LMFDB - Embedded newform 1152.2.r.f.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(193,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1152.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			193.3
Root			$0.500000 - 2.74530i$ of defining polynomial
Character	$\chi$	$=$	1152.193
Dual form			1152.2.r.f.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.524648 + 1.65068i) q^{3} +(-2.98735 - 1.72474i) q^{5} +(2.02166 + 3.50162i) q^{7} +(-2.44949 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.524648 + 1.65068i) q^{3} +(-2.98735 - 1.72474i) q^{5} +(2.02166 + 3.50162i) q^{7} +(-2.44949 - 1.73205i) q^{9} +(3.50162 - 2.02166i) q^{11} +(0.866025 + 0.500000i) q^{13} +(4.41431 - 4.02627i) q^{15} +6.44949 q^{17} +(-6.84072 + 1.50000i) q^{21} +(-1.11295 + 1.92768i) q^{23} +(3.44949 + 5.97469i) q^{25} +(4.14418 - 3.13461i) q^{27} +(-5.10867 + 2.94949i) q^{29} +(-2.93038 + 5.07556i) q^{31} +(1.50000 + 6.84072i) q^{33} -13.9474i q^{35} +3.55051i q^{37} +(-1.27970 + 1.16721i) q^{39} +(-4.17423 + 7.22999i) q^{41} +(-8.93092 + 5.15627i) q^{43} +(4.33013 + 9.39898i) q^{45} +(-2.02166 - 3.50162i) q^{47} +(-4.67423 + 8.09601i) q^{49} +(-3.38371 + 10.6460i) q^{51} -3.34847i q^{53} -13.9474 q^{55} +(1.92768 + 1.11295i) q^{59} +(-1.64456 + 0.949490i) q^{61} +(1.11295 - 12.0788i) q^{63} +(-1.72474 - 2.98735i) q^{65} +(13.6527 + 7.88242i) q^{67} +(-2.59808 - 2.84847i) q^{69} +13.5389 q^{71} +3.55051 q^{73} +(-11.6721 + 2.55940i) q^{75} +(14.1582 + 8.17423i) q^{77} +(4.74781 + 8.22345i) q^{79} +(3.00000 + 8.48528i) q^{81} +(-1.92768 + 1.11295i) q^{83} +(-19.2669 - 11.1237i) q^{85} +(-2.18841 - 9.98022i) q^{87} +4.44949 q^{89} +4.04332i q^{91} +(-6.84072 - 7.50000i) q^{93} +(-8.17423 - 14.1582i) q^{97} +(-12.0788 - 1.11295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 64 q^{17} + 16 q^{25} + 24 q^{33} - 8 q^{41} - 16 q^{49} - 8 q^{65} + 96 q^{73} + 48 q^{81} + 32 q^{89} - 72 q^{97}+O(q^{100}) $ 16 * q + 64 * q^17 + 16 * q^25 + 24 * q^33 - 8 * q^41 - 16 * q^49 - 8 * q^65 + 96 * q^73 + 48 * q^81 + 32 * q^89 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.524648	+	1.65068i	−0.302905	+	0.953021i
$3$	−0.524648	+	1.65068i	−0.302905	+	0.953021i
$4$		0			0
$5$	−2.98735	−	1.72474i	−1.33598	−	0.771329i	−0.349773	−	0.936835i	$-0.613741\pi$
$5$	−2.98735	−	1.72474i	−1.33598	−	0.771329i	−0.986209	+	0.165505i	$0.947075\pi$
$6$		0			0
$7$	2.02166	+	3.50162i	0.764116	+	1.32349i	0.940712	+	0.339205i	$0.110158\pi$
$7$	2.02166	+	3.50162i	0.764116	+	1.32349i	−0.176596	+	0.984283i	$0.556509\pi$
$8$		0			0
$9$	−2.44949	−	1.73205i	−0.816497	−	0.577350i
$10$		0			0
$11$	3.50162	−	2.02166i	1.05578	−	0.609554i	0.131517	−	0.991314i	$-0.458015\pi$
$11$	3.50162	−	2.02166i	1.05578	−	0.609554i	0.924262	+	0.381760i	$0.124682\pi$
$12$		0			0
$13$	0.866025	+	0.500000i	0.240192	+	0.138675i	0.615265	−	0.788320i	$-0.289049\pi$
$13$	0.866025	+	0.500000i	0.240192	+	0.138675i	−0.375073	+	0.926995i	$0.622382\pi$
$14$		0			0
$15$	4.41431	−	4.02627i	1.13977	−	1.03958i
$16$		0			0
$17$	6.44949			1.56423			0.782116	−	0.623133i	$-0.214141\pi$
$17$	6.44949			1.56423			0.782116	+	0.623133i	$0.214141\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−6.84072	+	1.50000i	−1.49277	+	0.327327i
$22$		0			0
$23$	−1.11295	+	1.92768i	−0.232065	+	0.401949i	−0.958416	−	0.285376i	$-0.907882\pi$
$23$	−1.11295	+	1.92768i	−0.232065	+	0.401949i	0.726351	+	0.687324i	$0.241215\pi$
$24$		0			0
$25$	3.44949	+	5.97469i	0.689898	+	1.19494i
$26$		0			0
$27$	4.14418	−	3.13461i	0.797548	−	0.603256i
$28$		0			0
$29$	−5.10867	+	2.94949i	−0.948655	+	0.547706i	−0.892663	−	0.450725i	$-0.851166\pi$
$29$	−5.10867	+	2.94949i	−0.948655	+	0.547706i	−0.0559925	+	0.998431i	$0.517832\pi$
$30$		0			0
$31$	−2.93038	+	5.07556i	−0.526311	+	0.911598i	0.473219	+	0.880945i	$0.343092\pi$
$31$	−2.93038	+	5.07556i	−0.526311	+	0.911598i	−0.999530	+	0.0306532i	$0.990241\pi$
$32$		0			0
$33$	1.50000	+	6.84072i	0.261116	+	1.19082i
$34$		0			0
$35$		−	13.9474i		−	2.35754i
$36$		0			0
$37$			3.55051i			0.583700i	0.956464	+	0.291850i	$0.0942709\pi$
$37$			3.55051i			0.583700i	−0.956464	+	0.291850i	$0.905729\pi$
$38$		0			0
$39$	−1.27970	+	1.16721i	−0.204916	+	0.186903i
$40$		0			0
$41$	−4.17423	+	7.22999i	−0.651906	+	1.12913i	0.330754	+	0.943717i	$0.392697\pi$
$41$	−4.17423	+	7.22999i	−0.651906	+	1.12913i	−0.982660	+	0.185417i	$0.940636\pi$
$42$		0			0
$43$	−8.93092	+	5.15627i	−1.36195	+	0.786324i	−0.989884	−	0.141881i	$-0.954685\pi$
$43$	−8.93092	+	5.15627i	−1.36195	+	0.786324i	−0.372069	+	0.928205i	$0.621352\pi$
$44$		0			0
$45$	4.33013	+	9.39898i	0.645497	+	1.40112i
$46$		0			0
$47$	−2.02166	−	3.50162i	−0.294890	−	0.510764i	0.680070	−	0.733148i	$-0.261950\pi$
$47$	−2.02166	−	3.50162i	−0.294890	−	0.510764i	−0.974959	+	0.222384i	$0.928616\pi$
$48$		0			0
$49$	−4.67423	+	8.09601i	−0.667748	+	1.15657i
$50$		0			0
$51$	−3.38371	+	10.6460i	−0.473814	+	1.49074i
$52$		0			0
$53$		−	3.34847i		−	0.459948i	−0.973197	−	0.229974i	$-0.926136\pi$
$53$		−	3.34847i		−	0.459948i	0.973197	−	0.229974i	$-0.0738641\pi$
$54$		0			0
$55$	−13.9474			−1.88067
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.92768	+	1.11295i	0.250962	+	0.144893i	0.620205	−	0.784440i	$-0.287049\pi$
$59$	1.92768	+	1.11295i	0.250962	+	0.144893i	−0.369242	+	0.929333i	$0.620383\pi$
$60$		0			0
$61$	−1.64456	+	0.949490i	−0.210565	+	0.121570i	−0.601574	−	0.798817i	$-0.705459\pi$
$61$	−1.64456	+	0.949490i	−0.210565	+	0.121570i	0.391009	+	0.920387i	$0.372126\pi$
$62$		0			0
$63$	1.11295	−	12.0788i	0.140218	−	1.52179i
$64$		0			0
$65$	−1.72474	−	2.98735i	−0.213928	−	0.370535i
$66$		0			0
$67$	13.6527	+	7.88242i	1.66795	+	0.962991i	0.968742	+	0.248072i	$0.0797968\pi$
$67$	13.6527	+	7.88242i	1.66795	+	0.962991i	0.699207	+	0.714919i	$0.253537\pi$
$68$		0			0
$69$	−2.59808	−	2.84847i	−0.312772	−	0.342915i
$70$		0			0
$71$	13.5389			1.60678			0.803389	−	0.595455i	$-0.203028\pi$
$71$	13.5389			1.60678			0.803389	+	0.595455i	$0.203028\pi$
$72$		0			0
$73$	3.55051			0.415556			0.207778	−	0.978176i	$-0.433377\pi$
$73$	3.55051			0.415556			0.207778	+	0.978176i	$0.433377\pi$
$74$		0			0
$75$	−11.6721	+	2.55940i	−1.34777	+	0.295534i
$76$		0			0
$77$	14.1582	+	8.17423i	1.61348	+	0.931540i
$78$		0			0
$79$	4.74781	+	8.22345i	0.534170	+	0.925210i	0.999203	+	0.0399168i	$0.0127093\pi$
$79$	4.74781	+	8.22345i	0.534170	+	0.925210i	−0.465033	+	0.885294i	$0.653957\pi$
$80$		0			0
