LMFDB - Embedded newform 912.2.bn.f.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.28235666434$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.f.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(3.00000 + 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(3.00000 + 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} -3.46410i q^{11} +(4.50000 - 2.59808i) q^{13} +(3.00000 + 5.19615i) q^{15} +(-3.00000 - 1.73205i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.50000 - 0.866025i) q^{21} +(3.50000 + 6.06218i) q^{25} +5.19615i q^{27} +(-3.00000 - 5.19615i) q^{29} +1.73205i q^{31} +(3.00000 - 5.19615i) q^{33} +(-3.00000 - 1.73205i) q^{35} +5.19615i q^{37} +9.00000 q^{39} +(-6.00000 + 10.3923i) q^{41} +(-0.500000 + 0.866025i) q^{43} +10.3923i q^{45} +(-6.00000 + 3.46410i) q^{47} -6.00000 q^{49} +(-3.00000 - 5.19615i) q^{51} +(-6.00000 - 10.3923i) q^{53} +(6.00000 - 10.3923i) q^{55} +(4.50000 + 6.06218i) q^{57} +(-3.50000 - 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{63} +18.0000 q^{65} +(-7.50000 + 4.33013i) q^{67} +(3.00000 - 5.19615i) q^{71} +(3.50000 - 6.06218i) q^{73} +12.1244i q^{75} +3.46410i q^{77} +(-4.50000 - 2.59808i) q^{79} +(-4.50000 + 7.79423i) q^{81} +10.3923i q^{83} +(-6.00000 - 10.3923i) q^{85} -10.3923i q^{87} +(-4.50000 + 2.59808i) q^{91} +(-1.50000 + 2.59808i) q^{93} +(9.00000 + 12.1244i) q^{95} +(6.00000 + 3.46410i) q^{97} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 6 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 6 * q^5 - 2 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} + 6 q^{5} - 2 q^{7} + 3 q^{9} + 9 q^{13} + 6 q^{15} - 6 q^{17} + 8 q^{19} - 3 q^{21} + 7 q^{25} - 6 q^{29} + 6 q^{33} - 6 q^{35} + 18 q^{39} - 12 q^{41} - q^{43} - 12 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 12 q^{55} + 9 q^{57} - 7 q^{61} - 3 q^{63} + 36 q^{65} - 15 q^{67} + 6 q^{71} + 7 q^{73} - 9 q^{79} - 9 q^{81} - 12 q^{85} - 9 q^{91} - 3 q^{93} + 18 q^{95} + 12 q^{97} + 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 6 * q^5 - 2 * q^7 + 3 * q^9 + 9 * q^13 + 6 * q^15 - 6 * q^17 + 8 * q^19 - 3 * q^21 + 7 * q^25 - 6 * q^29 + 6 * q^33 - 6 * q^35 + 18 * q^39 - 12 * q^41 - q^43 - 12 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 12 * q^55 + 9 * q^57 - 7 * q^61 - 3 * q^63 + 36 * q^65 - 15 * q^67 + 6 * q^71 + 7 * q^73 - 9 * q^79 - 9 * q^81 - 12 * q^85 - 9 * q^91 - 3 * q^93 + 18 * q^95 + 12 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		0			0
$5$	3.00000	+	1.73205i	1.34164	+	0.774597i	0.987048	−	0.160424i	$-0.0512862\pi$
$5$	3.00000	+	1.73205i	1.34164	+	0.774597i	0.354593	+	0.935021i	$0.384620\pi$
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$		0			0
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$		0			0
$17$	−3.00000	−	1.73205i	−0.727607	−	0.420084i	0.0899392	−	0.995947i	$-0.471333\pi$
$17$	−3.00000	−	1.73205i	−0.727607	−	0.420084i	−0.817546	+	0.575863i	$0.804666\pi$
$18$		0			0
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$		0			0
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$	3.50000	+	6.06218i	0.700000	+	1.21244i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$		0			0
$35$	−3.00000	−	1.73205i	−0.507093	−	0.292770i
$36$		0			0
$37$			5.19615i			0.854242i	0.904194	+	0.427121i	$0.140472\pi$
$37$			5.19615i			0.854242i	−0.904194	+	0.427121i	$0.859528\pi$
$38$		0			0
$39$	9.00000			1.44115
$40$		0			0
$41$	−6.00000	+	10.3923i	−0.937043	+	1.62301i	−0.166092	+	0.986110i	$0.553115\pi$
$41$	−6.00000	+	10.3923i	−0.937043	+	1.62301i	−0.770950	+	0.636895i	$0.780218\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$			10.3923i			1.54919i
$46$		0			0
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.869069	−	0.494690i	$-0.835282\pi$
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.00612051	+	0.999981i	$0.501948\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$		0			0
$55$	6.00000	−	10.3923i	0.809040	−	1.40130i
$56$		0			0
$57$	4.50000	+	6.06218i	0.596040	+	0.802955i
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$	−1.50000	−	2.59808i	−0.188982	−	0.327327i
$64$		0			0
$65$	18.0000			2.23263
$66$		0			0
$67$	−7.50000	+	4.33013i	−0.916271	+	0.529009i	−0.882443	−	0.470418i	$-0.844103\pi$
$67$	−7.50000	+	4.33013i	−0.916271	+	0.529009i	−0.0338274	+	0.999428i	$0.510770\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$			12.1244i			1.40000i
$76$		0			0
$77$			3.46410i			0.394771i
$78$		0			0
$79$	−4.50000	−	2.59808i	−0.506290	−	0.292306i	0.225018	−	0.974355i	$-0.427756\pi$
$79$	−4.50000	−	2.59808i	−0.506290	−	0.292306i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$			10.3923i			1.14070i	0.821401	+	0.570352i	$0.193193\pi$
$83$			10.3923i			1.14070i	−0.821401	+	0.570352i	$0.806807\pi$
$84$		0			0
$85$	−6.00000	−	10.3923i	−0.650791	−	1.12720i
$86$		0			0
$87$		−	10.3923i		−	1.11417i
$88$		0			0
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−4.50000	+	2.59808i	−0.471728	+	0.272352i
$92$		0			0
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$		0			0
$95$	9.00000	+	12.1244i	0.923381	+	1.24393i
$96$		0			0
