LMFDB - Embedded newform 936.2.g.b.469.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	936.469
Dual form			936.2.g.b.469.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +3.46410i q^{5} -4.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.26795 - 4.73205i) q^{10} +1.26795i q^{11} +1.00000i q^{13} +(6.46410 + 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +1.46410 q^{17} -2.73205i q^{19} +(-3.46410 + 6.00000i) q^{20} +(0.464102 - 1.73205i) q^{22} -4.00000 q^{23} -7.00000 q^{25} +(0.366025 - 1.36603i) q^{26} +(-8.19615 - 4.73205i) q^{28} -2.00000i q^{29} -3.26795 q^{31} +(-1.46410 - 5.46410i) q^{32} +(-2.00000 - 0.535898i) q^{34} -16.3923i q^{35} +4.92820i q^{37} +(-1.00000 + 3.73205i) q^{38} +(6.92820 - 6.92820i) q^{40} +4.92820 q^{41} -7.46410i q^{43} +(-1.26795 + 2.19615i) q^{44} +(5.46410 + 1.46410i) q^{46} -3.26795 q^{47} +15.3923 q^{49} +(9.56218 + 2.56218i) q^{50} +(-1.00000 + 1.73205i) q^{52} -10.9282i q^{53} -4.39230 q^{55} +(9.46410 + 9.46410i) q^{56} +(-0.732051 + 2.73205i) q^{58} -0.196152i q^{59} -10.9282i q^{61} +(4.46410 + 1.19615i) q^{62} +8.00000i q^{64} -3.46410 q^{65} -2.73205i q^{67} +(2.53590 + 1.46410i) q^{68} +(-6.00000 + 22.3923i) q^{70} -2.19615 q^{71} -0.535898 q^{73} +(1.80385 - 6.73205i) q^{74} +(2.73205 - 4.73205i) q^{76} -6.00000i q^{77} -1.46410 q^{79} +(-12.0000 + 6.92820i) q^{80} +(-6.73205 - 1.80385i) q^{82} -6.73205i q^{83} +5.07180i q^{85} +(-2.73205 + 10.1962i) q^{86} +(2.53590 - 2.53590i) q^{88} -17.3205 q^{89} -4.73205i q^{91} +(-6.92820 - 4.00000i) q^{92} +(4.46410 + 1.19615i) q^{94} +9.46410 q^{95} -14.3923 q^{97} +(-21.0263 - 5.63397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 12 q^{7} - 8 q^{8} + 12 q^{10} + 12 q^{14} + 8 q^{16} - 8 q^{17} - 12 q^{22} - 16 q^{23} - 28 q^{25} - 2 q^{26} - 12 q^{28} - 20 q^{31} + 8 q^{32} - 8 q^{34} - 4 q^{38} - 8 q^{41} - 12 q^{44}+ \cdots - 46 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 12 * q^7 - 8 * q^8 + 12 * q^10 + 12 * q^14 + 8 * q^16 - 8 * q^17 - 12 * q^22 - 16 * q^23 - 28 * q^25 - 2 * q^26 - 12 * q^28 - 20 * q^31 + 8 * q^32 - 8 * q^34 - 4 * q^38 - 8 * q^41 - 12 * q^44 + 8 * q^46 - 20 * q^47 + 20 * q^49 + 14 * q^50 - 4 * q^52 + 24 * q^55 + 24 * q^56 + 4 * q^58 + 4 * q^62 + 24 * q^68 - 24 * q^70 + 12 * q^71 - 16 * q^73 + 28 * q^74 + 4 * q^76 + 8 * q^79 - 48 * q^80 - 20 * q^82 - 4 * q^86 + 24 * q^88 + 4 * q^94 + 24 * q^95 - 16 * q^97 - 46 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$			3.46410i			1.54919i	0.632456	+	0.774597i	$0.282047\pi$
$5$			3.46410i			1.54919i	−0.632456	+	0.774597i	$0.717953\pi$
$6$		0			0
$7$	−4.73205			−1.78855			−0.894274	−	0.447521i	$-0.852307\pi$
$7$	−4.73205			−1.78855			−0.894274	+	0.447521i	$0.852307\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	1.26795	−	4.73205i	0.400961	−	1.49641i
$11$			1.26795i			0.382301i	0.981561	+	0.191151i	$0.0612219\pi$
$11$			1.26795i			0.382301i	−0.981561	+	0.191151i	$0.938778\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	6.46410	+	1.73205i	1.72760	+	0.462910i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.46410			0.355097			0.177548	−	0.984112i	$-0.443183\pi$
$17$	1.46410			0.355097			0.177548	+	0.984112i	$0.443183\pi$
$18$		0			0
$19$		−	2.73205i		−	0.626775i	−0.949625	−	0.313388i	$-0.898536\pi$
$19$		−	2.73205i		−	0.626775i	0.949625	−	0.313388i	$-0.101464\pi$
$20$	−3.46410	+	6.00000i	−0.774597	+	1.34164i
$21$		0			0
$22$	0.464102	−	1.73205i	0.0989468	−	0.369274i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	−7.00000			−1.40000
$26$	0.366025	−	1.36603i	0.0717835	−	0.267900i
$27$		0			0
$28$	−8.19615	−	4.73205i	−1.54893	−	0.894274i
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	−3.26795			−0.586941			−0.293471	−	0.955968i	$-0.594810\pi$
$31$	−3.26795			−0.586941			−0.293471	+	0.955968i	$0.594810\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$	−2.00000	−	0.535898i	−0.342997	−	0.0919058i
$35$		−	16.3923i		−	2.77081i
$36$		0			0
$37$			4.92820i			0.810192i	0.914274	+	0.405096i	$0.132762\pi$
$37$			4.92820i			0.810192i	−0.914274	+	0.405096i	$0.867238\pi$
$38$	−1.00000	+	3.73205i	−0.162221	+	0.605419i
$39$		0			0
$40$	6.92820	−	6.92820i	1.09545	−	1.09545i
$41$	4.92820			0.769656			0.384828	−	0.922988i	$-0.374261\pi$
$41$	4.92820			0.769656			0.384828	+	0.922988i	$0.374261\pi$
$42$		0			0
$43$		−	7.46410i		−	1.13826i	−0.822246	−	0.569132i	$-0.807279\pi$
$43$		−	7.46410i		−	1.13826i	0.822246	−	0.569132i	$-0.192721\pi$
$44$	−1.26795	+	2.19615i	−0.191151	+	0.331082i
$45$		0			0
$46$	5.46410	+	1.46410i	0.805638	+	0.215870i
$47$	−3.26795			−0.476679			−0.238340	−	0.971182i	$-0.576603\pi$
$47$	−3.26795			−0.476679			−0.238340	+	0.971182i	$0.576603\pi$
$48$		0			0
$49$	15.3923			2.19890
$50$	9.56218	+	2.56218i	1.35230	+	0.362347i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$		−	10.9282i		−	1.50110i	−0.660811	−	0.750552i	$-0.729788\pi$
$53$		−	10.9282i		−	1.50110i	0.660811	−	0.750552i	$-0.270212\pi$
$54$		0			0
$55$	−4.39230			−0.592258
$56$	9.46410	+	9.46410i	1.26469	+	1.26469i
$57$		0			0
$58$	−0.732051	+	2.73205i	−0.0961230	+	0.358736i
$59$		−	0.196152i		−	0.0255369i	−0.999918	−	0.0127684i	$-0.995936\pi$
$59$		−	0.196152i		−	0.0255369i	0.999918	−	0.0127684i	$-0.00406443\pi$
$60$		0			0
$61$		−	10.9282i		−	1.39921i	−0.714528	−	0.699607i	$-0.753359\pi$
$61$		−	10.9282i		−	1.39921i	0.714528	−	0.699607i	$-0.246641\pi$
$62$	4.46410	+	1.19615i	0.566941	+	0.151912i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−3.46410			−0.429669
$66$		0			0
$67$		−	2.73205i		−	0.333773i	−0.985976	−	0.166887i	$-0.946629\pi$
$67$		−	2.73205i		−	0.333773i	0.985976	−	0.166887i	$-0.0533714\pi$
$68$	2.53590	+	1.46410i	0.307523	+	0.177548i
$69$		0			0
$70$	−6.00000	+	22.3923i	−0.717137	+	2.67639i
$71$	−2.19615			−0.260635			−0.130318	−	0.991472i	$-0.541600\pi$
$71$	−2.19615			−0.260635			−0.130318	+	0.991472i	$0.541600\pi$
$72$		0			0
$73$	−0.535898			−0.0627222			−0.0313611	−	0.999508i	$-0.509984\pi$
$73$	−0.535898			−0.0627222			−0.0313611	+	0.999508i	$0.509984\pi$
$74$	1.80385	−	6.73205i	0.209693	−	0.782585i
$75$		0			0
$76$	2.73205	−	4.73205i	0.313388	−	0.542803i
$77$		−	6.00000i		−	0.683763i
$78$		0			0
$79$	−1.46410			−0.164724			−0.0823622	−	0.996602i	$-0.526246\pi$
$79$	−1.46410			−0.164724			−0.0823622	+	0.996602i	$0.526246\pi$
$80$	−12.0000	+	6.92820i	−1.34164	+	0.774597i
$81$		0			0
$82$	−6.73205	−	1.80385i	−0.743431	−	0.199202i