$81$	3.00000	+	8.48528i	0.333333	+	0.942809i
$82$		0			0
$83$	−1.92768	+	1.11295i	−0.211590	+	0.122162i	−0.602050	−	0.798458i	$-0.705649\pi$
$83$	−1.92768	+	1.11295i	−0.211590	+	0.122162i	0.390460	+	0.920620i	$0.372316\pi$
$84$		0			0
$85$	−19.2669	−	11.1237i	−2.08978	−	1.20654i
$86$		0			0
$87$	−2.18841	−	9.98022i	−0.234623	−	1.06999i
$88$		0			0
$89$	4.44949			0.471645			0.235822	−	0.971796i	$-0.424222\pi$
$89$	4.44949			0.471645			0.235822	+	0.971796i	$0.424222\pi$
$90$		0			0
$91$			4.04332i			0.423856i
$92$		0			0
$93$	−6.84072	−	7.50000i	−0.709349	−	0.777714i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.17423	−	14.1582i	−0.829968	−	1.43755i	−0.898063	−	0.439868i	$-0.855025\pi$
$97$	−8.17423	−	14.1582i	−0.829968	−	1.43755i	0.0680949	−	0.997679i	$-0.478308\pi$
$98$		0			0
$99$	−12.0788	−	1.11295i	−1.21397	−	0.111855i
$100$		0			0
$101$	−12.4261	+	7.17423i	−1.23645	+	0.713863i	−0.968366	−	0.249533i	$-0.919723\pi$
$101$	−12.4261	+	7.17423i	−1.23645	+	0.713863i	−0.268081	+	0.963396i	$0.586389\pi$
$102$		0			0
$103$	4.24755	−	7.35698i	0.418524	−	0.724905i	−0.577267	−	0.816555i	$-0.695881\pi$
$103$	4.24755	−	7.35698i	0.418524	−	0.724905i	0.995791	+	0.0916506i	$0.0292143\pi$
$104$		0			0
$105$	23.0227	+	7.31747i	2.24679	+	0.714112i
$106$		0			0
$107$			4.45178i			0.430370i	0.976573	+	0.215185i	$0.0690355\pi$
$107$			4.45178i			0.430370i	−0.976573	+	0.215185i	$0.930965\pi$
$108$		0			0
$109$			11.3485i			1.08699i	0.839414	+	0.543493i	$0.182899\pi$
$109$			11.3485i			1.08699i	−0.839414	+	0.543493i	$0.817101\pi$
$110$		0			0
$111$	−5.86076	−	1.86277i	−0.556278	−	0.176806i
$112$		0			0
$113$	−5.39898	+	9.35131i	−0.507893	+	0.879697i	0.492065	+	0.870558i	$0.336242\pi$
$113$	−5.39898	+	9.35131i	−0.507893	+	0.879697i	−0.999958	+	0.00913847i	$0.997091\pi$
$114$		0			0
$115$	6.64951	−	3.83909i	0.620070	−	0.357997i
$116$		0			0
$117$	−1.25529	−	2.72474i	−0.116052	−	0.251903i
$118$		0			0
$119$	13.0387	+	22.5837i	1.19525	+	2.07024i
$120$		0			0
$121$	2.67423	−	4.63191i	0.243112	−	0.421083i
$122$		0			0
$123$	−9.74439	−	10.6835i	−0.878622	−	0.963301i
$124$		0			0
$125$		−	6.55051i		−	0.585895i
$126$		0			0
$127$	−12.5384			−1.11261			−0.556303	−	0.830980i	$-0.687781\pi$
$127$	−12.5384			−1.11261			−0.556303	+	0.830980i	$0.687781\pi$
$128$		0			0
$129$	−3.82577	−	17.4473i	−0.336840	−	1.53615i
$130$		0			0
$131$	−1.22021	−	0.704487i	−0.106610	−	0.0615513i	0.445747	−	0.895159i	$-0.352938\pi$
$131$	−1.22021	−	0.704487i	−0.106610	−	0.0615513i	−0.552357	+	0.833608i	$0.686271\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−17.7865	+	2.21650i	−1.53082	+	0.190766i
$136$		0			0
$137$	−0.724745	−	1.25529i	−0.0619191	−	0.107247i	0.833404	−	0.552664i	$-0.186389\pi$
$137$	−0.724745	−	1.25529i	−0.0619191	−	0.107247i	−0.895323	+	0.445417i	$0.853055\pi$
$138$		0			0
$139$	15.2267	+	8.79114i	1.29151	+	0.745654i	0.978922	−	0.204234i	$-0.0654704\pi$
$139$	15.2267	+	8.79114i	1.29151	+	0.745654i	0.312589	+	0.949888i	$0.398804\pi$
$140$		0			0
$141$	6.84072	−	1.50000i	0.576092	−	0.126323i
$142$		0			0
$143$	4.04332			0.338120
$144$		0			0
$145$	20.3485			1.68985
$146$		0			0
$147$	−10.9116	−	11.9632i	−0.899974	−	0.986710i
$148$		0			0
$149$	−0.0874863	−	0.0505103i	−0.00716716	−	0.00413796i	0.496412	−	0.868087i	$-0.334650\pi$
$149$	−0.0874863	−	0.0505103i	−0.00716716	−	0.00413796i	−0.503579	+	0.863949i	$0.667984\pi$
$150$		0			0
$151$	−11.0170	−	19.0820i	−0.896553	−	1.55288i	−0.831871	−	0.554969i	$-0.812730\pi$
$151$	−11.0170	−	19.0820i	−0.896553	−	1.55288i	−0.0646820	−	0.997906i	$-0.520603\pi$
$152$		0			0
$153$	−15.7980	−	11.1708i	−1.27719	−	0.903109i
$154$		0			0
$155$	17.5081	−	10.1083i	1.40628	−	0.811919i
$156$		0			0
$157$	8.00853	+	4.62372i	0.639150	+	0.369013i	0.784287	−	0.620398i	$-0.213029\pi$
$157$	8.00853	+	4.62372i	0.639150	+	0.369013i	−0.145137	+	0.989412i	$0.546362\pi$
$158$		0			0
$159$	5.52725	+	1.75677i	0.438340	+	0.139321i
$160$		0			0
$161$	−9.00000			−0.709299
$162$		0			0
$163$			11.7215i			0.918100i	0.888410	+	0.459050i	$0.151810\pi$
$163$			11.7215i			0.918100i	−0.888410	+	0.459050i	$0.848190\pi$
$164$		0			0
$165$	7.31747	−	23.0227i	0.569664	−	1.79232i
$166$		0			0
$167$	9.69985	−	16.8006i	0.750597	−	1.30007i	−0.196937	−	0.980416i	$-0.563099\pi$
$167$	9.69985	−	16.8006i	0.750597	−	1.30007i	0.947534	−	0.319656i	$-0.103567\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.25529	−	0.724745i	0.0954383	−	0.0551013i	−0.451521	−	0.892260i	$-0.649118\pi$
$173$	1.25529	−	0.724745i	0.0954383	−	0.0551013i	0.546960	+	0.837159i	$0.315785\pi$
$174$		0			0
$175$	−13.9474	+	24.1576i	−1.05432	+	1.82614i
$176$		0			0
$177$	−2.84847	+	2.59808i	−0.214104	+	0.195283i
$178$		0			0
$179$		−	3.63487i		−	0.271683i	−0.990731	−	0.135841i	$-0.956626\pi$
$179$		−	3.63487i		−	0.271683i	0.990731	−	0.135841i	$-0.0433737\pi$
$180$		0			0
$181$		−	5.34847i		−	0.397549i	−0.980045	−	0.198774i	$-0.936304\pi$
$181$		−	5.34847i		−	0.397549i	0.980045	−	0.198774i	$-0.0636961\pi$
$182$		0			0
$183$	−0.704487	−	3.21280i	−0.0520772	−	0.237497i
$184$		0			0
$185$	6.12372	−	10.6066i	0.450225	−	0.779813i
$186$		0			0
$187$	22.5837	−	13.0387i	1.65148	−	0.953483i
$188$		0			0
$189$	19.3543	+	8.17423i	1.40782	+	0.594588i
$190$		0			0
$191$	10.1083	+	17.5081i	0.731412	+	1.26684i	0.956280	+	0.292453i	$0.0944715\pi$
$191$	10.1083	+	17.5081i	0.731412	+	1.26684i	−0.224868	+	0.974389i	$0.572195\pi$
$192$		0			0
$193$	−4.82577	+	8.35847i	−0.347366	+	0.601656i	−0.985781	−	0.168037i	$-0.946257\pi$
$193$	−4.82577	+	8.35847i	−0.347366	+	0.601656i	0.638415	+	0.769693i	$0.279591\pi$
$194$		0			0
$195$	5.83604	−	1.27970i	0.417927	−	0.0916411i
$196$		0			0
$197$		−	2.89898i		−	0.206544i	−0.994653	−	0.103272i	$-0.967069\pi$
$197$		−	2.89898i		−	0.206544i	0.994653	−	0.103272i	$-0.0329312\pi$
$198$		0			0
$199$	2.63435			0.186744			0.0933721	−	0.995631i	$-0.470235\pi$
$199$	2.63435			0.186744			0.0933721	+	0.995631i	$0.470235\pi$
$200$		0			0
$201$	−20.1742	+	18.4008i	−1.42298	+	1.29789i
$202$		0			0
$203$	−20.6560	−	11.9257i	−1.44977	−	0.837023i
$204$		0			0
$205$	24.9398	−	14.3990i	1.74187	−	1.00567i
$206$		0			0
$207$	6.06499	−	2.79415i	0.421546	−	0.194207i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	3.50162	+	2.02166i	0.241062	+	0.139177i	0.615665	−	0.788008i	$-0.288888\pi$
$211$	3.50162	+	2.02166i	0.241062	+	0.139177i	−0.374603	+	0.927185i	$0.622221\pi$
$212$		0			0
