LMFDB - Embedded newform 810.3.g.k.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(163,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("810.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 54 x^{9} + 921 x^{8} - 1350 x^{7} + 1458 x^{6} - 18792 x^{5} + 231804 x^{4} - 552420 x^{3} + \cdots + 656100 $ x^12 - 54x^9 + 921x^8 - 1350x^7 + 1458x^6 - 18792x^5 + 231804x^4 - 552420x^3 + 583200x^2 + 874800*x + 656100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.1
Root			$-3.83690 + 3.83690i$ of defining polynomial
Character	$\chi$	$=$	810.163
Dual form			810.3.g.k.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.31004 + 2.53448i) q^{5} +(-2.41180 + 2.41180i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.77556 + 6.84452i) q^{10} +1.28274 q^{11} +(-2.89064 - 2.89064i) q^{13} +4.82359i q^{14} -4.00000 q^{16} +(19.6659 - 19.6659i) q^{17} +17.2032i q^{19} +(5.06896 + 8.62007i) q^{20} +(1.28274 - 1.28274i) q^{22} +(21.8181 + 21.8181i) q^{23} +(12.1528 - 21.8474i) q^{25} -5.78128 q^{26} +(4.82359 + 4.82359i) q^{28} -53.2302i q^{29} +26.7530 q^{31} +(-4.00000 + 4.00000i) q^{32} -39.3319i q^{34} +(4.28229 - 16.5076i) q^{35} +(6.39867 - 6.39867i) q^{37} +(17.2032 + 17.2032i) q^{38} +(13.6890 + 3.55112i) q^{40} +49.5039 q^{41} +(32.2949 + 32.2949i) q^{43} -2.56548i q^{44} +43.6362 q^{46} +(8.02075 - 8.02075i) q^{47} +37.3665i q^{49} +(-9.69454 - 34.0002i) q^{50} +(-5.78128 + 5.78128i) q^{52} +(0.174975 + 0.174975i) q^{53} +(-5.52865 + 3.25107i) q^{55} +9.64719 q^{56} +(-53.2302 - 53.2302i) q^{58} -102.072i q^{59} +52.6841 q^{61} +(26.7530 - 26.7530i) q^{62} +8.00000i q^{64} +(19.7850 + 5.13250i) q^{65} +(42.0158 - 42.0158i) q^{67} +(-39.3319 - 39.3319i) q^{68} +(-12.2253 - 20.7899i) q^{70} +5.54275 q^{71} +(-48.9018 - 48.9018i) q^{73} -12.7973i q^{74} +34.4065 q^{76} +(-3.09370 + 3.09370i) q^{77} +97.8287i q^{79} +(17.2401 - 10.1379i) q^{80} +(49.5039 - 49.5039i) q^{82} +(-50.9676 - 50.9676i) q^{83} +(-34.9180 + 134.604i) q^{85} +64.5897 q^{86} +(-2.56548 - 2.56548i) q^{88} +46.9573i q^{89} +13.9433 q^{91} +(43.6362 - 43.6362i) q^{92} -16.0415i q^{94} +(-43.6012 - 74.1466i) q^{95} +(-112.883 + 112.883i) q^{97} +(37.3665 + 37.3665i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 6 q^{7} - 24 q^{8} - 6 q^{10} + 12 q^{11} - 48 q^{16} - 18 q^{17} - 12 q^{20} + 12 q^{22} + 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} - 48 q^{32} - 168 q^{35} + 66 q^{37} + 36 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 12 * q^2 + 6 * q^7 - 24 * q^8 - 6 * q^10 + 12 * q^11 - 48 * q^16 - 18 * q^17 - 12 * q^20 + 12 * q^22 + 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 - 48 * q^32 - 168 * q^35 + 66 * q^37 + 36 * q^38 - 12 * q^40 - 24 * q^41 - 108 * q^43 + 108 * q^46 - 48 * q^47 - 54 * q^50 + 192 * q^53 - 276 * q^55 - 24 * q^56 - 60 * q^58 + 456 * q^61 + 72 * q^62 - 264 * q^65 - 12 * q^67 + 36 * q^68 - 174 * q^70 - 84 * q^71 - 216 * q^73 + 72 * q^76 + 48 * q^77 - 24 * q^82 + 246 * q^83 - 324 * q^85 - 216 * q^86 - 24 * q^88 + 612 * q^91 + 108 * q^92 - 432 * q^95 + 102 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−4.31004	+	2.53448i	−0.862007	+	0.506896i
$5$	−4.31004	+	2.53448i	−0.862007	+	0.506896i
$6$		0			0
$7$	−2.41180	+	2.41180i	−0.344542	+	0.344542i	−0.858072	−	0.513530i	$-0.828338\pi$
$7$	−2.41180	+	2.41180i	−0.344542	+	0.344542i	0.513530	+	0.858072i	$0.328338\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−1.77556	+	6.84452i	−0.177556	+	0.684452i
$11$	1.28274			0.116613			0.0583063	−	0.998299i	$-0.481430\pi$
$11$	1.28274			0.116613			0.0583063	+	0.998299i	$0.481430\pi$
$12$		0			0
$13$	−2.89064	−	2.89064i	−0.222357	−	0.222357i	0.587133	−	0.809490i	$-0.300256\pi$
$13$	−2.89064	−	2.89064i	−0.222357	−	0.222357i	−0.809490	+	0.587133i	$0.800256\pi$
$14$			4.82359i			0.344542i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	19.6659	−	19.6659i	1.15682	−	1.15682i	0.171664	−	0.985156i	$-0.445086\pi$
$17$	19.6659	−	19.6659i	1.15682	−	1.15682i	0.985156	−	0.171664i	$-0.0549142\pi$
$18$		0			0
$19$			17.2032i			0.905434i	0.891654	+	0.452717i	$0.149545\pi$
$19$			17.2032i			0.905434i	−0.891654	+	0.452717i	$0.850455\pi$
$20$	5.06896	+	8.62007i	0.253448	+	0.431004i
$21$		0			0
$22$	1.28274	−	1.28274i	0.0583063	−	0.0583063i
$23$	21.8181	+	21.8181i	0.948613	+	0.948613i	0.998743	−	0.0501301i	$-0.0159636\pi$
$23$	21.8181	+	21.8181i	0.948613	+	0.948613i	−0.0501301	+	0.998743i	$0.515964\pi$
$24$		0			0
$25$	12.1528	−	21.8474i	0.486114	−	0.873896i
$26$	−5.78128			−0.222357
$27$		0			0
$28$	4.82359	+	4.82359i	0.172271	+	0.172271i
$29$		−	53.2302i		−	1.83552i	−0.397131	−	0.917762i	$-0.629994\pi$
$29$		−	53.2302i		−	1.83552i	0.397131	−	0.917762i	$-0.370006\pi$
$30$		0			0
$31$	26.7530			0.863001			0.431501	−	0.902113i	$-0.357984\pi$
$31$	26.7530			0.863001			0.431501	+	0.902113i	$0.357984\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	39.3319i		−	1.15682i
$35$	4.28229	−	16.5076i	0.122351	−	0.471645i
$36$		0			0
$37$	6.39867	−	6.39867i	0.172937	−	0.172937i	−0.615332	−	0.788268i	$-0.710978\pi$
$37$	6.39867	−	6.39867i	0.172937	−	0.172937i	0.788268	+	0.615332i	$0.210978\pi$
$38$	17.2032	+	17.2032i	0.452717	+	0.452717i
$39$		0			0
$40$	13.6890	+	3.55112i	0.342226	+	0.0887780i
$41$	49.5039			1.20741			0.603706	−	0.797207i	$-0.293690\pi$
$41$	49.5039			1.20741			0.603706	+	0.797207i	$0.293690\pi$
$42$		0			0
$43$	32.2949	+	32.2949i	0.751043	+	0.751043i	0.974674	−	0.223631i	$-0.0717909\pi$
$43$	32.2949	+	32.2949i	0.751043	+	0.751043i	−0.223631	+	0.974674i	$0.571791\pi$
$44$		−	2.56548i		−	0.0583063i
$45$		0			0
$46$	43.6362			0.948613
$47$	8.02075	−	8.02075i	0.170654	−	0.170654i	−0.616613	−	0.787267i	$-0.711495\pi$
$47$	8.02075	−	8.02075i	0.170654	−	0.170654i	0.787267	+	0.616613i	$0.211495\pi$
$48$		0			0
$49$			37.3665i			0.762581i
$50$	−9.69454	−	34.0002i	−0.193891	−	0.680005i
$51$		0			0
$52$	−5.78128	+	5.78128i	−0.111178	+	0.111178i
$53$	0.174975	+	0.174975i	0.00330142	+	0.00330142i	0.708756	−	0.705454i	$-0.249257\pi$
$53$	0.174975	+	0.174975i	0.00330142	+	0.00330142i	−0.705454	+	0.708756i	$0.749257\pi$
$54$		0			0
$55$	−5.52865	+	3.25107i	−0.100521	+	0.0591104i
$56$	9.64719			0.172271
$57$		0			0
$58$	−53.2302	−	53.2302i	−0.917762	−	0.917762i
$59$		−	102.072i		−	1.73004i	−0.501737	−	0.865020i	$-0.667306\pi$
$59$		−	102.072i		−	1.73004i	0.501737	−	0.865020i	$-0.332694\pi$
$60$		0			0
$61$	52.6841			0.863674			0.431837	−	0.901952i	$-0.357866\pi$
$61$	52.6841			0.863674			0.431837	+	0.901952i	$0.357866\pi$
$62$	26.7530	−	26.7530i	0.431501	−	0.431501i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	19.7850	+	5.13250i	0.304385	+	0.0789615i
$66$		0			0
$67$	42.0158	−	42.0158i	0.627102	−	0.627102i	−0.320236	−	0.947338i	$-0.603762\pi$
$67$	42.0158	−	42.0158i	0.627102	−	0.627102i	0.947338	+	0.320236i	$0.103762\pi$
$68$	−39.3319	−	39.3319i	−0.578410	−	0.578410i
$69$		0			0
$70$	−12.2253	−	20.7899i	−0.174647	−	0.296998i
$71$	5.54275			0.0780669			0.0390335	−	0.999238i	$-0.487572\pi$
