LMFDB - Embedded newform 850.2.o.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [850,2,Mod(49,850)] 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([4, 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("850.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.o (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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			49.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	850.49
Dual form			850.2.o.a.399.1

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

Character values

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

$n$	$477$	$751$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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
$3$	−1.70711	+	0.707107i	−0.985599	+	0.408248i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−1.70711	+	0.707107i	−0.985599	+	0.408248i	−0.169102	+	0.985599i	$0.554087\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	0.707107	−	1.70711i	0.288675	−	0.696923i
$7$	−0.585786	+	1.41421i	−0.221406	+	0.534522i	−0.995081	−	0.0990602i	$-0.968416\pi$
$7$	−0.585786	+	1.41421i	−0.221406	+	0.534522i	0.773675	+	0.633583i	$0.218416\pi$
$8$	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	−0.426401	−	0.904534i	$-0.640219\pi$
$11$	1.70711	−	4.12132i	0.514712	−	1.24262i	0.941113	−	0.338091i	$-0.109781\pi$
$12$	0.707107	+	1.70711i	0.204124	+	0.492799i
$13$	0.828427			0.229764			0.114882	−	0.993379i	$-0.463351\pi$
$13$	0.828427			0.229764			0.114882	+	0.993379i	$0.463351\pi$
$14$	−0.585786	−	1.41421i	−0.156558	−	0.377964i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.53553	−	2.12132i	−0.857493	−	0.514496i
$17$	−3.53553	−	2.12132i	−0.857493	−	0.514496i
$18$			0.414214i			0.0976311i
$19$	−0.585786	−	0.585786i	−0.134389	−	0.134389i	0.636713	−	0.771101i	$-0.280294\pi$
$19$	−0.585786	−	0.585786i	−0.134389	−	0.134389i	−0.771101	+	0.636713i	$0.780294\pi$
$20$		0			0
$21$		−	2.82843i		−	0.617213i
$22$	1.70711	+	4.12132i	0.363956	+	0.878668i
$23$	2.82843	+	1.17157i	0.589768	+	0.244290i	0.657551	−	0.753410i	$-0.271593\pi$
$23$	2.82843	+	1.17157i	0.589768	+	0.244290i	−0.0677829	+	0.997700i	$0.521593\pi$
$24$	−1.70711	−	0.707107i	−0.348462	−	0.144338i
$25$		0			0
$26$	−0.585786	+	0.585786i	−0.114882	+	0.114882i
$27$	1.82843	−	4.41421i	0.351881	−	0.849516i
$28$	1.41421	+	0.585786i	0.267261	+	0.110703i
$29$	1.41421	−	0.585786i	0.262613	−	0.108778i	−0.247492	−	0.968890i	$-0.579606\pi$
$29$	1.41421	−	0.585786i	0.262613	−	0.108778i	0.510105	+	0.860112i	$0.329606\pi$
$30$		0			0
$31$	−1.41421	−	3.41421i	−0.254000	−	0.613211i	0.744520	−	0.667601i	$-0.232679\pi$
$31$	−1.41421	−	3.41421i	−0.254000	−	0.613211i	−0.998520	+	0.0543898i	$0.982679\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$			8.24264i			1.43486i
$34$	4.00000	−	1.00000i	0.685994	−	0.171499i
$35$		0			0
$36$	−0.292893	−	0.292893i	−0.0488155	−	0.0488155i
$37$	−2.00000	+	0.828427i	−0.328798	+	0.136193i	−0.540975	−	0.841039i	$-0.681945\pi$
$37$	−2.00000	+	0.828427i	−0.328798	+	0.136193i	0.212177	+	0.977231i	$0.431945\pi$
$38$	0.828427			0.134389
$39$	−1.41421	+	0.585786i	−0.226455	+	0.0938009i
$40$		0			0
$41$	10.3640	+	4.29289i	1.61858	+	0.670437i	0.993884	−	0.110432i	$-0.0352233\pi$
$41$	10.3640	+	4.29289i	1.61858	+	0.670437i	0.624695	+	0.780869i	$0.285223\pi$
$42$	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
$47$	9.65685			1.40860			0.704298	−	0.709904i	$-0.251262\pi$
$47$	9.65685			1.40860			0.704298	+	0.709904i	$0.251262\pi$
$48$	1.70711	−	0.707107i	0.246400	−	0.102062i
$49$	3.29289	+	3.29289i	0.470413	+	0.470413i
$50$		0			0
$51$	7.53553	+	1.12132i	1.05519	+	0.157016i
$52$		−	0.828427i		−	0.114882i
$53$	0.585786	−	0.585786i	0.0804640	−	0.0804640i	−0.665729	−	0.746193i	$-0.731879\pi$
$53$	0.585786	−	0.585786i	0.0804640	−	0.0804640i	0.746193	+	0.665729i	$0.231879\pi$
$54$	1.82843	+	4.41421i	0.248817	+	0.600698i
$55$		0			0
$56$	−1.41421	+	0.585786i	−0.188982	+	0.0782790i
$57$	1.41421	+	0.585786i	0.187317	+	0.0775893i
$58$	−0.585786	+	1.41421i	−0.0769175	+	0.185695i
$59$	−0.414214	+	0.414214i	−0.0539260	+	0.0539260i	−0.733556	−	0.679630i	$-0.762141\pi$
$59$	−0.414214	+	0.414214i	−0.0539260	+	0.0539260i	0.679630	+	0.733556i	$0.262141\pi$
$60$		0			0
$61$	6.82843	+	2.82843i	0.874291	+	0.362143i	0.774280	−	0.632843i	$-0.218112\pi$
$61$	6.82843	+	2.82843i	0.874291	+	0.362143i	0.100011	+	0.994986i	$0.468112\pi$
$62$	3.41421	+	1.41421i	0.433606	+	0.179605i
$63$	0.242641	+	0.585786i	0.0305699	+	0.0738022i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−5.82843	−	5.82843i	−0.717430	−	0.717430i
$67$		−	7.41421i		−	0.905790i	−0.891564	−	0.452895i	$-0.850391\pi$
$67$		−	7.41421i		−	0.905790i	0.891564	−	0.452895i	$-0.149609\pi$
$68$	−2.12132	+	3.53553i	−0.257248	+	0.428746i
$69$	−5.65685			−0.681005
$70$		0			0
$71$	0.828427	+	2.00000i	0.0983162	+	0.237356i	0.965383	−	0.260835i	$-0.0839978\pi$
$71$	0.828427	+	2.00000i	0.0983162	+	0.237356i	−0.867067	+	0.498191i	$0.833998\pi$
$72$	0.414214			0.0488155
$73$	2.05025	+	4.94975i	0.239964	+	0.579324i	0.997279	−	0.0737261i	$-0.0234891\pi$
$73$	2.05025	+	4.94975i	0.239964	+	0.579324i	−0.757315	+	0.653050i	$0.773489\pi$
$74$	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
$78$	0.585786	−	1.41421i	0.0663273	−	0.160128i
$79$	2.00000	−	4.82843i	0.225018	−	0.543240i	−0.770540	−	0.637391i	$-0.780014\pi$
$79$	2.00000	−	4.82843i	0.225018	−	0.543240i	0.995558	+	0.0941507i	$0.0300136\pi$
$80$		0			0
$81$			10.0711i			1.11901i
$82$	−10.3640	+	4.29289i	−1.14451	+	0.474071i
$83$	4.41421	−	4.41421i	0.484523	−	0.484523i	−0.422050	−	0.906573i	$-0.638689\pi$
$83$	4.41421	−	4.41421i	0.484523	−	0.484523i	0.906573	+	0.422050i	$0.138689\pi$
$84$	−2.82843			−0.308607
$85$		0			0
$86$	−1.75736			−0.189501
$87$	−2.00000	+	2.00000i	−0.214423	+	0.214423i
$88$	4.12132	−	1.70711i	0.439334	−	0.181978i
$89$			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
$92$	1.17157	−	2.82843i	0.122145	−	0.294884i
$93$	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
$97$	−2.12132	−	5.12132i	−0.215387	−	0.519991i	0.778848	−	0.627213i	$-0.215804\pi$
$97$	−2.12132	−	5.12132i	−0.215387	−	0.519991i	−0.994235	+	0.107222i	$0.965804\pi$
$98$	−4.65685			−0.470413
$99$	−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	$0.430673\pi$
$102$	−6.12132	+	4.53553i	−0.606101	+	0.449085i
$103$		−	12.4853i		−	1.23021i	−0.788445	−	0.615106i	$-0.789113\pi$
