LMFDB - Embedded newform 855.2.k.a.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.a.676.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{7} +(-1.00000 + 1.73205i) q^{10} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 - 4.33013i) q^{19} +2.00000 q^{20} +(1.00000 + 1.73205i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{26} +(2.00000 - 3.46410i) q^{28} +(-2.50000 + 4.33013i) q^{29} +9.00000 q^{31} +(4.00000 - 6.92820i) q^{32} +(2.00000 - 3.46410i) q^{34} +(1.00000 + 1.73205i) q^{35} -6.00000 q^{37} +(-8.00000 + 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{41} +(5.00000 + 8.66025i) q^{43} +(1.00000 - 1.73205i) q^{44} +8.00000 q^{46} -3.00000 q^{49} +2.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(0.500000 + 0.866025i) q^{55} +10.0000 q^{58} +(3.50000 + 6.06218i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-9.00000 - 15.5885i) q^{62} -8.00000 q^{64} +2.00000 q^{65} +(-4.00000 + 6.92820i) q^{67} -4.00000 q^{68} +(2.00000 - 3.46410i) q^{70} +(1.50000 + 2.59808i) q^{71} +(1.00000 + 1.73205i) q^{73} +(6.00000 + 10.3923i) q^{74} +(7.00000 + 5.19615i) q^{76} +2.00000 q^{77} +(5.50000 + 9.52628i) q^{79} +(2.00000 - 3.46410i) q^{80} +(6.00000 - 10.3923i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{85} +(10.0000 - 17.3205i) q^{86} +(7.50000 - 12.9904i) q^{89} +(2.00000 - 3.46410i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(-4.00000 + 1.73205i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(3.00000 + 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} - q^{5} - 4 q^{7} - 2 q^{10} - 2 q^{11} - 2 q^{13} + 4 q^{14} + 4 q^{16} + 2 q^{17} + q^{19} + 4 q^{20} + 2 q^{22} - 4 q^{23} - q^{25} + 8 q^{26} + 4 q^{28} - 5 q^{29} + 18 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 - q^5 - 4 * q^7 - 2 * q^10 - 2 * q^11 - 2 * q^13 + 4 * q^14 + 4 * q^16 + 2 * q^17 + q^19 + 4 * q^20 + 2 * q^22 - 4 * q^23 - q^25 + 8 * q^26 + 4 * q^28 - 5 * q^29 + 18 * q^31 + 8 * q^32 + 4 * q^34 + 2 * q^35 - 12 * q^37 - 16 * q^38 + 6 * q^41 + 10 * q^43 + 2 * q^44 + 16 * q^46 - 6 * q^49 + 4 * q^50 - 4 * q^52 - 2 * q^53 + q^55 + 20 * q^58 + 7 * q^59 + 7 * q^61 - 18 * q^62 - 16 * q^64 + 4 * q^65 - 8 * q^67 - 8 * q^68 + 4 * q^70 + 3 * q^71 + 2 * q^73 + 12 * q^74 + 14 * q^76 + 4 * q^77 + 11 * q^79 + 4 * q^80 + 12 * q^82 - 12 * q^83 + 2 * q^85 + 20 * q^86 + 15 * q^89 + 4 * q^91 - 8 * q^92 - 8 * q^95 - 8 * q^97 + 6 * q^98

Character values

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

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

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 $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		0			0
$9$		0			0
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$20$	2.00000			0.447214
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.00000			0.784465
$27$		0			0
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$		0			0
$31$	9.00000			1.61645			0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000			1.61645			0.808224	+	0.588875i	$0.200429\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$		0			0
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	−8.00000	+	3.46410i	−1.29777	+	0.561951i
$39$		0			0
$40$		0			0
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	8.00000			1.17954
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	2.00000			0.282843
$51$		0			0
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	0.500000	+	0.866025i	0.0674200	+	0.116775i
$56$		0			0
$57$		0			0
$58$	10.0000			1.31306
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−9.00000	−	15.5885i	−1.14300	−	1.97974i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	2.00000			0.248069
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	2.00000	−	3.46410i	0.239046	−	0.414039i
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$		0			0
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	6.00000	+	10.3923i	0.697486	+	1.20808i
$75$		0			0
$76$	7.00000	+	5.19615i	0.802955	+	0.596040i
$77$	2.00000			0.227921
$78$		0			0
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$		0			0
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	10.0000	−	17.3205i	1.07833	−	1.86772i
$87$		0			0
$88$		0			0
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$	2.00000	−	3.46410i	0.209657	−	0.363137i
$92$	−4.00000	−	6.92820i	−0.417029	−	0.722315i
$93$		0			0
$94$		0			0
$95$	−4.00000	+	1.73205i	−0.410391	+	0.177705i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$		0			0
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	−3.50000	+	6.06218i	−0.348263	+	0.603209i	−0.985941	−	0.167094i	$-0.946562\pi$
$101$	−3.50000	+	6.06218i	−0.348263	+	0.603209i	0.637678	+	0.770303i	$0.279895\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$		0			0
$106$	4.00000			0.388514
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.0957826	−	0.995402i	$-0.530535\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$		0			0
$112$	−4.00000	−	6.92820i	−0.377964	−	0.654654i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$		0			0
$115$	4.00000			0.373002
$116$	−5.00000	−	8.66025i	−0.464238	−	0.804084i
$117$		0			0
$118$	7.00000	−	12.1244i	0.644402	−	1.11614i
$119$	−2.00000	−	3.46410i	−0.183340	−	0.317554i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	−14.0000			−1.26750
$123$		0			0
$124$	−9.00000	+	15.5885i	−0.808224	+	1.39988i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.00000	+	3.46410i	−0.177471	+	0.307389i	−0.941014	−	0.338368i	$-0.890125\pi$
