LMFDB - Embedded newform 300.2.o.a.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(109,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, 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("300.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.o (of order $10$, degree $4$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	300.229
Dual form			300.2.o.a.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{3} +(-0.921600 + 2.03732i) q^{5} -4.41540i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{3} +(-0.921600 + 2.03732i) q^{5} -4.41540i q^{7} +(-0.309017 - 0.951057i) q^{9} +(1.37568 - 4.23392i) q^{11} +(5.46646 - 1.77616i) q^{13} +(1.10652 + 1.94309i) q^{15} +(3.86196 + 5.31553i) q^{17} +(-2.25162 + 1.63590i) q^{19} +(-3.57213 - 2.59531i) q^{21} +(1.25059 + 0.406341i) q^{23} +(-3.30131 - 3.75518i) q^{25} +(-0.951057 - 0.309017i) q^{27} +(-3.91985 - 2.84794i) q^{29} +(0.159486 - 0.115873i) q^{31} +(-2.61671 - 3.60159i) q^{33} +(8.99556 + 4.06923i) q^{35} +(-7.80690 + 2.53662i) q^{37} +(1.77616 - 5.46646i) q^{39} +(2.42573 + 7.46564i) q^{41} -0.412792i q^{43} +(2.22239 + 0.246929i) q^{45} +(-4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +6.57035 q^{51} +(-0.185420 + 0.255208i) q^{53} +(7.35800 + 6.70469i) q^{55} +2.78315i q^{57} +(-0.778419 - 2.39573i) q^{59} +(2.88348 - 8.87444i) q^{61} +(-4.19929 + 1.36443i) q^{63} +(-1.41929 + 12.7738i) q^{65} +(7.02151 + 9.66428i) q^{67} +(1.06382 - 0.772907i) q^{69} +(-0.411990 - 0.299328i) q^{71} +(14.9990 + 4.87346i) q^{73} +(-4.97846 + 0.463572i) q^{75} +(-18.6945 - 6.07420i) q^{77} +(-2.77617 - 2.01700i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(3.15732 + 4.34568i) q^{83} +(-14.3886 + 2.96923i) q^{85} +(-4.60806 + 1.49725i) q^{87} +(-3.50585 + 10.7899i) q^{89} +(-7.84246 - 24.1366i) q^{91} -0.197136i q^{93} +(-1.25774 - 6.09490i) q^{95} +(2.98572 - 4.10948i) q^{97} -4.45181 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^5 + 6 * q^9	$ 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{10}\right)$

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
$5$	−0.921600	+	2.03732i	−0.412152	+	0.911115i
$5$	−0.921600	+	2.03732i	−0.412152	+	0.911115i
$6$		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	−0.497659	−	0.867373i	$-0.665807\pi$
$11$	1.37568	−	4.23392i	0.414785	−	1.27658i	0.912443	−	0.409203i	$-0.134193\pi$
$12$		0			0
$13$	5.46646	−	1.77616i	1.51612	−	0.492619i	0.571452	−	0.820635i	$-0.306380\pi$
$13$	5.46646	−	1.77616i	1.51612	−	0.492619i	0.944672	+	0.328017i	$0.106380\pi$
$14$		0			0
$15$	1.10652	+	1.94309i	0.285702	+	0.501705i
$16$		0			0
$17$	3.86196	+	5.31553i	0.936662	+	1.28921i	0.957203	+	0.289416i	$0.0934611\pi$
$17$	3.86196	+	5.31553i	0.936662	+	1.28921i	−0.0205412	+	0.999789i	$0.506539\pi$
$18$		0			0
$19$	−2.25162	+	1.63590i	−0.516557	+	0.375301i	−0.815305	−	0.579031i	$-0.803431\pi$
$19$	−2.25162	+	1.63590i	−0.516557	+	0.375301i	0.298748	+	0.954332i	$0.403431\pi$
$20$		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	$-0.356224\pi$
$23$	1.25059	+	0.406341i	0.260766	+	0.0847280i	−0.175716	+	0.984441i	$0.556224\pi$
$24$		0			0
$25$	−3.30131	−	3.75518i	−0.660261	−	0.751036i
$26$		0			0
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$		0			0
$29$	−3.91985	−	2.84794i	−0.727899	−	0.528849i	0.160999	−	0.986954i	$-0.448528\pi$
$29$	−3.91985	−	2.84794i	−0.727899	−	0.528849i	−0.888898	+	0.458105i	$0.848528\pi$
$30$		0			0
$31$	0.159486	−	0.115873i	0.0286446	−	0.0208115i	−0.573371	−	0.819296i	$-0.694365\pi$
$31$	0.159486	−	0.115873i	0.0286446	−	0.0208115i	0.602015	+	0.798484i	$0.294365\pi$
$32$		0			0
$33$	−2.61671	−	3.60159i	−0.455510	−	0.626956i
$34$		0			0
$35$	8.99556	+	4.06923i	1.52053	+	0.687826i
$36$		0			0
$37$	−7.80690	+	2.53662i	−1.28345	+	0.417017i	−0.869793	−	0.493417i	$-0.835748\pi$
$37$	−7.80690	+	2.53662i	−1.28345	+	0.417017i	−0.413654	+	0.910434i	$0.635748\pi$
$38$		0			0
$39$	1.77616	−	5.46646i	0.284413	−	0.875335i
$40$		0			0
$41$	2.42573	+	7.46564i	0.378836	+	1.16594i	0.940854	+	0.338813i	$0.110025\pi$
$41$	2.42573	+	7.46564i	0.378836	+	1.16594i	−0.562018	+	0.827125i	$0.689975\pi$
$42$		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
$45$	2.22239	+	0.246929i	0.331295	+	0.0368100i
$46$		0			0
$47$	−4.58154	+	6.30595i	−0.668287	+	0.919818i	−0.999720	−	0.0236610i	$-0.992468\pi$
$47$	−4.58154	+	6.30595i	−0.668287	+	0.919818i	0.331433	+	0.943479i	$0.392468\pi$
$48$		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	$-0.806897\pi$
$53$	−0.185420	+	0.255208i	−0.0254694	+	0.0350556i	0.796092	+	0.605175i	$0.206897\pi$
$54$		0			0
$55$	7.35800	+	6.70469i	0.992153	+	0.904060i
$56$		0			0
$57$			2.78315i			0.368638i
$58$		0			0
$59$	−0.778419	−	2.39573i	−0.101342	−	0.311897i	0.887513	−	0.460783i	$-0.152431\pi$
$59$	−0.778419	−	2.39573i	−0.101342	−	0.311897i	−0.988854	+	0.148886i	$0.952431\pi$
$60$		0			0
$61$	2.88348	−	8.87444i	0.369192	−	1.13626i	−0.578123	−	0.815950i	$-0.696214\pi$
$61$	2.88348	−	8.87444i	0.369192	−	1.13626i	0.947314	−	0.320305i	$-0.103786\pi$
