LMFDB - Embedded newform 9360.2.a.cc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9360,2,Mod(1,9360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9360.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9360.a (trivial)

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:	yes
Analytic conductor:	$74.7399762919$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 520)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.44949$ of defining polynomial
Character	$\chi$	$=$	9360.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{5} -2.00000 q^{7} +O(q^{10})$	$q-1.00000 q^{5} -2.00000 q^{7} -4.44949 q^{11} -1.00000 q^{13} -6.89898 q^{17} -0.449490 q^{19} +6.44949 q^{23} +1.00000 q^{25} -4.00000 q^{29} +4.44949 q^{31} +2.00000 q^{35} +4.89898 q^{37} -10.8990 q^{41} -11.3485 q^{43} -2.00000 q^{47} -3.00000 q^{49} -1.10102 q^{53} +4.44949 q^{55} +9.34847 q^{59} -5.79796 q^{61} +1.00000 q^{65} +5.10102 q^{67} -3.55051 q^{71} -14.6969 q^{73} +8.89898 q^{77} -4.89898 q^{79} +2.00000 q^{83} +6.89898 q^{85} -6.00000 q^{89} +2.00000 q^{91} +0.449490 q^{95} +7.79796 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 2 * q - 2 * q^5 - 4 * q^7	$ 2 q - 2 q^{5} - 4 q^{7} - 4 q^{11} - 2 q^{13} - 4 q^{17} + 4 q^{19} + 8 q^{23} + 2 q^{25} - 8 q^{29} + 4 q^{31} + 4 q^{35} - 12 q^{41} - 8 q^{43} - 4 q^{47} - 6 q^{49} - 12 q^{53} + 4 q^{55} + 4 q^{59} + 8 q^{61} + 2 q^{65} + 20 q^{67} - 12 q^{71} + 8 q^{77} + 4 q^{83} + 4 q^{85} - 12 q^{89} + 4 q^{91} - 4 q^{95} - 4 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 - 4 * q^7 - 4 * q^11 - 2 * q^13 - 4 * q^17 + 4 * q^19 + 8 * q^23 + 2 * q^25 - 8 * q^29 + 4 * q^31 + 4 * q^35 - 12 * q^41 - 8 * q^43 - 4 * q^47 - 6 * q^49 - 12 * q^53 + 4 * q^55 + 4 * q^59 + 8 * q^61 + 2 * q^65 + 20 * q^67 - 12 * q^71 + 8 * q^77 + 4 * q^83 + 4 * q^85 - 12 * q^89 + 4 * q^91 - 4 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

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	0
$3$	0	0
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	−4.44949	−1.34157	−0.670786	−	0.741651i	$-0.734043\pi$
$11$	−4.44949	−1.34157	−0.670786	+	0.741651i	$0.734043\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−6.89898	−1.67325	−0.836624	−	0.547777i	$-0.815474\pi$
$17$	−6.89898	−1.67325	−0.836624	+	0.547777i	$0.815474\pi$
$18$	0	0
$19$	−0.449490	−0.103120	−0.0515600	−	0.998670i	$-0.516419\pi$
$19$	−0.449490	−0.103120	−0.0515600	+	0.998670i	$0.516419\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	6.44949	1.34481	0.672406	−	0.740183i	$-0.265261\pi$
$23$	6.44949	1.34481	0.672406	+	0.740183i	$0.265261\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	0	0
$31$	4.44949	0.799152	0.399576	−	0.916700i	$-0.369157\pi$
$31$	4.44949	0.799152	0.399576	+	0.916700i	$0.369157\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	2.00000	0.338062
$36$	0	0
$37$	4.89898	0.805387	0.402694	−	0.915335i	$-0.368074\pi$
$37$	4.89898	0.805387	0.402694	+	0.915335i	$0.368074\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−10.8990	−1.70213	−0.851067	−	0.525057i	$-0.824044\pi$
$41$	−10.8990	−1.70213	−0.851067	+	0.525057i	$0.824044\pi$
$42$	0	0
$43$	−11.3485	−1.73063	−0.865313	−	0.501232i	$-0.832880\pi$
$43$	−11.3485	−1.73063	−0.865313	+	0.501232i	$0.832880\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−1.10102	−0.151237	−0.0756184	−	0.997137i	$-0.524093\pi$
$53$	−1.10102	−0.151237	−0.0756184	+	0.997137i	$0.524093\pi$
$54$	0	0
$55$	4.44949	0.599969
$56$	0	0
$57$	0	0
$58$	0	0
$59$	9.34847	1.21707	0.608534	−	0.793528i	$-0.291758\pi$
$59$	9.34847	1.21707	0.608534	+	0.793528i	$0.291758\pi$
$60$	0	0
$61$	−5.79796	−0.742353	−0.371176	−	0.928562i	$-0.621045\pi$
$61$	−5.79796	−0.742353	−0.371176	+	0.928562i	$0.621045\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	1.00000	0.124035
$66$	0	0
$67$	5.10102	0.623189	0.311594	−	0.950215i	$-0.399137\pi$
$67$	5.10102	0.623189	0.311594	+	0.950215i	$0.399137\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−3.55051	−0.421368	−0.210684	−	0.977554i	$-0.567569\pi$
$71$	−3.55051	−0.421368	−0.210684	+	0.977554i	$0.567569\pi$
$72$	0	0
$73$	−14.6969	−1.72015	−0.860073	−	0.510171i	$-0.829582\pi$
$73$	−14.6969	−1.72015	−0.860073	+	0.510171i	$0.829582\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	8.89898	1.01413
