LMFDB - Embedded newform 525.2.b.i.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(251,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("525.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.b (of order $2$, degree $1$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.624529833984.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} - 2x^{4} - 18x^{2} + 81 $ x^8 - 2x^6 - 2x^4 - 18*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.6
Root			$1.70166 + 0.323042i$ of defining polynomial
Character	$\chi$	$=$	525.251
Dual form			525.2.b.i.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.09941i q^{2} +(1.70166 + 0.323042i) q^{3} +0.791288 q^{4} +(-0.355157 + 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} +3.06878i q^{8} +(2.79129 + 1.09941i) q^{9} +O(q^{10})$	\(q+1.09941i q^{2} +(1.70166 + 0.323042i) q^{3} +0.791288 q^{4} +(-0.355157 + 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} +3.06878i q^{8} +(2.79129 + 1.09941i) q^{9} -3.06878i q^{11} +(1.34650 + 0.255619i) q^{12} +2.44949i q^{13} +(2.69300 + 1.09941i) q^{14} -1.79129 q^{16} -2.69300 q^{17} +(-1.20871 + 3.06878i) q^{18} -4.38774i q^{19} +(2.49295 - 3.84515i) q^{21} +3.37386 q^{22} +5.26761i q^{23} +(-0.991345 + 5.22202i) q^{24} -2.69300 q^{26} +(4.39466 + 2.77253i) q^{27} +(0.791288 - 1.93825i) q^{28} +5.26761i q^{29} -6.83723i q^{31} +4.16820i q^{32} +(0.991345 - 5.22202i) q^{33} -2.96073i q^{34} +(2.20871 + 0.869953i) q^{36} -8.58258 q^{37} +4.82395 q^{38} +(-0.791288 + 4.16820i) q^{39} -10.2100 q^{41} +(4.22742 + 2.74078i) q^{42} +6.58258 q^{43} -2.42829i q^{44} -5.79129 q^{46} -2.69300 q^{47} +(-3.04816 - 0.578661i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(-4.58258 - 0.869953i) q^{51} +1.93825i q^{52} -3.93874i q^{53} +(-3.04816 + 4.83156i) q^{54} +(7.51695 + 3.06878i) q^{56} +(1.41742 - 7.46644i) q^{57} -5.79129 q^{58} +7.51695 q^{59} +6.83723i q^{61} +7.51695 q^{62} +(5.48429 - 5.73782i) q^{63} -8.16515 q^{64} +(5.74117 + 1.08990i) q^{66} -4.16515 q^{67} -2.13094 q^{68} +(-1.70166 + 8.96368i) q^{69} -3.06878i q^{71} +(-3.37386 + 8.56585i) q^{72} +16.1240i q^{73} -9.43581i q^{74} -3.47197i q^{76} +(-7.51695 - 3.06878i) q^{77} +(-4.58258 - 0.869953i) q^{78} +0.582576 q^{79} +(6.58258 + 6.13756i) q^{81} -11.2250i q^{82} -15.5960 q^{83} +(1.97264 - 3.04262i) q^{84} +7.23698i q^{86} +(-1.70166 + 8.96368i) q^{87} +9.41742 q^{88} -7.51695 q^{89} +(6.00000 + 2.44949i) q^{91} +4.16820i q^{92} +(2.20871 - 11.6346i) q^{93} -2.96073i q^{94} +(-1.34650 + 7.09285i) q^{96} -11.7362i q^{97} +(5.38601 - 5.49707i) q^{98} +(3.37386 - 8.56585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9	$ 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9} + 4 q^{16} - 28 q^{18} - 12 q^{21} - 28 q^{22} - 12 q^{28} + 36 q^{36} - 32 q^{37} + 12 q^{39} + 16 q^{43} - 28 q^{46} - 40 q^{49} + 48 q^{57} - 28 q^{58} + 4 q^{63} + 8 q^{64} + 40 q^{67} + 28 q^{72} - 32 q^{79} + 16 q^{81} + 60 q^{84} + 112 q^{88} + 48 q^{91} + 36 q^{93} - 28 q^{99}+O(q^{100}) $ 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9 + 4 * q^16 - 28 * q^18 - 12 * q^21 - 28 * q^22 - 12 * q^28 + 36 * q^36 - 32 * q^37 + 12 * q^39 + 16 * q^43 - 28 * q^46 - 40 * q^49 + 48 * q^57 - 28 * q^58 + 4 * q^63 + 8 * q^64 + 40 * q^67 + 28 * q^72 - 32 * q^79 + 16 * q^81 + 60 * q^84 + 112 * q^88 + 48 * q^91 + 36 * q^93 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.09941i			0.777403i	0.921364	+	0.388702i	$0.127076\pi$
$2$			1.09941i			0.777403i	−0.921364	+	0.388702i	$0.872924\pi$
$3$	1.70166	+	0.323042i	0.982453	+	0.186508i
$3$	1.70166	+	0.323042i	0.982453	+	0.186508i
$4$	0.791288			0.395644
$5$		0			0
$5$		0			0
$6$	−0.355157	+	1.87083i	−0.144992	+	0.763763i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$			3.06878i			1.08498i
$9$	2.79129	+	1.09941i	0.930429	+	0.366471i
$10$		0			0
$11$		−	3.06878i		−	0.925273i	−0.886548	−	0.462636i	$-0.846904\pi$
$11$		−	3.06878i		−	0.925273i	0.886548	−	0.462636i	$-0.153096\pi$
$12$	1.34650	+	0.255619i	0.388702	+	0.0737909i
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$	2.69300	+	1.09941i	0.719736	+	0.293831i
$15$		0			0
$16$	−1.79129			−0.447822
$17$	−2.69300			−0.653150			−0.326575	−	0.945171i	$-0.605894\pi$
$17$	−2.69300			−0.653150			−0.326575	+	0.945171i	$0.605894\pi$
$18$	−1.20871	+	3.06878i	−0.284896	+	0.723319i
$19$		−	4.38774i		−	1.00662i	−0.864107	−	0.503308i	$-0.832116\pi$
$19$		−	4.38774i		−	1.00662i	0.864107	−	0.503308i	$-0.167884\pi$
$20$		0			0
$21$	2.49295	−	3.84515i	0.544006	−	0.839082i
$22$	3.37386			0.719310
$23$			5.26761i			1.09837i	0.835700	+	0.549186i	$0.185062\pi$
$23$			5.26761i			1.09837i	−0.835700	+	0.549186i	$0.814938\pi$
$24$	−0.991345	+	5.22202i	−0.202358	+	1.06594i
$25$		0			0
$26$	−2.69300			−0.528142
$27$	4.39466	+	2.77253i	0.845753	+	0.533574i
$28$	0.791288	−	1.93825i	0.149539	−	0.366295i
$29$			5.26761i			0.978171i	0.872236	+	0.489085i	$0.162669\pi$
$29$			5.26761i			0.978171i	−0.872236	+	0.489085i	$0.837331\pi$
$30$		0			0
$31$		−	6.83723i		−	1.22800i	−0.789305	−	0.614001i	$-0.789559\pi$
$31$		−	6.83723i		−	1.22800i	0.789305	−	0.614001i	$-0.210441\pi$
$32$			4.16820i			0.736840i
$33$	0.991345	−	5.22202i	0.172571	−	0.909037i
$34$		−	2.96073i		−	0.507761i
$35$		0			0
$36$	2.20871	+	0.869953i	0.368119	+	0.144992i
$37$	−8.58258			−1.41097			−0.705483	−	0.708726i	$-0.749270\pi$
$37$	−8.58258			−1.41097			−0.705483	+	0.708726i	$0.749270\pi$
$38$	4.82395			0.782547
$39$	−0.791288	+	4.16820i	−0.126707	+	0.667446i
$40$		0			0
$41$	−10.2100			−1.59453			−0.797264	−	0.603631i	$-0.793720\pi$
$41$	−10.2100			−1.59453			−0.797264	+	0.603631i	$0.793720\pi$
$42$	4.22742	+	2.74078i	0.652305	+	0.422912i
$43$	6.58258			1.00383			0.501917	−	0.864916i	$-0.332628\pi$
$43$	6.58258			1.00383			0.501917	+	0.864916i	$0.332628\pi$
$44$		−	2.42829i		−	0.366079i
$45$		0			0
$46$	−5.79129			−0.853879
$47$	−2.69300			−0.392815			−0.196408	−	0.980522i	$-0.562928\pi$
$47$	−2.69300			−0.392815			−0.196408	+	0.980522i	$0.562928\pi$
$48$	−3.04816	−	0.578661i	−0.439964	−	0.0835225i
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$	−4.58258	−	0.869953i	−0.641689	−	0.121818i
$52$			1.93825i			0.268787i
$53$		−	3.93874i		−	0.541027i	−0.962716	−	0.270513i	$-0.912807\pi$
$53$		−	3.93874i		−	0.541027i	0.962716	−	0.270513i	$-0.0871935\pi$
$54$	−3.04816	+	4.83156i	−0.414802	+	0.657492i
$55$		0			0
$56$	7.51695	+	3.06878i	1.00449	+	0.410083i
$57$	1.41742	−	7.46644i	0.187742	−	0.988954i
$58$	−5.79129			−0.760433
$59$	7.51695			0.978624			0.489312	−	0.872109i	$-0.337248\pi$
$59$	7.51695			0.978624			0.489312	+	0.872109i	$0.337248\pi$
$60$		0			0
$61$			6.83723i			0.875418i	0.899117	+	0.437709i	$0.144210\pi$
$61$			6.83723i			0.875418i	−0.899117	+	0.437709i	$0.855790\pi$
$62$	7.51695			0.954654
$63$	5.48429	−	5.73782i	0.690956	−	0.722897i
$64$	−8.16515			−1.02064
$65$		0			0
$66$	5.74117	+	1.08990i	0.706689	+	0.134157i
$67$	−4.16515			−0.508854			−0.254427	−	0.967092i	$-0.581887\pi$