$62$		0			0
$63$	−4.19929	+	1.36443i	−0.529061	+	0.171902i
$64$		0			0
$65$	−1.41929	+	12.7738i	−0.176042	+	1.58440i
$66$		0			0
$67$	7.02151	+	9.66428i	0.857814	+	1.18068i	0.982086	+	0.188431i	$0.0603403\pi$
$67$	7.02151	+	9.66428i	0.857814	+	1.18068i	−0.124273	+	0.992248i	$0.539660\pi$
$68$		0			0
$69$	1.06382	−	0.772907i	0.128068	−	0.0930471i
$70$		0			0
$71$	−0.411990	−	0.299328i	−0.0488942	−	0.0355237i	0.563070	−	0.826409i	$-0.309620\pi$
$71$	−0.411990	−	0.299328i	−0.0488942	−	0.0355237i	−0.611964	+	0.790886i	$0.709620\pi$
$72$		0			0
$73$	14.9990	+	4.87346i	1.75549	+	0.570395i	0.996718	−	0.0809557i	$-0.0257972\pi$
$73$	14.9990	+	4.87346i	1.75549	+	0.570395i	0.758777	+	0.651351i	$0.225797\pi$
$74$		0			0
$75$	−4.97846	+	0.463572i	−0.574863	+	0.0535287i
$76$		0			0
$77$	−18.6945	−	6.07420i	−2.13043	−	0.692219i
$78$		0			0
$79$	−2.77617	−	2.01700i	−0.312343	−	0.226930i	0.420558	−	0.907266i	$-0.361834\pi$
$79$	−2.77617	−	2.01700i	−0.312343	−	0.226930i	−0.732901	+	0.680335i	$0.761834\pi$
$80$		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	$-0.104746\pi$
$83$	3.15732	+	4.34568i	0.346561	+	0.477000i	−0.599783	+	0.800163i	$0.704746\pi$
$84$		0			0
$85$	−14.3886	+	2.96923i	−1.56066	+	0.322058i
$86$		0			0
$87$	−4.60806	+	1.49725i	−0.494036	+	0.160522i
$88$		0			0
$89$	−3.50585	+	10.7899i	−0.371619	+	1.14373i	0.574112	+	0.818777i	$0.305347\pi$
$89$	−3.50585	+	10.7899i	−0.371619	+	1.14373i	−0.945731	+	0.324950i	$0.894653\pi$
$90$		0			0
$91$	−7.84246	−	24.1366i	−0.822114	−	2.53021i
$92$		0			0
$93$		−	0.197136i		−	0.0204420i
$94$		0			0
$95$	−1.25774	−	6.09490i	−0.129042	−	0.625324i
$96$		0			0
$97$	2.98572	−	4.10948i	0.303153	−	0.417255i	−0.630077	−	0.776532i	$-0.716977\pi$
$97$	2.98572	−	4.10948i	0.303153	−	0.417255i	0.933231	+	0.359277i	$0.116977\pi$
$98$		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	$-0.849530\pi$
$103$	−1.84898	+	2.54490i	−0.182185	+	0.250757i	0.708150	+	0.706062i	$0.249530\pi$
$104$		0			0
$105$	8.57954	−	4.88573i	0.837277	−	0.476798i
$106$		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	0.978938	+	0.204157i	$0.0654453\pi$
$109$	3.20477	+	9.86326i	0.306961	+	0.944729i	−0.671977	+	0.740572i	$0.734555\pi$
$110$		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	$-0.440273\pi$
$113$	9.72574	−	3.16009i	0.914921	−	0.297276i	0.728382	+	0.685172i	$0.240273\pi$
$114$		0			0
$115$	−1.98039	+	2.17336i	−0.184672	+	0.202667i
$116$		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
$125$	10.6930	−	3.26502i	0.956408	−	0.292032i
$126$		0			0
$127$	10.7590	+	3.49582i	0.954709	+	0.310204i	0.744628	−	0.667480i	$-0.232627\pi$
$127$	10.7590	+	3.49582i	0.954709	+	0.310204i	0.210081	+	0.977684i	$0.432627\pi$
$128$		0			0
$129$	−0.333956	−	0.242633i	−0.0294031	−	0.0213626i
$130$		0			0
$131$	7.64816	−	5.55671i	0.668223	−	0.485492i	−0.201207	−	0.979549i	$-0.564486\pi$
$131$	7.64816	−	5.55671i	0.668223	−	0.485492i	0.869430	+	0.494056i	$0.164486\pi$
$132$		0			0
$133$	7.22314	+	9.94180i	0.626326	+	0.862063i
$134$		0			0
$135$	1.50606	−	1.65281i	0.129621	−	0.142251i
$136$		0			0
$137$	7.99861	−	2.59891i	0.683367	−	0.222039i	0.0532983	−	0.998579i	$-0.483027\pi$
$137$	7.99861	−	2.59891i	0.683367	−	0.222039i	0.630069	+	0.776539i	$0.283027\pi$
$138$		0			0
$139$	−3.65307	+	11.2430i	−0.309849	+	0.953617i	0.667974	+	0.744185i	$0.267162\pi$
$139$	−3.65307	+	11.2430i	−0.309849	+	0.953617i	−0.977823	+	0.209433i	$0.932838\pi$
$140$		0			0
$141$	2.40866	+	7.41309i	0.202846	+	0.624295i
$142$		0			0
$143$		−	25.5880i		−	2.13978i
$144$		0			0
$145$	9.41469	−	5.36131i	0.781847	−	0.445233i
$146$		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
$155$	0.0890883	+	0.431713i	0.00715574	+	0.0346760i
$156$		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	$-0.793114\pi$
$163$	−13.8458	+	4.49876i	−1.08448	+	0.352370i	−0.288371	+	0.957519i	$0.593114\pi$
$164$		0			0
$165$	9.74913	−	2.01183i	0.758969	−	0.156621i
$166$		0			0
$167$	−5.85918	−	8.06448i	−0.453397	−	0.624048i	0.519726	−	0.854333i	$-0.326034\pi$
$167$	−5.85918	−	8.06448i	−0.453397	−	0.624048i	−0.973123	+	0.230285i	$0.926034\pi$
$168$		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	$-0.535661\pi$
$173$	−10.3427	−	3.36056i	−0.786344	−	0.255499i	−0.674547	+	0.738232i	$0.735661\pi$
$174$		0			0
$175$	−16.5806	+	14.5766i	−1.25338	+	1.10189i
$176$		0			0
$177$	−2.39573	−	0.778419i	−0.180074	−	0.0585096i
$178$		0			0
$179$	−20.3662	−	14.7969i	−1.52224	−	1.10597i	−0.960364	−	0.278749i	$-0.910080\pi$
$179$	−20.3662	−	14.7969i	−1.52224	−	1.10597i	−0.561875	−	0.827222i	$-0.689920\pi$
$180$		0			0
$181$	6.14184	−	4.46231i	0.456520	−	0.331681i	−0.335645	−	0.941989i	$-0.608954\pi$
$181$	6.14184	−	4.46231i	0.456520	−	0.331681i	0.792164	+	0.610308i	$0.208954\pi$
$182$		0			0
$183$	−5.48470	−	7.54905i	−0.405441	−	0.558042i
$184$		0			0
$185$	2.02696	−	18.2429i	0.149025	−	1.34124i
$186$		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	0.950921	−	0.309433i	$-0.100139\pi$
