LMFDB - Embedded newform 792.2.f.h.397.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(397,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.397"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	20.0.74831334220841134637329678336.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2x^{18} + 5x^{16} - 8x^{14} + 28x^{12} - 64x^{10} + 112x^{8} - 128x^{6} + 320x^{4} - 512x^{2} + 1024 $ x^20 - 2x^18 + 5x^16 - 8x^14 + 28x^12 - 64x^10 + 112x^8 - 128x^6 + 320x^4 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			397.18
Root			$-1.25295 + 0.655834i$ of defining polynomial
Character	$\chi$	$=$	792.397
Dual form			792.2.f.h.397.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25295 + 0.655834i) q^{2} +(1.13976 + 1.64345i) q^{4} -2.54164i q^{5} +4.84329 q^{7} +(0.350232 + 2.80666i) q^{8} +(1.66690 - 3.18455i) q^{10} -1.00000i q^{11} -4.85572i q^{13} +(6.06840 + 3.17640i) q^{14} +(-1.40188 + 3.74630i) q^{16} -7.15011 q^{17} -1.80543i q^{19} +(4.17707 - 2.89687i) q^{20} +(0.655834 - 1.25295i) q^{22} +3.29371 q^{23} -1.45995 q^{25} +(3.18455 - 6.08398i) q^{26} +(5.52021 + 7.95973i) q^{28} +4.82588i q^{29} -0.623337 q^{31} +(-4.21343 + 3.77452i) q^{32} +(-8.95872 - 4.68929i) q^{34} -12.3099i q^{35} +10.3565i q^{37} +(1.18407 - 2.26212i) q^{38} +(7.13353 - 0.890165i) q^{40} +6.34400 q^{41} +6.34400i q^{43} +(1.64345 - 1.13976i) q^{44} +(4.12685 + 2.16012i) q^{46} -6.08486 q^{47} +16.4575 q^{49} +(-1.82924 - 0.957485i) q^{50} +(7.98016 - 5.53438i) q^{52} -4.47736i q^{53} -2.54164 q^{55} +(1.69628 + 13.5935i) q^{56} +(-3.16498 + 6.04659i) q^{58} +7.75087i q^{59} +2.14112i q^{61} +(-0.781009 - 0.408805i) q^{62} +(-7.75467 + 1.96597i) q^{64} -12.3415 q^{65} -9.21748i q^{67} +(-8.14943 - 11.7509i) q^{68} +(8.07327 - 15.4237i) q^{70} -0.911979 q^{71} +0.0991030 q^{73} +(-6.79213 + 12.9761i) q^{74} +(2.96715 - 2.05777i) q^{76} -4.84329i q^{77} -7.99086 q^{79} +(9.52175 + 3.56308i) q^{80} +(7.94870 + 4.16061i) q^{82} -1.41148i q^{83} +18.1730i q^{85} +(-4.16061 + 7.94870i) q^{86} +(2.80666 - 0.350232i) q^{88} -14.5622 q^{89} -23.5177i q^{91} +(3.75404 + 5.41305i) q^{92} +(-7.62403 - 3.99066i) q^{94} -4.58877 q^{95} -2.04425 q^{97} +(20.6204 + 10.7934i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 8 q^{10} - 12 q^{16} - 12 q^{25} + 24 q^{28} + 40 q^{31} - 24 q^{34} - 32 q^{40} + 40 q^{46} + 36 q^{49} + 56 q^{52} - 16 q^{55} + 24 q^{58} + 4 q^{64} + 56 q^{70} - 56 q^{73} - 8 q^{76}+ \cdots + 8 q^{97}+O(q^{100}) $ 20 * q + 4 * q^4 + 8 * q^10 - 12 * q^16 - 12 * q^25 + 24 * q^28 + 40 * q^31 - 24 * q^34 - 32 * q^40 + 40 * q^46 + 36 * q^49 + 56 * q^52 - 16 * q^55 + 24 * q^58 + 4 * q^64 + 56 * q^70 - 56 * q^73 - 8 * q^76 - 16 * q^79 - 32 * q^82 + 12 * q^88 - 24 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$1$	$1$	$-1$

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 $

$2$	1.25295	+	0.655834i	0.885969	+	0.463745i
$2$	1.25295	+	0.655834i	0.885969	+	0.463745i
$3$		0			0
$3$		0			0
$4$	1.13976	+	1.64345i	0.569882	+	0.821727i
$5$		−	2.54164i		−	1.13666i	−0.822802	−	0.568329i	$-0.807590\pi$
$5$		−	2.54164i		−	1.13666i	0.822802	−	0.568329i	$-0.192410\pi$
$6$		0			0
$7$	4.84329			1.83059			0.915296	−	0.402781i	$-0.131956\pi$
$7$	4.84329			1.83059			0.915296	+	0.402781i	$0.131956\pi$
$8$	0.350232	+	2.80666i	0.123826	+	0.992304i
$9$		0			0
$10$	1.66690	−	3.18455i	0.527119	−	1.00704i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		0			0
$13$		−	4.85572i		−	1.34674i	−0.739308	−	0.673368i	$-0.764847\pi$
$13$		−	4.85572i		−	1.34674i	0.739308	−	0.673368i	$-0.235153\pi$
$14$	6.06840	+	3.17640i	1.62185	+	0.848928i
$15$		0			0
$16$	−1.40188	+	3.74630i	−0.350470	+	0.936574i
$17$	−7.15011			−1.73416			−0.867078	−	0.498172i	$-0.834005\pi$
$17$	−7.15011			−1.73416			−0.867078	+	0.498172i	$0.834005\pi$
$18$		0			0
$19$		−	1.80543i		−	0.414195i	−0.978320	−	0.207097i	$-0.933598\pi$
$19$		−	1.80543i		−	0.414195i	0.978320	−	0.207097i	$-0.0664017\pi$
$20$	4.17707	−	2.89687i	0.934022	−	0.647760i
$21$		0			0
$22$	0.655834	−	1.25295i	0.139824	−	0.267130i
$23$	3.29371			0.686785			0.343393	−	0.939192i	$-0.388424\pi$
$23$	3.29371			0.686785			0.343393	+	0.939192i	$0.388424\pi$
$24$		0			0
$25$	−1.45995			−0.291990
$26$	3.18455	−	6.08398i	0.624542	−	1.19317i
$27$		0			0
$28$	5.52021	+	7.95973i	1.04322	+	1.50425i
$29$			4.82588i			0.896144i	0.893997	+	0.448072i	$0.147889\pi$
$29$			4.82588i			0.896144i	−0.893997	+	0.448072i	$0.852111\pi$
$30$		0			0
$31$	−0.623337			−0.111955			−0.0559773	−	0.998432i	$-0.517827\pi$
$31$	−0.623337			−0.111955			−0.0559773	+	0.998432i	$0.517827\pi$
$32$	−4.21343	+	3.77452i	−0.744837	+	0.667247i
$33$		0			0
$34$	−8.95872	−	4.68929i	−1.53641	−	0.804206i
$35$		−	12.3099i		−	2.08076i
$36$		0			0
$37$			10.3565i			1.70259i	0.524685	+	0.851297i	$0.324183\pi$
$37$			10.3565i			1.70259i	−0.524685	+	0.851297i	$0.675817\pi$
$38$	1.18407	−	2.26212i	0.192081	−	0.366964i
$39$		0			0
$40$	7.13353	−	0.890165i	1.12791	−	0.140747i
$41$	6.34400			0.990766			0.495383	−	0.868675i	$-0.335028\pi$
$41$	6.34400			0.990766			0.495383	+	0.868675i	$0.335028\pi$
$42$		0			0
$43$			6.34400i			0.967450i	0.875220	+	0.483725i	$0.160717\pi$
$43$			6.34400i			0.967450i	−0.875220	+	0.483725i	$0.839283\pi$
$44$	1.64345	−	1.13976i	0.247760	−	0.171826i
$45$		0			0
$46$	4.12685	+	2.16012i	0.608470	+	0.318493i
$47$	−6.08486			−0.887569			−0.443784	−	0.896134i	$-0.646364\pi$
$47$	−6.08486			−0.887569			−0.443784	+	0.896134i	$0.646364\pi$
$48$		0			0
$49$	16.4575			2.35107
$50$	−1.82924	−	0.957485i	−0.258694	−	0.135409i
$51$		0			0
$52$	7.98016	−	5.53438i	1.10665	−	0.767480i
$53$		−	4.47736i		−	0.615013i	−0.951546	−	0.307506i	$-0.900505\pi$
$53$		−	4.47736i		−	0.615013i	0.951546	−	0.307506i	$-0.0994945\pi$
$54$		0			0
$55$	−2.54164			−0.342715
$56$	1.69628	+	13.5935i	0.226675	+	1.81650i
$57$		0			0
$58$	−3.16498	+	6.04659i	−0.415582	+	0.793956i
$59$			7.75087i			1.00908i	0.863389	+	0.504539i	$0.168337\pi$
$59$			7.75087i			1.00908i	−0.863389	+	0.504539i	$0.831663\pi$
$60$		0			0
$61$			2.14112i			0.274142i	0.990561	+	0.137071i	$0.0437689\pi$
$61$			2.14112i			0.274142i	−0.990561	+	0.137071i	$0.956231\pi$
$62$	−0.781009	−	0.408805i	−0.0991882	−	0.0519183i
$63$		0			0
$64$	−7.75467	+	1.96597i	−0.969334	+	0.245746i
$65$	−12.3415			−1.53078
$66$		0			0
$67$		−	9.21748i		−	1.12609i	−0.826425	−	0.563047i	$-0.809629\pi$
$67$		−	9.21748i		−	1.12609i	0.826425	−	0.563047i	$-0.190371\pi$
$68$	−8.14943	−	11.7509i	−0.988264	−	1.42500i
$69$		0			0
$70$	8.07327	−	15.4237i	0.964940	−	1.84349i
