LMFDB - Embedded newform 925.2.y.a.193.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.10
Character	$\chi$	$=$	925.193
Dual form			925.2.y.a.532.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.926614 - 0.534981i) q^{2} +(-0.561303 - 2.09481i) q^{3} +(-0.427591 + 0.740609i) q^{4} +(-1.64079 - 1.64079i) q^{6} +(0.642189 + 2.39668i) q^{7} +3.05494i q^{8} +(-1.47509 + 0.851645i) q^{9} -5.02991i q^{11} +(1.79144 + 0.480016i) q^{12} +(-3.98890 - 2.30299i) q^{13} +(1.87724 + 1.87724i) q^{14} +(0.779151 + 1.34953i) q^{16} +(-2.61653 - 4.53196i) q^{17} +(-0.911227 + 1.57829i) q^{18} +(-1.96405 - 7.32995i) q^{19} +(4.66013 - 2.69053i) q^{21} +(-2.69090 - 4.66078i) q^{22} +3.90190i q^{23} +(6.39951 - 1.71474i) q^{24} -4.92823 q^{26} +(-1.98852 - 1.98852i) q^{27} +(-2.04960 - 0.549188i) q^{28} +(-2.46568 - 2.46568i) q^{29} +(6.59621 - 6.59621i) q^{31} +(-3.84736 - 2.22127i) q^{32} +(-10.5367 + 2.82330i) q^{33} +(-4.84903 - 2.79959i) q^{34} -1.45662i q^{36} +(4.23183 + 4.36939i) q^{37} +(-5.74130 - 5.74130i) q^{38} +(-2.58535 + 9.64866i) q^{39} +(2.12301 + 1.22572i) q^{41} +(2.87876 - 4.98616i) q^{42} +2.84795i q^{43} +(3.72519 + 2.15074i) q^{44} +(2.08744 + 3.61556i) q^{46} +(3.77465 - 3.77465i) q^{47} +(2.38967 - 2.38967i) q^{48} +(0.730503 - 0.421756i) q^{49} +(-8.02493 + 8.02493i) q^{51} +(3.41123 - 1.96948i) q^{52} +(0.509586 - 1.90180i) q^{53} +(-2.90640 - 0.778769i) q^{54} +(-7.32171 + 1.96185i) q^{56} +(-14.2524 + 8.22864i) q^{57} +(-3.60383 - 0.965642i) q^{58} +(-12.3239 - 3.30218i) q^{59} +(3.14132 + 11.7236i) q^{61} +(2.58330 - 9.64099i) q^{62} +(-2.98841 - 2.98841i) q^{63} -7.86996 q^{64} +(-8.25304 + 8.25304i) q^{66} +(1.37987 - 0.369735i) q^{67} +4.47521 q^{68} +(8.17374 - 2.19015i) q^{69} +(0.476267 - 0.824919i) q^{71} +(-2.60172 - 4.50631i) q^{72} +(-5.74703 + 5.74703i) q^{73} +(6.25882 + 1.78479i) q^{74} +(6.26844 + 1.67962i) q^{76} +(12.0551 - 3.23015i) q^{77} +(2.76623 + 10.3237i) q^{78} +(2.65009 + 9.89027i) q^{79} +(-5.60434 + 9.70700i) q^{81} +2.62295 q^{82} +(0.433112 - 1.61639i) q^{83} +4.60178i q^{84} +(1.52360 + 2.63895i) q^{86} +(-3.78114 + 6.54913i) q^{87} +15.3660 q^{88} +(0.934359 - 3.48707i) q^{89} +(2.95791 - 11.0391i) q^{91} +(-2.88978 - 1.66842i) q^{92} +(-17.5203 - 10.1153i) q^{93} +(1.47828 - 5.51702i) q^{94} +(-2.49361 + 9.30629i) q^{96} -10.8774 q^{97} +(0.451263 - 0.781611i) q^{98} +(4.28369 + 7.41958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 36 q^{4} + 8 q^{14} - 72 q^{16} + 16 q^{19} - 36 q^{21} - 4 q^{24} + 8 q^{26} + 24 q^{31} + 60 q^{34} - 24 q^{41} + 24 q^{44} + 12 q^{49} + 84 q^{51} + 28 q^{54} + 104 q^{56} + 4 q^{59} - 24 q^{61}+ \cdots + 120 q^{99}+O(q^{100}) $ 56 * q + 36 * q^4 + 8 * q^14 - 72 * q^16 + 16 * q^19 - 36 * q^21 - 4 * q^24 + 8 * q^26 + 24 * q^31 + 60 * q^34 - 24 * q^41 + 24 * q^44 + 12 * q^49 + 84 * q^51 + 28 * q^54 + 104 * q^56 + 4 * q^59 - 24 * q^61 - 344 * q^64 - 124 * q^66 - 52 * q^69 - 72 * q^71 - 48 * q^74 + 40 * q^76 + 100 * q^79 + 44 * q^81 + 40 * q^86 + 32 * q^89 - 4 * q^91 - 140 * q^94 - 132 * q^96 + 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.926614	−	0.534981i	0.655215	−	0.378289i	−0.135236	−	0.990813i	$-0.543179\pi$
$2$	0.926614	−	0.534981i	0.655215	−	0.378289i	0.790451	+	0.612525i	$0.209846\pi$
$3$	−0.561303	−	2.09481i	−0.324068	−	1.20944i	−0.915245	−	0.402897i	$-0.868003\pi$
$3$	−0.561303	−	2.09481i	−0.324068	−	1.20944i	0.591177	−	0.806542i	$-0.298663\pi$
$4$	−0.427591	+	0.740609i	−0.213795	+	0.370304i
$5$		0			0
$5$		0			0
$6$	−1.64079	−	1.64079i	−0.669852	−	0.669852i
$7$	0.642189	+	2.39668i	0.242725	+	0.905860i	0.974513	+	0.224329i	$0.0720190\pi$
$7$	0.642189	+	2.39668i	0.242725	+	0.905860i	−0.731789	+	0.681531i	$0.761314\pi$
$8$			3.05494i			1.08008i
$9$	−1.47509	+	0.851645i	−0.491697	+	0.283882i
$10$		0			0
$11$		−	5.02991i		−	1.51657i	−0.651921	−	0.758287i	$-0.726037\pi$
$11$		−	5.02991i		−	1.51657i	0.651921	−	0.758287i	$-0.273963\pi$
$12$	1.79144	+	0.480016i	0.517145	+	0.138569i
$13$	−3.98890	−	2.30299i	−1.10632	−	0.638735i	−0.168447	−	0.985711i	$-0.553875\pi$
$13$	−3.98890	−	2.30299i	−1.10632	−	0.638735i	−0.937874	+	0.346976i	$0.887209\pi$
$14$	1.87724	+	1.87724i	0.501714	+	0.501714i
$15$		0			0
$16$	0.779151	+	1.34953i	0.194788	+	0.337382i
$17$	−2.61653	−	4.53196i	−0.634602	−	1.09916i	−0.986599	−	0.163161i	$-0.947831\pi$
$17$	−2.61653	−	4.53196i	−0.634602	−	1.09916i	0.351998	−	0.936001i	$-0.385502\pi$
$18$	−0.911227	+	1.57829i	−0.214778	+	0.372007i
$19$	−1.96405	−	7.32995i	−0.450585	−	1.68161i	−0.700754	−	0.713403i	$-0.747153\pi$
$19$	−1.96405	−	7.32995i	−0.450585	−	1.68161i	0.250169	−	0.968202i	$-0.419514\pi$
$20$		0			0
$21$	4.66013	−	2.69053i	1.01692	−	0.587121i
$22$	−2.69090	−	4.66078i	−0.573703	−	0.993682i
$23$			3.90190i			0.813602i	0.913517	+	0.406801i	$0.133356\pi$
$23$			3.90190i			0.813602i	−0.913517	+	0.406801i	$0.866644\pi$
$24$	6.39951	−	1.71474i	1.30629	−	0.350021i
$25$		0			0
$26$	−4.92823			−0.966505
$27$	−1.98852	−	1.98852i	−0.382690	−	0.382690i
$28$	−2.04960	−	0.549188i	−0.387338	−	0.103787i
$29$	−2.46568	−	2.46568i	−0.457865	−	0.457865i	0.440089	−	0.897954i	$-0.354947\pi$
$29$	−2.46568	−	2.46568i	−0.457865	−	0.457865i	−0.897954	+	0.440089i	$0.854947\pi$
$30$		0			0
$31$	6.59621	−	6.59621i	1.18471	−	1.18471i	0.206206	−	0.978509i	$-0.433888\pi$
$31$	6.59621	−	6.59621i	1.18471	−	1.18471i	0.978509	−	0.206206i	$-0.0661117\pi$
$32$	−3.84736	−	2.22127i	−0.680123	−	0.392669i
$33$	−10.5367	+	2.82330i	−1.83420	+	0.491473i
$34$	−4.84903	−	2.79959i	−0.831601	−	0.480125i
$35$		0			0
$36$		−	1.45662i		−	0.242770i
$37$	4.23183	+	4.36939i	0.695709	+	0.718323i
$37$	4.23183	+	4.36939i	0.695709	+	0.718323i
$38$	−5.74130	−	5.74130i	−0.931362	−	0.931362i
$39$	−2.58535	+	9.64866i	−0.413987	+	1.54502i
$40$		0			0
$41$	2.12301	+	1.22572i	0.331558	+	0.191425i	0.656533	−	0.754298i	$-0.272022\pi$
$41$	2.12301	+	1.22572i	0.331558	+	0.191425i	−0.324975	+	0.945723i	$0.605356\pi$
$42$	2.87876	−	4.98616i	0.444203	−	0.769381i
$43$			2.84795i			0.434308i	0.976137	+	0.217154i	$0.0696773\pi$
$43$			2.84795i			0.434308i	−0.976137	+	0.217154i	$0.930323\pi$
$44$	3.72519	+	2.15074i	0.561594	+	0.324237i
$45$		0			0
$46$	2.08744	+	3.61556i	0.307777	+	0.533085i
$47$	3.77465	−	3.77465i	0.550590	−	0.550590i	−0.376021	−	0.926611i	$-0.622708\pi$
$47$	3.77465	−	3.77465i	0.550590	−	0.550590i	0.926611	+	0.376021i	$0.122708\pi$
$48$	2.38967	−	2.38967i	0.344919	−	0.344919i
$49$	0.730503	−	0.421756i	0.104358	−	0.0602509i
$50$		0			0
$51$	−8.02493	+	8.02493i	−1.12372	+	1.12372i
$52$	3.41123	−	1.96948i	0.473053	−	0.273117i
$53$	0.509586	−	1.90180i	0.0699970	−	0.261233i	−0.922055	−	0.387058i	$-0.873491\pi$
$53$	0.509586	−	1.90180i	0.0699970	−	0.261233i	0.992052	+	0.125826i	$0.0401580\pi$
$54$	−2.90640	−	0.778769i	−0.395511	−	0.105977i
$55$		0			0
$56$	−7.32171	+	1.96185i	−0.978404	+	0.262163i
$57$	−14.2524	+	8.22864i	−1.88778	+	1.08991i
$58$	−3.60383	−	0.965642i	−0.473206	−	0.126795i
$59$	−12.3239	−	3.30218i	−1.60443	−	0.429907i	−0.658057	−	0.752968i	$-0.728621\pi$
$59$	−12.3239	−	3.30218i	−1.60443	−	0.429907i	−0.946378	+	0.323061i	$0.895288\pi$
$60$		0			0
$61$	3.14132	+	11.7236i	0.402205	+	1.50105i	0.809153	+	0.587597i	$0.199926\pi$
$61$	3.14132	+	11.7236i	0.402205	+	1.50105i	−0.406949	+	0.913451i	$0.633407\pi$
$62$	2.58330	−	9.64099i	0.328079	−	1.22441i
$63$	−2.98841	−	2.98841i	−0.376504	−	0.376504i
$64$	−7.86996			−0.983745
$65$		0			0
$66$	−8.25304	+	8.25304i	−1.01588	+	1.01588i
$67$	1.37987	−	0.369735i	0.168578	−	0.0451703i	−0.173543	−	0.984826i	$-0.555521\pi$
$67$	1.37987	−	0.369735i	0.168578	−	0.0451703i	0.342121	+	0.939656i	$0.388855\pi$
$68$	4.47521			0.542700
$69$	8.17374	−	2.19015i	0.984002	−	0.263663i
$70$		0			0
$71$	0.476267	−	0.824919i	0.0565225	−	0.0978999i	−0.836380	−	0.548151i	$-0.815332\pi$
$71$	0.476267	−	0.824919i	0.0565225	−	0.0978999i	0.892902	+	0.450251i	$0.148665\pi$
$72$	−2.60172	−	4.50631i	−0.306616	−	0.531074i
$73$	−5.74703	+	5.74703i	−0.672639	+	0.672639i	−0.958324	−	0.285685i	$-0.907779\pi$
$73$	−5.74703	+	5.74703i	−0.672639	+	0.672639i	0.285685	+	0.958324i	$0.407779\pi$