$83$		−	6.73205i		−	0.738939i	−0.929243	−	0.369469i	$-0.879539\pi$
$83$		−	6.73205i		−	0.738939i	0.929243	−	0.369469i	$-0.120461\pi$
$84$		0			0
$85$			5.07180i			0.550114i
$86$	−2.73205	+	10.1962i	−0.294605	+	1.09948i
$87$		0			0
$88$	2.53590	−	2.53590i	0.270328	−	0.270328i
$89$	−17.3205			−1.83597			−0.917985	−	0.396615i	$-0.870185\pi$
$89$	−17.3205			−1.83597			−0.917985	+	0.396615i	$0.870185\pi$
$90$		0			0
$91$		−	4.73205i		−	0.496054i
$92$	−6.92820	−	4.00000i	−0.722315	−	0.417029i
$93$		0			0
$94$	4.46410	+	1.19615i	0.460437	+	0.123374i
$95$	9.46410			0.970996
$96$		0			0
$97$	−14.3923			−1.46132			−0.730659	−	0.682743i	$-0.760787\pi$
$97$	−14.3923			−1.46132			−0.730659	+	0.682743i	$0.760787\pi$
$98$	−21.0263	−	5.63397i	−2.12397	−	0.569117i
$99$		0			0
$100$	−12.1244	−	7.00000i	−1.21244	−	0.700000i
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$		0			0
$103$	−6.92820			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$104$	2.00000	−	2.00000i	0.196116	−	0.196116i
$105$		0			0
$106$	−4.00000	+	14.9282i	−0.388514	+	1.44996i
$107$			8.92820i			0.863122i	0.902084	+	0.431561i	$0.142037\pi$
$107$			8.92820i			0.863122i	−0.902084	+	0.431561i	$0.857963\pi$
$108$		0			0
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	6.00000	+	1.60770i	0.572078	+	0.153288i
$111$		0			0
$112$	−9.46410	−	16.3923i	−0.894274	−	1.54893i
$113$	−9.46410			−0.890308			−0.445154	−	0.895454i	$-0.646851\pi$
$113$	−9.46410			−0.890308			−0.445154	+	0.895454i	$0.646851\pi$
$114$		0			0
$115$		−	13.8564i		−	1.29212i
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$		0			0
$118$	−0.0717968	+	0.267949i	−0.00660943	+	0.0246667i
$119$	−6.92820			−0.635107
$120$		0			0
$121$	9.39230			0.853846
$122$	−4.00000	+	14.9282i	−0.362143	+	1.35154i
$123$		0			0
$124$	−5.66025	−	3.26795i	−0.508306	−	0.293471i
$125$		−	6.92820i		−	0.619677i
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	4.73205	+	1.26795i	0.415028	+	0.111207i
$131$			7.85641i			0.686417i	0.939259	+	0.343209i	$0.111514\pi$
$131$			7.85641i			0.686417i	−0.939259	+	0.343209i	$0.888486\pi$
$132$		0			0
$133$			12.9282i			1.12102i
$134$	−1.00000	+	3.73205i	−0.0863868	+	0.322400i
$135$		0			0
$136$	−2.92820	−	2.92820i	−0.251091	−	0.251091i
$137$	0.928203			0.0793018			0.0396509	−	0.999214i	$-0.487375\pi$
$137$	0.928203			0.0793018			0.0396509	+	0.999214i	$0.487375\pi$
$138$		0			0
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$	16.3923	−	28.3923i	1.38540	−	2.39959i
$141$		0			0
$142$	3.00000	+	0.803848i	0.251754	+	0.0674574i
$143$	−1.26795			−0.106031
$144$		0			0
$145$	6.92820			0.575356
$146$	0.732051	+	0.196152i	0.0605850	+	0.0162337i
$147$		0			0
$148$	−4.92820	+	8.53590i	−0.405096	+	0.701647i
$149$		−	0.928203i		−	0.0760414i	−0.999277	−	0.0380207i	$-0.987895\pi$
$149$		−	0.928203i		−	0.0760414i	0.999277	−	0.0380207i	$-0.0121053\pi$
$150$		0			0
$151$	17.1244			1.39356			0.696780	−	0.717285i	$-0.254615\pi$
$151$	17.1244			1.39356			0.696780	+	0.717285i	$0.254615\pi$
$152$	−5.46410	+	5.46410i	−0.443197	+	0.443197i
$153$		0			0
$154$	−2.19615	+	8.19615i	−0.176971	+	0.660465i
$155$		−	11.3205i		−	0.909285i
$156$		0			0
$157$		−	3.07180i		−	0.245156i	−0.992459	−	0.122578i	$-0.960884\pi$
$157$		−	3.07180i		−	0.245156i	0.992459	−	0.122578i	$-0.0391162\pi$
$158$	2.00000	+	0.535898i	0.159111	+	0.0426338i
$159$		0			0
$160$	18.9282	−	5.07180i	1.49641	−	0.400961i
$161$	18.9282			1.49175
$162$		0			0
$163$			13.2679i			1.03923i	0.854402	+	0.519613i	$0.173924\pi$
$163$			13.2679i			1.03923i	−0.854402	+	0.519613i	$0.826076\pi$
$164$	8.53590	+	4.92820i	0.666542	+	0.384828i
$165$		0			0
$166$	−2.46410	+	9.19615i	−0.191251	+	0.713760i
$167$	−11.6603			−0.902298			−0.451149	−	0.892449i	$-0.648986\pi$
$167$	−11.6603			−0.902298			−0.451149	+	0.892449i	$0.648986\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	1.85641	−	6.92820i	0.142380	−	0.531369i
$171$		0			0
$172$	7.46410	−	12.9282i	0.569132	−	0.985766i
$173$			6.92820i			0.526742i	0.964695	+	0.263371i	$0.0848343\pi$
$173$			6.92820i			0.526742i	−0.964695	+	0.263371i	$0.915166\pi$
$174$		0			0
$175$	33.1244			2.50397
$176$	−4.39230	+	2.53590i	−0.331082	+	0.191151i
$177$		0			0
$178$	23.6603	+	6.33975i	1.77341	+	0.475184i
$179$		−	10.3923i		−	0.776757i	−0.921500	−	0.388379i	$-0.873035\pi$
$179$		−	10.3923i		−	0.776757i	0.921500	−	0.388379i	$-0.126965\pi$
$180$		0			0
$181$			4.92820i			0.366310i	0.983084	+	0.183155i	$0.0586311\pi$
$181$			4.92820i			0.366310i	−0.983084	+	0.183155i	$0.941369\pi$
$182$	−1.73205	+	6.46410i	−0.128388	+	0.479151i
$183$		0			0
$184$	8.00000	+	8.00000i	0.589768	+	0.589768i
$185$	−17.0718			−1.25514
$186$		0			0
$187$			1.85641i			0.135754i
$188$	−5.66025	−	3.26795i	−0.412816	−	0.238340i
$189$		0			0
$190$	−12.9282	−	3.46410i	−0.937910	−	0.251312i
$191$	21.4641			1.55309			0.776544	−	0.630063i	$-0.216971\pi$
$191$	21.4641			1.55309			0.776544	+	0.630063i	$0.216971\pi$
$192$		0			0
$193$	−22.3923			−1.61183			−0.805917	−	0.592029i	$-0.798327\pi$
$193$	−22.3923			−1.61183			−0.805917	+	0.592029i	$0.798327\pi$
$194$	19.6603	+	5.26795i	1.41152	+	0.378217i
$195$		0			0
$196$	26.6603	+	15.3923i	1.90430	+	1.09945i
$197$			16.9282i			1.20608i	0.797709	+	0.603042i	$0.206045\pi$
$197$			16.9282i			1.20608i	−0.797709	+	0.603042i	$0.793955\pi$
$198$		0			0
$199$	−24.7846			−1.75693			−0.878467	−	0.477803i	$-0.841433\pi$
$199$	−24.7846			−1.75693			−0.878467	+	0.477803i	$0.841433\pi$
$200$	14.0000	+	14.0000i	0.989949	+	0.989949i
$201$		0			0
$202$	4.39230	−	16.3923i	0.309041	−	1.15336i
$203$			9.46410i			0.664250i
$204$		0			0
$205$			17.0718i			1.19235i
$206$	9.46410	+	2.53590i	0.659395	+	0.176684i
$207$		0			0
$208$	−3.46410	+	2.00000i	−0.240192	+	0.138675i
$209$	3.46410			0.239617
$210$		0			0
$211$			19.8564i			1.36697i	0.729964	+	0.683486i	$0.239537\pi$
$211$			19.8564i			1.36697i	−0.729964	+	0.683486i	$0.760463\pi$
$212$	10.9282	−	18.9282i	0.750552	−	1.29999i
$213$		0			0
$214$	3.26795	−	12.1962i	0.223392	−	0.833712i
$215$	25.8564			1.76339
$216$		0			0
$217$	15.4641			1.04977
$218$	−0.732051	+	2.73205i	−0.0495807	+	0.185038i
$219$		0			0
$220$	−7.60770	−	4.39230i	−0.512911	−	0.296129i
$221$			1.46410i			0.0984861i
$222$		0			0
$223$	10.1962			0.682785			0.341392	−	0.939921i	$-0.389101\pi$
$223$	10.1962			0.682785			0.341392	+	0.939921i	$0.389101\pi$
$224$	6.92820	+	25.8564i	0.462910	+	1.72760i
