LMFDB - Embedded newform 3024.2.r.g.1009.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1009,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.r (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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1009.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	3024.1009
Dual form			3024.2.r.g.2017.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29679 + 2.24611i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-1.29679 + 2.24611i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.25729 - 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +0.945916 q^{17} +4.05408 q^{19} +(0.136673 - 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +(1.23025 + 2.13086i) q^{29} +(1.16372 - 2.01561i) q^{31} +2.59358 q^{35} +1.78074 q^{37} +(-3.20321 + 5.54812i) q^{41} +(-5.21780 - 9.03749i) q^{43} +(6.08113 + 10.5328i) q^{47} +(-0.500000 + 0.866025i) q^{49} +6.27335 q^{53} +11.7089 q^{55} +(1.36333 - 2.36135i) q^{59} +(1.13667 + 1.96878i) q^{61} +(-1.29679 - 2.24611i) q^{65} +(-7.90856 + 13.6980i) q^{67} +3.27335 q^{71} -1.50739 q^{73} +(-2.25729 + 3.90975i) q^{77} +(7.35447 + 12.7383i) q^{79} +(0.472958 + 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +14.3566 q^{89} +1.00000 q^{91} +(-5.25729 + 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q - 5 * q^5 - 3 * q^7	$ 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59} + 6 q^{61} - 5 q^{65} + 18 q^{71} + 6 q^{73} + 2 q^{77} + 15 q^{79} + 12 q^{83} - 9 q^{85} + 4 q^{89} + 6 q^{91} - 16 q^{95} - 3 q^{97}+O(q^{100}) $ 6 * q - 5 * q^5 - 3 * q^7 + 2 * q^11 - 3 * q^13 + 24 * q^17 + 6 * q^19 - 6 * q^25 + q^29 - 3 * q^31 + 10 * q^35 - 6 * q^37 - 22 * q^41 - 3 * q^43 + 9 * q^47 - 3 * q^49 + 36 * q^53 + 12 * q^55 + 9 * q^59 + 6 * q^61 - 5 * q^65 + 18 * q^71 + 6 * q^73 + 2 * q^77 + 15 * q^79 + 12 * q^83 - 9 * q^85 + 4 * q^89 + 6 * q^91 - 16 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	−1.29679	+	2.24611i	−0.579942	+	1.00449i	0.415543	+	0.909573i	$0.363591\pi$
$5$	−1.29679	+	2.24611i	−0.579942	+	1.00449i	−0.995485	+	0.0949156i	$0.969742\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.25729	−	3.90975i	−0.680600	−	1.17883i	−0.974798	−	0.223089i	$-0.928386\pi$
$11$	−2.25729	−	3.90975i	−0.680600	−	1.17883i	0.294198	−	0.955744i	$-0.404947\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.945916			0.229418			0.114709	−	0.993399i	$-0.463406\pi$
$17$	0.945916			0.229418			0.114709	+	0.993399i	$0.463406\pi$
$18$		0			0
$19$	4.05408			0.930071			0.465035	−	0.885292i	$-0.346042\pi$
$19$	4.05408			0.930071			0.465035	+	0.885292i	$0.346042\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.136673	−	0.236725i	0.0284983	−	0.0493605i	−0.851425	−	0.524477i	$-0.824261\pi$
$23$	0.136673	−	0.236725i	0.0284983	−	0.0493605i	0.879923	+	0.475117i	$0.157594\pi$
$24$		0			0
$25$	−0.863327	−	1.49533i	−0.172665	−	0.299065i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.23025	+	2.13086i	0.228452	+	0.395691i	0.957350	−	0.288932i	$-0.0933002\pi$
$29$	1.23025	+	2.13086i	0.228452	+	0.395691i	−0.728897	+	0.684623i	$0.759967\pi$
$30$		0			0
$31$	1.16372	−	2.01561i	0.209009	−	0.362015i	−0.742393	−	0.669964i	$-0.766309\pi$
$31$	1.16372	−	2.01561i	0.209009	−	0.362015i	0.951403	+	0.307949i	$0.0996427\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.59358			0.438395
$36$		0			0
$37$	1.78074			0.292752			0.146376	−	0.989229i	$-0.453239\pi$
$37$	1.78074			0.292752			0.146376	+	0.989229i	$0.453239\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	0.499743	+	0.866174i	$0.333428\pi$
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	−1.00000		0.000297253i	$0.999905\pi$
$42$		0			0
$43$	−5.21780	−	9.03749i	−0.795707	−	1.37820i	−0.922389	−	0.386262i	$-0.873766\pi$
$43$	−5.21780	−	9.03749i	−0.795707	−	1.37820i	0.126682	−	0.991943i	$-0.459567\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.843377	+	0.537323i	$0.180564\pi$
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.0436467	+	0.999047i	$0.486102\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.27335			0.861710			0.430855	−	0.902421i	$-0.358212\pi$
$53$	6.27335			0.861710			0.430855	+	0.902421i	$0.358212\pi$
$54$		0			0
$55$	11.7089			1.57883
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.36333	−	2.36135i	0.177490	−	0.307422i	−0.763530	−	0.645772i	$-0.776536\pi$
$59$	1.36333	−	2.36135i	0.177490	−	0.307422i	0.941020	+	0.338350i	$0.109869\pi$
$60$		0			0
$61$	1.13667	+	1.96878i	0.145536	+	0.252076i	0.929573	−	0.368639i	$-0.120176\pi$
$61$	1.13667	+	1.96878i	0.145536	+	0.252076i	−0.784037	+	0.620714i	$0.786843\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.29679	−	2.24611i	−0.160847	−	0.278595i
$66$		0			0
$67$	−7.90856	+	13.6980i	−0.966184	+	1.67348i	−0.259784	+	0.965667i	$0.583651\pi$
$67$	−7.90856	+	13.6980i	−0.966184	+	1.67348i	−0.706400	+	0.707813i	$0.749682\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.27335			0.388475			0.194237	−	0.980955i	$-0.437777\pi$
$71$	3.27335			0.388475			0.194237	+	0.980955i	$0.437777\pi$
$72$		0			0
$73$	−1.50739			−0.176427			−0.0882134	−	0.996102i	$-0.528116\pi$
$73$	−1.50739			−0.176427			−0.0882134	+	0.996102i	$0.528116\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.25729	+	3.90975i	−0.257243	+	0.445557i
$78$		0			0
$79$	7.35447	+	12.7383i	0.827443	+	1.43317i	0.900038	+	0.435811i	$0.143539\pi$
$79$	7.35447	+	12.7383i	0.827443	+	1.43317i	−0.0725952	+	0.997361i	$0.523128\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.472958	+	0.819187i	0.0519139	+	0.0899175i	0.890815	−	0.454367i	$-0.150135\pi$
$83$	0.472958	+	0.819187i	0.0519139	+	0.0899175i	−0.838901	+	0.544285i	$0.816801\pi$
$84$		0			0
$85$	−1.22665	+	2.12463i	−0.133049	+	0.230448i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	14.3566			1.52180			0.760899	−	0.648871i	$-0.224758\pi$
