LMFDB - Embedded newform 400.2.bi.c.303.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} - 64 x^{13} + 66 x^{12} - 28 x^{11} + 160 x^{10} - 392 x^{9} + 419 x^{8} + \cdots + 1 $ x^16 - 8x^15 + 32x^14 - 64x^13 + 66x^12 - 28x^11 + 160x^10 - 392x^9 + 419x^8 + 164x^7 + 200x^6 - 576x^5 + 726x^4 + 668x^3 + 288x^2 + 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			303.1
Root			$1.04676 + 1.04676i$ of defining polynomial
Character	$\chi$	$=$	400.303
Dual form			400.2.bi.c.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13351 + 0.337915i) q^{3} +2.23607 q^{5} +(-1.09351 - 1.09351i) q^{7} +(1.58450 - 0.514836i) q^{9} +O(q^{10})$	\(q+(-2.13351 + 0.337915i) q^{3} +2.23607 q^{5} +(-1.09351 - 1.09351i) q^{7} +(1.58450 - 0.514836i) q^{9} +(1.97819 + 0.642752i) q^{11} +(0.587785 - 1.15359i) q^{13} +(-4.77067 + 0.755600i) q^{15} +(-0.224514 + 1.41753i) q^{17} +(6.56626 - 4.77067i) q^{19} +(2.70254 + 1.96351i) q^{21} +(2.41210 + 4.73400i) q^{23} +5.00000 q^{25} +(2.56742 - 1.30816i) q^{27} +(3.65359 - 5.02874i) q^{29} +(3.63007 + 4.99637i) q^{31} +(-4.43767 - 0.702858i) q^{33} +(-2.44517 - 2.44517i) q^{35} +(0.658904 + 0.335729i) q^{37} +(-0.864229 + 2.65982i) q^{39} +(2.49411 + 7.67609i) q^{41} +(-2.49767 + 2.49767i) q^{43} +(3.54306 - 1.15121i) q^{45} +(-1.64967 - 10.4156i) q^{47} -4.60845i q^{49} -3.10017i q^{51} +(-1.37633 - 8.68983i) q^{53} +(4.42336 + 1.43724i) q^{55} +(-12.3971 + 12.3971i) q^{57} +(1.75249 + 5.39361i) q^{59} +(-1.25148 + 3.85166i) q^{61} +(-2.29566 - 1.16970i) q^{63} +(1.31433 - 2.57951i) q^{65} +(-4.77067 - 0.755600i) q^{67} +(-6.74591 - 9.28496i) q^{69} +(-2.26680 + 3.11998i) q^{71} +(-11.3066 + 5.76101i) q^{73} +(-10.6675 + 1.68957i) q^{75} +(-1.46032 - 2.86603i) q^{77} +(-12.6026 - 9.15634i) q^{79} +(-9.07914 + 6.59638i) q^{81} +(0.0651353 - 0.411248i) q^{83} +(-0.502029 + 3.16968i) q^{85} +(-6.09569 + 11.9635i) q^{87} +(0.613243 + 0.199255i) q^{89} +(-1.90422 + 0.618720i) q^{91} +(-9.43314 - 9.43314i) q^{93} +(14.6826 - 10.6675i) q^{95} +(-17.7541 + 2.81198i) q^{97} +3.46535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{9}+O(q^{10}) $ 16 * q + 20 * q^9	$ 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93} - 80 q^{97}+O(q^{100}) $ 16 * q + 20 * q^9 + 20 * q^21 + 80 * q^25 + 20 * q^29 - 20 * q^33 - 40 * q^37 - 12 * q^41 + 20 * q^45 - 40 * q^53 + 20 * q^57 - 12 * q^61 - 60 * q^69 - 40 * q^73 - 100 * q^77 - 24 * q^81 - 60 * q^89 - 100 * q^93 - 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$-1$

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
$3$	−2.13351	+	0.337915i	−1.23178	+	0.195095i	−0.738187	−	0.674597i	$-0.764318\pi$
$3$	−2.13351	+	0.337915i	−1.23178	+	0.195095i	−0.493595	+	0.869692i	$0.664318\pi$
$4$		0			0
$5$	2.23607			1.00000
$5$	2.23607			1.00000
$6$		0			0
$7$	−1.09351	−	1.09351i	−0.413310	−	0.413310i	0.469580	−	0.882890i	$-0.344405\pi$
$7$	−1.09351	−	1.09351i	−0.413310	−	0.413310i	−0.882890	+	0.469580i	$0.844405\pi$
$8$		0			0
$9$	1.58450	−	0.514836i	0.528168	−	0.171612i
$10$		0			0
$11$	1.97819	+	0.642752i	0.596446	+	0.193797i	0.591655	−	0.806192i	$-0.298475\pi$
$11$	1.97819	+	0.642752i	0.596446	+	0.193797i	0.00479106	+	0.999989i	$0.498475\pi$
$12$		0			0
$13$	0.587785	−	1.15359i	0.163022	−	0.319949i	−0.795017	−	0.606588i	$-0.792538\pi$
$13$	0.587785	−	1.15359i	0.163022	−	0.319949i	0.958039	+	0.286639i	$0.0925379\pi$
$14$		0			0
$15$	−4.77067	+	0.755600i	−1.23178	+	0.195095i
$16$		0			0
$17$	−0.224514	+	1.41753i	−0.0544526	+	0.343800i	0.945388	+	0.325947i	$0.105683\pi$
$17$	−0.224514	+	1.41753i	−0.0544526	+	0.343800i	−0.999841	+	0.0178532i	$0.994317\pi$
$18$		0			0
$19$	6.56626	−	4.77067i	1.50640	−	1.09447i	0.538663	−	0.842521i	$-0.318930\pi$
$19$	6.56626	−	4.77067i	1.50640	−	1.09447i	0.967741	−	0.251945i	$-0.0810703\pi$
$20$		0			0
$21$	2.70254	+	1.96351i	0.589742	+	0.428473i
$22$		0			0
$23$	2.41210	+	4.73400i	0.502957	+	0.987108i	0.993298	+	0.115578i	$0.0368719\pi$
$23$	2.41210	+	4.73400i	0.502957	+	0.987108i	−0.490342	+	0.871530i	$0.663128\pi$
$24$		0			0
$25$	5.00000			1.00000
$26$		0			0
$27$	2.56742	−	1.30816i	0.494100	−	0.251756i
$28$		0			0
$29$	3.65359	−	5.02874i	0.678455	−	0.933814i	−0.321459	−	0.946924i	$-0.604173\pi$
$29$	3.65359	−	5.02874i	0.678455	−	0.933814i	0.999914	+	0.0131100i	$0.00417316\pi$
$30$		0			0
$31$	3.63007	+	4.99637i	0.651980	+	0.897374i	0.999183	−	0.0404162i	$-0.0128684\pi$
$31$	3.63007	+	4.99637i	0.651980	+	0.897374i	−0.347203	+	0.937790i	$0.612868\pi$
$32$		0			0
$33$	−4.43767	−	0.702858i	−0.772500	−	0.122352i
$34$		0			0
$35$	−2.44517	−	2.44517i	−0.413310	−	0.413310i
$36$		0			0
$37$	0.658904	+	0.335729i	0.108323	+	0.0551934i	0.507313	−	0.861762i	$-0.330639\pi$
$37$	0.658904	+	0.335729i	0.108323	+	0.0551934i	−0.398989	+	0.916956i	$0.630639\pi$
$38$		0			0
$39$	−0.864229	+	2.65982i	−0.138387	+	0.425913i
$40$		0			0
$41$	2.49411	+	7.67609i	0.389515	+	1.19880i	0.933152	+	0.359483i	$0.117047\pi$
$41$	2.49411	+	7.67609i	0.389515	+	1.19880i	−0.543637	+	0.839321i	$0.682953\pi$
$42$		0			0
$43$	−2.49767	+	2.49767i	−0.380892	+	0.380892i	−0.871423	−	0.490532i	$-0.836803\pi$
$43$	−2.49767	+	2.49767i	−0.380892	+	0.380892i	0.490532	+	0.871423i	$0.336803\pi$
$44$		0			0
$45$	3.54306	−	1.15121i	0.528168	−	0.171612i
$46$		0			0
$47$	−1.64967	−	10.4156i	−0.240629	−	1.51927i	−0.751569	−	0.659655i	$-0.770703\pi$
$47$	−1.64967	−	10.4156i	−0.240629	−	1.51927i	0.510940	−	0.859616i	$-0.329297\pi$
$48$		0			0
$49$		−	4.60845i		−	0.658350i
$50$		0			0
$51$		−	3.10017i		−	0.434111i
$52$		0			0
$53$	−1.37633	−	8.68983i	−0.189054	−	1.19364i	−0.881505	−	0.472175i	$-0.843469\pi$
$53$	−1.37633	−	8.68983i	−0.189054	−	1.19364i	0.692451	−	0.721465i	$-0.256531\pi$
$54$		0			0
$55$	4.42336	+	1.43724i	0.596446	+	0.193797i
$56$		0			0
$57$	−12.3971	+	12.3971i	−1.64204	+	1.64204i
$58$		0			0
$59$	1.75249	+	5.39361i	0.228155	+	0.702188i	0.997956	+	0.0639045i	$0.0203553\pi$
$59$	1.75249	+	5.39361i	0.228155	+	0.702188i	−0.769801	+	0.638284i	$0.779645\pi$
$60$		0			0
$61$	−1.25148	+	3.85166i	−0.160236	+	0.493155i	−0.998654	−	0.0518731i	$-0.983481\pi$
$61$	−1.25148	+	3.85166i	−0.160236	+	0.493155i	0.838418	+	0.545028i	$0.183481\pi$
$62$		0			0
$63$	−2.29566	−	1.16970i	−0.289226	−	0.147368i
$64$		0			0
$65$	1.31433	−	2.57951i	0.163022	−	0.319949i
$66$		0			0
$67$	−4.77067	−	0.755600i	−0.582830	−	0.0923112i	−0.141945	−	0.989875i	$-0.545336\pi$
$67$	−4.77067	−	0.755600i	−0.582830	−	0.0923112i	−0.440885	+	0.897563i	$0.645336\pi$
$68$		0			0
$69$	−6.74591	−	9.28496i	−0.812113	−	1.11778i
$70$		0			0
$71$	−2.26680	+	3.11998i	−0.269020	+	0.370274i	−0.922058	−	0.387051i	$-0.873494\pi$
$71$	−2.26680	+	3.11998i	−0.269020	+	0.370274i	0.653039	+	0.757324i	$0.273494\pi$
$72$		0			0
$73$	−11.3066	+	5.76101i	−1.32334	+	0.674275i	−0.965718	−	0.259592i	$-0.916412\pi$
