LMFDB - Embedded newform 1500.2.m.d.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, 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 $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.d.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} -4.41540 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} -4.41540 q^{7} +(0.309017 - 0.951057i) q^{9} +(1.37568 + 4.23392i) q^{11} +(1.77616 - 5.46646i) q^{13} +(5.31553 + 3.86196i) q^{17} +(2.25162 + 1.63590i) q^{19} +(-3.57213 + 2.59531i) q^{21} +(-0.406341 - 1.25059i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(3.91985 - 2.84794i) q^{29} +(0.159486 + 0.115873i) q^{31} +(3.60159 + 2.61671i) q^{33} +(2.53662 - 7.80690i) q^{37} +(-1.77616 - 5.46646i) q^{39} +(2.42573 - 7.46564i) q^{41} +0.412792 q^{43} +(6.30595 - 4.58154i) q^{47} +12.4958 q^{49} +6.57035 q^{51} +(-0.255208 + 0.185420i) q^{53} +2.78315 q^{57} +(0.778419 - 2.39573i) q^{59} +(2.88348 + 8.87444i) q^{61} +(-1.36443 + 4.19929i) q^{63} +(9.66428 + 7.02151i) q^{67} +(-1.06382 - 0.772907i) q^{69} +(-0.411990 + 0.299328i) q^{71} +(-4.87346 - 14.9990i) q^{73} +(-6.07420 - 18.6945i) q^{77} +(2.77617 - 2.01700i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.34568 - 3.15732i) q^{83} +(1.49725 - 4.60806i) q^{87} +(3.50585 + 10.7899i) q^{89} +(-7.84246 + 24.1366i) q^{91} +0.197136 q^{93} +(-4.10948 + 2.98572i) q^{97} +4.45181 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.41540			−1.66886			−0.834432	−	0.551111i	$-0.814204\pi$
$7$	−4.41540			−1.66886			−0.834432	+	0.551111i	$0.814204\pi$
$8$		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
$13$	1.77616	−	5.46646i	0.492619	−	1.51612i	−0.328017	−	0.944672i	$-0.606380\pi$
$13$	1.77616	−	5.46646i	0.492619	−	1.51612i	0.820635	−	0.571452i	$-0.193620\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.31553	+	3.86196i	1.28921	+	0.936662i	0.999789	−	0.0205412i	$-0.00653891\pi$
$17$	5.31553	+	3.86196i	1.28921	+	0.936662i	0.289416	+	0.957203i	$0.406539\pi$
$18$		0			0
$19$	2.25162	+	1.63590i	0.516557	+	0.375301i	0.815305	−	0.579031i	$-0.196569\pi$
$19$	2.25162	+	1.63590i	0.516557	+	0.375301i	−0.298748	+	0.954332i	$0.596569\pi$
$20$		0			0
$21$	−3.57213	+	2.59531i	−0.779503	+	0.566342i
$22$		0			0
$23$	−0.406341	−	1.25059i	−0.0847280	−	0.260766i	0.899713	−	0.436482i	$-0.143776\pi$
$23$	−0.406341	−	1.25059i	−0.0847280	−	0.260766i	−0.984441	+	0.175716i	$0.943776\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$		0			0
$29$	3.91985	−	2.84794i	0.727899	−	0.528849i	−0.160999	−	0.986954i	$-0.551472\pi$
$29$	3.91985	−	2.84794i	0.727899	−	0.528849i	0.888898	+	0.458105i	$0.151472\pi$
$30$		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
$33$	3.60159	+	2.61671i	0.626956	+	0.455510i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.53662	−	7.80690i	0.417017	−	1.28345i	−0.493417	−	0.869793i	$-0.664252\pi$
$37$	2.53662	−	7.80690i	0.417017	−	1.28345i	0.910434	−	0.413654i	$-0.135748\pi$
$38$		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
$43$	0.412792			0.0629502			0.0314751	−	0.999505i	$-0.489980\pi$
$43$	0.412792			0.0629502			0.0314751	+	0.999505i	$0.489980\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.30595	−	4.58154i	0.919818	−	0.668287i	−0.0236610	−	0.999720i	$-0.507532\pi$
$47$	6.30595	−	4.58154i	0.919818	−	0.668287i	0.943479	+	0.331433i	$0.107532\pi$
$48$		0			0
$49$	12.4958			1.78511
$50$		0			0
$51$	6.57035			0.920034
$52$		0			0
$53$	−0.255208	+	0.185420i	−0.0350556	+	0.0254694i	−0.605175	−	0.796092i	$-0.706897\pi$
$53$	−0.255208	+	0.185420i	−0.0350556	+	0.0254694i	0.570120	+	0.821562i	$0.306897\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.78315			0.368638
$58$		0			0
$59$	0.778419	−	2.39573i	0.101342	−	0.311897i	−0.887513	−	0.460783i	$-0.847569\pi$
$59$	0.778419	−	2.39573i	0.101342	−	0.311897i	0.988854	+	0.148886i	$0.0475687\pi$
$60$		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
$63$	−1.36443	+	4.19929i	−0.171902	+	0.529061i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	9.66428	+	7.02151i	1.18068	+	0.857814i	0.992248	−	0.124273i	$-0.0396597\pi$
$67$	9.66428	+	7.02151i	1.18068	+	0.857814i	0.188431	+	0.982086i	$0.439660\pi$
$68$		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
$73$	−4.87346	−	14.9990i	−0.570395	−	1.75549i	−0.651351	−	0.758777i	$-0.725797\pi$
$73$	−4.87346	−	14.9990i	−0.570395	−	1.75549i	0.0809557	−	0.996718i	$-0.474203\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.07420	−	18.6945i	−0.692219	−	2.13043i
$78$		0			0
$79$	2.77617	−	2.01700i	0.312343	−	0.226930i	−0.420558	−	0.907266i	$-0.638166\pi$
$79$	2.77617	−	2.01700i	0.312343	−	0.226930i	0.732901	+	0.680335i	$0.238166\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−4.34568	−	3.15732i	−0.477000	−	0.346561i	0.323163	−	0.946343i	$-0.395254\pi$
$83$	−4.34568	−	3.15732i	−0.477000	−	0.346561i	−0.800163	+	0.599783i	$0.795254\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.49725	−	4.60806i	0.160522	−	0.494036i
$88$		0			0