$71$	−0.911979			−0.108232			−0.0541160	−	0.998535i	$-0.517234\pi$
$71$	−0.911979			−0.108232			−0.0541160	+	0.998535i	$0.517234\pi$
$72$		0			0
$73$	0.0991030			0.0115991			0.00579956	−	0.999983i	$-0.498154\pi$
$73$	0.0991030			0.0115991			0.00579956	+	0.999983i	$0.498154\pi$
$74$	−6.79213	+	12.9761i	−0.789569	+	1.50844i
$75$		0			0
$76$	2.96715	−	2.05777i	0.340355	−	0.236042i
$77$		−	4.84329i		−	0.551945i
$78$		0			0
$79$	−7.99086			−0.899042			−0.449521	−	0.893270i	$-0.648405\pi$
$79$	−7.99086			−0.899042			−0.449521	+	0.893270i	$0.648405\pi$
$80$	9.52175	+	3.56308i	1.06456	+	0.398364i
$81$		0			0
$82$	7.94870	+	4.16061i	0.877788	+	0.459462i
$83$		−	1.41148i		−	0.154930i	−0.996995	−	0.0774652i	$-0.975317\pi$
$83$		−	1.41148i		−	0.154930i	0.996995	−	0.0774652i	$-0.0246827\pi$
$84$		0			0
$85$			18.1730i			1.97114i
$86$	−4.16061	+	7.94870i	−0.448650	+	0.857131i
$87$		0			0
$88$	2.80666	−	0.350232i	0.299191	−	0.0373349i
$89$	−14.5622			−1.54359			−0.771793	−	0.635874i	$-0.780640\pi$
$89$	−14.5622			−1.54359			−0.771793	+	0.635874i	$0.780640\pi$
$90$		0			0
$91$		−	23.5177i		−	2.46532i
$92$	3.75404	+	5.41305i	0.391386	+	0.564350i
$93$		0			0
$94$	−7.62403	−	3.99066i	−0.786358	−	0.411605i
$95$	−4.58877			−0.470798
$96$		0			0
$97$	−2.04425			−0.207562			−0.103781	−	0.994600i	$-0.533094\pi$
$97$	−2.04425			−0.207562			−0.103781	+	0.994600i	$0.533094\pi$
$98$	20.6204	+	10.7934i	2.08298	+	1.09030i
$99$		0			0
$100$	−1.66400	−	2.39936i	−0.166400	−	0.239936i
$101$			1.90917i			0.189970i	0.995479	+	0.0949848i	$0.0302802\pi$
$101$			1.90917i			0.189970i	−0.995479	+	0.0949848i	$0.969720\pi$
$102$		0			0
$103$	−19.5566			−1.92697			−0.963484	−	0.267764i	$-0.913715\pi$
$103$	−19.5566			−1.92697			−0.963484	+	0.267764i	$0.913715\pi$
$104$	13.6284	−	1.70063i	1.33637	−	0.166761i
$105$		0			0
$106$	2.93640	−	5.60990i	0.285209	−	0.544882i
$107$			9.52320i			0.920643i	0.887752	+	0.460321i	$0.152266\pi$
$107$			9.52320i			0.920643i	−0.887752	+	0.460321i	$0.847734\pi$
$108$		0			0
$109$			17.8559i			1.71028i	0.518396	+	0.855141i	$0.326529\pi$
$109$			17.8559i			1.71028i	−0.518396	+	0.855141i	$0.673471\pi$
$110$	−3.18455	−	1.66690i	−0.303635	−	0.158932i
$111$		0			0
$112$	−6.78972	+	18.1444i	−0.641568	+	1.71449i
$113$	−0.584117			−0.0549491			−0.0274746	−	0.999623i	$-0.508747\pi$
$113$	−0.584117			−0.0549491			−0.0274746	+	0.999623i	$0.508747\pi$
$114$		0			0
$115$		−	8.37142i		−	0.780639i
$116$	−7.93112	+	5.50037i	−0.736386	+	0.510696i
$117$		0			0
$118$	−5.08329	+	9.71145i	−0.467954	+	0.894011i
$119$	−34.6301			−3.17453
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−1.40422	+	2.68271i	−0.127132	+	0.242881i
$123$		0			0
$124$	−0.710456	−	1.02442i	−0.0638008	−	0.0919961i
$125$		−	8.99754i		−	0.804765i
$126$		0			0
$127$	12.5593			1.11446			0.557231	−	0.830358i	$-0.311864\pi$
$127$	12.5593			1.11446			0.557231	+	0.830358i	$0.311864\pi$
$128$	−11.0056	−	2.62253i	−0.972763	−	0.231801i
$129$		0			0
$130$	−15.4633	−	8.09399i	−1.35622	−	0.709890i
$131$		−	13.2298i		−	1.15590i	−0.816074	−	0.577948i	$-0.803854\pi$
$131$		−	13.2298i		−	1.15590i	0.816074	−	0.577948i	$-0.196146\pi$
$132$		0			0
$133$		−	8.74425i		−	0.758222i
$134$	6.04514	−	11.5490i	0.522220	−	0.997685i
$135$		0			0
$136$	−2.50420	−	20.0679i	−0.214733	−	1.72081i
$137$	8.14943			0.696253			0.348126	−	0.937448i	$-0.386818\pi$
$137$	8.14943			0.696253			0.348126	+	0.937448i	$0.386818\pi$
$138$		0			0
$139$		−	15.2150i		−	1.29052i	−0.763963	−	0.645260i	$-0.776749\pi$
$139$		−	15.2150i		−	1.29052i	0.763963	−	0.645260i	$-0.223251\pi$
$140$	20.2308	−	14.0304i	1.70981	−	1.18579i
$141$		0			0
$142$	−1.14266	−	0.598107i	−0.0958901	−	0.0501920i
$143$	−4.85572			−0.406056
$144$		0			0
$145$	12.2657			1.01861
$146$	0.124171	+	0.0649951i	0.0102765	+	0.00537903i
$147$		0			0
$148$	−17.0204	+	11.8039i	−1.39907	+	0.970277i
$149$		−	18.6759i		−	1.52999i	−0.644039	−	0.764993i	$-0.722742\pi$
$149$		−	18.6759i		−	1.52999i	0.644039	−	0.764993i	$-0.277258\pi$
$150$		0			0
$151$	−3.92339			−0.319281			−0.159641	−	0.987175i	$-0.551034\pi$
$151$	−3.92339			−0.319281			−0.159641	+	0.987175i	$0.551034\pi$
$152$	5.06724	−	0.632321i	0.411007	−	0.0512880i
$153$		0			0
$154$	3.17640	−	6.06840i	0.255961	−	0.489006i
$155$			1.58430i			0.127254i
$156$		0			0
$157$			8.19964i			0.654402i	0.944955	+	0.327201i	$0.106105\pi$
$157$			8.19964i			0.654402i	−0.944955	+	0.327201i	$0.893895\pi$
$158$	−10.0121	−	5.24068i	−0.796524	−	0.416926i
$159$		0			0
$160$	9.59348	+	10.7090i	0.758431	+	0.846624i
$161$	15.9524			1.25722
$162$		0			0
$163$			1.15259i			0.0902776i	0.998981	+	0.0451388i	$0.0143730\pi$
$163$			1.15259i			0.0902776i	−0.998981	+	0.0451388i	$0.985627\pi$
$164$	7.23065	+	10.4261i	0.564619	+	0.814139i
$165$		0			0
$166$	0.925698	−	1.76852i	0.0718481	−	0.137263i
$167$	17.9481			1.38887			0.694434	−	0.719556i	$-0.255655\pi$
$167$	17.9481			1.38887			0.694434	+	0.719556i	$0.255655\pi$
$168$		0			0
$169$	−10.5781			−0.813697
$170$	−11.9185	+	22.7699i	−0.914106	+	1.74637i
$171$		0			0
$172$	−10.4261	+	7.23065i	−0.794980	+	0.551332i
$173$		−	0.697316i		−	0.0530160i	−0.999649	−	0.0265080i	$-0.991561\pi$
$173$		−	0.697316i		−	0.0530160i	0.999649	−	0.0265080i	$-0.00843874\pi$
$174$		0			0
$175$	−7.07096			−0.534515
$176$	3.74630	+	1.40188i	0.282388	+	0.105671i
$177$		0			0
$178$	−18.2456	−	9.55036i	−1.36757	−	0.715830i
$179$		−	18.2551i		−	1.36445i	−0.731143	−	0.682224i	$-0.761013\pi$
$179$		−	18.2551i		−	1.36445i	0.731143	−	0.682224i	$-0.238987\pi$
$180$		0			0
$181$			10.0236i			0.745048i	0.928023	+	0.372524i	$0.121508\pi$
$181$			10.0236i			0.745048i	−0.928023	+	0.372524i	$0.878492\pi$
$182$	15.4237	−	29.4665i	1.14328	−	2.18420i
$183$		0			0
$184$	1.15356	+	9.24431i	0.0850417	+	0.681500i
$185$	26.3225			1.93527
$186$		0			0
$187$			7.15011i			0.522868i
$188$	−6.93530	−	10.0002i	−0.505809	−	0.729339i
$189$		0			0
$190$	−5.74949	−	3.00947i	−0.417112	−	0.218330i
$191$	13.3380			0.965106			0.482553	−	0.875867i	$-0.339710\pi$
$191$	13.3380			0.965106			0.482553	+	0.875867i	$0.339710\pi$
$192$		0			0
$193$	−12.0590			−0.868028			−0.434014	−	0.900906i	$-0.642903\pi$
$193$	−12.0590			−0.868028			−0.434014	+	0.900906i	$0.642903\pi$
$194$	−2.56134	−	1.34069i	−0.183893	−	0.0962558i
$195$		0			0
$196$	18.7576	+	27.0471i	1.33983	+	1.93194i
$197$			25.4806i			1.81541i	0.419604	+	0.907707i	$0.362169\pi$
$197$			25.4806i			1.81541i	−0.419604	+	0.907707i	$0.637831\pi$
$198$		0			0
$199$	−10.7899			−0.764876			−0.382438	−	0.923981i	$-0.624916\pi$