$191$	−0.00373697	−	0.0115012i	−0.000270398	−	0.000832198i	−0.951192	+	0.308601i	$0.900139\pi$
$192$		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
$195$	9.50000	+	8.65650i	0.680309	+	0.619905i
$196$		0			0
$197$	−5.79877	+	7.98132i	−0.413145	+	0.568646i	−0.963982	−	0.265967i	$-0.914309\pi$
$197$	−5.79877	+	7.98132i	−0.413145	+	0.568646i	0.550837	+	0.834613i	$0.314309\pi$
$198$		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
$205$	−17.4454	−	1.93835i	−1.21844	−	0.135381i
$206$		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	0.721667	+	0.692240i	$0.243376\pi$
$211$	−3.90836	+	12.0287i	−0.269062	+	0.828089i	−0.990730	+	0.135849i	$0.956624\pi$
$212$		0			0
$213$	−0.484323	+	0.157366i	−0.0331853	+	0.0107826i
$214$		0			0
$215$	0.840987	+	0.380429i	0.0573548	+	0.0259450i
$216$		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	$-0.343865\pi$
$223$	4.98335	+	1.61919i	0.333710	+	0.108429i	−0.137369	+	0.990520i	$0.543865\pi$
$224$		0			0
$225$	−2.55123	+	4.30014i	−0.170082	+	0.286676i
$226$		0			0
$227$	−7.38873	−	2.40074i	−0.490407	−	0.159343i	0.0533663	−	0.998575i	$-0.483005\pi$
$227$	−7.38873	−	2.40074i	−0.490407	−	0.159343i	−0.543773	+	0.839232i	$0.683005\pi$
$228$		0			0
$229$	−4.84757	−	3.52196i	−0.320336	−	0.232738i	0.415983	−	0.909373i	$-0.363438\pi$
$229$	−4.84757	−	3.52196i	−0.320336	−	0.232738i	−0.736319	+	0.676635i	$0.763438\pi$
$230$		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	$-0.361857\pi$
$233$	−8.73631	−	12.0245i	−0.572334	−	0.787751i	−0.992829	+	0.119544i	$0.961857\pi$
$234$		0			0
$235$	−8.62486	−	15.1456i	−0.562624	−	0.987991i
$236$		0			0
$237$	−3.26358	+	1.06040i	−0.211992	+	0.0688804i
$238$		0			0
$239$	6.55140	−	20.1631i	0.423775	−	1.30424i	−0.480388	−	0.877056i	$-0.659504\pi$
$239$	6.55140	−	20.1631i	0.423775	−	1.30424i	0.904163	−	0.427188i	$-0.140496\pi$
$240$		0			0
$241$	4.96162	+	15.2703i	0.319606	+	0.983647i	0.973817	+	0.227334i	$0.0730010\pi$
$241$	4.96162	+	15.2703i	0.319606	+	0.983647i	−0.654210	+	0.756313i	$0.726999\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	11.5161	−	25.4578i	0.735736	−	1.62644i
$246$		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
$255$	−6.05524	+	13.3859i	−0.379194	+	0.838256i
$256$		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	$-0.683264\pi$
$263$	−7.97729	+	2.59198i	−0.491901	+	0.159828i	0.0525547	+	0.998618i	$0.483264\pi$
$264$		0			0
$265$	−0.349057	−	0.612958i	−0.0214424	−	0.0376537i
$266$		0			0
$267$	6.66852	+	9.17843i	0.408107	+	0.561711i
$268$		0			0
$269$	−4.47812	+	3.25354i	−0.273036	+	0.198372i	−0.715874	−	0.698229i	$-0.753972\pi$
$269$	−4.47812	+	3.25354i	−0.273036	+	0.198372i	0.442838	+	0.896601i	$0.353972\pi$
$270$		0			0
$271$	−12.8227	−	9.31623i	−0.778923	−	0.565921i	0.125733	−	0.992064i	$-0.459872\pi$
$271$	−12.8227	−	9.31623i	−0.778923	−	0.565921i	−0.904656	+	0.426144i	$0.859872\pi$
$272$		0			0
$273$	−24.1366	−	7.84246i	−1.46081	−	0.474647i
$274$		0			0
$275$	−20.4407	+	8.81152i	−1.23262	+	0.531355i
$276$		0			0
$277$	8.26699	+	2.68611i	0.496715	+	0.161393i	0.546652	−	0.837360i	$-0.315902\pi$
$277$	8.26699	+	2.68611i	0.496715	+	0.161393i	−0.0499369	+	0.998752i	$0.515902\pi$
$278$		0			0
$279$	−0.159486	−	0.115873i	−0.00954819	−	0.00693716i
$280$		0			0
$281$	−8.72120	+	6.33633i	−0.520263	+	0.377994i	−0.816703	−	0.577058i	$-0.804201\pi$
$281$	−8.72120	+	6.33633i	−0.520263	+	0.377994i	0.296440	+	0.955052i	$0.404201\pi$
$282$		0			0
$283$	−5.78686	−	7.96493i	−0.343993	−	0.473466i	0.601609	−	0.798791i	$-0.294527\pi$
$283$	−5.78686	−	7.96493i	−0.343993	−	0.473466i	−0.945602	+	0.325324i	$0.894527\pi$
$284$		0			0
$285$	−5.67016	−	2.56496i	−0.335871	−	0.151935i
$286$		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
$295$	5.59824	+	0.622019i	0.325942	+	0.0362153i
$296$		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
$305$	15.4226	+	14.0532i	0.883096	+	0.804686i
$306$		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	0.465153	+	0.885230i	$0.345999\pi$
$311$	−7.60939	+	23.4193i	−0.431489	+	1.32799i	−0.896642	+	0.442756i	$0.854001\pi$
$312$		0			0
$313$	21.4458	−	6.96817i	1.21219	−	0.393864i	0.367957	−	0.929843i	$-0.380057\pi$
$313$	21.4458	−	6.96817i	1.21219	−	0.393864i	0.844232	+	0.535979i	$0.180057\pi$
$314$		0			0
$315$	1.09029	−	9.81275i	0.0614309	−	0.552886i
$316$		0			0
$317$	0.954767	+	1.31412i	0.0536251	+	0.0738086i	0.834987	−	0.550269i	$-0.185475\pi$
$317$	0.954767	+	1.31412i	0.0536251	+	0.0738086i	−0.781362	+	0.624078i	$0.785475\pi$
$318$		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
$325$	−24.7163	−	14.6639i	−1.37101	−	0.813407i
$326$		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	−0.369071	−	0.929401i	$-0.620324\pi$
$331$	7.29178	−	5.29779i	0.400793	−	0.291193i	0.769864	+	0.638208i	$0.220324\pi$
$332$		0			0
$333$	4.82493	+	6.64095i	0.264405	+	0.363922i
$334$		0			0
$335$	−26.1602	+	5.39842i	−1.42928	+	0.294947i
$336$		0			0
$337$	25.6482	−	8.33361i	1.39715	−	0.453961i	0.488880	−	0.872351i	$-0.337406\pi$
$337$	25.6482	−	8.33361i	1.39715	−	0.453961i	0.908267	+	0.418390i	$0.137406\pi$
