LMFDB - Embedded newform 1500.2.o.c.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.3
Character	$\chi$	$=$	1500.349
Dual form			1500.2.o.c.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{3} -4.41540i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{3} -4.41540i q^{7} +(-0.309017 + 0.951057i) q^{9} +(1.37568 + 4.23392i) q^{11} +(-5.46646 - 1.77616i) q^{13} +(-3.86196 + 5.31553i) q^{17} +(-2.25162 - 1.63590i) q^{19} +(-3.57213 + 2.59531i) q^{21} +(-1.25059 + 0.406341i) q^{23} +(0.951057 - 0.309017i) q^{27} +(-3.91985 + 2.84794i) q^{29} +(0.159486 + 0.115873i) q^{31} +(2.61671 - 3.60159i) q^{33} +(7.80690 + 2.53662i) q^{37} +(1.77616 + 5.46646i) q^{39} +(2.42573 - 7.46564i) q^{41} -0.412792i q^{43} +(4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +6.57035 q^{51} +(0.185420 + 0.255208i) q^{53} +2.78315i q^{57} +(-0.778419 + 2.39573i) q^{59} +(2.88348 + 8.87444i) q^{61} +(4.19929 + 1.36443i) q^{63} +(-7.02151 + 9.66428i) q^{67} +(1.06382 + 0.772907i) q^{69} +(-0.411990 + 0.299328i) q^{71} +(-14.9990 + 4.87346i) q^{73} +(18.6945 - 6.07420i) q^{77} +(-2.77617 + 2.01700i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-3.15732 + 4.34568i) q^{83} +(4.60806 + 1.49725i) q^{87} +(-3.50585 - 10.7899i) q^{89} +(-7.84246 + 24.1366i) q^{91} -0.197136i q^{93} +(-2.98572 - 4.10948i) q^{97} -4.45181 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

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
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	4.41540i		−	1.66886i	−0.551111	−	0.834432i	$-0.685796\pi$
$7$		−	4.41540i		−	1.66886i	0.551111	−	0.834432i	$-0.314204\pi$
$8$		0			0
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	1.37568	+	4.23392i	0.414785	+	1.27658i	0.912443	+	0.409203i	$0.134193\pi$
$11$	1.37568	+	4.23392i	0.414785	+	1.27658i	−0.497659	+	0.867373i	$0.665807\pi$
$12$		0			0
$13$	−5.46646	−	1.77616i	−1.51612	−	0.492619i	−0.571452	−	0.820635i	$-0.693620\pi$
$13$	−5.46646	−	1.77616i	−1.51612	−	0.492619i	−0.944672	+	0.328017i	$0.893620\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.86196	+	5.31553i	−0.936662	+	1.28921i	0.0205412	+	0.999789i	$0.493461\pi$
$17$	−3.86196	+	5.31553i	−0.936662	+	1.28921i	−0.957203	+	0.289416i	$0.906539\pi$
$18$		0			0
$19$	−2.25162	−	1.63590i	−0.516557	−	0.375301i	0.298748	−	0.954332i	$-0.403431\pi$
$19$	−2.25162	−	1.63590i	−0.516557	−	0.375301i	−0.815305	+	0.579031i	$0.803431\pi$
$20$		0			0
$21$	−3.57213	+	2.59531i	−0.779503	+	0.566342i
$22$		0			0
$23$	−1.25059	+	0.406341i	−0.260766	+	0.0847280i	−0.436482	−	0.899713i	$-0.643776\pi$
$23$	−1.25059	+	0.406341i	−0.260766	+	0.0847280i	0.175716	+	0.984441i	$0.443776\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$		0			0
$29$	−3.91985	+	2.84794i	−0.727899	+	0.528849i	−0.888898	−	0.458105i	$-0.848528\pi$
$29$	−3.91985	+	2.84794i	−0.727899	+	0.528849i	0.160999	+	0.986954i	$0.448528\pi$
$30$		0			0
$31$	0.159486	+	0.115873i	0.0286446	+	0.0208115i	0.602015	−	0.798484i	$-0.294365\pi$
$31$	0.159486	+	0.115873i	0.0286446	+	0.0208115i	−0.573371	+	0.819296i	$0.694365\pi$
$32$		0			0
$33$	2.61671	−	3.60159i	0.455510	−	0.626956i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.80690	+	2.53662i	1.28345	+	0.417017i	0.869793	−	0.493417i	$-0.164252\pi$
$37$	7.80690	+	2.53662i	1.28345	+	0.417017i	0.413654	+	0.910434i	$0.364252\pi$
$38$		0			0
$39$	1.77616	+	5.46646i	0.284413	+	0.875335i
$40$		0			0
$41$	2.42573	−	7.46564i	0.378836	−	1.16594i	−0.562018	−	0.827125i	$-0.689975\pi$
$41$	2.42573	−	7.46564i	0.378836	−	1.16594i	0.940854	−	0.338813i	$-0.110025\pi$
$42$		0			0
$43$		−	0.412792i		−	0.0629502i	−0.999505	−	0.0314751i	$-0.989980\pi$
$43$		−	0.412792i		−	0.0629502i	0.999505	−	0.0314751i	$-0.0100205\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.58154	+	6.30595i	0.668287	+	0.919818i	0.999720	−	0.0236610i	$-0.00753223\pi$
$47$	4.58154	+	6.30595i	0.668287	+	0.919818i	−0.331433	+	0.943479i	$0.607532\pi$
$48$		0			0
$49$	−12.4958			−1.78511
$50$		0			0
$51$	6.57035			0.920034
$52$		0			0
$53$	0.185420	+	0.255208i	0.0254694	+	0.0350556i	0.821562	−	0.570120i	$-0.193103\pi$
$53$	0.185420	+	0.255208i	0.0254694	+	0.0350556i	−0.796092	+	0.605175i	$0.793103\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			2.78315i			0.368638i
$58$		0			0
$59$	−0.778419	+	2.39573i	−0.101342	+	0.311897i	−0.988854	−	0.148886i	$-0.952431\pi$
$59$	−0.778419	+	2.39573i	−0.101342	+	0.311897i	0.887513	+	0.460783i	$0.152431\pi$
$60$		0			0
$61$	2.88348	+	8.87444i	0.369192	+	1.13626i	0.947314	+	0.320305i	$0.103786\pi$
$61$	2.88348	+	8.87444i	0.369192	+	1.13626i	−0.578123	+	0.815950i	$0.696214\pi$
$62$		0			0
$63$	4.19929	+	1.36443i	0.529061	+	0.171902i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.02151	+	9.66428i	−0.857814	+	1.18068i	0.124273	+	0.992248i	$0.460340\pi$
$67$	−7.02151	+	9.66428i	−0.857814	+	1.18068i	−0.982086	+	0.188431i	$0.939660\pi$
$68$		0			0
$69$	1.06382	+	0.772907i	0.128068	+	0.0930471i
$70$		0			0
$71$	−0.411990	+	0.299328i	−0.0488942	+	0.0355237i	−0.611964	−	0.790886i	$-0.709620\pi$
$71$	−0.411990	+	0.299328i	−0.0488942	+	0.0355237i	0.563070	+	0.826409i	$0.309620\pi$
$72$		0			0
$73$	−14.9990	+	4.87346i	−1.75549	+	0.570395i	−0.996718	−	0.0809557i	$-0.974203\pi$
$73$	−14.9990	+	4.87346i	−1.75549	+	0.570395i	−0.758777	+	0.651351i	$0.774203\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	18.6945	−	6.07420i	2.13043	−	0.692219i
$78$		0			0
$79$	−2.77617	+	2.01700i	−0.312343	+	0.226930i	−0.732901	−	0.680335i	$-0.761834\pi$
$79$	−2.77617	+	2.01700i	−0.312343	+	0.226930i	0.420558	+	0.907266i	$0.361834\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−3.15732	+	4.34568i	−0.346561	+	0.477000i	−0.946343	−	0.323163i	$-0.895254\pi$
$83$	−3.15732	+	4.34568i	−0.346561	+	0.477000i	0.599783	+	0.800163i	$0.295254\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.60806	+	1.49725i	0.494036	+	0.160522i
$88$		0			0
$89$	−3.50585	−	10.7899i	−0.371619	−	1.14373i	−0.945731	−	0.324950i	$-0.894653\pi$
$89$	−3.50585	−	10.7899i	−0.371619	−	1.14373i	0.574112	−	0.818777i	$-0.305347\pi$
$90$		0			0
$91$	−7.84246	+	24.1366i	−0.822114	+	2.53021i