$78$	0	0
$79$	−4.89898	−0.551178	−0.275589	−	0.961276i	$-0.588873\pi$
$79$	−4.89898	−0.551178	−0.275589	+	0.961276i	$0.588873\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	0	0
$85$	6.89898	0.748299
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0.449490	0.0461167
$96$	0	0
$97$	7.79796	0.791763	0.395881	−	0.918302i	$-0.370439\pi$
$97$	7.79796	0.791763	0.395881	+	0.918302i	$0.370439\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	15.7980	1.57196	0.785978	−	0.618255i	$-0.212160\pi$
$101$	15.7980	1.57196	0.785978	+	0.618255i	$0.212160\pi$
$102$	0	0
$103$	−11.3485	−1.11820	−0.559099	−	0.829101i	$-0.688853\pi$
$103$	−11.3485	−1.11820	−0.559099	+	0.829101i	$0.688853\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−12.2474	−1.18401	−0.592003	−	0.805936i	$-0.701663\pi$
$107$	−12.2474	−1.18401	−0.592003	+	0.805936i	$0.701663\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−1.10102	−0.103575	−0.0517876	−	0.998658i	$-0.516492\pi$
$113$	−1.10102	−0.103575	−0.0517876	+	0.998658i	$0.516492\pi$
$114$	0	0
$115$	−6.44949	−0.601418
$116$	0	0
$117$	0	0
$118$	0	0
$119$	13.7980	1.26486
$120$	0	0
$121$	8.79796	0.799814
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−4.65153	−0.412757	−0.206378	−	0.978472i	$-0.566168\pi$
$127$	−4.65153	−0.412757	−0.206378	+	0.978472i	$0.566168\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	19.5959	1.71210	0.856052	−	0.516890i	$-0.172910\pi$
$131$	19.5959	1.71210	0.856052	+	0.516890i	$0.172910\pi$
$132$	0	0
$133$	0.898979	0.0779514
$134$	0	0
$135$	0	0
$136$	0	0
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	0	0
$139$	16.8990	1.43335	0.716676	−	0.697406i	$-0.245662\pi$
$139$	16.8990	1.43335	0.716676	+	0.697406i	$0.245662\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	4.44949	0.372085
$144$	0	0
$145$	4.00000	0.332182
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−11.7980	−0.966526	−0.483263	−	0.875475i	$-0.660549\pi$
$149$	−11.7980	−0.966526	−0.483263	+	0.875475i	$0.660549\pi$
$150$	0	0
$151$	2.65153	0.215779	0.107889	−	0.994163i	$-0.465591\pi$
$151$	2.65153	0.215779	0.107889	+	0.994163i	$0.465591\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−4.44949	−0.357392
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−12.8990	−1.01658
$162$	0	0
$163$	9.10102	0.712847	0.356423	−	0.934325i	$-0.383996\pi$
$163$	9.10102	0.712847	0.356423	+	0.934325i	$0.383996\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−6.89898	−0.524520	−0.262260	−	0.964997i	$-0.584468\pi$
$173$	−6.89898	−0.524520	−0.262260	+	0.964997i	$0.584468\pi$
$174$	0	0
$175$	−2.00000	−0.151186
$176$	0	0
$177$	0	0
$178$	0	0
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0	0
$181$	5.79796	0.430959	0.215479	−	0.976508i	$-0.430869\pi$
$181$	5.79796	0.430959	0.215479	+	0.976508i	$0.430869\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−4.89898	−0.360180
$186$	0	0
$187$	30.6969	2.24478
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−1.79796	−0.130096	−0.0650479	−	0.997882i	$-0.520720\pi$
$191$	−1.79796	−0.130096	−0.0650479	+	0.997882i	$0.520720\pi$
$192$	0	0
$193$	0.202041	0.0145432	0.00727162	−	0.999974i	$-0.497685\pi$
$193$	0.202041	0.0145432	0.00727162	+	0.999974i	$0.497685\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	23.7980	1.69553	0.847767	−	0.530369i	$-0.177946\pi$
$197$	23.7980	1.69553	0.847767	+	0.530369i	$0.177946\pi$
$198$	0	0
$199$	−5.79796	−0.411006	−0.205503	−	0.978656i	$-0.565883\pi$
$199$	−5.79796	−0.411006	−0.205503	+	0.978656i	$0.565883\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	8.00000	0.561490
$204$	0	0
$205$	10.8990	0.761218
$206$	0	0
$207$	0	0
$208$	0	0
$209$	2.00000	0.138343
$210$	0	0
$211$	25.7980	1.77600	0.888002	−	0.459839i	$-0.152093\pi$
$211$	25.7980	1.77600	0.888002	+	0.459839i	$0.152093\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	11.3485	0.773959
$216$	0	0
$217$	−8.89898	−0.604102
$218$	0	0
$219$	0	0
$220$	0	0
$221$	6.89898	0.464076
$222$	0	0
$223$	17.5959	1.17831	0.589155	−	0.808020i	$-0.299461\pi$
$223$	17.5959	1.17831	0.589155	+	0.808020i	$0.299461\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	22.8990	1.51986	0.759929	−	0.650006i	$-0.225234\pi$
$227$	22.8990	1.51986	0.759929	+	0.650006i	$0.225234\pi$
$228$	0	0
