LMFDB - Embedded newform 792.2.r.f.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(289,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

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

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

chi := DirichletCharacter("792.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.r (of order $5$, degree $4$, 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:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 264)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			577.2
Root			$1.71634 - 0.232753i$ of defining polynomial
Character	$\chi$	$=$	792.577
Dual form			792.2.r.f.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.464601 - 1.42989i) q^{5} +(-2.96808 + 2.15644i) q^{7} +O(q^{10})$	$q+(0.464601 - 1.42989i) q^{5} +(-2.96808 + 2.15644i) q^{7} +(-2.46808 - 2.21553i) q^{11} +(1.53888 + 4.73618i) q^{13} +(-2.17879 + 6.70563i) q^{17} +(-3.37540 - 2.45238i) q^{19} +1.12151 q^{23} +(2.21634 + 1.61027i) q^{25} +(-5.82781 + 4.23415i) q^{29} +(1.60835 + 4.94999i) q^{31} +(1.70450 + 5.24592i) q^{35} +(3.52536 - 2.56132i) q^{37} +(1.20723 + 0.877104i) q^{41} -9.12151 q^{43} +(2.65343 + 1.92783i) q^{47} +(1.99616 - 6.14356i) q^{49} +(-0.226382 - 0.696733i) q^{53} +(-4.31465 + 2.49976i) q^{55} +(-11.1049 + 8.06819i) q^{59} +(3.25795 - 10.0269i) q^{61} +7.48721 q^{65} +12.5655 q^{67} +(0.549742 - 1.69193i) q^{71} +(-12.0639 + 8.76492i) q^{73} +(12.1031 + 1.25361i) q^{77} +(-1.64339 - 5.05784i) q^{79} +(-1.86009 + 5.72476i) q^{83} +(8.57607 + 6.23088i) q^{85} -5.96435 q^{89} +(-14.7808 - 10.7389i) q^{91} +(-5.07485 + 3.68710i) q^{95} +(0.961121 + 2.95803i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{5} - 5 q^{7}+O(q^{10}) $ 8 * q + q^5 - 5 * q^7	$ 8 q + q^{5} - 5 q^{7} - q^{11} - q^{13} + 4 q^{17} - 2 q^{19} - 16 q^{23} + 7 q^{25} + 7 q^{29} + 29 q^{31} + 20 q^{35} + 13 q^{37} + 23 q^{41} - 48 q^{43} + 15 q^{47} - 11 q^{49} - 9 q^{53} - 22 q^{55} - 12 q^{59} + 9 q^{61} - 42 q^{65} + 38 q^{67} + 41 q^{71} - 25 q^{73} + 55 q^{77} + 11 q^{79} - 23 q^{83} + 23 q^{85} - 12 q^{89} - 35 q^{91} - 29 q^{95} + 21 q^{97}+O(q^{100}) $ 8 * q + q^5 - 5 * q^7 - q^11 - q^13 + 4 * q^17 - 2 * q^19 - 16 * q^23 + 7 * q^25 + 7 * q^29 + 29 * q^31 + 20 * q^35 + 13 * q^37 + 23 * q^41 - 48 * q^43 + 15 * q^47 - 11 * q^49 - 9 * q^53 - 22 * q^55 - 12 * q^59 + 9 * q^61 - 42 * q^65 + 38 * q^67 + 41 * q^71 - 25 * q^73 + 55 * q^77 + 11 * q^79 - 23 * q^83 + 23 * q^85 - 12 * q^89 - 35 * q^91 - 29 * q^95 + 21 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	0.464601	−	1.42989i	0.207776	−	0.639468i	−0.791812	−	0.610765i	$-0.790862\pi$
$5$	0.464601	−	1.42989i	0.207776	−	0.639468i	0.999588	−	0.0287035i	$-0.00913787\pi$
$6$		0			0
$7$	−2.96808	+	2.15644i	−1.12183	+	0.815057i	−0.984485	−	0.175467i	$-0.943857\pi$
$7$	−2.96808	+	2.15644i	−1.12183	+	0.815057i	−0.137344	+	0.990523i	$0.543857\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.46808	−	2.21553i	−0.744154	−	0.668008i
$11$	−2.46808	−	2.21553i	−0.744154	−	0.668008i
$12$		0			0
$13$	1.53888	+	4.73618i	0.426808	+	1.31358i	0.901252	+	0.433295i	$0.142649\pi$
$13$	1.53888	+	4.73618i	0.426808	+	1.31358i	−0.474444	+	0.880286i	$0.657351\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.17879	+	6.70563i	−0.528434	+	1.62635i	0.228988	+	0.973429i	$0.426458\pi$
$17$	−2.17879	+	6.70563i	−0.528434	+	1.62635i	−0.757423	+	0.652925i	$0.773542\pi$
$18$		0			0
$19$	−3.37540	−	2.45238i	−0.774371	−	0.562613i	0.128913	−	0.991656i	$-0.458851\pi$
$19$	−3.37540	−	2.45238i	−0.774371	−	0.562613i	−0.903284	+	0.429042i	$0.858851\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.12151			0.233852			0.116926	−	0.993141i	$-0.462696\pi$
$23$	1.12151			0.233852			0.116926	+	0.993141i	$0.462696\pi$
$24$		0			0
$25$	2.21634	+	1.61027i	0.443268	+	0.322053i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.82781	+	4.23415i	−1.08220	+	0.786263i	−0.978065	−	0.208301i	$-0.933207\pi$
$29$	−5.82781	+	4.23415i	−1.08220	+	0.786263i	−0.104133	+	0.994563i	$0.533207\pi$
$30$		0			0
$31$	1.60835	+	4.94999i	0.288868	+	0.889044i	0.985213	+	0.171336i	$0.0548085\pi$
$31$	1.60835	+	4.94999i	0.288868	+	0.889044i	−0.696345	+	0.717707i	$0.745192\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.70450	+	5.24592i	0.288114	+	0.886723i
$36$		0			0
$37$	3.52536	−	2.56132i	0.579565	−	0.421079i	−0.259002	−	0.965877i	$-0.583394\pi$
$37$	3.52536	−	2.56132i	0.579565	−	0.421079i	0.838567	+	0.544798i	$0.183394\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.20723	+	0.877104i	0.188538	+	0.136981i	0.678050	−	0.735016i	$-0.262825\pi$
$41$	1.20723	+	0.877104i	0.188538	+	0.136981i	−0.489512	+	0.871996i	$0.662825\pi$
$42$		0			0
$43$	−9.12151			−1.39102			−0.695509	−	0.718517i	$-0.744821\pi$
$43$	−9.12151			−1.39102			−0.695509	+	0.718517i	$0.744821\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.65343	+	1.92783i	0.387043	+	0.281203i	0.764243	−	0.644929i	$-0.223113\pi$
$47$	2.65343	+	1.92783i	0.387043	+	0.281203i	−0.377200	+	0.926132i	$0.623113\pi$
$48$		0			0
$49$	1.99616	−	6.14356i	0.285166	−	0.877652i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.226382	−	0.696733i	−0.0310960	−	0.0957036i	0.934304	−	0.356477i	$-0.116022\pi$
$53$	−0.226382	−	0.696733i	−0.0310960	−	0.0957036i	−0.965400	+	0.260774i	$0.916022\pi$
$54$		0			0
$55$	−4.31465	+	2.49976i	−0.581787	+	0.337067i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.1049	+	8.06819i	−1.44574	+	1.05039i	−0.458932	+	0.888471i	$0.651768\pi$
$59$	−11.1049	+	8.06819i	−1.44574	+	1.05039i	−0.986804	+	0.161918i	$0.948232\pi$
$60$		0			0
$61$	3.25795	−	10.0269i	0.417137	−	1.28382i	−0.493188	−	0.869923i	$-0.664169\pi$
$61$	3.25795	−	10.0269i	0.417137	−	1.28382i	0.910325	−	0.413894i	$-0.135831\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.48721			0.928674
$66$		0			0
$67$	12.5655			1.53511			0.767557	−	0.640980i	$-0.221472\pi$
$67$	12.5655			1.53511			0.767557	+	0.640980i	$0.221472\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.549742	−	1.69193i	0.0652424	−	0.200795i	−0.913121	−	0.407688i	$-0.866335\pi$