$92$		0			0
$93$		−	0.197136i		−	0.0204420i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.98572	−	4.10948i	−0.303153	−	0.417255i	0.630077	−	0.776532i	$-0.283023\pi$
$97$	−2.98572	−	4.10948i	−0.303153	−	0.417255i	−0.933231	+	0.359277i	$0.883023\pi$
$98$		0			0
$99$	−4.45181			−0.447424
$100$		0			0
$101$	−11.1860			−1.11305			−0.556525	−	0.830831i	$-0.687866\pi$
$101$	−11.1860			−1.11305			−0.556525	+	0.830831i	$0.687866\pi$
$102$		0			0
$103$	1.84898	+	2.54490i	0.182185	+	0.250757i	0.890335	−	0.455305i	$-0.150470\pi$
$103$	1.84898	+	2.54490i	0.182185	+	0.250757i	−0.708150	+	0.706062i	$0.750470\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			7.74013i			0.748266i	0.927375	+	0.374133i	$0.122060\pi$
$107$			7.74013i			0.748266i	−0.927375	+	0.374133i	$0.877940\pi$
$108$		0			0
$109$	3.20477	−	9.86326i	0.306961	−	0.944729i	−0.671977	−	0.740572i	$-0.734555\pi$
$109$	3.20477	−	9.86326i	0.306961	−	0.944729i	0.978938	−	0.204157i	$-0.0654453\pi$
$110$		0			0
$111$	−2.53662	−	7.80690i	−0.240765	−	0.740998i
$112$		0			0
$113$	−9.72574	−	3.16009i	−0.914921	−	0.297276i	−0.186539	−	0.982447i	$-0.559727\pi$
$113$	−9.72574	−	3.16009i	−0.914921	−	0.297276i	−0.728382	+	0.685172i	$0.759727\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.37846	−	4.65005i	0.312339	−	0.429897i
$118$		0			0
$119$	23.4702	+	17.0521i	2.15151	+	1.56316i
$120$		0			0
$121$	−7.13440	+	5.18344i	−0.648582	+	0.471222i
$122$		0			0
$123$	−7.46564	+	2.42573i	−0.673154	+	0.218721i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−10.7590	+	3.49582i	−0.954709	+	0.310204i	−0.744628	−	0.667480i	$-0.767373\pi$
$127$	−10.7590	+	3.49582i	−0.954709	+	0.310204i	−0.210081	+	0.977684i	$0.567373\pi$
$128$		0			0
$129$	−0.333956	+	0.242633i	−0.0294031	+	0.0213626i
$130$		0			0
$131$	7.64816	+	5.55671i	0.668223	+	0.485492i	0.869430	−	0.494056i	$-0.164486\pi$
$131$	7.64816	+	5.55671i	0.668223	+	0.485492i	−0.201207	+	0.979549i	$0.564486\pi$
$132$		0			0
$133$	−7.22314	+	9.94180i	−0.626326	+	0.862063i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.99861	−	2.59891i	−0.683367	−	0.222039i	−0.0532983	−	0.998579i	$-0.516973\pi$
$137$	−7.99861	−	2.59891i	−0.683367	−	0.222039i	−0.630069	+	0.776539i	$0.716973\pi$
$138$		0			0
$139$	−3.65307	−	11.2430i	−0.309849	−	0.953617i	−0.977823	−	0.209433i	$-0.932838\pi$
$139$	−3.65307	−	11.2430i	−0.309849	−	0.953617i	0.667974	−	0.744185i	$-0.267162\pi$
$140$		0			0
$141$	2.40866	−	7.41309i	0.202846	−	0.624295i
$142$		0			0
$143$		−	25.5880i		−	2.13978i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.34482	+	10.1093i	0.605791	+	0.833799i
$148$		0			0
$149$	−10.6355			−0.871294			−0.435647	−	0.900118i	$-0.643480\pi$
$149$	−10.6355			−0.871294			−0.435647	+	0.900118i	$0.643480\pi$
$150$		0			0
$151$	4.41657			0.359415			0.179707	−	0.983720i	$-0.442485\pi$
$151$	4.41657			0.359415			0.179707	+	0.983720i	$0.442485\pi$
$152$		0			0
$153$	−3.86196	−	5.31553i	−0.312221	−	0.429735i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	13.5289i		−	1.07972i	−0.841754	−	0.539861i	$-0.818477\pi$
$157$		−	13.5289i		−	1.07972i	0.841754	−	0.539861i	$-0.181523\pi$
$158$		0			0
$159$	0.0974809	−	0.300015i	0.00773074	−	0.0237928i
$160$		0			0
$161$	1.79416	+	5.52186i	0.141400	+	0.435183i
$162$		0			0
$163$	13.8458	+	4.49876i	1.08448	+	0.352370i	0.796112	−	0.605149i	$-0.206886\pi$
$163$	13.8458	+	4.49876i	1.08448	+	0.352370i	0.288371	+	0.957519i	$0.406886\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.85918	−	8.06448i	0.453397	−	0.624048i	−0.519726	−	0.854333i	$-0.673966\pi$
$167$	5.85918	−	8.06448i	0.453397	−	0.624048i	0.973123	+	0.230285i	$0.0739659\pi$
$168$		0			0
$169$	16.2103	+	11.7774i	1.24694	+	0.905957i
$170$		0			0
$171$	2.25162	−	1.63590i	0.172186	−	0.125100i
$172$		0			0
$173$	10.3427	−	3.36056i	0.786344	−	0.255499i	0.111798	−	0.993731i	$-0.464339\pi$
$173$	10.3427	−	3.36056i	0.786344	−	0.255499i	0.674547	+	0.738232i	$0.264339\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.39573	−	0.778419i	0.180074	−	0.0585096i
$178$		0			0
$179$	−20.3662	+	14.7969i	−1.52224	+	1.10597i	−0.561875	+	0.827222i	$0.689920\pi$
$179$	−20.3662	+	14.7969i	−1.52224	+	1.10597i	−0.960364	+	0.278749i	$0.910080\pi$
$180$		0			0
$181$	6.14184	+	4.46231i	0.456520	+	0.331681i	0.792164	−	0.610308i	$-0.208954\pi$
$181$	6.14184	+	4.46231i	0.456520	+	0.331681i	−0.335645	+	0.941989i	$0.608954\pi$
$182$		0			0
$183$	5.48470	−	7.54905i	0.405441	−	0.558042i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−27.8184	−	9.03874i	−2.03428	−	0.660978i
$188$		0			0
$189$	−1.36443	−	4.19929i	−0.0992479	−	0.305454i
$190$		0			0
$191$	−0.00373697	+	0.0115012i	−0.000270398	+	0.000832198i	−0.951192	−	0.308601i	$-0.900139\pi$
$191$	−0.00373697	+	0.0115012i	−0.000270398	+	0.000832198i	0.950921	+	0.309433i	$0.100139\pi$
$192$		0			0
$193$			12.7841i			0.920219i	0.887862	+	0.460110i	$0.152190\pi$
$193$			12.7841i			0.920219i	−0.887862	+	0.460110i	$0.847810\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.79877	+	7.98132i	0.413145	+	0.568646i	0.963982	−	0.265967i	$-0.0856914\pi$
$197$	5.79877	+	7.98132i	0.413145	+	0.568646i	−0.550837	+	0.834613i	$0.685691\pi$
$198$		0			0
$199$	0.295640			0.0209573			0.0104787	−	0.999945i	$-0.496664\pi$
$199$	0.295640			0.0209573			0.0104787	+	0.999945i	$0.496664\pi$
$200$		0			0
$201$	11.9457			0.842585
$202$		0			0
$203$	12.5748	+	17.3077i	0.882578	+	1.21476i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	1.31495i		−	0.0913952i
$208$		0			0
$209$	3.82874	−	11.7837i	0.264840	−	0.815093i
$210$		0			0
$211$	−3.90836	−	12.0287i	−0.269062	−	0.828089i	−0.990730	−	0.135849i	$-0.956624\pi$
$211$	−3.90836	−	12.0287i	−0.269062	−	0.828089i	0.721667	−	0.692240i	$-0.243376\pi$
$212$		0			0
$213$	0.484323	+	0.157366i	0.0331853	+	0.0107826i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.511628	−	0.704195i	0.0347315	−	0.0478039i
$218$		0			0
$219$	12.7589	+	9.26986i	0.862165	+	0.626399i
$220$		0			0
$221$	30.5525	−	22.1977i	2.05518	−	1.49318i
$222$		0			0
$223$	−4.98335	+	1.61919i	−0.333710	+	0.108429i	−0.471079	−	0.882091i	$-0.656135\pi$