$225$		0			0
$226$	12.9282	+	3.46410i	0.859971	+	0.230429i
$227$		−	27.1244i		−	1.80031i	−0.435573	−	0.900153i	$-0.643454\pi$
$227$		−	27.1244i		−	1.80031i	0.435573	−	0.900153i	$-0.356546\pi$
$228$		0			0
$229$			29.3205i			1.93755i	0.247934	+	0.968777i	$0.420248\pi$
$229$			29.3205i			1.93755i	−0.247934	+	0.968777i	$0.579752\pi$
$230$	−5.07180	+	18.9282i	−0.334424	+	1.24809i
$231$		0			0
$232$	−4.00000	+	4.00000i	−0.262613	+	0.262613i
$233$	−3.07180			−0.201240			−0.100620	−	0.994925i	$-0.532083\pi$
$233$	−3.07180			−0.201240			−0.100620	+	0.994925i	$0.532083\pi$
$234$		0			0
$235$		−	11.3205i		−	0.738469i
$236$	0.196152	−	0.339746i	0.0127684	−	0.0221156i
$237$		0			0
$238$	9.46410	+	2.53590i	0.613467	+	0.164378i
$239$	−15.2679			−0.987602			−0.493801	−	0.869575i	$-0.664393\pi$
$239$	−15.2679			−0.987602			−0.493801	+	0.869575i	$0.664393\pi$
$240$		0			0
$241$	−9.60770			−0.618886			−0.309443	−	0.950918i	$-0.600143\pi$
$241$	−9.60770			−0.618886			−0.309443	+	0.950918i	$0.600143\pi$
$242$	−12.8301	−	3.43782i	−0.824752	−	0.220992i
$243$		0			0
$244$	10.9282	−	18.9282i	0.699607	−	1.21175i
$245$			53.3205i			3.40652i
$246$		0			0
$247$	2.73205			0.173836
$248$	6.53590	+	6.53590i	0.415030	+	0.415030i
$249$		0			0
$250$	−2.53590	+	9.46410i	−0.160384	+	0.598562i
$251$			14.3923i			0.908434i	0.890891	+	0.454217i	$0.150081\pi$
$251$			14.3923i			0.908434i	−0.890891	+	0.454217i	$0.849919\pi$
$252$		0			0
$253$		−	5.07180i		−	0.318861i
$254$	5.46410	+	1.46410i	0.342848	+	0.0918659i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−3.85641			−0.240556			−0.120278	−	0.992740i	$-0.538379\pi$
$257$	−3.85641			−0.240556			−0.120278	+	0.992740i	$0.538379\pi$
$258$		0			0
$259$		−	23.3205i		−	1.44907i
$260$	−6.00000	−	3.46410i	−0.372104	−	0.214834i
$261$		0			0
$262$	2.87564	−	10.7321i	0.177658	−	0.663028i
$263$	−7.32051			−0.451402			−0.225701	−	0.974197i	$-0.572467\pi$
$263$	−7.32051			−0.451402			−0.225701	+	0.974197i	$0.572467\pi$
$264$		0			0
$265$	37.8564			2.32550
$266$	4.73205	−	17.6603i	0.290141	−	1.08282i
$267$		0			0
$268$	2.73205	−	4.73205i	0.166887	−	0.289056i
$269$		−	19.8564i		−	1.21067i	−0.795972	−	0.605333i	$-0.793040\pi$
$269$		−	19.8564i		−	1.21067i	0.795972	−	0.605333i	$-0.206960\pi$
$270$		0			0
$271$	−9.80385			−0.595541			−0.297771	−	0.954637i	$-0.596243\pi$
$271$	−9.80385			−0.595541			−0.297771	+	0.954637i	$0.596243\pi$
$272$	2.92820	+	5.07180i	0.177548	+	0.307523i
$273$		0			0
$274$	−1.26795	−	0.339746i	−0.0765996	−	0.0205248i
$275$		−	8.87564i		−	0.535221i
$276$		0			0
$277$		−	25.8564i		−	1.55356i	−0.629771	−	0.776780i	$-0.716851\pi$
$277$		−	25.8564i		−	1.55356i	0.629771	−	0.776780i	$-0.283149\pi$
$278$	−3.66025	+	13.6603i	−0.219527	+	0.819288i
$279$		0			0
$280$	−32.7846	+	32.7846i	−1.95926	+	1.95926i
$281$	25.3205			1.51049			0.755247	−	0.655440i	$-0.227517\pi$
$281$	25.3205			1.51049			0.755247	+	0.655440i	$0.227517\pi$
$282$		0			0
$283$			12.5359i			0.745182i	0.927996	+	0.372591i	$0.121531\pi$
$283$			12.5359i			0.745182i	−0.927996	+	0.372591i	$0.878469\pi$
$284$	−3.80385	−	2.19615i	−0.225717	−	0.130318i
$285$		0			0
$286$	1.73205	+	0.464102i	0.102418	+	0.0274429i
$287$	−23.3205			−1.37657
$288$		0			0
$289$	−14.8564			−0.873906
$290$	−9.46410	−	2.53590i	−0.555751	−	0.148913i
$291$		0			0
$292$	−0.928203	−	0.535898i	−0.0543190	−	0.0313611i
$293$		−	19.0718i		−	1.11419i	−0.830450	−	0.557093i	$-0.811917\pi$
$293$		−	19.0718i		−	1.11419i	0.830450	−	0.557093i	$-0.188083\pi$
$294$		0			0
$295$	0.679492			0.0395615
$296$	9.85641	−	9.85641i	0.572892	−	0.572892i
$297$		0			0
$298$	−0.339746	+	1.26795i	−0.0196810	+	0.0734503i
$299$		−	4.00000i		−	0.231326i
$300$		0			0
$301$			35.3205i			2.03584i
$302$	−23.3923	−	6.26795i	−1.34608	−	0.360680i
$303$		0			0
$304$	9.46410	−	5.46410i	0.542803	−	0.313388i
$305$	37.8564			2.16765
$306$		0			0
$307$		−	2.73205i		−	0.155926i	−0.996956	−	0.0779632i	$-0.975158\pi$
$307$		−	2.73205i		−	0.155926i	0.996956	−	0.0779632i	$-0.0248417\pi$
$308$	6.00000	−	10.3923i	0.341882	−	0.592157i
$309$		0			0
$310$	−4.14359	+	15.4641i	−0.235340	+	0.878302i
$311$	−14.9282			−0.846501			−0.423250	−	0.906013i	$-0.639111\pi$
$311$	−14.9282			−0.846501			−0.423250	+	0.906013i	$0.639111\pi$
$312$		0			0
$313$	−20.3923			−1.15264			−0.576321	−	0.817224i	$-0.695512\pi$
$313$	−20.3923			−1.15264			−0.576321	+	0.817224i	$0.695512\pi$
$314$	−1.12436	+	4.19615i	−0.0634511	+	0.236803i
$315$		0			0
$316$	−2.53590	−	1.46410i	−0.142655	−	0.0823622i
$317$			3.46410i			0.194563i	0.995257	+	0.0972817i	$0.0310148\pi$
$317$			3.46410i			0.194563i	−0.995257	+	0.0972817i	$0.968985\pi$
$318$		0			0
$319$	2.53590			0.141983
$320$	−27.7128			−1.54919
$321$		0			0
$322$	−25.8564	−	6.92820i	−1.44092	−	0.386094i
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$		−	7.00000i		−	0.388290i
$326$	4.85641	−	18.1244i	0.268971	−	1.00382i
$327$		0			0
$328$	−9.85641	−	9.85641i	−0.544229	−	0.544229i
$329$	15.4641			0.852564
$330$		0			0
$331$		−	27.5167i		−	1.51245i	−0.654310	−	0.756226i	$-0.727041\pi$
$331$		−	27.5167i		−	1.51245i	0.654310	−	0.756226i	$-0.272959\pi$
$332$	6.73205	−	11.6603i	0.369469	−	0.639940i
$333$		0			0
$334$	15.9282	+	4.26795i	0.871553	+	0.233532i
$335$	9.46410			0.517079
$336$		0			0
$337$	−5.46410			−0.297649			−0.148824	−	0.988864i	$-0.547549\pi$
$337$	−5.46410			−0.297649			−0.148824	+	0.988864i	$0.547549\pi$
$338$	1.36603	+	0.366025i	0.0743020	+	0.0199092i
$339$		0			0
$340$	−5.07180	+	8.78461i	−0.275057	+	0.476412i
$341$		−	4.14359i		−	0.224388i
$342$		0			0
$343$	−39.7128			−2.14429
$344$	−14.9282	+	14.9282i	−0.804875	+	0.804875i
$345$		0			0
$346$	2.53590	−	9.46410i	0.136331	−	0.508793i
$347$			20.9282i			1.12348i	0.827312	+	0.561742i	$0.189869\pi$
$347$			20.9282i			1.12348i	−0.827312	+	0.561742i	$0.810131\pi$
$348$		0			0
$349$			30.3923i			1.62686i	0.581661	+	0.813431i	$0.302403\pi$
$349$			30.3923i			1.62686i	−0.581661	+	0.813431i	$0.697597\pi$
$350$	−45.2487	−	12.1244i	−2.41865	−	0.648074i
$351$		0			0
$352$	6.92820	−	1.85641i	0.369274	−	0.0989468i
$353$	24.9282			1.32679			0.663397	−	0.748267i	$-0.269114\pi$
$353$	24.9282			1.32679			0.663397	+	0.748267i	$0.269114\pi$
$354$		0			0
$355$		−	7.60770i		−	0.403775i
$356$	−30.0000	−	17.3205i	−1.59000	−	0.917985i
$357$		0			0
$358$	−3.80385	+	14.1962i	−0.201040	+	0.750290i
$359$	13.5167			0.713382			0.356691	−	0.934222i	$-0.383905\pi$
