LMFDB - Embedded newform 912.2.bh.f.767.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(239,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("912.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bh (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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			767.5
Character	$\chi$	$=$	912.767
Dual form			912.2.bh.f.239.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.631725 - 1.61274i) q^{3} +(1.81928 - 1.05036i) q^{5} +3.85684i q^{7} +(-2.20185 + 2.03761i) q^{9} +2.41989 q^{11} +(2.57207 - 4.45496i) q^{13} +(-2.84324 - 2.27048i) q^{15} +(2.36265 - 1.36408i) q^{17} +(1.37962 + 4.13481i) q^{19} +(6.22008 - 2.43646i) q^{21} +(-2.33855 + 4.05049i) q^{23} +(-0.293478 + 0.508318i) q^{25} +(4.67710 + 2.26379i) q^{27} +(6.26345 + 3.61620i) q^{29} -2.26379i q^{31} +(-1.52870 - 3.90265i) q^{33} +(4.05108 + 7.01668i) q^{35} -4.73110 q^{37} +(-8.80952 - 1.33377i) q^{39} +(10.1642 - 5.86833i) q^{41} +(8.19167 - 4.72946i) q^{43} +(-1.86555 + 6.01973i) q^{45} +(2.29646 - 3.97759i) q^{47} -7.87524 q^{49} +(-3.69244 - 2.94861i) q^{51} +(-8.79637 - 5.07859i) q^{53} +(4.40246 - 2.54176i) q^{55} +(5.79682 - 4.83703i) q^{57} +(-6.43172 - 11.1401i) q^{59} +(1.57207 - 2.72291i) q^{61} +(-7.85875 - 8.49218i) q^{63} -10.8064i q^{65} +(-1.92814 - 1.11321i) q^{67} +(8.00969 + 1.21268i) q^{69} +(-1.29128 - 2.23657i) q^{71} +(7.23110 + 12.5246i) q^{73} +(1.00518 + 0.152185i) q^{75} +9.33313i q^{77} +(-5.16883 + 2.98423i) q^{79} +(0.696268 - 8.97303i) q^{81} -12.8578 q^{83} +(2.86555 - 4.96328i) q^{85} +(1.87521 - 12.3857i) q^{87} +(5.45784 + 3.15109i) q^{89} +(17.1821 + 9.92007i) q^{91} +(-3.65091 + 1.43009i) q^{93} +(6.85297 + 6.07328i) q^{95} +(-1.20652 - 2.08976i) q^{97} +(-5.32823 + 4.93079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) $ 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.631725	−	1.61274i	−0.364726	−	0.931115i
$3$	−0.631725	−	1.61274i	−0.364726	−	0.931115i
$4$		0			0
$5$	1.81928	−	1.05036i	0.813607	−	0.469736i	−0.0345998	−	0.999401i	$-0.511016\pi$
$5$	1.81928	−	1.05036i	0.813607	−	0.469736i	0.848207	+	0.529665i	$0.177682\pi$
$6$		0			0
$7$			3.85684i			1.45775i	0.684647	+	0.728875i	$0.259956\pi$
$7$			3.85684i			1.45775i	−0.684647	+	0.728875i	$0.740044\pi$
$8$		0			0
$9$	−2.20185	+	2.03761i	−0.733949	+	0.679204i
$10$		0			0
$11$	2.41989			0.729624			0.364812	−	0.931081i	$-0.381133\pi$
$11$	2.41989			0.729624			0.364812	+	0.931081i	$0.381133\pi$
$12$		0			0
$13$	2.57207	−	4.45496i	0.713364	−	1.23558i	−0.250223	−	0.968188i	$-0.580504\pi$
$13$	2.57207	−	4.45496i	0.713364	−	1.23558i	0.963587	−	0.267395i	$-0.0861627\pi$
$14$		0			0
$15$	−2.84324	−	2.27048i	−0.734122	−	0.586236i
$16$		0			0
$17$	2.36265	−	1.36408i	0.573027	−	0.330837i	−0.185331	−	0.982676i	$-0.559336\pi$
$17$	2.36265	−	1.36408i	0.573027	−	0.330837i	0.758357	+	0.651839i	$0.226002\pi$
$18$		0			0
$19$	1.37962	+	4.13481i	0.316507	+	0.948590i
$19$	1.37962	+	4.13481i	0.316507	+	0.948590i
$20$		0			0
$21$	6.22008	−	2.43646i	1.35733	−	0.531680i
$22$		0			0
$23$	−2.33855	+	4.05049i	−0.487621	+	0.844585i	−0.999899	−	0.0142354i	$-0.995469\pi$
$23$	−2.33855	+	4.05049i	−0.487621	+	0.844585i	0.512278	+	0.858820i	$0.328802\pi$
$24$		0			0
$25$	−0.293478	+	0.508318i	−0.0586955	+	0.101664i
$26$		0			0
$27$	4.67710	+	2.26379i	0.900108	+	0.435667i
$28$		0			0
$29$	6.26345	+	3.61620i	1.16309	+	0.671512i	0.952043	−	0.305964i	$-0.0989786\pi$
$29$	6.26345	+	3.61620i	1.16309	+	0.671512i	0.211049	+	0.977475i	$0.432312\pi$
$30$		0			0
$31$		−	2.26379i		−	0.406589i	−0.979118	−	0.203295i	$-0.934835\pi$
$31$		−	2.26379i		−	0.406589i	0.979118	−	0.203295i	$-0.0651649\pi$
$32$		0			0
$33$	−1.52870	−	3.90265i	−0.266113	−	0.679363i
$34$		0			0
$35$	4.05108	+	7.01668i	0.684758	+	1.18604i
$36$		0			0
$37$	−4.73110			−0.777788			−0.388894	−	0.921283i	$-0.627143\pi$
$37$	−4.73110			−0.777788			−0.388894	+	0.921283i	$0.627143\pi$
$38$		0			0
$39$	−8.80952	−	1.33377i	−1.41065	−	0.213574i
$40$		0			0
$41$	10.1642	−	5.86833i	1.58739	−	0.916479i	0.593652	−	0.804722i	$-0.297685\pi$
$41$	10.1642	−	5.86833i	1.58739	−	0.916479i	0.993736	−	0.111757i	$-0.0356479\pi$
$42$		0			0
$43$	8.19167	−	4.72946i	1.24922	−	0.721236i	0.278264	−	0.960505i	$-0.410241\pi$
$43$	8.19167	−	4.72946i	1.24922	−	0.721236i	0.970953	+	0.239269i	$0.0769077\pi$
$44$		0			0
$45$	−1.86555	+	6.01973i	−0.278100	+	0.897368i
$46$		0			0
$47$	2.29646	−	3.97759i	0.334974	−	0.580192i	−0.648506	−	0.761210i	$-0.724606\pi$
$47$	2.29646	−	3.97759i	0.334974	−	0.580192i	0.983480	+	0.181018i	$0.0579392\pi$
$48$		0			0
$49$	−7.87524			−1.12503
$50$		0			0
$51$	−3.69244	−	2.94861i	−0.517045	−	0.412888i
$52$		0			0
$53$	−8.79637	−	5.07859i	−1.20827	−	0.697598i	−0.245893	−	0.969297i	$-0.579081\pi$
$53$	−8.79637	−	5.07859i	−1.20827	−	0.697598i	−0.962382	+	0.271699i	$0.912414\pi$
$54$		0			0
$55$	4.40246	−	2.54176i	0.593627	−	0.342731i
$56$		0			0
$57$	5.79682	−	4.83703i	0.767808	−	0.640680i
$58$		0			0
$59$	−6.43172	−	11.1401i	−0.837338	−	1.45031i	−0.892112	−	0.451813i	$-0.850777\pi$
$59$	−6.43172	−	11.1401i	−0.837338	−	1.45031i	0.0547744	−	0.998499i	$-0.482556\pi$
$60$		0			0
$61$	1.57207	−	2.72291i	0.201283	−	0.348632i	−0.747659	−	0.664083i	$-0.768822\pi$
$61$	1.57207	−	2.72291i	0.201283	−	0.348632i	0.948942	+	0.315450i	$0.102156\pi$
$62$		0			0
$63$	−7.85875	−	8.49218i	−0.990110	−	1.06991i
$64$		0			0
$65$		−	10.8064i		−	1.34037i
$66$		0			0
$67$	−1.92814	−	1.11321i	−0.235559	−	0.136000i	0.377575	−	0.925979i	$-0.376758\pi$
$67$	−1.92814	−	1.11321i	−0.235559	−	0.136000i	−0.613134	+	0.789979i	$0.710091\pi$
$68$		0			0
$69$	8.00969	+	1.21268i	0.964253	+	0.145989i
$70$		0			0
$71$	−1.29128	−	2.23657i	−0.153247	−	0.265432i	0.779172	−	0.626810i	$-0.215640\pi$
$71$	−1.29128	−	2.23657i	−0.153247	−	0.265432i	−0.932419	+	0.361378i	$0.882306\pi$
$72$		0			0
$73$	7.23110	+	12.5246i	0.846336	+	1.46590i	0.884456	+	0.466624i	$0.154530\pi$
$73$	7.23110	+	12.5246i	0.846336	+	1.46590i	−0.0381202	+	0.999273i	$0.512137\pi$
$74$		0			0
$75$	1.00518	+	0.152185i	0.116068	+	0.0175729i
$76$		0			0
$77$			9.33313i			1.06361i
$78$		0			0
$79$	−5.16883	+	2.98423i	−0.581539	+	0.335752i	−0.761745	−	0.647877i	$-0.775657\pi$
$79$	−5.16883	+	2.98423i	−0.581539	+	0.335752i	0.180206	+	0.983629i	$0.442324\pi$
$80$		0			0
$81$	0.696268	−	8.97303i	0.0773632	−	0.997003i
$82$		0			0
$83$	−12.8578			−1.41132			−0.705662	−	0.708549i	$-0.749350\pi$