$71$	0.549742	−	1.69193i	0.0652424	−	0.200795i	0.978364	+	0.206893i	$0.0663351\pi$
$72$		0			0
$73$	−12.0639	+	8.76492i	−1.41197	+	1.02586i	−0.418938	+	0.908015i	$0.637598\pi$
$73$	−12.0639	+	8.76492i	−1.41197	+	1.02586i	−0.993032	+	0.117842i	$0.962402\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	12.1031	+	1.25361i	1.37928	+	0.142863i
$78$		0			0
$79$	−1.64339	−	5.05784i	−0.184896	−	0.569051i	0.815051	−	0.579390i	$-0.196709\pi$
$79$	−1.64339	−	5.05784i	−0.184896	−	0.569051i	−0.999947	+	0.0103384i	$0.996709\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.86009	+	5.72476i	−0.204171	+	0.628374i	0.795575	+	0.605855i	$0.207169\pi$
$83$	−1.86009	+	5.72476i	−0.204171	+	0.628374i	−0.999746	+	0.0225195i	$0.992831\pi$
$84$		0			0
$85$	8.57607	+	6.23088i	0.930206	+	0.675834i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.96435			−0.632220			−0.316110	−	0.948722i	$-0.602377\pi$
$89$	−5.96435			−0.632220			−0.316110	+	0.948722i	$0.602377\pi$
$90$		0			0
$91$	−14.7808	−	10.7389i	−1.54945	−	1.12574i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.07485	+	3.68710i	−0.520669	+	0.378288i
$96$		0			0
$97$	0.961121	+	2.95803i	0.0975870	+	0.300342i	0.987919	−	0.154969i	$-0.0495279\pi$
$97$	0.961121	+	2.95803i	0.0975870	+	0.300342i	−0.890332	+	0.455311i	$0.849528\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.99401	−	6.13694i	−0.198412	−	0.610649i	−0.999920	−	0.0126647i	$-0.995969\pi$
$101$	−1.99401	−	6.13694i	−0.198412	−	0.610649i	0.801508	−	0.597984i	$-0.204031\pi$
$102$		0			0
$103$	−2.30809	+	1.67692i	−0.227423	+	0.165232i	−0.695662	−	0.718370i	$-0.744889\pi$
$103$	−2.30809	+	1.67692i	−0.227423	+	0.165232i	0.468239	+	0.883602i	$0.344889\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.40076	−	1.74426i	−0.232090	−	0.168624i	0.465662	−	0.884963i	$-0.345816\pi$
$107$	−2.40076	−	1.74426i	−0.232090	−	0.168624i	−0.697752	+	0.716339i	$0.745816\pi$
$108$		0			0
$109$	−4.70124			−0.450298			−0.225149	−	0.974324i	$-0.572287\pi$
$109$	−4.70124			−0.450298			−0.225149	+	0.974324i	$0.572287\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.392582	−	0.285228i	−0.0369310	−	0.0268320i	0.569167	−	0.822222i	$-0.307266\pi$
$113$	−0.392582	−	0.285228i	−0.0369310	−	0.0268320i	−0.606098	+	0.795390i	$0.707266\pi$
$114$		0			0
$115$	0.521056	−	1.60365i	0.0485888	−	0.149541i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.99344	−	24.6013i	−0.732757	−	2.25520i
$120$		0			0
$121$	1.18285	+	10.9362i	0.107531	+	0.994202i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.41393	−	6.83962i	0.842007	−	0.611754i
$126$		0			0
$127$	0.428380	−	1.31842i	0.0380126	−	0.116991i	−0.930250	−	0.366927i	$-0.880410\pi$
$127$	0.428380	−	1.31842i	0.0380126	−	0.116991i	0.968262	+	0.249937i	$0.0804098\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.503480			−0.0439892			−0.0219946	−	0.999758i	$-0.507002\pi$
$131$	−0.503480			−0.0439892			−0.0219946	+	0.999758i	$0.507002\pi$
$132$		0			0
$133$	15.3069			1.32727
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.85005	−	8.77154i	0.243496	−	0.749403i	−0.752384	−	0.658724i	$-0.771096\pi$
$137$	2.85005	−	8.77154i	0.243496	−	0.749403i	0.995880	−	0.0906789i	$-0.0289037\pi$
$138$		0			0
$139$	12.9909	−	9.43846i	1.10188	−	0.800560i	0.120511	−	0.992712i	$-0.461547\pi$
$139$	12.9909	−	9.43846i	1.10188	−	0.800560i	0.981365	+	0.192152i	$0.0615466\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.69508	−	15.0987i	0.559871	−	1.26262i
$144$		0			0
$145$	3.34679	+	10.3003i	0.277935	+	0.855397i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.08228	−	12.5640i	0.334433	−	1.02928i	−0.632567	−	0.774506i	$-0.717999\pi$
$149$	4.08228	−	12.5640i	0.334433	−	1.02928i	0.967000	−	0.254775i	$-0.0820012\pi$
$150$		0			0
$151$	13.3820	+	9.72260i	1.08901	+	0.791214i	0.979232	−	0.202742i	$-0.0649853\pi$
$151$	13.3820	+	9.72260i	1.08901	+	0.791214i	0.109780	+	0.993956i	$0.464985\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.82520			0.628535
$156$		0			0
$157$	−9.15401	−	6.65078i	−0.730569	−	0.530790i	0.159174	−	0.987251i	$-0.449117\pi$
$157$	−9.15401	−	6.65078i	−0.730569	−	0.530790i	−0.889744	+	0.456461i	$0.849117\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.32874	+	2.41847i	−0.262342	+	0.190602i
$162$		0			0
$163$	4.91138	+	15.1157i	0.384689	+	1.18395i	0.936706	+	0.350118i	$0.113858\pi$
$163$	4.91138	+	15.1157i	0.384689	+	1.18395i	−0.552017	+	0.833833i	$0.686142\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.80518	+	5.55578i	0.139689	+	0.429919i	0.996290	−	0.0860608i	$-0.0274279\pi$
$167$	1.80518	+	5.55578i	0.139689	+	0.429919i	−0.856601	+	0.515980i	$0.827428\pi$
$168$		0			0
$169$	−9.54606	+	6.93562i	−0.734312	+	0.533509i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.8758	+	9.35482i	0.978929	+	0.711234i	0.957469	−	0.288536i	$-0.0931685\pi$
$173$	12.8758	+	9.35482i	0.978929	+	0.711234i	0.0214602	+	0.999770i	$0.493168\pi$
$174$		0			0
$175$	−10.0507			−0.759763
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.26300	−	0.917624i	−0.0944012	−	0.0685865i	0.539583	−	0.841932i	$-0.318582\pi$
$179$	−1.26300	−	0.917624i	−0.0944012	−	0.0685865i	−0.633985	+	0.773346i	$0.718582\pi$
$180$		0			0
$181$	7.47074	−	22.9926i	0.555296	−	1.70902i	−0.139866	−	0.990171i	$-0.544667\pi$
$181$	7.47074	−	22.9926i	0.555296	−	1.70902i	0.695161	−	0.718854i	$-0.255333\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.02454	−	6.23088i	−0.148847	−	0.458104i
$186$		0			0
$187$	20.2340	−	11.7229i	1.47965	−	0.857260i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.46152	−	6.14765i	0.612254	−	0.444829i	−0.237953	−	0.971277i	$-0.576477\pi$
$191$	8.46152	−	6.14765i	0.612254	−	0.444829i	0.850207	+	0.526448i	$0.176477\pi$
$192$		0			0
$193$	6.36461	−	19.5883i	0.458135	−	1.40999i	−0.409281	−	0.912409i	$-0.634220\pi$
$193$	6.36461	−	19.5883i	0.458135	−	1.40999i	0.867415	−	0.497585i	$-0.165780\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.1986			1.08285			0.541426	−	0.840748i	$-0.317885\pi$
$197$	15.1986			1.08285			0.541426	+	0.840748i	$0.317885\pi$
