LMFDB - Embedded newform 900.2.w.c.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(109,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.w (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.3
Character	$\chi$	$=$	900.289
Dual form			900.2.w.c.109.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913250 + 2.04107i) q^{5} +4.62675i q^{7} +(-4.00366 + 2.90883i) q^{11} +(2.21170 - 3.04414i) q^{13} +(-2.55872 + 0.831378i) q^{17} +(-1.81426 - 5.58371i) q^{19} +(-3.92540 - 5.40285i) q^{23} +(-3.33195 - 3.72802i) q^{25} +(0.370972 - 1.14173i) q^{29} +(1.02048 + 3.14072i) q^{31} +(-9.44353 - 4.22538i) q^{35} +(1.10342 - 1.51873i) q^{37} +(-2.45366 - 1.78269i) q^{41} +10.6626i q^{43} +(-0.246527 - 0.0801015i) q^{47} -14.4068 q^{49} +(9.31711 + 3.02731i) q^{53} +(-2.28079 - 10.8282i) q^{55} +(7.78643 + 5.65717i) q^{59} +(-5.07552 + 3.68758i) q^{61} +(4.19348 + 7.29430i) q^{65} +(-2.43521 + 0.791247i) q^{67} +(-2.68143 + 8.25259i) q^{71} +(2.86534 + 3.94381i) q^{73} +(-13.4584 - 18.5239i) q^{77} +(-3.85443 + 11.8627i) q^{79} +(8.45513 - 2.74724i) q^{83} +(0.639846 - 5.98178i) q^{85} +(-11.7934 + 8.56841i) q^{89} +(14.0845 + 10.2330i) q^{91} +(13.0536 + 1.39629i) q^{95} +(-3.79176 - 1.23202i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67}+ \cdots - 40 q^{97}+O(q^{100}) $ 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$5$	−0.913250	+	2.04107i	−0.408418	+	0.912795i
$5$	−0.913250	+	2.04107i	−0.408418	+	0.912795i
$6$		0			0
$7$			4.62675i			1.74875i	0.485254	+	0.874373i	$0.338727\pi$
$7$			4.62675i			1.74875i	−0.485254	+	0.874373i	$0.661273\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.00366	+	2.90883i	−1.20715	+	0.877045i	−0.994969	−	0.100185i	$-0.968056\pi$
$11$	−4.00366	+	2.90883i	−1.20715	+	0.877045i	−0.212180	+	0.977231i	$0.568056\pi$
$12$		0			0
$13$	2.21170	−	3.04414i	0.613415	−	0.844294i	−0.383438	−	0.923567i	$-0.625260\pi$
$13$	2.21170	−	3.04414i	0.613415	−	0.844294i	0.996853	+	0.0792730i	$0.0252599\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.55872	+	0.831378i	−0.620580	+	0.201639i	−0.602398	−	0.798196i	$-0.705788\pi$
$17$	−2.55872	+	0.831378i	−0.620580	+	0.201639i	−0.0181824	+	0.999835i	$0.505788\pi$
$18$		0			0
$19$	−1.81426	−	5.58371i	−0.416219	−	1.28099i	−0.911156	−	0.412062i	$-0.864809\pi$
$19$	−1.81426	−	5.58371i	−0.416219	−	1.28099i	0.494937	−	0.868929i	$-0.335191\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.92540	−	5.40285i	−0.818502	−	1.12657i	−0.989955	−	0.141379i	$-0.954846\pi$
$23$	−3.92540	−	5.40285i	−0.818502	−	1.12657i	0.171453	−	0.985192i	$-0.445154\pi$
$24$		0			0
$25$	−3.33195	−	3.72802i	−0.666390	−	0.745603i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.370972	−	1.14173i	0.0688878	−	0.212015i	−0.910686	−	0.413099i	$-0.864446\pi$
$29$	0.370972	−	1.14173i	0.0688878	−	0.212015i	0.979574	+	0.201084i	$0.0644464\pi$
$30$		0			0
$31$	1.02048	+	3.14072i	0.183284	+	0.564090i	0.999915	−	0.0130708i	$-0.00416068\pi$
$31$	1.02048	+	3.14072i	0.183284	+	0.564090i	−0.816631	+	0.577161i	$0.804161\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9.44353	−	4.22538i	−1.59625	−	0.714219i
$36$		0			0
$37$	1.10342	−	1.51873i	0.181401	−	0.249677i	−0.708627	−	0.705584i	$-0.750685\pi$
$37$	1.10342	−	1.51873i	0.181401	−	0.249677i	0.890028	+	0.455907i	$0.150685\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.45366	−	1.78269i	−0.383198	−	0.278410i	0.379464	−	0.925206i	$-0.376108\pi$
$41$	−2.45366	−	1.78269i	−0.383198	−	0.278410i	−0.762663	+	0.646797i	$0.776108\pi$
$42$		0			0
$43$			10.6626i			1.62603i	0.582244	+	0.813014i	$0.302175\pi$
$43$			10.6626i			1.62603i	−0.582244	+	0.813014i	$0.697825\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.246527	−	0.0801015i	−0.0359597	−	0.0116840i	0.290982	−	0.956729i	$-0.406018\pi$
$47$	−0.246527	−	0.0801015i	−0.0359597	−	0.0116840i	−0.326942	+	0.945045i	$0.606018\pi$
$48$		0			0
$49$	−14.4068			−2.05811
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.31711	+	3.02731i	1.27980	+	0.415833i	0.868511	−	0.495670i	$-0.165078\pi$
$53$	9.31711	+	3.02731i	1.27980	+	0.415833i	0.411292	+	0.911504i	$0.365078\pi$
$54$		0			0
$55$	−2.28079	−	10.8282i	−0.307542	−	1.46008i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.78643	+	5.65717i	1.01371	+	0.736501i	0.964983	−	0.262311i	$-0.0844847\pi$
$59$	7.78643	+	5.65717i	1.01371	+	0.736501i	0.0487233	+	0.998812i	$0.484485\pi$
$60$		0			0
$61$	−5.07552	+	3.68758i	−0.649854	+	0.472147i	−0.863222	−	0.504825i	$-0.831557\pi$
$61$	−5.07552	+	3.68758i	−0.649854	+	0.472147i	0.213367	+	0.976972i	$0.431557\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.19348	+	7.29430i	0.520138	+	0.904747i
$66$		0			0
$67$	−2.43521	+	0.791247i	−0.297508	+	0.0966662i	−0.453968	−	0.891018i	$-0.649992\pi$
$67$	−2.43521	+	0.791247i	−0.297508	+	0.0966662i	0.156460	+	0.987684i	$0.449992\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.68143	+	8.25259i	−0.318227	+	0.979403i	0.656178	+	0.754606i	$0.272172\pi$
$71$	−2.68143	+	8.25259i	−0.318227	+	0.979403i	−0.974406	+	0.224797i	$0.927828\pi$
$72$		0			0
$73$	2.86534	+	3.94381i	0.335363	+	0.461588i	0.943080	−	0.332566i	$-0.107914\pi$
$73$	2.86534	+	3.94381i	0.335363	+	0.461588i	−0.607717	+	0.794154i	$0.707914\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−13.4584	−	18.5239i	−1.53373	−	2.11100i
$78$		0			0
$79$	−3.85443	+	11.8627i	−0.433657	+	1.33466i	0.460800	+	0.887504i	$0.347563\pi$
$79$	−3.85443	+	11.8627i	−0.433657	+	1.33466i	−0.894457	+	0.447155i	$0.852437\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.45513	−	2.74724i	0.928071	−	0.301549i	0.194298	−	0.980943i	$-0.437757\pi$
$83$	8.45513	−	2.74724i	0.928071	−	0.301549i	0.733774	+	0.679394i	$0.237757\pi$
$84$		0			0
$85$	0.639846	−	5.98178i	0.0694011	−	0.648816i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.7934	+	8.56841i	−1.25010	+	0.908249i	−0.998228	−	0.0595118i	$-0.981046\pi$
