LMFDB - Embedded newform 2548.2.k.i.1569.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(393,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("2548.393");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.k (of order $3$, degree $2$, 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 19 x^{16} - 16 x^{15} + 244 x^{14} - 181 x^{13} + 1600 x^{12} - 607 x^{11} + \cdots + 1296 $ x^18 - x^17 + 19x^16 - 16x^15 + 244x^14 - 181x^13 + 1600x^12 - 607x^11 + 7069x^10 - 1482x^9 + 17139x^8 + 5442x^7 + 25305x^6 + 13059x^5 + 28116x^4 + 18981x^3 + 15021x^2 + 4644x + 1296
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1569.3
Root			$-0.520270 + 0.901135i$ of defining polynomial
Character	$\chi$	$=$	2548.1569
Dual form			2548.2.k.i.393.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.520270 + 0.901135i) q^{3} +3.18009 q^{5} +(0.958637 + 1.66041i) q^{9} +(0.852470 - 1.47652i) q^{11} +(2.78983 + 2.28404i) q^{13} +(-1.65451 + 2.86569i) q^{15} +(-1.40001 - 2.42488i) q^{17} +(2.74455 + 4.75370i) q^{19} +(-2.73500 + 4.73716i) q^{23} +5.11296 q^{25} -5.11663 q^{27} +(3.81432 - 6.60660i) q^{29} +2.51962 q^{31} +(0.887030 + 1.53638i) q^{33} +(-3.95043 + 6.84235i) q^{37} +(-3.50970 + 1.32569i) q^{39} +(4.19364 - 7.26359i) q^{41} +(5.61467 + 9.72490i) q^{43} +(3.04855 + 5.28024i) q^{45} -6.25007 q^{47} +2.91353 q^{51} -1.84212 q^{53} +(2.71093 - 4.69547i) q^{55} -5.71163 q^{57} +(-1.34710 - 2.33325i) q^{59} +(-3.38846 - 5.86899i) q^{61} +(8.87191 + 7.26345i) q^{65} +(-1.79166 + 3.10325i) q^{67} +(-2.84588 - 4.92921i) q^{69} +(-2.00501 - 3.47278i) q^{71} +11.7029 q^{73} +(-2.66012 + 4.60746i) q^{75} +13.2439 q^{79} +(-0.213883 + 0.370457i) q^{81} -8.55336 q^{83} +(-4.45215 - 7.71134i) q^{85} +(3.96896 + 6.87444i) q^{87} +(0.105061 - 0.181971i) q^{89} +(-1.31088 + 2.27052i) q^{93} +(8.72791 + 15.1172i) q^{95} +(-6.33077 - 10.9652i) q^{97} +3.26884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{3} - 10 q^{9} + 2 q^{11} - 4 q^{13} - 10 q^{15} + 6 q^{17} + q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{27} + 2 q^{29} + 14 q^{31} + 14 q^{33} - 8 q^{37} + 11 q^{39} - 7 q^{41} - 2 q^{43} + 10 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) $ 18 * q + q^3 - 10 * q^9 + 2 * q^11 - 4 * q^13 - 10 * q^15 + 6 * q^17 + q^19 + 6 * q^23 + 10 * q^25 + 4 * q^27 + 2 * q^29 + 14 * q^31 + 14 * q^33 - 8 * q^37 + 11 * q^39 - 7 * q^41 - 2 * q^43 + 10 * q^45 - 24 * q^47 - 28 * q^51 - 26 * q^53 + q^55 - 2 * q^57 + 8 * q^59 + q^61 + 4 * q^65 + 29 * q^67 + 17 * q^69 + 7 * q^71 + 18 * q^73 + 59 * q^75 + 4 * q^79 - 13 * q^81 + 30 * q^83 - 46 * q^85 - 26 * q^87 - 13 * q^89 + 3 * q^93 - 14 * q^95 + 24 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.520270	+	0.901135i	−0.300378	+	0.520270i	−0.976222	−	0.216775i	$-0.930446\pi$
$3$	−0.520270	+	0.901135i	−0.300378	+	0.520270i	0.675843	+	0.737045i	$0.263780\pi$
$4$		0			0
$5$	3.18009			1.42218			0.711089	−	0.703102i	$-0.248202\pi$
$5$	3.18009			1.42218			0.711089	+	0.703102i	$0.248202\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.958637	+	1.66041i	0.319546	+	0.553470i
$10$		0			0
$11$	0.852470	−	1.47652i	0.257029	−	0.445188i	−0.708415	−	0.705796i	$-0.750590\pi$
$11$	0.852470	−	1.47652i	0.257029	−	0.445188i	0.965445	+	0.260608i	$0.0839229\pi$
$12$		0			0
$13$	2.78983	+	2.28404i	0.773760	+	0.633479i
$13$	2.78983	+	2.28404i	0.773760	+	0.633479i
$14$		0			0
$15$	−1.65451	+	2.86569i	−0.427192	+	0.739917i
$16$		0			0
$17$	−1.40001	−	2.42488i	−0.339552	−	0.588121i	0.644797	−	0.764354i	$-0.276942\pi$
$17$	−1.40001	−	2.42488i	−0.339552	−	0.588121i	−0.984348	+	0.176233i	$0.943609\pi$
$18$		0			0
$19$	2.74455	+	4.75370i	0.629643	+	1.09057i	0.987623	+	0.156844i	$0.0501321\pi$
$19$	2.74455	+	4.75370i	0.629643	+	1.09057i	−0.357981	+	0.933729i	$0.616535\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.73500	+	4.73716i	−0.570287	+	0.987766i	0.426249	+	0.904606i	$0.359835\pi$
$23$	−2.73500	+	4.73716i	−0.570287	+	0.987766i	−0.996536	+	0.0831603i	$0.973499\pi$
$24$		0			0
$25$	5.11296			1.02259
$26$		0			0
$27$	−5.11663			−0.984695
$28$		0			0
$29$	3.81432	−	6.60660i	0.708302	−	1.22682i	−0.257185	−	0.966362i	$-0.582795\pi$
$29$	3.81432	−	6.60660i	0.708302	−	1.22682i	0.965487	−	0.260453i	$-0.0838718\pi$
$30$		0			0
$31$	2.51962			0.452537			0.226269	−	0.974065i	$-0.427347\pi$
$31$	2.51962			0.452537			0.226269	+	0.974065i	$0.427347\pi$
$32$		0			0
$33$	0.887030	+	1.53638i	0.154412	+	0.267450i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.95043	+	6.84235i	−0.649447	+	1.12487i	0.333808	+	0.942641i	$0.391666\pi$
$37$	−3.95043	+	6.84235i	−0.649447	+	1.12487i	−0.983255	+	0.182234i	$0.941667\pi$
$38$		0			0
$39$	−3.50970	+	1.32569i	−0.562001	+	0.212281i
$40$		0			0
$41$	4.19364	−	7.26359i	0.654936	−	1.13438i	−0.326974	−	0.945033i	$-0.606029\pi$
$41$	4.19364	−	7.26359i	0.654936	−	1.13438i	0.981910	−	0.189349i	$-0.0606379\pi$
$42$		0			0
$43$	5.61467	+	9.72490i	0.856230	+	1.48303i	0.875499	+	0.483219i	$0.160533\pi$
$43$	5.61467	+	9.72490i	0.856230	+	1.48303i	−0.0192697	+	0.999814i	$0.506134\pi$
$44$		0			0
$45$	3.04855	+	5.28024i	0.454451	+	0.787132i
$46$		0			0
$47$	−6.25007			−0.911666			−0.455833	−	0.890065i	$-0.650659\pi$
$47$	−6.25007			−0.911666			−0.455833	+	0.890065i	$0.650659\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.91353			0.407976
$52$		0			0
$53$	−1.84212			−0.253035			−0.126517	−	0.991964i	$-0.540380\pi$
$53$	−1.84212			−0.253035			−0.126517	+	0.991964i	$0.540380\pi$
$54$		0			0
$55$	2.71093	−	4.69547i	0.365542	−	0.633137i
$56$		0			0
$57$	−5.71163			−0.756524
$58$		0			0
$59$	−1.34710	−	2.33325i	−0.175378	−	0.303764i	0.764914	−	0.644132i	$-0.222781\pi$
$59$	−1.34710	−	2.33325i	−0.175378	−	0.303764i	−0.940292	+	0.340369i	$0.889448\pi$
$60$		0			0
$61$	−3.38846	−	5.86899i	−0.433848	−	0.751447i	0.563353	−	0.826217i	$-0.309511\pi$
$61$	−3.38846	−	5.86899i	−0.433848	−	0.751447i	−0.997201	+	0.0747693i	$0.976178\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.87191	+	7.26345i	1.10042	+	0.900920i
$66$		0			0
$67$	−1.79166	+	3.10325i	−0.218887	+	0.379123i	−0.954468	−	0.298314i	$-0.903576\pi$
$67$	−1.79166	+	3.10325i	−0.218887	+	0.379123i	0.735581	+	0.677437i	$0.236909\pi$
$68$		0			0
$69$	−2.84588	−	4.92921i	−0.342604	−	0.593407i
