LMFDB - Embedded newform 1600.2.s.d.943.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (of order $4$, degree $2$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.1
Root			$0.235136 + 1.39453i$ of defining polynomial
Character	$\chi$	$=$	1600.943
Dual form			1600.2.s.d.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.96561 q^{3} +(-0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +O(q^{10})$	$q-2.96561 q^{3} +(-0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +(-2.95966 - 2.95966i) q^{11} -1.55822i q^{13} +(-0.299668 + 0.299668i) q^{17} +(2.26261 + 2.26261i) q^{19} +(0.341344 - 0.341344i) q^{21} +(4.14573 + 4.14573i) q^{23} -8.28846 q^{27} +(0.289656 - 0.289656i) q^{29} -4.18508i q^{31} +(8.77721 + 8.77721i) q^{33} +1.63643i q^{37} +4.62107i q^{39} -7.61648i q^{41} -6.72651i q^{43} +(4.38366 + 4.38366i) q^{47} +6.97350i q^{49} +(0.888698 - 0.888698i) q^{51} -11.4324 q^{53} +(-6.71003 - 6.71003i) q^{57} +(-1.63497 + 1.63497i) q^{59} +(-1.23034 - 1.23034i) q^{61} +(-0.666993 + 0.666993i) q^{63} -2.49337i q^{67} +(-12.2946 - 12.2946i) q^{69} -8.00096 q^{71} +(1.12102 - 1.12102i) q^{73} +0.681319 q^{77} -3.62218 q^{79} +7.19579 q^{81} +1.62629 q^{83} +(-0.859007 + 0.859007i) q^{87} -15.7149 q^{89} +(0.179352 + 0.179352i) q^{91} +12.4113i q^{93} +(-9.69217 + 9.69217i) q^{97} +(-17.1508 - 17.1508i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^7 + 10 * q^9	$ 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.96561			−1.71220			−0.856099	−	0.516813i	$-0.827118\pi$
$3$	−2.96561			−1.71220			−0.856099	+	0.516813i	$0.827118\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.115101	+	0.115101i	−0.0435040	+	0.0435040i	−0.728524	−	0.685020i	$-0.759793\pi$
$7$	−0.115101	+	0.115101i	−0.0435040	+	0.0435040i	0.685020	+	0.728524i	$0.259793\pi$
$8$		0			0
$9$	5.79486			1.93162
$10$		0			0
$11$	−2.95966	−	2.95966i	−0.892372	−	0.892372i	0.102374	−	0.994746i	$-0.467356\pi$
$11$	−2.95966	−	2.95966i	−0.892372	−	0.892372i	−0.994746	+	0.102374i	$0.967356\pi$
$12$		0			0
$13$		−	1.55822i		−	0.432172i	−0.976374	−	0.216086i	$-0.930671\pi$
$13$		−	1.55822i		−	0.432172i	0.976374	−	0.216086i	$-0.0693292\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.299668	+	0.299668i	−0.0726801	+	0.0726801i	−0.742512	−	0.669832i	$-0.766366\pi$
$17$	−0.299668	+	0.299668i	−0.0726801	+	0.0726801i	0.669832	+	0.742512i	$0.266366\pi$
$18$		0			0
$19$	2.26261	+	2.26261i	0.519079	+	0.519079i	0.917293	−	0.398214i	$-0.130370\pi$
$19$	2.26261	+	2.26261i	0.519079	+	0.519079i	−0.398214	+	0.917293i	$0.630370\pi$
$20$		0			0
$21$	0.341344	−	0.341344i	0.0744874	−	0.0744874i
$22$		0			0
$23$	4.14573	+	4.14573i	0.864444	+	0.864444i	0.991851	−	0.127406i	$-0.0406652\pi$
$23$	4.14573	+	4.14573i	0.864444	+	0.864444i	−0.127406	+	0.991851i	$0.540665\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−8.28846			−1.59511
$28$		0			0
$29$	0.289656	−	0.289656i	0.0537878	−	0.0537878i	−0.679701	−	0.733489i	$-0.737891\pi$
$29$	0.289656	−	0.289656i	0.0537878	−	0.0537878i	0.733489	+	0.679701i	$0.237891\pi$
$30$		0			0
$31$		−	4.18508i		−	0.751663i	−0.926688	−	0.375832i	$-0.877357\pi$
$31$		−	4.18508i		−	0.751663i	0.926688	−	0.375832i	$-0.122643\pi$
$32$		0			0
$33$	8.77721	+	8.77721i	1.52792	+	1.52792i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			1.63643i			0.269027i	0.990912	+	0.134514i	$0.0429472\pi$
$37$			1.63643i			0.269027i	−0.990912	+	0.134514i	$0.957053\pi$
$38$		0			0
$39$			4.62107i			0.739964i
$40$		0			0
$41$		−	7.61648i		−	1.18949i	−0.803913	−	0.594747i	$-0.797252\pi$
$41$		−	7.61648i		−	1.18949i	0.803913	−	0.594747i	$-0.202748\pi$
$42$		0			0
$43$		−	6.72651i		−	1.02578i	−0.858453	−	0.512892i	$-0.828574\pi$
$43$		−	6.72651i		−	1.02578i	0.858453	−	0.512892i	$-0.171426\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.38366	+	4.38366i	0.639423	+	0.639423i	0.950413	−	0.310990i	$-0.100661\pi$
$47$	4.38366	+	4.38366i	0.639423	+	0.639423i	−0.310990	+	0.950413i	$0.600661\pi$
$48$		0			0
$49$			6.97350i			0.996215i
$50$		0			0
$51$	0.888698	−	0.888698i	0.124443	−	0.124443i
$52$		0			0
$53$	−11.4324			−1.57036			−0.785182	−	0.619265i	$-0.787431\pi$
$53$	−11.4324			−1.57036			−0.785182	+	0.619265i	$0.787431\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.71003	−	6.71003i	−0.888766	−	0.888766i
$58$		0			0
$59$	−1.63497	+	1.63497i	−0.212855	+	0.212855i	−0.805479	−	0.592624i	$-0.798092\pi$
$59$	−1.63497	+	1.63497i	−0.212855	+	0.212855i	0.592624	+	0.805479i	$0.298092\pi$
$60$		0			0
$61$	−1.23034	−	1.23034i	−0.157528	−	0.157528i	0.623942	−	0.781471i	$-0.285530\pi$
$61$	−1.23034	−	1.23034i	−0.157528	−	0.157528i	−0.781471	+	0.623942i	$0.785530\pi$
$62$		0			0
$63$	−0.666993	+	0.666993i	−0.0840332	+	0.0840332i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	2.49337i		−	0.304614i	−0.988333	−	0.152307i	$-0.951330\pi$
$67$		−	2.49337i		−	0.304614i	0.988333	−	0.152307i	$-0.0486702\pi$
$68$		0			0
$69$	−12.2946	−	12.2946i	−1.48010	−	1.48010i
$70$		0			0
$71$	−8.00096			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$71$	−8.00096			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$72$		0			0
$73$	1.12102	−	1.12102i	0.131205	−	0.131205i	−0.638454	−	0.769660i	$-0.720426\pi$
$73$	1.12102	−	1.12102i	0.131205	−	0.131205i	0.769660	+	0.638454i	$0.220426\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.681319			0.0776435
$78$		0			0
$79$	−3.62218			−0.407527			−0.203763	−	0.979020i	$-0.565317\pi$
$79$	−3.62218			−0.407527			−0.203763	+	0.979020i	$0.565317\pi$
$80$		0			0
$81$	7.19579			0.799532
$82$		0			0
$83$	1.62629			0.178509			0.0892545	−	0.996009i	$-0.471552\pi$
$83$	1.62629			0.178509			0.0892545	+	0.996009i	$0.471552\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.859007	+	0.859007i	−0.0920953	+	0.0920953i
$88$		0			0
$89$	−15.7149			−1.66577			−0.832887	−	0.553443i	$-0.813314\pi$
