LMFDB - Embedded newform 700.5.o.a.649.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,5,Mod(549,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.549"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.32905425960566784.37
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 $ x^12 + 36x^10 + 432x^8 + 2040x^6 + 3780x^4 + 2592*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.3
Root			$0.802567i$ of defining polynomial
Character	$\chi$	$=$	700.649
Dual form			700.5.o.a.549.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.784623 - 1.35901i) q^{3} +(-24.5667 - 42.3967i) q^{7} +(39.2687 - 68.0154i) q^{9} +(-11.7557 - 20.3615i) q^{11} +136.269 q^{13} +(131.251 + 227.333i) q^{17} +(387.162 + 223.528i) q^{19} +(-38.3418 + 66.6517i) q^{21} +(648.800 + 374.585i) q^{23} -250.353 q^{27} -406.524 q^{29} +(-584.199 + 337.287i) q^{31} +(-18.4476 + 31.9521i) q^{33} +(645.476 + 372.666i) q^{37} +(-106.920 - 185.191i) q^{39} -2476.20i q^{41} -2636.68i q^{43} +(-334.343 + 579.099i) q^{47} +(-1193.96 + 2083.09i) q^{49} +(205.964 - 356.741i) q^{51} +(-1757.36 + 1014.61i) q^{53} -701.541i q^{57} +(1014.22 - 585.561i) q^{59} +(-2022.05 - 1167.43i) q^{61} +(-3848.33 + 6.04891i) q^{63} +(6546.78 - 3779.79i) q^{67} -1175.63i q^{69} +7575.36 q^{71} +(1896.12 + 3284.18i) q^{73} +(-574.460 + 998.615i) q^{77} +(3897.33 - 6750.37i) q^{79} +(-2984.33 - 5169.02i) q^{81} +2181.41 q^{83} +(318.968 + 552.469i) q^{87} +(-8050.38 - 4647.89i) q^{89} +(-3347.69 - 5777.37i) q^{91} +(916.751 + 529.287i) q^{93} +9981.90 q^{97} -1846.52 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 180 q^{9} + 270 q^{11} + 1494 q^{19} + 4338 q^{21} + 1080 q^{29} - 10710 q^{31} - 13176 q^{39} - 16860 q^{49} - 1782 q^{51} + 5886 q^{59} + 8082 q^{61} + 4536 q^{71} + 15546 q^{79} - 14958 q^{81}+ \cdots - 16200 q^{99}+O(q^{100}) $ 12 * q - 180 * q^9 + 270 * q^11 + 1494 * q^19 + 4338 * q^21 + 1080 * q^29 - 10710 * q^31 - 13176 * q^39 - 16860 * q^49 - 1782 * q^51 + 5886 * q^59 + 8082 * q^61 + 4536 * q^71 + 15546 * q^79 - 14958 * q^81 - 29970 * q^89 - 41904 * q^91 - 16200 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.784623	−	1.35901i	−0.0871803	−	0.151001i	0.819138	−	0.573597i	$-0.194452\pi$
$3$	−0.784623	−	1.35901i	−0.0871803	−	0.151001i	−0.906318	+	0.422596i	$0.861119\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−24.5667	−	42.3967i	−0.501361	−	0.865238i
$7$	−24.5667	−	42.3967i	−0.501361	−	0.865238i
$8$		0			0
$9$	39.2687	−	68.0154i	0.484799	−	0.839697i
$10$		0			0
$11$	−11.7557	−	20.3615i	−0.0971545	−	0.168276i	0.813351	−	0.581773i	$-0.197641\pi$
$11$	−11.7557	−	20.3615i	−0.0971545	−	0.168276i	−0.910506	+	0.413496i	$0.864307\pi$
$12$		0			0
$13$	136.269			0.806328			0.403164	−	0.915128i	$-0.367910\pi$
$13$	136.269			0.806328			0.403164	+	0.915128i	$0.367910\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	131.251	+	227.333i	0.454154	+	0.786618i	0.998639	−	0.0521523i	$-0.0166081\pi$
$17$	131.251	+	227.333i	0.454154	+	0.786618i	−0.544485	+	0.838771i	$0.683275\pi$
$18$		0			0
$19$	387.162	+	223.528i	1.07247	+	0.619191i	0.928855	−	0.370442i	$-0.120794\pi$
$19$	387.162	+	223.528i	1.07247	+	0.619191i	0.143615	+	0.989634i	$0.454127\pi$
$20$		0			0
$21$	−38.3418	+	66.6517i	−0.0869429	+	0.151138i
$22$		0			0
$23$	648.800	+	374.585i	1.22646	+	0.708100i	0.966288	−	0.257462i	$-0.0828861\pi$
$23$	648.800	+	374.585i	1.22646	+	0.708100i	0.260176	+	0.965561i	$0.416219\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−250.353			−0.343420
$28$		0			0
$29$	−406.524			−0.483382			−0.241691	−	0.970353i	$-0.577702\pi$
$29$	−406.524			−0.483382			−0.241691	+	0.970353i	$0.577702\pi$
$30$		0			0
$31$	−584.199	+	337.287i	−0.607907	+	0.350975i	−0.772146	−	0.635445i	$-0.780817\pi$
$31$	−584.199	+	337.287i	−0.607907	+	0.350975i	0.164239	+	0.986421i	$0.447483\pi$
$32$		0			0
$33$	−18.4476	+	31.9521i	−0.0169399	+	0.0293408i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	645.476	+	372.666i	0.471495	+	0.272218i	0.716865	−	0.697212i	$-0.245576\pi$
$37$	645.476	+	372.666i	0.471495	+	0.272218i	−0.245370	+	0.969429i	$0.578910\pi$
$38$		0			0
$39$	−106.920	−	185.191i	−0.0702959	−	0.121756i
$40$		0			0
$41$		−	2476.20i		−	1.47305i	−0.676410	−	0.736526i	$-0.736465\pi$
$41$		−	2476.20i		−	1.47305i	0.676410	−	0.736526i	$-0.263535\pi$
$42$		0			0
$43$		−	2636.68i		−	1.42601i	−0.701161	−	0.713003i	$-0.747335\pi$
$43$		−	2636.68i		−	1.42601i	0.701161	−	0.713003i	$-0.252665\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−334.343	+	579.099i	−0.151355	+	0.262154i	−0.931726	−	0.363163i	$-0.881697\pi$
$47$	−334.343	+	579.099i	−0.151355	+	0.262154i	0.780371	+	0.625317i	$0.215030\pi$
$48$		0			0
$49$	−1193.96	+	2083.09i	−0.497275	+	0.867593i
$50$		0			0
$51$	205.964	−	356.741i	0.0791866	−	0.137155i
$52$		0			0
$53$	−1757.36	+	1014.61i	−0.625617	+	0.361200i	−0.779053	−	0.626959i	$-0.784300\pi$
$53$	−1757.36	+	1014.61i	−0.625617	+	0.361200i	0.153436	+	0.988159i	$0.450966\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	701.541i		−	0.215925i
$58$		0			0
$59$	1014.22	−	585.561i	0.291359	−	0.168216i	−0.347195	−	0.937793i	$-0.612866\pi$
$59$	1014.22	−	585.561i	0.291359	−	0.168216i	0.638555	+	0.769576i	$0.279533\pi$
$60$		0			0
$61$	−2022.05	−	1167.43i	−0.543416	−	0.313741i	0.203047	−	0.979169i	$-0.434916\pi$
$61$	−2022.05	−	1167.43i	−0.543416	−	0.313741i	−0.746462	+	0.665428i	$0.768249\pi$
$62$		0			0
$63$	−3848.33	+	6.04891i	−0.969597	+	0.00152404i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6546.78	−	3779.79i	1.45841	−	0.842011i	0.459472	−	0.888192i	$-0.348039\pi$
$67$	6546.78	−	3779.79i	1.45841	−	0.842011i	0.998933	+	0.0461815i	$0.0147052\pi$
$68$		0			0
$69$		−	1175.63i		−	0.246929i
$70$		0			0
$71$	7575.36			1.50275			0.751375	−	0.659876i	$-0.229391\pi$
$71$	7575.36			1.50275			0.751375	+	0.659876i	$0.229391\pi$
$72$		0			0
$73$	1896.12	+	3284.18i	0.355812	+	0.616284i	0.987257	−	0.159137i	$-0.0508710\pi$
$73$	1896.12	+	3284.18i	0.355812	+	0.616284i	−0.631445	+	0.775421i	$0.717538\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−574.460	+	998.615i	−0.0968898	+	0.168429i
$78$		0			0
