LMFDB - Embedded newform 525.2.g.d.524.1

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:	$8$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			524.1
Root			$-0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	525.524
Dual form			525.2.g.d.524.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52434 q^{2} +(0.396143 - 1.68614i) q^{3} +4.37228 q^{4} +(-1.00000 + 4.25639i) q^{6} +(1.73205 - 2.00000i) q^{7} -5.98844 q^{8} +(-2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q-2.52434 q^{2} +(0.396143 - 1.68614i) q^{3} +4.37228 q^{4} +(-1.00000 + 4.25639i) q^{6} +(1.73205 - 2.00000i) q^{7} -5.98844 q^{8} +(-2.68614 - 1.33591i) q^{9} +0.792287i q^{11} +(1.73205 - 7.37228i) q^{12} -5.84096 q^{13} +(-4.37228 + 5.04868i) q^{14} +6.37228 q^{16} -1.37228i q^{17} +(6.78073 + 3.37228i) q^{18} -3.46410i q^{19} +(-2.68614 - 3.71277i) q^{21} -2.00000i q^{22} +1.87953 q^{23} +(-2.37228 + 10.0974i) q^{24} +14.7446 q^{26} +(-3.31662 + 4.00000i) q^{27} +(7.57301 - 8.74456i) q^{28} -4.25639i q^{29} -3.46410i q^{31} -4.10891 q^{32} +(1.33591 + 0.313859i) q^{33} +3.46410i q^{34} +(-11.7446 - 5.84096i) q^{36} +4.74456i q^{37} +8.74456i q^{38} +(-2.31386 + 9.84868i) q^{39} -6.00000 q^{41} +(6.78073 + 9.37228i) q^{42} +6.74456i q^{43} +3.46410i q^{44} -4.74456 q^{46} -7.37228i q^{47} +(2.52434 - 10.7446i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-2.31386 - 0.543620i) q^{51} -25.5383 q^{52} -8.51278 q^{53} +(8.37228 - 10.0974i) q^{54} +(-10.3723 + 11.9769i) q^{56} +(-5.84096 - 1.37228i) q^{57} +10.7446i q^{58} -2.74456 q^{59} -6.92820i q^{61} +8.74456i q^{62} +(-7.32435 + 3.05842i) q^{63} -2.37228 q^{64} +(-3.37228 - 0.792287i) q^{66} -6.74456i q^{67} -6.00000i q^{68} +(0.744563 - 3.16915i) q^{69} +13.5615i q^{71} +(16.0858 + 8.00000i) q^{72} -6.92820 q^{73} -11.9769i q^{74} -15.1460i q^{76} +(1.58457 + 1.37228i) q^{77} +(5.84096 - 24.8614i) q^{78} -3.37228 q^{79} +(5.43070 + 7.17687i) q^{81} +15.1460 q^{82} -5.48913i q^{83} +(-11.7446 - 16.2333i) q^{84} -17.0256i q^{86} +(-7.17687 - 1.68614i) q^{87} -4.74456i q^{88} -3.25544 q^{89} +(-10.1168 + 11.6819i) q^{91} +8.21782 q^{92} +(-5.84096 - 1.37228i) q^{93} +18.6101i q^{94} +(-1.62772 + 6.92820i) q^{96} -1.08724 q^{97} +(2.52434 + 17.4891i) q^{98} +(1.05842 - 2.12819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) $ 8 * q + 12 * q^4 - 8 * q^6 - 10 * q^9	$ 8 q + 12 q^{4} - 8 q^{6} - 10 q^{9} - 12 q^{14} + 28 q^{16} - 10 q^{21} + 4 q^{24} + 72 q^{26} - 48 q^{36} - 30 q^{39} - 48 q^{41} + 8 q^{46} - 8 q^{49} - 30 q^{51} + 44 q^{54} - 60 q^{56} + 24 q^{59} + 4 q^{64} - 4 q^{66} - 40 q^{69} - 4 q^{79} - 14 q^{81} - 48 q^{84} - 72 q^{89} - 12 q^{91} - 36 q^{96} - 26 q^{99}+O(q^{100}) $ 8 * q + 12 * q^4 - 8 * q^6 - 10 * q^9 - 12 * q^14 + 28 * q^16 - 10 * q^21 + 4 * q^24 + 72 * q^26 - 48 * q^36 - 30 * q^39 - 48 * q^41 + 8 * q^46 - 8 * q^49 - 30 * q^51 + 44 * q^54 - 60 * q^56 + 24 * q^59 + 4 * q^64 - 4 * q^66 - 40 * q^69 - 4 * q^79 - 14 * q^81 - 48 * q^84 - 72 * q^89 - 12 * q^91 - 36 * q^96 - 26 * 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 $

$2$	−2.52434			−1.78498			−0.892488	−	0.451071i	$-0.851042\pi$
$2$	−2.52434			−1.78498			−0.892488	+	0.451071i	$0.851042\pi$
$3$	0.396143	−	1.68614i	0.228714	−	0.973494i
$3$	0.396143	−	1.68614i	0.228714	−	0.973494i
$4$	4.37228			2.18614
$5$		0			0
$5$		0			0
$6$	−1.00000	+	4.25639i	−0.408248	+	1.73766i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$	−5.98844			−2.11723
$9$	−2.68614	−	1.33591i	−0.895380	−	0.445302i
$10$		0			0
$11$			0.792287i			0.238884i	0.992841	+	0.119442i	$0.0381105\pi$
$11$			0.792287i			0.238884i	−0.992841	+	0.119442i	$0.961890\pi$
$12$	1.73205	−	7.37228i	0.500000	−	2.12819i
$13$	−5.84096			−1.61999			−0.809996	−	0.586436i	$-0.800531\pi$
$13$	−5.84096			−1.61999			−0.809996	+	0.586436i	$0.800531\pi$
$14$	−4.37228	+	5.04868i	−1.16854	+	1.34932i
$15$		0			0
$16$	6.37228			1.59307
$17$		−	1.37228i		−	0.332827i	−0.986056	−	0.166414i	$-0.946781\pi$
$17$		−	1.37228i		−	0.332827i	0.986056	−	0.166414i	$-0.0532187\pi$
$18$	6.78073	+	3.37228i	1.59823	+	0.794854i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	−2.68614	−	3.71277i	−0.586164	−	0.810192i
$22$		−	2.00000i		−	0.426401i
$23$	1.87953			0.391909			0.195954	−	0.980613i	$-0.437220\pi$
$23$	1.87953			0.391909			0.195954	+	0.980613i	$0.437220\pi$
$24$	−2.37228	+	10.0974i	−0.484240	+	2.06111i
$25$		0			0
$26$	14.7446			2.89165
$27$	−3.31662	+	4.00000i	−0.638285	+	0.769800i
$28$	7.57301	−	8.74456i	1.43117	−	1.65257i
$29$		−	4.25639i		−	0.790392i	−0.918597	−	0.395196i	$-0.870677\pi$
$29$		−	4.25639i		−	0.790392i	0.918597	−	0.395196i	$-0.129323\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	−4.10891			−0.726360
$33$	1.33591	+	0.313859i	0.232552	+	0.0546359i
$34$			3.46410i			0.594089i
$35$		0			0
$36$	−11.7446	−	5.84096i	−1.95743	−	0.973494i
$37$			4.74456i			0.780001i	0.920815	+	0.390001i	$0.127525\pi$
$37$			4.74456i			0.780001i	−0.920815	+	0.390001i	$0.872475\pi$
$38$			8.74456i			1.41856i
$39$	−2.31386	+	9.84868i	−0.370514	+	1.57705i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	6.78073	+	9.37228i	1.04629	+	1.44617i
$43$			6.74456i			1.02854i	0.857629	+	0.514268i	$0.171936\pi$
$43$			6.74456i			1.02854i	−0.857629	+	0.514268i	$0.828064\pi$
$44$			3.46410i			0.522233i
$45$		0			0
$46$	−4.74456			−0.699548
$47$		−	7.37228i		−	1.07536i	−0.843150	−	0.537679i	$-0.819301\pi$
$47$		−	7.37228i		−	1.07536i	0.843150	−	0.537679i	$-0.180699\pi$
$48$	2.52434	−	10.7446i	0.364357	−	1.55084i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−2.31386	−	0.543620i	−0.324005	−	0.0761221i
$52$	−25.5383			−3.54153
$53$	−8.51278			−1.16932			−0.584660	−	0.811278i	$-0.698772\pi$
$53$	−8.51278			−1.16932			−0.584660	+	0.811278i	$0.698772\pi$
$54$	8.37228	−	10.0974i	1.13932	−	1.37408i
$55$		0			0
$56$	−10.3723	+	11.9769i	−1.38605	+	1.60048i
$57$	−5.84096	−	1.37228i	−0.773654	−	0.181763i
$58$			10.7446i			1.41083i
$59$	−2.74456			−0.357312			−0.178656	−	0.983912i	$-0.557175\pi$
$59$	−2.74456			−0.357312			−0.178656	+	0.983912i	$0.557175\pi$
$60$		0			0
$61$		−	6.92820i		−	0.887066i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$		−	6.92820i		−	0.887066i	0.896258	−	0.443533i	$-0.146275\pi$
$62$			8.74456i			1.11056i
$63$	−7.32435	+	3.05842i	−0.922781	+	0.385325i
$64$	−2.37228			−0.296535
$65$		0			0
$66$	−3.37228	−	0.792287i	−0.415099	−	0.0975238i
$67$		−	6.74456i		−	0.823979i	−0.911188	−	0.411990i	$-0.864834\pi$
$67$		−	6.74456i		−	0.823979i	0.911188	−	0.411990i	$-0.135166\pi$
$68$		−	6.00000i		−	0.727607i
$69$	0.744563	−	3.16915i	0.0896348	−	0.381521i
$70$		0			0
$71$			13.5615i			1.60945i	0.593649	+	0.804724i	$0.297687\pi$
$71$			13.5615i			1.60945i	−0.593649	+	0.804724i	$0.702313\pi$
$72$	16.0858	+	8.00000i	1.89573	+	0.942809i
$73$	−6.92820			−0.810885			−0.405442	−	0.914121i	$-0.632883\pi$
$73$	−6.92820			−0.810885			−0.405442	+	0.914121i	$0.632883\pi$
$74$		−	11.9769i		−	1.39228i
