LMFDB - Embedded newform 3024.2.q.g.2305.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.g.2881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59097 - 2.75564i) q^{5} +(2.56238 + 0.658939i) q^{7} +O(q^{10})$	$q+(-1.59097 - 2.75564i) q^{5} +(2.56238 + 0.658939i) q^{7} +(-1.59097 + 2.75564i) q^{11} +(2.85185 - 4.93955i) q^{13} +(0.760877 + 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(-1.11956 - 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(3.54063 + 6.13255i) q^{29} +9.42107 q^{31} +(-2.26088 - 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(2.80150 - 4.85235i) q^{41} +(-3.41423 - 5.91362i) q^{43} -5.82846 q^{47} +(6.13160 + 3.37690i) q^{49} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} -1.12476 q^{59} +3.12476 q^{61} -18.1488 q^{65} -10.9669 q^{67} +8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(-5.89248 + 6.01266i) q^{77} +4.13844 q^{79} +(-4.03379 - 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-0.112725 + 0.195246i) q^{89} +(10.5624 - 10.7778i) q^{91} -4.08126 q^{95} +(7.42107 + 12.8537i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{5} - 2 q^{7}+O(q^{10}) $ 6 * q - q^5 - 2 * q^7	$ 6 q - q^{5} - 2 q^{7} - q^{11} + 8 q^{13} + 4 q^{17} + 3 q^{19} - 7 q^{23} + 2 q^{25} + 5 q^{29} + 40 q^{31} - 13 q^{35} + 3 q^{37} + 6 q^{43} + 18 q^{47} + 12 q^{49} - 15 q^{53} + 26 q^{55} + 28 q^{59} - 16 q^{61} - 24 q^{65} + 2 q^{67} + 14 q^{71} + 19 q^{73} - 10 q^{77} + 10 q^{79} + 2 q^{83} - 2 q^{85} + 9 q^{89} + 46 q^{91} + 8 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q - q^5 - 2 * q^7 - q^11 + 8 * q^13 + 4 * q^17 + 3 * q^19 - 7 * q^23 + 2 * q^25 + 5 * q^29 + 40 * q^31 - 13 * q^35 + 3 * q^37 + 6 * q^43 + 18 * q^47 + 12 * q^49 - 15 * q^53 + 26 * q^55 + 28 * q^59 - 16 * q^61 - 24 * q^65 + 2 * q^67 + 14 * q^71 + 19 * q^73 - 10 * q^77 + 10 * q^79 + 2 * q^83 - 2 * q^85 + 9 * q^89 + 46 * q^91 + 8 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	−0.964292	−	0.264840i	$-0.914681\pi$
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	0.252788	−	0.967522i	$-0.418652\pi$
$6$		0			0
$7$	2.56238	+	0.658939i	0.968489	+	0.249055i
$7$	2.56238	+	0.658939i	0.968489	+	0.249055i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.59097	+	2.75564i	−0.479696	+	0.830858i	−0.999729	−	0.0232884i	$-0.992586\pi$
$11$	−1.59097	+	2.75564i	−0.479696	+	0.830858i	0.520033	+	0.854146i	$0.325920\pi$
$12$		0			0
$13$	2.85185	−	4.93955i	0.790960	−	1.36998i	−0.134412	−	0.990925i	$-0.542915\pi$
$13$	2.85185	−	4.93955i	0.790960	−	1.36998i	0.925373	−	0.379058i	$-0.123752\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	0.943421	−	0.331596i	$-0.107587\pi$
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	−0.758882	+	0.651229i	$0.774254\pi$
$18$		0			0
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	−0.783037	−	0.621975i	$-0.786330\pi$
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	0.930165	+	0.367142i	$0.119664\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.11956	−	1.93914i	−0.233445	−	0.404338i	0.725375	−	0.688354i	$-0.241666\pi$
$23$	−1.11956	−	1.93914i	−0.233445	−	0.404338i	−0.958820	+	0.284016i	$0.908333\pi$
$24$		0			0
$25$	−2.56238	+	4.43818i	−0.512476	+	0.887635i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.54063	+	6.13255i	0.657478	+	1.13879i	0.981266	+	0.192656i	$0.0617101\pi$
$29$	3.54063	+	6.13255i	0.657478	+	1.13879i	−0.323788	+	0.946130i	$0.604957\pi$
$30$		0			0
$31$	9.42107			1.69207			0.846037	−	0.533125i	$-0.178982\pi$
$31$	9.42107			1.69207			0.846037	+	0.533125i	$0.178982\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.26088	−	8.10936i	−0.382158	−	1.37073i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	−0.559976	−	0.828509i	$-0.689190\pi$
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	0.997498	+	0.0706992i	$0.0225230\pi$
$42$		0			0
$43$	−3.41423	−	5.91362i	−0.520665	−	0.901819i	−0.999711	−	0.0240288i	$-0.992351\pi$
$43$	−3.41423	−	5.91362i	−0.520665	−	0.901819i	0.479046	−	0.877790i	$-0.340983\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.82846			−0.850168			−0.425084	−	0.905154i	$-0.639755\pi$
$47$	−5.82846			−0.850168			−0.425084	+	0.905154i	$0.639755\pi$
$48$		0			0
$49$	6.13160	+	3.37690i	0.875943	+	0.482415i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	0.786694	−	0.617343i	$-0.211791\pi$
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	−0.927982	+	0.372626i	$0.878458\pi$
$54$		0			0
$55$	10.1248			1.36522
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.12476			−0.146432			−0.0732159	−	0.997316i	$-0.523326\pi$
$59$	−1.12476			−0.146432			−0.0732159	+	0.997316i	$0.523326\pi$
$60$		0			0
$61$	3.12476			0.400085			0.200042	−	0.979787i	$-0.435892\pi$
$61$	3.12476			0.400085			0.200042	+	0.979787i	$0.435892\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−18.1488			−2.25109
$66$		0			0
$67$	−10.9669			−1.33982			−0.669910	−	0.742442i	$-0.733667\pi$
$67$	−10.9669			−1.33982			−0.669910	+	0.742442i	$0.733667\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.69002			1.03132			0.515658	−	0.856794i	$-0.327548\pi$
$71$	8.69002			1.03132			0.515658	+	0.856794i	$0.327548\pi$
$72$		0			0
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	0.683302	−	0.730136i	$-0.260543\pi$
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	−0.973967	+	0.226689i	$0.927210\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.89248	+	6.01266i	−0.671510	+	0.685206i
$78$		0			0
$79$	4.13844			0.465610			0.232805	−	0.972523i	$-0.425210\pi$
$79$	4.13844			0.465610			0.232805	+	0.972523i	$0.425210\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.03379	−	6.98673i	−0.442766	−	0.766893i	0.555127	−	0.831765i	$-0.312669\pi$
$83$	−4.03379	−	6.98673i	−0.442766	−	0.766893i	−0.997894	+	0.0648718i	$0.979336\pi$