$89$	3.50585	+	10.7899i	0.371619	+	1.14373i	0.945731	+	0.324950i	$0.105347\pi$
$89$	3.50585	+	10.7899i	0.371619	+	1.14373i	−0.574112	+	0.818777i	$0.694653\pi$
$90$		0			0
$91$	−7.84246	+	24.1366i	−0.822114	+	2.53021i
$92$		0			0
$93$	0.197136			0.0204420
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4.10948	+	2.98572i	−0.417255	+	0.303153i	−0.776532	−	0.630077i	$-0.783023\pi$
$97$	−4.10948	+	2.98572i	−0.417255	+	0.303153i	0.359277	+	0.933231i	$0.383023\pi$
$98$		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
$103$	−2.54490	+	1.84898i	−0.250757	+	0.182185i	−0.706062	−	0.708150i	$-0.749530\pi$
$103$	−2.54490	+	1.84898i	−0.250757	+	0.182185i	0.455305	+	0.890335i	$0.349530\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.74013			0.748266			0.374133	−	0.927375i	$-0.377940\pi$
$107$	7.74013			0.748266			0.374133	+	0.927375i	$0.377940\pi$
$108$		0			0
$109$	−3.20477	+	9.86326i	−0.306961	+	0.944729i	0.671977	+	0.740572i	$0.265445\pi$
$109$	−3.20477	+	9.86326i	−0.306961	+	0.944729i	−0.978938	+	0.204157i	$0.934555\pi$
$110$		0			0
$111$	−2.53662	−	7.80690i	−0.240765	−	0.740998i
$112$		0			0
$113$	3.16009	−	9.72574i	0.297276	−	0.914921i	−0.685172	−	0.728382i	$-0.740273\pi$
$113$	3.16009	−	9.72574i	0.297276	−	0.914921i	0.982447	−	0.186539i	$-0.0597272\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.65005	−	3.37846i	−0.429897	−	0.312339i
$118$		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
$123$	−2.42573	−	7.46564i	−0.218721	−	0.673154i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.49582	+	10.7590i	0.310204	+	0.954709i	0.977684	+	0.210081i	$0.0673729\pi$
$127$	3.49582	+	10.7590i	0.310204	+	0.954709i	−0.667480	+	0.744628i	$0.732627\pi$
$128$		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
$133$	−9.94180	−	7.22314i	−0.862063	−	0.626326i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.59891	+	7.99861i	−0.222039	+	0.683367i	0.776539	+	0.630069i	$0.216973\pi$
$137$	−2.59891	+	7.99861i	−0.222039	+	0.683367i	−0.998579	+	0.0532983i	$0.983027\pi$
$138$		0			0
$139$	3.65307	+	11.2430i	0.309849	+	0.953617i	0.977823	+	0.209433i	$0.0671617\pi$
$139$	3.65307	+	11.2430i	0.309849	+	0.953617i	−0.667974	+	0.744185i	$0.732838\pi$
$140$		0			0
$141$	2.40866	−	7.41309i	0.202846	−	0.624295i
$142$		0			0
$143$	25.5880			2.13978
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.1093	−	7.34482i	0.833799	−	0.605791i
$148$		0			0
$149$	10.6355			0.871294			0.435647	−	0.900118i	$-0.356520\pi$
$149$	10.6355			0.871294			0.435647	+	0.900118i	$0.356520\pi$
$150$		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
$153$	5.31553	−	3.86196i	0.429735	−	0.312221i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−13.5289			−1.07972			−0.539861	−	0.841754i	$-0.681523\pi$
$157$	−13.5289			−1.07972			−0.539861	+	0.841754i	$0.681523\pi$
$158$		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
$163$	−4.49876	+	13.8458i	−0.352370	+	1.08448i	0.605149	+	0.796112i	$0.293114\pi$
$163$	−4.49876	+	13.8458i	−0.352370	+	1.08448i	−0.957519	+	0.288371i	$0.906886\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.06448	−	5.85918i	−0.624048	−	0.453397i	0.230285	−	0.973123i	$-0.426034\pi$
$167$	−8.06448	−	5.85918i	−0.624048	−	0.453397i	−0.854333	+	0.519726i	$0.826034\pi$
$168$		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
$173$	3.36056	+	10.3427i	0.255499	+	0.786344i	0.993731	+	0.111798i	$0.0356608\pi$
$173$	3.36056	+	10.3427i	0.255499	+	0.786344i	−0.738232	+	0.674547i	$0.764339\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.778419	−	2.39573i	−0.0585096	−	0.180074i
$178$		0			0
$179$	20.3662	−	14.7969i	1.52224	−	1.10597i	0.561875	−	0.827222i	$-0.310080\pi$
$179$	20.3662	−	14.7969i	1.52224	−	1.10597i	0.960364	−	0.278749i	$-0.0899198\pi$
$180$		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
$183$	7.54905	+	5.48470i	0.558042	+	0.405441i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.03874	+	27.8184i	−0.660978	+	2.03428i
$188$		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
$193$	−12.7841			−0.920219			−0.460110	−	0.887862i	$-0.652190\pi$
$193$	−12.7841			−0.920219			−0.460110	+	0.887862i	$0.652190\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.98132	−	5.79877i	0.568646	−	0.413145i	−0.265967	−	0.963982i	$-0.585691\pi$
$197$	7.98132	−	5.79877i	0.568646	−	0.413145i	0.834613	+	0.550837i	$0.185691\pi$
$198$		0			0
$199$	−0.295640			−0.0209573			−0.0104787	−	0.999945i	$-0.503336\pi$
$199$	−0.295640			−0.0209573			−0.0104787	+	0.999945i	$0.503336\pi$
$200$		0			0
$201$	11.9457			0.842585
$202$		0			0
$203$	−17.3077	+	12.5748i	−1.21476	+	0.882578i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.31495			−0.0913952
$208$		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
$213$	−0.157366	+	0.484323i	−0.0107826	+	0.0331853i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.704195	−	0.511628i	−0.0478039	−	0.0347315i
$218$		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
$223$	−1.61919	−	4.98335i	−0.108429	−	0.333710i	0.882091	−	0.471079i	$-0.156135\pi$
