LMFDB - Embedded newform 900.3.u.d.149.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.u (of order $6$, degree $2$, not 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.7
Character	$\chi$	$=$	900.149
Dual form			900.3.u.d.749.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.708005 + 2.91526i) q^{3} +(-8.59526 + 4.96248i) q^{7} +(-7.99746 - 4.12804i) q^{9} +O(q^{10})$	\(q+(-0.708005 + 2.91526i) q^{3} +(-8.59526 + 4.96248i) q^{7} +(-7.99746 - 4.12804i) q^{9} +(3.59076 - 2.07313i) q^{11} +(-1.06217 - 0.613246i) q^{13} -21.0247 q^{17} +9.84025 q^{19} +(-8.38141 - 28.5709i) q^{21} +(-1.34068 + 2.32213i) q^{23} +(17.6965 - 20.3920i) q^{27} +(0.321704 - 0.185736i) q^{29} +(22.1854 - 38.4263i) q^{31} +(3.50142 + 11.9358i) q^{33} +33.0624i q^{37} +(2.53980 - 2.66233i) q^{39} +(-34.2494 - 19.7739i) q^{41} +(25.2682 - 14.5886i) q^{43} +(-39.6069 - 68.6012i) q^{47} +(24.7524 - 42.8724i) q^{49} +(14.8856 - 61.2924i) q^{51} +92.8471 q^{53} +(-6.96695 + 28.6869i) q^{57} +(53.3228 + 30.7859i) q^{59} +(12.6725 + 21.9495i) q^{61} +(89.2255 - 4.20566i) q^{63} +(-31.0774 - 17.9426i) q^{67} +(-5.82040 - 5.55252i) q^{69} +16.7821i q^{71} +62.4649i q^{73} +(-20.5757 + 35.6382i) q^{77} +(-71.9430 - 124.609i) q^{79} +(46.9187 + 66.0276i) q^{81} +(-8.20517 - 14.2118i) q^{83} +(0.313699 + 1.06935i) q^{87} -155.682i q^{89} +12.1729 q^{91} +(96.3152 + 91.8823i) q^{93} +(-90.6538 + 52.3390i) q^{97} +(-37.2749 + 1.75696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	−0.708005	+	2.91526i	−0.236002	+	0.971753i
$3$	−0.708005	+	2.91526i	−0.236002	+	0.971753i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−8.59526	+	4.96248i	−1.22789	+	0.708925i	−0.966589	−	0.256331i	$-0.917486\pi$
$7$	−8.59526	+	4.96248i	−1.22789	+	0.708925i	−0.261306	+	0.965256i	$0.584153\pi$
$8$		0			0
$9$	−7.99746	−	4.12804i	−0.888606	−	0.458671i
$10$		0			0
$11$	3.59076	−	2.07313i	0.326433	−	0.188466i	−0.327823	−	0.944739i	$-0.606315\pi$
$11$	3.59076	−	2.07313i	0.326433	−	0.188466i	0.654256	+	0.756273i	$0.272982\pi$
$12$		0			0
$13$	−1.06217	−	0.613246i	−0.0817057	−	0.0471728i	0.458591	−	0.888648i	$-0.348354\pi$
$13$	−1.06217	−	0.613246i	−0.0817057	−	0.0471728i	−0.540296	+	0.841475i	$0.681688\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−21.0247			−1.23675			−0.618373	−	0.785885i	$-0.712208\pi$
$17$	−21.0247			−1.23675			−0.618373	+	0.785885i	$0.712208\pi$
$18$		0			0
$19$	9.84025			0.517908			0.258954	−	0.965890i	$-0.416622\pi$
$19$	9.84025			0.517908			0.258954	+	0.965890i	$0.416622\pi$
$20$		0			0
$21$	−8.38141	−	28.5709i	−0.399115	−	1.36052i
$22$		0			0
$23$	−1.34068	+	2.32213i	−0.0582906	+	0.100962i	−0.893698	−	0.448669i	$-0.851898\pi$
$23$	−1.34068	+	2.32213i	−0.0582906	+	0.100962i	0.835408	+	0.549631i	$0.185232\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	17.6965	−	20.3920i	0.655427	−	0.755259i
$28$		0			0
$29$	0.321704	−	0.185736i	0.0110932	−	0.00640468i	−0.494443	−	0.869210i	$-0.664628\pi$
$29$	0.321704	−	0.185736i	0.0110932	−	0.00640468i	0.505536	+	0.862805i	$0.331295\pi$
$30$		0			0
$31$	22.1854	−	38.4263i	0.715659	−	1.23956i	−0.247046	−	0.969004i	$-0.579460\pi$
$31$	22.1854	−	38.4263i	0.715659	−	1.23956i	0.962705	−	0.270554i	$-0.0872069\pi$
$32$		0			0
$33$	3.50142	+	11.9358i	0.106104	+	0.361690i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			33.0624i			0.893579i	0.894639	+	0.446790i	$0.147433\pi$
$37$			33.0624i			0.893579i	−0.894639	+	0.446790i	$0.852567\pi$
$38$		0			0
$39$	2.53980	−	2.66233i	0.0651230	−	0.0682649i
$40$		0			0
$41$	−34.2494	−	19.7739i	−0.835351	−	0.482290i	0.0203301	−	0.999793i	$-0.493528\pi$
$41$	−34.2494	−	19.7739i	−0.835351	−	0.482290i	−0.855681	+	0.517503i	$0.826862\pi$
$42$		0			0
$43$	25.2682	−	14.5886i	0.587633	−	0.339270i	−0.176528	−	0.984296i	$-0.556487\pi$
$43$	25.2682	−	14.5886i	0.587633	−	0.339270i	0.764161	+	0.645026i	$0.223153\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−39.6069	−	68.6012i	−0.842700	−	1.45960i	−0.887604	−	0.460608i	$-0.847632\pi$
$47$	−39.6069	−	68.6012i	−0.842700	−	1.45960i	0.0449040	−	0.998991i	$-0.485702\pi$
$48$		0			0
$49$	24.7524	−	42.8724i	0.505150	−	0.874946i
$50$		0			0
$51$	14.8856	−	61.2924i	0.291874	−	1.20181i
$52$		0			0
$53$	92.8471			1.75183			0.875916	−	0.482463i	$-0.160258\pi$
$53$	92.8471			1.75183			0.875916	+	0.482463i	$0.160258\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.96695	+	28.6869i	−0.122227	+	0.503279i
$58$		0			0
$59$	53.3228	+	30.7859i	0.903776	+	0.521796i	0.878424	−	0.477883i	$-0.158596\pi$
$59$	53.3228	+	30.7859i	0.903776	+	0.521796i	0.0253530	+	0.999679i	$0.491929\pi$
$60$		0			0
$61$	12.6725	+	21.9495i	0.207747	+	0.359828i	0.951004	−	0.309177i	$-0.100054\pi$
$61$	12.6725	+	21.9495i	0.207747	+	0.359828i	−0.743258	+	0.669005i	$0.766720\pi$
$62$		0			0
$63$	89.2255	−	4.20566i	1.41628	−	0.0667564i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−31.0774	−	17.9426i	−0.463842	−	0.267799i	0.249816	−	0.968293i	$-0.419630\pi$
$67$	−31.0774	−	17.9426i	−0.463842	−	0.267799i	−0.713658	+	0.700494i	$0.752963\pi$
$68$		0			0
$69$	−5.82040	−	5.55252i	−0.0843537	−	0.0804713i
$70$		0			0
$71$			16.7821i			0.236368i	0.992992	+	0.118184i	$0.0377073\pi$
$71$			16.7821i			0.236368i	−0.992992	+	0.118184i	$0.962293\pi$
$72$		0			0
$73$			62.4649i			0.855684i	0.903854	+	0.427842i	$0.140726\pi$
$73$			62.4649i			0.855684i	−0.903854	+	0.427842i	$0.859274\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−20.5757	+	35.6382i	−0.267217	+	0.462833i
$78$		0			0
$79$	−71.9430	−	124.609i	−0.910671	−	1.57733i	−0.813118	−	0.582098i	$-0.802232\pi$
$79$	−71.9430	−	124.609i	−0.910671	−	1.57733i	−0.0975527	−	0.995230i	$-0.531101\pi$
$80$		0			0
$81$	46.9187	+	66.0276i	0.579243	+	0.815155i
$82$		0			0
$83$	−8.20517	−	14.2118i	−0.0988575	−	0.171226i	0.812355	−	0.583164i	$-0.198185\pi$
$83$	−8.20517	−	14.2118i	−0.0988575	−	0.171226i	−0.911212	+	0.411938i	$0.864852\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.313699	+	1.06935i	0.00360574	+	0.0122914i
$88$		0			0
$89$		−	155.682i		−	1.74924i	−0.484809	−	0.874620i	$-0.661111\pi$