$71$	5.54275			0.0780669			0.0390335	+	0.999238i	$0.487572\pi$
$72$		0			0
$73$	−48.9018	−	48.9018i	−0.669888	−	0.669888i	0.287802	−	0.957690i	$-0.407075\pi$
$73$	−48.9018	−	48.9018i	−0.669888	−	0.669888i	−0.957690	+	0.287802i	$0.907075\pi$
$74$		−	12.7973i		−	0.172937i
$75$		0			0
$76$	34.4065			0.452717
$77$	−3.09370	+	3.09370i	−0.0401780	+	0.0401780i
$78$		0			0
$79$			97.8287i			1.23834i	0.785258	+	0.619169i	$0.212530\pi$
$79$			97.8287i			1.23834i	−0.785258	+	0.619169i	$0.787470\pi$
$80$	17.2401	−	10.1379i	0.215502	−	0.126724i
$81$		0			0
$82$	49.5039	−	49.5039i	0.603706	−	0.603706i
$83$	−50.9676	−	50.9676i	−0.614068	−	0.614068i	0.329935	−	0.944003i	$-0.392973\pi$
$83$	−50.9676	−	50.9676i	−0.614068	−	0.614068i	−0.944003	+	0.329935i	$0.892973\pi$
$84$		0			0
$85$	−34.9180	+	134.604i	−0.410800	+	1.58357i
$86$	64.5897			0.751043
$87$		0			0
$88$	−2.56548	−	2.56548i	−0.0291531	−	0.0291531i
$89$			46.9573i			0.527610i	0.964576	+	0.263805i	$0.0849776\pi$
$89$			46.9573i			0.527610i	−0.964576	+	0.263805i	$0.915022\pi$
$90$		0			0
$91$	13.9433			0.153223
$92$	43.6362	−	43.6362i	0.474306	−	0.474306i
$93$		0			0
$94$		−	16.0415i		−	0.170654i
$95$	−43.6012	−	74.1466i	−0.458961	−	0.780491i
$96$		0			0
$97$	−112.883	+	112.883i	−1.16374	+	1.16374i	−0.180087	+	0.983651i	$0.557638\pi$
$97$	−112.883	+	112.883i	−1.16374	+	1.16374i	−0.983651	+	0.180087i	$0.942362\pi$
$98$	37.3665	+	37.3665i	0.381291	+	0.381291i
$99$		0			0
$100$	−43.6948	−	24.3057i	−0.436948	−	0.243057i
$101$	74.3351			0.735991			0.367995	−	0.929828i	$-0.380044\pi$
$101$	74.3351			0.735991			0.367995	+	0.929828i	$0.380044\pi$
$102$		0			0
$103$	−11.2285	−	11.2285i	−0.109015	−	0.109015i	0.650495	−	0.759510i	$-0.274561\pi$
$103$	−11.2285	−	11.2285i	−0.109015	−	0.109015i	−0.759510	+	0.650495i	$0.774561\pi$
$104$			11.5626i			0.111178i
$105$		0			0
$106$	0.349951			0.00330142
$107$	114.528	−	114.528i	1.07035	−	1.07035i	0.0730234	−	0.997330i	$-0.476735\pi$
$107$	114.528	−	114.528i	1.07035	−	1.07035i	0.997330	−	0.0730234i	$-0.0232648\pi$
$108$		0			0
$109$		−	80.1875i		−	0.735665i	−0.929892	−	0.367833i	$-0.880100\pi$
$109$		−	80.1875i		−	0.735665i	0.929892	−	0.367833i	$-0.119900\pi$
$110$	−2.27758	+	8.77972i	−0.0207052	+	0.0798156i
$111$		0			0
$112$	9.64719	−	9.64719i	0.0861356	−	0.0861356i
$113$	105.659	+	105.659i	0.935037	+	0.935037i	0.998015	−	0.0629775i	$-0.0200596\pi$
$113$	105.659	+	105.659i	0.935037	+	0.935037i	−0.0629775	+	0.998015i	$0.520060\pi$
$114$		0			0
$115$	−149.334	−	38.7393i	−1.29856	−	0.336864i
$116$	−106.460			−0.917762
$117$		0			0
$118$	−102.072	−	102.072i	−0.865020	−	0.865020i
$119$			94.8604i			0.797146i
$120$		0			0
$121$	−119.355			−0.986402
$122$	52.6841	−	52.6841i	0.431837	−	0.431837i
$123$		0			0
$124$		−	53.5061i		−	0.431501i
$125$	2.99251	+	124.964i	0.0239401	+	0.999713i
$126$		0			0
$127$	−111.415	+	111.415i	−0.877284	+	0.877284i	−0.993253	−	0.115969i	$-0.963003\pi$
$127$	−111.415	+	111.415i	−0.877284	+	0.877284i	0.115969	+	0.993253i	$0.463003\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	24.9175	−	14.6525i	0.191673	−	0.112712i
$131$	−4.10096			−0.0313051			−0.0156525	−	0.999877i	$-0.504983\pi$
$131$	−4.10096			−0.0313051			−0.0156525	+	0.999877i	$0.504983\pi$
$132$		0			0
$133$	−41.4907	−	41.4907i	−0.311960	−	0.311960i
$134$		−	84.0317i		−	0.627102i
$135$		0			0
$136$	−78.6637			−0.578410
$137$	98.5110	−	98.5110i	0.719058	−	0.719058i	−0.249354	−	0.968412i	$-0.580218\pi$
$137$	98.5110	−	98.5110i	0.719058	−	0.719058i	0.968412	+	0.249354i	$0.0802183\pi$
$138$		0			0
$139$		−	23.3971i		−	0.168324i	−0.996452	−	0.0841621i	$-0.973179\pi$
$139$		−	23.3971i		−	0.168324i	0.996452	−	0.0841621i	$-0.0268214\pi$
$140$	−33.0152	−	8.56458i	−0.235823	−	0.0611756i
$141$		0			0
$142$	5.54275	−	5.54275i	0.0390335	−	0.0390335i
$143$	−3.70793	−	3.70793i	−0.0259296	−	0.0259296i
$144$		0			0
$145$	134.911	+	229.424i	0.930419	+	1.58224i
$146$	−97.8036			−0.669888
$147$		0			0
$148$	−12.7973	−	12.7973i	−0.0864685	−	0.0864685i
$149$		−	225.492i		−	1.51337i	−0.653782	−	0.756683i	$-0.726819\pi$
$149$		−	225.492i		−	1.51337i	0.653782	−	0.756683i	$-0.273181\pi$
$150$		0			0
$151$	248.688			1.64694			0.823470	−	0.567360i	$-0.192035\pi$
$151$	248.688			1.64694			0.823470	+	0.567360i	$0.192035\pi$
$152$	34.4065	−	34.4065i	0.226359	−	0.226359i
$153$		0			0
$154$			6.18740i			0.0401780i
$155$	−115.307	+	67.8050i	−0.743914	+	0.437452i
$156$		0			0
$157$	−38.1875	+	38.1875i	−0.243232	+	0.243232i	−0.818186	−	0.574954i	$-0.805020\pi$
$157$	−38.1875	+	38.1875i	−0.243232	+	0.243232i	0.574954	+	0.818186i	$0.305020\pi$
$158$	97.8287	+	97.8287i	0.619169	+	0.619169i
$159$		0			0
$160$	7.10224	−	27.3781i	0.0443890	−	0.171113i
$161$	−105.242			−0.653674
$162$		0			0
$163$	115.074	+	115.074i	0.705977	+	0.705977i	0.965687	−	0.259709i	$-0.0836268\pi$
$163$	115.074	+	115.074i	0.705977	+	0.705977i	−0.259709	+	0.965687i	$0.583627\pi$
$164$		−	99.0078i		−	0.603706i
$165$		0			0
$166$	−101.935			−0.614068
$167$	−221.357	+	221.357i	−1.32549	+	1.32549i	−0.416238	+	0.909256i	$0.636652\pi$
$167$	−221.357	+	221.357i	−1.32549	+	1.32549i	−0.909256	+	0.416238i	$0.863348\pi$
$168$		0			0
$169$		−	152.288i		−	0.901115i
$170$	99.6857	+	169.522i	0.586387	+	0.997187i
$171$		0			0
$172$	64.5897	−	64.5897i	0.375522	−	0.375522i
$173$	153.233	+	153.233i	0.885742	+	0.885742i	0.994111	−	0.108369i	$-0.0345628\pi$
$173$	153.233	+	153.233i	0.885742	+	0.885742i	−0.108369	+	0.994111i	$0.534563\pi$
$174$		0			0
$175$	23.3813	+	82.0016i	0.133607	+	0.468581i
$176$	−5.13095			−0.0291531
$177$		0			0
$178$	46.9573	+	46.9573i	0.263805	+	0.263805i
$179$		−	164.771i		−	0.920507i	−0.887788	−	0.460254i	$-0.847759\pi$
$179$		−	164.771i		−	0.920507i	0.887788	−	0.460254i	$-0.152241\pi$
$180$		0			0
$181$	−5.29281			−0.0292421			−0.0146210	−	0.999893i	$-0.504654\pi$
$181$	−5.29281			−0.0292421			−0.0146210	+	0.999893i	$0.504654\pi$
$182$	13.9433	−	13.9433i	0.0766113	−	0.0766113i
$183$		0			0
$184$		−	87.2724i		−	0.474306i
$185$	−11.3612	+	43.7958i	−0.0614120	+	0.236734i
$186$		0			0
$187$	25.2262	−	25.2262i	0.134900	−	0.134900i
$188$	−16.0415	−	16.0415i	−0.0853271	−	0.0853271i
$189$		0			0
$190$	−117.748	−	30.5454i	−0.619726	−	0.160765i
$191$	−79.4156			−0.415789			−0.207894	−	0.978151i	$-0.566661\pi$
$191$	−79.4156			−0.415789			−0.207894	+	0.978151i	$0.566661\pi$
$192$		0			0
$193$	−120.146	−	120.146i	−0.622519	−	0.622519i	0.323656	−	0.946175i	$-0.395088\pi$
$193$	−120.146	−	120.146i	−0.622519	−	0.622519i	−0.946175	+	0.323656i	$0.895088\pi$
$194$			225.765i			1.16374i
$195$		0			0
$196$	74.7329			0.381291
$197$	−38.1732	+	38.1732i	−0.193773	+	0.193773i	−0.797324	−	0.603551i	$-0.793752\pi$
$197$	−38.1732	+	38.1732i	−0.193773	+	0.193773i	0.603551	+	0.797324i	$0.293752\pi$
$198$		0			0
$199$			90.0401i			0.452463i	0.974074	+	0.226231i	$0.0726405\pi$
$199$			90.0401i			0.452463i	−0.974074	+	0.226231i	$0.927359\pi$
$200$	−68.0005	+	19.3891i	−0.340002	+	0.0969454i
$201$		0			0
