LMFDB - Embedded newform 912.2.bn.n.449.8

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			449.8
Root			$1.25083 + 1.19809i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.n.65.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66299 - 0.484201i) q^{3} +(1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(2.53110 - 1.61045i) q^{9} +O(q^{10})$	\(q+(1.66299 - 0.484201i) q^{3} +(1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(2.53110 - 1.61045i) q^{9} -4.73011i q^{11} +(2.73150 + 1.57703i) q^{13} +(1.80617 - 1.88567i) q^{15} +(-3.56436 + 2.05788i) q^{17} +(-3.27583 + 2.87557i) q^{19} +(5.03567 - 1.46620i) q^{21} +(-5.45589 - 3.14996i) q^{23} +(-1.36367 + 2.36194i) q^{25} +(3.42942 - 3.90373i) q^{27} +(-3.81794 + 6.61287i) q^{29} -7.27292i q^{31} +(-2.29032 - 7.86614i) q^{33} +(3.95335 - 2.28247i) q^{35} -1.63254i q^{37} +(5.30608 + 1.30000i) q^{39} +(5.98623 + 10.3684i) q^{41} +(5.45011 + 9.43986i) q^{43} +(2.09061 - 4.01041i) q^{45} +(-2.43127 - 1.40370i) q^{47} +2.16925 q^{49} +(-4.93108 + 5.14811i) q^{51} +(2.08557 - 3.61231i) q^{53} +(-3.56541 - 6.17546i) q^{55} +(-4.05533 + 6.36822i) q^{57} +(-3.79395 - 6.57132i) q^{59} +(3.68771 - 6.38730i) q^{61} +(7.66436 - 4.87656i) q^{63} +4.75488 q^{65} +(2.81536 + 1.62545i) q^{67} +(-10.5983 - 2.59661i) q^{69} +(1.03794 + 1.79776i) q^{71} +(-1.24172 - 2.15072i) q^{73} +(-1.12411 + 4.58818i) q^{75} -14.3231i q^{77} +(-5.72981 + 3.30811i) q^{79} +(3.81292 - 8.15240i) q^{81} +12.7535i q^{83} +(-3.10233 + 5.37340i) q^{85} +(-3.14725 + 12.8458i) q^{87} +(1.41608 - 2.45273i) q^{89} +(8.27121 + 4.77538i) q^{91} +(-3.52156 - 12.0948i) q^{93} +(-2.10930 + 6.22347i) q^{95} +(-6.24590 + 3.60607i) q^{97} +(-7.61759 - 11.9724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * 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
$3$	1.66299	−	0.484201i	0.960130	−	0.279554i
$3$	1.66299	−	0.484201i	0.960130	−	0.279554i
$4$		0			0
$5$	1.30557	−	0.753769i	0.583867	−	0.337096i	−0.178802	−	0.983885i	$-0.557222\pi$
$5$	1.30557	−	0.753769i	0.583867	−	0.337096i	0.762669	+	0.646790i	$0.223889\pi$
$6$		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
$9$	2.53110	−	1.61045i	0.843699	−	0.536816i
$10$		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	0.828427	−	0.560097i	$-0.189236\pi$
$13$	2.73150	+	1.57703i	0.757583	+	0.437391i	−0.0708442	+	0.997487i	$0.522569\pi$
$14$		0			0
$15$	1.80617	−	1.88567i	0.466352	−	0.486878i
$16$		0			0
$17$	−3.56436	+	2.05788i	−0.864484	+	0.499110i	−0.865511	−	0.500890i	$-0.833006\pi$
$17$	−3.56436	+	2.05788i	−0.864484	+	0.499110i	0.00102753	+	0.999999i	$0.499673\pi$
$18$		0			0
$19$	−3.27583	+	2.87557i	−0.751527	+	0.659702i
$19$	−3.27583	+	2.87557i	−0.751527	+	0.659702i
$20$		0			0
$21$	5.03567	−	1.46620i	1.09887	−	0.319951i
$22$		0			0
$23$	−5.45589	−	3.14996i	−1.13763	−	0.656812i	−0.191788	−	0.981436i	$-0.561429\pi$
$23$	−5.45589	−	3.14996i	−1.13763	−	0.656812i	−0.945843	+	0.324625i	$0.894762\pi$
$24$		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	0.256264	+	0.966607i	$0.417508\pi$
$29$	−3.81794	+	6.61287i	−0.708974	+	1.22798i	−0.965238	+	0.261372i	$0.915825\pi$
$30$		0			0
$31$		−	7.27292i		−	1.30625i	−0.757248	−	0.653127i	$-0.773457\pi$
$31$		−	7.27292i		−	1.30625i	0.757248	−	0.653127i	$-0.226543\pi$
$32$		0			0
$33$	−2.29032	−	7.86614i	−0.398694	−	1.36932i
$34$		0			0
$35$	3.95335	−	2.28247i	0.668238	−	0.385808i
$36$		0			0
$37$		−	1.63254i		−	0.268388i	−0.990955	−	0.134194i	$-0.957155\pi$
$37$		−	1.63254i		−	0.268388i	0.990955	−	0.134194i	$-0.0428445\pi$
$38$		0			0
$39$	5.30608	+	1.30000i	0.849653	+	0.208167i
$40$		0			0
$41$	5.98623	+	10.3684i	0.934891	+	1.61928i	0.774827	+	0.632173i	$0.217837\pi$
$41$	5.98623	+	10.3684i	0.934891	+	1.61928i	0.160064	+	0.987107i	$0.448830\pi$
$42$		0			0
$43$	5.45011	+	9.43986i	0.831134	+	1.43957i	0.897140	+	0.441747i	$0.145641\pi$
$43$	5.45011	+	9.43986i	0.831134	+	1.43957i	−0.0660061	+	0.997819i	$0.521026\pi$
$44$		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	$-0.398972\pi$
$47$	−2.43127	−	1.40370i	−0.354638	−	0.204750i	−0.666726	+	0.745303i	$0.732305\pi$
$48$		0			0
$49$	2.16925			0.309892
$50$		0			0
$51$	−4.93108	+	5.14811i	−0.690489	+	0.720880i
$52$		0			0
$53$	2.08557	−	3.61231i	0.286475	−	0.496190i	−0.686491	−	0.727139i	$-0.740850\pi$
$53$	2.08557	−	3.61231i	0.286475	−	0.496190i	0.972966	+	0.230949i	$0.0741831\pi$
$54$		0			0
$55$	−3.56541	−	6.17546i	−0.480759	−	0.832700i
$56$		0			0
$57$	−4.05533	+	6.36822i	−0.537142	+	0.843492i
$58$		0			0
$59$	−3.79395	−	6.57132i	−0.493931	−	0.855513i	0.506045	−	0.862507i	$-0.331107\pi$
$59$	−3.79395	−	6.57132i	−0.493931	−	0.855513i	−0.999976	+	0.00699432i	$0.997774\pi$
$60$		0			0
$61$	3.68771	−	6.38730i	0.472163	−	0.817810i	−0.527330	−	0.849661i	$-0.676807\pi$
$61$	3.68771	−	6.38730i	0.472163	−	0.817810i	0.999493	+	0.0318509i	$0.0101402\pi$
$62$		0			0
$63$	7.66436	−	4.87656i	0.965618	−	0.614389i
$64$		0			0
$65$	4.75488			0.589770
$66$		0			0
$67$	2.81536	+	1.62545i	0.343951	+	0.198580i	0.662018	−	0.749488i	$-0.269700\pi$