$199$	−10.7899			−0.764876			−0.382438	+	0.923981i	$0.624916\pi$
$200$	−0.511321	−	4.09758i	−0.0361559	−	0.289743i
$201$		0			0
$202$	−1.25210	+	2.39209i	−0.0880974	+	0.168307i
$203$			23.3732i			1.64048i
$204$		0			0
$205$		−	16.1242i		−	1.12616i
$206$	−24.5034	−	12.8259i	−1.70723	−	0.893622i
$207$		0			0
$208$	18.1910	+	6.80714i	1.26132	+	0.471990i
$209$	−1.80543			−0.124884
$210$		0			0
$211$		−	21.3658i		−	1.47088i	−0.677589	−	0.735441i	$-0.736975\pi$
$211$		−	21.3658i		−	1.47088i	0.677589	−	0.735441i	$-0.263025\pi$
$212$	7.35833	−	5.10313i	0.505372	−	0.350484i
$213$		0			0
$214$	−6.24564	+	11.9321i	−0.426943	+	0.815661i
$215$	16.1242			1.09966
$216$		0			0
$217$	−3.01900			−0.204943
$218$	−11.7105	+	22.3725i	−0.793134	+	1.51526i
$219$		0			0
$220$	−2.89687	−	4.17707i	−0.195307	−	0.281618i
$221$			34.7190i			2.33545i
$222$		0			0
$223$	−4.27192			−0.286069			−0.143034	−	0.989718i	$-0.545686\pi$
$223$	−4.27192			−0.286069			−0.143034	+	0.989718i	$0.545686\pi$
$224$	−20.4069	+	18.2811i	−1.36349	+	1.22146i
$225$		0			0
$226$	−0.731869	−	0.383084i	−0.0486832	−	0.0254824i
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$		0			0
$229$		−	18.2440i		−	1.20559i	−0.797894	−	0.602797i	$-0.794053\pi$
$229$		−	18.2440i		−	1.20559i	0.797894	−	0.602797i	$-0.205947\pi$
$230$	5.49027	−	10.4890i	0.362017	−	0.691622i
$231$		0			0
$232$	−13.5446	+	1.69018i	−0.889247	+	0.110966i
$233$	−13.5657			−0.888721			−0.444360	−	0.895848i	$-0.646569\pi$
$233$	−13.5657			−0.888721			−0.444360	+	0.895848i	$0.646569\pi$
$234$		0			0
$235$			15.4656i			1.00886i
$236$	−12.7382	+	8.83416i	−0.829186	+	0.575055i
$237$		0			0
$238$	−43.3897	−	22.7116i	−2.81254	−	1.47217i
$239$	−2.66440			−0.172346			−0.0861728	−	0.996280i	$-0.527464\pi$
$239$	−2.66440			−0.172346			−0.0861728	+	0.996280i	$0.527464\pi$
$240$		0			0
$241$	10.2657			0.661270			0.330635	−	0.943759i	$-0.392737\pi$
$241$	10.2657			0.661270			0.330635	+	0.943759i	$0.392737\pi$
$242$	−1.25295	−	0.655834i	−0.0805426	−	0.0421586i
$243$		0			0
$244$	−3.51883	+	2.44037i	−0.225270	+	0.156229i
$245$		−	41.8291i		−	2.67236i
$246$		0			0
$247$	−8.76669			−0.557811
$248$	−0.218313	−	1.74949i	−0.0138629	−	0.111093i
$249$		0			0
$250$	5.90090	−	11.2735i	0.373205	−	0.712997i
$251$			21.9871i			1.38781i	0.720065	+	0.693906i	$0.244112\pi$
$251$			21.9871i			1.38781i	−0.720065	+	0.693906i	$0.755888\pi$
$252$		0			0
$253$		−	3.29371i		−	0.207074i
$254$	15.7362	+	8.23685i	0.987378	+	0.516826i
$255$		0			0
$256$	−12.0695	−	10.5037i	−0.754342	−	0.656482i
$257$	17.0204			1.06171			0.530853	−	0.847464i	$-0.321872\pi$
$257$	17.0204			1.06171			0.530853	+	0.847464i	$0.321872\pi$
$258$		0			0
$259$			50.1594i			3.11676i
$260$	−14.0664	−	20.2827i	−0.872361	−	1.25788i
$261$		0			0
$262$	8.67657	−	16.5763i	0.536040	−	1.02409i
$263$	20.8876			1.28799			0.643993	−	0.765031i	$-0.277277\pi$
$263$	20.8876			1.28799			0.643993	+	0.765031i	$0.277277\pi$
$264$		0			0
$265$	−11.3798			−0.699059
$266$	5.73478	−	10.9561i	0.351622	−	0.671761i
$267$		0			0
$268$	15.1485	−	10.5057i	0.925342	−	0.641741i
$269$			24.3916i			1.48718i	0.668634	+	0.743592i	$0.266879\pi$
$269$			24.3916i			1.48718i	−0.668634	+	0.743592i	$0.733121\pi$
$270$		0			0
$271$	−12.0583			−0.732492			−0.366246	−	0.930518i	$-0.619357\pi$
$271$	−12.0583			−0.732492			−0.366246	+	0.930518i	$0.619357\pi$
$272$	10.0236	−	26.7864i	0.607770	−	1.62417i
$273$		0			0
$274$	10.2108	+	5.34467i	0.616858	+	0.322884i
$275$			1.45995i			0.0880383i
$276$		0			0
$277$		−	0.142476i		−	0.00856054i	−0.999991	−	0.00428027i	$-0.998638\pi$
$277$		−	0.142476i		−	0.00856054i	0.999991	−	0.00428027i	$-0.00136246\pi$
$278$	9.97852	−	19.0636i	0.598472	−	1.14336i
$279$		0			0
$280$	34.5498	−	4.31133i	2.06474	−	0.257651i
$281$	−9.14875			−0.545769			−0.272884	−	0.962047i	$-0.587978\pi$
$281$	−9.14875			−0.545769			−0.272884	+	0.962047i	$0.587978\pi$
$282$		0			0
$283$		−	7.37210i		−	0.438226i	−0.975699	−	0.219113i	$-0.929684\pi$
$283$		−	7.37210i		−	0.438226i	0.975699	−	0.219113i	$-0.0703163\pi$
$284$	−1.03944	−	1.49879i	−0.0616794	−	0.0889371i
$285$		0			0
$286$	−6.08398	−	3.18455i	−0.359753	−	0.188306i
$287$	30.7258			1.81369
$288$		0			0
$289$	34.1240			2.00730
$290$	15.3683	+	8.04425i	0.902456	+	0.472375i
$291$		0			0
$292$	0.112954	+	0.162871i	0.00661013	+	0.00953131i
$293$		−	4.38597i		−	0.256231i	−0.991759	−	0.128116i	$-0.959107\pi$
$293$		−	4.38597i		−	0.256231i	0.991759	−	0.128116i	$-0.0408928\pi$
$294$		0			0
$295$	19.6999			1.14698
$296$	−29.0671	+	3.62717i	−1.68949	+	0.210825i
$297$		0			0
$298$	12.2483	−	23.3999i	0.709523	−	1.35552i
$299$		−	15.9933i		−	0.924918i
$300$		0			0
$301$			30.7258i			1.77101i
$302$	−4.91581	−	2.57310i	−0.282873	−	0.148065i
$303$		0			0
$304$	6.76369	+	2.53100i	0.387924	+	0.145163i
$305$	5.44196			0.311606
$306$		0			0
$307$		−	27.3791i		−	1.56261i	−0.624150	−	0.781304i	$-0.714555\pi$
$307$		−	27.3791i		−	1.56261i	0.624150	−	0.781304i	$-0.285445\pi$
$308$	7.95973	−	5.52021i	0.453548	−	0.314543i
$309$		0			0
$310$	−1.03904	+	1.98505i	−0.0590134	+	0.112743i
$311$	−15.0540			−0.853634			−0.426817	−	0.904338i	$-0.640365\pi$
$311$	−15.0540			−0.853634			−0.426817	+	0.904338i	$0.640365\pi$
$312$		0			0
$313$	−21.0355			−1.18900			−0.594500	−	0.804096i	$-0.702650\pi$
$313$	−21.0355			−1.18900			−0.594500	+	0.804096i	$0.702650\pi$
$314$	−5.37760	+	10.2737i	−0.303476	+	0.579780i
$315$		0			0
$316$	−9.10769	−	13.1326i	−0.512348	−	0.738767i
$317$			3.29178i			0.184885i	0.995718	+	0.0924425i	$0.0294674\pi$
$317$			3.29178i			0.184885i	−0.995718	+	0.0924425i	$0.970533\pi$
$318$		0			0
$319$	4.82588			0.270198
$320$	4.99678	+	19.7096i	0.279329	+	1.10180i
$321$		0			0
$322$	19.9875	+	10.4621i	1.11386	+	0.583031i
$323$			12.9090i			0.718279i
$324$		0			0
$325$			7.08911i			0.393233i
$326$	−0.755906	+	1.44413i	−0.0418658	+	0.0799831i
$327$		0			0
$328$	2.22187	+	17.8054i	0.122682	+	0.983141i
$329$	−29.4708			−1.62478
$330$		0			0
$331$		−	12.6880i		−	0.697395i	−0.937235	−	0.348698i	$-0.886624\pi$
$331$		−	12.6880i		−	0.697395i	0.937235	−	0.348698i	$-0.113376\pi$
$332$	2.31971	−	1.60876i	0.127310	−	0.0882919i
$333$		0			0
$334$	22.4881	+	11.7710i	1.23049	+	0.644080i
$335$	−23.4275			−1.27998
$336$		0			0
$337$	−6.48274			−0.353137			−0.176569	−	0.984288i	$-0.556500\pi$
$337$	−6.48274			−0.353137			−0.176569	+	0.984288i	$0.556500\pi$
$338$	−13.2538	−	6.93745i	−0.720910	−	0.377348i
$339$		0			0
$340$	−29.8665	+	20.7129i	−1.61974	+	1.12332i
$341$			0.623337i			0.0337556i
$342$		0			0