$70$		0			0
$71$	−2.00501	−	3.47278i	−0.237951	−	0.412143i	0.722175	−	0.691710i	$-0.243142\pi$
$71$	−2.00501	−	3.47278i	−0.237951	−	0.412143i	−0.960126	+	0.279567i	$0.909809\pi$
$72$		0			0
$73$	11.7029			1.36972			0.684862	−	0.728673i	$-0.259862\pi$
$73$	11.7029			1.36972			0.684862	+	0.728673i	$0.259862\pi$
$74$		0			0
$75$	−2.66012	+	4.60746i	−0.307164	+	0.532024i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	13.2439			1.49005			0.745027	−	0.667034i	$-0.232436\pi$
$79$	13.2439			1.49005			0.745027	+	0.667034i	$0.232436\pi$
$80$		0			0
$81$	−0.213883	+	0.370457i	−0.0237648	+	0.0411618i
$82$		0			0
$83$	−8.55336			−0.938853			−0.469426	−	0.882972i	$-0.655539\pi$
$83$	−8.55336			−0.938853			−0.469426	+	0.882972i	$0.655539\pi$
$84$		0			0
$85$	−4.45215	−	7.71134i	−0.482903	−	0.836413i
$86$		0			0
$87$	3.96896	+	6.87444i	0.425517	+	0.737017i
$88$		0			0
$89$	0.105061	−	0.181971i	0.0111364	−	0.0192889i	−0.860403	−	0.509613i	$-0.829788\pi$
$89$	0.105061	−	0.181971i	0.0111364	−	0.0192889i	0.871540	+	0.490325i	$0.163122\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.31088	+	2.27052i	−0.135932	+	0.235442i
$94$		0			0
$95$	8.72791	+	15.1172i	0.895464	+	1.55099i
$96$		0			0
$97$	−6.33077	−	10.9652i	−0.642792	−	1.11335i	−0.984807	−	0.173654i	$-0.944443\pi$
$97$	−6.33077	−	10.9652i	−0.642792	−	1.11335i	0.342015	−	0.939695i	$-0.388891\pi$
$98$		0			0
$99$	3.26884			0.328531
$100$		0			0
$101$	5.77693	−	10.0059i	0.574826	−	0.995628i	−0.421234	−	0.906952i	$-0.638403\pi$
$101$	5.77693	−	10.0059i	0.574826	−	0.995628i	0.996061	−	0.0886761i	$-0.0282636\pi$
$102$		0			0
$103$	12.2027			1.20237			0.601183	−	0.799111i	$-0.294696\pi$
$103$	12.2027			1.20237			0.601183	+	0.799111i	$0.294696\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.13656	−	1.96858i	0.109875	−	0.190310i	−0.805844	−	0.592128i	$-0.798288\pi$
$107$	1.13656	−	1.96858i	0.109875	−	0.190310i	0.915720	+	0.401818i	$0.131621\pi$
$108$		0			0
$109$	−4.85215			−0.464751			−0.232376	−	0.972626i	$-0.574650\pi$
$109$	−4.85215			−0.464751			−0.232376	+	0.972626i	$0.574650\pi$
$110$		0			0
$111$	−4.11058	−	7.11974i	−0.390159	−	0.675776i
$112$		0			0
$113$	−0.333301	−	0.577294i	−0.0313543	−	0.0543072i	0.849922	−	0.526908i	$-0.176649\pi$
$113$	−0.333301	−	0.577294i	−0.0313543	−	0.0543072i	−0.881277	+	0.472601i	$0.843315\pi$
$114$		0			0
$115$	−8.69754	+	15.0646i	−0.811050	+	1.40478i
$116$		0			0
$117$	−1.11801	+	6.82183i	−0.103360	+	0.630678i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.04659	+	7.00890i	0.367872	+	0.637172i
$122$		0			0
$123$	4.36365	+	7.55807i	0.393457	+	0.681488i
$124$		0			0
$125$	0.359215			0.0321292
$126$		0			0
$127$	−9.03831	+	15.6548i	−0.802020	+	1.38914i	0.116264	+	0.993218i	$0.462908\pi$
$127$	−9.03831	+	15.6548i	−0.802020	+	1.38914i	−0.918284	+	0.395922i	$0.870425\pi$
$128$		0			0
$129$	−11.6846			−1.02877
$130$		0			0
$131$	−18.7051			−1.63427			−0.817135	−	0.576446i	$-0.804439\pi$
$131$	−18.7051			−1.63427			−0.817135	+	0.576446i	$0.804439\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−16.2713			−1.40041
$136$		0			0
$137$	11.2574	+	19.4984i	0.961786	+	1.66586i	0.718012	+	0.696031i	$0.245052\pi$
$137$	11.2574	+	19.4984i	0.961786	+	1.66586i	0.243775	+	0.969832i	$0.421614\pi$
$138$		0			0
$139$	−3.61314	−	6.25815i	−0.306463	−	0.530809i	0.671123	−	0.741346i	$-0.265812\pi$
$139$	−3.61314	−	6.25815i	−0.306463	−	0.530809i	−0.977586	+	0.210537i	$0.932479\pi$
$140$		0			0
$141$	3.25173	−	5.63215i	0.273845	−	0.474313i
$142$		0			0
$143$	5.75068	−	2.17217i	0.480896	−	0.181646i
$144$		0			0
$145$	12.1299	−	21.0096i	1.00733	−	1.74475i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.74931	+	6.49399i	0.307155	+	0.532009i	0.977739	−	0.209825i	$-0.0672895\pi$
$149$	3.74931	+	6.49399i	0.307155	+	0.532009i	−0.670584	+	0.741834i	$0.733956\pi$
$150$		0			0
$151$	−1.98514			−0.161549			−0.0807743	−	0.996732i	$-0.525739\pi$
$151$	−1.98514			−0.161549			−0.0807743	+	0.996732i	$0.525739\pi$
$152$		0			0
$153$	2.68420	−	4.64917i	0.217005	−	0.375863i
$154$		0			0
$155$	8.01261			0.643589
$156$		0			0
$157$	−4.02469			−0.321205			−0.160603	−	0.987019i	$-0.551344\pi$
$157$	−4.02469			−0.321205			−0.160603	+	0.987019i	$0.551344\pi$
$158$		0			0
$159$	0.958401	−	1.66000i	0.0760061	−	0.131646i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.99358	+	3.45298i	0.156149	+	0.270458i	0.933477	−	0.358638i	$-0.116759\pi$
$163$	1.99358	+	3.45298i	0.156149	+	0.270458i	−0.777328	+	0.629096i	$0.783425\pi$
$164$		0			0
$165$	2.82083	+	4.88583i	0.219602	+	0.380361i
$166$		0			0
$167$	1.98915	−	3.44532i	0.153925	−	0.266607i	−0.778742	−	0.627345i	$-0.784142\pi$
$167$	1.98915	−	3.44532i	0.153925	−	0.266607i	0.932667	+	0.360738i	$0.117475\pi$
$168$		0			0
$169$	2.56631	+	12.7442i	0.197409	+	0.980321i
$170$		0			0
$171$	−5.26206	+	9.11415i	−0.402399	+	0.696976i
$172$		0			0
$173$	11.3603	+	19.6766i	0.863706	+	1.49598i	0.868326	+	0.495993i	$0.165196\pi$
$173$	11.3603	+	19.6766i	0.863706	+	1.49598i	−0.00462066	+	0.999989i	$0.501471\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.80343			0.210719
$178$		0			0
$179$	2.06510	−	3.57686i	0.154353	−	0.267347i	−0.778470	−	0.627681i	$-0.784004\pi$
$179$	2.06510	−	3.57686i	0.154353	−	0.267347i	0.932823	+	0.360334i	$0.117337\pi$
$180$		0			0
$181$	−2.63446			−0.195818			−0.0979091	−	0.995195i	$-0.531215\pi$
$181$	−2.63446			−0.195818			−0.0979091	+	0.995195i	$0.531215\pi$
$182$		0			0
$183$	7.05167			0.521274
$184$		0			0
$185$	−12.5627	+	21.7593i	−0.923629	+	1.59977i
$186$		0			0
$187$	−4.77386			−0.349099
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.34005	+	4.05309i	0.169320	+	0.293271i	0.938181	−	0.346145i	$-0.112509\pi$
$191$	2.34005	+	4.05309i	0.169320	+	0.293271i	−0.768861	+	0.639416i	$0.779176\pi$
$192$		0			0
$193$	8.96829	−	15.5335i	0.645551	−	1.11813i	−0.338622	−	0.940922i	$-0.609961\pi$
$193$	8.96829	−	15.5335i	0.645551	−	1.11813i	0.984174	−	0.177206i	$-0.0567057\pi$
$194$		0			0
$195$	−11.1611	+	4.21583i	−0.799266	+	0.301902i
$196$		0			0
$197$	11.3526	−	19.6632i	0.808838	−	1.40095i	−0.104832	−	0.994490i	$-0.533430\pi$
$197$	11.3526	−	19.6632i	0.808838	−	1.40095i	0.913669	−	0.406458i	$-0.133236\pi$
$198$		0			0
$199$	−3.97980	−	6.89322i	−0.282121	−	0.488648i	0.689786	−	0.724013i	$-0.257705\pi$
