LMFDB - Embedded newform 324.2.b.b.323.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,2,Mod(323,324)] 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("324.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.170772624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.8
Root			$0.335728 - 1.37379i$ of defining polynomial
Character	$\chi$	$=$	324.323
Dual form			324.2.b.b.323.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35760 + 0.396143i) q^{2} +(1.68614 + 1.07561i) q^{4} +2.52434i q^{5} -1.27582i q^{7} +(1.86301 + 2.12819i) q^{8} +(-1.00000 + 3.42703i) q^{10} +0.505408 q^{11} -2.37228 q^{13} +(0.505408 - 1.73205i) q^{14} +(1.68614 + 3.62725i) q^{16} +0.792287i q^{17} -4.70285i q^{19} +(-2.71519 + 4.25639i) q^{20} +(0.686141 + 0.200214i) q^{22} +3.22060 q^{23} -1.37228 q^{25} +(-3.22060 - 0.939764i) q^{26} +(1.37228 - 2.15121i) q^{28} +2.52434i q^{29} -8.12989i q^{31} +(0.852189 + 5.59230i) q^{32} +(-0.313859 + 1.07561i) q^{34} +3.22060 q^{35} -6.74456 q^{37} +(1.86301 - 6.38458i) q^{38} +(-5.37228 + 4.70285i) q^{40} -6.78073i q^{41} -7.72946i q^{43} +(0.852189 + 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +1.19897 q^{47} +5.37228 q^{49} +(-1.86301 - 0.543620i) q^{50} +(-4.00000 - 2.55164i) q^{52} +1.87953i q^{53} +1.27582i q^{55} +(2.71519 - 2.37686i) q^{56} +(-1.00000 + 3.42703i) q^{58} -12.3770 q^{59} -2.37228 q^{61} +(3.22060 - 11.0371i) q^{62} +(-1.05842 + 7.92967i) q^{64} -5.98844i q^{65} +7.72946i q^{67} +(-0.852189 + 1.33591i) q^{68} +(4.37228 + 1.27582i) q^{70} -11.8716 q^{71} +3.37228 q^{73} +(-9.15640 - 2.67181i) q^{74} +(5.05842 - 7.92967i) q^{76} -0.644810i q^{77} +9.88067i q^{79} +(-9.15640 + 4.25639i) q^{80} +(2.68614 - 9.20550i) q^{82} -7.64018 q^{83} -2.00000 q^{85} +(3.06198 - 10.4935i) q^{86} +(0.941578 + 1.07561i) q^{88} -11.9769i q^{89} +3.02661i q^{91} +(5.43039 + 3.46410i) q^{92} +(1.62772 + 0.474964i) q^{94} +11.8716 q^{95} +10.4891 q^{97} +(7.29339 + 2.12819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 8 q^{10} + 4 q^{13} + 2 q^{16} - 6 q^{22} + 12 q^{25} - 12 q^{28} - 14 q^{34} - 8 q^{37} - 20 q^{40} + 12 q^{46} + 20 q^{49} - 32 q^{52} - 8 q^{58} + 4 q^{61} + 26 q^{64} + 12 q^{70} + 4 q^{73}+ \cdots - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 8 * q^10 + 4 * q^13 + 2 * q^16 - 6 * q^22 + 12 * q^25 - 12 * q^28 - 14 * q^34 - 8 * q^37 - 20 * q^40 + 12 * q^46 + 20 * q^49 - 32 * q^52 - 8 * q^58 + 4 * q^61 + 26 * q^64 + 12 * q^70 + 4 * q^73 + 6 * q^76 + 10 * q^82 - 16 * q^85 + 42 * q^88 + 36 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.35760	+	0.396143i	0.959966	+	0.280116i
$2$	1.35760	+	0.396143i	0.959966	+	0.280116i
$3$		0			0
$3$		0			0
$4$	1.68614	+	1.07561i	0.843070	+	0.537803i
$5$			2.52434i			1.12892i	0.825461	+	0.564459i	$0.190915\pi$
$5$			2.52434i			1.12892i	−0.825461	+	0.564459i	$0.809085\pi$
$6$		0			0
$7$		−	1.27582i		−	0.482215i	−0.970498	−	0.241107i	$-0.922489\pi$
$7$		−	1.27582i		−	0.482215i	0.970498	−	0.241107i	$-0.0775106\pi$
$8$	1.86301	+	2.12819i	0.658672	+	0.752430i
$9$		0			0
$10$	−1.00000	+	3.42703i	−0.316228	+	1.08372i
$11$	0.505408			0.152386			0.0761931	−	0.997093i	$-0.475723\pi$
$11$	0.505408			0.152386			0.0761931	+	0.997093i	$0.475723\pi$
$12$		0			0
$13$	−2.37228			−0.657952			−0.328976	−	0.944338i	$-0.606704\pi$
$13$	−2.37228			−0.657952			−0.328976	+	0.944338i	$0.606704\pi$
$14$	0.505408	−	1.73205i	0.135076	−	0.462910i
$15$		0			0
$16$	1.68614	+	3.62725i	0.421535	+	0.906812i
$17$			0.792287i			0.192158i	0.995374	+	0.0960789i	$0.0306301\pi$
$17$			0.792287i			0.192158i	−0.995374	+	0.0960789i	$0.969370\pi$
$18$		0			0
$19$		−	4.70285i		−	1.07891i	−0.842015	−	0.539454i	$-0.818631\pi$
$19$		−	4.70285i		−	1.07891i	0.842015	−	0.539454i	$-0.181369\pi$
$20$	−2.71519	+	4.25639i	−0.607136	+	0.951757i
$21$		0			0
$22$	0.686141	+	0.200214i	0.146286	+	0.0426858i
$23$	3.22060			0.671542			0.335771	−	0.941944i	$-0.391003\pi$
$23$	3.22060			0.671542			0.335771	+	0.941944i	$0.391003\pi$
$24$		0			0
$25$	−1.37228			−0.274456
$26$	−3.22060	−	0.939764i	−0.631612	−	0.184303i
$27$		0			0
$28$	1.37228	−	2.15121i	0.259337	−	0.406541i
$29$			2.52434i			0.468758i	0.972145	+	0.234379i	$0.0753056\pi$
$29$			2.52434i			0.468758i	−0.972145	+	0.234379i	$0.924694\pi$
$30$		0			0
$31$		−	8.12989i		−	1.46017i	−0.683356	−	0.730086i	$-0.739480\pi$
$31$		−	8.12989i		−	1.46017i	0.683356	−	0.730086i	$-0.260520\pi$
$32$	0.852189	+	5.59230i	0.150647	+	0.988588i
$33$		0			0
$34$	−0.313859	+	1.07561i	−0.0538264	+	0.184465i
$35$	3.22060			0.544381
$36$		0			0
$37$	−6.74456			−1.10880			−0.554400	−	0.832251i	$-0.687052\pi$
$37$	−6.74456			−1.10880			−0.554400	+	0.832251i	$0.687052\pi$
$38$	1.86301	−	6.38458i	0.302219	−	1.03572i
$39$		0			0
$40$	−5.37228	+	4.70285i	−0.849432	+	0.743587i
$41$		−	6.78073i		−	1.05897i	−0.848319	−	0.529486i	$-0.822385\pi$
$41$		−	6.78073i		−	1.05897i	0.848319	−	0.529486i	$-0.177615\pi$
$42$		0			0
$43$		−	7.72946i		−	1.17873i	−0.807866	−	0.589366i	$-0.799378\pi$
$43$		−	7.72946i		−	1.17873i	0.807866	−	0.589366i	$-0.200622\pi$
$44$	0.852189	+	0.543620i	0.128472	+	0.0819538i
$45$		0			0
$46$	4.37228	+	1.27582i	0.644658	+	0.188110i
$47$	1.19897			0.174888			0.0874439	−	0.996169i	$-0.472130\pi$
$47$	1.19897			0.174888			0.0874439	+	0.996169i	$0.472130\pi$
$48$		0			0
$49$	5.37228			0.767469
$50$	−1.86301	−	0.543620i	−0.263469	−	0.0768795i
$51$		0			0
$52$	−4.00000	−	2.55164i	−0.554700	−	0.353849i
$53$			1.87953i			0.258173i	0.991633	+	0.129086i	$0.0412045\pi$
$53$			1.87953i			0.258173i	−0.991633	+	0.129086i	$0.958796\pi$
$54$		0			0
$55$			1.27582i			0.172032i
$56$	2.71519	−	2.37686i	0.362833	−	0.317621i
$57$		0			0
$58$	−1.00000	+	3.42703i	−0.131306	+	0.449992i
$59$	−12.3770			−1.61135			−0.805674	−	0.592359i	$-0.798197\pi$
$59$	−12.3770			−1.61135			−0.805674	+	0.592359i	$0.798197\pi$
$60$		0			0
$61$	−2.37228			−0.303739			−0.151870	−	0.988401i	$-0.548529\pi$
$61$	−2.37228			−0.303739			−0.151870	+	0.988401i	$0.548529\pi$
$62$	3.22060	−	11.0371i	0.409017	−	1.40172i
$63$		0			0
$64$	−1.05842	+	7.92967i	−0.132303	+	0.991209i
$65$		−	5.98844i		−	0.742774i
$66$		0			0
$67$			7.72946i			0.944304i	0.881517	+	0.472152i	$0.156523\pi$
$67$			7.72946i			0.944304i	−0.881517	+	0.472152i	$0.843477\pi$
$68$	−0.852189	+	1.33591i	−0.103343	+	0.162003i
$69$		0			0
$70$	4.37228	+	1.27582i	0.522588	+	0.152490i
$71$	−11.8716			−1.40890			−0.704450	−	0.709754i	$-0.748806\pi$
$71$	−11.8716			−1.40890			−0.704450	+	0.709754i	$0.748806\pi$
$72$		0			0
$73$	3.37228			0.394696			0.197348	−	0.980334i	$-0.436767\pi$
$73$	3.37228			0.394696			0.197348	+	0.980334i	$0.436767\pi$
$74$	−9.15640	−	2.67181i	−1.06441	−	0.310592i
$75$		0			0
$76$	5.05842	−	7.92967i	0.580241	−	0.909596i
