LMFDB - Embedded newform 640.2.ba.a.207.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(207,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("640.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.ba (of order $8$, degree $4$, not 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			207.2
Character	$\chi$	$=$	640.207
Dual form			640.2.ba.a.303.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54622 - 1.05468i) q^{3} +(2.21873 + 0.277906i) q^{5} +3.70855 q^{7} +(3.24959 + 3.24959i) q^{9} +O(q^{10})$	\(q+(-2.54622 - 1.05468i) q^{3} +(2.21873 + 0.277906i) q^{5} +3.70855 q^{7} +(3.24959 + 3.24959i) q^{9} +(-1.62306 + 3.91841i) q^{11} +(-2.41888 - 1.00193i) q^{13} +(-5.35629 - 3.04767i) q^{15} +(-2.57998 + 2.57998i) q^{17} +(0.820706 + 1.98136i) q^{19} +(-9.44280 - 3.91133i) q^{21} +5.30550 q^{23} +(4.84554 + 1.23320i) q^{25} +(-1.68286 - 4.06279i) q^{27} +(2.00240 + 4.83422i) q^{29} +1.44002i q^{31} +(8.26535 - 8.26535i) q^{33} +(8.22827 + 1.03063i) q^{35} +(8.58562 - 3.55628i) q^{37} +(5.10230 + 5.10230i) q^{39} +(1.63341 - 1.63341i) q^{41} +(-2.43161 - 5.87042i) q^{43} +(6.30688 + 8.11304i) q^{45} +(2.96683 + 2.96683i) q^{47} +6.75333 q^{49} +(9.29026 - 3.84815i) q^{51} +(2.41336 - 0.999648i) q^{53} +(-4.69009 + 8.24285i) q^{55} -5.91057i q^{57} +(-2.10156 + 5.07362i) q^{59} +(-6.83341 + 2.83049i) q^{61} +(12.0513 + 12.0513i) q^{63} +(-5.08841 - 2.89524i) q^{65} +(3.49753 - 8.44379i) q^{67} +(-13.5090 - 5.59561i) q^{69} +(2.44190 - 2.44190i) q^{71} +7.04282i q^{73} +(-11.0372 - 8.25050i) q^{75} +(-6.01920 + 14.5316i) q^{77} -0.203871i q^{79} -1.66719i q^{81} +(2.40680 - 5.81053i) q^{83} +(-6.44127 + 5.00729i) q^{85} -14.4209i q^{87} +(-1.94360 + 1.94360i) q^{89} +(-8.97054 - 3.71572i) q^{91} +(1.51876 - 3.66661i) q^{93} +(1.27029 + 4.62419i) q^{95} +(3.62241 + 3.62241i) q^{97} +(-18.0075 + 7.45896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 4 q^{5} + 8 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 4 * q^5 + 8 * q^7	$ 88 q + 4 q^{3} - 4 q^{5} + 8 q^{7} + 8 q^{11} - 4 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} + 8 q^{23} - 4 q^{25} - 8 q^{27} - 8 q^{33} + 48 q^{35} - 4 q^{37} - 8 q^{41} - 28 q^{43} - 4 q^{45} + 8 q^{47} + 40 q^{49} - 8 q^{51} - 4 q^{53} - 28 q^{55} - 40 q^{61} + 56 q^{63} - 8 q^{65} + 28 q^{67} - 24 q^{69} - 24 q^{71} + 16 q^{75} - 32 q^{77} - 36 q^{83} - 4 q^{85} + 8 q^{91} + 8 q^{93} - 8 q^{97}+O(q^{100}) $ 88 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 + 8 * q^11 - 4 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 + 8 * q^23 - 4 * q^25 - 8 * q^27 - 8 * q^33 + 48 * q^35 - 4 * q^37 - 8 * q^41 - 28 * q^43 - 4 * q^45 + 8 * q^47 + 40 * q^49 - 8 * q^51 - 4 * q^53 - 28 * q^55 - 40 * q^61 + 56 * q^63 - 8 * q^65 + 28 * q^67 - 24 * q^69 - 24 * q^71 + 16 * q^75 - 32 * q^77 - 36 * q^83 - 4 * q^85 + 8 * q^91 + 8 * q^93 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.54622	−	1.05468i	−1.47006	−	0.608920i	−0.503190	−	0.864176i	$-0.667840\pi$
$3$	−2.54622	−	1.05468i	−1.47006	−	0.608920i	−0.966874	+	0.255256i	$0.917840\pi$
$4$		0			0
$5$	2.21873	+	0.277906i	0.992247	+	0.124284i
$5$	2.21873	+	0.277906i	0.992247	+	0.124284i
$6$		0			0
$7$	3.70855			1.40170			0.700850	−	0.713309i	$-0.252804\pi$
$7$	3.70855			1.40170			0.700850	+	0.713309i	$0.252804\pi$
$8$		0			0
$9$	3.24959	+	3.24959i	1.08320	+	1.08320i
$10$		0			0
$11$	−1.62306	+	3.91841i	−0.489371	+	1.18145i	0.465666	+	0.884961i	$0.345815\pi$
$11$	−1.62306	+	3.91841i	−0.489371	+	1.18145i	−0.955037	+	0.296486i	$0.904185\pi$
$12$		0			0
$13$	−2.41888	−	1.00193i	−0.670877	−	0.277886i	0.0211303	−	0.999777i	$-0.493274\pi$
$13$	−2.41888	−	1.00193i	−0.670877	−	0.277886i	−0.692008	+	0.721890i	$0.743274\pi$
$14$		0			0
$15$	−5.35629	−	3.04767i	−1.38299	−	0.786904i
$16$		0			0
$17$	−2.57998	+	2.57998i	−0.625737	+	0.625737i	−0.946993	−	0.321256i	$-0.895895\pi$
$17$	−2.57998	+	2.57998i	−0.625737	+	0.625737i	0.321256	+	0.946993i	$0.395895\pi$
$18$		0			0
$19$	0.820706	+	1.98136i	0.188283	+	0.454555i	0.989629	−	0.143646i	$-0.0458825\pi$
$19$	0.820706	+	1.98136i	0.188283	+	0.454555i	−0.801346	+	0.598201i	$0.795883\pi$
$20$		0			0
$21$	−9.44280	−	3.91133i	−2.06059	−	0.853523i
$22$		0			0
$23$	5.30550			1.10627			0.553137	−	0.833091i	$-0.313431\pi$
$23$	5.30550			1.10627			0.553137	+	0.833091i	$0.313431\pi$
$24$		0			0
$25$	4.84554	+	1.23320i	0.969107	+	0.246640i
$26$		0			0
$27$	−1.68286	−	4.06279i	−0.323867	−	0.781883i
$28$		0			0
$29$	2.00240	+	4.83422i	0.371837	+	0.897693i	0.993439	+	0.114360i	$0.0364818\pi$
$29$	2.00240	+	4.83422i	0.371837	+	0.897693i	−0.621603	+	0.783333i	$0.713518\pi$
$30$		0			0
$31$			1.44002i			0.258635i	0.991603	+	0.129317i	$0.0412786\pi$
$31$			1.44002i			0.258635i	−0.991603	+	0.129317i	$0.958721\pi$
$32$		0			0
$33$	8.26535	−	8.26535i	1.43881	−	1.43881i
$34$		0			0
$35$	8.22827	+	1.03063i	1.39083	+	0.174208i
$36$		0			0
$37$	8.58562	−	3.55628i	1.41147	−	0.584649i	0.458766	−	0.888557i	$-0.348292\pi$
$37$	8.58562	−	3.55628i	1.41147	−	0.584649i	0.952701	+	0.303908i	$0.0982915\pi$
$38$		0			0
$39$	5.10230	+	5.10230i	0.817021	+	0.817021i
$40$		0			0
$41$	1.63341	−	1.63341i	0.255096	−	0.255096i	−0.567960	−	0.823056i	$-0.692267\pi$
$41$	1.63341	−	1.63341i	0.255096	−	0.255096i	0.823056	+	0.567960i	$0.192267\pi$
$42$		0			0
$43$	−2.43161	−	5.87042i	−0.370817	−	0.895231i	−0.993612	−	0.112847i	$-0.964003\pi$
$43$	−2.43161	−	5.87042i	−0.370817	−	0.895231i	0.622796	−	0.782385i	$-0.285997\pi$
$44$		0			0
$45$	6.30688	+	8.11304i	0.940174	+	1.20942i
$46$		0			0
$47$	2.96683	+	2.96683i	0.432757	+	0.432757i	0.889565	−	0.456808i	$-0.151007\pi$
$47$	2.96683	+	2.96683i	0.432757	+	0.432757i	−0.456808	+	0.889565i	$0.651007\pi$
$48$		0			0
$49$	6.75333			0.964762
$50$		0			0
$51$	9.29026	−	3.84815i	1.30090	−	0.538849i
$52$		0			0
$53$	2.41336	−	0.999648i	0.331501	−	0.137312i	−0.210724	−	0.977546i	$-0.567582\pi$
$53$	2.41336	−	0.999648i	0.331501	−	0.137312i	0.542225	+	0.840233i	$0.317582\pi$
$54$		0			0
$55$	−4.69009	+	8.24285i	−0.632411	+	1.11147i
$56$		0			0
$57$		−	5.91057i		−	0.782874i
$58$		0			0
$59$	−2.10156	+	5.07362i	−0.273600	+	0.660529i	−0.999632	−	0.0271319i	$-0.991363\pi$
$59$	−2.10156	+	5.07362i	−0.273600	+	0.660529i	0.726032	+	0.687661i	$0.241363\pi$
$60$		0			0
$61$	−6.83341	+	2.83049i	−0.874928	+	0.362407i	−0.774528	−	0.632540i	$-0.782012\pi$
$61$	−6.83341	+	2.83049i	−0.874928	+	0.362407i	−0.100401	+	0.994947i	$0.532012\pi$
$62$		0			0
$63$	12.0513	+	12.0513i	1.51832	+	1.51832i
$64$		0			0
$65$	−5.08841	−	2.89524i	−0.631139	−	0.359111i
$66$		0			0
$67$	3.49753	−	8.44379i	0.427291	−	1.03157i	−0.552852	−	0.833280i	$-0.686460\pi$
$67$	3.49753	−	8.44379i	0.427291	−	1.03157i	0.980143	−	0.198293i	$-0.0635397\pi$
$68$		0			0
