LMFDB - Embedded newform 525.2.g.f.524.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(524,525)]

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, 1, 1]))

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

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

chi := DirichletCharacter("525.524");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.g (of order $2$, degree $1$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
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} + 32x^{14} + 386x^{12} + 2208x^{10} + 6263x^{8} + 8496x^{6} + 4790x^{4} + 704x^{2} + 25 $ x^16 + 32x^14 + 386x^12 + 2208x^10 + 6263x^8 + 8496x^6 + 4790x^4 + 704*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			524.12
Root			$2.37862i$ of defining polynomial
Character	$\chi$	$=$	525.524
Dual form			525.2.g.f.524.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.09941 q^{2} +(0.323042 + 1.70166i) q^{3} -0.791288 q^{4} +(0.355157 + 1.87083i) q^{6} +(2.44949 + 1.00000i) q^{7} -3.06878 q^{8} +(-2.79129 + 1.09941i) q^{9} +O(q^{10})$	\(q+1.09941 q^{2} +(0.323042 + 1.70166i) q^{3} -0.791288 q^{4} +(0.355157 + 1.87083i) q^{6} +(2.44949 + 1.00000i) q^{7} -3.06878 q^{8} +(-2.79129 + 1.09941i) q^{9} +3.06878i q^{11} +(-0.255619 - 1.34650i) q^{12} +2.44949 q^{13} +(2.69300 + 1.09941i) q^{14} -1.79129 q^{16} +2.69300i q^{17} +(-3.06878 + 1.20871i) q^{18} +4.38774i q^{19} +(-0.910371 + 4.49124i) q^{21} +3.37386i q^{22} -5.26761 q^{23} +(-0.991345 - 5.22202i) q^{24} +2.69300 q^{26} +(-2.77253 - 4.39466i) q^{27} +(-1.93825 - 0.791288i) q^{28} +5.26761i q^{29} -6.83723i q^{31} +4.16820 q^{32} +(-5.22202 + 0.991345i) q^{33} +2.96073i q^{34} +(2.20871 - 0.869953i) q^{36} -8.58258i q^{37} +4.82395i q^{38} +(0.791288 + 4.16820i) q^{39} +10.2100 q^{41} +(-1.00088 + 4.93773i) q^{42} -6.58258i q^{43} -2.42829i q^{44} -5.79129 q^{46} +2.69300i q^{47} +(-0.578661 - 3.04816i) q^{48} +(5.00000 + 4.89898i) q^{49} +(-4.58258 + 0.869953i) q^{51} -1.93825 q^{52} +3.93874 q^{53} +(-3.04816 - 4.83156i) q^{54} +(-7.51695 - 3.06878i) q^{56} +(-7.46644 + 1.41742i) q^{57} +5.79129i q^{58} +7.51695 q^{59} +6.83723i q^{61} -7.51695i q^{62} +(-7.93665 - 0.0982834i) q^{63} +8.16515 q^{64} +(-5.74117 + 1.08990i) q^{66} -4.16515i q^{67} -2.13094i q^{68} +(-1.70166 - 8.96368i) q^{69} +3.06878i q^{71} +(8.56585 - 3.37386i) q^{72} +16.1240 q^{73} -9.43581i q^{74} -3.47197i q^{76} +(-3.06878 + 7.51695i) q^{77} +(0.869953 + 4.58258i) q^{78} -0.582576 q^{79} +(6.58258 - 6.13756i) q^{81} +11.2250 q^{82} -15.5960i q^{83} +(0.720366 - 3.55386i) q^{84} -7.23698i q^{86} +(-8.96368 + 1.70166i) q^{87} -9.41742i q^{88} -7.51695 q^{89} +(6.00000 + 2.44949i) q^{91} +4.16820 q^{92} +(11.6346 - 2.20871i) q^{93} +2.96073i q^{94} +(1.34650 + 7.09285i) q^{96} +11.7362 q^{97} +(5.49707 + 5.38601i) q^{98} +(-3.37386 - 8.56585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 24 * q^4 - 8 * q^9	$ 16 q + 24 q^{4} - 8 q^{9} + 8 q^{16} - 24 q^{21} + 72 q^{36} - 24 q^{39} - 56 q^{46} + 80 q^{49} - 16 q^{64} + 64 q^{79} + 32 q^{81} - 120 q^{84} + 96 q^{91} + 56 q^{99}+O(q^{100}) $ 16 * q + 24 * q^4 - 8 * q^9 + 8 * q^16 - 24 * q^21 + 72 * q^36 - 24 * q^39 - 56 * q^46 + 80 * q^49 - 16 * q^64 + 64 * q^79 + 32 * q^81 - 120 * q^84 + 96 * q^91 + 56 * 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 $

$2$	1.09941			0.777403			0.388702	−	0.921364i	$-0.372924\pi$
$2$	1.09941			0.777403			0.388702	+	0.921364i	$0.372924\pi$
$3$	0.323042	+	1.70166i	0.186508	+	0.982453i
$3$	0.323042	+	1.70166i	0.186508	+	0.982453i
$4$	−0.791288			−0.395644
$5$		0			0
$5$		0			0
$6$	0.355157	+	1.87083i	0.144992	+	0.763763i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$8$	−3.06878			−1.08498
$9$	−2.79129	+	1.09941i	−0.930429	+	0.366471i
$10$		0			0
$11$			3.06878i			0.925273i	0.886548	+	0.462636i	$0.153096\pi$
$11$			3.06878i			0.925273i	−0.886548	+	0.462636i	$0.846904\pi$
$12$	−0.255619	−	1.34650i	−0.0737909	−	0.388702i
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	2.69300	+	1.09941i	0.719736	+	0.293831i
$15$		0			0
$16$	−1.79129			−0.447822
$17$			2.69300i			0.653150i	0.945171	+	0.326575i	$0.105894\pi$
$17$			2.69300i			0.653150i	−0.945171	+	0.326575i	$0.894106\pi$
$18$	−3.06878	+	1.20871i	−0.723319	+	0.284896i
$19$			4.38774i			1.00662i	0.864107	+	0.503308i	$0.167884\pi$
$19$			4.38774i			1.00662i	−0.864107	+	0.503308i	$0.832116\pi$
$20$		0			0
$21$	−0.910371	+	4.49124i	−0.198659	+	0.980069i
$22$			3.37386i			0.719310i
$23$	−5.26761			−1.09837			−0.549186	−	0.835700i	$-0.685062\pi$
$23$	−5.26761			−1.09837			−0.549186	+	0.835700i	$0.685062\pi$
$24$	−0.991345	−	5.22202i	−0.202358	−	1.06594i
$25$		0			0
$26$	2.69300			0.528142
$27$	−2.77253	−	4.39466i	−0.533574	−	0.845753i
$28$	−1.93825	−	0.791288i	−0.366295	−	0.149539i
$29$			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	$-0.210441\pi$
$32$	4.16820			0.736840
$33$	−5.22202	+	0.991345i	−0.909037	+	0.172571i
$34$			2.96073i			0.507761i
$35$		0			0
$36$	2.20871	−	0.869953i	0.368119	−	0.144992i
$37$		−	8.58258i		−	1.41097i	−0.708726	−	0.705483i	$-0.750730\pi$
$37$		−	8.58258i		−	1.41097i	0.708726	−	0.705483i	$-0.249270\pi$
$38$			4.82395i			0.782547i
$39$	0.791288	+	4.16820i	0.126707	+	0.667446i
$40$		0			0
$41$	10.2100			1.59453			0.797264	−	0.603631i	$-0.206280\pi$
$41$	10.2100			1.59453			0.797264	+	0.603631i	$0.206280\pi$
$42$	−1.00088	+	4.93773i	−0.154438	+	0.761909i
$43$		−	6.58258i		−	1.00383i	−0.864916	−	0.501917i	$-0.832628\pi$
$43$		−	6.58258i		−	1.00383i	0.864916	−	0.501917i	$-0.167372\pi$
$44$		−	2.42829i		−	0.366079i
$45$		0			0
$46$	−5.79129			−0.853879
$47$			2.69300i			0.392815i	0.980522	+	0.196408i	$0.0629276\pi$
$47$			2.69300i			0.392815i	−0.980522	+	0.196408i	$0.937072\pi$
$48$	−0.578661	−	3.04816i	−0.0835225	−	0.439964i
$49$	5.00000	+	4.89898i	0.714286	+	0.699854i
$50$		0			0
$51$	−4.58258	+	0.869953i	−0.641689	+	0.121818i
$52$	−1.93825			−0.268787
$53$	3.93874			0.541027			0.270513	−	0.962716i	$-0.412807\pi$
$53$	3.93874			0.541027			0.270513	+	0.962716i	$0.412807\pi$
$54$	−3.04816	−	4.83156i	−0.414802	−	0.657492i
$55$		0			0
$56$	−7.51695	−	3.06878i	−1.00449	−	0.410083i
$57$	−7.46644	+	1.41742i	−0.988954	+	0.187742i
$58$			5.79129i			0.760433i
$59$	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	$0.855790\pi$
$62$		−	7.51695i		−	0.954654i
$63$	−7.93665	−	0.0982834i	−0.999923	−	0.0123825i
$64$	8.16515			1.02064