$77$		−	0.644810i		−	0.0734829i
$78$		0			0
$79$			9.88067i			1.11166i	0.831295	+	0.555831i	$0.187600\pi$
$79$			9.88067i			1.11166i	−0.831295	+	0.555831i	$0.812400\pi$
$80$	−9.15640	+	4.25639i	−1.02372	+	0.475879i
$81$		0			0
$82$	2.68614	−	9.20550i	0.296635	−	1.01658i
$83$	−7.64018			−0.838618			−0.419309	−	0.907844i	$-0.637728\pi$
$83$	−7.64018			−0.838618			−0.419309	+	0.907844i	$0.637728\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	3.06198	−	10.4935i	0.330181	−	1.13154i
$87$		0			0
$88$	0.941578	+	1.07561i	0.100373	+	0.114660i
$89$		−	11.9769i		−	1.26955i	−0.772698	−	0.634773i	$-0.781093\pi$
$89$		−	11.9769i		−	1.26955i	0.772698	−	0.634773i	$-0.218907\pi$
$90$		0			0
$91$			3.02661i			0.317274i
$92$	5.43039	+	3.46410i	0.566157	+	0.361158i
$93$		0			0
$94$	1.62772	+	0.474964i	0.167886	+	0.0489888i
$95$	11.8716			1.21800
$96$		0			0
$97$	10.4891			1.06501			0.532505	−	0.846427i	$-0.321251\pi$
$97$	10.4891			1.06501			0.532505	+	0.846427i	$0.321251\pi$
$98$	7.29339	+	2.12819i	0.736744	+	0.214980i
$99$		0			0
$100$	−2.31386	−	1.47603i	−0.231386	−	0.147603i
$101$			1.23472i			0.122859i	0.998111	+	0.0614295i	$0.0195659\pi$
$101$			1.23472i			0.122859i	−0.998111	+	0.0614295i	$0.980434\pi$
$102$		0			0
$103$		−	0.474964i		−	0.0467996i	−0.999726	−	0.0233998i	$-0.992551\pi$
$103$		−	0.474964i		−	0.0467996i	0.999726	−	0.0233998i	$-0.00744907\pi$
$104$	−4.41957	−	5.04868i	−0.433375	−	0.495063i
$105$		0			0
$106$	−0.744563	+	2.55164i	−0.0723183	+	0.247837i
$107$	12.5652			1.21472			0.607360	−	0.794427i	$-0.292229\pi$
$107$	12.5652			1.21472			0.607360	+	0.794427i	$0.292229\pi$
$108$		0			0
$109$	13.4891			1.29202			0.646012	−	0.763327i	$-0.276436\pi$
$109$	13.4891			1.29202			0.646012	+	0.763327i	$0.276436\pi$
$110$	−0.505408	+	1.73205i	−0.0481888	+	0.165145i
$111$		0			0
$112$	4.62772	−	2.15121i	0.437278	−	0.203271i
$113$			7.27806i			0.684662i	0.939579	+	0.342331i	$0.111216\pi$
$113$			7.27806i			0.684662i	−0.939579	+	0.342331i	$0.888784\pi$
$114$		0			0
$115$			8.12989i			0.758116i
$116$	−2.71519	+	4.25639i	−0.252099	+	0.395196i
$117$		0			0
$118$	−16.8030	−	4.90307i	−1.54684	−	0.451364i
$119$	1.01082			0.0926614
$120$		0			0
$121$	−10.7446			−0.976778
$122$	−3.22060	−	0.939764i	−0.291580	−	0.0850822i
$123$		0			0
$124$	8.74456	−	13.7081i	0.785285	−	1.23103i
$125$			9.15759i			0.819080i
$126$		0			0
$127$			7.65492i			0.679265i	0.940558	+	0.339632i	$0.110303\pi$
$127$			7.65492i			0.679265i	−0.940558	+	0.339632i	$0.889697\pi$
$128$	−4.57820	+	10.3460i	−0.404660	+	0.914467i
$129$		0			0
$130$	2.37228	−	8.12989i	0.208063	−	0.713038i
$131$	7.64018			0.667525			0.333763	−	0.942657i	$-0.391682\pi$
$131$	7.64018			0.667525			0.333763	+	0.942657i	$0.391682\pi$
$132$		0			0
$133$	−6.00000			−0.520266
$134$	−3.06198	+	10.4935i	−0.264514	+	0.906500i
$135$		0			0
$136$	−1.68614	+	1.47603i	−0.144585	+	0.126569i
$137$		−	5.49111i		−	0.469137i	−0.972100	−	0.234568i	$-0.924632\pi$
$137$		−	5.49111i		−	0.469137i	0.972100	−	0.234568i	$-0.0753677\pi$
$138$		0			0
$139$			15.3844i			1.30489i	0.757838	+	0.652443i	$0.226256\pi$
$139$			15.3844i			1.30489i	−0.757838	+	0.652443i	$0.773744\pi$
$140$	5.43039	+	3.46410i	0.458952	+	0.292770i
$141$		0			0
$142$	−16.1168	−	4.70285i	−1.35250	−	0.394655i
$143$	−1.19897			−0.100263
$144$		0			0
$145$	−6.37228			−0.529189
$146$	4.57820	+	1.33591i	0.378895	+	0.110560i
$147$		0			0
$148$	−11.3723	−	7.25450i	−0.934796	−	0.596316i
$149$			12.9166i			1.05817i	0.848568	+	0.529086i	$0.177465\pi$
$149$			12.9166i			1.05817i	−0.848568	+	0.529086i	$0.822535\pi$
$150$		0			0
$151$		−	3.02661i		−	0.246302i	−0.992388	−	0.123151i	$-0.960700\pi$
$151$		−	3.02661i		−	0.246302i	0.992388	−	0.123151i	$-0.0392999\pi$
$152$	10.0086	−	8.76144i	0.811804	−	0.710647i
$153$		0			0
$154$	0.255437	−	0.875393i	0.0205837	−	0.0705411i
$155$	20.5226			1.64841
$156$		0			0
$157$	11.8614			0.946643			0.473322	−	0.880890i	$-0.343055\pi$
$157$	11.8614			0.946643			0.473322	+	0.880890i	$0.343055\pi$
$158$	−3.91416	+	13.4140i	−0.311394	+	1.06716i
$159$		0			0
$160$	−14.1168	+	2.15121i	−1.11603	+	0.170068i
$161$		−	4.10891i		−	0.323828i
$162$		0			0
$163$		−	1.75079i		−	0.137132i	−0.997647	−	0.0685660i	$-0.978158\pi$
$163$		−	1.75079i		−	0.137132i	0.997647	−	0.0685660i	$-0.0218424\pi$
$164$	7.29339	−	11.4333i	0.569518	−	0.892787i
$165$		0			0
$166$	−10.3723	−	3.02661i	−0.805045	−	0.234910i
$167$	−17.4901			−1.35343			−0.676714	−	0.736246i	$-0.736597\pi$
$167$	−17.4901			−1.35343			−0.676714	+	0.736246i	$0.736597\pi$
$168$		0			0
$169$	−7.37228			−0.567099
$170$	−2.71519	−	0.792287i	−0.208246	−	0.0607656i
$171$		0			0
$172$	8.31386	−	13.0330i	0.633926	−	0.993754i
$173$			17.6704i			1.34345i	0.740799	+	0.671726i	$0.234447\pi$
$173$			17.6704i			1.34345i	−0.740799	+	0.671726i	$0.765553\pi$
$174$		0			0
$175$			1.75079i			0.132347i
$176$	0.852189	+	1.83324i	0.0642362	+	0.138186i
$177$		0			0
$178$	4.74456	−	16.2598i	0.355620	−	1.21872i
$179$	−8.83915			−0.660669			−0.330334	−	0.943864i	$-0.607162\pi$
$179$	−8.83915			−0.660669			−0.330334	+	0.943864i	$0.607162\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	−1.19897	+	4.10891i	−0.0888736	+	0.304573i
$183$		0			0
$184$	6.00000	+	6.85407i	0.442326	+	0.505289i
$185$		−	17.0256i		−	1.25174i
$186$		0			0
$187$			0.400428i			0.0292822i
$188$	2.02163	+	1.28962i	0.147443	+	0.0940552i
$189$		0			0
$190$	16.1168	+	4.70285i	1.16924	+	0.341181i
$191$	−15.0922			−1.09203			−0.546017	−	0.837774i	$-0.683856\pi$
$191$	−15.0922			−1.09203			−0.546017	+	0.837774i	$0.683856\pi$
$192$		0			0
$193$	7.74456			0.557466			0.278733	−	0.960369i	$-0.410086\pi$
$193$	7.74456			0.557466			0.278733	+	0.960369i	$0.410086\pi$
$194$	14.2400	+	4.15520i	1.02237	+	0.298326i
$195$		0			0
$196$	9.05842	+	5.77846i	0.647030	+	0.412747i
$197$			23.9538i			1.70663i	0.521392	+	0.853317i	$0.325413\pi$
$197$			23.9538i			1.70663i	−0.521392	+	0.853317i	$0.674587\pi$
$198$		0			0
$199$			12.9073i			0.914973i	0.889217	+	0.457486i	$0.151250\pi$
$199$			12.9073i			0.914973i	−0.889217	+	0.457486i	$0.848750\pi$
$200$	−2.55657	−	2.92048i	−0.180777	−	0.206509i
$201$		0			0
$202$	−0.489125	+	1.67625i	−0.0344147	+	0.117940i
$203$	3.22060			0.226042
$204$		0			0
$205$	17.1168			1.19549
$206$	0.188154	−	0.644810i	0.0131093	−	0.0449261i
$207$		0			0
$208$	−4.00000	−	8.60485i	−0.277350	−	0.596639i
$209$		−	2.37686i		−	0.164411i
$210$		0			0
$211$		−	17.5356i		−	1.20720i	−0.797287	−	0.603600i	$-0.793732\pi$
$211$		−	17.5356i		−	1.20720i	0.797287	−	0.603600i	$-0.206268\pi$
$212$	−2.02163	+	3.16915i	−0.138846	+	0.217658i
$213$		0			0
$214$	17.0584	+	4.97760i	1.16609	+	0.340262i
$215$	19.5118			1.33069
$216$		0			0
$217$	−10.3723			−0.704116