$89$	−11.7934	+	8.56841i	−1.25010	+	0.908249i	−0.251870	+	0.967761i	$0.581046\pi$
$90$		0			0
$91$	14.0845	+	10.2330i	1.47646	+	1.07271i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	13.0536	+	1.39629i	1.33927	+	0.143256i
$96$		0			0
$97$	−3.79176	−	1.23202i	−0.384995	−	0.125092i	0.110123	−	0.993918i	$-0.464875\pi$
$97$	−3.79176	−	1.23202i	−0.384995	−	0.125092i	−0.495119	+	0.868825i	$0.664875\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.36896			−0.932246			−0.466123	−	0.884720i	$-0.654350\pi$
$101$	−9.36896			−0.932246			−0.466123	+	0.884720i	$0.654350\pi$
$102$		0			0
$103$	−9.91391	−	3.22123i	−0.976847	−	0.317397i	−0.223270	−	0.974757i	$-0.571673\pi$
$103$	−9.91391	−	3.22123i	−0.976847	−	0.317397i	−0.753577	+	0.657360i	$0.771673\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			0.220683i			0.0213342i	0.999943	+	0.0106671i	$0.00339551\pi$
$107$			0.220683i			0.0213342i	−0.999943	+	0.0106671i	$0.996604\pi$
$108$		0			0
$109$	5.40941	+	3.93017i	0.518127	+	0.376442i	0.815898	−	0.578196i	$-0.196243\pi$
$109$	5.40941	+	3.93017i	0.518127	+	0.376442i	−0.297771	+	0.954637i	$0.596243\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.64782	−	7.77355i	0.531302	−	0.731274i	−0.456026	−	0.889966i	$-0.650728\pi$
$113$	5.64782	−	7.77355i	0.531302	−	0.731274i	0.987328	+	0.158692i	$0.0507277\pi$
$114$		0			0
$115$	14.6125	−	3.07787i	1.36262	−	0.287013i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.84658	−	11.8385i	−0.352615	−	1.08524i
$120$		0			0
$121$	4.16882	−	12.8303i	0.378984	−	1.16639i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.6521	−	3.39614i	0.952749	−	0.303760i
$126$		0			0
$127$	−9.40003	−	12.9380i	−0.834118	−	1.14806i	−0.987143	−	0.159842i	$-0.948902\pi$
$127$	−9.40003	−	12.9380i	−0.834118	−	1.14806i	0.153025	−	0.988222i	$-0.451098\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.80795	+	11.7197i	0.332702	+	1.02395i	0.967843	+	0.251556i	$0.0809422\pi$
$131$	3.80795	+	11.7197i	0.332702	+	1.02395i	−0.635140	+	0.772397i	$0.719058\pi$
$132$		0			0
$133$	25.8344	−	8.39411i	2.24013	−	0.727862i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.34717	−	4.60698i	0.285968	−	0.393601i	−0.641731	−	0.766930i	$-0.721784\pi$
$137$	3.34717	−	4.60698i	0.285968	−	0.393601i	0.927699	+	0.373329i	$0.121784\pi$
$138$		0			0
$139$	−14.5598	+	10.5783i	−1.23495	+	0.897242i	−0.997251	−	0.0740969i	$-0.976393\pi$
$139$	−14.5598	+	10.5783i	−1.23495	+	0.897242i	−0.237697	+	0.971339i	$0.576393\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			18.6212i			1.55718i
$144$		0			0
$145$	1.99157	+	1.79987i	0.165391	+	0.149471i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.09001			−0.0892972			−0.0446486	−	0.999003i	$-0.514217\pi$
$149$	−1.09001			−0.0892972			−0.0446486	+	0.999003i	$0.514217\pi$
$150$		0			0
$151$	11.3789			0.926004			0.463002	−	0.886357i	$-0.346772\pi$
$151$	11.3789			0.926004			0.463002	+	0.886357i	$0.346772\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.34239	−	0.785384i	−0.589755	−	0.0630836i
$156$		0			0
$157$		−	3.98415i		−	0.317970i	−0.987281	−	0.158985i	$-0.949178\pi$
$157$		−	3.98415i		−	0.317970i	0.987281	−	0.158985i	$-0.0508221\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	24.9976	−	18.1618i	1.97009	−	1.43135i
$162$		0			0
$163$	−12.8322	+	17.6620i	−1.00509	+	1.38339i	−0.0829441	+	0.996554i	$0.526432\pi$
$163$	−12.8322	+	17.6620i	−1.00509	+	1.38339i	−0.922148	+	0.386837i	$0.873568\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.7118	+	4.78015i	−1.13843	+	0.369899i	−0.816775	−	0.576957i	$-0.804240\pi$
$167$	−14.7118	+	4.78015i	−1.13843	+	0.369899i	−0.321658	+	0.946856i	$0.604240\pi$
$168$		0			0
$169$	−0.357976	−	1.10174i	−0.0275366	−	0.0847490i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.0925	−	13.8911i	−0.767317	−	1.05612i	−0.996570	−	0.0827547i	$-0.973628\pi$
$173$	−10.0925	−	13.8911i	−0.767317	−	1.05612i	0.229253	−	0.973367i	$-0.426372\pi$
$174$		0			0
$175$	17.2486	−	15.4161i	1.30387	−	1.16535i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.46392	+	13.7385i	−0.333649	+	1.02687i	0.633734	+	0.773551i	$0.281521\pi$
$179$	−4.46392	+	13.7385i	−0.333649	+	1.02687i	−0.967384	+	0.253316i	$0.918479\pi$
$180$		0			0
$181$	3.83071	+	11.7897i	0.284734	+	0.876322i	0.986478	+	0.163893i	$0.0524051\pi$
$181$	3.83071	+	11.7897i	0.284734	+	0.876322i	−0.701744	+	0.712429i	$0.747595\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.09213	+	3.63913i	0.153817	+	0.267554i
$186$		0			0
$187$	7.82590	−	10.7714i	0.572287	−	0.787685i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.33930	−	0.973056i	−0.0969081	−	0.0704078i	0.538276	−	0.842769i	$-0.319076\pi$
$191$	−1.33930	−	0.973056i	−0.0969081	−	0.0704078i	−0.635184	+	0.772361i	$0.719076\pi$
$192$		0			0
$193$		−	16.3253i		−	1.17512i	−0.809181	−	0.587560i	$-0.800089\pi$
$193$		−	16.3253i		−	1.17512i	0.809181	−	0.587560i	$-0.199911\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.9652	+	4.21264i	0.923730	+	0.300138i	0.731996	−	0.681309i	$-0.238589\pi$
$197$	12.9652	+	4.21264i	0.923730	+	0.300138i	0.191734	+	0.981447i	$0.438589\pi$
$198$		0			0
$199$	6.07817			0.430870			0.215435	−	0.976518i	$-0.430883\pi$
$199$	6.07817			0.430870			0.215435	+	0.976518i	$0.430883\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.28252	+	1.71639i	0.370760	+	0.120467i
$204$		0			0
$205$	5.87941	−	3.38006i	0.410636	−	0.236074i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	23.5057	+	17.0779i	1.62593	+	1.18130i
$210$		0			0
$211$	−13.8200	+	10.0408i	−0.951409	+	0.691239i	−0.951140	−	0.308761i	$-0.900086\pi$
$211$	−13.8200	+	10.0408i	−0.951409	+	0.691239i	−0.000268984		1.00000i	$0.500086\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−21.7631	−	9.73760i	−1.48423	−	0.664099i
$216$		0			0
$217$	−14.5313	+	4.72151i	−0.986450	+	0.320517i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.12828	+	9.62787i	−0.210431	+	0.647640i