$103$		−	12.4853i		−	1.23021i	0.788445	−	0.615106i	$-0.210887\pi$
$104$	0.585786	+	0.585786i	0.0574411	+	0.0574411i
$105$		0			0
$106$			0.828427i			0.0804640i
$107$	4.46447	+	10.7782i	0.431596	+	1.04197i	0.978773	+	0.204948i	$0.0657026\pi$
$107$	4.46447	+	10.7782i	0.431596	+	1.04197i	−0.547177	+	0.837017i	$0.684297\pi$
$108$	−4.41421	−	1.82843i	−0.424758	−	0.175940i
$109$	9.07107	+	3.75736i	0.868851	+	0.359890i	0.772163	−	0.635425i	$-0.219175\pi$
$109$	9.07107	+	3.75736i	0.868851	+	0.359890i	0.0966881	+	0.995315i	$0.469175\pi$
$110$		0			0
$111$	2.82843	−	2.82843i	0.268462	−	0.268462i
$112$	0.585786	−	1.41421i	0.0553516	−	0.133631i
$113$	8.53553	+	3.53553i	0.802955	+	0.332595i	0.746140	−	0.665790i	$-0.231905\pi$
$113$	8.53553	+	3.53553i	0.802955	+	0.332595i	0.0568160	+	0.998385i	$0.481905\pi$
$114$	−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
$118$		−	0.585786i		−	0.0539260i
$119$	5.07107	−	3.75736i	0.464864	−	0.344437i
$120$		0			0
$121$	−6.29289	−	6.29289i	−0.572081	−	0.572081i
$122$	−6.82843	+	2.82843i	−0.618217	+	0.256074i
$123$	−20.7279			−1.86897
$124$	−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	0.171363	−	0.985208i	$-0.445183\pi$
$127$	−9.17157	−	9.17157i	−0.813845	−	0.813845i	−0.985208	+	0.171363i	$0.945183\pi$
$128$	−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	−0.377377	−	0.926060i	$-0.623174\pi$
$131$	0.121320	−	0.0502525i	0.0105998	−	0.00439058i	0.387977	+	0.921669i	$0.373174\pi$
$132$	8.24264			0.717430
$133$	1.17157	−	0.485281i	0.101588	−	0.0420792i
$134$	5.24264	+	5.24264i	0.452895	+	0.452895i
$135$		0			0
$136$	−1.00000	−	4.00000i	−0.0857493	−	0.342997i
$137$		−	2.34315i		−	0.200188i	−0.994978	−	0.100094i	$-0.968086\pi$
$137$		−	2.34315i		−	0.200188i	0.994978	−	0.100094i	$-0.0319144\pi$
$138$	4.00000	−	4.00000i	0.340503	−	0.340503i
$139$	0.707107	+	1.70711i	0.0599760	+	0.144795i	0.951027	−	0.309109i	$-0.100031\pi$
$139$	0.707107	+	1.70711i	0.0599760	+	0.144795i	−0.891051	+	0.453904i	$0.850031\pi$
$140$		0			0
$141$	−16.4853	+	6.82843i	−1.38831	+	0.575057i
$142$	−2.00000	−	0.828427i	−0.167836	−	0.0695201i
$143$	1.41421	−	3.41421i	0.118262	−	0.285511i
$144$	−0.292893	+	0.292893i	−0.0244078	+	0.0244078i
$145$		0			0
$146$	−4.94975	−	2.05025i	−0.409644	−	0.169680i
$147$	−7.94975	−	3.29289i	−0.655684	−	0.271593i
$148$	0.828427	+	2.00000i	0.0680963	+	0.164399i
$149$		−	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	−0.943897	−	0.330240i	$-0.892870\pi$
$151$	−15.6569	−	15.6569i	−1.27414	−	1.27414i	−0.330240	−	0.943897i	$-0.607130\pi$
$152$		−	0.828427i		−	0.0671943i
$153$	−1.65685	+	0.414214i	−0.133949	+	0.0334872i
$154$	−6.82843			−0.550250
$155$		0			0
$156$	0.585786	+	1.41421i	0.0469005	+	0.113228i
$157$	−13.3137			−1.06255			−0.531275	−	0.847200i	$-0.678287\pi$
$157$	−13.3137			−1.06255			−0.531275	+	0.847200i	$0.678287\pi$
$158$	2.00000	+	4.82843i	0.159111	+	0.384129i
$159$	−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
$163$	8.70711	−	21.0208i	0.681993	−	1.64648i	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	8.70711	−	21.0208i	0.681993	−	1.64648i	0.760319	−	0.649550i	$-0.225042\pi$
$164$	4.29289	−	10.3640i	0.335219	−	0.809289i
$165$		0			0
$166$			6.24264i			0.484523i
$167$	18.2426	−	7.55635i	1.41166	−	0.584728i	0.458908	−	0.888484i	$-0.348241\pi$
$167$	18.2426	−	7.55635i	1.41166	−	0.584728i	0.952750	+	0.303756i	$0.0982407\pi$
$168$	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
$173$	−5.41421	+	2.24264i	−0.411635	+	0.170505i	−0.578884	−	0.815410i	$-0.696512\pi$
$173$	−5.41421	+	2.24264i	−0.411635	+	0.170505i	0.167249	+	0.985915i	$0.446512\pi$
$174$		−	2.82843i		−	0.214423i
$175$		0			0
$176$	−1.70711	+	4.12132i	−0.128678	+	0.310656i
$177$	0.414214	−	1.00000i	0.0311342	−	0.0751646i
$178$	−10.6569	−	10.6569i	−0.798765	−	0.798765i
$179$	18.2426	−	18.2426i	1.36352	−	1.36352i	0.494132	−	0.869387i	$-0.335486\pi$
$179$	18.2426	−	18.2426i	1.36352	−	1.36352i	0.869387	−	0.494132i	$-0.164514\pi$
$180$		0			0
$181$	2.34315	−	5.65685i	0.174165	−	0.420471i	−0.812559	−	0.582879i	$-0.801926\pi$
$181$	2.34315	−	5.65685i	0.174165	−	0.420471i	0.986724	+	0.162408i	$0.0519262\pi$
$182$	−0.485281	−	1.17157i	−0.0359714	−	0.0868428i
$183$	−13.6569			−1.00954
$184$	1.17157	+	2.82843i	0.0863695	+	0.208514i
$185$		0			0
$186$	−6.82843			−0.500685
$187$	−14.7782	+	10.9497i	−1.08069	+	0.800725i
$188$		−	9.65685i		−	0.704298i
$189$	5.17157	+	5.17157i	0.376177	+	0.376177i
$190$		0			0
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	−0.707107	−	1.70711i	−0.0510310	−	0.123200i
$193$	−11.3640	−	4.70711i	−0.817996	−	0.338825i	−0.0658565	−	0.997829i	$-0.520978\pi$
$193$	−11.3640	−	4.70711i	−0.817996	−	0.338825i	−0.752139	+	0.659004i	$0.770978\pi$
$194$	5.12132	+	2.12132i	0.367689	+	0.152302i
$195$		0			0
$196$	3.29289	−	3.29289i	0.235207	−	0.235207i
$197$	7.65685	−	18.4853i	0.545528	−	1.31702i	−0.375246	−	0.926925i	$-0.622442\pi$
$197$	7.65685	−	18.4853i	0.545528	−	1.31702i	0.920774	−	0.390096i	$-0.127558\pi$
$198$	1.70711	+	0.707107i	0.121319	+	0.0502519i
$199$	19.3137	−	8.00000i	1.36911	−	0.567105i	0.427565	−	0.903985i	$-0.359372\pi$
$199$	19.3137	−	8.00000i	1.36911	−	0.567105i	0.941548	+	0.336880i	$0.109372\pi$
$200$		0			0
$201$	5.24264	+	12.6569i	0.369787	+	0.892746i
$202$	−3.07107	+	3.07107i	−0.216080	+	0.216080i
$203$			2.34315i			0.164457i
$204$	1.12132	−	7.53553i	0.0785081	−	0.527593i
$205$		0			0
$206$	8.82843	+	8.82843i	0.615106	+	0.615106i
$207$	1.17157	−	0.485281i	0.0814299	−	0.0337294i
$208$	−0.828427			−0.0574411
$209$	−3.41421	+	1.41421i	−0.236166	+	0.0978232i
$210$		0			0
$211$	−0.121320	−	0.0502525i	−0.00835204	−	0.00345953i	0.378504	−	0.925600i	$-0.376439\pi$
$211$	−0.121320	−	0.0502525i	−0.00835204	−	0.00345953i	−0.386856	+	0.922140i	$0.626439\pi$
$212$	−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
$217$	5.65685			0.384012
$218$	−9.07107	+	3.75736i	−0.614370	+	0.254480i
$219$	−7.00000	−	7.00000i	−0.473016	−	0.473016i
$220$		0			0
$221$	−2.92893	−	1.75736i	−0.197021	−	0.118213i
$222$			4.00000i			0.268462i
$223$	−17.3137	+	17.3137i	−1.15941	+	1.15941i	−0.174809	+	0.984602i	$0.555931\pi$
$223$	−17.3137	+	17.3137i	−1.15941	+	1.15941i	−0.984602	+	0.174809i	$0.944069\pi$
$224$	0.585786	+	1.41421i	0.0391395	+	0.0944911i
$225$		0			0
$226$	−8.53553	+	3.53553i	−0.567775	+	0.235180i
$227$	18.7782	+	7.77817i	1.24635	+	0.516256i	0.905694	−	0.423932i	$-0.139350\pi$
