LMFDB - Embedded newform 912.2.bn.o.65.6

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.6
Root			$1.25083 - 1.19809i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.o.449.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25083 + 1.19809i) q^{3} +(-1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(0.129140 + 2.99722i) q^{9} +O(q^{10})$	\(q+(1.25083 + 1.19809i) q^{3} +(-1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(0.129140 + 2.99722i) q^{9} -4.73011i q^{11} +(2.73150 - 1.57703i) q^{13} +(-0.729951 - 2.50703i) q^{15} +(3.56436 + 2.05788i) q^{17} +(-3.27583 - 2.87557i) q^{19} +(3.78760 + 3.62792i) q^{21} +(5.45589 - 3.14996i) q^{23} +(-1.36367 - 2.36194i) q^{25} +(-3.42942 + 3.90373i) q^{27} +(3.81794 + 6.61287i) q^{29} +7.27292i q^{31} +(5.66712 - 5.91655i) q^{33} +(-3.95335 - 2.28247i) q^{35} +1.63254i q^{37} +(5.30608 + 1.30000i) q^{39} +(-5.98623 + 10.3684i) q^{41} +(5.45011 - 9.43986i) q^{43} +(2.09061 - 4.01041i) q^{45} +(2.43127 - 1.40370i) q^{47} +2.16925 q^{49} +(1.99286 + 6.84449i) q^{51} +(-2.08557 - 3.61231i) q^{53} +(-3.56541 + 6.17546i) q^{55} +(-0.652293 - 7.52160i) q^{57} +(3.79395 - 6.57132i) q^{59} +(3.68771 + 6.38730i) q^{61} +(0.391044 + 9.07581i) q^{63} -4.75488 q^{65} +(2.81536 - 1.62545i) q^{67} +(10.5983 + 2.59661i) q^{69} +(-1.03794 + 1.79776i) q^{71} +(-1.24172 + 2.15072i) q^{73} +(1.12411 - 4.58818i) q^{75} -14.3231i q^{77} +(-5.72981 - 3.30811i) q^{79} +(-8.96665 + 0.774119i) q^{81} +12.7535i q^{83} +(-3.10233 - 5.37340i) q^{85} +(-3.14725 + 12.8458i) q^{87} +(-1.41608 - 2.45273i) q^{89} +(8.27121 - 4.77538i) q^{91} +(-8.71364 + 9.09717i) q^{93} +(2.10930 + 6.22347i) q^{95} +(-6.24590 - 3.60607i) q^{97} +(14.1772 - 0.610844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * 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
$3$	1.25083	+	1.19809i	0.722166	+	0.691720i
$3$	1.25083	+	1.19809i	0.722166	+	0.691720i
$4$		0			0
$5$	−1.30557	−	0.753769i	−0.583867	−	0.337096i	0.178802	−	0.983885i	$-0.442778\pi$
$5$	−1.30557	−	0.753769i	−0.583867	−	0.337096i	−0.762669	+	0.646790i	$0.776111\pi$
$6$		0			0
$7$	3.02808			1.14451			0.572253	−	0.820077i	$-0.306070\pi$
$7$	3.02808			1.14451			0.572253	+	0.820077i	$0.306070\pi$
$8$		0			0
$9$	0.129140	+	2.99722i	0.0430465	+	0.999073i
$10$		0			0
$11$		−	4.73011i		−	1.42618i	−0.701072	−	0.713091i	$-0.747295\pi$
$11$		−	4.73011i		−	1.42618i	0.701072	−	0.713091i	$-0.252705\pi$
$12$		0			0
$13$	2.73150	−	1.57703i	0.757583	−	0.437391i	−0.0708442	−	0.997487i	$-0.522569\pi$
$13$	2.73150	−	1.57703i	0.757583	−	0.437391i	0.828427	+	0.560097i	$0.189236\pi$
$14$		0			0
$15$	−0.729951	−	2.50703i	−0.188473	−	0.647311i
$16$		0			0
$17$	3.56436	+	2.05788i	0.864484	+	0.499110i	0.865511	−	0.500890i	$-0.166994\pi$
$17$	3.56436	+	2.05788i	0.864484	+	0.499110i	−0.00102753	+	0.999999i	$0.500327\pi$
$18$		0			0
$19$	−3.27583	−	2.87557i	−0.751527	−	0.659702i
$19$	−3.27583	−	2.87557i	−0.751527	−	0.659702i
$20$		0			0
$21$	3.78760	+	3.62792i	0.826522	+	0.791677i
$22$		0			0
$23$	5.45589	−	3.14996i	1.13763	−	0.656812i	0.191788	−	0.981436i	$-0.438571\pi$
$23$	5.45589	−	3.14996i	1.13763	−	0.656812i	0.945843	+	0.324625i	$0.105238\pi$
$24$		0			0
$25$	−1.36367	−	2.36194i	−0.272733	−	0.472388i
$26$		0			0
$27$	−3.42942	+	3.90373i	−0.659992	+	0.751272i
$28$		0			0
$29$	3.81794	+	6.61287i	0.708974	+	1.22798i	0.965238	+	0.261372i	$0.0841749\pi$
$29$	3.81794	+	6.61287i	0.708974	+	1.22798i	−0.256264	+	0.966607i	$0.582492\pi$
$30$		0			0
$31$			7.27292i			1.30625i	0.757248	+	0.653127i	$0.226543\pi$
$31$			7.27292i			1.30625i	−0.757248	+	0.653127i	$0.773457\pi$
$32$		0			0
$33$	5.66712	−	5.91655i	0.986518	−	1.02994i
$34$		0			0
$35$	−3.95335	−	2.28247i	−0.668238	−	0.385808i
$36$		0			0
$37$			1.63254i			0.268388i	0.990955	+	0.134194i	$0.0428445\pi$
$37$			1.63254i			0.268388i	−0.990955	+	0.134194i	$0.957155\pi$
$38$		0			0
$39$	5.30608	+	1.30000i	0.849653	+	0.208167i
$40$		0			0
$41$	−5.98623	+	10.3684i	−0.934891	+	1.61928i	−0.160064	+	0.987107i	$0.551170\pi$
$41$	−5.98623	+	10.3684i	−0.934891	+	1.61928i	−0.774827	+	0.632173i	$0.782163\pi$
$42$		0			0
$43$	5.45011	−	9.43986i	0.831134	−	1.43957i	−0.0660061	−	0.997819i	$-0.521026\pi$
$43$	5.45011	−	9.43986i	0.831134	−	1.43957i	0.897140	−	0.441747i	$-0.145641\pi$
$44$		0			0
$45$	2.09061	−	4.01041i	0.311650	−	0.597836i
$46$		0			0
$47$	2.43127	−	1.40370i	0.354638	−	0.204750i	−0.312088	−	0.950053i	$-0.601028\pi$
$47$	2.43127	−	1.40370i	0.354638	−	0.204750i	0.666726	+	0.745303i	$0.267695\pi$
$48$		0			0
$49$	2.16925			0.309892
$50$		0			0
$51$	1.99286	+	6.84449i	0.279056	+	0.958421i
$52$		0			0
$53$	−2.08557	−	3.61231i	−0.286475	−	0.496190i	0.686491	−	0.727139i	$-0.259150\pi$
$53$	−2.08557	−	3.61231i	−0.286475	−	0.496190i	−0.972966	+	0.230949i	$0.925817\pi$
$54$		0			0
$55$	−3.56541	+	6.17546i	−0.480759	+	0.832700i
$56$		0			0
$57$	−0.652293	−	7.52160i	−0.0863983	−	0.996261i
$58$		0			0
$59$	3.79395	−	6.57132i	0.493931	−	0.855513i	−0.506045	−	0.862507i	$-0.668893\pi$
$59$	3.79395	−	6.57132i	0.493931	−	0.855513i	0.999976	+	0.00699432i	$0.00222638\pi$
$60$		0			0
$61$	3.68771	+	6.38730i	0.472163	+	0.817810i	0.999493	−	0.0318509i	$-0.0101402\pi$
$61$	3.68771	+	6.38730i	0.472163	+	0.817810i	−0.527330	+	0.849661i	$0.676807\pi$
$62$		0			0
$63$	0.391044	+	9.07581i	0.0492670	+	1.14344i
$64$		0			0
$65$	−4.75488			−0.589770
$66$		0			0
$67$	2.81536	−	1.62545i	0.343951	−	0.198580i	−0.318067	−	0.948068i	$-0.603034\pi$
$67$	2.81536	−	1.62545i	0.343951	−	0.198580i	0.662018	+	0.749488i	$0.269700\pi$
$68$		0			0
$69$	10.5983	+	2.59661i	1.27589	+	0.312595i
$70$		0			0
$71$	−1.03794	+	1.79776i	−0.123180	+	0.213355i	−0.921020	−	0.389515i	$-0.872643\pi$
$71$	−1.03794	+	1.79776i	−0.123180	+	0.213355i	0.797840	+	0.602869i	$0.205976\pi$
$72$		0			0
$73$	−1.24172	+	2.15072i	−0.145332	+	0.251723i	−0.929497	−	0.368830i	$-0.879759\pi$
$73$	−1.24172	+	2.15072i	−0.145332	+	0.251723i	0.784164	+	0.620553i	$0.213092\pi$
$74$		0			0
$75$	1.12411	−	4.58818i	0.129802	−	0.529797i
$76$		0			0
$77$		−	14.3231i		−	1.63227i
$78$		0			0
$79$	−5.72981	−	3.30811i	−0.644654	−	0.372191i	0.141751	−	0.989902i	$-0.454727\pi$
$79$	−5.72981	−	3.30811i	−0.644654	−	0.372191i	−0.786405	+	0.617711i	$0.788060\pi$
$80$		0			0
$81$	−8.96665	+	0.774119i	−0.996294	+	0.0860132i
$82$		0			0
$83$			12.7535i			1.39987i	0.714204	+	0.699937i	$0.246789\pi$
