LMFDB - Embedded newform 400.2.u.g.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - x^{15} + 12 x^{14} - 18 x^{13} + 100 x^{12} + 23 x^{11} + 567 x^{10} + 556 x^{9} + 3841 x^{8} + \cdots + 6400 $ x^16 - x^15 + 12x^14 - 18x^13 + 100x^12 + 23x^11 + 567x^10 + 556x^9 + 3841x^8 + 1155x^7 + 7575x^6 - 875x^5 + 7485x^4 + 900x^3 + 2000x^2 + 1600x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			241.2
Root			$0.372462 + 1.14632i$ of defining polynomial
Character	$\chi$	$=$	400.241
Dual form			400.2.u.g.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.372462 - 1.14632i) q^{3} +(0.388572 - 2.20205i) q^{5} -1.59935 q^{7} +(1.25173 - 0.909432i) q^{9} +O(q^{10})$	\(q+(-0.372462 - 1.14632i) q^{3} +(0.388572 - 2.20205i) q^{5} -1.59935 q^{7} +(1.25173 - 0.909432i) q^{9} +(-2.86042 - 2.07822i) q^{11} +(-2.38530 + 1.73302i) q^{13} +(-2.66898 + 0.374751i) q^{15} +(-0.357732 + 1.10099i) q^{17} +(0.866689 - 2.66739i) q^{19} +(0.595698 + 1.83337i) q^{21} +(2.55625 + 1.85723i) q^{23} +(-4.69802 - 1.71131i) q^{25} +(-4.43408 - 3.22155i) q^{27} +(-3.04006 - 9.35636i) q^{29} +(-0.572270 + 1.76126i) q^{31} +(-1.31690 + 4.05302i) q^{33} +(-0.621463 + 3.52185i) q^{35} +(-3.63802 + 2.64318i) q^{37} +(2.87503 + 2.08883i) q^{39} +(6.49601 - 4.71963i) q^{41} +11.5345 q^{43} +(-1.51623 - 3.10974i) q^{45} +(-0.728491 - 2.24207i) q^{47} -4.44208 q^{49} +1.39533 q^{51} +(2.15111 + 6.62042i) q^{53} +(-5.68781 + 5.49124i) q^{55} -3.38050 q^{57} +(11.1170 - 8.07696i) q^{59} +(1.96004 + 1.42405i) q^{61} +(-2.00195 + 1.45450i) q^{63} +(2.88933 + 5.92594i) q^{65} +(4.27388 - 13.1537i) q^{67} +(1.17687 - 3.62203i) q^{69} +(1.07380 + 3.30482i) q^{71} +(2.63248 + 1.91261i) q^{73} +(-0.211872 + 6.02284i) q^{75} +(4.57481 + 3.32380i) q^{77} +(3.06650 + 9.43770i) q^{79} +(-0.607051 + 1.86831i) q^{81} +(-3.97495 + 12.2336i) q^{83} +(2.28542 + 1.21556i) q^{85} +(-9.59308 + 6.96978i) q^{87} +(8.85248 + 6.43171i) q^{89} +(3.81493 - 2.77171i) q^{91} +2.23212 q^{93} +(-5.53696 - 2.94497i) q^{95} +(-2.21345 - 6.81231i) q^{97} -5.47046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) $ 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9	$ 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9} + 10 q^{11} + q^{13} + 10 q^{15} - 4 q^{17} - 3 q^{21} - 11 q^{23} + 9 q^{25} - 13 q^{27} + 5 q^{29} + 9 q^{31} + 16 q^{33} - 24 q^{35} + 30 q^{37} - 14 q^{39} - 2 q^{41} + 42 q^{43} - 77 q^{45} + 16 q^{47} + 18 q^{49} - 100 q^{51} + 11 q^{53} + 24 q^{55} - 64 q^{57} + 53 q^{59} + 4 q^{61} + 38 q^{63} + 37 q^{65} + 14 q^{67} - 7 q^{69} + 6 q^{71} - 24 q^{73} + 15 q^{75} + 23 q^{77} + 22 q^{79} - 6 q^{81} - 33 q^{83} + 8 q^{85} - 37 q^{87} + 20 q^{89} + 27 q^{91} + 40 q^{93} + 24 q^{95} + 11 q^{97} - 122 q^{99}+O(q^{100}) $ 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9 + 10 * q^11 + q^13 + 10 * q^15 - 4 * q^17 - 3 * q^21 - 11 * q^23 + 9 * q^25 - 13 * q^27 + 5 * q^29 + 9 * q^31 + 16 * q^33 - 24 * q^35 + 30 * q^37 - 14 * q^39 - 2 * q^41 + 42 * q^43 - 77 * q^45 + 16 * q^47 + 18 * q^49 - 100 * q^51 + 11 * q^53 + 24 * q^55 - 64 * q^57 + 53 * q^59 + 4 * q^61 + 38 * q^63 + 37 * q^65 + 14 * q^67 - 7 * q^69 + 6 * q^71 - 24 * q^73 + 15 * q^75 + 23 * q^77 + 22 * q^79 - 6 * q^81 - 33 * q^83 + 8 * q^85 - 37 * q^87 + 20 * q^89 + 27 * q^91 + 40 * q^93 + 24 * q^95 + 11 * q^97 - 122 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.372462	−	1.14632i	−0.215041	−	0.661829i	−0.999151	−	0.0412064i	$-0.986880\pi$
$3$	−0.372462	−	1.14632i	−0.215041	−	0.661829i	0.784109	−	0.620623i	$-0.213120\pi$
$4$		0			0
$5$	0.388572	−	2.20205i	0.173775	−	0.984785i
$5$	0.388572	−	2.20205i	0.173775	−	0.984785i
$6$		0			0
$7$	−1.59935			−0.604498			−0.302249	−	0.953229i	$-0.597737\pi$
$7$	−1.59935			−0.604498			−0.302249	+	0.953229i	$0.597737\pi$
$8$		0			0
$9$	1.25173	−	0.909432i	0.417242	−	0.303144i
$10$		0			0
$11$	−2.86042	−	2.07822i	−0.862449	−	0.626606i	0.0661014	−	0.997813i	$-0.478944\pi$
$11$	−2.86042	−	2.07822i	−0.862449	−	0.626606i	−0.928550	+	0.371207i	$0.878944\pi$
$12$		0			0
$13$	−2.38530	+	1.73302i	−0.661563	+	0.480654i	−0.867190	−	0.497977i	$-0.834076\pi$
$13$	−2.38530	+	1.73302i	−0.661563	+	0.480654i	0.205627	+	0.978630i	$0.434076\pi$
$14$		0			0
$15$	−2.66898	+	0.374751i	−0.689128	+	0.0967604i
$16$		0			0
$17$	−0.357732	+	1.10099i	−0.0867628	+	0.267028i	−0.985020	−	0.172443i	$-0.944834\pi$
$17$	−0.357732	+	1.10099i	−0.0867628	+	0.267028i	0.898257	+	0.439471i	$0.144834\pi$
$18$		0			0
$19$	0.866689	−	2.66739i	0.198832	−	0.611942i	−0.801078	−	0.598559i	$-0.795740\pi$
$19$	0.866689	−	2.66739i	0.198832	−	0.611942i	0.999910	−	0.0133828i	$-0.00425999\pi$
$20$		0			0
$21$	0.595698	+	1.83337i	0.129992	+	0.400074i
$22$		0			0
$23$	2.55625	+	1.85723i	0.533015	+	0.387258i	0.821484	−	0.570231i	$-0.193146\pi$
$23$	2.55625	+	1.85723i	0.533015	+	0.387258i	−0.288469	+	0.957489i	$0.593146\pi$
$24$		0			0
$25$	−4.69802	−	1.71131i	−0.939605	−	0.342262i
$26$		0			0
$27$	−4.43408	−	3.22155i	−0.853339	−	0.619987i
$28$		0			0
$29$	−3.04006	−	9.35636i	−0.564526	−	1.73743i	−0.669356	−	0.742942i	$-0.733430\pi$
$29$	−3.04006	−	9.35636i	−0.564526	−	1.73743i	0.104830	−	0.994490i	$-0.466570\pi$
$30$		0			0
$31$	−0.572270	+	1.76126i	−0.102783	+	0.316332i	−0.989204	−	0.146547i	$-0.953184\pi$
$31$	−0.572270	+	1.76126i	−0.102783	+	0.316332i	0.886421	+	0.462880i	$0.153184\pi$
$32$		0			0
$33$	−1.31690	+	4.05302i	−0.229244	+	0.705540i
$34$		0			0
$35$	−0.621463	+	3.52185i	−0.105046	+	0.595301i
$36$		0			0
$37$	−3.63802	+	2.64318i	−0.598087	+	0.434535i	−0.845199	−	0.534451i	$-0.820518\pi$
$37$	−3.63802	+	2.64318i	−0.598087	+	0.434535i	0.247112	+	0.968987i	$0.420518\pi$
$38$		0			0
$39$	2.87503	+	2.08883i	0.460374	+	0.334481i
$40$		0			0
$41$	6.49601	−	4.71963i	1.01451	−	0.737082i	0.0493568	−	0.998781i	$-0.484283\pi$
$41$	6.49601	−	4.71963i	1.01451	−	0.737082i	0.965149	+	0.261699i	$0.0842829\pi$
$42$		0			0
$43$	11.5345			1.75899			0.879496	−	0.475906i	$-0.157880\pi$
$43$	11.5345			1.75899			0.879496	+	0.475906i	$0.157880\pi$
$44$		0			0
$45$	−1.51623	−	3.10974i	−0.226026	−	0.463573i
$46$		0			0
$47$	−0.728491	−	2.24207i	−0.106261	−	0.327039i	0.883763	−	0.467935i	$-0.155002\pi$
$47$	−0.728491	−	2.24207i	−0.106261	−	0.327039i	−0.990024	+	0.140896i	$0.955002\pi$
$48$		0			0
$49$	−4.44208			−0.634583
$50$		0			0
$51$	1.39533			0.195385
$52$		0			0
$53$	2.15111	+	6.62042i	0.295477	+	0.909385i	0.983061	+	0.183280i	$0.0586714\pi$
$53$	2.15111	+	6.62042i	0.295477	+	0.909385i	−0.687584	+	0.726105i	$0.741329\pi$
$54$		0			0
$55$	−5.68781	+	5.49124i	−0.766944	+	0.740439i
$56$		0			0
$57$	−3.38050			−0.447758
$58$		0			0
$59$	11.1170	−	8.07696i	1.44731	−	1.05153i	0.460856	−	0.887475i	$-0.347543\pi$
$59$	11.1170	−	8.07696i	1.44731	−	1.05153i	0.986451	−	0.164055i	$-0.0524574\pi$
$60$		0			0
$61$	1.96004	+	1.42405i	0.250958	+	0.182331i	0.706151	−	0.708061i	$-0.250430\pi$
$61$	1.96004	+	1.42405i	0.250958	+	0.182331i	−0.455194	+	0.890393i	$0.650430\pi$
