LMFDB - Embedded newform 1500.2.m.c.901.6

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			901.6
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.c.601.6

$q$-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	$-0.185796\pi$
$7$	4.41540			1.66886			0.834432	+	0.551111i	$0.185796\pi$
$8$		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	$0.393620\pi$
$13$	−1.77616	+	5.46646i	−0.492619	+	1.51612i	−0.820635	+	0.571452i	$0.806380\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.31553	−	3.86196i	−1.28921	−	0.936662i	−0.289416	−	0.957203i	$-0.593461\pi$
$17$	−5.31553	−	3.86196i	−1.28921	−	0.936662i	−0.999789	+	0.0205412i	$0.993461\pi$
$18$		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	0.984441	−	0.175716i	$-0.0562241\pi$
$23$	0.406341	+	1.25059i	0.0847280	+	0.260766i	−0.899713	+	0.436482i	$0.856224\pi$
$24$		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	$0.335748\pi$
$37$	−2.53662	+	7.80690i	−0.417017	+	1.28345i	−0.910434	+	0.413654i	$0.864252\pi$
$38$		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	$-0.510020\pi$
$43$	−0.412792			−0.0629502			−0.0314751	+	0.999505i	$0.510020\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.30595	+	4.58154i	−0.919818	+	0.668287i	−0.943479	−	0.331433i	$-0.892468\pi$
$47$	−6.30595	+	4.58154i	−0.919818	+	0.668287i	0.0236610	+	0.999720i	$0.492468\pi$
$48$		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	−0.570120	−	0.821562i	$-0.693103\pi$
$53$	0.255208	−	0.185420i	0.0350556	−	0.0254694i	0.605175	+	0.796092i	$0.293103\pi$
$54$		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	−0.188431	−	0.982086i	$-0.560340\pi$
$67$	−9.66428	−	7.02151i	−1.18068	−	0.857814i	−0.992248	+	0.124273i	$0.960340\pi$
$68$		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	$0.274203\pi$
$73$	4.87346	+	14.9990i	0.570395	+	1.75549i	−0.0809557	+	0.996718i	$0.525797\pi$
$74$		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	0.800163	−	0.599783i	$-0.204746\pi$
$83$	4.34568	+	3.15732i	0.477000	+	0.346561i	−0.323163	+	0.946343i	$0.604746\pi$
$84$		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	−0.359277	−	0.933231i	$-0.616977\pi$
$97$	4.10948	−	2.98572i	0.417255	−	0.303153i	0.776532	+	0.630077i	$0.216977\pi$
$98$		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	−0.455305	−	0.890335i	$-0.650470\pi$
$103$	2.54490	−	1.84898i	0.250757	−	0.182185i	0.706062	+	0.708150i	$0.250470\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.74013			−0.748266			−0.374133	−	0.927375i	$-0.622060\pi$
$107$	−7.74013			−0.748266			−0.374133	+	0.927375i	$0.622060\pi$
$108$		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	$0.259727\pi$
$113$	−3.16009	+	9.72574i	−0.297276	+	0.914921i	−0.982447	+	0.186539i	$0.940273\pi$
$114$		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	$-0.932627\pi$
$127$	−3.49582	−	10.7590i	−0.310204	−	0.954709i	0.667480	−	0.744628i	$-0.267373\pi$
$128$		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	$-0.783027\pi$
$137$	2.59891	−	7.99861i	0.222039	−	0.683367i	0.998579	−	0.0532983i	$-0.0169734\pi$
$138$		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	$-0.318477\pi$
$157$	13.5289			1.07972			0.539861	+	0.841754i	$0.318477\pi$
$158$		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	$-0.706886\pi$
$163$	4.49876	−	13.8458i	0.352370	−	1.08448i	0.957519	−	0.288371i	$-0.0931135\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.06448	+	5.85918i	0.624048	+	0.453397i	0.854333	−	0.519726i	$-0.173966\pi$
$167$	8.06448	+	5.85918i	0.624048	+	0.453397i	−0.230285	+	0.973123i	$0.573966\pi$
$168$		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	$-0.964339\pi$
$173$	−3.36056	−	10.3427i	−0.255499	−	0.786344i	0.738232	−	0.674547i	$-0.235661\pi$
$174$		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	$-0.347810\pi$
$193$	12.7841			0.920219			0.460110	+	0.887862i	$0.347810\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.98132	+	5.79877i	−0.568646	+	0.413145i	−0.834613	−	0.550837i	$-0.814309\pi$
$197$	−7.98132	+	5.79877i	−0.568646	+	0.413145i	0.265967	+	0.963982i	$0.414309\pi$