$223$	−1.61919	−	4.98335i	−0.108429	−	0.333710i	−0.990520	+	0.137369i	$0.956135\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.40074	−	7.38873i	−0.159343	−	0.490407i	0.839232	−	0.543773i	$-0.183005\pi$
$227$	−2.40074	−	7.38873i	−0.159343	−	0.490407i	−0.998575	+	0.0533663i	$0.983005\pi$
$228$		0			0
$229$	4.84757	−	3.52196i	0.320336	−	0.232738i	−0.415983	−	0.909373i	$-0.636562\pi$
$229$	4.84757	−	3.52196i	0.320336	−	0.232738i	0.736319	+	0.676635i	$0.236562\pi$
$230$		0			0
$231$	−15.9025	−	11.5538i	−1.04630	−	0.760185i
$232$		0			0
$233$	12.0245	+	8.73631i	0.787751	+	0.572334i	0.907295	−	0.420494i	$-0.138143\pi$
$233$	12.0245	+	8.73631i	0.787751	+	0.572334i	−0.119544	+	0.992829i	$0.538143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.06040	−	3.26358i	0.0688804	−	0.211992i
$238$		0			0
$239$	−6.55140	−	20.1631i	−0.423775	−	1.30424i	−0.904163	−	0.427188i	$-0.859504\pi$
$239$	−6.55140	−	20.1631i	−0.423775	−	1.30424i	0.480388	−	0.877056i	$-0.340496\pi$
$240$		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
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	12.9418	−	9.40278i	0.823468	−	0.598284i
$248$		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
$253$	4.73590	−	3.44084i	0.297744	−	0.216323i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.22940			−0.263823			−0.131911	−	0.991262i	$-0.542111\pi$
$257$	−4.22940			−0.263823			−0.131911	+	0.991262i	$0.542111\pi$
$258$		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
$263$	−2.59198	+	7.97729i	−0.159828	+	0.491901i	−0.998618	−	0.0525547i	$-0.983264\pi$
$263$	−2.59198	+	7.97729i	−0.159828	+	0.491901i	0.838790	+	0.544455i	$0.183264\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	9.17843	+	6.66852i	0.561711	+	0.408107i
$268$		0			0
$269$	4.47812	+	3.25354i	0.273036	+	0.198372i	0.715874	−	0.698229i	$-0.246028\pi$
$269$	4.47812	+	3.25354i	0.273036	+	0.198372i	−0.442838	+	0.896601i	$0.646028\pi$
$270$		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
$273$	7.84246	+	24.1366i	0.474647	+	1.46081i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.68611	+	8.26699i	0.161393	+	0.496715i	0.998752	−	0.0499369i	$-0.0159020\pi$
$277$	2.68611	+	8.26699i	0.161393	+	0.496715i	−0.837360	+	0.546652i	$0.815902\pi$
$278$		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
$283$	7.96493	+	5.78686i	0.473466	+	0.343993i	0.798791	−	0.601609i	$-0.205473\pi$
$283$	7.96493	+	5.78686i	0.473466	+	0.343993i	−0.325324	+	0.945602i	$0.605473\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.7106	+	32.9638i	−0.632226	+	1.94579i
$288$		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
$293$	−9.77733			−0.571198			−0.285599	−	0.958349i	$-0.592192\pi$
$293$	−9.77733			−0.571198			−0.285599	+	0.958349i	$0.592192\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.60159	−	2.61671i	0.208985	−	0.151837i
$298$		0			0
$299$	−7.55803			−0.437092
$300$		0			0
$301$	−1.82264			−0.105055
$302$		0			0
$303$	−9.04967	+	6.57497i	−0.519890	+	0.377722i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−32.7301			−1.86801			−0.934003	−	0.357265i	$-0.883709\pi$
$307$	−32.7301			−1.86801			−0.934003	+	0.357265i	$0.883709\pi$
$308$		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
$313$	6.96817	−	21.4458i	0.393864	−	1.21219i	−0.535979	−	0.844232i	$-0.680057\pi$
$313$	6.96817	−	21.4458i	0.393864	−	1.21219i	0.929843	−	0.367957i	$-0.119943\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.31412	+	0.954767i	0.0738086	+	0.0536251i	0.624078	−	0.781362i	$-0.285475\pi$
$317$	1.31412	+	0.954767i	0.0738086	+	0.0536251i	−0.550269	+	0.834987i	$0.685475\pi$
$318$		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
$323$	5.65078	+	17.3913i	0.314418	+	0.967679i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.20477	+	9.86326i	0.177224	+	0.545440i
$328$		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
$333$	−6.64095	−	4.82493i	−0.363922	−	0.264405i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8.33361	+	25.6482i	−0.453961	+	1.39715i	0.418390	+	0.908267i	$0.362594\pi$
$337$	−8.33361	+	25.6482i	−0.453961	+	1.39715i	−0.872351	+	0.488880i	$0.837406\pi$
$338$		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
$343$	−24.2660			−1.31024
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−21.2325	+	15.4263i	−1.13982	+	0.828127i	−0.987094	−	0.160142i	$-0.948805\pi$
$347$	−21.2325	+	15.4263i	−1.13982	+	0.828127i	−0.152725	+	0.988269i	$0.548805\pi$
$348$		0			0
$349$	18.2310			0.975885			0.487943	−	0.872876i	$-0.337748\pi$
$349$	18.2310			0.975885			0.487943	+	0.872876i	$0.337748\pi$
$350$		0			0
$351$	−5.74778			−0.306794
$352$		0			0
$353$	3.59982	−	2.61542i	0.191599	−	0.139205i	−0.487850	−	0.872927i	$-0.662219\pi$
$353$	3.59982	−	2.61542i	0.191599	−	0.139205i	0.679449	+	0.733723i	$0.262219\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−29.0107			−1.53541
$358$		0			0
$359$	−9.98964	+	30.7449i	−0.527233	+	1.62266i	0.232625	+	0.972567i	$0.425269\pi$
$359$	−9.98964	+	30.7449i	−0.527233	+	1.62266i	−0.759858	+	0.650089i	$0.774731\pi$
