LMFDB - Embedded newform 825.2.f.g.626.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(626,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, 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("825.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.f (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:	$6.58765816676$
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} - 2 x^{15} - 17 x^{14} + 26 x^{13} + 191 x^{12} - 390 x^{11} - 539 x^{10} + 1484 x^{9} + \cdots + 102940 $ x^16 - 2x^15 - 17x^14 + 26x^13 + 191x^12 - 390x^11 - 539x^10 + 1484x^9 + 1787x^8 - 704x^7 + 14278x^6 - 10982x^5 + 73951x^4 + 70936x^3 + 207288x^2 + 119752*x + 102940
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.3
Root			$-0.411184 + 0.840091i$ of defining polynomial
Character	$\chi$	$=$	825.626
Dual form			825.2.f.g.626.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92586 q^{2} +(1.51468 - 0.840091i) q^{3} +1.70894 q^{4} +(-2.91706 + 1.61790i) q^{6} +3.14352i q^{7} +0.560539 q^{8} +(1.58849 - 2.54493i) q^{9} +O(q^{10})$	\(q-1.92586 q^{2} +(1.51468 - 0.840091i) q^{3} +1.70894 q^{4} +(-2.91706 + 1.61790i) q^{6} +3.14352i q^{7} +0.560539 q^{8} +(1.58849 - 2.54493i) q^{9} +(0.166374 - 3.31245i) q^{11} +(2.58849 - 1.43567i) q^{12} -1.94903i q^{13} -6.05398i q^{14} -4.49740 q^{16} -3.57551 q^{17} +(-3.05922 + 4.90119i) q^{18} -6.65886i q^{19} +(2.64084 + 4.76142i) q^{21} +(-0.320413 + 6.37932i) q^{22} +3.98060i q^{23} +(0.849035 - 0.470903i) q^{24} +3.75357i q^{26} +(0.268081 - 5.18923i) q^{27} +5.37209i q^{28} +4.99736 q^{29} +6.03356 q^{31} +7.54030 q^{32} +(-2.53076 - 5.15706i) q^{33} +6.88593 q^{34} +(2.71464 - 4.34914i) q^{36} +9.52676 q^{37} +12.8240i q^{38} +(-1.63736 - 2.95216i) q^{39} -0.227791 q^{41} +(-5.08590 - 9.16983i) q^{42} -7.57380i q^{43} +(0.284323 - 5.66078i) q^{44} -7.66608i q^{46} +4.32448i q^{47} +(-6.81211 + 3.77823i) q^{48} -2.88172 q^{49} +(-5.41574 + 3.00375i) q^{51} -3.33078i q^{52} +1.53503i q^{53} +(-0.516287 + 9.99374i) q^{54} +1.76206i q^{56} +(-5.59404 - 10.0860i) q^{57} -9.62423 q^{58} -5.56495i q^{59} -5.46437i q^{61} -11.6198 q^{62} +(8.00005 + 4.99346i) q^{63} -5.52676 q^{64} +(4.87388 + 9.93178i) q^{66} -6.46805 q^{67} -6.11033 q^{68} +(3.34407 + 6.02932i) q^{69} -9.07047i q^{71} +(0.890413 - 1.42653i) q^{72} -13.0382i q^{73} -18.3472 q^{74} -11.3796i q^{76} +(10.4128 + 0.523000i) q^{77} +(3.15334 + 5.68544i) q^{78} +11.5641i q^{79} +(-3.95337 - 8.08522i) q^{81} +0.438693 q^{82} +5.54979 q^{83} +(4.51305 + 8.13699i) q^{84} +14.5861i q^{86} +(7.56939 - 4.19824i) q^{87} +(0.0932591 - 1.85676i) q^{88} +3.01648i q^{89} +6.12682 q^{91} +6.80261i q^{92} +(9.13890 - 5.06874i) q^{93} -8.32835i q^{94} +(11.4211 - 6.33453i) q^{96} -5.38853 q^{97} +5.54979 q^{98} +(-8.16568 - 5.68522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9	$ 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9} + 6 q^{12} + 32 q^{16} + 28 q^{22} + 2 q^{27} - 12 q^{31} - 20 q^{33} + 28 q^{34} - 36 q^{36} + 4 q^{37} + 58 q^{42} - 40 q^{48} - 28 q^{49} - 16 q^{58} + 60 q^{64} - 30 q^{66} - 44 q^{67} + 44 q^{69} - 44 q^{78} - 26 q^{81} - 8 q^{82} + 76 q^{88} + 64 q^{91} - 14 q^{93} - 108 q^{97} + 14 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9 + 6 * q^12 + 32 * q^16 + 28 * q^22 + 2 * q^27 - 12 * q^31 - 20 * q^33 + 28 * q^34 - 36 * q^36 + 4 * q^37 + 58 * q^42 - 40 * q^48 - 28 * q^49 - 16 * q^58 + 60 * q^64 - 30 * q^66 - 44 * q^67 + 44 * q^69 - 44 * q^78 - 26 * q^81 - 8 * q^82 + 76 * q^88 + 64 * q^91 - 14 * q^93 - 108 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.92586			−1.36179			−0.680895	−	0.732381i	$-0.738409\pi$
$2$	−1.92586			−1.36179			−0.680895	+	0.732381i	$0.738409\pi$
$3$	1.51468	−	0.840091i	0.874499	−	0.485027i
$3$	1.51468	−	0.840091i	0.874499	−	0.485027i
$4$	1.70894			0.854471
$5$		0			0
$5$		0			0
$6$	−2.91706	+	1.61790i	−1.19088	+	0.660504i
$7$			3.14352i			1.18814i	0.804414	+	0.594070i	$0.202480\pi$
$7$			3.14352i			1.18814i	−0.804414	+	0.594070i	$0.797520\pi$
$8$	0.560539			0.198180
$9$	1.58849	−	2.54493i	0.529498	−	0.848311i
$10$		0			0
$11$	0.166374	−	3.31245i	0.0501637	−	0.998741i
$11$	0.166374	−	3.31245i	0.0501637	−	0.998741i
$12$	2.58849	−	1.43567i	0.747234	−	0.414441i
$13$		−	1.94903i		−	0.540564i	−0.962781	−	0.270282i	$-0.912883\pi$
$13$		−	1.94903i		−	0.540564i	0.962781	−	0.270282i	$-0.0871170\pi$
$14$		−	6.05398i		−	1.61800i
$15$		0			0
$16$	−4.49740			−1.12435
$17$	−3.57551			−0.867188			−0.433594	−	0.901108i	$-0.642755\pi$
$17$	−3.57551			−0.867188			−0.433594	+	0.901108i	$0.642755\pi$
$18$	−3.05922	+	4.90119i	−0.721065	+	1.15522i
$19$		−	6.65886i		−	1.52765i	−0.645426	−	0.763823i	$-0.723320\pi$
$19$		−	6.65886i		−	1.52765i	0.645426	−	0.763823i	$-0.276680\pi$
$20$		0			0
$21$	2.64084	+	4.76142i	0.576279	+	1.03903i
$22$	−0.320413	+	6.37932i	−0.0683123	+	1.36008i
$23$			3.98060i			0.830012i	0.909819	+	0.415006i	$0.136221\pi$
$23$			3.98060i			0.830012i	−0.909819	+	0.415006i	$0.863779\pi$
$24$	0.849035	−	0.470903i	0.173309	−	0.0961228i
$25$		0			0
$26$			3.75357i			0.736135i
$27$	0.268081	−	5.18923i	0.0515923	−	0.998668i
$28$			5.37209i			1.01523i
$29$	4.99736			0.927987			0.463993	−	0.885839i	$-0.346416\pi$
$29$	4.99736			0.927987			0.463993	+	0.885839i	$0.346416\pi$
$30$		0			0
$31$	6.03356			1.08366			0.541830	−	0.840488i	$-0.317732\pi$
$31$	6.03356			1.08366			0.541830	+	0.840488i	$0.317732\pi$
$32$	7.54030			1.33295
$33$	−2.53076	−	5.15706i	−0.440548	−	0.897729i
$34$	6.88593			1.18093
$35$		0			0
$36$	2.71464	−	4.34914i	0.452441	−	0.724857i
$37$	9.52676			1.56619			0.783095	−	0.621903i	$-0.213640\pi$
$37$	9.52676			1.56619			0.783095	+	0.621903i	$0.213640\pi$
$38$			12.8240i			2.08033i
$39$	−1.63736	−	2.95216i	−0.262188	−	0.472723i
$40$		0			0
$41$	−0.227791			−0.0355749			−0.0177875	−	0.999842i	$-0.505662\pi$
$41$	−0.227791			−0.0355749			−0.0177875	+	0.999842i	$0.505662\pi$
$42$	−5.08590	−	9.16983i	−0.784771	−	1.41494i
$43$		−	7.57380i		−	1.15499i	−0.816393	−	0.577497i	$-0.804029\pi$
$43$		−	7.57380i		−	1.15499i	0.816393	−	0.577497i	$-0.195971\pi$
$44$	0.284323	−	5.66078i	0.0428634	−	0.853395i
$45$		0			0
$46$		−	7.66608i		−	1.13030i
$47$			4.32448i			0.630790i	0.948960	+	0.315395i	$0.102137\pi$
$47$			4.32448i			0.630790i	−0.948960	+	0.315395i	$0.897863\pi$
$48$	−6.81211	+	3.77823i	−0.983244	+	0.545340i
$49$	−2.88172			−0.411674
$50$		0			0
$51$	−5.41574	+	3.00375i	−0.758355	+	0.420609i
$52$		−	3.33078i		−	0.461896i
$53$			1.53503i			0.210853i	0.994427	+	0.105426i	$0.0336208\pi$
$53$			1.53503i			0.210853i	−0.994427	+	0.105426i	$0.966379\pi$
$54$	−0.516287	+	9.99374i	−0.0702578	+	1.35998i
$55$		0			0
$56$			1.76206i			0.235466i
$57$	−5.59404	−	10.0860i	−0.740949	−	1.33593i
$58$	−9.62423			−1.26372
$59$		−	5.56495i		−	0.724495i	−0.932082	−	0.362248i	$-0.882010\pi$
$59$		−	5.56495i		−	0.724495i	0.932082	−	0.362248i	$-0.117990\pi$
$60$		0			0
$61$		−	5.46437i		−	0.699641i	−0.936817	−	0.349820i	$-0.886243\pi$
