LMFDB - Embedded newform 912.2.bn.g.449.1

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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.g.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.41421i) q^{3} +(-1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.41421i) q^{3} +(-1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.00000 + 2.82843i) q^{9} -0.317837i q^{11} +(-3.00000 - 1.73205i) q^{13} +(2.22474 + 1.02494i) q^{15} +(5.44949 - 3.14626i) q^{17} +(4.17423 + 1.25529i) q^{19} +(4.44949 + 6.29253i) q^{21} +(6.12372 + 3.53553i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 - 1.41421i) q^{27} +(1.22474 - 2.12132i) q^{29} +4.24264i q^{31} +(-0.449490 + 0.317837i) q^{33} +(5.44949 - 3.14626i) q^{35} +0.778539i q^{37} +(0.550510 + 5.97469i) q^{39} +(1.50000 + 2.59808i) q^{41} +(0.449490 + 0.778539i) q^{43} +(-0.775255 - 4.17121i) q^{45} +(-5.57321 - 3.21770i) q^{47} +12.7980 q^{49} +(-9.89898 - 4.56048i) q^{51} +(0.550510 - 0.953512i) q^{53} +(0.224745 + 0.389270i) q^{55} +(-2.39898 - 7.15855i) q^{57} +(3.27526 + 5.67291i) q^{59} +(3.22474 - 5.58542i) q^{61} +(4.44949 - 12.5851i) q^{63} +4.89898 q^{65} +(5.17423 + 2.98735i) q^{67} +(-1.12372 - 12.1958i) q^{69} +(3.00000 + 5.19615i) q^{71} +(5.39898 + 9.35131i) q^{73} +(5.17423 - 0.476756i) q^{75} +1.41421i q^{77} +(-7.34847 + 4.24264i) q^{79} +(-7.00000 - 5.65685i) q^{81} -14.1742i q^{83} +(-4.44949 + 7.70674i) q^{85} +(-4.22474 + 0.389270i) q^{87} +(-8.44949 + 14.6349i) q^{89} +(13.3485 + 7.70674i) q^{91} +(6.00000 - 4.24264i) q^{93} +(-6.00000 + 1.41421i) q^{95} +(-11.8485 + 6.84072i) q^{97} +(0.898979 + 0.317837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 8 * q^7 - 4 * q^9	$ 4 q - 4 q^{3} - 8 q^{7} - 4 q^{9} - 12 q^{13} + 4 q^{15} + 12 q^{17} + 2 q^{19} + 8 q^{21} - 6 q^{25} + 20 q^{27} + 8 q^{33} + 12 q^{35} + 12 q^{39} + 6 q^{41} - 8 q^{43} - 8 q^{45} + 12 q^{47} + 12 q^{49} - 20 q^{51} + 12 q^{53} - 4 q^{55} + 10 q^{57} + 18 q^{59} + 8 q^{61} + 8 q^{63} + 6 q^{67} + 20 q^{69} + 12 q^{71} + 2 q^{73} + 6 q^{75} - 28 q^{81} - 8 q^{85} - 12 q^{87} - 24 q^{89} + 24 q^{91} + 24 q^{93} - 24 q^{95} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 8 * q^7 - 4 * q^9 - 12 * q^13 + 4 * q^15 + 12 * q^17 + 2 * q^19 + 8 * q^21 - 6 * q^25 + 20 * q^27 + 8 * q^33 + 12 * q^35 + 12 * q^39 + 6 * q^41 - 8 * q^43 - 8 * q^45 + 12 * q^47 + 12 * q^49 - 20 * q^51 + 12 * q^53 - 4 * q^55 + 10 * q^57 + 18 * q^59 + 8 * q^61 + 8 * q^63 + 6 * q^67 + 20 * q^69 + 12 * q^71 + 2 * q^73 + 6 * q^75 - 28 * q^81 - 8 * q^85 - 12 * q^87 - 24 * q^89 + 24 * q^91 + 24 * q^93 - 24 * q^95 - 18 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$		0			0
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$		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
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		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	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$		0			0
$15$	2.22474	+	1.02494i	0.574427	+	0.264639i
$16$		0			0
$17$	5.44949	−	3.14626i	1.32170	−	0.763081i	0.337696	−	0.941255i	$-0.390352\pi$
$17$	5.44949	−	3.14626i	1.32170	−	0.763081i	0.983999	+	0.178174i	$0.0570190\pi$
$18$		0			0
$19$	4.17423	+	1.25529i	0.957635	+	0.287984i
$19$	4.17423	+	1.25529i	0.957635	+	0.287984i
$20$		0			0
$21$	4.44949	+	6.29253i	0.970958	+	1.37314i
$22$		0			0
$23$	6.12372	+	3.53553i	1.27688	+	0.737210i	0.976274	−	0.216537i	$-0.0694763\pi$
$23$	6.12372	+	3.53553i	1.27688	+	0.737210i	0.300610	+	0.953747i	$0.402810\pi$
$24$		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	$-0.760301\pi$
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	0.957046	+	0.289938i	$0.0936346\pi$
$30$		0			0
$31$			4.24264i			0.762001i	0.924575	+	0.381000i	$0.124420\pi$
$31$			4.24264i			0.762001i	−0.924575	+	0.381000i	$0.875580\pi$
$32$		0			0
$33$	−0.449490	+	0.317837i	−0.0782461	+	0.0553284i
$34$		0			0
$35$	5.44949	−	3.14626i	0.921132	−	0.531816i
$36$		0			0
$37$			0.778539i			0.127991i	0.997950	+	0.0639955i	$0.0203843\pi$
$37$			0.778539i			0.127991i	−0.997950	+	0.0639955i	$0.979616\pi$
$38$		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	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	0.449490	+	0.778539i	0.0685465	+	0.118726i	0.898262	−	0.439461i	$-0.144831\pi$
$43$	0.449490	+	0.778539i	0.0685465	+	0.118726i	−0.829715	+	0.558187i	$0.811497\pi$
$44$		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	$-0.488845\pi$
$47$	−5.57321	−	3.21770i	−0.812937	−	0.469349i	−0.847975	+	0.530037i	$0.822178\pi$
$48$		0			0
$49$	12.7980			1.82828
$50$		0			0
$51$	−9.89898	−	4.56048i	−1.38613	−	0.638595i
$52$		0			0
$53$	0.550510	−	0.953512i	0.0756184	−	0.130975i	−0.825737	−	0.564056i	$-0.809240\pi$
$53$	0.550510	−	0.953512i	0.0756184	−	0.130975i	0.901355	+	0.433081i	$0.142574\pi$
$54$		0			0
$55$	0.224745	+	0.389270i	0.0303046	+	0.0524891i
$56$		0			0
$57$	−2.39898	−	7.15855i	−0.317753	−	0.948174i
$58$		0			0
$59$	3.27526	+	5.67291i	0.426402	+	0.738550i	0.996550	−	0.0829920i	$-0.0264476\pi$
$59$	3.27526	+	5.67291i	0.426402	+	0.738550i	−0.570148	+	0.821542i	$0.693114\pi$
$60$		0			0