$360$		0			0
$361$	−3.47769	−	10.7032i	−0.183036	−	0.563328i
$362$		0			0
$363$	−2.72510	+	8.38699i	−0.143031	+	0.440203i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.64378	−	3.37390i	−0.242403	−	0.176116i	0.459950	−	0.887945i	$-0.347867\pi$
$367$	−4.64378	−	3.37390i	−0.242403	−	0.176116i	−0.702353	+	0.711829i	$0.747867\pi$
$368$		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
$373$	−0.321953	−	0.990868i	−0.0166701	−	0.0513052i	0.942375	−	0.334557i	$-0.108587\pi$
$373$	−0.321953	−	0.990868i	−0.0166701	−	0.0513052i	−0.959046	+	0.283252i	$0.908587\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.60587	−	26.4861i	−0.443225	−	1.36411i
$378$		0			0
$379$	3.84230	−	2.79159i	0.197366	−	0.143395i	−0.484713	−	0.874673i	$-0.661076\pi$
$379$	3.84230	−	2.79159i	0.197366	−	0.143395i	0.682079	+	0.731279i	$0.261076\pi$
$380$		0			0
$381$	9.15217	+	6.64944i	0.468880	+	0.340661i
$382$		0			0
$383$	8.91536	+	6.47739i	0.455553	+	0.330979i	0.791784	−	0.610801i	$-0.209152\pi$
$383$	8.91536	+	6.47739i	0.455553	+	0.330979i	−0.336231	+	0.941780i	$0.609152\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.127560	−	0.392588i	0.00648422	−	0.0199564i
$388$		0			0
$389$	−10.2628	−	31.5856i	−0.520344	−	1.60145i	−0.773344	−	0.633987i	$-0.781417\pi$
$389$	−10.2628	−	31.5856i	−0.520344	−	1.60145i	0.253000	−	0.967466i	$-0.418583\pi$
$390$		0			0
$391$	2.66981	−	8.21682i	0.135018	−	0.415542i
$392$		0			0
$393$	9.45365			0.476873
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.22008	−	1.61299i	0.111423	−	0.0809534i	−0.530678	−	0.847573i	$-0.678063\pi$
$397$	2.22008	−	1.61299i	0.111423	−	0.0809534i	0.642101	+	0.766620i	$0.278063\pi$
$398$		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
$403$	0.916691	−	0.666015i	0.0456636	−	0.0331766i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	36.5434			1.81139
$408$		0			0
$409$	−2.03102	+	6.25083i	−0.100427	+	0.309084i	−0.988630	−	0.150368i	$-0.951954\pi$
$409$	−2.03102	+	6.25083i	−0.100427	+	0.309084i	0.888203	+	0.459452i	$0.151954\pi$
$410$		0			0
$411$	2.59891	+	7.99861i	0.128195	+	0.394542i
$412$		0			0
$413$	−3.43703	+	10.5781i	−0.169125	+	0.520514i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	9.56385	+	6.94855i	0.468344	+	0.340272i
$418$		0			0
$419$	−28.5125	−	20.7155i	−1.39293	−	1.01202i	−0.995537	−	0.0943704i	$-0.969916\pi$
$419$	−28.5125	−	20.7155i	−1.39293	−	1.01202i	−0.397389	−	0.917650i	$-0.630084\pi$
$420$		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
$423$	−2.40866	−	7.41309i	−0.117113	−	0.360437i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.7317	−	39.1842i	−0.616131	−	1.89626i
$428$		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
$433$	−5.48367	−	3.98412i	−0.263529	−	0.191465i	0.448173	−	0.893947i	$-0.352075\pi$
$433$	−5.48367	−	3.98412i	−0.263529	−	0.191465i	−0.711701	+	0.702482i	$0.752075\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.13091	−	3.48059i	0.0540988	−	0.166499i
$438$		0			0
$439$	−5.23618	−	16.1153i	−0.249909	−	0.769142i	−0.994790	−	0.101944i	$-0.967494\pi$
$439$	−5.23618	−	16.1153i	−0.249909	−	0.769142i	0.744881	−	0.667197i	$-0.232506\pi$
$440$		0			0
$441$	3.86140	−	11.8842i	0.183876	−	0.565913i
$442$		0			0
$443$	−23.8927			−1.13517			−0.567587	−	0.823313i	$-0.692123\pi$
$443$	−23.8927			−1.13517			−0.567587	+	0.823313i	$0.692123\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.60430	−	6.25139i	0.406969	−	0.295681i
$448$		0			0
$449$	6.39281			0.301695			0.150848	−	0.988557i	$-0.451800\pi$
$449$	6.39281			0.301695			0.150848	+	0.988557i	$0.451800\pi$
$450$		0			0
$451$	34.9460			1.64554
$452$		0			0
$453$	3.57308	−	2.59599i	0.167878	−	0.121970i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.89482			0.275748			0.137874	−	0.990450i	$-0.455973\pi$
$457$	5.89482			0.275748			0.137874	+	0.990450i	$0.455973\pi$
$458$		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
$463$	−9.22757	+	28.3995i	−0.428842	+	1.31984i	0.470426	+	0.882440i	$0.344100\pi$
$463$	−9.22757	+	28.3995i	−0.428842	+	1.31984i	−0.899267	+	0.437399i	$0.855900\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	21.1569	+	15.3714i	0.979022	+	0.711301i	0.957490	−	0.288467i	$-0.0931455\pi$
$467$	21.1569	+	15.3714i	0.979022	+	0.711301i	0.0215325	+	0.999768i	$0.493145\pi$
$468$		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
$473$	0.567871	+	1.74773i	0.0261108	+	0.0803606i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.0974809	+	0.300015i	0.00446334	+	0.0137368i
$478$		0			0
$479$	−1.25147	+	0.909247i	−0.0571812	+	0.0415446i	−0.616009	−	0.787739i	$-0.711251\pi$
$479$	−1.25147	+	0.909247i	−0.0571812	+	0.0415446i	0.558827	+	0.829284i	$0.311251\pi$
$480$		0			0
$481$	−38.1707	−	27.7326i	−1.74043	−	1.26450i
$482$		0			0
$483$	4.69717	+	3.41269i	0.213729	+	0.155283i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.85619	+	11.8681i	−0.174741	+	0.537797i	−0.999622	−	0.0275101i	$-0.991242\pi$