$79$	3897.33	−	6750.37i	0.624472	−	1.08162i	−0.364171	−	0.931332i	$-0.618647\pi$
$79$	3897.33	−	6750.37i	0.624472	−	1.08162i	0.988643	−	0.150285i	$-0.0480192\pi$
$80$		0			0
$81$	−2984.33	−	5169.02i	−0.454860	−	0.787840i
$82$		0			0
$83$	2181.41			0.316651			0.158326	−	0.987387i	$-0.449390\pi$
$83$	2181.41			0.316651			0.158326	+	0.987387i	$0.449390\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	318.968	+	552.469i	0.0421414	+	0.0729910i
$88$		0			0
$89$	−8050.38	−	4647.89i	−1.01633	−	0.586781i	−0.103294	−	0.994651i	$-0.532938\pi$
$89$	−8050.38	−	4647.89i	−1.01633	−	0.586781i	−0.913040	+	0.407870i	$0.866272\pi$
$90$		0			0
$91$	−3347.69	−	5777.37i	−0.404261	−	0.697666i
$92$		0			0
$93$	916.751	+	529.287i	0.105995	+	0.0611963i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9981.90			1.06089			0.530444	−	0.847720i	$-0.322025\pi$
$97$	9981.90			1.06089			0.530444	+	0.847720i	$0.322025\pi$
$98$		0			0
$99$	−1846.52			−0.188402
$100$		0			0
$101$	−675.552	+	390.030i	−0.0662241	+	0.0382345i	−0.532746	−	0.846275i	$-0.678840\pi$
$101$	−675.552	+	390.030i	−0.0662241	+	0.0382345i	0.466522	+	0.884509i	$0.345507\pi$
$102$		0			0
$103$	−1376.35	+	2383.90i	−0.129734	+	0.224706i	−0.923573	−	0.383422i	$-0.874746\pi$
$103$	−1376.35	+	2383.90i	−0.129734	+	0.224706i	0.793840	+	0.608127i	$0.208079\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12868.2	+	7429.46i	1.12396	+	0.648917i	0.942408	−	0.334464i	$-0.108555\pi$
$107$	12868.2	+	7429.46i	1.12396	+	0.648917i	0.181550	+	0.983382i	$0.441889\pi$
$108$		0			0
$109$	1378.33	+	2387.33i	0.116011	+	0.200937i	0.918183	−	0.396155i	$-0.129656\pi$
$109$	1378.33	+	2387.33i	0.116011	+	0.200937i	−0.802172	+	0.597092i	$0.796323\pi$
$110$		0			0
$111$		−	1169.61i		−	0.0949281i
$112$		0			0
$113$			6264.79i			0.490625i	0.969444	+	0.245312i	$0.0788905\pi$
$113$			6264.79i			0.490625i	−0.969444	+	0.245312i	$0.921109\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5351.13	−	9268.43i	0.390907	−	0.677071i
$118$		0			0
$119$	6413.76	−	11149.4i	0.452917	−	0.787331i
$120$		0			0
$121$	7044.11	−	12200.8i	0.481122	−	0.833328i
$122$		0			0
$123$	−3365.17	+	1942.88i	−0.222432	+	0.128421i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	12855.0i		−	0.797010i	−0.917166	−	0.398505i	$-0.869529\pi$
$127$		−	12855.0i		−	0.797010i	0.917166	−	0.398505i	$-0.130471\pi$
$128$		0			0
$129$	−3583.27	+	2068.80i	−0.215328	+	0.124320i
$130$		0			0
$131$	−21412.5	−	12362.5i	−1.24774	−	0.720383i	−0.277082	−	0.960846i	$-0.589367\pi$
$131$	−21412.5	−	12362.5i	−1.24774	−	0.720383i	−0.970658	+	0.240464i	$0.922701\pi$
$132$		0			0
$133$	−34.4320	−	21905.7i	−0.00194652	−	1.23838i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1145.02	+	661.078i	−0.0610059	+	0.0352218i	−0.530193	−	0.847877i	$-0.677880\pi$
$137$	−1145.02	+	661.078i	−0.0610059	+	0.0352218i	0.469187	+	0.883099i	$0.344547\pi$
$138$		0			0
$139$			5119.78i			0.264985i	0.991184	+	0.132493i	$0.0422981\pi$
$139$			5119.78i			0.264985i	−0.991184	+	0.132493i	$0.957702\pi$
$140$		0			0
$141$	1049.33			0.0527807
$142$		0			0
$143$	−1601.94	−	2774.64i	−0.0783384	−	0.135686i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3767.74	−	11.8445i	0.174360	−	0.000548128i
$148$		0			0
$149$	5104.93	−	8842.00i	0.229942	−	0.398270i	−0.727849	−	0.685737i	$-0.759480\pi$
$149$	5104.93	−	8842.00i	0.229942	−	0.398270i	0.957791	+	0.287467i	$0.0928132\pi$
$150$		0			0
$151$	−14672.1	−	25412.8i	−0.643483	−	1.11455i	−0.984650	−	0.174543i	$-0.944155\pi$
$151$	−14672.1	−	25412.8i	−0.643483	−	1.11455i	0.341166	−	0.940003i	$-0.389178\pi$
$152$		0			0
$153$	20616.2			0.880695
$154$		0			0
$155$		0			0
$156$		0			0
$157$	15030.2	+	26033.1i	0.609770	+	1.05615i	0.991278	+	0.131787i	$0.0420716\pi$
$157$	15030.2	+	26033.1i	0.609770	+	1.05615i	−0.381508	+	0.924366i	$0.624595\pi$
$158$		0			0
$159$	2757.73	+	1592.17i	0.109083	+	0.0629791i
$160$		0			0
$161$	−57.7005	−	36709.3i	−0.00222602	−	1.41620i
$162$		0			0
$163$	−26742.3	−	15439.7i	−1.00652	−	0.581115i	−0.0963500	−	0.995348i	$-0.530717\pi$
$163$	−26742.3	−	15439.7i	−1.00652	−	0.581115i	−0.910171	+	0.414232i	$0.864050\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12858.8			0.461070			0.230535	−	0.973064i	$-0.425952\pi$
$167$	12858.8			0.461070			0.230535	+	0.973064i	$0.425952\pi$
$168$		0			0
$169$	−9991.63			−0.349835
$170$		0			0
$171$	30406.7	−	17555.3i	1.03987	−	0.600367i
$172$		0			0
$173$	−7845.51	+	13588.8i	−0.262137	+	0.454035i	−0.966810	−	0.255498i	$-0.917761\pi$
$173$	−7845.51	+	13588.8i	−0.262137	+	0.454035i	0.704672	+	0.709533i	$0.251094\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1591.56	−	918.890i	−0.0508016	−	0.0293303i
$178$		0			0
$179$	−15993.2	−	27701.0i	−0.499148	−	0.864550i	0.500851	−	0.865533i	$-0.333020\pi$
$179$	−15993.2	−	27701.0i	−0.499148	−	0.864550i	−1.00000		0.000983488i	$0.999687\pi$
$180$		0			0
$181$		−	47967.6i		−	1.46417i	−0.681215	−	0.732083i	$-0.738548\pi$
$181$		−	47967.6i		−	1.46417i	0.681215	−	0.732083i	$-0.261452\pi$
$182$		0			0
$183$			3663.97i			0.109408i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3085.88	−	5344.91i	0.0882462	−	0.152847i
$188$		0			0
$189$	6150.35	+	10614.2i	0.172177	+	0.297141i
$190$		0			0
$191$	−2227.93	+	3858.88i	−0.0610709	+	0.105778i	−0.894944	−	0.446178i	$-0.852785\pi$
$191$	−2227.93	+	3858.88i	−0.0610709	+	0.105778i	0.833873	+	0.551956i	$0.186118\pi$
$192$		0			0
$193$	−25460.9	+	14699.9i	−0.683533	+	0.394638i	−0.801185	−	0.598417i	$-0.795797\pi$
$193$	−25460.9	+	14699.9i	−0.683533	+	0.394638i	0.117652	+	0.993055i	$0.462463\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	23816.0i		−	0.613671i	−0.951763	−	0.306836i	$-0.900730\pi$
$197$		−	23816.0i		−	0.613671i	0.951763	−	0.306836i	$-0.0992701\pi$
$198$		0			0
$199$	42280.9	−	24410.9i	1.06767	−	0.616421i	0.140128	−	0.990133i	$-0.455249\pi$
$199$	42280.9	−	24410.9i	1.06767	−	0.616421i	0.927545	+	0.373713i	$0.121915\pi$
$200$		0			0
$201$	−10273.5	−	5931.41i	−0.254288	−	0.146813i
$202$		0			0
$203$	9986.94	+	17235.3i	0.242349	+	0.418241i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	50955.1	−	29418.9i	1.18918	−	0.686572i
$208$		0			0
$209$		−	10510.9i		−	0.240629i