$61$		−	5.46437i		−	0.699641i	0.936817	−	0.349820i	$-0.113757\pi$
$62$	−11.6198			−1.47572
$63$	8.00005	+	4.99346i	1.00791	+	0.629117i
$64$	−5.52676			−0.690845
$65$		0			0
$66$	4.87388	+	9.93178i	0.599934	+	1.22252i
$67$	−6.46805			−0.790198			−0.395099	−	0.918639i	$-0.629290\pi$
$67$	−6.46805			−0.790198			−0.395099	+	0.918639i	$0.629290\pi$
$68$	−6.11033			−0.740987
$69$	3.34407	+	6.02932i	0.402578	+	0.725845i
$70$		0			0
$71$		−	9.07047i		−	1.07647i	−0.842796	−	0.538233i	$-0.819092\pi$
$71$		−	9.07047i		−	1.07647i	0.842796	−	0.538233i	$-0.180908\pi$
$72$	0.890413	−	1.42653i	0.104936	−	0.168119i
$73$		−	13.0382i		−	1.52600i	−0.646397	−	0.763001i	$-0.723725\pi$
$73$		−	13.0382i		−	1.52600i	0.646397	−	0.763001i	$-0.276275\pi$
$74$	−18.3472			−2.13282
$75$		0			0
$76$		−	11.3796i		−	1.30533i
$77$	10.4128	+	0.523000i	1.18664	+	0.0596014i
$78$	3.15334	+	5.68544i	0.357045	+	0.643749i
$79$			11.5641i			1.30107i	0.759477	+	0.650534i	$0.225455\pi$
$79$			11.5641i			1.30107i	−0.759477	+	0.650534i	$0.774545\pi$
$80$		0			0
$81$	−3.95337	−	8.08522i	−0.439263	−	0.898358i
$82$	0.438693			0.0484456
$83$	5.54979			0.609169			0.304584	−	0.952485i	$-0.401482\pi$
$83$	5.54979			0.609169			0.304584	+	0.952485i	$0.401482\pi$
$84$	4.51305	+	8.13699i	0.492414	+	0.887818i
$85$		0			0
$86$			14.5861i			1.57286i
$87$	7.56939	−	4.19824i	0.811524	−	0.450098i
$88$	0.0932591	−	1.85676i	0.00994145	−	0.197931i
$89$			3.01648i			0.319746i	0.987138	+	0.159873i	$0.0511085\pi$
$89$			3.01648i			0.319746i	−0.987138	+	0.159873i	$0.948891\pi$
$90$		0			0
$91$	6.12682			0.642266
$92$			6.80261i			0.709221i
$93$	9.13890	−	5.06874i	0.947660	−	0.525604i
$94$		−	8.32835i		−	0.859004i
$95$		0			0
$96$	11.4211	−	6.33453i	1.16566	−	0.646516i
$97$	−5.38853			−0.547122			−0.273561	−	0.961855i	$-0.588202\pi$
$97$	−5.38853			−0.547122			−0.273561	+	0.961855i	$0.588202\pi$
$98$	5.54979			0.560614
$99$	−8.16568	−	5.68522i	−0.820682	−	0.571386i
$100$		0			0
$101$	−13.8138			−1.37452			−0.687261	−	0.726411i	$-0.741187\pi$
$101$	−13.8138			−1.37452			−0.687261	+	0.726411i	$0.741187\pi$
$102$	10.4300	−	5.78481i	1.03272	−	0.572781i
$103$	−5.67018			−0.558700			−0.279350	−	0.960189i	$-0.590119\pi$
$103$	−5.67018			−0.558700			−0.279350	+	0.960189i	$0.590119\pi$
$104$		−	1.09251i		−	0.107129i
$105$		0			0
$106$		−	2.95626i		−	0.287137i
$107$	20.5657			1.98817			0.994083	−	0.108626i	$-0.0346452\pi$
$107$	20.5657			1.98817			0.994083	+	0.108626i	$0.0346452\pi$
$108$	0.458135	−	8.86809i	0.0440841	−	0.853333i
$109$			4.61755i			0.442281i	0.975242	+	0.221140i	$0.0709779\pi$
$109$			4.61755i			0.442281i	−0.975242	+	0.221140i	$0.929022\pi$
$110$		0			0
$111$	14.4300	−	8.00334i	1.36963	−	0.759644i
$112$		−	14.1377i		−	1.33588i
$113$		−	15.6135i		−	1.46879i	−0.678721	−	0.734396i	$-0.737465\pi$
$113$		−	15.6135i		−	1.46879i	0.678721	−	0.734396i	$-0.262535\pi$
$114$	10.7734	+	19.4243i	1.00902	+	1.81925i
$115$		0			0
$116$	8.54020			0.792938
$117$	−4.96016	−	3.09603i	−0.458567	−	0.286228i
$118$			10.7173i			0.986610i
$119$		−	11.2397i		−	1.03034i
$120$		0			0
$121$	−10.9446	−	1.10221i	−0.994967	−	0.100201i
$122$			10.5236i			0.952763i
$123$	−0.345029	+	0.191365i	−0.0311102	+	0.0172548i
$124$	10.3110			0.925956
$125$		0			0
$126$	−15.4070	−	9.61672i	−1.37256	−	0.856726i
$127$		−	5.09255i		−	0.451891i	−0.974140	−	0.225946i	$-0.927453\pi$
$127$		−	5.09255i		−	0.451891i	0.974140	−	0.225946i	$-0.0725471\pi$
$128$	−4.43682			−0.392164
$129$	−6.36268	−	11.4719i	−0.560203	−	1.01004i
$130$		0			0
$131$	19.9887			1.74643			0.873213	−	0.487340i	$-0.162033\pi$
$131$	19.9887			1.74643			0.873213	+	0.487340i	$0.162033\pi$
$132$	−4.32491	−	8.81311i	−0.376435	−	0.767083i
$133$	20.9322			1.81506
$134$	12.4566			1.07608
$135$		0			0
$136$	−2.00421			−0.171860
$137$			21.6535i			1.84998i	0.379985	+	0.924992i	$0.375929\pi$
$137$			21.6535i			1.84998i	−0.379985	+	0.924992i	$0.624071\pi$
$138$	−6.44021	−	11.6116i	−0.548227	−	0.988448i
$139$		−	3.05124i		−	0.258803i	−0.991592	−	0.129402i	$-0.958694\pi$
$139$		−	3.05124i		−	0.258803i	0.991592	−	0.129402i	$-0.0413056\pi$
$140$		0			0
$141$	3.63296	+	6.55019i	0.305950	+	0.551626i
$142$			17.4685i			1.46592i
$143$	−6.45607	−	0.324268i	−0.539884	−	0.0271167i
$144$	−7.14410	+	11.4456i	−0.595342	+	0.953799i
$145$		0			0
$146$			25.1097i			2.07809i
$147$	−4.36488	+	2.42091i	−0.360009	+	0.199673i
$148$	16.2807			1.33826
$149$	7.40267			0.606450			0.303225	−	0.952919i	$-0.401937\pi$
$149$	7.40267			0.606450			0.303225	+	0.952919i	$0.401937\pi$
$150$		0			0
$151$			20.9947i			1.70853i	0.519842	+	0.854263i	$0.325991\pi$
$151$			20.9947i			1.70853i	−0.519842	+	0.854263i	$0.674009\pi$
$152$		−	3.73255i		−	0.302750i
$153$	−5.67967	+	9.09943i	−0.459174	+	0.735645i
$154$	−20.0535	−	1.00723i	−1.61596	−	0.0811646i
$155$		0			0
$156$	−2.79816	−	5.04506i	−0.224032	−	0.403928i
$157$	−8.18120			−0.652931			−0.326465	−	0.945209i	$-0.605858\pi$
$157$	−8.18120			−0.652931			−0.326465	+	0.945209i	$0.605858\pi$
$158$		−	22.2709i		−	1.77178i
$159$	1.28957	+	2.32508i	0.102269	+	0.184391i
$160$		0			0
$161$	−12.5131			−0.986170
$162$	7.61364	+	15.5710i	0.598184	+	1.22337i
$163$	−1.00421			−0.0786558			−0.0393279	−	0.999226i	$-0.512522\pi$
$163$	−1.00421			−0.0786558			−0.0393279	+	0.999226i	$0.512522\pi$
$164$	−0.389281			−0.0303977
$165$		0			0
$166$	−10.6881			−0.829560
$167$	−23.6454			−1.82973			−0.914866	−	0.403757i	$-0.867704\pi$
$167$	−23.6454			−1.82973			−0.914866	+	0.403757i	$0.867704\pi$
$168$	1.48029	+	2.66896i	0.114207	+	0.205915i
$169$	9.20127			0.707790
$170$		0			0
$171$	−16.9463	−	10.5776i	−1.29592	−	0.808886i
$172$		−	12.9432i		−	0.986909i
$173$	11.5535			0.878397			0.439198	−	0.898390i	$-0.355262\pi$
$173$	11.5535			0.878397			0.439198	+	0.898390i	$0.355262\pi$
$174$	−14.5776	+	8.08522i	−1.10512	+	0.612939i
$175$		0			0
$176$	−0.748251	+	14.8974i	−0.0564015	+	1.12294i
$177$	−4.67507	−	8.42911i	−0.351399	−	0.633570i
$178$		−	5.80933i		−	0.435427i
$179$			18.2085i			1.36096i	0.732765	+	0.680482i	$0.238230\pi$
$179$			18.2085i			1.36096i	−0.732765	+	0.680482i	$0.761770\pi$
$180$		0			0
$181$	4.02935			0.299500			0.149750	−	0.988724i	$-0.452153\pi$
$181$	4.02935			0.299500			0.149750	+	0.988724i	$0.452153\pi$
$182$	−11.7994			−0.874631
$183$	−4.59057	−	8.27675i	−0.339344	−	0.611835i
$184$			2.23128i			0.164492i
$185$		0			0
$186$	−17.6003	+	9.76170i	−1.29051	+	0.715762i
$187$	−0.594872	+	11.8437i	−0.0435013	+	0.866096i
$188$			7.39028i			0.538992i
$189$	16.3125	+	0.842719i	1.18656	+	0.0612988i
$190$		0			0
$191$		−	0.475086i		−	0.0343760i	−0.999852	−	0.0171880i	$-0.994529\pi$
$191$		−	0.475086i		−	0.0343760i	0.999852	−	0.0171880i	$-0.00547138\pi$
$192$	−8.37125	+	4.64298i	−0.604143	+	0.335078i
$193$			7.01473i			0.504931i	0.967606	+	0.252466i	$0.0812414\pi$
$193$			7.01473i			0.504931i	−0.967606	+	0.252466i	$0.918759\pi$
$194$	10.3776			0.745065
$195$		0			0
$196$	−4.92469			−0.351764
$197$	−8.52444			−0.607342			−0.303671	−	0.952777i	$-0.598212\pi$