$67$	2.81536	+	1.62545i	0.343951	+	0.198580i	−0.318067	+	0.948068i	$0.603034\pi$
$68$		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	$-0.127357\pi$
$71$	1.03794	+	1.79776i	0.123180	+	0.213355i	−0.797840	+	0.602869i	$0.794024\pi$
$72$		0			0
$73$	−1.24172	−	2.15072i	−0.145332	−	0.251723i	0.784164	−	0.620553i	$-0.213092\pi$
$73$	−1.24172	−	2.15072i	−0.145332	−	0.251723i	−0.929497	+	0.368830i	$0.879759\pi$
$74$		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	−0.786405	−	0.617711i	$-0.788060\pi$
$79$	−5.72981	+	3.30811i	−0.644654	+	0.372191i	0.141751	+	0.989902i	$0.454727\pi$
$80$		0			0
$81$	3.81292	−	8.15240i	0.423657	−	0.905823i
$82$		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	$-0.785372\pi$
$89$	1.41608	−	2.45273i	0.150105	−	0.259989i	0.931266	+	0.364341i	$0.118706\pi$
$90$		0			0
$91$	8.27121	+	4.77538i	0.867058	+	0.500596i
$92$		0			0
$93$	−3.52156	−	12.0948i	−0.365168	−	1.25417i
$94$		0			0
$95$	−2.10930	+	6.22347i	−0.216409	+	0.638514i
$96$		0			0
$97$	−6.24590	+	3.60607i	−0.634175	+	0.366141i	−0.782367	−	0.622817i	$-0.785988\pi$
$97$	−6.24590	+	3.60607i	−0.634175	+	0.366141i	0.148192	+	0.988959i	$0.452655\pi$
$98$		0			0
$99$	−7.61759	−	11.9724i	−0.765597	−	1.20327i
$100$		0			0
$101$	−3.42875	−	1.97959i	−0.341173	−	0.196976i	0.319618	−	0.947547i	$-0.396446\pi$
$101$	−3.42875	−	1.97959i	−0.341173	−	0.196976i	−0.660791	+	0.750570i	$0.729779\pi$
$102$		0			0
$103$		−	3.57546i		−	0.352301i	−0.984363	−	0.176151i	$-0.943635\pi$
$103$		−	3.57546i		−	0.352301i	0.984363	−	0.176151i	$-0.0563645\pi$
$104$		0			0
$105$	5.46923	−	5.70995i	0.533742	−	0.557234i
$106$		0			0
$107$	15.0716			1.45702			0.728511	−	0.685034i	$-0.240213\pi$
$107$	15.0716			1.45702			0.728511	+	0.685034i	$0.240213\pi$
$108$		0			0
$109$	0.544313	−	0.314259i	0.0521357	−	0.0301006i	−0.473706	−	0.880683i	$-0.657084\pi$
$109$	0.544313	−	0.314259i	0.0521357	−	0.0301006i	0.525841	+	0.850583i	$0.323751\pi$
$110$		0			0
$111$	−0.790478	−	2.71491i	−0.0750289	−	0.257687i
$112$		0			0
$113$	7.49162			0.704752			0.352376	−	0.935859i	$-0.385374\pi$
$113$	7.49162			0.704752			0.352376	+	0.935859i	$0.385374\pi$
$114$		0			0
$115$	−9.49736			−0.885633
$116$		0			0
$117$	9.45344	−	0.407315i	0.873971	−	0.0376563i
$118$		0			0
$119$	−10.7931	+	6.23143i	−0.989406	+	0.571234i
$120$		0			0
$121$	−11.3739			−1.03399
$122$		0			0
$123$	14.9755	+	14.3441i	1.35029	+	1.29337i
$124$		0			0
$125$			11.6492i			1.04194i
$126$		0			0
$127$	3.33995	+	1.92832i	0.296373	+	0.171111i	0.640812	−	0.767698i	$-0.278598\pi$
$127$	3.33995	+	1.92832i	0.296373	+	0.171111i	−0.344439	+	0.938809i	$0.611931\pi$
$128$		0			0
$129$	13.6343	+	13.0595i	1.20043	+	1.14982i
$130$		0			0
$131$	−3.16271	+	1.82599i	−0.276327	+	0.159538i	−0.631760	−	0.775164i	$-0.717667\pi$
$131$	−3.16271	+	1.82599i	−0.276327	+	0.159538i	0.355432	+	0.934702i	$0.384334\pi$
$132$		0			0
$133$	−9.91947	+	8.70746i	−0.860127	+	0.755032i
$134$		0			0
$135$	1.53483	−	7.68156i	0.132097	−	0.661123i
$136$		0			0
$137$	−8.50779	−	4.91198i	−0.726870	−	0.419659i	0.0904061	−	0.995905i	$-0.471184\pi$
$137$	−8.50779	−	4.91198i	−0.726870	−	0.419659i	−0.817276	+	0.576246i	$0.804517\pi$
$138$		0			0
$139$	−9.41572	+	16.3085i	−0.798631	+	1.38327i	0.121876	+	0.992545i	$0.461109\pi$
$139$	−9.41572	+	16.3085i	−0.798631	+	1.38327i	−0.920508	+	0.390725i	$0.872224\pi$
$140$		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
$147$	3.60745	−	1.05035i	0.297537	−	0.0866316i
$148$		0			0
$149$	7.39978	−	4.27227i	0.606214	−	0.349998i	−0.165268	−	0.986249i	$-0.552849\pi$
$149$	7.39978	−	4.27227i	0.606214	−	0.349998i	0.771482	+	0.636251i	$0.219516\pi$
$150$		0			0
$151$		−	12.5741i		−	1.02326i	−0.859205	−	0.511632i	$-0.829041\pi$
$151$		−	12.5741i		−	1.02326i	0.859205	−	0.511632i	$-0.170959\pi$
$152$		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	0.938449	+	0.345419i	$0.112263\pi$
$157$	9.62759	+	16.6755i	0.768366	+	1.33085i	−0.170083	+	0.985430i	$0.554404\pi$
$158$		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
$165$	−8.91942	−	8.54339i	−0.694376	−	0.665102i
$166$		0			0
$167$	10.7662	−	18.6475i	0.833110	−	1.44299i	−0.0624500	−	0.998048i	$-0.519891\pi$
$167$	10.7662	−	18.6475i	0.833110	−	1.44299i	0.895560	−	0.444941i	$-0.146775\pi$
$168$		0			0
$169$	−1.52592	−	2.64297i	−0.117379	−	0.203306i
$170$		0			0
$171$	−3.66049	+	12.5539i	−0.279925	+	0.960022i
$172$		0			0
$173$	8.27489	+	14.3325i	0.629128	+	1.08968i	0.987727	+	0.156191i	$0.0499214\pi$
$173$	8.27489	+	14.3325i	0.629128	+	1.08968i	−0.358599	+	0.933492i	$0.616745\pi$
$174$		0			0
$175$	−4.12928	+	7.15213i	−0.312145	+	0.540650i
$176$		0			0
$177$	−9.49116	−	9.09103i	−0.713399	−	0.683323i
$178$		0			0
$179$	−12.4745			−0.932389			−0.466194	−	0.884682i	$-0.654375\pi$
$179$	−12.4745			−0.932389			−0.466194	+	0.884682i	$0.654375\pi$
$180$		0			0
$181$	−3.33803	−	1.92721i	−0.248114	−	0.143249i	0.370786	−	0.928718i	$-0.379088\pi$
$181$	−3.33803	−	1.92721i	−0.248114	−	0.143249i	−0.618900	+	0.785469i	$0.712422\pi$
$182$		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	−0.475498	−	0.879717i	$-0.657732\pi$