$487$	−3.85619	+	11.8681i	−0.174741	+	0.537797i	0.824881	+	0.565307i	$0.191242\pi$
$488$		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
$493$	31.8347			1.43376
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.81910	−	1.32165i	0.0815978	−	0.0592843i
$498$		0			0
$499$	−30.9281			−1.38453			−0.692267	−	0.721642i	$-0.743388\pi$
$499$	−30.9281			−1.38453			−0.692267	+	0.721642i	$0.743388\pi$
$500$		0			0
$501$	−9.96824			−0.445348
$502$		0			0
$503$	25.5273	−	18.5467i	1.13821	−	0.826956i	0.151338	−	0.988482i	$-0.451642\pi$
$503$	25.5273	−	18.5467i	1.13821	−	0.826956i	0.986868	+	0.161526i	$0.0516417\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−20.0370			−0.889873
$508$		0			0
$509$	−2.23276	+	6.87172i	−0.0989652	+	0.304583i	−0.988267	−	0.152738i	$-0.951191\pi$
$509$	−2.23276	+	6.87172i	−0.0989652	+	0.304583i	0.889302	+	0.457321i	$0.151191\pi$
$510$		0			0
$511$	21.5183	+	66.2264i	0.951912	+	2.92968i
$512$		0			0
$513$	0.860042	−	2.64694i	0.0379718	−	0.116865i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	28.0729	+	20.3962i	1.23464	+	0.897022i
$518$		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
$523$	6.29007	+	19.3589i	0.275046	+	0.846504i	0.989207	+	0.146523i	$0.0468082\pi$
$523$	6.29007	+	19.3589i	0.275046	+	0.846504i	−0.714162	+	0.699981i	$0.753192\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.400255	+	1.23186i	0.0174354	+	0.0536606i
$528$		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
$533$	−36.5022	−	26.5204i	−1.58108	−	1.14873i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.77918	−	23.9419i	0.335697	−	1.03317i
$538$		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
$543$	7.59173			0.325792
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−12.4100	+	9.01637i	−0.530612	+	0.385512i	−0.820587	−	0.571522i	$-0.806353\pi$
$547$	−12.4100	+	9.01637i	−0.530612	+	0.385512i	0.289975	+	0.957034i	$0.406353\pi$
$548$		0			0
$549$	9.33114			0.398243
$550$		0			0
$551$	13.4850			0.574478
$552$		0			0
$553$	−12.2579	+	8.90587i	−0.521258	+	0.378716i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−28.6722			−1.21488			−0.607441	−	0.794365i	$-0.707804\pi$
$557$	−28.6722			−1.21488			−0.607441	+	0.794365i	$0.707804\pi$
$558$		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
$563$	−2.27127	+	6.99026i	−0.0957227	+	0.294604i	−0.987441	−	0.157986i	$-0.949500\pi$
$563$	−2.27127	+	6.99026i	−0.0957227	+	0.294604i	0.891719	+	0.452590i	$0.149500\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.57213	+	2.59531i	0.150016	+	0.108993i
$568$		0			0
$569$	25.1830	+	18.2965i	1.05572	+	0.767029i	0.973293	−	0.229568i	$-0.0737312\pi$
$569$	25.1830	+	18.2965i	1.05572	+	0.767029i	0.0824322	+	0.996597i	$0.473731\pi$
$570$		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
$573$	0.00373697	+	0.0115012i	0.000156114	+	0.000480470i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.73333	+	20.7231i	0.280312	+	0.862712i	0.987765	+	0.155951i	$0.0498443\pi$
$577$	6.73333	+	20.7231i	0.280312	+	0.862712i	−0.707453	+	0.706761i	$0.750156\pi$
$578$		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
$583$	−1.13614	−	0.825453i	−0.0470541	−	0.0341868i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.22724	−	25.3208i	0.339575	−	1.04510i	−0.624850	−	0.780745i	$-0.714840\pi$
$587$	8.22724	−	25.3208i	0.339575	−	1.04510i	0.964425	−	0.264358i	$-0.0851601\pi$
$588$		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
$593$	5.23169			0.214840			0.107420	−	0.994214i	$-0.465741\pi$
$593$	5.23169			0.214840			0.107420	+	0.994214i	$0.465741\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.239178	+	0.173773i	−0.00978889	+	0.00711204i
$598$		0			0
$599$	39.5405			1.61558			0.807790	−	0.589471i	$-0.200664\pi$
$599$	39.5405			1.61558			0.807790	+	0.589471i	$0.200664\pi$
$600$		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
$603$	9.66428	−	7.02151i	0.393560	−	0.285938i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.6524			−0.757078			−0.378539	−	0.925585i	$-0.623573\pi$
$607$	−18.6524			−0.757078			−0.378539	+	0.925585i	$0.623573\pi$
$608$		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
$613$	3.30887	−	10.1837i	0.133644	−	0.411314i	−0.861733	−	0.507363i	$-0.830620\pi$
$613$	3.30887	−	10.1837i	0.133644	−	0.411314i	0.995377	+	0.0960485i	$0.0306204\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.5376	+	9.83565i	0.545004	+	0.395968i	0.825940	−	0.563758i	$-0.190645\pi$
$617$	13.5376	+	9.83565i	0.545004	+	0.395968i	−0.280936	+	0.959726i	$0.590645\pi$
$618$		0			0
$619$	−18.5531	−	13.4796i	−0.745711	−	0.541791i	0.148783	−	0.988870i	$-0.452464\pi$
$619$	−18.5531	−	13.4796i	−0.745711	−	0.541791i	−0.894495	+	0.447079i	$0.852464\pi$
$620$		0			0
$621$	−1.06382	+	0.772907i	−0.0426894	+	0.0310157i
$622$		0			0
$623$	−15.4797	−	47.6417i	−0.620182	−	1.90872i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.82874	+	11.7837i	0.152905	+	0.470594i
$628$		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