$229$	−18.8990	−1.24888	−0.624440	−	0.781073i	$-0.714673\pi$
$229$	−18.8990	−1.24888	−0.624440	+	0.781073i	$0.714673\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	25.5959	1.67684	0.838422	−	0.545021i	$-0.183478\pi$
$233$	25.5959	1.67684	0.838422	+	0.545021i	$0.183478\pi$
$234$	0	0
$235$	2.00000	0.130466
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−11.1464	−0.721003	−0.360501	−	0.932759i	$-0.617394\pi$
$239$	−11.1464	−0.721003	−0.360501	+	0.932759i	$0.617394\pi$
$240$	0	0
$241$	−0.696938	−0.0448938	−0.0224469	−	0.999748i	$-0.507146\pi$
$241$	−0.696938	−0.0448938	−0.0224469	+	0.999748i	$0.507146\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	3.00000	0.191663
$246$	0	0
$247$	0.449490	0.0286003
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−14.6969	−0.927663	−0.463831	−	0.885924i	$-0.653526\pi$
$251$	−14.6969	−0.927663	−0.463831	+	0.885924i	$0.653526\pi$
$252$	0	0
$253$	−28.6969	−1.80416
$254$	0	0
$255$	0	0
$256$	0	0
$257$	3.79796	0.236910	0.118455	−	0.992959i	$-0.462206\pi$
$257$	3.79796	0.236910	0.118455	+	0.992959i	$0.462206\pi$
$258$	0	0
$259$	−9.79796	−0.608816
$260$	0	0
$261$	0	0
$262$	0	0
$263$	26.4495	1.63095	0.815473	−	0.578796i	$-0.196477\pi$
$263$	26.4495	1.63095	0.815473	+	0.578796i	$0.196477\pi$
$264$	0	0
$265$	1.10102	0.0676352
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−26.0000	−1.58525	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000	−1.58525	−0.792624	+	0.609711i	$0.791286\pi$
$270$	0	0
$271$	−3.55051	−0.215678	−0.107839	−	0.994168i	$-0.534393\pi$
$271$	−3.55051	−0.215678	−0.107839	+	0.994168i	$0.534393\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−4.44949	−0.268314
$276$	0	0
$277$	−22.4949	−1.35159	−0.675794	−	0.737091i	$-0.736199\pi$
$277$	−22.4949	−1.35159	−0.675794	+	0.737091i	$0.736199\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	6.89898	0.411559	0.205779	−	0.978598i	$-0.434027\pi$
$281$	6.89898	0.411559	0.205779	+	0.978598i	$0.434027\pi$
$282$	0	0
$283$	6.44949	0.383382	0.191691	−	0.981455i	$-0.438603\pi$
$283$	6.44949	0.383382	0.191691	+	0.981455i	$0.438603\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	21.7980	1.28669
$288$	0	0
$289$	30.5959	1.79976
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−28.4949	−1.66469	−0.832345	−	0.554258i	$-0.813002\pi$
$293$	−28.4949	−1.66469	−0.832345	+	0.554258i	$0.813002\pi$
$294$	0	0
$295$	−9.34847	−0.544289
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−6.44949	−0.372984
$300$	0	0
$301$	22.6969	1.30823
$302$	0	0
$303$	0	0
$304$	0	0
$305$	5.79796	0.331990
$306$	0	0
$307$	−7.79796	−0.445053	−0.222527	−	0.974927i	$-0.571430\pi$
$307$	−7.79796	−0.445053	−0.222527	+	0.974927i	$0.571430\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	3.10102	0.175843	0.0879214	−	0.996127i	$-0.471978\pi$
$311$	3.10102	0.175843	0.0879214	+	0.996127i	$0.471978\pi$
$312$	0	0
$313$	−22.4949	−1.27149	−0.635743	−	0.771900i	$-0.719306\pi$
$313$	−22.4949	−1.27149	−0.635743	+	0.771900i	$0.719306\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−26.6969	−1.49945	−0.749725	−	0.661750i	$-0.769814\pi$
$317$	−26.6969	−1.49945	−0.749725	+	0.661750i	$0.769814\pi$
$318$	0	0
$319$	17.7980	0.996494
$320$	0	0
$321$	0	0
$322$	0	0
$323$	3.10102	0.172545
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	0	0
$327$	0	0
$328$	0	0
$329$	4.00000	0.220527
$330$	0	0
$331$	3.55051	0.195154	0.0975768	−	0.995228i	$-0.468891\pi$
$331$	3.55051	0.195154	0.0975768	+	0.995228i	$0.468891\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−5.10102	−0.278699
$336$	0	0
$337$	−16.6969	−0.909540	−0.454770	−	0.890609i	$-0.650279\pi$
$337$	−16.6969	−0.909540	−0.454770	+	0.890609i	$0.650279\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	−19.7980	−1.07212
$342$	0	0
$343$	20.0000	1.07990
$344$	0	0
$345$	0	0
$346$	0	0
$347$	20.2474	1.08694	0.543470	−	0.839429i	$-0.317110\pi$
$347$	20.2474	1.08694	0.543470	+	0.839429i	$0.317110\pi$
$348$	0	0
$349$	20.6969	1.10788	0.553941	−	0.832556i	$-0.313123\pi$
$349$	20.6969	1.10788	0.553941	+	0.832556i	$0.313123\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	28.4949	1.51663	0.758315	−	0.651888i	$-0.226023\pi$
$353$	28.4949	1.51663	0.758315	+	0.651888i	$0.226023\pi$
$354$	0	0
$355$	3.55051	0.188442