$198$		0			0
$199$	−26.6069			−1.88611			−0.943055	−	0.332637i	$-0.892062\pi$
$199$	−26.6069			−1.88611			−0.943055	+	0.332637i	$0.892062\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.16673	−	25.1346i	0.573192	−	1.76410i
$204$		0			0
$205$	1.81505	−	1.31871i	0.126768	−	0.0921026i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.89746	+	13.5310i	0.200421	+	0.935957i
$210$		0			0
$211$	0.0615785	+	0.189519i	0.00423924	+	0.0130470i	0.953154	−	0.302486i	$-0.0978166\pi$
$211$	0.0615785	+	0.189519i	0.00423924	+	0.0130470i	−0.948915	+	0.315533i	$0.897817\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.23786	+	13.0428i	−0.289020	+	0.889512i
$216$		0			0
$217$	−15.4480	−	11.2237i	−1.04868	−	0.761912i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−35.1120			−2.36189
$222$		0			0
$223$	−5.47655	−	3.97894i	−0.366737	−	0.266450i	0.389120	−	0.921187i	$-0.372779\pi$
$223$	−5.47655	−	3.97894i	−0.366737	−	0.266450i	−0.755856	+	0.654737i	$0.772779\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.48085	+	1.80244i	−0.164660	+	0.119632i	−0.667064	−	0.745001i	$-0.732449\pi$
$227$	−2.48085	+	1.80244i	−0.164660	+	0.119632i	0.502404	+	0.864633i	$0.332449\pi$
$228$		0			0
$229$	5.19160	+	15.9781i	0.343071	+	1.05586i	0.962609	+	0.270896i	$0.0873200\pi$
$229$	5.19160	+	15.9781i	0.343071	+	1.05586i	−0.619538	+	0.784967i	$0.712680\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.88294	−	24.2612i	−0.516429	−	1.58940i	−0.780668	−	0.624946i	$-0.785121\pi$
$233$	−7.88294	−	24.2612i	−0.516429	−	1.58940i	0.264239	−	0.964457i	$-0.414879\pi$
$234$		0			0
$235$	3.98938	−	2.89846i	0.260239	−	0.189074i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	17.4236	+	12.6590i	1.12704	+	0.818842i	0.985261	−	0.171056i	$-0.0547179\pi$
$239$	17.4236	+	12.6590i	1.12704	+	0.818842i	0.141779	+	0.989898i	$0.454718\pi$
$240$		0			0
$241$	−7.53167			−0.485158			−0.242579	−	0.970132i	$-0.577993\pi$
$241$	−7.53167			−0.485158			−0.242579	+	0.970132i	$0.577993\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.85723	−	5.70861i	−0.501980	−	0.364710i
$246$		0			0
$247$	6.42056	−	19.7604i	0.408530	−	1.25733i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.15133	+	28.1649i	0.577627	+	1.77775i	0.627056	+	0.778974i	$0.284260\pi$
$251$	9.15133	+	28.1649i	0.577627	+	1.77775i	−0.0494295	+	0.998778i	$0.515740\pi$
$252$		0			0
$253$	−2.76799	−	2.48475i	−0.174022	−	0.156215i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.92960	+	4.30811i	−0.369878	+	0.268732i	−0.757160	−	0.653229i	$-0.773414\pi$
$257$	−5.92960	+	4.30811i	−0.369878	+	0.268732i	0.387282	+	0.921961i	$0.373414\pi$
$258$		0			0
$259$	−4.94022	+	15.2044i	−0.306970	+	0.944757i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.5747			−0.960378			−0.480189	−	0.877165i	$-0.659432\pi$
$263$	−15.5747			−0.960378			−0.480189	+	0.877165i	$0.659432\pi$
$264$		0			0
$265$	−1.10143			−0.0676604
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.91679	+	18.2100i	−0.360753	+	1.11028i	0.591845	+	0.806052i	$0.298400\pi$
$269$	−5.91679	+	18.2100i	−0.360753	+	1.11028i	−0.952598	+	0.304232i	$0.901600\pi$
$270$		0			0
$271$	5.73729	−	4.16838i	0.348515	−	0.253211i	−0.399731	−	0.916633i	$-0.630896\pi$
$271$	5.73729	−	4.16838i	0.348515	−	0.253211i	0.748246	+	0.663421i	$0.230896\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.90251	−	8.88464i	−0.114726	−	0.535764i
$276$		0			0
$277$	−0.176133	−	0.542080i	−0.0105828	−	0.0325704i	0.945626	−	0.325257i	$-0.105451\pi$
$277$	−0.176133	−	0.542080i	−0.0105828	−	0.0325704i	−0.956208	+	0.292686i	$0.905451\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.16957	+	25.1434i	−0.487356	+	1.49993i	0.341184	+	0.939997i	$0.389172\pi$
$281$	−8.16957	+	25.1434i	−0.487356	+	1.49993i	−0.828540	+	0.559930i	$0.810828\pi$
$282$		0			0
$283$	6.96866	+	5.06302i	0.414244	+	0.300966i	0.775318	−	0.631572i	$-0.217590\pi$
$283$	6.96866	+	5.06302i	0.414244	+	0.300966i	−0.361074	+	0.932537i	$0.617590\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.47458			−0.323154
$288$		0			0
$289$	−26.4650	−	19.2280i	−1.55677	−	1.13106i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	19.3238	−	14.0396i	1.12891	−	0.820200i	0.143373	−	0.989669i	$-0.454205\pi$
$293$	19.3238	−	14.0396i	1.12891	−	0.820200i	0.985536	+	0.169469i	$0.0542052\pi$
$294$		0			0
$295$	6.37731	+	19.6273i	0.371301	+	1.14275i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.72587	+	5.31170i	0.0998099	+	0.307183i
$300$		0			0
$301$	27.0734	−	19.6700i	1.56048	−	1.13376i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12.8238	−	9.31704i	−0.734289	−	0.533492i
$306$		0			0
$307$	−11.3425			−0.647351			−0.323676	−	0.946168i	$-0.604919\pi$
$307$	−11.3425			−0.647351			−0.323676	+	0.946168i	$0.604919\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	21.6462	+	15.7269i	1.22744	+	0.891788i	0.996696	−	0.0812259i	$-0.0258835\pi$
$311$	21.6462	+	15.7269i	1.22744	+	0.891788i	0.230745	+	0.973014i	$0.425884\pi$
$312$		0			0
$313$	−5.24134	+	16.1312i	−0.296258	+	0.911789i	0.686538	+	0.727094i	$0.259130\pi$
$313$	−5.24134	+	16.1312i	−0.296258	+	0.911789i	−0.982796	+	0.184695i	$0.940870\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.87709	+	24.2432i	0.442421	+	1.36163i	0.885287	+	0.465045i	$0.153962\pi$
$317$	7.87709	+	24.2432i	0.442421	+	1.36163i	−0.442866	+	0.896588i	$0.646038\pi$
$318$		0			0
$319$	23.7644	+	2.46147i	1.33055	+	0.137816i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	23.7990	−	17.2910i	1.32421	−	0.962097i
$324$		0			0
$325$	−4.21583	+	12.9750i	−0.233852	+	0.719724i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−12.0329			−0.663393
$330$		0			0
$331$	−8.27007			−0.454564			−0.227282	−	0.973829i	$-0.572984\pi$
$331$	−8.27007			−0.454564			−0.227282	+	0.973829i	$0.572984\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.83792	−	17.9673i	0.318960	−	0.981657i
$336$		0			0
$337$	−19.8692	+	14.4358i	−1.08234	+	0.786368i	−0.978090	−	0.208183i	$-0.933245\pi$
$337$	−19.8692	+	14.4358i	−1.08234	+	0.786368i	−0.104253	+	0.994551i	$0.533245\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.99731	−	15.7803i	0.378926	−	0.854552i