$202$	74.3351	−	74.3351i	0.367995	−	0.367995i
$203$	128.380	+	128.380i	0.632416	+	0.632416i
$204$		0			0
$205$	−213.364	+	125.467i	−1.04080	+	0.612032i
$206$	−22.4570			−0.109015
$207$		0			0
$208$	11.5626	+	11.5626i	0.0555892	+	0.0555892i
$209$			22.0673i			0.105585i
$210$		0			0
$211$	371.619			1.76123			0.880614	−	0.473834i	$-0.157130\pi$
$211$	371.619			1.76123			0.880614	+	0.473834i	$0.157130\pi$
$212$	0.349951	−	0.349951i	0.00165071	−	0.00165071i
$213$		0			0
$214$		−	229.056i		−	1.07035i
$215$	−221.043	−	57.3415i	−1.02811	−	0.266704i
$216$		0			0
$217$	−64.5229	+	64.5229i	−0.297341	+	0.297341i
$218$	−80.1875	−	80.1875i	−0.367833	−	0.367833i
$219$		0			0
$220$	6.50214	+	11.0573i	0.0295552	+	0.0502604i
$221$	−113.694			−0.514453
$222$		0			0
$223$	−153.940	−	153.940i	−0.690315	−	0.690315i	0.271986	−	0.962301i	$-0.412319\pi$
$223$	−153.940	−	153.940i	−0.690315	−	0.690315i	−0.962301	+	0.271986i	$0.912319\pi$
$224$		−	19.2944i		−	0.0861356i
$225$		0			0
$226$	211.318			0.935037
$227$	−24.8343	+	24.8343i	−0.109402	+	0.109402i	−0.759689	−	0.650287i	$-0.774649\pi$
$227$	−24.8343	+	24.8343i	−0.109402	+	0.109402i	0.650287	+	0.759689i	$0.274649\pi$
$228$		0			0
$229$			140.049i			0.611569i	0.952101	+	0.305784i	$0.0989187\pi$
$229$			140.049i			0.611569i	−0.952101	+	0.305784i	$0.901081\pi$
$230$	−188.074	+	110.595i	−0.817711	+	0.480848i
$231$		0			0
$232$	−106.460	+	106.460i	−0.458881	+	0.458881i
$233$	−127.973	−	127.973i	−0.549239	−	0.549239i	0.376982	−	0.926221i	$-0.376962\pi$
$233$	−127.973	−	127.973i	−0.549239	−	0.549239i	−0.926221	+	0.376982i	$0.876962\pi$
$234$		0			0
$235$	−14.2413	+	54.8981i	−0.0606013	+	0.233609i
$236$	−204.145			−0.865020
$237$		0			0
$238$	94.8604	+	94.8604i	0.398573	+	0.398573i
$239$			72.0469i			0.301452i	0.988576	+	0.150726i	$0.0481611\pi$
$239$			72.0469i			0.301452i	−0.988576	+	0.150726i	$0.951839\pi$
$240$		0			0
$241$	268.481			1.11403			0.557014	−	0.830503i	$-0.311947\pi$
$241$	268.481			1.11403			0.557014	+	0.830503i	$0.311947\pi$
$242$	−119.355	+	119.355i	−0.493201	+	0.493201i
$243$		0			0
$244$		−	105.368i		−	0.431837i
$245$	−94.7045	−	161.051i	−0.386549	−	0.657351i
$246$		0			0
$247$	49.7284	−	49.7284i	0.201329	−	0.201329i
$248$	−53.5061	−	53.5061i	−0.215750	−	0.215750i
$249$		0			0
$250$	127.957	+	121.972i	0.511827	+	0.487887i
$251$	251.209			1.00083			0.500416	−	0.865785i	$-0.333180\pi$
$251$	251.209			1.00083			0.500416	+	0.865785i	$0.333180\pi$
$252$		0			0
$253$	27.9869	+	27.9869i	0.110620	+	0.110620i
$254$			222.830i			0.877284i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−57.1178	+	57.1178i	−0.222248	+	0.222248i	−0.809445	−	0.587196i	$-0.800232\pi$
$257$	−57.1178	+	57.1178i	−0.222248	+	0.222248i	0.587196	+	0.809445i	$0.300232\pi$
$258$		0			0
$259$			30.8646i			0.119168i
$260$	10.2650	−	39.5700i	0.0394808	−	0.152192i
$261$		0			0
$262$	−4.10096	+	4.10096i	−0.0156525	+	0.0156525i
$263$	101.458	+	101.458i	0.385771	+	0.385771i	0.873176	−	0.487405i	$-0.162057\pi$
$263$	101.458	+	101.458i	0.385771	+	0.385771i	−0.487405	+	0.873176i	$0.662057\pi$
$264$		0			0
$265$	−1.19762	−	0.310679i	−0.00451933	−	0.00117237i
$266$	−82.9815			−0.311960
$267$		0			0
$268$	−84.0317	−	84.0317i	−0.313551	−	0.313551i
$269$			341.458i			1.26936i	0.772775	+	0.634680i	$0.218868\pi$
$269$			341.458i			1.26936i	−0.772775	+	0.634680i	$0.781132\pi$
$270$		0			0
$271$	157.125			0.579798			0.289899	−	0.957057i	$-0.406378\pi$
$271$	157.125			0.579798			0.289899	+	0.957057i	$0.406378\pi$
$272$	−78.6637	+	78.6637i	−0.289205	+	0.289205i
$273$		0			0
$274$		−	197.022i		−	0.719058i
$275$	15.5889	−	28.0245i	0.0566869	−	0.101907i
$276$		0			0
$277$	−118.189	+	118.189i	−0.426677	+	0.426677i	−0.887495	−	0.460818i	$-0.847556\pi$
$277$	−118.189	+	118.189i	−0.426677	+	0.426677i	0.460818	+	0.887495i	$0.347556\pi$
$278$	−23.3971	−	23.3971i	−0.0841621	−	0.0841621i
$279$		0			0
$280$	−41.5797	+	24.4506i	−0.148499	+	0.0873235i
$281$	−201.462			−0.716946			−0.358473	−	0.933540i	$-0.616702\pi$
$281$	−201.462			−0.716946			−0.358473	+	0.933540i	$0.616702\pi$
$282$		0			0
$283$	−42.0512	−	42.0512i	−0.148591	−	0.148591i	0.628897	−	0.777488i	$-0.283507\pi$
$283$	−42.0512	−	42.0512i	−0.148591	−	0.148591i	−0.777488	+	0.628897i	$0.783507\pi$
$284$		−	11.0855i		−	0.0390335i
$285$		0			0
$286$	−7.41586			−0.0259296
$287$	−119.393	+	119.393i	−0.416005	+	0.416005i
$288$		0			0
$289$		−	484.497i		−	1.67646i
$290$	364.335	+	94.5134i	1.25633	+	0.325908i
$291$		0			0
$292$	−97.8036	+	97.8036i	−0.334944	+	0.334944i
$293$	−227.907	−	227.907i	−0.777841	−	0.777841i	0.201623	−	0.979463i	$-0.435379\pi$
$293$	−227.907	−	227.907i	−0.777841	−	0.777841i	−0.979463	+	0.201623i	$0.935379\pi$
$294$		0			0
$295$	258.700	+	439.936i	0.876950	+	1.49131i
$296$	−25.5947			−0.0864685
$297$		0			0
$298$	−225.492	−	225.492i	−0.756683	−	0.756683i
$299$		−	126.136i		−	0.421861i
$300$		0			0
$301$	−155.777			−0.517533
$302$	248.688	−	248.688i	0.823470	−	0.823470i
$303$		0			0
$304$		−	68.8130i		−	0.226359i
$305$	−227.070	+	133.527i	−0.744493	+	0.437792i
$306$		0			0
$307$	65.6054	−	65.6054i	0.213698	−	0.213698i	−0.592138	−	0.805837i	$-0.701716\pi$
$307$	65.6054	−	65.6054i	0.213698	−	0.213698i	0.805837	+	0.592138i	$0.201716\pi$
$308$	6.18740	+	6.18740i	0.0200890	+	0.0200890i
$309$		0			0
$310$	−47.5016	+	183.112i	−0.153231	+	0.590683i
$311$	−243.797			−0.783914			−0.391957	−	0.919983i	$-0.628202\pi$
$311$	−243.797			−0.783914			−0.391957	+	0.919983i	$0.628202\pi$
$312$		0			0
$313$	166.484	+	166.484i	0.531897	+	0.531897i	0.921136	−	0.389240i	$-0.127262\pi$
$313$	166.484	+	166.484i	0.531897	+	0.531897i	−0.389240	+	0.921136i	$0.627262\pi$
$314$			76.3749i			0.243232i
$315$		0			0
$316$	195.657			0.619169
$317$	−334.850	+	334.850i	−1.05631	+	1.05631i	−0.0579912	+	0.998317i	$0.518470\pi$
$317$	−334.850	+	334.850i	−1.05631	+	1.05631i	−0.998317	+	0.0579912i	$0.981530\pi$
$318$		0			0
$319$		−	68.2804i		−	0.214045i
$320$	−20.2758	−	34.4803i	−0.0633619	−	0.107751i
$321$		0			0
$322$	−105.242	+	105.242i	−0.326837	+	0.326837i
$323$	338.318	+	338.318i	1.04742	+	1.04742i
$324$		0			0
$325$	−98.2824	+	28.0234i	−0.302407	+	0.0862259i
$326$	230.149			0.705977
$327$		0			0
$328$	−99.0078	−	99.0078i	−0.301853	−	0.301853i
$329$			38.6888i			0.117595i
$330$		0			0
$331$	−246.161			−0.743690			−0.371845	−	0.928295i	$-0.621275\pi$
$331$	−246.161			−0.743690			−0.371845	+	0.928295i	$0.621275\pi$
$332$	−101.935	+	101.935i	−0.307034	+	0.307034i
$333$		0			0
$334$			442.715i			1.32549i
$335$	−74.6016	+	287.578i	−0.222691	+	0.858442i
$336$		0			0
$337$	−318.765	+	318.765i	−0.945889	+	0.945889i	−0.998609	−	0.0527200i	$-0.983211\pi$
$337$	−318.765	+	318.765i	−0.945889	+	0.945889i	0.0527200	+	0.998609i	$0.483211\pi$
$338$	−152.288	−	152.288i	−0.450557	−	0.450557i
$339$		0			0
$340$	269.207	+	69.8360i	0.791787	+	0.205400i
$341$	34.3171			0.100637
$342$		0			0
$343$	−208.298	−	208.298i	−0.607284	−	0.607284i
$344$		−	129.179i		−	0.375522i
$345$		0			0
$346$	306.467			0.885742