$89$		−	155.682i		−	1.74924i	0.484809	−	0.874620i	$-0.338889\pi$
$90$		0			0
$91$	12.1729			0.133768
$92$		0			0
$93$	96.3152	+	91.8823i	1.03565	+	0.987981i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−90.6538	+	52.3390i	−0.934576	+	0.539577i	−0.888256	−	0.459349i	$-0.848083\pi$
$97$	−90.6538	+	52.3390i	−0.934576	+	0.539577i	−0.0463198	+	0.998927i	$0.514749\pi$
$98$		0			0
$99$	−37.2749	+	1.75696i	−0.376514	+	0.0177470i
$100$		0			0
$101$	89.5942	−	51.7272i	0.887071	−	0.512151i	0.0140876	−	0.999901i	$-0.495516\pi$
$101$	89.5942	−	51.7272i	0.887071	−	0.512151i	0.872983	+	0.487750i	$0.162182\pi$
$102$		0			0
$103$	100.747	+	58.1660i	0.978122	+	0.564719i	0.901703	−	0.432357i	$-0.142318\pi$
$103$	100.747	+	58.1660i	0.978122	+	0.564719i	0.0764192	+	0.997076i	$0.475651\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	191.681			1.79141			0.895704	−	0.444651i	$-0.146672\pi$
$107$	191.681			1.79141			0.895704	+	0.444651i	$0.146672\pi$
$108$		0			0
$109$	−140.403			−1.28810			−0.644050	−	0.764983i	$-0.722747\pi$
$109$	−140.403			−1.28810			−0.644050	+	0.764983i	$0.722747\pi$
$110$		0			0
$111$	−96.3855	−	23.4084i	−0.868338	−	0.210886i
$112$		0			0
$113$	59.4080	−	102.898i	0.525735	−	0.910599i	−0.473816	−	0.880624i	$-0.657124\pi$
$113$	59.4080	−	102.898i	0.525735	−	0.910599i	0.999551	−	0.0299752i	$-0.00954282\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.96319	+	9.28910i	0.0509674	+	0.0793940i
$118$		0			0
$119$	180.713	−	104.335i	1.51859	−	0.876761i
$120$		0			0
$121$	−51.9043	+	89.9009i	−0.428961	+	0.742982i
$122$		0			0
$123$	81.8948	−	85.8458i	0.665811	−	0.697933i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	135.134i		−	1.06405i	−0.846729	−	0.532025i	$-0.821431\pi$
$127$		−	135.134i		−	1.06405i	0.846729	−	0.532025i	$-0.178569\pi$
$128$		0			0
$129$	24.6395	+	83.9922i	0.191004	+	0.651102i
$130$		0			0
$131$	−125.310	−	72.3475i	−0.956561	−	0.552271i	−0.0614484	−	0.998110i	$-0.519572\pi$
$131$	−125.310	−	72.3475i	−0.956561	−	0.552271i	−0.895113	+	0.445839i	$0.852905\pi$
$132$		0			0
$133$	−84.5796	+	48.8320i	−0.635937	+	0.367158i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−59.4296	−	102.935i	−0.433793	−	0.751351i	0.563404	−	0.826182i	$-0.309492\pi$
$137$	−59.4296	−	102.935i	−0.433793	−	0.751351i	−0.997196	+	0.0748310i	$0.976158\pi$
$138$		0			0
$139$	69.8533	−	120.989i	0.502542	−	0.870428i	−0.497454	−	0.867490i	$-0.665732\pi$
$139$	69.8533	−	120.989i	0.502542	−	0.870428i	0.999996	−	0.00293743i	$-0.000935013\pi$
$140$		0			0
$141$	228.032	−	66.8943i	1.61725	−	0.474428i
$142$		0			0
$143$	−5.08535			−0.0355619
$144$		0			0
$145$		0			0
$146$		0			0
$147$	107.459	+	102.513i	0.731015	+	0.697370i
$148$		0			0
$149$	207.246	+	119.654i	1.39091	+	0.803045i	0.993417	−	0.114558i	$-0.0365452\pi$
$149$	207.246	+	119.654i	1.39091	+	0.803045i	0.397498	+	0.917603i	$0.369879\pi$
$150$		0			0
$151$	−26.5794	−	46.0369i	−0.176022	−	0.304880i	0.764492	−	0.644633i	$-0.222990\pi$
$151$	−26.5794	−	46.0369i	−0.176022	−	0.304880i	−0.940515	+	0.339753i	$0.889656\pi$
$152$		0			0
$153$	168.144	+	86.7906i	1.09898	+	0.567259i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−75.2959	−	43.4721i	−0.479591	−	0.276892i	0.240655	−	0.970611i	$-0.422638\pi$
$157$	−75.2959	−	43.4721i	−0.479591	−	0.276892i	−0.720246	+	0.693719i	$0.755971\pi$
$158$		0			0
$159$	−65.7362	+	270.673i	−0.413436	+	1.70235i
$160$		0			0
$161$		−	26.6124i		−	0.165295i
$162$		0			0
$163$			45.5616i			0.279519i	0.990185	+	0.139760i	$0.0446329\pi$
$163$			45.5616i			0.279519i	−0.990185	+	0.139760i	$0.955367\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	40.9028	−	70.8458i	0.244927	−	0.424226i	−0.717184	−	0.696884i	$-0.754569\pi$
$167$	40.9028	−	70.8458i	0.244927	−	0.424226i	0.962111	+	0.272658i	$0.0879026\pi$
$168$		0			0
$169$	−83.7479	−	145.056i	−0.495549	−	0.858317i
$170$		0			0
$171$	−78.6970	−	40.6209i	−0.460216	−	0.237549i
$172$		0			0
$173$	−107.264	−	185.787i	−0.620025	−	1.07391i	−0.989481	−	0.144666i	$-0.953789\pi$
$173$	−107.264	−	185.787i	−0.620025	−	1.07391i	0.369456	−	0.929248i	$-0.379544\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−127.502	+	133.653i	−0.720349	+	0.755103i
$178$		0			0
$179$			14.6923i			0.0820800i	0.999158	+	0.0410400i	$0.0130671\pi$
$179$			14.6923i			0.0820800i	−0.999158	+	0.0410400i	$0.986933\pi$
$180$		0			0
$181$	93.0954			0.514339			0.257170	−	0.966366i	$-0.417210\pi$
$181$	93.0954			0.514339			0.257170	+	0.966366i	$0.417210\pi$
$182$		0			0
$183$	−72.9607	+	21.4034i	−0.398692	+	0.116958i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−75.4947	+	43.5869i	−0.403715	+	0.233085i
$188$		0			0
$189$	−50.9116	+	263.093i	−0.269373	+	1.39203i
$190$		0			0
$191$	−179.363	+	103.555i	−0.939072	+	0.542173i	−0.889669	−	0.456606i	$-0.849065\pi$
$191$	−179.363	+	103.555i	−0.939072	+	0.542173i	−0.0494024	+	0.998779i	$0.515732\pi$
$192$		0			0
$193$	−225.655	−	130.282i	−1.16920	−	0.675037i	−0.215708	−	0.976458i	$-0.569206\pi$
$193$	−225.655	−	130.282i	−1.16920	−	0.675037i	−0.953491	+	0.301421i	$0.902539\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−156.721			−0.795537			−0.397768	−	0.917486i	$-0.630215\pi$
$197$	−156.721			−0.795537			−0.397768	+	0.917486i	$0.630215\pi$
$198$		0			0
$199$	−144.623			−0.726748			−0.363374	−	0.931643i	$-0.618375\pi$
$199$	−144.623			−0.726748			−0.363374	+	0.931643i	$0.618375\pi$
$200$		0			0
$201$	74.3101	−	77.8953i	0.369702	−	0.387539i
$202$		0			0
$203$	−1.84342	+	3.19289i	−0.00908087	+	0.0157285i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	20.3079	−	13.0368i	0.0981058	−	0.0629795i
$208$		0			0
$209$	35.3340	−	20.4001i	0.169062	−	0.0976082i
$210$		0			0
$211$	11.9568	−	20.7098i	0.0566673	−	0.0981506i	−0.836300	−	0.548272i	$-0.815286\pi$
$211$	11.9568	−	20.7098i	0.0566673	−	0.0981506i	0.892967	+	0.450121i	$0.148619\pi$
$212$		0			0
$213$	−48.9243	−	11.8818i	−0.229691	−	0.0557833i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			440.379i			2.02940i
$218$		0			0
$219$	−182.101	−	44.2255i	−0.831513	−	0.201943i
$220$		0			0
