{9} -0.317837i q^{11} +(-3.00000 + 1.73205i) q^{13} +(2.00000 - 1.41421i) q^{15} +(-5.44949 - 3.14626i) q^{17} +(4.17423 - 1.25529i) q^{19} +(-3.22474 + 6.99964i) q^{21} +(-6.12372 + 3.53553i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-5.00000 + 1.41421i) q^{27} +(-1.22474 - 2.12132i) q^{29} -4.24264i q^{31} +(-0.500000 - 0.230351i) q^{33} +(-5.44949 - 3.14626i) q^{35} -0.778539i q^{37} +(0.550510 + 5.97469i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(0.449490 - 0.778539i) q^{43} +(-0.775255 - 4.17121i) q^{45} +(5.57321 - 3.21770i) q^{47} +12.7980 q^{49} +(-8.89898 + 6.29253i) q^{51} +(-0.550510 - 0.953512i) q^{53} +(0.224745 - 0.389270i) q^{55} +(1.05051 - 7.47639i) q^{57} +(-3.27526 + 5.67291i) q^{59} +(3.22474 + 5.58542i) q^{61} +(8.67423 + 10.1459i) q^{63} -4.89898 q^{65} +(5.17423 - 2.98735i) q^{67} +(1.12372 + 12.1958i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(5.39898 - 9.35131i) q^{73} +(-5.17423 + 0.476756i) q^{75} +1.41421i q^{77} +(-7.34847 - 4.24264i) q^{79} +(-1.39898 + 8.89060i) q^{81} -14.1742i q^{83} +(-4.44949 - 7.70674i) q^{85} +(-4.22474 + 0.389270i) q^{87} +(8.44949 + 14.6349i) q^{89} +(13.3485 - 7.70674i) q^{91} +(-6.67423 - 3.07483i) q^{93} +(6.00000 + 1.41421i) q^{95} +(-11.8485 - 6.84072i) q^{97} +(-0.724745 + 0.619620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9	$ 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9} - 12 q^{13} + 8 q^{15} - 12 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{25} - 20 q^{27} - 2 q^{33} - 12 q^{35} + 12 q^{39} - 6 q^{41} - 8 q^{43} - 8 q^{45} - 12 q^{47} + 12 q^{49} - 16 q^{51} - 12 q^{53} - 4 q^{55} + 14 q^{57} - 18 q^{59} + 8 q^{61} + 20 q^{63} + 6 q^{67} - 20 q^{69} - 12 q^{71} + 2 q^{73} - 6 q^{75} + 14 q^{81} - 8 q^{85} - 12 q^{87} + 24 q^{89} + 24 q^{91} - 12 q^{93} + 24 q^{95} - 18 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9 - 12 * q^13 + 8 * q^15 - 12 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^25 - 20 * q^27 - 2 * q^33 - 12 * q^35 + 12 * q^39 - 6 * q^41 - 8 * q^43 - 8 * q^45 - 12 * q^47 + 12 * q^49 - 16 * q^51 - 12 * q^53 - 4 * q^55 + 14 * q^57 - 18 * q^59 + 8 * q^61 + 20 * q^63 + 6 * q^67 - 20 * q^69 - 12 * q^71 + 2 * q^73 - 6 * q^75 + 14 * q^81 - 8 * q^85 - 12 * q^87 + 24 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 18 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$3$	0.724745	−	1.57313i	0.418432	−	0.908248i
$3$	0.724745	−	1.57313i	0.418432	−	0.908248i
$4$		0			0
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	0.748203	−	0.663470i	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$		0			0
$7$	−4.44949			−1.68175			−0.840875	−	0.541230i	$-0.817959\pi$
$7$	−4.44949			−1.68175			−0.840875	+	0.541230i	$0.817959\pi$
$8$		0			0
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$		0			0
$11$		−	0.317837i		−	0.0958315i	−0.998851	−	0.0479158i	$-0.984742\pi$
$11$		−	0.317837i		−	0.0958315i	0.998851	−	0.0479158i	$-0.0152579\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$		0			0
$15$	2.00000	−	1.41421i	0.516398	−	0.365148i
$16$		0			0
$17$	−5.44949	−	3.14626i	−1.32170	−	0.763081i	−0.337696	−	0.941255i	$-0.609648\pi$
$17$	−5.44949	−	3.14626i	−1.32170	−	0.763081i	−0.983999	+	0.178174i	$0.942981\pi$
$18$		0			0
$19$	4.17423	−	1.25529i	0.957635	−	0.287984i
$19$	4.17423	−	1.25529i	0.957635	−	0.287984i
$20$		0			0
$21$	−3.22474	+	6.99964i	−0.703697	+	1.52745i
$22$		0			0
$23$	−6.12372	+	3.53553i	−1.27688	+	0.737210i	−0.976274	−	0.216537i	$-0.930524\pi$
$23$	−6.12372	+	3.53553i	−1.27688	+	0.737210i	−0.300610	+	0.953747i	$0.597190\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		0			0
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$		0			0
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$		0			0
$31$		−	4.24264i		−	0.762001i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$		−	4.24264i		−	0.762001i	0.924575	−	0.381000i	$-0.124420\pi$
$32$		0			0
$33$	−0.500000	−	0.230351i	−0.0870388	−	0.0400989i
$34$		0			0
$35$	−5.44949	−	3.14626i	−0.921132	−	0.531816i
$36$		0			0
$37$		−	0.778539i		−	0.127991i	−0.997950	−	0.0639955i	$-0.979616\pi$
$37$		−	0.778539i		−	0.127991i	0.997950	−	0.0639955i	$-0.0203843\pi$
$38$		0			0
$39$	0.550510	+	5.97469i	0.0881522	+	0.956716i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	0.449490	−	0.778539i	0.0685465	−	0.118726i	−0.829715	−	0.558187i	$-0.811497\pi$
$43$	0.449490	−	0.778539i	0.0685465	−	0.118726i	0.898262	+	0.439461i	$0.144831\pi$
$44$		0			0
$45$	−0.775255	−	4.17121i	−0.115568	−	0.621807i
$46$		0			0
$47$	5.57321	−	3.21770i	0.812937	−	0.469349i	−0.0350379	−	0.999386i	$-0.511155\pi$
$47$	5.57321	−	3.21770i	0.812937	−	0.469349i	0.847975	+	0.530037i	$0.177822\pi$
$48$		0			0
$49$	12.7980			1.82828
$50$		0			0
$51$	−8.89898	+	6.29253i	−1.24611	+	0.881130i
$52$		0			0
$53$	−0.550510	−	0.953512i	−0.0756184	−	0.130975i	0.825737	−	0.564056i	$-0.190760\pi$
$53$	−0.550510	−	0.953512i	−0.0756184	−	0.130975i	−0.901355	+	0.433081i	$0.857426\pi$
$54$		0			0
$55$	0.224745	−	0.389270i	0.0303046	−	0.0524891i
$56$		0			0
$57$	1.05051	−	7.47639i	0.139143	−	0.990272i
$58$		0			0
$59$	−3.27526	+	5.67291i	−0.426402	+	0.738550i	−0.996550	−	0.0829920i	$-0.973552\pi$
$59$	−3.27526	+	5.67291i	−0.426402	+	0.738550i	0.570148	+	0.821542i	$0.306886\pi$
$60$		0			0
$61$	3.22474	+	5.58542i	0.412886	+	0.715140i	0.995204	−	0.0978213i	$-0.0311874\pi$
$61$	3.22474	+	5.58542i	0.412886	+	0.715140i	−0.582318	+	0.812961i	$0.697854\pi$
$62$		0			0
$63$	8.67423	+	10.1459i	1.09285	+	1.27826i
$64$		0			0
$65$	−4.89898			−0.607644
$66$		0			0
$67$	5.17423	−	2.98735i	0.632133	−	0.364962i	−0.149444	−	0.988770i	$-0.547749\pi$
$67$	5.17423	−	2.98735i	0.632133	−	0.364962i	0.781578	+	0.623808i	$0.214415\pi$
$68$		0			0
$69$	1.12372	+	12.1958i	0.135281	+	1.46820i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	5.39898	−	9.35131i	0.631903	−	1.09449i	−0.355260	−	0.934768i	$-0.615608\pi$
$73$	5.39898	−	9.35131i	0.631903	−	1.09449i	0.987162	−	0.159720i	$-0.0510591\pi$
$74$		0			0
$75$	−5.17423	+	0.476756i	−0.597469	+	0.0550510i
$76$		0			0
$77$			1.41421i			0.161165i
$78$		0			0
$79$	−7.34847	−	4.24264i	−0.826767	−	0.477334i	0.0259772	−	0.999663i	$-0.491730\pi$
$79$	−7.34847	−	4.24264i	−0.826767	−	0.477334i	−0.852745	+	0.522328i	$0.825064\pi$
$80$		0			0
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$		0			0
$83$		−	14.1742i		−	1.55583i	−0.628372	−	0.777913i	$-0.716279\pi$