$342$		0			0
$343$	−0.612514	−	1.88512i	−0.0330726	−	0.101787i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.50660	−	13.8699i	0.241927	−	0.744575i	−0.754199	−	0.656645i	$-0.771975\pi$
$347$	4.50660	−	13.8699i	0.241927	−	0.744575i	0.996127	−	0.0879300i	$-0.0280252\pi$
$348$		0			0
$349$	22.3044	+	16.2051i	1.19393	+	0.867437i	0.993674	−	0.112307i	$-0.0358241\pi$
$349$	22.3044	+	16.2051i	1.19393	+	0.867437i	0.200251	+	0.979745i	$0.435824\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.4334			0.661763			0.330881	−	0.943672i	$-0.392654\pi$
$353$	12.4334			0.661763			0.330881	+	0.943672i	$0.392654\pi$
$354$		0			0
$355$	−2.16387	−	1.57215i	−0.114846	−	0.0834408i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.5918	+	19.3201i	−1.40346	+	1.01967i	−0.409228	+	0.912432i	$0.634202\pi$
$359$	−26.5918	+	19.3201i	−1.40346	+	1.01967i	−0.994233	+	0.107242i	$0.965798\pi$
$360$		0			0
$361$	−0.492109	−	1.51456i	−0.0259005	−	0.0797135i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.92802	+	21.3223i	0.362629	+	1.11606i
$366$		0			0
$367$	11.6177	−	8.44074i	0.606438	−	0.440603i	−0.241720	−	0.970346i	$-0.577712\pi$
$367$	11.6177	−	8.44074i	0.606438	−	0.440603i	0.848158	+	0.529743i	$0.177712\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.17438	+	1.57978i	0.112888	+	0.0820181i
$372$		0			0
$373$	11.4836			0.594599			0.297300	−	0.954784i	$-0.403914\pi$
$373$	11.4836			0.594599			0.297300	+	0.954784i	$0.403914\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.0220	−	21.0857i	−1.49471	−	1.08597i
$378$		0			0
$379$	−2.41665	+	7.43770i	−0.124135	+	0.382049i	−0.993743	−	0.111695i	$-0.964372\pi$
$379$	−2.41665	+	7.43770i	−0.124135	+	0.382049i	0.869607	+	0.493744i	$0.164372\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.45181	+	7.54589i	0.125281	+	0.385577i	0.993952	−	0.109813i	$-0.0350252\pi$
$383$	2.45181	+	7.54589i	0.125281	+	0.385577i	−0.868671	+	0.495390i	$0.835025\pi$
$384$		0			0
$385$	7.41565	−	16.7237i	0.377937	−	0.852321i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−26.0811	+	18.9490i	−1.32236	+	0.960754i	−0.322465	+	0.946581i	$0.604511\pi$
$389$	−26.0811	+	18.9490i	−1.32236	+	0.960754i	−0.999900	+	0.0141725i	$0.995489\pi$
$390$		0			0
$391$	−2.44354	+	7.52046i	−0.123575	+	0.380326i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.99570			−0.402307
$396$		0			0
$397$	−19.2617			−0.966716			−0.483358	−	0.875423i	$-0.660583\pi$
$397$	−19.2617			−0.966716			−0.483358	+	0.875423i	$0.660583\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.43157	+	19.7943i	−0.321177	+	0.988482i	0.651959	+	0.758254i	$0.273947\pi$
$401$	−6.43157	+	19.7943i	−0.321177	+	0.988482i	−0.973137	+	0.230228i	$0.926053\pi$
$402$		0			0
$403$	−20.9690	+	15.2349i	−1.04454	+	0.758903i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.3756	−	1.48899i	−0.712570	−	0.0738064i
$408$		0			0
$409$	4.60103	+	14.1605i	0.227506	+	0.700193i	0.998027	+	0.0627783i	$0.0199961\pi$
$409$	4.60103	+	14.1605i	0.227506	+	0.700193i	−0.770521	+	0.637415i	$0.780004\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	15.5617	−	47.8941i	0.765743	−	2.35671i
$414$		0			0
$415$	7.32161	+	5.31946i	0.359404	+	0.261122i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.7133			−0.523379			−0.261690	−	0.965152i	$-0.584280\pi$
$419$	−10.7133			−0.523379			−0.261690	+	0.965152i	$0.584280\pi$
$420$		0			0
$421$	−10.0654	−	7.31293i	−0.490557	−	0.356410i	0.314842	−	0.949144i	$-0.398049\pi$
$421$	−10.0654	−	7.31293i	−0.490557	−	0.356410i	−0.805398	+	0.592734i	$0.798049\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.6268	+	11.3535i	−0.758011	+	0.550727i
$426$		0			0
$427$	11.9526	+	36.7863i	0.578426	+	1.78021i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.04056	+	18.5909i	0.290964	+	0.895494i	0.984547	+	0.175118i	$0.0560308\pi$
$431$	6.04056	+	18.5909i	0.290964	+	0.895494i	−0.693584	+	0.720376i	$0.743969\pi$
$432$		0			0
$433$	−31.1448	+	22.6280i	−1.49672	+	1.08743i	−0.525058	+	0.851067i	$0.675956\pi$
$433$	−31.1448	+	22.6280i	−1.49672	+	1.08743i	−0.971664	+	0.236365i	$0.924044\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.78556	−	2.75037i	−0.181088	−	0.131568i
$438$		0			0
$439$	7.52715			0.359251			0.179626	−	0.983735i	$-0.442511\pi$
$439$	7.52715			0.359251			0.179626	+	0.983735i	$0.442511\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.0758	−	11.6798i	−0.763786	−	0.554923i	0.136284	−	0.990670i	$-0.456484\pi$
$443$	−16.0758	−	11.6798i	−0.763786	−	0.554923i	−0.900069	+	0.435747i	$0.856484\pi$
$444$		0			0
$445$	−2.77104	+	8.52840i	−0.131360	+	0.404285i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.57929	+	7.93824i	0.121724	+	0.374629i	0.993290	−	0.115650i	$-0.0368950\pi$
$449$	2.57929	+	7.93824i	0.121724	+	0.374629i	−0.871566	+	0.490279i	$0.836895\pi$
$450$		0			0
$451$	−1.03629	−	4.83942i	−0.0487970	−	0.227879i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−22.2226	+	16.1457i	−1.04181	+	0.756922i
$456$		0			0
$457$	−3.37038	+	10.3730i	−0.157660	+	0.485226i	−0.998421	−	0.0561801i	$-0.982108\pi$
$457$	−3.37038	+	10.3730i	−0.157660	+	0.485226i	0.840761	+	0.541406i	$0.182108\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.9763			0.604368			0.302184	−	0.953250i	$-0.402284\pi$
$461$	12.9763			0.604368			0.302184	+	0.953250i	$0.402284\pi$
$462$		0			0
$463$	20.4036			0.948238			0.474119	−	0.880461i	$-0.342767\pi$
$463$	20.4036			0.948238			0.474119	+	0.880461i	$0.342767\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.67283	+	23.6145i	−0.355056	+	1.09275i	0.600921	+	0.799309i	$0.294801\pi$
$467$	−7.67283	+	23.6145i	−0.355056	+	1.09275i	−0.955977	+	0.293442i	$0.905199\pi$
$468$		0			0
$469$	−37.2953	+	27.0966i	−1.72214	+	1.25121i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.5126	+	20.2090i	1.03513	+	0.929211i
$474$		0			0
$475$	−3.53207	−	10.8706i	−0.162063	−	0.498777i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.75737	−	5.40863i	0.0802963	−	0.247127i	−0.902847	−	0.429961i	$-0.858527\pi$
