LMFDB - Embedded newform 855.2.n.d.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 101x^{16} + 2922x^{12} + 18746x^{8} + 4405x^{4} + 1 $ x^20 + 101x^16 + 2922x^12 + 18746x^8 + 4405x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.1
Root			$-1.88195 + 1.88195i$ of defining polynomial
Character	$\chi$	$=$	855.647
Dual form			855.2.n.d.818.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88195 + 1.88195i) q^{2} -5.08350i q^{4} +(-1.88195 - 1.20758i) q^{5} +(0.476855 + 0.476855i) q^{7} +(5.80302 + 5.80302i) q^{8} +O(q^{10})$	\(q+(-1.88195 + 1.88195i) q^{2} -5.08350i q^{4} +(-1.88195 - 1.20758i) q^{5} +(0.476855 + 0.476855i) q^{7} +(5.80302 + 5.80302i) q^{8} +(5.81436 - 1.26914i) q^{10} +1.63041i q^{11} +(1.47686 - 1.47686i) q^{13} -1.79484 q^{14} -11.6750 q^{16} +(-0.157152 + 0.157152i) q^{17} -1.00000i q^{19} +(-6.13873 + 9.56692i) q^{20} +(-3.06836 - 3.06836i) q^{22} +(2.14764 + 2.14764i) q^{23} +(2.08350 + 4.54522i) q^{25} +5.55875i q^{26} +(2.42410 - 2.42410i) q^{28} -6.74307 q^{29} -9.97799 q^{31} +(10.3658 - 10.3658i) q^{32} -0.591507i q^{34} +(-0.321579 - 1.47326i) q^{35} +(2.12112 + 2.12112i) q^{37} +(1.88195 + 1.88195i) q^{38} +(-3.91341 - 17.9286i) q^{40} -11.5734i q^{41} +(4.42410 - 4.42410i) q^{43} +8.28821 q^{44} -8.08350 q^{46} +(8.80543 - 8.80543i) q^{47} -6.54522i q^{49} +(-12.4750 - 4.63283i) q^{50} +(-7.50760 - 7.50760i) q^{52} +(-6.03021 - 6.03021i) q^{53} +(1.96885 - 3.06836i) q^{55} +5.53440i q^{56} +(12.6902 - 12.6902i) q^{58} -6.37177 q^{59} -3.03722 q^{61} +(18.7781 - 18.7781i) q^{62} +15.6659i q^{64} +(-4.56279 + 0.995955i) q^{65} +(3.59798 + 3.59798i) q^{67} +(0.798885 + 0.798885i) q^{68} +(3.37781 + 2.16741i) q^{70} -3.73956i q^{71} +(-8.16054 + 8.16054i) q^{73} -7.98371 q^{74} -5.08350 q^{76} +(-0.777471 + 0.777471i) q^{77} +8.50800i q^{79} +(21.9718 + 14.0985i) q^{80} +(21.7806 + 21.7806i) q^{82} +(-6.53329 - 6.53329i) q^{83} +(0.485528 - 0.105980i) q^{85} +16.6519i q^{86} +(-9.46131 + 9.46131i) q^{88} +9.13388 q^{89} +1.40849 q^{91} +(10.9175 - 10.9175i) q^{92} +33.1429i q^{94} +(-1.20758 + 1.88195i) q^{95} +(-11.1056 - 11.1056i) q^{97} +(12.3178 + 12.3178i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q + 28 q^{10} + 20 q^{13} - 76 q^{16} + 32 q^{22} - 32 q^{25} - 16 q^{28} - 16 q^{31} + 4 q^{37} - 64 q^{40} + 24 q^{43} - 88 q^{46} - 12 q^{52} + 40 q^{55} + 116 q^{58} + 32 q^{61} + 24 q^{67} - 16 q^{70} + 20 q^{73} - 28 q^{76} + 92 q^{82} - 16 q^{85} - 32 q^{88} + 112 q^{91} - 36 q^{97}+O(q^{100}) $ 20 * q + 28 * q^10 + 20 * q^13 - 76 * q^16 + 32 * q^22 - 32 * q^25 - 16 * q^28 - 16 * q^31 + 4 * q^37 - 64 * q^40 + 24 * q^43 - 88 * q^46 - 12 * q^52 + 40 * q^55 + 116 * q^58 + 32 * q^61 + 24 * q^67 - 16 * q^70 + 20 * q^73 - 28 * q^76 + 92 * q^82 - 16 * q^85 - 32 * q^88 + 112 * q^91 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.88195	+	1.88195i	−1.33074	+	1.33074i	−0.426037	+	0.904706i	$0.640091\pi$
$2$	−1.88195	+	1.88195i	−1.33074	+	1.33074i	−0.904706	+	0.426037i	$0.859909\pi$
$3$		0			0
$3$		0			0
$4$		−	5.08350i		−	2.54175i
$5$	−1.88195	−	1.20758i	−0.841636	−	0.540046i
$5$	−1.88195	−	1.20758i	−0.841636	−	0.540046i
$6$		0			0
$7$	0.476855	+	0.476855i	0.180234	+	0.180234i	0.791458	−	0.611224i	$-0.209322\pi$
$7$	0.476855	+	0.476855i	0.180234	+	0.180234i	−0.611224	+	0.791458i	$0.709322\pi$
$8$	5.80302	+	5.80302i	2.05168	+	2.05168i
$9$		0			0
$10$	5.81436	−	1.26914i	1.83866	−	0.401338i
$11$			1.63041i			0.491588i	0.969322	+	0.245794i	$0.0790487\pi$
$11$			1.63041i			0.491588i	−0.969322	+	0.245794i	$0.920951\pi$
$12$		0			0
$13$	1.47686	−	1.47686i	0.409606	−	0.409606i	−0.471995	−	0.881601i	$-0.656466\pi$
$13$	1.47686	−	1.47686i	0.409606	−	0.409606i	0.881601	+	0.471995i	$0.156466\pi$
$14$	−1.79484			−0.479691
$15$		0			0
$16$	−11.6750			−2.91875
$17$	−0.157152	+	0.157152i	−0.0381151	+	0.0381151i	−0.725907	−	0.687792i	$-0.758580\pi$
$17$	−0.157152	+	0.157152i	−0.0381151	+	0.0381151i	0.687792	+	0.725907i	$0.258580\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−6.13873	+	9.56692i	−1.37266	+	2.13923i
$21$		0			0
$22$	−3.06836	−	3.06836i	−0.654177	−	0.654177i
$23$	2.14764	+	2.14764i	0.447813	+	0.447813i	0.894627	−	0.446814i	$-0.147441\pi$
$23$	2.14764	+	2.14764i	0.447813	+	0.447813i	−0.446814	+	0.894627i	$0.647441\pi$
$24$		0			0
$25$	2.08350	+	4.54522i	0.416701	+	0.909044i
$26$			5.55875i			1.09016i
$27$		0			0
$28$	2.42410	−	2.42410i	0.458111	−	0.458111i
$29$	−6.74307			−1.25216			−0.626079	−	0.779760i	$-0.715341\pi$
$29$	−6.74307			−1.25216			−0.626079	+	0.779760i	$0.715341\pi$
$30$		0			0
$31$	−9.97799			−1.79210			−0.896050	−	0.443954i	$-0.853575\pi$
$31$	−9.97799			−1.79210			−0.896050	+	0.443954i	$0.853575\pi$
$32$	10.3658	−	10.3658i	1.83243	−	1.83243i
$33$		0			0
$34$		−	0.591507i		−	0.101443i
$35$	−0.321579	−	1.47326i	−0.0543568	−	0.249026i
$36$		0			0
$37$	2.12112	+	2.12112i	0.348710	+	0.348710i	0.859629	−	0.510919i	$-0.170695\pi$
$37$	2.12112	+	2.12112i	0.348710	+	0.348710i	−0.510919	+	0.859629i	$0.670695\pi$
$38$	1.88195	+	1.88195i	0.305293	+	0.305293i
$39$		0			0
$40$	−3.91341	−	17.9286i	−0.618764	−	2.83476i
$41$		−	11.5734i		−	1.80746i	−0.428103	−	0.903730i	$-0.640818\pi$
$41$		−	11.5734i		−	1.80746i	0.428103	−	0.903730i	$-0.359182\pi$
$42$		0			0
$43$	4.42410	−	4.42410i	0.674668	−	0.674668i	−0.284120	−	0.958789i	$-0.591702\pi$
$43$	4.42410	−	4.42410i	0.674668	−	0.674668i	0.958789	+	0.284120i	$0.0917015\pi$
$44$	8.28821			1.24949
$45$		0			0
$46$	−8.08350			−1.19185
$47$	8.80543	−	8.80543i	1.28440	−	1.28440i	0.346270	−	0.938135i	$-0.387448\pi$
$47$	8.80543	−	8.80543i	1.28440	−	1.28440i	0.938135	−	0.346270i	$-0.112552\pi$
$48$		0			0
$49$		−	6.54522i		−	0.935031i
$50$	−12.4750	−	4.63283i	−1.76422	−	0.655181i
$51$		0			0
$52$	−7.50760	−	7.50760i	−1.04112	−	1.04112i
$53$	−6.03021	−	6.03021i	−0.828313	−	0.828313i	0.158971	−	0.987283i	$-0.449182\pi$
$53$	−6.03021	−	6.03021i	−0.828313	−	0.828313i	−0.987283	+	0.158971i	$0.949182\pi$
$54$		0			0
$55$	1.96885	−	3.06836i	0.265480	−	0.413738i
$56$			5.53440i			0.739565i
$57$		0			0
$58$	12.6902	−	12.6902i	1.66630	−	1.66630i
$59$	−6.37177			−0.829534			−0.414767	−	0.909928i	$-0.636137\pi$
$59$	−6.37177			−0.829534			−0.414767	+	0.909928i	$0.636137\pi$
$60$		0			0
$61$	−3.03722			−0.388876			−0.194438	−	0.980915i	$-0.562288\pi$
$61$	−3.03722			−0.388876			−0.194438	+	0.980915i	$0.562288\pi$
$62$	18.7781	−	18.7781i	2.38482	−	2.38482i
$63$		0			0
$64$			15.6659i			1.95824i
$65$	−4.56279	+	0.995955i	−0.565945	+	0.123533i
$66$		0			0
$67$	3.59798	+	3.59798i	0.439563	+	0.439563i	0.891865	−	0.452302i	$-0.149397\pi$
$67$	3.59798	+	3.59798i	0.439563	+	0.439563i	−0.452302	+	0.891865i	$0.649397\pi$
$68$	0.798885	+	0.798885i	0.0968791	+	0.0968791i
$69$		0			0
$70$	3.37781	+	2.16741i	0.403725	+	0.259055i
$71$		−	3.73956i		−	0.443804i	−0.975069	−	0.221902i	$-0.928774\pi$