$84$		0			0
$85$	2.42107	−	4.19341i	0.262602	−	0.454839i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	−0.871938	−	0.489616i	$-0.837137\pi$
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	0.859989	+	0.510312i	$0.170470\pi$
$90$		0			0
$91$	10.5624	−	10.7778i	1.10724	−	1.12982i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.08126			−0.418728
$96$		0			0
$97$	7.42107	+	12.8537i	0.753495	+	1.30509i	0.946119	+	0.323819i	$0.104967\pi$
$97$	7.42107	+	12.8537i	0.753495	+	1.30509i	−0.192624	+	0.981273i	$0.561700\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.29467	−	16.0988i	0.924854	−	1.60189i	0.133058	−	0.991108i	$-0.457520\pi$
$101$	9.29467	−	16.0988i	0.924854	−	1.60189i	0.791796	−	0.610786i	$-0.209146\pi$
$102$		0			0
$103$	−0.141315	−	0.244765i	−0.0139242	−	0.0241174i	0.858979	−	0.512010i	$-0.171099\pi$
$103$	−0.141315	−	0.244765i	−0.0139242	−	0.0241174i	−0.872904	+	0.487893i	$0.837766\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	−0.448322	−	0.893872i	$-0.647978\pi$
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	0.998277	−	0.0586780i	$-0.0186885\pi$
$108$		0			0
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.60752	−	2.78431i	0.151223	−	0.261926i	−0.780454	−	0.625213i	$-0.785012\pi$
$113$	1.60752	−	2.78431i	0.151223	−	0.261926i	0.931677	+	0.363287i	$0.118345\pi$
$114$		0			0
$115$	−3.56238	+	6.17023i	−0.332194	+	0.575377i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.08126	+	3.87828i	0.0991186	+	0.355521i
$120$		0			0
$121$	0.437618	+	0.757977i	0.0397835	+	0.0689070i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.396990			0.0355079
$126$		0			0
$127$	−20.1053			−1.78406			−0.892030	−	0.451976i	$-0.850719\pi$
$127$	−20.1053			−1.78406			−0.892030	+	0.451976i	$0.850719\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.18194	−	5.51129i	−0.278008	−	0.481523i	0.692882	−	0.721051i	$-0.256341\pi$
$131$	−3.18194	−	5.51129i	−0.278008	−	0.481523i	−0.970890	+	0.239528i	$0.923007\pi$
$132$		0			0
$133$	2.37524	−	2.42368i	0.205959	−	0.210160i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.37072	−	2.37416i	0.117109	−	0.202838i	−0.801512	−	0.597979i	$-0.795971\pi$
$137$	1.37072	−	2.37416i	0.117109	−	0.202838i	0.918621	+	0.395140i	$0.129304\pi$
$138$		0			0
$139$	3.98345	−	6.89953i	0.337872	−	0.585211i	−0.646161	−	0.763202i	$-0.723626\pi$
$139$	3.98345	−	6.89953i	0.337872	−	0.585211i	0.984032	+	0.177991i	$0.0569597\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.07442	+	15.7174i	0.758841	+	1.31435i
$144$		0			0
$145$	11.2661	−	19.5134i	0.935597	−	1.62050i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.6300	−	20.1437i	−0.952764	−	1.65024i	−0.739404	−	0.673262i	$-0.764893\pi$
$149$	−11.6300	−	20.1437i	−0.952764	−	1.65024i	−0.213360	−	0.976974i	$-0.568441\pi$
$150$		0			0
$151$	−4.06238	+	7.03625i	−0.330592	+	0.572602i	−0.982628	−	0.185586i	$-0.940582\pi$
$151$	−4.06238	+	7.03625i	−0.330592	+	0.572602i	0.652036	+	0.758188i	$0.273915\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.9887	−	25.9611i	−1.20392	−	2.08525i
$156$		0			0
$157$	−11.2632			−0.898901			−0.449451	−	0.893305i	$-0.648380\pi$
$157$	−11.2632			−0.898901			−0.449451	+	0.893305i	$0.648380\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.59097	−	5.70653i	−0.125386	−	0.449738i
$162$		0			0
$163$	1.99028	−	3.44727i	0.155891	−	0.270011i	−0.777492	−	0.628893i	$-0.783508\pi$
$163$	1.99028	−	3.44727i	0.155891	−	0.270011i	0.933383	+	0.358881i	$0.116842\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.61956	−	4.53721i	0.202708	−	0.351100i	−0.746692	−	0.665170i	$-0.768359\pi$
$167$	2.61956	−	4.53721i	0.202708	−	0.351100i	0.949400	+	0.314070i	$0.101693\pi$
$168$		0			0
$169$	−9.76608	−	16.9153i	−0.751237	−	1.30118i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.55159			−0.193994			−0.0969968	−	0.995285i	$-0.530924\pi$
$173$	−2.55159			−0.193994			−0.0969968	+	0.995285i	$0.530924\pi$
$174$		0			0
$175$	−9.49028	+	9.68385i	−0.717398	+	0.732030i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	0.967041	−	0.254620i	$-0.0819504\pi$
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	−0.704028	+	0.710172i	$0.748617\pi$
$180$		0			0
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.18194			−0.233941
$186$		0			0
$187$	−4.84213			−0.354092
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.98057			0.143309			0.0716545	−	0.997430i	$-0.477172\pi$
$191$	1.98057			0.143309			0.0716545	+	0.997430i	$0.477172\pi$
$192$		0			0
$193$	−4.54583			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$193$	−4.54583			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.8148			1.55424			0.777120	−	0.629353i	$-0.216680\pi$
$197$	21.8148			1.55424			0.777120	+	0.629353i	$0.216680\pi$
$198$		0			0
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	0.561978	−	0.827152i	$-0.310041\pi$
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	−0.997324	+	0.0731106i	$0.976707\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.03147	+	18.0470i	0.353140	+	1.26665i
$204$		0			0
$205$	−17.8285			−1.24519
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.04063	+	3.53447i	0.141153	+	0.244485i
$210$		0			0
$211$	8.32846	−	14.4253i	0.573355	−	0.993080i	−0.422863	−	0.906193i	$-0.638975\pi$
$211$	8.32846	−	14.4253i	0.573355	−	0.993080i	0.996218	−	0.0868863i	$-0.0276917\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.8639	+	18.8168i	−0.740911	+	1.28330i
$216$		0			0
$217$	24.1404	+	6.20790i	1.63876	+	0.421420i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.67962			0.583854
$222$		0			0
$223$	5.32846	+	9.22916i	0.356820	+	0.618031i	0.987428	−	0.158071i	$-0.0505276\pi$
$223$	5.32846	+	9.22916i	0.356820	+	0.618031i	−0.630608	+	0.776102i	$0.717194\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.25404	−	12.5644i	0.481468	−	0.833926i	−0.518306	−	0.855195i	$-0.673437\pi$