$227$	18.7782	+	7.77817i	1.24635	+	0.516256i	0.340657	+	0.940188i	$0.389350\pi$
$228$	0.585786	−	1.41421i	0.0387947	−	0.0936586i
$229$	−13.0711	+	13.0711i	−0.863760	+	0.863760i	−0.991773	−	0.128012i	$-0.959140\pi$
$229$	−13.0711	+	13.0711i	−0.863760	+	0.863760i	0.128012	+	0.991773i	$0.459140\pi$
$230$		0			0
$231$	−11.6569	−	4.82843i	−0.766965	−	0.317687i
$232$	1.41421	+	0.585786i	0.0928477	+	0.0384588i
$233$	−4.02082	−	9.70711i	−0.263412	−	0.635934i	0.735733	−	0.677272i	$-0.236838\pi$
$233$	−4.02082	−	9.70711i	−0.263412	−	0.635934i	−0.999145	+	0.0413382i	$0.986838\pi$
$234$			0.343146i			0.0224321i
$235$		0			0
$236$	0.414214	+	0.414214i	0.0269630	+	0.0269630i
$237$			9.65685i			0.627280i
$238$	−0.928932	+	6.24264i	−0.0602137	+	0.404650i
$239$	−21.1716			−1.36948			−0.684738	−	0.728790i	$-0.740083\pi$
$239$	−21.1716			−1.36948			−0.684738	+	0.728790i	$0.740083\pi$
$240$		0			0
$241$	7.60660	+	18.3640i	0.489984	+	1.18293i	0.954728	+	0.297481i	$0.0961466\pi$
$241$	7.60660	+	18.3640i	0.489984	+	1.18293i	−0.464743	+	0.885445i	$0.653853\pi$
$242$	8.89949			0.572081
$243$	−1.63604	−	3.94975i	−0.104952	−	0.253376i
$244$	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
$248$	1.41421	−	3.41421i	0.0898027	−	0.216803i
$249$	−4.41421	+	10.6569i	−0.279739	+	0.675351i
$250$		0			0
$251$			18.7279i			1.18210i	0.806636	+	0.591048i	$0.201286\pi$
$251$			18.7279i			1.18210i	−0.806636	+	0.591048i	$0.798714\pi$
$252$	0.585786	−	0.242641i	0.0369011	−	0.0152849i
$253$	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	$0.332761\pi$
$258$	3.00000	−	1.24264i	0.186772	−	0.0773634i
$259$		−	3.31371i		−	0.205904i
$260$		0			0
$261$	0.242641	−	0.585786i	0.0150191	−	0.0362593i
$262$	−0.0502525	+	0.121320i	−0.00310461	+	0.00749520i
$263$	−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
$267$	−10.6569	−	25.7279i	−0.652189	−	1.57452i
$268$	−7.41421			−0.452895
$269$	−2.92893	−	7.07107i	−0.178580	−	0.431131i	0.809089	−	0.587686i	$-0.199961\pi$
$269$	−2.92893	−	7.07107i	−0.178580	−	0.431131i	−0.987669	+	0.156555i	$0.949961\pi$
$270$		0			0
$271$	−14.8284			−0.900763			−0.450381	−	0.892836i	$-0.648712\pi$
$271$	−14.8284			−0.900763			−0.450381	+	0.892836i	$0.648712\pi$
$272$	3.53553	+	2.12132i	0.214373	+	0.128624i
$273$		−	2.34315i		−	0.141814i
$274$	1.65685	+	1.65685i	0.100094	+	0.100094i
$275$		0			0
$276$			5.65685i			0.340503i
$277$	9.07107	+	21.8995i	0.545028	+	1.31581i	0.921137	+	0.389238i	$0.127262\pi$
$277$	9.07107	+	21.8995i	0.545028	+	1.31581i	−0.376110	+	0.926575i	$0.622738\pi$
$278$	−1.70711	−	0.707107i	−0.102385	−	0.0424094i
$279$	−1.41421	−	0.585786i	−0.0846668	−	0.0350701i
$280$		0			0
$281$	10.1421	−	10.1421i	0.605029	−	0.605029i	−0.336614	−	0.941643i	$-0.609282\pi$
$281$	10.1421	−	10.1421i	0.605029	−	0.605029i	0.941643	+	0.336614i	$0.109282\pi$
$282$	6.82843	−	16.4853i	0.406627	−	0.981684i
$283$	−1.05025	−	0.435029i	−0.0624310	−	0.0258598i	0.351249	−	0.936282i	$-0.385757\pi$
$283$	−1.05025	−	0.435029i	−0.0624310	−	0.0258598i	−0.413680	+	0.910422i	$0.635757\pi$
$284$	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
$288$		−	0.414214i		−	0.0244078i
$289$	8.00000	+	15.0000i	0.470588	+	0.882353i
$290$		0			0
$291$	7.24264	+	7.24264i	0.424571	+	0.424571i
$292$	4.94975	−	2.05025i	0.289662	−	0.119982i
$293$	22.0000			1.28525			0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000			1.28525			0.642627	+	0.766179i	$0.277845\pi$
$294$	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
$302$	22.1421			1.27414
$303$	−7.41421	+	3.07107i	−0.425935	+	0.176428i
$304$	0.585786	+	0.585786i	0.0335972	+	0.0335972i
$305$		0			0
$306$	0.878680	−	1.46447i	0.0502308	−	0.0837180i
$307$			6.34315i			0.362022i	0.983481	+	0.181011i	$0.0579370\pi$
$307$			6.34315i			0.362022i	−0.983481	+	0.181011i	$0.942063\pi$
$308$	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	−0.740207	−	0.672379i	$-0.765272\pi$
$311$	−13.8995	+	5.75736i	−0.788168	+	0.326470i	−0.0479613	+	0.998849i	$0.515272\pi$
$312$	−1.41421	−	0.585786i	−0.0800641	−	0.0331636i
$313$	5.19239	−	12.5355i	0.293491	−	0.708550i	−0.706509	−	0.707705i	$-0.749731\pi$
$313$	5.19239	−	12.5355i	0.293491	−	0.708550i	1.00000		0.000845724i	$-0.000269202\pi$
$314$	9.41421	−	9.41421i	0.531275	−	0.531275i
$315$		0			0
$316$	−4.82843	−	2.00000i	−0.271620	−	0.112509i
$317$	20.4853	+	8.48528i	1.15057	+	0.476581i	0.874724	−	0.484622i	$-0.161043\pi$
$317$	20.4853	+	8.48528i	1.15057	+	0.476581i	0.275844	+	0.961202i	$0.411043\pi$
$318$	−0.585786	−	1.41421i	−0.0328493	−	0.0793052i
$319$		−	6.82843i		−	0.382319i
$320$		0			0
$321$	−15.2426	−	15.2426i	−0.850761	−	0.850761i
$322$		−	4.68629i		−	0.261157i
$323$	0.828427	+	3.31371i	0.0460949	+	0.184380i
$324$	10.0711			0.559504
$325$		0			0
$326$	8.70711	+	21.0208i	0.482242	+	1.16424i
$327$	−18.1421			−1.00326
$328$	4.29289	+	10.3640i	0.237035	+	0.572254i
$329$	−5.65685	+	13.6569i	−0.311872	+	0.752927i
$330$		0			0
$331$	19.5858	−	19.5858i	1.07653	−	1.07653i	0.0797144	−	0.996818i	$-0.474599\pi$
$331$	19.5858	−	19.5858i	1.07653	−	1.07653i	0.996818	−	0.0797144i	$-0.0254008\pi$
$332$	−4.41421	−	4.41421i	−0.242261	−	0.242261i
$333$	−0.343146	+	0.828427i	−0.0188043	+	0.0453975i
$334$	−7.55635	+	18.2426i	−0.413465	+	0.998193i
$335$		0			0
$336$			2.82843i			0.154303i
$337$	−10.7782	+	4.46447i	−0.587125	+	0.243195i	−0.656413	−	0.754402i	$-0.727927\pi$
$337$	−10.7782	+	4.46447i	−0.587125	+	0.243195i	0.0692885	+	0.997597i	$0.477927\pi$
$338$	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
$343$	−16.4853	+	6.82843i	−0.890122	+	0.368700i
$344$			1.75736i			0.0947505i
$345$		0			0
$346$	2.24264	−	5.41421i	0.120565	−	0.291070i
$347$	6.19239	−	14.9497i	0.332425	−	0.802544i	−0.665974	−	0.745975i	$-0.731984\pi$
$347$	6.19239	−	14.9497i	0.332425	−	0.802544i	0.998399	−	0.0565694i	$-0.0180162\pi$
$348$	2.00000	+	2.00000i	0.107211	+	0.107211i
$349$	13.8995	−	13.8995i	0.744023	−	0.744023i	−0.229327	−	0.973350i	$-0.573652\pi$
$349$	13.8995	−	13.8995i	0.744023	−	0.744023i	0.973350	+	0.229327i	$0.0736524\pi$
$350$		0			0
$351$	1.51472	−	3.65685i	0.0808497	−	0.195188i
$352$	−1.70711	−	4.12132i	−0.0909891	−	0.219667i
$353$	14.3848			0.765624			0.382812	−	0.923826i	$-0.374956\pi$
$353$	14.3848			0.765624			0.382812	+	0.923826i	$0.374956\pi$
$354$	0.414214	+	1.00000i	0.0220152	+	0.0531494i
$355$		0			0
$356$	15.0711			0.798765
$357$	−6.00000	+	10.0000i	−0.317554	+	0.529256i