$75$		0			0
$76$		−	15.1460i		−	1.73737i
$77$	1.58457	+	1.37228i	0.180579	+	0.156386i
$78$	5.84096	−	24.8614i	0.661359	−	2.81500i
$79$	−3.37228			−0.379411			−0.189706	−	0.981841i	$-0.560753\pi$
$79$	−3.37228			−0.379411			−0.189706	+	0.981841i	$0.560753\pi$
$80$		0			0
$81$	5.43070	+	7.17687i	0.603411	+	0.797430i
$82$	15.1460			1.67260
$83$		−	5.48913i		−	0.602510i	−0.953544	−	0.301255i	$-0.902594\pi$
$83$		−	5.48913i		−	0.602510i	0.953544	−	0.301255i	$-0.0974055\pi$
$84$	−11.7446	−	16.2333i	−1.28144	−	1.77119i
$85$		0			0
$86$		−	17.0256i		−	1.83591i
$87$	−7.17687	−	1.68614i	−0.769441	−	0.180773i
$88$		−	4.74456i		−	0.505772i
$89$	−3.25544			−0.345076			−0.172538	−	0.985003i	$-0.555197\pi$
$89$	−3.25544			−0.345076			−0.172538	+	0.985003i	$0.555197\pi$
$90$		0			0
$91$	−10.1168	+	11.6819i	−1.06053	+	1.22460i
$92$	8.21782			0.856767
$93$	−5.84096	−	1.37228i	−0.605680	−	0.142299i
$94$			18.6101i			1.91949i
$95$		0			0
$96$	−1.62772	+	6.92820i	−0.166128	+	0.707107i
$97$	−1.08724			−0.110393			−0.0551963	−	0.998476i	$-0.517578\pi$
$97$	−1.08724			−0.110393			−0.0551963	+	0.998476i	$0.517578\pi$
$98$	2.52434	+	17.4891i	0.254997	+	1.76667i
$99$	1.05842	−	2.12819i	0.106375	−	0.213892i
$100$		0			0
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$	5.84096	+	1.37228i	0.578341	+	0.135876i
$103$	16.2333			1.59951			0.799756	−	0.600326i	$-0.204962\pi$
$103$	16.2333			1.59951			0.799756	+	0.600326i	$0.204962\pi$
$104$	34.9783			3.42990
$105$		0			0
$106$	21.4891			2.08721
$107$	−6.63325			−0.641260			−0.320630	−	0.947204i	$-0.603895\pi$
$107$	−6.63325			−0.641260			−0.320630	+	0.947204i	$0.603895\pi$
$108$	−14.5012	+	17.4891i	−1.39538	+	1.68289i
$109$	−0.116844			−0.0111916			−0.00559581	−	0.999984i	$-0.501781\pi$
$109$	−0.116844			−0.0111916			−0.00559581	+	0.999984i	$0.501781\pi$
$110$		0			0
$111$	8.00000	+	1.87953i	0.759326	+	0.178397i
$112$	11.0371	−	12.7446i	1.04291	−	1.20425i
$113$	10.0974			0.949879			0.474939	−	0.880018i	$-0.342470\pi$
$113$	10.0974			0.949879			0.474939	+	0.880018i	$0.342470\pi$
$114$	14.7446	+	3.46410i	1.38095	+	0.324443i
$115$		0			0
$116$		−	18.6101i		−	1.72791i
$117$	15.6896	+	7.80298i	1.45051	+	0.721386i
$118$	6.92820			0.637793
$119$	−2.74456	−	2.37686i	−0.251594	−	0.217886i
$120$		0			0
$121$	10.3723			0.942935
$122$			17.4891i			1.58339i
$123$	−2.37686	+	10.1168i	−0.214314	+	0.912205i
$124$		−	15.1460i		−	1.36015i
$125$		0			0
$126$	18.4891	−	7.72049i	1.64714	−	0.687796i
$127$			10.7446i			0.953426i	0.879059	+	0.476713i	$0.158172\pi$
$127$			10.7446i			0.953426i	−0.879059	+	0.476713i	$0.841828\pi$
$128$	14.2063			1.25567
$129$	11.3723	+	2.67181i	1.00127	+	0.235240i
$130$		0			0
$131$	−17.4891			−1.52803			−0.764016	−	0.645197i	$-0.776775\pi$
$131$	−17.4891			−1.52803			−0.764016	+	0.645197i	$0.776775\pi$
$132$	5.84096	+	1.37228i	0.508391	+	0.119442i
$133$	−6.92820	−	6.00000i	−0.600751	−	0.520266i
$134$			17.0256i			1.47078i
$135$		0			0
$136$			8.21782i			0.704673i
$137$	13.2665			1.13343			0.566717	−	0.823913i	$-0.308213\pi$
$137$	13.2665			1.13343			0.566717	+	0.823913i	$0.308213\pi$
$138$	−1.87953	+	8.00000i	−0.159996	+	0.681005i
$139$		−	1.28962i		−	0.109384i	−0.998503	−	0.0546921i	$-0.982582\pi$
$139$		−	1.28962i		−	0.109384i	0.998503	−	0.0546921i	$-0.0174177\pi$
$140$		0			0
$141$	−12.4307	−	2.92048i	−1.04685	−	0.245949i
$142$		−	34.2337i		−	2.87283i
$143$		−	4.62772i		−	0.386989i
$144$	−17.1168	−	8.51278i	−1.42640	−	0.709398i
$145$		0			0
$146$	17.4891			1.44741
$147$	−12.0781	−	1.05842i	−0.996182	−	0.0872972i
$148$			20.7446i			1.70519i
$149$		−	10.0974i		−	0.827207i	−0.910457	−	0.413604i	$-0.864270\pi$
$149$		−	10.0974i		−	0.827207i	0.910457	−	0.413604i	$-0.135730\pi$
$150$		0			0
$151$	3.37228			0.274432			0.137216	−	0.990541i	$-0.456184\pi$
$151$	3.37228			0.274432			0.137216	+	0.990541i	$0.456184\pi$
$152$			20.7446i			1.68261i
$153$	−1.83324	+	3.68614i	−0.148209	+	0.298007i
$154$	−4.00000	−	3.46410i	−0.322329	−	0.279145i
$155$		0			0
$156$	−10.1168	+	43.0612i	−0.809996	+	3.44766i
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$	8.51278			0.677240
$159$	−3.37228	+	14.3537i	−0.267439	+	1.13833i
$160$		0			0
$161$	3.25544	−	3.75906i	0.256564	−	0.296255i
$162$	−13.7089	−	18.1168i	−1.07708	−	1.42339i
$163$		−	8.00000i		−	0.626608i	−0.949653	−	0.313304i	$-0.898564\pi$
$163$		−	8.00000i		−	0.626608i	0.949653	−	0.313304i	$-0.101436\pi$
$164$	−26.2337			−2.04851
$165$		0			0
$166$			13.8564i			1.07547i
$167$		−	22.1168i		−	1.71145i	−0.517429	−	0.855726i	$-0.673111\pi$
$167$		−	22.1168i		−	1.71145i	0.517429	−	0.855726i	$-0.326889\pi$
$168$	16.0858	+	22.2337i	1.24105	+	1.71537i
$169$	21.1168			1.62437
$170$		0			0
$171$	−4.62772	+	9.30506i	−0.353890	+	0.711576i
$172$			29.4891i			2.24852i
$173$		−	16.1168i		−	1.22534i	−0.790338	−	0.612670i	$-0.790095\pi$
$173$		−	16.1168i		−	1.22534i	0.790338	−	0.612670i	$-0.209905\pi$
$174$	18.1168	+	4.25639i	1.37343	+	0.322676i
$175$		0			0
$176$			5.04868i			0.380558i
$177$	−1.08724	+	4.62772i	−0.0817220	+	0.347841i
$178$	8.21782			0.615952
$179$		−	6.63325i		−	0.495792i	−0.968787	−	0.247896i	$-0.920261\pi$
$179$		−	6.63325i		−	0.495792i	0.968787	−	0.247896i	$-0.0797392\pi$
$180$		0			0
$181$			18.6101i			1.38328i	0.722242	+	0.691640i	$0.243111\pi$
$181$			18.6101i			1.38328i	−0.722242	+	0.691640i	$0.756889\pi$
$182$	25.5383	−	29.4891i	1.89303	−	2.18588i
$183$	−11.6819	−	2.74456i	−0.863553	−	0.202884i
$184$	−11.2554			−0.829762
$185$		0			0
$186$	14.7446	+	3.46410i	1.08112	+	0.254000i
$187$	1.08724			0.0795069
$188$		−	32.2337i		−	2.35088i
$189$	2.25544	+	13.5615i	0.164059	+	0.986451i
$190$		0			0
$191$		−	15.6434i		−	1.13191i	−0.824435	−	0.565957i	$-0.808507\pi$
$191$		−	15.6434i		−	1.13191i	0.824435	−	0.565957i	$-0.191493\pi$
$192$	−0.939764	+	4.00000i	−0.0678216	+	0.288675i
$193$		−	22.2337i		−	1.60042i	−0.599723	−	0.800208i	$-0.704722\pi$
$193$		−	22.2337i		−	1.60042i	0.599723	−	0.800208i	$-0.295278\pi$
$194$	2.74456			0.197048
$195$		0			0
$196$	−4.37228	−	30.2921i	−0.312306	−	2.16372i
$197$	22.3692			1.59374			0.796869	−	0.604152i	$-0.206488\pi$
$197$	22.3692			1.59374			0.796869	+	0.604152i	$0.206488\pi$
$198$	−2.67181	+	5.37228i	−0.189878	+	0.381791i
$199$			12.9715i			0.919528i	0.888041	+	0.459764i	$0.152066\pi$
$199$			12.9715i			0.919528i	−0.888041	+	0.459764i	$0.847934\pi$
$200$		0			0
$201$	−11.3723	−	2.67181i	−0.802139	−	0.188455i
$202$	−15.1460			−1.06567
$203$	−8.51278	−	7.37228i	−0.597480	−	0.517433i
$204$	−10.1168	−	2.37686i	−0.708321	−	0.166414i
$205$		0			0
$206$	−40.9783			−2.85509
$207$	−5.04868	−	2.51087i	−0.350907	−	0.174518i
$208$	−37.2203			−2.58076
$209$	2.74456			0.189845
$210$		0			0
$211$	6.11684			0.421101			0.210550	−	0.977583i	$-0.432474\pi$
$211$	6.11684			0.421101			0.210550	+	0.977583i	$0.432474\pi$
$212$	−37.2203			−2.55630
$213$	22.8665	+	5.37228i	1.56679	+	0.368103i
$214$	16.7446			1.14463
$215$		0			0
$216$	19.8614	−	23.9538i	1.35140	−	1.62985i
