LMFDB - Embedded newform 855.2.n.d.818.1

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			818.1
Root			$-1.88195 - 1.88195i$ of defining polynomial
Character	$\chi$	$=$	855.818
Dual form			855.2.n.d.647.1

$q$-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 $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.904706	−	0.426037i	$-0.859909\pi$
$2$	−1.88195	−	1.88195i	−1.33074	−	1.33074i	−0.426037	−	0.904706i	$-0.640091\pi$
$3$		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	−0.611224	−	0.791458i	$-0.709322\pi$
$7$	0.476855	−	0.476855i	0.180234	−	0.180234i	0.791458	+	0.611224i	$0.209322\pi$
$8$	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	$-0.920951\pi$
$11$		−	1.63041i		−	0.491588i	0.969322	−	0.245794i	$-0.0790487\pi$
$12$		0			0
$13$	1.47686	+	1.47686i	0.409606	+	0.409606i	0.881601	−	0.471995i	$-0.156466\pi$
$13$	1.47686	+	1.47686i	0.409606	+	0.409606i	−0.471995	+	0.881601i	$0.656466\pi$
$14$	−1.79484			−0.479691
$15$		0			0
$16$	−11.6750			−2.91875
$17$	−0.157152	−	0.157152i	−0.0381151	−	0.0381151i	0.687792	−	0.725907i	$-0.258580\pi$
$17$	−0.157152	−	0.157152i	−0.0381151	−	0.0381151i	−0.725907	+	0.687792i	$0.758580\pi$
$18$		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	−0.446814	−	0.894627i	$-0.647441\pi$
$23$	2.14764	−	2.14764i	0.447813	−	0.447813i	0.894627	+	0.446814i	$0.147441\pi$
$24$		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	−0.510919	−	0.859629i	$-0.670695\pi$
$37$	2.12112	−	2.12112i	0.348710	−	0.348710i	0.859629	+	0.510919i	$0.170695\pi$
$38$	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	$0.359182\pi$
$41$			11.5734i			1.80746i	−0.428103	+	0.903730i	$0.640818\pi$
$42$		0			0
$43$	4.42410	+	4.42410i	0.674668	+	0.674668i	0.958789	−	0.284120i	$-0.0917015\pi$
$43$	4.42410	+	4.42410i	0.674668	+	0.674668i	−0.284120	+	0.958789i	$0.591702\pi$
$44$	8.28821			1.24949
$45$		0			0
$46$	−8.08350			−1.19185
$47$	8.80543	+	8.80543i	1.28440	+	1.28440i	0.938135	+	0.346270i	$0.112552\pi$
$47$	8.80543	+	8.80543i	1.28440	+	1.28440i	0.346270	+	0.938135i	$0.387448\pi$
$48$		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	−0.987283	−	0.158971i	$-0.949182\pi$
$53$	−6.03021	+	6.03021i	−0.828313	+	0.828313i	0.158971	+	0.987283i	$0.449182\pi$
$54$		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	−0.452302	−	0.891865i	$-0.649397\pi$
$67$	3.59798	−	3.59798i	0.439563	−	0.439563i	0.891865	+	0.452302i	$0.149397\pi$
$68$	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	$0.0712265\pi$
$71$			3.73956i			0.443804i	−0.975069	+	0.221902i	$0.928774\pi$
$72$		0			0
$73$	−8.16054	−	8.16054i	−0.955119	−	0.955119i	0.0439162	−	0.999035i	$-0.486017\pi$
$73$	−8.16054	−	8.16054i	−0.955119	−	0.955119i	−0.999035	+	0.0439162i	$0.986017\pi$
$74$	−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	$-0.841140\pi$
$79$		−	8.50800i		−	0.957225i	0.878026	−	0.478613i	$-0.158860\pi$
$80$	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	−0.968015	−	0.250893i	$-0.919276\pi$
$83$	−6.53329	+	6.53329i	−0.717122	+	0.717122i	0.250893	+	0.968015i	$0.419276\pi$
$84$		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	−0.137034	+	0.990566i	$0.543757\pi$
$97$	−11.1056	+	11.1056i	−1.12760	+	1.12760i	−0.990566	+	0.137034i	$0.956243\pi$