$633$	−10.2322	−	7.43414i	−0.406694	−	0.295481i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	22.1945	−	68.3076i	0.879377	−	2.70645i
$638$		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
$643$	−3.63816			−0.143475			−0.0717376	−	0.997424i	$-0.522854\pi$
$643$	−3.63816			−0.143475			−0.0717376	+	0.997424i	$0.522854\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.09695	+	6.60932i	−0.357638	+	0.259839i	−0.752066	−	0.659088i	$-0.770943\pi$
$647$	−9.09695	+	6.60932i	−0.357638	+	0.259839i	0.394428	+	0.918927i	$0.370943\pi$
$648$		0			0
$649$	11.2142			0.440195
$650$		0			0
$651$	−0.870433			−0.0341150
$652$		0			0
$653$	−1.63604	+	1.18866i	−0.0640233	+	0.0465157i	−0.619337	−	0.785126i	$-0.712598\pi$
$653$	−1.63604	+	1.18866i	−0.0640233	+	0.0465157i	0.555313	+	0.831641i	$0.312598\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−15.7708			−0.615279
$658$		0			0
$659$	−0.245610	+	0.755909i	−0.00956760	+	0.0294460i	−0.955726	−	0.294257i	$-0.904928\pi$
$659$	−0.245610	+	0.755909i	−0.00956760	+	0.0294460i	0.946159	+	0.323703i	$0.104928\pi$
$660$		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
$663$	11.6700	−	35.9166i	0.453226	−	1.39489i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.15440	−	3.74489i	−0.199579	−	0.145003i
$668$		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
$673$	10.8469	+	33.3834i	0.418118	+	1.28683i	0.909432	+	0.415852i	$0.136517\pi$
$673$	10.8469	+	33.3834i	0.418118	+	1.28683i	−0.491314	+	0.870982i	$0.663483\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.8621	−	36.5079i	−0.455899	−	1.40311i	−0.870077	−	0.492916i	$-0.835931\pi$
$677$	−11.8621	−	36.5079i	−0.455899	−	1.40311i	0.414178	−	0.910196i	$-0.364069\pi$
$678$		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
$683$	6.76730	+	4.91673i	0.258944	+	0.188134i	0.709681	−	0.704523i	$-0.248839\pi$
$683$	6.76730	+	4.91673i	0.258944	+	0.188134i	−0.450738	+	0.892657i	$0.648839\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.85161	−	5.69866i	0.0706432	−	0.217417i
$688$		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
$693$	−19.6565			−0.746689
$694$		0			0
$695$		0			0
$696$		0			0
$697$	41.7261	−	30.3158i	1.58049	−	1.14829i
$698$		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
$703$	18.4828	−	13.4285i	0.697091	−	0.506467i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	49.3907			1.85753
$708$		0			0
$709$	−3.00734	+	9.25565i	−0.112943	+	0.347603i	−0.991512	−	0.130012i	$-0.958499\pi$
$709$	−3.00734	+	9.25565i	−0.112943	+	0.347603i	0.878569	+	0.477615i	$0.158499\pi$
$710$		0			0
$711$	−1.06040	−	3.26358i	−0.0397681	−	0.122394i
$712$		0			0
$713$	0.0801044	−	0.246536i	0.00299993	−	0.00923285i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.1518	−	12.4615i	−0.640545	−	0.465383i
$718$		0			0
$719$	−15.1579	−	11.0129i	−0.565294	−	0.410710i	0.268099	−	0.963391i	$-0.413605\pi$
$719$	−15.1579	−	11.0129i	−0.565294	−	0.410710i	−0.833393	+	0.552681i	$0.813605\pi$
$720$		0			0
$721$	11.2368	−	8.16399i	0.418479	−	0.304043i
$722$		0			0
$723$	−4.96162	−	15.2703i	−0.184525	−	0.567909i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	11.7376	+	36.1247i	0.435324	+	1.33979i	0.892754	+	0.450544i	$0.148770\pi$
$727$	11.7376	+	36.1247i	0.435324	+	1.33979i	−0.457430	+	0.889246i	$0.651230\pi$
$728$		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
$733$	−21.3271	−	15.4951i	−0.787735	−	0.572323i	0.119555	−	0.992828i	$-0.461853\pi$
$733$	−21.3271	−	15.4951i	−0.787735	−	0.572323i	−0.907290	+	0.420505i	$0.861853\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.4335	+	50.5772i	−0.605337	+	1.86303i
$738$		0			0
$739$	−10.2081	−	31.4174i	−0.375513	−	1.15571i	−0.943132	−	0.332418i	$-0.892136\pi$
$739$	−10.2081	−	31.4174i	−0.375513	−	1.15571i	0.567619	−	0.823291i	$-0.307864\pi$
$740$		0			0
$741$	4.94333	−	15.2140i	0.181598	−	0.558901i
$742$		0			0
$743$	−40.2017			−1.47486			−0.737428	−	0.675425i	$-0.763960\pi$
$743$	−40.2017			−1.47486			−0.737428	+	0.675425i	$0.763960\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.34568	+	3.15732i	−0.159000	+	0.115520i
$748$		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
$753$	−19.5274	+	14.1875i	−0.711617	+	0.517020i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	24.4003			0.886845			0.443422	−	0.896313i	$-0.353764\pi$
$757$	24.4003			0.886845			0.443422	+	0.896313i	$0.353764\pi$
$758$		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
$763$	14.1503	−	43.5502i	0.512276	−	1.57662i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.7136	−	8.51040i	−0.422952	−	0.307293i
$768$		0			0
$769$	33.2679	+	24.1706i	1.19967	+	0.871613i	0.994252	−	0.107061i	$-0.0341439\pi$
$769$	33.2679	+	24.1706i	1.19967	+	0.871613i	0.205420	+	0.978674i	$0.434144\pi$
$770$		0			0
$771$	−3.42166	+	2.48598i	−0.123228	+	0.0895304i
$772$		0			0
$773$	−1.48856	−	4.58131i	−0.0535397	−	0.164778i	0.920711	−	0.390244i	$-0.127609\pi$
$773$	−1.48856	−	4.58131i	−0.0535397	−	0.164778i	−0.974251	+	0.225466i	$0.927609\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	11.2002	+	34.4706i	0.401804	+	1.23663i