$213$	−7.10318	+	22.3485i	−0.486702	+	1.53129i
$214$		0			0
$215$	35.5730			2.42606
$216$		0			0
$217$	−23.6969			−1.60865
$218$		0			0
$219$	−1.86277	+	5.86076i	−0.125874	+	0.396033i
$220$		0			0
$221$	5.58542	+	3.22474i	0.375716	+	0.216920i
$222$		0			0
$223$	5.65653	+	9.79739i	0.378789	+	0.656082i	0.990886	−	0.134701i	$-0.0430072\pi$
$223$	5.65653	+	9.79739i	0.378789	+	0.656082i	−0.612097	+	0.790782i	$0.709674\pi$
$224$		0			0
$225$	1.89898	−	20.6096i	0.126599	−	1.37398i
$226$		0			0
$227$	7.35698	−	4.24755i	0.488300	−	0.281920i	−0.235569	−	0.971858i	$-0.575695\pi$
$227$	7.35698	−	4.24755i	0.488300	−	0.281920i	0.723869	+	0.689938i	$0.242362\pi$
$228$		0			0
$229$	18.2259	+	10.5227i	1.20440	+	0.695360i	0.961530	−	0.274699i	$-0.0885783\pi$
$229$	18.2259	+	10.5227i	1.20440	+	0.695360i	0.242868	+	0.970059i	$0.421912\pi$
$230$		0			0
$231$	−20.9211	+	19.0820i	−1.37651	+	1.25551i
$232$		0			0
$233$	2.89898			0.189918			0.0949592	−	0.995481i	$-0.469728\pi$
$233$	2.89898			0.189918			0.0949592	+	0.995481i	$0.469728\pi$
$234$		0			0
$235$			13.9474i			0.909828i
$236$		0			0
$237$	−16.0652	+	3.52270i	−1.04355	+	0.228824i
$238$		0			0
$239$	−2.93038	+	5.07556i	−0.189550	+	0.328311i	−0.945100	−	0.326780i	$-0.894036\pi$
$239$	−2.93038	+	5.07556i	−0.189550	+	0.328311i	0.755550	+	0.655091i	$0.227370\pi$
$240$		0			0
$241$	0.949490	+	1.64456i	0.0611620	+	0.105936i	0.894985	−	0.446096i	$-0.147186\pi$
$241$	0.949490	+	1.64456i	0.0611620	+	0.105936i	−0.833823	+	0.552032i	$0.813853\pi$
$242$		0			0
$243$	−15.5804	+	0.500258i	−0.999485	+	0.0320915i
$244$		0			0
$245$	27.9271	−	16.1237i	1.78420	−	1.03011i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.825765	−	3.76588i	−0.0523308	−	0.238653i
$250$		0			0
$251$		−	11.7215i		−	0.739855i	−0.929061	−	0.369928i	$-0.879382\pi$
$251$		−	11.7215i		−	0.739855i	0.929061	−	0.369928i	$-0.120618\pi$
$252$		0			0
$253$			9.00000i			0.565825i
$254$		0			0
$255$	28.4700	−	25.9674i	1.78286	−	1.62614i
$256$		0			0
$257$	7.29796	−	12.6404i	0.455234	−	0.788489i	−0.543467	−	0.839430i	$-0.682889\pi$
$257$	7.29796	−	12.6404i	0.455234	−	0.788489i	0.998702	+	0.0509415i	$0.0162222\pi$
$258$		0			0
$259$	−12.4325	+	7.17793i	−0.772521	+	0.446015i
$260$		0			0
$261$	17.6223	+	1.62372i	1.09079	+	0.100506i
$262$		0			0
$263$	2.93038	+	5.07556i	0.180695	+	0.312973i	0.942117	−	0.335283i	$-0.108832\pi$
$263$	2.93038	+	5.07556i	0.180695	+	0.312973i	−0.761423	+	0.648256i	$0.775499\pi$
$264$		0			0
$265$	−5.77526	+	10.0030i	−0.354771	+	0.614482i
$266$		0			0
$267$	−2.33441	+	7.34468i	−0.142864	+	0.449487i
$268$		0			0
$269$		−	11.5505i		−	0.704247i	−0.935954	−	0.352124i	$-0.885460\pi$
$269$		−	11.5505i		−	0.704247i	0.935954	−	0.352124i	$-0.114540\pi$
$270$		0			0
$271$	11.7215			0.712031			0.356016	−	0.934480i	$-0.384135\pi$
$271$	11.7215			0.712031			0.356016	+	0.934480i	$0.384135\pi$
$272$		0			0
$273$	−6.67423	−	2.12132i	−0.403943	−	0.128388i
$274$		0			0
$275$	24.1576	+	13.9474i	1.45676	+	0.841060i
$276$		0			0
$277$	21.0864	−	12.1742i	1.26696	−	0.731479i	0.292547	−	0.956251i	$-0.405497\pi$
$277$	21.0864	−	12.1742i	1.26696	−	0.731479i	0.974411	+	0.224772i	$0.0721638\pi$
$278$		0			0
$279$	15.9691	−	7.35698i	0.956043	−	0.440451i
$280$		0			0
$281$	−11.6237	−	20.1329i	−0.693413	−	1.20103i	−0.970713	−	0.240243i	$-0.922773\pi$
$281$	−11.6237	−	20.1329i	−0.693413	−	1.20103i	0.277299	−	0.960784i	$-0.410561\pi$
$282$		0			0
$283$	−1.92768	−	1.11295i	−0.114589	−	0.0661578i	0.441610	−	0.897207i	$-0.354407\pi$
$283$	−1.92768	−	1.11295i	−0.114589	−	0.0661578i	−0.556199	+	0.831049i	$0.687741\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−33.7556			−1.99253
$288$		0			0
$289$	24.5959			1.44682
$290$		0			0
$291$	27.6592	−	6.06499i	1.62141	−	0.355536i
$292$		0			0
$293$	−18.5758	−	10.7247i	−1.08521	−	0.626546i	−0.152913	−	0.988240i	$-0.548865\pi$
$293$	−18.5758	−	10.7247i	−1.08521	−	0.626546i	−0.932297	+	0.361693i	$0.882199\pi$
$294$		0			0
$295$	−3.83909	−	6.64951i	−0.223521	−	0.387149i
$296$		0			0
$297$	8.17423	−	19.3543i	0.474317	−	1.12305i
$298$		0			0
$299$	−1.92768	+	1.11295i	−0.111481	+	0.0643633i
$300$		0			0
$301$	−36.1106	−	20.8485i	−2.08138	−	1.20169i
$302$		0			0
$303$	−5.32302	−	24.2755i	−0.305800	−	1.39459i
$304$		0			0
$305$	6.55051			0.375081
$306$		0			0
$307$			0.816917i			0.0466239i	0.999728	+	0.0233120i	$0.00742110\pi$
$307$			0.816917i			0.0466239i	−0.999728	+	0.0233120i	$0.992579\pi$
$308$		0			0
$309$	9.91555	+	10.8712i	0.564076	+	0.618439i
$310$		0			0
$311$	−11.4255	+	19.7895i	−0.647880	+	1.12216i	0.335749	+	0.941952i	$0.391011\pi$
$311$	−11.4255	+	19.7895i	−0.647880	+	1.12216i	−0.983628	+	0.180209i	$0.942323\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$		0			0
$315$	−24.1576	+	34.1640i	−1.36113	+	1.92492i
$316$		0			0
$317$	−1.04100	+	0.601021i	−0.0584683	+	0.0337567i	−0.528949	−	0.848654i	$-0.677414\pi$
$317$	−1.04100	+	0.601021i	−0.0584683	+	0.0337567i	0.470481	+	0.882410i	$0.344080\pi$
$318$		0			0
$319$	−11.9257	+	20.6560i	−0.667713	+	1.15651i
$320$		0			0
$321$	−7.34847	−	2.33562i	−0.410152	−	0.130361i
$322$		0			0
$323$		0			0
$324$		0			0
$325$			6.89898i			0.382687i
$326$		0			0
$327$	−18.7327	−	5.95395i	−1.03592	−	0.329254i
$328$		0			0
$329$	8.17423	−	14.1582i	0.450660	−	0.780566i
$330$		0			0
$331$	−3.50162	+	2.02166i	−0.192467	+	0.111121i	−0.593137	−	0.805102i	$-0.702111\pi$
$331$	−3.50162	+	2.02166i	−0.192467	+	0.111121i	0.400670	+	0.916222i	$0.368777\pi$
$332$		0			0
$333$	6.14966	−	8.69694i	0.337000	−	0.476589i
$334$		0			0
$335$	−27.1903	−	47.0950i	−1.48557	−	2.57308i
$336$		0			0
$337$	−11.8485	+	20.5222i	−0.645427	+	1.11791i	0.338775	+	0.940867i	$0.389987\pi$
$337$	−11.8485	+	20.5222i	−0.645427	+	1.11791i	−0.984203	+	0.177046i	$0.943346\pi$
$338$		0			0
$339$	−12.6035	−	13.8181i	−0.684526	−	0.750498i
$340$		0			0
$341$			23.6969i			1.28326i
$342$		0			0
$343$	−9.49562			−0.512715
$344$		0			0
$345$	2.84847	+	12.9904i	0.153356	+	0.699379i
$346$		0			0
$347$	−7.35698	−	4.24755i	−0.394943	−	0.228021i	0.289357	−	0.957221i	$-0.406559\pi$
$347$	−7.35698	−	4.24755i	−0.394943	−	0.228021i	−0.684300	+	0.729201i	$0.739892\pi$
$348$		0			0
$349$	14.1582	−	8.17423i	0.757871	−	0.437557i	−0.0706601	−	0.997500i	$-0.522511\pi$
$349$	14.1582	−	8.17423i	0.757871	−	0.437557i	0.828531	+	0.559944i	$0.189177\pi$
$350$		0			0
$351$	5.15627	−	0.642559i	0.275221	−	0.0342973i
$352$		0			0