$127$	−2.00000	+	3.46410i	−0.177471	+	0.307389i	0.763542	+	0.645758i	$0.223458\pi$
$128$		0			0
$129$		0			0
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	8.00000	+	13.8564i	0.698963	+	1.21064i	0.968826	+	0.247741i	$0.0796882\pi$
$131$	8.00000	+	13.8564i	0.698963	+	1.21064i	−0.269863	+	0.962899i	$0.586978\pi$
$132$		0			0
$133$	−1.00000	+	8.66025i	−0.0867110	+	0.750939i
$134$	16.0000			1.38219
$135$		0			0
$136$		0			0
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	−4.00000			−0.338062
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$		0			0
$145$	5.00000			0.415227
$146$	2.00000	−	3.46410i	0.165521	−	0.286691i
$147$		0			0
$148$	6.00000	−	10.3923i	0.493197	−	0.854242i
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	−3.00000			−0.244137			−0.122068	−	0.992522i	$-0.538953\pi$
$151$	−3.00000			−0.244137			−0.122068	+	0.992522i	$0.538953\pi$
$152$		0			0
$153$		0			0
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$	−4.50000	−	7.79423i	−0.361449	−	0.626048i
$156$		0			0
$157$	−6.00000	−	10.3923i	−0.478852	−	0.829396i	0.520854	−	0.853646i	$-0.325614\pi$
$157$	−6.00000	−	10.3923i	−0.478852	−	0.829396i	−0.999706	+	0.0242497i	$0.992280\pi$
$158$	11.0000	−	19.0526i	0.875113	−	1.51574i
$159$		0			0
$160$	−8.00000			−0.632456
$161$	4.00000	−	6.92820i	0.315244	−	0.546019i
$162$		0			0
$163$	−18.0000			−1.40987			−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000			−1.40987			−0.704934	+	0.709273i	$0.749024\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	−0.902120	−	0.431486i	$-0.857990\pi$
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	0.824737	+	0.565516i	$0.191323\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−20.0000			−1.52499
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$	−30.0000			−2.24860
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$		0			0
$181$	−5.00000	+	8.66025i	−0.371647	+	0.643712i	−0.989819	−	0.142331i	$-0.954540\pi$
$181$	−5.00000	+	8.66025i	−0.371647	+	0.643712i	0.618172	+	0.786043i	$0.287874\pi$
$182$	−8.00000			−0.592999
$183$		0			0
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$		0			0
$189$		0			0
$190$	7.00000	+	5.19615i	0.507833	+	0.376969i
$191$	−15.0000			−1.08536			−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000			−1.08536			−0.542681	+	0.839939i	$0.682591\pi$
$192$		0			0
$193$	13.0000	+	22.5167i	0.935760	+	1.62078i	0.773272	+	0.634074i	$0.218619\pi$
$193$	13.0000	+	22.5167i	0.935760	+	1.62078i	0.162488	+	0.986710i	$0.448048\pi$
$194$	−8.00000	+	13.8564i	−0.574367	+	0.994832i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$		0			0
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$		0			0
$201$		0			0
$202$	14.0000			0.985037
$203$	5.00000	−	8.66025i	0.350931	−	0.607831i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$		0			0
$208$	−8.00000			−0.554700
$209$	−0.500000	+	4.33013i	−0.0345857	+	0.299521i
$210$		0			0
$211$	13.5000	+	23.3827i	0.929378	+	1.60973i	0.784364	+	0.620301i	$0.212990\pi$
$211$	13.5000	+	23.3827i	0.929378	+	1.60973i	0.145014	+	0.989430i	$0.453677\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$		0			0
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$	−18.0000			−1.22192
$218$	−19.0000	+	32.9090i	−1.28684	+	2.22888i
$219$		0			0
$220$	−2.00000			−0.134840
$221$	−4.00000			−0.269069
$222$		0			0
$223$	6.00000	+	10.3923i	0.401790	+	0.695920i	0.993942	−	0.109906i	$-0.0350549\pi$
$223$	6.00000	+	10.3923i	0.401790	+	0.695920i	−0.592152	+	0.805826i	$0.701722\pi$
$224$	−8.00000	+	13.8564i	−0.534522	+	0.925820i
$225$		0			0
$226$	−10.0000	−	17.3205i	−0.665190	−	1.15214i
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$		0			0
$229$	−11.0000			−0.726900			−0.363450	−	0.931614i	$-0.618401\pi$
$229$	−11.0000			−0.726900			−0.363450	+	0.931614i	$0.618401\pi$
$230$	−4.00000	−	6.92820i	−0.263752	−	0.456832i
$231$		0			0
$232$		0			0
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$		0			0
$236$	−14.0000			−0.911322
$237$		0			0
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$	−27.0000			−1.74648			−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000			−1.74648			−0.873242	+	0.487286i	$0.837987\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	10.0000	+	17.3205i	0.642824	+	1.11340i
$243$		0			0
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$		0			0
$247$	7.00000	+	5.19615i	0.445399	+	0.330623i
$248$		0			0
$249$		0			0
$250$	−1.00000	−	1.73205i	−0.0632456	−	0.109545i
$251$	−8.50000	+	14.7224i	−0.536515	+	0.929272i	0.462573	+	0.886581i	$0.346926\pi$
$251$	−8.50000	+	14.7224i	−0.536515	+	0.929272i	−0.999088	+	0.0426905i	$0.986407\pi$
$252$		0			0
$253$	2.00000	−	3.46410i	0.125739	−	0.217786i
$254$	8.00000			0.501965
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	11.0000	−	19.0526i	0.686161	−	1.18847i	−0.286909	−	0.957958i	$-0.592628\pi$
$257$	11.0000	−	19.0526i	0.686161	−	1.18847i	0.973070	−	0.230508i	$-0.0740389\pi$
$258$		0			0
$259$	12.0000			0.745644
$260$	−2.00000	+	3.46410i	−0.124035	+	0.214834i
$261$		0			0
$262$	16.0000	−	27.7128i	0.988483	−	1.71210i
$263$	10.0000	+	17.3205i	0.616626	+	1.06803i	0.990097	+	0.140386i	$0.0448344\pi$
$263$	10.0000	+	17.3205i	0.616626	+	1.06803i	−0.373470	+	0.927642i	$0.621832\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	16.0000	−	6.92820i	0.981023	−	0.424795i
$267$		0			0
$268$	−8.00000	−	13.8564i	−0.488678	−	0.846415i
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	0.880866	−	0.473366i	$-0.156961\pi$
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	−0.850380	+	0.526169i	$0.823628\pi$