$359$	13.5167			0.713382			0.356691	+	0.934222i	$0.383905\pi$
$360$		0			0
$361$	11.5359			0.607153
$362$	1.80385	−	6.73205i	0.0948081	−	0.353829i
$363$		0			0
$364$	4.73205	−	8.19615i	0.248027	−	0.429595i
$365$		−	1.85641i		−	0.0971688i
$366$		0			0
$367$	26.2487			1.37017			0.685086	−	0.728462i	$-0.259765\pi$
$367$	26.2487			1.37017			0.685086	+	0.728462i	$0.259765\pi$
$368$	−8.00000	−	13.8564i	−0.417029	−	0.722315i
$369$		0			0
$370$	23.3205	+	6.24871i	1.21238	+	0.324855i
$371$			51.7128i			2.68480i
$372$		0			0
$373$			26.7846i			1.38685i	0.720527	+	0.693427i	$0.243900\pi$
$373$			26.7846i			1.38685i	−0.720527	+	0.693427i	$0.756100\pi$
$374$	0.679492	−	2.53590i	0.0351357	−	0.131128i
$375$		0			0
$376$	6.53590	+	6.53590i	0.337063	+	0.337063i
$377$	2.00000			0.103005
$378$		0			0
$379$		−	16.5885i		−	0.852092i	−0.904702	−	0.426046i	$-0.859906\pi$
$379$		−	16.5885i		−	0.852092i	0.904702	−	0.426046i	$-0.140094\pi$
$380$	16.3923	+	9.46410i	0.840907	+	0.485498i
$381$		0			0
$382$	−29.3205	−	7.85641i	−1.50017	−	0.401969i
$383$	27.6603			1.41337			0.706686	−	0.707527i	$-0.250189\pi$
$383$	27.6603			1.41337			0.706686	+	0.707527i	$0.250189\pi$
$384$		0			0
$385$	20.7846			1.05928
$386$	30.5885	+	8.19615i	1.55691	+	0.417173i
$387$		0			0
$388$	−24.9282	−	14.3923i	−1.26554	−	0.730659i
$389$		−	2.00000i		−	0.101404i	−0.998714	−	0.0507020i	$-0.983854\pi$
$389$		−	2.00000i		−	0.101404i	0.998714	−	0.0507020i	$-0.0161459\pi$
$390$		0			0
$391$	−5.85641			−0.296171
$392$	−30.7846	−	30.7846i	−1.55486	−	1.55486i
$393$		0			0
$394$	6.19615	−	23.1244i	0.312158	−	1.16499i
$395$		−	5.07180i		−	0.255190i
$396$		0			0
$397$		−	11.4641i		−	0.575367i	−0.957726	−	0.287683i	$-0.907115\pi$
$397$		−	11.4641i		−	0.575367i	0.957726	−	0.287683i	$-0.0928851\pi$
$398$	33.8564	+	9.07180i	1.69707	+	0.454728i
$399$		0			0
$400$	−14.0000	−	24.2487i	−0.700000	−	1.21244i
$401$	−11.4641			−0.572490			−0.286245	−	0.958156i	$-0.592407\pi$
$401$	−11.4641			−0.572490			−0.286245	+	0.958156i	$0.592407\pi$
$402$		0			0
$403$		−	3.26795i		−	0.162788i
$404$	−12.0000	+	20.7846i	−0.597022	+	1.03407i
$405$		0			0
$406$	3.46410	−	12.9282i	0.171920	−	0.641616i
$407$	−6.24871			−0.309737
$408$		0			0
$409$	−0.928203			−0.0458967			−0.0229483	−	0.999737i	$-0.507305\pi$
$409$	−0.928203			−0.0458967			−0.0229483	+	0.999737i	$0.507305\pi$
$410$	6.24871	−	23.3205i	0.308602	−	1.15172i
$411$		0			0
$412$	−12.0000	−	6.92820i	−0.591198	−	0.341328i
$413$			0.928203i			0.0456739i
$414$		0			0
$415$	23.3205			1.14476
$416$	5.46410	−	1.46410i	0.267900	−	0.0717835i
$417$		0			0
$418$	−4.73205	−	1.26795i	−0.231452	−	0.0620174i
$419$		−	10.7846i		−	0.526863i	−0.964678	−	0.263431i	$-0.915146\pi$
$419$		−	10.7846i		−	0.526863i	0.964678	−	0.263431i	$-0.0848542\pi$
$420$		0			0
$421$		−	24.2487i		−	1.18181i	−0.806741	−	0.590905i	$-0.798771\pi$
$421$		−	24.2487i		−	1.18181i	0.806741	−	0.590905i	$-0.201229\pi$
$422$	7.26795	−	27.1244i	0.353798	−	1.32039i
$423$		0			0
$424$	−21.8564	+	21.8564i	−1.06144	+	1.06144i
$425$	−10.2487			−0.497136
$426$		0			0
$427$			51.7128i			2.50256i
$428$	−8.92820	+	15.4641i	−0.431561	+	0.747486i
$429$		0			0
$430$	−35.3205	−	9.46410i	−1.70331	−	0.456400i
$431$	−14.8756			−0.716535			−0.358267	−	0.933619i	$-0.616632\pi$
$431$	−14.8756			−0.716535			−0.358267	+	0.933619i	$0.616632\pi$
$432$		0			0
$433$	34.7846			1.67164			0.835821	−	0.549002i	$-0.184992\pi$
$433$	34.7846			1.67164			0.835821	+	0.549002i	$0.184992\pi$
$434$	−21.1244	−	5.66025i	−1.01400	−	0.271701i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$			10.9282i			0.522767i
$438$		0			0
$439$	−10.9282			−0.521575			−0.260787	−	0.965396i	$-0.583982\pi$
$439$	−10.9282			−0.521575			−0.260787	+	0.965396i	$0.583982\pi$
$440$	8.78461	+	8.78461i	0.418790	+	0.418790i
$441$		0			0
$442$	0.535898	−	2.00000i	0.0254901	−	0.0951303i
$443$			30.0000i			1.42534i	0.701498	+	0.712672i	$0.252515\pi$
$443$			30.0000i			1.42534i	−0.701498	+	0.712672i	$0.747485\pi$
$444$		0			0
$445$		−	60.0000i		−	2.84427i
$446$	−13.9282	−	3.73205i	−0.659520	−	0.176718i
$447$		0			0
$448$		−	37.8564i		−	1.78855i
$449$	−38.3923			−1.81184			−0.905922	−	0.423444i	$-0.860821\pi$
$449$	−38.3923			−1.81184			−0.905922	+	0.423444i	$0.860821\pi$
$450$		0			0
$451$			6.24871i			0.294240i
$452$	−16.3923	−	9.46410i	−0.771029	−	0.445154i
$453$		0			0
$454$	−9.92820	+	37.0526i	−0.465954	+	1.73896i
$455$	16.3923			0.768483
$456$		0			0
$457$	−14.0000			−0.654892			−0.327446	−	0.944870i	$-0.606188\pi$
$457$	−14.0000			−0.654892			−0.327446	+	0.944870i	$0.606188\pi$
$458$	10.7321	−	40.0526i	0.501476	−	1.87153i
$459$		0			0
$460$	13.8564	−	24.0000i	0.646058	−	1.11901i
$461$		−	7.07180i		−	0.329366i	−0.986347	−	0.164683i	$-0.947340\pi$
$461$		−	7.07180i		−	0.329366i	0.986347	−	0.164683i	$-0.0526602\pi$
$462$		0			0
$463$	−15.6603			−0.727794			−0.363897	−	0.931439i	$-0.618554\pi$
$463$	−15.6603			−0.727794			−0.363897	+	0.931439i	$0.618554\pi$
$464$	6.92820	−	4.00000i	0.321634	−	0.185695i
$465$		0			0
$466$	4.19615	+	1.12436i	0.194383	+	0.0520848i
$467$			12.2487i			0.566803i	0.959001	+	0.283401i	$0.0914629\pi$
$467$			12.2487i			0.566803i	−0.959001	+	0.283401i	$0.908537\pi$
$468$		0			0
$469$			12.9282i			0.596969i
$470$	−4.14359	+	15.4641i	−0.191130	+	0.713306i
$471$		0			0
$472$	−0.392305	+	0.392305i	−0.0180573	+	0.0180573i
$473$	9.46410			0.435160
$474$		0			0
$475$			19.1244i			0.877486i
$476$	−12.0000	−	6.92820i	−0.550019	−	0.317554i
$477$		0			0
$478$	20.8564	+	5.58846i	0.953950	+	0.255610i
$479$	−24.7321			−1.13004			−0.565018	−	0.825078i	$-0.691131\pi$
$479$	−24.7321			−1.13004			−0.565018	+	0.825078i	$0.691131\pi$
$480$		0			0
$481$	−4.92820			−0.224707
$482$	13.1244	+	3.51666i	0.597798	+	0.160179i
$483$		0			0
$484$	16.2679	+	9.39230i	0.739452	+	0.426923i
$485$		−	49.8564i		−	2.26386i
$486$		0			0
$487$	16.4449			0.745188			0.372594	−	0.927994i	$-0.378468\pi$
$487$	16.4449			0.745188			0.372594	+	0.927994i	$0.378468\pi$
$488$	−21.8564	+	21.8564i	−0.989393	+	0.989393i
$489$		0			0
$490$	19.5167	−	72.8372i	0.881673	−	3.29045i
$491$		−	24.2487i		−	1.09433i	−0.837025	−	0.547165i	$-0.815707\pi$
$491$		−	24.2487i		−	1.09433i	0.837025	−	0.547165i	$-0.184293\pi$
$492$		0			0
$493$		−	2.92820i		−	0.131880i
$494$	−3.73205	−	1.00000i	−0.167913	−	0.0449921i
$495$		0			0
$496$	−6.53590	−	11.3205i	−0.293471	−	0.508306i
$497$	10.3923			0.466159