$98$	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	$0.159017\pi$
$101$			9.62867i			0.958089i	−0.877791	+	0.479044i	$0.840983\pi$
$102$		0			0
$103$	3.03722	+	3.03722i	0.299266	+	0.299266i	0.840726	−	0.541460i	$-0.182128\pi$
$103$	3.03722	+	3.03722i	0.299266	+	0.299266i	−0.541460	+	0.840726i	$0.682128\pi$
$104$	17.1404			1.68076
$105$		0			0
$106$	22.6971			2.20454
$107$	−5.25131	−	5.25131i	−0.507663	−	0.507663i	0.406145	−	0.913809i	$-0.366873\pi$
$107$	−5.25131	−	5.25131i	−0.507663	−	0.507663i	−0.913809	+	0.406145i	$0.866873\pi$
$108$		0			0
$109$			16.3167i			1.56285i	0.623997	+	0.781427i	$0.285508\pi$
$109$			16.3167i			1.56285i	−0.623997	+	0.781427i	$0.714492\pi$
$110$	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	−0.727580	−	0.686023i	$-0.759355\pi$
$113$	−0.441752	+	0.441752i	−0.0415565	+	0.0415565i	0.686023	+	0.727580i	$0.259355\pi$
$114$		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	−0.985925	−	0.167188i	$-0.946531\pi$
$127$	−9.22670	+	9.22670i	−0.818737	+	0.818737i	0.167188	+	0.985925i	$0.446531\pi$
$128$	−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	$0.0889066\pi$
$131$			6.31085i			0.551382i	−0.961246	+	0.275691i	$0.911093\pi$
$132$		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	0.548631	−	0.836065i	$-0.315149\pi$
$137$	−3.36433	−	3.36433i	−0.287434	−	0.287434i	−0.836065	+	0.548631i	$0.815149\pi$
$138$		0			0
$139$		−	0.122863i		−	0.0104211i	−0.999986	−	0.00521056i	$-0.998341\pi$
$139$		−	0.122863i		−	0.0104211i	0.999986	−	0.00521056i	$-0.00165858\pi$
$140$	−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	−0.573903	−	0.818924i	$-0.694571\pi$
$157$	3.07010	−	3.07010i	0.245021	−	0.245021i	0.818924	+	0.573903i	$0.194571\pi$
$158$	−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	0.527797	−	0.849371i	$-0.323018\pi$
$163$	−4.10558	−	4.10558i	−0.321574	−	0.321574i	−0.849371	+	0.527797i	$0.823018\pi$
$164$	−58.8334			−4.59412
$165$		0			0
$166$	24.5907			1.90861
$167$	−16.3089	−	16.3089i	−1.26202	−	1.26202i	−0.950112	−	0.311909i	$-0.899032\pi$
$167$	−16.3089	−	16.3089i	−1.26202	−	1.26202i	−0.311909	−	0.950112i	$-0.600968\pi$
$168$		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	−0.683688	−	0.729775i	$-0.739625\pi$
$173$	0.606179	−	0.606179i	0.0460869	−	0.0460869i	0.729775	+	0.683688i	$0.239625\pi$
$174$		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	$0.267513\pi$
$191$			20.5900i			1.48984i	−0.667152	+	0.744921i	$0.732487\pi$
$192$		0			0
$193$	15.9931	+	15.9931i	1.15121	+	1.15121i	0.986310	+	0.164900i	$0.0527303\pi$
$193$	15.9931	+	15.9931i	1.15121	+	1.15121i	0.164900	+	0.986310i	$0.447270\pi$
$194$	41.8004			3.00109
$195$		0			0
$196$	−33.2726			−2.37662
$197$	−7.34631	−	7.34631i	−0.523403	−	0.523403i	0.395194	−	0.918598i	$-0.370677\pi$
$197$	−7.34631	−	7.34631i	−0.523403	−	0.523403i	−0.918598	+	0.395194i	$0.870677\pi$
$198$		0			0
$199$			23.2748i			1.64991i	0.565201	+	0.824953i	$0.308799\pi$
$199$			23.2748i			1.64991i	−0.565201	+	0.824953i	$0.691201\pi$
$200$	−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	0.825151	−	0.564912i	$-0.191090\pi$
$223$	3.88621	+	3.88621i	0.260240	+	0.260240i	−0.564912	+	0.825151i	$0.691090\pi$
$224$	9.88598			0.660535
$225$		0			0
$226$	1.66271			0.110602
$227$	−2.84343	−	2.84343i	−0.188725	−	0.188725i	0.606420	−	0.795145i	$-0.292605\pi$