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−5.75255	−0.303608	−0.151804	−	0.988411i	$-0.548508\pi$
$359$	−5.75255	−0.303608	−0.151804	+	0.988411i	$0.548508\pi$
$360$	0	0
$361$	−18.7980	−0.989366
$362$	0	0
$363$	0	0
$364$	0	0
$365$	14.6969	0.769273
$366$	0	0
$367$	−34.9444	−1.82408	−0.912041	−	0.410099i	$-0.865494\pi$
$367$	−34.9444	−1.82408	−0.912041	+	0.410099i	$0.865494\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	2.20204	0.114324
$372$	0	0
$373$	29.5959	1.53242	0.766209	−	0.642591i	$-0.222141\pi$
$373$	29.5959	1.53242	0.766209	+	0.642591i	$0.222141\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	4.00000	0.206010
$378$	0	0
$379$	16.4495	0.844954	0.422477	−	0.906374i	$-0.361161\pi$
$379$	16.4495	0.844954	0.422477	+	0.906374i	$0.361161\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−25.5959	−1.30789	−0.653945	−	0.756542i	$-0.726887\pi$
$383$	−25.5959	−1.30789	−0.653945	+	0.756542i	$0.726887\pi$
$384$	0	0
$385$	−8.89898	−0.453534
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−1.59592	−0.0809163	−0.0404581	−	0.999181i	$-0.512882\pi$
$389$	−1.59592	−0.0809163	−0.0404581	+	0.999181i	$0.512882\pi$
$390$	0	0
$391$	−44.4949	−2.25020
$392$	0	0
$393$	0	0
$394$	0	0
$395$	4.89898	0.246494
$396$	0	0
$397$	30.6969	1.54064	0.770318	−	0.637660i	$-0.220098\pi$
$397$	30.6969	1.54064	0.770318	+	0.637660i	$0.220098\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	−4.44949	−0.221645
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−21.7980	−1.08048
$408$	0	0
$409$	−6.89898	−0.341133	−0.170566	−	0.985346i	$-0.554560\pi$
$409$	−6.89898	−0.341133	−0.170566	+	0.985346i	$0.554560\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−18.6969	−0.920016
$414$	0	0
$415$	−2.00000	−0.0981761
$416$	0	0
$417$	0	0
$418$	0	0
$419$	38.6969	1.89047	0.945235	−	0.326392i	$-0.105833\pi$
$419$	38.6969	1.89047	0.945235	+	0.326392i	$0.105833\pi$
$420$	0	0
$421$	−3.79796	−0.185101	−0.0925506	−	0.995708i	$-0.529502\pi$
$421$	−3.79796	−0.185101	−0.0925506	+	0.995708i	$0.529502\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−6.89898	−0.334650
$426$	0	0
$427$	11.5959	0.561166
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−32.0454	−1.54357	−0.771786	−	0.635882i	$-0.780637\pi$
$431$	−32.0454	−1.54357	−0.771786	+	0.635882i	$0.780637\pi$
$432$	0	0
$433$	11.7980	0.566974	0.283487	−	0.958976i	$-0.408509\pi$
$433$	11.7980	0.566974	0.283487	+	0.958976i	$0.408509\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−2.89898	−0.138677
$438$	0	0
$439$	17.7980	0.849450	0.424725	−	0.905322i	$-0.360371\pi$
$439$	17.7980	0.849450	0.424725	+	0.905322i	$0.360371\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−22.0454	−1.04741	−0.523704	−	0.851900i	$-0.675450\pi$
$443$	−22.0454	−1.04741	−0.523704	+	0.851900i	$0.675450\pi$
$444$	0	0
$445$	6.00000	0.284427
$446$	0	0
$447$	0	0
$448$	0	0
$449$	20.6969	0.976749	0.488374	−	0.872634i	$-0.337590\pi$
$449$	20.6969	0.976749	0.488374	+	0.872634i	$0.337590\pi$
$450$	0	0
$451$	48.4949	2.28354
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−2.00000	−0.0937614
$456$	0	0
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	32.6969	1.52285	0.761424	−	0.648254i	$-0.224501\pi$
$461$	32.6969	1.52285	0.761424	+	0.648254i	$0.224501\pi$
$462$	0	0
$463$	22.8990	1.06421	0.532103	−	0.846680i	$-0.321402\pi$
$463$	22.8990	1.06421	0.532103	+	0.846680i	$0.321402\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	22.9444	1.06174	0.530870	−	0.847453i	$-0.321865\pi$
$467$	22.9444	1.06174	0.530870	+	0.847453i	$0.321865\pi$
$468$	0	0
$469$	−10.2020	−0.471086
$470$	0	0
$471$	0	0
$472$	0	0
$473$	50.4949	2.32176
$474$	0	0
$475$	−0.449490	−0.0206240
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−9.34847	−0.427142	−0.213571	−	0.976927i	$-0.568510\pi$
$479$	−9.34847	−0.427142	−0.213571	+	0.976927i	$0.568510\pi$
$480$	0	0
$481$	−4.89898	−0.223374
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−7.79796	−0.354087
$486$	0	0
$487$	6.89898	0.312623	0.156311	−	0.987708i	$-0.450040\pi$
$487$	6.89898	0.312623	0.156311	+	0.987708i	$0.450040\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−34.2929	−1.54761	−0.773807	−	0.633421i	$-0.781650\pi$
$491$	−34.2929	−1.54761	−0.773807	+	0.633421i	$0.781650\pi$
$492$	0	0
$493$	27.5959	1.24286
$494$	0	0
$495$	0	0
$496$	0	0
$497$	7.10102	0.318524