$498$		0			0
$499$		−	10.7321i		−	0.480433i	−0.970719	−	0.240216i	$-0.922782\pi$
$499$		−	10.7321i		−	0.480433i	0.970719	−	0.240216i	$-0.0772184\pi$
$500$	6.92820	−	12.0000i	0.309839	−	0.536656i
$501$		0			0
$502$	5.26795	−	19.6603i	0.235120	−	0.877480i
$503$	−37.4641			−1.67044			−0.835221	−	0.549915i	$-0.814660\pi$
$503$	−37.4641			−1.67044			−0.835221	+	0.549915i	$0.814660\pi$
$504$		0			0
$505$	−41.5692			−1.84981
$506$	−1.85641	+	6.92820i	−0.0825273	+	0.307996i
$507$		0			0
$508$	−6.92820	−	4.00000i	−0.307389	−	0.177471i
$509$			6.39230i			0.283334i	0.989914	+	0.141667i	$0.0452462\pi$
$509$			6.39230i			0.283334i	−0.989914	+	0.141667i	$0.954754\pi$
$510$		0			0
$511$	2.53590			0.112182
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	5.26795	+	1.41154i	0.232359	+	0.0622605i
$515$		−	24.0000i		−	1.05757i
$516$		0			0
$517$		−	4.14359i		−	0.182235i
$518$	−8.53590	+	31.8564i	−0.375046	+	1.39969i
$519$		0			0
$520$	6.92820	+	6.92820i	0.303822	+	0.303822i
$521$	−37.1769			−1.62875			−0.814375	−	0.580339i	$-0.802920\pi$
$521$	−37.1769			−1.62875			−0.814375	+	0.580339i	$0.802920\pi$
$522$		0			0
$523$			14.0000i			0.612177i	0.952003	+	0.306089i	$0.0990204\pi$
$523$			14.0000i			0.612177i	−0.952003	+	0.306089i	$0.900980\pi$
$524$	−7.85641	+	13.6077i	−0.343209	+	0.594455i
$525$		0			0
$526$	10.0000	+	2.67949i	0.436021	+	0.116831i
$527$	−4.78461			−0.208421
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−51.7128	−	13.8564i	−2.24626	−	0.601884i
$531$		0			0
$532$	−12.9282	+	22.3923i	−0.560509	+	0.970830i
$533$			4.92820i			0.213464i
$534$		0			0
$535$	−30.9282			−1.33714
$536$	−5.46410	+	5.46410i	−0.236013	+	0.236013i
$537$		0			0
$538$	−7.26795	+	27.1244i	−0.313344	+	1.16941i
$539$			19.5167i			0.840642i
$540$		0			0
$541$		−	16.9282i		−	0.727800i	−0.931438	−	0.363900i	$-0.881445\pi$
$541$		−	16.9282i		−	0.727800i	0.931438	−	0.363900i	$-0.118555\pi$
$542$	13.3923	+	3.58846i	0.575249	+	0.154137i
$543$		0			0
$544$	−2.14359	−	8.00000i	−0.0919058	−	0.342997i
$545$	6.92820			0.296772
$546$		0			0
$547$			15.8564i			0.677971i	0.940792	+	0.338985i	$0.110084\pi$
$547$			15.8564i			0.677971i	−0.940792	+	0.338985i	$0.889916\pi$
$548$	1.60770	+	0.928203i	0.0686773	+	0.0396509i
$549$		0			0
$550$	−3.24871	+	12.1244i	−0.138526	+	0.516984i
$551$	−5.46410			−0.232779
$552$		0			0
$553$	6.92820			0.294617
$554$	−9.46410	+	35.3205i	−0.402091	+	1.50062i
$555$		0			0
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$			6.78461i			0.287473i	0.989616	+	0.143737i	$0.0459118\pi$
$557$			6.78461i			0.287473i	−0.989616	+	0.143737i	$0.954088\pi$
$558$		0			0
$559$	7.46410			0.315698
$560$	56.7846	−	32.7846i	2.39959	−	1.38540i
$561$		0			0
$562$	−34.5885	−	9.26795i	−1.45903	−	0.390945i
$563$			0.535898i			0.0225854i	0.999936	+	0.0112927i	$0.00359466\pi$
$563$			0.535898i			0.0225854i	−0.999936	+	0.0112927i	$0.996405\pi$
$564$		0			0
$565$		−	32.7846i		−	1.37926i
$566$	4.58846	−	17.1244i	0.192867	−	0.719790i
$567$		0			0
$568$	4.39230	+	4.39230i	0.184297	+	0.184297i
$569$	14.0000			0.586911			0.293455	−	0.955973i	$-0.405195\pi$
$569$	14.0000			0.586911			0.293455	+	0.955973i	$0.405195\pi$
$570$		0			0
$571$			37.3205i			1.56181i	0.624647	+	0.780907i	$0.285243\pi$
$571$			37.3205i			1.56181i	−0.624647	+	0.780907i	$0.714757\pi$
$572$	−2.19615	−	1.26795i	−0.0918257	−	0.0530156i
$573$		0			0
$574$	31.8564	+	8.53590i	1.32966	+	0.356282i
$575$	28.0000			1.16768
$576$		0			0
$577$	−20.9282			−0.871253			−0.435626	−	0.900128i	$-0.643473\pi$
$577$	−20.9282			−0.871253			−0.435626	+	0.900128i	$0.643473\pi$
$578$	20.2942	+	5.43782i	0.844129	+	0.226184i
$579$		0			0
$580$	12.0000	+	6.92820i	0.498273	+	0.287678i
$581$			31.8564i			1.32163i
$582$		0			0
$583$	13.8564			0.573874
$584$	1.07180	+	1.07180i	0.0443513	+	0.0443513i
$585$		0			0
$586$	−6.98076	+	26.0526i	−0.288373	+	1.07622i
$587$			21.6603i			0.894014i	0.894530	+	0.447007i	$0.147510\pi$
$587$			21.6603i			0.894014i	−0.894530	+	0.447007i	$0.852490\pi$
$588$		0			0
$589$			8.92820i			0.367880i
$590$	−0.928203	−	0.248711i	−0.0382135	−	0.0102393i
$591$		0			0
$592$	−17.0718	+	9.85641i	−0.701647	+	0.405096i
$593$	−19.8564			−0.815405			−0.407702	−	0.913115i	$-0.633670\pi$
$593$	−19.8564			−0.815405			−0.407702	+	0.913115i	$0.633670\pi$
$594$		0			0
$595$		−	24.0000i		−	0.983904i
$596$	0.928203	−	1.60770i	0.0380207	−	0.0658538i
$597$		0			0
$598$	−1.46410	+	5.46410i	−0.0598716	+	0.223444i
$599$	−17.1769			−0.701830			−0.350915	−	0.936407i	$-0.614129\pi$
$599$	−17.1769			−0.701830			−0.350915	+	0.936407i	$0.614129\pi$
$600$		0			0
$601$	16.3923			0.668656			0.334328	−	0.942457i	$-0.391491\pi$
$601$	16.3923			0.668656			0.334328	+	0.942457i	$0.391491\pi$
$602$	12.9282	−	48.2487i	0.526914	−	1.96647i
$603$		0			0
$604$	29.6603	+	17.1244i	1.20686	+	0.696780i
$605$			32.5359i			1.32277i
$606$		0			0
$607$	−27.3205			−1.10891			−0.554453	−	0.832215i	$-0.687072\pi$
$607$	−27.3205			−1.10891			−0.554453	+	0.832215i	$0.687072\pi$
$608$	−14.9282	+	4.00000i	−0.605419	+	0.162221i
$609$		0			0
$610$	−51.7128	−	13.8564i	−2.09379	−	0.561029i
$611$		−	3.26795i		−	0.132207i
$612$		0			0
$613$		−	44.6410i		−	1.80303i	−0.432744	−	0.901517i	$-0.642455\pi$
$613$		−	44.6410i		−	1.80303i	0.432744	−	0.901517i	$-0.357545\pi$
$614$	−1.00000	+	3.73205i	−0.0403567	+	0.150613i
$615$		0			0
$616$	−12.0000	+	12.0000i	−0.483494	+	0.483494i
$617$	−6.67949			−0.268906			−0.134453	−	0.990920i	$-0.542928\pi$
$617$	−6.67949			−0.268906			−0.134453	+	0.990920i	$0.542928\pi$
$618$		0			0
$619$			12.5885i			0.505973i	0.967470	+	0.252986i	$0.0814128\pi$
$619$			12.5885i			0.505973i	−0.967470	+	0.252986i	$0.918587\pi$
$620$	11.3205	−	19.6077i	0.454643	−	0.787464i
$621$		0			0
$622$	20.3923	+	5.46410i	0.817657	+	0.219091i
$623$	81.9615			3.28372
$624$		0			0
$625$	−11.0000			−0.440000
$626$	27.8564	+	7.46410i	1.11337	+	0.298325i
$627$		0			0
$628$	3.07180	−	5.32051i	0.122578	−	0.212311i
$629$			7.21539i			0.287696i
$630$		0			0
$631$	−3.94744			−0.157145			−0.0785726	−	0.996908i	$-0.525036\pi$
$631$	−3.94744			−0.157145			−0.0785726	+	0.996908i	$0.525036\pi$
$632$	2.92820	+	2.92820i	0.116478	+	0.116478i
$633$		0			0
$634$	1.26795	−	4.73205i	0.0503567	−	0.187934i
$635$		−	13.8564i		−	0.549875i
$636$		0			0
$637$			15.3923i			0.609865i
$638$	−3.46410	−	0.928203i	−0.137145	−	0.0367479i
$639$		0			0
$640$	37.8564	+	10.1436i	1.49641	+	0.400961i