$67$	−4.16515			−0.508854			−0.254427	+	0.967092i	$0.581887\pi$
$68$	−2.13094			−0.258415
$69$	−1.70166	+	8.96368i	−0.204856	+	1.07910i
$70$		0			0
$71$		−	3.06878i		−	0.364197i	−0.983280	−	0.182099i	$-0.941711\pi$
$71$		−	3.06878i		−	0.364197i	0.983280	−	0.182099i	$-0.0582890\pi$
$72$	−3.37386	+	8.56585i	−0.397614	+	1.00950i
$73$			16.1240i			1.88717i	0.331136	+	0.943583i	$0.392568\pi$
$73$			16.1240i			1.88717i	−0.331136	+	0.943583i	$0.607432\pi$
$74$		−	9.43581i		−	1.09689i
$75$		0			0
$76$		−	3.47197i		−	0.398262i
$77$	−7.51695	−	3.06878i	−0.856636	−	0.349720i
$78$	−4.58258	−	0.869953i	−0.518875	−	0.0985028i
$79$	0.582576			0.0655449			0.0327724	−	0.999463i	$-0.489566\pi$
$79$	0.582576			0.0655449			0.0327724	+	0.999463i	$0.489566\pi$
$80$		0			0
$81$	6.58258	+	6.13756i	0.731397	+	0.681952i
$82$		−	11.2250i		−	1.23959i
$83$	−15.5960			−1.71188			−0.855940	−	0.517076i	$-0.827021\pi$
$83$	−15.5960			−1.71188			−0.855940	+	0.517076i	$0.827021\pi$
$84$	1.97264	−	3.04262i	0.215233	−	0.331978i
$85$		0			0
$86$			7.23698i			0.780384i
$87$	−1.70166	+	8.96368i	−0.182437	+	0.961007i
$88$	9.41742			1.00390
$89$	−7.51695			−0.796795			−0.398398	−	0.917213i	$-0.630434\pi$
$89$	−7.51695			−0.796795			−0.398398	+	0.917213i	$0.630434\pi$
$90$		0			0
$91$	6.00000	+	2.44949i	0.628971	+	0.256776i
$92$			4.16820i			0.434565i
$93$	2.20871	−	11.6346i	0.229033	−	1.20646i
$94$		−	2.96073i		−	0.305376i
$95$		0			0
$96$	−1.34650	+	7.09285i	−0.137427	+	0.723911i
$97$		−	11.7362i		−	1.19163i	−0.803121	−	0.595816i	$-0.796829\pi$
$97$		−	11.7362i		−	1.19163i	0.803121	−	0.595816i	$-0.203171\pi$
$98$	5.38601	−	5.49707i	0.544069	−	0.555288i
$99$	3.37386	−	8.56585i	0.339086	−	0.860901i
$100$		0			0
$101$	18.2890			1.81982			0.909910	−	0.414805i	$-0.136150\pi$
$101$	18.2890			1.81982			0.909910	+	0.414805i	$0.136150\pi$
$102$	0.956439	−	5.03815i	0.0947016	−	0.498851i
$103$		−	4.38774i		−	0.432337i	−0.976356	−	0.216168i	$-0.930644\pi$
$103$		−	4.38774i		−	0.432337i	0.976356	−	0.216168i	$-0.0693561\pi$
$104$	−7.51695			−0.737098
$105$		0			0
$106$	4.33030			0.420596
$107$		−	10.5352i		−	1.01848i	−0.860625	−	0.509239i	$-0.829927\pi$
$107$		−	10.5352i		−	1.01848i	0.860625	−	0.509239i	$-0.170073\pi$
$108$	3.47744	+	2.19387i	0.334617	+	0.211105i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	−14.6046	−	2.77253i	−1.38621	−	0.263157i
$112$	−1.79129	+	4.38774i	−0.169261	+	0.414603i
$113$		−	18.0017i		−	1.69345i	−0.532028	−	0.846727i	$-0.678570\pi$
$113$		−	18.0017i		−	1.69345i	0.532028	−	0.846727i	$-0.321430\pi$
$114$	8.20871	+	1.55834i	0.768816	+	0.145952i
$115$		0			0
$116$			4.16820i			0.387007i
$117$	−2.69300	+	6.83723i	−0.248968	+	0.632102i
$118$			8.26424i			0.760785i
$119$	−2.69300	+	6.59649i	−0.246867	+	0.604699i
$120$		0			0
$121$	1.58258			0.143871
$122$	−7.51695			−0.680553
$123$	−17.3739	−	3.29824i	−1.56655	−	0.297393i
$124$		−	5.41022i		−	0.485852i
$125$		0			0
$126$	6.30824	+	6.02951i	0.561983	+	0.537151i
$127$	8.16515			0.724540			0.362270	−	0.932073i	$-0.382002\pi$
$127$	8.16515			0.724540			0.362270	+	0.932073i	$0.382002\pi$
$128$		−	0.640492i		−	0.0566120i
$129$	11.2013	+	2.12645i	0.986219	+	0.187223i
$130$		0			0
$131$	−2.69300			−0.235289			−0.117644	−	0.993056i	$-0.537534\pi$
$131$	−2.69300			−0.235289			−0.117644	+	0.993056i	$0.537534\pi$
$132$	0.784439	−	4.13212i	0.0682767	−	0.359655i
$133$	−10.7477	−	4.38774i	−0.931946	−	0.380465i
$134$		−	4.57923i		−	0.395585i
$135$		0			0
$136$		−	8.26424i		−	0.708653i
$137$		−	10.5352i		−	0.900085i	−0.893007	−	0.450042i	$-0.851409\pi$
$137$		−	10.5352i		−	0.900085i	0.893007	−	0.450042i	$-0.148591\pi$
$138$	−9.85480	−	1.87083i	−0.838896	−	0.159256i
$139$			2.44949i			0.207763i	0.994590	+	0.103882i	$0.0331263\pi$
$139$			2.44949i			0.207763i	−0.994590	+	0.103882i	$0.966874\pi$
$140$		0			0
$141$	−4.58258	−	0.869953i	−0.385922	−	0.0732633i
$142$	3.37386			0.283128
$143$	7.51695			0.628599
$144$	−5.00000	−	1.96937i	−0.416667	−	0.164114i
$145$		0			0
$146$	−17.7269			−1.46709
$147$	−6.92572	−	9.95160i	−0.571224	−	0.820794i
$148$	−6.79129			−0.558240
$149$		−	18.0017i		−	1.47475i	−0.675482	−	0.737377i	$-0.736064\pi$
$149$		−	18.0017i		−	1.47475i	0.675482	−	0.737377i	$-0.263936\pi$
$150$		0			0
$151$	−4.16515			−0.338955			−0.169478	−	0.985534i	$-0.554208\pi$
$151$	−4.16515			−0.338955			−0.169478	+	0.985534i	$0.554208\pi$
$152$	13.4650			1.09216
$153$	−7.51695	−	2.96073i	−0.607709	−	0.239361i
$154$	3.37386	−	8.26424i	0.271874	−	0.665952i
$155$		0			0
$156$	−0.626136	+	3.29824i	−0.0501310	+	0.264071i
$157$			1.93825i			0.154689i	0.997004	+	0.0773447i	$0.0246442\pi$
$157$			1.93825i			0.154689i	−0.997004	+	0.0773447i	$0.975356\pi$
$158$			0.640492i			0.0509548i
$159$	1.27238	−	6.70239i	0.100906	−	0.531534i
$160$		0			0
$161$	12.9030	+	5.26761i	1.01690	+	0.415146i
$162$	−6.74773	+	7.23698i	−0.530152	+	0.568591i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−8.07901			−0.630865
$165$		0			0
$166$		−	17.1464i		−	1.33082i
$167$	18.2890			1.41524			0.707621	−	0.706592i	$-0.249768\pi$
$167$	18.2890			1.41524			0.707621	+	0.706592i	$0.249768\pi$
$168$	11.7999	+	7.65031i	0.910385	+	0.590234i
$169$	7.00000			0.538462
$170$		0			0
$171$	4.82395	−	12.2474i	0.368896	−	0.936586i
$172$	5.20871			0.397161
$173$	−8.07901			−0.614236			−0.307118	−	0.951671i	$-0.599365\pi$
$173$	−8.07901			−0.614236			−0.307118	+	0.951671i	$0.599365\pi$
$174$	−9.85480	−	1.87083i	−0.747090	−	0.141827i
$175$		0			0
$176$			5.49707i			0.414357i
$177$	12.7913	+	2.42829i	0.961452	+	0.182521i
$178$		−	8.26424i		−	0.619431i
$179$			14.4740i			1.08183i	0.841076	+	0.540917i	$0.181923\pi$
$179$			14.4740i			1.08183i	−0.841076	+	0.540917i	$0.818077\pi$
$180$		0			0
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	−2.69300	+	6.59649i	−0.199619	+	0.488964i
$183$	−2.20871	+	11.6346i	−0.163273	+	0.860057i
$184$	−16.1652			−1.19171
$185$		0			0
$186$	12.7913	+	2.42829i	0.937903	+	0.178051i
$187$			8.26424i			0.604341i
$188$	−2.13094			−0.155415
$189$	11.1860	−	7.99215i	0.813658	−	0.581343i
$190$		0			0
$191$		−	17.1317i		−	1.23961i	−0.784757	−	0.619803i	$-0.787212\pi$
$191$		−	17.1317i		−	1.23961i	0.784757	−	0.619803i	$-0.212788\pi$
$192$	−13.8943	−	2.63769i	−1.00274	−	0.190359i
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	12.9030			0.926379
$195$		0			0
$196$	−3.95644	−	3.87650i	−0.282603	−	0.276893i
$197$			3.52770i			0.251339i	0.992072	+	0.125669i	$0.0401078\pi$
$197$			3.52770i			0.251339i	−0.992072	+	0.125669i	$0.959892\pi$
$198$	9.41742	+	3.70927i	0.669267	+	0.263607i
$199$			7.85971i			0.557160i	0.960413	+	0.278580i	$0.0898637\pi$
$199$			7.85971i			0.557160i	−0.960413	+	0.278580i	$0.910136\pi$
$200$		0			0
$201$	−7.08767	−	1.34552i	−0.499926	−	0.0949056i
$202$			20.1072i			1.41473i
$203$	12.9030	+	5.26761i	0.905610	+	0.369714i
$204$	−3.62614	−	0.688383i	−0.253880	−	0.0481965i
$205$		0			0
$206$	4.82395			0.336100
$207$	−5.79129	+	14.7034i	−0.402522	+	1.02196i