$83$	−12.8578			−1.41132			−0.705662	+	0.708549i	$0.749350\pi$
$84$		0			0
$85$	2.86555	−	4.96328i	0.310812	−	0.538343i
$86$		0			0
$87$	1.87521	−	12.3857i	0.201044	−	1.32789i
$88$		0			0
$89$	5.45784	+	3.15109i	0.578530	+	0.334015i	0.760549	−	0.649280i	$-0.224930\pi$
$89$	5.45784	+	3.15109i	0.578530	+	0.334015i	−0.182019	+	0.983295i	$0.558263\pi$
$90$		0			0
$91$	17.1821	+	9.92007i	1.80117	+	1.03991i
$92$		0			0
$93$	−3.65091	+	1.43009i	−0.378581	+	0.148294i
$94$		0			0
$95$	6.85297	+	6.07328i	0.703100	+	0.623105i
$96$		0			0
$97$	−1.20652	−	2.08976i	−0.122504	−	0.212183i	0.798251	−	0.602325i	$-0.205759\pi$
$97$	−1.20652	−	2.08976i	−0.122504	−	0.212183i	−0.920754	+	0.390143i	$0.872426\pi$
$98$		0			0
$99$	−5.32823	+	4.93079i	−0.535507	+	0.495564i
$100$		0			0
$101$	7.99077	+	4.61347i	0.795111	+	0.459058i	0.841759	−	0.539854i	$-0.181520\pi$
$101$	7.99077	+	4.61347i	0.795111	+	0.459058i	−0.0466475	+	0.998911i	$0.514854\pi$
$102$		0			0
$103$		−	0.670744i		−	0.0660904i	−0.999454	−	0.0330452i	$-0.989479\pi$
$103$		−	0.670744i		−	0.0660904i	0.999454	−	0.0330452i	$-0.0105205\pi$
$104$		0			0
$105$	8.75690	−	10.9659i	0.854586	−	1.07017i
$106$		0			0
$107$	4.83978			0.467879			0.233939	−	0.972251i	$-0.424838\pi$
$107$	4.83978			0.467879			0.233939	+	0.972251i	$0.424838\pi$
$108$		0			0
$109$	4.35066	+	7.53557i	0.416718	+	0.721777i	0.995607	−	0.0936295i	$-0.0298469\pi$
$109$	4.35066	+	7.53557i	0.416718	+	0.721777i	−0.578889	+	0.815406i	$0.696514\pi$
$110$		0			0
$111$	2.98875	+	7.63002i	0.283680	+	0.724209i
$112$		0			0
$113$		−	1.27668i		−	0.120100i	−0.998195	−	0.0600499i	$-0.980874\pi$
$113$		−	1.27668i		−	0.120100i	0.998195	−	0.0600499i	$-0.0191260\pi$
$114$		0			0
$115$			9.82529i			0.916213i
$116$		0			0
$117$	3.41417	+	15.0500i	0.315640	+	1.39138i
$118$		0			0
$119$	5.26103	+	9.11237i	0.482278	+	0.835329i
$120$		0			0
$121$	−5.14414			−0.467649
$122$		0			0
$123$	−15.8851	−	12.6851i	−1.43231	−	1.14378i
$124$		0			0
$125$			11.7367i			1.04976i
$126$		0			0
$127$	7.12933	+	4.11612i	0.632626	+	0.365247i	0.781768	−	0.623569i	$-0.214318\pi$
$127$	7.12933	+	4.11612i	0.632626	+	0.365247i	−0.149142	+	0.988816i	$0.547651\pi$
$128$		0			0
$129$	−12.8023	−	10.2233i	−1.12718	−	0.900111i
$130$		0			0
$131$	−4.39099	−	7.60543i	−0.383643	−	0.664489i	0.607937	−	0.793985i	$-0.291997\pi$
$131$	−4.39099	−	7.60543i	−0.383643	−	0.664489i	−0.991580	+	0.129496i	$0.958664\pi$
$132$		0			0
$133$	−15.9473	+	5.32098i	−1.38281	+	0.461388i
$134$		0			0
$135$	10.8868	−	0.794170i	0.936983	−	0.0683513i
$136$		0			0
$137$	−16.6169	−	9.59375i	−1.41967	−	0.819649i	−0.423405	−	0.905941i	$-0.639165\pi$
$137$	−16.6169	−	9.59375i	−1.41967	−	0.819649i	−0.996270	+	0.0862912i	$0.972498\pi$
$138$		0			0
$139$	6.13173	+	3.54016i	0.520087	+	0.300272i	0.736970	−	0.675925i	$-0.236256\pi$
$139$	6.13173	+	3.54016i	0.520087	+	0.300272i	−0.216883	+	0.976198i	$0.569589\pi$
$140$		0			0
$141$	−7.86555	−	1.19085i	−0.662399	−	0.100288i
$142$		0			0
$143$	6.22412	−	10.7805i	0.520487	−	0.901511i
$144$		0			0
$145$	15.1933			1.26173
$146$		0			0
$147$	4.97498	+	12.7007i	0.410330	+	1.04754i
$148$		0			0
$149$	−14.6462	+	8.45599i	−1.19986	+	0.692742i	−0.960525	−	0.278194i	$-0.910264\pi$
$149$	−14.6462	+	8.45599i	−1.19986	+	0.692742i	−0.239339	+	0.970936i	$0.576931\pi$
$150$		0			0
$151$			20.0297i			1.62999i	0.579465	+	0.814997i	$0.303262\pi$
$151$			20.0297i			1.62999i	−0.579465	+	0.814997i	$0.696738\pi$
$152$		0			0
$153$	−2.42273	+	7.81765i	−0.195867	+	0.632020i
$154$		0			0
$155$	−2.37780	−	4.11848i	−0.190990	−	0.330804i
$156$		0			0
$157$	−2.08696	−	3.61471i	−0.166557	−	0.288485i	0.770650	−	0.637259i	$-0.219932\pi$
$157$	−2.08696	−	3.61471i	−0.166557	−	0.288485i	−0.937207	+	0.348773i	$0.886598\pi$
$158$		0			0
$159$	−2.63355	+	17.3945i	−0.208854	+	1.37947i
$160$		0			0
$161$	−15.6221	−	9.01941i	−1.23119	−	0.710829i
$162$		0			0
$163$			1.40349i			0.109930i	0.998488	+	0.0549650i	$0.0175047\pi$
$163$			1.40349i			0.109930i	−0.998488	+	0.0549650i	$0.982495\pi$
$164$		0			0
$165$	−6.88033	−	5.49432i	−0.535633	−	0.427732i
$166$		0			0
$167$	2.42272	−	4.19627i	0.187475	−	0.324717i	−0.756932	−	0.653493i	$-0.773303\pi$
$167$	2.42272	−	4.19627i	0.187475	−	0.324717i	0.944408	+	0.328776i	$0.106636\pi$
$168$		0			0
$169$	−6.73110	−	11.6586i	−0.517777	−	0.896816i
$170$		0			0
$171$	−11.4629	−	6.29309i	−0.876586	−	0.481244i
$172$		0			0
$173$	0.975880	−	0.563425i	0.0741948	−	0.0428364i	−0.462444	−	0.886649i	$-0.653027\pi$
$173$	0.975880	−	0.563425i	0.0741948	−	0.0428364i	0.536638	+	0.843812i	$0.319694\pi$
$174$		0			0
$175$	−1.96050	−	1.13190i	−0.148200	−	0.0855634i
$176$		0			0
$177$	−13.9029	+	17.4101i	−1.04501	+	1.30862i
$178$		0			0
$179$	−4.75561			−0.355451			−0.177725	−	0.984080i	$-0.556874\pi$
$179$	−4.75561			−0.355451			−0.177725	+	0.984080i	$0.556874\pi$
$180$		0			0
$181$	−6.35066	+	10.9997i	−0.472041	+	0.817599i	−0.999488	−	0.0319886i	$-0.989816\pi$
$181$	−6.35066	+	10.9997i	−0.472041	+	0.817599i	0.527447	+	0.849588i	$0.323149\pi$
$182$		0			0
$183$	−5.38445	−	0.815211i	−0.398030	−	0.0602621i
$184$		0			0
$185$	−8.60719	+	4.96937i	−0.632814	+	0.365355i
$186$		0			0
$187$	5.71735	−	3.30091i	0.418094	−	0.241387i
$188$		0			0
$189$	−8.73110	+	18.0388i	−0.635094	+	1.31213i
$190$		0			0
$191$	−5.27275			−0.381523			−0.190761	−	0.981636i	$-0.561096\pi$
$191$	−5.27275			−0.381523			−0.190761	+	0.981636i	$0.561096\pi$
$192$		0			0
$193$	0.159026	+	0.275441i	0.0114469	+	0.0198267i	0.871692	−	0.490054i	$-0.163023\pi$
$193$	0.159026	+	0.275441i	0.0114469	+	0.0198267i	−0.860245	+	0.509881i	$0.829690\pi$
$194$		0			0
$195$	−17.4279	+	6.82669i	−1.24804	+	0.488869i
$196$		0			0
$197$			20.0334i			1.42732i	0.700493	+	0.713659i	$0.252964\pi$
$197$			20.0334i			1.42732i	−0.700493	+	0.713659i	$0.747036\pi$
$198$		0			0
$199$	−4.20593	−	2.42829i	−0.298150	−	0.172137i	0.343461	−	0.939167i	$-0.388401\pi$
$199$	−4.20593	−	2.42829i	−0.298150	−	0.172137i	−0.641612	+	0.767030i	$0.721734\pi$
$200$		0			0
$201$	−0.577265	+	3.81282i	−0.0407171	+	0.268936i
$202$		0			0
$203$	−13.9471	+	24.1571i	−0.978896	+	1.69550i
$204$		0			0
$205$	12.3277	−	21.3523i	0.861007	−	1.49131i
$206$		0			0
$207$	−3.10419	−	13.6836i	−0.215756	−	0.951077i
$208$		0			0
$209$	3.33853	+	10.0058i	0.230931	+	0.692114i
$210$		0			0
$211$	16.7330	−	9.66079i	1.15195	−	0.665076i	0.202586	−	0.979265i	$-0.435066\pi$