$270$		0			0
$271$	−13.5000	−	23.3827i	−0.820067	−	1.42040i	−0.905632	−	0.424064i	$-0.860603\pi$
$271$	−13.5000	−	23.3827i	−0.820067	−	1.42040i	0.0855654	−	0.996333i	$-0.472730\pi$
$272$	−4.00000	+	6.92820i	−0.242536	+	0.420084i
$273$		0			0
$274$	12.0000			0.724947
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$	40.0000			2.39904
$279$		0			0
$280$		0			0
$281$	−13.0000	+	22.5167i	−0.775515	+	1.34323i	0.158990	+	0.987280i	$0.449176\pi$
$281$	−13.0000	+	22.5167i	−0.775515	+	1.34323i	−0.934505	+	0.355951i	$0.884157\pi$
$282$		0			0
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−4.00000			−0.236525
$287$	−6.00000	−	10.3923i	−0.354169	−	0.613438i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$		0			0
$292$	−4.00000			−0.234082
$293$	4.00000			0.233682			0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000			0.233682			0.116841	+	0.993151i	$0.462723\pi$
$294$		0			0
$295$	3.50000	−	6.06218i	0.203778	−	0.352954i
$296$		0			0
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$		0			0
$301$	−10.0000	−	17.3205i	−0.576390	−	0.998337i
$302$	3.00000	+	5.19615i	0.172631	+	0.299005i
$303$		0			0
$304$	16.0000	−	6.92820i	0.917663	−	0.397360i
$305$	−7.00000			−0.400819
$306$		0			0
$307$	12.0000	+	20.7846i	0.684876	+	1.18624i	0.973476	+	0.228790i	$0.0734771\pi$
$307$	12.0000	+	20.7846i	0.684876	+	1.18624i	−0.288600	+	0.957450i	$0.593190\pi$
$308$	−2.00000	+	3.46410i	−0.113961	+	0.197386i
$309$		0			0
$310$	−9.00000	+	15.5885i	−0.511166	+	0.885365i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	10.0000	−	17.3205i	0.565233	−	0.979013i	−0.431795	−	0.901972i	$-0.642119\pi$
$313$	10.0000	−	17.3205i	0.565233	−	0.979013i	0.997028	−	0.0770410i	$-0.0245472\pi$
$314$	−12.0000	+	20.7846i	−0.677199	+	1.17294i
$315$		0			0
$316$	−22.0000			−1.23760
$317$	16.0000	−	27.7128i	0.898650	−	1.55651i	0.0694277	−	0.997587i	$-0.477883\pi$
$317$	16.0000	−	27.7128i	0.898650	−	1.55651i	0.829222	−	0.558920i	$-0.188784\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$		0			0
$322$	−16.0000			−0.891645
$323$	8.00000	−	3.46410i	0.445132	−	0.192748i
$324$		0			0
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	18.0000	+	31.1769i	0.996928	+	1.72673i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$	4.00000			0.218870
$335$	8.00000			0.437087
$336$		0			0
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	0.954164	−	0.299285i	$-0.0967480\pi$
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	−0.736270	+	0.676688i	$0.763415\pi$
$338$	9.00000	−	15.5885i	0.489535	−	0.847900i
$339$		0			0
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−9.00000			−0.487377
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$		0			0
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	−11.0000	−	19.0526i	−0.590511	−	1.02279i	−0.994164	−	0.107883i	$-0.965593\pi$
$347$	−11.0000	−	19.0526i	−0.590511	−	1.02279i	0.403653	−	0.914912i	$-0.367740\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	−4.00000	+	6.92820i	−0.213201	+	0.369274i
$353$	14.0000			0.745145			0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000			0.745145			0.372572	+	0.928003i	$0.378476\pi$
$354$		0			0
$355$	1.50000	−	2.59808i	0.0796117	−	0.137892i
$356$	15.0000	+	25.9808i	0.794998	+	1.37698i
$357$		0			0
$358$	−3.00000	−	5.19615i	−0.158555	−	0.274625i
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	0.740951	−	0.671559i	$-0.234375\pi$
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	−0.952063	+	0.305903i	$0.901042\pi$
$360$		0			0
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	20.0000			1.05118
$363$		0			0
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$		0			0
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	−0.477677	−	0.878536i	$-0.658521\pi$
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	0.999673	−	0.0255875i	$-0.00814566\pi$
$368$	−16.0000			−0.834058
$369$		0			0
$370$	6.00000	−	10.3923i	0.311925	−	0.540270i
$371$	2.00000	−	3.46410i	0.103835	−	0.179847i
$372$		0			0
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$		0			0
$376$		0			0
$377$	−5.00000	−	8.66025i	−0.257513	−	0.446026i
$378$		0			0
$379$	31.0000			1.59236			0.796182	−	0.605058i	$-0.206850\pi$
$379$	31.0000			1.59236			0.796182	+	0.605058i	$0.206850\pi$
$380$	1.00000	−	8.66025i	0.0512989	−	0.444262i
$381$		0			0
$382$	15.0000	+	25.9808i	0.767467	+	1.32929i
$383$	13.0000	+	22.5167i	0.664269	+	1.15055i	0.979483	+	0.201527i	$0.0645904\pi$
$383$	13.0000	+	22.5167i	0.664269	+	1.15055i	−0.315214	+	0.949021i	$0.602076\pi$
$384$		0			0
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$	26.0000	−	45.0333i	1.32337	−	2.29214i
$387$		0			0
$388$	16.0000			0.812277
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	−0.0561516	−	0.998422i	$-0.517883\pi$
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	0.892735	−	0.450582i	$-0.148784\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		0			0
$393$		0			0
$394$	10.0000	+	17.3205i	0.503793	+	0.872595i
$395$	5.50000	−	9.52628i	0.276735	−	0.479319i
$396$		0			0
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$	−6.00000			−0.300753
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$		0			0
$403$	−9.00000	+	15.5885i	−0.448322	+	0.776516i
$404$	−7.00000	−	12.1244i	−0.348263	−	0.603209i
$405$		0			0
$406$	−20.0000			−0.992583
$407$	6.00000			0.297409
$408$		0			0
$409$	14.5000	−	25.1147i	0.716979	−	1.24184i	−0.245212	−	0.969469i	$-0.578858\pi$
$409$	14.5000	−	25.1147i	0.716979	−	1.24184i	0.962191	−	0.272374i	$-0.0878089\pi$