$71$		−	3.73956i		−	0.443804i	0.975069	−	0.221902i	$-0.0712265\pi$
$72$		0			0
$73$	−8.16054	+	8.16054i	−0.955119	+	0.955119i	−0.999035	−	0.0439162i	$-0.986017\pi$
$73$	−8.16054	+	8.16054i	−0.955119	+	0.955119i	0.0439162	+	0.999035i	$0.486017\pi$
$74$	−7.98371			−0.928087
$75$		0			0
$76$	−5.08350			−0.583118
$77$	−0.777471	+	0.777471i	−0.0886010	+	0.0886010i
$78$		0			0
$79$			8.50800i			0.957225i	0.878026	+	0.478613i	$0.158860\pi$
$79$			8.50800i			0.957225i	−0.878026	+	0.478613i	$0.841140\pi$
$80$	21.9718	+	14.0985i	2.45653	+	1.57626i
$81$		0			0
$82$	21.7806	+	21.7806i	2.40526	+	2.40526i
$83$	−6.53329	−	6.53329i	−0.717122	−	0.717122i	0.250893	−	0.968015i	$-0.419276\pi$
$83$	−6.53329	−	6.53329i	−0.717122	−	0.717122i	−0.968015	+	0.250893i	$0.919276\pi$
$84$		0			0
$85$	0.485528	−	0.105980i	0.0526629	−	0.0114951i
$86$			16.6519i			1.79562i
$87$		0			0
$88$	−9.46131	+	9.46131i	−1.00858	+	1.00858i
$89$	9.13388			0.968189			0.484095	−	0.875016i	$-0.339149\pi$
$89$	9.13388			0.968189			0.484095	+	0.875016i	$0.339149\pi$
$90$		0			0
$91$	1.40849			0.147650
$92$	10.9175	−	10.9175i	1.13823	−	1.13823i
$93$		0			0
$94$			33.1429i			3.41842i
$95$	−1.20758	+	1.88195i	−0.123895	+	0.193084i
$96$		0			0
$97$	−11.1056	−	11.1056i	−1.12760	−	1.12760i	−0.990566	−	0.137034i	$-0.956243\pi$
$97$	−11.1056	−	11.1056i	−1.12760	−	1.12760i	−0.137034	−	0.990566i	$-0.543757\pi$
$98$	12.3178	+	12.3178i	1.24429	+	1.24429i
$99$		0			0
$100$	23.1056	−	10.5915i	2.31056	−	1.05915i
$101$		−	9.62867i		−	0.958089i	−0.877791	−	0.479044i	$-0.840983\pi$
$101$		−	9.62867i		−	0.958089i	0.877791	−	0.479044i	$-0.159017\pi$
$102$		0			0
$103$	3.03722	−	3.03722i	0.299266	−	0.299266i	−0.541460	−	0.840726i	$-0.682128\pi$
$103$	3.03722	−	3.03722i	0.299266	−	0.299266i	0.840726	+	0.541460i	$0.182128\pi$
$104$	17.1404			1.68076
$105$		0			0
$106$	22.6971			2.20454
$107$	−5.25131	+	5.25131i	−0.507663	+	0.507663i	−0.913809	−	0.406145i	$-0.866873\pi$
$107$	−5.25131	+	5.25131i	−0.507663	+	0.507663i	0.406145	+	0.913809i	$0.366873\pi$
$108$		0			0
$109$		−	16.3167i		−	1.56285i	−0.623997	−	0.781427i	$-0.714492\pi$
$109$		−	16.3167i		−	1.56285i	0.623997	−	0.781427i	$-0.285508\pi$
$110$	2.06923	+	9.47981i	0.197293	+	0.903864i
$111$		0			0
$112$	−5.56729	−	5.56729i	−0.526060	−	0.526060i
$113$	−0.441752	−	0.441752i	−0.0415565	−	0.0415565i	0.686023	−	0.727580i	$-0.259355\pi$
$113$	−0.441752	−	0.441752i	−0.0415565	−	0.0415565i	−0.727580	+	0.686023i	$0.759355\pi$
$114$		0			0
$115$	−1.44831	−	6.63519i	−0.135056	−	0.618735i
$116$			34.2784i			3.18267i
$117$		0			0
$118$	11.9914	−	11.9914i	1.10390	−	1.10390i
$119$	−0.149878			−0.0137393
$120$		0			0
$121$	8.34175			0.758341
$122$	5.71590	−	5.71590i	0.517493	−	0.517493i
$123$		0			0
$124$			50.7231i			4.55507i
$125$	1.56765	−	11.0699i	0.140215	−	0.990121i
$126$		0			0
$127$	−9.22670	−	9.22670i	−0.818737	−	0.818737i	0.167188	−	0.985925i	$-0.446531\pi$
$127$	−9.22670	−	9.22670i	−0.818737	−	0.818737i	−0.985925	+	0.167188i	$0.946531\pi$
$128$	−8.75096	−	8.75096i	−0.773483	−	0.773483i
$129$		0			0
$130$	6.71263	−	10.4613i	0.588737	−	0.917518i
$131$		−	6.31085i		−	0.551382i	−0.961246	−	0.275691i	$-0.911093\pi$
$131$		−	6.31085i		−	0.551382i	0.961246	−	0.275691i	$-0.0889066\pi$
$132$		0			0
$133$	0.476855	−	0.476855i	0.0413486	−	0.0413486i
$134$	−13.5425			−1.16989
$135$		0			0
$136$	−1.82392			−0.156400
$137$	−3.36433	+	3.36433i	−0.287434	+	0.287434i	−0.836065	−	0.548631i	$-0.815149\pi$
$137$	−3.36433	+	3.36433i	−0.287434	+	0.287434i	0.548631	+	0.836065i	$0.315149\pi$
$138$		0			0
$139$			0.122863i			0.0104211i	0.999986	+	0.00521056i	$0.00165858\pi$
$139$			0.122863i			0.0104211i	−0.999986	+	0.00521056i	$0.998341\pi$
$140$	−7.48933	+	1.63475i	−0.632964	+	0.138162i
$141$		0			0
$142$	7.03768	+	7.03768i	0.590589	+	0.590589i
$143$	2.40788	+	2.40788i	0.201357	+	0.201357i
$144$		0			0
$145$	12.6902	+	8.14279i	1.05386	+	0.676222i
$146$		−	30.7155i		−	2.54204i
$147$		0			0
$148$	10.7827	−	10.7827i	0.886335	−	0.886335i
$149$	−20.7879			−1.70301			−0.851507	−	0.524343i	$-0.824311\pi$
$149$	−20.7879			−1.70301			−0.851507	+	0.524343i	$0.824311\pi$
$150$		0			0
$151$	−1.30297			−0.106035			−0.0530173	−	0.998594i	$-0.516884\pi$
$151$	−1.30297			−0.106035			−0.0530173	+	0.998594i	$0.516884\pi$
$152$	5.80302	−	5.80302i	0.470687	−	0.470687i
$153$		0			0
$154$		−	2.92633i		−	0.235810i
$155$	18.7781	+	12.0492i	1.50829	+	0.967816i
$156$		0			0
$157$	3.07010	+	3.07010i	0.245021	+	0.245021i	0.818924	−	0.573903i	$-0.194571\pi$
$157$	3.07010	+	3.07010i	0.245021	+	0.245021i	−0.573903	+	0.818924i	$0.694571\pi$
$158$	−16.0117	−	16.0117i	−1.27382	−	1.27382i
$159$		0			0
$160$	−32.0255	+	6.99045i	−2.53184	+	0.552643i
$161$			2.04822i			0.161423i
$162$		0			0
$163$	−4.10558	+	4.10558i	−0.321574	+	0.321574i	−0.849371	−	0.527797i	$-0.823018\pi$
$163$	−4.10558	+	4.10558i	−0.321574	+	0.321574i	0.527797	+	0.849371i	$0.323018\pi$
$164$	−58.8334			−4.59412
$165$		0			0
$166$	24.5907			1.90861
$167$	−16.3089	+	16.3089i	−1.26202	+	1.26202i	−0.311909	+	0.950112i	$0.600968\pi$
$167$	−16.3089	+	16.3089i	−1.26202	+	1.26202i	−0.950112	+	0.311909i	$0.899032\pi$
$168$		0			0
$169$			8.63780i			0.664446i
$170$	−0.714292	+	1.11319i	−0.0547837	+	0.0853778i
$171$		0			0
$172$	−22.4899	−	22.4899i	−1.71484	−	1.71484i
$173$	0.606179	+	0.606179i	0.0460869	+	0.0460869i	0.729775	−	0.683688i	$-0.239625\pi$
$173$	0.606179	+	0.606179i	0.0460869	+	0.0460869i	−0.683688	+	0.729775i	$0.739625\pi$
$174$		0			0
$175$	−1.17388	+	3.16094i	−0.0887371	+	0.238945i
$176$		−	19.0351i		−	1.43482i
$177$		0			0
$178$	−17.1895	+	17.1895i	−1.28841	+	1.28841i
$179$	22.0930			1.65131			0.825655	−	0.564175i	$-0.190806\pi$
$179$	22.0930			1.65131			0.825655	+	0.564175i	$0.190806\pi$
$180$		0			0
$181$	−21.9516			−1.63165			−0.815824	−	0.578301i	$-0.803716\pi$
$181$	−21.9516			−1.63165			−0.815824	+	0.578301i	$0.803716\pi$
$182$	−2.65072	+	2.65072i	−0.196484	+	0.196484i
$183$		0			0
$184$			24.9255i			1.83753i
$185$	−1.43043	−	6.55328i	−0.105167	−	0.481807i
$186$		0			0
$187$	−0.256223	−	0.256223i	−0.0187369	−	0.0187369i
$188$	−44.7625	−	44.7625i	−3.26464	−	3.26464i
$189$		0			0
$190$	−1.26914	−	5.81436i	−0.0920733	−	0.421818i
$191$		−	20.5900i		−	1.48984i	−0.667152	−	0.744921i	$-0.732487\pi$
$191$		−	20.5900i		−	1.48984i	0.667152	−	0.744921i	$-0.267513\pi$
$192$		0			0
$193$	15.9931	−	15.9931i	1.15121	−	1.15121i	0.164900	−	0.986310i	$-0.447270\pi$
$193$	15.9931	−	15.9931i	1.15121	−	1.15121i	0.986310	−	0.164900i	$-0.0527303\pi$
$194$	41.8004			3.00109
$195$		0			0
$196$	−33.2726			−2.37662
$197$	−7.34631	+	7.34631i	−0.523403	+	0.523403i	−0.918598	−	0.395194i	$-0.870677\pi$
$197$	−7.34631	+	7.34631i	−0.523403	+	0.523403i	0.395194	+	0.918598i	$0.370677\pi$
$198$		0			0
$199$		−	23.2748i		−	1.64991i	−0.565201	−	0.824953i	$-0.691201\pi$
$199$		−	23.2748i		−	1.64991i	0.565201	−	0.824953i	$-0.308799\pi$