$198$		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	0.990520	−	0.137369i	$-0.0438647\pi$
$223$	1.61919	+	4.98335i	0.108429	+	0.333710i	−0.882091	+	0.471079i	$0.843865\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.40074	+	7.38873i	0.159343	+	0.490407i	0.998575	−	0.0533663i	$-0.0169951\pi$
$227$	2.40074	+	7.38873i	0.159343	+	0.490407i	−0.839232	+	0.543773i	$0.816995\pi$
$228$		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	0.119544	−	0.992829i	$-0.461857\pi$
$233$	−12.0245	−	8.73631i	−0.787751	−	0.572334i	−0.907295	+	0.420494i	$0.861857\pi$
$234$		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	$-0.457889\pi$
$257$	4.22940			0.263823			0.131911	+	0.991262i	$0.457889\pi$
$258$		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	−0.838790	−	0.544455i	$-0.816736\pi$
$263$	2.59198	−	7.97729i	0.159828	−	0.491901i	0.998618	+	0.0525547i	$0.0167364\pi$
$264$		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	0.837360	−	0.546652i	$-0.184098\pi$
$277$	−2.68611	−	8.26699i	−0.161393	−	0.496715i	−0.998752	+	0.0499369i	$0.984098\pi$
$278$		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	0.325324	−	0.945602i	$-0.394527\pi$
$283$	−7.96493	−	5.78686i	−0.473466	−	0.343993i	−0.798791	+	0.601609i	$0.794527\pi$
$284$		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	$-0.407808\pi$
$293$	9.77733			0.571198			0.285599	+	0.958349i	$0.407808\pi$
$294$		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	$-0.116291\pi$
$307$	32.7301			1.86801			0.934003	+	0.357265i	$0.116291\pi$
$308$		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	$0.319943\pi$
$313$	−6.96817	+	21.4458i	−0.393864	+	1.21219i	−0.929843	+	0.367957i	$0.880057\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.31412	−	0.954767i	−0.0738086	−	0.0536251i	0.550269	−	0.834987i	$-0.314525\pi$
$317$	−1.31412	−	0.954767i	−0.0738086	−	0.0536251i	−0.624078	+	0.781362i	$0.714525\pi$
$318$		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	$-0.637406\pi$
$337$	8.33361	−	25.6482i	0.453961	−	1.39715i	0.872351	−	0.488880i	$-0.162594\pi$
$338$		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	0.152725	−	0.988269i	$-0.451195\pi$
$347$	21.2325	−	15.4263i	1.13982	−	0.828127i	0.987094	+	0.160142i	$0.0511952\pi$
$348$		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	−0.679449	−	0.733723i	$-0.737781\pi$
$353$	−3.59982	+	2.61542i	−0.191599	+	0.139205i	0.487850	+	0.872927i	$0.337781\pi$
$354$		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	0.702353	−	0.711829i	$-0.252133\pi$
$367$	4.64378	+	3.37390i	0.242403	+	0.176116i	−0.459950	+	0.887945i	$0.652133\pi$
$368$		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	0.959046	−	0.283252i	$-0.0914133\pi$
$373$	0.321953	+	0.990868i	0.0166701	+	0.0513052i	−0.942375	+	0.334557i	$0.891413\pi$
$374$		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	0.336231	−	0.941780i	$-0.390848\pi$
$383$	−8.91536	−	6.47739i	−0.455553	−	0.330979i	−0.791784	+	0.610801i	$0.790848\pi$
$384$		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	−0.642101	−	0.766620i	$-0.721937\pi$
$397$	−2.22008	+	1.61299i	−0.111423	+	0.0809534i	0.530678	+	0.847573i	$0.321937\pi$
$398$		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	0.711701	−	0.702482i	$-0.247925\pi$
$433$	5.48367	+	3.98412i	0.263529	+	0.191465i	−0.448173	+	0.893947i	$0.647925\pi$
$434$		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	$-0.307877\pi$
$443$	23.8927			1.13517			0.567587	+	0.823313i	$0.307877\pi$
$444$		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	$-0.544027\pi$
$457$	−5.89482			−0.275748			−0.137874	+	0.990450i	$0.544027\pi$
$458$		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	$-0.655900\pi$
$463$	9.22757	−	28.3995i	0.428842	−	1.31984i	0.899267	−	0.437399i	$-0.144100\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−21.1569	−	15.3714i	−0.979022	−	0.711301i	−0.0215325	−	0.999768i	$-0.506855\pi$
$467$	−21.1569	−	15.3714i	−0.979022	−	0.711301i	−0.957490	+	0.288467i	$0.906855\pi$
$468$		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	−0.824881	−	0.565307i	$-0.808758\pi$