$227$	−2.84343	−	2.84343i	−0.188725	−	0.188725i	−0.795145	+	0.606420i	$0.792605\pi$
$228$		0			0
$229$		−	4.50241i		−	0.297528i	−0.988873	−	0.148764i	$-0.952471\pi$
$229$		−	4.50241i		−	0.297528i	0.988873	−	0.148764i	$-0.0475294\pi$
$230$	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	−0.825638	−	0.564200i	$-0.809185\pi$
$233$	−3.99068	+	3.99068i	−0.261438	+	0.261438i	0.564200	+	0.825638i	$0.309185\pi$
$234$		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	$0.136595\pi$
$251$			13.1838i			0.832155i	−0.909329	+	0.416077i	$0.863405\pi$
$252$		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	0.996606	−	0.0823226i	$-0.0262338\pi$
$257$	14.6571	+	14.6571i	0.914283	+	0.914283i	−0.0823226	+	0.996606i	$0.526234\pi$
$258$		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	0.0212734	−	0.999774i	$-0.493228\pi$
$263$	16.5586	−	16.5586i	1.02105	−	1.02105i	0.999774	−	0.0212734i	$-0.00677204\pi$
$264$		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	−0.0724702	−	0.997371i	$-0.523088\pi$
$277$	15.3934	−	15.3934i	0.924900	−	0.924900i	0.997371	+	0.0724702i	$0.0230882\pi$
$278$	−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	$0.0701598\pi$
$281$			7.32992i			0.437266i	−0.975807	+	0.218633i	$0.929840\pi$
$282$		0			0
$283$	14.2020	+	14.2020i	0.844223	+	0.844223i	0.989405	−	0.145182i	$-0.0463769\pi$
$283$	14.2020	+	14.2020i	0.844223	+	0.844223i	−0.145182	+	0.989405i	$0.546377\pi$
$284$	−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	0.0992495	−	0.995063i	$-0.468356\pi$
$293$	18.7316	−	18.7316i	1.09431	−	1.09431i	0.995063	−	0.0992495i	$-0.0316442\pi$
$294$		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	−0.0462367	+	0.998931i	$0.514723\pi$
$307$	−18.3128	+	18.3128i	−1.04517	+	1.04517i	−0.998931	+	0.0462367i	$0.985277\pi$
$308$	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	$-0.950618\pi$
$311$		−	5.44980i		−	0.309030i	0.987990	−	0.154515i	$-0.0493815\pi$
$312$		0			0
$313$	2.34279	+	2.34279i	0.132423	+	0.132423i	0.770211	−	0.637789i	$-0.220151\pi$
$313$	2.34279	+	2.34279i	0.132423	+	0.132423i	−0.637789	+	0.770211i	$0.720151\pi$
$314$	−11.5556			−0.652120
$315$		0			0
$316$	43.2505			2.43303
$317$	−19.5088	−	19.5088i	−1.09572	−	1.09572i	−0.994905	−	0.100819i	$-0.967854\pi$
$317$	−19.5088	−	19.5088i	−1.09572	−	1.09572i	−0.100819	−	0.994905i	$-0.532146\pi$
$318$		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	−0.722619	−	0.691247i	$-0.757062\pi$
$337$	−0.575904	+	0.575904i	−0.0313715	+	0.0313715i	0.691247	+	0.722619i	$0.257062\pi$
$338$	−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	0.718787	−	0.695230i	$-0.244698\pi$
$347$	0.438815	+	0.438815i	0.0235568	+	0.0235568i	−0.695230	+	0.718787i	$0.744698\pi$
$348$		0			0
$349$			6.41542i			0.343410i	0.985148	+	0.171705i	$0.0549276\pi$
$349$			6.41542i			0.343410i	−0.985148	+	0.171705i	$0.945072\pi$
$350$	−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	−0.699873	−	0.714267i	$-0.746760\pi$
$353$	0.270434	−	0.270434i	0.0143938	−	0.0143938i	0.714267	+	0.699873i	$0.246760\pi$
$354$		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	−0.237228	−	0.971454i	$-0.576239\pi$
$367$	14.0658	−	14.0658i	0.734227	−	0.734227i	0.971454	+	0.237228i	$0.0762387\pi$
