LMFDB - Embedded newform 850.2.l.a.501.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [850,2,Mod(151,850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(850, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("850.151"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,0,0,-4,0,4,-4,0,8,0,-4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			501.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	850.501
Dual form			850.2.l.a.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 1.70711i) q^{3} -1.00000i q^{4} +(0.707107 + 1.70711i) q^{6} +(-1.41421 + 0.585786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.292893 - 0.292893i) q^{9} +(1.70711 + 4.12132i) q^{11} +(-1.70711 - 0.707107i) q^{12} +0.828427i q^{13} +(0.585786 - 1.41421i) q^{14} -1.00000 q^{16} +(2.12132 + 3.53553i) q^{17} +0.414214 q^{18} +(0.585786 - 0.585786i) q^{19} +2.82843i q^{21} +(-4.12132 - 1.70711i) q^{22} +(1.17157 + 2.82843i) q^{23} +(1.70711 - 0.707107i) q^{24} +(-0.585786 - 0.585786i) q^{26} +(4.41421 - 1.82843i) q^{27} +(0.585786 + 1.41421i) q^{28} +(-1.41421 - 0.585786i) q^{29} +(-1.41421 + 3.41421i) q^{31} +(0.707107 - 0.707107i) q^{32} +8.24264 q^{33} +(-4.00000 - 1.00000i) q^{34} +(-0.292893 + 0.292893i) q^{36} +(-0.828427 + 2.00000i) q^{37} +0.828427i q^{38} +(1.41421 + 0.585786i) q^{39} +(10.3640 - 4.29289i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(1.24264 + 1.24264i) q^{43} +(4.12132 - 1.70711i) q^{44} +(-2.82843 - 1.17157i) q^{46} -9.65685i q^{47} +(-0.707107 + 1.70711i) q^{48} +(-3.29289 + 3.29289i) q^{49} +(7.53553 - 1.12132i) q^{51} +0.828427 q^{52} +(-0.585786 + 0.585786i) q^{53} +(-1.82843 + 4.41421i) q^{54} +(-1.41421 - 0.585786i) q^{56} +(-0.585786 - 1.41421i) q^{57} +(1.41421 - 0.585786i) q^{58} +(0.414214 + 0.414214i) q^{59} +(6.82843 - 2.82843i) q^{61} +(-1.41421 - 3.41421i) q^{62} +(0.585786 + 0.242641i) q^{63} +1.00000i q^{64} +(-5.82843 + 5.82843i) q^{66} +7.41421 q^{67} +(3.53553 - 2.12132i) q^{68} +5.65685 q^{69} +(0.828427 - 2.00000i) q^{71} -0.414214i q^{72} +(4.94975 + 2.05025i) q^{73} +(-0.828427 - 2.00000i) q^{74} +(-0.585786 - 0.585786i) q^{76} +(-4.82843 - 4.82843i) q^{77} +(-1.41421 + 0.585786i) q^{78} +(-2.00000 - 4.82843i) q^{79} -10.0711i q^{81} +(-4.29289 + 10.3640i) q^{82} +(-4.41421 + 4.41421i) q^{83} +2.82843 q^{84} -1.75736 q^{86} +(-2.00000 + 2.00000i) q^{87} +(-1.70711 + 4.12132i) q^{88} +15.0711i q^{89} +(-0.485281 - 1.17157i) q^{91} +(2.82843 - 1.17157i) q^{92} +(4.82843 + 4.82843i) q^{93} +(6.82843 + 6.82843i) q^{94} +(-0.707107 - 1.70711i) q^{96} +(5.12132 + 2.12132i) q^{97} -4.65685i q^{98} +(0.707107 - 1.70711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9} + 4 q^{11} - 4 q^{12} + 8 q^{14} - 4 q^{16} - 4 q^{18} + 8 q^{19} - 8 q^{22} + 16 q^{23} + 4 q^{24} - 8 q^{26} + 12 q^{27} + 8 q^{28} + 16 q^{33} - 16 q^{34} - 4 q^{36} + 8 q^{37} + 16 q^{41}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^9 + 4 * q^11 - 4 * q^12 + 8 * q^14 - 4 * q^16 - 4 * q^18 + 8 * q^19 - 8 * q^22 + 16 * q^23 + 4 * q^24 - 8 * q^26 + 12 * q^27 + 8 * q^28 + 16 * q^33 - 16 * q^34 - 4 * q^36 + 8 * q^37 + 16 * q^41 - 8 * q^42 - 12 * q^43 + 8 * q^44 - 16 * q^49 + 16 * q^51 - 8 * q^52 - 8 * q^53 + 4 * q^54 - 8 * q^57 - 4 * q^59 + 16 * q^61 + 8 * q^63 - 12 * q^66 + 24 * q^67 - 8 * q^71 + 8 * q^74 - 8 * q^76 - 8 * q^77 - 8 * q^79 - 20 * q^82 - 12 * q^83 - 24 * q^86 - 8 * q^87 - 4 * q^88 + 32 * q^91 + 8 * q^93 + 16 * q^94 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	−	1.70711i	0.408248	−	0.985599i	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	0.707107	−	1.70711i	0.408248	−	0.985599i	0.985599	−	0.169102i	$-0.0540867\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	0.707107	+	1.70711i	0.288675	+	0.696923i
$7$	−1.41421	+	0.585786i	−0.534522	+	0.221406i	−0.633583	−	0.773675i	$-0.718416\pi$
$7$	−1.41421	+	0.585786i	−0.534522	+	0.221406i	0.0990602	+	0.995081i	$0.468416\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.292893	−	0.292893i	−0.0976311	−	0.0976311i
$10$		0			0
$11$	1.70711	+	4.12132i	0.514712	+	1.24262i	0.941113	+	0.338091i	$0.109781\pi$
$11$	1.70711	+	4.12132i	0.514712	+	1.24262i	−0.426401	+	0.904534i	$0.640219\pi$
$12$	−1.70711	−	0.707107i	−0.492799	−	0.204124i
$13$			0.828427i			0.229764i	0.993379	+	0.114882i	$0.0366490\pi$
$13$			0.828427i			0.229764i	−0.993379	+	0.114882i	$0.963351\pi$
$14$	0.585786	−	1.41421i	0.156558	−	0.377964i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.12132	+	3.53553i	0.514496	+	0.857493i
$17$	2.12132	+	3.53553i	0.514496	+	0.857493i
$18$	0.414214			0.0976311
$19$	0.585786	−	0.585786i	0.134389	−	0.134389i	−0.636713	−	0.771101i	$-0.719706\pi$
$19$	0.585786	−	0.585786i	0.134389	−	0.134389i	0.771101	+	0.636713i	$0.219706\pi$
$20$		0			0
$21$			2.82843i			0.617213i
$22$	−4.12132	−	1.70711i	−0.878668	−	0.363956i
$23$	1.17157	+	2.82843i	0.244290	+	0.589768i	0.997700	−	0.0677829i	$-0.0215925\pi$
$23$	1.17157	+	2.82843i	0.244290	+	0.589768i	−0.753410	+	0.657551i	$0.771593\pi$
$24$	1.70711	−	0.707107i	0.348462	−	0.144338i
$25$		0			0
$26$	−0.585786	−	0.585786i	−0.114882	−	0.114882i
$27$	4.41421	−	1.82843i	0.849516	−	0.351881i
$28$	0.585786	+	1.41421i	0.110703	+	0.267261i
$29$	−1.41421	−	0.585786i	−0.262613	−	0.108778i	0.247492	−	0.968890i	$-0.420394\pi$
$29$	−1.41421	−	0.585786i	−0.262613	−	0.108778i	−0.510105	+	0.860112i	$0.670394\pi$
$30$		0			0
$31$	−1.41421	+	3.41421i	−0.254000	+	0.613211i	−0.998520	−	0.0543898i	$-0.982679\pi$
$31$	−1.41421	+	3.41421i	−0.254000	+	0.613211i	0.744520	+	0.667601i	$0.232679\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	8.24264			1.43486
$34$	−4.00000	−	1.00000i	−0.685994	−	0.171499i
$35$		0			0
$36$	−0.292893	+	0.292893i	−0.0488155	+	0.0488155i
$37$	−0.828427	+	2.00000i	−0.136193	+	0.328798i	−0.977231	−	0.212177i	$-0.931945\pi$
$37$	−0.828427	+	2.00000i	−0.136193	+	0.328798i	0.841039	+	0.540975i	$0.181945\pi$
$38$			0.828427i			0.134389i
$39$	1.41421	+	0.585786i	0.226455	+	0.0938009i
$40$		0			0
$41$	10.3640	−	4.29289i	1.61858	−	0.670437i	0.624695	−	0.780869i	$-0.285223\pi$
$41$	10.3640	−	4.29289i	1.61858	−	0.670437i	0.993884	+	0.110432i	$0.0352233\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	1.24264	+	1.24264i	0.189501	+	0.189501i	0.795480	−	0.605979i	$-0.207219\pi$
$43$	1.24264	+	1.24264i	0.189501	+	0.189501i	−0.605979	+	0.795480i	$0.707219\pi$
$44$	4.12132	−	1.70711i	0.621312	−	0.257356i
$45$		0			0
$46$	−2.82843	−	1.17157i	−0.417029	−	0.172739i
$47$		−	9.65685i		−	1.40860i	−0.709904	−	0.704298i	$-0.751262\pi$
$47$		−	9.65685i		−	1.40860i	0.709904	−	0.704298i	$-0.248738\pi$
$48$	−0.707107	+	1.70711i	−0.102062	+	0.246400i
$49$	−3.29289	+	3.29289i	−0.470413	+	0.470413i
$50$		0			0
$51$	7.53553	−	1.12132i	1.05519	−	0.157016i
$52$	0.828427			0.114882
$53$	−0.585786	+	0.585786i	−0.0804640	+	0.0804640i	−0.746193	−	0.665729i	$-0.768121\pi$
$53$	−0.585786	+	0.585786i	−0.0804640	+	0.0804640i	0.665729	+	0.746193i	$0.268121\pi$
$54$	−1.82843	+	4.41421i	−0.248817	+	0.600698i
$55$		0			0
$56$	−1.41421	−	0.585786i	−0.188982	−	0.0782790i
$57$	−0.585786	−	1.41421i	−0.0775893	−	0.187317i
$58$	1.41421	−	0.585786i	0.185695	−	0.0769175i
$59$	0.414214	+	0.414214i	0.0539260	+	0.0539260i	0.733556	−	0.679630i	$-0.237859\pi$
$59$	0.414214	+	0.414214i	0.0539260	+	0.0539260i	−0.679630	+	0.733556i	$0.737859\pi$
$60$		0			0
$61$	6.82843	−	2.82843i	0.874291	−	0.362143i	0.100011	−	0.994986i	$-0.468112\pi$
$61$	6.82843	−	2.82843i	0.874291	−	0.362143i	0.774280	+	0.632843i	$0.218112\pi$
$62$	−1.41421	−	3.41421i	−0.179605	−	0.433606i
$63$	0.585786	+	0.242641i	0.0738022	+	0.0305699i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−5.82843	+	5.82843i	−0.717430	+	0.717430i
$67$	7.41421			0.905790			0.452895	−	0.891564i	$-0.350391\pi$
$67$	7.41421			0.905790			0.452895	+	0.891564i	$0.350391\pi$
$68$	3.53553	−	2.12132i	0.428746	−	0.257248i
$69$	5.65685			0.681005
$70$		0			0
$71$	0.828427	−	2.00000i	0.0983162	−	0.237356i	−0.867067	−	0.498191i	$-0.833998\pi$
$71$	0.828427	−	2.00000i	0.0983162	−	0.237356i	0.965383	+	0.260835i	$0.0839978\pi$
$72$		−	0.414214i		−	0.0488155i