$211$	16.7330	−	9.66079i	1.15195	−	0.665076i	0.949361	+	0.314188i	$0.101732\pi$
$212$		0			0
$213$	−2.79126	+	3.49540i	−0.191254	+	0.239501i
$214$		0			0
$215$	9.93530	−	17.2084i	0.677582	−	1.17361i
$216$		0			0
$217$	8.73110			0.592705
$218$		0			0
$219$	15.6309	−	19.5740i	1.05624	−	1.32269i
$220$		0			0
$221$		−	14.0340i		−	0.944029i
$222$		0			0
$223$	−22.5151	+	12.9991i	−1.50772	+	0.870483i	−0.507761	+	0.861498i	$0.669527\pi$
$223$	−22.5151	+	12.9991i	−1.50772	+	0.870483i	−0.999960	+	0.00898445i	$0.997140\pi$
$224$		0			0
$225$	−0.389562	−	1.71723i	−0.0259708	−	0.114482i
$226$		0			0
$227$	28.6526			1.90174			0.950869	−	0.309593i	$-0.100193\pi$
$227$	28.6526			1.90174			0.950869	+	0.309593i	$0.100193\pi$
$228$		0			0
$229$	24.6257			1.62731			0.813657	−	0.581346i	$-0.197474\pi$
$229$	24.6257			1.62731			0.813657	+	0.581346i	$0.197474\pi$
$230$		0			0
$231$	15.0519	−	5.89597i	0.990342	−	0.387926i
$232$		0			0
$233$	2.88712	−	1.66688i	0.189141	−	0.109201i	−0.402439	−	0.915447i	$-0.631838\pi$
$233$	2.88712	−	1.66688i	0.189141	−	0.109201i	0.591581	+	0.806246i	$0.298504\pi$
$234$		0			0
$235$		−	9.64848i		−	0.629397i
$236$		0			0
$237$	8.07805	+	6.45076i	0.524726	+	0.419022i
$238$		0			0
$239$	−25.6427			−1.65869			−0.829344	−	0.558738i	$-0.811286\pi$
$239$	−25.6427			−1.65869			−0.829344	+	0.558738i	$0.811286\pi$
$240$		0			0
$241$	6.08696	−	10.5429i	0.392095	−	0.679129i	−0.600630	−	0.799527i	$-0.705084\pi$
$241$	6.08696	−	10.5429i	0.392095	−	0.679129i	0.992726	+	0.120398i	$0.0384170\pi$
$242$		0			0
$243$	−14.9110	+	4.54558i	−0.956541	+	0.291599i
$244$		0			0
$245$	−14.3273	+	8.27185i	−0.915336	+	0.528469i
$246$		0			0
$247$	21.9689	+	4.48887i	1.39785	+	0.285620i
$248$		0			0
$249$	8.12257	+	20.7362i	0.514747	+	1.31410i
$250$		0			0
$251$	0.707354	−	1.22517i	0.0446478	−	0.0773322i	−0.842838	−	0.538167i	$-0.819117\pi$
$251$	0.707354	−	1.22517i	0.0446478	−	0.0773322i	0.887486	+	0.460835i	$0.152450\pi$
$252$		0			0
$253$	−5.65903	+	9.80172i	−0.355780	+	0.616229i
$254$		0			0
$255$	−9.81470	−	1.48596i	−0.614620	−	0.0930541i
$256$		0			0
$257$	−17.6847	−	10.2103i	−1.10314	−	0.636899i	−0.166097	−	0.986109i	$-0.553116\pi$
$257$	−17.6847	−	10.2103i	−1.10314	−	0.636899i	−0.937044	+	0.349210i	$0.886450\pi$
$258$		0			0
$259$		−	18.2471i		−	1.13382i
$260$		0			0
$261$	−21.1596	+	4.80015i	−1.30974	+	0.297122i
$262$		0			0
$263$	0.881757	+	1.52725i	0.0543715	+	0.0941741i	0.891930	−	0.452173i	$-0.149351\pi$
$263$	0.881757	+	1.52725i	0.0543715	+	0.0941741i	−0.837559	+	0.546347i	$0.816018\pi$
$264$		0			0
$265$	−21.3374			−1.31075
$266$		0			0
$267$	1.63402	−	10.7927i	0.100001	−	0.660502i
$268$		0			0
$269$	−16.2574	+	9.38622i	−0.991232	+	0.572288i	−0.905642	−	0.424043i	$-0.860611\pi$
$269$	−16.2574	+	9.38622i	−0.991232	+	0.572288i	−0.0855895	+	0.996330i	$0.527277\pi$
$270$		0			0
$271$	13.8096	−	7.97297i	0.838872	−	0.484323i	−0.0180084	−	0.999838i	$-0.505733\pi$
$271$	13.8096	−	7.97297i	0.838872	−	0.484323i	0.856881	+	0.515515i	$0.172399\pi$
$272$		0			0
$273$	5.14414	−	33.9769i	0.311338	−	2.05638i
$274$		0			0
$275$	−0.710183	+	1.23007i	−0.0428256	+	0.0741762i
$276$		0			0
$277$	1.85586			0.111508			0.0557539	−	0.998445i	$-0.482244\pi$
$277$	1.85586			0.111508			0.0557539	+	0.998445i	$0.482244\pi$
$278$		0			0
$279$	4.61273	+	4.98453i	0.276157	+	0.298416i
$280$		0			0
$281$	10.1831	+	5.87924i	0.607475	+	0.350726i	0.771977	−	0.635651i	$-0.219268\pi$
$281$	10.1831	+	5.87924i	0.607475	+	0.350726i	−0.164501	+	0.986377i	$0.552602\pi$
$282$		0			0
$283$	4.49955	−	2.59782i	0.267471	−	0.154424i	−0.360267	−	0.932849i	$-0.617314\pi$
$283$	4.49955	−	2.59782i	0.267471	−	0.154424i	0.627738	+	0.778425i	$0.283981\pi$
$284$		0			0
$285$	5.46542	−	14.8887i	0.323743	−	0.881929i
$286$		0			0
$287$	22.6332	+	39.2019i	1.33600	+	2.31401i
$288$		0			0
$289$	−4.77859	+	8.27677i	−0.281094	+	0.486869i
$290$		0			0
$291$	−2.60804	+	3.26596i	−0.152886	+	0.191454i
$292$		0			0
$293$		−	13.8592i		−	0.809663i	−0.914391	−	0.404832i	$-0.867330\pi$
$293$		−	13.8592i		−	0.809663i	0.914391	−	0.404832i	$-0.132670\pi$
$294$		0			0
$295$	−23.4022	−	13.5113i	−1.36253	−	0.786656i
$296$		0			0
$297$	11.3181	+	5.47813i	0.656740	+	0.317873i
$298$		0			0
$299$	12.0298	+	20.8363i	0.695703	+	1.20499i
$300$		0			0
$301$	18.2408	+	31.5940i	1.05138	+	1.82105i
$302$		0			0
$303$	2.39236	−	15.8015i	0.137437	−	0.907770i
$304$		0			0
$305$		−	6.60498i		−	0.378200i
$306$		0			0
$307$	−23.9294	+	13.8156i	−1.36572	+	0.788500i	−0.990378	−	0.138386i	$-0.955809\pi$
$307$	−23.9294	+	13.8156i	−1.36572	+	0.788500i	−0.375344	+	0.926886i	$0.622475\pi$
$308$		0			0
$309$	−1.08173	+	0.423726i	−0.0615377	+	0.0241049i
$310$		0			0
$311$	−21.6341			−1.22676			−0.613379	−	0.789789i	$-0.710190\pi$
$311$	−21.6341			−1.22676			−0.613379	+	0.789789i	$0.710190\pi$
$312$		0			0
$313$	2.20652	−	3.82181i	0.124720	−	0.216021i	−0.796903	−	0.604107i	$-0.793530\pi$
$313$	2.20652	−	3.82181i	0.124720	−	0.216021i	0.921623	+	0.388085i	$0.126863\pi$
$314$		0			0
$315$	−23.2171	−	7.19513i	−1.30814	−	0.405399i
$316$		0			0
$317$	−4.07107	−	2.35044i	−0.228654	−	0.132014i	0.381297	−	0.924453i	$-0.375478\pi$
$317$	−4.07107	−	2.35044i	−0.228654	−	0.132014i	−0.609951	+	0.792439i	$0.708811\pi$
$318$		0			0
$319$	15.1568	+	8.75080i	0.848620	+	0.489951i
$320$		0			0
$321$	−3.05741	−	7.80529i	−0.170648	−	0.435649i
$322$		0			0
$323$	8.89975	+	7.88719i	0.495196	+	0.438855i
$324$		0			0
$325$	1.50969	+	2.61486i	0.0837425	+	0.145046i
$326$		0			0
$327$	9.40448	−	11.7769i	0.520069	−	0.651263i
$328$		0			0
$329$	15.3410	+	8.85710i	0.845774	+	0.488308i
$330$		0			0
$331$			13.4679i			0.740265i	0.928979	+	0.370133i	$0.120688\pi$
$331$			13.4679i			0.740265i	−0.928979	+	0.370133i	$0.879312\pi$
$332$		0			0
$333$	10.4172	−	9.64014i	0.570857	−	0.528277i
$334$		0			0
$335$	−4.67710			−0.255537
$336$		0			0
$337$	−9.71621	−	16.8290i	−0.529276	−	0.916733i	−0.999417	−	0.0341414i	$-0.989130\pi$
$337$	−9.71621	−	16.8290i	−0.529276	−	0.916733i	0.470141	−	0.882591i	$-0.344203\pi$
$338$		0			0
$339$	−2.05895	+	0.806509i	−0.111827	+	0.0438035i
$340$		0			0
$341$		−	5.47813i		−	0.296657i
$342$		0			0
$343$		−	3.37566i		−	0.182268i
$344$		0			0
$345$	15.8456	−	6.20688i	0.853100	−	0.334167i
$346$		0			0
$347$	−14.5339	−	25.1734i	−0.780220	−	1.35138i	−0.931814	−	0.362937i	$-0.881774\pi$
$347$	−14.5339	−	25.1734i	−0.780220	−	1.35138i	0.151594	−	0.988443i	$-0.451559\pi$