$218$	18.3128	+	5.34363i	1.24030	+	0.361916i
$219$		0			0
$220$	−1.37228	+	2.15121i	−0.0925192	+	0.145035i
$221$		−	1.87953i		−	0.126431i
$222$		0			0
$223$			8.12989i			0.544418i	0.962238	+	0.272209i	$0.0877541\pi$
$223$			8.12989i			0.544418i	−0.962238	+	0.272209i	$0.912246\pi$
$224$	7.13477	−	1.08724i	0.476712	−	0.0726443i
$225$		0			0
$226$	−2.88316	+	9.88067i	−0.191785	+	0.657253i
$227$	−14.3986			−0.955671			−0.477835	−	0.878449i	$-0.658578\pi$
$227$	−14.3986			−0.955671			−0.477835	+	0.878449i	$0.658578\pi$
$228$		0			0
$229$	3.62772			0.239726			0.119863	−	0.992790i	$-0.461754\pi$
$229$	3.62772			0.239726			0.119863	+	0.992790i	$0.461754\pi$
$230$	−3.22060	+	11.0371i	−0.212360	+	0.727766i
$231$		0			0
$232$	−5.37228	+	4.70285i	−0.352708	+	0.308758i
$233$		−	4.84630i		−	0.317491i	−0.987320	−	0.158746i	$-0.949255\pi$
$233$		−	4.84630i		−	0.317491i	0.987320	−	0.158746i	$-0.0507450\pi$
$234$		0			0
$235$			3.02661i			0.197434i
$236$	−20.8694	−	13.3128i	−1.35848	−	0.866589i
$237$		0			0
$238$	1.37228	+	0.400428i	0.0889518	+	0.0259559i
$239$	12.0597			0.780080			0.390040	−	0.920798i	$-0.372461\pi$
$239$	12.0597			0.780080			0.390040	+	0.920798i	$0.372461\pi$
$240$		0			0
$241$	−6.48913			−0.418001			−0.209001	−	0.977916i	$-0.567021\pi$
$241$	−6.48913			−0.418001			−0.209001	+	0.977916i	$0.567021\pi$
$242$	−14.5868	−	4.25639i	−0.937674	−	0.273611i
$243$		0			0
$244$	−4.00000	−	2.55164i	−0.256074	−	0.163352i
$245$			13.5615i			0.866409i
$246$		0			0
$247$			11.1565i			0.709871i
$248$	17.3020	−	15.1460i	1.09868	−	0.961774i
$249$		0			0
$250$	−3.62772	+	12.4323i	−0.229437	+	0.786289i
$251$	−11.1780			−0.705551			−0.352776	−	0.935708i	$-0.614762\pi$
$251$	−11.1780			−0.705551			−0.352776	+	0.935708i	$0.614762\pi$
$252$		0			0
$253$	1.62772			0.102334
$254$	−3.03245	+	10.3923i	−0.190273	+	0.652071i
$255$		0			0
$256$	−10.3139	+	12.2321i	−0.644616	+	0.764506i
$257$		−	14.9985i		−	0.935584i	−0.883839	−	0.467792i	$-0.845050\pi$
$257$		−	14.9985i		−	0.935584i	0.883839	−	0.467792i	$-0.154950\pi$
$258$		0			0
$259$			8.60485i			0.534680i
$260$	6.44121	−	10.0974i	0.399467	−	0.626211i
$261$		0			0
$262$	10.3723	+	3.02661i	0.640802	+	0.186984i
$263$	27.9746			1.72499			0.862494	−	0.506067i	$-0.168901\pi$
$263$	27.9746			1.72499			0.862494	+	0.506067i	$0.168901\pi$
$264$		0			0
$265$	−4.74456			−0.291456
$266$	−8.14558	−	2.37686i	−0.499438	−	0.145735i
$267$		0			0
$268$	−8.31386	+	13.0330i	−0.507850	+	0.796115i
$269$		−	21.4843i		−	1.30992i	−0.755663	−	0.654961i	$-0.772685\pi$
$269$		−	21.4843i		−	1.30992i	0.755663	−	0.654961i	$-0.227315\pi$
$270$		0			0
$271$		−	29.9679i		−	1.82042i	−0.414146	−	0.910211i	$-0.635920\pi$
$271$		−	29.9679i		−	1.82042i	0.414146	−	0.910211i	$-0.364080\pi$
$272$	−2.87382	+	1.33591i	−0.174251	+	0.0810013i
$273$		0			0
$274$	2.17527	−	7.45471i	0.131413	−	0.450356i
$275$	−0.693562			−0.0418234
$276$		0			0
$277$	6.37228			0.382873			0.191437	−	0.981505i	$-0.438685\pi$
$277$	6.37228			0.382873			0.191437	+	0.981505i	$0.438685\pi$
$278$	−6.09442	+	20.8858i	−0.365519	+	1.25265i
$279$		0			0
$280$	6.00000	+	6.85407i	0.358569	+	0.409609i
$281$		−	23.0140i		−	1.37290i	−0.727177	−	0.686450i	$-0.759168\pi$
$281$		−	23.0140i		−	1.37290i	0.727177	−	0.686450i	$-0.240832\pi$
$282$		0			0
$283$		−	9.88067i		−	0.587345i	−0.955906	−	0.293673i	$-0.905122\pi$
$283$		−	9.88067i		−	0.587345i	0.955906	−	0.293673i	$-0.0948775\pi$
$284$	−20.0172	−	12.7692i	−1.18780	−	0.757711i
$285$		0			0
$286$	−1.62772	−	0.474964i	−0.0962490	−	0.0280852i
$287$	−8.65099			−0.510652
$288$		0			0
$289$	16.3723			0.963075
$290$	−8.65099	−	2.52434i	−0.508004	−	0.148234i
$291$		0			0
$292$	5.68614	+	3.62725i	0.332756	+	0.212269i
$293$			23.3089i			1.36172i	0.732412	+	0.680862i	$0.238395\pi$
$293$			23.3089i			1.36172i	−0.732412	+	0.680862i	$0.761605\pi$
$294$		0			0
$295$		−	31.2437i		−	1.81908i
$296$	−12.5652	−	14.3537i	−0.730335	−	0.834294i
$297$		0			0
$298$	−5.11684	+	17.5356i	−0.296411	+	1.01581i
$299$	−7.64018			−0.441843
$300$		0			0
$301$	−9.86141			−0.568402
$302$	1.19897	−	4.10891i	0.0689930	−	0.236441i
$303$		0			0
$304$	17.0584	−	7.92967i	0.978368	−	0.454798i
$305$		−	5.98844i		−	0.342897i
$306$		0			0
$307$			1.20128i			0.0685609i	0.999412	+	0.0342805i	$0.0109140\pi$
$307$			1.20128i			0.0685609i	−0.999412	+	0.0342805i	$0.989086\pi$
$308$	0.693562	−	1.08724i	0.0395194	−	0.0619513i
$309$		0			0
$310$	27.8614	+	8.12989i	1.58242	+	0.461747i
$311$	−19.1355			−1.08507			−0.542536	−	0.840032i	$-0.682536\pi$
$311$	−19.1355			−1.08507			−0.542536	+	0.840032i	$0.682536\pi$
$312$		0			0
$313$	−18.4891			−1.04507			−0.522534	−	0.852619i	$-0.675013\pi$
$313$	−18.4891			−1.04507			−0.522534	+	0.852619i	$0.675013\pi$
$314$	16.1030	+	4.69882i	0.908746	+	0.265170i
$315$		0			0
$316$	−10.6277	+	16.6602i	−0.597856	+	0.937210i
$317$		−	32.5214i		−	1.82659i	−0.407303	−	0.913293i	$-0.633531\pi$
$317$		−	32.5214i		−	1.82659i	0.407303	−	0.913293i	$-0.366469\pi$
$318$		0			0
$319$			1.27582i			0.0714323i
$320$	−20.0172	−	2.67181i	−1.11899	−	0.149359i
$321$		0			0
$322$	1.62772	−	5.57825i	0.0907092	−	0.310864i
$323$	3.72601			0.207321
$324$		0			0
$325$	3.25544			0.180579
$326$	0.693562	−	2.37686i	0.0384129	−	0.131642i
$327$		0			0
$328$	14.4307	−	12.6325i	0.796802	−	0.697515i
$329$		−	1.52967i		−	0.0843335i
$330$		0			0
$331$		−	27.7422i		−	1.52485i	−0.647078	−	0.762424i	$-0.724009\pi$
$331$		−	27.7422i		−	1.52485i	0.647078	−	0.762424i	$-0.275991\pi$
$332$	−12.8824	−	8.21782i	−0.707014	−	0.451012i
$333$		0			0
$334$	−23.7446	−	6.92860i	−1.29924	−	0.379116i
$335$	−19.5118			−1.06604
$336$		0			0
$337$	−15.7446			−0.857661			−0.428830	−	0.903385i	$-0.641074\pi$
$337$	−15.7446			−0.857661			−0.428830	+	0.903385i	$0.641074\pi$
$338$	−10.0086	−	2.92048i	−0.544395	−	0.158853i
$339$		0			0
$340$	−3.37228	−	2.15121i	−0.182888	−	0.116666i
$341$		−	4.10891i		−	0.222510i
$342$		0			0
$343$		−	15.7848i		−	0.852300i
$344$	16.4498	−	14.4000i	0.886913	−	0.776397i
$345$		0			0
$346$	−7.00000	+	23.9892i	−0.376322	+	1.28967i
$347$	6.94661			0.372914			0.186457	−	0.982463i	$-0.440300\pi$
$347$	6.94661			0.372914			0.186457	+	0.982463i	$0.440300\pi$
$348$		0			0
$349$	−5.62772			−0.301245			−0.150622	−	0.988591i	$-0.548128\pi$
$349$	−5.62772			−0.301245			−0.150622	+	0.988591i	$0.548128\pi$
$350$	−0.693562	+	2.37686i	−0.0370725	+	0.127049i
$351$		0			0
$352$	0.430703	+	2.82639i	0.0229566	+	0.150647i
$353$			8.36530i			0.445240i	0.974905	+	0.222620i	$0.0714609\pi$
$353$			8.36530i			0.445240i	−0.974905	+	0.222620i	$0.928539\pi$
$354$		0			0
$355$		−	29.9679i		−	1.59053i
$356$	12.8824	−	20.1947i	0.682766	−	1.07032i
$357$		0			0
$358$	−12.0000	−	3.50157i	−0.634220	−	0.185064i