$208$		−	4.38774i		−	0.304235i
$209$	−13.4650			−0.931395
$210$		0			0
$211$	−14.7477			−1.01528			−0.507638	−	0.861571i	$-0.669481\pi$
$211$	−14.7477			−1.01528			−0.507638	+	0.861571i	$0.669481\pi$
$212$		−	3.11667i		−	0.214054i
$213$	0.991345	−	5.22202i	0.0679259	−	0.357807i
$214$	11.5826			0.791769
$215$		0			0
$216$	−8.50830	+	13.4863i	−0.578916	+	0.917624i
$217$	−16.7477	−	6.83723i	−1.13691	−	0.464141i
$218$			5.49707i			0.372309i
$219$	−5.20871	+	27.4375i	−0.351972	+	1.85405i
$220$		0			0
$221$		−	6.59649i		−	0.443728i
$222$	3.04816	−	16.0565i	0.204579	−	1.07764i
$223$			2.44949i			0.164030i	0.996631	+	0.0820150i	$0.0261355\pi$
$223$			2.44949i			0.164030i	−0.996631	+	0.0820150i	$0.973864\pi$
$224$	10.2100	+	4.16820i	0.682181	+	0.278499i
$225$		0			0
$226$	19.7913			1.31650
$227$	−2.69300			−0.178741			−0.0893705	−	0.995998i	$-0.528486\pi$
$227$	−2.69300			−0.178741			−0.0893705	+	0.995998i	$0.528486\pi$
$228$	1.12159	−	5.90810i	0.0742792	−	0.391274i
$229$			3.87650i			0.256167i	0.991763	+	0.128083i	$0.0408825\pi$
$229$			3.87650i			0.256167i	−0.991763	+	0.128083i	$0.959118\pi$
$230$		0			0
$231$	−11.7999	−	7.65031i	−0.776379	−	0.503354i
$232$	−16.1652			−1.06129
$233$			5.26761i			0.345093i	0.985001	+	0.172546i	$0.0551995\pi$
$233$			5.26761i			0.345093i	−0.985001	+	0.172546i	$0.944801\pi$
$234$	−7.51695	−	2.96073i	−0.491398	−	0.193549i
$235$		0			0
$236$	5.94807			0.387186
$237$	0.991345	+	0.188196i	0.0643948	+	0.0122247i
$238$	−7.25227	−	2.96073i	−0.470095	−	0.191915i
$239$			14.4740i			0.936242i	0.883664	+	0.468121i	$0.155069\pi$
$239$			14.4740i			0.936242i	−0.883664	+	0.468121i	$0.844931\pi$
$240$		0			0
$241$			19.0847i			1.22935i	0.788780	+	0.614676i	$0.210713\pi$
$241$			19.0847i			1.22935i	−0.788780	+	0.614676i	$0.789287\pi$
$242$			1.73991i			0.111845i
$243$	9.21861	+	12.5705i	0.591374	+	0.806397i
$244$			5.41022i			0.346354i
$245$		0			0
$246$	3.62614	−	19.1011i	0.231194	−	1.21784i
$247$	10.7477			0.683861
$248$	20.9820			1.33236
$249$	−26.5390	−	5.03815i	−1.68184	−	0.319280i
$250$		0			0
$251$	−17.7269			−1.11891			−0.559456	−	0.828860i	$-0.688990\pi$
$251$	−17.7269			−1.11891			−0.559456	+	0.828860i	$0.688990\pi$
$252$	4.33965	−	4.54026i	0.273372	−	0.286010i
$253$	16.1652			1.01629
$254$			8.97689i			0.563260i
$255$		0			0
$256$	−15.6261			−0.976634
$257$	4.82395			0.300909			0.150455	−	0.988617i	$-0.451926\pi$
$257$	4.82395			0.300909			0.150455	+	0.988617i	$0.451926\pi$
$258$	−2.33785	+	12.3149i	−0.145548	+	0.766690i
$259$	−8.58258	+	21.0229i	−0.533295	+	1.30630i
$260$		0			0
$261$	−5.79129	+	14.7034i	−0.358472	+	0.910119i
$262$		−	2.96073i		−	0.182914i
$263$			28.5369i			1.75966i	0.475289	+	0.879830i	$0.342344\pi$
$263$			28.5369i			1.75966i	−0.475289	+	0.879830i	$0.657656\pi$
$264$	16.0252	+	3.04222i	0.986286	+	0.187236i
$265$		0			0
$266$	4.82395	−	11.8162i	0.295775	−	0.724498i
$267$	−12.7913	−	2.42829i	−0.782814	−	0.148609i
$268$	−3.29583			−0.201325
$269$	20.9820			1.27929			0.639647	−	0.768669i	$-0.279081\pi$
$269$	20.9820			1.27929			0.639647	+	0.768669i	$0.279081\pi$
$270$		0			0
$271$			25.9219i			1.57464i	0.616542	+	0.787322i	$0.288533\pi$
$271$			25.9219i			1.57464i	−0.616542	+	0.787322i	$0.711467\pi$
$272$	4.82395			0.292495
$273$	9.41867	+	6.10645i	0.570044	+	0.369579i
$274$	11.5826			0.699729
$275$		0			0
$276$	−1.34650	+	7.09285i	−0.0810499	+	0.426939i
$277$	18.7477			1.12644			0.563221	−	0.826306i	$-0.309562\pi$
$277$	18.7477			1.12644			0.563221	+	0.826306i	$0.309562\pi$
$278$	−2.69300			−0.161516
$279$	7.51695	−	19.0847i	0.450028	−	1.14257i
$280$		0			0
$281$			15.3439i			0.915341i	0.889122	+	0.457670i	$0.151316\pi$
$281$			15.3439i			0.915341i	−0.889122	+	0.457670i	$0.848684\pi$
$282$	0.956439	−	5.03815i	0.0569551	−	0.300017i
$283$		−	23.4724i		−	1.39529i	−0.716443	−	0.697645i	$-0.754231\pi$
$283$		−	23.4724i		−	1.39529i	0.716443	−	0.697645i	$-0.245769\pi$
$284$		−	2.42829i		−	0.144093i
$285$		0			0
$286$			8.26424i			0.488675i
$287$	−10.2100	+	25.0092i	−0.602675	+	1.47625i
$288$	−4.58258	+	11.6346i	−0.270031	+	0.685578i
$289$	−9.74773			−0.573396
$290$		0			0
$291$	3.79129	−	19.9710i	0.222249	−	1.17072i
$292$			12.7587i			0.746646i
$293$	−2.13094			−0.124491			−0.0622455	−	0.998061i	$-0.519826\pi$
$293$	−2.13094			−0.124491			−0.0622455	+	0.998061i	$0.519826\pi$
$294$	10.9409	−	7.61424i	0.638088	−	0.444071i
$295$		0			0
$296$		−	26.3381i		−	1.53087i
$297$	8.50830	−	13.4863i	0.493701	−	0.782552i
$298$	19.7913			1.14648
$299$	−12.9030			−0.746197
$300$		0			0
$301$	6.58258	−	16.1240i	0.379413	−	0.929369i
$302$		−	4.57923i		−	0.263505i
$303$	31.1216	+	5.90810i	1.78789	+	0.339412i
$304$			7.85971i			0.450785i
$305$		0			0
$306$	3.25507	−	8.26424i	0.186080	−	0.472435i
$307$		−	13.1632i		−	0.751265i	−0.926769	−	0.375632i	$-0.877426\pi$
$307$		−	13.1632i		−	0.751265i	0.926769	−	0.375632i	$-0.122574\pi$
$308$	−5.94807	−	2.42829i	−0.338923	−	0.138365i
$309$	1.41742	−	7.46644i	0.0806345	−	0.424751i
$310$		0			0
$311$	12.3409			0.699788			0.349894	−	0.936789i	$-0.386218\pi$
$311$	12.3409			0.699788			0.349894	+	0.936789i	$0.386218\pi$
$312$	−12.7913	−	2.42829i	−0.724164	−	0.137475i
$313$			22.9612i			1.29784i	0.760855	+	0.648921i	$0.224780\pi$
$313$			22.9612i			1.29784i	−0.760855	+	0.648921i	$0.775220\pi$
$314$	−2.13094			−0.120256
$315$		0			0
$316$	0.460985			0.0259324
$317$		−	1.32888i		−	0.0746371i	−0.999303	−	0.0373185i	$-0.988118\pi$
$317$		−	1.32888i		−	0.0746371i	0.999303	−	0.0373185i	$-0.0118816\pi$
$318$	7.36870	+	1.39887i	0.413216	+	0.0784447i
$319$	16.1652			0.905075
$320$		0			0
$321$	3.40332	−	17.9274i	0.189955	−	1.00061i
$322$	−5.79129	+	14.1857i	−0.322736	+	0.790538i
$323$			11.8162i			0.657471i
$324$	5.20871	+	4.85658i	0.289373	+	0.269810i
$325$		0			0
$326$		−	4.39766i		−	0.243564i
$327$	8.50830	+	1.61521i	0.470510	+	0.0893213i
$328$		−	31.3321i		−	1.73003i
$329$	−2.69300	+	6.59649i	−0.148470	+	0.363676i
$330$		0			0
$331$	17.0000			0.934405			0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000			0.934405			0.467202	+	0.884150i	$0.345262\pi$
$332$	−12.3409			−0.677295
$333$	−23.9564	−	9.43581i	−1.31280	−	0.517079i
$334$			20.1072i			1.10021i
$335$		0			0
$336$	−4.46559	+	6.88778i	−0.243618	+	0.375759i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$			7.69590i			0.418602i
$339$	5.81529	−	30.6327i	0.315843	−	1.66374i
$340$		0			0
$341$	−20.9820			−1.13624
$342$	13.4650	+	5.30352i	0.728105	+	0.286781i
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$			20.2005i			1.08914i
$345$		0			0
$346$		−	8.88218i		−	0.477509i
$347$			3.52770i			0.189377i	0.995507	+	0.0946886i	$0.0301855\pi$
$347$			3.52770i			0.189377i	−0.995507	+	0.0946886i	$0.969814\pi$
$348$	−1.34650	+	7.09285i	−0.0721801	+	0.380217i
$349$			9.28672i			0.497107i	0.968618	+	0.248553i	$0.0799551\pi$
$349$			9.28672i			0.497107i	−0.968618	+	0.248553i	$0.920045\pi$
$350$		0			0
$351$	−6.79129	+	10.7647i	−0.362492	+	0.574576i
$352$	12.7913			0.681778