$69$	−13.5090	−	5.59561i	−1.62629	−	0.673632i
$70$		0			0
$71$	2.44190	−	2.44190i	0.289800	−	0.289800i	−0.547201	−	0.837001i	$-0.684307\pi$
$71$	2.44190	−	2.44190i	0.289800	−	0.289800i	0.837001	+	0.547201i	$0.184307\pi$
$72$		0			0
$73$			7.04282i			0.824300i	0.911116	+	0.412150i	$0.135222\pi$
$73$			7.04282i			0.824300i	−0.911116	+	0.412150i	$0.864778\pi$
$74$		0			0
$75$	−11.0372	−	8.25050i	−1.27447	−	0.952685i
$76$		0			0
$77$	−6.01920	+	14.5316i	−0.685951	+	1.65603i
$78$		0			0
$79$		−	0.203871i		−	0.0229372i	−0.999934	−	0.0114686i	$-0.996349\pi$
$79$		−	0.203871i		−	0.0229372i	0.999934	−	0.0114686i	$-0.00365066\pi$
$80$		0			0
$81$		−	1.66719i		−	0.185243i
$82$		0			0
$83$	2.40680	−	5.81053i	0.264181	−	0.637789i	−0.735008	−	0.678058i	$-0.762822\pi$
$83$	2.40680	−	5.81053i	0.264181	−	0.637789i	0.999189	+	0.0402696i	$0.0128217\pi$
$84$		0			0
$85$	−6.44127	+	5.00729i	−0.698654	+	0.543117i
$86$		0			0
$87$		−	14.4209i		−	1.54608i
$88$		0			0
$89$	−1.94360	+	1.94360i	−0.206021	+	0.206021i	−0.802574	−	0.596553i	$-0.796537\pi$
$89$	−1.94360	+	1.94360i	−0.206021	+	0.206021i	0.596553	+	0.802574i	$0.296537\pi$
$90$		0			0
$91$	−8.97054	−	3.71572i	−0.940368	−	0.389513i
$92$		0			0
$93$	1.51876	−	3.66661i	0.157488	−	0.380209i
$94$		0			0
$95$	1.27029	+	4.62419i	0.130329	+	0.474431i
$96$		0			0
$97$	3.62241	+	3.62241i	0.367800	+	0.367800i	0.866674	−	0.498874i	$-0.166253\pi$
$97$	3.62241	+	3.62241i	0.367800	+	0.367800i	−0.498874	+	0.866674i	$0.666253\pi$
$98$		0			0
$99$	−18.0075	+	7.45896i	−1.80982	+	0.749653i
$100$		0			0
$101$	0.775088	−	1.87123i	0.0771241	−	0.186194i	−0.880615	−	0.473833i	$-0.842870\pi$
$101$	0.775088	−	1.87123i	0.0771241	−	0.186194i	0.957739	+	0.287639i	$0.0928702\pi$
$102$		0			0
$103$		−	3.85297i		−	0.379645i	−0.981818	−	0.189822i	$-0.939209\pi$
$103$		−	3.85297i		−	0.379645i	0.981818	−	0.189822i	$-0.0607912\pi$
$104$		0			0
$105$	−19.8640	−	11.3024i	−1.93853	−	1.10300i
$106$		0			0
$107$	17.3854	−	7.20128i	1.68071	−	0.696174i	0.681353	−	0.731955i	$-0.261392\pi$
$107$	17.3854	−	7.20128i	1.68071	−	0.696174i	0.999360	+	0.0357808i	$0.0113918\pi$
$108$		0			0
$109$	0.773533	−	0.320408i	0.0740910	−	0.0306895i	−0.345330	−	0.938481i	$-0.612233\pi$
$109$	0.773533	−	0.320408i	0.0740910	−	0.0306895i	0.419421	+	0.907792i	$0.362233\pi$
$110$		0			0
$111$	−25.6117			−2.43095
$112$		0			0
$113$	−10.6418	−	10.6418i	−1.00110	−	1.00110i	−0.999999	−	0.00110032i	$-0.999650\pi$
$113$	−10.6418	−	10.6418i	−1.00110	−	1.00110i	−0.00110032	−	0.999999i	$-0.500350\pi$
$114$		0			0
$115$	11.7715	+	1.47443i	1.09770	+	0.137492i
$116$		0			0
$117$	−4.60450	−	11.1162i	−0.425686	−	1.02770i
$118$		0			0
$119$	−9.56798	+	9.56798i	−0.877095	+	0.877095i
$120$		0			0
$121$	−4.94147	−	4.94147i	−0.449225	−	0.449225i
$122$		0			0
$123$	−5.88176	+	2.43631i	−0.530341	+	0.219674i
$124$		0			0
$125$	10.4082	+	4.08274i	0.930940	+	0.365172i
$126$		0			0
$127$	−12.9680	+	12.9680i	−1.15073	+	1.15073i	−0.164320	+	0.986407i	$0.552543\pi$
$127$	−12.9680	+	12.9680i	−1.15073	+	1.15073i	−0.986407	+	0.164320i	$0.947457\pi$
$128$		0			0
$129$			17.5120i			1.54184i
$130$		0			0
$131$	8.35611	+	20.1734i	0.730076	+	1.76256i	0.642344	+	0.766416i	$0.277962\pi$
$131$	8.35611	+	20.1734i	0.730076	+	1.76256i	0.0877325	+	0.996144i	$0.472038\pi$
$132$		0			0
$133$	3.04363	+	7.34797i	0.263916	+	0.637150i
$134$		0			0
$135$	−2.60474	−	9.48191i	−0.224180	−	0.816073i
$136$		0			0
$137$	−1.88186			−0.160778			−0.0803892	−	0.996764i	$-0.525616\pi$
$137$	−1.88186			−0.160778			−0.0803892	+	0.996764i	$0.525616\pi$
$138$		0			0
$139$	0.549075	+	0.227434i	0.0465719	+	0.0192907i	0.405848	−	0.913941i	$-0.366976\pi$
$139$	0.549075	+	0.227434i	0.0465719	+	0.0192907i	−0.359276	+	0.933231i	$0.616976\pi$
$140$		0			0
$141$	−4.42516	−	10.6833i	−0.372666	−	0.899695i
$142$		0			0
$143$	7.85198	−	7.85198i	0.656616	−	0.656616i
$144$		0			0
$145$	3.09933	+	11.2823i	0.257385	+	0.936946i
$146$		0			0
$147$	−17.1955	−	7.12261i	−1.41826	−	0.587463i
$148$		0			0
$149$	−3.54082	+	8.54830i	−0.290076	+	0.700304i	−0.999992	−	0.00398147i	$-0.998733\pi$
$149$	−3.54082	+	8.54830i	−0.290076	+	0.700304i	0.709917	+	0.704286i	$0.248733\pi$
$150$		0			0
$151$	−7.95693	−	7.95693i	−0.647526	−	0.647526i	0.304869	−	0.952394i	$-0.401387\pi$
$151$	−7.95693	−	7.95693i	−0.647526	−	0.647526i	−0.952394	+	0.304869i	$0.901387\pi$
$152$		0			0
$153$	−16.7677			−1.35559
$154$		0			0
$155$	−0.400190	+	3.19501i	−0.0321440	+	0.256629i
$156$		0			0
$157$	−11.4649	−	4.74892i	−0.914999	−	0.379005i	−0.125031	−	0.992153i	$-0.539903\pi$
$157$	−11.4649	−	4.74892i	−0.914999	−	0.379005i	−0.789968	+	0.613148i	$0.789903\pi$
$158$		0			0
$159$	−7.19928			−0.570940
$160$		0			0
$161$	19.6757			1.55066
$162$		0			0
$163$	−11.2235	−	4.64892i	−0.879091	−	0.364131i	−0.102947	−	0.994687i	$-0.532827\pi$
$163$	−11.2235	−	4.64892i	−0.879091	−	0.364131i	−0.776144	+	0.630555i	$0.782827\pi$
$164$		0			0
$165$	20.6356	−	16.0416i	1.60648	−	1.24884i
$166$		0			0
$167$	−17.1661			−1.32835			−0.664175	−	0.747578i	$-0.731217\pi$
$167$	−17.1661			−1.32835			−0.664175	+	0.747578i	$0.731217\pi$
$168$		0			0
$169$	−4.34527	−	4.34527i	−0.334251	−	0.334251i
$170$		0			0
$171$	−3.77165	+	9.10556i	−0.288425	+	0.696320i
$172$		0			0
$173$	5.63214	+	2.33291i	0.428204	+	0.177368i	0.586368	−	0.810045i	$-0.300557\pi$
$173$	5.63214	+	2.33291i	0.428204	+	0.177368i	−0.158164	+	0.987413i	$0.550557\pi$
$174$		0			0
$175$	17.9699	+	4.57338i	1.35840	+	0.345715i
$176$		0			0
$177$	10.7021	−	10.7021i	0.804419	−	0.804419i
$178$		0			0
$179$	−3.97779	−	9.60324i	−0.297314	−	0.717780i	−0.999980	−	0.00626044i	$-0.998007\pi$
$179$	−3.97779	−	9.60324i	−0.297314	−	0.717780i	0.702666	−	0.711520i	$-0.251993\pi$
$180$		0			0
$181$	22.2181	+	9.20303i	1.65146	+	0.684056i	0.997378	−	0.0723710i	$-0.0230566\pi$
$181$	22.2181	+	9.20303i	1.65146	+	0.684056i	0.654079	+	0.756427i	$0.273057\pi$
$182$		0			0
$183$	20.3847			1.50688
$184$		0			0
$185$	20.0375	−	5.50443i	1.47319	−	0.404694i
$186$		0			0
$187$	−5.92197	−	14.2969i	−0.433057	−	1.04549i
$188$		0			0
$189$	−6.24097	−	15.0670i	−0.453964	−	1.09597i
$190$		0			0
$191$		−	8.62257i		−	0.623907i	−0.950097	−	0.311954i	$-0.899017\pi$
$191$		−	8.62257i		−	0.623907i	0.950097	−	0.311954i	$-0.100983\pi$
$192$		0			0
$193$	13.1126	−	13.1126i	0.943862	−	0.943862i	−0.0546439	−	0.998506i	$-0.517402\pi$
$193$	13.1126	−	13.1126i	0.943862	−	0.943862i	0.998506	+	0.0546439i	$0.0174024\pi$
$194$		0			0
$195$	9.90266	+	12.7386i	0.709145	+	0.912229i
$196$		0			0
$197$	−10.3876	+	4.30267i	−0.740083	+	0.306552i	−0.720688	−	0.693260i	$-0.756174\pi$
$197$	−10.3876	+	4.30267i	−0.740083	+	0.306552i	−0.0193947	+	0.999812i	$0.506174\pi$
$198$		0			0
$199$	−1.56365	−	1.56365i	−0.110844	−	0.110844i	0.649510	−	0.760353i	$-0.274974\pi$