$359$	1.38712			0.0732096			0.0366048	−	0.999330i	$-0.488346\pi$
$359$	1.38712			0.0732096			0.0366048	+	0.999330i	$0.488346\pi$
$360$		0			0
$361$	−3.11684			−0.164044
$362$	−5.43039	−	1.58457i	−0.285415	−	0.0832834i
$363$		0			0
$364$	−3.25544	+	5.10328i	−0.170631	+	0.267485i
$365$			8.51278i			0.445579i
$366$		0			0
$367$			6.37910i			0.332987i	0.986043	+	0.166493i	$0.0532444\pi$
$367$			6.37910i			0.332987i	−0.986043	+	0.166493i	$0.946756\pi$
$368$	5.43039	+	11.6819i	0.283079	+	0.608962i
$369$		0			0
$370$	6.74456	−	23.1138i	0.350633	−	1.20163i
$371$	2.39794			0.124495
$372$		0			0
$373$	−19.8614			−1.02838			−0.514192	−	0.857675i	$-0.671908\pi$
$373$	−19.8614			−1.02838			−0.514192	+	0.857675i	$0.671908\pi$
$374$	−0.158627	+	0.543620i	−0.00820241	+	0.0281099i
$375$		0			0
$376$	2.23369	+	2.55164i	0.115194	+	0.131591i
$377$		−	5.98844i		−	0.308420i
$378$		0			0
$379$			6.45364i			0.331501i	0.986168	+	0.165751i	$0.0530047\pi$
$379$			6.45364i			0.331501i	−0.986168	+	0.165751i	$0.946995\pi$
$380$	20.0172	+	12.7692i	1.02686	+	0.655044i
$381$		0			0
$382$	−20.4891	−	5.97868i	−1.04831	−	0.305896i
$383$	−8.65099			−0.442045			−0.221023	−	0.975269i	$-0.570939\pi$
$383$	−8.65099			−0.442045			−0.221023	+	0.975269i	$0.570939\pi$
$384$		0			0
$385$	1.62772			0.0829562
$386$	10.5140	+	3.06796i	0.535148	+	0.156155i
$387$		0			0
$388$	17.6861	+	11.2822i	0.897878	+	0.572766i
$389$			31.5268i			1.59847i	0.601018	+	0.799235i	$0.294762\pi$
$389$			31.5268i			1.59847i	−0.601018	+	0.799235i	$0.705238\pi$
$390$		0			0
$391$			2.55164i			0.129042i
$392$	10.0086	+	11.4333i	0.505510	+	0.577467i
$393$		0			0
$394$	−9.48913	+	32.5196i	−0.478055	+	1.63831i
$395$	−24.9422			−1.25498
$396$		0			0
$397$	−18.7446			−0.940763			−0.470381	−	0.882463i	$-0.655884\pi$
$397$	−18.7446			−0.940763			−0.470381	+	0.882463i	$0.655884\pi$
$398$	−5.11313	+	17.5229i	−0.256298	+	0.878343i
$399$		0			0
$400$	−2.31386	−	4.97760i	−0.115693	−	0.248880i
$401$		−	4.60625i		−	0.230025i	−0.993364	−	0.115012i	$-0.963309\pi$
$401$		−	4.60625i		−	0.230025i	0.993364	−	0.115012i	$-0.0366908\pi$
$402$		0			0
$403$			19.2864i			0.960723i
$404$	−1.32807	+	2.08191i	−0.0660740	+	0.103579i
$405$		0			0
$406$	4.37228	+	1.27582i	0.216993	+	0.0633179i
$407$	−3.40876			−0.168966
$408$		0			0
$409$	13.7446			0.679625			0.339812	−	0.940493i	$-0.389636\pi$
$409$	13.7446			0.679625			0.339812	+	0.940493i	$0.389636\pi$
$410$	23.2378	+	6.78073i	1.14763	+	0.334876i
$411$		0			0
$412$	0.510875	−	0.800857i	0.0251690	−	0.0394554i
$413$			15.7908i			0.777016i
$414$		0			0
$415$		−	19.2864i		−	0.946731i
$416$	−2.02163	−	13.2665i	−0.0991187	−	0.650444i
$417$		0			0
$418$	0.941578	−	3.22682i	0.0460541	−	0.157829i
$419$	26.9638			1.31727			0.658634	−	0.752464i	$-0.271135\pi$
$419$	26.9638			1.31727			0.658634	+	0.752464i	$0.271135\pi$
$420$		0			0
$421$	−10.6060			−0.516903			−0.258452	−	0.966024i	$-0.583212\pi$
$421$	−10.6060			−0.516903			−0.258452	+	0.966024i	$0.583212\pi$
$422$	6.94661	−	23.8063i	0.338156	−	1.15887i
$423$		0			0
$424$	−4.00000	+	3.50157i	−0.194257	+	0.170051i
$425$		−	1.08724i		−	0.0527389i
$426$		0			0
$427$			3.02661i			0.146468i
$428$	21.1866	+	13.5152i	1.02409	+	0.653280i
$429$		0			0
$430$	26.4891	+	7.72946i	1.27742	+	0.372748i
$431$	31.1952			1.50262			0.751310	−	0.659949i	$-0.229422\pi$
$431$	31.1952			1.50262			0.751310	+	0.659949i	$0.229422\pi$
$432$		0			0
$433$	−8.62772			−0.414622			−0.207311	−	0.978275i	$-0.566471\pi$
$433$	−8.62772			−0.414622			−0.207311	+	0.978275i	$0.566471\pi$
$434$	−14.0814	−	4.10891i	−0.675928	−	0.197234i
$435$		0			0
$436$	22.7446	+	14.5090i	1.08927	+	0.694855i
$437$		−	15.1460i		−	0.724533i
$438$		0			0
$439$		−	6.52818i		−	0.311573i	−0.987791	−	0.155786i	$-0.950209\pi$
$439$		−	6.52818i		−	0.311573i	0.987791	−	0.155786i	$-0.0497912\pi$
$440$	−2.71519	+	2.37686i	−0.129442	+	0.113312i
$441$		0			0
$442$	0.744563	−	2.55164i	0.0354152	−	0.121369i
$443$	12.3770			0.588049			0.294025	−	0.955798i	$-0.405005\pi$
$443$	12.3770			0.588049			0.294025	+	0.955798i	$0.405005\pi$
$444$		0			0
$445$	30.2337			1.43321
$446$	−3.22060	+	11.0371i	−0.152500	+	0.522623i
$447$		0			0
$448$	10.1168	+	1.35036i	0.477976	+	0.0637984i
$449$			19.4024i			0.915657i	0.889041	+	0.457828i	$0.151373\pi$
$449$			19.4024i			0.915657i	−0.889041	+	0.457828i	$0.848627\pi$
$450$		0			0
$451$		−	3.42703i		−	0.161373i
$452$	−7.82833	+	12.2718i	−0.368214	+	0.577218i
$453$		0			0
$454$	−19.5475	−	5.70393i	−0.917412	−	0.267698i
$455$	−7.64018			−0.358177
$456$		0			0
$457$	39.9783			1.87010			0.935052	−	0.354511i	$-0.115353\pi$
$457$	39.9783			1.87010			0.935052	+	0.354511i	$0.115353\pi$
$458$	4.92498	+	1.43710i	0.230129	+	0.0671511i
$459$		0			0
$460$	−8.74456	+	13.7081i	−0.407717	+	0.639145i
$461$			0.349857i			0.0162944i	0.999967	+	0.00814722i	$0.00259337\pi$
$461$			0.349857i			0.0162944i	−0.999967	+	0.00814722i	$0.997407\pi$
$462$		0			0
$463$			4.77739i			0.222024i	0.993819	+	0.111012i	$0.0354092\pi$
$463$			4.77739i			0.222024i	−0.993819	+	0.111012i	$0.964591\pi$
$464$	−9.15640	+	4.25639i	−0.425075	+	0.197598i
$465$		0			0
$466$	1.91983	−	6.57932i	0.0889343	−	0.304781i
$467$	−5.11313			−0.236608			−0.118304	−	0.992977i	$-0.537746\pi$
$467$	−5.11313			−0.236608			−0.118304	+	0.992977i	$0.537746\pi$
$468$		0			0
$469$	9.86141			0.455357
$470$	−1.19897	+	4.10891i	−0.0553044	+	0.189530i
$471$		0			0
$472$	−23.0584	−	26.3407i	−1.06135	−	1.21243i
$473$		−	3.90653i		−	0.179623i
$474$		0			0
$475$			6.45364i			0.296113i
$476$	1.70438	+	1.08724i	0.0781201	+	0.0498336i
$477$		0			0
$478$	16.3723	+	4.77739i	0.748851	+	0.218513i
$479$	13.0706			0.597209			0.298605	−	0.954377i	$-0.403479\pi$
$479$	13.0706			0.597209			0.298605	+	0.954377i	$0.403479\pi$
$480$		0			0
$481$	16.0000			0.729537
$482$	−8.80962	−	2.57062i	−0.401267	−	0.117089i
$483$		0			0
$484$	−18.1168	−	11.5569i	−0.823493	−	0.525315i
$485$			26.4781i			1.20231i
$486$		0			0
$487$			42.8752i			1.94286i	0.237325	+	0.971430i	$0.423729\pi$
$487$			42.8752i			1.94286i	−0.237325	+	0.971430i	$0.576271\pi$
$488$	−4.41957	−	5.04868i	−0.200065	−	0.228543i
$489$		0			0
$490$	−5.37228	+	18.4110i	−0.242695	+	0.831724i
$491$	−13.7641			−0.621166			−0.310583	−	0.950546i	$-0.600524\pi$
$491$	−13.7641			−0.621166			−0.310583	+	0.950546i	$0.600524\pi$
$492$		0			0
$493$	−2.00000			−0.0900755
$494$	−4.41957	+	15.1460i	−0.198846	+	0.681452i
$495$		0			0
$496$	29.4891	−	13.7081i	1.32410	−	0.615513i
$497$			15.1460i			0.679392i
$498$		0			0
$499$		−	3.42703i		−	0.153415i	−0.997054	−	0.0767076i	$-0.975559\pi$
$499$		−	3.42703i		−	0.153415i	0.997054	−	0.0767076i	$-0.0244408\pi$
$500$	−9.84996	+	15.4410i	−0.440504	+	0.690542i
$501$		0			0
$502$	−15.1753	−	4.42810i	−0.677305	−	0.197636i