$89$	14.3566			1.52180			0.760899	+	0.648871i	$0.224758\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.25729	+	9.10590i	−0.539387	+	0.934246i
$96$		0			0
$97$	5.74484	+	9.95036i	0.583300	+	1.01031i	0.995085	+	0.0990246i	$0.0315722\pi$
$97$	5.74484	+	9.95036i	0.583300	+	1.01031i	−0.411785	+	0.911281i	$0.635094\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.83988	−	3.18677i	−0.183075	−	0.317096i	0.759851	−	0.650097i	$-0.225272\pi$
$101$	−1.83988	−	3.18677i	−0.183075	−	0.317096i	−0.942926	+	0.333002i	$0.891939\pi$
$102$		0			0
$103$	−4.86333	+	8.42353i	−0.479198	+	0.829995i	−0.999715	−	0.0238560i	$-0.992406\pi$
$103$	−4.86333	+	8.42353i	−0.479198	+	0.829995i	0.520518	+	0.853851i	$0.325739\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.37432			−0.132860			−0.0664301	−	0.997791i	$-0.521161\pi$
$107$	−1.37432			−0.132860			−0.0664301	+	0.997791i	$0.521161\pi$
$108$		0			0
$109$	−3.39922			−0.325587			−0.162793	−	0.986660i	$-0.552050\pi$
$109$	−3.39922			−0.325587			−0.162793	+	0.986660i	$0.552050\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.19436	−	8.99689i	0.488644	−	0.846356i	−0.511271	−	0.859420i	$-0.670825\pi$
$113$	5.19436	−	8.99689i	0.488644	−	0.846356i	0.999915	+	0.0130636i	$0.00415840\pi$
$114$		0			0
$115$	0.354473	+	0.613964i	0.0330547	+	0.0572525i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.472958	−	0.819187i	−0.0433560	−	0.0750948i
$120$		0			0
$121$	−4.69076	+	8.12463i	−0.426432	+	0.738603i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.48968			−0.759340
$126$		0			0
$127$	−0.672570			−0.0596809			−0.0298405	−	0.999555i	$-0.509500\pi$
$127$	−0.672570			−0.0596809			−0.0298405	+	0.999555i	$0.509500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.95691	+	6.85356i	−0.345717	+	0.598799i	−0.985484	−	0.169770i	$-0.945697\pi$
$131$	−3.95691	+	6.85356i	−0.345717	+	0.598799i	0.639767	+	0.768569i	$0.279031\pi$
$132$		0			0
$133$	−2.02704	−	3.51094i	−0.175767	−	0.304437i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.83628	−	3.18054i	−0.156884	−	0.271732i	0.776859	−	0.629674i	$-0.216812\pi$
$137$	−1.83628	−	3.18054i	−0.156884	−	0.271732i	−0.933744	+	0.357943i	$0.883478\pi$
$138$		0			0
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	−0.906289	−	0.422658i	$-0.861097\pi$
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	0.819177	+	0.573541i	$0.194431\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.51459			0.377529
$144$		0			0
$145$	−6.38151			−0.529956
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.77188	+	11.7292i	−0.554774	+	0.960897i	0.443147	+	0.896449i	$0.353862\pi$
$149$	−6.77188	+	11.7292i	−0.554774	+	0.960897i	−0.997921	+	0.0644482i	$0.979471\pi$
$150$		0			0
$151$	4.96410	+	8.59808i	0.403973	+	0.699702i	0.994201	−	0.107535i	$-0.0342956\pi$
$151$	4.96410	+	8.59808i	0.403973	+	0.699702i	−0.590228	+	0.807236i	$0.700962\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.01819	+	5.22765i	0.242427	+	0.419895i
$156$		0			0
$157$	−3.02704	+	5.24299i	−0.241584	+	0.418436i	−0.961166	−	0.275972i	$-0.911000\pi$
$157$	−3.02704	+	5.24299i	−0.241584	+	0.418436i	0.719581	+	0.694408i	$0.244334\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.273346			−0.0215427
$162$		0			0
$163$	−17.8171			−1.39554			−0.697772	−	0.716320i	$-0.745825\pi$
$163$	−17.8171			−1.39554			−0.697772	+	0.716320i	$0.745825\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.23385	−	7.33325i	0.327625	−	0.567464i	−0.654415	−	0.756136i	$-0.727085\pi$
$167$	4.23385	−	7.33325i	0.327625	−	0.567464i	0.982040	+	0.188672i	$0.0604183\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.67830	+	15.0313i	0.659799	+	1.14281i	0.980667	+	0.195682i	$0.0626920\pi$
$173$	8.67830	+	15.0313i	0.659799	+	1.14281i	−0.320868	+	0.947124i	$0.603975\pi$
$174$		0			0
$175$	−0.863327	+	1.49533i	−0.0652614	+	0.113036i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.3494			−0.848295			−0.424147	−	0.905593i	$-0.639426\pi$
$179$	−11.3494			−0.848295			−0.424147	+	0.905593i	$0.639426\pi$
$180$		0			0
$181$	21.8889			1.62699			0.813495	−	0.581572i	$-0.197562\pi$
$181$	21.8889			1.62699			0.813495	+	0.581572i	$0.197562\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.30924	+	3.99973i	−0.169779	+	0.294066i
$186$		0			0
$187$	−2.13521	−	3.69829i	−0.156142	−	0.270446i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.350874	+	0.607731i	0.0253883	+	0.0439739i	0.878440	−	0.477852i	$-0.158584\pi$
$191$	0.350874	+	0.607731i	0.0253883	+	0.0439739i	−0.853052	+	0.521826i	$0.825251\pi$
$192$		0			0
$193$	−6.07227	+	10.5175i	−0.437092	+	0.757065i	−0.997464	−	0.0711760i	$-0.977325\pi$
$193$	−6.07227	+	10.5175i	−0.437092	+	0.757065i	0.560372	+	0.828241i	$0.310658\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.4107			1.16921			0.584607	−	0.811317i	$-0.301249\pi$
$197$	16.4107			1.16921			0.584607	+	0.811317i	$0.301249\pi$
$198$		0			0
$199$	−22.7060			−1.60959			−0.804794	−	0.593555i	$-0.797724\pi$
$199$	−22.7060			−1.60959			−0.804794	+	0.593555i	$0.797724\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.23025	−	2.13086i	0.0863468	−	0.149557i
$204$		0			0
$205$	−8.30778	−	14.3895i	−0.580241	−	1.00501i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.15126	−	15.8505i	−0.633006	−	1.09640i
$210$		0			0
$211$	2.28074	−	3.95035i	0.157012	−	0.271954i	−0.776778	−	0.629775i	$-0.783147\pi$
$211$	2.28074	−	3.95035i	0.157012	−	0.271954i	0.933790	+	0.357822i	$0.116480\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	27.0656			1.84586
$216$		0			0
$217$	−2.32743			−0.157996
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.472958	+	0.819187i	−0.0318146	+	0.0551045i
$222$		0			0
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	0.998131	−	0.0611159i	$-0.0194659\pi$
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	−0.551993	+	0.833849i	$0.686133\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.690757	−	1.19643i	−0.0458472	−	0.0794096i	0.842191	−	0.539179i	$-0.181265\pi$