$338$		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
$345$	0.594243	+	2.87964i	0.0319929	+	0.155035i
$346$		0			0
$347$	15.4263	−	21.2325i	0.828127	−	1.13982i	−0.160142	−	0.987094i	$-0.551195\pi$
$347$	15.4263	−	21.2325i	0.828127	−	1.13982i	0.988269	−	0.152725i	$-0.0488048\pi$
$348$		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	$-0.762219\pi$
$353$	2.61542	−	3.59982i	0.139205	−	0.191599i	0.872927	+	0.487850i	$0.162219\pi$
$354$		0			0
$355$	0.989516	−	0.563492i	0.0525181	−	0.0299071i
$356$		0			0
$357$		−	29.0107i		−	1.53541i
$358$		0			0
$359$	9.98964	+	30.7449i	0.527233	+	1.62266i	0.759858	+	0.650089i	$0.225269\pi$
$359$	9.98964	+	30.7449i	0.527233	+	1.62266i	−0.232625	+	0.972567i	$0.574731\pi$
$360$		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
$365$	−23.7518	+	26.0662i	−1.24323	+	1.36437i
$366$		0			0
$367$	−3.37390	−	4.64378i	−0.176116	−	0.242403i	0.711829	−	0.702353i	$-0.247867\pi$
$367$	−3.37390	−	4.64378i	−0.176116	−	0.242403i	−0.887945	+	0.459950i	$0.847867\pi$
$368$		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	$-0.391413\pi$
$373$	0.990868	+	0.321953i	0.0513052	+	0.0166701i	−0.283252	+	0.959046i	$0.591413\pi$
$374$		0			0
$375$	3.64371	−	10.5699i	0.188160	−	0.545829i
$376$		0			0
$377$	−26.4861	−	8.60587i	−1.36411	−	0.443225i
$378$		0			0
$379$	−3.84230	−	2.79159i	−0.197366	−	0.143395i	0.484713	−	0.874673i	$-0.338924\pi$
$379$	−3.84230	−	2.79159i	−0.197366	−	0.143395i	−0.682079	+	0.731279i	$0.738924\pi$
$380$		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	$-0.290848\pi$
$383$	−6.47739	−	8.91536i	−0.330979	−	0.455553i	−0.941780	+	0.336231i	$0.890848\pi$
$384$		0			0
$385$	29.6039	−	32.4885i	1.50875	−	1.65577i
$386$		0			0
$387$	−0.392588	+	0.127560i	−0.0199564	+	0.00648422i
$388$		0			0
$389$	10.2628	−	31.5856i	0.520344	−	1.60145i	−0.253000	−	0.967466i	$-0.581417\pi$
$389$	10.2628	−	31.5856i	0.520344	−	1.60145i	0.773344	−	0.633987i	$-0.218583\pi$
$390$		0			0
$391$	2.66981	+	8.21682i	0.135018	+	0.415542i
$392$		0			0
$393$		−	9.45365i		−	0.476873i
$394$		0			0
$395$	6.66778	−	3.79705i	0.335493	−	0.191050i
$396$		0			0
$397$	−1.61299	+	2.22008i	−0.0809534	+	0.111423i	−0.847573	−	0.530678i	$-0.821937\pi$
$397$	−1.61299	+	2.22008i	−0.0809534	+	0.111423i	0.766620	+	0.642101i	$0.221937\pi$
$398$		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
$405$	−0.451913	−	2.18993i	−0.0224558	−	0.108818i
$406$		0			0
$407$			36.5434i			1.81139i
$408$		0			0
$409$	2.03102	+	6.25083i	0.100427	+	0.309084i	0.988630	−	0.150368i	$-0.0480459\pi$
$409$	2.03102	+	6.25083i	0.100427	+	0.309084i	−0.888203	+	0.459452i	$0.848046\pi$
$410$		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
$415$	−11.7633	+	2.42748i	−0.577438	+	0.119160i
$416$		0			0
$417$	6.94855	+	9.56385i	0.340272	+	0.468344i
$418$		0			0
$419$	28.5125	−	20.7155i	1.39293	−	1.01202i	0.397389	−	0.917650i	$-0.369916\pi$
$419$	28.5125	−	20.7155i	1.39293	−	1.01202i	0.995537	−	0.0943704i	$-0.0300838\pi$
$420$		0			0
$421$	−5.07520	−	3.68735i	−0.247350	−	0.179710i	0.457201	−	0.889363i	$-0.348852\pi$
$421$	−5.07520	−	3.68735i	−0.247350	−	0.179710i	−0.704552	+	0.709653i	$0.748852\pi$
$422$		0			0
$423$	7.41309	+	2.40866i	0.360437	+	0.117113i
$424$		0			0
$425$	7.21127	−	32.0505i	0.349798	−	1.55468i
$426$		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	−0.288612	−	0.957446i	$-0.593194\pi$
$431$	11.0609	−	8.03624i	0.532787	−	0.387092i	0.821399	+	0.570354i	$0.193194\pi$
$432$		0			0
$433$	3.98412	+	5.48367i	0.191465	+	0.263529i	0.893947	−	0.448173i	$-0.147925\pi$
$433$	3.98412	+	5.48367i	0.191465	+	0.263529i	−0.702482	+	0.711701i	$0.747925\pi$
$434$		0			0
$435$	1.19642	−	10.7679i	0.0573641	−	0.516283i
$436$		0			0
$437$	−3.48059	+	1.13091i	−0.166499	+	0.0540988i
$438$		0			0
$439$	5.23618	−	16.1153i	0.249909	−	0.769142i	−0.744881	−	0.667197i	$-0.767494\pi$
$439$	5.23618	−	16.1153i	0.249909	−	0.769142i	0.994790	−	0.101944i	$-0.0325063\pi$
$440$		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
$445$	−18.7514	−	17.0865i	−0.888902	−	0.809977i
$446$		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
$455$	56.4015	+	6.26675i	2.64414	+	0.293790i
$456$		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	0.602050	+	0.798458i	$0.294351\pi$
$461$	−7.60801	+	23.4151i	−0.354340	+	1.09055i	−0.956391	+	0.292090i	$0.905649\pi$
$462$		0			0
$463$	−28.3995	+	9.22757i	−1.31984	+	0.428842i	−0.882440	−	0.470426i	$-0.844100\pi$
$463$	−28.3995	+	9.22757i	−1.31984	+	0.428842i	−0.437399	+	0.899267i	$0.644100\pi$
$464$		0			0
$465$	0.401628	+	0.181680i	0.0186250	+	0.00842522i
$466$		0			0
$467$	15.3714	+	21.1569i	0.711301	+	0.979022i	0.999768	+	0.0215325i	$0.00685454\pi$
$467$	15.3714	+	21.1569i	0.711301	+	0.979022i	−0.288467	+	0.957490i	$0.593145\pi$
$468$		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
$475$	13.5764	+	3.05464i	0.622927	+	0.140157i
$476$		0			0
$477$	0.300015	+	0.0974809i	0.0137368	+	0.00446334i
$478$		0			0
