LMFDB - Embedded newform 2548.2.l.n.1537.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(373,2548)]

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, 2, 4]))

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

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

chi := DirichletCharacter("2548.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.l (of order $3$, degree $2$, 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:	$20.3458824350$
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:	$\Z[a_1, \ldots, a_{25}]$
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			1537.7
Root			$-0.520270 - 0.901135i$ of defining polynomial
Character	$\chi$	$=$	2548.1537
Dual form			2548.2.l.n.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.04054 q^{3} +(-1.59004 - 2.75404i) q^{5} -1.91727 q^{9} -1.70494 q^{11} +(2.78983 - 2.28404i) q^{13} +(-1.65451 - 2.86569i) q^{15} +(-1.40001 - 2.42488i) q^{17} -5.48910 q^{19} +(-2.73500 + 4.73716i) q^{23} +(-2.55648 + 4.42795i) q^{25} -5.11663 q^{27} +(3.81432 + 6.60660i) q^{29} +(-1.25981 + 2.18206i) q^{31} -1.77406 q^{33} +(-3.95043 + 6.84235i) q^{37} +(2.90293 - 2.37664i) q^{39} +(4.19364 + 7.26359i) q^{41} +(5.61467 - 9.72490i) q^{43} +(3.04855 + 5.28024i) q^{45} +(3.12503 + 5.41272i) q^{47} +(-1.45676 - 2.52319i) q^{51} +(0.921060 - 1.59532i) q^{53} +(2.71093 + 4.69547i) q^{55} -5.71163 q^{57} +(-1.34710 - 2.33325i) q^{59} +6.77693 q^{61} +(-10.7263 - 4.05157i) q^{65} +3.58333 q^{67} +(-2.84588 + 4.92921i) q^{69} +(-2.00501 + 3.47278i) q^{71} +(-5.85146 + 10.1350i) q^{73} +(-2.66012 + 4.60746i) q^{75} +(-6.62195 - 11.4695i) q^{79} +0.427766 q^{81} -8.55336 q^{83} +(-4.45215 + 7.71134i) q^{85} +(3.96896 + 6.87444i) q^{87} +(0.105061 - 0.181971i) q^{89} +(-1.31088 + 2.27052i) q^{93} +(8.72791 + 15.1172i) q^{95} +(-6.33077 + 10.9652i) q^{97} +3.26884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} + 20 q^{9} - 4 q^{11} - 4 q^{13} - 10 q^{15} + 6 q^{17} - 2 q^{19} + 6 q^{23} - 5 q^{25} + 4 q^{27} + 2 q^{29} - 7 q^{31} - 28 q^{33} - 8 q^{37} + 17 q^{39} - 7 q^{41} - 2 q^{43} + 10 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) $ 18 * q - 2 * q^3 + 20 * q^9 - 4 * q^11 - 4 * q^13 - 10 * q^15 + 6 * q^17 - 2 * q^19 + 6 * q^23 - 5 * q^25 + 4 * q^27 + 2 * q^29 - 7 * q^31 - 28 * q^33 - 8 * q^37 + 17 * q^39 - 7 * q^41 - 2 * q^43 + 10 * q^45 + 12 * q^47 + 14 * q^51 + 13 * q^53 + q^55 - 2 * q^57 + 8 * q^59 - 2 * q^61 + 10 * q^65 - 58 * q^67 + 17 * q^69 + 7 * q^71 - 9 * q^73 + 59 * q^75 - 2 * q^79 + 26 * 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 $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

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

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
$3$	1.04054			0.600757			0.300378	−	0.953820i	$-0.402887\pi$
$3$	1.04054			0.600757			0.300378	+	0.953820i	$0.402887\pi$
$4$		0			0
$5$	−1.59004	−	2.75404i	−0.711089	−	1.23164i	−0.964449	−	0.264270i	$-0.914869\pi$
$5$	−1.59004	−	2.75404i	−0.711089	−	1.23164i	0.253359	−	0.967372i	$-0.418464\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.91727			−0.639092
$10$		0			0
$11$	−1.70494			−0.514059			−0.257029	−	0.966404i	$-0.582744\pi$
$11$	−1.70494			−0.514059			−0.257029	+	0.966404i	$0.582744\pi$
$12$		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
$19$	−5.48910			−1.25929			−0.629643	−	0.776885i	$-0.716799\pi$
$19$	−5.48910			−1.25929			−0.629643	+	0.776885i	$0.716799\pi$
$20$		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
$25$	−2.55648	+	4.42795i	−0.511296	+	0.885590i
$26$		0			0
$27$	−5.11663			−0.984695
$28$		0			0
$29$	3.81432	+	6.60660i	0.708302	+	1.22682i	0.965487	+	0.260453i	$0.0838718\pi$
$29$	3.81432	+	6.60660i	0.708302	+	1.22682i	−0.257185	+	0.966362i	$0.582795\pi$
$30$		0			0
$31$	−1.25981	+	2.18206i	−0.226269	+	0.391909i	−0.956699	−	0.291078i	$-0.905986\pi$
$31$	−1.25981	+	2.18206i	−0.226269	+	0.391909i	0.730431	+	0.682987i	$0.239319\pi$
$32$		0			0
$33$	−1.77406			−0.308824
$34$		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
$39$	2.90293	−	2.37664i	0.464841	−	0.380567i
$40$		0			0
$41$	4.19364	+	7.26359i	0.654936	+	1.13438i	0.981910	+	0.189349i	$0.0606379\pi$
$41$	4.19364	+	7.26359i	0.654936	+	1.13438i	−0.326974	+	0.945033i	$0.606029\pi$
$42$		0			0
$43$	5.61467	−	9.72490i	0.856230	−	1.48303i	−0.0192697	−	0.999814i	$-0.506134\pi$
$43$	5.61467	−	9.72490i	0.856230	−	1.48303i	0.875499	−	0.483219i	$-0.160533\pi$
$44$		0			0
$45$	3.04855	+	5.28024i	0.454451	+	0.787132i
$46$		0			0
$47$	3.12503	+	5.41272i	0.455833	+	0.789526i	0.998736	−	0.0502697i	$-0.0160081\pi$
$47$	3.12503	+	5.41272i	0.455833	+	0.789526i	−0.542903	+	0.839796i	$0.682675\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.45676	−	2.52319i	−0.203988	−	0.353317i