$227$	−0.690757	−	1.19643i	−0.0458472	−	0.0794096i	−0.888038	+	0.459769i	$0.847932\pi$
$228$		0			0
$229$	8.98968	−	15.5706i	0.594055	−	1.02893i	−0.399625	−	0.916679i	$-0.630859\pi$
$229$	8.98968	−	15.5706i	0.594055	−	1.02893i	0.993679	−	0.112254i	$-0.0358072\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.9823			1.24357			0.621786	−	0.783187i	$-0.286408\pi$
$233$	18.9823			1.24357			0.621786	+	0.783187i	$0.286408\pi$
$234$		0			0
$235$	−31.5438			−2.05769
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.44592	+	4.23645i	−0.158213	+	0.274033i	−0.934224	−	0.356686i	$-0.883907\pi$
$239$	−2.44592	+	4.23645i	−0.158213	+	0.274033i	0.776011	+	0.630719i	$0.217240\pi$
$240$		0			0
$241$	13.0797	+	22.6546i	0.842535	+	1.45931i	0.887745	+	0.460336i	$0.152271\pi$
$241$	13.0797	+	22.6546i	0.842535	+	1.45931i	−0.0452094	+	0.998978i	$0.514396\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.29679	−	2.24611i	−0.0828489	−	0.143498i
$246$		0			0
$247$	−2.02704	+	3.51094i	−0.128978	+	0.223396i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.4576			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$251$	18.4576			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$252$		0			0
$253$	−1.23405			−0.0775838
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.86693	+	10.1618i	−0.365969	+	0.633876i	−0.988931	−	0.148375i	$-0.952596\pi$
$257$	−5.86693	+	10.1618i	−0.365969	+	0.633876i	0.622962	+	0.782252i	$0.285929\pi$
$258$		0			0
$259$	−0.890369	−	1.54216i	−0.0553248	−	0.0958254i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.76089	+	6.51406i	0.231907	+	0.401674i	0.958369	−	0.285532i	$-0.0921703\pi$
$263$	3.76089	+	6.51406i	0.231907	+	0.401674i	−0.726463	+	0.687206i	$0.758837\pi$
$264$		0			0
$265$	−8.13521	+	14.0906i	−0.499742	+	0.865579i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.8348			1.14838			0.574190	−	0.818722i	$-0.305317\pi$
$269$	18.8348			1.14838			0.574190	+	0.818722i	$0.305317\pi$
$270$		0			0
$271$	23.9823			1.45682			0.728410	−	0.685141i	$-0.240260\pi$
$271$	23.9823			1.45682			0.728410	+	0.685141i	$0.240260\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.89757	+	6.75078i	−0.235032	+	0.407088i
$276$		0			0
$277$	−3.58113	−	6.20269i	−0.215169	−	0.372684i	0.738156	−	0.674630i	$-0.235697\pi$
$277$	−3.58113	−	6.20269i	−0.215169	−	0.372684i	−0.953325	+	0.301947i	$0.902364\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.44085	+	12.8879i	0.443884	+	0.768830i	0.997974	−	0.0636271i	$-0.0202668\pi$
$281$	7.44085	+	12.8879i	0.443884	+	0.768830i	−0.554090	+	0.832457i	$0.686933\pi$
$282$		0			0
$283$	9.99854	−	17.3180i	0.594351	−	1.02945i	−0.399287	−	0.916826i	$-0.630742\pi$
$283$	9.99854	−	17.3180i	0.594351	−	1.02945i	0.993638	−	0.112621i	$-0.0359245\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.40642			0.378159
$288$		0			0
$289$	−16.1052			−0.947367
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	−0.557625	−	0.830093i	$-0.688287\pi$
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	0.997694	+	0.0678705i	$0.0216205\pi$
$294$		0			0
$295$	3.53590	+	6.12435i	0.205868	+	0.356574i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.136673	+	0.236725i	0.00790401	+	0.0136901i
$300$		0			0
$301$	−5.21780	+	9.03749i	−0.300749	+	0.520912i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.89610			−0.337610
$306$		0			0
$307$	27.2704			1.55641			0.778203	−	0.628013i	$-0.216132\pi$
$307$	27.2704			1.55641			0.778203	+	0.628013i	$0.216132\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.99115	−	13.8411i	0.453136	−	0.784855i	−0.545443	−	0.838148i	$-0.683638\pi$
$311$	7.99115	−	13.8411i	0.453136	−	0.784855i	0.998579	+	0.0532931i	$0.0169718\pi$
$312$		0			0
$313$	−5.79893	−	10.0440i	−0.327775	−	0.567722i	0.654295	−	0.756239i	$-0.272965\pi$
$313$	−5.79893	−	10.0440i	−0.327775	−	0.567722i	−0.982070	+	0.188517i	$0.939632\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.00885	−	1.74739i	−0.0566629	−	0.0981430i	0.836303	−	0.548268i	$-0.184713\pi$
$317$	−1.00885	−	1.74739i	−0.0566629	−	0.0981430i	−0.892965	+	0.450125i	$0.851379\pi$
$318$		0			0
$319$	5.55408	−	9.61996i	0.310969	−	0.538614i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.83482			0.213375
$324$		0			0
$325$	1.72665			0.0957775
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.08113	−	10.5328i	0.335263	−	0.580693i
$330$		0			0
$331$	−9.85447	−	17.0684i	−0.541651	−	0.938167i	−0.998809	−	0.0487815i	$-0.984466\pi$
$331$	−9.85447	−	17.0684i	−0.541651	−	0.938167i	0.457159	−	0.889385i	$-0.348867\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−20.5115	−	35.5269i	−1.12066	−	1.94104i
$336$		0			0
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	−0.133929	−	0.990991i	$-0.542759\pi$
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	0.925188	−	0.379509i	$-0.123907\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−10.5074			−0.569007
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.5416	+	25.1868i	−0.780636	+	1.35210i	0.150936	+	0.988544i	$0.451771\pi$
$347$	−14.5416	+	25.1868i	−0.780636	+	1.35210i	−0.931572	+	0.363557i	$0.881562\pi$
$348$		0			0
$349$	−12.3815	−	21.4454i	−0.662767	−	1.14795i	−0.979885	−	0.199561i	$-0.936049\pi$
$349$	−12.3815	−	21.4454i	−0.662767	−	1.14795i	0.317118	−	0.948386i	$-0.397285\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.6513	−	28.8408i	−0.886257	−	1.53504i	−0.844266	−	0.535925i	$-0.819963\pi$
$353$	−16.6513	−	28.8408i	−0.886257	−	1.53504i	−0.0419914	−	0.999118i	$-0.513370\pi$
$354$		0			0
$355$	−4.24484	+	7.35228i	−0.225293	+	0.390219i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	25.5366			1.34777			0.673884	−	0.738837i	$-0.264625\pi$
$359$	25.5366			1.34777			0.673884	+	0.738837i	$0.264625\pi$
$360$		0			0
$361$	−2.56440			−0.134968
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.95477	−	3.38576i	0.102317	−	0.177219i