$353$	−7.17423	−	12.4261i	−0.381846	−	0.661377i	0.609480	−	0.792801i	$-0.291378\pi$
$353$	−7.17423	−	12.4261i	−0.381846	−	0.661377i	−0.991326	+	0.131425i	$0.958045\pi$
$354$		0			0
$355$	−40.4455	−	23.3512i	−2.14662	−	1.23935i
$356$		0			0
$357$	−44.1191	+	9.67423i	−2.33503	+	0.512015i
$358$		0			0
$359$	−16.9902			−0.896709			−0.448355	−	0.893856i	$-0.647990\pi$
$359$	−16.9902			−0.896709			−0.448355	+	0.893856i	$0.647990\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	6.24277	+	6.84443i	0.327661	+	0.359239i
$364$		0			0
$365$	−10.6066	−	6.12372i	−0.555175	−	0.320530i
$366$		0			0
$367$	8.79114	+	15.2267i	0.458894	+	0.794827i	0.998903	−	0.0468322i	$-0.0149126\pi$
$367$	8.79114	+	15.2267i	0.458894	+	0.794827i	−0.540009	+	0.841659i	$0.681579\pi$
$368$		0			0
$369$	22.7474	−	10.4798i	1.18418	−	0.545556i
$370$		0			0
$371$	11.7251	−	6.76947i	0.608735	−	0.351454i
$372$		0			0
$373$	−7.79423	−	4.50000i	−0.403570	−	0.233001i	0.284453	−	0.958690i	$-0.408188\pi$
$373$	−7.79423	−	4.50000i	−0.403570	−	0.233001i	−0.688023	+	0.725689i	$0.741521\pi$
$374$		0			0
$375$	10.8128	+	3.43671i	0.558370	+	0.177471i
$376$		0			0
$377$	−5.89898			−0.303813
$378$		0			0
$379$			6.26922i			0.322028i	0.986952	+	0.161014i	$0.0514764\pi$
$379$			6.26922i			0.322028i	−0.986952	+	0.161014i	$0.948524\pi$
$380$		0			0
$381$	6.57826	−	20.6969i	0.337014	−	1.06034i
$382$		0			0
$383$	10.5168	−	18.2156i	0.537382	−	0.930773i	−0.461662	−	0.887056i	$-0.652747\pi$
$383$	10.5168	−	18.2156i	0.537382	−	0.930773i	0.999044	−	0.0437167i	$-0.0139199\pi$
$384$		0			0
$385$	−28.1969	−	48.8385i	−1.43705	−	2.48904i
$386$		0			0
$387$	30.8071	+	2.83858i	1.56601	+	0.144293i
$388$		0			0
$389$	31.4787	−	18.1742i	1.59603	−	0.921470i	0.603792	−	0.797142i	$-0.293656\pi$
$389$	31.4787	−	18.1742i	1.59603	−	0.921470i	0.992241	−	0.124329i	$-0.0396777\pi$
$390$		0			0
$391$	−7.17793	+	12.4325i	−0.363004	+	0.628741i
$392$		0			0
$393$	1.80306	−	1.64456i	0.0909524	−	0.0829573i
$394$		0			0
$395$		−	32.7551i		−	1.64809i
$396$		0			0
$397$		−	0.247449i		−	0.0124191i	−0.999981	−	0.00620955i	$-0.998023\pi$
$397$		−	0.247449i		−	0.0124191i	0.999981	−	0.00620955i	$-0.00197657\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.62372	+	6.27647i	−0.180960	+	0.313432i	−0.942208	−	0.335029i	$-0.891254\pi$
$401$	−3.62372	+	6.27647i	−0.180960	+	0.313432i	0.761248	+	0.648461i	$0.224587\pi$
$402$		0			0
$403$	−5.07556	+	2.93038i	−0.252832	+	0.145973i
$404$		0			0
$405$	5.67291	−	30.5227i	0.281889	−	1.51669i
$406$		0			0
$407$	7.17793	+	12.4325i	0.355797	+	0.616258i
$408$		0			0
$409$	8.29796	−	14.3725i	0.410308	−	0.710674i	−0.584616	−	0.811310i	$-0.698755\pi$
$409$	8.29796	−	14.3725i	0.410308	−	0.710674i	0.994923	+	0.100637i	$0.0320880\pi$
$410$		0			0
$411$	2.45233	−	0.537734i	0.120964	−	0.0265245i
$412$		0			0
$413$			9.00000i			0.442861i
$414$		0			0
$415$	7.67819			0.376907
$416$		0			0
$417$	−22.5000	+	20.5222i	−1.10183	+	1.00497i
$418$		0			0
$419$	−20.6560	−	11.9257i	−1.00911	−	0.582611i	−0.0981799	−	0.995169i	$-0.531302\pi$
$419$	−20.6560	−	11.9257i	−1.00911	−	0.582611i	−0.910931	+	0.412558i	$0.864635\pi$
$420$		0			0
$421$	−3.20164	+	1.84847i	−0.156039	+	0.0900889i	−0.575986	−	0.817459i	$-0.695382\pi$
$421$	−3.20164	+	1.84847i	−0.156039	+	0.0900889i	0.419948	+	0.907548i	$0.362048\pi$
$422$		0			0
$423$	−1.11295	+	12.0788i	−0.0541133	+	0.587292i
$424$		0			0
$425$	22.2474	+	38.5337i	1.07916	+	1.86916i
$426$		0			0
$427$	−6.64951	−	3.83909i	−0.321792	−	0.185787i
$428$		0			0
$429$	−2.12132	+	6.67423i	−0.102418	+	0.322235i
$430$		0			0
$431$	0.816917			0.0393495			0.0196748	−	0.999806i	$-0.493737\pi$
$431$	0.816917			0.0393495			0.0196748	+	0.999806i	$0.493737\pi$
$432$		0			0
$433$	−8.04541			−0.386638			−0.193319	−	0.981136i	$-0.561925\pi$
$433$	−8.04541			−0.386638			−0.193319	+	0.981136i	$0.561925\pi$
$434$		0			0
$435$	−10.6758	+	33.5888i	−0.511864	+	1.61046i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−14.6519	−	25.3778i	−0.699297	−	1.21122i	−0.968711	−	0.248193i	$-0.920163\pi$
$439$	−14.6519	−	25.3778i	−0.699297	−	1.21122i	0.269414	−	0.963024i	$-0.413170\pi$
$440$		0			0
$441$	25.4722	−	11.7351i	1.21296	−	0.558814i
$442$		0			0
$443$	−12.7863	+	7.38216i	−0.607494	+	0.350737i	−0.771984	−	0.635642i	$-0.780736\pi$
$443$	−12.7863	+	7.38216i	−0.607494	+	0.350737i	0.164490	+	0.986379i	$0.447402\pi$
$444$		0			0
$445$	−13.2922	−	7.67423i	−0.630109	−	0.363794i
$446$		0			0
$447$	0.129276	−	0.117912i	0.00611453	−	0.00557704i
$448$		0			0
$449$	−29.3485			−1.38504			−0.692520	−	0.721399i	$-0.743500\pi$
$449$	−29.3485			−1.38504			−0.692520	+	0.721399i	$0.743500\pi$
$450$		0			0
$451$			33.7556i			1.58949i
$452$		0			0
$453$	37.2784	−	8.17423i	1.75149	−	0.384059i
$454$		0			0
$455$	6.97370	−	12.0788i	0.326932	−	0.566263i
$456$		0			0
$457$	10.0732	+	17.4473i	0.471205	+	0.816151i	0.999457	−	0.0329363i	$-0.0104858\pi$
$457$	10.0732	+	17.4473i	0.471205	+	0.816151i	−0.528252	+	0.849087i	$0.677153\pi$
$458$		0			0
$459$	26.7279	−	20.2166i	1.24755	−	0.943631i
$460$		0			0
$461$	−25.1147	+	14.5000i	−1.16971	+	0.675332i	−0.953612	−	0.301039i	$-0.902666\pi$
$461$	−25.1147	+	14.5000i	−1.16971	+	0.675332i	−0.216098	+	0.976372i	$0.569333\pi$
$462$		0			0
$463$	11.0170	−	19.0820i	0.512005	−	0.886818i	−0.487899	−	0.872900i	$-0.662236\pi$
$463$	11.0170	−	19.0820i	0.512005	−	0.886818i	0.999903	−	0.0139177i	$-0.00443028\pi$
$464$		0			0
$465$	7.50000	+	34.2036i	0.347804	+	1.58615i
$466$		0			0
$467$			23.4430i			1.08481i	0.840116	+	0.542407i	$0.182487\pi$
$467$			23.4430i			1.08481i	−0.840116	+	0.542407i	$0.817513\pi$
$468$		0			0
$469$			63.7423i			2.94335i
$470$		0			0
$471$	−11.8339	+	10.7937i	−0.545279	+	0.497347i
$472$		0			0
$473$	−20.8485	+	36.1106i	−0.958614	+	1.66037i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.79972	+	8.20204i	−0.265551	+	0.375546i
$478$		0			0
$479$	−6.97370	−	12.0788i	−0.318637	−	0.551895i	0.661567	−	0.749886i	$-0.269892\pi$
$479$	−6.97370	−	12.0788i	−0.318637	−	0.551895i	−0.980204	+	0.197991i	$0.936558\pi$
$480$		0			0
$481$	−1.77526	+	3.07483i	−0.0809447	+	0.140200i
$482$		0			0
$483$	4.72183	−	14.8561i	0.214851	−	0.675977i
$484$		0			0
$485$			56.3939i			2.56071i
$486$		0			0
$487$	40.4332			1.83221			0.916103	−	0.400944i	$-0.131318\pi$
$487$	40.4332			1.83221			0.916103	+	0.400944i	$0.131318\pi$
$488$		0			0
$489$	−19.3485	−	6.14966i	−0.874968	−	0.278097i
$490$		0			0