$348$		0			0
$349$	−17.2231			−0.921929			−0.460965	−	0.887419i	$-0.652496\pi$
$349$	−17.2231			−0.921929			−0.460965	+	0.887419i	$0.652496\pi$
$350$		0			0
$351$	22.1149	−	15.0136i	1.18041	−	0.801368i
$352$		0			0
$353$		−	2.53153i		−	0.134740i	−0.997728	−	0.0673699i	$-0.978539\pi$
$353$		−	2.53153i		−	0.134740i	0.997728	−	0.0673699i	$-0.0214608\pi$
$354$		0			0
$355$	−4.69842	−	2.71263i	−0.249366	−	0.143972i
$356$		0			0
$357$	11.3723	−	14.2412i	0.601888	−	0.753722i
$358$		0			0
$359$	−9.73053	−	16.8538i	−0.513558	−	0.889508i	−0.999876	−	0.0157266i	$-0.994994\pi$
$359$	−9.73053	−	16.8538i	−0.513558	−	0.889508i	0.486318	−	0.873782i	$-0.338339\pi$
$360$		0			0
$361$	−15.1933	+	11.4089i	−0.799647	+	0.600471i
$362$		0			0
$363$	3.24968	+	8.29615i	0.170564	+	0.435435i
$364$		0			0
$365$	26.3108	+	15.1905i	1.37717	+	0.795109i
$366$		0			0
$367$	−6.76631	−	3.90653i	−0.353199	−	0.203919i	0.312895	−	0.949788i	$-0.398701\pi$
$367$	−6.76631	−	3.90653i	−0.353199	−	0.203919i	−0.666093	+	0.745869i	$0.732035\pi$
$368$		0			0
$369$	−10.4227	+	33.6320i	−0.542586	+	1.75081i
$370$		0			0
$371$	19.5873	−	33.9262i	1.01692	−	1.76136i
$372$		0			0
$373$	−24.7207			−1.27999			−0.639995	−	0.768379i	$-0.721064\pi$
$373$	−24.7207			−1.27999			−0.639995	+	0.768379i	$0.721064\pi$
$374$		0			0
$375$	18.9282	−	7.41433i	0.977445	−	0.382875i
$376$		0			0
$377$	32.2201	−	18.6023i	1.65942	−	0.958065i
$378$		0			0
$379$		−	33.0438i		−	1.69735i	−0.528918	−	0.848673i	$-0.677402\pi$
$379$		−	33.0438i		−	1.69735i	0.528918	−	0.848673i	$-0.322598\pi$
$380$		0			0
$381$	2.13445	−	14.0980i	0.109351	−	0.722263i
$382$		0			0
$383$	−9.02601	−	15.6335i	−0.461207	−	0.798835i	0.537814	−	0.843064i	$-0.319250\pi$
$383$	−9.02601	−	15.6335i	−0.461207	−	0.798835i	−0.999021	+	0.0442288i	$0.985917\pi$
$384$		0			0
$385$	9.80317	+	16.9796i	0.499616	+	0.865360i
$386$		0			0
$387$	−8.39999	+	27.1050i	−0.426996	+	1.37782i
$388$		0			0
$389$	17.9847	+	10.3835i	0.911862	+	0.526464i	0.881030	−	0.473061i	$-0.156851\pi$
$389$	17.9847	+	10.3835i	0.911862	+	0.526464i	0.0308324	+	0.999525i	$0.490184\pi$
$390$		0			0
$391$			12.7598i			0.645292i
$392$		0			0
$393$	−9.49166	+	11.8861i	−0.478791	+	0.599572i
$394$		0			0
$395$	−6.26904	+	10.8583i	−0.315429	+	0.546340i
$396$		0			0
$397$	−11.4473	−	19.8273i	−0.574524	−	0.995105i	−0.996093	−	0.0883085i	$-0.971854\pi$
$397$	−11.4473	−	19.8273i	−0.574524	−	0.995105i	0.421569	−	0.906796i	$-0.361479\pi$
$398$		0			0
$399$	18.6557	+	22.3574i	0.933951	+	1.11927i
$400$		0			0
$401$	−14.7245	+	8.50121i	−0.735308	+	0.424530i	−0.820361	−	0.571846i	$-0.806227\pi$
$401$	−14.7245	+	8.50121i	−0.735308	+	0.424530i	0.0850530	+	0.996376i	$0.472894\pi$
$402$		0			0
$403$	−10.0851	−	5.82264i	−0.502375	−	0.290046i
$404$		0			0
$405$	−8.15822	−	17.0558i	−0.405385	−	0.847509i
$406$		0			0
$407$	−11.4487			−0.567492
$408$		0			0
$409$	8.81286	−	15.2643i	0.435768	−	0.754772i	−0.561590	−	0.827416i	$-0.689810\pi$
$409$	8.81286	−	15.2643i	0.435768	−	0.754772i	0.997358	+	0.0726436i	$0.0231436\pi$
$410$		0			0
$411$	−4.97492	+	32.8593i	−0.245395	+	1.62083i
$412$		0			0
$413$	42.9655	−	24.8061i	2.11419	−	1.22063i
$414$		0			0
$415$	−23.3919	+	13.5053i	−1.14826	+	0.662950i
$416$		0			0
$417$	1.83578	−	12.1253i	0.0898985	−	0.593778i
$418$		0			0
$419$	6.26014			0.305828			0.152914	−	0.988240i	$-0.451134\pi$
$419$	6.26014			0.305828			0.152914	+	0.988240i	$0.451134\pi$
$420$		0			0
$421$	7.11153	+	12.3175i	0.346595	+	0.600320i	0.985642	−	0.168848i	$-0.0540046\pi$
$421$	7.11153	+	12.3175i	0.346595	+	0.600320i	−0.639047	+	0.769167i	$0.720671\pi$
$422$		0			0
$423$	3.04833	+	13.4374i	0.148215	+	0.653347i
$424$		0			0
$425$			1.60130i			0.0776746i
$426$		0			0
$427$	10.5018	+	6.06323i	0.508219	+	0.293420i
$428$		0			0
$429$	−21.3181	−	3.22757i	−1.02925	−	0.155829i
$430$		0			0
$431$	−10.3145	+	17.8652i	−0.496830	+	0.860535i	−0.999993	−	0.00365638i	$-0.998836\pi$
$431$	−10.3145	+	17.8652i	−0.496830	+	0.860535i	0.503163	+	0.864191i	$0.332169\pi$
$432$		0			0
$433$	4.98512	−	8.63447i	0.239569	−	0.414946i	−0.721021	−	0.692913i	$-0.756327\pi$
$433$	4.98512	−	8.63447i	0.239569	−	0.414946i	0.960591	+	0.277966i	$0.0896604\pi$
$434$		0			0
$435$	−9.59798	−	24.5028i	−0.460188	−	1.17482i
$436$		0			0
$437$	−19.9743	−	4.08132i	−0.955500	−	0.195236i
$438$		0			0
$439$	−23.0612	+	13.3144i	−1.10065	+	0.635462i	−0.936393	−	0.350954i	$-0.885857\pi$
$439$	−23.0612	+	13.3144i	−1.10065	+	0.635462i	−0.164261	+	0.986417i	$0.552524\pi$
$440$		0			0
$441$	17.3401	−	16.0467i	0.825718	−	0.764128i
$442$		0			0
$443$	−0.870033	+	1.50694i	−0.0413365	+	0.0715969i	−0.885953	−	0.463774i	$-0.846495\pi$
$443$	−0.870033	+	1.50694i	−0.0413365	+	0.0715969i	0.844617	+	0.535371i	$0.179828\pi$
$444$		0			0
$445$	13.2391			0.627595
$446$		0			0
$447$	22.8897	+	18.2786i	1.08264	+	0.864550i
$448$		0			0
$449$		−	10.7002i		−	0.504976i	−0.967600	−	0.252488i	$-0.918751\pi$
$449$		−	10.7002i		−	0.504976i	0.967600	−	0.252488i	$-0.0812488\pi$
$450$		0			0
$451$	24.5963	−	14.2007i	1.15820	−	0.668685i
$452$		0			0
$453$	32.3027	−	12.6533i	1.51771	−	0.594502i
$454$		0			0
$455$	41.6787			1.95393
$456$		0			0
$457$	−30.3374			−1.41913			−0.709563	−	0.704642i	$-0.751107\pi$
$457$	−30.3374			−1.41913			−0.709563	+	0.704642i	$0.751107\pi$
$458$		0			0
$459$	14.1383	−	1.03137i	0.659921	−	0.0481401i
$460$		0			0
$461$	−18.5875	+	10.7315i	−0.865707	+	0.499816i	−0.865919	−	0.500184i	$-0.833266\pi$
$461$	−18.5875	+	10.7315i	−0.865707	+	0.499816i	0.000212046		1.00000i	$0.499933\pi$
$462$		0			0
$463$		−	22.9242i		−	1.06538i	−0.846311	−	0.532688i	$-0.821182\pi$
$463$		−	22.9242i		−	1.06538i	0.846311	−	0.532688i	$-0.178818\pi$
$464$		0			0
$465$	−5.13991	+	6.43652i	−0.238357	+	0.298486i
$466$		0			0
$467$	−12.1957			−0.564352			−0.282176	−	0.959363i	$-0.591056\pi$
$467$	−12.1957			−0.564352			−0.282176	+	0.959363i	$0.591056\pi$
$468$		0			0
$469$	4.29348	−	7.43652i	0.198254	−	0.343387i
$470$		0			0
$471$	−4.51120	+	5.64921i	−0.207865	+	0.260302i
$472$		0			0
$473$	19.8229	−	11.4448i	0.911459	−	0.526231i
$474$		0			0
$475$	−2.50669	−	0.512187i	−0.115015	−	0.0235008i
$476$		0			0
$477$	29.7165	−	6.74132i	1.36062	−	0.308664i
$478$		0			0
$479$	−2.45914	+	4.25936i	−0.112361	+	0.194615i	−0.916722	−	0.399526i	$-0.869175\pi$
$479$	−2.45914	+	4.25936i	−0.112361	+	0.194615i	0.804361	+	0.594141i	$0.202508\pi$
$480$		0			0
$481$	−12.1687	+	21.0768i	−0.554846	+	0.961021i