$74$	6.25882	+	1.78479i	0.727573	+	0.207478i
$75$		0			0
$76$	6.26844	+	1.67962i	0.719039	+	0.192666i
$77$	12.0551	−	3.23015i	1.37380	−	0.368110i
$78$	2.76623	+	10.3237i	0.313214	+	1.16893i
$79$	2.65009	+	9.89027i	0.298158	+	1.11274i	0.938676	+	0.344799i	$0.112053\pi$
$79$	2.65009	+	9.89027i	0.298158	+	1.11274i	−0.640518	+	0.767943i	$0.721280\pi$
$80$		0			0
$81$	−5.60434	+	9.70700i	−0.622704	+	1.07856i
$82$	2.62295			0.289656
$83$	0.433112	−	1.61639i	0.0475402	−	0.177422i	−0.938073	−	0.346436i	$-0.887392\pi$
$83$	0.433112	−	1.61639i	0.0475402	−	0.177422i	0.985614	+	0.169014i	$0.0540583\pi$
$84$			4.60178i			0.502095i
$85$		0			0
$86$	1.52360	+	2.63895i	0.164294	+	0.284565i
$87$	−3.78114	+	6.54913i	−0.405381	+	0.702140i
$88$	15.3660			1.63803
$89$	0.934359	−	3.48707i	0.0990418	−	0.369629i	−0.898559	−	0.438852i	$-0.855385\pi$
$89$	0.934359	−	3.48707i	0.0990418	−	0.369629i	0.997601	+	0.0692228i	$0.0220519\pi$
$90$		0			0
$91$	2.95791	−	11.0391i	0.310073	−	1.15721i
$92$	−2.88978	−	1.66842i	−0.301281	−	0.173944i
$93$	−17.5203	−	10.1153i	−1.81677	−	1.04891i
$94$	1.47828	−	5.51702i	0.152473	−	0.569037i
$95$		0			0
$96$	−2.49361	+	9.30629i	−0.254503	+	0.949820i
$97$	−10.8774			−1.10443			−0.552215	−	0.833702i	$-0.686217\pi$
$97$	−10.8774			−1.10443			−0.552215	+	0.833702i	$0.686217\pi$
$98$	0.451263	−	0.781611i	0.0455845	−	0.0789546i
$99$	4.28369	+	7.41958i	0.430527	+	0.745695i
$100$		0			0
$101$		−	12.2409i		−	1.21802i	−0.793164	−	0.609008i	$-0.791568\pi$
$101$		−	12.2409i		−	1.21802i	0.793164	−	0.609008i	$-0.208432\pi$
$102$	−3.14283	+	11.7292i	−0.311187	+	1.16136i
$103$	10.9612			1.08004			0.540021	−	0.841651i	$-0.318416\pi$
$103$	10.9612			1.08004			0.540021	+	0.841651i	$0.318416\pi$
$104$	7.03549	−	12.1858i	0.689887	−	1.19492i
$105$		0			0
$106$	−0.545238	−	2.03485i	−0.0529582	−	0.197643i
$107$	2.32616	+	8.68135i	0.224878	+	0.839257i	0.982453	+	0.186509i	$0.0597174\pi$
$107$	2.32616	+	8.68135i	0.224878	+	0.839257i	−0.757575	+	0.652748i	$0.773616\pi$
$108$	2.32298	−	0.622441i	0.223529	−	0.0598944i
$109$	5.88902	+	1.57796i	0.564066	+	0.151141i	0.529574	−	0.848264i	$-0.322352\pi$
$109$	5.88902	+	1.57796i	0.564066	+	0.151141i	0.0344922	+	0.999405i	$0.489019\pi$
$110$		0			0
$111$	6.77770	−	11.3174i	0.643311	−	1.07420i
$112$	−2.73403	+	2.73403i	−0.258341	+	0.258341i
$113$	−1.55938	−	2.70092i	−0.146694	−	0.254081i	0.783310	−	0.621632i	$-0.213530\pi$
$113$	−1.55938	−	2.70092i	−0.146694	−	0.254081i	−0.930004	+	0.367550i	$0.880197\pi$
$114$	−8.80433	+	15.2495i	−0.824601	+	1.42825i
$115$		0			0
$116$	2.88041	−	0.771803i	0.267439	−	0.0716601i
$117$	7.84532			0.725300
$118$	−13.1861	+	3.53321i	−1.21388	+	0.325258i
$119$	9.18136	−	9.18136i	0.841654	−	0.841654i
$120$		0			0
$121$	−14.3000			−1.30000
$122$	9.18267	+	9.18267i	0.831360	+	0.831360i
$123$	1.37600	−	5.13530i	0.124070	−	0.463034i
$124$	2.06473	+	7.70569i	0.185419	+	0.691992i
$125$		0			0
$126$	−4.36784	−	1.17036i	−0.389118	−	0.104264i
$127$	−7.08705	−	1.89897i	−0.628874	−	0.168506i	−0.0697154	−	0.997567i	$-0.522209\pi$
$127$	−7.08705	−	1.89897i	−0.628874	−	0.168506i	−0.559159	+	0.829061i	$0.688876\pi$
$128$	0.402302	−	0.232269i	0.0355588	−	0.0205299i
$129$	5.96590	−	1.59856i	0.525269	−	0.140745i
$130$		0			0
$131$	15.5092	+	4.15568i	1.35505	+	0.363084i	0.861995	−	0.506916i	$-0.169215\pi$
$131$	15.5092	+	4.15568i	1.35505	+	0.363084i	0.493052	+	0.870000i	$0.335881\pi$
$132$	2.41443	−	9.01079i	0.210150	−	0.784289i
$133$	16.3063	−	9.41442i	1.41393	−	0.816334i
$134$	1.08081	−	1.08081i	0.0933674	−	0.0933674i
$135$		0			0
$136$	13.8448	−	7.99333i	1.18719	−	0.685422i
$137$	11.5120	−	11.5120i	0.983540	−	0.983540i	−0.0163269	−	0.999867i	$-0.505197\pi$
$137$	11.5120	−	11.5120i	0.983540	−	0.983540i	0.999867	+	0.0163269i	$0.00519724\pi$
$138$	6.40221	−	6.40221i	0.544993	−	0.544993i
$139$	0.497367	+	0.861465i	0.0421861	+	0.0730685i	0.886348	−	0.463021i	$-0.153234\pi$
$139$	0.497367	+	0.861465i	0.0421861	+	0.0730685i	−0.844161	+	0.536089i	$0.819901\pi$
$140$		0			0
$141$	−10.0259	−	5.78846i	−0.844334	−	0.487476i
$142$		−	1.01918i		−	0.0855273i
$143$	−11.5838	+	20.0638i	−0.968689	+	1.67782i
$144$	−2.29864	−	1.32712i	−0.191553	−	0.110593i
$145$		0			0
$146$	−2.25073	+	8.39983i	−0.186271	+	0.695175i
$147$	−1.29353	−	1.29353i	−0.106689	−	0.106689i
$148$	−5.04550	+	1.26582i	−0.414738	+	0.104050i
$149$		−	13.2762i		−	1.08763i	−0.839206	−	0.543814i	$-0.816980\pi$
$149$		−	13.2762i		−	1.08763i	0.839206	−	0.543814i	$-0.183020\pi$
$150$		0			0
$151$	6.69165	+	3.86343i	0.544559	+	0.314401i	0.746924	−	0.664909i	$-0.231530\pi$
$151$	6.69165	+	3.86343i	0.544559	+	0.314401i	−0.202366	+	0.979310i	$0.564863\pi$
$152$	22.3925	−	6.00006i	1.81627	−	0.486669i
$153$	7.71924	+	4.45671i	0.624064	+	0.360303i
$154$	9.44234	−	9.44234i	0.760886	−	0.760886i
$155$		0			0
$156$	−6.04041	−	6.04041i	−0.483620	−	0.483620i
$157$	−15.3229	−	4.10576i	−1.22290	−	0.327675i	−0.411089	−	0.911595i	$-0.634851\pi$
$157$	−15.3229	−	4.10576i	−1.22290	−	0.327675i	−0.811811	+	0.583920i	$0.801518\pi$
$158$	7.74672	+	7.74672i	0.616296	+	0.616296i
$159$	−4.26994			−0.338629
$160$		0			0
$161$	−9.35161	+	2.50576i	−0.737010	+	0.197481i
$162$			11.9929i			0.942248i
$163$	0.821552	+	1.42297i	0.0643489	+	0.111456i	0.896405	−	0.443236i	$-0.146170\pi$
$163$	0.821552	+	1.42297i	0.0643489	+	0.111456i	−0.832056	+	0.554692i	$0.812836\pi$
$164$	−1.81556	+	1.04821i	−0.141771	+	0.0818516i
$165$		0			0
$166$	−0.463413	−	1.72948i	−0.0359678	−	0.134234i
$167$	−9.72982	+	16.8526i	−0.752916	+	1.30409i	0.193487	+	0.981103i	$0.438020\pi$
$167$	−9.72982	+	16.8526i	−0.752916	+	1.30409i	−0.946404	+	0.322987i	$0.895313\pi$
$168$	8.21939	+	14.2364i	0.634139	+	1.09836i
$169$	4.10754	+	7.11447i	0.315965	+	0.547267i
$170$		0			0
$171$	9.13967	+	9.13967i	0.698928	+	0.698928i
$172$	−2.10921	−	1.21776i	−0.160826	−	0.0928530i
$173$	4.88196	+	1.30812i	0.371168	+	0.0994542i	0.439581	−	0.898203i	$-0.355127\pi$
$173$	4.88196	+	1.30812i	0.371168	+	0.0994542i	−0.0684130	+	0.997657i	$0.521794\pi$
$174$			8.09135i			0.613404i
$175$		0			0
$176$	6.78800	−	3.91906i	0.511665	−	0.295410i
$177$			27.6697i			2.07979i
$178$	−0.999728	−	3.73104i	−0.0749328	−	0.279653i
$179$	6.16119	+	6.16119i	0.460509	+	0.460509i	0.898822	−	0.438313i	$-0.144424\pi$
$179$	6.16119	+	6.16119i	0.460509	+	0.460509i	−0.438313	+	0.898822i	$0.644424\pi$
$180$		0			0
$181$	8.91593	−	15.4428i	0.662716	−	1.14786i	−0.317183	−	0.948364i	$-0.602737\pi$
$181$	8.91593	−	15.4428i	0.662716	−	1.14786i	0.979899	−	0.199494i	$-0.0639297\pi$
$182$	−3.16485	−	11.8114i	−0.234594	−	0.875518i
$183$	22.7954	−	13.1609i	1.68508	−	0.972884i
$184$	−11.9201			−0.878758
$185$		0			0
$186$	−21.6461			−1.58717
$187$	−22.7953	+	13.1609i	−1.66696	+	0.962420i
$188$	1.18154	+	4.40955i	0.0861723	+	0.321600i
$189$	3.48883	−	6.04284i	0.253775	−	0.439552i
$190$		0			0
$191$	−9.29165	−	9.29165i	−0.672320	−	0.672320i	0.285930	−	0.958250i	$-0.407697\pi$
$191$	−9.29165	−	9.29165i	−0.672320	−	0.672320i	−0.958250	+	0.285930i	$0.907697\pi$
$192$	4.41743	+	16.4861i	0.318800	+	1.18978i
$193$			0.877457i			0.0631607i	0.999501	+	0.0315804i	$0.0100540\pi$
$193$			0.877457i			0.0631607i	−0.999501	+	0.0315804i	$0.989946\pi$
$194$	−10.0791	+	5.81918i	−0.723639	+	0.417793i
$195$		0			0
$196$			0.721356i			0.0515255i
$197$	−3.55020	−	0.951274i	−0.252941	−	0.0677755i	0.130120	−	0.991498i	$-0.458464\pi$
$197$	−3.55020	−	0.951274i	−0.252941	−	0.0677755i	−0.383062	+	0.923723i	$0.625130\pi$
$198$	7.93866	+	4.58339i	0.564176	+	0.325727i
$199$	6.52995	+	6.52995i	0.462896	+	0.462896i	0.899604	−	0.436708i	$-0.143856\pi$
$199$	6.52995	+	6.52995i	0.462896	+	0.462896i	−0.436708	+	0.899604i	$0.643856\pi$
$200$		0			0
$201$	−1.54905	−	2.68303i	−0.109261	−	0.189246i
$202$	−6.54865	−	11.3426i	−0.460762	−	0.798062i
$203$	4.32602	−	7.49288i	0.303627	−	0.525897i
$204$	−2.51195	−	9.37472i	−0.175872	−	0.656362i
$205$		0			0
$206$	10.1568	−	5.86405i	0.707660	−	0.408568i
$207$	−3.32303	−	5.75566i	−0.230967	−	0.400046i
$208$		−	7.17751i		−	0.497671i
$209$	−36.8690	+	9.87901i	−2.55028	+	0.683345i