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	0.772655	−	0.634826i	$-0.218928\pi$
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	−0.163448	+	0.986552i	$0.552261\pi$
$98$		0			0
$99$	9.00000	−	5.19615i	0.904534	−	0.522233i
$100$		0			0
$101$	9.00000	−	5.19615i	0.895533	−	0.517036i	0.0197851	−	0.999804i	$-0.493702\pi$
$101$	9.00000	−	5.19615i	0.895533	−	0.517036i	0.875748	+	0.482768i	$0.160368\pi$
$102$		0			0
$103$		−	8.66025i		−	0.853320i	−0.904412	−	0.426660i	$-0.859690\pi$
$103$		−	8.66025i		−	0.853320i	0.904412	−	0.426660i	$-0.140310\pi$
$104$		0			0
$105$	−3.00000	−	5.19615i	−0.292770	−	0.507093i
$106$		0			0
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$		0			0
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$	−4.50000	+	7.79423i	−0.427121	+	0.739795i
$112$		0			0
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	13.5000	+	7.79423i	1.24808	+	0.720577i
$118$		0			0
$119$	3.00000	+	1.73205i	0.275010	+	0.158777i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$		0			0
$123$	−18.0000	+	10.3923i	−1.62301	+	0.937043i
$124$		0			0
$125$			6.92820i			0.619677i
$126$		0			0
$127$	9.00000	−	5.19615i	0.798621	−	0.461084i	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	9.00000	−	5.19615i	0.798621	−	0.461084i	0.842989	+	0.537931i	$0.180794\pi$
$128$		0			0
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$		0			0
$131$	−3.00000	−	1.73205i	−0.262111	−	0.151330i	0.363186	−	0.931717i	$-0.381689\pi$
$131$	−3.00000	−	1.73205i	−0.262111	−	0.151330i	−0.625297	+	0.780387i	$0.715022\pi$
$132$		0			0
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$		0			0
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$		0			0
$137$	−3.00000	+	1.73205i	−0.256307	+	0.147979i	−0.622649	−	0.782501i	$-0.713943\pi$
$137$	−3.00000	+	1.73205i	−0.256307	+	0.147979i	0.366342	+	0.930480i	$0.380610\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$	−12.0000			−1.01058
$142$		0			0
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$		0			0
$145$		−	20.7846i		−	1.72607i
$146$		0			0
$147$	−9.00000	−	5.19615i	−0.742307	−	0.428571i
$148$		0			0
$149$	15.0000	+	8.66025i	1.22885	+	0.709476i	0.966789	−	0.255576i	$-0.0822652\pi$
$149$	15.0000	+	8.66025i	1.22885	+	0.709476i	0.262059	+	0.965052i	$0.415599\pi$
$150$		0			0
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$		0			0
$153$		−	10.3923i		−	0.840168i
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$		0			0
$159$		−	20.7846i		−	1.64833i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$		0			0
$165$	18.0000	−	10.3923i	1.40130	−	0.809040i
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$		0			0
$171$	1.50000	+	12.9904i	0.114708	+	0.993399i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−3.50000	−	6.06218i	−0.264575	−	0.458258i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−6.00000	+	3.46410i	−0.445976	+	0.257485i	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−6.00000	+	3.46410i	−0.445976	+	0.257485i	0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$		−	12.1244i		−	0.896258i
$184$		0			0
$185$	−9.00000	+	15.5885i	−0.661693	+	1.14609i
$186$		0			0
$187$	−6.00000	+	10.3923i	−0.438763	+	0.759961i
$188$		0			0
$189$		−	5.19615i		−	0.377964i
$190$		0			0
$191$		−	17.3205i		−	1.25327i	−0.779314	−	0.626634i	$-0.784432\pi$
$191$		−	17.3205i		−	1.25327i	0.779314	−	0.626634i	$-0.215568\pi$
$192$		0			0
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	−0.827788	+	0.561041i	$0.810401\pi$
$194$		0			0
$195$	27.0000	+	15.5885i	1.93351	+	1.11631i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.844446	−	0.535641i	$-0.820070\pi$
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.0416556	−	0.999132i	$-0.513263\pi$
$200$		0			0
$201$	−15.0000			−1.05802
$202$		0			0
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		0			0
$205$	−36.0000	+	20.7846i	−2.51435	+	1.45166i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000	−	13.8564i	0.415029	−	0.958468i
$210$		0			0
$211$	19.5000	+	11.2583i	1.34244	+	0.775055i	0.987164	−	0.159708i	$-0.0510552\pi$
$211$	19.5000	+	11.2583i	1.34244	+	0.775055i	0.355271	+	0.934763i	$0.384389\pi$
$212$		0			0
$213$	9.00000	−	5.19615i	0.616670	−	0.356034i
$214$		0			0
$215$	−3.00000	+	1.73205i	−0.204598	+	0.118125i
$216$		0			0
$217$		−	1.73205i		−	0.117579i
$218$		0			0
$219$	10.5000	−	6.06218i	0.709524	−	0.409644i
$220$		0			0
$221$	−18.0000			−1.21081
$222$		0			0
$223$	−16.5000	−	9.52628i	−1.10492	−	0.637927i	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	−16.5000	−	9.52628i	−1.10492	−	0.637927i	−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$	−10.5000	+	18.1865i	−0.700000	+	1.21244i
$226$		0			0
$227$	−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
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$		0			0
$233$	15.0000	+	8.66025i	0.982683	+	0.567352i	0.903079	−	0.429474i	$-0.141301\pi$
$233$	15.0000	+	8.66025i	0.982683	+	0.567352i	0.0796037	+	0.996827i	$0.474635\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$		0			0
$237$	−4.50000	−	7.79423i	−0.292306	−	0.506290i
$238$		0			0