$210$		0			0
$211$	−9582.07			−0.215226			−0.107613	−	0.994193i	$-0.534321\pi$
$211$	−9582.07			−0.215226			−0.107613	+	0.994193i	$0.534321\pi$
$212$		0			0
$213$	−5943.80	−	10295.0i	−0.131010	−	0.226916i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	28651.7	+	16482.1i	0.608458	+	0.350019i
$218$		0			0
$219$	2975.48	−	5153.68i	0.0620396	−	0.107456i
$220$		0			0
$221$	17885.5	+	30978.5i	0.366197	+	0.634273i
$222$		0			0
$223$	54978.9			1.10557			0.552785	−	0.833324i	$-0.313565\pi$
$223$	54978.9			1.10557			0.552785	+	0.833324i	$0.313565\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4340.66	+	7518.24i	0.0842372	+	0.145903i	0.905066	−	0.425271i	$-0.139821\pi$
$227$	4340.66	+	7518.24i	0.0842372	+	0.145903i	−0.820829	+	0.571174i	$0.806488\pi$
$228$		0			0
$229$	6262.86	+	3615.86i	0.119427	+	0.0689511i	0.558523	−	0.829489i	$-0.311368\pi$
$229$	6262.86	+	3615.86i	0.119427	+	0.0689511i	−0.439097	+	0.898440i	$0.644701\pi$
$230$		0			0
$231$	1807.86	−	2.84164i	0.0338798	−	5.32531e-5i
$232$		0			0
$233$	−7660.79	−	4422.96i	−0.141111	−	0.0814707i	0.427782	−	0.903882i	$-0.359295\pi$
$233$	−7660.79	−	4422.96i	−0.141111	−	0.0814707i	−0.568894	+	0.822411i	$0.692628\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−12231.7			−0.217767
$238$		0			0
$239$	−88491.7			−1.54920			−0.774599	−	0.632453i	$-0.782048\pi$
$239$	−88491.7			−1.54920			−0.774599	+	0.632453i	$0.782048\pi$
$240$		0			0
$241$	−53365.8	+	30810.7i	−0.918816	+	0.530479i	−0.883257	−	0.468889i	$-0.844654\pi$
$241$	−53365.8	+	30810.7i	−0.918816	+	0.530479i	−0.0355589	+	0.999368i	$0.511321\pi$
$242$		0			0
$243$	−14822.5	+	25673.3i	−0.251020	+	0.434779i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	52758.4	+	30460.0i	0.864763	+	0.499271i
$248$		0			0
$249$	−1711.59	−	2964.55i	−0.0276058	−	0.0478146i
$250$		0			0
$251$		−	57796.3i		−	0.917386i	−0.888595	−	0.458693i	$-0.848318\pi$
$251$		−	57796.3i		−	0.917386i	0.888595	−	0.458693i	$-0.151682\pi$
$252$		0			0
$253$		−	17614.0i		−	0.275180i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	35065.0	−	60734.3i	0.530893	−	0.919534i	−0.468457	−	0.883486i	$-0.655190\pi$
$257$	35065.0	−	60734.3i	0.530893	−	0.919534i	0.999350	−	0.0360479i	$-0.0114769\pi$
$258$		0			0
$259$	−57.4050	−	36521.2i	−0.000855756	−	0.544435i
$260$		0			0
$261$	−15963.7	+	27649.9i	−0.234343	+	0.405894i
$262$		0			0
$263$	19262.0	−	11120.9i	0.278477	−	0.160779i	−0.354257	−	0.935148i	$-0.615266\pi$
$263$	19262.0	−	11120.9i	0.278477	−	0.160779i	0.632734	+	0.774369i	$0.281933\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			14587.4i			0.204623i
$268$		0			0
$269$	−40332.3	+	23285.9i	−0.557376	+	0.321801i	−0.752092	−	0.659058i	$-0.770955\pi$
$269$	−40332.3	+	23285.9i	−0.557376	+	0.321801i	0.194715	+	0.980860i	$0.437622\pi$
$270$		0			0
$271$	71958.3	+	41545.1i	0.979811	+	0.565694i	0.902213	−	0.431291i	$-0.141942\pi$
$271$	71958.3	+	41545.1i	0.979811	+	0.565694i	0.0775980	+	0.996985i	$0.475275\pi$
$272$		0			0
$273$	−5224.82	+	9082.59i	−0.0701045	+	0.121866i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	7818.59	−	4514.06i	0.101899	−	0.0588313i	−0.448185	−	0.893941i	$-0.647929\pi$
$277$	7818.59	−	4514.06i	0.101899	−	0.0588313i	0.550083	+	0.835110i	$0.314596\pi$
$278$		0			0
$279$			52979.4i			0.680610i
$280$		0			0
$281$	64188.4			0.812912			0.406456	−	0.913670i	$-0.366764\pi$
$281$	64188.4			0.812912			0.406456	+	0.913670i	$0.366764\pi$
$282$		0			0
$283$	11295.1	+	19563.7i	0.141032	+	0.244274i	0.927885	−	0.372865i	$-0.121625\pi$
$283$	11295.1	+	19563.7i	0.141032	+	0.244274i	−0.786854	+	0.617140i	$0.788291\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−104983.	+	60832.0i	−1.27454	+	0.738530i
$288$		0			0
$289$	7307.06	−	12656.2i	0.0874877	−	0.151533i
$290$		0			0
$291$	−7832.02	−	13565.5i	−0.0924885	−	0.160195i
$292$		0			0
$293$	−130473.			−1.51980			−0.759900	−	0.650040i	$-0.774752\pi$
$293$	−130473.			−1.51980			−0.759900	+	0.650040i	$0.774752\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2943.08	+	5097.56i	0.0333648	+	0.0577896i
$298$		0			0
$299$	88411.6	+	51044.5i	0.988933	+	0.570961i
$300$		0			0
$301$	−111787.	+	64774.5i	−1.23383	+	0.714943i
$302$		0			0
$303$	1060.11	+	612.053i	0.0115469	+	0.00666659i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−56173.9			−0.596015			−0.298008	−	0.954563i	$-0.596322\pi$
$307$	−56173.9			−0.596015			−0.298008	+	0.954563i	$0.596322\pi$
$308$		0			0
$309$	4319.65			0.0452410
$310$		0			0
$311$	40087.2	−	23144.4i	0.414462	−	0.239290i	−0.278243	−	0.960511i	$-0.589752\pi$
$311$	40087.2	−	23144.4i	0.414462	−	0.239290i	0.692705	+	0.721221i	$0.256419\pi$
$312$		0			0
$313$	69174.4	−	119814.i	0.706085	−	1.22298i	−0.260213	−	0.965551i	$-0.583793\pi$
$313$	69174.4	−	119814.i	0.706085	−	1.22298i	0.966299	−	0.257424i	$-0.0828737\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−50493.9	−	29152.7i	−0.502482	−	0.290108i	0.227256	−	0.973835i	$-0.427025\pi$
$317$	−50493.9	−	29152.7i	−0.502482	−	0.290108i	−0.729738	+	0.683727i	$0.760358\pi$
$318$		0			0
$319$	4778.97	+	8277.42i	0.0469627	+	0.0813418i
$320$		0			0
$321$		−	23317.3i		−	0.226291i
$322$		0			0
$323$			117353.i			1.12483i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2162.93	−	3746.31i	0.0202278	−	0.0350355i
$328$		0			0
$329$	32765.6	−	51.5018i	0.302709	−	0.000475806i
$330$		0			0
$331$	−494.602	+	856.675i	−0.00451440	+	0.00781916i	−0.868274	−	0.496085i	$-0.834770\pi$
$331$	−494.602	+	856.675i	−0.00451440	+	0.00781916i	0.863759	+	0.503904i	$0.168104\pi$
$332$		0			0
$333$	50694.1	−	29268.2i	0.457161	−	0.263942i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			55958.7i			0.492728i	0.969177	+	0.246364i	$0.0792359\pi$
$337$			55958.7i			0.492728i	−0.969177	+	0.246364i	$0.920764\pi$
$338$		0			0
$339$	8513.89	−	4915.49i	0.0740847	−	0.0427728i
$340$		0			0
$341$	13735.3	+	7930.09i	0.118122	+	0.0681976i
$342$		0			0
$343$	117648.	−	554.769i	0.999989	−	0.00471546i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−113141.	+	65322.2i	−0.939641	+	0.542502i	−0.889848	−	0.456257i	$-0.849190\pi$
$347$	−113141.	+	65322.2i	−0.939641	+	0.542502i	−0.0497936	+	0.998760i	$0.515856\pi$