$778$		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
$783$	−3.91985	−	2.84794i	−0.140084	−	0.101777i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	12.4590	−	38.3447i	0.444114	−	1.36684i	−0.439339	−	0.898321i	$-0.644787\pi$
$787$	12.4590	−	38.3447i	0.444114	−	1.36684i	0.883453	−	0.468520i	$-0.155213\pi$
$788$		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
$793$	53.6333			1.90457
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.4289	+	17.7487i	−0.865318	+	0.628690i	−0.929326	−	0.369259i	$-0.879611\pi$
$797$	−24.4289	+	17.7487i	−0.865318	+	0.628690i	0.0640088	+	0.997949i	$0.479611\pi$
$798$		0			0
$799$	51.2132			1.81179
$800$		0			0
$801$	11.3452			0.400862
$802$		0			0
$803$	56.8001	−	41.2677i	2.00443	−	1.45630i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.53526			0.194850
$808$		0			0
$809$	3.36218	−	10.3477i	0.118208	−	0.363807i	−0.874395	−	0.485216i	$-0.838741\pi$
$809$	3.36218	−	10.3477i	0.118208	−	0.363807i	0.992603	+	0.121409i	$0.0387411\pi$
$810$		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
$813$	−4.89783	+	15.0740i	−0.171774	+	0.528667i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.929450	+	0.675285i	0.0325173	+	0.0236252i
$818$		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
$823$	7.03293	+	21.6451i	0.245152	+	0.754502i	0.995611	+	0.0935845i	$0.0298325\pi$
$823$	7.03293	+	21.6451i	0.245152	+	0.754502i	−0.750459	+	0.660917i	$0.770167\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.4761	−	44.5530i	−0.503385	−	1.54926i	−0.803469	−	0.595346i	$-0.797015\pi$
$827$	−14.4761	−	44.5530i	−0.503385	−	1.54926i	0.300084	−	0.953913i	$-0.402985\pi$
$828$		0			0
$829$	11.1652	−	8.11202i	0.387785	−	0.281742i	−0.376762	−	0.926310i	$-0.622963\pi$
$829$	11.1652	−	8.11202i	0.387785	−	0.281742i	0.764547	+	0.644568i	$0.222963\pi$
$830$		0			0
$831$	7.03232	+	5.10928i	0.243949	+	0.177239i
$832$		0			0
$833$	66.4215	+	48.2581i	2.30137	+	1.67204i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.0609183	−	0.187487i	0.00210564	−	0.00648051i
$838$		0			0
$839$	−3.27210	−	10.0705i	−0.112966	−	0.347672i	0.878552	−	0.477647i	$-0.158510\pi$
$839$	−3.27210	−	10.0705i	−0.112966	−	0.347672i	−0.991517	+	0.129975i	$0.958510\pi$
$840$		0			0
$841$	−1.70701	+	5.25362i	−0.0588623	+	0.181159i
$842$		0			0
$843$	−10.7800			−0.371283
$844$		0			0
$845$		0			0
$846$		0			0
$847$	31.5012	−	22.8870i	1.08239	−	0.786406i
$848$		0			0
$849$	9.84520			0.337886
$850$		0			0
$851$	−10.7940			−0.370012
$852$		0			0
$853$	−18.3240	+	13.3131i	−0.627401	+	0.455834i	−0.855499	−	0.517805i	$-0.826749\pi$
$853$	−18.3240	+	13.3131i	−0.627401	+	0.455834i	0.228098	+	0.973638i	$0.426749\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	39.4749			1.34844			0.674218	−	0.738533i	$-0.264481\pi$
$857$	39.4749			1.34844			0.674218	+	0.738533i	$0.264481\pi$
$858$		0			0
$859$	13.7012	−	42.1679i	0.467478	−	1.43875i	−0.388361	−	0.921507i	$-0.626959\pi$
$859$	13.7012	−	42.1679i	0.467478	−	1.43875i	0.855839	−	0.517242i	$-0.173041\pi$
$860$		0			0
$861$	10.7106	+	32.9638i	0.365016	+	1.12340i
$862$		0			0
$863$	1.55610	−	4.78917i	0.0529701	−	0.163025i	−0.921072	−	0.389393i	$-0.872685\pi$
$863$	1.55610	−	4.78917i	0.0529701	−	0.163025i	0.974042	+	0.226367i	$0.0726850\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	21.1716	+	15.3821i	0.719026	+	0.522403i
$868$		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
$873$	1.56968	+	4.83099i	0.0531257	+	0.163504i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.40602	−	16.6380i	−0.182548	−	0.561826i	0.817349	−	0.576143i	$-0.195443\pi$
$877$	−5.40602	−	16.6380i	−0.182548	−	0.561826i	−0.999898	+	0.0143164i	$0.995443\pi$
$878$		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
$883$	24.5572	+	17.8419i	0.826416	+	0.600427i	0.918543	−	0.395321i	$-0.129367\pi$
$883$	24.5572	+	17.8419i	0.826416	+	0.600427i	−0.0921269	+	0.995747i	$0.529367\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.2689	+	50.0705i	−0.546256	+	1.68120i	0.171729	+	0.985144i	$0.445065\pi$
$887$	−16.2689	+	50.0705i	−0.546256	+	1.68120i	−0.717985	+	0.696058i	$0.754935\pi$
$888$		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
$893$	21.6935			0.725947
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.11458	+	4.44250i	−0.204160	+	0.148331i
$898$		0			0
$899$	0.955163			0.0318565
$900$		0			0
$901$	−2.07265			−0.0690500
$902$		0			0
$903$	−1.47455	+	1.07132i	−0.0490699	+	0.0356513i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−8.79799			−0.292133			−0.146066	−	0.989275i	$-0.546661\pi$
$907$	−8.79799			−0.292133			−0.146066	+	0.989275i	$0.546661\pi$
$908$		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
$913$	7.38956	−	22.7427i	0.244559	−	0.752675i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−33.7697	−	24.5351i	−1.11517	−	0.810221i
$918$		0			0
$919$	27.0858	+	19.6790i	0.893478	+	0.649150i	0.936782	−	0.349912i	$-0.113789\pi$
$919$	27.0858	+	19.6790i	0.893478	+	0.649150i	−0.0433046	+	0.999062i	$0.513789\pi$