$222$		0			0
$223$	0.460700	+	0.634100i	0.0308508	+	0.0424624i	0.824164	−	0.566352i	$-0.191646\pi$
$223$	0.460700	+	0.634100i	0.0308508	+	0.0424624i	−0.793313	+	0.608814i	$0.791646\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.0771	+	19.3755i	0.934331	+	1.28600i	0.958146	+	0.286280i	$0.0924186\pi$
$227$	14.0771	+	19.3755i	0.934331	+	1.28600i	−0.0238153	+	0.999716i	$0.507581\pi$
$228$		0			0
$229$	1.71005	−	5.26299i	0.113003	−	0.347788i	−0.878522	−	0.477702i	$-0.841470\pi$
$229$	1.71005	−	5.26299i	0.113003	−	0.347788i	0.991525	+	0.129914i	$0.0414700\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.863314	+	0.280508i	−0.0565576	+	0.0183767i	−0.337159	−	0.941448i	$-0.609466\pi$
$233$	−0.863314	+	0.280508i	−0.0565576	+	0.0183767i	0.280602	+	0.959824i	$0.409466\pi$
$234$		0			0
$235$	0.388634	−	0.430027i	0.0253517	−	0.0280519i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.09227	−	6.60592i	0.588130	−	0.427302i	−0.253516	−	0.967331i	$-0.581587\pi$
$239$	9.09227	−	6.60592i	0.588130	−	0.427302i	0.841646	+	0.540030i	$0.181587\pi$
$240$		0			0
$241$	16.3840	+	11.9037i	1.05539	+	0.766783i	0.973229	−	0.229837i	$-0.0738193\pi$
$241$	16.3840	+	11.9037i	1.05539	+	0.766783i	0.0821564	+	0.996619i	$0.473819\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.1570	−	29.4053i	0.840570	−	1.87864i
$246$		0			0
$247$	−21.0102	−	6.82663i	−1.33685	−	0.434368i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	30.6919			1.93725			0.968627	−	0.248520i	$-0.0799442\pi$
$251$	30.6919			1.93725			0.968627	+	0.248520i	$0.0799442\pi$
$252$		0			0
$253$	31.4319	+	10.2129i	1.97611	+	0.642077i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	4.77543i		−	0.297883i	−0.988846	−	0.148941i	$-0.952413\pi$
$257$		−	4.77543i		−	0.297883i	0.988846	−	0.148941i	$-0.0475866\pi$
$258$		0			0
$259$	7.02676	+	5.10524i	0.436622	+	0.317224i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.711022	−	0.978638i	0.0438435	−	0.0603454i	−0.786532	−	0.617549i	$-0.788126\pi$
$263$	0.711022	−	0.978638i	0.0438435	−	0.0603454i	0.830376	+	0.557204i	$0.188126\pi$
$264$		0			0
$265$	−14.6878	+	16.2522i	−0.902265	+	0.998364i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.88763	−	24.2756i	−0.480917	−	1.48011i	−0.837808	−	0.545965i	$-0.816163\pi$
$269$	−7.88763	−	24.2756i	−0.480917	−	1.48011i	0.356891	−	0.934146i	$-0.383837\pi$
$270$		0			0
$271$	−1.81499	+	5.58596i	−0.110253	+	0.339323i	−0.990927	−	0.134399i	$-0.957090\pi$
$271$	−1.81499	+	5.58596i	−0.110253	+	0.339323i	0.880675	+	0.473722i	$0.157090\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	24.1842	+	5.23364i	1.45836	+	0.315600i
$276$		0			0
$277$	2.88332	+	3.96855i	0.173242	+	0.238447i	0.886805	−	0.462144i	$-0.152920\pi$
$277$	2.88332	+	3.96855i	0.173242	+	0.238447i	−0.713563	+	0.700591i	$0.752920\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.400257	+	1.23186i	0.0238773	+	0.0734868i	0.962285	−	0.272043i	$-0.0876993\pi$
$281$	0.400257	+	1.23186i	0.0238773	+	0.0734868i	−0.938408	+	0.345530i	$0.887699\pi$
$282$		0			0
$283$	28.7501	−	9.34149i	1.70902	−	0.555294i	0.718849	−	0.695166i	$-0.244669\pi$
$283$	28.7501	−	9.34149i	1.70902	−	0.555294i	0.990169	+	0.139873i	$0.0446693\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.24807	−	11.3525i	0.486868	−	0.670116i
$288$		0			0
$289$	−7.89744	+	5.73783i	−0.464555	+	0.337519i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			8.06831i			0.471356i	0.971831	+	0.235678i	$0.0757310\pi$
$293$			8.06831i			0.471356i	−0.971831	+	0.235678i	$0.924269\pi$
$294$		0			0
$295$	−18.6576	+	10.7263i	−1.08629	+	0.624506i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−25.1289			−1.45324
$300$		0			0
$301$	−49.3331			−2.84351
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.89140	−	13.7272i	−0.165561	−	0.786017i
$306$		0			0
$307$		−	14.7750i		−	0.843255i	−0.906769	−	0.421628i	$-0.861459\pi$
$307$		−	14.7750i		−	0.843255i	0.906769	−	0.421628i	$-0.138541\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.40552	+	5.38043i	−0.419929	+	0.305096i	−0.777609	−	0.628748i	$-0.783568\pi$
$311$	−7.40552	+	5.38043i	−0.419929	+	0.305096i	0.357680	+	0.933844i	$0.383568\pi$
$312$		0			0
$313$	7.79128	−	10.7238i	0.440389	−	0.606144i	−0.529909	−	0.848054i	$-0.677774\pi$
$313$	7.79128	−	10.7238i	0.440389	−	0.606144i	0.970299	+	0.241910i	$0.0777740\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.751858	+	0.244293i	−0.0422286	+	0.0137209i	−0.330055	−	0.943962i	$-0.607067\pi$
$317$	−0.751858	+	0.244293i	−0.0422286	+	0.0137209i	0.287827	+	0.957683i	$0.407067\pi$
$318$		0			0
$319$	1.83587	+	5.65021i	0.102789	+	0.316351i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	9.28434	+	12.7788i	0.516595	+	0.711032i
$324$		0			0
$325$	−18.7179	+	1.89768i	−1.03828	+	0.105264i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.370610	−	1.14062i	0.0204324	−	0.0628844i
$330$		0			0
$331$	−1.04253	−	3.20858i	−0.0573026	−	0.176359i	0.918308	−	0.395866i	$-0.129555\pi$
$331$	−1.04253	−	3.20858i	−0.0573026	−	0.176359i	−0.975611	+	0.219506i	$0.929555\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.608960	−	5.69304i	0.0332711	−	0.311044i
$336$		0			0
$337$	−10.6189	+	14.6157i	−0.578449	+	0.796166i	−0.993524	−	0.113621i	$-0.963755\pi$
$337$	−10.6189	+	14.6157i	−0.578449	+	0.796166i	0.415076	+	0.909787i	$0.363755\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13.2215	−	9.60597i	−0.715983	−	0.520192i
$342$		0			0
$343$		−	34.2694i		−	1.85037i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.90284	+	0.943191i	0.155833	+	0.0506332i	0.385895	−	0.922543i	$-0.373893\pi$
$347$	2.90284	+	0.943191i	0.155833	+	0.0506332i	−0.230062	+	0.973176i	$0.573893\pi$
$348$		0			0
$349$	0.628744			0.0336559			0.0168280	−	0.999858i	$-0.494643\pi$
$349$	0.628744			0.0336559			0.0168280	+	0.999858i	$0.494643\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.9651	+	5.83721i	0.956184	+	0.310683i	0.745226	−	0.666812i	$-0.232342\pi$