$200$	−14.2854	+	38.4666i	−1.01013	+	2.72000i
$201$		0			0
$202$	18.1207	+	18.1207i	1.27497	+	1.27497i
$203$	−3.21547	−	3.21547i	−0.225682	−	0.225682i
$204$		0			0
$205$	−13.9758	+	21.7806i	−0.976111	+	1.52122i
$206$			11.4318i			0.796491i
$207$		0			0
$208$	−17.2423	+	17.2423i	−1.19554	+	1.19554i
$209$	1.63041			0.112778
$210$		0			0
$211$	−7.80948			−0.537626			−0.268813	−	0.963192i	$-0.586631\pi$
$211$	−7.80948			−0.537626			−0.268813	+	0.963192i	$0.586631\pi$
$212$	−30.6546	+	30.6546i	−2.10537	+	2.10537i
$213$		0			0
$214$		−	19.7654i		−	1.35114i
$215$	−13.6684	+	2.98350i	−0.932177	+	0.203473i
$216$		0			0
$217$	−4.75806	−	4.75806i	−0.322998	−	0.322998i
$218$	30.7072	+	30.7072i	2.07976	+	2.07976i
$219$		0			0
$220$	−15.5980	−	10.0087i	−1.05162	−	0.674785i
$221$			0.464183i			0.0312243i
$222$		0			0
$223$	3.88621	−	3.88621i	0.260240	−	0.260240i	−0.564912	−	0.825151i	$-0.691090\pi$
$223$	3.88621	−	3.88621i	0.260240	−	0.260240i	0.825151	+	0.564912i	$0.191090\pi$
$224$	9.88598			0.660535
$225$		0			0
$226$	1.66271			0.110602
$227$	−2.84343	+	2.84343i	−0.188725	+	0.188725i	−0.795145	−	0.606420i	$-0.792605\pi$
$227$	−2.84343	+	2.84343i	−0.188725	+	0.188725i	0.606420	+	0.795145i	$0.292605\pi$
$228$		0			0
$229$			4.50241i			0.297528i	0.988873	+	0.148764i	$0.0475294\pi$
$229$			4.50241i			0.297528i	−0.988873	+	0.148764i	$0.952471\pi$
$230$	15.2128	+	9.76147i	1.00310	+	0.643652i
$231$		0			0
$232$	−39.1302	−	39.1302i	−2.56902	−	2.56902i
$233$	−3.99068	−	3.99068i	−0.261438	−	0.261438i	0.564200	−	0.825638i	$-0.309185\pi$
$233$	−3.99068	−	3.99068i	−0.261438	−	0.261438i	−0.825638	+	0.564200i	$0.809185\pi$
$234$		0			0
$235$	−27.2047	+	5.93817i	−1.77464	+	0.387363i
$236$			32.3909i			2.10847i
$237$		0			0
$238$	0.282063	−	0.282063i	0.0182835	−	0.0182835i
$239$	25.0722			1.62178			0.810892	−	0.585195i	$-0.198982\pi$
$239$	25.0722			1.62178			0.810892	+	0.585195i	$0.198982\pi$
$240$		0			0
$241$	−7.80190			−0.502565			−0.251282	−	0.967914i	$-0.580852\pi$
$241$	−7.80190			−0.502565			−0.251282	+	0.967914i	$0.580852\pi$
$242$	−15.6988	+	15.6988i	−1.00916	+	1.00916i
$243$		0			0
$244$			15.4397i			0.988426i
$245$	−7.90387	+	12.3178i	−0.504960	+	0.786956i
$246$		0			0
$247$	−1.47686	−	1.47686i	−0.0939701	−	0.0939701i
$248$	−57.9024	−	57.9024i	−3.67681	−	3.67681i
$249$		0			0
$250$	17.8828	+	23.7833i	1.13101	+	1.50419i
$251$		−	13.1838i		−	0.832155i	−0.909329	−	0.416077i	$-0.863405\pi$
$251$		−	13.1838i		−	0.832155i	0.909329	−	0.416077i	$-0.136595\pi$
$252$		0			0
$253$	−3.50153	+	3.50153i	−0.220139	+	0.220139i
$254$	34.7285			2.17906
$255$		0			0
$256$	1.60595			0.100372
$257$	14.6571	−	14.6571i	0.914283	−	0.914283i	−0.0823226	−	0.996606i	$-0.526234\pi$
$257$	14.6571	−	14.6571i	0.914283	−	0.914283i	0.996606	+	0.0823226i	$0.0262338\pi$
$258$		0			0
$259$			2.02294i			0.125699i
$260$	5.06294	+	23.1950i	0.313990	+	1.43849i
$261$		0			0
$262$	11.8767	+	11.8767i	0.733747	+	0.733747i
$263$	16.5586	+	16.5586i	1.02105	+	1.02105i	0.999774	+	0.0212734i	$0.00677204\pi$
$263$	16.5586	+	16.5586i	1.02105	+	1.02105i	0.0212734	+	0.999774i	$0.493228\pi$
$264$		0			0
$265$	4.06662	+	18.6305i	0.249811	+	1.14446i
$266$			1.79484i			0.110049i
$267$		0			0
$268$	18.2903	−	18.2903i	1.11726	−	1.11726i
$269$	−4.70940			−0.287137			−0.143569	−	0.989640i	$-0.545858\pi$
$269$	−4.70940			−0.287137			−0.143569	+	0.989640i	$0.545858\pi$
$270$		0			0
$271$	−20.2112			−1.22774			−0.613870	−	0.789407i	$-0.710388\pi$
$271$	−20.2112			−1.22774			−0.613870	+	0.789407i	$0.710388\pi$
$272$	1.83476	−	1.83476i	0.111248	−	0.111248i
$273$		0			0
$274$		−	12.6630i		−	0.765002i
$275$	−7.41058	+	3.39697i	−0.446875	+	0.204845i
$276$		0			0
$277$	15.3934	+	15.3934i	0.924900	+	0.924900i	0.997371	−	0.0724702i	$-0.0230882\pi$
$277$	15.3934	+	15.3934i	0.924900	+	0.924900i	−0.0724702	+	0.997371i	$0.523088\pi$
$278$	−0.231223	−	0.231223i	−0.0138678	−	0.0138678i
$279$		0			0
$280$	6.68322	−	10.4155i	0.399399	−	0.622444i
$281$		−	7.32992i		−	0.437266i	−0.975807	−	0.218633i	$-0.929840\pi$
$281$		−	7.32992i		−	0.437266i	0.975807	−	0.218633i	$-0.0701598\pi$
$282$		0			0
$283$	14.2020	−	14.2020i	0.844223	−	0.844223i	−0.145182	−	0.989405i	$-0.546377\pi$
$283$	14.2020	−	14.2020i	0.844223	−	0.844223i	0.989405	+	0.145182i	$0.0463769\pi$
$284$	−19.0101			−1.12804
$285$		0			0
$286$	−9.06306			−0.535910
$287$	5.51883	−	5.51883i	0.325766	−	0.325766i
$288$		0			0
$289$			16.9506i			0.997094i
$290$	−39.2067	+	8.55793i	−2.30229	+	0.502539i
$291$		0			0
$292$	41.4841	+	41.4841i	2.42768	+	2.42768i
$293$	18.7316	+	18.7316i	1.09431	+	1.09431i	0.995063	+	0.0992495i	$0.0316442\pi$
$293$	18.7316	+	18.7316i	1.09431	+	1.09431i	0.0992495	+	0.995063i	$0.468356\pi$
$294$		0			0
$295$	11.9914	+	7.69442i	0.698166	+	0.447987i
$296$			24.6178i			1.43088i
$297$		0			0
$298$	39.1219	−	39.1219i	2.26627	−	2.26627i
$299$	6.34349			0.366854
$300$		0			0
$301$	4.21931			0.243197
$302$	2.45214	−	2.45214i	0.141105	−	0.141105i
$303$		0			0
$304$			11.6750i			0.669608i
$305$	5.71590	+	3.66768i	0.327292	+	0.210011i
$306$		0			0
$307$	−18.3128	−	18.3128i	−1.04517	−	1.04517i	−0.998931	−	0.0462367i	$-0.985277\pi$
$307$	−18.3128	−	18.3128i	−1.04517	−	1.04517i	−0.0462367	−	0.998931i	$-0.514723\pi$
$308$	3.95228	+	3.95228i	0.225202	+	0.225202i
$309$		0			0
$310$	−58.0156	+	12.6635i	−3.29507	+	0.719238i
$311$			5.44980i			0.309030i	0.987990	+	0.154515i	$0.0493815\pi$
$311$			5.44980i			0.309030i	−0.987990	+	0.154515i	$0.950618\pi$
$312$		0			0
$313$	2.34279	−	2.34279i	0.132423	−	0.132423i	−0.637789	−	0.770211i	$-0.720151\pi$
$313$	2.34279	−	2.34279i	0.132423	−	0.132423i	0.770211	+	0.637789i	$0.220151\pi$
$314$	−11.5556			−0.652120
$315$		0			0
$316$	43.2505			2.43303
$317$	−19.5088	+	19.5088i	−1.09572	+	1.09572i	−0.100819	+	0.994905i	$0.532146\pi$
$317$	−19.5088	+	19.5088i	−1.09572	+	1.09572i	−0.994905	+	0.100819i	$0.967854\pi$
$318$		0			0
$319$		−	10.9940i		−	0.615545i
$320$	18.9179	−	29.4826i	1.05754	−	1.64813i
$321$		0			0
$322$	−3.85466	−	3.85466i	−0.214812	−	0.214812i
$323$	0.157152	+	0.157152i	0.00874420	+	0.00874420i
$324$		0			0
$325$	9.78966	+	3.63559i	0.543033	+	0.201666i
$326$		−	15.4530i		−	0.855864i
$327$		0			0
$328$	67.1606	−	67.1606i	3.70832	−	3.70832i
$329$	8.39784			0.462988
$330$		0			0
$331$	−3.53576			−0.194343			−0.0971715	−	0.995268i	$-0.530980\pi$
$331$	−3.53576			−0.194343			−0.0971715	+	0.995268i	$0.530980\pi$
$332$	−33.2120	+	33.2120i	−1.82275	+	1.82275i
$333$		0			0
$334$		−	61.3852i		−	3.35885i
$335$	−2.42639	−	11.1161i	−0.132568	−	0.607336i
$336$		0			0
$337$	−0.575904	−	0.575904i	−0.0313715	−	0.0313715i	0.691247	−	0.722619i	$-0.257062\pi$
$337$	−0.575904	−	0.575904i	−0.0313715	−	0.0313715i	−0.722619	+	0.691247i	$0.757062\pi$
$338$	−16.2559	−	16.2559i	−0.884207	−	0.884207i
$339$		0			0
$340$	−0.538748	−	2.46818i	−0.0292177	−	0.133856i
$341$		−	16.2682i		−	0.880974i