$348$		0			0
$349$			110948.i			0.910899i	0.890262	+	0.455450i	$0.150522\pi$
$349$			110948.i			0.910899i	−0.890262	+	0.455450i	$0.849478\pi$
$350$		0			0
$351$	−34115.5			−0.276910
$352$		0			0
$353$	8503.18	+	14727.9i	0.0682389	+	0.118193i	0.898126	−	0.439738i	$-0.144929\pi$
$353$	8503.18	+	14727.9i	0.0682389	+	0.118193i	−0.829887	+	0.557931i	$0.811595\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−20184.5	+	31.7265i	−0.158373	+	0.000248935i
$358$		0			0
$359$	35732.4	−	61890.3i	0.277251	−	0.480212i	−0.693450	−	0.720505i	$-0.743910\pi$
$359$	35732.4	−	61890.3i	0.277251	−	0.480212i	0.970701	+	0.240293i	$0.0772434\pi$
$360$		0			0
$361$	34769.0	+	60221.8i	0.266795	+	0.462103i
$362$		0			0
$363$	−22107.9			−0.167777
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−85183.8	−	147543.i	−0.632448	−	1.09543i	−0.987050	−	0.160415i	$-0.948717\pi$
$367$	−85183.8	−	147543.i	−0.632448	−	1.09543i	0.354602	−	0.935017i	$-0.384617\pi$
$368$		0			0
$369$	−168420.	−	97237.2i	−1.23692	−	0.714134i
$370$		0			0
$371$	86188.6	+	49580.5i	0.626184	+	0.360216i
$372$		0			0
$373$	−130503.	−	75346.0i	−0.938001	−	0.541555i	−0.0486680	−	0.998815i	$-0.515498\pi$
$373$	−130503.	−	75346.0i	−0.938001	−	0.541555i	−0.889333	+	0.457260i	$0.848831\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−55396.8			−0.389764
$378$		0			0
$379$	211477.			1.47226			0.736129	−	0.676841i	$-0.236652\pi$
$379$	211477.			1.47226			0.736129	+	0.676841i	$0.236652\pi$
$380$		0			0
$381$	−17470.0	+	10086.3i	−0.120349	+	0.0694836i
$382$		0			0
$383$	59333.6	−	102769.i	0.404486	−	0.700590i	−0.589776	−	0.807567i	$-0.700784\pi$
$383$	59333.6	−	102769.i	0.404486	−	0.700590i	0.994261	+	0.106977i	$0.0341172\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−179335.	−	103539.i	−1.19741	−	0.691326i
$388$		0			0
$389$	107858.	+	186816.i	0.712778	+	1.23457i	0.963810	+	0.266588i	$0.0858964\pi$
$389$	107858.	+	186816.i	0.712778	+	1.23457i	−0.251033	+	0.967979i	$0.580770\pi$
$390$		0			0
$391$			196658.i			1.28635i
$392$		0			0
$393$			38799.6i			0.251213i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−77371.1	+	134011.i	−0.490905	+	0.850273i	−0.999945	−	0.0104699i	$-0.996667\pi$
$397$	−77371.1	+	134011.i	−0.490905	+	0.850273i	0.509040	+	0.860743i	$0.330001\pi$
$398$		0			0
$399$	−29743.0	+	17234.5i	−0.186827	+	0.108256i
$400$		0			0
$401$	−100029.	+	173255.i	−0.622067	+	1.07745i	0.367033	+	0.930208i	$0.380374\pi$
$401$	−100029.	+	173255.i	−0.622067	+	1.07745i	−0.989100	+	0.147244i	$0.952960\pi$
$402$		0			0
$403$	−79608.5	+	45962.0i	−0.490173	+	0.283001i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	17523.8i		−	0.105789i
$408$		0			0
$409$	−190382.	+	109917.i	−1.13810	+	0.657080i	−0.945958	−	0.324288i	$-0.894875\pi$
$409$	−190382.	+	109917.i	−1.13810	+	0.657080i	−0.192137	+	0.981368i	$0.561542\pi$
$410$		0			0
$411$	1796.82	+	1037.39i	0.0106370	+	0.00614129i
$412$		0			0
$413$	−49741.9	−	28614.4i	−0.291623	−	0.167758i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6957.81	−	4017.10i	0.0400130	−	0.0231015i
$418$		0			0
$419$			31359.8i			0.178626i	0.996004	+	0.0893132i	$0.0284672\pi$
$419$			31359.8i			0.178626i	−0.996004	+	0.0893132i	$0.971533\pi$
$420$		0			0
$421$	−73690.7			−0.415766			−0.207883	−	0.978154i	$-0.566657\pi$
$421$	−73690.7			−0.415766			−0.207883	+	0.978154i	$0.566657\pi$
$422$		0			0
$423$	26258.5	+	45481.0i	0.146753	+	0.254184i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	179.830	+	114408.i	0.000986291	+	0.627481i
$428$		0			0
$429$	−2513.84	+	4354.10i	−0.0136591	+	0.0236583i
$430$		0			0
$431$	132586.	+	229646.i	0.713746	+	1.23624i	0.963441	+	0.267920i	$0.0863364\pi$
$431$	132586.	+	229646.i	0.713746	+	1.23624i	−0.249695	+	0.968325i	$0.580330\pi$
$432$		0			0
$433$	124873.			0.666027			0.333014	−	0.942922i	$-0.391934\pi$
$433$	124873.			0.666027			0.333014	+	0.942922i	$0.391934\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	167460.	+	290050.i	0.876898	+	1.51883i
$438$		0			0
$439$	120989.	+	69852.8i	0.627792	+	0.362456i	0.779896	−	0.625909i	$-0.215272\pi$
$439$	120989.	+	69852.8i	0.627792	+	0.362456i	−0.152105	+	0.988364i	$0.548605\pi$
$440$		0			0
$441$	94797.1	+	163008.i	0.487437	+	0.838169i
$442$		0			0
$443$	191556.	+	110595.i	0.976087	+	0.563544i	0.901087	−	0.433639i	$-0.142771\pi$
$443$	191556.	+	110595.i	0.976087	+	0.563544i	0.0750005	+	0.997183i	$0.476104\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−16021.8			−0.0801855
$448$		0			0
$449$	−255878.			−1.26923			−0.634615	−	0.772828i	$-0.718841\pi$
$449$	−255878.			−1.26923			−0.634615	+	0.772828i	$0.718841\pi$
$450$		0			0
$451$	−50419.0	+	29109.4i	−0.247880	+	0.143114i
$452$		0			0
$453$	−23024.1	+	39878.9i	−0.112198	+	0.194333i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−277065.	−	159964.i	−1.32663	−	0.765929i	−0.341852	−	0.939754i	$-0.611054\pi$
$457$	−277065.	−	159964.i	−1.32663	−	0.765929i	−0.984777	+	0.173825i	$0.944387\pi$
$458$		0			0
$459$	−32859.0	−	56913.5i	−0.155966	−	0.270141i
$460$		0			0
$461$			369557.i			1.73892i	0.494002	+	0.869461i	$0.335534\pi$
$461$			369557.i			1.73892i	−0.494002	+	0.869461i	$0.664466\pi$
$462$		0			0
$463$			32715.0i			0.152611i	0.997084	+	0.0763053i	$0.0243124\pi$
$463$			32715.0i			0.152611i	−0.997084	+	0.0763053i	$0.975688\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	153186.	−	265325.i	0.702400	−	1.21659i	−0.265222	−	0.964187i	$-0.585445\pi$
$467$	153186.	−	265325.i	0.702400	−	1.21659i	0.967622	−	0.252405i	$-0.0812214\pi$
$468$		0			0
$469$	−321083.	−	184705.i	−1.45973	−	0.839717i
$470$		0			0
$471$	23586.1	−	40852.3i	0.106320	−	0.184151i
$472$		0			0
$473$	−53686.7	+	30996.0i	−0.239963	+	0.138543i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			159370.i			0.700438i
$478$		0			0
$479$	226801.	−	130944.i	0.988493	−	0.570707i	0.0836697	−	0.996494i	$-0.473336\pi$
$479$	226801.	−	130944.i	0.988493	−	0.570707i	0.904824	+	0.425787i	$0.140003\pi$
$480$		0			0
$481$	87958.7	+	50783.0i	0.380180	+	0.219497i
$482$		0			0
$483$	−49842.8	+	28881.3i	−0.213653	+	0.123801i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−71235.3	+	41127.7i	−0.300357	+	0.173411i	−0.642603	−	0.766199i	$-0.722146\pi$