$61$	3.22474	−	5.58542i	0.412886	−	0.715140i	−0.582318	−	0.812961i	$-0.697854\pi$
$61$	3.22474	−	5.58542i	0.412886	−	0.715140i	0.995204	+	0.0978213i	$0.0311874\pi$
$62$		0			0
$63$	4.44949	−	12.5851i	0.560583	−	1.58557i
$64$		0			0
$65$	4.89898			0.607644
$66$		0			0
$67$	5.17423	+	2.98735i	0.632133	+	0.364962i	0.781578	−	0.623808i	$-0.214415\pi$
$67$	5.17423	+	2.98735i	0.632133	+	0.364962i	−0.149444	+	0.988770i	$0.547749\pi$
$68$		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	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	5.39898	+	9.35131i	0.631903	+	1.09449i	0.987162	+	0.159720i	$0.0510591\pi$
$73$	5.39898	+	9.35131i	0.631903	+	1.09449i	−0.355260	+	0.934768i	$0.615608\pi$
$74$		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	−0.852745	−	0.522328i	$-0.825064\pi$
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	0.0259772	+	0.999663i	$0.491730\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		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	−0.0626387	+	0.998036i	$0.519952\pi$
$89$	−8.44949	+	14.6349i	−0.895644	+	1.55130i	−0.833005	+	0.553265i	$0.813382\pi$
$90$		0			0
$91$	13.3485	+	7.70674i	1.39930	+	0.807886i
$92$		0			0
$93$	6.00000	−	4.24264i	0.622171	−	0.439941i
$94$		0			0
$95$	−6.00000	+	1.41421i	−0.615587	+	0.145095i
$96$		0			0
$97$	−11.8485	+	6.84072i	−1.20303	+	0.694570i	−0.961228	−	0.275756i	$-0.911072\pi$
$97$	−11.8485	+	6.84072i	−1.20303	+	0.694570i	−0.241802	+	0.970326i	$0.577738\pi$
$98$		0			0
$99$	0.898979	+	0.317837i	0.0903508	+	0.0319438i
$100$		0			0
$101$	8.57321	+	4.94975i	0.853067	+	0.492518i	0.861684	−	0.507445i	$-0.169410\pi$
$101$	8.57321	+	4.94975i	0.853067	+	0.492518i	−0.00861771	+	0.999963i	$0.502743\pi$
$102$		0			0
$103$		−	11.9494i		−	1.17741i	−0.808349	−	0.588704i	$-0.799638\pi$
$103$		−	11.9494i		−	1.17741i	0.808349	−	0.588704i	$-0.200362\pi$
$104$		0			0
$105$	−9.89898	−	4.56048i	−0.966041	−	0.445057i
$106$		0			0
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$		0			0
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$	1.10102	−	0.778539i	0.104504	−	0.0738957i
$112$		0			0
$113$	−0.797959			−0.0750657			−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	−0.797959			−0.0750657			−0.0375328	+	0.999295i	$0.511950\pi$
$114$		0			0
$115$	−10.0000			−0.932505
$116$		0			0
$117$	7.89898	−	6.75323i	0.730261	−	0.624336i
$118$		0			0
$119$	−24.2474	+	13.9993i	−2.22276	+	1.28331i
$120$		0			0
$121$	10.8990			0.990816
$122$		0			0
$123$	2.17423	−	4.71940i	0.196044	−	0.425534i
$124$		0			0
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	9.00000	+	5.19615i	0.798621	+	0.461084i	0.842989	−	0.537931i	$-0.180794\pi$
$127$	9.00000	+	5.19615i	0.798621	+	0.461084i	−0.0443678	+	0.999015i	$0.514127\pi$
$128$		0			0
$129$	0.651531	−	1.41421i	0.0573641	−	0.124515i
$130$		0			0
$131$	19.0732	−	11.0119i	1.66643	−	0.962116i	0.696898	−	0.717171i	$-0.254563\pi$
$131$	19.0732	−	11.0119i	1.66643	−	0.962116i	0.969537	−	0.244946i	$-0.0787702\pi$
$132$		0			0
$133$	−18.5732	−	5.58542i	−1.61050	−	0.484318i
$134$		0			0
$135$	−5.12372	+	5.26758i	−0.440980	+	0.453362i
$136$		0			0
$137$	6.39898	+	3.69445i	0.546702	+	0.315638i	0.747791	−	0.663935i	$-0.231115\pi$
$137$	6.39898	+	3.69445i	0.546702	+	0.315638i	−0.201089	+	0.979573i	$0.564448\pi$
$138$		0			0
$139$	0.174235	−	0.301783i	0.0147784	−	0.0255969i	−0.858542	−	0.512744i	$-0.828629\pi$
$139$	0.174235	−	0.301783i	0.0147784	−	0.0255969i	0.873320	+	0.487147i	$0.161962\pi$
$140$		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
$147$	−12.7980	−	18.0990i	−1.05556	−	1.49278i
$148$		0			0
$149$	−4.22474	+	2.43916i	−0.346105	+	0.199824i	−0.662968	−	0.748648i	$-0.730704\pi$
$149$	−4.22474	+	2.43916i	−0.346105	+	0.199824i	0.316864	+	0.948471i	$0.397370\pi$
$150$		0			0
$151$			18.0990i			1.47288i	0.676503	+	0.736440i	$0.263495\pi$
$151$			18.0990i			1.47288i	−0.676503	+	0.736440i	$0.736505\pi$
$152$		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	0.949684	+	0.313209i	$0.101404\pi$
$157$	9.34847	+	16.1920i	0.746089	+	1.29226i	−0.203595	+	0.979055i	$0.565263\pi$
$158$		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
$165$	0.325765	−	0.707107i	0.0253608	−	0.0550482i
$166$		0			0
$167$	2.44949	−	4.24264i	0.189547	−	0.328305i	−0.755552	−	0.655089i	$-0.772631\pi$
$167$	2.44949	−	4.24264i	0.189547	−	0.328305i	0.945099	+	0.326783i	$0.105965\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	−7.72474	+	10.5512i	−0.590726	+	0.806872i
$172$		0			0
$173$	−5.44949	−	9.43879i	−0.414317	−	0.717618i	0.581039	−	0.813875i	$-0.302646\pi$
$173$	−5.44949	−	9.43879i	−0.414317	−	0.717618i	−0.995356	+	0.0962572i	$0.969313\pi$
$174$		0			0
$175$	6.67423	−	11.5601i	0.504525	−	0.873862i
$176$		0			0
$177$	4.74745	−	10.3048i	0.356840	−	0.774558i
$178$		0			0
$179$	−22.3485			−1.67040			−0.835202	−	0.549944i	$-0.814649\pi$
$179$	−22.3485			−1.67040			−0.835202	+	0.549944i	$0.814649\pi$
$180$		0			0
$181$	11.3258	+	6.53893i	0.841838	+	0.486035i	0.857888	−	0.513836i	$-0.171776\pi$
$181$	11.3258	+	6.53893i	0.841838	+	0.486035i	−0.0160509	+	0.999871i	$0.505109\pi$