$197$	−8.52444			−0.607342			−0.303671	+	0.952777i	$0.598212\pi$
$198$	15.7260	+	10.9489i	1.11760	+	0.778107i
$199$	18.9740			1.34503			0.672515	−	0.740083i	$-0.265214\pi$
$199$	18.9740			1.34503			0.672515	+	0.740083i	$0.265214\pi$
$200$		0			0
$201$	−9.79700	+	5.43375i	−0.691027	+	0.383267i
$202$	26.6034			1.87181
$203$			15.7093i			1.10258i
$204$	−9.25518	+	5.13323i	−0.647992	+	0.359398i
$205$		0			0
$206$	10.9200			0.760831
$207$	10.1304	+	6.32316i	0.704109	+	0.439490i
$208$			8.76558i			0.607784i
$209$	−22.0571	−	1.10786i	−1.52572	−	0.0766323i
$210$		0			0
$211$			6.72698i			0.463105i	0.972822	+	0.231552i	$0.0743804\pi$
$211$			6.72698i			0.463105i	−0.972822	+	0.231552i	$0.925620\pi$
$212$			2.62328i			0.180168i
$213$	−7.62002	−	13.7388i	−0.522115	−	0.941369i
$214$	−39.6068			−2.70746
$215$		0			0
$216$	0.150270	−	2.90877i	0.0102246	−	0.197916i
$217$			18.9666i			1.28754i
$218$		−	8.89275i		−	0.602293i
$219$	−10.9533	−	19.7486i	−0.740152	−	1.33449i
$220$		0			0
$221$			6.96878i			0.468771i
$222$	−27.7901	+	15.4133i	−1.86515	+	1.03447i
$223$	−22.6915			−1.51953			−0.759767	−	0.650196i	$-0.774687\pi$
$223$	−22.6915			−1.51953			−0.759767	+	0.650196i	$0.774687\pi$
$224$			23.7031i			1.58373i
$225$		0			0
$226$			30.0694i			2.00019i
$227$	−11.0750			−0.735075			−0.367538	−	0.930009i	$-0.619799\pi$
$227$	−11.0750			−0.735075			−0.367538	+	0.930009i	$0.619799\pi$
$228$	−9.55989	−	17.2364i	−0.633119	−	1.14151i
$229$	−11.0715			−0.731623			−0.365811	−	0.930689i	$-0.619208\pi$
$229$	−11.0715			−0.731623			−0.365811	+	0.930689i	$0.619208\pi$
$230$		0			0
$231$	16.2113	−	7.95548i	1.06663	−	0.523432i
$232$	2.80122			0.183909
$233$	−17.5686			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$233$	−17.5686			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$234$	9.55258	+	5.96252i	0.624471	+	0.389782i
$235$		0			0
$236$		−	9.51018i		−	0.619060i
$237$	9.71493	+	17.5160i	0.631053	+	1.13778i
$238$			21.6461i			1.40311i
$239$	9.94630			0.643373			0.321686	−	0.946846i	$-0.395750\pi$
$239$	9.94630			0.643373			0.321686	+	0.946846i	$0.395750\pi$
$240$		0			0
$241$			25.3569i			1.63338i	0.577077	+	0.816690i	$0.304193\pi$
$241$			25.3569i			1.63338i	−0.577077	+	0.816690i	$0.695807\pi$
$242$	21.0779	+	2.12271i	1.35494	+	0.136453i
$243$	−12.7804	−	8.92532i	−0.819863	−	0.572559i
$244$		−	9.33828i		−	0.597822i
$245$		0			0
$246$	0.664479	−	0.368542i	0.0423656	−	0.0234974i
$247$	−12.9783			−0.825791
$248$	3.38205			0.214760
$249$	8.40615	−	4.66233i	0.532718	−	0.295463i
$250$		0			0
$251$		−	16.9540i		−	1.07013i	−0.844811	−	0.535065i	$-0.820287\pi$
$251$		−	16.9540i		−	1.07013i	0.844811	−	0.535065i	$-0.179713\pi$
$252$	13.6716	+	8.53354i	0.861231	+	0.537562i
$253$	13.1855	+	0.662268i	0.828967	+	0.0416365i
$254$			9.80755i			0.615380i
$255$		0			0
$256$	19.5982			1.22489
$257$			24.4076i			1.52250i	0.648456	+	0.761252i	$0.275415\pi$
$257$			24.4076i			1.52250i	−0.648456	+	0.761252i	$0.724585\pi$
$258$	12.2536	+	22.0932i	0.762879	+	1.37546i
$259$			29.9476i			1.86085i
$260$		0			0
$261$	7.93828	−	12.7180i	0.491367	−	0.787222i
$262$	−38.4956			−2.37826
$263$	7.74352			0.477486			0.238743	−	0.971083i	$-0.423265\pi$
$263$	7.74352			0.477486			0.238743	+	0.971083i	$0.423265\pi$
$264$	−1.41859	−	2.89073i	−0.0873080	−	0.177912i
$265$		0			0
$266$	−40.3126			−2.47172
$267$	2.53412	+	4.56900i	0.155086	+	0.279618i
$268$	−11.0535			−0.675201
$269$		−	2.65825i		−	0.162076i	−0.996711	−	0.0810380i	$-0.974176\pi$
$269$		−	2.65825i		−	0.162076i	0.996711	−	0.0810380i	$-0.0258235\pi$
$270$		0			0
$271$		−	24.9768i		−	1.51724i	−0.651536	−	0.758618i	$-0.725875\pi$
$271$		−	24.9768i		−	1.51724i	0.651536	−	0.758618i	$-0.274125\pi$
$272$	16.0805			0.975023
$273$	9.28016	−	5.14709i	0.561661	−	0.311516i
$274$		−	41.7017i		−	2.51929i
$275$		0			0
$276$	5.71481	+	10.3038i	0.343991	+	0.620213i
$277$		−	2.13359i		−	0.128195i	−0.997944	−	0.0640974i	$-0.979583\pi$
$277$		−	2.13359i		−	0.128195i	0.997944	−	0.0640974i	$-0.0204168\pi$
$278$			5.87627i			0.352435i
$279$	9.58428	−	15.3550i	0.573796	−	0.919281i
$280$		0			0
$281$	15.6347			0.932687			0.466343	−	0.884604i	$-0.345571\pi$
$281$	15.6347			0.932687			0.466343	+	0.884604i	$0.345571\pi$
$282$	−6.99657	−	12.6148i	−0.416640	−	0.751198i
$283$			10.4619i			0.621898i	0.950427	+	0.310949i	$0.100647\pi$
$283$			10.4619i			0.621898i	−0.950427	+	0.310949i	$0.899353\pi$
$284$		−	15.5009i		−	0.919809i
$285$		0			0
$286$	12.4335	+	0.624496i	0.735208	+	0.0369272i
$287$		−	0.716065i		−	0.0422680i
$288$	11.9777	−	19.1895i	0.705794	−	1.13075i
$289$	−4.21575			−0.247985
$290$		0			0
$291$	−8.16188	+	4.52685i	−0.478458	+	0.265369i
$292$		−	22.2815i		−	1.30392i
$293$	−5.82601			−0.340359			−0.170180	−	0.985413i	$-0.554435\pi$
$293$	−5.82601			−0.340359			−0.170180	+	0.985413i	$0.554435\pi$
$294$	8.40615	−	4.66233i	0.490256	−	0.271913i
$295$		0			0
$296$	5.34012			0.310388
$297$	−17.1445	−	1.75136i	−0.994823	−	0.101624i
$298$	−14.2565			−0.825857
$299$	7.75832			0.448675
$300$		0			0
$301$	23.8084			1.37229
$302$		−	40.4329i		−	2.32665i
$303$	−20.9234	+	11.6048i	−1.20202	+	0.666680i
$304$			29.9476i			1.71761i
$305$		0			0
$306$	10.9383	−	17.5242i	0.625299	−	1.00179i
$307$		−	5.36118i		−	0.305979i	−0.988228	−	0.152989i	$-0.951110\pi$
$307$		−	5.36118i		−	0.305979i	0.988228	−	0.152989i	$-0.0488900\pi$
$308$	17.7948	+	0.893777i	1.01395	+	0.0509276i
$309$	−8.58849	+	4.76347i	−0.488582	+	0.270984i
$310$		0			0
$311$		−	23.4789i		−	1.33136i	−0.746236	−	0.665682i	$-0.768141\pi$
$311$		−	23.4789i		−	1.33136i	0.746236	−	0.665682i	$-0.231859\pi$
$312$	−0.917806	−	1.65480i	−0.0519605	−	0.0936845i
$313$	7.19792			0.406851			0.203425	−	0.979090i	$-0.434793\pi$
$313$	7.19792			0.406851			0.203425	+	0.979090i	$0.434793\pi$
$314$	15.7559			0.889154
$315$		0			0
$316$			19.7624i			1.11172i
$317$			10.9777i			0.616568i	0.951294	+	0.308284i	$0.0997547\pi$
$317$			10.9777i			0.616568i	−0.951294	+	0.308284i	$0.900245\pi$
$318$	−2.48353	−	4.47778i	−0.139269	−	0.251101i
$319$	0.831431	−	16.5535i	0.0465512	−	0.926819i
$320$		0			0
$321$	31.1505	−	17.2771i	1.73865	−	0.964313i
$322$	24.0985			1.34296
$323$			23.8088i			1.32476i
$324$	−6.75608	−	13.8172i	−0.375338	−	0.767621i
$325$		0			0
$326$	1.93397			0.107113
$327$	3.87916	+	6.99409i	0.214518	+	0.386774i
$328$	−0.127685			−0.00705025
$329$	−13.5941			−0.749467
$330$		0			0
$331$	−11.8021			−0.648701			−0.324350	−	0.945937i	$-0.605146\pi$
$331$	−11.8021			−0.648701			−0.324350	+	0.945937i	$0.605146\pi$
$332$	9.48427			0.520517
$333$	15.1332	−	24.2450i	0.829294	−	1.32862i
$334$	45.5377			2.49171
$335$		0			0
$336$	−11.8769	−	21.4140i	−0.647940	−	1.16823i
$337$		−	24.2305i		−	1.31992i	−0.751301	−	0.659960i	$-0.770573\pi$
$337$		−	24.2305i		−	1.31992i	0.751301	−	0.659960i	$-0.229427\pi$
$338$	−17.7204			−0.963861
$339$	−13.1167	−	23.6494i	−0.712404	−	1.28446i
$340$		0			0
$341$	1.00383	−	19.9859i	0.0543604	−	1.08230i
