LMFDB - Embedded newform 3024.2.q.i.2305.2

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.2
Root			$1.19343 + 2.06709i$ of defining polynomial
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.i.2881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46043 - 2.52954i) q^{5} +(0.138560 - 2.64212i) q^{7} +O(q^{10})$	$q+(-1.46043 - 2.52954i) q^{5} +(0.138560 - 2.64212i) q^{7} +(0.676857 - 1.17235i) q^{11} +(-0.733001 + 1.26960i) q^{13} +(-1.65514 - 2.86678i) q^{17} +(1.10329 - 1.91096i) q^{19} +(-1.31415 - 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +(-0.521720 - 0.903646i) q^{29} -3.27458 q^{31} +(-6.88572 + 3.50815i) q^{35} +(5.43773 - 9.41842i) q^{37} +(0.904289 - 1.56627i) q^{41} +(2.17129 + 3.76078i) q^{43} +3.97914 q^{47} +(-6.96160 - 0.732185i) q^{49} +(3.22743 + 5.59008i) q^{53} -3.95402 q^{55} -12.2140 q^{59} +0.559734 q^{61} +4.28200 q^{65} -12.8118 q^{67} +12.9177 q^{71} +(5.22772 + 9.05467i) q^{73} +(-3.00371 - 1.95078i) q^{77} -0.767677 q^{79} +(-0.983707 - 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(-3.20356 + 5.54872i) q^{89} +(3.25286 + 2.11259i) q^{91} -6.44514 q^{95} +(-4.14143 - 7.17316i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 10 * q - 4 * q^5 + 4 * q^7	$ 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * 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
$5$	−1.46043	−	2.52954i	−0.653125	−	1.13125i	−0.982360	−	0.186998i	$-0.940124\pi$
$5$	−1.46043	−	2.52954i	−0.653125	−	1.13125i	0.329235	−	0.944248i	$-0.393209\pi$
$6$		0			0
$7$	0.138560	−	2.64212i	0.0523708	−	0.998628i
$7$	0.138560	−	2.64212i	0.0523708	−	0.998628i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.676857	−	1.17235i	0.204080	−	0.353477i	−0.745759	−	0.666216i	$-0.767913\pi$
$11$	0.676857	−	1.17235i	0.204080	−	0.353477i	0.949839	+	0.312738i	$0.101246\pi$
$12$		0			0
$13$	−0.733001	+	1.26960i	−0.203298	+	0.352123i	−0.949589	−	0.313497i	$-0.898499\pi$
$13$	−0.733001	+	1.26960i	−0.203298	+	0.352123i	0.746291	+	0.665620i	$0.231833\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.65514	−	2.86678i	−0.401430	−	0.695297i	0.592469	−	0.805593i	$-0.298153\pi$
$17$	−1.65514	−	2.86678i	−0.401430	−	0.695297i	−0.993899	+	0.110297i	$0.964820\pi$
$18$		0			0
$19$	1.10329	−	1.91096i	0.253113	−	0.438404i	−0.711268	−	0.702921i	$-0.751879\pi$
$19$	1.10329	−	1.91096i	0.253113	−	0.438404i	0.964381	+	0.264516i	$0.0852123\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.31415	−	2.27617i	−0.274019	−	0.474614i	0.695868	−	0.718169i	$-0.255020\pi$
$23$	−1.31415	−	2.27617i	−0.274019	−	0.474614i	−0.969887	+	0.243555i	$0.921686\pi$
$24$		0			0
$25$	−1.76573	+	3.05833i	−0.353146	+	0.611666i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.521720	−	0.903646i	−0.0968810	−	0.167803i	0.813511	−	0.581549i	$-0.197553\pi$
$29$	−0.521720	−	0.903646i	−0.0968810	−	0.167803i	−0.910392	+	0.413747i	$0.864220\pi$
$30$		0			0
$31$	−3.27458			−0.588132			−0.294066	−	0.955785i	$-0.595009\pi$
$31$	−3.27458			−0.588132			−0.294066	+	0.955785i	$0.595009\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.88572	+	3.50815i	−1.16390	+	0.592985i
$36$		0			0
$37$	5.43773	−	9.41842i	0.893957	−	1.54838i	0.0588664	−	0.998266i	$-0.481251\pi$
$37$	5.43773	−	9.41842i	0.893957	−	1.54838i	0.835090	−	0.550113i	$-0.185415\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.904289	−	1.56627i	0.141226	−	0.244611i	−0.786732	−	0.617294i	$-0.788229\pi$
$41$	0.904289	−	1.56627i	0.141226	−	0.244611i	0.927959	+	0.372683i	$0.121562\pi$
$42$		0			0
$43$	2.17129	+	3.76078i	0.331118	+	0.573514i	0.982731	−	0.185038i	$-0.0592408\pi$