$487$	−71235.3	+	41127.7i	−0.300357	+	0.173411i	0.342246	+	0.939610i	$0.388812\pi$
$488$		0			0
$489$			48457.2i			0.202647i
$490$		0			0
$491$	−102923.			−0.426924			−0.213462	−	0.976951i	$-0.568474\pi$
$491$	−102923.			−0.426924			−0.213462	+	0.976951i	$0.568474\pi$
$492$		0			0
$493$	−53356.5	−	92416.2i	−0.219530	−	0.380237i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−186101.	−	321170.i	−0.753420	−	1.30024i
$498$		0			0
$499$	75028.2	−	129953.i	0.301317	−	0.521896i	−0.675118	−	0.737710i	$-0.735907\pi$
$499$	75028.2	−	129953.i	0.301317	−	0.521896i	0.976434	+	0.215814i	$0.0692405\pi$
$500$		0			0
$501$	−10089.3	−	17475.2i	−0.0401962	−	0.0696219i
$502$		0			0
$503$	91806.6			0.362859			0.181430	−	0.983404i	$-0.441928\pi$
$503$	91806.6			0.362859			0.181430	+	0.983404i	$0.441928\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7839.66	+	13578.7i	0.0304987	+	0.0528253i
$508$		0			0
$509$	412600.	+	238215.i	1.59255	+	0.919460i	0.992867	+	0.119224i	$0.0380405\pi$
$509$	412600.	+	238215.i	1.59255	+	0.919460i	0.599684	+	0.800237i	$0.295293\pi$
$510$		0			0
$511$	92656.9	−	161071.i	0.354843	−	0.616843i
$512$		0			0
$513$	−96927.3	−	55961.0i	−0.368308	−	0.212643i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	15721.7			0.0588192
$518$		0			0
$519$	24623.1			0.0914128
$520$		0			0
$521$	147768.	−	85314.0i	0.544384	−	0.314300i	−0.202470	−	0.979289i	$-0.564897\pi$
$521$	147768.	−	85314.0i	0.544384	−	0.314300i	0.746854	+	0.664988i	$0.231563\pi$
$522$		0			0
$523$	−49098.2	+	85040.5i	−0.179499	+	0.310901i	−0.941709	−	0.336428i	$-0.890781\pi$
$523$	−49098.2	+	85040.5i	−0.179499	+	0.310901i	0.762210	+	0.647330i	$0.224114\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−153353.	−	88538.3i	−0.552167	−	0.318794i
$528$		0			0
$529$	140707.	+	243711.i	0.502810	+	0.870892i
$530$		0			0
$531$		−	91977.0i		−	0.326205i
$532$		0			0
$533$		−	337430.i		−	1.18776i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−25097.3	+	43469.7i	−0.0870318	+	0.150743i
$538$		0			0
$539$	56450.5	−	177.461i	0.194308	−	0.000610838i
$540$		0			0
$541$	52833.7	−	91510.6i	0.180516	−	0.312663i	−0.761540	−	0.648118i	$-0.775557\pi$
$541$	52833.7	−	91510.6i	0.180516	−	0.312663i	0.942056	+	0.335454i	$0.108890\pi$
$542$		0			0
$543$	−65188.2	+	37636.4i	−0.221090	+	0.127646i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			127121.i			0.424855i	0.977177	+	0.212428i	$0.0681370\pi$
$547$			127121.i			0.424855i	−0.977177	+	0.212428i	$0.931863\pi$
$548$		0			0
$549$	−158807.	+	91687.0i	−0.526895	+	0.304203i
$550$		0			0
$551$	−157391.	−	90869.5i	−0.518413	−	0.299306i
$552$		0			0
$553$	−381938.	+	600.340i	−1.24894	+	0.00196312i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26407.6	+	15246.5i	−0.0851176	+	0.0491427i	−0.541955	−	0.840408i	$-0.682316\pi$
$557$	−26407.6	+	15246.5i	−0.0851176	+	0.0491427i	0.456837	+	0.889550i	$0.348982\pi$
$558$		0			0
$559$		−	359300.i		−	1.14983i
$560$		0			0
$561$	−9685.01			−0.0307733
$562$		0			0
$563$	265237.	+	459404.i	0.836791	+	1.44936i	0.892564	+	0.450921i	$0.148905\pi$
$563$	265237.	+	459404.i	0.836791	+	1.44936i	−0.0557725	+	0.998444i	$0.517762\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−145834.	+	253511.i	−0.453621	+	0.788554i
$568$		0			0
$569$	−169366.	+	293351.i	−0.523121	+	0.906072i	0.476517	+	0.879165i	$0.341899\pi$
$569$	−169366.	+	293351.i	−0.523121	+	0.906072i	−0.999638	+	0.0269067i	$0.991434\pi$
$570$		0			0
$571$	53455.6	+	92587.8i	0.163954	+	0.283976i	0.936283	−	0.351246i	$-0.114242\pi$
$571$	53455.6	+	92587.8i	0.163954	+	0.283976i	−0.772330	+	0.635222i	$0.780909\pi$
$572$		0			0
$573$	6992.33			0.0212967
$574$		0			0
$575$		0			0
$576$		0			0
$577$	60238.8	+	104337.i	0.180936	+	0.313390i	0.942200	−	0.335052i	$-0.108754\pi$
$577$	60238.8	+	104337.i	0.180936	+	0.313390i	−0.761264	+	0.648443i	$0.775421\pi$
$578$		0			0
$579$	39954.4	+	23067.7i	0.119181	+	0.0688093i
$580$		0			0
$581$	−53590.0	−	92484.6i	−0.158757	−	0.273979i
$582$		0			0
$583$	41317.9	+	23854.9i	0.121563	+	0.0701844i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	525818.			1.52602			0.763008	−	0.646389i	$-0.223722\pi$
$587$	525818.			1.52602			0.763008	+	0.646389i	$0.223722\pi$
$588$		0			0
$589$	−301573.			−0.869283
$590$		0			0
$591$	−32366.0	+	18686.5i	−0.0926648	+	0.0535000i
$592$		0			0
$593$	37113.8	−	64283.0i	0.105542	−	0.182804i	−0.808417	−	0.588610i	$-0.799676\pi$
$593$	37113.8	−	64283.0i	0.105542	−	0.182804i	0.913960	+	0.405805i	$0.133009\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−66349.1	−	38306.7i	−0.186160	−	0.107480i
$598$		0			0
$599$	10990.7	+	19036.5i	0.0306318	+	0.0530558i	0.880935	−	0.473237i	$-0.156915\pi$
$599$	10990.7	+	19036.5i	0.0306318	+	0.0530558i	−0.850303	+	0.526293i	$0.823581\pi$
$600$		0			0
$601$		−	77418.2i		−	0.214336i	−0.994241	−	0.107168i	$-0.965822\pi$
$601$		−	77418.2i		−	0.214336i	0.994241	−	0.107168i	$-0.0341782\pi$
$602$		0			0
$603$		−	593710.i		−	1.63282i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	89931.2	−	155765.i	0.244081	−	0.422760i	−0.717792	−	0.696257i	$-0.754847\pi$
$607$	89931.2	−	155765.i	0.244081	−	0.422760i	0.961873	+	0.273498i	$0.0881805\pi$
$608$		0			0
$609$	15586.9	−	27095.5i	0.0420266	−	0.0730572i
$610$		0			0
$611$	−45560.7	+	78913.5i	−0.122042	+	0.211382i
$612$		0			0
$613$	544968.	−	314637.i	1.45027	−	0.837316i	0.451777	−	0.892131i	$-0.350790\pi$
$613$	544968.	−	314637.i	1.45027	−	0.837316i	0.998497	+	0.0548147i	$0.0174568\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			52877.1i			0.138899i	0.997585	+	0.0694493i	$0.0221242\pi$
$617$			52877.1i			0.138899i	−0.997585	+	0.0694493i	$0.977876\pi$
$618$		0			0
$619$	−447040.	+	258099.i	−1.16672	+	0.673603i	−0.952904	−	0.303271i	$-0.901921\pi$
$619$	−447040.	+	258099.i	−1.16672	+	0.673603i	−0.213811	+	0.976875i	$0.568588\pi$
$620$		0			0
$621$	−162429.	−	93778.6i	−0.421193	−	0.243176i
$622$		0			0
$623$	715.955	+	455493.i	0.00184463	+	1.17356i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−14284.4	+	8247.09i	−0.0363351	+	0.0209781i
$628$		0			0
$629$			195651.i			0.494515i
$630$		0			0