$227$	7.25404	−	12.5644i	0.481468	−	0.833926i	0.999774	+	0.0212688i	$0.00677059\pi$
$228$		0			0
$229$	−5.12476	−	8.87635i	−0.338654	−	0.586566i	0.645526	−	0.763738i	$-0.276638\pi$
$229$	−5.12476	−	8.87635i	−0.338654	−	0.586566i	−0.984180	+	0.177173i	$0.943305\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	−0.883191	−	0.469014i	$-0.844610\pi$
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	0.847773	+	0.530359i	$0.177943\pi$
$234$		0			0
$235$	9.27292	+	16.0612i	0.604898	+	1.04771i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.16019	+	10.6698i	−0.398470	+	0.690170i	−0.993537	−	0.113506i	$-0.963792\pi$
$239$	−6.16019	+	10.6698i	−0.398470	+	0.690170i	0.595068	+	0.803676i	$0.297125\pi$
$240$		0			0
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	−0.577107	−	0.816668i	$-0.695819\pi$
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	0.995809	+	0.0914555i	$0.0291519\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.449657	−	22.2691i	−0.0287275	−	1.42272i
$246$		0			0
$247$	−3.65787	−	6.33561i	−0.232744	−	0.403125i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.83009	+	6.63392i	0.238915	+	0.413813i	0.960403	−	0.278614i	$-0.0898750\pi$
$257$	3.83009	+	6.63392i	0.238915	+	0.413813i	−0.721488	+	0.692427i	$0.756542\pi$
$258$		0			0
$259$	1.85185	−	1.88962i	0.115068	−	0.117415i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.54746	−	2.68029i	0.0954208	−	0.165274i	−0.814363	−	0.580355i	$-0.802914\pi$
$263$	1.54746	−	2.68029i	0.0954208	−	0.165274i	0.909784	+	0.415082i	$0.136247\pi$
$264$		0			0
$265$	−3.27292	+	5.66886i	−0.201054	+	0.348235i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	0.905855	+	0.423587i	$0.139229\pi$
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	−0.0860906	+	0.996287i	$0.527437\pi$
$270$		0			0
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	−0.301759	−	0.953384i	$-0.597574\pi$
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	0.976534	−	0.215362i	$-0.0690930\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.15335	−	14.1220i	−0.491666	−	0.851590i
$276$		0			0
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	−0.557928	−	0.829889i	$-0.688404\pi$
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	0.997669	+	0.0682357i	$0.0217370\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.6992	−	20.2636i	−0.697915	−	1.20882i	−0.969188	−	0.246322i	$-0.920778\pi$
$281$	−11.6992	−	20.2636i	−0.697915	−	1.20882i	0.271273	−	0.962502i	$-0.412555\pi$
$282$		0			0
$283$	26.1248			1.55296			0.776478	−	0.630144i	$-0.217004\pi$
$283$	26.1248			1.55296			0.776478	+	0.630144i	$0.217004\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.3759	−	10.5876i	0.612471	−	0.624963i
$288$		0			0
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	0.189678	+	0.981846i	$0.439255\pi$
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	−0.945143	+	0.326657i	$0.894078\pi$
$294$		0			0
$295$	1.78947	+	3.09945i	0.104187	+	0.180457i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.7713			−0.738582
$300$		0			0
$301$	−4.85185	−	17.4027i	−0.279656	−	1.00308i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.97141	−	8.61073i	−0.284662	−	0.493049i
$306$		0			0
$307$	−3.53216			−0.201591			−0.100795	−	0.994907i	$-0.532139\pi$
$307$	−3.53216			−0.201591			−0.100795	+	0.994907i	$0.532139\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.70370			0.0966078			0.0483039	−	0.998833i	$-0.484618\pi$
$311$	1.70370			0.0966078			0.0483039	+	0.998833i	$0.484618\pi$
$312$		0			0
$313$	−2.84213			−0.160647			−0.0803234	−	0.996769i	$-0.525595\pi$
$313$	−2.84213			−0.160647			−0.0803234	+	0.996769i	$0.525595\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	24.9201			1.39965			0.699827	−	0.714313i	$-0.253261\pi$
$317$	24.9201			1.39965			0.699827	+	0.714313i	$0.253261\pi$
$318$		0			0
$319$	−22.5322			−1.26156
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.95185			0.108604
$324$		0			0
$325$	14.6150	+	25.3140i	0.810697	+	1.40417i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.9347	−	3.84060i	−0.823379	−	0.211739i
$330$		0			0
$331$	7.17154			0.394183			0.197092	−	0.980385i	$-0.436850\pi$
$331$	7.17154			0.394183			0.197092	+	0.980385i	$0.436850\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.4480	+	30.2209i	0.953287	+	1.65114i
$336$		0			0
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	0.398651	+	0.917103i	$0.369478\pi$
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	−0.993560	+	0.113309i	$0.963855\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.9887	+	25.9611i	−0.811681	+	1.40587i
$342$		0			0
$343$	13.4863	+	12.6933i	0.728193	+	0.685372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.11109			−0.113329			−0.0566646	−	0.998393i	$-0.518047\pi$
$347$	−2.11109			−0.113329			−0.0566646	+	0.998393i	$0.518047\pi$
$348$		0			0
$349$	18.1082	+	31.3643i	0.969310	+	1.67889i	0.697559	+	0.716527i	$0.254269\pi$
$349$	18.1082	+	31.3643i	0.969310	+	1.67889i	0.271751	+	0.962368i	$0.412397\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.24433	+	9.08344i	−0.279127	+	0.483463i	−0.971168	−	0.238396i	$-0.923378\pi$
$353$	−5.24433	+	9.08344i	−0.279127	+	0.483463i	0.692041	+	0.721858i	$0.256712\pi$
$354$		0			0
$355$	−13.8256	−	23.9466i	−0.733786	−	1.27095i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	−0.0195047	−	0.999810i	$-0.506209\pi$
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	0.875613	−	0.483013i	$-0.160458\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.90219	+	13.6870i	−0.413620	+	0.716410i
$366$		0			0
$367$	−9.05555	+	15.6847i	−0.472696	+	0.818733i	−0.999512	−	0.0312465i	$-0.990052\pi$