$199$	−1.56365	−	1.56365i	−0.110844	−	0.110844i	−0.760353	+	0.649510i	$0.774974\pi$
$200$		0			0
$201$	−17.8110	+	17.8110i	−1.25629	+	1.25629i
$202$		0			0
$203$	7.42600	+	17.9280i	0.521203	+	1.25830i
$204$		0			0
$205$	4.07804	−	3.17017i	0.284822	−	0.221414i
$206$		0			0
$207$	17.2407	+	17.2407i	1.19831	+	1.19831i
$208$		0			0
$209$	−9.09585			−0.629173
$210$		0			0
$211$	4.96614	−	2.05704i	0.341883	−	0.141613i	−0.205134	−	0.978734i	$-0.565763\pi$
$211$	4.96614	−	2.05704i	0.341883	−	0.141613i	0.547017	+	0.837121i	$0.315763\pi$
$212$		0			0
$213$	−8.79305	+	3.64220i	−0.602490	+	0.249559i
$214$		0			0
$215$	−3.76366	−	13.7007i	−0.256679	−	0.934377i
$216$		0			0
$217$			5.34037i			0.362528i
$218$		0			0
$219$	7.42793	−	17.9326i	0.501933	−	1.21177i
$220$		0			0
$221$	8.82564	−	3.65570i	0.593677	−	0.245909i
$222$		0			0
$223$	−17.0444	−	17.0444i	−1.14138	−	1.14138i	−0.988198	−	0.153181i	$-0.951048\pi$
$223$	−17.0444	−	17.0444i	−1.14138	−	1.14138i	−0.153181	−	0.988198i	$-0.548952\pi$
$224$		0			0
$225$	11.7386	+	19.7534i	0.782574	+	1.31689i
$226$		0			0
$227$	−9.95905	+	24.0433i	−0.661005	+	1.59581i	0.135225	+	0.990815i	$0.456824\pi$
$227$	−9.95905	+	24.0433i	−0.661005	+	1.59581i	−0.796231	+	0.604993i	$0.793176\pi$
$228$		0			0
$229$	−15.6688	−	6.49021i	−1.03542	−	0.428885i	−0.200755	−	0.979642i	$-0.564339\pi$
$229$	−15.6688	−	6.49021i	−1.03542	−	0.428885i	−0.834666	+	0.550756i	$0.814339\pi$
$230$		0			0
$231$	30.6525	−	30.6525i	2.01678	−	2.01678i
$232$		0			0
$233$			22.4264i			1.46920i	0.678500	+	0.734600i	$0.262630\pi$
$233$			22.4264i			1.46920i	−0.678500	+	0.734600i	$0.737370\pi$
$234$		0			0
$235$	5.75810	+	7.40711i	0.375617	+	0.483186i
$236$		0			0
$237$	−0.215019	+	0.519101i	−0.0139670	+	0.0337192i
$238$		0			0
$239$			5.46064i			0.353219i	0.984281	+	0.176610i	$0.0565130\pi$
$239$			5.46064i			0.353219i	−0.984281	+	0.176610i	$0.943487\pi$
$240$		0			0
$241$		−	25.7625i		−	1.65951i	−0.558127	−	0.829755i	$-0.688480\pi$
$241$		−	25.7625i		−	1.65951i	0.558127	−	0.829755i	$-0.311520\pi$
$242$		0			0
$243$	−6.80694	+	16.4334i	−0.436665	+	1.05420i
$244$		0			0
$245$	14.9838	+	1.87679i	0.957282	+	0.119904i
$246$		0			0
$247$		−	5.61497i		−	0.357272i
$248$		0			0
$249$	−12.2565	+	12.2565i	−0.776725	+	0.776725i
$250$		0			0
$251$	−7.97245	−	3.30230i	−0.503217	−	0.208439i	0.116610	−	0.993178i	$-0.462797\pi$
$251$	−7.97245	−	3.30230i	−0.503217	−	0.208439i	−0.619827	+	0.784739i	$0.712797\pi$
$252$		0			0
$253$	−8.61115	+	20.7891i	−0.541378	+	1.30700i
$254$		0			0
$255$	21.6820	−	5.95619i	1.35778	−	0.372991i
$256$		0			0
$257$	−15.1455	−	15.1455i	−0.944747	−	0.944747i	0.0538042	−	0.998552i	$-0.482865\pi$
$257$	−15.1455	−	15.1455i	−0.944747	−	0.944747i	−0.998552	+	0.0538042i	$0.982865\pi$
$258$		0			0
$259$	31.8402	−	13.1886i	1.97845	−	0.819502i
$260$		0			0
$261$	−9.20226	+	22.2162i	−0.569606	+	1.37515i
$262$		0			0
$263$			6.87330i			0.423826i	0.977289	+	0.211913i	$0.0679693\pi$
$263$			6.87330i			0.423826i	−0.977289	+	0.211913i	$0.932031\pi$
$264$		0			0
$265$	5.63242	−	1.54726i	0.345997	−	0.0950475i
$266$		0			0
$267$	6.99873	−	2.89897i	0.428315	−	0.177414i
$268$		0			0
$269$	20.3252	−	8.41897i	1.23925	−	0.513314i	0.335769	−	0.941944i	$-0.391004\pi$
$269$	20.3252	−	8.41897i	1.23925	−	0.513314i	0.903480	+	0.428631i	$0.141004\pi$
$270$		0			0
$271$	−12.4734			−0.757703			−0.378851	−	0.925457i	$-0.623681\pi$
$271$	−12.4734			−0.757703			−0.378851	+	0.925457i	$0.623681\pi$
$272$		0			0
$273$	18.9221	+	18.9221i	1.14522	+	1.14522i
$274$		0			0
$275$	−12.6968	+	16.9853i	−0.765645	+	1.02425i
$276$		0			0
$277$	−8.98606	−	21.6943i	−0.539920	−	1.30348i	−0.924778	−	0.380507i	$-0.875750\pi$
$277$	−8.98606	−	21.6943i	−0.539920	−	1.30348i	0.384858	−	0.922976i	$-0.374250\pi$
$278$		0			0
$279$	−4.67946	+	4.67946i	−0.280152	+	0.280152i
$280$		0			0
$281$	5.32879	+	5.32879i	0.317889	+	0.317889i	0.847956	−	0.530067i	$-0.177833\pi$
$281$	5.32879	+	5.32879i	0.317889	+	0.317889i	−0.530067	+	0.847956i	$0.677833\pi$
$282$		0			0
$283$	−10.2587	+	4.24930i	−0.609818	+	0.252595i	−0.666151	−	0.745817i	$-0.732059\pi$
$283$	−10.2587	+	4.24930i	−0.609818	+	0.252595i	0.0563329	+	0.998412i	$0.482059\pi$
$284$		0			0
$285$	1.64259	−	13.1140i	0.0972984	−	0.776804i
$286$		0			0
$287$	6.05759	−	6.05759i	0.357568	−	0.357568i
$288$		0			0
$289$			3.68741i			0.216906i
$290$		0			0
$291$	−5.40299	−	13.0440i	−0.316729	−	0.764651i
$292$		0			0
$293$	−4.25127	−	10.2635i	−0.248362	−	0.599598i	0.749704	−	0.661774i	$-0.230196\pi$
$293$	−4.25127	−	10.2635i	−0.248362	−	0.599598i	−0.998065	+	0.0621758i	$0.980196\pi$
$294$		0			0
$295$	−6.07280	+	10.6730i	−0.353572	+	0.621404i
$296$		0			0
$297$	18.6511			1.08224
$298$		0			0
$299$	−12.8334	−	5.31576i	−0.742174	−	0.307418i
$300$		0			0
$301$	−9.01774	−	21.7708i	−0.519774	−	1.25485i
$302$		0			0
$303$	−3.94710	+	3.94710i	−0.226755	+	0.226755i
$304$		0			0
$305$	−15.9481	+	4.38105i	−0.913186	+	0.250858i
$306$		0			0
$307$	0.897767	+	0.371867i	0.0512383	+	0.0212236i	0.408155	−	0.912912i	$-0.366172\pi$
$307$	0.897767	+	0.371867i	0.0512383	+	0.0212236i	−0.356917	+	0.934136i	$0.616172\pi$
$308$		0			0
$309$	−4.06366	+	9.81054i	−0.231173	+	0.558102i
$310$		0			0
$311$	6.73409	+	6.73409i	0.381855	+	0.381855i	0.871770	−	0.489915i	$-0.162972\pi$
$311$	6.73409	+	6.73409i	0.381855	+	0.381855i	−0.489915	+	0.871770i	$0.662972\pi$
$312$		0			0
$313$	−7.44365			−0.420740			−0.210370	−	0.977622i	$-0.567467\pi$
$313$	−7.44365			−0.420740			−0.210370	+	0.977622i	$0.567467\pi$
$314$		0			0
$315$	23.3894	+	30.0876i	1.31784	+	1.69525i
$316$		0			0
$317$	−5.47419	−	2.26749i	−0.307461	−	0.127355i	0.223618	−	0.974677i	$-0.428213\pi$
$317$	−5.47419	−	2.26749i	−0.307461	−	0.127355i	−0.531079	+	0.847322i	$0.678213\pi$
$318$		0			0
$319$	−22.1925			−1.24254
$320$		0			0
$321$	−51.8623			−2.89467
$322$		0			0
$323$	−7.22927	−	2.99446i	−0.402248	−	0.166616i
$324$		0			0
$325$	−10.4852	−	7.83787i	−0.581614	−	0.434767i
$326$		0			0
$327$	−2.30752			−0.127606
$328$		0			0
$329$	11.0026	+	11.0026i	0.606596	+	0.606596i
$330$		0			0
$331$	6.91960	−	16.7054i	0.380336	−	0.918212i	−0.611565	−	0.791195i	$-0.709460\pi$
$331$	6.91960	−	16.7054i	0.380336	−	0.918212i	0.991900	−	0.127018i	$-0.0405404\pi$
$332$		0			0
$333$	39.4562	+	16.3433i	2.16219	+	0.895607i
$334$		0			0
$335$	10.1067	−	17.7625i	0.552186	−	0.970469i
$336$		0			0
$337$	−5.47917	+	5.47917i	−0.298470	+	0.298470i	−0.840414	−	0.541945i	$-0.817688\pi$
$337$	−5.47917	+	5.47917i	−0.298470	+	0.298470i	0.541945	+	0.840414i	$0.317688\pi$
$338$		0			0
$339$	15.8728	+	38.3202i	0.862090	+	2.08127i
$340$		0			0
$341$	−5.64258	−	2.33724i	−0.305563	−	0.126568i
$342$		0			0
$343$	−0.914780			−0.0493935
$344$		0			0