$193$	0.675302	−	0.389886i	0.0486093	−	0.0280646i	0.524108	+	0.851652i	$0.324399\pi$
$194$		0			0
$195$	7.90733	−	2.30232i	0.566256	−	0.164872i
$196$		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	−0.664075	−	0.747666i	$-0.731175\pi$
$199$	4.45011	−	7.70781i	0.315460	−	0.546392i	0.979535	+	0.201273i	$0.0645079\pi$
$200$		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
$207$	−18.8822	+	0.813568i	−1.31241	+	0.0565469i
$208$		0			0
$209$	13.6018	+	15.4950i	0.940854	+	1.07181i
$210$		0			0
$211$	−16.8902	+	9.75157i	−1.16277	+	0.671326i	−0.951966	−	0.306203i	$-0.900942\pi$
$211$	−16.8902	+	9.75157i	−1.16277	+	0.671326i	−0.210804	+	0.977528i	$0.567608\pi$
$212$		0			0
$213$	2.59656	+	2.48709i	0.177913	+	0.170413i
$214$		0			0
$215$	14.2309	+	8.21624i	0.970542	+	0.560343i
$216$		0			0
$217$		−	22.0230i		−	1.49502i
$218$		0			0
$219$	−3.10636	−	2.97540i	−0.209908	−	0.201059i
$220$		0			0
$221$	−12.9814			−0.873224
$222$		0			0
$223$	−6.24954	+	3.60817i	−0.418500	+	0.241621i	−0.694435	−	0.719555i	$-0.744346\pi$
$223$	−6.24954	+	3.60817i	−0.418500	+	0.241621i	0.275935	+	0.961176i	$0.411012\pi$
$224$		0			0
$225$	0.352206	+	8.17441i	0.0234804	+	0.544961i
$226$		0			0
$227$	7.69814			0.510944			0.255472	−	0.966816i	$-0.417769\pi$
$227$	7.69814			0.510944			0.255472	+	0.966816i	$0.417769\pi$
$228$		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
$231$	−6.93528	−	23.8193i	−0.456308	−	1.56719i
$232$		0			0
$233$	−4.28304	+	2.47281i	−0.280591	+	0.161999i	−0.633691	−	0.773586i	$-0.718461\pi$
$233$	−4.28304	+	2.47281i	−0.280591	+	0.161999i	0.353100	+	0.935586i	$0.385128\pi$
$234$		0			0
$235$	−4.23225			−0.276082
$236$		0			0
$237$	−7.92684	+	8.27574i	−0.514904	+	0.537567i
$238$		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	−0.313916	−	0.949451i	$-0.601641\pi$
$241$	−20.0747	−	11.5901i	−1.29312	−	0.746584i	−0.979206	+	0.202866i	$0.934974\pi$
$242$		0			0
$243$	2.39345	−	15.4036i	0.153540	−	0.988142i
$244$		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
$249$	6.17524	+	21.2089i	0.391340	+	1.34406i
$250$		0			0
$251$	20.0791	+	11.5927i	1.26738	+	0.731724i	0.974492	−	0.224421i	$-0.0720492\pi$
$251$	20.0791	+	11.5927i	1.26738	+	0.731724i	0.292891	+	0.956146i	$0.405383\pi$
$252$		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	$-0.950279\pi$
$257$	−5.75817	+	9.97345i	−0.359185	+	0.622127i	0.628640	+	0.777697i	$0.283612\pi$
$258$		0			0
$259$		−	4.94346i		−	0.307172i
$260$		0			0
$261$	0.986094	+	22.8864i	0.0610377	+	1.41663i
$262$		0			0
$263$	−20.4618	+	11.8136i	−1.26173	+	0.728458i	−0.973408	−	0.229076i	$-0.926430\pi$
$263$	−20.4618	+	11.8136i	−1.26173	+	0.728458i	−0.288318	+	0.957535i	$0.593096\pi$
$264$		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	0.910643	+	0.413195i	$0.135587\pi$
$269$	13.3368	+	23.1000i	0.813159	+	1.40843i	−0.0974838	+	0.995237i	$0.531079\pi$
$270$		0			0
$271$	−5.65442	−	9.79375i	−0.343482	−	0.594928i	0.641595	−	0.767044i	$-0.278273\pi$
$271$	−5.65442	−	9.79375i	−0.343482	−	0.594928i	−0.985077	+	0.172116i	$0.944940\pi$
$272$		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
$279$	−11.7127	−	18.4085i	−0.701218	−	1.10209i
$280$		0			0
$281$	5.95572	−	10.3156i	0.355289	−	0.615378i	−0.631879	−	0.775067i	$-0.717716\pi$
$281$	5.95572	−	10.3156i	0.355289	−	0.615378i	0.987167	+	0.159689i	$0.0510492\pi$
$282$		0			0
$283$	6.16698	+	10.6815i	0.366589	+	0.634951i	0.989030	−	0.147716i	$-0.0471922\pi$
$283$	6.16698	+	10.6815i	0.366589	+	0.634951i	−0.622441	+	0.782667i	$0.713859\pi$
$284$		0			0
$285$	−0.494336	+	11.3709i	−0.0292819	+	0.673555i
$286$		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
$291$	−8.64083	+	9.02115i	−0.506535	+	0.528829i
$292$		0			0
$293$	−16.4438			−0.960657			−0.480329	−	0.877089i	$-0.659483\pi$
$293$	−16.4438			−0.960657			−0.480329	+	0.877089i	$0.659483\pi$
$294$		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	−0.822333	−	0.569006i	$-0.807328\pi$
$307$	−12.9786	+	7.49319i	−0.740727	+	0.427659i	0.0816069	+	0.996665i	$0.473995\pi$
$308$		0			0
$309$	−1.73124	−	5.94598i	−0.0984871	−	0.338255i
$310$		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	−0.661075	−	0.750320i	$-0.729900\pi$
$313$	5.64826	−	9.78307i	0.319259	−	0.552972i	0.980334	+	0.197348i	$0.0632328\pi$
$314$		0			0
$315$	6.33053	−	12.1438i	0.356685	−	0.684227i
$316$		0			0
$317$	16.2051	−	28.0680i	0.910168	−	1.57646i	0.0963424	−	0.995348i	$-0.469286\pi$
$317$	16.2051	−	28.0680i	0.910168	−	1.57646i	0.813826	−	0.581109i	$-0.197381\pi$
$318$		0			0
$319$	31.2796	+	18.0593i	1.75132	+	1.01113i
$320$		0			0
$321$	25.0639	−	7.29766i	1.39893	−	0.407316i
$322$		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
$327$	0.753025	−	0.786169i	0.0416424	−	0.0434752i
$328$		0			0
$329$	−7.36208	−	4.25050i	−0.405885	−	0.234338i
$330$		0			0
$331$		−	24.7762i		−	1.36183i	−0.732365	−	0.680913i	$-0.761583\pi$
$331$		−	24.7762i		−	1.36183i	0.732365	−	0.680913i	$-0.238417\pi$
$332$		0			0
$333$	−2.62912	−	4.13212i	−0.144075	−	0.226439i
$334$		0			0
$335$	4.90085			0.267762
$336$		0			0