$498$	0	0
$499$	−6.65153	−0.297763	−0.148882	−	0.988855i	$-0.547567\pi$
$499$	−6.65153	−0.297763	−0.148882	+	0.988855i	$0.547567\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	26.9444	1.20139	0.600695	−	0.799478i	$-0.294890\pi$
$503$	26.9444	1.20139	0.600695	+	0.799478i	$0.294890\pi$
$504$	0	0
$505$	−15.7980	−0.703000
$506$	0	0
$507$	0	0
$508$	0	0
$509$	−17.1010	−0.757989	−0.378995	−	0.925399i	$-0.623730\pi$
$509$	−17.1010	−0.757989	−0.378995	+	0.925399i	$0.623730\pi$
$510$	0	0
$511$	29.3939	1.30031
$512$	0	0
$513$	0	0
$514$	0	0
$515$	11.3485	0.500073
$516$	0	0
$517$	8.89898	0.391377
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−25.7980	−1.13023	−0.565115	−	0.825012i	$-0.691168\pi$
$521$	−25.7980	−1.13023	−0.565115	+	0.825012i	$0.691168\pi$
$522$	0	0
$523$	24.6515	1.07794	0.538968	−	0.842326i	$-0.318814\pi$
$523$	24.6515	1.07794	0.538968	+	0.842326i	$0.318814\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−30.6969	−1.33718
$528$	0	0
$529$	18.5959	0.808518
$530$	0	0
$531$	0	0
$532$	0	0
$533$	10.8990	0.472087
$534$	0	0
$535$	12.2474	0.529503
$536$	0	0
$537$	0	0
$538$	0	0
$539$	13.3485	0.574959
$540$	0	0
$541$	14.8990	0.640557	0.320279	−	0.947323i	$-0.396223\pi$
$541$	14.8990	0.640557	0.320279	+	0.947323i	$0.396223\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	10.0000	0.428353
$546$	0	0
$547$	−15.3485	−0.656253	−0.328127	−	0.944634i	$-0.606417\pi$
$547$	−15.3485	−0.656253	−0.328127	+	0.944634i	$0.606417\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	1.79796	0.0765956
$552$	0	0
$553$	9.79796	0.416652
$554$	0	0
$555$	0	0
$556$	0	0
$557$	30.6969	1.30067	0.650336	−	0.759647i	$-0.274628\pi$
$557$	30.6969	1.30067	0.650336	+	0.759647i	$0.274628\pi$
$558$	0	0
$559$	11.3485	0.479989
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−32.2474	−1.35907	−0.679534	−	0.733644i	$-0.737818\pi$
$563$	−32.2474	−1.35907	−0.679534	+	0.733644i	$0.737818\pi$
$564$	0	0
$565$	1.10102	0.0463203
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−29.7980	−1.24920	−0.624598	−	0.780947i	$-0.714737\pi$
$569$	−29.7980	−1.24920	−0.624598	+	0.780947i	$0.714737\pi$
$570$	0	0
$571$	20.4949	0.857685	0.428842	−	0.903379i	$-0.358922\pi$
$571$	20.4949	0.857685	0.428842	+	0.903379i	$0.358922\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	6.44949	0.268962
$576$	0	0
$577$	36.8990	1.53612	0.768062	−	0.640375i	$-0.221221\pi$
$577$	36.8990	1.53612	0.768062	+	0.640375i	$0.221221\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	−4.00000	−0.165948
$582$	0	0
$583$	4.89898	0.202895
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−1.10102	−0.0454440	−0.0227220	−	0.999742i	$-0.507233\pi$
$587$	−1.10102	−0.0454440	−0.0227220	+	0.999742i	$0.507233\pi$
$588$	0	0
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	−13.7980	−0.565661
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−19.1010	−0.780447	−0.390223	−	0.920720i	$-0.627602\pi$
$599$	−19.1010	−0.780447	−0.390223	+	0.920720i	$0.627602\pi$
$600$	0	0
$601$	5.59592	0.228262	0.114131	−	0.993466i	$-0.463592\pi$
$601$	5.59592	0.228262	0.114131	+	0.993466i	$0.463592\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−8.79796	−0.357688
$606$	0	0
$607$	−26.4495	−1.07355	−0.536776	−	0.843725i	$-0.680358\pi$
$607$	−26.4495	−1.07355	−0.536776	+	0.843725i	$0.680358\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	2.00000	0.0809113
$612$	0	0
$613$	−33.1918	−1.34061	−0.670303	−	0.742088i	$-0.733836\pi$
$613$	−33.1918	−1.34061	−0.670303	+	0.742088i	$0.733836\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−23.3939	−0.941802	−0.470901	−	0.882186i	$-0.656071\pi$
$617$	−23.3939	−0.941802	−0.470901	+	0.882186i	$0.656071\pi$
$618$	0	0
$619$	−9.34847	−0.375747	−0.187873	−	0.982193i	$-0.560159\pi$
$619$	−9.34847	−0.375747	−0.187873	+	0.982193i	$0.560159\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	12.0000	0.480770
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−33.7980	−1.34761
$630$	0	0
$631$	11.5505	0.459819	0.229909	−	0.973212i	$-0.426157\pi$
$631$	11.5505	0.459819	0.229909	+	0.973212i	$0.426157\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	4.65153	0.184590
$636$	0	0
$637$	3.00000	0.118864
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−23.3939	−0.924003	−0.462001	−	0.886879i	$-0.652868\pi$