$73$	4.94975	+	2.05025i	0.579324	+	0.239964i	0.653050	−	0.757315i	$-0.273489\pi$
$73$	4.94975	+	2.05025i	0.579324	+	0.239964i	−0.0737261	+	0.997279i	$0.523489\pi$
$74$	−0.828427	−	2.00000i	−0.0963027	−	0.232495i
$75$		0			0
$76$	−0.585786	−	0.585786i	−0.0671943	−	0.0671943i
$77$	−4.82843	−	4.82843i	−0.550250	−	0.550250i
$78$	−1.41421	+	0.585786i	−0.160128	+	0.0663273i
$79$	−2.00000	−	4.82843i	−0.225018	−	0.543240i	0.770540	−	0.637391i	$-0.219986\pi$
$79$	−2.00000	−	4.82843i	−0.225018	−	0.543240i	−0.995558	+	0.0941507i	$0.969986\pi$
$80$		0			0
$81$		−	10.0711i		−	1.11901i
$82$	−4.29289	+	10.3640i	−0.474071	+	1.14451i
$83$	−4.41421	+	4.41421i	−0.484523	+	0.484523i	−0.906573	−	0.422050i	$-0.861311\pi$
$83$	−4.41421	+	4.41421i	−0.484523	+	0.484523i	0.422050	+	0.906573i	$0.361311\pi$
$84$	2.82843			0.308607
$85$		0			0
$86$	−1.75736			−0.189501
$87$	−2.00000	+	2.00000i	−0.214423	+	0.214423i
$88$	−1.70711	+	4.12132i	−0.181978	+	0.439334i
$89$			15.0711i			1.59753i	0.601643	+	0.798765i	$0.294513\pi$
$89$			15.0711i			1.59753i	−0.601643	+	0.798765i	$0.705487\pi$
$90$		0			0
$91$	−0.485281	−	1.17157i	−0.0508713	−	0.122814i
$92$	2.82843	−	1.17157i	0.294884	−	0.122145i
$93$	4.82843	+	4.82843i	0.500685	+	0.500685i
$94$	6.82843	+	6.82843i	0.704298	+	0.704298i
$95$		0			0
$96$	−0.707107	−	1.70711i	−0.0721688	−	0.174231i
$97$	5.12132	+	2.12132i	0.519991	+	0.215387i	0.627213	−	0.778848i	$-0.284196\pi$
$97$	5.12132	+	2.12132i	0.519991	+	0.215387i	−0.107222	+	0.994235i	$0.534196\pi$
$98$		−	4.65685i		−	0.470413i
$99$	0.707107	−	1.70711i	0.0710669	−	0.171571i
$100$		0			0
$101$	4.34315			0.432159			0.216080	−	0.976376i	$-0.430673\pi$
$101$	4.34315			0.432159			0.216080	+	0.976376i	$0.430673\pi$
$102$	−4.53553	+	6.12132i	−0.449085	+	0.606101i
$103$	−12.4853			−1.23021			−0.615106	−	0.788445i	$-0.710887\pi$
$103$	−12.4853			−1.23021			−0.615106	+	0.788445i	$0.710887\pi$
$104$	−0.585786	+	0.585786i	−0.0574411	+	0.0574411i
$105$		0			0
$106$		−	0.828427i		−	0.0804640i
$107$	−10.7782	−	4.46447i	−1.04197	−	0.431596i	−0.204948	−	0.978773i	$-0.565703\pi$
$107$	−10.7782	−	4.46447i	−1.04197	−	0.431596i	−0.837017	+	0.547177i	$0.815703\pi$
$108$	−1.82843	−	4.41421i	−0.175940	−	0.424758i
$109$	−9.07107	+	3.75736i	−0.868851	+	0.359890i	−0.772163	−	0.635425i	$-0.780825\pi$
$109$	−9.07107	+	3.75736i	−0.868851	+	0.359890i	−0.0966881	+	0.995315i	$0.530825\pi$
$110$		0			0
$111$	2.82843	+	2.82843i	0.268462	+	0.268462i
$112$	1.41421	−	0.585786i	0.133631	−	0.0553516i
$113$	3.53553	+	8.53553i	0.332595	+	0.802955i	0.998385	+	0.0568160i	$0.0180948\pi$
$113$	3.53553	+	8.53553i	0.332595	+	0.802955i	−0.665790	+	0.746140i	$0.731905\pi$
$114$	1.41421	+	0.585786i	0.132453	+	0.0548639i
$115$		0			0
$116$	−0.585786	+	1.41421i	−0.0543889	+	0.131306i
$117$	0.242641	−	0.242641i	0.0224321	−	0.0224321i
$118$	−0.585786			−0.0539260
$119$	−5.07107	−	3.75736i	−0.464864	−	0.344437i
$120$		0			0
$121$	−6.29289	+	6.29289i	−0.572081	+	0.572081i
$122$	−2.82843	+	6.82843i	−0.256074	+	0.618217i
$123$		−	20.7279i		−	1.86897i
$124$	3.41421	+	1.41421i	0.306605	+	0.127000i
$125$		0			0
$126$	−0.585786	+	0.242641i	−0.0521860	+	0.0216162i
$127$	9.17157	+	9.17157i	0.813845	+	0.813845i	0.985208	−	0.171363i	$-0.0548169\pi$
$127$	9.17157	+	9.17157i	0.813845	+	0.813845i	−0.171363	+	0.985208i	$0.554817\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.00000	−	1.24264i	0.264135	−	0.109408i
$130$		0			0
$131$	0.121320	+	0.0502525i	0.0105998	+	0.00439058i	0.387977	−	0.921669i	$-0.373174\pi$
$131$	0.121320	+	0.0502525i	0.0105998	+	0.00439058i	−0.377377	+	0.926060i	$0.623174\pi$
$132$		−	8.24264i		−	0.717430i
$133$	−0.485281	+	1.17157i	−0.0420792	+	0.101588i
$134$	−5.24264	+	5.24264i	−0.452895	+	0.452895i
$135$		0			0
$136$	−1.00000	+	4.00000i	−0.0857493	+	0.342997i
$137$	2.34315			0.200188			0.100094	−	0.994978i	$-0.468086\pi$
$137$	2.34315			0.200188			0.100094	+	0.994978i	$0.468086\pi$
$138$	−4.00000	+	4.00000i	−0.340503	+	0.340503i
$139$	−0.707107	+	1.70711i	−0.0599760	+	0.144795i	−0.951027	−	0.309109i	$-0.899969\pi$
$139$	−0.707107	+	1.70711i	−0.0599760	+	0.144795i	0.891051	+	0.453904i	$0.149969\pi$
$140$		0			0
$141$	−16.4853	−	6.82843i	−1.38831	−	0.575057i
$142$	0.828427	+	2.00000i	0.0695201	+	0.167836i
$143$	−3.41421	+	1.41421i	−0.285511	+	0.118262i
$144$	0.292893	+	0.292893i	0.0244078	+	0.0244078i
$145$		0			0
$146$	−4.94975	+	2.05025i	−0.409644	+	0.169680i
$147$	3.29289	+	7.94975i	0.271593	+	0.655684i
$148$	2.00000	+	0.828427i	0.164399	+	0.0680963i
$149$		−	15.6569i		−	1.28266i	−0.767265	−	0.641330i	$-0.778383\pi$
$149$		−	15.6569i		−	1.28266i	0.767265	−	0.641330i	$-0.221617\pi$
$150$		0			0
$151$	−15.6569	+	15.6569i	−1.27414	+	1.27414i	−0.330240	+	0.943897i	$0.607130\pi$
$151$	−15.6569	+	15.6569i	−1.27414	+	1.27414i	−0.943897	+	0.330240i	$0.892870\pi$
$152$	0.828427			0.0671943
$153$	0.414214	−	1.65685i	0.0334872	−	0.133949i
$154$	6.82843			0.550250
$155$		0			0
$156$	0.585786	−	1.41421i	0.0469005	−	0.113228i
$157$			13.3137i			1.06255i	0.847200	+	0.531275i	$0.178287\pi$
$157$			13.3137i			1.06255i	−0.847200	+	0.531275i	$0.821713\pi$
$158$	4.82843	+	2.00000i	0.384129	+	0.159111i
$159$	0.585786	+	1.41421i	0.0464559	+	0.112154i
$160$		0			0
$161$	−3.31371	−	3.31371i	−0.261157	−	0.261157i
$162$	7.12132	+	7.12132i	0.559504	+	0.559504i
$163$	−21.0208	+	8.70711i	−1.64648	+	0.681993i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$	−21.0208	+	8.70711i	−1.64648	+	0.681993i	−0.649550	+	0.760319i	$0.725042\pi$
$164$	−4.29289	−	10.3640i	−0.335219	−	0.809289i
$165$		0			0
$166$		−	6.24264i		−	0.484523i
$167$	7.55635	−	18.2426i	0.584728	−	1.41166i	−0.303756	−	0.952750i	$-0.598241\pi$
$167$	7.55635	−	18.2426i	0.584728	−	1.41166i	0.888484	−	0.458908i	$-0.151759\pi$
$168$	−2.00000	+	2.00000i	−0.154303	+	0.154303i
$169$	12.3137			0.947208
$170$		0			0
$171$	−0.343146			−0.0262410
$172$	1.24264	−	1.24264i	0.0947505	−	0.0947505i
$173$	2.24264	−	5.41421i	0.170505	−	0.411635i	−0.815410	−	0.578884i	$-0.803488\pi$
$173$	2.24264	−	5.41421i	0.170505	−	0.411635i	0.985915	+	0.167249i	$0.0534884\pi$
$174$		−	2.82843i		−	0.214423i
$175$		0			0
$176$	−1.70711	−	4.12132i	−0.128678	−	0.310656i
$177$	1.00000	−	0.414214i	0.0751646	−	0.0311342i
$178$	−10.6569	−	10.6569i	−0.798765	−	0.798765i
$179$	−18.2426	−	18.2426i	−1.36352	−	1.36352i	−0.869387	−	0.494132i	$-0.835486\pi$
$179$	−18.2426	−	18.2426i	−1.36352	−	1.36352i	−0.494132	−	0.869387i	$-0.664514\pi$
$180$		0			0
$181$	2.34315	+	5.65685i	0.174165	+	0.420471i	0.986724	−	0.162408i	$-0.0519262\pi$
$181$	2.34315	+	5.65685i	0.174165	+	0.420471i	−0.812559	+	0.582879i	$0.801926\pi$
$182$	1.17157	+	0.485281i	0.0868428	+	0.0359714i
$183$		−	13.6569i		−	1.00954i
$184$	−1.17157	+	2.82843i	−0.0863695	+	0.208514i
$185$		0			0
$186$	−6.82843			−0.500685
$187$	−10.9497	+	14.7782i	−0.800725	+	1.08069i
$188$	−9.65685			−0.704298
$189$	−5.17157	+	5.17157i	−0.376177	+	0.376177i
$190$		0			0
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$	1.70711	+	0.707107i	0.123200	+	0.0510310i
$193$	−4.70711	−	11.3640i	−0.338825	−	0.817996i	−0.997829	−	0.0658565i	$-0.979022\pi$
$193$	−4.70711	−	11.3640i	−0.338825	−	0.817996i	0.659004	−	0.752139i	$-0.270978\pi$
$194$	−5.12132	+	2.12132i	−0.367689	+	0.152302i
$195$		0			0
$196$	3.29289	+	3.29289i	0.235207	+	0.235207i
$197$	18.4853	−	7.65685i	1.31702	−	0.545528i	0.390096	−	0.920774i	$-0.372442\pi$
$197$	18.4853	−	7.65685i	1.31702	−	0.545528i	0.926925	+	0.375246i	$0.122442\pi$
$198$	0.707107	+	1.70711i	0.0502519	+	0.121319i
$199$	−19.3137	−	8.00000i	−1.36911	−	0.567105i	−0.427565	−	0.903985i	$-0.640628\pi$
$199$	−19.3137	−	8.00000i	−1.36911	−	0.567105i	−0.941548	+	0.336880i	$0.890628\pi$
$200$		0			0
$201$	5.24264	−	12.6569i	0.369787	−	0.892746i
$202$	−3.07107	+	3.07107i	−0.216080	+	0.216080i
$203$	2.34315			0.164457
$204$	−1.12132	−	7.53553i	−0.0785081	−	0.527593i
$205$		0			0
$206$	8.82843	−	8.82843i	0.615106	−	0.615106i
$207$	0.485281	−	1.17157i	0.0337294	−	0.0814299i
$208$		−	0.828427i		−	0.0574411i
$209$	3.41421	+	1.41421i	0.236166	+	0.0978232i
$210$		0			0
$211$	−0.121320	+	0.0502525i	−0.00835204	+	0.00345953i	−0.386856	−	0.922140i	$-0.626439\pi$