$199$	−3.97980	−	6.89322i	−0.282121	−	0.488648i	−0.971907	+	0.235366i	$0.924371\pi$
$200$		0			0
$201$	−1.86430	−	3.22906i	−0.131498	−	0.227761i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	13.3361	−	23.0989i	0.931436	−	1.61329i
$206$		0			0
$207$	−10.4875			−0.728931
$208$		0			0
$209$	9.35859			0.647347
$210$		0			0
$211$	−5.08147	+	8.80136i	−0.349823	+	0.605911i	−0.986218	−	0.165453i	$-0.947092\pi$
$211$	−5.08147	+	8.80136i	−0.349823	+	0.605911i	0.636395	+	0.771363i	$0.280425\pi$
$212$		0			0
$213$	4.17259			0.285901
$214$		0			0
$215$	17.8552	+	30.9260i	1.21771	+	2.10914i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.08869	+	10.5459i	−0.411435	+	0.712627i
$220$		0			0
$221$	1.63275	−	9.96269i	0.109831	−	0.670163i
$222$		0			0
$223$	−1.33387	+	2.31033i	−0.0893224	+	0.154711i	−0.907225	−	0.420646i	$-0.861803\pi$
$223$	−1.33387	+	2.31033i	−0.0893224	+	0.154711i	0.817902	+	0.575357i	$0.195137\pi$
$224$		0			0
$225$	4.90147	+	8.48960i	0.326765	+	0.565973i
$226$		0			0
$227$	−12.5757	−	21.7817i	−0.834677	−	1.44570i	−0.894293	−	0.447482i	$-0.852321\pi$
$227$	−12.5757	−	21.7817i	−0.834677	−	1.44570i	0.0596159	−	0.998221i	$-0.481012\pi$
$228$		0			0
$229$	12.3075			0.813301			0.406651	−	0.913584i	$-0.366697\pi$
$229$	12.3075			0.813301			0.406651	+	0.913584i	$0.366697\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−21.1440			−1.38519			−0.692594	−	0.721327i	$-0.743532\pi$
$233$	−21.1440			−1.38519			−0.692594	+	0.721327i	$0.743532\pi$
$234$		0			0
$235$	−19.8758			−1.29655
$236$		0			0
$237$	−6.89041	+	11.9345i	−0.447580	+	0.775231i
$238$		0			0
$239$	−27.3984			−1.77225			−0.886127	−	0.463443i	$-0.846614\pi$
$239$	−27.3984			−1.77225			−0.886127	+	0.463443i	$0.846614\pi$
$240$		0			0
$241$	8.57805	+	14.8576i	0.552561	+	0.957064i	0.998089	+	0.0617955i	$0.0196827\pi$
$241$	8.57805	+	14.8576i	0.552561	+	0.957064i	−0.445528	+	0.895268i	$0.646984\pi$
$242$		0			0
$243$	−7.89749	−	13.6789i	−0.506624	−	0.877499i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.20082	+	19.5307i	−0.203663	+	1.24271i
$248$		0			0
$249$	4.45006	−	7.70773i	0.282011	−	0.488457i
$250$		0			0
$251$	13.4469	+	23.2907i	0.848759	+	1.47009i	0.882317	+	0.470656i	$0.155983\pi$
$251$	13.4469	+	23.2907i	0.848759	+	1.47009i	−0.0335582	+	0.999437i	$0.510684\pi$
$252$		0			0
$253$	4.66301	+	8.07658i	0.293161	+	0.507770i
$254$		0			0
$255$	9.26528			0.580214
$256$		0			0
$257$	−5.65006	+	9.78619i	−0.352441	+	0.610446i	−0.986677	−	0.162694i	$-0.947982\pi$
$257$	−5.65006	+	9.78619i	−0.352441	+	0.610446i	0.634235	+	0.773140i	$0.281315\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	14.6262			0.905340
$262$		0			0
$263$	0.498739	−	0.863842i	0.0307536	−	0.0532668i	−0.850239	−	0.526397i	$-0.823543\pi$
$263$	0.498739	−	0.863842i	0.0307536	−	0.0532668i	0.880993	+	0.473130i	$0.156876\pi$
$264$		0			0
$265$	−5.85810			−0.359860
$266$		0			0
$267$	0.109320	+	0.189348i	0.00669029	+	0.0115879i
$268$		0			0
$269$	6.56406	+	11.3693i	0.400218	+	0.693198i	0.993752	−	0.111611i	$-0.0356010\pi$
$269$	6.56406	+	11.3693i	0.400218	+	0.693198i	−0.593534	+	0.804809i	$0.702268\pi$
$270$		0			0
$271$	3.22120	−	5.57928i	0.195674	−	0.338917i	−0.751447	−	0.659793i	$-0.770644\pi$
$271$	3.22120	−	5.57928i	0.195674	−	0.338917i	0.947121	+	0.320876i	$0.103977\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.35864	−	7.54939i	0.262836	−	0.455246i
$276$		0			0
$277$	11.9907	+	20.7685i	0.720451	+	1.24786i	0.960819	+	0.277175i	$0.0893983\pi$
$277$	11.9907	+	20.7685i	0.720451	+	1.24786i	−0.240369	+	0.970682i	$0.577268\pi$
$278$		0			0
$279$	2.41540	+	4.18360i	0.144606	+	0.250466i
$280$		0			0
$281$	−10.3602			−0.618035			−0.309018	−	0.951056i	$-0.600000\pi$
$281$	−10.3602			−0.618035			−0.309018	+	0.951056i	$0.600000\pi$
$282$		0			0
$283$	14.9565	−	25.9054i	0.889071	−	1.53992i	0.0480964	−	0.998843i	$-0.484685\pi$
$283$	14.9565	−	25.9054i	0.889071	−	1.53992i	0.840975	−	0.541074i	$-0.181982\pi$
$284$		0			0
$285$	−18.1635			−1.07591
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.57996	−	7.93272i	0.269409	−	0.466631i
$290$		0			0
$291$	13.1748			0.772323
$292$		0			0
$293$	−0.184399	−	0.319389i	−0.0107727	−	0.0186589i	0.860589	−	0.509300i	$-0.170096\pi$
$293$	−0.184399	−	0.319389i	−0.0107727	−	0.0186589i	−0.871362	+	0.490642i	$0.836762\pi$
$294$		0			0
$295$	−4.28391	−	7.41995i	−0.249419	−	0.432006i
$296$		0			0
$297$	−4.36177	+	7.55481i	−0.253096	+	0.438374i
$298$		0			0
$299$	−18.4501	+	6.96902i	−1.06699	+	0.403029i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6.01113	+	10.4116i	0.345331	+	0.598130i
$304$		0			0
$305$	−10.7756	−	18.6639i	−0.617010	−	1.06869i
$306$		0			0
$307$	13.8684			0.791511			0.395756	−	0.918356i	$-0.370483\pi$
$307$	13.8684			0.791511			0.395756	+	0.918356i	$0.370483\pi$
$308$		0			0
$309$	−6.34869	+	10.9963i	−0.361165	+	0.625555i
$310$		0			0
$311$	1.18119			0.0669791			0.0334895	−	0.999439i	$-0.489338\pi$
$311$	1.18119			0.0669791			0.0334895	+	0.999439i	$0.489338\pi$
$312$		0			0
$313$	10.5862			0.598368			0.299184	−	0.954195i	$-0.403286\pi$
$313$	10.5862			0.598368			0.299184	+	0.954195i	$0.403286\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.48888			0.476783			0.238392	−	0.971169i	$-0.423380\pi$
$317$	8.48888			0.476783			0.238392	+	0.971169i	$0.423380\pi$
$318$		0			0
$319$	−6.50319	−	11.2639i	−0.364109	−	0.630655i
$320$		0			0
$321$	1.18264	+	2.04839i	0.0660084	+	0.114330i
$322$		0			0
$323$	7.68478	−	13.3104i	0.427592	−	0.740612i
$324$		0			0
$325$	14.2643	+	11.6782i	0.791240	+	0.647790i
$326$		0			0
$327$	2.52443	−	4.37244i	0.139601	−	0.241796i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.17210	−	3.76219i	−0.119389	−	0.206788i	0.800136	−	0.599818i	$-0.204760\pi$
$331$	−2.17210	−	3.76219i	−0.119389	−	0.206788i	−0.919526	+	0.393030i	$0.871427\pi$
$332$		0			0
$333$	−15.1481			−0.830112
$334$		0			0
$335$	−5.69765	+	9.86862i	−0.311296	+	0.539180i
$336$		0			0
$337$	8.59397			0.468143			0.234072	−	0.972219i	$-0.424795\pi$
$337$	8.59397			0.468143			0.234072	+	0.972219i	$0.424795\pi$
$338$		0			0
$339$	0.693626			0.0376726
$340$		0			0
$341$	2.14790	−	3.72027i	0.116315	−	0.201464i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.05015	−	15.6753i	−0.487244	−	0.843931i