$83$			12.7535i			1.39987i	−0.714204	+	0.699937i	$0.753211\pi$
$84$		0			0
$85$	−3.10233	−	5.37340i	−0.336495	−	0.582827i
$86$		0			0
$87$	−3.14725	+	12.8458i	−0.337421	+	1.37722i
$88$		0			0
$89$	−1.41608	−	2.45273i	−0.150105	−	0.259989i	0.781161	−	0.624330i	$-0.214628\pi$
$89$	−1.41608	−	2.45273i	−0.150105	−	0.259989i	−0.931266	+	0.364341i	$0.881294\pi$
$90$		0			0
$91$	8.27121	−	4.77538i	0.867058	−	0.500596i
$92$		0			0
$93$	−8.71364	+	9.09717i	−0.903563	+	0.943332i
$94$		0			0
$95$	2.10930	+	6.22347i	0.216409	+	0.638514i
$96$		0			0
$97$	−6.24590	−	3.60607i	−0.634175	−	0.366141i	0.148192	−	0.988959i	$-0.452655\pi$
$97$	−6.24590	−	3.60607i	−0.634175	−	0.366141i	−0.782367	+	0.622817i	$0.785988\pi$
$98$		0			0
$99$	14.1772	−	0.610844i	1.42486	−	0.0613921i
$100$		0			0
$101$	3.42875	−	1.97959i	0.341173	−	0.196976i	−0.319618	−	0.947547i	$-0.603554\pi$
$101$	3.42875	−	1.97959i	0.341173	−	0.196976i	0.660791	+	0.750570i	$0.270221\pi$
$102$		0			0
$103$			3.57546i			0.352301i	0.984363	+	0.176151i	$0.0563645\pi$
$103$			3.57546i			0.352301i	−0.984363	+	0.176151i	$0.943635\pi$
$104$		0			0
$105$	−2.21035	−	7.59146i	−0.215708	−	0.740851i
$106$		0			0
$107$	−15.0716			−1.45702			−0.728511	−	0.685034i	$-0.759787\pi$
$107$	−15.0716			−1.45702			−0.728511	+	0.685034i	$0.759787\pi$
$108$		0			0
$109$	0.544313	+	0.314259i	0.0521357	+	0.0301006i	0.525841	−	0.850583i	$-0.323751\pi$
$109$	0.544313	+	0.314259i	0.0521357	+	0.0301006i	−0.473706	+	0.880683i	$0.657084\pi$
$110$		0			0
$111$	−1.95594	+	2.04203i	−0.185649	+	0.193821i
$112$		0			0
$113$	−7.49162			−0.704752			−0.352376	−	0.935859i	$-0.614626\pi$
$113$	−7.49162			−0.704752			−0.352376	+	0.935859i	$0.614626\pi$
$114$		0			0
$115$	−9.49736			−0.885633
$116$		0			0
$117$	5.07946	+	7.98326i	0.469597	+	0.738053i
$118$		0			0
$119$	10.7931	+	6.23143i	0.989406	+	0.571234i
$120$		0			0
$121$	−11.3739			−1.03399
$122$		0			0
$123$	−19.9101	+	5.79708i	−1.79523	+	0.522705i
$124$		0			0
$125$			11.6492i			1.04194i
$126$		0			0
$127$	3.33995	−	1.92832i	0.296373	−	0.171111i	−0.344439	−	0.938809i	$-0.611931\pi$
$127$	3.33995	−	1.92832i	0.296373	−	0.171111i	0.640812	+	0.767698i	$0.278598\pi$
$128$		0			0
$129$	18.1270	−	5.27790i	1.59599	−	0.464693i
$130$		0			0
$131$	3.16271	+	1.82599i	0.276327	+	0.159538i	0.631760	−	0.775164i	$-0.282333\pi$
$131$	3.16271	+	1.82599i	0.276327	+	0.159538i	−0.355432	+	0.934702i	$0.615666\pi$
$132$		0			0
$133$	−9.91947	−	8.70746i	−0.860127	−	0.755032i
$134$		0			0
$135$	7.41984	−	2.51158i	0.638598	−	0.216162i
$136$		0			0
$137$	8.50779	−	4.91198i	0.726870	−	0.419659i	−0.0904061	−	0.995905i	$-0.528816\pi$
$137$	8.50779	−	4.91198i	0.726870	−	0.419659i	0.817276	+	0.576246i	$0.195483\pi$
$138$		0			0
$139$	−9.41572	−	16.3085i	−0.798631	−	1.38327i	−0.920508	−	0.390725i	$-0.872224\pi$
$139$	−9.41572	−	16.3085i	−0.798631	−	1.38327i	0.121876	−	0.992545i	$-0.461109\pi$
$140$		0			0
$141$	4.72287	+	1.15711i	0.397737	+	0.0974465i
$142$		0			0
$143$	−7.45954	−	12.9203i	−0.623798	−	1.08045i
$144$		0			0
$145$		−	11.5114i		−	0.955968i
$146$		0			0
$147$	2.71335	+	2.59896i	0.223794	+	0.214359i
$148$		0			0
$149$	−7.39978	−	4.27227i	−0.606214	−	0.349998i	0.165268	−	0.986249i	$-0.447151\pi$
$149$	−7.39978	−	4.27227i	−0.606214	−	0.349998i	−0.771482	+	0.636251i	$0.780484\pi$
$150$		0			0
$151$			12.5741i			1.02326i	0.859205	+	0.511632i	$0.170959\pi$
$151$			12.5741i			1.02326i	−0.859205	+	0.511632i	$0.829041\pi$
$152$		0			0
$153$	−5.70763	+	10.9489i	−0.461434	+	0.885167i
$154$		0			0
$155$	5.48210	−	9.49527i	0.440333	−	0.762679i
$156$		0			0
$157$	9.62759	−	16.6755i	0.768366	−	1.33085i	−0.170083	−	0.985430i	$-0.554404\pi$
$157$	9.62759	−	16.6755i	0.768366	−	1.33085i	0.938449	−	0.345419i	$-0.112263\pi$
$158$		0			0
$159$	1.71920	−	7.01709i	0.136342	−	0.556492i
$160$		0			0
$161$	16.5208	−	9.53831i	1.30202	−	0.751724i
$162$		0			0
$163$	−11.1480			−0.873177			−0.436589	−	0.899661i	$-0.643813\pi$
$163$	−11.1480			−0.873177			−0.436589	+	0.899661i	$0.643813\pi$
$164$		0			0
$165$	−11.8585	+	3.45275i	−0.923183	+	0.268796i
$166$		0			0
$167$	−10.7662	−	18.6475i	−0.833110	−	1.44299i	−0.895560	−	0.444941i	$-0.853225\pi$
$167$	−10.7662	−	18.6475i	−0.833110	−	1.44299i	0.0624500	−	0.998048i	$-0.480109\pi$
$168$		0			0
$169$	−1.52592	+	2.64297i	−0.117379	+	0.203306i
$170$		0			0
$171$	8.19568	−	10.1897i	0.626740	−	0.779229i
$172$		0			0
$173$	−8.27489	+	14.3325i	−0.629128	+	1.08968i	0.358599	+	0.933492i	$0.383255\pi$
$173$	−8.27489	+	14.3325i	−0.629128	+	1.08968i	−0.987727	+	0.156191i	$0.950079\pi$
$174$		0			0
$175$	−4.12928	−	7.15213i	−0.312145	−	0.540650i
$176$		0			0
$177$	12.6186	−	3.67407i	0.948475	−	0.276160i
$178$		0			0
$179$	12.4745			0.932389			0.466194	−	0.884682i	$-0.345625\pi$
$179$	12.4745			0.932389			0.466194	+	0.884682i	$0.345625\pi$
$180$		0			0
$181$	−3.33803	+	1.92721i	−0.248114	+	0.143249i	−0.618900	−	0.785469i	$-0.712422\pi$
$181$	−3.33803	+	1.92721i	−0.248114	+	0.143249i	0.370786	+	0.928718i	$0.379088\pi$
$182$		0			0
$183$	−3.03990	+	12.4076i	−0.224716	+	0.917198i
$184$		0			0
$185$	1.23056	−	2.13139i	0.0904724	−	0.156703i
$186$		0			0
$187$	9.73401	−	16.8598i	0.711821	−	1.23291i
$188$		0			0
$189$	−10.3845	+	11.8208i	−0.755365	+	0.859835i
$190$		0			0
$191$			7.74165i			0.560166i	0.959976	+	0.280083i	$0.0903620\pi$
$191$			7.74165i			0.560166i	−0.959976	+	0.280083i	$0.909638\pi$
$192$		0			0
$193$	0.675302	+	0.389886i	0.0486093	+	0.0280646i	0.524108	−	0.851652i	$-0.324399\pi$
$193$	0.675302	+	0.389886i	0.0486093	+	0.0280646i	−0.475498	+	0.879717i	$0.657732\pi$
$194$		0			0
$195$	−5.94753	−	5.69679i	−0.425912	−	0.407956i
$196$		0			0
$197$		−	7.65061i		−	0.545084i	−0.962144	−	0.272542i	$-0.912136\pi$
$197$		−	7.65061i		−	0.545084i	0.962144	−	0.272542i	$-0.0878643\pi$
$198$		0			0
$199$	4.45011	+	7.70781i	0.315460	+	0.546392i	0.979535	−	0.201273i	$-0.0645079\pi$
$199$	4.45011	+	7.70781i	0.315460	+	0.546392i	−0.664075	+	0.747666i	$0.731175\pi$
$200$		0			0
$201$	5.46897	+	1.33991i	0.385751	+	0.0945100i
$202$		0			0
$203$	11.5610	+	20.0243i	0.811424	+	1.40543i
$204$		0			0
$205$	15.6308	−	9.02446i	1.09170	−	0.630295i
$206$		0			0
$207$	10.1457	+	15.9457i	0.705174	+	1.10830i
$208$		0			0
$209$	−13.6018	+	15.4950i	−0.940854	+	1.07181i
$210$		0			0
$211$	−16.8902	−	9.75157i	−1.16277	−	0.671326i	−0.210804	−	0.977528i	$-0.567608\pi$
$211$	−16.8902	−	9.75157i	−1.16277	−	0.671326i	−0.951966	+	0.306203i	$0.900942\pi$