$239$			24.2487i			1.56852i	0.620433	+	0.784259i	$0.286957\pi$
$239$			24.2487i			1.56852i	−0.620433	+	0.784259i	$0.713043\pi$
$240$		0			0
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		0			0
$245$	−18.0000	−	10.3923i	−1.14998	−	0.663940i
$246$		0			0
$247$	22.5000	−	2.59808i	1.43164	−	0.165312i
$248$		0			0
$249$	−9.00000	+	15.5885i	−0.570352	+	0.987878i
$250$		0			0
$251$	6.00000	−	3.46410i	0.378717	−	0.218652i	−0.298543	−	0.954396i	$-0.596501\pi$
$251$	6.00000	−	3.46410i	0.378717	−	0.218652i	0.677260	+	0.735744i	$0.263167\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		−	20.7846i		−	1.30158i
$256$		0			0
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$		−	5.19615i		−	0.322873i
$260$		0			0
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$		0			0
$263$	21.0000	+	12.1244i	1.29492	+	0.747620i	0.979521	−	0.201341i	$-0.0645299\pi$
$263$	21.0000	+	12.1244i	1.29492	+	0.747620i	0.315394	+	0.948961i	$0.397863\pi$
$264$		0			0
$265$		−	41.5692i		−	2.55358i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$		0			0
$273$	−9.00000			−0.544705
$274$		0			0
$275$	21.0000	−	12.1244i	1.26635	−	0.731126i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$	−4.50000	+	2.59808i	−0.269408	+	0.155543i
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$		0			0
$285$	3.00000	+	25.9808i	0.177705	+	1.53897i
$286$		0			0
$287$	6.00000	−	10.3923i	0.354169	−	0.613438i
$288$		0			0
$289$	−2.50000	−	4.33013i	−0.147059	−	0.254713i
$290$		0			0
$291$	6.00000	+	10.3923i	0.351726	+	0.609208i
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	18.0000			1.04447
$298$		0			0
$299$		0			0
$300$		0			0
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$		0			0
$303$	18.0000			1.03407
$304$		0			0
$305$		−	24.2487i		−	1.38848i
$306$		0			0
$307$	−27.0000	−	15.5885i	−1.54097	−	0.889680i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$	−27.0000	−	15.5885i	−1.54097	−	0.889680i	−0.542194	−	0.840254i	$-0.682406\pi$
$308$		0			0
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$		0			0
$311$			13.8564i			0.785725i	0.919597	+	0.392862i	$0.128515\pi$
$311$			13.8564i			0.785725i	−0.919597	+	0.392862i	$0.871485\pi$
$312$		0			0
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$		0			0
$315$		−	10.3923i		−	0.585540i
$316$		0			0
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$	−18.0000	+	10.3923i	−1.00781	+	0.581857i
$320$		0			0
$321$	27.0000	+	15.5885i	1.50699	+	0.870063i
$322$		0			0
$323$	−9.00000	−	12.1244i	−0.500773	−	0.674617i
$324$		0			0
$325$	31.5000	+	18.1865i	1.74731	+	1.00881i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.00000	−	3.46410i	0.330791	−	0.190982i
$330$		0			0
$331$		−	5.19615i		−	0.285606i	−0.989751	−	0.142803i	$-0.954388\pi$
$331$		−	5.19615i		−	0.285606i	0.989751	−	0.142803i	$-0.0456116\pi$
$332$		0			0
$333$	−13.5000	+	7.79423i	−0.739795	+	0.427121i
$334$		0			0
$335$	−30.0000			−1.63908
$336$		0			0
$337$	1.50000	+	0.866025i	0.0817102	+	0.0471754i	0.540298	−	0.841473i	$-0.318311\pi$
$337$	1.50000	+	0.866025i	0.0817102	+	0.0471754i	−0.458588	+	0.888649i	$0.651645\pi$
$338$		0			0
$339$	−18.0000	−	10.3923i	−0.977626	−	0.564433i
$340$		0			0
$341$	6.00000			0.324918
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−21.0000	−	12.1244i	−1.12734	−	0.650870i	−0.184075	−	0.982912i	$-0.558929\pi$
$347$	−21.0000	−	12.1244i	−1.12734	−	0.650870i	−0.943264	+	0.332043i	$0.892262\pi$
$348$		0			0
$349$	−7.00000			−0.374701			−0.187351	−	0.982293i	$-0.559990\pi$
$349$	−7.00000			−0.374701			−0.187351	+	0.982293i	$0.559990\pi$
$350$		0			0
$351$	13.5000	+	23.3827i	0.720577	+	1.24808i
$352$		0			0
$353$			10.3923i			0.553127i	0.960996	+	0.276563i	$0.0891955\pi$
$353$			10.3923i			0.553127i	−0.960996	+	0.276563i	$0.910804\pi$
$354$		0			0
$355$	18.0000	−	10.3923i	0.955341	−	0.551566i
$356$		0			0
$357$	3.00000	+	5.19615i	0.158777	+	0.275010i
$358$		0			0
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	−1.50000	−	0.866025i	−0.0787296	−	0.0454545i
$364$		0			0
$365$	21.0000	−	12.1244i	1.09919	−	0.634618i
$366$		0			0
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$		0			0
$369$	−36.0000			−1.87409
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$		−	6.92820i		−	0.358729i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$		−	6.92820i		−	0.358729i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$		0			0
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$		0			0
$377$	−27.0000	−	15.5885i	−1.39057	−	0.802846i
$378$		0			0
$379$		−	12.1244i		−	0.622786i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$		−	12.1244i		−	0.622786i	0.950281	−	0.311393i	$-0.100796\pi$
$380$		0			0
$381$	18.0000			0.922168
$382$		0			0
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$		0			0
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$		0			0
$387$	−3.00000			−0.152499
$388$		0			0
$389$	−24.0000	+	13.8564i	−1.21685	+	0.702548i	−0.964242	−	0.265022i	$-0.914621\pi$
$389$	−24.0000	+	13.8564i	−1.21685	+	0.702548i	−0.252606	+	0.967569i	$0.581288\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−3.00000	−	5.19615i	−0.151330	−	0.262111i