$65$		0			0
$66$	−5.74117	+	1.08990i	−0.706689	+	0.134157i
$67$		−	4.16515i		−	0.508854i	−0.967092	−	0.254427i	$-0.918113\pi$
$67$		−	4.16515i		−	0.508854i	0.967092	−	0.254427i	$-0.0818869\pi$
$68$		−	2.13094i		−	0.258415i
$69$	−1.70166	−	8.96368i	−0.204856	−	1.07910i
$70$		0			0
$71$			3.06878i			0.364197i	0.983280	+	0.182099i	$0.0582890\pi$
$71$			3.06878i			0.364197i	−0.983280	+	0.182099i	$0.941711\pi$
$72$	8.56585	−	3.37386i	1.00950	−	0.397614i
$73$	16.1240			1.88717			0.943583	−	0.331136i	$-0.107432\pi$
$73$	16.1240			1.88717			0.943583	+	0.331136i	$0.107432\pi$
$74$		−	9.43581i		−	1.09689i
$75$		0			0
$76$		−	3.47197i		−	0.398262i
$77$	−3.06878	+	7.51695i	−0.349720	+	0.856636i
$78$	0.869953	+	4.58258i	0.0985028	+	0.518875i
$79$	−0.582576			−0.0655449			−0.0327724	−	0.999463i	$-0.510434\pi$
$79$	−0.582576			−0.0655449			−0.0327724	+	0.999463i	$0.510434\pi$
$80$		0			0
$81$	6.58258	−	6.13756i	0.731397	−	0.681952i
$82$	11.2250			1.23959
$83$		−	15.5960i		−	1.71188i	−0.517076	−	0.855940i	$-0.672979\pi$
$83$		−	15.5960i		−	1.71188i	0.517076	−	0.855940i	$-0.327021\pi$
$84$	0.720366	−	3.55386i	0.0785983	−	0.387758i
$85$		0			0
$86$		−	7.23698i		−	0.780384i
$87$	−8.96368	+	1.70166i	−0.961007	+	0.182437i
$88$		−	9.41742i		−	1.00390i
$89$	−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
$92$	4.16820			0.434565
$93$	11.6346	−	2.20871i	1.20646	−	0.229033i
$94$			2.96073i			0.305376i
$95$		0			0
$96$	1.34650	+	7.09285i	0.137427	+	0.723911i
$97$	11.7362			1.19163			0.595816	−	0.803121i	$-0.296829\pi$
$97$	11.7362			1.19163			0.595816	+	0.803121i	$0.296829\pi$
$98$	5.49707	+	5.38601i	0.555288	+	0.544069i
$99$	−3.37386	−	8.56585i	−0.339086	−	0.860901i
$100$		0			0
$101$	−18.2890			−1.81982			−0.909910	−	0.414805i	$-0.863850\pi$
$101$	−18.2890			−1.81982			−0.909910	+	0.414805i	$0.863850\pi$
$102$	−5.03815	+	0.956439i	−0.498851	+	0.0947016i
$103$	−4.38774			−0.432337			−0.216168	−	0.976356i	$-0.569356\pi$
$103$	−4.38774			−0.432337			−0.216168	+	0.976356i	$0.569356\pi$
$104$	−7.51695			−0.737098
$105$		0			0
$106$	4.33030			0.420596
$107$	−10.5352			−1.01848			−0.509239	−	0.860625i	$-0.670073\pi$
$107$	−10.5352			−1.01848			−0.509239	+	0.860625i	$0.670073\pi$
$108$	2.19387	+	3.47744i	0.211105	+	0.334617i
$109$	−5.00000			−0.478913			−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000			−0.478913			−0.239457	+	0.970907i	$0.576969\pi$
$110$		0			0
$111$	14.6046	−	2.77253i	1.38621	−	0.263157i
$112$	−4.38774	−	1.79129i	−0.414603	−	0.169261i
$113$	18.0017			1.69345			0.846727	−	0.532028i	$-0.178570\pi$
$113$	18.0017			1.69345			0.846727	+	0.532028i	$0.178570\pi$
$114$	−8.20871	+	1.55834i	−0.768816	+	0.145952i
$115$		0			0
$116$		−	4.16820i		−	0.387007i
$117$	−6.83723	+	2.69300i	−0.632102	+	0.248968i
$118$	8.26424			0.760785
$119$	−2.69300	+	6.59649i	−0.246867	+	0.604699i
$120$		0			0
$121$	1.58258			0.143871
$122$			7.51695i			0.680553i
$123$	3.29824	+	17.3739i	0.297393	+	1.56655i
$124$			5.41022i			0.485852i
$125$		0			0
$126$	−8.72566	−	0.108054i	−0.777344	−	0.00962623i
$127$			8.16515i			0.724540i	0.932073	+	0.362270i	$0.117998\pi$
$127$			8.16515i			0.724540i	−0.932073	+	0.362270i	$0.882002\pi$
$128$	0.640492			0.0566120
$129$	11.2013	−	2.12645i	0.986219	−	0.187223i
$130$		0			0
$131$	2.69300			0.235289			0.117644	−	0.993056i	$-0.462466\pi$
$131$	2.69300			0.235289			0.117644	+	0.993056i	$0.462466\pi$
$132$	4.13212	−	0.784439i	0.359655	−	0.0682767i
$133$	−4.38774	+	10.7477i	−0.380465	+	0.931946i
$134$		−	4.57923i		−	0.395585i
$135$		0			0
$136$		−	8.26424i		−	0.708653i
$137$	−10.5352			−0.900085			−0.450042	−	0.893007i	$-0.648591\pi$
$137$	−10.5352			−0.900085			−0.450042	+	0.893007i	$0.648591\pi$
$138$	−1.87083	−	9.85480i	−0.159256	−	0.838896i
$139$		−	2.44949i		−	0.207763i	−0.994590	−	0.103882i	$-0.966874\pi$
$139$		−	2.44949i		−	0.207763i	0.994590	−	0.103882i	$-0.0331263\pi$
$140$		0			0
$141$	−4.58258	+	0.869953i	−0.385922	+	0.0732633i
$142$			3.37386i			0.283128i
$143$			7.51695i			0.628599i
$144$	5.00000	−	1.96937i	0.416667	−	0.164114i
$145$		0			0
$146$	17.7269			1.46709
$147$	−6.72118	+	10.0909i	−0.554354	+	0.832281i
$148$			6.79129i			0.558240i
$149$		−	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	$0.554208\pi$
$152$		−	13.4650i		−	1.09216i
$153$	−2.96073	−	7.51695i	−0.239361	−	0.607709i
$154$	−3.37386	+	8.26424i	−0.271874	+	0.665952i
$155$		0			0
$156$	−0.626136	−	3.29824i	−0.0501310	−	0.264071i
$157$	−1.93825			−0.154689			−0.0773447	−	0.997004i	$-0.524644\pi$
$157$	−1.93825			−0.154689			−0.0773447	+	0.997004i	$0.524644\pi$
$158$	−0.640492			−0.0509548
$159$	1.27238	+	6.70239i	0.100906	+	0.531534i
$160$		0			0
$161$	−12.9030	−	5.26761i	−1.01690	−	0.415146i
$162$	7.23698	−	6.74773i	0.568591	−	0.530152i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	−8.07901			−0.630865
$165$		0			0
$166$		−	17.1464i		−	1.33082i
$167$		−	18.2890i		−	1.41524i	−0.706592	−	0.707621i	$-0.749768\pi$
$167$		−	18.2890i		−	1.41524i	0.706592	−	0.707621i	$-0.250232\pi$
$168$	2.79373	−	13.7826i	0.215541	−	1.06335i
$169$	−7.00000			−0.538462
$170$		0			0
$171$	−4.82395	−	12.2474i	−0.368896	−	0.936586i
$172$			5.20871i			0.397161i
$173$		−	8.07901i		−	0.614236i	−0.951671	−	0.307118i	$-0.900635\pi$
$173$		−	8.07901i		−	0.614236i	0.951671	−	0.307118i	$-0.0993646\pi$
$174$	−9.85480	+	1.87083i	−0.747090	+	0.141827i
$175$		0			0
$176$		−	5.49707i		−	0.414357i
$177$	2.42829	+	12.7913i	0.182521	+	0.961452i
$178$	−8.26424			−0.619431
$179$			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	$0.849577\pi$
$182$	6.59649	+	2.69300i	0.488964	+	0.199619i
$183$	−11.6346	+	2.20871i	−0.860057	+	0.163273i
$184$	16.1652			1.19171
$185$		0			0
$186$	12.7913	−	2.42829i	0.937903	−	0.178051i
$187$	−8.26424			−0.604341
$188$		−	2.13094i		−	0.155415i
$189$	−2.39662	−	13.5372i	−0.174329	−	0.984688i
$190$		0			0
$191$			17.1317i			1.23961i	0.784757	+	0.619803i	$0.212788\pi$
$191$			17.1317i			1.23961i	−0.784757	+	0.619803i	$0.787212\pi$
$192$	2.63769	+	13.8943i	0.190359	+	1.00274i
$193$		−	11.0000i		−	0.791797i	−0.918294	−	0.395899i	$-0.870433\pi$
$193$		−	11.0000i		−	0.791797i	0.918294	−	0.395899i	$-0.129567\pi$
$194$	12.9030			0.926379
$195$		0			0
$196$	−3.95644	−	3.87650i	−0.282603	−	0.276893i
$197$	3.52770			0.251339			0.125669	−	0.992072i	$-0.459892\pi$
$197$	3.52770			0.251339			0.125669	+	0.992072i	$0.459892\pi$