$358$			25.7990i			1.36352i
$359$	−8.00000	−	8.00000i	−0.422224	−	0.422224i	0.463745	−	0.885969i	$-0.346505\pi$
$359$	−8.00000	−	8.00000i	−0.422224	−	0.422224i	−0.885969	+	0.463745i	$0.846505\pi$
$360$		0			0
$361$		−	18.3137i		−	0.963879i
$362$	2.34315	+	5.65685i	0.123153	+	0.297318i
$363$	15.1924	+	6.29289i	0.797394	+	0.330291i
$364$	1.17157	+	0.485281i	0.0614071	+	0.0254357i
$365$		0			0
$366$	9.65685	−	9.65685i	0.504772	−	0.504772i
$367$	−7.17157	+	17.3137i	−0.374353	+	0.903768i	0.618649	+	0.785668i	$0.287680\pi$
$367$	−7.17157	+	17.3137i	−0.374353	+	0.903768i	−0.993002	+	0.118100i	$0.962320\pi$
$368$	−2.82843	−	1.17157i	−0.147442	−	0.0610725i
$369$	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
$373$			10.4853i			0.542907i	0.962452	+	0.271454i	$0.0875044\pi$
$373$			10.4853i			0.542907i	−0.962452	+	0.271454i	$0.912496\pi$
$374$	2.70711	−	18.1924i	0.139981	−	0.940706i
$375$		0			0
$376$	6.82843	+	6.82843i	0.352149	+	0.352149i
$377$	1.17157	−	0.485281i	0.0603391	−	0.0249933i
$378$	−7.31371			−0.376177
$379$	−8.60660	+	3.56497i	−0.442091	+	0.183120i	−0.592614	−	0.805486i	$-0.701904\pi$
$379$	−8.60660	+	3.56497i	−0.442091	+	0.183120i	0.150523	+	0.988606i	$0.451904\pi$
$380$		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
$387$	0.727922			0.0370024
$388$	−5.12132	+	2.12132i	−0.259996	+	0.107694i
$389$	−2.24264	−	2.24264i	−0.113706	−	0.113706i	0.647964	−	0.761671i	$-0.275621\pi$
$389$	−2.24264	−	2.24264i	−0.113706	−	0.113706i	−0.761671	+	0.647964i	$0.775621\pi$
$390$		0			0
$391$	−7.51472	−	10.1421i	−0.380036	−	0.512910i
$392$			4.65685i			0.235207i
$393$	−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
$397$	7.65685	+	3.17157i	0.384286	+	0.159177i	0.566459	−	0.824090i	$-0.308313\pi$
$397$	7.65685	+	3.17157i	0.384286	+	0.159177i	−0.182173	+	0.983267i	$0.558313\pi$
$398$	−8.00000	+	19.3137i	−0.401004	+	0.968109i
$399$	−1.65685	+	1.65685i	−0.0829465	+	0.0829465i
$400$		0			0
$401$	−22.1924	−	9.19239i	−1.10823	−	0.459046i	−0.247905	−	0.968784i	$-0.579742\pi$
$401$	−22.1924	−	9.19239i	−1.10823	−	0.459046i	−0.860330	+	0.509738i	$0.829742\pi$
$402$	−12.6569	−	5.24264i	−0.631267	−	0.261479i
$403$	−1.17157	−	2.82843i	−0.0583602	−	0.140894i
$404$		−	4.34315i		−	0.216080i
$405$		0			0
$406$	−1.65685	−	1.65685i	−0.0822283	−	0.0822283i
$407$			9.65685i			0.478672i
$408$	4.53553	+	6.12132i	0.224542	+	0.303051i
$409$	−15.5563			−0.769212			−0.384606	−	0.923081i	$-0.625663\pi$
$409$	−15.5563			−0.769212			−0.384606	+	0.923081i	$0.625663\pi$
$410$		0			0
$411$	1.65685	+	4.00000i	0.0817266	+	0.197305i
$412$	−12.4853			−0.615106
$413$	−0.343146	−	0.828427i	−0.0168851	−	0.0407642i
$414$	−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
$418$	1.41421	−	3.41421i	0.0691714	−	0.166995i
$419$	6.60660	−	15.9497i	0.322754	−	0.779196i	−0.676338	−	0.736591i	$-0.736434\pi$
$419$	6.60660	−	15.9497i	0.322754	−	0.779196i	0.999092	−	0.0426051i	$-0.0135657\pi$
$420$		0			0
$421$			15.6569i			0.763068i	0.924355	+	0.381534i	$0.124604\pi$
$421$			15.6569i			0.763068i	−0.924355	+	0.381534i	$0.875396\pi$
$422$	0.121320	−	0.0502525i	0.00590578	−	0.00244625i
$423$	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
$428$	10.7782	−	4.46447i	0.520983	−	0.215798i
$429$			6.82843i			0.329680i
$430$		0			0
$431$	−5.51472	+	13.3137i	−0.265635	+	0.641299i	−0.999268	−	0.0382464i	$-0.987823\pi$
$431$	−5.51472	+	13.3137i	−0.265635	+	0.641299i	0.733634	+	0.679545i	$0.237823\pi$
$432$	−1.82843	+	4.41421i	−0.0879702	+	0.212379i
$433$	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
$437$	−0.970563	−	2.34315i	−0.0464283	−	0.112088i
$438$	9.89949			0.473016
$439$	8.82843	+	21.3137i	0.421358	+	1.01725i	0.981947	+	0.189154i	$0.0605745\pi$
$439$	8.82843	+	21.3137i	0.421358	+	1.01725i	−0.560590	+	0.828094i	$0.689425\pi$
$440$		0			0
$441$	1.92893			0.0918539
$442$	3.31371	−	0.828427i	0.157617	−	0.0394043i
$443$			36.8701i			1.75175i	0.482539	+	0.875875i	$0.339715\pi$
$443$			36.8701i			1.75175i	−0.482539	+	0.875875i	$0.660285\pi$
$444$	−2.82843	−	2.82843i	−0.134231	−	0.134231i
$445$		0			0
$446$		−	24.4853i		−	1.15941i
$447$	11.0711	+	26.7279i	0.523644	+	1.26419i
$448$	−1.41421	−	0.585786i	−0.0668153	−	0.0276758i
$449$	−5.12132	−	2.12132i	−0.241690	−	0.100111i	0.258551	−	0.965998i	$-0.416755\pi$
$449$	−5.12132	−	2.12132i	−0.241690	−	0.100111i	−0.500241	+	0.865886i	$0.666755\pi$
$450$		0			0
$451$	35.3848	−	35.3848i	1.66620	−	1.66620i
$452$	3.53553	−	8.53553i	0.166298	−	0.401478i
$453$	37.7990	+	15.6569i	1.77595	+	0.735623i
$454$	−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	$0.287089\pi$
$458$		−	18.4853i		−	0.863760i
$459$	−15.8284	+	11.7279i	−0.738808	+	0.547413i
$460$		0			0
$461$	−24.7279	−	24.7279i	−1.15169	−	1.15169i	−0.986213	−	0.165481i	$-0.947082\pi$
$461$	−24.7279	−	24.7279i	−1.15169	−	1.15169i	−0.165481	−	0.986213i	$-0.552918\pi$
$462$	11.6569	−	4.82843i	0.542326	−	0.224639i
$463$	−3.31371			−0.154001			−0.0770005	−	0.997031i	$-0.524534\pi$
$463$	−3.31371			−0.154001			−0.0770005	+	0.997031i	$0.524534\pi$
$464$	−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	0.665276	−	0.746597i	$-0.268314\pi$
$467$	−1.75736	−	1.75736i	−0.0813209	−	0.0813209i	−0.746597	+	0.665276i	$0.768314\pi$
$468$	−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
$472$	−0.585786			−0.0269630
$473$	7.24264	−	3.00000i	0.333017	−	0.137940i
$474$	−6.82843	−	6.82843i	−0.313640	−	0.313640i
$475$		0			0
$476$	−3.75736	−	5.07107i	−0.172218	−	0.232432i
$477$		−	0.343146i		−	0.0157116i
$478$	14.9706	−	14.9706i	0.684738	−	0.684738i
$479$	−9.51472	−	22.9706i	−0.434739	−	1.04955i	−0.977740	−	0.209820i	$-0.932712\pi$
$479$	−9.51472	−	22.9706i	−0.434739	−	1.04955i	0.543001	−	0.839732i	$-0.317288\pi$
$480$		0			0
$481$	−1.65685	+	0.686292i	−0.0755461	+	0.0312922i
$482$	−18.3640	−	7.60660i	−0.836456	−	0.346471i
$483$	3.31371	−	8.00000i	0.150779	−	0.364013i
$484$	−6.29289	+	6.29289i	−0.286041	+	0.286041i
$485$		0			0
$486$	3.94975	+	1.63604i	0.179164	+	0.0742122i
$487$	20.4853	+	8.48528i	0.928277	+	0.384505i	0.795024	−	0.606577i	$-0.207458\pi$
$487$	20.4853	+	8.48528i	0.928277	+	0.384505i	0.133252	+	0.991082i	$0.457458\pi$
$488$	2.82843	+	6.82843i	0.128037	+	0.309108i
$489$			42.0416i			1.90119i
$490$		0			0
$491$	10.9289	+	10.9289i	0.493216	+	0.493216i	0.909318	−	0.416102i	$-0.136604\pi$
$491$	10.9289	+	10.9289i	0.493216	+	0.493216i	−0.416102	+	0.909318i	$0.636604\pi$