$43$	2.17129	+	3.76078i	0.331118	+	0.573514i	−0.651613	+	0.758551i	$0.725907\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.97914			0.580417			0.290209	−	0.956963i	$-0.406275\pi$
$47$	3.97914			0.580417			0.290209	+	0.956963i	$0.406275\pi$
$48$		0			0
$49$	−6.96160	−	0.732185i	−0.994515	−	0.104598i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.22743	+	5.59008i	0.443322	+	0.767856i	0.997934	−	0.0642533i	$-0.0204666\pi$
$53$	3.22743	+	5.59008i	0.443322	+	0.767856i	−0.554612	+	0.832109i	$0.687133\pi$
$54$		0			0
$55$	−3.95402			−0.533160
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.2140			−1.59013			−0.795064	−	0.606526i	$-0.792563\pi$
$59$	−12.2140			−1.59013			−0.795064	+	0.606526i	$0.792563\pi$
$60$		0			0
$61$	0.559734			0.0716666			0.0358333	−	0.999358i	$-0.488591\pi$
$61$	0.559734			0.0716666			0.0358333	+	0.999358i	$0.488591\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.28200			0.531117
$66$		0			0
$67$	−12.8118			−1.56521			−0.782603	−	0.622521i	$-0.786109\pi$
$67$	−12.8118			−1.56521			−0.782603	+	0.622521i	$0.786109\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.9177			1.53305			0.766525	−	0.642214i	$-0.221984\pi$
$71$	12.9177			1.53305			0.766525	+	0.642214i	$0.221984\pi$
$72$		0			0
$73$	5.22772	+	9.05467i	0.611858	+	1.05977i	0.990927	+	0.134401i	$0.0429109\pi$
$73$	5.22772	+	9.05467i	0.611858	+	1.05977i	−0.379069	+	0.925368i	$0.623756\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.00371	−	1.95078i	−0.342304	−	0.222312i
$78$		0			0
$79$	−0.767677			−0.0863704			−0.0431852	−	0.999067i	$-0.513751\pi$
$79$	−0.767677			−0.0863704			−0.0431852	+	0.999067i	$0.513751\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.983707	−	1.70383i	−0.107976	−	0.187020i	0.806974	−	0.590587i	$-0.201104\pi$
$83$	−0.983707	−	1.70383i	−0.107976	−	0.187020i	−0.914950	+	0.403567i	$0.867770\pi$
$84$		0			0
$85$	−4.83443	+	8.37348i	−0.524368	+	0.908232i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.20356	+	5.54872i	−0.339576	+	0.588163i	−0.984353	−	0.176208i	$-0.943617\pi$
$89$	−3.20356	+	5.54872i	−0.339576	+	0.588163i	0.644777	+	0.764371i	$0.276950\pi$
$90$		0			0
$91$	3.25286	+	2.11259i	0.340992	+	0.221460i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.44514			−0.661258
$96$		0			0
$97$	−4.14143	−	7.17316i	−0.420498	−	0.728324i	0.575490	−	0.817809i	$-0.304811\pi$
$97$	−4.14143	−	7.17316i	−0.420498	−	0.728324i	−0.995988	+	0.0894847i	$0.971478\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.11331	+	14.0527i	−0.807305	+	1.39829i	0.107419	+	0.994214i	$0.465741\pi$
$101$	−8.11331	+	14.0527i	−0.807305	+	1.39829i	−0.914724	+	0.404079i	$0.867592\pi$
$102$		0			0
$103$	−1.11342	−	1.92849i	−0.109708	−	0.190020i	0.805944	−	0.591992i	$-0.201658\pi$
$103$	−1.11342	−	1.92849i	−0.109708	−	0.190020i	−0.915652	+	0.401972i	$0.868325\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.75403	+	15.1624i	−0.846284	+	1.46581i	0.0382175	+	0.999269i	$0.487832\pi$
$107$	−8.75403	+	15.1624i	−0.846284	+	1.46581i	−0.884501	+	0.466537i	$0.845501\pi$
$108$		0			0
$109$	−7.79917	−	13.5086i	−0.747025	−	1.29388i	−0.949243	−	0.314544i	$-0.898148\pi$
$109$	−7.79917	−	13.5086i	−0.747025	−	1.29388i	0.202218	−	0.979341i	$-0.435185\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.844555	−	1.46281i	0.0794491	−	0.137610i	−0.823563	−	0.567224i	$-0.808017\pi$
$113$	0.844555	−	1.46281i	0.0794491	−	0.137610i	0.903012	+	0.429615i	$0.141351\pi$
$114$		0			0
$115$	−3.83845	+	6.64839i	−0.357937	+	0.619966i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.80372	+	3.97585i	−0.715366	+	0.364466i
$120$		0			0
$121$	4.58373	+	7.93925i	0.416703	+	0.721750i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.28942			−0.383657
$126$		0			0
$127$	3.96918			0.352208			0.176104	−	0.984372i	$-0.443650\pi$