$641$	−23.3939	−0.924003	−0.462001	+	0.886879i	$0.652868\pi$
$642$	0	0
$643$	30.0000	1.18308	0.591542	−	0.806274i	$-0.298519\pi$
$643$	30.0000	1.18308	0.591542	+	0.806274i	$0.298519\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−38.9444	−1.53106	−0.765531	−	0.643399i	$-0.777524\pi$
$647$	−38.9444	−1.53106	−0.765531	+	0.643399i	$0.777524\pi$
$648$	0	0
$649$	−41.5959	−1.63278
$650$	0	0
$651$	0	0
$652$	0	0
$653$	24.2020	0.947099	0.473550	−	0.880767i	$-0.342972\pi$
$653$	24.2020	0.947099	0.473550	+	0.880767i	$0.342972\pi$
$654$	0	0
$655$	−19.5959	−0.765676
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−14.6969	−0.572511	−0.286256	−	0.958153i	$-0.592411\pi$
$659$	−14.6969	−0.572511	−0.286256	+	0.958153i	$0.592411\pi$
$660$	0	0
$661$	20.2020	0.785768	0.392884	−	0.919588i	$-0.371477\pi$
$661$	20.2020	0.785768	0.392884	+	0.919588i	$0.371477\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−0.898979	−0.0348609
$666$	0	0
$667$	−25.7980	−0.998901
$668$	0	0
$669$	0	0
$670$	0	0
$671$	25.7980	0.995919
$672$	0	0
$673$	−10.8990	−0.420125	−0.210062	−	0.977688i	$-0.567367\pi$
$673$	−10.8990	−0.420125	−0.210062	+	0.977688i	$0.567367\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	11.3031	0.434412	0.217206	−	0.976126i	$-0.430306\pi$
$677$	11.3031	0.434412	0.217206	+	0.976126i	$0.430306\pi$
$678$	0	0
$679$	−15.5959	−0.598516
$680$	0	0
$681$	0	0
$682$	0	0
$683$	6.49490	0.248520	0.124260	−	0.992250i	$-0.460344\pi$
$683$	6.49490	0.248520	0.124260	+	0.992250i	$0.460344\pi$
$684$	0	0
$685$	−14.0000	−0.534913
$686$	0	0
$687$	0	0
$688$	0	0
$689$	1.10102	0.0419455
$690$	0	0
$691$	29.3485	1.11647	0.558234	−	0.829683i	$-0.311479\pi$
$691$	29.3485	1.11647	0.558234	+	0.829683i	$0.311479\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−16.8990	−0.641015
$696$	0	0
$697$	75.1918	2.84809
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−41.1918	−1.55579	−0.777897	−	0.628392i	$-0.783714\pi$
$701$	−41.1918	−1.55579	−0.777897	+	0.628392i	$0.783714\pi$
$702$	0	0
$703$	−2.20204	−0.0830516
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−31.5959	−1.18829
$708$	0	0
$709$	36.2929	1.36301	0.681503	−	0.731815i	$-0.261326\pi$
$709$	36.2929	1.36301	0.681503	+	0.731815i	$0.261326\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	28.6969	1.07471
$714$	0	0
$715$	−4.44949	−0.166401
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	0	0
$721$	22.6969	0.845278
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−4.00000	−0.148556
$726$	0	0
$727$	26.0454	0.965971	0.482985	−	0.875628i	$-0.339552\pi$
$727$	26.0454	0.965971	0.482985	+	0.875628i	$0.339552\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	78.2929	2.89577
$732$	0	0
$733$	−6.00000	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−22.6969	−0.836052
$738$	0	0
$739$	−18.2474	−0.671243	−0.335622	−	0.941997i	$-0.608946\pi$
$739$	−18.2474	−0.671243	−0.335622	+	0.941997i	$0.608946\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	23.3939	0.858238	0.429119	−	0.903248i	$-0.358824\pi$
$743$	23.3939	0.858238	0.429119	+	0.903248i	$0.358824\pi$
$744$	0	0
$745$	11.7980	0.432244
$746$	0	0
$747$	0	0
$748$	0	0
$749$	24.4949	0.895024
$750$	0	0
$751$	−40.8990	−1.49242	−0.746212	−	0.665708i	$-0.768130\pi$
$751$	−40.8990	−1.49242	−0.746212	+	0.665708i	$0.768130\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−2.65153	−0.0964991
$756$	0	0
$757$	−22.4949	−0.817591	−0.408795	−	0.912626i	$-0.634051\pi$
$757$	−22.4949	−0.817591	−0.408795	+	0.912626i	$0.634051\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	49.5959	1.79785	0.898925	−	0.438102i	$-0.144349\pi$
$761$	49.5959	1.79785	0.898925	+	0.438102i	$0.144349\pi$
$762$	0	0
$763$	20.0000	0.724049
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−9.34847	−0.337554
$768$	0	0
$769$	−19.3939	−0.699361	−0.349681	−	0.936869i	$-0.613710\pi$
$769$	−19.3939	−0.699361	−0.349681	+	0.936869i	$0.613710\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	44.0908	1.58584	0.792918	−	0.609328i	$-0.208561\pi$
$773$	44.0908	1.58584	0.792918	+	0.609328i	$0.208561\pi$
$774$	0	0
$775$	4.44949	0.159830
$776$	0	0
$777$	0	0
$778$	0	0
$779$	4.89898	0.175524
$780$	0	0
$781$	15.7980	0.565295
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−10.0000	−0.356915
$786$	0	0