$89$	−15.7149			−1.66577			−0.832887	+	0.553443i	$0.813314\pi$
$90$		0			0
$91$	0.179352	+	0.179352i	0.0188012	+	0.0188012i
$92$		0			0
$93$			12.4113i			1.28700i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.69217	+	9.69217i	−0.984091	+	0.984091i	−0.999875	−	0.0157848i	$-0.994975\pi$
$97$	−9.69217	+	9.69217i	−0.984091	+	0.984091i	0.0157848	+	0.999875i	$0.494975\pi$
$98$		0			0
$99$	−17.1508	−	17.1508i	−1.72372	−	1.72372i
$100$		0			0
$101$	−12.8067	+	12.8067i	−1.27432	+	1.27432i	−0.330516	+	0.943800i	$0.607223\pi$
$101$	−12.8067	+	12.8067i	−1.27432	+	1.27432i	−0.943800	+	0.330516i	$0.892777\pi$
$102$		0			0
$103$	−4.33738	−	4.33738i	−0.427375	−	0.427375i	0.460358	−	0.887733i	$-0.347721\pi$
$103$	−4.33738	−	4.33738i	−0.427375	−	0.427375i	−0.887733	+	0.460358i	$0.847721\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.9807			−1.15822			−0.579108	−	0.815251i	$-0.696599\pi$
$107$	−11.9807			−1.15822			−0.579108	+	0.815251i	$0.696599\pi$
$108$		0			0
$109$	4.01503	−	4.01503i	0.384570	−	0.384570i	−0.488175	−	0.872746i	$-0.662337\pi$
$109$	4.01503	−	4.01503i	0.384570	−	0.384570i	0.872746	+	0.488175i	$0.162337\pi$
$110$		0			0
$111$		−	4.85301i		−	0.460628i
$112$		0			0
$113$	−6.47754	−	6.47754i	−0.609356	−	0.609356i	0.333422	−	0.942778i	$-0.391797\pi$
$113$	−6.47754	−	6.47754i	−0.609356	−	0.609356i	−0.942778	+	0.333422i	$0.891797\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	9.02966i		−	0.834792i
$118$		0			0
$119$		−	0.0689840i		−	0.00632375i
$120$		0			0
$121$			6.51921i			0.592655i
$122$		0			0
$123$			22.5875i			2.03665i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−12.2756	−	12.2756i	−1.08928	−	1.08928i	−0.995603	−	0.0936781i	$-0.970138\pi$
$127$	−12.2756	−	12.2756i	−1.08928	−	1.08928i	−0.0936781	−	0.995603i	$-0.529862\pi$
$128$		0			0
$129$			19.9482i			1.75634i
$130$		0			0
$131$	−7.99562	+	7.99562i	−0.698581	+	0.698581i	−0.964104	−	0.265524i	$-0.914455\pi$
$131$	−7.99562	+	7.99562i	−0.698581	+	0.698581i	0.265524	+	0.964104i	$0.414455\pi$
$132$		0			0
$133$	−0.520857			−0.0451641
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.08551	+	3.08551i	0.263613	+	0.263613i	0.826520	−	0.562907i	$-0.190317\pi$
$137$	3.08551	+	3.08551i	0.263613	+	0.263613i	−0.562907	+	0.826520i	$0.690317\pi$
$138$		0			0
$139$	−12.2206	+	12.2206i	−1.03654	+	1.03654i	−0.0372284	+	0.999307i	$0.511853\pi$
$139$	−12.2206	+	12.2206i	−1.03654	+	1.03654i	−0.999307	+	0.0372284i	$0.988147\pi$
$140$		0			0
$141$	−13.0002	−	13.0002i	−1.09482	−	1.09482i
$142$		0			0
$143$	−4.61180	+	4.61180i	−0.385658	+	0.385658i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	20.6807i		−	1.70572i
$148$		0			0
$149$	2.59172	+	2.59172i	0.212322	+	0.212322i	0.805253	−	0.592931i	$-0.202029\pi$
$149$	2.59172	+	2.59172i	0.212322	+	0.212322i	−0.592931	+	0.805253i	$0.702029\pi$
$150$		0			0
$151$	16.9594			1.38014			0.690068	−	0.723745i	$-0.257581\pi$
$151$	16.9594			1.38014			0.690068	+	0.723745i	$0.257581\pi$
$152$		0			0
$153$	−1.73653	+	1.73653i	−0.140390	+	0.140390i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.55235			−0.682552			−0.341276	−	0.939963i	$-0.610859\pi$
$157$	−8.55235			−0.682552			−0.341276	+	0.939963i	$0.610859\pi$
$158$		0			0
$159$	33.9041			2.68877
$160$		0			0
$161$	−0.954354			−0.0752136
$162$		0			0
$163$	−3.57797			−0.280248			−0.140124	−	0.990134i	$-0.544750\pi$
$163$	−3.57797			−0.280248			−0.140124	+	0.990134i	$0.544750\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.482874	−	0.482874i	0.0373659	−	0.0373659i	−0.688177	−	0.725543i	$-0.741589\pi$
$167$	0.482874	−	0.482874i	0.0373659	−	0.0373659i	0.725543	+	0.688177i	$0.241589\pi$
$168$		0			0
$169$	10.5720			0.813227
$170$		0			0
$171$	13.1115	+	13.1115i	1.00266	+	1.00266i
$172$		0			0
$173$		−	11.8189i		−	0.898576i	−0.893387	−	0.449288i	$-0.851678\pi$
$173$		−	11.8189i		−	0.898576i	0.893387	−	0.449288i	$-0.148322\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.84870	−	4.84870i	0.364451	−	0.364451i
$178$		0			0
$179$	4.71524	+	4.71524i	0.352433	+	0.352433i	0.861014	−	0.508581i	$-0.169830\pi$
$179$	4.71524	+	4.71524i	0.352433	+	0.352433i	−0.508581	+	0.861014i	$0.669830\pi$
$180$		0			0
$181$	13.1843	−	13.1843i	0.979983	−	0.979983i	−0.0198205	−	0.999804i	$-0.506309\pi$
$181$	13.1843	−	13.1843i	0.979983	−	0.979983i	0.999804	+	0.0198205i	$0.00630948\pi$
$182$		0			0
$183$	3.64870	+	3.64870i	0.269720	+	0.269720i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.77383			0.129715
$188$		0			0
$189$	0.954008	−	0.954008i	0.0693939	−	0.0693939i
$190$		0			0
$191$		−	13.9872i		−	1.01208i	−0.862510	−	0.506040i	$-0.831109\pi$
$191$		−	13.9872i		−	1.01208i	0.862510	−	0.506040i	$-0.168891\pi$
$192$		0			0
$193$	−3.88875	−	3.88875i	−0.279919	−	0.279919i	0.553158	−	0.833076i	$-0.313423\pi$
$193$	−3.88875	−	3.88875i	−0.279919	−	0.279919i	−0.833076	+	0.553158i	$0.813423\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	22.3277i		−	1.59078i	−0.606097	−	0.795391i	$-0.707266\pi$
$197$		−	22.3277i		−	1.59078i	0.606097	−	0.795391i	$-0.292734\pi$
$198$		0			0
$199$		−	9.83847i		−	0.697431i	−0.937229	−	0.348715i	$-0.886618\pi$
$199$		−	9.83847i		−	0.697431i	0.937229	−	0.348715i	$-0.113382\pi$
$200$		0			0
$201$			7.39437i			0.521559i
$202$		0			0
$203$			0.0666793i			0.00467997i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	24.0239	+	24.0239i	1.66978	+	1.66978i
$208$		0			0
$209$		−	13.3931i		−	0.926423i
$210$		0			0
$211$	−11.0531	+	11.0531i	−0.760925	+	0.760925i	−0.976490	−	0.215565i	$-0.930841\pi$
$211$	−11.0531	+	11.0531i	−0.760925	+	0.760925i	0.215565	+	0.976490i	$0.430841\pi$
$212$		0			0
$213$	23.7278			1.62580
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.481706	+	0.481706i	0.0327004	+	0.0327004i
$218$		0			0
$219$	−3.32451	+	3.32451i	−0.224650	+	0.224650i
$220$		0			0