$353$	17.9651	+	5.83721i	0.956184	+	0.310683i	0.210958	+	0.977495i	$0.432342\pi$
$354$		0			0
$355$	−14.3953	−	13.0097i	−0.764024	−	0.690482i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.4087	−	17.0074i	−1.23546	−	0.897617i	−0.238176	−	0.971222i	$-0.576550\pi$
$359$	−23.4087	−	17.0074i	−1.23546	−	0.897617i	−0.997287	+	0.0736053i	$0.976550\pi$
$360$		0			0
$361$	−12.5149	+	9.09264i	−0.658681	+	0.478560i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.6664	+	2.24669i	−0.558303	+	0.117597i
$366$		0			0
$367$	5.11949	−	1.66342i	0.267235	−	0.0868299i	−0.172334	−	0.985038i	$-0.555131\pi$
$367$	5.11949	−	1.66342i	0.267235	−	0.0868299i	0.439570	+	0.898209i	$0.355131\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−14.0066	+	43.1079i	−0.727187	+	2.23805i
$372$		0			0
$373$	6.46415	+	8.89714i	0.334701	+	0.460677i	0.942884	−	0.333120i	$-0.108101\pi$
$373$	6.46415	+	8.89714i	0.334701	+	0.460677i	−0.608183	+	0.793797i	$0.708101\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.65513	−	3.65447i	−0.136746	−	0.188215i
$378$		0			0
$379$	−2.18405	+	6.72183i	−0.112187	+	0.345277i	−0.991350	−	0.131245i	$-0.958103\pi$
$379$	−2.18405	+	6.72183i	−0.112187	+	0.345277i	0.879163	+	0.476522i	$0.158103\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.70484	−	2.50346i	0.393699	−	0.127921i	−0.105476	−	0.994422i	$-0.533637\pi$
$383$	7.70484	−	2.50346i	0.393699	−	0.127921i	0.499175	+	0.866501i	$0.333637\pi$
$384$		0			0
$385$	50.0996	−	10.5526i	2.55331	−	0.537812i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−26.7325	+	19.4223i	−1.35539	+	0.984750i	−0.356669	+	0.934231i	$0.616088\pi$
$389$	−26.7325	+	19.4223i	−1.35539	+	0.984750i	−0.998723	+	0.0505192i	$0.983912\pi$
$390$		0			0
$391$	14.5358	+	10.5609i	0.735107	+	0.534086i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.6926	−	18.7008i	−1.04116	−	0.940938i
$396$		0			0
$397$	11.7615	+	3.82155i	0.590294	+	0.191798i	0.588907	−	0.808201i	$-0.299559\pi$
$397$	11.7615	+	3.82155i	0.590294	+	0.191798i	0.00138688	+	0.999999i	$0.499559\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.7983			0.738993			0.369496	−	0.929232i	$-0.379530\pi$
$401$	14.7983			0.738993			0.369496	+	0.929232i	$0.379530\pi$
$402$		0			0
$403$	11.8178	+	3.83984i	0.588687	+	0.191276i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			9.29012i			0.460494i
$408$		0			0
$409$	−19.1618	−	13.9219i	−0.947491	−	0.688392i	0.00272132	−	0.999996i	$-0.499134\pi$
$409$	−19.1618	−	13.9219i	−0.947491	−	0.688392i	−0.950212	+	0.311604i	$0.899134\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−26.1743	+	36.0258i	−1.28795	+	1.77272i
$414$		0			0
$415$	−2.11433	+	19.7664i	−0.103789	+	0.970297i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.477059	+	1.46824i	0.0233058	+	0.0717280i	0.962033	−	0.272933i	$-0.0879938\pi$
$419$	0.477059	+	1.46824i	0.0233058	+	0.0717280i	−0.938727	+	0.344661i	$0.887994\pi$
$420$		0			0
$421$	−5.43760	+	16.7352i	−0.265013	+	0.815625i	0.726678	+	0.686978i	$0.241063\pi$
$421$	−5.43760	+	16.7352i	−0.265013	+	0.815625i	−0.991691	+	0.128647i	$0.958937\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	11.6249	+	6.76883i	0.563891	+	0.328337i
$426$		0			0
$427$	−17.0615	−	23.4832i	−0.825665	−	1.13643i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.83527	−	14.8814i	−0.232907	−	0.716814i	−0.997392	−	0.0721724i	$-0.977007\pi$
$431$	−4.83527	−	14.8814i	−0.232907	−	0.716814i	0.764485	−	0.644641i	$-0.222993\pi$
$432$		0			0
$433$	0.217772	−	0.0707586i	0.0104655	−	0.00340044i	−0.303780	−	0.952742i	$-0.598249\pi$
$433$	0.217772	−	0.0707586i	0.0104655	−	0.00340044i	0.314245	+	0.949342i	$0.398249\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.0462	+	31.7204i	−1.10245	+	1.51739i
$438$		0			0
$439$	15.7111	−	11.4147i	0.749848	−	0.544796i	−0.145932	−	0.989295i	$-0.546618\pi$
$439$	15.7111	−	11.4147i	0.749848	−	0.544796i	0.895780	+	0.444498i	$0.146618\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	12.7980i		−	0.608051i	−0.952664	−	0.304026i	$-0.901669\pi$
$443$		−	12.7980i		−	0.608051i	0.952664	−	0.304026i	$-0.0983309\pi$
$444$		0			0
$445$	−6.71842	−	31.8963i	−0.318483	−	1.51203i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−21.1499			−0.998124			−0.499062	−	0.866566i	$-0.666322\pi$
$449$	−21.1499			−0.998124			−0.499062	+	0.866566i	$0.666322\pi$
$450$		0			0
$451$	15.0092			0.706755
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−33.7489	+	19.4022i	−1.58217	+	0.909589i
$456$		0			0
$457$		−	8.97118i		−	0.419654i	−0.977739	−	0.209827i	$-0.932710\pi$
$457$		−	8.97118i		−	0.419654i	0.977739	−	0.209827i	$-0.0672901\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.2764	−	16.1847i	1.03751	−	0.753797i	0.0677146	−	0.997705i	$-0.478429\pi$
$461$	22.2764	−	16.1847i	1.03751	−	0.753797i	0.969799	+	0.243907i	$0.0784293\pi$
$462$		0			0
$463$	−17.2815	+	23.7859i	−0.803140	+	1.10543i	0.189206	+	0.981937i	$0.439409\pi$
$463$	−17.2815	+	23.7859i	−0.803140	+	1.10543i	−0.992346	+	0.123489i	$0.960591\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.6119	−	4.09785i	0.583609	−	0.189626i	−0.00230768	−	0.999997i	$-0.500735\pi$
$467$	12.6119	−	4.09785i	0.583609	−	0.189626i	0.585917	+	0.810371i	$0.300735\pi$
$468$		0			0
$469$	−3.66090	−	11.2671i	−0.169045	−	0.520266i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−31.0156	−	42.6893i	−1.42610	−	1.96286i
$474$		0			0
$475$	−14.7711	+	25.3682i	−0.677747	+	1.16397i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.58057	+	17.1752i	−0.254983	+	0.784757i	0.738850	+	0.673870i	$0.235369\pi$
$479$	−5.58057	+	17.1752i	−0.254983	+	0.784757i	−0.993833	+	0.110887i	$0.964631\pi$
$480$		0			0
$481$	−2.18279	−	6.71793i	−0.0995266	−	0.306311i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.97746	−	6.61412i	0.271423	−	0.300332i