$182$		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	−0.749432	−	0.662081i	$-0.769673\pi$
$193$	−7.65153	+	4.41761i	−0.550769	+	0.317987i	0.198663	+	0.980068i	$0.436340\pi$
$194$		0			0
$195$	−4.89898	−	6.92820i	−0.350823	−	0.496139i
$196$		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	−0.717471	−	0.696588i	$-0.754700\pi$
$199$	3.44949	−	5.97469i	0.244528	−	0.423535i	0.961999	+	0.273054i	$0.0880337\pi$
$200$		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
$207$	−16.1237	+	13.7850i	−1.12068	+	0.958122i
$208$		0			0
$209$	0.398979	−	1.32673i	0.0275980	−	0.0917716i
$210$		0			0
$211$	−13.3485	+	7.70674i	−0.918947	+	0.530554i	−0.883299	−	0.468810i	$-0.844683\pi$
$211$	−13.3485	+	7.70674i	−0.918947	+	0.530554i	−0.0356477	+	0.999364i	$0.511349\pi$
$212$		0			0
$213$	4.34847	−	9.43879i	0.297952	−	0.646735i
$214$		0			0
$215$	−1.10102	−	0.635674i	−0.0750890	−	0.0433526i
$216$		0			0
$217$		−	18.8776i		−	1.28149i
$218$		0			0
$219$	7.82577	−	16.9866i	0.528816	−	1.14785i
$220$		0			0
$221$	−21.7980			−1.46629
$222$		0			0
$223$	8.32577	−	4.80688i	0.557534	−	0.321893i	−0.194621	−	0.980879i	$-0.562348\pi$
$223$	8.32577	−	4.80688i	0.557534	−	0.321893i	0.752155	+	0.658986i	$0.229014\pi$
$224$		0			0
$225$	−5.84847	−	6.84072i	−0.389898	−	0.456048i
$226$		0			0
$227$	5.44949			0.361695			0.180848	−	0.983511i	$-0.442116\pi$
$227$	5.44949			0.361695			0.180848	+	0.983511i	$0.442116\pi$
$228$		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
$231$	2.00000	−	1.41421i	0.131590	−	0.0930484i
$232$		0			0
$233$	5.60102	−	3.23375i	0.366935	−	0.211850i	−0.305184	−	0.952294i	$-0.598718\pi$
$233$	5.60102	−	3.23375i	0.366935	−	0.211850i	0.672119	+	0.740443i	$0.265384\pi$
$234$		0			0
$235$	9.10102			0.593685
$236$		0			0
$237$	13.3485	+	6.14966i	0.867076	+	0.399464i
$238$		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	0.757141	−	0.653251i	$-0.226595\pi$
$241$	8.84847	+	5.10867i	0.569980	+	0.329078i	−0.187161	+	0.982329i	$0.559929\pi$
$242$		0			0
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$		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
$249$	−20.0454	+	14.1742i	−1.27033	+	0.898256i
$250$		0			0
$251$	−5.72474	−	3.30518i	−0.361343	−	0.208621i	0.308327	−	0.951280i	$-0.400231\pi$
$251$	−5.72474	−	3.30518i	−0.361343	−	0.208621i	−0.669670	+	0.742659i	$0.733564\pi$
$252$		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	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$		−	3.46410i		−	0.215249i
$260$		0			0
$261$	4.77526	+	5.58542i	0.295581	+	0.345729i
$262$		0			0
$263$	10.2247	−	5.90326i	0.630485	−	0.364011i	−0.150455	−	0.988617i	$-0.548074\pi$
$263$	10.2247	−	5.90326i	0.630485	−	0.364011i	0.780940	+	0.624606i	$0.214741\pi$
$264$		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	0.949377	+	0.314138i	$0.101715\pi$
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	−0.202637	+	0.979254i	$0.564951\pi$
$270$		0			0
$271$	12.0227	+	20.8239i	0.730327	+	1.26496i	0.956743	+	0.290933i	$0.0939658\pi$
$271$	12.0227	+	20.8239i	0.730327	+	1.26496i	−0.226416	+	0.974031i	$0.572701\pi$
$272$		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
$279$	−12.0000	−	4.24264i	−0.718421	−	0.254000i
$280$		0			0
$281$	8.29796	−	14.3725i	0.495015	−	0.857391i	−0.504969	−	0.863138i	$-0.668496\pi$
$281$	8.29796	−	14.3725i	0.495015	−	0.857391i	0.999983	+	0.00574696i	$0.00182932\pi$
$282$		0			0
$283$	−2.27526	−	3.94086i	−0.135250	−	0.234260i	0.790443	−	0.612536i	$-0.209850\pi$
$283$	−2.27526	−	3.94086i	−0.135250	−	0.234260i	−0.925693	+	0.378276i	$0.876517\pi$
$284$		0			0
$285$	8.00000	+	7.07107i	0.473879	+	0.418854i
$286$		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
$291$	21.5227	+	9.91555i	1.26168	+	0.581260i
$292$		0			0
$293$	4.65153			0.271745			0.135873	−	0.990726i	$-0.456616\pi$
$293$	4.65153			0.271745			0.135873	+	0.990726i	$0.456616\pi$
$294$		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	−0.396094	−	0.918210i	$-0.629635\pi$
$307$	3.52270	−	2.03383i	0.201051	−	0.116077i	0.597146	+	0.802133i	$0.296301\pi$
$308$		0			0
$309$	−16.8990	+	11.9494i	−0.961349	+	0.679777i
$310$		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	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$		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	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−0.674235	−	0.389270i	−0.0377499	−	0.0217949i
$320$		0			0
$321$	−4.89898	−	6.92820i	−0.273434	−	0.386695i
$322$		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	$-0.866570\pi$
$331$		−	14.8099i		−	0.814027i	0.913422	−	0.407013i	$-0.133430\pi$
$332$		0			0
$333$	−2.20204	−	0.778539i	−0.120671	−	0.0426637i
$334$		0			0
$335$	−8.44949			−0.461645
$336$		0			0
$337$	−3.15153	+	1.81954i	−0.171675	+	0.0991165i	−0.583375	−	0.812203i	$-0.698268\pi$
$337$	−3.15153	+	1.81954i	−0.171675	+	0.0991165i	0.411701	+	0.911319i	$0.364935\pi$
$338$		0			0
$339$	0.797959	+	1.12848i	0.0433392	+	0.0612909i
$340$		0			0
$341$	1.34847			0.0730237
$342$		0			0
$343$	−25.7980			−1.39296
$344$		0			0
$345$	10.0000	+	14.1421i	0.538382	+	0.761387i
$346$		0			0
$347$	5.72474	−	3.30518i	0.307320	−	0.177432i	−0.338406	−	0.941000i	$-0.609888\pi$