$198$	−3.70927	−	9.41742i	−0.263607	−	0.669267i
$199$		−	7.85971i		−	0.557160i	−0.960413	−	0.278580i	$-0.910136\pi$
$199$		−	7.85971i		−	0.557160i	0.960413	−	0.278580i	$-0.0898637\pi$
$200$		0			0
$201$	7.08767	−	1.34552i	0.499926	−	0.0949056i
$202$	−20.1072			−1.41473
$203$	−5.26761	+	12.9030i	−0.369714	+	0.905610i
$204$	3.62614	−	0.688383i	0.253880	−	0.0481965i
$205$		0			0
$206$	−4.82395			−0.336100
$207$	14.7034	−	5.79129i	1.02196	−	0.402522i
$208$	−4.38774			−0.304235
$209$	−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	$0.669481\pi$
$212$	−3.11667			−0.214054
$213$	−5.22202	+	0.991345i	−0.357807	+	0.0679259i
$214$	−11.5826			−0.791769
$215$		0			0
$216$	8.50830	+	13.4863i	0.578916	+	0.917624i
$217$	6.83723	−	16.7477i	0.464141	−	1.13691i
$218$	−5.49707			−0.372309
$219$	5.20871	+	27.4375i	0.351972	+	1.85405i
$220$		0			0
$221$			6.59649i			0.443728i
$222$	16.0565	−	3.04816i	1.07764	−	0.204579i
$223$	2.44949			0.164030			0.0820150	−	0.996631i	$-0.473864\pi$
$223$	2.44949			0.164030			0.0820150	+	0.996631i	$0.473864\pi$
$224$	10.2100	+	4.16820i	0.682181	+	0.278499i
$225$		0			0
$226$	19.7913			1.31650
$227$			2.69300i			0.178741i	0.995998	+	0.0893705i	$0.0284855\pi$
$227$			2.69300i			0.178741i	−0.995998	+	0.0893705i	$0.971514\pi$
$228$	5.90810	−	1.12159i	0.391274	−	0.0742792i
$229$		−	3.87650i		−	0.256167i	−0.991763	−	0.128083i	$-0.959118\pi$
$229$		−	3.87650i		−	0.256167i	0.991763	−	0.128083i	$-0.0408825\pi$
$230$		0			0
$231$	−13.7826	−	2.79373i	−0.906831	−	0.183814i
$232$		−	16.1652i		−	1.06129i
$233$	−5.26761			−0.345093			−0.172546	−	0.985001i	$-0.555199\pi$
$233$	−5.26761			−0.345093			−0.172546	+	0.985001i	$0.555199\pi$
$234$	−7.51695	+	2.96073i	−0.491398	+	0.193549i
$235$		0			0
$236$	−5.94807			−0.387186
$237$	−0.188196	−	0.991345i	−0.0122247	−	0.0643948i
$238$	−2.96073	+	7.25227i	−0.191915	+	0.470095i
$239$			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	$0.789287\pi$
$242$	1.73991			0.111845
$243$	12.5705	+	9.21861i	0.806397	+	0.591374i
$244$		−	5.41022i		−	0.346354i
$245$		0			0
$246$	3.62614	+	19.1011i	0.231194	+	1.21784i
$247$			10.7477i			0.683861i
$248$			20.9820i			1.33236i
$249$	26.5390	−	5.03815i	1.68184	−	0.319280i
$250$		0			0
$251$	17.7269			1.11891			0.559456	−	0.828860i	$-0.311010\pi$
$251$	17.7269			1.11891			0.559456	+	0.828860i	$0.311010\pi$
$252$	6.28017	+	0.0777705i	0.395614	+	0.00489908i
$253$		−	16.1652i		−	1.01629i
$254$			8.97689i			0.563260i
$255$		0			0
$256$	−15.6261			−0.976634
$257$		−	4.82395i		−	0.300909i	−0.988617	−	0.150455i	$-0.951926\pi$
$257$		−	4.82395i		−	0.300909i	0.988617	−	0.150455i	$-0.0480738\pi$
$258$	12.3149	−	2.33785i	0.766690	−	0.145548i
$259$	8.58258	−	21.0229i	0.533295	−	1.30630i
$260$		0			0
$261$	−5.79129	−	14.7034i	−0.358472	−	0.910119i
$262$	2.96073			0.182914
$263$	−28.5369			−1.75966			−0.879830	−	0.475289i	$-0.842344\pi$
$263$	−28.5369			−1.75966			−0.879830	+	0.475289i	$0.842344\pi$
$264$	16.0252	−	3.04222i	0.986286	−	0.187236i
$265$		0			0
$266$	−4.82395	+	11.8162i	−0.295775	+	0.724498i
$267$	−2.42829	−	12.7913i	−0.148609	−	0.782814i
$268$			3.29583i			0.201325i
$269$	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	$0.711467\pi$
$272$		−	4.82395i		−	0.292495i
$273$	−2.22995	+	11.0012i	−0.134962	+	0.665826i
$274$	−11.5826			−0.699729
$275$		0			0
$276$	1.34650	+	7.09285i	0.0810499	+	0.426939i
$277$			18.7477i			1.12644i	0.826306	+	0.563221i	$0.190438\pi$
$277$			18.7477i			1.12644i	−0.826306	+	0.563221i	$0.809562\pi$
$278$		−	2.69300i		−	0.161516i
$279$	7.51695	+	19.0847i	0.450028	+	1.14257i
$280$		0			0
$281$		−	15.3439i		−	0.915341i	−0.889122	−	0.457670i	$-0.848684\pi$
$281$		−	15.3439i		−	0.915341i	0.889122	−	0.457670i	$-0.151316\pi$
$282$	−5.03815	+	0.956439i	−0.300017	+	0.0569551i
$283$	−23.4724			−1.39529			−0.697645	−	0.716443i	$-0.745769\pi$
$283$	−23.4724			−1.39529			−0.697645	+	0.716443i	$0.745769\pi$
$284$		−	2.42829i		−	0.144093i
$285$		0			0
$286$			8.26424i			0.488675i
$287$	25.0092	+	10.2100i	1.47625	+	0.602675i
$288$	−11.6346	+	4.58258i	−0.685578	+	0.270031i
$289$	9.74773			0.573396
$290$		0			0
$291$	3.79129	+	19.9710i	0.222249	+	1.17072i
$292$	−12.7587			−0.746646
$293$		−	2.13094i		−	0.124491i	−0.998061	−	0.0622455i	$-0.980174\pi$
$293$		−	2.13094i		−	0.124491i	0.998061	−	0.0622455i	$-0.0198262\pi$
$294$	−7.38937	+	11.0941i	−0.430957	+	0.647018i
$295$		0			0
$296$			26.3381i			1.53087i
$297$	13.4863	−	8.50830i	0.782552	−	0.493701i
$298$		−	19.7913i		−	1.14648i
$299$	−12.9030			−0.746197
$300$		0			0
$301$	6.58258	−	16.1240i	0.379413	−	0.929369i
$302$	−4.57923			−0.263505
$303$	−5.90810	−	31.1216i	−0.339412	−	1.78789i
$304$		−	7.85971i		−	0.450785i
$305$		0			0
$306$	−3.25507	−	8.26424i	−0.186080	−	0.472435i
$307$	13.1632			0.751265			0.375632	−	0.926769i	$-0.377426\pi$
$307$	13.1632			0.751265			0.375632	+	0.926769i	$0.377426\pi$
$308$	2.42829	−	5.94807i	0.138365	−	0.338923i
$309$	−1.41742	−	7.46644i	−0.0806345	−	0.424751i
$310$		0			0
$311$	−12.3409			−0.699788			−0.349894	−	0.936789i	$-0.613782\pi$
$311$	−12.3409			−0.699788			−0.349894	+	0.936789i	$0.613782\pi$
$312$	−2.42829	−	12.7913i	−0.137475	−	0.724164i
$313$	22.9612			1.29784			0.648921	−	0.760855i	$-0.275220\pi$
$313$	22.9612			1.29784			0.648921	+	0.760855i	$0.275220\pi$
$314$	−2.13094			−0.120256
$315$		0			0
$316$	0.460985			0.0259324
$317$	−1.32888			−0.0746371			−0.0373185	−	0.999303i	$-0.511882\pi$
$317$	−1.32888			−0.0746371			−0.0373185	+	0.999303i	$0.511882\pi$
$318$	1.39887	+	7.36870i	0.0784447	+	0.413216i
$319$	−16.1652			−0.905075
$320$		0			0
$321$	−3.40332	−	17.9274i	−0.189955	−	1.00061i
$322$	−14.1857	−	5.79129i	−0.790538	−	0.322736i
$323$	−11.8162			−0.657471
$324$	−5.20871	+	4.85658i	−0.289373	+	0.269810i
$325$		0			0
$326$			4.39766i			0.243564i
$327$	−1.61521	−	8.50830i	−0.0893213	−	0.470510i
$328$	−31.3321			−1.73003
$329$	−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	$0.345262\pi$
$332$			12.3409i			0.677295i
$333$	9.43581	+	23.9564i	0.517079	+	1.31280i
$334$		−	20.1072i		−	1.10021i
$335$		0			0
$336$	1.63074	−	8.04510i	0.0889640	−	0.438896i
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$	−7.69590			−0.418602
$339$	5.81529	+	30.6327i	0.315843	+	1.66374i
$340$		0			0
$341$	20.9820			1.13624
$342$	−5.30352	−	13.4650i	−0.286781	−	0.728105i
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$			20.2005i			1.08914i
$345$		0			0