$62$		0			0
$63$	−2.00195	+	1.45450i	−0.252222	+	0.183250i
$64$		0			0
$65$	2.88933	+	5.92594i	0.358378	+	0.735023i
$66$		0			0
$67$	4.27388	−	13.1537i	0.522138	−	1.60698i	−0.247769	−	0.968819i	$-0.579697\pi$
$67$	4.27388	−	13.1537i	0.522138	−	1.60698i	0.769907	−	0.638156i	$-0.220303\pi$
$68$		0			0
$69$	1.17687	−	3.62203i	0.141678	−	0.436042i
$70$		0			0
$71$	1.07380	+	3.30482i	0.127437	+	0.392210i	0.994337	−	0.106271i	$-0.0338912\pi$
$71$	1.07380	+	3.30482i	0.127437	+	0.392210i	−0.866900	+	0.498482i	$0.833891\pi$
$72$		0			0
$73$	2.63248	+	1.91261i	0.308108	+	0.223854i	0.731084	−	0.682287i	$-0.239015\pi$
$73$	2.63248	+	1.91261i	0.308108	+	0.223854i	−0.422976	+	0.906141i	$0.639015\pi$
$74$		0			0
$75$	−0.211872	+	6.02284i	−0.0244649	+	0.695458i
$76$		0			0
$77$	4.57481	+	3.32380i	0.521348	+	0.378782i
$78$		0			0
$79$	3.06650	+	9.43770i	0.345008	+	1.06182i	0.961580	+	0.274526i	$0.0885210\pi$
$79$	3.06650	+	9.43770i	0.345008	+	1.06182i	−0.616572	+	0.787299i	$0.711479\pi$
$80$		0			0
$81$	−0.607051	+	1.86831i	−0.0674501	+	0.207590i
$82$		0			0
$83$	−3.97495	+	12.2336i	−0.436307	+	1.34282i	0.455434	+	0.890270i	$0.349484\pi$
$83$	−3.97495	+	12.2336i	−0.436307	+	1.34282i	−0.891741	+	0.452546i	$0.850516\pi$
$84$		0			0
$85$	2.28542	+	1.21556i	0.247888	+	0.131845i
$86$		0			0
$87$	−9.59308	+	6.96978i	−1.02849	+	0.747239i
$88$		0			0
$89$	8.85248	+	6.43171i	0.938361	+	0.681759i	0.948026	−	0.318194i	$-0.103076\pi$
$89$	8.85248	+	6.43171i	0.938361	+	0.681759i	−0.00966436	+	0.999953i	$0.503076\pi$
$90$		0			0
$91$	3.81493	−	2.77171i	0.399913	−	0.290554i
$92$		0			0
$93$	2.23212			0.231461
$94$		0			0
$95$	−5.53696	−	2.94497i	−0.568080	−	0.302147i
$96$		0			0
$97$	−2.21345	−	6.81231i	−0.224742	−	0.691685i	−0.998318	−	0.0579809i	$-0.981534\pi$
$97$	−2.21345	−	6.81231i	−0.224742	−	0.691685i	0.773576	−	0.633704i	$-0.218466\pi$
$98$		0			0
$99$	−5.47046			−0.549802
$100$		0			0
$101$	18.4139			1.83225			0.916124	−	0.400896i	$-0.131301\pi$
$101$	18.4139			1.83225			0.916124	+	0.400896i	$0.131301\pi$
$102$		0			0
$103$	−0.579455	−	1.78338i	−0.0570954	−	0.175722i	0.918442	−	0.395556i	$-0.129448\pi$
$103$	−0.579455	−	1.78338i	−0.0570954	−	0.175722i	−0.975537	+	0.219835i	$0.929448\pi$
$104$		0			0
$105$	4.26864	−	0.599359i	0.416577	−	0.0584914i
$106$		0			0
$107$	6.86223			0.663397			0.331699	−	0.943385i	$-0.392378\pi$
$107$	6.86223			0.663397			0.331699	+	0.943385i	$0.392378\pi$
$108$		0			0
$109$	−2.56393	+	1.86280i	−0.245580	+	0.178424i	−0.703766	−	0.710432i	$-0.748499\pi$
$109$	−2.56393	+	1.86280i	−0.245580	+	0.178424i	0.458186	+	0.888857i	$0.348499\pi$
$110$		0			0
$111$	4.38496	+	3.18586i	0.416202	+	0.302388i
$112$		0			0
$113$	0.108692	−	0.0789696i	0.0102249	−	0.00742883i	−0.582661	−	0.812715i	$-0.697988\pi$
$113$	0.108692	−	0.0789696i	0.0102249	−	0.00742883i	0.592886	+	0.805286i	$0.297988\pi$
$114$		0			0
$115$	5.08299	−	4.90732i	0.473991	−	0.457610i
$116$		0			0
$117$	−1.40968	+	4.33854i	−0.130325	+	0.401098i
$118$		0			0
$119$	0.572139	−	1.76086i	0.0524479	−	0.161418i
$120$		0			0
$121$	0.463826	+	1.42751i	0.0421660	+	0.129774i
$122$		0			0
$123$	−7.82973	−	5.68863i	−0.705983	−	0.512927i
$124$		0			0
$125$	−5.59390	+	9.68030i	−0.500334	+	0.865833i
$126$		0			0
$127$	−9.49674	−	6.89978i	−0.842699	−	0.612257i	0.0804241	−	0.996761i	$-0.474373\pi$
$127$	−9.49674	−	6.89978i	−0.842699	−	0.612257i	−0.923123	+	0.384504i	$0.874373\pi$
$128$		0			0
$129$	−4.29616	−	13.2222i	−0.378256	−	1.16415i
$130$		0			0
$131$	−0.664422	+	2.04488i	−0.0580508	+	0.178662i	−0.975877	−	0.218320i	$-0.929942\pi$
$131$	−0.664422	+	2.04488i	−0.0580508	+	0.178662i	0.917826	+	0.396982i	$0.129942\pi$
$132$		0			0
$133$	−1.38614	+	4.26610i	−0.120194	+	0.369918i
$134$		0			0
$135$	−8.81696	+	8.51225i	−0.758843	+	0.732618i
$136$		0			0
$137$	12.7949	−	9.29605i	1.09314	−	0.794215i	0.113216	−	0.993570i	$-0.463885\pi$
$137$	12.7949	−	9.29605i	1.09314	−	0.794215i	0.979927	+	0.199355i	$0.0638847\pi$
$138$		0			0
$139$	−16.0382	−	11.6525i	−1.36035	−	0.988349i	−0.998423	−	0.0561417i	$-0.982120\pi$
$139$	−16.0382	−	11.6525i	−1.36035	−	0.988349i	−0.361924	−	0.932208i	$-0.617880\pi$
$140$		0			0
$141$	−2.29879	+	1.67017i	−0.193593	+	0.140654i
$142$		0			0
$143$	10.4245			0.871744
$144$		0			0
$145$	−21.7844	+	3.05875i	−1.80910	+	0.254015i
$146$		0			0
$147$	1.65451	+	5.09205i	0.136461	+	0.419985i
$148$		0			0
$149$	9.45736			0.774777			0.387388	−	0.921917i	$-0.373377\pi$
$149$	9.45736			0.774777			0.387388	+	0.921917i	$0.373377\pi$
$150$		0			0
$151$	19.5082			1.58755			0.793777	−	0.608209i	$-0.208112\pi$
$151$	19.5082			1.58755			0.793777	+	0.608209i	$0.208112\pi$
$152$		0			0
$153$	0.553490	+	1.70347i	0.0447470	+	0.137717i
$154$		0			0
$155$	3.65602	+	1.94454i	0.293659	+	0.156189i
$156$		0			0
$157$	−14.9261			−1.19123			−0.595616	−	0.803270i	$-0.703092\pi$
$157$	−14.9261			−1.19123			−0.595616	+	0.803270i	$0.703092\pi$
$158$		0			0
$159$	6.78793	−	4.93172i	0.538317	−	0.391111i
$160$		0			0
$161$	−4.08834	−	2.97035i	−0.322207	−	0.234097i
$162$		0			0
$163$	−8.73705	+	6.34784i	−0.684339	+	0.497201i	−0.874794	−	0.484495i	$-0.839004\pi$
$163$	−8.73705	+	6.34784i	−0.684339	+	0.497201i	0.190456	+	0.981696i	$0.439004\pi$
$164$		0			0
$165$	8.41322	+	4.47478i	0.654968	+	0.348361i
$166$		0			0
$167$	−3.99854	+	12.3062i	−0.309416	+	0.952285i	0.668576	+	0.743644i	$0.266904\pi$
$167$	−3.99854	+	12.3062i	−0.309416	+	0.952285i	−0.977992	+	0.208642i	$0.933096\pi$
$168$		0			0
$169$	−1.33093	+	4.09619i	−0.102379	+	0.315091i
$170$		0			0
$171$	−1.34096	−	4.12704i	−0.102546	−	0.315603i
$172$		0			0
$173$	−17.5346	−	12.7396i	−1.33313	−	0.968575i	−0.999667	−	0.0258121i	$-0.991783\pi$
$173$	−17.5346	−	12.7396i	−1.33313	−	0.968575i	−0.333463	−	0.942763i	$-0.608217\pi$
$174$		0			0
$175$	7.51379	+	2.73698i	0.567989	+	0.206896i
$176$		0			0
$177$	−13.3994	−	9.73527i	−1.00716	−	0.731747i
$178$		0			0
$179$	−1.49437	−	4.59920i	−0.111694	−	0.343760i	0.879549	−	0.475809i	$-0.157845\pi$
$179$	−1.49437	−	4.59920i	−0.111694	−	0.343760i	−0.991243	+	0.132048i	$0.957845\pi$
$180$		0			0
$181$	−0.992136	+	3.05348i	−0.0737449	+	0.226963i	−0.981134	−	0.193328i	$-0.938072\pi$
$181$	−0.992136	+	3.05348i	−0.0737449	+	0.226963i	0.907389	+	0.420291i	$0.138072\pi$
$182$		0			0
$183$	0.902381	−	2.77724i	0.0667059	−	0.205300i
$184$		0			0
$185$	4.40677	+	9.03816i	0.323992	+	0.664498i
$186$		0			0
$187$	3.31135	−	2.40584i	0.242150	−	0.175932i
$188$		0			0
$189$	7.09165	+	5.15239i	0.515842	+	0.374781i
$190$		0			0
$191$	11.0932	−	8.05971i	0.802679	−	0.583180i	−0.109020	−	0.994040i	$-0.534771\pi$
$191$	11.0932	−	8.05971i	0.802679	−	0.583180i	0.911699	+	0.410859i	$0.134771\pi$
$192$		0			0
$193$	19.7184			1.41936			0.709682	−	0.704522i	$-0.248838\pi$
$193$	19.7184			1.41936			0.709682	+	0.704522i	$0.248838\pi$
$194$		0			0
$195$	5.71687	−	5.51930i	0.409394	−	0.395245i
$196$		0			0