$492$			20.7279i			0.934487i
$493$	−6.24264	−	0.928932i	−0.281154	−	0.0418370i
$494$	0.686292			0.0308777
$495$		0			0
$496$	1.41421	+	3.41421i	0.0635001	+	0.153303i
$497$	−3.31371			−0.148640
$498$	−4.41421	−	10.6569i	−0.197806	−	0.477545i
$499$	14.0919	−	34.0208i	0.630839	−	1.52298i	−0.207730	−	0.978186i	$-0.566608\pi$
$499$	14.0919	−	34.0208i	0.630839	−	1.52298i	0.838569	−	0.544795i	$-0.183392\pi$
$500$		0			0
$501$	−25.7990	+	25.7990i	−1.15261	+	1.15261i
$502$	−13.2426	−	13.2426i	−0.591048	−	0.591048i
$503$	4.62742	−	11.1716i	0.206326	−	0.498116i	−0.786513	−	0.617574i	$-0.788116\pi$
$503$	4.62742	−	11.1716i	0.206326	−	0.498116i	0.992839	+	0.119458i	$0.0381157\pi$
$504$	−0.242641	+	0.585786i	−0.0108081	+	0.0260930i
$505$		0			0
$506$			13.6569i			0.607121i
$507$	21.0208	−	8.70711i	0.933567	−	0.386696i
$508$	−9.17157	+	9.17157i	−0.406923	+	0.406923i
$509$	−16.6274			−0.736997			−0.368499	−	0.929628i	$-0.620128\pi$
$509$	−16.6274			−0.736997			−0.368499	+	0.929628i	$0.620128\pi$
$510$		0			0
$511$	−8.20101			−0.362791
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.65685	+	1.51472i	−0.161454	+	0.0668765i
$514$		−	8.24264i		−	0.363567i
$515$		0			0
$516$	−1.24264	+	3.00000i	−0.0547042	+	0.132068i
$517$	16.4853	−	39.7990i	0.725022	−	1.75036i
$518$	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	−0.293720	−	0.955892i	$-0.594893\pi$
$521$	13.4645	−	32.5061i	0.589889	−	1.42412i	0.883609	−	0.468226i	$-0.155107\pi$
$522$	0.242641	+	0.585786i	0.0106201	+	0.0256392i
$523$	−23.2132			−1.01504			−0.507521	−	0.861639i	$-0.669438\pi$
$523$	−23.2132			−1.01504			−0.507521	+	0.861639i	$0.669438\pi$
$524$	−0.0502525	−	0.121320i	−0.00219529	−	0.00529990i
$525$		0			0
$526$	8.00000			0.348817
$527$	−2.24264	+	15.0711i	−0.0976910	+	0.656506i
$528$		−	8.24264i		−	0.358715i
$529$	−9.63604	−	9.63604i	−0.418958	−	0.418958i
$530$		0			0
$531$			0.242641i			0.0105297i
$532$	−0.485281	−	1.17157i	−0.0210396	−	0.0507941i
$533$	8.58579	+	3.55635i	0.371892	+	0.154043i
$534$	25.7279	+	10.6569i	1.11336	+	0.461167i
$535$		0			0
$536$	5.24264	−	5.24264i	0.226448	−	0.226448i
$537$	−18.2426	+	44.0416i	−0.787228	+	1.90054i
$538$	7.07107	+	2.92893i	0.304855	+	0.126275i
$539$	19.1924	−	7.94975i	0.826675	−	0.342420i
$540$		0			0
$541$	7.79899	+	18.8284i	0.335305	+	0.809497i	0.998153	+	0.0607439i	$0.0193473\pi$
$541$	7.79899	+	18.8284i	0.335305	+	0.809497i	−0.662849	+	0.748753i	$0.730653\pi$
$542$	10.4853	−	10.4853i	0.450381	−	0.450381i
$543$			11.3137i			0.485518i
$544$	−4.00000	+	1.00000i	−0.171499	+	0.0428746i
$545$		0			0
$546$	1.65685	+	1.65685i	0.0709068	+	0.0709068i
$547$	22.6777	−	9.39340i	0.969627	−	0.401633i	0.159054	−	0.987270i	$-0.449156\pi$
$547$	22.6777	−	9.39340i	0.969627	−	0.401633i	0.810573	+	0.585637i	$0.199156\pi$
$548$	−2.34315			−0.100094
$549$	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
$557$	41.1127			1.74200			0.871000	−	0.491282i	$-0.163472\pi$
$557$	41.1127			1.74200			0.871000	+	0.491282i	$0.163472\pi$
$558$	1.41421	−	0.585786i	0.0598684	−	0.0247983i
$559$	1.02944	+	1.02944i	0.0435406	+	0.0435406i
$560$		0			0
$561$	17.4853	−	29.1421i	0.738229	−	1.23038i
$562$			14.3431i			0.605029i
$563$	−5.92893	+	5.92893i	−0.249875	+	0.249875i	−0.820919	−	0.571044i	$-0.806538\pi$
$563$	−5.92893	+	5.92893i	−0.249875	+	0.249875i	0.571044	+	0.820919i	$0.306538\pi$
$564$	6.82843	+	16.4853i	0.287529	+	0.694156i
$565$		0			0
$566$	1.05025	−	0.435029i	0.0441454	−	0.0182856i
$567$	−14.2426	−	5.89949i	−0.598135	−	0.247755i
$568$	−0.828427	+	2.00000i	−0.0347600	+	0.0839181i
$569$	−3.48528	+	3.48528i	−0.146111	+	0.146111i	−0.776378	−	0.630267i	$-0.782945\pi$
$569$	−3.48528	+	3.48528i	−0.146111	+	0.146111i	0.630267	+	0.776378i	$0.282945\pi$
$570$		0			0
$571$	2.22183	+	0.920310i	0.0929805	+	0.0385138i	0.428689	−	0.903452i	$-0.358976\pi$
$571$	2.22183	+	0.920310i	0.0929805	+	0.0385138i	−0.335708	+	0.941966i	$0.608976\pi$
$572$	−3.41421	−	1.41421i	−0.142755	−	0.0591312i
$573$	−2.00000	−	4.82843i	−0.0835512	−	0.201710i
$574$		−	17.1716i		−	0.716728i
$575$		0			0
$576$	0.292893	+	0.292893i	0.0122039	+	0.0122039i
$577$		−	16.6274i		−	0.692208i	−0.938196	−	0.346104i	$-0.887504\pi$
$577$		−	16.6274i		−	0.692208i	0.938196	−	0.346104i	$-0.112496\pi$
$578$	−16.2635	−	4.94975i	−0.676471	−	0.205882i
$579$	22.7279			0.944540
$580$		0			0
$581$	3.65685	+	8.82843i	0.151712	+	0.366265i
$582$	−10.2426			−0.424571
$583$	−1.41421	−	3.41421i	−0.0585707	−	0.141402i
$584$	−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	0.661516	−	0.749931i	$-0.269913\pi$
$587$	−2.14214	−	2.14214i	−0.0884154	−	0.0884154i	−0.749931	+	0.661516i	$0.769913\pi$
$588$	−3.29289	+	7.94975i	−0.135797	+	0.327842i
$589$	−1.17157	+	2.82843i	−0.0482738	+	0.116543i
$590$		0			0
$591$			36.9706i			1.52077i
$592$	2.00000	−	0.828427i	0.0821995	−	0.0340481i
$593$	−3.00000	+	3.00000i	−0.123195	+	0.123195i	−0.766016	−	0.642821i	$-0.777764\pi$
$593$	−3.00000	+	3.00000i	−0.123195	+	0.123195i	0.642821	+	0.766016i	$0.277764\pi$
$594$	21.3137			0.874512
$595$		0			0
$596$	−15.6569			−0.641330
$597$	−27.3137	+	27.3137i	−1.11788	+	1.11788i
$598$	−2.34315	+	0.970563i	−0.0958184	+	0.0396893i
$599$		−	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	−0.999972	−	0.00749419i	$-0.997615\pi$
$601$	−7.05025	+	17.0208i	−0.287586	+	0.694294i	0.712386	+	0.701788i	$0.247615\pi$
$602$	1.02944	−	2.48528i	0.0419567	−	0.101293i
$603$	−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
$607$	3.75736	+	9.07107i	0.152507	+	0.368183i	0.981606	−	0.190918i	$-0.0611464\pi$
$607$	3.75736	+	9.07107i	0.152507	+	0.368183i	−0.829100	+	0.559101i	$0.811146\pi$
$608$	−0.828427			−0.0335972
$609$	−1.65685	−	4.00000i	−0.0671391	−	0.162088i
$610$		0			0
$611$	8.00000			0.323645
$612$	0.414214	+	1.65685i	0.0167436	+	0.0669744i
$613$		−	37.7990i		−	1.52669i	−0.645993	−	0.763343i	$-0.723556\pi$
$613$		−	37.7990i		−	1.52669i	0.645993	−	0.763343i	$-0.276444\pi$
$614$	−4.48528	−	4.48528i	−0.181011	−	0.181011i
$615$		0			0
$616$			6.82843i			0.275125i
$617$	−6.92031	−	16.7071i	−0.278601	−	0.672603i	0.721196	−	0.692731i	$-0.243593\pi$
$617$	−6.92031	−	16.7071i	−0.278601	−	0.672603i	−0.999797	+	0.0201281i	$0.993593\pi$
$618$	−21.3137	−	8.82843i	−0.857363	−	0.355131i
$619$	−5.12132	−	2.12132i	−0.205843	−	0.0852631i	0.277380	−	0.960760i	$-0.410534\pi$
$619$	−5.12132	−	2.12132i	−0.205843	−	0.0852631i	−0.483223	+	0.875497i	$0.660534\pi$
