LMFDB - Embedded newform 456.2.bf.a.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(65,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, 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("456.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bf (of order $6$, degree $2$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	456.449
Dual form			456.2.bf.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 1.26217i) q^{5} +3.37228 q^{7} +(2.68614 + 1.33591i) q^{9} +O(q^{10})$	\(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 1.26217i) q^{5} +3.37228 q^{7} +(2.68614 + 1.33591i) q^{9} -3.46410i q^{11} +(2.87228 + 1.65831i) q^{13} +(-4.18614 + 1.26217i) q^{15} +(-2.18614 + 1.26217i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(5.68614 + 1.33591i) q^{21} +(7.93070 + 4.57879i) q^{23} +(0.686141 - 1.18843i) q^{25} +(4.00000 + 3.31662i) q^{27} +(0.186141 - 0.322405i) q^{29} +7.72049i q^{31} +(1.37228 - 5.84096i) q^{33} +(-7.37228 + 4.25639i) q^{35} -11.1846i q^{37} +(4.18614 + 3.93398i) q^{39} +(-3.18614 - 5.51856i) q^{41} +(-5.87228 - 10.1711i) q^{43} +(-7.55842 + 0.469882i) q^{45} +(-0.813859 - 0.469882i) q^{47} +4.37228 q^{49} +(-4.18614 + 1.26217i) q^{51} +(2.81386 - 4.87375i) q^{53} +(4.37228 + 7.57301i) q^{55} +(-7.43070 + 1.33591i) q^{57} +(-0.813859 - 1.40965i) q^{59} +(0.500000 - 0.866025i) q^{61} +(9.05842 + 4.50506i) q^{63} -8.37228 q^{65} +(-1.24456 - 0.718549i) q^{67} +(11.5584 + 10.8622i) q^{69} +(-6.18614 - 10.7147i) q^{71} +(-2.87228 - 4.97494i) q^{73} +(1.62772 - 1.73205i) q^{75} -11.6819i q^{77} +(-12.9891 + 7.49927i) q^{79} +(5.43070 + 7.17687i) q^{81} +3.46410i q^{83} +(3.18614 - 5.51856i) q^{85} +(0.441578 - 0.469882i) q^{87} +(0.813859 - 1.40965i) q^{89} +(9.68614 + 5.59230i) q^{91} +(-3.05842 + 13.0178i) q^{93} +(6.55842 - 8.83518i) q^{95} +(2.44158 - 1.40965i) q^{97} +(4.62772 - 9.30506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9	$ 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} - 11 q^{15} - 3 q^{17} - 16 q^{19} + 17 q^{21} + 3 q^{23} - 3 q^{25} + 16 q^{27} - 5 q^{29} - 6 q^{33} - 18 q^{35} + 11 q^{39} - 7 q^{41} - 12 q^{43} - 13 q^{45} - 9 q^{47} + 6 q^{49} - 11 q^{51} + 17 q^{53} + 6 q^{55} - q^{57} - 9 q^{59} + 2 q^{61} + 19 q^{63} - 22 q^{65} + 18 q^{67} + 29 q^{69} - 19 q^{71} + 18 q^{75} - 6 q^{79} - 7 q^{81} + 7 q^{85} + 19 q^{87} + 9 q^{89} + 33 q^{91} + 5 q^{93} + 9 q^{95} + 27 q^{97} + 30 q^{99}+O(q^{100}) $ 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9 - 11 * q^15 - 3 * q^17 - 16 * q^19 + 17 * q^21 + 3 * q^23 - 3 * q^25 + 16 * q^27 - 5 * q^29 - 6 * q^33 - 18 * q^35 + 11 * q^39 - 7 * q^41 - 12 * q^43 - 13 * q^45 - 9 * q^47 + 6 * q^49 - 11 * q^51 + 17 * q^53 + 6 * q^55 - q^57 - 9 * q^59 + 2 * q^61 + 19 * q^63 - 22 * q^65 + 18 * q^67 + 29 * q^69 - 19 * q^71 + 18 * q^75 - 6 * q^79 - 7 * q^81 + 7 * q^85 + 19 * q^87 + 9 * q^89 + 33 * q^91 + 5 * q^93 + 9 * q^95 + 27 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	1.68614	+	0.396143i	0.973494	+	0.228714i
$3$	1.68614	+	0.396143i	0.973494	+	0.228714i
$4$		0			0
$5$	−2.18614	+	1.26217i	−0.977672	+	0.564459i	−0.901566	−	0.432641i	$-0.857582\pi$
$5$	−2.18614	+	1.26217i	−0.977672	+	0.564459i	−0.0761054	+	0.997100i	$0.524249\pi$
$6$		0			0
$7$	3.37228			1.27460			0.637301	−	0.770615i	$-0.280051\pi$
$7$	3.37228			1.27460			0.637301	+	0.770615i	$0.280051\pi$
$8$		0			0
$9$	2.68614	+	1.33591i	0.895380	+	0.445302i
$10$		0			0
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$		0			0
$13$	2.87228	+	1.65831i	0.796628	+	0.459933i	0.842291	−	0.539024i	$-0.181207\pi$
$13$	2.87228	+	1.65831i	0.796628	+	0.459933i	−0.0456630	+	0.998957i	$0.514540\pi$
$14$		0			0
$15$	−4.18614	+	1.26217i	−1.08086	+	0.325891i
$16$		0			0
$17$	−2.18614	+	1.26217i	−0.530217	+	0.306121i	−0.741105	−	0.671389i	$-0.765698\pi$
$17$	−2.18614	+	1.26217i	−0.530217	+	0.306121i	0.210888	+	0.977510i	$0.432365\pi$
$18$		0			0
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$		0			0
$21$	5.68614	+	1.33591i	1.24082	+	0.291519i
$22$		0			0
$23$	7.93070	+	4.57879i	1.65367	+	0.954744i	0.975547	+	0.219793i	$0.0705381\pi$
$23$	7.93070	+	4.57879i	1.65367	+	0.954744i	0.678119	+	0.734952i	$0.262795\pi$
$24$		0			0
$25$	0.686141	−	1.18843i	0.137228	−	0.237686i
$26$		0			0
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$		0			0
$29$	0.186141	−	0.322405i	0.0345655	−	0.0598691i	−0.848225	−	0.529636i	$-0.822329\pi$
$29$	0.186141	−	0.322405i	0.0345655	−	0.0598691i	0.882791	+	0.469767i	$0.155662\pi$
$30$		0			0
$31$			7.72049i			1.38664i	0.720629	+	0.693320i	$0.243853\pi$
$31$			7.72049i			1.38664i	−0.720629	+	0.693320i	$0.756147\pi$
$32$		0			0
$33$	1.37228	−	5.84096i	0.238884	−	1.01678i
$34$		0			0
$35$	−7.37228	+	4.25639i	−1.24614	+	0.719461i
$36$		0			0
$37$		−	11.1846i		−	1.83874i	−0.393399	−	0.919368i	$-0.628701\pi$
$37$		−	11.1846i		−	1.83874i	0.393399	−	0.919368i	$-0.371299\pi$
$38$		0			0
$39$	4.18614	+	3.93398i	0.670319	+	0.629942i
$40$		0			0
$41$	−3.18614	−	5.51856i	−0.497592	−	0.861854i	0.502405	−	0.864633i	$-0.332449\pi$
$41$	−3.18614	−	5.51856i	−0.497592	−	0.861854i	−0.999996	+	0.00277878i	$0.999115\pi$
$42$		0			0
$43$	−5.87228	−	10.1711i	−0.895515	−	1.55108i	−0.833167	−	0.553022i	$-0.813474\pi$
$43$	−5.87228	−	10.1711i	−0.895515	−	1.55108i	−0.0623480	−	0.998054i	$-0.519859\pi$
$44$		0			0
$45$	−7.55842	+	0.469882i	−1.12674	+	0.0700459i
$46$		0			0
$47$	−0.813859	−	0.469882i	−0.118714	−	0.0685393i	0.439467	−	0.898259i	$-0.355167\pi$
$47$	−0.813859	−	0.469882i	−0.118714	−	0.0685393i	−0.558181	+	0.829719i	$0.688501\pi$
$48$		0			0
$49$	4.37228			0.624612
$50$		0			0
$51$	−4.18614	+	1.26217i	−0.586177	+	0.176739i
$52$		0			0
$53$	2.81386	−	4.87375i	0.386513	−	0.669461i	−0.605465	−	0.795872i	$-0.707013\pi$
$53$	2.81386	−	4.87375i	0.386513	−	0.669461i	0.991978	+	0.126412i	$0.0403460\pi$
$54$		0			0
$55$	4.37228	+	7.57301i	0.589558	+	1.02114i
$56$		0			0
$57$	−7.43070	+	1.33591i	−0.984221	+	0.176945i
$58$		0			0
$59$	−0.813859	−	1.40965i	−0.105955	−	0.183520i	0.808173	−	0.588946i	$-0.200457\pi$
$59$	−0.813859	−	1.40965i	−0.105955	−	0.183520i	−0.914128	+	0.405425i	$0.867123\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	9.05842	+	4.50506i	1.14125	+	0.567584i
$64$		0			0
$65$	−8.37228			−1.03845
$66$		0			0
$67$	−1.24456	−	0.718549i	−0.152048	−	0.0877847i	0.422046	−	0.906574i	$-0.361312\pi$
$67$	−1.24456	−	0.718549i	−0.152048	−	0.0877847i	−0.574094	+	0.818790i	$0.694645\pi$
$68$		0			0
$69$	11.5584	+	10.8622i	1.39147	+	1.30765i
$70$		0			0
$71$	−6.18614	−	10.7147i	−0.734160	−	1.27160i	−0.955091	−	0.296313i	$-0.904243\pi$