$347$	188.142	−	188.142i	0.542197	−	0.542197i	−0.381975	−	0.924172i	$-0.624756\pi$
$347$	188.142	−	188.142i	0.542197	−	0.542197i	0.924172	+	0.381975i	$0.124756\pi$
$348$		0			0
$349$		−	114.626i		−	0.328442i	−0.986424	−	0.164221i	$-0.947489\pi$
$349$		−	114.626i		−	0.328442i	0.986424	−	0.164221i	$-0.0525110\pi$
$350$	105.383	+	58.6204i	0.301094	+	0.167487i
$351$		0			0
$352$	−5.13095	+	5.13095i	−0.0145766	+	0.0145766i
$353$	72.6933	+	72.6933i	0.205930	+	0.205930i	0.802535	−	0.596605i	$-0.203484\pi$
$353$	72.6933	+	72.6933i	0.205930	+	0.205930i	−0.596605	+	0.802535i	$0.703484\pi$
$354$		0			0
$355$	−23.8895	+	14.0480i	−0.0672943	+	0.0395718i
$356$	93.9146			0.263805
$357$		0			0
$358$	−164.771	−	164.771i	−0.460254	−	0.460254i
$359$			190.904i			0.531767i	0.964005	+	0.265883i	$0.0856636\pi$
$359$			190.904i			0.531767i	−0.964005	+	0.265883i	$0.914336\pi$
$360$		0			0
$361$	65.0483			0.180189
$362$	−5.29281	+	5.29281i	−0.0146210	+	0.0146210i
$363$		0			0
$364$		−	27.8865i		−	0.0766113i
$365$	334.709	+	86.8281i	0.917011	+	0.237885i
$366$		0			0
$367$	370.526	−	370.526i	1.00961	−	1.00961i	0.00965302	−	0.999953i	$-0.496927\pi$
$367$	370.526	−	370.526i	1.00961	−	1.00961i	0.999953	−	0.00965302i	$-0.00307270\pi$
$368$	−87.2724	−	87.2724i	−0.237153	−	0.237153i
$369$		0			0
$370$	32.4346	+	55.1570i	0.0876610	+	0.149073i
$371$	−0.844010			−0.00227496
$372$		0			0
$373$	155.325	+	155.325i	0.416421	+	0.416421i	0.883968	−	0.467547i	$-0.154862\pi$
$373$	155.325	+	155.325i	0.416421	+	0.416421i	−0.467547	+	0.883968i	$0.654862\pi$
$374$		−	50.4524i		−	0.134900i
$375$		0			0
$376$	−32.0830			−0.0853271
$377$	−153.869	+	153.869i	−0.408141	+	0.408141i
$378$		0			0
$379$		−	542.378i		−	1.43108i	−0.698574	−	0.715538i	$-0.746181\pi$
$379$		−	542.378i		−	1.43108i	0.698574	−	0.715538i	$-0.253819\pi$
$380$	−148.293	+	87.2025i	−0.390245	+	0.229480i
$381$		0			0
$382$	−79.4156	+	79.4156i	−0.207894	+	0.207894i
$383$	238.639	+	238.639i	0.623079	+	0.623079i	0.946317	−	0.323239i	$-0.104772\pi$
$383$	238.639	+	238.639i	0.623079	+	0.623079i	−0.323239	+	0.946317i	$0.604772\pi$
$384$		0			0
$385$	5.49305	−	21.1749i	0.0142677	−	0.0549997i
$386$	−240.292			−0.622519
$387$		0			0
$388$	225.765	+	225.765i	0.581869	+	0.581869i
$389$		−	174.765i		−	0.449269i	−0.974443	−	0.224634i	$-0.927881\pi$
$389$		−	174.765i		−	0.449269i	0.974443	−	0.224634i	$-0.0721188\pi$
$390$		0			0
$391$	858.146			2.19475
$392$	74.7329	−	74.7329i	0.190645	−	0.190645i
$393$		0			0
$394$			76.3465i			0.193773i
$395$	−247.945	−	421.645i	−0.627708	−	1.06746i
$396$		0			0
$397$	−249.989	+	249.989i	−0.629695	+	0.629695i	−0.947991	−	0.318296i	$-0.896889\pi$
$397$	−249.989	+	249.989i	−0.629695	+	0.629695i	0.318296	+	0.947991i	$0.396889\pi$
$398$	90.0401	+	90.0401i	0.226231	+	0.226231i
$399$		0			0
$400$	−48.6114	+	87.3896i	−0.121528	+	0.218474i
$401$	131.561			0.328081			0.164041	−	0.986454i	$-0.447547\pi$
$401$	131.561			0.328081			0.164041	+	0.986454i	$0.447547\pi$
$402$		0			0
$403$	−77.3334	−	77.3334i	−0.191894	−	0.191894i
$404$		−	148.670i		−	0.367995i
$405$		0			0
$406$	256.761			0.632416
$407$	8.20781	−	8.20781i	0.0201666	−	0.0201666i
$408$		0			0
$409$		−	457.799i		−	1.11931i	−0.828725	−	0.559656i	$-0.810933\pi$
$409$		−	457.799i		−	1.11931i	0.828725	−	0.559656i	$-0.189067\pi$
$410$	−87.8971	+	338.830i	−0.214383	+	0.826415i
$411$		0			0
$412$	−22.4570	+	22.4570i	−0.0545074	+	0.0545074i
$413$	246.178	+	246.178i	0.596072	+	0.596072i
$414$		0			0
$415$	348.849	+	90.4961i	0.840600	+	0.218063i
$416$	23.1251			0.0555892
$417$		0			0
$418$	22.0673	+	22.0673i	0.0527925	+	0.0527925i
$419$			205.557i			0.490590i	0.969448	+	0.245295i	$0.0788849\pi$
$419$			205.557i			0.490590i	−0.969448	+	0.245295i	$0.921115\pi$
$420$		0			0
$421$	−67.9739			−0.161458			−0.0807291	−	0.996736i	$-0.525725\pi$
$421$	−67.9739			−0.161458			−0.0807291	+	0.996736i	$0.525725\pi$
$422$	371.619	−	371.619i	0.880614	−	0.880614i
$423$		0			0
$424$		−	0.699901i		−	0.00165071i
$425$	−190.652	−	668.646i	−0.448593	−	1.57328i
$426$		0			0
$427$	−127.063	+	127.063i	−0.297572	+	0.297572i
$428$	−229.056	−	229.056i	−0.535177	−	0.535177i
$429$		0			0
$430$	−278.384	+	163.701i	−0.647405	+	0.380701i
$431$	99.6045			0.231101			0.115550	−	0.993302i	$-0.463137\pi$
$431$	99.6045			0.231101			0.115550	+	0.993302i	$0.463137\pi$
$432$		0			0
$433$	−459.635	−	459.635i	−1.06151	−	1.06151i	−0.997980	−	0.0635322i	$-0.979763\pi$
$433$	−459.635	−	459.635i	−1.06151	−	1.06151i	−0.0635322	−	0.997980i	$-0.520237\pi$
$434$			129.046i			0.297341i
$435$		0			0
$436$	−160.375			−0.367833
$437$	−375.342	+	375.342i	−0.858906	+	0.858906i
$438$		0			0
$439$		−	58.3325i		−	0.132876i	−0.997791	−	0.0664379i	$-0.978837\pi$
$439$		−	58.3325i		−	0.132876i	0.997791	−	0.0664379i	$-0.0211634\pi$
$440$	17.5594	+	4.55515i	0.0399078	+	0.0103526i
$441$		0			0
$442$	−113.694	+	113.694i	−0.257227	+	0.257227i
$443$	−171.243	−	171.243i	−0.386554	−	0.386554i	0.486903	−	0.873456i	$-0.338127\pi$
$443$	−171.243	−	171.243i	−0.386554	−	0.386554i	−0.873456	+	0.486903i	$0.838127\pi$
$444$		0			0
$445$	−119.012	−	202.388i	−0.267443	−	0.454804i
$446$	−307.880			−0.690315
$447$		0			0
$448$	−19.2944	−	19.2944i	−0.0430678	−	0.0430678i
$449$		−	769.773i		−	1.71442i	−0.514970	−	0.857208i	$-0.672197\pi$
$449$		−	769.773i		−	1.71442i	0.514970	−	0.857208i	$-0.327803\pi$
$450$		0			0
$451$	63.5005			0.140799
$452$	211.318	−	211.318i	0.467519	−	0.467519i
$453$		0			0
$454$			49.6687i			0.109402i
$455$	−60.0960	+	35.3389i	−0.132079	+	0.0776679i
$456$		0			0
$457$	−12.7691	+	12.7691i	−0.0279411	+	0.0279411i	−0.720939	−	0.692998i	$-0.756289\pi$
$457$	−12.7691	+	12.7691i	−0.0279411	+	0.0279411i	0.692998	+	0.720939i	$0.256289\pi$
$458$	140.049	+	140.049i	0.305784	+	0.305784i
$459$		0			0
$460$	−77.4786	+	298.668i	−0.168432	+	0.649279i
$461$	589.157			1.27800			0.638999	−	0.769208i	$-0.279349\pi$
$461$	589.157			1.27800			0.638999	+	0.769208i	$0.279349\pi$
$462$		0			0
$463$	−463.077	−	463.077i	−1.00017	−	1.00017i	−1.00000		0.000165541i	$-0.999947\pi$
$463$	−463.077	−	463.077i	−1.00017	−	1.00017i	−0.000165541	−	1.00000i	$-0.500053\pi$
$464$			212.921i			0.458881i
$465$		0			0
$466$	−255.945			−0.549239
$467$	−61.7235	+	61.7235i	−0.132170	+	0.132170i	−0.770097	−	0.637927i	$-0.779792\pi$
$467$	−61.7235	+	61.7235i	−0.132170	+	0.132170i	0.637927	+	0.770097i	$0.279792\pi$
$468$		0			0
$469$			202.667i			0.432126i
$470$	40.6568	+	69.1394i	0.0865038	+	0.147105i
$471$		0			0
$472$	−204.145	+	204.145i	−0.432510	+	0.432510i
$473$	41.4258	+	41.4258i	0.0875810	+	0.0875810i
$474$		0			0
$475$	375.846	+	209.068i	0.791255	+	0.440144i
$476$	189.721			0.398573
$477$		0			0
$478$	72.0469	+	72.0469i	0.150726	+	0.150726i
$479$		−	163.627i		−	0.341602i	−0.985306	−	0.170801i	$-0.945365\pi$
$479$		−	163.627i		−	0.341602i	0.985306	−	0.170801i	$-0.0546355\pi$
$480$		0			0
$481$	−36.9925			−0.0769074
$482$	268.481	−	268.481i	0.557014	−	0.557014i
$483$		0			0
$484$			238.709i			0.493201i