$211$	−0.121320	+	0.0502525i	−0.00835204	+	0.00345953i	0.378504	+	0.925600i	$0.376439\pi$
$212$	0.585786	+	0.585786i	0.0402320	+	0.0402320i
$213$	−2.82843	−	2.82843i	−0.193801	−	0.193801i
$214$	10.7782	−	4.46447i	0.736781	−	0.305185i
$215$		0			0
$216$	4.41421	+	1.82843i	0.300349	+	0.124409i
$217$		−	5.65685i		−	0.384012i
$218$	3.75736	−	9.07107i	0.254480	−	0.614370i
$219$	7.00000	−	7.00000i	0.473016	−	0.473016i
$220$		0			0
$221$	−2.92893	+	1.75736i	−0.197021	+	0.118213i
$222$	−4.00000			−0.268462
$223$	17.3137	−	17.3137i	1.15941	−	1.15941i	0.174809	−	0.984602i	$-0.444069\pi$
$223$	17.3137	−	17.3137i	1.15941	−	1.15941i	0.984602	−	0.174809i	$-0.0559309\pi$
$224$	−0.585786	+	1.41421i	−0.0391395	+	0.0944911i
$225$		0			0
$226$	−8.53553	−	3.53553i	−0.567775	−	0.235180i
$227$	−7.77817	−	18.7782i	−0.516256	−	1.24635i	−0.940188	−	0.340657i	$-0.889350\pi$
$227$	−7.77817	−	18.7782i	−0.516256	−	1.24635i	0.423932	−	0.905694i	$-0.360650\pi$
$228$	−1.41421	+	0.585786i	−0.0936586	+	0.0387947i
$229$	13.0711	+	13.0711i	0.863760	+	0.863760i	0.991773	−	0.128012i	$-0.0408596\pi$
$229$	13.0711	+	13.0711i	0.863760	+	0.863760i	−0.128012	+	0.991773i	$0.540860\pi$
$230$		0			0
$231$	−11.6569	+	4.82843i	−0.766965	+	0.317687i
$232$	−0.585786	−	1.41421i	−0.0384588	−	0.0928477i
$233$	−9.70711	−	4.02082i	−0.635934	−	0.263412i	0.0413382	−	0.999145i	$-0.486838\pi$
$233$	−9.70711	−	4.02082i	−0.635934	−	0.263412i	−0.677272	+	0.735733i	$0.736838\pi$
$234$			0.343146i			0.0224321i
$235$		0			0
$236$	0.414214	−	0.414214i	0.0269630	−	0.0269630i
$237$	−9.65685			−0.627280
$238$	6.24264	−	0.928932i	0.404650	−	0.0602137i
$239$	21.1716			1.36948			0.684738	−	0.728790i	$-0.259917\pi$
$239$	21.1716			1.36948			0.684738	+	0.728790i	$0.259917\pi$
$240$		0			0
$241$	7.60660	−	18.3640i	0.489984	−	1.18293i	−0.464743	−	0.885445i	$-0.653853\pi$
$241$	7.60660	−	18.3640i	0.489984	−	1.18293i	0.954728	−	0.297481i	$-0.0961466\pi$
$242$		−	8.89949i		−	0.572081i
$243$	−3.94975	−	1.63604i	−0.253376	−	0.104952i
$244$	−2.82843	−	6.82843i	−0.181071	−	0.437145i
$245$		0			0
$246$	14.6569	+	14.6569i	0.934487	+	0.934487i
$247$	0.485281	+	0.485281i	0.0308777	+	0.0308777i
$248$	−3.41421	+	1.41421i	−0.216803	+	0.0898027i
$249$	4.41421	+	10.6569i	0.279739	+	0.675351i
$250$		0			0
$251$		−	18.7279i		−	1.18210i	−0.806636	−	0.591048i	$-0.798714\pi$
$251$		−	18.7279i		−	1.18210i	0.806636	−	0.591048i	$-0.201286\pi$
$252$	0.242641	−	0.585786i	0.0152849	−	0.0369011i
$253$	−9.65685	+	9.65685i	−0.607121	+	0.607121i
$254$	−12.9706			−0.813845
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.82843	+	5.82843i	−0.363567	+	0.363567i	−0.865124	−	0.501557i	$-0.832761\pi$
$257$	−5.82843	+	5.82843i	−0.363567	+	0.363567i	0.501557	+	0.865124i	$0.332761\pi$
$258$	−1.24264	+	3.00000i	−0.0773634	+	0.186772i
$259$		−	3.31371i		−	0.205904i
$260$		0			0
$261$	0.242641	+	0.585786i	0.0150191	+	0.0362593i
$262$	−0.121320	+	0.0502525i	−0.00749520	+	0.00310461i
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$	5.82843	+	5.82843i	0.358715	+	0.358715i
$265$		0			0
$266$	−0.485281	−	1.17157i	−0.0297545	−	0.0718337i
$267$	25.7279	+	10.6569i	1.57452	+	0.652189i
$268$		−	7.41421i		−	0.452895i
$269$	2.92893	−	7.07107i	0.178580	−	0.431131i	−0.809089	−	0.587686i	$-0.800039\pi$
$269$	2.92893	−	7.07107i	0.178580	−	0.431131i	0.987669	+	0.156555i	$0.0500390\pi$
$270$		0			0
$271$	−14.8284			−0.900763			−0.450381	−	0.892836i	$-0.648712\pi$
$271$	−14.8284			−0.900763			−0.450381	+	0.892836i	$0.648712\pi$
$272$	−2.12132	−	3.53553i	−0.128624	−	0.214373i
$273$	−2.34315			−0.141814
$274$	−1.65685	+	1.65685i	−0.100094	+	0.100094i
$275$		0			0
$276$		−	5.65685i		−	0.340503i
$277$	−21.8995	−	9.07107i	−1.31581	−	0.545028i	−0.389238	−	0.921137i	$-0.627262\pi$
$277$	−21.8995	−	9.07107i	−1.31581	−	0.545028i	−0.926575	+	0.376110i	$0.877262\pi$
$278$	−0.707107	−	1.70711i	−0.0424094	−	0.102385i
$279$	1.41421	−	0.585786i	0.0846668	−	0.0350701i
$280$		0			0
$281$	10.1421	+	10.1421i	0.605029	+	0.605029i	0.941643	−	0.336614i	$-0.109282\pi$
$281$	10.1421	+	10.1421i	0.605029	+	0.605029i	−0.336614	+	0.941643i	$0.609282\pi$
$282$	16.4853	−	6.82843i	0.981684	−	0.406627i
$283$	−0.435029	−	1.05025i	−0.0258598	−	0.0624310i	0.910422	−	0.413680i	$-0.135757\pi$
$283$	−0.435029	−	1.05025i	−0.0258598	−	0.0624310i	−0.936282	+	0.351249i	$0.885757\pi$
$284$	−2.00000	−	0.828427i	−0.118678	−	0.0491581i
$285$		0			0
$286$	1.41421	−	3.41421i	0.0836242	−	0.201887i
$287$	−12.1421	+	12.1421i	−0.716728	+	0.716728i
$288$	−0.414214			−0.0244078
$289$	−8.00000	+	15.0000i	−0.470588	+	0.882353i
$290$		0			0
$291$	7.24264	−	7.24264i	0.424571	−	0.424571i
$292$	2.05025	−	4.94975i	0.119982	−	0.289662i
$293$			22.0000i			1.28525i	0.766179	+	0.642627i	$0.222155\pi$
$293$			22.0000i			1.28525i	−0.766179	+	0.642627i	$0.777845\pi$
$294$	−7.94975	−	3.29289i	−0.463639	−	0.192045i
$295$		0			0
$296$	−2.00000	+	0.828427i	−0.116248	+	0.0481513i
$297$	15.0711	+	15.0711i	0.874512	+	0.874512i
$298$	11.0711	+	11.0711i	0.641330	+	0.641330i
$299$	−2.34315	+	0.970563i	−0.135508	+	0.0561291i
$300$		0			0
$301$	−2.48528	−	1.02944i	−0.143249	−	0.0593358i
$302$		−	22.1421i		−	1.27414i
$303$	3.07107	−	7.41421i	0.176428	−	0.425935i
$304$	−0.585786	+	0.585786i	−0.0335972	+	0.0335972i
$305$		0			0
$306$	0.878680	+	1.46447i	0.0502308	+	0.0837180i
$307$	−6.34315			−0.362022			−0.181011	−	0.983481i	$-0.557937\pi$
$307$	−6.34315			−0.362022			−0.181011	+	0.983481i	$0.557937\pi$
$308$	−4.82843	+	4.82843i	−0.275125	+	0.275125i
$309$	−8.82843	+	21.3137i	−0.502232	+	1.21249i
$310$		0			0
$311$	−13.8995	−	5.75736i	−0.788168	−	0.326470i	−0.0479613	−	0.998849i	$-0.515272\pi$
$311$	−13.8995	−	5.75736i	−0.788168	−	0.326470i	−0.740207	+	0.672379i	$0.765272\pi$
$312$	0.585786	+	1.41421i	0.0331636	+	0.0800641i
$313$	−12.5355	+	5.19239i	−0.708550	+	0.293491i	−0.707705	−	0.706509i	$-0.750269\pi$
$313$	−12.5355	+	5.19239i	−0.708550	+	0.293491i	−0.000845724		1.00000i	$0.500269\pi$
$314$	−9.41421	−	9.41421i	−0.531275	−	0.531275i
$315$		0			0
$316$	−4.82843	+	2.00000i	−0.271620	+	0.112509i
$317$	−8.48528	−	20.4853i	−0.476581	−	1.15057i	−0.961202	−	0.275844i	$-0.911043\pi$
$317$	−8.48528	−	20.4853i	−0.476581	−	1.15057i	0.484622	−	0.874724i	$-0.338957\pi$
$318$	−1.41421	−	0.585786i	−0.0793052	−	0.0328493i
$319$		−	6.82843i		−	0.382319i
$320$		0			0
$321$	−15.2426	+	15.2426i	−0.850761	+	0.850761i
$322$	4.68629			0.261157
$323$	3.31371	+	0.828427i	0.184380	+	0.0460949i
$324$	−10.0711			−0.559504
$325$		0			0
$326$	8.70711	−	21.0208i	0.482242	−	1.16424i
$327$			18.1421i			1.00326i
$328$	10.3640	+	4.29289i	0.572254	+	0.237035i
$329$	5.65685	+	13.6569i	0.311872	+	0.752927i
$330$		0			0
$331$	19.5858	+	19.5858i	1.07653	+	1.07653i	0.996818	+	0.0797144i	$0.0254008\pi$
$331$	19.5858	+	19.5858i	1.07653	+	1.07653i	0.0797144	+	0.996818i	$0.474599\pi$
$332$	4.41421	+	4.41421i	0.242261	+	0.242261i
$333$	0.828427	−	0.343146i	0.0453975	−	0.0188043i
$334$	7.55635	+	18.2426i	0.413465	+	0.998193i
$335$		0			0
$336$		−	2.82843i		−	0.154303i
$337$	−4.46447	+	10.7782i	−0.243195	+	0.587125i	−0.997597	−	0.0692885i	$-0.977927\pi$
$337$	−4.46447	+	10.7782i	−0.243195	+	0.587125i	0.754402	+	0.656413i	$0.227927\pi$
$338$	−8.70711	+	8.70711i	−0.473604	+	0.473604i
$339$	17.0711			0.927173
$340$		0			0
$341$	−16.4853			−0.892728
$342$	0.242641	−	0.242641i	0.0131205	−	0.0131205i
$343$	6.82843	−	16.4853i	0.368700	−	0.890122i
$344$			1.75736i			0.0947505i
$345$		0			0
$346$	2.24264	+	5.41421i	0.120565	+	0.291070i
$347$	14.9497	−	6.19239i	0.802544	−	0.332425i	0.0565694	−	0.998399i	$-0.481984\pi$
$347$	14.9497	−	6.19239i	0.802544	−	0.332425i	0.745975	+	0.665974i	$0.231984\pi$
$348$	2.00000	+	2.00000i	0.107211	+	0.107211i
$349$	−13.8995	−	13.8995i	−0.744023	−	0.744023i	0.229327	−	0.973350i	$-0.426348\pi$
$349$	−13.8995	−	13.8995i	−0.744023	−	0.744023i	−0.973350	+	0.229327i	$0.926348\pi$
$350$		0			0
$351$	1.51472	+	3.65685i	0.0808497	+	0.195188i
$352$	4.12132	+	1.70711i	0.219667	+	0.0909891i
$353$			14.3848i			0.765624i	0.923826	+	0.382812i	$0.125044\pi$
$353$			14.3848i			0.765624i	−0.923826	+	0.382812i	$0.874956\pi$