$346$		0			0
$347$	−10.4098	−	18.0304i	−0.558829	−	0.967920i	−0.997595	−	0.0693188i	$-0.977917\pi$
$347$	−10.4098	−	18.0304i	−0.558829	−	0.967920i	0.438765	−	0.898602i	$-0.355416\pi$
$348$		0			0
$349$	0.115786	−	0.200546i	0.00619786	−	0.0107350i	−0.862910	−	0.505358i	$-0.831360\pi$
$349$	0.115786	−	0.200546i	0.00619786	−	0.0107350i	0.869108	+	0.494623i	$0.164694\pi$
$350$		0			0
$351$	−14.2745	−	11.6866i	−0.761917	−	0.623784i
$352$		0			0
$353$	−9.09972	+	15.7612i	−0.484329	+	0.838883i	−0.999838	−	0.0180014i	$-0.994270\pi$
$353$	−9.09972	+	15.7612i	−0.484329	+	0.838883i	0.515509	+	0.856884i	$0.327603\pi$
$354$		0			0
$355$	−6.37611	−	11.0437i	−0.338409	−	0.586141i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.54298			0.239769			0.119885	−	0.992788i	$-0.461748\pi$
$359$	4.54298			0.239769			0.119885	+	0.992788i	$0.461748\pi$
$360$		0			0
$361$	−5.56510	+	9.63904i	−0.292900	+	0.507318i
$362$		0			0
$363$	−8.42128			−0.442003
$364$		0			0
$365$	37.2163			1.94799
$366$		0			0
$367$	5.01139	−	8.67998i	0.261592	−	0.453091i	−0.705073	−	0.709135i	$-0.749086\pi$
$367$	5.01139	−	8.67998i	0.261592	−	0.453091i	0.966665	+	0.256044i	$0.0824190\pi$
$368$		0			0
$369$	16.0807			0.837128
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−4.21567	−	7.30176i	−0.218279	−	0.378071i	0.736003	−	0.676979i	$-0.236711\pi$
$373$	−4.21567	−	7.30176i	−0.218279	−	0.378071i	−0.954282	+	0.298908i	$0.903378\pi$
$374$		0			0
$375$	−0.186889	+	0.323702i	−0.00965092	+	0.0167159i
$376$		0			0
$377$	25.7311	−	9.71923i	1.32522	−	0.500566i
$378$		0			0
$379$	−5.15804	+	8.93398i	−0.264951	+	0.458908i	−0.967551	−	0.252677i	$-0.918689\pi$
$379$	−5.15804	+	8.93398i	−0.264951	+	0.458908i	0.702600	+	0.711585i	$0.252022\pi$
$380$		0			0
$381$	−9.40473	−	16.2895i	−0.481819	−	0.834535i
$382$		0			0
$383$	−1.09813	−	1.90201i	−0.0561116	−	0.0971881i	0.836605	−	0.547806i	$-0.184537\pi$
$383$	−1.09813	−	1.90201i	−0.0561116	−	0.0971881i	−0.892717	+	0.450618i	$0.851204\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.7649	+	18.6453i	−0.547209	+	0.947794i
$388$		0			0
$389$	−32.7955			−1.66280			−0.831398	−	0.555677i	$-0.812459\pi$
$389$	−32.7955			−1.66280			−0.831398	+	0.555677i	$0.812459\pi$
$390$		0			0
$391$	15.3161			0.774568
$392$		0			0
$393$	9.73170	−	16.8558i	0.490899	−	0.850262i
$394$		0			0
$395$	42.1167			2.11912
$396$		0			0
$397$	−2.75848	−	4.77782i	−0.138444	−	0.239792i	0.788464	−	0.615081i	$-0.210877\pi$
$397$	−2.75848	−	4.77782i	−0.138444	−	0.239792i	−0.926908	+	0.375289i	$0.877543\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.66790	−	16.7453i	0.482792	−	0.836220i	−0.517013	−	0.855977i	$-0.672956\pi$
$401$	9.66790	−	16.7453i	0.482792	−	0.836220i	0.999805	+	0.0197577i	$0.00628949\pi$
$402$		0			0
$403$	7.02931	+	5.75492i	0.350155	+	0.286673i
$404$		0			0
$405$	−0.680167	+	1.17808i	−0.0337978	+	0.0585395i
$406$		0			0
$407$	6.73525	+	11.6658i	0.333854	+	0.578252i
$408$		0			0
$409$	−18.0322	−	31.2326i	−0.891633	−	1.54435i	−0.837918	−	0.545797i	$-0.816227\pi$
$409$	−18.0322	−	31.2326i	−0.891633	−	1.54435i	−0.0537150	−	0.998556i	$-0.517106\pi$
$410$		0			0
$411$	−23.4276			−1.15560
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−27.2004			−1.33522
$416$		0			0
$417$	7.51925			0.368219
$418$		0			0
$419$	4.22915	−	7.32510i	0.206607	−	0.357854i	−0.744036	−	0.668139i	$-0.767091\pi$
$419$	4.22915	−	7.32510i	0.206607	−	0.357854i	0.950644	+	0.310285i	$0.100424\pi$
$420$		0			0
$421$	−40.2697			−1.96262			−0.981312	−	0.192424i	$-0.938365\pi$
$421$	−40.2697			−1.96262			−0.981312	+	0.192424i	$0.938365\pi$
$422$		0			0
$423$	−5.99155	−	10.3777i	−0.291319	−	0.504579i
$424$		0			0
$425$	−7.15818	−	12.3983i	−0.347223	−	0.601407i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.03449	+	6.31226i	−0.0499458	+	0.304759i
$430$		0			0
$431$	6.53799	−	11.3241i	0.314924	−	0.545464i	−0.664498	−	0.747290i	$-0.731354\pi$
$431$	6.53799	−	11.3241i	0.314924	−	0.545464i	0.979421	+	0.201827i	$0.0646877\pi$
$432$		0			0
$433$	−9.78438	−	16.9470i	−0.470207	−	0.814423i	0.529212	−	0.848490i	$-0.322488\pi$
$433$	−9.78438	−	16.9470i	−0.470207	−	0.814423i	−0.999420	+	0.0340664i	$0.989154\pi$
$434$		0			0
$435$	12.6216	+	21.8613i	0.605161	+	1.04817i
$436$		0			0
$437$	−30.0254			−1.43631
$438$		0			0
$439$	7.19768	−	12.4667i	0.343527	−	0.595006i	−0.641558	−	0.767074i	$-0.721712\pi$
$439$	7.19768	−	12.4667i	0.343527	−	0.595006i	0.985085	+	0.172069i	$0.0550451\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.63764			0.410386			0.205193	−	0.978721i	$-0.434218\pi$
$443$	8.63764			0.410386			0.205193	+	0.978721i	$0.434218\pi$
$444$		0			0
$445$	0.334103	−	0.578684i	0.0158380	−	0.0274322i
$446$		0			0
$447$	−7.80262			−0.369051
$448$		0			0
$449$	−11.4447	−	19.8228i	−0.540110	−	0.935498i	−0.998897	−	0.0469519i	$-0.985049\pi$
$449$	−11.4447	−	19.8228i	−0.540110	−	0.935498i	0.458787	−	0.888546i	$-0.348284\pi$
$450$		0			0
$451$	−7.14990	−	12.3840i	−0.336676	−	0.583140i
$452$		0			0
$453$	1.03281	−	1.78888i	0.0485257	−	0.0840490i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.9024	−	22.3476i	0.603548	−	1.04538i	−0.388732	−	0.921351i	$-0.627087\pi$
$457$	12.9024	−	22.3476i	0.603548	−	1.04538i	0.992279	−	0.124024i	$-0.0395800\pi$
$458$		0			0
$459$	7.16331	+	12.4072i	0.334355	+	0.579119i
$460$		0			0
$461$	3.84106	+	6.65291i	0.178896	+	0.309857i	0.941503	−	0.337005i	$-0.109414\pi$
$461$	3.84106	+	6.65291i	0.178896	+	0.309857i	−0.762607	+	0.646862i	$0.776081\pi$
$462$		0			0
$463$	7.95930			0.369900			0.184950	−	0.982748i	$-0.440788\pi$
$463$	7.95930			0.369900			0.184950	+	0.982748i	$0.440788\pi$
$464$		0			0
$465$	−4.16873	+	7.22044i	−0.193320	+	0.334840i
$466$		0			0
$467$	−21.5156			−0.995621			−0.497810	−	0.867286i	$-0.665862\pi$
$467$	−21.5156			−0.995621			−0.497810	+	0.867286i	$0.665862\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.09393	−	3.62679i	0.0964831	−	0.167114i
$472$		0			0
$473$	19.1454			0.880305
$474$		0			0
$475$	14.0328	+	24.3055i	0.643867	+	1.11521i
$476$		0			0
$477$	−1.76593	−	3.05867i	−0.0808562	−	0.140047i
$478$		0			0
$479$	16.7505	−	29.0126i	0.765348	−	1.32562i	−0.174715	−	0.984619i	$-0.555900\pi$
$479$	16.7505	−	29.0126i	0.765348	−	1.32562i	0.940063	−	0.341002i	$-0.110766\pi$
$480$		0			0