$368$	−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	−0.994641	−	0.103386i	$-0.967032\pi$
$373$	−21.2064	−	21.2064i	−1.09803	−	1.09803i	−0.103386	−	0.994641i	$-0.532968\pi$
$374$	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	$-0.977565\pi$
$379$		−	2.74198i		−	0.140846i	0.997517	−	0.0704229i	$-0.0224349\pi$
$380$	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	−0.262386	−	0.964963i	$-0.584509\pi$
$383$	13.7497	−	13.7497i	0.702578	−	0.702578i	0.964963	+	0.262386i	$0.0845092\pi$
$384$		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	−0.912743	−	0.408534i	$-0.866040\pi$
$397$	−10.0463	+	10.0463i	−0.504209	+	0.504209i	0.408534	+	0.912743i	$0.366040\pi$
$398$	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	$-0.971721\pi$
$401$		−	3.55335i		−	0.177446i	0.996056	−	0.0887230i	$-0.0282786\pi$
$402$		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	$-0.772108\pi$
$409$		−	26.5469i		−	1.31266i	0.754473	−	0.656331i	$-0.227892\pi$
$410$	−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	$-0.644952\pi$
$431$		−	37.2898i		−	1.79619i	0.439805	−	0.898094i	$-0.355048\pi$
$432$		0			0
$433$	−2.40415	−	2.40415i	−0.115536	−	0.115536i	0.646975	−	0.762511i	$-0.276034\pi$
$433$	−2.40415	−	2.40415i	−0.115536	−	0.115536i	−0.762511	+	0.646975i	$0.776034\pi$
$434$	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	$-0.944867\pi$
$439$		−	7.22183i		−	0.344679i	0.985038	−	0.172340i	$-0.0551327\pi$
$440$	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	−0.797549	−	0.603255i	$-0.793870\pi$
$443$	−4.08942	+	4.08942i	−0.194294	+	0.194294i	0.603255	+	0.797549i	$0.293870\pi$
$444$		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	0.240660	−	0.970610i	$-0.422636\pi$
$457$	25.8940	−	25.8940i	1.21127	−	1.21127i	0.970610	−	0.240660i	$-0.0773638\pi$
$458$	−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	$-0.951777\pi$
$461$		−	6.48072i		−	0.301837i	0.988546	−	0.150919i	$-0.0482231\pi$
$462$		0			0
$463$	19.5257	+	19.5257i	0.907437	+	0.907437i	0.996065	−	0.0886282i	$-0.0282483\pi$
$463$	19.5257	+	19.5257i	0.907437	+	0.907437i	−0.0886282	+	0.996065i	$0.528248\pi$
$464$	78.7255			3.65474
$465$		0			0
$466$	15.0206			0.695814
$467$	0.256295	+	0.256295i	0.0118599	+	0.0118599i	0.713012	−	0.701152i	$-0.247331\pi$
$467$	0.256295	+	0.256295i	0.0118599	+	0.0118599i	−0.701152	+	0.713012i	$0.747331\pi$
$468$		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	−0.143181	+	0.989697i	$0.545733\pi$
$487$	−25.0004	+	25.0004i	−1.13288	+	1.13288i	−0.989697	+	0.143181i	$0.954267\pi$
$488$	−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	$0.166651\pi$
$491$			22.1567i			0.999917i	−0.866049	+	0.499958i	$0.833349\pi$
$492$		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	$0.124637\pi$
$499$			17.0499i			0.763258i	−0.924316	+	0.381629i	$0.875363\pi$
$500$	−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	−0.949308	−	0.314347i	$-0.898214\pi$
$503$	−14.2407	+	14.2407i	−0.634961	+	0.634961i	0.314347	+	0.949308i	$0.398214\pi$
$504$		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	$-0.868216\pi$
$521$		−	18.3647i		−	0.804573i	0.915514	−	0.402287i	$-0.131784\pi$
$522$		0			0
$523$	14.5341	+	14.5341i	0.635531	+	0.635531i	0.949450	−	0.313919i	$-0.101642\pi$
$523$	14.5341	+	14.5341i	0.635531	+	0.635531i	−0.313919	+	0.949450i	$0.601642\pi$