$491$	29.9406	+	17.2862i	1.35120	+	0.780117i	0.988418	−	0.151756i	$-0.0484928\pi$
$491$	29.9406	+	17.2862i	1.35120	+	0.780117i	0.362785	+	0.931873i	$0.381826\pi$
$492$		0			0
$493$	−32.9483	+	19.0227i	−1.48392	+	0.856739i
$494$		0			0
$495$	34.1640	+	24.1576i	1.53556	+	1.08580i
$496$		0			0
$497$	27.3712	+	47.4083i	1.22776	+	2.12655i
$498$		0			0
$499$	9.63839	+	5.56473i	0.431474	+	0.249111i	0.699974	−	0.714168i	$-0.253195\pi$
$499$	9.63839	+	5.56473i	0.431474	+	0.249111i	−0.268501	+	0.963280i	$0.586528\pi$
$500$		0			0
$501$	22.6435	+	24.8258i	1.01164	+	1.10913i
$502$		0			0
$503$	6.26922			0.279530			0.139765	−	0.990185i	$-0.455365\pi$
$503$	6.26922			0.279530			0.139765	+	0.990185i	$0.455365\pi$
$504$		0			0
$505$	49.4949			2.20249
$506$		0			0
$507$	20.3023	−	4.45178i	0.901655	−	0.197711i
$508$		0			0
$509$	3.72656	+	2.15153i	0.165177	+	0.0953649i	0.580310	−	0.814396i	$-0.302932\pi$
$509$	3.72656	+	2.15153i	0.165177	+	0.0953649i	−0.415133	+	0.909761i	$0.636265\pi$
$510$		0			0
$511$	7.17793	+	12.4325i	0.317533	+	0.549983i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.3778	+	14.6519i	−1.11828	+	0.645639i
$516$		0			0
$517$	−14.1582	−	8.17423i	−0.622676	−	0.359502i
$518$		0			0
$519$	0.537734	+	2.45233i	0.0236039	+	0.107645i
$520$		0			0
$521$	−33.3939			−1.46301			−0.731506	−	0.681835i	$-0.761182\pi$
$521$	−33.3939			−1.46301			−0.731506	+	0.681835i	$0.761182\pi$
$522$		0			0
$523$		−	34.9809i		−	1.52961i	−0.644262	−	0.764805i	$-0.722835\pi$
$523$		−	34.9809i		−	1.52961i	0.644262	−	0.764805i	$-0.277165\pi$
$524$		0			0
$525$	−32.5590	−	35.6969i	−1.42099	−	1.55794i
$526$		0			0
$527$	−18.8994	+	32.7348i	−0.823273	+	1.42595i
$528$		0			0
$529$	9.02270	+	15.6278i	0.392291	+	0.679469i
$530$		0			0
$531$	−2.79415	−	6.06499i	−0.121256	−	0.263198i
$532$		0			0
$533$	−7.22999	+	4.17423i	−0.313165	+	0.180806i
$534$		0			0
$535$	7.67819	−	13.2990i	0.331957	−	0.574967i
$536$		0			0
$537$	6.00000	+	1.90702i	0.258919	+	0.0822941i
$538$		0			0
$539$			37.7989i			1.62811i
$540$		0			0
$541$			7.30306i			0.313983i	0.987600	+	0.156992i	$0.0501796\pi$
$541$			7.30306i			0.313983i	−0.987600	+	0.156992i	$0.949820\pi$
$542$		0			0
$543$	8.82861	+	2.80606i	0.378872	+	0.120420i
$544$		0			0
$545$	19.5732	−	33.9018i	0.838424	−	1.45219i
$546$		0			0
$547$	11.2123	−	6.47344i	0.479405	−	0.276785i	−0.240764	−	0.970584i	$-0.577398\pi$
$547$	11.2123	−	6.47344i	0.479405	−	0.276785i	0.720168	+	0.693799i	$0.244065\pi$
$548$		0			0
$549$	5.67291	+	0.522704i	0.242114	+	0.0223085i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−19.1969	+	33.2501i	−0.816337	+	1.41394i
$554$		0			0
$555$	14.2953	+	15.6730i	0.606802	+	0.665283i
$556$		0			0
$557$		−	37.1464i		−	1.57394i	−0.616988	−	0.786972i	$-0.711647\pi$
$557$		−	37.1464i		−	1.57394i	0.616988	−	0.786972i	$-0.288353\pi$
$558$		0			0
$559$	−10.3125			−0.436174
$560$		0			0
$561$	9.67423	+	44.1191i	0.408447	+	1.86271i
$562$		0			0
$563$	5.94204	+	3.43064i	0.250427	+	0.144584i	0.619960	−	0.784634i	$-0.287149\pi$
$563$	5.94204	+	3.43064i	0.250427	+	0.144584i	−0.369533	+	0.929218i	$0.620482\pi$
$564$		0			0
$565$	32.2572	−	18.6237i	1.35707	−	0.783506i
$566$		0			0
$567$	−23.6473	+	27.6592i	−0.993091	+	1.16158i
$568$		0			0
$569$	6.74745	+	11.6869i	0.282868	+	0.489941i	0.972090	−	0.234609i	$-0.0753809\pi$
$569$	6.74745	+	11.6869i	0.282868	+	0.489941i	−0.689222	+	0.724550i	$0.742048\pi$
$570$		0			0
$571$	−12.9453	−	7.47396i	−0.541743	−	0.312775i	0.204042	−	0.978962i	$-0.434592\pi$
$571$	−12.9453	−	7.47396i	−0.541743	−	0.312775i	−0.745785	+	0.666187i	$0.767925\pi$
$572$		0			0
$573$	−34.2036	+	7.50000i	−1.42888	+	0.313317i
$574$		0			0
$575$	−15.3564			−0.640405
$576$		0			0
$577$	−26.0454			−1.08428			−0.542142	−	0.840287i	$-0.682387\pi$
$577$	−26.0454			−1.08428			−0.542142	+	0.840287i	$0.682387\pi$
$578$		0			0
$579$	−11.2653	−	12.3510i	−0.468171	−	0.513292i
$580$		0			0
$581$	−7.79423	−	4.50000i	−0.323359	−	0.186691i
$582$		0			0
$583$	−6.76947	−	11.7251i	−0.280363	−	0.485603i
$584$		0			0
$585$	−0.949490	+	10.3048i	−0.0392566	+	0.426052i
$586$		0			0
$587$	−21.5225	+	12.4260i	−0.888327	+	0.512876i	−0.873395	−	0.487013i	$-0.838087\pi$
$587$	−21.5225	+	12.4260i	−0.888327	+	0.512876i	−0.0149322	+	0.999889i	$0.504753\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	4.78529	+	1.52094i	0.196840	+	0.0625632i
$592$		0			0
$593$	7.75255			0.318359			0.159180	−	0.987250i	$-0.449115\pi$
$593$	7.75255			0.318359			0.159180	+	0.987250i	$0.449115\pi$
$594$		0			0
$595$		−	89.9536i		−	3.68774i
$596$		0			0
$597$	−1.38211	+	4.34847i	−0.0565658	+	0.177971i
$598$		0			0
$599$	−5.65653	+	9.79739i	−0.231119	+	0.400311i	−0.958138	−	0.286307i	$-0.907572\pi$
$599$	−5.65653	+	9.79739i	−0.231119	+	0.400311i	0.727018	+	0.686618i	$0.240905\pi$
$600$		0			0
$601$	−16.5227	−	28.6182i	−0.673975	−	1.16736i	−0.976767	−	0.214303i	$-0.931252\pi$
$601$	−16.5227	−	28.6182i	−0.673975	−	1.16736i	0.302792	−	0.953057i	$-0.402081\pi$
$602$		0			0
$603$	−19.7895	−	42.9552i	−0.805892	−	1.74927i
$604$		0			0
$605$	−15.9777	+	9.22474i	−0.649587	+	0.375039i
$606$		0			0
$607$	15.5606	−	26.9518i	0.631586	−	1.09394i	−0.355642	−	0.934622i	$-0.615738\pi$
$607$	15.5606	−	26.9518i	0.631586	−	1.09394i	0.987228	−	0.159316i	$-0.0509289\pi$
$608$		0			0
$609$	30.5227	−	27.8396i	1.23684	−	1.12812i
$610$		0			0
$611$		−	4.04332i		−	0.163575i
$612$		0			0
$613$		−	36.7423i		−	1.48401i	−0.670395	−	0.742005i	$-0.733875\pi$
$613$		−	36.7423i		−	1.48401i	0.670395	−	0.742005i	$-0.266125\pi$
$614$		0			0
$615$	10.6835	+	48.7220i	0.430801	+	1.96466i
$616$		0			0
$617$	14.2753	−	24.7255i	0.574700	−	0.995410i	−0.421374	−	0.906887i	$-0.638452\pi$
$617$	14.2753	−	24.7255i	0.574700	−	0.995410i	0.996074	−	0.0885229i	$-0.0282146\pi$
$618$		0			0
$619$	−2.79415	+	1.61320i	−0.112306	+	0.0648401i	−0.555101	−	0.831783i	$-0.687320\pi$
$619$	−2.79415	+	1.61320i	−0.112306	+	0.0648401i	0.442795	+	0.896623i	$0.353987\pi$
$620$		0			0
$621$	1.43027	+	11.4773i	0.0573947	+	0.460568i
$622$		0			0
$623$	8.99536	+	15.5804i	0.360392	+	0.624217i
$624$		0			0
$625$	5.94949	−	10.3048i	0.237980	−	0.412193i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			22.8990i			0.913042i
$630$		0			0
$631$	11.7215			0.466626			0.233313	−	0.972402i	$-0.425043\pi$
$631$	11.7215			0.466626			0.233313	+	0.972402i	$0.425043\pi$
$632$		0			0
$633$	−5.17423	+	4.71940i	−0.205657	+	0.187579i
$634$		0			0