$210$		0			0
$211$	22.5445			1.55203			0.776015	−	0.630714i	$-0.217238\pi$
$211$	22.5445			1.55203			0.776015	+	0.630714i	$0.217238\pi$
$212$	1.19060	+	1.19060i	0.0817705	+	0.0817705i
$213$	−1.99538	−	0.534660i	−0.136721	−	0.0366343i
$214$	6.79981	+	6.79981i	0.464825	+	0.464825i
$215$		0			0
$216$	6.07479	−	6.07479i	0.413337	−	0.413337i
$217$	20.0450	+	11.5730i	1.36075	+	0.785627i
$218$	6.30103	−	1.68835i	0.426759	−	0.114350i
$219$	15.2648	+	8.81311i	1.03150	+	0.595535i
$220$		0			0
$221$			24.1034i			1.62137i
$222$	0.225703	−	14.1128i	0.0151482	−	0.947192i
$223$	−13.5560	−	13.5560i	−0.907775	−	0.907775i	0.0883170	−	0.996092i	$-0.471851\pi$
$223$	−13.5560	−	13.5560i	−0.907775	−	0.907775i	−0.996092	+	0.0883170i	$0.971851\pi$
$224$	2.85295	−	10.6474i	0.190621	−	0.711407i
$225$		0			0
$226$	−2.88988	−	1.66848i	−0.192232	−	0.110985i
$227$	8.02252	−	13.8954i	0.532473	−	0.922271i	−0.466808	−	0.884359i	$-0.654596\pi$
$227$	8.02252	−	13.8954i	0.532473	−	0.922271i	0.999281	−	0.0379118i	$-0.0120706\pi$
$228$		−	14.0740i		−	0.932071i
$229$	−8.12112	−	4.68873i	−0.536659	−	0.309840i	0.207065	−	0.978327i	$-0.433609\pi$
$229$	−8.12112	−	4.68873i	−0.536659	−	0.309840i	−0.743724	+	0.668487i	$0.766942\pi$
$230$		0			0
$231$	−13.5331	−	23.4400i	−0.890413	−	1.54224i
$232$	7.53249	−	7.53249i	0.494533	−	0.494533i
$233$	15.0519	−	15.0519i	0.986082	−	0.986082i	−0.0138229	−	0.999904i	$-0.504400\pi$
$233$	15.0519	−	15.0519i	0.986082	−	0.986082i	0.999904	+	0.0138229i	$0.00440012\pi$
$234$	7.26959	−	4.19710i	0.475228	−	0.274373i
$235$		0			0
$236$	7.71521	−	7.71521i	0.502217	−	0.502217i
$237$	19.2307	−	11.1029i	1.24917	−	0.721209i
$238$	3.59573	−	13.4194i	0.233076	−	0.869853i
$239$	−2.43829	−	0.653338i	−0.157720	−	0.0422609i	0.179095	−	0.983832i	$-0.442683\pi$
$239$	−2.43829	−	0.653338i	−0.157720	−	0.0422609i	−0.336815	+	0.941571i	$0.609350\pi$
$240$		0			0
$241$	−17.7868	+	4.76596i	−1.14575	+	0.307002i	−0.781260	−	0.624206i	$-0.785423\pi$
$241$	−17.7868	+	4.76596i	−1.14575	+	0.307002i	−0.364488	+	0.931208i	$0.618756\pi$
$242$	−13.2505	+	7.65021i	−0.851778	+	0.491774i
$243$	15.3310	+	4.10792i	0.983481	+	0.263523i
$244$	−10.0258	−	2.68640i	−0.641834	−	0.171979i
$245$		0			0
$246$	−1.47227	−	5.49457i	−0.0938683	−	0.350321i
$247$	−9.04640	+	33.7616i	−0.575609	+	2.14820i
$248$	20.1510	+	20.1510i	1.27959	+	1.27959i
$249$	−3.62915			−0.229988
$250$		0			0
$251$	−11.9106	+	11.9106i	−0.751792	+	0.751792i	−0.974814	−	0.223021i	$-0.928408\pi$
$251$	−11.9106	+	11.9106i	−0.751792	+	0.751792i	0.223021	+	0.974814i	$0.428408\pi$
$252$	3.49106	−	0.935426i	0.219916	−	0.0589263i
$253$	19.6262			1.23389
$254$	−7.58288	+	2.03183i	−0.475792	+	0.127488i
$255$		0			0
$256$	8.11848	−	14.0616i	0.507405	−	0.878851i
$257$	7.08231	+	12.2669i	0.441783	+	0.765190i	0.997822	−	0.0659662i	$-0.0210129\pi$
$257$	7.08231	+	12.2669i	0.441783	+	0.765190i	−0.556039	+	0.831156i	$0.687680\pi$
$258$	4.67289	−	4.67289i	0.290922	−	0.290922i
$259$	−7.75440	+	12.9483i	−0.481835	+	0.804570i
$260$		0			0
$261$	5.73699	+	1.53722i	0.355111	+	0.0951516i
$262$	16.5943	−	4.44642i	1.02520	−	0.274701i
$263$	2.56405	+	9.56915i	0.158106	+	0.590059i	0.998819	+	0.0485788i	$0.0154692\pi$
$263$	2.56405	+	9.56915i	0.158106	+	0.590059i	−0.840714	+	0.541480i	$0.817864\pi$
$264$	−8.62500	−	32.1889i	−0.530832	−	1.98109i
$265$		0			0
$266$	10.0731	−	17.4471i	0.617620	−	1.06975i
$267$	−7.82922			−0.479140
$268$	−0.316190	+	1.18004i	−0.0193144	+	0.0720823i
$269$		−	20.3700i		−	1.24198i	−0.783819	−	0.620989i	$-0.786731\pi$
$269$		−	20.3700i		−	1.24198i	0.783819	−	0.620989i	$-0.213269\pi$
$270$		0			0
$271$	6.96002	+	12.0551i	0.422791	+	0.732296i	0.996211	−	0.0869658i	$-0.0277171\pi$
$271$	6.96002	+	12.0551i	0.422791	+	0.732296i	−0.573420	+	0.819261i	$0.694384\pi$
$272$	4.07734	−	7.06216i	0.247225	−	0.428206i
$273$	−24.7850			−1.50006
$274$	4.50850	−	16.8259i	0.272368	−	1.01649i
$275$		0			0
$276$	−1.87297	+	6.99003i	−0.112740	+	0.420750i
$277$	−9.65077	−	5.57187i	−0.579858	−	0.334781i	0.181219	−	0.983443i	$-0.441996\pi$
$277$	−9.65077	−	5.57187i	−0.579858	−	0.334781i	−0.761077	+	0.648661i	$0.775329\pi$
$278$	0.921735	+	0.532164i	0.0552820	+	0.0319171i
$279$	−4.11239	+	15.3476i	−0.246202	+	0.918840i
$280$		0			0
$281$	−5.29526	+	19.7622i	−0.315889	+	1.17891i	0.607270	+	0.794495i	$0.292264\pi$
$281$	−5.29526	+	19.7622i	−0.315889	+	1.17891i	−0.923159	+	0.384418i	$0.874402\pi$
$282$	−12.3869			−0.737627
$283$	2.40691	−	4.16889i	0.143076	−	0.247815i	−0.785577	−	0.618763i	$-0.787634\pi$
$283$	2.40691	−	4.16889i	0.143076	−	0.247815i	0.928653	+	0.370948i	$0.120967\pi$
$284$	0.407295	+	0.705456i	0.0241685	+	0.0418611i
$285$		0			0
$286$			24.7885i			1.46578i
$287$	−1.57429	+	5.87532i	−0.0929272	+	0.346809i
$288$	7.56695			0.445887
$289$	−5.19245	+	8.99359i	−0.305438	+	0.529034i
$290$		0			0
$291$	6.10550	+	22.7860i	0.357910	+	1.33574i
$292$	−1.79892	−	6.71368i	−0.105274	−	0.392888i
$293$	7.58300	−	2.03186i	0.443004	−	0.118702i	−0.0304202	−	0.999537i	$-0.509685\pi$
$293$	7.58300	−	2.03186i	0.443004	−	0.118702i	0.473424	+	0.880835i	$0.343018\pi$
$294$	−1.89062	−	0.506590i	−0.110263	−	0.0295450i
$295$		0			0
$296$	−13.3482	+	12.9280i	−0.775849	+	0.751424i
$297$	−10.0020	+	10.0020i	−0.580378	+	0.580378i
$298$	−7.10251	−	12.3019i	−0.411438	−	0.712631i
$299$	8.98604	−	15.5643i	0.519676	−	0.900106i
$300$		0			0
$301$	−6.82562	+	1.82892i	−0.393422	+	0.105417i
$302$	8.26744			0.475738
$303$	−25.6424	+	6.87085i	−1.47312	+	0.394720i
$304$	8.36168	−	8.36168i	0.479575	−	0.479575i
$305$		0			0
$306$	9.53701			0.545195
$307$	21.3204	+	21.3204i	1.21682	+	1.21682i	0.968739	+	0.248083i	$0.0798006\pi$
$307$	21.3204	+	21.3204i	1.21682	+	1.21682i	0.248083	+	0.968739i	$0.420199\pi$
$308$	−2.76236	+	10.3093i	−0.157400	+	0.587426i
$309$	−6.15257	−	22.9617i	−0.350007	−	1.30625i
$310$		0			0
$311$	10.2124	+	2.73640i	0.579092	+	0.155167i	0.536463	−	0.843924i	$-0.319760\pi$
$311$	10.2124	+	2.73640i	0.579092	+	0.155167i	0.0426287	+	0.999091i	$0.486427\pi$
$312$	−29.4760	−	7.89808i	−1.66875	−	0.447141i
$313$	−21.1567	+	12.2148i	−1.19585	+	0.690423i	−0.959627	−	0.281277i	$-0.909242\pi$
$313$	−21.1567	+	12.2148i	−1.19585	+	0.690423i	−0.236220	+	0.971699i	$0.575909\pi$
$314$	−16.3949	+	4.39300i	−0.925218	+	0.247911i
$315$		0			0
$316$	−8.45798	−	2.26631i	−0.475798	−	0.127490i
$317$	−1.05570	+	3.93993i	−0.0592940	+	0.221288i	−0.989215	−	0.146471i	$-0.953208\pi$
$317$	−1.05570	+	3.93993i	−0.0592940	+	0.221288i	0.929921	+	0.367760i	$0.119875\pi$
$318$	−3.95659	+	2.28434i	−0.221875	+	0.128099i
$319$	−12.4021	+	12.4021i	−0.694387	+	0.694387i
$320$		0			0
$321$	16.8801	−	9.74573i	0.942155	−	0.543953i
$322$	−7.32480	+	7.32480i	−0.408195	+	0.408195i
$323$	−28.0800	+	28.0800i	−1.56242	+	1.56242i
$324$	−4.79273	−	8.30124i	−0.266263	−	0.461180i
$325$		0			0
$326$	1.52252	+	0.879029i	0.0843248	+	0.0486849i
$327$		−	13.2221i		−	0.731183i
$328$	−3.74449	+	6.48565i	−0.206755	+	0.358110i
$329$	11.4707	+	6.62260i	0.632399	+	0.365116i
$330$		0			0
$331$	−2.85231	+	10.6450i	−0.156777	+	0.585101i	0.842169	+	0.539213i	$0.181278\pi$
$331$	−2.85231	+	10.6450i	−0.156777	+	0.585101i	−0.998947	+	0.0458877i	$0.985388\pi$
$332$	1.01192	+	1.01192i	0.0555364	+	0.0555364i
$333$	−9.96351	−	2.84123i	−0.545997	−	0.155699i
$334$			20.8211i			1.13928i
$335$		0			0
$336$	7.26189	+	4.19265i	0.396168	+	0.228728i
$337$	24.2549	−	6.49907i	1.32125	−	0.354027i	0.471802	−	0.881705i	$-0.343604\pi$
$337$	24.2549	−	6.49907i	1.32125	−	0.354027i	0.849445	+	0.527678i	$0.176937\pi$
$338$	7.61222	+	4.39492i	0.414050	+	0.239052i
$339$	−4.78264	+	4.78264i	−0.259757	+	0.259757i
$340$		0			0
$341$	−33.1783	−	33.1783i	−1.79671	−	1.79671i
$342$	13.3585	+	3.57940i	0.722345	+	0.193552i
$343$	13.7614	+	13.7614i	0.743045	+	0.743045i
$344$	−8.70029			−0.469088
$345$		0			0
$346$	5.22351	−	1.39963i	0.280817	−	0.0752448i
$347$		−	28.0694i		−	1.50685i	−0.657536	−	0.753423i	$-0.728401\pi$
$347$		−	28.0694i		−	1.50685i	0.657536	−	0.753423i	$-0.271599\pi$
$348$	−3.23356	−	5.60069i	−0.173337	−	0.300229i
