LMFDB - Embedded newform 1216.2.n.e.255.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(255,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1216.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.n (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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.31726512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 10x^{4} + 3x^{3} + 84x^{2} - 27x + 9 $ x^6 - x^5 + 10x^4 + 3x^3 + 84x^2 - 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			255.3
Root			$1.69617 - 2.93786i$ of defining polynomial
Character	$\chi$	$=$	1216.255
Dual form			1216.2.n.e.639.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69617 - 2.93786i) q^{3} +(1.19617 - 2.07183i) q^{5} +1.22147i q^{7} +(-4.25400 - 7.36814i) q^{9} +O(q^{10})$	\(q+(1.69617 - 2.93786i) q^{3} +(1.19617 - 2.07183i) q^{5} +1.22147i q^{7} +(-4.25400 - 7.36814i) q^{9} -2.95353i q^{11} +(-3.00000 + 1.73205i) q^{13} +(-4.05783 - 7.02836i) q^{15} +(0.138344 - 0.239619i) q^{17} +(1.30383 + 4.15933i) q^{19} +(3.58852 + 2.07183i) q^{21} +(-1.05783 + 0.610737i) q^{23} +(-0.361656 - 0.626406i) q^{25} -18.6850 q^{27} +(6.58852 - 3.80388i) q^{29} -8.90034 q^{31} +(-8.67703 - 5.00969i) q^{33} +(2.53069 + 1.46109i) q^{35} -7.60776i q^{37} +11.7514i q^{39} +(8.26200 + 4.77007i) q^{41} +(3.00000 + 1.73205i) q^{43} -20.3541 q^{45} +(4.05783 - 2.34279i) q^{47} +5.50800 q^{49} +(-0.469311 - 0.812871i) q^{51} +(6.00000 - 3.46410i) q^{53} +(-6.11921 - 3.53292i) q^{55} +(14.4310 + 3.22448i) q^{57} +(3.44217 - 5.96202i) q^{59} +(3.19617 + 5.53593i) q^{61} +(9.00000 - 5.19615i) q^{63} +8.28732i q^{65} +(-3.83452 - 6.64158i) q^{67} +4.14366i q^{69} +(-3.00000 + 5.19615i) q^{71} +(1.75400 - 3.03802i) q^{73} -2.45372 q^{75} +3.60766 q^{77} +(-0.392344 + 0.679560i) q^{79} +(-18.9310 + 32.7895i) q^{81} +8.31866i q^{83} +(-0.330967 - 0.573252i) q^{85} -25.8082i q^{87} +(-2.58497 + 1.49243i) q^{89} +(-2.11566 - 3.66442i) q^{91} +(-15.0965 + 26.1479i) q^{93} +(10.1770 + 2.27396i) q^{95} +(-5.67703 - 3.27764i) q^{97} +(-21.7620 + 12.5643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} - 2 q^{5} - 10 q^{9}+O(q^{10}) $ 6 * q + q^3 - 2 * q^5 - 10 * q^9	$ 6 q + q^{3} - 2 q^{5} - 10 q^{9} - 18 q^{13} - 18 q^{15} - 2 q^{17} + 17 q^{19} - 6 q^{21} - 5 q^{25} - 26 q^{27} + 12 q^{29} - 4 q^{31} + 3 q^{33} - 6 q^{35} + 3 q^{41} + 18 q^{43} - 12 q^{45} + 18 q^{47} + 2 q^{49} - 24 q^{51} + 36 q^{53} + 12 q^{55} + 16 q^{57} + 27 q^{59} + 10 q^{61} + 54 q^{63} - 11 q^{67} - 18 q^{71} - 5 q^{73} + 46 q^{75} + 40 q^{77} + 16 q^{79} - 43 q^{81} - 26 q^{85} - 24 q^{89} - 32 q^{93} + 6 q^{95} + 21 q^{97} - 84 q^{99}+O(q^{100}) $ 6 * q + q^3 - 2 * q^5 - 10 * q^9 - 18 * q^13 - 18 * q^15 - 2 * q^17 + 17 * q^19 - 6 * q^21 - 5 * q^25 - 26 * q^27 + 12 * q^29 - 4 * q^31 + 3 * q^33 - 6 * q^35 + 3 * q^41 + 18 * q^43 - 12 * q^45 + 18 * q^47 + 2 * q^49 - 24 * q^51 + 36 * q^53 + 12 * q^55 + 16 * q^57 + 27 * q^59 + 10 * q^61 + 54 * q^63 - 11 * q^67 - 18 * q^71 - 5 * q^73 + 46 * q^75 + 40 * q^77 + 16 * q^79 - 43 * q^81 - 26 * q^85 - 24 * q^89 - 32 * q^93 + 6 * q^95 + 21 * q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	1.69617	−	2.93786i	0.979285	−	1.69617i	0.314286	−	0.949328i	$-0.398235\pi$
$3$	1.69617	−	2.93786i	0.979285	−	1.69617i	0.664999	−	0.746844i	$-0.268432\pi$
$4$		0			0
$5$	1.19617	−	2.07183i	0.534944	−	0.926551i	−0.464222	−	0.885719i	$-0.653666\pi$
$5$	1.19617	−	2.07183i	0.534944	−	0.926551i	0.999166	−	0.0408319i	$-0.0130008\pi$
$6$		0			0
$7$			1.22147i			0.461674i	0.972992	+	0.230837i	$0.0741464\pi$
$7$			1.22147i			0.461674i	−0.972992	+	0.230837i	$0.925854\pi$
$8$		0			0
$9$	−4.25400	−	7.36814i	−1.41800	−	2.45605i
$10$		0			0
$11$		−	2.95353i		−	0.890521i	−0.895401	−	0.445261i	$-0.853111\pi$
$11$		−	2.95353i		−	0.890521i	0.895401	−	0.445261i	$-0.146889\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$		0			0
$15$	−4.05783	−	7.02836i	−1.04773	−	1.81472i
$16$		0			0
$17$	0.138344	−	0.239619i	0.0335534	−	0.0581162i	−0.848761	−	0.528777i	$-0.822651\pi$
$17$	0.138344	−	0.239619i	0.0335534	−	0.0581162i	0.882314	+	0.470660i	$0.155984\pi$
$18$		0			0
$19$	1.30383	+	4.15933i	0.299119	+	0.954216i
$19$	1.30383	+	4.15933i	0.299119	+	0.954216i
$20$		0			0
$21$	3.58852	+	2.07183i	0.783079	+	0.452111i
$22$		0			0
$23$	−1.05783	+	0.610737i	−0.220572	+	0.127348i	−0.606215	−	0.795301i	$-0.707313\pi$
$23$	−1.05783	+	0.610737i	−0.220572	+	0.127348i	0.385643	+	0.922648i	$0.373980\pi$
$24$		0			0
$25$	−0.361656	−	0.626406i	−0.0723311	−	0.125281i
$26$		0			0
$27$	−18.6850			−3.59594
$28$		0			0
$29$	6.58852	−	3.80388i	1.22346	−	0.706363i	0.257804	−	0.966197i	$-0.417001\pi$
$29$	6.58852	−	3.80388i	1.22346	−	0.706363i	0.965653	+	0.259834i	$0.0836679\pi$
$30$		0			0
$31$	−8.90034			−1.59855			−0.799275	−	0.600966i	$-0.794783\pi$
$31$	−8.90034			−1.59855			−0.799275	+	0.600966i	$0.794783\pi$
$32$		0			0
$33$	−8.67703	−	5.00969i	−1.51048	−	0.872075i
$34$		0			0
$35$	2.53069	+	1.46109i	0.427764	+	0.246970i
$36$		0			0
$37$		−	7.60776i		−	1.25071i	−0.780341	−	0.625354i	$-0.784954\pi$
$37$		−	7.60776i		−	1.25071i	0.780341	−	0.625354i	$-0.215046\pi$
$38$		0			0
$39$			11.7514i			1.88173i
$40$		0			0
$41$	8.26200	+	4.77007i	1.29031	+	0.744959i	0.978709	−	0.205254i	$-0.0658021\pi$
$41$	8.26200	+	4.77007i	1.29031	+	0.744959i	0.311599	+	0.950214i	$0.399135\pi$
$42$		0			0
$43$	3.00000	+	1.73205i	0.457496	+	0.264135i	0.710991	−	0.703201i	$-0.248247\pi$
$43$	3.00000	+	1.73205i	0.457496	+	0.264135i	−0.253495	+	0.967337i	$0.581580\pi$
$44$		0			0
$45$	−20.3541			−3.03421
$46$		0			0
$47$	4.05783	−	2.34279i	0.591895	−	0.341731i	−0.173951	−	0.984754i	$-0.555654\pi$
$47$	4.05783	−	2.34279i	0.591895	−	0.341731i	0.765846	+	0.643023i	$0.222320\pi$
$48$		0			0
$49$	5.50800			0.786857
$50$		0			0
$51$	−0.469311	−	0.812871i	−0.0657167	−	0.113825i
$52$		0			0
$53$	6.00000	−	3.46410i	0.824163	−	0.475831i	−0.0276867	−	0.999617i	$-0.508814\pi$
$53$	6.00000	−	3.46410i	0.824163	−	0.475831i	0.851850	+	0.523786i	$0.175481\pi$
$54$		0			0
$55$	−6.11921	−	3.53292i	−0.825113	−	0.476379i
$56$		0			0
$57$	14.4310	+	3.22448i	1.91144	+	0.427093i
$58$		0			0
$59$	3.44217	−	5.96202i	0.448133	−	0.776188i	−0.550132	−	0.835078i	$-0.685423\pi$
$59$	3.44217	−	5.96202i	0.448133	−	0.776188i	0.998265	+	0.0588893i	$0.0187559\pi$
$60$		0			0
$61$	3.19617	+	5.53593i	0.409228	+	0.708804i	0.994803	−	0.101814i	$-0.0324648\pi$
$61$	3.19617	+	5.53593i	0.409228	+	0.708804i	−0.585576	+	0.810618i	$0.699131\pi$
$62$		0			0
$63$	9.00000	−	5.19615i	1.13389	−	0.654654i