$83$		−	14.1742i		−	1.55583i	0.628372	−	0.777913i	$-0.283721\pi$
$84$		0			0
$85$	−4.44949	−	7.70674i	−0.482615	−	0.835914i
$86$		0			0
$87$	−4.22474	+	0.389270i	−0.452940	+	0.0417341i
$88$		0			0
$89$	8.44949	+	14.6349i	0.895644	+	1.55130i	0.833005	+	0.553265i	$0.186618\pi$
$89$	8.44949	+	14.6349i	0.895644	+	1.55130i	0.0626387	+	0.998036i	$0.480048\pi$
$90$		0			0
$91$	13.3485	−	7.70674i	1.39930	−	0.807886i
$92$		0			0
$93$	−6.67423	−	3.07483i	−0.692086	−	0.318845i
$94$		0			0
$95$	6.00000	+	1.41421i	0.615587	+	0.145095i
$96$		0			0
$97$	−11.8485	−	6.84072i	−1.20303	−	0.694570i	−0.241802	−	0.970326i	$-0.577738\pi$
$97$	−11.8485	−	6.84072i	−1.20303	−	0.694570i	−0.961228	+	0.275756i	$0.911072\pi$
$98$		0			0
$99$	−0.724745	+	0.619620i	−0.0728396	+	0.0622742i
$100$		0			0
$101$	−8.57321	+	4.94975i	−0.853067	+	0.492518i	−0.861684	−	0.507445i	$-0.830590\pi$
$101$	−8.57321	+	4.94975i	−0.853067	+	0.492518i	0.00861771	+	0.999963i	$0.497257\pi$
$102$		0			0
$103$			11.9494i			1.17741i	0.808349	+	0.588704i	$0.200362\pi$
$103$			11.9494i			1.17741i	−0.808349	+	0.588704i	$0.799638\pi$
$104$		0			0
$105$	−8.89898	+	6.29253i	−0.868451	+	0.614088i
$106$		0			0
$107$	−4.89898			−0.473602			−0.236801	−	0.971558i	$-0.576099\pi$
$107$	−4.89898			−0.473602			−0.236801	+	0.971558i	$0.576099\pi$
$108$		0			0
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$	−1.22474	−	0.564242i	−0.116248	−	0.0535555i
$112$		0			0
$113$	0.797959			0.0750657			0.0375328	−	0.999295i	$-0.488050\pi$
$113$	0.797959			0.0750657			0.0375328	+	0.999295i	$0.488050\pi$
$114$		0			0
$115$	−10.0000			−0.932505
$116$		0			0
$117$	9.79796	+	3.46410i	0.905822	+	0.320256i
$118$		0			0
$119$	24.2474	+	13.9993i	2.22276	+	1.28331i
$120$		0			0
$121$	10.8990			0.990816
$122$		0			0
$123$	3.00000	+	4.24264i	0.270501	+	0.382546i
$124$		0			0
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	9.00000	−	5.19615i	0.798621	−	0.461084i	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	9.00000	−	5.19615i	0.798621	−	0.461084i	0.842989	+	0.537931i	$0.180794\pi$
$128$		0			0
$129$	−0.898979	−	1.27135i	−0.0791507	−	0.111936i
$130$		0			0
$131$	−19.0732	−	11.0119i	−1.66643	−	0.962116i	−0.969537	−	0.244946i	$-0.921230\pi$
$131$	−19.0732	−	11.0119i	−1.66643	−	0.962116i	−0.696898	−	0.717171i	$-0.745437\pi$
$132$		0			0
$133$	−18.5732	+	5.58542i	−1.61050	+	0.484318i
$134$		0			0
$135$	−7.12372	−	1.80348i	−0.613113	−	0.155219i
$136$		0			0
$137$	−6.39898	+	3.69445i	−0.546702	+	0.315638i	−0.747791	−	0.663935i	$-0.768885\pi$
$137$	−6.39898	+	3.69445i	−0.546702	+	0.315638i	0.201089	+	0.979573i	$0.435552\pi$
$138$		0			0
$139$	0.174235	+	0.301783i	0.0147784	+	0.0255969i	0.873320	−	0.487147i	$-0.161962\pi$
$139$	0.174235	+	0.301783i	0.0147784	+	0.0255969i	−0.858542	+	0.512744i	$0.828629\pi$
$140$		0			0
$141$	−1.02270	−	11.0994i	−0.0861272	−	0.934739i
$142$		0			0
$143$	0.550510	+	0.953512i	0.0460360	+	0.0797367i
$144$		0			0
$145$		−	3.46410i		−	0.287678i
$146$		0			0
$147$	9.27526	−	20.1329i	0.765010	−	1.66053i
$148$		0			0
$149$	4.22474	+	2.43916i	0.346105	+	0.199824i	0.662968	−	0.748648i	$-0.269296\pi$
$149$	4.22474	+	2.43916i	0.346105	+	0.199824i	−0.316864	+	0.948471i	$0.602630\pi$
$150$		0			0
$151$		−	18.0990i		−	1.47288i	−0.676503	−	0.736440i	$-0.736505\pi$
$151$		−	18.0990i		−	1.47288i	0.676503	−	0.736440i	$-0.263495\pi$
$152$		0			0
$153$	3.44949	+	18.5597i	0.278875	+	1.50047i
$154$		0			0
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	9.34847	−	16.1920i	0.746089	−	1.29226i	−0.203595	−	0.979055i	$-0.565263\pi$
$157$	9.34847	−	16.1920i	0.746089	−	1.29226i	0.949684	−	0.313209i	$-0.101404\pi$
$158$		0			0
$159$	−1.89898	+	0.174973i	−0.150599	+	0.0138762i
$160$		0			0
$161$	27.2474	−	15.7313i	2.14740	−	1.23980i
$162$		0			0
$163$	−3.65153			−0.286010			−0.143005	−	0.989722i	$-0.545676\pi$
$163$	−3.65153			−0.286010			−0.143005	+	0.989722i	$0.545676\pi$
$164$		0			0
$165$	−0.449490	−	0.635674i	−0.0349927	−	0.0494872i
$166$		0			0
$167$	−2.44949	−	4.24264i	−0.189547	−	0.328305i	0.755552	−	0.655089i	$-0.227369\pi$
$167$	−2.44949	−	4.24264i	−0.189547	−	0.328305i	−0.945099	+	0.326783i	$0.894035\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	−11.0000	−	7.07107i	−0.841191	−	0.540738i
$172$		0			0
$173$	5.44949	−	9.43879i	0.414317	−	0.717618i	−0.581039	−	0.813875i	$-0.697354\pi$
$173$	5.44949	−	9.43879i	0.414317	−	0.717618i	0.995356	+	0.0962572i	$0.0306871\pi$
$174$		0			0
$175$	6.67423	+	11.5601i	0.504525	+	0.873862i
$176$		0			0
$177$	6.55051	+	9.26382i	0.492367	+	0.696311i
$178$		0			0
$179$	22.3485			1.67040			0.835202	−	0.549944i	$-0.185351\pi$
$179$	22.3485			1.67040			0.835202	+	0.549944i	$0.185351\pi$
$180$		0			0
$181$	11.3258	−	6.53893i	0.841838	−	0.486035i	−0.0160509	−	0.999871i	$-0.505109\pi$
$181$	11.3258	−	6.53893i	0.841838	−	0.486035i	0.857888	+	0.513836i	$0.171776\pi$
$182$		0			0
$183$	11.1237	−	1.02494i	0.822289	−	0.0757660i
$184$		0			0
$185$	0.550510	−	0.953512i	0.0404743	−	0.0701036i
$186$		0			0
$187$	−1.00000	+	1.73205i	−0.0731272	+	0.126660i
$188$		0			0
$189$	22.2474	−	6.29253i	1.61826	−	0.457714i
$190$		0			0
$191$			19.5133i			1.41193i	0.708247	+	0.705965i	$0.249486\pi$
$191$			19.5133i			1.41193i	−0.708247	+	0.705965i	$0.750514\pi$
$192$		0			0
$193$	−7.65153	−	4.41761i	−0.550769	−	0.317987i	0.198663	−	0.980068i	$-0.436340\pi$
$193$	−7.65153	−	4.41761i	−0.550769	−	0.317987i	−0.749432	+	0.662081i	$0.769673\pi$
$194$		0			0
$195$	−3.55051	+	7.70674i	−0.254257	+	0.551891i
$196$		0			0
$197$			0.492810i			0.0351113i	0.999846	+	0.0175556i	$0.00558842\pi$
$197$			0.492810i			0.0351113i	−0.999846	+	0.0175556i	$0.994412\pi$
$198$		0			0
$199$	3.44949	+	5.97469i	0.244528	+	0.423535i	0.961999	−	0.273054i	$-0.0880337\pi$
$199$	3.44949	+	5.97469i	0.244528	+	0.423535i	−0.717471	+	0.696588i	$0.754700\pi$
$200$		0			0
$201$	−0.949490	−	10.3048i	−0.0669718	−	0.726846i
$202$		0			0
$203$	5.44949	+	9.43879i	0.382479	+	0.662473i
$204$		0			0
$205$	−3.67423	+	2.12132i	−0.256620	+	0.148159i
$206$		0			0
$207$	20.0000	+	7.07107i	1.39010	+	0.491473i
$208$		0			0
$209$	−0.398979	−	1.32673i	−0.0275980	−	0.0917716i
$210$		0			0
$211$	−13.3485	−	7.70674i	−0.918947	−	0.530554i	−0.0356477	−	0.999364i	$-0.511349\pi$
$211$	−13.3485	−	7.70674i	−0.918947	−	0.530554i	−0.883299	+	0.468810i	$0.844683\pi$
$212$		0			0
$213$	6.00000	+	8.48528i	0.411113	+	0.581402i