$347$	5.72474	−	3.30518i	0.307320	−	0.177432i	0.645727	+	0.763569i	$0.276555\pi$
$348$		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
$351$	−17.4495	−	4.41761i	−0.931385	−	0.235795i
$352$		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
$357$	44.0454	+	20.2918i	2.33113	+	1.07396i
$358$		0			0
$359$	−20.8207	+	12.0208i	−1.09887	+	0.634434i	−0.935925	−	0.352200i	$-0.885434\pi$
$359$	−20.8207	+	12.0208i	−1.09887	+	0.634434i	−0.162948	+	0.986635i	$0.552100\pi$
$360$		0			0
$361$	15.8485	+	10.4798i	0.834130	+	0.551568i
$362$		0			0
$363$	−10.8990	−	15.4135i	−0.572048	−	0.808998i
$364$		0			0
$365$	−13.2247	−	7.63531i	−0.692215	−	0.399650i
$366$		0			0
$367$	−11.6742	+	20.2204i	−0.609390	+	1.05549i	0.381951	+	0.924183i	$0.375252\pi$
$367$	−11.6742	+	20.2204i	−0.609390	+	1.05549i	−0.991341	+	0.131312i	$0.958081\pi$
$368$		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	$0.229032\pi$
$373$			25.4558i			1.31805i	−0.752119	+	0.659027i	$0.770968\pi$
$374$		0			0
$375$	−16.0000	+	11.3137i	−0.826236	+	0.584237i
$376$		0			0
$377$	−7.34847	+	4.24264i	−0.378465	+	0.218507i
$378$		0			0
$379$			15.4135i			0.791738i	0.918307	+	0.395869i	$0.129556\pi$
$379$			15.4135i			0.791738i	−0.918307	+	0.395869i	$0.870444\pi$
$380$		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	$-0.0366150\pi$
$383$	7.77526	+	13.4671i	0.397297	+	0.688139i	−0.596094	+	0.802914i	$0.703282\pi$
$384$		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	$-0.0994912\pi$
$389$	22.8990	+	13.2207i	1.16102	+	0.670318i	0.209475	+	0.977814i	$0.432824\pi$
$390$		0			0
$391$	44.4949			2.25020
$392$		0			0
$393$	−34.6464	−	15.9617i	−1.74768	−	0.805160i
$394$		0			0
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$		0			0
$397$	−4.67423	−	8.09601i	−0.234593	−	0.406327i	0.724561	−	0.689210i	$-0.242042\pi$
$397$	−4.67423	−	8.09601i	−0.234593	−	0.406327i	−0.959154	+	0.282883i	$0.908709\pi$
$398$		0			0
$399$	10.6742	+	31.8519i	0.534380	+	1.59459i
$400$		0			0
$401$	−6.39898	−	11.0834i	−0.319550	−	0.553476i	0.660844	−	0.750523i	$-0.270198\pi$
$401$	−6.39898	−	11.0834i	−0.319550	−	0.553476i	−0.980394	+	0.197047i	$0.936865\pi$
$402$		0			0
$403$	7.34847	−	12.7279i	0.366053	−	0.634023i
$404$		0			0
$405$	12.5732	+	1.97846i	0.624768	+	0.0983103i
$406$		0			0
$407$	0.247449			0.0122656
$408$		0			0
$409$	17.8485	+	10.3048i	0.882550	+	0.509540i	0.871498	−	0.490398i	$-0.163149\pi$
$409$	17.8485	+	10.3048i	0.882550	+	0.509540i	0.0110517	+	0.999939i	$0.496482\pi$
$410$		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	−0.974660	−	0.223690i	$-0.928190\pi$
$421$	−26.0227	+	15.0242i	−1.26827	+	0.732235i	−0.293609	+	0.955926i	$0.594856\pi$
$422$		0			0
$423$	14.6742	−	12.5457i	0.713486	−	0.609994i
$424$		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	−0.140029	−	0.990147i	$-0.544720\pi$
$431$	16.3485	−	28.3164i	0.787478	−	1.36395i	0.927507	−	0.373805i	$-0.121947\pi$
$432$		0			0
$433$	11.6969	+	6.75323i	0.562119	+	0.324540i	0.753996	−	0.656880i	$-0.228124\pi$
$433$	11.6969	+	6.75323i	0.562119	+	0.324540i	−0.191877	+	0.981419i	$0.561457\pi$
$434$		0			0
$435$	4.89898	−	3.46410i	0.234888	−	0.166091i
$436$		0			0
$437$	21.1237	+	22.4452i	1.01048	+	1.07370i
$438$		0			0
$439$	2.32577	−	1.34278i	0.111003	−	0.0640875i	−0.443471	−	0.896289i	$-0.646253\pi$
$439$	2.32577	−	1.34278i	0.111003	−	0.0640875i	0.554474	+	0.832201i	$0.312920\pi$
$440$		0			0
$441$	−12.7980	+	36.1981i	−0.609427	+	1.72372i
$442$		0			0
$443$	25.3207	+	14.6189i	1.20302	+	0.694564i	0.961226	−	0.275763i	$-0.0889304\pi$
$443$	25.3207	+	14.6189i	1.20302	+	0.694564i	0.241795	+	0.970327i	$0.422264\pi$
$444$		0			0
$445$		−	23.8988i		−	1.13291i
$446$		0			0
$447$	7.67423	+	3.53553i	0.362979	+	0.167225i
$448$		0			0
$449$	−11.2020			−0.528657			−0.264329	−	0.964433i	$-0.585150\pi$
$449$	−11.2020			−0.528657			−0.264329	+	0.964433i	$0.585150\pi$
$450$		0			0
$451$	0.825765	−	0.476756i	0.0388838	−	0.0224496i
$452$		0			0
$453$	25.5959	−	18.0990i	1.20260	−	0.850367i
$454$		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
$459$	22.7980	−	23.4381i	1.06412	−	1.09400i
$460$		0			0
$461$	8.75255	−	5.05329i	0.407647	−	0.235355i	−0.282131	−	0.959376i	$-0.591041\pi$
$461$	8.75255	−	5.05329i	0.407647	−	0.235355i	0.689778	+	0.724021i	$0.257708\pi$
$462$		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
$465$	−4.34847	+	9.43879i	−0.201655	+	0.437714i
$466$		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
$471$	13.5505	−	29.4128i	0.624375	−	1.35527i
$472$		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
$477$	2.14643	+	2.51059i	0.0982782	+	0.114952i
$478$		0			0
$479$	35.1464	+	20.2918i	1.60588	+	0.927156i	0.990278	+	0.139099i	$0.0444208\pi$
$479$	35.1464	+	20.2918i	1.60588	+	0.927156i	0.615603	+	0.788057i	$0.288913\pi$
$480$		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	$-0.877713\pi$
$487$		−	16.5420i		−	0.749588i	0.927108	−	0.374794i	$-0.122287\pi$
$488$		0			0
$489$	3.65153	+	5.16404i	0.165128	+	0.233526i
$490$		0			0
$491$	−4.10102	+	2.36773i	−0.185076	+	0.106854i	−0.589676	−	0.807640i	$-0.700744\pi$