$486$		0			0
$487$	8.26258	−	11.3725i	0.374413	−	0.515336i	−0.579681	−	0.814844i	$-0.696823\pi$
$487$	8.26258	−	11.3725i	0.374413	−	0.515336i	0.954094	+	0.299508i	$0.0968226\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−22.0310	−	16.0065i	−0.994247	−	0.722363i	−0.0334000	−	0.999442i	$-0.510634\pi$
$491$	−22.0310	−	16.0065i	−0.994247	−	0.722363i	−0.960847	+	0.277079i	$0.910634\pi$
$492$		0			0
$493$			3.22980i			0.145463i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−38.1827	−	12.4063i	−1.71273	−	0.556499i
$498$		0			0
$499$	8.17654			0.366032			0.183016	−	0.983110i	$-0.441414\pi$
$499$	8.17654			0.366032			0.183016	+	0.983110i	$0.441414\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.45805	+	3.07311i	0.421714	+	0.137023i	0.512183	−	0.858876i	$-0.328837\pi$
$503$	9.45805	+	3.07311i	0.421714	+	0.137023i	−0.0904697	+	0.995899i	$0.528837\pi$
$504$		0			0
$505$	8.55620	−	19.1227i	0.380746	−	0.850950i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.9758	−	10.1540i	−0.619464	−	0.450067i	0.233270	−	0.972412i	$-0.425057\pi$
$509$	−13.9758	−	10.1540i	−0.619464	−	0.450067i	−0.852734	+	0.522345i	$0.825057\pi$
$510$		0			0
$511$	−18.2470	+	13.2572i	−0.807200	+	0.586465i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.6286	−	17.2932i	0.688680	−	0.762031i
$516$		0			0
$517$	1.22001	−	0.396406i	0.0536561	−	0.0174339i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.43786	−	10.5807i	0.150615	−	0.463547i	−0.847075	−	0.531474i	$-0.821638\pi$
$521$	3.43786	−	10.5807i	0.150615	−	0.463547i	0.997690	+	0.0679269i	$0.0216385\pi$
$522$		0			0
$523$	−2.20585	−	3.03609i	−0.0964551	−	0.132759i	0.758062	−	0.652183i	$-0.226147\pi$
$523$	−2.20585	−	3.03609i	−0.0964551	−	0.132759i	−0.854517	+	0.519424i	$0.826147\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.22225	−	7.18781i	−0.227485	−	0.313106i
$528$		0			0
$529$	−6.67462	+	20.5424i	−0.290201	+	0.893146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−10.8535	+	3.52653i	−0.470119	+	0.152751i
$534$		0			0
$535$	−0.450429	−	0.201538i	−0.0194738	−	0.00871326i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	57.6799	−	41.9069i	2.48445	−	1.80506i
$540$		0			0
$541$	−15.2752	−	11.0981i	−0.656731	−	0.477143i	0.208826	−	0.977953i	$-0.433036\pi$
$541$	−15.2752	−	11.0981i	−0.656731	−	0.477143i	−0.865557	+	0.500810i	$0.833036\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.9619	+	7.45177i	−0.555226	+	0.319199i
$546$		0			0
$547$	0.147706	+	0.0479926i	0.00631545	+	0.00205201i	0.312173	−	0.950025i	$-0.398943\pi$
$547$	0.147706	+	0.0479926i	0.00631545	+	0.00205201i	−0.305858	+	0.952077i	$0.598943\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.04815			−0.300261
$552$		0			0
$553$	−54.8858	−	17.8335i	−2.33398	−	0.758356i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			19.0371i			0.806626i	0.915062	+	0.403313i	$0.132141\pi$
$557$			19.0371i			0.806626i	−0.915062	+	0.403313i	$0.867859\pi$
$558$		0			0
$559$	32.4584	+	23.5824i	1.37285	+	0.997430i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.2630	+	25.1369i	−0.769694	+	1.05939i	0.226652	+	0.973976i	$0.427222\pi$
$563$	−18.2630	+	25.1369i	−0.769694	+	1.05939i	−0.996345	+	0.0854166i	$0.972778\pi$
$564$		0			0
$565$	10.7085	+	18.6268i	0.450510	+	0.783635i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.1573	+	37.4162i	0.509659	+	1.56857i	0.792794	+	0.609490i	$0.208626\pi$
$569$	12.1573	+	37.4162i	0.509659	+	1.56857i	−0.283135	+	0.959080i	$0.591374\pi$
$570$		0			0
$571$	8.78632	−	27.0415i	0.367696	−	1.13165i	−0.580580	−	0.814203i	$-0.697174\pi$
$571$	8.78632	−	27.0415i	0.367696	−	1.13165i	0.948276	−	0.317448i	$-0.102826\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.06267	+	32.6360i	−0.294534	+	1.36101i
$576$		0			0
$577$	13.2014	+	18.1701i	0.549581	+	0.756433i	0.989955	−	0.141381i	$-0.0451544\pi$
$577$	13.2014	+	18.1701i	0.549581	+	0.756433i	−0.440375	+	0.897814i	$0.645154\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.7108	+	39.1198i	0.527332	+	1.62296i
$582$		0			0
$583$	−46.1085	+	14.9815i	−1.90962	+	0.620472i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.45335	−	13.0114i	0.390182	−	0.537039i	−0.568064	−	0.822984i	$-0.692308\pi$
$587$	9.45335	−	13.0114i	0.390182	−	0.537039i	0.958246	+	0.285945i	$0.0923076\pi$
$588$		0			0
$589$	15.6854	−	11.3961i	0.646307	−	0.469570i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			20.4648i			0.840389i	0.907434	+	0.420194i	$0.138038\pi$
$593$			20.4648i			0.840389i	−0.907434	+	0.420194i	$0.861962\pi$
$594$		0			0
$595$	27.6762	+	2.96041i	1.13461	+	0.121365i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	18.5688			0.758699			0.379349	−	0.925253i	$-0.376148\pi$
$599$	18.5688			0.758699			0.379349	+	0.925253i	$0.376148\pi$
$600$		0			0
$601$	47.2047			1.92552			0.962761	−	0.270355i	$-0.0871409\pi$
$601$	47.2047			1.92552			0.962761	+	0.270355i	$0.0871409\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	22.3804	+	20.2261i	0.909894	+	0.822310i
$606$		0			0
$607$			0.0786576i			0.00319261i	0.999999	+	0.00159631i	$0.000508121\pi$
$607$			0.0786576i			0.00319261i	−0.999999	+	0.00159631i	$0.999492\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.789085	+	0.573304i	−0.0319230	+	0.0231934i
$612$		0			0
$613$	−3.12162	+	4.29654i	−0.126081	+	0.173536i	−0.867391	−	0.497627i	$-0.834205\pi$
$613$	−3.12162	+	4.29654i	−0.126081	+	0.173536i	0.741310	+	0.671163i	$0.234205\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	28.9429	−	9.40411i	1.16520	−	0.378595i	0.338349	−	0.941021i	$-0.390132\pi$
$617$	28.9429	−	9.40411i	1.16520	−	0.378595i	0.826848	+	0.562426i	$0.190132\pi$
$618$		0			0
$619$	9.77918	+	30.0972i	0.393058	+	1.20971i	0.930463	+	0.366385i	$0.119405\pi$
$619$	9.77918	+	30.0972i	0.393058	+	1.20971i	−0.537405	+	0.843324i	$0.680595\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−39.6439	−	54.5651i	−1.58830	−	2.18610i