$394$		0			0
$395$	−9.00000	−	15.5885i	−0.452839	−	0.784340i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$		0			0
$399$	−4.50000	−	6.06218i	−0.225282	−	0.303488i
$400$		0			0
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$		0			0
$403$	4.50000	+	7.79423i	0.224161	+	0.388258i
$404$		0			0
$405$	−27.0000	+	15.5885i	−1.34164	+	0.774597i
$406$		0			0
$407$	18.0000			0.892227
$408$		0			0
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.483582	−	0.875299i	$-0.339335\pi$
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.999822	+	0.0188549i	$0.00600205\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.0000	+	31.1769i	−0.883585	+	1.53041i
$416$		0			0
$417$		−	8.66025i		−	0.424094i
$418$		0			0
$419$			10.3923i			0.507697i	0.967244	+	0.253849i	$0.0816965\pi$
$419$			10.3923i			0.507697i	−0.967244	+	0.253849i	$0.918303\pi$
$420$		0			0
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	0.763056	−	0.646332i	$-0.223698\pi$
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	−0.178212	+	0.983992i	$0.557031\pi$
$422$		0			0
$423$	−18.0000	−	10.3923i	−0.875190	−	0.505291i
$424$		0			0
$425$		−	24.2487i		−	1.17624i
$426$		0			0
$427$	3.50000	+	6.06218i	0.169377	+	0.293369i
$428$		0			0
$429$		−	31.1769i		−	1.50524i
$430$		0			0
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	−16.5000	+	9.52628i	−0.792939	+	0.457804i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	−16.5000	+	9.52628i	−0.792939	+	0.457804i	0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	18.0000	−	31.1769i	0.863034	−	1.49482i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	7.50000	+	4.33013i	0.357955	+	0.206666i	0.668184	−	0.743996i	$-0.267072\pi$
$439$	7.50000	+	4.33013i	0.357955	+	0.206666i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	−9.00000	−	15.5885i	−0.428571	−	0.742307i
$442$		0			0
$443$	21.0000	−	12.1244i	0.997740	−	0.576046i	0.0901612	−	0.995927i	$-0.471262\pi$
$443$	21.0000	−	12.1244i	0.997740	−	0.576046i	0.907579	+	0.419882i	$0.137928\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	15.0000	+	25.9808i	0.709476	+	1.22885i
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	36.0000	+	20.7846i	1.69517	+	0.978709i
$452$		0			0
$453$	3.00000	−	5.19615i	0.140952	−	0.244137i
$454$		0			0
$455$	−18.0000			−0.843853
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$		0			0
$459$	9.00000	−	15.5885i	0.420084	−	0.727607i
$460$		0			0
$461$	6.00000	+	3.46410i	0.279448	+	0.161339i	0.633173	−	0.774010i	$-0.281752\pi$
$461$	6.00000	+	3.46410i	0.279448	+	0.161339i	−0.353726	+	0.935349i	$0.615085\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$		0			0
$465$	−9.00000	+	5.19615i	−0.417365	+	0.240966i
$466$		0			0
$467$			27.7128i			1.28240i	0.767375	+	0.641198i	$0.221562\pi$
$467$			27.7128i			1.28240i	−0.767375	+	0.641198i	$0.778438\pi$
$468$		0			0
$469$	7.50000	−	4.33013i	0.346318	−	0.199947i
$470$		0			0
$471$	−10.5000	+	6.06218i	−0.483814	+	0.279330i
$472$		0			0
$473$	3.00000	+	1.73205i	0.137940	+	0.0796398i
$474$		0			0
$475$	3.50000	+	30.3109i	0.160591	+	1.39076i
$476$		0			0
$477$	18.0000	−	31.1769i	0.824163	−	1.42749i
$478$		0			0
$479$	−9.00000	+	5.19615i	−0.411220	+	0.237418i	−0.691314	−	0.722554i	$-0.742968\pi$
$479$	−9.00000	+	5.19615i	−0.411220	+	0.237418i	0.280094	+	0.959973i	$0.409635\pi$
$480$		0			0
$481$	13.5000	+	23.3827i	0.615547	+	1.06616i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	12.0000	+	20.7846i	0.544892	+	0.943781i
$486$		0			0
$487$		−	3.46410i		−	0.156973i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$		−	3.46410i		−	0.156973i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$		0			0
$489$	16.5000	+	9.52628i	0.746156	+	0.430793i
$490$		0			0
$491$	9.00000	+	5.19615i	0.406164	+	0.234499i	0.689140	−	0.724628i	$-0.257988\pi$
$491$	9.00000	+	5.19615i	0.406164	+	0.234499i	−0.282976	+	0.959127i	$0.591322\pi$
$492$		0			0
$493$			20.7846i			0.936092i
$494$		0			0
$495$	36.0000			1.61808
$496$		0			0
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$		0			0
$501$		−	20.7846i		−	0.928588i
$502$		0			0
$503$	27.0000	−	15.5885i	1.20387	−	0.695055i	0.242457	−	0.970162i	$-0.422047\pi$
$503$	27.0000	−	15.5885i	1.20387	−	0.695055i	0.961414	+	0.275107i	$0.0887134\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$	21.0000	−	12.1244i	0.932643	−	0.538462i
$508$		0			0
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	−3.50000	+	6.06218i	−0.154831	+	0.268175i
$512$		0			0
$513$	−9.00000	+	20.7846i	−0.397360	+	0.917663i
$514$		0			0
$515$	15.0000	−	25.9808i	0.660979	−	1.14485i
$516$		0			0
$517$	12.0000	+	20.7846i	0.527759	+	0.914106i
$518$		0			0
$519$	9.00000	−	5.19615i	0.395056	−	0.228086i
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	4.50000	−	2.59808i	0.196771	−	0.113606i	−0.398377	−	0.917222i	$-0.630427\pi$
$523$	4.50000	−	2.59808i	0.196771	−	0.113606i	0.595149	+	0.803616i	$0.297093\pi$
$524$		0			0
$525$		−	12.1244i		−	0.529150i
$526$		0			0
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$		0			0
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			62.3538i			2.70084i