$342$	32.6363	+	20.3709i	1.76477	+	1.10153i
$343$			12.9459i			0.699013i
$344$		−	4.24541i		−	0.228897i
$345$		0			0
$346$	−22.2505			−1.19619
$347$	−1.60887			−0.0863685			−0.0431843	−	0.999067i	$-0.513750\pi$
$347$	−1.60887			−0.0863685			−0.0431843	+	0.999067i	$0.513750\pi$
$348$	12.9356	−	7.17454i	0.693423	−	0.384596i
$349$			35.5992i			1.90558i	0.303629	+	0.952790i	$0.401802\pi$
$349$			35.5992i			1.90558i	−0.303629	+	0.952790i	$0.598198\pi$
$350$		0			0
$351$	−10.1140	−	0.522499i	−0.539844	−	0.0278889i
$352$	1.25451	−	24.9768i	0.0668656	−	1.33127i
$353$			12.0586i			0.641817i	0.947110	+	0.320908i	$0.103988\pi$
$353$			12.0586i			0.641817i	−0.947110	+	0.320908i	$0.896012\pi$
$354$	9.00353	+	16.2333i	0.478532	+	0.862790i
$355$		0			0
$356$			5.15499i			0.273214i
$357$	−9.44235	−	17.0245i	−0.499742	−	0.901031i
$358$		−	35.0670i		−	1.85335i
$359$	−22.4611			−1.18545			−0.592725	−	0.805405i	$-0.701948\pi$
$359$	−22.4611			−1.18545			−0.592725	+	0.805405i	$0.701948\pi$
$360$		0			0
$361$	−25.3404			−1.33370
$362$	−7.75998			−0.407855
$363$	−17.5036	+	7.52500i	−0.918698	+	0.394960i
$364$	10.4704			0.548797
$365$		0			0
$366$	8.84079	+	15.9399i	0.462116	+	0.833191i
$367$	13.6953			0.714890			0.357445	−	0.933934i	$-0.383648\pi$
$367$	13.6953			0.714890			0.357445	+	0.933934i	$0.383648\pi$
$368$		−	17.9024i		−	0.933225i
$369$	−0.361844	+	0.579712i	−0.0188369	+	0.0301786i
$370$		0			0
$371$	−4.82540			−0.250522
$372$	15.6178	−	8.66218i	0.809748	−	0.449113i
$373$			11.1841i			0.579092i	0.957164	+	0.289546i	$0.0935043\pi$
$373$			11.1841i			0.579092i	−0.957164	+	0.289546i	$0.906496\pi$
$374$	1.14564	−	22.8093i	0.0592396	−	1.17944i
$375$		0			0
$376$			2.42404i			0.125010i
$377$		−	9.74002i		−	0.501637i
$378$	−31.4155	−	1.62296i	−1.61584	−	0.0834760i
$379$	−8.14256			−0.418255			−0.209128	−	0.977888i	$-0.567062\pi$
$379$	−8.14256			−0.418255			−0.209128	+	0.977888i	$0.567062\pi$
$380$		0			0
$381$	−4.27821	−	7.71357i	−0.219179	−	0.395178i
$382$			0.914949i			0.0468129i
$383$		−	6.33460i		−	0.323683i	−0.986817	−	0.161841i	$-0.948257\pi$
$383$		−	6.33460i		−	0.323683i	0.986817	−	0.161841i	$-0.0517433\pi$
$384$	−6.72036	+	3.72734i	−0.342947	+	0.190210i
$385$		0			0
$386$		−	13.5094i		−	0.687610i
$387$	−19.2748	−	12.0309i	−0.979795	−	0.611567i
$388$	−9.20868			−0.467500
$389$			27.5735i			1.39803i	0.715106	+	0.699016i	$0.246378\pi$
$389$			27.5735i			1.39803i	−0.715106	+	0.699016i	$0.753622\pi$
$390$		0			0
$391$		−	14.2327i		−	0.719777i
$392$	−1.61532			−0.0815858
$393$	30.2765	−	16.7924i	1.52725	−	0.847063i
$394$	16.4169			0.827071
$395$		0			0
$396$	−13.9547	−	9.71570i	−0.701248	−	0.488232i
$397$	−3.66683			−0.184033			−0.0920165	−	0.995757i	$-0.529331\pi$
$397$	−3.66683			−0.184033			−0.0920165	+	0.995757i	$0.529331\pi$
$398$	−36.5413			−1.83165
$399$	31.7056	−	17.5850i	1.58727	−	0.880351i
$400$		0			0
$401$			24.7658i			1.23675i	0.785885	+	0.618373i	$0.212208\pi$
$401$			24.7658i			1.23675i	−0.785885	+	0.618373i	$0.787792\pi$
$402$	18.8677	−	10.4646i	0.941034	−	0.521929i
$403$		−	11.7596i		−	0.585788i
$404$	−23.6069			−1.17449
$405$		0			0
$406$		−	30.2540i		−	1.50148i
$407$	1.58500	−	31.5569i	0.0785658	−	1.56422i
$408$	−3.03573	+	1.68372i	−0.150291	+	0.0833565i
$409$			13.0140i			0.643502i	0.946824	+	0.321751i	$0.104271\pi$
$409$			13.0140i			0.643502i	−0.946824	+	0.321751i	$0.895729\pi$
$410$		0			0
$411$	18.1909	+	32.7981i	0.897292	+	1.61781i
$412$	−9.69001			−0.477392
$413$	17.4935			0.860801
$414$	−19.5097	−	12.1775i	−0.958848	−	0.598493i
$415$		0			0
$416$		−	14.6963i		−	0.720544i
$417$	−2.56332	−	4.62165i	−0.125526	−	0.226323i
$418$	42.4790	+	2.13359i	2.07771	+	0.104357i
$419$		−	19.0092i		−	0.928661i	−0.885662	−	0.464331i	$-0.846295\pi$
$419$		−	19.0092i		−	0.928661i	0.885662	−	0.464331i	$-0.153705\pi$
$420$		0			0
$421$	0.202133			0.00985138			0.00492569	−	0.999988i	$-0.498432\pi$
$421$	0.202133			0.00985138			0.00492569	+	0.999988i	$0.498432\pi$
$422$		−	12.9552i		−	0.630651i
$423$	11.0055	+	6.86941i	0.535106	+	0.334002i
$424$			0.860445i			0.0417869i
$425$		0			0
$426$	14.6751	+	26.4591i	0.711011	+	1.28195i
$427$	17.1774			0.831270
$428$	35.1456			1.69883
$429$	−10.0513	+	4.93253i	−0.485280	+	0.238145i
$430$		0			0
$431$	−30.7310			−1.48026			−0.740131	−	0.672463i	$-0.765236\pi$
$431$	−30.7310			−1.48026			−0.740131	+	0.672463i	$0.765236\pi$
$432$	−1.20567	+	23.3381i	−0.0580078	+	1.12285i
$433$	19.2649			0.925813			0.462907	−	0.886407i	$-0.346806\pi$
$433$	19.2649			0.925813			0.462907	+	0.886407i	$0.346806\pi$
$434$		−	36.5271i		−	1.75336i
$435$		0			0
$436$			7.89112i			0.377916i
$437$	26.5062			1.26797
$438$	21.0944	+	38.0331i	1.00793	+	1.81729i
$439$			19.7189i			0.941130i	0.882365	+	0.470565i	$0.155950\pi$
$439$			19.7189i			0.941130i	−0.882365	+	0.470565i	$0.844050\pi$
$440$		0			0
$441$	−4.57760	+	7.33379i	−0.217981	+	0.349228i
$442$		−	13.4209i		−	0.638367i
$443$			25.6834i			1.22026i	0.792302	+	0.610129i	$0.208882\pi$
$443$			25.6834i			1.22026i	−0.792302	+	0.610129i	$0.791118\pi$
$444$	24.6600	−	13.6772i	1.17031	−	0.649093i
$445$		0			0
$446$	43.7006			2.06929
$447$	11.2127	−	6.21891i	0.530340	−	0.294145i
$448$		−	17.3735i		−	0.820819i
$449$			16.9075i			0.797916i	0.916969	+	0.398958i	$0.130628\pi$
$449$			16.9075i			0.797916i	−0.916969	+	0.398958i	$0.869372\pi$
$450$		0			0
$451$	−0.0378984	+	0.754545i	−0.00178457	+	0.0355301i
$452$		−	26.6825i		−	1.25504i
$453$	17.6375	+	31.8002i	0.828680	+	1.49410i
$454$	21.3290			1.00102
$455$		0			0
$456$	−3.13568	−	5.65360i	−0.146842	−	0.264754i
$457$			26.5623i			1.24253i	0.783600	+	0.621265i	$0.213381\pi$
$457$			26.5623i			1.24253i	−0.783600	+	0.621265i	$0.786619\pi$
$458$	21.3221			0.996316
$459$	−0.958526	+	18.5541i	−0.0447402	+	0.866033i
$460$		0			0
$461$	24.1584			1.12517			0.562585	−	0.826739i	$-0.309807\pi$
$461$	24.1584			1.12517			0.562585	+	0.826739i	$0.309807\pi$
$462$	−31.2208	+	15.3212i	−1.45252	+	0.712805i
$463$	−21.0922			−0.980235			−0.490118	−	0.871656i	$-0.663046\pi$
$463$	−21.0922			−0.980235			−0.490118	+	0.871656i	$0.663046\pi$
$464$	−22.4751			−1.04338
$465$		0			0
$466$	33.8348			1.56737
$467$		−	30.1009i		−	1.39291i	−0.717603	−	0.696453i	$-0.754761\pi$
$467$		−	30.1009i		−	1.39291i	0.717603	−	0.696453i	$-0.245239\pi$
$468$	−8.47662	−	5.29093i	−0.391832	−	0.244573i
$469$		−	20.3324i		−	0.938865i
$470$		0			0
$471$	−12.3919	+	6.87295i	−0.570988	+	0.316689i
$472$		−	3.11937i		−	0.143581i
$473$	−25.0878	−	1.26008i	−1.15354	−	0.0579387i
$474$	−18.7096	−	33.7333i	−0.859361	−	1.54942i
$475$		0			0
$476$		−	19.2080i		−	0.880395i
$477$	3.90655	+	2.43839i	0.178869	+	0.111646i
$478$	−19.1552			−0.876138
$479$	12.9591			0.592119			0.296059	−	0.955170i	$-0.404327\pi$
$479$	12.9591			0.592119			0.296059	+	0.955170i	$0.404327\pi$
$480$		0			0
$481$		−	18.5680i		−	0.846626i
$482$		−	48.8338i		−	2.22432i
$483$	−18.9533	+	10.5121i	−0.862405	+	0.478319i
$484$	−18.7037	−	1.88361i	−0.850170	−	0.0856188i
$485$		0			0