$491$	−4.10102	+	2.36773i	−0.185076	+	0.106854i	0.404599	+	0.914494i	$0.367411\pi$
$492$		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	0.893157	−	0.449745i	$-0.148485\pi$
$499$	1.27526	+	2.20881i	0.0570883	+	0.0988798i	−0.836069	+	0.548624i	$0.815152\pi$
$500$		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	$-0.220598\pi$
$503$	13.4722	+	7.77817i	0.600695	+	0.346812i	−0.168620	+	0.985681i	$0.553931\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$		0			0
$507$	−0.724745	+	1.57313i	−0.0321870	+	0.0698653i
$508$		0			0
$509$	20.6969	−	35.8481i	0.917376	−	1.58894i	0.113990	−	0.993482i	$-0.463637\pi$
$509$	20.6969	−	35.8481i	0.917376	−	1.58894i	0.803385	−	0.595459i	$-0.203030\pi$
$510$		0			0
$511$	−24.0227	−	41.6085i	−1.06270	−	1.84065i
$512$		0			0
$513$	22.6464	+	0.373215i	0.999864	+	0.0164779i
$514$		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
$519$	−7.89898	+	17.1455i	−0.346727	+	0.752605i
$520$		0			0
$521$	16.1010			0.705399			0.352699	−	0.935737i	$-0.385264\pi$
$521$	16.1010			0.705399			0.352699	+	0.935737i	$0.385264\pi$
$522$		0			0
$523$	−23.6969	−	13.6814i	−1.03619	−	0.598247i	−0.117442	−	0.993080i	$-0.537469\pi$
$523$	−23.6969	−	13.6814i	−1.03619	−	0.598247i	−0.918753	+	0.394832i	$0.870803\pi$
$524$		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
$537$	22.3485	+	31.6055i	0.964408	+	1.36388i
$538$		0			0
$539$		−	4.06767i		−	0.175207i
$540$		0			0
$541$	9.34847	−	16.1920i	0.401922	−	0.696149i	−0.592036	−	0.805912i	$-0.701676\pi$
$541$	9.34847	−	16.1920i	0.401922	−	0.696149i	0.993958	+	0.109762i	$0.0350089\pi$
$542$		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	−0.184958	−	0.982746i	$-0.559215\pi$
$547$	−26.3939	−	15.2385i	−1.12852	−	0.651552i	−0.943562	+	0.331195i	$0.892548\pi$
$548$		0			0
$549$	12.5732	+	14.7064i	0.536612	+	0.627653i
$550$		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
$555$	−0.797959	+	1.73205i	−0.0338715	+	0.0735215i
$556$		0			0
$557$	24.2474	+	13.9993i	1.02740	+	0.593168i	0.916238	−	0.400634i	$-0.131210\pi$
$557$	24.2474	+	13.9993i	1.02740	+	0.593168i	0.111159	+	0.993803i	$0.464544\pi$
$558$		0			0
$559$		−	3.11416i		−	0.131715i
$560$		0			0
$561$	−1.44949	+	3.14626i	−0.0611975	+	0.132835i
$562$		0			0
$563$	−22.8434			−0.962733			−0.481367	−	0.876519i	$-0.659859\pi$
$563$	−22.8434			−0.962733			−0.481367	+	0.876519i	$0.659859\pi$
$564$		0			0
$565$	0.977296	−	0.564242i	0.0411152	−	0.0237378i
$566$		0			0
$567$	31.1464	+	25.1701i	1.30803	+	1.05705i
$568$		0			0
$569$	−34.2929			−1.43763			−0.718816	−	0.695201i	$-0.755315\pi$
$569$	−34.2929			−1.43763			−0.718816	+	0.695201i	$0.755315\pi$
$570$		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
$573$	27.5959	−	19.5133i	1.15284	−	0.815178i
$574$		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
$579$	13.8990	+	6.40329i	0.577622	+	0.266111i
$580$		0			0
$581$			63.0682i			2.61651i
$582$		0			0
$583$	−0.303062	−	0.174973i	−0.0125515	−	0.00724663i
$584$		0			0
$585$	−4.89898	+	13.8564i	−0.202548	+	0.572892i
$586$		0			0
$587$	−4.10102	+	2.36773i	−0.169267	+	0.0977265i	−0.582240	−	0.813017i	$-0.697824\pi$
$587$	−4.10102	+	2.36773i	−0.169267	+	0.0977265i	0.412973	+	0.910743i	$0.364490\pi$
$588$		0			0
$589$	−5.32577	+	17.7098i	−0.219444	+	0.729719i
$590$		0			0
$591$	0.696938	−	0.492810i	0.0286682	−	0.0202715i
$592$		0			0
$593$	24.0959	+	13.9118i	0.989501	+	0.571289i	0.905125	−	0.425145i	$-0.139777\pi$
$593$	24.0959	+	13.9118i	0.989501	+	0.571289i	0.0843757	+	0.996434i	$0.473110\pi$
$594$		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	−0.398038	−	0.917369i	$-0.630309\pi$
$599$	14.5732	−	25.2415i	0.595445	−	1.03134i	0.993484	−	0.113973i	$-0.0363577\pi$
$600$		0			0
$601$		−	31.0019i		−	1.26460i	−0.774725	−	0.632298i	$-0.782112\pi$
$601$		−	31.0019i		−	1.26460i	0.774725	−	0.632298i	$-0.217888\pi$
$602$		0			0
$603$	−13.6237	+	11.6476i	−0.554801	+	0.474327i
$604$		0			0
$605$	−13.3485	+	7.70674i	−0.542692	+	0.313324i
$606$		0			0
$607$		−	36.9766i		−	1.50084i	−0.660964	−	0.750418i	$-0.729852\pi$
$607$		−	36.9766i		−	1.50084i	0.660964	−	0.750418i	$-0.270148\pi$
$608$		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	−0.996612	−	0.0822481i	$-0.973790\pi$
$613$	−14.1010	−	24.4237i	−0.569535	−	0.986463i	0.427077	−	0.904215i	$-0.359543\pi$
$614$		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	$-0.430650\pi$
$617$	−12.9495	−	7.47639i	−0.521327	−	0.300988i	−0.737477	+	0.675372i	$0.763983\pi$
$618$		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
$621$	35.6186	+	9.01742i	1.42933	+	0.361856i
$622$		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
$627$	−2.27526	+	0.762485i	−0.0908649	+	0.0304507i
$628$		0			0
$629$	2.44949	+	4.24264i	0.0976676	+	0.169165i
$630$		0			0
$631$	−4.87628	+	8.44596i	−0.194121	+	0.336228i	−0.946612	−	0.322375i	$-0.895519\pi$
$631$	−4.87628	+	8.44596i	−0.194121	+	0.336228i	0.752491	+	0.658603i	$0.228852\pi$
$632$		0			0
$633$	24.2474	+	11.1708i	0.963750	+	0.444001i
$634$		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	−0.985490	−	0.169736i	$-0.945708\pi$
$641$	−16.1969	−	28.0539i	−0.639741	−	1.10806i	0.345749	−	0.938327i	$-0.387625\pi$