$624$		0			0
$625$	−2.79622	+	24.8431i	−0.111849	+	0.993725i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.56070	+	4.80335i	−0.0622293	+	0.191522i
$630$		0			0
$631$	−10.4722	−	32.2301i	−0.416891	−	1.28306i	−0.910548	−	0.413403i	$-0.864340\pi$
$631$	−10.4722	−	32.2301i	−0.416891	−	1.28306i	0.493657	−	0.869657i	$-0.335660\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	34.9920	−	7.37048i	1.38862	−	0.292489i
$636$		0			0
$637$	−31.8635	+	43.8564i	−1.26248	+	1.73765i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−39.6699	−	28.8219i	−1.56687	−	1.13840i	−0.930080	−	0.367358i	$-0.880263\pi$
$641$	−39.6699	−	28.8219i	−1.56687	−	1.13840i	−0.636788	−	0.771039i	$-0.719737\pi$
$642$		0			0
$643$			14.2509i			0.562000i	0.959708	+	0.281000i	$0.0906660\pi$
$643$			14.2509i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−40.2623	−	13.0820i	−1.58287	−	0.514307i	−0.620079	−	0.784539i	$-0.712899\pi$
$647$	−40.2623	−	13.0820i	−1.58287	−	0.514307i	−0.962795	+	0.270233i	$0.912899\pi$
$648$		0			0
$649$	−47.6300			−1.86964
$650$		0			0
$651$		0			0
$652$		0			0
$653$	44.7274	+	14.5328i	1.75032	+	0.568713i	0.996126	−	0.0879407i	$-0.0280286\pi$
$653$	44.7274	+	14.5328i	1.75032	+	0.568713i	0.754192	+	0.656654i	$0.228029\pi$
$654$		0			0
$655$	−27.3983	−	2.93068i	−1.07054	−	0.114511i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.05013	+	6.57531i	0.352543	+	0.256138i	0.749935	−	0.661511i	$-0.230085\pi$
$659$	9.05013	+	6.57531i	0.352543	+	0.256138i	−0.397392	+	0.917649i	$0.630085\pi$
$660$		0			0
$661$	37.7102	−	27.3981i	1.46676	−	1.06566i	0.485218	−	0.874393i	$-0.338740\pi$
$661$	37.7102	−	27.3981i	1.46676	−	1.06566i	0.981538	−	0.191268i	$-0.0612599\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.46029	+	60.3958i	−0.250519	+	2.34205i
$666$		0			0
$667$	−7.62483	+	2.47746i	−0.295235	+	0.0959276i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	9.59412	−	29.5277i	0.370377	−	1.13990i
$672$		0			0
$673$	−8.07264	−	11.1110i	−0.311178	−	0.428299i	0.624570	−	0.780968i	$-0.285274\pi$
$673$	−8.07264	−	11.1110i	−0.311178	−	0.428299i	−0.935748	+	0.352669i	$0.885274\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.6428	+	29.7888i	0.831801	+	1.14488i	0.987585	+	0.157085i	$0.0502095\pi$
$677$	21.6428	+	29.7888i	0.831801	+	1.14488i	−0.155784	+	0.987791i	$0.549790\pi$
$678$		0			0
$679$	5.70024	−	17.5435i	0.218755	−	0.673259i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	28.6179	−	9.29850i	1.09503	−	0.355797i	0.294843	−	0.955546i	$-0.404733\pi$
$683$	28.6179	−	9.29850i	1.09503	−	0.355797i	0.800189	+	0.599748i	$0.204733\pi$
$684$		0			0
$685$	6.34638	+	11.0391i	0.242483	+	0.421784i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	29.8222	−	21.6671i	1.13614	−	0.825451i
$690$		0			0
$691$	6.76839	+	4.91752i	0.257482	+	0.187071i	0.709036	−	0.705172i	$-0.249130\pi$
$691$	6.76839	+	4.91752i	0.257482	+	0.187071i	−0.451554	+	0.892244i	$0.649130\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.29438	−	39.3783i	−0.314624	−	1.49370i
$696$		0			0
$697$	7.76033	+	2.52148i	0.293943	+	0.0955080i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.42495			0.129359			0.0646794	−	0.997906i	$-0.479398\pi$
$701$	3.42495			0.129359			0.0646794	+	0.997906i	$0.479398\pi$
$702$		0			0
$703$	−10.4820	−	3.40581i	−0.395336	−	0.128453i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	43.3478i		−	1.63026i
$708$		0			0
$709$	−40.0330	−	29.0857i	−1.50347	−	1.09234i	−0.968973	−	0.247168i	$-0.920500\pi$
$709$	−40.0330	−	29.0857i	−1.50347	−	1.09234i	−0.534499	−	0.845169i	$-0.679500\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.9630	−	17.8421i	0.485469	−	0.668191i
$714$		0			0
$715$	−38.0072	−	17.0058i	−1.42139	−	0.635980i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	8.08148	+	24.8722i	0.301388	+	0.927578i	0.981000	+	0.194006i	$0.0621481\pi$
$719$	8.08148	+	24.8722i	0.301388	+	0.927578i	−0.679612	+	0.733572i	$0.737852\pi$
$720$		0			0
$721$	14.9038	−	45.8692i	0.555046	−	1.70826i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.49247	+	2.42121i	−0.203985	+	0.0899216i
$726$		0			0
$727$	20.3475	+	28.0059i	0.754647	+	1.03868i	0.997640	+	0.0686545i	$0.0218706\pi$
$727$	20.3475	+	28.0059i	0.754647	+	1.03868i	−0.242994	+	0.970028i	$0.578129\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.86463	−	27.2825i	−0.327870	−	1.00908i
$732$		0			0
$733$	16.6104	−	5.39704i	0.613518	−	0.199344i	0.0142577	−	0.999898i	$-0.495461\pi$
$733$	16.6104	−	5.39704i	0.613518	−	0.199344i	0.599260	+	0.800554i	$0.295461\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.44814	−	10.2515i	0.274356	−	0.377618i
$738$		0			0
$739$	16.2358	−	11.7960i	0.597243	−	0.433922i	−0.247656	−	0.968848i	$-0.579660\pi$
$739$	16.2358	−	11.7960i	0.597243	−	0.433922i	0.844899	+	0.534926i	$0.179660\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			5.84644i			0.214485i	0.994233	+	0.107243i	$0.0342022\pi$
$743$			5.84644i			0.214485i	−0.994233	+	0.107243i	$0.965798\pi$
$744$		0			0
$745$	0.995453	−	2.22479i	0.0364706	−	0.0815101i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.02104			−0.0373081
$750$		0			0
$751$	−32.7925			−1.19662			−0.598308	−	0.801266i	$-0.704160\pi$
$751$	−32.7925			−1.19662			−0.598308	+	0.801266i	$0.704160\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.3918	+	23.2252i	−0.378196	+	0.845252i
$756$		0			0
$757$			22.6371i			0.822759i	0.911464	+	0.411379i	$0.134953\pi$
$757$			22.6371i			0.822759i	−0.911464	+	0.411379i	$0.865047\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−29.3923	+	21.3547i	−1.06547	+	0.774109i	−0.975092	−	0.221799i	$-0.928807\pi$
$761$	−29.3923	+	21.3547i	−1.06547	+	0.774109i	−0.0903767	+	0.995908i	$0.528807\pi$
$762$		0			0
$763$	−18.1839	+	25.0280i	−0.658301	+	0.906073i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	34.4425	−	11.1910i	1.24365	−	0.404085i
$768$		0			0