$346$		−	8.88218i		−	0.477509i
$347$	3.52770			0.189377			0.0946886	−	0.995507i	$-0.469814\pi$
$347$	3.52770			0.189377			0.0946886	+	0.995507i	$0.469814\pi$
$348$	7.09285	−	1.34650i	0.380217	−	0.0721801i
$349$		−	9.28672i		−	0.497107i	−0.968618	−	0.248553i	$-0.920045\pi$
$349$		−	9.28672i		−	0.497107i	0.968618	−	0.248553i	$-0.0799551\pi$
$350$		0			0
$351$	−6.79129	−	10.7647i	−0.362492	−	0.574576i
$352$			12.7913i			0.681778i
$353$		−	30.6299i		−	1.63026i	−0.579276	−	0.815132i	$-0.696665\pi$
$353$		−	30.6299i		−	1.63026i	0.579276	−	0.815132i	$-0.303335\pi$
$354$	2.66970	+	14.0629i	0.141893	+	0.747436i
$355$		0			0
$356$	5.94807			0.315247
$357$	−12.0949	−	2.45163i	−0.640131	−	0.129754i
$358$			15.9129i			0.841022i
$359$		−	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
$362$			13.4650i			0.707706i
$363$	0.511238	+	2.69300i	0.0268331	+	0.141346i
$364$	−4.74773	−	1.93825i	−0.248849	−	0.101592i
$365$		0			0
$366$	−12.7913	+	2.42829i	−0.668611	+	0.126929i
$367$	0.915775			0.0478031			0.0239015	−	0.999714i	$-0.492391\pi$
$367$	0.915775			0.0478031			0.0239015	+	0.999714i	$0.492391\pi$
$368$	9.43581			0.491875
$369$	−28.4989	+	11.2250i	−1.48359	+	0.584349i
$370$		0			0
$371$	9.64789	+	3.93874i	0.500894	+	0.204489i
$372$	−9.20635	+	1.74773i	−0.477327	+	0.0906154i
$373$			26.9129i			1.39350i	0.717316	+	0.696748i	$0.245370\pi$
$373$			26.9129i			1.39350i	−0.717316	+	0.696748i	$0.754630\pi$
$374$	−9.08583			−0.469817
$375$		0			0
$376$		−	8.26424i		−	0.426196i
$377$			12.9030i			0.664536i
$378$	−2.63488	−	14.8830i	−0.135524	−	0.765499i
$379$	−17.3303			−0.890198			−0.445099	−	0.895481i	$-0.646831\pi$
$379$	−17.3303			−0.890198			−0.445099	+	0.895481i	$0.646831\pi$
$380$		0			0
$381$	−13.8943	+	2.63769i	−0.711827	+	0.135133i
$382$			18.8348i			0.963675i
$383$			27.9369i			1.42751i	0.700397	+	0.713753i	$0.253006\pi$
$383$			27.9369i			1.42751i	−0.700397	+	0.713753i	$0.746994\pi$
$384$	0.206906	+	1.08990i	0.0105586	+	0.0556187i
$385$		0			0
$386$		−	12.0936i		−	0.615546i
$387$	7.23698	+	18.3739i	0.367876	+	0.933996i
$388$	−9.28672			−0.471462
$389$		−	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
$392$	−15.3439	−	15.0339i	−0.774985	−	0.759327i
$393$	0.869953	+	4.58258i	0.0438833	+	0.231160i
$394$	3.87841			0.195391
$395$		0			0
$396$	2.66970	+	6.77806i	0.134157	+	0.340610i
$397$	−8.77548			−0.440429			−0.220214	−	0.975451i	$-0.570676\pi$
$397$	−8.77548			−0.440429			−0.220214	+	0.975451i	$0.570676\pi$
$398$		−	8.64108i		−	0.433138i
$399$	−19.7064	−	3.99447i	−0.986554	−	0.199974i
$400$		0			0
$401$		−	20.2005i		−	1.00876i	−0.863481	−	0.504382i	$-0.831720\pi$
$401$		−	20.2005i		−	1.00876i	0.863481	−	0.504382i	$-0.168280\pi$
$402$	7.79228	−	1.47928i	0.388644	−	0.0737799i
$403$		−	16.7477i		−	0.834264i
$404$	14.4718			0.720001
$405$		0			0
$406$	−5.79129	+	14.1857i	−0.287417	+	0.704024i
$407$	26.3381			1.30553
$408$	14.0629	−	2.66970i	0.696219	−	0.132170i
$409$			31.7367i			1.56928i	0.619954	+	0.784639i	$0.287151\pi$
$409$			31.7367i			1.56928i	−0.619954	+	0.784639i	$0.712849\pi$
$410$		0			0
$411$	−3.40332	−	17.9274i	−0.167873	−	0.884291i
$412$	3.47197			0.171052
$413$	18.4127	+	7.51695i	0.906029	+	0.369885i
$414$	16.1652	−	6.36703i	0.794474	−	0.312922i
$415$		0			0
$416$	10.2100			0.500584
$417$	4.16820	−	0.791288i	0.204117	−	0.0387495i
$418$	−14.8036			−0.724070
$419$	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	$0.436240\pi$
$422$	−16.2139			−0.789279
$423$	−2.96073	−	7.51695i	−0.143956	−	0.365487i
$424$	−12.0871			−0.587003
$425$		0			0
$426$	−5.74117	+	1.08990i	−0.278160	+	0.0528058i
$427$	−6.83723	+	16.7477i	−0.330877	+	0.810479i
$428$	8.33639			0.402955
$429$	−12.7913	+	2.42829i	−0.617569	+	0.117239i
$430$		0			0
$431$		−	34.2634i		−	1.65041i	−0.564833	−	0.825205i	$-0.691059\pi$
$431$		−	34.2634i		−	1.65041i	0.564833	−	0.825205i	$-0.308941\pi$
$432$	4.96640	+	7.87211i	0.238946	+	0.378747i
$433$	1.02248			0.0491371			0.0245685	−	0.999698i	$-0.492179\pi$
$433$	1.02248			0.0491371			0.0245685	+	0.999698i	$0.492179\pi$
$434$	7.51695	−	18.4127i	0.360825	−	0.883838i
$435$		0			0
$436$	3.95644			0.189479
$437$		−	23.1129i		−	1.10564i
$438$	5.72653	+	30.1652i	0.273624	+	1.44135i
$439$		−	26.9444i		−	1.28599i	−0.765872	−	0.642993i	$-0.777693\pi$
$439$		−	26.9444i		−	1.28599i	0.765872	−	0.642993i	$-0.222307\pi$
$440$		0			0
$441$	−19.3424	−	8.17739i	−0.921069	−	0.389400i
$442$			7.25227i			0.344955i
$443$	3.93874			0.187135			0.0935675	−	0.995613i	$-0.470173\pi$
$443$	3.93874			0.187135			0.0935675	+	0.995613i	$0.470173\pi$
$444$	−11.5565	+	2.19387i	−0.548445	+	0.104116i
$445$		0			0
$446$	2.69300			0.127517
$447$	30.6327	−	5.81529i	1.44888	−	0.275054i
$448$	20.0005	+	8.16515i	0.944933	+	0.385767i
$449$		−	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
$452$	−14.2445			−0.670005
$453$	−1.34552	−	7.08767i	−0.0632180	−	0.333008i
$454$			2.96073i			0.138954i
$455$		0			0
$456$	22.9129	−	4.34977i	1.07299	−	0.203696i
$457$		−	34.1652i		−	1.59818i	−0.601213	−	0.799089i	$-0.705315\pi$
$457$		−	34.1652i		−	1.59818i	0.601213	−	0.799089i	$-0.294685\pi$
$458$		−	4.26188i		−	0.199145i
$459$	11.8348	−	7.46644i	0.552403	−	0.348504i
$460$		0			0
$461$	−33.3229			−1.55200			−0.776000	−	0.630732i	$-0.782755\pi$
$461$	−33.3229			−1.55200			−0.776000	+	0.630732i	$0.782755\pi$
$462$	−15.1528	−	3.07147i	−0.704973	−	0.142898i
$463$		−	12.7477i		−	0.592437i	−0.955120	−	0.296219i	$-0.904274\pi$
$463$		−	12.7477i		−	0.592437i	0.955120	−	0.296219i	$-0.0957257\pi$
$464$		−	9.43581i		−	0.438046i
$465$		0			0
$466$	−5.79129			−0.268276
$467$			16.1580i			0.747704i	0.927488	+	0.373852i	$0.121963\pi$
$467$			16.1580i			0.747704i	−0.927488	+	0.373852i	$0.878037\pi$
$468$	5.41022	−	2.13094i	0.250087	−	0.0985028i
$469$	4.16515	−	10.2025i	0.192329	−	0.471107i
$470$		0			0
$471$	−0.626136	−	3.29824i	−0.0288508	−	0.151975i
$472$	−23.0679			−1.06179
$473$	20.2005			0.928820
$474$	−0.206906	−	1.08990i	−0.00950350	−	0.0500607i
$475$		0			0
$476$	2.13094	−	5.21972i	0.0976716	−	0.239245i
$477$	−10.9941	+	4.33030i	−0.503387	+	0.198271i
$478$			15.9129i			0.727838i
$479$	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
$482$			20.9820i			0.955703i
$483$	4.79548	−	23.6581i	0.218202	−	1.07648i
$484$	−1.25227			−0.0569215
$485$		0			0
$486$	13.8202	+	10.1351i	0.626896	+	0.459736i
$487$		−	21.8348i		−	0.989431i	−0.869055	−	0.494716i	$-0.835272\pi$