$64$		0			0
$65$			8.28732i			1.02792i
$66$		0			0
$67$	−3.83452	−	6.64158i	−0.468461	−	0.811398i	0.530889	−	0.847441i	$-0.321858\pi$
$67$	−3.83452	−	6.64158i	−0.468461	−	0.811398i	−0.999350	+	0.0360433i	$0.988525\pi$
$68$		0			0
$69$			4.14366i			0.498838i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	1.75400	−	3.03802i	0.205290	−	0.355573i	−0.744935	−	0.667137i	$-0.767520\pi$
$73$	1.75400	−	3.03802i	0.205290	−	0.355573i	0.950225	+	0.311564i	$0.100853\pi$
$74$		0			0
$75$	−2.45372			−0.283331
$76$		0			0
$77$	3.60766			0.411131
$78$		0			0
$79$	−0.392344	+	0.679560i	−0.0441422	+	0.0764565i	−0.887252	−	0.461284i	$-0.847389\pi$
$79$	−0.392344	+	0.679560i	−0.0441422	+	0.0764565i	0.843110	+	0.537741i	$0.180722\pi$
$80$		0			0
$81$	−18.9310	+	32.7895i	−2.10345	+	3.64328i
$82$		0			0
$83$			8.31866i			0.913092i	0.889700	+	0.456546i	$0.150914\pi$
$83$			8.31866i			0.913092i	−0.889700	+	0.456546i	$0.849086\pi$
$84$		0			0
$85$	−0.330967	−	0.573252i	−0.0358984	−	0.0621779i
$86$		0			0
$87$		−	25.8082i		−	2.76692i
$88$		0			0
$89$	−2.58497	+	1.49243i	−0.274006	+	0.158197i	−0.630707	−	0.776021i	$-0.717235\pi$
$89$	−2.58497	+	1.49243i	−0.274006	+	0.158197i	0.356701	+	0.934219i	$0.383902\pi$
$90$		0			0
$91$	−2.11566	−	3.66442i	−0.221781	−	0.384136i
$92$		0			0
$93$	−15.0965	+	26.1479i	−1.56544	+	2.71141i
$94$		0			0
$95$	10.1770	+	2.27396i	1.04414	+	0.233304i
$96$		0			0
$97$	−5.67703	−	3.27764i	−0.576415	−	0.332794i	0.183292	−	0.983058i	$-0.441325\pi$
$97$	−5.67703	−	3.27764i	−0.576415	−	0.332794i	−0.759708	+	0.650265i	$0.774658\pi$
$98$		0			0
$99$	−21.7620	+	12.5643i	−2.18716	+	1.26276i
$100$		0			0
$101$	−8.09652	−	14.0236i	−0.805634	−	1.39540i	−0.915863	−	0.401492i	$-0.868492\pi$
$101$	−8.09652	−	14.0236i	−0.805634	−	1.39540i	0.110229	−	0.993906i	$-0.464842\pi$
$102$		0			0
$103$	2.55338			0.251592			0.125796	−	0.992056i	$-0.459852\pi$
$103$	2.55338			0.251592			0.125796	+	0.992056i	$0.459852\pi$
$104$		0			0
$105$	8.58497	−	4.95653i	0.837807	−	0.483708i
$106$		0			0
$107$	−4.23131			−0.409056			−0.204528	−	0.978861i	$-0.565566\pi$
$107$	−4.23131			−0.409056			−0.204528	+	0.978861i	$0.565566\pi$
$108$		0			0
$109$	7.17703	+	4.14366i	0.687435	+	0.396891i	0.802650	−	0.596450i	$-0.203422\pi$
$109$	7.17703	+	4.14366i	0.687435	+	0.396891i	−0.115215	+	0.993341i	$0.536756\pi$
$110$		0			0
$111$	−22.3505	−	12.9041i	−2.12142	−	1.22480i
$112$		0			0
$113$			1.73205i			0.162938i	0.996676	+	0.0814688i	$0.0259611\pi$
$113$			1.73205i			0.162938i	−0.996676	+	0.0814688i	$0.974039\pi$
$114$		0			0
$115$			2.92219i			0.272495i
$116$		0			0
$117$	25.5240	+	14.7363i	2.35969	+	1.36237i
$118$		0			0
$119$	0.292689	+	0.168984i	0.0268307	+	0.0154907i
$120$		0			0
$121$	2.27669			0.206972
$122$		0			0
$123$	28.0275	−	16.1817i	2.52716	−	1.45906i
$124$		0			0
$125$	10.2313			0.915116
$126$		0			0
$127$	4.27669	+	7.40744i	0.379495	+	0.657304i	0.990989	−	0.133945i	$-0.0427645\pi$
$127$	4.27669	+	7.40744i	0.379495	+	0.657304i	−0.611494	+	0.791249i	$0.709431\pi$
$128$		0			0
$129$	10.1770	−	5.87571i	0.896038	−	0.517328i
$130$		0			0
$131$	−5.97286	−	3.44843i	−0.521851	−	0.301291i	0.215840	−	0.976429i	$-0.430751\pi$
$131$	−5.97286	−	3.44843i	−0.521851	−	0.301291i	−0.737692	+	0.675138i	$0.764084\pi$
$132$		0			0
$133$	−5.08052	+	1.59259i	−0.440537	+	0.138095i
$134$		0			0
$135$	−22.3505	+	38.7122i	−1.92363	+	3.33182i
$136$		0			0
$137$	−2.10766	−	3.65057i	−0.180069	−	0.311889i	0.761835	−	0.647771i	$-0.224299\pi$
$137$	−2.10766	−	3.65057i	−0.180069	−	0.311889i	−0.941904	+	0.335882i	$0.890965\pi$
$138$		0			0
$139$	−3.44217	+	1.98734i	−0.291961	+	0.168564i	−0.638826	−	0.769351i	$-0.720580\pi$
$139$	−3.44217	+	1.98734i	−0.291961	+	0.168564i	0.346865	+	0.937915i	$0.387246\pi$
$140$		0			0
$141$		−	15.8951i		−	1.33861i
$142$		0			0
$143$	5.11566	+	8.86058i	0.427793	+	0.740959i
$144$		0			0
$145$		−	18.2004i		−	1.51146i
$146$		0			0
$147$	9.34252	−	16.1817i	0.770558	−	1.33465i
$148$		0			0
$149$	3.31183	−	5.73625i	0.271316	−	0.469932i	−0.697883	−	0.716211i	$-0.745875\pi$
$149$	3.31183	−	5.73625i	0.271316	−	0.469932i	0.969199	+	0.246279i	$0.0792080\pi$
$150$		0			0
$151$	−7.22241			−0.587751			−0.293876	−	0.955844i	$-0.594945\pi$
$151$	−7.22241			−0.587751			−0.293876	+	0.955844i	$0.594945\pi$
$152$		0			0
$153$	−2.35407			−0.190315
$154$		0			0
$155$	−10.6463	+	18.4400i	−0.855135	+	1.48114i
$156$		0			0
$157$	−5.50800	+	9.54014i	−0.439586	+	0.761386i	−0.997657	−	0.0684073i	$-0.978208\pi$
$157$	−5.50800	+	9.54014i	−0.439586	+	0.761386i	0.558071	+	0.829793i	$0.311542\pi$
$158$		0			0
$159$		−	23.5029i		−	1.86390i
$160$		0			0
$161$	−0.746000	−	1.29211i	−0.0587930	−	0.101833i
$162$		0			0
$163$			2.61556i			0.204866i	0.994740	+	0.102433i	$0.0326628\pi$
$163$			2.61556i			0.204866i	−0.994740	+	0.102433i	$0.967337\pi$
$164$		0			0
$165$	−20.7585	+	11.9849i	−1.61604	+	0.933023i
$166$		0			0
$167$	6.29269	+	10.8993i	0.486943	+	0.843410i	0.999887	−	0.0150120i	$-0.00477865\pi$
$167$	6.29269	+	10.8993i	0.486943	+	0.843410i	−0.512944	+	0.858422i	$0.671445\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	25.1001	−	27.3006i	1.91945	−	2.08773i
$172$		0			0
$173$	−15.0000	−	8.66025i	−1.14043	−	0.658427i	−0.193892	−	0.981023i	$-0.562111\pi$
$173$	−15.0000	−	8.66025i	−1.14043	−	0.658427i	−0.946537	+	0.322596i	$0.895445\pi$
$174$		0			0
$175$	0.765139	−	0.441753i	0.0578391	−	0.0333934i
$176$		0			0
$177$	−11.6770	−	20.2252i	−0.877700	−	1.52022i
$178$		0			0
$179$	2.40834			0.180008			0.0900041	−	0.995941i	$-0.471312\pi$
$179$	2.40834			0.180008			0.0900041	+	0.995941i	$0.471312\pi$
$180$		0			0
$181$	15.9355	−	9.20036i	1.18448	−	0.683857i	0.227430	−	0.973795i	$-0.426968\pi$
$181$	15.9355	−	9.20036i	1.18448	−	0.683857i	0.957046	+	0.289937i	$0.0936345\pi$
$182$		0			0
$183$	21.6850			1.60300
$184$		0			0
$185$	−15.7620	−	9.10020i	−1.15885	−	0.669060i
$186$		0			0
$187$	−0.707722	−	0.408603i	−0.0517537	−	0.0298800i
$188$		0			0
$189$		−	22.8233i		−	1.66015i
$190$		0			0
$191$			2.04231i			0.147776i	0.997267	+	0.0738880i	$0.0235407\pi$
$191$			2.04231i			0.147776i	−0.997267	+	0.0738880i	$0.976459\pi$
$192$		0			0
$193$	9.41503	+	5.43577i	0.677709	+	0.391275i	0.798991	−	0.601343i	$-0.205367\pi$
$193$	9.41503	+	5.43577i	0.677709	+	0.391275i	−0.121282	+	0.992618i	$0.538701\pi$
$194$		0			0
$195$	24.3470	+	14.0567i	1.74352	+	1.00662i
$196$		0			0
$197$	4.16103			0.296461			0.148231	−	0.988953i	$-0.452642\pi$
$197$	4.16103			0.296461			0.148231	+	0.988953i	$0.452642\pi$
$198$		0			0