$524$	−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	−0.410008	−	0.912082i	$-0.634474\pi$
$547$	11.7425	−	11.7425i	0.502074	−	0.502074i	0.912082	+	0.410008i	$0.134474\pi$
$548$	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	0.383979	−	0.923342i	$-0.374554\pi$
$557$	−12.7294	−	12.7294i	−0.539363	−	0.539363i	−0.923342	+	0.383979i	$0.874554\pi$
$558$		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	−0.307073	−	0.951686i	$-0.599350\pi$
$563$	15.2951	−	15.2951i	0.644613	−	0.644613i	0.951686	+	0.307073i	$0.0993497\pi$
$564$		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	−0.110143	−	0.993916i	$-0.535131\pi$
$577$	21.2290	−	21.2290i	0.883773	−	0.883773i	0.993916	+	0.110143i	$0.0351307\pi$
$578$	−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	0.215733	−	0.976452i	$-0.430786\pi$
$587$	−18.4308	−	18.4308i	−0.760720	−	0.760720i	−0.976452	+	0.215733i	$0.930786\pi$
$588$		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	−0.578996	−	0.815331i	$-0.696555\pi$
$593$	5.75514	−	5.75514i	0.236335	−	0.236335i	0.815331	+	0.578996i	$0.196555\pi$
$594$		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	−0.706005	−	0.708207i	$-0.749504\pi$
$607$	0.0542610	−	0.0542610i	0.00220239	−	0.00220239i	0.708207	+	0.706005i	$0.249504\pi$
$608$	−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	0.659924	−	0.751332i	$-0.270588\pi$
$613$	−2.26315	−	2.26315i	−0.0914080	−	0.0914080i	−0.751332	+	0.659924i	$0.770588\pi$
$614$	68.9277			2.78170
$615$		0			0
$616$	−9.02335			−0.363561
$617$	−23.9841	−	23.9841i	−0.965563	−	0.965563i	0.0338632	−	0.999426i	$-0.489219\pi$
$617$	−23.9841	−	23.9841i	−0.965563	−	0.965563i	−0.999426	+	0.0338632i	$0.989219\pi$
$618$		0			0
$619$			15.9948i			0.642883i	0.946929	+	0.321442i	$0.104167\pi$
$619$			15.9948i			0.642883i	−0.946929	+	0.321442i	$0.895833\pi$
$620$	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	$0.0379582\pi$
$641$			6.02400i			0.237934i	−0.992898	+	0.118967i	$0.962042\pi$
$642$		0			0
$643$	24.1402	+	24.1402i	0.951996	+	0.951996i	0.998899	−	0.0469033i	$-0.0149353\pi$
$643$	24.1402	+	24.1402i	0.951996	+	0.951996i	−0.0469033	+	0.998899i	$0.514935\pi$
$644$	10.4122			0.410296
$645$		0			0
$646$	−0.591507			−0.0232726
$647$	27.5027	+	27.5027i	1.08124	+	1.08124i	0.996394	+	0.0848489i	$0.0270408\pi$
$647$	27.5027	+	27.5027i	1.08124	+	1.08124i	0.0848489	+	0.996394i	$0.472959\pi$
$648$		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	−0.552846	−	0.833283i	$-0.686458\pi$
$653$	7.16626	−	7.16626i	0.280437	−	0.280437i	0.833283	+	0.552846i	$0.186458\pi$
$654$		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	0.755961	−	0.654616i	$-0.227170\pi$
$673$	2.62912	+	2.62912i	0.101345	+	0.101345i	−0.654616	+	0.755961i	$0.727170\pi$
$674$	2.16765			0.0834947
$675$		0			0
$676$	43.9103			1.68886
$677$	−21.6623	−	21.6623i	−0.832549	−	0.832549i	0.155316	−	0.987865i	$-0.450361\pi$
$677$	−21.6623	−	21.6623i	−0.832549	−	0.832549i	−0.987865	+	0.155316i	$0.950361\pi$
$678$		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	−0.777817	−	0.628490i	$-0.783673\pi$
$683$	−3.90256	+	3.90256i	−0.149327	+	0.149327i	0.628490	+	0.777817i	$0.283673\pi$
$684$		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	$0.117968\pi$