$631$	193439.			0.485831			0.242915	−	0.970047i	$-0.421896\pi$
$631$	193439.			0.485831			0.242915	+	0.970047i	$0.421896\pi$
$632$		0			0
$633$	7518.31	+	13022.1i	0.0187635	+	0.0324993i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−162700.	+	283862.i	−0.400967	+	0.699565i
$638$		0			0
$639$	297475.	−	515242.i	0.728532	−	1.26185i
$640$		0			0
$641$	−376563.	−	652226.i	−0.916477	−	1.58738i	−0.804725	−	0.593648i	$-0.797687\pi$
$641$	−376563.	−	652226.i	−0.916477	−	1.58738i	−0.111751	−	0.993736i	$-0.535646\pi$
$642$		0			0
$643$	−7110.23			−0.0171974			−0.00859868	−	0.999963i	$-0.502737\pi$
$643$	−7110.23			−0.0171974			−0.00859868	+	0.999963i	$0.502737\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	197343.	+	341808.i	0.471426	+	0.816534i	0.999466	−	0.0326859i	$-0.0104061\pi$
$647$	197343.	+	341808.i	0.471426	+	0.816534i	−0.528040	+	0.849220i	$0.677073\pi$
$648$		0			0
$649$	−23845.8	−	13767.4i	−0.0566137	−	0.0326860i
$650$		0			0
$651$	−81.5306	−	51870.0i	−0.000192380	−	0.122392i
$652$		0			0
$653$	−200186.	−	115578.i	−0.469470	−	0.271049i	0.246548	−	0.969131i	$-0.420704\pi$
$653$	−200186.	−	115578.i	−0.469470	−	0.271049i	−0.716018	+	0.698082i	$0.754037\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	297833.			0.689989
$658$		0			0
$659$	772498.			1.77880			0.889399	−	0.457131i	$-0.151123\pi$
$659$	772498.			1.77880			0.889399	+	0.457131i	$0.151123\pi$
$660$		0			0
$661$	−195287.	+	112749.i	−0.446962	+	0.258053i	−0.706546	−	0.707667i	$-0.749748\pi$
$661$	−195287.	+	112749.i	−0.446962	+	0.258053i	0.259584	+	0.965720i	$0.416414\pi$
$662$		0			0
$663$	28066.7	−	48612.9i	0.0638504	−	0.110592i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−263753.	−	152278.i	−0.592851	−	0.342282i
$668$		0			0
$669$	−43137.7	−	74716.6i	−0.0963839	−	0.166942i
$670$		0			0
$671$			54895.8i			0.121925i
$672$		0			0
$673$			59564.6i			0.131510i	0.997836	+	0.0657549i	$0.0209455\pi$
$673$			59564.6i			0.131510i	−0.997836	+	0.0657549i	$0.979054\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	396715.	−	687131.i	0.865569	−	1.49921i	−0.000912440	−	1.00000i	$-0.500290\pi$
$677$	396715.	−	687131.i	0.865569	−	1.49921i	0.866481	−	0.499210i	$-0.166376\pi$
$678$		0			0
$679$	−245222.	−	423199.i	−0.531888	−	0.917921i
$680$		0			0
$681$	6811.56	−	11798.0i	0.0146876	−	0.0254397i
$682$		0			0
$683$	−80201.3	+	46304.3i	−0.171925	+	0.0992612i	−0.583493	−	0.812118i	$-0.698315\pi$
$683$	−80201.3	+	46304.3i	−0.171925	+	0.0992612i	0.411568	+	0.911379i	$0.364981\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	11348.4i		−	0.0240447i
$688$		0			0
$689$	−239474.	+	138261.i	−0.504453	+	0.291246i
$690$		0			0
$691$	−162273.	−	93688.2i	−0.339852	−	0.196213i	0.320355	−	0.947298i	$-0.396198\pi$
$691$	−162273.	−	93688.2i	−0.339852	−	0.196213i	−0.660206	+	0.751084i	$0.729531\pi$
$692$		0			0
$693$	45362.9	+	78286.5i	0.0944571	+	0.163012i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	562921.	−	325003.i	1.15873	−	0.668993i
$698$		0			0
$699$			13881.4i			0.0284105i
$700$		0			0
$701$	326056.			0.663522			0.331761	−	0.943363i	$-0.392357\pi$
$701$	326056.			0.663522			0.331761	+	0.943363i	$0.392357\pi$
$702$		0			0
$703$	166603.	+	288564.i	0.337110	+	0.583891i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	33132.0	+	19059.4i	0.0662841	+	0.0381303i
$708$		0			0
$709$	32372.6	−	56070.9i	0.0643998	−	0.111544i	−0.832028	−	0.554734i	$-0.812820\pi$
$709$	32372.6	−	56070.9i	0.0643998	−	0.111544i	0.896428	+	0.443190i	$0.146153\pi$
$710$		0			0
$711$	−306086.	−	530157.i	−0.605487	−	1.04873i
$712$		0			0
$713$	−505371.			−0.994102
$714$		0			0
$715$		0			0
$716$		0			0
$717$	69432.6	+	120261.i	0.135060	+	0.233930i
$718$		0			0
$719$	616355.	+	355853.i	1.19227	+	0.688355i	0.958820	−	0.284014i	$-0.0916664\pi$
$719$	616355.	+	355853.i	1.19227	+	0.688355i	0.233446	+	0.972370i	$0.425000\pi$
$720$		0			0
$721$	134882.	−	212.011i	0.259468	−	0.000407838i
$722$		0			0
$723$	83744.0	+	48349.6i	0.160205	+	0.0924946i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	763134.			1.44388			0.721941	−	0.691954i	$-0.243250\pi$
$727$	763134.			1.44388			0.721941	+	0.691954i	$0.243250\pi$
$728$		0			0
$729$	−436942.			−0.822183
$730$		0			0
$731$	599404.	−	346066.i	1.12172	−	0.647626i
$732$		0			0
$733$	10304.6	−	17848.0i	0.0191788	−	0.0332187i	−0.856277	−	0.516517i	$-0.827228\pi$
$733$	10304.6	−	17848.0i	0.0191788	−	0.0332187i	0.875456	+	0.483299i	$0.160561\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−153924.	−	88868.0i	−0.283381	−	0.163610i
$738$		0			0
$739$	−393194.	−	681032.i	−0.719976	−	1.24703i	−0.961009	−	0.276518i	$-0.910819\pi$
$739$	−393194.	−	681032.i	−0.719976	−	1.24703i	0.241033	−	0.970517i	$-0.422514\pi$
$740$		0			0
$741$		−	95598.6i		−	0.174107i
$742$		0			0
$743$			740479.i			1.34133i	0.741761	+	0.670664i	$0.233991\pi$
$743$			740479.i			1.34133i	−0.741761	+	0.670664i	$0.766009\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	85661.3	−	148370.i	0.153512	−	0.265891i
$748$		0			0
$749$	−1144.42	−	728086.i	−0.00203997	−	1.29783i
$750$		0			0
$751$	247292.	−	428322.i	0.438460	−	0.759436i	−0.559111	−	0.829093i	$-0.688857\pi$
$751$	247292.	−	428322.i	0.438460	−	0.759436i	0.997571	+	0.0696574i	$0.0221906\pi$
$752$		0			0
$753$	−78545.5	+	45348.3i	−0.138526	+	0.0799780i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			139399.i			0.243258i	0.992576	+	0.121629i	$0.0388118\pi$
$757$			139399.i			0.243258i	−0.992576	+	0.121629i	$0.961188\pi$
$758$		0			0
$759$	−23937.5	+	13820.3i	−0.0415524	+	0.0239903i
$760$		0			0
$761$	−207340.	−	119708.i	−0.358025	−	0.206706i	0.310189	−	0.950675i	$-0.399608\pi$
$761$	−207340.	−	119708.i	−0.358025	−	0.206706i	−0.668214	+	0.743969i	$0.732941\pi$
$762$		0			0
$763$	67354.1	−	117085.i	0.115695	−	0.201119i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	138208.	−	79794.1i	0.234931	−	0.135638i
$768$		0			0
$769$		−	98701.5i		−	0.166906i	−0.996512	−	0.0834528i	$-0.973405\pi$
$769$		−	98701.5i		−	0.166906i	0.996512	−	0.0834528i	$-0.0265948\pi$
$770$		0			0
$771$	−110051.			−0.185134
$772$		0			0
$773$	−293248.	−	507921.i	−0.490769	−	0.850036i	0.509175	−	0.860663i	$-0.329951\pi$