$221$	22.3319	+	12.8933i	0.101049	+	0.0583408i
$222$		0			0
$223$	−379.853	+	219.308i	−1.70338	+	0.983446i	−0.761087	+	0.648650i	$0.775334\pi$
$223$	−379.853	+	219.308i	−1.70338	+	0.983446i	−0.942291	+	0.334796i	$0.891333\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−214.307	−	371.191i	−0.944085	−	1.63520i	−0.757573	−	0.652750i	$-0.773615\pi$
$227$	−214.307	−	371.191i	−0.944085	−	1.63520i	−0.186512	−	0.982453i	$-0.559718\pi$
$228$		0			0
$229$	−29.1308	+	50.4560i	−0.127209	+	0.220332i	−0.922594	−	0.385772i	$-0.873935\pi$
$229$	−29.1308	+	50.4560i	−0.127209	+	0.220332i	0.795386	+	0.606104i	$0.207268\pi$
$230$		0			0
$231$	−89.3267	−	85.2155i	−0.386696	−	0.368898i
$232$		0			0
$233$	−283.668			−1.21746			−0.608730	−	0.793378i	$-0.708321\pi$
$233$	−283.668			−1.21746			−0.608730	+	0.793378i	$0.708321\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	414.203	−	121.509i	1.74769	−	0.512695i
$238$		0			0
$239$	218.485	+	126.142i	0.914161	+	0.527791i	0.881768	−	0.471684i	$-0.156354\pi$
$239$	218.485	+	126.142i	0.914161	+	0.527791i	0.0323937	+	0.999475i	$0.489687\pi$
$240$		0			0
$241$	119.975	+	207.803i	0.497822	+	0.862253i	0.999997	−	0.00251337i	$-0.000800031\pi$
$241$	119.975	+	207.803i	0.497822	+	0.862253i	−0.502175	+	0.864766i	$0.667467\pi$
$242$		0			0
$243$	−225.706	+	90.0321i	−0.928831	+	0.370503i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−10.4521	−	6.03450i	−0.0423160	−	0.0244312i
$248$		0			0
$249$	47.2403	−	13.8582i	0.189720	−	0.0556553i
$250$		0			0
$251$			21.5862i			0.0860008i	0.999075	+	0.0430004i	$0.0136917\pi$
$251$			21.5862i			0.0860008i	−0.999075	+	0.0430004i	$0.986308\pi$
$252$		0			0
$253$			11.1176i			0.0439432i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−27.5100	+	47.6487i	−0.107043	+	0.185403i	−0.914571	−	0.404426i	$-0.867471\pi$
$257$	−27.5100	+	47.6487i	−0.107043	+	0.185403i	0.807528	+	0.589829i	$0.200805\pi$
$258$		0			0
$259$	−164.072	−	284.180i	−0.633481	−	1.09722i
$260$		0			0
$261$	−3.33953	+	0.157409i	−0.0127951	+	0.000603101i
$262$		0			0
$263$	−86.2155	−	149.330i	−0.327815	−	0.567793i	0.654263	−	0.756267i	$-0.272979\pi$
$263$	−86.2155	−	149.330i	−0.327815	−	0.567793i	−0.982078	+	0.188474i	$0.939646\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	453.854	+	110.224i	1.69983	+	0.412824i
$268$		0			0
$269$			220.556i			0.819910i	0.912106	+	0.409955i	$0.134456\pi$
$269$			220.556i			0.819910i	−0.912106	+	0.409955i	$0.865544\pi$
$270$		0			0
$271$	176.241			0.650337			0.325168	−	0.945656i	$-0.394579\pi$
$271$	176.241			0.650337			0.325168	+	0.945656i	$0.394579\pi$
$272$		0			0
$273$	−8.61846	+	35.4871i	−0.0315695	+	0.129989i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−330.454	+	190.788i	−1.19297	+	0.688764i	−0.958980	−	0.283474i	$-0.908513\pi$
$277$	−330.454	+	190.788i	−1.19297	+	0.688764i	−0.233994	+	0.972238i	$0.575180\pi$
$278$		0			0
$279$	−336.052	+	215.730i	−1.20449	+	0.773227i
$280$		0			0
$281$	−435.222	+	251.276i	−1.54883	+	0.894219i	−0.550602	+	0.834768i	$0.685602\pi$
$281$	−435.222	+	251.276i	−1.54883	+	0.894219i	−0.998231	+	0.0594516i	$0.981065\pi$
$282$		0			0
$283$	−297.181	−	171.577i	−1.05011	−	0.606280i	−0.127428	−	0.991848i	$-0.540672\pi$
$283$	−297.181	−	171.577i	−1.05011	−	0.606280i	−0.922680	+	0.385568i	$0.874006\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	392.510			1.36763
$288$		0			0
$289$	153.037			0.529541
$290$		0			0
$291$	−88.3983	−	301.336i	−0.303774	−	1.03552i
$292$		0			0
$293$	239.902	−	415.522i	0.818777	−	1.41816i	−0.0878060	−	0.996138i	$-0.527986\pi$
$293$	239.902	−	415.522i	0.818777	−	1.41816i	0.906583	−	0.422027i	$-0.138681\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	21.2688	−	109.910i	0.0716123	−	0.370067i
$298$		0			0
$299$	2.84808	−	1.64434i	0.00952534	−	0.00549946i
$300$		0			0
$301$	−144.791	+	250.786i	−0.481034	+	0.833176i
$302$		0			0
$303$	87.3650	+	297.813i	0.288333	+	0.982882i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			170.593i			0.555679i	0.960627	+	0.277840i	$0.0896184\pi$
$307$			170.593i			0.555679i	−0.960627	+	0.277840i	$0.910382\pi$
$308$		0			0
$309$	−240.898	+	252.520i	−0.779605	+	0.817218i
$310$		0			0
$311$	360.862	+	208.344i	1.16033	+	0.669916i	0.951383	−	0.308011i	$-0.0996634\pi$
$311$	360.862	+	208.344i	1.16033	+	0.669916i	0.208946	+	0.977927i	$0.432997\pi$
$312$		0			0
$313$	−68.4691	+	39.5306i	−0.218751	+	0.126296i	−0.605372	−	0.795943i	$-0.706976\pi$
$313$	−68.4691	+	39.5306i	−0.218751	+	0.126296i	0.386621	+	0.922239i	$0.373642\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−105.129	−	182.089i	−0.331637	−	0.574413i	0.651196	−	0.758910i	$-0.274268\pi$
$317$	−105.129	−	182.089i	−0.331637	−	0.574413i	−0.982833	+	0.184497i	$0.940934\pi$
$318$		0			0
$319$	0.770107	−	1.33387i	0.00241413	−	0.00418140i
$320$		0			0
$321$	−135.711	+	558.798i	−0.422775	+	1.74081i
$322$		0			0
$323$	−206.888			−0.640521
$324$		0			0
$325$		0			0
$326$		0			0
$327$	99.4060	−	409.311i	0.303994	−	1.25171i
$328$		0			0
$329$	680.863	+	393.097i	2.06949	+	1.19482i
$330$		0			0
$331$	285.288	+	494.133i	0.861896	+	1.49285i	0.870096	+	0.492881i	$0.164056\pi$
$331$	285.288	+	494.133i	0.861896	+	1.49285i	−0.00820039	+	0.999966i	$0.502610\pi$
$332$		0			0
$333$	136.483	−	264.415i	0.409858	−	0.794040i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	114.911	+	66.3441i	0.340983	+	0.196867i	0.660707	−	0.750644i	$-0.270257\pi$
$337$	114.911	+	66.3441i	0.340983	+	0.196867i	−0.319723	+	0.947511i	$0.603590\pi$
$338$		0			0
$339$	257.912	+	246.042i	0.760803	+	0.725787i
$340$		0			0
$341$		−	183.973i		−	0.539510i
$342$		0			0
$343$			5.00939i			0.0146046i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	92.6758	−	160.519i	0.267077	−	0.462591i	−0.701029	−	0.713133i	$-0.747275\pi$
$347$	92.6758	−	160.519i	0.267077	−	0.462591i	0.968106	+	0.250542i	$0.0806088\pi$
$348$		0			0
$349$	36.8894	+	63.8943i	0.105700	+	0.183078i	0.914024	−	0.405660i	$-0.132958\pi$
$349$	36.8894	+	63.8943i	0.105700	+	0.183078i	−0.808324	+	0.588738i	$0.799625\pi$
$350$		0			0
$351$	−31.3021	+	10.8075i	−0.0891798	+	0.0307906i