$337$	19.9671	−	11.5280i	1.08768	−	0.627969i	0.154719	−	0.987959i	$-0.450553\pi$
$337$	19.9671	−	11.5280i	1.08768	−	0.627969i	0.932957	+	0.359989i	$0.117220\pi$
$338$		0			0
$339$	12.4585	−	3.62745i	0.676654	−	0.197016i
$340$		0			0
$341$	−34.4017			−1.86296
$342$		0			0
$343$	−14.6279			−0.789832
$344$		0			0
$345$	−15.7940	+	4.59863i	−0.850323	+	0.247582i
$346$		0			0
$347$	−20.6226	+	11.9065i	−1.10708	+	0.639173i	−0.938071	−	0.346442i	$-0.887390\pi$
$347$	−20.6226	+	11.9065i	−1.10708	+	0.639173i	−0.169008	+	0.985615i	$0.554056\pi$
$348$		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
$351$	15.5238	−	5.25473i	0.828599	−	0.280477i
$352$		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
$357$	−14.9317	+	15.5889i	−0.790268	+	0.825051i
$358$		0			0
$359$	−9.67780	+	5.58748i	−0.510775	+	0.294896i	−0.733152	−	0.680065i	$-0.761952\pi$
$359$	−9.67780	+	5.58748i	−0.510775	+	0.294896i	0.222377	+	0.974961i	$0.428618\pi$
$360$		0			0
$361$	2.46215	−	18.8398i	0.129587	−	0.991568i
$362$		0			0
$363$	−18.9148	+	5.50727i	−0.992767	+	0.289056i
$364$		0			0
$365$	−3.24230	−	1.87194i	−0.169710	−	0.0979818i
$366$		0			0
$367$	14.2255	−	24.6393i	0.742566	−	1.28616i	−0.208757	−	0.977968i	$-0.566942\pi$
$367$	14.2255	−	24.6393i	0.742566	−	1.28616i	0.951323	−	0.308195i	$-0.0997250\pi$
$368$		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	$-0.755643\pi$
$373$		−	26.8245i		−	1.38892i	0.719531	−	0.694461i	$-0.244357\pi$
$374$		0			0
$375$	5.64058	+	19.3726i	0.291278	+	1.00040i
$376$		0			0
$377$	−20.8574	+	12.0421i	−1.07421	+	0.620197i
$378$		0			0
$379$		−	4.29692i		−	0.220718i	−0.993892	−	0.110359i	$-0.964800\pi$
$379$		−	4.29692i		−	0.220718i	0.993892	−	0.110359i	$-0.0352001\pi$
$380$		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	$-0.330303\pi$
$383$	−9.62338	−	16.6682i	−0.491732	−	0.851704i	−0.999955	+	0.00952143i	$0.996969\pi$
$384$		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	$-0.290659\pi$
$389$	4.56610	+	2.63624i	0.231510	+	0.133663i	−0.379758	+	0.925086i	$0.623993\pi$
$390$		0			0
$391$	25.9290			1.31128
$392$		0			0
$393$	−4.37542	+	4.56800i	−0.220711	+	0.230425i
$394$		0			0
$395$	−4.98709	+	8.63790i	−0.250928	+	0.434620i
$396$		0			0
$397$	6.69534	+	11.5967i	0.336030	+	0.582020i	0.983682	−	0.179916i	$-0.0575825\pi$
$397$	6.69534	+	11.5967i	0.336030	+	0.582020i	−0.647653	+	0.761936i	$0.724249\pi$
$398$		0			0
$399$	−12.2799	+	19.2835i	−0.614762	+	0.965381i
$400$		0			0
$401$	−9.18871	−	15.9153i	−0.458862	−	0.794773i	0.540039	−	0.841640i	$-0.318409\pi$
$401$	−9.18871	−	15.9153i	−0.458862	−	0.794773i	−0.998901	+	0.0468675i	$0.985076\pi$
$402$		0			0
$403$	11.4696	−	19.8660i	0.571344	−	0.989596i
$404$		0			0
$405$	−1.16701	−	13.5176i	−0.0579893	−	0.671693i
$406$		0			0
$407$	−7.72209			−0.382770
$408$		0			0
$409$	18.7518	+	10.8264i	0.927216	+	0.535329i	0.885930	−	0.463819i	$-0.153521\pi$
$409$	18.7518	+	10.8264i	0.927216	+	0.535329i	0.0412862	+	0.999147i	$0.486854\pi$
$410$		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	0.271812	−	0.962350i	$-0.412377\pi$
$421$	25.4660	−	14.7028i	1.24114	−	0.716571i	0.969326	+	0.245779i	$0.0790437\pi$
$422$		0			0
$423$	−8.41437	+	0.362546i	−0.409121	+	0.0176276i
$424$		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	0.0967066	+	0.995313i	$0.469169\pi$
$431$	−16.8910	+	29.2561i	−0.813613	+	1.40922i	−0.910320	+	0.413906i	$0.864164\pi$
$432$		0			0
$433$	19.5716	+	11.2997i	0.940552	+	0.543028i	0.890133	−	0.455700i	$-0.150611\pi$
$433$	19.5716	+	11.2997i	0.940552	+	0.543028i	0.0504190	+	0.998728i	$0.483944\pi$
$434$		0			0
$435$	5.57382	+	19.1434i	0.267244	+	0.917853i
$436$		0			0
$437$	26.9305	−	5.37007i	1.28826	−	0.256885i
$438$		0			0
$439$	−18.9504	+	10.9410i	−0.904455	+	0.522187i	−0.878643	−	0.477480i	$-0.841550\pi$
$439$	−18.9504	+	10.9410i	−0.904455	+	0.522187i	−0.0258118	+	0.999667i	$0.508217\pi$
$440$		0			0
$441$	5.49058	−	3.49346i	0.261456	−	0.166355i
$442$		0			0
$443$	9.62663	+	5.55794i	0.457375	+	0.264066i	0.710940	−	0.703253i	$-0.248270\pi$
$443$	9.62663	+	5.55794i	0.457375	+	0.264066i	−0.253565	+	0.967318i	$0.581603\pi$
$444$		0			0
$445$		−	4.26960i		−	0.202398i
$446$		0			0
$447$	10.2372	−	10.6877i	0.484201	−	0.505513i
$448$		0			0
$449$	4.07831			0.192468			0.0962338	−	0.995359i	$-0.469320\pi$
$449$	4.07831			0.192468			0.0962338	+	0.995359i	$0.469320\pi$
$450$		0			0
$451$	49.0439	−	28.3155i	2.30939	−	1.33332i
$452$		0			0
$453$	−6.08838	−	20.9106i	−0.286057	−	0.982466i
$454$		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
$459$	−4.19027	+	20.9716i	−0.195585	+	0.978871i
$460$		0			0
$461$	32.2126	−	18.5980i	1.50029	−	0.866194i	0.500292	−	0.865857i	$-0.333226\pi$
$461$	32.2126	−	18.5980i	1.50029	−	0.866194i	1.00000		0.000337526i	$-0.000107438\pi$
$462$		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
$465$	−13.7143	−	13.1361i	−0.635986	−	0.609174i
$466$		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
$471$	24.0849	+	23.0695i	1.10977	+	1.06299i
$472$		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
$477$	−0.538659	−	12.5018i	−0.0246635	−	0.572419i