$366$		0			0
$367$	13.7252	+	23.7727i	0.716449	+	1.24093i	0.962398	+	0.271644i	$0.0875672\pi$
$367$	13.7252	+	23.7727i	0.716449	+	1.24093i	−0.245949	+	0.969283i	$0.579100\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.13667	−	5.43288i	−0.162848	−	0.282061i
$372$		0			0
$373$	−8.16372	+	14.1400i	−0.422701	+	0.732140i	−0.996203	−	0.0870646i	$-0.972251\pi$
$373$	−8.16372	+	14.1400i	−0.422701	+	0.732140i	0.573502	+	0.819204i	$0.305585\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.46050			−0.126722
$378$		0			0
$379$	−12.0364			−0.618267			−0.309134	−	0.951019i	$-0.600039\pi$
$379$	−12.0364			−0.618267			−0.309134	+	0.951019i	$0.600039\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.21780	−	10.7695i	0.317715	−	0.550298i	−0.662296	−	0.749242i	$-0.730418\pi$
$383$	6.21780	−	10.7695i	0.317715	−	0.550298i	0.980011	+	0.198944i	$0.0637512\pi$
$384$		0			0
$385$	−5.85447	−	10.1402i	−0.298372	−	0.516795i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.3004	+	17.8408i	0.522250	+	0.904564i	0.999665	+	0.0258860i	$0.00824070\pi$
$389$	10.3004	+	17.8408i	0.522250	+	0.904564i	−0.477414	+	0.878678i	$0.658426\pi$
$390$		0			0
$391$	0.129281	−	0.223922i	0.00653803	−	0.0113242i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−38.1488			−1.91948
$396$		0			0
$397$	−23.6372			−1.18631			−0.593157	−	0.805087i	$-0.702119\pi$
$397$	−23.6372			−1.18631			−0.593157	+	0.805087i	$0.702119\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.28220	+	2.22084i	−0.0640300	+	0.110903i	−0.896263	−	0.443522i	$-0.853729\pi$
$401$	−1.28220	+	2.22084i	−0.0640300	+	0.110903i	0.832233	+	0.554426i	$0.187062\pi$
$402$		0			0
$403$	1.16372	+	2.01561i	0.0579688	+	0.100405i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.01965	−	6.96224i	−0.199247	−	0.345105i
$408$		0			0
$409$	17.1623	−	29.7259i	0.848619	−	1.46985i	−0.0338223	−	0.999428i	$-0.510768\pi$
$409$	17.1623	−	29.7259i	0.848619	−	1.46985i	0.882441	−	0.470423i	$-0.155899\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.72665			−0.134170
$414$		0			0
$415$	−2.45331			−0.120428
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.02850	+	3.51347i	−0.0990989	+	0.171644i	−0.911312	−	0.411717i	$-0.864929\pi$
$419$	−2.02850	+	3.51347i	−0.0990989	+	0.171644i	0.812213	+	0.583361i	$0.198263\pi$
$420$		0			0
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	0.999879	+	0.0155624i	$0.00495387\pi$
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	−0.486462	+	0.873702i	$0.661713\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.816635	−	1.41445i	−0.0396126	−	0.0686110i
$426$		0			0
$427$	1.13667	−	1.96878i	0.0550075	−	0.0952757i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	22.6185			1.08949			0.544747	−	0.838600i	$-0.316626\pi$
$431$	22.6185			1.08949			0.544747	+	0.838600i	$0.316626\pi$
$432$		0			0
$433$	2.41789			0.116196			0.0580982	−	0.998311i	$-0.481496\pi$
$433$	2.41789			0.116196			0.0580982	+	0.998311i	$0.481496\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.554084	−	0.959702i	0.0265054	−	0.0459088i
$438$		0			0
$439$	−11.7448	−	20.3427i	−0.560551	−	0.970902i	−0.997448	−	0.0713911i	$-0.977256\pi$
$439$	−11.7448	−	20.3427i	−0.560551	−	0.970902i	0.436898	−	0.899511i	$-0.356077\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.70895	+	11.6202i	0.318752	+	0.552094i	0.980228	−	0.197872i	$-0.0634031\pi$
$443$	6.70895	+	11.6202i	0.318752	+	0.552094i	−0.661476	+	0.749966i	$0.730070\pi$
$444$		0			0
$445$	−18.6175	+	32.2465i	−0.882554	+	1.52863i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.16225			0.432393			0.216197	−	0.976350i	$-0.430635\pi$
$449$	9.16225			0.432393			0.216197	+	0.976350i	$0.430635\pi$
$450$		0			0
$451$	28.9224			1.36190
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.29679	+	2.24611i	−0.0607944	+	0.105299i
$456$		0			0
$457$	−4.40856	−	7.63584i	−0.206224	−	0.357190i	0.744298	−	0.667847i	$-0.232784\pi$
$457$	−4.40856	−	7.63584i	−0.206224	−	0.357190i	−0.950522	+	0.310658i	$0.899451\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	0.792579	−	0.609769i	$-0.208738\pi$
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	−0.924365	+	0.381509i	$0.875405\pi$
$462$		0			0
$463$	7.86333	−	13.6197i	0.365440	−	0.632960i	−0.623407	−	0.781898i	$-0.714252\pi$
$463$	7.86333	−	13.6197i	0.365440	−	0.632960i	0.988847	+	0.148937i	$0.0475853\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−21.9971			−1.01790			−0.508952	−	0.860795i	$-0.669967\pi$
$467$	−21.9971			−1.01790			−0.508952	+	0.860795i	$0.669967\pi$
$468$		0			0
$469$	15.8171			0.730366
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−23.5562	+	40.8006i	−1.08312	+	1.87601i
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.4875	−	21.6291i	−0.570571	−	0.988257i	−0.996507	−	0.0835043i	$-0.973389\pi$
$479$	−12.4875	−	21.6291i	−0.570571	−	0.988257i	0.425937	−	0.904753i	$-0.359945\pi$
$480$		0			0
$481$	−0.890369	+	1.54216i	−0.0405973	+	0.0703166i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−29.7994			−1.35312
$486$		0			0
$487$	17.5979			0.797435			0.398717	−	0.917074i	$-0.369455\pi$
$487$	17.5979			0.797435			0.398717	+	0.917074i	$0.369455\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.89757	+	11.9469i	−0.311283	+	0.539158i	−0.978640	−	0.205580i	$-0.934092\pi$
$491$	−6.89757	+	11.9469i	−0.311283	+	0.539158i	0.667358	+	0.744737i	$0.267425\pi$
$492$		0			0
$493$	1.16372	+	2.01561i	0.0524111	+	0.0907787i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.63667	−	2.83480i	−0.0734148	−	0.127158i
$498$		0			0
$499$	6.54377	−	11.3341i	0.292939	−	0.507386i	−0.681564	−	0.731758i	$-0.738700\pi$
$499$	6.54377	−	11.3341i	0.292939	−	0.507386i	0.974503	+	0.224373i	$0.0720333\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.3068			−0.994611			−0.497305	−	0.867576i	$-0.665677\pi$
$503$	−22.3068			−0.994611			−0.497305	+	0.867576i	$0.665677\pi$