$410$	−12.0000			−0.592638
$411$		0			0
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	−7.00000	−	12.1244i	−0.344447	−	0.596601i
$414$		0			0
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$	8.00000	+	13.8564i	0.392232	+	0.679366i
$417$		0			0
$418$	8.00000	−	3.46410i	0.391293	−	0.169435i
$419$	5.00000			0.244266			0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000			0.244266			0.122133	+	0.992514i	$0.461027\pi$
$420$		0			0
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	0.938623	−	0.344946i	$-0.112103\pi$
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	−0.768043	+	0.640398i	$0.778769\pi$
$422$	27.0000	−	46.7654i	1.31434	−	2.27650i
$423$		0			0
$424$		0			0
$425$	−2.00000			−0.0970143
$426$		0			0
$427$	−7.00000	+	12.1244i	−0.338754	+	0.586739i
$428$		0			0
$429$		0			0
$430$	−20.0000			−0.964486
$431$	11.5000	−	19.9186i	0.553936	−	0.959444i	−0.444050	−	0.896002i	$-0.646459\pi$
$431$	11.5000	−	19.9186i	0.553936	−	0.959444i	0.997985	−	0.0634424i	$-0.0202079\pi$
$432$		0			0
$433$	−3.00000	+	5.19615i	−0.144171	+	0.249711i	−0.929063	−	0.369921i	$-0.879385\pi$
$433$	−3.00000	+	5.19615i	−0.144171	+	0.249711i	0.784892	+	0.619632i	$0.212718\pi$
$434$	18.0000	+	31.1769i	0.864028	+	1.49654i
$435$		0			0
$436$	38.0000			1.81987
$437$	14.0000	+	10.3923i	0.669711	+	0.497131i
$438$		0			0
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$		0			0
$441$		0			0
$442$	4.00000	+	6.92820i	0.190261	+	0.329541i
$443$	−4.00000	+	6.92820i	−0.190046	+	0.329169i	−0.945265	−	0.326303i	$-0.894197\pi$
$443$	−4.00000	+	6.92820i	−0.190046	+	0.329169i	0.755219	+	0.655472i	$0.227530\pi$
$444$		0			0
$445$	−15.0000			−0.711068
$446$	12.0000	−	20.7846i	0.568216	−	0.984180i
$447$		0			0
$448$	16.0000			0.755929
$449$	39.0000			1.84052			0.920262	−	0.391303i	$-0.127976\pi$
$449$	39.0000			1.84052			0.920262	+	0.391303i	$0.127976\pi$
$450$		0			0
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	−10.0000	+	17.3205i	−0.470360	+	0.814688i
$453$		0			0
$454$	18.0000	+	31.1769i	0.844782	+	1.46321i
$455$	−4.00000			−0.187523
$456$		0			0
$457$	−8.00000			−0.374224			−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000			−0.374224			−0.187112	+	0.982339i	$0.559913\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$		0			0
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	0.828978	−	0.559281i	$-0.188923\pi$
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	−0.898840	+	0.438276i	$0.855589\pi$
$462$		0			0
$463$	−10.0000			−0.464739			−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000			−0.464739			−0.232370	+	0.972628i	$0.574648\pi$
$464$	−20.0000			−0.928477
$465$		0			0
$466$	−24.0000	+	41.5692i	−1.11178	+	1.92566i
$467$	38.0000			1.75843			0.879215	−	0.476425i	$-0.158068\pi$
$467$	38.0000			1.75843			0.879215	+	0.476425i	$0.158068\pi$
$468$		0			0
$469$	8.00000	−	13.8564i	0.369406	−	0.639829i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	3.50000	+	2.59808i	0.160591	+	0.119208i
$476$	8.00000			0.366679
$477$		0			0
$478$	27.0000	+	46.7654i	1.23495	+	2.13900i
$479$	2.50000	−	4.33013i	0.114228	−	0.197849i	−0.803243	−	0.595652i	$-0.796894\pi$
$479$	2.50000	−	4.33013i	0.114228	−	0.197849i	0.917471	+	0.397803i	$0.130227\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	10.0000			0.455488
$483$		0			0
$484$	10.0000	−	17.3205i	0.454545	−	0.787296i
$485$	−4.00000	+	6.92820i	−0.181631	+	0.314594i
$486$		0			0
$487$	14.0000			0.634401			0.317200	−	0.948359i	$-0.397257\pi$
$487$	14.0000			0.634401			0.317200	+	0.948359i	$0.397257\pi$
$488$		0			0
$489$		0			0
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	−0.950365	−	0.311136i	$-0.899290\pi$
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	0.205731	−	0.978609i	$-0.434043\pi$
$492$		0			0
$493$	−10.0000			−0.450377
$494$	2.00000	−	17.3205i	0.0899843	−	0.779287i
$495$		0			0
$496$	18.0000	+	31.1769i	0.808224	+	1.39988i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	−1.00000	+	1.73205i	−0.0447214	+	0.0774597i
$501$		0			0
$502$	34.0000			1.51749
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.322151	+	0.946688i	$0.604406\pi$
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.658781	+	0.752335i	$0.728928\pi$
$504$		0			0
$505$	7.00000			0.311496
$506$	−8.00000			−0.355643
$507$		0			0
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	32.0000			1.41421
$513$		0			0
$514$	−44.0000			−1.94076
$515$	4.00000	+	6.92820i	0.176261	+	0.305293i
$516$		0			0
$517$		0			0
$518$	−12.0000	−	20.7846i	−0.527250	−	0.913223i
$519$		0			0
$520$		0			0
$521$	−21.0000			−0.920027			−0.460013	−	0.887912i	$-0.652155\pi$
$521$	−21.0000			−0.920027			−0.460013	+	0.887912i	$0.652155\pi$
$522$		0			0
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	−0.518766	−	0.854916i	$-0.673608\pi$
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	0.999762	+	0.0218062i	$0.00694167\pi$
$524$	−32.0000			−1.39793
$525$		0			0
$526$	20.0000	−	34.6410i	0.872041	−	1.51042i
$527$	9.00000	+	15.5885i	0.392046	+	0.679044i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−2.00000	−	3.46410i	−0.0868744	−	0.150471i
$531$		0			0
$532$	−14.0000	−	10.3923i	−0.606977	−	0.450564i
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	3.00000			0.129219
$540$		0			0
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	−0.980993	−	0.194043i	$-0.937840\pi$
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	0.658543	+	0.752543i	$0.271173\pi$
$542$	−27.0000	+	46.7654i	−1.15975	+	2.00874i