$635$	37.4566	+	21.6256i	1.48642	+	0.858186i
$636$		0			0
$637$	−8.09601	+	4.67423i	−0.320776	+	0.185200i
$638$		0			0
$639$	−33.1635	−	23.4501i	−1.31193	−	0.927673i
$640$		0			0
$641$	−1.29796	−	2.24813i	−0.0512663	−	0.0887958i	0.839253	−	0.543740i	$-0.182992\pi$
$641$	−1.29796	−	2.24813i	−0.0512663	−	0.0887958i	−0.890520	+	0.454945i	$0.849659\pi$
$642$		0			0
$643$	30.8071	+	17.7865i	1.21491	+	0.701431i	0.963826	−	0.266533i	$-0.0858782\pi$
$643$	30.8071	+	17.7865i	1.21491	+	0.701431i	0.251088	+	0.967964i	$0.419211\pi$
$644$		0			0
$645$	−18.6633	+	58.7196i	−0.734866	+	2.31208i
$646$		0			0
$647$	29.5286			1.16089			0.580445	−	0.814299i	$-0.302878\pi$
$647$	29.5286			1.16089			0.580445	+	0.814299i	$0.302878\pi$
$648$		0			0
$649$	9.00000			0.353281
$650$		0			0
$651$	12.4325	−	39.1161i	0.487270	−	1.53308i
$652$		0			0
$653$	−2.63740	−	1.52270i	−0.103209	−	0.0595880i	0.447507	−	0.894281i	$-0.352312\pi$
$653$	−2.63740	−	1.52270i	−0.103209	−	0.0595880i	−0.550716	+	0.834693i	$0.685645\pi$
$654$		0			0
$655$	2.43012	+	4.20909i	0.0949527	+	0.164463i
$656$		0			0
$657$	−8.69694	−	6.14966i	−0.339300	−	0.239921i
$658$		0			0
$659$	2.79415	−	1.61320i	0.108845	−	0.0628415i	−0.444589	−	0.895734i	$-0.646650\pi$
$659$	2.79415	−	1.61320i	0.108845	−	0.0628415i	0.553434	+	0.832893i	$0.313317\pi$
$660$		0			0
$661$	−23.5970	−	13.6237i	−0.917816	−	0.529901i	−0.0348785	−	0.999392i	$-0.511104\pi$
$661$	−23.5970	−	13.6237i	−0.917816	−	0.529901i	−0.882938	+	0.469490i	$0.844438\pi$
$662$		0			0
$663$	−8.25340	+	7.52789i	−0.320536	+	0.292359i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	13.1305i		−	0.508415i
$668$		0			0
$669$	−19.1400	+	4.19694i	−0.739997	+	0.162263i
$670$		0			0
$671$	−3.83909	+	6.64951i	−0.148207	+	0.256701i
$672$		0			0
$673$	23.8712	+	41.3461i	0.920166	+	1.59377i	0.799156	+	0.601123i	$0.205280\pi$
$673$	23.8712	+	41.3461i	0.920166	+	1.59377i	0.121010	+	0.992651i	$0.461387\pi$
$674$		0			0
$675$	33.0236	+	13.9474i	1.27108	+	0.536836i
$676$		0			0
$677$	15.2867	−	8.82577i	0.587515	−	0.339202i	−0.176600	−	0.984283i	$-0.556510\pi$
$677$	15.2867	−	8.82577i	0.587515	−	0.339202i	0.764114	+	0.645081i	$0.223176\pi$
$678$		0			0
$679$	33.0511	−	57.2461i	1.26838	−	2.19691i
$680$		0			0
$681$	3.15153	+	14.3725i	0.120767	+	0.550755i
$682$		0			0
$683$			11.7215i			0.448511i	0.974530	+	0.224256i	$0.0719951\pi$
$683$			11.7215i			0.448511i	−0.974530	+	0.224256i	$0.928005\pi$
$684$		0			0
$685$			5.00000i			0.191040i
$686$		0			0
$687$	−26.9318	+	24.5643i	−1.02751	+	0.937188i
$688$		0			0
$689$	1.67423	−	2.89986i	0.0637833	−	0.110476i
$690$		0			0
$691$	40.7992	−	23.5555i	1.55208	−	0.896092i	0.554104	−	0.832448i	$-0.313061\pi$
$691$	40.7992	−	23.5555i	1.55208	−	0.896092i	0.997973	−	0.0636443i	$-0.0202723\pi$
$692$		0			0
$693$	−20.5222	−	44.5454i	−0.779572	−	1.69214i
$694$		0			0
$695$	−30.3249	−	52.5243i	−1.15029	−	1.99236i
$696$		0			0
$697$	−26.9217	+	46.6297i	−1.01973	+	1.76623i
$698$		0			0
$699$	−1.52094	+	4.78529i	−0.0575273	+	0.180996i
$700$		0			0
$701$		−	39.1464i		−	1.47854i	−0.673409	−	0.739270i	$-0.735171\pi$
$701$		−	39.1464i		−	1.47854i	0.673409	−	0.739270i	$-0.264829\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−23.0227	−	7.31747i	−0.867085	−	0.275592i
$706$		0			0
$707$	−50.2429	−	29.0078i	−1.88958	−	1.09095i
$708$		0			0
$709$	−25.7576	+	14.8712i	−0.967348	+	0.558499i	−0.898427	−	0.439123i	$-0.855289\pi$
$709$	−25.7576	+	14.8712i	−0.967348	+	0.558499i	−0.0689213	+	0.997622i	$0.521956\pi$
$710$		0			0
$711$	2.61372	−	28.3667i	0.0980221	−	1.06383i
$712$		0			0
$713$	−6.52270	−	11.2977i	−0.244277	−	0.423100i
$714$		0			0
$715$	−12.0788	−	6.97370i	−0.451722	−	0.260802i
$716$		0			0
$717$	−6.84072	−	7.50000i	−0.255471	−	0.280093i
$718$		0			0
$719$	−3.63487			−0.135558			−0.0677788	−	0.997700i	$-0.521591\pi$
$719$	−3.63487			−0.135558			−0.0677788	+	0.997700i	$0.521591\pi$
$720$		0			0
$721$	34.3485			1.27920
$722$		0			0
$723$	−3.21280	+	0.704487i	−0.119485	+	0.0262002i
$724$		0			0
$725$	−35.2446	−	20.3485i	−1.30895	−	0.755723i
$726$		0			0
$727$	9.19959	+	15.9342i	0.341194	+	0.590965i	0.984655	−	0.174514i	$-0.0558353\pi$
$727$	9.19959	+	15.9342i	0.341194	+	0.590965i	−0.643461	+	0.765479i	$0.722502\pi$
$728$		0			0
$729$	7.34847	−	25.9808i	0.272166	−	0.962250i
$730$		0			0
$731$	−57.5999	+	33.2553i	−2.13041	+	1.22999i
$732$		0			0
$733$	−17.0580	−	9.84847i	−0.630053	−	0.363762i	0.150719	−	0.988577i	$-0.451841\pi$
$733$	−17.0580	−	9.84847i	−0.630053	−	0.363762i	−0.780773	+	0.624815i	$0.785174\pi$
$734$		0			0
$735$	11.9632	+	54.5580i	0.441270	+	2.01240i
$736$		0			0
$737$	63.7423			2.34798
$738$		0			0
$739$			24.4435i			0.899170i	0.893237	+	0.449585i	$0.148428\pi$
$739$			24.4435i			0.899170i	−0.893237	+	0.449585i	$0.851572\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.43012	−	4.20909i	0.0891525	−	0.154417i	−0.818001	−	0.575217i	$-0.804917\pi$
$743$	2.43012	−	4.20909i	0.0891525	−	0.154417i	0.907153	+	0.420801i	$0.138251\pi$
$744$		0			0
$745$	0.174235	+	0.301783i	0.00638346	+	0.0110565i
$746$		0			0
$747$	6.64951	+	0.612688i	0.243293	+	0.0224171i
$748$		0			0
$749$	−15.5885	+	9.00000i	−0.569590	+	0.328853i
$750$		0			0
$751$	9.69985	−	16.8006i	0.353953	−	0.613064i	−0.632986	−	0.774164i	$-0.718171\pi$
$751$	9.69985	−	16.8006i	0.353953	−	0.613064i	0.986938	+	0.161100i	$0.0515041\pi$
$752$		0			0
$753$	19.3485	+	6.14966i	0.705097	+	0.224106i
$754$		0			0
$755$			76.0062i			2.76615i
$756$		0			0
$757$			45.3939i			1.64987i	0.565229	+	0.824934i	$0.308788\pi$
$757$			45.3939i			1.64987i	−0.565229	+	0.824934i	$0.691212\pi$
$758$		0			0
$759$	−14.8561	−	4.72183i	−0.539243	−	0.171392i
$760$		0			0
$761$	3.72474	−	6.45145i	0.135022	−	0.233865i	−0.790584	−	0.612354i	$-0.790223\pi$
$761$	3.72474	−	6.45145i	0.135022	−	0.233865i	0.925606	+	0.378489i	$0.123556\pi$
$762$		0			0
$763$	−39.7380	+	22.9428i	−1.43861	+	0.830584i
$764$		0			0
$765$	27.9271	+	60.6186i	1.00971	+	2.19167i
$766$		0			0
$767$	1.11295	+	1.92768i	0.0401861	+	0.0696044i
$768$		0			0
$769$	−2.15153	+	3.72656i	−0.0775862	+	0.134383i	−0.902208	−	0.431301i	$-0.858055\pi$
$769$	−2.15153	+	3.72656i	−0.0775862	+	0.134383i	0.824622	+	0.565684i	$0.191388\pi$
$770$		0			0
$771$	17.0365	+	18.6784i	0.613553	+	0.672685i
$772$		0			0
$773$		−	33.8434i		−	1.21726i	−0.793454	−	0.608631i	$-0.791719\pi$
$773$		−	33.8434i		−	1.21726i	0.793454	−	0.608631i	$-0.208281\pi$
$774$		0			0