$481$	−26.6492	+	10.0660i	−1.21510	+	0.458972i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.1324	−	34.8703i	−0.914165	−	1.58338i
$486$		0			0
$487$	−7.62298	−	13.2034i	−0.345430	−	0.598303i	0.640001	−	0.768374i	$-0.278934\pi$
$487$	−7.62298	−	13.2034i	−0.345430	−	0.598303i	−0.985432	+	0.170071i	$0.945600\pi$
$488$		0			0
$489$	−4.14880			−0.187615
$490$		0			0
$491$	10.9575	−	18.9790i	0.494507	−	0.856510i	−0.505473	−	0.862842i	$-0.668682\pi$
$491$	10.9575	−	18.9790i	0.494507	−	0.856510i	0.999980	+	0.00633175i	$0.00201547\pi$
$492$		0			0
$493$	−21.3603			−0.962020
$494$		0			0
$495$	10.3952			0.467229
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−36.3127			−1.62558			−0.812791	−	0.582555i	$-0.802053\pi$
$499$	−36.3127			−1.62558			−0.812791	+	0.582555i	$0.802053\pi$
$500$		0			0
$501$	2.06980	+	3.58499i	0.0924717	+	0.160166i
$502$		0			0
$503$	−13.2906	−	23.0199i	−0.592597	−	1.02641i	−0.993881	−	0.110454i	$-0.964769\pi$
$503$	−13.2906	−	23.0199i	−0.592597	−	1.02641i	0.401285	−	0.915953i	$-0.368564\pi$
$504$		0			0
$505$	18.3711	−	31.8198i	0.817505	−	1.41596i
$506$		0			0
$507$	−12.8194	−	4.31782i	−0.569329	−	0.191761i
$508$		0			0
$509$	17.5859	−	30.4597i	0.779483	−	1.35010i	−0.152757	−	0.988264i	$-0.548815\pi$
$509$	17.5859	−	30.4597i	0.779483	−	1.35010i	0.932240	−	0.361841i	$-0.117852\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−14.0428	−	24.3229i	−0.620006	−	1.07388i
$514$		0			0
$515$	38.8056			1.70998
$516$		0			0
$517$	−5.32800	+	9.22836i	−0.234325	+	0.405863i
$518$		0			0
$519$	−23.6417			−1.03775
$520$		0			0
$521$	−7.61490			−0.333615			−0.166807	−	0.985989i	$-0.553346\pi$
$521$	−7.61490			−0.333615			−0.166807	+	0.985989i	$0.553346\pi$
$522$		0			0
$523$	19.0037	−	32.9154i	0.830975	−	1.43929i	−0.0662915	−	0.997800i	$-0.521117\pi$
$523$	19.0037	−	32.9154i	0.830975	−	1.43929i	0.897266	−	0.441490i	$-0.145550\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.52749	−	6.10979i	−0.153660	−	0.266146i
$528$		0			0
$529$	−3.46046	−	5.99369i	−0.150455	−	0.260595i
$530$		0			0
$531$	2.58277	−	4.47349i	0.112083	−	0.194133i
$532$		0			0
$533$	28.2899	−	10.6858i	1.22537	−	0.462852i
$534$		0			0
$535$	3.61436	−	6.26026i	0.156262	−	0.270654i
$536$		0			0
$537$	2.14882	+	3.72187i	0.0927286	+	0.160611i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.91225			−0.383168			−0.191584	−	0.981476i	$-0.561362\pi$
$541$	−8.91225			−0.383168			−0.191584	+	0.981476i	$0.561362\pi$
$542$		0			0
$543$	1.37063	−	2.37401i	0.0588195	−	0.101878i
$544$		0			0
$545$	−15.4303			−0.660960
$546$		0			0
$547$	−16.7066			−0.714321			−0.357161	−	0.934043i	$-0.616255\pi$
$547$	−16.7066			−0.714321			−0.357161	+	0.934043i	$0.616255\pi$
$548$		0			0
$549$	6.49662	−	11.2525i	0.277269	−	0.480244i
$550$		0			0
$551$	41.8744			1.78391
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−13.0720	−	22.6414i	−0.554876	−	0.961074i
$556$		0			0
$557$	18.3262	−	31.7419i	0.776507	−	1.34495i	−0.157437	−	0.987529i	$-0.550323\pi$
$557$	18.3262	−	31.7419i	0.776507	−	1.34495i	0.933944	−	0.357420i	$-0.116343\pi$
$558$		0			0
$559$	−6.54808	+	39.9550i	−0.276954	+	1.68992i
$560$		0			0
$561$	2.48370	−	4.30189i	0.104862	−	0.181626i
$562$		0			0
$563$	−1.96094	−	3.39646i	−0.0826440	−	0.143144i	0.821741	−	0.569861i	$-0.193003\pi$
$563$	−1.96094	−	3.39646i	−0.0826440	−	0.143144i	−0.904385	+	0.426718i	$0.859670\pi$
$564$		0			0
$565$	−1.05993	−	1.83585i	−0.0445914	−	0.0772346i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.00915	−	1.74790i	0.0423058	−	0.0732757i	−0.844097	−	0.536190i	$-0.819863\pi$
$569$	1.00915	−	1.74790i	0.0423058	−	0.0732757i	0.886403	+	0.462914i	$0.153196\pi$
$570$		0			0
$571$	5.56366			0.232832			0.116416	−	0.993201i	$-0.462859\pi$
$571$	5.56366			0.232832			0.116416	+	0.993201i	$0.462859\pi$
$572$		0			0
$573$	−4.86984			−0.203441
$574$		0			0
$575$	−13.9839	+	24.2209i	−0.583171	+	1.01008i
$576$		0			0
$577$	1.08138			0.0450186			0.0225093	−	0.999747i	$-0.492834\pi$
$577$	1.08138			0.0450186			0.0225093	+	0.999747i	$0.492834\pi$
$578$		0			0
$579$	9.33187	+	16.1633i	0.387819	+	0.671723i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.57035	+	2.71993i	−0.0650374	+	0.112648i
$584$		0			0
$585$	−3.55536	+	21.6940i	−0.146996	+	0.896937i
$586$		0			0
$587$	11.3515	−	19.6613i	0.468526	−	0.811510i	−0.530827	−	0.847480i	$-0.678119\pi$
$587$	11.3515	−	19.6613i	0.468526	−	0.811510i	0.999353	+	0.0359699i	$0.0114520\pi$
$588$		0			0
$589$	6.91522	+	11.9775i	0.284937	+	0.493525i
$590$		0			0
$591$	11.8128	+	20.4604i	0.485915	+	0.841629i
$592$		0			0
$593$	−22.0550			−0.905692			−0.452846	−	0.891589i	$-0.649591\pi$
$593$	−22.0550			−0.905692			−0.452846	+	0.891589i	$0.649591\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.28230			0.338972
$598$		0			0
$599$	6.16283			0.251807			0.125903	−	0.992043i	$-0.459817\pi$
$599$	6.16283			0.251807			0.125903	+	0.992043i	$0.459817\pi$
$600$		0			0
$601$	9.13735	−	15.8264i	0.372720	−	0.645571i	−0.617263	−	0.786757i	$-0.711758\pi$
$601$	9.13735	−	15.8264i	0.372720	−	0.645571i	0.989983	+	0.141187i	$0.0450917\pi$
$602$		0			0
$603$	−6.87023			−0.279777
$604$		0			0
$605$	12.8685	+	22.2889i	0.523179	+	0.906173i
$606$		0			0
$607$	7.45389	+	12.9105i	0.302544	+	0.524022i	0.976712	−	0.214557i	$-0.0688307\pi$
$607$	7.45389	+	12.9105i	0.302544	+	0.524022i	−0.674167	+	0.738579i	$0.735497\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.4366	−	14.2754i	−0.705411	−	0.577521i
$612$		0			0
$613$	−2.32174	+	4.02137i	−0.0937742	+	0.162422i	−0.909096	−	0.416586i	$-0.863227\pi$
$613$	−2.32174	+	4.02137i	−0.0937742	+	0.162422i	0.815322	+	0.579008i	$0.196560\pi$
$614$		0			0
$615$	13.8768	+	24.0353i	0.559566	+	0.969197i
$616$		0			0
$617$	−5.34393	−	9.25597i	−0.215139	−	0.372631i	0.738177	−	0.674607i	$-0.235687\pi$
$617$	−5.34393	−	9.25597i	−0.215139	−	0.372631i	−0.953315	+	0.301976i	$0.902354\pi$
$618$		0			0
$619$	20.5826			0.827283			0.413642	−	0.910440i	$-0.364257\pi$
$619$	20.5826			0.827283			0.413642	+	0.910440i	$0.364257\pi$
$620$		0			0
$621$	13.9940	−	24.2383i	0.561559	−	0.972648i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−24.4225			−0.976898
$626$		0			0
$627$	−4.86900	+	8.43335i	−0.194449	+	0.336796i
$628$		0			0
$629$	22.1225			0.882083