$482$		0			0
$483$	−4.67710	+	30.8921i	−0.212815	+	1.40564i
$484$		0			0
$485$	−4.39001	−	2.53457i	−0.199340	−	0.115089i
$486$		0			0
$487$			8.01806i			0.363333i	0.983360	+	0.181666i	$0.0581491\pi$
$487$			8.01806i			0.363333i	−0.983360	+	0.181666i	$0.941851\pi$
$488$		0			0
$489$	2.26346	−	0.886620i	0.102357	−	0.0400943i
$490$		0			0
$491$	21.8417	+	37.8309i	0.985702	+	1.70729i	0.638775	+	0.769394i	$0.279442\pi$
$491$	21.8417	+	37.8309i	0.985702	+	1.70729i	0.346927	+	0.937892i	$0.387225\pi$
$492$		0			0
$493$	19.7311			0.888644
$494$		0			0
$495$	−4.51442	+	14.5671i	−0.202908	+	0.654741i
$496$		0			0
$497$	8.62609	−	4.98028i	0.386933	−	0.223396i
$498$		0			0
$499$	6.34959	−	3.66594i	0.284247	−	0.164110i	−0.351098	−	0.936339i	$-0.614191\pi$
$499$	6.34959	−	3.66594i	0.284247	−	0.164110i	0.635344	+	0.772229i	$0.280858\pi$
$500$		0			0
$501$	−8.29797	−	1.25632i	−0.370726	−	0.0561283i
$502$		0			0
$503$	21.0166	−	36.4018i	0.937083	−	1.62308i	0.166206	−	0.986091i	$-0.446848\pi$
$503$	21.0166	−	36.4018i	0.937083	−	1.62308i	0.770877	−	0.636984i	$-0.219818\pi$
$504$		0			0
$505$	19.3833			0.862544
$506$		0			0
$507$	−14.5501	+	18.2205i	−0.646191	+	0.809202i
$508$		0			0
$509$	21.3800	+	12.3437i	0.947650	+	0.547126i	0.892350	−	0.451344i	$-0.149055\pi$
$509$	21.3800	+	12.3437i	0.947650	+	0.547126i	0.0553000	+	0.998470i	$0.482388\pi$
$510$		0			0
$511$	−48.3055	+	27.8892i	−2.13691	+	1.23375i
$512$		0			0
$513$	−2.90773	+	22.4621i	−0.128379	+	0.991725i
$514$		0			0
$515$	−0.704524	−	1.22027i	−0.0310451	−	0.0537716i
$516$		0			0
$517$	5.55719	−	9.62533i	0.244405	−	0.423322i
$518$		0			0
$519$	−1.52514	−	1.21791i	−0.0669464	−	0.0534603i
$520$		0			0
$521$			15.6978i			0.687735i	0.939018	+	0.343867i	$0.111737\pi$
$521$			15.6978i			0.687735i	−0.939018	+	0.343867i	$0.888263\pi$
$522$		0			0
$523$	−5.52082	−	3.18745i	−0.241409	−	0.139377i	0.374415	−	0.927261i	$-0.377843\pi$
$523$	−5.52082	−	3.18745i	−0.241409	−	0.139377i	−0.615824	+	0.787884i	$0.711177\pi$
$524$		0			0
$525$	−0.586955	+	3.87682i	−0.0256168	+	0.169198i
$526$		0			0
$527$	−3.08799	−	5.34855i	−0.134515	−	0.232986i
$528$		0			0
$529$	0.562381	+	0.974072i	0.0244513	+	0.0423510i
$530$		0			0
$531$	36.8608	+	11.4234i	1.59962	+	0.495732i
$532$		0			0
$533$		−	60.3750i		−	2.61513i
$534$		0			0
$535$	8.80491	−	5.08352i	0.380670	−	0.219780i
$536$		0			0
$537$	3.00423	+	7.66955i	0.129642	+	0.330965i
$538$		0			0
$539$	−19.0572			−0.820852
$540$		0			0
$541$	9.05719	−	15.6875i	0.389399	−	0.674459i	−0.602970	−	0.797764i	$-0.706016\pi$
$541$	9.05719	−	15.6875i	0.389399	−	0.674459i	0.992369	+	0.123305i	$0.0393494\pi$
$542$		0			0
$543$	21.7515	+	3.29319i	0.933445	+	0.141324i
$544$		0			0
$545$	15.8302	+	9.13955i	0.678090	+	0.391495i
$546$		0			0
$547$	−28.0335	−	16.1852i	−1.19863	−	0.692028i	−0.238379	−	0.971172i	$-0.576616\pi$
$547$	−28.0335	−	16.1852i	−1.19863	−	0.692028i	−0.960249	+	0.279144i	$0.909949\pi$
$548$		0			0
$549$	2.08677	+	9.19870i	0.0890611	+	0.392591i
$550$		0			0
$551$	−6.31112	+	30.8871i	−0.268863	+	1.31584i
$552$		0			0
$553$	−11.5097	−	19.9354i	−0.489442	−	0.847738i
$554$		0			0
$555$	13.4517	+	10.7419i	0.570991	+	0.455967i
$556$		0			0
$557$	16.6547	+	9.61557i	0.705681	+	0.407425i	0.809460	−	0.587175i	$-0.199760\pi$
$557$	16.6547	+	9.61557i	0.705681	+	0.407425i	−0.103779	+	0.994600i	$0.533093\pi$
$558$		0			0
$559$		−	48.6580i		−	2.05802i
$560$		0			0
$561$	−8.93529	−	7.13531i	−0.377248	−	0.301253i
$562$		0			0
$563$	−21.0441			−0.886903			−0.443452	−	0.896298i	$-0.646246\pi$
$563$	−21.0441			−0.886903			−0.443452	+	0.896298i	$0.646246\pi$
$564$		0			0
$565$	−1.34097	−	2.32264i	−0.0564152	−	0.0977140i
$566$		0			0
$567$	34.6076	+	2.68540i	1.45338	+	0.112776i
$568$		0			0
$569$			11.8647i			0.497392i	0.968582	+	0.248696i	$0.0800021\pi$
$569$			11.8647i			0.497392i	−0.968582	+	0.248696i	$0.919998\pi$
$570$		0			0
$571$			0.291628i			0.0122042i	0.999981	+	0.00610212i	$0.00194238\pi$
$571$			0.291628i			0.0122042i	−0.999981	+	0.00610212i	$0.998058\pi$
$572$		0			0
$573$	3.33093	+	8.50357i	0.139151	+	0.355242i
$574$		0			0
$575$	−1.37262	−	2.37745i	−0.0572423	−	0.0991466i
$576$		0			0
$577$	22.2424			0.925965			0.462982	−	0.886367i	$-0.346779\pi$
$577$	22.2424			0.925965			0.462982	+	0.886367i	$0.346779\pi$
$578$		0			0
$579$	0.343754	−	0.430470i	0.0142859	−	0.0178897i
$580$		0			0
$581$		−	49.5904i		−	2.05736i
$582$		0			0
$583$	−21.2862	−	12.2896i	−0.881586	−	0.508984i
$584$		0			0
$585$	22.0193	+	23.7941i	0.910387	+	0.983765i
$586$		0			0
$587$	−21.6369	−	37.4763i	−0.893052	−	1.54681i	−0.836197	−	0.548429i	$-0.815226\pi$
$587$	−21.6369	−	37.4763i	−0.893052	−	1.54681i	−0.0568545	−	0.998382i	$-0.518107\pi$
$588$		0			0
$589$	9.36035	−	3.12318i	0.385687	−	0.128688i
$590$		0			0
$591$	32.3086	−	12.6556i	1.32900	−	0.520581i
$592$		0			0
$593$	−10.1831	−	5.87924i	−0.418171	−	0.241431i	0.276123	−	0.961122i	$-0.410950\pi$
$593$	−10.1831	−	5.87924i	−0.418171	−	0.241431i	−0.694295	+	0.719691i	$0.744284\pi$
$594$		0			0
$595$	19.1426	+	11.0520i	0.784769	+	0.453087i
$596$		0			0
$597$	−1.25921	+	8.31707i	−0.0515362	+	0.340395i
$598$		0			0
$599$	18.2119	−	31.5439i	0.744117	−	1.28885i	−0.206490	−	0.978449i	$-0.566204\pi$
$599$	18.2119	−	31.5439i	0.744117	−	1.28885i	0.950606	−	0.310399i	$-0.100463\pi$
$600$		0			0
$601$	35.7401			1.45787			0.728934	−	0.684584i	$-0.240016\pi$
$601$	35.7401			1.45787			0.728934	+	0.684584i	$0.240016\pi$
$602$		0			0
$603$	6.51376	−	1.47768i	0.265261	−	0.0601756i
$604$		0			0
$605$	−9.35864	+	5.40321i	−0.380483	+	0.219672i
$606$		0			0
$607$		−	4.03366i		−	0.163721i	−0.996644	−	0.0818606i	$-0.973914\pi$
$607$		−	4.03366i		−	0.163721i	0.996644	−	0.0818606i	$-0.0260862\pi$
$608$		0			0
$609$	47.7699	+	7.23240i	1.93573	+	0.293072i
$610$		0			0
$611$	−11.8133	−	20.4613i	−0.477916	−	0.827776i
$612$		0			0
$613$	−21.7831	−	37.7294i	−0.879811	−	1.52388i	−0.851548	−	0.524276i	$-0.824336\pi$
$613$	−21.7831	−	37.7294i	−0.879811	−	1.52388i	−0.0282624	−	0.999601i	$-0.508997\pi$
$614$		0			0
$615$	−42.2234	−	6.39266i	−1.70261	−	0.257777i
$616$		0			0
$617$	18.7714	+	10.8377i	0.755710	+	0.436309i	0.827753	−	0.561092i	$-0.189619\pi$
$617$	18.7714	+	10.8377i	0.755710	+	0.436309i	−0.0720436	+	0.997401i	$0.522952\pi$
$618$		0			0
$619$			30.4136i			1.22243i	0.791466	+	0.611213i	$0.209318\pi$
$619$			30.4136i			1.22243i	−0.791466	+	0.611213i	$0.790682\pi$