$199$	14.3541	−	8.28732i	1.01753	−	0.587473i	0.104144	−	0.994562i	$-0.466790\pi$
$199$	14.3541	−	8.28732i	1.01753	−	0.587473i	0.913388	+	0.407089i	$0.133456\pi$
$200$		0			0
$201$	−26.0160			−1.83503
$202$		0			0
$203$	4.64634	+	8.04770i	0.326109	+	0.564838i
$204$		0			0
$205$	19.7655	−	11.4116i	1.38049	−	0.797024i
$206$		0			0
$207$	9.00000	+	5.19615i	0.625543	+	0.361158i
$208$		0			0
$209$	12.2847	−	3.85089i	0.849750	−	0.266372i
$210$		0			0
$211$	−5.03869	+	8.72726i	−0.346878	+	0.600810i	−0.985693	−	0.168550i	$-0.946091\pi$
$211$	−5.03869	+	8.72726i	−0.346878	+	0.600810i	0.638815	+	0.769360i	$0.279425\pi$
$212$		0			0
$213$	10.1770	+	17.6271i	0.697319	+	1.20779i
$214$		0			0
$215$	7.17703	−	4.14366i	0.489470	−	0.282595i
$216$		0			0
$217$		−	10.8715i		−	0.738008i
$218$		0			0
$219$	−5.95017	−	10.3060i	−0.402075	−	0.696415i
$220$		0			0
$221$			0.958477i			0.0644742i
$222$		0			0
$223$	2.78114	−	4.81707i	0.186239	−	0.322575i	−0.757754	−	0.652540i	$-0.773704\pi$
$223$	2.78114	−	4.81707i	0.186239	−	0.322575i	0.943993	+	0.329965i	$0.107037\pi$
$224$		0			0
$225$	−3.07697	+	5.32946i	−0.205131	+	0.355298i
$226$		0			0
$227$	−16.1770			−1.07371			−0.536854	−	0.843675i	$-0.680387\pi$
$227$	−16.1770			−1.07371			−0.536854	+	0.843675i	$0.680387\pi$
$228$		0			0
$229$	−6.78469			−0.448345			−0.224172	−	0.974549i	$-0.571968\pi$
$229$	−6.78469			−0.448345			−0.224172	+	0.974549i	$0.571968\pi$
$230$		0			0
$231$	6.11921	−	10.5988i	0.402614	−	0.697348i
$232$		0			0
$233$	5.53869	−	9.59329i	0.362852	−	0.628477i	−0.625577	−	0.780162i	$-0.715137\pi$
$233$	5.53869	−	9.59329i	0.362852	−	0.628477i	0.988429	+	0.151685i	$0.0484699\pi$
$234$		0			0
$235$		−	11.2095i		−	0.731228i
$236$		0			0
$237$	1.33097	+	2.30530i	0.0864556	+	0.149746i
$238$		0			0
$239$		−	2.38027i		−	0.153967i	−0.997032	−	0.0769835i	$-0.975471\pi$
$239$		−	2.38027i		−	0.153967i	0.997032	−	0.0769835i	$-0.0245289\pi$
$240$		0			0
$241$	18.4390	−	10.6458i	1.18776	−	0.685755i	0.229965	−	0.973199i	$-0.426139\pi$
$241$	18.4390	−	10.6458i	1.18776	−	0.685755i	0.957797	+	0.287444i	$0.0928055\pi$
$242$		0			0
$243$	36.1930	+	62.6882i	2.32178	+	4.02145i
$244$		0			0
$245$	6.58852	−	11.4116i	0.420925	−	0.729063i
$246$		0			0
$247$	−11.1157	−	10.2197i	−0.707272	−	0.650264i
$248$		0			0
$249$	24.4390	+	14.1099i	1.54876	+	0.894177i
$250$		0			0
$251$	−3.85720	+	2.22696i	−0.243465	+	0.140564i	−0.616768	−	0.787145i	$-0.711558\pi$
$251$	−3.85720	+	2.22696i	−0.243465	+	0.140564i	0.373303	+	0.927709i	$0.378225\pi$
$252$		0			0
$253$	1.80383	+	3.12432i	0.113406	+	0.196424i
$254$		0			0
$255$	−2.24551			−0.140619
$256$		0			0
$257$	−4.08497	+	2.35846i	−0.254813	+	0.147117i	−0.621966	−	0.783044i	$-0.713666\pi$
$257$	−4.08497	+	2.35846i	−0.254813	+	0.147117i	0.367153	+	0.930161i	$0.380333\pi$
$258$		0			0
$259$	9.29269			0.577420
$260$		0			0
$261$	−56.0551	−	32.3634i	−3.46972	−	2.00325i
$262$		0			0
$263$	24.7589	+	14.2945i	1.52670	+	0.881439i	0.999498	+	0.0316971i	$0.0100912\pi$
$263$	24.7589	+	14.2945i	1.52670	+	0.881439i	0.527199	+	0.849742i	$0.323242\pi$
$264$		0			0
$265$		−	16.5746i		−	1.01817i
$266$		0			0
$267$			10.1257i			0.619682i
$268$		0			0
$269$	9.83007	+	5.67539i	0.599350	+	0.346035i	0.768786	−	0.639506i	$-0.220861\pi$
$269$	9.83007	+	5.67539i	0.599350	+	0.346035i	−0.169436	+	0.985541i	$0.554195\pi$
$270$		0			0
$271$	4.35052	+	2.51177i	0.264275	+	0.152579i	0.626283	−	0.779596i	$-0.284575\pi$
$271$	4.35052	+	2.51177i	0.264275	+	0.152579i	−0.362008	+	0.932175i	$0.617909\pi$
$272$		0			0
$273$	−14.3541			−0.868748
$274$		0			0
$275$	−1.85011	+	1.06816i	−0.111566	+	0.0644124i
$276$		0			0
$277$	−28.4243			−1.70785			−0.853927	−	0.520393i	$-0.825785\pi$
$277$	−28.4243			−1.70785			−0.853927	+	0.520393i	$0.825785\pi$
$278$		0			0
$279$	37.8621	+	65.5790i	2.26674	+	3.92611i
$280$		0			0
$281$	−13.9150	+	8.03385i	−0.830101	+	0.479259i	−0.853887	−	0.520458i	$-0.825761\pi$
$281$	−13.9150	+	8.03385i	−0.830101	+	0.479259i	0.0237861	+	0.999717i	$0.492428\pi$
$282$		0			0
$283$	−17.0885	−	9.86606i	−1.01581	−	0.586476i	−0.102920	−	0.994690i	$-0.532819\pi$
$283$	−17.0885	−	9.86606i	−1.01581	−	0.586476i	−0.912887	+	0.408213i	$0.866152\pi$
$284$		0			0
$285$	23.9426	−	26.0416i	1.41824	−	1.54257i
$286$		0			0
$287$	−5.82652	+	10.0918i	−0.343928	+	0.595701i
$288$		0			0
$289$	8.46172	+	14.6561i	0.497748	+	0.862125i
$290$		0			0
$291$	−19.2585	+	11.1189i	−1.12895	+	0.651800i
$292$		0			0
$293$			14.9366i			0.872606i	0.899800	+	0.436303i	$0.143712\pi$
$293$			14.9366i			0.872606i	−0.899800	+	0.436303i	$0.856288\pi$
$294$		0			0
$295$	−8.23486	−	14.2632i	−0.479452	−	0.830435i
$296$		0			0
$297$			55.1867i			3.20226i
$298$		0			0
$299$	2.11566	−	3.66442i	0.122352	−	0.211919i
$300$		0			0
$301$	−2.11566	+	3.66442i	−0.121944	+	0.211214i
$302$		0			0
$303$	−54.9323			−3.15578
$304$		0			0
$305$	15.2927			0.875657
$306$		0			0
$307$	11.0658	−	19.1666i	0.631560	−	1.09389i	−0.355673	−	0.934611i	$-0.615748\pi$
$307$	11.0658	−	19.1666i	0.631560	−	1.09389i	0.987233	−	0.159284i	$-0.0509185\pi$
$308$		0			0
$309$	4.33097	−	7.50146i	0.246380	−	0.426743i
$310$		0			0
$311$			26.8293i			1.52135i	0.649133	+	0.760675i	$0.275132\pi$
$311$			26.8293i			1.52135i	−0.649133	+	0.760675i	$0.724868\pi$
$312$		0			0
$313$	0.246000	+	0.426084i	0.0139047	+	0.0240837i	0.872894	−	0.487910i	$-0.162241\pi$
$313$	0.246000	+	0.426084i	0.0139047	+	0.0240837i	−0.858989	+	0.511994i	$0.828907\pi$
$314$		0			0
$315$		−	24.8620i		−	1.40081i
$316$		0			0
$317$	13.5240	−	7.80809i	0.759584	−	0.438546i	−0.0695627	−	0.997578i	$-0.522160\pi$
$317$	13.5240	−	7.80809i	0.759584	−	0.438546i	0.829146	+	0.559032i	$0.188827\pi$
$318$		0			0
$319$	−11.2349	−	19.4593i	−0.629031	−	1.08951i
$320$		0			0
$321$	−7.17703	+	12.4310i	−0.400583	+	0.693830i
$322$		0			0
$323$	1.17703	+	0.262997i	0.0654919	+	0.0146336i
$324$		0			0
$325$	2.16993	+	1.25281i	0.120366	+	0.0694935i
$326$		0			0
$327$	24.3470	−	14.0567i	1.34639	−	0.777339i
$328$		0			0
$329$	2.86166	+	4.95653i	0.157768	+	0.273263i
$330$		0			0
$331$	−27.1930			−1.49466			−0.747332	−	0.664451i	$-0.768666\pi$
$331$	−27.1930			−1.49466			−0.747332	+	0.664451i	$0.768666\pi$
$332$		0			0
$333$	−56.0551	+	32.3634i	−3.07180	+	1.77350i
$334$		0			0
$335$	−18.3470			−1.00240
$336$		0			0
$337$	18.0240	+	10.4062i	0.981830	+	0.566860i	0.902822	−	0.430014i	$-0.141491\pi$
$337$	18.0240	+	10.4062i	0.981830	+	0.566860i	0.0790078	+	0.996874i	$0.474825\pi$
$338$		0			0
$339$	5.08852	+	2.93786i	0.276370	+	0.159562i
$340$		0			0
$341$			26.2874i			1.42354i
$342$		0			0
$343$			15.2782i			0.824945i