$71$	−6.18614	−	10.7147i	−0.734160	−	1.27160i	0.220931	−	0.975289i	$-0.429090\pi$
$72$		0			0
$73$	−2.87228	−	4.97494i	−0.336175	−	0.582272i	0.647535	−	0.762036i	$-0.275800\pi$
$73$	−2.87228	−	4.97494i	−0.336175	−	0.582272i	−0.983710	+	0.179764i	$0.942467\pi$
$74$		0			0
$75$	1.62772	−	1.73205i	0.187953	−	0.200000i
$76$		0			0
$77$		−	11.6819i		−	1.33128i
$78$		0			0
$79$	−12.9891	+	7.49927i	−1.46139	+	0.843734i	−0.999076	−	0.0429815i	$-0.986314\pi$
$79$	−12.9891	+	7.49927i	−1.46139	+	0.843734i	−0.462315	+	0.886716i	$0.652981\pi$
$80$		0			0
$81$	5.43070	+	7.17687i	0.603411	+	0.797430i
$82$		0			0
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$	3.18614	−	5.51856i	0.345585	−	0.598572i
$86$		0			0
$87$	0.441578	−	0.469882i	0.0473421	−	0.0503766i
$88$		0			0
$89$	0.813859	−	1.40965i	0.0862689	−	0.149422i	−0.819662	−	0.572847i	$-0.805839\pi$
$89$	0.813859	−	1.40965i	0.0862689	−	0.149422i	0.905931	+	0.423425i	$0.139172\pi$
$90$		0			0
$91$	9.68614	+	5.59230i	1.01538	+	0.586232i
$92$		0			0
$93$	−3.05842	+	13.0178i	−0.317144	+	1.34989i
$94$		0			0
$95$	6.55842	−	8.83518i	0.672880	−	0.906471i
$96$		0			0
$97$	2.44158	−	1.40965i	0.247905	−	0.143128i	−0.370900	−	0.928673i	$-0.620951\pi$
$97$	2.44158	−	1.40965i	0.247905	−	0.143128i	0.618804	+	0.785545i	$0.287617\pi$
$98$		0			0
$99$	4.62772	−	9.30506i	0.465103	−	0.935194i
$100$		0			0
$101$	−2.18614	−	1.26217i	−0.217529	−	0.125590i	0.387277	−	0.921964i	$-0.373416\pi$
$101$	−2.18614	−	1.26217i	−0.217529	−	0.125590i	−0.604806	+	0.796373i	$0.706749\pi$
$102$		0			0
$103$			9.30506i			0.916855i	0.888732	+	0.458428i	$0.151587\pi$
$103$			9.30506i			0.916855i	−0.888732	+	0.458428i	$0.848413\pi$
$104$		0			0
$105$	−14.1168	+	4.25639i	−1.37766	+	0.415381i
$106$		0			0
$107$	5.25544			0.508062			0.254031	−	0.967196i	$-0.418243\pi$
$107$	5.25544			0.508062			0.254031	+	0.967196i	$0.418243\pi$
$108$		0			0
$109$	−3.55842	+	2.05446i	−0.340835	+	0.196781i	−0.660641	−	0.750702i	$-0.729716\pi$
$109$	−3.55842	+	2.05446i	−0.340835	+	0.196781i	0.319806	+	0.947483i	$0.396382\pi$
$110$		0			0
$111$	4.43070	−	18.8588i	0.420544	−	1.79000i
$112$		0			0
$113$	−3.25544			−0.306246			−0.153123	−	0.988207i	$-0.548933\pi$
$113$	−3.25544			−0.306246			−0.153123	+	0.988207i	$0.548933\pi$
$114$		0			0
$115$	−23.1168			−2.15566
$116$		0			0
$117$	5.50000	+	8.29156i	0.508475	+	0.766555i
$118$		0			0
$119$	−7.37228	+	4.25639i	−0.675816	+	0.390183i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$		0			0
$123$	−3.18614	−	10.5672i	−0.287285	−	0.952815i
$124$		0			0
$125$		−	9.15759i		−	0.819080i
$126$		0			0
$127$	3.30298	+	1.90698i	0.293092	+	0.169217i	0.639336	−	0.768928i	$-0.279209\pi$
$127$	3.30298	+	1.90698i	0.293092	+	0.169217i	−0.346243	+	0.938145i	$0.612543\pi$
$128$		0			0
$129$	−5.87228	−	19.4762i	−0.517026	−	1.71478i
$130$		0			0
$131$	−15.3030	+	8.83518i	−1.33703	+	0.771933i	−0.986366	−	0.164569i	$-0.947377\pi$
$131$	−15.3030	+	8.83518i	−1.33703	+	0.771933i	−0.350662	+	0.936502i	$0.614044\pi$
$132$		0			0
$133$	−13.4891	+	5.84096i	−1.16966	+	0.506476i
$134$		0			0
$135$	−12.9307	−	2.20193i	−1.11290	−	0.189512i
$136$		0			0
$137$	−14.1861	−	8.19037i	−1.21200	−	0.699751i	−0.248808	−	0.968553i	$-0.580039\pi$
$137$	−14.1861	−	8.19037i	−1.21200	−	0.699751i	−0.963195	+	0.268802i	$0.913372\pi$
$138$		0			0
$139$	3.24456	−	5.61975i	0.275200	−	0.476661i	−0.694985	−	0.719024i	$-0.744589\pi$
$139$	3.24456	−	5.61975i	0.275200	−	0.476661i	0.970186	+	0.242363i	$0.0779225\pi$
$140$		0			0
$141$	−1.18614	−	1.11469i	−0.0998911	−	0.0938740i
$142$		0			0
$143$	5.74456	−	9.94987i	0.480384	−	0.832050i
$144$		0			0
$145$			0.939764i			0.0780431i
$146$		0			0
$147$	7.37228	+	1.73205i	0.608056	+	0.142857i
$148$		0			0
$149$	6.55842	−	3.78651i	0.537287	−	0.310203i	−0.206692	−	0.978406i	$-0.566270\pi$
$149$	6.55842	−	3.78651i	0.537287	−	0.310203i	0.743979	+	0.668203i	$0.232936\pi$
$150$		0			0
$151$			0.294954i			0.0240030i	0.999928	+	0.0120015i	$0.00382029\pi$
$151$			0.294954i			0.0240030i	−0.999928	+	0.0120015i	$0.996180\pi$
$152$		0			0
$153$	−7.55842	+	0.469882i	−0.611062	+	0.0379877i
$154$		0			0
$155$	−9.74456	−	16.8781i	−0.782702	−	1.35568i
$156$		0			0
$157$	1.24456	+	2.15565i	0.0993269	+	0.172039i	0.911406	−	0.411508i	$-0.134998\pi$
$157$	1.24456	+	2.15565i	0.0993269	+	0.172039i	−0.812079	+	0.583547i	$0.801664\pi$
$158$		0			0
$159$	6.67527	−	7.10313i	0.529383	−	0.563315i
$160$		0			0
$161$	26.7446	+	15.4410i	2.10777	+	1.21692i
$162$		0			0
$163$	15.3723			1.20405			0.602025	−	0.798477i	$-0.294361\pi$
$163$	15.3723			1.20405			0.602025	+	0.798477i	$0.294361\pi$
$164$		0			0
$165$	4.37228	+	14.5012i	0.340382	+	1.12892i
$166$		0			0
$167$	−0.441578	+	0.764836i	−0.0341703	+	0.0591848i	−0.882605	−	0.470116i	$-0.844212\pi$
$167$	−0.441578	+	0.764836i	−0.0341703	+	0.0591848i	0.848434	+	0.529300i	$0.177546\pi$
$168$		0			0
$169$	−1.00000	−	1.73205i	−0.0769231	−	0.133235i
$170$		0			0
$171$	−13.0584	−	0.691097i	−0.998602	−	0.0528495i
$172$		0			0
$173$	6.93070	+	12.0043i	0.526932	+	0.912672i	0.999507	+	0.0313823i	$0.00999094\pi$
$173$	6.93070	+	12.0043i	0.526932	+	0.912672i	−0.472576	+	0.881290i	$0.656676\pi$
$174$		0			0
$175$	2.31386	−	4.00772i	0.174911	−	0.302955i
$176$		0			0
$177$	−0.813859	−	2.69927i	−0.0611734	−	0.202889i
$178$		0			0
$179$	−1.48913			−0.111302			−0.0556512	−	0.998450i	$-0.517723\pi$
$179$	−1.48913			−0.111302			−0.0556512	+	0.998450i	$0.517723\pi$
$180$		0			0
$181$	−18.3030	−	10.5672i	−1.36045	−	0.785456i	−0.370766	−	0.928726i	$-0.620905\pi$
$181$	−18.3030	−	10.5672i	−1.36045	−	0.785456i	−0.989684	+	0.143270i	$0.954238\pi$
$182$		0			0
$183$	1.18614	−	1.26217i	0.0876820	−	0.0933022i
$184$		0			0
$185$	14.1168	+	24.4511i	1.03789	+	1.79768i
$186$		0			0
$187$	4.37228	+	7.57301i	0.319733	+	0.553794i
$188$		0			0
$189$	13.4891	+	11.1846i	0.981189	+	0.813559i
$190$		0			0
$191$			6.63325i			0.479965i	0.970777	+	0.239983i	$0.0771417\pi$
$191$			6.63325i			0.479965i	−0.970777	+	0.239983i	$0.922858\pi$
$192$		0			0
$193$	13.5000	−	7.79423i	0.971751	−	0.561041i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	13.5000	−	7.79423i	0.971751	−	0.561041i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$	−14.1168	−	3.31662i	−1.01093	−	0.237508i
$196$		0			0
$197$			23.3639i			1.66461i	0.554321	+	0.832303i	$0.312978\pi$
$197$			23.3639i			1.66461i	−0.554321	+	0.832303i	$0.687022\pi$
$198$		0			0
$199$	1.24456	−	2.15565i	0.0882247	−	0.152810i	−0.818536	−	0.574455i	$-0.805214\pi$
$199$	1.24456	−	2.15565i	0.0882247	−	0.152810i	0.906761	+	0.421645i	$0.138547\pi$
$200$		0			0
$201$	−1.81386	−	1.70460i	−0.127940	−	0.120233i