$221$	0.466948	+	0.466948i	0.0314103	+	0.0314103i
$222$		0			0
$223$	5.93975	−	5.93975i	0.397755	−	0.397755i	−0.479686	−	0.877440i	$-0.659249\pi$
$223$	5.93975	−	5.93975i	0.397755	−	0.397755i	0.877440	+	0.479686i	$0.159249\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			23.2105i			1.54054i	0.637720	+	0.770269i	$0.279878\pi$
$227$			23.2105i			1.54054i	−0.637720	+	0.770269i	$0.720122\pi$
$228$		0			0
$229$	5.59944	+	5.59944i	0.370021	+	0.370021i	0.867485	−	0.497464i	$-0.165735\pi$
$229$	5.59944	+	5.59944i	0.370021	+	0.370021i	−0.497464	+	0.867485i	$0.665735\pi$
$230$		0			0
$231$	−2.02053			−0.132941
$232$		0			0
$233$	−3.01998	+	3.01998i	−0.197845	+	0.197845i	−0.799076	−	0.601230i	$-0.794677\pi$
$233$	−3.01998	+	3.01998i	−0.197845	+	0.197845i	0.601230	+	0.799076i	$0.294677\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	10.7420			0.697766
$238$		0			0
$239$	0.00138865			8.98241e−5			4.49120e−5	−	1.00000i	$-0.499986\pi$
$239$	0.00138865			8.98241e−5			4.49120e−5		1.00000i	$0.499986\pi$
$240$		0			0
$241$	−12.8578			−0.828245			−0.414123	−	0.910221i	$-0.635912\pi$
$241$	−12.8578			−0.828245			−0.414123	+	0.910221i	$0.635912\pi$
$242$		0			0
$243$	3.52546			0.226158
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.52565	−	3.52565i	0.224332	−	0.224332i
$248$		0			0
$249$	−4.82296			−0.305643
$250$		0			0
$251$	9.14111	+	9.14111i	0.576982	+	0.576982i	0.934071	−	0.357089i	$-0.116231\pi$
$251$	9.14111	+	9.14111i	0.576982	+	0.576982i	−0.357089	+	0.934071i	$0.616231\pi$
$252$		0			0
$253$		−	24.5399i		−	1.54281i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−21.2733	+	21.2733i	−1.32699	+	1.32699i	−0.419013	+	0.907980i	$0.637624\pi$
$257$	−21.2733	+	21.2733i	−1.32699	+	1.32699i	−0.907980	+	0.419013i	$0.862376\pi$
$258$		0			0
$259$	−0.188354	−	0.188354i	−0.0117038	−	0.0117038i
$260$		0			0
$261$	1.67851	−	1.67851i	0.103897	−	0.103897i
$262$		0			0
$263$	−16.7214	−	16.7214i	−1.03108	−	1.03108i	−0.999501	−	0.0315818i	$-0.989946\pi$
$263$	−16.7214	−	16.7214i	−1.03108	−	1.03108i	−0.0315818	−	0.999501i	$-0.510054\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	46.6043			2.85213
$268$		0			0
$269$	15.9096	−	15.9096i	0.970026	−	0.970026i	−0.0295378	−	0.999564i	$-0.509404\pi$
$269$	15.9096	−	15.9096i	0.970026	−	0.970026i	0.999564	+	0.0295378i	$0.00940355\pi$
$270$		0			0
$271$			12.3601i			0.750824i	0.926858	+	0.375412i	$0.122499\pi$
$271$			12.3601i			0.750824i	−0.926858	+	0.375412i	$0.877501\pi$
$272$		0			0
$273$	−0.531889	−	0.531889i	−0.0321914	−	0.0321914i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			21.0270i			1.26339i	0.775217	+	0.631695i	$0.217641\pi$
$277$			21.0270i			1.26339i	−0.775217	+	0.631695i	$0.782359\pi$
$278$		0			0
$279$		−	24.2520i		−	1.45193i
$280$		0			0
$281$		−	10.6807i		−	0.637158i	−0.947896	−	0.318579i	$-0.896794\pi$
$281$		−	10.6807i		−	0.637158i	0.947896	−	0.318579i	$-0.103206\pi$
$282$		0			0
$283$			12.5946i			0.748673i	0.927293	+	0.374336i	$0.122129\pi$
$283$			12.5946i			0.748673i	−0.927293	+	0.374336i	$0.877871\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.876663	+	0.876663i	0.0517478	+	0.0517478i
$288$		0			0
$289$			16.8204i			0.989435i
$290$		0			0
$291$	28.7432	−	28.7432i	1.68496	−	1.68496i
$292$		0			0
$293$	−3.43132			−0.200460			−0.100230	−	0.994964i	$-0.531958\pi$
$293$	−3.43132			−0.200460			−0.100230	+	0.994964i	$0.531958\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	24.5310	+	24.5310i	1.42344	+	1.42344i
$298$		0			0
$299$	6.45996	−	6.45996i	0.373589	−	0.373589i
$300$		0			0
$301$	0.774227	+	0.774227i	0.0446257	+	0.0446257i
$302$		0			0
$303$	37.9798	−	37.9798i	2.18188	−	2.18188i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			11.8104i			0.674053i	0.941495	+	0.337027i	$0.109421\pi$
$307$			11.8104i			0.674053i	−0.941495	+	0.337027i	$0.890579\pi$
$308$		0			0
$309$	12.8630	+	12.8630i	0.731750	+	0.731750i
$310$		0			0
$311$	−22.6262			−1.28301			−0.641506	−	0.767118i	$-0.721690\pi$
$311$	−22.6262			−1.28301			−0.641506	+	0.767118i	$0.721690\pi$
$312$		0			0
$313$	−7.08945	+	7.08945i	−0.400719	+	0.400719i	−0.878486	−	0.477767i	$-0.841446\pi$
$313$	−7.08945	+	7.08945i	−0.400719	+	0.400719i	0.477767	+	0.878486i	$0.341446\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.1265			1.41124			0.705621	−	0.708589i	$-0.250668\pi$
$317$	25.1265			1.41124			0.705621	+	0.708589i	$0.250668\pi$
$318$		0			0
$319$	−1.71457			−0.0959974
$320$		0			0
$321$	35.5300			1.98309
$322$		0			0
$323$	−1.35606			−0.0754535
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.9070	+	11.9070i	−0.658460	+	0.658460i
$328$		0			0
$329$	−1.00913			−0.0556349
$330$		0			0
$331$	−5.80829	−	5.80829i	−0.319253	−	0.319253i	0.529227	−	0.848480i	$-0.322482\pi$
$331$	−5.80829	−	5.80829i	−0.319253	−	0.319253i	−0.848480	+	0.529227i	$0.822482\pi$
$332$		0			0
$333$			9.48287i			0.519658i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.41679	−	7.41679i	0.404019	−	0.404019i	−0.475628	−	0.879647i	$-0.657779\pi$
$337$	7.41679	−	7.41679i	0.404019	−	0.404019i	0.879647	+	0.475628i	$0.157779\pi$
$338$		0			0
$339$	19.2099	+	19.2099i	1.04334	+	1.04334i
$340$		0			0
$341$	−12.3864	+	12.3864i	−0.670763	+	0.670763i
$342$		0			0
$343$	−1.60836	−	1.60836i	−0.0868434	−	0.0868434i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−18.2493			−0.979673			−0.489837	−	0.871814i	$-0.662944\pi$
$347$	−18.2493			−0.979673			−0.489837	+	0.871814i	$0.662944\pi$
$348$		0			0
$349$	−19.4413	+	19.4413i	−1.04067	+	1.04067i	−0.0415330	+	0.999137i	$0.513224\pi$
$349$	−19.4413	+	19.4413i	−1.04067	+	1.04067i	−0.999137	+	0.0415330i	$0.986776\pi$
$350$		0			0
$351$			12.9152i			0.689364i
$352$		0			0
$353$	1.13598	+	1.13598i	0.0604622	+	0.0604622i	0.736691	−	0.676229i	$-0.236387\pi$