$52$		0			0
$53$	0.921060	−	1.59532i	0.126517	−	0.219134i	−0.795808	−	0.605549i	$-0.792953\pi$
$53$	0.921060	−	1.59532i	0.126517	−	0.219134i	0.922325	+	0.386415i	$0.126287\pi$
$54$		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
$61$	6.77693			0.867697			0.433848	−	0.900986i	$-0.357155\pi$
$61$	6.77693			0.867697			0.433848	+	0.900986i	$0.357155\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.7263	−	4.05157i	−1.33043	−	0.502536i
$66$		0			0
$67$	3.58333			0.437773			0.218887	−	0.975750i	$-0.429757\pi$
$67$	3.58333			0.437773			0.218887	+	0.975750i	$0.429757\pi$
$68$		0			0
$69$	−2.84588	+	4.92921i	−0.342604	+	0.593407i
$70$		0			0
$71$	−2.00501	+	3.47278i	−0.237951	+	0.412143i	−0.960126	−	0.279567i	$-0.909809\pi$
$71$	−2.00501	+	3.47278i	−0.237951	+	0.412143i	0.722175	+	0.691710i	$0.243142\pi$
$72$		0			0
$73$	−5.85146	+	10.1350i	−0.684862	+	1.18622i	0.288618	+	0.957444i	$0.406804\pi$
$73$	−5.85146	+	10.1350i	−0.684862	+	1.18622i	−0.973480	+	0.228771i	$0.926529\pi$
$74$		0			0
$75$	−2.66012	+	4.60746i	−0.307164	+	0.532024i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.62195	−	11.4695i	−0.745027	−	1.29043i	−0.950182	−	0.311696i	$-0.899103\pi$
$79$	−6.62195	−	11.4695i	−0.745027	−	1.29043i	0.205155	−	0.978730i	$-0.434230\pi$
$80$		0			0
$81$	0.427766			0.0475296
$82$		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	0.342015	+	0.939695i	$0.388891\pi$
$97$	−6.33077	+	10.9652i	−0.642792	+	1.11335i	−0.984807	+	0.173654i	$0.944443\pi$
$98$		0			0
$99$	3.26884			0.328531
$100$		0			0
$101$	−11.5539			−1.14965			−0.574826	−	0.818276i	$-0.694930\pi$
$101$	−11.5539			−1.14965			−0.574826	+	0.818276i	$0.694930\pi$
$102$		0			0
$103$	−6.10134	−	10.5678i	−0.601183	−	1.04128i	−0.992642	−	0.121084i	$-0.961363\pi$
$103$	−6.10134	−	10.5678i	−0.601183	−	1.04128i	0.391459	−	0.920195i	$-0.371970\pi$
$104$		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
$109$	2.42607	−	4.20208i	0.232376	−	0.402487i	−0.726131	−	0.687556i	$-0.758683\pi$
$109$	2.42607	−	4.20208i	0.232376	−	0.402487i	0.958507	+	0.285070i	$0.0920168\pi$
$110$		0			0
$111$	−4.11058	+	7.11974i	−0.390159	+	0.675776i
$112$		0			0
$113$	−0.333301	+	0.577294i	−0.0313543	+	0.0543072i	−0.881277	−	0.472601i	$-0.843315\pi$
$113$	−0.333301	+	0.577294i	−0.0313543	+	0.0543072i	0.849922	+	0.526908i	$0.176649\pi$
$114$		0			0
$115$	17.3951			1.62210
$116$		0			0
$117$	−5.34887	+	4.37913i	−0.494503	+	0.404851i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−8.09318			−0.735743
$122$		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	−0.918284	−	0.395922i	$-0.870425\pi$
$127$	−9.03831	−	15.6548i	−0.802020	−	1.38914i	0.116264	−	0.993218i	$-0.462908\pi$
$128$		0			0
$129$	5.84230	−	10.1192i	0.514386	−	0.890942i
$130$		0			0
$131$	9.35254	+	16.1991i	0.817135	+	1.41532i	0.907785	+	0.419437i	$0.137772\pi$
$131$	9.35254	+	16.1991i	0.817135	+	1.41532i	−0.0906496	+	0.995883i	$0.528894\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	8.13566	+	14.0914i	0.700206	+	1.21279i
$136$		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	−0.977586	−	0.210537i	$-0.932479\pi$
$139$	−3.61314	+	6.25815i	−0.306463	+	0.530809i	0.671123	+	0.741346i	$0.265812\pi$
$140$		0			0
$141$	3.25173	+	5.63215i	0.273845	+	0.474313i
$142$		0			0
$143$	−4.75650	+	3.89415i	−0.397758	+	0.325646i
$144$		0			0
$145$	12.1299	−	21.0096i	1.00733	−	1.74475i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.49862			−0.614311			−0.307155	−	0.951659i	$-0.599377\pi$
$149$	−7.49862			−0.614311			−0.307155	+	0.951659i	$0.599377\pi$
$150$		0			0
$151$	0.992571	−	1.71918i	0.0807743	−	0.139905i	−0.822808	−	0.568319i	$-0.807594\pi$
$151$	0.992571	−	1.71918i	0.0807743	−	0.139905i	0.903583	+	0.428414i	$0.140927\pi$
$152$		0			0
$153$	2.68420	+	4.64917i	0.217005	+	0.375863i
$154$		0			0
$155$	8.01261			0.643589
$156$		0			0
$157$	2.01235	−	3.48549i	0.160603	−	0.278172i	−0.774482	−	0.632596i	$-0.781990\pi$
$157$	2.01235	−	3.48549i	0.160603	−	0.278172i	0.935085	+	0.354424i	$0.115323\pi$
$158$		0			0
$159$	0.958401	−	1.66000i	0.0760061	−	0.131646i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.98715			−0.312298			−0.156149	−	0.987734i	$-0.549908\pi$
$163$	−3.98715			−0.312298			−0.156149	+	0.987734i	$0.549908\pi$
$164$		0			0
$165$	2.82083	+	4.88583i	0.219602	+	0.380361i
$166$		0			0
$167$	1.98915	+	3.44532i	0.153925	+	0.266607i	0.932667	−	0.360738i	$-0.117475\pi$
$167$	1.98915	+	3.44532i	0.153925	+	0.266607i	−0.778742	+	0.627345i	$0.784142\pi$
$168$		0			0
$169$	2.56631	−	12.7442i	0.197409	−	0.980321i
$170$		0			0
$171$	10.5241			0.804799
$172$		0			0
$173$	−22.7206			−1.72741			−0.863706	−	0.503996i	$-0.831863\pi$
$173$	−22.7206			−1.72741			−0.863706	+	0.503996i	$0.831863\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.40172	−	2.42784i	−0.105359	−	0.182488i