$701$			19.1785i			0.724361i	−0.932108	+	0.362180i	$0.882032\pi$
$702$		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	$0.102375\pi$
$709$			16.8339i			0.632211i	−0.948724	+	0.316105i	$0.897625\pi$
$710$	−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	−0.574925	−	0.818206i	$-0.694969\pi$
$727$	6.55956	−	6.55956i	0.243281	−	0.243281i	0.818206	+	0.574925i	$0.194969\pi$
$728$	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	0.156722	−	0.987643i	$-0.449907\pi$
$733$	−22.4963	−	22.4963i	−0.830921	−	0.830921i	−0.987643	+	0.156722i	$0.949907\pi$
$734$	−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	$0.330979\pi$
$739$			46.8827i			1.72461i	−0.506391	+	0.862304i	$0.669021\pi$
$740$	−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	−0.763488	−	0.645822i	$-0.776515\pi$
$743$	−3.20736	+	3.20736i	−0.117667	+	0.117667i	0.645822	+	0.763488i	$0.276515\pi$
$744$		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	−0.0121498	+	0.999926i	$0.503868\pi$
$757$	−27.8459	+	27.8459i	−1.01208	+	1.01208i	−0.999926	+	0.0121498i	$0.996132\pi$
$758$	−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	$-0.939989\pi$
$761$		−	10.3401i		−	0.374828i	0.982281	−	0.187414i	$-0.0600106\pi$
$762$		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	$-0.731585\pi$
$769$		−	41.4192i		−	1.49362i	0.665040	−	0.746808i	$-0.268415\pi$
$770$	−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	−0.554287	−	0.832326i	$-0.687009\pi$
$773$	7.73027	−	7.73027i	0.278038	−	0.278038i	0.832326	+	0.554287i	$0.187009\pi$
$774$		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	−0.580567	−	0.814213i	$-0.697169\pi$
$787$	6.55459	−	6.55459i	0.233646	−	0.233646i	0.814213	+	0.580567i	$0.197169\pi$
$788$	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	0.741627	−	0.670812i	$-0.234054\pi$
$797$	1.99918	+	1.99918i	0.0708147	+	0.0708147i	−0.670812	+	0.741627i	$0.734054\pi$
$798$		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	$0.167956\pi$
$821$			28.8539i			1.00701i	−0.863992	+	0.503505i	$0.832044\pi$
$822$		0			0
$823$	19.3679	+	19.3679i	0.675124	+	0.675124i	0.958893	−	0.283769i	$-0.0915849\pi$
$823$	19.3679	+	19.3679i	0.675124	+	0.675124i	−0.283769	+	0.958893i	$0.591585\pi$
$824$	35.2500			1.22799
$825$		0			0
$826$	11.4363			0.397920
$827$	16.2098	+	16.2098i	0.563669	+	0.563669i	0.930348	−	0.366679i	$-0.119505\pi$
$827$	16.2098	+	16.2098i	0.563669	+	0.563669i	−0.366679	+	0.930348i	$0.619505\pi$
$828$		0			0
$829$			45.7957i			1.59055i	0.606248	+	0.795276i	$0.292674\pi$
$829$			45.7957i			1.59055i	−0.606248	+	0.795276i	$0.707326\pi$
$830$	−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	0.996822	−	0.0796640i	$-0.0253847\pi$
$853$	26.7867	+	26.7867i	0.917158	+	0.917158i	−0.0796640	+	0.996822i	$0.525385\pi$
$854$	5.45132			0.186540
$855$		0			0
$856$	−60.9469			−2.08312
$857$	−25.9045	−	25.9045i	−0.884880	−	0.884880i	0.109146	−	0.994026i	$-0.465188\pi$
$857$	−25.9045	−	25.9045i	−0.884880	−	0.884880i	−0.994026	+	0.109146i	$0.965188\pi$
$858$		0			0
$859$		−	45.3372i		−	1.54689i	−0.633865	−	0.773443i	$-0.718533\pi$
$859$		−	45.3372i		−	1.54689i	0.633865	−	0.773443i	$-0.281467\pi$
$860$	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	−0.901918	−	0.431907i	$-0.857841\pi$
$863$	−13.8075	+	13.8075i	−0.470011	+	0.470011i	0.431907	+	0.901918i	$0.357841\pi$