$353$	−30.6299			−1.63026			−0.815132	−	0.579276i	$-0.803335\pi$
$353$	−30.6299			−1.63026			−0.815132	+	0.579276i	$0.803335\pi$
$354$	−2.66970	+	14.0629i	−0.141893	+	0.747436i
$355$		0			0
$356$	−5.94807			−0.315247
$357$	−6.71352	+	10.3550i	−0.355317	+	0.548046i
$358$	−15.9129			−0.841022
$359$		−	18.0017i		−	0.950091i	−0.879961	−	0.475046i	$-0.842432\pi$
$359$		−	18.0017i		−	0.950091i	0.879961	−	0.475046i	$-0.157568\pi$
$360$		0			0
$361$	−0.252273			−0.0132775
$362$	−13.4650			−0.707706
$363$	2.69300	+	0.511238i	0.141346	+	0.0268331i
$364$	4.74773	+	1.93825i	0.248849	+	0.101592i
$365$		0			0
$366$	−12.7913	−	2.42829i	−0.668611	−	0.126929i
$367$		−	0.915775i		−	0.0478031i	−0.999714	−	0.0239015i	$-0.992391\pi$
$367$		−	0.915775i		−	0.0478031i	0.999714	−	0.0239015i	$-0.00760882\pi$
$368$		−	9.43581i		−	0.491875i
$369$	−28.4989	−	11.2250i	−1.48359	−	0.584349i
$370$		0			0
$371$	−9.64789	−	3.93874i	−0.500894	−	0.204489i
$372$	1.74773	−	9.20635i	0.0906154	−	0.477327i
$373$	−26.9129			−1.39350			−0.696748	−	0.717316i	$-0.745370\pi$
$373$	−26.9129			−1.39350			−0.696748	+	0.717316i	$0.745370\pi$
$374$	−9.08583			−0.469817
$375$		0			0
$376$		−	8.26424i		−	0.426196i
$377$	−12.9030			−0.664536
$378$	8.78669	+	12.2980i	0.451938	+	0.632541i
$379$	17.3303			0.890198			0.445099	−	0.895481i	$-0.353169\pi$
$379$	17.3303			0.890198			0.445099	+	0.895481i	$0.353169\pi$
$380$		0			0
$381$	13.8943	+	2.63769i	0.711827	+	0.135133i
$382$	18.8348			0.963675
$383$	27.9369			1.42751			0.713753	−	0.700397i	$-0.246994\pi$
$383$	27.9369			1.42751			0.713753	+	0.700397i	$0.246994\pi$
$384$	0.206906	−	1.08990i	0.0105586	−	0.0556187i
$385$		0			0
$386$			12.0936i			0.615546i
$387$	18.3739	+	7.23698i	0.933996	+	0.367876i
$388$		−	9.28672i		−	0.471462i
$389$		−	13.1451i		−	0.666482i	−0.942842	−	0.333241i	$-0.891858\pi$
$389$		−	13.1451i		−	0.666482i	0.942842	−	0.333241i	$-0.108142\pi$
$390$		0			0
$391$		−	14.1857i		−	0.717402i
$392$	15.0339	−	15.3439i	0.759327	−	0.774985i
$393$	−4.58258	−	0.869953i	−0.231160	−	0.0438833i
$394$	−3.87841			−0.195391
$395$		0			0
$396$	2.66970	−	6.77806i	0.134157	−	0.340610i
$397$			8.77548i			0.440429i	0.975451	+	0.220214i	$0.0706757\pi$
$397$			8.77548i			0.440429i	−0.975451	+	0.220214i	$0.929324\pi$
$398$	−8.64108			−0.433138
$399$	−16.8715	−	10.9384i	−0.844634	−	0.547605i
$400$		0			0
$401$			20.2005i			1.00876i	0.863481	+	0.504382i	$0.168280\pi$
$401$			20.2005i			1.00876i	−0.863481	+	0.504382i	$0.831720\pi$
$402$	1.47928	−	7.79228i	0.0737799	−	0.388644i
$403$	16.7477			0.834264
$404$	14.4718			0.720001
$405$		0			0
$406$	−5.79129	+	14.1857i	−0.287417	+	0.704024i
$407$			26.3381i			1.30553i
$408$	2.66970	−	14.0629i	0.132170	−	0.696219i
$409$		−	31.7367i		−	1.56928i	−0.619954	−	0.784639i	$-0.712849\pi$
$409$		−	31.7367i		−	1.56928i	0.619954	−	0.784639i	$-0.287151\pi$
$410$		0			0
$411$	3.40332	−	17.9274i	0.167873	−	0.884291i
$412$		−	3.47197i		−	0.171052i
$413$	7.51695	−	18.4127i	0.369885	−	0.906029i
$414$	−16.1652	−	6.36703i	−0.794474	−	0.312922i
$415$		0			0
$416$	−10.2100			−0.500584
$417$	−0.791288	+	4.16820i	−0.0387495	+	0.204117i
$418$		−	14.8036i		−	0.724070i
$419$	20.9820			1.02504			0.512518	−	0.858676i	$-0.328713\pi$
$419$	20.9820			1.02504			0.512518	+	0.858676i	$0.328713\pi$
$420$		0			0
$421$	8.16515			0.397945			0.198973	−	0.980005i	$-0.436240\pi$
$421$	8.16515			0.397945			0.198973	+	0.980005i	$0.436240\pi$
$422$		−	16.2139i		−	0.789279i
$423$	−7.51695	−	2.96073i	−0.365487	−	0.143956i
$424$	12.0871			0.587003
$425$		0			0
$426$	5.74117	+	1.08990i	0.278160	+	0.0528058i
$427$	16.7477	+	6.83723i	0.810479	+	0.330877i
$428$		−	8.33639i		−	0.402955i
$429$	12.7913	+	2.42829i	0.617569	+	0.117239i
$430$		0			0
$431$			34.2634i			1.65041i	0.564833	+	0.825205i	$0.308941\pi$
$431$			34.2634i			1.65041i	−0.564833	+	0.825205i	$0.691059\pi$
$432$	−7.87211	−	4.96640i	−0.378747	−	0.238946i
$433$			1.02248i			0.0491371i	0.999698	+	0.0245685i	$0.00782120\pi$
$433$			1.02248i			0.0491371i	−0.999698	+	0.0245685i	$0.992179\pi$
$434$	7.51695	−	18.4127i	0.360825	−	0.883838i
$435$		0			0
$436$	3.95644			0.189479
$437$	23.1129			1.10564
$438$	−30.1652	−	5.72653i	−1.44135	−	0.273624i
$439$			26.9444i			1.28599i	0.765872	+	0.642993i	$0.222307\pi$
$439$			26.9444i			1.28599i	−0.765872	+	0.642993i	$0.777693\pi$
$440$		0			0
$441$	−8.57043	−	19.1715i	−0.408116	−	0.912930i
$442$	7.25227			0.344955
$443$		−	3.93874i		−	0.187135i	−0.995613	−	0.0935675i	$-0.970173\pi$
$443$		−	3.93874i		−	0.187135i	0.995613	−	0.0935675i	$-0.0298271\pi$
$444$	−11.5565	−	2.19387i	−0.548445	−	0.104116i
$445$		0			0
$446$	−2.69300			−0.127517
$447$	5.81529	−	30.6327i	0.275054	−	1.44888i
$448$	−8.16515	+	20.0005i	−0.385767	+	0.944933i
$449$		−	36.4144i		−	1.71850i	−0.511556	−	0.859250i	$-0.670931\pi$
$449$		−	36.4144i		−	1.71850i	0.511556	−	0.859250i	$-0.329069\pi$
$450$		0			0
$451$			31.3321i			1.47537i
$452$		−	14.2445i		−	0.670005i
$453$	−7.08767	−	1.34552i	−0.333008	−	0.0632180i
$454$		−	2.96073i		−	0.138954i
$455$		0			0
$456$	22.9129	+	4.34977i	1.07299	+	0.203696i
$457$	−34.1652			−1.59818			−0.799089	−	0.601213i	$-0.794685\pi$
$457$	−34.1652			−1.59818			−0.799089	+	0.601213i	$0.794685\pi$
$458$	−4.26188			−0.199145
$459$	−11.8348	−	7.46644i	−0.552403	−	0.348504i
$460$		0			0
$461$	33.3229			1.55200			0.776000	−	0.630732i	$-0.217245\pi$
$461$	33.3229			1.55200			0.776000	+	0.630732i	$0.217245\pi$
$462$	8.41086	−	12.9730i	0.391309	−	0.603560i
$463$	12.7477			0.592437			0.296219	−	0.955120i	$-0.404274\pi$
$463$	12.7477			0.592437			0.296219	+	0.955120i	$0.404274\pi$
$464$		−	9.43581i		−	0.438046i
$465$		0			0
$466$	−5.79129			−0.268276
$467$	−16.1580			−0.747704			−0.373852	−	0.927488i	$-0.621963\pi$
$467$	−16.1580			−0.747704			−0.373852	+	0.927488i	$0.621963\pi$
$468$	−2.13094	+	5.41022i	−0.0985028	+	0.250087i
$469$	−4.16515	+	10.2025i	−0.192329	+	0.471107i
$470$		0			0
$471$	−0.626136	+	3.29824i	−0.0288508	+	0.151975i
$472$			23.0679i			1.06179i
$473$		−	20.2005i		−	0.928820i
$474$	−0.206906	+	1.08990i	−0.00950350	+	0.0500607i
$475$		0			0
$476$	−2.13094	+	5.21972i	−0.0976716	+	0.239245i
$477$	4.33030	−	10.9941i	0.198271	−	0.503387i
$478$	−15.9129			−0.727838
$479$	7.51695			0.343458			0.171729	−	0.985144i	$-0.445065\pi$
$479$	7.51695			0.343458			0.171729	+	0.985144i	$0.445065\pi$
$480$		0			0
$481$		−	21.0229i		−	0.958563i
$482$	−20.9820			−0.955703
$483$	20.2548	+	13.1319i	0.921624	+	0.597521i
$484$	1.25227			0.0569215
$485$		0			0
$486$	−13.8202	+	10.1351i	−0.626896	+	0.459736i
$487$	−21.8348			−0.989431			−0.494716	−	0.869055i	$-0.664728\pi$
$487$	−21.8348			−0.989431			−0.494716	+	0.869055i	$0.664728\pi$
$488$	−20.9820			−0.949809
$489$	−6.80664	−	1.29217i	−0.307807	−	0.0584338i
$490$		0			0
$491$		−	26.3381i		−	1.18862i	−0.804236	−	0.594310i	$-0.797425\pi$
$491$		−	26.3381i		−	1.18862i	0.804236	−	0.594310i	$-0.202575\pi$
$492$	−13.7477	−	2.60986i	−0.619795	−	0.117662i
$493$		−	14.1857i		−	0.638892i