$787$	−38.0000	−1.35455	−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000	−1.35455	−0.677277	+	0.735728i	$0.736840\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	2.20204	0.0782956
$792$	0	0
$793$	5.79796	0.205892
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−8.20204	−0.290531	−0.145266	−	0.989393i	$-0.546404\pi$
$797$	−8.20204	−0.290531	−0.145266	+	0.989393i	$0.546404\pi$
$798$	0	0
$799$	13.7980	0.488137
$800$	0	0
$801$	0	0
$802$	0	0
$803$	65.3939	2.30770
$804$	0	0
$805$	12.8990	0.454629
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−12.0000	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$810$	0	0
$811$	−9.84337	−0.345647	−0.172824	−	0.984953i	$-0.555289\pi$
$811$	−9.84337	−0.345647	−0.172824	+	0.984953i	$0.555289\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−9.10102	−0.318795
$816$	0	0
$817$	5.10102	0.178462
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−25.1918	−0.879201	−0.439601	−	0.898193i	$-0.644880\pi$
$821$	−25.1918	−0.879201	−0.439601	+	0.898193i	$0.644880\pi$
$822$	0	0
$823$	−25.5505	−0.890635	−0.445317	−	0.895373i	$-0.646909\pi$
$823$	−25.5505	−0.890635	−0.445317	+	0.895373i	$0.646909\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−21.1918	−0.736912	−0.368456	−	0.929645i	$-0.620114\pi$
$827$	−21.1918	−0.736912	−0.368456	+	0.929645i	$0.620114\pi$
$828$	0	0
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	20.6969	0.717106
$834$	0	0
$835$	−18.0000	−0.622916
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−24.4495	−0.844090	−0.422045	−	0.906575i	$-0.638688\pi$
$839$	−24.4495	−0.844090	−0.422045	+	0.906575i	$0.638688\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	−17.5959	−0.604603
$848$	0	0
$849$	0	0
$850$	0	0
$851$	31.5959	1.08309
$852$	0	0
$853$	10.6969	0.366256	0.183128	−	0.983089i	$-0.441378\pi$
$853$	10.6969	0.366256	0.183128	+	0.983089i	$0.441378\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	23.3939	0.799120	0.399560	−	0.916707i	$-0.369163\pi$
$857$	23.3939	0.799120	0.399560	+	0.916707i	$0.369163\pi$
$858$	0	0
$859$	1.30306	0.0444599	0.0222299	−	0.999753i	$-0.492923\pi$
$859$	1.30306	0.0444599	0.0222299	+	0.999753i	$0.492923\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−35.3939	−1.20482	−0.602411	−	0.798186i	$-0.705793\pi$
$863$	−35.3939	−1.20482	−0.602411	+	0.798186i	$0.705793\pi$
$864$	0	0
$865$	6.89898	0.234572
$866$	0	0
$867$	0	0
$868$	0	0
$869$	21.7980	0.739445
$870$	0	0
$871$	−5.10102	−0.172841
$872$	0	0
$873$	0	0
$874$	0	0
$875$	2.00000	0.0676123
$876$	0	0
$877$	−21.5959	−0.729242	−0.364621	−	0.931156i	$-0.618802\pi$
$877$	−21.5959	−0.729242	−0.364621	+	0.931156i	$0.618802\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	9.79796	0.330102	0.165051	−	0.986285i	$-0.447221\pi$
$881$	9.79796	0.330102	0.165051	+	0.986285i	$0.447221\pi$
$882$	0	0
$883$	−3.34847	−0.112685	−0.0563425	−	0.998412i	$-0.517944\pi$
$883$	−3.34847	−0.112685	−0.0563425	+	0.998412i	$0.517944\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−20.2474	−0.679843	−0.339921	−	0.940454i	$-0.610400\pi$
$887$	−20.2474	−0.679843	−0.339921	+	0.940454i	$0.610400\pi$
$888$	0	0
$889$	9.30306	0.312015
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0.898979	0.0300832
$894$	0	0
$895$	−8.00000	−0.267411
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−17.7980	−0.593595
$900$	0	0
$901$	7.59592	0.253057
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−5.79796	−0.192731
$906$	0	0
$907$	19.8434	0.658888	0.329444	−	0.944175i	$-0.393139\pi$
$907$	19.8434	0.658888	0.329444	+	0.944175i	$0.393139\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	9.39388	0.311233	0.155617	−	0.987818i	$-0.450264\pi$
$911$	9.39388	0.311233	0.155617	+	0.987818i	$0.450264\pi$
$912$	0	0
$913$	−8.89898	−0.294513
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−39.1918	−1.29423
$918$	0	0
$919$	20.8990	0.689394	0.344697	−	0.938714i	$-0.387982\pi$
$919$	20.8990	0.689394	0.344697	+	0.938714i	$0.387982\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	3.55051	0.116866
$924$	0	0
$925$	4.89898	0.161077
$926$	0	0
$927$	0	0
$928$	0	0
$929$	4.69694	0.154102	0.0770508	−	0.997027i	$-0.475450\pi$
$929$	4.69694	0.154102	0.0770508	+	0.997027i	$0.475450\pi$
$930$	0	0
$931$	1.34847	0.0441943