$479$	1.75737	−	5.40863i	0.0802963	−	0.247127i	0.983144	+	0.182834i	$0.0585273\pi$
$480$		0			0
$481$	17.5560	+	12.7552i	0.800484	+	0.581586i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.67620			0.212335
$486$		0			0
$487$	17.2618	+	12.5414i	0.782208	+	0.568307i	0.905641	−	0.424046i	$-0.139390\pi$
$487$	17.2618	+	12.5414i	0.782208	+	0.568307i	−0.123433	+	0.992353i	$0.539390\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.4255	−	11.2073i	0.696142	−	0.505777i	−0.182531	−	0.983200i	$-0.558429\pi$
$491$	15.4255	−	11.2073i	0.696142	−	0.505777i	0.878673	+	0.477423i	$0.158429\pi$
$492$		0			0
$493$	−15.6951	−	48.3045i	−0.706871	−	2.17552i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.01687	+	6.20727i	0.0904688	+	0.278434i
$498$		0			0
$499$	1.08432	−	0.787804i	0.0485408	−	0.0352670i	−0.563250	−	0.826286i	$-0.690449\pi$
$499$	1.08432	−	0.787804i	0.0485408	−	0.0352670i	0.611791	+	0.791019i	$0.290449\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.8297	+	15.1337i	0.928751	+	0.674777i	0.945687	−	0.325079i	$-0.105391\pi$
$503$	20.8297	+	15.1337i	0.928751	+	0.674777i	−0.0169355	+	0.999857i	$0.505391\pi$
$504$		0			0
$505$	−9.70160			−0.431716
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.5745	−	14.2217i	−0.867626	−	0.630367i	0.0623227	−	0.998056i	$-0.480149\pi$
$509$	−19.5745	−	14.2217i	−0.867626	−	0.630367i	−0.929949	+	0.367689i	$0.880149\pi$
$510$		0			0
$511$	16.9056	−	52.0300i	0.747858	−	2.30167i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.32548	+	4.07942i	0.0584078	+	0.179761i
$516$		0			0
$517$	−2.27772	−	10.6368i	−0.100174	−	0.467806i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.3445	−	7.51569i	0.453199	−	0.329268i	−0.337659	−	0.941269i	$-0.609635\pi$
$521$	10.3445	−	7.51569i	0.453199	−	0.329268i	0.790857	+	0.612000i	$0.209635\pi$
$522$		0			0
$523$	4.35266	−	13.3961i	0.190329	−	0.585771i	−0.809671	−	0.586884i	$-0.800354\pi$
$523$	4.35266	−	13.3961i	0.190329	−	0.585771i	0.999999	+	0.00111298i	$0.000354273\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−36.6970			−1.59855
$528$		0			0
$529$	−21.7422			−0.945313
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.29634	+	7.06742i	−0.0994657	+	0.306124i
$534$		0			0
$535$	−3.60950	+	2.62245i	−0.156052	+	0.113379i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.5379	+	10.7402i	−0.798486	+	0.462615i
$540$		0			0
$541$	−1.99319	−	6.13442i	−0.0856940	−	0.263739i	0.899023	−	0.437902i	$-0.144278\pi$
$541$	−1.99319	−	6.13442i	−0.0856940	−	0.263739i	−0.984717	+	0.174163i	$0.944278\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.18420	+	6.72228i	−0.0935609	+	0.287951i
$546$		0			0
$547$	7.11861	+	5.17197i	0.304370	+	0.221138i	0.729477	−	0.684005i	$-0.239764\pi$
$547$	7.11861	+	5.17197i	0.304370	+	0.221138i	−0.425107	+	0.905143i	$0.639764\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	30.0550			1.28038
$552$		0			0
$553$	15.7846	+	11.4682i	0.671231	+	0.487678i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.9265	+	9.39167i	−0.547714	+	0.397938i	−0.826942	−	0.562287i	$-0.809922\pi$
$557$	−12.9265	+	9.39167i	−0.547714	+	0.397938i	0.279228	+	0.960225i	$0.409922\pi$
$558$		0			0
$559$	−14.0369	−	43.2012i	−0.593698	−	1.82721i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.295851	−	0.910536i	−0.0124686	−	0.0383745i	0.944629	−	0.328141i	$-0.106422\pi$
$563$	−0.295851	−	0.910536i	−0.0124686	−	0.0383745i	−0.957097	+	0.289767i	$0.906422\pi$
$564$		0			0
$565$	−0.590240	+	0.428834i	−0.0248316	+	0.0180412i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.2624	+	11.8153i	0.681755	+	0.495324i	0.873940	−	0.486035i	$-0.161557\pi$
$569$	16.2624	+	11.8153i	0.681755	+	0.495324i	−0.192184	+	0.981359i	$0.561557\pi$
$570$		0			0
$571$	3.31936			0.138911			0.0694555	−	0.997585i	$-0.477874\pi$
$571$	3.31936			0.138911			0.0694555	+	0.997585i	$0.477874\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.48566	+	1.80594i	0.103659	+	0.0753127i
$576$		0			0
$577$	13.5449	−	41.6869i	0.563882	−	1.73545i	−0.107368	−	0.994219i	$-0.534242\pi$
$577$	13.5449	−	41.6869i	0.563882	−	1.73545i	0.671250	−	0.741231i	$-0.265758\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.82420	−	21.0027i	−0.283115	−	0.871340i
$582$		0			0
$583$	−0.984903	+	2.22115i	−0.0407905	+	0.0919906i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	27.7797	−	20.1831i	1.14659	−	0.833047i	0.158567	−	0.987348i	$-0.449313\pi$
$587$	27.7797	−	20.1831i	1.14659	−	0.833047i	0.988024	+	0.154301i	$0.0493127\pi$
$588$		0			0
$589$	6.71040	−	20.6525i	0.276497	−	0.850971i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16.3665			0.672091			0.336046	−	0.941846i	$-0.390910\pi$
$593$	16.3665			0.672091			0.336046	+	0.941846i	$0.390910\pi$
$594$		0			0
$595$	−38.8910			−1.59437
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.29374	−	22.4478i	0.298014	−	0.917194i	−0.684178	−	0.729315i	$-0.739839\pi$
$599$	7.29374	−	22.4478i	0.298014	−	0.917194i	0.982192	−	0.187879i	$-0.0601611\pi$
$600$		0			0
$601$	−14.0269	+	10.1911i	−0.572169	+	0.415705i	−0.835893	−	0.548893i	$-0.815049\pi$
$601$	−14.0269	+	10.1911i	−0.572169	+	0.415705i	0.263723	+	0.964598i	$0.415049\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.1872	+	3.38963i	0.658103	+	0.137808i
$606$		0			0
$607$	8.47418	+	26.0808i	0.343956	+	1.05859i	0.962140	+	0.272555i	$0.0878687\pi$
$607$	8.47418	+	26.0808i	0.343956	+	1.05859i	−0.618184	+	0.786033i	$0.712131\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.04725	+	15.5338i	−0.204190	+	0.628432i
$612$		0			0
$613$	37.6375	+	27.3452i	1.52016	+	1.10446i	0.961406	+	0.275133i	$0.0887219\pi$
$613$	37.6375	+	27.3452i	1.52016	+	1.10446i	0.558758	+	0.829331i	$0.311278\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	38.9398			1.56766			0.783828	−	0.620978i	$-0.213265\pi$
$617$	38.9398			1.56766			0.783828	+	0.620978i	$0.213265\pi$
$618$		0			0
$619$	7.83918	+	5.69550i	0.315083	+	0.228921i	0.734075	−	0.679069i	$-0.237616\pi$
$619$	7.83918	+	5.69550i	0.315083	+	0.228921i	−0.418991	+	0.907990i	$0.637616\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	17.7027	−	12.8618i	0.709243	−	0.515295i