$197$	−6.67522	−	20.5442i	−0.475589	−	1.46371i	−0.845161	−	0.534512i	$-0.820496\pi$
$197$	−6.67522	−	20.5442i	−0.475589	−	1.46371i	0.369572	−	0.929202i	$-0.379504\pi$
$198$		0			0
$199$	−24.2188			−1.71683			−0.858413	−	0.512960i	$-0.828549\pi$
$199$	−24.2188			−1.71683			−0.858413	+	0.512960i	$0.828549\pi$
$200$		0			0
$201$	−16.6702			−1.17582
$202$		0			0
$203$	4.86213	+	14.9641i	0.341255	+	1.05027i
$204$		0			0
$205$	−7.86867	−	16.1384i	−0.549572	−	1.12716i
$206$		0			0
$207$	4.88875			0.339791
$208$		0			0
$209$	−8.02251	+	5.82870i	−0.554929	+	0.403179i
$210$		0			0
$211$	1.68226	+	1.22223i	0.115812	+	0.0841421i	0.644184	−	0.764871i	$-0.277197\pi$
$211$	1.68226	+	1.22223i	0.115812	+	0.0841421i	−0.528372	+	0.849013i	$0.677197\pi$
$212$		0			0
$213$	3.38844	−	2.46185i	0.232172	−	0.168683i
$214$		0			0
$215$	4.48198	−	25.3995i	0.305668	−	1.73223i
$216$		0			0
$217$	0.915260	−	2.81688i	0.0621319	−	0.191222i
$218$		0			0
$219$	1.21196	−	3.73004i	0.0818970	−	0.252053i
$220$		0			0
$221$	−1.05473	−	3.24614i	−0.0709491	−	0.218359i
$222$		0			0
$223$	−15.8396	−	11.5081i	−1.06070	−	0.770642i	−0.0864809	−	0.996254i	$-0.527562\pi$
$223$	−15.8396	−	11.5081i	−1.06070	−	0.770642i	−0.974217	+	0.225611i	$0.927562\pi$
$224$		0			0
$225$	−7.43696	+	2.13044i	−0.495797	+	0.142030i
$226$		0			0
$227$	5.30621	+	3.85518i	0.352185	+	0.255878i	0.749785	−	0.661681i	$-0.230157\pi$
$227$	5.30621	+	3.85518i	0.352185	+	0.255878i	−0.397600	+	0.917559i	$0.630157\pi$
$228$		0			0
$229$	−4.68231	−	14.4107i	−0.309416	−	0.952285i	−0.977992	−	0.208641i	$-0.933096\pi$
$229$	−4.68231	−	14.4107i	−0.309416	−	0.952285i	0.668576	−	0.743644i	$-0.266904\pi$
$230$		0			0
$231$	2.10619	−	6.48219i	0.138577	−	0.426497i
$232$		0			0
$233$	−0.532402	+	1.63857i	−0.0348788	+	0.107346i	−0.966980	−	0.254851i	$-0.917973\pi$
$233$	−0.532402	+	1.63857i	−0.0348788	+	0.107346i	0.932101	+	0.362198i	$0.117973\pi$
$234$		0			0
$235$	−5.22021	+	0.732968i	−0.340529	+	0.0478136i
$236$		0			0
$237$	9.67649	−	7.03038i	0.628556	−	0.456672i
$238$		0			0
$239$	6.55820	+	4.76481i	0.424215	+	0.308210i	0.779331	−	0.626612i	$-0.215559\pi$
$239$	6.55820	+	4.76481i	0.424215	+	0.308210i	−0.355117	+	0.934822i	$0.615559\pi$
$240$		0			0
$241$	−3.19595	+	2.32199i	−0.205869	+	0.149573i	−0.685943	−	0.727656i	$-0.740610\pi$
$241$	−3.19595	+	2.32199i	−0.205869	+	0.149573i	0.480074	+	0.877228i	$0.340610\pi$
$242$		0			0
$243$	−14.0747			−0.902892
$244$		0			0
$245$	−1.72607	+	9.78166i	−0.110274	+	0.624928i
$246$		0			0
$247$	2.55534	+	7.86452i	0.162592	+	0.500408i
$248$		0			0
$249$	15.5042			0.982539
$250$		0			0
$251$	−21.2264			−1.33980			−0.669899	−	0.742452i	$-0.733663\pi$
$251$	−21.2264			−1.33980			−0.669899	+	0.742452i	$0.733663\pi$
$252$		0			0
$253$	−3.45223	−	10.6249i	−0.217040	−	0.667981i
$254$		0			0
$255$	0.542185	−	3.07257i	0.0339529	−	0.192412i
$256$		0			0
$257$	0.186373			0.0116256			0.00581282	−	0.999983i	$-0.498150\pi$
$257$	0.186373			0.0116256			0.00581282	+	0.999983i	$0.498150\pi$
$258$		0			0
$259$	5.81847	−	4.22737i	0.361542	−	0.262676i
$260$		0			0
$261$	−12.3143	−	8.94686i	−0.762236	−	0.553797i
$262$		0			0
$263$	8.03986	−	5.84130i	0.495759	−	0.360190i	−0.311636	−	0.950202i	$-0.600877\pi$
$263$	8.03986	−	5.84130i	0.495759	−	0.360190i	0.807395	+	0.590012i	$0.200877\pi$
$264$		0			0
$265$	15.4143	−	2.16432i	0.946895	−	0.132953i
$266$		0			0
$267$	4.07558	−	12.5434i	0.249422	−	0.767641i
$268$		0			0
$269$	−8.72173	+	26.8427i	−0.531773	+	1.63663i	0.218747	+	0.975782i	$0.429803\pi$
$269$	−8.72173	+	26.8427i	−0.531773	+	1.63663i	−0.750520	+	0.660848i	$0.770197\pi$
$270$		0			0
$271$	1.30854	+	4.02727i	0.0794881	+	0.244639i	0.982902	−	0.184131i	$-0.0589470\pi$
$271$	1.30854	+	4.02727i	0.0794881	+	0.244639i	−0.903414	+	0.428770i	$0.858947\pi$
$272$		0			0
$273$	−4.59819	−	3.34078i	−0.278295	−	0.202193i
$274$		0			0
$275$	9.88185	+	14.6586i	0.595898	+	0.883945i
$276$		0			0
$277$	15.0058	+	10.9024i	0.901614	+	0.655061i	0.938880	−	0.344245i	$-0.111865\pi$
$277$	15.0058	+	10.9024i	0.901614	+	0.655061i	−0.0372663	+	0.999305i	$0.511865\pi$
$278$		0			0
$279$	0.885426	+	2.72506i	0.0530091	+	0.163145i
$280$		0			0
$281$	−1.02897	+	3.16685i	−0.0613834	+	0.188919i	−0.977046	−	0.213030i	$-0.931667\pi$
$281$	−1.02897	+	3.16685i	−0.0613834	+	0.188919i	0.915662	+	0.401948i	$0.131667\pi$
$282$		0			0
$283$	−6.72318	+	20.6918i	−0.399651	+	1.23000i	0.525628	+	0.850714i	$0.323830\pi$
$283$	−6.72318	+	20.6918i	−0.399651	+	1.23000i	−0.925279	+	0.379286i	$0.876170\pi$
$284$		0			0
$285$	−1.31357	+	7.44402i	−0.0778091	+	0.440946i
$286$		0			0
$287$	−10.3894	+	7.54834i	−0.613267	+	0.445564i
$288$		0			0
$289$	12.6691	+	9.20463i	0.745241	+	0.541449i
$290$		0			0
$291$	−6.98466	+	5.07466i	−0.409448	+	0.297482i
$292$		0			0
$293$	22.9801			1.34251			0.671257	−	0.741225i	$-0.265755\pi$
$293$	22.9801			1.34251			0.671257	+	0.741225i	$0.265755\pi$
$294$		0			0
$295$	−13.4661	−	27.6186i	−0.784026	−	1.60802i
$296$		0			0
$297$	5.98825	+	18.4300i	0.347474	+	1.06941i
$298$		0			0
$299$	−9.31604			−0.538760
$300$		0			0
$301$	−18.4477			−1.06331
$302$		0			0
$303$	−6.85847	−	21.1082i	−0.394009	−	1.21263i
$304$		0			0
$305$	3.89745	−	3.76276i	0.223167	−	0.215455i
$306$		0			0
$307$	−0.166588			−0.00950768			−0.00475384	−	0.999989i	$-0.501513\pi$
$307$	−0.166588			−0.00950768			−0.00475384	+	0.999989i	$0.501513\pi$
$308$		0			0
$309$	−1.82850	+	1.32848i	−0.104020	+	0.0755748i
$310$		0			0
$311$	−6.42513	−	4.66813i	−0.364335	−	0.264705i	0.390523	−	0.920593i	$-0.372294\pi$
$311$	−6.42513	−	4.66813i	−0.364335	−	0.264705i	−0.754858	+	0.655888i	$0.772294\pi$
$312$		0			0
$313$	9.65596	−	7.01546i	0.545787	−	0.396537i	−0.280443	−	0.959871i	$-0.590481\pi$
$313$	9.65596	−	7.01546i	0.545787	−	0.396537i	0.826230	+	0.563333i	$0.190481\pi$
$314$		0			0
$315$	2.42498	+	4.97356i	0.136632	+	0.280229i
$316$		0			0
$317$	−3.09875	+	9.53696i	−0.174043	+	0.535649i	−0.999588	−	0.0286866i	$-0.990868\pi$
$317$	−3.09875	+	9.53696i	−0.174043	+	0.535649i	0.825546	+	0.564335i	$0.190868\pi$
$318$		0			0
$319$	−10.7487	+	33.0810i	−0.601810	+	1.85218i
$320$		0			0
$321$	−2.55592	−	7.86633i	−0.142658	−	0.439056i
$322$		0			0
$323$	2.62672	+	1.90842i	0.146155	+	0.106188i
$324$		0			0
$325$	14.1719	−	4.05979i	0.786117	−	0.225197i
$326$		0			0
$327$	3.09034	+	2.24526i	0.170896	+	0.124163i
$328$		0			0
$329$	1.16511	+	3.58585i	0.0642348	+	0.197694i
$330$		0			0
$331$	−10.0080	+	30.8015i	−0.550090	+	1.69300i	0.158481	+	0.987362i	$0.449340\pi$
$331$	−10.0080	+	30.8015i	−0.550090	+	1.69300i	−0.708570	+	0.705640i	$0.750660\pi$
$332$		0			0
$333$	−2.15001	+	6.61707i	−0.117820	+	0.362613i
$334$		0			0
$335$	−27.3043	−	14.5224i	−1.49179	−	0.793446i
$336$		0			0
$337$	−8.21206	+	5.96641i	−0.447339	+	0.325011i	−0.788544	−	0.614978i	$-0.789165\pi$
$337$	−8.21206	+	5.96641i	−0.447339	+	0.325011i	0.341205	+	0.939989i	$0.389165\pi$
$338$		0			0
$339$	−0.131008	−	0.0951831i	−0.00711540	−	0.00516964i