$920$		0			0
$921$	−26.4792	+	19.2383i	−0.872520	+	0.633923i
$922$		0			0
$923$	0.904506	+	2.78378i	0.0297722	+	0.0916294i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.972067	+	2.99171i	0.0319269	+	0.0982608i
$928$		0			0
$929$	1.51966	−	1.10410i	0.0498585	−	0.0362244i	−0.562577	−	0.826745i	$-0.690190\pi$
$929$	1.51966	−	1.10410i	0.0498585	−	0.0362244i	0.612435	+	0.790521i	$0.290190\pi$
$930$		0			0
$931$	28.1357	+	20.4418i	0.922110	+	0.669952i
$932$		0			0
$933$	−19.9216	−	14.4739i	−0.652205	−	0.473855i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.707094	−	2.17621i	0.0230997	−	0.0710937i	−0.938842	−	0.344348i	$-0.888100\pi$
$937$	0.707094	−	2.17621i	0.0230997	−	0.0710937i	0.961942	+	0.273254i	$0.0881000\pi$
$938$		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
$943$	−10.3221			−0.336135
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.0060	−	25.4333i	1.13754	−	0.826472i	0.150766	−	0.988569i	$-0.451826\pi$
$947$	35.0060	−	25.4333i	1.13754	−	0.826472i	0.986775	+	0.162098i	$0.0518260\pi$
$948$		0			0
$949$	−90.6473			−2.94253
$950$		0			0
$951$	1.62435			0.0526731
$952$		0			0
$953$	−28.1986	+	20.4875i	−0.913441	+	0.663654i	−0.941883	−	0.335942i	$-0.890945\pi$
$953$	−28.1986	+	20.4875i	−0.913441	+	0.663654i	0.0284419	+	0.999595i	$0.490945\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	21.5699			0.697257
$958$		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
$963$	2.39183	−	7.36130i	0.0770757	−	0.237215i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−28.2952	−	20.5577i	−0.909912	−	0.661090i	0.0310806	−	0.999517i	$-0.490105\pi$
$967$	−28.2952	−	20.5577i	−0.909912	−	0.661090i	−0.940993	+	0.338427i	$0.890105\pi$
$968$		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
$973$	−16.1297	−	49.6423i	−0.517096	−	1.59146i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.76386	−	14.6616i	−0.152409	−	0.469067i	0.845480	−	0.534007i	$-0.179314\pi$
$977$	−4.76386	−	14.6616i	−0.152409	−	0.469067i	−0.997889	+	0.0649398i	$0.979314\pi$
$978$		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
$983$	−47.5297	−	34.5324i	−1.51596	−	1.10141i	−0.963443	−	0.267912i	$-0.913666\pi$
$983$	−47.5297	−	34.5324i	−1.51596	−	1.10141i	−0.552520	−	0.833500i	$-0.686334\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.6352	+	32.7318i	−0.338522	+	1.04186i
$988$		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
$993$	9.01314			0.286023
$994$		0			0
$995$		0			0
$996$		0			0
$997$	9.54368	−	6.93389i	0.302251	−	0.219598i	−0.426313	−	0.904576i	$-0.640188\pi$
$997$	9.54368	−	6.93389i	0.302251	−	0.219598i	0.728564	+	0.684977i	$0.240188\pi$
$998$		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.m.d.901.1		24
5.2	odd	4		1500.2.o.c.349.3		24
5.3	odd	4		300.2.o.a.169.4	✓	24
5.4	even	2		1500.2.m.c.901.6		24
15.8	even	4		900.2.w.c.469.5		24
25.2	odd	20		7500.2.d.g.1249.14		24
25.3	odd	20		1500.2.o.c.649.3		24
25.4	even	10		1500.2.m.c.601.6		24
25.11	even	5		7500.2.a.m.1.2		12
25.14	even	10		7500.2.a.n.1.11		12
25.21	even	5	inner	1500.2.m.d.601.1		24
25.22	odd	20		300.2.o.a.229.4	yes	24
25.23	odd	20		7500.2.d.g.1249.11		24
75.47	even	20		900.2.w.c.829.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.4	✓	24	5.3	odd	4
300.2.o.a.229.4	yes	24	25.22	odd	20
900.2.w.c.469.5		24	15.8	even	4
900.2.w.c.829.5		24	75.47	even	20
1500.2.m.c.601.6		24	25.4	even	10
1500.2.m.c.901.6		24	5.4	even	2
1500.2.m.d.601.1		24	25.21	even	5	inner
1500.2.m.d.901.1		24	1.1	even	1	trivial
1500.2.o.c.349.3		24	5.2	odd	4
1500.2.o.c.649.3		24	25.3	odd	20
7500.2.a.m.1.2		12	25.11	even	5
7500.2.a.n.1.11		12	25.14	even	10
7500.2.d.g.1249.11		24	25.23	odd	20
7500.2.d.g.1249.14		24	25.2	odd	20

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.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} -4.41540 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} -4.41540 q^{7} +(0.309017 - 0.951057i) q^{9} +(1.37568 + 4.23392i) q^{11} +(1.77616 - 5.46646i) q^{13} +(5.31553 + 3.86196i) q^{17} +(2.25162 + 1.63590i) q^{19} +(-3.57213 + 2.59531i) q^{21} +(-0.406341 - 1.25059i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(3.91985 - 2.84794i) q^{29} +(0.159486 + 0.115873i) q^{31} +(3.60159 + 2.61671i) q^{33} +(2.53662 - 7.80690i) q^{37} +(-1.77616 - 5.46646i) q^{39} +(2.42573 - 7.46564i) q^{41} +0.412792 q^{43} +(6.30595 - 4.58154i) q^{47} +12.4958 q^{49} +6.57035 q^{51} +(-0.255208 + 0.185420i) q^{53} +2.78315 q^{57} +(0.778419 - 2.39573i) q^{59} +(2.88348 + 8.87444i) q^{61} +(-1.36443 + 4.19929i) q^{63} +(9.66428 + 7.02151i) q^{67} +(-1.06382 - 0.772907i) q^{69} +(-0.411990 + 0.299328i) q^{71} +(-4.87346 - 14.9990i) q^{73} +(-6.07420 - 18.6945i) q^{77} +(2.77617 - 2.01700i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.34568 - 3.15732i) q^{83} +(1.49725 - 4.60806i) q^{87} +(3.50585 + 10.7899i) q^{89} +(-7.84246 + 24.1366i) q^{91} +0.197136 q^{93} +(-4.10948 + 2.98572i) q^{97} +4.45181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more