$212$		0			0
$213$	−3.45216	+	1.00514i	−0.236538	+	0.0688711i
$214$		0			0
$215$	−14.2309	+	8.21624i	−0.970542	+	0.560343i
$216$		0			0
$217$			22.0230i			1.49502i
$218$		0			0
$219$	−4.12995	+	1.20249i	−0.279076	+	0.0812565i
$220$		0			0
$221$	12.9814			0.873224
$222$		0			0
$223$	−6.24954	−	3.60817i	−0.418500	−	0.241621i	0.275935	−	0.961176i	$-0.411012\pi$
$223$	−6.24954	−	3.60817i	−0.418500	−	0.241621i	−0.694435	+	0.719555i	$0.744346\pi$
$224$		0			0
$225$	6.90314	−	4.39223i	0.460210	−	0.292815i
$226$		0			0
$227$	−7.69814			−0.510944			−0.255472	−	0.966816i	$-0.582231\pi$
$227$	−7.69814			−0.510944			−0.255472	+	0.966816i	$0.582231\pi$
$228$		0			0
$229$	−19.2143			−1.26972			−0.634860	−	0.772627i	$-0.718942\pi$
$229$	−19.2143			−1.26972			−0.634860	+	0.772627i	$0.718942\pi$
$230$		0			0
$231$	17.1605	−	17.9158i	1.12908	−	1.17877i
$232$		0			0
$233$	4.28304	+	2.47281i	0.280591	+	0.161999i	0.633691	−	0.773586i	$-0.281539\pi$
$233$	4.28304	+	2.47281i	0.280591	+	0.161999i	−0.353100	+	0.935586i	$0.614872\pi$
$234$		0			0
$235$	−4.23225			−0.276082
$236$		0			0
$237$	−3.20358	−	11.0027i	−0.208095	−	0.714703i
$238$		0			0
$239$		−	25.0859i		−	1.62267i	−0.584582	−	0.811335i	$-0.698741\pi$
$239$		−	25.0859i		−	1.62267i	0.584582	−	0.811335i	$-0.301259\pi$
$240$		0			0
$241$	−20.0747	+	11.5901i	−1.29312	+	0.746584i	−0.979206	−	0.202866i	$-0.934974\pi$
$241$	−20.0747	+	11.5901i	−1.29312	+	0.746584i	−0.313916	+	0.949451i	$0.601641\pi$
$242$		0			0
$243$	−12.1432	−	9.77460i	−0.778986	−	0.627041i
$244$		0			0
$245$	−2.83209	−	1.63511i	−0.180936	−	0.104463i
$246$		0			0
$247$	−13.4828	−	2.68854i	−0.857892	−	0.171068i
$248$		0			0
$249$	−15.2799	+	15.9524i	−0.968321	+	1.01094i
$250$		0			0
$251$	−20.0791	+	11.5927i	−1.26738	+	0.731724i	−0.974492	−	0.224421i	$-0.927951\pi$
$251$	−20.0791	+	11.5927i	−1.26738	+	0.731724i	−0.292891	+	0.956146i	$0.594617\pi$
$252$		0			0
$253$	−14.8996	−	25.8069i	−0.936732	−	1.62247i
$254$		0			0
$255$	2.55736	−	10.4381i	0.160148	−	0.653658i
$256$		0			0
$257$	5.75817	+	9.97345i	0.359185	+	0.622127i	0.987825	−	0.155570i	$-0.0497214\pi$
$257$	5.75817	+	9.97345i	0.359185	+	0.622127i	−0.628640	+	0.777697i	$0.716388\pi$
$258$		0			0
$259$			4.94346i			0.307172i
$260$		0			0
$261$	−19.3272	+	12.2972i	−1.19632	+	0.761177i
$262$		0			0
$263$	20.4618	+	11.8136i	1.26173	+	0.728458i	0.973408	−	0.229076i	$-0.0735705\pi$
$263$	20.4618	+	11.8136i	1.26173	+	0.728458i	0.288318	+	0.957535i	$0.406904\pi$
$264$		0			0
$265$			6.28815i			0.386278i
$266$		0			0
$267$	1.16732	−	4.76455i	0.0714391	−	0.291585i
$268$		0			0
$269$	−13.3368	+	23.1000i	−0.813159	+	1.40843i	0.0974838	+	0.995237i	$0.468921\pi$
$269$	−13.3368	+	23.1000i	−0.813159	+	1.40843i	−0.910643	+	0.413195i	$0.864413\pi$
$270$		0			0
$271$	−5.65442	+	9.79375i	−0.343482	+	0.594928i	−0.985077	−	0.172116i	$-0.944940\pi$
$271$	−5.65442	+	9.79375i	−0.343482	+	0.594928i	0.641595	+	0.767044i	$0.278273\pi$
$272$		0			0
$273$	16.0672	+	3.93650i	0.972432	+	0.238248i
$274$		0			0
$275$	−11.1722	+	6.45029i	−0.673710	+	0.388967i
$276$		0			0
$277$	−13.2302			−0.794924			−0.397462	−	0.917619i	$-0.630109\pi$
$277$	−13.2302			−0.794924			−0.397462	+	0.917619i	$0.630109\pi$
$278$		0			0
$279$	−21.7985	+	0.939221i	−1.30504	+	0.0562297i
$280$		0			0
$281$	−5.95572	−	10.3156i	−0.355289	−	0.615378i	0.631879	−	0.775067i	$-0.282284\pi$
$281$	−5.95572	−	10.3156i	−0.355289	−	0.615378i	−0.987167	+	0.159689i	$0.948951\pi$
$282$		0			0
$283$	6.16698	−	10.6815i	0.366589	−	0.634951i	−0.622441	−	0.782667i	$-0.713859\pi$
$283$	6.16698	−	10.6815i	0.366589	−	0.634951i	0.989030	+	0.147716i	$0.0471922\pi$
$284$		0			0
$285$	−4.81794	+	10.3116i	−0.285390	+	0.610808i
$286$		0			0
$287$	−18.1267	+	31.3965i	−1.06999	+	1.85327i
$288$		0			0
$289$	−0.0302375	−	0.0523729i	−0.00177868	−	0.00308076i
$290$		0			0
$291$	−3.49213	−	11.9938i	−0.204712	−	0.703086i
$292$		0			0
$293$	16.4438			0.960657			0.480329	−	0.877089i	$-0.340517\pi$
$293$	16.4438			0.960657			0.480329	+	0.877089i	$0.340517\pi$
$294$		0			0
$295$	−9.90651	+	5.71952i	−0.576779	+	0.333004i
$296$		0			0
$297$	18.4650	+	16.2215i	1.07145	+	0.941268i
$298$		0			0
$299$	9.93519	−	17.2082i	0.574567	−	0.995179i
$300$		0			0
$301$	16.5033	−	28.5846i	0.951237	−	1.64759i
$302$		0			0
$303$	6.66050	+	1.63184i	0.382636	+	0.0937467i
$304$		0			0
$305$		−	11.1187i		−	0.636656i
$306$		0			0
$307$	−12.9786	−	7.49319i	−0.740727	−	0.427659i	0.0816069	−	0.996665i	$-0.473995\pi$
$307$	−12.9786	−	7.49319i	−0.740727	−	0.427659i	−0.822333	+	0.569006i	$0.807328\pi$
$308$		0			0
$309$	−4.28374	+	4.47229i	−0.243694	+	0.254420i
$310$		0			0
$311$			6.90288i			0.391427i	0.980661	+	0.195713i	$0.0627022\pi$
$311$			6.90288i			0.391427i	−0.980661	+	0.195713i	$0.937298\pi$
$312$		0			0
$313$	5.64826	+	9.78307i	0.319259	+	0.552972i	0.980334	−	0.197348i	$-0.0632328\pi$
$313$	5.64826	+	9.78307i	0.319259	+	0.552972i	−0.661075	+	0.750320i	$0.729900\pi$
$314$		0			0
$315$	6.33053	−	12.1438i	0.356685	−	0.684227i
$316$		0			0
$317$	−16.2051	−	28.0680i	−0.910168	−	1.57646i	−0.813826	−	0.581109i	$-0.802619\pi$
$317$	−16.2051	−	28.0680i	−0.910168	−	1.57646i	−0.0963424	−	0.995348i	$-0.530714\pi$
$318$		0			0
$319$	31.2796	−	18.0593i	1.75132	−	1.01113i
$320$		0			0
$321$	−18.8519	−	18.0571i	−1.05221	−	1.00785i
$322$		0			0
$323$	−5.75864	−	16.9909i	−0.320420	−	0.945396i
$324$		0			0
$325$	−7.44972	−	4.30110i	−0.413236	−	0.238582i
$326$		0			0
$327$	0.304330	+	1.04522i	0.0168295	+	0.0578010i
$328$		0			0
$329$	7.36208	−	4.25050i	0.405885	−	0.234338i
$330$		0			0
$331$			24.7762i			1.36183i	0.732365	+	0.680913i	$0.238417\pi$
$331$			24.7762i			1.36183i	−0.732365	+	0.680913i	$0.761583\pi$
$332$		0			0
$333$	−4.89308	+	0.210826i	−0.268139	+	0.0115532i
$334$		0			0
$335$	−4.90085			−0.267762
$336$		0			0
$337$	19.9671	+	11.5280i	1.08768	+	0.627969i	0.932957	−	0.359989i	$-0.117220\pi$
$337$	19.9671	+	11.5280i	1.08768	+	0.627969i	0.154719	+	0.987959i	$0.450553\pi$
$338$		0			0
$339$	−9.37072	−	8.97566i	−0.508948	−	0.487491i
$340$		0			0
$341$	34.4017			1.86296
$342$		0			0
$343$	−14.6279			−0.789832
$344$		0			0
$345$	−11.8796	−	11.3787i	−0.639574	−	0.612610i
$346$		0			0
$347$	20.6226	+	11.9065i	1.10708	+	0.639173i	0.938071	−	0.346442i	$-0.112610\pi$
$347$	20.6226	+	11.9065i	1.10708	+	0.639173i	0.169008	+	0.985615i	$0.445944\pi$
$348$		0			0
$349$	19.9071			1.06560			0.532802	−	0.846240i	$-0.321139\pi$