$479$	1.25147	+	0.909247i	0.0571812	+	0.0415446i	0.616009	−	0.787739i	$-0.288749\pi$
$479$	1.25147	+	0.909247i	0.0571812	+	0.0415446i	−0.558827	+	0.829284i	$0.688749\pi$
$480$		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
$485$	5.62068	+	9.87015i	0.255222	+	0.448180i
$486$		0			0
$487$	11.8681	−	3.85619i	0.537797	−	0.174741i	−0.0275101	−	0.999622i	$-0.508758\pi$
$487$	11.8681	−	3.85619i	0.537797	−	0.174741i	0.565307	+	0.824881i	$0.308758\pi$
$488$		0			0
$489$	−4.49876	+	13.8458i	−0.203441	+	0.626126i
$490$		0			0
$491$	−5.46864	−	16.8307i	−0.246796	−	0.759561i	−0.995336	−	0.0964706i	$-0.969245\pi$
$491$	−5.46864	−	16.8307i	−0.246796	−	0.759561i	0.748540	−	0.663090i	$-0.230755\pi$
$492$		0			0
$493$		−	31.8347i		−	1.43376i
$494$		0			0
$495$	4.10279	−	9.06974i	0.184407	−	0.407654i
$496$		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	−0.161526	−	0.986868i	$-0.551642\pi$
$503$	18.5467	−	25.5273i	0.826956	−	1.13821i	0.988482	−	0.151338i	$-0.0483583\pi$
$504$		0			0
$505$	10.3090	−	22.7894i	0.458746	−	1.01412i
$506$		0			0
$507$		−	20.0370i		−	0.889873i
$508$		0			0
$509$	2.23276	+	6.87172i	0.0989652	+	0.304583i	0.988267	−	0.152738i	$-0.0488090\pi$
$509$	2.23276	+	6.87172i	0.0989652	+	0.304583i	−0.889302	+	0.457321i	$0.848809\pi$
$510$		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
$515$	−3.48075	−	6.11234i	−0.153380	−	0.269342i
$516$		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	0.743061	−	0.669224i	$-0.233373\pi$
$521$	7.67413	+	5.57558i	0.336210	+	0.244271i	−0.406851	+	0.913494i	$0.633373\pi$
$522$		0			0
$523$	−19.3589	−	6.29007i	−0.846504	−	0.275046i	−0.146523	−	0.989207i	$-0.546808\pi$
$523$	−19.3589	−	6.29007i	−0.846504	−	0.275046i	−0.699981	+	0.714162i	$0.746808\pi$
$524$		0			0
$525$	2.04686	+	21.9819i	0.0893321	+	0.959369i
$526$		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
$535$	−15.7691	−	7.13330i	−0.681757	−	0.308400i
$536$		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	0.916480	+	0.400081i	$0.131018\pi$
$541$	9.54086	+	29.3638i	0.410194	+	1.26245i	−0.506286	+	0.862366i	$0.668982\pi$
$542$		0			0
$543$		−	7.59173i		−	0.325792i
$544$		0			0
$545$	−23.0481	−	2.56086i	−0.987271	−	0.109695i
$546$		0			0
$547$	9.01637	−	12.4100i	0.385512	−	0.530612i	−0.571522	−	0.820587i	$-0.693647\pi$
$547$	9.01637	−	12.4100i	0.385512	−	0.530612i	0.957034	+	0.289975i	$0.0936469\pi$
$548$		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
$555$	−13.5674	−	12.3627i	−0.575903	−	0.524769i
$556$		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	$-0.649500\pi$
$563$	−6.99026	+	2.27127i	−0.294604	+	0.0957227i	0.157986	+	0.987441i	$0.449500\pi$
$564$		0			0
$565$	−2.52516	+	22.7267i	−0.106234	+	0.956121i
$566$		0			0
$567$	2.59531	+	3.57213i	0.108993	+	0.150016i
$568$		0			0
$569$	−25.1830	+	18.2965i	−1.05572	+	0.767029i	−0.973293	−	0.229568i	$-0.926269\pi$
$569$	−25.1830	+	18.2965i	−1.05572	+	0.767029i	−0.0824322	+	0.996597i	$0.526269\pi$
$570$		0			0
$571$	−10.5055	−	7.63268i	−0.439641	−	0.319418i	0.345851	−	0.938289i	$-0.387590\pi$
$571$	−10.5055	−	7.63268i	−0.439641	−	0.319418i	−0.785492	+	0.618872i	$0.787590\pi$
$572$		0			0
$573$	−0.0115012	−	0.00373697i	−0.000480470	−	0.000156114i
$574$		0			0
$575$	−2.60269	−	6.03765i	−0.108540	−	0.251787i
$576$		0			0
$577$	20.7231	+	6.73333i	0.862712	+	0.280312i	0.706761	−	0.707453i	$-0.250156\pi$
$577$	20.7231	+	6.73333i	0.862712	+	0.280312i	0.155951	+	0.987765i	$0.450156\pi$
$578$		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
$585$	12.5872	−	2.59750i	0.520417	−	0.107393i
$586$		0			0
$587$	−25.3208	+	8.22724i	−1.04510	+	0.339575i	−0.780745	−	0.624850i	$-0.785160\pi$
$587$	−25.3208	+	8.22724i	−1.04510	+	0.339575i	−0.264358	+	0.964425i	$0.585160\pi$
$588$		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
$595$	13.1103	+	63.5314i	0.537472	+	2.60453i
$596$		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
$605$	17.1354	−	9.75796i	0.696652	−	0.396717i
$606$		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	$-0.530620\pi$
$613$	10.1837	−	3.30887i	0.411314	−	0.133644i	0.507363	+	0.861733i	$0.330620\pi$
$614$		0			0
$615$	−11.8223	+	12.9743i	−0.476722	+	0.523175i
$616$		0			0
$617$	9.83565	+	13.5376i	0.395968	+	0.545004i	0.959726	−	0.280936i	$-0.0906449\pi$
$617$	9.83565	+	13.5376i	0.395968	+	0.545004i	−0.563758	+	0.825940i	$0.690645\pi$
$618$		0			0
$619$	18.5531	−	13.4796i	0.745711	−	0.541791i	−0.148783	−	0.988870i	$-0.547536\pi$
$619$	18.5531	−	13.4796i	0.745711	−	0.541791i	0.894495	+	0.447079i	$0.147536\pi$
$620$		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
$625$	−3.20277	+	24.7940i	−0.128111	+	0.991760i
$626$		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	−0.796479	−	0.604666i	$-0.793307\pi$
$631$	−11.7443	+	8.53273i	−0.467533	+	0.339683i	0.328946	+	0.944349i	$0.393307\pi$
$632$		0			0
$633$	7.43414	+	10.2322i	0.295481	+	0.406694i
$634$		0			0
$635$	−17.0376	+	18.6978i	−0.676117	+	0.741999i
$636$		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	−0.934611	−	0.355672i	$-0.884252\pi$