$367$	−9.05555	+	15.6847i	−0.472696	+	0.818733i	0.526816	+	0.849979i	$0.323386\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.46169	−	5.24284i	−0.0758874	−	0.272195i
$372$		0			0
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	0.976621	−	0.214971i	$-0.0689656\pi$
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	−0.674480	+	0.738293i	$0.735632\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	40.3893			2.08016
$378$		0			0
$379$	−14.2690			−0.732947			−0.366474	−	0.930428i	$-0.619435\pi$
$379$	−14.2690			−0.732947			−0.366474	+	0.930428i	$0.619435\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.824893	+	1.42876i	0.0421501	+	0.0730061i	0.886331	−	0.463053i	$-0.153246\pi$
$383$	0.824893	+	1.42876i	0.0421501	+	0.0730061i	−0.844181	+	0.536059i	$0.819913\pi$
$384$		0			0
$385$	25.9435	+	6.67160i	1.32220	+	0.340016i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.0338	+	27.7713i	−0.812946	+	1.40806i	0.0978483	+	0.995201i	$0.468804\pi$
$389$	−16.0338	+	27.7713i	−0.812946	+	1.40806i	−0.910794	+	0.412862i	$0.864529\pi$
$390$		0			0
$391$	1.70370	−	2.95089i	0.0861596	−	0.149233i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.58414	−	11.4041i	−0.331284	−	0.573800i
$396$		0			0
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.210660	+	0.977559i	$0.567561\pi$
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.741261	+	0.671217i	$0.765772\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.30959	+	9.19647i	0.265148	+	0.459250i	0.967602	−	0.252479i	$-0.0812458\pi$
$401$	5.30959	+	9.19647i	0.265148	+	0.459250i	−0.702454	+	0.711729i	$0.747913\pi$
$402$		0			0
$403$	26.8675	−	46.5358i	1.33836	−	2.31811i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.59097	+	2.75564i	0.0788615	+	0.136592i
$408$		0			0
$409$	5.54583			0.274224			0.137112	−	0.990556i	$-0.456218\pi$
$409$	5.54583			0.274224			0.137112	+	0.990556i	$0.456218\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.88207	−	0.741150i	−0.141818	−	0.0364696i
$414$		0			0
$415$	−12.8353	+	22.2314i	−0.630060	+	1.09130i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.77455	−	4.80566i	0.135546	−	0.234772i	−0.790260	−	0.612772i	$-0.790055\pi$
$419$	2.77455	−	4.80566i	0.135546	−	0.234772i	0.925806	+	0.378000i	$0.123388\pi$
$420$		0			0
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	0.770537	−	0.637396i	$-0.219988\pi$
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	−0.937269	+	0.348606i	$0.886655\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.79863			−0.378289
$426$		0			0
$427$	8.00684	+	2.05903i	0.387478	+	0.0996433i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	0.921321	+	0.388803i	$0.127111\pi$
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	−0.123947	+	0.992289i	$0.539555\pi$
$432$		0			0
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.87197			−0.137385
$438$		0			0
$439$	8.83422			0.421634			0.210817	−	0.977526i	$-0.432388\pi$
$439$	8.83422			0.421634			0.210817	+	0.977526i	$0.432388\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.5185			0.832328			0.416164	−	0.909290i	$-0.363374\pi$
$443$	17.5185			0.832328			0.416164	+	0.909290i	$0.363374\pi$
$444$		0			0
$445$	0.717370			0.0340066
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.2301			−1.47384			−0.736920	−	0.675980i	$-0.763720\pi$
$449$	−31.2301			−1.47384			−0.736920	+	0.675980i	$0.763720\pi$
$450$		0			0
$451$	8.91423	+	15.4399i	0.419755	+	0.727036i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−46.5043	−	11.9590i	−2.18015	−	0.560645i
$456$		0			0
$457$	−32.1248			−1.50273			−0.751367	−	0.659885i	$-0.770605\pi$
$457$	−32.1248			−1.50273			−0.751367	+	0.659885i	$0.770605\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	0.835901	−	0.548880i	$-0.184946\pi$
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	−0.893295	+	0.449472i	$0.851612\pi$
$462$		0			0
$463$	−15.1735	+	26.2812i	−0.705171	+	1.22139i	0.261459	+	0.965215i	$0.415796\pi$
$463$	−15.1735	+	26.2812i	−0.705171	+	1.22139i	−0.966630	+	0.256177i	$0.917537\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	−0.989465	−	0.144774i	$-0.953754\pi$
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	0.620110	+	0.784515i	$0.287088\pi$
$468$		0			0
$469$	−28.1014	−	7.22651i	−1.29760	−	0.333689i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	21.7278			0.999044
$474$		0			0
$475$	3.28659	+	5.69254i	0.150799	+	0.261192i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.5865	−	20.0683i	0.529399	−	0.916946i	−0.470013	−	0.882659i	$-0.655751\pi$
$479$	11.5865	−	20.0683i	0.529399	−	0.916946i	0.999412	−	0.0342863i	$-0.0109158\pi$
$480$		0			0
$481$	−2.85185	−	4.93955i	−0.130033	−	0.225224i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	23.6134	−	40.8996i	1.07223	−	1.85716i
$486$		0			0
$487$	−1.70658	−	2.95588i	−0.0773323	−	0.133943i	0.824766	−	0.565474i	$-0.191307\pi$
$487$	−1.70658	−	2.95588i	−0.0773323	−	0.133943i	−0.902098	+	0.431531i	$0.857974\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.58414	+	16.6002i	−0.432526	+	0.749157i	−0.997090	−	0.0762323i	$-0.975711\pi$
$491$	−9.58414	+	16.6002i	−0.432526	+	0.749157i	0.564564	+	0.825389i	$0.309044\pi$
$492$		0			0
$493$	−5.38796	+	9.33223i	−0.242662	+	0.420302i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.2672	+	5.72619i	0.998819	+	0.256855i
$498$		0			0
$499$	20.5848	+	35.6540i	0.921503	+	1.59609i	0.797090	+	0.603860i	$0.206371\pi$
$499$	20.5848	+	35.6540i	0.921503	+	1.59609i	0.124413	+	0.992231i	$0.460295\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.38564	+	11.0603i	0.283039	+	0.490237i	0.972132	−	0.234436i	$-0.0753242\pi$
$509$	6.38564	+	11.0603i	0.283039	+	0.490237i	−0.689093	+	0.724673i	$0.741991\pi$
$510$		0			0
$511$	−3.52915	−	12.6584i	−0.156120	−	0.559975i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.449657	+	0.778828i	−0.0198142	+	0.0343193i