$217$	−6.92820	−	6.00000i	−0.470317	−	0.407307i
$218$	0.294954			0.0199768
$219$	−2.74456	+	11.6819i	−0.185460	+	0.789391i
$220$		0			0
$221$			8.01544i			0.539177i
$222$	−20.1947	−	4.74456i	−1.35538	−	0.318434i
$223$	−20.9870			−1.40539			−0.702696	−	0.711490i	$-0.748021\pi$
$223$	−20.9870			−1.40539			−0.702696	+	0.711490i	$0.748021\pi$
$224$	−7.11684	+	8.21782i	−0.475514	+	0.549076i
$225$		0			0
$226$	−25.4891			−1.69551
$227$		−	15.6060i		−	1.03580i	−0.855440	−	0.517902i	$-0.826713\pi$
$227$		−	15.6060i		−	1.03580i	0.855440	−	0.517902i	$-0.173287\pi$
$228$	−25.5383	−	6.00000i	−1.69132	−	0.397360i
$229$		−	4.75372i		−	0.314135i	−0.987588	−	0.157067i	$-0.949796\pi$
$229$		−	4.75372i		−	0.314135i	0.987588	−	0.157067i	$-0.0502040\pi$
$230$		0			0
$231$	2.94158	−	2.12819i	0.193542	−	0.140025i
$232$			25.4891i			1.67344i
$233$	−3.75906			−0.246264			−0.123132	−	0.992390i	$-0.539294\pi$
$233$	−3.75906			−0.246264			−0.123132	+	0.992390i	$0.539294\pi$
$234$	−39.6060	−	19.6974i	−2.58912	−	1.28766i
$235$		0			0
$236$	−12.0000			−0.781133
$237$	−1.33591	+	5.68614i	−0.0867765	+	0.369355i
$238$	6.92820	+	6.00000i	0.449089	+	0.388922i
$239$			15.6434i			1.01188i	0.862567	+	0.505942i	$0.168855\pi$
$239$			15.6434i			1.01188i	−0.862567	+	0.505942i	$0.831145\pi$
$240$		0			0
$241$		−	23.3639i		−	1.50500i	−0.658593	−	0.752499i	$-0.728848\pi$
$241$		−	23.3639i		−	1.50500i	0.658593	−	0.752499i	$-0.271152\pi$
$242$	−26.1831			−1.68312
$243$	14.2525	−	6.31386i	0.914302	−	0.405034i
$244$		−	30.2921i		−	1.93925i
$245$		0			0
$246$	6.00000	−	25.5383i	0.382546	−	1.62826i
$247$			20.2337i			1.28744i
$248$			20.7446i			1.31728i
$249$	−9.25544	−	2.17448i	−0.586540	−	0.137802i
$250$		0			0
$251$	17.4891			1.10390			0.551952	−	0.833876i	$-0.313883\pi$
$251$	17.4891			1.10390			0.551952	+	0.833876i	$0.313883\pi$
$252$	−32.0241	+	13.3723i	−2.01733	+	0.842375i
$253$			1.48913i			0.0936205i
$254$		−	27.1229i		−	1.70184i
$255$		0			0
$256$	−31.1168			−1.94480
$257$			23.4891i			1.46521i	0.680653	+	0.732606i	$0.261696\pi$
$257$			23.4891i			1.46521i	−0.680653	+	0.732606i	$0.738304\pi$
$258$	−28.7075	−	6.74456i	−1.78725	−	0.419898i
$259$	9.48913	+	8.21782i	0.589626	+	0.510631i
$260$		0			0
$261$	−5.68614	+	11.4333i	−0.351963	+	0.707701i
$262$	44.1485			2.72750
$263$	13.5615			0.836235			0.418118	−	0.908393i	$-0.362690\pi$
$263$	13.5615			0.836235			0.418118	+	0.908393i	$0.362690\pi$
$264$	−8.00000	−	1.87953i	−0.492366	−	0.115677i
$265$		0			0
$266$	17.4891	+	15.1460i	1.07233	+	0.928662i
$267$	−1.28962	+	5.48913i	−0.0789235	+	0.335929i
$268$		−	29.4891i		−	1.80134i
$269$	8.74456			0.533165			0.266583	−	0.963812i	$-0.414105\pi$
$269$	8.74456			0.533165			0.266583	+	0.963812i	$0.414105\pi$
$270$		0			0
$271$		−	15.1460i		−	0.920056i	−0.887905	−	0.460028i	$-0.847839\pi$
$271$		−	15.1460i		−	0.920056i	0.887905	−	0.460028i	$-0.152161\pi$
$272$		−	8.74456i		−	0.530217i
$273$	15.6896	+	21.6861i	0.949581	+	1.31250i
$274$	−33.4891			−2.02315
$275$		0			0
$276$	3.25544	−	13.8564i	0.195954	−	0.834058i
$277$		−	6.23369i		−	0.374546i	−0.982308	−	0.187273i	$-0.940035\pi$
$277$		−	6.23369i		−	0.374546i	0.982308	−	0.187273i	$-0.0599649\pi$
$278$			3.25544i			0.195248i
$279$	−4.62772	+	9.30506i	−0.277054	+	0.557080i
$280$		0			0
$281$		−	4.84630i		−	0.289106i	−0.989497	−	0.144553i	$-0.953826\pi$
$281$		−	4.84630i		−	0.289106i	0.989497	−	0.144553i	$-0.0461744\pi$
$282$	31.3793	+	7.37228i	1.86861	+	0.439013i
$283$	9.30506			0.553129			0.276564	−	0.960995i	$-0.410804\pi$
$283$	9.30506			0.553129			0.276564	+	0.960995i	$0.410804\pi$
$284$			59.2945i			3.51848i
$285$		0			0
$286$			11.6819i			0.690767i
$287$	−10.3923	+	12.0000i	−0.613438	+	0.708338i
$288$	11.0371	+	5.48913i	0.650368	+	0.323450i
$289$	15.1168			0.889226
$290$		0			0
$291$	−0.430703	+	1.83324i	−0.0252483	+	0.107466i
$292$	−30.2921			−1.77271
$293$			28.1168i			1.64260i	0.570494	+	0.821302i	$0.306752\pi$
$293$			28.1168i			1.64260i	−0.570494	+	0.821302i	$0.693248\pi$
$294$	30.4891	+	2.67181i	1.77816	+	0.155823i
$295$		0			0
$296$		−	28.4125i		−	1.65144i
$297$	−3.16915	−	2.62772i	−0.183893	−	0.152476i
$298$			25.4891i			1.47655i
$299$	−10.9783			−0.634889
$300$		0			0
$301$	13.4891	+	11.6819i	0.777500	+	0.673335i
$302$	−8.51278			−0.489855
$303$	2.37686	−	10.1168i	0.136547	−	0.581198i
$304$		−	22.0742i		−	1.26604i
$305$		0			0
$306$	4.62772	−	9.30506i	0.264549	−	0.531935i
$307$	−7.13058			−0.406964			−0.203482	−	0.979079i	$-0.565226\pi$
$307$	−7.13058			−0.406964			−0.203482	+	0.979079i	$0.565226\pi$
$308$	6.92820	+	6.00000i	0.394771	+	0.341882i
$309$	6.43070	−	27.3716i	0.365830	−	1.55711i
$310$		0			0
$311$	20.2337			1.14735			0.573674	−	0.819084i	$-0.305518\pi$
$311$	20.2337			1.14735			0.573674	+	0.819084i	$0.305518\pi$
$312$	13.8564	−	58.9783i	0.784465	−	3.33899i
$313$	24.4511			1.38206			0.691029	−	0.722827i	$-0.257158\pi$
$313$	24.4511			1.38206			0.691029	+	0.722827i	$0.257158\pi$
$314$		0			0
$315$		0			0
$316$	−14.7446			−0.829446
$317$	8.51278			0.478125			0.239063	−	0.971004i	$-0.423160\pi$
$317$	8.51278			0.478125			0.239063	+	0.971004i	$0.423160\pi$
$318$	8.51278	−	36.2337i	0.477373	−	2.03188i
$319$	3.37228			0.188812
$320$		0			0
$321$	−2.62772	+	11.1846i	−0.146665	+	0.624263i
$322$	−8.21782	+	9.48913i	−0.457961	+	0.528808i
$323$	−4.75372			−0.264504
$324$	23.7446	+	31.3793i	1.31914	+	1.74329i
$325$		0			0
$326$			20.1947i			1.11848i
$327$	−0.0462870	+	0.197015i	−0.00255968	+	0.0108950i
$328$	35.9306			1.98394
$329$	−14.7446	−	12.7692i	−0.812894	−	0.703987i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$		−	24.0000i		−	1.31717i
$333$	6.33830	−	12.7446i	0.347336	−	0.698398i
$334$			55.8304i			3.05490i
$335$		0			0
$336$	−17.1168	−	23.6588i	−0.933800	−	1.29069i
$337$		−	18.2337i		−	0.993252i	−0.867965	−	0.496626i	$-0.834572\pi$
$337$		−	18.2337i		−	0.993252i	0.867965	−	0.496626i	$-0.165428\pi$
$338$	−53.3060			−2.89947
$339$	4.00000	−	17.0256i	0.217250	−	0.924701i
$340$		0			0
$341$	2.74456			0.148626
$342$	11.6819	−	23.4891i	0.631686	−	1.27015i
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		−	40.3894i		−	2.17765i
$345$		0			0
$346$			40.6844i			2.18720i
$347$	−18.3152			−0.983210			−0.491605	−	0.870818i	$-0.663590\pi$
$347$	−18.3152			−0.983210			−0.491605	+	0.870818i	$0.663590\pi$
$348$	−31.3793	−	7.37228i	−1.68211	−	0.395196i
$349$			4.75372i			0.254461i	0.991873	+	0.127230i	$0.0406088\pi$
$349$			4.75372i			0.254461i	−0.991873	+	0.127230i	$0.959391\pi$
$350$		0			0
$351$	19.3723	−	23.3639i	1.03402	−	1.24707i
$352$		−	3.25544i		−	0.173515i
$353$		−	7.88316i		−	0.419578i	−0.977747	−	0.209789i	$-0.932722\pi$
$353$		−	7.88316i		−	0.419578i	0.977747	−	0.209789i	$-0.0672777\pi$
$354$	2.74456	−	11.6819i	0.145872	−	0.620887i
$355$		0			0
$356$	−14.2337			−0.754384
$357$	−5.09496	+	3.68614i	−0.269654	+	0.195091i
$358$			16.7446i			0.884978i
$359$			9.80240i			0.517351i	0.965964	+	0.258675i	$0.0832860\pi$