$504$		0			0
$505$	9.54377			0.424692
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.94659	+	13.7639i	−0.352226	+	0.610074i	−0.986639	−	0.162920i	$-0.947909\pi$
$509$	−7.94659	+	13.7639i	−0.352226	+	0.610074i	0.634413	+	0.772994i	$0.281242\pi$
$510$		0			0
$511$	0.753696	+	1.30544i	0.0333415	+	0.0577492i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.6134	−	21.8471i	−0.555814	−	0.962698i
$516$		0			0
$517$	27.4538	−	47.5514i	1.20742	−	2.09131i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.41789			−0.193551			−0.0967756	−	0.995306i	$-0.530853\pi$
$521$	−4.41789			−0.193551			−0.0967756	+	0.995306i	$0.530853\pi$
$522$		0			0
$523$	−25.2733			−1.10513			−0.552563	−	0.833471i	$-0.686350\pi$
$523$	−25.2733			−1.10513			−0.552563	+	0.833471i	$0.686350\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.10078	−	1.90660i	0.0479506	−	0.0830528i
$528$		0			0
$529$	11.4626	+	19.8539i	0.498376	+	0.863212i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.20321	−	5.54812i	−0.138746	−	0.240316i
$534$		0			0
$535$	1.78220	−	3.08686i	0.0770513	−	0.133457i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.51459			0.194457
$540$		0			0
$541$	−3.43852			−0.147834			−0.0739168	−	0.997264i	$-0.523550\pi$
$541$	−3.43852			−0.147834			−0.0739168	+	0.997264i	$0.523550\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.40808	−	7.63501i	0.188821	−	0.327048i
$546$		0			0
$547$	−3.46410	−	6.00000i	−0.148114	−	0.256542i	0.782416	−	0.622756i	$-0.213987\pi$
$547$	−3.46410	−	6.00000i	−0.148114	−	0.256542i	−0.930531	+	0.366214i	$0.880654\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.98755	+	8.63868i	0.212477	+	0.368020i
$552$		0			0
$553$	7.35447	−	12.7383i	0.312744	−	0.541688i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−33.5835			−1.42298			−0.711488	−	0.702698i	$-0.751979\pi$
$557$	−33.5835			−1.42298			−0.711488	+	0.702698i	$0.751979\pi$
$558$		0			0
$559$	10.4356			0.441379
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−21.2396	+	36.7880i	−0.895142	+	1.55043i	−0.0615128	+	0.998106i	$0.519593\pi$
$563$	−21.2396	+	36.7880i	−0.895142	+	1.55043i	−0.833629	+	0.552325i	$0.813741\pi$
$564$		0			0
$565$	13.4720	+	23.3341i	0.566770	+	0.981675i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.20175	+	9.00969i	0.218069	+	0.377706i	0.954217	−	0.299114i	$-0.0966910\pi$
$569$	5.20175	+	9.00969i	0.218069	+	0.377706i	−0.736149	+	0.676820i	$0.763358\pi$
$570$		0			0
$571$	8.92480	−	15.4582i	0.373491	−	0.646906i	−0.616609	−	0.787270i	$-0.711494\pi$
$571$	8.92480	−	15.4582i	0.373491	−	0.646906i	0.990100	+	0.140364i	$0.0448272\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.471974			−0.0196827
$576$		0			0
$577$	11.9430			0.497193			0.248597	−	0.968607i	$-0.420031\pi$
$577$	11.9430			0.497193			0.248597	+	0.968607i	$0.420031\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.472958	−	0.819187i	0.0196216	−	0.0339856i
$582$		0			0
$583$	−14.1608	−	24.5272i	−0.586480	−	1.01581i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.9299	−	20.6631i	−0.492398	−	0.852859i	0.507563	−	0.861614i	$-0.330546\pi$
$587$	−11.9299	−	20.6631i	−0.492398	−	0.852859i	−0.999962	+	0.00875568i	$0.997213\pi$
$588$		0			0
$589$	4.71780	−	8.17147i	0.194394	−	0.336699i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.5801			−0.804060			−0.402030	−	0.915626i	$-0.631695\pi$
$593$	−19.5801			−0.804060			−0.402030	+	0.915626i	$0.631695\pi$
$594$		0			0
$595$	2.45331			0.100576
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.27335	+	16.0619i	−0.378899	+	0.656272i	−0.990902	−	0.134583i	$-0.957030\pi$
$599$	−9.27335	+	16.0619i	−0.378899	+	0.656272i	0.612004	+	0.790855i	$0.290364\pi$
$600$		0			0
$601$	9.09931	+	15.7605i	0.371169	+	0.642883i	0.989746	−	0.142841i	$-0.0456238\pi$
$601$	9.09931	+	15.7605i	0.371169	+	0.642883i	−0.618577	+	0.785724i	$0.712290\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−12.1659	−	21.0719i	−0.494612	−	0.856693i
$606$		0			0
$607$	−11.1549	+	19.3208i	−0.452762	+	0.784206i	−0.998556	−	0.0537125i	$-0.982895\pi$
$607$	−11.1549	+	19.3208i	−0.452762	+	0.784206i	0.545795	+	0.837919i	$0.316228\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.1623			−0.492032
$612$		0			0
$613$	10.2370			0.413467			0.206734	−	0.978397i	$-0.433717\pi$
$613$	10.2370			0.413467			0.206734	+	0.978397i	$0.433717\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.66372	+	9.80984i	−0.228013	+	0.394929i	−0.957219	−	0.289364i	$-0.906556\pi$
$617$	−5.66372	+	9.80984i	−0.228013	+	0.394929i	0.729206	+	0.684294i	$0.239889\pi$
$618$		0			0
$619$	4.31663	+	7.47663i	0.173500	+	0.300511i	0.939641	−	0.342161i	$-0.111159\pi$
$619$	4.31663	+	7.47663i	0.173500	+	0.300511i	−0.766141	+	0.642672i	$0.777826\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.17830	−	12.4332i	−0.287593	−	0.498125i
$624$		0			0
$625$	15.3260	−	26.5454i	0.613039	−	1.06181i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.68443			0.0671626
$630$		0			0
$631$	14.8535			0.591308			0.295654	−	0.955295i	$-0.404462\pi$
$631$	14.8535			0.591308			0.295654	+	0.955295i	$0.404462\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.872181	−	1.51066i	0.0346115	−	0.0599488i
$636$		0			0
$637$	−0.500000	−	0.866025i	−0.0198107	−	0.0343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.0797	−	29.5828i	−0.674606	−	1.16845i	−0.976584	−	0.215137i	$-0.930980\pi$
$641$	−17.0797	−	29.5828i	−0.674606	−	1.16845i	0.301978	−	0.953315i	$-0.402353\pi$
$642$		0			0
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	−0.952852	−	0.303437i	$-0.901866\pi$
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	0.739210	+	0.673475i	$0.235199\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	32.9692			1.29615			0.648077	−	0.761575i	$-0.275573\pi$
$647$	32.9692			1.29615			0.648077	+	0.761575i	$0.275573\pi$
$648$		0			0
$649$	−12.3097			−0.483199