$223$	−4.98335	+	1.61919i	−0.333710	+	0.108429i	0.137369	+	0.990520i	$0.456135\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.38873	−	2.40074i	0.490407	−	0.159343i	−0.0533663	−	0.998575i	$-0.516995\pi$
$227$	7.38873	−	2.40074i	0.490407	−	0.159343i	0.543773	+	0.839232i	$0.316995\pi$
$228$		0			0
$229$	−4.84757	+	3.52196i	−0.320336	+	0.232738i	−0.736319	−	0.676635i	$-0.763438\pi$
$229$	−4.84757	+	3.52196i	−0.320336	+	0.232738i	0.415983	+	0.909373i	$0.363438\pi$
$230$		0			0
$231$	−15.9025	−	11.5538i	−1.04630	−	0.760185i
$232$		0			0
$233$	8.73631	−	12.0245i	0.572334	−	0.787751i	−0.420494	−	0.907295i	$-0.638143\pi$
$233$	8.73631	−	12.0245i	0.572334	−	0.787751i	0.992829	+	0.119544i	$0.0381434\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.26358	+	1.06040i	0.211992	+	0.0688804i
$238$		0			0
$239$	6.55140	+	20.1631i	0.423775	+	1.30424i	0.904163	+	0.427188i	$0.140496\pi$
$239$	6.55140	+	20.1631i	0.423775	+	1.30424i	−0.480388	+	0.877056i	$0.659504\pi$
$240$		0			0
$241$	4.96162	−	15.2703i	0.319606	−	0.983647i	−0.654210	−	0.756313i	$-0.726999\pi$
$241$	4.96162	−	15.2703i	0.319606	−	0.983647i	0.973817	−	0.227334i	$-0.0730010\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.40278	+	12.9418i	0.598284	+	0.823468i
$248$		0			0
$249$	5.37155			0.340408
$250$		0			0
$251$	−24.1371			−1.52352			−0.761761	−	0.647858i	$-0.775665\pi$
$251$	−24.1371			−1.52352			−0.761761	+	0.647858i	$0.775665\pi$
$252$		0			0
$253$	−3.44084	−	4.73590i	−0.216323	−	0.297744i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	4.22940i		−	0.263823i	−0.991262	−	0.131911i	$-0.957889\pi$
$257$		−	4.22940i		−	0.263823i	0.991262	−	0.131911i	$-0.0421114\pi$
$258$		0			0
$259$	11.2002	−	34.4706i	0.695945	−	2.14190i
$260$		0			0
$261$	−1.49725	−	4.60806i	−0.0926775	−	0.285232i
$262$		0			0
$263$	7.97729	+	2.59198i	0.491901	+	0.159828i	0.544455	−	0.838790i	$-0.316736\pi$
$263$	7.97729	+	2.59198i	0.491901	+	0.159828i	−0.0525547	+	0.998618i	$0.516736\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.66852	+	9.17843i	−0.408107	+	0.561711i
$268$		0			0
$269$	−4.47812	−	3.25354i	−0.273036	−	0.198372i	0.442838	−	0.896601i	$-0.353972\pi$
$269$	−4.47812	−	3.25354i	−0.273036	−	0.198372i	−0.715874	+	0.698229i	$0.753972\pi$
$270$		0			0
$271$	−12.8227	+	9.31623i	−0.778923	+	0.565921i	−0.904656	−	0.426144i	$-0.859872\pi$
$271$	−12.8227	+	9.31623i	−0.778923	+	0.565921i	0.125733	+	0.992064i	$0.459872\pi$
$272$		0			0
$273$	24.1366	−	7.84246i	1.46081	−	0.474647i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−8.26699	+	2.68611i	−0.496715	+	0.161393i	−0.546652	−	0.837360i	$-0.684098\pi$
$277$	−8.26699	+	2.68611i	−0.496715	+	0.161393i	0.0499369	+	0.998752i	$0.484098\pi$
$278$		0			0
$279$	−0.159486	+	0.115873i	−0.00954819	+	0.00693716i
$280$		0			0
$281$	−8.72120	−	6.33633i	−0.520263	−	0.377994i	0.296440	−	0.955052i	$-0.404201\pi$
$281$	−8.72120	−	6.33633i	−0.520263	−	0.377994i	−0.816703	+	0.577058i	$0.804201\pi$
$282$		0			0
$283$	5.78686	−	7.96493i	0.343993	−	0.473466i	−0.601609	−	0.798791i	$-0.705473\pi$
$283$	5.78686	−	7.96493i	0.343993	−	0.473466i	0.945602	+	0.325324i	$0.105473\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−32.9638	−	10.7106i	−1.94579	−	0.632226i
$288$		0			0
$289$	−8.08684	−	24.8887i	−0.475696	−	1.46404i
$290$		0			0
$291$	−1.56968	+	4.83099i	−0.0920165	+	0.283198i
$292$		0			0
$293$			9.77733i			0.571198i	0.958349	+	0.285599i	$0.0921925\pi$
$293$			9.77733i			0.571198i	−0.958349	+	0.285599i	$0.907808\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.61671	+	3.60159i	0.151837	+	0.208985i
$298$		0			0
$299$	7.55803			0.437092
$300$		0			0
$301$	−1.82264			−0.105055
$302$		0			0
$303$	6.57497	+	9.04967i	0.377722	+	0.519890i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	32.7301i		−	1.86801i	−0.357265	−	0.934003i	$-0.616291\pi$
$307$		−	32.7301i		−	1.86801i	0.357265	−	0.934003i	$-0.383709\pi$
$308$		0			0
$309$	0.972067	−	2.99171i	0.0552989	−	0.170193i
$310$		0			0
$311$	−7.60939	−	23.4193i	−0.431489	−	1.32799i	−0.896642	−	0.442756i	$-0.854001\pi$
$311$	−7.60939	−	23.4193i	−0.431489	−	1.32799i	0.465153	−	0.885230i	$-0.345999\pi$
$312$		0			0
$313$	−21.4458	−	6.96817i	−1.21219	−	0.393864i	−0.367957	−	0.929843i	$-0.619943\pi$
$313$	−21.4458	−	6.96817i	−1.21219	−	0.393864i	−0.844232	+	0.535979i	$0.819943\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.954767	+	1.31412i	−0.0536251	+	0.0738086i	−0.834987	−	0.550269i	$-0.814525\pi$
$317$	−0.954767	+	1.31412i	−0.0536251	+	0.0738086i	0.781362	+	0.624078i	$0.214525\pi$
$318$		0			0
$319$	−17.4504	−	12.6785i	−0.977037	−	0.709859i
$320$		0			0
$321$	6.26189	−	4.54953i	0.349505	−	0.253930i
$322$		0			0
$323$	17.3913	−	5.65078i	0.967679	−	0.314418i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.86326	+	3.20477i	−0.545440	+	0.177224i
$328$		0			0
$329$	27.8433	−	20.2293i	1.53505	−	1.11528i
$330$		0			0
$331$	7.29178	+	5.29779i	0.400793	+	0.291193i	0.769864	−	0.638208i	$-0.220324\pi$
$331$	7.29178	+	5.29779i	0.400793	+	0.291193i	−0.369071	+	0.929401i	$0.620324\pi$
$332$		0			0
$333$	−4.82493	+	6.64095i	−0.264405	+	0.363922i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−25.6482	−	8.33361i	−1.39715	−	0.453961i	−0.488880	−	0.872351i	$-0.662594\pi$
$337$	−25.6482	−	8.33361i	−1.39715	−	0.453961i	−0.908267	+	0.418390i	$0.862594\pi$
$338$		0			0
$339$	3.16009	+	9.72574i	0.171632	+	0.528230i
$340$		0			0
$341$	−0.271197	+	0.834657i	−0.0146861	+	0.0451992i
$342$		0			0
$343$			24.2660i			1.31024i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.4263	−	21.2325i	−0.828127	−	1.13982i	−0.988269	−	0.152725i	$-0.951195\pi$
$347$	−15.4263	−	21.2325i	−0.828127	−	1.13982i	0.160142	−	0.987094i	$-0.448805\pi$
$348$		0			0
$349$	−18.2310			−0.975885			−0.487943	−	0.872876i	$-0.662252\pi$
$349$	−18.2310			−0.975885			−0.487943	+	0.872876i	$0.662252\pi$
$350$		0			0
$351$	−5.74778			−0.306794
$352$		0			0
$353$	−2.61542	−	3.59982i	−0.139205	−	0.191599i	0.733723	−	0.679449i	$-0.237781\pi$
$353$	−2.61542	−	3.59982i	−0.139205	−	0.191599i	−0.872927	+	0.487850i	$0.837781\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	29.0107i		−	1.53541i