$773$	−293248.	−	507921.i	−0.490769	−	0.850036i	−0.999944	+	0.0106268i	$0.996617\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−49587.5	+	28733.4i	−0.0821354	+	0.0475932i
$778$		0			0
$779$	553500.	−	958690.i	0.912100	−	1.57980i
$780$		0			0
$781$	−89053.6	−	154245.i	−0.145999	−	0.252877i
$782$		0			0
$783$	101775.			0.166003
$784$		0			0
$785$		0			0
$786$		0			0
$787$	74787.4	+	129536.i	0.120748	+	0.209141i	0.920063	−	0.391771i	$-0.128137\pi$
$787$	74787.4	+	129536.i	0.120748	+	0.209141i	−0.799315	+	0.600912i	$0.794804\pi$
$788$		0			0
$789$	−30226.8	−	17451.4i	−0.0485554	−	0.0280335i
$790$		0			0
$791$	265606.	−	153905.i	0.424507	−	0.245980i
$792$		0			0
$793$	−275544.	−	159085.i	−0.438171	−	0.252978i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	241092.			0.379547			0.189774	−	0.981828i	$-0.439225\pi$
$797$	241092.			0.379547			0.189774	+	0.981828i	$0.439225\pi$
$798$		0			0
$799$	−175531.			−0.274954
$800$		0			0
$801$	−632256.	+	365033.i	−0.985436	+	0.568941i
$802$		0			0
$803$	44580.4	−	77215.6i	0.0691374	−	0.119750i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	63291.3	+	36541.3i	0.0971845	+	0.0561095i
$808$		0			0
$809$	100933.	+	174820.i	0.154218	+	0.267113i	0.932774	−	0.360462i	$-0.117381\pi$
$809$	100933.	+	174820.i	0.154218	+	0.267113i	−0.778556	+	0.627575i	$0.784048\pi$
$810$		0			0
$811$		−	1.16747e6i		−	1.77503i	−0.460779	−	0.887515i	$-0.652430\pi$
$811$		−	1.16747e6i		−	1.77503i	0.460779	−	0.887515i	$-0.347570\pi$
$812$		0			0
$813$		−	130389.i		−	0.197270i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	589373.	−	1.02082e6i	0.882970	−	1.52935i
$818$		0			0
$819$	−524410.	+	824.281i	−0.781814	+	0.00122887i
$820$		0			0
$821$	324585.	−	562198.i	0.481551	−	0.834071i	−0.518225	−	0.855245i	$-0.673407\pi$
$821$	324585.	−	562198.i	0.481551	−	0.834071i	0.999776	+	0.0211734i	$0.00674022\pi$
$822$		0			0
$823$	−425193.	+	245486.i	−0.627750	+	0.362432i	−0.779880	−	0.625929i	$-0.784720\pi$
$823$	−425193.	+	245486.i	−0.627750	+	0.362432i	0.152130	+	0.988360i	$0.451387\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			709017.i			1.03668i	0.855174	+	0.518341i	$0.173450\pi$
$827$			709017.i			1.03668i	−0.855174	+	0.518341i	$0.826550\pi$
$828$		0			0
$829$	−534645.	+	308677.i	−0.777958	+	0.449154i	−0.835706	−	0.549177i	$-0.814941\pi$
$829$	−534645.	+	308677.i	−0.777958	+	0.449154i	0.0577480	+	0.998331i	$0.481608\pi$
$830$		0			0
$831$	−12269.3	−	7083.68i	−0.0177671	−	0.0102579i
$832$		0			0
$833$	−630262.	+	1981.33i	−0.908304	+	0.00285540i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	146256.	−	84441.0i	0.208768	−	0.120532i
$838$		0			0
$839$			493961.i			0.701728i	0.936426	+	0.350864i	$0.114112\pi$
$839$			493961.i			0.701728i	−0.936426	+	0.350864i	$0.885888\pi$
$840$		0			0
$841$	−542019.			−0.766342
$842$		0			0
$843$	−50363.7	−	87232.4i	−0.0708699	−	0.122750i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−690322.	+	1085.07i	−0.962243	+	0.00151248i
$848$		0			0
$849$	17724.8	−	30700.2i	0.0245904	−	0.0425918i
$850$		0			0
$851$	279190.	+	483571.i	0.385514	+	0.667730i
$852$		0			0
$853$	505142.			0.694249			0.347124	−	0.937819i	$-0.387158\pi$
$853$	505142.			0.694249			0.347124	+	0.937819i	$0.387158\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	560018.	+	969980.i	0.762501	+	1.32069i	0.941557	+	0.336852i	$0.109362\pi$
$857$	560018.	+	969980.i	0.762501	+	1.32069i	−0.179056	+	0.983839i	$0.557304\pi$
$858$		0			0
$859$	605141.	+	349379.i	0.820107	+	0.473489i	0.850453	−	0.526050i	$-0.176328\pi$
$859$	605141.	+	349379.i	0.820107	+	0.473489i	−0.0303463	+	0.999539i	$0.509661\pi$
$860$		0			0
$861$	165043.	+	94941.9i	0.222633	+	0.128071i
$862$		0			0
$863$	−830576.	−	479533.i	−1.11521	−	0.643868i	−0.175038	−	0.984562i	$-0.556005\pi$
$863$	−830576.	−	479533.i	−1.11521	−	0.643868i	−0.940175	+	0.340693i	$0.889338\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−22933.1			−0.0305088
$868$		0			0
$869$	−183263.			−0.242681
$870$		0			0
$871$	892127.	−	515069.i	1.17595	−	0.678937i
$872$		0			0
$873$	391976.	−	678923.i	0.514318	−	0.890824i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−863326.	−	498442.i	−1.12247	−	0.648060i	−0.180442	−	0.983586i	$-0.557753\pi$
$877$	−863326.	−	498442.i	−1.12247	−	0.648060i	−0.942031	+	0.335526i	$0.891086\pi$
$878$		0			0
$879$	102372.	+	177314.i	0.132497	+	0.229491i
$880$		0			0
$881$		−	494568.i		−	0.637198i	−0.947890	−	0.318599i	$-0.896788\pi$
$881$		−	494568.i		−	0.637198i	0.947890	−	0.318599i	$-0.103212\pi$
$882$		0			0
$883$			887278.i			1.13799i	0.822341	+	0.568995i	$0.192667\pi$
$883$			887278.i			1.13799i	−0.822341	+	0.568995i	$0.807333\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	312960.	−	542062.i	0.397779	−	0.688973i	−0.595673	−	0.803227i	$-0.703115\pi$
$887$	312960.	−	542062.i	0.397779	−	0.688973i	0.993452	+	0.114254i	$0.0364479\pi$
$888$		0			0
$889$	−545008.	+	315804.i	−0.689604	+	0.399589i
$890$		0			0
$891$	−70165.8	+	121531.i	−0.0883833	+	0.153084i
$892$		0			0
$893$	−258890.	+	149470.i	−0.324647	+	0.187435i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	160203.i		−	0.199106i
$898$		0			0
$899$	237491.	−	137115.i	0.293851	−	0.169655i
$900$		0			0
$901$	−461309.	−	266337.i	−0.568253	−	0.328081i
$902$		0			0
$903$	175739.	+	101095.i	0.215523	+	0.123981i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.09835e6	−	634131.i	1.33513	−	0.770840i	0.349052	−	0.937103i	$-0.386504\pi$
$907$	1.09835e6	−	634131.i	1.33513	−	0.770840i	0.986081	+	0.166263i	$0.0531702\pi$
$908$		0			0
$909$			61263.9i			0.0741442i
$910$		0			0
$911$	−1.09985e6			−1.32525			−0.662625	−	0.748951i	$-0.730558\pi$
$911$	−1.09985e6			−1.32525			−0.662625	+	0.748951i	$0.730558\pi$
$912$		0			0
$913$	−25644.0	−	44416.7i	−0.0307641	−	0.0532850i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1904.30	+	1.21152e6i	0.00226463	+	1.44076i
$918$		0			0
$919$	430660.	−	745925.i	0.509922	−	0.883211i	−0.490012	−	0.871716i	$-0.663008\pi$
$919$	430660.	−	745925.i	0.509922	−	0.883211i	0.999934	−	0.0114950i	$-0.00365905\pi$
$920$		0			0
$921$	44075.3	+	76340.6i	0.0519608	+	0.0899987i
$922$		0			0