$503$	19.3236			0.861597			0.430799	−	0.902448i	$-0.358232\pi$
$503$	19.3236			0.861597			0.430799	+	0.902448i	$0.358232\pi$
$504$		0			0
$505$	−3.11684			−0.138698
$506$	2.20979	+	0.644810i	0.0982370	+	0.0286653i
$507$		0			0
$508$	−8.23369	+	12.9073i	−0.365311	+	0.572668i
$509$		−	14.7962i		−	0.655829i	−0.944707	−	0.327914i	$-0.893654\pi$
$509$		−	14.7962i		−	0.655829i	0.944707	−	0.327914i	$-0.106346\pi$
$510$		0			0
$511$		−	4.30243i		−	0.190328i
$512$	−18.8477	+	12.5205i	−0.832960	+	0.553333i
$513$		0			0
$514$	5.94158	−	20.3620i	0.262072	−	0.898129i
$515$	1.19897			0.0528329
$516$		0			0
$517$	0.605969			0.0266505
$518$	−3.40876	+	11.6819i	−0.149772	+	0.513274i
$519$		0			0
$520$	12.7446	−	11.1565i	0.558886	−	0.489245i
$521$		−	26.0357i		−	1.14064i	−0.821421	−	0.570322i	$-0.806819\pi$
$521$		−	26.0357i		−	1.14064i	0.821421	−	0.570322i	$-0.193181\pi$
$522$		0			0
$523$			9.40571i			0.411283i	0.978627	+	0.205641i	$0.0659281\pi$
$523$			9.40571i			0.411283i	−0.978627	+	0.205641i	$0.934072\pi$
$524$	12.8824	+	8.21782i	0.562771	+	0.358997i
$525$		0			0
$526$	37.9783	+	11.0820i	1.65593	+	0.483196i
$527$	6.44121			0.280583
$528$		0			0
$529$	−12.6277			−0.549031
$530$	−6.44121	−	1.87953i	−0.279788	−	0.0816415i
$531$		0			0
$532$	−10.1168	−	6.45364i	−0.438621	−	0.279801i
$533$			16.0858i			0.696753i
$534$		0			0
$535$			31.7187i			1.37132i
$536$	−16.4498	+	14.4000i	−0.710523	+	0.621986i
$537$		0			0
$538$	8.51087	−	29.1671i	0.366930	−	1.25748i
$539$	2.71519			0.116952
$540$		0			0
$541$	−8.97825			−0.386005			−0.193003	−	0.981198i	$-0.561823\pi$
$541$	−8.97825			−0.386005			−0.193003	+	0.981198i	$0.561823\pi$
$542$	11.8716	−	40.6844i	0.509929	−	1.74754i
$543$		0			0
$544$	−4.43070	+	0.675178i	−0.189965	+	0.0289480i
$545$			34.0511i			1.45859i
$546$		0			0
$547$			22.2385i			0.950848i	0.879757	+	0.475424i	$0.157705\pi$
$547$			22.2385i			0.950848i	−0.879757	+	0.475424i	$0.842295\pi$
$548$	5.90627	−	9.25878i	0.252303	−	0.395515i
$549$		0			0
$550$	−0.941578	−	0.274750i	−0.0401490	−	0.0117154i
$551$	11.8716			0.505747
$552$		0			0
$553$	12.6060			0.536060
$554$	8.65099	+	2.52434i	0.367545	+	0.107249i
$555$		0			0
$556$	−16.5475	+	25.9402i	−0.701772	+	1.10011i
$557$		−	7.22316i		−	0.306055i	−0.988222	−	0.153027i	$-0.951098\pi$
$557$		−	7.22316i		−	0.306055i	0.988222	−	0.153027i	$-0.0489023\pi$
$558$		0			0
$559$			18.3365i			0.775549i
$560$	5.43039	+	11.6819i	0.229476	+	0.493651i
$561$		0			0
$562$	9.11684	−	31.2437i	0.384571	−	1.31794i
$563$	15.7858			0.665290			0.332645	−	0.943052i	$-0.392059\pi$
$563$	15.7858			0.665290			0.332645	+	0.943052i	$0.392059\pi$
$564$		0			0
$565$	−18.3723			−0.772928
$566$	3.91416	−	13.4140i	0.164525	−	0.563831i
$567$		0			0
$568$	−22.1168	−	25.2651i	−0.928002	−	1.06010i
$569$		−	25.3909i		−	1.06444i	−0.846606	−	0.532220i	$-0.821358\pi$
$569$		−	25.3909i		−	1.06444i	0.846606	−	0.532220i	$-0.178642\pi$
$570$		0			0
$571$			4.22789i			0.176932i	0.996079	+	0.0884659i	$0.0281964\pi$
$571$			4.22789i			0.176932i	−0.996079	+	0.0884659i	$0.971804\pi$
$572$	−2.02163	−	1.28962i	−0.0845287	−	0.0539217i
$573$		0			0
$574$	−11.7446	−	3.42703i	−0.490209	−	0.143042i
$575$	−4.41957			−0.184309
$576$		0			0
$577$	31.8397			1.32550			0.662751	−	0.748840i	$-0.269389\pi$
$577$	31.8397			1.32550			0.662751	+	0.748840i	$0.269389\pi$
$578$	22.2270	+	6.48577i	0.924520	+	0.269773i
$579$		0			0
$580$	−10.7446	−	6.85407i	−0.446144	−	0.284600i
$581$			9.74749i			0.404394i
$582$		0			0
$583$			0.949929i			0.0393420i
$584$	6.28258	+	7.17687i	0.259975	+	0.296981i
$585$		0			0
$586$	−9.23369	+	31.6442i	−0.381440	+	1.30721i
$587$	−3.91416			−0.161555			−0.0807774	−	0.996732i	$-0.525740\pi$
$587$	−3.91416			−0.161555			−0.0807774	+	0.996732i	$0.525740\pi$
$588$		0			0
$589$	−38.2337			−1.57539
$590$	12.3770	−	42.4164i	0.509553	−	1.74626i
$591$		0			0
$592$	−11.3723	−	24.4642i	−0.467398	−	1.00547i
$593$			8.80773i			0.361690i	0.983512	+	0.180845i	$0.0578833\pi$
$593$			8.80773i			0.361690i	−0.983512	+	0.180845i	$0.942117\pi$
$594$		0			0
$595$			2.55164i			0.104607i
$596$	−13.8932	+	21.7793i	−0.569089	+	0.892114i
$597$		0			0
$598$	−10.3723	−	3.02661i	−0.424154	−	0.123767i
$599$	0.188154			0.00768776			0.00384388	−	0.999993i	$-0.498776\pi$
$599$	0.188154			0.00768776			0.00384388	+	0.999993i	$0.498776\pi$
$600$		0			0
$601$	15.9783			0.651766			0.325883	−	0.945410i	$-0.394338\pi$
$601$	15.9783			0.651766			0.325883	+	0.945410i	$0.394338\pi$
$602$	−13.3878	−	3.90653i	−0.545647	−	0.159218i
$603$		0			0
$604$	3.25544	−	5.10328i	0.132462	−	0.207650i
$605$		−	27.1229i		−	1.10270i
$606$		0			0
$607$		−	3.97653i		−	0.161403i	−0.996738	−	0.0807013i	$-0.974284\pi$
$607$		−	3.97653i		−	0.161403i	0.996738	−	0.0807013i	$-0.0257160\pi$
$608$	26.2998	−	4.00772i	1.06660	−	0.162535i
$609$		0			0
$610$	2.37228	−	8.12989i	0.0960509	−	0.329170i
$611$	−2.84429			−0.115068
$612$		0			0
$613$	4.23369			0.170997			0.0854985	−	0.996338i	$-0.472752\pi$
$613$	4.23369			0.170997			0.0854985	+	0.996338i	$0.472752\pi$
$614$	−0.475881	+	1.63086i	−0.0192050	+	0.0658162i
$615$		0			0
$616$	1.37228	−	1.20128i	0.0552908	−	0.0484011i
$617$			4.90120i			0.197315i	0.995121	+	0.0986574i	$0.0314548\pi$
$617$			4.90120i			0.197315i	−0.995121	+	0.0986574i	$0.968545\pi$
$618$		0			0
$619$			9.33117i			0.375052i	0.982260	+	0.187526i	$0.0600468\pi$
$619$			9.33117i			0.375052i	−0.982260	+	0.187526i	$0.939953\pi$
$620$	34.6040	+	22.0742i	1.38973	+	0.886522i
$621$		0			0
$622$	−25.9783	−	7.58039i	−1.04163	−	0.303946i
$623$	−15.2804			−0.612194
$624$		0			0
$625$	−29.9783			−1.19913
$626$	−25.1008	−	7.32435i	−1.00323	−	0.292740i
$627$		0			0
$628$	20.0000	+	12.7582i	0.798087	+	0.509108i
$629$		−	5.34363i		−	0.213064i
$630$		0			0
$631$		−	42.8752i		−	1.70683i	−0.521228	−	0.853417i	$-0.674526\pi$
$631$		−	42.8752i		−	1.70683i	0.521228	−	0.853417i	$-0.325474\pi$
$632$	−21.0280	+	18.4077i	−0.836449	+	0.732221i
$633$		0			0
$634$	12.8832	−	44.1510i	0.511655	−	1.75346i
$635$	−19.3236			−0.766834
$636$		0			0
$637$	−12.7446			−0.504958
$638$	−0.505408	+	1.73205i	−0.0200093	+	0.0685725i
$639$		0			0
$640$	−26.1168	−	11.5569i	−1.03236	−	0.456827i
$641$			20.9321i			0.826768i	0.910557	+	0.413384i	$0.135653\pi$
$641$			20.9321i			0.826768i	−0.910557	+	0.413384i	$0.864347\pi$
$642$		0			0
$643$			35.9466i			1.41760i	0.705412	+	0.708798i	$0.250762\pi$
$643$			35.9466i			1.41760i	−0.705412	+	0.708798i	$0.749238\pi$
$644$	4.41957	−	6.92820i	0.174156	−	0.273009i
$645$		0			0
$646$	5.05842	+	1.47603i	0.199021	+	0.0580738i
$647$	−46.0993			−1.81235			−0.906174	−	0.422904i	$-0.861011\pi$
$647$	−46.0993			−1.81235			−0.906174	+	0.422904i	$0.861011\pi$
$648$		0			0
$649$	−6.25544			−0.245547