$202$		0			0
$203$	0.627719	−	1.08724i	0.0440572	−	0.0763093i
$204$		0			0
$205$	13.9307	+	8.04290i	0.972963	+	0.561740i
$206$		0			0
$207$	15.1861	+	22.8940i	1.05551	+	1.59124i
$208$		0			0
$209$	6.00000	+	13.8564i	0.415029	+	0.958468i
$210$		0			0
$211$	9.98913	−	5.76722i	0.687680	−	0.397032i	−0.115062	−	0.993358i	$-0.536707\pi$
$211$	9.98913	−	5.76722i	0.687680	−	0.397032i	0.802742	+	0.596326i	$0.203373\pi$
$212$		0			0
$213$	−6.18614	−	20.5171i	−0.423867	−	1.40581i
$214$		0			0
$215$	25.6753	+	14.8236i	1.75104	+	1.01096i
$216$		0			0
$217$			26.0357i			1.76742i
$218$		0			0
$219$	−2.87228	−	9.52628i	−0.194091	−	0.643726i
$220$		0			0
$221$	−8.37228			−0.563181
$222$		0			0
$223$	18.7337	−	10.8159i	1.25450	−	0.724286i	0.282501	−	0.959267i	$-0.408836\pi$
$223$	18.7337	−	10.8159i	1.25450	−	0.724286i	0.972000	+	0.234981i	$0.0755028\pi$
$224$		0			0
$225$	3.43070	−	2.27567i	0.228714	−	0.151711i
$226$		0			0
$227$	−18.7446			−1.24412			−0.622060	−	0.782969i	$-0.713704\pi$
$227$	−18.7446			−1.24412			−0.622060	+	0.782969i	$0.713704\pi$
$228$		0			0
$229$	−3.88316			−0.256606			−0.128303	−	0.991735i	$-0.540953\pi$
$229$	−3.88316			−0.256606			−0.128303	+	0.991735i	$0.540953\pi$
$230$		0			0
$231$	4.62772	−	19.6974i	0.304482	−	1.29599i
$232$		0			0
$233$	12.5584	−	7.25061i	0.822730	−	0.475003i	−0.0286273	−	0.999590i	$-0.509114\pi$
$233$	12.5584	−	7.25061i	0.822730	−	0.475003i	0.851357	+	0.524587i	$0.175780\pi$
$234$		0			0
$235$	2.37228			0.154751
$236$		0			0
$237$	−24.8723	+	7.49927i	−1.61563	+	0.487130i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	17.6168	+	10.1711i	1.13480	+	0.655177i	0.945138	−	0.326672i	$-0.105927\pi$
$241$	17.6168	+	10.1711i	1.13480	+	0.655177i	0.189663	+	0.981849i	$0.439261\pi$
$242$		0			0
$243$	6.31386	+	14.2525i	0.405034	+	0.914302i
$244$		0			0
$245$	−9.55842	+	5.51856i	−0.610665	+	0.352568i
$246$		0			0
$247$	−14.3614	−	1.65831i	−0.913794	−	0.105516i
$248$		0			0
$249$	−1.37228	+	5.84096i	−0.0869648	+	0.370156i
$250$		0			0
$251$	19.9307	+	11.5070i	1.25801	+	0.726315i	0.972688	−	0.232115i	$-0.0745646\pi$
$251$	19.9307	+	11.5070i	1.25801	+	0.726315i	0.285327	+	0.958430i	$0.407898\pi$
$252$		0			0
$253$	15.8614	−	27.4728i	0.997198	−	1.72720i
$254$		0			0
$255$	7.55842	−	8.04290i	0.473327	−	0.503666i
$256$		0			0
$257$	9.55842	−	16.5557i	0.596238	−	1.03271i	−0.397133	−	0.917761i	$-0.629995\pi$
$257$	9.55842	−	16.5557i	0.596238	−	1.03271i	0.993371	−	0.114953i	$-0.0366719\pi$
$258$		0			0
$259$		−	37.7176i		−	2.34366i
$260$		0			0
$261$	0.930703	−	0.617359i	0.0576091	−	0.0382135i
$262$		0			0
$263$	10.9307	−	6.31084i	0.674016	−	0.389143i	−0.123581	−	0.992335i	$-0.539438\pi$
$263$	10.9307	−	6.31084i	0.674016	−	0.389143i	0.797597	+	0.603191i	$0.206104\pi$
$264$		0			0
$265$			14.2063i			0.872684i
$266$		0			0
$267$	1.93070	−	2.05446i	0.118157	−	0.125731i
$268$		0			0
$269$	−7.93070	−	13.7364i	−0.483544	−	0.837522i	0.516278	−	0.856421i	$-0.327317\pi$
$269$	−7.93070	−	13.7364i	−0.483544	−	0.837522i	−0.999821	+	0.0188992i	$0.993984\pi$
$270$		0			0
$271$	9.93070	+	17.2005i	0.603247	+	1.04485i	0.992326	+	0.123650i	$0.0394601\pi$
$271$	9.93070	+	17.2005i	0.603247	+	1.04485i	−0.389079	+	0.921205i	$0.627207\pi$
$272$		0			0
$273$	14.1168	+	13.2665i	0.854390	+	0.802925i
$274$		0			0
$275$	−4.11684	−	2.37686i	−0.248255	−	0.143330i
$276$		0			0
$277$	−19.4891			−1.17099			−0.585494	−	0.810677i	$-0.699099\pi$
$277$	−19.4891			−1.17099			−0.585494	+	0.810677i	$0.699099\pi$
$278$		0			0
$279$	−10.3139	+	20.7383i	−0.617475	+	1.24157i
$280$		0			0
$281$	−7.30298	+	12.6491i	−0.435660	+	0.754584i	−0.997349	−	0.0727635i	$-0.976818\pi$
$281$	−7.30298	+	12.6491i	−0.435660	+	0.754584i	0.561690	+	0.827348i	$0.310151\pi$
$282$		0			0
$283$	−0.0692967	−	0.120025i	−0.00411926	−	0.00713477i	0.863958	−	0.503563i	$-0.167978\pi$
$283$	−0.0692967	−	0.120025i	−0.00411926	−	0.00713477i	−0.868078	+	0.496428i	$0.834645\pi$
$284$		0			0
$285$	14.5584	−	12.2993i	0.862366	−	0.728547i
$286$		0			0
$287$	−10.7446	−	18.6101i	−0.634231	−	1.09852i
$288$		0			0
$289$	−5.31386	+	9.20387i	−0.312580	+	0.541404i
$290$		0			0
$291$	4.67527	−	1.40965i	0.274069	−	0.0826349i
$292$		0			0
$293$	−20.7446			−1.21191			−0.605955	−	0.795499i	$-0.707209\pi$
$293$	−20.7446			−1.21191			−0.605955	+	0.795499i	$0.707209\pi$
$294$		0			0
$295$	3.55842	+	2.05446i	0.207179	+	0.119615i
$296$		0			0
$297$	11.4891	−	13.8564i	0.666667	−	0.804030i
$298$		0			0
$299$	15.1861	+	26.3032i	0.878237	+	1.52115i
$300$		0			0
$301$	−19.8030	−	34.2998i	−1.14143	−	1.97701i
$302$		0			0
$303$	−3.18614	−	2.99422i	−0.183039	−	0.172013i
$304$		0			0
$305$			2.52434i			0.144543i
$306$		0			0
$307$	−26.7921	+	15.4684i	−1.52911	+	0.882830i	−0.529707	+	0.848181i	$0.677698\pi$
$307$	−26.7921	+	15.4684i	−1.52911	+	0.882830i	−0.999400	+	0.0346493i	$0.988969\pi$
$308$		0			0
$309$	−3.68614	+	15.6896i	−0.209697	+	0.892553i
$310$		0			0
$311$			18.9051i			1.07201i	0.844215	+	0.536004i	$0.180067\pi$
$311$			18.9051i			1.07201i	−0.844215	+	0.536004i	$0.819933\pi$
$312$		0			0
$313$	9.67527	−	16.7581i	0.546878	−	0.947221i	−0.451608	−	0.892217i	$-0.649149\pi$
$313$	9.67527	−	16.7581i	0.546878	−	0.947221i	0.998486	−	0.0550045i	$-0.0175173\pi$
$314$		0			0
$315$	−25.4891	+	1.58457i	−1.43615	+	0.0892806i
$316$		0			0
$317$	−7.81386	+	13.5340i	−0.438870	+	0.760145i	−0.997603	−	0.0692026i	$-0.977954\pi$
$317$	−7.81386	+	13.5340i	−0.438870	+	0.760145i	0.558733	+	0.829348i	$0.311288\pi$
$318$		0			0
$319$	−1.11684	−	0.644810i	−0.0625313	−	0.0361024i
$320$		0			0
$321$	8.86141	+	2.08191i	0.494595	+	0.116201i
$322$		0			0
$323$	6.55842	−	8.83518i	0.364920	−	0.491603i
$324$		0			0
$325$	3.94158	−	2.27567i	0.218639	−	0.126232i
$326$		0			0
$327$	−6.81386	+	2.05446i	−0.376807	+	0.113612i
$328$		0			0
$329$	−2.74456	−	1.58457i	−0.151313	−	0.0873604i
$330$		0			0
$331$		−	2.96677i		−	0.163068i	−0.996671	−	0.0815342i	$-0.974018\pi$
$331$		−	2.96677i		−	0.163068i	0.996671	−	0.0815342i	$-0.0259820\pi$
$332$		0			0
$333$	14.9416	−	30.0434i	0.818793	−	1.64637i
$334$		0			0
$335$	3.62772			0.198203
$336$		0			0
$337$	−24.7337	+	14.2800i	−1.34733	+	0.777881i	−0.987871	−	0.155280i	$-0.950372\pi$
$337$	−24.7337	+	14.2800i	−1.34733	+	0.777881i	−0.359459	+	0.933161i	$0.617039\pi$
$338$		0			0
$339$	−5.48913	−	1.28962i	−0.298128	−	0.0700426i
$340$		0			0
$341$	26.7446			1.44830
$342$		0			0
$343$	−8.86141			−0.478471
$344$		0			0
$345$	−38.9783	−	9.15759i	−2.09852	−	0.493028i
$346$		0			0
$347$	−24.0475	+	13.8839i	−1.29094	+	0.745325i	−0.978821	−	0.204718i	$-0.934372\pi$