$354$	−0.414214	+	1.00000i	−0.0220152	+	0.0531494i
$355$		0			0
$356$	15.0711			0.798765
$357$	−10.0000	+	6.00000i	−0.529256	+	0.317554i
$358$	25.7990			1.36352
$359$	8.00000	−	8.00000i	0.422224	−	0.422224i	−0.463745	−	0.885969i	$-0.653495\pi$
$359$	8.00000	−	8.00000i	0.422224	−	0.422224i	0.885969	+	0.463745i	$0.153495\pi$
$360$		0			0
$361$			18.3137i			0.963879i
$362$	−5.65685	−	2.34315i	−0.297318	−	0.123153i
$363$	6.29289	+	15.1924i	0.330291	+	0.797394i
$364$	−1.17157	+	0.485281i	−0.0614071	+	0.0254357i
$365$		0			0
$366$	9.65685	+	9.65685i	0.504772	+	0.504772i
$367$	−17.3137	+	7.17157i	−0.903768	+	0.374353i	−0.785668	−	0.618649i	$-0.787680\pi$
$367$	−17.3137	+	7.17157i	−0.903768	+	0.374353i	−0.118100	+	0.993002i	$0.537680\pi$
$368$	−1.17157	−	2.82843i	−0.0610725	−	0.147442i
$369$	−4.29289	−	1.77817i	−0.223479	−	0.0925681i
$370$		0			0
$371$	0.485281	−	1.17157i	0.0251946	−	0.0608250i
$372$	4.82843	−	4.82843i	0.250342	−	0.250342i
$373$	10.4853			0.542907			0.271454	−	0.962452i	$-0.412496\pi$
$373$	10.4853			0.542907			0.271454	+	0.962452i	$0.412496\pi$
$374$	−2.70711	−	18.1924i	−0.139981	−	0.940706i
$375$		0			0
$376$	6.82843	−	6.82843i	0.352149	−	0.352149i
$377$	0.485281	−	1.17157i	0.0249933	−	0.0603391i
$378$		−	7.31371i		−	0.376177i
$379$	8.60660	+	3.56497i	0.442091	+	0.183120i	0.592614	−	0.805486i	$-0.298096\pi$
$379$	8.60660	+	3.56497i	0.442091	+	0.183120i	−0.150523	+	0.988606i	$0.548096\pi$
$380$		0			0
$381$	22.1421	−	9.17157i	1.13438	−	0.469874i
$382$	2.00000	+	2.00000i	0.102329	+	0.102329i
$383$	21.3137	+	21.3137i	1.08908	+	1.08908i	0.995623	+	0.0934562i	$0.0297915\pi$
$383$	21.3137	+	21.3137i	1.08908	+	1.08908i	0.0934562	+	0.995623i	$0.470208\pi$
$384$	−1.70711	+	0.707107i	−0.0871154	+	0.0360844i
$385$		0			0
$386$	11.3640	+	4.70711i	0.578410	+	0.239585i
$387$		−	0.727922i		−	0.0370024i
$388$	2.12132	−	5.12132i	0.107694	−	0.259996i
$389$	2.24264	−	2.24264i	0.113706	−	0.113706i	−0.647964	−	0.761671i	$-0.724379\pi$
$389$	2.24264	−	2.24264i	0.113706	−	0.113706i	0.761671	+	0.647964i	$0.224379\pi$
$390$		0			0
$391$	−7.51472	+	10.1421i	−0.380036	+	0.512910i
$392$	−4.65685			−0.235207
$393$	0.171573	−	0.171573i	0.00865471	−	0.00865471i
$394$	−7.65685	+	18.4853i	−0.385747	+	0.931275i
$395$		0			0
$396$	−1.70711	−	0.707107i	−0.0857853	−	0.0355335i
$397$	−3.17157	−	7.65685i	−0.159177	−	0.384286i	0.824090	−	0.566459i	$-0.191687\pi$
$397$	−3.17157	−	7.65685i	−0.159177	−	0.384286i	−0.983267	+	0.182173i	$0.941687\pi$
$398$	19.3137	−	8.00000i	0.968109	−	0.401004i
$399$	1.65685	+	1.65685i	0.0829465	+	0.0829465i
$400$		0			0
$401$	−22.1924	+	9.19239i	−1.10823	+	0.459046i	−0.860330	−	0.509738i	$-0.829742\pi$
$401$	−22.1924	+	9.19239i	−1.10823	+	0.459046i	−0.247905	+	0.968784i	$0.579742\pi$
$402$	5.24264	+	12.6569i	0.261479	+	0.631267i
$403$	−2.82843	−	1.17157i	−0.140894	−	0.0583602i
$404$		−	4.34315i		−	0.216080i
$405$		0			0
$406$	−1.65685	+	1.65685i	−0.0822283	+	0.0822283i
$407$	−9.65685			−0.478672
$408$	6.12132	+	4.53553i	0.303051	+	0.224542i
$409$	15.5563			0.769212			0.384606	−	0.923081i	$-0.374337\pi$
$409$	15.5563			0.769212			0.384606	+	0.923081i	$0.374337\pi$
$410$		0			0
$411$	1.65685	−	4.00000i	0.0817266	−	0.197305i
$412$			12.4853i			0.615106i
$413$	−0.828427	−	0.343146i	−0.0407642	−	0.0168851i
$414$	0.485281	+	1.17157i	0.0238503	+	0.0575797i
$415$		0			0
$416$	0.585786	+	0.585786i	0.0287205	+	0.0287205i
$417$	2.41421	+	2.41421i	0.118225	+	0.118225i
$418$	−3.41421	+	1.41421i	−0.166995	+	0.0691714i
$419$	−6.60660	−	15.9497i	−0.322754	−	0.779196i	−0.999092	−	0.0426051i	$-0.986434\pi$
$419$	−6.60660	−	15.9497i	−0.322754	−	0.779196i	0.676338	−	0.736591i	$-0.263566\pi$
$420$		0			0
$421$		−	15.6569i		−	0.763068i	−0.924355	−	0.381534i	$-0.875396\pi$
$421$		−	15.6569i		−	0.763068i	0.924355	−	0.381534i	$-0.124604\pi$
$422$	0.0502525	−	0.121320i	0.00244625	−	0.00590578i
$423$	−2.82843	+	2.82843i	−0.137523	+	0.137523i
$424$	−0.828427			−0.0402320
$425$		0			0
$426$	4.00000			0.193801
$427$	−8.00000	+	8.00000i	−0.387147	+	0.387147i
$428$	−4.46447	+	10.7782i	−0.215798	+	0.520983i
$429$			6.82843i			0.329680i
$430$		0			0
$431$	−5.51472	−	13.3137i	−0.265635	−	0.641299i	0.733634	−	0.679545i	$-0.237823\pi$
$431$	−5.51472	−	13.3137i	−0.265635	−	0.641299i	−0.999268	+	0.0382464i	$0.987823\pi$
$432$	−4.41421	+	1.82843i	−0.212379	+	0.0879702i
$433$	9.17157	+	9.17157i	0.440758	+	0.440758i	0.892267	−	0.451509i	$-0.149114\pi$
$433$	9.17157	+	9.17157i	0.440758	+	0.440758i	−0.451509	+	0.892267i	$0.649114\pi$
$434$	4.00000	+	4.00000i	0.192006	+	0.192006i
$435$		0			0
$436$	3.75736	+	9.07107i	0.179945	+	0.434425i
$437$	2.34315	+	0.970563i	0.112088	+	0.0464283i
$438$			9.89949i			0.473016i
$439$	−8.82843	+	21.3137i	−0.421358	+	1.01725i	0.560590	+	0.828094i	$0.310575\pi$
$439$	−8.82843	+	21.3137i	−0.421358	+	1.01725i	−0.981947	+	0.189154i	$0.939425\pi$
$440$		0			0
$441$	1.92893			0.0918539
$442$	0.828427	−	3.31371i	0.0394043	−	0.157617i
$443$	36.8701			1.75175			0.875875	−	0.482539i	$-0.160285\pi$
$443$	36.8701			1.75175			0.875875	+	0.482539i	$0.160285\pi$
$444$	2.82843	−	2.82843i	0.134231	−	0.134231i
$445$		0			0
$446$			24.4853i			1.15941i
$447$	−26.7279	−	11.0711i	−1.26419	−	0.523644i
$448$	−0.585786	−	1.41421i	−0.0276758	−	0.0668153i
$449$	5.12132	−	2.12132i	0.241690	−	0.100111i	−0.258551	−	0.965998i	$-0.583245\pi$
$449$	5.12132	−	2.12132i	0.241690	−	0.100111i	0.500241	+	0.865886i	$0.333245\pi$
$450$		0			0
$451$	35.3848	+	35.3848i	1.66620	+	1.66620i
$452$	8.53553	−	3.53553i	0.401478	−	0.166298i
$453$	15.6569	+	37.7990i	0.735623	+	1.77595i
$454$	18.7782	+	7.77817i	0.881303	+	0.365048i
$455$		0			0
$456$	0.585786	−	1.41421i	0.0274320	−	0.0662266i
$457$	−3.51472	+	3.51472i	−0.164412	+	0.164412i	−0.784518	−	0.620106i	$-0.787089\pi$
$457$	−3.51472	+	3.51472i	−0.164412	+	0.164412i	0.620106	+	0.784518i	$0.287089\pi$
$458$	−18.4853			−0.863760
$459$	15.8284	+	11.7279i	0.738808	+	0.547413i
$460$		0			0
$461$	−24.7279	+	24.7279i	−1.15169	+	1.15169i	−0.165481	+	0.986213i	$0.552918\pi$
$461$	−24.7279	+	24.7279i	−1.15169	+	1.15169i	−0.986213	+	0.165481i	$0.947082\pi$
$462$	4.82843	−	11.6569i	0.224639	−	0.542326i
$463$		−	3.31371i		−	0.154001i	−0.997031	−	0.0770005i	$-0.975466\pi$
$463$		−	3.31371i		−	0.154001i	0.997031	−	0.0770005i	$-0.0245343\pi$
$464$	1.41421	+	0.585786i	0.0656532	+	0.0271945i
$465$		0			0
$466$	9.70711	−	4.02082i	0.449673	−	0.186261i
$467$	1.75736	+	1.75736i	0.0813209	+	0.0813209i	0.746597	−	0.665276i	$-0.231686\pi$
$467$	1.75736	+	1.75736i	0.0813209	+	0.0813209i	−0.665276	+	0.746597i	$0.731686\pi$
$468$	−0.242641	−	0.242641i	−0.0112161	−	0.0112161i
$469$	−10.4853	+	4.34315i	−0.484165	+	0.200548i
$470$		0			0
$471$	22.7279	+	9.41421i	1.04725	+	0.433784i
$472$			0.585786i			0.0269630i
$473$	−3.00000	+	7.24264i	−0.137940	+	0.333017i
$474$	6.82843	−	6.82843i	0.313640	−	0.313640i
$475$		0			0
$476$	−3.75736	+	5.07107i	−0.172218	+	0.232432i
$477$	0.343146			0.0157116
$478$	−14.9706	+	14.9706i	−0.684738	+	0.684738i
$479$	9.51472	−	22.9706i	0.434739	−	1.04955i	−0.543001	−	0.839732i	$-0.682712\pi$
$479$	9.51472	−	22.9706i	0.434739	−	1.04955i	0.977740	−	0.209820i	$-0.0672878\pi$
$480$		0			0
$481$	−1.65685	−	0.686292i	−0.0755461	−	0.0312922i
$482$	7.60660	+	18.3640i	0.346471	+	0.836456i
$483$	−8.00000	+	3.31371i	−0.364013	+	0.150779i
$484$	6.29289	+	6.29289i	0.286041	+	0.286041i
$485$		0			0
$486$	3.94975	−	1.63604i	0.179164	−	0.0742122i
$487$	−8.48528	−	20.4853i	−0.384505	−	0.928277i	−0.991082	−	0.133252i	$-0.957458\pi$
$487$	−8.48528	−	20.4853i	−0.384505	−	0.928277i	0.606577	−	0.795024i	$-0.292542\pi$
$488$	6.82843	+	2.82843i	0.309108	+	0.128037i
$489$			42.0416i			1.90119i
$490$		0			0
$491$	10.9289	−	10.9289i	0.493216	−	0.493216i	−0.416102	−	0.909318i	$-0.636604\pi$
$491$	10.9289	−	10.9289i	0.493216	−	0.493216i	0.909318	+	0.416102i	$0.136604\pi$
$492$	−20.7279			−0.934487
$493$	−0.928932	−	6.24264i	−0.0418370	−	0.281154i
$494$	−0.686292			−0.0308777
$495$		0			0
$496$	1.41421	−	3.41421i	0.0635001	−	0.153303i
$497$			3.31371i			0.148640i
$498$	−10.6569	−	4.41421i	−0.477545	−	0.197806i