$344$		0			0
$345$	8.58497	+	4.95653i	0.462199	+	0.266851i
$346$		0			0
$347$	22.5649	+	13.0279i	1.21135	+	0.699373i	0.963053	−	0.269312i	$-0.0867962\pi$
$347$	22.5649	+	13.0279i	1.21135	+	0.699373i	0.248296	+	0.968684i	$0.420130\pi$
$348$		0			0
$349$	24.3541			1.30364			0.651822	−	0.758372i	$-0.274005\pi$
$349$	24.3541			1.30364			0.651822	+	0.758372i	$0.274005\pi$
$350$		0			0
$351$	56.0551	−	32.3634i	2.99200	−	1.72743i
$352$		0			0
$353$	18.0160			0.958895			0.479447	−	0.877571i	$-0.340837\pi$
$353$	18.0160			0.958895			0.479447	+	0.877571i	$0.340837\pi$
$354$		0			0
$355$	7.17703	+	12.4310i	0.380917	+	0.659768i
$356$		0			0
$357$	0.992901	−	0.573252i	0.0525499	−	0.0303397i
$358$		0			0
$359$	−24.1192	−	13.9252i	−1.27296	−	0.734946i	−0.297418	−	0.954747i	$-0.596126\pi$
$359$	−24.1192	−	13.9252i	−1.27296	−	0.734946i	−0.975545	+	0.219802i	$0.929459\pi$
$360$		0			0
$361$	−15.6001	+	10.8461i	−0.821056	+	0.570848i
$362$		0			0
$363$	3.86166	−	6.68858i	0.202684	−	0.351060i
$364$		0			0
$365$	−4.19617	−	7.26798i	−0.219638	−	0.380424i
$366$		0			0
$367$	26.1806	−	15.1154i	1.36662	−	0.789016i	0.376121	−	0.926571i	$-0.377258\pi$
$367$	26.1806	−	15.1154i	1.36662	−	0.789016i	0.990494	+	0.137555i	$0.0439243\pi$
$368$		0			0
$369$		−	81.1675i		−	4.22541i
$370$		0			0
$371$	4.23131	+	7.32885i	0.219679	+	0.380495i
$372$		0			0
$373$			10.7929i			0.558838i	0.960169	+	0.279419i	$0.0901418\pi$
$373$			10.7929i			0.558838i	−0.960169	+	0.279419i	$0.909858\pi$
$374$		0			0
$375$	17.3541	−	30.0581i	0.896160	−	1.55219i
$376$		0			0
$377$	−13.1770	+	22.8233i	−0.678652	+	1.17546i
$378$		0			0
$379$	20.5080			1.05343			0.526713	−	0.850043i	$-0.323424\pi$
$379$	20.5080			1.05343			0.526713	+	0.850043i	$0.323424\pi$
$380$		0			0
$381$	29.0160			1.48653
$382$		0			0
$383$	7.05783	−	12.2245i	0.360638	−	0.624644i	−0.627428	−	0.778675i	$-0.715892\pi$
$383$	7.05783	−	12.2245i	0.360638	−	0.624644i	0.988066	+	0.154031i	$0.0492256\pi$
$384$		0			0
$385$	4.31538	−	7.47445i	0.219932	−	0.380933i
$386$		0			0
$387$		−	29.4726i		−	1.49818i
$388$		0			0
$389$	−3.27669	−	5.67539i	−0.166135	−	0.287754i	0.770923	−	0.636928i	$-0.219795\pi$
$389$	−3.27669	−	5.67539i	−0.166135	−	0.287754i	−0.937058	+	0.349175i	$0.886462\pi$
$390$		0			0
$391$			0.337968i			0.0170918i
$392$		0			0
$393$	−20.2620	+	11.6983i	−1.02208	+	0.590100i
$394$		0			0
$395$	0.938623	+	1.62574i	0.0472272	+	0.0818000i
$396$		0			0
$397$	10.6045	−	18.3676i	0.532225	−	0.921842i	−0.467067	−	0.884222i	$-0.654689\pi$
$397$	10.6045	−	18.3676i	0.532225	−	0.921842i	0.999292	−	0.0376194i	$-0.0119775\pi$
$398$		0			0
$399$	−3.93862	+	17.6271i	−0.197178	+	0.882461i
$400$		0			0
$401$	5.33007	+	3.07731i	0.266171	+	0.153674i	0.627146	−	0.778902i	$-0.284223\pi$
$401$	5.33007	+	3.07731i	0.266171	+	0.153674i	−0.360975	+	0.932575i	$0.617556\pi$
$402$		0			0
$403$	26.7010	−	15.4158i	1.33007	−	0.767918i
$404$		0			0
$405$	45.2896	+	78.4438i	2.25046	+	3.89790i
$406$		0			0
$407$	−22.4697			−1.11378
$408$		0			0
$409$	−9.09207	+	5.24931i	−0.449574	+	0.259562i	−0.707650	−	0.706563i	$-0.750245\pi$
$409$	−9.09207	+	5.24931i	−0.449574	+	0.259562i	0.258076	+	0.966125i	$0.416911\pi$
$410$		0			0
$411$	−14.2998			−0.705356
$412$		0			0
$413$	7.28245	+	4.20453i	0.358346	+	0.206891i
$414$		0			0
$415$	17.2349	+	9.95055i	0.846026	+	0.488453i
$416$		0			0
$417$			13.4835i			0.660289i
$418$		0			0
$419$			36.3381i			1.77523i	0.460584	+	0.887616i	$0.347640\pi$
$419$			36.3381i			1.77523i	−0.460584	+	0.887616i	$0.652360\pi$
$420$		0			0
$421$	−18.2896	−	10.5595i	−0.891378	−	0.514637i	−0.0169851	−	0.999856i	$-0.505407\pi$
$421$	−18.2896	−	10.5595i	−0.891378	−	0.514637i	−0.874393	+	0.485218i	$0.838740\pi$
$422$		0			0
$423$	−34.5240	−	19.9324i	−1.67861	−	0.969148i
$424$		0			0
$425$	−0.200132			−0.00970783
$426$		0			0
$427$	−6.76200	+	3.90404i	−0.327236	+	0.188930i
$428$		0			0
$429$	34.7081			1.67572
$430$		0			0
$431$	7.23131	+	12.5250i	0.348320	+	0.603308i	0.985951	−	0.167034i	$-0.0534189\pi$
$431$	7.23131	+	12.5250i	0.348320	+	0.603308i	−0.637631	+	0.770342i	$0.720086\pi$
$432$		0			0
$433$	−31.2931	+	18.0671i	−1.50385	+	0.868248i	−0.503860	+	0.863785i	$0.668087\pi$
$433$	−31.2931	+	18.0671i	−1.50385	+	0.868248i	−0.999990	+	0.00446329i	$0.998579\pi$
$434$		0			0
$435$	−53.4701	−	30.8710i	−2.56370	−	1.48015i
$436$		0			0
$437$	−3.91948	−	3.60356i	−0.187494	−	0.172382i
$438$		0			0
$439$	7.84252	−	13.5836i	0.374303	−	0.648312i	−0.615920	−	0.787809i	$-0.711215\pi$
$439$	7.84252	−	13.5836i	0.374303	−	0.648312i	0.990222	+	0.139497i	$0.0445487\pi$
$440$		0			0
$441$	−23.4310	−	40.5837i	−1.11576	−	1.93256i
$442$		0			0
$443$	14.6739	−	8.47198i	0.697178	−	0.402516i	−0.109118	−	0.994029i	$-0.534803\pi$
$443$	14.6739	−	8.47198i	0.697178	−	0.402516i	0.806295	+	0.591513i	$0.201469\pi$
$444$		0			0
$445$			7.14082i			0.338507i
$446$		0			0
$447$	−11.2349	−	19.4593i	−0.531391	−	0.920396i
$448$		0			0
$449$		−	17.8275i		−	0.841330i	−0.907216	−	0.420665i	$-0.861797\pi$
$449$		−	17.8275i		−	0.841330i	0.907216	−	0.420665i	$-0.138203\pi$
$450$		0			0
$451$	14.0885	−	24.4020i	0.663402	−	1.14905i
$452$		0			0
$453$	−12.2505	+	21.2184i	−0.575576	+	0.996928i
$454$		0			0
$455$	−10.1228			−0.474562
$456$		0			0
$457$	19.8301			0.927611			0.463806	−	0.885937i	$-0.346484\pi$
$457$	19.8301			0.927611			0.463806	+	0.885937i	$0.346484\pi$
$458$		0			0
$459$	−2.58497	+	4.47729i	−0.120656	+	0.208982i
$460$		0			0
$461$	−16.4537	+	28.4987i	−0.766326	+	1.32732i	0.173216	+	0.984884i	$0.444584\pi$
$461$	−16.4537	+	28.4987i	−0.766326	+	1.32732i	−0.939543	+	0.342432i	$0.888749\pi$
$462$		0			0
$463$			21.3979i			0.994443i	0.867624	+	0.497222i	$0.165646\pi$
$463$			21.3979i			0.994443i	−0.867624	+	0.497222i	$0.834354\pi$
$464$		0			0
$465$	36.1161	+	62.5549i	1.67484	+	2.90091i
$466$		0			0
$467$			8.79790i			0.407118i	0.979063	+	0.203559i	$0.0652509\pi$
$467$			8.79790i			0.407118i	−0.979063	+	0.203559i	$0.934749\pi$
$468$		0			0
$469$	8.11252	−	4.68376i	0.374601	−	0.216276i
$470$		0			0
$471$	18.6850	+	32.3634i	0.860961	+	1.49123i
$472$		0			0
$473$	5.11566	−	8.86058i	0.235218	−	0.407410i
$474$		0			0
$475$	2.13389	−	2.32097i	0.0979097	−	0.106493i
$476$		0			0
$477$	−51.0480	−	29.4726i	−2.33733	−	1.34946i
$478$		0			0
$479$	−2.11566	+	1.22147i	−0.0966668	+	0.0558106i	−0.547554	−	0.836770i	$-0.684441\pi$
$479$	−2.11566	+	1.22147i	−0.0966668	+	0.0558106i	0.450887	+	0.892581i	$0.351108\pi$
$480$		0			0
$481$	13.1770	+	22.8233i	0.600821	+	1.04065i
$482$		0			0
$483$	−5.06138			−0.230301
$484$		0			0