$347$	−24.0475	+	13.8839i	−1.29094	+	0.745325i	−0.312119	+	0.950043i	$0.601039\pi$
$348$		0			0
$349$	9.60597			0.514196			0.257098	−	0.966385i	$-0.417234\pi$
$349$	9.60597			0.514196			0.257098	+	0.966385i	$0.417234\pi$
$350$		0			0
$351$	5.98913	+	16.1595i	0.319676	+	0.862532i
$352$		0			0
$353$		−	11.0920i		−	0.590369i	−0.955440	−	0.295184i	$-0.904619\pi$
$353$		−	11.0920i		−	0.590369i	0.955440	−	0.295184i	$-0.0953810\pi$
$354$		0			0
$355$	27.0475	+	15.6159i	1.43553	+	0.828806i
$356$		0			0
$357$	−14.1168	+	4.25639i	−0.747143	+	0.225272i
$358$		0			0
$359$	18.3030	−	10.5672i	0.965995	−	0.557717i	0.0679818	−	0.997687i	$-0.478344\pi$
$359$	18.3030	−	10.5672i	0.965995	−	0.557717i	0.898013	+	0.439969i	$0.145011\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$		0			0
$363$	−1.68614	−	0.396143i	−0.0884994	−	0.0207921i
$364$		0			0
$365$	12.5584	+	7.25061i	0.657338	+	0.379514i
$366$		0			0
$367$	−7.61684	+	13.1928i	−0.397596	+	0.688657i	−0.993429	−	0.114452i	$-0.963489\pi$
$367$	−7.61684	+	13.1928i	−0.397596	+	0.688657i	0.595833	+	0.803109i	$0.296822\pi$
$368$		0			0
$369$	−1.18614	−	19.0800i	−0.0617480	−	0.993266i
$370$		0			0
$371$	9.48913	−	16.4356i	0.492651	−	0.853296i
$372$		0			0
$373$			6.92820i			0.358729i	0.983783	+	0.179364i	$0.0574041\pi$
$373$			6.92820i			0.358729i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$	3.62772	−	15.4410i	0.187335	−	0.797369i
$376$		0			0
$377$	1.06930	−	0.617359i	0.0550716	−	0.0317956i
$378$		0			0
$379$		−	12.4742i		−	0.640757i	−0.947290	−	0.320379i	$-0.896190\pi$
$379$		−	12.4742i		−	0.640757i	0.947290	−	0.320379i	$-0.103810\pi$
$380$		0			0
$381$	4.81386	+	4.52389i	0.246621	+	0.231766i
$382$		0			0
$383$	15.3030	+	26.5055i	0.781946	+	1.35437i	0.930807	+	0.365512i	$0.119106\pi$
$383$	15.3030	+	26.5055i	0.781946	+	1.35437i	−0.148861	+	0.988858i	$0.547561\pi$
$384$		0			0
$385$	14.7446	+	25.5383i	0.751452	+	1.30155i
$386$		0			0
$387$	−2.18614	−	35.1658i	−0.111128	−	1.78758i
$388$		0			0
$389$	22.1644	+	12.7966i	1.12378	+	0.648814i	0.942363	−	0.334592i	$-0.108599\pi$
$389$	22.1644	+	12.7966i	1.12378	+	0.648814i	0.181416	+	0.983406i	$0.441932\pi$
$390$		0			0
$391$	−23.1168			−1.16907
$392$		0			0
$393$	−29.3030	+	8.83518i	−1.47814	+	0.445676i
$394$		0			0
$395$	18.9307	−	32.7889i	0.952507	−	1.64979i
$396$		0			0
$397$	12.6168	+	21.8530i	0.633221	+	1.09677i	0.986889	+	0.161400i	$0.0516010\pi$
$397$	12.6168	+	21.8530i	0.633221	+	1.09677i	−0.353668	+	0.935371i	$0.615066\pi$
$398$		0			0
$399$	−25.0584	+	4.50506i	−1.25449	+	0.225535i
$400$		0			0
$401$	−16.6753	−	28.8824i	−0.832723	−	1.44232i	−0.895871	−	0.444314i	$-0.853447\pi$
$401$	−16.6753	−	28.8824i	−0.832723	−	1.44232i	0.0631479	−	0.998004i	$-0.479886\pi$
$402$		0			0
$403$	−12.8030	+	22.1754i	−0.637762	+	1.10464i
$404$		0			0
$405$	−20.9307	−	8.83518i	−1.04006	−	0.439024i
$406$		0			0
$407$	−38.7446			−1.92050
$408$		0			0
$409$	−11.7921	−	6.80818i	−0.583082	−	0.336643i	0.179275	−	0.983799i	$-0.442625\pi$
$409$	−11.7921	−	6.80818i	−0.583082	−	0.336643i	−0.762357	+	0.647156i	$0.775958\pi$
$410$		0			0
$411$	−20.6753	−	19.4299i	−1.01984	−	0.958405i
$412$		0			0
$413$	−2.74456	−	4.75372i	−0.135051	−	0.233915i
$414$		0			0
$415$	−4.37228	−	7.57301i	−0.214627	−	0.371745i
$416$		0			0
$417$	7.69702	−	8.19037i	0.376924	−	0.401084i
$418$		0			0
$419$		−	10.9822i		−	0.536516i	−0.963347	−	0.268258i	$-0.913552\pi$
$419$		−	10.9822i		−	0.536516i	0.963347	−	0.268258i	$-0.0864480\pi$
$420$		0			0
$421$	−17.7921	+	10.2723i	−0.867134	+	0.500640i	−0.866395	−	0.499359i	$-0.833569\pi$
$421$	−17.7921	+	10.2723i	−0.867134	+	0.500640i	−0.000739475		1.00000i	$0.500235\pi$
$422$		0			0
$423$	−1.55842	−	2.34941i	−0.0757731	−	0.114232i
$424$		0			0
$425$			3.46410i			0.168034i
$426$		0			0
$427$	1.68614	−	2.92048i	0.0815981	−	0.141332i
$428$		0			0
$429$	13.6277	−	14.5012i	0.657952	−	0.700125i
$430$		0			0
$431$	4.06930	−	7.04823i	0.196011	−	0.339501i	−0.751220	−	0.660051i	$-0.770534\pi$
$431$	4.06930	−	7.04823i	0.196011	−	0.339501i	0.947232	+	0.320550i	$0.103868\pi$
$432$		0			0
$433$	−30.7337	−	17.7441i	−1.47697	−	0.852727i	−0.477305	−	0.878738i	$-0.658386\pi$
$433$	−30.7337	−	17.7441i	−1.47697	−	0.852727i	−0.999662	+	0.0260105i	$0.991720\pi$
$434$		0			0
$435$	−0.372281	+	1.58457i	−0.0178495	+	0.0759745i
$436$		0			0
$437$	−39.6535	−	4.57879i	−1.89688	−	0.219033i
$438$		0			0
$439$	4.50000	−	2.59808i	0.214773	−	0.123999i	−0.388755	−	0.921341i	$-0.627095\pi$
$439$	4.50000	−	2.59808i	0.214773	−	0.123999i	0.603528	+	0.797342i	$0.293761\pi$
$440$		0			0
$441$	11.7446	+	5.84096i	0.559265	+	0.278141i
$442$		0			0
$443$	23.5367	+	13.5889i	1.11826	+	0.645628i	0.940956	−	0.338528i	$-0.109929\pi$
$443$	23.5367	+	13.5889i	1.11826	+	0.645628i	0.177305	+	0.984156i	$0.443262\pi$
$444$		0			0
$445$			4.10891i			0.194781i
$446$		0			0
$447$	12.5584	−	3.78651i	0.593993	−	0.179096i
$448$		0			0
$449$	30.4674			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$449$	30.4674			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$450$		0			0
$451$	−19.1168	+	11.0371i	−0.900177	+	0.519717i
$452$		0			0
$453$	−0.116844	+	0.497333i	−0.00548981	+	0.0233668i
$454$		0			0
$455$	−28.2337			−1.32362
$456$		0			0
$457$	30.6277			1.43270			0.716352	−	0.697739i	$-0.245810\pi$
$457$	30.6277			1.43270			0.716352	+	0.697739i	$0.245810\pi$
$458$		0			0
$459$	−12.9307	−	2.20193i	−0.603554	−	0.102777i
$460$		0			0
$461$	25.9307	−	14.9711i	1.20771	−	0.697274i	0.245454	−	0.969408i	$-0.421063\pi$
$461$	25.9307	−	14.9711i	1.20771	−	0.697274i	0.962259	+	0.272135i	$0.0877296\pi$
$462$		0			0
$463$	23.3723			1.08620			0.543101	−	0.839667i	$-0.317250\pi$
$463$	23.3723			1.08620			0.543101	+	0.839667i	$0.317250\pi$
$464$		0			0
$465$	−9.74456	−	32.3191i	−0.451893	−	1.49876i
$466$		0			0
$467$			42.2689i			1.95597i	0.208668	+	0.977986i	$0.433087\pi$
$467$			42.2689i			1.95597i	−0.208668	+	0.977986i	$0.566913\pi$
$468$		0			0
$469$	−4.19702	−	2.42315i	−0.193800	−	0.111891i
$470$		0			0
$471$	1.24456	+	4.12775i	0.0573464	+	0.190197i
$472$		0			0
$473$	−35.2337	+	20.3422i	−1.62005	+	0.935334i
$474$		0			0
$475$	−0.686141	+	5.94215i	−0.0314823	+	0.272645i
$476$		0			0
$477$	14.0693	−	9.33252i	0.644189	−	0.427307i
$478$		0			0
$479$	−22.9307	−	13.2390i	−1.04773	−	0.604908i	−0.125717	−	0.992066i	$-0.540123\pi$
$479$	−22.9307	−	13.2390i	−1.04773	−	0.604908i	−0.922013	+	0.387159i	$0.873457\pi$
$480$		0			0
$481$	18.5475	−	32.1253i	0.845695	−	1.46479i
$482$		0			0
$483$	38.9783	+	36.6303i	1.77357	+	1.66674i
$484$		0			0
$485$	−3.55842	+	6.16337i	−0.161580	+	0.279864i
$486$		0			0
$487$		−	13.5615i		−	0.614528i	−0.951624	−	0.307264i	$-0.900587\pi$