$478$		0			0
$479$	−0.0351091	−	0.0202702i	−0.00160417	−	0.000926170i	0.499198	−	0.866488i	$-0.333628\pi$
$479$	−0.0351091	−	0.0202702i	−0.00160417	−	0.000926170i	−0.500802	+	0.865562i	$0.666961\pi$
$480$		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	$0.0111926\pi$
$487$			1.55162i			0.0703108i	−0.999382	+	0.0351554i	$0.988807\pi$
$488$		0			0
$489$	−18.5390	+	5.39787i	−0.838364	+	0.244100i
$490$		0			0
$491$	38.3422	−	22.1369i	1.73036	−	0.999024i	0.843100	−	0.537756i	$-0.180728\pi$
$491$	38.3422	−	22.1369i	1.73036	−	0.999024i	0.887261	−	0.461268i	$-0.152605\pi$
$492$		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	0.952274	−	0.305244i	$-0.0987382\pi$
$499$	4.73098	+	8.19429i	0.211788	+	0.366827i	−0.740486	+	0.672071i	$0.765405\pi$
$500$		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	$-0.487499\pi$
$503$	−18.0870	−	10.4426i	−0.806461	−	0.465611i	−0.845725	+	0.533618i	$0.820832\pi$
$504$		0			0
$505$	−5.96860			−0.265599
$506$		0			0
$507$	−3.81733	−	3.65640i	−0.169534	−	0.162386i
$508$		0			0
$509$	2.46000	−	4.26084i	0.109038	−	0.188859i	−0.806343	−	0.591448i	$-0.798556\pi$
$509$	2.46000	−	4.26084i	0.109038	−	0.188859i	0.915381	+	0.402589i	$0.131890\pi$
$510$		0			0
$511$	−3.76003	−	6.51256i	−0.166334	−	0.288099i
$512$		0			0
$513$	−0.00875496	+	22.6495i	−0.000386541	+	1.00000i
$514$		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
$519$	20.7009	+	19.8282i	0.908670	+	0.870362i
$520$		0			0
$521$	−24.1951			−1.06001			−0.530003	−	0.847996i	$-0.677809\pi$
$521$	−24.1951			−1.06001			−0.530003	+	0.847996i	$0.677809\pi$
$522$		0			0
$523$	8.01170	+	4.62555i	0.350327	+	0.202261i	0.664829	−	0.746995i	$-0.268504\pi$
$523$	8.01170	+	4.62555i	0.350327	+	0.202261i	−0.314502	+	0.949257i	$0.601838\pi$
$524$		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
$537$	−20.7450	+	6.04017i	−0.895214	+	0.260653i
$538$		0			0
$539$		−	10.2608i		−	0.441963i
$540$		0			0
$541$	15.3145	−	26.5254i	0.658420	−	1.14042i	−0.322605	−	0.946534i	$-0.604559\pi$
$541$	15.3145	−	26.5254i	0.658420	−	1.14042i	0.981025	−	0.193883i	$-0.0621081\pi$
$542$		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	0.160497	−	0.987036i	$-0.448690\pi$
$547$	−14.3615	−	8.29162i	−0.614054	−	0.354524i	−0.774550	+	0.632512i	$0.782024\pi$
$548$		0			0
$549$	−0.952458	−	22.1057i	−0.0406499	−	0.943450i
$550$		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
$555$	−3.07843	−	2.94865i	−0.130672	−	0.125163i
$556$		0			0
$557$	−26.6376	−	15.3792i	−1.12867	−	0.651639i	−0.185071	−	0.982725i	$-0.559252\pi$
$557$	−26.6376	−	15.3792i	−1.12867	−	0.651639i	−0.943601	+	0.331086i	$0.892585\pi$
$558$		0			0
$559$			34.3800i			1.45412i
$560$		0			0
$561$	24.3511	+	23.3245i	1.02811	+	0.984762i
$562$		0			0
$563$	−5.05699			−0.213127			−0.106563	−	0.994306i	$-0.533985\pi$
$563$	−5.05699			−0.213127			−0.106563	+	0.994306i	$0.533985\pi$
$564$		0			0
$565$	9.78080	−	5.64695i	0.411481	−	0.237569i
$566$		0			0
$567$	11.5458	−	24.6861i	0.484878	−	1.03672i
$568$		0			0
$569$	5.76398			0.241639			0.120819	−	0.992675i	$-0.461448\pi$
$569$	5.76398			0.241639			0.120819	+	0.992675i	$0.461448\pi$
$570$		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
$573$	3.74852	+	12.8743i	0.156596	+	0.537832i
$574$		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
$579$	0.934240	−	0.975360i	0.0388257	−	0.0405346i
$580$		0			0
$581$			38.6185i			1.60216i
$582$		0			0
$583$	−17.0866	−	9.86497i	−0.707656	−	0.408565i
$584$		0			0
$585$	12.0351	−	7.65748i	0.497589	−	0.316598i
$586$		0			0
$587$	−9.73427	+	5.62008i	−0.401776	+	0.231966i	−0.687250	−	0.726421i	$-0.741182\pi$
$587$	−9.73427	+	5.62008i	−0.401776	+	0.231966i	0.285474	+	0.958387i	$0.407849\pi$
$588$		0			0
$589$	20.9138	+	23.8249i	0.861739	+	0.981686i
$590$		0			0
$591$	−3.70444	−	12.7229i	−0.152380	−	0.523351i
$592$		0			0
$593$	9.74801	+	5.62802i	0.400303	+	0.231115i	0.686615	−	0.727022i	$-0.259096\pi$
$593$	9.74801	+	5.62802i	0.400303	+	0.231115i	−0.286312	+	0.958136i	$0.592429\pi$
$594$		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	$-0.757581\pi$
$599$	5.76971	−	9.99344i	0.235744	−	0.408321i	0.959489	+	0.281747i	$0.0909139\pi$
$600$		0			0
$601$		−	45.3443i		−	1.84963i	−0.380415	−	0.924816i	$-0.624219\pi$
$601$		−	45.3443i		−	1.84963i	0.380415	−	0.924816i	$-0.375781\pi$
$602$		0			0
$603$	9.74365	−	0.419819i	0.396792	−	0.0170964i
$604$		0			0
$605$	−14.8494	+	8.57330i	−0.603714	+	0.348554i
$606$		0			0
$607$		−	19.0689i		−	0.773984i	−0.922083	−	0.386992i	$-0.873514\pi$
$607$		−	19.0689i		−	0.773984i	0.922083	−	0.386992i	$-0.126486\pi$
$608$		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	0.502927	−	0.864329i	$-0.332257\pi$
$613$	−12.3068	−	21.3160i	−0.497067	−	0.860946i	−0.999994	+	0.00338287i	$0.998923\pi$
$614$		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	$-0.126862\pi$
$617$	25.9907	+	15.0058i	1.04635	+	0.604109i	0.124723	+	0.992192i	$0.460196\pi$
$618$		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
$621$	−31.0071	+	10.4958i	−1.24427	+	0.421180i
$622$		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