$349$	7.20930	−	4.16229i	0.385905	−	0.222802i	−0.294479	−	0.955658i	$-0.595146\pi$
$349$	7.20930	−	4.16229i	0.385905	−	0.222802i	0.680384	+	0.732855i	$0.261813\pi$
$350$		0			0
$351$	3.35245	+	12.5115i	0.178941	+	0.667816i
$352$	−11.1728	+	19.3519i	−0.595512	+	1.03146i
$353$	−10.8303	−	18.7587i	−0.576441	−	0.998425i	−0.995883	−	0.0906428i	$-0.971108\pi$
$353$	−10.8303	−	18.7587i	−0.576441	−	0.998425i	0.419443	−	0.907782i	$-0.362225\pi$
$354$	14.8028	+	25.6392i	0.786759	+	1.36271i
$355$		0			0
$356$	2.18304	+	2.18304i	0.115701	+	0.115701i
$357$	−24.3867	−	14.0797i	−1.29068	−	0.745176i
$358$	9.00516	+	2.41293i	0.475938	+	0.127527i
$359$			12.6259i			0.666370i	0.942861	+	0.333185i	$0.108123\pi$
$359$			12.6259i			0.666370i	−0.942861	+	0.333185i	$0.891877\pi$
$360$		0			0
$361$	−33.4162	+	19.2928i	−1.75875	+	1.01541i
$362$		−	19.0794i		−	1.00279i
$363$	8.02661	+	29.9557i	0.421288	+	1.57227i
$364$	6.91086	+	6.91086i	0.362228	+	0.362228i
$365$		0			0
$366$	14.0817	−	24.3902i	0.736062	−	1.27490i
$367$	2.92473	+	10.9152i	0.152669	+	0.569770i	0.999294	+	0.0375790i	$0.0119646\pi$
$367$	2.92473	+	10.9152i	0.152669	+	0.569770i	−0.846624	+	0.532191i	$0.821369\pi$
$368$	−5.26573	+	3.04017i	−0.274495	+	0.158480i
$369$	−4.17551			−0.217368
$370$		0			0
$371$	4.88526			0.253630
$372$	14.9830	−	8.65045i	0.776833	−	0.448505i
$373$	−3.65968	−	13.6581i	−0.189491	−	0.707191i	−0.993624	−	0.112741i	$-0.964037\pi$
$373$	−3.65968	−	13.6581i	−0.189491	−	0.707191i	0.804133	−	0.594449i	$-0.202630\pi$
$374$	−14.0817	+	24.3901i	−0.728145	+	1.26118i
$375$		0			0
$376$	11.5313	+	11.5313i	0.594683	+	0.594683i
$377$	4.15691	+	15.5138i	0.214092	+	0.799001i
$378$		−	7.46584i		−	0.384001i
$379$	27.8783	−	16.0956i	1.43201	−	0.826774i	0.434739	−	0.900556i	$-0.356840\pi$
$379$	27.8783	−	16.0956i	1.43201	−	0.826774i	0.997274	+	0.0737827i	$0.0235071\pi$
$380$		0			0
$381$			15.9119i			0.815193i
$382$	−13.5806	−	3.63892i	−0.694845	−	0.186183i
$383$	27.8000	+	16.0504i	1.42052	+	0.820135i	0.996343	−	0.0854465i	$-0.0272317\pi$
$383$	27.8000	+	16.0504i	1.42052	+	0.820135i	0.424172	+	0.905581i	$0.360565\pi$
$384$	−0.712374	−	0.712374i	−0.0363532	−	0.0363532i
$385$		0			0
$386$	0.469423	+	0.813064i	0.0238930	+	0.0413839i
$387$	−2.42544	−	4.20098i	−0.123292	−	0.213548i
$388$	4.65106	−	8.05588i	0.236122	−	0.408975i
$389$	5.37479	+	20.0590i	0.272513	+	1.01703i	0.957490	+	0.288467i	$0.0931454\pi$
$389$	5.37479	+	20.0590i	0.272513	+	1.01703i	−0.684977	+	0.728564i	$0.740188\pi$
$390$		0			0
$391$	17.6833	−	10.2094i	0.894281	−	0.516313i
$392$	1.28844	+	2.23164i	0.0650760	+	0.112715i
$393$		−	34.8215i		−	1.75651i
$394$	−3.79858	+	1.01783i	−0.191370	+	0.0512774i
$395$		0			0
$396$	−7.32667			−0.368179
$397$	−14.9552	−	14.9552i	−0.750580	−	0.750580i	0.224008	−	0.974587i	$-0.428086\pi$
$397$	−14.9552	−	14.9552i	−0.750580	−	0.750580i	−0.974587	+	0.224008i	$0.928086\pi$
$398$	9.54414	+	2.55735i	0.478405	+	0.128188i
$399$	−28.8742	−	28.8742i	−1.44552	−	1.44552i
$400$		0			0
$401$	−0.727039	+	0.727039i	−0.0363066	+	0.0363066i	−0.725027	−	0.688720i	$-0.758173\pi$
$401$	−0.727039	+	0.727039i	−0.0363066	+	0.0363066i	0.688720	+	0.725027i	$0.258173\pi$
$402$	−2.87074	−	1.65742i	−0.143180	−	0.0826647i
$403$	−41.5026	+	11.1206i	−2.06739	+	0.553957i
$404$	9.06572	+	5.23410i	0.451037	+	0.260406i
$405$		0			0
$406$		−	9.25735i		−	0.459434i
$407$	21.9776	−	21.2857i	1.08939	−	1.05509i
$408$	−24.5157	−	24.5157i	−1.21371	−	1.21371i
$409$	0.0739583	−	0.276016i	0.00365700	−	0.0136481i	−0.964073	−	0.265637i	$-0.914418\pi$
$409$	0.0739583	−	0.276016i	0.00365700	−	0.0136481i	0.967730	+	0.251989i	$0.0810845\pi$
$410$		0			0
$411$	−30.5773	−	17.6538i	−1.50827	−	0.870798i
$412$	−4.68692	+	8.11799i	−0.230908	+	0.399945i
$413$		−	31.6571i		−	1.55774i
$414$	−6.15834	−	3.55552i	−0.302666	−	0.174744i
$415$		0			0
$416$	10.2312	+	17.7209i	0.501623	+	0.868837i
$417$	1.52543	−	1.52543i	0.0747007	−	0.0747007i
$418$	−28.8782	+	28.8782i	−1.41248	+	1.41248i
$419$	33.0662	−	19.0908i	1.61539	−	0.932645i	0.627297	−	0.778780i	$-0.284161\pi$
$419$	33.0662	−	19.0908i	1.61539	−	0.932645i	0.988092	−	0.153865i	$-0.0491721\pi$
$420$		0			0
$421$	6.96708	−	6.96708i	0.339555	−	0.339555i	−0.516645	−	0.856200i	$-0.672819\pi$
$421$	6.96708	−	6.96708i	0.339555	−	0.339555i	0.856200	+	0.516645i	$0.172819\pi$
$422$	20.8901	−	12.0609i	1.01691	−	0.587116i
$423$	−2.35330	+	8.78263i	−0.114421	+	0.427026i
$424$	5.80988	+	1.55675i	0.282153	+	0.0756026i
$425$		0			0
$426$	−2.13498	+	0.572066i	−0.103440	+	0.0277167i
$427$	−26.0803	+	15.0575i	−1.26212	+	0.728683i
$428$	−7.42413	−	1.98929i	−0.358859	−	0.0961559i
$429$	48.5319	+	13.0041i	2.34314	+	0.627843i
$430$		0			0
$431$	−3.09363	−	11.5456i	−0.149015	−	0.556131i	−0.999544	−	0.0302026i	$-0.990385\pi$
$431$	−3.09363	−	11.5456i	−0.149015	−	0.556131i	0.850529	−	0.525928i	$-0.176282\pi$
$432$	1.13421	−	4.23291i	0.0545695	−	0.203656i
$433$	−22.4771	−	22.4771i	−1.08018	−	1.08018i	−0.996492	−	0.0836882i	$-0.973330\pi$
$433$	−22.4771	−	22.4771i	−1.08018	−	1.08018i	−0.0836882	−	0.996492i	$-0.526670\pi$
$434$	24.7653			1.18877
$435$		0			0
$436$	−3.68674	+	3.68674i	−0.176563	+	0.176563i
$437$	28.6007	−	7.66354i	1.36816	−	0.366597i
$438$	18.8594			0.901136
$439$	−7.28246	+	1.95133i	−0.347573	+	0.0931319i	−0.428382	−	0.903598i	$-0.640916\pi$
$439$	−7.28246	+	1.95133i	−0.347573	+	0.0931319i	0.0808091	+	0.996730i	$0.474250\pi$
$440$		0			0
$441$	−0.718373	+	1.24426i	−0.0342082	+	0.0592504i
$442$	12.8949	+	22.3345i	0.613345	+	1.06235i
$443$	−10.5608	+	10.5608i	−0.501757	+	0.501757i	−0.911984	−	0.410227i	$-0.865450\pi$
$443$	−10.5608	+	10.5608i	−0.501757	+	0.501757i	0.410227	+	0.911984i	$0.365450\pi$
$444$	5.48371	+	9.85886i	0.260246	+	0.467881i
$445$		0			0
$446$	−19.8134	−	5.30897i	−0.938189	−	0.251387i
$447$	−27.8111	+	7.45197i	−1.31542	+	0.352466i
$448$	−5.05400	−	18.8618i	−0.238779	−	0.891136i
$449$	3.96580	+	14.8006i	0.187158	+	0.698483i	0.994158	+	0.107932i	$0.0344228\pi$
$449$	3.96580	+	14.8006i	0.187158	+	0.698483i	−0.807000	+	0.590551i	$0.798910\pi$
$450$		0			0
$451$	6.16525	−	10.6785i	0.290310	−	0.502832i
$452$	2.66710			0.125450
$453$	4.33710	−	16.1863i	0.203775	−	0.760498i
$454$		−	17.1676i		−	0.805714i
$455$		0			0
$456$	−25.1380	−	43.5402i	−1.17719	−	2.03896i
$457$	9.76779	−	16.9183i	0.456918	−	0.791405i	−0.541878	−	0.840457i	$-0.682287\pi$
$457$	9.76779	−	16.9183i	0.456918	−	0.791405i	0.998796	+	0.0490521i	$0.0156200\pi$
$458$	−10.0335			−0.468836
$459$	−3.80887	+	14.2149i	−0.177783	+	0.663494i
$460$		0			0
$461$	0.0440321	−	0.164330i	0.00205078	−	0.00765362i	−0.964893	−	0.262644i	$-0.915406\pi$
$461$	0.0440321	−	0.164330i	0.00205078	−	0.00765362i	0.966944	+	0.254990i	$0.0820722\pi$
$462$	−25.0799	−	14.4799i	−1.16682	−	0.673666i
$463$	10.7568	+	6.21046i	0.499912	+	0.288624i	0.728677	−	0.684857i	$-0.240135\pi$
$463$	10.7568	+	6.21046i	0.499912	+	0.288624i	−0.228765	+	0.973482i	$0.573469\pi$
$464$	1.40637	−	5.24864i	0.0652891	−	0.243662i
$465$		0			0
$466$	5.89482	−	21.9998i	0.273072	−	1.01912i
$467$	33.8170			1.56486			0.782432	−	0.622736i	$-0.213979\pi$
$467$	33.8170			1.56486			0.782432	+	0.622736i	$0.213979\pi$
$468$	−3.35459	+	5.81032i	−0.155066	+	0.268582i
$469$	1.77227	+	3.06967i	0.0818360	+	0.141744i
$470$		0			0
$471$			34.4031i			1.58521i
$472$	10.0879	−	37.6487i	0.464335	−	1.73292i
$473$	14.3249			0.658660
$474$	11.8796	−	20.5762i	0.545650	−	0.945094i
$475$		0			0
$476$	2.87393	+	10.7257i	0.131726	+	0.491610i
$477$	0.867973	+	3.23932i	0.0397417	+	0.148318i
$478$	−2.60888	+	0.699047i	−0.119327	+	0.0319737i
$479$	−3.60990	−	0.967271i	−0.164941	−	0.0441957i	0.175404	−	0.984497i	$-0.443877\pi$
$479$	−3.60990	−	0.967271i	−0.164941	−	0.0441957i	−0.340344	+	0.940301i	$0.610544\pi$
$480$		0			0
$481$	−6.81769	−	27.1749i	−0.310860	−	1.23907i
$482$	−13.9318	+	13.9318i	−0.634576	+	0.634576i
$483$	10.4982	+	18.1834i	0.477683	+	0.827371i
$484$	6.11453	−	10.5907i	0.277933	−	0.481395i
$485$		0			0
$486$	16.4035	−	4.39531i	0.744080	−	0.199376i
$487$	−19.2166			−0.870789			−0.435394	−	0.900240i	$-0.643391\pi$