$486$	24.6133	+	17.1889i	1.11648	+	0.779705i
$487$	18.2097			0.825160			0.412580	−	0.910921i	$-0.364628\pi$
$487$	18.2097			0.825160			0.412580	+	0.910921i	$0.364628\pi$
$488$		−	3.06299i		−	0.138655i
$489$	−1.52105	+	0.843628i	−0.0687845	+	0.0381502i
$490$		0			0
$491$	7.17488			0.323798			0.161899	−	0.986807i	$-0.448238\pi$
$491$	7.17488			0.323798			0.161899	+	0.986807i	$0.448238\pi$
$492$	−0.589635	+	0.327031i	−0.0265828	+	0.0147437i
$493$	−17.8681			−0.804739
$494$	24.9945			1.12455
$495$		0			0
$496$	−27.1354			−1.21841
$497$	28.5132			1.27899
$498$	−16.1891	+	8.97900i	−0.725450	+	0.402359i
$499$	0.0852025			0.00381419			0.00190709	−	0.999998i	$-0.499393\pi$
$499$	0.0852025			0.00381419			0.00190709	+	0.999998i	$0.499393\pi$
$500$		0			0
$501$	−35.8151	+	19.8642i	−1.60010	+	0.887469i
$502$			32.6511i			1.45729i
$503$	5.41861			0.241604			0.120802	−	0.992677i	$-0.461453\pi$
$503$	5.41861			0.241604			0.120802	+	0.992677i	$0.461453\pi$
$504$	4.48434	+	2.79903i	0.199748	+	0.124679i
$505$		0			0
$506$	−25.3935	−	1.27544i	−1.12888	−	0.0567001i
$507$	13.9370	−	7.72990i	0.618962	−	0.343297i
$508$		−	8.70287i		−	0.386128i
$509$			16.1518i			0.715917i	0.933737	+	0.357959i	$0.116527\pi$
$509$			16.1518i			0.715917i	−0.933737	+	0.357959i	$0.883473\pi$
$510$		0			0
$511$	40.9858			1.81310
$512$	−28.8698			−1.27588
$513$	−34.5544	−	1.78511i	−1.52561	−	0.0788147i
$514$		−	47.0056i		−	2.07333i
$515$		0			0
$516$	−10.8735	−	19.6048i	−0.478677	−	0.863051i
$517$	14.3246	+	0.719481i	0.629996	+	0.0316428i
$518$		−	57.6748i		−	2.53409i
$519$	17.4998	−	9.70600i	0.768158	−	0.426046i
$520$		0			0
$521$			9.39333i			0.411529i	0.978602	+	0.205765i	$0.0659681\pi$
$521$			9.39333i			0.411529i	−0.978602	+	0.205765i	$0.934032\pi$
$522$	−15.2880	+	24.4930i	−0.669139	+	1.07203i
$523$			8.06475i			0.352647i	0.984332	+	0.176324i	$0.0564205\pi$
$523$			8.06475i			0.352647i	−0.984332	+	0.176324i	$0.943580\pi$
$524$	34.1596			1.49227
$525$		0			0
$526$	−14.9130			−0.650236
$527$	−21.5731			−0.939737
$528$	11.3818	+	23.1934i	0.495330	+	1.00936i
$529$	7.15483			0.311080
$530$		0			0
$531$	−14.1624	−	8.83990i	−0.614597	−	0.383619i
$532$	35.7720			1.55091
$533$			0.443971i			0.0192305i
$534$	−4.88036	−	8.79925i	−0.211194	−	0.380781i
$535$		0			0
$536$	−3.62559			−0.156602
$537$	15.2968	+	27.5799i	0.660104	+	1.19016i
$538$			5.11941i			0.220713i
$539$	−0.479443	+	9.54555i	−0.0206511	+	0.411156i
$540$		0			0
$541$		−	10.6333i		−	0.457159i	−0.973525	−	0.228580i	$-0.926592\pi$
$541$		−	10.6333i		−	0.457159i	0.973525	−	0.228580i	$-0.0734081\pi$
$542$			48.1019i			2.06615i
$543$	6.10317	−	3.38502i	0.261912	−	0.145265i
$544$	−26.9604			−1.15592
$545$		0			0
$546$	−17.8723	+	9.91258i	−0.764864	+	0.424219i
$547$		−	7.05753i		−	0.301758i	−0.988552	−	0.150879i	$-0.951790\pi$
$547$		−	7.05753i		−	0.301758i	0.988552	−	0.150879i	$-0.0482104\pi$
$548$			37.0046i			1.58076i
$549$	−13.9065	−	8.68012i	−0.593513	−	0.370458i
$550$		0			0
$551$		−	33.2767i		−	1.41764i
$552$	1.87448	+	3.37967i	0.0797831	+	0.143848i
$553$	−36.3521			−1.54585
$554$			4.10899i			0.174574i
$555$		0			0
$556$		−	5.21440i		−	0.221140i
$557$	−17.5612			−0.744094			−0.372047	−	0.928214i	$-0.621344\pi$
$557$	−17.5612			−0.744094			−0.372047	+	0.928214i	$0.621344\pi$
$558$	−18.4580	+	29.5716i	−0.781389	+	1.25187i
$559$	−14.7616			−0.624349
$560$		0			0
$561$	9.04873	+	18.4391i	0.382038	+	0.778500i
$562$	−30.1102			−1.27012
$563$	15.5944			0.657224			0.328612	−	0.944465i	$-0.393419\pi$
$563$	15.5944			0.657224			0.328612	+	0.944465i	$0.393419\pi$
$564$	6.20851	+	11.1939i	0.261425	+	0.471348i
$565$		0			0
$566$		−	20.1482i		−	0.846894i
$567$	25.4161	−	12.4275i	1.06737	−	0.521906i
$568$		−	5.08435i		−	0.213334i
$569$	26.0344			1.09142			0.545710	−	0.837974i	$-0.316260\pi$
$569$	26.0344			1.09142			0.545710	+	0.837974i	$0.316260\pi$
$570$		0			0
$571$			3.95528i			0.165523i	0.996569	+	0.0827616i	$0.0263740\pi$
$571$			3.95528i			0.165523i	−0.996569	+	0.0827616i	$0.973626\pi$
$572$	−11.0330	−	0.554156i	−0.461315	−	0.0231704i
$573$	−0.399115	−	0.719601i	−0.0166733	−	0.0300618i
$574$			1.37904i			0.0575601i
$575$		0			0
$576$	−8.77922	+	14.0652i	−0.365801	+	0.586051i
$577$	−22.9607			−0.955868			−0.477934	−	0.878396i	$-0.658614\pi$
$577$	−22.9607			−0.955868			−0.477934	+	0.878396i	$0.658614\pi$
$578$	8.11895			0.337704
$579$	5.89301	+	10.6250i	0.244905	+	0.441562i
$580$		0			0
$581$			17.4459i			0.723777i
$582$	15.7186	−	8.71809i	0.651559	−	0.361377i
$583$	5.08472	+	0.255389i	0.210587	+	0.0105772i
$584$		−	7.30840i		−	0.302424i
$585$		0			0
$586$	11.2201			0.463497
$587$		−	23.6143i		−	0.974667i	−0.873216	−	0.487334i	$-0.837970\pi$
$587$		−	23.6143i		−	0.974667i	0.873216	−	0.487334i	$-0.162030\pi$
$588$	−7.45932	+	4.13719i	−0.307617	+	0.170615i
$589$		−	40.1766i		−	1.65545i
$590$		0			0
$591$	−12.9118	+	7.16131i	−0.531120	+	0.294577i
$592$	−42.8457			−1.76095
$593$	−23.7191			−0.974025			−0.487013	−	0.873395i	$-0.661913\pi$
$593$	−23.7191			−0.974025			−0.487013	+	0.873395i	$0.661913\pi$
$594$	33.0179	+	3.37287i	1.35474	+	0.138391i
$595$		0			0
$596$	12.6507			0.518194
$597$	28.7395	−	15.9399i	1.17623	−	0.652376i
$598$	−14.9414			−0.611001
$599$		−	18.5481i		−	0.757854i	−0.925427	−	0.378927i	$-0.876293\pi$
$599$		−	18.5481i		−	0.757854i	0.925427	−	0.378927i	$-0.123707\pi$
$600$		0			0
$601$			26.1336i			1.06601i	0.846112	+	0.533005i	$0.178937\pi$
$601$			26.1336i			1.06601i	−0.846112	+	0.533005i	$0.821063\pi$
$602$	−45.8517			−1.86878
$603$	−10.2745	+	16.4607i	−0.418408	+	0.670334i
$604$			35.8787i			1.45988i
$605$		0			0
$606$	40.2956	−	22.3493i	1.63690	−	0.907878i
$607$			29.4153i			1.19393i	0.802267	+	0.596966i	$0.203627\pi$
$607$			29.4153i			1.19393i	−0.802267	+	0.596966i	$0.796373\pi$
$608$		−	50.2097i		−	2.03627i
$609$	13.1972	+	23.7945i	0.534780	+	0.964203i
$610$		0			0
$611$	8.42855			0.340983
$612$	−9.70623	+	15.5504i	−0.392351	+	0.628587i
$613$			12.5605i			0.507312i	0.967294	+	0.253656i	$0.0816331\pi$
$613$			12.5605i			0.507312i	−0.967294	+	0.253656i	$0.918367\pi$
$614$			10.3249i			0.416678i
$615$		0			0
$616$	5.83675	+	0.293162i	0.235169	+	0.0118118i
$617$			11.1299i			0.448073i	0.974581	+	0.224037i	$0.0719235\pi$
$617$			11.1299i			0.448073i	−0.974581	+	0.224037i	$0.928077\pi$
$618$	16.5402	−	9.17378i	0.665346	−	0.369023i
$619$	25.4913			1.02458			0.512292	−	0.858811i	$-0.328797\pi$
$619$	25.4913			1.02458			0.512292	+	0.858811i	$0.328797\pi$
$620$		0			0
$621$	20.6563	+	1.06712i	0.828907	+	0.0428222i
$622$			45.2170i			1.81304i
$623$	−9.48237			−0.379903
$624$	7.36389	+	13.2770i	0.294791	+	0.531507i
$625$		0			0
$626$	−13.8622			−0.554045
$627$	−34.3401	+	16.8519i	−1.37141	+	0.673002i
$628$	−13.9812			−0.557910
$629$	−34.0630			−1.35818
$630$		0			0
$631$	8.00941			0.318849			0.159425	−	0.987210i	$-0.449036\pi$
$631$	8.00941			0.318849			0.159425	+	0.987210i	$0.449036\pi$
$632$			6.48215i			0.257846i
$633$	5.65128	+	10.1892i	0.224618	+	0.404985i