$485$	−13.5814	+	7.84124i	−0.616700	+	0.356052i
$486$		0			0
$487$	−25.0231			−1.13390			−0.566952	−	0.823751i	$-0.691878\pi$
$487$	−25.0231			−1.13390			−0.566952	+	0.823751i	$0.691878\pi$
$488$		0			0
$489$	7.68413	+	4.43644i	0.347488	+	0.200623i
$490$		0			0
$491$	36.6397	+	21.1539i	1.65352	+	0.954663i	0.975607	+	0.219525i	$0.0704508\pi$
$491$	36.6397	+	21.1539i	1.65352	+	0.954663i	0.677918	+	0.735138i	$0.262883\pi$
$492$		0			0
$493$		−	2.10498i		−	0.0948036i
$494$		0			0
$495$			60.1162i			2.70202i
$496$		0			0
$497$	−6.34697	−	3.66442i	−0.284700	−	0.164372i
$498$		0			0
$499$	21.2113	+	12.2463i	0.949547	+	0.548221i	0.892940	−	0.450175i	$-0.148639\pi$
$499$	21.2113	+	12.2463i	0.949547	+	0.548221i	0.0566067	+	0.998397i	$0.481972\pi$
$500$		0			0
$501$	42.6939			1.90742
$502$		0			0
$503$	−32.9288	+	19.0114i	−1.46822	+	0.847679i	−0.999366	−	0.0355959i	$-0.988667\pi$
$503$	−32.9288	+	19.0114i	−1.46822	+	0.847679i	−0.468856	+	0.883275i	$0.655334\pi$
$504$		0			0
$505$	−38.7393			−1.72388
$506$		0			0
$507$	1.69617	+	2.93786i	0.0753297	+	0.130475i
$508$		0			0
$509$	−9.34697	+	5.39647i	−0.414297	+	0.239195i	−0.692634	−	0.721289i	$-0.743550\pi$
$509$	−9.34697	+	5.39647i	−0.414297	+	0.239195i	0.278337	+	0.960483i	$0.410217\pi$
$510$		0			0
$511$	3.71086	+	2.14247i	0.164159	+	0.0947771i
$512$		0			0
$513$	−24.3621	−	77.7172i	−1.07561	−	3.43130i
$514$		0			0
$515$	3.05428	−	5.29017i	0.134588	−	0.233113i
$516$		0			0
$517$	−6.91948	−	11.9849i	−0.304319	−	0.527095i
$518$		0			0
$519$	−50.8852	+	29.3786i	−2.23361	+	1.28958i
$520$		0			0
$521$		−	13.4835i		−	0.590722i	−0.955386	−	0.295361i	$-0.904560\pi$
$521$		−	13.4835i		−	0.590722i	0.955386	−	0.295361i	$-0.0954399\pi$
$522$		0			0
$523$	−12.7393	−	22.0651i	−0.557051	−	0.964841i	−0.997741	−	0.0671814i	$-0.978599\pi$
$523$	−12.7393	−	22.0651i	−0.557051	−	0.964841i	0.440690	−	0.897660i	$-0.354734\pi$
$524$		0			0
$525$		−	2.99716i		−	0.130807i
$526$		0			0
$527$	−1.23131	+	2.13269i	−0.0536368	+	0.0929016i
$528$		0			0
$529$	−10.7540	+	18.6265i	−0.467565	+	0.809847i
$530$		0			0
$531$	−58.5720			−2.54181
$532$		0			0
$533$	−33.0480			−1.43147
$534$		0			0
$535$	−5.06138	+	8.76656i	−0.218822	+	0.379012i
$536$		0			0
$537$	4.08497	−	7.07537i	0.176279	−	0.305325i
$538$		0			0
$539$		−	16.2680i		−	0.700713i
$540$		0			0
$541$	15.5080	+	26.8606i	0.666741	+	1.15483i	0.978810	+	0.204770i	$0.0656446\pi$
$541$	15.5080	+	26.8606i	0.666741	+	1.15483i	−0.312069	+	0.950059i	$0.601022\pi$
$542$		0			0
$543$		−	62.4216i		−	2.67877i
$544$		0			0
$545$	17.1699	−	9.91307i	0.735479	−	0.424629i
$546$		0			0
$547$	−9.83897	−	17.0416i	−0.420684	−	0.728646i	0.575323	−	0.817927i	$-0.304877\pi$
$547$	−9.83897	−	17.0416i	−0.420684	−	0.728646i	−0.996007	+	0.0892807i	$0.971543\pi$
$548$		0			0
$549$	27.1930	−	47.0997i	1.16057	−	2.01017i
$550$		0			0
$551$	24.4119	+	22.4442i	1.03998	+	0.956156i
$552$		0			0
$553$	−0.830066	−	0.479239i	−0.0352980	−	0.0203793i
$554$		0			0
$555$	−53.4701	+	30.8710i	−2.26968	+	1.31040i
$556$		0			0
$557$	−9.56938	−	16.5746i	−0.405468	−	0.702290i	0.588908	−	0.808200i	$-0.299558\pi$
$557$	−9.56938	−	16.5746i	−0.405468	−	0.702290i	−0.994376	+	0.105910i	$0.966225\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$		0			0
$561$	−2.40084	+	1.38612i	−0.101363	+	0.0585222i
$562$		0			0
$563$	−38.4083			−1.61872			−0.809359	−	0.587314i	$-0.800185\pi$
$563$	−38.4083			−1.61872			−0.809359	+	0.587314i	$0.800185\pi$
$564$		0			0
$565$	3.58852	+	2.07183i	0.150970	+	0.0871626i
$566$		0			0
$567$	−40.0516	−	23.1238i	−1.68201	−	0.971107i
$568$		0			0
$569$		−	34.7750i		−	1.45785i	−0.684596	−	0.728923i	$-0.740021\pi$
$569$		−	34.7750i		−	1.45785i	0.684596	−	0.728923i	$-0.259979\pi$
$570$		0			0
$571$			30.9257i			1.29420i	0.762405	+	0.647100i	$0.224019\pi$
$571$			30.9257i			1.29420i	−0.762405	+	0.647100i	$0.775981\pi$
$572$		0			0
$573$	6.00000	+	3.46410i	0.250654	+	0.144715i
$574$		0			0
$575$	0.765139	+	0.441753i	0.0319085	+	0.0184224i
$576$		0			0
$577$	−27.7847			−1.15669			−0.578346	−	0.815792i	$-0.696302\pi$
$577$	−27.7847			−1.15669			−0.578346	+	0.815792i	$0.696302\pi$
$578$		0			0
$579$	31.9390	−	18.4400i	1.32734	−	0.766341i
$580$		0			0
$581$	−10.1610			−0.421551
$582$		0			0
$583$	−10.2313	−	17.7212i	−0.423738	−	0.733935i
$584$		0			0
$585$	61.0622	−	35.2543i	2.52461	−	1.45758i
$586$		0			0
$587$	14.0614	+	8.11834i	0.580375	+	0.335080i	0.761282	−	0.648420i	$-0.224570\pi$
$587$	14.0614	+	8.11834i	0.580375	+	0.335080i	−0.180907	+	0.983500i	$0.557903\pi$
$588$		0			0
$589$	−11.6045	−	37.0195i	−0.478156	−	1.52536i
$590$		0			0
$591$	7.05783	−	12.2245i	0.290320	−	0.502849i
$592$		0			0
$593$	5.57697	+	9.65959i	0.229019	+	0.396672i	0.957518	−	0.288375i	$-0.0931150\pi$
$593$	5.57697	+	9.65959i	0.229019	+	0.396672i	−0.728499	+	0.685047i	$0.759782\pi$
$594$		0			0
$595$	0.700213	−	0.404268i	0.0287059	−	0.0165734i
$596$		0			0
$597$		−	56.2269i		−	2.30121i
$598$		0			0
$599$	7.00355	+	12.1305i	0.286157	+	0.495639i	0.972889	−	0.231272i	$-0.0742887\pi$
$599$	7.00355	+	12.1305i	0.286157	+	0.495639i	−0.686732	+	0.726911i	$0.740955\pi$
$600$		0			0
$601$			35.5486i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$601$			35.5486i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$602$		0			0
$603$	−32.6241	+	56.5065i	−1.32855	+	2.30112i
$604$		0			0
$605$	2.72331	−	4.71691i	0.110718	−	0.191770i
$606$		0			0
$607$	−7.13166			−0.289465			−0.144732	−	0.989471i	$-0.546232\pi$
$607$	−7.13166			−0.289465			−0.144732	+	0.989471i	$0.546232\pi$
$608$		0			0
$609$	31.5240			1.27742
$610$		0			0
$611$	−8.11566	+	14.0567i	−0.328324	+	0.568674i
$612$		0			0
$613$	8.90034	−	15.4158i	0.359482	−	0.622640i	−0.628393	−	0.777896i	$-0.716287\pi$
$613$	8.90034	−	15.4158i	0.359482	−	0.622640i	0.987874	+	0.155256i	$0.0496202\pi$
$614$		0			0
$615$		−	77.4245i		−	3.12206i
$616$		0			0
$617$	−12.2847	−	21.2777i	−0.494563	−	0.856608i	0.505417	−	0.862875i	$-0.331339\pi$
$617$	−12.2847	−	21.2777i	−0.494563	−	0.856608i	−0.999980	+	0.00626683i	$0.998005\pi$
$618$		0			0
$619$		−	21.6804i		−	0.871409i	−0.900090	−	0.435705i	$-0.856499\pi$
$619$		−	21.6804i		−	0.871409i	0.900090	−	0.435705i	$-0.143501\pi$
$620$		0			0
$621$	19.7655	−	11.4116i	0.793164	−	0.457934i
$622$		0			0
$623$	−1.82297	−	3.15747i	−0.0730356	−	0.126501i
$624$		0			0
$625$	14.0467	−	24.3296i	0.561868	−	0.973183i
$626$		0			0
$627$	9.52359	−	42.6224i	0.380336	−	1.70218i
$628$		0			0
$629$	−1.82297	−	1.05249i	−0.0726865	−	0.0419655i
$630$		0			0
$631$	36.7589	−	21.2227i	1.46335	−	0.844864i	0.464183	−	0.885739i	$-0.346348\pi$