$494$			11.8162i			0.531636i
$495$		0			0
$496$			12.2474i			0.549927i
$497$	−7.51695	−	3.06878i	−0.337181	−	0.137654i
$498$	5.53901	−	29.1774i	0.248209	−	1.30747i
$499$	3.25227			0.145592			0.0727959	−	0.997347i	$-0.476808\pi$
$499$	3.25227			0.145592			0.0727959	+	0.997347i	$0.476808\pi$
$500$		0			0
$501$	31.1216	+	5.90810i	1.39041	+	0.263955i
$502$		−	19.4892i		−	0.869846i
$503$	5.38601			0.240150			0.120075	−	0.992765i	$-0.461686\pi$
$503$	5.38601			0.240150			0.120075	+	0.992765i	$0.461686\pi$
$504$	17.6081	+	16.8301i	0.784328	+	0.749672i
$505$		0			0
$506$			17.7722i			0.790071i
$507$	11.9116	+	2.26129i	0.529013	+	0.100428i
$508$	6.46099			0.286660
$509$	−22.5509			−0.999549			−0.499774	−	0.866156i	$-0.666584\pi$
$509$	−22.5509			−0.999549			−0.499774	+	0.866156i	$0.666584\pi$
$510$		0			0
$511$	39.4955	+	16.1240i	1.74718	+	0.713282i
$512$		−	18.4606i		−	0.815850i
$513$	12.1652	−	19.2826i	0.537105	−	0.851350i
$514$			5.30352i			0.233928i
$515$		0			0
$516$	8.86345	+	1.68263i	0.390192	+	0.0740738i
$517$			8.26424i			0.363461i
$518$	−23.1129	−	9.43581i	−1.01552	−	0.414586i
$519$	−13.7477	−	2.60986i	−0.603458	−	0.114560i
$520$		0			0
$521$	−16.1580			−0.707896			−0.353948	−	0.935265i	$-0.615161\pi$
$521$	−16.1580			−0.707896			−0.353948	+	0.935265i	$0.615161\pi$
$522$	−16.1652	−	6.36703i	−0.707529	−	0.278677i
$523$			14.6969i			0.642652i	0.946969	+	0.321326i	$0.104129\pi$
$523$			14.6969i			0.642652i	−0.946969	+	0.321326i	$0.895871\pi$
$524$	−2.13094			−0.0930906
$525$		0			0
$526$	−31.3739			−1.36797
$527$			18.4127i			0.802070i
$528$	−1.77578	+	9.35414i	−0.0772811	+	0.407087i
$529$	−4.74773			−0.206423
$530$		0			0
$531$	20.9820	+	8.26424i	0.910540	+	0.358638i
$532$	−8.50455	−	3.47197i	−0.368719	−	0.150529i
$533$		−	25.0092i		−	1.08327i
$534$	2.66970	−	14.0629i	0.115529	−	0.608562i
$535$		0			0
$536$		−	12.7819i		−	0.552096i
$537$	−4.67569	+	24.6297i	−0.201771	+	1.06285i
$538$			23.0679i			0.994527i
$539$	−15.0339	+	15.3439i	−0.647556	+	0.660909i
$540$		0			0
$541$	−8.58258			−0.368994			−0.184497	−	0.982833i	$-0.559066\pi$
$541$	−8.58258			−0.368994			−0.184497	+	0.982833i	$0.559066\pi$
$542$	−28.4989			−1.22413
$543$	−3.95644	+	20.8410i	−0.169787	+	0.894372i
$544$		−	11.2250i		−	0.481267i
$545$		0			0
$546$	−6.71352	+	10.3550i	−0.287312	+	0.443154i
$547$	4.66970			0.199662			0.0998309	−	0.995004i	$-0.468170\pi$
$547$	4.66970			0.199662			0.0998309	+	0.995004i	$0.468170\pi$
$548$		−	8.33639i		−	0.356113i
$549$	−7.51695	+	19.0847i	−0.320816	+	0.814514i
$550$		0			0
$551$	23.1129			0.984643
$552$	−27.5076	−	5.22202i	−1.17080	−	0.222264i
$553$	0.582576	−	1.42701i	0.0247736	−	0.0606828i
$554$			20.6115i			0.875700i
$555$		0			0
$556$			1.93825i			0.0822002i
$557$		−	6.18546i		−	0.262086i	−0.991377	−	0.131043i	$-0.958167\pi$
$557$		−	6.18546i		−	0.262086i	0.991377	−	0.131043i	$-0.0418326\pi$
$558$	20.9820	+	8.26424i	0.888238	+	0.349853i
$559$			16.1240i			0.681970i
$560$		0			0
$561$	−2.66970	+	14.0629i	−0.112715	+	0.593737i
$562$	−16.8693			−0.711589
$563$	−9.64789			−0.406610			−0.203305	−	0.979115i	$-0.565168\pi$
$563$	−9.64789			−0.406610			−0.203305	+	0.979115i	$0.565168\pi$
$564$	−3.62614	−	0.688383i	−0.152688	−	0.0289862i
$565$		0			0
$566$	25.8059			1.08470
$567$	21.6165	−	9.98639i	0.907807	−	0.419389i
$568$	9.41742			0.395146
$569$			0.411031i			0.0172313i	0.999963	+	0.00861566i	$0.00274248\pi$
$569$			0.411031i			0.0172313i	−0.999963	+	0.00861566i	$0.997258\pi$
$570$		0			0
$571$	−29.7477			−1.24490			−0.622452	−	0.782658i	$-0.713863\pi$
$571$	−29.7477			−1.24490			−0.622452	+	0.782658i	$0.713863\pi$
$572$	5.94807			0.248701
$573$	5.53426	−	29.1523i	0.231197	−	1.21786i
$574$	−27.4955	−	11.2250i	−1.14764	−	0.468521i
$575$		0			0
$576$	−22.7913	−	8.97689i	−0.949637	−	0.374037i
$577$		−	23.9837i		−	0.998453i	−0.866472	−	0.499226i	$-0.833618\pi$
$577$		−	23.9837i		−	0.998453i	0.866472	−	0.499226i	$-0.166382\pi$
$578$		−	10.7168i		−	0.445760i
$579$	18.7183	+	3.55346i	0.777904	+	0.147677i
$580$		0			0
$581$	−15.5960	+	38.2022i	−0.647030	+	1.58489i
$582$	21.9564	+	4.16820i	0.910124	+	0.172777i
$583$	−12.0871			−0.500597
$584$	−49.4809			−2.04753
$585$		0			0
$586$		−	2.34279i		−	0.0967797i
$587$	3.25507			0.134351			0.0671755	−	0.997741i	$-0.478601\pi$
$587$	3.25507			0.134351			0.0671755	+	0.997741i	$0.478601\pi$
$588$	−5.48024	−	7.87458i	−0.226001	−	0.324742i
$589$	−30.0000			−1.23613
$590$		0			0
$591$	−1.13960	+	6.00295i	−0.0468767	+	0.246928i
$592$	15.3739			0.631862
$593$	5.38601			0.221177			0.110588	−	0.993866i	$-0.464726\pi$
$593$	5.38601			0.221177			0.110588	+	0.993866i	$0.464726\pi$
$594$	14.8270	+	9.35414i	0.608359	+	0.383805i
$595$		0			0
$596$		−	14.2445i		−	0.583477i
$597$	−2.53901	+	13.3745i	−0.103915	+	0.547384i
$598$		−	14.1857i		−	0.580096i
$599$		−	36.4144i		−	1.48785i	−0.668263	−	0.743925i	$-0.732962\pi$
$599$		−	36.4144i		−	1.48785i	0.668263	−	0.743925i	$-0.267038\pi$
$600$		0			0
$601$		−	2.85403i		−	0.116418i	−0.998304	−	0.0582091i	$-0.981461\pi$
$601$		−	2.85403i		−	0.116418i	0.998304	−	0.0582091i	$-0.0185390\pi$
$602$	17.7269	+	7.23698i	0.722495	+	0.294957i
$603$	−11.6261	−	4.57923i	−0.473453	−	0.186481i
$604$	−3.29583			−0.134106
$605$		0			0
$606$	−6.49545	+	34.2155i	−0.263860	+	1.38991i
$607$			21.0229i			0.853294i	0.904418	+	0.426647i	$0.140305\pi$
$607$			21.0229i			0.853294i	−0.904418	+	0.426647i	$0.859695\pi$
$608$	18.2890			0.741716
$609$	20.2548	+	13.1319i	0.820765	+	0.532130i
$610$		0			0
$611$		−	6.59649i		−	0.266865i
$612$	−5.94807	−	2.34279i	−0.240437	−	0.0947016i
$613$	36.5826			1.47756			0.738778	−	0.673949i	$-0.235403\pi$
$613$	36.5826			1.47756			0.738778	+	0.673949i	$0.235403\pi$
$614$	14.4718			0.584036
$615$		0			0
$616$	9.41742	−	23.0679i	0.379439	−	0.929432i
$617$		−	1.32888i		−	0.0534985i	−0.999642	−	0.0267493i	$-0.991484\pi$
$617$		−	1.32888i		−	0.0534985i	0.999642	−	0.0267493i	$-0.00851557\pi$
$618$	8.20871	+	1.55834i	0.330203	+	0.0626855i
$619$			13.2699i			0.533363i	0.963785	+	0.266682i	$0.0859272\pi$
$619$			13.2699i			0.533363i	−0.963785	+	0.266682i	$0.914073\pi$
$620$		0			0
$621$	−14.6046	+	23.1494i	−0.586063	+	0.928953i
$622$			13.5678i			0.544018i
$623$	−7.51695	+	18.4127i	−0.301160	+	0.737689i
$624$	1.41742	−	7.46644i	0.0567424	−	0.298897i
$625$		0			0
$626$	−25.2439			−1.00895
$627$	−22.9129	−	4.34977i	−0.915052	−	0.173713i
$628$			1.53371i			0.0612019i
$629$	23.1129			0.921572
$630$		0			0
$631$	33.7477			1.34348			0.671738	−	0.740789i	$-0.265548\pi$
$631$	33.7477			1.34348			0.671738	+	0.740789i	$0.265548\pi$
$632$			1.78780i			0.0711148i
$633$	−25.0956	−	4.76413i	−0.997461	−	0.189357i
$634$	1.46099			0.0580231
$635$		0			0
$636$	1.00682	−	5.30352i	0.0399229	−	0.210298i
$637$	12.0000	−	12.2474i	0.475457	−	0.485262i
$638$			17.7722i			0.703608i
$639$	3.37386	−	8.56585i	0.133468	−	0.338860i
$640$		0			0
$641$			1.78780i			0.0706138i	0.999377	+	0.0353069i	$0.0112409\pi$