$487$		−	13.5615i		−	0.614528i	0.951624	−	0.307264i	$-0.0994135\pi$
$488$		0			0
$489$	25.9198	+	6.08963i	1.17214	+	0.275383i
$490$		0			0
$491$	7.67527	−	4.43132i	0.346380	−	0.199983i	−0.316710	−	0.948522i	$-0.602578\pi$
$491$	7.67527	−	4.43132i	0.346380	−	0.199983i	0.663090	+	0.748540i	$0.269245\pi$
$492$		0			0
$493$			0.939764i			0.0423248i
$494$		0			0
$495$	1.62772	+	26.1831i	0.0731605	+	1.17684i
$496$		0			0
$497$	−20.8614	−	36.1330i	−0.935762	−	1.62079i
$498$		0			0
$499$	6.12772	+	10.6135i	0.274314	+	0.475126i	0.969962	−	0.243257i	$-0.0782158\pi$
$499$	6.12772	+	10.6135i	0.274314	+	0.475126i	−0.695648	+	0.718383i	$0.744882\pi$
$500$		0			0
$501$	−1.04755	+	1.11469i	−0.0468010	+	0.0498008i
$502$		0			0
$503$	33.8139	+	19.5224i	1.50769	+	0.870463i	0.999960	+	0.00894369i	$0.00284690\pi$
$503$	33.8139	+	19.5224i	1.50769	+	0.870463i	0.507725	+	0.861519i	$0.330486\pi$
$504$		0			0
$505$	6.37228			0.283563
$506$		0			0
$507$	−1.00000	−	3.31662i	−0.0444116	−	0.147296i
$508$		0			0
$509$	3.55842	−	6.16337i	0.157724	−	0.273186i	−0.776323	−	0.630335i	$-0.782918\pi$
$509$	3.55842	−	6.16337i	0.157724	−	0.273186i	0.934048	+	0.357148i	$0.116251\pi$
$510$		0			0
$511$	−9.68614	−	16.7769i	−0.428490	−	0.742166i
$512$		0			0
$513$	−21.7446	−	6.33830i	−0.960046	−	0.279843i
$514$		0			0
$515$	−11.7446	−	20.3422i	−0.517527	−	0.896384i
$516$		0			0
$517$	−1.62772	+	2.81929i	−0.0715870	+	0.123992i
$518$		0			0
$519$	6.93070	+	22.9865i	0.304224	+	1.00900i
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$		0			0
$523$	−1.24456	−	0.718549i	−0.0544209	−	0.0314199i	0.472543	−	0.881308i	$-0.343336\pi$
$523$	−1.24456	−	0.718549i	−0.0544209	−	0.0314199i	−0.526964	+	0.849888i	$0.676670\pi$
$524$		0			0
$525$	5.48913	−	5.84096i	0.239565	−	0.254921i
$526$		0			0
$527$	−9.74456	−	16.8781i	−0.424480	−	0.735221i
$528$		0			0
$529$	30.4307	+	52.7075i	1.32307	+	2.29163i
$530$		0			0
$531$	−0.302985	−	4.87375i	−0.0131484	−	0.211503i
$532$		0			0
$533$		−	21.1345i		−	0.915435i
$534$		0			0
$535$	−11.4891	+	6.63325i	−0.496718	+	0.286780i
$536$		0			0
$537$	−2.51087	−	0.589907i	−0.108352	−	0.0254564i
$538$		0			0
$539$		−	15.1460i		−	0.652386i
$540$		0			0
$541$	−14.9891	+	25.9619i	−0.644433	+	1.11619i	0.339999	+	0.940426i	$0.389573\pi$
$541$	−14.9891	+	25.9619i	−0.644433	+	1.11619i	−0.984432	+	0.175765i	$0.943760\pi$
$542$		0			0
$543$	−26.6753	−	25.0684i	−1.14475	−	1.07579i
$544$		0			0
$545$	5.18614	−	8.98266i	0.222150	−	0.384775i
$546$		0			0
$547$	−18.3832	−	10.6135i	−0.786007	−	0.453801i	0.0525479	−	0.998618i	$-0.483266\pi$
$547$	−18.3832	−	10.6135i	−0.786007	−	0.453801i	−0.838555	+	0.544817i	$0.816599\pi$
$548$		0			0
$549$	2.50000	−	1.65831i	0.106697	−	0.0707750i
$550$		0			0
$551$	−0.186141	+	1.61203i	−0.00792986	+	0.0686746i
$552$		0			0
$553$	−43.8030	+	25.2897i	−1.86269	+	1.07543i
$554$		0			0
$555$	14.1168	+	46.8203i	0.599227	+	1.98741i
$556$		0			0
$557$	13.0693	+	7.54556i	0.553764	+	0.319716i	0.750639	−	0.660713i	$-0.229746\pi$
$557$	13.0693	+	7.54556i	0.553764	+	0.319716i	−0.196875	+	0.980429i	$0.563079\pi$
$558$		0			0
$559$		−	38.9523i		−	1.64751i
$560$		0			0
$561$	4.37228	+	14.5012i	0.184598	+	0.612242i
$562$		0			0
$563$	13.7228			0.578348			0.289174	−	0.957277i	$-0.406619\pi$
$563$	13.7228			0.578348			0.289174	+	0.957277i	$0.406619\pi$
$564$		0			0
$565$	7.11684	−	4.10891i	0.299408	−	0.172863i
$566$		0			0
$567$	18.3139	+	24.2024i	0.769110	+	1.01641i
$568$		0			0
$569$	−27.2554			−1.14261			−0.571304	−	0.820739i	$-0.693562\pi$
$569$	−27.2554			−1.14261			−0.571304	+	0.820739i	$0.693562\pi$
$570$		0			0
$571$	15.3723			0.643310			0.321655	−	0.946857i	$-0.395761\pi$
$571$	15.3723			0.643310			0.321655	+	0.946857i	$0.395761\pi$
$572$		0			0
$573$	−2.62772	+	11.1846i	−0.109775	+	0.467243i
$574$		0			0
$575$	10.8832	−	6.28339i	0.453859	−	0.262036i
$576$		0			0
$577$	−4.51087			−0.187790			−0.0938951	−	0.995582i	$-0.529932\pi$
$577$	−4.51087			−0.187790			−0.0938951	+	0.995582i	$0.529932\pi$
$578$		0			0
$579$	25.8505	−	7.79423i	1.07431	−	0.323917i
$580$		0			0
$581$			11.6819i			0.484648i
$582$		0			0
$583$	−16.8832	−	9.74749i	−0.699229	−	0.403700i
$584$		0			0
$585$	−22.4891	−	11.1846i	−0.929811	−	0.462426i
$586$		0			0
$587$	−41.1861	+	23.7788i	−1.69993	+	0.981457i	−0.754127	+	0.656729i	$0.771940\pi$
$587$	−41.1861	+	23.7788i	−1.69993	+	0.981457i	−0.945807	+	0.324728i	$0.894727\pi$
$588$		0			0
$589$	−13.3723	−	30.8820i	−0.550995	−	1.27247i
$590$		0			0
$591$	−9.25544	+	39.3947i	−0.380718	+	1.62048i
$592$		0			0
$593$	−27.0475	−	15.6159i	−1.11071	−	0.641269i	−0.171697	−	0.985150i	$-0.554925\pi$
$593$	−27.0475	−	15.6159i	−1.11071	−	0.641269i	−0.939013	+	0.343881i	$0.888258\pi$
$594$		0			0
$595$	10.7446	−	18.6101i	0.440484	−	0.762941i
$596$		0			0
$597$	2.95245	−	3.14170i	0.120836	−	0.128581i
$598$		0			0
$599$	−8.55842	+	14.8236i	−0.349688	+	0.605677i	−0.986194	−	0.165595i	$-0.947046\pi$
$599$	−8.55842	+	14.8236i	−0.349688	+	0.605677i	0.636506	+	0.771272i	$0.280379\pi$
$600$		0			0
$601$		−	22.2766i		−	0.908682i	−0.890828	−	0.454341i	$-0.849875\pi$
$601$		−	22.2766i		−	0.908682i	0.890828	−	0.454341i	$-0.150125\pi$
$602$		0			0
$603$	−2.38316	−	3.59274i	−0.0970496	−	0.146308i
$604$		0			0
$605$	2.18614	−	1.26217i	0.0888793	−	0.0513145i
$606$		0			0
$607$			0.792287i			0.0321579i	0.999871	+	0.0160790i	$0.00511832\pi$
$607$			0.792287i			0.0321579i	−0.999871	+	0.0160790i	$0.994882\pi$
$608$		0			0
$609$	1.48913	−	1.58457i	0.0603424	−	0.0642102i
$610$		0			0
$611$	−1.55842	−	2.69927i	−0.0630470	−	0.109201i
$612$		0			0
$613$	−12.5584	−	21.7518i	−0.507230	−	0.878548i	−0.999965	−	0.00836857i	$-0.997336\pi$
$613$	−12.5584	−	21.7518i	−0.507230	−	0.878548i	0.492735	−	0.870179i	$-0.335997\pi$
$614$		0			0
$615$	20.3030	+	19.0800i	0.818695	+	0.769380i
$616$		0			0
$617$	12.5584	+	7.25061i	0.505583	+	0.291898i	0.731016	−	0.682360i	$-0.239046\pi$
$617$	12.5584	+	7.25061i	0.505583	+	0.291898i	−0.225433	+	0.974259i	$0.572380\pi$
$618$		0			0
$619$	3.13859			0.126151			0.0630754	−	0.998009i	$-0.479909\pi$
$619$	3.13859			0.126151			0.0630754	+	0.998009i	$0.479909\pi$
$620$		0			0
$621$	16.5367	+	44.6183i	0.663594	+	1.79047i
$622$		0			0
$623$	2.74456	−	4.75372i	0.109959	−	0.190454i
$624$		0			0
$625$	14.9891	+	25.9619i	0.599565	+	1.03848i
$626$		0			0
$627$	4.62772	+	25.7407i	0.184813	+	1.02798i
$628$		0			0
$629$	14.1168	+	24.4511i	0.562875	+	0.974929i
$630$		0			0
$631$	12.6168	−	21.8530i	0.502269	−	0.869955i	−0.497728	−	0.867333i	$-0.665832\pi$
$631$	12.6168	−	21.8530i	0.502269	−	0.869955i	0.999997	−	0.00262157i	$-0.000834473\pi$