$630$		0			0
$631$	−21.9750	−	38.0619i	−0.874812	−	1.51522i	−0.856963	−	0.515379i	$-0.827651\pi$
$631$	−21.9750	−	38.0619i	−0.874812	−	1.51522i	−0.0178498	−	0.999841i	$-0.505682\pi$
$632$		0			0
$633$	−5.28748	−	9.15818i	−0.210158	−	0.364005i
$634$		0			0
$635$	−28.7426	+	49.7837i	−1.14062	+	1.97560i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.84415	−	6.65827i	0.152072	−	0.263397i
$640$		0			0
$641$	−24.3981	−	42.2587i	−0.963666	−	1.66912i	−0.713157	−	0.701005i	$-0.752735\pi$
$641$	−24.3981	−	42.2587i	−0.963666	−	1.66912i	−0.250509	−	0.968114i	$-0.580598\pi$
$642$		0			0
$643$	2.08350	+	3.60873i	0.0821653	+	0.142315i	0.904180	−	0.427152i	$-0.140483\pi$
$643$	2.08350	+	3.60873i	0.0821653	+	0.142315i	−0.822014	+	0.569467i	$0.807150\pi$
$644$		0			0
$645$	−37.1580			−1.46310
$646$		0			0
$647$	8.13081	−	14.0830i	0.319655	−	0.553659i	−0.660761	−	0.750596i	$-0.729766\pi$
$647$	8.13081	−	14.0830i	0.319655	−	0.553659i	0.980416	+	0.196938i	$0.0630996\pi$
$648$		0			0
$649$	−4.59346			−0.180309
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.91378	+	6.77886i	−0.153158	+	0.265277i	−0.932387	−	0.361462i	$-0.882278\pi$
$653$	−3.91378	+	6.77886i	−0.153158	+	0.265277i	0.779229	+	0.626740i	$0.215611\pi$
$654$		0			0
$655$	−59.4838			−2.32422
$656$		0			0
$657$	11.2189	+	19.4316i	0.437690	+	0.758100i
$658$		0			0
$659$	20.3114	+	35.1805i	0.791221	+	1.37044i	0.925211	+	0.379453i	$0.123888\pi$
$659$	20.3114	+	35.1805i	0.791221	+	1.37044i	−0.133990	+	0.990983i	$0.542779\pi$
$660$		0			0
$661$	−15.4342	+	26.7328i	−0.600320	+	1.03979i	0.392452	+	0.919773i	$0.371627\pi$
$661$	−15.4342	+	26.7328i	−0.600320	+	1.03979i	−0.992772	+	0.120013i	$0.961706\pi$
$662$		0			0
$663$	8.12825	+	6.65462i	0.315675	+	0.258444i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.8644	+	36.1381i	0.807871	+	1.39927i
$668$		0			0
$669$	−1.38794	−	2.40399i	−0.0536610	−	0.0929436i
$670$		0			0
$671$	−11.5543			−0.446047
$672$		0			0
$673$	−13.5310	+	23.4364i	−0.521581	+	0.903405i	0.478104	+	0.878303i	$0.341324\pi$
$673$	−13.5310	+	23.4364i	−0.521581	+	0.903405i	−0.999685	+	0.0251020i	$0.992009\pi$
$674$		0			0
$675$	−26.1611			−1.00694
$676$		0			0
$677$	−16.8472			−0.647490			−0.323745	−	0.946144i	$-0.604942\pi$
$677$	−16.8472			−0.647490			−0.323745	+	0.946144i	$0.604942\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	26.1710			1.00288
$682$		0			0
$683$	−9.89038	−	17.1306i	−0.378445	−	0.655486i	0.612391	−	0.790555i	$-0.290208\pi$
$683$	−9.89038	−	17.1306i	−0.378445	−	0.655486i	−0.990836	+	0.135069i	$0.956874\pi$
$684$		0			0
$685$	35.7996	+	62.0067i	1.36783	+	2.36915i
$686$		0			0
$687$	−6.40322	+	11.0907i	−0.244298	+	0.423137i
$688$		0			0
$689$	−5.13920	−	4.20748i	−0.195788	−	0.160292i
$690$		0			0
$691$	−4.64021	+	8.03707i	−0.176522	+	0.305745i	−0.940687	−	0.339276i	$-0.889818\pi$
$691$	−4.64021	+	8.03707i	−0.176522	+	0.305745i	0.764165	+	0.645021i	$0.223151\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.4901	−	19.9015i	−0.435845	−	0.754905i
$696$		0			0
$697$	−23.4845			−0.889539
$698$		0			0
$699$	11.0006	−	19.0536i	0.416081	−	0.720673i
$700$		0			0
$701$	34.6015			1.30688			0.653441	−	0.756977i	$-0.273325\pi$
$701$	34.6015			1.30688			0.653441	+	0.756977i	$0.273325\pi$
$702$		0			0
$703$	−43.3686			−1.63568
$704$		0			0
$705$	10.3408	−	17.9107i	0.389456	−	0.674558i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.55823	+	13.0912i	0.283855	+	0.491652i	0.972331	−	0.233608i	$-0.0750531\pi$
$709$	7.55823	+	13.0912i	0.283855	+	0.491652i	−0.688476	+	0.725260i	$0.741720\pi$
$710$		0			0
$711$	12.6961	+	21.9903i	0.476141	+	0.824700i
$712$		0			0
$713$	−6.89116	+	11.9358i	−0.258076	+	0.447001i
$714$		0			0
$715$	18.2877	−	6.90769i	0.683920	−	0.258333i
$716$		0			0
$717$	14.2546	−	24.6896i	0.532346	−	0.922051i
$718$		0			0
$719$	−10.6380	−	18.4255i	−0.396730	−	0.687157i	0.596590	−	0.802546i	$-0.296522\pi$
$719$	−10.6380	−	18.4255i	−0.396730	−	0.687157i	−0.993320	+	0.115389i	$0.963188\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−17.8516			−0.663909
$724$		0			0
$725$	19.5025	−	33.7793i	0.724304	−	1.25453i
$726$		0			0
$727$	−10.5609			−0.391684			−0.195842	−	0.980635i	$-0.562744\pi$
$727$	−10.5609			−0.391684			−0.195842	+	0.980635i	$0.562744\pi$
$728$		0			0
$729$	15.1520			0.561186
$730$		0			0
$731$	15.7212	−	27.2299i	0.581468	−	1.00713i
$732$		0			0
$733$	−8.81656			−0.325647			−0.162824	−	0.986655i	$-0.552060\pi$
$733$	−8.81656			−0.325647			−0.162824	+	0.986655i	$0.552060\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.05468	+	5.29086i	0.112521	+	0.194891i
$738$		0			0
$739$	−14.5384	+	25.1812i	−0.534803	+	0.926307i	0.464369	+	0.885642i	$0.346281\pi$
$739$	−14.5384	+	25.1812i	−0.534803	+	0.926307i	−0.999173	+	0.0406651i	$0.987052\pi$
$740$		0			0
$741$	−15.9345	−	13.0456i	−0.585368	−	0.479242i
$742$		0			0
$743$	−19.3225	+	33.4675i	−0.708872	+	1.22780i	0.256404	+	0.966570i	$0.417462\pi$
$743$	−19.3225	+	33.4675i	−0.708872	+	1.22780i	−0.965276	+	0.261233i	$0.915871\pi$
$744$		0			0
$745$	11.9231	+	20.6515i	0.436830	+	0.756611i
$746$		0			0
$747$	−8.19957	−	14.2021i	−0.300006	−	0.519626i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	20.1942	−	34.9775i	0.736898	−	1.27635i	−0.216987	−	0.976174i	$-0.569623\pi$
$751$	20.1942	−	34.9775i	0.736898	−	1.27635i	0.953885	−	0.300171i	$-0.0970437\pi$
$752$		0			0
$753$	−27.9840			−1.01979
$754$		0			0
$755$	−6.31293			−0.229751
$756$		0			0
$757$	11.2192	−	19.4322i	0.407768	−	0.706275i	−0.586871	−	0.809680i	$-0.699641\pi$
$757$	11.2192	−	19.4322i	0.407768	−	0.706275i	0.994639	+	0.103405i	$0.0329739\pi$
$758$		0			0
$759$	−9.70411			−0.352237
$760$		0			0
$761$	−8.58250	−	14.8653i	−0.311115	−	0.538868i	0.667489	−	0.744620i	$-0.267369\pi$
$761$	−8.58250	−	14.8653i	−0.311115	−	0.538868i	−0.978604	+	0.205752i	$0.934036\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	8.53599	−	14.7848i	0.308619	−	0.534544i
$766$		0			0
$767$	1.57105	−	9.58622i	0.0567274	−	0.346138i
$768$		0			0
$769$	−21.4658	+	37.1798i	−0.774076	+	1.34074i	0.161236	+	0.986916i	$0.448452\pi$
$769$	−21.4658	+	37.1798i	−0.774076	+	1.34074i	−0.935312	+	0.353823i	$0.884881\pi$
$770$		0			0
$771$	−5.87912	−	10.1829i	−0.211731	−	0.366729i
$772$		0			0