$642$		0			0
$643$	−12.0732	−	20.9114i	−0.476121	−	0.824666i	0.523505	−	0.852023i	$-0.324624\pi$
$643$	−12.0732	−	20.9114i	−0.476121	−	0.824666i	−0.999626	+	0.0273569i	$0.991291\pi$
$644$		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
$651$	−26.6969	+	18.8776i	−1.04634	+	0.739871i
$652$		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	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$		0			0
$661$	−25.7196	−	14.8492i	−1.00038	−	0.577569i	−0.0920180	−	0.995757i	$-0.529332\pi$
$661$	−25.7196	−	14.8492i	−1.00038	−	0.577569i	−0.908360	+	0.418189i	$0.862665\pi$
$662$		0			0
$663$	21.7980	+	30.8270i	0.846563	+	1.19722i
$664$		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
$669$	−15.1237	−	6.96753i	−0.584717	−	0.269380i
$670$		0			0
$671$	−1.77526	−	1.02494i	−0.0685330	−	0.0395675i
$672$		0			0
$673$			3.46410i			0.133531i	0.997769	+	0.0667657i	$0.0212680\pi$
$673$			3.46410i			0.133531i	−0.997769	+	0.0667657i	$0.978732\pi$
$674$		0			0
$675$	−3.82577	+	15.1117i	−0.147254	+	0.581650i
$676$		0			0
$677$	3.30306			0.126947			0.0634735	−	0.997984i	$-0.479782\pi$
$677$	3.30306			0.126947			0.0634735	+	0.997984i	$0.479782\pi$
$678$		0			0
$679$	52.7196	−	30.4377i	2.02319	−	1.16809i
$680$		0			0
$681$	−5.44949	−	7.70674i	−0.208825	−	0.295323i
$682$		0			0
$683$	−41.3939			−1.58389			−0.791946	−	0.610591i	$-0.790932\pi$
$683$	−41.3939			−1.58389			−0.791946	+	0.610591i	$0.790932\pi$
$684$		0			0
$685$	−10.4495			−0.399254
$686$		0			0
$687$	8.89898	+	12.5851i	0.339517	+	0.480150i
$688$		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
$693$	−4.00000	−	1.41421i	−0.151947	−	0.0537215i
$694$		0			0
$695$			0.492810i			0.0186933i
$696$		0			0
$697$	16.3485	+	9.43879i	0.619242	+	0.357520i
$698$		0			0
$699$	−10.1742	−	4.68729i	−0.384825	−	0.177290i
$700$		0			0
$701$	−8.57321	+	4.94975i	−0.323806	+	0.186949i	−0.653088	−	0.757282i	$-0.726527\pi$
$701$	−8.57321	+	4.94975i	−0.323806	+	0.186949i	0.329282	+	0.944232i	$0.393193\pi$
$702$		0			0
$703$	−0.977296	+	3.24980i	−0.0368594	+	0.122569i
$704$		0			0
$705$	−9.10102	−	12.8708i	−0.342764	−	0.484742i
$706$		0			0
$707$	−38.1464	−	22.0239i	−1.43464	−	0.828292i
$708$		0			0
$709$	1.32577	−	2.29629i	0.0497902	−	0.0862391i	−0.840056	−	0.542499i	$-0.817478\pi$
$709$	1.32577	−	2.29629i	0.0497902	−	0.0862391i	0.889846	+	0.456260i	$0.150811\pi$
$710$		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
$717$	10.2020	−	7.21393i	0.381002	−	0.269409i
$718$		0			0
$719$	−8.14643	+	4.70334i	−0.303811	+	0.175405i	−0.644153	−	0.764896i	$-0.722790\pi$
$719$	−8.14643	+	4.70334i	−0.303811	+	0.175405i	0.340343	+	0.940301i	$0.389457\pi$
$720$		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	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$		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
$735$	28.4722	+	13.1172i	1.05021	+	0.483835i
$736$		0			0
$737$	0.949490	−	1.64456i	0.0349749	−	0.0605783i
$738$		0			0
$739$	4.82577	+	8.35847i	0.177519	+	0.307471i	0.941030	−	0.338323i	$-0.109860\pi$
$739$	4.82577	+	8.35847i	0.177519	+	0.307471i	−0.763511	+	0.645794i	$0.776526\pi$
$740$		0			0
$741$	−5.20204	+	25.6308i	−0.191102	+	0.941572i
$742$		0			0
$743$	−9.67423	−	16.7563i	−0.354913	−	0.614728i	0.632190	−	0.774814i	$-0.282156\pi$
$743$	−9.67423	−	16.7563i	−0.354913	−	0.614728i	−0.987103	+	0.160086i	$0.948823\pi$
$744$		0			0
$745$	3.44949	−	5.97469i	0.126380	−	0.218896i
$746$		0			0
$747$	40.0908	+	14.1742i	1.46685	+	0.518608i
$748$		0			0
$749$	−21.7980			−0.796480
$750$		0			0
$751$	11.6969	+	6.75323i	0.426827	+	0.246429i	0.697994	−	0.716103i	$-0.254076\pi$
$751$	11.6969	+	6.75323i	0.426827	+	0.246429i	−0.271167	+	0.962532i	$0.587409\pi$
$752$		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	0.634235	−	0.773140i	$-0.281315\pi$
$757$	−9.69694	−	16.7956i	−0.352441	−	0.610446i	−0.986677	+	0.162694i	$0.947982\pi$
$758$		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
$765$	−17.3485	−	20.2918i	−0.627235	−	0.733652i
$766$		0			0
$767$		−	22.6916i		−	0.819347i
$768$		0			0
$769$	17.7980	−	30.8270i	0.641811	−	1.11165i	−0.343217	−	0.939256i	$-0.611517\pi$
$769$	17.7980	−	30.8270i	0.641811	−	1.11165i	0.985028	−	0.172393i	$-0.0551499\pi$
$770$		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	$-0.847360\pi$
$773$	−1.22474	+	2.12132i	−0.0440510	+	0.0762986i	0.843159	+	0.537664i	$0.180693\pi$
$774$		0			0
$775$	−11.0227	−	6.36396i	−0.395947	−	0.228600i
$776$		0			0
$777$	−4.89898	+	3.46410i	−0.175750	+	0.124274i
$778$		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
$783$	3.12372	−	12.3387i	0.111633	−	0.440947i
$784$		0			0
$785$	−22.8990	−	13.2207i	−0.817300	−	0.471868i
$786$		0			0
$787$			17.9241i			0.638924i	0.947599	+	0.319462i	$0.103502\pi$
$787$			17.9241i			0.638924i	−0.947599	+	0.319462i	$0.896498\pi$
$788$		0			0
$789$	−18.5732	−	8.55671i	−0.661224	−	0.304627i
$790$		0			0
$791$	3.55051			0.126242
$792$		0			0
$793$	−19.3485	+	11.1708i	−0.687084	+	0.396688i
$794$		0			0
$795$	2.20204	−	1.55708i	0.0780983	−	0.0552239i
$796$		0			0
$797$	−22.6515			−0.802358			−0.401179	−	0.916000i	$-0.631400\pi$