$359$			9.80240i			0.517351i	−0.965964	+	0.258675i	$0.916714\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		−	46.9783i		−	2.46912i
$363$	4.10891	−	17.4891i	0.215662	−	0.917941i
$364$	−44.2337	+	51.0767i	−2.31848	+	2.67714i
$365$		0			0
$366$	29.4891	+	6.92820i	1.54142	+	0.362143i
$367$	25.3360			1.32253			0.661263	−	0.750154i	$-0.270021\pi$
$367$	25.3360			1.32253			0.661263	+	0.750154i	$0.270021\pi$
$368$	11.9769			0.624338
$369$	16.1168	+	8.01544i	0.839009	+	0.417267i
$370$		0			0
$371$	−14.7446	+	17.0256i	−0.765500	+	0.883923i
$372$	−25.5383	−	6.00000i	−1.32410	−	0.311086i
$373$			24.7446i			1.28122i	0.767864	+	0.640612i	$0.221319\pi$
$373$			24.7446i			1.28122i	−0.767864	+	0.640612i	$0.778681\pi$
$374$	−2.74456			−0.141918
$375$		0			0
$376$			44.1485i			2.27678i
$377$			24.8614i			1.28043i
$378$	−5.69349	−	34.2337i	−0.292841	−	1.76079i
$379$	−1.48913			−0.0764912			−0.0382456	−	0.999268i	$-0.512177\pi$
$379$	−1.48913			−0.0764912			−0.0382456	+	0.999268i	$0.512177\pi$
$380$		0			0
$381$	18.1168	+	4.25639i	0.928154	+	0.218061i
$382$			39.4891i			2.02044i
$383$			17.4891i			0.893653i	0.894621	+	0.446826i	$0.147446\pi$
$383$			17.4891i			0.893653i	−0.894621	+	0.446826i	$0.852554\pi$
$384$	5.62772	−	23.9538i	0.287188	−	1.22239i
$385$		0			0
$386$			56.1253i			2.85670i
$387$	9.01011	−	18.1168i	0.458010	−	0.920931i
$388$	−4.75372			−0.241334
$389$		−	13.7638i		−	0.697854i	−0.937150	−	0.348927i	$-0.886546\pi$
$389$		−	13.7638i		−	0.697854i	0.937150	−	0.348927i	$-0.113454\pi$
$390$		0			0
$391$		−	2.57924i		−	0.130438i
$392$	5.98844	+	41.4891i	0.302462	+	2.09552i
$393$	−6.92820	+	29.4891i	−0.349482	+	1.48753i
$394$	−56.4674			−2.84479
$395$		0			0
$396$	4.62772	−	9.30506i	0.232552	−	0.467597i
$397$	3.66648			0.184015			0.0920077	−	0.995758i	$-0.470672\pi$
$397$	3.66648			0.184015			0.0920077	+	0.995758i	$0.470672\pi$
$398$		−	32.7446i		−	1.64134i
$399$	−12.8614	+	9.30506i	−0.643876	+	0.465836i
$400$		0			0
$401$		−	2.67181i		−	0.133424i	−0.997772	−	0.0667120i	$-0.978749\pi$
$401$		−	2.67181i		−	0.133424i	0.997772	−	0.0667120i	$-0.0212509\pi$
$402$	28.7075	+	6.74456i	1.43180	+	0.336388i
$403$			20.2337i			1.00791i
$404$	26.2337			1.30517
$405$		0			0
$406$	21.4891	+	18.6101i	1.06649	+	0.923605i
$407$	−3.75906			−0.186329
$408$	13.8564	+	3.25544i	0.685994	+	0.161168i
$409$		−	35.0458i		−	1.73290i	−0.499262	−	0.866451i	$-0.666396\pi$
$409$		−	35.0458i		−	1.73290i	0.499262	−	0.866451i	$-0.333604\pi$
$410$		0			0
$411$	5.25544	−	22.3692i	0.259232	−	1.10339i
$412$	70.9764			3.49676
$413$	−4.75372	+	5.48913i	−0.233915	+	0.270102i
$414$	12.7446	+	6.33830i	0.626361	+	0.311510i
$415$		0			0
$416$	24.0000			1.17670
$417$	−2.17448	−	0.510875i	−0.106485	−	0.0250176i
$418$	−6.92820			−0.338869
$419$	2.74456			0.134081			0.0670403	−	0.997750i	$-0.478644\pi$
$419$	2.74456			0.134081			0.0670403	+	0.997750i	$0.478644\pi$
$420$		0			0
$421$	−25.6060			−1.24796			−0.623979	−	0.781441i	$-0.714485\pi$
$421$	−25.6060			−1.24796			−0.623979	+	0.781441i	$0.714485\pi$
$422$	−15.4410			−0.751655
$423$	−9.84868	+	19.8030i	−0.478859	+	0.962854i
$424$	50.9783			2.47572
$425$		0			0
$426$	−57.7228	−	13.5615i	−2.79668	−	0.657055i
$427$	−13.8564	−	12.0000i	−0.670559	−	0.580721i
$428$	−29.0024			−1.40189
$429$	−7.80298	−	1.83324i	−0.376732	−	0.0885097i
$430$		0			0
$431$		−	31.6742i		−	1.52569i	−0.646579	−	0.762847i	$-0.723801\pi$
$431$		−	31.6742i		−	1.52569i	0.646579	−	0.762847i	$-0.276199\pi$
$432$	−21.1345	+	25.4891i	−1.01683	+	1.22635i
$433$	2.57924			0.123950			0.0619752	−	0.998078i	$-0.480260\pi$
$433$	2.57924			0.123950			0.0619752	+	0.998078i	$0.480260\pi$
$434$	17.4891	+	15.1460i	0.839505	+	0.727033i
$435$		0			0
$436$	−0.510875			−0.0244665
$437$		−	6.51087i		−	0.311457i
$438$	6.92820	−	29.4891i	0.331042	−	1.40904i
$439$			1.28962i			0.0615502i	0.999526	+	0.0307751i	$0.00979757\pi$
$439$			1.28962i			0.0615502i	−0.999526	+	0.0307751i	$0.990202\pi$
$440$		0			0
$441$	−6.56930	+	19.9460i	−0.312824	+	0.949811i
$442$		−	20.2337i		−	0.962418i
$443$	6.63325			0.315155			0.157578	−	0.987507i	$-0.449632\pi$
$443$	6.63325			0.315155			0.157578	+	0.987507i	$0.449632\pi$
$444$	34.9783	+	8.21782i	1.65999	+	0.390001i
$445$		0			0
$446$	52.9783			2.50859
$447$	−17.0256	−	4.00000i	−0.805281	−	0.189194i
$448$	−4.10891	+	4.74456i	−0.194128	+	0.224160i
$449$			28.2101i			1.33132i	0.746256	+	0.665660i	$0.231850\pi$
$449$			28.2101i			1.33132i	−0.746256	+	0.665660i	$0.768150\pi$
$450$		0			0
$451$		−	4.75372i		−	0.223844i
$452$	44.1485			2.07657
$453$	1.33591	−	5.68614i	0.0627664	−	0.267158i
$454$			39.3947i			1.84889i
$455$		0			0
$456$	34.9783	+	8.21782i	1.63801	+	0.384835i
$457$		−	32.9783i		−	1.54266i	−0.636437	−	0.771329i	$-0.719592\pi$
$457$		−	32.9783i		−	1.54266i	0.636437	−	0.771329i	$-0.280408\pi$
$458$			12.0000i			0.560723i
$459$	5.48913	+	4.55134i	0.256210	+	0.212438i
$460$		0			0
$461$	−8.74456			−0.407275			−0.203637	−	0.979046i	$-0.565276\pi$
$461$	−8.74456			−0.407275			−0.203637	+	0.979046i	$0.565276\pi$
$462$	−7.42554	+	5.37228i	−0.345467	+	0.249941i
$463$		−	36.4674i		−	1.69478i	−0.530969	−	0.847391i	$-0.678172\pi$
$463$		−	36.4674i		−	1.69478i	0.530969	−	0.847391i	$-0.321828\pi$
$464$		−	27.1229i		−	1.25915i
$465$		0			0
$466$	9.48913			0.439575
$467$		−	13.8832i		−	0.642436i	−0.947005	−	0.321218i	$-0.895908\pi$
$467$		−	13.8832i		−	0.642436i	0.947005	−	0.321218i	$-0.104092\pi$
$468$	68.5996	+	34.1168i	3.17102	+	1.57705i
$469$	−13.4891	−	11.6819i	−0.622870	−	0.539421i
$470$		0			0
$471$		0			0
$472$	16.4356			0.756512
$473$	−5.34363			−0.245700
$474$	3.37228	−	14.3537i	0.154894	−	0.659289i
$475$		0			0
$476$	−12.0000	−	10.3923i	−0.550019	−	0.476331i
$477$	22.8665	+	11.3723i	1.04699	+	0.520701i
$478$		−	39.4891i		−	1.80619i
$479$	−18.5109			−0.845783			−0.422892	−	0.906180i	$-0.638985\pi$
$479$	−18.5109			−0.845783			−0.422892	+	0.906180i	$0.638985\pi$
$480$		0			0
$481$		−	27.7128i		−	1.26360i
$482$			58.9783i			2.68639i
$483$	−5.04868	−	6.97825i	−0.229723	−	0.317521i
$484$	45.3505			2.06139
$485$		0			0
$486$	−35.9783	+	15.9383i	−1.63201	+	0.722977i
$487$			14.5109i			0.657550i	0.944408	+	0.328775i	$0.106636\pi$
$487$			14.5109i			0.657550i	−0.944408	+	0.328775i	$0.893364\pi$
$488$			41.4891i			1.87812i
$489$	−13.4891	−	3.16915i	−0.609999	−	0.143314i
$490$		0			0
$491$		−	10.8896i		−	0.491442i	−0.969341	−	0.245721i	$-0.920975\pi$
$491$		−	10.8896i		−	0.491442i	0.969341	−	0.245721i	$-0.0790248\pi$
$492$	−10.3923	+	44.2337i	−0.468521	+	1.99421i
$493$	−5.84096			−0.263064
$494$		−	51.0767i		−	2.29805i
$495$		0			0
$496$		−	22.0742i		−	0.991162i
$497$	27.1229	+	23.4891i	1.21663	+	1.05363i
$498$	23.3639	+	5.48913i	1.04696	+	0.245974i
$499$	10.3505			0.463353			0.231677	−	0.972793i	$-0.425579\pi$
$499$	10.3505			0.463353			0.231677	+	0.972793i	$0.425579\pi$
$500$		0			0
$501$	−37.2921	−	8.76144i	−1.66609	−	0.391432i
$502$	−44.1485			−1.97044
$503$			27.6060i			1.23089i	0.788180	+	0.615445i	$0.211024\pi$