$485$	200.430	−	772.627i	0.413257	−	1.59304i
$486$		0			0
$487$	−359.366	+	359.366i	−0.737918	+	0.737918i	−0.972175	−	0.234257i	$-0.924734\pi$
$487$	−359.366	+	359.366i	−0.737918	+	0.737918i	0.234257	+	0.972175i	$0.424734\pi$
$488$	−105.368	−	105.368i	−0.215918	−	0.215918i
$489$		0			0
$490$	−255.755	−	66.3464i	−0.521950	−	0.135401i
$491$	57.0287			0.116148			0.0580740	−	0.998312i	$-0.481504\pi$
$491$	57.0287			0.116148			0.0580740	+	0.998312i	$0.481504\pi$
$492$		0			0
$493$	−1046.82	−	1046.82i	−2.12337	−	2.12337i
$494$		−	99.4567i		−	0.201329i
$495$		0			0
$496$	−107.012			−0.215750
$497$	−13.3680	+	13.3680i	−0.0268974	+	0.0268974i
$498$		0			0
$499$		−	886.807i		−	1.77717i	−0.458715	−	0.888584i	$-0.651690\pi$
$499$		−	886.807i		−	1.77717i	0.458715	−	0.888584i	$-0.348310\pi$
$500$	249.928	−	5.98502i	0.499857	−	0.0119700i
$501$		0			0
$502$	251.209	−	251.209i	0.500416	−	0.500416i
$503$	−70.9445	−	70.9445i	−0.141043	−	0.141043i	0.633060	−	0.774103i	$-0.281799\pi$
$503$	−70.9445	−	70.9445i	−0.141043	−	0.141043i	−0.774103	+	0.633060i	$0.781799\pi$
$504$		0			0
$505$	−320.387	+	188.401i	−0.634429	+	0.373070i
$506$	55.9738			0.110620
$507$		0			0
$508$	222.830	+	222.830i	0.438642	+	0.438642i
$509$		−	220.529i		−	0.433260i	−0.976254	−	0.216630i	$-0.930493\pi$
$509$		−	220.529i		−	0.433260i	0.976254	−	0.216630i	$-0.0695065\pi$
$510$		0			0
$511$	235.882			0.461609
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$			114.236i			0.222248i
$515$	76.8538	+	19.9369i	0.149231	+	0.0387124i
$516$		0			0
$517$	10.2885	−	10.2885i	0.0199004	−	0.0199004i
$518$	30.8646	+	30.8646i	0.0595841	+	0.0595841i
$519$		0			0
$520$	−29.3050	−	49.8350i	−0.0563558	−	0.0958366i
$521$	315.280			0.605144			0.302572	−	0.953127i	$-0.402155\pi$
$521$	315.280			0.605144			0.302572	+	0.953127i	$0.402155\pi$
$522$		0			0
$523$	550.337	+	550.337i	1.05227	+	1.05227i	0.998556	+	0.0537127i	$0.0171055\pi$
$523$	550.337	+	550.337i	1.05227	+	1.05227i	0.0537127	+	0.998556i	$0.482894\pi$
$524$			8.20193i			0.0156525i
$525$		0			0
$526$	202.915			0.385771
$527$	526.123	−	526.123i	0.998337	−	0.998337i
$528$		0			0
$529$			423.058i			0.799732i
$530$	−1.50830	+	0.886942i	−0.00284585	+	0.00167348i
$531$		0			0
$532$	−82.9815	+	82.9815i	−0.155980	+	0.155980i
$533$	−143.098	−	143.098i	−0.268476	−	0.268476i
$534$		0			0
$535$	−203.351	+	783.887i	−0.380095	+	1.46521i
$536$	−168.063			−0.313551
$537$		0			0
$538$	341.458	+	341.458i	0.634680	+	0.634680i
$539$			47.9314i			0.0889265i
$540$		0			0
$541$	86.5875			0.160051			0.0800254	−	0.996793i	$-0.474500\pi$
$541$	86.5875			0.160051			0.0800254	+	0.996793i	$0.474500\pi$
$542$	157.125	−	157.125i	0.289899	−	0.289899i
$543$		0			0
$544$			157.327i			0.289205i
$545$	203.233	+	345.611i	0.372905	+	0.634149i
$546$		0			0
$547$	359.715	−	359.715i	0.657614	−	0.657614i	−0.297201	−	0.954815i	$-0.596053\pi$
$547$	359.715	−	359.715i	0.657614	−	0.657614i	0.954815	+	0.297201i	$0.0960532\pi$
$548$	−197.022	−	197.022i	−0.359529	−	0.359529i
$549$		0			0
$550$	−12.4356	−	43.6134i	−0.0226101	−	0.0792971i
$551$	915.732			1.66195
$552$		0			0
$553$	−235.943	−	235.943i	−0.426660	−	0.426660i
$554$			236.379i			0.426677i
$555$		0			0
$556$	−46.7941			−0.0841621
$557$	−145.517	+	145.517i	−0.261252	+	0.261252i	−0.825563	−	0.564311i	$-0.809142\pi$
$557$	−145.517	+	145.517i	−0.261252	+	0.261252i	0.564311	+	0.825563i	$0.309142\pi$
$558$		0			0
$559$		−	186.706i		−	0.333999i
$560$	−17.1292	+	66.0303i	−0.0305878	+	0.117911i
$561$		0			0
$562$	−201.462	+	201.462i	−0.358473	+	0.358473i
$563$	−362.028	−	362.028i	−0.643033	−	0.643033i	0.308267	−	0.951300i	$-0.400251\pi$
$563$	−362.028	−	362.028i	−0.643033	−	0.643033i	−0.951300	+	0.308267i	$0.900251\pi$
$564$		0			0
$565$	−723.186	−	187.604i	−1.27998	−	0.332043i
$566$	−84.1024			−0.148591
$567$		0			0
$568$	−11.0855	−	11.0855i	−0.0195167	−	0.0195167i
$569$			386.149i			0.678646i	0.940670	+	0.339323i	$0.110198\pi$
$569$			386.149i			0.678646i	−0.940670	+	0.339323i	$0.889802\pi$
$570$		0			0
$571$	153.581			0.268968			0.134484	−	0.990916i	$-0.457062\pi$
$571$	153.581			0.268968			0.134484	+	0.990916i	$0.457062\pi$
$572$	−7.41586	+	7.41586i	−0.0129648	+	0.0129648i
$573$		0			0
$574$			238.787i			0.416005i
$575$	741.820	−	211.516i	1.29012	−	0.367855i
$576$		0			0
$577$	−115.299	+	115.299i	−0.199825	+	0.199825i	−0.799925	−	0.600100i	$-0.795127\pi$
$577$	−115.299	+	115.299i	−0.199825	+	0.199825i	0.600100	+	0.799925i	$0.295127\pi$
$578$	−484.497	−	484.497i	−0.838231	−	0.838231i
$579$		0			0
$580$	458.848	−	269.822i	0.791118	−	0.465209i
$581$	245.847			0.423145
$582$		0			0
$583$	0.224447	+	0.224447i	0.000384987	+	0.000384987i
$584$			195.607i			0.334944i
$585$		0			0
$586$	−455.815			−0.777841
$587$	159.506	−	159.506i	0.271731	−	0.271731i	−0.558066	−	0.829797i	$-0.688456\pi$
$587$	159.506	−	159.506i	0.271731	−	0.271731i	0.829797	+	0.558066i	$0.188456\pi$
$588$		0			0
$589$			460.239i			0.781391i
$590$	698.636	+	181.236i	1.18413	+	0.307179i
$591$		0			0
$592$	−25.5947	+	25.5947i	−0.0432342	+	0.0432342i
$593$	−250.553	−	250.553i	−0.422518	−	0.422518i	0.463552	−	0.886070i	$-0.346575\pi$
$593$	−250.553	−	250.553i	−0.422518	−	0.422518i	−0.886070	+	0.463552i	$0.846575\pi$
$594$		0			0
$595$	−240.422	−	408.852i	−0.404070	−	0.687146i
$596$	−450.983			−0.756683
$597$		0			0
$598$	−126.136	−	126.136i	−0.210930	−	0.210930i
$599$		−	450.877i		−	0.752716i	−0.926474	−	0.376358i	$-0.877176\pi$
$599$		−	450.877i		−	0.752716i	0.926474	−	0.376358i	$-0.122824\pi$
$600$		0			0
$601$	−368.430			−0.613028			−0.306514	−	0.951866i	$-0.599163\pi$
$601$	−368.430			−0.613028			−0.306514	+	0.951866i	$0.599163\pi$
$602$	−155.777	+	155.777i	−0.258766	+	0.258766i
$603$		0			0
$604$		−	497.376i		−	0.823470i
$605$	514.423	−	302.502i	0.850285	−	0.500003i
$606$		0			0
$607$	−443.996	+	443.996i	−0.731459	+	0.731459i	−0.970909	−	0.239450i	$-0.923033\pi$
$607$	−443.996	+	443.996i	−0.731459	+	0.731459i	0.239450	+	0.970909i	$0.423033\pi$
$608$	−68.8130	−	68.8130i	−0.113179	−	0.113179i
$609$		0			0
$610$	−93.5437	+	360.597i	−0.153350	+	0.591143i
$611$	−46.3701			−0.0758922
$612$		0			0
$613$	−530.799	−	530.799i	−0.865904	−	0.865904i	0.126112	−	0.992016i	$-0.459750\pi$
$613$	−530.799	−	530.799i	−0.865904	−	0.865904i	−0.992016	+	0.126112i	$0.959750\pi$
$614$		−	131.211i		−	0.213698i
$615$		0			0
$616$	12.3748			0.0200890
$617$	292.377	−	292.377i	0.473868	−	0.473868i	−0.429296	−	0.903164i	$-0.641238\pi$
$617$	292.377	−	292.377i	0.473868	−	0.473868i	0.903164	+	0.429296i	$0.141238\pi$
$618$		0			0
$619$		−	359.571i		−	0.580890i	−0.956892	−	0.290445i	$-0.906197\pi$
$619$		−	359.571i		−	0.580890i	0.956892	−	0.290445i	$-0.0938034\pi$
$620$	135.610	+	230.613i	0.218726	+	0.371957i
$621$		0			0
$622$	−243.797	+	243.797i	−0.391957	+	0.391957i
$623$	−113.251	−	113.251i	−0.181784	−	0.181784i
$624$		0			0
$625$	−329.617	−	531.016i	−0.527387	−	0.849625i
$626$	332.967			0.531897
$627$		0			0
$628$	76.3749	+	76.3749i	0.121616	+	0.121616i
$629$		−	251.671i		−	0.400113i