$641$	−26.2487			−1.03676			−0.518381	−	0.855150i	$-0.673465\pi$
$641$	−26.2487			−1.03676			−0.518381	+	0.855150i	$0.673465\pi$
$642$		0			0
$643$		−	9.26795i		−	0.365492i	−0.983160	−	0.182746i	$-0.941501\pi$
$643$		−	9.26795i		−	0.365492i	0.983160	−	0.182746i	$-0.0584986\pi$
$644$	32.7846	+	18.9282i	1.29189	+	0.745876i
$645$		0			0
$646$	−1.46410	+	5.46410i	−0.0576043	+	0.214982i
$647$	−10.1436			−0.398786			−0.199393	−	0.979920i	$-0.563897\pi$
$647$	−10.1436			−0.398786			−0.199393	+	0.979920i	$0.563897\pi$
$648$		0			0
$649$	0.248711			0.00976277
$650$	−2.56218	+	9.56218i	−0.100497	+	0.375059i
$651$		0			0
$652$	−13.2679	+	22.9808i	−0.519613	+	0.899996i
$653$			16.9282i			0.662452i	0.943551	+	0.331226i	$0.107462\pi$
$653$			16.9282i			0.662452i	−0.943551	+	0.331226i	$0.892538\pi$
$654$		0			0
$655$	−27.2154			−1.06339
$656$	9.85641	+	17.0718i	0.384828	+	0.666542i
$657$		0			0
$658$	−21.1244	−	5.66025i	−0.823513	−	0.220660i
$659$		−	14.0000i		−	0.545363i	−0.962104	−	0.272681i	$-0.912090\pi$
$659$		−	14.0000i		−	0.545363i	0.962104	−	0.272681i	$-0.0879105\pi$
$660$		0			0
$661$		−	17.3205i		−	0.673690i	−0.941560	−	0.336845i	$-0.890640\pi$
$661$		−	17.3205i		−	0.673690i	0.941560	−	0.336845i	$-0.109360\pi$
$662$	−10.0718	+	37.5885i	−0.391451	+	1.46092i
$663$		0			0
$664$	−13.4641	+	13.4641i	−0.522508	+	0.522508i
$665$	−44.7846			−1.73667
$666$		0			0
$667$			8.00000i			0.309761i
$668$	−20.1962	−	11.6603i	−0.781413	−	0.451149i
$669$		0			0
$670$	−12.9282	−	3.46410i	−0.499460	−	0.133830i
$671$	13.8564			0.534921
$672$		0			0
$673$	−29.1769			−1.12469			−0.562344	−	0.826904i	$-0.690100\pi$
$673$	−29.1769			−1.12469			−0.562344	+	0.826904i	$0.690100\pi$
$674$	7.46410	+	2.00000i	0.287506	+	0.0770371i
$675$		0			0
$676$	−1.73205	−	1.00000i	−0.0666173	−	0.0384615i
$677$		−	34.9282i		−	1.34240i	−0.741276	−	0.671200i	$-0.765779\pi$
$677$		−	34.9282i		−	1.34240i	0.741276	−	0.671200i	$-0.234221\pi$
$678$		0			0
$679$	68.1051			2.61363
$680$	10.1436	−	10.1436i	0.388989	−	0.388989i
$681$		0			0
$682$	−1.51666	+	5.66025i	−0.0580759	+	0.216742i
$683$			28.1962i			1.07890i	0.842019	+	0.539448i	$0.181367\pi$
$683$			28.1962i			1.07890i	−0.842019	+	0.539448i	$0.818633\pi$
$684$		0			0
$685$			3.21539i			0.122854i
$686$	54.2487	+	14.5359i	2.07123	+	0.554983i
$687$		0			0
$688$	25.8564	−	14.9282i	0.985766	−	0.569132i
$689$	10.9282			0.416331
$690$		0			0
$691$			46.8372i			1.78177i	0.454229	+	0.890885i	$0.349915\pi$
$691$			46.8372i			1.78177i	−0.454229	+	0.890885i	$0.650085\pi$
$692$	−6.92820	+	12.0000i	−0.263371	+	0.456172i
$693$		0			0
$694$	7.66025	−	28.5885i	0.290779	−	1.08520i
$695$	34.6410			1.31401
$696$		0			0
$697$	7.21539			0.273302
$698$	11.1244	−	41.5167i	0.421063	−	1.57143i
$699$		0			0
$700$	57.3731	+	33.1244i	2.16850	+	1.25198i
$701$		−	28.6410i		−	1.08176i	−0.841101	−	0.540878i	$-0.818092\pi$
$701$		−	28.6410i		−	1.08176i	0.841101	−	0.540878i	$-0.181908\pi$
$702$		0			0
$703$	13.4641			0.507808
$704$	−10.1436			−0.382301
$705$		0			0
$706$	−34.0526	−	9.12436i	−1.28158	−	0.343400i
$707$		−	56.7846i		−	2.13561i
$708$		0			0
$709$		−	5.32051i		−	0.199816i	−0.994997	−	0.0999079i	$-0.968145\pi$
$709$		−	5.32051i		−	0.199816i	0.994997	−	0.0999079i	$-0.0318548\pi$
$710$	−2.78461	+	10.3923i	−0.104505	+	0.390016i
$711$		0			0
$712$	34.6410	+	34.6410i	1.29823	+	1.29823i
$713$	13.0718			0.489543
$714$		0			0
$715$		−	4.39230i		−	0.164263i
$716$	10.3923	−	18.0000i	0.388379	−	0.672692i
$717$		0			0
$718$	−18.4641	−	4.94744i	−0.689074	−	0.184637i
$719$	−17.0718			−0.636671			−0.318335	−	0.947978i	$-0.603124\pi$
$719$	−17.0718			−0.636671			−0.318335	+	0.947978i	$0.603124\pi$
$720$		0			0
$721$	32.7846			1.22096
$722$	−15.7583	−	4.22243i	−0.586464	−	0.157143i
$723$		0			0
$724$	−4.92820	+	8.53590i	−0.183155	+	0.317234i
$725$			14.0000i			0.519947i
$726$		0			0
$727$	−9.07180			−0.336454			−0.168227	−	0.985748i	$-0.553804\pi$
$727$	−9.07180			−0.336454			−0.168227	+	0.985748i	$0.553804\pi$
$728$	−9.46410	+	9.46410i	−0.350763	+	0.350763i
$729$		0			0
$730$	−0.679492	+	2.53590i	−0.0251491	+	0.0938578i
$731$		−	10.9282i		−	0.404194i
$732$		0			0
$733$			2.67949i			0.0989693i	0.998775	+	0.0494846i	$0.0157579\pi$
$733$			2.67949i			0.0989693i	−0.998775	+	0.0494846i	$0.984242\pi$
$734$	−35.8564	−	9.60770i	−1.32348	−	0.354626i
$735$		0			0
$736$	5.85641	+	21.8564i	0.215870	+	0.805638i
$737$	3.46410			0.127602
$738$		0			0
$739$		−	53.7654i		−	1.97779i	−0.148612	−	0.988896i	$-0.547481\pi$
$739$		−	53.7654i		−	1.97779i	0.148612	−	0.988896i	$-0.452519\pi$
$740$	−29.5692	−	17.0718i	−1.08699	−	0.627572i
$741$		0			0
$742$	18.9282	−	70.6410i	0.694876	−	2.59331i
$743$	21.8038			0.799906			0.399953	−	0.916536i	$-0.369027\pi$
$743$	21.8038			0.799906			0.399953	+	0.916536i	$0.369027\pi$
$744$		0			0
$745$	3.21539			0.117803
$746$	9.80385	−	36.5885i	0.358944	−	1.33960i
$747$		0			0
$748$	−1.85641	+	3.21539i	−0.0678769	+	0.117566i
$749$		−	42.2487i		−	1.54373i
$750$		0			0
$751$	14.9282			0.544738			0.272369	−	0.962193i	$-0.412193\pi$
$751$	14.9282			0.544738			0.272369	+	0.962193i	$0.412193\pi$
$752$	−6.53590	−	11.3205i	−0.238340	−	0.412816i
$753$		0			0
$754$	−2.73205	−	0.732051i	−0.0994954	−	0.0266597i
$755$			59.3205i			2.15889i
$756$		0			0
$757$		−	0.784610i		−	0.0285171i	−0.999898	−	0.0142586i	$-0.995461\pi$
$757$		−	0.784610i		−	0.0285171i	0.999898	−	0.0142586i	$-0.00453880\pi$
$758$	−6.07180	+	22.6603i	−0.220538	+	0.823057i
$759$		0			0
$760$	−18.9282	−	18.9282i	−0.686598	−	0.686598i
$761$	22.7846			0.825941			0.412971	−	0.910744i	$-0.364491\pi$
$761$	22.7846			0.825941			0.412971	+	0.910744i	$0.364491\pi$
$762$		0			0
$763$			9.46410i			0.342623i
$764$	37.1769	+	21.4641i	1.34501	+	0.776544i
$765$		0			0
$766$	−37.7846	−	10.1244i	−1.36521	−	0.365808i
$767$	0.196152			0.00708265
$768$		0			0
$769$	24.5359			0.884787			0.442394	−	0.896821i	$-0.354129\pi$
$769$	24.5359			0.884787			0.442394	+	0.896821i	$0.354129\pi$
$770$	−28.3923	−	7.60770i	−1.02319	−	0.274162i
$771$		0			0
$772$	−38.7846	−	22.3923i	−1.39589	−	0.805917i
$773$		−	20.5359i		−	0.738625i	−0.929305	−	0.369312i	$-0.879593\pi$
$773$		−	20.5359i		−	0.738625i	0.929305	−	0.369312i	$-0.120407\pi$
$774$		0			0
$775$	22.8756			0.821717
$776$	28.7846	+	28.7846i	1.03331	+	1.03331i
$777$		0			0
$778$	−0.732051	+	2.73205i	−0.0262453	+	0.0979488i
$779$		−	13.4641i		−	0.482402i
$780$		0			0