$534$		0			0
$535$	54.0000	+	31.1769i	2.33462	+	1.34790i
$536$		0			0
$537$	−18.0000	−	10.3923i	−0.776757	−	0.448461i
$538$		0			0
$539$			20.7846i			0.895257i
$540$		0			0
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	0.971250	−	0.238062i	$-0.0765123\pi$
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	−0.691793	+	0.722096i	$0.743179\pi$
$542$		0			0
$543$	−12.0000			−0.514969
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−22.5000	+	12.9904i	−0.962031	+	0.555429i	−0.896797	−	0.442441i	$-0.854112\pi$
$547$	−22.5000	+	12.9904i	−0.962031	+	0.555429i	−0.0652331	+	0.997870i	$0.520779\pi$
$548$		0			0
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$		0			0
$551$	−3.00000	−	25.9808i	−0.127804	−	1.10682i
$552$		0			0
$553$	4.50000	+	2.59808i	0.191359	+	0.110481i
$554$		0			0
$555$	−27.0000	+	15.5885i	−1.14609	+	0.661693i
$556$		0			0
$557$	−3.00000	+	1.73205i	−0.127114	+	0.0733893i	−0.562209	−	0.826995i	$-0.690048\pi$
$557$	−3.00000	+	1.73205i	−0.127114	+	0.0733893i	0.435095	+	0.900385i	$0.356715\pi$
$558$		0			0
$559$			5.19615i			0.219774i
$560$		0			0
$561$	−18.0000	+	10.3923i	−0.759961	+	0.438763i
$562$		0			0
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$		0			0
$565$	−36.0000	−	20.7846i	−1.51453	−	0.874415i
$566$		0			0
$567$	4.50000	−	7.79423i	0.188982	−	0.327327i
$568$		0			0
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	−5.00000			−0.209243			−0.104622	−	0.994512i	$-0.533363\pi$
$571$	−5.00000			−0.209243			−0.104622	+	0.994512i	$0.533363\pi$
$572$		0			0
$573$	15.0000	−	25.9808i	0.626634	−	1.08536i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$		0			0
$579$	−10.5000	−	18.1865i	−0.436365	−	0.755807i
$580$		0			0
$581$		−	10.3923i		−	0.431145i
$582$		0			0
$583$	−36.0000	+	20.7846i	−1.49097	+	0.860811i
$584$		0			0
$585$	27.0000	+	46.7654i	1.11631	+	1.93351i
$586$		0			0
$587$	−6.00000	−	3.46410i	−0.247647	−	0.142979i	0.371040	−	0.928617i	$-0.379001\pi$
$587$	−6.00000	−	3.46410i	−0.247647	−	0.142979i	−0.618686	+	0.785638i	$0.712335\pi$
$588$		0			0
$589$	−3.00000	+	6.92820i	−0.123613	+	0.285472i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−36.0000	+	20.7846i	−1.47834	+	0.853522i	−0.999700	−	0.0244882i	$-0.992204\pi$
$593$	−36.0000	+	20.7846i	−1.47834	+	0.853522i	−0.478643	+	0.878010i	$0.658871\pi$
$594$		0			0
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$		0			0
$597$		−	43.3013i		−	1.77220i
$598$		0			0
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$			1.73205i			0.0706518i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$			1.73205i			0.0706518i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−22.5000	−	12.9904i	−0.916271	−	0.529009i
$604$		0			0
$605$	−3.00000	−	1.73205i	−0.121967	−	0.0704179i
$606$		0			0
$607$		−	32.9090i		−	1.33573i	−0.744281	−	0.667867i	$-0.767208\pi$
$607$		−	32.9090i		−	1.33573i	0.744281	−	0.667867i	$-0.232792\pi$
$608$		0			0
$609$			10.3923i			0.421117i
$610$		0			0
$611$	−18.0000	+	31.1769i	−0.728202	+	1.26128i
$612$		0			0
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	−0.171564	−	0.985173i	$-0.554882\pi$
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	0.938967	−	0.344008i	$-0.111785\pi$
$614$		0			0
$615$	−72.0000			−2.90332
$616$		0			0
$617$	33.0000	−	19.0526i	1.32853	−	0.767027i	0.343458	−	0.939168i	$-0.388402\pi$
$617$	33.0000	−	19.0526i	1.32853	−	0.767027i	0.985072	+	0.172141i	$0.0550685\pi$
$618$		0			0
$619$	17.0000			0.683288			0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000			0.683288			0.341644	+	0.939829i	$0.389016\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$		0			0
$627$	21.0000	−	15.5885i	0.838659	−	0.622543i
$628$		0			0
$629$	9.00000	−	15.5885i	0.358854	−	0.621552i
$630$		0			0
$631$	6.50000	+	11.2583i	0.258761	+	0.448187i	0.965910	−	0.258877i	$-0.0833525\pi$
$631$	6.50000	+	11.2583i	0.258761	+	0.448187i	−0.707149	+	0.707064i	$0.750019\pi$
$632$		0			0
$633$	19.5000	+	33.7750i	0.775055	+	1.34244i
$634$		0			0
$635$	36.0000			1.42862
$636$		0			0
$637$	−27.0000	+	15.5885i	−1.06978	+	0.617637i
$638$		0			0
$639$	18.0000			0.712069
$640$		0			0
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	−0.525584	−	0.850741i	$-0.676153\pi$
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	0.999556	+	0.0297987i	$0.00948663\pi$
$642$		0			0
$643$	2.50000	−	4.33013i	0.0985904	−	0.170764i	−0.812511	−	0.582946i	$-0.801900\pi$
$643$	2.50000	−	4.33013i	0.0985904	−	0.170764i	0.911101	+	0.412182i	$0.135233\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$			38.1051i			1.49807i	0.662532	+	0.749033i	$0.269482\pi$
$647$			38.1051i			1.49807i	−0.662532	+	0.749033i	$0.730518\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	1.50000	−	2.59808i	0.0587896	−	0.101827i
$652$		0			0
$653$			17.3205i			0.677804i	0.940822	+	0.338902i	$0.110055\pi$
$653$			17.3205i			0.677804i	−0.940822	+	0.338902i	$0.889945\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$		0			0
$657$	21.0000			0.819288
$658$		0			0
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	0.918523	−	0.395367i	$-0.129383\pi$