$620$		0			0
$621$	10.3431	−	10.3431i	0.415056	−	0.415056i
$622$	5.75736	−	13.8995i	0.230849	−	0.557319i
$623$	−21.3137	−	8.82843i	−0.853916	−	0.353703i
$624$	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
$628$			13.3137i			0.531275i
$629$	8.82843	+	1.31371i	0.352012	+	0.0523810i
$630$		0			0
$631$	−21.6569	−	21.6569i	−0.862146	−	0.862146i	0.129441	−	0.991587i	$-0.458682\pi$
$631$	−21.6569	−	21.6569i	−0.862146	−	0.862146i	−0.991587	+	0.129441i	$0.958682\pi$
$632$	4.82843	−	2.00000i	0.192065	−	0.0795557i
$633$	0.242641			0.00964410
$634$	−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	−0.631889	−	0.775059i	$-0.717720\pi$
$641$	−13.4350	+	5.56497i	−0.530652	+	0.219803i	0.101237	+	0.994862i	$0.467720\pi$
$642$	21.5563			0.850761
$643$	−12.3640	+	5.12132i	−0.487587	+	0.201965i	−0.612913	−	0.790150i	$-0.710002\pi$
$643$	−12.3640	+	5.12132i	−0.487587	+	0.201965i	0.125326	+	0.992116i	$0.460002\pi$
$644$	3.31371	+	3.31371i	0.130578	+	0.130578i
$645$		0			0
$646$	−2.92893	−	1.75736i	−0.115237	−	0.0691424i
$647$			12.4853i			0.490847i	0.969416	+	0.245424i	$0.0789270\pi$
$647$			12.4853i			0.490847i	−0.969416	+	0.245424i	$0.921073\pi$
$648$	−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
$652$	−21.0208	−	8.70711i	−0.823239	−	0.340997i
$653$	−9.89949	+	23.8995i	−0.387397	+	0.935260i	0.603092	+	0.797671i	$0.293935\pi$
$653$	−9.89949	+	23.8995i	−0.387397	+	0.935260i	−0.990490	+	0.137588i	$0.956065\pi$
$654$	12.8284	−	12.8284i	0.501631	−	0.501631i
$655$		0			0
$656$	−10.3640	−	4.29289i	−0.404645	−	0.167609i
$657$	2.05025	+	0.849242i	0.0799880	+	0.0331321i
$658$	−5.65685	−	13.6569i	−0.220527	−	0.532400i
$659$			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	0.909896	−	0.414837i	$-0.136161\pi$
$661$	12.7279	+	12.7279i	0.495059	+	0.495059i	−0.414837	+	0.909896i	$0.636161\pi$
$662$			27.6985i			1.07653i
$663$	6.24264	+	0.928932i	0.242444	+	0.0360767i
$664$	6.24264			0.242261
$665$		0			0
$666$	−0.343146	−	0.828427i	−0.0132966	−	0.0321009i
$667$	4.68629			0.181454
$668$	−7.55635	−	18.2426i	−0.292364	−	0.705829i
$669$	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
$673$	0.393398	−	0.949747i	0.0151644	−	0.0366101i	−0.916116	−	0.400913i	$-0.868693\pi$
$673$	0.393398	−	0.949747i	0.0151644	−	0.0366101i	0.931280	+	0.364303i	$0.118693\pi$
$674$	4.46447	−	10.7782i	0.171965	−	0.415160i
$675$		0			0
$676$			12.3137i			0.473604i
$677$	10.8284	−	4.48528i	0.416170	−	0.172383i	−0.164766	−	0.986333i	$-0.552687\pi$
$677$	10.8284	−	4.48528i	0.416170	−	0.172383i	0.580936	+	0.813949i	$0.302687\pi$
$678$	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
$683$	−10.0208	+	4.15076i	−0.383436	+	0.158824i	−0.566071	−	0.824356i	$-0.691537\pi$
$683$	−10.0208	+	4.15076i	−0.383436	+	0.158824i	0.182635	+	0.983181i	$0.441537\pi$
$684$			0.343146i			0.0131205i
$685$		0			0
$686$	6.82843	−	16.4853i	0.260711	−	0.629411i
$687$	13.0711	−	31.5563i	0.498692	−	1.20395i
$688$	−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	0.0712988	+	0.997455i	$0.477286\pi$
$691$	−17.9914	+	43.4350i	−0.684424	+	1.65235i	−0.755723	+	0.654891i	$0.772714\pi$
$692$	2.24264	+	5.41421i	0.0852524	+	0.205818i
$693$	2.82843			0.107443
$694$	6.19239	+	14.9497i	0.235060	+	0.567485i
$695$		0			0
$696$	−2.82843			−0.107211
$697$	−27.5355	−	37.1630i	−1.04298	−	1.40765i
$698$			19.6569i			0.744023i
$699$	13.7279	+	13.7279i	0.519238	+	0.519238i
$700$		0			0
$701$		−	1.51472i		−	0.0572101i	−0.999591	−	0.0286051i	$-0.990893\pi$
$701$		−	1.51472i		−	0.0572101i	0.999591	−	0.0286051i	$-0.00910652\pi$
$702$	1.51472	+	3.65685i	0.0571694	+	0.138019i
$703$	1.65685	+	0.686292i	0.0624894	+	0.0258840i
$704$	4.12132	+	1.70711i	0.155328	+	0.0643390i
$705$		0			0
$706$	−10.1716	+	10.1716i	−0.382812	+	0.382812i
$707$	−2.54416	+	6.14214i	−0.0956828	+	0.230999i
$708$	−1.00000	−	0.414214i	−0.0375823	−	0.0155671i
$709$	5.75736	−	2.38478i	0.216222	−	0.0895622i	−0.271943	−	0.962313i	$-0.587666\pi$
$709$	5.75736	−	2.38478i	0.216222	−	0.0895622i	0.488165	+	0.872751i	$0.337666\pi$
$710$		0			0
$711$	−0.828427	−	2.00000i	−0.0310684	−	0.0750059i
$712$	−10.6569	+	10.6569i	−0.399382	+	0.399382i
$713$		−	11.3137i		−	0.423702i
$714$	−2.82843	−	11.3137i	−0.105851	−	0.423405i
$715$		0			0
$716$	−18.2426	−	18.2426i	−0.681759	−	0.681759i
$717$	36.1421	−	14.9706i	1.34975	−	0.559086i
$718$	11.3137			0.422224
$719$	−4.00000	+	1.65685i	−0.149175	+	0.0617902i	−0.456022	−	0.889969i	$-0.650726\pi$
$719$	−4.00000	+	1.65685i	−0.149175	+	0.0617902i	0.306847	+	0.951759i	$0.400726\pi$
$720$		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
$727$	−32.2843			−1.19736			−0.598679	−	0.800989i	$-0.704307\pi$
$727$	−32.2843			−1.19736			−0.598679	+	0.800989i	$0.704307\pi$
$728$	−1.17157	+	0.485281i	−0.0434214	+	0.0179857i
$729$	−15.7782	−	15.7782i	−0.584377	−	0.584377i
$730$		0			0
$731$	−1.75736	−	7.02944i	−0.0649983	−	0.259993i
$732$			13.6569i			0.504772i
$733$	−9.89949	+	9.89949i	−0.365646	+	0.365646i	−0.865887	−	0.500240i	$-0.833245\pi$
$733$	−9.89949	+	9.89949i	−0.365646	+	0.365646i	0.500240	+	0.865887i	$0.333245\pi$
$734$	−7.17157	−	17.3137i	−0.264708	−	0.639061i
$735$		0			0
$736$	2.82843	−	1.17157i	0.104257	−	0.0431847i
$737$	−30.5563	−	12.6569i	−1.12556	−	0.466221i
$738$	−1.77817	+	4.29289i	−0.0654555	+	0.158024i
$739$	0.485281	−	0.485281i	0.0178514	−	0.0178514i	−0.698125	−	0.715976i	$-0.745982\pi$
$739$	0.485281	−	0.485281i	0.0178514	−	0.0178514i	0.715976	+	0.698125i	$0.245982\pi$
$740$		0			0
$741$	1.17157	+	0.485281i	0.0430388	+	0.0178273i
$742$	−1.17157	−	0.485281i	−0.0430098	−	0.0178152i
$743$	−9.89949	−	23.8995i	−0.363177	−	0.876787i	−0.994832	−	0.101537i	$-0.967624\pi$
$743$	−9.89949	−	23.8995i	−0.363177	−	0.876787i	0.631654	−	0.775250i	$-0.282376\pi$
$744$			6.82843i			0.250342i
$745$		0			0
$746$	−7.41421	−	7.41421i	−0.271454	−	0.271454i
$747$		−	2.58579i		−	0.0946090i
$748$	10.9497	+	14.7782i	0.400362	+	0.540344i
$749$	−17.8579			−0.652512
$750$		0			0
$751$	9.51472	+	22.9706i	0.347197	+	0.838208i	0.996949	+	0.0780611i	$0.0248729\pi$
$751$	9.51472	+	22.9706i	0.347197	+	0.838208i	−0.649752	+	0.760147i	$0.725127\pi$
$752$	−9.65685			−0.352149
$753$	−13.2426	−	31.9706i	−0.482589	−	1.16507i
$754$	−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	0.551939	−	0.833885i	$-0.313888\pi$
$757$	−7.75736	−	7.75736i	−0.281946	−	0.281946i	−0.833885	+	0.551939i	$0.813888\pi$