$641$	−9.81208	−	30.1985i	−0.387554	−	1.19277i	0.547057	−	0.837095i	$-0.315748\pi$
$642$		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
$645$	0.802093	−	0.456762i	0.0315824	−	0.0179850i
$646$		0			0
$647$	6.60932	−	9.09695i	0.259839	−	0.357638i	−0.659088	−	0.752066i	$-0.729057\pi$
$647$	6.60932	−	9.09695i	0.259839	−	0.357638i	0.918927	+	0.394428i	$0.129057\pi$
$648$		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	$-0.812598\pi$
$653$	−1.18866	+	1.63604i	−0.0465157	+	0.0640233i	0.785126	+	0.619337i	$0.212598\pi$
$654$		0			0
$655$	4.27223	+	20.7028i	0.166930	+	0.808925i
$656$		0			0
$657$		−	15.7708i		−	0.615279i
$658$		0			0
$659$	0.245610	+	0.755909i	0.00956760	+	0.0294460i	0.955726	−	0.294257i	$-0.0950721\pi$
$659$	0.245610	+	0.755909i	0.00956760	+	0.0294460i	−0.946159	+	0.323703i	$0.895072\pi$
$660$		0			0
$661$	12.6628	−	38.9722i	0.492527	−	1.51584i	−0.328249	−	0.944591i	$-0.606459\pi$
$661$	12.6628	−	38.9722i	0.492527	−	1.51584i	0.820776	−	0.571250i	$-0.193541\pi$
$662$		0			0
$663$	35.9166	−	11.6700i	1.39489	−	0.453226i
$664$		0			0
$665$	−26.9114	+	5.55345i	−1.04358	+	0.215353i
$666$		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	$-0.636517\pi$
$673$	−33.3834	−	10.8469i	−1.28683	−	0.418118i	−0.870982	+	0.491314i	$0.836517\pi$
$674$		0			0
$675$	1.97931	+	4.59155i	0.0761838	+	0.176729i
$676$		0			0
$677$	−36.5079	−	11.8621i	−1.40311	−	0.455899i	−0.492916	−	0.870077i	$-0.664069\pi$
$677$	−36.5079	−	11.8621i	−1.40311	−	0.455899i	−0.910196	+	0.414178i	$0.864069\pi$
$678$		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	$-0.251161\pi$
$683$	−4.91673	−	6.76730i	−0.188134	−	0.258944i	−0.892657	+	0.450738i	$0.851161\pi$
$684$		0			0
$685$	−2.07673	+	18.6908i	−0.0793479	+	0.714140i
$686$		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	0.979462	−	0.201631i	$-0.0646241\pi$
$691$	1.80183	+	5.54547i	0.0685450	+	0.210960i	−0.910917	+	0.412590i	$0.864624\pi$
$692$		0			0
$693$			19.6565i			0.746689i
$694$		0			0
$695$	−19.5388	−	17.8040i	−0.741150	−	0.675344i
$696$		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
$705$	−17.3226	−	1.92471i	−0.652408	−	0.0724888i
$706$		0			0
$707$			49.3907i			1.85753i
$708$		0			0
$709$	3.00734	+	9.25565i	0.112943	+	0.347603i	0.991512	−	0.130012i	$-0.0415015\pi$
$709$	3.00734	+	9.25565i	0.112943	+	0.347603i	−0.878569	+	0.477615i	$0.841501\pi$
$710$		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
$715$	52.1309	+	23.5819i	1.94958	+	0.881914i
$716$		0			0
$717$	−12.4615	−	17.1518i	−0.465383	−	0.640545i
$718$		0			0
$719$	15.1579	−	11.0129i	0.565294	−	0.410710i	−0.268099	−	0.963391i	$-0.586395\pi$
$719$	15.1579	−	11.0129i	0.565294	−	0.410710i	0.833393	+	0.552681i	$0.186395\pi$
$720$		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
$725$	2.24610	+	24.1217i	0.0834181	+	0.895857i
$726$		0			0
$727$	36.1247	+	11.7376i	1.33979	+	0.435324i	0.889246	−	0.457430i	$-0.151230\pi$
$727$	36.1247	+	11.7376i	1.33979	+	0.435324i	0.450544	+	0.892754i	$0.351230\pi$
$728$		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	$-0.0381469\pi$
$733$	15.4951	+	21.3271i	0.572323	+	0.787735i	−0.420505	+	0.907290i	$0.638147\pi$
$734$		0			0
$735$	−13.8268	−	24.2804i	−0.510009	−	0.895597i
$736$		0			0
$737$	50.5772	−	16.4335i	1.86303	−	0.605337i
$738$		0			0
$739$	10.2081	−	31.4174i	0.375513	−	1.15571i	−0.567619	−	0.823291i	$-0.692136\pi$
$739$	10.2081	−	31.4174i	0.375513	−	1.15571i	0.943132	−	0.332418i	$-0.107864\pi$
$740$		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
$745$	9.80168	−	21.6679i	0.359106	−	0.793849i
$746$		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
$755$	−4.07031	+	8.99793i	−0.148134	+	0.327468i
$756$		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	−0.657362	−	0.753575i	$-0.728328\pi$
$761$	8.75574	−	26.9474i	0.317395	−	0.976842i	0.974757	−	0.223267i	$-0.0716723\pi$
$762$		0			0
$763$	43.5502	−	14.1503i	1.57662	−	0.512276i
$764$		0			0
$765$	7.27022	+	12.7668i	0.262856	+	0.461585i
$766$		0			0
$767$	−8.51040	−	11.7136i	−0.307293	−	0.422952i
$768$		0			0
$769$	−33.2679	+	24.1706i	−1.19967	+	0.871613i	−0.994252	−	0.107061i	$-0.965856\pi$
$769$	−33.2679	+	24.1706i	−1.19967	+	0.871613i	−0.205420	+	0.978674i	$0.565856\pi$
$770$		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	$-0.372391\pi$
$773$	4.58131	+	1.48856i	0.164778	+	0.0535397i	−0.225466	+	0.974251i	$0.572391\pi$
$774$		0			0
$775$	−0.961638	−	0.216366i	−0.0345431	−	0.00777208i
$776$		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
$785$	27.5626	+	12.4682i	0.983751	+	0.445010i
$786$		0			0
$787$	−38.3447	+	12.4590i	−1.36684	+	0.444114i	−0.898321	−	0.439339i	$-0.855213\pi$
$787$	−38.3447	+	12.4590i	−1.36684	+	0.444114i	−0.468520	+	0.883453i	$0.655213\pi$
$788$		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
$795$	−0.701064	−	0.0778950i	−0.0248642	−	0.00276265i
$796$		0			0
$797$	17.7487	−	24.4289i	0.628690	−	0.865318i	−0.369259	−	0.929326i	$-0.620389\pi$
$797$	17.7487	−	24.4289i	0.628690	−	0.865318i	0.997949	+	0.0640088i	$0.0203886\pi$