$214$		0			0
$215$	1.10102	−	0.635674i	0.0750890	−	0.0433526i
$216$		0			0
$217$			18.8776i			1.28149i
$218$		0			0
$219$	−10.7980	−	15.2706i	−0.729658	−	1.03189i
$220$		0			0
$221$	21.7980			1.46629
$222$		0			0
$223$	8.32577	+	4.80688i	0.557534	+	0.321893i	0.752155	−	0.658986i	$-0.229014\pi$
$223$	8.32577	+	4.80688i	0.557534	+	0.321893i	−0.194621	+	0.980879i	$0.562348\pi$
$224$		0			0
$225$	−3.00000	+	8.48528i	−0.200000	+	0.565685i
$226$		0			0
$227$	−5.44949			−0.361695			−0.180848	−	0.983511i	$-0.557884\pi$
$227$	−5.44949			−0.361695			−0.180848	+	0.983511i	$0.557884\pi$
$228$		0			0
$229$	−8.89898			−0.588061			−0.294031	−	0.955796i	$-0.594997\pi$
$229$	−8.89898			−0.588061			−0.294031	+	0.955796i	$0.594997\pi$
$230$		0			0
$231$	2.22474	+	1.02494i	0.146377	+	0.0674364i
$232$		0			0
$233$	−5.60102	−	3.23375i	−0.366935	−	0.211850i	0.305184	−	0.952294i	$-0.401282\pi$
$233$	−5.60102	−	3.23375i	−0.366935	−	0.211850i	−0.672119	+	0.740443i	$0.734616\pi$
$234$		0			0
$235$	9.10102			0.593685
$236$		0			0
$237$	−12.0000	+	8.48528i	−0.779484	+	0.551178i
$238$		0			0
$239$			7.21393i			0.466630i	0.972401	+	0.233315i	$0.0749574\pi$
$239$			7.21393i			0.466630i	−0.972401	+	0.233315i	$0.925043\pi$
$240$		0			0
$241$	8.84847	−	5.10867i	0.569980	−	0.329078i	−0.187161	−	0.982329i	$-0.559929\pi$
$241$	8.84847	−	5.10867i	0.569980	−	0.329078i	0.757141	+	0.653251i	$0.226595\pi$
$242$		0			0
$243$	12.9722	+	8.64420i	0.832167	+	0.554526i
$244$		0			0
$245$	15.6742	+	9.04952i	1.00139	+	0.578153i
$246$		0			0
$247$	−10.3485	+	10.9959i	−0.658457	+	0.699651i
$248$		0			0
$249$	−22.2980	−	10.2727i	−1.41308	−	0.651007i
$250$		0			0
$251$	5.72474	−	3.30518i	0.361343	−	0.208621i	−0.308327	−	0.951280i	$-0.599769\pi$
$251$	5.72474	−	3.30518i	0.361343	−	0.208621i	0.669670	+	0.742659i	$0.266436\pi$
$252$		0			0
$253$	1.12372	+	1.94635i	0.0706479	+	0.122366i
$254$		0			0
$255$	−15.3485	+	1.41421i	−0.961158	+	0.0885615i
$256$		0			0
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		0			0
$259$			3.46410i			0.215249i
$260$		0			0
$261$	−2.44949	+	6.92820i	−0.151620	+	0.428845i
$262$		0			0
$263$	−10.2247	−	5.90326i	−0.630485	−	0.364011i	0.150455	−	0.988617i	$-0.451926\pi$
$263$	−10.2247	−	5.90326i	−0.630485	−	0.364011i	−0.780940	+	0.624606i	$0.785259\pi$
$264$		0			0
$265$		−	1.55708i		−	0.0956506i
$266$		0			0
$267$	29.1464	−	2.68556i	1.78373	−	0.164354i
$268$		0			0
$269$	−12.2474	+	21.2132i	−0.746740	+	1.29339i	0.202637	+	0.979254i	$0.435049\pi$
$269$	−12.2474	+	21.2132i	−0.746740	+	1.29339i	−0.949377	+	0.314138i	$0.898285\pi$
$270$		0			0
$271$	12.0227	−	20.8239i	0.730327	−	1.26496i	−0.226416	−	0.974031i	$-0.572701\pi$
$271$	12.0227	−	20.8239i	0.730327	−	1.26496i	0.956743	−	0.290933i	$-0.0939658\pi$
$272$		0			0
$273$	−2.44949	−	26.5843i	−0.148250	−	1.60896i
$274$		0			0
$275$	−0.825765	+	0.476756i	−0.0497955	+	0.0287495i
$276$		0			0
$277$	−4.24745			−0.255204			−0.127602	−	0.991825i	$-0.540728\pi$
$277$	−4.24745			−0.255204			−0.127602	+	0.991825i	$0.540728\pi$
$278$		0			0
$279$	−9.67423	+	8.27098i	−0.579181	+	0.495171i
$280$		0			0
$281$	−8.29796	−	14.3725i	−0.495015	−	0.857391i	0.504969	−	0.863138i	$-0.331504\pi$
$281$	−8.29796	−	14.3725i	−0.495015	−	0.857391i	−0.999983	+	0.00574696i	$0.998171\pi$
$282$		0			0
$283$	−2.27526	+	3.94086i	−0.135250	+	0.234260i	−0.925693	−	0.378276i	$-0.876517\pi$
$283$	−2.27526	+	3.94086i	−0.135250	+	0.234260i	0.790443	+	0.612536i	$0.209850\pi$
$284$		0			0
$285$	6.57321	−	8.41385i	0.389364	−	0.498393i
$286$		0			0
$287$	6.67423	−	11.5601i	0.393968	−	0.682372i
$288$		0			0
$289$	11.2980	+	19.5686i	0.664586	+	1.15110i
$290$		0			0
$291$	−19.3485	+	13.6814i	−1.13423	+	0.802020i
$292$		0			0
$293$	−4.65153			−0.271745			−0.135873	−	0.990726i	$-0.543384\pi$
$293$	−4.65153			−0.271745			−0.135873	+	0.990726i	$0.543384\pi$
$294$		0			0
$295$	−8.02270	+	4.63191i	−0.467100	+	0.269680i
$296$		0			0
$297$	0.449490	+	1.58919i	0.0260820	+	0.0922139i
$298$		0			0
$299$	12.2474	−	21.2132i	0.708288	−	1.22679i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$		0			0
$303$	1.57321	+	17.0741i	0.0903788	+	0.980882i
$304$		0			0
$305$			9.12096i			0.522264i
$306$		0			0
$307$	3.52270	+	2.03383i	0.201051	+	0.116077i	0.597146	−	0.802133i	$-0.296301\pi$
$307$	3.52270	+	2.03383i	0.201051	+	0.116077i	−0.396094	+	0.918210i	$0.629635\pi$
$308$		0			0
$309$	18.7980	+	8.66025i	1.06938	+	0.492665i
$310$		0			0
$311$		−	15.5563i		−	0.882120i	−0.897478	−	0.441060i	$-0.854603\pi$
$311$		−	15.5563i		−	0.882120i	0.897478	−	0.441060i	$-0.145397\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$		0			0
$315$	3.44949	+	18.5597i	0.194357	+	1.04572i
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	−0.674235	+	0.389270i	−0.0377499	+	0.0217949i
$320$		0			0
$321$	−3.55051	+	7.70674i	−0.198170	+	0.430148i
$322$		0			0
$323$	−26.6969	−	6.29253i	−1.48546	−	0.350126i
$324$		0			0
$325$	9.00000	+	5.19615i	0.499230	+	0.288231i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−24.7980	+	14.3171i	−1.36716	+	0.789328i
$330$		0			0
$331$			14.8099i			0.814027i	0.913422	+	0.407013i	$0.133430\pi$
$331$			14.8099i			0.814027i	−0.913422	+	0.407013i	$0.866570\pi$
$332$		0			0
$333$	−1.77526	+	1.51775i	−0.0972834	+	0.0831724i
$334$		0			0
$335$	8.44949			0.461645
$336$		0			0
$337$	−3.15153	−	1.81954i	−0.171675	−	0.0991165i	0.411701	−	0.911319i	$-0.364935\pi$
$337$	−3.15153	−	1.81954i	−0.171675	−	0.0991165i	−0.583375	+	0.812203i	$0.698268\pi$
$338$		0			0
$339$	0.578317	−	1.25529i	0.0314099	−	0.0681783i
$340$		0			0
$341$	−1.34847			−0.0730237
$342$		0			0
$343$	−25.7980			−1.39296
$344$		0			0
$345$	−7.24745	+	15.7313i	−0.390190	+	0.846946i
$346$		0			0
$347$	−5.72474	−	3.30518i	−0.307320	−	0.177432i	0.338406	−	0.941000i	$-0.390112\pi$
$347$	−5.72474	−	3.30518i	−0.307320	−	0.177432i	−0.645727	+	0.763569i	$0.723445\pi$
$348$		0			0
$349$	−16.4949			−0.882952			−0.441476	−	0.897273i	$-0.645545\pi$
$349$	−16.4949			−0.882952			−0.441476	+	0.897273i	$0.645545\pi$
$350$		0			0
$351$	12.5505	−	12.9029i	0.669897	−	0.688706i
$352$		0			0
$353$			14.6028i			0.777231i	0.921400	+	0.388615i	$0.127046\pi$
$353$			14.6028i			0.777231i	−0.921400	+	0.388615i	$0.872954\pi$
$354$		0			0
$355$	−7.34847	+	4.24264i	−0.390016	+	0.225176i
$356$		0			0
$357$	39.5959	−	27.9985i	2.09564	−	1.48184i
$358$		0			0
$359$	20.8207	+	12.0208i	1.09887	+	0.634434i	0.935925	−	0.352200i	$-0.114566\pi$