$775$	−40.4332			−1.45240
$776$		0			0
$777$	−5.32577	−	24.2880i	−0.191061	−	0.871328i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	47.4083	−	27.3712i	1.69640	−	0.979418i
$782$		0			0
$783$	−11.9257	+	28.2369i	−0.426191	+	1.00910i
$784$		0			0
$785$	−15.9495	−	27.6253i	−0.569262	−	0.985990i
$786$		0			0
$787$	−10.6639	−	6.15679i	−0.380126	−	0.219466i	0.297747	−	0.954645i	$-0.403765\pi$
$787$	−10.6639	−	6.15679i	−0.380126	−	0.219466i	−0.677873	+	0.735179i	$0.737098\pi$
$788$		0			0
$789$	−9.91555	+	2.17423i	−0.353003	+	0.0774048i
$790$		0			0
$791$	−43.6596			−1.55236
$792$		0			0
$793$	−1.89898			−0.0674347
$794$		0			0
$795$	−13.4818	−	14.7812i	−0.478152	−	0.524234i
$796$		0			0
$797$	−0.0874863	−	0.0505103i	−0.00309892	−	0.00178917i	0.498450	−	0.866919i	$-0.333903\pi$
$797$	−0.0874863	−	0.0505103i	−0.00309892	−	0.00178917i	−0.501549	+	0.865129i	$0.667236\pi$
$798$		0			0
$799$	−13.0387	−	22.5837i	−0.461276	−	0.798953i
$800$		0			0
$801$	−10.8990	−	7.70674i	−0.385097	−	0.272304i
$802$		0			0
$803$	12.4325	−	7.17793i	0.438735	−	0.253304i
$804$		0			0
$805$	26.8861	+	15.5227i	0.947611	+	0.547103i
$806$		0			0
$807$	19.0662	+	6.05995i	0.671162	+	0.213320i
$808$		0			0
$809$	39.6413			1.39371			0.696857	−	0.717210i	$-0.254581\pi$
$809$	39.6413			1.39371			0.696857	+	0.717210i	$0.254581\pi$
$810$		0			0
$811$			16.1733i			0.567921i	0.958836	+	0.283961i	$0.0916485\pi$
$811$			16.1733i			0.567921i	−0.958836	+	0.283961i	$0.908352\pi$
$812$		0			0
$813$	−6.14966	+	19.3485i	−0.215678	+	0.678580i
$814$		0			0
$815$	20.2166	−	35.0162i	0.708157	−	1.22656i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	7.00324	−	9.90408i	0.244713	−	0.346077i
$820$		0			0
$821$	−11.6869	+	6.74745i	−0.407876	+	0.235488i	−0.689877	−	0.723927i	$-0.742335\pi$
$821$	−11.6869	+	6.74745i	−0.407876	+	0.235488i	0.282000	+	0.959414i	$0.409002\pi$
$822$		0			0
$823$	21.3296	−	36.9439i	0.743502	−	1.28778i	−0.207389	−	0.978258i	$-0.566497\pi$
$823$	21.3296	−	36.9439i	0.743502	−	1.28778i	0.950891	−	0.309525i	$-0.100170\pi$
$824$		0			0
$825$	−35.6969	+	32.5590i	−1.24281	+	1.13356i
$826$		0			0
$827$			39.6163i			1.37759i	0.724954	+	0.688797i	$0.241861\pi$
$827$			39.6163i			1.37759i	−0.724954	+	0.688797i	$0.758139\pi$
$828$		0			0
$829$		−	27.3485i		−	0.949852i	−0.880026	−	0.474926i	$-0.842475\pi$
$829$		−	27.3485i		−	0.949852i	0.880026	−	0.474926i	$-0.157525\pi$
$830$		0			0
$831$	9.03284	+	41.1941i	0.313346	+	1.42901i
$832$		0			0
$833$	−30.1464	+	52.2151i	−1.04451	+	1.80915i
$834$		0			0
$835$	−57.9536	+	33.4595i	−2.00557	+	1.15792i
$836$		0			0
$837$	3.76588	+	30.2196i	0.130168	+	1.04454i
$838$		0			0
$839$	15.9691	+	27.6592i	0.551313	+	0.954903i	0.998180	+	0.0603023i	$0.0192065\pi$
$839$	15.9691	+	27.6592i	0.551313	+	0.954903i	−0.446867	+	0.894601i	$0.647460\pi$
$840$		0			0
$841$	2.89898	−	5.02118i	0.0999648	−	0.173144i
$842$		0			0
$843$	39.3313	−	8.62438i	1.35464	−	0.297040i
$844$		0			0
$845$			41.3939i			1.42399i
$846$		0			0
$847$	21.6256			0.743064
$848$		0			0
$849$	2.84847	−	2.59808i	0.0977592	−	0.0891657i
$850$		0			0
$851$	−6.84424	−	3.95153i	−0.234618	−	0.135457i
$852$		0			0
$853$	30.3895	−	17.5454i	1.04052	−	0.600743i	0.120538	−	0.992709i	$-0.461538\pi$
$853$	30.3895	−	17.5454i	1.04052	−	0.600743i	0.919980	+	0.391965i	$0.128205\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.9722	−	24.2005i	−0.477281	−	0.826675i	0.522380	−	0.852713i	$-0.325044\pi$
$857$	−13.9722	−	24.2005i	−0.477281	−	0.826675i	−0.999661	+	0.0260378i	$0.991711\pi$
$858$		0			0
$859$	−24.5113	−	14.1516i	−0.836316	−	0.482848i	0.0196940	−	0.999806i	$-0.493731\pi$
$859$	−24.5113	−	14.1516i	−0.836316	−	0.482848i	−0.856010	+	0.516959i	$0.827064\pi$
$860$		0			0
$861$	17.7098	−	55.7196i	0.603548	−	1.89892i
$862$		0			0
$863$	−36.7984			−1.25263			−0.626316	−	0.779570i	$-0.715438\pi$
$863$	−36.7984			−1.25263			−0.626316	+	0.779570i	$0.715438\pi$
$864$		0			0
$865$	−5.00000			−0.170005
$866$		0			0
$867$	−12.9042	+	40.6000i	−0.438249	+	1.37885i
$868$		0			0
$869$	33.2501	+	19.1969i	1.12793	+	0.651212i
$870$		0			0
$871$	7.88242	+	13.6527i	0.267086	+	0.462606i
$872$		0			0
$873$	−4.50000	+	48.8385i	−0.152302	+	1.65293i
$874$		0			0
$875$	22.9374	−	13.2429i	0.775426	−	0.447692i
$876$		0			0
$877$	29.9609	+	17.2980i	1.01171	+	0.584111i	0.911692	−	0.410875i	$-0.134777\pi$
$877$	29.9609	+	17.2980i	1.01171	+	0.584111i	0.100018	+	0.994986i	$0.468110\pi$
$878$		0			0
$879$	27.4489	−	25.0360i	0.925828	−	0.844443i
$880$		0			0
$881$	−44.0454			−1.48393			−0.741964	−	0.670440i	$-0.766105\pi$
$881$	−44.0454			−1.48393			−0.741964	+	0.670440i	$0.766105\pi$
$882$		0			0
$883$		−	43.2512i		−	1.45552i	−0.685833	−	0.727759i	$-0.740562\pi$
$883$		−	43.2512i		−	1.45552i	0.685833	−	0.727759i	$-0.259438\pi$
$884$		0			0
$885$	12.9904	−	2.84847i	0.436667	−	0.0957502i
$886$		0			0
$887$	15.4688	−	26.7928i	0.519392	−	0.899613i	−0.480354	−	0.877075i	$-0.659492\pi$
$887$	15.4688	−	26.7928i	0.519392	−	0.899613i	0.999746	−	0.0225384i	$-0.00717479\pi$
$888$		0			0
$889$	−25.3485	−	43.9048i	−0.850160	−	1.47252i
$890$		0			0
$891$	27.6592	+	23.6473i	0.926619	+	0.792213i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−6.26922	+	10.8586i	−0.209557	+	0.362963i
$896$		0			0
$897$	−0.825765	−	3.76588i	−0.0275715	−	0.125739i
$898$		0			0
$899$		−	34.5725i		−	1.15306i
$900$		0			0
$901$		−	21.5959i		−	0.719464i
$902$		0			0
$903$	53.3595	−	48.6690i	1.77569	−	1.61960i
$904$		0			0
$905$	−9.22474	+	15.9777i	−0.306641	+	0.531118i
$906$		0			0
$907$	−29.2332	+	16.8778i	−0.970672	+	0.560418i	−0.899441	−	0.437042i	$-0.856026\pi$
$907$	−29.2332	+	16.8778i	−0.970672	+	0.560418i	−0.0712308	+	0.997460i	$0.522693\pi$
$908$		0			0
$909$	42.8638	+	3.94949i	1.42170	+	0.130996i
$910$		0			0
$911$	−11.0170	−	19.0820i	−0.365010	−	0.632217i	0.623767	−	0.781610i	$-0.285601\pi$
$911$	−11.0170	−	19.0820i	−0.365010	−	0.632217i	−0.988778	+	0.149393i	$0.952268\pi$
$912$		0			0
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$		0			0
$915$	−3.43671	+	10.8128i	−0.113614	+	0.357460i
$916$		0			0
$917$		−	5.69694i		−	0.188129i
$918$		0			0
$919$	8.08665			0.266754			0.133377	−	0.991065i	$-0.457418\pi$
$919$	8.08665			0.266754			0.133377	+	0.991065i	$0.457418\pi$
$920$		0			0
$921$	−1.34847	−	0.428594i	−0.0444336	−	0.0141226i
$922$		0			0
$923$	11.7251	+	6.76947i	0.385935	+	0.222820i
$924$		0			0
$925$	−21.2132	+	12.2474i	−0.697486	+	0.402694i