$516$		0			0
$517$	9.27292	−	16.0612i	0.407822	−	0.706369i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	0.930942	−	0.365168i	$-0.118988\pi$
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	−0.781716	+	0.623635i	$0.785655\pi$
$522$		0			0
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	0.339148	+	0.940733i	$0.389861\pi$
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	−0.984273	+	0.176656i	$0.943472\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.16827	+	12.4158i	0.312255	+	0.540841i
$528$		0			0
$529$	8.99316	−	15.5766i	0.391007	−	0.677244i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−15.9789	−	27.6763i	−0.692125	−	1.19879i
$534$		0			0
$535$	−36.2028			−1.56518
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.0607	+	11.5239i	−0.821004	+	0.496371i
$540$		0			0
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.03379	+	12.1829i	−0.301295	+	0.521857i
$546$		0			0
$547$	−17.6150	−	30.5102i	−0.753165	−	1.30452i	−0.946281	−	0.323344i	$-0.895193\pi$
$547$	−17.6150	−	30.5102i	−0.753165	−	1.30452i	0.193116	−	0.981176i	$-0.438141\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.08263			0.386933
$552$		0			0
$553$	10.6043	+	2.72698i	0.450939	+	0.115963i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	0.928532	−	0.371252i	$-0.121071\pi$
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	−0.785779	+	0.618507i	$0.787738\pi$
$558$		0			0
$559$	−38.9475			−1.64730
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.45993			−0.0615286			−0.0307643	−	0.999527i	$-0.509794\pi$
$563$	−1.45993			−0.0615286			−0.0307643	+	0.999527i	$0.509794\pi$
$564$		0			0
$565$	−10.2301			−0.430383
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.5653			−0.820218			−0.410109	−	0.912036i	$-0.634509\pi$
$569$	−19.5653			−0.820218			−0.410109	+	0.912036i	$0.634509\pi$
$570$		0			0
$571$	21.9259			0.917569			0.458785	−	0.888547i	$-0.348285\pi$
$571$	21.9259			0.917569			0.458785	+	0.888547i	$0.348285\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	11.4750			0.478540
$576$		0			0
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	0.999853	+	0.0171554i	$0.00546099\pi$
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	−0.485069	+	0.874476i	$0.661206\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.73229	−	20.5607i	−0.237815	−	0.853001i
$582$		0			0
$583$	6.54583			0.271101
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.0796	−	31.3148i	−0.746226	−	1.29250i	−0.949620	−	0.313404i	$-0.898531\pi$
$587$	−18.0796	−	31.3148i	−0.746226	−	1.29250i	0.203394	−	0.979097i	$-0.434803\pi$
$588$		0			0
$589$	6.04187	−	10.4648i	0.248951	−	0.431196i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	−0.668204	−	0.743978i	$-0.732937\pi$
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	0.978406	+	0.206693i	$0.0662700\pi$
$594$		0			0
$595$	8.96690	−	9.14978i	0.367607	−	0.375105i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.45417			−0.222851			−0.111426	−	0.993773i	$-0.535542\pi$
$599$	−5.45417			−0.222851			−0.111426	+	0.993773i	$0.535542\pi$
$600$		0			0
$601$	−3.36840	−	5.83424i	−0.137400	−	0.237984i	0.789112	−	0.614250i	$-0.210541\pi$
$601$	−3.36840	−	5.83424i	−0.137400	−	0.237984i	−0.926512	+	0.376266i	$0.877208\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.39248	−	2.41184i	0.0566122	−	0.0980553i
$606$		0			0
$607$	3.33530	+	5.77690i	0.135376	+	0.234477i	0.925741	−	0.378159i	$-0.123443\pi$
$607$	3.33530	+	5.77690i	0.135376	+	0.234477i	−0.790365	+	0.612636i	$0.790109\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.6219	+	28.7899i	−0.672449	+	1.16472i
$612$		0			0
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.2483	+	29.8749i	−0.694390	+	1.20272i	0.275996	+	0.961159i	$0.410992\pi$
$617$	−17.2483	+	29.8749i	−0.694390	+	1.20272i	−0.970386	+	0.241560i	$0.922341\pi$
$618$		0			0
$619$	−8.22421	+	14.2447i	−0.330559	+	0.572545i	−0.982622	−	0.185620i	$-0.940571\pi$
$619$	−8.22421	+	14.2447i	−0.330559	+	0.572545i	0.652063	+	0.758165i	$0.273904\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.417500	+	0.426015i	−0.0167268	+	0.0170679i
$624$		0			0
$625$	12.1803	+	21.0969i	0.487212	+	0.843877i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.52175			0.0606763
$630$		0			0
$631$	30.0118			1.19475			0.597375	−	0.801962i	$-0.296210\pi$
$631$	30.0118			1.19475			0.597375	+	0.801962i	$0.296210\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	31.9870	+	55.4031i	1.26937	+	2.19861i
$636$		0			0
$637$	34.1668	−	20.6569i	1.35374	−	0.818456i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.9497	−	24.1615i	0.550978	−	0.954322i	−0.447226	−	0.894421i	$-0.647588\pi$
$641$	13.9497	−	24.1615i	0.550978	−	0.954322i	0.998204	−	0.0599014i	$-0.0190786\pi$
$642$		0			0
$643$	−14.2524	+	24.6859i	−0.562060	+	0.973516i	0.435257	+	0.900306i	$0.356658\pi$
$643$	−14.2524	+	24.6859i	−0.562060	+	0.973516i	−0.997317	+	0.0732100i	$0.976676\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	0.982224	−	0.187711i	$-0.0601069\pi$
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	−0.653675	+	0.756776i	$0.726774\pi$
$648$		0			0
$649$	1.78947	−	3.09945i	0.0702427	−	0.121664i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.0825	+	33.0519i	0.746756	+	1.29342i	0.949370	+	0.314161i	$0.101723\pi$
$653$	19.0825	+	33.0519i	0.746756	+	1.29342i	−0.202614	+	0.979259i	$0.564944\pi$
$654$		0			0
$655$	−10.1248	+	17.5366i	−0.395607	+	0.685212i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.37072	+	7.57031i	0.170259	+	0.294898i	0.938510	−	0.345251i	$-0.112206\pi$
$659$	4.37072	+	7.57031i	0.170259	+	0.294898i	−0.768251	+	0.640148i	$0.778873\pi$
$660$		0			0
$661$	−20.0837			−0.781167			−0.390584	−	0.920567i	$-0.627727\pi$