$758$	3.56497	−	8.60660i	0.129486	−	0.312606i
$759$	−9.65685	+	23.3137i	−0.350522	+	0.846234i
$760$		0			0
$761$			53.2548i			1.93049i	0.261354	+	0.965243i	$0.415831\pi$
$761$			53.2548i			1.93049i	−0.261354	+	0.965243i	$0.584169\pi$
$762$	−22.1421	+	9.17157i	−0.802125	+	0.332251i
$763$	−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
$768$	−1.70711	+	0.707107i	−0.0615999	+	0.0255155i
$769$		−	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
$772$	−4.70711	+	11.3640i	−0.169412	+	0.408998i
$773$	−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
$777$	2.34315	+	5.65685i	0.0840599	+	0.202939i
$778$	3.17157			0.113706
$779$	−3.55635	−	8.58579i	−0.127419	−	0.307618i
$780$		0			0
$781$	9.65685			0.345549
$782$	12.4853	+	1.85786i	0.446473	+	0.0664371i
$783$		−	7.31371i		−	0.261371i
$784$	−3.29289	−	3.29289i	−0.117603	−	0.117603i
$785$		0			0
$786$		−	0.242641i		−	0.00865471i
$787$	−7.29289	−	17.6066i	−0.259964	−	0.627608i	0.738972	−	0.673736i	$-0.235312\pi$
$787$	−7.29289	−	17.6066i	−0.259964	−	0.627608i	−0.998936	+	0.0461286i	$0.985312\pi$
$788$	−18.4853	−	7.65685i	−0.658511	−	0.272764i
$789$	13.6569	+	5.65685i	0.486197	+	0.201389i
$790$		0			0
$791$	−10.0000	+	10.0000i	−0.355559	+	0.355559i
$792$	0.707107	−	1.70711i	0.0251259	−	0.0606594i
$793$	5.65685	+	2.34315i	0.200881	+	0.0832075i
$794$	−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	$0.406698\pi$
$798$		−	2.34315i		−	0.0829465i
$799$	−34.1421	−	20.4853i	−1.20786	−	0.724717i
$800$		0			0
$801$	4.41421	+	4.41421i	0.155969	+	0.155969i
$802$	22.1924	−	9.19239i	0.783640	−	0.324595i
$803$	23.8995			0.843395
$804$	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	$-0.0682601\pi$
$809$	43.1630	+	17.8787i	1.51753	+	0.628581i	0.540434	+	0.841386i	$0.318260\pi$
$810$		0			0
$811$	45.5061	−	18.8492i	1.59794	−	0.661886i	0.606813	−	0.794844i	$-0.292447\pi$
$811$	45.5061	−	18.8492i	1.59794	−	0.661886i	0.991122	+	0.132958i	$0.0424475\pi$
$812$	2.34315			0.0822283
$813$	25.3137	−	10.4853i	0.887791	−	0.367735i
$814$	−6.82843	−	6.82843i	−0.239336	−	0.239336i
$815$		0			0
$816$	−7.53553	−	1.12132i	−0.263796	−	0.0392541i
$817$		−	1.45584i		−	0.0509335i
$818$	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	−0.388663	−	0.921380i	$-0.627063\pi$
$821$	−0.343146	+	0.142136i	−0.0119759	+	0.00496057i	0.376687	+	0.926340i	$0.377063\pi$
$822$	−4.00000	−	1.65685i	−0.139516	−	0.0577894i
$823$	16.6863	−	40.2843i	0.581648	−	1.40422i	−0.309671	−	0.950844i	$-0.600219\pi$
$823$	16.6863	−	40.2843i	0.581648	−	1.40422i	0.891319	−	0.453378i	$-0.149781\pi$
$824$	8.82843	−	8.82843i	0.307553	−	0.307553i
$825$		0			0
$826$	0.828427	+	0.343146i	0.0288247	+	0.0119396i
$827$	−22.0919	−	9.15076i	−0.768210	−	0.318203i	−0.0360629	−	0.999350i	$-0.511482\pi$
$827$	−22.0919	−	9.15076i	−0.768210	−	0.318203i	−0.732147	+	0.681147i	$0.761482\pi$
$828$	−0.485281	−	1.17157i	−0.0168647	−	0.0407150i
$829$			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
$832$			0.828427i			0.0287205i
$833$	−4.65685	−	18.6274i	−0.161350	−	0.645402i
$834$	3.41421			0.118225
$835$		0			0
$836$	1.41421	+	3.41421i	0.0489116	+	0.118083i
$837$	−17.6569			−0.610310
$838$	6.60660	+	15.9497i	0.228221	+	0.550975i
$839$	−18.5269	+	44.7279i	−0.639620	+	1.54418i	0.187566	+	0.982252i	$0.439940\pi$
$839$	−18.5269	+	44.7279i	−0.639620	+	1.54418i	−0.827187	+	0.561927i	$0.810060\pi$
$840$		0			0
$841$	−18.8492	+	18.8492i	−0.649974	+	0.649974i
$842$	−11.0711	−	11.0711i	−0.381534	−	0.381534i
$843$	−10.1421	+	24.4853i	−0.349314	+	0.843318i
$844$	−0.0502525	+	0.121320i	−0.00172976	+	0.00417602i
$845$		0			0
$846$			4.00000i			0.137523i
$847$	12.5858	−	5.21320i	0.432453	−	0.179128i
$848$	−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
$853$	−35.0711	+	14.5269i	−1.20081	+	0.497392i	−0.891261	−	0.453491i	$-0.850178\pi$
$853$	−35.0711	+	14.5269i	−1.20081	+	0.497392i	−0.309550	+	0.950883i	$0.600178\pi$
$854$		−	11.3137i		−	0.387147i
$855$		0			0
$856$	−4.46447	+	10.7782i	−0.152592	+	0.368390i
$857$	15.4056	−	37.1924i	0.526245	−	1.27047i	−0.407721	−	0.913106i	$-0.633676\pi$
$857$	15.4056	−	37.1924i	0.526245	−	1.27047i	0.933966	−	0.357361i	$-0.116324\pi$
$858$	−4.82843	−	4.82843i	−0.164840	−	0.164840i
$859$	−0.556349	+	0.556349i	−0.0189824	+	0.0189824i	−0.716534	−	0.697552i	$-0.754273\pi$
$859$	−0.556349	+	0.556349i	−0.0189824	+	0.0189824i	0.697552	+	0.716534i	$0.254273\pi$
$860$		0			0
$861$	12.1421	−	29.3137i	0.413803	−	0.999009i
$862$	−5.51472	−	13.3137i	−0.187832	−	0.453467i
$863$	−0.970563			−0.0330383			−0.0165192	−	0.999864i	$-0.505258\pi$
$863$	−0.970563			−0.0330383			−0.0165192	+	0.999864i	$0.505258\pi$
$864$	−1.82843	−	4.41421i	−0.0622044	−	0.150175i
$865$		0			0
$866$	−12.9706			−0.440758
$867$	−24.2635	−	19.9497i	−0.824030	−	0.677529i
$868$		−	5.65685i		−	0.192006i
$869$	−16.4853	−	16.4853i	−0.559225	−	0.559225i
$870$		0			0
$871$		−	6.14214i		−	0.208118i
$872$	3.75736	+	9.07107i	0.127240	+	0.307185i
$873$	−2.12132	−	0.878680i	−0.0717958	−	0.0297388i
$874$	2.34315	+	0.970563i	0.0792581	+	0.0328298i
$875$		0			0
$876$	−7.00000	+	7.00000i	−0.236508	+	0.236508i
$877$	−4.10051	+	9.89949i	−0.138464	+	0.334282i	−0.977867	−	0.209228i	$-0.932905\pi$
$877$	−4.10051	+	9.89949i	−0.138464	+	0.334282i	0.839403	+	0.543510i	$0.182905\pi$
$878$	−21.3137	−	8.82843i	−0.719303	−	0.297945i
$879$	−37.5563	+	15.5563i	−1.26674	+	0.524703i
$880$		0			0
$881$	−6.92031	−	16.7071i	−0.233151	−	0.562877i	0.763394	−	0.645934i	$-0.223532\pi$
$881$	−6.92031	−	16.7071i	−0.233151	−	0.562877i	−0.996545	+	0.0830568i	$0.973532\pi$
$882$	−1.36396	+	1.36396i	−0.0459270	+	0.0459270i
$883$		−	34.5269i		−	1.16192i	−0.813931	−	0.580962i	$-0.802677\pi$
$883$		−	34.5269i		−	1.16192i	0.813931	−	0.580962i	$-0.197323\pi$
$884$	−1.75736	+	2.92893i	−0.0591064	+	0.0985106i
$885$		0			0
$886$	−26.0711	−	26.0711i	−0.875875	−	0.875875i
$887$	2.34315	−	0.970563i	0.0786751	−	0.0325883i	−0.342999	−	0.939336i	$-0.611443\pi$
$887$	2.34315	−	0.970563i	0.0786751	−	0.0325883i	0.421674	+	0.906748i	$0.361443\pi$
$888$	4.00000			0.134231
$889$	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
$897$	−4.68629			−0.156471
$898$	5.12132	−	2.12132i	0.170901	−	0.0707894i
$899$	−4.00000	−	4.00000i	−0.133407	−	0.133407i
$900$		0			0
$901$	−3.31371	+	0.828427i	−0.110396	+	0.0275989i
$902$			50.0416i			1.66620i
$903$	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