$352$		0			0
$353$	71.4437	+	123.744i	0.202390	+	0.350550i	0.949298	−	0.314377i	$-0.101796\pi$
$353$	71.4437	+	123.744i	0.202390	+	0.350550i	−0.746908	+	0.664928i	$0.768462\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	176.217	+	600.694i	0.493604	+	1.68262i
$358$		0			0
$359$		−	275.684i		−	0.767923i	−0.923349	−	0.383961i	$-0.874560\pi$
$359$		−	275.684i		−	0.767923i	0.923349	−	0.383961i	$-0.125440\pi$
$360$		0			0
$361$	−264.169			−0.731771
$362$		0			0
$363$	−225.336	−	214.965i	−0.620759	−	0.592189i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	434.689	−	250.968i	1.18444	−	0.683836i	0.227401	−	0.973801i	$-0.426977\pi$
$367$	434.689	−	250.968i	1.18444	−	0.683836i	0.957037	+	0.289965i	$0.0936437\pi$
$368$		0			0
$369$	192.281	+	299.524i	0.521086	+	0.811717i
$370$		0			0
$371$	−798.046	+	460.752i	−2.15107	+	1.24192i
$372$		0			0
$373$	6.03444	+	3.48399i	0.0161781	+	0.00934045i	0.508067	−	0.861317i	$-0.330360\pi$
$373$	6.03444	+	3.48399i	0.0161781	+	0.00934045i	−0.491889	+	0.870658i	$0.663693\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.455607			−0.00120851
$378$		0			0
$379$	−682.804			−1.80159			−0.900797	−	0.434240i	$-0.857017\pi$
$379$	−682.804			−1.80159			−0.900797	+	0.434240i	$0.857017\pi$
$380$		0			0
$381$	393.951	+	95.6757i	1.03399	+	0.251117i
$382$		0			0
$383$	92.4032	−	160.047i	0.241262	−	0.417877i	−0.719812	−	0.694169i	$-0.755772\pi$
$383$	92.4032	−	160.047i	0.241262	−	0.417877i	0.961074	+	0.276291i	$0.0891055\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−262.304	+	12.3637i	−0.677787	+	0.0319476i
$388$		0			0
$389$	18.7375	−	10.8181i	0.0481683	−	0.0278100i	−0.475722	−	0.879595i	$-0.657813\pi$
$389$	18.7375	−	10.8181i	0.0481683	−	0.0278100i	0.523891	+	0.851785i	$0.324480\pi$
$390$		0			0
$391$	28.1875	−	48.8221i	0.0720907	−	0.124865i
$392$		0			0
$393$	299.631	−	314.087i	0.762421	−	0.799204i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	113.001i		−	0.284637i	−0.989821	−	0.142318i	$-0.954544\pi$
$397$		−	113.001i		−	0.284637i	0.989821	−	0.142318i	$-0.0454557\pi$
$398$		0			0
$399$	−82.4752	−	281.145i	−0.206705	−	0.704623i
$400$		0			0
$401$	407.847	+	235.471i	1.01708	+	0.587209i	0.913256	−	0.407387i	$-0.133560\pi$
$401$	407.847	+	235.471i	1.01708	+	0.587209i	0.103820	+	0.994596i	$0.466893\pi$
$402$		0			0
$403$	−47.1296	+	27.2103i	−0.116947	+	0.0675193i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	68.5426	+	118.719i	0.168409	+	0.291694i
$408$		0			0
$409$	160.550	−	278.081i	0.392543	−	0.679904i	−0.600241	−	0.799819i	$-0.704929\pi$
$409$	160.550	−	278.081i	0.392543	−	0.679904i	0.992784	+	0.119915i	$0.0382621\pi$
$410$		0			0
$411$	342.159	−	100.374i	0.832503	−	0.244219i
$412$		0			0
$413$	−611.098			−1.47966
$414$		0			0
$415$		0			0
$416$		0			0
$417$	303.259	+	289.302i	0.727240	+	0.693769i
$418$		0			0
$419$	−608.628	−	351.391i	−1.45257	−	0.838643i	−0.453945	−	0.891030i	$-0.649984\pi$
$419$	−608.628	−	351.391i	−1.45257	−	0.838643i	−0.998627	+	0.0523870i	$0.983317\pi$
$420$		0			0
$421$	−100.762	−	174.525i	−0.239340	−	0.414549i	0.721185	−	0.692742i	$-0.243598\pi$
$421$	−100.762	−	174.525i	−0.239340	−	0.414549i	−0.960525	+	0.278193i	$0.910264\pi$
$422$		0			0
$423$	33.5665	+	712.133i	0.0793534	+	1.68353i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−217.848	−	125.774i	−0.510182	−	0.294554i
$428$		0			0
$429$	3.60046	−	14.8251i	0.00839267	−	0.0345574i
$430$		0			0
$431$		−	499.638i		−	1.15925i	−0.814883	−	0.579626i	$-0.803199\pi$
$431$		−	499.638i		−	1.15925i	0.814883	−	0.579626i	$-0.196801\pi$
$432$		0			0
$433$			552.323i			1.27557i	0.770213	+	0.637786i	$0.220150\pi$
$433$			552.323i			1.27557i	−0.770213	+	0.637786i	$0.779850\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.1927	+	22.8504i	−0.0301892	+	0.0522892i
$438$		0			0
$439$	−295.077	−	511.088i	−0.672157	−	1.16421i	−0.977291	−	0.211901i	$-0.932035\pi$
$439$	−295.077	−	511.088i	−0.672157	−	1.16421i	0.305134	−	0.952309i	$-0.401299\pi$
$440$		0			0
$441$	−374.935	+	240.691i	−0.850192	+	0.545785i
$442$		0			0
$443$	85.3062	+	147.755i	0.192565	+	0.333532i	0.946100	−	0.323876i	$-0.104986\pi$
$443$	85.3062	+	147.755i	0.192565	+	0.333532i	−0.753535	+	0.657408i	$0.771653\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−495.553	+	519.461i	−1.10862	+	1.16211i
$448$		0			0
$449$		−	285.994i		−	0.636957i	−0.947930	−	0.318478i	$-0.896828\pi$
$449$		−	285.994i		−	0.636957i	0.947930	−	0.318478i	$-0.103172\pi$
$450$		0			0
$451$	−163.975			−0.363582
$452$		0			0
$453$	153.028	−	44.8915i	0.337809	−	0.0990981i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−205.226	+	118.487i	−0.449073	+	0.259272i	−0.707438	−	0.706775i	$-0.750149\pi$
$457$	−205.226	+	118.487i	−0.449073	+	0.259272i	0.258366	+	0.966047i	$0.416816\pi$
$458$		0			0
$459$	−372.064	+	428.735i	−0.810597	+	0.934063i
$460$		0			0
$461$	562.490	−	324.754i	1.22015	−	0.704455i	0.255202	−	0.966888i	$-0.417858\pi$
$461$	562.490	−	324.754i	1.22015	−	0.704455i	0.964950	+	0.262432i	$0.0845247\pi$
$462$		0			0
$463$	−240.689	−	138.962i	−0.519846	−	0.300133i	0.217026	−	0.976166i	$-0.430364\pi$
$463$	−240.689	−	138.962i	−0.519846	−	0.300133i	−0.736872	+	0.676033i	$0.763698\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	593.440			1.27075			0.635375	−	0.772204i	$-0.280846\pi$
$467$	593.440			1.27075			0.635375	+	0.772204i	$0.280846\pi$
$468$		0			0
$469$	356.158			0.759399
$470$		0			0
$471$	180.042	−	188.728i	0.382255	−	0.400697i
$472$		0			0
$473$	60.4881	−	104.768i	0.127882	−	0.221498i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−742.541	−	383.276i	−1.55669	−	0.803514i
$478$		0			0
$479$	490.726	−	283.321i	1.02448	−	0.591484i	0.109082	−	0.994033i	$-0.465209\pi$
$479$	490.726	−	283.321i	1.02448	−	0.591484i	0.915399	+	0.402549i	$0.131876\pi$
$480$		0			0
$481$	20.2754	−	35.1181i	0.0421526	−	0.0730105i
$482$		0			0
$483$	77.5821	+	18.8417i	0.160626	+	0.0390098i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	651.371i		−	1.33752i	−0.743479	−	0.668759i	$-0.766826\pi$
$487$		−	651.371i		−	1.33752i	0.743479	−	0.668759i	$-0.233174\pi$