$340$		0			0
$341$	5.29722	−	3.84865i	0.286860	−	0.208416i
$342$		0			0
$343$	18.2999			0.988101
$344$		0			0
$345$	−7.51859	−	3.99894i	−0.404787	−	0.215296i
$346$		0			0
$347$	10.3220	+	31.7678i	0.554114	+	1.70539i	0.698272	+	0.715832i	$0.253953\pi$
$347$	10.3220	+	31.7678i	0.554114	+	1.70539i	−0.144158	+	0.989555i	$0.546047\pi$
$348$		0			0
$349$	5.59021			0.299237			0.149619	−	0.988744i	$-0.452195\pi$
$349$	5.59021			0.299237			0.149619	+	0.988744i	$0.452195\pi$
$350$		0			0
$351$	16.1596			0.862537
$352$		0			0
$353$	−7.71318	−	23.7387i	−0.410531	−	1.26348i	−0.916188	−	0.400750i	$-0.868750\pi$
$353$	−7.71318	−	23.7387i	−0.410531	−	1.26348i	0.505656	−	0.862735i	$-0.331250\pi$
$354$		0			0
$355$	7.69463	−	1.08040i	0.408388	−	0.0573417i
$356$		0			0
$357$	−2.23161			−0.118110
$358$		0			0
$359$	29.9147	−	21.7343i	1.57884	−	1.14709i	0.660830	−	0.750536i	$-0.270204\pi$
$359$	29.9147	−	21.7343i	1.57884	−	1.14709i	0.918009	−	0.396558i	$-0.129796\pi$
$360$		0			0
$361$	9.00748	+	6.54432i	0.474078	+	0.344438i
$362$		0			0
$363$	1.46363	−	1.06339i	0.0768206	−	0.0558134i
$364$		0			0
$365$	5.23456	−	5.05366i	0.273990	−	0.264521i
$366$		0			0
$367$	−1.07356	+	3.30408i	−0.0560394	+	0.172472i	−0.975159	−	0.221508i	$-0.928902\pi$
$367$	−1.07356	+	3.30408i	−0.0560394	+	0.172472i	0.919119	+	0.393980i	$0.128902\pi$
$368$		0			0
$369$	3.83904	−	11.8154i	0.199853	−	0.615083i
$370$		0			0
$371$	−3.44037	−	10.5884i	−0.178615	−	0.549721i
$372$		0			0
$373$	11.6934	+	8.49575i	0.605461	+	0.439893i	0.847813	−	0.530295i	$-0.177919\pi$
$373$	11.6934	+	8.49575i	0.605461	+	0.439893i	−0.242352	+	0.970188i	$0.577919\pi$
$374$		0			0
$375$	13.1803	+	2.80686i	0.680626	+	0.144946i
$376$		0			0
$377$	23.4662	+	17.0492i	1.20857	+	0.878079i
$378$		0			0
$379$	1.37239	+	4.22379i	0.0704950	+	0.216961i	0.980097	−	0.198519i	$-0.0636133\pi$
$379$	1.37239	+	4.22379i	0.0704950	+	0.216961i	−0.909602	+	0.415481i	$0.863613\pi$
$380$		0			0
$381$	−4.37219	+	13.4562i	−0.223994	+	0.689383i
$382$		0			0
$383$	0.726319	−	2.23538i	0.0371132	−	0.114223i	−0.930784	−	0.365571i	$-0.880874\pi$
$383$	0.726319	−	2.23538i	0.0371132	−	0.114223i	0.967897	+	0.251348i	$0.0808739\pi$
$384$		0			0
$385$	9.09680	−	8.78242i	0.463616	−	0.447593i
$386$		0			0
$387$	14.4380	−	10.4898i	0.733926	−	0.533228i
$388$		0			0
$389$	−3.70812	−	2.69411i	−0.188009	−	0.136597i	0.489799	−	0.871835i	$-0.337070\pi$
$389$	−3.70812	−	2.69411i	−0.188009	−	0.136597i	−0.677808	+	0.735239i	$0.737070\pi$
$390$		0			0
$391$	−2.95923	+	2.15001i	−0.149655	+	0.108731i
$392$		0			0
$393$	2.59156			0.130727
$394$		0			0
$395$	21.9738	−	3.08534i	1.10562	−	0.155240i
$396$		0			0
$397$	−1.21194	−	3.72998i	−0.0608258	−	0.187202i	0.916026	−	0.401118i	$-0.131378\pi$
$397$	−1.21194	−	3.72998i	−0.0608258	−	0.187202i	−0.976852	+	0.213916i	$0.931378\pi$
$398$		0			0
$399$	5.40661			0.270669
$400$		0			0
$401$	4.06725			0.203109			0.101554	−	0.994830i	$-0.467618\pi$
$401$	4.06725			0.203109			0.101554	+	0.994830i	$0.467618\pi$
$402$		0			0
$403$	−1.68727	−	5.19290i	−0.0840491	−	0.258677i
$404$		0			0
$405$	3.87823	+	2.06273i	0.192711	+	0.102498i
$406$		0			0
$407$	15.8993			0.788101
$408$		0			0
$409$	−9.51161	+	6.91059i	−0.470319	+	0.341707i	−0.797566	−	0.603232i	$-0.793879\pi$
$409$	−9.51161	+	6.91059i	−0.470319	+	0.341707i	0.327247	+	0.944939i	$0.393879\pi$
$410$		0			0
$411$	−15.4219	−	11.2047i	−0.760706	−	0.552685i
$412$		0			0
$413$	−17.7799	+	12.9179i	−0.874894	+	0.635648i
$414$		0			0
$415$	25.3945	+	13.5067i	1.24657	+	0.663017i
$416$		0			0
$417$	−7.38383	+	22.7251i	−0.361588	+	1.11285i
$418$		0			0
$419$	−4.97447	+	15.3098i	−0.243019	+	0.747934i	0.752937	+	0.658092i	$0.228636\pi$
$419$	−4.97447	+	15.3098i	−0.243019	+	0.747934i	−0.995956	+	0.0898423i	$0.971364\pi$
$420$		0			0
$421$	−0.159992	−	0.492406i	−0.00779756	−	0.0239984i	0.947082	−	0.320992i	$-0.104016\pi$
$421$	−0.159992	−	0.492406i	−0.00779756	−	0.0239984i	−0.954880	+	0.296993i	$0.904016\pi$
$422$		0			0
$423$	−2.95088	−	2.14394i	−0.143477	−	0.104242i
$424$		0			0
$425$	3.56476	−	4.56027i	0.172916	−	0.221205i
$426$		0			0
$427$	−3.13479	−	2.27756i	−0.151703	−	0.110219i
$428$		0			0
$429$	−3.88275	−	11.9499i	−0.187461	−	0.576946i
$430$		0			0
$431$	6.24332	−	19.2150i	0.300730	−	0.925553i	−0.680506	−	0.732743i	$-0.738240\pi$
$431$	6.24332	−	19.2150i	0.300730	−	0.925553i	0.981236	−	0.192810i	$-0.0617601\pi$
$432$		0			0
$433$	−10.3203	+	31.7627i	−0.495963	+	1.52642i	0.319488	+	0.947590i	$0.396489\pi$
$433$	−10.3203	+	31.7627i	−0.495963	+	1.52642i	−0.815451	+	0.578827i	$0.803511\pi$
$434$		0			0
$435$	11.6202	+	23.8327i	0.557145	+	1.14269i
$436$		0			0
$437$	7.16943	−	5.20889i	0.342960	−	0.249175i
$438$		0			0
$439$	19.6723	+	14.2928i	0.938909	+	0.682157i	0.948158	−	0.317800i	$-0.102944\pi$
$439$	19.6723	+	14.2928i	0.938909	+	0.682157i	−0.00924884	+	0.999957i	$0.502944\pi$
$440$		0			0
$441$	−5.56026	+	4.03977i	−0.264775	+	0.192370i
$442$		0			0
$443$	18.2746			0.868252			0.434126	−	0.900852i	$-0.357057\pi$
$443$	18.2746			0.868252			0.434126	+	0.900852i	$0.357057\pi$
$444$		0			0
$445$	17.6027	−	16.9944i	0.834450	−	0.805612i
$446$		0			0
$447$	−3.52251	−	10.8412i	−0.166609	−	0.512770i
$448$		0			0
$449$	−36.1354			−1.70534			−0.852668	−	0.522454i	$-0.825017\pi$
$449$	−36.1354			−1.70534			−0.852668	+	0.522454i	$0.825017\pi$
$450$		0			0
$451$	−28.3897			−1.33682
$452$		0			0
$453$	−7.26607	−	22.3627i	−0.341390	−	1.05069i
$454$		0			0
$455$	−4.62106	−	9.47766i	−0.216639	−	0.444320i
$456$		0			0
$457$	9.25903			0.433119			0.216560	−	0.976269i	$-0.430516\pi$
$457$	9.25903			0.433119			0.216560	+	0.976269i	$0.430516\pi$
$458$		0			0
$459$	5.13309	−	3.72941i	0.239592	−	0.174074i
$460$		0			0
$461$	−4.65453	−	3.38171i	−0.216783	−	0.157502i	0.474094	−	0.880474i	$-0.342776\pi$
$461$	−4.65453	−	3.38171i	−0.216783	−	0.157502i	−0.690877	+	0.722972i	$0.742776\pi$
$462$		0			0
$463$	22.5798	−	16.4052i	1.04937	−	0.762415i	0.0772808	−	0.997009i	$-0.475376\pi$
$463$	22.5798	−	16.4052i	1.04937	−	0.762415i	0.972093	+	0.234594i	$0.0753762\pi$
$464$		0			0
$465$	0.867341	−	4.91524i	0.0402220	−	0.227939i
$466$		0			0
$467$	−0.730903	+	2.24949i	−0.0338222	+	0.104094i	−0.966542	−	0.256507i	$-0.917428\pi$
$467$	−0.730903	+	2.24949i	−0.0338222	+	0.104094i	0.932720	+	0.360601i	$0.117428\pi$
$468$		0			0
$469$	−6.83544	+	21.0373i	−0.315631	+	0.971413i
$470$		0			0
$471$	5.55941	+	17.1101i	0.256164	+	0.788391i
$472$		0			0
$473$	−32.9935	−	23.9711i	−1.51704	−	1.10219i
$474$		0			0
$475$	−8.63646	+	11.0483i	−0.396268	+	0.506931i
$476$		0			0
$477$	8.71342	+	6.33067i	0.398960	+	0.289861i
$478$		0			0
$479$	3.16821	+	9.75074i	0.144759	+	0.445523i	0.996980	−	0.0776594i	$-0.0247447\pi$
$479$	3.16821	+	9.75074i	0.144759	+	0.445523i	−0.852221	+	0.523182i	$0.824745\pi$
$480$		0			0
$481$	4.09708	−	12.6095i	0.186811	−	0.574945i
$482$		0			0
$483$	−1.88223	+	5.79290i	−0.0856443	+	0.263586i
$484$		0			0