$353$	1.13598	+	1.13598i	0.0604622	+	0.0604622i	−0.676229	+	0.736691i	$0.736387\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			0.204580i			0.0108275i
$358$		0			0
$359$			28.4140i			1.49963i	0.661645	+	0.749817i	$0.269859\pi$
$359$			28.4140i			1.49963i	−0.661645	+	0.749817i	$0.730141\pi$
$360$		0			0
$361$		−	8.76116i		−	0.461114i
$362$		0			0
$363$		−	19.3334i		−	1.01474i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.29692	−	2.29692i	−0.119898	−	0.119898i	0.644612	−	0.764510i	$-0.277019\pi$
$367$	−2.29692	−	2.29692i	−0.119898	−	0.119898i	−0.764510	+	0.644612i	$0.777019\pi$
$368$		0			0
$369$		−	44.1364i		−	2.29765i
$370$		0			0
$371$	1.31588	−	1.31588i	0.0683172	−	0.0683172i
$372$		0			0
$373$	18.0787			0.936081			0.468040	−	0.883707i	$-0.344960\pi$
$373$	18.0787			0.936081			0.468040	+	0.883707i	$0.344960\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.451348	−	0.451348i	−0.0232456	−	0.0232456i
$378$		0			0
$379$	2.79031	−	2.79031i	0.143328	−	0.143328i	−0.631802	−	0.775130i	$-0.717684\pi$
$379$	2.79031	−	2.79031i	0.143328	−	0.143328i	0.775130	+	0.631802i	$0.217684\pi$
$380$		0			0
$381$	36.4046	+	36.4046i	1.86506	+	1.86506i
$382$		0			0
$383$	−8.12206	+	8.12206i	−0.415018	+	0.415018i	−0.883482	−	0.468464i	$-0.844807\pi$
$383$	−8.12206	+	8.12206i	−0.415018	+	0.415018i	0.468464	+	0.883482i	$0.344807\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	38.9792i		−	1.98142i
$388$		0			0
$389$	−14.4341	−	14.4341i	−0.731839	−	0.731839i	0.239145	−	0.970984i	$-0.423133\pi$
$389$	−14.4341	−	14.4341i	−0.731839	−	0.731839i	−0.970984	+	0.239145i	$0.923133\pi$
$390$		0			0
$391$	−2.48468			−0.125656
$392$		0			0
$393$	23.7119	−	23.7119i	1.19611	−	1.19611i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	35.1624			1.76475			0.882374	−	0.470549i	$-0.155944\pi$
$397$	35.1624			1.76475			0.882374	+	0.470549i	$0.155944\pi$
$398$		0			0
$399$	1.54466			0.0773298
$400$		0			0
$401$	−23.5164			−1.17435			−0.587176	−	0.809459i	$-0.699760\pi$
$401$	−23.5164			−1.17435			−0.587176	+	0.809459i	$0.699760\pi$
$402$		0			0
$403$	−6.52128			−0.324848
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.84328	−	4.84328i	0.240072	−	0.240072i
$408$		0			0
$409$	23.2595			1.15011			0.575054	−	0.818115i	$-0.304981\pi$
$409$	23.2595			1.15011			0.575054	+	0.818115i	$0.304981\pi$
$410$		0			0
$411$	−9.15043	−	9.15043i	−0.451357	−	0.451357i
$412$		0			0
$413$		−	0.376374i		−	0.0185201i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	36.2415	−	36.2415i	1.77475	−	1.77475i
$418$		0			0
$419$	−6.63975	−	6.63975i	−0.324373	−	0.324373i	0.526069	−	0.850442i	$-0.323665\pi$
$419$	−6.63975	−	6.63975i	−0.324373	−	0.324373i	−0.850442	+	0.526069i	$0.823665\pi$
$420$		0			0
$421$	7.28216	−	7.28216i	0.354911	−	0.354911i	−0.507022	−	0.861933i	$-0.669254\pi$
$421$	7.28216	−	7.28216i	0.354911	−	0.354911i	0.861933	+	0.507022i	$0.169254\pi$
$422$		0			0
$423$	25.4027	+	25.4027i	1.23512	+	1.23512i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.283225			0.0137062
$428$		0			0
$429$	13.6768	−	13.6768i	0.660323	−	0.660323i
$430$		0			0
$431$		−	11.7250i		−	0.564771i	−0.959301	−	0.282386i	$-0.908874\pi$
$431$		−	11.7250i		−	0.564771i	0.959301	−	0.282386i	$-0.0911258\pi$
$432$		0			0
$433$	20.8827	+	20.8827i	1.00356	+	1.00356i	0.999994	+	0.00356603i	$0.00113511\pi$
$433$	20.8827	+	20.8827i	1.00356	+	1.00356i	0.00356603	+	0.999994i	$0.498865\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			18.7604i			0.897430i
$438$		0			0
$439$		−	7.53661i		−	0.359703i	−0.983694	−	0.179851i	$-0.942438\pi$
$439$		−	7.53661i		−	0.359703i	0.983694	−	0.179851i	$-0.0575617\pi$
$440$		0			0
$441$			40.4105i			1.92431i
$442$		0			0
$443$		−	25.7280i		−	1.22237i	−0.791486	−	0.611187i	$-0.790692\pi$
$443$		−	25.7280i		−	1.22237i	0.791486	−	0.611187i	$-0.209308\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.68604	−	7.68604i	−0.363537	−	0.363537i
$448$		0			0
$449$		−	2.33824i		−	0.110348i	−0.998477	−	0.0551741i	$-0.982429\pi$
$449$		−	2.33824i		−	0.110348i	0.998477	−	0.0551741i	$-0.0175714\pi$
$450$		0			0
$451$	−22.5422	+	22.5422i	−1.06147	+	1.06147i
$452$		0			0
$453$	−50.2950			−2.36306
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.4561	−	10.4561i	−0.489115	−	0.489115i	0.418912	−	0.908027i	$-0.362412\pi$
$457$	−10.4561	−	10.4561i	−0.489115	−	0.489115i	−0.908027	+	0.418912i	$0.862412\pi$
$458$		0			0
$459$	2.48378	−	2.48378i	0.115933	−	0.115933i
$460$		0			0
$461$	15.6903	+	15.6903i	0.730769	+	0.730769i	0.970772	−	0.240003i	$-0.0771484\pi$
$461$	15.6903	+	15.6903i	0.730769	+	0.730769i	−0.240003	+	0.970772i	$0.577148\pi$
$462$		0			0
$463$	−19.6332	+	19.6332i	−0.912434	+	0.912434i	−0.996463	−	0.0840297i	$-0.973221\pi$
$463$	−19.6332	+	19.6332i	−0.912434	+	0.912434i	0.0840297	+	0.996463i	$0.473221\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			24.4862i			1.13309i	0.824032	+	0.566543i	$0.191719\pi$
$467$			24.4862i			1.13309i	−0.824032	+	0.566543i	$0.808281\pi$
$468$		0			0
$469$	0.286989	+	0.286989i	0.0132519	+	0.0132519i
$470$		0			0
$471$	25.3630			1.16866
$472$		0			0
$473$	−19.9082	+	19.9082i	−0.915380	+	0.915380i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−66.2493			−3.03335
$478$		0			0
$479$	−37.0609			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$479$	−37.0609			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$480$		0			0
$481$	2.54991			0.116266
$482$		0			0
$483$	2.83024			0.128781
$484$		0			0
$485$		0			0
$486$		0			0
$487$	20.1912	−	20.1912i	0.914950	−	0.914950i	−0.0817061	−	0.996656i	$-0.526037\pi$
$487$	20.1912	−	20.1912i	0.914950	−	0.914950i	0.996656	+	0.0817061i	$0.0260369\pi$
$488$		0			0
$489$	10.6109			0.479840
$490$		0			0
$491$	7.45822	+	7.45822i	0.336585	+	0.336585i	0.855080	−	0.518496i	$-0.173508\pi$
$491$	7.45822	+	7.45822i	0.336585	+	0.336585i	−0.518496	+	0.855080i	$0.673508\pi$
$492$		0			0