$343$	45.8054			2.47326
$344$	−17.8054	+	2.22187i	−0.960005	+	0.119795i
$345$		0			0
$346$	0.457324	−	0.873702i	0.0245859	−	0.0469705i
$347$		−	27.0102i		−	1.44998i	−0.688759	−	0.724991i	$-0.741844\pi$
$347$		−	27.0102i		−	1.44998i	0.688759	−	0.724991i	$-0.258156\pi$
$348$		0			0
$349$			2.22276i			0.118981i	0.998229	+	0.0594907i	$0.0189477\pi$
$349$			2.22276i			0.118981i	−0.998229	+	0.0594907i	$0.981052\pi$
$350$	−8.85956	−	4.63738i	−0.473563	−	0.247878i
$351$		0			0
$352$	3.77452	+	4.21343i	0.201182	+	0.224577i
$353$	−25.9731			−1.38241			−0.691204	−	0.722660i	$-0.742919\pi$
$353$	−25.9731			−1.38241			−0.691204	+	0.722660i	$0.742919\pi$
$354$		0			0
$355$			2.31792i			0.123023i
$356$	−16.5974	−	23.9322i	−0.879661	−	1.26841i
$357$		0			0
$358$	11.9723	−	22.8727i	0.632756	−	1.20886i
$359$	15.6003			0.823352			0.411676	−	0.911330i	$-0.364944\pi$
$359$	15.6003			0.823352			0.411676	+	0.911330i	$0.364944\pi$
$360$		0			0
$361$	15.7404			0.828443
$362$	−6.57381	+	12.5591i	−0.345512	+	0.660089i
$363$		0			0
$364$	38.6502	−	26.8046i	2.02582	−	1.40494i
$365$		−	0.251884i		−	0.0131842i
$366$		0			0
$367$	2.56706			0.133999			0.0669997	−	0.997753i	$-0.478657\pi$
$367$	2.56706			0.133999			0.0669997	+	0.997753i	$0.478657\pi$
$368$	−4.61738	+	12.3392i	−0.240698	+	0.643225i
$369$		0			0
$370$	32.9807	+	17.2632i	1.71458	+	0.897469i
$371$		−	21.6852i		−	1.12584i
$372$		0			0
$373$		−	20.9799i		−	1.08630i	−0.839636	−	0.543149i	$-0.817232\pi$
$373$		−	20.9799i		−	1.08630i	0.839636	−	0.543149i	$-0.182768\pi$
$374$	−4.68929	+	8.95872i	−0.242477	+	0.463244i
$375$		0			0
$376$	−2.13112	−	17.0781i	−0.109904	−	0.880738i
$377$	23.4332			1.20687
$378$		0			0
$379$		−	2.32082i		−	0.119213i	−0.998222	−	0.0596063i	$-0.981015\pi$
$379$		−	2.32082i		−	0.119213i	0.998222	−	0.0596063i	$-0.0189845\pi$
$380$	−5.23011	−	7.54143i	−0.268299	−	0.386867i
$381$		0			0
$382$	16.7119	+	8.74754i	0.855054	+	0.447563i
$383$	7.30839			0.373441			0.186721	−	0.982413i	$-0.440214\pi$
$383$	7.30839			0.373441			0.186721	+	0.982413i	$0.440214\pi$
$384$		0			0
$385$	−12.3099			−0.627372
$386$	−15.1094	−	7.90873i	−0.769046	−	0.402544i
$387$		0			0
$388$	−2.32996	−	3.35963i	−0.118286	−	0.170559i
$389$			12.4190i			0.629669i	0.949147	+	0.314835i	$0.101949\pi$
$389$			12.4190i			0.629669i	−0.949147	+	0.314835i	$0.898051\pi$
$390$		0			0
$391$	−23.5504			−1.19099
$392$	5.76394	+	46.1906i	0.291123	+	2.33298i
$393$		0			0
$394$	−16.7110	+	31.9258i	−0.841889	+	1.60840i
$395$			20.3099i			1.02190i
$396$		0			0
$397$			12.8462i			0.644731i	0.946615	+	0.322366i	$0.104478\pi$
$397$			12.8462i			0.644731i	−0.946615	+	0.322366i	$0.895522\pi$
$398$	−13.5192	−	7.07639i	−0.677657	−	0.354707i
$399$		0			0
$400$	2.04667	−	5.46940i	0.102334	−	0.273470i
$401$	6.73490			0.336325			0.168163	−	0.985759i	$-0.446217\pi$
$401$	6.73490			0.336325			0.168163	+	0.985759i	$0.446217\pi$
$402$		0			0
$403$			3.02675i			0.150773i
$404$	−3.13763	+	2.17600i	−0.156103	+	0.108260i
$405$		0			0
$406$	−15.3289	+	29.2854i	−0.760762	+	1.45341i
$407$	10.3565			0.513351
$408$		0			0
$409$	6.06964			0.300124			0.150062	−	0.988677i	$-0.452053\pi$
$409$	6.06964			0.300124			0.150062	+	0.988677i	$0.452053\pi$
$410$	10.5748	−	20.2028i	0.522251	−	0.997744i
$411$		0			0
$412$	−22.2899	−	32.1404i	−1.09814	−	1.58344i
$413$			37.5397i			1.84721i
$414$		0			0
$415$	−3.58748			−0.176103
$416$	18.3280	+	20.4593i	0.898605	+	1.00310i
$417$		0			0
$418$	−2.26212	−	1.18407i	−0.110644	−	0.0579145i
$419$			18.3756i			0.897708i	0.893605	+	0.448854i	$0.148168\pi$
$419$			18.3756i			0.897708i	−0.893605	+	0.448854i	$0.851832\pi$
$420$		0			0
$421$			14.8185i			0.722208i	0.932525	+	0.361104i	$0.117600\pi$
$421$			14.8185i			0.722208i	−0.932525	+	0.361104i	$0.882400\pi$
$422$	14.0124	−	26.7702i	0.682114	−	1.30316i
$423$		0			0
$424$	12.5664	−	1.56812i	0.610279	−	0.0761544i
$425$	10.4388			0.506356
$426$		0			0
$427$			10.3701i			0.501843i
$428$	−15.6509	+	10.8542i	−0.756517	+	0.524657i
$429$		0			0
$430$	20.2028	+	10.5748i	0.974264	+	0.509961i
$431$	31.7144			1.52763			0.763815	−	0.645435i	$-0.223324\pi$
$431$	31.7144			1.52763			0.763815	+	0.645435i	$0.223324\pi$
$432$		0			0
$433$	14.8878			0.715464			0.357732	−	0.933824i	$-0.383550\pi$
$433$	14.8878			0.715464			0.357732	+	0.933824i	$0.383550\pi$
$434$	−3.78266	−	1.97996i	−0.181573	−	0.0950413i
$435$		0			0
$436$	−29.3453	+	20.3515i	−1.40538	+	0.974658i
$437$		−	5.94657i		−	0.284463i
$438$		0			0
$439$	29.4357			1.40489			0.702446	−	0.711737i	$-0.252091\pi$
$439$	29.4357			1.40489			0.702446	+	0.711737i	$0.252091\pi$
$440$	−0.890165	−	7.13353i	−0.0424370	−	0.340078i
$441$		0			0
$442$	−22.7699	+	43.5011i	−1.08305	+	2.06914i
$443$			3.34361i			0.158860i	0.996840	+	0.0794298i	$0.0253100\pi$
$443$			3.34361i			0.158860i	−0.996840	+	0.0794298i	$0.974690\pi$
$444$		0			0
$445$			37.0118i			1.75453i
$446$	−5.35250	−	2.80167i	−0.253448	−	0.132663i
$447$		0			0
$448$	−37.5582	+	9.52175i	−1.77446	+	0.449860i
$449$	19.2984			0.910749			0.455374	−	0.890300i	$-0.349505\pi$
$449$	19.2984			0.910749			0.455374	+	0.890300i	$0.349505\pi$
$450$		0			0
$451$		−	6.34400i		−	0.298727i
$452$	−0.665755	−	0.959970i	−0.0313145	−	0.0451532i
$453$		0			0
$454$	−2.62334	+	5.01180i	−0.123119	+	0.235215i
$455$	−59.7736			−2.80223
$456$		0			0
$457$	2.68162			0.125441			0.0627205	−	0.998031i	$-0.480022\pi$
$457$	2.68162			0.125441			0.0627205	+	0.998031i	$0.480022\pi$
$458$	11.9650	−	22.8588i	0.559088	−	1.06812i
$459$		0			0
$460$	13.7580	−	9.54144i	0.641472	−	0.444872i
$461$			0.240855i			0.0112177i	0.999984	+	0.00560887i	$0.00178537\pi$
$461$			0.240855i			0.0112177i	−0.999984	+	0.00560887i	$0.998215\pi$
$462$		0			0
$463$	−2.80818			−0.130507			−0.0652536	−	0.997869i	$-0.520786\pi$
$463$	−2.80818			−0.130507			−0.0652536	+	0.997869i	$0.520786\pi$
$464$	−18.0792	−	6.76531i	−0.839305	−	0.314072i
$465$		0			0
$466$	−16.9972	−	8.89687i	−0.787379	−	0.412140i
$467$			0.198206i			0.00917188i	0.999989	+	0.00458594i	$0.00145975\pi$
$467$			0.198206i			0.00917188i	−0.999989	+	0.00458594i	$0.998540\pi$
$468$		0			0
$469$		−	44.6430i		−	2.06142i
$470$	−10.1428	+	19.3776i	−0.467854	+	0.893820i
$471$		0			0
$472$	−21.7541	+	2.71460i	−1.00131	+	0.124950i
$473$	6.34400			0.291697
$474$		0			0
$475$			2.63584i			0.120941i
$476$	−39.4701	−	56.9129i	−1.80911	−	2.60860i
$477$		0			0
$478$	−3.33836	−	1.74740i	−0.152693	−	0.0799244i
$479$	−0.634324			−0.0289830			−0.0144915	−	0.999895i	$-0.504613\pi$
$479$	−0.634324			−0.0289830			−0.0144915	+	0.999895i	$0.504613\pi$