$359$	20.8207	+	12.0208i	1.09887	+	0.634434i	0.162948	+	0.986635i	$0.447900\pi$
$360$		0			0
$361$	15.8485	−	10.4798i	0.834130	−	0.551568i
$362$		0			0
$363$	7.89898	−	17.1455i	0.414589	−	0.899907i
$364$		0			0
$365$	13.2247	−	7.63531i	0.692215	−	0.399650i
$366$		0			0
$367$	−11.6742	−	20.2204i	−0.609390	−	1.05549i	−0.991341	−	0.131312i	$-0.958081\pi$
$367$	−11.6742	−	20.2204i	−0.609390	−	1.05549i	0.381951	−	0.924183i	$-0.375252\pi$
$368$		0			0
$369$	8.84847	−	1.64456i	0.460633	−	0.0856126i
$370$		0			0
$371$	2.44949	+	4.24264i	0.127171	+	0.220267i
$372$		0			0
$373$		−	25.4558i		−	1.31805i	−0.752119	−	0.659027i	$-0.770968\pi$
$373$		−	25.4558i		−	1.31805i	0.752119	−	0.659027i	$-0.229032\pi$
$374$		0			0
$375$	−17.7980	−	8.19955i	−0.919083	−	0.423423i
$376$		0			0
$377$	7.34847	+	4.24264i	0.378465	+	0.218507i
$378$		0			0
$379$		−	15.4135i		−	0.791738i	−0.918307	−	0.395869i	$-0.870444\pi$
$379$		−	15.4135i		−	0.791738i	0.918307	−	0.395869i	$-0.129556\pi$
$380$		0			0
$381$	−1.65153	−	17.9241i	−0.0846105	−	0.918278i
$382$		0			0
$383$	−7.77526	+	13.4671i	−0.397297	+	0.688139i	−0.993391	−	0.114776i	$-0.963385\pi$
$383$	−7.77526	+	13.4671i	−0.397297	+	0.688139i	0.596094	+	0.802914i	$0.296718\pi$
$384$		0			0
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$		0			0
$387$	−2.65153	+	0.492810i	−0.134785	+	0.0250509i
$388$		0			0
$389$	−22.8990	+	13.2207i	−1.16102	+	0.670318i	−0.951549	−	0.307496i	$-0.900509\pi$
$389$	−22.8990	+	13.2207i	−1.16102	+	0.670318i	−0.209475	+	0.977814i	$0.567176\pi$
$390$		0			0
$391$	44.4949			2.25020
$392$		0			0
$393$	−31.1464	+	22.0239i	−1.57113	+	1.11096i
$394$		0			0
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$		0			0
$397$	−4.67423	+	8.09601i	−0.234593	+	0.406327i	−0.959154	−	0.282883i	$-0.908709\pi$
$397$	−4.67423	+	8.09601i	−0.234593	+	0.406327i	0.724561	+	0.689210i	$0.242042\pi$
$398$		0			0
$399$	−4.67423	+	33.2661i	−0.234004	+	1.66539i
$400$		0			0
$401$	6.39898	−	11.0834i	0.319550	−	0.553476i	−0.660844	−	0.750523i	$-0.729802\pi$
$401$	6.39898	−	11.0834i	0.319550	−	0.553476i	0.980394	+	0.197047i	$0.0631350\pi$
$402$		0			0
$403$	7.34847	+	12.7279i	0.366053	+	0.634023i
$404$		0			0
$405$	−8.00000	+	9.89949i	−0.397523	+	0.491910i
$406$		0			0
$407$	−0.247449			−0.0122656
$408$		0			0
$409$	17.8485	−	10.3048i	0.882550	−	0.509540i	0.0110517	−	0.999939i	$-0.496482\pi$
$409$	17.8485	−	10.3048i	0.882550	−	0.509540i	0.871498	+	0.490398i	$0.163149\pi$
$410$		0			0
$411$	1.17423	+	12.7440i	0.0579207	+	0.628614i
$412$		0			0
$413$	14.5732	−	25.2415i	0.717101	−	1.24206i
$414$		0			0
$415$	10.0227	−	17.3598i	0.491995	−	0.852161i
$416$		0			0
$417$	0.601021	−	0.0553782i	0.0294321	−	0.00271188i
$418$		0			0
$419$			3.74983i			0.183191i	0.995796	+	0.0915956i	$0.0291967\pi$
$419$			3.74983i			0.183191i	−0.995796	+	0.0915956i	$0.970803\pi$
$420$		0			0
$421$	−26.0227	−	15.0242i	−1.26827	−	0.732235i	−0.293609	−	0.955926i	$-0.594856\pi$
$421$	−26.0227	−	15.0242i	−1.26827	−	0.732235i	−0.974660	+	0.223690i	$0.928190\pi$
$422$		0			0
$423$	−18.2020	−	6.43539i	−0.885014	−	0.312900i
$424$		0			0
$425$			18.8776i			0.915697i
$426$		0			0
$427$	−14.3485	−	24.8523i	−0.694371	−	1.20269i
$428$		0			0
$429$	1.89898	−	0.174973i	0.0916836	−	0.00844776i
$430$		0			0
$431$	−16.3485	−	28.3164i	−0.787478	−	1.36395i	−0.927507	−	0.373805i	$-0.878053\pi$
$431$	−16.3485	−	28.3164i	−0.787478	−	1.36395i	0.140029	−	0.990147i	$-0.455280\pi$
$432$		0			0
$433$	11.6969	−	6.75323i	0.562119	−	0.324540i	−0.191877	−	0.981419i	$-0.561457\pi$
$433$	11.6969	−	6.75323i	0.562119	−	0.324540i	0.753996	+	0.656880i	$0.228124\pi$
$434$		0			0
$435$	−5.44949	−	2.51059i	−0.261283	−	0.120374i
$436$		0			0
$437$	−21.1237	+	22.4452i	−1.01048	+	1.07370i
$438$		0			0
$439$	2.32577	+	1.34278i	0.111003	+	0.0640875i	0.554474	−	0.832201i	$-0.312920\pi$
$439$	2.32577	+	1.34278i	0.111003	+	0.0640875i	−0.443471	+	0.896289i	$0.646253\pi$
$440$		0			0
$441$	−24.9495	−	29.1824i	−1.18807	−	1.38964i
$442$		0			0
$443$	−25.3207	+	14.6189i	−1.20302	+	0.694564i	−0.961226	−	0.275763i	$-0.911070\pi$
$443$	−25.3207	+	14.6189i	−1.20302	+	0.694564i	−0.241795	+	0.970327i	$0.577736\pi$
$444$		0			0
$445$			23.8988i			1.13291i
$446$		0			0
$447$	6.89898	−	4.87832i	0.326311	−	0.230736i
$448$		0			0
$449$	11.2020			0.528657			0.264329	−	0.964433i	$-0.414850\pi$
$449$	11.2020			0.528657			0.264329	+	0.964433i	$0.414850\pi$
$450$		0			0
$451$	0.825765	+	0.476756i	0.0388838	+	0.0224496i
$452$		0			0
$453$	−28.4722	−	13.1172i	−1.33774	−	0.616299i
$454$		0			0
$455$	21.7980			1.02190
$456$		0			0
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$		0			0
$459$	31.6969	+	8.02458i	1.47949	+	0.374555i
$460$		0			0
$461$	−8.75255	−	5.05329i	−0.407647	−	0.235355i	0.282131	−	0.959376i	$-0.408959\pi$
$461$	−8.75255	−	5.05329i	−0.407647	−	0.235355i	−0.689778	+	0.724021i	$0.742292\pi$
$462$		0			0
$463$	0.202041			0.00938964			0.00469482	−	0.999989i	$-0.498506\pi$
$463$	0.202041			0.00938964			0.00469482	+	0.999989i	$0.498506\pi$
$464$		0			0
$465$	−6.00000	−	8.48528i	−0.278243	−	0.393496i
$466$		0			0
$467$			32.4162i			1.50004i	0.661415	+	0.750020i	$0.269956\pi$
$467$			32.4162i			1.50004i	−0.661415	+	0.750020i	$0.730044\pi$
$468$		0			0
$469$	−23.0227	+	13.2922i	−1.06309	+	0.613775i
$470$		0			0
$471$	−18.6969	−	26.4415i	−0.861509	−	1.21836i
$472$		0			0
$473$	−0.247449	−	0.142865i	−0.0113777	−	0.00656892i
$474$		0			0
$475$	−9.52270	−	8.96204i	−0.436932	−	0.411206i
$476$		0			0
$477$	−1.10102	+	3.11416i	−0.0504123	+	0.142587i
$478$		0			0
$479$	−35.1464	+	20.2918i	−1.60588	+	0.927156i	−0.615603	+	0.788057i	$0.711087\pi$
$479$	−35.1464	+	20.2918i	−1.60588	+	0.927156i	−0.990278	+	0.139099i	$0.955579\pi$
$480$		0			0
$481$	1.34847	+	2.33562i	0.0614849	+	0.106495i
$482$		0			0
$483$	−5.00000	−	54.2650i	−0.227508	−	2.46914i
$484$		0			0
$485$	−9.67423	−	16.7563i	−0.439284	−	0.760863i
$486$		0			0
$487$			16.5420i			0.749588i	0.927108	+	0.374794i	$0.122287\pi$
$487$			16.5420i			0.749588i	−0.927108	+	0.374794i	$0.877713\pi$
$488$		0			0
$489$	−2.64643	+	5.74434i	−0.119676	+	0.259768i
$490$		0			0
$491$	4.10102	+	2.36773i	0.185076	+	0.106854i	0.589676	−	0.807640i	$-0.299256\pi$
$491$	4.10102	+	2.36773i	0.185076	+	0.106854i	−0.404599	+	0.914494i	$0.632589\pi$
$492$		0			0
$493$			15.4135i			0.694188i
$494$		0			0
$495$	−1.32577	+	0.246405i	−0.0595887	+	0.0110751i