$487$		−	21.8348i		−	0.989431i	0.869055	−	0.494716i	$-0.164728\pi$
$488$		−	20.9820i		−	0.949809i
$489$	−6.80664	+	1.29217i	−0.307807	+	0.0584338i
$490$		0			0
$491$			26.3381i			1.18862i	0.804236	+	0.594310i	$0.202575\pi$
$491$			26.3381i			1.18862i	−0.804236	+	0.594310i	$0.797425\pi$
$492$	−2.60986	−	13.7477i	−0.117662	−	0.619795i
$493$	−14.1857			−0.638892
$494$			11.8162i			0.531636i
$495$		0			0
$496$			12.2474i			0.549927i
$497$	−3.06878	+	7.51695i	−0.137654	+	0.337181i
$498$	29.1774	−	5.53901i	1.30747	−	0.248209i
$499$	−3.25227			−0.145592			−0.0727959	−	0.997347i	$-0.523192\pi$
$499$	−3.25227			−0.145592			−0.0727959	+	0.997347i	$0.523192\pi$
$500$		0			0
$501$	31.1216	−	5.90810i	1.39041	−	0.263955i
$502$	19.4892			0.869846
$503$			5.38601i			0.240150i	0.992765	+	0.120075i	$0.0383135\pi$
$503$			5.38601i			0.240150i	−0.992765	+	0.120075i	$0.961686\pi$
$504$	24.3558	+	0.301610i	1.08490	+	0.0134348i
$505$		0			0
$506$		−	17.7722i		−	0.790071i
$507$	−2.26129	−	11.9116i	−0.100428	−	0.529013i
$508$		−	6.46099i		−	0.286660i
$509$	−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
$512$	−18.4606			−0.815850
$513$	19.2826	−	12.1652i	0.851350	−	0.537105i
$514$		−	5.30352i		−	0.233928i
$515$		0			0
$516$	−8.86345	+	1.68263i	−0.390192	+	0.0740738i
$517$	−8.26424			−0.363461
$518$	9.43581	−	23.1129i	0.414586	−	1.01552i
$519$	13.7477	−	2.60986i	0.603458	−	0.114560i
$520$		0			0
$521$	16.1580			0.707896			0.353948	−	0.935265i	$-0.384839\pi$
$521$	16.1580			0.707896			0.353948	+	0.935265i	$0.384839\pi$
$522$	−6.36703	−	16.1652i	−0.278677	−	0.707529i
$523$	14.6969			0.642652			0.321326	−	0.946969i	$-0.395871\pi$
$523$	14.6969			0.642652			0.321326	+	0.946969i	$0.395871\pi$
$524$	−2.13094			−0.0930906
$525$		0			0
$526$	−31.3739			−1.36797
$527$	18.4127			0.802070
$528$	9.35414	−	1.77578i	0.407087	−	0.0772811i
$529$	4.74773			0.206423
$530$		0			0
$531$	−20.9820	+	8.26424i	−0.910540	+	0.358638i
$532$	3.47197	−	8.50455i	0.150529	−	0.368719i
$533$	25.0092			1.08327
$534$	−2.66970	−	14.0629i	−0.115529	−	0.608562i
$535$		0			0
$536$			12.7819i			0.552096i
$537$	−24.6297	+	4.67569i	−1.06285	+	0.201771i
$538$	23.0679			0.994527
$539$	−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	$0.559066\pi$
$542$			28.4989i			1.22413i
$543$	−20.8410	+	3.95644i	−0.894372	+	0.169787i
$544$			11.2250i			0.481267i
$545$		0			0
$546$	−2.45163	+	12.0949i	−0.104920	+	0.517615i
$547$			4.66970i			0.199662i	0.995004	+	0.0998309i	$0.0318302\pi$
$547$			4.66970i			0.199662i	−0.995004	+	0.0998309i	$0.968170\pi$
$548$	8.33639			0.356113
$549$	−7.51695	−	19.0847i	−0.320816	−	0.814514i
$550$		0			0
$551$	−23.1129			−0.984643
$552$	5.22202	+	27.5076i	0.222264	+	1.17080i
$553$	−1.42701	−	0.582576i	−0.0606828	−	0.0247736i
$554$			20.6115i			0.875700i
$555$		0			0
$556$			1.93825i			0.0822002i
$557$	−6.18546			−0.262086			−0.131043	−	0.991377i	$-0.541833\pi$
$557$	−6.18546			−0.262086			−0.131043	+	0.991377i	$0.541833\pi$
$558$	8.26424	+	20.9820i	0.349853	+	0.888238i
$559$		−	16.1240i		−	0.681970i
$560$		0			0
$561$	−2.66970	−	14.0629i	−0.112715	−	0.593737i
$562$		−	16.8693i		−	0.711589i
$563$		−	9.64789i		−	0.406610i	−0.979115	−	0.203305i	$-0.934832\pi$
$563$		−	9.64789i		−	0.406610i	0.979115	−	0.203305i	$-0.0651683\pi$
$564$	3.62614	−	0.688383i	0.152688	−	0.0289862i
$565$		0			0
$566$	−25.8059			−1.08470
$567$	22.2615	−	8.45133i	0.934896	−	0.354922i
$568$		−	9.41742i		−	0.395146i
$569$			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	$0.713863\pi$
$572$		−	5.94807i		−	0.248701i
$573$	−29.1523	+	5.53426i	−1.21786	+	0.231197i
$574$	27.4955	+	11.2250i	1.14764	+	0.468521i
$575$		0			0
$576$	−22.7913	+	8.97689i	−0.949637	+	0.374037i
$577$	23.9837			0.998453			0.499226	−	0.866472i	$-0.333618\pi$
$577$	23.9837			0.998453			0.499226	+	0.866472i	$0.333618\pi$
$578$	10.7168			0.445760
$579$	18.7183	−	3.55346i	0.777904	−	0.147677i
$580$		0			0
$581$	15.5960	−	38.2022i	0.647030	−	1.58489i
$582$	4.16820	+	21.9564i	0.172777	+	0.910124i
$583$			12.0871i			0.500597i
$584$	−49.4809			−2.04753
$585$		0			0
$586$		−	2.34279i		−	0.0967797i
$587$		−	3.25507i		−	0.134351i	−0.997741	−	0.0671755i	$-0.978601\pi$
$587$		−	3.25507i		−	0.134351i	0.997741	−	0.0671755i	$-0.0213987\pi$
$588$	5.31839	−	7.98478i	0.219327	−	0.329287i
$589$	30.0000			1.23613
$590$		0			0
$591$	1.13960	+	6.00295i	0.0468767	+	0.246928i
$592$			15.3739i			0.631862i
$593$			5.38601i			0.221177i	0.993866	+	0.110588i	$0.0352735\pi$
$593$			5.38601i			0.221177i	−0.993866	+	0.110588i	$0.964726\pi$
$594$	14.8270	−	9.35414i	0.608359	−	0.383805i
$595$		0			0
$596$			14.2445i			0.583477i
$597$	13.3745	−	2.53901i	0.547384	−	0.103915i
$598$	−14.1857			−0.580096
$599$		−	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	$-0.0185390\pi$
$602$	7.23698	−	17.7269i	0.294957	−	0.722495i
$603$	4.57923	+	11.6261i	0.186481	+	0.473453i
$604$	3.29583			0.134106
$605$		0			0
$606$	−6.49545	−	34.2155i	−0.263860	−	1.38991i
$607$	−21.0229			−0.853294			−0.426647	−	0.904418i	$-0.640305\pi$
$607$	−21.0229			−0.853294			−0.426647	+	0.904418i	$0.640305\pi$
$608$			18.2890i			0.741716i
$609$	−23.6581	−	4.79548i	−0.958675	−	0.194323i
$610$		0			0
$611$			6.59649i			0.266865i
$612$	2.34279	+	5.94807i	0.0947016	+	0.240437i
$613$		−	36.5826i		−	1.47756i	−0.673949	−	0.738778i	$-0.735403\pi$
$613$		−	36.5826i		−	1.47756i	0.673949	−	0.738778i	$-0.264597\pi$
$614$	14.4718			0.584036
$615$		0			0
$616$	9.41742	−	23.0679i	0.379439	−	0.929432i
$617$	−1.32888			−0.0534985			−0.0267493	−	0.999642i	$-0.508516\pi$
$617$	−1.32888			−0.0534985			−0.0267493	+	0.999642i	$0.508516\pi$
$618$	−1.55834	−	8.20871i	−0.0626855	−	0.330203i
$619$		−	13.2699i		−	0.533363i	−0.963785	−	0.266682i	$-0.914073\pi$
$619$		−	13.2699i		−	0.533363i	0.963785	−	0.266682i	$-0.0859272\pi$
$620$		0			0
$621$	14.6046	+	23.1494i	0.586063	+	0.928953i
$622$	−13.5678			−0.544018
$623$	−18.4127	−	7.51695i	−0.737689	−	0.301160i
$624$	−1.41742	−	7.46644i	−0.0567424	−	0.298897i
$625$		0			0
$626$	25.2439			1.00895
$627$	−4.34977	−	22.9129i	−0.173713	−	0.915052i
$628$	1.53371			0.0612019
$629$	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	$0.265548\pi$
$632$	1.78780			0.0711148
$633$	−4.76413	−	25.0956i	−0.189357	−	0.997461i
$634$	−1.46099			−0.0580231
$635$		0			0
$636$	−1.00682	−	5.30352i	−0.0399229	−	0.210298i
$637$	12.2474	+	12.0000i	0.485262	+	0.475457i