$543$		0			0
$544$	16.0000			0.685994
$545$	−9.50000	+	16.4545i	−0.406935	+	0.704833i
$546$		0			0
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$		0			0
$550$	−2.00000			−0.0852803
$551$	17.5000	+	12.9904i	0.745525	+	0.553409i
$552$		0			0
$553$	−11.0000	−	19.0526i	−0.467768	−	0.810197i
$554$	8.00000	+	13.8564i	0.339887	+	0.588702i
$555$		0			0
$556$	−20.0000	−	34.6410i	−0.848189	−	1.46911i
$557$	−16.0000	+	27.7128i	−0.677942	+	1.17423i	0.297658	+	0.954673i	$0.403795\pi$
$557$	−16.0000	+	27.7128i	−0.677942	+	1.17423i	−0.975600	+	0.219557i	$0.929539\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	−4.00000	+	6.92820i	−0.169031	+	0.292770i
$561$		0			0
$562$	52.0000			2.19349
$563$	42.0000			1.77009			0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000			1.77009			0.885044	+	0.465506i	$0.154128\pi$
$564$		0			0
$565$	−5.00000	−	8.66025i	−0.210352	−	0.364340i
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$		0			0
$568$		0			0
$569$	39.0000			1.63497			0.817483	−	0.575953i	$-0.195369\pi$
$569$	39.0000			1.63497			0.817483	+	0.575953i	$0.195369\pi$
$570$		0			0
$571$	−15.0000			−0.627730			−0.313865	−	0.949468i	$-0.601624\pi$
$571$	−15.0000			−0.627730			−0.313865	+	0.949468i	$0.601624\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$		0			0
$574$	−12.0000	+	20.7846i	−0.500870	+	0.867533i
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$		0			0
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$	−26.0000			−1.08146
$579$		0			0
$580$	−5.00000	+	8.66025i	−0.207614	+	0.359597i
$581$	12.0000			0.497844
$582$		0			0
$583$	1.00000	−	1.73205i	0.0414158	−	0.0717342i
$584$		0			0
$585$		0			0
$586$	−4.00000	−	6.92820i	−0.165238	−	0.286201i
$587$	11.0000	+	19.0526i	0.454019	+	0.786383i	0.998631	−	0.0523045i	$-0.0166566\pi$
$587$	11.0000	+	19.0526i	0.454019	+	0.786383i	−0.544613	+	0.838688i	$0.683323\pi$
$588$		0			0
$589$	4.50000	−	38.9711i	0.185419	−	1.60578i
$590$	−14.0000			−0.576371
$591$		0			0
$592$	−12.0000	−	20.7846i	−0.493197	−	0.854242i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	−18.0000			−0.737309
$597$		0			0
$598$	−8.00000	+	13.8564i	−0.327144	+	0.566631i
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$		0			0
$601$	−15.0000			−0.611863			−0.305931	−	0.952054i	$-0.598968\pi$
$601$	−15.0000			−0.611863			−0.305931	+	0.952054i	$0.598968\pi$
$602$	−20.0000	+	34.6410i	−0.815139	+	1.41186i
$603$		0			0
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	−10.0000			−0.405887			−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000			−0.405887			−0.202944	+	0.979190i	$0.565051\pi$
$608$	−28.0000	−	20.7846i	−1.13555	−	0.842927i
$609$		0			0
$610$	7.00000	+	12.1244i	0.283422	+	0.490901i
$611$		0			0
$612$		0			0
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	0.920229	−	0.391381i	$-0.128002\pi$
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	−0.799060	+	0.601251i	$0.794669\pi$
$614$	24.0000	−	41.5692i	0.968561	−	1.67760i
$615$		0			0
$616$		0			0
$617$	−12.0000	+	20.7846i	−0.483102	+	0.836757i	−0.999812	−	0.0194037i	$-0.993823\pi$
$617$	−12.0000	+	20.7846i	−0.483102	+	0.836757i	0.516710	+	0.856161i	$0.327157\pi$
$618$		0			0
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$	18.0000			0.722897
$621$		0			0
$622$	24.0000	+	41.5692i	0.962312	+	1.66677i
$623$	−15.0000	+	25.9808i	−0.600962	+	1.04090i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−40.0000			−1.59872
$627$		0			0
$628$	24.0000			0.957704
$629$	−6.00000	−	10.3923i	−0.239236	−	0.414368i
$630$		0			0
$631$	1.50000	−	2.59808i	0.0597141	−	0.103428i	−0.834623	−	0.550822i	$-0.814314\pi$
$631$	1.50000	−	2.59808i	0.0597141	−	0.103428i	0.894337	+	0.447394i	$0.147648\pi$
$632$		0			0
$633$		0			0
$634$	−64.0000			−2.54176
$635$	4.00000			0.158735
$636$		0			0
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$	−10.0000			−0.395904
$639$		0			0
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	−22.0000	−	38.1051i	−0.867595	−	1.50272i	−0.864447	−	0.502724i	$-0.832331\pi$
$643$	−22.0000	−	38.1051i	−0.867595	−	1.50272i	−0.00314839	−	0.999995i	$-0.501002\pi$
$644$	8.00000	+	13.8564i	0.315244	+	0.546019i
$645$		0			0
$646$	−14.0000	−	10.3923i	−0.550823	−	0.408880i
$647$	−6.00000			−0.235884			−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000			−0.235884			−0.117942	+	0.993020i	$0.537630\pi$
$648$		0			0
$649$	−3.50000	−	6.06218i	−0.137387	−	0.237961i
$650$	−2.00000	+	3.46410i	−0.0784465	+	0.135873i
$651$		0			0
$652$	18.0000	−	31.1769i	0.704934	−	1.22098i
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$		0			0
$655$	8.00000	−	13.8564i	0.312586	−	0.541415i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$		0			0
$658$		0			0
$659$	20.0000	−	34.6410i	0.779089	−	1.34942i	−0.153378	−	0.988168i	$-0.549015\pi$
$659$	20.0000	−	34.6410i	0.779089	−	1.34942i	0.932467	−	0.361255i	$-0.117652\pi$
$660$		0			0
$661$	−4.50000	+	7.79423i	−0.175030	+	0.303160i	−0.940172	−	0.340701i	$-0.889335\pi$
$661$	−4.50000	+	7.79423i	−0.175030	+	0.303160i	0.765142	+	0.643862i	$0.222669\pi$
$662$	−8.00000	−	13.8564i	−0.310929	−	0.538545i
$663$		0			0
$664$		0			0
$665$	8.00000	−	3.46410i	0.310227	−	0.134332i
$666$		0			0
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	−2.00000	−	3.46410i	−0.0773823	−	0.134030i
$669$		0			0
$670$	−8.00000	−	13.8564i	−0.309067	−	0.535320i
$671$	−3.50000	+	6.06218i	−0.135116	+	0.234028i
$672$		0			0
$673$	36.0000			1.38770			0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000			1.38770			0.693849	+	0.720121i	$0.255914\pi$