$923$	1.03229e6			1.21171
$924$		0			0
$925$		0			0
$926$		0			0
$927$	108095.	+	187226.i	0.125790	+	0.217874i
$928$		0			0
$929$	326247.	+	188359.i	0.378021	+	0.218250i	0.676957	−	0.736023i	$-0.263298\pi$
$929$	326247.	+	188359.i	0.378021	+	0.218250i	−0.298936	+	0.954273i	$0.596632\pi$
$930$		0			0
$931$	−927884.	+	539610.i	−1.07052	+	0.622560i
$932$		0			0
$933$	−62906.7	−	36319.2i	−0.0722659	−	0.0417227i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	417813.			0.475885			0.237943	−	0.971279i	$-0.423527\pi$
$937$	417813.			0.475885			0.237943	+	0.971279i	$0.423527\pi$
$938$		0			0
$939$	−217103.			−0.246227
$940$		0			0
$941$	213031.	−	122994.i	0.240582	−	0.138900i	−0.374862	−	0.927081i	$-0.622310\pi$
$941$	213031.	−	122994.i	0.240582	−	0.138900i	0.615444	+	0.788180i	$0.288977\pi$
$942$		0			0
$943$	927546.	−	1.60656e6i	1.04307	−	1.80665i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.25221e6	−	722964.i	−1.39630	−	0.806152i	−0.402294	−	0.915511i	$-0.631787\pi$
$947$	−1.25221e6	−	722964.i	−1.39630	−	0.806152i	−0.994002	+	0.109359i	$0.965120\pi$
$948$		0			0
$949$	258384.	+	447533.i	0.286901	+	0.496928i
$950$		0			0
$951$			91495.4i			0.101167i
$952$		0			0
$953$			907377.i			0.999084i	0.866290	+	0.499542i	$0.166498\pi$
$953$			907377.i			0.999084i	−0.866290	+	0.499542i	$0.833502\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7499.38	−	12989.3i	0.00818845	−	0.0141828i
$958$		0			0
$959$	56156.9	+	32304.6i	0.0610612	+	0.0351259i
$960$		0			0
$961$	−234235.	+	405707.i	−0.253633	+	0.439305i
$962$		0			0
$963$	1.01064e6	−	583491.i	1.08979	−	0.629189i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			50286.2i			0.0537770i	0.999638	+	0.0268885i	$0.00855990\pi$
$967$			50286.2i			0.0537770i	−0.999638	+	0.0268885i	$0.991440\pi$
$968$		0			0
$969$	159483.	−	92077.6i	0.169851	−	0.0980633i
$970$		0			0
$971$	677500.	+	391155.i	0.718573	+	0.414868i	0.814227	−	0.580546i	$-0.197161\pi$
$971$	677500.	+	391155.i	0.718573	+	0.414868i	−0.0956544	+	0.995415i	$0.530494\pi$
$972$		0			0
$973$	217062.	−	125776.i	0.229275	−	0.132853i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.10629e6	+	638714.i	−1.15899	+	0.669141i	−0.951061	−	0.309004i	$-0.900004\pi$
$977$	−1.10629e6	+	638714.i	−1.15899	+	0.669141i	−0.207925	+	0.978145i	$0.566671\pi$
$978$		0			0
$979$			218557.i			0.228033i
$980$		0			0
$981$	216501.			0.224968
$982$		0			0
$983$	786638.	+	1.36250e6i	0.814081	+	1.41003i	0.909986	+	0.414639i	$0.136092\pi$
$983$	786638.	+	1.36250e6i	0.814081	+	1.41003i	−0.0959049	+	0.995391i	$0.530574\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−25778.6	−	44488.2i	−0.0264621	−	0.0456679i
$988$		0			0
$989$	987661.	−	1.71068e6i	1.00975	−	1.74894i
$990$		0			0
$991$	−162173.	−	280892.i	−0.165132	−	0.286017i	0.771570	−	0.636144i	$-0.219472\pi$
$991$	−162173.	−	280892.i	−0.165132	−	0.286017i	−0.936702	+	0.350127i	$0.886138\pi$
$992$		0			0
$993$	1552.30			0.00157427
$994$		0			0
$995$		0			0
$996$		0			0
$997$	907185.	+	1.57129e6i	0.912652	+	1.58076i	0.810303	+	0.586012i	$0.199303\pi$
$997$	907185.	+	1.57129e6i	0.912652	+	1.58076i	0.102350	+	0.994748i	$0.467364\pi$
$998$		0			0
$999$	−161597.	−	93298.2i	−0.161921	−	0.0934851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.5.o.a.649.3		12
5.2	odd	4		28.5.h.a.5.2	✓	6
5.3	odd	4		700.5.s.a.201.2		6
5.4	even	2	inner	700.5.o.a.649.4		12
7.3	odd	6	inner	700.5.o.a.549.4		12
15.2	even	4		252.5.z.f.145.1		6
20.7	even	4		112.5.s.c.33.2		6
35.2	odd	12		196.5.b.a.97.3		6
35.3	even	12		700.5.s.a.101.2		6
35.12	even	12		196.5.b.a.97.4		6
35.17	even	12		28.5.h.a.17.2	yes	6
35.24	odd	6	inner	700.5.o.a.549.3		12
35.27	even	4		196.5.h.c.117.2		6
35.32	odd	12		196.5.h.c.129.2		6
105.17	odd	12		252.5.z.f.73.1		6
140.47	odd	12		784.5.c.e.97.3		6
140.87	odd	12		112.5.s.c.17.2		6
140.107	even	12		784.5.c.e.97.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.5.h.a.5.2	✓	6	5.2	odd	4
28.5.h.a.17.2	yes	6	35.17	even	12
112.5.s.c.17.2		6	140.87	odd	12
112.5.s.c.33.2		6	20.7	even	4
196.5.b.a.97.3		6	35.2	odd	12
196.5.b.a.97.4		6	35.12	even	12
196.5.h.c.117.2		6	35.27	even	4
196.5.h.c.129.2		6	35.32	odd	12
252.5.z.f.73.1		6	105.17	odd	12
252.5.z.f.145.1		6	15.2	even	4
700.5.o.a.549.3		12	35.24	odd	6	inner
700.5.o.a.549.4		12	7.3	odd	6	inner
700.5.o.a.649.3		12	1.1	even	1	trivial
700.5.o.a.649.4		12	5.4	even	2	inner
700.5.s.a.101.2		6	35.3	even	12
700.5.s.a.201.2		6	5.3	odd	4
784.5.c.e.97.3		6	140.47	odd	12
784.5.c.e.97.4		6	140.107	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.784623 - 1.35901i) q^{3} +(-24.5667 - 42.3967i) q^{7} +(39.2687 - 68.0154i) q^{9} +(-11.7557 - 20.3615i) q^{11} +136.269 q^{13} +(131.251 + 227.333i) q^{17} +(387.162 + 223.528i) q^{19} +(-38.3418 + 66.6517i) q^{21} +(648.800 + 374.585i) q^{23} -250.353 q^{27} -406.524 q^{29} +(-584.199 + 337.287i) q^{31} +(-18.4476 + 31.9521i) q^{33} +(645.476 + 372.666i) q^{37} +(-106.920 - 185.191i) q^{39} -2476.20i q^{41} -2636.68i q^{43} +(-334.343 + 579.099i) q^{47} +(-1193.96 + 2083.09i) q^{49} +(205.964 - 356.741i) q^{51} +(-1757.36 + 1014.61i) q^{53} -701.541i q^{57} +(1014.22 - 585.561i) q^{59} +(-2022.05 - 1167.43i) q^{61} +(-3848.33 + 6.04891i) q^{63} +(6546.78 - 3779.79i) q^{67} -1175.63i q^{69} +7575.36 q^{71} +(1896.12 + 3284.18i) q^{73} +(-574.460 + 998.615i) q^{77} +(3897.33 - 6750.37i) q^{79} +(-2984.33 - 5169.02i) q^{81} +2181.41 q^{83} +(318.968 + 552.469i) q^{87} +(-8050.38 - 4647.89i) q^{89} +(-3347.69 - 5777.37i) q^{91} +(916.751 + 529.287i) q^{93} +9981.90 q^{97} -1846.52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 180 q^{9} + 270 q^{11} + 1494 q^{19} + 4338 q^{21} + 1080 q^{29} - 10710 q^{31} - 13176 q^{39} - 16860 q^{49} - 1782 q^{51} + 5886 q^{59} + 8082 q^{61} + 4536 q^{71} + 15546 q^{79} - 14958 q^{81}+ \cdots - 16200 q^{99}+O(q^{100}) \) 12 * q - 180 * q^9 + 270 * q^11 + 1494 * q^19 + 4338 * q^21 + 1080 * q^29 - 10710 * q^31 - 13176 * q^39 - 16860 * q^49 - 1782 * q^51 + 5886 * q^59 + 8082 * q^61 + 4536 * q^71 + 15546 * q^79 - 14958 * q^81 - 29970 * q^89 - 41904 * q^91 - 16200 * q^99

Introduction

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