$864$		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	0.0788216	−	0.996889i	$-0.474884\pi$
$877$	31.8563	−	31.8563i	1.07571	−	1.07571i	0.996889	−	0.0788216i	$-0.0251158\pi$
$878$	−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	$0.166810\pi$
$881$			29.7048i			1.00078i	−0.865800	+	0.500391i	$0.833190\pi$
$882$		0			0
$883$	13.4220	+	13.4220i	0.451687	+	0.451687i	0.895914	−	0.444227i	$-0.146522\pi$
$883$	13.4220	+	13.4220i	0.451687	+	0.451687i	−0.444227	+	0.895914i	$0.646522\pi$
$884$	2.35968			0.0793645
$885$		0			0
$886$	15.3922			0.517111
$887$	26.1586	+	26.1586i	0.878319	+	0.878319i	0.993361	−	0.115041i	$-0.0367001\pi$
$887$	26.1586	+	26.1586i	0.878319	+	0.878319i	−0.115041	+	0.993361i	$0.536700\pi$
$888$		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	−0.437055	−	0.899435i	$-0.643979\pi$
$907$	13.9252	−	13.9252i	0.462380	−	0.462380i	0.899435	+	0.437055i	$0.143979\pi$
$908$	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	$0.102882\pi$
$911$			19.1730i			0.635230i	−0.948220	+	0.317615i	$0.897118\pi$
$912$		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	$-0.818237\pi$
$919$		−	32.7703i		−	1.08099i	0.841347	−	0.540496i	$-0.181763\pi$
$920$	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	−0.810347	−	0.585951i	$-0.800721\pi$
$937$	−6.86887	+	6.86887i	−0.224396	+	0.224396i	0.585951	+	0.810347i	$0.300721\pi$
$938$	−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	$0.177863\pi$
$941$			32.5252i			1.06029i	−0.847907	+	0.530145i	$0.822137\pi$
$942$		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	−0.909045	−	0.416698i	$-0.863187\pi$
$947$	−40.7976	−	40.7976i	−1.32574	−	1.32574i	−0.416698	−	0.909045i	$-0.636813\pi$
$948$		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	0.0265934	−	0.999646i	$-0.491534\pi$
$953$	31.6807	−	31.6807i	1.02624	−	1.02624i	0.999646	−	0.0265934i	$-0.00846593\pi$
$954$		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	−0.756226	−	0.654311i	$-0.772959\pi$
$967$	−3.16921	+	3.16921i	−0.101915	+	0.101915i	0.654311	+	0.756226i	$0.272959\pi$
$968$	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	$-0.747493\pi$
$971$		−	44.4138i		−	1.42531i	0.701516	−	0.712654i	$-0.252507\pi$
$972$		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	0.635997	−	0.771691i	$-0.280589\pi$
$977$	−4.24140	−	4.24140i	−0.135694	−	0.135694i	−0.771691	+	0.635997i	$0.780589\pi$
$978$		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	−0.975545	−	0.219800i	$-0.929460\pi$
$983$	−23.6947	+	23.6947i	−0.755745	+	0.755745i	0.219800	+	0.975545i	$0.429460\pi$
$984$		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	−0.996605	−	0.0823298i	$-0.973764\pi$
$997$	−28.8685	+	28.8685i	−0.914275	+	0.914275i	0.0823298	+	0.996605i	$0.473764\pi$
$998$	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.818.1	yes	20
3.2	odd	2	inner	855.2.n.d.818.10	yes	20
5.2	odd	4	inner	855.2.n.d.647.10	yes	20
15.2	even	4	inner	855.2.n.d.647.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.d.647.1	✓	20	15.2	even	4	inner
855.2.n.d.647.10	yes	20	5.2	odd	4	inner
855.2.n.d.818.1	yes	20	1.1	even	1	trivial
855.2.n.d.818.10	yes	20	3.2	odd	2	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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