$797$	−22.6515			−0.802358			−0.401179	+	0.916000i	$0.631400\pi$
$798$		0			0
$799$	−40.4949			−1.43261
$800$		0			0
$801$	−32.9444	−	38.5337i	−1.16403	−	1.36152i
$802$		0			0
$803$	2.97219	−	1.71600i	0.104886	−	0.0605562i
$804$		0			0
$805$	44.4949			1.56824
$806$		0			0
$807$	17.7526	−	38.5337i	0.624919	−	1.35645i
$808$		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	0.446402	−	0.894832i	$-0.352705\pi$
$811$	−3.00000	−	1.73205i	−0.105344	−	0.0608205i	−0.551746	+	0.834012i	$0.686038\pi$
$812$		0			0
$813$	17.4268	−	37.8266i	0.611184	−	1.32664i
$814$		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
$819$	−35.1464	+	30.0484i	−1.22812	+	1.04998i
$820$		0			0
$821$	0.550510	+	0.317837i	0.0192129	+	0.0110926i	0.509576	−	0.860426i	$-0.329802\pi$
$821$	0.550510	+	0.317837i	0.0192129	+	0.0110926i	−0.490363	+	0.871518i	$0.663136\pi$
$822$		0			0
$823$	−9.65153	+	16.7169i	−0.336431	+	0.582716i	−0.983759	−	0.179496i	$-0.942553\pi$
$823$	−9.65153	+	16.7169i	−0.336431	+	0.582716i	0.647327	+	0.762212i	$0.275887\pi$
$824$		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	$-0.815351\pi$
$827$	1.62372	−	2.81237i	0.0564624	−	0.0977958i	0.892875	+	0.450304i	$0.148685\pi$
$828$		0			0
$829$			36.1981i			1.25721i	0.777724	+	0.628606i	$0.216374\pi$
$829$			36.1981i			1.25721i	−0.777724	+	0.628606i	$0.783626\pi$
$830$		0			0
$831$	4.24745	+	6.00680i	0.147342	+	0.208374i
$832$		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	$-0.174077\pi$
$839$	−0.674235	−	1.16781i	−0.0232772	−	0.0403172i	−0.877429	+	0.479706i	$0.840743\pi$
$840$		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
$849$	−3.29796	+	7.15855i	−0.113186	+	0.245681i
$850$		0			0
$851$	−2.75255	+	4.76756i	−0.0943562	+	0.163430i
$852$		0			0
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$		0			0
$855$	2.00000	−	18.3848i	0.0683986	−	0.628746i
$856$		0			0
$857$	11.2980	+	19.5686i	0.385931	+	0.668452i	0.991898	−	0.127038i	$-0.0405470\pi$
$857$	11.2980	+	19.5686i	0.385931	+	0.668452i	−0.605967	+	0.795490i	$0.707214\pi$
$858$		0			0
$859$	−22.4217	+	38.8355i	−0.765018	+	1.32505i	0.175219	+	0.984529i	$0.443937\pi$
$859$	−22.4217	+	38.8355i	−0.765018	+	1.32505i	−0.940237	+	0.340521i	$0.889397\pi$
$860$		0			0
$861$	−9.67423	+	20.9989i	−0.329697	+	0.715641i
$862$		0			0
$863$	31.3485			1.06711			0.533557	−	0.845764i	$-0.320855\pi$
$863$	31.3485			1.06711			0.533557	+	0.845764i	$0.320855\pi$
$864$		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	−0.493720	−	0.869621i	$-0.664363\pi$
$877$	0.371173	−	0.214297i	0.0125336	−	0.00723629i	0.506254	+	0.862385i	$0.331030\pi$
$878$		0			0
$879$	−4.65153	−	6.57826i	−0.156892	−	0.221879i
$880$		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	−0.239744	−	0.970836i	$-0.577063\pi$
$883$	21.4217	−	37.1034i	0.720897	−	1.24863i	0.960641	−	0.277794i	$-0.0896033\pi$
$884$		0			0
$885$	1.47219	+	15.9777i	0.0494872	+	0.537085i
$886$		0			0
$887$	−16.0454	+	27.7915i	−0.538752	+	0.933146i	0.460220	+	0.887805i	$0.347771\pi$
$887$	−16.0454	+	27.7915i	−0.538752	+	0.933146i	−0.998972	+	0.0453408i	$0.985563\pi$
$888$		0			0
$889$	−40.0454	−	23.1202i	−1.34308	−	0.775428i
$890$		0			0
$891$	−1.79796	+	2.22486i	−0.0602339	+	0.0745356i
$892$		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
$897$	−17.7526	+	38.5337i	−0.592740	+	1.28660i
$898$		0			0
$899$	9.00000	+	5.19615i	0.300167	+	0.173301i
$900$		0			0
$901$		−	6.92820i		−	0.230812i
$902$		0			0
$903$	−2.89898	+	6.29253i	−0.0964720	+	0.209402i
$904$		0			0
$905$	−18.4949			−0.614791
$906$		0			0
$907$	−47.9166	+	27.6647i	−1.59104	+	0.918590i	−0.597916	+	0.801559i	$0.704004\pi$
$907$	−47.9166	+	27.6647i	−1.59104	+	0.918590i	−0.993128	+	0.117031i	$0.962662\pi$
$908$		0			0
$909$	−22.5732	+	19.2990i	−0.748706	+	0.640106i
$910$		0			0
$911$	−43.3485			−1.43620			−0.718099	−	0.695941i	$-0.754988\pi$
$911$	−43.3485			−1.43620			−0.718099	+	0.695941i	$0.754988\pi$
$912$		0			0
$913$	−4.50510			−0.149097
$914$		0			0
$915$	12.8990	−	9.12096i	0.426427	−	0.301529i
$916$		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
$921$	−6.39898	−	2.94802i	−0.210854	−	0.0971406i
$922$		0			0
$923$		−	20.7846i		−	0.684134i
$924$		0			0
$925$	−2.02270	−	1.16781i	−0.0665061	−	0.0383973i
$926$		0			0
$927$	33.7980	+	11.9494i	1.11007	+	0.392469i
$928$		0			0
$929$	−15.0959	+	8.71563i	−0.495281	+	0.285951i	−0.726763	−	0.686889i	$-0.758976\pi$
$929$	−15.0959	+	8.71563i	−0.495281	+	0.285951i	0.231482	+	0.972839i	$0.425643\pi$
$930$		0			0
$931$	53.4217	+	16.0652i	1.75082	+	0.526516i
$932$		0			0
$933$	−22.0000	+	15.5563i	−0.720248	+	0.509292i
$934$		0			0
$935$	2.44949	+	1.41421i	0.0801069	+	0.0462497i
$936$		0			0
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	−0.990430	−	0.138017i	$-0.955927\pi$
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	0.614741	+	0.788729i	$0.289260\pi$
$938$		0			0
$939$	−32.7702	+	3.01945i	−1.06941	+	0.0985362i
$940$		0			0
$941$	27.4949	−	47.6226i	0.896308	−	1.55245i	0.0641307	−	0.997942i	$-0.479573\pi$
$941$	27.4949	−	47.6226i	0.896308	−	1.55245i	0.832177	−	0.554510i	$-0.187094\pi$
$942$		0			0