$488$		0			0
$489$	−132.824	−	32.2578i	−0.271623	−	0.0659670i
$490$		0			0
$491$	−138.817	−	80.1462i	−0.282724	−	0.163231i	0.351932	−	0.936025i	$-0.385525\pi$
$491$	−138.817	−	80.1462i	−0.282724	−	0.163231i	−0.634656	+	0.772795i	$0.718858\pi$
$492$		0			0
$493$	−6.76372	+	3.90503i	−0.0137195	+	0.00792096i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−83.2810	−	144.247i	−0.167567	−	0.290235i
$498$		0			0
$499$	−278.706	+	482.733i	−0.558530	+	0.967402i	0.439090	+	0.898443i	$0.355301\pi$
$499$	−278.706	+	482.733i	−0.558530	+	0.967402i	−0.997620	+	0.0689585i	$0.978032\pi$
$500$		0			0
$501$	177.574	+	169.402i	0.354440	+	0.338127i
$502$		0			0
$503$	288.388			0.573337			0.286668	−	0.958030i	$-0.407452\pi$
$503$	288.388			0.573337			0.286668	+	0.958030i	$0.407452\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	482.168	−	141.447i	0.951022	−	0.278987i
$508$		0			0
$509$	575.821	+	332.451i	1.13128	+	0.653145i	0.944256	−	0.329211i	$-0.106783\pi$
$509$	575.821	+	332.451i	1.13128	+	0.653145i	0.187023	+	0.982356i	$0.440116\pi$
$510$		0			0
$511$	−309.981	−	536.902i	−0.606616	−	1.05069i
$512$		0			0
$513$	174.138	−	200.662i	0.339451	−	0.391155i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−284.438	−	164.220i	−0.550170	−	0.317641i
$518$		0			0
$519$	617.561	−	181.165i	1.18991	−	0.349065i
$520$		0			0
$521$		−	865.738i		−	1.66168i	−0.556508	−	0.830842i	$-0.687859\pi$
$521$		−	865.738i		−	1.66168i	0.556508	−	0.830842i	$-0.312141\pi$
$522$		0			0
$523$		−	515.707i		−	0.986056i	−0.870013	−	0.493028i	$-0.835890\pi$
$523$		−	515.707i		−	0.986056i	0.870013	−	0.493028i	$-0.164110\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−466.442	+	807.901i	−0.885089	+	1.53302i
$528$		0			0
$529$	260.905	+	451.901i	0.493204	+	0.854255i
$530$		0			0
$531$	−299.361	−	466.328i	−0.563769	−	0.878207i
$532$		0			0
$533$	24.2525	+	42.0066i	0.0455020	+	0.0788117i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−42.8319	−	10.4022i	−0.0797615	−	0.0193710i
$538$		0			0
$539$		−	205.259i		−	0.380815i
$540$		0			0
$541$	117.923			0.217973			0.108987	−	0.994043i	$-0.465239\pi$
$541$	117.923			0.217973			0.108987	+	0.994043i	$0.465239\pi$
$542$		0			0
$543$	−65.9120	+	271.397i	−0.121385	+	0.499811i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−402.413	+	232.333i	−0.735673	+	0.424741i	−0.820494	−	0.571655i	$-0.806301\pi$
$547$	−402.413	+	232.333i	−0.735673	+	0.424741i	0.0848212	+	0.996396i	$0.472968\pi$
$548$		0			0
$549$	−10.7399	−	227.853i	−0.0195626	−	0.415032i
$550$		0			0
$551$	3.16564	−	1.82769i	0.00574527	−	0.00331703i
$552$		0			0
$553$	1236.74	+	714.031i	2.23642	+	1.29120i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.93254			0.0142415			0.00712077	−	0.999975i	$-0.497733\pi$
$557$	7.93254			0.0142415			0.00712077	+	0.999975i	$0.497733\pi$
$558$		0			0
$559$	−35.7856			−0.0640173
$560$		0			0
$561$	−73.6163	−	250.946i	−0.131223	−	0.447319i
$562$		0			0
$563$	210.651	−	364.857i	0.374157	−	0.648059i	−0.616043	−	0.787712i	$-0.711265\pi$
$563$	210.651	−	364.857i	0.374157	−	0.648059i	0.990201	+	0.139653i	$0.0445987\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−730.938	−	334.692i	−1.28913	−	0.590285i
$568$		0			0
$569$	−945.149	+	545.682i	−1.66107	+	0.959019i	−0.688864	+	0.724891i	$0.741890\pi$
$569$	−945.149	+	545.682i	−1.66107	+	0.959019i	−0.972206	+	0.234128i	$0.924776\pi$
$570$		0			0
$571$	65.5170	−	113.479i	0.114741	−	0.198737i	−0.802935	−	0.596066i	$-0.796730\pi$
$571$	65.5170	−	113.479i	0.114741	−	0.198737i	0.917676	+	0.397329i	$0.130063\pi$
$572$		0			0
$573$	−174.900	−	596.206i	−0.305236	−	1.04050i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			71.2517i			0.123487i	0.998092	+	0.0617433i	$0.0196660\pi$
$577$			71.2517i			0.123487i	−0.998092	+	0.0617433i	$0.980334\pi$
$578$		0			0
$579$	539.571	−	565.603i	0.931902	−	0.976862i
$580$		0			0
$581$	141.051	+	81.4359i	0.242773	+	0.140165i
$582$		0			0
$583$	333.392	−	192.484i	0.571856	−	0.330161i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−365.167	−	632.488i	−0.622090	−	1.07749i	−0.989096	−	0.147273i	$-0.952950\pi$
$587$	−365.167	−	632.488i	−0.622090	−	1.07749i	0.367006	−	0.930219i	$-0.380383\pi$
$588$		0			0
$589$	218.310	−	378.124i	0.370646	−	0.641977i
$590$		0			0
$591$	110.959	−	456.881i	0.187748	−	0.773065i
$592$		0			0
$593$	0.291939			0.000492309			0.000246154	−	1.00000i	$-0.499922\pi$
$593$	0.291939			0.000492309			0.000246154		1.00000i	$0.499922\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	102.394	−	421.613i	0.171514	−	0.706219i
$598$		0			0
$599$	−109.992	−	63.5040i	−0.183626	−	0.106017i	0.405369	−	0.914153i	$-0.367143\pi$
$599$	−109.992	−	63.5040i	−0.183626	−	0.106017i	−0.588995	+	0.808136i	$0.700476\pi$
$600$		0			0
$601$	−276.284	−	478.537i	−0.459707	−	0.796235i	0.539239	−	0.842153i	$-0.318712\pi$
$601$	−276.284	−	478.537i	−0.459707	−	0.796235i	−0.998945	+	0.0459177i	$0.985379\pi$
$602$		0			0
$603$	174.473	+	271.783i	0.289341	+	0.450719i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	453.430	+	261.788i	0.747002	+	0.431282i	0.824610	−	0.565702i	$-0.191395\pi$
$607$	453.430	+	261.788i	0.747002	+	0.431282i	−0.0776075	+	0.996984i	$0.524728\pi$
$608$		0			0
$609$	−8.00296	−	7.63462i	−0.0131411	−	0.0125363i
$610$		0			0
$611$			97.1551i			0.159010i
$612$		0			0
$613$		−	345.873i		−	0.564230i	−0.959381	−	0.282115i	$-0.908964\pi$
$613$		−	345.873i		−	0.564230i	0.959381	−	0.282115i	$-0.0910360\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−409.184	+	708.728i	−0.663183	+	1.14867i	0.316591	+	0.948562i	$0.397462\pi$
$617$	−409.184	+	708.728i	−0.663183	+	1.14867i	−0.979774	+	0.200105i	$0.935872\pi$
$618$		0			0
$619$	485.889	+	841.584i	0.784958	+	1.35959i	0.929024	+	0.370019i	$0.120649\pi$
$619$	485.889	+	841.584i	0.784958	+	1.35959i	−0.144067	+	0.989568i	$0.546018\pi$
$620$		0			0
$621$	23.6274	+	68.4329i	0.0380474	+	0.110198i
$622$		0			0
$623$	772.570	+	1338.13i	1.24008	+	2.14788i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	34.4549	+	117.451i	0.0549520	+	0.187322i
$628$		0			0