$499$	−14.0919	−	34.0208i	−0.630839	−	1.52298i	−0.838569	−	0.544795i	$-0.816608\pi$
$499$	−14.0919	−	34.0208i	−0.630839	−	1.52298i	0.207730	−	0.978186i	$-0.433392\pi$
$500$		0			0
$501$	−25.7990	−	25.7990i	−1.15261	−	1.15261i
$502$	13.2426	+	13.2426i	0.591048	+	0.591048i
$503$	−11.1716	+	4.62742i	−0.498116	+	0.206326i	−0.617574	−	0.786513i	$-0.711884\pi$
$503$	−11.1716	+	4.62742i	−0.498116	+	0.206326i	0.119458	+	0.992839i	$0.461884\pi$
$504$	0.242641	+	0.585786i	0.0108081	+	0.0260930i
$505$		0			0
$506$		−	13.6569i		−	0.607121i
$507$	8.70711	−	21.0208i	0.386696	−	0.933567i
$508$	9.17157	−	9.17157i	0.406923	−	0.406923i
$509$	16.6274			0.736997			0.368499	−	0.929628i	$-0.379872\pi$
$509$	16.6274			0.736997			0.368499	+	0.929628i	$0.379872\pi$
$510$		0			0
$511$	−8.20101			−0.362791
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.51472	−	3.65685i	0.0668765	−	0.161454i
$514$		−	8.24264i		−	0.363567i
$515$		0			0
$516$	−1.24264	−	3.00000i	−0.0547042	−	0.132068i
$517$	39.7990	−	16.4853i	1.75036	−	0.725022i
$518$	2.34315	+	2.34315i	0.102952	+	0.102952i
$519$	−7.65685	−	7.65685i	−0.336099	−	0.336099i
$520$		0			0
$521$	13.4645	+	32.5061i	0.589889	+	1.42412i	0.883609	+	0.468226i	$0.155107\pi$
$521$	13.4645	+	32.5061i	0.589889	+	1.42412i	−0.293720	+	0.955892i	$0.594893\pi$
$522$	−0.585786	−	0.242641i	−0.0256392	−	0.0106201i
$523$		−	23.2132i		−	1.01504i	−0.861639	−	0.507521i	$-0.830562\pi$
$523$		−	23.2132i		−	1.01504i	0.861639	−	0.507521i	$-0.169438\pi$
$524$	0.0502525	−	0.121320i	0.00219529	−	0.00529990i
$525$		0			0
$526$	8.00000			0.348817
$527$	−15.0711	+	2.24264i	−0.656506	+	0.0976910i
$528$	−8.24264			−0.358715
$529$	9.63604	−	9.63604i	0.418958	−	0.418958i
$530$		0			0
$531$		−	0.242641i		−	0.0105297i
$532$	1.17157	+	0.485281i	0.0507941	+	0.0210396i
$533$	3.55635	+	8.58579i	0.154043	+	0.371892i
$534$	−25.7279	+	10.6569i	−1.11336	+	0.461167i
$535$		0			0
$536$	5.24264	+	5.24264i	0.226448	+	0.226448i
$537$	−44.0416	+	18.2426i	−1.90054	+	0.787228i
$538$	2.92893	+	7.07107i	0.126275	+	0.304855i
$539$	−19.1924	−	7.94975i	−0.826675	−	0.342420i
$540$		0			0
$541$	7.79899	−	18.8284i	0.335305	−	0.809497i	−0.662849	−	0.748753i	$-0.730653\pi$
$541$	7.79899	−	18.8284i	0.335305	−	0.809497i	0.998153	−	0.0607439i	$-0.0193473\pi$
$542$	10.4853	−	10.4853i	0.450381	−	0.450381i
$543$	11.3137			0.485518
$544$	4.00000	+	1.00000i	0.171499	+	0.0428746i
$545$		0			0
$546$	1.65685	−	1.65685i	0.0709068	−	0.0709068i
$547$	9.39340	−	22.6777i	0.401633	−	0.969627i	−0.585637	−	0.810573i	$-0.699156\pi$
$547$	9.39340	−	22.6777i	0.401633	−	0.969627i	0.987270	−	0.159054i	$-0.0508443\pi$
$548$		−	2.34315i		−	0.100094i
$549$	−2.82843	−	1.17157i	−0.120714	−	0.0500015i
$550$		0			0
$551$	−1.17157	+	0.485281i	−0.0499107	+	0.0206737i
$552$	4.00000	+	4.00000i	0.170251	+	0.170251i
$553$	5.65685	+	5.65685i	0.240554	+	0.240554i
$554$	21.8995	−	9.07107i	0.930420	−	0.385393i
$555$		0			0
$556$	1.70711	+	0.707107i	0.0723975	+	0.0299880i
$557$		−	41.1127i		−	1.74200i	−0.491282	−	0.871000i	$-0.663472\pi$
$557$		−	41.1127i		−	1.74200i	0.491282	−	0.871000i	$-0.336528\pi$
$558$	−0.585786	+	1.41421i	−0.0247983	+	0.0598684i
$559$	−1.02944	+	1.02944i	−0.0435406	+	0.0435406i
$560$		0			0
$561$	17.4853	+	29.1421i	0.738229	+	1.23038i
$562$	−14.3431			−0.605029
$563$	5.92893	−	5.92893i	0.249875	−	0.249875i	−0.571044	−	0.820919i	$-0.693462\pi$
$563$	5.92893	−	5.92893i	0.249875	−	0.249875i	0.820919	+	0.571044i	$0.193462\pi$
$564$	−6.82843	+	16.4853i	−0.287529	+	0.694156i
$565$		0			0
$566$	1.05025	+	0.435029i	0.0441454	+	0.0182856i
$567$	5.89949	+	14.2426i	0.247755	+	0.598135i
$568$	2.00000	−	0.828427i	0.0839181	−	0.0347600i
$569$	3.48528	+	3.48528i	0.146111	+	0.146111i	0.776378	−	0.630267i	$-0.217055\pi$
$569$	3.48528	+	3.48528i	0.146111	+	0.146111i	−0.630267	+	0.776378i	$0.717055\pi$
$570$		0			0
$571$	2.22183	−	0.920310i	0.0929805	−	0.0385138i	−0.335708	−	0.941966i	$-0.608976\pi$
$571$	2.22183	−	0.920310i	0.0929805	−	0.0385138i	0.428689	+	0.903452i	$0.358976\pi$
$572$	1.41421	+	3.41421i	0.0591312	+	0.142755i
$573$	−4.82843	−	2.00000i	−0.201710	−	0.0835512i
$574$		−	17.1716i		−	0.716728i
$575$		0			0
$576$	0.292893	−	0.292893i	0.0122039	−	0.0122039i
$577$	16.6274			0.692208			0.346104	−	0.938196i	$-0.387504\pi$
$577$	16.6274			0.692208			0.346104	+	0.938196i	$0.387504\pi$
$578$	−4.94975	−	16.2635i	−0.205882	−	0.676471i
$579$	−22.7279			−0.944540
$580$		0			0
$581$	3.65685	−	8.82843i	0.151712	−	0.366265i
$582$			10.2426i			0.424571i
$583$	−3.41421	−	1.41421i	−0.141402	−	0.0585707i
$584$	2.05025	+	4.94975i	0.0848401	+	0.204822i
$585$		0			0
$586$	−15.5563	−	15.5563i	−0.642627	−	0.642627i
$587$	2.14214	+	2.14214i	0.0884154	+	0.0884154i	0.749931	−	0.661516i	$-0.230087\pi$
$587$	2.14214	+	2.14214i	0.0884154	+	0.0884154i	−0.661516	+	0.749931i	$0.730087\pi$
$588$	7.94975	−	3.29289i	0.327842	−	0.135797i
$589$	1.17157	+	2.82843i	0.0482738	+	0.116543i
$590$		0			0
$591$		−	36.9706i		−	1.52077i
$592$	0.828427	−	2.00000i	0.0340481	−	0.0821995i
$593$	3.00000	−	3.00000i	0.123195	−	0.123195i	−0.642821	−	0.766016i	$-0.722236\pi$
$593$	3.00000	−	3.00000i	0.123195	−	0.123195i	0.766016	+	0.642821i	$0.222236\pi$
$594$	−21.3137			−0.874512
$595$		0			0
$596$	−15.6569			−0.641330
$597$	−27.3137	+	27.3137i	−1.11788	+	1.11788i
$598$	0.970563	−	2.34315i	0.0396893	−	0.0958184i
$599$		−	26.3431i		−	1.07635i	−0.842833	−	0.538176i	$-0.819114\pi$
$599$		−	26.3431i		−	1.07635i	0.842833	−	0.538176i	$-0.180886\pi$
$600$		0			0
$601$	−7.05025	−	17.0208i	−0.287586	−	0.694294i	0.712386	−	0.701788i	$-0.247615\pi$
$601$	−7.05025	−	17.0208i	−0.287586	−	0.694294i	−0.999972	+	0.00749419i	$0.997615\pi$
$602$	2.48528	−	1.02944i	0.101293	−	0.0419567i
$603$	−2.17157	−	2.17157i	−0.0884333	−	0.0884333i
$604$	15.6569	+	15.6569i	0.637068	+	0.637068i
$605$		0			0
$606$	3.07107	+	7.41421i	0.124754	+	0.301182i
$607$	−9.07107	−	3.75736i	−0.368183	−	0.152507i	0.190918	−	0.981606i	$-0.438854\pi$
$607$	−9.07107	−	3.75736i	−0.368183	−	0.152507i	−0.559101	+	0.829100i	$0.688854\pi$
$608$		−	0.828427i		−	0.0335972i
$609$	1.65685	−	4.00000i	0.0671391	−	0.162088i
$610$		0			0
$611$	8.00000			0.323645
$612$	−1.65685	−	0.414214i	−0.0669744	−	0.0167436i
$613$	−37.7990			−1.52669			−0.763343	−	0.645993i	$-0.776444\pi$
$613$	−37.7990			−1.52669			−0.763343	+	0.645993i	$0.776444\pi$
$614$	4.48528	−	4.48528i	0.181011	−	0.181011i
$615$		0			0
$616$		−	6.82843i		−	0.275125i
$617$	16.7071	+	6.92031i	0.672603	+	0.278601i	0.692731	−	0.721196i	$-0.256407\pi$
$617$	16.7071	+	6.92031i	0.672603	+	0.278601i	−0.0201281	+	0.999797i	$0.506407\pi$
$618$	−8.82843	−	21.3137i	−0.355131	−	0.857363i
$619$	5.12132	−	2.12132i	0.205843	−	0.0852631i	−0.277380	−	0.960760i	$-0.589466\pi$
$619$	5.12132	−	2.12132i	0.205843	−	0.0852631i	0.483223	+	0.875497i	$0.339466\pi$
$620$		0			0
$621$	10.3431	+	10.3431i	0.415056	+	0.415056i
$622$	13.8995	−	5.75736i	0.557319	−	0.230849i
$623$	−8.82843	−	21.3137i	−0.353703	−	0.853916i
$624$	−1.41421	−	0.585786i	−0.0566139	−	0.0234502i
$625$		0			0
$626$	5.19239	−	12.5355i	0.207530	−	0.501021i
$627$	4.82843	−	4.82843i	0.192829	−	0.192829i
$628$	13.3137			0.531275
$629$	−8.82843	+	1.31371i	−0.352012	+	0.0523810i
$630$		0			0
$631$	−21.6569	+	21.6569i	−0.862146	+	0.862146i	−0.991587	−	0.129441i	$-0.958682\pi$
$631$	−21.6569	+	21.6569i	−0.862146	+	0.862146i	0.129441	+	0.991587i	$0.458682\pi$
$632$	2.00000	−	4.82843i	0.0795557	−	0.192065i
$633$			0.242641i			0.00964410i
$634$	20.4853	+	8.48528i	0.813574	+	0.336994i
$635$		0			0
$636$	1.41421	−	0.585786i	0.0560772	−	0.0232279i
$637$	−2.72792	−	2.72792i	−0.108084	−	0.108084i
$638$	4.82843	+	4.82843i	0.191159	+	0.191159i
$639$	−0.828427	+	0.343146i	−0.0327721	+	0.0135746i
$640$		0			0
$641$	−13.4350	−	5.56497i	−0.530652	−	0.219803i	0.101237	−	0.994862i	$-0.467720\pi$
$641$	−13.4350	−	5.56497i	−0.530652	−	0.219803i	−0.631889	+	0.775059i	$0.717720\pi$
$642$		−	21.5563i		−	0.850761i
$643$	5.12132	−	12.3640i	0.201965	−	0.487587i	−0.790150	−	0.612913i	$-0.789998\pi$
$643$	5.12132	−	12.3640i	0.201965	−	0.487587i	0.992116	+	0.125326i	$0.0399976\pi$
$644$	−3.31371	+	3.31371i	−0.130578	+	0.130578i
$645$		0			0