$349$	19.9071			1.06560			0.532802	+	0.846240i	$0.321139\pi$
$350$		0			0
$351$	−3.21117	+	16.0714i	−0.171399	+	0.857826i
$352$		0			0
$353$		−	7.30433i		−	0.388770i	−0.980925	−	0.194385i	$-0.937729\pi$
$353$		−	7.30433i		−	0.388770i	0.980925	−	0.194385i	$-0.0622711\pi$
$354$		0			0
$355$	2.71019	−	1.56473i	0.143842	−	0.0830471i
$356$		0			0
$357$	6.03453	+	20.7256i	0.319381	+	1.09692i
$358$		0			0
$359$	9.67780	+	5.58748i	0.510775	+	0.294896i	0.733152	−	0.680065i	$-0.238048\pi$
$359$	9.67780	+	5.58748i	0.510775	+	0.294896i	−0.222377	+	0.974961i	$0.571382\pi$
$360$		0			0
$361$	2.46215	+	18.8398i	0.129587	+	0.991568i
$362$		0			0
$363$	−14.2268	−	13.6270i	−0.746714	−	0.715233i
$364$		0			0
$365$	3.24230	−	1.87194i	0.169710	−	0.0979818i
$366$		0			0
$367$	14.2255	+	24.6393i	0.742566	+	1.28616i	0.951323	+	0.308195i	$0.0997250\pi$
$367$	14.2255	+	24.6393i	0.742566	+	1.28616i	−0.208757	+	0.977968i	$0.566942\pi$
$368$		0			0
$369$	−31.8496	−	16.6031i	−1.65802	−	0.864320i
$370$		0			0
$371$	−6.31527	−	10.9384i	−0.327872	−	0.567892i
$372$		0			0
$373$			26.8245i			1.38892i	0.719531	+	0.694461i	$0.244357\pi$
$373$			26.8245i			1.38892i	−0.719531	+	0.694461i	$0.755643\pi$
$374$		0			0
$375$	−13.9569	+	14.5712i	−0.720731	+	0.752453i
$376$		0			0
$377$	20.8574	+	12.0421i	1.07421	+	0.620197i
$378$		0			0
$379$			4.29692i			0.220718i	0.993892	+	0.110359i	$0.0352001\pi$
$379$			4.29692i			0.220718i	−0.993892	+	0.110359i	$0.964800\pi$
$380$		0			0
$381$	6.48802	+	1.58958i	0.332391	+	0.0814367i
$382$		0			0
$383$	9.62338	−	16.6682i	0.491732	−	0.851704i	−0.508223	−	0.861225i	$-0.669697\pi$
$383$	9.62338	−	16.6682i	0.491732	−	0.851704i	0.999955	+	0.00952143i	$0.00303081\pi$
$384$		0			0
$385$	−10.7963	+	18.6998i	−0.550232	+	0.953029i
$386$		0			0
$387$	28.9972	+	15.1161i	1.47401	+	0.768395i
$388$		0			0
$389$	−4.56610	+	2.63624i	−0.231510	+	0.133663i	−0.611269	−	0.791423i	$-0.709341\pi$
$389$	−4.56610	+	2.63624i	−0.231510	+	0.133663i	0.379758	+	0.925086i	$0.376007\pi$
$390$		0			0
$391$	25.9290			1.31128
$392$		0			0
$393$	1.76830	+	6.07323i	0.0891987	+	0.306354i
$394$		0			0
$395$	4.98709	+	8.63790i	0.250928	+	0.434620i
$396$		0			0
$397$	6.69534	−	11.5967i	0.336030	−	0.582020i	−0.647653	−	0.761936i	$-0.724249\pi$
$397$	6.69534	−	11.5967i	0.336030	−	0.582020i	0.983682	+	0.179916i	$0.0575825\pi$
$398$		0			0
$399$	−1.97519	−	22.7760i	−0.0988833	−	1.14023i
$400$		0			0
$401$	9.18871	−	15.9153i	0.458862	−	0.794773i	−0.540039	−	0.841640i	$-0.681591\pi$
$401$	9.18871	−	15.9153i	0.458862	−	0.794773i	0.998901	+	0.0468675i	$0.0149238\pi$
$402$		0			0
$403$	11.4696	+	19.8660i	0.571344	+	0.989596i
$404$		0			0
$405$	12.2900	+	5.74811i	0.610697	+	0.285626i
$406$		0			0
$407$	7.72209			0.382770
$408$		0			0
$409$	18.7518	−	10.8264i	0.927216	−	0.535329i	0.0412862	−	0.999147i	$-0.486854\pi$
$409$	18.7518	−	10.8264i	0.927216	−	0.535329i	0.885930	+	0.463819i	$0.153521\pi$
$410$		0			0
$411$	16.5268	+	4.04910i	0.815207	+	0.199728i
$412$		0			0
$413$	11.4884	−	19.8985i	0.565306	−	0.979139i
$414$		0			0
$415$	9.61316	−	16.6505i	0.471892	−	0.817340i
$416$		0			0
$417$	7.76169	−	31.6801i	0.380092	−	1.55138i
$418$		0			0
$419$			20.3881i			0.996022i	0.867171	+	0.498011i	$0.165936\pi$
$419$			20.3881i			0.996022i	−0.867171	+	0.498011i	$0.834064\pi$
$420$		0			0
$421$	25.4660	+	14.7028i	1.24114	+	0.716571i	0.969326	−	0.245779i	$-0.0790437\pi$
$421$	25.4660	+	14.7028i	1.24114	+	0.716571i	0.271812	+	0.962350i	$0.412377\pi$
$422$		0			0
$423$	4.52116	+	7.10579i	0.219826	+	0.345495i
$424$		0			0
$425$		−	11.2251i		−	0.544495i
$426$		0			0
$427$	11.1667	+	19.3412i	0.540393	+	0.935988i
$428$		0			0
$429$	6.14915	−	25.0983i	0.296884	−	1.21176i
$430$		0			0
$431$	16.8910	+	29.2561i	0.813613	+	1.40922i	0.910320	+	0.413906i	$0.135836\pi$
$431$	16.8910	+	29.2561i	0.813613	+	1.40922i	−0.0967066	+	0.995313i	$0.530831\pi$
$432$		0			0
$433$	19.5716	−	11.2997i	0.940552	−	0.543028i	0.0504190	−	0.998728i	$-0.483944\pi$
$433$	19.5716	−	11.2997i	0.940552	−	0.543028i	0.890133	+	0.455700i	$0.150611\pi$
$434$		0			0
$435$	13.7917	−	14.3987i	0.661262	−	0.690367i
$436$		0			0
$437$	−26.9305	−	5.37007i	−1.28826	−	0.256885i
$438$		0			0
$439$	−18.9504	−	10.9410i	−0.904455	−	0.522187i	−0.0258118	−	0.999667i	$-0.508217\pi$
$439$	−18.9504	−	10.9410i	−0.904455	−	0.522187i	−0.878643	+	0.477480i	$0.841550\pi$
$440$		0			0
$441$	0.280136	+	6.50171i	0.0133398	+	0.309605i
$442$		0			0
$443$	−9.62663	+	5.55794i	−0.457375	+	0.264066i	−0.710940	−	0.703253i	$-0.751730\pi$
$443$	−9.62663	+	5.55794i	−0.457375	+	0.264066i	0.253565	+	0.967318i	$0.418397\pi$
$444$		0			0
$445$			4.26960i			0.202398i
$446$		0			0
$447$	−4.13727	−	14.2095i	−0.195686	−	0.672087i
$448$		0			0
$449$	−4.07831			−0.192468			−0.0962338	−	0.995359i	$-0.530680\pi$
$449$	−4.07831			−0.192468			−0.0962338	+	0.995359i	$0.530680\pi$
$450$		0			0
$451$	49.0439	+	28.3155i	2.30939	+	1.33332i
$452$		0			0
$453$	−15.0649	+	15.7280i	−0.707812	+	0.738966i
$454$		0			0
$455$	−14.3981			−0.674995
$456$		0			0
$457$	−24.3241			−1.13783			−0.568916	−	0.822396i	$-0.692637\pi$
$457$	−24.3241			−1.13783			−0.568916	+	0.822396i	$0.692637\pi$
$458$		0			0
$459$	−20.2571	+	6.85693i	−0.945520	+	0.320054i
$460$		0			0
$461$	−32.2126	−	18.5980i	−1.50029	−	0.866194i	−1.00000		0.000337526i	$-0.999893\pi$
$461$	−32.2126	−	18.5980i	−1.50029	−	0.866194i	−0.500292	−	0.865857i	$-0.666774\pi$
$462$		0			0
$463$	30.4951			1.41723			0.708615	−	0.705596i	$-0.249321\pi$
$463$	30.4951			1.41723			0.708615	+	0.705596i	$0.249321\pi$
$464$		0			0
$465$	18.2334	−	5.30888i	0.845553	−	0.246193i
$466$		0			0
$467$		−	2.73788i		−	0.126694i	−0.997992	−	0.0633469i	$-0.979823\pi$
$467$		−	2.73788i		−	0.126694i	0.997992	−	0.0633469i	$-0.0201775\pi$
$468$		0			0
$469$	8.52512	−	4.92198i	0.393654	−	0.227276i
$470$		0			0
$471$	32.0213	−	9.32339i	1.47546	−	0.429599i
$472$		0			0
$473$	−44.6516	−	25.7796i	−2.05308	−	1.18535i
$474$		0			0
$475$	−2.32479	+	11.6586i	−0.106669	+	0.534935i
$476$		0			0
$477$	10.5576	−	6.71740i	0.483398	−	0.307569i
$478$		0			0
$479$	0.0351091	−	0.0202702i	0.00160417	−	0.000926170i	−0.499198	−	0.866488i	$-0.666372\pi$
$479$	0.0351091	−	0.0202702i	0.00160417	−	0.000926170i	0.500802	+	0.865562i	$0.333039\pi$
$480$		0			0
$481$	2.57457	+	4.45929i	0.117390	+	0.203326i
$482$		0			0
$483$	32.0925	+	7.86274i	1.46026	+	0.357767i