$641$			1.78780i			0.0706138i	−0.999377	+	0.0353069i	$0.988759\pi$
$642$	19.7096	+	3.74166i	0.777876	+	0.147671i
$643$		−	20.6184i		−	0.813110i	−0.913626	−	0.406555i	$-0.866730\pi$
$643$		−	20.6184i		−	0.813110i	0.913626	−	0.406555i	$-0.133270\pi$
$644$	10.2100	+	4.16820i	0.402329	+	0.164250i
$645$		0			0
$646$	−12.9909			−0.511120
$647$	40.8398			1.60558			0.802790	−	0.596263i	$-0.203348\pi$
$647$	40.8398			1.60558			0.802790	+	0.596263i	$0.203348\pi$
$648$	−18.8348	+	20.2005i	−0.739903	+	0.793550i
$649$		−	23.0679i		−	0.905494i
$650$		0			0
$651$	−26.2902	−	17.0449i	−1.03039	−	0.668041i
$652$	−3.16515			−0.123957
$653$			14.4740i			0.566410i	0.959059	+	0.283205i	$0.0913976\pi$
$653$			14.4740i			0.566410i	−0.959059	+	0.283205i	$0.908602\pi$
$654$	−1.77578	+	9.35414i	−0.0694387	+	0.365776i
$655$		0			0
$656$	18.2890			0.714064
$657$	−17.7269	+	45.0066i	−0.691592	+	1.75587i
$658$	−7.25227	−	2.96073i	−0.282723	−	0.115421i
$659$			14.4740i			0.563825i	0.959440	+	0.281913i	$0.0909688\pi$
$659$			14.4740i			0.563825i	−0.959440	+	0.281913i	$0.909031\pi$
$660$		0			0
$661$		−	43.5796i		−	1.69505i	−0.530756	−	0.847525i	$-0.678092\pi$
$661$		−	43.5796i		−	1.69505i	0.530756	−	0.847525i	$-0.321908\pi$
$662$			18.6900i			0.726409i
$663$	2.13094	−	11.2250i	0.0827589	−	0.435942i
$664$		−	47.8606i		−	1.85735i
$665$		0			0
$666$	10.3739	−	26.3381i	0.401979	−	1.02058i
$667$	−27.7477			−1.07440
$668$	14.4718			0.559932
$669$	−0.791288	+	4.16820i	−0.0305930	+	0.161152i
$670$		0			0
$671$	20.9820			0.810000
$672$	16.0274	+	10.3911i	0.618269	+	0.400845i
$673$	−7.49545			−0.288929			−0.144464	−	0.989510i	$-0.546146\pi$
$673$	−7.49545			−0.288929			−0.144464	+	0.989510i	$0.546146\pi$
$674$			2.19883i			0.0846957i
$675$		0			0
$676$	5.53901			0.213039
$677$	10.7720			0.414002			0.207001	−	0.978341i	$-0.433630\pi$
$677$	10.7720			0.414002			0.207001	+	0.978341i	$0.433630\pi$
$678$	33.6780	+	6.39342i	1.29340	+	0.245538i
$679$	−28.7477	−	11.7362i	−1.10324	−	0.450394i
$680$		0			0
$681$	−4.58258	−	0.869953i	−0.175605	−	0.0333367i
$682$		−	23.0679i		−	0.883315i
$683$			10.1242i			0.387391i	0.981062	+	0.193696i	$0.0620474\pi$
$683$			10.1242i			0.387391i	−0.981062	+	0.193696i	$0.937953\pi$
$684$	3.81713	−	9.69126i	0.145952	−	0.370554i
$685$		0			0
$686$	−8.07901	−	18.6900i	−0.308458	−	0.713589i
$687$	−1.25227	+	6.59649i	−0.0477772	+	0.251672i
$688$	−11.7913			−0.449539
$689$	9.64789			0.367555
$690$		0			0
$691$			6.83723i			0.260101i	0.991507	+	0.130050i	$0.0415139\pi$
$691$			6.83723i			0.260101i	−0.991507	+	0.130050i	$0.958486\pi$
$692$	−6.39283			−0.243019
$693$	−17.6081	−	16.8301i	−0.668877	−	0.639323i
$694$	−3.87841			−0.147222
$695$		0			0
$696$	−27.5076	−	5.22202i	−1.04267	−	0.197940i
$697$	27.4955			1.04146
$698$	−10.2100			−0.386452
$699$	−1.70166	+	8.96368i	−0.0643627	+	0.339037i
$700$		0			0
$701$		−	17.1317i		−	0.647056i	−0.946219	−	0.323528i	$-0.895131\pi$
$701$		−	17.1317i		−	0.647056i	0.946219	−	0.323528i	$-0.104869\pi$
$702$	−11.8348	−	7.46644i	−0.446678	−	0.281803i
$703$			37.6581i			1.42030i
$704$			25.0571i			0.944374i
$705$		0			0
$706$		−	33.6749i		−	1.26737i
$707$	18.2890	−	44.7986i	0.687827	−	1.68483i
$708$	10.1216	+	1.92148i	0.380393	+	0.0722135i
$709$	23.4955			0.882390			0.441195	−	0.897411i	$-0.354555\pi$
$709$	23.4955			0.882390			0.441195	+	0.897411i	$0.354555\pi$
$710$		0			0
$711$	1.62614	+	0.640492i	0.0609849	+	0.0240203i
$712$		−	23.0679i		−	0.864506i
$713$	36.0159			1.34881
$714$	−11.3845	−	7.38094i	−0.426053	−	0.276225i
$715$		0			0
$716$			11.4531i			0.428021i
$717$	−4.67569	+	24.6297i	−0.174617	+	0.919815i
$718$	19.7913			0.738604
$719$	5.94807			0.221826			0.110913	−	0.993830i	$-0.464623\pi$
$719$	5.94807			0.221826			0.110913	+	0.993830i	$0.464623\pi$
$720$		0			0
$721$	−10.7477	−	4.38774i	−0.400266	−	0.163408i
$722$		−	0.277352i		−	0.0103220i
$723$	−6.16515	+	32.4756i	−0.229284	+	1.20778i
$724$			9.69126i			0.360173i
$725$		0			0
$726$	−0.562063	+	2.96073i	−0.0208601	+	0.109883i
$727$			11.3317i			0.420269i	0.977673	+	0.210134i	$0.0673901\pi$
$727$			11.3317i			0.420269i	−0.977673	+	0.210134i	$0.932610\pi$
$728$	−7.51695	+	18.4127i	−0.278597	+	0.682420i
$729$	11.6261	+	24.3687i	0.430598	+	0.902544i
$730$		0			0
$731$	−17.7269			−0.655653
$732$	−1.74773	+	9.20635i	−0.0645979	+	0.340276i
$733$		−	12.6520i		−	0.467312i	−0.972319	−	0.233656i	$-0.924931\pi$
$733$		−	12.6520i		−	0.467312i	0.972319	−	0.233656i	$-0.0750689\pi$
$734$	1.00682			0.0371623
$735$		0			0
$736$	−21.9564			−0.809325
$737$			12.7819i			0.470829i
$738$	12.3409	−	31.3321i	0.454275	−	1.15335i
$739$	50.8258			1.86966			0.934828	−	0.355101i	$-0.115554\pi$
$739$	50.8258			1.86966			0.934828	+	0.355101i	$0.115554\pi$
$740$		0			0
$741$	18.2890	+	3.47197i	0.671862	+	0.127546i
$742$	4.33030	−	10.6070i	0.158970	−	0.389396i
$743$			14.4740i			0.530998i	0.964111	+	0.265499i	$0.0855367\pi$
$743$			14.4740i			0.530998i	−0.964111	+	0.265499i	$0.914463\pi$
$744$	35.7042	+	6.77806i	1.30898	+	0.248496i
$745$		0			0
$746$		−	29.5884i		−	1.08331i
$747$	−43.5328	−	17.1464i	−1.59278	−	0.627355i
$748$			6.53940i			0.239104i
$749$	−25.8059	−	10.5352i	−0.942928	−	0.384949i
$750$		0			0
$751$	−11.2523			−0.410601			−0.205301	−	0.978699i	$-0.565817\pi$
$751$	−11.2523			−0.410601			−0.205301	+	0.978699i	$0.565817\pi$
$752$	4.82395			0.175911
$753$	−30.1652	−	5.72653i	−1.09928	−	0.208686i
$754$		−	14.1857i		−	0.516613i
$755$		0			0
$756$	8.85131	−	6.32409i	0.321919	−	0.230005i
$757$	33.7477			1.22658			0.613291	−	0.789857i	$-0.289845\pi$
$757$	33.7477			1.22658			0.613291	+	0.789857i	$0.289845\pi$
$758$			19.0532i			0.692043i
$759$	27.5076	+	5.22202i	0.998462	+	0.189547i
$760$		0			0
$761$	−4.26188			−0.154493			−0.0772466	−	0.997012i	$-0.524613\pi$
$761$	−4.26188			−0.154493			−0.0772466	+	0.997012i	$0.524613\pi$
$762$	−2.89991	+	15.2756i	−0.105053	+	0.553377i
$763$	5.00000	−	12.2474i	0.181012	−	0.443387i
$764$		−	13.5561i		−	0.490443i
$765$		0			0
$766$			30.7142i			1.10975i
$767$			18.4127i			0.664844i
$768$	−26.5904	−	5.04790i	−0.959497	−	0.182150i
$769$		−	30.3097i		−	1.09299i	−0.837461	−	0.546497i	$-0.815961\pi$
$769$		−	30.3097i		−	1.09299i	0.837461	−	0.546497i	$-0.184039\pi$
$770$		0			0
$771$	8.20871	+	1.55834i	0.295630	+	0.0561221i
$772$	8.70417			0.313270
$773$	−15.5960			−0.560948			−0.280474	−	0.959862i	$-0.590492\pi$
$773$	−15.5960			−0.560948			−0.280474	+	0.959862i	$0.590492\pi$
$774$	−7.95644	+	20.2005i	−0.285988	+	0.726092i
$775$		0			0
$776$	36.0159			1.29289
$777$	−21.3959	+	33.0013i	−0.767574	+	1.18392i
$778$	14.4519			0.518125
$779$			44.7986i			1.60508i
$780$		0			0
$781$	−9.41742			−0.336982
$782$	15.5960			0.557711
$783$	−14.6046	+	23.1494i	−0.521926	+	0.827291i
$784$	8.95644	+	8.77548i	0.319873	+	0.313410i
$785$		0			0
$786$	0.956439	−	5.03815i	0.0341151	−	0.179705i
$787$		−	6.32599i		−	0.225497i	−0.993624	−	0.112749i	$-0.964035\pi$
$787$		−	6.32599i		−	0.225497i	0.993624	−	0.112749i	$-0.0359655\pi$