$634$		−	21.1415i		−	0.839636i
$635$		0			0
$636$	2.20379	+	3.97342i	0.0873861	+	0.157556i
$637$			5.61657i			0.222536i
$638$	−1.60122	+	31.8798i	−0.0633930	+	1.26213i
$639$	−23.0837	−	14.4084i	−0.913178	−	0.569987i
$640$		0			0
$641$			5.53239i			0.218516i	0.994013	+	0.109258i	$0.0348475\pi$
$641$			5.53239i			0.218516i	−0.994013	+	0.109258i	$0.965152\pi$
$642$	−59.9915	+	33.2733i	−2.36767	+	1.31319i
$643$	39.0347			1.53938			0.769689	−	0.638419i	$-0.220411\pi$
$643$	39.0347			1.53938			0.769689	+	0.638419i	$0.220411\pi$
$644$	−21.3841			−0.842653
$645$		0			0
$646$		−	45.8524i		−	1.80404i
$647$			13.9123i			0.546948i	0.961879	+	0.273474i	$0.0881728\pi$
$647$			13.9123i			0.546948i	−0.961879	+	0.273474i	$0.911827\pi$
$648$	−2.21602	−	4.53208i	−0.0870534	−	0.178037i
$649$	−18.4336	−	0.925864i	−0.723583	−	0.0363433i
$650$		0			0
$651$	15.9337	+	28.7283i	0.624491	+	1.12595i
$652$	−1.71614			−0.0672091
$653$		−	11.2114i		−	0.438735i	−0.975642	−	0.219368i	$-0.929601\pi$
$653$		−	11.2114i		−	0.438735i	0.975642	−	0.219368i	$-0.0703994\pi$
$654$	−7.47072	−	13.4697i	−0.292128	−	0.526705i
$655$		0			0
$656$	1.02447			0.0399987
$657$	−33.1813	−	20.7111i	−1.29453	−	0.808016i
$658$	26.1803			1.02062
$659$	17.7213			0.690325			0.345163	−	0.938543i	$-0.387824\pi$
$659$	17.7213			0.690325			0.345163	+	0.938543i	$0.387824\pi$
$660$		0			0
$661$	−12.6323			−0.491339			−0.245669	−	0.969354i	$-0.579008\pi$
$661$	−12.6323			−0.491339			−0.245669	+	0.969354i	$0.579008\pi$
$662$	22.7292			0.883394
$663$	5.85441	+	10.5555i	0.227366	+	0.409940i
$664$	3.11087			0.120725
$665$		0			0
$666$	−29.1444	+	46.6924i	−1.12932	+	1.80929i
$667$			19.8925i			0.770241i
$668$	−40.4085			−1.56345
$669$	−34.3703	+	19.0629i	−1.32883	+	0.737015i
$670$		0			0
$671$	−18.1004	−	0.909129i	−0.698760	−	0.0350965i
$672$	19.9127	+	35.9025i	0.768150	+	1.38497i
$673$		−	28.9430i		−	1.11567i	−0.829951	−	0.557836i	$-0.811632\pi$
$673$		−	28.9430i		−	1.11567i	0.829951	−	0.557836i	$-0.188368\pi$
$674$			46.6646i			1.79745i
$675$		0			0
$676$	15.7244			0.604786
$677$	−22.5741			−0.867594			−0.433797	−	0.901011i	$-0.642826\pi$
$677$	−22.5741			−0.867594			−0.433797	+	0.901011i	$0.642826\pi$
$678$	25.2610	+	45.5454i	0.970144	+	1.74916i
$679$		−	16.9389i		−	0.650057i
$680$		0			0
$681$	−16.7751	+	9.30403i	−0.642823	+	0.356531i
$682$	−1.93323	+	38.4900i	−0.0740274	+	1.47386i
$683$		−	18.2535i		−	0.698452i	−0.937039	−	0.349226i	$-0.886445\pi$
$683$		−	18.2535i		−	0.698452i	0.937039	−	0.349226i	$-0.113555\pi$
$684$	−28.9603	−	18.0764i	−1.10732	−	0.691169i
$685$		0			0
$686$		−	24.9320i		−	0.951908i
$687$	−16.7697	+	9.30104i	−0.639804	+	0.354857i
$688$			34.0624i			1.29862i
$689$	2.99183			0.113980
$690$		0			0
$691$	−43.3199			−1.64797			−0.823984	−	0.566614i	$-0.808253\pi$
$691$	−43.3199			−1.64797			−0.823984	+	0.566614i	$0.808253\pi$
$692$	19.7443			0.750564
$693$	17.8716	−	25.6690i	0.678886	−	0.975084i
$694$	3.09845			0.117616
$695$		0			0
$696$	4.24294	−	2.35328i	0.160828	−	0.0892007i
$697$	0.814467			0.0308501
$698$		−	68.5591i		−	2.59500i
$699$	−26.6108	+	14.7593i	−1.00651	+	0.558247i
$700$		0			0
$701$	−47.2425			−1.78433			−0.892163	−	0.451714i	$-0.850813\pi$
$701$	−47.2425			−1.78433			−0.892163	+	0.451714i	$0.850813\pi$
$702$	19.4781	+	1.00626i	0.735155	+	0.0379789i
$703$		−	63.4373i		−	2.39258i
$704$	−0.919509	+	18.3071i	−0.0346553	+	0.689975i
$705$		0			0
$706$		−	23.2233i		−	0.874020i
$707$		−	43.4239i		−	1.63312i
$708$	−7.98941	−	14.4048i	−0.300261	−	0.541367i
$709$	−33.8224			−1.27023			−0.635113	−	0.772419i	$-0.719047\pi$
$709$	−33.8224			−1.27023			−0.635113	+	0.772419i	$0.719047\pi$
$710$		0			0
$711$	29.4300	+	18.3696i	1.10371	+	0.688913i
$712$			1.69085i			0.0633675i
$713$			24.0172i			0.899451i
$714$	18.1847	+	32.7868i	0.680544	+	1.22702i
$715$		0			0
$716$			31.1172i			1.16290i
$717$	15.0654	−	8.35580i	0.562629	−	0.312053i
$718$	43.2569			1.61433
$719$			7.16751i			0.267303i	0.991028	+	0.133652i	$0.0426703\pi$
$719$			7.16751i			0.267303i	−0.991028	+	0.133652i	$0.957330\pi$
$720$		0			0
$721$		−	17.8243i		−	0.663813i
$722$	48.8020			1.81622
$723$	21.3021	+	38.4075i	0.792233	+	1.42839i
$724$	6.88593			0.255914
$725$		0			0
$726$	33.7094	−	14.4921i	1.25107	−	0.537852i
$727$	−6.99011			−0.259249			−0.129624	−	0.991563i	$-0.541377\pi$
$727$	−6.99011			−0.259249			−0.129624	+	0.991563i	$0.541377\pi$
$728$	3.43432			0.127284
$729$	−26.8563	−	2.78227i	−0.994676	−	0.103047i
$730$		0			0
$731$			27.0802i			1.00160i
$732$	−7.84501	−	14.1445i	−0.289960	−	0.522795i
$733$			9.54467i			0.352540i	0.984342	+	0.176270i	$0.0564032\pi$
$733$			9.54467i			0.352540i	−0.984342	+	0.176270i	$0.943597\pi$
$734$	−26.3753			−0.973530
$735$		0			0
$736$			30.0149i			1.10636i
$737$	−1.07612	+	21.4251i	−0.0396392	+	0.789203i
$738$	0.696862	−	1.11644i	0.0256518	−	0.0410969i
$739$		−	33.8456i		−	1.24503i	−0.782607	−	0.622516i	$-0.786111\pi$
$739$		−	33.8456i		−	1.24503i	0.782607	−	0.622516i	$-0.213889\pi$
$740$		0			0
$741$	−19.6580	+	10.9030i	−0.722154	+	0.400531i
$742$	9.29306			0.341159
$743$	46.4146			1.70279			0.851393	−	0.524528i	$-0.175758\pi$
$743$	46.4146			1.70279			0.851393	+	0.524528i	$0.175758\pi$
$744$	5.12271	−	2.84123i	0.187808	−	0.104164i
$745$		0			0
$746$		−	21.5391i		−	0.788602i
$747$	8.81582	−	14.1239i	0.322554	−	0.516765i
$748$	−1.01660	+	20.2402i	−0.0371706	+	0.740054i
$749$			64.6488i			2.36222i
$750$		0			0
$751$	−21.7960			−0.795348			−0.397674	−	0.917527i	$-0.630183\pi$
$751$	−21.7960			−0.795348			−0.397674	+	0.917527i	$0.630183\pi$
$752$		−	19.4489i		−	0.709230i
$753$	−14.2429	−	25.6799i	−0.519041	−	0.935828i
$754$			18.7579i			0.683124i
$755$		0			0
$756$	27.8770	+	1.44016i	1.01388	+	0.0523780i
$757$	32.0990			1.16666			0.583328	−	0.812236i	$-0.301750\pi$
$757$	32.0990			1.16666			0.583328	+	0.812236i	$0.301750\pi$
$758$	15.6814			0.569576
$759$	20.5282	−	10.0739i	0.745126	−	0.365660i
$760$		0			0
$761$	5.58080			0.202304			0.101152	−	0.994871i	$-0.467747\pi$
$761$	5.58080			0.202304			0.101152	+	0.994871i	$0.467747\pi$
$762$	8.23923	+	14.8553i	0.298476	+	0.538150i
$763$	−14.5154			−0.525491
$764$		−	0.811894i		−	0.0293733i
$765$		0			0
$766$			12.1996i			0.440788i
$767$	−10.8463			−0.391636
$768$	29.6850	−	16.4643i	1.07116	−	0.594104i
$769$		−	4.91350i		−	0.177185i	−0.996068	−	0.0885926i	$-0.971763\pi$
$769$		−	4.91350i		−	0.177185i	0.996068	−	0.0885926i	$-0.0282369\pi$
$770$		0			0
$771$	20.5046	+	36.9696i	0.738455	+	1.33143i
$772$			11.9878i			0.431449i
$773$			7.96546i			0.286498i	0.989687	+	0.143249i	$0.0457549\pi$
$773$			7.96546i			0.286498i	−0.989687	+	0.143249i	$0.954245\pi$
$774$	37.1206	+	23.1699i	1.33427	+	0.832826i
$775$		0			0
$776$	−3.02048			−0.108429
$777$	25.1587	+	45.3609i	0.902562	+	1.62731i
$778$		−	53.1027i		−	1.90382i
$779$			1.51683i			0.0543459i
$780$		0			0
$781$	−30.0455	−	1.50909i	−1.07511	−	0.0539995i
$782$			27.4101i			0.980184i
$783$	1.33970	−	25.9325i	0.0478769	−	0.926751i