$345$	−28.4178	−	16.1694i	−1.52996	−	0.870531i
$346$		0			0
$347$	6.97500	+	16.8391i	0.374438	+	0.903973i	0.992987	+	0.118226i	$0.0377209\pi$
$347$	6.97500	+	16.8391i	0.374438	+	0.903973i	−0.618549	+	0.785746i	$0.712279\pi$
$348$		0			0
$349$	1.95879	+	4.72895i	0.104852	+	0.253135i	0.967595	−	0.252508i	$-0.0812554\pi$
$349$	1.95879	+	4.72895i	0.104852	+	0.253135i	−0.862743	+	0.505643i	$0.831255\pi$
$350$		0			0
$351$			11.5135i			0.614546i
$352$		0			0
$353$	0.763353	−	0.763353i	0.0406292	−	0.0406292i	−0.686500	−	0.727130i	$-0.740854\pi$
$353$	0.763353	−	0.763353i	0.0406292	−	0.0406292i	0.727130	+	0.686500i	$0.240854\pi$
$354$		0			0
$355$	6.09654	−	4.73930i	0.323571	−	0.251536i
$356$		0			0
$357$	34.4534	−	14.2711i	1.82347	−	0.755305i
$358$		0			0
$359$	13.3030	+	13.3030i	0.702107	+	0.702107i	0.964862	−	0.262756i	$-0.0846313\pi$
$359$	13.3030	+	13.3030i	0.702107	+	0.702107i	−0.262756	+	0.964862i	$0.584631\pi$
$360$		0			0
$361$	10.1828	−	10.1828i	0.535937	−	0.535937i
$362$		0			0
$363$	7.37042	+	17.7938i	0.386847	+	0.933931i
$364$		0			0
$365$	−1.95725	+	15.6261i	−0.102447	+	0.817909i
$366$		0			0
$367$	−8.06357	−	8.06357i	−0.420915	−	0.420915i	0.464604	−	0.885519i	$-0.346197\pi$
$367$	−8.06357	−	8.06357i	−0.420915	−	0.420915i	−0.885519	+	0.464604i	$0.846197\pi$
$368$		0			0
$369$	10.6158			0.552638
$370$		0			0
$371$	8.95008	−	3.70724i	0.464665	−	0.192471i
$372$		0			0
$373$	16.0127	−	6.63267i	0.829105	−	0.343427i	0.0725569	−	0.997364i	$-0.476884\pi$
$373$	16.0127	−	6.63267i	0.829105	−	0.343427i	0.756549	+	0.653938i	$0.226884\pi$
$374$		0			0
$375$	−22.1957	−	21.3729i	−1.14618	−	1.10369i
$376$		0			0
$377$		−	13.6997i		−	0.705570i
$378$		0			0
$379$	9.60968	−	23.1998i	0.493616	−	1.19170i	−0.459251	−	0.888307i	$-0.651882\pi$
$379$	9.60968	−	23.1998i	0.493616	−	1.19170i	0.952867	−	0.303388i	$-0.0981180\pi$
$380$		0			0
$381$	46.6967	−	19.3424i	2.39234	−	0.990941i
$382$		0			0
$383$	6.46368	+	6.46368i	0.330278	+	0.330278i	0.852692	−	0.522414i	$-0.174968\pi$
$383$	6.46368	+	6.46368i	0.330278	+	0.330278i	−0.522414	+	0.852692i	$0.674968\pi$
$384$		0			0
$385$	−17.3934	+	30.5690i	−0.886451	+	1.55794i
$386$		0			0
$387$	11.1747	−	26.9782i	0.568043	−	1.37138i
$388$		0			0
$389$	24.1362	+	9.99755i	1.22375	+	0.506896i	0.898602	−	0.438766i	$-0.144584\pi$
$389$	24.1362	+	9.99755i	1.22375	+	0.506896i	0.325153	+	0.945661i	$0.394584\pi$
$390$		0			0
$391$	−13.6881	+	13.6881i	−0.692236	+	0.692236i
$392$		0			0
$393$		−	60.1791i		−	3.03563i
$394$		0			0
$395$	0.0566570	−	0.452334i	0.00285072	−	0.0227594i
$396$		0			0
$397$	−10.7897	+	26.0485i	−0.541517	+	1.30734i	0.382135	+	0.924106i	$0.375189\pi$
$397$	−10.7897	+	26.0485i	−0.541517	+	1.30734i	−0.923652	+	0.383232i	$0.874811\pi$
$398$		0			0
$399$		−	21.9196i		−	1.09735i
$400$		0			0
$401$			34.5054i			1.72312i	0.507659	+	0.861558i	$0.330511\pi$
$401$			34.5054i			1.72312i	−0.507659	+	0.861558i	$0.669489\pi$
$402$		0			0
$403$	1.44280	−	3.48323i	0.0718711	−	0.173512i
$404$		0			0
$405$	0.463323	−	3.69905i	0.0230227	−	0.183807i
$406$		0			0
$407$			39.4141i			1.95368i
$408$		0			0
$409$	13.2323	−	13.2323i	0.654297	−	0.654297i	−0.299728	−	0.954025i	$-0.596896\pi$
$409$	13.2323	−	13.2323i	0.654297	−	0.654297i	0.954025	+	0.299728i	$0.0968959\pi$
$410$		0			0
$411$	4.79164	+	1.98476i	0.236354	+	0.0979012i
$412$		0			0
$413$	−7.79375	+	18.8158i	−0.383505	+	0.925864i
$414$		0			0
$415$	6.95483	−	12.2231i	0.341399	−	0.600010i
$416$		0			0
$417$	−1.15820	−	1.15820i	−0.0567172	−	0.0567172i
$418$		0			0
$419$	23.2713	−	9.63930i	1.13688	−	0.470911i	0.266765	−	0.963761i	$-0.414045\pi$
$419$	23.2713	−	9.63930i	1.13688	−	0.470911i	0.870114	+	0.492851i	$0.164045\pi$
$420$		0			0
$421$	−9.47180	+	22.8669i	−0.461627	+	1.11447i	0.506102	+	0.862474i	$0.331086\pi$
$421$	−9.47180	+	22.8669i	−0.461627	+	1.11447i	−0.967729	+	0.251993i	$0.918914\pi$
$422$		0			0
$423$			19.2820i			0.937522i
$424$		0			0
$425$	−15.6830	+	9.31976i	−0.760738	+	0.452075i
$426$		0			0
$427$	−25.3420	+	10.4970i	−1.22639	+	0.507986i
$428$		0			0
$429$	−28.2743	+	11.7116i	−1.36509	+	0.565440i
$430$		0			0
$431$	−6.73695			−0.324508			−0.162254	−	0.986749i	$-0.551876\pi$
$431$	−6.73695			−0.324508			−0.162254	+	0.986749i	$0.551876\pi$
$432$		0			0
$433$	−24.2565	−	24.2565i	−1.16569	−	1.16569i	−0.983208	−	0.182486i	$-0.941586\pi$
$433$	−24.2565	−	24.2565i	−1.16569	−	1.16569i	−0.182486	−	0.983208i	$-0.558414\pi$
$434$		0			0
$435$	4.00767	−	31.9961i	0.192153	−	1.53410i
$436$		0			0
$437$	4.35426	+	10.5121i	0.208292	+	0.502862i
$438$		0			0
$439$	−11.7908	+	11.7908i	−0.562745	+	0.562745i	−0.930086	−	0.367341i	$-0.880268\pi$
$439$	−11.7908	+	11.7908i	−0.562745	+	0.562745i	0.367341	+	0.930086i	$0.380268\pi$
$440$		0			0
$441$	21.9455	+	21.9455i	1.04503	+	1.04503i
$442$		0			0
$443$	17.3149	−	7.17207i	0.822656	−	0.340755i	0.0686646	−	0.997640i	$-0.478126\pi$
$443$	17.3149	−	7.17207i	0.822656	−	0.340755i	0.753991	+	0.656885i	$0.228126\pi$
$444$		0			0
$445$	−4.85247	+	3.77219i	−0.230029	+	0.178819i
$446$		0			0
$447$	18.0315	−	18.0315i	0.852859	−	0.852859i
$448$		0			0
$449$		−	34.5622i		−	1.63109i	−0.578693	−	0.815546i	$-0.696437\pi$
$449$		−	34.5622i		−	1.63109i	0.578693	−	0.815546i	$-0.303563\pi$
$450$		0			0
$451$	3.74926	+	9.05151i	0.176546	+	0.426219i
$452$		0			0
$453$	11.8681	+	28.6522i	0.557612	+	1.34620i
$454$		0			0
$455$	−18.8706	−	10.7372i	−0.884667	−	0.503366i
$456$		0			0
$457$	39.6621			1.85532			0.927658	−	0.373430i	$-0.121818\pi$
$457$	39.6621			1.85532			0.927658	+	0.373430i	$0.121818\pi$
$458$		0			0
$459$	14.8236	+	6.14016i	0.691909	+	0.286598i
$460$		0			0
$461$	−5.87134	−	14.1747i	−0.273456	−	0.660180i	0.726171	−	0.687514i	$-0.241298\pi$
$461$	−5.87134	−	14.1747i	−0.273456	−	0.660180i	−0.999626	+	0.0273342i	$0.991298\pi$
$462$		0			0
$463$	19.2066	−	19.2066i	0.892605	−	0.892605i	−0.102163	−	0.994768i	$-0.532576\pi$
$463$	19.2066	−	19.2066i	0.892605	−	0.892605i	0.994768	+	0.102163i	$0.0325764\pi$
$464$		0			0
$465$	4.38869	−	7.71314i	0.203521	−	0.357688i
$466$		0			0
$467$	−13.7733	−	5.70508i	−0.637352	−	0.264000i	0.0405215	−	0.999179i	$-0.487098\pi$
$467$	−13.7733	−	5.70508i	−0.637352	−	0.264000i	−0.677873	+	0.735179i	$0.737098\pi$
$468$		0			0
$469$	12.9708	−	31.3142i	0.598934	−	1.44595i
$470$		0			0
$471$	24.1836	+	24.1836i	1.11432	+	1.11432i
$472$		0			0
$473$	26.9494			1.23913
$474$		0			0
$475$	1.53335	+	10.6128i	0.0703549	+	0.486951i
$476$		0			0
$477$	11.0909	+	4.59400i	0.507817	+	0.210345i
$478$		0			0
$479$	9.35639			0.427504			0.213752	−	0.976888i	$-0.431432\pi$
$479$	9.35639			0.427504			0.213752	+	0.976888i	$0.431432\pi$
$480$		0			0
$481$	−24.3308			−1.10939
$482$		0			0
$483$	−50.0988	−	20.7516i	−2.27957	−	0.944230i
$484$		0			0