$650$	4.41957	+	1.28962i	0.173350	+	0.0505831i
$651$		0			0
$652$	1.88316	−	2.95207i	0.0737501	−	0.115612i
$653$		−	4.40387i		−	0.172337i	−0.996281	−	0.0861683i	$-0.972538\pi$
$653$		−	4.40387i		−	0.172337i	0.996281	−	0.0861683i	$-0.0274623\pi$
$654$		0			0
$655$			19.2864i			0.753581i
$656$	24.5954	−	11.4333i	0.960288	−	0.446394i
$657$		0			0
$658$	0.605969	−	2.07668i	0.0236231	−	0.0809573i
$659$	−12.0597			−0.469781			−0.234891	−	0.972022i	$-0.575473\pi$
$659$	−12.0597			−0.469781			−0.234891	+	0.972022i	$0.575473\pi$
$660$		0			0
$661$	15.6277			0.607848			0.303924	−	0.952696i	$-0.401703\pi$
$661$	15.6277			0.607848			0.303924	+	0.952696i	$0.401703\pi$
$662$	10.9899	−	37.6627i	0.427134	−	1.46380i
$663$		0			0
$664$	−14.2337	−	16.2598i	−0.552374	−	0.631002i
$665$		−	15.1460i		−	0.587338i
$666$		0			0
$667$			8.12989i			0.314791i
$668$	−29.4908	−	18.8125i	−1.14103	−	0.727878i
$669$		0			0
$670$	−26.4891	−	7.72946i	−1.02336	−	0.298615i
$671$	−1.19897			−0.0462857
$672$		0			0
$673$	29.8614			1.15107			0.575536	−	0.817776i	$-0.304793\pi$
$673$	29.8614			1.15107			0.575536	+	0.817776i	$0.304793\pi$
$674$	−21.3748	−	6.23711i	−0.823326	−	0.240244i
$675$		0			0
$676$	−12.4307	−	7.92967i	−0.478104	−	0.304987i
$677$		−	3.51900i		−	0.135246i	−0.997711	−	0.0676232i	$-0.978458\pi$
$677$		−	3.51900i		−	0.135246i	0.997711	−	0.0676232i	$-0.0215416\pi$
$678$		0			0
$679$		−	13.3822i		−	0.513563i
$680$	−3.72601	−	4.25639i	−0.142886	−	0.163225i
$681$		0			0
$682$	1.62772	−	5.57825i	0.0623286	−	0.213602i
$683$	20.0172			0.765936			0.382968	−	0.923762i	$-0.374902\pi$
$683$	20.0172			0.765936			0.382968	+	0.923762i	$0.374902\pi$
$684$		0			0
$685$	13.8614			0.529617
$686$	6.25305	−	21.4294i	0.238743	−	0.818179i
$687$		0			0
$688$	28.0367	−	13.0330i	1.06889	−	0.496877i
$689$		−	4.45877i		−	0.169866i
$690$		0			0
$691$		−	20.0872i		−	0.764155i	−0.924130	−	0.382077i	$-0.875209\pi$
$691$		−	20.0872i		−	0.764155i	0.924130	−	0.382077i	$-0.124791\pi$
$692$	−19.0064	+	29.7947i	−0.722513	+	1.13263i
$693$		0			0
$694$	9.43070	+	2.75186i	0.357985	+	0.104459i
$695$	−38.8354			−1.47311
$696$		0			0
$697$	5.37228			0.203490
$698$	−7.64018	−	2.22938i	−0.289185	−	0.0843834i
$699$		0			0
$700$	−1.88316	+	2.95207i	−0.0711766	+	0.111578i
$701$		−	32.7615i		−	1.23738i	−0.785634	−	0.618692i	$-0.787663\pi$
$701$		−	32.7615i		−	1.23738i	0.785634	−	0.618692i	$-0.212337\pi$
$702$		0			0
$703$			31.7187i			1.19629i
$704$	−0.534935	+	4.00772i	−0.0201611	+	0.151047i
$705$		0			0
$706$	−3.31386	+	11.3567i	−0.124719	+	0.427415i
$707$	1.57528			0.0592444
$708$		0			0
$709$	23.8614			0.896134			0.448067	−	0.894000i	$-0.352113\pi$
$709$	23.8614			0.896134			0.448067	+	0.894000i	$0.352113\pi$
$710$	11.8716	−	40.6844i	0.445533	−	1.52686i
$711$		0			0
$712$	25.4891	−	22.3130i	0.955245	−	0.836215i
$713$		−	26.1831i		−	0.980566i
$714$		0			0
$715$		−	3.02661i		−	0.113189i
$716$	−14.9040	−	9.50744i	−0.556990	−	0.355310i
$717$		0			0
$718$	1.88316	+	0.549500i	0.0702788	+	0.0205072i
$719$	−16.2912			−0.607558			−0.303779	−	0.952743i	$-0.598248\pi$
$719$	−16.2912			−0.607558			−0.303779	+	0.952743i	$0.598248\pi$
$720$		0			0
$721$	−0.605969			−0.0225675
$722$	−4.23142	−	1.23472i	−0.157477	−	0.0459514i
$723$		0			0
$724$	−6.74456	−	4.30243i	−0.250660	−	0.159898i
$725$		−	3.46410i		−	0.128654i
$726$		0			0
$727$			38.0978i			1.41297i	0.707728	+	0.706485i	$0.249720\pi$
$727$			38.0978i			1.41297i	−0.707728	+	0.706485i	$0.750280\pi$
$728$	−6.44121	+	5.63858i	−0.238727	+	0.208980i
$729$		0			0
$730$	−3.37228	+	11.5569i	−0.124814	+	0.427741i
$731$	6.12395			0.226503
$732$		0			0
$733$	0.372281			0.0137505			0.00687526	−	0.999976i	$-0.497812\pi$
$733$	0.372281			0.0137505			0.00687526	+	0.999976i	$0.497812\pi$
$734$	−2.52704	+	8.66025i	−0.0932748	+	0.319656i
$735$		0			0
$736$	2.74456	+	18.0106i	0.101166	+	0.663878i
$737$			3.90653i			0.143899i
$738$		0			0
$739$		−	6.45364i		−	0.237401i	−0.992930	−	0.118700i	$-0.962127\pi$
$739$		−	6.45364i		−	0.237401i	0.992930	−	0.118700i	$-0.0378728\pi$
$740$	18.3128	−	28.7075i	0.673192	−	1.05531i
$741$		0			0
$742$	3.25544	+	0.949929i	0.119511	+	0.0348730i
$743$	21.1571			0.776179			0.388089	−	0.921622i	$-0.373135\pi$
$743$	21.1571			0.776179			0.388089	+	0.921622i	$0.373135\pi$
$744$		0			0
$745$	−32.6060			−1.19459
$746$	−26.9638	−	7.86797i	−0.987215	−	0.288067i
$747$		0			0
$748$	−0.430703	+	0.675178i	−0.0157481	+	0.0246870i
$749$		−	16.0309i		−	0.585756i
$750$		0			0
$751$		−	21.6890i		−	0.791441i	−0.918371	−	0.395721i	$-0.870495\pi$
$751$		−	21.6890i		−	0.791441i	0.918371	−	0.395721i	$-0.129505\pi$
$752$	2.02163	+	4.34896i	0.0737213	+	0.158590i
$753$		0			0
$754$	2.37228	−	8.12989i	0.0863934	−	0.296073i
$755$	7.64018			0.278054
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−2.55657	+	8.76144i	−0.0928587	+	0.318230i
$759$		0			0
$760$	22.1168	+	25.2651i	0.802262	+	0.916460i
$761$		−	17.3754i		−	0.629858i	−0.949115	−	0.314929i	$-0.898019\pi$
$761$		−	17.3754i		−	0.629858i	0.949115	−	0.314929i	$-0.101981\pi$
$762$		0			0
$763$		−	17.2097i		−	0.623033i
$764$	−25.4476	−	16.2333i	−0.920661	−	0.587299i
$765$		0			0
$766$	−11.7446	−	3.42703i	−0.424348	−	0.123824i
$767$	29.3617			1.06019
$768$		0			0
$769$	8.09509			0.291917			0.145958	−	0.989291i	$-0.453373\pi$
$769$	8.09509			0.291917			0.145958	+	0.989291i	$0.453373\pi$
$770$	2.20979	+	0.644810i	0.0796352	+	0.0232373i
$771$		0			0
$772$	13.0584	+	8.33010i	0.469983	+	0.299807i
$773$		−	0.699713i		−	0.0251669i	−0.999921	−	0.0125835i	$-0.995994\pi$
$773$		−	0.699713i		−	0.0251669i	0.999921	−	0.0125835i	$-0.00400555\pi$
$774$		0			0
$775$			11.1565i			0.400753i
$776$	19.5413	+	22.3229i	0.701492	+	0.801345i
$777$		0			0
$778$	−12.4891	+	42.8007i	−0.447757	+	1.53448i
$779$	−31.8888			−1.14253
$780$		0			0
$781$	−6.00000			−0.214697
$782$	−1.01082	+	3.46410i	−0.0361467	+	0.123876i
$783$		0			0
$784$	9.05842	+	19.4866i	0.323515	+	0.695950i
$785$			29.9422i			1.06868i
$786$		0			0
$787$			34.7453i			1.23854i	0.785180	+	0.619268i	$0.212571\pi$
$787$			34.7453i			1.23854i	−0.785180	+	0.619268i	$0.787429\pi$
$788$	−25.7648	+	40.3894i	−0.917834	+	1.43881i
$789$		0			0
$790$	−33.8614	−	9.88067i	−1.20473	−	0.351539i
$791$	9.28550			0.330154
$792$		0			0
$793$	5.62772			0.199846
$794$	−25.4476	−	7.42554i	−0.903100	−	0.263522i
$795$		0			0
$796$	−13.8832	+	21.7635i	−0.492075	+	0.771386i
$797$		−	23.8989i		−	0.846541i	−0.906003	−	0.423270i	$-0.860882\pi$
$797$		−	23.8989i		−	0.846541i	0.906003	−	0.423270i	$-0.139118\pi$
$798$		0			0
$799$			0.949929i			0.0336061i
$800$	−1.16944	−	7.67420i	−0.0413461	−	0.271324i
$801$		0			0
$802$	1.82473	−	6.25343i	0.0644336	−	0.220816i
$803$	1.70438			0.0601462
$804$		0			0