$646$	−2.92893	+	1.75736i	−0.115237	+	0.0691424i
$647$	−12.4853			−0.490847			−0.245424	−	0.969416i	$-0.578927\pi$
$647$	−12.4853			−0.490847			−0.245424	+	0.969416i	$0.578927\pi$
$648$	7.12132	−	7.12132i	0.279752	−	0.279752i
$649$	−1.00000	+	2.41421i	−0.0392534	+	0.0947662i
$650$		0			0
$651$	−9.65685	−	4.00000i	−0.378482	−	0.156772i
$652$	8.70711	+	21.0208i	0.340997	+	0.823239i
$653$	23.8995	−	9.89949i	0.935260	−	0.387397i	0.137588	−	0.990490i	$-0.456065\pi$
$653$	23.8995	−	9.89949i	0.935260	−	0.387397i	0.797671	+	0.603092i	$0.206065\pi$
$654$	−12.8284	−	12.8284i	−0.501631	−	0.501631i
$655$		0			0
$656$	−10.3640	+	4.29289i	−0.404645	+	0.167609i
$657$	−0.849242	−	2.05025i	−0.0331321	−	0.0799880i
$658$	−13.6569	−	5.65685i	−0.532400	−	0.220527i
$659$			39.3137i			1.53144i	0.643171	+	0.765722i	$0.277618\pi$
$659$			39.3137i			1.53144i	−0.643171	+	0.765722i	$0.722382\pi$
$660$		0			0
$661$	12.7279	−	12.7279i	0.495059	−	0.495059i	−0.414837	−	0.909896i	$-0.636161\pi$
$661$	12.7279	−	12.7279i	0.495059	−	0.495059i	0.909896	+	0.414837i	$0.136161\pi$
$662$	−27.6985			−1.07653
$663$	0.928932	+	6.24264i	0.0360767	+	0.242444i
$664$	−6.24264			−0.242261
$665$		0			0
$666$	−0.343146	+	0.828427i	−0.0132966	+	0.0321009i
$667$		−	4.68629i		−	0.181454i
$668$	−18.2426	−	7.55635i	−0.705829	−	0.292364i
$669$	−17.3137	−	41.7990i	−0.669387	−	1.61604i
$670$		0			0
$671$	23.3137	+	23.3137i	0.900016	+	0.900016i
$672$	2.00000	+	2.00000i	0.0771517	+	0.0771517i
$673$	−0.949747	+	0.393398i	−0.0366101	+	0.0151644i	−0.400913	−	0.916116i	$-0.631307\pi$
$673$	−0.949747	+	0.393398i	−0.0366101	+	0.0151644i	0.364303	+	0.931280i	$0.381307\pi$
$674$	−4.46447	−	10.7782i	−0.171965	−	0.415160i
$675$		0			0
$676$		−	12.3137i		−	0.473604i
$677$	4.48528	−	10.8284i	0.172383	−	0.416170i	−0.813949	−	0.580936i	$-0.802687\pi$
$677$	4.48528	−	10.8284i	0.172383	−	0.416170i	0.986333	+	0.164766i	$0.0526867\pi$
$678$	−12.0711	+	12.0711i	−0.463587	+	0.463587i
$679$	−8.48528			−0.325635
$680$		0			0
$681$	−37.5563			−1.43916
$682$	11.6569	−	11.6569i	0.446364	−	0.446364i
$683$	4.15076	−	10.0208i	0.158824	−	0.383436i	−0.824356	−	0.566071i	$-0.808463\pi$
$683$	4.15076	−	10.0208i	0.158824	−	0.383436i	0.983181	+	0.182635i	$0.0584628\pi$
$684$			0.343146i			0.0131205i
$685$		0			0
$686$	6.82843	+	16.4853i	0.260711	+	0.629411i
$687$	31.5563	−	13.0711i	1.20395	−	0.498692i
$688$	−1.24264	−	1.24264i	−0.0473752	−	0.0473752i
$689$	−0.485281	−	0.485281i	−0.0184877	−	0.0184877i
$690$		0			0
$691$	−17.9914	−	43.4350i	−0.684424	−	1.65235i	−0.755723	−	0.654891i	$-0.772714\pi$
$691$	−17.9914	−	43.4350i	−0.684424	−	1.65235i	0.0712988	−	0.997455i	$-0.477286\pi$
$692$	−5.41421	−	2.24264i	−0.205818	−	0.0852524i
$693$			2.82843i			0.107443i
$694$	−6.19239	+	14.9497i	−0.235060	+	0.567485i
$695$		0			0
$696$	−2.82843			−0.107211
$697$	37.1630	+	27.5355i	1.40765	+	1.04298i
$698$	19.6569			0.744023
$699$	−13.7279	+	13.7279i	−0.519238	+	0.519238i
$700$		0			0
$701$			1.51472i			0.0572101i	0.999591	+	0.0286051i	$0.00910652\pi$
$701$			1.51472i			0.0572101i	−0.999591	+	0.0286051i	$0.990893\pi$
$702$	−3.65685	−	1.51472i	−0.138019	−	0.0571694i
$703$	0.686292	+	1.65685i	0.0258840	+	0.0624894i
$704$	−4.12132	+	1.70711i	−0.155328	+	0.0643390i
$705$		0			0
$706$	−10.1716	−	10.1716i	−0.382812	−	0.382812i
$707$	−6.14214	+	2.54416i	−0.230999	+	0.0956828i
$708$	−0.414214	−	1.00000i	−0.0155671	−	0.0375823i
$709$	−5.75736	−	2.38478i	−0.216222	−	0.0895622i	0.271943	−	0.962313i	$-0.412334\pi$
$709$	−5.75736	−	2.38478i	−0.216222	−	0.0895622i	−0.488165	+	0.872751i	$0.662334\pi$
$710$		0			0
$711$	−0.828427	+	2.00000i	−0.0310684	+	0.0750059i
$712$	−10.6569	+	10.6569i	−0.399382	+	0.399382i
$713$	−11.3137			−0.423702
$714$	2.82843	−	11.3137i	0.105851	−	0.423405i
$715$		0			0
$716$	−18.2426	+	18.2426i	−0.681759	+	0.681759i
$717$	14.9706	−	36.1421i	0.559086	−	1.34975i
$718$			11.3137i			0.422224i
$719$	4.00000	+	1.65685i	0.149175	+	0.0617902i	0.456022	−	0.889969i	$-0.349274\pi$
$719$	4.00000	+	1.65685i	0.149175	+	0.0617902i	−0.306847	+	0.951759i	$0.599274\pi$
$720$		0			0
$721$	17.6569	−	7.31371i	0.657576	−	0.272377i
$722$	−12.9497	−	12.9497i	−0.481940	−	0.481940i
$723$	−25.9706	−	25.9706i	−0.965856	−	0.965856i
$724$	5.65685	−	2.34315i	0.210235	−	0.0870823i
$725$		0			0
$726$	−15.1924	−	6.29289i	−0.563842	−	0.233551i
$727$			32.2843i			1.19736i	0.800989	+	0.598679i	$0.204307\pi$
$727$			32.2843i			1.19736i	−0.800989	+	0.598679i	$0.795693\pi$
$728$	0.485281	−	1.17157i	0.0179857	−	0.0434214i
$729$	15.7782	−	15.7782i	0.584377	−	0.584377i
$730$		0			0
$731$	−1.75736	+	7.02944i	−0.0649983	+	0.259993i
$732$	−13.6569			−0.504772
$733$	9.89949	−	9.89949i	0.365646	−	0.365646i	−0.500240	−	0.865887i	$-0.666755\pi$
$733$	9.89949	−	9.89949i	0.365646	−	0.365646i	0.865887	+	0.500240i	$0.166755\pi$
$734$	7.17157	−	17.3137i	0.264708	−	0.639061i
$735$		0			0
$736$	2.82843	+	1.17157i	0.104257	+	0.0431847i
$737$	12.6569	+	30.5563i	0.466221	+	1.12556i
$738$	4.29289	−	1.77817i	0.158024	−	0.0654555i
$739$	−0.485281	−	0.485281i	−0.0178514	−	0.0178514i	0.698125	−	0.715976i	$-0.254018\pi$
$739$	−0.485281	−	0.485281i	−0.0178514	−	0.0178514i	−0.715976	+	0.698125i	$0.754018\pi$
$740$		0			0
$741$	1.17157	−	0.485281i	0.0430388	−	0.0178273i
$742$	0.485281	+	1.17157i	0.0178152	+	0.0430098i
$743$	−23.8995	−	9.89949i	−0.876787	−	0.363177i	−0.101537	−	0.994832i	$-0.532376\pi$
$743$	−23.8995	−	9.89949i	−0.876787	−	0.363177i	−0.775250	+	0.631654i	$0.782376\pi$
$744$			6.82843i			0.250342i
$745$		0			0
$746$	−7.41421	+	7.41421i	−0.271454	+	0.271454i
$747$	2.58579			0.0946090
$748$	14.7782	+	10.9497i	0.540344	+	0.400362i
$749$	17.8579			0.652512
$750$		0			0
$751$	9.51472	−	22.9706i	0.347197	−	0.838208i	−0.649752	−	0.760147i	$-0.725127\pi$
$751$	9.51472	−	22.9706i	0.347197	−	0.838208i	0.996949	−	0.0780611i	$-0.0248729\pi$
$752$			9.65685i			0.352149i
$753$	−31.9706	−	13.2426i	−1.16507	−	0.482589i
$754$	0.485281	+	1.17157i	0.0176729	+	0.0426662i
$755$		0			0
$756$	5.17157	+	5.17157i	0.188088	+	0.188088i
$757$	7.75736	+	7.75736i	0.281946	+	0.281946i	0.833885	−	0.551939i	$-0.186112\pi$
$757$	7.75736	+	7.75736i	0.281946	+	0.281946i	−0.551939	+	0.833885i	$0.686112\pi$
$758$	−8.60660	+	3.56497i	−0.312606	+	0.129486i
$759$	9.65685	+	23.3137i	0.350522	+	0.846234i
$760$		0			0
$761$		−	53.2548i		−	1.93049i	−0.261354	−	0.965243i	$-0.584169\pi$
$761$		−	53.2548i		−	1.93049i	0.261354	−	0.965243i	$-0.415831\pi$
$762$	−9.17157	+	22.1421i	−0.332251	+	0.802125i
$763$	10.6274	−	10.6274i	0.384738	−	0.384738i
$764$	−2.82843			−0.102329
$765$		0			0
$766$	−30.1421			−1.08908
$767$	−0.343146	+	0.343146i	−0.0123903	+	0.0123903i
$768$	0.707107	−	1.70711i	0.0255155	−	0.0615999i
$769$		−	26.3431i		−	0.949958i	−0.879997	−	0.474979i	$-0.842456\pi$
$769$		−	26.3431i		−	0.949958i	0.879997	−	0.474979i	$-0.157544\pi$
$770$		0			0
$771$	5.82843	+	14.0711i	0.209906	+	0.506757i
$772$	−11.3640	+	4.70711i	−0.408998	+	0.169412i
$773$	−2.58579	−	2.58579i	−0.0930043	−	0.0930043i	0.659074	−	0.752078i	$-0.270948\pi$
$773$	−2.58579	−	2.58579i	−0.0930043	−	0.0930043i	−0.752078	+	0.659074i	$0.770948\pi$
$774$	0.514719	+	0.514719i	0.0185012	+	0.0185012i
$775$		0			0
$776$	2.12132	+	5.12132i	0.0761510	+	0.183845i
$777$	−5.65685	−	2.34315i	−0.202939	−	0.0840599i
$778$			3.17157i			0.113706i
$779$	3.55635	−	8.58579i	0.127419	−	0.307618i
$780$		0			0
$781$	9.65685			0.345549
$782$	−1.85786	−	12.4853i	−0.0664371	−	0.446473i
$783$	−7.31371			−0.261371
$784$	3.29289	−	3.29289i	0.117603	−	0.117603i
$785$		0			0
$786$			0.242641i			0.00865471i
$787$	17.6066	+	7.29289i	0.627608	+	0.259964i	0.673736	−	0.738972i	$-0.264688\pi$
$787$	17.6066	+	7.29289i	0.627608	+	0.259964i	−0.0461286	+	0.998936i	$0.514688\pi$
$788$	−7.65685	−	18.4853i	−0.272764	−	0.658511i
$789$	−13.6569	+	5.65685i	−0.486197	+	0.201389i
$790$		0			0
$791$	−10.0000	−	10.0000i	−0.355559	−	0.355559i
$792$	1.70711	−	0.707107i	0.0606594	−	0.0251259i
$793$	2.34315	+	5.65685i	0.0832075	+	0.200881i
$794$	7.65685	+	3.17157i	0.271732	+	0.112555i
$795$		0			0
$796$	−8.00000	+	19.3137i	−0.283552	+	0.684556i
$797$	−18.8701	+	18.8701i	−0.668412	+	0.668412i	−0.957348	−	0.288937i	$-0.906698\pi$