$485$	7.03047	+	9.04385i	0.319237	+	0.410660i
$486$		0			0
$487$	5.49190			0.248862			0.124431	−	0.992228i	$-0.460289\pi$
$487$	5.49190			0.248862			0.124431	+	0.992228i	$0.460289\pi$
$488$		0			0
$489$	23.6744	+	23.6744i	1.07059	+	1.07059i
$490$		0			0
$491$	3.70433	−	8.94304i	0.167174	−	0.403594i	−0.817985	−	0.575240i	$-0.804909\pi$
$491$	3.70433	−	8.94304i	0.167174	−	0.403594i	0.985159	+	0.171646i	$0.0549087\pi$
$492$		0			0
$493$	−17.6384	−	7.30605i	−0.794392	−	0.329048i
$494$		0			0
$495$	−42.0267	+	11.5450i	−1.88896	+	0.518910i
$496$		0			0
$497$	9.05590	−	9.05590i	0.406213	−	0.406213i
$498$		0			0
$499$	−3.58828	−	8.66289i	−0.160634	−	0.387804i	0.822986	−	0.568062i	$-0.192307\pi$
$499$	−3.58828	−	8.66289i	−0.160634	−	0.387804i	−0.983619	+	0.180258i	$0.942307\pi$
$500$		0			0
$501$	43.7086	+	18.1047i	1.95276	+	0.808859i
$502$		0			0
$503$	0.633548			0.0282485			0.0141243	−	0.999900i	$-0.495504\pi$
$503$	0.633548			0.0282485			0.0141243	+	0.999900i	$0.495504\pi$
$504$		0			0
$505$	2.23974	−	3.93635i	0.0996670	−	0.175165i
$506$		0			0
$507$	6.48116	+	15.6469i	0.287838	+	0.694903i
$508$		0			0
$509$	−7.69272	−	18.5719i	−0.340974	−	0.823183i	−0.997618	−	0.0689828i	$-0.978025\pi$
$509$	−7.69272	−	18.5719i	−0.340974	−	0.823183i	0.656644	−	0.754201i	$-0.271975\pi$
$510$		0			0
$511$			26.1187i			1.15542i
$512$		0			0
$513$	6.66871	−	6.66871i	0.294431	−	0.294431i
$514$		0			0
$515$	1.07077	−	8.54872i	0.0471836	−	0.376701i
$516$		0			0
$517$	−16.4406	+	6.80993i	−0.723058	+	0.299501i
$518$		0			0
$519$	−11.8802	−	11.8802i	−0.521484	−	0.521484i
$520$		0			0
$521$	−1.28598	+	1.28598i	−0.0563400	+	0.0563400i	−0.734715	−	0.678375i	$-0.762684\pi$
$521$	−1.28598	+	1.28598i	−0.0563400	+	0.0563400i	0.678375	+	0.734715i	$0.262684\pi$
$522$		0			0
$523$	−1.71691	−	4.14499i	−0.0750754	−	0.181248i	0.881886	−	0.471462i	$-0.156274\pi$
$523$	−1.71691	−	4.14499i	−0.0750754	−	0.181248i	−0.956962	+	0.290214i	$0.906274\pi$
$524$		0			0
$525$	−40.9320	−	30.5974i	−1.78642	−	1.33538i
$526$		0			0
$527$	−3.71522	−	3.71522i	−0.161837	−	0.161837i
$528$		0			0
$529$	5.14833			0.223841
$530$		0			0
$531$	−23.3164	+	9.65797i	−1.01185	+	0.419120i
$532$		0			0
$533$	−5.58760	+	2.31446i	−0.242026	+	0.100250i
$534$		0			0
$535$	40.5749	−	11.1462i	1.75420	−	0.481891i
$536$		0			0
$537$			28.6473i			1.23622i
$538$		0			0
$539$	−10.9611	+	26.4624i	−0.472127	+	1.13981i
$540$		0			0
$541$	−19.1096	+	7.91546i	−0.821587	+	0.340312i	−0.753567	−	0.657372i	$-0.771668\pi$
$541$	−19.1096	+	7.91546i	−0.821587	+	0.340312i	−0.0680201	+	0.997684i	$0.521668\pi$
$542$		0			0
$543$	−46.8659	−	46.8659i	−2.01121	−	2.01121i
$544$		0			0
$545$	1.80531	−	0.495929i	0.0773308	−	0.0212433i
$546$		0			0
$547$	7.69432	−	18.5757i	0.328985	−	0.794241i	−0.669683	−	0.742647i	$-0.733570\pi$
$547$	7.69432	−	18.5757i	0.328985	−	0.794241i	0.998668	−	0.0515935i	$-0.0164300\pi$
$548$		0			0
$549$	−31.4037	−	13.0078i	−1.34028	−	0.555161i
$550$		0			0
$551$	−7.93496	+	7.93496i	−0.338041	+	0.338041i
$552$		0			0
$553$		−	0.756064i		−	0.0321511i
$554$		0			0
$555$	−56.8254	−	7.11765i	−2.41210	−	0.302127i
$556$		0			0
$557$	8.02477	−	19.3735i	0.340021	−	0.820882i	−0.657692	−	0.753287i	$-0.728467\pi$
$557$	8.02477	−	19.3735i	0.340021	−	0.820882i	0.997713	−	0.0675954i	$-0.0215327\pi$
$558$		0			0
$559$			16.6362i			0.703635i
$560$		0			0
$561$			42.6489i			1.80064i
$562$		0			0
$563$	15.8057	−	38.1583i	0.666129	−	1.60818i	−0.121901	−	0.992542i	$-0.538899\pi$
$563$	15.8057	−	38.1583i	0.666129	−	1.60818i	0.788030	−	0.615636i	$-0.211101\pi$
$564$		0			0
$565$	−20.6539	−	26.5688i	−0.868918	−	1.11776i
$566$		0			0
$567$		−	6.18286i		−	0.259656i
$568$		0			0
$569$	−15.6674	+	15.6674i	−0.656811	+	0.656811i	−0.954624	−	0.297813i	$-0.903743\pi$
$569$	−15.6674	+	15.6674i	−0.656811	+	0.656811i	0.297813	+	0.954624i	$0.403743\pi$
$570$		0			0
$571$	−23.0913	−	9.56473i	−0.966340	−	0.400271i	−0.156992	−	0.987600i	$-0.550180\pi$
$571$	−23.0913	−	9.56473i	−0.966340	−	0.400271i	−0.809349	+	0.587329i	$0.800180\pi$
$572$		0			0
$573$	−9.09406	+	21.9550i	−0.379910	+	0.917183i
$574$		0			0
$575$	25.7080	+	6.54274i	1.07210	+	0.272851i
$576$		0			0
$577$	27.8886	+	27.8886i	1.16102	+	1.16102i	0.984254	+	0.176762i	$0.0565624\pi$
$577$	27.8886	+	27.8886i	1.16102	+	1.16102i	0.176762	+	0.984254i	$0.443438\pi$
$578$		0			0
$579$	−47.2171	+	19.5579i	−1.96227	+	0.812800i
$580$		0			0
$581$	8.92574	−	21.5486i	0.370302	−	0.893988i
$582$		0			0
$583$			11.0791i			0.458848i
$584$		0			0
$585$	−7.12687	−	25.9436i	−0.294660	−	1.07263i
$586$		0			0
$587$	−33.2273	+	13.7632i	−1.37144	+	0.568067i	−0.942177	−	0.335114i	$-0.891225\pi$
$587$	−33.2273	+	13.7632i	−1.37144	+	0.568067i	−0.429258	+	0.903182i	$0.641225\pi$
$588$		0			0
$589$	−2.85319	+	1.18183i	−0.117564	+	0.0486965i
$590$		0			0
$591$	30.9870			1.27463
$592$		0			0
$593$	−15.2714	−	15.2714i	−0.627123	−	0.627123i	0.320220	−	0.947343i	$-0.396243\pi$
$593$	−15.2714	−	15.2714i	−0.627123	−	0.627123i	−0.947343	+	0.320220i	$0.896243\pi$
$594$		0			0
$595$	−23.8878	+	18.5698i	−0.979303	+	0.761286i
$596$		0			0
$597$	2.33225	+	5.63054i	0.0954525	+	0.230443i
$598$		0			0
$599$	−5.68644	+	5.68644i	−0.232342	+	0.232342i	−0.813669	−	0.581328i	$-0.802533\pi$
$599$	−5.68644	+	5.68644i	−0.232342	+	0.232342i	0.581328	+	0.813669i	$0.302533\pi$
$600$		0			0
$601$	0.490584	+	0.490584i	0.0200113	+	0.0200113i	0.717042	−	0.697030i	$-0.245496\pi$
$601$	0.490584	+	0.490584i	0.0200113	+	0.0200113i	−0.697030	+	0.717042i	$0.745496\pi$
$602$		0			0
$603$	38.8044	−	16.0733i	1.58024	−	0.654555i
$604$		0			0
$605$	−9.59053	−	12.3371i	−0.389911	−	0.501573i
$606$		0			0
$607$	−5.39237	+	5.39237i	−0.218870	+	0.218870i	−0.808022	−	0.589152i	$-0.799462\pi$
$607$	−5.39237	+	5.39237i	−0.218870	+	0.218870i	0.589152	+	0.808022i	$0.299462\pi$
$608$		0			0
$609$		−	53.4807i		−	2.16715i
$610$		0			0
$611$	−4.20385	−	10.1490i	−0.170070	−	0.410584i
$612$		0			0
$613$	−13.9134	−	33.5899i	−0.561956	−	1.35668i	−0.908200	−	0.418537i	$-0.862543\pi$
$613$	−13.9134	−	33.5899i	−0.561956	−	1.35668i	0.346244	−	0.938145i	$-0.387457\pi$
$614$		0			0
$615$	−13.7271	+	3.77093i	−0.553531	+	0.152058i
$616$		0			0
$617$	−9.87023			−0.397360			−0.198680	−	0.980064i	$-0.563666\pi$
$617$	−9.87023			−0.397360			−0.198680	+	0.980064i	$0.563666\pi$
$618$		0			0
$619$	28.4293	+	11.7758i	1.14267	+	0.473309i	0.872069	−	0.489383i	$-0.162778\pi$
$619$	28.4293	+	11.7758i	1.14267	+	0.473309i	0.270599	+	0.962692i	$0.412778\pi$
$620$		0			0
$621$	−8.92842	−	21.5551i	−0.358285	−	0.864977i
$622$		0			0
$623$	−7.20795	+	7.20795i	−0.288780	+	0.288780i
$624$		0			0
$625$	21.9584	+	11.9510i	0.878338	+	0.478041i
$626$		0			0
$627$	23.1601	+	9.59321i	0.924924	+	0.383116i
$628$		0			0
$629$	−12.9756	+	31.3259i	−0.517371	+	1.24904i