$496$		0			0
$497$	13.3485	−	23.1202i	0.598761	−	1.03708i
$498$		0			0
$499$	1.27526	−	2.20881i	0.0570883	−	0.0988798i	−0.836069	−	0.548624i	$-0.815152\pi$
$499$	1.27526	−	2.20881i	0.0570883	−	0.0988798i	0.893157	+	0.449745i	$0.148485\pi$
$500$		0			0
$501$	−8.44949	+	0.778539i	−0.377495	+	0.0347826i
$502$		0			0
$503$	−13.4722	+	7.77817i	−0.600695	+	0.346812i	−0.769315	−	0.638870i	$-0.779402\pi$
$503$	−13.4722	+	7.77817i	−0.600695	+	0.346812i	0.168620	+	0.985681i	$0.446069\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$		0			0
$507$	1.00000	+	1.41421i	0.0444116	+	0.0628074i
$508$		0			0
$509$	−20.6969	−	35.8481i	−0.917376	−	1.58894i	−0.803385	−	0.595459i	$-0.796970\pi$
$509$	−20.6969	−	35.8481i	−0.917376	−	1.58894i	−0.113990	−	0.993482i	$-0.536363\pi$
$510$		0			0
$511$	−24.0227	+	41.6085i	−1.06270	+	1.84065i
$512$		0			0
$513$	−19.0959	+	12.1797i	−0.843105	+	0.537748i
$514$		0			0
$515$	−8.44949	+	14.6349i	−0.372329	+	0.644893i
$516$		0			0
$517$	−1.02270	−	1.77138i	−0.0449785	−	0.0779050i
$518$		0			0
$519$	−10.8990	−	15.4135i	−0.478412	−	0.676577i
$520$		0			0
$521$	−16.1010			−0.705399			−0.352699	−	0.935737i	$-0.614736\pi$
$521$	−16.1010			−0.705399			−0.352699	+	0.935737i	$0.614736\pi$
$522$		0			0
$523$	−23.6969	+	13.6814i	−1.03619	+	0.598247i	−0.918753	−	0.394832i	$-0.870803\pi$
$523$	−23.6969	+	13.6814i	−1.03619	+	0.598247i	−0.117442	+	0.993080i	$0.537469\pi$
$524$		0			0
$525$	23.0227	−	2.12132i	1.00479	−	0.0925820i
$526$		0			0
$527$	−13.3485	+	23.1202i	−0.581468	+	1.00713i
$528$		0			0
$529$	13.5000	−	23.3827i	0.586957	−	1.01664i
$530$		0			0
$531$	19.3207	−	3.59091i	0.838445	−	0.155832i
$532$		0			0
$533$		−	10.3923i		−	0.450141i
$534$		0			0
$535$	−6.00000	−	3.46410i	−0.259403	−	0.149766i
$536$		0			0
$537$	16.1969	−	35.1571i	0.698949	−	1.51714i
$538$		0			0
$539$		−	4.06767i		−	0.175207i
$540$		0			0
$541$	9.34847	+	16.1920i	0.401922	+	0.696149i	0.993958	−	0.109762i	$-0.0350089\pi$
$541$	9.34847	+	16.1920i	0.401922	+	0.696149i	−0.592036	+	0.805912i	$0.701676\pi$
$542$		0			0
$543$	−2.07832	−	22.5560i	−0.0891891	−	0.967970i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−26.3939	+	15.2385i	−1.12852	+	0.651552i	−0.943562	−	0.331195i	$-0.892548\pi$
$547$	−26.3939	+	15.2385i	−1.12852	+	0.651552i	−0.184958	+	0.982746i	$0.559215\pi$
$548$		0			0
$549$	6.44949	−	18.2419i	0.275258	−	0.778546i
$550$		0			0
$551$	−7.77526	−	7.31747i	−0.331237	−	0.311735i
$552$		0			0
$553$	32.6969	+	18.8776i	1.39042	+	0.802757i
$554$		0			0
$555$	−1.10102	−	1.55708i	−0.0467357	−	0.0660943i
$556$		0			0
$557$	−24.2474	+	13.9993i	−1.02740	+	0.593168i	−0.916238	−	0.400634i	$-0.868790\pi$
$557$	−24.2474	+	13.9993i	−1.02740	+	0.593168i	−0.111159	+	0.993803i	$0.535456\pi$
$558$		0			0
$559$			3.11416i			0.131715i
$560$		0			0
$561$	2.00000	+	2.82843i	0.0844401	+	0.119416i
$562$		0			0
$563$	22.8434			0.962733			0.481367	−	0.876519i	$-0.340141\pi$
$563$	22.8434			0.962733			0.481367	+	0.876519i	$0.340141\pi$
$564$		0			0
$565$	0.977296	+	0.564242i	0.0411152	+	0.0237378i
$566$		0			0
$567$	6.22474	−	39.5587i	0.261415	−	1.66131i
$568$		0			0
$569$	34.2929			1.43763			0.718816	−	0.695201i	$-0.244685\pi$
$569$	34.2929			1.43763			0.718816	+	0.695201i	$0.244685\pi$
$570$		0			0
$571$	11.0454			0.462236			0.231118	−	0.972926i	$-0.425762\pi$
$571$	11.0454			0.462236			0.231118	+	0.972926i	$0.425762\pi$
$572$		0			0
$573$	30.6969	+	14.1421i	1.28238	+	0.590796i
$574$		0			0
$575$	18.3712	+	10.6066i	0.766131	+	0.442326i
$576$		0			0
$577$	−20.5959			−0.857419			−0.428710	−	0.903442i	$-0.641032\pi$
$577$	−20.5959			−0.857419			−0.428710	+	0.903442i	$0.641032\pi$
$578$		0			0
$579$	−12.4949	+	8.83523i	−0.519270	+	0.367179i
$580$		0			0
$581$			63.0682i			2.61651i
$582$		0			0
$583$	−0.303062	+	0.174973i	−0.0125515	+	0.00724663i
$584$		0			0
$585$	9.55051	+	11.1708i	0.394865	+	0.461858i
$586$		0			0
$587$	4.10102	+	2.36773i	0.169267	+	0.0977265i	0.582240	−	0.813017i	$-0.302176\pi$
$587$	4.10102	+	2.36773i	0.169267	+	0.0977265i	−0.412973	+	0.910743i	$0.635510\pi$
$588$		0			0
$589$	−5.32577	−	17.7098i	−0.219444	−	0.729719i
$590$		0			0
$591$	0.775255	+	0.357161i	0.0318897	+	0.0146917i
$592$		0			0
$593$	−24.0959	+	13.9118i	−0.989501	+	0.571289i	−0.905125	−	0.425145i	$-0.860223\pi$
$593$	−24.0959	+	13.9118i	−0.989501	+	0.571289i	−0.0843757	+	0.996434i	$0.526890\pi$
$594$		0			0
$595$	19.7980	+	34.2911i	0.811637	+	1.40580i
$596$		0			0
$597$	11.8990	−	1.09638i	0.486993	−	0.0448717i
$598$		0			0
$599$	−14.5732	−	25.2415i	−0.595445	−	1.03134i	−0.993484	−	0.113973i	$-0.963642\pi$
$599$	−14.5732	−	25.2415i	−0.595445	−	1.03134i	0.398038	−	0.917369i	$-0.369691\pi$
$600$		0			0
$601$			31.0019i			1.26460i	0.774725	+	0.632298i	$0.217888\pi$
$601$			31.0019i			1.26460i	−0.774725	+	0.632298i	$0.782112\pi$
$602$		0			0
$603$	−16.8990	−	5.97469i	−0.688180	−	0.243308i
$604$		0			0
$605$	13.3485	+	7.70674i	0.542692	+	0.313324i
$606$		0			0
$607$			36.9766i			1.50084i	0.660964	+	0.750418i	$0.270148\pi$
$607$			36.9766i			1.50084i	−0.660964	+	0.750418i	$0.729852\pi$
$608$		0			0
$609$	18.7980	−	1.73205i	0.761732	−	0.0701862i
$610$		0			0
$611$	−11.1464	+	19.3062i	−0.450936	+	0.781044i
$612$		0			0
$613$	−14.1010	+	24.4237i	−0.569535	+	0.986463i	0.427077	+	0.904215i	$0.359543\pi$
$613$	−14.1010	+	24.4237i	−0.569535	+	0.986463i	−0.996612	+	0.0822481i	$0.973790\pi$
$614$		0			0
$615$	0.674235	+	7.31747i	0.0271878	+	0.295069i
$616$		0			0
$617$	12.9495	−	7.47639i	0.521327	−	0.300988i	−0.216151	−	0.976360i	$-0.569350\pi$
$617$	12.9495	−	7.47639i	0.521327	−	0.300988i	0.737477	+	0.675372i	$0.236017\pi$
$618$		0			0
$619$	1.30306			0.0523745			0.0261872	−	0.999657i	$-0.491663\pi$
$619$	1.30306			0.0523745			0.0261872	+	0.999657i	$0.491663\pi$
$620$		0			0
$621$	25.6186	−	26.3379i	1.02804	−	1.05690i
$622$		0			0
$623$	−37.5959	−	65.1180i	−1.50625	−	2.60890i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$		0			0
$627$	−2.37628	−	0.333891i	−0.0948993	−	0.0133343i
$628$		0			0
$629$	−2.44949	+	4.24264i	−0.0976676	+	0.169165i
$630$		0			0
$631$	−4.87628	−	8.44596i	−0.194121	−	0.336228i	0.752491	−	0.658603i	$-0.228852\pi$
$631$	−4.87628	−	8.44596i	−0.194121	−	0.336228i	−0.946612	+	0.322375i	$0.895519\pi$
$632$		0			0
$633$	−21.7980	+	15.4135i	−0.866391	+	0.612631i
$634$		0			0
$635$	14.6969			0.583230
$636$		0			0
$637$	−38.3939	+	22.1667i	−1.52122	+	0.878277i