$487$	−19.2166			−0.870789			−0.435394	+	0.900240i	$0.643391\pi$
$488$	−35.8147	+	9.59653i	−1.62126	+	0.434414i
$489$	2.51971	−	2.51971i	0.113945	−	0.113945i
$490$		0			0
$491$	−1.12142			−0.0506089			−0.0253045	−	0.999680i	$-0.508056\pi$
$491$	−1.12142			−0.0506089			−0.0253045	+	0.999680i	$0.508056\pi$
$492$	3.21488	+	3.21488i	0.144938	+	0.144938i
$493$	−4.72284	+	17.6259i	−0.212706	+	0.793830i
$494$	9.67930	+	36.1237i	0.435492	+	1.62528i
$495$		0			0
$496$	14.0412	+	3.76233i	0.630469	+	0.168934i
$497$	2.28292	+	0.611707i	0.102403	+	0.0274388i
$498$	−3.36282	+	1.94152i	−0.150691	+	0.0870018i
$499$	1.54366	−	0.413621i	0.0691035	−	0.0185162i	−0.224102	−	0.974566i	$-0.571945\pi$
$499$	1.54366	−	0.413621i	0.0691035	−	0.0185162i	0.293205	+	0.956050i	$0.405278\pi$
$500$		0			0
$501$	40.7643	+	10.9228i	1.82121	+	0.487993i
$502$	−4.66460	+	17.4085i	−0.208191	+	0.776980i
$503$	33.1979	−	19.1668i	1.48022	−	0.854607i	0.480474	−	0.877009i	$-0.340465\pi$
$503$	33.1979	−	19.1668i	1.48022	−	0.854607i	0.999749	+	0.0224019i	$0.00713133\pi$
$504$	9.12940	−	9.12940i	0.406656	−	0.406656i
$505$		0			0
$506$	18.1859	−	10.4996i	0.808462	−	0.466766i
$507$	12.5979	−	12.5979i	0.559492	−	0.559492i
$508$	4.43675	−	4.43675i	0.196849	−	0.196849i
$509$	0.0135360	+	0.0234450i	0.000599970	+	0.00103918i	0.866325	−	0.499480i	$-0.166476\pi$
$509$	0.0135360	+	0.0234450i	0.000599970	+	0.00103918i	−0.865725	+	0.500519i	$0.833142\pi$
$510$		0			0
$511$	−17.4645	−	10.0831i	−0.772583	−	0.446051i
$512$		−	16.4438i		−	0.726722i
$513$	−10.6702	+	18.4813i	−0.471099	+	0.815968i
$514$	13.1251	+	7.57780i	0.578925	+	0.334243i
$515$		0			0
$516$	−1.36706	+	5.10193i	−0.0601814	+	0.224600i
$517$	−18.9862	−	18.9862i	−0.835010	−	0.835010i
$518$	−0.258227	+	16.1466i	−0.0113459	+	0.709439i
$519$		−	10.9610i		−	0.481135i
$520$		0			0
$521$	−13.0122	−	7.51259i	−0.570074	−	0.329133i	0.187105	−	0.982340i	$-0.440090\pi$
$521$	−13.0122	−	7.51259i	−0.570074	−	0.329133i	−0.757179	+	0.653207i	$0.773423\pi$
$522$	6.13836	−	1.64477i	0.268669	−	0.0719896i
$523$	18.0764	+	10.4364i	0.790427	+	0.456353i	0.840113	−	0.542412i	$-0.182489\pi$
$523$	18.0764	+	10.4364i	0.790427	+	0.456353i	−0.0496857	+	0.998765i	$0.515822\pi$
$524$	−9.70934	+	9.70934i	−0.424154	+	0.424154i
$525$		0			0
$526$	7.49519	+	7.49519i	0.326806	+	0.326806i
$527$	−47.1530	−	12.6346i	−2.05401	−	0.550372i
$528$	−12.0198	−	12.0198i	−0.523095	−	0.523095i
$529$	7.77518			0.338051
$530$		0			0
$531$	20.9912	−	5.62457i	0.910939	−	0.244085i
$532$			16.1021i			0.698114i
$533$	−5.64564	−	9.77854i	−0.244540	−	0.423556i
$534$	−7.25466	+	4.18848i	−0.313940	+	0.181253i
$535$		0			0
$536$	1.12952	+	4.21541i	0.0487877	+	0.182078i
$537$	9.44823	−	16.3648i	0.407721	−	0.706194i
$538$	−10.8975	−	18.8751i	−0.469827	−	0.813763i
$539$	−2.12139	−	3.67436i	−0.0913749	−	0.158266i
$540$		0			0
$541$	−12.1070	−	12.1070i	−0.520520	−	0.520520i	0.397209	−	0.917728i	$-0.369979\pi$
$541$	−12.1070	−	12.1070i	−0.520520	−	0.520520i	−0.917728	+	0.397209i	$0.869979\pi$
$542$	12.8985	+	7.44696i	0.554038	+	0.319874i
$543$	−37.3544	−	10.0091i	−1.60303	−	0.429530i
$544$			23.2481i			0.996755i
$545$		0			0
$546$	−22.9662	+	13.2595i	−0.982862	+	0.567455i
$547$		−	14.1115i		−	0.603364i	−0.953409	−	0.301682i	$-0.902452\pi$
$547$		−	14.1115i		−	0.603364i	0.953409	−	0.301682i	$-0.0975482\pi$
$548$	3.60348	+	13.4484i	0.153933	+	0.574485i
$549$	−14.6180	−	14.6180i	−0.623883	−	0.623883i
$550$		0			0
$551$	−13.2306	+	22.9160i	−0.563642	+	0.976256i
$552$	6.69076	+	24.9702i	0.284778	+	1.06280i
$553$	−22.0020	+	12.7028i	−0.935619	+	0.540180i
$554$	−11.9234			−0.506576
$555$		0			0
$556$	−0.850678			−0.0360768
$557$	13.4266	−	7.75186i	0.568904	−	0.328457i	−0.187807	−	0.982206i	$-0.560138\pi$
$557$	13.4266	−	7.75186i	0.568904	−	0.328457i	0.756712	+	0.653749i	$0.226805\pi$
$558$	4.40010	+	16.4214i	0.186271	+	0.695173i
$559$	6.55879	−	11.3602i	0.277407	−	0.480484i
$560$		0			0
$561$	40.3647	+	40.3647i	1.70420	+	1.70420i
$562$	5.66573	+	21.1448i	0.238994	+	0.891939i
$563$		−	25.2519i		−	1.06424i	−0.846669	−	0.532119i	$-0.821396\pi$
$563$		−	25.2519i		−	1.06424i	0.846669	−	0.532119i	$-0.178604\pi$
$564$	8.57397	−	4.95019i	0.361029	−	0.208440i
$565$		0			0
$566$		−	5.15061i		−	0.216496i
$567$	−26.8636	−	7.19808i	−1.12817	−	0.302291i
$568$	2.52007	+	1.45497i	0.105740	+	0.0610490i
$569$	−27.4188	−	27.4188i	−1.14945	−	1.14945i	−0.986660	−	0.162794i	$-0.947949\pi$
$569$	−27.4188	−	27.4188i	−1.14945	−	1.14945i	−0.162794	−	0.986660i	$-0.552051\pi$
$570$		0			0
$571$	−12.8765	−	22.3027i	−0.538864	−	0.933340i	−0.998966	−	0.0454735i	$-0.985520\pi$
$571$	−12.8765	−	22.3027i	−0.538864	−	0.933340i	0.460102	−	0.887866i	$-0.347813\pi$
$572$	−9.90628	−	17.1582i	−0.414202	−	0.717420i
$573$	−14.2488	+	24.6797i	−0.595253	+	1.03101i
$574$	1.68443	+	6.28636i	0.0703066	+	0.262388i
$575$		0			0
$576$	11.6089	−	6.70241i	0.483705	−	0.279267i
$577$	−20.6569	−	35.7788i	−0.859959	−	1.48949i	−0.871967	−	0.489565i	$-0.837156\pi$
$577$	−20.6569	−	35.7788i	−0.859959	−	1.48949i	0.0120080	−	0.999928i	$-0.496178\pi$
$578$			11.1114i			0.462175i
$579$	1.83811	−	0.492519i	0.0763890	−	0.0204684i
$580$		0			0
$581$	4.15212			0.172259
$582$	17.8475	+	17.8475i	0.739804	+	0.739804i
$583$	−9.56588	−	2.56317i	−0.396178	−	0.106156i
$584$	−17.5568	−	17.5568i	−0.726505	−	0.726505i
$585$		0			0
$586$	5.93951	−	5.93951i	0.245359	−	0.245359i
$587$	−10.6262	−	6.13506i	−0.438591	−	0.253221i	0.264409	−	0.964411i	$-0.414823\pi$
$587$	−10.6262	−	6.13506i	−0.438591	−	0.253221i	−0.703000	+	0.711190i	$0.748157\pi$
$588$	1.51110	−	0.404899i	0.0623169	−	0.0166978i
$589$	−61.3052	−	35.3946i	−2.52604	−	1.45841i
$590$		0			0
$591$			7.97095i			0.327881i
$592$	−2.59938	+	9.11540i	−0.106834	+	0.374640i
$593$	9.41692	+	9.41692i	0.386707	+	0.386707i	0.873511	−	0.486804i	$-0.161838\pi$
$593$	9.41692	+	9.41692i	0.386707	+	0.386707i	−0.486804	+	0.873511i	$0.661838\pi$
$594$	−3.91713	+	14.6189i	−0.160722	+	0.599822i
$595$		0			0
$596$	9.83247	+	5.67678i	0.402754	+	0.232530i
$597$	10.0137	−	17.3443i	0.409835	−	0.709854i
$598$		−	19.2294i		−	0.786351i
$599$	32.1246	+	18.5471i	1.31257	+	0.757815i	0.982522	−	0.186148i	$-0.0596003\pi$
$599$	32.1246	+	18.5471i	1.31257	+	0.757815i	0.330052	+	0.943963i	$0.392934\pi$
$600$		0			0
$601$	9.28898	+	16.0890i	0.378905	+	0.656283i	0.990903	−	0.134576i	$-0.0429672\pi$
$601$	9.28898	+	16.0890i	0.378905	+	0.656283i	−0.611998	+	0.790859i	$0.709634\pi$
$602$	−5.34628	+	5.34628i	−0.217898	+	0.217898i
$603$	−1.72055	+	1.72055i	−0.0700663	+	0.0700663i
$604$	−5.72258	+	3.30393i	−0.232848	+	0.134435i
$605$		0			0
$606$	−20.0848	+	20.0848i	−0.815890	+	0.815890i
$607$	34.6826	−	20.0240i	1.40772	−	0.812749i	0.412555	−	0.910933i	$-0.364637\pi$
$607$	34.6826	−	20.0240i	1.40772	−	0.812749i	0.995168	+	0.0981835i	$0.0313032\pi$
$608$	−8.72540	+	32.5636i	−0.353862	+	1.32063i
$609$	−18.1244	−	4.85641i	−0.734437	−	0.196792i
$610$		0			0
$611$	−23.7497	+	6.36372i	−0.960811	+	0.257448i
$612$	−6.60135	+	3.81129i	−0.266844	+	0.154062i
$613$	5.64923	+	1.51371i	0.228170	+	0.0611381i	0.371093	−	0.928596i	$-0.378983\pi$
$613$	5.64923	+	1.51371i	0.228170	+	0.0611381i	−0.142922	+	0.989734i	$0.545650\pi$
$614$	31.1619	+	8.34979i	1.25759	+	0.336970i
$615$		0			0
$616$	9.86790	+	36.8275i	0.397589	+	1.48382i
$617$	3.47987	−	12.9870i	0.140094	−	0.522839i	−0.859831	−	0.510579i	$-0.829431\pi$
$617$	3.47987	−	12.9870i	0.140094	−	0.522839i	0.999925	−	0.0122593i	$-0.00390237\pi$
$618$	−17.9851	−	17.9851i	−0.723468	−	0.723468i
$619$	−28.9680			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$619$	−28.9680			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$620$		0			0
$621$	7.75899	−	7.75899i	0.311357	−	0.311357i
$622$	10.9269	−	2.92785i	0.438128	−	0.117396i
$623$	8.95744			0.358872
$624$	−15.0355	+	4.02876i	−0.601903	+	0.161279i
$625$		0			0
$626$	−13.0694	+	22.6369i	−0.522358	+	0.904751i
$627$	41.3893	+	71.6884i	1.65293	+	2.86296i
$628$	9.59268	−	9.59268i	0.382790	−	0.382790i
$629$	8.72919	−	30.6111i	0.348056	−	1.22055i
$630$		0			0
$631$	−42.1539	−	11.2951i	−1.67812	−	0.449651i	−0.710839	−	0.703355i	$-0.751685\pi$