$342$		0			0
$343$	6.45911	−	6.45911i	0.348759	−	0.348759i
$344$	51.3462			2.76840
$345$		0			0
$346$	−2.28160			−0.122660
$347$	0.438815	−	0.438815i	0.0235568	−	0.0235568i	−0.695230	−	0.718787i	$-0.744698\pi$
$347$	0.438815	−	0.438815i	0.0235568	−	0.0235568i	0.718787	+	0.695230i	$0.244698\pi$
$348$		0			0
$349$		−	6.41542i		−	0.343410i	−0.985148	−	0.171705i	$-0.945072\pi$
$349$		−	6.41542i		−	0.343410i	0.985148	−	0.171705i	$-0.0549276\pi$
$350$	−3.73956	−	8.15794i	−0.199888	−	0.436060i
$351$		0			0
$352$	16.9006	+	16.9006i	0.900802	+	0.900802i
$353$	0.270434	+	0.270434i	0.0143938	+	0.0143938i	0.714267	−	0.699873i	$-0.246760\pi$
$353$	0.270434	+	0.270434i	0.0143938	+	0.0143938i	−0.699873	+	0.714267i	$0.746760\pi$
$354$		0			0
$355$	−4.51581	+	7.03768i	−0.239674	+	0.373521i
$356$		−	46.4321i		−	2.46090i
$357$		0			0
$358$	−41.5781	+	41.5781i	−2.19747	+	2.19747i
$359$	8.50134			0.448684			0.224342	−	0.974511i	$-0.427977\pi$
$359$	8.50134			0.448684			0.224342	+	0.974511i	$0.427977\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	41.3119	−	41.3119i	2.17130	−	2.17130i
$363$		0			0
$364$		−	7.16008i		−	0.375290i
$365$	25.2123	−	5.50327i	1.31967	−	0.288054i
$366$		0			0
$367$	14.0658	+	14.0658i	0.734227	+	0.734227i	0.971454	−	0.237228i	$-0.0762387\pi$
$367$	14.0658	+	14.0658i	0.734227	+	0.734227i	−0.237228	+	0.971454i	$0.576239\pi$
$368$	−25.0737	−	25.0737i	−1.30706	−	1.30706i
$369$		0			0
$370$	15.0250	+	9.64096i	0.781111	+	0.501210i
$371$		−	5.75107i		−	0.298581i
$372$		0			0
$373$	−21.2064	+	21.2064i	−1.09803	+	1.09803i	−0.103386	+	0.994641i	$0.532968\pi$
$373$	−21.2064	+	21.2064i	−1.09803	+	1.09803i	−0.994641	+	0.103386i	$0.967032\pi$
$374$	0.964401			0.0498680
$375$		0			0
$376$	102.196			5.27036
$377$	−9.95854	+	9.95854i	−0.512891	+	0.512891i
$378$		0			0
$379$			2.74198i			0.140846i	0.997517	+	0.0704229i	$0.0224349\pi$
$379$			2.74198i			0.140846i	−0.997517	+	0.0704229i	$0.977565\pi$
$380$	9.56692	+	6.13873i	0.490773	+	0.314910i
$381$		0			0
$382$	38.7495	+	38.7495i	1.98260	+	1.98260i
$383$	13.7497	+	13.7497i	0.702578	+	0.702578i	0.964963	−	0.262386i	$-0.0845092\pi$
$383$	13.7497	+	13.7497i	0.702578	+	0.702578i	−0.262386	+	0.964963i	$0.584509\pi$
$384$		0			0
$385$	2.40202	−	0.524307i	0.122418	−	0.0267212i
$386$			60.1967i			3.06393i
$387$		0			0
$388$	−56.4553	+	56.4553i	−2.86608	+	2.86608i
$389$	8.95723			0.454150			0.227075	−	0.973877i	$-0.427084\pi$
$389$	8.95723			0.454150			0.227075	+	0.973877i	$0.427084\pi$
$390$		0			0
$391$	−0.675012			−0.0341368
$392$	37.9820	−	37.9820i	1.91838	−	1.91838i
$393$		0			0
$394$		−	27.6509i		−	1.39303i
$395$	10.2741	−	16.0117i	0.516945	−	0.805635i
$396$		0			0
$397$	−10.0463	−	10.0463i	−0.504209	−	0.504209i	0.408534	−	0.912743i	$-0.366040\pi$
$397$	−10.0463	−	10.0463i	−0.504209	−	0.504209i	−0.912743	+	0.408534i	$0.866040\pi$
$398$	43.8021	+	43.8021i	2.19560	+	2.19560i
$399$		0			0
$400$	−24.3249	−	53.0655i	−1.21625	−	2.65327i
$401$			3.55335i			0.177446i	0.996056	+	0.0887230i	$0.0282786\pi$
$401$			3.55335i			0.177446i	−0.996056	+	0.0887230i	$0.971721\pi$
$402$		0			0
$403$	−14.7360	+	14.7360i	−0.734055	+	0.734055i
$404$	−48.9474			−2.43522
$405$		0			0
$406$	12.1027			0.600649
$407$	−3.45830	+	3.45830i	−0.171422	+	0.171422i
$408$		0			0
$409$			26.5469i			1.31266i	0.754473	+	0.656331i	$0.227892\pi$
$409$			26.5469i			1.31266i	−0.754473	+	0.656331i	$0.772108\pi$
$410$	−14.6883	−	67.2919i	−0.725403	−	3.32331i
$411$		0			0
$412$	−15.4397	−	15.4397i	−0.760659	−	0.760659i
$413$	−3.03841	−	3.03841i	−0.149511	−	0.149511i
$414$		0			0
$415$	4.40589	+	20.1848i	0.216277	+	0.990834i
$416$		−	30.6176i		−	1.50115i
$417$		0			0
$418$	−3.06836	+	3.06836i	−0.150079	+	0.150079i
$419$	28.5178			1.39319			0.696593	−	0.717466i	$-0.254698\pi$
$419$	28.5178			1.39319			0.696593	+	0.717466i	$0.254698\pi$
$420$		0			0
$421$	−23.6279			−1.15155			−0.575777	−	0.817607i	$-0.695300\pi$
$421$	−23.6279			−1.15155			−0.575777	+	0.817607i	$0.695300\pi$
$422$	14.6971	−	14.6971i	0.715442	−	0.715442i
$423$		0			0
$424$		−	69.9868i		−	3.39886i
$425$	−1.04172	−	0.386864i	−0.0505308	−	0.0187657i
$426$		0			0
$427$	−1.44831	−	1.44831i	−0.0700887	−	0.0700887i
$428$	26.6951	+	26.6951i	1.29035	+	1.29035i
$429$		0			0
$430$	20.1085	−	31.3381i	0.969717	−	1.51126i
$431$			37.2898i			1.79619i	0.439805	+	0.898094i	$0.355048\pi$
$431$			37.2898i			1.79619i	−0.439805	+	0.898094i	$0.644952\pi$
$432$		0			0
$433$	−2.40415	+	2.40415i	−0.115536	+	0.115536i	−0.762511	−	0.646975i	$-0.776034\pi$
$433$	−2.40415	+	2.40415i	−0.115536	+	0.115536i	0.646975	+	0.762511i	$0.276034\pi$
$434$	17.9089			0.859654
$435$		0			0
$436$	−82.9459			−3.97239
$437$	2.14764	−	2.14764i	0.102735	−	0.102735i
$438$		0			0
$439$			7.22183i			0.344679i	0.985038	+	0.172340i	$0.0551327\pi$
$439$			7.22183i			0.344679i	−0.985038	+	0.172340i	$0.944867\pi$
$440$	29.2310	−	6.38047i	1.39354	−	0.304177i
$441$		0			0
$442$	−0.873571	−	0.873571i	−0.0415515	−	0.0415515i
$443$	−4.08942	−	4.08942i	−0.194294	−	0.194294i	0.603255	−	0.797549i	$-0.293870\pi$
$443$	−4.08942	−	4.08942i	−0.194294	−	0.194294i	−0.797549	+	0.603255i	$0.793870\pi$
$444$		0			0
$445$	−17.1895	−	11.0299i	−0.814863	−	0.522867i
$446$			14.6273i			0.692625i
$447$		0			0
$448$	−7.47039	+	7.47039i	−0.352943	+	0.352943i
$449$	−12.6672			−0.597804			−0.298902	−	0.954284i	$-0.596620\pi$
$449$	−12.6672			−0.597804			−0.298902	+	0.954284i	$0.596620\pi$
$450$		0			0
$451$	18.8694			0.888525
$452$	−2.24565	+	2.24565i	−0.105626	+	0.105626i
$453$		0			0
$454$		−	10.7024i		−	0.502288i
$455$	−2.65072	−	1.70087i	−0.124268	−	0.0797378i
$456$		0			0
$457$	25.8940	+	25.8940i	1.21127	+	1.21127i	0.970610	+	0.240660i	$0.0773638\pi$
$457$	25.8940	+	25.8940i	1.21127	+	1.21127i	0.240660	+	0.970610i	$0.422636\pi$
$458$	−8.47333	−	8.47333i	−0.395933	−	0.395933i
$459$		0			0
$460$	−33.7300	+	7.36250i	−1.57267	+	0.343278i
$461$			6.48072i			0.301837i	0.988546	+	0.150919i	$0.0482231\pi$
$461$			6.48072i			0.301837i	−0.988546	+	0.150919i	$0.951777\pi$
$462$		0			0
$463$	19.5257	−	19.5257i	0.907437	−	0.907437i	−0.0886282	−	0.996065i	$-0.528248\pi$
$463$	19.5257	−	19.5257i	0.907437	−	0.907437i	0.996065	+	0.0886282i	$0.0282483\pi$
$464$	78.7255			3.65474
$465$		0			0
$466$	15.0206			0.695814
$467$	0.256295	−	0.256295i	0.0118599	−	0.0118599i	−0.701152	−	0.713012i	$-0.747331\pi$
$467$	0.256295	−	0.256295i	0.0118599	−	0.0118599i	0.713012	+	0.701152i	$0.247331\pi$
$468$		0			0
$469$			3.43143i			0.158449i
$470$	40.0226	−	62.3733i	1.84611	−	2.87707i
$471$		0			0
$472$	−36.9755	−	36.9755i	−1.70194	−	1.70194i
$473$	7.21310	+	7.21310i	0.331659	+	0.331659i
$474$		0			0
$475$	4.54522	−	2.08350i	0.208549	−	0.0955978i
$476$			0.761905i			0.0349219i
$477$		0			0
$478$	−47.1847	+	47.1847i	−2.15818	+	2.15818i
$479$	−9.00550			−0.411472			−0.205736	−	0.978608i	$-0.565959\pi$
$479$	−9.00550			−0.411472			−0.205736	+	0.978608i	$0.565959\pi$