$805$	10.3723			0.365575
$806$	−7.64018	+	26.1831i	−0.269114	+	0.922262i
$807$		0			0
$808$	−2.62772	+	2.30029i	−0.0924428	+	0.0809238i
$809$			35.8381i			1.26000i	0.776595	+	0.630000i	$0.216945\pi$
$809$			35.8381i			1.26000i	−0.776595	+	0.630000i	$0.783055\pi$
$810$		0			0
$811$		−	1.20128i		−	0.0421828i	−0.999778	−	0.0210914i	$-0.993286\pi$
$811$		−	1.20128i		−	0.0421828i	0.999778	−	0.0210914i	$-0.00671410\pi$
$812$	5.43039	+	3.46410i	0.190569	+	0.121566i
$813$		0			0
$814$	−4.62772	−	1.35036i	−0.162201	−	0.0473300i
$815$	4.41957			0.154811
$816$		0			0
$817$	−36.3505			−1.27174
$818$	18.6596	+	5.44482i	0.652417	+	0.190374i
$819$		0			0
$820$	28.8614	+	18.4110i	1.00788	+	0.642940i
$821$		−	18.2603i		−	0.637288i	−0.947874	−	0.318644i	$-0.896773\pi$
$821$		−	18.2603i		−	0.637288i	0.947874	−	0.318644i	$-0.103227\pi$
$822$		0			0
$823$		−	14.0340i		−	0.489195i	−0.969625	−	0.244598i	$-0.921344\pi$
$823$		−	14.0340i		−	0.489195i	0.969625	−	0.244598i	$-0.0786559\pi$
$824$	1.01082	−	0.884861i	0.0352135	−	0.0308256i
$825$		0			0
$826$	−6.25544	+	21.4376i	−0.217655	+	0.745909i
$827$	47.4864			1.65126			0.825632	−	0.564210i	$-0.190819\pi$
$827$	47.4864			1.65126			0.825632	+	0.564210i	$0.190819\pi$
$828$		0			0
$829$	−48.2337			−1.67523			−0.837613	−	0.546265i	$-0.816049\pi$
$829$	−48.2337			−1.67523			−0.837613	+	0.546265i	$0.816049\pi$
$830$	7.64018	−	26.1831i	0.265194	−	0.908830i
$831$		0			0
$832$	2.51087	−	18.8114i	0.0870489	−	0.652169i
$833$			4.25639i			0.147475i
$834$		0			0
$835$		−	44.1510i		−	1.52791i
$836$	2.55657	−	4.00772i	0.0884207	−	0.138610i
$837$		0			0
$838$	36.6060	+	10.6815i	1.26453	+	0.368987i
$839$	42.6205			1.47142			0.735711	−	0.677296i	$-0.236848\pi$
$839$	42.6205			1.47142			0.735711	+	0.677296i	$0.236848\pi$
$840$		0			0
$841$	22.6277			0.780266
$842$	−14.3986	−	4.20149i	−0.496210	−	0.144793i
$843$		0			0
$844$	18.8614	−	29.5675i	0.649236	−	1.01775i
$845$		−	18.6101i		−	0.640208i
$846$		0			0
$847$			13.7081i			0.471017i
$848$	−6.81751	+	3.16915i	−0.234114	+	0.108829i
$849$		0			0
$850$	0.430703	−	1.47603i	0.0147730	−	0.0506276i
$851$	−21.7216			−0.744605
$852$		0			0
$853$	44.6060			1.52728			0.763640	−	0.645643i	$-0.223410\pi$
$853$	44.6060			1.52728			0.763640	+	0.645643i	$0.223410\pi$
$854$	−1.19897	+	4.10891i	−0.0410279	+	0.140604i
$855$		0			0
$856$	23.4090	+	26.7411i	0.800102	+	0.913992i
$857$			37.5701i			1.28337i	0.766968	+	0.641685i	$0.221764\pi$
$857$			37.5701i			1.28337i	−0.766968	+	0.641685i	$0.778236\pi$
$858$		0			0
$859$			1.82532i			0.0622791i	0.999515	+	0.0311396i	$0.00991364\pi$
$859$			1.82532i			0.0622791i	−0.999515	+	0.0311396i	$0.990086\pi$
$860$	32.8996	+	20.9870i	1.12187	+	0.715650i
$861$		0			0
$862$	42.3505	+	12.3578i	1.44246	+	0.420908i
$863$	−40.0344			−1.36279			−0.681393	−	0.731918i	$-0.738625\pi$
$863$	−40.0344			−1.36279			−0.681393	+	0.731918i	$0.738625\pi$
$864$		0			0
$865$	−44.6060			−1.51665
$866$	−11.7130	−	3.41781i	−0.398023	−	0.116142i
$867$		0			0
$868$	−17.4891	−	11.1565i	−0.593620	−	0.378676i
$869$			4.99377i			0.169402i
$870$		0			0
$871$		−	18.3365i		−	0.621307i
$872$	25.1303	+	28.7075i	0.851020	+	0.972158i
$873$		0			0
$874$	6.00000	−	20.5622i	0.202953	−	0.695527i
$875$	11.6834			0.394972
$876$		0			0
$877$	21.6277			0.730316			0.365158	−	0.930946i	$-0.381015\pi$
$877$	21.6277			0.730316			0.365158	+	0.930946i	$0.381015\pi$
$878$	2.58609	−	8.86263i	0.0872765	−	0.299099i
$879$		0			0
$880$	−4.62772	+	2.15121i	−0.156000	+	0.0725174i
$881$			52.9562i			1.78414i	0.451898	+	0.892070i	$0.350747\pi$
$881$			52.9562i			1.78414i	−0.451898	+	0.892070i	$0.649253\pi$
$882$		0			0
$883$		−	20.0127i		−	0.673481i	−0.941597	−	0.336741i	$-0.890675\pi$
$883$		−	20.0127i		−	0.673481i	0.941597	−	0.336741i	$-0.109325\pi$
$884$	2.02163	−	3.16915i	0.0679949	−	0.106590i
$885$		0			0
$886$	16.8030	+	4.90307i	0.564507	+	0.164722i
$887$	19.5118			0.655141			0.327571	−	0.944827i	$-0.393770\pi$
$887$	19.5118			0.655141			0.327571	+	0.944827i	$0.393770\pi$
$888$		0			0
$889$	9.76631			0.327552
$890$	41.0452	+	11.9769i	1.37584	+	0.401466i
$891$		0			0
$892$	−8.74456	+	13.7081i	−0.292790	+	0.458982i
$893$		−	5.63858i		−	0.188688i
$894$		0			0
$895$		−	22.3130i		−	0.745841i
$896$	13.1997	+	5.84096i	0.440970	+	0.195133i
$897$		0			0
$898$	−7.68614	+	26.3407i	−0.256490	+	0.878999i
$899$	20.5226			0.684467
$900$		0			0
$901$	−1.48913			−0.0496100
$902$	1.35760	−	4.65253i	0.0452030	−	0.154912i
$903$		0			0
$904$	−15.4891	+	13.5591i	−0.515161	+	0.450968i
$905$		−	10.0974i		−	0.335647i
$906$		0			0
$907$			29.8934i			0.992593i	0.868153	+	0.496297i	$0.165307\pi$
$907$			29.8934i			0.992593i	−0.868153	+	0.496297i	$0.834693\pi$
$908$	−24.2781	−	15.4873i	−0.805698	−	0.513963i
$909$		0			0
$910$	−10.3723	−	3.02661i	−0.343838	−	0.100331i
$911$	−35.8029			−1.18620			−0.593102	−	0.805127i	$-0.702097\pi$
$911$	−35.8029			−1.18620			−0.593102	+	0.805127i	$0.702097\pi$
$912$		0			0
$913$	−3.86141			−0.127794
$914$	54.2744	+	15.8371i	1.79524	+	0.523846i
$915$		0			0
$916$	6.11684	+	3.90200i	0.202106	+	0.128926i
$917$		−	9.74749i		−	0.321891i
$918$		0			0
$919$		−	36.9711i		−	1.21956i	−0.792570	−	0.609781i	$-0.791257\pi$
$919$		−	36.9711i		−	1.21956i	0.792570	−	0.609781i	$-0.208743\pi$
$920$	−17.3020	+	15.1460i	−0.570429	+	0.499350i
$921$		0			0
$922$	−0.138593	+	0.474964i	−0.00456433	+	0.0156421i
$923$	28.1628			0.926989
$924$		0			0
$925$	9.25544			0.304317
$926$	−1.89253	+	6.48577i	−0.0621925	+	0.213136i
$927$		0			0
$928$	−14.1168	+	2.15121i	−0.463408	+	0.0706170i
$929$			18.5552i			0.608777i	0.952548	+	0.304389i	$0.0984521\pi$
$929$			18.5552i			0.608777i	−0.952548	+	0.304389i	$0.901548\pi$
$930$		0			0
$931$		−	25.2651i		−	0.828029i
$932$	5.21271	−	8.17154i	0.170748	−	0.267668i
$933$		0			0
$934$	−6.94158	−	2.02554i	−0.227135	−	0.0662775i
$935$	−1.01082			−0.0330572
$936$		0			0
$937$	45.7228			1.49370			0.746850	−	0.664993i	$-0.231565\pi$
$937$	45.7228			1.49370			0.746850	+	0.664993i	$0.231565\pi$
$938$	13.3878	+	3.90653i	0.437128	+	0.127553i
$939$		0			0
$940$	−3.25544	+	5.10328i	−0.106181	+	0.166451i
$941$		−	13.5065i		−	0.440301i	−0.975466	−	0.220150i	$-0.929345\pi$
$941$		−	13.5065i		−	0.440301i	0.975466	−	0.220150i	$-0.0706548\pi$
$942$		0			0
$943$		−	21.8380i		−	0.711144i
$944$	−20.8694	−	44.8945i	−0.679240	−	1.46119i
$945$		0			0
$946$	1.54755	−	5.30350i	0.0503151	−	0.172432i
$947$	6.57031			0.213506			0.106753	−	0.994286i	$-0.465955\pi$
$947$	6.57031			0.213506			0.106753	+	0.994286i	$0.465955\pi$
$948$		0			0
$949$	−8.00000			−0.259691
$950$	−2.55657	+	8.76144i	−0.0829460	+	0.284259i
$951$		0			0
$952$	1.88316	+	2.15121i	0.0610334	+	0.0697212i
$953$			10.2997i			0.333641i	0.985987	+	0.166821i	$0.0533500\pi$