$631$	−42.1539	−	11.2951i	−1.67812	−	0.449651i	−0.967282	+	0.253704i	$0.918351\pi$
$632$	−30.2141	+	8.09585i	−1.20185	+	0.322036i
$633$	−12.6543	−	47.2265i	−0.502964	−	1.87709i
$634$	1.12956	+	4.21557i	0.0448605	+	0.167422i
$635$		0			0
$636$	1.82579	−	3.16236i	0.0723972	−	0.125396i
$637$	−3.88521			−0.153937
$638$	−4.85709	+	18.1269i	−0.192294	+	0.717651i
$639$			1.62244i			0.0641828i
$640$		0			0
$641$	−21.3625	−	37.0010i	−0.843770	−	1.46145i	−0.886685	−	0.462374i	$-0.846998\pi$
$641$	−21.3625	−	37.0010i	−0.843770	−	1.46145i	0.0429152	−	0.999079i	$-0.486335\pi$
$642$	10.4276	−	18.0611i	0.411543	−	0.712813i
$643$	4.82705			0.190360			0.0951802	−	0.995460i	$-0.469657\pi$
$643$	4.82705			0.190360			0.0951802	+	0.995460i	$0.469657\pi$
$644$	2.14288	−	7.99732i	0.0844412	−	0.315139i
$645$		0			0
$646$	−10.9971	+	41.0417i	−0.432674	+	1.61476i
$647$	−16.3059	−	9.41423i	−0.641052	−	0.370112i	0.143967	−	0.989582i	$-0.454014\pi$
$647$	−16.3059	−	9.41423i	−0.641052	−	0.370112i	−0.785020	+	0.619471i	$0.787347\pi$
$648$	−29.6542	−	17.1209i	−1.16493	−	0.672572i
$649$	−16.6096	+	61.9881i	−0.651986	+	2.43324i
$650$		0			0
$651$	12.9919	−	48.4865i	0.509193	−	1.90034i
$652$	−1.40515			−0.0550300
$653$	−17.1768	+	29.7510i	−0.672178	+	1.16425i	0.305107	+	0.952318i	$0.401308\pi$
$653$	−17.1768	+	29.7510i	−0.672178	+	1.16425i	−0.977285	+	0.211929i	$0.932025\pi$
$654$	−7.07357	−	12.2518i	−0.276598	−	0.479082i
$655$		0			0
$656$			3.82008i			0.149149i
$657$	3.58297	−	13.3718i	0.139785	−	0.521684i
$658$	14.1719			0.552477
$659$	−12.6706	+	21.9461i	−0.493575	+	0.854897i	−0.999973	−	0.00740321i	$-0.997643\pi$
$659$	−12.6706	+	21.9461i	−0.493575	+	0.854897i	0.506398	+	0.862300i	$0.330977\pi$
$660$		0			0
$661$	1.57712	+	5.88590i	0.0613430	+	0.228935i	0.989791	−	0.142528i	$-0.0455230\pi$
$661$	1.57712	+	5.88590i	0.0613430	+	0.228935i	−0.928448	+	0.371463i	$0.878856\pi$
$662$	3.05187	+	11.3897i	0.118614	+	0.442674i
$663$	50.4920	−	13.5293i	1.96095	−	0.525434i
$664$	4.93798	+	1.32313i	0.191631	+	0.0513473i
$665$		0			0
$666$	−10.7523	+	2.69756i	−0.416645	+	0.104528i
$667$	9.62084	−	9.62084i	0.372520	−	0.372520i
$668$	−8.32077	−	14.4120i	−0.321940	−	0.557617i
$669$	−20.7882	+	36.0062i	−0.803718	+	1.39208i
$670$		0			0
$671$	58.9684	−	15.8005i	2.27645	−	0.609973i
$672$	−23.9056			−0.922178
$673$	0.698464	−	0.187153i	0.0269238	−	0.00721421i	−0.245332	−	0.969439i	$-0.578897\pi$
$673$	0.698464	−	0.187153i	0.0269238	−	0.00721421i	0.272256	+	0.962225i	$0.412230\pi$
$674$	18.9980	−	18.9980i	0.731776	−	0.731776i
$675$		0			0
$676$	−7.02539			−0.270207
$677$	19.6540	+	19.6540i	0.755365	+	0.755365i	0.975475	−	0.220110i	$-0.0706417\pi$
$677$	19.6540	+	19.6540i	0.755365	+	0.755365i	−0.220110	+	0.975475i	$0.570642\pi$
$678$	−1.87304	+	6.99028i	−0.0719336	+	0.268460i
$679$	−6.98532	−	26.0696i	−0.268072	−	1.00046i
$680$		0			0
$681$	−33.6113	−	9.00612i	−1.28799	−	0.345115i
$682$	−48.4933	−	12.9937i	−1.85690	−	0.497556i
$683$	30.1277	−	17.3942i	1.15280	−	0.665571i	0.203235	−	0.979130i	$-0.434855\pi$
$683$	30.1277	−	17.3942i	1.15280	−	0.665571i	0.949569	+	0.313559i	$0.101521\pi$
$684$	−10.6770	+	2.86088i	−0.408244	+	0.109389i
$685$		0			0
$686$	20.1136	+	5.38942i	0.767940	+	0.205769i
$687$	−5.26359	+	19.6440i	−0.200819	+	0.749465i
$688$	−3.84338	+	2.21898i	−0.146528	+	0.0845978i
$689$	−6.41252	+	6.41252i	−0.244298	+	0.244298i
$690$		0			0
$691$	−24.4409	+	14.1110i	−0.929777	+	0.536807i	−0.886741	−	0.462267i	$-0.847036\pi$
$691$	−24.4409	+	14.1110i	−0.929777	+	0.536807i	−0.0430357	+	0.999074i	$0.513703\pi$
$692$	−3.05628	+	3.05628i	−0.116182	+	0.116182i
$693$	−15.0314	+	15.0314i	−0.570996	+	0.570996i
$694$	−15.0166	−	26.0095i	−0.570023	−	0.987309i
$695$		0			0
$696$	−20.0072	−	11.5511i	−0.758369	−	0.437845i
$697$		−	12.8285i		−	0.485915i
$698$	4.45350	−	7.71368i	0.168567	−	0.291967i
$699$	−39.9795	−	23.0822i	−1.51216	−	0.873048i
$700$		0			0
$701$	−1.93774	+	7.23174i	−0.0731874	+	0.273139i	−0.992816	−	0.119650i	$-0.961823\pi$
$701$	−1.93774	+	7.23174i	−0.0731874	+	0.273139i	0.919629	+	0.392789i	$0.128490\pi$
$702$	9.79985	+	9.79985i	0.369872	+	0.369872i
$703$	23.7159	−	39.6009i	0.894461	−	1.49357i
$704$			39.5852i			1.49192i
$705$		0			0
$706$	−20.0711	−	11.5880i	−0.755385	−	0.436122i
$707$	29.3376	−	7.86097i	1.10335	−	0.295642i
$708$	−20.4925	−	11.8313i	−0.770154	−	0.444649i
$709$	5.54419	−	5.54419i	0.208216	−	0.208216i	−0.595293	−	0.803509i	$-0.702964\pi$
$709$	5.54419	−	5.54419i	0.208216	−	0.208216i	0.803509	+	0.595293i	$0.202964\pi$
$710$		0			0
$711$	−12.3321	−	12.3321i	−0.462491	−	0.462491i
$712$	10.6528	+	2.85441i	0.399230	+	0.106973i
$713$	25.7378	+	25.7378i	0.963887	+	0.963887i
$714$	−30.1295			−1.12757
$715$		0			0
$716$	−7.19750	+	1.92856i	−0.268983	+	0.0720738i
$717$			5.47448i			0.204448i
$718$	6.75463	+	11.6994i	0.252080	+	0.436616i
$719$	35.4199	−	20.4497i	1.32094	−	0.762645i	0.337061	−	0.941483i	$-0.390567\pi$
$719$	35.4199	−	20.4497i	1.32094	−	0.762645i	0.983879	+	0.178838i	$0.0572338\pi$
$720$		0			0
$721$	7.03918	+	26.2706i	0.262153	+	0.978368i
$722$	−20.6426	+	35.7540i	−0.768238	+	1.33063i
$723$	19.9675	+	34.5848i	0.742601	+	1.28622i
$724$	7.62474	+	13.2064i	0.283371	+	0.490813i
$725$		0			0
$726$	23.4633	+	23.4633i	0.870805	+	0.870805i
$727$	−15.9454	−	9.20610i	−0.591384	−	0.341435i	0.174261	−	0.984700i	$-0.444246\pi$
$727$	−15.9454	−	9.20610i	−0.591384	−	0.341435i	−0.765644	+	0.643264i	$0.777580\pi$
$728$	33.7237	+	9.03623i	1.24988	+	0.334905i
$729$		−	0.795201i		−	0.0294519i
$730$		0			0
$731$	12.9068	−	7.45173i	0.477374	−	0.275612i
$732$			22.5100i			0.831993i
$733$	9.63447	+	35.9563i	0.355857	+	1.32808i	0.879402	+	0.476079i	$0.157943\pi$
$733$	9.63447	+	35.9563i	0.355857	+	1.32808i	−0.523545	+	0.851998i	$0.675391\pi$
$734$	8.54953	+	8.54953i	0.315569	+	0.315569i
$735$		0			0
$736$	8.66719	−	15.0120i	0.319477	−	0.553350i
$737$	−1.85973	−	6.94061i	−0.0685041	−	0.255661i
$738$	−3.86909	+	2.23382i	−0.142423	+	0.0822280i
$739$	4.83340			0.177799			0.0888997	−	0.996041i	$-0.471665\pi$
$739$	4.83340			0.177799			0.0888997	+	0.996041i	$0.471665\pi$
$740$		0			0
$741$	75.8020			2.78465
$742$	4.52675	−	2.61352i	0.166182	−	0.0959454i
$743$	0.700312	+	2.61360i	0.0256919	+	0.0958836i	0.977581	−	0.210558i	$-0.0675282\pi$
$743$	0.700312	+	2.61360i	0.0256919	+	0.0958836i	−0.951889	+	0.306442i	$0.900861\pi$
$744$	30.9017	−	53.5233i	1.13291	−	1.96226i
$745$		0			0
$746$	−10.6979	−	10.6979i	−0.391680	−	0.391680i
$747$	0.737715	+	2.75319i	0.0269916	+	0.100734i
$748$		−	22.5099i		−	0.823044i
$749$	−19.3126	+	11.1501i	−0.705667	+	0.407417i
$750$		0			0
$751$			44.2080i			1.61317i	0.591116	+	0.806586i	$0.298687\pi$
$751$			44.2080i			1.61317i	−0.591116	+	0.806586i	$0.701313\pi$
$752$	8.03503	+	2.15298i	0.293007	+	0.0785111i
$753$	31.6360	+	18.2650i	1.15288	+	0.665615i
$754$	12.1514	+	12.1514i	0.442529	+	0.442529i
$755$		0			0
$756$	2.98359	+	5.16772i	0.108512	+	0.187948i
$757$	13.8005	+	23.9032i	0.501588	+	0.868776i	0.999998	+	0.00183500i	$0.000584100\pi$
$757$	13.8005	+	23.9032i	0.501588	+	0.868776i	−0.498410	+	0.866941i	$0.666083\pi$
$758$	17.2216	−	29.8288i	0.625518	−	1.08343i
$759$	−11.0162	−	41.1131i	−0.399864	−	1.49231i
$760$		0			0
$761$	31.2157	−	18.0224i	1.13157	−	0.653311i	0.187239	−	0.982314i	$-0.440046\pi$
$761$	31.2157	−	18.0224i	1.13157	−	0.653311i	0.944329	+	0.329003i	$0.106713\pi$
$762$	8.51258	+	14.7442i	0.308378	+	0.534127i
$763$			15.1274i			0.547650i
$764$	10.8545	−	2.90845i	0.392702	−	0.105224i
$765$		0			0
$766$	34.3465			1.24099
$767$	41.5539	+	41.5539i	1.50042	+	1.50042i
$768$	−34.0133	−	9.11385i	−1.22735	−	0.328868i
$769$	17.1512	+	17.1512i	0.618489	+	0.618489i	0.945144	−	0.326655i	$-0.105921\pi$
$769$	17.1512	+	17.1512i	0.618489	+	0.618489i	−0.326655	+	0.945144i	$0.605921\pi$
$770$		0			0
$771$	21.7216	−	21.7216i	0.782283	−	0.782283i
$772$	−0.649852	−	0.375192i	−0.0233887	−	0.0135035i
$773$	−46.7592	+	12.5291i	−1.68181	+	0.450640i	−0.968256	−	0.249961i	$-0.919582\pi$
$773$	−46.7592	+	12.5291i	−1.68181	+	0.450640i	−0.713554	+	0.700600i	$0.752916\pi$