$493$			0.173601i			0.00781860i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.920917	−	0.920917i	0.0413088	−	0.0413088i
$498$		0			0
$499$	−8.17420	−	8.17420i	−0.365927	−	0.365927i	0.500062	−	0.865990i	$-0.333311\pi$
$499$	−8.17420	−	8.17420i	−0.365927	−	0.365927i	−0.865990	+	0.500062i	$0.833311\pi$
$500$		0			0
$501$	−1.43202	+	1.43202i	−0.0639778	+	0.0639778i
$502$		0			0
$503$	−29.2327	−	29.2327i	−1.30342	−	1.30342i	−0.926072	−	0.377348i	$-0.876836\pi$
$503$	−29.2327	−	29.2327i	−1.30342	−	1.30342i	−0.377348	−	0.926072i	$-0.623164\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−31.3523			−1.39241
$508$		0			0
$509$	−20.0340	+	20.0340i	−0.887992	+	0.887992i	−0.994330	−	0.106338i	$-0.966088\pi$
$509$	−20.0340	+	20.0340i	−0.887992	+	0.887992i	0.106338	+	0.994330i	$0.466088\pi$
$510$		0			0
$511$			0.258061i			0.0114159i
$512$		0			0
$513$	−18.7536	−	18.7536i	−0.827991	−	0.827991i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	25.9483i		−	1.14121i
$518$		0			0
$519$			35.0504i			1.53854i
$520$		0			0
$521$			5.89264i			0.258161i	0.991634	+	0.129081i	$0.0412026\pi$
$521$			5.89264i			0.258161i	−0.991634	+	0.129081i	$0.958797\pi$
$522$		0			0
$523$		−	24.6537i		−	1.07803i	−0.842296	−	0.539015i	$-0.818797\pi$
$523$		−	24.6537i		−	1.07803i	0.842296	−	0.539015i	$-0.181203\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.25413	+	1.25413i	0.0546309	+	0.0546309i
$528$		0			0
$529$			11.3742i			0.494528i
$530$		0			0
$531$	−9.47444	+	9.47444i	−0.411156	+	0.411156i
$532$		0			0
$533$	−11.8681			−0.514066
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−13.9836	−	13.9836i	−0.603435	−	0.603435i
$538$		0			0
$539$	20.6392	−	20.6392i	0.888994	−	0.888994i
$540$		0			0
$541$	−27.1762	−	27.1762i	−1.16840	−	1.16840i	−0.982585	−	0.185812i	$-0.940508\pi$
$541$	−27.1762	−	27.1762i	−1.16840	−	1.16840i	−0.185812	−	0.982585i	$-0.559492\pi$
$542$		0			0
$543$	−39.0996	+	39.0996i	−1.67792	+	1.67792i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	3.69225i		−	0.157869i	−0.996880	−	0.0789347i	$-0.974848\pi$
$547$		−	3.69225i		−	0.157869i	0.996880	−	0.0789347i	$-0.0251519\pi$
$548$		0			0
$549$	−7.12962	−	7.12962i	−0.304285	−	0.304285i
$550$		0			0
$551$	1.31076			0.0558402
$552$		0			0
$553$	0.416915	−	0.416915i	0.0177290	−	0.0177290i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.2117			−0.517426			−0.258713	−	0.965954i	$-0.583298\pi$
$557$	−12.2117			−0.517426			−0.258713	+	0.965954i	$0.583298\pi$
$558$		0			0
$559$	−10.4814			−0.443315
$560$		0			0
$561$	−5.26049			−0.222098
$562$		0			0
$563$	−12.2211			−0.515057			−0.257528	−	0.966271i	$-0.582908\pi$
$563$	−12.2211			−0.515057			−0.257528	+	0.966271i	$0.582908\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.828241	+	0.828241i	−0.0347829	+	0.0347829i
$568$		0			0
$569$	−30.9592			−1.29788			−0.648938	−	0.760841i	$-0.724787\pi$
$569$	−30.9592			−1.29788			−0.648938	+	0.760841i	$0.724787\pi$
$570$		0			0
$571$	−30.1508	−	30.1508i	−1.26177	−	1.26177i	−0.950233	−	0.311539i	$-0.899156\pi$
$571$	−30.1508	−	30.1508i	−1.26177	−	1.26177i	−0.311539	−	0.950233i	$-0.600844\pi$
$572$		0			0
$573$			41.4806i			1.73288i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.98215	+	1.98215i	−0.0825181	+	0.0825181i	−0.747161	−	0.664643i	$-0.768584\pi$
$577$	−1.98215	+	1.98215i	−0.0825181	+	0.0825181i	0.664643	+	0.747161i	$0.268584\pi$
$578$		0			0
$579$	11.5325	+	11.5325i	0.479276	+	0.479276i
$580$		0			0
$581$	−0.187188	+	0.187188i	−0.00776586	+	0.00776586i
$582$		0			0
$583$	33.8361	+	33.8361i	1.40135	+	1.40135i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	26.9680			1.11309			0.556544	−	0.830818i	$-0.312127\pi$
$587$	26.9680			1.11309			0.556544	+	0.830818i	$0.312127\pi$
$588$		0			0
$589$	9.46923	−	9.46923i	0.390173	−	0.390173i
$590$		0			0
$591$			66.2153i			2.72373i
$592$		0			0
$593$	−16.6701	−	16.6701i	−0.684560	−	0.684560i	0.276464	−	0.961024i	$-0.410837\pi$
$593$	−16.6701	−	16.6701i	−0.684560	−	0.684560i	−0.961024	+	0.276464i	$0.910837\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			29.1771i			1.19414i
$598$		0			0
$599$		−	28.8376i		−	1.17827i	−0.808033	−	0.589137i	$-0.799468\pi$
$599$		−	28.8376i		−	1.17827i	0.808033	−	0.589137i	$-0.200532\pi$
$600$		0			0
$601$			1.91377i			0.0780642i	0.999238	+	0.0390321i	$0.0124275\pi$
$601$			1.91377i			0.0780642i	−0.999238	+	0.0390321i	$0.987573\pi$
$602$		0			0
$603$		−	14.4487i		−	0.588397i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−7.89049	−	7.89049i	−0.320265	−	0.320265i	0.528604	−	0.848869i	$-0.322716\pi$
$607$	−7.89049	−	7.89049i	−0.320265	−	0.320265i	−0.848869	+	0.528604i	$0.822716\pi$
$608$		0			0
$609$		−	0.197745i		−	0.00801303i
$610$		0			0
$611$	6.83071	−	6.83071i	0.276341	−	0.276341i
$612$		0			0
$613$	40.1035			1.61976			0.809882	−	0.586592i	$-0.199531\pi$
$613$	40.1035			1.61976			0.809882	+	0.586592i	$0.199531\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.5821	−	14.5821i	−0.587052	−	0.587052i	0.349780	−	0.936832i	$-0.386256\pi$
$617$	−14.5821	−	14.5821i	−0.587052	−	0.587052i	−0.936832	+	0.349780i	$0.886256\pi$
$618$		0			0
$619$	4.01752	−	4.01752i	0.161478	−	0.161478i	−0.621743	−	0.783221i	$-0.713575\pi$
$619$	4.01752	−	4.01752i	0.161478	−	0.161478i	0.783221	+	0.621743i	$0.213575\pi$
$620$		0			0
$621$	−34.3617	−	34.3617i	−1.37889	−	1.37889i
$622$		0			0
$623$	1.80880	−	1.80880i	0.0724679	−	0.0724679i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			39.7189i			1.58622i
$628$		0			0
$629$	−0.490385	−	0.490385i	−0.0195529	−	0.0195529i
$630$		0			0
$631$	26.9309			1.07210			0.536052	−	0.844185i	$-0.319915\pi$
$631$	26.9309			1.07210			0.536052	+	0.844185i	$0.319915\pi$
$632$		0			0
$633$	32.7791	−	32.7791i	1.30285	−	1.30285i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	10.8662			0.430536
$638$		0			0
$639$	−46.3644			−1.83415