$630$		0			0
$631$	−3.97486	−	3.97486i	−0.158236	−	0.158236i	0.623548	−	0.781785i	$-0.285690\pi$
$631$	−3.97486	−	3.97486i	−0.158236	−	0.158236i	−0.781785	+	0.623548i	$0.785690\pi$
$632$		0			0
$633$	−14.8144			−0.588821
$634$		0			0
$635$	−32.3765	+	25.1687i	−1.28482	+	0.998789i
$636$		0			0
$637$	−16.3355	−	6.76639i	−0.647237	−	0.268094i
$638$		0			0
$639$	15.8703			0.627821
$640$		0			0
$641$	−22.0503			−0.870935			−0.435468	−	0.900204i	$-0.643417\pi$
$641$	−22.0503			−0.870935			−0.435468	+	0.900204i	$0.643417\pi$
$642$		0			0
$643$	23.3820	+	9.68514i	0.922096	+	0.381945i	0.792675	−	0.609645i	$-0.208688\pi$
$643$	23.3820	+	9.68514i	0.922096	+	0.381945i	0.129422	+	0.991590i	$0.458688\pi$
$644$		0			0
$645$	−4.86669	+	38.8544i	−0.191626	+	1.52989i
$646$		0			0
$647$	3.30587			0.129967			0.0649836	−	0.997886i	$-0.479300\pi$
$647$	3.30587			0.129967			0.0649836	+	0.997886i	$0.479300\pi$
$648$		0			0
$649$	−16.4696	−	16.4696i	−0.646488	−	0.646488i
$650$		0			0
$651$	5.63239	−	13.5978i	0.220751	−	0.532939i
$652$		0			0
$653$	−32.7223	−	13.5540i	−1.28052	−	0.530410i	−0.364376	−	0.931252i	$-0.618718\pi$
$653$	−32.7223	−	13.5540i	−1.28052	−	0.530410i	−0.916147	+	0.400842i	$0.868718\pi$
$654$		0			0
$655$	12.9336	+	47.0816i	0.505359	+	1.83963i
$656$		0			0
$657$	−22.8863	+	22.8863i	−0.892879	+	0.892879i
$658$		0			0
$659$	−10.1544	−	24.5149i	−0.395559	−	0.954964i	−0.988706	−	0.149870i	$-0.952115\pi$
$659$	−10.1544	−	24.5149i	−0.395559	−	0.954964i	0.593147	−	0.805094i	$-0.297885\pi$
$660$		0			0
$661$	−29.1101	−	12.0578i	−1.13225	−	0.468994i	−0.263705	−	0.964603i	$-0.584945\pi$
$661$	−29.1101	−	12.0578i	−1.13225	−	0.468994i	−0.868545	+	0.495610i	$0.834945\pi$
$662$		0			0
$663$	−26.3276			−1.02248
$664$		0			0
$665$	4.71095	+	17.1490i	0.182683	+	0.665010i
$666$		0			0
$667$	10.6237	+	25.6480i	0.411353	+	0.993094i
$668$		0			0
$669$	25.4225	+	61.3753i	0.982891	+	2.37291i
$670$		0			0
$671$		−	31.3702i		−	1.21103i
$672$		0			0
$673$	12.1579	−	12.1579i	0.468654	−	0.468654i	−0.432824	−	0.901478i	$-0.642483\pi$
$673$	12.1579	−	12.1579i	0.468654	−	0.468654i	0.901478	+	0.432824i	$0.142483\pi$
$674$		0			0
$675$	−3.14414	−	21.7617i	−0.121018	−	0.837607i
$676$		0			0
$677$	−38.8974	+	16.1118i	−1.49495	+	0.619228i	−0.972387	−	0.233375i	$-0.925023\pi$
$677$	−38.8974	+	16.1118i	−1.49495	+	0.619228i	−0.522561	+	0.852602i	$0.675023\pi$
$678$		0			0
$679$	13.4339	+	13.4339i	0.515546	+	0.515546i
$680$		0			0
$681$	50.7160	−	50.7160i	1.94344	−	1.94344i
$682$		0			0
$683$	−10.9032	−	26.3227i	−0.417200	−	1.00721i	−0.983155	−	0.182774i	$-0.941492\pi$
$683$	−10.9032	−	26.3227i	−0.417200	−	1.00721i	0.565955	−	0.824436i	$-0.308508\pi$
$684$		0			0
$685$	−4.17535	−	0.522982i	−0.159532	−	0.0199821i
$686$		0			0
$687$	33.0511	+	33.0511i	1.26098	+	1.26098i
$688$		0			0
$689$	−6.83923			−0.260554
$690$		0			0
$691$	−19.5933	+	8.11580i	−0.745363	+	0.308740i	−0.722848	−	0.691007i	$-0.757167\pi$
$691$	−19.5933	+	8.11580i	−0.745363	+	0.308740i	−0.0225151	+	0.999747i	$0.507167\pi$
$692$		0			0
$693$	−66.7817	+	27.6619i	−2.53683	+	1.05079i
$694$		0			0
$695$	1.15504	+	0.657207i	0.0438133	+	0.0249293i
$696$		0			0
$697$			8.42834i			0.319246i
$698$		0			0
$699$	23.6527	−	57.1026i	0.894626	−	2.15982i
$700$		0			0
$701$	17.3571	−	7.18953i	0.655567	−	0.271545i	−0.0300049	−	0.999550i	$-0.509552\pi$
$701$	17.3571	−	7.18953i	0.655567	−	0.271545i	0.685572	+	0.728005i	$0.259552\pi$
$702$		0			0
$703$	14.0925	+	14.0925i	0.531511	+	0.531511i
$704$		0			0
$705$	−6.84929	−	24.9331i	−0.257959	−	0.939036i
$706$		0			0
$707$	2.87445	−	6.93954i	0.108105	−	0.260988i
$708$		0			0
$709$	0.650888	+	0.269607i	0.0244446	+	0.0101253i	0.394872	−	0.918736i	$-0.370789\pi$
$709$	0.650888	+	0.269607i	0.0244446	+	0.0101253i	−0.370428	+	0.928861i	$0.620789\pi$
$710$		0			0
$711$	0.662496	−	0.662496i	0.0248455	−	0.0248455i
$712$		0			0
$713$			7.64001i			0.286121i
$714$		0			0
$715$	19.6036	−	15.2393i	0.733132	−	0.569918i
$716$		0			0
$717$	5.75923	−	13.9040i	0.215082	−	0.519255i
$718$		0			0
$719$		−	41.3849i		−	1.54340i	−0.635989	−	0.771698i	$-0.719408\pi$
$719$		−	41.3849i		−	1.54340i	0.635989	−	0.771698i	$-0.280592\pi$
$720$		0			0
$721$		−	14.2889i		−	0.532148i
$722$		0			0
$723$	−27.1713	+	65.5972i	−1.01051	+	2.43959i
$724$		0			0
$725$	3.74115	+	25.8938i	0.138943	+	0.961670i
$726$		0			0
$727$			31.9347i			1.18439i	0.805794	+	0.592196i	$0.201739\pi$
$727$			31.9347i			1.18439i	−0.805794	+	0.592196i	$0.798261\pi$
$728$		0			0
$729$	31.1273	−	31.1273i	1.15286	−	1.15286i
$730$		0			0
$731$	21.4191	+	8.87207i	0.792213	+	0.328145i
$732$		0			0
$733$	17.7686	−	42.8973i	0.656299	−	1.58445i	−0.147177	−	0.989110i	$-0.547019\pi$
$733$	17.7686	−	42.8973i	0.656299	−	1.58445i	0.803476	−	0.595337i	$-0.202981\pi$
$734$		0			0
$735$	−36.1728	−	20.5819i	−1.33425	−	0.759175i
$736$		0			0
$737$	27.4095	+	27.4095i	1.00964	+	1.00964i
$738$		0			0
$739$	−26.2226	+	10.8618i	−0.964616	+	0.399557i	−0.808705	−	0.588214i	$-0.799831\pi$
$739$	−26.2226	+	10.8618i	−0.964616	+	0.399557i	−0.155911	+	0.987771i	$0.549831\pi$
$740$		0			0
$741$	−5.92200	+	14.2970i	−0.217550	+	0.525213i
$742$		0			0
$743$		−	4.46895i		−	0.163950i	−0.996634	−	0.0819749i	$-0.973877\pi$
$743$		−	4.46895i		−	0.163950i	0.996634	−	0.0819749i	$-0.0261227\pi$
$744$		0			0
$745$	−10.2318	+	17.9824i	−0.374863	+	0.658823i
$746$		0			0
$747$	26.7029	−	11.0607i	0.977010	−	0.404691i
$748$		0			0
$749$	64.4747	−	26.7063i	2.35585	−	0.975827i
$750$		0			0
$751$	16.8523			0.614949			0.307474	−	0.951556i	$-0.400516\pi$
$751$	16.8523			0.614949			0.307474	+	0.951556i	$0.400516\pi$
$752$		0			0
$753$	16.8168	+	16.8168i	0.612837	+	0.612837i
$754$		0			0
$755$	−15.4430	−	19.8656i	−0.562029	−	0.722982i
$756$		0			0
$757$	14.0127	+	33.8297i	0.509302	+	1.22956i	0.944286	+	0.329125i	$0.106754\pi$
$757$	14.0127	+	33.8297i	0.509302	+	1.22956i	−0.434985	+	0.900438i	$0.643246\pi$
$758$		0			0
$759$	43.8518	−	43.8518i	1.59172	−	1.59172i
$760$		0			0
$761$	21.9685	+	21.9685i	0.796356	+	0.796356i	0.982519	−	0.186163i	$-0.0596051\pi$
$761$	21.9685	+	21.9685i	0.796356	+	0.796356i	−0.186163	+	0.982519i	$0.559605\pi$
$762$		0			0
$763$	2.86869	−	1.18825i	0.103853	−	0.0430175i
$764$		0			0
$765$	−37.2031	−	4.65986i	−1.34508	−	0.168478i
$766$		0			0
$767$	10.1669	−	10.1669i	0.367104	−	0.367104i
$768$		0			0
$769$			17.3648i			0.626192i	0.949721	+	0.313096i	$0.101366\pi$
$769$			17.3648i			0.626192i	−0.949721	+	0.313096i	$0.898634\pi$
$770$		0			0
$771$	22.5901	+	54.5373i	0.813563	+	1.96411i
$772$		0			0
$773$	−3.66118	−	8.83886i	−0.131683	−	0.317912i	0.844261	−	0.535933i	$-0.180040\pi$
$773$	−3.66118	−	8.83886i	−0.131683	−	0.317912i	−0.975944	+	0.218021i	$0.930040\pi$
$774$		0			0