$73$	−11.3066	+	5.76101i	−1.32334	+	0.674275i	−0.357620	+	0.933867i	$0.616412\pi$
$74$		0			0
$75$	−10.6675	+	1.68957i	−1.23178	+	0.195095i
$76$		0			0
$77$	−1.46032	−	2.86603i	−0.166419	−	0.326615i
$78$		0			0
$79$	−12.6026	−	9.15634i	−1.41791	−	1.03017i	−0.992113	−	0.125349i	$-0.959995\pi$
$79$	−12.6026	−	9.15634i	−1.41791	−	1.03017i	−0.425793	−	0.904820i	$-0.640005\pi$
$80$		0			0
$81$	−9.07914	+	6.59638i	−1.00879	+	0.732931i
$82$		0			0
$83$	0.0651353	−	0.411248i	0.00714952	−	0.0451403i	−0.983856	−	0.178964i	$-0.942726\pi$
$83$	0.0651353	−	0.411248i	0.00714952	−	0.0451403i	0.991005	+	0.133823i	$0.0427255\pi$
$84$		0			0
$85$	−0.502029	+	3.16968i	−0.0544526	+	0.343800i
$86$		0			0
$87$	−6.09569	+	11.9635i	−0.653526	+	1.28262i
$88$		0			0
$89$	0.613243	+	0.199255i	0.0650036	+	0.0211210i	0.341338	−	0.939941i	$-0.389120\pi$
$89$	0.613243	+	0.199255i	0.0650036	+	0.0211210i	−0.276335	+	0.961061i	$0.589120\pi$
$90$		0			0
$91$	−1.90422	+	0.618720i	−0.199617	+	0.0648594i
$92$		0			0
$93$	−9.43314	−	9.43314i	−0.978171	−	0.978171i
$94$		0			0
$95$	14.6826	−	10.6675i	1.50640	−	1.09447i
$96$		0			0
$97$	−17.7541	+	2.81198i	−1.80266	+	0.285513i	−0.965301	−	0.261141i	$-0.915901\pi$
$97$	−17.7541	+	2.81198i	−1.80266	+	0.285513i	−0.837358	+	0.546655i	$0.815901\pi$
$98$		0			0
$99$	3.46535			0.348281
$100$		0			0
$101$	11.9596			1.19002			0.595012	−	0.803717i	$-0.297147\pi$
$101$	11.9596			1.19002			0.595012	+	0.803717i	$0.297147\pi$
$102$		0			0
$103$	13.3780	−	2.11887i	1.31818	−	0.208779i	0.542579	−	0.840005i	$-0.317448\pi$
$103$	13.3780	−	2.11887i	1.31818	−	0.208779i	0.775599	+	0.631226i	$0.217448\pi$
$104$		0			0
$105$	6.04306	+	4.39054i	0.589742	+	0.428473i
$106$		0			0
$107$	12.3834	+	12.3834i	1.19715	+	1.19715i	0.975018	+	0.222128i	$0.0713001\pi$
$107$	12.3834	+	12.3834i	1.19715	+	1.19715i	0.222128	+	0.975018i	$0.428700\pi$
$108$		0			0
$109$	0.113299	−	0.0368132i	0.0108521	−	0.00352607i	−0.303586	−	0.952804i	$-0.598184\pi$
$109$	0.113299	−	0.0368132i	0.0108521	−	0.00352607i	0.314438	+	0.949278i	$0.398184\pi$
$110$		0			0
$111$	−1.51923	−	0.493626i	−0.144199	−	0.0468529i
$112$		0			0
$113$	−0.492916	+	0.967401i	−0.0463696	+	0.0910055i	−0.913029	−	0.407895i	$-0.866263\pi$
$113$	−0.492916	+	0.967401i	−0.0463696	+	0.0910055i	0.866659	+	0.498901i	$0.166263\pi$
$114$		0			0
$115$	5.39361	+	10.5856i	0.502957	+	0.987108i
$116$		0			0
$117$	0.337436	−	2.13049i	0.0311959	−	0.196963i
$118$		0			0
$119$	1.79559	−	1.30458i	0.164602	−	0.119590i
$120$		0			0
$121$	−5.39910	−	3.92267i	−0.490827	−	0.356607i
$122$		0			0
$123$	−7.91507	−	15.5342i	−0.713678	−	1.40067i
$124$		0			0
$125$	11.1803			1.00000
$126$		0			0
$127$	10.1516	−	5.17252i	0.900813	−	0.458987i	0.0586921	−	0.998276i	$-0.481307\pi$
$127$	10.1516	−	5.17252i	0.900813	−	0.458987i	0.842121	+	0.539289i	$0.181307\pi$
$128$		0			0
$129$	4.48481	−	6.17281i	0.394865	−	0.543485i
$130$		0			0
$131$	−8.78574	−	12.0925i	−0.767614	−	1.05653i	−0.996542	−	0.0830864i	$-0.973522\pi$
$131$	−8.78574	−	12.0925i	−0.767614	−	1.05653i	0.228929	−	0.973443i	$-0.426478\pi$
$132$		0			0
$133$	−12.3971	−	1.96351i	−1.07497	−	0.170258i
$134$		0			0
$135$	5.74092	−	2.92514i	0.494100	−	0.251756i
$136$		0			0
$137$	12.2633	+	6.24846i	1.04772	+	0.533842i	0.891096	−	0.453815i	$-0.149937\pi$
$137$	12.2633	+	6.24846i	1.04772	+	0.533842i	0.156629	+	0.987658i	$0.449937\pi$
$138$		0			0
$139$	−4.77489	+	14.6956i	−0.405001	+	1.24646i	0.515894	+	0.856653i	$0.327460\pi$
$139$	−4.77489	+	14.6956i	−0.405001	+	1.24646i	−0.920895	+	0.389812i	$0.872540\pi$
$140$		0			0
$141$	7.03916	+	21.6643i	0.592804	+	1.82446i
$142$		0			0
$143$	1.90422	−	1.90422i	0.159239	−	0.159239i
$144$		0			0
$145$	8.16968	−	11.2446i	0.678455	−	0.933814i
$146$		0			0
$147$	1.55726	+	9.83217i	0.128441	+	0.810944i
$148$		0			0
$149$		−	11.8636i		−	0.971902i	−0.873986	−	0.485951i	$-0.838473\pi$
$149$		−	11.8636i		−	0.971902i	0.873986	−	0.485951i	$-0.161527\pi$
$150$		0			0
$151$		−	7.18238i		−	0.584493i	−0.956343	−	0.292247i	$-0.905597\pi$
$151$		−	7.18238i		−	0.584493i	0.956343	−	0.292247i	$-0.0944028\pi$
$152$		0			0
$153$	0.374050	+	2.36166i	0.0302402	+	0.190929i
$154$		0			0
$155$	8.11709	+	11.1722i	0.651980	+	0.897374i
$156$		0			0
$157$	−11.9970	+	11.9970i	−0.957463	+	0.957463i	−0.999132	−	0.0416681i	$-0.986733\pi$
$157$	−11.9970	+	11.9970i	−0.957463	+	0.957463i	0.0416681	+	0.999132i	$0.486733\pi$
$158$		0			0
$159$	5.87284	+	18.0747i	0.465747	+	1.43342i
$160$		0			0
$161$	2.53904	−	7.81436i	0.200104	−	0.615858i
$162$		0			0
$163$	1.12659	+	0.574027i	0.0882415	+	0.0449613i	0.497554	−	0.867433i	$-0.334232\pi$
$163$	1.12659	+	0.574027i	0.0882415	+	0.0449613i	−0.409313	+	0.912394i	$0.634232\pi$
$164$		0			0
$165$	−9.92294	−	1.57164i	−0.772500	−	0.122352i
$166$		0			0
$167$	−13.4234	−	2.12605i	−1.03873	−	0.164519i	−0.386305	−	0.922371i	$-0.626249\pi$
$167$	−13.4234	−	2.12605i	−1.03873	−	0.164519i	−0.652426	+	0.757852i	$0.726249\pi$
$168$		0			0
$169$	6.65592	+	9.16109i	0.511994	+	0.704699i
$170$		0			0
$171$	7.94815	−	10.9397i	0.607810	−	0.836579i
$172$		0			0
$173$	12.9584	−	6.60262i	0.985207	−	0.501988i	0.114305	−	0.993446i	$-0.463536\pi$
$173$	12.9584	−	6.60262i	0.985207	−	0.501988i	0.870901	+	0.491458i	$0.163536\pi$
$174$		0			0
$175$	−5.46757	−	5.46757i	−0.413310	−	0.413310i
$176$		0			0
$177$	−5.56153	−	10.9151i	−0.418030	−	0.820431i
$178$		0			0
$179$	−18.0481	−	13.1127i	−1.34898	−	0.980090i	−0.999062	−	0.0433097i	$-0.986210\pi$
$179$	−18.0481	−	13.1127i	−1.34898	−	0.980090i	−0.349917	−	0.936781i	$-0.613790\pi$
$180$		0			0
$181$	−2.16125	+	1.57024i	−0.160645	+	0.116715i	−0.665203	−	0.746662i	$-0.731655\pi$
$181$	−2.16125	+	1.57024i	−0.160645	+	0.116715i	0.504559	+	0.863377i	$0.331655\pi$
$182$		0			0
$183$	1.36851	−	8.64044i	0.101163	−	0.638720i
$184$		0			0
$185$	1.47335	+	0.750712i	0.108323	+	0.0551934i
$186$		0			0
$187$	−1.35525	+	2.65982i	−0.0991055	+	0.194506i
$188$		0			0
$189$	−4.23801	−	1.37701i	−0.308270	−	0.100163i
$190$		0			0
$191$	−14.3940	+	4.67689i	−1.04151	+	0.338408i	−0.779332	−	0.626611i	$-0.784442\pi$
$191$	−14.3940	+	4.67689i	−1.04151	+	0.338408i	−0.262181	+	0.965019i	$0.584442\pi$
$192$		0			0
$193$	3.63824	+	3.63824i	0.261886	+	0.261886i	0.825820	−	0.563934i	$-0.190713\pi$
$193$	3.63824	+	3.63824i	0.261886	+	0.261886i	−0.563934	+	0.825820i	$0.690713\pi$
$194$		0			0
$195$	−1.93247	+	5.94754i	−0.138387	+	0.425913i
$196$		0			0
$197$	17.6977	−	2.80304i	1.26091	−	0.199708i	0.510034	−	0.860154i	$-0.329633\pi$
$197$	17.6977	−	2.80304i	1.26091	−	0.199708i	0.750874	+	0.660446i	$0.229633\pi$
$198$		0			0
$199$	−16.2327			−1.15071			−0.575353	−	0.817905i	$-0.695135\pi$
$199$	−16.2327			−1.15071			−0.575353	+	0.817905i	$0.695135\pi$
$200$		0			0