$638$		0			0
$639$	17.6969	−	3.28913i	0.700080	−	0.130116i
$640$		0			0
$641$	16.1969	−	28.0539i	0.639741	−	1.10806i	−0.345749	−	0.938327i	$-0.612375\pi$
$641$	16.1969	−	28.0539i	0.639741	−	1.10806i	0.985490	−	0.169736i	$-0.0542916\pi$
$642$		0			0
$643$	−12.0732	+	20.9114i	−0.476121	+	0.824666i	−0.999626	−	0.0273569i	$-0.991291\pi$
$643$	−12.0732	+	20.9114i	−0.476121	+	0.824666i	0.523505	+	0.852023i	$0.324624\pi$
$644$		0			0
$645$	−0.202041	−	2.19275i	−0.00795536	−	0.0863396i
$646$		0			0
$647$		−	7.84961i		−	0.308600i	−0.988024	−	0.154300i	$-0.950688\pi$
$647$		−	7.84961i		−	0.308600i	0.988024	−	0.154300i	$-0.0493122\pi$
$648$		0			0
$649$	1.80306	+	1.04100i	0.0707764	+	0.0408627i
$650$		0			0
$651$	29.6969	+	13.6814i	1.16391	+	0.536218i
$652$		0			0
$653$		−	19.5133i		−	0.763613i	−0.924242	−	0.381806i	$-0.875302\pi$
$653$		−	19.5133i		−	0.763613i	0.924242	−	0.381806i	$-0.124698\pi$
$654$		0			0
$655$	−15.5732	−	26.9736i	−0.608496	−	1.05395i
$656$		0			0
$657$	−31.8485	+	5.91931i	−1.24253	+	0.230934i
$658$		0			0
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	0.999309	−	0.0371821i	$-0.0118382\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$		0			0
$661$	−25.7196	+	14.8492i	−1.00038	+	0.577569i	−0.908360	−	0.418189i	$-0.862665\pi$
$661$	−25.7196	+	14.8492i	−1.00038	+	0.577569i	−0.0920180	+	0.995757i	$0.529332\pi$
$662$		0			0
$663$	15.7980	−	34.2911i	0.613542	−	1.33175i
$664$		0			0
$665$	−26.6969	−	6.29253i	−1.03526	−	0.244014i
$666$		0			0
$667$	15.0000	+	8.66025i	0.580802	+	0.335326i
$668$		0			0
$669$	13.5959	−	9.61377i	0.525649	−	0.371690i
$670$		0			0
$671$	1.77526	−	1.02494i	0.0685330	−	0.0395675i
$672$		0			0
$673$		−	3.46410i		−	0.133531i	−0.997769	−	0.0667657i	$-0.978732\pi$
$673$		−	3.46410i		−	0.133531i	0.997769	−	0.0667657i	$-0.0212680\pi$
$674$		0			0
$675$	11.1742	+	10.8691i	0.430096	+	0.418350i
$676$		0			0
$677$	−3.30306			−0.126947			−0.0634735	−	0.997984i	$-0.520218\pi$
$677$	−3.30306			−0.126947			−0.0634735	+	0.997984i	$0.520218\pi$
$678$		0			0
$679$	52.7196	+	30.4377i	2.02319	+	1.16809i
$680$		0			0
$681$	−3.94949	+	8.57277i	−0.151345	+	0.328509i
$682$		0			0
$683$	41.3939			1.58389			0.791946	−	0.610591i	$-0.209068\pi$
$683$	41.3939			1.58389			0.791946	+	0.610591i	$0.209068\pi$
$684$		0			0
$685$	−10.4495			−0.399254
$686$		0			0
$687$	−6.44949	+	13.9993i	−0.246063	+	0.534106i
$688$		0			0
$689$	3.30306	+	1.90702i	0.125837	+	0.0726518i
$690$		0			0
$691$	40.0000			1.52167			0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000			1.52167			0.760836	+	0.648944i	$0.224789\pi$
$692$		0			0
$693$	3.22474	−	2.75699i	0.122498	−	0.104730i
$694$		0			0
$695$			0.492810i			0.0186933i
$696$		0			0
$697$	16.3485	−	9.43879i	0.619242	−	0.357520i
$698$		0			0
$699$	−9.14643	+	6.46750i	−0.345950	+	0.244623i
$700$		0			0
$701$	8.57321	+	4.94975i	0.323806	+	0.186949i	0.653088	−	0.757282i	$-0.273473\pi$
$701$	8.57321	+	4.94975i	0.323806	+	0.186949i	−0.329282	+	0.944232i	$0.606807\pi$
$702$		0			0
$703$	−0.977296	−	3.24980i	−0.0368594	−	0.122569i
$704$		0			0
$705$	6.59592	−	14.3171i	0.248417	−	0.539213i
$706$		0			0
$707$	38.1464	−	22.0239i	1.43464	−	0.828292i
$708$		0			0
$709$	1.32577	+	2.29629i	0.0497902	+	0.0862391i	0.889846	−	0.456260i	$-0.150811\pi$
$709$	1.32577	+	2.29629i	0.0497902	+	0.0862391i	−0.840056	+	0.542499i	$0.817478\pi$
$710$		0			0
$711$	4.65153	+	25.0273i	0.174446	+	0.938595i
$712$		0			0
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$			1.55708i			0.0582314i
$716$		0			0
$717$	11.3485	+	5.22826i	0.423816	+	0.195253i
$718$		0			0
$719$	8.14643	+	4.70334i	0.303811	+	0.175405i	0.644153	−	0.764896i	$-0.277210\pi$
$719$	8.14643	+	4.70334i	0.303811	+	0.175405i	−0.340343	+	0.940301i	$0.610543\pi$
$720$		0			0
$721$		−	53.1687i		−	1.98010i
$722$		0			0
$723$	−1.62372	−	17.6223i	−0.0603870	−	0.655380i
$724$		0			0
$725$	−3.67423	+	6.36396i	−0.136458	+	0.236352i
$726$		0			0
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$	−4.89898	+	2.82843i	−0.181195	+	0.104613i
$732$		0			0
$733$	24.0454			0.888137			0.444069	−	0.895993i	$-0.353535\pi$
$733$	24.0454			0.888137			0.444069	+	0.895993i	$0.353535\pi$
$734$		0			0
$735$	25.5959	−	18.0990i	0.944120	−	0.667593i
$736$		0			0
$737$	−0.949490	−	1.64456i	−0.0349749	−	0.0605783i
$738$		0			0
$739$	4.82577	−	8.35847i	0.177519	−	0.307471i	−0.763511	−	0.645794i	$-0.776526\pi$
$739$	4.82577	−	8.35847i	0.177519	−	0.307471i	0.941030	+	0.338323i	$0.109860\pi$
$740$		0			0
$741$	9.79796	+	24.2487i	0.359937	+	0.890799i
$742$		0			0
$743$	9.67423	−	16.7563i	0.354913	−	0.614728i	−0.632190	−	0.774814i	$-0.717844\pi$
$743$	9.67423	−	16.7563i	0.354913	−	0.614728i	0.987103	+	0.160086i	$0.0511771\pi$
$744$		0			0
$745$	3.44949	+	5.97469i	0.126380	+	0.218896i
$746$		0			0
$747$	−32.3207	+	27.6325i	−1.18255	+	1.01102i
$748$		0			0
$749$	21.7980			0.796480
$750$		0			0
$751$	11.6969	−	6.75323i	0.426827	−	0.246429i	−0.271167	−	0.962532i	$-0.587409\pi$
$751$	11.6969	−	6.75323i	0.426827	−	0.246429i	0.697994	+	0.716103i	$0.254076\pi$
$752$		0			0
$753$	−1.05051	−	11.4012i	−0.0382827	−	0.415483i
$754$		0			0
$755$	12.7980	−	22.1667i	0.465765	−	0.806729i
$756$		0			0
$757$	−9.69694	+	16.7956i	−0.352441	+	0.610446i	−0.986677	−	0.162694i	$-0.947982\pi$
$757$	−9.69694	+	16.7956i	−0.352441	+	0.610446i	0.634235	+	0.773140i	$0.281315\pi$
$758$		0			0
$759$	3.87628	−	0.357161i	0.140700	−	0.0129641i
$760$		0			0
$761$			41.9657i			1.52126i	0.649188	+	0.760628i	$0.275109\pi$
$761$			41.9657i			1.52126i	−0.649188	+	0.760628i	$0.724891\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−8.89898	+	25.1701i	−0.321743	+	0.910027i
$766$		0			0
$767$		−	22.6916i		−	0.819347i
$768$		0			0
$769$	17.7980	+	30.8270i	0.641811	+	1.11165i	0.985028	+	0.172393i	$0.0551499\pi$
$769$	17.7980	+	30.8270i	0.641811	+	1.11165i	−0.343217	+	0.939256i	$0.611517\pi$
$770$		0			0
$771$	−25.8712	+	2.38378i	−0.931728	+	0.0858497i
$772$		0			0
$773$	1.22474	+	2.12132i	0.0440510	+	0.0762986i	0.887210	−	0.461365i	$-0.152640\pi$
$773$	1.22474	+	2.12132i	0.0440510	+	0.0762986i	−0.843159	+	0.537664i	$0.819307\pi$
$774$		0			0
$775$	−11.0227	+	6.36396i	−0.395947	+	0.228600i
$776$		0			0
$777$	5.44949	+	2.51059i	0.195499	+	0.0900669i
$778$		0			0
$779$	−3.00000	+	12.7279i	−0.107486	+	0.456025i
$780$		0			0
$781$	1.65153	+	0.953512i	0.0590964	+	0.0341193i
$782$		0			0