$784$	12.9603			0.462866
$785$		0			0
$786$	−58.3083	+	32.3398i	−2.07979	+	1.15352i
$787$		−	41.9921i		−	1.49686i	−0.663215	−	0.748429i	$-0.730809\pi$
$787$		−	41.9921i		−	1.49686i	0.663215	−	0.748429i	$-0.269191\pi$
$788$	−14.5678			−0.518956
$789$	11.7289	−	6.50526i	0.417561	−	0.231594i
$790$		0			0
$791$	49.0813			1.74513
$792$	−4.57718	−	3.18678i	−0.162643	−	0.113237i
$793$	−10.6502			−0.378201
$794$	7.06181			0.250614
$795$		0			0
$796$	32.4254			1.14929
$797$		−	12.8380i		−	0.454745i	−0.973808	−	0.227372i	$-0.926987\pi$
$797$		−	12.8380i		−	0.454745i	0.973808	−	0.227372i	$-0.0730134\pi$
$798$	−61.0606	+	33.8663i	−2.16152	+	1.19885i
$799$		−	15.4622i		−	0.547014i
$800$		0			0
$801$	7.67675	+	4.79167i	0.271244	+	0.169305i
$802$		−	47.6956i		−	1.68419i
$803$	−43.1883	−	2.16921i	−1.52408	−	0.0765499i
$804$	−16.7425	+	9.28596i	−0.590463	+	0.327490i
$805$		0			0
$806$			22.6474i			0.797720i
$807$	−2.23317	−	4.02638i	−0.0786112	−	0.141735i
$808$	−7.74316			−0.272403
$809$	30.6914			1.07905			0.539526	−	0.841969i	$-0.318603\pi$
$809$	30.6914			1.07905			0.539526	+	0.841969i	$0.318603\pi$
$810$		0			0
$811$		−	43.6321i		−	1.53213i	−0.642764	−	0.766064i	$-0.722212\pi$
$811$		−	43.6321i		−	1.53213i	0.642764	−	0.766064i	$-0.277788\pi$
$812$			26.8463i			0.942120i
$813$	−20.9828	−	37.8319i	−0.735900	−	1.32682i
$814$	−3.05250	+	60.7742i	−0.106990	+	2.13013i
$815$		0			0
$816$	24.3568	−	13.5091i	0.852657	−	0.472912i
$817$	−50.4329			−1.76442
$818$		−	25.0632i		−	0.876314i
$819$	9.73243	−	15.5924i	0.340078	−	0.544841i
$820$		0			0
$821$	29.5532			1.03141			0.515706	−	0.856765i	$-0.327530\pi$
$821$	29.5532			1.03141			0.515706	+	0.856765i	$0.327530\pi$
$822$	−35.0332	−	63.1646i	−1.22192	−	2.20312i
$823$	31.0653			1.08287			0.541434	−	0.840743i	$-0.317882\pi$
$823$	31.0653			1.08287			0.541434	+	0.840743i	$0.317882\pi$
$824$	−3.17836			−0.110723
$825$		0			0
$826$	−33.6901			−1.17223
$827$	49.7363			1.72950			0.864751	−	0.502201i	$-0.167476\pi$
$827$	49.7363			1.72950			0.864751	+	0.502201i	$0.167476\pi$
$828$	17.3122	+	10.8059i	0.601640	+	0.375531i
$829$	−21.6199			−0.750890			−0.375445	−	0.926845i	$-0.622510\pi$
$829$	−21.6199			−0.750890			−0.375445	+	0.926845i	$0.622510\pi$
$830$		0			0
$831$	−1.79241	−	3.23169i	−0.0621779	−	0.112106i
$832$			10.7718i			0.373446i
$833$	10.3036			0.356999
$834$	4.93660	+	8.90066i	0.170941	+	0.308204i
$835$		0			0
$836$	−37.6943	−	1.89327i	−1.30369	−	0.0654801i
$837$	1.61749	−	31.3096i	0.0559085	−	1.08222i
$838$			36.6091i			1.26464i
$839$			2.37523i			0.0820019i	0.999159	+	0.0410010i	$0.0130547\pi$
$839$			2.37523i			0.0820019i	−0.999159	+	0.0410010i	$0.986945\pi$
$840$		0			0
$841$	−4.02637			−0.138840
$842$	−0.389281			−0.0134155
$843$	23.6815	−	13.1346i	0.815634	−	0.452378i
$844$			11.4960i			0.395709i
$845$		0			0
$846$	−21.1951	−	13.2295i	−0.728702	−	0.454841i
$847$	3.46482	−	34.4047i	0.119053	−	1.18216i
$848$		−	6.90366i		−	0.237073i
$849$	8.78898	+	15.8465i	0.301637	+	0.543849i
$850$		0			0
$851$			37.9222i			1.29996i
$852$	−13.0222	−	23.4789i	−0.446132	−	0.804372i
$853$		−	1.30039i		−	0.0445244i	−0.999752	−	0.0222622i	$-0.992913\pi$
$853$		−	1.30039i		−	0.0445244i	0.999752	−	0.0222622i	$-0.00708687\pi$
$854$	−33.0812			−1.13202
$855$		0			0
$856$	11.5279			0.394015
$857$	−13.6826			−0.467389			−0.233694	−	0.972310i	$-0.575081\pi$
$857$	−13.6826			−0.467389			−0.233694	+	0.972310i	$0.575081\pi$
$858$	19.3574	−	9.49936i	0.660850	−	0.324303i
$859$	24.6408			0.840734			0.420367	−	0.907354i	$-0.361901\pi$
$859$	24.6408			0.840734			0.420367	+	0.907354i	$0.361901\pi$
$860$		0			0
$861$	−0.601559	−	1.08461i	−0.0205011	−	0.0369633i
$862$	59.1837			2.01580
$863$			56.6992i			1.93006i	0.262135	+	0.965031i	$0.415573\pi$
$863$			56.6992i			1.93006i	−0.262135	+	0.965031i	$0.584427\pi$
$864$	2.02141	−	39.1283i	0.0687698	−	1.33117i
$865$		0			0
$866$	−37.1016			−1.26076
$867$	−6.38550	+	3.54161i	−0.216863	+	0.120279i
$868$			32.4129i			1.10016i
$869$	38.3056	+	1.92397i	1.29943	+	0.0652663i
$870$		0			0
$871$			12.6064i			0.427153i
$872$			2.58831i			0.0876514i
$873$	−8.55965	+	13.7134i	−0.289700	+	0.464130i
$874$	−51.0473			−1.72670
$875$		0			0
$876$	−18.7185	−	33.7492i	−0.632438	−	1.14028i
$877$		−	40.8654i		−	1.37993i	−0.723845	−	0.689963i	$-0.757627\pi$
$877$		−	40.8654i		−	1.37993i	0.723845	−	0.689963i	$-0.242373\pi$
$878$		−	37.9758i		−	1.28162i
$879$	−8.82452	+	4.89438i	−0.297644	+	0.165083i
$880$		0			0
$881$			46.8633i			1.57887i	0.613837	+	0.789433i	$0.289625\pi$
$881$			46.8633i			1.57887i	−0.613837	+	0.789433i	$0.710375\pi$
$882$	8.81582	−	14.1239i	0.296844	−	0.475575i
$883$	−9.41752			−0.316925			−0.158462	−	0.987365i	$-0.550654\pi$
$883$	−9.41752			−0.316925			−0.158462	+	0.987365i	$0.550654\pi$
$884$			11.9092i			0.400551i
$885$		0			0
$886$		−	49.4627i		−	1.66173i
$887$	21.2410			0.713203			0.356602	−	0.934257i	$-0.383935\pi$
$887$	21.2410			0.713203			0.356602	+	0.934257i	$0.383935\pi$
$888$	8.08855	−	4.48618i	0.271434	−	0.150546i
$889$	16.0085			0.536909
$890$		0			0
$891$	−27.4396	+	11.7502i	−0.919262	+	0.393645i
$892$	−38.7784			−1.29840
$893$	28.7961			0.963625
$894$	−21.5940	+	11.9768i	−0.722212	+	0.400563i
$895$		0			0
$896$		−	13.9472i		−	0.465945i
$897$	11.7513	−	6.51769i	0.392366	−	0.217619i
$898$		−	32.5616i		−	1.08659i
$899$	30.1519			1.00562
$900$		0			0
$901$		−	5.48852i		−	0.182849i
$902$	0.0729872	−	1.45315i	0.00243021	−	0.0483846i
$903$	36.0621	−	20.0012i	1.20007	−	0.665599i
$904$		−	8.75196i		−	0.291086i
$905$		0			0
$906$	−33.9673	−	61.2428i	−1.12849	−	2.03466i
$907$	39.4518			1.30998			0.654988	−	0.755639i	$-0.272674\pi$
$907$	39.4518			1.30998			0.654988	+	0.755639i	$0.272674\pi$
$908$	−18.9266			−0.628100
$909$	−21.9431	+	35.1551i	−0.727807	+	1.16602i
$910$		0			0
$911$		−	43.9566i		−	1.45635i	−0.685393	−	0.728174i	$-0.740369\pi$
$911$		−	43.9566i		−	1.45635i	0.685393	−	0.728174i	$-0.259631\pi$
$912$	25.1587	+	45.3609i	0.833087	+	1.50205i
$913$	0.923341	−	18.3834i	0.0305581	−	0.608402i
$914$		−	51.1552i		−	1.69206i
$915$		0			0
$916$	−18.9205			−0.625150
$917$			62.8350i			2.07500i
$918$	1.84599	−	35.7327i	0.0609267	−	1.17935i
$919$		−	13.4719i		−	0.444397i	−0.975001	−	0.222199i	$-0.928677\pi$
$919$		−	13.4719i		−	0.444397i	0.975001	−	0.222199i	$-0.0713234\pi$
$920$		0			0
$921$	−4.50388	−	8.12045i	−0.148408	−	0.267578i
$922$	−46.5258			−1.53224
$923$	−17.6786			−0.581899
$924$	27.7042	−	13.5955i	0.911401	−	0.447257i
$925$		0			0
$926$	40.6206			1.33487
$927$	−9.00705	+	14.4302i	−0.295830	+	0.473951i
$928$	37.6816			1.23696
$929$			28.0769i			0.921172i	0.887615	+	0.460586i	$0.152361\pi$
$929$			28.0769i			0.921172i	−0.887615	+	0.460586i	$0.847639\pi$
$930$		0			0
$931$			19.1890i			0.628893i
$932$	−30.0238			−0.983462
$933$	−19.7244	−	35.5629i	−0.645747	−	1.16428i
$934$			57.9702i			1.89684i
$935$		0			0
$936$	−2.78036	−	1.73544i	−0.0908789	−	0.0567247i
$937$		−	12.1672i		−	0.397485i	−0.980052	−	0.198743i	$-0.936314\pi$