$638$	−17.7722			−0.703608
$639$	−3.37386	−	8.56585i	−0.133468	−	0.338860i
$640$		0			0
$641$		−	1.78780i		−	0.0706138i	−0.999377	−	0.0353069i	$-0.988759\pi$
$641$		−	1.78780i		−	0.0706138i	0.999377	−	0.0353069i	$-0.0112409\pi$
$642$	−3.74166	−	19.7096i	−0.147671	−	0.777876i
$643$	−20.6184			−0.813110			−0.406555	−	0.913626i	$-0.633270\pi$
$643$	−20.6184			−0.813110			−0.406555	+	0.913626i	$0.633270\pi$
$644$	10.2100	+	4.16820i	0.402329	+	0.164250i
$645$		0			0
$646$	−12.9909			−0.511120
$647$		−	40.8398i		−	1.60558i	−0.596263	−	0.802790i	$-0.703348\pi$
$647$		−	40.8398i		−	1.60558i	0.596263	−	0.802790i	$-0.296652\pi$
$648$	−20.2005	+	18.8348i	−0.793550	+	0.739903i
$649$			23.0679i			0.905494i
$650$		0			0
$651$	30.7076	+	6.22442i	1.20353	+	0.243954i
$652$		−	3.16515i		−	0.123957i
$653$	−14.4740			−0.566410			−0.283205	−	0.959059i	$-0.591398\pi$
$653$	−14.4740			−0.566410			−0.283205	+	0.959059i	$0.591398\pi$
$654$	−1.77578	−	9.35414i	−0.0694387	−	0.365776i
$655$		0			0
$656$	−18.2890			−0.714064
$657$	−45.0066	+	17.7269i	−1.75587	+	0.691592i
$658$	−2.96073	+	7.25227i	−0.115421	+	0.282723i
$659$			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	$-0.321908\pi$
$662$	18.6900			0.726409
$663$	−11.2250	+	2.13094i	−0.435942	+	0.0827589i
$664$			47.8606i			1.85735i
$665$		0			0
$666$	10.3739	+	26.3381i	0.401979	+	1.02058i
$667$		−	27.7477i		−	1.07440i
$668$			14.4718i			0.559932i
$669$	0.791288	+	4.16820i	0.0305930	+	0.161152i
$670$		0			0
$671$	−20.9820			−0.810000
$672$	−3.79461	+	18.7204i	−0.146380	+	0.722154i
$673$			7.49545i			0.288929i	0.989510	+	0.144464i	$0.0461459\pi$
$673$			7.49545i			0.288929i	−0.989510	+	0.144464i	$0.953854\pi$
$674$			2.19883i			0.0846957i
$675$		0			0
$676$	5.53901			0.213039
$677$		−	10.7720i		−	0.414002i	−0.978341	−	0.207001i	$-0.933630\pi$
$677$		−	10.7720i		−	0.414002i	0.978341	−	0.207001i	$-0.0663704\pi$
$678$	6.39342	+	33.6780i	0.245538	+	1.29340i
$679$	28.7477	+	11.7362i	1.10324	+	0.450394i
$680$		0			0
$681$	−4.58258	+	0.869953i	−0.175605	+	0.0333367i
$682$	23.0679			0.883315
$683$	−10.1242			−0.387391			−0.193696	−	0.981062i	$-0.562047\pi$
$683$	−10.1242			−0.387391			−0.193696	+	0.981062i	$0.562047\pi$
$684$	3.81713	+	9.69126i	0.145952	+	0.370554i
$685$		0			0
$686$	8.07901	+	18.6900i	0.308458	+	0.713589i
$687$	6.59649	−	1.25227i	0.251672	−	0.0477772i
$688$			11.7913i			0.449539i
$689$	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	$0.958486\pi$
$692$			6.39283i			0.243019i
$693$	0.301610	−	24.3558i	0.0114572	−	0.925202i
$694$	3.87841			0.147222
$695$		0			0
$696$	27.5076	−	5.22202i	1.04267	−	0.197940i
$697$			27.4955i			1.04146i
$698$		−	10.2100i		−	0.386452i
$699$	−1.70166	−	8.96368i	−0.0643627	−	0.339037i
$700$		0			0
$701$			17.1317i			0.647056i	0.946219	+	0.323528i	$0.104869\pi$
$701$			17.1317i			0.647056i	−0.946219	+	0.323528i	$0.895131\pi$
$702$	−7.46644	−	11.8348i	−0.281803	−	0.446678i
$703$	37.6581			1.42030
$704$			25.0571i			0.944374i
$705$		0			0
$706$		−	33.6749i		−	1.26737i
$707$	−44.7986	−	18.2890i	−1.68483	−	0.687827i
$708$	−1.92148	−	10.1216i	−0.0722135	−	0.380393i
$709$	−23.4955			−0.882390			−0.441195	−	0.897411i	$-0.645445\pi$
$709$	−23.4955			−0.882390			−0.441195	+	0.897411i	$0.645445\pi$
$710$		0			0
$711$	1.62614	−	0.640492i	0.0609849	−	0.0240203i
$712$	23.0679			0.864506
$713$			36.0159i			1.34881i
$714$	−13.2973	−	2.69536i	−0.497640	−	0.100871i
$715$		0			0
$716$		−	11.4531i		−	0.428021i
$717$	−24.6297	+	4.67569i	−0.919815	+	0.174617i
$718$		−	19.7913i		−	0.738604i
$719$	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
$722$	−0.277352			−0.0103220
$723$	−32.4756	+	6.16515i	−1.20778	+	0.229284i
$724$		−	9.69126i		−	0.360173i
$725$		0			0
$726$	0.562063	+	2.96073i	0.0208601	+	0.109883i
$727$	−11.3317			−0.420269			−0.210134	−	0.977673i	$-0.567390\pi$
$727$	−11.3317			−0.420269			−0.210134	+	0.977673i	$0.567390\pi$
$728$	−18.4127	−	7.51695i	−0.682420	−	0.278597i
$729$	−11.6261	+	24.3687i	−0.430598	+	0.902544i
$730$		0			0
$731$	17.7269			0.655653
$732$	9.20635	−	1.74773i	0.340276	−	0.0645979i
$733$	−12.6520			−0.467312			−0.233656	−	0.972319i	$-0.575069\pi$
$733$	−12.6520			−0.467312			−0.233656	+	0.972319i	$0.575069\pi$
$734$	1.00682			0.0371623
$735$		0			0
$736$	−21.9564			−0.809325
$737$	12.7819			0.470829
$738$	−31.3321	+	12.3409i	−1.15335	+	0.454275i
$739$	−50.8258			−1.86966			−0.934828	−	0.355101i	$-0.884446\pi$
$739$	−50.8258			−1.86966			−0.934828	+	0.355101i	$0.884446\pi$
$740$		0			0
$741$	−18.2890	+	3.47197i	−0.671862	+	0.127546i
$742$	10.6070	+	4.33030i	0.389396	+	0.158970i
$743$	−14.4740			−0.530998			−0.265499	−	0.964111i	$-0.585537\pi$
$743$	−14.4740			−0.530998			−0.265499	+	0.964111i	$0.585537\pi$
$744$	−35.7042	+	6.77806i	−1.30898	+	0.248496i
$745$		0			0
$746$			29.5884i			1.08331i
$747$	17.1464	+	43.5328i	0.627355	+	1.59278i
$748$	6.53940			0.239104
$749$	−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	$0.565817\pi$
$752$		−	4.82395i		−	0.175911i
$753$	5.72653	+	30.1652i	0.208686	+	1.09928i
$754$			14.1857i			0.516613i
$755$		0			0
$756$	1.89642	+	10.7118i	0.0689721	+	0.389586i
$757$			33.7477i			1.22658i	0.789857	+	0.613291i	$0.210155\pi$
$757$			33.7477i			1.22658i	−0.789857	+	0.613291i	$0.789845\pi$
$758$	−19.0532			−0.692043
$759$	27.5076	−	5.22202i	0.998462	−	0.189547i
$760$		0			0
$761$	4.26188			0.154493			0.0772466	−	0.997012i	$-0.475387\pi$
$761$	4.26188			0.154493			0.0772466	+	0.997012i	$0.475387\pi$
$762$	−15.2756	+	2.89991i	−0.553377	+	0.105053i
$763$	−12.2474	−	5.00000i	−0.443387	−	0.181012i
$764$		−	13.5561i		−	0.490443i
$765$		0			0
$766$			30.7142i			1.10975i
$767$	18.4127			0.664844
$768$	−5.04790	−	26.5904i	−0.182150	−	0.959497i
$769$			30.3097i			1.09299i	0.837461	+	0.546497i	$0.184039\pi$
$769$			30.3097i			1.09299i	−0.837461	+	0.546497i	$0.815961\pi$
$770$		0			0
$771$	8.20871	−	1.55834i	0.295630	−	0.0561221i
$772$			8.70417i			0.313270i
$773$		−	15.5960i		−	0.560948i	−0.959862	−	0.280474i	$-0.909508\pi$
$773$		−	15.5960i		−	0.560948i	0.959862	−	0.280474i	$-0.0904916\pi$
$774$	7.95644	+	20.2005i	0.285988	+	0.726092i
$775$		0			0
$776$	−36.0159			−1.29289
$777$	38.5464	+	7.81333i	1.38284	+	0.280302i
$778$		−	14.4519i		−	0.518125i
$779$			44.7986i			1.60508i
$780$		0			0
$781$	−9.41742			−0.336982
$782$		−	15.5960i		−	0.557711i
$783$	23.1494	−	14.6046i	0.827291	−	0.521926i