$632$		0			0
$633$	19.1277	−	5.76722i	0.760259	−	0.229227i
$634$		0			0
$635$	−9.62772			−0.382064
$636$		0			0
$637$	12.5584	+	7.25061i	0.497583	+	0.287280i
$638$		0			0
$639$	−2.30298	−	37.0453i	−0.0911047	−	1.46549i
$640$		0			0
$641$	−13.1861	−	22.8391i	−0.520821	−	0.902089i	−0.999707	−	0.0242115i	$-0.992292\pi$
$641$	−13.1861	−	22.8391i	−0.520821	−	0.902089i	0.478886	−	0.877877i	$-0.341041\pi$
$642$		0			0
$643$	1.50000	+	2.59808i	0.0591542	+	0.102458i	0.894086	−	0.447895i	$-0.147826\pi$
$643$	1.50000	+	2.59808i	0.0591542	+	0.102458i	−0.834932	+	0.550353i	$0.814493\pi$
$644$		0			0
$645$	37.4198	+	35.1658i	1.47340	+	1.38465i
$646$		0			0
$647$		−	17.9104i		−	0.704131i	−0.935975	−	0.352066i	$-0.885479\pi$
$647$		−	17.9104i		−	0.704131i	0.935975	−	0.352066i	$-0.114521\pi$
$648$		0			0
$649$	−4.88316	+	2.81929i	−0.191681	+	0.110667i
$650$		0			0
$651$	−10.3139	+	43.8998i	−0.404232	+	1.72057i
$652$		0			0
$653$		−	2.17448i		−	0.0850940i	−0.999094	−	0.0425470i	$-0.986453\pi$
$653$		−	2.17448i		−	0.0850940i	0.999094	−	0.0425470i	$-0.0135472\pi$
$654$		0			0
$655$	22.3030	−	38.6299i	0.871450	−	1.50940i
$656$		0			0
$657$	−1.06930	−	17.2005i	−0.0417172	−	0.671055i
$658$		0			0
$659$	−12.0475	+	20.8670i	−0.469306	+	0.812862i	−0.999384	−	0.0350871i	$-0.988829\pi$
$659$	−12.0475	+	20.8670i	−0.469306	+	0.812862i	0.530078	+	0.847949i	$0.322162\pi$
$660$		0			0
$661$	−24.3030	−	14.0313i	−0.945277	−	0.545756i	−0.0536661	−	0.998559i	$-0.517091\pi$
$661$	−24.3030	−	14.0313i	−0.945277	−	0.545756i	−0.891610	+	0.452803i	$0.850424\pi$
$662$		0			0
$663$	−14.1168	−	3.31662i	−0.548253	−	0.128807i
$664$		0			0
$665$	22.1168	−	29.7947i	0.857654	−	1.15539i
$666$		0			0
$667$	2.95245	−	1.70460i	0.114319	−	0.0660024i
$668$		0			0
$669$	35.8723	−	10.8159i	1.38690	−	0.418167i
$670$		0			0
$671$	−3.00000	−	1.73205i	−0.115814	−	0.0668651i
$672$		0			0
$673$		−	2.08191i		−	0.0802516i	−0.999195	−	0.0401258i	$-0.987224\pi$
$673$		−	2.08191i		−	0.0802516i	0.999195	−	0.0401258i	$-0.0127759\pi$
$674$		0			0
$675$	6.68614	−	2.47805i	0.257350	−	0.0953802i
$676$		0			0
$677$	−15.2554			−0.586314			−0.293157	−	0.956064i	$-0.594706\pi$
$677$	−15.2554			−0.586314			−0.293157	+	0.956064i	$0.594706\pi$
$678$		0			0
$679$	8.23369	−	4.75372i	0.315980	−	0.182431i
$680$		0			0
$681$	−31.6060	−	7.42554i	−1.21114	−	0.284547i
$682$		0			0
$683$	6.74456			0.258074			0.129037	−	0.991640i	$-0.458811\pi$
$683$	6.74456			0.258074			0.129037	+	0.991640i	$0.458811\pi$
$684$		0			0
$685$	41.3505			1.57992
$686$		0			0
$687$	−6.54755	−	1.53829i	−0.249805	−	0.0586893i
$688$		0			0
$689$	16.1644	−	9.33252i	0.615814	−	0.355541i
$690$		0			0
$691$	49.9565			1.90043			0.950217	−	0.311588i	$-0.100861\pi$
$691$	49.9565			1.90043			0.950217	+	0.311588i	$0.100861\pi$
$692$		0			0
$693$	15.6060	−	31.3793i	0.592822	−	1.19200i
$694$		0			0
$695$			16.3807i			0.621357i
$696$		0			0
$697$	13.9307	+	8.04290i	0.527663	+	0.304646i
$698$		0			0
$699$	24.0475	−	7.25061i	0.909562	−	0.274243i
$700$		0			0
$701$	−5.44158	+	3.14170i	−0.205526	+	0.118660i	−0.599230	−	0.800577i	$-0.704527\pi$
$701$	−5.44158	+	3.14170i	−0.205526	+	0.118660i	0.393705	+	0.919237i	$0.371193\pi$
$702$		0			0
$703$	19.3723	+	44.7384i	0.730639	+	1.68734i
$704$		0			0
$705$	4.00000	+	0.939764i	0.150649	+	0.0353936i
$706$		0			0
$707$	−7.37228	−	4.25639i	−0.277263	−	0.160078i
$708$		0			0
$709$	11.2446	−	19.4762i	0.422298	−	0.731442i	−0.573865	−	0.818950i	$-0.694557\pi$
$709$	11.2446	−	19.4762i	0.422298	−	0.731442i	0.996164	+	0.0875073i	$0.0278901\pi$
$710$		0			0
$711$	−44.9090	+	2.79184i	−1.68422	+	0.104702i
$712$		0			0
$713$	−35.3505	+	61.2289i	−1.32389	+	2.29304i
$714$		0			0
$715$			29.0024i			1.08463i
$716$		0			0
$717$	−4.11684	+	17.5229i	−0.153746	+	0.654404i
$718$		0			0
$719$	0.813859	−	0.469882i	0.0303518	−	0.0175236i	−0.484747	−	0.874654i	$-0.661088\pi$
$719$	0.813859	−	0.469882i	0.0303518	−	0.0175236i	0.515099	+	0.857131i	$0.327755\pi$
$720$		0			0
$721$			31.3793i			1.16863i
$722$		0			0
$723$	25.6753	+	24.1287i	0.954873	+	0.897355i
$724$		0			0
$725$	−0.255437	−	0.442430i	−0.00948671	−	0.0164315i
$726$		0			0
$727$	−11.1277	−	19.2738i	−0.412704	−	0.714825i	0.582480	−	0.812845i	$-0.302082\pi$
$727$	−11.1277	−	19.2738i	−0.412704	−	0.714825i	−0.995184	+	0.0980202i	$0.968749\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$		0			0
$731$	25.6753	+	14.8236i	0.949634	+	0.548271i
$732$		0			0
$733$	20.9783			0.774849			0.387425	−	0.921901i	$-0.373365\pi$
$733$	20.9783			0.774849			0.387425	+	0.921901i	$0.373365\pi$
$734$		0			0
$735$	−18.3030	+	5.51856i	−0.675116	+	0.203555i
$736$		0			0
$737$	−2.48913	+	4.31129i	−0.0916881	+	0.158808i
$738$		0			0
$739$	−3.75544	−	6.50461i	−0.138146	−	0.239276i	0.788649	−	0.614844i	$-0.210781\pi$
$739$	−3.75544	−	6.50461i	−0.138146	−	0.239276i	−0.926795	+	0.375568i	$0.877448\pi$
$740$		0			0
$741$	−23.5584	−	8.48533i	−0.865440	−	0.311716i
$742$		0			0
$743$	−8.18614	−	14.1788i	−0.300320	−	0.520170i	0.675888	−	0.737004i	$-0.263760\pi$
$743$	−8.18614	−	14.1788i	−0.300320	−	0.520170i	−0.976208	+	0.216834i	$0.930427\pi$
$744$		0			0
$745$	−9.55842	+	16.5557i	−0.350193	+	0.606553i
$746$		0			0
$747$	−4.62772	+	9.30506i	−0.169319	+	0.340454i
$748$		0			0
$749$	17.7228			0.647578
$750$		0			0
$751$	2.01087	+	1.16098i	0.0733779	+	0.0423647i	0.536240	−	0.844066i	$-0.319844\pi$
$751$	2.01087	+	1.16098i	0.0733779	+	0.0423647i	−0.462862	+	0.886430i	$0.653178\pi$
$752$		0			0
$753$	29.0475	+	27.2978i	1.05855	+	0.994788i
$754$		0			0
$755$	−0.372281	−	0.644810i	−0.0135487	−	0.0234670i
$756$		0			0
$757$	7.12772	+	12.3456i	0.259061	+	0.448707i	0.965991	−	0.258577i	$-0.0832535\pi$
$757$	7.12772	+	12.3456i	0.259061	+	0.448707i	−0.706929	+	0.707284i	$0.749920\pi$
$758$		0			0
$759$	37.6277	−	40.0395i	1.36580	−	1.45334i
$760$		0			0
$761$			19.6048i			0.710673i	0.934738	+	0.355337i	$0.115634\pi$
$761$			19.6048i			0.710673i	−0.934738	+	0.355337i	$0.884366\pi$
$762$		0			0
$763$	−12.0000	+	6.92820i	−0.434429	+	0.250818i
$764$		0			0
$765$	15.9307	−	10.5672i	0.575976	−	0.382059i
$766$		0			0
$767$		−	5.39853i		−	0.194930i
$768$		0			0
$769$	15.8723	−	27.4916i	0.572369	−	0.991372i	−0.423953	−	0.905684i	$-0.639358\pi$
$769$	15.8723	−	27.4916i	0.572369	−	0.991372i	0.996322	−	0.0856881i	$-0.0273089\pi$
$770$		0			0
$771$	22.6753	−	24.1287i	0.816630	−	0.868973i
$772$		0			0
$773$	18.8139	−	32.5866i	0.676687	−	1.17206i	−0.299285	−	0.954164i	$-0.596748\pi$
$773$	18.8139	−	32.5866i	0.676687	−	1.17206i	0.975973	−	0.217893i	$-0.0699185\pi$
$774$		0			0
$775$	9.17527	+	5.29734i	0.329585	+	0.190286i
$776$		0			0