$358$		0			0
$359$	9.98964	−	30.7449i	0.527233	−	1.62266i	−0.232625	−	0.972567i	$-0.574731\pi$
$359$	9.98964	−	30.7449i	0.527233	−	1.62266i	0.759858	−	0.650089i	$-0.225269\pi$
$360$		0			0
$361$	−3.47769	−	10.7032i	−0.183036	−	0.563328i
$362$		0			0
$363$	8.38699	+	2.72510i	0.440203	+	0.143031i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.37390	−	4.64378i	0.176116	−	0.242403i	−0.711829	−	0.702353i	$-0.752133\pi$
$367$	3.37390	−	4.64378i	0.176116	−	0.242403i	0.887945	+	0.459950i	$0.152133\pi$
$368$		0			0
$369$	6.35066	+	4.61402i	0.330602	+	0.240196i
$370$		0			0
$371$	1.12685	−	0.818702i	0.0585030	−	0.0425049i
$372$		0			0
$373$	−0.990868	+	0.321953i	−0.0513052	+	0.0166701i	−0.334557	−	0.942375i	$-0.608587\pi$
$373$	−0.990868	+	0.321953i	−0.0513052	+	0.0166701i	0.283252	+	0.959046i	$0.408587\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	26.4861	−	8.60587i	1.36411	−	0.443225i
$378$		0			0
$379$	−3.84230	+	2.79159i	−0.197366	+	0.143395i	−0.682079	−	0.731279i	$-0.738924\pi$
$379$	−3.84230	+	2.79159i	−0.197366	+	0.143395i	0.484713	+	0.874673i	$0.338924\pi$
$380$		0			0
$381$	9.15217	+	6.64944i	0.468880	+	0.340661i
$382$		0			0
$383$	6.47739	−	8.91536i	0.330979	−	0.455553i	−0.610801	−	0.791784i	$-0.709152\pi$
$383$	6.47739	−	8.91536i	0.330979	−	0.455553i	0.941780	+	0.336231i	$0.109152\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.392588	+	0.127560i	0.0199564	+	0.00648422i
$388$		0			0
$389$	10.2628	+	31.5856i	0.520344	+	1.60145i	0.773344	+	0.633987i	$0.218583\pi$
$389$	10.2628	+	31.5856i	0.520344	+	1.60145i	−0.253000	+	0.967466i	$0.581417\pi$
$390$		0			0
$391$	2.66981	−	8.21682i	0.135018	−	0.415542i
$392$		0			0
$393$		−	9.45365i		−	0.476873i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.61299	+	2.22008i	0.0809534	+	0.111423i	0.847573	−	0.530678i	$-0.178063\pi$
$397$	1.61299	+	2.22008i	0.0809534	+	0.111423i	−0.766620	+	0.642101i	$0.778063\pi$
$398$		0			0
$399$	12.2887			0.615207
$400$		0			0
$401$	−2.11503			−0.105619			−0.0528097	−	0.998605i	$-0.516818\pi$
$401$	−2.11503			−0.105619			−0.0528097	+	0.998605i	$0.516818\pi$
$402$		0			0
$403$	−0.666015	−	0.916691i	−0.0331766	−	0.0456636i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			36.5434i			1.81139i
$408$		0			0
$409$	2.03102	−	6.25083i	0.100427	−	0.309084i	−0.888203	−	0.459452i	$-0.848046\pi$
$409$	2.03102	−	6.25083i	0.100427	−	0.309084i	0.988630	+	0.150368i	$0.0480459\pi$
$410$		0			0
$411$	2.59891	+	7.99861i	0.128195	+	0.394542i
$412$		0			0
$413$	10.5781	+	3.43703i	0.520514	+	0.169125i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.94855	+	9.56385i	−0.340272	+	0.468344i
$418$		0			0
$419$	28.5125	+	20.7155i	1.39293	+	1.01202i	0.995537	+	0.0943704i	$0.0300838\pi$
$419$	28.5125	+	20.7155i	1.39293	+	1.01202i	0.397389	+	0.917650i	$0.369916\pi$
$420$		0			0
$421$	−5.07520	+	3.68735i	−0.247350	+	0.179710i	−0.704552	−	0.709653i	$-0.748852\pi$
$421$	−5.07520	+	3.68735i	−0.247350	+	0.179710i	0.457201	+	0.889363i	$0.348852\pi$
$422$		0			0
$423$	−7.41309	+	2.40866i	−0.360437	+	0.117113i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	39.1842	−	12.7317i	1.89626	−	0.616131i
$428$		0			0
$429$	−20.7011	+	15.0403i	−0.999461	+	0.726151i
$430$		0			0
$431$	11.0609	+	8.03624i	0.532787	+	0.387092i	0.821399	−	0.570354i	$-0.193194\pi$
$431$	11.0609	+	8.03624i	0.532787	+	0.387092i	−0.288612	+	0.957446i	$0.593194\pi$
$432$		0			0
$433$	−3.98412	+	5.48367i	−0.191465	+	0.263529i	−0.893947	−	0.448173i	$-0.852075\pi$
$433$	−3.98412	+	5.48367i	−0.191465	+	0.263529i	0.702482	+	0.711701i	$0.252075\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.48059	+	1.13091i	0.166499	+	0.0540988i
$438$		0			0
$439$	5.23618	+	16.1153i	0.249909	+	0.769142i	0.994790	+	0.101944i	$0.0325063\pi$
$439$	5.23618	+	16.1153i	0.249909	+	0.769142i	−0.744881	+	0.667197i	$0.767494\pi$
$440$		0			0
$441$	3.86140	−	11.8842i	0.183876	−	0.565913i
$442$		0			0
$443$			23.8927i			1.13517i	0.823313	+	0.567587i	$0.192123\pi$
$443$			23.8927i			1.13517i	−0.823313	+	0.567587i	$0.807877\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.25139	+	8.60430i	0.295681	+	0.406969i
$448$		0			0
$449$	−6.39281			−0.301695			−0.150848	−	0.988557i	$-0.548200\pi$
$449$	−6.39281			−0.301695			−0.150848	+	0.988557i	$0.548200\pi$
$450$		0			0
$451$	34.9460			1.64554
$452$		0			0
$453$	−2.59599	−	3.57308i	−0.121970	−	0.167878i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			5.89482i			0.275748i	0.990450	+	0.137874i	$0.0440269\pi$
$457$			5.89482i			0.275748i	−0.990450	+	0.137874i	$0.955973\pi$
$458$		0			0
$459$	−2.03035	+	6.24878i	−0.0947687	+	0.291668i
$460$		0			0
$461$	−7.60801	−	23.4151i	−0.354340	−	1.09055i	−0.956391	−	0.292090i	$-0.905649\pi$
$461$	−7.60801	−	23.4151i	−0.354340	−	1.09055i	0.602050	−	0.798458i	$-0.294351\pi$
$462$		0			0
$463$	28.3995	+	9.22757i	1.31984	+	0.428842i	0.882440	−	0.470426i	$-0.155900\pi$
$463$	28.3995	+	9.22757i	1.31984	+	0.428842i	0.437399	+	0.899267i	$0.355900\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.3714	+	21.1569i	−0.711301	+	0.979022i	0.288467	+	0.957490i	$0.406855\pi$
$467$	−15.3714	+	21.1569i	−0.711301	+	0.979022i	−0.999768	+	0.0215325i	$0.993145\pi$
$468$		0			0
$469$	42.6716	+	31.0028i	1.97039	+	1.43157i
$470$		0			0
$471$	−10.9451	+	7.95207i	−0.504323	+	0.366412i
$472$		0			0
$473$	1.74773	−	0.567871i	0.0803606	−	0.0261108i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.300015	+	0.0974809i	−0.0137368	+	0.00446334i
$478$		0			0
$479$	1.25147	−	0.909247i	0.0571812	−	0.0415446i	−0.558827	−	0.829284i	$-0.688749\pi$
$479$	1.25147	−	0.909247i	0.0571812	−	0.0415446i	0.616009	+	0.787739i	$0.288749\pi$
$480$		0			0
$481$	−38.1707	−	27.7326i	−1.74043	−	1.26450i
$482$		0			0
$483$	3.41269	−	4.69717i	0.155283	−	0.213729i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−11.8681	−	3.85619i	−0.537797	−	0.174741i	0.0275101	−	0.999622i	$-0.491242\pi$
$487$	−11.8681	−	3.85619i	−0.537797	−	0.174741i	−0.565307	+	0.824881i	$0.691242\pi$
$488$		0			0