$485$	−15.8611	+	2.22705i	−0.720216	+	0.101125i
$486$		0			0
$487$	−13.5930	+	9.87586i	−0.615955	+	0.447518i	−0.851506	−	0.524344i	$-0.824311\pi$
$487$	−13.5930	+	9.87586i	−0.615955	+	0.447518i	0.235551	+	0.971862i	$0.424311\pi$
$488$		0			0
$489$	10.5309	+	7.65114i	0.476223	+	0.345996i
$490$		0			0
$491$	−22.7142	+	16.5028i	−1.02508	+	0.744762i	−0.967318	−	0.253568i	$-0.918396\pi$
$491$	−22.7142	+	16.5028i	−1.02508	+	0.744762i	−0.0577599	+	0.998331i	$0.518396\pi$
$492$		0			0
$493$	11.3887			0.512923
$494$		0			0
$495$	−2.12567	+	12.0462i	−0.0955416	+	0.541437i
$496$		0			0
$497$	−1.71739	−	5.28557i	−0.0770353	−	0.237090i
$498$		0			0
$499$	−29.2059			−1.30743			−0.653717	−	0.756739i	$-0.726791\pi$
$499$	−29.2059			−1.30743			−0.653717	+	0.756739i	$0.726791\pi$
$500$		0			0
$501$	15.5962			0.696787
$502$		0			0
$503$	−9.53123	−	29.3341i	−0.424977	−	1.30794i	−0.903017	−	0.429606i	$-0.858653\pi$
$503$	−9.53123	−	29.3341i	−0.424977	−	1.30794i	0.478040	−	0.878338i	$-0.341347\pi$
$504$		0			0
$505$	7.15511	−	40.5482i	0.318398	−	1.80437i
$506$		0			0
$507$	5.19127			0.230552
$508$		0			0
$509$	−2.55341	+	1.85516i	−0.113178	+	0.0822287i	−0.642935	−	0.765921i	$-0.722283\pi$
$509$	−2.55341	+	1.85516i	−0.113178	+	0.0822287i	0.529757	+	0.848150i	$0.322283\pi$
$510$		0			0
$511$	−4.21026	−	3.05893i	−0.186251	−	0.135319i
$512$		0			0
$513$	−12.4361	+	9.03536i	−0.549068	+	0.398921i
$514$		0			0
$515$	−4.15225	+	0.583016i	−0.182970	+	0.0256908i
$516$		0			0
$517$	−2.57571	+	7.92721i	−0.113279	+	0.348638i
$518$		0			0
$519$	−8.07273	+	24.8453i	−0.354353	+	1.09059i
$520$		0			0
$521$	7.57661	+	23.3184i	0.331937	+	1.02160i	0.968211	+	0.250135i	$0.0804750\pi$
$521$	7.57661	+	23.3184i	0.331937	+	1.02160i	−0.636274	+	0.771464i	$0.719525\pi$
$522$		0			0
$523$	−10.5366	−	7.65528i	−0.460733	−	0.334742i	0.333086	−	0.942896i	$-0.391910\pi$
$523$	−10.5366	−	7.65528i	−0.460733	−	0.334742i	−0.793819	+	0.608155i	$0.791910\pi$
$524$		0			0
$525$	0.338858	−	9.63264i	0.0147890	−	0.420403i
$526$		0			0
$527$	−1.73441	−	1.26012i	−0.0755520	−	0.0548918i
$528$		0			0
$529$	−4.02226	−	12.3792i	−0.174881	−	0.538227i
$530$		0			0
$531$	6.56996	−	20.2203i	0.285112	−	0.877485i
$532$		0			0
$533$	−7.31571	+	22.5154i	−0.316879	+	0.975252i
$534$		0			0
$535$	2.66647	−	15.1110i	0.115282	−	0.653304i
$536$		0			0
$537$	−4.71556	+	3.42606i	−0.203492	+	0.147845i
$538$		0			0
$539$	12.7062	+	9.23160i	0.547295	+	0.397633i
$540$		0			0
$541$	−21.0579	+	15.2995i	−0.905351	+	0.657776i	−0.939835	−	0.341629i	$-0.889021\pi$
$541$	−21.0579	+	15.2995i	−0.905351	+	0.657776i	0.0344839	+	0.999405i	$0.489021\pi$
$542$		0			0
$543$	3.86980			0.166069
$544$		0			0
$545$	3.10571	+	6.36973i	0.133034	+	0.272849i
$546$		0			0
$547$	−7.49421	−	23.0648i	−0.320429	−	0.986180i	−0.973462	−	0.228850i	$-0.926503\pi$
$547$	−7.49421	−	23.0648i	−0.320429	−	0.986180i	0.653032	−	0.757330i	$-0.273497\pi$
$548$		0			0
$549$	3.74851			0.159983
$550$		0			0
$551$	−27.5919			−1.17545
$552$		0			0
$553$	−4.90440	−	15.0942i	−0.208556	−	0.641871i
$554$		0			0
$555$	8.71928	−	8.41794i	0.370113	−	0.357322i
$556$		0			0
$557$	24.7393			1.04824			0.524118	−	0.851646i	$-0.324395\pi$
$557$	24.7393			1.04824			0.524118	+	0.851646i	$0.324395\pi$
$558$		0			0
$559$	−27.5132	+	19.9895i	−1.16368	+	0.845466i
$560$		0			0
$561$	−3.99122	−	2.89979i	−0.168509	−	0.122429i
$562$		0			0
$563$	−6.10487	+	4.43545i	−0.257290	+	0.186932i	−0.708951	−	0.705257i	$-0.750831\pi$
$563$	−6.10487	+	4.43545i	−0.257290	+	0.186932i	0.451662	+	0.892189i	$0.350831\pi$
$564$		0			0
$565$	−0.131660	−	0.270031i	−0.00553898	−	0.0113603i
$566$		0			0
$567$	0.970888	−	2.98808i	0.0407734	−	0.125488i
$568$		0			0
$569$	0.0729216	−	0.224430i	0.00305703	−	0.00940858i	−0.949516	−	0.313718i	$-0.898426\pi$
$569$	0.0729216	−	0.224430i	0.00305703	−	0.00940858i	0.952573	+	0.304309i	$0.0984255\pi$
$570$		0			0
$571$	−5.31068	−	16.3446i	−0.222245	−	0.684001i	−0.998560	−	0.0536545i	$-0.982913\pi$
$571$	−5.31068	−	16.3446i	−0.222245	−	0.684001i	0.776314	−	0.630346i	$-0.217087\pi$
$572$		0			0
$573$	−13.3708	−	9.71448i	−0.558575	−	0.405828i
$574$		0			0
$575$	−8.83104	−	13.0998i	−0.368280	−	0.546300i
$576$		0			0
$577$	−6.15985	−	4.47539i	−0.256438	−	0.186313i	0.452137	−	0.891948i	$-0.350662\pi$
$577$	−6.15985	−	4.47539i	−0.256438	−	0.186313i	−0.708575	+	0.705635i	$0.750662\pi$
$578$		0			0
$579$	−7.34438	−	22.6037i	−0.305222	−	0.939377i
$580$		0			0
$581$	6.35734	−	19.5659i	0.263747	−	0.811729i
$582$		0			0
$583$	7.60560	−	23.4076i	0.314992	−	0.969445i
$584$		0			0
$585$	9.00590	+	4.79001i	0.372348	+	0.198042i
$586$		0			0
$587$	16.4411	−	11.9451i	0.678596	−	0.493029i	−0.194296	−	0.980943i	$-0.562242\pi$
$587$	16.4411	−	11.9451i	0.678596	−	0.493029i	0.872892	+	0.487914i	$0.162242\pi$
$588$		0			0
$589$	4.20201	+	3.05294i	0.173141	+	0.125794i
$590$		0			0
$591$	−21.0640	+	15.3039i	−0.866457	+	0.629518i
$592$		0			0
$593$	−17.3712			−0.713348			−0.356674	−	0.934229i	$-0.616089\pi$
$593$	−17.3712			−0.713348			−0.356674	+	0.934229i	$0.616089\pi$
$594$		0			0
$595$	−3.65518	−	1.94410i	−0.149848	−	0.0797003i
$596$		0			0
$597$	9.02059	+	27.7625i	0.369188	+	1.13624i
$598$		0			0
$599$	11.1550			0.455779			0.227890	−	0.973687i	$-0.426817\pi$
$599$	11.1550			0.455779			0.227890	+	0.973687i	$0.426817\pi$
$600$		0			0
$601$	8.30269			0.338674			0.169337	−	0.985558i	$-0.445837\pi$
$601$	8.30269			0.338674			0.169337	+	0.985558i	$0.445837\pi$
$602$		0			0
$603$	−6.61263	−	20.3516i	−0.269287	−	0.828781i
$604$		0			0
$605$	3.32368	−	0.466677i	0.135127	−	0.0189731i
$606$		0			0
$607$	−4.56913			−0.185455			−0.0927275	−	0.995692i	$-0.529559\pi$
$607$	−4.56913			−0.185455			−0.0927275	+	0.995692i	$0.529559\pi$
$608$		0			0
$609$	15.3427	−	11.1471i	0.621718	−	0.451704i
$610$		0			0
$611$	5.62322	+	4.08551i	0.227491	+	0.165282i
$612$		0			0
$613$	23.6078	−	17.1521i	0.953510	−	0.692765i	0.00187525	−	0.999998i	$-0.499403\pi$
$613$	23.6078	−	17.1521i	0.953510	−	0.692765i	0.951634	+	0.307233i	$0.0994031\pi$
$614$		0			0
$615$	−15.5691	+	15.0310i	−0.627805	+	0.606108i
$616$		0			0
$617$	9.42696	−	29.0132i	0.379515	−	1.16803i	−0.560866	−	0.827906i	$-0.689532\pi$
$617$	9.42696	−	29.0132i	0.379515	−	1.16803i	0.940382	−	0.340121i	$-0.110468\pi$
$618$		0			0
$619$	4.12667	−	12.7006i	0.165865	−	0.510480i	−0.833234	−	0.552921i	$-0.813513\pi$
$619$	4.12667	−	12.7006i	0.165865	−	0.510480i	0.999099	+	0.0424406i	$0.0135133\pi$
$620$		0			0
$621$	−5.35148	−	16.4702i	−0.214748	−	0.660925i
$622$		0			0
$623$	−14.1582	−	10.2866i	−0.567237	−	0.412122i
$624$		0			0
$625$	19.1428	+	16.0795i	0.765714	+	0.643181i
$626$		0			0
$627$	9.66965	+	7.02541i	0.386168	+	0.280568i
$628$		0			0
$629$	−1.60866	−	4.95096i	−0.0641416	−	0.197408i
$630$		0			0
$631$	−0.142339	+	0.438075i	−0.00566643	+	0.0174395i	−0.953850	−	0.300284i	$-0.902918\pi$
$631$	−0.142339	+	0.438075i	−0.00566643	+	0.0174395i	0.948183	+	0.317724i	$0.102918\pi$