$777$	14.9416	−	63.5972i	0.536026	−	2.28154i
$778$		0			0
$779$	22.3030	+	16.5557i	0.799087	+	0.593169i
$780$		0			0
$781$	−37.1168	+	21.4294i	−1.32815	+	0.766805i
$782$		0			0
$783$	1.81386	−	0.672262i	0.0648220	−	0.0240247i
$784$		0			0
$785$	−5.44158	−	3.14170i	−0.194218	−	0.112132i
$786$		0			0
$787$			2.37686i			0.0847259i	0.999102	+	0.0423630i	$0.0134886\pi$
$787$			2.37686i			0.0847259i	−0.999102	+	0.0423630i	$0.986511\pi$
$788$		0			0
$789$	20.9307	−	6.31084i	0.745153	−	0.224672i
$790$		0			0
$791$	−10.9783			−0.390342
$792$		0			0
$793$	2.87228	−	1.65831i	0.101998	−	0.0588884i
$794$		0			0
$795$	−5.62772	+	23.9538i	−0.199595	+	0.849552i
$796$		0			0
$797$	−24.5109			−0.868220			−0.434110	−	0.900860i	$-0.642937\pi$
$797$	−24.5109			−0.868220			−0.434110	+	0.900860i	$0.642937\pi$
$798$		0			0
$799$	2.37228			0.0839253
$800$		0			0
$801$	4.06930	−	2.69927i	0.143782	−	0.0953739i
$802$		0			0
$803$	−17.2337	+	9.94987i	−0.608164	+	0.351123i
$804$		0			0
$805$	−77.9565			−2.74761
$806$		0			0
$807$	−7.93070	−	26.3032i	−0.279174	−	0.925915i
$808$		0			0
$809$		−	1.58457i		−	0.0557107i	−0.999612	−	0.0278553i	$-0.991132\pi$
$809$		−	1.58457i		−	0.0557107i	0.999612	−	0.0278553i	$-0.00886777\pi$
$810$		0			0
$811$	−1.67527	−	0.967215i	−0.0588265	−	0.0339635i	0.470298	−	0.882508i	$-0.344146\pi$
$811$	−1.67527	−	0.967215i	−0.0588265	−	0.0339635i	−0.529125	+	0.848544i	$0.677480\pi$
$812$		0			0
$813$	9.93070	+	32.9364i	0.348285	+	1.15513i
$814$		0			0
$815$	−33.6060	+	19.4024i	−1.17717	+	0.679637i
$816$		0			0
$817$	41.1060	+	30.5133i	1.43812	+	1.06752i
$818$		0			0
$819$	18.5475	+	27.9615i	0.648104	+	0.977053i
$820$		0			0
$821$	−15.9090	−	9.18504i	−0.555226	−	0.320560i	0.196001	−	0.980604i	$-0.437204\pi$
$821$	−15.9090	−	9.18504i	−0.555226	−	0.320560i	−0.751227	+	0.660044i	$0.770538\pi$
$822$		0			0
$823$	−17.9307	+	31.0569i	−0.625025	+	1.08258i	0.363511	+	0.931590i	$0.381578\pi$
$823$	−17.9307	+	31.0569i	−0.625025	+	1.08258i	−0.988536	+	0.150985i	$0.951755\pi$
$824$		0			0
$825$	−6.00000	−	5.63858i	−0.208893	−	0.196310i
$826$		0			0
$827$	16.9307	−	29.3248i	0.588738	−	1.01972i	−0.405660	−	0.914024i	$-0.632958\pi$
$827$	16.9307	−	29.3248i	0.588738	−	1.01972i	0.994398	−	0.105700i	$-0.0337084\pi$
$828$		0			0
$829$			5.25106i			0.182377i	0.995834	+	0.0911883i	$0.0290665\pi$
$829$			5.25106i			0.182377i	−0.995834	+	0.0911883i	$0.970933\pi$
$830$		0			0
$831$	−32.8614	−	7.72049i	−1.13995	−	0.267821i
$832$		0			0
$833$	−9.55842	+	5.51856i	−0.331180	+	0.191207i
$834$		0			0
$835$		−	2.22938i		−	0.0771510i
$836$		0			0
$837$	−25.6060	+	30.8820i	−0.885072	+	1.06744i
$838$		0			0
$839$	−4.18614	−	7.25061i	−0.144522	−	0.250319i	0.784673	−	0.619910i	$-0.212831\pi$
$839$	−4.18614	−	7.25061i	−0.144522	−	0.250319i	−0.929194	+	0.369591i	$0.879498\pi$
$840$		0			0
$841$	14.4307	+	24.9947i	0.497610	+	0.861887i
$842$		0			0
$843$	−17.3247	+	18.4352i	−0.596696	+	0.634942i
$844$		0			0
$845$	4.37228	+	2.52434i	0.150411	+	0.0868399i
$846$		0			0
$847$	−3.37228			−0.115873
$848$		0			0
$849$	−0.0692967	−	0.229831i	−0.00237826	−	0.00788778i
$850$		0			0
$851$	51.2119	−	88.7017i	1.75552	−	3.04065i
$852$		0			0
$853$	−0.872281	−	1.51084i	−0.0298663	−	0.0517300i	0.850706	−	0.525642i	$-0.176175\pi$
$853$	−0.872281	−	1.51084i	−0.0298663	−	0.0517300i	−0.880572	+	0.473912i	$0.842841\pi$
$854$		0			0
$855$	29.4198	−	14.9711i	1.00614	−	0.512001i
$856$		0			0
$857$	−5.18614	−	8.98266i	−0.177155	−	0.306842i	0.763750	−	0.645512i	$-0.223356\pi$
$857$	−5.18614	−	8.98266i	−0.177155	−	0.306842i	−0.940905	+	0.338671i	$0.890023\pi$
$858$		0			0
$859$	20.6168	−	35.7094i	0.703438	−	1.21839i	−0.263815	−	0.964573i	$-0.584981\pi$
$859$	20.6168	−	35.7094i	0.703438	−	1.21839i	0.967252	−	0.253816i	$-0.0816859\pi$
$860$		0			0
$861$	−10.7446	−	35.6357i	−0.366174	−	1.21446i
$862$		0			0
$863$	−33.4891			−1.13998			−0.569992	−	0.821651i	$-0.693054\pi$
$863$	−33.4891			−1.13998			−0.569992	+	0.821651i	$0.693054\pi$
$864$		0			0
$865$	−30.3030	−	17.4954i	−1.03033	−	0.594863i
$866$		0			0
$867$	−12.6060	+	13.4140i	−0.428121	+	0.455563i
$868$		0			0
$869$	25.9783	+	44.9956i	0.881252	+	1.52637i
$870$		0			0
$871$	−2.38316	−	4.12775i	−0.0807502	−	0.139863i
$872$		0			0
$873$	8.44158	−	0.524785i	0.285704	−	0.0177613i
$874$		0			0
$875$		−	30.8820i		−	1.04400i
$876$		0			0
$877$	−11.3614	+	6.55951i	−0.383647	+	0.221499i	−0.679404	−	0.733764i	$-0.737762\pi$
$877$	−11.3614	+	6.55951i	−0.383647	+	0.221499i	0.295757	+	0.955263i	$0.404428\pi$
$878$		0			0
$879$	−34.9783	−	8.21782i	−1.17979	−	0.277180i
$880$		0			0
$881$			15.4410i			0.520220i	0.965579	+	0.260110i	$0.0837588\pi$
$881$			15.4410i			0.520220i	−0.965579	+	0.260110i	$0.916241\pi$
$882$		0			0
$883$	−4.12772	+	7.14942i	−0.138909	+	0.240597i	−0.927084	−	0.374854i	$-0.877693\pi$
$883$	−4.12772	+	7.14942i	−0.138909	+	0.240597i	0.788175	+	0.615451i	$0.211026\pi$
$884$		0			0
$885$	5.18614	+	4.87375i	0.174330	+	0.163829i
$886$		0			0
$887$	18.3030	−	31.7017i	0.614554	−	1.06444i	−0.375908	−	0.926657i	$-0.622669\pi$
$887$	18.3030	−	31.7017i	0.614554	−	1.06444i	0.990463	−	0.137782i	$-0.0439974\pi$
$888$		0			0
$889$	11.1386	+	6.43087i	0.373576	+	0.215684i
$890$		0			0
$891$	24.8614	−	18.8125i	0.832888	−	0.630243i
$892$		0			0
$893$	4.06930	+	0.469882i	0.136174	+	0.0157240i
$894$		0			0
$895$	3.25544	−	1.87953i	0.108817	−	0.0628257i
$896$		0			0
$897$	15.1861	+	50.3667i	0.507050	+	1.68170i
$898$		0			0
$899$	2.48913	+	1.43710i	0.0830170	+	0.0479299i
$900$		0			0
$901$			14.2063i			0.473279i
$902$		0			0
$903$	−19.8030	−	65.6791i	−0.659002	−	2.18566i
$904$		0			0
$905$	53.3505			1.77343
$906$		0			0
$907$	17.4416	−	10.0699i	0.579138	−	0.334366i	−0.181653	−	0.983363i	$-0.558145\pi$
$907$	17.4416	−	10.0699i	0.579138	−	0.334366i	0.760791	+	0.648997i	$0.224811\pi$
$908$		0			0
$909$	−4.18614	−	6.31084i	−0.138846	−	0.209317i
$910$		0			0
$911$	−13.4891			−0.446915			−0.223457	−	0.974714i	$-0.571734\pi$
$911$	−13.4891			−0.446915			−0.223457	+	0.974714i	$0.571734\pi$
$912$		0			0
$913$	12.0000			0.397142
$914$		0			0
$915$	−1.00000	+	4.25639i	−0.0330590	+	0.140712i
$916$		0			0
$917$	−51.6060	+	29.7947i	−1.70418	+	0.983908i
$918$		0			0
$919$	−8.86141			−0.292311			−0.146155	−	0.989262i	$-0.546690\pi$
$919$	−8.86141			−0.292311			−0.146155	+	0.989262i	$0.546690\pi$
$920$		0			0
$921$	−51.3030	+	15.4684i	−1.69049	+	0.509702i
$922$		0			0
$923$		−	41.0342i		−	1.35066i
$924$		0			0
$925$	−13.2921	−	7.67420i	−0.437042	−	0.252326i
$926$		0			0
$927$	−12.4307	+	24.9947i	−0.408278	+	0.820934i
$928$		0			0
$929$	−20.1861	+	11.6545i	−0.662286	+	0.382371i	−0.793147	−	0.609030i	$-0.791559\pi$