$178$		0			0
$179$	−4.13020			−0.308706			−0.154353	−	0.988016i	$-0.549329\pi$
$179$	−4.13020			−0.308706			−0.154353	+	0.988016i	$0.549329\pi$
$180$		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
$185$	25.1254			1.84726
$186$		0			0
$187$	2.38693	+	4.13428i	0.174550	+	0.302329i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.68011			−0.338641			−0.169320	−	0.985561i	$-0.554157\pi$
$191$	−4.68011			−0.338641			−0.169320	+	0.985561i	$0.554157\pi$
$192$		0			0
$193$	−17.9366			−1.29110			−0.645551	−	0.763717i	$-0.723372\pi$
$193$	−17.9366			−1.29110			−0.645551	+	0.763717i	$0.723372\pi$
$194$		0			0
$195$	−11.1611	−	4.21583i	−0.799266	−	0.301902i
$196$		0			0
$197$	11.3526	+	19.6632i	0.808838	+	1.40095i	0.913669	+	0.406458i	$0.133236\pi$
$197$	11.3526	+	19.6632i	0.808838	+	1.40095i	−0.104832	+	0.994490i	$0.533430\pi$
$198$		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
$201$	3.72860			0.262995
$202$		0			0
$203$		0			0
$204$		0			0
$205$	13.3361	−	23.0989i	0.931436	−	1.61329i
$206$		0			0
$207$	5.24375	−	9.08244i	0.364466	−	0.631273i
$208$		0			0
$209$	9.35859			0.647347
$210$		0			0
$211$	−5.08147	−	8.80136i	−0.349823	−	0.605911i	0.636395	−	0.771363i	$-0.280425\pi$
$211$	−5.08147	−	8.80136i	−0.349823	−	0.605911i	−0.986218	+	0.165453i	$0.947092\pi$
$212$		0			0
$213$	−2.08629	+	3.61357i	−0.142951	+	0.247598i
$214$		0			0
$215$	−35.7103			−2.43542
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.08869	+	10.5459i	−0.411435	+	0.712627i
$220$		0			0
$221$	−9.44432	−	3.56734i	−0.635294	−	0.239965i
$222$		0			0
$223$	−1.33387	−	2.31033i	−0.0893224	−	0.154711i	0.817902	−	0.575357i	$-0.195137\pi$
$223$	−1.33387	−	2.31033i	−0.0893224	−	0.154711i	−0.907225	+	0.420646i	$0.861803\pi$
$224$		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
$229$	−6.15374	−	10.6586i	−0.406651	−	0.704339i	0.587862	−	0.808962i	$-0.299970\pi$
$229$	−6.15374	−	10.6586i	−0.406651	−	0.704339i	−0.994512	+	0.104622i	$0.966637\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.5720	+	18.3112i	0.692594	+	1.19961i	0.970985	+	0.239141i	$0.0768657\pi$
$233$	10.5720	+	18.3112i	0.692594	+	1.19961i	−0.278391	+	0.960468i	$0.589801\pi$
$234$		0			0
$235$	9.93788	−	17.2129i	0.648276	−	1.12285i
$236$		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
$243$	15.7950			1.01325
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−15.3137	+	12.5373i	−0.974385	+	0.797731i
$248$		0			0
$249$	−8.90012			−0.564022
$250$		0			0
$251$	13.4469	−	23.2907i	0.848759	−	1.47009i	−0.0335582	−	0.999437i	$-0.510684\pi$
$251$	13.4469	−	23.2907i	0.848759	−	1.47009i	0.882317	−	0.470656i	$-0.155983\pi$
$252$		0			0
$253$	4.66301	−	8.07658i	0.293161	−	0.507770i
$254$		0			0
$255$	−4.63264	+	8.02397i	−0.290107	+	0.502480i
$256$		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
$261$	−7.31310	−	12.6667i	−0.452670	−	0.784047i
$262$		0			0
$263$	−0.997479			−0.0615072			−0.0307536	−	0.999527i	$-0.509791\pi$
$263$	−0.997479			−0.0615072			−0.0307536	+	0.999527i	$0.509791\pi$
$264$		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
$283$	−29.9130			−1.77814			−0.889071	−	0.457769i	$-0.848649\pi$
$283$	−29.9130			−1.77814			−0.889071	+	0.457769i	$0.848649\pi$
$284$		0			0
$285$	9.08174	+	15.7300i	0.537956	+	0.931767i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.57996	−	7.93272i	0.269409	−	0.466631i
$290$		0			0
$291$	−6.58742	+	11.4098i	−0.386162	+	0.668852i
$292$		0			0
$293$	−0.184399	+	0.319389i	−0.0107727	+	0.0186589i	−0.871362	−	0.490642i	$-0.836762\pi$
$293$	−0.184399	+	0.319389i	−0.0107727	+	0.0186589i	0.860589	+	0.509300i	$0.170096\pi$
$294$		0			0
$295$	−4.28391	+	7.41995i	−0.249419	+	0.432006i
$296$		0			0
$297$	8.72354			0.506191
$298$		0			0
$299$	3.18968	+	19.4627i	0.184464	+	1.12556i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−12.0223			−0.690661
$304$		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
$311$	−0.590595	+	1.02294i	−0.0334895	+	0.0580056i	−0.882284	−	0.470717i	$-0.843995\pi$
$311$	−0.590595	+	1.02294i	−0.0334895	+	0.0580056i	0.848795	+	0.528722i	$0.177329\pi$
$312$		0			0
$313$	−5.29311	−	9.16793i	−0.299184	−	0.518202i	0.676765	−	0.736199i	$-0.263381\pi$
$313$	−5.29311	−	9.16793i	−0.299184	−	0.518202i	−0.975950	+	0.217997i	$0.930048\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.24444	−	7.35159i	−0.238392	−	0.412906i	0.721861	−	0.692038i	$-0.243287\pi$
$317$	−4.24444	−	7.35159i	−0.238392	−	0.412906i	−0.960253	+	0.279131i	$0.909953\pi$
$318$		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
$325$	2.98148	+	18.1923i	0.165383	+	1.00913i
$326$		0			0
$327$	2.52443	−	4.37244i	0.139601	−	0.241796i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.34420			0.238779			0.119389	−	0.992848i	$-0.461906\pi$