$627$	30.1224	+	19.1822i	1.20297	+	0.766062i
$628$		0			0
$629$	3.35958	+	5.81896i	0.133955	+	0.232017i
$630$		0			0
$631$	−11.6963	+	20.2585i	−0.465620	+	0.806478i	−0.999229	−	0.0392531i	$-0.987502\pi$
$631$	−11.6963	+	20.2585i	−0.465620	+	0.806478i	0.533609	+	0.845731i	$0.320835\pi$
$632$		0			0
$633$	−23.3666	+	24.3951i	−0.928739	+	0.969617i
$634$		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	$-0.164925\pi$
$641$	0.138525	+	0.239932i	0.00547140	+	0.00947675i	−0.863277	+	0.504731i	$0.831592\pi$
$642$		0			0
$643$	−9.96549	−	17.2607i	−0.393001	−	0.680697i	0.599843	−	0.800118i	$-0.295230\pi$
$643$	−9.96549	−	17.2607i	−0.393001	−	0.680697i	−0.992844	+	0.119421i	$0.961896\pi$
$644$		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
$651$	−10.6635	−	36.6240i	−0.417937	−	1.43541i
$652$		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	$-0.920934\pi$
$659$	−6.97599	+	12.0828i	−0.271746	+	0.470678i	0.697563	+	0.716523i	$0.254268\pi$
$660$		0			0
$661$	16.1466	+	9.32226i	0.628031	+	0.362594i	0.779989	−	0.625793i	$-0.215225\pi$
$661$	16.1466	+	9.32226i	0.628031	+	0.362594i	−0.151958	+	0.988387i	$0.548558\pi$
$662$		0			0
$663$	−21.5880	+	6.28562i	−0.838409	+	0.244113i
$664$		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
$669$	−8.64586	+	9.02640i	−0.334268	+	0.348981i
$670$		0			0
$671$	−30.2126	−	17.4433i	−1.16634	−	0.673389i
$672$		0			0
$673$		−	7.16700i		−	0.276268i	−0.990414	−	0.138134i	$-0.955890\pi$
$673$		−	7.16700i		−	0.276268i	0.990414	−	0.138134i	$-0.0441104\pi$
$674$		0			0
$675$	4.54378	+	13.4235i	0.174890	+	0.516669i
$676$		0			0
$677$	−4.36818			−0.167883			−0.0839415	−	0.996471i	$-0.526751\pi$
$677$	−4.36818			−0.167883			−0.0839415	+	0.996471i	$0.526751\pi$
$678$		0			0
$679$	−18.9131	+	10.9195i	−0.725817	+	0.419051i
$680$		0			0
$681$	12.8020	−	3.72745i	0.490572	−	0.142836i
$682$		0			0
$683$	7.77593			0.297538			0.148769	−	0.988872i	$-0.452469\pi$
$683$	7.77593			0.297538			0.148769	+	0.988872i	$0.452469\pi$
$684$		0			0
$685$	−14.8100			−0.565860
$686$		0			0
$687$	−31.9533	+	9.30361i	−1.21910	+	0.354955i
$688$		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
$693$	−23.0666	−	36.2532i	−0.876229	−	1.37715i
$694$		0			0
$695$			28.3891i			1.07686i
$696$		0			0
$697$	−42.6741	−	24.6379i	−1.61640	−	0.933227i
$698$		0			0
$699$	−5.92533	+	6.18613i	−0.224117	+	0.233981i
$700$		0			0
$701$	−36.7393	+	21.2115i	−1.38762	+	0.801146i	−0.993047	−	0.117717i	$-0.962442\pi$
$701$	−36.7393	+	21.2115i	−1.38762	+	0.801146i	−0.394578	+	0.918863i	$0.629109\pi$
$702$		0			0
$703$	4.69449	+	5.34793i	0.177056	+	0.201701i
$704$		0			0
$705$	−7.03821	+	2.04926i	−0.265074	+	0.0771796i
$706$		0			0
$707$	−10.3825	−	5.99434i	−0.390474	−	0.225440i
$708$		0			0
$709$	−18.5339	+	32.1016i	−0.696055	+	1.20560i	0.273769	+	0.961795i	$0.411730\pi$
$709$	−18.5339	+	32.1016i	−0.696055	+	1.20560i	−0.969824	+	0.243807i	$0.921604\pi$
$710$		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
$717$	−12.1466	−	41.7176i	−0.453623	−	1.55797i
$718$		0			0
$719$	26.3198	−	15.1958i	0.981564	−	0.566706i	0.0788219	−	0.996889i	$-0.474884\pi$
$719$	26.3198	−	15.1958i	0.981564	−	0.566706i	0.902742	+	0.430183i	$0.141551\pi$
$720$		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	−0.917084	−	0.398693i	$-0.869464\pi$
$727$	−21.6734	−	37.5394i	−0.803821	−	1.39226i	0.113264	−	0.993565i	$-0.463869\pi$
$728$		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
$735$	3.91803	−	4.09048i	0.144519	−	0.150880i
$736$		0			0
$737$	7.68854	−	13.3169i	0.283211	−	0.490536i
$738$		0			0
$739$	18.5865	+	32.1927i	0.683715	+	1.18423i	0.973839	+	0.227240i	$0.0729702\pi$
$739$	18.5865	+	32.1927i	0.683715	+	1.18423i	−0.290124	+	0.956989i	$0.593696\pi$
$740$		0			0
$741$	−21.1201	+	10.9994i	−0.775865	+	0.404074i
$742$		0			0
$743$	−9.98139	−	17.2883i	−0.366182	−	0.634245i	0.622783	−	0.782394i	$-0.286002\pi$
$743$	−9.98139	−	17.2883i	−0.366182	−	0.634245i	−0.988965	+	0.148149i	$0.952668\pi$
$744$		0			0
$745$	6.44060	−	11.1554i	0.235965	−	0.408704i
$746$		0			0
$747$	20.5388	+	32.2803i	0.751475	+	1.18107i
$748$		0			0
$749$	45.6378			1.66757
$750$		0			0
$751$	13.2494	+	7.64954i	0.483477	+	0.279136i	0.721864	−	0.692035i	$-0.243285\pi$
$751$	13.2494	+	7.64954i	0.483477	+	0.279136i	−0.238387	+	0.971170i	$0.576619\pi$
$752$		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	0.999942	+	0.0107682i	$0.00342770\pi$
$757$	14.0126	+	24.2705i	0.509297	+	0.882128i	−0.490645	+	0.871359i	$0.663239\pi$
$758$		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
$765$	0.801268	+	18.5968i	0.0289699	+	0.672367i
$766$		0			0
$767$		−	23.9328i		−	0.864163i
$768$		0			0
$769$	−13.8355	+	23.9637i	−0.498919	+	0.864153i	−0.999999	−	0.00124761i	$-0.999603\pi$
$769$	−13.8355	+	23.9637i	−0.498919	+	0.864153i	0.501080	+	0.865401i	$0.332936\pi$
$770$		0			0
$771$	−4.74665	+	19.3739i	−0.170946	+	0.697734i
$772$		0			0
$773$	14.1290	−	24.4721i	0.508183	−	0.880199i	−0.491772	−	0.870724i	$-0.663651\pi$
$773$	14.1290	−	24.4721i	0.508183	−	0.880199i	0.999955	−	0.00947520i	$-0.00301610\pi$