$769$	−4.51902	−	13.9081i	−0.162960	−	0.501539i	0.835920	−	0.548851i	$-0.184935\pi$
$769$	−4.51902	−	13.9081i	−0.162960	−	0.501539i	−0.998880	+	0.0473119i	$0.984935\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.9422	−	24.6953i	−0.645336	−	0.888229i	0.353550	−	0.935416i	$-0.384975\pi$
$773$	−17.9422	−	24.6953i	−0.645336	−	0.888229i	−0.998886	+	0.0471864i	$0.984975\pi$
$774$		0			0
$775$	8.30846	−	14.2691i	0.298449	−	0.512561i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.50245	+	16.9348i	−0.197146	+	0.606752i
$780$		0			0
$781$	−13.2699	−	40.8404i	−0.474833	−	1.46138i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.13194	+	3.63852i	0.290241	+	0.129865i
$786$		0			0
$787$	28.8905	−	39.7644i	1.02984	−	1.41745i	0.124766	−	0.992186i	$-0.460182\pi$
$787$	28.8905	−	39.7644i	1.02984	−	1.41745i	0.905070	−	0.425262i	$-0.139818\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	35.9663	+	26.1310i	1.27881	+	0.929112i
$792$		0			0
$793$			23.6065i			0.838290i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	42.3529	+	13.7613i	1.50022	+	0.487450i	0.940081	−	0.340951i	$-0.110749\pi$
$797$	42.3529	+	13.7613i	1.50022	+	0.487450i	0.560136	+	0.828401i	$0.310749\pi$
$798$		0			0
$799$	0.697388			0.0246718
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−22.9437	−	7.45487i	−0.809667	−	0.263077i
$804$		0			0
$805$	14.2405	+	67.6082i	0.501913	+	2.38288i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	24.5060	+	17.8046i	0.861584	+	0.625978i	0.928316	−	0.371793i	$-0.121257\pi$
$809$	24.5060	+	17.8046i	0.861584	+	0.625978i	−0.0667312	+	0.997771i	$0.521257\pi$
$810$		0			0
$811$	−5.05382	+	3.67182i	−0.177464	+	0.128935i	−0.672971	−	0.739669i	$-0.734982\pi$
$811$	−5.05382	+	3.67182i	−0.177464	+	0.128935i	0.495507	+	0.868604i	$0.334982\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−24.3304	−	42.3211i	−0.852255	−	1.48244i
$816$		0			0
$817$	59.5367	−	19.3447i	2.08293	−	0.676784i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.95524	−	18.3284i	0.207839	−	0.639664i	−0.791745	−	0.610851i	$-0.790827\pi$
$821$	5.95524	−	18.3284i	0.207839	−	0.639664i	0.999585	−	0.0288127i	$-0.00917263\pi$
$822$		0			0
$823$	−4.44218	−	6.11414i	−0.154845	−	0.213126i	0.724546	−	0.689227i	$-0.242050\pi$
$823$	−4.44218	−	6.11414i	−0.154845	−	0.213126i	−0.879391	+	0.476101i	$0.842050\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.4412	−	25.3821i	−0.641262	−	0.882621i	0.357420	−	0.933944i	$-0.383656\pi$
$827$	−18.4412	−	25.3821i	−0.641262	−	0.882621i	−0.998682	+	0.0513225i	$0.983656\pi$
$828$		0			0
$829$	−8.55625	+	26.3334i	−0.297171	+	0.914597i	0.685313	+	0.728249i	$0.259665\pi$
$829$	−8.55625	+	26.3334i	−0.297171	+	0.914597i	−0.982484	+	0.186349i	$0.940335\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	36.8629	−	11.9775i	1.27723	−	0.414996i
$834$		0			0
$835$	3.67890	−	34.3933i	0.127314	−	1.19023i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	30.5642	−	22.2062i	1.05519	−	0.766643i	0.0819999	−	0.996632i	$-0.473869\pi$
$839$	30.5642	−	22.2062i	1.05519	−	0.766643i	0.973193	+	0.229990i	$0.0738693\pi$
$840$		0			0
$841$	22.2956	+	16.1987i	0.768812	+	0.558575i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.57565	+	0.275506i	0.0886049	+	0.00947770i
$846$		0			0
$847$	59.3626	+	19.2881i	2.03972	+	0.662747i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12.5368			−0.429756
$852$		0			0
$853$	46.9508	+	15.2552i	1.60756	+	0.522329i	0.968962	−	0.247208i	$-0.0795131\pi$
$853$	46.9508	+	15.2552i	1.60756	+	0.522329i	0.638602	+	0.769537i	$0.279513\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			15.7692i			0.538667i	0.963047	+	0.269333i	$0.0868034\pi$
$857$			15.7692i			0.538667i	−0.963047	+	0.269333i	$0.913197\pi$
$858$		0			0
$859$	7.60223	+	5.52335i	0.259385	+	0.188454i	0.709876	−	0.704327i	$-0.248751\pi$
$859$	7.60223	+	5.52335i	0.259385	+	0.188454i	−0.450491	+	0.892781i	$0.648751\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.5040	+	14.4575i	−0.357560	+	0.492140i	−0.949467	−	0.313867i	$-0.898375\pi$
$863$	−10.5040	+	14.4575i	−0.357560	+	0.492140i	0.591907	+	0.806007i	$0.298375\pi$
$864$		0			0
$865$	37.5697	−	7.91343i	1.27741	−	0.269065i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−19.0748	−	58.7061i	−0.647068	−	1.99147i
$870$		0			0
$871$	−2.97728	+	9.16312i	−0.100881	+	0.310481i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.7131	+	49.2844i	0.531199	+	1.66612i
$876$		0			0
$877$	10.4069	+	14.3238i	0.351415	+	0.483681i	0.947732	−	0.319068i	$-0.103370\pi$
$877$	10.4069	+	14.3238i	0.351415	+	0.483681i	−0.596317	+	0.802749i	$0.703370\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	9.82007	+	30.2231i	0.330847	+	1.01824i	0.968732	+	0.248110i	$0.0798094\pi$
$881$	9.82007	+	30.2231i	0.330847	+	1.01824i	−0.637885	+	0.770131i	$0.720191\pi$
$882$		0			0
$883$	32.9158	−	10.6950i	1.10771	−	0.359916i	0.302643	−	0.953104i	$-0.402131\pi$
$883$	32.9158	−	10.6950i	1.10771	−	0.359916i	0.805064	+	0.593188i	$0.202131\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.7639	+	23.0735i	−0.562876	+	0.774732i	−0.991689	−	0.128661i	$-0.958932\pi$
$887$	−16.7639	+	23.0735i	−0.562876	+	0.774732i	0.428813	+	0.903393i	$0.358932\pi$
$888$		0			0
$889$	59.8610	−	43.4916i	2.00767	−	1.45866i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			1.52186i			0.0509271i
$894$		0			0
$895$	−23.9647	−	21.6579i	−0.801051	−	0.723944i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.96444			0.132221
$900$		0			0
$901$	−26.3567			−0.878069
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−27.5620	−	2.94819i	−0.916193	−	0.0980013i
$906$		0			0
$907$			7.01754i			0.233013i	0.993190	+	0.116507i	$0.0371697\pi$
$907$			7.01754i			0.233013i	−0.993190	+	0.116507i	$0.962830\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.9145	+	12.2891i	−0.560403	+	0.407157i	−0.831606	−	0.555365i	$-0.812578\pi$