$331$	4.34420			0.238779			0.119389	+	0.992848i	$0.461906\pi$
$332$		0			0
$333$	7.57406	−	13.1187i	0.415056	−	0.718898i
$334$		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
$339$	−0.346813	+	0.600698i	−0.0188363	+	0.0326254i
$340$		0			0
$341$	2.14790	−	3.72027i	0.116315	−	0.201464i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	18.1003			0.974487
$346$		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	0.869108	−	0.494623i	$-0.164694\pi$
$349$	0.115786	+	0.200546i	0.00619786	+	0.0107350i	−0.862910	+	0.505358i	$0.831360\pi$
$350$		0			0
$351$	−14.2745	+	11.6866i	−0.761917	+	0.623784i
$352$		0			0
$353$	18.1994			0.968659			0.484329	−	0.874886i	$-0.339064\pi$
$353$	18.1994			0.968659			0.484329	+	0.874886i	$0.339064\pi$
$354$		0			0
$355$	12.7522			0.676817
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.27149	−	3.93434i	−0.119885	−	0.207646i	0.799837	−	0.600217i	$-0.204919\pi$
$359$	−2.27149	−	3.93434i	−0.119885	−	0.207646i	−0.919722	+	0.392571i	$0.871586\pi$
$360$		0			0
$361$	11.1302			0.585800
$362$		0			0
$363$	−8.42128			−0.442003
$364$		0			0
$365$	37.2163			1.94799
$366$		0			0
$367$	−10.0228			−0.523185			−0.261592	−	0.965178i	$-0.584248\pi$
$367$	−10.0228			−0.523185			−0.261592	+	0.965178i	$0.584248\pi$
$368$		0			0
$369$	−8.04036	−	13.9263i	−0.418564	−	0.724974i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	8.43135			0.436559			0.218279	−	0.975886i	$-0.429956\pi$
$373$	8.43135			0.436559			0.218279	+	0.975886i	$0.429956\pi$
$374$		0			0
$375$	0.373778			0.0193018
$376$		0			0
$377$	25.7311	+	9.71923i	1.32522	+	0.500566i
$378$		0			0
$379$	−5.15804	−	8.93398i	−0.264951	−	0.458908i	0.702600	−	0.711585i	$-0.252022\pi$
$379$	−5.15804	−	8.93398i	−0.264951	−	0.458908i	−0.967551	+	0.252677i	$0.918689\pi$
$380$		0			0
$381$	−9.40473	−	16.2895i	−0.481819	−	0.834535i
$382$		0			0
$383$	2.19625			0.112223			0.0561116	−	0.998425i	$-0.482130\pi$
$383$	2.19625			0.112223			0.0561116	+	0.998425i	$0.482130\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.7649	+	18.6453i	−0.547209	+	0.947794i
$388$		0			0
$389$	16.3977	−	28.4017i	0.831398	−	1.44002i	−0.0655315	−	0.997851i	$-0.520874\pi$
$389$	16.3977	−	28.4017i	0.831398	−	1.44002i	0.896930	−	0.442173i	$-0.145792\pi$
$390$		0			0
$391$	15.3161			0.774568
$392$		0			0
$393$	9.73170	+	16.8558i	0.490899	+	0.850262i
$394$		0			0
$395$	−21.0584	+	36.4742i	−1.05956	+	1.83521i
$396$		0			0
$397$	5.51695			0.276888			0.138444	−	0.990370i	$-0.455790\pi$
$397$	5.51695			0.276888			0.138444	+	0.990370i	$0.455790\pi$
$398$		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
$403$	1.46925	+	8.96502i	0.0731884	+	0.446580i
$404$		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
$411$	11.7138	+	20.2889i	0.577799	+	1.00078i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	13.6002	+	23.5563i	0.667608	+	1.15633i
$416$		0			0
$417$	−3.75962	+	6.51186i	−0.184110	+	0.318887i
$418$		0			0
$419$	4.22915	+	7.32510i	0.206607	+	0.357854i	0.950644	−	0.310285i	$-0.100424\pi$
$419$	4.22915	+	7.32510i	0.206607	+	0.357854i	−0.744036	+	0.668139i	$0.767091\pi$
$420$		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
$425$	14.3164			0.694445
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.94933	+	4.05203i	−0.238956	+	0.195634i
$430$		0			0
$431$	−13.0760			−0.629847			−0.314924	−	0.949117i	$-0.601979\pi$
$431$	−13.0760			−0.629847			−0.314924	+	0.949117i	$0.601979\pi$
$432$		0			0
$433$	−9.78438	+	16.9470i	−0.470207	+	0.814423i	−0.999420	−	0.0340664i	$-0.989154\pi$
$433$	−9.78438	+	16.9470i	−0.470207	+	0.814423i	0.529212	+	0.848490i	$0.322488\pi$
$434$		0			0
$435$	12.6216	−	21.8613i	0.605161	−	1.04817i
$436$		0			0
$437$	15.0127	−	26.0027i	0.718154	−	1.24388i
$438$		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
$443$	−4.31882	−	7.48041i	−0.205193	−	0.355405i	0.745001	−	0.667063i	$-0.232449\pi$
$443$	−4.31882	−	7.48041i	−0.205193	−	0.355405i	−0.950194	+	0.311658i	$0.899116\pi$
$444$		0			0
$445$	−0.668206			−0.0316760
$446$		0			0
$447$	−7.80262			−0.369051
$448$		0			0
$449$	−11.4447	+	19.8228i	−0.540110	+	0.935498i	0.458787	+	0.888546i	$0.348284\pi$
$449$	−11.4447	+	19.8228i	−0.540110	+	0.935498i	−0.998897	+	0.0469519i	$0.985049\pi$
$450$		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	−0.762607	−	0.646862i	$-0.776081\pi$
$461$	3.84106	−	6.65291i	0.178896	−	0.309857i	0.941503	+	0.337005i	$0.109414\pi$
$462$		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
$465$	8.33745			0.386640
$466$		0			0
$467$	10.7578	+	18.6330i	0.497810	+	0.862233i	0.999997	−	0.00252639i	$-0.000804175\pi$
$467$	10.7578	+	18.6330i	0.497810	+	0.862233i	−0.502186	+	0.864759i	$0.667471\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.09393	−	3.62679i	0.0964831	−	0.167114i