$489$	−4.49876	−	13.8458i	−0.203441	−	0.626126i
$490$		0			0
$491$	−5.46864	+	16.8307i	−0.246796	+	0.759561i	0.748540	+	0.663090i	$0.230755\pi$
$491$	−5.46864	+	16.8307i	−0.246796	+	0.759561i	−0.995336	+	0.0964706i	$0.969245\pi$
$492$		0			0
$493$		−	31.8347i		−	1.43376i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.32165	+	1.81910i	0.0592843	+	0.0815978i
$498$		0			0
$499$	30.9281			1.38453			0.692267	−	0.721642i	$-0.256612\pi$
$499$	30.9281			1.38453			0.692267	+	0.721642i	$0.256612\pi$
$500$		0			0
$501$	−9.96824			−0.445348
$502$		0			0
$503$	−18.5467	−	25.5273i	−0.826956	−	1.13821i	−0.988482	−	0.151338i	$-0.951642\pi$
$503$	−18.5467	−	25.5273i	−0.826956	−	1.13821i	0.161526	−	0.986868i	$-0.448358\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	20.0370i		−	0.889873i
$508$		0			0
$509$	2.23276	−	6.87172i	0.0989652	−	0.304583i	−0.889302	−	0.457321i	$-0.848809\pi$
$509$	2.23276	−	6.87172i	0.0989652	−	0.304583i	0.988267	+	0.152738i	$0.0488090\pi$
$510$		0			0
$511$	21.5183	+	66.2264i	0.951912	+	2.92968i
$512$		0			0
$513$	−2.64694	−	0.860042i	−0.116865	−	0.0379718i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−20.3962	+	28.0729i	−0.897022	+	1.23464i
$518$		0			0
$519$	−8.79806	−	6.39217i	−0.386192	−	0.280585i
$520$		0			0
$521$	7.67413	−	5.57558i	0.336210	−	0.244271i	−0.406851	−	0.913494i	$-0.633373\pi$
$521$	7.67413	−	5.57558i	0.336210	−	0.244271i	0.743061	+	0.669224i	$0.233373\pi$
$522$		0			0
$523$	19.3589	−	6.29007i	0.846504	−	0.275046i	0.146523	−	0.989207i	$-0.453192\pi$
$523$	19.3589	−	6.29007i	0.846504	−	0.275046i	0.699981	+	0.714162i	$0.253192\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.23186	+	0.400255i	−0.0536606	+	0.0174354i
$528$		0			0
$529$	−17.2085	+	12.5027i	−0.748197	+	0.543597i
$530$		0			0
$531$	−2.03793	−	1.48064i	−0.0884385	−	0.0642544i
$532$		0			0
$533$	−26.5204	+	36.5022i	−1.14873	+	1.58108i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	23.9419	+	7.77918i	1.03317	+	0.335697i
$538$		0			0
$539$	−17.1902	−	52.9061i	−0.740435	−	2.27883i
$540$		0			0
$541$	9.54086	−	29.3638i	0.410194	−	1.26245i	−0.506286	−	0.862366i	$-0.668982\pi$
$541$	9.54086	−	29.3638i	0.410194	−	1.26245i	0.916480	−	0.400081i	$-0.131018\pi$
$542$		0			0
$543$		−	7.59173i		−	0.325792i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−9.01637	−	12.4100i	−0.385512	−	0.530612i	0.571522	−	0.820587i	$-0.306353\pi$
$547$	−9.01637	−	12.4100i	−0.385512	−	0.530612i	−0.957034	+	0.289975i	$0.906353\pi$
$548$		0			0
$549$	−9.33114			−0.398243
$550$		0			0
$551$	13.4850			0.574478
$552$		0			0
$553$	8.90587	+	12.2579i	0.378716	+	0.521258i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	28.6722i		−	1.21488i	−0.794365	−	0.607441i	$-0.792196\pi$
$557$		−	28.6722i		−	1.21488i	0.794365	−	0.607441i	$-0.207804\pi$
$558$		0			0
$559$	−0.733185	+	2.25651i	−0.0310104	+	0.0954403i
$560$		0			0
$561$	9.03874	+	27.8184i	0.381616	+	1.17449i
$562$		0			0
$563$	6.99026	+	2.27127i	0.294604	+	0.0957227i	0.452590	−	0.891719i	$-0.350500\pi$
$563$	6.99026	+	2.27127i	0.294604	+	0.0957227i	−0.157986	+	0.987441i	$0.550500\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.59531	+	3.57213i	−0.108993	+	0.150016i
$568$		0			0
$569$	−25.1830	−	18.2965i	−1.05572	−	0.767029i	−0.0824322	−	0.996597i	$-0.526269\pi$
$569$	−25.1830	−	18.2965i	−1.05572	−	0.767029i	−0.973293	+	0.229568i	$0.926269\pi$
$570$		0			0
$571$	−10.5055	+	7.63268i	−0.439641	+	0.319418i	−0.785492	−	0.618872i	$-0.787590\pi$
$571$	−10.5055	+	7.63268i	−0.439641	+	0.319418i	0.345851	+	0.938289i	$0.387590\pi$
$572$		0			0
$573$	0.0115012	−	0.00373697i	0.000480470	−	0.000156114i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−20.7231	+	6.73333i	−0.862712	+	0.280312i	−0.706761	−	0.707453i	$-0.749844\pi$
$577$	−20.7231	+	6.73333i	−0.862712	+	0.280312i	−0.155951	+	0.987765i	$0.549844\pi$
$578$		0			0
$579$	10.3426	−	7.51430i	0.429822	−	0.312284i
$580$		0			0
$581$	19.1879	+	13.9408i	0.796048	+	0.578363i
$582$		0			0
$583$	−0.825453	+	1.13614i	−0.0341868	+	0.0470541i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	25.3208	+	8.22724i	1.04510	+	0.339575i	0.780745	−	0.624850i	$-0.214840\pi$
$587$	25.3208	+	8.22724i	1.04510	+	0.339575i	0.264358	+	0.964425i	$0.414840\pi$
$588$		0			0
$589$	−0.169545	−	0.521806i	−0.00698598	−	0.0215006i
$590$		0			0
$591$	3.04859	−	9.38261i	0.125402	−	0.385949i
$592$		0			0
$593$		−	5.23169i		−	0.214840i	−0.994214	−	0.107420i	$-0.965741\pi$
$593$		−	5.23169i		−	0.214840i	0.994214	−	0.107420i	$-0.0342589\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.173773	−	0.239178i	−0.00711204	−	0.00978889i
$598$		0			0
$599$	−39.5405			−1.61558			−0.807790	−	0.589471i	$-0.799336\pi$
$599$	−39.5405			−1.61558			−0.807790	+	0.589471i	$0.799336\pi$
$600$		0			0
$601$	−45.5789			−1.85920			−0.929602	−	0.368565i	$-0.879849\pi$
$601$	−45.5789			−1.85920			−0.929602	+	0.368565i	$0.879849\pi$
$602$		0			0
$603$	−7.02151	−	9.66428i	−0.285938	−	0.393560i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	18.6524i		−	0.757078i	−0.925585	−	0.378539i	$-0.876427\pi$
$607$		−	18.6524i		−	0.757078i	0.925585	−	0.378539i	$-0.123573\pi$
$608$		0			0
$609$	6.61096	−	20.3464i	0.267890	−	0.824480i
$610$		0			0
$611$	−13.8444	−	42.6088i	−0.560086	−	1.72377i
$612$		0			0
$613$	−10.1837	−	3.30887i	−0.411314	−	0.133644i	0.0960485	−	0.995377i	$-0.469380\pi$
$613$	−10.1837	−	3.30887i	−0.411314	−	0.133644i	−0.507363	+	0.861733i	$0.669380\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.83565	+	13.5376i	−0.395968	+	0.545004i	−0.959726	−	0.280936i	$-0.909355\pi$
$617$	−9.83565	+	13.5376i	−0.395968	+	0.545004i	0.563758	+	0.825940i	$0.309355\pi$
$618$		0			0
$619$	18.5531	+	13.4796i	0.745711	+	0.541791i	0.894495	−	0.447079i	$-0.147536\pi$
$619$	18.5531	+	13.4796i	0.745711	+	0.541791i	−0.148783	+	0.988870i	$0.547536\pi$
$620$		0			0
$621$	−1.06382	+	0.772907i	−0.0426894	+	0.0310157i
$622$		0			0
$623$	−47.6417	+	15.4797i	−1.90872	+	0.620182i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−11.7837	+	3.82874i	−0.470594	+	0.152905i
$628$		0			0
$629$	−43.6334	+	31.7015i	−1.73978	+	1.26402i