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.96557	+	3.40446i	−0.0769185	+	0.133227i	−0.901919	−	0.431905i	$-0.857841\pi$
$653$	−1.96557	+	3.40446i	−0.0769185	+	0.133227i	0.825000	+	0.565132i	$0.191175\pi$
$654$		0			0
$655$	−10.2626	−	17.7753i	−0.400991	−	0.694537i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.40856	−	14.5640i	−0.327551	−	0.567335i	0.654474	−	0.756084i	$-0.272890\pi$
$659$	−8.40856	−	14.5640i	−0.327551	−	0.567335i	−0.982025	+	0.188749i	$0.939557\pi$
$660$		0			0
$661$	8.51080	−	14.7411i	0.331032	−	0.573364i	−0.651683	−	0.758492i	$-0.725937\pi$
$661$	8.51080	−	14.7411i	0.331032	−	0.573364i	0.982714	+	0.185128i	$0.0592700\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.5146			0.407738
$666$		0			0
$667$	0.672570			0.0260420
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.13161	−	8.88821i	0.198104	−	0.343126i
$672$		0			0
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	−0.997979	−	0.0635501i	$-0.979758\pi$
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	0.443953	−	0.896050i	$-0.353576\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.01819	−	5.22765i	−0.115998	−	0.200915i	0.802180	−	0.597082i	$-0.203673\pi$
$677$	−3.01819	−	5.22765i	−0.115998	−	0.200915i	−0.918178	+	0.396167i	$0.870340\pi$
$678$		0			0
$679$	5.74484	−	9.95036i	0.220467	−	0.381860i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	20.5113			0.784842			0.392421	−	0.919786i	$-0.371638\pi$
$683$	20.5113			0.784842			0.392421	+	0.919786i	$0.371638\pi$
$684$		0			0
$685$	9.52510			0.363935
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.13667	+	5.43288i	−0.119498	+	0.206976i
$690$		0			0
$691$	−7.50146	−	12.9929i	−0.285369	−	0.494274i	0.687330	−	0.726346i	$-0.258783\pi$
$691$	−7.50146	−	12.9929i	−0.285369	−	0.494274i	−0.972699	+	0.232072i	$0.925450\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.66372	−	4.61369i	−0.101040	−	0.175007i
$696$		0			0
$697$	−3.02997	+	5.24806i	−0.114768	+	0.198784i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−38.5113			−1.45455			−0.727275	−	0.686346i	$-0.759214\pi$
$701$	−38.5113			−1.45455			−0.727275	+	0.686346i	$0.759214\pi$
$702$		0			0
$703$	7.21926			0.272280
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.83988	+	3.18677i	−0.0691959	+	0.119851i
$708$		0			0
$709$	−3.82004	−	6.61650i	−0.143465	−	0.248488i	0.785334	−	0.619072i	$-0.212491\pi$
$709$	−3.82004	−	6.61650i	−0.143465	−	0.248488i	−0.928799	+	0.370584i	$0.879158\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.318097	−	0.550960i	−0.0119128	−	0.0206336i
$714$		0			0
$715$	−5.85447	+	10.1402i	−0.218945	+	0.379224i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−30.0364			−1.12017			−0.560084	−	0.828436i	$-0.689231\pi$
$719$	−30.0364			−1.12017			−0.560084	+	0.828436i	$0.689231\pi$
$720$		0			0
$721$	9.72665			0.362240
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.12422	−	3.67926i	0.0788916	−	0.136644i
$726$		0			0
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	0.896291	−	0.443466i	$-0.146251\pi$
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	−0.832199	+	0.554478i	$0.812918\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.93560	−	8.54871i	−0.182550	−	0.316185i
$732$		0			0
$733$	−19.2630	+	33.3645i	−0.711496	+	1.23235i	0.252799	+	0.967519i	$0.418649\pi$
$733$	−19.2630	+	33.3645i	−0.711496	+	1.23235i	−0.964295	+	0.264829i	$0.914685\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	71.4078			2.63034
$738$		0			0
$739$	−45.1239			−1.65991			−0.829955	−	0.557830i	$-0.811634\pi$
$739$	−45.1239			−1.65991			−0.829955	+	0.557830i	$0.811634\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.74338	+	8.21577i	−0.174018	+	0.301407i	−0.939821	−	0.341668i	$-0.889008\pi$
$743$	−4.74338	+	8.21577i	−0.174018	+	0.301407i	0.765803	+	0.643075i	$0.222342\pi$
$744$		0			0
$745$	−17.5634	−	30.4207i	−0.643474	−	1.11453i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.687159	+	1.19019i	0.0251082	+	0.0434887i
$750$		0			0
$751$	−4.91595	+	8.51467i	−0.179386	+	0.310705i	−0.941670	−	0.336537i	$-0.890744\pi$
$751$	−4.91595	+	8.51467i	−0.179386	+	0.310705i	0.762285	+	0.647242i	$0.224078\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−25.7496			−0.937124
$756$		0			0
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.4897	−	19.9007i	0.416501	−	0.721400i	−0.579084	−	0.815268i	$-0.696590\pi$
$761$	11.4897	−	19.9007i	0.416501	−	0.721400i	0.995585	+	0.0938675i	$0.0299230\pi$
$762$		0			0
$763$	1.69961	+	2.94381i	0.0615301	+	0.106573i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.36333	+	2.36135i	0.0492269	+	0.0852635i
$768$		0			0
$769$	−3.04329	+	5.27113i	−0.109744	+	0.190082i	−0.915666	−	0.401939i	$-0.868336\pi$
$769$	−3.04329	+	5.27113i	−0.109744	+	0.190082i	0.805923	+	0.592021i	$0.201670\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	41.8214			1.50421			0.752105	−	0.659043i	$-0.229038\pi$
$773$	41.8214			1.50421			0.752105	+	0.659043i	$0.229038\pi$
$774$		0			0
$775$	−4.01867			−0.144355
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.9861	+	22.4926i	−0.465275	+	0.805880i
$780$		0			0
$781$	−7.38891	−	12.7980i	−0.264396	−	0.457947i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.85087	−	13.5981i	−0.280210	−	0.485337i
$786$		0			0
$787$	16.1460	−	27.9657i	0.575543	−	0.996870i	−0.420439	−	0.907321i	$-0.638124\pi$
$787$	16.1460	−	27.9657i	0.575543	−	0.996870i	0.995982	−	0.0895491i	$-0.0285426\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.3887			−0.369380
$792$		0			0
$793$	−2.27335			−0.0807289
$794$		0			0
$795$		0			0
$796$		0			0
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	−0.0774101	−	0.996999i	$-0.524665\pi$
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	0.902132	−	0.431461i	$-0.142002\pi$
$798$		0			0
$799$	5.75223	+	9.96316i	0.203499	+	0.352471i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.40263	+	5.89352i	0.120076	+	0.207978i