$629$		−	695.127i		−	1.10513i
$630$		0			0
$631$	965.757			1.53052			0.765259	−	0.643722i	$-0.222611\pi$
$631$	965.757			1.53052			0.765259	+	0.643722i	$0.222611\pi$
$632$		0			0
$633$	51.9089	+	49.5198i	0.0820045	+	0.0782303i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−52.5826	+	30.3586i	−0.0825473	+	0.0476587i
$638$		0			0
$639$	69.2773	−	134.214i	0.108415	−	0.210038i
$640$		0			0
$641$	16.5863	−	9.57610i	0.0258757	−	0.0149393i	−0.487006	−	0.873398i	$-0.661911\pi$
$641$	16.5863	−	9.57610i	0.0258757	−	0.0149393i	0.512882	+	0.858459i	$0.328578\pi$
$642$		0			0
$643$	−142.839	−	82.4679i	−0.222144	−	0.128255i	0.384799	−	0.923001i	$-0.374271\pi$
$643$	−142.839	−	82.4679i	−0.222144	−	0.128255i	−0.606943	+	0.794746i	$0.707604\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	630.208			0.974047			0.487023	−	0.873389i	$-0.338083\pi$
$647$	630.208			0.974047			0.487023	+	0.873389i	$0.338083\pi$
$648$		0			0
$649$	255.293			0.393363
$650$		0			0
$651$	−1283.82	−	311.790i	−1.97207	−	0.478941i
$652$		0			0
$653$	−271.342	+	469.978i	−0.415531	+	0.719722i	−0.995484	−	0.0949286i	$-0.969738\pi$
$653$	−271.342	+	469.978i	−0.415531	+	0.719722i	0.579953	+	0.814650i	$0.303071\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	257.857	−	499.560i	0.392477	−	0.760366i
$658$		0			0
$659$	−659.562	+	380.799i	−1.00085	+	0.577843i	−0.908501	−	0.417883i	$-0.862772\pi$
$659$	−659.562	+	380.799i	−1.00085	+	0.577843i	−0.0923527	+	0.995726i	$0.529439\pi$
$660$		0			0
$661$	284.021	−	491.939i	0.429684	−	0.744234i	−0.567161	−	0.823607i	$-0.691958\pi$
$661$	284.021	−	491.939i	0.429684	−	0.744234i	0.996845	+	0.0793725i	$0.0252916\pi$
$662$		0			0
$663$	−53.3984	+	55.9746i	−0.0805406	+	0.0844263i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			0.996051i			0.00149333i
$668$		0			0
$669$	−370.402	−	1262.64i	−0.553666	−	1.88736i
$670$		0			0
$671$	91.0082	+	52.5436i	0.135631	+	0.0783064i
$672$		0			0
$673$	581.286	−	335.606i	0.863724	−	0.498671i	−0.00153386	−	0.999999i	$-0.500488\pi$
$673$	581.286	−	335.606i	0.863724	−	0.498671i	0.865257	+	0.501328i	$0.167155\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−611.750	−	1059.58i	−0.903619	−	1.56511i	−0.822760	−	0.568389i	$-0.807567\pi$
$677$	−611.750	−	1059.58i	−0.903619	−	1.56511i	−0.0808588	−	0.996726i	$-0.525766\pi$
$678$		0			0
$679$	519.462	−	899.735i	0.765040	−	1.32509i
$680$		0			0
$681$	1233.85	−	361.956i	1.81182	−	0.531506i
$682$		0			0
$683$	1094.61			1.60265			0.801325	−	0.598229i	$-0.204129\pi$
$683$	1094.61			1.60265			0.801325	+	0.598229i	$0.204129\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−126.467	−	120.647i	−0.184086	−	0.175614i
$688$		0			0
$689$	−98.6198	−	56.9382i	−0.143135	−	0.0826389i
$690$		0			0
$691$	160.830	+	278.566i	0.232750	+	0.403134i	0.958616	−	0.284701i	$-0.0918944\pi$
$691$	160.830	+	278.566i	0.232750	+	0.403134i	−0.725867	+	0.687835i	$0.758561\pi$
$692$		0			0
$693$	311.669	−	200.077i	0.449739	−	0.288712i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	720.083	+	415.740i	1.03312	+	0.596471i
$698$		0			0
$699$	200.838	−	826.966i	0.287323	−	1.18307i
$700$		0			0
$701$		−	162.214i		−	0.231404i	−0.993284	−	0.115702i	$-0.963088\pi$
$701$		−	162.214i		−	0.231404i	0.993284	−	0.115702i	$-0.0369118\pi$
$702$		0			0
$703$			325.343i			0.462792i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−513.390	+	889.218i	−0.726153	+	1.25773i
$708$		0			0
$709$	−508.270	−	880.350i	−0.716883	−	1.24168i	−0.962229	−	0.272242i	$-0.912235\pi$
$709$	−508.270	−	880.350i	−0.716883	−	1.24168i	0.245346	−	0.969436i	$-0.421099\pi$
$710$		0			0
$711$	60.9711	+	1293.54i	0.0857540	+	1.81932i
$712$		0			0
$713$	59.4873	+	103.035i	0.0834324	+	0.144509i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−522.425	+	547.630i	−0.728626	+	0.763779i
$718$		0			0
$719$		−	210.621i		−	0.292937i	−0.989215	−	0.146468i	$-0.953209\pi$
$719$		−	210.621i		−	0.292937i	0.989215	−	0.146468i	$-0.0467906\pi$
$720$		0			0
$721$	−1154.59			−1.60137
$722$		0			0
$723$	−690.742	+	202.633i	−0.955383	+	0.280267i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	997.857	−	576.113i	1.37257	−	0.792453i	0.381318	−	0.924444i	$-0.375470\pi$
$727$	997.857	−	576.113i	1.37257	−	0.792453i	0.991251	+	0.131991i	$0.0421371\pi$
$728$		0			0
$729$	−102.666	−	721.735i	−0.140831	−	0.990034i
$730$		0			0
$731$	−531.256	+	306.721i	−0.726753	+	0.419591i
$732$		0			0
$733$	−35.8676	−	20.7081i	−0.0489325	−	0.0282512i	0.475334	−	0.879805i	$-0.342327\pi$
$733$	−35.8676	−	20.7081i	−0.0489325	−	0.0282512i	−0.524267	+	0.851554i	$0.675661\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−148.789			−0.201884
$738$		0			0
$739$	880.919			1.19204			0.596021	−	0.802969i	$-0.296748\pi$
$739$	880.919			1.19204			0.596021	+	0.802969i	$0.296748\pi$
$740$		0			0
$741$	24.9922	−	26.1980i	0.0337277	−	0.0353549i
$742$		0			0
$743$	−49.8112	+	86.2755i	−0.0670406	+	0.116118i	−0.897597	−	0.440816i	$-0.854689\pi$
$743$	−49.8112	+	86.2755i	−0.0670406	+	0.116118i	0.830557	+	0.556934i	$0.188022\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.95381	+	147.529i	0.00930898	+	0.197496i
$748$		0			0
$749$	−1647.55	+	951.211i	−2.19966	+	1.26997i
$750$		0			0
$751$	267.844	−	463.919i	0.356650	−	0.617736i	−0.630749	−	0.775987i	$-0.717252\pi$
$751$	267.844	−	463.919i	0.356650	−	0.617736i	0.987399	+	0.158251i	$0.0505856\pi$
$752$		0			0
$753$	−62.9293	−	15.2831i	−0.0835715	−	0.0202963i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			965.475i			1.27540i	0.770286	+	0.637698i	$0.220113\pi$
$757$			965.475i			1.27540i	−0.770286	+	0.637698i	$0.779887\pi$
$758$		0			0
$759$	−32.4108	−	7.87134i	−0.0427019	−	0.0103707i
$760$		0			0
$761$	953.700	+	550.619i	1.25322	+	0.723547i	0.971748	−	0.236023i	$-0.0758440\pi$
$761$	953.700	+	550.619i	1.25322	+	0.723547i	0.281472	+	0.959569i	$0.409177\pi$
$762$		0			0
$763$	1206.80	−	696.746i	1.58165	−	0.913167i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.7587	−	65.4000i	−0.0492291	−	0.0852673i
$768$		0			0
$769$	−666.991	+	1155.26i	−0.867348	+	1.50229i	−0.00265113	+	0.999996i	$0.500844\pi$