$487$	3.85619	−	11.8681i	0.174741	−	0.537797i	0.999622	+	0.0275101i	$0.00875783\pi$
$488$		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	−0.986868	−	0.161526i	$-0.948358\pi$
$503$	−25.5273	+	18.5467i	−1.13821	+	0.826956i	−0.151338	+	0.988482i	$0.548358\pi$
$504$		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	$-0.953192\pi$
$523$	−6.29007	−	19.3589i	−0.275046	−	0.846504i	0.714162	−	0.699981i	$-0.246808\pi$
$524$		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	−0.289975	−	0.957034i	$-0.593647\pi$
$547$	12.4100	−	9.01637i	0.530612	−	0.385512i	0.820587	+	0.571522i	$0.193647\pi$
$548$		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	$-0.292196\pi$
$557$	28.6722			1.21488			0.607441	+	0.794365i	$0.292196\pi$
$558$		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	−0.891719	−	0.452590i	$-0.850500\pi$
$563$	2.27127	−	6.99026i	0.0957227	−	0.294604i	0.987441	+	0.157986i	$0.0505001\pi$
$564$		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	$-0.950156\pi$
$577$	−6.73333	−	20.7231i	−0.280312	−	0.862712i	0.707453	−	0.706761i	$-0.249844\pi$
$578$		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	$0.285160\pi$
$587$	−8.22724	+	25.3208i	−0.339575	+	1.04510i	−0.964425	+	0.264358i	$0.914840\pi$
$588$		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	$-0.534259\pi$
$593$	−5.23169			−0.214840			−0.107420	+	0.994214i	$0.534259\pi$
$594$		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	$-0.376427\pi$
$607$	18.6524			0.757078			0.378539	+	0.925585i	$0.376427\pi$
$608$		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	−0.995377	−	0.0960485i	$-0.969380\pi$
$613$	−3.30887	+	10.1837i	−0.133644	+	0.411314i	0.861733	+	0.507363i	$0.169380\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.5376	−	9.83565i	−0.545004	−	0.395968i	0.280936	−	0.959726i	$-0.409355\pi$
$617$	−13.5376	−	9.83565i	−0.545004	−	0.395968i	−0.825940	+	0.563758i	$0.809355\pi$
$618$		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	$-0.477146\pi$
$643$	3.63816			0.143475			0.0717376	+	0.997424i	$0.477146\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.09695	−	6.60932i	0.357638	−	0.259839i	−0.394428	−	0.918927i	$-0.629057\pi$
$647$	9.09695	−	6.60932i	0.357638	−	0.259839i	0.752066	+	0.659088i	$0.229057\pi$
$648$		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	−0.555313	−	0.831641i	$-0.687402\pi$
$653$	1.63604	−	1.18866i	0.0640233	−	0.0465157i	0.619337	+	0.785126i	$0.287402\pi$
$654$		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	$-0.863483\pi$
$673$	−10.8469	−	33.3834i	−0.418118	−	1.28683i	0.491314	−	0.870982i	$-0.336517\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.8621	+	36.5079i	0.455899	+	1.40311i	0.870077	+	0.492916i	$0.164069\pi$
$677$	11.8621	+	36.5079i	0.455899	+	1.40311i	−0.414178	+	0.910196i	$0.635931\pi$
$678$		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	0.450738	−	0.892657i	$-0.351161\pi$
$683$	−6.76730	−	4.91673i	−0.258944	−	0.188134i	−0.709681	+	0.704523i	$0.751161\pi$
$684$		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	$-0.851230\pi$
$727$	−11.7376	−	36.1247i	−0.435324	−	1.33979i	0.457430	−	0.889246i	$-0.348770\pi$
$728$		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	0.907290	−	0.420505i	$-0.138147\pi$
$733$	21.3271	+	15.4951i	0.787735	+	0.572323i	−0.119555	+	0.992828i	$0.538147\pi$
$734$		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	$-0.236040\pi$
$743$	40.2017			1.47486			0.737428	+	0.675425i	$0.236040\pi$
$744$		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	$-0.646236\pi$
$757$	−24.4003			−0.886845			−0.443422	+	0.896313i	$0.646236\pi$
$758$		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	0.974251	−	0.225466i	$-0.0723905\pi$
$773$	1.48856	+	4.58131i	0.0535397	+	0.164778i	−0.920711	+	0.390244i	$0.872391\pi$
$774$		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	$0.355213\pi$
$787$	−12.4590	+	38.3447i	−0.444114	+	1.36684i	−0.883453	+	0.468520i	$0.844787\pi$
$788$		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	−0.0640088	−	0.997949i	$-0.520389\pi$