$632$		0			0
$633$	0.774495	−	2.38365i	0.0307834	−	0.0947416i
$634$		0			0
$635$	−18.8838	+	18.2312i	−0.749382	+	0.723483i
$636$		0			0
$637$	10.5957	−	7.69821i	0.419816	−	0.305014i
$638$		0			0
$639$	4.34962	+	3.16018i	0.172068	+	0.125015i
$640$		0			0
$641$	22.0956	−	16.0534i	0.872724	−	0.634071i	−0.0585926	−	0.998282i	$-0.518661\pi$
$641$	22.0956	−	16.0534i	0.872724	−	0.634071i	0.931316	+	0.364211i	$0.118661\pi$
$642$		0			0
$643$	13.8667			0.546848			0.273424	−	0.961894i	$-0.411844\pi$
$643$	13.8667			0.546848			0.273424	+	0.961894i	$0.411844\pi$
$644$		0			0
$645$	−30.7853	+	4.32256i	−1.21217	+	0.170201i
$646$		0			0
$647$	−9.54913	−	29.3892i	−0.375415	−	1.15541i	−0.943198	−	0.332231i	$-0.892199\pi$
$647$	−9.54913	−	29.3892i	−0.375415	−	1.15541i	0.567783	−	0.823178i	$-0.307801\pi$
$648$		0			0
$649$	−48.5849			−1.90712
$650$		0			0
$651$	−3.56995			−0.139917
$652$		0			0
$653$	−4.64737	−	14.3031i	−0.181866	−	0.559725i	0.818015	−	0.575198i	$-0.195075\pi$
$653$	−4.64737	−	14.3031i	−0.181866	−	0.559725i	−0.999880	+	0.0154722i	$0.995075\pi$
$654$		0			0
$655$	4.24475	+	2.25767i	0.165856	+	0.0882146i
$656$		0			0
$657$	5.03453			0.196416
$658$		0			0
$659$	0.112275	−	0.0815727i	0.00437362	−	0.00317762i	−0.585596	−	0.810603i	$-0.699140\pi$
$659$	0.112275	−	0.0815727i	0.00437362	−	0.00317762i	0.589970	+	0.807425i	$0.299140\pi$
$660$		0			0
$661$	23.8045	+	17.2950i	0.925888	+	0.672697i	0.944983	−	0.327120i	$-0.106078\pi$
$661$	23.8045	+	17.2950i	0.925888	+	0.672697i	−0.0190943	+	0.999818i	$0.506078\pi$
$662$		0			0
$663$	−3.32827	+	2.41813i	−0.129259	+	0.0939123i
$664$		0			0
$665$	8.85554	+	4.71003i	0.343403	+	0.182647i
$666$		0			0
$667$	9.60569	−	29.5633i	0.371934	−	1.14470i
$668$		0			0
$669$	−7.29238	+	22.4436i	−0.281940	+	0.867721i
$670$		0			0
$671$	−2.64705	−	8.14678i	−0.102188	−	0.314503i
$672$		0			0
$673$	22.1214	+	16.0722i	0.852719	+	0.619537i	0.925894	−	0.377782i	$-0.123313\pi$
$673$	22.1214	+	16.0722i	0.852719	+	0.619537i	−0.0731753	+	0.997319i	$0.523313\pi$
$674$		0			0
$675$	15.3184	+	22.7230i	0.589604	+	0.874608i
$676$		0			0
$677$	−14.5307	−	10.5571i	−0.558458	−	0.405744i	0.272436	−	0.962174i	$-0.412171\pi$
$677$	−14.5307	−	10.5571i	−0.558458	−	0.405744i	−0.830894	+	0.556430i	$0.812171\pi$
$678$		0			0
$679$	3.54009	+	10.8953i	0.135856	+	0.418122i
$680$		0			0
$681$	2.44292	−	7.51853i	0.0936128	−	0.288111i
$682$		0			0
$683$	−8.43526	+	25.9611i	−0.322766	+	0.993372i	0.649673	+	0.760214i	$0.274906\pi$
$683$	−8.43526	+	25.9611i	−0.322766	+	0.993372i	−0.972439	+	0.233158i	$0.925094\pi$
$684$		0			0
$685$	−15.4986	−	31.7872i	−0.592171	−	1.21453i
$686$		0			0
$687$	−14.7753	+	10.7349i	−0.563712	+	0.409561i
$688$		0			0
$689$	−16.6044	−	12.0638i	−0.632576	−	0.459593i
$690$		0			0
$691$	30.5969	−	22.2300i	1.16396	−	0.845667i	0.173688	−	0.984801i	$-0.444432\pi$
$691$	30.5969	−	22.2300i	1.16396	−	0.845667i	0.990274	+	0.139134i	$0.0444317\pi$
$692$		0			0
$693$	8.74918			0.332354
$694$		0			0
$695$	−31.8913	+	30.7892i	−1.20971	+	1.16790i
$696$		0			0
$697$	2.87241	+	8.84038i	0.108800	+	0.334853i
$698$		0			0
$699$	2.07662			0.0785451
$700$		0			0
$701$	−34.1068			−1.28820			−0.644098	−	0.764943i	$-0.722767\pi$
$701$	−34.1068			−1.28820			−0.644098	+	0.764943i	$0.722767\pi$
$702$		0			0
$703$	3.89736	+	11.9948i	0.146992	+	0.452394i
$704$		0			0
$705$	2.78455	+	5.71103i	0.104872	+	0.215090i
$706$		0			0
$707$	−29.4502			−1.10759
$708$		0			0
$709$	17.2989	−	12.5684i	0.649673	−	0.472015i	−0.213487	−	0.976946i	$-0.568482\pi$
$709$	17.2989	−	12.5684i	0.649673	−	0.472015i	0.863160	+	0.504931i	$0.168482\pi$
$710$		0			0
$711$	12.4214	+	9.02465i	0.465838	+	0.338451i
$712$		0			0
$713$	−4.73393	+	3.43940i	−0.177287	+	0.128807i
$714$		0			0
$715$	4.05069	−	22.9553i	0.151487	−	0.858481i
$716$		0			0
$717$	3.01932	−	9.29252i	0.112759	−	0.347036i
$718$		0			0
$719$	8.20972	−	25.2669i	0.306171	−	0.942298i	−0.673067	−	0.739582i	$-0.735023\pi$
$719$	8.20972	−	25.2669i	0.306171	−	0.942298i	0.979238	−	0.202716i	$-0.0649767\pi$
$720$		0			0
$721$	0.926752	+	2.85225i	0.0345140	+	0.106223i
$722$		0			0
$723$	3.85212	+	2.79873i	0.143262	+	0.104086i
$724$		0			0
$725$	−1.72932	+	49.1589i	−0.0642252	+	1.82571i
$726$		0			0
$727$	−1.12942	−	0.820574i	−0.0418880	−	0.0304334i	0.566644	−	0.823963i	$-0.308241\pi$
$727$	−1.12942	−	0.820574i	−0.0418880	−	0.0304334i	−0.608532	+	0.793529i	$0.708241\pi$
$728$		0			0
$729$	7.06345	+	21.7391i	0.261609	+	0.805150i
$730$		0			0
$731$	−4.12625	+	12.6993i	−0.152615	+	0.469701i
$732$		0			0
$733$	4.72195	−	14.5327i	0.174409	−	0.536776i	−0.825197	−	0.564845i	$-0.808936\pi$
$733$	4.72195	−	14.5327i	0.174409	−	0.536776i	0.999606	+	0.0280692i	$0.00893587\pi$
$734$		0			0
$735$	11.8558	−	1.66467i	0.437309	−	0.0614024i
$736$		0			0
$737$	−39.5612	+	28.7429i	−1.45726	+	1.05876i
$738$		0			0
$739$	25.0588	+	18.2063i	0.921802	+	0.669728i	0.943972	−	0.330026i	$-0.107057\pi$
$739$	25.0588	+	18.2063i	0.921802	+	0.669728i	−0.0221698	+	0.999754i	$0.507057\pi$
$740$		0			0
$741$	8.06351	−	5.85848i	0.296220	−	0.215217i
$742$		0			0
$743$	−9.18330			−0.336902			−0.168451	−	0.985710i	$-0.553877\pi$
$743$	−9.18330			−0.336902			−0.168451	+	0.985710i	$0.553877\pi$
$744$		0			0
$745$	3.67486	−	20.8255i	0.134637	−	0.762989i
$746$		0			0
$747$	6.15012	+	18.9281i	0.225021	+	0.692543i
$748$		0			0
$749$	−10.9751			−0.401022
$750$		0			0
$751$	45.3438			1.65462			0.827309	−	0.561747i	$-0.189871\pi$
$751$	45.3438			1.65462			0.827309	+	0.561747i	$0.189871\pi$
$752$		0			0
$753$	7.90604	+	24.3323i	0.288112	+	0.886718i
$754$		0			0
$755$	7.58034	−	42.9579i	0.275877	−	1.56340i
$756$		0			0
$757$	−45.4782			−1.65293			−0.826467	−	0.562985i	$-0.809653\pi$
$757$	−45.4782			−1.65293			−0.826467	+	0.562985i	$0.809653\pi$
$758$		0			0
$759$	−10.8937	+	7.91474i	−0.395416	+	0.287287i
$760$		0			0
$761$	0.515120	+	0.374257i	0.0186731	+	0.0135668i	0.597083	−	0.802180i	$-0.296326\pi$
$761$	0.515120	+	0.374257i	0.0186731	+	0.0135668i	−0.578410	+	0.815747i	$0.696326\pi$
$762$		0			0
$763$	4.10062	−	2.97928i	0.148453	−	0.107857i
$764$		0			0
$765$	3.96618	−	0.556891i	0.143398	−	0.0201344i
$766$		0			0
$767$	−12.5198	+	38.5319i	−0.452063	+	1.39131i
$768$		0			0
$769$	2.87386	−	8.84482i	0.103634	−	0.318952i	−0.885774	−	0.464118i	$-0.846371\pi$
$769$	2.87386	−	8.84482i	0.103634	−	0.318952i	0.989407	+	0.145165i	$0.0463714\pi$
$770$		0			0
$771$	−0.0694170	−	0.213644i	−0.00249999	−	0.00769419i
$772$		0			0
$773$	−5.91821	−	4.29983i	−0.212863	−	0.154654i	0.476245	−	0.879313i	$-0.341998\pi$
$773$	−5.91821	−	4.29983i	−0.212863	−	0.154654i	−0.689108	+	0.724658i	$0.741998\pi$
$774$		0			0
$775$	5.70260	−	7.29513i	0.204844	−	0.262049i
$776$		0			0
$777$	−7.01308	−	5.09530i	−0.251593	−	0.182793i
$778$		0			0
$779$	−6.95909	−	21.4179i	−0.249335	−	0.767375i
$780$		0			0
$781$	3.79661	−	11.6848i	0.135853	−	0.418114i
$782$		0			0
$783$	−16.6621	+	51.2806i	−0.595454	+	1.83262i