$781$		−	2.78461i		−	0.0996412i
$782$	8.00000	+	2.14359i	0.286079	+	0.0766547i
$783$		0			0
$784$	30.7846	+	53.3205i	1.09945	+	1.90430i
$785$	10.6410			0.379794
$786$		0			0
$787$		−	4.87564i		−	0.173798i	−0.996217	−	0.0868990i	$-0.972304\pi$
$787$		−	4.87564i		−	0.173798i	0.996217	−	0.0868990i	$-0.0276957\pi$
$788$	−16.9282	+	29.3205i	−0.603042	+	1.04450i
$789$		0			0
$790$	−1.85641	+	6.92820i	−0.0660480	+	0.246494i
$791$	44.7846			1.59236
$792$		0			0
$793$	10.9282			0.388072
$794$	−4.19615	+	15.6603i	−0.148916	+	0.555762i
$795$		0			0
$796$	−42.9282	−	24.7846i	−1.52155	−	0.878467i
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$		0			0
$799$	−4.78461			−0.169267
$800$	10.2487	+	38.2487i	0.362347	+	1.35230i
$801$		0			0
$802$	15.6603	+	4.19615i	0.552983	+	0.148171i
$803$		−	0.679492i		−	0.0239787i
$804$		0			0
$805$			65.5692i			2.31101i
$806$	−1.19615	+	4.46410i	−0.0421327	+	0.157241i
$807$		0			0
$808$	24.0000	−	24.0000i	0.844317	−	0.844317i
$809$	−1.46410			−0.0514751			−0.0257375	−	0.999669i	$-0.508193\pi$
$809$	−1.46410			−0.0514751			−0.0257375	+	0.999669i	$0.508193\pi$
$810$		0			0
$811$			52.5885i			1.84663i	0.384043	+	0.923315i	$0.374531\pi$
$811$			52.5885i			1.84663i	−0.384043	+	0.923315i	$0.625469\pi$
$812$	−9.46410	+	16.3923i	−0.332125	+	0.575257i
$813$		0			0
$814$	8.53590	+	2.28719i	0.299183	+	0.0801659i
$815$	−45.9615			−1.60996
$816$		0			0
$817$	−20.3923			−0.713436
$818$	1.26795	+	0.339746i	0.0443328	+	0.0118789i
$819$		0			0
$820$	−17.0718	+	29.5692i	−0.596173	+	1.03260i
$821$		−	0.248711i		−	0.00868008i	−0.999991	−	0.00434004i	$-0.998619\pi$
$821$		−	0.248711i		−	0.00868008i	0.999991	−	0.00434004i	$-0.00138148\pi$
$822$		0			0
$823$	20.0000			0.697156			0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000			0.697156			0.348578	+	0.937280i	$0.386665\pi$
$824$	13.8564	+	13.8564i	0.482711	+	0.482711i
$825$		0			0
$826$	0.339746	−	1.26795i	0.0118213	−	0.0441176i
$827$		−	5.26795i		−	0.183185i	−0.995797	−	0.0915923i	$-0.970804\pi$
$827$		−	5.26795i		−	0.183185i	0.995797	−	0.0915923i	$-0.0291956\pi$
$828$		0			0
$829$			12.7846i			0.444028i	0.975043	+	0.222014i	$0.0712630\pi$
$829$			12.7846i			0.444028i	−0.975043	+	0.222014i	$0.928737\pi$
$830$	−31.8564	−	8.53590i	−1.10575	−	0.296285i
$831$		0			0
$832$	−8.00000			−0.277350
$833$	22.5359			0.780823
$834$		0			0
$835$		−	40.3923i		−	1.39783i
$836$	6.00000	+	3.46410i	0.207514	+	0.119808i
$837$		0			0
$838$	−3.94744	+	14.7321i	−0.136362	+	0.508910i
$839$	−30.9808			−1.06957			−0.534787	−	0.844987i	$-0.679608\pi$
$839$	−30.9808			−1.06957			−0.534787	+	0.844987i	$0.679608\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	−8.87564	+	33.1244i	−0.305875	+	1.14154i
$843$		0			0
$844$	−19.8564	+	34.3923i	−0.683486	+	1.18383i
$845$		−	3.46410i		−	0.119169i
$846$		0			0
$847$	−44.4449			−1.52714
$848$	37.8564	−	21.8564i	1.29999	−	0.750552i
$849$		0			0
$850$	14.0000	+	3.75129i	0.480196	+	0.128668i
$851$		−	19.7128i		−	0.675747i
$852$		0			0
$853$			7.17691i			0.245733i	0.992423	+	0.122866i	$0.0392087\pi$
$853$			7.17691i			0.245733i	−0.992423	+	0.122866i	$0.960791\pi$
$854$	18.9282	−	70.6410i	0.647710	−	2.41729i
$855$		0			0
$856$	17.8564	−	17.8564i	0.610319	−	0.610319i
$857$	−19.8564			−0.678282			−0.339141	−	0.940736i	$-0.610136\pi$
$857$	−19.8564			−0.678282			−0.339141	+	0.940736i	$0.610136\pi$
$858$		0			0
$859$			18.0000i			0.614152i	0.951685	+	0.307076i	$0.0993506\pi$
$859$			18.0000i			0.614152i	−0.951685	+	0.307076i	$0.900649\pi$
$860$	44.7846	+	25.8564i	1.52714	+	0.881696i
$861$		0			0
$862$	20.3205	+	5.44486i	0.692119	+	0.185453i
$863$	−4.73205			−0.161081			−0.0805404	−	0.996751i	$-0.525665\pi$
$863$	−4.73205			−0.161081			−0.0805404	+	0.996751i	$0.525665\pi$
$864$		0			0
$865$	−24.0000			−0.816024
$866$	−47.5167	−	12.7321i	−1.61468	−	0.432653i
$867$		0			0
$868$	26.7846	+	15.4641i	0.909129	+	0.524886i
$869$		−	1.85641i		−	0.0629743i
$870$		0			0
$871$	2.73205			0.0925720
$872$	−4.00000	+	4.00000i	−0.135457	+	0.135457i
$873$		0			0
$874$	4.00000	−	14.9282i	0.135302	−	0.504954i
$875$			32.7846i			1.10832i
$876$		0			0
$877$		−	16.5359i		−	0.558378i	−0.960236	−	0.279189i	$-0.909934\pi$
$877$		−	16.5359i		−	0.558378i	0.960236	−	0.279189i	$-0.0900655\pi$
$878$	14.9282	+	4.00000i	0.503802	+	0.134993i
$879$		0			0
$880$	−8.78461	−	15.2154i	−0.296129	−	0.512911i
$881$	−21.7128			−0.731523			−0.365762	−	0.930709i	$-0.619191\pi$
$881$	−21.7128			−0.731523			−0.365762	+	0.930709i	$0.619191\pi$
$882$		0			0
$883$			24.5359i			0.825699i	0.910799	+	0.412849i	$0.135466\pi$
$883$			24.5359i			0.825699i	−0.910799	+	0.412849i	$0.864534\pi$
$884$	−1.46410	+	2.53590i	−0.0492431	+	0.0852915i
$885$		0			0
$886$	10.9808	−	40.9808i	0.368906	−	1.37678i
$887$	18.2487			0.612732			0.306366	−	0.951914i	$-0.400887\pi$
$887$	18.2487			0.612732			0.306366	+	0.951914i	$0.400887\pi$
$888$		0			0
$889$	18.9282			0.634832
$890$	−21.9615	+	81.9615i	−0.736152	+	2.74736i
$891$		0			0
$892$	17.6603	+	10.1962i	0.591309	+	0.341392i
$893$			8.92820i			0.298771i
$894$		0			0
$895$	36.0000			1.20335
$896$	−13.8564	+	51.7128i	−0.462910	+	1.72760i
$897$		0			0
$898$	52.4449	+	14.0526i	1.75011	+	0.468940i
$899$			6.53590i			0.217984i
$900$		0			0
$901$		−	16.0000i		−	0.533037i
$902$	2.28719	−	8.53590i	0.0761550	−	0.284214i
$903$		0			0
$904$	18.9282	+	18.9282i	0.629543	+	0.629543i
$905$	−17.0718			−0.567486
$906$		0			0
$907$		−	54.1051i		−	1.79653i	−0.439453	−	0.898265i	$-0.644828\pi$
$907$		−	54.1051i		−	1.79653i	0.439453	−	0.898265i	$-0.355172\pi$
$908$	27.1244	−	46.9808i	0.900153	−	1.55911i
$909$		0			0
$910$	−22.3923	−	6.00000i	−0.742298	−	0.198898i
$911$	31.3205			1.03769			0.518847	−	0.854867i	$-0.326361\pi$
$911$	31.3205			1.03769			0.518847	+	0.854867i	$0.326361\pi$
$912$		0			0
$913$	8.53590			0.282497
$914$	19.1244	+	5.12436i	0.632577	+	0.169499i
$915$		0			0
$916$	−29.3205	+	50.7846i	−0.968777	+	1.67797i
$917$		−	37.1769i		−	1.22769i
$918$		0			0
$919$	−0.679492			−0.0224144			−0.0112072	−	0.999937i	$-0.503567\pi$
$919$	−0.679492			−0.0224144			−0.0112072	+	0.999937i	$0.503567\pi$
$920$	−27.7128	+	27.7128i	−0.913664	+	0.913664i
$921$		0			0
$922$	−2.58846	+	9.66025i	−0.0852463	+	0.318144i
$923$		−	2.19615i		−	0.0722872i
$924$		0			0
$925$		−	34.4974i		−	1.13427i
$926$	21.3923	+	5.73205i	0.702995	+	0.188367i
$927$		0			0
$928$	−10.9282	+	2.92820i	−0.358736	+	0.0961230i