$480$		0			0
$481$	50.2882			2.29294
$482$	12.8624	+	6.73258i	0.585865	+	0.306661i
$483$		0			0
$484$	−1.13976	−	1.64345i	−0.0518074	−	0.0747024i
$485$			5.19575i			0.235927i
$486$		0			0
$487$	−24.7182			−1.12009			−0.560044	−	0.828463i	$-0.689216\pi$
$487$	−24.7182			−1.12009			−0.560044	+	0.828463i	$0.689216\pi$
$488$	−6.00939	+	0.749889i	−0.272032	+	0.0339459i
$489$		0			0
$490$	27.4329	−	52.4097i	1.23929	−	2.36763i
$491$			30.5099i			1.37689i	0.725288	+	0.688446i	$0.241707\pi$
$491$			30.5099i			1.37689i	−0.725288	+	0.688446i	$0.758293\pi$
$492$		0			0
$493$		−	34.5056i		−	1.55405i
$494$	−10.9842	−	5.74949i	−0.494203	−	0.258682i
$495$		0			0
$496$	0.873843	−	2.33520i	0.0392367	−	0.104854i
$497$	−4.41698			−0.198129
$498$		0			0
$499$		−	30.1394i		−	1.34923i	−0.738171	−	0.674613i	$-0.764310\pi$
$499$		−	30.1394i		−	1.34923i	0.738171	−	0.674613i	$-0.235690\pi$
$500$	14.7870	−	10.2551i	0.661297	−	0.458621i
$501$		0			0
$502$	−14.4199	+	27.5487i	−0.643591	+	1.22956i
$503$	28.4586			1.26890			0.634452	−	0.772962i	$-0.281226\pi$
$503$	28.4586			1.26890			0.634452	+	0.772962i	$0.281226\pi$
$504$		0			0
$505$	4.85243			0.215930
$506$	2.16012	−	4.12685i	0.0960293	−	0.183461i
$507$		0			0
$508$	14.3147	+	20.6407i	0.635111	+	0.915783i
$509$			8.27915i			0.366967i	0.983023	+	0.183484i	$0.0587374\pi$
$509$			8.27915i			0.366967i	−0.983023	+	0.183484i	$0.941263\pi$
$510$		0			0
$511$	0.479985			0.0212333
$512$	−8.23373	−	21.0762i	−0.363883	−	0.931445i
$513$		0			0
$514$	21.3257	+	11.1626i	0.940638	+	0.492360i
$515$			49.7059i			2.19030i
$516$		0			0
$517$			6.08486i			0.267612i
$518$	−32.8963	+	62.8472i	−1.44538	+	2.76135i
$519$		0			0
$520$	−4.32240	−	34.6384i	−0.189550	−	1.51900i
$521$	14.9245			0.653855			0.326927	−	0.945050i	$-0.393987\pi$
$521$	14.9245			0.653855			0.326927	+	0.945050i	$0.393987\pi$
$522$		0			0
$523$			28.0034i			1.22450i	0.790663	+	0.612252i	$0.209736\pi$
$523$			28.0034i			1.22450i	−0.790663	+	0.612252i	$0.790264\pi$
$524$	21.7426	−	15.0789i	0.949830	−	0.658723i
$525$		0			0
$526$	26.1711	+	13.6988i	1.14112	+	0.597297i
$527$	4.45692			0.194147
$528$		0			0
$529$	−12.1515			−0.528326
$530$	−14.2584	−	7.46329i	−0.619344	−	0.324185i
$531$		0			0
$532$	14.3708	−	9.96637i	0.623052	−	0.432097i
$533$		−	30.8047i		−	1.33430i
$534$		0			0
$535$	24.2046			1.04646
$536$	25.8703	−	3.22826i	1.11743	−	0.139440i
$537$		0			0
$538$	−15.9969	+	30.5615i	−0.689673	+	1.31760i
$539$		−	16.4575i		−	0.708874i
$540$		0			0
$541$		−	42.3272i		−	1.81979i	−0.414842	−	0.909893i	$-0.636163\pi$
$541$		−	42.3272i		−	1.81979i	0.414842	−	0.909893i	$-0.363837\pi$
$542$	−15.1085	−	7.90827i	−0.648965	−	0.339689i
$543$		0			0
$544$	30.1265	−	26.9882i	1.29166	−	1.15711i
$545$	45.3832			1.94400
$546$		0			0
$547$			5.55376i			0.237462i	0.992926	+	0.118731i	$0.0378826\pi$
$547$			5.55376i			0.237462i	−0.992926	+	0.118731i	$0.962117\pi$
$548$	9.28842	+	13.3932i	0.396782	+	0.572130i
$549$		0			0
$550$	−0.957485	+	1.82924i	−0.0408273	+	0.0779992i
$551$	8.71281			0.371178
$552$		0			0
$553$	−38.7021			−1.64578
$554$	0.0934404	−	0.178515i	0.00396990	−	0.00758437i
$555$		0			0
$556$	25.0052	−	17.3415i	1.06045	−	0.735443i
$557$		−	6.05429i		−	0.256528i	−0.991740	−	0.128264i	$-0.959059\pi$
$557$		−	6.05429i		−	0.256528i	0.991740	−	0.128264i	$-0.0409405\pi$
$558$		0			0
$559$	30.8047			1.30290
$560$	46.1166	+	17.2570i	1.94878	+	0.729243i
$561$		0			0
$562$	−11.4629	−	6.00006i	−0.483534	−	0.253097i
$563$		−	36.5314i		−	1.53961i	−0.638277	−	0.769806i	$-0.720353\pi$
$563$		−	36.5314i		−	1.53961i	0.638277	−	0.769806i	$-0.279647\pi$
$564$		0			0
$565$			1.48462i			0.0624583i
$566$	4.83488	−	9.23687i	0.203225	−	0.388255i
$567$		0			0
$568$	−0.319404	−	2.55961i	−0.0134019	−	0.107399i
$569$	−39.1923			−1.64303			−0.821514	−	0.570188i	$-0.806870\pi$
$569$	−39.1923			−1.64303			−0.821514	+	0.570188i	$0.806870\pi$
$570$		0			0
$571$			0.253449i			0.0106065i	0.999986	+	0.00530325i	$0.00168808\pi$
$571$			0.253449i			0.0106065i	−0.999986	+	0.00530325i	$0.998312\pi$
$572$	−5.53438	−	7.98016i	−0.231404	−	0.333667i
$573$		0			0
$574$	38.4979	+	20.1511i	1.60687	+	0.841089i
$575$	−4.80864			−0.200534
$576$		0			0
$577$	−25.2484			−1.05111			−0.525553	−	0.850761i	$-0.676142\pi$
$577$	−25.2484			−1.05111			−0.525553	+	0.850761i	$0.676142\pi$
$578$	42.7557	+	22.3797i	1.77840	+	0.930873i
$579$		0			0
$580$	13.9800	+	20.1581i	0.580486	+	0.837018i
$581$		−	6.83622i		−	0.283614i
$582$		0			0
$583$	−4.47736			−0.185433
$584$	0.0347091	+	0.278148i	0.00143627	+	0.0115099i
$585$		0			0
$586$	2.87647	−	5.49540i	0.118826	−	0.227013i
$587$		−	39.1304i		−	1.61509i	−0.589809	−	0.807543i	$-0.700797\pi$
$587$		−	39.1304i		−	1.61509i	0.589809	−	0.807543i	$-0.299203\pi$
$588$		0			0
$589$			1.12539i			0.0463710i
$590$	24.6830	+	12.9199i	1.01618	+	0.531904i
$591$		0			0
$592$	−38.7984	−	14.5185i	−1.59460	−	0.596708i
$593$	25.4476			1.04501			0.522504	−	0.852637i	$-0.324998\pi$
$593$	25.4476			1.04501			0.522504	+	0.852637i	$0.324998\pi$
$594$		0			0
$595$			88.0173i			3.60836i
$596$	30.6929	−	21.2861i	1.25723	−	0.871911i
$597$		0			0
$598$	10.4890	−	20.0388i	0.428926	−	0.819448i
$599$	37.0670			1.51452			0.757259	−	0.653115i	$-0.226538\pi$
$599$	37.0670			1.51452			0.757259	+	0.653115i	$0.226538\pi$
$600$		0			0
$601$	30.5587			1.24652			0.623259	−	0.782016i	$-0.285808\pi$
$601$	30.5587			1.24652			0.623259	+	0.782016i	$0.285808\pi$
$602$	−20.1511	+	38.4979i	−0.821296	+	1.56906i
$603$		0			0
$604$	−4.47174	−	6.44792i	−0.181953	−	0.262362i
$605$			2.54164i			0.103332i
$606$		0			0
$607$	15.4063			0.625322			0.312661	−	0.949865i	$-0.398780\pi$
$607$	15.4063			0.625322			0.312661	+	0.949865i	$0.398780\pi$
$608$	6.81464	+	7.60707i	0.276370	+	0.308508i
$609$		0			0
$610$	6.81850	+	3.56902i	0.276073	+	0.144506i
$611$			29.5464i			1.19532i
$612$		0			0
$613$		−	24.0437i		−	0.971116i	−0.874205	−	0.485558i	$-0.838617\pi$
$613$		−	24.0437i		−	0.971116i	0.874205	−	0.485558i	$-0.161383\pi$
$614$	17.9562	−	34.3046i	0.724652	−	1.38442i
$615$		0			0
$616$	13.5935	−	1.69628i	0.547697	−	0.0683450i
$617$	−8.77372			−0.353217			−0.176608	−	0.984281i	$-0.556513\pi$
$617$	−8.77372			−0.353217			−0.176608	+	0.984281i	$0.556513\pi$
$618$		0			0
$619$			1.81682i			0.0730242i	0.999333	+	0.0365121i	$0.0116248\pi$
$619$			1.81682i			0.0730242i	−0.999333	+	0.0365121i	$0.988375\pi$
$620$	−2.60372	+	1.80573i	−0.104568	+	0.0725197i
$621$		0			0
$622$	−18.8619	−	9.87293i	−0.756293	−	0.395868i
$623$	−70.5288			−2.82568
$624$		0			0