$775$	−1.77583	+	6.97766i	−0.0637896	+	0.250645i
$776$		0			0
$777$	−94.9821			−3.40746
$778$		0			0
$779$	4.57693	+	1.89583i	0.163985	+	0.0679250i
$780$		0			0
$781$	5.60502	+	13.5317i	0.200563	+	0.484203i
$782$		0			0
$783$	16.2707	−	16.2707i	0.581466	−	0.581466i
$784$		0			0
$785$	−24.1178	−	13.7227i	−0.860801	−	0.489786i
$786$		0			0
$787$	32.0088	+	13.2585i	1.14099	+	0.472614i	0.871503	−	0.490390i	$-0.163146\pi$
$787$	32.0088	+	13.2585i	1.14099	+	0.472614i	0.269488	+	0.963004i	$0.413146\pi$
$788$		0			0
$789$	7.24913	−	17.5010i	0.258076	−	0.623050i
$790$		0			0
$791$	−39.4658	−	39.4658i	−1.40324	−	1.40324i
$792$		0			0
$793$	19.3652			0.687677
$794$		0			0
$795$	−15.9733	−	2.00073i	−0.566513	−	0.0709584i
$796$		0			0
$797$	−37.8964	−	15.6972i	−1.34236	−	0.556023i	−0.408203	−	0.912891i	$-0.633844\pi$
$797$	−37.8964	−	15.6972i	−1.34236	−	0.556023i	−0.934155	+	0.356868i	$0.883844\pi$
$798$		0			0
$799$	−15.3087			−0.541584
$800$		0			0
$801$	−12.6318			−0.446323
$802$		0			0
$803$	−27.5967	−	11.4309i	−0.973867	−	0.403389i
$804$		0			0
$805$	43.6551	+	5.46801i	1.53864	+	0.192722i
$806$		0			0
$807$	−60.6318			−2.13434
$808$		0			0
$809$	−4.54672	−	4.54672i	−0.159854	−	0.159854i	0.622648	−	0.782502i	$-0.286057\pi$
$809$	−4.54672	−	4.54672i	−0.159854	−	0.159854i	−0.782502	+	0.622648i	$0.786057\pi$
$810$		0			0
$811$	8.69312	−	20.9871i	0.305257	−	0.736955i	−0.694589	−	0.719407i	$-0.744414\pi$
$811$	8.69312	−	20.9871i	0.305257	−	0.736955i	0.999846	−	0.0175486i	$-0.00558619\pi$
$812$		0			0
$813$	31.7600	+	13.1554i	1.11387	+	0.461381i
$814$		0			0
$815$	−23.6099	−	13.4338i	−0.827020	−	0.470565i
$816$		0			0
$817$	9.63579	−	9.63579i	0.337114	−	0.337114i
$818$		0			0
$819$	−17.0760	−	41.2251i	−0.596684	−	1.44052i
$820$		0			0
$821$	9.76690	+	4.04558i	0.340867	+	0.141192i	0.546549	−	0.837427i	$-0.315941\pi$
$821$	9.76690	+	4.04558i	0.340867	+	0.141192i	−0.205682	+	0.978619i	$0.565941\pi$
$822$		0			0
$823$	32.4078			1.12966			0.564832	−	0.825206i	$-0.308941\pi$
$823$	32.4078			1.12966			0.564832	+	0.825206i	$0.308941\pi$
$824$		0			0
$825$	50.2429	−	29.8572i	1.74923	−	1.03950i
$826$		0			0
$827$	6.17678	+	14.9121i	0.214788	+	0.518543i	0.994147	−	0.108034i	$-0.0344554\pi$
$827$	6.17678	+	14.9121i	0.214788	+	0.518543i	−0.779360	+	0.626577i	$0.784455\pi$
$828$		0			0
$829$	2.07649	+	5.01309i	0.0721194	+	0.174112i	0.955829	−	0.293925i	$-0.0949616\pi$
$829$	2.07649	+	5.01309i	0.0721194	+	0.174112i	−0.883709	+	0.468037i	$0.844962\pi$
$830$		0			0
$831$			64.7159i			2.24497i
$832$		0			0
$833$	−17.4235	+	17.4235i	−0.603687	+	0.603687i
$834$		0			0
$835$	−38.0869	−	4.77056i	−1.31805	−	0.165092i
$836$		0			0
$837$	5.85048	−	2.42335i	0.202222	−	0.0837632i
$838$		0			0
$839$	31.8237	+	31.8237i	1.09868	+	1.09868i	0.994566	+	0.104110i	$0.0331994\pi$
$839$	31.8237	+	31.8237i	1.09868	+	1.09868i	0.104110	+	0.994566i	$0.466801\pi$
$840$		0			0
$841$	1.14598	−	1.14598i	0.0395166	−	0.0395166i
$842$		0			0
$843$	−7.94812	−	19.1885i	−0.273748	−	0.660885i
$844$		0			0
$845$	−8.43340	−	10.8486i	−0.290118	−	0.373202i
$846$		0			0
$847$	−18.3257	−	18.3257i	−0.629678	−	0.629678i
$848$		0			0
$849$	30.6027			1.05028
$850$		0			0
$851$	45.5510	−	18.8679i	1.56147	−	0.646782i
$852$		0			0
$853$	42.6825	−	17.6797i	1.46142	−	0.605341i	0.496537	−	0.868015i	$-0.334605\pi$
$853$	42.6825	−	17.6797i	1.46142	−	0.605341i	0.964884	+	0.262675i	$0.0846046\pi$
$854$		0			0
$855$	−10.8988	+	19.1546i	−0.372730	+	0.655074i
$856$		0			0
$857$		−	44.9421i		−	1.53519i	−0.640934	−	0.767596i	$-0.721453\pi$
$857$		−	44.9421i		−	1.53519i	0.640934	−	0.767596i	$-0.278547\pi$
$858$		0			0
$859$	15.0404	−	36.3106i	0.513170	−	1.23890i	−0.428859	−	0.903372i	$-0.641084\pi$
$859$	15.0404	−	36.3106i	0.513170	−	1.23890i	0.942029	−	0.335531i	$-0.108916\pi$
$860$		0			0
$861$	−21.8128	+	9.03516i	−0.743378	+	0.307917i
$862$		0			0
$863$	38.7485	+	38.7485i	1.31901	+	1.31901i	0.914558	+	0.404455i	$0.132539\pi$
$863$	38.7485	+	38.7485i	1.31901	+	1.31901i	0.404455	+	0.914558i	$0.367461\pi$
$864$		0			0
$865$	11.8479	+	6.74131i	0.402840	+	0.229211i
$866$		0			0
$867$	3.88904	−	9.38897i	0.132079	−	0.318866i
$868$		0			0
$869$	0.798850	+	0.330894i	0.0270991	+	0.0112248i
$870$		0			0
$871$	−16.9202	+	16.9202i	−0.573320	+	0.573320i
$872$		0			0
$873$			23.5427i			0.796800i
$874$		0			0
$875$	38.5994	+	15.1411i	1.30490	+	0.511861i
$876$		0			0
$877$	6.21828	−	15.0122i	0.209976	−	0.506928i	−0.783443	−	0.621464i	$-0.786538\pi$
$877$	6.21828	−	15.0122i	0.209976	−	0.506928i	0.993419	+	0.114536i	$0.0365382\pi$
$878$		0			0
$879$			30.6168i			1.03268i
$880$		0			0
$881$		−	29.0942i		−	0.980208i	−0.871664	−	0.490104i	$-0.836959\pi$
$881$		−	29.0942i		−	0.980208i	0.871664	−	0.490104i	$-0.163041\pi$
$882$		0			0
$883$	−13.2835	+	32.0692i	−0.447025	+	1.07921i	0.526406	+	0.850233i	$0.323539\pi$
$883$	−13.2835	+	32.0692i	−0.447025	+	1.07921i	−0.973431	+	0.228980i	$0.926461\pi$
$884$		0			0
$885$	26.7193	−	20.7709i	0.898159	−	0.698207i
$886$		0			0
$887$		−	33.3087i		−	1.11840i	−0.829034	−	0.559199i	$-0.811109\pi$
$887$		−	33.3087i		−	1.11840i	0.829034	−	0.559199i	$-0.188891\pi$
$888$		0			0
$889$	−48.0926	+	48.0926i	−1.61297	+	1.61297i
$890$		0			0
$891$	6.53274	+	2.70595i	0.218855	+	0.0906527i
$892$		0			0
$893$	−3.44347	+	8.31327i	−0.115231	+	0.278193i
$894$		0			0
$895$	−6.15685	−	22.4125i	−0.205801	−	0.749166i
$896$		0			0
$897$	27.0702	+	27.0702i	0.903849	+	0.903849i
$898$		0			0
$899$	−6.96137	+	2.88349i	−0.232175	+	0.0961699i
$900$		0			0
$901$	−3.64736	+	8.80551i	−0.121511	+	0.293354i
$902$		0			0
$903$			64.9441i			2.16120i
$904$		0			0
$905$	46.7384	+	26.5936i	1.55364	+	0.884001i
$906$		0			0
$907$	0.145961	−	0.0604591i	0.00484656	−	0.00200751i	−0.380259	−	0.924880i	$-0.624165\pi$
$907$	0.145961	−	0.0604591i	0.00484656	−	0.00200751i	0.385105	+	0.922873i	$0.374165\pi$
$908$		0			0
$909$	8.59943	−	3.56200i	0.285225	−	0.118144i
$910$		0			0
$911$	7.19740			0.238461			0.119230	−	0.992867i	$-0.461957\pi$
$911$	7.19740			0.238461			0.119230	+	0.992867i	$0.461957\pi$
$912$		0			0
$913$	18.8617	+	18.8617i	0.624231	+	0.624231i
$914$		0			0
$915$	45.2281	+	5.66503i	1.49519	+	0.187280i
$916$		0			0
$917$	30.9890	+	74.8141i	1.02335	+	2.47058i
$918$		0			0
$919$	18.9346	−	18.9346i	0.624593	−	0.624593i	−0.322109	−	0.946703i	$-0.604392\pi$
$919$	18.9346	−	18.9346i	0.624593	−	0.624593i	0.946703	+	0.322109i	$0.104392\pi$
$920$		0			0
$921$	−1.89372	−	1.89372i	−0.0624000	−	0.0624000i
$922$		0			0
$923$	−8.35329	+	3.46004i	−0.274952	+	0.113889i
$924$		0			0
$925$	45.9875	−	6.64431i	1.51206	−	0.218463i
$926$		0			0
$927$	12.5206	−	12.5206i	0.411230	−	0.411230i
$928$		0			0
$929$			1.41239i			0.0463390i	0.999732	+	0.0231695i	$0.00737573\pi$