$773$	3.36534	+	5.82893i	0.121043	+	0.209652i	0.920179	−	0.391498i	$-0.128043\pi$
$773$	3.36534	+	5.82893i	0.121043	+	0.209652i	−0.799136	+	0.601150i	$0.794710\pi$
$774$		0			0
$775$	12.8827			0.462761
$776$		0			0
$777$		0			0
$778$		0			0
$779$	46.0386			1.64950
$780$		0			0
$781$	−6.83685			−0.244642
$782$		0			0
$783$	−19.5165	+	33.8035i	−0.697461	+	1.20804i
$784$		0			0
$785$	−12.7989			−0.456811
$786$		0			0
$787$	19.1240	+	33.1238i	0.681699	+	1.18074i	0.974462	+	0.224552i	$0.0720918\pi$
$787$	19.1240	+	33.1238i	0.681699	+	1.18074i	−0.292764	+	0.956185i	$0.594575\pi$
$788$		0			0
$789$	0.518959	+	0.898863i	0.0184754	+	0.0320004i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.95178	−	24.1129i	0.140332	−	0.856274i
$794$		0			0
$795$	3.04780	−	5.27894i	0.108094	−	0.187225i
$796$		0			0
$797$	21.3120	+	36.9134i	0.754909	+	1.30754i	0.945420	+	0.325855i	$0.105652\pi$
$797$	21.3120	+	36.9134i	0.754909	+	1.30754i	−0.190511	+	0.981685i	$0.561015\pi$
$798$		0			0
$799$	8.75014	+	15.1557i	0.309558	+	0.536170i
$800$		0			0
$801$	0.402862			0.0142344
$802$		0			0
$803$	9.97640	−	17.2796i	0.352059	−	0.609785i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−13.6604			−0.480867
$808$		0			0
$809$	18.7448	−	32.4670i	0.659033	−	1.14148i	−0.321833	−	0.946797i	$-0.604299\pi$
$809$	18.7448	−	32.4670i	0.659033	−	1.14148i	0.980866	−	0.194683i	$-0.0623678\pi$
$810$		0			0
$811$	25.4069			0.892156			0.446078	−	0.894994i	$-0.352820\pi$
$811$	25.4069			0.892156			0.446078	+	0.894994i	$0.352820\pi$
$812$		0			0
$813$	3.35179	+	5.80547i	0.117552	+	0.203607i
$814$		0			0
$815$	6.33975	+	10.9808i	0.222072	+	0.384640i
$816$		0			0
$817$	−30.8195	+	53.3809i	−1.07824	+	1.86756i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.0406154	−	0.0703480i	0.00141749	−	0.00245516i	−0.865316	−	0.501227i	$-0.832882\pi$
$821$	0.0406154	−	0.0703480i	0.00141749	−	0.00245516i	0.866733	+	0.498772i	$0.166215\pi$
$822$		0			0
$823$	0.624767	+	1.08213i	0.0217780	+	0.0377206i	0.876709	−	0.481021i	$-0.159734\pi$
$823$	0.624767	+	1.08213i	0.0217780	+	0.0377206i	−0.854931	+	0.518742i	$0.826401\pi$
$824$		0			0
$825$	4.53535	+	7.85545i	0.157901	+	0.273492i
$826$		0			0
$827$	32.9535			1.14591			0.572954	−	0.819588i	$-0.305798\pi$
$827$	32.9535			1.14591			0.572954	+	0.819588i	$0.305798\pi$
$828$		0			0
$829$	−8.61206	+	14.9165i	−0.299109	+	0.518072i	−0.975932	−	0.218073i	$-0.930023\pi$
$829$	−8.61206	+	14.9165i	−0.299109	+	0.518072i	0.676823	+	0.736146i	$0.263356\pi$
$830$		0			0
$831$	−24.9536			−0.865631
$832$		0			0
$833$		0			0
$834$		0			0
$835$	6.32569	−	10.9564i	0.218909	−	0.379162i
$836$		0			0
$837$	−12.8920			−0.445611
$838$		0			0
$839$	−14.7357	−	25.5229i	−0.508731	−	0.881149i	−0.999949	−	0.0101117i	$-0.996781\pi$
$839$	−14.7357	−	25.5229i	−0.508731	−	0.881149i	0.491217	−	0.871037i	$-0.336552\pi$
$840$		0			0
$841$	−14.5981	−	25.2847i	−0.503383	−	0.871886i
$842$		0			0
$843$	5.39008	−	9.33590i	0.185644	−	0.321545i
$844$		0			0
$845$	8.16110	+	40.5276i	0.280750	+	1.39419i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	15.5628	+	26.9556i	0.534115	+	0.925115i
$850$		0			0
$851$	−21.6089	−	37.4276i	−0.740742	−	1.28300i
$852$		0			0
$853$	−17.8668			−0.611747			−0.305873	−	0.952072i	$-0.598948\pi$
$853$	−17.8668			−0.611747			−0.305873	+	0.952072i	$0.598948\pi$
$854$		0			0
$855$	−16.7338	+	28.9838i	−0.572284	+	0.991225i
$856$		0			0
$857$	−20.1614			−0.688701			−0.344351	−	0.938841i	$-0.611901\pi$
$857$	−20.1614			−0.688701			−0.344351	+	0.938841i	$0.611901\pi$
$858$		0			0
$859$	−11.9734			−0.408526			−0.204263	−	0.978916i	$-0.565480\pi$
$859$	−11.9734			−0.408526			−0.204263	+	0.978916i	$0.565480\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	39.7010			1.35144			0.675719	−	0.737160i	$-0.263833\pi$
$863$	39.7010			1.35144			0.675719	+	0.737160i	$0.263833\pi$
$864$		0			0
$865$	36.1267	+	62.5732i	1.22834	+	2.12755i
$866$		0			0
$867$	4.76564	+	8.25432i	0.161849	+	0.280331i
$868$		0			0
$869$	11.2900	−	19.5549i	0.382988	−	0.663355i
$870$		0			0
$871$	−12.0864	+	4.56532i	−0.409532	+	0.154690i
$872$		0			0
$873$	12.1378	−	21.0233i	0.410803	−	0.711532i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	22.8328	+	39.5476i	0.771010	+	1.33543i	0.937010	+	0.349302i	$0.113581\pi$
$877$	22.8328	+	39.5476i	0.771010	+	1.33543i	−0.166000	+	0.986126i	$0.553085\pi$
$878$		0			0
$879$	0.383750			0.0129436
$880$		0			0
$881$	16.6420	−	28.8249i	0.560685	−	0.971134i	−0.436752	−	0.899582i	$-0.643871\pi$
$881$	16.6420	−	28.8249i	0.560685	−	0.971134i	0.997437	−	0.0715523i	$-0.0227953\pi$
$882$		0			0
$883$	32.3115			1.08737			0.543685	−	0.839289i	$-0.317029\pi$
$883$	32.3115			1.08737			0.543685	+	0.839289i	$0.317029\pi$
$884$		0			0
$885$	8.91516			0.299680
$886$		0			0
$887$	−16.7530	+	29.0170i	−0.562509	+	0.974295i	0.434767	+	0.900543i	$0.356831\pi$
$887$	−16.7530	+	29.0170i	−0.562509	+	0.974295i	−0.997277	+	0.0737520i	$0.976503\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.364658	+	0.631606i	0.0122165	+	0.0211596i
$892$		0			0
$893$	−17.1536	−	29.7109i	−0.574024	−	0.994239i
$894$		0			0
$895$	6.56721	−	11.3747i	0.219517	−	0.380215i
$896$		0			0
$897$	3.31899	−	20.2518i	0.110818	−	0.676187i
$898$		0			0
$899$	9.61064	−	16.6461i	0.320533	−	0.555179i
$900$		0			0
$901$	2.57898	+	4.46693i	0.0859183	+	0.148815i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.37783			−0.278488
$906$		0			0
$907$	19.4451	−	33.6798i	0.645663	−	1.11832i	−0.338485	−	0.940972i	$-0.609915\pi$
$907$	19.4451	−	33.6798i	0.645663	−	1.11832i	0.984148	−	0.177349i	$-0.0567521\pi$
$908$		0			0
$909$	22.1519			0.734733
$910$		0			0
$911$	−41.0133			−1.35883			−0.679415	−	0.733754i	$-0.737766\pi$
$911$	−41.0133			−1.35883			−0.679415	+	0.733754i	$0.737766\pi$
$912$		0			0
$913$	−7.29148	+	12.6292i	−0.241313	+	0.417966i
$914$		0			0
$915$	22.4249			0.741345
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−11.9574	−	20.7108i	−0.394438	−	0.683186i	0.598592	−	0.801054i	$-0.295727\pi$
$919$	−11.9574	−	20.7108i	−0.394438	−	0.683186i	−0.993029	+	0.117868i	$0.962394\pi$
$920$		0			0
$921$	−7.21532	+	12.4973i	−0.237753	+	0.411800i
$922$		0			0
$923$	2.33833	−	14.2680i	0.0769671	−	0.469637i
$924$		0			0
$925$	−20.1984	+	34.9846i	−0.664119	+	1.15029i
$926$		0			0