$201$	10.4336			0.735929
$202$		0			0
$203$	−9.49426	+	1.50374i	−0.666366	+	0.105542i
$204$		0			0
$205$	5.57701	+	17.1643i	0.389515	+	1.19880i
$206$		0			0
$207$	6.25921	+	6.25921i	0.435045	+	0.435045i
$208$		0			0
$209$	16.0557	−	5.21680i	1.11059	−	0.360853i
$210$		0			0
$211$	−8.37973	−	2.72274i	−0.576885	−	0.187441i	0.00601989	−	0.999982i	$-0.498084\pi$
$211$	−8.37973	−	2.72274i	−0.576885	−	0.187441i	−0.582904	+	0.812541i	$0.698084\pi$
$212$		0			0
$213$	3.78195	−	7.42249i	0.259135	−	0.508581i
$214$		0			0
$215$	−5.58497	+	5.58497i	−0.380892	+	0.380892i
$216$		0			0
$217$	1.49406	−	9.43314i	0.101424	−	0.640363i
$218$		0			0
$219$	22.1760	−	16.1118i	1.49852	−	1.08874i
$220$		0			0
$221$	1.50328	+	1.09220i	0.101122	+	0.0734692i
$222$		0			0
$223$	7.30040	+	14.3278i	0.488871	+	0.959463i	0.995268	+	0.0971632i	$0.0309769\pi$
$223$	7.30040	+	14.3278i	0.488871	+	0.959463i	−0.506397	+	0.862300i	$0.669023\pi$
$224$		0			0
$225$	7.92252	−	2.57418i	0.528168	−	0.171612i
$226$		0			0
$227$	−0.576597	+	0.293791i	−0.0382701	+	0.0194996i	−0.473021	−	0.881051i	$-0.656836\pi$
$227$	−0.576597	+	0.293791i	−0.0382701	+	0.0194996i	0.434751	+	0.900551i	$0.356836\pi$
$228$		0			0
$229$	−5.99225	+	8.24762i	−0.395979	+	0.545018i	−0.959729	−	0.280927i	$-0.909358\pi$
$229$	−5.99225	+	8.24762i	−0.395979	+	0.545018i	0.563750	+	0.825945i	$0.309358\pi$
$230$		0			0
$231$	4.08407	+	5.62124i	0.268712	+	0.369851i
$232$		0			0
$233$	17.9968	+	2.85041i	1.17901	+	0.186736i	0.715019	−	0.699105i	$-0.246418\pi$
$233$	17.9968	+	2.85041i	1.17901	+	0.186736i	0.463988	+	0.885841i	$0.346418\pi$
$234$		0			0
$235$	−3.68877	−	23.2900i	−0.240629	−	1.51927i
$236$		0			0
$237$	29.9819	+	15.2765i	1.94753	+	0.992317i
$238$		0			0
$239$	−1.61300	+	4.96431i	−0.104336	+	0.321114i	−0.989574	−	0.144024i	$-0.953996\pi$
$239$	−1.61300	+	4.96431i	−0.104336	+	0.321114i	0.885238	+	0.465139i	$0.153996\pi$
$240$		0			0
$241$	−3.64658	−	11.2230i	−0.234897	−	0.722937i	−0.997135	−	0.0756411i	$-0.975900\pi$
$241$	−3.64658	−	11.2230i	−0.234897	−	0.722937i	0.762239	−	0.647296i	$-0.224100\pi$
$242$		0			0
$243$	11.0289	−	11.0289i	0.707502	−	0.707502i
$244$		0			0
$245$		−	10.3048i		−	0.658350i
$246$		0			0
$247$	−1.64386	−	10.3789i	−0.104596	−	0.660395i
$248$		0			0
$249$			0.899411i			0.0569978i
$250$		0			0
$251$			24.6761i			1.55754i	0.627309	+	0.778770i	$0.284156\pi$
$251$			24.6761i			1.55754i	−0.627309	+	0.778770i	$0.715844\pi$
$252$		0			0
$253$	1.72879	+	10.9151i	0.108688	+	0.686228i
$254$		0			0
$255$		−	6.93219i		−	0.434111i
$256$		0			0
$257$	−12.0883	+	12.0883i	−0.754048	+	0.754048i	−0.975232	−	0.221184i	$-0.929008\pi$
$257$	−12.0883	+	12.0883i	−0.754048	+	0.754048i	0.221184	+	0.975232i	$0.429008\pi$
$258$		0			0
$259$	−0.353397	−	1.08765i	−0.0219590	−	0.0675830i
$260$		0			0
$261$	3.20015	−	9.84906i	0.198084	−	0.609641i
$262$		0			0
$263$	2.34594	+	1.19532i	0.144657	+	0.0737064i	0.524821	−	0.851213i	$-0.324132\pi$
$263$	2.34594	+	1.19532i	0.144657	+	0.0737064i	−0.380164	+	0.924919i	$0.624132\pi$
$264$		0			0
$265$	−3.07758	−	19.4311i	−0.189054	−	1.19364i
$266$		0			0
$267$	−1.37569	−	0.217888i	−0.0841909	−	0.0133345i
$268$		0			0
$269$	−2.07991	−	2.86275i	−0.126814	−	0.174545i	0.740889	−	0.671628i	$-0.234405\pi$
$269$	−2.07991	−	2.86275i	−0.126814	−	0.174545i	−0.867703	+	0.497083i	$0.834405\pi$
$270$		0			0
$271$	−6.34057	+	8.72704i	−0.385162	+	0.530130i	−0.956943	−	0.290276i	$-0.906253\pi$
$271$	−6.34057	+	8.72704i	−0.385162	+	0.530130i	0.571781	+	0.820406i	$0.306253\pi$
$272$		0			0
$273$	3.85360	−	1.96351i	0.233231	−	0.118837i
$274$		0			0
$275$	9.89093	+	3.21376i	0.596446	+	0.193797i
$276$		0			0
$277$	−10.2663	−	20.1488i	−0.616843	−	1.21062i	−0.962249	−	0.272170i	$-0.912259\pi$
$277$	−10.2663	−	20.1488i	−0.616843	−	1.21062i	0.345406	−	0.938453i	$-0.387741\pi$
$278$		0			0
$279$	8.32417	+	6.04786i	0.498355	+	0.362076i
$280$		0			0
$281$	−7.65058	+	5.55847i	−0.456395	+	0.331590i	−0.792115	−	0.610371i	$-0.791020\pi$
$281$	−7.65058	+	5.55847i	−0.456395	+	0.331590i	0.335720	+	0.941962i	$0.391020\pi$
$282$		0			0
$283$	−2.32550	+	14.6826i	−0.138236	+	0.872791i	0.816933	+	0.576732i	$0.195672\pi$
$283$	−2.32550	+	14.6826i	−0.138236	+	0.872791i	−0.955170	+	0.296059i	$0.904328\pi$
$284$		0			0
$285$	−27.7208	+	27.7208i	−1.64204	+	1.64204i
$286$		0			0
$287$	5.66657	−	11.1213i	0.334487	−	0.656467i
$288$		0			0
$289$	14.2090	+	4.61678i	0.835823	+	0.271575i
$290$		0			0
$291$	36.9284	−	11.9988i	2.16478	−	0.703380i
$292$		0			0
$293$	−3.58180	−	3.58180i	−0.209251	−	0.209251i	0.594698	−	0.803949i	$-0.297272\pi$
$293$	−3.58180	−	3.58180i	−0.209251	−	0.209251i	−0.803949	+	0.594698i	$0.797272\pi$
$294$		0			0
$295$	3.91869	+	12.0605i	0.228155	+	0.702188i
$296$		0			0
$297$	5.91966	−	0.937581i	0.343493	−	0.0544040i
$298$		0			0
$299$	6.87891			0.397818
$300$		0			0
$301$	5.46248			0.314852
$302$		0			0
$303$	−25.5159	+	4.04132i	−1.46585	+	0.232168i
$304$		0			0
$305$	−2.79840	+	8.61258i	−0.160236	+	0.493155i
$306$		0			0
$307$	−11.8995	−	11.8995i	−0.679142	−	0.679142i	0.280664	−	0.959806i	$-0.409445\pi$
$307$	−11.8995	−	11.8995i	−0.679142	−	0.679142i	−0.959806	+	0.280664i	$0.909445\pi$
$308$		0			0
$309$	−27.8262	+	9.04127i	−1.58297	+	0.514340i
$310$		0			0
$311$	22.4967	+	7.30962i	1.27567	+	0.414490i	0.867053	−	0.498215i	$-0.166011\pi$
$311$	22.4967	+	7.30962i	1.27567	+	0.414490i	0.408617	+	0.912706i	$0.366011\pi$
$312$		0			0
$313$	−12.1258	+	23.7983i	−0.685392	+	1.34516i	0.241709	+	0.970349i	$0.422292\pi$
$313$	−12.1258	+	23.7983i	−0.685392	+	1.34516i	−0.927102	+	0.374810i	$0.877708\pi$
$314$		0			0
$315$	−5.13325	−	2.61552i	−0.289226	−	0.147368i
$316$		0			0
$317$	4.33894	−	27.3950i	0.243699	−	1.53866i	−0.497555	−	0.867433i	$-0.665769\pi$
$317$	4.33894	−	27.3950i	0.243699	−	1.53866i	0.741254	−	0.671225i	$-0.234231\pi$
$318$		0			0
$319$	10.4597	−	7.59943i	0.585632	−	0.425486i
$320$		0			0
$321$	−30.6045	−	22.2355i	−1.70818	−	1.24106i
$322$		0			0
$323$	5.28833	+	10.3789i	0.294250	+	0.577499i
$324$		0			0
$325$	2.93893	−	5.76797i	0.163022	−	0.319949i
$326$		0			0
$327$	−0.229286	+	0.116827i	−0.0126795	+	0.00646054i
$328$		0			0
$329$	−9.58567	+	13.1935i	−0.528475	+	0.727383i
$330$		0			0
$331$	0.490278	+	0.674810i	0.0269481	+	0.0370909i	0.822278	−	0.569085i	$-0.192703\pi$
$331$	0.490278	+	0.674810i	0.0269481	+	0.0370909i	−0.795330	+	0.606176i	$0.792703\pi$
$332$		0			0
$333$	1.21688	+	0.192735i	0.0666847	+	0.0105618i
$334$		0			0
$335$	−10.6675	−	1.68957i	−0.582830	−	0.0923112i
$336$		0			0
$337$	2.30371	+	1.17380i	0.125491	+	0.0639408i	0.515609	−	0.856824i	$-0.327566\pi$
$337$	2.30371	+	1.17380i	0.125491	+	0.0639408i	−0.390118	+	0.920765i	$0.627566\pi$
$338$		0			0
$339$	0.724741	−	2.23052i	0.0393625	−	0.121145i
$340$		0			0