$798$		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
$805$	9.59626	+	8.74421i	0.338224	+	0.308193i
$806$		0			0
$807$			5.53526i			0.194850i
$808$		0			0
$809$	−3.36218	−	10.3477i	−0.118208	−	0.363807i	0.874395	−	0.485216i	$-0.161259\pi$
$809$	−3.36218	−	10.3477i	−0.118208	−	0.363807i	−0.992603	+	0.121409i	$0.961259\pi$
$810$		0			0
$811$	−14.6035	+	44.9451i	−0.512799	+	1.57823i	0.274451	+	0.961601i	$0.411504\pi$
$811$	−14.6035	+	44.9451i	−0.512799	+	1.57823i	−0.787250	+	0.616633i	$0.788496\pi$
$812$		0			0
$813$	−15.0740	+	4.89783i	−0.528667	+	0.171774i
$814$		0			0
$815$	3.59486	−	32.3542i	0.125923	−	1.13332i
$816$		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	0.178454	−	0.983948i	$-0.442890\pi$
$821$	−20.1200	−	14.6180i	−0.702191	−	0.510172i	−0.880645	+	0.473777i	$0.842890\pi$
$822$		0			0
$823$	−21.6451	−	7.03293i	−0.754502	−	0.245152i	−0.0935845	−	0.995611i	$-0.529833\pi$
$823$	−21.6451	−	7.03293i	−0.754502	−	0.245152i	−0.660917	+	0.750459i	$0.729833\pi$
$824$		0			0
$825$	−4.88607	+	21.7162i	−0.170111	+	0.756059i
$826$		0			0
$827$	−44.5530	−	14.4761i	−1.54926	−	0.503385i	−0.595346	−	0.803469i	$-0.702985\pi$
$827$	−44.5530	−	14.4761i	−1.54926	−	0.503385i	−0.953913	+	0.300084i	$0.902985\pi$
$828$		0			0
$829$	−11.1652	−	8.11202i	−0.387785	−	0.281742i	0.376762	−	0.926310i	$-0.377037\pi$
$829$	−11.1652	−	8.11202i	−0.387785	−	0.281742i	−0.764547	+	0.644568i	$0.777037\pi$
$830$		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
$835$	21.8297	−	4.50478i	0.755448	−	0.155894i
$836$		0			0
$837$	−0.187487	+	0.0609183i	−0.00648051	+	0.00210564i
$838$		0			0
$839$	3.27210	−	10.0705i	0.112966	−	0.347672i	−0.878552	−	0.477647i	$-0.841490\pi$
$839$	3.27210	−	10.0705i	0.112966	−	0.347672i	0.991517	+	0.129975i	$0.0414897\pi$
$840$		0			0
$841$	−1.70701	−	5.25362i	−0.0588623	−	0.181159i
$842$		0			0
$843$			10.7800i			0.371283i
$844$		0			0
$845$	9.05497	+	43.8795i	0.311501	+	1.50950i
$846$		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	$-0.926749\pi$
$853$	−13.3131	+	18.3240i	−0.455834	+	0.627401i	0.517805	+	0.855499i	$0.326749\pi$
$854$		0			0
$855$	−5.40793	+	3.07961i	−0.184947	+	0.105321i
$856$		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	−0.855839	−	0.517242i	$-0.826959\pi$
$859$	−13.7012	−	42.1679i	−0.467478	−	1.43875i	0.388361	−	0.921507i	$-0.373041\pi$
$860$		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	$-0.572685\pi$
$863$	4.78917	−	1.55610i	0.163025	−	0.0529701i	0.389393	+	0.921072i	$0.372685\pi$
$864$		0			0
$865$	16.3784	−	17.9743i	0.556882	−	0.611146i
$866$		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
$875$	−14.4164	−	47.2137i	−0.487363	−	1.59612i
$876$		0			0
$877$	−16.6380	−	5.40602i	−0.561826	−	0.182548i	0.0143164	−	0.999898i	$-0.495443\pi$
$877$	−16.6380	−	5.40602i	−0.561826	−	0.182548i	−0.576143	+	0.817349i	$0.695443\pi$
$878$		0			0
$879$	7.91003	+	5.74697i	0.266799	+	0.193840i
$880$		0			0
$881$	43.8856	−	31.8848i	1.47855	−	1.07423i	0.500523	−	0.865723i	$-0.333141\pi$
$881$	43.8856	−	31.8848i	1.47855	−	1.07423i	0.978022	−	0.208503i	$-0.0668590\pi$
$882$		0			0
$883$	−17.8419	−	24.5572i	−0.600427	−	0.826416i	0.395321	−	0.918543i	$-0.370633\pi$
$883$	−17.8419	−	24.5572i	−0.600427	−	0.826416i	−0.995747	+	0.0921269i	$0.970633\pi$
$884$		0			0
$885$	3.79379	−	4.16346i	0.127527	−	0.139953i
$886$		0			0
$887$	50.0705	−	16.2689i	1.68120	−	0.546256i	0.696058	−	0.717985i	$-0.254935\pi$
$887$	50.0705	−	16.2689i	1.68120	−	0.546256i	0.985144	+	0.171729i	$0.0549355\pi$
$888$		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
$895$	48.9154	−	27.8555i	1.63506	−	0.931106i
$896$		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
$905$	3.43081	+	16.6253i	0.114044	+	0.552645i
$906$		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	0.649795	+	0.760110i	$0.274855\pi$
$911$	−9.73942	+	29.9749i	−0.322682	+	0.993112i	−0.972476	+	0.233002i	$0.925145\pi$
$912$		0			0
$913$	22.7427	−	7.38956i	0.752675	−	0.244559i
$914$		0			0
$915$	20.4345	−	4.21686i	0.675544	−	0.139405i
$916$		0			0
$917$	−24.5351	−	33.7697i	−0.810221	−	1.11517i
$918$		0			0
$919$	−27.0858	+	19.6790i	−0.893478	+	0.649150i	−0.936782	−	0.349912i	$-0.886211\pi$
$919$	−27.0858	+	19.6790i	−0.893478	+	0.649150i	0.0433046	+	0.999062i	$0.486211\pi$
$920$		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
$925$	35.2984	+	20.9422i	1.16060	+	0.688575i
$926$		0			0
$927$	2.99171	+	0.972067i	0.0982608	+	0.0319269i
$928$		0			0
$929$	−1.51966	−	1.10410i	−0.0498585	−	0.0362244i	0.562577	−	0.826745i	$-0.309810\pi$
$929$	−1.51966	−	1.10410i	−0.0498585	−	0.0362244i	−0.612435	+	0.790521i	$0.709810\pi$
$930$		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
$935$	−7.22267	+	65.0049i	−0.236207	+	2.12589i
$936$		0			0
$937$	−2.17621	+	0.707094i	−0.0710937	+	0.0230997i	−0.344348	−	0.938842i	$-0.611900\pi$
$937$	−2.17621	+	0.707094i	−0.0710937	+	0.0230997i	0.273254	+	0.961942i	$0.411900\pi$
$938$		0			0
$939$	6.96817	−	21.4458i	0.227398	−	0.699858i
$940$		0			0