$797$	24.4289	−	17.7487i	0.865318	−	0.628690i	0.929326	+	0.369259i	$0.120389\pi$
$798$		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	$-0.970167\pi$
$823$	−7.03293	−	21.6451i	−0.245152	−	0.754502i	0.750459	−	0.660917i	$-0.229833\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.4761	+	44.5530i	0.503385	+	1.54926i	0.803469	+	0.595346i	$0.202985\pi$
$827$	14.4761	+	44.5530i	0.503385	+	1.54926i	−0.300084	+	0.953913i	$0.597015\pi$
$828$		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	−0.228098	−	0.973638i	$-0.573251\pi$
$853$	18.3240	−	13.3131i	0.627401	−	0.455834i	0.855499	+	0.517805i	$0.173251\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−39.4749			−1.34844			−0.674218	−	0.738533i	$-0.735519\pi$
$857$	−39.4749			−1.34844			−0.674218	+	0.738533i	$0.735519\pi$
$858$		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	−0.974042	−	0.226367i	$-0.927315\pi$
$863$	−1.55610	+	4.78917i	−0.0529701	+	0.163025i	0.921072	+	0.389393i	$0.127315\pi$
$864$		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	0.999898	−	0.0143164i	$-0.00455722\pi$
$877$	5.40602	+	16.6380i	0.182548	+	0.561826i	−0.817349	+	0.576143i	$0.804557\pi$
$878$		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	0.0921269	−	0.995747i	$-0.470633\pi$
$883$	−24.5572	−	17.8419i	−0.826416	−	0.600427i	−0.918543	+	0.395321i	$0.870633\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.2689	−	50.0705i	0.546256	−	1.68120i	−0.171729	−	0.985144i	$-0.554935\pi$
$887$	16.2689	−	50.0705i	0.546256	−	1.68120i	0.717985	−	0.696058i	$-0.245065\pi$
$888$		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	$-0.453339\pi$
$907$	8.79799			0.292133			0.146066	+	0.989275i	$0.453339\pi$
$908$		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	−0.961942	−	0.273254i	$-0.911900\pi$
$937$	−0.707094	+	2.17621i	−0.0230997	+	0.0710937i	0.938842	+	0.344348i	$0.111900\pi$
$938$		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	−0.986775	−	0.162098i	$-0.948174\pi$
$947$	−35.0060	+	25.4333i	−1.13754	+	0.826472i	−0.150766	+	0.988569i	$0.548174\pi$
$948$		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	−0.0284419	−	0.999595i	$-0.509055\pi$
$953$	28.1986	−	20.4875i	0.913441	−	0.663654i	0.941883	+	0.335942i	$0.109055\pi$
$954$		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	0.940993	−	0.338427i	$-0.109895\pi$
$967$	28.2952	+	20.5577i	0.909912	+	0.661090i	−0.0310806	+	0.999517i	$0.509895\pi$
$968$		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	0.997889	−	0.0649398i	$-0.0206855\pi$
$977$	4.76386	+	14.6616i	0.152409	+	0.469067i	−0.845480	+	0.534007i	$0.820686\pi$
$978$		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	$0.0863337\pi$
$983$	47.5297	+	34.5324i	1.51596	+	1.10141i	0.552520	+	0.833500i	$0.313666\pi$
$984$		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	−0.728564	−	0.684977i	$-0.759812\pi$
$997$	−9.54368	+	6.93389i	−0.302251	+	0.219598i	0.426313	+	0.904576i	$0.359812\pi$
$998$		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.c.901.6		24
5.2	odd	4		300.2.o.a.169.4	✓	24
5.3	odd	4		1500.2.o.c.349.3		24
5.4	even	2		1500.2.m.d.901.1		24
15.2	even	4		900.2.w.c.469.5		24
25.2	odd	20		7500.2.d.g.1249.11		24
25.3	odd	20		300.2.o.a.229.4	yes	24
25.4	even	10		1500.2.m.d.601.1		24
25.11	even	5		7500.2.a.n.1.11		12
25.14	even	10		7500.2.a.m.1.2		12
25.21	even	5	inner	1500.2.m.c.601.6		24
25.22	odd	20		1500.2.o.c.649.3		24
25.23	odd	20		7500.2.d.g.1249.14		24
75.53	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	5.2	odd	4
300.2.o.a.229.4	yes	24	25.3	odd	20
900.2.w.c.469.5		24	15.2	even	4
900.2.w.c.829.5		24	75.53	even	20
1500.2.m.c.601.6		24	25.21	even	5	inner
1500.2.m.c.901.6		24	1.1	even	1	trivial
1500.2.m.d.601.1		24	25.4	even	10
1500.2.m.d.901.1		24	5.4	even	2
1500.2.o.c.349.3		24	5.3	odd	4
1500.2.o.c.649.3		24	25.22	odd	20
7500.2.a.m.1.2		12	25.14	even	10
7500.2.a.n.1.11		12	25.11	even	5
7500.2.d.g.1249.11		24	25.2	odd	20
7500.2.d.g.1249.14		24	25.23	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

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