$804$		0			0
$805$	0.354473	−	0.613964i	0.0124935	−	0.0216394i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.8023			0.379790			0.189895	−	0.981804i	$-0.439185\pi$
$809$	10.8023			0.379790			0.189895	+	0.981804i	$0.439185\pi$
$810$		0			0
$811$	−5.58307			−0.196048			−0.0980240	−	0.995184i	$-0.531252\pi$
$811$	−5.58307			−0.196048			−0.0980240	+	0.995184i	$0.531252\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.1050	−	40.0191i	0.809335	−	1.40181i
$816$		0			0
$817$	−21.1534	−	36.6388i	−0.740064	−	1.28183i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.8940	−	27.5292i	−0.554703	−	0.960774i	−0.997927	−	0.0643630i	$-0.979498\pi$
$821$	−15.8940	−	27.5292i	−0.554703	−	0.960774i	0.443223	−	0.896411i	$-0.353835\pi$
$822$		0			0
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	0.360623	+	0.932712i	$0.382564\pi$
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	−0.988063	+	0.154047i	$0.950769\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.9224			0.553675			0.276837	−	0.960917i	$-0.410714\pi$
$827$	15.9224			0.553675			0.276837	+	0.960917i	$0.410714\pi$
$828$		0			0
$829$	35.4720			1.23199			0.615996	−	0.787749i	$-0.288754\pi$
$829$	35.4720			1.23199			0.615996	+	0.787749i	$0.288754\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.472958	+	0.819187i	−0.0163870	+	0.0283832i
$834$		0			0
$835$	10.9808	+	19.0194i	0.380007	+	0.658192i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	27.3391	+	47.3527i	0.943850	+	1.63480i	0.758037	+	0.652212i	$0.226159\pi$
$839$	27.3391	+	47.3527i	0.943850	+	1.63480i	0.185814	+	0.982585i	$0.440508\pi$
$840$		0			0
$841$	11.4730	−	19.8717i	0.395619	−	0.685233i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−31.1230			−1.07066
$846$		0			0
$847$	9.38151			0.322353
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.243379	−	0.421545i	0.00834292	−	0.0144504i
$852$		0			0
$853$	1.09884	+	1.90324i	0.0376234	+	0.0651656i	0.884224	−	0.467063i	$-0.154688\pi$
$853$	1.09884	+	1.90324i	0.0376234	+	0.0651656i	−0.846601	+	0.532229i	$0.821355\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.88823	−	13.6628i	−0.269457	−	0.466713i	0.699265	−	0.714863i	$-0.253511\pi$
$857$	−7.88823	−	13.6628i	−0.269457	−	0.466713i	−0.968722	+	0.248150i	$0.920178\pi$
$858$		0			0
$859$	2.78813	−	4.82918i	0.0951298	−	0.164770i	−0.814533	−	0.580117i	$-0.803007\pi$
$859$	2.78813	−	4.82918i	0.0951298	−	0.164770i	0.909663	+	0.415348i	$0.136340\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	23.1268			0.787247			0.393623	−	0.919272i	$-0.371221\pi$
$863$	23.1268			0.787247			0.393623	+	0.919272i	$0.371221\pi$
$864$		0			0
$865$	−45.0157			−1.53058
$866$		0			0
$867$		0			0
$868$		0			0
$869$	33.2024	−	57.5083i	1.12631	−	1.95083i
$870$		0			0
$871$	−7.90856	−	13.6980i	−0.267971	−	0.464140i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.24484	+	7.35228i	0.143502	+	0.248552i
$876$		0			0
$877$	−1.96264	+	3.39939i	−0.0662737	+	0.114789i	−0.897258	−	0.441506i	$-0.854444\pi$
$877$	−1.96264	+	3.39939i	−0.0662737	+	0.114789i	0.830985	+	0.556295i	$0.187778\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.1986			−0.916345			−0.458173	−	0.888863i	$-0.651496\pi$
$881$	−27.1986			−0.916345			−0.458173	+	0.888863i	$0.651496\pi$
$882$		0			0
$883$	−8.21341			−0.276403			−0.138202	−	0.990404i	$-0.544132\pi$
$883$	−8.21341			−0.276403			−0.138202	+	0.990404i	$0.544132\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.24057	−	5.61283i	0.108808	−	0.188460i	−0.806480	−	0.591262i	$-0.798630\pi$
$887$	3.24057	−	5.61283i	0.108808	−	0.188460i	0.915287	+	0.402801i	$0.131963\pi$
$888$		0			0
$889$	0.336285	+	0.582462i	0.0112786	+	0.0195352i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	24.6534	+	42.7009i	0.824995	+	1.42893i
$894$		0			0
$895$	14.7178	−	25.4920i	0.491962	−	0.852103i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.72665			0.190995
$900$		0			0
$901$	5.93406			0.197692
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−28.3853	+	49.1648i	−0.943560	+	1.63429i
$906$		0			0
$907$	5.06440	+	8.77180i	0.168161	+	0.291263i	0.937773	−	0.347248i	$-0.112884\pi$
$907$	5.06440	+	8.77180i	0.168161	+	0.291263i	−0.769613	+	0.638511i	$0.779551\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22.9612	−	39.7699i	−0.760738	−	1.31764i	−0.942471	−	0.334289i	$-0.891504\pi$
$911$	−22.9612	−	39.7699i	−0.760738	−	1.31764i	0.181733	−	0.983348i	$-0.441829\pi$
$912$		0			0
$913$	2.13521	−	3.69829i	0.0706652	−	0.122396i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.91381			0.261337
$918$		0			0
$919$	4.92432			0.162438			0.0812192	−	0.996696i	$-0.474119\pi$
$919$	4.92432			0.162438			0.0812192	+	0.996696i	$0.474119\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.63667	+	2.83480i	−0.0538718	+	0.0933086i
$924$		0			0
$925$	−1.53736	−	2.66278i	−0.0505481	−	0.0875518i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.00379324	+	0.00657009i	0.000124452	+	0.000215558i	0.866088	−	0.499892i	$-0.166627\pi$
$929$	0.00379324	+	0.00657009i	0.000124452	+	0.000215558i	−0.865963	+	0.500108i	$0.833294\pi$
$930$		0			0
$931$	−2.02704	+	3.51094i	−0.0664336	+	0.115066i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11.0757			0.362213
$936$		0			0
$937$	21.1623			0.691341			0.345670	−	0.938356i	$-0.387652\pi$
$937$	21.1623			0.691341			0.345670	+	0.938356i	$0.387652\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.27908	−	3.94748i	0.0742959	−	0.128684i	−0.826484	−	0.562960i	$-0.809662\pi$
$941$	2.27908	−	3.94748i	0.0742959	−	0.128684i	0.900780	+	0.434276i	$0.142996\pi$
$942$		0			0
$943$	0.875585	+	1.51656i	0.0285130	+	0.0493859i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.86760	−	11.8950i	−0.223167	−	0.386537i	0.732601	−	0.680658i	$-0.238306\pi$
$947$	−6.86760	−	11.8950i	−0.223167	−	0.386537i	−0.955768	+	0.294122i	$0.904973\pi$