$480$		0			0
$481$	6.26518			0.285668
$482$	14.6828	−	14.6828i	0.668784	−	0.668784i
$483$		0			0
$484$		−	42.4053i		−	1.92752i
$485$	7.48933	+	34.3111i	0.340073	+	1.55798i
$486$		0			0
$487$	−25.0004	−	25.0004i	−1.13288	−	1.13288i	−0.989697	−	0.143181i	$-0.954267\pi$
$487$	−25.0004	−	25.0004i	−1.13288	−	1.13288i	−0.143181	−	0.989697i	$-0.545733\pi$
$488$	−17.6250	−	17.6250i	−0.797847	−	0.797847i
$489$		0			0
$490$	−8.30682	−	38.0563i	−0.375264	−	1.71921i
$491$		−	22.1567i		−	0.999917i	−0.866049	−	0.499958i	$-0.833349\pi$
$491$		−	22.1567i		−	0.999917i	0.866049	−	0.499958i	$-0.166651\pi$
$492$		0			0
$493$	1.05969	−	1.05969i	0.0477261	−	0.0477261i
$494$	5.55875			0.250100
$495$		0			0
$496$	116.493			5.23070
$497$	1.78323	−	1.78323i	0.0799887	−	0.0799887i
$498$		0			0
$499$		−	17.0499i		−	0.763258i	−0.924316	−	0.381629i	$-0.875363\pi$
$499$		−	17.0499i		−	0.763258i	0.924316	−	0.381629i	$-0.124637\pi$
$500$	−56.2738	−	7.96915i	−2.51664	−	0.356391i
$501$		0			0
$502$	24.8113	+	24.8113i	1.10738	+	1.10738i
$503$	−14.2407	−	14.2407i	−0.634961	−	0.634961i	0.314347	−	0.949308i	$-0.398214\pi$
$503$	−14.2407	−	14.2407i	−0.634961	−	0.634961i	−0.949308	+	0.314347i	$0.898214\pi$
$504$		0			0
$505$	−11.6274	+	18.1207i	−0.517412	+	0.806361i
$506$		−	13.1795i		−	0.585898i
$507$		0			0
$508$	−46.9040	+	46.9040i	−2.08103	+	2.08103i
$509$	−9.37529			−0.415552			−0.207776	−	0.978176i	$-0.566623\pi$
$509$	−9.37529			−0.415552			−0.207776	+	0.978176i	$0.566623\pi$
$510$		0			0
$511$	−7.78279			−0.344291
$512$	14.4796	−	14.4796i	0.639914	−	0.639914i
$513$		0			0
$514$			55.1679i			2.43335i
$515$	−9.38358	+	2.04822i	−0.413490	+	0.0902555i
$516$		0			0
$517$	14.3565	+	14.3565i	0.631398	+	0.631398i
$518$	−3.80707	−	3.80707i	−0.167273	−	0.167273i
$519$		0			0
$520$	−32.2575	−	20.6984i	−1.41459	−	0.907686i
$521$			18.3647i			0.804573i	0.915514	+	0.402287i	$0.131784\pi$
$521$			18.3647i			0.804573i	−0.915514	+	0.402287i	$0.868216\pi$
$522$		0			0
$523$	14.5341	−	14.5341i	0.635531	−	0.635531i	−0.313919	−	0.949450i	$-0.601642\pi$
$523$	14.5341	−	14.5341i	0.635531	−	0.635531i	0.949450	+	0.313919i	$0.101642\pi$
$524$	−32.0812			−1.40148
$525$		0			0
$526$	−62.3251			−2.71750
$527$	1.56807	−	1.56807i	0.0683060	−	0.0683060i
$528$		0			0
$529$		−	13.7753i		−	0.598927i
$530$	−42.7150	−	27.4086i	−1.85542	−	1.19055i
$531$		0			0
$532$	−2.42410	−	2.42410i	−0.105098	−	0.105098i
$533$	−17.0922	−	17.0922i	−0.740346	−	0.740346i
$534$		0			0
$535$	16.2241	−	3.54135i	0.701429	−	0.153106i
$536$			41.7582i			1.80368i
$537$		0			0
$538$	8.86287	−	8.86287i	0.382106	−	0.382106i
$539$	10.6714			0.459650
$540$		0			0
$541$	−5.96891			−0.256624			−0.128312	−	0.991734i	$-0.540956\pi$
$541$	−5.96891			−0.256624			−0.128312	+	0.991734i	$0.540956\pi$
$542$	38.0365	−	38.0365i	1.63381	−	1.63381i
$543$		0			0
$544$			3.25802i			0.139687i
$545$	−19.7037	+	30.7072i	−0.844013	+	1.31535i
$546$		0			0
$547$	11.7425	+	11.7425i	0.502074	+	0.502074i	0.912082	−	0.410008i	$-0.134474\pi$
$547$	11.7425	+	11.7425i	0.502074	+	0.502074i	−0.410008	+	0.912082i	$0.634474\pi$
$548$	17.1026	+	17.1026i	0.730587	+	0.730587i
$549$		0			0
$550$	7.55343	−	20.3393i	0.322079	−	0.867272i
$551$			6.74307i			0.287265i
$552$		0			0
$553$	−4.05709	+	4.05709i	−0.172525	+	0.172525i
$554$	−57.9394			−2.46161
$555$		0			0
$556$	0.624575			0.0264879
$557$	−12.7294	+	12.7294i	−0.539363	+	0.539363i	−0.923342	−	0.383979i	$-0.874554\pi$
$557$	−12.7294	+	12.7294i	−0.539363	+	0.539363i	0.383979	+	0.923342i	$0.374554\pi$
$558$		0			0
$559$		−	13.0675i		−	0.552696i
$560$	3.75444	+	17.2003i	0.158654	+	0.726847i
$561$		0			0
$562$	13.7946	+	13.7946i	0.581889	+	0.581889i
$563$	15.2951	+	15.2951i	0.644613	+	0.644613i	0.951686	−	0.307073i	$-0.0993497\pi$
$563$	15.2951	+	15.2951i	0.644613	+	0.644613i	−0.307073	+	0.951686i	$0.599350\pi$
$564$		0			0
$565$	0.297907	+	1.36481i	0.0125330	+	0.0574179i
$566$			53.4551i			2.24689i
$567$		0			0
$568$	21.7007	−	21.7007i	0.910542	−	0.910542i
$569$	26.8248			1.12456			0.562278	−	0.826949i	$-0.309925\pi$
$569$	26.8248			1.12456			0.562278	+	0.826949i	$0.309925\pi$
$570$		0			0
$571$	31.7300			1.32786			0.663929	−	0.747796i	$-0.268888\pi$
$571$	31.7300			1.32786			0.663929	+	0.747796i	$0.268888\pi$
$572$	12.2405	−	12.2405i	0.511801	−	0.511801i
$573$		0			0
$574$			20.7724i			0.867022i
$575$	−5.28686	+	14.2361i	−0.220477	+	0.593686i
$576$		0			0
$577$	21.2290	+	21.2290i	0.883773	+	0.883773i	0.993916	−	0.110143i	$-0.0351307\pi$
$577$	21.2290	+	21.2290i	0.883773	+	0.883773i	−0.110143	+	0.993916i	$0.535131\pi$
$578$	−31.9003	−	31.9003i	−1.32688	−	1.32688i
$579$		0			0
$580$	41.3939	−	64.5105i	1.71879	−	2.67865i
$581$		−	6.23087i		−	0.258500i
$582$		0			0
$583$	9.83173	−	9.83173i	0.407188	−	0.407188i
$584$	−94.7115			−3.91919
$585$		0			0
$586$	−70.5041			−2.91250
$587$	−18.4308	+	18.4308i	−0.760720	+	0.760720i	−0.976452	−	0.215733i	$-0.930786\pi$
$587$	−18.4308	+	18.4308i	−0.760720	+	0.760720i	0.215733	+	0.976452i	$0.430786\pi$
$588$		0			0
$589$			9.97799i			0.411136i
$590$	−37.0478	+	8.08669i	−1.52523	+	0.332924i
$591$		0			0
$592$	−24.7641	−	24.7641i	−1.01780	−	1.01780i
$593$	5.75514	+	5.75514i	0.236335	+	0.236335i	0.815331	−	0.578996i	$-0.196555\pi$
$593$	5.75514	+	5.75514i	0.236335	+	0.236335i	−0.578996	+	0.815331i	$0.696555\pi$
$594$		0			0
$595$	0.282063	+	0.180989i	0.0115635	+	0.00741985i
$596$			105.676i			4.32864i
$597$		0			0
$598$	−11.9382	+	11.9382i	−0.488188	+	0.488188i
$599$	41.5907			1.69935			0.849674	−	0.527308i	$-0.176799\pi$
$599$	41.5907			1.69935			0.849674	+	0.527308i	$0.176799\pi$
$600$		0			0
$601$	26.6848			1.08850			0.544248	−	0.838925i	$-0.316815\pi$
$601$	26.6848			1.08850			0.544248	+	0.838925i	$0.316815\pi$
$602$	−7.94054	+	7.94054i	−0.323632	+	0.323632i
$603$		0			0
$604$			6.62368i			0.269514i
$605$	−15.6988	−	10.0733i	−0.638247	−	0.409539i
$606$		0			0
$607$	0.0542610	+	0.0542610i	0.00220239	+	0.00220239i	0.708207	−	0.706005i	$-0.249504\pi$
$607$	0.0542610	+	0.0542610i	0.00220239	+	0.00220239i	−0.706005	+	0.708207i	$0.749504\pi$
$608$	−10.3658	−	10.3658i	−0.420389	−	0.420389i
$609$		0			0
$610$	−17.6595	+	3.85466i	−0.715011	+	0.156071i
$611$		−	26.0087i		−	1.05220i
$612$		0			0
$613$	−2.26315	+	2.26315i	−0.0914080	+	0.0914080i	−0.751332	−	0.659924i	$-0.770588\pi$
$613$	−2.26315	+	2.26315i	−0.0914080	+	0.0914080i	0.659924	+	0.751332i	$0.270588\pi$
$614$	68.9277			2.78170
$615$		0			0
$616$	−9.02335			−0.363561
$617$	−23.9841	+	23.9841i	−0.965563	+	0.965563i	−0.999426	−	0.0338632i	$-0.989219\pi$
$617$	−23.9841	+	23.9841i	−0.965563	+	0.965563i	0.0338632	+	0.999426i	$0.489219\pi$
$618$		0			0
$619$		−	15.9948i		−	0.642883i	−0.946929	−	0.321442i	$-0.895833\pi$
$619$		−	15.9948i		−	0.642883i	0.946929	−	0.321442i	$-0.104167\pi$
$620$	61.2522	−	95.4586i	2.45995	−	3.83371i
$621$		0			0