$631$	36.7589	−	21.2227i	1.46335	−	0.844864i	0.999164	+	0.0408755i	$0.0130147\pi$
$632$		0			0
$633$	17.0930	+	29.6059i	0.679384	+	1.17673i
$634$		0			0
$635$	20.4626			0.812034
$636$		0			0
$637$	−16.5240	+	9.54014i	−0.654705	+	0.377994i
$638$		0			0
$639$	51.0480			2.01943
$640$		0			0
$641$	−11.7451	−	6.78104i	−0.463903	−	0.267835i	0.249781	−	0.968302i	$-0.419641\pi$
$641$	−11.7451	−	6.78104i	−0.463903	−	0.267835i	−0.713684	+	0.700468i	$0.752975\pi$
$642$		0			0
$643$	−26.4355	−	15.2625i	−1.04251	−	0.601896i	−0.121969	−	0.992534i	$-0.538921\pi$
$643$	−26.4355	−	15.2625i	−1.04251	−	0.601896i	−0.920544	+	0.390638i	$0.872254\pi$
$644$		0			0
$645$		−	28.1135i		−	1.10697i
$646$		0			0
$647$		−	20.7219i		−	0.814663i	−0.913280	−	0.407332i	$-0.866459\pi$
$647$		−	20.7219i		−	0.814663i	0.913280	−	0.407332i	$-0.133541\pi$
$648$		0			0
$649$	−17.6090	−	10.1665i	−0.691212	−	0.399072i
$650$		0			0
$651$	−31.9390	−	18.4400i	−1.25179	−	0.722721i
$652$		0			0
$653$	35.9234			1.40579			0.702896	−	0.711292i	$-0.251890\pi$
$653$	35.9234			1.40579			0.702896	+	0.711292i	$0.251890\pi$
$654$		0			0
$655$	−14.2891	+	8.24984i	−0.558323	+	0.322348i
$656$		0			0
$657$	−29.8461			−1.16441
$658$		0			0
$659$	18.5854	+	32.1908i	0.723984	+	1.25398i	0.959391	+	0.282079i	$0.0910242\pi$
$659$	18.5854	+	32.1908i	0.723984	+	1.25398i	−0.235408	+	0.971897i	$0.575642\pi$
$660$		0			0
$661$	−12.1054	+	6.98907i	−0.470846	+	0.271843i	−0.716594	−	0.697491i	$-0.754300\pi$
$661$	−12.1054	+	6.98907i	−0.470846	+	0.271843i	0.245748	+	0.969334i	$0.420967\pi$
$662$		0			0
$663$	2.81587	+	1.62574i	0.109359	+	0.0631386i
$664$		0			0
$665$	−2.77759	+	12.4310i	−0.107710	+	0.482053i
$666$		0			0
$667$	−4.64634	+	8.04770i	−0.179907	+	0.311608i
$668$		0			0
$669$	−9.43458	−	16.3412i	−0.364762	−	0.631786i
$670$		0			0
$671$	16.3505	−	9.43998i	0.631205	−	0.364426i
$672$		0			0
$673$		−	1.62574i		−	0.0626678i	−0.999509	−	0.0313339i	$-0.990024\pi$
$673$		−	1.62574i		−	0.0626678i	0.999509	−	0.0313339i	$-0.00997552\pi$
$674$		0			0
$675$	6.75755	+	11.7044i	0.260098	+	0.450503i
$676$		0			0
$677$			44.6881i			1.71750i	0.512392	+	0.858752i	$0.328759\pi$
$677$			44.6881i			1.71750i	−0.512392	+	0.858752i	$0.671241\pi$
$678$		0			0
$679$	4.00355	−	6.93435i	0.153642	−	0.266116i
$680$		0			0
$681$	−27.4390	+	47.5258i	−1.05147	+	1.82119i
$682$		0			0
$683$	−15.5374			−0.594521			−0.297261	−	0.954796i	$-0.596073\pi$
$683$	−15.5374			−0.594521			−0.297261	+	0.954796i	$0.596073\pi$
$684$		0			0
$685$	−10.0845			−0.385308
$686$		0			0
$687$	−11.5080	+	19.9324i	−0.439058	+	0.760470i
$688$		0			0
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$		−	6.18234i		−	0.235187i	−0.993062	−	0.117594i	$-0.962482\pi$
$691$		−	6.18234i		−	0.235187i	0.993062	−	0.117594i	$-0.0375180\pi$
$692$		0			0
$693$	−15.3470	−	26.5817i	−0.582983	−	1.00976i
$694$		0			0
$695$			9.50880i			0.360689i
$696$		0			0
$697$	2.28600	−	1.31982i	0.0865885	−	0.0499919i
$698$		0			0
$699$	−18.7891	−	32.5437i	−0.710671	−	1.23092i
$700$		0			0
$701$	−6.60452	+	11.4394i	−0.249449	+	0.432059i	−0.963373	−	0.268165i	$-0.913583\pi$
$701$	−6.60452	+	11.4394i	−0.249449	+	0.432059i	0.713924	+	0.700223i	$0.246916\pi$
$702$		0			0
$703$	31.6432	−	9.91921i	1.19345	−	0.374110i
$704$		0			0
$705$	−32.9319	−	19.0133i	−1.24029	−	0.716081i
$706$		0			0
$707$	17.1294	−	9.88969i	0.644219	−	0.371940i
$708$		0			0
$709$	−6.42748	−	11.1327i	−0.241389	−	0.418098i	0.719721	−	0.694263i	$-0.244270\pi$
$709$	−6.42748	−	11.1327i	−0.241389	−	0.418098i	−0.961110	+	0.276165i	$0.910936\pi$
$710$		0			0
$711$	6.67613			0.250374
$712$		0			0
$713$	9.41503	−	5.43577i	0.352596	−	0.203571i
$714$		0			0
$715$	24.4768			0.915381
$716$		0			0
$717$	−6.99290	−	4.03735i	−0.261155	−	0.150778i
$718$		0			0
$719$	−38.2998	−	22.1124i	−1.42834	−	0.824653i	−0.431351	−	0.902184i	$-0.641963\pi$
$719$	−38.2998	−	22.1124i	−1.42834	−	0.824653i	−0.996990	+	0.0775310i	$0.975296\pi$
$720$		0			0
$721$			3.11888i			0.116153i
$722$		0			0
$723$		−	72.2283i		−	2.68620i
$724$		0			0
$725$	−4.76555	−	2.75139i	−0.176988	−	0.102184i
$726$		0			0
$727$	7.47600	+	4.31627i	0.277269	+	0.160082i	0.632187	−	0.774816i	$-0.282158\pi$
$727$	7.47600	+	4.31627i	0.277269	+	0.160082i	−0.354917	+	0.934898i	$0.615491\pi$
$728$		0			0
$729$	131.972			4.88786
$730$		0			0
$731$	0.830066	−	0.479239i	0.0307011	−	0.0177253i
$732$		0			0
$733$	−33.8532			−1.25040			−0.625198	−	0.780467i	$-0.714982\pi$
$733$	−33.8532			−1.25040			−0.625198	+	0.780467i	$0.714982\pi$
$734$		0			0
$735$	−22.3505	−	38.7122i	−0.824411	−	1.42792i
$736$		0			0
$737$	−19.6161	+	11.3253i	−0.722567	+	0.417174i
$738$		0			0
$739$	2.26514	+	1.30778i	0.0833245	+	0.0481074i	0.541083	−	0.840969i	$-0.318014\pi$
$739$	2.26514	+	1.30778i	0.0833245	+	0.0481074i	−0.457759	+	0.889076i	$0.651348\pi$
$740$		0			0
$741$	−48.8781	+	15.3218i	−1.79558	+	0.562862i
$742$		0			0
$743$	−18.4119	+	31.8903i	−0.675467	+	1.16994i	0.300865	+	0.953667i	$0.402725\pi$
$743$	−18.4119	+	31.8903i	−0.675467	+	1.16994i	−0.976332	+	0.216276i	$0.930609\pi$
$744$		0			0
$745$	−7.92303	−	13.7231i	−0.290277	−	0.502775i
$746$		0			0
$747$	61.2931	−	35.3876i	2.24260	−	1.29476i
$748$		0			0
$749$		−	5.16844i		−	0.188851i
$750$		0			0
$751$	−15.3923	−	26.6603i	−0.561675	−	0.972849i	−0.997351	−	0.0727454i	$-0.976824\pi$
$751$	−15.3923	−	26.6603i	−0.561675	−	0.972849i	0.435676	−	0.900104i	$-0.356509\pi$
$752$		0			0
$753$			15.1092i			0.550611i
$754$		0			0
$755$	−8.63925	+	14.9636i	−0.314414	+	0.544582i
$756$		0			0
$757$	−7.37634	+	12.7762i	−0.268098	+	0.464359i	−0.968371	−	0.249516i	$-0.919728\pi$
$757$	−7.37634	+	12.7762i	−0.268098	+	0.464359i	0.700273	+	0.713875i	$0.253062\pi$
$758$		0			0
$759$	12.2384			0.444226
$760$		0			0
$761$	−4.80069			−0.174025			−0.0870124	−	0.996207i	$-0.527732\pi$
$761$	−4.80069			−0.174025			−0.0870124	+	0.996207i	$0.527732\pi$
$762$		0			0
$763$	−5.06138	+	8.76656i	−0.183234	+	0.317371i
$764$		0			0
$765$	−2.81587	+	4.87723i	−0.101808	+	0.176337i
$766$		0			0
$767$			23.8481i			0.861104i
$768$		0			0
$769$	3.86166	+	6.68858i	0.139255	+	0.241197i	0.927215	−	0.374530i	$-0.122196\pi$
$769$	3.86166	+	6.68858i	0.139255	+	0.241197i	−0.787960	+	0.615727i	$0.788863\pi$
$770$		0			0
$771$			16.0014i			0.576276i
$772$		0			0
$773$	−44.2966	+	25.5747i	−1.59324	+	0.919857i	−0.600493	+	0.799630i	$0.705029\pi$
$773$	−44.2966	+	25.5747i	−1.59324	+	0.919857i	−0.992746	+	0.120228i	$0.961638\pi$
$774$		0			0
$775$	3.21886	+	5.57523i	0.115625	+	0.200268i
$776$		0			0