$484$		0			0
$485$	5.43629	+	9.41593i	0.246849	+	0.427555i
$486$		0			0
$487$		−	1.55162i		−	0.0703108i	−0.999382	−	0.0351554i	$-0.988807\pi$
$487$		−	1.55162i		−	0.0703108i	0.999382	−	0.0351554i	$-0.0111926\pi$
$488$		0			0
$489$	−13.9442	−	13.3563i	−0.630579	−	0.603994i
$490$		0			0
$491$	−38.3422	−	22.1369i	−1.73036	−	0.999024i	−0.887261	−	0.461268i	$-0.847395\pi$
$491$	−38.3422	−	22.1369i	−1.73036	−	0.999024i	−0.843100	−	0.537756i	$-0.819272\pi$
$492$		0			0
$493$			31.4275i			1.41542i
$494$		0			0
$495$	−18.9697	−	9.88881i	−0.852623	−	0.444469i
$496$		0			0
$497$	−3.14295	+	5.44375i	−0.140981	+	0.244186i
$498$		0			0
$499$	4.73098	−	8.19429i	0.211788	−	0.366827i	−0.740486	−	0.672071i	$-0.765405\pi$
$499$	4.73098	−	8.19429i	0.211788	−	0.366827i	0.952274	+	0.305244i	$0.0987382\pi$
$500$		0			0
$501$	8.87489	−	36.2237i	0.396501	−	1.61836i
$502$		0			0
$503$	18.0870	−	10.4426i	0.806461	−	0.465611i	−0.0392643	−	0.999229i	$-0.512501\pi$
$503$	18.0870	−	10.4426i	0.806461	−	0.465611i	0.845725	+	0.533618i	$0.179168\pi$
$504$		0			0
$505$	−5.96860			−0.265599
$506$		0			0
$507$	−5.07520	+	1.47771i	−0.225397	+	0.0656272i
$508$		0			0
$509$	−2.46000	−	4.26084i	−0.109038	−	0.188859i	0.806343	−	0.591448i	$-0.201444\pi$
$509$	−2.46000	−	4.26084i	−0.109038	−	0.188859i	−0.915381	+	0.402589i	$0.868110\pi$
$510$		0			0
$511$	−3.76003	+	6.51256i	−0.166334	+	0.288099i
$512$		0			0
$513$	22.4597	−	2.92640i	0.991618	−	0.129204i
$514$		0			0
$515$	2.69507	−	4.66800i	0.118759	−	0.205697i
$516$		0			0
$517$	−6.63964	−	11.5002i	−0.292011	−	0.505778i
$518$		0			0
$519$	−27.5222	+	8.01343i	−1.20809	+	0.351750i
$520$		0			0
$521$	24.1951			1.06001			0.530003	−	0.847996i	$-0.322191\pi$
$521$	24.1951			1.06001			0.530003	+	0.847996i	$0.322191\pi$
$522$		0			0
$523$	8.01170	−	4.62555i	0.350327	−	0.202261i	−0.314502	−	0.949257i	$-0.601838\pi$
$523$	8.01170	−	4.62555i	0.350327	−	0.202261i	0.664829	+	0.746995i	$0.268504\pi$
$524$		0			0
$525$	3.40390	−	13.8934i	0.148559	−	0.606356i
$526$		0			0
$527$	−14.9668	+	25.9233i	−0.651965	+	1.12924i
$528$		0			0
$529$	8.34446	−	14.4530i	0.362803	−	0.628393i
$530$		0			0
$531$	20.1856	+	10.5227i	0.875982	+	0.456646i
$532$		0			0
$533$			37.7619i			1.63565i
$534$		0			0
$535$	19.6769	+	11.3605i	0.850706	+	0.491156i
$536$		0			0
$537$	15.6035	+	14.9456i	0.673339	+	0.644952i
$538$		0			0
$539$		−	10.2608i		−	0.441963i
$540$		0			0
$541$	15.3145	+	26.5254i	0.658420	+	1.14042i	0.981025	+	0.193883i	$0.0621081\pi$
$541$	15.3145	+	26.5254i	0.658420	+	1.14042i	−0.322605	+	0.946534i	$0.604559\pi$
$542$		0			0
$543$	−6.48429	−	1.58867i	−0.278267	−	0.0681762i
$544$		0			0
$545$	−0.473758	−	0.820572i	−0.0202935	−	0.0351495i
$546$		0			0
$547$	−14.3615	+	8.29162i	−0.614054	+	0.354524i	−0.774550	−	0.632512i	$-0.782024\pi$
$547$	−14.3615	+	8.29162i	−0.614054	+	0.354524i	0.160497	+	0.987036i	$0.448690\pi$
$548$		0			0
$549$	−18.6679	+	11.8777i	−0.796727	+	0.506929i
$550$		0			0
$551$	6.50885	−	32.6414i	0.277286	−	1.39057i
$552$		0			0
$553$	−17.3503	−	10.0172i	−0.737809	−	0.425975i
$554$		0			0
$555$	4.09282	−	1.19168i	0.173731	−	0.0505838i
$556$		0			0
$557$	26.6376	−	15.3792i	1.12867	−	0.651639i	0.185071	−	0.982725i	$-0.440748\pi$
$557$	26.6376	−	15.3792i	1.12867	−	0.651639i	0.943601	+	0.331086i	$0.107415\pi$
$558$		0			0
$559$		−	34.3800i		−	1.45412i
$560$		0			0
$561$	32.3752	−	9.42644i	1.36688	−	0.397984i
$562$		0			0
$563$	5.05699			0.213127			0.106563	−	0.994306i	$-0.466015\pi$
$563$	5.05699			0.213127			0.106563	+	0.994306i	$0.466015\pi$
$564$		0			0
$565$	9.78080	+	5.64695i	0.411481	+	0.237569i
$566$		0			0
$567$	−27.1517	+	2.34409i	−1.14026	+	0.0984426i
$568$		0			0
$569$	−5.76398			−0.241639			−0.120819	−	0.992675i	$-0.538552\pi$
$569$	−5.76398			−0.241639			−0.120819	+	0.992675i	$0.538552\pi$
$570$		0			0
$571$	−26.2790			−1.09974			−0.549871	−	0.835250i	$-0.685323\pi$
$571$	−26.2790			−1.09974			−0.549871	+	0.835250i	$0.685323\pi$
$572$		0			0
$573$	−9.27522	+	9.68347i	−0.387478	+	0.404533i
$574$		0			0
$575$	−14.8800	−	8.59098i	−0.620539	−	0.358269i
$576$		0			0
$577$	34.3220			1.42884			0.714422	−	0.699715i	$-0.246690\pi$
$577$	34.3220			1.42884			0.714422	+	0.699715i	$0.246690\pi$
$578$		0			0
$579$	0.377566	+	1.29676i	0.0156911	+	0.0538913i
$580$		0			0
$581$			38.6185i			1.60216i
$582$		0			0
$583$	−17.0866	+	9.86497i	−0.707656	+	0.408565i
$584$		0			0
$585$	−0.614043	−	14.2514i	−0.0253875	−	0.589223i
$586$		0			0
$587$	9.73427	+	5.62008i	0.401776	+	0.231966i	0.687250	−	0.726421i	$-0.258818\pi$
$587$	9.73427	+	5.62008i	0.401776	+	0.231966i	−0.285474	+	0.958387i	$0.592151\pi$
$588$		0			0
$589$	20.9138	−	23.8249i	0.861739	−	0.981686i
$590$		0			0
$591$	9.16616	−	9.56960i	0.377045	−	0.393641i
$592$		0			0
$593$	−9.74801	+	5.62802i	−0.400303	+	0.231115i	−0.686615	−	0.727022i	$-0.740904\pi$
$593$	−9.74801	+	5.62802i	−0.400303	+	0.231115i	0.286312	+	0.958136i	$0.407571\pi$
$594$		0			0
$595$	−9.39411	−	16.2711i	−0.385121	−	0.667049i
$596$		0			0
$597$	−3.66837	+	14.9728i	−0.150136	+	0.612796i
$598$		0			0
$599$	−5.76971	−	9.99344i	−0.235744	−	0.408321i	0.723745	−	0.690068i	$-0.242419\pi$
$599$	−5.76971	−	9.99344i	−0.235744	−	0.408321i	−0.959489	+	0.281747i	$0.909086\pi$
$600$		0			0
$601$			45.3443i			1.84963i	0.380415	+	0.924816i	$0.375781\pi$
$601$			45.3443i			1.84963i	−0.380415	+	0.924816i	$0.624219\pi$
$602$		0			0
$603$	5.23540	+	8.22834i	0.213202	+	0.335084i
$604$		0			0
$605$	14.8494	+	8.57330i	0.603714	+	0.348554i
$606$		0			0
$607$			19.0689i			0.773984i	0.922083	+	0.386992i	$0.126486\pi$
$607$			19.0689i			0.773984i	−0.922083	+	0.386992i	$0.873514\pi$
$608$		0			0
$609$	−9.53013	+	38.8981i	−0.386180	+	1.57623i
$610$		0			0
$611$	4.42736	−	7.66841i	0.179112	−	0.310231i
$612$		0			0
$613$	−12.3068	+	21.3160i	−0.497067	+	0.860946i	−0.999994	−	0.00338287i	$-0.998923\pi$
$613$	−12.3068	+	21.3160i	−0.497067	+	0.860946i	0.502927	+	0.864329i	$0.332257\pi$
$614$		0			0
$615$	30.3636	+	7.43916i	1.22438	+	0.299976i
$616$		0			0
$617$	−25.9907	+	15.0058i	−1.04635	+	0.604109i	−0.921625	−	0.388082i	$-0.873138\pi$
$617$	−25.9907	+	15.0058i	−1.04635	+	0.604109i	−0.124723	+	0.992192i	$0.539804\pi$
$618$		0			0
$619$	−1.81932			−0.0731247			−0.0365624	−	0.999331i	$-0.511641\pi$
$619$	−1.81932			−0.0731247			−0.0365624	+	0.999331i	$0.511641\pi$
$620$		0			0
$621$	−6.41396	+	32.1008i	−0.257383	+	1.28816i
$622$		0			0