$472$		0			0
$473$	−9.57269	+	16.5804i	−0.440153	+	0.762367i
$474$		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
$479$	−33.5009			−1.53070			−0.765348	−	0.643617i	$-0.777433\pi$
$479$	−33.5009			−1.53070			−0.765348	+	0.643617i	$0.777433\pi$
$480$		0			0
$481$	4.60717	+	28.1119i	0.210069	+	1.28179i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	40.2648			1.82833
$486$		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	0.999980	−	0.00633175i	$-0.00201547\pi$
$491$	10.9575	+	18.9790i	0.494507	+	0.856510i	−0.505473	+	0.862842i	$0.668682\pi$
$492$		0			0
$493$	10.6802	−	18.4986i	0.481010	−	0.833134i
$494$		0			0
$495$	−5.19760	−	9.00250i	−0.233615	−	0.404632i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	18.1564	+	31.4478i	0.812791	+	1.40780i	0.910903	+	0.412620i	$0.135386\pi$
$499$	18.1564	+	31.4478i	0.812791	+	1.40780i	−0.0981123	+	0.995175i	$0.531280\pi$
$500$		0			0
$501$	2.06980	+	3.58499i	0.0924717	+	0.160166i
$502$		0			0
$503$	−13.2906	+	23.0199i	−0.592597	+	1.02641i	0.401285	+	0.915953i	$0.368564\pi$
$503$	−13.2906	+	23.0199i	−0.592597	+	1.02641i	−0.993881	+	0.110454i	$0.964769\pi$
$504$		0			0
$505$	18.3711	+	31.8198i	0.817505	+	1.41596i
$506$		0			0
$507$	2.67035	−	13.2608i	0.118595	−	0.588934i
$508$		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
$513$	28.0857			1.24001
$514$		0			0
$515$	−19.4028	+	33.6066i	−0.854989	+	1.48089i
$516$		0			0
$517$	−5.32800	−	9.22836i	−0.234325	−	0.405863i
$518$		0			0
$519$	−23.6417			−1.03775
$520$		0			0
$521$	3.80745	−	6.59470i	0.166807	−	0.288919i	−0.770488	−	0.637454i	$-0.779988\pi$
$521$	3.80745	−	6.59470i	0.166807	−	0.288919i	0.937296	+	0.348535i	$0.113321\pi$
$522$		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
$527$	7.05497			0.307319
$528$		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
$535$	−7.22872			−0.312525
$536$		0			0
$537$	−4.29765			−0.185457
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.45613	+	7.71824i	0.191584	+	0.331833i	0.945775	−	0.324822i	$-0.105304\pi$
$541$	4.45613	+	7.71824i	0.191584	+	0.331833i	−0.754191	+	0.656655i	$0.771971\pi$
$542$		0			0
$543$	−2.74127			−0.117639
$544$		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
$549$	−12.9932			−0.554538
$550$		0			0
$551$	−20.9372	−	36.2643i	−0.891955	−	1.54491i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	26.1440			1.10975
$556$		0			0
$557$	−36.6524			−1.55301			−0.776507	−	0.630109i	$-0.783010\pi$
$557$	−36.6524			−1.55301			−0.776507	+	0.630109i	$0.783010\pi$
$558$		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
$565$	2.11985			0.0891828
$566$		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
$571$	−2.78183	+	4.81827i	−0.116416	+	0.201639i	−0.918345	−	0.395781i	$-0.870474\pi$
$571$	−2.78183	+	4.81827i	−0.116416	+	0.201639i	0.801929	+	0.597420i	$0.203807\pi$
$572$		0			0
$573$	−4.86984			−0.203441
$574$		0			0
$575$	−13.9839	−	24.2209i	−0.583171	−	1.01008i
$576$		0			0
$577$	−0.540691	+	0.936505i	−0.0225093	+	0.0389872i	−0.877061	−	0.480380i	$-0.840499\pi$
$577$	−0.540691	+	0.936505i	−0.0225093	+	0.0389872i	0.854551	+	0.519367i	$0.173832\pi$
$578$		0			0
$579$	−18.6637			−0.775638
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.57035	+	2.71993i	−0.0650374	+	0.112648i
$584$		0			0
$585$	20.5652	+	7.76798i	0.850268	+	0.321166i
$586$		0			0
$587$	11.3515	+	19.6613i	0.468526	+	0.811510i	0.999353	−	0.0359699i	$-0.0114520\pi$
$587$	11.3515	+	19.6613i	0.468526	+	0.811510i	−0.530827	+	0.847480i	$0.678119\pi$
$588$		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
$593$	11.0275	+	19.1002i	0.452846	+	0.784352i	0.998561	−	0.0536184i	$-0.0170755\pi$
$593$	11.0275	+	19.1002i	0.452846	+	0.784352i	−0.545716	+	0.837970i	$0.683742\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.14115	−	7.17268i	−0.169486	−	0.293558i
$598$		0			0
$599$	−3.08142	+	5.33717i	−0.125903	+	0.218071i	−0.922086	−	0.386986i	$-0.873516\pi$
$599$	−3.08142	+	5.33717i	−0.125903	+	0.218071i	0.796182	+	0.605057i	$0.206850\pi$
$600$		0			0
$601$	9.13735	+	15.8264i	0.372720	+	0.645571i	0.989983	−	0.141187i	$-0.0450917\pi$
$601$	9.13735	+	15.8264i	0.372720	+	0.645571i	−0.617263	+	0.786757i	$0.711758\pi$
$602$		0			0
$603$	−6.87023			−0.279777
$604$		0			0
$605$	12.8685	+	22.2889i	0.523179	+	0.906173i
$606$		0			0
$607$	−14.9078			−0.605088			−0.302544	−	0.953135i	$-0.597836\pi$
$607$	−14.9078			−0.605088			−0.302544	+	0.953135i	$0.597836\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	21.0812	+	7.96286i	0.852853	+	0.322143i
$612$		0			0
$613$	4.64348			0.187548			0.0937742	−	0.995593i	$-0.470107\pi$
$613$	4.64348			0.187548			0.0937742	+	0.995593i	$0.470107\pi$
$614$		0			0
$615$	13.8768	−	24.0353i	0.559566	−	0.969197i
$616$		0			0