$503$			27.6060i			1.23089i	−0.788180	+	0.615445i	$0.788976\pi$
$504$	43.8614	−	18.3152i	1.95374	−	0.815823i
$505$		0			0
$506$		−	3.75906i		−	0.167110i
$507$	8.36530	−	35.6060i	0.371516	−	1.58132i
$508$			46.9783i			2.08432i
$509$	38.2337			1.69468			0.847339	−	0.531052i	$-0.178203\pi$
$509$	38.2337			1.69468			0.847339	+	0.531052i	$0.178203\pi$
$510$		0			0
$511$	−12.0000	+	13.8564i	−0.530849	+	0.612971i
$512$	50.1369			2.21576
$513$	13.8564	+	11.4891i	0.611775	+	0.507257i
$514$		−	59.2945i		−	2.61537i
$515$		0			0
$516$	49.7228	+	11.6819i	2.18892	+	0.514268i
$517$	5.84096			0.256885
$518$	−23.9538	−	20.7446i	−1.05247	−	0.911464i
$519$	−27.1753	−	6.38458i	−1.19286	−	0.280252i
$520$		0			0
$521$	34.4674			1.51004			0.755022	−	0.655700i	$-0.227626\pi$
$521$	34.4674			1.51004			0.755022	+	0.655700i	$0.227626\pi$
$522$	14.3537	−	28.8614i	0.628246	−	1.26323i
$523$	−10.3923			−0.454424			−0.227212	−	0.973845i	$-0.572961\pi$
$523$	−10.3923			−0.454424			−0.227212	+	0.973845i	$0.572961\pi$
$524$	−76.4674			−3.34049
$525$		0			0
$526$	−34.2337			−1.49266
$527$	−4.75372			−0.207075
$528$	8.51278	+	2.00000i	0.370471	+	0.0870388i
$529$	−19.4674			−0.846408
$530$		0			0
$531$	7.37228	+	3.66648i	0.319930	+	0.159112i
$532$	−30.2921	−	26.2337i	−1.31333	−	1.13737i
$533$	35.0458			1.51800
$534$	3.25544	−	13.8564i	0.140877	−	0.599625i
$535$		0			0
$536$			40.3894i			1.74456i
$537$	−11.1846	−	2.62772i	−0.482651	−	0.113394i
$538$	−22.0742			−0.951688
$539$	5.48913	−	0.792287i	0.236433	−	0.0341262i
$540$		0			0
$541$	18.6277			0.800868			0.400434	−	0.916326i	$-0.368859\pi$
$541$	18.6277			0.800868			0.400434	+	0.916326i	$0.368859\pi$
$542$			38.2337i			1.64228i
$543$	31.3793	+	7.37228i	1.34661	+	0.316375i
$544$			5.63858i			0.241752i
$545$		0			0
$546$	−39.6060	−	54.7431i	−1.69498	−	2.34279i
$547$			42.9783i			1.83762i	0.394703	+	0.918809i	$0.370847\pi$
$547$			42.9783i			1.83762i	−0.394703	+	0.918809i	$0.629153\pi$
$548$	58.0049			2.47785
$549$	−9.25544	+	18.6101i	−0.395012	+	0.794261i
$550$		0			0
$551$	−14.7446			−0.628139
$552$	−4.45877	+	18.9783i	−0.189778	+	0.807768i
$553$	−5.84096	+	6.74456i	−0.248383	+	0.286808i
$554$			15.7359i			0.668556i
$555$		0			0
$556$		−	5.63858i		−	0.239129i
$557$	−30.8820			−1.30851			−0.654255	−	0.756274i	$-0.727018\pi$
$557$	−30.8820			−1.30851			−0.654255	+	0.756274i	$0.727018\pi$
$558$	11.6819	−	23.4891i	0.494535	−	0.994374i
$559$		−	39.3947i		−	1.66622i
$560$		0			0
$561$	0.430703	−	1.83324i	0.0181843	−	0.0773995i
$562$			12.2337i			0.516047i
$563$		−	5.48913i		−	0.231339i	−0.993288	−	0.115670i	$-0.963099\pi$
$563$		−	5.48913i		−	0.231339i	0.993288	−	0.115670i	$-0.0369014\pi$
$564$	−54.3505	−	12.7692i	−2.28857	−	0.537679i
$565$		0			0
$566$	−23.4891			−0.987322
$567$	23.7600	+	1.56930i	0.997826	+	0.0659043i
$568$		−	81.2119i		−	3.40758i
$569$			10.6873i			0.448033i	0.974585	+	0.224017i	$0.0719170\pi$
$569$			10.6873i			0.448033i	−0.974585	+	0.224017i	$0.928083\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		−	20.2337i		−	0.846013i
$573$	−26.3769	−	6.19702i	−1.10191	−	0.258884i
$574$	26.2337	−	30.2921i	1.09497	−	1.26437i
$575$		0			0
$576$	6.37228	+	3.16915i	0.265512	+	0.132048i
$577$	−12.7692			−0.531587			−0.265794	−	0.964030i	$-0.585634\pi$
$577$	−12.7692			−0.531587			−0.265794	+	0.964030i	$0.585634\pi$
$578$	−38.1600			−1.58725
$579$	−37.4891	−	8.80773i	−1.55799	−	0.366037i
$580$		0			0
$581$	−10.9783	−	9.50744i	−0.455455	−	0.394435i
$582$	1.08724	−	4.62772i	0.0450676	−	0.191825i
$583$		−	6.74456i		−	0.279331i
$584$	41.4891			1.71683
$585$		0			0
$586$		−	70.9764i		−	2.93201i
$587$		−	5.48913i		−	0.226560i	−0.993563	−	0.113280i	$-0.963864\pi$
$587$		−	5.48913i		−	0.226560i	0.993563	−	0.113280i	$-0.0361358\pi$
$588$	−52.8087	−	4.62772i	−2.17779	−	0.190844i
$589$	−12.0000			−0.494451
$590$		0			0
$591$	8.86141	−	37.7176i	0.364510	−	1.55149i
$592$			30.2337i			1.24260i
$593$			1.37228i			0.0563528i	0.999603	+	0.0281764i	$0.00897002\pi$
$593$			1.37228i			0.0563528i	−0.999603	+	0.0281764i	$0.991030\pi$
$594$	8.00000	+	6.63325i	0.328244	+	0.272166i
$595$		0			0
$596$		−	44.1485i		−	1.80839i
$597$	21.8719	+	5.13859i	0.895155	+	0.210309i
$598$	27.7128			1.13326
$599$			1.78695i			0.0730129i	0.999333	+	0.0365065i	$0.0116230\pi$
$599$			1.78695i			0.0730129i	−0.999333	+	0.0365065i	$0.988377\pi$
$600$		0			0
$601$		−	2.17448i		−	0.0886989i	−0.999016	−	0.0443495i	$-0.985878\pi$
$601$		−	2.17448i		−	0.0886989i	0.999016	−	0.0443495i	$-0.0141215\pi$
$602$	−34.0511	−	29.4891i	−1.38782	−	1.20189i
$603$	−9.01011	+	18.1168i	−0.366920	+	0.737775i
$604$	14.7446			0.599948
$605$		0			0
$606$	−6.00000	+	25.5383i	−0.243733	+	1.03742i
$607$	20.9870			0.851836			0.425918	−	0.904762i	$-0.359951\pi$
$607$	20.9870			0.851836			0.425918	+	0.904762i	$0.359951\pi$
$608$			14.2337i			0.577252i
$609$	−15.8030	+	11.4333i	−0.640369	+	0.463299i
$610$		0			0
$611$			43.0612i			1.74207i
$612$	−8.01544	+	16.1168i	−0.324005	+	0.651485i
$613$			4.51087i			0.182193i	0.995842	+	0.0910963i	$0.0290371\pi$
$613$			4.51087i			0.182193i	−0.995842	+	0.0910963i	$0.970963\pi$
$614$	18.0000			0.726421
$615$		0			0
$616$	−9.48913	−	8.21782i	−0.382328	−	0.331106i
$617$	−37.8102			−1.52218			−0.761090	−	0.648646i	$-0.775335\pi$
$617$	−37.8102			−1.52218			−0.761090	+	0.648646i	$0.775335\pi$
$618$	−16.2333	+	69.0951i	−0.652998	+	2.77941i
$619$		−	1.28962i		−	0.0518342i	−0.999664	−	0.0259171i	$-0.991749\pi$
$619$		−	1.28962i		−	0.0518342i	0.999664	−	0.0259171i	$-0.00825060\pi$
$620$		0			0
$621$	−6.23369	+	7.51811i	−0.250149	+	0.301691i
$622$	−51.0767			−2.04799
$623$	−5.63858	+	6.51087i	−0.225905	+	0.260853i
$624$	−14.7446	+	62.7586i	−0.590255	+	2.51235i
$625$		0			0
$626$	−61.7228			−2.46694
$627$	1.08724	−	4.62772i	0.0434202	−	0.184813i
$628$		0			0
$629$	6.51087			0.259606
$630$		0			0
$631$	−5.88316			−0.234205			−0.117102	−	0.993120i	$-0.537361\pi$
$631$	−5.88316			−0.234205			−0.117102	+	0.993120i	$0.537361\pi$
$632$	20.1947			0.803302
$633$	2.42315	−	10.3139i	0.0963115	−	0.409939i
$634$	−21.4891			−0.853442
$635$		0			0
$636$	−14.7446	+	62.7586i	−0.584660	+	2.48854i
$637$	5.84096	+	40.4674i	0.231427	+	1.60338i
$638$	−8.51278			−0.337024
$639$	18.1168	−	36.4280i	0.716691	−	1.44107i
$640$		0			0
$641$		−	29.7021i		−	1.17316i	−0.809890	−	0.586582i	$-0.800473\pi$
$641$		−	29.7021i		−	1.17316i	0.809890	−	0.586582i	$-0.199527\pi$
$642$	6.63325	−	28.2337i	0.261793	−	1.11429i
$643$	−39.5971			−1.56156			−0.780779	−	0.624807i	$-0.785178\pi$
$643$	−39.5971			−1.56156			−0.780779	+	0.624807i	$0.785178\pi$
$644$	14.2337	−	16.4356i	0.560886	−	0.647655i
$645$		0			0
$646$	12.0000			0.472134
$647$			12.0000i			0.471769i	0.971781	+	0.235884i	$0.0757987\pi$
$647$			12.0000i			0.471769i	−0.971781	+	0.235884i	$0.924201\pi$
$648$	−32.5214	−	42.9783i	−1.27756	−	1.68835i
$649$		−	2.17448i		−	0.0853559i
$650$		0			0
$651$	−12.8614	+	9.30506i	−0.504078	+	0.364694i
$652$		−	34.9783i		−	1.36985i