$774$	−4.49489	−	2.59513i	−0.161565	−	0.0932799i
$775$		0			0
$776$		−	33.2297i		−	1.19288i
$777$	31.4769	+	8.97606i	1.12923	+	0.322015i
$778$	15.7115	+	15.7115i	0.563286	+	0.563286i
$779$	4.81476	−	17.9689i	0.172507	−	0.643803i
$780$		0			0
$781$	−4.14927	−	2.39558i	−0.148472	−	0.0857206i
$782$	10.9237	−	18.9204i	0.390631	−	0.676593i
$783$			9.80609i			0.350441i
$784$	1.13834	+	0.657223i	0.0406552	+	0.0234723i
$785$		0			0
$786$	−18.6288	−	32.2661i	−0.664468	−	1.15089i
$787$	−29.7783	+	29.7783i	−1.06148	+	1.06148i	−0.0635008	+	0.997982i	$0.520227\pi$
$787$	−29.7783	+	29.7783i	−1.06148	+	1.06148i	−0.997982	+	0.0635008i	$0.979773\pi$
$788$	2.22256	−	2.22256i	0.0791753	−	0.0791753i
$789$	18.6063	−	10.7424i	0.662403	−	0.382439i
$790$		0			0
$791$	5.47184	−	5.47184i	0.194556	−	0.194556i
$792$	−22.6663	+	13.0864i	−0.805413	+	0.465005i
$793$	14.4689	−	53.9985i	0.513804	−	1.91754i
$794$	−21.8584	−	5.85695i	−0.775727	−	0.207855i
$795$		0			0
$796$	−7.62829	+	2.04399i	−0.270377	+	0.0724474i
$797$	21.0733	−	12.1667i	0.746455	−	0.430966i	−0.0779563	−	0.996957i	$-0.524839\pi$
$797$	21.0733	−	12.1667i	0.746455	−	0.430966i	0.824412	+	0.565991i	$0.191506\pi$
$798$	−42.2023	−	11.3081i	−1.49395	−	0.400302i
$799$	−26.9831	−	7.23010i	−0.954593	−	0.255782i
$800$		0			0
$801$	1.59148	+	5.93950i	0.0562323	+	0.209862i
$802$	−0.284733	+	1.06264i	−0.0100543	+	0.0375230i
$803$	28.9070	+	28.9070i	1.02011	+	1.02011i
$804$	2.64944			0.0934384
$805$		0			0
$806$	−32.5076	+	32.5076i	−1.14503	+	1.14503i
$807$	−42.6712	+	11.4337i	−1.50210	+	0.402486i
$808$	37.3952			1.31556
$809$	−16.9308	+	4.53660i	−0.595256	+	0.159498i	−0.543854	−	0.839180i	$-0.683036\pi$
$809$	−16.9308	+	4.53660i	−0.595256	+	0.159498i	−0.0514018	+	0.998678i	$0.516369\pi$
$810$		0			0
$811$	−17.0374	+	29.5096i	−0.598263	+	1.03622i	0.394814	+	0.918761i	$0.370809\pi$
$811$	−17.0374	+	29.5096i	−0.598263	+	1.03622i	−0.993077	+	0.117462i	$0.962524\pi$
$812$	3.69953	+	6.40778i	0.129828	+	0.224869i
$813$	21.3465	−	21.3465i	0.748654	−	0.748654i
$814$	8.97732	−	31.4813i	0.314655	−	1.10342i
$815$		0			0
$816$	−17.0825	−	4.57724i	−0.598007	−	0.160236i
$817$	20.8753	−	5.59352i	0.730334	−	0.195692i
$818$	−0.0791325	−	0.295327i	−0.00276680	−	0.0103259i
$819$	5.03818	+	18.8027i	0.176048	+	0.657021i
$820$		0			0
$821$	8.74075	−	15.1394i	0.305054	−	0.528370i	−0.672219	−	0.740352i	$-0.734659\pi$
$821$	8.74075	−	15.1394i	0.305054	−	0.528370i	0.977273	+	0.211983i	$0.0679920\pi$
$822$	−37.7778			−1.31765
$823$	−2.35099	+	8.77400i	−0.0819502	+	0.305842i	−0.994719	−	0.102634i	$-0.967273\pi$
$823$	−2.35099	+	8.77400i	−0.0819502	+	0.305842i	0.912769	+	0.408476i	$0.133940\pi$
$824$			33.4859i			1.16654i
$825$		0			0
$826$	−16.9359	−	29.3339i	−0.589276	−	1.02066i
$827$	22.8046	−	39.4988i	0.792994	−	1.37351i	−0.131111	−	0.991368i	$-0.541854\pi$
$827$	22.8046	−	39.4988i	0.792994	−	1.37351i	0.924105	−	0.382139i	$-0.124812\pi$
$828$	5.68359			0.197518
$829$	−1.07495	+	4.01177i	−0.0373346	+	0.139334i	−0.982077	−	0.188478i	$-0.939645\pi$
$829$	−1.07495	+	4.01177i	−0.0373346	+	0.139334i	0.944743	+	0.327812i	$0.106311\pi$
$830$		0			0
$831$	−6.25501	+	23.3440i	−0.216984	+	0.809795i
$832$	31.3925	+	18.1245i	1.08834	+	0.628352i
$833$	−3.82277	−	2.20708i	−0.132451	−	0.0764706i
$834$	0.597410	−	2.22956i	0.0206866	−	0.0772035i
$835$		0			0
$836$	8.44835	−	31.5297i	0.292192	−	1.09048i
$837$	−26.2333			−0.906757
$838$	20.4264	−	35.3796i	0.705618	−	1.22217i
$839$	6.83483	+	11.8383i	0.235964	+	0.408702i	0.959553	−	0.281530i	$-0.0908418\pi$
$839$	6.83483	+	11.8383i	0.235964	+	0.408702i	−0.723588	+	0.690232i	$0.757508\pi$
$840$		0			0
$841$		−	16.8408i		−	0.580719i
$842$	2.72854	−	10.1830i	0.0940317	−	0.350931i
$843$	44.3703			1.52819
$844$	−9.63984	+	16.6967i	−0.331817	+	0.574724i
$845$		0			0
$846$	2.51794	+	9.39708i	0.0865685	+	0.323078i
$847$	−9.18328	−	34.2725i	−0.315541	−	1.17762i
$848$	2.96358	−	0.794089i	0.101770	−	0.0272691i
$849$	−10.0840	−	2.70201i	−0.346083	−	0.0927328i
$850$		0			0
$851$	−17.0489	+	16.5122i	−0.584430	+	0.566031i
$852$	1.24918	−	1.24918i	0.0427962	−	0.0427962i
$853$	−1.01716	−	1.76178i	−0.0348271	−	0.0603222i	0.848087	−	0.529858i	$-0.177755\pi$
$853$	−1.01716	−	1.76178i	−0.0348271	−	0.0603222i	−0.882914	+	0.469536i	$0.844421\pi$
$854$	−16.1109	+	27.9050i	−0.551305	+	0.954888i
$855$		0			0
$856$	−26.5210	+	7.10627i	−0.906468	+	0.242887i
$857$	19.2528			0.657662			0.328831	−	0.944389i	$-0.393345\pi$
$857$	19.2528			0.657662			0.328831	+	0.944389i	$0.393345\pi$
$858$	51.9272	−	13.9139i	1.77277	−	0.475011i
$859$	1.92856	−	1.92856i	0.0658018	−	0.0658018i	−0.673440	−	0.739242i	$-0.735184\pi$
$859$	1.92856	−	1.92856i	0.0658018	−	0.0658018i	0.739242	+	0.673440i	$0.235184\pi$
$860$		0			0
$861$	13.1913			0.449559
$862$	−9.04326	−	9.04326i	−0.308015	−	0.308015i
$863$	12.5939	−	47.0010i	0.428701	−	1.59993i	−0.327005	−	0.945023i	$-0.606039\pi$
$863$	12.5939	−	47.0010i	0.428701	−	1.59993i	0.755706	−	0.654911i	$-0.227294\pi$
$864$	3.23350	+	12.0676i	0.110006	+	0.410547i
$865$		0			0
$866$	−32.8524	−	8.80278i	−1.11637	−	0.299131i
$867$	21.7544	+	5.82907i	0.738818	+	0.197966i
$868$	−17.1421	+	9.89702i	−0.581842	+	0.335927i
$869$	49.7471	−	13.3297i	1.68756	−	0.452179i
$870$		0			0
$871$	−6.35566	−	1.70299i	−0.215353	−	0.0577037i
$872$	−4.82056	+	17.9906i	−0.163245	+	0.609238i
$873$	16.0451	−	9.26365i	0.543045	−	0.313527i
$874$	22.4020	−	22.4020i	0.757759	−	0.757759i
$875$		0			0
$876$	−13.0541	+	7.53681i	−0.441058	+	0.254645i
$877$	−6.15212	+	6.15212i	−0.207742	+	0.207742i	−0.803307	−	0.595565i	$-0.796928\pi$
$877$	−6.15212	+	6.15212i	−0.207742	+	0.207742i	0.595565	+	0.803307i	$0.296928\pi$
$878$	−5.70411	+	5.70411i	−0.192504	+	0.192504i
$879$	−8.51272	−	14.7445i	−0.287127	−	0.497318i
$880$		0			0
$881$	19.1705	+	11.0681i	0.645871	+	0.372894i	0.786872	−	0.617116i	$-0.211699\pi$
$881$	19.1705	+	11.0681i	0.645871	+	0.372894i	−0.141002	+	0.990009i	$0.545032\pi$
$882$			1.53726i			0.0517624i
$883$	−1.18144	+	2.04631i	−0.0397585	+	0.0688637i	−0.885220	−	0.465173i	$-0.845992\pi$
$883$	−1.18144	+	2.04631i	−0.0397585	+	0.0688637i	0.845461	+	0.534037i	$0.179326\pi$
$884$	−17.8512	−	10.3064i	−0.600400	−	0.346641i
$885$		0			0
$886$	−4.13594	+	15.4356i	−0.138950	+	0.518567i
$887$	−17.5210	−	17.5210i	−0.588298	−	0.588298i	0.348872	−	0.937170i	$-0.386565\pi$
$887$	−17.5210	−	17.5210i	−0.588298	−	0.588298i	−0.937170	+	0.348872i	$0.886565\pi$
$888$	34.5740	+	20.7054i	1.16023	+	0.694829i
$889$		−	18.2049i		−	0.610573i
$890$		0			0
$891$	48.8253	+	28.1893i	1.63571	+	0.944377i
$892$	15.8361	−	4.24327i	0.530232	−	0.142075i
$893$	−35.0817	−	20.2544i	−1.17396	−	0.677788i
$894$	−21.7835	+	21.7835i	−0.728550	+	0.728550i
$895$		0			0
$896$	0.815030	+	0.815030i	0.0272282	+	0.0272282i
$897$	−37.6481	−	10.0878i	−1.25703	−	0.336821i
$898$	11.5928	+	11.5928i	0.386857	+	0.386857i
$899$	−32.5283			−1.08488
$900$		0			0
$901$	−9.95224	+	2.66669i	−0.331557	+	0.0888405i
$902$		−	13.1932i		−	0.439284i
$903$	7.66247	+	13.2718i	0.254991	+	0.441658i
$904$	8.25114	−	4.76380i	0.274429	−	0.158442i
$905$		0			0
$906$	−4.64053	−	17.3187i	−0.154171	−	0.575376i
$907$	−3.30636	+	5.72678i	−0.109786	+	0.190155i	−0.915683	−	0.401900i	$-0.868350\pi$
$907$	−3.30636	+	5.72678i	−0.109786	+	0.190155i	0.805898	+	0.592055i	$0.201683\pi$
$908$	6.86071	+	11.8831i	0.227681	+	0.394354i
$909$	10.4249	+	18.0565i	0.345772	+	0.598895i
$910$		0			0
$911$	−1.30394	−	1.30394i	−0.0432014	−	0.0432014i	0.685176	−	0.728377i	$-0.259725\pi$
$911$	−1.30394	−	1.30394i	−0.0432014	−	0.0432014i	−0.728377	+	0.685176i	$0.759725\pi$
$912$	−22.2096	−	12.8227i	−0.735432	−	0.424602i
$913$	−8.13031	−	2.17851i	−0.269074	−	0.0720982i
$914$		−	20.9023i		−	0.691387i
$915$		0			0
$916$	6.94503	−	4.00971i	0.229470	−	0.132485i
$917$			39.8394i			1.31561i
$918$	4.07534	+	15.2094i	0.134506	+	0.501984i
$919$	40.4446	+	40.4446i	1.33415	+	1.33415i	0.901623	+	0.432523i	$0.142376\pi$
$919$	40.4446	+	40.4446i	1.33415	+	1.33415i	0.432523	+	0.901623i	$0.357624\pi$
$920$		0			0
$921$	32.6951	−	56.6295i	1.07734	−	1.86601i