$623$	−4.28801	−	7.42706i	−0.171796	−	0.297559i
$624$		0			0
$625$	1.96250	−	3.39915i	0.0785000	−	0.135966i
$626$		0			0
$627$	−35.5780	+	3.08542i	−1.42085	+	0.123220i
$628$		0			0
$629$	−3.35958	+	5.81896i	−0.133955	+	0.232017i
$630$		0			0
$631$	−11.6963	−	20.2585i	−0.465620	−	0.806478i	0.533609	−	0.845731i	$-0.320835\pi$
$631$	−11.6963	−	20.2585i	−0.465620	−	0.806478i	−0.999229	+	0.0392531i	$0.987502\pi$
$632$		0			0
$633$	−9.44345	−	32.4336i	−0.375343	−	1.28912i
$634$		0			0
$635$	−5.81404			−0.230723
$636$		0			0
$637$	5.92531	−	3.42098i	0.234769	−	0.135544i
$638$		0			0
$639$	−5.52231	−	2.87876i	−0.218459	−	0.113882i
$640$		0			0
$641$	−0.138525	+	0.239932i	−0.00547140	+	0.00947675i	−0.868748	−	0.495254i	$-0.835075\pi$
$641$	−0.138525	+	0.239932i	−0.00547140	+	0.00947675i	0.863277	+	0.504731i	$0.168408\pi$
$642$		0			0
$643$	−9.96549	+	17.2607i	−0.393001	+	0.680697i	−0.992844	−	0.119421i	$-0.961896\pi$
$643$	−9.96549	+	17.2607i	−0.393001	+	0.680697i	0.599843	+	0.800118i	$0.295230\pi$
$644$		0			0
$645$	−27.6443	−	6.77292i	−1.08849	−	0.266683i
$646$		0			0
$647$		−	19.1151i		−	0.751494i	−0.926722	−	0.375747i	$-0.877386\pi$
$647$		−	19.1151i		−	0.751494i	0.926722	−	0.375747i	$-0.122614\pi$
$648$		0			0
$649$	−31.0830	−	17.9458i	−1.22012	−	0.704434i
$650$		0			0
$651$	−26.3856	+	27.5469i	−1.03413	+	1.07965i
$652$		0			0
$653$			23.0719i			0.902874i	0.892303	+	0.451437i	$0.149088\pi$
$653$			23.0719i			0.902874i	−0.892303	+	0.451437i	$0.850912\pi$
$654$		0			0
$655$	−2.75275	−	4.76790i	−0.107559	−	0.186297i
$656$		0			0
$657$	−6.60655	−	3.44397i	−0.257746	−	0.134362i
$658$		0			0
$659$	6.97599	+	12.0828i	0.271746	+	0.470678i	0.969309	−	0.245846i	$-0.0790656\pi$
$659$	6.97599	+	12.0828i	0.271746	+	0.470678i	−0.697563	+	0.716523i	$0.745732\pi$
$660$		0			0
$661$	16.1466	−	9.32226i	0.628031	−	0.362594i	−0.151958	−	0.988387i	$-0.548558\pi$
$661$	16.1466	−	9.32226i	0.628031	−	0.362594i	0.779989	+	0.625793i	$0.215225\pi$
$662$		0			0
$663$	16.2375	+	15.5530i	0.630613	+	0.604027i
$664$		0			0
$665$	6.38711	+	18.8451i	0.247682	+	0.730783i
$666$		0			0
$667$	41.6605	+	24.0527i	1.61310	+	0.931324i
$668$		0			0
$669$	−3.49416	−	12.0007i	−0.135092	−	0.463975i
$670$		0			0
$671$	30.2126	−	17.4433i	1.16634	−	0.673389i
$672$		0			0
$673$			7.16700i			0.276268i	0.990414	+	0.138134i	$0.0441104\pi$
$673$			7.16700i			0.276268i	−0.990414	+	0.138134i	$0.955890\pi$
$674$		0			0
$675$	13.8969	+	2.77670i	0.534894	+	0.106875i
$676$		0			0
$677$	4.36818			0.167883			0.0839415	−	0.996471i	$-0.473249\pi$
$677$	4.36818			0.167883			0.0839415	+	0.996471i	$0.473249\pi$
$678$		0			0
$679$	−18.9131	−	10.9195i	−0.725817	−	0.419051i
$680$		0			0
$681$	−9.62905	−	9.22310i	−0.368986	−	0.353430i
$682$		0			0
$683$	−7.77593			−0.297538			−0.148769	−	0.988872i	$-0.547531\pi$
$683$	−7.77593			−0.297538			−0.148769	+	0.988872i	$0.547531\pi$
$684$		0			0
$685$	−14.8100			−0.565860
$686$		0			0
$687$	−24.0338	−	23.0206i	−0.916948	−	0.878291i
$688$		0			0
$689$	−11.3935	−	6.57804i	−0.434057	−	0.250603i
$690$		0			0
$691$	−15.3029			−0.582150			−0.291075	−	0.956700i	$-0.594013\pi$
$691$	−15.3029			−0.582150			−0.291075	+	0.956700i	$0.594013\pi$
$692$		0			0
$693$	42.9296	−	1.84968i	1.63076	−	0.0702636i
$694$		0			0
$695$			28.3891i			1.07686i
$696$		0			0
$697$	−42.6741	+	24.6379i	−1.61640	+	0.933227i
$698$		0			0
$699$	2.39468	+	8.22455i	0.0905751	+	0.311081i
$700$		0			0
$701$	36.7393	+	21.2115i	1.38762	+	0.801146i	0.993047	−	0.117717i	$-0.0375575\pi$
$701$	36.7393	+	21.2115i	1.38762	+	0.801146i	0.394578	+	0.918863i	$0.370891\pi$
$702$		0			0
$703$	4.69449	−	5.34793i	0.177056	−	0.201701i
$704$		0			0
$705$	−5.29382	−	5.07064i	−0.199377	−	0.190971i
$706$		0			0
$707$	10.3825	−	5.99434i	0.390474	−	0.225440i
$708$		0			0
$709$	−18.5339	−	32.1016i	−0.696055	−	1.20560i	−0.969824	−	0.243807i	$-0.921604\pi$
$709$	−18.5339	−	32.1016i	−0.696055	−	1.20560i	0.273769	−	0.961795i	$-0.411730\pi$
$710$		0			0
$711$	9.17517	−	17.6007i	0.344096	−	0.660078i
$712$		0			0
$713$	22.9094	+	39.6802i	0.857963	+	1.48604i
$714$		0			0
$715$			22.4911i			0.841119i
$716$		0			0
$717$	30.0552	−	31.3781i	1.12243	−	1.17184i
$718$		0			0
$719$	−26.3198	−	15.1958i	−0.981564	−	0.566706i	−0.0788219	−	0.996889i	$-0.525116\pi$
$719$	−26.3198	−	15.1958i	−0.981564	−	0.566706i	−0.902742	+	0.430183i	$0.858449\pi$
$720$		0			0
$721$			10.8268i			0.403210i
$722$		0			0
$723$	−38.9960	−	9.55411i	−1.45028	−	0.355321i
$724$		0			0
$725$	10.4128	−	18.0355i	0.386721	−	0.669821i
$726$		0			0
$727$	−21.6734	+	37.5394i	−0.803821	+	1.39226i	0.113264	+	0.993565i	$0.463869\pi$
$727$	−21.6734	+	37.5394i	−0.803821	+	1.39226i	−0.917084	+	0.398693i	$0.869464\pi$
$728$		0			0
$729$	−3.47815	−	26.7750i	−0.128820	−	0.991668i
$730$		0			0
$731$	38.8523	−	22.4314i	1.43700	−	0.829654i
$732$		0			0
$733$	40.8632			1.50932			0.754658	−	0.656119i	$-0.227803\pi$
$733$	40.8632			1.50932			0.754658	+	0.656119i	$0.227803\pi$
$734$		0			0
$735$	−1.58345	−	5.43836i	−0.0584063	−	0.200597i
$736$		0			0
$737$	−7.68854	−	13.3169i	−0.283211	−	0.490536i
$738$		0			0
$739$	18.5865	−	32.1927i	0.683715	−	1.18423i	−0.290124	−	0.956989i	$-0.593696\pi$
$739$	18.5865	−	32.1927i	0.683715	−	1.18423i	0.973839	−	0.227240i	$-0.0729702\pi$
$740$		0			0
$741$	−13.6436	−	19.5166i	−0.501209	−	0.716960i
$742$		0			0
$743$	9.98139	−	17.2883i	0.366182	−	0.634245i	−0.622783	−	0.782394i	$-0.713998\pi$
$743$	9.98139	−	17.2883i	0.366182	−	0.634245i	0.988965	+	0.148149i	$0.0473316\pi$
$744$		0			0
$745$	6.44060	+	11.1554i	0.235965	+	0.408704i
$746$		0			0
$747$	−38.2249	+	1.64698i	−1.39858	+	0.0602597i
$748$		0			0
$749$	−45.6378			−1.66757
$750$		0			0
$751$	13.2494	−	7.64954i	0.483477	−	0.279136i	−0.238387	−	0.971170i	$-0.576619\pi$
$751$	13.2494	−	7.64954i	0.483477	−	0.279136i	0.721864	+	0.692035i	$0.243285\pi$
$752$		0			0
$753$	−39.0047	−	9.55624i	−1.42141	−	0.348249i
$754$		0			0
$755$	9.47794	−	16.4163i	0.344938	−	0.597449i
$756$		0			0
$757$	14.0126	−	24.2705i	0.509297	−	0.882128i	−0.490645	−	0.871359i	$-0.663239\pi$
$757$	14.0126	−	24.2705i	0.509297	−	0.882128i	0.999942	−	0.0107682i	$-0.00342770\pi$
$758$		0			0
$759$	12.2823	−	50.1312i	0.445818	−	1.81965i
$760$		0			0
$761$			38.4314i			1.39314i	0.717491	+	0.696568i	$0.245291\pi$
$761$			38.4314i			1.39314i	−0.717491	+	0.696568i	$0.754709\pi$
$762$		0			0
$763$	1.64822	+	0.951601i	0.0596696	+	0.0344503i