$622$	−10.2563	−	10.2563i	−0.411240	−	0.411240i
$623$	4.35554	+	4.35554i	0.174501	+	0.174501i
$624$		0			0
$625$	−16.3180	+	18.9400i	−0.652721	+	0.757599i
$626$			8.81806i			0.352441i
$627$		0			0
$628$	15.6069	−	15.6069i	0.622783	−	0.622783i
$629$	−0.666679			−0.0265822
$630$		0			0
$631$	14.1306			0.562529			0.281264	−	0.959630i	$-0.409246\pi$
$631$	14.1306			0.562529			0.281264	+	0.959630i	$0.409246\pi$
$632$	−49.3721	+	49.3721i	−1.96392	+	1.96392i
$633$		0			0
$634$		−	73.4294i		−	2.91625i
$635$	6.22226	+	28.5062i	0.246923	+	1.13123i
$636$		0			0
$637$	−9.66634	−	9.66634i	−0.382994	−	0.382994i
$638$	20.6902	+	20.6902i	0.819133	+	0.819133i
$639$		0			0
$640$	5.90143	+	27.0364i	0.233275	+	1.06871i
$641$		−	6.02400i		−	0.237934i	−0.992898	−	0.118967i	$-0.962042\pi$
$641$		−	6.02400i		−	0.237934i	0.992898	−	0.118967i	$-0.0379582\pi$
$642$		0			0
$643$	24.1402	−	24.1402i	0.951996	−	0.951996i	−0.0469033	−	0.998899i	$-0.514935\pi$
$643$	24.1402	−	24.1402i	0.951996	−	0.951996i	0.998899	+	0.0469033i	$0.0149353\pi$
$644$	10.4122			0.410296
$645$		0			0
$646$	−0.591507			−0.0232726
$647$	27.5027	−	27.5027i	1.08124	−	1.08124i	0.0848489	−	0.996394i	$-0.472959\pi$
$647$	27.5027	−	27.5027i	1.08124	−	1.08124i	0.996394	−	0.0848489i	$-0.0270408\pi$
$648$		0			0
$649$		−	10.3886i		−	0.407789i
$650$	−25.2657	+	11.5817i	−0.991003	+	0.454271i
$651$		0			0
$652$	20.8707	+	20.8707i	0.817361	+	0.817361i
$653$	7.16626	+	7.16626i	0.280437	+	0.280437i	0.833283	−	0.552846i	$-0.186458\pi$
$653$	7.16626	+	7.16626i	0.280437	+	0.280437i	−0.552846	+	0.833283i	$0.686458\pi$
$654$		0			0
$655$	−7.62085	+	11.8767i	−0.297771	+	0.464062i
$656$			135.119i			5.27553i
$657$		0			0
$658$	−15.8043	+	15.8043i	−0.616118	+	0.616118i
$659$	−28.3090			−1.10276			−0.551382	−	0.834253i	$-0.685899\pi$
$659$	−28.3090			−1.10276			−0.551382	+	0.834253i	$0.685899\pi$
$660$		0			0
$661$	−9.67275			−0.376226			−0.188113	−	0.982147i	$-0.560237\pi$
$661$	−9.67275			−0.376226			−0.188113	+	0.982147i	$0.560237\pi$
$662$	6.65414	−	6.65414i	0.258621	−	0.258621i
$663$		0			0
$664$		−	75.8256i		−	2.94260i
$665$	−1.47326	+	0.321579i	−0.0571306	+	0.0124703i
$666$		0			0
$667$	−14.4817	−	14.4817i	−0.560732	−	0.560732i
$668$	82.9064	+	82.9064i	3.20774	+	3.20774i
$669$		0			0
$670$	25.4863	+	16.3536i	0.984621	+	0.631794i
$671$		−	4.95192i		−	0.191167i
$672$		0			0
$673$	2.62912	−	2.62912i	0.101345	−	0.101345i	−0.654616	−	0.755961i	$-0.727170\pi$
$673$	2.62912	−	2.62912i	0.101345	−	0.101345i	0.755961	+	0.654616i	$0.227170\pi$
$674$	2.16765			0.0834947
$675$		0			0
$676$	43.9103			1.68886
$677$	−21.6623	+	21.6623i	−0.832549	+	0.832549i	−0.987865	−	0.155316i	$-0.950361\pi$
$677$	−21.6623	+	21.6623i	−0.832549	+	0.832549i	0.155316	+	0.987865i	$0.450361\pi$
$678$		0			0
$679$		−	10.5915i		−	0.406465i
$680$	3.43253	+	2.20252i	0.131631	+	0.0844629i
$681$		0			0
$682$	30.6161	+	30.6161i	1.17235	+	1.17235i
$683$	−3.90256	−	3.90256i	−0.149327	−	0.149327i	0.628490	−	0.777817i	$-0.283673\pi$
$683$	−3.90256	−	3.90256i	−0.149327	−	0.149327i	−0.777817	+	0.628490i	$0.783673\pi$
$684$		0			0
$685$	10.3942	−	2.26882i	0.397142	−	0.0866872i
$686$			24.3115i			0.928217i
$687$		0			0
$688$	−51.6514	+	51.6514i	−1.96919	+	1.96919i
$689$	−17.8115			−0.678563
$690$		0			0
$691$	−12.1711			−0.463010			−0.231505	−	0.972834i	$-0.574365\pi$
$691$	−12.1711			−0.463010			−0.231505	+	0.972834i	$0.574365\pi$
$692$	3.08151	−	3.08151i	0.117142	−	0.117142i
$693$		0			0
$694$			1.65166i			0.0626961i
$695$	0.148367	−	0.231223i	0.00562788	−	0.00877078i
$696$		0			0
$697$	1.81879	+	1.81879i	0.0688914	+	0.0688914i
$698$	12.0735	+	12.0735i	0.456990	+	0.456990i
$699$		0			0
$700$	16.0687	+	5.96743i	0.607338	+	0.225548i
$701$		−	19.1785i		−	0.724361i	−0.932108	−	0.362180i	$-0.882032\pi$
$701$		−	19.1785i		−	0.724361i	0.932108	−	0.362180i	$-0.117968\pi$
$702$		0			0
$703$	2.12112	−	2.12112i	0.0799996	−	0.0799996i
$704$	−25.5419			−0.962648
$705$		0			0
$706$	−1.01789			−0.0383088
$707$	4.59148	−	4.59148i	0.172680	−	0.172680i
$708$		0			0
$709$		−	16.8339i		−	0.632211i	−0.948724	−	0.316105i	$-0.897625\pi$
$709$		−	16.8339i		−	0.632211i	0.948724	−	0.316105i	$-0.102375\pi$
$710$	−4.74603	−	21.7431i	−0.178116	−	0.816006i
$711$		0			0
$712$	53.0040	+	53.0040i	1.98641	+	1.98641i
$713$	−21.4291	−	21.4291i	−0.802525	−	0.802525i
$714$		0			0
$715$	−1.62382	−	7.43924i	−0.0607273	−	0.278212i
$716$		−	112.310i		−	4.19722i
$717$		0			0
$718$	−15.9991	+	15.9991i	−0.597082	+	0.597082i
$719$	−29.8518			−1.11328			−0.556642	−	0.830753i	$-0.687910\pi$
$719$	−29.8518			−1.11328			−0.556642	+	0.830753i	$0.687910\pi$
$720$		0			0
$721$	2.89662			0.107876
$722$	1.88195	−	1.88195i	0.0700391	−	0.0700391i
$723$		0			0
$724$			111.591i			4.14724i
$725$	−14.0492	−	30.6487i	−0.521775	−	1.13827i
$726$		0			0
$727$	6.55956	+	6.55956i	0.243281	+	0.243281i	0.818206	−	0.574925i	$-0.194969\pi$
$727$	6.55956	+	6.55956i	0.243281	+	0.243281i	−0.574925	+	0.818206i	$0.694969\pi$
$728$	8.17350	+	8.17350i	0.302930	+	0.302930i
$729$		0			0
$730$	−37.0914	+	57.8052i	−1.37282	+	2.13947i
$731$			1.39052i			0.0514301i
$732$		0			0
$733$	−22.4963	+	22.4963i	−0.830921	+	0.830921i	−0.987643	−	0.156722i	$-0.949907\pi$
$733$	−22.4963	+	22.4963i	−0.830921	+	0.830921i	0.156722	+	0.987643i	$0.449907\pi$
$734$	−52.9422			−1.95413
$735$		0			0
$736$	44.5240			1.64118
$737$	−5.86619	+	5.86619i	−0.216084	+	0.216084i
$738$		0			0
$739$		−	46.8827i		−	1.72461i	−0.506391	−	0.862304i	$-0.669021\pi$
$739$		−	46.8827i		−	1.72461i	0.506391	−	0.862304i	$-0.330979\pi$
$740$	−33.3136	+	7.27161i	−1.22463	+	0.267310i
$741$		0			0
$742$	10.8233	+	10.8233i	0.397334	+	0.397334i
$743$	−3.20736	−	3.20736i	−0.117667	−	0.117667i	0.645822	−	0.763488i	$-0.276515\pi$
$743$	−3.20736	−	3.20736i	−0.117667	−	0.117667i	−0.763488	+	0.645822i	$0.776515\pi$
$744$		0			0
$745$	39.1219	+	25.1031i	1.43332	+	0.919706i
$746$		−	79.8191i		−	2.92238i
$747$		0			0
$748$	−1.30251	+	1.30251i	−0.0476246	+	0.0476246i
$749$	−5.00823			−0.182997
$750$		0			0
$751$	−10.3267			−0.376827			−0.188414	−	0.982090i	$-0.560335\pi$
$751$	−10.3267			−0.376827			−0.188414	+	0.982090i	$0.560335\pi$
$752$	−102.804	+	102.804i	−3.74886	+	3.74886i
$753$		0			0
$754$		−	37.4830i		−	1.36505i
$755$	2.45214	+	1.57344i	0.0892425	+	0.0572635i
$756$		0			0
$757$	−27.8459	−	27.8459i	−1.01208	−	1.01208i	−0.999926	−	0.0121498i	$-0.996132\pi$
$757$	−27.8459	−	27.8459i	−1.01208	−	1.01208i	−0.0121498	−	0.999926i	$-0.503868\pi$
$758$	−5.16027	−	5.16027i	−0.187430	−	0.187430i
$759$		0			0
$760$	−17.9286	+	3.91341i	−0.650339	+	0.141954i
$761$			10.3401i			0.374828i	0.982281	+	0.187414i	$0.0600106\pi$
$761$			10.3401i			0.374828i	−0.982281	+	0.187414i	$0.939989\pi$
$762$		0			0
$763$	7.78069	−	7.78069i	0.281680	−	0.281680i
$764$	−104.670			−3.78681
$765$		0			0
$766$	−51.7527			−1.86990
$767$	−9.41019	+	9.41019i	−0.339782	+	0.339782i