$777$	15.7620	−	27.3006i	0.565459	−	0.979403i
$778$		0			0
$779$	−9.06807	+	40.5837i	−0.324897	+	1.45406i
$780$		0			0
$781$	15.3470	+	8.86058i	0.549158	+	0.317056i
$782$		0			0
$783$	−123.107	+	71.0757i	−4.39947	+	2.54004i
$784$		0			0
$785$	13.1770	+	22.8233i	0.470308	+	0.814598i
$786$		0			0
$787$	−32.2090			−1.14813			−0.574064	−	0.818810i	$-0.694634\pi$
$787$	−32.2090			−1.14813			−0.574064	+	0.818810i	$0.694634\pi$
$788$		0			0
$789$	83.9906	−	48.4920i	2.99014	−	1.72636i
$790$		0			0
$791$	−2.11566			−0.0752241
$792$		0			0
$793$	−19.1770	−	11.0719i	−0.680996	−	0.393173i
$794$		0			0
$795$	−48.6939	−	28.1135i	−1.72700	−	0.997082i
$796$		0			0
$797$			46.5142i			1.64762i	0.566869	+	0.823808i	$0.308155\pi$
$797$			46.5142i			1.64762i	−0.566869	+	0.823808i	$0.691845\pi$
$798$		0			0
$799$		−	1.29645i		−	0.0458649i
$800$		0			0
$801$	21.9929	+	12.6976i	0.777081	+	0.448648i
$802$		0			0
$803$	−8.97286	−	5.18048i	−0.316645	−	0.182815i
$804$		0			0
$805$	−3.56938			−0.125804
$806$		0			0
$807$	33.3470	−	19.2529i	1.17387	−	0.677733i
$808$		0			0
$809$	6.36925			0.223931			0.111965	−	0.993712i	$-0.464285\pi$
$809$	6.36925			0.223931			0.111965	+	0.993712i	$0.464285\pi$
$810$		0			0
$811$	−26.3087	−	45.5680i	−0.923823	−	1.60011i	−0.793443	−	0.608644i	$-0.791714\pi$
$811$	−26.3087	−	45.5680i	−0.923823	−	1.60011i	−0.130380	−	0.991464i	$-0.541620\pi$
$812$		0			0
$813$	14.7585	−	8.52080i	0.517601	−	0.298837i
$814$		0			0
$815$	5.41899	+	3.12866i	0.189819	+	0.109592i
$816$		0			0
$817$	−3.29269	+	14.7363i	−0.115197	+	0.515557i
$818$		0			0
$819$	−18.0000	+	31.1769i	−0.628971	+	1.08941i
$820$		0			0
$821$	2.73931	+	4.74463i	0.0956026	+	0.165589i	0.909860	−	0.414915i	$-0.136189\pi$
$821$	2.73931	+	4.74463i	0.0956026	+	0.165589i	−0.814257	+	0.580504i	$0.802856\pi$
$822$		0			0
$823$	29.7553	−	17.1792i	1.03720	−	0.598831i	0.118165	−	0.992994i	$-0.462299\pi$
$823$	29.7553	−	17.1792i	1.03720	−	0.598831i	0.919040	+	0.394163i	$0.128966\pi$
$824$		0			0
$825$			7.24713i			0.252313i
$826$		0			0
$827$	−20.3812	−	35.3013i	−0.708724	−	1.22755i	−0.965331	−	0.261030i	$-0.915938\pi$
$827$	−20.3812	−	35.3013i	−0.708724	−	1.22755i	0.256607	−	0.966516i	$-0.417395\pi$
$828$		0			0
$829$			12.3093i			0.427518i	0.976886	+	0.213759i	$0.0685708\pi$
$829$			12.3093i			0.427518i	−0.976886	+	0.213759i	$0.931429\pi$
$830$		0			0
$831$	−48.2126	+	83.5066i	−1.67248	+	2.89681i
$832$		0			0
$833$	0.762000	−	1.31982i	0.0264017	−	0.0457292i
$834$		0			0
$835$	30.1086			1.04195
$836$		0			0
$837$	166.303			5.74828
$838$		0			0
$839$	−2.28914	+	3.96491i	−0.0790299	+	0.136884i	−0.902832	−	0.429994i	$-0.858516\pi$
$839$	−2.28914	+	3.96491i	−0.0790299	+	0.136884i	0.823802	+	0.566878i	$0.191849\pi$
$840$		0			0
$841$	14.4390	−	25.0091i	0.497898	−	0.862384i
$842$		0			0
$843$			54.5072i			1.87733i
$844$		0			0
$845$	1.19617	+	2.07183i	0.0411496	+	0.0712732i
$846$		0			0
$847$			2.78092i			0.0955534i
$848$		0			0
$849$	−57.9701	+	33.4691i	−1.98953	+	1.14866i
$850$		0			0
$851$	4.64634	+	8.04770i	0.159275	+	0.275872i
$852$		0			0
$853$	−15.5080	+	26.8606i	−0.530984	+	0.919691i	0.468362	+	0.883536i	$0.344844\pi$
$853$	−15.5080	+	26.8606i	−0.530984	+	0.919691i	−0.999346	+	0.0361545i	$0.988489\pi$
$854$		0			0
$855$	−26.5382	−	84.6593i	−0.907587	−	2.89529i
$856$		0			0
$857$	−33.8541	−	19.5457i	−1.15643	−	0.667667i	−0.205986	−	0.978555i	$-0.566040\pi$
$857$	−33.8541	−	19.5457i	−1.15643	−	0.667667i	−0.950447	+	0.310888i	$0.899374\pi$
$858$		0			0
$859$	−32.3269	+	18.6640i	−1.10298	+	0.636806i	−0.937002	−	0.349323i	$-0.886411\pi$
$859$	−32.3269	+	18.6640i	−1.10298	+	0.636806i	−0.165978	+	0.986129i	$0.553078\pi$
$860$		0			0
$861$	19.7655	+	34.2349i	0.673608	+	1.16672i
$862$		0			0
$863$	2.70103			0.0919443			0.0459721	−	0.998943i	$-0.485361\pi$
$863$	2.70103			0.0919443			0.0459721	+	0.998943i	$0.485361\pi$
$864$		0			0
$865$	−35.8852	+	20.7183i	−1.22013	+	0.704444i
$866$		0			0
$867$	57.4101			1.94975
$868$		0			0
$869$	2.00710	+	1.15880i	0.0680862	+	0.0393096i
$870$		0			0
$871$	23.0071	+	13.2832i	0.779566	+	0.450083i
$872$		0			0
$873$			55.7723i			1.88761i
$874$		0			0
$875$			12.4973i			0.422485i
$876$		0			0
$877$	−14.5956	−	8.42678i	−0.492859	−	0.284552i	0.232901	−	0.972500i	$-0.425178\pi$
$877$	−14.5956	−	8.42678i	−0.492859	−	0.284552i	−0.725760	+	0.687948i	$0.758512\pi$
$878$		0			0
$879$	43.8816	+	25.3351i	1.48009	+	0.854530i
$880$		0			0
$881$	23.0454			0.776418			0.388209	−	0.921571i	$-0.373094\pi$
$881$	23.0454			0.776418			0.388209	+	0.921571i	$0.373094\pi$
$882$		0			0
$883$	−18.5582	+	10.7146i	−0.624534	+	0.360575i	−0.778632	−	0.627480i	$-0.784086\pi$
$883$	−18.5582	+	10.7146i	−0.624534	+	0.360575i	0.154098	+	0.988056i	$0.450753\pi$
$884$		0			0
$885$	−55.8710			−1.87808
$886$		0			0
$887$	3.29269	+	5.70310i	0.110558	+	0.191492i	0.915995	−	0.401189i	$-0.131403\pi$
$887$	3.29269	+	5.70310i	0.110558	+	0.191492i	−0.805438	+	0.592681i	$0.798070\pi$
$888$		0			0
$889$	−9.04800	+	5.22387i	−0.303460	+	0.175203i
$890$		0			0
$891$	96.8446	+	55.9133i	3.24442	+	1.87317i
$892$		0			0
$893$	15.0351	+	13.8233i	0.503132	+	0.462578i
$894$		0			0
$895$	2.88079	−	4.98968i	0.0962944	−	0.166787i
$896$		0			0
$897$	−7.17703	−	12.4310i	−0.239634	−	0.415059i
$898$		0			0
$899$	−58.6401	+	33.8559i	−1.95576	+	1.12916i
$900$		0			0
$901$		−	1.91695i		−	0.0638630i
$902$		0			0
$903$	7.17703	+	12.4310i	0.238837	+	0.413677i
$904$		0			0
$905$		−	44.0208i		−	1.46330i
$906$		0			0
$907$	0.342517	−	0.593256i	0.0113731	−	0.0196987i	−0.860283	−	0.509817i	$-0.829713\pi$
$907$	0.342517	−	0.593256i	0.0113731	−	0.0196987i	0.871656	+	0.490118i	$0.163046\pi$
$908$		0			0
$909$	−68.8852	+	119.313i	−2.28478	+	3.95735i
$910$		0			0
$911$	36.3470			1.20423			0.602114	−	0.798410i	$-0.294325\pi$
$911$	36.3470			1.20423			0.602114	+	0.798410i	$0.294325\pi$
$912$		0			0
$913$	24.5694			0.813128
$914$		0			0
$915$	25.9390	−	44.9277i	0.857518	−	1.48526i
$916$		0			0
$917$	4.21217	−	7.29570i	0.139098	−	0.240925i
$918$		0			0
$919$		−	1.97963i		−	0.0653020i	−0.999467	−	0.0326510i	$-0.989605\pi$
$919$		−	1.97963i		−	0.0653020i	0.999467	−	0.0326510i	$-0.0103950\pi$
$920$		0			0
$921$	−37.5391	−	65.0196i	−1.23696	−	2.14247i
$922$		0			0
$923$		−	20.7846i		−	0.684134i
$924$		0			0
$925$	−4.76555	+	2.75139i	−0.156690	+	0.0904652i
$926$		0			0
$927$	−10.8621	−	18.8137i	−0.356757	−	0.617921i
$928$		0			0
$929$	−12.3390	+	21.3717i	−0.404828	+	0.701183i	−0.994301	−	0.106605i	$-0.966002\pi$
$929$	−12.3390	+	21.3717i	−0.404828	+	0.701183i	0.589473	+	0.807788i	$0.299335\pi$
$930$		0			0