$617$	−5.34393	+	9.25597i	−0.215139	+	0.372631i	−0.953315	−	0.301976i	$-0.902354\pi$
$617$	−5.34393	+	9.25597i	−0.215139	+	0.372631i	0.738177	+	0.674607i	$0.235687\pi$
$618$		0			0
$619$	−10.2913	+	17.8250i	−0.413642	+	0.716448i	−0.995285	−	0.0969957i	$-0.969077\pi$
$619$	−10.2913	+	17.8250i	−0.413642	+	0.716448i	0.581643	+	0.813444i	$0.302410\pi$
$620$		0			0
$621$	13.9940	−	24.2383i	0.561559	−	0.972648i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	12.2112	+	21.1505i	0.488449	+	0.846019i
$626$		0			0
$627$	9.73799			0.388898
$628$		0			0
$629$	22.1225			0.882083
$630$		0			0
$631$	−21.9750	+	38.0619i	−0.874812	+	1.51522i	−0.0178498	+	0.999841i	$0.505682\pi$
$631$	−21.9750	+	38.0619i	−0.874812	+	1.51522i	−0.856963	+	0.515379i	$0.827651\pi$
$632$		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	−0.822014	−	0.569467i	$-0.807150\pi$
$643$	2.08350	−	3.60873i	0.0821653	−	0.142315i	0.904180	+	0.427152i	$0.140483\pi$
$644$		0			0
$645$	−37.1580			−1.46310
$646$		0			0
$647$	−16.2616			−0.639310			−0.319655	−	0.947534i	$-0.603567\pi$
$647$	−16.2616			−0.639310			−0.319655	+	0.947534i	$0.603567\pi$
$648$		0			0
$649$	2.29673	+	3.97806i	0.0901546	+	0.156152i
$650$		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
$655$	29.7419	−	51.5145i	1.16211	−	2.01284i
$656$		0			0
$657$	11.2189	−	19.4316i	0.437690	−	0.758100i
$658$		0			0
$659$	20.3114	−	35.1805i	0.791221	−	1.37044i	−0.133990	−	0.990983i	$-0.542779\pi$
$659$	20.3114	−	35.1805i	0.791221	−	1.37044i	0.925211	−	0.379453i	$-0.123888\pi$
$660$		0			0
$661$	30.8684			1.20064			0.600320	−	0.799760i	$-0.295040\pi$
$661$	30.8684			1.20064			0.600320	+	0.799760i	$0.295040\pi$
$662$		0			0
$663$	−9.82720	−	3.71196i	−0.381657	−	0.144161i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−41.7287			−1.61574
$668$		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	−0.999685	−	0.0251020i	$-0.992009\pi$
$673$	−13.5310	−	23.4364i	−0.521581	−	0.903405i	0.478104	−	0.878303i	$-0.341324\pi$
$674$		0			0
$675$	13.0805	−	22.6562i	0.503470	−	0.872036i
$676$		0			0
$677$	8.42360	+	14.5901i	0.323745	+	0.560743i	0.981258	−	0.192701i	$-0.0617246\pi$
$677$	8.42360	+	14.5901i	0.323745	+	0.560743i	−0.657512	+	0.753444i	$0.728391\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−13.0855	−	22.6648i	−0.501438	−	0.868516i
$682$		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
$689$	−1.07418	−	6.55442i	−0.0409230	−	0.249704i
$690$		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
$695$	22.9802			0.871690
$696$		0			0
$697$	11.7422	−	20.3382i	0.444769	−	0.770363i
$698$		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
$703$	21.6843	−	37.5583i	0.817839	−	1.41654i
$704$		0			0
$705$	10.3408	−	17.9107i	0.389456	−	0.674558i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15.1165			−0.567711			−0.283855	−	0.958867i	$-0.591614\pi$
$709$	−15.1165			−0.567711			−0.283855	+	0.958867i	$0.591614\pi$
$710$		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
$717$	−28.5091			−1.06469
$718$		0			0
$719$	21.2760			0.793460			0.396730	−	0.917935i	$-0.370145\pi$
$719$	21.2760			0.793460			0.396730	+	0.917935i	$0.370145\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8.92581	+	15.4600i	0.331955	+	0.574962i
$724$		0			0
$725$	−39.0049			−1.44861
$726$		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
$731$	−31.4423			−1.16294
$732$		0			0
$733$	4.40828	+	7.63536i	0.162824	+	0.282019i	0.935880	−	0.352318i	$-0.114607\pi$
$733$	4.40828	+	7.63536i	0.162824	+	0.282019i	−0.773057	+	0.634337i	$0.781273\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.10936			−0.225041
$738$		0			0
$739$	29.0768			1.06961			0.534803	−	0.844977i	$-0.320386\pi$
$739$	29.0768			1.06961			0.534803	+	0.844977i	$0.320386\pi$
$740$		0			0
$741$	−15.9345	+	13.0456i	−0.585368	+	0.479242i
$742$		0			0
$743$	−19.3225	−	33.4675i	−0.708872	−	1.22780i	−0.965276	−	0.261233i	$-0.915871\pi$
$743$	−19.3225	−	33.4675i	−0.708872	−	1.22780i	0.256404	−	0.966570i	$-0.417462\pi$
$744$		0			0
$745$	11.9231	+	20.6515i	0.436830	+	0.756611i
$746$		0			0
$747$	16.3991			0.600013
$748$		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
$753$	13.9920	−	24.2349i	0.509897	−	0.883168i
$754$		0			0
$755$	−6.31293			−0.229751
$756$		0			0
$757$	11.2192	+	19.4322i	0.407768	+	0.706275i	0.994639	−	0.103405i	$-0.0329739\pi$
$757$	11.2192	+	19.4322i	0.407768	+	0.706275i	−0.586871	+	0.809680i	$0.699641\pi$
$758$		0			0
$759$	4.85206	−	8.40401i	0.176118	−	0.305046i
$760$		0			0
$761$	17.1650			0.622231			0.311115	−	0.950372i	$-0.399297\pi$
$761$	17.1650			0.622231			0.311115	+	0.950372i	$0.399297\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	8.53599	−	14.7848i	0.308619	−	0.534544i
$766$		0			0
$767$	−9.08744	−	3.43254i	−0.328128	−	0.123942i
$768$		0			0