$774$		0			0
$775$	17.1782	+	9.91783i	0.617059	+	0.356259i
$776$		0			0
$777$	−2.39363	−	8.22094i	−0.0858710	−	0.294925i
$778$		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
$783$	12.7215	+	37.5825i	0.454629	+	1.34309i
$784$		0			0
$785$	25.1389	+	14.5140i	0.897246	+	0.518025i
$786$		0			0
$787$		−	12.6007i		−	0.449167i	−0.974455	−	0.224584i	$-0.927898\pi$
$787$		−	12.6007i		−	0.449167i	0.974455	−	0.224584i	$-0.0721022\pi$
$788$		0			0
$789$	−28.3076	+	29.5536i	−1.00778	+	1.05214i
$790$		0			0
$791$	22.6852			0.806592
$792$		0			0
$793$	20.1460	−	11.6313i	0.715405	−	0.413039i
$794$		0			0
$795$	−3.04473	−	10.4572i	−0.107985	−	0.370877i
$796$		0			0
$797$	−14.2376			−0.504323			−0.252161	−	0.967685i	$-0.581141\pi$
$797$	−14.2376			−0.504323			−0.252161	+	0.967685i	$0.581141\pi$
$798$		0			0
$799$	11.5546			0.408771
$800$		0			0
$801$	−0.365745	−	8.48863i	−0.0129230	−	0.299931i
$802$		0			0
$803$	−10.1732	+	5.87347i	−0.359003	+	0.207270i
$804$		0			0
$805$	−28.7587			−1.01361
$806$		0			0
$807$	33.3641	+	31.9575i	1.17447	+	1.12496i
$808$		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	0.148702	−	0.988882i	$-0.452490\pi$
$811$	−18.0364	−	10.4133i	−0.633343	−	0.365661i	−0.782046	+	0.623221i	$0.785824\pi$
$812$		0			0
$813$	−14.1454	−	13.5491i	−0.496101	−	0.475186i
$814$		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
$819$	28.6257	−	1.23338i	1.00026	−	0.0430978i
$820$		0			0
$821$	7.21206	+	4.16388i	0.251703	+	0.145321i	0.620544	−	0.784172i	$-0.286912\pi$
$821$	7.21206	+	4.16388i	0.251703	+	0.145321i	−0.368841	+	0.929493i	$0.620245\pi$
$822$		0			0
$823$	−25.8342	+	44.7462i	−0.900524	+	1.55975i	−0.0737083	+	0.997280i	$0.523483\pi$
$823$	−25.8342	+	44.7462i	−0.900524	+	1.55975i	−0.826816	+	0.562473i	$0.809850\pi$
$824$		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	$-0.693091\pi$
$827$	12.2642	−	21.2422i	0.426468	−	0.738665i	0.996556	+	0.0829189i	$0.0264243\pi$
$828$		0			0
$829$			14.7185i			0.511194i	0.966783	+	0.255597i	$0.0822720\pi$
$829$			14.7185i			0.511194i	−0.966783	+	0.255597i	$0.917728\pi$
$830$		0			0
$831$	−22.0017	+	6.40607i	−0.763231	+	0.222224i
$832$		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	$-0.0588110\pi$
$839$	9.62790	+	16.6760i	0.332392	+	0.575720i	−0.650588	+	0.759430i	$0.725478\pi$
$840$		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
$849$	15.4277	+	14.7773i	0.529476	+	0.507154i
$850$		0			0
$851$	−5.14243	+	8.90696i	−0.176280	+	0.305327i
$852$		0			0
$853$	−15.4361	−	26.7361i	−0.528523	−	0.915428i	−0.999447	−	0.0332544i	$-0.989413\pi$
$853$	−15.4361	−	26.7361i	−0.528523	−	0.915428i	0.470924	−	0.882174i	$-0.343920\pi$
$854$		0			0
$855$	4.68373	+	19.1491i	0.160180	+	0.654886i
$856$		0			0
$857$	−20.2314	−	35.0419i	−0.691093	−	1.19701i	−0.971480	−	0.237121i	$-0.923796\pi$
$857$	−20.2314	−	35.0419i	−0.691093	−	1.19701i	0.280387	−	0.959887i	$-0.409537\pi$
$858$		0			0
$859$	−4.74515	+	8.21884i	−0.161902	+	0.280423i	−0.935551	−	0.353192i	$-0.885096\pi$
$859$	−4.74515	+	8.21884i	−0.161902	+	0.280423i	0.773649	+	0.633615i	$0.218430\pi$
$860$		0			0
$861$	45.3469	+	43.4351i	1.54542	+	1.48026i
$862$		0			0
$863$	41.2793			1.40516			0.702582	−	0.711602i	$-0.252030\pi$
$863$	41.2793			1.40516			0.702582	+	0.711602i	$0.252030\pi$
$864$		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	−0.635173	−	0.772370i	$-0.719071\pi$
$877$	−8.40653	+	4.85351i	−0.283868	+	0.163891i	0.351305	+	0.936261i	$0.385738\pi$
$878$		0			0
$879$	−27.3459	+	7.96211i	−0.922356	+	0.268555i
$880$		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	−0.737597	−	0.675242i	$-0.764039\pi$
$883$	6.41786	−	11.1161i	0.215978	−	0.374085i	0.953575	+	0.301157i	$0.0973727\pi$
$884$		0			0
$885$	−19.2439	−	4.71479i	−0.646875	−	0.158486i
$886$		0			0
$887$	−15.8426	+	27.4402i	−0.531943	+	0.921353i	0.467361	+	0.884066i	$0.345205\pi$
$887$	−15.8426	+	27.4402i	−0.531943	+	0.921353i	−0.999305	+	0.0372863i	$0.988129\pi$
$888$		0			0
$889$	10.1136	+	5.83911i	0.339201	+	0.195838i
$890$		0			0
$891$	−38.5617	−	18.0355i	−1.29187	−	0.604212i
$892$		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
$897$	−24.8544	−	23.8066i	−0.829865	−	0.794879i
$898$		0			0
$899$	48.0949	+	27.7676i	1.60405	+	0.926101i
$900$		0			0
$901$			17.1674i			0.571930i
$902$		0			0
$903$	41.2857	+	39.5451i	1.37390	+	1.31598i
$904$		0			0
$905$	−5.81069			−0.193154
$906$		0			0
$907$	27.1981	−	15.7028i	0.903096	−	0.521403i	0.0248929	−	0.999690i	$-0.492076\pi$
$907$	27.1981	−	15.7028i	0.903096	−	0.521403i	0.878204	+	0.478287i	$0.158742\pi$
$908$		0			0
$909$	−11.8665	+	0.511286i	−0.393587	+	0.0169583i
$910$		0			0
$911$	19.4773			0.645313			0.322656	−	0.946516i	$-0.395424\pi$
$911$	19.4773			0.645313			0.322656	+	0.946516i	$0.395424\pi$
$912$		0			0
$913$	60.3253			1.99647
$914$		0			0
$915$	−5.38370	−	18.4904i	−0.177979	−	0.611272i
$916$		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
$921$	−17.9551	+	18.7454i	−0.591640	+	0.617681i
$922$		0			0
$923$			6.54745i			0.215512i
$924$		0			0
$925$	3.85596	+	2.22624i	0.126783	+	0.0731983i