$630$		0			0
$631$	−11.7443	−	8.53273i	−0.467533	−	0.339683i	0.328946	−	0.944349i	$-0.393307\pi$
$631$	−11.7443	−	8.53273i	−0.467533	−	0.339683i	−0.796479	+	0.604666i	$0.793307\pi$
$632$		0			0
$633$	−7.43414	+	10.2322i	−0.295481	+	0.406694i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	68.3076	+	22.1945i	2.70645	+	0.879377i
$638$		0			0
$639$	−0.157366	−	0.484323i	−0.00622531	−	0.0191595i
$640$		0			0
$641$	−9.81208	+	30.1985i	−0.387554	+	1.19277i	0.547057	+	0.837095i	$0.315748\pi$
$641$	−9.81208	+	30.1985i	−0.387554	+	1.19277i	−0.934611	+	0.355672i	$0.884252\pi$
$642$		0			0
$643$			3.63816i			0.143475i	0.997424	+	0.0717376i	$0.0228544\pi$
$643$			3.63816i			0.143475i	−0.997424	+	0.0717376i	$0.977146\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.60932	−	9.09695i	−0.259839	−	0.357638i	0.659088	−	0.752066i	$-0.270943\pi$
$647$	−6.60932	−	9.09695i	−0.259839	−	0.357638i	−0.918927	+	0.394428i	$0.870943\pi$
$648$		0			0
$649$	−11.2142			−0.440195
$650$		0			0
$651$	−0.870433			−0.0341150
$652$		0			0
$653$	1.18866	+	1.63604i	0.0465157	+	0.0640233i	0.831641	−	0.555313i	$-0.187402\pi$
$653$	1.18866	+	1.63604i	0.0465157	+	0.0640233i	−0.785126	+	0.619337i	$0.787402\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	15.7708i		−	0.615279i
$658$		0			0
$659$	0.245610	−	0.755909i	0.00956760	−	0.0294460i	−0.946159	−	0.323703i	$-0.895072\pi$
$659$	0.245610	−	0.755909i	0.00956760	−	0.0294460i	0.955726	+	0.294257i	$0.0950721\pi$
$660$		0			0
$661$	12.6628	+	38.9722i	0.492527	+	1.51584i	0.820776	+	0.571250i	$0.193541\pi$
$661$	12.6628	+	38.9722i	0.492527	+	1.51584i	−0.328249	+	0.944591i	$0.606459\pi$
$662$		0			0
$663$	−35.9166	−	11.6700i	−1.39489	−	0.453226i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.74489	−	5.15440i	0.145003	−	0.199579i
$668$		0			0
$669$	4.23909	+	3.07988i	0.163893	+	0.119075i
$670$		0			0
$671$	−33.6069	+	24.4169i	−1.29738	+	0.942602i
$672$		0			0
$673$	33.3834	−	10.8469i	1.28683	−	0.418118i	0.415852	−	0.909432i	$-0.363483\pi$
$673$	33.3834	−	10.8469i	1.28683	−	0.418118i	0.870982	+	0.491314i	$0.163483\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	36.5079	−	11.8621i	1.40311	−	0.455899i	0.492916	−	0.870077i	$-0.335931\pi$
$677$	36.5079	−	11.8621i	1.40311	−	0.455899i	0.910196	+	0.414178i	$0.135931\pi$
$678$		0			0
$679$	−18.1450	+	13.1831i	−0.696342	+	0.505922i
$680$		0			0
$681$	−6.28523	−	4.56649i	−0.240850	−	0.174988i
$682$		0			0
$683$	4.91673	−	6.76730i	0.188134	−	0.258944i	−0.704523	−	0.709681i	$-0.748839\pi$
$683$	4.91673	−	6.76730i	0.188134	−	0.258944i	0.892657	+	0.450738i	$0.148839\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.69866	+	1.85161i	0.217417	+	0.0706432i
$688$		0			0
$689$	−0.560299	−	1.72442i	−0.0213457	−	0.0656953i
$690$		0			0
$691$	1.80183	−	5.54547i	0.0685450	−	0.210960i	−0.910917	−	0.412590i	$-0.864624\pi$
$691$	1.80183	−	5.54547i	0.0685450	−	0.210960i	0.979462	+	0.201631i	$0.0646241\pi$
$692$		0			0
$693$			19.6565i			0.746689i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	30.3158	+	41.7261i	1.14829	+	1.58049i
$698$		0			0
$699$	−14.8631			−0.562174
$700$		0			0
$701$	50.6649			1.91359			0.956793	−	0.290770i	$-0.0939114\pi$
$701$	50.6649			1.91359			0.956793	+	0.290770i	$0.0939114\pi$
$702$		0			0
$703$	−13.4285	−	18.4828i	−0.506467	−	0.697091i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			49.3907i			1.85753i
$708$		0			0
$709$	3.00734	−	9.25565i	0.112943	−	0.347603i	−0.878569	−	0.477615i	$-0.841501\pi$
$709$	3.00734	−	9.25565i	0.112943	−	0.347603i	0.991512	+	0.130012i	$0.0415015\pi$
$710$		0			0
$711$	−1.06040	−	3.26358i	−0.0397681	−	0.122394i
$712$		0			0
$713$	−0.246536	−	0.0801044i	−0.00923285	−	0.00299993i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.4615	−	17.1518i	0.465383	−	0.640545i
$718$		0			0
$719$	15.1579	+	11.0129i	0.565294	+	0.410710i	0.833393	−	0.552681i	$-0.186395\pi$
$719$	15.1579	+	11.0129i	0.565294	+	0.410710i	−0.268099	+	0.963391i	$0.586395\pi$
$720$		0			0
$721$	11.2368	−	8.16399i	0.418479	−	0.304043i
$722$		0			0
$723$	−15.2703	+	4.96162i	−0.567909	+	0.184525i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−36.1247	+	11.7376i	−1.33979	+	0.435324i	−0.889246	−	0.457430i	$-0.848770\pi$
$727$	−36.1247	+	11.7376i	−1.33979	+	0.435324i	−0.450544	+	0.892754i	$0.648770\pi$
$728$		0			0
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	2.19421	+	1.59418i	0.0811557	+	0.0589630i
$732$		0			0
$733$	−15.4951	+	21.3271i	−0.572323	+	0.787735i	−0.992828	−	0.119555i	$-0.961853\pi$
$733$	−15.4951	+	21.3271i	−0.572323	+	0.787735i	0.420505	+	0.907290i	$0.361853\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−50.5772	−	16.4335i	−1.86303	−	0.605337i
$738$		0			0
$739$	10.2081	+	31.4174i	0.375513	+	1.15571i	0.943132	+	0.332418i	$0.107864\pi$
$739$	10.2081	+	31.4174i	0.375513	+	1.15571i	−0.567619	+	0.823291i	$0.692136\pi$
$740$		0			0
$741$	4.94333	−	15.2140i	0.181598	−	0.558901i
$742$		0			0
$743$			40.2017i			1.47486i	0.675425	+	0.737428i	$0.263960\pi$
$743$			40.2017i			1.47486i	−0.675425	+	0.737428i	$0.736040\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.15732	−	4.34568i	−0.115520	−	0.159000i
$748$		0			0
$749$	34.1758			1.24876
$750$		0			0
$751$	30.5937			1.11638			0.558190	−	0.829713i	$-0.311496\pi$
$751$	30.5937			1.11638			0.558190	+	0.829713i	$0.311496\pi$
$752$		0			0
$753$	14.1875	+	19.5274i	0.517020	+	0.711617i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			24.4003i			0.886845i	0.896313	+	0.443422i	$0.146236\pi$
$757$			24.4003i			0.886845i	−0.896313	+	0.443422i	$0.853764\pi$
$758$		0			0
$759$	−1.80895	+	5.56739i	−0.0656609	+	0.202083i
$760$		0			0
$761$	8.75574	+	26.9474i	0.317395	+	0.976842i	0.974757	+	0.223267i	$0.0716723\pi$
$761$	8.75574	+	26.9474i	0.317395	+	0.976842i	−0.657362	+	0.753575i	$0.728328\pi$
$762$		0			0
$763$	−43.5502	−	14.1503i	−1.57662	−	0.512276i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.51040	−	11.7136i	0.307293	−	0.422952i
$768$		0			0
$769$	−33.2679	−	24.1706i	−1.19967	−	0.871613i	−0.205420	−	0.978674i	$-0.565856\pi$