$674$	8.00000	−	13.8564i	0.308148	−	0.533729i
$675$		0			0
$676$	−18.0000			−0.692308
$677$	−46.0000			−1.76792			−0.883962	−	0.467559i	$-0.845134\pi$
$677$	−46.0000			−1.76792			−0.883962	+	0.467559i	$0.845134\pi$
$678$		0			0
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$		0			0
$681$		0			0
$682$	9.00000	+	15.5885i	0.344628	+	0.596913i
$683$	24.0000			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$	−20.0000	−	34.6410i	−0.763604	−	1.32260i
$687$		0			0
$688$	−20.0000	+	34.6410i	−0.762493	+	1.32068i
$689$	−2.00000	−	3.46410i	−0.0761939	−	0.131972i
$690$		0			0
$691$	23.0000			0.874961			0.437481	−	0.899228i	$-0.355871\pi$
$691$	23.0000			0.874961			0.437481	+	0.899228i	$0.355871\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−22.0000	+	38.1051i	−0.835109	+	1.44645i
$695$	20.0000			0.758643
$696$		0			0
$697$	−6.00000	+	10.3923i	−0.227266	+	0.393637i
$698$	−6.00000	−	10.3923i	−0.227103	−	0.393355i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−11.0000	−	19.0526i	−0.415464	−	0.719605i	0.580013	−	0.814607i	$-0.303048\pi$
$701$	−11.0000	−	19.0526i	−0.415464	−	0.719605i	−0.995477	+	0.0950021i	$0.969714\pi$
$702$		0			0
$703$	−3.00000	+	25.9808i	−0.113147	+	0.979883i
$704$	8.00000			0.301511
$705$		0			0
$706$	−14.0000	−	24.2487i	−0.526897	−	0.912612i
$707$	7.00000	−	12.1244i	0.263262	−	0.455983i
$708$		0			0
$709$	13.5000	−	23.3827i	0.507003	−	0.878155i	−0.492964	−	0.870050i	$-0.664087\pi$
$709$	13.5000	−	23.3827i	0.507003	−	0.878155i	0.999967	−	0.00810550i	$-0.00258009\pi$
$710$	−6.00000			−0.225176
$711$		0			0
$712$		0			0
$713$	−18.0000	+	31.1769i	−0.674105	+	1.16758i
$714$		0			0
$715$	−2.00000			−0.0747958
$716$	−3.00000	+	5.19615i	−0.112115	+	0.194189i
$717$		0			0
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	−13.5000	−	23.3827i	−0.503465	−	0.872027i	−0.999992	−	0.00400572i	$-0.998725\pi$
$719$	−13.5000	−	23.3827i	−0.503465	−	0.872027i	0.496527	−	0.868021i	$-0.334608\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	11.0000	+	36.3731i	0.409378	+	1.35367i
$723$		0			0
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$	−2.50000	−	4.33013i	−0.0928477	−	0.160817i
$726$		0			0
$727$	1.00000	+	1.73205i	0.0370879	+	0.0642382i	0.883974	−	0.467537i	$-0.154858\pi$
$727$	1.00000	+	1.73205i	0.0370879	+	0.0642382i	−0.846886	+	0.531775i	$0.821525\pi$
$728$		0			0
$729$		0			0
$730$	−4.00000			−0.148047
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$		0			0
$733$	10.0000			0.369358			0.184679	−	0.982799i	$-0.440875\pi$
$733$	10.0000			0.369358			0.184679	+	0.982799i	$0.440875\pi$
$734$	−40.0000			−1.47643
$735$		0			0
$736$	16.0000	+	27.7128i	0.589768	+	1.02151i
$737$	4.00000	−	6.92820i	0.147342	−	0.255204i
$738$		0			0
$739$	26.5000	+	45.8993i	0.974818	+	1.68843i	0.680534	+	0.732717i	$0.261748\pi$
$739$	26.5000	+	45.8993i	0.974818	+	1.68843i	0.294285	+	0.955718i	$0.404919\pi$
$740$	−12.0000			−0.441129
$741$		0			0
$742$	−8.00000			−0.293689
$743$	11.0000	+	19.0526i	0.403551	+	0.698971i	0.994152	−	0.107993i	$-0.0344425\pi$
$743$	11.0000	+	19.0526i	0.403551	+	0.698971i	−0.590601	+	0.806964i	$0.701109\pi$
$744$		0			0
$745$	4.50000	−	7.79423i	0.164867	−	0.285558i
$746$	32.0000	+	55.4256i	1.17160	+	2.02928i
$747$		0			0
$748$	4.00000			0.146254
$749$		0			0
$750$		0			0
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	−0.837359	−	0.546653i	$-0.815902\pi$
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	0.892095	+	0.451848i	$0.149235\pi$
$752$		0			0
$753$		0			0
$754$	−10.0000	+	17.3205i	−0.364179	+	0.630776i
$755$	1.50000	+	2.59808i	0.0545906	+	0.0945537i
$756$		0			0
$757$	7.00000	+	12.1244i	0.254419	+	0.440667i	0.964738	−	0.263213i	$-0.0847823\pi$
$757$	7.00000	+	12.1244i	0.254419	+	0.440667i	−0.710318	+	0.703881i	$0.751449\pi$
$758$	−31.0000	−	53.6936i	−1.12597	−	1.95024i
$759$		0			0
$760$		0			0
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		0			0
$763$	19.0000	+	32.9090i	0.687846	+	1.19138i
$764$	15.0000	−	25.9808i	0.542681	−	0.939951i
$765$		0			0
$766$	26.0000	−	45.0333i	0.939418	−	1.62712i
$767$	−14.0000			−0.505511
$768$		0			0
$769$	21.5000	−	37.2391i	0.775310	−	1.34288i	−0.159310	−	0.987229i	$-0.550927\pi$
$769$	21.5000	−	37.2391i	0.775310	−	1.34288i	0.934620	−	0.355647i	$-0.115740\pi$
$770$	−2.00000	+	3.46410i	−0.0720750	+	0.124838i
$771$		0			0
$772$	−52.0000			−1.87152
$773$	10.0000	−	17.3205i	0.359675	−	0.622975i	−0.628231	−	0.778027i	$-0.716221\pi$
$773$	10.0000	−	17.3205i	0.359675	−	0.622975i	0.987906	+	0.155051i	$0.0495542\pi$
$774$		0			0
$775$	−4.50000	+	7.79423i	−0.161645	+	0.279977i
$776$		0			0
$777$		0			0
$778$	−66.0000			−2.36621
$779$	24.0000	−	10.3923i	0.859889	−	0.372343i
$780$		0			0
$781$	−1.50000	−	2.59808i	−0.0536742	−	0.0929665i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$		0			0
$784$	−6.00000	−	10.3923i	−0.214286	−	0.371154i
$785$	−6.00000	+	10.3923i	−0.214149	+	0.370917i
$786$		0			0
$787$	−8.00000			−0.285169			−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000			−0.285169			−0.142585	+	0.989783i	$0.545541\pi$
$788$	10.0000	−	17.3205i	0.356235	−	0.617018i
$789$		0			0
$790$	−22.0000			−0.782725
$791$	−20.0000			−0.711118
$792$		0			0
$793$	7.00000	+	12.1244i	0.248577	+	0.430548i
$794$	20.0000	−	34.6410i	0.709773	−	1.22936i
$795$		0			0
$796$	3.00000	+	5.19615i	0.106332	+	0.184173i
$797$	−10.0000			−0.354218			−0.177109	−	0.984191i	$-0.556675\pi$
$797$	−10.0000			−0.354218			−0.177109	+	0.984191i	$0.556675\pi$
$798$		0			0