$640$		0			0
$641$	18.6880			0.738131			0.369065	−	0.929403i	$-0.379678\pi$
$641$	18.6880			0.738131			0.369065	+	0.929403i	$0.379678\pi$
$642$		0			0
$643$	29.6249			1.16829			0.584146	−	0.811648i	$-0.301429\pi$
$643$	29.6249			1.16829			0.584146	+	0.811648i	$0.301429\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.04426	+	5.04426i	−0.198310	+	0.198310i	−0.799275	−	0.600965i	$-0.794783\pi$
$647$	−5.04426	+	5.04426i	−0.198310	+	0.198310i	0.600965	+	0.799275i	$0.294783\pi$
$648$		0			0
$649$	9.67794			0.379893
$650$		0			0
$651$	−1.42855	−	1.42855i	−0.0559895	−	0.0559895i
$652$		0			0
$653$		−	3.04934i		−	0.119330i	−0.998218	−	0.0596649i	$-0.980997\pi$
$653$		−	3.04934i		−	0.119330i	0.998218	−	0.0596649i	$-0.0190032\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.49615	−	6.49615i	0.253439	−	0.253439i
$658$		0			0
$659$	−22.0441	−	22.0441i	−0.858718	−	0.858718i	0.132469	−	0.991187i	$-0.457709\pi$
$659$	−22.0441	−	22.0441i	−0.858718	−	0.858718i	−0.991187	+	0.132469i	$0.957709\pi$
$660$		0			0
$661$	8.09788	−	8.09788i	0.314971	−	0.314971i	−0.531861	−	0.846832i	$-0.678507\pi$
$661$	8.09788	−	8.09788i	0.314971	−	0.314971i	0.846832	+	0.531861i	$0.178507\pi$
$662$		0			0
$663$	−1.38479	−	1.38479i	−0.0537807	−	0.0537807i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.40167			0.0929931
$668$		0			0
$669$	−17.6150	+	17.6150i	−0.681035	+	0.681035i
$670$		0			0
$671$			7.28276i			0.281148i
$672$		0			0
$673$	27.1768	+	27.1768i	1.04759	+	1.04759i	0.998810	+	0.0487786i	$0.0155329\pi$
$673$	27.1768	+	27.1768i	1.04759	+	1.04759i	0.0487786	+	0.998810i	$0.484467\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			28.6501i			1.10111i	0.834798	+	0.550557i	$0.185585\pi$
$677$			28.6501i			1.10111i	−0.834798	+	0.550557i	$0.814415\pi$
$678$		0			0
$679$		−	2.23115i		−	0.0856238i
$680$		0			0
$681$		−	68.8334i		−	2.63770i
$682$		0			0
$683$			30.8472i			1.18034i	0.807281	+	0.590168i	$0.200938\pi$
$683$			30.8472i			1.18034i	−0.807281	+	0.590168i	$0.799062\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−16.6058	−	16.6058i	−0.633549	−	0.633549i
$688$		0			0
$689$			17.8142i			0.678668i
$690$		0			0
$691$	−0.253186	+	0.253186i	−0.00963164	+	0.00963164i	−0.711906	−	0.702275i	$-0.752168\pi$
$691$	−0.253186	+	0.253186i	−0.00963164	+	0.00963164i	0.702275	+	0.711906i	$0.252168\pi$
$692$		0			0
$693$	3.94815			0.149978
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.28241	+	2.28241i	0.0864525	+	0.0864525i
$698$		0			0
$699$	8.95608	−	8.95608i	0.338750	−	0.338750i
$700$		0			0
$701$	10.5238	+	10.5238i	0.397479	+	0.397479i	0.877343	−	0.479864i	$-0.159314\pi$
$701$	10.5238	+	10.5238i	0.397479	+	0.397479i	−0.479864	+	0.877343i	$0.659314\pi$
$702$		0			0
$703$	−3.70261	+	3.70261i	−0.139646	+	0.139646i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	2.94813i		−	0.110876i
$708$		0			0
$709$	1.58968	+	1.58968i	0.0597015	+	0.0597015i	0.736327	−	0.676626i	$-0.236558\pi$
$709$	1.58968	+	1.58968i	0.0597015	+	0.0597015i	−0.676626	+	0.736327i	$0.736558\pi$
$710$		0			0
$711$	−20.9900			−0.787186
$712$		0			0
$713$	17.3502	−	17.3502i	0.649771	−	0.649771i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.00411819			−0.000153797
$718$		0			0
$719$	22.8919			0.853722			0.426861	−	0.904317i	$-0.359619\pi$
$719$	22.8919			0.853722			0.426861	+	0.904317i	$0.359619\pi$
$720$		0			0
$721$	0.998472			0.0371850
$722$		0			0
$723$	38.1313			1.41812
$724$		0			0
$725$		0			0
$726$		0			0
$727$	20.1893	−	20.1893i	0.748780	−	0.748780i	−0.225470	−	0.974250i	$-0.572392\pi$
$727$	20.1893	−	20.1893i	0.748780	−	0.748780i	0.974250	+	0.225470i	$0.0723919\pi$
$728$		0			0
$729$	−32.0425			−1.18676
$730$		0			0
$731$	2.01572	+	2.01572i	0.0745540	+	0.0745540i
$732$		0			0
$733$			14.3253i			0.529118i	0.964370	+	0.264559i	$0.0852263\pi$
$733$			14.3253i			0.529118i	−0.964370	+	0.264559i	$0.914774\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.37954	+	7.37954i	−0.271829	+	0.271829i
$738$		0			0
$739$	32.3401	+	32.3401i	1.18965	+	1.18965i	0.977164	+	0.212487i	$0.0681564\pi$
$739$	32.3401	+	32.3401i	1.18965	+	1.18965i	0.212487	+	0.977164i	$0.431844\pi$
$740$		0			0
$741$	−10.4557	+	10.4557i	−0.384100	+	0.384100i
$742$		0			0
$743$	−6.06842	−	6.06842i	−0.222629	−	0.222629i	0.586976	−	0.809605i	$-0.300318\pi$
$743$	−6.06842	−	6.06842i	−0.222629	−	0.222629i	−0.809605	+	0.586976i	$0.800318\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	9.42414			0.344811
$748$		0			0
$749$	1.37898	−	1.37898i	0.0503870	−	0.0503870i
$750$		0			0
$751$		−	49.6431i		−	1.81150i	−0.423810	−	0.905751i	$-0.639308\pi$
$751$		−	49.6431i		−	1.81150i	0.423810	−	0.905751i	$-0.360692\pi$
$752$		0			0
$753$	−27.1090	−	27.1090i	−0.987907	−	0.987907i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	9.18443i		−	0.333814i	−0.985973	−	0.166907i	$-0.946622\pi$
$757$		−	9.18443i		−	0.333814i	0.985973	−	0.166907i	$-0.0533779\pi$
$758$		0			0
$759$			72.7759i			2.64160i
$760$		0			0
$761$		−	4.75310i		−	0.172300i	−0.996282	−	0.0861499i	$-0.972544\pi$
$761$		−	4.75310i		−	0.172300i	0.996282	−	0.0861499i	$-0.0274564\pi$
$762$		0			0
$763$			0.924267i			0.0334607i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.54765	+	2.54765i	0.0919902	+	0.0919902i
$768$		0			0
$769$		−	19.4153i		−	0.700135i	−0.936724	−	0.350067i	$-0.886159\pi$
$769$		−	19.4153i		−	0.700135i	0.936724	−	0.350067i	$-0.113841\pi$
$770$		0			0
$771$	63.0884	−	63.0884i	2.27207	−	2.27207i
$772$		0			0
$773$	−26.0890			−0.938356			−0.469178	−	0.883104i	$-0.655450\pi$
$773$	−26.0890			−0.938356			−0.469178	+	0.883104i	$0.655450\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.558586	+	0.558586i	0.0200392	+	0.0200392i
$778$		0			0
$779$	17.2331	−	17.2331i	0.617442	−	0.617442i
$780$		0			0
$781$	23.6802	+	23.6802i	0.847343	+	0.847343i
$782$		0			0