$769$	−33.2679	−	24.1706i	−1.19967	−	0.871613i	−0.994252	+	0.107061i	$0.965856\pi$
$770$		0			0
$771$	−3.42166	+	2.48598i	−0.123228	+	0.0895304i
$772$		0			0
$773$	−4.58131	+	1.48856i	−0.164778	+	0.0535397i	−0.390244	−	0.920711i	$-0.627609\pi$
$773$	−4.58131	+	1.48856i	−0.164778	+	0.0535397i	0.225466	+	0.974251i	$0.427609\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−34.4706	+	11.2002i	−1.23663	+	0.401804i
$778$		0			0
$779$	−17.6749	+	12.8415i	−0.633268	+	0.460096i
$780$		0			0
$781$	−1.83410	−	1.33255i	−0.0656293	−	0.0476825i
$782$		0			0
$783$	−2.84794	+	3.91985i	−0.101777	+	0.140084i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	38.3447	+	12.4590i	1.36684	+	0.444114i	0.898321	−	0.439339i	$-0.144787\pi$
$787$	38.3447	+	12.4590i	1.36684	+	0.444114i	0.468520	+	0.883453i	$0.344787\pi$
$788$		0			0
$789$	−2.59198	−	7.97729i	−0.0922769	−	0.283999i
$790$		0			0
$791$	−13.9530	+	42.9430i	−0.496113	+	1.52688i
$792$		0			0
$793$		−	53.6333i		−	1.90457i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.7487	−	24.4289i	−0.628690	−	0.865318i	0.369259	−	0.929326i	$-0.379611\pi$
$797$	−17.7487	−	24.4289i	−0.628690	−	0.865318i	−0.997949	+	0.0640088i	$0.979611\pi$
$798$		0			0
$799$	−51.2132			−1.81179
$800$		0			0
$801$	11.3452			0.400862
$802$		0			0
$803$	−41.2677	−	56.8001i	−1.45630	−	2.00443i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			5.53526i			0.194850i
$808$		0			0
$809$	−3.36218	+	10.3477i	−0.118208	+	0.363807i	−0.992603	−	0.121409i	$-0.961259\pi$
$809$	−3.36218	+	10.3477i	−0.118208	+	0.363807i	0.874395	+	0.485216i	$0.161259\pi$
$810$		0			0
$811$	−14.6035	−	44.9451i	−0.512799	−	1.57823i	−0.787250	−	0.616633i	$-0.788496\pi$
$811$	−14.6035	−	44.9451i	−0.512799	−	1.57823i	0.274451	−	0.961601i	$-0.411504\pi$
$812$		0			0
$813$	15.0740	+	4.89783i	0.528667	+	0.171774i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.675285	+	0.929450i	−0.0236252	+	0.0325173i
$818$		0			0
$819$	−20.5318	−	14.9173i	−0.717440	−	0.521251i
$820$		0			0
$821$	−20.1200	+	14.6180i	−0.702191	+	0.510172i	−0.880645	−	0.473777i	$-0.842890\pi$
$821$	−20.1200	+	14.6180i	−0.702191	+	0.510172i	0.178454	+	0.983948i	$0.442890\pi$
$822$		0			0
$823$	21.6451	−	7.03293i	0.754502	−	0.245152i	0.0935845	−	0.995611i	$-0.470167\pi$
$823$	21.6451	−	7.03293i	0.754502	−	0.245152i	0.660917	+	0.750459i	$0.270167\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	44.5530	−	14.4761i	1.54926	−	0.503385i	0.595346	−	0.803469i	$-0.297015\pi$
$827$	44.5530	−	14.4761i	1.54926	−	0.503385i	0.953913	+	0.300084i	$0.0970148\pi$
$828$		0			0
$829$	−11.1652	+	8.11202i	−0.387785	+	0.281742i	−0.764547	−	0.644568i	$-0.777037\pi$
$829$	−11.1652	+	8.11202i	−0.387785	+	0.281742i	0.376762	+	0.926310i	$0.377037\pi$
$830$		0			0
$831$	7.03232	+	5.10928i	0.243949	+	0.177239i
$832$		0			0
$833$	48.2581	−	66.4215i	1.67204	−	2.30137i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.187487	+	0.0609183i	0.00648051	+	0.00210564i
$838$		0			0
$839$	3.27210	+	10.0705i	0.112966	+	0.347672i	0.991517	−	0.129975i	$-0.0414897\pi$
$839$	3.27210	+	10.0705i	0.112966	+	0.347672i	−0.878552	+	0.477647i	$0.841490\pi$
$840$		0			0
$841$	−1.70701	+	5.25362i	−0.0588623	+	0.181159i
$842$		0			0
$843$			10.7800i			0.371283i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	22.8870	+	31.5012i	0.786406	+	1.08239i
$848$		0			0
$849$	−9.84520			−0.337886
$850$		0			0
$851$	−10.7940			−0.370012
$852$		0			0
$853$	13.3131	+	18.3240i	0.455834	+	0.627401i	0.973638	−	0.228098i	$-0.0732506\pi$
$853$	13.3131	+	18.3240i	0.455834	+	0.627401i	−0.517805	+	0.855499i	$0.673251\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			39.4749i			1.34844i	0.738533	+	0.674218i	$0.235519\pi$
$857$			39.4749i			1.34844i	−0.738533	+	0.674218i	$0.764481\pi$
$858$		0			0
$859$	−13.7012	+	42.1679i	−0.467478	+	1.43875i	0.388361	+	0.921507i	$0.373041\pi$
$859$	−13.7012	+	42.1679i	−0.467478	+	1.43875i	−0.855839	+	0.517242i	$0.826959\pi$
$860$		0			0
$861$	10.7106	+	32.9638i	0.365016	+	1.12340i
$862$		0			0
$863$	−4.78917	−	1.55610i	−0.163025	−	0.0529701i	0.226367	−	0.974042i	$-0.427315\pi$
$863$	−4.78917	−	1.55610i	−0.163025	−	0.0529701i	−0.389393	+	0.921072i	$0.627315\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.3821	+	21.1716i	−0.522403	+	0.719026i
$868$		0			0
$869$	−12.3590	−	8.97931i	−0.419249	−	0.304602i
$870$		0			0
$871$	55.5481	−	40.3581i	1.88218	−	1.36748i
$872$		0			0
$873$	4.83099	−	1.56968i	0.163504	−	0.0531257i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	16.6380	−	5.40602i	0.561826	−	0.182548i	−0.0143164	−	0.999898i	$-0.504557\pi$
$877$	16.6380	−	5.40602i	0.561826	−	0.182548i	0.576143	+	0.817349i	$0.304557\pi$
$878$		0			0
$879$	7.91003	−	5.74697i	0.266799	−	0.193840i
$880$		0			0
$881$	43.8856	+	31.8848i	1.47855	+	1.07423i	0.978022	+	0.208503i	$0.0668590\pi$
$881$	43.8856	+	31.8848i	1.47855	+	1.07423i	0.500523	+	0.865723i	$0.333141\pi$
$882$		0			0
$883$	17.8419	−	24.5572i	0.600427	−	0.826416i	−0.395321	−	0.918543i	$-0.629367\pi$
$883$	17.8419	−	24.5572i	0.600427	−	0.826416i	0.995747	+	0.0921269i	$0.0293665\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−50.0705	−	16.2689i	−1.68120	−	0.546256i	−0.696058	−	0.717985i	$-0.745065\pi$
$887$	−50.0705	−	16.2689i	−1.68120	−	0.546256i	−0.985144	+	0.171729i	$0.945065\pi$
$888$		0			0
$889$	15.4354	+	47.5054i	0.517688	+	1.59328i
$890$		0			0
$891$	1.37568	−	4.23392i	0.0460872	−	0.141842i
$892$		0			0
$893$		−	21.6935i		−	0.725947i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−4.44250	−	6.11458i	−0.148331	−	0.204160i
$898$		0			0
$899$	−0.955163			−0.0318565
$900$		0			0
$901$	−2.07265			−0.0690500
$902$		0			0
$903$	1.07132	+	1.47455i	0.0356513	+	0.0490699i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	8.79799i		−	0.292133i	−0.989275	−	0.146066i	$-0.953339\pi$
$907$		−	8.79799i		−	0.292133i	0.989275	−	0.146066i	$-0.0466613\pi$
$908$		0			0
$909$	3.45667	−	10.6385i	0.114650	−	0.352858i
$910$		0			0
$911$	−9.73942	−	29.9749i	−0.322682	−	0.993112i	−0.972476	−	0.233002i	$-0.925145\pi$
$911$	−9.73942	−	29.9749i	−0.322682	−	0.993112i	0.649795	−	0.760110i	$-0.274855\pi$