$784$		0			0
$785$	−5.79986	+	32.8679i	−0.207006	+	1.17311i
$786$		0			0
$787$	23.0553	−	16.7507i	0.821833	−	0.597097i	−0.0954038	−	0.995439i	$-0.530414\pi$
$787$	23.0553	−	16.7507i	0.821833	−	0.597097i	0.917237	+	0.398342i	$0.130414\pi$
$788$		0			0
$789$	−9.69055	−	7.04060i	−0.344993	−	0.250652i
$790$		0			0
$791$	−0.173837	+	0.126300i	−0.00618094	+	0.00449071i
$792$		0			0
$793$	−7.14320			−0.253662
$794$		0			0
$795$	−8.22227	−	16.8637i	−0.291614	−	0.598092i
$796$		0			0
$797$	−1.53076	−	4.71121i	−0.0542225	−	0.166880i	0.920278	−	0.391265i	$-0.127962\pi$
$797$	−1.53076	−	4.71121i	−0.0542225	−	0.166880i	−0.974500	+	0.224386i	$0.927962\pi$
$798$		0			0
$799$	2.72909			0.0965482
$800$		0			0
$801$	16.9301			0.598195
$802$		0			0
$803$	−3.55518	−	10.9417i	−0.125460	−	0.386125i
$804$		0			0
$805$	−8.12948	+	7.84853i	−0.286526	+	0.276624i
$806$		0			0
$807$	34.0189			1.19752
$808$		0			0
$809$	22.0656	−	16.0316i	0.775787	−	0.563642i	−0.127925	−	0.991784i	$-0.540832\pi$
$809$	22.0656	−	16.0316i	0.775787	−	0.563642i	0.903712	+	0.428142i	$0.140832\pi$
$810$		0			0
$811$	40.8986	+	29.7146i	1.43614	+	1.04342i	0.988831	+	0.149042i	$0.0476189\pi$
$811$	40.8986	+	29.7146i	1.43614	+	1.04342i	0.447313	+	0.894378i	$0.352381\pi$
$812$		0			0
$813$	4.12917	−	3.00002i	0.144816	−	0.105215i
$814$		0			0
$815$	10.5833	+	21.7060i	0.370716	+	0.760328i
$816$		0			0
$817$	9.99681	−	30.7670i	0.349744	−	1.07640i
$818$		0			0
$819$	2.25457	−	6.93884i	0.0787809	−	0.242463i
$820$		0			0
$821$	−4.73239	−	14.5648i	−0.165162	−	0.508315i	0.833886	−	0.551936i	$-0.186111\pi$
$821$	−4.73239	−	14.5648i	−0.165162	−	0.508315i	−0.999048	+	0.0436206i	$0.986111\pi$
$822$		0			0
$823$	17.6552	+	12.8272i	0.615421	+	0.447129i	0.851319	−	0.524649i	$-0.175803\pi$
$823$	17.6552	+	12.8272i	0.615421	+	0.447129i	−0.235898	+	0.971778i	$0.575803\pi$
$824$		0			0
$825$	13.1228	−	16.7875i	0.456878	−	0.584467i
$826$		0			0
$827$	23.7315	+	17.2419i	0.825224	+	0.599560i	0.918204	−	0.396108i	$-0.129639\pi$
$827$	23.7315	+	17.2419i	0.825224	+	0.599560i	−0.0929802	+	0.995668i	$0.529639\pi$
$828$		0			0
$829$	13.2985	+	40.9287i	0.461877	+	1.42151i	0.862868	+	0.505430i	$0.168666\pi$
$829$	13.2985	+	40.9287i	0.461877	+	1.42151i	−0.400990	+	0.916082i	$0.631334\pi$
$830$		0			0
$831$	6.90852	−	21.2622i	0.239654	−	0.737579i
$832$		0			0
$833$	1.58907	−	4.89066i	0.0550581	−	0.169451i
$834$		0			0
$835$	25.5452	+	13.5868i	0.884028	+	0.470192i
$836$		0			0
$837$	8.21149	−	5.96600i	0.283831	−	0.206215i
$838$		0			0
$839$	−24.4386	−	17.7556i	−0.843713	−	0.612993i	0.0796927	−	0.996819i	$-0.474606\pi$
$839$	−24.4386	−	17.7556i	−0.843713	−	0.612993i	−0.923405	+	0.383826i	$0.874606\pi$
$840$		0			0
$841$	−54.8379	+	39.8421i	−1.89096	+	1.37387i
$842$		0			0
$843$	4.01348			0.138232
$844$		0			0
$845$	8.50283	+	4.52244i	0.292506	+	0.155577i
$846$		0			0
$847$	−0.741821	−	2.28309i	−0.0254893	−	0.0784479i
$848$		0			0
$849$	26.2236			0.899992
$850$		0			0
$851$	−14.2087			−0.487067
$852$		0			0
$853$	16.8447	+	51.8426i	0.576751	+	1.77506i	0.630138	+	0.776483i	$0.282998\pi$
$853$	16.8447	+	51.8426i	0.576751	+	1.77506i	−0.0533875	+	0.998574i	$0.517002\pi$
$854$		0			0
$855$	−9.60900	+	1.34920i	−0.328621	+	0.0461416i
$856$		0			0
$857$	28.3459			0.968276			0.484138	−	0.874992i	$-0.339133\pi$
$857$	28.3459			0.968276			0.484138	+	0.874992i	$0.339133\pi$
$858$		0			0
$859$	3.62806	−	2.63594i	0.123788	−	0.0899372i	−0.524169	−	0.851615i	$-0.675624\pi$
$859$	3.62806	−	2.63594i	0.123788	−	0.0899372i	0.647957	+	0.761677i	$0.275624\pi$
$860$		0			0
$861$	12.5225	+	9.09812i	0.426765	+	0.310063i
$862$		0			0
$863$	−18.7437	+	13.6181i	−0.638044	+	0.463566i	−0.859178	−	0.511677i	$-0.829024\pi$
$863$	−18.7437	+	13.6181i	−0.638044	+	0.463566i	0.221133	+	0.975244i	$0.429024\pi$
$864$		0			0
$865$	−34.8667	+	33.6617i	−1.18550	+	1.14453i
$866$		0			0
$867$	5.83271	−	17.9512i	0.198089	−	0.609656i
$868$		0			0
$869$	10.8421	−	33.3686i	0.367794	−	1.13195i
$870$		0			0
$871$	12.6011	+	38.7821i	0.426971	+	1.31408i
$872$		0			0
$873$	−8.96597	−	6.51416i	−0.303452	−	0.220471i
$874$		0			0
$875$	8.94661	−	15.4822i	0.302451	−	0.523394i
$876$		0			0
$877$	−27.1415	−	19.7195i	−0.916505	−	0.665880i	0.0261468	−	0.999658i	$-0.491676\pi$
$877$	−27.1415	−	19.7195i	−0.916505	−	0.665880i	−0.942652	+	0.333778i	$0.891676\pi$
$878$		0			0
$879$	−8.55924	−	26.3426i	−0.288696	−	0.888515i
$880$		0			0
$881$	−2.53650	+	7.80655i	−0.0854569	+	0.263009i	−0.984649	−	0.174544i	$-0.944155\pi$
$881$	−2.53650	+	7.80655i	−0.0854569	+	0.263009i	0.899192	+	0.437553i	$0.144155\pi$
$882$		0			0
$883$	−1.81874	+	5.59752i	−0.0612056	+	0.188371i	−0.976984	−	0.213312i	$-0.931575\pi$
$883$	−1.81874	+	5.59752i	−0.0612056	+	0.188371i	0.915778	+	0.401684i	$0.131575\pi$
$884$		0			0
$885$	−26.6442	+	25.7234i	−0.895634	+	0.864681i
$886$		0			0
$887$	−21.1004	+	15.3304i	−0.708484	+	0.514744i	−0.882684	−	0.469967i	$-0.844266\pi$
$887$	−21.1004	+	15.3304i	−0.708484	+	0.514744i	0.174200	+	0.984710i	$0.444266\pi$
$888$		0			0
$889$	15.1886	+	11.0352i	0.509410	+	0.370108i
$890$		0			0
$891$	5.61917	−	4.08257i	0.188249	−	0.136771i
$892$		0			0
$893$	−6.61185			−0.221257
$894$		0			0
$895$	−10.7083	+	1.50355i	−0.357940	+	0.0502583i
$896$		0			0
$897$	3.46987	+	10.6792i	0.115856	+	0.356567i
$898$		0			0
$899$	18.2188			0.607630
$900$		0			0
$901$	−8.05851			−0.268468
$902$		0			0
$903$	6.87107	+	21.1470i	0.228655	+	0.703727i
$904$		0			0
$905$	6.33839	+	3.37123i	0.210695	+	0.112063i
$906$		0			0
$907$	−55.9049			−1.85629			−0.928146	−	0.372216i	$-0.878598\pi$
$907$	−55.9049			−1.85629			−0.928146	+	0.372216i	$0.878598\pi$
$908$		0			0
$909$	23.0491	−	16.7462i	0.764491	−	0.555435i
$910$		0			0
$911$	9.01861	+	6.55240i	0.298800	+	0.217091i	0.727076	−	0.686557i	$-0.240879\pi$
$911$	9.01861	+	6.55240i	0.298800	+	0.217091i	−0.428276	+	0.903648i	$0.640879\pi$
$912$		0			0
$913$	36.7941	−	26.7325i	1.21771	−	0.884717i
$914$		0			0
$915$	−5.76498	−	3.06625i	−0.190584	−	0.101367i
$916$		0			0
$917$	1.06264	−	3.27048i	0.0350916	−	0.108001i
$918$		0			0
$919$	0.0872351	−	0.268482i	0.00287762	−	0.00885640i	−0.949607	−	0.313442i	$-0.898518\pi$
$919$	0.0872351	−	0.268482i	0.00287762	−	0.00885640i	0.952485	+	0.304585i	$0.0985179\pi$
$920$		0			0
$921$	0.0620478	+	0.190964i	0.00204454	+	0.00629246i
$922$		0			0
$923$	−8.28867	−	6.02207i	−0.272825	−	0.198219i
$924$		0			0
$925$	21.6148	−	6.19193i	0.710690	−	0.203589i
$926$		0			0
$927$	−2.34718	−	1.70533i	−0.0770916	−	0.0560103i
$928$		0			0
$929$	1.82070	+	5.60354i	0.0597353	+	0.183846i	0.976471	−	0.215647i	$-0.0691861\pi$
$929$	1.82070	+	5.60354i	0.0597353	+	0.183846i	−0.916736	+	0.399493i	$0.869186\pi$
$930$		0			0
$931$	−3.84990	+	11.8488i	−0.126175	+	0.388328i
$932$		0			0
$933$	−2.95806	+	9.10396i	−0.0968424	+	0.298050i
$934$		0			0
$935$	−4.01107	−	8.22659i	−0.131176	−	0.269038i
$936$		0			0
$937$	−3.83443	+	2.78588i	−0.125265	+	0.0910107i	−0.648654	−	0.761084i	$-0.724668\pi$