$620$		0			0
$621$	−20.1071	+	13.6505i	−0.806869	+	0.547777i
$622$		0			0
$623$	−12.1532	+	21.0500i	−0.486910	+	0.843352i
$624$		0			0
$625$	10.8604	+	18.8107i	0.434414	+	0.752427i
$626$		0			0
$627$	14.0277	−	11.7051i	0.560211	−	0.467455i
$628$		0			0
$629$	−11.1779	+	6.45358i	−0.445693	+	0.257321i
$630$		0			0
$631$	−16.2515	−	9.38283i	−0.646963	−	0.373524i	0.140328	−	0.990105i	$-0.455184\pi$
$631$	−16.2515	−	9.38283i	−0.646963	−	0.373524i	−0.787292	+	0.616581i	$0.788517\pi$
$632$		0			0
$633$	−26.1510	−	20.8830i	−1.03941	−	0.830023i
$634$		0			0
$635$	17.2937			0.686279
$636$		0			0
$637$	−20.2557	+	35.0839i	−0.802559	+	1.39007i
$638$		0			0
$639$	7.40047	+	2.29345i	0.292758	+	0.0907274i
$640$		0			0
$641$	6.00121	−	3.46480i	0.237034	−	0.136851i	−0.376779	−	0.926303i	$-0.622968\pi$
$641$	6.00121	−	3.46480i	0.237034	−	0.136851i	0.613813	+	0.789452i	$0.289635\pi$
$642$		0			0
$643$	37.8250	−	21.8383i	1.49167	−	0.861218i	0.491719	−	0.870754i	$-0.336369\pi$
$643$	37.8250	−	21.8383i	1.49167	−	0.861218i	0.999955	+	0.00953590i	$0.00303542\pi$
$644$		0			0
$645$	−34.0291	−	5.15203i	−1.33989	−	0.202861i
$646$		0			0
$647$	−49.4320			−1.94337			−0.971687	−	0.236271i	$-0.924075\pi$
$647$	−49.4320			−1.94337			−0.971687	+	0.236271i	$0.924075\pi$
$648$		0			0
$649$	−15.5640	−	26.9577i	−0.610942	−	1.05818i
$650$		0			0
$651$	−5.51565	−	14.0810i	−0.216175	−	0.551877i
$652$		0			0
$653$			6.80160i			0.266167i	0.991105	+	0.133084i	$0.0424879\pi$
$653$			6.80160i			0.266167i	−0.991105	+	0.133084i	$0.957512\pi$
$654$		0			0
$655$	−15.9769	−	9.22427i	−0.624269	−	0.360422i
$656$		0			0
$657$	−41.4421	−	12.8431i	−1.61681	−	0.501059i
$658$		0			0
$659$	12.6862	−	21.9731i	0.494184	−	0.855952i	−0.505793	−	0.862655i	$-0.668800\pi$
$659$	12.6862	−	21.9731i	0.494184	−	0.855952i	0.999978	+	0.00670258i	$0.00213351\pi$
$660$		0			0
$661$	−8.56688	+	14.8383i	−0.333213	+	0.577142i	−0.983140	−	0.182855i	$-0.941466\pi$
$661$	−8.56688	+	14.8383i	−0.333213	+	0.577142i	0.649927	+	0.759997i	$0.274799\pi$
$662$		0			0
$663$	−22.6332	+	8.86562i	−0.878999	+	0.344312i
$664$		0			0
$665$	−23.4237	+	26.4308i	−0.908331	+	1.02494i
$666$		0			0
$667$	−29.2947	+	16.9133i	−1.13430	+	0.654887i
$668$		0			0
$669$	35.1874	+	28.0991i	1.36042	+	1.08637i
$670$		0			0
$671$	3.80424	−	6.58913i	0.146861	−	0.254371i
$672$		0			0
$673$	14.5870			0.562286			0.281143	−	0.959666i	$-0.409287\pi$
$673$	14.5870			0.562286			0.281143	+	0.959666i	$0.409287\pi$
$674$		0			0
$675$	−2.52335	+	1.71308i	−0.0971238	+	0.0659365i
$676$		0			0
$677$			2.25370i			0.0866167i	0.999062	+	0.0433083i	$0.0137898\pi$
$677$			2.25370i			0.0866167i	−0.999062	+	0.0433083i	$0.986210\pi$
$678$		0			0
$679$	8.05987	−	4.65337i	0.309309	−	0.178580i
$680$		0			0
$681$	−18.1005	−	46.2091i	−0.693614	−	1.77074i
$682$		0			0
$683$	21.4658			0.821365			0.410682	−	0.911778i	$-0.365291\pi$
$683$	21.4658			0.821365			0.410682	+	0.911778i	$0.365291\pi$
$684$		0			0
$685$	−40.3077			−1.54008
$686$		0			0
$687$	−15.5567	−	39.7148i	−0.593524	−	1.51522i
$688$		0			0
$689$	−45.2498	+	26.1250i	−1.72388	+	0.995282i
$690$		0			0
$691$		−	26.4019i		−	1.00438i	−0.864759	−	0.502188i	$-0.832529\pi$
$691$		−	26.4019i		−	1.00438i	0.864759	−	0.502188i	$-0.167471\pi$
$692$		0			0
$693$	−19.0173	−	20.5501i	−0.722408	−	0.780635i
$694$		0			0
$695$	14.8738			0.564195
$696$		0			0
$697$	16.0097	−	27.7296i	0.606410	−	1.05033i
$698$		0			0
$699$	−4.51210	−	3.60316i	−0.170663	−	0.136284i
$700$		0			0
$701$	17.0441	−	9.84042i	0.643747	−	0.371668i	−0.142309	−	0.989822i	$-0.545453\pi$
$701$	17.0441	−	9.84042i	0.643747	−	0.371668i	0.786057	+	0.618155i	$0.212119\pi$
$702$		0			0
$703$	−6.52712	−	19.5622i	−0.246175	−	0.737802i
$704$		0			0
$705$	−15.5605	+	6.09518i	−0.586041	+	0.229558i
$706$		0			0
$707$	−17.7934	+	30.8191i	−0.669191	+	1.15907i
$708$		0			0
$709$	−7.39816	+	12.8140i	−0.277844	+	0.481240i	−0.970849	−	0.239693i	$-0.922953\pi$
$709$	−7.39816	+	12.8140i	−0.277844	+	0.481240i	0.693005	+	0.720933i	$0.256286\pi$
$710$		0			0
$711$	5.30028	−	17.1029i	0.198776	−	0.641408i
$712$		0			0
$713$	9.16946	+	5.29399i	0.343399	+	0.198262i
$714$		0			0
$715$		−	26.1503i		−	0.977967i
$716$		0			0
$717$	16.1991	+	41.3549i	0.604967	+	1.54443i
$718$		0			0
$719$	15.6176	+	27.0504i	0.582437	+	1.00881i	0.995190	+	0.0979676i	$0.0312341\pi$
$719$	15.6176	+	27.0504i	0.582437	+	1.00881i	−0.412752	+	0.910843i	$0.635433\pi$
$720$		0			0
$721$	2.58696			0.0963432
$722$		0			0
$723$	−20.8482	−	3.15644i	−0.775354	−	0.117389i
$724$		0			0
$725$	−3.67636	+	2.12255i	−0.136537	+	0.0788295i
$726$		0			0
$727$	−33.8804	+	19.5608i	−1.25655	+	0.725471i	−0.972403	−	0.233309i	$-0.925045\pi$
$727$	−33.8804	+	19.5608i	−1.25655	+	0.725471i	−0.284150	+	0.958780i	$0.591711\pi$
$728$		0			0
$729$	16.7505	+	21.1760i	0.620388	+	0.784295i
$730$		0			0
$731$	12.9027	−	22.3481i	0.477223	−	0.826575i
$732$		0			0
$733$	36.4920			1.34786			0.673931	−	0.738795i	$-0.264605\pi$
$733$	36.4920			1.34786			0.673931	+	0.738795i	$0.264605\pi$
$734$		0			0
$735$	22.3912	+	17.8806i	0.825913	+	0.659536i
$736$		0			0
$737$	−4.66588	−	2.69384i	−0.171870	−	0.0992290i
$738$		0			0
$739$	19.4038	−	11.2028i	0.713782	−	0.412102i	−0.0986781	−	0.995119i	$-0.531461\pi$
$739$	19.4038	−	11.2028i	0.713782	−	0.412102i	0.812460	+	0.583017i	$0.198128\pi$
$740$		0			0
$741$	−6.63892	−	38.2658i	−0.243887	−	1.40573i
$742$		0			0
$743$	1.76634	+	3.05940i	0.0648008	+	0.112238i	0.896606	−	0.442830i	$-0.146025\pi$
$743$	1.76634	+	3.05940i	0.0648008	+	0.112238i	−0.831805	+	0.555068i	$0.812692\pi$
$744$		0			0
$745$	−17.7637	+	30.7676i	−0.650812	+	1.12724i
$746$		0			0
$747$	28.3109	−	26.1992i	1.03584	−	0.958577i
$748$		0			0
$749$			18.6663i			0.682050i
$750$		0			0
$751$	−17.9831	−	10.3826i	−0.656214	−	0.378865i	0.134619	−	0.990897i	$-0.457019\pi$
$751$	−17.9831	−	10.3826i	−0.656214	−	0.378865i	−0.790833	+	0.612032i	$0.790352\pi$
$752$		0			0
$753$	−2.42273	−	0.366804i	−0.0882894	−	0.0133671i
$754$		0			0
$755$	21.0385	+	36.4397i	0.765668	+	1.32618i
$756$		0			0
$757$	−11.5915	−	20.0770i	−0.421298	−	0.729710i	0.574768	−	0.818316i	$-0.305092\pi$
$757$	−11.5915	−	20.0770i	−0.421298	−	0.729710i	−0.996067	+	0.0886059i	$0.971759\pi$
$758$		0			0
$759$	19.3826	+	2.93454i	0.703542	+	0.106517i
$760$		0			0
$761$			27.6529i			1.00242i	0.865326	+	0.501209i	$0.167111\pi$
$761$			27.6529i			1.00242i	−0.865326	+	0.501209i	$0.832889\pi$