$783$	−2.40080	+	2.40080i	−0.0857977	+	0.0857977i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			14.2339i			0.507384i	0.967285	+	0.253692i	$0.0816449\pi$
$787$			14.2339i			0.507384i	−0.967285	+	0.253692i	$0.918355\pi$
$788$		0			0
$789$	49.5891	+	49.5891i	1.76542	+	1.76542i
$790$		0			0
$791$	1.49114			0.0530189
$792$		0			0
$793$	−1.91713	+	1.91713i	−0.0680794	+	0.0680794i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.8283			−0.702353			−0.351176	−	0.936309i	$-0.614218\pi$
$797$	−19.8283			−0.702353			−0.351176	+	0.936309i	$0.614218\pi$
$798$		0			0
$799$	−2.62729			−0.0929467
$800$		0			0
$801$	−91.0655			−3.21764
$802$		0			0
$803$	−6.63568			−0.234168
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−47.1817	+	47.1817i	−1.66088	+	1.66088i
$808$		0			0
$809$	21.3864			0.751907			0.375954	−	0.926639i	$-0.377315\pi$
$809$	21.3864			0.751907			0.375954	+	0.926639i	$0.377315\pi$
$810$		0			0
$811$	9.90624	+	9.90624i	0.347855	+	0.347855i	0.859310	−	0.511455i	$-0.170893\pi$
$811$	9.90624	+	9.90624i	0.347855	+	0.347855i	−0.511455	+	0.859310i	$0.670893\pi$
$812$		0			0
$813$		−	36.6553i		−	1.28556i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	15.2195	−	15.2195i	0.532463	−	0.532463i
$818$		0			0
$819$	1.03932	+	1.03932i	0.0363168	+	0.0363168i
$820$		0			0
$821$	22.6209	−	22.6209i	0.789474	−	0.789474i	−0.191934	−	0.981408i	$-0.561476\pi$
$821$	22.6209	−	22.6209i	0.789474	−	0.789474i	0.981408	+	0.191934i	$0.0614759\pi$
$822$		0			0
$823$	4.89892	+	4.89892i	0.170766	+	0.170766i	0.787316	−	0.616550i	$-0.211470\pi$
$823$	4.89892	+	4.89892i	0.170766	+	0.170766i	−0.616550	+	0.787316i	$0.711470\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.05434			0.0366630			0.0183315	−	0.999832i	$-0.494165\pi$
$827$	1.05434			0.0366630			0.0183315	+	0.999832i	$0.494165\pi$
$828$		0			0
$829$	11.7754	−	11.7754i	0.408978	−	0.408978i	−0.472404	−	0.881382i	$-0.656614\pi$
$829$	11.7754	−	11.7754i	0.408978	−	0.408978i	0.881382	+	0.472404i	$0.156614\pi$
$830$		0			0
$831$		−	62.3580i		−	2.16317i
$832$		0			0
$833$	−2.08973	−	2.08973i	−0.0724050	−	0.0724050i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			34.6879i			1.19899i
$838$		0			0
$839$		−	41.1678i		−	1.42127i	−0.703560	−	0.710636i	$-0.748407\pi$
$839$		−	41.1678i		−	1.42127i	0.703560	−	0.710636i	$-0.251593\pi$
$840$		0			0
$841$			28.8322i			0.994214i
$842$		0			0
$843$			31.6749i			1.09094i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.750366	−	0.750366i	−0.0257829	−	0.0257829i
$848$		0			0
$849$		−	37.3508i		−	1.28188i
$850$		0			0
$851$	−6.78419	+	6.78419i	−0.232559	+	0.232559i
$852$		0			0
$853$	−11.7179			−0.401212			−0.200606	−	0.979672i	$-0.564291\pi$
$853$	−11.7179			−0.401212			−0.200606	+	0.979672i	$0.564291\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.2154	+	12.2154i	0.417270	+	0.417270i	0.884262	−	0.466992i	$-0.154662\pi$
$857$	12.2154	+	12.2154i	0.417270	+	0.417270i	−0.466992	+	0.884262i	$0.654662\pi$
$858$		0			0
$859$	−17.2170	+	17.2170i	−0.587436	+	0.587436i	−0.936936	−	0.349500i	$-0.886351\pi$
$859$	−17.2170	+	17.2170i	−0.587436	+	0.587436i	0.349500	+	0.936936i	$0.386351\pi$
$860$		0			0
$861$	−2.59984	−	2.59984i	−0.0886024	−	0.0886024i
$862$		0			0
$863$	−11.1929	+	11.1929i	−0.381011	+	0.381011i	−0.871466	−	0.490455i	$-0.836831\pi$
$863$	−11.1929	+	11.1929i	−0.381011	+	0.381011i	0.490455	+	0.871466i	$0.336831\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	49.8828i		−	1.69411i
$868$		0			0
$869$	10.7204	+	10.7204i	0.363665	+	0.363665i
$870$		0			0
$871$	−3.88522			−0.131646
$872$		0			0
$873$	−56.1647	+	56.1647i	−1.90089	+	1.90089i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−43.1739			−1.45788			−0.728940	−	0.684578i	$-0.759987\pi$
$877$	−43.1739			−1.45788			−0.728940	+	0.684578i	$0.759987\pi$
$878$		0			0
$879$	10.1760			0.343227
$880$		0			0
$881$	−33.4204			−1.12596			−0.562981	−	0.826470i	$-0.690346\pi$
$881$	−33.4204			−1.12596			−0.562981	+	0.826470i	$0.690346\pi$
$882$		0			0
$883$	2.00362			0.0674270			0.0337135	−	0.999432i	$-0.489267\pi$
$883$	2.00362			0.0674270			0.0337135	+	0.999432i	$0.489267\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.1765	+	16.1765i	−0.543154	+	0.543154i	−0.924452	−	0.381298i	$-0.875477\pi$
$887$	−16.1765	+	16.1765i	−0.543154	+	0.543154i	0.381298	+	0.924452i	$0.375477\pi$
$888$		0			0
$889$	2.82586			0.0947762
$890$		0			0
$891$	−21.2971	−	21.2971i	−0.713480	−	0.713480i
$892$		0			0
$893$			19.8371i			0.663822i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−19.1577	+	19.1577i	−0.639658	+	0.639658i
$898$		0			0
$899$	−1.21223	−	1.21223i	−0.0404303	−	0.0404303i
$900$		0			0
$901$	3.42593	−	3.42593i	0.114134	−	0.114134i
$902$		0			0
$903$	−2.29606	−	2.29606i	−0.0764080	−	0.0764080i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−29.7116			−0.986559			−0.493279	−	0.869871i	$-0.664202\pi$
$907$	−29.7116			−0.986559			−0.493279	+	0.869871i	$0.664202\pi$
$908$		0			0
$909$	−74.2131	+	74.2131i	−2.46149	+	2.46149i
$910$		0			0
$911$			44.6931i			1.48075i	0.672195	+	0.740374i	$0.265352\pi$
$911$			44.6931i			1.48075i	−0.672195	+	0.740374i	$0.734648\pi$
$912$		0			0
$913$	−4.81328	−	4.81328i	−0.159296	−	0.159296i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1.84061i		−	0.0607821i
$918$		0			0
$919$		−	40.1278i		−	1.32369i	−0.749639	−	0.661847i	$-0.769773\pi$
$919$		−	40.1278i		−	1.32369i	0.749639	−	0.661847i	$-0.230227\pi$
$920$		0			0
$921$		−	35.0250i		−	1.15411i
$922$		0			0
$923$			12.4673i			0.410365i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−25.1345	−	25.1345i	−0.825525	−	0.825525i
$928$		0			0
$929$		−	27.7519i		−	0.910512i	−0.890361	−	0.455256i	$-0.849548\pi$
$929$		−	27.7519i		−	0.910512i	0.890361	−	0.455256i	$-0.150452\pi$
$930$		0			0
$931$	−15.7783	+	15.7783i	−0.517114	+	0.517114i