$783$	9.12372	+	8.87455i	0.326055	+	0.317151i
$784$		0			0
$785$	22.8990	−	13.2207i	0.817300	−	0.471868i
$786$		0			0
$787$		−	17.9241i		−	0.638924i	−0.947599	−	0.319462i	$-0.896498\pi$
$787$		−	17.9241i		−	0.638924i	0.947599	−	0.319462i	$-0.103502\pi$
$788$		0			0
$789$	−16.6969	+	11.8065i	−0.594427	+	0.420323i
$790$		0			0
$791$	−3.55051			−0.126242
$792$		0			0
$793$	−19.3485	−	11.1708i	−0.687084	−	0.396688i
$794$		0			0
$795$	−2.44949	−	1.12848i	−0.0868744	−	0.0400232i
$796$		0			0
$797$	22.6515			0.802358			0.401179	−	0.916000i	$-0.368600\pi$
$797$	22.6515			0.802358			0.401179	+	0.916000i	$0.368600\pi$
$798$		0			0
$799$	−40.4949			−1.43261
$800$		0			0
$801$	16.8990	−	47.7975i	0.597096	−	1.68884i
$802$		0			0
$803$	−2.97219	−	1.71600i	−0.104886	−	0.0605562i
$804$		0			0
$805$	44.4949			1.56824
$806$		0			0
$807$	24.4949	+	34.6410i	0.862261	+	1.21942i
$808$		0			0
$809$		−	2.36773i		−	0.0832448i	−0.999133	−	0.0416224i	$-0.986747\pi$
$809$		−	2.36773i		−	0.0832448i	0.999133	−	0.0416224i	$-0.0132526\pi$
$810$		0			0
$811$	−3.00000	+	1.73205i	−0.105344	+	0.0608205i	−0.551746	−	0.834012i	$-0.686038\pi$
$811$	−3.00000	+	1.73205i	−0.105344	+	0.0608205i	0.446402	+	0.894832i	$0.352705\pi$
$812$		0			0
$813$	−24.0454	−	34.0053i	−0.843309	−	1.19262i
$814$		0			0
$815$	−4.47219	−	2.58202i	−0.156654	−	0.0904443i
$816$		0			0
$817$	0.898979	−	3.81405i	0.0314513	−	0.133437i
$818$		0			0
$819$	−43.5959	−	15.4135i	−1.52336	−	0.538591i
$820$		0			0
$821$	−0.550510	+	0.317837i	−0.0192129	+	0.0110926i	−0.509576	−	0.860426i	$-0.670198\pi$
$821$	−0.550510	+	0.317837i	−0.0192129	+	0.0110926i	0.490363	+	0.871518i	$0.336864\pi$
$822$		0			0
$823$	−9.65153	−	16.7169i	−0.336431	−	0.582716i	0.647327	−	0.762212i	$-0.275887\pi$
$823$	−9.65153	−	16.7169i	−0.336431	−	0.582716i	−0.983759	+	0.179496i	$0.942553\pi$
$824$		0			0
$825$	0.151531	+	1.64456i	0.00527562	+	0.0572564i
$826$		0			0
$827$	−1.62372	−	2.81237i	−0.0564624	−	0.0977958i	0.836413	−	0.548100i	$-0.184649\pi$
$827$	−1.62372	−	2.81237i	−0.0564624	−	0.0977958i	−0.892875	+	0.450304i	$0.851315\pi$
$828$		0			0
$829$		−	36.1981i		−	1.25721i	−0.777724	−	0.628606i	$-0.783626\pi$
$829$		−	36.1981i		−	1.25721i	0.777724	−	0.628606i	$-0.216374\pi$
$830$		0			0
$831$	−3.07832	+	6.68180i	−0.106786	+	0.231789i
$832$		0			0
$833$	−69.7423	−	40.2658i	−2.41643	−	1.39513i
$834$		0			0
$835$		−	6.92820i		−	0.239760i
$836$		0			0
$837$	6.00000	+	21.2132i	0.207390	+	0.733236i
$838$		0			0
$839$	0.674235	−	1.16781i	0.0232772	−	0.0403172i	−0.854152	−	0.520023i	$-0.825923\pi$
$839$	0.674235	−	1.16781i	0.0232772	−	0.0403172i	0.877429	+	0.479706i	$0.159257\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$		0			0
$843$	−28.6237	+	2.63740i	−0.985853	+	0.0908369i
$844$		0			0
$845$	−1.22474	+	0.707107i	−0.0421325	+	0.0243252i
$846$		0			0
$847$	−48.4949			−1.66630
$848$		0			0
$849$	4.55051	+	6.43539i	0.156173	+	0.220862i
$850$		0			0
$851$	2.75255	+	4.76756i	0.0943562	+	0.163430i
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$		0			0
$855$	−8.47219	−	16.4384i	−0.289743	−	0.562182i
$856$		0			0
$857$	−11.2980	+	19.5686i	−0.385931	+	0.668452i	−0.991898	−	0.127038i	$-0.959453\pi$
$857$	−11.2980	+	19.5686i	−0.385931	+	0.668452i	0.605967	+	0.795490i	$0.292786\pi$
$858$		0			0
$859$	−22.4217	−	38.8355i	−0.765018	−	1.32505i	−0.940237	−	0.340521i	$-0.889397\pi$
$859$	−22.4217	−	38.8355i	−0.765018	−	1.32505i	0.175219	−	0.984529i	$-0.443937\pi$
$860$		0			0
$861$	−13.3485	−	18.8776i	−0.454915	−	0.643346i
$862$		0			0
$863$	−31.3485			−1.06711			−0.533557	−	0.845764i	$-0.679145\pi$
$863$	−31.3485			−1.06711			−0.533557	+	0.845764i	$0.679145\pi$
$864$		0			0
$865$	13.3485	−	7.70674i	0.453862	−	0.262037i
$866$		0			0
$867$	38.9722	−	3.59091i	1.32357	−	0.121954i
$868$		0			0
$869$	−1.34847	+	2.33562i	−0.0457437	+	0.0792304i
$870$		0			0
$871$	−10.3485	+	17.9241i	−0.350645	+	0.607334i
$872$		0			0
$873$	7.50000	+	40.3532i	0.253837	+	1.36575i
$874$		0			0
$875$			50.3402i			1.70181i
$876$		0			0
$877$	0.371173	+	0.214297i	0.0125336	+	0.00723629i	0.506254	−	0.862385i	$-0.331030\pi$
$877$	0.371173	+	0.214297i	0.0125336	+	0.00723629i	−0.493720	+	0.869621i	$0.664363\pi$
$878$		0			0
$879$	−3.37117	+	7.31747i	−0.113707	+	0.246812i
$880$		0			0
$881$		−	55.5364i		−	1.87107i	−0.353236	−	0.935534i	$-0.614919\pi$
$881$		−	55.5364i		−	1.87107i	0.353236	−	0.935534i	$-0.385081\pi$
$882$		0			0
$883$	21.4217	+	37.1034i	0.720897	+	1.24863i	0.960641	+	0.277794i	$0.0896033\pi$
$883$	21.4217	+	37.1034i	0.720897	+	1.24863i	−0.239744	+	0.970836i	$0.577063\pi$
$884$		0			0
$885$	1.47219	+	15.9777i	0.0494872	+	0.537085i
$886$		0			0
$887$	16.0454	+	27.7915i	0.538752	+	0.933146i	0.998972	+	0.0453408i	$0.0144374\pi$
$887$	16.0454	+	27.7915i	0.538752	+	0.933146i	−0.460220	+	0.887805i	$0.652229\pi$
$888$		0			0
$889$	−40.0454	+	23.1202i	−1.34308	+	0.775428i
$890$		0			0
$891$	2.82577	+	0.444648i	0.0946667	+	0.0148963i
$892$		0			0
$893$	19.2247	−	20.4274i	0.643332	−	0.683578i
$894$		0			0
$895$	27.3712	+	15.8028i	0.914917	+	0.528228i
$896$		0			0
$897$	−24.4949	−	34.6410i	−0.817861	−	1.15663i
$898$		0			0
$899$	−9.00000	+	5.19615i	−0.300167	+	0.173301i
$900$		0			0
$901$			6.92820i			0.230812i
$902$		0			0
$903$	4.00000	+	5.65685i	0.133112	+	0.188248i
$904$		0			0
$905$	18.4949			0.614791
$906$		0			0
$907$	−47.9166	−	27.6647i	−1.59104	−	0.918590i	−0.993128	−	0.117031i	$-0.962662\pi$
$907$	−47.9166	−	27.6647i	−1.59104	−	0.918590i	−0.597916	−	0.801559i	$-0.704004\pi$
$908$		0			0
$909$	28.0000	+	9.89949i	0.928701	+	0.328346i
$910$		0			0
$911$	43.3485			1.43620			0.718099	−	0.695941i	$-0.245012\pi$
$911$	43.3485			1.43620			0.718099	+	0.695941i	$0.245012\pi$
$912$		0			0
$913$	−4.50510			−0.149097
$914$		0			0
$915$	14.3485	+	6.61037i	0.474346	+	0.218532i
$916$		0			0
$917$	84.8661	+	48.9974i	2.80252	+	1.61804i
$918$		0			0
$919$	7.30306			0.240906			0.120453	−	0.992719i	$-0.461565\pi$
$919$	7.30306			0.240906			0.120453	+	0.992719i	$0.461565\pi$
$920$		0			0
$921$	5.75255	−	4.06767i	0.189553	−	0.134034i
$922$		0			0
$923$		−	20.7846i		−	0.684134i
$924$		0			0
$925$	−2.02270	+	1.16781i	−0.0665061	+	0.0383973i
$926$		0			0
$927$	27.2474	−	23.2952i	0.894924	−	0.765115i
$928$		0			0
$929$	15.0959	+	8.71563i	0.495281	+	0.285951i	0.726763	−	0.686889i	$-0.241024\pi$
$929$	15.0959	+	8.71563i	0.495281	+	0.285951i	−0.231482	+	0.972839i	$0.574357\pi$