$788$			2.79143i			0.0994406i
$789$	−9.21861	+	48.5601i	−0.328191	+	1.72878i
$790$		0			0
$791$	−44.0949	−	18.0017i	−1.56783	−	0.640065i
$792$	26.2867	+	10.3537i	0.934059	+	0.367901i
$793$	−16.7477			−0.594729
$794$	−9.64789			−0.342391
$795$		0			0
$796$			6.21929i			0.220437i
$797$	−17.7269			−0.627919			−0.313960	−	0.949436i	$-0.601656\pi$
$797$	−17.7269			−0.627919			−0.313960	+	0.949436i	$0.601656\pi$
$798$	12.0258	−	18.5488i	0.425710	−	0.656621i
$799$	7.25227			0.256567
$800$		0			0
$801$	−20.9820	−	8.26424i	−0.741362	−	0.292003i
$802$	−22.2087			−0.784217
$803$	49.4809			1.74614
$804$	−5.60839	−	1.06469i	−0.197793	−	0.0375488i
$805$		0			0
$806$			18.4127i			0.648559i
$807$	35.7042	+	6.77806i	1.25685	+	0.238599i
$808$			56.1249i			1.97447i
$809$			28.5369i			1.00330i	0.865070	+	0.501652i	$0.167274\pi$
$809$			28.5369i			1.00330i	−0.865070	+	0.501652i	$0.832726\pi$
$810$		0			0
$811$			13.6745i			0.480175i	0.970751	+	0.240088i	$0.0771762\pi$
$811$			13.6745i			0.480175i	−0.970751	+	0.240088i	$0.922824\pi$
$812$	10.2100	+	4.16820i	0.358299	+	0.146275i
$813$	−8.37386	+	44.1103i	−0.293684	+	1.54701i
$814$	−28.9564			−1.01492
$815$		0			0
$816$	8.20871	+	1.55834i	0.287362	+	0.0545527i
$817$		−	28.8826i		−	1.01048i
$818$	34.8917			1.21996
$819$	14.0547	+	13.4337i	0.491112	+	0.469412i
$820$		0			0
$821$		−	17.1317i		−	0.597901i	−0.954269	−	0.298950i	$-0.903363\pi$
$821$		−	17.1317i		−	0.597901i	0.954269	−	0.298950i	$-0.0966365\pi$
$822$	19.7096	+	3.74166i	0.687451	+	0.130505i
$823$	−2.25227			−0.0785093			−0.0392546	−	0.999229i	$-0.512498\pi$
$823$	−2.25227			−0.0785093			−0.0392546	+	0.999229i	$0.512498\pi$
$824$	13.4650			0.469076
$825$		0			0
$826$	20.2432	+	8.26424i	0.704350	+	0.287550i
$827$		−	14.8850i		−	0.517602i	−0.965931	−	0.258801i	$-0.916673\pi$
$827$		−	14.8850i		−	0.517602i	0.965931	−	0.258801i	$-0.0833273\pi$
$828$	−4.58258	+	11.6346i	−0.159256	+	0.404332i
$829$		−	15.2082i		−	0.528202i	−0.964495	−	0.264101i	$-0.914925\pi$
$829$		−	15.2082i		−	0.528202i	0.964495	−	0.264101i	$-0.0850752\pi$
$830$		0			0
$831$	31.9022	+	6.05630i	1.10668	+	0.210091i
$832$		−	20.0005i		−	0.693391i
$833$	13.4650	+	13.1930i	0.466535	+	0.457109i
$834$	−4.58258	−	0.869953i	−0.158682	−	0.0301240i
$835$		0			0
$836$	−10.6547			−0.368501
$837$	18.9564	−	30.0473i	0.655230	−	1.03859i
$838$			23.0679i			0.796867i
$839$	7.51695			0.259514			0.129757	−	0.991546i	$-0.458580\pi$
$839$	7.51695			0.259514			0.129757	+	0.991546i	$0.458580\pi$
$840$		0			0
$841$	1.25227			0.0431818
$842$			8.97689i			0.309364i
$843$	−4.95673	+	26.1101i	−0.170719	+	0.899280i
$844$	−11.6697			−0.401688
$845$		0			0
$846$	3.25507	−	8.26424i	0.111912	−	0.284131i
$847$	1.58258	−	3.87650i	0.0543779	−	0.133198i
$848$			7.05541i			0.242284i
$849$	7.58258	−	39.9421i	0.260233	−	1.37081i
$850$		0			0
$851$		−	45.2097i		−	1.54977i
$852$	0.784439	−	4.13212i	0.0268745	−	0.141564i
$853$			17.5510i			0.600934i	0.953792	+	0.300467i	$0.0971425\pi$
$853$			17.5510i			0.600934i	−0.953792	+	0.300467i	$0.902858\pi$
$854$	−7.51695	+	18.4127i	−0.257225	+	0.630069i
$855$		0			0
$856$	32.3303			1.10503
$857$	46.7879			1.59824			0.799122	−	0.601169i	$-0.205298\pi$
$857$	46.7879			1.59824			0.799122	+	0.601169i	$0.205298\pi$
$858$	−2.66970	+	14.0629i	−0.0911420	+	0.480100i
$859$		−	47.9673i		−	1.63662i	−0.574774	−	0.818312i	$-0.694910\pi$
$859$		−	47.9673i		−	1.63662i	0.574774	−	0.818312i	$-0.305090\pi$
$860$		0			0
$861$	−25.4529	+	39.2589i	−0.867432	+	1.33794i
$862$	−37.6697			−1.28303
$863$		−	22.8582i		−	0.778104i	−0.921216	−	0.389052i	$-0.872803\pi$
$863$		−	22.8582i		−	0.778104i	0.921216	−	0.389052i	$-0.127197\pi$
$864$	−11.5565	+	18.3178i	−0.393159	+	0.623185i
$865$		0			0
$866$	−1.12413			−0.0381993
$867$	−16.5873	−	3.14892i	−0.563335	−	0.106943i
$868$	−13.2523	−	5.41022i	−0.449811	−	0.183635i
$869$		−	1.78780i		−	0.0606469i
$870$		0			0
$871$		−	10.2025i		−	0.345698i
$872$			15.3439i			0.519610i
$873$	12.9030	−	32.7591i	0.436699	−	1.10873i
$874$			25.4107i			0.859529i
$875$		0			0
$876$	−4.12159	+	21.7109i	−0.139256	+	0.733545i
$877$	−31.4955			−1.06353			−0.531763	−	0.846893i	$-0.678470\pi$
$877$	−31.4955			−1.06353			−0.531763	+	0.846893i	$0.678470\pi$
$878$	−29.6230			−0.999729
$879$	−3.62614	−	0.688383i	−0.122307	−	0.0232186i
$880$		0			0
$881$	34.8917			1.17553			0.587766	−	0.809031i	$-0.300007\pi$
$881$	34.8917			1.17553			0.587766	+	0.809031i	$0.300007\pi$
$882$	21.0775	−	9.42246i	0.709715	−	0.317271i
$883$	15.4174			0.518838			0.259419	−	0.965765i	$-0.416469\pi$
$883$	15.4174			0.518838			0.259419	+	0.965765i	$0.416469\pi$
$884$		−	5.21972i		−	0.175558i
$885$		0			0
$886$	4.33030			0.145479
$887$	−40.2778			−1.35239			−0.676197	−	0.736721i	$-0.736373\pi$
$887$	−40.2778			−1.35239			−0.676197	+	0.736721i	$0.736373\pi$
$888$	8.50830	−	44.8184i	0.285520	−	1.50401i
$889$	8.16515	−	20.0005i	0.273850	−	0.670794i
$890$		0			0
$891$	18.8348	−	20.2005i	0.630991	−	0.676742i
$892$			1.93825i			0.0648975i
$893$			11.8162i			0.395414i
$894$	33.6780	+	6.39342i	1.12636	+	0.213828i
$895$		0			0
$896$	−1.56888	−	0.640492i	−0.0524126	−	0.0213973i
$897$	−21.9564	−	4.16820i	−0.733104	−	0.139172i
$898$	40.0345			1.33597
$899$	36.0159			1.20120
$900$		0			0
$901$			10.6070i			0.353371i
$902$	−34.4470			−1.14696
$903$	16.4100	−	25.3110i	0.546091	−	0.842298i
$904$	55.2432			1.83736
$905$		0			0
$906$	1.47928	−	7.79228i	0.0491459	−	0.258881i
$907$	−1.49545			−0.0496557			−0.0248279	−	0.999692i	$-0.507904\pi$
$907$	−1.49545			−0.0496557			−0.0248279	+	0.999692i	$0.507904\pi$
$908$	−2.13094			−0.0707178
$909$	51.0498	+	20.1072i	1.69321	+	0.666912i
$910$		0			0
$911$			10.4873i			0.347461i	0.984793	+	0.173730i	$0.0555821\pi$
$911$			10.4873i			0.347461i	−0.984793	+	0.173730i	$0.944418\pi$
$912$	−2.53901	+	13.3745i	−0.0840752	+	0.442875i
$913$			47.8606i			1.58396i
$914$		−	37.5617i		−	1.24243i
$915$		0			0
$916$			3.06743i			0.101351i
$917$	−2.69300	+	6.59649i	−0.0889308	+	0.217835i
$918$	8.20871	−	13.0114i	0.270928	−	0.429440i
$919$	−24.0780			−0.794261			−0.397130	−	0.917762i	$-0.629994\pi$
$919$	−24.0780			−0.794261			−0.397130	+	0.917762i	$0.629994\pi$
$920$		0			0
$921$	4.25227	−	22.3993i	0.140117	−	0.738083i
$922$			36.6356i			1.20653i
$923$	7.51695			0.247423
$924$	−9.33715	−	6.05360i	−0.307170	−	0.199149i
$925$		0			0
$926$			14.0150i			0.460563i
$927$	4.82395	−	12.2474i	0.158439	−	0.402259i
$928$	−21.9564			−0.720755
$929$	−7.51695			−0.246623			−0.123312	−	0.992368i	$-0.539351\pi$
$929$	−7.51695			−0.246623			−0.123312	+	0.992368i	$0.539351\pi$
$930$		0			0
$931$	−21.4955	+	21.9387i	−0.704485	+	0.719012i
$932$			4.16820i			0.136534i
$933$	21.0000	+	3.98663i	0.687509	+	0.130516i
$934$		−	17.7644i		−	0.581268i
$935$		0			0
$936$	−20.9820	−	8.26424i	−0.685817	−	0.270125i
$937$		−	36.2311i		−	1.18362i	−0.806078	−	0.591809i	$-0.798414\pi$
$937$		−	36.2311i		−	1.18362i	0.806078	−	0.591809i	$-0.201586\pi$
$938$	−11.2168	−	4.57923i	−0.366241	−	0.149517i