$341$	3.96954	+	12.2170i	0.214962	+	0.661587i
$342$		0			0
$343$	−12.6940	+	12.6940i	−0.685412	+	0.685412i
$344$		0			0
$345$	−15.0843	−	20.7618i	−0.812113	−	1.11778i
$346$		0			0
$347$	−4.47164	−	28.2328i	−0.240050	−	1.51562i	−0.753471	−	0.657481i	$-0.771622\pi$
$347$	−4.47164	−	28.2328i	−0.240050	−	1.51562i	0.513421	−	0.858137i	$-0.328378\pi$
$348$		0			0
$349$			35.3568i			1.89261i	0.323278	+	0.946304i	$0.395215\pi$
$349$			35.3568i			1.89261i	−0.323278	+	0.946304i	$0.604785\pi$
$350$		0			0
$351$		−	3.73068i		−	0.199129i
$352$		0			0
$353$	−0.796332	−	5.02784i	−0.0423845	−	0.267605i	0.957391	−	0.288795i	$-0.0932546\pi$
$353$	−0.796332	−	5.02784i	−0.0423845	−	0.267605i	−0.999775	+	0.0211898i	$0.993255\pi$
$354$		0			0
$355$	−5.06872	+	6.97649i	−0.269020	+	0.370274i
$356$		0			0
$357$	−3.39008	+	3.39008i	−0.179422	+	0.179422i
$358$		0			0
$359$	−6.93265	−	21.3365i	−0.365891	−	1.12610i	−0.949421	−	0.314006i	$-0.898329\pi$
$359$	−6.93265	−	21.3365i	−0.365891	−	1.12610i	0.583530	−	0.812092i	$-0.301671\pi$
$360$		0			0
$361$	14.4852	−	44.5809i	0.762379	−	2.34636i
$362$		0			0
$363$	12.8445	+	6.54462i	0.674164	+	0.343504i
$364$		0			0
$365$	−25.2824	+	12.8820i	−1.32334	+	0.674275i
$366$		0			0
$367$	−0.172176	−	0.0272700i	−0.00898752	−	0.00142348i	0.151939	−	0.988390i	$-0.451448\pi$
$367$	−0.172176	−	0.0272700i	−0.00898752	−	0.00142348i	−0.160927	+	0.986966i	$0.551448\pi$
$368$		0			0
$369$	7.90386	+	10.8787i	0.411458	+	0.566324i
$370$		0			0
$371$	−7.99741	+	11.0075i	−0.415205	+	0.571481i
$372$		0			0
$373$	2.30371	−	1.17380i	0.119281	−	0.0607769i	−0.393332	−	0.919397i	$-0.628678\pi$
$373$	2.30371	−	1.17380i	0.119281	−	0.0607769i	0.512613	+	0.858620i	$0.328678\pi$
$374$		0			0
$375$	−23.8534	+	3.77800i	−1.23178	+	0.195095i
$376$		0			0
$377$	−3.65359	−	7.17058i	−0.188170	−	0.369304i
$378$		0			0
$379$	10.2969	+	7.48117i	0.528918	+	0.384282i	0.819953	−	0.572431i	$-0.194000\pi$
$379$	10.2969	+	7.48117i	0.528918	+	0.384282i	−0.291035	+	0.956712i	$0.594000\pi$
$380$		0			0
$381$	−19.9108	+	14.4660i	−1.02006	+	0.741116i
$382$		0			0
$383$	−0.298010	+	1.88156i	−0.0152276	+	0.0961433i	−0.994132	−	0.108177i	$-0.965499\pi$
$383$	−0.298010	+	1.88156i	−0.0152276	+	0.0961433i	0.978904	+	0.204321i	$0.0654985\pi$
$384$		0			0
$385$	−3.26537	−	6.40865i	−0.166419	−	0.326615i
$386$		0			0
$387$	−2.67168	+	5.24346i	−0.135809	+	0.266540i
$388$		0			0
$389$	−26.3796	−	8.57124i	−1.33750	−	0.434579i	−0.449029	−	0.893517i	$-0.648230\pi$
$389$	−26.3796	−	8.57124i	−1.33750	−	0.434579i	−0.888468	+	0.458938i	$0.848230\pi$
$390$		0			0
$391$	−7.25212	+	2.35636i	−0.366755	+	0.119166i
$392$		0			0
$393$	22.8307	+	22.8307i	1.15166	+	1.15166i
$394$		0			0
$395$	−28.1803	−	20.4742i	−1.41791	−	1.03017i
$396$		0			0
$397$	4.84796	−	0.767841i	0.243312	−	0.0385369i	−0.0335872	−	0.999436i	$-0.510693\pi$
$397$	4.84796	−	0.767841i	0.243312	−	0.0385369i	0.276899	+	0.960899i	$0.410693\pi$
$398$		0			0
$399$	27.1128			1.35734
$400$		0			0
$401$	−7.28459			−0.363775			−0.181888	−	0.983319i	$-0.558221\pi$
$401$	−7.28459			−0.363775			−0.181888	+	0.983319i	$0.558221\pi$
$402$		0			0
$403$	7.89748	−	1.25084i	0.393401	−	0.0623087i
$404$		0			0
$405$	−20.3016	+	14.7500i	−1.00879	+	0.732931i
$406$		0			0
$407$	1.08765	+	1.08765i	0.0539126	+	0.0539126i
$408$		0			0
$409$	4.27878	−	1.39026i	0.211572	−	0.0687439i	−0.201313	−	0.979527i	$-0.564521\pi$
$409$	4.27878	−	1.39026i	0.211572	−	0.0687439i	0.412885	+	0.910783i	$0.364521\pi$
$410$		0			0
$411$	−28.2753	−	9.18720i	−1.39472	−	0.453171i
$412$		0			0
$413$	3.98162	−	7.81436i	0.195923	−	0.384520i
$414$		0			0
$415$	0.145647	−	0.919578i	0.00714952	−	0.0451403i
$416$		0			0
$417$	5.22141	−	32.9667i	0.255694	−	1.61439i
$418$		0			0
$419$	−23.8809	+	17.3505i	−1.16666	+	0.847626i	−0.990605	−	0.136755i	$-0.956333\pi$
$419$	−23.8809	+	17.3505i	−1.16666	+	0.847626i	−0.176052	+	0.984381i	$0.556333\pi$
$420$		0			0
$421$	−23.9460	−	17.3978i	−1.16706	−	0.847916i	−0.176403	−	0.984318i	$-0.556446\pi$
$421$	−23.9460	−	17.3978i	−1.16706	−	0.847916i	−0.990654	+	0.136402i	$0.956446\pi$
$422$		0			0
$423$	−7.97623	−	15.6542i	−0.387818	−	0.761135i
$424$		0			0
$425$	−1.12257	+	7.08763i	−0.0544526	+	0.343800i
$426$		0			0
$427$	5.58036	−	2.84333i	0.270052	−	0.137599i
$428$		0			0
$429$	−3.41921	+	4.70614i	−0.165081	+	0.227215i
$430$		0			0
$431$	2.79744	+	3.85035i	0.134748	+	0.185465i	0.871059	−	0.491179i	$-0.163434\pi$
$431$	2.79744	+	3.85035i	0.134748	+	0.185465i	−0.736311	+	0.676644i	$0.763434\pi$
$432$		0			0
$433$	13.7736	+	2.18153i	0.661918	+	0.104838i	0.478350	−	0.878169i	$-0.341235\pi$
$433$	13.7736	+	2.18153i	0.661918	+	0.104838i	0.183568	+	0.983007i	$0.441235\pi$
$434$		0			0
$435$	−13.6304	+	26.7511i	−0.653526	+	1.28262i
$436$		0			0
$437$	38.4228	+	19.5774i	1.83801	+	0.936514i
$438$		0			0
$439$	8.93487	−	27.4987i	0.426438	−	1.31244i	−0.475173	−	0.879892i	$-0.657614\pi$
$439$	8.93487	−	27.4987i	0.426438	−	1.31244i	0.901611	−	0.432548i	$-0.142386\pi$
$440$		0			0
$441$	−2.37260	−	7.30211i	−0.112981	−	0.347719i
$442$		0			0
$443$	−7.50224	+	7.50224i	−0.356442	+	0.356442i	−0.862500	−	0.506058i	$-0.831102\pi$
$443$	−7.50224	+	7.50224i	−0.356442	+	0.356442i	0.506058	+	0.862500i	$0.331102\pi$
$444$		0			0
$445$	1.37125	+	0.445547i	0.0650036	+	0.0211210i
$446$		0			0
$447$	4.00887	+	25.3110i	0.189613	+	1.19717i
$448$		0			0
$449$			5.26233i			0.248345i	0.992261	+	0.124172i	$0.0396275\pi$
$449$			5.26233i			0.248345i	−0.992261	+	0.124172i	$0.960372\pi$
$450$		0			0
$451$			16.7878i			0.790508i
$452$		0			0
$453$	2.42703	+	15.3237i	0.114032	+	0.719968i
$454$		0			0
$455$	−4.25797	+	1.38350i	−0.199617	+	0.0648594i
$456$		0			0
$457$	−17.0368	+	17.0368i	−0.796946	+	0.796946i	−0.982613	−	0.185666i	$-0.940556\pi$
$457$	−17.0368	+	17.0368i	−0.796946	+	0.796946i	0.185666	+	0.982613i	$0.440556\pi$
$458$		0			0
$459$	1.27794	+	3.93308i	0.0596489	+	0.183581i
$460$		0			0
$461$	1.01792	−	3.13284i	0.0474093	−	0.145911i	−0.924550	−	0.381062i	$-0.875559\pi$
$461$	1.01792	−	3.13284i	0.0474093	−	0.145911i	0.971959	+	0.235151i	$0.0755585\pi$
$462$		0			0
$463$	−22.9190	−	11.6778i	−1.06514	−	0.542714i	−0.168600	−	0.985685i	$-0.553925\pi$
$463$	−22.9190	−	11.6778i	−1.06514	−	0.542714i	−0.896536	+	0.442971i	$0.853925\pi$
$464$		0			0
$465$	−21.0931	−	21.0931i	−0.978171	−	0.978171i
$466$		0			0
$467$	15.2660	+	2.41790i	0.706428	+	0.111887i	0.499303	−	0.866427i	$-0.333589\pi$
$467$	15.2660	+	2.41790i	0.706428	+	0.111887i	0.207125	+	0.978315i	$0.433589\pi$
$468$		0			0
$469$	4.39054	+	6.04306i	0.202736	+	0.279042i
$470$		0			0
$471$	21.5417	−	29.6496i	0.992590	−	1.36618i
$472$		0			0
$473$	−6.54625	+	3.33548i	−0.300997	+	0.153366i
$474$		0			0
$475$	32.8313	−	23.8534i	1.50640	−	1.09447i
$476$		0			0