$653$	33.0564			1.29360			0.646799	−	0.762660i	$-0.276107\pi$
$653$	33.0564			1.29360			0.646799	+	0.762660i	$0.276107\pi$
$654$	0.116844	−	0.497333i	0.00456896	−	0.0194473i
$655$		0			0
$656$	−38.2337			−1.49277
$657$	18.6101	+	9.25544i	0.726050	+	0.361089i
$658$	37.2203	+	32.2337i	1.45100	+	1.25660i
$659$			20.3971i			0.794558i	0.917698	+	0.397279i	$0.130045\pi$
$659$			20.3971i			0.794558i	−0.917698	+	0.397279i	$0.869955\pi$
$660$		0			0
$661$			6.92820i			0.269476i	0.990881	+	0.134738i	$0.0430193\pi$
$661$			6.92820i			0.269476i	−0.990881	+	0.134738i	$0.956981\pi$
$662$	10.0974			0.392445
$663$	13.5152	+	3.17527i	0.524886	+	0.123317i
$664$			32.8713i			1.27565i
$665$		0			0
$666$	−16.0000	+	32.1716i	−0.619987	+	1.24662i
$667$		−	8.00000i		−	0.309761i
$668$		−	96.7011i		−	3.74148i
$669$	−8.31386	+	35.3870i	−0.321432	+	1.36814i
$670$		0			0
$671$	5.48913			0.211905
$672$	11.0371	+	15.2554i	0.425766	+	0.588491i
$673$		−	22.2337i		−	0.857046i	−0.903531	−	0.428523i	$-0.859034\pi$
$673$		−	22.2337i		−	0.857046i	0.903531	−	0.428523i	$-0.140966\pi$
$674$			46.0280i			1.77293i
$675$		0			0
$676$	92.3288			3.55111
$677$			21.6060i			0.830385i	0.909734	+	0.415192i	$0.136286\pi$
$677$			21.6060i			0.830385i	−0.909734	+	0.415192i	$0.863714\pi$
$678$	−10.0974	+	42.9783i	−0.387786	+	1.65057i
$679$	−1.88316	+	2.17448i	−0.0722689	+	0.0834489i
$680$		0			0
$681$	−26.3139	−	6.18220i	−1.00835	−	0.236903i
$682$	−6.92820			−0.265295
$683$	−51.7764			−1.98117			−0.990584	−	0.136906i	$-0.956284\pi$
$683$	−51.7764			−1.98117			−0.990584	+	0.136906i	$0.956284\pi$
$684$	−20.2337	+	40.6844i	−0.773654	+	1.55561i
$685$		0			0
$686$	39.3505	+	25.2434i	1.50241	+	0.963797i
$687$	−8.01544	−	1.88316i	−0.305808	−	0.0718469i
$688$			42.9783i			1.63853i
$689$	49.7228			1.89429
$690$		0			0
$691$			38.5099i			1.46498i	0.680775	+	0.732492i	$0.261643\pi$
$691$			38.5099i			1.46498i	−0.680775	+	0.732492i	$0.738357\pi$
$692$		−	70.4674i		−	2.67877i
$693$	−2.42315	−	5.80298i	−0.0920478	−	0.220437i
$694$	46.2337			1.75501
$695$		0			0
$696$	42.9783	+	10.0974i	1.62909	+	0.382739i
$697$			8.23369i			0.311873i
$698$		−	12.0000i		−	0.454207i
$699$	−1.48913	+	6.33830i	−0.0563239	+	0.239736i
$700$		0			0
$701$			45.8256i			1.73081i	0.501074	+	0.865405i	$0.332939\pi$
$701$			45.8256i			1.73081i	−0.501074	+	0.865405i	$0.667061\pi$
$702$	−48.9022	+	58.9783i	−1.84569	+	2.22599i
$703$	16.4356			0.619882
$704$		−	1.87953i		−	0.0708374i
$705$		0			0
$706$			19.8997i			0.748937i
$707$	10.3923	−	12.0000i	0.390843	−	0.451306i
$708$	−4.75372	+	20.2337i	−0.178656	+	0.760429i
$709$	−24.1168			−0.905727			−0.452864	−	0.891580i	$-0.649598\pi$
$709$	−24.1168			−0.905727			−0.452864	+	0.891580i	$0.649598\pi$
$710$		0			0
$711$	9.05842	+	4.50506i	0.339717	+	0.168953i
$712$	19.4950			0.730606
$713$		−	6.51087i		−	0.243834i
$714$	12.8614	−	9.30506i	0.481326	−	0.348233i
$715$		0			0
$716$		−	29.0024i		−	1.08387i
$717$	26.3769	+	6.19702i	0.985064	+	0.231432i
$718$		−	24.7446i		−	0.923459i
$719$	−40.4674			−1.50918			−0.754589	−	0.656197i	$-0.772164\pi$
$719$	−40.4674			−1.50918			−0.754589	+	0.656197i	$0.772164\pi$
$720$		0			0
$721$	28.1168	−	32.4665i	1.04713	−	1.20912i
$722$	−17.6704			−0.657623
$723$	−39.3947	−	9.25544i	−1.46511	−	0.344213i
$724$			81.3687i			3.02404i
$725$		0			0
$726$	−10.3723	+	44.1485i	−0.384951	+	1.63850i
$727$	3.46410			0.128476			0.0642382	−	0.997935i	$-0.479538\pi$
$727$	3.46410			0.128476			0.0642382	+	0.997935i	$0.479538\pi$
$728$	60.5841	−	69.9565i	2.24540	−	2.59276i
$729$	−5.00000	−	26.5330i	−0.185185	−	0.982704i
$730$		0			0
$731$	9.25544			0.342325
$732$	−51.0767	−	12.0000i	−1.88785	−	0.443533i
$733$	10.1899			0.376373			0.188187	−	0.982133i	$-0.439739\pi$
$733$	10.1899			0.376373			0.188187	+	0.982133i	$0.439739\pi$
$734$	−63.9565			−2.36068
$735$		0			0
$736$	−7.72281			−0.284667
$737$	5.34363			0.196835
$738$	−40.6844	−	20.2337i	−1.49761	−	0.744812i
$739$	8.62772			0.317376			0.158688	−	0.987329i	$-0.449274\pi$
$739$	8.62772			0.317376			0.158688	+	0.987329i	$0.449274\pi$
$740$		0			0
$741$	34.1168	+	8.01544i	1.25331	+	0.294455i
$742$	37.2203	−	42.9783i	1.36640	−	1.57778i
$743$	36.9253			1.35466			0.677329	−	0.735680i	$-0.263137\pi$
$743$	36.9253			1.35466			0.677329	+	0.735680i	$0.263137\pi$
$744$	34.9783	+	8.21782i	1.28236	+	0.301280i
$745$		0			0
$746$		−	62.4636i		−	2.28696i
$747$	−7.33296	+	14.7446i	−0.268299	+	0.539475i
$748$	4.75372			0.173813
$749$	−11.4891	+	13.2665i	−0.419804	+	0.484747i
$750$		0			0
$751$	−22.3505			−0.815582			−0.407791	−	0.913075i	$-0.633701\pi$
$751$	−22.3505			−0.815582			−0.407791	+	0.913075i	$0.633701\pi$
$752$		−	46.9783i		−	1.71312i
$753$	6.92820	−	29.4891i	0.252478	−	1.07464i
$754$		−	62.7586i		−	2.28553i
$755$		0			0
$756$	9.86141	+	59.2945i	0.358656	+	2.15652i
$757$		−	54.2337i		−	1.97116i	−0.169219	−	0.985578i	$-0.554125\pi$
$757$		−	54.2337i		−	1.97116i	0.169219	−	0.985578i	$-0.445875\pi$
$758$	3.75906			0.136535
$759$	2.51087	+	0.589907i	0.0911390	+	0.0214123i
$760$		0			0
$761$	−26.2337			−0.950970			−0.475485	−	0.879724i	$-0.657727\pi$
$761$	−26.2337			−0.950970			−0.475485	+	0.879724i	$0.657727\pi$
$762$	−45.7330	−	10.7446i	−1.65673	−	0.389234i
$763$	−0.202380	+	0.233688i	−0.00732664	+	0.00846007i
$764$		−	68.3972i		−	2.47452i
$765$		0			0
$766$		−	44.1485i		−	1.59515i
$767$	16.0309			0.578842
$768$	−12.3267	+	52.4674i	−0.444803	+	1.89325i
$769$			21.1894i			0.764108i	0.924140	+	0.382054i	$0.124783\pi$
$769$			21.1894i			0.764108i	−0.924140	+	0.382054i	$0.875217\pi$
$770$		0			0
$771$	39.6060	+	9.30506i	1.42637	+	0.335114i
$772$		−	97.2119i		−	3.49873i
$773$			46.6277i			1.67708i	0.544838	+	0.838541i	$0.316591\pi$
$773$			46.6277i			1.67708i	−0.544838	+	0.838541i	$0.683409\pi$
$774$	−22.7446	+	45.7330i	−0.817536	+	1.64384i
$775$		0			0
$776$	6.51087			0.233727
$777$	17.6155	−	12.7446i	0.631951	−	0.457209i
$778$			34.7446i			1.24565i
$779$			20.7846i			0.744686i
$780$		0			0
$781$	−10.7446			−0.384471
$782$			6.51087i			0.232828i
$783$	17.0256	+	14.1168i	0.608444	+	0.504495i
$784$	−6.37228	−	44.1485i	−0.227581	−	1.57673i
$785$		0			0
$786$	17.4891	−	74.4405i	0.623816	−	2.65521i
$787$	−46.5253			−1.65845			−0.829224	−	0.558916i	$-0.811217\pi$
$787$	−46.5253			−1.65845			−0.829224	+	0.558916i	$0.811217\pi$
$788$	97.8044			3.48414
$789$	5.37228	−	22.8665i	0.191258	−	0.814070i
$790$		0			0
$791$	17.4891	−	20.1947i	0.621842	−	0.718041i
$792$	−6.33830	+	12.7446i	−0.225222	+	0.452858i
$793$			40.4674i			1.43704i
$794$	−9.25544			−0.328463
$795$		0			0
$796$			56.7152i			2.01022i
$797$		−	42.8614i		−	1.51823i	−0.650957	−	0.759114i	$-0.725632\pi$
$797$		−	42.8614i		−	1.51823i	0.650957	−	0.759114i	$-0.274368\pi$
$798$	32.4665	−	23.4891i	1.14930	−	0.831506i
$799$	−10.1168			−0.357908
$800$		0			0
$801$	8.74456	+	4.34896i	0.308974	+	0.153663i
$802$			6.74456i			0.238159i
$803$		−	5.48913i		−	0.193707i
$804$	−49.7228	−	11.6819i	−1.75359	−	0.411990i