$784$	−8.95644	−	8.77548i	−0.319873	−	0.313410i
$785$		0			0
$786$	0.956439	+	5.03815i	0.0341151	+	0.179705i
$787$	6.32599			0.225497			0.112749	−	0.993624i	$-0.464035\pi$
$787$	6.32599			0.225497			0.112749	+	0.993624i	$0.464035\pi$
$788$	−2.79143			−0.0994406
$789$	−9.21861	−	48.5601i	−0.328191	−	1.72878i
$790$		0			0
$791$	44.0949	+	18.0017i	1.56783	+	0.640065i
$792$	10.3537	+	26.2867i	0.367901	+	0.934059i
$793$			16.7477i			0.594729i
$794$	−9.64789			−0.342391
$795$		0			0
$796$			6.21929i			0.220437i
$797$			17.7269i			0.627919i	0.949436	+	0.313960i	$0.101656\pi$
$797$			17.7269i			0.627919i	−0.949436	+	0.313960i	$0.898344\pi$
$798$	−21.6655	−	4.39158i	−0.766950	−	0.155460i
$799$	−7.25227			−0.256567
$800$		0			0
$801$	20.9820	−	8.26424i	0.741362	−	0.292003i
$802$		−	22.2087i		−	0.784217i
$803$			49.4809i			1.74614i
$804$	−5.60839	+	1.06469i	−0.197793	+	0.0375488i
$805$		0			0
$806$		−	18.4127i		−	0.648559i
$807$	6.77806	+	35.7042i	0.238599	+	1.25685i
$808$	56.1249			1.97447
$809$			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	$0.922824\pi$
$812$	4.16820	−	10.2100i	0.146275	−	0.358299i
$813$	−44.1103	+	8.37386i	−1.54701	+	0.293684i
$814$	28.9564			1.01492
$815$		0			0
$816$	8.20871	−	1.55834i	0.287362	−	0.0545527i
$817$	28.8826			1.01048
$818$			34.8917i			1.21996i
$819$	−19.4407	−	0.240744i	−0.679314	−	0.00841228i
$820$		0			0
$821$			17.1317i			0.597901i	0.954269	+	0.298950i	$0.0966365\pi$
$821$			17.1317i			0.597901i	−0.954269	+	0.298950i	$0.903363\pi$
$822$	−3.74166	−	19.7096i	−0.130505	−	0.687451i
$823$			2.25227i			0.0785093i	0.999229	+	0.0392546i	$0.0124984\pi$
$823$			2.25227i			0.0785093i	−0.999229	+	0.0392546i	$0.987502\pi$
$824$	13.4650			0.469076
$825$		0			0
$826$	20.2432	+	8.26424i	0.704350	+	0.287550i
$827$	−14.8850			−0.517602			−0.258801	−	0.965931i	$-0.583327\pi$
$827$	−14.8850			−0.517602			−0.258801	+	0.965931i	$0.583327\pi$
$828$	−11.6346	+	4.58258i	−0.404332	+	0.159256i
$829$			15.2082i			0.528202i	0.964495	+	0.264101i	$0.0850752\pi$
$829$			15.2082i			0.528202i	−0.964495	+	0.264101i	$0.914925\pi$
$830$		0			0
$831$	−31.9022	+	6.05630i	−1.10668	+	0.210091i
$832$	20.0005			0.693391
$833$	−13.1930	+	13.4650i	−0.457109	+	0.466535i
$834$	4.58258	−	0.869953i	0.158682	−	0.0301240i
$835$		0			0
$836$	10.6547			0.368501
$837$	−30.0473	+	18.9564i	−1.03859	+	0.655230i
$838$	23.0679			0.796867
$839$	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
$842$	8.97689			0.309364
$843$	26.1101	−	4.95673i	0.899280	−	0.170719i
$844$	11.6697			0.401688
$845$		0			0
$846$	−3.25507	−	8.26424i	−0.111912	−	0.284131i
$847$	3.87650	+	1.58258i	0.133198	+	0.0543779i
$848$	−7.05541			−0.242284
$849$	−7.58258	−	39.9421i	−0.260233	−	1.37081i
$850$		0			0
$851$			45.2097i			1.54977i
$852$	4.13212	−	0.784439i	0.141564	−	0.0268745i
$853$	17.5510			0.600934			0.300467	−	0.953792i	$-0.402858\pi$
$853$	17.5510			0.600934			0.300467	+	0.953792i	$0.402858\pi$
$854$	−7.51695	+	18.4127i	−0.257225	+	0.630069i
$855$		0			0
$856$	32.3303			1.10503
$857$		−	46.7879i		−	1.59824i	−0.601169	−	0.799122i	$-0.705298\pi$
$857$		−	46.7879i		−	1.59824i	0.601169	−	0.799122i	$-0.294702\pi$
$858$	−14.0629	+	2.66970i	−0.480100	+	0.0911420i
$859$			47.9673i			1.63662i	0.574774	+	0.818312i	$0.305090\pi$
$859$			47.9673i			1.63662i	−0.574774	+	0.818312i	$0.694910\pi$
$860$		0			0
$861$	−9.29485	+	45.8553i	−0.316768	+	1.56275i
$862$		−	37.6697i		−	1.28303i
$863$	22.8582			0.778104			0.389052	−	0.921216i	$-0.372803\pi$
$863$	22.8582			0.778104			0.389052	+	0.921216i	$0.372803\pi$
$864$	−11.5565	−	18.3178i	−0.393159	−	0.623185i
$865$		0			0
$866$	1.12413			0.0381993
$867$	3.14892	+	16.5873i	0.106943	+	0.563335i
$868$	−5.41022	+	13.2523i	−0.183635	+	0.449811i
$869$		−	1.78780i		−	0.0606469i
$870$		0			0
$871$		−	10.2025i		−	0.345698i
$872$	15.3439			0.519610
$873$	−32.7591	+	12.9030i	−1.10873	+	0.436699i
$874$		−	25.4107i		−	0.859529i
$875$		0			0
$876$	−4.12159	−	21.7109i	−0.139256	−	0.733545i
$877$		−	31.4955i		−	1.06353i	−0.846893	−	0.531763i	$-0.821530\pi$
$877$		−	31.4955i		−	1.06353i	0.846893	−	0.531763i	$-0.178470\pi$
$878$		−	29.6230i		−	0.999729i
$879$	3.62614	−	0.688383i	0.122307	−	0.0232186i
$880$		0			0
$881$	−34.8917			−1.17553			−0.587766	−	0.809031i	$-0.699993\pi$
$881$	−34.8917			−1.17553			−0.587766	+	0.809031i	$0.699993\pi$
$882$	−21.2654	−	8.99034i	−0.716042	−	0.302721i
$883$		−	15.4174i		−	0.518838i	−0.965765	−	0.259419i	$-0.916469\pi$
$883$		−	15.4174i		−	0.518838i	0.965765	−	0.259419i	$-0.0835310\pi$
$884$		−	5.21972i		−	0.175558i
$885$		0			0
$886$	4.33030			0.145479
$887$			40.2778i			1.35239i	0.736721	+	0.676197i	$0.236373\pi$
$887$			40.2778i			1.35239i	−0.736721	+	0.676197i	$0.763627\pi$
$888$	−44.8184	+	8.50830i	−1.50401	+	0.285520i
$889$	−8.16515	+	20.0005i	−0.273850	+	0.670794i
$890$		0			0
$891$	18.8348	+	20.2005i	0.630991	+	0.676742i
$892$	−1.93825			−0.0648975
$893$	−11.8162			−0.395414
$894$	33.6780	−	6.39342i	1.12636	−	0.213828i
$895$		0			0
$896$	1.56888	+	0.640492i	0.0524126	+	0.0213973i
$897$	−4.16820	−	21.9564i	−0.139172	−	0.733104i
$898$		−	40.0345i		−	1.33597i
$899$	36.0159			1.20120
$900$		0			0
$901$			10.6070i			0.353371i
$902$			34.4470i			1.14696i
$903$	29.5639	+	5.99259i	0.983826	+	0.199421i
$904$	−55.2432			−1.83736
$905$		0			0
$906$	−1.47928	−	7.79228i	−0.0491459	−	0.258881i
$907$		−	1.49545i		−	0.0496557i	−0.999692	−	0.0248279i	$-0.992096\pi$
$907$		−	1.49545i		−	0.0496557i	0.999692	−	0.0248279i	$-0.00790377\pi$
$908$		−	2.13094i		−	0.0707178i
$909$	51.0498	−	20.1072i	1.69321	−	0.666912i
$910$		0			0
$911$		−	10.4873i		−	0.347461i	−0.984793	−	0.173730i	$-0.944418\pi$
$911$		−	10.4873i		−	0.347461i	0.984793	−	0.173730i	$-0.0555821\pi$
$912$	13.3745	−	2.53901i	0.442875	−	0.0840752i
$913$	47.8606			1.58396
$914$		−	37.5617i		−	1.24243i
$915$		0			0
$916$			3.06743i			0.101351i
$917$	6.59649	+	2.69300i	0.217835	+	0.0889308i
$918$	13.0114	−	8.20871i	0.429440	−	0.270928i
$919$	24.0780			0.794261			0.397130	−	0.917762i	$-0.370006\pi$
$919$	24.0780			0.794261			0.397130	+	0.917762i	$0.370006\pi$
$920$		0			0
$921$	4.25227	+	22.3993i	0.140117	+	0.738083i
$922$	−36.6356			−1.20653
$923$			7.51695i			0.247423i
$924$	10.9060	+	2.21065i	0.358782	+	0.0727249i
$925$		0			0
$926$		−	14.0150i		−	0.460563i
$927$	12.2474	−	4.82395i	0.402259	−	0.158439i
$928$			21.9564i			0.720755i
$929$	−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