$762$		0			0
$763$	−29.0635	+	16.7798i	−1.05217	+	0.607471i
$764$		0			0
$765$	3.80373	+	16.7673i	0.137524	+	0.606221i
$766$		0			0
$767$	−66.1713			−2.38931
$768$		0			0
$769$	−15.3455	+	26.5791i	−0.553372	+	0.958468i	0.444656	+	0.895701i	$0.353326\pi$
$769$	−15.3455	+	26.5791i	−0.553372	+	0.958468i	−0.998028	+	0.0627669i	$0.980008\pi$
$770$		0			0
$771$	−5.29462	+	34.9709i	−0.190681	+	1.25945i
$772$		0			0
$773$	−26.8920	−	15.5261i	−0.967237	−	0.558434i	−0.0688440	−	0.997627i	$-0.521931\pi$
$773$	−26.8920	−	15.5261i	−0.967237	−	0.558434i	−0.898393	+	0.439193i	$0.855264\pi$
$774$		0			0
$775$	1.15073	+	0.664373i	0.0413353	+	0.0238650i
$776$		0			0
$777$	−29.4278	+	11.5271i	−1.05572	+	0.413534i
$778$		0			0
$779$	38.2872	+	33.9311i	1.37178	+	1.21571i
$780$		0			0
$781$	−3.12476	−	5.41225i	−0.111813	−	0.193665i
$782$		0			0
$783$	21.1084	+	31.0925i	0.754353	+	1.11115i
$784$		0			0
$785$	−7.59352	−	4.38412i	−0.271024	−	0.156476i
$786$		0			0
$787$		−	17.2100i		−	0.613470i	−0.951795	−	0.306735i	$-0.900764\pi$
$787$		−	17.2100i		−	0.613470i	0.951795	−	0.306735i	$-0.0992365\pi$
$788$		0			0
$789$	1.90602	−	2.38684i	0.0678562	−	0.0849739i
$790$		0			0
$791$	4.92394			0.175075
$792$		0			0
$793$	−8.08696	−	14.0070i	−0.287176	−	0.497404i
$794$		0			0
$795$	13.4794	+	34.4117i	0.478064	+	1.22046i
$796$		0			0
$797$		−	14.5989i		−	0.517119i	−0.965995	−	0.258560i	$-0.916752\pi$
$797$		−	14.5989i		−	0.517119i	0.965995	−	0.258560i	$-0.0832479\pi$
$798$		0			0
$799$		−	12.5302i		−	0.443287i
$800$		0			0
$801$	−18.4380	+	4.18276i	−0.651476	+	0.147790i
$802$		0			0
$803$	17.4984	+	30.3082i	0.617507	+	1.06955i
$804$		0			0
$805$	−37.8946			−1.33561
$806$		0			0
$807$	25.4077	+	20.2894i	0.894394	+	0.714222i
$808$		0			0
$809$			33.4557i			1.17624i	0.808774	+	0.588120i	$0.200132\pi$
$809$			33.4557i			1.17624i	−0.808774	+	0.588120i	$0.799868\pi$
$810$		0			0
$811$	47.1461	+	27.2198i	1.65552	+	0.955817i	0.974743	+	0.223329i	$0.0716923\pi$
$811$	47.1461	+	27.2198i	1.65552	+	0.955817i	0.680780	+	0.732488i	$0.261641\pi$
$812$		0			0
$813$	−21.5822	−	17.2345i	−0.756919	−	0.604441i
$814$		0			0
$815$	1.47417	+	2.55334i	0.0516381	+	0.0894398i
$816$		0			0
$817$	30.8568	+	27.3461i	1.07954	+	0.956719i
$818$		0			0
$819$	−58.0456	+	13.1679i	−2.02828	+	0.460124i
$820$		0			0
$821$	−29.8899	−	17.2570i	−1.04317	−	0.602272i	−0.122438	−	0.992476i	$-0.539071\pi$
$821$	−29.8899	−	17.2570i	−1.04317	−	0.602272i	−0.920728	+	0.390204i	$0.872404\pi$
$822$		0			0
$823$	−9.12453	−	5.26805i	−0.318061	−	0.183633i	0.332467	−	0.943115i	$-0.392119\pi$
$823$	−9.12453	−	5.26805i	−0.318061	−	0.183633i	−0.650528	+	0.759482i	$0.725452\pi$
$824$		0			0
$825$	2.43243	+	0.368272i	0.0846862	+	0.0128216i
$826$		0			0
$827$	11.5782	−	20.0541i	0.402614	−	0.697348i	−0.591427	−	0.806359i	$-0.701435\pi$
$827$	11.5782	−	20.0541i	0.402614	−	0.697348i	0.994041	+	0.109011i	$0.0347684\pi$
$828$		0			0
$829$	7.98961			0.277491			0.138745	−	0.990328i	$-0.455693\pi$
$829$	7.98961			0.277491			0.138745	+	0.990328i	$0.455693\pi$
$830$		0			0
$831$	−1.17239	−	2.99301i	−0.0406698	−	0.103826i
$832$		0			0
$833$	−18.6064	+	10.7424i	−0.644674	+	0.372203i
$834$		0			0
$835$		−	10.1789i		−	0.352256i
$836$		0			0
$837$	5.12476	−	10.5880i	0.177138	−	0.365974i
$838$		0			0
$839$	12.1808	+	21.0977i	0.420527	+	0.728375i	0.995991	−	0.0894527i	$-0.0285118\pi$
$839$	12.1808	+	21.0977i	0.420527	+	0.728375i	−0.575464	+	0.817827i	$0.695178\pi$
$840$		0			0
$841$	11.6538	+	20.1850i	0.401856	+	0.696035i
$842$		0			0
$843$	3.04873	−	20.1368i	0.105004	−	0.693548i
$844$		0			0
$845$	−24.4915	−	14.1402i	−0.842534	−	0.486437i
$846$		0			0
$847$		−	19.8401i		−	0.681716i
$848$		0			0
$849$	−7.03208	−	5.61550i	−0.241340	−	0.192723i
$850$		0			0
$851$	11.0639	−	19.1632i	0.379266	−	0.656907i
$852$		0			0
$853$	12.6933	+	21.9854i	0.434610	+	0.752767i	0.997264	−	0.0739261i	$-0.0235529\pi$
$853$	12.6933	+	21.9854i	0.434610	+	0.752767i	−0.562654	+	0.826693i	$0.690220\pi$
$854$		0			0
$855$	−27.4642	+	0.591260i	−0.939255	+	0.0202207i
$856$		0			0
$857$	−24.6024	+	14.2042i	−0.840401	+	0.485206i	−0.857400	−	0.514650i	$-0.827922\pi$
$857$	−24.6024	+	14.2042i	−0.840401	+	0.485206i	0.0169995	+	0.999855i	$0.494589\pi$
$858$		0			0
$859$	32.1077	+	18.5374i	1.09550	+	0.632487i	0.935035	−	0.354554i	$-0.115367\pi$
$859$	32.1077	+	18.5374i	1.09550	+	0.632487i	0.160465	+	0.987042i	$0.448701\pi$
$860$		0			0
$861$	48.9244	−	61.2663i	1.66734	−	2.08795i
$862$		0			0
$863$	7.15205			0.243459			0.121729	−	0.992563i	$-0.461156\pi$
$863$	7.15205			0.243459			0.121729	+	0.992563i	$0.461156\pi$
$864$		0			0
$865$	1.18360	−	2.05006i	0.0402436	−	0.0697040i
$866$		0			0
$867$	16.3670	+	2.47798i	0.555853	+	0.0841567i
$868$		0			0
$869$	−12.5080	+	7.22149i	−0.424305	+	0.244972i
$870$		0			0
$871$	−9.91861	+	5.72651i	−0.336079	+	0.194035i
$872$		0			0
$873$	6.91470	+	2.14290i	0.234027	+	0.0725263i
$874$		0			0
$875$	−45.2664			−1.53028
$876$		0			0
$877$	5.93243	+	10.2753i	0.200324	+	0.346971i	0.948633	−	0.316379i	$-0.102467\pi$
$877$	5.93243	+	10.2753i	0.200324	+	0.346971i	−0.748309	+	0.663350i	$0.769134\pi$
$878$		0			0
$879$	−22.3513	+	8.75520i	−0.753889	+	0.295306i
$880$		0			0
$881$		−	28.9982i		−	0.976975i	−0.872571	−	0.488488i	$-0.837549\pi$
$881$		−	28.9982i		−	0.976975i	0.872571	−	0.488488i	$-0.162451\pi$
$882$		0			0
$883$	19.4922	+	11.2538i	0.655966	+	0.378722i	0.790738	−	0.612155i	$-0.209697\pi$
$883$	19.4922	+	11.2538i	0.655966	+	0.378722i	−0.134772	+	0.990877i	$0.543030\pi$
$884$		0			0
$885$	−7.00639	+	46.2770i	−0.235517	+	1.55558i
$886$		0			0
$887$	−16.5442	+	28.6555i	−0.555501	+	0.962157i	0.442363	+	0.896836i	$0.354140\pi$
$887$	−16.5442	+	28.6555i	−0.555501	+	0.962157i	−0.997864	+	0.0653204i	$0.979193\pi$
$888$		0			0
$889$	−15.8752	+	27.4967i	−0.532438	+	0.922210i
$890$		0			0
$891$	1.68489	−	21.7137i	0.0564460	−	0.727437i
$892$		0			0
$893$	19.6148	+	4.00787i	0.656386	+	0.134118i
$894$		0			0
$895$	−8.65179	+	4.99511i	−0.289197	+	0.166968i
$896$		0			0
$897$	26.0039	−	32.5637i	0.868245	−	1.08727i
$898$		0			0
$899$	8.18633	−	14.1791i	0.273030	−	0.472901i
$900$		0			0
$901$	−27.7103			−0.923165
$902$		0			0
$903$	39.4296	−	49.3763i	1.31214	−	1.64314i
$904$		0			0
$905$			26.6820i			0.886940i
$906$		0			0
$907$	−32.1834	+	18.5811i	−1.06863	+	0.616976i	−0.927808	−	0.373058i	$-0.878309\pi$
$907$	−32.1834	+	18.5811i	−1.06863	+	0.616976i	−0.140826	+	0.990034i	$0.544976\pi$