$805$		0			0
$806$		−	51.0767i		−	1.79910i
$807$	3.46410	−	14.7446i	0.121942	−	0.519033i
$808$	−35.9306			−1.26404
$809$		−	36.7229i		−	1.29111i	−0.763714	−	0.645555i	$-0.776626\pi$
$809$		−	36.7229i		−	1.29111i	0.763714	−	0.645555i	$-0.223374\pi$
$810$		0			0
$811$			1.28962i			0.0452847i	0.999744	+	0.0226423i	$0.00720790\pi$
$811$			1.28962i			0.0452847i	−0.999744	+	0.0226423i	$0.992792\pi$
$812$	−37.2203	−	32.2337i	−1.30617	−	1.13118i
$813$	−25.5383	−	6.00000i	−0.895668	−	0.210429i
$814$	9.48913			0.332594
$815$		0			0
$816$	−14.7446	−	3.46410i	−0.516163	−	0.121268i
$817$	23.3639			0.817398
$818$			88.4674i			3.09319i
$819$	42.7812	−	17.8641i	1.49490	−	0.624223i
$820$		0			0
$821$		−	11.7745i		−	0.410933i	−0.978664	−	0.205466i	$-0.934129\pi$
$821$		−	11.7745i		−	0.410933i	0.978664	−	0.205466i	$-0.0658711\pi$
$822$	−13.2665	+	56.4674i	−0.462722	+	1.96953i
$823$			48.2337i			1.68132i	0.541563	+	0.840660i	$0.317833\pi$
$823$			48.2337i			1.68132i	−0.541563	+	0.840660i	$0.682167\pi$
$824$	−97.2119			−3.38654
$825$		0			0
$826$	12.0000	−	13.8564i	0.417533	−	0.482126i
$827$	−18.3152			−0.636881			−0.318441	−	0.947943i	$-0.603159\pi$
$827$	−18.3152			−0.636881			−0.318441	+	0.947943i	$0.603159\pi$
$828$	−22.0742	−	10.9783i	−0.767133	−	0.381521i
$829$			32.4665i			1.12761i	0.825908	+	0.563805i	$0.190663\pi$
$829$			32.4665i			1.12761i	−0.825908	+	0.563805i	$0.809337\pi$
$830$		0			0
$831$	−10.5109	−	2.46943i	−0.364618	−	0.0856637i
$832$	13.8564			0.480384
$833$	−9.50744	+	1.37228i	−0.329413	+	0.0475467i
$834$	5.48913	+	1.28962i	0.190073	+	0.0446559i
$835$		0			0
$836$	12.0000			0.415029
$837$	13.8564	+	11.4891i	0.478947	+	0.397122i
$838$	−6.92820			−0.239331
$839$	53.4891			1.84665			0.923325	−	0.384020i	$-0.125461\pi$
$839$	53.4891			1.84665			0.923325	+	0.384020i	$0.125461\pi$
$840$		0			0
$841$	10.8832			0.375281
$842$	64.6381			2.22758
$843$	−8.17154	−	1.91983i	−0.281443	−	0.0661224i
$844$	26.7446			0.920586
$845$		0			0
$846$	24.8614	−	49.9894i	0.854753	−	1.71867i
$847$	17.9653	−	20.7446i	0.617296	−	0.712792i
$848$	−54.2458			−1.86281
$849$	3.68614	−	15.6896i	0.126508	−	0.538467i
$850$		0			0
$851$			8.91754i			0.305689i
$852$	99.9788	+	23.4891i	3.42522	+	0.804724i
$853$	46.7277			1.59993			0.799963	−	0.600049i	$-0.204852\pi$
$853$	46.7277			1.59993			0.799963	+	0.600049i	$0.204852\pi$
$854$	34.9783	+	30.2921i	1.19693	+	1.03657i
$855$		0			0
$856$	39.7228			1.35770
$857$		−	22.4674i		−	0.767471i	−0.923443	−	0.383735i	$-0.874637\pi$
$857$		−	22.4674i		−	0.767471i	0.923443	−	0.383735i	$-0.125363\pi$
$858$	19.6974	+	4.62772i	0.672457	+	0.157988i
$859$			45.4381i			1.55033i	0.631760	+	0.775164i	$0.282333\pi$
$859$			45.4381i			1.55033i	−0.631760	+	0.775164i	$0.717667\pi$
$860$		0			0
$861$	16.1168	+	22.2766i	0.549261	+	0.759185i
$862$			79.9565i			2.72333i
$863$	−28.0078			−0.953395			−0.476698	−	0.879067i	$-0.658166\pi$
$863$	−28.0078			−0.953395			−0.476698	+	0.879067i	$0.658166\pi$
$864$	13.6277	−	16.4356i	0.463624	−	0.559152i
$865$		0			0
$866$	−6.51087			−0.221249
$867$	5.98844	−	25.4891i	0.203378	−	0.865656i
$868$	−30.2921	−	26.2337i	−1.02818	−	0.890429i
$869$		−	2.67181i		−	0.0906351i
$870$		0			0
$871$			39.3947i			1.33484i
$872$	0.699713			0.0236953
$873$	2.92048	+	1.45245i	0.0988433	+	0.0491581i
$874$			16.4356i			0.555944i
$875$		0			0
$876$	−12.0000	+	51.0767i	−0.405442	+	1.72572i
$877$			30.4674i			1.02881i	0.857547	+	0.514405i	$0.171987\pi$
$877$			30.4674i			1.02881i	−0.857547	+	0.514405i	$0.828013\pi$
$878$		−	3.25544i		−	0.109866i
$879$	47.4090	+	11.1383i	1.59906	+	0.375686i
$880$		0			0
$881$	−2.23369			−0.0752549			−0.0376274	−	0.999292i	$-0.511980\pi$
$881$	−2.23369			−0.0752549			−0.0376274	+	0.999292i	$0.511980\pi$
$882$	16.5831	−	50.3505i	0.558383	−	1.69539i
$883$		−	26.5109i		−	0.892162i	−0.894993	−	0.446081i	$-0.852819\pi$
$883$		−	26.5109i		−	0.892162i	0.894993	−	0.446081i	$-0.147181\pi$
$884$			35.0458i			1.17872i
$885$		0			0
$886$	−16.7446			−0.562545
$887$			41.4891i			1.39307i	0.717524	+	0.696534i	$0.245276\pi$
$887$			41.4891i			1.39307i	−0.717524	+	0.696534i	$0.754724\pi$
$888$	−47.9075	−	11.2554i	−1.60767	−	0.377708i
$889$	21.4891	+	18.6101i	0.720722	+	0.624164i
$890$		0			0
$891$	−5.68614	+	4.30268i	−0.190493	+	0.144145i
$892$	−91.7610			−3.07239
$893$	−25.5383			−0.854608
$894$	42.9783	+	10.0974i	1.43741	+	0.337706i
$895$		0			0
$896$	24.6060	−	28.4125i	0.822028	−	0.949196i
$897$	−4.34896	+	18.5109i	−0.145208	+	0.618060i
$898$		−	71.2119i		−	2.37637i
$899$	−14.7446			−0.491759
$900$		0			0
$901$			11.6819i			0.389181i
$902$			12.0000i			0.399556i
$903$	25.0410	−	18.1168i	0.833312	−	0.602891i
$904$	−60.4674			−2.01112
$905$		0			0
$906$	−3.37228	+	14.3537i	−0.112037	+	0.476871i
$907$			8.00000i			0.265636i	0.991140	+	0.132818i	$0.0424025\pi$
$907$			8.00000i			0.265636i	−0.991140	+	0.132818i	$0.957597\pi$
$908$		−	68.2337i		−	2.26441i
$909$	−16.1168	−	8.01544i	−0.534562	−	0.265855i
$910$		0			0
$911$		−	23.6588i		−	0.783851i	−0.919997	−	0.391926i	$-0.871809\pi$
$911$		−	23.6588i		−	0.783851i	0.919997	−	0.391926i	$-0.128191\pi$
$912$	−37.2203	−	8.74456i	−1.23249	−	0.289561i
$913$	4.34896			0.143930
$914$			83.2482i			2.75361i
$915$		0			0
$916$		−	20.7846i		−	0.686743i
$917$	−30.2921	+	34.9783i	−1.00033	+	1.15508i
$918$	−13.8564	−	11.4891i	−0.457330	−	0.379198i
$919$	11.3723			0.375137			0.187568	−	0.982252i	$-0.439939\pi$
$919$	11.3723			0.375137			0.187568	+	0.982252i	$0.439939\pi$
$920$		0			0
$921$	−2.82473	+	12.0232i	−0.0930782	+	0.396177i
$922$	22.0742			0.726976
$923$		−	79.2119i		−	2.60729i
$924$	12.8614	−	9.30506i	0.423109	−	0.306114i
$925$		0			0
$926$			92.0560i			3.02515i
$927$	−43.6048	−	21.6861i	−1.43217	−	0.712266i
$928$			17.4891i			0.574109i
$929$	−7.02175			−0.230376			−0.115188	−	0.993344i	$-0.536747\pi$
$929$	−7.02175			−0.230376			−0.115188	+	0.993344i	$0.536747\pi$
$930$		0			0
$931$	−24.0000	+	3.46410i	−0.786568	+	0.113531i
$932$	−16.4356			−0.538368
$933$	8.01544	−	34.1168i	0.262414	−	1.11694i
$934$			35.0458i			1.14673i
$935$		0			0
$936$	−93.9565	−	46.7277i	−3.07106	−	1.52734i
$937$	−49.9894			−1.63308			−0.816542	−	0.577287i	$-0.804112\pi$
$937$	−49.9894			−1.63308			−0.816542	+	0.577287i	$0.804112\pi$
$938$	34.0511	+	29.4891i	1.11181	+	0.962854i
$939$	9.68614	−	41.2280i	0.316095	−	1.34542i
$940$		0			0
$941$	−27.2554			−0.888502			−0.444251	−	0.895902i	$-0.646530\pi$
$941$	−27.2554			−0.888502			−0.444251	+	0.895902i	$0.646530\pi$
$942$		0			0
$943$	−11.2772			−0.367235
$944$	−17.4891			−0.569223
$945$		0			0
$946$	13.4891			0.438569
$947$	−48.2025			−1.56637			−0.783185	−	0.621789i	$-0.786406\pi$
$947$	−48.2025			−1.56637			−0.783185	+	0.621789i	$0.786406\pi$
$948$	−5.84096	+	24.8614i	−0.189706	+	0.807461i
$949$	40.4674			1.31363
$950$		0			0
$951$	3.37228	−	14.3537i	0.109354	−	0.465452i
$952$	16.4356	+	14.2337i	0.532682	+	0.461316i
$953$	−38.8048			−1.25701			−0.628506	−	0.777805i	$-0.716333\pi$