$929$			1.41239i			0.0463390i	−0.999732	+	0.0231695i	$0.992624\pi$
$930$		0			0
$931$	5.54250	+	13.3808i	0.181648	+	0.438537i
$932$		0			0
$933$	−10.0442	−	24.2488i	−0.328832	−	0.793871i
$934$		0			0
$935$	−9.16605	−	33.3667i	−0.299762	−	1.09121i
$936$		0			0
$937$	−12.6258			−0.412468			−0.206234	−	0.978503i	$-0.566121\pi$
$937$	−12.6258			−0.412468			−0.206234	+	0.978503i	$0.566121\pi$
$938$		0			0
$939$	18.9532	+	7.85068i	0.618515	+	0.256197i
$940$		0			0
$941$	11.3405	+	27.3783i	0.369688	+	0.892507i	0.993801	+	0.111172i	$0.0354606\pi$
$941$	11.3405	+	27.3783i	0.369688	+	0.892507i	−0.624113	+	0.781334i	$0.714539\pi$
$942$		0			0
$943$	8.66607	−	8.66607i	0.282206	−	0.282206i
$944$		0			0
$945$	−9.65981	−	35.1641i	−0.314234	−	1.14389i
$946$		0			0
$947$	−29.7484	−	12.3222i	−0.966694	−	0.400418i	−0.157213	−	0.987565i	$-0.550251\pi$
$947$	−29.7484	−	12.3222i	−0.966694	−	0.400418i	−0.809480	+	0.587147i	$0.800251\pi$
$948$		0			0
$949$	7.05644	−	17.0358i	0.229062	−	0.553004i
$950$		0			0
$951$	11.5471	+	11.5471i	0.374439	+	0.374439i
$952$		0			0
$953$	−60.5106			−1.96013			−0.980066	−	0.198673i	$-0.936337\pi$
$953$	−60.5106			−1.96013			−0.980066	+	0.198673i	$0.936337\pi$
$954$		0			0
$955$	2.39627	−	19.1312i	0.0775414	−	0.619070i
$956$		0			0
$957$	56.5071	+	23.4060i	1.82662	+	0.756609i
$958$		0			0
$959$	−6.97898			−0.225363
$960$		0			0
$961$	28.9264			0.933108
$962$		0			0
$963$	79.8967	+	33.0943i	2.57463	+	1.06645i
$964$		0			0
$965$	32.7373	−	25.4492i	1.05385	−	0.819237i
$966$		0			0
$967$	18.3324			0.589531			0.294766	−	0.955570i	$-0.404758\pi$
$967$	18.3324			0.589531			0.294766	+	0.955570i	$0.404758\pi$
$968$		0			0
$969$	15.2492	+	15.2492i	0.489873	+	0.489873i
$970$		0			0
$971$	−0.992401	+	2.39587i	−0.0318477	+	0.0768870i	−0.939003	−	0.343908i	$-0.888249\pi$
$971$	−0.992401	+	2.39587i	−0.0318477	+	0.0768870i	0.907156	+	0.420796i	$0.138249\pi$
$972$		0			0
$973$	2.03627	+	0.843451i	0.0652798	+	0.0270398i
$974$		0			0
$975$	18.4312	+	31.0155i	0.590271	+	0.993291i
$976$		0			0
$977$	21.9823	−	21.9823i	0.703276	−	0.703276i	−0.261836	−	0.965112i	$-0.584328\pi$
$977$	21.9823	−	21.9823i	0.703276	−	0.703276i	0.965112	+	0.261836i	$0.0843280\pi$
$978$		0			0
$979$	−4.46126	−	10.7704i	−0.142582	−	0.344224i
$980$		0			0
$981$	3.55486	+	1.47247i	0.113498	+	0.0470124i
$982$		0			0
$983$	−33.0141			−1.05299			−0.526493	−	0.850180i	$-0.676493\pi$
$983$	−33.0141			−1.05299			−0.526493	+	0.850180i	$0.676493\pi$
$984$		0			0
$985$	−24.2429	+	6.65969i	−0.772444	+	0.212195i
$986$		0			0
$987$	−16.4109	−	39.6195i	−0.522366	−	1.26110i
$988$		0			0
$989$	−12.9009	−	31.1455i	−0.410225	−	0.990370i
$990$		0			0
$991$			1.26612i			0.0402198i	0.999798	+	0.0201099i	$0.00640161\pi$
$991$			1.26612i			0.0402198i	−0.999798	+	0.0201099i	$0.993598\pi$
$992$		0			0
$993$	−35.2377	+	35.2377i	−1.11824	+	1.11824i
$994$		0			0
$995$	−3.03476	−	3.90386i	−0.0962084	−	0.123761i
$996$		0			0
$997$	−9.06030	+	3.75290i	−0.286943	+	0.118856i	−0.521512	−	0.853244i	$-0.674632\pi$
$997$	−9.06030	+	3.75290i	−0.286943	+	0.118856i	0.234570	+	0.972099i	$0.424632\pi$
$998$		0			0
$999$	−28.8968	−	28.8968i	−0.914255	−	0.914255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.ba.a.207.2		88
4.3	odd	2		160.2.ba.a.107.11	yes	88
5.3	odd	4		640.2.u.a.463.21		88
20.3	even	4		160.2.u.a.43.22	✓	88
20.7	even	4		800.2.v.b.43.1		88
20.19	odd	2		800.2.bb.b.107.12		88
32.3	odd	8		640.2.u.a.47.21		88
32.29	even	8		160.2.u.a.67.22	yes	88
160.3	even	8	inner	640.2.ba.a.303.2		88
160.29	even	8		800.2.v.b.707.1		88
160.93	odd	8		160.2.ba.a.3.11	yes	88
160.157	odd	8		800.2.bb.b.643.12		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.22	✓	88	20.3	even	4
160.2.u.a.67.22	yes	88	32.29	even	8
160.2.ba.a.3.11	yes	88	160.93	odd	8
160.2.ba.a.107.11	yes	88	4.3	odd	2
640.2.u.a.47.21		88	32.3	odd	8
640.2.u.a.463.21		88	5.3	odd	4
640.2.ba.a.207.2		88	1.1	even	1	trivial
640.2.ba.a.303.2		88	160.3	even	8	inner
800.2.v.b.43.1		88	20.7	even	4
800.2.v.b.707.1		88	160.29	even	8
800.2.bb.b.107.12		88	20.19	odd	2
800.2.bb.b.643.12		88	160.157	odd	8

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.ba (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.54622 - 1.05468i) q^{3} +(2.21873 + 0.277906i) q^{5} +3.70855 q^{7} +(3.24959 + 3.24959i) q^{9} +O(q^{10})\)	\(q+(-2.54622 - 1.05468i) q^{3} +(2.21873 + 0.277906i) q^{5} +3.70855 q^{7} +(3.24959 + 3.24959i) q^{9} +(-1.62306 + 3.91841i) q^{11} +(-2.41888 - 1.00193i) q^{13} +(-5.35629 - 3.04767i) q^{15} +(-2.57998 + 2.57998i) q^{17} +(0.820706 + 1.98136i) q^{19} +(-9.44280 - 3.91133i) q^{21} +5.30550 q^{23} +(4.84554 + 1.23320i) q^{25} +(-1.68286 - 4.06279i) q^{27} +(2.00240 + 4.83422i) q^{29} +1.44002i q^{31} +(8.26535 - 8.26535i) q^{33} +(8.22827 + 1.03063i) q^{35} +(8.58562 - 3.55628i) q^{37} +(5.10230 + 5.10230i) q^{39} +(1.63341 - 1.63341i) q^{41} +(-2.43161 - 5.87042i) q^{43} +(6.30688 + 8.11304i) q^{45} +(2.96683 + 2.96683i) q^{47} +6.75333 q^{49} +(9.29026 - 3.84815i) q^{51} +(2.41336 - 0.999648i) q^{53} +(-4.69009 + 8.24285i) q^{55} -5.91057i q^{57} +(-2.10156 + 5.07362i) q^{59} +(-6.83341 + 2.83049i) q^{61} +(12.0513 + 12.0513i) q^{63} +(-5.08841 - 2.89524i) q^{65} +(3.49753 - 8.44379i) q^{67} +(-13.5090 - 5.59561i) q^{69} +(2.44190 - 2.44190i) q^{71} +7.04282i q^{73} +(-11.0372 - 8.25050i) q^{75} +(-6.01920 + 14.5316i) q^{77} -0.203871i q^{79} -1.66719i q^{81} +(2.40680 - 5.81053i) q^{83} +(-6.44127 + 5.00729i) q^{85} -14.4209i q^{87} +(-1.94360 + 1.94360i) q^{89} +(-8.97054 - 3.71572i) q^{91} +(1.51876 - 3.66661i) q^{93} +(1.27029 + 4.62419i) q^{95} +(3.62241 + 3.62241i) q^{97} +(-18.0075 + 7.45896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 4 q^{5} + 8 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 4 * q^5 + 8 * q^7	\( 88 q + 4 q^{3} - 4 q^{5} + 8 q^{7} + 8 q^{11} - 4 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} + 8 q^{23} - 4 q^{25} - 8 q^{27} - 8 q^{33} + 48 q^{35} - 4 q^{37} - 8 q^{41} - 28 q^{43} - 4 q^{45} + 8 q^{47} + 40 q^{49} - 8 q^{51} - 4 q^{53} - 28 q^{55} - 40 q^{61} + 56 q^{63} - 8 q^{65} + 28 q^{67} - 24 q^{69} - 24 q^{71} + 16 q^{75} - 32 q^{77} - 36 q^{83} - 4 q^{85} + 8 q^{91} + 8 q^{93} - 8 q^{97}+O(q^{100}) \) 88 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 + 8 * q^11 - 4 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 + 8 * q^23 - 4 * q^25 - 8 * q^27 - 8 * q^33 + 48 * q^35 - 4 * q^37 - 8 * q^41 - 28 * q^43 - 4 * q^45 + 8 * q^47 + 40 * q^49 - 8 * q^51 - 4 * q^53 - 28 * q^55 - 40 * q^61 + 56 * q^63 - 8 * q^65 + 28 * q^67 - 24 * q^69 - 24 * q^71 + 16 * q^75 - 32 * q^77 - 36 * q^83 - 4 * q^85 + 8 * q^91 + 8 * q^93 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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