$932$		0			0
$933$	67.1004			2.19677
$934$		0			0
$935$		0			0
$936$		0			0
$937$	17.2805	+	17.2805i	0.564531	+	0.564531i	0.930591	−	0.366060i	$-0.119294\pi$
$937$	17.2805	+	17.2805i	0.564531	+	0.564531i	−0.366060	+	0.930591i	$0.619294\pi$
$938$		0			0
$939$	21.0245	−	21.0245i	0.686110	−	0.686110i
$940$		0			0
$941$	−4.81532	−	4.81532i	−0.156975	−	0.156975i	0.624250	−	0.781225i	$-0.285405\pi$
$941$	−4.81532	−	4.81532i	−0.156975	−	0.156975i	−0.781225	+	0.624250i	$0.785405\pi$
$942$		0			0
$943$	31.5759	−	31.5759i	1.02825	−	1.02825i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	3.37347i		−	0.109623i	−0.998497	−	0.0548115i	$-0.982544\pi$
$947$		−	3.37347i		−	0.109623i	0.998497	−	0.0548115i	$-0.0174558\pi$
$948$		0			0
$949$	−1.74680	−	1.74680i	−0.0567034	−	0.0567034i
$950$		0			0
$951$	−74.5153			−2.41632
$952$		0			0
$953$	−14.3663	+	14.3663i	−0.465369	+	0.465369i	−0.900410	−	0.435041i	$-0.856734\pi$
$953$	−14.3663	+	14.3663i	−0.465369	+	0.465369i	0.435041	+	0.900410i	$0.356734\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	5.08475			0.164366
$958$		0			0
$959$	−0.710289			−0.0229364
$960$		0			0
$961$	13.4851			0.435003
$962$		0			0
$963$	−69.4263			−2.23723
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.8576	+	11.8576i	−0.381315	+	0.381315i	−0.871576	−	0.490260i	$-0.836902\pi$
$967$	−11.8576	+	11.8576i	−0.381315	+	0.381315i	0.490260	+	0.871576i	$0.336902\pi$
$968$		0			0
$969$	4.02156			0.129191
$970$		0			0
$971$	14.6082	+	14.6082i	0.468799	+	0.468799i	0.901525	−	0.432726i	$-0.142448\pi$
$971$	14.6082	+	14.6082i	0.468799	+	0.468799i	−0.432726	+	0.901525i	$0.642448\pi$
$972$		0			0
$973$		−	2.81319i		−	0.0901869i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.9249	+	12.9249i	−0.413504	+	0.413504i	−0.882957	−	0.469454i	$-0.844451\pi$
$977$	−12.9249	+	12.9249i	−0.413504	+	0.413504i	0.469454	+	0.882957i	$0.344451\pi$
$978$		0			0
$979$	46.5108	+	46.5108i	1.48649	+	1.48649i
$980$		0			0
$981$	23.2665	−	23.2665i	0.742843	−	0.742843i
$982$		0			0
$983$	−0.133323	−	0.133323i	−0.00425235	−	0.00425235i	0.704977	−	0.709230i	$-0.250957\pi$
$983$	−0.133323	−	0.133323i	−0.00425235	−	0.00425235i	−0.709230	+	0.704977i	$0.750957\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.99268			0.0952580
$988$		0			0
$989$	27.8863	−	27.8863i	0.886733	−	0.886733i
$990$		0			0
$991$			47.9032i			1.52170i	0.648930	+	0.760848i	$0.275217\pi$
$991$			47.9032i			1.52170i	−0.648930	+	0.760848i	$0.724783\pi$
$992$		0			0
$993$	17.2251	+	17.2251i	0.546624	+	0.546624i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	54.9379i		−	1.73990i	−0.493138	−	0.869951i	$-0.664150\pi$
$997$		−	54.9379i		−	1.73990i	0.493138	−	0.869951i	$-0.335850\pi$
$998$		0			0
$999$		−	13.5635i		−	0.429129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.d.943.1		18
4.3	odd	2		400.2.s.d.243.5		18
5.2	odd	4		1600.2.j.d.1007.9		18
5.3	odd	4		320.2.j.b.47.1		18
5.4	even	2		320.2.s.b.303.9		18
16.5	even	4		400.2.j.d.43.9		18
16.11	odd	4		1600.2.j.d.143.1		18
20.3	even	4		80.2.j.b.67.1	yes	18
20.7	even	4		400.2.j.d.307.9		18
20.19	odd	2		80.2.s.b.3.5	yes	18
40.3	even	4		640.2.j.d.607.1		18
40.13	odd	4		640.2.j.c.607.9		18
40.19	odd	2		640.2.s.d.223.9		18
40.29	even	2		640.2.s.c.223.1		18
60.23	odd	4		720.2.bd.g.307.9		18
60.59	even	2		720.2.z.g.163.5		18
80.3	even	4		640.2.s.c.287.1		18
80.13	odd	4		640.2.s.d.287.9		18
80.19	odd	4		640.2.j.c.543.1		18
80.27	even	4	inner	1600.2.s.d.207.1		18
80.29	even	4		640.2.j.d.543.9		18
80.37	odd	4		400.2.s.d.107.5		18
80.43	even	4		320.2.s.b.207.9		18
80.53	odd	4		80.2.s.b.27.5	yes	18
80.59	odd	4		320.2.j.b.143.9		18
80.69	even	4		80.2.j.b.43.1	✓	18
240.53	even	4		720.2.z.g.667.5		18
240.149	odd	4		720.2.bd.g.523.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	80.69	even	4
80.2.j.b.67.1	yes	18	20.3	even	4
80.2.s.b.3.5	yes	18	20.19	odd	2
80.2.s.b.27.5	yes	18	80.53	odd	4
320.2.j.b.47.1		18	5.3	odd	4
320.2.j.b.143.9		18	80.59	odd	4
320.2.s.b.207.9		18	80.43	even	4
320.2.s.b.303.9		18	5.4	even	2
400.2.j.d.43.9		18	16.5	even	4
400.2.j.d.307.9		18	20.7	even	4
400.2.s.d.107.5		18	80.37	odd	4
400.2.s.d.243.5		18	4.3	odd	2
640.2.j.c.543.1		18	80.19	odd	4
640.2.j.c.607.9		18	40.13	odd	4
640.2.j.d.543.9		18	80.29	even	4
640.2.j.d.607.1		18	40.3	even	4
640.2.s.c.223.1		18	40.29	even	2
640.2.s.c.287.1		18	80.3	even	4
640.2.s.d.223.9		18	40.19	odd	2
640.2.s.d.287.9		18	80.13	odd	4
720.2.z.g.163.5		18	60.59	even	2
720.2.z.g.667.5		18	240.53	even	4
720.2.bd.g.307.9		18	60.23	odd	4
720.2.bd.g.523.9		18	240.149	odd	4
1600.2.j.d.143.1		18	16.11	odd	4
1600.2.j.d.1007.9		18	5.2	odd	4
1600.2.s.d.207.1		18	80.27	even	4	inner
1600.2.s.d.943.1		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.96561 q^{3} +(-0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +O(q^{10})\)	\(q-2.96561 q^{3} +(-0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +(-2.95966 - 2.95966i) q^{11} -1.55822i q^{13} +(-0.299668 + 0.299668i) q^{17} +(2.26261 + 2.26261i) q^{19} +(0.341344 - 0.341344i) q^{21} +(4.14573 + 4.14573i) q^{23} -8.28846 q^{27} +(0.289656 - 0.289656i) q^{29} -4.18508i q^{31} +(8.77721 + 8.77721i) q^{33} +1.63643i q^{37} +4.62107i q^{39} -7.61648i q^{41} -6.72651i q^{43} +(4.38366 + 4.38366i) q^{47} +6.97350i q^{49} +(0.888698 - 0.888698i) q^{51} -11.4324 q^{53} +(-6.71003 - 6.71003i) q^{57} +(-1.63497 + 1.63497i) q^{59} +(-1.23034 - 1.23034i) q^{61} +(-0.666993 + 0.666993i) q^{63} -2.49337i q^{67} +(-12.2946 - 12.2946i) q^{69} -8.00096 q^{71} +(1.12102 - 1.12102i) q^{73} +0.681319 q^{77} -3.62218 q^{79} +7.19579 q^{81} +1.62629 q^{83} +(-0.859007 + 0.859007i) q^{87} -15.7149 q^{89} +(0.179352 + 0.179352i) q^{91} +12.4113i q^{93} +(-9.69217 + 9.69217i) q^{97} +(-17.1508 - 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

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