$769$	−666.991	+	1155.26i	−0.867348	+	1.50229i	−0.864697	+	0.502294i	$0.832489\pi$
$770$		0			0
$771$	−119.431	−	113.934i	−0.154904	−	0.147774i
$772$		0			0
$773$	310.586			0.401793			0.200897	−	0.979612i	$-0.435614\pi$
$773$	310.586			0.401793			0.200897	+	0.979612i	$0.435614\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	944.622	−	277.110i	1.21573	−	0.356641i
$778$		0			0
$779$	−337.023	−	194.580i	−0.432635	−	0.249782i
$780$		0			0
$781$	34.7915	+	60.2607i	0.0445474	+	0.0771584i
$782$		0			0
$783$	1.90552	−	9.84705i	0.00243361	−	0.0125761i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−771.107	−	445.199i	−0.979806	−	0.565691i	−0.0775946	−	0.996985i	$-0.524724\pi$
$787$	−771.107	−	445.199i	−0.979806	−	0.565691i	−0.902212	+	0.431294i	$0.858057\pi$
$788$		0			0
$789$	496.375	−	145.614i	0.629119	−	0.184555i
$790$		0			0
$791$			1179.24i			1.49083i
$792$		0			0
$793$		−	31.0856i		−	0.0392000i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−365.720	+	633.446i	−0.458871	+	0.794788i	−0.998902	−	0.0468571i	$-0.985079\pi$
$797$	−365.720	+	633.446i	−0.458871	+	0.794788i	0.540030	+	0.841646i	$0.318413\pi$
$798$		0			0
$799$	832.723	+	1442.32i	1.04221	+	1.80515i
$800$		0			0
$801$	−642.662	+	1245.06i	−0.802325	+	1.55439i
$802$		0			0
$803$	129.498	+	224.297i	0.161267	+	0.279323i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−642.977	−	156.155i	−0.796750	−	0.193500i
$808$		0			0
$809$		−	630.726i		−	0.779637i	−0.920892	−	0.389818i	$-0.872538\pi$
$809$		−	630.726i		−	0.779637i	0.920892	−	0.389818i	$-0.127462\pi$
$810$		0			0
$811$	707.192			0.872000			0.436000	−	0.899947i	$-0.356395\pi$
$811$	707.192			0.872000			0.436000	+	0.899947i	$0.356395\pi$
$812$		0			0
$813$	−124.780	+	513.789i	−0.153481	+	0.631967i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	248.646	−	143.556i	0.304340	−	0.175711i
$818$		0			0
$819$	−97.3521	−	50.2501i	−0.118867	−	0.0613554i
$820$		0			0
$821$	573.638	−	331.190i	0.698706	−	0.403398i	−0.108159	−	0.994134i	$-0.534496\pi$
$821$	573.638	−	331.190i	0.698706	−	0.403398i	0.806865	+	0.590735i	$0.201162\pi$
$822$		0			0
$823$	630.973	+	364.292i	0.766674	+	0.442640i	0.831687	−	0.555245i	$-0.187375\pi$
$823$	630.973	+	364.292i	0.766674	+	0.442640i	−0.0650127	+	0.997884i	$0.520709\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1247.54			1.50851			0.754256	−	0.656581i	$-0.227998\pi$
$827$	1247.54			1.50851			0.754256	+	0.656581i	$0.227998\pi$
$828$		0			0
$829$	1302.23			1.57084			0.785421	−	0.618962i	$-0.212446\pi$
$829$	1302.23			1.57084			0.785421	+	0.618962i	$0.212446\pi$
$830$		0			0
$831$	−322.232	−	1098.44i	−0.387764	−	1.32183i
$832$		0			0
$833$	−520.411	+	901.378i	−0.624743	+	1.08209i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−390.983	−	1132.42i	−0.467124	−	1.35295i
$838$		0			0
$839$	209.274	−	120.824i	0.249432	−	0.144010i	−0.370072	−	0.929003i	$-0.620667\pi$
$839$	209.274	−	120.824i	0.249432	−	0.144010i	0.619504	+	0.784993i	$0.287334\pi$
$840$		0			0
$841$	−420.431	+	728.208i	−0.499918	+	0.865883i
$842$		0			0
$843$	−424.394	−	1446.69i	−0.503433	−	1.71612i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	1030.30i		−	1.21641i
$848$		0			0
$849$	710.597	−	744.880i	0.836982	−	0.877362i
$850$		0			0
$851$	−76.7753	−	44.3263i	−0.0902178	−	0.0520873i
$852$		0			0
$853$	−244.017	+	140.883i	−0.286069	+	0.165162i	−0.636168	−	0.771551i	$-0.719481\pi$
$853$	−244.017	+	140.883i	−0.286069	+	0.165162i	0.350099	+	0.936713i	$0.386148\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	278.587	+	482.527i	0.325072	+	0.563042i	0.981527	−	0.191324i	$-0.0612780\pi$
$857$	278.587	+	482.527i	0.325072	+	0.563042i	−0.656455	+	0.754365i	$0.727945\pi$
$858$		0			0
$859$	−647.267	+	1121.10i	−0.753512	+	1.30512i	0.192599	+	0.981278i	$0.438308\pi$
$859$	−647.267	+	1121.10i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$860$		0			0
$861$	−277.899	+	1144.27i	−0.322763	+	1.32900i
$862$		0			0
$863$	−440.129			−0.509998			−0.254999	−	0.966941i	$-0.582075\pi$
$863$	−440.129			−0.509998			−0.254999	+	0.966941i	$0.582075\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−108.351	+	446.144i	−0.124973	+	0.514583i
$868$		0			0
$869$	−516.661	−	298.294i	−0.594546	−	0.343261i
$870$		0			0
$871$	22.0064	+	38.1162i	0.0252657	+	0.0437614i
$872$		0			0
$873$	941.057	−	44.3568i	1.07796	−	0.0508097i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	427.869	+	247.030i	0.487878	+	0.281676i	0.723694	−	0.690121i	$-0.242443\pi$
$877$	427.869	+	247.030i	0.487878	+	0.281676i	−0.235816	+	0.971798i	$0.575776\pi$
$878$		0			0
$879$	1041.50	+	993.567i	1.18487	+	1.13034i
$880$		0			0
$881$		−	1182.99i		−	1.34279i	−0.741102	−	0.671393i	$-0.765696\pi$
$881$		−	1182.99i		−	1.34279i	0.741102	−	0.671393i	$-0.234304\pi$
$882$		0			0
$883$		−	1695.81i		−	1.92051i	−0.279117	−	0.960257i	$-0.590042\pi$
$883$		−	1695.81i		−	1.92051i	0.279117	−	0.960257i	$-0.409958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−545.638	+	945.072i	−0.615150	+	1.06547i	0.375209	+	0.926940i	$0.377571\pi$
$887$	−545.638	+	945.072i	−0.615150	+	1.06547i	−0.990358	+	0.138530i	$0.955762\pi$
$888$		0			0
$889$	670.601	+	1161.51i	0.754331	+	1.30654i
$890$		0			0
$891$	305.357	+	139.821i	0.342713	+	0.156926i
$892$		0			0
$893$	−389.742	−	675.053i	−0.436441	−	0.755938i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.77722	+	9.46708i	0.00309612	+	0.0105542i
$898$		0			0
$899$		−	16.4825i		−	0.0183343i
$900$		0			0
$901$	−1952.08			−2.16657
$902$		0			0
$903$	−628.592	−	599.662i	−0.696116	−	0.664077i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	988.183	−	570.527i	1.08951	−	0.629027i	0.156062	−	0.987747i	$-0.450120\pi$
$907$	988.183	−	570.527i	1.08951	−	0.629027i	0.933445	+	0.358720i	$0.116787\pi$
$908$		0			0
$909$	−930.057	+	43.8383i	−1.02317	+	0.0482270i
$910$		0			0
$911$	1054.65	−	608.900i	1.15768	−	0.668387i	0.206933	−	0.978355i	$-0.433652\pi$
$911$	1054.65	−	608.900i	1.15768	−	0.668387i	0.950747	+	0.309969i	$0.100319\pi$
$912$		0			0