$625$	−30.1683			−1.20673
$626$	−26.3565	−	13.7958i	−1.05342	−	0.551392i
$627$		0			0
$628$	−13.4757	+	9.34564i	−0.537740	+	0.372932i
$629$		−	74.0499i		−	2.95256i
$630$		0			0
$631$	2.72027			0.108292			0.0541461	−	0.998533i	$-0.482756\pi$
$631$	2.72027			0.108292			0.0541461	+	0.998533i	$0.482756\pi$
$632$	−2.79866	−	22.4276i	−0.111325	−	0.892123i
$633$		0			0
$634$	−2.15886	+	4.12444i	−0.0857395	+	0.163802i
$635$		−	31.9214i		−	1.26676i
$636$		0			0
$637$		−	79.9130i		−	3.16627i
$638$	6.04659	+	3.16498i	0.239387	+	0.125303i
$639$		0			0
$640$	−6.66553	+	27.9722i	−0.263478	+	1.10570i
$641$	6.10619			0.241180			0.120590	−	0.992702i	$-0.461521\pi$
$641$	6.10619			0.241180			0.120590	+	0.992702i	$0.461521\pi$
$642$		0			0
$643$			32.9170i			1.29812i	0.760737	+	0.649060i	$0.224838\pi$
$643$			32.9170i			1.29812i	−0.760737	+	0.649060i	$0.775162\pi$
$644$	18.1819	+	26.2170i	0.716469	+	1.03309i
$645$		0			0
$646$	−8.46619	+	16.1744i	−0.333098	+	0.636372i
$647$	−11.0567			−0.434684			−0.217342	−	0.976095i	$-0.569739\pi$
$647$	−11.0567			−0.434684			−0.217342	+	0.976095i	$0.569739\pi$
$648$		0			0
$649$	7.75087			0.304248
$650$	−4.64928	+	8.88230i	−0.182360	+	0.348392i
$651$		0			0
$652$	−1.89422	+	1.31368i	−0.0741835	+	0.0514475i
$653$		−	18.6278i		−	0.728963i	−0.931211	−	0.364482i	$-0.881246\pi$
$653$		−	18.6278i		−	0.728963i	0.931211	−	0.364482i	$-0.118754\pi$
$654$		0			0
$655$	−33.6255			−1.31386
$656$	−8.89352	+	23.7665i	−0.347234	+	0.927925i
$657$		0			0
$658$	−36.9254	−	19.3279i	−1.43950	−	0.753482i
$659$			26.2315i			1.02184i	0.859629	+	0.510918i	$0.170694\pi$
$659$			26.2315i			1.02184i	−0.859629	+	0.510918i	$0.829306\pi$
$660$		0			0
$661$			38.4922i			1.49717i	0.663038	+	0.748586i	$0.269267\pi$
$661$			38.4922i			1.49717i	−0.663038	+	0.748586i	$0.730733\pi$
$662$	8.32122	−	15.8974i	0.323413	−	0.617870i
$663$		0			0
$664$	3.96155	−	0.494347i	0.153738	−	0.0191844i
$665$	−22.2248			−0.861839
$666$		0			0
$667$			15.8950i			0.615459i
$668$	20.4566	+	29.4969i	0.791490	+	1.14127i
$669$		0			0
$670$	−29.3535	−	15.3646i	−1.13403	−	0.593586i
$671$	2.14112			0.0826570
$672$		0			0
$673$	−29.0436			−1.11955			−0.559773	−	0.828646i	$-0.689112\pi$
$673$	−29.0436			−1.11955			−0.559773	+	0.828646i	$0.689112\pi$
$674$	−8.12254	−	4.25160i	−0.312869	−	0.163766i
$675$		0			0
$676$	−12.0565	−	17.3845i	−0.463711	−	0.668636i
$677$		−	14.6056i		−	0.561340i	−0.959804	−	0.280670i	$-0.909443\pi$
$677$		−	14.6056i		−	0.561340i	0.959804	−	0.280670i	$-0.0905567\pi$
$678$		0			0
$679$	−9.90090			−0.379962
$680$	−51.0055	+	6.36478i	−1.95597	+	0.244078i
$681$		0			0
$682$	−0.408805	+	0.781009i	−0.0156540	+	0.0299064i
$683$		−	29.6575i		−	1.13481i	−0.823438	−	0.567406i	$-0.807947\pi$
$683$		−	29.6575i		−	1.13481i	0.823438	−	0.567406i	$-0.192053\pi$
$684$		0			0
$685$		−	20.7129i		−	0.791401i
$686$	57.3919	+	30.0408i	2.19123	+	1.14696i
$687$		0			0
$688$	−23.7665	−	8.89352i	−0.906089	−	0.339062i
$689$	−21.7408			−0.828259
$690$		0			0
$691$		−	16.6181i		−	0.632184i	−0.948729	−	0.316092i	$-0.897629\pi$
$691$		−	16.6181i		−	0.632184i	0.948729	−	0.316092i	$-0.102371\pi$
$692$	1.14601	−	0.794775i	0.0435646	−	0.0302128i
$693$		0			0
$694$	17.7142	−	33.8424i	0.672421	−	1.28464i
$695$	−38.6711			−1.46688
$696$		0			0
$697$	−45.3603			−1.71814
$698$	−1.45776	+	2.78500i	−0.0551770	+	0.105414i
$699$		0			0
$700$	−8.05923	−	11.6208i	−0.304610	−	0.439225i
$701$			36.9173i			1.39435i	0.716902	+	0.697174i	$0.245559\pi$
$701$			36.9173i			1.39435i	−0.716902	+	0.697174i	$0.754441\pi$
$702$		0			0
$703$	18.6979			0.705206
$704$	1.96597	+	7.75467i	0.0740951	+	0.292265i
$705$		0			0
$706$	−32.5429	−	17.0340i	−1.22477	−	0.641084i
$707$			9.24667i			0.347757i
$708$		0			0
$709$		−	1.80322i		−	0.0677215i	−0.999427	−	0.0338608i	$-0.989220\pi$
$709$		−	1.80322i		−	0.0677215i	0.999427	−	0.0338608i	$-0.0107803\pi$
$710$	−1.52017	+	2.90424i	−0.0570511	+	0.108994i
$711$		0			0
$712$	−5.10014	−	40.8710i	−0.191136	−	1.53171i
$713$	−2.05309			−0.0768887
$714$		0			0
$715$			12.3415i			0.461547i
$716$	30.0014	−	20.8065i	1.12120	−	0.777574i
$717$		0			0
$718$	19.5464	+	10.2312i	0.729464	+	0.381825i
$719$	−30.0049			−1.11899			−0.559496	−	0.828833i	$-0.689005\pi$
$719$	−30.0049			−1.11899			−0.559496	+	0.828833i	$0.689005\pi$
$720$		0			0
$721$	−94.7183			−3.52750
$722$	19.7219	+	10.3231i	0.733974	+	0.384186i
$723$		0			0
$724$	−16.4733	+	11.4245i	−0.612226	+	0.424589i
$725$		−	7.04555i		−	0.261665i
$726$		0			0
$727$	5.71187			0.211842			0.105921	−	0.994375i	$-0.466221\pi$
$727$	5.71187			0.211842			0.105921	+	0.994375i	$0.466221\pi$
$728$	66.0062	−	8.23666i	2.44635	−	0.305271i
$729$		0			0
$730$	0.165194	−	0.315598i	0.00611412	−	0.0116808i
$731$		−	45.3603i		−	1.67771i
$732$		0			0
$733$			13.4418i			0.496483i	0.968698	+	0.248242i	$0.0798527\pi$
$733$			13.4418i			0.496483i	−0.968698	+	0.248242i	$0.920147\pi$
$734$	3.21640	+	1.68357i	0.118719	+	0.0621415i
$735$		0			0
$736$	−13.8778	+	12.4322i	−0.511543	+	0.458255i
$737$	−9.21748			−0.339530
$738$		0			0
$739$		−	15.6188i		−	0.574548i	−0.957849	−	0.287274i	$-0.907251\pi$
$739$		−	15.6188i		−	0.574548i	0.957849	−	0.287274i	$-0.0927489\pi$
$740$	30.0014	+	43.2597i	1.10287	+	1.59026i
$741$		0			0
$742$	14.2219	−	27.1704i	0.522101	−	0.997457i
$743$	−41.2940			−1.51493			−0.757466	−	0.652875i	$-0.773563\pi$
$743$	−41.2940			−1.51493			−0.757466	+	0.652875i	$0.773563\pi$
$744$		0			0
$745$	−47.4674			−1.73907
$746$	13.7593	−	26.2867i	0.503765	−	0.962426i
$747$		0			0
$748$	−11.7509	+	8.14943i	−0.429654	+	0.297973i
$749$			46.1237i			1.68532i
$750$		0			0
$751$	5.34503			0.195043			0.0975215	−	0.995233i	$-0.468909\pi$
$751$	5.34503			0.195043			0.0975215	+	0.995233i	$0.468909\pi$
$752$	8.53025	−	22.7957i	0.311066	−	0.831274i
$753$		0			0
$754$	29.3606	+	15.3683i	1.06925	+	0.559679i
$755$			9.97187i			0.362913i
$756$		0			0
$757$		−	13.6401i		−	0.495757i	−0.968791	−	0.247878i	$-0.920267\pi$
$757$		−	13.6401i		−	0.495757i	0.968791	−	0.247878i	$-0.0797334\pi$
$758$	1.52207	−	2.90787i	0.0552842	−	0.105619i
$759$		0			0
$760$	−1.60713	−	12.8791i	−0.0582969	−	0.467174i
$761$	−29.1959			−1.05835			−0.529176	−	0.848512i	$-0.677499\pi$
$761$	−29.1959			−1.05835			−0.529176	+	0.848512i	$0.677499\pi$
$762$		0			0
$763$			86.4812i			3.13083i
$764$	15.2022	+	21.9204i	0.549996	+	0.793054i
$765$		0			0
$766$	9.15704	+	4.79309i	0.330857	+	0.173181i
$767$	37.6361			1.35896
$768$		0			0
$769$	23.4723			0.846432			0.423216	−	0.906029i	$-0.360901\pi$