$630$		0			0
$631$	1215.94			1.92701			0.963505	−	0.267690i	$-0.0862602\pi$
$631$	1215.94			1.92701			0.963505	+	0.267690i	$0.0862602\pi$
$632$	195.657	−	195.657i	0.309585	−	0.309585i
$633$		0			0
$634$			669.699i			1.05631i
$635$	197.824	−	762.582i	0.311534	−	1.20092i
$636$		0			0
$637$	108.013	−	108.013i	0.169565	−	0.169565i
$638$	−68.2804	−	68.2804i	−0.107023	−	0.107023i
$639$		0			0
$640$	−54.7561	−	14.2045i	−0.0855564	−	0.0221945i
$641$	−547.803			−0.854607			−0.427303	−	0.904108i	$-0.640536\pi$
$641$	−547.803			−0.854607			−0.427303	+	0.904108i	$0.640536\pi$
$642$		0			0
$643$	517.011	+	517.011i	0.804060	+	0.804060i	0.983727	−	0.179667i	$-0.0575021\pi$
$643$	517.011	+	517.011i	0.804060	+	0.804060i	−0.179667	+	0.983727i	$0.557502\pi$
$644$			210.483i			0.326837i
$645$		0			0
$646$	676.636			1.04742
$647$	−374.569	+	374.569i	−0.578932	+	0.578932i	−0.934609	−	0.355677i	$-0.884250\pi$
$647$	−374.569	+	374.569i	−0.578932	+	0.578932i	0.355677	+	0.934609i	$0.384250\pi$
$648$		0			0
$649$		−	130.932i		−	0.201744i
$650$	−70.2589	+	126.306i	−0.108091	+	0.194317i
$651$		0			0
$652$	230.149	−	230.149i	0.352989	−	0.352989i
$653$	−636.747	−	636.747i	−0.975110	−	0.975110i	0.0245879	−	0.999698i	$-0.492173\pi$
$653$	−636.747	−	636.747i	−0.975110	−	0.975110i	−0.999698	+	0.0245879i	$0.992173\pi$
$654$		0			0
$655$	17.6753	−	10.3938i	0.0269852	−	0.0158684i
$656$	−198.016			−0.301853
$657$		0			0
$658$	38.6888	+	38.6888i	0.0587976	+	0.0587976i
$659$		−	151.436i		−	0.229796i	−0.993377	−	0.114898i	$-0.963346\pi$
$659$		−	151.436i		−	0.229796i	0.993377	−	0.114898i	$-0.0366541\pi$
$660$		0			0
$661$	53.4047			0.0807938			0.0403969	−	0.999184i	$-0.487138\pi$
$661$	53.4047			0.0807938			0.0403969	+	0.999184i	$0.487138\pi$
$662$	−246.161	+	246.161i	−0.371845	+	0.371845i
$663$		0			0
$664$			203.871i			0.307034i
$665$	283.984	+	73.6693i	0.427044	+	0.110781i
$666$		0			0
$667$	1161.38	−	1161.38i	1.74120	−	1.74120i
$668$	442.715	+	442.715i	0.662747	+	0.662747i
$669$		0			0
$670$	212.976	+	362.180i	0.317875	+	0.540567i
$671$	67.5799			0.100715
$672$		0			0
$673$	472.441	+	472.441i	0.701992	+	0.701992i	0.964838	−	0.262846i	$-0.0846610\pi$
$673$	472.441	+	472.441i	0.701992	+	0.701992i	−0.262846	+	0.964838i	$0.584661\pi$
$674$			637.529i			0.945889i
$675$		0			0
$676$	−304.577			−0.450557
$677$	−381.070	+	381.070i	−0.562880	+	0.562880i	−0.930124	−	0.367245i	$-0.880301\pi$
$677$	−381.070	+	381.070i	−0.562880	+	0.562880i	0.367245	+	0.930124i	$0.380301\pi$
$678$		0			0
$679$		−	544.500i		−	0.801914i
$680$	339.044	−	199.371i	0.498593	−	0.293193i
$681$		0			0
$682$	34.3171	−	34.3171i	0.0503184	−	0.0503184i
$683$	40.8892	+	40.8892i	0.0598670	+	0.0598670i	0.736406	−	0.676539i	$-0.236521\pi$
$683$	40.8892	+	40.8892i	0.0598670	+	0.0598670i	−0.676539	+	0.736406i	$0.736521\pi$
$684$		0			0
$685$	−174.912	+	674.260i	−0.255346	+	0.984321i
$686$	−416.597			−0.607284
$687$		0			0
$688$	−129.179	−	129.179i	−0.187761	−	0.187761i
$689$		−	1.01158i		−	0.00146819i
$690$		0			0
$691$	805.111			1.16514			0.582570	−	0.812781i	$-0.302047\pi$
$691$	805.111			1.16514			0.582570	+	0.812781i	$0.302047\pi$
$692$	306.467	−	306.467i	0.442871	−	0.442871i
$693$		0			0
$694$		−	376.285i		−	0.542197i
$695$	59.2994	+	100.842i	0.0853228	+	0.145097i
$696$		0			0
$697$	973.540	−	973.540i	1.39676	−	1.39676i
$698$	−114.626	−	114.626i	−0.164221	−	0.164221i
$699$		0			0
$700$	164.003	−	46.7625i	0.234290	−	0.0668036i
$701$	1140.79			1.62738			0.813690	−	0.581299i	$-0.197455\pi$
$701$	1140.79			1.62738			0.813690	+	0.581299i	$0.197455\pi$
$702$		0			0
$703$	110.078	+	110.078i	0.156583	+	0.156583i
$704$			10.2619i			0.0145766i
$705$		0			0
$706$	145.387			0.205930
$707$	−179.281	+	179.281i	−0.253580	+	0.253580i
$708$		0			0
$709$		−	740.214i		−	1.04403i	−0.852938	−	0.522013i	$-0.825181\pi$
$709$		−	740.214i		−	1.04403i	0.852938	−	0.522013i	$-0.174819\pi$
$710$	−9.84149	+	37.9375i	−0.0138613	+	0.0534330i
$711$		0			0
$712$	93.9146	−	93.9146i	0.131903	−	0.131903i
$713$	583.700	+	583.700i	0.818654	+	0.818654i
$714$		0			0
$715$	25.3790	+	6.58365i	0.0354951	+	0.00920790i
$716$	−329.542			−0.460254
$717$		0			0
$718$	190.904	+	190.904i	0.265883	+	0.265883i
$719$			595.037i			0.827590i	0.910370	+	0.413795i	$0.135797\pi$
$719$			595.037i			0.827590i	−0.910370	+	0.413795i	$0.864203\pi$
$720$		0			0
$721$	54.1618			0.0751204
$722$	65.0483	−	65.0483i	0.0900946	−	0.0900946i
$723$		0			0
$724$			10.5856i			0.0146210i
$725$	−1162.94	−	646.898i	−1.60406	−	0.892274i
$726$		0			0
$727$	−780.586	+	780.586i	−1.07371	+	1.07371i	−0.0766498	+	0.997058i	$0.524422\pi$
$727$	−780.586	+	780.586i	−1.07371	+	1.07371i	−0.997058	+	0.0766498i	$0.975578\pi$
$728$	−27.8865	−	27.8865i	−0.0383057	−	0.0383057i
$729$		0			0
$730$	421.537	−	247.881i	0.577448	−	0.339563i
$731$	1270.22			1.73764
$732$		0			0
$733$	−154.394	−	154.394i	−0.210633	−	0.210633i	0.593903	−	0.804536i	$-0.297586\pi$
$733$	−154.394	−	154.394i	−0.210633	−	0.210633i	−0.804536	+	0.593903i	$0.797586\pi$
$734$		−	741.051i		−	1.00961i
$735$		0			0
$736$	−174.545			−0.237153
$737$	53.8953	−	53.8953i	0.0731279	−	0.0731279i
$738$		0			0
$739$			393.578i			0.532583i	0.963893	+	0.266291i	$0.0857983\pi$
$739$			393.578i			0.532583i	−0.963893	+	0.266291i	$0.914202\pi$
$740$	87.5915	+	22.7224i	0.118367	+	0.0307060i
$741$		0			0
$742$	−0.844010	+	0.844010i	−0.00113748	+	0.00113748i
$743$	682.919	+	682.919i	0.919138	+	0.919138i	0.996967	−	0.0778289i	$-0.0247988\pi$
$743$	682.919	+	682.919i	0.919138	+	0.919138i	−0.0778289	+	0.996967i	$0.524799\pi$
$744$		0			0
$745$	571.503	+	971.877i	0.767119	+	1.30453i
$746$	310.650			0.416421
$747$		0			0
$748$	−50.4524	−	50.4524i	−0.0674498	−	0.0674498i
$749$			552.436i			0.737564i
$750$		0			0
$751$	225.440			0.300186			0.150093	−	0.988672i	$-0.452043\pi$
$751$	225.440			0.300186			0.150093	+	0.988672i	$0.452043\pi$
$752$	−32.0830	+	32.0830i	−0.0426635	+	0.0426635i
$753$		0			0
$754$			307.738i			0.408141i
$755$	−1071.85	+	630.294i	−1.41967	+	0.834826i
$756$		0			0
$757$	257.146	−	257.146i	0.339691	−	0.339691i	−0.516560	−	0.856251i	$-0.672788\pi$
$757$	257.146	−	257.146i	0.339691	−	0.339691i	0.856251	+	0.516560i	$0.172788\pi$
$758$	−542.378	−	542.378i	−0.715538	−	0.715538i
$759$		0			0
$760$	−61.0908	+	235.496i	−0.0803826	+	0.309863i
$761$	811.313			1.06611			0.533057	−	0.846079i	$-0.321043\pi$
$761$	811.313			1.06611			0.533057	+	0.846079i	$0.321043\pi$
$762$		0			0
$763$	193.396	+	193.396i	0.253468	+	0.253468i
$764$			158.831i			0.207894i
$765$		0			0
$766$	477.278			0.623079
$767$	−295.054	+	295.054i	−0.384686	+	0.384686i
$768$		0			0
$769$			276.246i			0.359228i	0.983737	+	0.179614i	$0.0574848\pi$
$769$			276.246i			0.359228i	−0.983737	+	0.179614i	$0.942515\pi$
$770$	−15.6818	−	26.6679i	−0.0203660	−	0.0346337i
$771$		0			0
$772$	−240.292	+	240.292i	−0.311260	+	0.311260i
$773$	−246.810	−	246.810i	−0.319288	−	0.319288i	0.529205	−	0.848494i	$-0.322490\pi$
$773$	−246.810	−	246.810i	−0.319288	−	0.319288i	−0.848494	+	0.529205i	$0.822490\pi$