$768$		0			0
$769$			41.4192i			1.49362i	0.665040	+	0.746808i	$0.268415\pi$
$769$			41.4192i			1.49362i	−0.665040	+	0.746808i	$0.731585\pi$
$770$	−3.53378	+	5.50722i	−0.127348	+	0.198466i
$771$		0			0
$772$	−81.3011	−	81.3011i	−2.92609	−	2.92609i
$773$	7.73027	+	7.73027i	0.278038	+	0.278038i	0.832326	−	0.554287i	$-0.187009\pi$
$773$	7.73027	+	7.73027i	0.278038	+	0.278038i	−0.554287	+	0.832326i	$0.687009\pi$
$774$		0			0
$775$	−20.7892	−	45.3521i	−0.746770	−	1.62910i
$776$		−	128.892i		−	4.62694i
$777$		0			0
$778$	−16.8571	+	16.8571i	−0.604356	+	0.604356i
$779$	−11.5734			−0.414660
$780$		0			0
$781$	6.09702			0.218169
$782$	1.27034	−	1.27034i	0.0454274	−	0.0454274i
$783$		0			0
$784$			76.4155i			2.72913i
$785$	−2.07040	−	9.48519i	−0.0738958	−	0.338541i
$786$		0			0
$787$	6.55459	+	6.55459i	0.233646	+	0.233646i	0.814213	−	0.580567i	$-0.197169\pi$
$787$	6.55459	+	6.55459i	0.233646	+	0.233646i	−0.580567	+	0.814213i	$0.697169\pi$
$788$	37.3450	+	37.3450i	1.33036	+	1.33036i
$789$		0			0
$790$	10.7979	+	49.4686i	0.384171	+	1.76001i
$791$		−	0.421303i		−	0.0149798i
$792$		0			0
$793$	−4.48553	+	4.48553i	−0.159286	+	0.159286i
$794$	37.8133			1.34194
$795$		0			0
$796$	−118.318			−4.19365
$797$	1.99918	−	1.99918i	0.0708147	−	0.0708147i	−0.670812	−	0.741627i	$-0.734054\pi$
$797$	1.99918	−	1.99918i	0.0708147	−	0.0708147i	0.741627	+	0.670812i	$0.234054\pi$
$798$		0			0
$799$			2.76759i			0.0979103i
$800$	68.7121	+	25.5177i	2.42934	+	0.902185i
$801$		0			0
$802$	−6.68725	−	6.68725i	−0.236135	−	0.236135i
$803$	−13.3050	−	13.3050i	−0.469525	−	0.469525i
$804$		0			0
$805$	2.47339	−	3.85466i	0.0871756	−	0.135859i
$806$		−	55.4651i		−	1.95368i
$807$		0			0
$808$	55.8753	−	55.8753i	1.96569	−	1.96569i
$809$	14.1776			0.498458			0.249229	−	0.968445i	$-0.419823\pi$
$809$	14.1776			0.498458			0.249229	+	0.968445i	$0.419823\pi$
$810$		0			0
$811$	−31.0015			−1.08861			−0.544304	−	0.838888i	$-0.683206\pi$
$811$	−31.0015			−1.08861			−0.544304	+	0.838888i	$0.683206\pi$
$812$	−16.3459	+	16.3459i	−0.573627	+	0.573627i
$813$		0			0
$814$		−	13.0167i		−	0.456237i
$815$	12.6843	−	2.76870i	0.444312	−	0.0969833i
$816$		0			0
$817$	−4.42410	−	4.42410i	−0.154780	−	0.154780i
$818$	−49.9601	−	49.9601i	−1.74682	−	1.74682i
$819$		0			0
$820$	110.722	+	71.0460i	3.86657	+	2.48103i
$821$		−	28.8539i		−	1.00701i	−0.863992	−	0.503505i	$-0.832044\pi$
$821$		−	28.8539i		−	1.00701i	0.863992	−	0.503505i	$-0.167956\pi$
$822$		0			0
$823$	19.3679	−	19.3679i	0.675124	−	0.675124i	−0.283769	−	0.958893i	$-0.591585\pi$
$823$	19.3679	−	19.3679i	0.675124	−	0.675124i	0.958893	+	0.283769i	$0.0915849\pi$
$824$	35.2500			1.22799
$825$		0			0
$826$	11.4363			0.397920
$827$	16.2098	−	16.2098i	0.563669	−	0.563669i	−0.366679	−	0.930348i	$-0.619505\pi$
$827$	16.2098	−	16.2098i	0.563669	−	0.563669i	0.930348	+	0.366679i	$0.119505\pi$
$828$		0			0
$829$		−	45.7957i		−	1.59055i	−0.606248	−	0.795276i	$-0.707326\pi$
$829$		−	45.7957i		−	1.59055i	0.606248	−	0.795276i	$-0.292674\pi$
$830$	−46.2786	−	29.6952i	−1.60635	−	1.03074i
$831$		0			0
$832$	23.1363	+	23.1363i	0.802108	+	0.802108i
$833$	1.02860	+	1.02860i	0.0356388	+	0.0356388i
$834$		0			0
$835$	50.3869	−	10.9983i	1.74371	−	0.380613i
$836$		−	8.28821i		−	0.286654i
$837$		0			0
$838$	−53.6692	+	53.6692i	−1.85397	+	1.85397i
$839$	−14.0439			−0.484849			−0.242424	−	0.970170i	$-0.577943\pi$
$839$	−14.0439			−0.484849			−0.242424	+	0.970170i	$0.577943\pi$
$840$		0			0
$841$	16.4690			0.567897
$842$	44.4667	−	44.4667i	1.53242	−	1.53242i
$843$		0			0
$844$			39.6995i			1.36651i
$845$	10.4308	−	16.2559i	0.358831	−	0.559221i
$846$		0			0
$847$	3.97781	+	3.97781i	0.136679	+	0.136679i
$848$	70.4027	+	70.4027i	2.41764	+	2.41764i
$849$		0			0
$850$	2.68853	−	1.23241i	0.0922158	−	0.0422713i
$851$			9.11079i			0.312314i
$852$		0			0
$853$	26.7867	−	26.7867i	0.917158	−	0.917158i	−0.0796640	−	0.996822i	$-0.525385\pi$
$853$	26.7867	−	26.7867i	0.917158	−	0.917158i	0.996822	+	0.0796640i	$0.0253847\pi$
$854$	5.45132			0.186540
$855$		0			0
$856$	−60.9469			−2.08312
$857$	−25.9045	+	25.9045i	−0.884880	+	0.884880i	−0.994026	−	0.109146i	$-0.965188\pi$
$857$	−25.9045	+	25.9045i	−0.884880	+	0.884880i	0.109146	+	0.994026i	$0.465188\pi$
$858$		0			0
$859$			45.3372i			1.54689i	0.633865	+	0.773443i	$0.281467\pi$
$859$			45.3372i			1.54689i	−0.633865	+	0.773443i	$0.718533\pi$
$860$	15.1666	+	69.4833i	0.517178	+	2.36936i
$861$		0			0
$862$	−70.1777	−	70.1777i	−2.39026	−	2.39026i
$863$	−13.8075	−	13.8075i	−0.470011	−	0.470011i	0.431907	−	0.901918i	$-0.357841\pi$
$863$	−13.8075	−	13.8075i	−0.470011	−	0.470011i	−0.901918	+	0.431907i	$0.857841\pi$
$864$		0			0
$865$	−0.408792	−	1.87281i	−0.0138993	−	0.0636774i
$866$		−	9.04899i		−	0.307497i
$867$		0			0
$868$	−24.1876	+	24.1876i	−0.820981	+	0.820981i
$869$	−13.8716			−0.470560
$870$		0			0
$871$	10.6274			0.360095
$872$	94.6859	−	94.6859i	3.20647	−	3.20647i
$873$		0			0
$874$			8.08350i			0.273429i
$875$	6.02628	−	4.53119i	0.203725	−	0.153182i
$876$		0			0
$877$	31.8563	+	31.8563i	1.07571	+	1.07571i	0.996889	+	0.0788216i	$0.0251158\pi$
$877$	31.8563	+	31.8563i	1.07571	+	1.07571i	0.0788216	+	0.996889i	$0.474884\pi$
$878$	−13.5912	−	13.5912i	−0.458679	−	0.458679i
$879$		0			0
$880$	−22.9864	+	35.8232i	−0.774871	+	1.20760i
$881$		−	29.7048i		−	1.00078i	−0.865800	−	0.500391i	$-0.833190\pi$
$881$		−	29.7048i		−	1.00078i	0.865800	−	0.500391i	$-0.166810\pi$
$882$		0			0
$883$	13.4220	−	13.4220i	0.451687	−	0.451687i	−0.444227	−	0.895914i	$-0.646522\pi$
$883$	13.4220	−	13.4220i	0.451687	−	0.451687i	0.895914	+	0.444227i	$0.146522\pi$
$884$	2.35968			0.0793645
$885$		0			0
$886$	15.3922			0.517111
$887$	26.1586	−	26.1586i	0.878319	−	0.878319i	−0.115041	−	0.993361i	$-0.536700\pi$
$887$	26.1586	−	26.1586i	0.878319	−	0.878319i	0.993361	+	0.115041i	$0.0367001\pi$
$888$		0			0
$889$		−	8.79960i		−	0.295129i
$890$	53.1077	−	11.5922i	1.78017	−	0.388572i
$891$		0			0
$892$	−19.7556	−	19.7556i	−0.661465	−	0.661465i
$893$	−8.80543	−	8.80543i	−0.294663	−	0.294663i
$894$		0			0
$895$	−41.5781	−	26.6791i	−1.38980	−	0.891783i
$896$		−	8.34589i		−	0.278816i
$897$		0			0
$898$	23.8392	−	23.8392i	0.795524	−	0.795524i
$899$	67.2823			2.24399
$900$		0			0
$901$	1.89532			0.0631424
$902$	−35.5114	+	35.5114i	−1.18240	+	1.18240i
$903$		0			0
$904$		−	5.12699i		−	0.170521i
$905$	41.3119	+	26.5083i	1.37325	+	0.881164i
$906$		0			0
$907$	13.9252	+	13.9252i	0.462380	+	0.462380i	0.899435	−	0.437055i	$-0.143979\pi$
$907$	13.9252	+	13.9252i	0.462380	+	0.462380i	−0.437055	+	0.899435i	$0.643979\pi$
$908$	14.4546	+	14.4546i	0.479692	+	0.479692i
$909$		0			0
$910$	8.18948	−	1.78758i	0.271479	−	0.0592577i
$911$		−	19.1730i		−	0.635230i	−0.948220	−	0.317615i	$-0.897118\pi$
$911$		−	19.1730i		−	0.635230i	0.948220	−	0.317615i	$-0.102882\pi$
$912$		0			0
$913$	10.6520	−	10.6520i	0.352528	−	0.352528i
$914$	−97.4626			−3.22378