$932$	4.16820			0.136534
$933$	−3.98663	−	21.0000i	−0.130516	−	0.687509i
$934$			17.7644i			0.581268i
$935$		0			0
$936$	20.9820	−	8.26424i	0.685817	−	0.270125i
$937$	36.2311			1.18362			0.591809	−	0.806078i	$-0.298414\pi$
$937$	36.2311			1.18362			0.591809	+	0.806078i	$0.298414\pi$
$938$	4.57923	−	11.2168i	0.149517	−	0.366241i
$939$	7.41742	+	39.0721i	0.242058	+	1.27507i
$940$		0			0
$941$	25.2439			0.822926			0.411463	−	0.911426i	$-0.365018\pi$
$941$	25.2439			0.822926			0.411463	+	0.911426i	$0.365018\pi$
$942$	−0.688383	−	3.62614i	−0.0224287	−	0.118146i
$943$	−53.7821			−1.75139
$944$	−13.4650			−0.438249
$945$		0			0
$946$	22.2087			0.722068
$947$	−28.9479			−0.940681			−0.470340	−	0.882485i	$-0.655869\pi$
$947$	−28.9479			−0.940681			−0.470340	+	0.882485i	$0.655869\pi$
$948$	0.148917	+	0.784439i	0.00483662	+	0.0254774i
$949$	39.4955			1.28208
$950$		0			0
$951$	−0.429283	−	2.26129i	−0.0139204	−	0.0733275i
$952$	8.26424	−	20.2432i	0.267846	−	0.656085i
$953$	−5.26761			−0.170635			−0.0853173	−	0.996354i	$-0.527190\pi$
$953$	−5.26761			−0.170635			−0.0853173	+	0.996354i	$0.527190\pi$
$954$	−12.0871	+	4.76080i	−0.391335	+	0.154137i
$955$		0			0
$956$		−	11.4531i		−	0.370419i
$957$	−5.22202	−	27.5076i	−0.168804	−	0.889194i
$958$	8.26424			0.267006
$959$	−25.8059	−	10.5352i	−0.833317	−	0.340200i
$960$		0			0
$961$	−15.7477			−0.507991
$962$		−	23.1129i		−	0.745190i
$963$	29.4068	−	11.5826i	0.947622	−	0.373243i
$964$		−	15.1015i		−	0.486386i
$965$		0			0
$966$	5.27222	−	26.0101i	0.169631	−	0.836860i
$967$		−	14.7477i		−	0.474255i	−0.971479	−	0.237127i	$-0.923794\pi$
$967$		−	14.7477i		−	0.474255i	0.971479	−	0.237127i	$-0.0762059\pi$
$968$	−4.85658			−0.156096
$969$	−3.81713	−	20.1072i	−0.122624	−	0.645935i
$970$		0			0
$971$	−27.3748			−0.878499			−0.439250	−	0.898365i	$-0.644756\pi$
$971$	−27.3748			−0.878499			−0.439250	+	0.898365i	$0.644756\pi$
$972$	−9.94688	−	7.29457i	−0.319046	−	0.233974i
$973$	2.44949	−	6.00000i	0.0785270	−	0.192351i
$974$		−	24.0055i		−	0.769187i
$975$		0			0
$976$		−	12.2474i		−	0.392031i
$977$	−1.32888			−0.0425145			−0.0212572	−	0.999774i	$-0.506767\pi$
$977$	−1.32888			−0.0425145			−0.0212572	+	0.999774i	$0.506767\pi$
$978$	−7.48331	+	1.42063i	−0.239290	+	0.0454267i
$979$		−	23.0679i		−	0.737253i
$980$		0			0
$981$	13.9564	−	5.49707i	0.445595	−	0.175508i
$982$			28.9564i			0.924037i
$983$		−	15.5960i		−	0.497434i	−0.968576	−	0.248717i	$-0.919991\pi$
$983$		−	15.5960i		−	0.497434i	0.968576	−	0.248717i	$-0.0800089\pi$
$984$	−10.1216	−	53.3166i	−0.322665	−	1.69967i
$985$		0			0
$986$	−15.5960			−0.496677
$987$	−12.0949	−	2.45163i	−0.384986	−	0.0780364i
$988$		−	8.50455i		−	0.270566i
$989$			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	$0.732989\pi$
$992$		−	28.4989i		−	0.904842i
$993$	5.49171	+	28.9282i	0.174274	+	0.918009i
$994$	−3.37386	+	8.26424i	−0.107012	+	0.262126i
$995$		0			0
$996$	−21.0000	+	3.98663i	−0.665410	+	0.126321i
$997$	−25.0061			−0.791952			−0.395976	−	0.918261i	$-0.629594\pi$
$997$	−25.0061			−0.791952			−0.395976	+	0.918261i	$0.629594\pi$
$998$	−3.57560			−0.113184
$999$	−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.g.f.524.12		16
3.2	odd	2	inner	525.2.g.f.524.7		16
5.2	odd	4		525.2.b.h.251.6	yes	8
5.3	odd	4		525.2.b.i.251.3	yes	8
5.4	even	2	inner	525.2.g.f.524.5		16
7.6	odd	2	inner	525.2.g.f.524.9		16
15.2	even	4		525.2.b.h.251.3	✓	8
15.8	even	4		525.2.b.i.251.6	yes	8
15.14	odd	2	inner	525.2.g.f.524.10		16
21.20	even	2	inner	525.2.g.f.524.6		16
35.13	even	4		525.2.b.i.251.4	yes	8
35.27	even	4		525.2.b.h.251.5	yes	8
35.34	odd	2	inner	525.2.g.f.524.8		16
105.62	odd	4		525.2.b.h.251.4	yes	8
105.83	odd	4		525.2.b.i.251.5	yes	8
105.104	even	2	inner	525.2.g.f.524.11		16

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

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.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.09941 q^{2} +(0.323042 + 1.70166i) q^{3} -0.791288 q^{4} +(0.355157 + 1.87083i) q^{6} +(2.44949 + 1.00000i) q^{7} -3.06878 q^{8} +(-2.79129 + 1.09941i) q^{9} +O(q^{10})\)	\(q+1.09941 q^{2} +(0.323042 + 1.70166i) q^{3} -0.791288 q^{4} +(0.355157 + 1.87083i) q^{6} +(2.44949 + 1.00000i) q^{7} -3.06878 q^{8} +(-2.79129 + 1.09941i) q^{9} +3.06878i q^{11} +(-0.255619 - 1.34650i) q^{12} +2.44949 q^{13} +(2.69300 + 1.09941i) q^{14} -1.79129 q^{16} +2.69300i q^{17} +(-3.06878 + 1.20871i) q^{18} +4.38774i q^{19} +(-0.910371 + 4.49124i) q^{21} +3.37386i q^{22} -5.26761 q^{23} +(-0.991345 - 5.22202i) q^{24} +2.69300 q^{26} +(-2.77253 - 4.39466i) q^{27} +(-1.93825 - 0.791288i) q^{28} +5.26761i q^{29} -6.83723i q^{31} +4.16820 q^{32} +(-5.22202 + 0.991345i) q^{33} +2.96073i q^{34} +(2.20871 - 0.869953i) q^{36} -8.58258i q^{37} +4.82395i q^{38} +(0.791288 + 4.16820i) q^{39} +10.2100 q^{41} +(-1.00088 + 4.93773i) q^{42} -6.58258i q^{43} -2.42829i q^{44} -5.79129 q^{46} +2.69300i q^{47} +(-0.578661 - 3.04816i) q^{48} +(5.00000 + 4.89898i) q^{49} +(-4.58258 + 0.869953i) q^{51} -1.93825 q^{52} +3.93874 q^{53} +(-3.04816 - 4.83156i) q^{54} +(-7.51695 - 3.06878i) q^{56} +(-7.46644 + 1.41742i) q^{57} +5.79129i q^{58} +7.51695 q^{59} +6.83723i q^{61} -7.51695i q^{62} +(-7.93665 - 0.0982834i) q^{63} +8.16515 q^{64} +(-5.74117 + 1.08990i) q^{66} -4.16515i q^{67} -2.13094i q^{68} +(-1.70166 - 8.96368i) q^{69} +3.06878i q^{71} +(8.56585 - 3.37386i) q^{72} +16.1240 q^{73} -9.43581i q^{74} -3.47197i q^{76} +(-3.06878 + 7.51695i) q^{77} +(0.869953 + 4.58258i) q^{78} -0.582576 q^{79} +(6.58258 - 6.13756i) q^{81} +11.2250 q^{82} -15.5960i q^{83} +(0.720366 - 3.55386i) q^{84} -7.23698i q^{86} +(-8.96368 + 1.70166i) q^{87} -9.41742i q^{88} -7.51695 q^{89} +(6.00000 + 2.44949i) q^{91} +4.16820 q^{92} +(11.6346 - 2.20871i) q^{93} +2.96073i q^{94} +(1.34650 + 7.09285i) q^{96} +11.7362 q^{97} +(5.49707 + 5.38601i) q^{98} +(-3.37386 - 8.56585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 24 * q^4 - 8 * q^9	\( 16 q + 24 q^{4} - 8 q^{9} + 8 q^{16} - 24 q^{21} + 72 q^{36} - 24 q^{39} - 56 q^{46} + 80 q^{49} - 16 q^{64} + 64 q^{79} + 32 q^{81} - 120 q^{84} + 96 q^{91} + 56 q^{99}+O(q^{100}) \) 16 * q + 24 * q^4 - 8 * q^9 + 8 * q^16 - 24 * q^21 + 72 * q^36 - 24 * q^39 - 56 * q^46 + 80 * q^49 - 16 * q^64 + 64 * q^79 + 32 * q^81 - 120 * q^84 + 96 * q^91 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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