$911$	−16.9145	+	12.2891i	−0.560403	+	0.407157i	0.271203	+	0.962522i	$0.412578\pi$
$912$		0			0
$913$	−25.8602	+	35.5936i	−0.855849	+	1.17797i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−54.2240	+	17.6184i	−1.79063	+	0.581812i
$918$		0			0
$919$	−18.4658	−	56.8320i	−0.609132	−	1.87471i	−0.465406	−	0.885097i	$-0.654092\pi$
$919$	−18.4658	−	56.8320i	−0.609132	−	1.87471i	−0.143726	−	0.989618i	$-0.545908\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.1916	+	26.4149i	0.631698	+	0.869458i
$924$		0			0
$925$	−9.33837	+	0.946755i	−0.307044	+	0.0311291i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.4320	+	38.2618i	−0.407881	+	1.25533i	0.510585	+	0.859828i	$0.329429\pi$
$929$	−12.4320	+	38.2618i	−0.407881	+	1.25533i	−0.918466	+	0.395501i	$0.870571\pi$
$930$		0			0
$931$	26.1376	+	80.4434i	0.856626	+	2.63642i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	14.8383	+	25.8102i	0.485263	+	0.844085i
$936$		0			0
$937$	−29.0457	+	39.9780i	−0.948881	+	1.30602i	0.00314114	+	0.999995i	$0.499000\pi$
$937$	−29.0457	+	39.9780i	−0.948881	+	1.30602i	−0.952022	+	0.306028i	$0.901000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.0130	+	13.0872i	0.587207	+	0.426631i	0.841315	−	0.540545i	$-0.181782\pi$
$941$	18.0130	+	13.0872i	0.587207	+	0.426631i	−0.254108	+	0.967176i	$0.581782\pi$
$942$		0			0
$943$			20.2546i			0.659579i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	33.9316	+	11.0251i	1.10263	+	0.358266i	0.803114	−	0.595825i	$-0.203175\pi$
$947$	33.9316	+	11.0251i	1.10263	+	0.358266i	0.299516	+	0.954091i	$0.403175\pi$
$948$		0			0
$949$	18.3428			0.595433
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.66940	+	0.867341i	0.0864704	+	0.0280959i	0.351933	−	0.936025i	$-0.385525\pi$
$953$	2.66940	+	0.867341i	0.0864704	+	0.0280959i	−0.265462	+	0.964121i	$0.585525\pi$
$954$		0			0
$955$	3.20919	−	1.84496i	0.103847	−	0.0597014i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	21.3153	+	15.4865i	0.688308	+	0.500085i
$960$		0			0
$961$	16.2568	−	11.8113i	0.524413	−	0.381008i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	33.3211	+	14.9091i	1.07264	+	0.479940i
$966$		0			0
$967$	10.9640	−	3.56243i	0.352580	−	0.114560i	−0.127372	−	0.991855i	$-0.540654\pi$
$967$	10.9640	−	3.56243i	0.352580	−	0.114560i	0.479952	+	0.877295i	$0.340654\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.15578	+	22.0232i	−0.229640	+	0.706759i	0.768148	+	0.640273i	$0.221179\pi$
$971$	−7.15578	+	22.0232i	−0.229640	+	0.706759i	−0.997787	+	0.0664858i	$0.978821\pi$
$972$		0			0
$973$	−48.9433	−	67.3646i	−1.56905	−	2.15961i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.85551	+	6.68304i	0.155342	+	0.213809i	0.879593	−	0.475726i	$-0.157815\pi$
$977$	4.85551	+	6.68304i	0.155342	+	0.213809i	−0.724252	+	0.689536i	$0.757815\pi$
$978$		0			0
$979$	22.2927	−	68.6100i	0.712479	−	2.19278i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.8202	−	6.11506i	0.600271	−	0.195040i	0.00690994	−	0.999976i	$-0.497800\pi$
$983$	18.8202	−	6.11506i	0.600271	−	0.195040i	0.593361	+	0.804936i	$0.297800\pi$
$984$		0			0
$985$	−20.4387	+	22.6157i	−0.651232	+	0.720595i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	57.6083	−	41.8549i	1.83184	−	1.33091i
$990$		0			0
$991$	−17.3036	−	12.5718i	−0.549666	−	0.399355i	0.277997	−	0.960582i	$-0.410330\pi$
$991$	−17.3036	−	12.5718i	−0.549666	−	0.399355i	−0.827662	+	0.561227i	$0.810330\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.55089	+	12.4060i	−0.175975	+	0.393296i
$996$		0			0
$997$	−16.7226	−	5.43350i	−0.529610	−	0.172081i	0.0319923	−	0.999488i	$-0.489815\pi$
$997$	−16.7226	−	5.43350i	−0.529610	−	0.172081i	−0.561602	+	0.827407i	$0.689815\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.w.c.289.3		24
3.2	odd	2		300.2.o.a.289.2	yes	24
15.2	even	4		1500.2.m.d.301.1		24
15.8	even	4		1500.2.m.c.301.6		24
15.14	odd	2		1500.2.o.c.949.6		24
25.9	even	10	inner	900.2.w.c.109.3		24
75.29	odd	10		7500.2.d.g.1249.13		24
75.38	even	20		1500.2.m.c.1201.6		24
75.41	odd	10		1500.2.o.c.49.6		24
75.47	even	20		7500.2.a.m.1.1		12
75.53	even	20		7500.2.a.n.1.12		12
75.59	odd	10		300.2.o.a.109.2	✓	24
75.62	even	20		1500.2.m.d.1201.1		24
75.71	odd	10		7500.2.d.g.1249.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.2	✓	24	75.59	odd	10
300.2.o.a.289.2	yes	24	3.2	odd	2
900.2.w.c.109.3		24	25.9	even	10	inner
900.2.w.c.289.3		24	1.1	even	1	trivial
1500.2.m.c.301.6		24	15.8	even	4
1500.2.m.c.1201.6		24	75.38	even	20
1500.2.m.d.301.1		24	15.2	even	4
1500.2.m.d.1201.1		24	75.62	even	20
1500.2.o.c.49.6		24	75.41	odd	10
1500.2.o.c.949.6		24	15.14	odd	2
7500.2.a.m.1.1		12	75.47	even	20
7500.2.a.n.1.12		12	75.53	even	20
7500.2.d.g.1249.12		24	75.71	odd	10
7500.2.d.g.1249.13		24	75.29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913250 + 2.04107i) q^{5} +4.62675i q^{7} +(-4.00366 + 2.90883i) q^{11} +(2.21170 - 3.04414i) q^{13} +(-2.55872 + 0.831378i) q^{17} +(-1.81426 - 5.58371i) q^{19} +(-3.92540 - 5.40285i) q^{23} +(-3.33195 - 3.72802i) q^{25} +(0.370972 - 1.14173i) q^{29} +(1.02048 + 3.14072i) q^{31} +(-9.44353 - 4.22538i) q^{35} +(1.10342 - 1.51873i) q^{37} +(-2.45366 - 1.78269i) q^{41} +10.6626i q^{43} +(-0.246527 - 0.0801015i) q^{47} -14.4068 q^{49} +(9.31711 + 3.02731i) q^{53} +(-2.28079 - 10.8282i) q^{55} +(7.78643 + 5.65717i) q^{59} +(-5.07552 + 3.68758i) q^{61} +(4.19348 + 7.29430i) q^{65} +(-2.43521 + 0.791247i) q^{67} +(-2.68143 + 8.25259i) q^{71} +(2.86534 + 3.94381i) q^{73} +(-13.4584 - 18.5239i) q^{77} +(-3.85443 + 11.8627i) q^{79} +(8.45513 - 2.74724i) q^{83} +(0.639846 - 5.98178i) q^{85} +(-11.7934 + 8.56841i) q^{89} +(14.0845 + 10.2330i) q^{91} +(13.0536 + 1.39629i) q^{95} +(-3.79176 - 1.23202i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67}+ \cdots - 40 q^{97}+O(q^{100}) \) 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Introduction

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