$774$		0			0
$775$	325.126	−	584.484i	0.419517	−	0.754173i
$776$	451.530			0.581869
$777$		0			0
$778$	−174.765	−	174.765i	−0.224634	−	0.224634i
$779$			851.628i			1.09323i
$780$		0			0
$781$	7.10990			0.00910358
$782$	858.146	−	858.146i	1.09737	−	1.09737i
$783$		0			0
$784$		−	149.466i		−	0.190645i
$785$	67.8041	−	261.375i	0.0863747	−	0.332961i
$786$		0			0
$787$	237.350	−	237.350i	0.301588	−	0.301588i	−0.540047	−	0.841635i	$-0.681593\pi$
$787$	237.350	−	237.350i	0.301588	−	0.301588i	0.841635	+	0.540047i	$0.181593\pi$
$788$	76.3465	+	76.3465i	0.0968864	+	0.0968864i
$789$		0			0
$790$	−669.590	−	173.701i	−0.847583	−	0.219874i
$791$	−509.657			−0.644320
$792$		0			0
$793$	−152.291	−	152.291i	−0.192044	−	0.192044i
$794$			499.978i			0.629695i
$795$		0			0
$796$	180.080			0.226231
$797$	−539.640	+	539.640i	−0.677090	+	0.677090i	−0.959341	−	0.282251i	$-0.908919\pi$
$797$	−539.640	+	539.640i	−0.677090	+	0.677090i	0.282251	+	0.959341i	$0.408919\pi$
$798$		0			0
$799$		−	315.471i		−	0.394832i
$800$	38.7782	+	136.001i	0.0484727	+	0.170001i
$801$		0			0
$802$	131.561	−	131.561i	0.164041	−	0.164041i
$803$	−62.7282	−	62.7282i	−0.0781173	−	0.0781173i
$804$		0			0
$805$	453.595	−	266.732i	0.563472	−	0.331345i
$806$	−154.667			−0.191894
$807$		0			0
$808$	−148.670	−	148.670i	−0.183998	−	0.183998i
$809$		−	195.169i		−	0.241248i	−0.992698	−	0.120624i	$-0.961511\pi$
$809$		−	195.169i		−	0.241248i	0.992698	−	0.120624i	$-0.0384895\pi$
$810$		0			0
$811$	−1111.22			−1.37018			−0.685090	−	0.728459i	$-0.740237\pi$
$811$	−1111.22			−1.37018			−0.685090	+	0.728459i	$0.740237\pi$
$812$	256.761	−	256.761i	0.316208	−	0.316208i
$813$		0			0
$814$		−	16.4156i		−	0.0201666i
$815$	−787.628	−	204.321i	−0.966415	−	0.250701i
$816$		0			0
$817$	−555.577	+	555.577i	−0.680020	+	0.680020i
$818$	−457.799	−	457.799i	−0.559656	−	0.559656i
$819$		0			0
$820$	250.933	+	426.727i	0.306016	+	0.520399i
$821$	−1358.56			−1.65476			−0.827382	−	0.561639i	$-0.810171\pi$
$821$	−1358.56			−1.65476			−0.827382	+	0.561639i	$0.810171\pi$
$822$		0			0
$823$	791.386	+	791.386i	0.961587	+	0.961587i	0.999289	−	0.0377018i	$-0.0120037\pi$
$823$	791.386	+	791.386i	0.961587	+	0.961587i	−0.0377018	+	0.999289i	$0.512004\pi$
$824$			44.9141i			0.0545074i
$825$		0			0
$826$	492.356			0.596072
$827$	−346.428	+	346.428i	−0.418897	+	0.418897i	−0.884823	−	0.465926i	$-0.845721\pi$
$827$	−346.428	+	346.428i	−0.418897	+	0.418897i	0.465926	+	0.884823i	$0.345721\pi$
$828$		0			0
$829$			1353.95i			1.63324i	0.577178	+	0.816618i	$0.304154\pi$
$829$			1353.95i			1.63324i	−0.577178	+	0.816618i	$0.695846\pi$
$830$	439.345	−	258.353i	0.529331	−	0.311268i
$831$		0			0
$832$	23.1251	−	23.1251i	0.0277946	−	0.0277946i
$833$	734.846	+	734.846i	0.882168	+	0.882168i
$834$		0			0
$835$	393.033	−	1515.08i	0.470699	−	1.81447i
$836$	44.1345			0.0527925
$837$		0			0
$838$	205.557	+	205.557i	0.245295	+	0.245295i
$839$		−	1100.51i		−	1.31170i	−0.754892	−	0.655849i	$-0.772311\pi$
$839$		−	1100.51i		−	1.31170i	0.754892	−	0.655849i	$-0.227689\pi$
$840$		0			0
$841$	−1992.45			−2.36915
$842$	−67.9739	+	67.9739i	−0.0807291	+	0.0807291i
$843$		0			0
$844$		−	743.239i		−	0.880614i
$845$	385.972	+	656.369i	0.456771	+	0.776768i
$846$		0			0
$847$	287.859	−	287.859i	0.339857	−	0.339857i
$848$	−0.699901	−	0.699901i	−0.000825355	−	0.000825355i
$849$		0			0
$850$	−859.298	−	477.994i	−1.01094	−	0.562346i
$851$	279.213			0.328100
$852$		0			0
$853$	−27.6294	−	27.6294i	−0.0323908	−	0.0323908i	0.690726	−	0.723117i	$-0.257291\pi$
$853$	−27.6294	−	27.6294i	−0.0323908	−	0.0323908i	−0.723117	+	0.690726i	$0.757291\pi$
$854$			254.127i			0.297572i
$855$		0			0
$856$	−458.111			−0.535177
$857$	−642.173	+	642.173i	−0.749327	+	0.749327i	−0.974353	−	0.225026i	$-0.927753\pi$
$857$	−642.173	+	642.173i	−0.749327	+	0.749327i	0.225026	+	0.974353i	$0.427753\pi$
$858$		0			0
$859$			1289.26i			1.50089i	0.660935	+	0.750443i	$0.270160\pi$
$859$			1289.26i			1.50089i	−0.660935	+	0.750443i	$0.729840\pi$
$860$	−114.683	+	442.085i	−0.133352	+	0.514053i
$861$		0			0
$862$	99.6045	−	99.6045i	0.115550	−	0.115550i
$863$	−230.587	−	230.587i	−0.267193	−	0.267193i	0.560775	−	0.827968i	$-0.310503\pi$
$863$	−230.587	−	230.587i	−0.267193	−	0.267193i	−0.827968	+	0.560775i	$0.810503\pi$
$864$		0			0
$865$	−1048.81	−	272.075i	−1.21249	−	0.314537i
$866$	−919.269			−1.06151
$867$		0			0
$868$	129.046	+	129.046i	0.148670	+	0.148670i
$869$			125.489i			0.144406i
$870$		0			0
$871$	−242.905			−0.278881
$872$	−160.375	+	160.375i	−0.183916	+	0.183916i
$873$		0			0
$874$			750.684i			0.858906i
$875$	−308.605	−	294.171i	−0.352692	−	0.336195i
$876$		0			0
$877$	559.046	−	559.046i	0.637453	−	0.637453i	−0.312473	−	0.949926i	$-0.601158\pi$
$877$	559.046	−	559.046i	0.637453	−	0.637453i	0.949926	+	0.312473i	$0.101158\pi$
$878$	−58.3325	−	58.3325i	−0.0664379	−	0.0664379i
$879$		0			0
$880$	22.1146	−	13.0043i	0.0251302	−	0.0147776i
$881$	−569.305			−0.646204			−0.323102	−	0.946364i	$-0.604726\pi$
$881$	−569.305			−0.646204			−0.323102	+	0.946364i	$0.604726\pi$
$882$		0			0
$883$	34.5889	+	34.5889i	0.0391720	+	0.0391720i	0.726421	−	0.687249i	$-0.241182\pi$
$883$	34.5889	+	34.5889i	0.0391720	+	0.0391720i	−0.687249	+	0.726421i	$0.741182\pi$
$884$			227.388i			0.257227i
$885$		0			0
$886$	−342.487			−0.386554
$887$	−913.625	+	913.625i	−1.03002	+	1.03002i	−0.0304811	+	0.999535i	$0.509704\pi$
$887$	−913.625	+	913.625i	−1.03002	+	1.03002i	−0.999535	+	0.0304811i	$0.990296\pi$
$888$		0			0
$889$		−	537.421i		−	0.604523i
$890$	−321.400	−	83.3755i	−0.361124	−	0.0936803i
$891$		0			0
$892$	−307.880	+	307.880i	−0.345157	+	0.345157i
$893$	137.983	+	137.983i	0.154516	+	0.154516i
$894$		0			0
$895$	417.608	+	710.168i	0.466601	+	0.793484i
$896$	−38.5887			−0.0430678
$897$		0			0
$898$	−769.773	−	769.773i	−0.857208	−	0.857208i
$899$		−	1424.07i		−	1.58406i
$900$		0			0
$901$	6.88210			0.00763830
$902$	63.5005	−	63.5005i	0.0703997	−	0.0703997i
$903$		0			0
$904$		−	422.637i		−	0.467519i
$905$	22.8122	−	13.4145i	0.0252069	−	0.0148227i
$906$		0			0
$907$	90.9091	−	90.9091i	0.100230	−	0.100230i	−0.655213	−	0.755444i	$-0.727421\pi$
$907$	90.9091	−	90.9091i	0.100230	−	0.100230i	0.755444	+	0.655213i	$0.227421\pi$
$908$	49.6687	+	49.6687i	0.0547012	+	0.0547012i
$909$		0			0
$910$	−24.7571	+	95.4349i	−0.0272056	+	0.104873i
$911$	−1512.04			−1.65976			−0.829878	−	0.557945i	$-0.811590\pi$
$911$	−1512.04			−1.65976			−0.829878	+	0.557945i	$0.811590\pi$
$912$		0			0
$913$	−65.3781	−	65.3781i	−0.0716080	−	0.0716080i
$914$			25.5381i			0.0279411i
$915$		0			0
$916$	280.099			0.305784
$917$	9.89069	−	9.89069i	0.0107859	−	0.0107859i
$918$		0			0
$919$			1310.73i			1.42626i	0.701031	+	0.713131i	$0.252724\pi$
$919$			1310.73i			1.42626i	−0.701031	+	0.713131i	$0.747276\pi$
$920$	221.190	+	376.147i	0.240424	+	0.408856i
$921$		0			0
$922$	589.157	−	589.157i	0.638999	−	0.638999i
$923$	−16.0221	−	16.0221i	−0.0173587	−	0.0173587i
$924$		0			0