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	−0.801660	+	0.597781i	$0.796049\pi$
$660$		0			0
$661$	−12.0000	+	6.92820i	−0.466746	+	0.269476i	−0.714877	−	0.699251i	$-0.753517\pi$
$661$	−12.0000	+	6.92820i	−0.466746	+	0.269476i	0.248131	+	0.968727i	$0.420184\pi$
$662$		0			0
$663$	−27.0000	−	15.5885i	−1.04859	−	0.605406i
$664$		0			0
$665$	−9.00000	−	12.1244i	−0.349005	−	0.470162i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−16.5000	−	28.5788i	−0.637927	−	1.10492i
$670$		0			0
$671$	−21.0000	+	12.1244i	−0.810696	+	0.468056i
$672$		0			0
$673$		−	12.1244i		−	0.467360i	−0.972314	−	0.233680i	$-0.924923\pi$
$673$		−	12.1244i		−	0.467360i	0.972314	−	0.233680i	$-0.0750767\pi$
$674$		0			0
$675$	−31.5000	+	18.1865i	−1.21244	+	0.700000i
$676$		0			0
$677$	−36.0000			−1.38359			−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000			−1.38359			−0.691796	+	0.722093i	$0.743180\pi$
$678$		0			0
$679$	−6.00000	−	3.46410i	−0.230259	−	0.132940i
$680$		0			0
$681$	−27.0000	−	15.5885i	−1.03464	−	0.597351i
$682$		0			0
$683$	30.0000			1.14792			0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000			1.14792			0.573959	+	0.818884i	$0.305407\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	19.5000	+	11.2583i	0.743971	+	0.429532i
$688$		0			0
$689$	−54.0000	−	31.1769i	−2.05724	−	1.18775i
$690$		0			0
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$		0			0
$693$	−9.00000	+	5.19615i	−0.341882	+	0.197386i
$694$		0			0
$695$		−	17.3205i		−	0.657004i
$696$		0			0
$697$	36.0000	−	20.7846i	1.36360	−	0.787273i
$698$		0			0
$699$	15.0000	+	25.9808i	0.567352	+	0.982683i
$700$		0			0
$701$	−9.00000	−	5.19615i	−0.339925	−	0.196256i	0.320314	−	0.947312i	$-0.396212\pi$
$701$	−9.00000	−	5.19615i	−0.339925	−	0.196256i	−0.660239	+	0.751056i	$0.729545\pi$
$702$		0			0
$703$	−9.00000	+	20.7846i	−0.339441	+	0.783906i
$704$		0			0
$705$	−36.0000	−	20.7846i	−1.35584	−	0.782794i
$706$		0			0
$707$	−9.00000	+	5.19615i	−0.338480	+	0.195421i
$708$		0			0
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	0.961882	−	0.273466i	$-0.0881700\pi$
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	−0.717769	+	0.696281i	$0.754837\pi$
$710$		0			0
$711$		−	15.5885i		−	0.584613i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		−	62.3538i		−	2.33190i
$716$		0			0
$717$	−21.0000	+	36.3731i	−0.784259	+	1.35838i
$718$		0			0
$719$	−24.0000	−	13.8564i	−0.895049	−	0.516757i	−0.0194584	−	0.999811i	$-0.506194\pi$
$719$	−24.0000	−	13.8564i	−0.895049	−	0.516757i	−0.875591	+	0.483054i	$0.839528\pi$
$720$		0			0
$721$			8.66025i			0.322525i
$722$		0			0
$723$	−3.00000			−0.111571
$724$		0			0
$725$	21.0000	−	36.3731i	0.779920	−	1.35086i
$726$		0			0
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	0.286954	+	0.957944i	$0.407357\pi$
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	−0.973081	+	0.230463i	$0.925976\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	3.00000	−	1.73205i	0.110959	−	0.0640622i
$732$		0			0
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$		0			0
$735$	−18.0000	−	31.1769i	−0.663940	−	1.14998i
$736$		0			0
$737$	15.0000	+	25.9808i	0.552532	+	0.957014i
$738$		0			0
$739$	12.5000	−	21.6506i	0.459820	−	0.796431i	−0.539131	−	0.842222i	$-0.681247\pi$
$739$	12.5000	−	21.6506i	0.459820	−	0.796431i	0.998951	+	0.0457903i	$0.0145806\pi$
$740$		0			0
$741$	36.0000	+	15.5885i	1.32249	+	0.572656i
$742$		0			0
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		0			0
$745$	30.0000	+	51.9615i	1.09911	+	1.90372i
$746$		0			0
$747$	−27.0000	+	15.5885i	−0.987878	+	0.570352i
$748$		0			0
$749$	−18.0000			−0.657706
$750$		0			0
$751$	−31.5000	+	18.1865i	−1.14945	+	0.663636i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−31.5000	+	18.1865i	−1.14945	+	0.663636i	−0.200698	+	0.979653i	$0.564321\pi$
$752$		0			0
$753$	12.0000			0.437304
$754$		0			0
$755$	6.00000	−	10.3923i	0.218362	−	0.378215i
$756$		0			0
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	27.7128i		−	1.00459i	−0.864697	−	0.502294i	$-0.832489\pi$
$761$		−	27.7128i		−	1.00459i	0.864697	−	0.502294i	$-0.167511\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	18.0000	−	31.1769i	0.650791	−	1.12720i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−18.5000	−	32.0429i	−0.667127	−	1.15550i	−0.978704	−	0.205277i	$-0.934190\pi$
$769$	−18.5000	−	32.0429i	−0.667127	−	1.15550i	0.311577	−	0.950221i	$-0.399143\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	0.565402	−	0.824815i	$-0.308721\pi$
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	−0.997012	+	0.0772449i	$0.975388\pi$
$774$		0			0
$775$	−10.5000	+	6.06218i	−0.377171	+	0.217760i
$776$		0			0
$777$	4.50000	−	7.79423i	0.161437	−	0.279616i
$778$		0			0
$779$	−42.0000	+	31.1769i	−1.50481	+	1.11703i
$780$		0			0
$781$	−18.0000	−	10.3923i	−0.644091	−	0.371866i
$782$		0			0
$783$	27.0000	−	15.5885i	0.964901	−	0.557086i
$784$		0			0
$785$	−21.0000	+	12.1244i	−0.749522	+	0.432737i
$786$		0			0
$787$			25.9808i			0.926114i	0.886328	+	0.463057i	$0.153248\pi$
$787$			25.9808i			0.926114i	−0.886328	+	0.463057i	$0.846752\pi$