$907$	13.5355	+	5.60660i	0.449440	+	0.186164i	0.595910	−	0.803051i	$-0.296791\pi$
$907$	13.5355	+	5.60660i	0.449440	+	0.186164i	−0.146470	+	0.989215i	$0.546791\pi$
$908$	7.77817	−	18.7782i	0.258128	−	0.623176i
$909$	1.27208	−	1.27208i	0.0421922	−	0.0421922i
$910$		0			0
$911$	−21.5563	−	8.92893i	−0.714194	−	0.295829i	−0.00415500	−	0.999991i	$-0.501323\pi$
$911$	−21.5563	−	8.92893i	−0.714194	−	0.295829i	−0.710039	+	0.704163i	$0.751323\pi$
$912$	−1.41421	−	0.585786i	−0.0468293	−	0.0193973i
$913$	−10.6569	−	25.7279i	−0.352690	−	0.851470i
$914$		−	4.97056i		−	0.164412i
$915$		0			0
$916$	13.0711	+	13.0711i	0.431880	+	0.431880i
$917$			0.201010i			0.00663794i
$918$	2.89949	−	19.4853i	0.0956976	−	0.643110i
$919$	2.34315			0.0772932			0.0386466	−	0.999253i	$-0.487695\pi$
$919$	2.34315			0.0772932			0.0386466	+	0.999253i	$0.487695\pi$
$920$		0			0
$921$	−4.48528	−	10.8284i	−0.147795	−	0.356809i
$922$	34.9706			1.15169
$923$	0.686292	+	1.65685i	0.0225896	+	0.0545360i
$924$	−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
$928$	0.585786	−	1.41421i	0.0192294	−	0.0464238i
$929$	3.53553	−	8.53553i	0.115997	−	0.280042i	−0.855209	−	0.518284i	$-0.826571\pi$
$929$	3.53553	−	8.53553i	0.115997	−	0.280042i	0.971206	+	0.238242i	$0.0765711\pi$
$930$		0			0
$931$		−	3.85786i		−	0.126436i
$932$	−9.70711	+	4.02082i	−0.317967	+	0.131706i
$933$	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	$0.222337\pi$
$938$	−10.4853	+	4.34315i	−0.342357	+	0.141809i
$939$			25.0711i			0.818163i
$940$		0			0
$941$	7.51472	−	18.1421i	0.244973	−	0.591417i	−0.752791	−	0.658260i	$-0.771293\pi$
$941$	7.51472	−	18.1421i	0.244973	−	0.591417i	0.997763	+	0.0668433i	$0.0212928\pi$
$942$	−9.41421	+	22.7279i	−0.306732	+	0.740516i
$943$	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
$947$	−20.0208	−	48.3345i	−0.650589	−	1.57066i	−0.811925	−	0.583761i	$-0.801580\pi$
$947$	−20.0208	−	48.3345i	−0.650589	−	1.57066i	0.161336	−	0.986900i	$-0.448420\pi$
$948$	9.65685			0.313640
$949$	1.69848	+	4.10051i	0.0551352	+	0.133108i
$950$		0			0
$951$	−40.9706			−1.32856
$952$	6.24264	+	0.928932i	0.202325	+	0.0301069i
$953$			11.5563i			0.374347i	0.982327	+	0.187173i	$0.0599326\pi$
$953$			11.5563i			0.374347i	−0.982327	+	0.187173i	$0.940067\pi$
$954$	0.242641	+	0.242641i	0.00785578	+	0.00785578i
$955$		0			0
$956$			21.1716i			0.684738i
$957$	4.82843	+	11.6569i	0.156081	+	0.376813i
$958$	22.9706	+	9.51472i	0.742145	+	0.307407i
$959$	3.31371	+	1.37258i	0.107005	+	0.0443230i
$960$		0			0
$961$	12.2635	−	12.2635i	0.395595	−	0.395595i
$962$	0.686292	−	1.65685i	0.0221269	−	0.0534191i
$963$	4.46447	+	1.84924i	0.143865	+	0.0595910i
$964$	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	$0.320471\pi$
$968$		−	8.89949i		−	0.286041i
$969$	−3.75736	−	5.07107i	−0.120704	−	0.162906i
$970$		0			0
$971$	15.0416	+	15.0416i	0.482709	+	0.482709i	0.905996	−	0.423287i	$-0.139124\pi$
$971$	15.0416	+	15.0416i	0.482709	+	0.482709i	−0.423287	+	0.905996i	$0.639124\pi$
$972$	−3.94975	+	1.63604i	−0.126688	+	0.0524760i
$973$	−2.82843			−0.0906752
$974$	−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	0.951405	−	0.307943i	$-0.0996405\pi$
$977$	20.1127	+	20.1127i	0.643462	+	0.643462i	−0.307943	+	0.951405i	$0.599641\pi$
$978$	−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
$982$	−15.4558			−0.493216
$983$	24.9706	−	10.3431i	0.796437	−	0.329895i	0.0529088	−	0.998599i	$-0.483151\pi$
$983$	24.9706	−	10.3431i	0.796437	−	0.329895i	0.743529	+	0.668704i	$0.233151\pi$
$984$	−14.6569	−	14.6569i	−0.467243	−	0.467243i
$985$		0			0
$986$	5.07107	−	3.75736i	0.161496	−	0.119659i
$987$		−	27.3137i		−	0.869405i
$988$	−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	−0.934392	−	0.356245i	$-0.884057\pi$
$991$	−42.2843	+	17.5147i	−1.34320	+	0.556373i	−0.408812	+	0.912619i	$0.634057\pi$
$992$	−3.41421	−	1.41421i	−0.108401	−	0.0449013i
$993$	−19.5858	+	47.2843i	−0.621536	+	1.50052i
$994$	2.34315	−	2.34315i	0.0743201	−	0.0743201i
$995$		0			0
$996$	10.6569	+	4.41421i	0.337675	+	0.139870i
$997$	−10.9706	−	4.54416i	−0.347441	−	0.143915i	0.202137	−	0.979357i	$-0.435211\pi$
$997$	−10.9706	−	4.54416i	−0.347441	−	0.143915i	−0.549578	+	0.835442i	$0.685211\pi$
$998$	14.0919	+	34.0208i	0.446071	+	1.07691i
$999$			10.3431i			0.327243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.o.a.49.1		4
5.2	odd	4		850.2.l.a.151.1		4
5.3	odd	4		34.2.d.a.15.1	✓	4
5.4	even	2		850.2.o.b.49.1		4
15.8	even	4		306.2.l.c.253.1		4
17.8	even	8		850.2.o.b.399.1		4
20.3	even	4		272.2.v.b.49.1		4
85.3	even	16		578.2.b.d.577.1		4
85.8	odd	8		34.2.d.a.25.1	yes	4
85.13	odd	4		578.2.d.c.155.1		4
85.23	even	16		578.2.c.f.251.1		8
85.28	even	16		578.2.c.f.251.4		8
85.33	odd	4		578.2.d.b.423.1		4
85.38	odd	4		578.2.d.a.155.1		4
85.42	odd	8		850.2.l.a.501.1		4
85.43	odd	8		578.2.d.b.399.1		4
85.48	even	16		578.2.b.d.577.4		4
85.53	odd	8		578.2.d.a.179.1		4
85.58	even	16		578.2.c.f.327.1		8
85.59	even	8	inner	850.2.o.a.399.1		4
85.63	even	16		578.2.a.i.1.1		4
85.73	even	16		578.2.a.i.1.4		4
85.78	even	16		578.2.c.f.327.4		8
85.83	odd	8		578.2.d.c.179.1		4
255.8	even	8		306.2.l.c.127.1		4
255.158	odd	16		5202.2.a.bw.1.1		4
255.233	odd	16		5202.2.a.bw.1.4		4
340.63	odd	16		4624.2.a.bn.1.4		4
340.243	odd	16		4624.2.a.bn.1.1		4
340.263	even	8		272.2.v.b.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.d.a.15.1	✓	4	5.3	odd	4
34.2.d.a.25.1	yes	4	85.8	odd	8
272.2.v.b.49.1		4	20.3	even	4
272.2.v.b.161.1		4	340.263	even	8
306.2.l.c.127.1		4	255.8	even	8
306.2.l.c.253.1		4	15.8	even	4
578.2.a.i.1.1		4	85.63	even	16
578.2.a.i.1.4		4	85.73	even	16
578.2.b.d.577.1		4	85.3	even	16
578.2.b.d.577.4		4	85.48	even	16
578.2.c.f.251.1		8	85.23	even	16
578.2.c.f.251.4		8	85.28	even	16
578.2.c.f.327.1		8	85.58	even	16
578.2.c.f.327.4		8	85.78	even	16
578.2.d.a.155.1		4	85.38	odd	4
578.2.d.a.179.1		4	85.53	odd	8
578.2.d.b.399.1		4	85.43	odd	8
578.2.d.b.423.1		4	85.33	odd	4
578.2.d.c.155.1		4	85.13	odd	4
578.2.d.c.179.1		4	85.83	odd	8
850.2.l.a.151.1		4	5.2	odd	4
850.2.l.a.501.1		4	85.42	odd	8
850.2.o.a.49.1		4	1.1	even	1	trivial
850.2.o.a.399.1		4	85.59	even	8	inner
850.2.o.b.49.1		4	5.4	even	2
850.2.o.b.399.1		4	17.8	even	8
4624.2.a.bn.1.1		4	340.243	odd	16
4624.2.a.bn.1.4		4	340.63	odd	16
5202.2.a.bw.1.1		4	255.158	odd	16
5202.2.a.bw.1.4		4	255.233	odd	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.o (of order \(8\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more