$477$	−6.65464	−	13.0605i	−0.304695	−	0.597998i
$478$		0			0
$479$	13.7623	+	9.99889i	0.628815	+	0.456861i	0.855990	−	0.516993i	$-0.172949\pi$
$479$	13.7623	+	9.99889i	0.628815	+	0.456861i	−0.227174	+	0.973854i	$0.572949\pi$
$480$		0			0
$481$	0.774588	−	0.562771i	0.0353182	−	0.0256602i
$482$		0			0
$483$	−2.77648	+	17.5300i	−0.126334	+	0.797642i
$484$		0			0
$485$	−39.6994	+	6.28777i	−1.80266	+	0.285513i
$486$		0			0
$487$	0.292481	−	0.574027i	0.0132536	−	0.0260117i	−0.884285	−	0.466948i	$-0.845354\pi$
$487$	0.292481	−	0.574027i	0.0132536	−	0.0260117i	0.897538	+	0.440936i	$0.145354\pi$
$488$		0			0
$489$	−2.59757	−	0.844000i	−0.117466	−	0.0381670i
$490$		0			0
$491$	6.79316	−	2.20723i	0.306571	−	0.0996110i	−0.151691	−	0.988428i	$-0.548472\pi$
$491$	6.79316	−	2.20723i	0.306571	−	0.0996110i	0.458262	+	0.888817i	$0.348472\pi$
$492$		0			0
$493$	6.30808	+	6.30808i	0.284102	+	0.284102i
$494$		0			0
$495$	7.74877			0.348281
$496$		0			0
$497$	5.89052	−	0.932967i	0.264226	−	0.0418493i
$498$		0			0
$499$	−7.00996			−0.313809			−0.156904	−	0.987614i	$-0.550151\pi$
$499$	−7.00996			−0.313809			−0.156904	+	0.987614i	$0.550151\pi$
$500$		0			0
$501$	29.3573			1.31159
$502$		0			0
$503$	36.9779	−	5.85673i	1.64876	−	0.261139i	0.738223	−	0.674557i	$-0.235665\pi$
$503$	36.9779	−	5.85673i	1.64876	−	0.261139i	0.910541	+	0.413418i	$0.135665\pi$
$504$		0			0
$505$	26.7425			1.19002
$506$		0			0
$507$	−17.2961	−	17.2961i	−0.768148	−	0.768148i
$508$		0			0
$509$	−16.1516	+	5.24798i	−0.715908	+	0.232613i	−0.644248	−	0.764817i	$-0.722830\pi$
$509$	−16.1516	+	5.24798i	−0.715908	+	0.232613i	−0.0716597	+	0.997429i	$0.522830\pi$
$510$		0			0
$511$	18.6637	+	6.06420i	0.825633	+	0.268264i
$512$		0			0
$513$	10.6175	−	20.8381i	0.468775	−	0.920023i
$514$		0			0
$515$	29.9142	−	4.73794i	1.31818	−	0.208779i
$516$		0			0
$517$	3.43129	−	21.6643i	0.150908	−	0.952796i
$518$		0			0
$519$	−25.4157	+	18.4656i	−1.11562	+	0.810549i
$520$		0			0
$521$	−17.9038	−	13.0079i	−0.784381	−	0.569886i	0.121910	−	0.992541i	$-0.461098\pi$
$521$	−17.9038	−	13.0079i	−0.784381	−	0.569886i	−0.906291	+	0.422655i	$0.861098\pi$
$522$		0			0
$523$	−10.1329	−	19.8868i	−0.443079	−	0.869591i	−0.999258	−	0.0385282i	$-0.987733\pi$
$523$	−10.1329	−	19.8868i	−0.443079	−	0.869591i	0.556179	−	0.831063i	$-0.312267\pi$
$524$		0			0
$525$	13.5127	+	9.81754i	0.589742	+	0.428473i
$526$		0			0
$527$	−7.89748	+	4.02397i	−0.344020	+	0.175287i
$528$		0			0
$529$	−3.07353	+	4.23034i	−0.133632	+	0.183928i
$530$		0			0
$531$	5.55365	+	7.64394i	0.241008	+	0.331719i
$532$		0			0
$533$	10.3211	+	1.63470i	0.447056	+	0.0708067i
$534$		0			0
$535$	27.6900	+	27.6900i	1.19715	+	1.19715i
$536$		0			0
$537$	42.9368	+	21.8774i	1.85286	+	0.944078i
$538$		0			0
$539$	2.96209	−	9.11638i	0.127586	−	0.392670i
$540$		0			0
$541$	−2.55139	−	7.85237i	−0.109693	−	0.337600i	0.881110	−	0.472911i	$-0.156797\pi$
$541$	−2.55139	−	7.85237i	−0.109693	−	0.337600i	−0.990803	+	0.135311i	$0.956797\pi$
$542$		0			0
$543$	4.08045	−	4.08045i	0.175109	−	0.175109i
$544$		0			0
$545$	0.253345	−	0.0823169i	0.0108521	−	0.00352607i
$546$		0			0
$547$	2.71595	+	17.1478i	0.116126	+	0.733189i	0.975198	+	0.221334i	$0.0710412\pi$
$547$	2.71595	+	17.1478i	0.116126	+	0.733189i	−0.859072	+	0.511854i	$0.828959\pi$
$548$		0			0
$549$			6.74728i			0.287967i
$550$		0			0
$551$		−	50.4501i		−	2.14925i
$552$		0			0
$553$	3.76856	+	23.7937i	0.160255	+	1.01181i
$554$		0			0
$555$	−3.39709	−	1.10378i	−0.144199	−	0.0468529i
$556$		0			0
$557$	5.03147	−	5.03147i	0.213190	−	0.213190i	−0.592431	−	0.805621i	$-0.701832\pi$
$557$	5.03147	−	5.03147i	0.213190	−	0.213190i	0.805621	+	0.592431i	$0.201832\pi$
$558$		0			0
$559$	1.41320	+	4.34940i	0.0597722	+	0.183960i
$560$		0			0
$561$	1.99264	−	6.13271i	0.0841293	−	0.258923i
$562$		0			0
$563$	14.6956	+	7.48778i	0.619346	+	0.315572i	0.735362	−	0.677675i	$-0.237012\pi$
$563$	14.6956	+	7.48778i	0.619346	+	0.315572i	−0.116016	+	0.993247i	$0.537012\pi$
$564$		0			0
$565$	−1.10219	+	2.16318i	−0.0463696	+	0.0910055i
$566$		0			0
$567$	17.1414	+	2.71493i	0.719871	+	0.114016i
$568$		0			0
$569$	7.77574	+	10.7024i	0.325976	+	0.448667i	0.940280	−	0.340402i	$-0.110563\pi$
$569$	7.77574	+	10.7024i	0.325976	+	0.448667i	−0.614304	+	0.789069i	$0.710563\pi$
$570$		0			0
$571$	−20.2416	+	27.8602i	−0.847085	+	1.16591i	0.137413	+	0.990514i	$0.456121\pi$
$571$	−20.2416	+	27.8602i	−0.847085	+	1.16591i	−0.984498	+	0.175399i	$0.943879\pi$
$572$		0			0
$573$	29.1293	−	14.8421i	1.21690	−	0.620039i
$574$		0			0
$575$	12.0605	+	23.6700i	0.502957	+	0.987108i
$576$		0			0
$577$	−15.3634	−	30.1523i	−0.639586	−	1.25526i	−0.952228	−	0.305387i	$-0.901214\pi$
$577$	−15.3634	−	30.1523i	−0.639586	−	1.25526i	0.312643	−	0.949871i	$-0.398786\pi$
$578$		0			0
$579$	−8.99162	−	6.53280i	−0.373679	−	0.271494i
$580$		0			0
$581$	−0.520932	+	0.378479i	−0.0216119	+	0.0157020i
$582$		0			0
$583$	2.86276	−	18.0747i	0.118563	−	0.748579i
$584$		0			0
$585$	0.754529	−	4.76391i	0.0311959	−	0.196963i
$586$		0			0
$587$	−1.43724	+	2.82074i	−0.0593211	+	0.116424i	−0.918763	−	0.394808i	$-0.870811\pi$
$587$	−1.43724	+	2.82074i	−0.0593211	+	0.116424i	0.859442	+	0.511233i	$0.170811\pi$
$588$		0			0
$589$	47.6720	+	15.4896i	1.96429	+	0.638237i
$590$		0			0
$591$	−36.8110	+	11.9606i	−1.51420	+	0.491994i
$592$		0			0
$593$	11.1294	+	11.1294i	0.457031	+	0.457031i	0.897680	−	0.440649i	$-0.145252\pi$
$593$	11.1294	+	11.1294i	0.457031	+	0.457031i	−0.440649	+	0.897680i	$0.645252\pi$
$594$		0			0
$595$	4.01507	−	2.91712i	0.164602	−	0.119590i
$596$		0			0
$597$	34.6326	−	5.48526i	1.41742	−	0.224497i
$598$		0			0
$599$	−14.2365			−0.581688			−0.290844	−	0.956770i	$-0.593936\pi$
$599$	−14.2365			−0.581688			−0.290844	+	0.956770i	$0.593936\pi$
$600$		0			0
$601$	13.1694			0.537191			0.268596	−	0.963253i	$-0.413440\pi$
$601$	13.1694			0.537191			0.268596	+	0.963253i	$0.413440\pi$
$602$		0			0
$603$	−7.94815	+	1.25886i	−0.323674	+	0.0512649i
$604$		0			0
$605$	−12.0727	−	8.77136i	−0.490827	−	0.356607i
$606$		0			0
$607$	6.13622	+	6.13622i	0.249062	+	0.249062i	0.820585	−	0.571524i	$-0.193648\pi$
$607$	6.13622	+	6.13622i	0.249062	+	0.249062i	−0.571524	+	0.820585i	$0.693648\pi$
$608$		0			0
$609$	19.7479	−	6.41650i	0.800227	−	0.260010i
$610$		0			0
$611$	−12.9850	−	4.21909i	−0.525317	−	0.170686i
$612$		0			0
$613$	1.35119	−	2.65185i	0.0545739	−	0.107107i	−0.862109	−	0.506723i	$-0.830857\pi$
$613$	1.35119	−	2.65185i	0.0545739	−	0.107107i	0.916683	+	0.399616i	$0.130857\pi$
$614$		0			0
$615$	−17.6986	−	34.7355i	−0.713678	−	1.40067i
$616$		0			0
$617$	−0.207858	+	1.31236i	−0.00836804	+	0.0528337i	−0.991519	−	0.129962i	$-0.958515\pi$
$617$	−0.207858	+	1.31236i	−0.00836804	+	0.0528337i	0.983151	+	0.182795i	$0.0585146\pi$
$618$		0			0