$922$	−0.0471127	−	0.175827i	−0.00155157	−	0.00579055i
$923$	−3.79956	+	2.19368i	−0.125064	+	0.0722058i
$924$	23.1465			0.761464
$925$		0			0
$926$	13.2899			0.436733
$927$	−16.1688	+	9.33508i	−0.531054	+	0.306604i
$928$	4.00941	+	14.9633i	0.131615	+	0.491195i
$929$	−13.5950	+	23.5472i	−0.446036	+	0.772557i	−0.998124	−	0.0612287i	$-0.980498\pi$
$929$	−13.5950	+	23.5472i	−0.446036	+	0.772557i	0.552088	+	0.833786i	$0.313831\pi$
$930$		0			0
$931$	−4.52620	−	4.52620i	−0.148340	−	0.148340i
$932$	4.71151	+	17.5836i	0.154331	+	0.575970i
$933$		−	22.9290i		−	0.750661i
$934$	31.3353	−	18.0915i	1.02532	−	0.591970i
$935$		0			0
$936$			23.9670i			0.783385i
$937$	7.77806	+	2.08413i	0.254098	+	0.0680854i	0.383620	−	0.923491i	$-0.374677\pi$
$937$	7.77806	+	2.08413i	0.254098	+	0.0680854i	−0.129521	+	0.991577i	$0.541344\pi$
$938$	3.28443	+	1.89626i	0.107240	+	0.0619152i
$939$	37.4630	+	37.4630i	1.22256	+	1.22256i
$940$		0			0
$941$	17.3013	+	29.9668i	0.564008	+	0.976890i	0.997141	+	0.0755604i	$0.0240746\pi$
$941$	17.3013	+	29.9668i	0.564008	+	0.976890i	−0.433133	+	0.901330i	$0.642592\pi$
$942$	18.4050	+	31.8784i	0.599668	+	1.03865i
$943$	−4.78263	+	8.28376i	−0.155744	+	0.269756i
$944$	−5.14579	−	19.2043i	−0.167481	−	0.625048i
$945$		0			0
$946$	13.2737	−	7.66355i	0.431564	−	0.249163i
$947$	−17.1551	−	29.7135i	−0.557465	−	0.965558i	−0.997707	−	0.0676788i	$-0.978441\pi$
$947$	−17.1551	−	29.7135i	−0.557465	−	0.965558i	0.440242	−	0.897879i	$-0.354893\pi$
$948$			18.9899i			0.616764i
$949$	36.1597	−	9.68895i	1.17379	−	0.314517i
$950$		0			0
$951$	8.84596			0.286850
$952$	28.0485	+	28.0485i	0.909056	+	0.909056i
$953$	−0.726754	−	0.194733i	−0.0235419	−	0.00630802i	0.247029	−	0.969008i	$-0.420546\pi$
$953$	−0.726754	−	0.194733i	−0.0235419	−	0.00630802i	−0.270571	+	0.962700i	$0.587212\pi$
$954$	2.53725	+	2.53725i	0.0821465	+	0.0821465i
$955$		0			0
$956$	1.52646	−	1.52646i	0.0493692	−	0.0493692i
$957$	32.9415	+	19.0188i	1.06485	+	0.614790i
$958$	−3.86246	+	1.03494i	−0.124790	+	0.0334375i
$959$	34.9836	+	20.1978i	1.12968	+	0.652220i
$960$		0			0
$961$		−	56.0200i		−	1.80710i
$962$	−20.8554	−	21.5334i	−0.672406	−	0.694263i
$963$	−10.8247	−	10.8247i	−0.348822	−	0.348822i
$964$	4.07576	−	15.2109i	0.131271	−	0.489911i
$965$		0			0
$966$	19.4555	+	11.2326i	0.625970	+	0.361404i
$967$	−25.2004	+	43.6483i	−0.810389	+	1.40363i	0.102203	+	0.994764i	$0.467411\pi$
$967$	−25.2004	+	43.6483i	−0.810389	+	1.40363i	−0.912592	+	0.408871i	$0.865923\pi$
$968$		−	43.6855i		−	1.40410i
$969$	74.5838	+	43.0610i	2.39598	+	1.38332i
$970$		0			0
$971$	−15.0692	−	26.1007i	−0.483594	−	0.837610i	0.516228	−	0.856451i	$-0.327336\pi$
$971$	−15.0692	−	26.1007i	−0.483594	−	0.837610i	−0.999822	+	0.0188411i	$0.994002\pi$
$972$	−9.59773	+	9.59773i	−0.307847	+	0.307847i
$973$	−1.74525	+	1.74525i	−0.0559503	+	0.0559503i
$974$	−17.8064	+	10.2805i	−0.570554	+	0.329410i
$975$		0			0
$976$	−13.3737	+	13.3737i	−0.428082	+	0.428082i
$977$	−6.28185	+	3.62683i	−0.200974	+	0.116033i	−0.597110	−	0.802159i	$-0.703684\pi$
$977$	−6.28185	+	3.62683i	−0.200974	+	0.116033i	0.396136	+	0.918192i	$0.370351\pi$
$978$	0.986803	−	3.68280i	0.0315545	−	0.117763i
$979$	−17.5397	−	4.69974i	−0.560570	−	0.150204i
$980$		0			0
$981$	−10.0307	+	2.68772i	−0.320256	+	0.0858123i
$982$	−1.03912	+	0.599938i	−0.0331597	+	0.0191448i
$983$	7.23524	+	1.93868i	0.230768	+	0.0618342i	0.372350	−	0.928092i	$-0.378552\pi$
$983$	7.23524	+	1.93868i	0.230768	+	0.0618342i	−0.141582	+	0.989927i	$0.545219\pi$
$984$	15.6880	+	4.20359i	0.500115	+	0.134005i
$985$		0			0
$986$	5.05326	+	18.8590i	0.160929	+	0.600594i
$987$	7.43457	−	27.7462i	0.236645	−	0.883171i
$988$	−21.1360	−	21.1360i	−0.672426	−	0.672426i
$989$	−11.1124			−0.353354
$990$		0			0
$991$	−21.2828	+	21.2828i	−0.676072	+	0.676072i	−0.959109	−	0.283037i	$-0.908658\pi$
$991$	−21.2828	+	21.2828i	−0.676072	+	0.676072i	0.283037	+	0.959109i	$0.408658\pi$
$992$	−40.0300	+	10.7260i	−1.27095	+	0.340551i
$993$	23.9002			0.758450
$994$	2.44264	−	0.654503i	0.0774758	−	0.0207596i
$995$		0			0
$996$	1.55179	−	2.68778i	0.0491703	−	0.0851655i
$997$	−14.2217	−	24.6327i	−0.450406	−	0.780125i	0.548006	−	0.836475i	$-0.315387\pi$
$997$	−14.2217	−	24.6327i	−0.450406	−	0.780125i	−0.998411	+	0.0563494i	$0.982054\pi$
$998$	1.20909	−	1.20909i	0.0382732	−	0.0382732i
$999$	0.273534	−	17.1037i	0.00865423	−	0.541136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.a.193.10	yes	56
5.2	odd	4		925.2.t.a.82.10	yes	56
5.3	odd	4		925.2.t.a.82.5	✓	56
5.4	even	2	inner	925.2.y.a.193.5	yes	56
37.14	odd	12		925.2.t.a.643.10	yes	56
185.14	odd	12		925.2.t.a.643.5	yes	56
185.88	even	12	inner	925.2.y.a.532.5	yes	56
185.162	even	12	inner	925.2.y.a.532.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.a.82.5	✓	56	5.3	odd	4
925.2.t.a.82.10	yes	56	5.2	odd	4
925.2.t.a.643.5	yes	56	185.14	odd	12
925.2.t.a.643.10	yes	56	37.14	odd	12
925.2.y.a.193.5	yes	56	5.4	even	2	inner
925.2.y.a.193.10	yes	56	1.1	even	1	trivial
925.2.y.a.532.5	yes	56	185.88	even	12	inner
925.2.y.a.532.10	yes	56	185.162	even	12	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926614 - 0.534981i) q^{2} +(-0.561303 - 2.09481i) q^{3} +(-0.427591 + 0.740609i) q^{4} +(-1.64079 - 1.64079i) q^{6} +(0.642189 + 2.39668i) q^{7} +3.05494i q^{8} +(-1.47509 + 0.851645i) q^{9} -5.02991i q^{11} +(1.79144 + 0.480016i) q^{12} +(-3.98890 - 2.30299i) q^{13} +(1.87724 + 1.87724i) q^{14} +(0.779151 + 1.34953i) q^{16} +(-2.61653 - 4.53196i) q^{17} +(-0.911227 + 1.57829i) q^{18} +(-1.96405 - 7.32995i) q^{19} +(4.66013 - 2.69053i) q^{21} +(-2.69090 - 4.66078i) q^{22} +3.90190i q^{23} +(6.39951 - 1.71474i) q^{24} -4.92823 q^{26} +(-1.98852 - 1.98852i) q^{27} +(-2.04960 - 0.549188i) q^{28} +(-2.46568 - 2.46568i) q^{29} +(6.59621 - 6.59621i) q^{31} +(-3.84736 - 2.22127i) q^{32} +(-10.5367 + 2.82330i) q^{33} +(-4.84903 - 2.79959i) q^{34} -1.45662i q^{36} +(4.23183 + 4.36939i) q^{37} +(-5.74130 - 5.74130i) q^{38} +(-2.58535 + 9.64866i) q^{39} +(2.12301 + 1.22572i) q^{41} +(2.87876 - 4.98616i) q^{42} +2.84795i q^{43} +(3.72519 + 2.15074i) q^{44} +(2.08744 + 3.61556i) q^{46} +(3.77465 - 3.77465i) q^{47} +(2.38967 - 2.38967i) q^{48} +(0.730503 - 0.421756i) q^{49} +(-8.02493 + 8.02493i) q^{51} +(3.41123 - 1.96948i) q^{52} +(0.509586 - 1.90180i) q^{53} +(-2.90640 - 0.778769i) q^{54} +(-7.32171 + 1.96185i) q^{56} +(-14.2524 + 8.22864i) q^{57} +(-3.60383 - 0.965642i) q^{58} +(-12.3239 - 3.30218i) q^{59} +(3.14132 + 11.7236i) q^{61} +(2.58330 - 9.64099i) q^{62} +(-2.98841 - 2.98841i) q^{63} -7.86996 q^{64} +(-8.25304 + 8.25304i) q^{66} +(1.37987 - 0.369735i) q^{67} +4.47521 q^{68} +(8.17374 - 2.19015i) q^{69} +(0.476267 - 0.824919i) q^{71} +(-2.60172 - 4.50631i) q^{72} +(-5.74703 + 5.74703i) q^{73} +(6.25882 + 1.78479i) q^{74} +(6.26844 + 1.67962i) q^{76} +(12.0551 - 3.23015i) q^{77} +(2.76623 + 10.3237i) q^{78} +(2.65009 + 9.89027i) q^{79} +(-5.60434 + 9.70700i) q^{81} +2.62295 q^{82} +(0.433112 - 1.61639i) q^{83} +4.60178i q^{84} +(1.52360 + 2.63895i) q^{86} +(-3.78114 + 6.54913i) q^{87} +15.3660 q^{88} +(0.934359 - 3.48707i) q^{89} +(2.95791 - 11.0391i) q^{91} +(-2.88978 - 1.66842i) q^{92} +(-17.5203 - 10.1153i) q^{93} +(1.47828 - 5.51702i) q^{94} +(-2.49361 + 9.30629i) q^{96} -10.8774 q^{97} +(0.451263 - 0.781611i) q^{98} +(4.28369 + 7.41958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 36 q^{4} + 8 q^{14} - 72 q^{16} + 16 q^{19} - 36 q^{21} - 4 q^{24} + 8 q^{26} + 24 q^{31} + 60 q^{34} - 24 q^{41} + 24 q^{44} + 12 q^{49} + 84 q^{51} + 28 q^{54} + 104 q^{56} + 4 q^{59} - 24 q^{61}+ \cdots + 120 q^{99}+O(q^{100}) \) 56 * q + 36 * q^4 + 8 * q^14 - 72 * q^16 + 16 * q^19 - 36 * q^21 - 4 * q^24 + 8 * q^26 + 24 * q^31 + 60 * q^34 - 24 * q^41 + 24 * q^44 + 12 * q^49 + 84 * q^51 + 28 * q^54 + 104 * q^56 + 4 * q^59 - 24 * q^61 - 344 * q^64 - 124 * q^66 - 52 * q^69 - 72 * q^71 - 48 * q^74 + 40 * q^76 + 100 * q^79 + 44 * q^81 + 40 * q^86 + 32 * q^89 - 4 * q^91 - 140 * q^94 - 132 * q^96 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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