$927$	11.6979	+	20.2614i	0.384211	+	0.665473i
$928$		0			0
$929$	−7.74124	−	13.4082i	−0.253982	−	0.439909i	0.710637	−	0.703559i	$-0.248407\pi$
$929$	−7.74124	−	13.4082i	−0.253982	−	0.439909i	−0.964618	+	0.263650i	$0.915074\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.614538	+	1.06441i	−0.0201191	+	0.0348472i
$934$		0			0
$935$	−15.1813			−0.496481
$936$		0			0
$937$	−38.8172			−1.26810			−0.634052	−	0.773290i	$-0.718609\pi$
$937$	−38.8172			−1.26810			−0.634052	+	0.773290i	$0.718609\pi$
$938$		0			0
$939$	−5.50770	+	9.53961i	−0.179737	+	0.311313i
$940$		0			0
$941$	5.28344			0.172235			0.0861177	−	0.996285i	$-0.472554\pi$
$941$	5.28344			0.172235			0.0861177	+	0.996285i	$0.472554\pi$
$942$		0			0
$943$	22.9392	+	39.7319i	0.747003	+	1.29385i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.98486	+	6.90198i	−0.129491	+	0.224284i	−0.923479	−	0.383648i	$-0.874668\pi$
$947$	−3.98486	+	6.90198i	−0.129491	+	0.224284i	0.793989	+	0.607932i	$0.208001\pi$
$948$		0			0
$949$	32.6492	+	26.7300i	1.05984	+	0.867691i
$950$		0			0
$951$	−4.41651	+	7.64963i	−0.143215	+	0.248056i
$952$		0			0
$953$	−8.48138	−	14.6902i	−0.274739	−	0.475862i	0.695330	−	0.718690i	$-0.255258\pi$
$953$	−8.48138	−	14.6902i	−0.274739	−	0.475862i	−0.970069	+	0.242829i	$0.921925\pi$
$954$		0			0
$955$	7.44157	+	12.8892i	0.240804	+	0.417084i
$956$		0			0
$957$	13.5337			0.437482
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−24.6515			−0.795210
$962$		0			0
$963$	4.35820			0.140441
$964$		0			0
$965$	28.5199	−	49.3980i	0.918089	−	1.59018i
$966$		0			0
$967$	21.4177			0.688746			0.344373	−	0.938833i	$-0.388092\pi$
$967$	21.4177			0.688746			0.344373	+	0.938833i	$0.388092\pi$
$968$		0			0
$969$	7.99633	+	13.8500i	0.256879	+	0.444927i
$970$		0			0
$971$	−8.46512	−	14.6620i	−0.271659	−	0.470527i	0.697628	−	0.716460i	$-0.254239\pi$
$971$	−8.46512	−	14.6620i	−0.271659	−	0.470527i	−0.969287	+	0.245933i	$0.920906\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−17.9449	+	6.77822i	−0.574698	+	0.217077i
$976$		0			0
$977$	−20.4387	+	35.4008i	−0.653891	+	1.13257i	0.328279	+	0.944581i	$0.393531\pi$
$977$	−20.4387	+	35.4008i	−0.653891	+	1.13257i	−0.982171	+	0.187992i	$0.939802\pi$
$978$		0			0
$979$	−0.179123	−	0.310250i	−0.00572479	−	0.00991562i
$980$		0			0
$981$	−4.65145	−	8.05655i	−0.148509	−	0.257226i
$982$		0			0
$983$	8.53733			0.272299			0.136149	−	0.990688i	$-0.456527\pi$
$983$	8.53733			0.272299			0.136149	+	0.990688i	$0.456527\pi$
$984$		0			0
$985$	36.1022	−	62.5308i	1.15031	−	1.99240i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−61.4245			−1.95319
$990$		0			0
$991$	−17.5874	+	30.4623i	−0.558682	+	0.967666i	0.438924	+	0.898524i	$0.355360\pi$
$991$	−17.5874	+	30.4623i	−0.558682	+	0.967666i	−0.997607	+	0.0691423i	$0.977974\pi$
$992$		0			0
$993$	4.52032			0.143448
$994$		0			0
$995$	−12.6561	−	21.9211i	−0.401226	−	0.694944i
$996$		0			0
$997$	−20.3109	−	35.1795i	−0.643252	−	1.11414i	−0.984702	−	0.174245i	$-0.944251\pi$
$997$	−20.3109	−	35.1795i	−0.643252	−	1.11414i	0.341450	−	0.939900i	$-0.389082\pi$
$998$		0			0
$999$	20.2129	−	35.0097i	0.639507	−	1.10766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.k.i.1569.3		18
7.2	even	3		2548.2.i.n.165.3		18
7.3	odd	6		364.2.l.a.9.3	yes	18
7.4	even	3		2548.2.l.n.373.7		18
7.5	odd	6		364.2.i.a.165.7	✓	18
7.6	odd	2		2548.2.k.h.1569.7		18
13.3	even	3	inner	2548.2.k.i.393.3		18
21.5	even	6		3276.2.u.k.1621.1		18
21.17	even	6		3276.2.x.k.2557.1		18
91.3	odd	6		364.2.i.a.289.7	yes	18
91.16	even	3		2548.2.l.n.1537.7		18
91.55	odd	6		2548.2.k.h.393.7		18
91.68	odd	6		364.2.l.a.81.3	yes	18
91.81	even	3		2548.2.i.n.1745.3		18
273.68	even	6		3276.2.x.k.2629.1		18
273.185	even	6		3276.2.u.k.289.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.i.a.165.7	✓	18	7.5	odd	6
364.2.i.a.289.7	yes	18	91.3	odd	6
364.2.l.a.9.3	yes	18	7.3	odd	6
364.2.l.a.81.3	yes	18	91.68	odd	6
2548.2.i.n.165.3		18	7.2	even	3
2548.2.i.n.1745.3		18	91.81	even	3
2548.2.k.h.393.7		18	91.55	odd	6
2548.2.k.h.1569.7		18	7.6	odd	2
2548.2.k.i.393.3		18	13.3	even	3	inner
2548.2.k.i.1569.3		18	1.1	even	1	trivial
2548.2.l.n.373.7		18	7.4	even	3
2548.2.l.n.1537.7		18	91.16	even	3
3276.2.u.k.289.1		18	273.185	even	6
3276.2.u.k.1621.1		18	21.5	even	6
3276.2.x.k.2557.1		18	21.17	even	6
3276.2.x.k.2629.1		18	273.68	even	6

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.520270 + 0.901135i) q^{3} +3.18009 q^{5} +(0.958637 + 1.66041i) q^{9} +(0.852470 - 1.47652i) q^{11} +(2.78983 + 2.28404i) q^{13} +(-1.65451 + 2.86569i) q^{15} +(-1.40001 - 2.42488i) q^{17} +(2.74455 + 4.75370i) q^{19} +(-2.73500 + 4.73716i) q^{23} +5.11296 q^{25} -5.11663 q^{27} +(3.81432 - 6.60660i) q^{29} +2.51962 q^{31} +(0.887030 + 1.53638i) q^{33} +(-3.95043 + 6.84235i) q^{37} +(-3.50970 + 1.32569i) q^{39} +(4.19364 - 7.26359i) q^{41} +(5.61467 + 9.72490i) q^{43} +(3.04855 + 5.28024i) q^{45} -6.25007 q^{47} +2.91353 q^{51} -1.84212 q^{53} +(2.71093 - 4.69547i) q^{55} -5.71163 q^{57} +(-1.34710 - 2.33325i) q^{59} +(-3.38846 - 5.86899i) q^{61} +(8.87191 + 7.26345i) q^{65} +(-1.79166 + 3.10325i) q^{67} +(-2.84588 - 4.92921i) q^{69} +(-2.00501 - 3.47278i) q^{71} +11.7029 q^{73} +(-2.66012 + 4.60746i) q^{75} +13.2439 q^{79} +(-0.213883 + 0.370457i) q^{81} -8.55336 q^{83} +(-4.45215 - 7.71134i) q^{85} +(3.96896 + 6.87444i) q^{87} +(0.105061 - 0.181971i) q^{89} +(-1.31088 + 2.27052i) q^{93} +(8.72791 + 15.1172i) q^{95} +(-6.33077 - 10.9652i) q^{97} +3.26884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{3} - 10 q^{9} + 2 q^{11} - 4 q^{13} - 10 q^{15} + 6 q^{17} + q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{27} + 2 q^{29} + 14 q^{31} + 14 q^{33} - 8 q^{37} + 11 q^{39} - 7 q^{41} - 2 q^{43} + 10 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) \) 18 * q + q^3 - 10 * q^9 + 2 * q^11 - 4 * q^13 - 10 * q^15 + 6 * q^17 + q^19 + 6 * q^23 + 10 * q^25 + 4 * q^27 + 2 * q^29 + 14 * q^31 + 14 * q^33 - 8 * q^37 + 11 * q^39 - 7 * q^41 - 2 * q^43 + 10 * q^45 - 24 * q^47 - 28 * q^51 - 26 * q^53 + q^55 - 2 * q^57 + 8 * q^59 + q^61 + 4 * q^65 + 29 * q^67 + 17 * q^69 + 7 * q^71 + 18 * q^73 + 59 * q^75 + 4 * q^79 - 13 * q^81 + 30 * q^83 - 46 * q^85 - 26 * q^87 - 13 * q^89 + 3 * q^93 - 14 * q^95 + 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more