$931$	7.18148	+	22.9096i	0.235364	+	0.750832i
$932$		0			0
$933$	78.8206	+	45.5071i	2.58047	+	1.48984i
$934$		0			0
$935$	−1.69311	+	0.977520i	−0.0553707	+	0.0319683i
$936$		0			0
$937$	20.0921	+	34.8005i	0.656379	+	1.13688i	0.981546	+	0.191225i	$0.0612462\pi$
$937$	20.0921	+	34.8005i	0.656379	+	1.13688i	−0.325167	+	0.945657i	$0.605421\pi$
$938$		0			0
$939$	1.66903			0.0544668
$940$		0			0
$941$	−2.65303	+	1.53173i	−0.0864864	+	0.0499329i	−0.542619	−	0.839979i	$-0.682567\pi$
$941$	−2.65303	+	1.53173i	−0.0864864	+	0.0499329i	0.456133	+	0.889912i	$0.349234\pi$
$942$		0			0
$943$	−11.6530			−0.379475
$944$		0			0
$945$	−47.2860	−	27.3006i	−1.53821	−	0.888088i
$946$		0			0
$947$	9.93862	+	5.73807i	0.322962	+	0.186462i	0.652712	−	0.757606i	$-0.273631\pi$
$947$	9.93862	+	5.73807i	0.322962	+	0.186462i	−0.329750	+	0.944068i	$0.606965\pi$
$948$		0			0
$949$			12.1521i			0.394473i
$950$		0			0
$951$		−	52.9754i		−	1.71785i
$952$		0			0
$953$	1.91503	+	1.10564i	0.0620340	+	0.0358153i	0.530696	−	0.847562i	$-0.321931\pi$
$953$	1.91503	+	1.10564i	0.0620340	+	0.0358153i	−0.468662	+	0.883377i	$0.655264\pi$
$954$		0			0
$955$	4.23131	+	2.44295i	0.136922	+	0.0790520i
$956$		0			0
$957$	−76.2250			−2.46401
$958$		0			0
$959$	4.45907	−	2.57445i	0.143991	−	0.0831332i
$960$		0			0
$961$	48.2161			1.55536
$962$		0			0
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$		0			0
$965$	22.5240	−	13.0042i	0.725073	−	0.418621i
$966$		0			0
$967$	−25.7624	−	14.8739i	−0.828463	−	0.478313i	0.0248629	−	0.999691i	$-0.492085\pi$
$967$	−25.7624	−	14.8739i	−0.828463	−	0.478313i	−0.853326	+	0.521377i	$0.825418\pi$
$968$		0			0
$969$	2.76910	−	3.01187i	0.0889563	−	0.0967551i
$970$		0			0
$971$	5.85052	−	10.1334i	0.187752	−	0.325196i	−0.756748	−	0.653706i	$-0.773213\pi$
$971$	5.85052	−	10.1334i	0.187752	−	0.325196i	0.944500	+	0.328510i	$0.106547\pi$
$972$		0			0
$973$	−2.42748	−	4.20453i	−0.0778216	−	0.134791i
$974$		0			0
$975$	7.36116	−	4.24997i	0.235746	−	0.136108i
$976$		0			0
$977$			30.4588i			0.974462i	0.873273	+	0.487231i	$0.161993\pi$
$977$			30.4588i			0.974462i	−0.873273	+	0.487231i	$0.838007\pi$
$978$		0			0
$979$	4.40793	+	7.63477i	0.140878	+	0.244008i
$980$		0			0
$981$		−	70.5086i		−	2.25116i
$982$		0			0
$983$	15.3470	−	26.5817i	0.489492	−	0.847825i	−0.510435	−	0.859917i	$-0.670515\pi$
$983$	15.3470	−	26.5817i	0.489492	−	0.847825i	0.999927	+	0.0120911i	$0.00384881\pi$
$984$		0			0
$985$	4.97731	−	8.62096i	0.158590	−	0.274687i
$986$		0			0
$987$	19.4154			0.618000
$988$		0			0
$989$	−4.23131			−0.134548
$990$		0			0
$991$	−22.6690	+	39.2639i	−0.720106	+	1.24726i	0.240852	+	0.970562i	$0.422573\pi$
$991$	−22.6690	+	39.2639i	−0.720106	+	1.24726i	−0.960957	+	0.276697i	$0.910760\pi$
$992$		0			0
$993$	−46.1241	+	79.8892i	−1.46370	+	2.53521i
$994$		0			0
$995$		−	39.6523i		−	1.25706i
$996$		0			0
$997$	29.8972	+	51.7835i	0.946854	+	1.64000i	0.751996	+	0.659168i	$0.229091\pi$
$997$	29.8972	+	51.7835i	0.946854	+	1.64000i	0.194858	+	0.980831i	$0.437575\pi$
$998$		0			0
$999$			142.151i			4.49747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.n.e.255.3		6
4.3	odd	2		1216.2.n.d.255.1		6
8.3	odd	2		304.2.n.e.255.3	yes	6
8.5	even	2		304.2.n.d.255.1	yes	6
19.12	odd	6		1216.2.n.d.639.1		6
24.5	odd	2		2736.2.bm.l.559.3		6
24.11	even	2		2736.2.bm.m.559.3		6
76.31	even	6	inner	1216.2.n.e.639.3		6
152.69	odd	6		304.2.n.e.31.3	yes	6
152.107	even	6		304.2.n.d.31.1	✓	6
456.107	odd	6		2736.2.bm.l.1855.3		6
456.221	even	6		2736.2.bm.m.1855.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.n.d.31.1	✓	6	152.107	even	6
304.2.n.d.255.1	yes	6	8.5	even	2
304.2.n.e.31.3	yes	6	152.69	odd	6
304.2.n.e.255.3	yes	6	8.3	odd	2
1216.2.n.d.255.1		6	4.3	odd	2
1216.2.n.d.639.1		6	19.12	odd	6
1216.2.n.e.255.3		6	1.1	even	1	trivial
1216.2.n.e.639.3		6	76.31	even	6	inner
2736.2.bm.l.559.3		6	24.5	odd	2
2736.2.bm.l.1855.3		6	456.107	odd	6
2736.2.bm.m.559.3		6	24.11	even	2
2736.2.bm.m.1855.3		6	456.221	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.69617 - 2.93786i) q^{3} +(1.19617 - 2.07183i) q^{5} +1.22147i q^{7} +(-4.25400 - 7.36814i) q^{9} +O(q^{10})\)	\(q+(1.69617 - 2.93786i) q^{3} +(1.19617 - 2.07183i) q^{5} +1.22147i q^{7} +(-4.25400 - 7.36814i) q^{9} -2.95353i q^{11} +(-3.00000 + 1.73205i) q^{13} +(-4.05783 - 7.02836i) q^{15} +(0.138344 - 0.239619i) q^{17} +(1.30383 + 4.15933i) q^{19} +(3.58852 + 2.07183i) q^{21} +(-1.05783 + 0.610737i) q^{23} +(-0.361656 - 0.626406i) q^{25} -18.6850 q^{27} +(6.58852 - 3.80388i) q^{29} -8.90034 q^{31} +(-8.67703 - 5.00969i) q^{33} +(2.53069 + 1.46109i) q^{35} -7.60776i q^{37} +11.7514i q^{39} +(8.26200 + 4.77007i) q^{41} +(3.00000 + 1.73205i) q^{43} -20.3541 q^{45} +(4.05783 - 2.34279i) q^{47} +5.50800 q^{49} +(-0.469311 - 0.812871i) q^{51} +(6.00000 - 3.46410i) q^{53} +(-6.11921 - 3.53292i) q^{55} +(14.4310 + 3.22448i) q^{57} +(3.44217 - 5.96202i) q^{59} +(3.19617 + 5.53593i) q^{61} +(9.00000 - 5.19615i) q^{63} +8.28732i q^{65} +(-3.83452 - 6.64158i) q^{67} +4.14366i q^{69} +(-3.00000 + 5.19615i) q^{71} +(1.75400 - 3.03802i) q^{73} -2.45372 q^{75} +3.60766 q^{77} +(-0.392344 + 0.679560i) q^{79} +(-18.9310 + 32.7895i) q^{81} +8.31866i q^{83} +(-0.330967 - 0.573252i) q^{85} -25.8082i q^{87} +(-2.58497 + 1.49243i) q^{89} +(-2.11566 - 3.66442i) q^{91} +(-15.0965 + 26.1479i) q^{93} +(10.1770 + 2.27396i) q^{95} +(-5.67703 - 3.27764i) q^{97} +(-21.7620 + 12.5643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} - 2 q^{5} - 10 q^{9}+O(q^{10}) \) 6 * q + q^3 - 2 * q^5 - 10 * q^9	\( 6 q + q^{3} - 2 q^{5} - 10 q^{9} - 18 q^{13} - 18 q^{15} - 2 q^{17} + 17 q^{19} - 6 q^{21} - 5 q^{25} - 26 q^{27} + 12 q^{29} - 4 q^{31} + 3 q^{33} - 6 q^{35} + 3 q^{41} + 18 q^{43} - 12 q^{45} + 18 q^{47} + 2 q^{49} - 24 q^{51} + 36 q^{53} + 12 q^{55} + 16 q^{57} + 27 q^{59} + 10 q^{61} + 54 q^{63} - 11 q^{67} - 18 q^{71} - 5 q^{73} + 46 q^{75} + 40 q^{77} + 16 q^{79} - 43 q^{81} - 26 q^{85} - 24 q^{89} - 32 q^{93} + 6 q^{95} + 21 q^{97} - 84 q^{99}+O(q^{100}) \) 6 * q + q^3 - 2 * q^5 - 10 * q^9 - 18 * q^13 - 18 * q^15 - 2 * q^17 + 17 * q^19 - 6 * q^21 - 5 * q^25 - 26 * q^27 + 12 * q^29 - 4 * q^31 + 3 * q^33 - 6 * q^35 + 3 * q^41 + 18 * q^43 - 12 * q^45 + 18 * q^47 + 2 * q^49 - 24 * q^51 + 36 * q^53 + 12 * q^55 + 16 * q^57 + 27 * q^59 + 10 * q^61 + 54 * q^63 - 11 * q^67 - 18 * q^71 - 5 * q^73 + 46 * q^75 + 40 * q^77 + 16 * q^79 - 43 * q^81 - 26 * q^85 - 24 * q^89 - 32 * q^93 + 6 * q^95 + 21 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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