$769$	23.4723			0.846432			0.423216	+	0.906029i	$0.360901\pi$
$770$	−15.4237	−	8.07327i	−0.555832	−	0.290940i
$771$		0			0
$772$	−13.7444	−	19.8185i	−0.494673	−	0.713282i
$773$		−	4.20825i		−	0.151360i	−0.997132	−	0.0756802i	$-0.975887\pi$
$773$		−	4.20825i		−	0.151360i	0.997132	−	0.0756802i	$-0.0241128\pi$
$774$		0			0
$775$	0.910040			0.0326896
$776$	−0.715962	−	5.73751i	−0.0257015	−	0.205965i
$777$		0			0
$778$	−8.14481	+	15.5604i	−0.292006	+	0.557867i
$779$		−	11.4537i		−	0.410370i
$780$		0			0
$781$			0.911979i			0.0326332i
$782$	−29.5074	−	15.4451i	−1.05518	−	0.552317i
$783$		0			0
$784$	−23.0714	+	61.6546i	−0.823980	+	2.20195i
$785$	20.8405			0.743831
$786$		0			0
$787$			17.8152i			0.635042i	0.948251	+	0.317521i	$0.102850\pi$
$787$			17.8152i			0.635042i	−0.948251	+	0.317521i	$0.897150\pi$
$788$	−41.8761	+	29.0418i	−1.49177	+	1.03457i
$789$		0			0
$790$	−13.3199	+	25.4473i	−0.473902	+	0.905374i
$791$	−2.82905			−0.100590
$792$		0			0
$793$	10.3967			0.369197
$794$	−8.42497	+	16.0956i	−0.298991	+	0.571212i
$795$		0			0
$796$	−12.2979	−	17.7327i	−0.435889	−	0.628519i
$797$			35.5339i			1.25868i	0.777131	+	0.629338i	$0.216674\pi$
$797$			35.5339i			1.25868i	−0.777131	+	0.629338i	$0.783326\pi$
$798$		0			0
$799$	43.5074			1.53918
$800$	6.15140	−	5.51061i	0.217485	−	0.194829i
$801$		0			0
$802$	8.43849	+	4.41698i	0.297974	+	0.155969i
$803$		−	0.0991030i		−	0.00349727i
$804$		0			0
$805$		−	40.5453i		−	1.42903i
$806$	−1.98505	+	3.79236i	−0.0699203	+	0.133580i
$807$		0			0
$808$	−5.35839	+	0.668653i	−0.188508	+	0.0235231i
$809$	3.57918			0.125837			0.0629187	−	0.998019i	$-0.479959\pi$
$809$	3.57918			0.125837			0.0629187	+	0.998019i	$0.479959\pi$
$810$		0			0
$811$		−	14.0896i		−	0.494753i	−0.968919	−	0.247377i	$-0.920432\pi$
$811$		−	14.0896i		−	0.494753i	0.968919	−	0.247377i	$-0.0795685\pi$
$812$	−38.4127	+	26.6399i	−1.34802	+	0.934877i
$813$		0			0
$814$	12.9761	+	6.79213i	0.454813	+	0.238064i
$815$	2.92946			0.102615
$816$		0			0
$817$	11.4537			0.400713
$818$	7.60495	+	3.98068i	0.265901	+	0.139181i
$819$		0			0
$820$	26.4993	−	18.3777i	0.925397	−	0.641778i
$821$		−	47.8288i		−	1.66924i	−0.550829	−	0.834618i	$-0.685688\pi$
$821$		−	47.8288i		−	1.66924i	0.550829	−	0.834618i	$-0.314312\pi$
$822$		0			0
$823$	−31.6451			−1.10308			−0.551539	−	0.834149i	$-0.685959\pi$
$823$	−31.6451			−1.10308			−0.551539	+	0.834149i	$0.685959\pi$
$824$	−6.84935	−	54.8887i	−0.238608	−	1.91214i
$825$		0			0
$826$	−24.6198	+	47.0354i	−0.856634	+	1.63657i
$827$			25.5630i			0.888911i	0.895801	+	0.444456i	$0.146603\pi$
$827$			25.5630i			0.888911i	−0.895801	+	0.444456i	$0.853397\pi$
$828$		0			0
$829$			14.1148i			0.490228i	0.969494	+	0.245114i	$0.0788254\pi$
$829$			14.1148i			0.490228i	−0.969494	+	0.245114i	$0.921175\pi$
$830$	−4.49494	−	2.35279i	−0.156021	−	0.0816667i
$831$		0			0
$832$	9.54618	+	37.6546i	0.330954	+	1.30544i
$833$	−117.673			−4.07712
$834$		0			0
$835$		−	45.6177i		−	1.57867i
$836$	−2.05777	−	2.96715i	−0.0711694	−	0.102621i
$837$		0			0
$838$	−12.0514	+	23.0237i	−0.416308	+	0.795342i
$839$	6.13279			0.211727			0.105864	−	0.994381i	$-0.466239\pi$
$839$	6.13279			0.211727			0.105864	+	0.994381i	$0.466239\pi$
$840$		0			0
$841$	5.71084			0.196926
$842$	−9.71846	+	18.5668i	−0.334920	+	0.639854i
$843$		0			0
$844$	35.1137	−	24.3519i	1.20866	−	0.838228i
$845$			26.8856i			0.924894i
$846$		0			0
$847$	−4.84329			−0.166418
$848$	16.7735	+	6.27672i	0.576005	+	0.215543i
$849$		0			0
$850$	13.0793	+	6.84612i	0.448616	+	0.234820i
$851$			34.1112i			1.16932i
$852$		0			0
$853$			3.74773i			0.128320i	0.997940	+	0.0641599i	$0.0204368\pi$
$853$			3.74773i			0.128320i	−0.997940	+	0.0641599i	$0.979563\pi$
$854$	−6.80104	+	12.9932i	−0.232727	+	0.444617i
$855$		0			0
$856$	−26.7284	+	3.33533i	−0.913557	+	0.113999i
$857$	41.2567			1.40930			0.704652	−	0.709553i	$-0.251103\pi$
$857$	41.2567			1.40930			0.704652	+	0.709553i	$0.251103\pi$
$858$		0			0
$859$			9.21458i			0.314398i	0.987567	+	0.157199i	$0.0502463\pi$
$859$			9.21458i			0.314398i	−0.987567	+	0.157199i	$0.949754\pi$
$860$	18.3777	+	26.4993i	0.626676	+	0.903620i
$861$		0			0
$862$	39.7366	+	20.7994i	1.35343	+	0.708431i
$863$	−39.3004			−1.33780			−0.668901	−	0.743352i	$-0.733235\pi$
$863$	−39.3004			−1.33780			−0.668901	+	0.743352i	$0.733235\pi$
$864$		0			0
$865$	−1.77233			−0.0602610
$866$	18.6537	+	9.76395i	0.633879	+	0.331793i
$867$		0			0
$868$	−3.44095	−	4.96159i	−0.116793	−	0.168407i
$869$			7.99086i			0.271071i
$870$		0			0
$871$	−44.7575			−1.51655
$872$	−50.1153	+	6.25370i	−1.69712	+	0.211777i
$873$		0			0
$874$	3.89996	−	7.45075i	0.131918	−	0.252025i
$875$		−	43.5778i		−	1.47320i
$876$		0			0
$877$		−	19.2061i		−	0.648545i	−0.945964	−	0.324273i	$-0.894880\pi$
$877$		−	19.2061i		−	0.648545i	0.945964	−	0.324273i	$-0.105120\pi$
$878$	36.8815	+	19.3050i	1.24469	+	0.651511i
$879$		0			0
$880$	3.56308	−	9.52175i	0.120111	−	0.320978i
$881$	5.78843			0.195017			0.0975087	−	0.995235i	$-0.468913\pi$
$881$	5.78843			0.195017			0.0975087	+	0.995235i	$0.468913\pi$
$882$		0			0
$883$			27.1286i			0.912949i	0.889737	+	0.456474i	$0.150888\pi$
$883$			27.1286i			0.912949i	−0.889737	+	0.456474i	$0.849112\pi$
$884$	−57.0590	+	39.5714i	−1.91910	+	1.33093i
$885$		0			0
$886$	−2.19285	+	4.18937i	−0.0736703	+	0.140745i
$887$	9.55834			0.320938			0.160469	−	0.987041i	$-0.448699\pi$
$887$	9.55834			0.320938			0.160469	+	0.987041i	$0.448699\pi$
$888$		0			0
$889$	60.8286			2.04013
$890$	−24.2736	+	46.3739i	−0.813653	+	1.55446i
$891$		0			0
$892$	−4.86898	−	7.02070i	−0.163025	−	0.235070i
$893$			10.9858i			0.367626i
$894$		0			0
$895$	−46.3979			−1.55091
$896$	−53.3032	−	12.7017i	−1.78073	−	0.424333i
$897$		0			0
$898$	24.1799	+	12.6566i	0.806895	+	0.422355i
$899$		−	3.00815i		−	0.100327i
$900$		0			0
$901$			32.0136i			1.06653i
$902$	4.16061	−	7.94870i	0.138533	−	0.264663i
$903$		0			0
$904$	−0.204577	−	1.63942i	−0.00680412	−	0.0545262i
$905$	25.4764			0.846864
$906$		0			0
$907$		−	23.2370i		−	0.771571i	−0.922588	−	0.385786i	$-0.873930\pi$
$907$		−	23.2370i		−	0.771571i	0.922588	−	0.385786i	$-0.126070\pi$
$908$	−6.57381	+	4.55905i	−0.218160	+	0.151297i
$909$		0			0
$910$	−74.8933	−	39.2016i	−2.48269	−	1.29952i
$911$	30.9370			1.02499			0.512494	−	0.858691i	$-0.328722\pi$
$911$	30.9370			1.02499			0.512494	+	0.858691i	$0.328722\pi$
$912$		0			0
$913$	−1.41148			−0.0467132
$914$	3.35994	+	1.75870i	0.111137	+	0.0581726i
$915$		0			0
$916$	29.9831	−	20.7938i	0.990670	−	0.687046i
$917$		−	64.0759i		−	2.11597i
$918$		0			0