$943$			21.2132i			0.690797i
$944$		0			0
$945$	22.7980	−	23.4381i	0.741618	−	0.762440i
$946$		0			0
$947$	−11.4495	+	6.61037i	−0.372058	+	0.214808i	−0.674357	−	0.738405i	$-0.735579\pi$
$947$	−11.4495	+	6.61037i	−0.372058	+	0.214808i	0.302299	+	0.953213i	$0.402246\pi$
$948$		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	$-0.139816\pi$
$953$	2.60102	+	4.50510i	0.0842553	+	0.145934i	−0.820818	+	0.571189i	$0.806482\pi$
$954$		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
$963$	−4.89898	+	13.8564i	−0.157867	+	0.446516i
$964$		0			0
$965$	6.24745	−	10.8209i	0.201112	−	0.348337i
$966$		0			0
$967$	3.69694	+	6.40329i	0.118886	+	0.205916i	0.919326	−	0.393496i	$-0.128735\pi$
$967$	3.69694	+	6.40329i	0.118886	+	0.205916i	−0.800441	+	0.599412i	$0.795401\pi$
$968$		0			0
$969$	−35.5959	−	31.4626i	−1.14351	−	1.01073i
$970$		0			0
$971$	13.0732	+	22.6435i	0.419539	+	0.726664i	0.995893	−	0.0905368i	$-0.0288583\pi$
$971$	13.0732	+	22.6435i	0.419539	+	0.726664i	−0.576354	+	0.817200i	$0.695525\pi$
$972$		0			0
$973$	−0.775255	+	1.34278i	−0.0248535	+	0.0430476i
$974$		0			0
$975$	−16.3485	−	7.53177i	−0.523570	−	0.241210i
$976$		0			0
$977$	−49.8990			−1.59641			−0.798205	−	0.602386i	$-0.794217\pi$
$977$	−49.8990			−1.59641			−0.798205	+	0.602386i	$0.794217\pi$
$978$		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	−0.991368	−	0.131109i	$-0.958146\pi$
$983$	−19.1010	−	33.0839i	−0.609228	−	1.05521i	0.382140	−	0.924104i	$-0.375187\pi$
$984$		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	−0.996285	−	0.0861200i	$-0.972553\pi$
$991$	−44.6969	+	25.8058i	−1.41985	+	0.819748i	−0.423560	+	0.905868i	$0.639220\pi$
$992$		0			0
$993$	−20.9444	+	14.8099i	−0.664650	+	0.469979i
$994$		0			0
$995$			9.75663i			0.309306i
$996$		0			0
$997$	−29.7196	+	51.4759i	−0.941231	+	1.63026i	−0.178102	+	0.984012i	$0.556996\pi$
$997$	−29.7196	+	51.4759i	−0.941231	+	1.63026i	−0.763128	+	0.646247i	$0.776338\pi$
$998$		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.g.449.1		4
3.2	odd	2		912.2.bn.h.449.2		4
4.3	odd	2		114.2.h.e.107.2	yes	4
12.11	even	2		114.2.h.f.107.1	yes	4
19.8	odd	6		912.2.bn.h.65.2		4
57.8	even	6	inner	912.2.bn.g.65.2		4
76.27	even	6		114.2.h.f.65.1	yes	4
228.179	odd	6		114.2.h.e.65.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.e.65.1	✓	4	228.179	odd	6
114.2.h.e.107.2	yes	4	4.3	odd	2
114.2.h.f.65.1	yes	4	76.27	even	6
114.2.h.f.107.1	yes	4	12.11	even	2
912.2.bn.g.65.2		4	57.8	even	6	inner
912.2.bn.g.449.1		4	1.1	even	1	trivial
912.2.bn.h.65.2		4	19.8	odd	6
912.2.bn.h.449.2		4	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.41421i) q^{3} +(-1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.41421i) q^{3} +(-1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.00000 + 2.82843i) q^{9} -0.317837i q^{11} +(-3.00000 - 1.73205i) q^{13} +(2.22474 + 1.02494i) q^{15} +(5.44949 - 3.14626i) q^{17} +(4.17423 + 1.25529i) q^{19} +(4.44949 + 6.29253i) q^{21} +(6.12372 + 3.53553i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 - 1.41421i) q^{27} +(1.22474 - 2.12132i) q^{29} +4.24264i q^{31} +(-0.449490 + 0.317837i) q^{33} +(5.44949 - 3.14626i) q^{35} +0.778539i q^{37} +(0.550510 + 5.97469i) q^{39} +(1.50000 + 2.59808i) q^{41} +(0.449490 + 0.778539i) q^{43} +(-0.775255 - 4.17121i) q^{45} +(-5.57321 - 3.21770i) q^{47} +12.7980 q^{49} +(-9.89898 - 4.56048i) q^{51} +(0.550510 - 0.953512i) q^{53} +(0.224745 + 0.389270i) q^{55} +(-2.39898 - 7.15855i) q^{57} +(3.27526 + 5.67291i) q^{59} +(3.22474 - 5.58542i) q^{61} +(4.44949 - 12.5851i) q^{63} +4.89898 q^{65} +(5.17423 + 2.98735i) q^{67} +(-1.12372 - 12.1958i) q^{69} +(3.00000 + 5.19615i) q^{71} +(5.39898 + 9.35131i) q^{73} +(5.17423 - 0.476756i) q^{75} +1.41421i q^{77} +(-7.34847 + 4.24264i) q^{79} +(-7.00000 - 5.65685i) q^{81} -14.1742i q^{83} +(-4.44949 + 7.70674i) q^{85} +(-4.22474 + 0.389270i) q^{87} +(-8.44949 + 14.6349i) q^{89} +(13.3485 + 7.70674i) q^{91} +(6.00000 - 4.24264i) q^{93} +(-6.00000 + 1.41421i) q^{95} +(-11.8485 + 6.84072i) q^{97} +(0.898979 + 0.317837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 8 * q^7 - 4 * q^9	\( 4 q - 4 q^{3} - 8 q^{7} - 4 q^{9} - 12 q^{13} + 4 q^{15} + 12 q^{17} + 2 q^{19} + 8 q^{21} - 6 q^{25} + 20 q^{27} + 8 q^{33} + 12 q^{35} + 12 q^{39} + 6 q^{41} - 8 q^{43} - 8 q^{45} + 12 q^{47} + 12 q^{49} - 20 q^{51} + 12 q^{53} - 4 q^{55} + 10 q^{57} + 18 q^{59} + 8 q^{61} + 8 q^{63} + 6 q^{67} + 20 q^{69} + 12 q^{71} + 2 q^{73} + 6 q^{75} - 28 q^{81} - 8 q^{85} - 12 q^{87} - 24 q^{89} + 24 q^{91} + 24 q^{93} - 24 q^{95} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 8 * q^7 - 4 * q^9 - 12 * q^13 + 4 * q^15 + 12 * q^17 + 2 * q^19 + 8 * q^21 - 6 * q^25 + 20 * q^27 + 8 * q^33 + 12 * q^35 + 12 * q^39 + 6 * q^41 - 8 * q^43 - 8 * q^45 + 12 * q^47 + 12 * q^49 - 20 * q^51 + 12 * q^53 - 4 * q^55 + 10 * q^57 + 18 * q^59 + 8 * q^61 + 8 * q^63 + 6 * q^67 + 20 * q^69 + 12 * q^71 + 2 * q^73 + 6 * q^75 - 28 * q^81 - 8 * q^85 - 12 * q^87 - 24 * q^89 + 24 * q^91 + 24 * q^93 - 24 * q^95 - 18 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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