$769$	−21.4658	−	37.1798i	−0.774076	−	1.34074i	−0.935312	−	0.353823i	$-0.884881\pi$
$769$	−21.4658	−	37.1798i	−0.774076	−	1.34074i	0.161236	−	0.986916i	$-0.448452\pi$
$770$		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
$775$	−6.44136	−	11.1568i	−0.231380	−	0.400762i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.0193	−	39.8706i	−0.824752	−	1.42851i
$780$		0			0
$781$	3.41842	−	5.92088i	0.122321	−	0.211866i
$782$		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
$789$	−1.03792			−0.0369508
$790$		0			0
$791$		0			0
$792$		0			0
$793$	18.9065	−	15.4788i	0.671389	−	0.549668i
$794$		0			0
$795$	−6.09560			−0.216189
$796$		0			0
$797$	21.3120	−	36.9134i	0.754909	−	1.30754i	−0.190511	−	0.981685i	$-0.561015\pi$
$797$	21.3120	−	36.9134i	0.754909	−	1.30754i	0.945420	−	0.325855i	$-0.105652\pi$
$798$		0			0
$799$	8.75014	−	15.1557i	0.309558	−	0.536170i
$800$		0			0
$801$	−0.201431	+	0.348888i	−0.00711721	+	0.0123274i
$802$		0			0
$803$	9.97640	−	17.2796i	0.352059	−	0.609785i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.83018	+	11.8302i	0.240434	+	0.416443i
$808$		0			0
$809$	−37.4897			−1.31807			−0.659033	−	0.752114i	$-0.729034\pi$
$809$	−37.4897			−1.31807			−0.659033	+	0.752114i	$0.729034\pi$
$810$		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
$829$	17.2241			0.598218			0.299109	−	0.954219i	$-0.403311\pi$
$829$	17.2241			0.598218			0.299109	+	0.954219i	$0.403311\pi$
$830$		0			0
$831$	12.4768	+	21.6104i	0.432815	+	0.749658i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	6.32569	−	10.9564i	0.218909	−	0.379162i
$836$		0			0
$837$	6.44598	−	11.1648i	0.222806	−	0.385910i
$838$		0			0
$839$	−14.7357	+	25.5229i	−0.508731	+	0.881149i	0.491217	+	0.871037i	$0.336552\pi$
$839$	−14.7357	+	25.5229i	−0.508731	+	0.881149i	−0.999949	+	0.0101117i	$0.996781\pi$
$840$		0			0
$841$	−14.5981	+	25.2847i	−0.503383	+	0.871886i
$842$		0			0
$843$	−10.7802			−0.371289
$844$		0			0
$845$	−39.1785	+	13.1961i	−1.34778	+	0.453959i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−31.1257			−1.06823
$850$		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
$857$	10.0807	−	17.4603i	0.344351	−	0.596433i	−0.640885	−	0.767637i	$-0.721432\pi$
$857$	10.0807	−	17.4603i	0.344351	−	0.596433i	0.985236	+	0.171204i	$0.0547657\pi$
$858$		0			0
$859$	5.98669	+	10.3692i	0.204263	+	0.353794i	0.949898	−	0.312561i	$-0.101187\pi$
$859$	5.98669	+	10.3692i	0.204263	+	0.353794i	−0.745635	+	0.666355i	$0.767854\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.8505	−	34.3821i	−0.675719	−	1.17038i	−0.976258	−	0.216610i	$-0.930500\pi$
$863$	−19.8505	−	34.3821i	−0.675719	−	1.17038i	0.300540	−	0.953769i	$-0.402833\pi$
$864$		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
$871$	9.99688	−	8.18447i	0.338731	−	0.277320i
$872$		0			0
$873$	12.1378	−	21.0233i	0.410803	−	0.711532i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−45.6656			−1.54202			−0.771010	−	0.636823i	$-0.780248\pi$
$877$	−45.6656			−1.54202			−0.771010	+	0.636823i	$0.780248\pi$
$878$		0			0
$879$	−0.191875	+	0.332337i	−0.00647178	+	0.0112095i
$880$		0			0
$881$	16.6420	+	28.8249i	0.560685	+	0.971134i	0.997437	+	0.0715523i	$0.0227953\pi$
$881$	16.6420	+	28.8249i	0.560685	+	0.971134i	−0.436752	+	0.899582i	$0.643871\pi$
$882$		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
$885$	−4.45758	+	7.72076i	−0.149840	+	0.259530i
$886$		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
$891$	−0.729316			−0.0244330
$892$		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
$899$	−19.2213			−0.641066
$900$		0			0
$901$	−5.15796			−0.171837
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.18891	+	7.25541i	0.139244	+	0.241178i
$906$		0			0
$907$	−38.8901			−1.29133			−0.645663	−	0.763623i	$-0.723419\pi$
$907$	−38.8901			−1.29133			−0.645663	+	0.763623i	$0.723419\pi$
$908$		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
$913$	14.5830			0.482626
$914$		0			0
$915$	−11.2125	−	19.4206i	−0.370673	−	0.642024i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	23.9148			0.788875			0.394438	−	0.918923i	$-0.370939\pi$
$919$	23.9148			0.788875			0.394438	+	0.918923i	$0.370939\pi$
$920$		0			0
$921$	14.4306			0.475506
$922$		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
$929$	15.4825			0.507964			0.253982	−	0.967209i	$-0.418260\pi$
$929$	15.4825			0.507964			0.253982	+	0.967209i	$0.418260\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.614538	+	1.06441i	−0.0201191	+	0.0348472i
$934$		0			0
$935$	7.59064	−	13.1474i	0.248241	−	0.429965i
$936$		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
$941$	−2.64172	+	4.57560i	−0.0861177	+	0.149160i	−0.905867	−	0.423562i	$-0.860779\pi$
$941$	−2.64172	+	4.57560i	−0.0861177	+	0.149160i	0.819749	+	0.572723i	$0.194113\pi$