$912$		0			0
$913$	−22.7427	−	7.38956i	−0.752675	−	0.244559i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.5351	−	33.7697i	0.810221	−	1.11517i
$918$		0			0
$919$	−27.0858	−	19.6790i	−0.893478	−	0.649150i	0.0433046	−	0.999062i	$-0.486211\pi$
$919$	−27.0858	−	19.6790i	−0.893478	−	0.649150i	−0.936782	+	0.349912i	$0.886211\pi$
$920$		0			0
$921$	−26.4792	+	19.2383i	−0.872520	+	0.633923i
$922$		0			0
$923$	2.78378	−	0.904506i	0.0916294	−	0.0297722i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−2.99171	+	0.972067i	−0.0982608	+	0.0319269i
$928$		0			0
$929$	−1.51966	+	1.10410i	−0.0498585	+	0.0362244i	−0.612435	−	0.790521i	$-0.709810\pi$
$929$	−1.51966	+	1.10410i	−0.0498585	+	0.0362244i	0.562577	+	0.826745i	$0.309810\pi$
$930$		0			0
$931$	28.1357	+	20.4418i	0.922110	+	0.669952i
$932$		0			0
$933$	−14.4739	+	19.9216i	−0.473855	+	0.652205i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.17621	+	0.707094i	0.0710937	+	0.0230997i	0.344348	−	0.938842i	$-0.388100\pi$
$937$	2.17621	+	0.707094i	0.0710937	+	0.0230997i	−0.273254	+	0.961942i	$0.588100\pi$
$938$		0			0
$939$	6.96817	+	21.4458i	0.227398	+	0.699858i
$940$		0			0
$941$	−18.5837	+	57.1947i	−0.605811	+	1.86449i	−0.114691	+	0.993401i	$0.536588\pi$
$941$	−18.5837	+	57.1947i	−0.605811	+	1.86449i	−0.491119	+	0.871092i	$0.663412\pi$
$942$		0			0
$943$			10.3221i			0.336135i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.4333	+	35.0060i	0.826472	+	1.13754i	0.988569	+	0.150766i	$0.0481740\pi$
$947$	25.4333	+	35.0060i	0.826472	+	1.13754i	−0.162098	+	0.986775i	$0.551826\pi$
$948$		0			0
$949$	90.6473			2.94253
$950$		0			0
$951$	1.62435			0.0526731
$952$		0			0
$953$	20.4875	+	28.1986i	0.663654	+	0.913441i	0.999595	−	0.0284419i	$-0.00905456\pi$
$953$	20.4875	+	28.1986i	0.663654	+	0.913441i	−0.335942	+	0.941883i	$0.609055\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			21.5699i			0.697257i
$958$		0			0
$959$	−11.4752	+	35.3171i	−0.370554	+	1.14045i
$960$		0			0
$961$	−9.56752	−	29.4458i	−0.308630	−	0.949864i
$962$		0			0
$963$	−7.36130	−	2.39183i	−0.237215	−	0.0770757i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	20.5577	−	28.2952i	0.661090	−	0.909912i	−0.338427	−	0.940993i	$-0.609895\pi$
$967$	20.5577	−	28.2952i	0.661090	−	0.909912i	0.999517	+	0.0310806i	$0.00989486\pi$
$968$		0			0
$969$	−14.7939	−	10.7484i	−0.475250	−	0.345289i
$970$		0			0
$971$	48.1194	−	34.9608i	1.54422	−	1.12194i	0.596607	−	0.802533i	$-0.296515\pi$
$971$	48.1194	−	34.9608i	1.54422	−	1.12194i	0.947616	−	0.319411i	$-0.103485\pi$
$972$		0			0
$973$	−49.6423	+	16.1297i	−1.59146	+	0.517096i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.6616	−	4.76386i	0.469067	−	0.152409i	−0.0649398	−	0.997889i	$-0.520686\pi$
$977$	14.6616	−	4.76386i	0.469067	−	0.152409i	0.534007	+	0.845480i	$0.320686\pi$
$978$		0			0
$979$	40.8606	−	29.6870i	1.30591	−	0.948800i
$980$		0			0
$981$	8.39019	+	6.09583i	0.267878	+	0.194625i
$982$		0			0
$983$	−34.5324	+	47.5297i	−1.10141	+	1.51596i	−0.267912	+	0.963443i	$0.586334\pi$
$983$	−34.5324	+	47.5297i	−1.10141	+	1.51596i	−0.833500	+	0.552520i	$0.813666\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−32.7318	−	10.6352i	−1.04186	−	0.338522i
$988$		0			0
$989$	0.167734	+	0.516233i	0.00533364	+	0.0164153i
$990$		0			0
$991$	0.529181	−	1.62865i	0.0168100	−	0.0517358i	−0.942300	−	0.334771i	$-0.891341\pi$
$991$	0.529181	−	1.62865i	0.0168100	−	0.0517358i	0.959110	+	0.283035i	$0.0913412\pi$
$992$		0			0
$993$		−	9.01314i		−	0.286023i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.93389	+	9.54368i	0.219598	+	0.302251i	0.904576	−	0.426313i	$-0.140188\pi$
$997$	6.93389	+	9.54368i	0.219598	+	0.302251i	−0.684977	+	0.728564i	$0.740188\pi$
$998$		0			0
$999$	8.20866			0.259711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.c.349.3		24
5.2	odd	4		1500.2.m.c.901.6		24
5.3	odd	4		1500.2.m.d.901.1		24
5.4	even	2		300.2.o.a.169.4	✓	24
15.14	odd	2		900.2.w.c.469.5		24
25.2	odd	20		7500.2.a.n.1.11		12
25.3	odd	20		1500.2.m.d.601.1		24
25.4	even	10	inner	1500.2.o.c.649.3		24
25.11	even	5		7500.2.d.g.1249.14		24
25.14	even	10		7500.2.d.g.1249.11		24
25.21	even	5		300.2.o.a.229.4	yes	24
25.22	odd	20		1500.2.m.c.601.6		24
25.23	odd	20		7500.2.a.m.1.2		12
75.71	odd	10		900.2.w.c.829.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.4	✓	24	5.4	even	2
300.2.o.a.229.4	yes	24	25.21	even	5
900.2.w.c.469.5		24	15.14	odd	2
900.2.w.c.829.5		24	75.71	odd	10
1500.2.m.c.601.6		24	25.22	odd	20
1500.2.m.c.901.6		24	5.2	odd	4
1500.2.m.d.601.1		24	25.3	odd	20
1500.2.m.d.901.1		24	5.3	odd	4
1500.2.o.c.349.3		24	1.1	even	1	trivial
1500.2.o.c.649.3		24	25.4	even	10	inner
7500.2.a.m.1.2		12	25.23	odd	20
7500.2.a.n.1.11		12	25.2	odd	20
7500.2.d.g.1249.11		24	25.14	even	10
7500.2.d.g.1249.14		24	25.11	even	5

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{3} -4.41540i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{3} -4.41540i q^{7} +(-0.309017 + 0.951057i) q^{9} +(1.37568 + 4.23392i) q^{11} +(-5.46646 - 1.77616i) q^{13} +(-3.86196 + 5.31553i) q^{17} +(-2.25162 - 1.63590i) q^{19} +(-3.57213 + 2.59531i) q^{21} +(-1.25059 + 0.406341i) q^{23} +(0.951057 - 0.309017i) q^{27} +(-3.91985 + 2.84794i) q^{29} +(0.159486 + 0.115873i) q^{31} +(2.61671 - 3.60159i) q^{33} +(7.80690 + 2.53662i) q^{37} +(1.77616 + 5.46646i) q^{39} +(2.42573 - 7.46564i) q^{41} -0.412792i q^{43} +(4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +6.57035 q^{51} +(0.185420 + 0.255208i) q^{53} +2.78315i q^{57} +(-0.778419 + 2.39573i) q^{59} +(2.88348 + 8.87444i) q^{61} +(4.19929 + 1.36443i) q^{63} +(-7.02151 + 9.66428i) q^{67} +(1.06382 + 0.772907i) q^{69} +(-0.411990 + 0.299328i) q^{71} +(-14.9990 + 4.87346i) q^{73} +(18.6945 - 6.07420i) q^{77} +(-2.77617 + 2.01700i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-3.15732 + 4.34568i) q^{83} +(4.60806 + 1.49725i) q^{87} +(-3.50585 - 10.7899i) q^{89} +(-7.84246 + 24.1366i) q^{91} -0.197136i q^{93} +(-2.98572 - 4.10948i) q^{97} -4.45181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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