$619$	−35.8316	+	26.0332i	−1.44019	+	1.04636i	−0.452193	+	0.891920i	$0.649358\pi$
$619$	−35.8316	+	26.0332i	−1.44019	+	1.04636i	−0.988002	+	0.154443i	$0.950642\pi$
$620$		0			0
$621$	12.3857	+	8.99875i	0.497021	+	0.361107i
$622$		0			0
$623$	−0.452702	−	0.888478i	−0.0181371	−	0.0355961i
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	−32.4920	+	16.5555i	−1.29761	+	0.661164i
$628$		0			0
$629$	−0.623837	+	0.858638i	−0.0248740	+	0.0342361i
$630$		0			0
$631$	−17.4397	−	24.0037i	−0.694263	−	0.955571i	−0.999994	−	0.00345325i	$-0.998901\pi$
$631$	−17.4397	−	24.0037i	−0.694263	−	0.955571i	0.305731	−	0.952118i	$-0.401099\pi$
$632$		0			0
$633$	18.7983	+	2.97736i	0.747165	+	0.118339i
$634$		0			0
$635$	22.6998	−	11.5661i	0.900813	−	0.458987i
$636$		0			0
$637$	−5.31628	−	2.70878i	−0.210639	−	0.107326i
$638$		0			0
$639$	−1.98547	+	6.11065i	−0.0785440	+	0.241734i
$640$		0			0
$641$	7.95305	+	24.4770i	0.314127	+	0.966782i	0.976112	+	0.217266i	$0.0697139\pi$
$641$	7.95305	+	24.4770i	0.314127	+	0.966782i	−0.661986	+	0.749516i	$0.730286\pi$
$642$		0			0
$643$	25.5380	−	25.5380i	1.00712	−	1.00712i	0.00714543	−	0.999974i	$-0.497726\pi$
$643$	25.5380	−	25.5380i	1.00712	−	1.00712i	0.999974	−	0.00714543i	$-0.00227448\pi$
$644$		0			0
$645$	10.0283	−	13.8028i	0.394865	−	0.543485i
$646$		0			0
$647$	5.58725	+	35.2765i	0.219657	+	1.38686i	0.813165	+	0.582034i	$0.197743\pi$
$647$	5.58725	+	35.2765i	0.219657	+	1.38686i	−0.593507	+	0.804829i	$0.702257\pi$
$648$		0			0
$649$			11.7960i			0.463033i
$650$		0			0
$651$			20.6305i			0.808575i
$652$		0			0
$653$	−3.23230	−	20.4079i	−0.126490	−	0.798625i	−0.966615	−	0.256232i	$-0.917519\pi$
$653$	−3.23230	−	20.4079i	−0.126490	−	0.798625i	0.840125	−	0.542392i	$-0.182481\pi$
$654$		0			0
$655$	−19.6455	−	27.0397i	−0.767614	−	1.05653i
$656$		0			0
$657$	−14.9494	+	14.9494i	−0.583231	+	0.583231i
$658$		0			0
$659$	−6.79316	−	20.9072i	−0.264624	−	0.814429i	−0.991780	−	0.127956i	$-0.959158\pi$
$659$	−6.79316	−	20.9072i	−0.264624	−	0.814429i	0.727156	−	0.686472i	$-0.240842\pi$
$660$		0			0
$661$	12.2063	−	37.5671i	0.474770	−	1.46119i	−0.371497	−	0.928434i	$-0.621155\pi$
$661$	12.2063	−	37.5671i	0.474770	−	1.46119i	0.846267	−	0.532758i	$-0.178845\pi$
$662$		0			0
$663$	−3.57634	−	1.82223i	−0.138893	−	0.0707697i
$664$		0			0
$665$	−27.7208	−	4.39054i	−1.07497	−	0.170258i
$666$		0			0
$667$	32.6189	+	5.16632i	1.26301	+	0.200041i
$668$		0			0
$669$	−20.4171	−	28.1017i	−0.789369	−	1.08647i
$670$		0			0
$671$	−4.95132	+	6.81491i	−0.191144	+	0.263087i
$672$		0			0
$673$	−39.3732	+	20.0616i	−1.51772	+	0.773319i	−0.996773	−	0.0802679i	$-0.974422\pi$
$673$	−39.3732	+	20.0616i	−1.51772	+	0.773319i	−0.520951	+	0.853587i	$0.674422\pi$
$674$		0			0
$675$	12.8371	−	6.54082i	0.494100	−	0.251756i
$676$		0			0
$677$	5.52498	+	10.8434i	0.212342	+	0.416745i	0.972470	−	0.233029i	$-0.0748636\pi$
$677$	5.52498	+	10.8434i	0.212342	+	0.416745i	−0.760128	+	0.649774i	$0.774864\pi$
$678$		0			0
$679$	22.4893	+	16.3395i	0.863062	+	0.627051i
$680$		0			0
$681$	1.13090	−	0.821646i	0.0433361	−	0.0314855i
$682$		0			0
$683$	4.75906	−	30.0475i	0.182100	−	1.14974i	−0.712103	−	0.702075i	$-0.752257\pi$
$683$	4.75906	−	30.0475i	0.182100	−	1.14974i	0.894204	−	0.447661i	$-0.147743\pi$
$684$		0			0
$685$	27.4216	+	13.9720i	1.04772	+	0.533842i
$686$		0			0
$687$	9.99752	−	19.6212i	0.381429	−	0.748597i
$688$		0			0
$689$	−10.8335	−	3.52002i	−0.412724	−	0.134102i
$690$		0			0
$691$	5.35733	−	1.74070i	0.203803	−	0.0662194i	−0.205337	−	0.978691i	$-0.565829\pi$
$691$	5.35733	−	1.74070i	0.203803	−	0.0662194i	0.409139	+	0.912472i	$0.365829\pi$
$692$		0			0
$693$	−3.78941	−	3.78941i	−0.143948	−	0.143948i
$694$		0			0
$695$	−10.6770	+	32.8604i	−0.405001	+	1.24646i
$696$		0			0
$697$	−11.4410	+	1.81208i	−0.433359	+	0.0686374i
$698$		0			0
$699$	−39.3594			−1.48871
$700$		0			0
$701$	−3.54099			−0.133741			−0.0668707	−	0.997762i	$-0.521302\pi$
$701$	−3.54099			−0.133741			−0.0668707	+	0.997762i	$0.521302\pi$
$702$		0			0
$703$	5.92819	−	0.938933i	0.223586	−	0.0354125i
$704$		0			0
$705$	15.7400	+	48.4429i	0.592804	+	1.82446i
$706$		0			0
$707$	−13.0780	−	13.0780i	−0.491848	−	0.491848i
$708$		0			0
$709$	−15.2749	+	4.96312i	−0.573661	+	0.186394i	−0.581459	−	0.813576i	$-0.697518\pi$
$709$	−15.2749	+	4.96312i	−0.573661	+	0.186394i	0.00779779	+	0.999970i	$0.497518\pi$
$710$		0			0
$711$	−24.6829	−	8.01996i	−0.925682	−	0.300772i
$712$		0			0
$713$	−14.8967	+	29.2365i	−0.557887	+	1.09492i
$714$		0			0
$715$	4.25797	−	4.25797i	0.159239	−	0.159239i
$716$		0			0
$717$	1.76384	−	11.1365i	0.0658718	−	0.415898i
$718$		0			0
$719$	−3.56596	+	2.59082i	−0.132988	+	0.0966213i	−0.652290	−	0.757969i	$-0.726192\pi$
$719$	−3.56596	+	2.59082i	−0.132988	+	0.0966213i	0.519303	+	0.854590i	$0.326192\pi$
$720$		0			0
$721$	−16.9461	−	12.3121i	−0.631106	−	0.458525i
$722$		0			0
$723$	11.5724	+	22.7121i	0.430383	+	0.844674i
$724$		0			0
$725$	18.2680	−	25.1437i	0.678455	−	0.933814i
$726$		0			0
$727$	−31.6955	+	16.1497i	−1.17552	+	0.598959i	−0.928964	−	0.370169i	$-0.879300\pi$
$727$	−31.6955	+	16.1497i	−1.17552	+	0.598959i	−0.246558	+	0.969128i	$0.579300\pi$
$728$		0			0
$729$	−0.0142190	+	0.0195708i	−0.000526629	+	0.000724843i
$730$		0			0
$731$	−2.97975	−	4.10128i	−0.110210	−	0.151691i
$732$		0			0
$733$	−30.2273	−	4.78753i	−1.11647	−	0.176832i	−0.429184	−	0.903217i	$-0.641199\pi$
$733$	−30.2273	−	4.78753i	−1.11647	−	0.176832i	−0.687287	+	0.726386i	$0.741199\pi$
$734$		0			0
$735$	3.48215	+	21.9854i	0.128441	+	0.810944i
$736$		0			0
$737$	−8.95161	−	4.56107i	−0.329737	−	0.168009i
$738$		0			0
$739$	−3.17748	+	9.77928i	−0.116886	+	0.359737i	−0.992336	−	0.123572i	$-0.960565\pi$
$739$	−3.17748	+	9.77928i	−0.116886	+	0.359737i	0.875450	+	0.483309i	$0.160565\pi$
$740$		0			0
$741$	7.01438	+	21.5881i	0.257680	+	0.793057i
$742$		0			0
$743$	−19.2467	+	19.2467i	−0.706091	+	0.706091i	−0.965711	−	0.259620i	$-0.916403\pi$
$743$	−19.2467	+	19.2467i	−0.706091	+	0.706091i	0.259620	+	0.965711i	$0.416403\pi$
$744$		0			0
$745$		−	26.5278i		−	0.971902i
$746$		0			0
$747$	−0.108518	−	0.685157i	−0.00397048	−	0.0250686i
$748$		0			0
$749$		−	27.0828i		−	0.989583i
$750$		0			0
$751$		−	35.8460i		−	1.30804i	−0.756477	−	0.654020i	$-0.773081\pi$
$751$		−	35.8460i		−	1.30804i	0.756477	−	0.654020i	$-0.226919\pi$
$752$		0			0
$753$	−8.33841	−	52.6466i	−0.303869	−	1.91855i
$754$		0			0
$755$		−	16.0603i		−	0.584493i
$756$		0			0
$757$	−13.4501	+	13.4501i	−0.488851	+	0.488851i	−0.907944	−	0.419093i	$-0.862348\pi$
$757$	−13.4501	+	13.4501i	−0.488851	+	0.488851i	0.419093	+	0.907944i	$0.362348\pi$
$758$		0			0
$759$	−7.37676	−	22.7033i	−0.267759	−	0.824078i
$760$		0			0
$761$	−8.62231	+	26.5368i	−0.312559	+	0.961957i	0.664189	+	0.747565i	$0.268777\pi$