$937$	−3.83443	+	2.78588i	−0.125265	+	0.0910107i	0.523388	+	0.852094i	$0.324668\pi$
$938$		0			0
$939$	−11.6385	−	8.45583i	−0.379807	−	0.275946i
$940$		0			0
$941$	9.49301	−	6.89708i	0.309463	−	0.224838i	−0.422203	−	0.906501i	$-0.638743\pi$
$941$	9.49301	−	6.89708i	0.309463	−	0.224838i	0.731666	+	0.681663i	$0.238743\pi$
$942$		0			0
$943$	25.3708			0.826188
$944$		0			0
$945$	14.1014	−	13.6141i	0.458719	−	0.442866i
$946$		0			0
$947$	8.35893	+	25.7261i	0.271629	+	0.835987i	0.990092	+	0.140422i	$0.0448460\pi$
$947$	8.35893	+	25.7261i	0.271629	+	0.835987i	−0.718463	+	0.695565i	$0.755154\pi$
$948$		0			0
$949$	−9.59384			−0.311429
$950$		0			0
$951$	12.0866			0.391934
$952$		0			0
$953$	3.12461	+	9.61655i	0.101216	+	0.311511i	0.988824	−	0.149089i	$-0.0476342\pi$
$953$	3.12461	+	9.61655i	0.101216	+	0.311511i	−0.887608	+	0.460600i	$0.847634\pi$
$954$		0			0
$955$	−13.4373	−	27.5596i	−0.434822	−	0.891808i
$956$		0			0
$957$	41.9249			1.35524
$958$		0			0
$959$	−20.4636	+	14.8676i	−0.660803	+	0.480101i
$960$		0			0
$961$	22.3050	+	16.2055i	0.719515	+	0.522758i
$962$		0			0
$963$	8.58964	−	6.24074i	0.276797	−	0.201105i
$964$		0			0
$965$	7.66204	−	43.4210i	0.246650	−	1.39777i
$966$		0			0
$967$	−17.0533	+	52.4847i	−0.548398	+	1.68780i	0.164373	+	0.986398i	$0.447440\pi$
$967$	−17.0533	+	52.4847i	−0.548398	+	1.68780i	−0.712771	+	0.701397i	$0.752560\pi$
$968$		0			0
$969$	1.20931	−	3.72188i	0.0388487	−	0.119564i
$970$		0			0
$971$	−12.6530	−	38.9419i	−0.406054	−	1.24971i	−0.920012	−	0.391891i	$-0.871821\pi$
$971$	−12.6530	−	38.9419i	−0.406054	−	1.24971i	0.513957	−	0.857816i	$-0.328179\pi$
$972$		0			0
$973$	25.6508	+	18.6364i	0.822326	+	0.597455i
$974$		0			0
$975$	−9.93234	−	14.7335i	−0.318089	−	0.471848i
$976$		0			0
$977$	−12.9047	−	9.37583i	−0.412859	−	0.299959i	0.361900	−	0.932217i	$-0.382128\pi$
$977$	−12.9047	−	9.37583i	−0.412859	−	0.299959i	−0.774758	+	0.632258i	$0.782128\pi$
$978$		0			0
$979$	−11.9553	−	36.7947i	−0.382094	−	1.17596i
$980$		0			0
$981$	−1.51524	+	4.66344i	−0.0483780	+	0.148892i
$982$		0			0
$983$	−13.3748	+	41.1633i	−0.426588	+	1.31290i	0.474877	+	0.880052i	$0.342493\pi$
$983$	−13.3748	+	41.1633i	−0.426588	+	1.31290i	−0.901465	+	0.432852i	$0.857507\pi$
$984$		0			0
$985$	−47.8331	+	6.71624i	−1.52409	+	0.213997i
$986$		0			0
$987$	3.67658	−	2.67119i	0.117027	−	0.0850249i
$988$		0			0
$989$	29.4850	+	21.4221i	0.937570	+	0.681184i
$990$		0			0
$991$	−11.5901	+	8.42071i	−0.368172	+	0.267493i	−0.756452	−	0.654049i	$-0.773069\pi$
$991$	−11.5901	+	8.42071i	−0.368172	+	0.267493i	0.388281	+	0.921541i	$0.373069\pi$
$992$		0			0
$993$	39.0360			1.23877
$994$		0			0
$995$	−9.41075	+	53.3309i	−0.298341	+	1.69070i
$996$		0			0
$997$	−7.34905	−	22.6180i	−0.232747	−	0.716321i	−0.997412	−	0.0718934i	$-0.977096\pi$
$997$	−7.34905	−	22.6180i	−0.232747	−	0.716321i	0.764666	−	0.644427i	$-0.222904\pi$
$998$		0			0
$999$	24.6464			0.779777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.g.241.2		16
4.3	odd	2		200.2.m.c.41.3	✓	16
20.3	even	4		1000.2.q.d.49.4		32
20.7	even	4		1000.2.q.d.49.5		32
20.19	odd	2		1000.2.m.c.201.2		16
25.6	even	5		10000.2.a.bk.1.3		8
25.11	even	5	inner	400.2.u.g.161.2		16
25.19	even	10		10000.2.a.bh.1.6		8
100.11	odd	10		200.2.m.c.161.3	yes	16
100.19	odd	10		5000.2.a.m.1.3		8
100.23	even	20		1000.2.q.d.449.5		32
100.27	even	20		1000.2.q.d.449.4		32
100.31	odd	10		5000.2.a.l.1.6		8
100.39	odd	10		1000.2.m.c.801.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.c.41.3	✓	16	4.3	odd	2
200.2.m.c.161.3	yes	16	100.11	odd	10
400.2.u.g.161.2		16	25.11	even	5	inner
400.2.u.g.241.2		16	1.1	even	1	trivial
1000.2.m.c.201.2		16	20.19	odd	2
1000.2.m.c.801.2		16	100.39	odd	10
1000.2.q.d.49.4		32	20.3	even	4
1000.2.q.d.49.5		32	20.7	even	4
1000.2.q.d.449.4		32	100.27	even	20
1000.2.q.d.449.5		32	100.23	even	20
5000.2.a.l.1.6		8	100.31	odd	10
5000.2.a.m.1.3		8	100.19	odd	10
10000.2.a.bh.1.6		8	25.19	even	10
10000.2.a.bk.1.3		8	25.6	even	5

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.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.372462 - 1.14632i) q^{3} +(0.388572 - 2.20205i) q^{5} -1.59935 q^{7} +(1.25173 - 0.909432i) q^{9} +O(q^{10})\)	\(q+(-0.372462 - 1.14632i) q^{3} +(0.388572 - 2.20205i) q^{5} -1.59935 q^{7} +(1.25173 - 0.909432i) q^{9} +(-2.86042 - 2.07822i) q^{11} +(-2.38530 + 1.73302i) q^{13} +(-2.66898 + 0.374751i) q^{15} +(-0.357732 + 1.10099i) q^{17} +(0.866689 - 2.66739i) q^{19} +(0.595698 + 1.83337i) q^{21} +(2.55625 + 1.85723i) q^{23} +(-4.69802 - 1.71131i) q^{25} +(-4.43408 - 3.22155i) q^{27} +(-3.04006 - 9.35636i) q^{29} +(-0.572270 + 1.76126i) q^{31} +(-1.31690 + 4.05302i) q^{33} +(-0.621463 + 3.52185i) q^{35} +(-3.63802 + 2.64318i) q^{37} +(2.87503 + 2.08883i) q^{39} +(6.49601 - 4.71963i) q^{41} +11.5345 q^{43} +(-1.51623 - 3.10974i) q^{45} +(-0.728491 - 2.24207i) q^{47} -4.44208 q^{49} +1.39533 q^{51} +(2.15111 + 6.62042i) q^{53} +(-5.68781 + 5.49124i) q^{55} -3.38050 q^{57} +(11.1170 - 8.07696i) q^{59} +(1.96004 + 1.42405i) q^{61} +(-2.00195 + 1.45450i) q^{63} +(2.88933 + 5.92594i) q^{65} +(4.27388 - 13.1537i) q^{67} +(1.17687 - 3.62203i) q^{69} +(1.07380 + 3.30482i) q^{71} +(2.63248 + 1.91261i) q^{73} +(-0.211872 + 6.02284i) q^{75} +(4.57481 + 3.32380i) q^{77} +(3.06650 + 9.43770i) q^{79} +(-0.607051 + 1.86831i) q^{81} +(-3.97495 + 12.2336i) q^{83} +(2.28542 + 1.21556i) q^{85} +(-9.59308 + 6.96978i) q^{87} +(8.85248 + 6.43171i) q^{89} +(3.81493 - 2.77171i) q^{91} +2.23212 q^{93} +(-5.53696 - 2.94497i) q^{95} +(-2.21345 - 6.81231i) q^{97} -5.47046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) \) 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9	\( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9} + 10 q^{11} + q^{13} + 10 q^{15} - 4 q^{17} - 3 q^{21} - 11 q^{23} + 9 q^{25} - 13 q^{27} + 5 q^{29} + 9 q^{31} + 16 q^{33} - 24 q^{35} + 30 q^{37} - 14 q^{39} - 2 q^{41} + 42 q^{43} - 77 q^{45} + 16 q^{47} + 18 q^{49} - 100 q^{51} + 11 q^{53} + 24 q^{55} - 64 q^{57} + 53 q^{59} + 4 q^{61} + 38 q^{63} + 37 q^{65} + 14 q^{67} - 7 q^{69} + 6 q^{71} - 24 q^{73} + 15 q^{75} + 23 q^{77} + 22 q^{79} - 6 q^{81} - 33 q^{83} + 8 q^{85} - 37 q^{87} + 20 q^{89} + 27 q^{91} + 40 q^{93} + 24 q^{95} + 11 q^{97} - 122 q^{99}+O(q^{100}) \) 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9 + 10 * q^11 + q^13 + 10 * q^15 - 4 * q^17 - 3 * q^21 - 11 * q^23 + 9 * q^25 - 13 * q^27 + 5 * q^29 + 9 * q^31 + 16 * q^33 - 24 * q^35 + 30 * q^37 - 14 * q^39 - 2 * q^41 + 42 * q^43 - 77 * q^45 + 16 * q^47 + 18 * q^49 - 100 * q^51 + 11 * q^53 + 24 * q^55 - 64 * q^57 + 53 * q^59 + 4 * q^61 + 38 * q^63 + 37 * q^65 + 14 * q^67 - 7 * q^69 + 6 * q^71 - 24 * q^73 + 15 * q^75 + 23 * q^77 + 22 * q^79 - 6 * q^81 - 33 * q^83 + 8 * q^85 - 37 * q^87 + 20 * q^89 + 27 * q^91 + 40 * q^93 + 24 * q^95 + 11 * q^97 - 122 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more