$661$	−20.0837			−0.781167			−0.390584	+	0.920567i	$0.627727\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.4577	−	2.68930i	−0.405534	−	0.104286i
$666$		0			0
$667$	7.92790	−	13.7315i	0.306970	−	0.531687i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.97141	+	8.61073i	−0.191919	+	0.332414i
$672$		0			0
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	−0.981561	−	0.191148i	$-0.938779\pi$
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	0.325242	−	0.945631i	$-0.394554\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.717370			0.0275708			0.0137854	−	0.999905i	$-0.495612\pi$
$677$	0.717370			0.0275708			0.0137854	+	0.999905i	$0.495612\pi$
$678$		0			0
$679$	10.5458	+	37.8260i	0.404712	+	1.45163i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	0.591260	−	0.806481i	$-0.298631\pi$
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	−0.994063	+	0.108806i	$0.965297\pi$
$684$		0			0
$685$	−8.72313			−0.333294
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−11.7335			−0.447012
$690$		0			0
$691$	−5.84789			−0.222464			−0.111232	−	0.993794i	$-0.535480\pi$
$691$	−5.84789			−0.222464			−0.111232	+	0.993794i	$0.535480\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−25.3502			−0.961588
$696$		0			0
$697$	8.52640			0.322960
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.2711			−0.387935			−0.193967	−	0.981008i	$-0.562136\pi$
$701$	−10.2711			−0.387935			−0.193967	+	0.981008i	$0.562136\pi$
$702$		0			0
$703$	−0.641315	−	1.11079i	−0.0241877	−	0.0418942i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.4246	−	35.1268i	1.29467	−	1.32108i
$708$		0			0
$709$	43.4854			1.63313			0.816564	−	0.577255i	$-0.195876\pi$
$709$	43.4854			1.63313			0.816564	+	0.577255i	$0.195876\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.5475	−	18.2687i	−0.395006	−	0.684170i
$714$		0			0
$715$	28.8743	−	50.0117i	1.07984	−	1.87033i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.200830	−	0.979626i	$-0.435636\pi$
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.747966	−	0.663737i	$-0.231031\pi$
$720$		0			0
$721$	−0.200818	−	0.720299i	−0.00747886	−	0.0268253i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−36.2898			−1.34777
$726$		0			0
$727$	−6.07210	−	10.5172i	−0.225202	−	0.390061i	0.731178	−	0.682186i	$-0.238971\pi$
$727$	−6.07210	−	10.5172i	−0.225202	−	0.390061i	−0.956380	+	0.292126i	$0.905637\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.19562	−	8.99907i	0.192167	−	0.332843i
$732$		0			0
$733$	23.0848	+	39.9841i	0.852657	+	1.47685i	0.878801	+	0.477188i	$0.158344\pi$
$733$	23.0848	+	39.9841i	0.852657	+	1.47685i	−0.0261440	+	0.999658i	$0.508323\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.4480	−	30.2209i	0.642706	−	1.11320i
$738$		0			0
$739$	2.49604	+	4.32327i	0.0918184	+	0.159034i	0.908276	−	0.418371i	$-0.137399\pi$
$739$	2.49604	+	4.32327i	0.0918184	+	0.159034i	−0.816458	+	0.577405i	$0.804065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.7060	+	27.2036i	−0.576198	+	0.998004i	0.419712	+	0.907657i	$0.362131\pi$
$743$	−15.7060	+	27.2036i	−0.576198	+	0.998004i	−0.995910	+	0.0903470i	$0.971202\pi$
$744$		0			0
$745$	−37.0059	+	64.0961i	−1.35579	+	2.34830i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	21.0695	−	21.4992i	0.769863	−	0.785565i
$750$		0			0
$751$	1.64815	+	2.85468i	0.0601419	+	0.104169i	0.894529	−	0.447010i	$-0.147511\pi$
$751$	1.64815	+	2.85468i	0.0601419	+	0.104169i	−0.834387	+	0.551179i	$0.814178\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	25.8525			0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.03379	+	12.1829i	0.254975	+	0.441629i	0.964889	−	0.262659i	$-0.0845995\pi$
$761$	7.03379	+	12.1829i	0.254975	+	0.441629i	−0.709914	+	0.704288i	$0.751266\pi$
$762$		0			0
$763$	−3.14132	−	11.2673i	−0.113723	−	0.407905i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.20765	+	5.55582i	−0.115822	+	0.200609i
$768$		0			0
$769$	11.3461	−	19.6520i	0.409151	−	0.708669i	−0.585644	−	0.810568i	$-0.699158\pi$
$769$	11.3461	−	19.6520i	0.409151	−	0.708669i	0.994795	+	0.101899i	$0.0324918\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	0.860071	−	0.510175i	$-0.170419\pi$
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	−0.871860	+	0.489756i	$0.837086\pi$
$774$		0			0
$775$	−24.1404	+	41.8123i	−0.867148	+	1.50194i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.59329	−	6.22377i	−0.128743	−	0.222990i
$780$		0			0
$781$	−13.8256	+	23.9466i	−0.494718	+	0.856877i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.9194	+	31.0374i	0.639572	+	1.10777i
$786$		0			0
$787$	−0.540073			−0.0192515			−0.00962576	−	0.999954i	$-0.503064\pi$
$787$	−0.540073			−0.0192515			−0.00962576	+	0.999954i	$0.503064\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.95378	−	6.07521i	0.211692	−	0.216010i
$792$		0			0
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	−0.553312	−	0.832974i	$-0.686636\pi$
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	0.998033	+	0.0626954i	$0.0199697\pi$
$798$		0			0
$799$	−4.43474	−	7.68119i	−0.156890	−	0.271741i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.8044			0.557725
$804$		0			0
$805$	−13.1940	+	13.4631i	−0.465027	+	0.474511i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	0.999889	+	0.0148817i	$0.00473717\pi$
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	−0.487057	+	0.873370i	$0.661929\pi$
$810$		0			0
$811$	15.4290			0.541785			0.270892	−	0.962610i	$-0.412681\pi$
$811$	15.4290			0.541785			0.270892	+	0.962610i	$0.412681\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−12.6659			−0.443669
$816$		0			0
$817$	−8.75839			−0.306417
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.48727			−0.296208			−0.148104	−	0.988972i	$-0.547317\pi$