$764$		0			0
$765$	15.7046	−	9.99230i	0.567802	−	0.361272i
$766$		0			0
$767$		−	23.9328i		−	0.864163i
$768$		0			0
$769$	−13.8355	−	23.9637i	−0.498919	−	0.864153i	0.501080	−	0.865401i	$-0.332936\pi$
$769$	−13.8355	−	23.9637i	−0.498919	−	0.864153i	−0.999999	+	0.00124761i	$0.999603\pi$
$770$		0			0
$771$	−4.74665	+	19.3739i	−0.170946	+	0.697734i
$772$		0			0
$773$	−14.1290	−	24.4721i	−0.508183	−	0.880199i	−0.999955	−	0.00947520i	$-0.996984\pi$
$773$	−14.1290	−	24.4721i	−0.508183	−	0.880199i	0.491772	−	0.870724i	$-0.336349\pi$
$774$		0			0
$775$	17.1782	−	9.91783i	0.617059	−	0.356259i
$776$		0			0
$777$	−5.92273	+	6.18341i	−0.212477	+	0.221829i
$778$		0			0
$779$	49.4251	−	16.7515i	1.77084	−	0.600183i
$780$		0			0
$781$	8.50359	+	4.90955i	0.304282	+	0.175677i
$782$		0			0
$783$	−38.9082	−	7.77411i	−1.39046	−	0.277824i
$784$		0			0
$785$	−25.1389	+	14.5140i	−0.897246	+	0.518025i
$786$		0			0
$787$			12.6007i			0.449167i	0.974455	+	0.224584i	$0.0721022\pi$
$787$			12.6007i			0.449167i	−0.974455	+	0.224584i	$0.927898\pi$
$788$		0			0
$789$	11.4403	+	39.2919i	0.407287	+	1.39883i
$790$		0			0
$791$	−22.6852			−0.806592
$792$		0			0
$793$	20.1460	+	11.6313i	0.715405	+	0.413039i
$794$		0			0
$795$	−7.53380	+	7.86539i	−0.267196	+	0.278957i
$796$		0			0
$797$	14.2376			0.504323			0.252161	−	0.967685i	$-0.418859\pi$
$797$	14.2376			0.504323			0.252161	+	0.967685i	$0.418859\pi$
$798$		0			0
$799$	11.5546			0.408771
$800$		0			0
$801$	7.16850	−	4.56106i	0.253286	−	0.161157i
$802$		0			0
$803$	10.1732	+	5.87347i	0.359003	+	0.207270i
$804$		0			0
$805$	−28.7587			−1.01361
$806$		0			0
$807$	−44.3580	+	12.9154i	−1.56148	+	0.454643i
$808$		0			0
$809$			4.75216i			0.167077i	0.996505	+	0.0835385i	$0.0266221\pi$
$809$			4.75216i			0.167077i	−0.996505	+	0.0835385i	$0.973378\pi$
$810$		0			0
$811$	−18.0364	+	10.4133i	−0.633343	+	0.365661i	−0.782046	−	0.623221i	$-0.785824\pi$
$811$	−18.0364	+	10.4133i	−0.633343	+	0.365661i	0.148702	+	0.988882i	$0.452490\pi$
$812$		0			0
$813$	−18.8065	+	5.47576i	−0.659574	+	0.192043i
$814$		0			0
$815$	14.5544	+	8.40300i	0.509819	+	0.294344i
$816$		0			0
$817$	−44.9987	+	15.2512i	−1.57430	+	0.533573i
$818$		0			0
$819$	15.3810	+	24.1739i	0.537456	+	0.844705i
$820$		0			0
$821$	−7.21206	+	4.16388i	−0.251703	+	0.145321i	−0.620544	−	0.784172i	$-0.713088\pi$
$821$	−7.21206	+	4.16388i	−0.251703	+	0.145321i	0.368841	+	0.929493i	$0.379755\pi$
$822$		0			0
$823$	−25.8342	−	44.7462i	−0.900524	−	1.55975i	−0.826816	−	0.562473i	$-0.809850\pi$
$823$	−25.8342	−	44.7462i	−0.900524	−	1.55975i	−0.0737083	−	0.997280i	$-0.523483\pi$
$824$		0			0
$825$	−21.7026	−	5.31718i	−0.755587	−	0.185121i
$826$		0			0
$827$	−12.2642	−	21.2422i	−0.426468	−	0.738665i	0.570088	−	0.821584i	$-0.306909\pi$
$827$	−12.2642	−	21.2422i	−0.426468	−	0.738665i	−0.996556	+	0.0829189i	$0.973576\pi$
$828$		0			0
$829$		−	14.7185i		−	0.511194i	−0.966783	−	0.255597i	$-0.917728\pi$
$829$		−	14.7185i		−	0.511194i	0.966783	−	0.255597i	$-0.0822720\pi$
$830$		0			0
$831$	−16.5487	−	15.8510i	−0.574067	−	0.549865i
$832$		0			0
$833$	7.73197	+	4.46406i	0.267897	+	0.154670i
$834$		0			0
$835$			32.4608i			1.12335i
$836$		0			0
$837$	−28.3915	−	24.9419i	−0.981353	−	0.862118i
$838$		0			0
$839$	−9.62790	+	16.6760i	−0.332392	+	0.575720i	−0.982980	−	0.183711i	$-0.941189\pi$
$839$	−9.62790	+	16.6760i	−0.332392	+	0.575720i	0.650588	+	0.759430i	$0.274522\pi$
$840$		0			0
$841$	−14.6534	+	25.3803i	−0.505288	+	0.875184i
$842$		0			0
$843$	4.90950	−	20.0386i	0.169092	−	0.690165i
$844$		0			0
$845$	3.98438	−	2.30038i	0.137067	−	0.0791356i
$846$		0			0
$847$	−34.4411			−1.18341
$848$		0			0
$849$	20.5113	−	5.97212i	0.703946	−	0.204963i
$850$		0			0
$851$	5.14243	+	8.90696i	0.176280	+	0.305327i
$852$		0			0
$853$	−15.4361	+	26.7361i	−0.528523	+	0.915428i	0.470924	+	0.882174i	$0.343920\pi$
$853$	−15.4361	+	26.7361i	−0.528523	+	0.915428i	−0.999447	+	0.0332544i	$0.989413\pi$
$854$		0			0
$855$	−18.3807	+	7.12572i	−0.628607	+	0.243694i
$856$		0			0
$857$	20.2314	−	35.0419i	0.691093	−	1.19701i	−0.280387	−	0.959887i	$-0.590463\pi$
$857$	20.2314	−	35.0419i	0.691093	−	1.19701i	0.971480	−	0.237121i	$-0.0762037\pi$
$858$		0			0
$859$	−4.74515	−	8.21884i	−0.161902	−	0.280423i	0.773649	−	0.633615i	$-0.218430\pi$
$859$	−4.74515	−	8.21884i	−0.161902	−	0.280423i	−0.935551	+	0.353192i	$0.885096\pi$
$860$		0			0
$861$	−60.2894	+	17.5540i	−2.05466	+	0.598238i
$862$		0			0
$863$	−41.2793			−1.40516			−0.702582	−	0.711602i	$-0.747970\pi$
$863$	−41.2793			−1.40516			−0.702582	+	0.711602i	$0.747970\pi$
$864$		0			0
$865$	21.6068	−	12.4747i	0.734654	−	0.424153i
$866$		0			0
$867$	0.0249258	−	0.101737i	0.000846524	−	0.00345517i
$868$		0			0
$869$	−15.6477	+	27.1026i	−0.530812	+	0.919393i
$870$		0			0
$871$	5.12678	−	8.87984i	0.173714	−	0.300882i
$872$		0			0
$873$	10.0016	−	19.1860i	0.338503	−	0.649349i
$874$		0			0
$875$			35.2748i			1.19251i
$876$		0			0
$877$	−8.40653	−	4.85351i	−0.283868	−	0.163891i	0.351305	−	0.936261i	$-0.385738\pi$
$877$	−8.40653	−	4.85351i	−0.283868	−	0.163891i	−0.635173	+	0.772370i	$0.719071\pi$
$878$		0			0
$879$	20.5684	+	19.7012i	0.693754	+	0.664506i
$880$		0			0
$881$		−	8.06513i		−	0.271721i	−0.990728	−	0.135860i	$-0.956620\pi$
$881$		−	8.06513i		−	0.271721i	0.990728	−	0.135860i	$-0.0433799\pi$
$882$		0			0
$883$	6.41786	+	11.1161i	0.215978	+	0.374085i	0.953575	−	0.301157i	$-0.0973727\pi$
$883$	6.41786	+	11.1161i	0.215978	+	0.374085i	−0.737597	+	0.675242i	$0.764039\pi$
$884$		0			0
$885$	−19.2439	−	4.71479i	−0.646875	−	0.158486i
$886$		0			0
$887$	15.8426	+	27.4402i	0.531943	+	0.921353i	0.999305	+	0.0372863i	$0.0118713\pi$
$887$	15.8426	+	27.4402i	0.531943	+	0.921353i	−0.467361	+	0.884066i	$0.654795\pi$
$888$		0			0
$889$	10.1136	−	5.83911i	0.339201	−	0.195838i
$890$		0			0
$891$	3.66167	+	42.4132i	0.122670	+	1.42090i
$892$		0			0
$893$	−12.0009	−	2.39303i	−0.401594	−	0.0800798i
$894$		0			0
$895$	−16.2863	−	9.40289i	−0.544391	−	0.314304i
$896$		0			0
$897$	33.0443	−	9.62126i	1.10332	−	0.321245i
$898$		0			0
$899$	−48.0949	+	27.7676i	−1.60405	+	0.926101i
$900$		0			0
$901$		−	17.1674i		−	0.571930i
$902$		0			0
$903$	54.8899	−	15.9819i	1.82662	−	0.531844i
$904$		0			0
$905$	5.81069			0.193154
$906$		0			0
$907$	27.1981	+	15.7028i	0.903096	+	0.521403i	0.878204	−	0.478287i	$-0.158742\pi$
$907$	27.1981	+	15.7028i	0.903096	+	0.521403i	0.0248929	+	0.999690i	$0.492076\pi$
$908$		0			0