$925$	−62.0321	−	217.556i	−0.0670618	−	0.235196i
$926$	−926.153			−1.00017
$927$		0			0
$928$	212.921	+	212.921i	0.229441	+	0.229441i
$929$			520.108i			0.559858i	0.960021	+	0.279929i	$0.0903109\pi$
$929$			520.108i			0.559858i	−0.960021	+	0.279929i	$0.909689\pi$
$930$		0			0
$931$	−642.825			−0.690467
$932$	−255.945	+	255.945i	−0.274619	+	0.274619i
$933$		0			0
$934$			123.447i			0.132170i
$935$	−44.7907	+	172.661i	−0.0479045	+	0.184664i
$936$		0			0
$937$	−845.208	+	845.208i	−0.902037	+	0.902037i	−0.995612	−	0.0935755i	$-0.970170\pi$
$937$	−845.208	+	845.208i	−0.902037	+	0.902037i	0.0935755	+	0.995612i	$0.470170\pi$
$938$	202.667	+	202.667i	0.216063	+	0.216063i
$939$		0			0
$940$	109.796	+	28.4826i	0.116804	+	0.0303007i
$941$	1260.99			1.34005			0.670025	−	0.742339i	$-0.266283\pi$
$941$	1260.99			1.34005			0.670025	+	0.742339i	$0.266283\pi$
$942$		0			0
$943$	1080.08	+	1080.08i	1.14537	+	1.14537i
$944$			408.289i			0.432510i
$945$		0			0
$946$	82.8517			0.0875810
$947$	−425.531	+	425.531i	−0.449347	+	0.449347i	−0.895137	−	0.445790i	$-0.852923\pi$
$947$	−425.531	+	425.531i	−0.449347	+	0.449347i	0.445790	+	0.895137i	$0.352923\pi$
$948$		0			0
$949$			282.715i			0.297908i
$950$	584.914	−	166.778i	0.615699	−	0.175555i
$951$		0			0
$952$	189.721	−	189.721i	0.199287	−	0.199287i
$953$	211.288	+	211.288i	0.221708	+	0.221708i	0.809217	−	0.587509i	$-0.199891\pi$
$953$	211.288	+	211.288i	0.221708	+	0.221708i	−0.587509	+	0.809217i	$0.699891\pi$
$954$		0			0
$955$	342.284	−	201.277i	0.358413	−	0.210761i
$956$	144.094			0.150726
$957$		0			0
$958$	−163.627	−	163.627i	−0.170801	−	0.170801i
$959$			475.177i			0.495492i
$960$		0			0
$961$	−245.275			−0.255229
$962$	−36.9925	+	36.9925i	−0.0384537	+	0.0384537i
$963$		0			0
$964$		−	536.961i		−	0.557014i
$965$	822.343	+	213.327i	0.852169	+	0.221064i
$966$		0			0
$967$	−491.943	+	491.943i	−0.508731	+	0.508731i	−0.914137	−	0.405406i	$-0.867130\pi$
$967$	−491.943	+	491.943i	−0.508731	+	0.508731i	0.405406	+	0.914137i	$0.367130\pi$
$968$	238.709	+	238.709i	0.246600	+	0.246600i
$969$		0			0
$970$	−572.197	−	973.056i	−0.589894	−	1.00315i
$971$	−1004.59			−1.03459			−0.517297	−	0.855806i	$-0.673062\pi$
$971$	−1004.59			−1.03459			−0.517297	+	0.855806i	$0.673062\pi$
$972$		0			0
$973$	56.4290	+	56.4290i	0.0579948	+	0.0579948i
$974$			718.732i			0.737918i
$975$		0			0
$976$	−210.736			−0.215918
$977$	−1119.23	+	1119.23i	−1.14558	+	1.14558i	−0.158167	+	0.987412i	$0.550558\pi$
$977$	−1119.23	+	1119.23i	−1.14558	+	1.14558i	−0.987412	+	0.158167i	$0.949442\pi$
$978$		0			0
$979$			60.2339i			0.0615259i
$980$	−322.102	+	189.409i	−0.328675	+	0.193274i
$981$		0			0
$982$	57.0287	−	57.0287i	0.0580740	−	0.0580740i
$983$	−579.607	−	579.607i	−0.589631	−	0.589631i	0.347900	−	0.937532i	$-0.386895\pi$
$983$	−579.607	−	579.607i	−0.589631	−	0.589631i	−0.937532	+	0.347900i	$0.886895\pi$
$984$		0			0
$985$	67.7788	−	261.277i	0.0688110	−	0.265256i
$986$	−2093.64			−2.12337
$987$		0			0
$988$	−99.4567	−	99.4567i	−0.100665	−	0.100665i
$989$			1409.22i			1.42490i
$990$		0			0
$991$	−570.979			−0.576164			−0.288082	−	0.957606i	$-0.593018\pi$
$991$	−570.979			−0.576164			−0.288082	+	0.957606i	$0.593018\pi$
$992$	−107.012	+	107.012i	−0.107875	+	0.107875i
$993$		0			0
$994$			26.7360i			0.0268974i
$995$	−228.205	−	388.076i	−0.229351	−	0.390026i
$996$		0			0
$997$	−835.111	+	835.111i	−0.837624	+	0.837624i	−0.988546	−	0.150922i	$-0.951776\pi$
$997$	−835.111	+	835.111i	−0.837624	+	0.837624i	0.150922	+	0.988546i	$0.451776\pi$
$998$	−886.807	−	886.807i	−0.888584	−	0.888584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.g.k.163.1		12
3.2	odd	2		810.3.g.i.163.6		12
5.2	odd	4	inner	810.3.g.k.487.1		12
9.2	odd	6		270.3.l.b.253.4		24
9.4	even	3		90.3.k.a.43.4	yes	24
9.5	odd	6		270.3.l.b.73.1		24
9.7	even	3		90.3.k.a.13.6	yes	24
15.2	even	4		810.3.g.i.487.6		12
45.2	even	12		270.3.l.b.37.1		24
45.7	odd	12		90.3.k.a.67.4	yes	24
45.22	odd	12		90.3.k.a.7.6	✓	24
45.32	even	12		270.3.l.b.127.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.6	✓	24	45.22	odd	12
90.3.k.a.13.6	yes	24	9.7	even	3
90.3.k.a.43.4	yes	24	9.4	even	3
90.3.k.a.67.4	yes	24	45.7	odd	12
270.3.l.b.37.1		24	45.2	even	12
270.3.l.b.73.1		24	9.5	odd	6
270.3.l.b.127.4		24	45.32	even	12
270.3.l.b.253.4		24	9.2	odd	6
810.3.g.i.163.6		12	3.2	odd	2
810.3.g.i.487.6		12	15.2	even	4
810.3.g.k.163.1		12	1.1	even	1	trivial
810.3.g.k.487.1		12	5.2	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.31004 + 2.53448i) q^{5} +(-2.41180 + 2.41180i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.77556 + 6.84452i) q^{10} +1.28274 q^{11} +(-2.89064 - 2.89064i) q^{13} +4.82359i q^{14} -4.00000 q^{16} +(19.6659 - 19.6659i) q^{17} +17.2032i q^{19} +(5.06896 + 8.62007i) q^{20} +(1.28274 - 1.28274i) q^{22} +(21.8181 + 21.8181i) q^{23} +(12.1528 - 21.8474i) q^{25} -5.78128 q^{26} +(4.82359 + 4.82359i) q^{28} -53.2302i q^{29} +26.7530 q^{31} +(-4.00000 + 4.00000i) q^{32} -39.3319i q^{34} +(4.28229 - 16.5076i) q^{35} +(6.39867 - 6.39867i) q^{37} +(17.2032 + 17.2032i) q^{38} +(13.6890 + 3.55112i) q^{40} +49.5039 q^{41} +(32.2949 + 32.2949i) q^{43} -2.56548i q^{44} +43.6362 q^{46} +(8.02075 - 8.02075i) q^{47} +37.3665i q^{49} +(-9.69454 - 34.0002i) q^{50} +(-5.78128 + 5.78128i) q^{52} +(0.174975 + 0.174975i) q^{53} +(-5.52865 + 3.25107i) q^{55} +9.64719 q^{56} +(-53.2302 - 53.2302i) q^{58} -102.072i q^{59} +52.6841 q^{61} +(26.7530 - 26.7530i) q^{62} +8.00000i q^{64} +(19.7850 + 5.13250i) q^{65} +(42.0158 - 42.0158i) q^{67} +(-39.3319 - 39.3319i) q^{68} +(-12.2253 - 20.7899i) q^{70} +5.54275 q^{71} +(-48.9018 - 48.9018i) q^{73} -12.7973i q^{74} +34.4065 q^{76} +(-3.09370 + 3.09370i) q^{77} +97.8287i q^{79} +(17.2401 - 10.1379i) q^{80} +(49.5039 - 49.5039i) q^{82} +(-50.9676 - 50.9676i) q^{83} +(-34.9180 + 134.604i) q^{85} +64.5897 q^{86} +(-2.56548 - 2.56548i) q^{88} +46.9573i q^{89} +13.9433 q^{91} +(43.6362 - 43.6362i) q^{92} -16.0415i q^{94} +(-43.6012 - 74.1466i) q^{95} +(-112.883 + 112.883i) q^{97} +(37.3665 + 37.3665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 6 q^{7} - 24 q^{8} - 6 q^{10} + 12 q^{11} - 48 q^{16} - 18 q^{17} - 12 q^{20} + 12 q^{22} + 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} - 48 q^{32} - 168 q^{35} + 66 q^{37} + 36 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 12 * q^2 + 6 * q^7 - 24 * q^8 - 6 * q^10 + 12 * q^11 - 48 * q^16 - 18 * q^17 - 12 * q^20 + 12 * q^22 + 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 - 48 * q^32 - 168 * q^35 + 66 * q^37 + 36 * q^38 - 12 * q^40 - 24 * q^41 - 108 * q^43 + 108 * q^46 - 48 * q^47 - 54 * q^50 + 192 * q^53 - 276 * q^55 - 24 * q^56 - 60 * q^58 + 456 * q^61 + 72 * q^62 - 264 * q^65 - 12 * q^67 + 36 * q^68 - 174 * q^70 - 84 * q^71 - 216 * q^73 + 72 * q^76 + 48 * q^77 - 24 * q^82 + 246 * q^83 - 324 * q^85 - 216 * q^86 - 24 * q^88 + 612 * q^91 + 108 * q^92 - 432 * q^95 + 102 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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