$929$	−27.4641			−0.901068			−0.450534	−	0.892759i	$-0.648766\pi$
$929$	−27.4641			−0.901068			−0.450534	+	0.892759i	$0.648766\pi$
$930$		0			0
$931$		−	42.0526i		−	1.37822i
$932$	−5.32051	−	3.07180i	−0.174279	−	0.100620i
$933$		0			0
$934$	4.48334	−	16.7321i	0.146699	−	0.547489i
$935$	−6.43078			−0.210309
$936$		0			0
$937$	41.7128			1.36270			0.681349	−	0.731959i	$-0.261394\pi$
$937$	41.7128			1.36270			0.681349	+	0.731959i	$0.261394\pi$
$938$	4.73205	−	17.6603i	0.154507	−	0.576628i
$939$		0			0
$940$	11.3205	−	19.6077i	0.369234	−	0.639532i
$941$			16.2487i			0.529693i	0.964291	+	0.264846i	$0.0853213\pi$
$941$			16.2487i			0.529693i	−0.964291	+	0.264846i	$0.914679\pi$
$942$		0			0
$943$	−19.7128			−0.641938
$944$	0.679492	−	0.392305i	0.0221156	−	0.0127684i
$945$		0			0
$946$	−12.9282	−	3.46410i	−0.420332	−	0.112628i
$947$		−	10.4449i		−	0.339412i	−0.985495	−	0.169706i	$-0.945718\pi$
$947$		−	10.4449i		−	0.339412i	0.985495	−	0.169706i	$-0.0542819\pi$
$948$		0			0
$949$		−	0.535898i		−	0.0173960i
$950$	7.00000	−	26.1244i	0.227110	−	0.847586i
$951$		0			0
$952$	13.8564	+	13.8564i	0.449089	+	0.449089i
$953$	4.14359			0.134224			0.0671121	−	0.997745i	$-0.478621\pi$
$953$	4.14359			0.134224			0.0671121	+	0.997745i	$0.478621\pi$
$954$		0			0
$955$			74.3538i			2.40603i
$956$	−26.4449	−	15.2679i	−0.855288	−	0.493801i
$957$		0			0
$958$	33.7846	+	9.05256i	1.09153	+	0.292475i
$959$	−4.39230			−0.141835
$960$		0			0
$961$	−20.3205			−0.655500
$962$	6.73205	+	1.80385i	0.217050	+	0.0581584i
$963$		0			0
$964$	−16.6410	−	9.60770i	−0.535971	−	0.309443i
$965$		−	77.5692i		−	2.49704i
$966$		0			0
$967$	42.9808			1.38217			0.691084	−	0.722774i	$-0.257133\pi$
$967$	42.9808			1.38217			0.691084	+	0.722774i	$0.257133\pi$
$968$	−18.7846	−	18.7846i	−0.603760	−	0.603760i
$969$		0			0
$970$	−18.2487	+	68.1051i	−0.585931	+	2.18672i
$971$			43.8564i			1.40742i	0.710488	+	0.703710i	$0.248474\pi$
$971$			43.8564i			1.40742i	−0.710488	+	0.703710i	$0.751526\pi$
$972$		0			0
$973$			47.3205i			1.51703i
$974$	−22.4641	−	6.01924i	−0.719796	−	0.192869i
$975$		0			0
$976$	37.8564	−	21.8564i	1.21175	−	0.699607i
$977$	37.6077			1.20318			0.601588	−	0.798806i	$-0.294535\pi$
$977$	37.6077			1.20318			0.601588	+	0.798806i	$0.294535\pi$
$978$		0			0
$979$		−	21.9615i		−	0.701893i
$980$	−53.3205	+	92.3538i	−1.70326	+	2.95013i
$981$		0			0
$982$	−8.87564	+	33.1244i	−0.283233	+	1.05704i
$983$	−5.80385			−0.185114			−0.0925570	−	0.995707i	$-0.529504\pi$
$983$	−5.80385			−0.185114			−0.0925570	+	0.995707i	$0.529504\pi$
$984$		0			0
$985$	−58.6410			−1.86846
$986$	−1.07180	+	4.00000i	−0.0341330	+	0.127386i
$987$		0			0
$988$	4.73205	+	2.73205i	0.150547	+	0.0869181i
$989$			29.8564i			0.949378i
$990$		0			0
$991$	−43.3205			−1.37612			−0.688061	−	0.725653i	$-0.741538\pi$
$991$	−43.3205			−1.37612			−0.688061	+	0.725653i	$0.741538\pi$
$992$	4.78461	+	17.8564i	0.151912	+	0.566941i
$993$		0			0
$994$	−14.1962	−	3.80385i	−0.450275	−	0.120651i
$995$		−	85.8564i		−	2.72183i
$996$		0			0
$997$		−	49.5692i		−	1.56987i	−0.619576	−	0.784936i	$-0.712696\pi$
$997$		−	49.5692i		−	1.56987i	0.619576	−	0.784936i	$-0.287304\pi$
$998$	−3.92820	+	14.6603i	−0.124345	+	0.464062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.b.469.1		4
3.2	odd	2		104.2.b.b.53.4	yes	4
4.3	odd	2		3744.2.g.b.1873.4		4
8.3	odd	2		3744.2.g.b.1873.2		4
8.5	even	2	inner	936.2.g.b.469.2		4
12.11	even	2		416.2.b.b.209.1		4
24.5	odd	2		104.2.b.b.53.3	✓	4
24.11	even	2		416.2.b.b.209.4		4
48.5	odd	4		3328.2.a.bd.1.2		2
48.11	even	4		3328.2.a.m.1.2		2
48.29	odd	4		3328.2.a.n.1.1		2
48.35	even	4		3328.2.a.bc.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.b.53.3	✓	4	24.5	odd	2
104.2.b.b.53.4	yes	4	3.2	odd	2
416.2.b.b.209.1		4	12.11	even	2
416.2.b.b.209.4		4	24.11	even	2
936.2.g.b.469.1		4	1.1	even	1	trivial
936.2.g.b.469.2		4	8.5	even	2	inner
3328.2.a.m.1.2		2	48.11	even	4
3328.2.a.n.1.1		2	48.29	odd	4
3328.2.a.bc.1.1		2	48.35	even	4
3328.2.a.bd.1.2		2	48.5	odd	4
3744.2.g.b.1873.2		4	8.3	odd	2
3744.2.g.b.1873.4		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +3.46410i q^{5} -4.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.26795 - 4.73205i) q^{10} +1.26795i q^{11} +1.00000i q^{13} +(6.46410 + 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +1.46410 q^{17} -2.73205i q^{19} +(-3.46410 + 6.00000i) q^{20} +(0.464102 - 1.73205i) q^{22} -4.00000 q^{23} -7.00000 q^{25} +(0.366025 - 1.36603i) q^{26} +(-8.19615 - 4.73205i) q^{28} -2.00000i q^{29} -3.26795 q^{31} +(-1.46410 - 5.46410i) q^{32} +(-2.00000 - 0.535898i) q^{34} -16.3923i q^{35} +4.92820i q^{37} +(-1.00000 + 3.73205i) q^{38} +(6.92820 - 6.92820i) q^{40} +4.92820 q^{41} -7.46410i q^{43} +(-1.26795 + 2.19615i) q^{44} +(5.46410 + 1.46410i) q^{46} -3.26795 q^{47} +15.3923 q^{49} +(9.56218 + 2.56218i) q^{50} +(-1.00000 + 1.73205i) q^{52} -10.9282i q^{53} -4.39230 q^{55} +(9.46410 + 9.46410i) q^{56} +(-0.732051 + 2.73205i) q^{58} -0.196152i q^{59} -10.9282i q^{61} +(4.46410 + 1.19615i) q^{62} +8.00000i q^{64} -3.46410 q^{65} -2.73205i q^{67} +(2.53590 + 1.46410i) q^{68} +(-6.00000 + 22.3923i) q^{70} -2.19615 q^{71} -0.535898 q^{73} +(1.80385 - 6.73205i) q^{74} +(2.73205 - 4.73205i) q^{76} -6.00000i q^{77} -1.46410 q^{79} +(-12.0000 + 6.92820i) q^{80} +(-6.73205 - 1.80385i) q^{82} -6.73205i q^{83} +5.07180i q^{85} +(-2.73205 + 10.1962i) q^{86} +(2.53590 - 2.53590i) q^{88} -17.3205 q^{89} -4.73205i q^{91} +(-6.92820 - 4.00000i) q^{92} +(4.46410 + 1.19615i) q^{94} +9.46410 q^{95} -14.3923 q^{97} +(-21.0263 - 5.63397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 12 q^{7} - 8 q^{8} + 12 q^{10} + 12 q^{14} + 8 q^{16} - 8 q^{17} - 12 q^{22} - 16 q^{23} - 28 q^{25} - 2 q^{26} - 12 q^{28} - 20 q^{31} + 8 q^{32} - 8 q^{34} - 4 q^{38} - 8 q^{41} - 12 q^{44}+ \cdots - 46 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 12 * q^7 - 8 * q^8 + 12 * q^10 + 12 * q^14 + 8 * q^16 - 8 * q^17 - 12 * q^22 - 16 * q^23 - 28 * q^25 - 2 * q^26 - 12 * q^28 - 20 * q^31 + 8 * q^32 - 8 * q^34 - 4 * q^38 - 8 * q^41 - 12 * q^44 + 8 * q^46 - 20 * q^47 + 20 * q^49 + 14 * q^50 - 4 * q^52 + 24 * q^55 + 24 * q^56 + 4 * q^58 + 4 * q^62 + 24 * q^68 - 24 * q^70 + 12 * q^71 - 16 * q^73 + 28 * q^74 + 4 * q^76 + 8 * q^79 - 48 * q^80 - 20 * q^82 - 4 * q^86 + 24 * q^88 + 4 * q^94 + 24 * q^95 - 16 * q^97 - 46 * q^98

Introduction

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