$939$	−7.41742	+	39.0721i	−0.242058	+	1.27507i
$940$		0			0
$941$	−25.2439			−0.822926			−0.411463	−	0.911426i	$-0.634982\pi$
$941$	−25.2439			−0.822926			−0.411463	+	0.911426i	$0.634982\pi$
$942$	−3.62614	−	0.688383i	−0.118146	−	0.0224287i
$943$		−	53.7821i		−	1.75139i
$944$	−13.4650			−0.438249
$945$		0			0
$946$	22.2087			0.722068
$947$		−	28.9479i		−	0.940681i	−0.882485	−	0.470340i	$-0.844131\pi$
$947$		−	28.9479i		−	0.940681i	0.882485	−	0.470340i	$-0.155869\pi$
$948$	0.784439	+	0.148917i	0.0254774	+	0.00483662i
$949$	−39.4955			−1.28208
$950$		0			0
$951$	0.429283	−	2.26129i	0.0139204	−	0.0733275i
$952$	−20.2432	−	8.26424i	−0.656085	−	0.267846i
$953$			5.26761i			0.170635i	0.996354	+	0.0853173i	$0.0271904\pi$
$953$			5.26761i			0.170635i	−0.996354	+	0.0853173i	$0.972810\pi$
$954$	12.0871	+	4.76080i	0.391335	+	0.154137i
$955$		0			0
$956$			11.4531i			0.370419i
$957$	27.5076	+	5.22202i	0.889194	+	0.168804i
$958$			8.26424i			0.267006i
$959$	−25.8059	−	10.5352i	−0.833317	−	0.340200i
$960$		0			0
$961$	−15.7477			−0.507991
$962$	23.1129			0.745190
$963$	11.5826	−	29.4068i	0.373243	−	0.947622i
$964$			15.1015i			0.486386i
$965$		0			0
$966$	−14.4374	+	22.2684i	−0.464515	+	0.716474i
$967$	−14.7477			−0.474255			−0.237127	−	0.971479i	$-0.576206\pi$
$967$	−14.7477			−0.474255			−0.237127	+	0.971479i	$0.576206\pi$
$968$			4.85658i			0.156096i
$969$	−3.81713	+	20.1072i	−0.122624	+	0.645935i
$970$		0			0
$971$	27.3748			0.878499			0.439250	−	0.898365i	$-0.355244\pi$
$971$	27.3748			0.878499			0.439250	+	0.898365i	$0.355244\pi$
$972$	7.29457	+	9.94688i	0.233974	+	0.319046i
$973$	6.00000	+	2.44949i	0.192351	+	0.0785270i
$974$		−	24.0055i		−	0.769187i
$975$		0			0
$976$		−	12.2474i		−	0.392031i
$977$		−	1.32888i		−	0.0425145i	−0.999774	−	0.0212572i	$-0.993233\pi$
$977$		−	1.32888i		−	0.0425145i	0.999774	−	0.0212572i	$-0.00676690\pi$
$978$	1.42063	−	7.48331i	0.0454267	−	0.239290i
$979$			23.0679i			0.737253i
$980$		0			0
$981$	13.9564	+	5.49707i	0.445595	+	0.175508i
$982$	28.9564			0.924037
$983$	−15.5960			−0.497434			−0.248717	−	0.968576i	$-0.580009\pi$
$983$	−15.5960			−0.497434			−0.248717	+	0.968576i	$0.580009\pi$
$984$	10.1216	−	53.3166i	0.322665	−	1.69967i
$985$		0			0
$986$	15.5960			0.496677
$987$	−6.71352	+	10.3550i	−0.213694	+	0.329604i
$988$	8.50455			0.270566
$989$			34.6744i			1.10258i
$990$		0			0
$991$	−42.0780			−1.33665			−0.668326	−	0.743868i	$-0.732989\pi$
$991$	−42.0780			−1.33665			−0.668326	+	0.743868i	$0.732989\pi$
$992$	28.4989			0.904842
$993$	28.9282	+	5.49171i	0.918009	+	0.174274i
$994$	3.37386	−	8.26424i	0.107012	−	0.262126i
$995$		0			0
$996$	−21.0000	−	3.98663i	−0.665410	−	0.126321i
$997$			25.0061i			0.791952i	0.918261	+	0.395976i	$0.129594\pi$
$997$			25.0061i			0.791952i	−0.918261	+	0.395976i	$0.870406\pi$
$998$			3.57560i			0.113184i
$999$	−37.7175	−	23.7955i	−1.19333	−	0.752855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.b.i.251.6	yes	8
3.2	odd	2	inner	525.2.b.i.251.3	yes	8
5.2	odd	4		525.2.g.f.524.7		16
5.3	odd	4		525.2.g.f.524.10		16
5.4	even	2		525.2.b.h.251.3	✓	8
7.6	odd	2	inner	525.2.b.i.251.5	yes	8
15.2	even	4		525.2.g.f.524.12		16
15.8	even	4		525.2.g.f.524.5		16
15.14	odd	2		525.2.b.h.251.6	yes	8
21.20	even	2	inner	525.2.b.i.251.4	yes	8
35.13	even	4		525.2.g.f.524.11		16
35.27	even	4		525.2.g.f.524.6		16
35.34	odd	2		525.2.b.h.251.4	yes	8
105.62	odd	4		525.2.g.f.524.9		16
105.83	odd	4		525.2.g.f.524.8		16
105.104	even	2		525.2.b.h.251.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.b.h.251.3	✓	8	5.4	even	2
525.2.b.h.251.4	yes	8	35.34	odd	2
525.2.b.h.251.5	yes	8	105.104	even	2
525.2.b.h.251.6	yes	8	15.14	odd	2
525.2.b.i.251.3	yes	8	3.2	odd	2	inner
525.2.b.i.251.4	yes	8	21.20	even	2	inner
525.2.b.i.251.5	yes	8	7.6	odd	2	inner
525.2.b.i.251.6	yes	8	1.1	even	1	trivial
525.2.g.f.524.5		16	15.8	even	4
525.2.g.f.524.6		16	35.27	even	4
525.2.g.f.524.7		16	5.2	odd	4
525.2.g.f.524.8		16	105.83	odd	4
525.2.g.f.524.9		16	105.62	odd	4
525.2.g.f.524.10		16	5.3	odd	4
525.2.g.f.524.11		16	35.13	even	4
525.2.g.f.524.12		16	15.2	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.09941i q^{2} +(1.70166 + 0.323042i) q^{3} +0.791288 q^{4} +(-0.355157 + 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} +3.06878i q^{8} +(2.79129 + 1.09941i) q^{9} +O(q^{10})\)	\(q+1.09941i q^{2} +(1.70166 + 0.323042i) q^{3} +0.791288 q^{4} +(-0.355157 + 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} +3.06878i q^{8} +(2.79129 + 1.09941i) q^{9} -3.06878i q^{11} +(1.34650 + 0.255619i) q^{12} +2.44949i q^{13} +(2.69300 + 1.09941i) q^{14} -1.79129 q^{16} -2.69300 q^{17} +(-1.20871 + 3.06878i) q^{18} -4.38774i q^{19} +(2.49295 - 3.84515i) q^{21} +3.37386 q^{22} +5.26761i q^{23} +(-0.991345 + 5.22202i) q^{24} -2.69300 q^{26} +(4.39466 + 2.77253i) q^{27} +(0.791288 - 1.93825i) q^{28} +5.26761i q^{29} -6.83723i q^{31} +4.16820i q^{32} +(0.991345 - 5.22202i) q^{33} -2.96073i q^{34} +(2.20871 + 0.869953i) q^{36} -8.58258 q^{37} +4.82395 q^{38} +(-0.791288 + 4.16820i) q^{39} -10.2100 q^{41} +(4.22742 + 2.74078i) q^{42} +6.58258 q^{43} -2.42829i q^{44} -5.79129 q^{46} -2.69300 q^{47} +(-3.04816 - 0.578661i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(-4.58258 - 0.869953i) q^{51} +1.93825i q^{52} -3.93874i q^{53} +(-3.04816 + 4.83156i) q^{54} +(7.51695 + 3.06878i) q^{56} +(1.41742 - 7.46644i) q^{57} -5.79129 q^{58} +7.51695 q^{59} +6.83723i q^{61} +7.51695 q^{62} +(5.48429 - 5.73782i) q^{63} -8.16515 q^{64} +(5.74117 + 1.08990i) q^{66} -4.16515 q^{67} -2.13094 q^{68} +(-1.70166 + 8.96368i) q^{69} -3.06878i q^{71} +(-3.37386 + 8.56585i) q^{72} +16.1240i q^{73} -9.43581i q^{74} -3.47197i q^{76} +(-7.51695 - 3.06878i) q^{77} +(-4.58258 - 0.869953i) q^{78} +0.582576 q^{79} +(6.58258 + 6.13756i) q^{81} -11.2250i q^{82} -15.5960 q^{83} +(1.97264 - 3.04262i) q^{84} +7.23698i q^{86} +(-1.70166 + 8.96368i) q^{87} +9.41742 q^{88} -7.51695 q^{89} +(6.00000 + 2.44949i) q^{91} +4.16820i q^{92} +(2.20871 - 11.6346i) q^{93} -2.96073i q^{94} +(-1.34650 + 7.09285i) q^{96} -11.7362i q^{97} +(5.38601 - 5.49707i) q^{98} +(3.37386 - 8.56585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9	\( 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9} + 4 q^{16} - 28 q^{18} - 12 q^{21} - 28 q^{22} - 12 q^{28} + 36 q^{36} - 32 q^{37} + 12 q^{39} + 16 q^{43} - 28 q^{46} - 40 q^{49} + 48 q^{57} - 28 q^{58} + 4 q^{63} + 8 q^{64} + 40 q^{67} + 28 q^{72} - 32 q^{79} + 16 q^{81} + 60 q^{84} + 112 q^{88} + 48 q^{91} + 36 q^{93} - 28 q^{99}+O(q^{100}) \) 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9 + 4 * q^16 - 28 * q^18 - 12 * q^21 - 28 * q^22 - 12 * q^28 + 36 * q^36 - 32 * q^37 + 12 * q^39 + 16 * q^43 - 28 * q^46 - 40 * q^49 + 48 * q^57 - 28 * q^58 + 4 * q^63 + 8 * q^64 + 40 * q^67 + 28 * q^72 - 32 * q^79 + 16 * q^81 + 60 * q^84 + 112 * q^88 + 48 * q^91 + 36 * q^93 - 28 * q^99

Introduction

L-functions

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