$913$	−58.9256	−	34.0207i	−0.0645407	−	0.0372626i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1436.09			1.56608
$918$		0			0
$919$	−444.333			−0.483496			−0.241748	−	0.970339i	$-0.577721\pi$
$919$	−444.333			−0.483496			−0.241748	+	0.970339i	$0.577721\pi$
$920$		0			0
$921$	−497.324	−	120.781i	−0.539983	−	0.131141i
$922$		0			0
$923$	10.2916	−	17.8256i	0.0111502	−	0.0193126i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−565.605	−	881.066i	−0.610145	−	0.950448i
$928$		0			0
$929$	−742.230	+	428.527i	−0.798956	+	0.461277i	−0.843106	−	0.537748i	$-0.819275\pi$
$929$	−742.230	+	428.527i	−0.798956	+	0.461277i	0.0441502	+	0.999025i	$0.485942\pi$
$930$		0			0
$931$	243.570	−	421.875i	0.261621	−	0.453142i
$932$		0			0
$933$	−862.869	+	904.498i	−0.924832	+	0.969451i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	986.255i		−	1.05257i	−0.850309	−	0.526283i	$-0.823585\pi$
$937$		−	986.255i		−	1.05257i	0.850309	−	0.526283i	$-0.176415\pi$
$938$		0			0
$939$	−66.7656	−	227.593i	−0.0711028	−	0.242378i
$940$		0			0
$941$	−872.937	−	503.990i	−0.927669	−	0.535590i	−0.0415955	−	0.999135i	$-0.513244\pi$
$941$	−872.937	−	503.990i	−0.927669	−	0.535590i	−0.886074	+	0.463545i	$0.846577\pi$
$942$		0			0
$943$	91.8352	−	53.0211i	0.0973862	−	0.0562260i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	448.223	+	776.345i	0.473308	+	0.819794i	0.999533	−	0.0305512i	$-0.00972627\pi$
$947$	448.223	+	776.345i	0.473308	+	0.819794i	−0.526225	+	0.850346i	$0.676393\pi$
$948$		0			0
$949$	38.3064	−	66.3486i	0.0403650	−	0.0699142i
$950$		0			0
$951$	605.268	−	177.558i	0.636454	−	0.186707i
$952$		0			0
$953$	−952.038			−0.998991			−0.499495	−	0.866317i	$-0.666481\pi$
$953$	−952.038			−0.998991			−0.499495	+	0.866317i	$0.666481\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.34332	+	3.18944i	0.00349354	+	0.00333275i
$958$		0			0
$959$	1021.63	+	589.836i	1.06530	+	0.615053i
$960$		0			0
$961$	−503.887	−	872.757i	−0.524336	−	0.908176i
$962$		0			0
$963$	−1532.96	−	791.264i	−1.59186	−	0.821666i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−664.429	−	383.608i	−0.687104	−	0.396700i	0.115422	−	0.993317i	$-0.463178\pi$
$967$	−664.429	−	383.608i	−0.687104	−	0.396700i	−0.802526	+	0.596617i	$0.796511\pi$
$968$		0			0
$969$	146.478	−	603.133i	0.151164	−	0.622428i
$970$		0			0
$971$			1004.22i			1.03421i	0.855921	+	0.517106i	$0.172991\pi$
$971$			1004.22i			1.03421i	−0.855921	+	0.517106i	$0.827009\pi$
$972$		0			0
$973$			1386.58i			1.42506i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−359.892	+	623.351i	−0.368364	+	0.638026i	−0.989310	−	0.145828i	$-0.953415\pi$
$977$	−359.892	+	623.351i	−0.368364	+	0.638026i	0.620946	+	0.783854i	$0.286749\pi$
$978$		0			0
$979$	−322.749	−	559.018i	−0.329673	−	0.571010i
$980$		0			0
$981$	1122.87	+	579.588i	1.14461	+	0.590814i
$982$		0			0
$983$	382.287	+	662.141i	0.388899	+	0.673592i	0.992302	−	0.123844i	$-0.0395223\pi$
$983$	382.287	+	662.141i	0.388899	+	0.673592i	−0.603403	+	0.797436i	$0.706189\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1628.03	+	1706.58i	−1.64948	+	1.72906i
$988$		0			0
$989$			78.2348i			0.0791050i
$990$		0			0
$991$	512.381			0.517035			0.258517	−	0.966007i	$-0.416766\pi$
$991$	512.381			0.517035			0.258517	+	0.966007i	$0.416766\pi$
$992$		0			0
$993$	−1642.51	+	481.839i	−1.65409	+	0.485235i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1192.69	−	688.601i	1.19628	−	0.690674i	0.236557	−	0.971618i	$-0.423981\pi$
$997$	1192.69	−	688.601i	1.19628	−	0.690674i	0.959724	+	0.280944i	$0.0906475\pi$
$998$		0			0
$999$	674.208	+	585.090i	0.674883	+	0.585676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.d.149.7		32
3.2	odd	2		2700.3.u.d.449.2		32
5.2	odd	4		900.3.p.d.401.8	yes	16
5.3	odd	4		900.3.p.e.401.1	yes	16
5.4	even	2	inner	900.3.u.d.149.10		32
9.2	odd	6	inner	900.3.u.d.749.10		32
9.7	even	3		2700.3.u.d.2249.15		32
15.2	even	4		2700.3.p.e.2501.1		16
15.8	even	4		2700.3.p.d.2501.8		16
15.14	odd	2		2700.3.u.d.449.15		32
45.2	even	12		900.3.p.d.101.8	✓	16
45.7	odd	12		2700.3.p.e.1601.1		16
45.29	odd	6	inner	900.3.u.d.749.7		32
45.34	even	6		2700.3.u.d.2249.2		32
45.38	even	12		900.3.p.e.101.1	yes	16
45.43	odd	12		2700.3.p.d.1601.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.8	✓	16	45.2	even	12
900.3.p.d.401.8	yes	16	5.2	odd	4
900.3.p.e.101.1	yes	16	45.38	even	12
900.3.p.e.401.1	yes	16	5.3	odd	4
900.3.u.d.149.7		32	1.1	even	1	trivial
900.3.u.d.149.10		32	5.4	even	2	inner
900.3.u.d.749.7		32	45.29	odd	6	inner
900.3.u.d.749.10		32	9.2	odd	6	inner
2700.3.p.d.1601.8		16	45.43	odd	12
2700.3.p.d.2501.8		16	15.8	even	4
2700.3.p.e.1601.1		16	45.7	odd	12
2700.3.p.e.2501.1		16	15.2	even	4
2700.3.u.d.449.2		32	3.2	odd	2
2700.3.u.d.449.15		32	15.14	odd	2
2700.3.u.d.2249.2		32	45.34	even	6
2700.3.u.d.2249.15		32	9.7	even	3

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.708005 + 2.91526i) q^{3} +(-8.59526 + 4.96248i) q^{7} +(-7.99746 - 4.12804i) q^{9} +O(q^{10})\)	\(q+(-0.708005 + 2.91526i) q^{3} +(-8.59526 + 4.96248i) q^{7} +(-7.99746 - 4.12804i) q^{9} +(3.59076 - 2.07313i) q^{11} +(-1.06217 - 0.613246i) q^{13} -21.0247 q^{17} +9.84025 q^{19} +(-8.38141 - 28.5709i) q^{21} +(-1.34068 + 2.32213i) q^{23} +(17.6965 - 20.3920i) q^{27} +(0.321704 - 0.185736i) q^{29} +(22.1854 - 38.4263i) q^{31} +(3.50142 + 11.9358i) q^{33} +33.0624i q^{37} +(2.53980 - 2.66233i) q^{39} +(-34.2494 - 19.7739i) q^{41} +(25.2682 - 14.5886i) q^{43} +(-39.6069 - 68.6012i) q^{47} +(24.7524 - 42.8724i) q^{49} +(14.8856 - 61.2924i) q^{51} +92.8471 q^{53} +(-6.96695 + 28.6869i) q^{57} +(53.3228 + 30.7859i) q^{59} +(12.6725 + 21.9495i) q^{61} +(89.2255 - 4.20566i) q^{63} +(-31.0774 - 17.9426i) q^{67} +(-5.82040 - 5.55252i) q^{69} +16.7821i q^{71} +62.4649i q^{73} +(-20.5757 + 35.6382i) q^{77} +(-71.9430 - 124.609i) q^{79} +(46.9187 + 66.0276i) q^{81} +(-8.20517 - 14.2118i) q^{83} +(0.313699 + 1.06935i) q^{87} -155.682i q^{89} +12.1729 q^{91} +(96.3152 + 91.8823i) q^{93} +(-90.6538 + 52.3390i) q^{97} +(-37.2749 + 1.75696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

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