$926$		0			0
$927$	−23.1470	+	10.6639i	−0.760247	+	0.350247i
$928$		0			0
$929$	−6.37628	−	11.0440i	−0.209199	−	0.362343i	0.742264	−	0.670108i	$-0.233752\pi$
$929$	−6.37628	−	11.0440i	−0.209199	−	0.362343i	−0.951462	+	0.307765i	$0.900419\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−26.6718	−	29.2423i	−0.873196	−	0.957351i
$934$		0			0
$935$	−89.9536			−2.94180
$936$		0			0
$937$	18.0454			0.589518			0.294759	−	0.955572i	$-0.404761\pi$
$937$	18.0454			0.589518			0.294759	+	0.955572i	$0.404761\pi$
$938$		0			0
$939$	18.6104	−	4.08080i	0.607328	−	0.133172i
$940$		0			0
$941$	47.4957	+	27.4217i	1.54832	+	0.893921i	0.998271	+	0.0587874i	$0.0187234\pi$
$941$	47.4957	+	27.4217i	1.54832	+	0.893921i	0.550047	+	0.835134i	$0.314610\pi$
$942$		0			0
$943$	−9.29139	−	16.0932i	−0.302569	−	0.524066i
$944$		0			0
$945$	−43.7196	−	57.8006i	−1.42220	−	1.88025i
$946$		0			0
$947$	−11.2123	+	6.47344i	−0.364352	+	0.210359i	−0.670988	−	0.741468i	$-0.734130\pi$
$947$	−11.2123	+	6.47344i	−0.364352	+	0.210359i	0.306636	+	0.951827i	$0.400797\pi$
$948$		0			0
$949$	3.07483	+	1.77526i	0.0998133	+	0.0576272i
$950$		0			0
$951$	−0.445935	−	2.03368i	−0.0144604	−	0.0659466i
$952$		0			0
$953$	40.4495			1.31029			0.655144	−	0.755504i	$-0.272608\pi$
$953$	40.4495			1.31029			0.655144	+	0.755504i	$0.272608\pi$
$954$		0			0
$955$		−	69.7370i		−	2.25664i
$956$		0			0
$957$	−27.8396	−	30.5227i	−0.899927	−	0.986659i
$958$		0			0
$959$	2.93038	−	5.07556i	0.0946269	−	0.163899i
$960$		0			0
$961$	−1.67423	−	2.89986i	−0.0540076	−	0.0935439i
$962$		0			0
$963$	7.71071	−	10.9046i	0.248474	−	0.351396i
$964$		0			0
$965$	28.8325	−	16.6464i	0.928150	−	0.535867i
$966$		0			0
$967$	−17.6947	+	30.6481i	−0.569023	+	0.985577i	0.427640	+	0.903949i	$0.359345\pi$
$967$	−17.6947	+	30.6481i	−0.569023	+	0.985577i	−0.996663	+	0.0816278i	$0.973988\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	2.63435i		−	0.0845403i	−0.999106	−	0.0422702i	$-0.986541\pi$
$971$		−	2.63435i		−	0.0845403i	0.999106	−	0.0422702i	$-0.0134590\pi$
$972$		0			0
$973$			71.0908i			2.27907i
$974$		0			0
$975$	−11.3880	−	3.61953i	−0.364708	−	0.115918i
$976$		0			0
$977$	−15.8485	+	27.4504i	−0.507037	+	0.878215i	0.492929	+	0.870069i	$0.335926\pi$
$977$	−15.8485	+	27.4504i	−0.507037	+	0.878215i	−0.999967	+	0.00814530i	$0.997407\pi$
$978$		0			0
$979$	15.5804	−	8.99536i	0.497953	−	0.287493i
$980$		0			0
$981$	19.6561	−	27.7980i	0.627572	−	0.887521i
$982$		0			0
$983$	−12.8345	−	22.2299i	−0.409356	−	0.709025i	0.585462	−	0.810700i	$-0.300913\pi$
$983$	−12.8345	−	22.2299i	−0.409356	−	0.709025i	−0.994818	+	0.101675i	$0.967580\pi$
$984$		0			0
$985$	−5.00000	+	8.66025i	−0.159313	+	0.275939i
$986$		0			0
$987$	19.0820	+	20.9211i	0.607388	+	0.665926i
$988$		0			0
$989$		−	22.9546i		−	0.729914i
$990$		0			0
$991$	61.8752			1.96553			0.982766	−	0.184855i	$-0.0591815\pi$
$991$	61.8752			1.96553			0.982766	+	0.184855i	$0.0591815\pi$
$992$		0			0
$993$	−1.50000	−	6.84072i	−0.0476011	−	0.217084i
$994$		0			0
$995$	−7.86971	−	4.54358i	−0.249487	−	0.144041i
$996$		0			0
$997$	8.00853	−	4.62372i	0.253633	−	0.146435i	−0.367794	−	0.929907i	$-0.619887\pi$
$997$	8.00853	−	4.62372i	0.253633	−	0.146435i	0.621426	+	0.783473i	$0.286553\pi$
$998$		0			0
$999$	11.1295	+	14.7140i	0.352120	+	0.465529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.r.f.193.3	✓	16
3.2	odd	2		3456.2.r.e.577.8		16
4.3	odd	2	inner	1152.2.r.f.193.5	yes	16
8.3	odd	2	inner	1152.2.r.f.193.4	yes	16
8.5	even	2	inner	1152.2.r.f.193.6	yes	16
9.2	odd	6		3456.2.r.e.2881.2		16
9.7	even	3	inner	1152.2.r.f.961.6	yes	16
12.11	even	2		3456.2.r.e.577.7		16
24.5	odd	2		3456.2.r.e.577.2		16
24.11	even	2		3456.2.r.e.577.1		16
36.7	odd	6	inner	1152.2.r.f.961.4	yes	16
36.11	even	6		3456.2.r.e.2881.1		16
72.11	even	6		3456.2.r.e.2881.7		16
72.29	odd	6		3456.2.r.e.2881.8		16
72.43	odd	6	inner	1152.2.r.f.961.5	yes	16
72.61	even	6	inner	1152.2.r.f.961.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.r.f.193.3	✓	16	1.1	even	1	trivial
1152.2.r.f.193.4	yes	16	8.3	odd	2	inner
1152.2.r.f.193.5	yes	16	4.3	odd	2	inner
1152.2.r.f.193.6	yes	16	8.5	even	2	inner
1152.2.r.f.961.3	yes	16	72.61	even	6	inner
1152.2.r.f.961.4	yes	16	36.7	odd	6	inner
1152.2.r.f.961.5	yes	16	72.43	odd	6	inner
1152.2.r.f.961.6	yes	16	9.7	even	3	inner
3456.2.r.e.577.1		16	24.11	even	2
3456.2.r.e.577.2		16	24.5	odd	2
3456.2.r.e.577.7		16	12.11	even	2
3456.2.r.e.577.8		16	3.2	odd	2
3456.2.r.e.2881.1		16	36.11	even	6
3456.2.r.e.2881.2		16	9.2	odd	6
3456.2.r.e.2881.7		16	72.11	even	6
3456.2.r.e.2881.8		16	72.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.524648 + 1.65068i) q^{3} +(-2.98735 - 1.72474i) q^{5} +(2.02166 + 3.50162i) q^{7} +(-2.44949 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.524648 + 1.65068i) q^{3} +(-2.98735 - 1.72474i) q^{5} +(2.02166 + 3.50162i) q^{7} +(-2.44949 - 1.73205i) q^{9} +(3.50162 - 2.02166i) q^{11} +(0.866025 + 0.500000i) q^{13} +(4.41431 - 4.02627i) q^{15} +6.44949 q^{17} +(-6.84072 + 1.50000i) q^{21} +(-1.11295 + 1.92768i) q^{23} +(3.44949 + 5.97469i) q^{25} +(4.14418 - 3.13461i) q^{27} +(-5.10867 + 2.94949i) q^{29} +(-2.93038 + 5.07556i) q^{31} +(1.50000 + 6.84072i) q^{33} -13.9474i q^{35} +3.55051i q^{37} +(-1.27970 + 1.16721i) q^{39} +(-4.17423 + 7.22999i) q^{41} +(-8.93092 + 5.15627i) q^{43} +(4.33013 + 9.39898i) q^{45} +(-2.02166 - 3.50162i) q^{47} +(-4.67423 + 8.09601i) q^{49} +(-3.38371 + 10.6460i) q^{51} -3.34847i q^{53} -13.9474 q^{55} +(1.92768 + 1.11295i) q^{59} +(-1.64456 + 0.949490i) q^{61} +(1.11295 - 12.0788i) q^{63} +(-1.72474 - 2.98735i) q^{65} +(13.6527 + 7.88242i) q^{67} +(-2.59808 - 2.84847i) q^{69} +13.5389 q^{71} +3.55051 q^{73} +(-11.6721 + 2.55940i) q^{75} +(14.1582 + 8.17423i) q^{77} +(4.74781 + 8.22345i) q^{79} +(3.00000 + 8.48528i) q^{81} +(-1.92768 + 1.11295i) q^{83} +(-19.2669 - 11.1237i) q^{85} +(-2.18841 - 9.98022i) q^{87} +4.44949 q^{89} +4.04332i q^{91} +(-6.84072 - 7.50000i) q^{93} +(-8.17423 - 14.1582i) q^{97} +(-12.0788 - 1.11295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 64 q^{17} + 16 q^{25} + 24 q^{33} - 8 q^{41} - 16 q^{49} - 8 q^{65} + 96 q^{73} + 48 q^{81} + 32 q^{89} - 72 q^{97}+O(q^{100}) \) 16 * q + 64 * q^17 + 16 * q^25 + 24 * q^33 - 8 * q^41 - 16 * q^49 - 8 * q^65 + 96 * q^73 + 48 * q^81 + 32 * q^89 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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