$942$		0			0
$943$	−45.8784			−1.49401
$944$		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
$949$	6.82424	+	41.6400i	0.221524	+	1.35169i
$950$		0			0
$951$	−4.41651	−	7.64963i	−0.143215	−	0.248056i
$952$		0			0
$953$	−8.48138	+	14.6902i	−0.274739	+	0.475862i	−0.970069	−	0.242829i	$-0.921925\pi$
$953$	−8.48138	+	14.6902i	−0.274739	+	0.475862i	0.695330	+	0.718690i	$0.255258\pi$
$954$		0			0
$955$	7.44157	+	12.8892i	0.240804	+	0.417084i
$956$		0			0
$957$	−6.76684	−	11.7205i	−0.218741	−	0.378870i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.3258	+	21.3488i	0.397605	+	0.688672i
$962$		0			0
$963$	−2.17910	+	3.77431i	−0.0702204	+	0.121625i
$964$		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
$971$	16.9302			0.543318			0.271659	−	0.962394i	$-0.412428\pi$
$971$	16.9302			0.543318			0.271659	+	0.962394i	$0.412428\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.10235	+	18.9299i	0.0993547	+	0.606241i
$976$		0			0
$977$	40.8774			1.30778			0.653891	−	0.756588i	$-0.273135\pi$
$977$	40.8774			1.30778			0.653891	+	0.756588i	$0.273135\pi$
$978$		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
$983$	−4.26867	+	7.39355i	−0.136149	+	0.235817i	−0.926036	−	0.377435i	$-0.876806\pi$
$983$	−4.26867	+	7.39355i	−0.136149	+	0.235817i	0.789887	+	0.613253i	$0.210139\pi$
$984$		0			0
$985$	36.1022	−	62.5308i	1.15031	−	1.99240i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30.7123	+	53.1952i	0.976593	+	1.69151i
$990$		0			0
$991$	35.1748			1.11736			0.558682	−	0.829382i	$-0.311307\pi$
$991$	35.1748			1.11736			0.558682	+	0.829382i	$0.311307\pi$
$992$		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.l.n.1537.7		18
7.2	even	3		2548.2.i.n.1745.3		18
7.3	odd	6		2548.2.k.h.393.7		18
7.4	even	3		2548.2.k.i.393.3		18
7.5	odd	6		364.2.i.a.289.7	yes	18
7.6	odd	2		364.2.l.a.81.3	yes	18
13.9	even	3		2548.2.i.n.165.3		18
21.5	even	6		3276.2.u.k.289.1		18
21.20	even	2		3276.2.x.k.2629.1		18
91.9	even	3	inner	2548.2.l.n.373.7		18
91.48	odd	6		364.2.i.a.165.7	✓	18
91.61	odd	6		364.2.l.a.9.3	yes	18
91.74	even	3		2548.2.k.i.1569.3		18
91.87	odd	6		2548.2.k.h.1569.7		18
273.152	even	6		3276.2.x.k.2557.1		18
273.230	even	6		3276.2.u.k.1621.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.i.a.165.7	✓	18	91.48	odd	6
364.2.i.a.289.7	yes	18	7.5	odd	6
364.2.l.a.9.3	yes	18	91.61	odd	6
364.2.l.a.81.3	yes	18	7.6	odd	2
2548.2.i.n.165.3		18	13.9	even	3
2548.2.i.n.1745.3		18	7.2	even	3
2548.2.k.h.393.7		18	7.3	odd	6
2548.2.k.h.1569.7		18	91.87	odd	6
2548.2.k.i.393.3		18	7.4	even	3
2548.2.k.i.1569.3		18	91.74	even	3
2548.2.l.n.373.7		18	91.9	even	3	inner
2548.2.l.n.1537.7		18	1.1	even	1	trivial
3276.2.u.k.289.1		18	21.5	even	6
3276.2.u.k.1621.1		18	273.230	even	6
3276.2.x.k.2557.1		18	273.152	even	6
3276.2.x.k.2629.1		18	21.20	even	2

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.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.04054 q^{3} +(-1.59004 - 2.75404i) q^{5} -1.91727 q^{9} -1.70494 q^{11} +(2.78983 - 2.28404i) q^{13} +(-1.65451 - 2.86569i) q^{15} +(-1.40001 - 2.42488i) q^{17} -5.48910 q^{19} +(-2.73500 + 4.73716i) q^{23} +(-2.55648 + 4.42795i) q^{25} -5.11663 q^{27} +(3.81432 + 6.60660i) q^{29} +(-1.25981 + 2.18206i) q^{31} -1.77406 q^{33} +(-3.95043 + 6.84235i) q^{37} +(2.90293 - 2.37664i) q^{39} +(4.19364 + 7.26359i) q^{41} +(5.61467 - 9.72490i) q^{43} +(3.04855 + 5.28024i) q^{45} +(3.12503 + 5.41272i) q^{47} +(-1.45676 - 2.52319i) q^{51} +(0.921060 - 1.59532i) q^{53} +(2.71093 + 4.69547i) q^{55} -5.71163 q^{57} +(-1.34710 - 2.33325i) q^{59} +6.77693 q^{61} +(-10.7263 - 4.05157i) q^{65} +3.58333 q^{67} +(-2.84588 + 4.92921i) q^{69} +(-2.00501 + 3.47278i) q^{71} +(-5.85146 + 10.1350i) q^{73} +(-2.66012 + 4.60746i) q^{75} +(-6.62195 - 11.4695i) q^{79} +0.427766 q^{81} -8.55336 q^{83} +(-4.45215 + 7.71134i) q^{85} +(3.96896 + 6.87444i) q^{87} +(0.105061 - 0.181971i) q^{89} +(-1.31088 + 2.27052i) q^{93} +(8.72791 + 15.1172i) q^{95} +(-6.33077 + 10.9652i) q^{97} +3.26884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} + 20 q^{9} - 4 q^{11} - 4 q^{13} - 10 q^{15} + 6 q^{17} - 2 q^{19} + 6 q^{23} - 5 q^{25} + 4 q^{27} + 2 q^{29} - 7 q^{31} - 28 q^{33} - 8 q^{37} + 17 q^{39} - 7 q^{41} - 2 q^{43} + 10 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) \) 18 * q - 2 * q^3 + 20 * q^9 - 4 * q^11 - 4 * q^13 - 10 * q^15 + 6 * q^17 - 2 * q^19 + 6 * q^23 - 5 * q^25 + 4 * q^27 + 2 * q^29 - 7 * q^31 - 28 * q^33 - 8 * q^37 + 17 * q^39 - 7 * q^41 - 2 * q^43 + 10 * q^45 + 12 * q^47 + 14 * q^51 + 13 * q^53 + q^55 - 2 * q^57 + 8 * q^59 - 2 * q^61 + 10 * q^65 - 58 * q^67 + 17 * q^69 + 7 * q^71 - 9 * q^73 + 59 * q^75 - 2 * q^79 + 26 * 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

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