$908$		0			0
$909$	−26.9949	+	6.12393i	−0.895365	+	0.203118i
$910$		0			0
$911$	0.180469			0.00597922			0.00298961	−	0.999996i	$-0.499048\pi$
$911$	0.180469			0.00597922			0.00298961	+	0.999996i	$0.499048\pi$
$912$		0			0
$913$	−31.1144			−1.02974
$914$		0			0
$915$	−10.6521	+	4.17253i	−0.352147	+	0.137939i
$916$		0			0
$917$	29.3329	−	16.9354i	0.968659	−	0.559255i
$918$		0			0
$919$			43.0085i			1.41872i	0.704846	+	0.709360i	$0.251016\pi$
$919$			43.0085i			1.41872i	−0.704846	+	0.709360i	$0.748984\pi$
$920$		0			0
$921$	37.3978	+	29.8641i	1.23230	+	0.984057i
$922$		0			0
$923$	−13.2851			−0.437284
$924$		0			0
$925$	1.38847	−	2.40490i	0.0456526	−	0.0790727i
$926$		0			0
$927$	1.36672	+	1.47688i	0.0448889	+	0.0485070i
$928$		0			0
$929$	−26.0080	+	15.0157i	−0.853296	+	0.492651i	−0.861762	−	0.507313i	$-0.830639\pi$
$929$	−26.0080	+	15.0157i	−0.853296	+	0.492651i	0.00846555	+	0.999964i	$0.497305\pi$
$930$		0			0
$931$	−10.8648	−	32.5626i	−0.356081	−	1.06720i
$932$		0			0
$933$	13.6668	+	34.8901i	0.447431	+	1.14225i
$934$		0			0
$935$	6.93431	−	12.0106i	0.226776	−	0.392788i
$936$		0			0
$937$	10.4473	−	18.0953i	0.341299	−	0.591147i	−0.643375	−	0.765551i	$-0.722467\pi$
$937$	10.4473	−	18.0953i	0.341299	−	0.591147i	0.984674	+	0.174404i	$0.0557999\pi$
$938$		0			0
$939$	−7.55749	−	1.14421i	−0.246629	−	0.0373399i
$940$		0			0
$941$	−19.5365	−	11.2794i	−0.636872	−	0.367698i	0.146536	−	0.989205i	$-0.453187\pi$
$941$	−19.5365	−	11.2794i	−0.636872	−	0.367698i	−0.783409	+	0.621507i	$0.786521\pi$
$942$		0			0
$943$			54.8935i			1.78758i
$944$		0			0
$945$	3.06299	+	41.9885i	0.0996391	+	1.36589i
$946$		0			0
$947$	12.7343	+	22.0565i	0.413811	+	0.716741i	0.995303	−	0.0968108i	$-0.0308642\pi$
$947$	12.7343	+	22.0565i	0.413811	+	0.716741i	−0.581492	+	0.813552i	$0.697531\pi$
$948$		0			0
$949$	74.3956			2.41498
$950$		0			0
$951$	−1.21884	+	8.05040i	−0.0395236	+	0.261052i
$952$		0			0
$953$	−27.1758	+	15.6900i	−0.880311	+	0.508248i	−0.870761	−	0.491707i	$-0.836373\pi$
$953$	−27.1758	+	15.6900i	−0.880311	+	0.508248i	−0.00955016	+	0.999954i	$0.503040\pi$
$954$		0			0
$955$	−9.59262	+	5.53830i	−0.310410	+	0.179215i
$956$		0			0
$957$	4.53781	−	29.9721i	0.146686	−	0.968861i
$958$		0			0
$959$	37.0016	−	64.0886i	1.19484	−	2.06953i
$960$		0			0
$961$	25.8752			0.834685
$962$		0			0
$963$	−10.6565	+	9.86159i	−0.343399	+	0.317785i
$964$		0			0
$965$	0.578626	+	0.334070i	0.0186266	+	0.0107541i
$966$		0			0
$967$	7.55709	−	4.36309i	0.243020	−	0.140307i	−0.373544	−	0.927612i	$-0.621858\pi$
$967$	7.55709	−	4.36309i	0.243020	−	0.140307i	0.616564	+	0.787305i	$0.288524\pi$
$968$		0			0
$969$	7.09778	−	19.3355i	0.228014	−	0.621146i
$970$		0			0
$971$	−4.14415	−	7.17787i	−0.132992	−	0.230349i	0.791837	−	0.610733i	$-0.209125\pi$
$971$	−4.14415	−	7.17787i	−0.132992	−	0.230349i	−0.924829	+	0.380384i	$0.875792\pi$
$972$		0			0
$973$	−13.6538	+	23.6491i	−0.437722	+	0.758156i
$974$		0			0
$975$	3.26338	−	4.08661i	0.104512	−	0.130876i
$976$		0			0
$977$		−	27.3720i		−	0.875707i	−0.899046	−	0.437853i	$-0.855739\pi$
$977$		−	27.3720i		−	0.875707i	0.899046	−	0.437853i	$-0.144261\pi$
$978$		0			0
$979$	13.2074	+	7.62528i	0.422109	+	0.243705i
$980$		0			0
$981$	−24.9341	−	7.72721i	−0.796084	−	0.246711i
$982$		0			0
$983$	10.1821	+	17.6360i	0.324760	+	0.562501i	0.981464	−	0.191648i	$-0.0613832\pi$
$983$	10.1821	+	17.6360i	0.324760	+	0.562501i	−0.656704	+	0.754149i	$0.728050\pi$
$984$		0			0
$985$	21.0423	+	36.4463i	0.670464	+	1.16128i
$986$		0			0
$987$	4.59293	−	30.3362i	0.146195	−	0.965611i
$988$		0			0
$989$			44.2403i			1.40676i
$990$		0			0
$991$	39.5977	−	22.8617i	1.25786	−	0.726227i	0.285204	−	0.958467i	$-0.407939\pi$
$991$	39.5977	−	22.8617i	1.25786	−	0.726227i	0.972659	+	0.232240i	$0.0746053\pi$
$992$		0			0
$993$	21.7203	−	8.50804i	0.689272	−	0.269994i
$994$		0			0
$995$	−10.2024			−0.323436
$996$		0			0
$997$	12.2609	−	21.2364i	0.388305	−	0.672565i	−0.603916	−	0.797048i	$-0.706394\pi$
$997$	12.2609	−	21.2364i	0.388305	−	0.672565i	0.992222	+	0.124483i	$0.0397272\pi$
$998$		0			0
$999$	−22.1278	−	10.7102i	−0.700093	−	0.338857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bh.f.767.5	yes	24
3.2	odd	2	inner	912.2.bh.f.767.9	yes	24
4.3	odd	2	inner	912.2.bh.f.767.8	yes	24
12.11	even	2	inner	912.2.bh.f.767.4	yes	24
19.11	even	3	inner	912.2.bh.f.239.4	✓	24
57.11	odd	6	inner	912.2.bh.f.239.8	yes	24
76.11	odd	6	inner	912.2.bh.f.239.9	yes	24
228.11	even	6	inner	912.2.bh.f.239.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bh.f.239.4	✓	24	19.11	even	3	inner
912.2.bh.f.239.5	yes	24	228.11	even	6	inner
912.2.bh.f.239.8	yes	24	57.11	odd	6	inner
912.2.bh.f.239.9	yes	24	76.11	odd	6	inner
912.2.bh.f.767.4	yes	24	12.11	even	2	inner
912.2.bh.f.767.5	yes	24	1.1	even	1	trivial
912.2.bh.f.767.8	yes	24	4.3	odd	2	inner
912.2.bh.f.767.9	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631725 - 1.61274i) q^{3} +(1.81928 - 1.05036i) q^{5} +3.85684i q^{7} +(-2.20185 + 2.03761i) q^{9} +2.41989 q^{11} +(2.57207 - 4.45496i) q^{13} +(-2.84324 - 2.27048i) q^{15} +(2.36265 - 1.36408i) q^{17} +(1.37962 + 4.13481i) q^{19} +(6.22008 - 2.43646i) q^{21} +(-2.33855 + 4.05049i) q^{23} +(-0.293478 + 0.508318i) q^{25} +(4.67710 + 2.26379i) q^{27} +(6.26345 + 3.61620i) q^{29} -2.26379i q^{31} +(-1.52870 - 3.90265i) q^{33} +(4.05108 + 7.01668i) q^{35} -4.73110 q^{37} +(-8.80952 - 1.33377i) q^{39} +(10.1642 - 5.86833i) q^{41} +(8.19167 - 4.72946i) q^{43} +(-1.86555 + 6.01973i) q^{45} +(2.29646 - 3.97759i) q^{47} -7.87524 q^{49} +(-3.69244 - 2.94861i) q^{51} +(-8.79637 - 5.07859i) q^{53} +(4.40246 - 2.54176i) q^{55} +(5.79682 - 4.83703i) q^{57} +(-6.43172 - 11.1401i) q^{59} +(1.57207 - 2.72291i) q^{61} +(-7.85875 - 8.49218i) q^{63} -10.8064i q^{65} +(-1.92814 - 1.11321i) q^{67} +(8.00969 + 1.21268i) q^{69} +(-1.29128 - 2.23657i) q^{71} +(7.23110 + 12.5246i) q^{73} +(1.00518 + 0.152185i) q^{75} +9.33313i q^{77} +(-5.16883 + 2.98423i) q^{79} +(0.696268 - 8.97303i) q^{81} -12.8578 q^{83} +(2.86555 - 4.96328i) q^{85} +(1.87521 - 12.3857i) q^{87} +(5.45784 + 3.15109i) q^{89} +(17.1821 + 9.92007i) q^{91} +(-3.65091 + 1.43009i) q^{93} +(6.85297 + 6.07328i) q^{95} +(-1.20652 - 2.08976i) q^{97} +(-5.32823 + 4.93079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) \) 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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