$919$	44.8067			1.47804			0.739019	−	0.673684i	$-0.235289\pi$
$919$	44.8067			1.47804			0.739019	+	0.673684i	$0.235289\pi$
$920$	23.4957	−	2.93194i	0.774632	−	0.0966633i
$921$		0			0
$922$	−0.157961	+	0.301779i	−0.00520217	+	0.00993857i
$923$			4.42832i			0.145760i
$924$		0			0
$925$		−	15.1199i		−	0.497140i
$926$	−3.51851	−	1.84170i	−0.115625	−	0.0605221i
$927$		0			0
$928$	−18.2154	−	20.3335i	−0.597949	−	0.667481i
$929$	−39.2081			−1.28638			−0.643189	−	0.765708i	$-0.722389\pi$
$929$	−39.2081			−1.28638			−0.643189	+	0.765708i	$0.722389\pi$
$930$		0			0
$931$		−	29.7129i		−	0.973802i
$932$	−15.4617	−	22.2947i	−0.506465	−	0.730286i
$933$		0			0
$934$	−0.129990	+	0.248342i	−0.00425341	+	0.00812600i
$935$	18.1730			0.594321
$936$		0			0
$937$	55.8729			1.82529			0.912644	−	0.408756i	$-0.134037\pi$
$937$	55.8729			1.82529			0.912644	+	0.408756i	$0.134037\pi$
$938$	29.2784	−	55.9354i	0.955973	−	1.82635i
$939$		0			0
$940$	−25.4169	+	17.6271i	−0.829009	+	0.574932i
$941$		−	43.3369i		−	1.41274i	−0.707842	−	0.706371i	$-0.750331\pi$
$941$		−	43.3369i		−	1.41274i	0.707842	−	0.706371i	$-0.249669\pi$
$942$		0			0
$943$	20.8953			0.680443
$944$	−29.0371	−	10.8658i	−0.945076	−	0.353651i
$945$		0			0
$946$	7.94870	+	4.16061i	0.258435	+	0.135273i
$947$		−	6.07170i		−	0.197304i	−0.995122	−	0.0986519i	$-0.968547\pi$
$947$		−	6.07170i		−	0.197304i	0.995122	−	0.0986519i	$-0.0314530\pi$
$948$		0			0
$949$		−	0.481217i		−	0.0156210i
$950$	−1.72868	+	3.30258i	−0.0560856	+	0.107150i
$951$		0			0
$952$	−12.1286	−	97.1948i	−0.393089	−	3.15010i
$953$	14.0254			0.454326			0.227163	−	0.973857i	$-0.427055\pi$
$953$	14.0254			0.454326			0.227163	+	0.973857i	$0.427055\pi$
$954$		0			0
$955$		−	33.9005i		−	1.09699i
$956$	−3.03678	−	4.37882i	−0.0982166	−	0.141621i
$957$		0			0
$958$	−0.794775	−	0.416011i	−0.0256780	−	0.0134407i
$959$	39.4701			1.27456
$960$		0			0
$961$	−30.6115			−0.987466
$962$	63.0085	+	32.9807i	2.03148	+	1.06334i
$963$		0			0
$964$	11.7004	+	16.8712i	0.376846	+	0.543384i
$965$			30.6498i			0.986651i
$966$		0			0
$967$	−7.68589			−0.247162			−0.123581	−	0.992335i	$-0.539438\pi$
$967$	−7.68589			−0.247162			−0.123581	+	0.992335i	$0.539438\pi$
$968$	−0.350232	−	2.80666i	−0.0112569	−	0.0902095i
$969$		0			0
$970$	−3.40755	+	6.51001i	−0.109410	+	0.209024i
$971$			26.3648i			0.846086i	0.906110	+	0.423043i	$0.139038\pi$
$971$			26.3648i			0.846086i	−0.906110	+	0.423043i	$0.860962\pi$
$972$		0			0
$973$		−	73.6907i		−	2.36242i
$974$	−30.9707	−	16.2110i	−0.992364	−	0.519435i
$975$		0			0
$976$	−8.02126	−	3.00159i	−0.256754	−	0.0960786i
$977$	−58.2530			−1.86368			−0.931840	−	0.362870i	$-0.881797\pi$
$977$	−58.2530			−1.86368			−0.931840	+	0.362870i	$0.881797\pi$
$978$		0			0
$979$			14.5622i			0.465409i
$980$	68.7441	−	47.6752i	2.19595	−	1.52293i
$981$		0			0
$982$	−20.0094	+	38.2273i	−0.638527	+	1.21988i
$983$	−28.7987			−0.918537			−0.459268	−	0.888298i	$-0.651888\pi$
$983$	−28.7987			−0.918537			−0.459268	+	0.888298i	$0.651888\pi$
$984$		0			0
$985$	64.7625			2.06350
$986$	22.6299	−	43.2338i	0.720684	−	1.37684i
$987$		0			0
$988$	−9.99195	−	14.4076i	−0.317886	−	0.458368i
$989$			20.8953i			0.664430i
$990$		0			0
$991$	−32.1947			−1.02270			−0.511349	−	0.859373i	$-0.670854\pi$
$991$	−32.1947			−1.02270			−0.511349	+	0.859373i	$0.670854\pi$
$992$	2.62639	−	2.35279i	0.0833879	−	0.0747013i
$993$		0			0
$994$	−5.53425	−	2.89681i	−0.175536	−	0.0918811i
$995$			27.4241i			0.869402i
$996$		0			0
$997$			32.6398i			1.03371i	0.856072	+	0.516856i	$0.172898\pi$
$997$			32.6398i			1.03371i	−0.856072	+	0.516856i	$0.827102\pi$
$998$	19.7665	−	37.7632i	0.625697	−	1.19537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.f.h.397.18	yes	20
3.2	odd	2	inner	792.2.f.h.397.3	✓	20
4.3	odd	2		3168.2.f.h.1585.3		20
8.3	odd	2		3168.2.f.h.1585.18		20
8.5	even	2	inner	792.2.f.h.397.17	yes	20
12.11	even	2		3168.2.f.h.1585.17		20
24.5	odd	2	inner	792.2.f.h.397.4	yes	20
24.11	even	2		3168.2.f.h.1585.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.f.h.397.3	✓	20	3.2	odd	2	inner
792.2.f.h.397.4	yes	20	24.5	odd	2	inner
792.2.f.h.397.17	yes	20	8.5	even	2	inner
792.2.f.h.397.18	yes	20	1.1	even	1	trivial
3168.2.f.h.1585.3		20	4.3	odd	2
3168.2.f.h.1585.4		20	24.11	even	2
3168.2.f.h.1585.17		20	12.11	even	2
3168.2.f.h.1585.18		20	8.3	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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25295 + 0.655834i) q^{2} +(1.13976 + 1.64345i) q^{4} -2.54164i q^{5} +4.84329 q^{7} +(0.350232 + 2.80666i) q^{8} +(1.66690 - 3.18455i) q^{10} -1.00000i q^{11} -4.85572i q^{13} +(6.06840 + 3.17640i) q^{14} +(-1.40188 + 3.74630i) q^{16} -7.15011 q^{17} -1.80543i q^{19} +(4.17707 - 2.89687i) q^{20} +(0.655834 - 1.25295i) q^{22} +3.29371 q^{23} -1.45995 q^{25} +(3.18455 - 6.08398i) q^{26} +(5.52021 + 7.95973i) q^{28} +4.82588i q^{29} -0.623337 q^{31} +(-4.21343 + 3.77452i) q^{32} +(-8.95872 - 4.68929i) q^{34} -12.3099i q^{35} +10.3565i q^{37} +(1.18407 - 2.26212i) q^{38} +(7.13353 - 0.890165i) q^{40} +6.34400 q^{41} +6.34400i q^{43} +(1.64345 - 1.13976i) q^{44} +(4.12685 + 2.16012i) q^{46} -6.08486 q^{47} +16.4575 q^{49} +(-1.82924 - 0.957485i) q^{50} +(7.98016 - 5.53438i) q^{52} -4.47736i q^{53} -2.54164 q^{55} +(1.69628 + 13.5935i) q^{56} +(-3.16498 + 6.04659i) q^{58} +7.75087i q^{59} +2.14112i q^{61} +(-0.781009 - 0.408805i) q^{62} +(-7.75467 + 1.96597i) q^{64} -12.3415 q^{65} -9.21748i q^{67} +(-8.14943 - 11.7509i) q^{68} +(8.07327 - 15.4237i) q^{70} -0.911979 q^{71} +0.0991030 q^{73} +(-6.79213 + 12.9761i) q^{74} +(2.96715 - 2.05777i) q^{76} -4.84329i q^{77} -7.99086 q^{79} +(9.52175 + 3.56308i) q^{80} +(7.94870 + 4.16061i) q^{82} -1.41148i q^{83} +18.1730i q^{85} +(-4.16061 + 7.94870i) q^{86} +(2.80666 - 0.350232i) q^{88} -14.5622 q^{89} -23.5177i q^{91} +(3.75404 + 5.41305i) q^{92} +(-7.62403 - 3.99066i) q^{94} -4.58877 q^{95} -2.04425 q^{97} +(20.6204 + 10.7934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 8 q^{10} - 12 q^{16} - 12 q^{25} + 24 q^{28} + 40 q^{31} - 24 q^{34} - 32 q^{40} + 40 q^{46} + 36 q^{49} + 56 q^{52} - 16 q^{55} + 24 q^{58} + 4 q^{64} + 56 q^{70} - 56 q^{73} - 8 q^{76}+ \cdots + 8 q^{97}+O(q^{100}) \) 20 * q + 4 * q^4 + 8 * q^10 - 12 * q^16 - 12 * q^25 + 24 * q^28 + 40 * q^31 - 24 * q^34 - 32 * q^40 + 40 * q^46 + 36 * q^49 + 56 * q^52 - 16 * q^55 + 24 * q^58 + 4 * q^64 + 56 * q^70 - 56 * q^73 - 8 * q^76 - 16 * q^79 - 32 * q^82 + 12 * q^88 - 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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