$926$		0			0
$927$	−5.75810	−	9.04985i	−0.189121	−	0.297236i
$928$		0			0
$929$	−15.6693	+	9.04670i	−0.514094	+	0.296812i	−0.734515	−	0.678592i	$-0.762590\pi$
$929$	−15.6693	+	9.04670i	−0.514094	+	0.296812i	0.220421	+	0.975405i	$0.429257\pi$
$930$		0			0
$931$	−7.10609	+	6.23783i	−0.232893	+	0.204437i
$932$		0			0
$933$	3.34238	+	11.4795i	0.109425	+	0.375820i
$934$		0			0
$935$	25.4168	+	14.6744i	0.831217	+	0.479903i
$936$		0			0
$937$	−4.21971	+	7.30875i	−0.137852	+	0.238766i	−0.926683	−	0.375843i	$-0.877353\pi$
$937$	−4.21971	+	7.30875i	−0.137852	+	0.238766i	0.788831	+	0.614610i	$0.210686\pi$
$938$		0			0
$939$	4.65605	−	19.0041i	0.151944	−	0.620175i
$940$		0			0
$941$	22.5257	−	39.0157i	0.734318	−	1.27188i	−0.220704	−	0.975341i	$-0.570836\pi$
$941$	22.5257	−	39.0157i	0.734318	−	1.27188i	0.955022	−	0.296535i	$-0.0958311\pi$
$942$		0			0
$943$		−	75.4254i		−	2.45619i
$944$		0			0
$945$	4.64757	−	23.2603i	0.151186	−	0.756659i
$946$		0			0
$947$	−24.8376	+	14.3400i	−0.807114	+	0.465988i	−0.845953	−	0.533258i	$-0.820968\pi$
$947$	−24.8376	+	14.3400i	−0.807114	+	0.465988i	0.0388385	+	0.999246i	$0.487634\pi$
$948$		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	$-0.116103\pi$
$953$	4.88327	+	8.45808i	0.158185	+	0.273984i	−0.776029	+	0.630697i	$0.782769\pi$
$954$		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
$963$	38.1476	−	24.2719i	1.22929	−	0.782152i
$964$		0			0
$965$	0.587767	−	1.01804i	0.0189209	−	0.0327720i
$966$		0			0
$967$	24.9019	+	43.1314i	0.800793	+	1.38701i	0.919095	+	0.394036i	$0.128921\pi$
$967$	24.9019	+	43.1314i	0.800793	+	1.38701i	−0.118302	+	0.992978i	$0.537745\pi$
$968$		0			0
$969$	1.34960	−	31.0440i	0.0433554	−	0.997278i
$970$		0			0
$971$	−0.668663	−	1.15816i	−0.0214584	−	0.0371671i	0.855097	−	0.518468i	$-0.173498\pi$
$971$	−0.668663	−	1.15816i	−0.0214584	−	0.0371671i	−0.876555	+	0.481301i	$0.840164\pi$
$972$		0			0
$973$	−28.5115	+	49.3834i	−0.914038	+	1.58316i
$974$		0			0
$975$	−10.3062	+	10.7599i	−0.330064	+	0.344591i
$976$		0			0
$977$	−16.6842			−0.533774			−0.266887	−	0.963728i	$-0.585995\pi$
$977$	−16.6842			−0.533774			−0.266887	+	0.963728i	$0.585995\pi$
$978$		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	$-0.252540\pi$
$983$	−8.35612	−	14.4732i	−0.266519	−	0.461624i	−0.967960	+	0.251103i	$0.919207\pi$
$984$		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	−0.556189	−	0.831056i	$-0.687737\pi$
$991$	−3.60663	+	2.08229i	−0.114568	+	0.0661460i	0.441621	+	0.897202i	$0.354404\pi$
$992$		0			0
$993$	−11.9967	−	41.2027i	−0.380703	−	1.30753i
$994$		0			0
$995$		−	13.4174i		−	0.425360i
$996$		0			0
$997$	14.2059	−	24.6053i	0.449904	−	0.779257i	−0.548475	−	0.836167i	$-0.684791\pi$
$997$	14.2059	−	24.6053i	0.449904	−	0.779257i	0.998379	+	0.0569097i	$0.0181247\pi$
$998$		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.n.449.8		16
3.2	odd	2		912.2.bn.o.449.6		16
4.3	odd	2		456.2.bf.d.449.1	yes	16
12.11	even	2		456.2.bf.c.449.3	yes	16
19.8	odd	6		912.2.bn.o.65.6		16
57.8	even	6	inner	912.2.bn.n.65.8		16
76.27	even	6		456.2.bf.c.65.3	✓	16
228.179	odd	6		456.2.bf.d.65.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.3	✓	16	76.27	even	6
456.2.bf.c.449.3	yes	16	12.11	even	2
456.2.bf.d.65.1	yes	16	228.179	odd	6
456.2.bf.d.449.1	yes	16	4.3	odd	2
912.2.bn.n.65.8		16	57.8	even	6	inner
912.2.bn.n.449.8		16	1.1	even	1	trivial
912.2.bn.o.65.6		16	19.8	odd	6
912.2.bn.o.449.6		16	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)

\(f(q)\)	\(=\)	\(q+(1.66299 - 0.484201i) q^{3} +(1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(2.53110 - 1.61045i) q^{9} +O(q^{10})\)	\(q+(1.66299 - 0.484201i) q^{3} +(1.30557 - 0.753769i) q^{5} +3.02808 q^{7} +(2.53110 - 1.61045i) q^{9} -4.73011i q^{11} +(2.73150 + 1.57703i) q^{13} +(1.80617 - 1.88567i) q^{15} +(-3.56436 + 2.05788i) q^{17} +(-3.27583 + 2.87557i) q^{19} +(5.03567 - 1.46620i) q^{21} +(-5.45589 - 3.14996i) q^{23} +(-1.36367 + 2.36194i) q^{25} +(3.42942 - 3.90373i) q^{27} +(-3.81794 + 6.61287i) q^{29} -7.27292i q^{31} +(-2.29032 - 7.86614i) q^{33} +(3.95335 - 2.28247i) q^{35} -1.63254i q^{37} +(5.30608 + 1.30000i) q^{39} +(5.98623 + 10.3684i) q^{41} +(5.45011 + 9.43986i) q^{43} +(2.09061 - 4.01041i) q^{45} +(-2.43127 - 1.40370i) q^{47} +2.16925 q^{49} +(-4.93108 + 5.14811i) q^{51} +(2.08557 - 3.61231i) q^{53} +(-3.56541 - 6.17546i) q^{55} +(-4.05533 + 6.36822i) q^{57} +(-3.79395 - 6.57132i) q^{59} +(3.68771 - 6.38730i) q^{61} +(7.66436 - 4.87656i) q^{63} +4.75488 q^{65} +(2.81536 + 1.62545i) q^{67} +(-10.5983 - 2.59661i) q^{69} +(1.03794 + 1.79776i) q^{71} +(-1.24172 - 2.15072i) q^{73} +(-1.12411 + 4.58818i) q^{75} -14.3231i q^{77} +(-5.72981 + 3.30811i) q^{79} +(3.81292 - 8.15240i) q^{81} +12.7535i q^{83} +(-3.10233 + 5.37340i) q^{85} +(-3.14725 + 12.8458i) q^{87} +(1.41608 - 2.45273i) q^{89} +(8.27121 + 4.77538i) q^{91} +(-3.52156 - 12.0948i) q^{93} +(-2.10930 + 6.22347i) q^{95} +(-6.24590 + 3.60607i) q^{97} +(-7.61759 - 11.9724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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