$915$		0			0
$916$	22.8880			0.756242
$917$	3.00936	−	3.00936i	0.0993779	−	0.0993779i
$918$		0			0
$919$			32.7703i			1.08099i	0.841347	+	0.540496i	$0.181763\pi$
$919$			32.7703i			1.08099i	−0.841347	+	0.540496i	$0.818237\pi$
$920$	30.0995	−	46.9087i	0.992353	−	1.54653i
$921$		0			0
$922$	−12.1964	−	12.1964i	−0.401668	−	0.401668i
$923$	−5.52279	−	5.52279i	−0.181785	−	0.181785i
$924$		0			0
$925$	−5.22159	+	14.0603i	−0.171685	+	0.462301i
$926$			73.4930i			2.41513i
$927$		0			0
$928$	−69.8974	+	69.8974i	−2.29449	+	2.29449i
$929$	5.45239			0.178887			0.0894436	−	0.995992i	$-0.471491\pi$
$929$	5.45239			0.178887			0.0894436	+	0.995992i	$0.471491\pi$
$930$		0			0
$931$	−6.54522			−0.214511
$932$	−20.2867	+	20.2867i	−0.664512	+	0.664512i
$933$		0			0
$934$			0.964669i			0.0315649i
$935$	0.172791	+	0.791611i	0.00565086	+	0.0258884i
$936$		0			0
$937$	−6.86887	−	6.86887i	−0.224396	−	0.224396i	0.585951	−	0.810347i	$-0.300721\pi$
$937$	−6.86887	−	6.86887i	−0.224396	−	0.224396i	−0.810347	+	0.585951i	$0.800721\pi$
$938$	−6.45779	−	6.45779i	−0.210854	−	0.210854i
$939$		0			0
$940$	30.1867	+	138.295i	0.984582	+	4.51069i
$941$		−	32.5252i		−	1.06029i	−0.847907	−	0.530145i	$-0.822137\pi$
$941$		−	32.5252i		−	1.06029i	0.847907	−	0.530145i	$-0.177863\pi$
$942$		0			0
$943$	24.8554	−	24.8554i	0.809404	−	0.809404i
$944$	74.3905			2.42121
$945$		0			0
$946$	−27.1495			−0.882705
$947$	−40.7976	+	40.7976i	−1.32574	+	1.32574i	−0.416698	+	0.909045i	$0.636813\pi$
$947$	−40.7976	+	40.7976i	−1.32574	+	1.32574i	−0.909045	+	0.416698i	$0.863187\pi$
$948$		0			0
$949$			24.1039i			0.782445i
$950$	−4.63283	+	12.4750i	−0.150309	+	0.404741i
$951$		0			0
$952$	−0.869744	−	0.869744i	−0.0281886	−	0.0281886i
$953$	31.6807	+	31.6807i	1.02624	+	1.02624i	0.999646	+	0.0265934i	$0.00846593\pi$
$953$	31.6807	+	31.6807i	1.02624	+	1.02624i	0.0265934	+	0.999646i	$0.491534\pi$
$954$		0			0
$955$	−24.8641	+	38.7495i	−0.804583	+	1.25390i
$956$		−	127.455i		−	4.12218i
$957$		0			0
$958$	16.9479	−	16.9479i	0.547563	−	0.547563i
$959$	−3.20860			−0.103611
$960$		0			0
$961$	68.5602			2.21162
$962$	−11.7908	+	11.7908i	−0.380150	+	0.380150i
$963$		0			0
$964$			39.6610i			1.27740i
$965$	−49.4113	+	10.7854i	−1.59061	+	0.347193i
$966$		0			0
$967$	−3.16921	−	3.16921i	−0.101915	−	0.101915i	0.654311	−	0.756226i	$-0.272959\pi$
$967$	−3.16921	−	3.16921i	−0.101915	−	0.101915i	−0.756226	+	0.654311i	$0.772959\pi$
$968$	48.4073	+	48.4073i	1.55587	+	1.55587i
$969$		0			0
$970$	−78.6664	−	50.4773i	−2.52583	−	1.62073i
$971$			44.4138i			1.42531i	0.701516	+	0.712654i	$0.252507\pi$
$971$			44.4138i			1.42531i	−0.701516	+	0.712654i	$0.747493\pi$
$972$		0			0
$973$	−0.0585879	+	0.0585879i	−0.00187824	+	0.00187824i
$974$	94.0993			3.01514
$975$		0			0
$976$	35.4595			1.13503
$977$	−4.24140	+	4.24140i	−0.135694	+	0.135694i	−0.771691	−	0.635997i	$-0.780589\pi$
$977$	−4.24140	+	4.24140i	−0.135694	+	0.135694i	0.635997	+	0.771691i	$0.280589\pi$
$978$		0			0
$979$			14.8920i			0.475950i
$980$	62.6176	+	40.1794i	2.00025	+	1.28348i
$981$		0			0
$982$	41.6978	+	41.6978i	1.33063	+	1.33063i
$983$	−23.6947	−	23.6947i	−0.755745	−	0.755745i	0.219800	−	0.975545i	$-0.429460\pi$
$983$	−23.6947	−	23.6947i	−0.755745	−	0.755745i	−0.975545	+	0.219800i	$0.929460\pi$
$984$		0			0
$985$	22.6967	−	4.95417i	0.723176	−	0.157853i
$986$			3.98858i			0.127022i
$987$		0			0
$988$	−7.50760	+	7.50760i	−0.238849	+	0.238849i
$989$	19.0027			0.604251
$990$		0			0
$991$	18.1359			0.576107			0.288053	−	0.957614i	$-0.406992\pi$
$991$	18.1359			0.576107			0.288053	+	0.957614i	$0.406992\pi$
$992$	−103.430	+	103.430i	−3.28390	+	3.28390i
$993$		0			0
$994$			6.71191i			0.212889i
$995$	−28.1062	+	43.8021i	−0.891025	+	1.38862i
$996$		0			0
$997$	−28.8685	−	28.8685i	−0.914275	−	0.914275i	0.0823298	−	0.996605i	$-0.473764\pi$
$997$	−28.8685	−	28.8685i	−0.914275	−	0.914275i	−0.996605	+	0.0823298i	$0.973764\pi$
$998$	32.0871	+	32.0871i	1.01570	+	1.01570i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.d.647.1	✓	20
3.2	odd	2	inner	855.2.n.d.647.10	yes	20
5.3	odd	4	inner	855.2.n.d.818.10	yes	20
15.8	even	4	inner	855.2.n.d.818.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.d.647.1	✓	20	1.1	even	1	trivial
855.2.n.d.647.10	yes	20	3.2	odd	2	inner
855.2.n.d.818.1	yes	20	15.8	even	4	inner
855.2.n.d.818.10	yes	20	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88195 + 1.88195i) q^{2} -5.08350i q^{4} +(-1.88195 - 1.20758i) q^{5} +(0.476855 + 0.476855i) q^{7} +(5.80302 + 5.80302i) q^{8} +O(q^{10})\)	\(q+(-1.88195 + 1.88195i) q^{2} -5.08350i q^{4} +(-1.88195 - 1.20758i) q^{5} +(0.476855 + 0.476855i) q^{7} +(5.80302 + 5.80302i) q^{8} +(5.81436 - 1.26914i) q^{10} +1.63041i q^{11} +(1.47686 - 1.47686i) q^{13} -1.79484 q^{14} -11.6750 q^{16} +(-0.157152 + 0.157152i) q^{17} -1.00000i q^{19} +(-6.13873 + 9.56692i) q^{20} +(-3.06836 - 3.06836i) q^{22} +(2.14764 + 2.14764i) q^{23} +(2.08350 + 4.54522i) q^{25} +5.55875i q^{26} +(2.42410 - 2.42410i) q^{28} -6.74307 q^{29} -9.97799 q^{31} +(10.3658 - 10.3658i) q^{32} -0.591507i q^{34} +(-0.321579 - 1.47326i) q^{35} +(2.12112 + 2.12112i) q^{37} +(1.88195 + 1.88195i) q^{38} +(-3.91341 - 17.9286i) q^{40} -11.5734i q^{41} +(4.42410 - 4.42410i) q^{43} +8.28821 q^{44} -8.08350 q^{46} +(8.80543 - 8.80543i) q^{47} -6.54522i q^{49} +(-12.4750 - 4.63283i) q^{50} +(-7.50760 - 7.50760i) q^{52} +(-6.03021 - 6.03021i) q^{53} +(1.96885 - 3.06836i) q^{55} +5.53440i q^{56} +(12.6902 - 12.6902i) q^{58} -6.37177 q^{59} -3.03722 q^{61} +(18.7781 - 18.7781i) q^{62} +15.6659i q^{64} +(-4.56279 + 0.995955i) q^{65} +(3.59798 + 3.59798i) q^{67} +(0.798885 + 0.798885i) q^{68} +(3.37781 + 2.16741i) q^{70} -3.73956i q^{71} +(-8.16054 + 8.16054i) q^{73} -7.98371 q^{74} -5.08350 q^{76} +(-0.777471 + 0.777471i) q^{77} +8.50800i q^{79} +(21.9718 + 14.0985i) q^{80} +(21.7806 + 21.7806i) q^{82} +(-6.53329 - 6.53329i) q^{83} +(0.485528 - 0.105980i) q^{85} +16.6519i q^{86} +(-9.46131 + 9.46131i) q^{88} +9.13388 q^{89} +1.40849 q^{91} +(10.9175 - 10.9175i) q^{92} +33.1429i q^{94} +(-1.20758 + 1.88195i) q^{95} +(-11.1056 - 11.1056i) q^{97} +(12.3178 + 12.3178i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q + 28 q^{10} + 20 q^{13} - 76 q^{16} + 32 q^{22} - 32 q^{25} - 16 q^{28} - 16 q^{31} + 4 q^{37} - 64 q^{40} + 24 q^{43} - 88 q^{46} - 12 q^{52} + 40 q^{55} + 116 q^{58} + 32 q^{61} + 24 q^{67} - 16 q^{70} + 20 q^{73} - 28 q^{76} + 92 q^{82} - 16 q^{85} - 32 q^{88} + 112 q^{91} - 36 q^{97}+O(q^{100}) \) 20 * q + 28 * q^10 + 20 * q^13 - 76 * q^16 + 32 * q^22 - 32 * q^25 - 16 * q^28 - 16 * q^31 + 4 * q^37 - 64 * q^40 + 24 * q^43 - 88 * q^46 - 12 * q^52 + 40 * q^55 + 116 * q^58 + 32 * q^61 + 24 * q^67 - 16 * q^70 + 20 * q^73 - 28 * q^76 + 92 * q^82 - 16 * q^85 - 32 * q^88 + 112 * q^91 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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