$624$		0			0
$625$	−1.17338	−	3.61129i	−0.0469352	−	0.144452i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.49426	+	29.2203i	0.378561	+	1.16509i
$630$		0			0
$631$	−9.60276	+	6.97681i	−0.382280	+	0.277743i	−0.762285	−	0.647242i	$-0.775922\pi$
$631$	−9.60276	+	6.97681i	−0.382280	+	0.277743i	0.380005	+	0.924985i	$0.375922\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.68617	−	1.22508i	−0.0669138	−	0.0486157i
$636$		0			0
$637$	32.1689			1.27458
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−29.9683	−	21.7733i	−1.18368	−	0.859993i	−0.191097	−	0.981571i	$-0.561204\pi$
$641$	−29.9683	−	21.7733i	−1.18368	−	0.859993i	−0.992582	+	0.121579i	$0.961204\pi$
$642$		0			0
$643$	3.04487	−	9.37113i	0.120078	−	0.369561i	−0.872894	−	0.487909i	$-0.837760\pi$
$643$	3.04487	−	9.37113i	0.120078	−	0.369561i	0.992972	+	0.118348i	$0.0377598\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.3003	+	31.7011i	0.404947	+	1.24630i	0.920940	+	0.389705i	$0.127423\pi$
$647$	10.3003	+	31.7011i	0.404947	+	1.24630i	−0.515993	+	0.856593i	$0.672577\pi$
$648$		0			0
$649$	45.2831	+	4.69033i	1.77752	+	0.184111i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.58769	−	1.88007i	0.101264	−	0.0735727i	−0.536001	−	0.844217i	$-0.680066\pi$
$653$	2.58769	−	1.88007i	0.101264	−	0.0735727i	0.637265	+	0.770645i	$0.280066\pi$
$654$		0			0
$655$	−0.233917	+	0.719923i	−0.00913990	+	0.0281297i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−42.6114			−1.65990			−0.829952	−	0.557835i	$-0.811632\pi$
$659$	−42.6114			−1.65990			−0.829952	+	0.557835i	$0.811632\pi$
$660$		0			0
$661$	16.4734			0.640742			0.320371	−	0.947292i	$-0.396192\pi$
$661$	16.4734			0.640742			0.320371	+	0.947292i	$0.396192\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.11158	−	21.8872i	0.275775	−	0.848749i
$666$		0			0
$667$	−6.53597	+	4.74866i	−0.253074	+	0.183869i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−30.2558	+	17.5292i	−1.16801	+	0.676707i
$672$		0			0
$673$	1.93785	+	5.96408i	0.0746985	+	0.229898i	0.981434	−	0.191802i	$-0.0614333\pi$
$673$	1.93785	+	5.96408i	0.0746985	+	0.229898i	−0.906735	+	0.421701i	$0.861433\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.05069	−	18.6221i	0.232547	−	0.715706i	−0.764890	−	0.644160i	$-0.777207\pi$
$677$	6.05069	−	18.6221i	0.232547	−	0.715706i	0.997437	−	0.0715453i	$-0.0227931\pi$
$678$		0			0
$679$	−9.23148	−	6.70706i	−0.354272	−	0.257393i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.5225			−0.402632			−0.201316	−	0.979526i	$-0.564522\pi$
$683$	−10.5225			−0.402632			−0.201316	+	0.979526i	$0.564522\pi$
$684$		0			0
$685$	−11.2182	−	8.15053i	−0.428627	−	0.311416i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.95148	−	2.14437i	0.112442	−	0.0816942i
$690$		0			0
$691$	−0.223656	−	0.688343i	−0.00850829	−	0.0261858i	0.946712	−	0.322081i	$-0.104382\pi$
$691$	−0.223656	−	0.688343i	−0.00850829	−	0.0261858i	−0.955221	+	0.295895i	$0.904382\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.46041	−	22.9608i	−0.282989	−	0.870952i
$696$		0			0
$697$	−8.51184	+	6.18421i	−0.322409	+	0.234244i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−5.51815	−	4.00917i	−0.208418	−	0.151424i	0.478680	−	0.877990i	$-0.341115\pi$
$701$	−5.51815	−	4.00917i	−0.208418	−	0.151424i	−0.687097	+	0.726565i	$0.741115\pi$
$702$		0			0
$703$	−18.1808			−0.685703
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19.1523	+	13.9150i	0.720297	+	0.523327i
$708$		0			0
$709$	−2.09602	+	6.45089i	−0.0787177	+	0.242268i	−0.982670	−	0.185366i	$-0.940653\pi$
$709$	−2.09602	+	6.45089i	−0.0787177	+	0.242268i	0.903952	+	0.427634i	$0.140653\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.80378	+	5.55148i	0.0675523	+	0.207905i
$714$		0			0
$715$	−18.4790	−	16.5881i	−0.691077	−	0.620361i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.5885	−	11.3257i	0.581352	−	0.422377i	−0.257859	−	0.966183i	$-0.583017\pi$
$719$	15.5885	−	11.3257i	0.581352	−	0.422377i	0.839211	+	0.543805i	$0.183017\pi$
$720$		0			0
$721$	3.23441	−	9.95449i	0.120456	−	0.370724i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19.7345			−0.732922
$726$		0			0
$727$	−31.5105			−1.16866			−0.584330	−	0.811516i	$-0.698643\pi$
$727$	−31.5105			−1.16866			−0.584330	+	0.811516i	$0.698643\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	19.8739	−	61.1655i	0.735062	−	2.26229i
$732$		0			0
$733$	16.7520	−	12.1710i	0.618748	−	0.449547i	−0.233736	−	0.972300i	$-0.575095\pi$
$733$	16.7520	−	12.1710i	0.618748	−	0.449547i	0.852484	+	0.522754i	$0.175095\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31.0126	−	27.8392i	−1.14236	−	1.02547i
$738$		0			0
$739$	2.47309	+	7.61140i	0.0909742	+	0.279990i	0.986184	−	0.165656i	$-0.0529741\pi$
$739$	2.47309	+	7.61140i	0.0909742	+	0.279990i	−0.895209	+	0.445646i	$0.852974\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.82300	−	24.0767i	0.286998	−	0.883290i	−0.698794	−	0.715323i	$-0.746280\pi$
$743$	7.82300	−	24.0767i	0.286998	−	0.883290i	0.985793	−	0.167967i	$-0.0537202\pi$
$744$		0			0
$745$	−16.0685	−	11.6745i	−0.588705	−	0.427719i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.8870			0.397804
$750$		0			0
$751$	−11.3309	−	8.23241i	−0.413472	−	0.300405i	0.361534	−	0.932359i	$-0.382253\pi$
$751$	−11.3309	−	8.23241i	−0.413472	−	0.300405i	−0.775006	+	0.631954i	$0.782253\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.1196	−	14.6177i	0.732227	−	0.531994i
$756$		0			0
$757$	−1.45345	−	4.47326i	−0.0528265	−	0.162583i	0.921163	−	0.389178i	$-0.127241\pi$
$757$	−1.45345	−	4.47326i	−0.0528265	−	0.162583i	−0.973989	+	0.226594i	$0.927241\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.74316	−	23.8310i	−0.280689	−	0.863873i	−0.987658	−	0.156628i	$-0.949938\pi$
$761$	−7.74316	−	23.8310i	−0.280689	−	0.863873i	0.706968	−	0.707245i	$-0.250062\pi$
$762$		0			0
$763$	13.9537	−	10.1379i	0.505157	−	0.367018i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−55.3015	−	40.1789i	−1.99682	−	1.45078i
$768$		0			0