$761$	−8.62231	+	26.5368i	−0.312559	+	0.961957i	−0.976748	+	0.214392i	$0.931223\pi$
$762$		0			0
$763$	−0.164150	−	0.0836388i	−0.00594264	−	0.00302793i
$764$		0			0
$765$	0.836402	+	5.28084i	0.0302402	+	0.190929i
$766$		0			0
$767$	7.25212	+	1.14862i	0.261859	+	0.0414744i
$768$		0			0
$769$	14.0782	+	19.3770i	0.507675	+	0.698754i	0.983525	−	0.180772i	$-0.0578596\pi$
$769$	14.0782	+	19.3770i	0.507675	+	0.698754i	−0.475850	+	0.879526i	$0.657860\pi$
$770$		0			0
$771$	21.7057	−	29.8753i	0.781711	−	1.07593i
$772$		0			0
$773$	10.9140	−	5.56097i	0.392550	−	0.200014i	−0.246563	−	0.969127i	$-0.579301\pi$
$773$	10.9140	−	5.56097i	0.392550	−	0.200014i	0.639114	+	0.769112i	$0.279301\pi$
$774$		0			0
$775$	18.1504	+	24.9818i	0.651980	+	0.897374i
$776$		0			0
$777$	1.12151	+	2.20108i	0.0402339	+	0.0789634i
$778$		0			0
$779$	52.9971	+	38.5046i	1.89882	+	1.37957i
$780$		0			0
$781$	−6.48953	+	4.71492i	−0.232214	+	0.168713i
$782$		0			0
$783$	2.80188	−	17.6904i	0.100131	−	0.632203i
$784$		0			0
$785$	−26.8261	+	26.8261i	−0.957463	+	0.957463i
$786$		0			0
$787$	20.7644	−	40.7524i	0.740171	−	1.45267i	−0.145988	−	0.989286i	$-0.546636\pi$
$787$	20.7644	−	40.7524i	0.740171	−	1.45267i	0.886159	−	0.463381i	$-0.153364\pi$
$788$		0			0
$789$	−5.40900	−	1.75749i	−0.192565	−	0.0625683i
$790$		0			0
$791$	1.59688	−	0.518857i	0.0567784	−	0.0184484i
$792$		0			0
$793$	3.70765	+	3.70765i	0.131662	+	0.131662i
$794$		0			0
$795$	13.1321	+	40.4164i	0.465747	+	1.43342i
$796$		0			0
$797$	−35.6100	+	5.64007i	−1.26137	+	0.199781i	−0.751074	−	0.660217i	$-0.770464\pi$
$797$	−35.6100	+	5.64007i	−1.26137	+	0.199781i	−0.510296	+	0.859999i	$0.670464\pi$
$798$		0			0
$799$	15.1347			0.535429
$800$		0			0
$801$	1.07427			0.0379574
$802$		0			0
$803$	−26.0695	+	4.12900i	−0.919972	+	0.145709i
$804$		0			0
$805$	5.67747	−	17.4734i	0.200104	−	0.615858i
$806$		0			0
$807$	5.40487	+	5.40487i	0.190261	+	0.190261i
$808$		0			0
$809$	−13.7893	+	4.48043i	−0.484807	+	0.157524i	−0.541215	−	0.840884i	$-0.682035\pi$
$809$	−13.7893	+	4.48043i	−0.484807	+	0.157524i	0.0564074	+	0.998408i	$0.482035\pi$
$810$		0			0
$811$	39.9508	+	12.9808i	1.40286	+	0.455817i	0.910115	−	0.414356i	$-0.135993\pi$
$811$	39.9508	+	12.9808i	1.40286	+	0.455817i	0.492747	+	0.870173i	$0.335993\pi$
$812$		0			0
$813$	10.5787	−	20.7618i	0.371010	−	0.728148i
$814$		0			0
$815$	2.51914	+	1.28356i	0.0882415	+	0.0449613i
$816$		0			0
$817$	−4.48481	+	28.3160i	−0.156904	+	0.990650i
$818$		0			0
$819$	−2.69871	+	1.96073i	−0.0943005	+	0.0685133i
$820$		0			0
$821$	11.0469	+	8.02604i	0.385539	+	0.280111i	0.763625	−	0.645660i	$-0.223418\pi$
$821$	11.0469	+	8.02604i	0.385539	+	0.280111i	−0.378086	+	0.925771i	$0.623418\pi$
$822$		0			0
$823$	18.4620	+	36.2338i	0.643546	+	1.26303i	0.950328	+	0.311250i	$0.100748\pi$
$823$	18.4620	+	36.2338i	0.643546	+	1.26303i	−0.306783	+	0.951780i	$0.599252\pi$
$824$		0			0
$825$	−22.1884	−	3.51429i	−0.772500	−	0.122352i
$826$		0			0
$827$	18.8913	−	9.62561i	0.656916	−	0.334715i	−0.0935597	−	0.995614i	$-0.529825\pi$
$827$	18.8913	−	9.62561i	0.656916	−	0.334715i	0.750475	+	0.660898i	$0.229825\pi$
$828$		0			0
$829$	26.6711	−	36.7096i	0.926324	−	1.27498i	−0.0349524	−	0.999389i	$-0.511128\pi$
$829$	26.6711	−	36.7096i	0.926324	−	1.27498i	0.961276	−	0.275587i	$-0.0888721\pi$
$830$		0			0
$831$	28.7118	+	39.5185i	0.996003	+	1.37088i
$832$		0			0
$833$	6.53260	+	1.03466i	0.226341	+	0.0358489i
$834$		0			0
$835$	−30.0155	−	4.75400i	−1.03873	−	0.164519i
$836$		0			0
$837$	15.8560	+	8.07903i	0.548063	+	0.279252i
$838$		0			0
$839$	5.95905	−	18.3401i	0.205729	−	0.633169i	−0.793953	−	0.607979i	$-0.791981\pi$
$839$	5.95905	−	18.3401i	0.205729	−	0.633169i	0.999683	−	0.0251909i	$-0.00801935\pi$
$840$		0			0
$841$	−2.97799	−	9.16531i	−0.102689	−	0.316045i
$842$		0			0
$843$	14.4443	−	14.4443i	0.497488	−	0.497488i
$844$		0			0
$845$	14.8831	+	20.4848i	0.511994	+	0.704699i
$846$		0			0
$847$	1.61449	+	10.1935i	0.0554745	+	0.350252i
$848$		0			0
$849$		−	32.1113i		−	1.10206i
$850$		0			0
$851$			3.92906i			0.134687i
$852$		0			0
$853$	8.19839	+	51.7626i	0.280707	+	1.77232i	0.576532	+	0.817075i	$0.304406\pi$
$853$	8.19839	+	51.7626i	0.280707	+	1.77232i	−0.295824	+	0.955242i	$0.595594\pi$
$854$		0			0
$855$	17.7726	−	24.4619i	0.607810	−	0.836579i
$856$		0			0
$857$	−23.2770	+	23.2770i	−0.795126	+	0.795126i	−0.982322	−	0.187197i	$-0.940060\pi$
$857$	−23.2770	+	23.2770i	−0.795126	+	0.795126i	0.187197	+	0.982322i	$0.440060\pi$
$858$		0			0
$859$	−8.16487	−	25.1289i	−0.278582	−	0.857387i	−0.988249	−	0.152850i	$-0.951155\pi$
$859$	−8.16487	−	25.1289i	−0.278582	−	0.857387i	0.709668	−	0.704537i	$-0.248845\pi$
$860$		0			0
$861$	−8.33163	+	25.6421i	−0.283941	+	0.873881i
$862$		0			0
$863$	−36.8460	−	18.7740i	−1.25425	−	0.639074i	−0.304630	−	0.952471i	$-0.598533\pi$
$863$	−36.8460	−	18.7740i	−1.25425	−	0.639074i	−0.949622	+	0.313397i	$0.898533\pi$
$864$		0			0
$865$	28.9758	−	14.7639i	0.985207	−	0.501988i
$866$		0			0
$867$	−31.8751	−	5.04852i	−1.08253	−	0.171457i
$868$		0			0
$869$	−19.0451	−	26.2133i	−0.646060	−	0.889226i
$870$		0			0
$871$	−3.67578	+	5.05928i	−0.124549	+	0.171427i
$872$		0			0
$873$	−26.6838	+	13.5961i	−0.903109	+	0.460157i
$874$		0			0
$875$	−12.2259	−	12.2259i	−0.413310	−	0.413310i
$876$		0			0
$877$	−15.4990	−	30.4186i	−0.523365	−	1.02716i	−0.989781	−	0.142597i	$-0.954455\pi$
$877$	−15.4990	−	30.4186i	−0.523365	−	1.02716i	0.466415	−	0.884566i	$-0.345545\pi$
$878$		0			0
$879$	8.85214	+	6.43145i	0.298575	+	0.216928i
$880$		0			0
$881$	−44.5882	+	32.3952i	−1.50221	+	1.09142i	−0.532724	+	0.846289i	$0.678832\pi$
$881$	−44.5882	+	32.3952i	−1.50221	+	1.09142i	−0.969489	+	0.245133i	$0.921168\pi$
$882$		0			0
$883$	−0.941392	+	5.94371i	−0.0316804	+	0.200022i	−0.998452	−	0.0556195i	$-0.982287\pi$
$883$	−0.941392	+	5.94371i	−0.0316804	+	0.200022i	0.966772	+	0.255641i	$0.0822866\pi$
$884$		0			0
$885$	−12.4360	−	24.4069i	−0.418030	−	0.820431i
$886$		0			0
$887$	−12.0513	+	23.6519i	−0.404642	+	0.794154i	−0.999956	−	0.00933862i	$-0.997027\pi$
$887$	−12.0513	+	23.6519i	−0.404642	+	0.794154i	0.595315	+	0.803493i	$0.297027\pi$
$888$		0			0
$889$	−16.7572	−	5.44474i	−0.562018	−	0.182611i
$890$		0			0
$891$	−22.2001	+	7.21324i	−0.743730	+	0.241652i
$892$		0			0
$893$	−60.5215	−	60.5215i	−2.02528	−	2.02528i
$894$		0			0
$895$	−40.3568	−	29.3209i	−1.34898	−	0.980090i
$896$		0			0
$897$	−14.6762	+	2.32448i	−0.490024	+	0.0776123i
$898$		0			0
$899$	38.3882			1.28032
$900$		0			0
$901$	12.6271			0.420668
$902$		0			0
$903$	−11.6543	+	1.84585i	−0.387829	+	0.0614261i
$904$		0			0
$905$	−4.83271	+	3.51117i	−0.160645	+	0.116715i
$906$		0			0
$907$	6.26798	+	6.26798i	0.208125	+	0.208125i	0.803470	−	0.595345i	$-0.202985\pi$
$907$	6.26798	+	6.26798i	0.208125	+	0.208125i	−0.595345	+	0.803470i	$0.702985\pi$