$821$	−8.48727			−0.296208			−0.148104	+	0.988972i	$0.547317\pi$
$822$		0			0
$823$	−29.0974			−1.01427			−0.507136	−	0.861866i	$-0.669296\pi$
$823$	−29.0974			−1.01427			−0.507136	+	0.861866i	$0.669296\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.9396			−0.902007			−0.451003	−	0.892522i	$-0.648934\pi$
$827$	−25.9396			−0.902007			−0.451003	+	0.892522i	$0.648934\pi$
$828$		0			0
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	0.914941	−	0.403588i	$-0.132237\pi$
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	−0.806988	+	0.590568i	$0.798904\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.215047	+	10.6501i	0.00745093	+	0.369004i
$834$		0			0
$835$	−16.6706			−0.576910
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.2947	+	36.8834i	0.735174	+	1.27336i	0.954647	+	0.297740i	$0.0962327\pi$
$839$	21.2947	+	36.8834i	0.735174	+	1.27336i	−0.219474	+	0.975618i	$0.570434\pi$
$840$		0			0
$841$	−10.5721	+	18.3114i	−0.364555	+	0.631428i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−31.0751	+	53.8237i	−1.06902	+	1.85159i
$846$		0			0
$847$	0.621885	+	2.23059i	0.0213682	+	0.0766440i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.23912			−0.0767562
$852$		0			0
$853$	−10.6969	−	18.5275i	−0.366254	−	0.634370i	0.622723	−	0.782442i	$-0.286026\pi$
$853$	−10.6969	−	18.5275i	−0.366254	−	0.634370i	−0.988976	+	0.148073i	$0.952693\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.4218	+	31.9074i	−0.629275	+	1.08994i	0.358422	+	0.933560i	$0.383315\pi$
$857$	−18.4218	+	31.9074i	−0.629275	+	1.08994i	−0.987697	+	0.156377i	$0.950019\pi$
$858$		0			0
$859$	−8.81875	−	15.2745i	−0.300892	−	0.521160i	0.675446	−	0.737409i	$-0.263951\pi$
$859$	−8.81875	−	15.2745i	−0.300892	−	0.521160i	−0.976338	+	0.216249i	$0.930618\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	−0.872428	−	0.488743i	$-0.837456\pi$
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	0.859478	+	0.511173i	$0.170789\pi$
$864$		0			0
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.58414	+	11.4041i	−0.223351	+	0.386856i
$870$		0			0
$871$	−31.2759	+	54.1715i	−1.05974	+	1.83553i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.01724	+	0.261592i	0.0343890	+	0.00884343i
$876$		0			0
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	0.968234	+	0.250044i	$0.0804451\pi$
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	−0.267573	+	0.963538i	$0.586222\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−8.35486			−0.281482			−0.140741	−	0.990046i	$-0.544949\pi$
$881$	−8.35486			−0.281482			−0.140741	+	0.990046i	$0.544949\pi$
$882$		0			0
$883$	−35.6181			−1.19864			−0.599322	−	0.800508i	$-0.704563\pi$
$883$	−35.6181			−1.19864			−0.599322	+	0.800508i	$0.704563\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.5550	+	32.1382i	0.623016	+	1.07909i	0.988921	+	0.148443i	$0.0474260\pi$
$887$	18.5550	+	32.1382i	0.623016	+	1.07909i	−0.365905	+	0.930652i	$0.619241\pi$
$888$		0			0
$889$	−51.5175	−	13.2482i	−1.72784	−	0.444330i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.73788	+	6.47420i	−0.125083	+	0.216651i
$894$		0			0
$895$	11.1969	−	19.3935i	0.374270	−	0.648254i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	33.3565	+	57.7751i	1.11250	+	1.92691i
$900$		0			0
$901$	1.56526	−	2.71111i	0.0521464	−	0.0903202i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.6300	+	35.7321i	0.685763	+	1.18778i
$906$		0			0
$907$	−24.0751	+	41.6993i	−0.799401	+	1.38460i	0.120606	+	0.992700i	$0.461516\pi$
$907$	−24.0751	+	41.6993i	−0.799401	+	1.38460i	−0.920007	+	0.391902i	$0.871817\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	17.4428	+	30.2119i	0.577906	+	1.00096i	0.995719	+	0.0924301i	$0.0294635\pi$
$911$	17.4428	+	30.2119i	0.577906	+	1.00096i	−0.417813	+	0.908533i	$0.637203\pi$
$912$		0			0
$913$	25.6706			0.849573
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.52175	−	16.2187i	−0.149321	−	0.535590i
$918$		0			0
$919$	25.8675	−	44.8037i	0.853289	−	1.47794i	−0.0249351	−	0.999689i	$-0.507938\pi$
$919$	25.8675	−	44.8037i	0.853289	−	1.47794i	0.878224	−	0.478250i	$-0.158729\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.7826	−	42.9248i	0.815730	−	1.41289i
$924$		0			0
$925$	2.56238	+	4.43818i	0.0842506	+	0.145926i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	50.8285			1.66763			0.833814	−	0.552046i	$-0.186153\pi$
$929$	50.8285			1.66763			0.833814	+	0.552046i	$0.186153\pi$
$930$		0			0
$931$	7.68332	−	4.64526i	0.251811	−	0.152242i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.70370	+	13.3432i	0.251938	+	0.436369i
$936$		0			0
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.15787			−0.0377454			−0.0188727	−	0.999822i	$-0.506008\pi$
$941$	−1.15787			−0.0377454			−0.0188727	+	0.999822i	$0.506008\pi$
$942$		0			0
$943$	−12.5458			−0.408548
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.81479			0.318938			0.159469	−	0.987203i	$-0.449022\pi$
$947$	9.81479			0.318938			0.159469	+	0.987203i	$0.449022\pi$
$948$		0			0
$949$	−28.3297			−0.919620
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.53791			−0.211784			−0.105892	−	0.994378i	$-0.533770\pi$
$953$	−6.53791			−0.211784			−0.105892	+	0.994378i	$0.533770\pi$
$954$		0			0
$955$	−3.15103	−	5.45774i	−0.101965	−	0.176608i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.07674	−	5.18029i	0.163937	−	0.167280i
$960$		0			0
$961$	57.7565			1.86311
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.23229	+	12.5267i	0.232816	+	0.403248i
$966$		0			0
$967$	−14.4445	+	25.0185i	−0.464502	+	0.804542i	−0.999179	−	0.0405151i	$-0.987100\pi$
$967$	−14.4445	+	25.0185i	−0.464502	+	0.804542i	0.534677	+	0.845057i	$0.320433\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	−0.820030	−	0.572320i	$-0.806043\pi$
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	0.905659	+	0.424007i	$0.139377\pi$