$797$	−18.8701	+	18.8701i	−0.668412	+	0.668412i	0.288937	+	0.957348i	$0.406698\pi$
$798$	−2.34315			−0.0829465
$799$	34.1421	−	20.4853i	1.20786	−	0.724717i
$800$		0			0
$801$	4.41421	−	4.41421i	0.155969	−	0.155969i
$802$	9.19239	−	22.1924i	0.324595	−	0.783640i
$803$			23.8995i			0.843395i
$804$	−12.6569	−	5.24264i	−0.446373	−	0.184894i
$805$		0			0
$806$	2.82843	−	1.17157i	0.0996271	−	0.0412669i
$807$	−10.0000	−	10.0000i	−0.352017	−	0.352017i
$808$	3.07107	+	3.07107i	0.108040	+	0.108040i
$809$	−43.1630	+	17.8787i	−1.51753	+	0.628581i	−0.977095	−	0.212806i	$-0.931740\pi$
$809$	−43.1630	+	17.8787i	−1.51753	+	0.628581i	−0.540434	+	0.841386i	$0.681740\pi$
$810$		0			0
$811$	45.5061	+	18.8492i	1.59794	+	0.661886i	0.991122	−	0.132958i	$-0.0424475\pi$
$811$	45.5061	+	18.8492i	1.59794	+	0.661886i	0.606813	+	0.794844i	$0.292447\pi$
$812$		−	2.34315i		−	0.0822283i
$813$	−10.4853	+	25.3137i	−0.367735	+	0.887791i
$814$	6.82843	−	6.82843i	0.239336	−	0.239336i
$815$		0			0
$816$	−7.53553	+	1.12132i	−0.263796	+	0.0392541i
$817$	1.45584			0.0509335
$818$	−11.0000	+	11.0000i	−0.384606	+	0.384606i
$819$	−0.201010	+	0.485281i	−0.00702386	+	0.0169571i
$820$		0			0
$821$	−0.343146	−	0.142136i	−0.0119759	−	0.00496057i	0.376687	−	0.926340i	$-0.377063\pi$
$821$	−0.343146	−	0.142136i	−0.0119759	−	0.00496057i	−0.388663	+	0.921380i	$0.627063\pi$
$822$	1.65685	+	4.00000i	0.0577894	+	0.139516i
$823$	−40.2843	+	16.6863i	−1.40422	+	0.581648i	−0.950844	−	0.309671i	$-0.899781\pi$
$823$	−40.2843	+	16.6863i	−1.40422	+	0.581648i	−0.453378	+	0.891319i	$0.649781\pi$
$824$	−8.82843	−	8.82843i	−0.307553	−	0.307553i
$825$		0			0
$826$	0.828427	−	0.343146i	0.0288247	−	0.0119396i
$827$	9.15076	+	22.0919i	0.318203	+	0.768210i	0.999350	+	0.0360629i	$0.0114817\pi$
$827$	9.15076	+	22.0919i	0.318203	+	0.768210i	−0.681147	+	0.732147i	$0.738518\pi$
$828$	−1.17157	−	0.485281i	−0.0407150	−	0.0168647i
$829$			20.1421i			0.699565i	0.936831	+	0.349783i	$0.113745\pi$
$829$			20.1421i			0.699565i	−0.936831	+	0.349783i	$0.886255\pi$
$830$		0			0
$831$	−30.9706	+	30.9706i	−1.07436	+	1.07436i
$832$	−0.828427			−0.0287205
$833$	−18.6274	−	4.65685i	−0.645402	−	0.161350i
$834$	−3.41421			−0.118225
$835$		0			0
$836$	1.41421	−	3.41421i	0.0489116	−	0.118083i
$837$			17.6569i			0.610310i
$838$	15.9497	+	6.60660i	0.550975	+	0.228221i
$839$	18.5269	+	44.7279i	0.639620	+	1.54418i	0.827187	+	0.561927i	$0.189940\pi$
$839$	18.5269	+	44.7279i	0.639620	+	1.54418i	−0.187566	+	0.982252i	$0.560060\pi$
$840$		0			0
$841$	−18.8492	−	18.8492i	−0.649974	−	0.649974i
$842$	11.0711	+	11.0711i	0.381534	+	0.381534i
$843$	24.4853	−	10.1421i	0.843318	−	0.349314i
$844$	0.0502525	+	0.121320i	0.00172976	+	0.00417602i
$845$		0			0
$846$		−	4.00000i		−	0.137523i
$847$	5.21320	−	12.5858i	0.179128	−	0.432453i
$848$	0.585786	−	0.585786i	0.0201160	−	0.0201160i
$849$	−2.10051			−0.0720891
$850$		0			0
$851$	−6.62742			−0.227185
$852$	−2.82843	+	2.82843i	−0.0969003	+	0.0969003i
$853$	14.5269	−	35.0711i	0.497392	−	1.20081i	−0.453491	−	0.891261i	$-0.649822\pi$
$853$	14.5269	−	35.0711i	0.497392	−	1.20081i	0.950883	−	0.309550i	$-0.100178\pi$
$854$		−	11.3137i		−	0.387147i
$855$		0			0
$856$	−4.46447	−	10.7782i	−0.152592	−	0.368390i
$857$	37.1924	−	15.4056i	1.27047	−	0.526245i	0.357361	−	0.933966i	$-0.383676\pi$
$857$	37.1924	−	15.4056i	1.27047	−	0.526245i	0.913106	+	0.407721i	$0.133676\pi$
$858$	−4.82843	−	4.82843i	−0.164840	−	0.164840i
$859$	0.556349	+	0.556349i	0.0189824	+	0.0189824i	0.716534	−	0.697552i	$-0.245727\pi$
$859$	0.556349	+	0.556349i	0.0189824	+	0.0189824i	−0.697552	+	0.716534i	$0.745727\pi$
$860$		0			0
$861$	12.1421	+	29.3137i	0.413803	+	0.999009i
$862$	13.3137	+	5.51472i	0.453467	+	0.187832i
$863$		−	0.970563i		−	0.0330383i	−0.999864	−	0.0165192i	$-0.994742\pi$
$863$		−	0.970563i		−	0.0330383i	0.999864	−	0.0165192i	$-0.00525845\pi$
$864$	1.82843	−	4.41421i	0.0622044	−	0.150175i
$865$		0			0
$866$	−12.9706			−0.440758
$867$	19.9497	+	24.2635i	0.677529	+	0.824030i
$868$	−5.65685			−0.192006
$869$	16.4853	−	16.4853i	0.559225	−	0.559225i
$870$		0			0
$871$			6.14214i			0.208118i
$872$	−9.07107	−	3.75736i	−0.307185	−	0.127240i
$873$	−0.878680	−	2.12132i	−0.0297388	−	0.0717958i
$874$	−2.34315	+	0.970563i	−0.0792581	+	0.0328298i
$875$		0			0
$876$	−7.00000	−	7.00000i	−0.236508	−	0.236508i
$877$	−9.89949	+	4.10051i	−0.334282	+	0.138464i	−0.543510	−	0.839403i	$-0.682905\pi$
$877$	−9.89949	+	4.10051i	−0.334282	+	0.138464i	0.209228	+	0.977867i	$0.432905\pi$
$878$	−8.82843	−	21.3137i	−0.297945	−	0.719303i
$879$	37.5563	+	15.5563i	1.26674	+	0.524703i
$880$		0			0
$881$	−6.92031	+	16.7071i	−0.233151	+	0.562877i	−0.996545	−	0.0830568i	$-0.973532\pi$
$881$	−6.92031	+	16.7071i	−0.233151	+	0.562877i	0.763394	+	0.645934i	$0.223532\pi$
$882$	−1.36396	+	1.36396i	−0.0459270	+	0.0459270i
$883$	−34.5269			−1.16192			−0.580962	−	0.813931i	$-0.697323\pi$
$883$	−34.5269			−1.16192			−0.580962	+	0.813931i	$0.697323\pi$
$884$	1.75736	+	2.92893i	0.0591064	+	0.0985106i
$885$		0			0
$886$	−26.0711	+	26.0711i	−0.875875	+	0.875875i
$887$	0.970563	−	2.34315i	0.0325883	−	0.0786751i	−0.906748	−	0.421674i	$-0.861443\pi$
$887$	0.970563	−	2.34315i	0.0325883	−	0.0786751i	0.939336	+	0.342999i	$0.111443\pi$
$888$			4.00000i			0.134231i
$889$	−18.3431	−	7.59798i	−0.615209	−	0.254828i
$890$		0			0
$891$	41.5061	−	17.1924i	1.39051	−	0.575967i
$892$	−17.3137	−	17.3137i	−0.579706	−	0.579706i
$893$	−5.65685	−	5.65685i	−0.189299	−	0.189299i
$894$	26.7279	−	11.0711i	0.893915	−	0.370272i
$895$		0			0
$896$	1.41421	+	0.585786i	0.0472456	+	0.0195698i
$897$			4.68629i			0.156471i
$898$	−2.12132	+	5.12132i	−0.0707894	+	0.170901i
$899$	4.00000	−	4.00000i	0.133407	−	0.133407i
$900$		0			0
$901$	−3.31371	−	0.828427i	−0.110396	−	0.0275989i
$902$	−50.0416			−1.66620
$903$	−3.51472	+	3.51472i	−0.116963	+	0.116963i
$904$	−3.53553	+	8.53553i	−0.117590	+	0.283888i
$905$		0			0
$906$	−37.7990	−	15.6569i	−1.25579	−	0.520164i
$907$	−5.60660	−	13.5355i	−0.186164	−	0.449440i	0.803051	−	0.595910i	$-0.203209\pi$
$907$	−5.60660	−	13.5355i	−0.186164	−	0.449440i	−0.989215	+	0.146470i	$0.953209\pi$
$908$	−18.7782	+	7.77817i	−0.623176	+	0.258128i
$909$	−1.27208	−	1.27208i	−0.0421922	−	0.0421922i
$910$		0			0
$911$	−21.5563	+	8.92893i	−0.714194	+	0.295829i	−0.710039	−	0.704163i	$-0.751323\pi$
$911$	−21.5563	+	8.92893i	−0.714194	+	0.295829i	−0.00415500	+	0.999991i	$0.501323\pi$
$912$	0.585786	+	1.41421i	0.0193973	+	0.0468293i
$913$	−25.7279	−	10.6569i	−0.851470	−	0.352690i
$914$		−	4.97056i		−	0.164412i
$915$		0			0
$916$	13.0711	−	13.0711i	0.431880	−	0.431880i
$917$	−0.201010			−0.00663794
$918$	−19.4853	+	2.89949i	−0.643110	+	0.0956976i
$919$	−2.34315			−0.0772932			−0.0386466	−	0.999253i	$-0.512305\pi$
$919$	−2.34315			−0.0772932			−0.0386466	+	0.999253i	$0.512305\pi$
$920$		0			0
$921$	−4.48528	+	10.8284i	−0.147795	+	0.356809i
$922$		−	34.9706i		−	1.15169i
$923$	1.65685	+	0.686292i	0.0545360	+	0.0225896i
$924$	4.82843	+	11.6569i	0.158844	+	0.383482i
$925$		0			0
$926$	2.34315	+	2.34315i	0.0770005	+	0.0770005i
$927$	3.65685	+	3.65685i	0.120107	+	0.120107i
$928$	−1.41421	+	0.585786i	−0.0464238	+	0.0192294i
$929$	−3.53553	−	8.53553i	−0.115997	−	0.280042i	0.855209	−	0.518284i	$-0.173429\pi$
$929$	−3.53553	−	8.53553i	−0.115997	−	0.280042i	−0.971206	+	0.238242i	$0.923429\pi$
$930$		0			0
$931$			3.85786i			0.126436i
$932$	−4.02082	+	9.70711i	−0.131706	+	0.317967i
$933$	−19.6569	+	19.6569i	−0.643537	+	0.643537i
$934$	−2.48528			−0.0813209
$935$		0			0
$936$	0.343146			0.0112161
$937$	3.75736	−	3.75736i	0.122748	−	0.122748i	−0.643064	−	0.765812i	$-0.722337\pi$
$937$	3.75736	−	3.75736i	0.122748	−	0.122748i	0.765812	+	0.643064i	$0.222337\pi$
$938$	4.34315	−	10.4853i	0.141809	−	0.342357i
$939$			25.0711i			0.818163i
$940$		0			0
$941$	7.51472	+	18.1421i	0.244973	+	0.591417i	0.997763	−	0.0668433i	$-0.0212928\pi$
$941$	7.51472	+	18.1421i	0.244973	+	0.591417i	−0.752791	+	0.658260i	$0.771293\pi$
$942$	−22.7279	+	9.41421i	−0.740516	+	0.306732i
$943$	24.2843	+	24.2843i	0.790805	+	0.790805i
$944$	−0.414214	−	0.414214i	−0.0134815	−	0.0134815i