$908$		0			0
$909$	18.9500	−	6.15723i	0.628532	−	0.204222i
$910$		0			0
$911$	26.9318	+	8.75066i	0.892289	+	0.289922i	0.719051	−	0.694958i	$-0.244577\pi$
$911$	26.9318	+	8.75066i	0.892289	+	0.289922i	0.173239	+	0.984880i	$0.444577\pi$
$912$		0			0
$913$	0.393180	−	0.771659i	0.0130124	−	0.0255382i
$914$		0			0
$915$	3.06009	−	19.3206i	0.101163	−	0.638720i
$916$		0			0
$917$	−3.61603	+	22.8307i	−0.119412	+	0.753936i
$918$		0			0
$919$	4.48628	−	3.25947i	0.147989	−	0.107520i	−0.511327	−	0.859386i	$-0.670846\pi$
$919$	4.48628	−	3.25947i	0.147989	−	0.107520i	0.659316	+	0.751866i	$0.270846\pi$
$920$		0			0
$921$	29.4088	+	21.3667i	0.969052	+	0.704057i
$922$		0			0
$923$	2.26680	+	4.44885i	0.0746126	+	0.146436i
$924$		0			0
$925$	3.29452	+	1.67864i	0.108323	+	0.0551934i
$926$		0			0
$927$	20.1067	−	10.2449i	0.660390	−	0.336485i
$928$		0			0
$929$	−17.5674	+	24.1794i	−0.576367	+	0.793301i	−0.993291	−	0.115640i	$-0.963108\pi$
$929$	−17.5674	+	24.1794i	−0.576367	+	0.793301i	0.416924	+	0.908941i	$0.363108\pi$
$930$		0			0
$931$	−21.9854	−	30.2603i	−0.720543	−	0.991742i
$932$		0			0
$933$	−50.4669	−	7.99317i	−1.65221	−	0.261685i
$934$		0			0
$935$	−3.03043	+	5.94754i	−0.0991055	+	0.194506i
$936$		0			0
$937$	−7.89497	−	4.02269i	−0.257918	−	0.131416i	0.320252	−	0.947333i	$-0.396233\pi$
$937$	−7.89497	−	4.02269i	−0.257918	−	0.131416i	−0.578169	+	0.815917i	$0.696233\pi$
$938$		0			0
$939$	17.8288	−	54.8713i	0.581820	−	1.79066i
$940$		0			0
$941$	5.47621	+	16.8541i	0.178519	+	0.549427i	0.999777	−	0.0211316i	$-0.00672691\pi$
$941$	5.47621	+	16.8541i	0.178519	+	0.549427i	−0.821257	+	0.570558i	$0.806727\pi$
$942$		0			0
$943$	−30.3226	+	30.3226i	−0.987440	+	0.987440i
$944$		0			0
$945$	−9.47647	−	3.07909i	−0.308270	−	0.100163i
$946$		0			0
$947$	4.11089	+	25.9552i	0.133586	+	0.843429i	0.959925	+	0.280256i	$0.0904195\pi$
$947$	4.11089	+	25.9552i	0.133586	+	0.843429i	−0.826339	+	0.563173i	$0.809581\pi$
$948$		0			0
$949$			16.4295i			0.533323i
$950$		0			0
$951$			59.9137i			1.94283i
$952$		0			0
$953$	−6.06258	−	38.2776i	−0.196386	−	1.23993i	−0.867068	−	0.498189i	$-0.833998\pi$
$953$	−6.06258	−	38.2776i	−0.196386	−	1.23993i	0.670682	−	0.741745i	$-0.266002\pi$
$954$		0			0
$955$	−32.1860	+	10.4579i	−1.04151	+	0.338408i
$956$		0			0
$957$	−19.7479	+	19.7479i	−0.638360	+	0.638360i
$958$		0			0
$959$	−6.57731	−	20.2429i	−0.212392	−	0.653677i
$960$		0			0
$961$	−2.20672	+	6.79160i	−0.0711846	+	0.219084i
$962$		0			0
$963$	25.9969	+	13.2461i	0.837738	+	0.426849i
$964$		0			0
$965$	8.13535	+	8.13535i	0.261886	+	0.261886i
$966$		0			0
$967$	−2.10550	−	0.333478i	−0.0677082	−	0.0107239i	0.122488	−	0.992470i	$-0.460913\pi$
$967$	−2.10550	−	0.333478i	−0.0677082	−	0.0107239i	−0.190197	+	0.981746i	$0.560913\pi$
$968$		0			0
$969$	−14.7899	−	20.3565i	−0.475120	−	0.653946i
$970$		0			0
$971$	−3.46609	+	4.77067i	−0.111232	+	0.153098i	−0.861003	−	0.508599i	$-0.830164\pi$
$971$	−3.46609	+	4.77067i	−0.111232	+	0.153098i	0.749771	+	0.661697i	$0.230164\pi$
$972$		0			0
$973$	21.2913	−	10.8484i	0.682566	−	0.347785i
$974$		0			0
$975$	−4.32114	+	13.2991i	−0.138387	+	0.425913i
$976$		0			0
$977$	1.00851	+	1.97931i	0.0322650	+	0.0633237i	0.906576	−	0.422042i	$-0.138687\pi$
$977$	1.00851	+	1.97931i	0.0322650	+	0.0633237i	−0.874311	+	0.485366i	$0.838687\pi$
$978$		0			0
$979$	1.08504	+	0.788326i	0.0346780	+	0.0251950i
$980$		0			0
$981$	0.160571	−	0.116661i	0.00512662	−	0.00372471i
$982$		0			0
$983$	−2.06018	+	13.0074i	−0.0657094	+	0.414873i	0.932805	+	0.360382i	$0.117354\pi$
$983$	−2.06018	+	13.0074i	−0.0657094	+	0.414873i	−0.998514	+	0.0544909i	$0.982646\pi$
$984$		0			0
$985$	39.5732	−	6.26779i	1.26091	−	0.199708i
$986$		0			0
$987$	15.9928	−	31.3877i	0.509057	−	0.999081i
$988$		0			0
$989$	−17.8486	−	5.79937i	−0.567553	−	0.184409i
$990$		0			0
$991$	10.4376	−	3.39139i	0.331562	−	0.107731i	−0.138505	−	0.990362i	$-0.544230\pi$
$991$	10.4376	−	3.39139i	0.331562	−	0.107731i	0.470067	+	0.882631i	$0.344230\pi$
$992$		0			0
$993$	−1.27404	−	1.27404i	−0.0404304	−	0.0404304i
$994$		0			0
$995$	−36.2974			−1.15071
$996$		0			0
$997$	−36.0905	+	5.71617i	−1.14300	+	0.181033i	−0.699086	−	0.715038i	$-0.746409\pi$
$997$	−36.0905	+	5.71617i	−1.14300	+	0.181033i	−0.443911	+	0.896071i	$0.646409\pi$
$998$		0			0
$999$	2.13087			0.0674178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.c.303.1	✓	16
4.3	odd	2	inner	400.2.bi.c.303.2	yes	16
25.17	odd	20	inner	400.2.bi.c.367.2	yes	16
100.67	even	20	inner	400.2.bi.c.367.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.c.303.1	✓	16	1.1	even	1	trivial
400.2.bi.c.303.2	yes	16	4.3	odd	2	inner
400.2.bi.c.367.1	yes	16	100.67	even	20	inner
400.2.bi.c.367.2	yes	16	25.17	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13351 + 0.337915i) q^{3} +2.23607 q^{5} +(-1.09351 - 1.09351i) q^{7} +(1.58450 - 0.514836i) q^{9} +O(q^{10})\)	\(q+(-2.13351 + 0.337915i) q^{3} +2.23607 q^{5} +(-1.09351 - 1.09351i) q^{7} +(1.58450 - 0.514836i) q^{9} +(1.97819 + 0.642752i) q^{11} +(0.587785 - 1.15359i) q^{13} +(-4.77067 + 0.755600i) q^{15} +(-0.224514 + 1.41753i) q^{17} +(6.56626 - 4.77067i) q^{19} +(2.70254 + 1.96351i) q^{21} +(2.41210 + 4.73400i) q^{23} +5.00000 q^{25} +(2.56742 - 1.30816i) q^{27} +(3.65359 - 5.02874i) q^{29} +(3.63007 + 4.99637i) q^{31} +(-4.43767 - 0.702858i) q^{33} +(-2.44517 - 2.44517i) q^{35} +(0.658904 + 0.335729i) q^{37} +(-0.864229 + 2.65982i) q^{39} +(2.49411 + 7.67609i) q^{41} +(-2.49767 + 2.49767i) q^{43} +(3.54306 - 1.15121i) q^{45} +(-1.64967 - 10.4156i) q^{47} -4.60845i q^{49} -3.10017i q^{51} +(-1.37633 - 8.68983i) q^{53} +(4.42336 + 1.43724i) q^{55} +(-12.3971 + 12.3971i) q^{57} +(1.75249 + 5.39361i) q^{59} +(-1.25148 + 3.85166i) q^{61} +(-2.29566 - 1.16970i) q^{63} +(1.31433 - 2.57951i) q^{65} +(-4.77067 - 0.755600i) q^{67} +(-6.74591 - 9.28496i) q^{69} +(-2.26680 + 3.11998i) q^{71} +(-11.3066 + 5.76101i) q^{73} +(-10.6675 + 1.68957i) q^{75} +(-1.46032 - 2.86603i) q^{77} +(-12.6026 - 9.15634i) q^{79} +(-9.07914 + 6.59638i) q^{81} +(0.0651353 - 0.411248i) q^{83} +(-0.502029 + 3.16968i) q^{85} +(-6.09569 + 11.9635i) q^{87} +(0.613243 + 0.199255i) q^{89} +(-1.90422 + 0.618720i) q^{91} +(-9.43314 - 9.43314i) q^{93} +(14.6826 - 10.6675i) q^{95} +(-17.7541 + 2.81198i) q^{97} +3.46535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{9}+O(q^{10}) \) 16 * q + 20 * q^9	\( 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93} - 80 q^{97}+O(q^{100}) \) 16 * q + 20 * q^9 + 20 * q^21 + 80 * q^25 + 20 * q^29 - 20 * q^33 - 40 * q^37 - 12 * q^41 + 20 * q^45 - 40 * q^53 + 20 * q^57 - 12 * q^61 - 60 * q^69 - 40 * q^73 - 100 * q^77 - 24 * q^81 - 60 * q^89 - 100 * q^93 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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