$930$		0			0
$931$	53.4217	−	16.0652i	1.75082	−	0.526516i
$932$		0			0
$933$	−24.4722	−	11.2744i	−0.801184	−	0.369107i
$934$		0			0
$935$	−2.44949	+	1.41421i	−0.0801069	+	0.0462497i
$936$		0			0
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$		0			0
$939$	32.7702	−	3.01945i	1.06941	−	0.0985362i
$940$		0			0
$941$	−27.4949	−	47.6226i	−0.896308	−	1.55245i	−0.832177	−	0.554510i	$-0.812906\pi$
$941$	−27.4949	−	47.6226i	−0.896308	−	1.55245i	−0.0641307	−	0.997942i	$-0.520427\pi$
$942$		0			0
$943$		−	21.2132i		−	0.690797i
$944$		0			0
$945$	31.6969	+	8.02458i	1.03110	+	0.261040i
$946$		0			0
$947$	11.4495	+	6.61037i	0.372058	+	0.214808i	0.674357	−	0.738405i	$-0.264421\pi$
$947$	11.4495	+	6.61037i	0.372058	+	0.214808i	−0.302299	+	0.953213i	$0.597754\pi$
$948$		0			0
$949$			37.4052i			1.21423i
$950$		0			0
$951$	−10.3485	+	0.953512i	−0.335572	+	0.0309197i
$952$		0			0
$953$	−2.60102	+	4.50510i	−0.0842553	+	0.145934i	−0.905074	−	0.425255i	$-0.860184\pi$
$953$	−2.60102	+	4.50510i	−0.0842553	+	0.145934i	0.820818	+	0.571189i	$0.193518\pi$
$954$		0			0
$955$	−13.7980	+	23.8988i	−0.446491	+	0.773346i
$956$		0			0
$957$	0.123724	+	1.34278i	0.00399944	+	0.0434060i
$958$		0			0
$959$	28.4722	−	16.4384i	0.919415	−	0.530825i
$960$		0			0
$961$	13.0000			0.419355
$962$		0			0
$963$	9.55051	+	11.1708i	0.307761	+	0.359975i
$964$		0			0
$965$	−6.24745	−	10.8209i	−0.201112	−	0.348337i
$966$		0			0
$967$	3.69694	−	6.40329i	0.118886	−	0.205916i	−0.800441	−	0.599412i	$-0.795401\pi$
$967$	3.69694	−	6.40329i	0.118886	−	0.205916i	0.919326	+	0.393496i	$0.128735\pi$
$968$		0			0
$969$	−29.2474	+	37.4373i	−0.939563	+	1.20266i
$970$		0			0
$971$	−13.0732	+	22.6435i	−0.419539	+	0.726664i	−0.995893	−	0.0905368i	$-0.971142\pi$
$971$	−13.0732	+	22.6435i	−0.419539	+	0.726664i	0.576354	+	0.817200i	$0.304475\pi$
$972$		0			0
$973$	−0.775255	−	1.34278i	−0.0248535	−	0.0430476i
$974$		0			0
$975$	14.6969	−	10.3923i	0.470679	−	0.332820i
$976$		0			0
$977$	49.8990			1.59641			0.798205	−	0.602386i	$-0.205783\pi$
$977$	49.8990			1.59641			0.798205	+	0.602386i	$0.205783\pi$
$978$		0			0
$979$	4.65153	−	2.68556i	0.148664	−	0.0858310i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.1010	−	33.0839i	0.609228	−	1.05521i	−0.382140	−	0.924104i	$-0.624813\pi$
$983$	19.1010	−	33.0839i	0.609228	−	1.05521i	0.991368	−	0.131109i	$-0.0418539\pi$
$984$		0			0
$985$	−0.348469	+	0.603566i	−0.0111032	+	0.0192312i
$986$		0			0
$987$	4.55051	+	49.3867i	0.144844	+	1.57200i
$988$		0			0
$989$			6.35674i			0.202133i
$990$		0			0
$991$	−44.6969	−	25.8058i	−1.41985	−	0.819748i	−0.423560	−	0.905868i	$-0.639220\pi$
$991$	−44.6969	−	25.8058i	−1.41985	−	0.819748i	−0.996285	+	0.0861200i	$0.972553\pi$
$992$		0			0
$993$	23.2980	+	10.7334i	0.739338	+	0.340615i
$994$		0			0
$995$			9.75663i			0.309306i
$996$		0			0
$997$	−29.7196	−	51.4759i	−0.941231	−	1.63026i	−0.763128	−	0.646247i	$-0.776338\pi$
$997$	−29.7196	−	51.4759i	−0.941231	−	1.63026i	−0.178102	−	0.984012i	$-0.556996\pi$
$998$		0			0
$999$	1.10102	+	3.89270i	0.0348347	+	0.123159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.h.65.2		4
3.2	odd	2		912.2.bn.g.65.2		4
4.3	odd	2		114.2.h.f.65.1	yes	4
12.11	even	2		114.2.h.e.65.1	✓	4
19.12	odd	6		912.2.bn.g.449.1		4
57.50	even	6	inner	912.2.bn.h.449.2		4
76.31	even	6		114.2.h.e.107.2	yes	4
228.107	odd	6		114.2.h.f.107.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.e.65.1	✓	4	12.11	even	2
114.2.h.e.107.2	yes	4	76.31	even	6
114.2.h.f.65.1	yes	4	4.3	odd	2
114.2.h.f.107.1	yes	4	228.107	odd	6
912.2.bn.g.65.2		4	3.2	odd	2
912.2.bn.g.449.1		4	19.12	odd	6
912.2.bn.h.65.2		4	1.1	even	1	trivial
912.2.bn.h.449.2		4	57.50	even	6	inner

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.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.724745 - 1.57313i) q^{3} +(1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.724745 - 1.57313i) q^{3} +(1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.94949 - 2.28024i) q^{9} -0.317837i q^{11} +(-3.00000 + 1.73205i) q^{13} +(2.00000 - 1.41421i) q^{15} +(-5.44949 - 3.14626i) q^{17} +(4.17423 - 1.25529i) q^{19} +(-3.22474 + 6.99964i) q^{21} +(-6.12372 + 3.53553i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-5.00000 + 1.41421i) q^{27} +(-1.22474 - 2.12132i) q^{29} -4.24264i q^{31} +(-0.500000 - 0.230351i) q^{33} +(-5.44949 - 3.14626i) q^{35} -0.778539i q^{37} +(0.550510 + 5.97469i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(0.449490 - 0.778539i) q^{43} +(-0.775255 - 4.17121i) q^{45} +(5.57321 - 3.21770i) q^{47} +12.7980 q^{49} +(-8.89898 + 6.29253i) q^{51} +(-0.550510 - 0.953512i) q^{53} +(0.224745 - 0.389270i) q^{55} +(1.05051 - 7.47639i) q^{57} +(-3.27526 + 5.67291i) q^{59} +(3.22474 + 5.58542i) q^{61} +(8.67423 + 10.1459i) q^{63} -4.89898 q^{65} +(5.17423 - 2.98735i) q^{67} +(1.12372 + 12.1958i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(5.39898 - 9.35131i) q^{73} +(-5.17423 + 0.476756i) q^{75} +1.41421i q^{77} +(-7.34847 - 4.24264i) q^{79} +(-1.39898 + 8.89060i) q^{81} -14.1742i q^{83} +(-4.44949 - 7.70674i) q^{85} +(-4.22474 + 0.389270i) q^{87} +(8.44949 + 14.6349i) q^{89} +(13.3485 - 7.70674i) q^{91} +(-6.67423 - 3.07483i) q^{93} +(6.00000 + 1.41421i) q^{95} +(-11.8485 - 6.84072i) q^{97} +(-0.724745 + 0.619620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9	\( 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9} - 12 q^{13} + 8 q^{15} - 12 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{25} - 20 q^{27} - 2 q^{33} - 12 q^{35} + 12 q^{39} - 6 q^{41} - 8 q^{43} - 8 q^{45} - 12 q^{47} + 12 q^{49} - 16 q^{51} - 12 q^{53} - 4 q^{55} + 14 q^{57} - 18 q^{59} + 8 q^{61} + 20 q^{63} + 6 q^{67} - 20 q^{69} - 12 q^{71} + 2 q^{73} - 6 q^{75} + 14 q^{81} - 8 q^{85} - 12 q^{87} + 24 q^{89} + 24 q^{91} - 12 q^{93} + 24 q^{95} - 18 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9 - 12 * q^13 + 8 * q^15 - 12 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^25 - 20 * q^27 - 2 * q^33 - 12 * q^35 + 12 * q^39 - 6 * q^41 - 8 * q^43 - 8 * q^45 - 12 * q^47 + 12 * q^49 - 16 * q^51 - 12 * q^53 - 4 * q^55 + 14 * q^57 - 18 * q^59 + 8 * q^61 + 20 * q^63 + 6 * q^67 - 20 * q^69 - 12 * q^71 + 2 * q^73 - 6 * q^75 + 14 * q^81 - 8 * q^85 - 12 * q^87 + 24 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 18 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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