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−30.6969	−1.00390
$936$	0	0
$937$	39.3939	1.28694	0.643471	−	0.765471i	$-0.277494\pi$
$937$	39.3939	1.28694	0.643471	+	0.765471i	$0.277494\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	52.6969	1.71787	0.858936	−	0.512084i	$-0.171126\pi$
$941$	52.6969	1.71787	0.858936	+	0.512084i	$0.171126\pi$
$942$	0	0
$943$	−70.2929	−2.28905
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−28.2020	−0.916443	−0.458222	−	0.888838i	$-0.651513\pi$
$947$	−28.2020	−0.916443	−0.458222	+	0.888838i	$0.651513\pi$
$948$	0	0
$949$	14.6969	0.477083
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−21.1918	−0.686471	−0.343235	−	0.939249i	$-0.611523\pi$
$953$	−21.1918	−0.686471	−0.343235	+	0.939249i	$0.611523\pi$
$954$	0	0
$955$	1.79796	0.0581806
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−28.0000	−0.904167
$960$	0	0
$961$	−11.2020	−0.361356
$962$	0	0
$963$	0	0
$964$	0	0
$965$	−0.202041	−0.00650393
$966$	0	0
$967$	−34.8990	−1.12228	−0.561138	−	0.827722i	$-0.689636\pi$
$967$	−34.8990	−1.12228	−0.561138	+	0.827722i	$0.689636\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−11.5959	−0.372131	−0.186065	−	0.982537i	$-0.559574\pi$
$971$	−11.5959	−0.372131	−0.186065	+	0.982537i	$0.559574\pi$
$972$	0	0
$973$	−33.7980	−1.08351
$974$	0	0
$975$	0	0
$976$	0	0
$977$	30.6969	0.982082	0.491041	−	0.871136i	$-0.336617\pi$
$977$	30.6969	0.982082	0.491041	+	0.871136i	$0.336617\pi$
$978$	0	0
$979$	26.6969	0.853238
$980$	0	0
$981$	0	0
$982$	0	0
$983$	49.1010	1.56608	0.783040	−	0.621972i	$-0.213668\pi$
$983$	49.1010	1.56608	0.783040	+	0.621972i	$0.213668\pi$
$984$	0	0
$985$	−23.7980	−0.758266
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−73.1918	−2.32736
$990$	0	0
$991$	49.7980	1.58188	0.790942	−	0.611891i	$-0.209591\pi$
$991$	49.7980	1.58188	0.790942	+	0.611891i	$0.209591\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	5.79796	0.183808
$996$	0	0
$997$	34.8990	1.10526	0.552631	−	0.833426i	$-0.313624\pi$
$997$	34.8990	1.10526	0.552631	+	0.833426i	$0.313624\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9360.2.a.cc.1.1		2
3.2	odd	2		1040.2.a.k.1.2		2
4.3	odd	2		4680.2.a.z.1.2		2
12.11	even	2		520.2.a.f.1.1	✓	2
15.14	odd	2		5200.2.a.bv.1.1		2
24.5	odd	2		4160.2.a.ba.1.1		2
24.11	even	2		4160.2.a.bg.1.2		2
60.23	odd	4		2600.2.d.h.1249.1		4
60.47	odd	4		2600.2.d.h.1249.4		4
60.59	even	2		2600.2.a.q.1.2		2
156.155	even	2		6760.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.a.f.1.1	✓	2	12.11	even	2
1040.2.a.k.1.2		2	3.2	odd	2
2600.2.a.q.1.2		2	60.59	even	2
2600.2.d.h.1249.1		4	60.23	odd	4
2600.2.d.h.1249.4		4	60.47	odd	4
4160.2.a.ba.1.1		2	24.5	odd	2
4160.2.a.bg.1.2		2	24.11	even	2
4680.2.a.z.1.2		2	4.3	odd	2
5200.2.a.bv.1.1		2	15.14	odd	2
6760.2.a.s.1.1		2	156.155	even	2
9360.2.a.cc.1.1		2	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9360.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{5} -2.00000 q^{7} +O(q^{10})\)	\(q-1.00000 q^{5} -2.00000 q^{7} -4.44949 q^{11} -1.00000 q^{13} -6.89898 q^{17} -0.449490 q^{19} +6.44949 q^{23} +1.00000 q^{25} -4.00000 q^{29} +4.44949 q^{31} +2.00000 q^{35} +4.89898 q^{37} -10.8990 q^{41} -11.3485 q^{43} -2.00000 q^{47} -3.00000 q^{49} -1.10102 q^{53} +4.44949 q^{55} +9.34847 q^{59} -5.79796 q^{61} +1.00000 q^{65} +5.10102 q^{67} -3.55051 q^{71} -14.6969 q^{73} +8.89898 q^{77} -4.89898 q^{79} +2.00000 q^{83} +6.89898 q^{85} -6.00000 q^{89} +2.00000 q^{91} +0.449490 q^{95} +7.79796 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 2 * q - 2 * q^5 - 4 * q^7	\( 2 q - 2 q^{5} - 4 q^{7} - 4 q^{11} - 2 q^{13} - 4 q^{17} + 4 q^{19} + 8 q^{23} + 2 q^{25} - 8 q^{29} + 4 q^{31} + 4 q^{35} - 12 q^{41} - 8 q^{43} - 4 q^{47} - 6 q^{49} - 12 q^{53} + 4 q^{55} + 4 q^{59} + 8 q^{61} + 2 q^{65} + 20 q^{67} - 12 q^{71} + 8 q^{77} + 4 q^{83} + 4 q^{85} - 12 q^{89} + 4 q^{91} - 4 q^{95} - 4 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 - 4 * q^7 - 4 * q^11 - 2 * q^13 - 4 * q^17 + 4 * q^19 + 8 * q^23 + 2 * q^25 - 8 * q^29 + 4 * q^31 + 4 * q^35 - 12 * q^41 - 8 * q^43 - 4 * q^47 - 6 * q^49 - 12 * q^53 + 4 * q^55 + 4 * q^59 + 8 * q^61 + 2 * q^65 + 20 * q^67 - 12 * q^71 + 8 * q^77 + 4 * q^83 + 4 * q^85 - 12 * q^89 + 4 * q^91 - 4 * q^95 - 4 * q^97

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