$799$		0			0
$800$	4.00000	+	6.92820i	0.141421	+	0.244949i
$801$		0			0
$802$	−27.0000	+	46.7654i	−0.953403	+	1.65134i
$803$	−1.00000	−	1.73205i	−0.0352892	−	0.0611227i
$804$		0			0
$805$	−8.00000			−0.281963
$806$	36.0000			1.26805
$807$		0			0
$808$		0			0
$809$	1.00000			0.0351581			0.0175791	−	0.999845i	$-0.494404\pi$
$809$	1.00000			0.0351581			0.0175791	+	0.999845i	$0.494404\pi$
$810$		0			0
$811$	−24.5000	+	42.4352i	−0.860311	+	1.49010i	0.0113172	+	0.999936i	$0.496398\pi$
$811$	−24.5000	+	42.4352i	−0.860311	+	1.49010i	−0.871629	+	0.490167i	$0.836936\pi$
$812$	10.0000	+	17.3205i	0.350931	+	0.607831i
$813$		0			0
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	9.00000	+	15.5885i	0.315256	+	0.546040i
$816$		0			0
$817$	40.0000	−	17.3205i	1.39942	−	0.605968i
$818$	−58.0000			−2.02792
$819$		0			0
$820$	6.00000	+	10.3923i	0.209529	+	0.362915i
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	−0.928846	+	0.370465i	$0.879198\pi$
$822$		0			0
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	−0.637419	−	0.770517i	$-0.719998\pi$
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	0.985997	+	0.166762i	$0.0533313\pi$
$824$		0			0
$825$		0			0
$826$	−14.0000	+	24.2487i	−0.487122	+	0.843721i
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	−0.742646	−	0.669684i	$-0.766429\pi$
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	0.951286	+	0.308308i	$0.0997628\pi$
$828$		0			0
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	8.00000	−	13.8564i	0.277350	−	0.480384i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	2.00000			0.0692129
$836$	−7.00000	−	5.19615i	−0.242100	−	0.179713i
$837$		0			0
$838$	−5.00000	−	8.66025i	−0.172722	−	0.299164i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$		0			0
$844$	−54.0000			−1.85876
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	20.0000			0.687208
$848$	−8.00000			−0.274721
$849$		0			0
$850$	2.00000	+	3.46410i	0.0685994	+	0.118818i
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$		0			0
$853$	1.00000	+	1.73205i	0.0342393	+	0.0593043i	0.882637	−	0.470055i	$-0.155766\pi$
$853$	1.00000	+	1.73205i	0.0342393	+	0.0593043i	−0.848398	+	0.529359i	$0.822432\pi$
$854$	28.0000			0.958140
$855$		0			0
$856$		0			0
$857$	5.00000	+	8.66025i	0.170797	+	0.295829i	0.938699	−	0.344739i	$-0.112033\pi$
$857$	5.00000	+	8.66025i	0.170797	+	0.295829i	−0.767902	+	0.640567i	$0.778699\pi$
$858$		0			0
$859$	−22.5000	+	38.9711i	−0.767690	+	1.32968i	0.171122	+	0.985250i	$0.445261\pi$
$859$	−22.5000	+	38.9711i	−0.767690	+	1.32968i	−0.938813	+	0.344428i	$0.888073\pi$
$860$	10.0000	+	17.3205i	0.340997	+	0.590624i
$861$		0			0
$862$	−46.0000			−1.56677
$863$	38.0000			1.29354			0.646768	−	0.762687i	$-0.276120\pi$
$863$	38.0000			1.29354			0.646768	+	0.762687i	$0.276120\pi$
$864$		0			0
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	12.0000			0.407777
$867$		0			0
$868$	18.0000	−	31.1769i	0.610960	−	1.05821i
$869$	−5.50000	−	9.52628i	−0.186575	−	0.323157i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$		0			0
$873$		0			0
$874$	4.00000	−	34.6410i	0.135302	−	1.17175i
$875$	−2.00000			−0.0676123
$876$		0			0
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	0.589135	−	0.808035i	$-0.299469\pi$
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	−0.994346	+	0.106188i	$0.966135\pi$
$878$	25.0000	−	43.3013i	0.843709	−	1.46135i
$879$		0			0
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	1.00000			0.0336909			0.0168454	−	0.999858i	$-0.494638\pi$
$881$	1.00000			0.0336909			0.0168454	+	0.999858i	$0.494638\pi$
$882$		0			0
$883$	14.0000	−	24.2487i	0.471138	−	0.816034i	−0.528317	−	0.849047i	$-0.677177\pi$
$883$	14.0000	−	24.2487i	0.471138	−	0.816034i	0.999455	+	0.0330128i	$0.0105102\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$		0			0
$886$	16.0000			0.537531
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$		0			0
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$	15.0000	+	25.9808i	0.502801	+	0.870877i
$891$		0			0
$892$	−24.0000			−0.803579
$893$		0			0
$894$		0			0
$895$	−1.50000	−	2.59808i	−0.0501395	−	0.0868441i
$896$		0			0
$897$		0			0
$898$	−39.0000	−	67.5500i	−1.30145	−	2.25417i
$899$	−22.5000	+	38.9711i	−0.750417	+	1.29976i
$900$		0			0
$901$	−4.00000			−0.133259
$902$	−6.00000	+	10.3923i	−0.199778	+	0.346026i
$903$		0			0
$904$		0			0
$905$	10.0000			0.332411
$906$		0			0
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$	18.0000	−	31.1769i	0.597351	−	1.03464i
$909$		0			0
$910$	4.00000	+	6.92820i	0.132599	+	0.229668i
$911$	9.00000			0.298183			0.149092	−	0.988823i	$-0.452365\pi$
$911$	9.00000			0.298183			0.149092	+	0.988823i	$0.452365\pi$
$912$		0			0
$913$	6.00000			0.198571
$914$	8.00000	+	13.8564i	0.264616	+	0.458329i
$915$		0			0
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$	−16.0000	−	27.7128i	−0.528367	−	0.915158i
$918$		0			0
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$		0			0
$921$		0			0
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	−6.00000			−0.197492
$924$		0			0
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	10.0000	+	17.3205i	0.328620	+	0.569187i
$927$		0			0
$928$	20.0000	+	34.6410i	0.656532	+	1.13715i
$929$	−5.50000	−	9.52628i	−0.180449	−	0.312547i	0.761584	−	0.648066i	$-0.224422\pi$
$929$	−5.50000	−	9.52628i	−0.180449	−	0.312547i	−0.942034	+	0.335519i	$0.891088\pi$
$930$		0			0
$931$	−1.50000	+	12.9904i	−0.0491605	+	0.425743i
$932$	48.0000			1.57229
$933$		0			0
$934$	−38.0000	−	65.8179i	−1.24340	−	2.15363i