$769$	0.757190			0.0273050			0.0136525	−	0.999907i	$-0.495654\pi$
$769$	0.757190			0.0273050			0.0136525	+	0.999907i	$0.495654\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.83542	+	5.69276i	0.281820	+	0.204755i	0.719711	−	0.694274i	$-0.244274\pi$
$773$	7.83542	+	5.69276i	0.281820	+	0.204755i	−0.437891	+	0.899028i	$0.644274\pi$
$774$		0			0
$775$	−4.40615	+	13.5607i	−0.158273	+	0.487116i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.92390	−	5.92116i	−0.0689310	−	0.212148i
$780$		0			0
$781$	−5.10533	+	2.95785i	−0.182683	+	0.105840i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−13.7629	+	9.99931i	−0.491218	+	0.356891i
$786$		0			0
$787$	−9.38462	+	28.8829i	−0.334526	+	1.02956i	0.632429	+	0.774618i	$0.282058\pi$
$787$	−9.38462	+	28.8829i	−0.334526	+	1.02956i	−0.966955	+	0.254946i	$0.917942\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.78029			0.0632999
$792$		0			0
$793$	52.5029			1.86443
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.40180	−	4.31431i	0.0496544	−	0.152821i	−0.923155	−	0.384428i	$-0.874399\pi$
$797$	1.40180	−	4.31431i	0.0496544	−	0.152821i	0.972809	+	0.231608i	$0.0743986\pi$
$798$		0			0
$799$	−18.7086	+	13.5926i	−0.661863	+	0.480871i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	49.1936	+	5.09536i	1.73600	+	0.179811i
$804$		0			0
$805$	1.91163	+	5.88338i	0.0673759	+	0.207362i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.2054	−	37.5643i	0.429118	−	1.32069i	−0.469878	−	0.882732i	$-0.655702\pi$
$809$	12.2054	−	37.5643i	0.429118	−	1.32069i	0.898996	−	0.437958i	$-0.144298\pi$
$810$		0			0
$811$	−0.459260	−	0.333672i	−0.0161268	−	0.0117168i	0.579693	−	0.814835i	$-0.303173\pi$
$811$	−0.459260	−	0.333672i	−0.0161268	−	0.0117168i	−0.595819	+	0.803118i	$0.703173\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.8956			0.837028
$816$		0			0
$817$	30.7888	+	22.3694i	1.07716	+	0.782605i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.08077	−	3.69140i	0.177320	−	0.128831i	−0.495585	−	0.868560i	$-0.665046\pi$
$821$	5.08077	−	3.69140i	0.177320	−	0.128831i	0.672905	+	0.739729i	$0.265046\pi$
$822$		0			0
$823$	−10.0854	−	31.0396i	−0.351555	−	1.08197i	−0.957980	−	0.286834i	$-0.907397\pi$
$823$	−10.0854	−	31.0396i	−0.351555	−	1.08197i	0.606426	−	0.795140i	$-0.292603\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.42454	−	13.6173i	−0.153856	−	0.473522i	0.844187	−	0.536049i	$-0.180084\pi$
$827$	−4.42454	−	13.6173i	−0.153856	−	0.473522i	−0.998043	+	0.0625276i	$0.980084\pi$
$828$		0			0
$829$	4.50058	−	3.26986i	0.156311	−	0.113567i	−0.506880	−	0.862016i	$-0.669201\pi$
$829$	4.50058	−	3.26986i	0.156311	−	0.113567i	0.663192	+	0.748450i	$0.269201\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	36.8472	+	26.7711i	1.27668	+	0.927563i
$834$		0			0
$835$	8.78286			0.303944
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.1697	+	13.9276i	0.661812	+	0.480835i	0.867274	−	0.497830i	$-0.165870\pi$
$839$	19.1697	+	13.9276i	0.661812	+	0.480835i	−0.205462	+	0.978665i	$0.565870\pi$
$840$		0			0
$841$	7.07385	−	21.7711i	0.243926	−	0.750727i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.48209	+	16.8722i	0.188590	+	0.580420i
$846$		0			0
$847$	−27.0940	−	29.9088i	−0.930963	−	1.02768i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.95374	−	2.87256i	0.135532	−	0.0984700i
$852$		0			0
$853$	−13.7889	+	42.4378i	−0.472122	+	1.45304i	0.377679	+	0.925937i	$0.376722\pi$
$853$	−13.7889	+	42.4378i	−0.472122	+	1.45304i	−0.849800	+	0.527105i	$0.823278\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.2787			0.761025			0.380512	−	0.924776i	$-0.375748\pi$
$857$	22.2787			0.761025			0.380512	+	0.924776i	$0.375748\pi$
$858$		0			0
$859$	9.11149			0.310880			0.155440	−	0.987845i	$-0.450320\pi$
$859$	9.11149			0.310880			0.155440	+	0.987845i	$0.450320\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.22867	−	13.0145i	0.143946	−	0.443019i	−0.852928	−	0.522028i	$-0.825176\pi$
$863$	4.22867	−	13.0145i	0.143946	−	0.443019i	0.996874	+	0.0790092i	$0.0251756\pi$
$864$		0			0
$865$	19.3585	−	14.0648i	0.658209	−	0.478217i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.14978	+	16.1241i	−0.242540	+	0.546974i
$870$		0			0
$871$	19.3367	+	59.5123i	0.655200	+	2.01650i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.1921	+	40.6011i	−0.445974	+	1.37257i
$876$		0			0
$877$	1.11276	+	0.808467i	0.0375752	+	0.0273000i	0.606414	−	0.795149i	$-0.292607\pi$
$877$	1.11276	+	0.808467i	0.0375752	+	0.0273000i	−0.568839	+	0.822449i	$0.692607\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.2582			0.884663			0.442331	−	0.896852i	$-0.354152\pi$
$881$	26.2582			0.884663			0.442331	+	0.896852i	$0.354152\pi$
$882$		0			0
$883$	24.0840	+	17.4981i	0.810491	+	0.588856i	0.913973	−	0.405775i	$-0.132998\pi$
$883$	24.0840	+	17.4981i	0.810491	+	0.588856i	−0.103482	+	0.994631i	$0.532998\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.743204	−	0.539970i	0.0249544	−	0.0181304i	−0.575238	−	0.817986i	$-0.695091\pi$
$887$	0.743204	−	0.539970i	0.0249544	−	0.0181304i	0.600193	+	0.799856i	$0.295091\pi$
$888$		0			0
$889$	1.57162	+	4.83695i	0.0527104	+	0.162226i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.22864	−	13.0144i	−0.141506	−	0.435511i
$894$		0			0
$895$	−1.89890	+	1.37963i	−0.0634731	+	0.0461159i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.3322	−	22.0376i	−1.01163	−	0.734995i
$900$		0			0
$901$	5.16527			0.172080
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−29.4060	−	21.3647i	−0.977490	−	0.710188i
$906$		0			0
$907$	16.4685	−	50.6848i	0.546827	−	1.68296i	−0.169779	−	0.985482i	$-0.554305\pi$
$907$	16.4685	−	50.6848i	0.546827	−	1.68296i	0.716606	−	0.697478i	$-0.245695\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.99666	−	15.3781i	−0.165547	−	0.509500i	0.833530	−	0.552475i	$-0.186316\pi$
$911$	−4.99666	−	15.3781i	−0.165547	−	0.509500i	−0.999076	+	0.0429748i	$0.986316\pi$
$912$		0			0
$913$	17.2742	−	10.0081i	0.571694	−	0.331220i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.49437	−	1.08572i	0.0493484	−	0.0358537i
$918$		0			0