$788$		0			0
$789$	21.0000	+	36.3731i	0.747620	+	1.29492i
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$	−31.5000	−	18.1865i	−1.11860	−	0.645823i
$794$		0			0
$795$	36.0000	−	62.3538i	1.27679	−	2.21146i
$796$		0			0
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−21.0000	−	12.1244i	−0.741074	−	0.427859i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			3.46410i			0.121791i	0.998144	+	0.0608957i	$0.0193957\pi$
$809$			3.46410i			0.121791i	−0.998144	+	0.0608957i	$0.980604\pi$
$810$		0			0
$811$	27.0000	−	15.5885i	0.948098	−	0.547385i	0.0556086	−	0.998453i	$-0.482290\pi$
$811$	27.0000	−	15.5885i	0.948098	−	0.547385i	0.892490	+	0.451068i	$0.148957\pi$
$812$		0			0
$813$	12.0000	−	6.92820i	0.420858	−	0.242983i
$814$		0			0
$815$	33.0000	+	19.0526i	1.15594	+	0.667382i
$816$		0			0
$817$	−3.50000	+	2.59808i	−0.122449	+	0.0908952i
$818$		0			0
$819$	−13.5000	−	7.79423i	−0.471728	−	0.272352i
$820$		0			0
$821$	−21.0000	+	12.1244i	−0.732905	+	0.423143i	−0.819484	−	0.573102i	$-0.805740\pi$
$821$	−21.0000	+	12.1244i	−0.732905	+	0.423143i	0.0865789	+	0.996245i	$0.472407\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$	42.0000			1.46225
$826$		0			0
$827$	3.00000	+	5.19615i	0.104320	+	0.180688i	0.913460	−	0.406928i	$-0.133400\pi$
$827$	3.00000	+	5.19615i	0.104320	+	0.180688i	−0.809140	+	0.587616i	$0.800067\pi$
$828$		0			0
$829$		−	50.2295i		−	1.74454i	−0.489023	−	0.872271i	$-0.662647\pi$
$829$		−	50.2295i		−	1.74454i	0.489023	−	0.872271i	$-0.337353\pi$
$830$		0			0
$831$	−3.00000	−	1.73205i	−0.104069	−	0.0600842i
$832$		0			0
$833$	18.0000	+	10.3923i	0.623663	+	0.360072i
$834$		0			0
$835$		−	41.5692i		−	1.43856i
$836$		0			0
$837$	−9.00000			−0.311086
$838$		0			0
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$		−	10.3923i		−	0.357930i
$844$		0			0
$845$	42.0000	−	24.2487i	1.44484	−	0.834181i
$846$		0			0
$847$	1.00000			0.0343604
$848$		0			0
$849$	−42.0000	+	24.2487i	−1.44144	+	0.832214i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−2.50000	+	4.33013i	−0.0855984	+	0.148261i	−0.905646	−	0.424034i	$-0.860614\pi$
$853$	−2.50000	+	4.33013i	−0.0855984	+	0.148261i	0.820048	+	0.572295i	$0.193947\pi$
$854$		0			0
$855$	−18.0000	+	41.5692i	−0.615587	+	1.42164i
$856$		0			0
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	−0.993248	−	0.116011i	$-0.962989\pi$
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	0.396156	−	0.918183i	$-0.370344\pi$
$860$		0			0
$861$	18.0000	−	10.3923i	0.613438	−	0.354169i
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	18.0000	−	10.3923i	0.612018	−	0.353349i
$866$		0			0
$867$		−	8.66025i		−	0.294118i
$868$		0			0
$869$	−9.00000	+	15.5885i	−0.305304	+	0.528802i
$870$		0			0
$871$	−22.5000	+	38.9711i	−0.762383	+	1.32049i
$872$		0			0
$873$			20.7846i			0.703452i
$874$		0			0
$875$		−	6.92820i		−	0.234216i
$876$		0			0
$877$	4.50000	+	2.59808i	0.151954	+	0.0877308i	0.574049	−	0.818821i	$-0.305372\pi$
$877$	4.50000	+	2.59808i	0.151954	+	0.0877308i	−0.422095	+	0.906552i	$0.638705\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			38.1051i			1.28379i	0.766791	+	0.641897i	$0.221852\pi$
$881$			38.1051i			1.28379i	−0.766791	+	0.641897i	$0.778148\pi$
$882$		0			0
$883$	6.50000	+	11.2583i	0.218742	+	0.378873i	0.954424	−	0.298455i	$-0.0964712\pi$
$883$	6.50000	+	11.2583i	0.218742	+	0.378873i	−0.735681	+	0.677328i	$0.763138\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$	−9.00000	+	5.19615i	−0.301850	+	0.174273i
$890$		0			0
$891$	27.0000	+	15.5885i	0.904534	+	0.522233i
$892$		0			0
$893$	−30.0000	+	3.46410i	−1.00391	+	0.115922i
$894$		0			0
$895$	−36.0000	−	20.7846i	−1.20335	−	0.694753i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.00000	−	5.19615i	0.300167	−	0.173301i
$900$		0			0
$901$			41.5692i			1.38487i
$902$		0			0
$903$	1.50000	−	0.866025i	0.0499169	−	0.0288195i
$904$		0			0
$905$	−24.0000			−0.797787
$906$		0			0
$907$	−21.0000	−	12.1244i	−0.697294	−	0.402583i	0.109045	−	0.994037i	$-0.465221\pi$
$907$	−21.0000	−	12.1244i	−0.697294	−	0.402583i	−0.806339	+	0.591454i	$0.798554\pi$
$908$		0			0
$909$	27.0000	+	15.5885i	0.895533	+	0.517036i
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$		0			0
$915$	21.0000	−	36.3731i	0.694239	−	1.20246i
$916$		0			0
$917$	3.00000	+	1.73205i	0.0990687	+	0.0571974i
$918$		0			0
$919$	53.0000			1.74831			0.874154	−	0.485648i	$-0.161416\pi$
$919$	53.0000			1.74831			0.874154	+	0.485648i	$0.161416\pi$
$920$		0			0
$921$	−27.0000	−	46.7654i	−0.889680	−	1.54097i
$922$		0			0
$923$		−	31.1769i		−	1.02620i
$924$		0			0
$925$	−31.5000	+	18.1865i	−1.03571	+	0.597970i
$926$		0			0
$927$	22.5000	−	12.9904i	0.738997	−	0.426660i
$928$		0			0
$929$	45.0000	+	25.9808i	1.47640	+	0.852401i	0.999645	−	0.0266341i	$-0.00847889\pi$
$929$	45.0000	+	25.9808i	1.47640	+	0.852401i	0.476757	+	0.879035i	$0.341812\pi$
$930$		0			0
$931$	−24.0000	−	10.3923i	−0.786568	−	0.340594i
$932$		0			0
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$		0			0
$935$	−36.0000	+	20.7846i	−1.17733	+	0.679729i
$936$		0			0
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$		0			0