$941$	−18.5837	−	57.1947i	−0.605811	−	1.86449i	−0.491119	−	0.871092i	$-0.663412\pi$
$941$	−18.5837	−	57.1947i	−0.605811	−	1.86449i	−0.114691	−	0.993401i	$-0.536588\pi$
$942$		0			0
$943$			10.3221i			0.336135i
$944$		0			0
$945$	−7.29782	−	6.64985i	−0.237398	−	0.216320i
$946$		0			0
$947$	−25.4333	+	35.0060i	−0.826472	+	1.13754i	0.162098	+	0.986775i	$0.448174\pi$
$947$	−25.4333	+	35.0060i	−0.826472	+	1.13754i	−0.988569	+	0.150766i	$0.951826\pi$
$948$		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	$-0.990945\pi$
$953$	−20.4875	+	28.1986i	−0.663654	+	0.913441i	0.335942	+	0.941883i	$0.390945\pi$
$954$		0			0
$955$	0.0268756	+	0.00298613i	0.000869673	+	9.66290e-5i
$956$		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
$965$	−26.0452	−	11.7818i	−0.838426	−	0.379271i
$966$		0			0
$967$	−20.5577	−	28.2952i	−0.661090	−	0.909912i	0.338427	−	0.940993i	$-0.390105\pi$
$967$	−20.5577	−	28.2952i	−0.661090	−	0.909912i	−0.999517	+	0.0310806i	$0.990105\pi$
$968$		0			0
$969$	−14.7939	+	10.7484i	−0.475250	+	0.345289i
$970$		0			0
$971$	48.1194	+	34.9608i	1.54422	+	1.12194i	0.947616	+	0.319411i	$0.103485\pi$
$971$	48.1194	+	34.9608i	1.54422	+	1.12194i	0.596607	+	0.802533i	$0.296515\pi$
$972$		0			0
$973$	49.6423	+	16.1297i	1.59146	+	0.517096i
$974$		0			0
$975$	−26.3912	+	11.3767i	−0.845195	+	0.364345i
$976$		0			0
$977$	−14.6616	−	4.76386i	−0.469067	−	0.152409i	0.0649398	−	0.997889i	$-0.479314\pi$
$977$	−14.6616	−	4.76386i	−0.469067	−	0.152409i	−0.534007	+	0.845480i	$0.679314\pi$
$978$		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	0.833500	+	0.552520i	$0.186334\pi$
$983$	34.5324	+	47.5297i	1.10141	+	1.51596i	0.267912	+	0.963443i	$0.413666\pi$
$984$		0			0
$985$	−10.9163	−	19.1695i	−0.347823	−	0.610791i
$986$		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	0.959110	−	0.283035i	$-0.0913412\pi$
$991$	0.529181	+	1.62865i	0.0168100	+	0.0517358i	−0.942300	+	0.334771i	$0.891341\pi$
$992$		0			0
$993$		−	9.01314i		−	0.286023i
$994$		0			0
$995$	−0.272462	+	0.602311i	−0.00863762	+	0.0190945i
$996$		0			0
$997$	−6.93389	+	9.54368i	−0.219598	+	0.302251i	−0.904576	−	0.426313i	$-0.859812\pi$
$997$	−6.93389	+	9.54368i	−0.219598	+	0.302251i	0.684977	+	0.728564i	$0.259812\pi$
$998$		0			0
$999$	8.20866			0.259711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.o.a.229.4	yes	24
3.2	odd	2		900.2.w.c.829.5		24
5.2	odd	4		1500.2.m.c.601.6		24
5.3	odd	4		1500.2.m.d.601.1		24
5.4	even	2		1500.2.o.c.649.3		24
25.6	even	5		1500.2.o.c.349.3		24
25.8	odd	20		1500.2.m.d.901.1		24
25.9	even	10		7500.2.d.g.1249.11		24
25.12	odd	20		7500.2.a.n.1.11		12
25.13	odd	20		7500.2.a.m.1.2		12
25.16	even	5		7500.2.d.g.1249.14		24
25.17	odd	20		1500.2.m.c.901.6		24
25.19	even	10	inner	300.2.o.a.169.4	✓	24
75.44	odd	10		900.2.w.c.469.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.4	✓	24	25.19	even	10	inner
300.2.o.a.229.4	yes	24	1.1	even	1	trivial
900.2.w.c.469.5		24	75.44	odd	10
900.2.w.c.829.5		24	3.2	odd	2
1500.2.m.c.601.6		24	5.2	odd	4
1500.2.m.c.901.6		24	25.17	odd	20
1500.2.m.d.601.1		24	5.3	odd	4
1500.2.m.d.901.1		24	25.8	odd	20
1500.2.o.c.349.3		24	25.6	even	5
1500.2.o.c.649.3		24	5.4	even	2
7500.2.a.m.1.2		12	25.13	odd	20
7500.2.a.n.1.11		12	25.12	odd	20
7500.2.d.g.1249.11		24	25.9	even	10
7500.2.d.g.1249.14		24	25.16	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{3} +(-0.921600 + 2.03732i) q^{5} -4.41540i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{3} +(-0.921600 + 2.03732i) q^{5} -4.41540i q^{7} +(-0.309017 - 0.951057i) q^{9} +(1.37568 - 4.23392i) q^{11} +(5.46646 - 1.77616i) q^{13} +(1.10652 + 1.94309i) q^{15} +(3.86196 + 5.31553i) q^{17} +(-2.25162 + 1.63590i) q^{19} +(-3.57213 - 2.59531i) q^{21} +(1.25059 + 0.406341i) q^{23} +(-3.30131 - 3.75518i) q^{25} +(-0.951057 - 0.309017i) q^{27} +(-3.91985 - 2.84794i) q^{29} +(0.159486 - 0.115873i) q^{31} +(-2.61671 - 3.60159i) q^{33} +(8.99556 + 4.06923i) q^{35} +(-7.80690 + 2.53662i) q^{37} +(1.77616 - 5.46646i) q^{39} +(2.42573 + 7.46564i) q^{41} -0.412792i q^{43} +(2.22239 + 0.246929i) q^{45} +(-4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +6.57035 q^{51} +(-0.185420 + 0.255208i) q^{53} +(7.35800 + 6.70469i) q^{55} +2.78315i q^{57} +(-0.778419 - 2.39573i) q^{59} +(2.88348 - 8.87444i) q^{61} +(-4.19929 + 1.36443i) q^{63} +(-1.41929 + 12.7738i) q^{65} +(7.02151 + 9.66428i) q^{67} +(1.06382 - 0.772907i) q^{69} +(-0.411990 - 0.299328i) q^{71} +(14.9990 + 4.87346i) q^{73} +(-4.97846 + 0.463572i) q^{75} +(-18.6945 - 6.07420i) q^{77} +(-2.77617 - 2.01700i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(3.15732 + 4.34568i) q^{83} +(-14.3886 + 2.96923i) q^{85} +(-4.60806 + 1.49725i) q^{87} +(-3.50585 + 10.7899i) q^{89} +(-7.84246 - 24.1366i) q^{91} -0.197136i q^{93} +(-1.25774 - 6.09490i) q^{95} +(2.98572 - 4.10948i) q^{97} -4.45181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^5 + 6 * q^9	\( 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Introduction

L-functions

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