$972$		0			0
$973$	14.7535	−	15.0544i	0.472975	−	0.482622i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	48.0722			1.53797			0.768983	−	0.639269i	$-0.220763\pi$
$977$	48.0722			1.53797			0.768983	+	0.639269i	$0.220763\pi$
$978$		0			0
$979$	−0.358685	−	0.621261i	−0.0114636	−	0.0198556i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−14.7313	+	25.5154i	−0.469857	+	0.813816i	−0.999406	−	0.0344634i	$-0.989028\pi$
$983$	−14.7313	+	25.5154i	−0.469857	+	0.813816i	0.529549	+	0.848279i	$0.322361\pi$
$984$		0			0
$985$	−34.7067	−	60.1138i	−1.10585	−	1.91538i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.64488	+	13.2413i	−0.243093	+	0.421050i
$990$		0			0
$991$	−15.4142	−	26.6982i	−0.489649	−	0.848097i	0.510280	−	0.860008i	$-0.329542\pi$
$991$	−15.4142	−	26.6982i	−0.489649	−	0.848097i	−0.999929	+	0.0119112i	$0.996208\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−19.5413	+	33.8466i	−0.619501	+	1.07301i
$996$		0			0
$997$	−2.77292	+	4.80283i	−0.0878191	+	0.152107i	−0.906589	−	0.422015i	$-0.861323\pi$
$997$	−2.77292	+	4.80283i	−0.0878191	+	0.152107i	0.818770	+	0.574122i	$0.194656\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.g.2305.1		6
3.2	odd	2		1008.2.q.g.625.1		6
4.3	odd	2		378.2.e.d.37.1		6
7.4	even	3		3024.2.t.h.1873.3		6
9.2	odd	6		1008.2.t.h.961.3		6
9.7	even	3		3024.2.t.h.289.3		6
12.11	even	2		126.2.e.c.121.3	yes	6
21.11	odd	6		1008.2.t.h.193.3		6
28.3	even	6		2646.2.h.o.361.1		6
28.11	odd	6		378.2.h.c.361.3		6
28.19	even	6		2646.2.f.m.1765.3		6
28.23	odd	6		2646.2.f.l.1765.1		6
28.27	even	2		2646.2.e.p.1549.3		6
36.7	odd	6		378.2.h.c.289.3		6
36.11	even	6		126.2.h.d.79.1	yes	6
36.23	even	6		1134.2.g.m.163.3		6
36.31	odd	6		1134.2.g.l.163.1		6
63.11	odd	6		1008.2.q.g.529.1		6
63.25	even	3	inner	3024.2.q.g.2881.1		6
84.11	even	6		126.2.h.d.67.1	yes	6
84.23	even	6		882.2.f.n.589.2		6
84.47	odd	6		882.2.f.o.589.2		6
84.59	odd	6		882.2.h.p.67.3		6
84.83	odd	2		882.2.e.o.373.1		6
252.11	even	6		126.2.e.c.25.3	✓	6
252.23	even	6		7938.2.a.bv.1.1		3
252.47	odd	6		882.2.f.o.295.2		6
252.67	odd	6		1134.2.g.l.487.1		6
252.79	odd	6		2646.2.f.l.883.1		6
252.83	odd	6		882.2.h.p.79.3		6
252.95	even	6		1134.2.g.m.487.3		6
252.103	even	6		7938.2.a.bz.1.1		3
252.115	even	6		2646.2.e.p.2125.3		6
252.131	odd	6		7938.2.a.bw.1.3		3
252.151	odd	6		378.2.e.d.235.1		6
252.187	even	6		2646.2.f.m.883.3		6
252.191	even	6		882.2.f.n.295.2		6
252.223	even	6		2646.2.h.o.667.1		6
252.227	odd	6		882.2.e.o.655.1		6
252.247	odd	6		7938.2.a.ca.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	252.11	even	6
126.2.e.c.121.3	yes	6	12.11	even	2
126.2.h.d.67.1	yes	6	84.11	even	6
126.2.h.d.79.1	yes	6	36.11	even	6
378.2.e.d.37.1		6	4.3	odd	2
378.2.e.d.235.1		6	252.151	odd	6
378.2.h.c.289.3		6	36.7	odd	6
378.2.h.c.361.3		6	28.11	odd	6
882.2.e.o.373.1		6	84.83	odd	2
882.2.e.o.655.1		6	252.227	odd	6
882.2.f.n.295.2		6	252.191	even	6
882.2.f.n.589.2		6	84.23	even	6
882.2.f.o.295.2		6	252.47	odd	6
882.2.f.o.589.2		6	84.47	odd	6
882.2.h.p.67.3		6	84.59	odd	6
882.2.h.p.79.3		6	252.83	odd	6
1008.2.q.g.529.1		6	63.11	odd	6
1008.2.q.g.625.1		6	3.2	odd	2
1008.2.t.h.193.3		6	21.11	odd	6
1008.2.t.h.961.3		6	9.2	odd	6
1134.2.g.l.163.1		6	36.31	odd	6
1134.2.g.l.487.1		6	252.67	odd	6
1134.2.g.m.163.3		6	36.23	even	6
1134.2.g.m.487.3		6	252.95	even	6
2646.2.e.p.1549.3		6	28.27	even	2
2646.2.e.p.2125.3		6	252.115	even	6
2646.2.f.l.883.1		6	252.79	odd	6
2646.2.f.l.1765.1		6	28.23	odd	6
2646.2.f.m.883.3		6	252.187	even	6
2646.2.f.m.1765.3		6	28.19	even	6
2646.2.h.o.361.1		6	28.3	even	6
2646.2.h.o.667.1		6	252.223	even	6
3024.2.q.g.2305.1		6	1.1	even	1	trivial
3024.2.q.g.2881.1		6	63.25	even	3	inner
3024.2.t.h.289.3		6	9.7	even	3
3024.2.t.h.1873.3		6	7.4	even	3
7938.2.a.bv.1.1		3	252.23	even	6
7938.2.a.bw.1.3		3	252.131	odd	6
7938.2.a.bz.1.1		3	252.103	even	6
7938.2.a.ca.1.3		3	252.247	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.59097 - 2.75564i) q^{5} +(2.56238 + 0.658939i) q^{7} +O(q^{10})\)	\(q+(-1.59097 - 2.75564i) q^{5} +(2.56238 + 0.658939i) q^{7} +(-1.59097 + 2.75564i) q^{11} +(2.85185 - 4.93955i) q^{13} +(0.760877 + 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(-1.11956 - 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(3.54063 + 6.13255i) q^{29} +9.42107 q^{31} +(-2.26088 - 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(2.80150 - 4.85235i) q^{41} +(-3.41423 - 5.91362i) q^{43} -5.82846 q^{47} +(6.13160 + 3.37690i) q^{49} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} -1.12476 q^{59} +3.12476 q^{61} -18.1488 q^{65} -10.9669 q^{67} +8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(-5.89248 + 6.01266i) q^{77} +4.13844 q^{79} +(-4.03379 - 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-0.112725 + 0.195246i) q^{89} +(10.5624 - 10.7778i) q^{91} -4.08126 q^{95} +(7.42107 + 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{5} - 2 q^{7}+O(q^{10}) \) 6 * q - q^5 - 2 * q^7	\( 6 q - q^{5} - 2 q^{7} - q^{11} + 8 q^{13} + 4 q^{17} + 3 q^{19} - 7 q^{23} + 2 q^{25} + 5 q^{29} + 40 q^{31} - 13 q^{35} + 3 q^{37} + 6 q^{43} + 18 q^{47} + 12 q^{49} - 15 q^{53} + 26 q^{55} + 28 q^{59} - 16 q^{61} - 24 q^{65} + 2 q^{67} + 14 q^{71} + 19 q^{73} - 10 q^{77} + 10 q^{79} + 2 q^{83} - 2 q^{85} + 9 q^{89} + 46 q^{91} + 8 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q - q^5 - 2 * q^7 - q^11 + 8 * q^13 + 4 * q^17 + 3 * q^19 - 7 * q^23 + 2 * q^25 + 5 * q^29 + 40 * q^31 - 13 * q^35 + 3 * q^37 + 6 * q^43 + 18 * q^47 + 12 * q^49 - 15 * q^53 + 26 * q^55 + 28 * q^59 - 16 * q^61 - 24 * q^65 + 2 * q^67 + 14 * q^71 + 19 * q^73 - 10 * q^77 + 10 * q^79 + 2 * q^83 - 2 * q^85 + 9 * q^89 + 46 * q^91 + 8 * q^95 + 28 * q^97

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