$939$			24.2487i			0.791327i
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	9.00000	−	15.5885i	0.292770	−	0.507093i
$946$		0			0
$947$	27.0000	+	15.5885i	0.877382	+	0.506557i	0.869794	−	0.493414i	$-0.164251\pi$
$947$	27.0000	+	15.5885i	0.877382	+	0.506557i	0.00758776	+	0.999971i	$0.497585\pi$
$948$		0			0
$949$		−	36.3731i		−	1.18072i
$950$		0			0
$951$			10.3923i			0.336994i
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$		0			0
$955$	30.0000	−	51.9615i	0.970777	−	1.68144i
$956$		0			0
$957$	−36.0000			−1.16371
$958$		0			0
$959$	3.00000	−	1.73205i	0.0968751	−	0.0559308i
$960$		0			0
$961$	28.0000			0.903226
$962$		0			0
$963$	27.0000	+	46.7654i	0.870063	+	1.50699i
$964$		0			0
$965$	−21.0000	−	36.3731i	−0.676014	−	1.17089i
$966$		0			0
$967$	−14.5000	+	25.1147i	−0.466289	+	0.807635i	−0.999259	−	0.0384986i	$-0.987742\pi$
$967$	−14.5000	+	25.1147i	−0.466289	+	0.807635i	0.532970	+	0.846134i	$0.321076\pi$
$968$		0			0
$969$	−3.00000	−	25.9808i	−0.0963739	−	0.834622i
$970$		0			0
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	0.167258	+	0.985913i	$0.446509\pi$
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	−0.937455	+	0.348107i	$0.886825\pi$
$972$		0			0
$973$	2.50000	+	4.33013i	0.0801463	+	0.138817i
$974$		0			0
$975$	31.5000	+	54.5596i	1.00881	+	1.74731i
$976$		0			0
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	0.308165	+	0.951333i	$0.400285\pi$
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	−0.977961	+	0.208788i	$0.933048\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.0000			0.381964
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−31.5000	−	18.1865i	−1.00063	−	0.577714i	−0.0921957	−	0.995741i	$-0.529389\pi$
$991$	−31.5000	−	18.1865i	−1.00063	−	0.577714i	−0.908435	+	0.418027i	$0.862722\pi$
$992$		0			0
$993$	4.50000	−	7.79423i	0.142803	−	0.247342i
$994$		0			0
$995$		−	86.6025i		−	2.74549i
$996$		0			0
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	0.890511	+	0.454961i	$0.150347\pi$
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	−0.0512480	+	0.998686i	$0.516320\pi$
$998$		0			0
$999$	−27.0000			−0.854242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.f.65.1		2
3.2	odd	2		912.2.bn.c.65.1		2
4.3	odd	2		114.2.h.b.65.1	✓	2
12.11	even	2		114.2.h.c.65.1	yes	2
19.12	odd	6		912.2.bn.c.449.1		2
57.50	even	6	inner	912.2.bn.f.449.1		2
76.31	even	6		114.2.h.c.107.1	yes	2
228.107	odd	6		114.2.h.b.107.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.b.65.1	✓	2	4.3	odd	2
114.2.h.b.107.1	yes	2	228.107	odd	6
114.2.h.c.65.1	yes	2	12.11	even	2
114.2.h.c.107.1	yes	2	76.31	even	6
912.2.bn.c.65.1		2	3.2	odd	2
912.2.bn.c.449.1		2	19.12	odd	6
912.2.bn.f.65.1		2	1.1	even	1	trivial
912.2.bn.f.449.1		2	57.50	even	6	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(3.00000 + 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(3.00000 + 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} -3.46410i q^{11} +(4.50000 - 2.59808i) q^{13} +(3.00000 + 5.19615i) q^{15} +(-3.00000 - 1.73205i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.50000 - 0.866025i) q^{21} +(3.50000 + 6.06218i) q^{25} +5.19615i q^{27} +(-3.00000 - 5.19615i) q^{29} +1.73205i q^{31} +(3.00000 - 5.19615i) q^{33} +(-3.00000 - 1.73205i) q^{35} +5.19615i q^{37} +9.00000 q^{39} +(-6.00000 + 10.3923i) q^{41} +(-0.500000 + 0.866025i) q^{43} +10.3923i q^{45} +(-6.00000 + 3.46410i) q^{47} -6.00000 q^{49} +(-3.00000 - 5.19615i) q^{51} +(-6.00000 - 10.3923i) q^{53} +(6.00000 - 10.3923i) q^{55} +(4.50000 + 6.06218i) q^{57} +(-3.50000 - 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{63} +18.0000 q^{65} +(-7.50000 + 4.33013i) q^{67} +(3.00000 - 5.19615i) q^{71} +(3.50000 - 6.06218i) q^{73} +12.1244i q^{75} +3.46410i q^{77} +(-4.50000 - 2.59808i) q^{79} +(-4.50000 + 7.79423i) q^{81} +10.3923i q^{83} +(-6.00000 - 10.3923i) q^{85} -10.3923i q^{87} +(-4.50000 + 2.59808i) q^{91} +(-1.50000 + 2.59808i) q^{93} +(9.00000 + 12.1244i) q^{95} +(6.00000 + 3.46410i) q^{97} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 6 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 6 * q^5 - 2 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} + 6 q^{5} - 2 q^{7} + 3 q^{9} + 9 q^{13} + 6 q^{15} - 6 q^{17} + 8 q^{19} - 3 q^{21} + 7 q^{25} - 6 q^{29} + 6 q^{33} - 6 q^{35} + 18 q^{39} - 12 q^{41} - q^{43} - 12 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 12 q^{55} + 9 q^{57} - 7 q^{61} - 3 q^{63} + 36 q^{65} - 15 q^{67} + 6 q^{71} + 7 q^{73} - 9 q^{79} - 9 q^{81} - 12 q^{85} - 9 q^{91} - 3 q^{93} + 18 q^{95} + 12 q^{97} + 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 6 * q^5 - 2 * q^7 + 3 * q^9 + 9 * q^13 + 6 * q^15 - 6 * q^17 + 8 * q^19 - 3 * q^21 + 7 * q^25 - 6 * q^29 + 6 * q^33 - 6 * q^35 + 18 * q^39 - 12 * q^41 - q^43 - 12 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 12 * q^55 + 9 * q^57 - 7 * q^61 - 3 * q^63 + 36 * q^65 - 15 * q^67 + 6 * q^71 + 7 * q^73 - 9 * q^79 - 9 * q^81 - 12 * q^85 - 9 * q^91 - 3 * q^93 + 18 * q^95 + 12 * q^97 + 18 * q^99

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