$935$	−1.00000	+	1.73205i	−0.0327035	+	0.0566441i
$936$		0			0
$937$	9.00000	−	15.5885i	0.294017	−	0.509253i	−0.680739	−	0.732526i	$-0.738341\pi$
$937$	9.00000	−	15.5885i	0.294017	−	0.509253i	0.974756	+	0.223274i	$0.0716744\pi$
$938$	−32.0000			−1.04484
$939$		0			0
$940$		0			0
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$		0			0
$943$	−24.0000			−0.781548
$944$	−14.0000	+	24.2487i	−0.455661	+	0.789228i
$945$		0			0
$946$	−10.0000	+	17.3205i	−0.325128	+	0.563138i
$947$	10.0000	+	17.3205i	0.324956	+	0.562841i	0.981504	−	0.191444i	$-0.0613171\pi$
$947$	10.0000	+	17.3205i	0.324956	+	0.562841i	−0.656547	+	0.754285i	$0.727984\pi$
$948$		0			0
$949$	−4.00000			−0.129845
$950$	1.00000	−	8.66025i	0.0324443	−	0.280976i
$951$		0			0
$952$		0			0
$953$	−4.00000	−	6.92820i	−0.129573	−	0.224427i	0.793938	−	0.607998i	$-0.208027\pi$
$953$	−4.00000	−	6.92820i	−0.129573	−	0.224427i	−0.923511	+	0.383572i	$0.874694\pi$
$954$		0			0
$955$	7.50000	+	12.9904i	0.242694	+	0.420359i
$956$	27.0000	−	46.7654i	0.873242	−	1.51250i
$957$		0			0
$958$	−10.0000			−0.323085
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	50.0000			1.61290
$962$	−24.0000			−0.773791
$963$		0			0
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	13.0000	−	22.5167i	0.418485	−	0.724837i
$966$		0			0
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$		0			0
$969$		0			0
$970$	16.0000			0.513729
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	20.0000	−	34.6410i	0.641171	−	1.11054i
$974$	−14.0000	−	24.2487i	−0.448589	−	0.776979i
$975$		0			0
$976$	28.0000			0.896258
$977$	−18.0000			−0.575871			−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000			−0.575871			−0.287936	+	0.957650i	$0.592969\pi$
$978$		0			0
$979$	−7.50000	+	12.9904i	−0.239701	+	0.415174i
$980$	−6.00000			−0.191663
$981$		0			0
$982$	−33.0000	+	57.1577i	−1.05307	+	1.82397i
$983$	−7.00000	−	12.1244i	−0.223265	−	0.386707i	0.732532	−	0.680732i	$-0.238338\pi$
$983$	−7.00000	−	12.1244i	−0.223265	−	0.386707i	−0.955798	+	0.294025i	$0.905005\pi$
$984$		0			0
$985$	5.00000	+	8.66025i	0.159313	+	0.275939i
$986$	10.0000	+	17.3205i	0.318465	+	0.551597i
$987$		0			0
$988$	−16.0000	+	6.92820i	−0.509028	+	0.220416i
$989$	−40.0000			−1.27193
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$	36.0000	−	62.3538i	1.14300	−	1.97974i
$993$		0			0
$994$	−6.00000	+	10.3923i	−0.190308	+	0.329624i
$995$	−3.00000			−0.0951064
$996$		0			0
$997$	−26.0000	+	45.0333i	−0.823428	+	1.42622i	0.0796863	+	0.996820i	$0.474608\pi$
$997$	−26.0000	+	45.0333i	−0.823428	+	1.42622i	−0.903115	+	0.429400i	$0.858725\pi$
$998$	−20.0000	+	34.6410i	−0.633089	+	1.09654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.a.406.1		2
3.2	odd	2		285.2.i.c.121.1	yes	2
19.11	even	3	inner	855.2.k.a.676.1		2
57.11	odd	6		285.2.i.c.106.1	✓	2
57.26	odd	6		5415.2.a.b.1.1		1
57.50	even	6		5415.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.c.106.1	✓	2	57.11	odd	6
285.2.i.c.121.1	yes	2	3.2	odd	2
855.2.k.a.406.1		2	1.1	even	1	trivial
855.2.k.a.676.1		2	19.11	even	3	inner
5415.2.a.b.1.1		1	57.26	odd	6
5415.2.a.l.1.1		1	57.50	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{7} +(-1.00000 + 1.73205i) q^{10} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 - 4.33013i) q^{19} +2.00000 q^{20} +(1.00000 + 1.73205i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{26} +(2.00000 - 3.46410i) q^{28} +(-2.50000 + 4.33013i) q^{29} +9.00000 q^{31} +(4.00000 - 6.92820i) q^{32} +(2.00000 - 3.46410i) q^{34} +(1.00000 + 1.73205i) q^{35} -6.00000 q^{37} +(-8.00000 + 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{41} +(5.00000 + 8.66025i) q^{43} +(1.00000 - 1.73205i) q^{44} +8.00000 q^{46} -3.00000 q^{49} +2.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(0.500000 + 0.866025i) q^{55} +10.0000 q^{58} +(3.50000 + 6.06218i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-9.00000 - 15.5885i) q^{62} -8.00000 q^{64} +2.00000 q^{65} +(-4.00000 + 6.92820i) q^{67} -4.00000 q^{68} +(2.00000 - 3.46410i) q^{70} +(1.50000 + 2.59808i) q^{71} +(1.00000 + 1.73205i) q^{73} +(6.00000 + 10.3923i) q^{74} +(7.00000 + 5.19615i) q^{76} +2.00000 q^{77} +(5.50000 + 9.52628i) q^{79} +(2.00000 - 3.46410i) q^{80} +(6.00000 - 10.3923i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{85} +(10.0000 - 17.3205i) q^{86} +(7.50000 - 12.9904i) q^{89} +(2.00000 - 3.46410i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(-4.00000 + 1.73205i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(3.00000 + 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} - q^{5} - 4 q^{7} - 2 q^{10} - 2 q^{11} - 2 q^{13} + 4 q^{14} + 4 q^{16} + 2 q^{17} + q^{19} + 4 q^{20} + 2 q^{22} - 4 q^{23} - q^{25} + 8 q^{26} + 4 q^{28} - 5 q^{29} + 18 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 - q^5 - 4 * q^7 - 2 * q^10 - 2 * q^11 - 2 * q^13 + 4 * q^14 + 4 * q^16 + 2 * q^17 + q^19 + 4 * q^20 + 2 * q^22 - 4 * q^23 - q^25 + 8 * q^26 + 4 * q^28 - 5 * q^29 + 18 * q^31 + 8 * q^32 + 4 * q^34 + 2 * q^35 - 12 * q^37 - 16 * q^38 + 6 * q^41 + 10 * q^43 + 2 * q^44 + 16 * q^46 - 6 * q^49 + 4 * q^50 - 4 * q^52 - 2 * q^53 + q^55 + 20 * q^58 + 7 * q^59 + 7 * q^61 - 18 * q^62 - 16 * q^64 + 4 * q^65 - 8 * q^67 - 8 * q^68 + 4 * q^70 + 3 * q^71 + 2 * q^73 + 12 * q^74 + 14 * q^76 + 4 * q^77 + 11 * q^79 + 4 * q^80 + 12 * q^82 - 12 * q^83 + 2 * q^85 + 20 * q^86 + 15 * q^89 + 4 * q^91 - 8 * q^92 - 8 * q^95 - 8 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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