$953$	−38.8048			−1.25701			−0.628506	+	0.777805i	$0.716333\pi$
$954$	−57.7228	−	28.7075i	−1.86885	−	0.929439i
$955$		0			0
$956$			68.3972i			2.21212i
$957$	1.33591	−	5.68614i	0.0431838	−	0.183807i
$958$	46.7277			1.50970
$959$	22.9783	−	26.5330i	0.742006	−	0.856795i
$960$		0			0
$961$	19.0000			0.612903
$962$			69.9565i			2.25549i
$963$	17.8178	+	8.86141i	0.574172	+	0.285555i
$964$		−	102.153i		−	3.29014i
$965$		0			0
$966$	12.7446	+	17.6155i	0.410050	+	0.566768i
$967$		−	24.2337i		−	0.779303i	−0.920962	−	0.389651i	$-0.872595\pi$
$967$		−	24.2337i		−	0.779303i	0.920962	−	0.389651i	$-0.127405\pi$
$968$	−62.1138			−1.99641
$969$	−1.88316	+	8.01544i	−0.0604957	+	0.257493i
$970$		0			0
$971$	−43.2119			−1.38674			−0.693369	−	0.720583i	$-0.743874\pi$
$971$	−43.2119			−1.38674			−0.693369	+	0.720583i	$0.743874\pi$
$972$	62.3162	−	27.6060i	1.99879	−	0.885462i
$973$	−2.57924	−	2.23369i	−0.0826867	−	0.0716087i
$974$		−	36.6303i		−	1.17371i
$975$		0			0
$976$		−	44.1485i		−	1.41316i
$977$	38.8048			1.24148			0.620738	−	0.784018i	$-0.286833\pi$
$977$	38.8048			1.24148			0.620738	+	0.784018i	$0.286833\pi$
$978$	34.0511	+	8.00000i	1.08883	+	0.255812i
$979$		−	2.57924i		−	0.0824329i
$980$		0			0
$981$	0.313859	+	0.156093i	0.0100208	+	0.00498366i
$982$			27.4891i			0.877213i
$983$		−	11.1386i		−	0.355266i	−0.984097	−	0.177633i	$-0.943156\pi$
$983$		−	11.1386i		−	0.355266i	0.984097	−	0.177633i	$-0.0568440\pi$
$984$	14.2337	−	60.5841i	0.453753	−	1.93135i
$985$		0			0
$986$	14.7446			0.469563
$987$	−27.3716	+	19.8030i	−0.871247	+	0.630336i
$988$			88.4674i			2.81452i
$989$			12.6766i			0.403092i
$990$		0			0
$991$	2.51087			0.0797606			0.0398803	−	0.999204i	$-0.487302\pi$
$991$	2.51087			0.0797606			0.0398803	+	0.999204i	$0.487302\pi$
$992$			14.2337i			0.451920i
$993$	−1.58457	+	6.74456i	−0.0502849	+	0.214032i
$994$	−68.4674	−	59.2945i	−2.17165	−	1.88071i
$995$		0			0
$996$	−40.4674	−	9.50744i	−1.28226	−	0.301255i
$997$	−21.8719			−0.692688			−0.346344	−	0.938107i	$-0.612577\pi$
$997$	−21.8719			−0.692688			−0.346344	+	0.938107i	$0.612577\pi$
$998$	−26.1282			−0.827075
$999$	−18.9783	−	15.7359i	−0.600445	−	0.497863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.g.d.524.1		8
3.2	odd	2		525.2.g.e.524.8		8
5.2	odd	4		525.2.b.e.251.1		4
5.3	odd	4		105.2.b.d.41.4	yes	4
5.4	even	2	inner	525.2.g.d.524.8		8
7.6	odd	2		525.2.g.e.524.2		8
15.2	even	4		525.2.b.g.251.4		4
15.8	even	4		105.2.b.c.41.1	✓	4
15.14	odd	2		525.2.g.e.524.1		8
20.3	even	4		1680.2.f.g.881.1		4
21.20	even	2	inner	525.2.g.d.524.7		8
35.3	even	12		735.2.s.h.656.1		4
35.13	even	4		105.2.b.c.41.4	yes	4
35.18	odd	12		735.2.s.g.656.1		4
35.23	odd	12		735.2.s.j.521.2		4
35.27	even	4		525.2.b.g.251.1		4
35.33	even	12		735.2.s.i.521.2		4
35.34	odd	2		525.2.g.e.524.7		8
60.23	odd	4		1680.2.f.h.881.3		4
105.23	even	12		735.2.s.h.521.1		4
105.38	odd	12		735.2.s.j.656.2		4
105.53	even	12		735.2.s.i.656.2		4
105.62	odd	4		525.2.b.e.251.4		4
105.68	odd	12		735.2.s.g.521.1		4
105.83	odd	4		105.2.b.d.41.1	yes	4
105.104	even	2	inner	525.2.g.d.524.2		8
140.83	odd	4		1680.2.f.h.881.4		4
420.83	even	4		1680.2.f.g.881.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.1	✓	4	15.8	even	4
105.2.b.c.41.4	yes	4	35.13	even	4
105.2.b.d.41.1	yes	4	105.83	odd	4
105.2.b.d.41.4	yes	4	5.3	odd	4
525.2.b.e.251.1		4	5.2	odd	4
525.2.b.e.251.4		4	105.62	odd	4
525.2.b.g.251.1		4	35.27	even	4
525.2.b.g.251.4		4	15.2	even	4
525.2.g.d.524.1		8	1.1	even	1	trivial
525.2.g.d.524.2		8	105.104	even	2	inner
525.2.g.d.524.7		8	21.20	even	2	inner
525.2.g.d.524.8		8	5.4	even	2	inner
525.2.g.e.524.1		8	15.14	odd	2
525.2.g.e.524.2		8	7.6	odd	2
525.2.g.e.524.7		8	35.34	odd	2
525.2.g.e.524.8		8	3.2	odd	2
735.2.s.g.521.1		4	105.68	odd	12
735.2.s.g.656.1		4	35.18	odd	12
735.2.s.h.521.1		4	105.23	even	12
735.2.s.h.656.1		4	35.3	even	12
735.2.s.i.521.2		4	35.33	even	12
735.2.s.i.656.2		4	105.53	even	12
735.2.s.j.521.2		4	35.23	odd	12
735.2.s.j.656.2		4	105.38	odd	12
1680.2.f.g.881.1		4	20.3	even	4
1680.2.f.g.881.2		4	420.83	even	4
1680.2.f.h.881.3		4	60.23	odd	4
1680.2.f.h.881.4		4	140.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.52434 q^{2} +(0.396143 - 1.68614i) q^{3} +4.37228 q^{4} +(-1.00000 + 4.25639i) q^{6} +(1.73205 - 2.00000i) q^{7} -5.98844 q^{8} +(-2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q-2.52434 q^{2} +(0.396143 - 1.68614i) q^{3} +4.37228 q^{4} +(-1.00000 + 4.25639i) q^{6} +(1.73205 - 2.00000i) q^{7} -5.98844 q^{8} +(-2.68614 - 1.33591i) q^{9} +0.792287i q^{11} +(1.73205 - 7.37228i) q^{12} -5.84096 q^{13} +(-4.37228 + 5.04868i) q^{14} +6.37228 q^{16} -1.37228i q^{17} +(6.78073 + 3.37228i) q^{18} -3.46410i q^{19} +(-2.68614 - 3.71277i) q^{21} -2.00000i q^{22} +1.87953 q^{23} +(-2.37228 + 10.0974i) q^{24} +14.7446 q^{26} +(-3.31662 + 4.00000i) q^{27} +(7.57301 - 8.74456i) q^{28} -4.25639i q^{29} -3.46410i q^{31} -4.10891 q^{32} +(1.33591 + 0.313859i) q^{33} +3.46410i q^{34} +(-11.7446 - 5.84096i) q^{36} +4.74456i q^{37} +8.74456i q^{38} +(-2.31386 + 9.84868i) q^{39} -6.00000 q^{41} +(6.78073 + 9.37228i) q^{42} +6.74456i q^{43} +3.46410i q^{44} -4.74456 q^{46} -7.37228i q^{47} +(2.52434 - 10.7446i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-2.31386 - 0.543620i) q^{51} -25.5383 q^{52} -8.51278 q^{53} +(8.37228 - 10.0974i) q^{54} +(-10.3723 + 11.9769i) q^{56} +(-5.84096 - 1.37228i) q^{57} +10.7446i q^{58} -2.74456 q^{59} -6.92820i q^{61} +8.74456i q^{62} +(-7.32435 + 3.05842i) q^{63} -2.37228 q^{64} +(-3.37228 - 0.792287i) q^{66} -6.74456i q^{67} -6.00000i q^{68} +(0.744563 - 3.16915i) q^{69} +13.5615i q^{71} +(16.0858 + 8.00000i) q^{72} -6.92820 q^{73} -11.9769i q^{74} -15.1460i q^{76} +(1.58457 + 1.37228i) q^{77} +(5.84096 - 24.8614i) q^{78} -3.37228 q^{79} +(5.43070 + 7.17687i) q^{81} +15.1460 q^{82} -5.48913i q^{83} +(-11.7446 - 16.2333i) q^{84} -17.0256i q^{86} +(-7.17687 - 1.68614i) q^{87} -4.74456i q^{88} -3.25544 q^{89} +(-10.1168 + 11.6819i) q^{91} +8.21782 q^{92} +(-5.84096 - 1.37228i) q^{93} +18.6101i q^{94} +(-1.62772 + 6.92820i) q^{96} -1.08724 q^{97} +(2.52434 + 17.4891i) q^{98} +(1.05842 - 2.12819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) 8 * q + 12 * q^4 - 8 * q^6 - 10 * q^9	\( 8 q + 12 q^{4} - 8 q^{6} - 10 q^{9} - 12 q^{14} + 28 q^{16} - 10 q^{21} + 4 q^{24} + 72 q^{26} - 48 q^{36} - 30 q^{39} - 48 q^{41} + 8 q^{46} - 8 q^{49} - 30 q^{51} + 44 q^{54} - 60 q^{56} + 24 q^{59} + 4 q^{64} - 4 q^{66} - 40 q^{69} - 4 q^{79} - 14 q^{81} - 48 q^{84} - 72 q^{89} - 12 q^{91} - 36 q^{96} - 26 q^{99}+O(q^{100}) \) 8 * q + 12 * q^4 - 8 * q^6 - 10 * q^9 - 12 * q^14 + 28 * q^16 - 10 * q^21 + 4 * q^24 + 72 * q^26 - 48 * q^36 - 30 * q^39 - 48 * q^41 + 8 * q^46 - 8 * q^49 - 30 * q^51 + 44 * q^54 - 60 * q^56 + 24 * q^59 + 4 * q^64 - 4 * q^66 - 40 * q^69 - 4 * q^79 - 14 * q^81 - 48 * q^84 - 72 * q^89 - 12 * q^91 - 36 * q^96 - 26 * q^99

Introduction

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