$953$			10.2997i			0.333641i	−0.985987	+	0.166821i	$0.946650\pi$
$954$		0			0
$955$		−	38.0978i		−	1.23282i
$956$	20.3344	+	12.9715i	0.657663	+	0.419530i
$957$		0			0
$958$	17.7446	+	5.17782i	0.573301	+	0.167288i
$959$	−7.00567			−0.226225
$960$		0			0
$961$	−35.0951			−1.13210
$962$	21.7216	+	6.33830i	0.700331	+	0.204355i
$963$		0			0
$964$	−10.9416	−	6.97975i	−0.352404	−	0.224802i
$965$			19.5499i			0.629333i
$966$		0			0
$967$		−	46.8517i		−	1.50665i	−0.657648	−	0.753325i	$-0.728449\pi$
$967$		−	46.8517i		−	1.50665i	0.657648	−	0.753325i	$-0.271551\pi$
$968$	−20.0172	−	22.8665i	−0.643376	−	0.734958i
$969$		0			0
$970$	−10.4891	+	35.9466i	−0.336786	+	1.15418i
$971$	−37.0019			−1.18745			−0.593724	−	0.804669i	$-0.702343\pi$
$971$	−37.0019			−1.18745			−0.593724	+	0.804669i	$0.702343\pi$
$972$		0			0
$973$	19.6277			0.629236
$974$	−16.9847	+	58.2072i	−0.544226	+	1.86508i
$975$		0			0
$976$	−4.00000	−	8.60485i	−0.128037	−	0.275435i
$977$			54.6882i			1.74963i	0.484455	+	0.874816i	$0.339018\pi$
$977$			54.6882i			1.74963i	−0.484455	+	0.874816i	$0.660982\pi$
$978$		0			0
$979$		−	6.05321i		−	0.193461i
$980$	−14.5868	+	22.8665i	−0.465958	+	0.730444i
$981$		0			0
$982$	−18.6861	−	5.45257i	−0.596299	−	0.173998i
$983$	−34.4158			−1.09769			−0.548847	−	0.835923i	$-0.684933\pi$
$983$	−34.4158			−1.09769			−0.548847	+	0.835923i	$0.684933\pi$
$984$		0			0
$985$	−60.4674			−1.92665
$986$	−2.71519	−	0.792287i	−0.0864694	−	0.0252316i
$987$		0			0
$988$	−12.0000	+	18.8114i	−0.381771	+	0.598471i
$989$		−	24.8935i		−	0.791568i
$990$		0			0
$991$		−	7.65492i		−	0.243167i	−0.992581	−	0.121583i	$-0.961203\pi$
$991$		−	7.65492i		−	0.243167i	0.992581	−	0.121583i	$-0.0387972\pi$
$992$	45.4647	−	6.92820i	1.44351	−	0.219971i
$993$		0			0
$994$	−6.00000	+	20.5622i	−0.190308	+	0.652194i
$995$	−32.5823			−1.03293
$996$		0			0
$997$	−24.1386			−0.764477			−0.382238	−	0.924064i	$-0.624847\pi$
$997$	−24.1386			−0.764477			−0.382238	+	0.924064i	$0.624847\pi$
$998$	1.35760	−	4.65253i	0.0429740	−	0.147273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.b.b.323.8		8
3.2	odd	2	inner	324.2.b.b.323.1		8
4.3	odd	2	inner	324.2.b.b.323.2		8
8.3	odd	2		5184.2.c.j.5183.2		8
8.5	even	2		5184.2.c.j.5183.1		8
9.2	odd	6		108.2.h.a.71.2		8
9.4	even	3		108.2.h.a.35.1		8
9.5	odd	6		36.2.h.a.11.4	yes	8
9.7	even	3		36.2.h.a.23.3	yes	8
12.11	even	2	inner	324.2.b.b.323.7		8
24.5	odd	2		5184.2.c.j.5183.7		8
24.11	even	2		5184.2.c.j.5183.8		8
36.7	odd	6		36.2.h.a.23.4	yes	8
36.11	even	6		108.2.h.a.71.1		8
36.23	even	6		36.2.h.a.11.3	✓	8
36.31	odd	6		108.2.h.a.35.2		8
45.7	odd	12		900.2.o.a.599.8		16
45.14	odd	6		900.2.r.c.551.1		8
45.23	even	12		900.2.o.a.299.3		16
45.32	even	12		900.2.o.a.299.6		16
45.34	even	6		900.2.r.c.851.2		8
45.43	odd	12		900.2.o.a.599.1		16
72.5	odd	6		576.2.s.f.191.4		8
72.11	even	6		1728.2.s.f.1151.2		8
72.13	even	6		1728.2.s.f.575.2		8
72.29	odd	6		1728.2.s.f.1151.1		8
72.43	odd	6		576.2.s.f.383.4		8
72.59	even	6		576.2.s.f.191.1		8
72.61	even	6		576.2.s.f.383.1		8
72.67	odd	6		1728.2.s.f.575.1		8
180.7	even	12		900.2.o.a.599.3		16
180.23	odd	12		900.2.o.a.299.8		16
180.43	even	12		900.2.o.a.599.6		16
180.59	even	6		900.2.r.c.551.2		8
180.79	odd	6		900.2.r.c.851.1		8
180.167	odd	12		900.2.o.a.299.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.3	✓	8	36.23	even	6
36.2.h.a.11.4	yes	8	9.5	odd	6
36.2.h.a.23.3	yes	8	9.7	even	3
36.2.h.a.23.4	yes	8	36.7	odd	6
108.2.h.a.35.1		8	9.4	even	3
108.2.h.a.35.2		8	36.31	odd	6
108.2.h.a.71.1		8	36.11	even	6
108.2.h.a.71.2		8	9.2	odd	6
324.2.b.b.323.1		8	3.2	odd	2	inner
324.2.b.b.323.2		8	4.3	odd	2	inner
324.2.b.b.323.7		8	12.11	even	2	inner
324.2.b.b.323.8		8	1.1	even	1	trivial
576.2.s.f.191.1		8	72.59	even	6
576.2.s.f.191.4		8	72.5	odd	6
576.2.s.f.383.1		8	72.61	even	6
576.2.s.f.383.4		8	72.43	odd	6
900.2.o.a.299.1		16	180.167	odd	12
900.2.o.a.299.3		16	45.23	even	12
900.2.o.a.299.6		16	45.32	even	12
900.2.o.a.299.8		16	180.23	odd	12
900.2.o.a.599.1		16	45.43	odd	12
900.2.o.a.599.3		16	180.7	even	12
900.2.o.a.599.6		16	180.43	even	12
900.2.o.a.599.8		16	45.7	odd	12
900.2.r.c.551.1		8	45.14	odd	6
900.2.r.c.551.2		8	180.59	even	6
900.2.r.c.851.1		8	180.79	odd	6
900.2.r.c.851.2		8	45.34	even	6
1728.2.s.f.575.1		8	72.67	odd	6
1728.2.s.f.575.2		8	72.13	even	6
1728.2.s.f.1151.1		8	72.29	odd	6
1728.2.s.f.1151.2		8	72.11	even	6
5184.2.c.j.5183.1		8	8.5	even	2
5184.2.c.j.5183.2		8	8.3	odd	2
5184.2.c.j.5183.7		8	24.5	odd	2
5184.2.c.j.5183.8		8	24.11	even	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35760 + 0.396143i) q^{2} +(1.68614 + 1.07561i) q^{4} +2.52434i q^{5} -1.27582i q^{7} +(1.86301 + 2.12819i) q^{8} +(-1.00000 + 3.42703i) q^{10} +0.505408 q^{11} -2.37228 q^{13} +(0.505408 - 1.73205i) q^{14} +(1.68614 + 3.62725i) q^{16} +0.792287i q^{17} -4.70285i q^{19} +(-2.71519 + 4.25639i) q^{20} +(0.686141 + 0.200214i) q^{22} +3.22060 q^{23} -1.37228 q^{25} +(-3.22060 - 0.939764i) q^{26} +(1.37228 - 2.15121i) q^{28} +2.52434i q^{29} -8.12989i q^{31} +(0.852189 + 5.59230i) q^{32} +(-0.313859 + 1.07561i) q^{34} +3.22060 q^{35} -6.74456 q^{37} +(1.86301 - 6.38458i) q^{38} +(-5.37228 + 4.70285i) q^{40} -6.78073i q^{41} -7.72946i q^{43} +(0.852189 + 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +1.19897 q^{47} +5.37228 q^{49} +(-1.86301 - 0.543620i) q^{50} +(-4.00000 - 2.55164i) q^{52} +1.87953i q^{53} +1.27582i q^{55} +(2.71519 - 2.37686i) q^{56} +(-1.00000 + 3.42703i) q^{58} -12.3770 q^{59} -2.37228 q^{61} +(3.22060 - 11.0371i) q^{62} +(-1.05842 + 7.92967i) q^{64} -5.98844i q^{65} +7.72946i q^{67} +(-0.852189 + 1.33591i) q^{68} +(4.37228 + 1.27582i) q^{70} -11.8716 q^{71} +3.37228 q^{73} +(-9.15640 - 2.67181i) q^{74} +(5.05842 - 7.92967i) q^{76} -0.644810i q^{77} +9.88067i q^{79} +(-9.15640 + 4.25639i) q^{80} +(2.68614 - 9.20550i) q^{82} -7.64018 q^{83} -2.00000 q^{85} +(3.06198 - 10.4935i) q^{86} +(0.941578 + 1.07561i) q^{88} -11.9769i q^{89} +3.02661i q^{91} +(5.43039 + 3.46410i) q^{92} +(1.62772 + 0.474964i) q^{94} +11.8716 q^{95} +10.4891 q^{97} +(7.29339 + 2.12819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 8 q^{10} + 4 q^{13} + 2 q^{16} - 6 q^{22} + 12 q^{25} - 12 q^{28} - 14 q^{34} - 8 q^{37} - 20 q^{40} + 12 q^{46} + 20 q^{49} - 32 q^{52} - 8 q^{58} + 4 q^{61} + 26 q^{64} + 12 q^{70} + 4 q^{73}+ \cdots - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 8 * q^10 + 4 * q^13 + 2 * q^16 - 6 * q^22 + 12 * q^25 - 12 * q^28 - 14 * q^34 - 8 * q^37 - 20 * q^40 + 12 * q^46 + 20 * q^49 - 32 * q^52 - 8 * q^58 + 4 * q^61 + 26 * q^64 + 12 * q^70 + 4 * q^73 + 6 * q^76 + 10 * q^82 - 16 * q^85 + 42 * q^88 + 36 * q^94 - 8 * q^97

Introduction

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