$919$	−10.5559	+	32.4877i	−0.348206	+	1.07167i	0.611638	+	0.791137i	$0.290511\pi$
$919$	−10.5559	+	32.4877i	−0.348206	+	1.07167i	−0.959845	+	0.280532i	$0.909489\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.85928			0.291607
$924$		0			0
$925$	11.9378			0.392513
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.25138	+	10.0067i	−0.106674	+	0.328310i	−0.990120	−	0.140224i	$-0.955218\pi$
$929$	−3.25138	+	10.0067i	−0.106674	+	0.328310i	0.883445	+	0.468534i	$0.155218\pi$
$930$		0			0
$931$	−21.8042	+	15.8417i	−0.714603	+	0.519190i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.36173	−	34.3789i	−0.240754	−	1.12431i
$936$		0			0
$937$	−9.95266	−	30.6311i	−0.325139	−	1.00068i	−0.971378	−	0.237540i	$-0.923659\pi$
$937$	−9.95266	−	30.6311i	−0.325139	−	1.00068i	0.646239	−	0.763135i	$-0.276341\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.8389	−	36.4365i	0.385938	−	1.18780i	−0.549859	−	0.835258i	$-0.685319\pi$
$941$	11.8389	−	36.4365i	0.385938	−	1.18780i	0.935797	−	0.352539i	$-0.114681\pi$
$942$		0			0
$943$	1.35393	+	0.983684i	0.0440899	+	0.0320332i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.2459			−0.982860			−0.491430	−	0.870917i	$-0.663526\pi$
$947$	−30.2459			−0.982860			−0.491430	+	0.870917i	$0.663526\pi$
$948$		0			0
$949$	−60.0771	−	43.6486i	−1.95019	−	1.41689i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−45.8330	+	33.2996i	−1.48468	+	1.07868i	−0.508662	+	0.860966i	$0.669860\pi$
$953$	−45.8330	+	33.2996i	−1.48468	+	1.07868i	−0.976013	+	0.217713i	$0.930140\pi$
$954$		0			0
$955$	−4.85927	−	14.9553i	−0.157242	−	0.483942i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	10.4561	+	32.1806i	0.337645	+	1.03917i
$960$		0			0
$961$	3.16394	−	2.29874i	0.102063	−	0.0741529i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−25.0521	−	18.2014i	−0.806457	−	0.585925i
$966$		0			0
$967$	−36.7258			−1.18102			−0.590511	−	0.807030i	$-0.701074\pi$
$967$	−36.7258			−1.18102			−0.590511	+	0.807030i	$0.701074\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.6087	+	20.7855i	0.918098	+	0.667037i	0.943050	−	0.332652i	$-0.107943\pi$
$971$	28.6087	+	20.7855i	0.918098	+	0.667037i	−0.0249522	+	0.999689i	$0.507943\pi$
$972$		0			0
$973$	−18.2047	+	56.0283i	−0.583615	+	1.79618i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.47087	−	4.52689i	−0.0470574	−	0.144828i	0.924767	−	0.380534i	$-0.124260\pi$
$977$	−1.47087	−	4.52689i	−0.0470574	−	0.144828i	−0.971824	+	0.235706i	$0.924260\pi$
$978$		0			0
$979$	14.7205	+	13.2142i	0.470470	+	0.422328i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−43.1297	+	31.3356i	−1.37562	+	0.999449i	−0.378350	+	0.925663i	$0.623508\pi$
$983$	−43.1297	+	31.3356i	−1.37562	+	0.999449i	−0.997274	+	0.0737869i	$0.976492\pi$
$984$		0			0
$985$	7.06126	−	21.7323i	0.224991	−	0.692450i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−10.2299			−0.325292
$990$		0			0
$991$	48.5492			1.54222			0.771108	−	0.636705i	$-0.219703\pi$
$991$	48.5492			1.54222			0.771108	+	0.636705i	$0.219703\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.3616	+	38.0450i	−0.391888	+	1.20611i
$996$		0			0
$997$	11.4656	−	8.33023i	0.363118	−	0.263821i	−0.391233	−	0.920292i	$-0.627951\pi$
$997$	11.4656	−	8.33023i	0.363118	−	0.263821i	0.754352	+	0.656471i	$0.227951\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.r.f.577.2		8
3.2	odd	2		264.2.q.e.49.1	✓	8
11.3	even	5		8712.2.a.bz.1.3		4
11.8	odd	10		8712.2.a.cc.1.3		4
11.9	even	5	inner	792.2.r.f.361.2		8
12.11	even	2		528.2.y.k.49.1		8
33.8	even	10		2904.2.a.be.1.2		4
33.14	odd	10		2904.2.a.bb.1.2		4
33.20	odd	10		264.2.q.e.97.1	yes	8
132.47	even	10		5808.2.a.co.1.2		4
132.107	odd	10		5808.2.a.cl.1.2		4
132.119	even	10		528.2.y.k.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.e.49.1	✓	8	3.2	odd	2
264.2.q.e.97.1	yes	8	33.20	odd	10
528.2.y.k.49.1		8	12.11	even	2
528.2.y.k.97.1		8	132.119	even	10
792.2.r.f.361.2		8	11.9	even	5	inner
792.2.r.f.577.2		8	1.1	even	1	trivial
2904.2.a.bb.1.2		4	33.14	odd	10
2904.2.a.be.1.2		4	33.8	even	10
5808.2.a.cl.1.2		4	132.107	odd	10
5808.2.a.co.1.2		4	132.47	even	10
8712.2.a.bz.1.3		4	11.3	even	5
8712.2.a.cc.1.3		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.464601 - 1.42989i) q^{5} +(-2.96808 + 2.15644i) q^{7} +O(q^{10})\)	\(q+(0.464601 - 1.42989i) q^{5} +(-2.96808 + 2.15644i) q^{7} +(-2.46808 - 2.21553i) q^{11} +(1.53888 + 4.73618i) q^{13} +(-2.17879 + 6.70563i) q^{17} +(-3.37540 - 2.45238i) q^{19} +1.12151 q^{23} +(2.21634 + 1.61027i) q^{25} +(-5.82781 + 4.23415i) q^{29} +(1.60835 + 4.94999i) q^{31} +(1.70450 + 5.24592i) q^{35} +(3.52536 - 2.56132i) q^{37} +(1.20723 + 0.877104i) q^{41} -9.12151 q^{43} +(2.65343 + 1.92783i) q^{47} +(1.99616 - 6.14356i) q^{49} +(-0.226382 - 0.696733i) q^{53} +(-4.31465 + 2.49976i) q^{55} +(-11.1049 + 8.06819i) q^{59} +(3.25795 - 10.0269i) q^{61} +7.48721 q^{65} +12.5655 q^{67} +(0.549742 - 1.69193i) q^{71} +(-12.0639 + 8.76492i) q^{73} +(12.1031 + 1.25361i) q^{77} +(-1.64339 - 5.05784i) q^{79} +(-1.86009 + 5.72476i) q^{83} +(8.57607 + 6.23088i) q^{85} -5.96435 q^{89} +(-14.7808 - 10.7389i) q^{91} +(-5.07485 + 3.68710i) q^{95} +(0.961121 + 2.95803i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{5} - 5 q^{7}+O(q^{10}) \) 8 * q + q^5 - 5 * q^7	\( 8 q + q^{5} - 5 q^{7} - q^{11} - q^{13} + 4 q^{17} - 2 q^{19} - 16 q^{23} + 7 q^{25} + 7 q^{29} + 29 q^{31} + 20 q^{35} + 13 q^{37} + 23 q^{41} - 48 q^{43} + 15 q^{47} - 11 q^{49} - 9 q^{53} - 22 q^{55} - 12 q^{59} + 9 q^{61} - 42 q^{65} + 38 q^{67} + 41 q^{71} - 25 q^{73} + 55 q^{77} + 11 q^{79} - 23 q^{83} + 23 q^{85} - 12 q^{89} - 35 q^{91} - 29 q^{95} + 21 q^{97}+O(q^{100}) \) 8 * q + q^5 - 5 * q^7 - q^11 - q^13 + 4 * q^17 - 2 * q^19 - 16 * q^23 + 7 * q^25 + 7 * q^29 + 29 * q^31 + 20 * q^35 + 13 * q^37 + 23 * q^41 - 48 * q^43 + 15 * q^47 - 11 * q^49 - 9 * q^53 - 22 * q^55 - 12 * q^59 + 9 * q^61 - 42 * q^65 + 38 * q^67 + 41 * q^71 - 25 * q^73 + 55 * q^77 + 11 * q^79 - 23 * q^83 + 23 * q^85 - 12 * q^89 - 35 * q^91 - 29 * q^95 + 21 * q^97

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