$948$		0			0
$949$	0.753696	−	1.30544i	0.0244660	−	0.0423764i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.80699			−0.285286			−0.142643	−	0.989774i	$-0.545560\pi$
$953$	−8.80699			−0.285286			−0.142643	+	0.989774i	$0.545560\pi$
$954$		0			0
$955$	−1.82004			−0.0588951
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.83628	+	3.18054i	−0.0592967	+	0.102705i
$960$		0			0
$961$	12.7915	+	22.1556i	0.412630	+	0.714696i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−15.7489	−	27.2779i	−0.506976	−	0.878108i
$966$		0			0
$967$	19.1642	−	33.1934i	0.616279	−	1.06743i	−0.373880	−	0.927477i	$-0.621973\pi$
$967$	19.1642	−	33.1934i	0.616279	−	1.06743i	0.990159	−	0.139949i	$-0.0446939\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−31.0187			−0.995436			−0.497718	−	0.867339i	$-0.665829\pi$
$971$	−31.0187			−0.995436			−0.497718	+	0.867339i	$0.665829\pi$
$972$		0			0
$973$	2.05408			0.0658509
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.3712	+	45.6763i	−0.843689	+	1.46131i	0.0430652	+	0.999072i	$0.486288\pi$
$977$	−26.3712	+	45.6763i	−0.843689	+	1.46131i	−0.886755	+	0.462241i	$0.847046\pi$
$978$		0			0
$979$	−32.4071	−	56.1307i	−1.03574	−	1.79395i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.15146	+	15.8508i	0.291886	+	0.505562i	0.974256	−	0.225446i	$-0.0723838\pi$
$983$	9.15146	+	15.8508i	0.291886	+	0.505562i	−0.682370	+	0.731007i	$0.739050\pi$
$984$		0			0
$985$	−21.2812	+	36.8601i	−0.678076	+	1.17446i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.85253			−0.0907052
$990$		0			0
$991$	12.6008			0.400277			0.200138	−	0.979768i	$-0.435861\pi$
$991$	12.6008			0.400277			0.200138	+	0.979768i	$0.435861\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	29.4449	−	51.0001i	0.933467	−	1.61681i
$996$		0			0
$997$	−5.87120	−	10.1692i	−0.185943	−	0.322062i	0.757951	−	0.652311i	$-0.226201\pi$
$997$	−5.87120	−	10.1692i	−0.185943	−	0.322062i	−0.943894	+	0.330249i	$0.892867\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.g.1009.2		6
3.2	odd	2		1008.2.r.k.337.3		6
4.3	odd	2		189.2.f.a.64.1		6
9.2	odd	6		1008.2.r.k.673.3		6
9.4	even	3		9072.2.a.cd.1.2		3
9.5	odd	6		9072.2.a.bq.1.2		3
9.7	even	3	inner	3024.2.r.g.2017.2		6
12.11	even	2		63.2.f.b.22.3	✓	6
28.3	even	6		1323.2.h.e.226.3		6
28.11	odd	6		1323.2.h.d.226.3		6
28.19	even	6		1323.2.g.b.361.1		6
28.23	odd	6		1323.2.g.c.361.1		6
28.27	even	2		1323.2.f.c.442.1		6
36.7	odd	6		189.2.f.a.127.1		6
36.11	even	6		63.2.f.b.43.3	yes	6
36.23	even	6		567.2.a.d.1.1		3
36.31	odd	6		567.2.a.g.1.3		3
84.11	even	6		441.2.h.c.373.1		6
84.23	even	6		441.2.g.e.67.3		6
84.47	odd	6		441.2.g.d.67.3		6
84.59	odd	6		441.2.h.b.373.1		6
84.83	odd	2		441.2.f.d.148.3		6
252.11	even	6		441.2.g.e.79.3		6
252.47	odd	6		441.2.h.b.214.1		6
252.79	odd	6		1323.2.h.d.802.3		6
252.83	odd	6		441.2.f.d.295.3		6
252.115	even	6		1323.2.g.b.667.1		6
252.139	even	6		3969.2.a.p.1.3		3
252.151	odd	6		1323.2.g.c.667.1		6
252.167	odd	6		3969.2.a.m.1.1		3
252.187	even	6		1323.2.h.e.802.3		6
252.191	even	6		441.2.h.c.214.1		6
252.223	even	6		1323.2.f.c.883.1		6
252.227	odd	6		441.2.g.d.79.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	12.11	even	2
63.2.f.b.43.3	yes	6	36.11	even	6
189.2.f.a.64.1		6	4.3	odd	2
189.2.f.a.127.1		6	36.7	odd	6
441.2.f.d.148.3		6	84.83	odd	2
441.2.f.d.295.3		6	252.83	odd	6
441.2.g.d.67.3		6	84.47	odd	6
441.2.g.d.79.3		6	252.227	odd	6
441.2.g.e.67.3		6	84.23	even	6
441.2.g.e.79.3		6	252.11	even	6
441.2.h.b.214.1		6	252.47	odd	6
441.2.h.b.373.1		6	84.59	odd	6
441.2.h.c.214.1		6	252.191	even	6
441.2.h.c.373.1		6	84.11	even	6
567.2.a.d.1.1		3	36.23	even	6
567.2.a.g.1.3		3	36.31	odd	6
1008.2.r.k.337.3		6	3.2	odd	2
1008.2.r.k.673.3		6	9.2	odd	6
1323.2.f.c.442.1		6	28.27	even	2
1323.2.f.c.883.1		6	252.223	even	6
1323.2.g.b.361.1		6	28.19	even	6
1323.2.g.b.667.1		6	252.115	even	6
1323.2.g.c.361.1		6	28.23	odd	6
1323.2.g.c.667.1		6	252.151	odd	6
1323.2.h.d.226.3		6	28.11	odd	6
1323.2.h.d.802.3		6	252.79	odd	6
1323.2.h.e.226.3		6	28.3	even	6
1323.2.h.e.802.3		6	252.187	even	6
3024.2.r.g.1009.2		6	1.1	even	1	trivial
3024.2.r.g.2017.2		6	9.7	even	3	inner
3969.2.a.m.1.1		3	252.167	odd	6
3969.2.a.p.1.3		3	252.139	even	6
9072.2.a.bq.1.2		3	9.5	odd	6
9072.2.a.cd.1.2		3	9.4	even	3

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29679 + 2.24611i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-1.29679 + 2.24611i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.25729 - 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +0.945916 q^{17} +4.05408 q^{19} +(0.136673 - 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +(1.23025 + 2.13086i) q^{29} +(1.16372 - 2.01561i) q^{31} +2.59358 q^{35} +1.78074 q^{37} +(-3.20321 + 5.54812i) q^{41} +(-5.21780 - 9.03749i) q^{43} +(6.08113 + 10.5328i) q^{47} +(-0.500000 + 0.866025i) q^{49} +6.27335 q^{53} +11.7089 q^{55} +(1.36333 - 2.36135i) q^{59} +(1.13667 + 1.96878i) q^{61} +(-1.29679 - 2.24611i) q^{65} +(-7.90856 + 13.6980i) q^{67} +3.27335 q^{71} -1.50739 q^{73} +(-2.25729 + 3.90975i) q^{77} +(7.35447 + 12.7383i) q^{79} +(0.472958 + 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +14.3566 q^{89} +1.00000 q^{91} +(-5.25729 + 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q - 5 * q^5 - 3 * q^7	\( 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59} + 6 q^{61} - 5 q^{65} + 18 q^{71} + 6 q^{73} + 2 q^{77} + 15 q^{79} + 12 q^{83} - 9 q^{85} + 4 q^{89} + 6 q^{91} - 16 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q - 5 * q^5 - 3 * q^7 + 2 * q^11 - 3 * q^13 + 24 * q^17 + 6 * q^19 - 6 * q^25 + q^29 - 3 * q^31 + 10 * q^35 - 6 * q^37 - 22 * q^41 - 3 * q^43 + 9 * q^47 - 3 * q^49 + 36 * q^53 + 12 * q^55 + 9 * q^59 + 6 * q^61 - 5 * q^65 + 18 * q^71 + 6 * q^73 + 2 * q^77 + 15 * q^79 + 12 * q^83 - 9 * q^85 + 4 * q^89 + 6 * q^91 - 16 * q^95 - 3 * q^97

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