$945$		0			0
$946$	−3.00000	−	7.24264i	−0.0975384	−	0.235479i
$947$	48.3345	+	20.0208i	1.57066	+	0.650589i	0.986900	−	0.161336i	$-0.0515803\pi$
$947$	48.3345	+	20.0208i	1.57066	+	0.650589i	0.583761	+	0.811925i	$0.301580\pi$
$948$			9.65685i			0.313640i
$949$	−1.69848	+	4.10051i	−0.0551352	+	0.133108i
$950$		0			0
$951$	−40.9706			−1.32856
$952$	−0.928932	−	6.24264i	−0.0301069	−	0.202325i
$953$	11.5563			0.374347			0.187173	−	0.982327i	$-0.440067\pi$
$953$	11.5563			0.374347			0.187173	+	0.982327i	$0.440067\pi$
$954$	−0.242641	+	0.242641i	−0.00785578	+	0.00785578i
$955$		0			0
$956$		−	21.1716i		−	0.684738i
$957$	−11.6569	−	4.82843i	−0.376813	−	0.156081i
$958$	9.51472	+	22.9706i	0.307407	+	0.742145i
$959$	−3.31371	+	1.37258i	−0.107005	+	0.0443230i
$960$		0			0
$961$	12.2635	+	12.2635i	0.395595	+	0.395595i
$962$	1.65685	−	0.686292i	0.0534191	−	0.0221269i
$963$	1.84924	+	4.46447i	0.0595910	+	0.143865i
$964$	−18.3640	−	7.60660i	−0.591463	−	0.244992i
$965$		0			0
$966$	3.31371	−	8.00000i	0.106617	−	0.257396i
$967$	−9.65685	+	9.65685i	−0.310543	+	0.310543i	−0.845120	−	0.534577i	$-0.820471\pi$
$967$	−9.65685	+	9.65685i	−0.310543	+	0.310543i	0.534577	+	0.845120i	$0.320471\pi$
$968$	−8.89949			−0.286041
$969$	3.75736	−	5.07107i	0.120704	−	0.162906i
$970$		0			0
$971$	15.0416	−	15.0416i	0.482709	−	0.482709i	−0.423287	−	0.905996i	$-0.639124\pi$
$971$	15.0416	−	15.0416i	0.482709	−	0.482709i	0.905996	+	0.423287i	$0.139124\pi$
$972$	−1.63604	+	3.94975i	−0.0524760	+	0.126688i
$973$		−	2.82843i		−	0.0906752i
$974$	20.4853	+	8.48528i	0.656391	+	0.271886i
$975$		0			0
$976$	−6.82843	+	2.82843i	−0.218573	+	0.0905357i
$977$	−20.1127	−	20.1127i	−0.643462	−	0.643462i	0.307943	−	0.951405i	$-0.400359\pi$
$977$	−20.1127	−	20.1127i	−0.643462	−	0.643462i	−0.951405	+	0.307943i	$0.900359\pi$
$978$	−29.7279	−	29.7279i	−0.950594	−	0.950594i
$979$	−62.1127	+	25.7279i	−1.98513	+	0.822268i
$980$		0			0
$981$	3.75736	+	1.55635i	0.119963	+	0.0496904i
$982$			15.4558i			0.493216i
$983$	−10.3431	+	24.9706i	−0.329895	+	0.796437i	0.668704	+	0.743529i	$0.266849\pi$
$983$	−10.3431	+	24.9706i	−0.329895	+	0.796437i	−0.998599	+	0.0529088i	$0.983151\pi$
$984$	14.6569	−	14.6569i	0.467243	−	0.467243i
$985$		0			0
$986$	5.07107	+	3.75736i	0.161496	+	0.119659i
$987$	27.3137			0.869405
$988$	0.485281	−	0.485281i	0.0154389	−	0.0154389i
$989$	−2.05887	+	4.97056i	−0.0654684	+	0.158055i
$990$		0			0
$991$	−42.2843	−	17.5147i	−1.34320	−	0.556373i	−0.408812	−	0.912619i	$-0.634057\pi$
$991$	−42.2843	−	17.5147i	−1.34320	−	0.556373i	−0.934392	+	0.356245i	$0.884057\pi$
$992$	1.41421	+	3.41421i	0.0449013	+	0.108401i
$993$	47.2843	−	19.5858i	1.50052	−	0.621536i
$994$	−2.34315	−	2.34315i	−0.0743201	−	0.0743201i
$995$		0			0
$996$	10.6569	−	4.41421i	0.337675	−	0.139870i
$997$	4.54416	+	10.9706i	0.143915	+	0.347441i	0.979357	−	0.202137i	$-0.0647885\pi$
$997$	4.54416	+	10.9706i	0.143915	+	0.347441i	−0.835442	+	0.549578i	$0.814789\pi$
$998$	34.0208	+	14.0919i	1.07691	+	0.446071i
$999$			10.3431i			0.327243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.l.a.501.1		4
5.2	odd	4		850.2.o.a.399.1		4
5.3	odd	4		850.2.o.b.399.1		4
5.4	even	2		34.2.d.a.25.1	yes	4
15.14	odd	2		306.2.l.c.127.1		4
17.15	even	8	inner	850.2.l.a.151.1		4
20.19	odd	2		272.2.v.b.161.1		4
85.4	even	4		578.2.d.c.179.1		4
85.9	even	8		578.2.d.a.155.1		4
85.14	odd	16		578.2.c.f.327.4		8
85.19	even	8		578.2.d.b.423.1		4
85.24	odd	16		578.2.a.i.1.4		4
85.29	odd	16		578.2.c.f.251.4		8
85.32	odd	8		850.2.o.b.49.1		4
85.39	odd	16		578.2.c.f.251.1		8
85.44	odd	16		578.2.a.i.1.1		4
85.49	even	8		34.2.d.a.15.1	✓	4
85.54	odd	16		578.2.c.f.327.1		8
85.59	even	8		578.2.d.c.155.1		4
85.64	even	4		578.2.d.a.179.1		4
85.74	odd	16		578.2.b.d.577.4		4
85.79	odd	16		578.2.b.d.577.1		4
85.83	odd	8		850.2.o.a.49.1		4
85.84	even	2		578.2.d.b.399.1		4
255.44	even	16		5202.2.a.bw.1.4		4
255.134	odd	8		306.2.l.c.253.1		4
255.194	even	16		5202.2.a.bw.1.1		4
340.219	odd	8		272.2.v.b.49.1		4
340.279	even	16		4624.2.a.bn.1.1		4
340.299	even	16		4624.2.a.bn.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.d.a.15.1	✓	4	85.49	even	8
34.2.d.a.25.1	yes	4	5.4	even	2
272.2.v.b.49.1		4	340.219	odd	8
272.2.v.b.161.1		4	20.19	odd	2
306.2.l.c.127.1		4	15.14	odd	2
306.2.l.c.253.1		4	255.134	odd	8
578.2.a.i.1.1		4	85.44	odd	16
578.2.a.i.1.4		4	85.24	odd	16
578.2.b.d.577.1		4	85.79	odd	16
578.2.b.d.577.4		4	85.74	odd	16
578.2.c.f.251.1		8	85.39	odd	16
578.2.c.f.251.4		8	85.29	odd	16
578.2.c.f.327.1		8	85.54	odd	16
578.2.c.f.327.4		8	85.14	odd	16
578.2.d.a.155.1		4	85.9	even	8
578.2.d.a.179.1		4	85.64	even	4
578.2.d.b.399.1		4	85.84	even	2
578.2.d.b.423.1		4	85.19	even	8
578.2.d.c.155.1		4	85.59	even	8
578.2.d.c.179.1		4	85.4	even	4
850.2.l.a.151.1		4	17.15	even	8	inner
850.2.l.a.501.1		4	1.1	even	1	trivial
850.2.o.a.49.1		4	85.83	odd	8
850.2.o.a.399.1		4	5.2	odd	4
850.2.o.b.49.1		4	85.32	odd	8
850.2.o.b.399.1		4	5.3	odd	4
4624.2.a.bn.1.1		4	340.279	even	16
4624.2.a.bn.1.4		4	340.299	even	16
5202.2.a.bw.1.1		4	255.194	even	16
5202.2.a.bw.1.4		4	255.44	even	16

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 1.70711i) q^{3} -1.00000i q^{4} +(0.707107 + 1.70711i) q^{6} +(-1.41421 + 0.585786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.292893 - 0.292893i) q^{9} +(1.70711 + 4.12132i) q^{11} +(-1.70711 - 0.707107i) q^{12} +0.828427i q^{13} +(0.585786 - 1.41421i) q^{14} -1.00000 q^{16} +(2.12132 + 3.53553i) q^{17} +0.414214 q^{18} +(0.585786 - 0.585786i) q^{19} +2.82843i q^{21} +(-4.12132 - 1.70711i) q^{22} +(1.17157 + 2.82843i) q^{23} +(1.70711 - 0.707107i) q^{24} +(-0.585786 - 0.585786i) q^{26} +(4.41421 - 1.82843i) q^{27} +(0.585786 + 1.41421i) q^{28} +(-1.41421 - 0.585786i) q^{29} +(-1.41421 + 3.41421i) q^{31} +(0.707107 - 0.707107i) q^{32} +8.24264 q^{33} +(-4.00000 - 1.00000i) q^{34} +(-0.292893 + 0.292893i) q^{36} +(-0.828427 + 2.00000i) q^{37} +0.828427i q^{38} +(1.41421 + 0.585786i) q^{39} +(10.3640 - 4.29289i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(1.24264 + 1.24264i) q^{43} +(4.12132 - 1.70711i) q^{44} +(-2.82843 - 1.17157i) q^{46} -9.65685i q^{47} +(-0.707107 + 1.70711i) q^{48} +(-3.29289 + 3.29289i) q^{49} +(7.53553 - 1.12132i) q^{51} +0.828427 q^{52} +(-0.585786 + 0.585786i) q^{53} +(-1.82843 + 4.41421i) q^{54} +(-1.41421 - 0.585786i) q^{56} +(-0.585786 - 1.41421i) q^{57} +(1.41421 - 0.585786i) q^{58} +(0.414214 + 0.414214i) q^{59} +(6.82843 - 2.82843i) q^{61} +(-1.41421 - 3.41421i) q^{62} +(0.585786 + 0.242641i) q^{63} +1.00000i q^{64} +(-5.82843 + 5.82843i) q^{66} +7.41421 q^{67} +(3.53553 - 2.12132i) q^{68} +5.65685 q^{69} +(0.828427 - 2.00000i) q^{71} -0.414214i q^{72} +(4.94975 + 2.05025i) q^{73} +(-0.828427 - 2.00000i) q^{74} +(-0.585786 - 0.585786i) q^{76} +(-4.82843 - 4.82843i) q^{77} +(-1.41421 + 0.585786i) q^{78} +(-2.00000 - 4.82843i) q^{79} -10.0711i q^{81} +(-4.29289 + 10.3640i) q^{82} +(-4.41421 + 4.41421i) q^{83} +2.82843 q^{84} -1.75736 q^{86} +(-2.00000 + 2.00000i) q^{87} +(-1.70711 + 4.12132i) q^{88} +15.0711i q^{89} +(-0.485281 - 1.17157i) q^{91} +(2.82843 - 1.17157i) q^{92} +(4.82843 + 4.82843i) q^{93} +(6.82843 + 6.82843i) q^{94} +(-0.707107 - 1.70711i) q^{96} +(5.12132 + 2.12132i) q^{97} -4.65685i q^{98} +(0.707107 - 1.70711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9} + 4 q^{11} - 4 q^{12} + 8 q^{14} - 4 q^{16} - 4 q^{18} + 8 q^{19} - 8 q^{22} + 16 q^{23} + 4 q^{24} - 8 q^{26} + 12 q^{27} + 8 q^{28} + 16 q^{33} - 16 q^{34} - 4 q^{36} + 8 q^{37} + 16 q^{41}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^9 + 4 * q^11 - 4 * q^12 + 8 * q^14 - 4 * q^16 - 4 * q^18 + 8 * q^19 - 8 * q^22 + 16 * q^23 + 4 * q^24 - 8 * q^26 + 12 * q^27 + 8 * q^28 + 16 * q^33 - 16 * q^34 - 4 * q^36 + 8 * q^37 + 16 * q^41 - 8 * q^42 - 12 * q^43 + 8 * q^44 - 16 * q^49 + 16 * q^51 - 8 * q^52 - 8 * q^53 + 4 * q^54 - 8 * q^57 - 4 * q^59 + 16 * q^61 + 8 * q^63 - 12 * q^66 + 24 * q^67 - 8 * q^71 + 8 * q^74 - 8 * q^76 - 8 * q^77 - 8 * q^79 - 20 * q^82 - 12 * q^83 - 24 * q^86 - 8 * q^87 - 4 * q^88 + 32 * q^91 + 8 * q^93 + 16 * q^94 + 12 * q^97

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