$937$		−	12.1672i		−	0.397485i	0.980052	−	0.198743i	$-0.0636858\pi$
$938$			39.1575i			1.27854i
$939$	10.9025	−	6.04691i	0.355791	−	0.197333i
$940$		0			0
$941$	13.6502			0.444983			0.222491	−	0.974935i	$-0.428581\pi$
$941$	13.6502			0.444983			0.222491	+	0.974935i	$0.428581\pi$
$942$	23.8650	−	13.2363i	0.777565	−	0.431264i
$943$		−	0.906743i		−	0.0295276i
$944$			25.0278i			0.814586i
$945$		0			0
$946$	48.3157	+	2.42675i	1.57088	+	0.0789004i
$947$		−	50.8540i		−	1.65253i	−0.563279	−	0.826267i	$-0.690460\pi$
$947$		−	50.8540i		−	1.65253i	0.563279	−	0.826267i	$-0.309540\pi$
$948$	16.6023	+	29.9337i	0.539216	+	0.972202i
$949$	−25.4118			−0.824903
$950$		0			0
$951$	9.22225	+	16.6276i	0.299052	+	0.539188i
$952$		−	6.30028i		−	0.204193i
$953$	35.4121			1.14711			0.573555	−	0.819167i	$-0.305564\pi$
$953$	35.4121			1.14711			0.573555	+	0.819167i	$0.305564\pi$
$954$	−7.52348	−	4.69600i	−0.243582	−	0.152039i
$955$		0			0
$956$	16.9976			0.549743
$957$	−12.6471	−	25.7717i	−0.408823	−	0.833081i
$958$	−24.9575			−0.806341
$959$	−68.0683			−2.19804
$960$		0			0
$961$	5.40390			0.174319
$962$			35.7593i			1.15293i
$963$	32.6686	−	52.3384i	1.05273	−	1.68658i
$964$			43.3334i			1.39567i
$965$		0			0
$966$	36.5014	−	20.2449i	1.17441	−	0.651370i
$967$		−	11.2578i		−	0.362025i	−0.983481	−	0.181012i	$-0.942063\pi$
$967$		−	11.2578i		−	0.362025i	0.983481	−	0.181012i	$-0.0579374\pi$
$968$	−6.13489	−	0.617832i	−0.197183	−	0.0198579i
$969$	20.0015	+	36.0626i	0.642542	+	1.15850i
$970$		0			0
$971$		−	20.8811i		−	0.670105i	−0.942199	−	0.335053i	$-0.891246\pi$
$971$		−	20.8811i		−	0.670105i	0.942199	−	0.335053i	$-0.108754\pi$
$972$	−21.8410	−	15.2528i	−0.700549	−	0.489235i
$973$	9.59165			0.307494
$974$	−35.0693			−1.12369
$975$		0			0
$976$			24.5755i			0.786641i
$977$			35.2258i			1.12697i	0.826126	+	0.563486i	$0.190540\pi$
$977$			35.2258i			1.12697i	−0.826126	+	0.563486i	$0.809460\pi$
$978$	2.92934	−	1.62471i	0.0936699	−	0.0519525i
$979$	9.99194	+	0.501864i	0.319344	+	0.0160397i
$980$		0			0
$981$	11.7513	+	7.33495i	0.375192	+	0.234187i
$982$	−13.8178			−0.440944
$983$		−	31.1665i		−	0.994057i	−0.867734	−	0.497029i	$-0.834424\pi$
$983$		−	31.1665i		−	0.994057i	0.867734	−	0.497029i	$-0.165576\pi$
$984$	−0.193402	+	0.107267i	−0.00616544	+	0.00341956i
$985$		0			0
$986$	34.4115			1.09589
$987$	−20.5907	+	11.4203i	−0.655408	+	0.363511i
$988$	−22.1792			−0.705614
$989$	30.1483			0.958660
$990$		0			0
$991$	50.0530			1.58999			0.794993	−	0.606618i	$-0.207474\pi$
$991$	50.0530			1.58999			0.794993	+	0.606618i	$0.207474\pi$
$992$	45.4949			1.44446
$993$	−17.8763	+	9.91482i	−0.567288	+	0.314637i
$994$	−54.9125			−1.74172
$995$		0			0
$996$	14.3656	−	7.96765i	0.455192	−	0.252465i
$997$		−	1.07806i		−	0.0341426i	−0.999854	−	0.0170713i	$-0.994566\pi$
$997$		−	1.07806i		−	0.0341426i	0.999854	−	0.0170713i	$-0.00543422\pi$
$998$	−0.164088			−0.00519412
$999$	2.55394	−	49.4366i	0.0808032	−	1.56410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.f.g.626.3	yes	16
3.2	odd	2	inner	825.2.f.g.626.14	yes	16
5.2	odd	4		825.2.d.f.824.5		32
5.3	odd	4		825.2.d.f.824.28		32
5.4	even	2		825.2.f.e.626.14	yes	16
11.10	odd	2	inner	825.2.f.g.626.13	yes	16
15.2	even	4		825.2.d.f.824.27		32
15.8	even	4		825.2.d.f.824.6		32
15.14	odd	2		825.2.f.e.626.3	✓	16
33.32	even	2	inner	825.2.f.g.626.4	yes	16
55.32	even	4		825.2.d.f.824.25		32
55.43	even	4		825.2.d.f.824.8		32
55.54	odd	2		825.2.f.e.626.4	yes	16
165.32	odd	4		825.2.d.f.824.7		32
165.98	odd	4		825.2.d.f.824.26		32
165.164	even	2		825.2.f.e.626.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.d.f.824.5		32	5.2	odd	4
825.2.d.f.824.6		32	15.8	even	4
825.2.d.f.824.7		32	165.32	odd	4
825.2.d.f.824.8		32	55.43	even	4
825.2.d.f.824.25		32	55.32	even	4
825.2.d.f.824.26		32	165.98	odd	4
825.2.d.f.824.27		32	15.2	even	4
825.2.d.f.824.28		32	5.3	odd	4
825.2.f.e.626.3	✓	16	15.14	odd	2
825.2.f.e.626.4	yes	16	55.54	odd	2
825.2.f.e.626.13	yes	16	165.164	even	2
825.2.f.e.626.14	yes	16	5.4	even	2
825.2.f.g.626.3	yes	16	1.1	even	1	trivial
825.2.f.g.626.4	yes	16	33.32	even	2	inner
825.2.f.g.626.13	yes	16	11.10	odd	2	inner
825.2.f.g.626.14	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.92586 q^{2} +(1.51468 - 0.840091i) q^{3} +1.70894 q^{4} +(-2.91706 + 1.61790i) q^{6} +3.14352i q^{7} +0.560539 q^{8} +(1.58849 - 2.54493i) q^{9} +O(q^{10})\)	\(q-1.92586 q^{2} +(1.51468 - 0.840091i) q^{3} +1.70894 q^{4} +(-2.91706 + 1.61790i) q^{6} +3.14352i q^{7} +0.560539 q^{8} +(1.58849 - 2.54493i) q^{9} +(0.166374 - 3.31245i) q^{11} +(2.58849 - 1.43567i) q^{12} -1.94903i q^{13} -6.05398i q^{14} -4.49740 q^{16} -3.57551 q^{17} +(-3.05922 + 4.90119i) q^{18} -6.65886i q^{19} +(2.64084 + 4.76142i) q^{21} +(-0.320413 + 6.37932i) q^{22} +3.98060i q^{23} +(0.849035 - 0.470903i) q^{24} +3.75357i q^{26} +(0.268081 - 5.18923i) q^{27} +5.37209i q^{28} +4.99736 q^{29} +6.03356 q^{31} +7.54030 q^{32} +(-2.53076 - 5.15706i) q^{33} +6.88593 q^{34} +(2.71464 - 4.34914i) q^{36} +9.52676 q^{37} +12.8240i q^{38} +(-1.63736 - 2.95216i) q^{39} -0.227791 q^{41} +(-5.08590 - 9.16983i) q^{42} -7.57380i q^{43} +(0.284323 - 5.66078i) q^{44} -7.66608i q^{46} +4.32448i q^{47} +(-6.81211 + 3.77823i) q^{48} -2.88172 q^{49} +(-5.41574 + 3.00375i) q^{51} -3.33078i q^{52} +1.53503i q^{53} +(-0.516287 + 9.99374i) q^{54} +1.76206i q^{56} +(-5.59404 - 10.0860i) q^{57} -9.62423 q^{58} -5.56495i q^{59} -5.46437i q^{61} -11.6198 q^{62} +(8.00005 + 4.99346i) q^{63} -5.52676 q^{64} +(4.87388 + 9.93178i) q^{66} -6.46805 q^{67} -6.11033 q^{68} +(3.34407 + 6.02932i) q^{69} -9.07047i q^{71} +(0.890413 - 1.42653i) q^{72} -13.0382i q^{73} -18.3472 q^{74} -11.3796i q^{76} +(10.4128 + 0.523000i) q^{77} +(3.15334 + 5.68544i) q^{78} +11.5641i q^{79} +(-3.95337 - 8.08522i) q^{81} +0.438693 q^{82} +5.54979 q^{83} +(4.51305 + 8.13699i) q^{84} +14.5861i q^{86} +(7.56939 - 4.19824i) q^{87} +(0.0932591 - 1.85676i) q^{88} +3.01648i q^{89} +6.12682 q^{91} +6.80261i q^{92} +(9.13890 - 5.06874i) q^{93} -8.32835i q^{94} +(11.4211 - 6.33453i) q^{96} -5.38853 q^{97} +5.54979 q^{98} +(-8.16568 - 5.68522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9	\( 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9} + 6 q^{12} + 32 q^{16} + 28 q^{22} + 2 q^{27} - 12 q^{31} - 20 q^{33} + 28 q^{34} - 36 q^{36} + 4 q^{37} + 58 q^{42} - 40 q^{48} - 28 q^{49} - 16 q^{58} + 60 q^{64} - 30 q^{66} - 44 q^{67} + 44 q^{69} - 44 q^{78} - 26 q^{81} - 8 q^{82} + 76 q^{88} + 64 q^{91} - 14 q^{93} - 108 q^{97} + 14 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9 + 6 * q^12 + 32 * q^16 + 28 * q^22 + 2 * q^27 - 12 * q^31 - 20 * q^33 + 28 * q^34 - 36 * q^36 + 4 * q^37 + 58 * q^42 - 40 * q^48 - 28 * q^49 - 16 * q^58 + 60 * q^64 - 30 * q^66 - 44 * q^67 + 44 * q^69 - 44 * q^78 - 26 * q^81 - 8 * q^82 + 76 * q^88 + 64 * q^91 - 14 * q^93 - 108 * q^97 + 14 * q^99

Introduction

L-functions

Modular forms

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