$909$	6.37604	+	10.0211i	0.211480	+	0.332378i
$910$		0			0
$911$	−19.4773			−0.645313			−0.322656	−	0.946516i	$-0.604576\pi$
$911$	−19.4773			−0.645313			−0.322656	+	0.946516i	$0.604576\pi$
$912$		0			0
$913$	60.3253			1.99647
$914$		0			0
$915$	13.3213	−	13.9076i	0.440388	−	0.459771i
$916$		0			0
$917$	9.57693	+	5.52924i	0.316258	+	0.182592i
$918$		0			0
$919$	−9.69771			−0.319898			−0.159949	−	0.987125i	$-0.551133\pi$
$919$	−9.69771			−0.319898			−0.159949	+	0.987125i	$0.551133\pi$
$920$		0			0
$921$	−7.25642	−	24.9222i	−0.239107	−	0.821216i
$922$		0			0
$923$			6.54745i			0.215512i
$924$		0			0
$925$	3.85596	−	2.22624i	0.126783	−	0.0731983i
$926$		0			0
$927$	−10.7165	+	0.461734i	−0.351974	+	0.0151653i
$928$		0			0
$929$	15.6693	+	9.04670i	0.514094	+	0.296812i	0.734515	−	0.678592i	$-0.237410\pi$
$929$	15.6693	+	9.04670i	0.514094	+	0.296812i	−0.220421	+	0.975405i	$0.570743\pi$
$930$		0			0
$931$	−7.10609	−	6.23783i	−0.232893	−	0.204437i
$932$		0			0
$933$	−8.27030	+	8.63432i	−0.270758	+	0.282675i
$934$		0			0
$935$	−25.4168	+	14.6744i	−0.831217	+	0.479903i
$936$		0			0
$937$	−4.21971	−	7.30875i	−0.137852	−	0.238766i	0.788831	−	0.614610i	$-0.210686\pi$
$937$	−4.21971	−	7.30875i	−0.137852	−	0.238766i	−0.926683	+	0.375843i	$0.877353\pi$
$938$		0			0
$939$	−4.65605	+	19.0041i	−0.151944	+	0.620175i
$940$		0			0
$941$	−22.5257	−	39.0157i	−0.734318	−	1.27188i	−0.955022	−	0.296535i	$-0.904169\pi$
$941$	−22.5257	−	39.0157i	−0.734318	−	1.27188i	0.220704	−	0.975341i	$-0.429164\pi$
$942$		0			0
$943$			75.4254i			2.45619i
$944$		0			0
$945$	22.4678	−	7.60526i	0.730879	−	0.247399i
$946$		0			0
$947$	24.8376	+	14.3400i	0.807114	+	0.465988i	0.845953	−	0.533258i	$-0.179032\pi$
$947$	24.8376	+	14.3400i	0.807114	+	0.465988i	−0.0388385	+	0.999246i	$0.512366\pi$
$948$		0			0
$949$			7.83295i			0.254268i
$950$		0			0
$951$	13.3584	−	54.5235i	0.433175	−	1.76804i
$952$		0			0
$953$	−4.88327	+	8.45808i	−0.158185	+	0.273984i	−0.934214	−	0.356713i	$-0.883897\pi$
$953$	−4.88327	+	8.45808i	−0.158185	+	0.273984i	0.776029	+	0.630697i	$0.217231\pi$
$954$		0			0
$955$	5.83541	−	10.1072i	0.188829	−	0.327062i
$956$		0			0
$957$	60.7621	+	14.8869i	1.96416	+	0.481224i
$958$		0			0
$959$	25.7623	−	14.8738i	0.831907	−	0.480301i
$960$		0			0
$961$	−21.8953			−0.706301
$962$		0			0
$963$	−1.94633	−	45.1727i	−0.0627197	−	1.45567i
$964$		0			0
$965$	−0.587767	−	1.01804i	−0.0189209	−	0.0327720i
$966$		0			0
$967$	24.9019	−	43.1314i	0.800793	−	1.38701i	−0.118302	−	0.992978i	$-0.537745\pi$
$967$	24.9019	−	43.1314i	0.800793	−	1.38701i	0.919095	−	0.394036i	$-0.128921\pi$
$968$		0			0
$969$	13.1536	−	28.1520i	0.422554	−	0.904373i
$970$		0			0
$971$	0.668663	−	1.15816i	0.0214584	−	0.0371671i	−0.855097	−	0.518468i	$-0.826502\pi$
$971$	0.668663	−	1.15816i	0.0214584	−	0.0371671i	0.876555	+	0.481301i	$0.159836\pi$
$972$		0			0
$973$	−28.5115	−	49.3834i	−0.914038	−	1.58316i
$974$		0			0
$975$	−4.16519	−	14.3054i	−0.133393	−	0.458139i
$976$		0			0
$977$	16.6842			0.533774			0.266887	−	0.963728i	$-0.414005\pi$
$977$	16.6842			0.533774			0.266887	+	0.963728i	$0.414005\pi$
$978$		0			0
$979$	−11.6017	+	6.69823i	−0.370791	+	0.214076i
$980$		0			0
$981$	−0.871612	+	1.67201i	−0.0278284	+	0.0533831i
$982$		0			0
$983$	8.35612	−	14.4732i	0.266519	−	0.461624i	−0.701442	−	0.712727i	$-0.747460\pi$
$983$	8.35612	−	14.4732i	0.266519	−	0.461624i	0.967960	+	0.251103i	$0.0807932\pi$
$984$		0			0
$985$	−5.76679	+	9.98838i	−0.183745	+	0.318256i
$986$		0			0
$987$	14.3012	+	3.50383i	0.455212	+	0.111528i
$988$		0			0
$989$		−	68.6704i		−	2.18359i
$990$		0			0
$991$	−3.60663	−	2.08229i	−0.114568	−	0.0661460i	0.441621	−	0.897202i	$-0.354404\pi$
$991$	−3.60663	−	2.08229i	−0.114568	−	0.0661460i	−0.556189	+	0.831056i	$0.687737\pi$
$992$		0			0
$993$	−29.6843	+	30.9908i	−0.942002	+	0.983464i
$994$		0			0
$995$		−	13.4174i		−	0.425360i
$996$		0			0
$997$	14.2059	+	24.6053i	0.449904	+	0.779257i	0.998379	−	0.0569097i	$-0.0181247\pi$
$997$	14.2059	+	24.6053i	0.449904	+	0.779257i	−0.548475	+	0.836167i	$0.684791\pi$
$998$		0			0
$999$	−6.37299	−	5.59867i	−0.201633	−	0.177134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.o.65.6		16
3.2	odd	2		912.2.bn.n.65.8		16
4.3	odd	2		456.2.bf.c.65.3	✓	16
12.11	even	2		456.2.bf.d.65.1	yes	16
19.12	odd	6		912.2.bn.n.449.8		16
57.50	even	6	inner	912.2.bn.o.449.6		16
76.31	even	6		456.2.bf.d.449.1	yes	16
228.107	odd	6		456.2.bf.c.449.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.3	✓	16	4.3	odd	2
456.2.bf.c.449.3	yes	16	228.107	odd	6
456.2.bf.d.65.1	yes	16	12.11	even	2
456.2.bf.d.449.1	yes	16	76.31	even	6
912.2.bn.n.65.8		16	3.2	odd	2
912.2.bn.n.449.8		16	19.12	odd	6
912.2.bn.o.65.6		16	1.1	even	1	trivial
912.2.bn.o.449.6		16	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)

\(f(q)\)	\(=\)	\(q+(1.25083 + 1.19809i) q^{3} +(-1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(0.129140 + 2.99722i) q^{9} +O(q^{10})\)	\(q+(1.25083 + 1.19809i) q^{3} +(-1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(0.129140 + 2.99722i) q^{9} -4.73011i q^{11} +(2.73150 - 1.57703i) q^{13} +(-0.729951 - 2.50703i) q^{15} +(3.56436 + 2.05788i) q^{17} +(-3.27583 - 2.87557i) q^{19} +(3.78760 + 3.62792i) q^{21} +(5.45589 - 3.14996i) q^{23} +(-1.36367 - 2.36194i) q^{25} +(-3.42942 + 3.90373i) q^{27} +(3.81794 + 6.61287i) q^{29} +7.27292i q^{31} +(5.66712 - 5.91655i) q^{33} +(-3.95335 - 2.28247i) q^{35} +1.63254i q^{37} +(5.30608 + 1.30000i) q^{39} +(-5.98623 + 10.3684i) q^{41} +(5.45011 - 9.43986i) q^{43} +(2.09061 - 4.01041i) q^{45} +(2.43127 - 1.40370i) q^{47} +2.16925 q^{49} +(1.99286 + 6.84449i) q^{51} +(-2.08557 - 3.61231i) q^{53} +(-3.56541 + 6.17546i) q^{55} +(-0.652293 - 7.52160i) q^{57} +(3.79395 - 6.57132i) q^{59} +(3.68771 + 6.38730i) q^{61} +(0.391044 + 9.07581i) q^{63} -4.75488 q^{65} +(2.81536 - 1.62545i) q^{67} +(10.5983 + 2.59661i) q^{69} +(-1.03794 + 1.79776i) q^{71} +(-1.24172 + 2.15072i) q^{73} +(1.12411 - 4.58818i) q^{75} -14.3231i q^{77} +(-5.72981 - 3.30811i) q^{79} +(-8.96665 + 0.774119i) q^{81} +12.7535i q^{83} +(-3.10233 - 5.37340i) q^{85} +(-3.14725 + 12.8458i) q^{87} +(-1.41608 - 2.45273i) q^{89} +(8.27121 - 4.77538i) q^{91} +(-8.71364 + 9.09717i) q^{93} +(2.10930 + 6.22347i) q^{95} +(-6.24590 - 3.60607i) q^{97} +(14.1772 - 0.610844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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