$929$	−20.1861	+	11.6545i	−0.662286	+	0.382371i	0.130862	+	0.991401i	$0.458226\pi$
$930$		0			0
$931$	−17.4891	+	7.57301i	−0.573183	+	0.248195i
$932$		0			0
$933$	−7.48913	+	31.8766i	−0.245183	+	1.04359i
$934$		0			0
$935$	−19.1168	−	11.0371i	−0.625188	−	0.360952i
$936$		0			0
$937$	−16.9891	+	29.4260i	−0.555011	+	0.961306i	0.442892	+	0.896575i	$0.353952\pi$
$937$	−16.9891	+	29.4260i	−0.555011	+	0.961306i	−0.997903	+	0.0647316i	$0.979381\pi$
$938$		0			0
$939$	22.9525	−	24.4236i	0.749025	−	0.797035i
$940$		0			0
$941$	−7.69702	+	13.3316i	−0.250916	+	0.434598i	−0.963778	−	0.266705i	$-0.914065\pi$
$941$	−7.69702	+	13.3316i	−0.250916	+	0.434598i	0.712863	+	0.701304i	$0.247398\pi$
$942$		0			0
$943$		−	58.3547i		−	1.90029i
$944$		0			0
$945$	−43.6060	−	7.42554i	−1.41850	−	0.241553i
$946$		0			0
$947$	−3.81386	+	2.20193i	−0.123934	+	0.0715532i	−0.560685	−	0.828029i	$-0.689462\pi$
$947$	−3.81386	+	2.20193i	−0.123934	+	0.0715532i	0.436752	+	0.899582i	$0.356129\pi$
$948$		0			0
$949$		−	19.0526i		−	0.618472i
$950$		0			0
$951$	−18.5367	+	19.7248i	−0.601093	+	0.639621i
$952$		0			0
$953$	4.69702	+	8.13547i	0.152151	+	0.263534i	0.932018	−	0.362412i	$-0.118047\pi$
$953$	4.69702	+	8.13547i	0.152151	+	0.263534i	−0.779867	+	0.625945i	$0.784713\pi$
$954$		0			0
$955$	−8.37228	−	14.5012i	−0.270921	−	0.469248i
$956$		0			0
$957$	−1.62772	−	1.52967i	−0.0526167	−	0.0494472i
$958$		0			0
$959$	−47.8397	−	27.6202i	−1.54482	−	0.891904i
$960$		0			0
$961$	−28.6060			−0.922773
$962$		0			0
$963$	14.1168	+	7.02078i	0.454909	+	0.226241i
$964$		0			0
$965$	−19.6753	+	34.0786i	−0.633369	+	1.09703i
$966$		0			0
$967$	−3.87228	−	6.70699i	−0.124524	−	0.215682i	0.797023	−	0.603949i	$-0.206407\pi$
$967$	−3.87228	−	6.70699i	−0.124524	−	0.215682i	−0.921547	+	0.388267i	$0.873074\pi$
$968$		0			0
$969$	14.5584	−	12.2993i	0.467684	−	0.395110i
$970$		0			0
$971$	13.9307	+	24.1287i	0.447058	+	0.774326i	0.998193	−	0.0600894i	$-0.0191386\pi$
$971$	13.9307	+	24.1287i	0.447058	+	0.774326i	−0.551135	+	0.834416i	$0.685805\pi$
$972$		0			0
$973$	10.9416	−	18.9514i	0.350771	−	0.607553i
$974$		0			0
$975$	7.54755	−	2.27567i	0.241715	−	0.0728798i
$976$		0			0
$977$	37.2119			1.19052			0.595258	−	0.803535i	$-0.297050\pi$
$977$	37.2119			1.19052			0.595258	+	0.803535i	$0.297050\pi$
$978$		0			0
$979$	−4.88316	−	2.81929i	−0.156066	−	0.0901049i
$980$		0			0
$981$	−12.3030	+	0.764836i	−0.392804	+	0.0244193i
$982$		0			0
$983$	−12.9307	−	22.3966i	−0.412425	−	0.714342i	0.582729	−	0.812667i	$-0.301985\pi$
$983$	−12.9307	−	22.3966i	−0.412425	−	0.714342i	−0.995154	+	0.0983248i	$0.968652\pi$
$984$		0			0
$985$	−29.4891	−	51.0767i	−0.939602	−	1.62744i
$986$		0			0
$987$	−4.00000	−	3.75906i	−0.127321	−	0.119652i
$988$		0			0
$989$		−	107.552i		−	3.41995i
$990$		0			0
$991$	9.12772	−	5.26989i	0.289952	−	0.167404i	−0.347968	−	0.937506i	$-0.613128\pi$
$991$	9.12772	−	5.26989i	0.289952	−	0.167404i	0.637920	+	0.770103i	$0.279795\pi$
$992$		0			0
$993$	1.17527	−	5.00239i	0.0372959	−	0.158746i
$994$		0			0
$995$			6.28339i			0.199197i
$996$		0			0
$997$	−18.2446	+	31.6005i	−0.577811	+	1.00080i	0.417919	+	0.908484i	$0.362760\pi$
$997$	−18.2446	+	31.6005i	−0.577811	+	1.00080i	−0.995730	+	0.0923138i	$0.970574\pi$
$998$		0			0
$999$	37.0951	−	44.7384i	1.17364	−	1.41546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bf.a.449.2	yes	4
3.2	odd	2		456.2.bf.b.449.1	yes	4
4.3	odd	2		912.2.bn.j.449.1		4
12.11	even	2		912.2.bn.i.449.2		4
19.8	odd	6		456.2.bf.b.65.2	yes	4
57.8	even	6	inner	456.2.bf.a.65.2	✓	4
76.27	even	6		912.2.bn.i.65.1		4
228.179	odd	6		912.2.bn.j.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.a.65.2	✓	4	57.8	even	6	inner
456.2.bf.a.449.2	yes	4	1.1	even	1	trivial
456.2.bf.b.65.2	yes	4	19.8	odd	6
456.2.bf.b.449.1	yes	4	3.2	odd	2
912.2.bn.i.65.1		4	76.27	even	6
912.2.bn.i.449.2		4	12.11	even	2
912.2.bn.j.65.1		4	228.179	odd	6
912.2.bn.j.449.1		4	4.3	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 1.26217i) q^{5} +3.37228 q^{7} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\)	\(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 1.26217i) q^{5} +3.37228 q^{7} +(2.68614 + 1.33591i) q^{9} -3.46410i q^{11} +(2.87228 + 1.65831i) q^{13} +(-4.18614 + 1.26217i) q^{15} +(-2.18614 + 1.26217i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(5.68614 + 1.33591i) q^{21} +(7.93070 + 4.57879i) q^{23} +(0.686141 - 1.18843i) q^{25} +(4.00000 + 3.31662i) q^{27} +(0.186141 - 0.322405i) q^{29} +7.72049i q^{31} +(1.37228 - 5.84096i) q^{33} +(-7.37228 + 4.25639i) q^{35} -11.1846i q^{37} +(4.18614 + 3.93398i) q^{39} +(-3.18614 - 5.51856i) q^{41} +(-5.87228 - 10.1711i) q^{43} +(-7.55842 + 0.469882i) q^{45} +(-0.813859 - 0.469882i) q^{47} +4.37228 q^{49} +(-4.18614 + 1.26217i) q^{51} +(2.81386 - 4.87375i) q^{53} +(4.37228 + 7.57301i) q^{55} +(-7.43070 + 1.33591i) q^{57} +(-0.813859 - 1.40965i) q^{59} +(0.500000 - 0.866025i) q^{61} +(9.05842 + 4.50506i) q^{63} -8.37228 q^{65} +(-1.24456 - 0.718549i) q^{67} +(11.5584 + 10.8622i) q^{69} +(-6.18614 - 10.7147i) q^{71} +(-2.87228 - 4.97494i) q^{73} +(1.62772 - 1.73205i) q^{75} -11.6819i q^{77} +(-12.9891 + 7.49927i) q^{79} +(5.43070 + 7.17687i) q^{81} +3.46410i q^{83} +(3.18614 - 5.51856i) q^{85} +(0.441578 - 0.469882i) q^{87} +(0.813859 - 1.40965i) q^{89} +(9.68614 + 5.59230i) q^{91} +(-3.05842 + 13.0178i) q^{93} +(6.55842 - 8.83518i) q^{95} +(2.44158 - 1.40965i) q^{97} +(4.62772 - 9.30506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9	\( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} - 11 q^{15} - 3 q^{17} - 16 q^{19} + 17 q^{21} + 3 q^{23} - 3 q^{25} + 16 q^{27} - 5 q^{29} - 6 q^{33} - 18 q^{35} + 11 q^{39} - 7 q^{41} - 12 q^{43} - 13 q^{45} - 9 q^{47} + 6 q^{49} - 11 q^{51} + 17 q^{53} + 6 q^{55} - q^{57} - 9 q^{59} + 2 q^{61} + 19 q^{63} - 22 q^{65} + 18 q^{67} + 29 q^{69} - 19 q^{71} + 18 q^{75} - 6 q^{79} - 7 q^{81} + 7 q^{85} + 19 q^{87} + 9 q^{89} + 33 q^{91} + 5 q^{93} + 9 q^{95} + 27 q^{97} + 30 q^{99}+O(q^{100}) \) 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9 - 11 * q^15 - 3 * q^17 - 16 * q^19 + 17 * q^21 + 3 * q^23 - 3 * q^25 + 16 * q^27 - 5 * q^29 - 6 * q^33 - 18 * q^35 + 11 * q^39 - 7 * q^41 - 12 * q^43 - 13 * q^45 - 9 * q^47 + 6 * q^49 - 11 * q^51 + 17 * q^53 + 6 * q^55 - q^57 - 9 * q^59 + 2 * q^61 + 19 * q^63 - 22 * q^65 + 18 * q^67 + 29 * q^69 - 19 * q^71 + 18 * q^75 - 6 * q^79 - 7 * q^81 + 7 * q^85 + 19 * q^87 + 9 * q^89 + 33 * q^91 + 5 * q^93 + 9 * q^95 + 27 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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