$127$	3.96918			0.352208			0.176104	+	0.984372i	$0.443650\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.66432	−	4.61473i	−0.232782	−	0.403191i	0.725844	−	0.687860i	$-0.241450\pi$
$131$	−2.66432	−	4.61473i	−0.232782	−	0.403191i	−0.958626	+	0.284669i	$0.908116\pi$
$132$		0			0
$133$	−4.89611	−	3.17982i	−0.424547	−	0.275725i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.74772	+	6.49124i	−0.320189	+	0.554584i	−0.980527	−	0.196385i	$-0.937080\pi$
$137$	−3.74772	+	6.49124i	−0.320189	+	0.554584i	0.660338	+	0.750969i	$0.270413\pi$
$138$		0			0
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	0.396812	+	0.917900i	$0.370116\pi$
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	−0.993331	+	0.115300i	$0.963217\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.992275	+	1.71867i	0.0829782	+	0.143722i
$144$		0			0
$145$	−1.52388	+	2.63943i	−0.126551	+	0.219193i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.08986	+	1.88769i	0.0892846	+	0.154645i	0.907209	−	0.420680i	$-0.138209\pi$
$149$	1.08986	+	1.88769i	0.0892846	+	0.154645i	−0.817924	+	0.575326i	$0.804875\pi$
$150$		0			0
$151$	7.01387	−	12.1484i	0.570781	−	0.988621i	−0.425705	−	0.904862i	$-0.639974\pi$
$151$	7.01387	−	12.1484i	0.570781	−	0.988621i	0.996486	−	0.0837595i	$-0.0266927\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.78231	+	8.28320i	0.384124	+	0.665322i
$156$		0			0
$157$	2.96623			0.236731			0.118365	−	0.992970i	$-0.462235\pi$
$157$	2.96623			0.236731			0.118365	+	0.992970i	$0.462235\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.19601	+	3.15675i	−0.488314	+	0.248787i
$162$		0			0
$163$	0.194278	−	0.336499i	0.0152170	−	0.0263566i	−0.858317	−	0.513120i	$-0.828489\pi$
$163$	0.194278	−	0.336499i	0.0152170	−	0.0263566i	0.873534	+	0.486764i	$0.161823\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.64889	−	6.32006i	0.282360	−	0.489061i	−0.689606	−	0.724185i	$-0.742216\pi$
$167$	3.64889	−	6.32006i	0.282360	−	0.489061i	0.971965	+	0.235124i	$0.0755496\pi$
$168$		0			0
$169$	5.42542	+	9.39710i	0.417340	+	0.722854i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.05508			0.308302			0.154151	−	0.988047i	$-0.450736\pi$
$173$	4.05508			0.308302			0.154151	+	0.988047i	$0.450736\pi$
$174$		0			0
$175$	7.83582	+	5.08903i	0.592332	+	0.384695i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.29243	+	9.16675i	0.395575	+	0.685155i	0.993174	−	0.116639i	$-0.0372121\pi$
$179$	5.29243	+	9.16675i	0.395575	+	0.685155i	−0.597600	+	0.801795i	$0.703879\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−31.7657			−2.33546
$186$		0			0
$187$	−4.48117			−0.327695
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.28714			0.599637			0.299818	−	0.953996i	$-0.403074\pi$
$191$	8.28714			0.599637			0.299818	+	0.953996i	$0.403074\pi$
$192$		0			0
$193$	−18.7848			−1.35216			−0.676082	−	0.736827i	$-0.736323\pi$
$193$	−18.7848			−1.35216			−0.676082	+	0.736827i	$0.736323\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.99634			−0.427222			−0.213611	−	0.976919i	$-0.568522\pi$
$197$	−5.99634			−0.427222			−0.213611	+	0.976919i	$0.568522\pi$
$198$		0			0
$199$	−7.20434	−	12.4783i	−0.510702	−	0.884562i	−0.999923	−	0.0124022i	$-0.996052\pi$
$199$	−7.20434	−	12.4783i	−0.510702	−	0.884562i	0.489221	−	0.872160i	$-0.337281\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.45983	+	1.25324i	−0.172646	+	0.0879601i
$204$		0			0
$205$	−5.28261			−0.368954
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.49354	−	2.58690i	−0.103311	−	0.178939i
$210$		0			0
$211$	6.92418	−	11.9930i	0.476680	−	0.825634i	−0.522963	−	0.852356i	$-0.675173\pi$
$211$	6.92418	−	11.9930i	0.476680	−	0.825634i	0.999643	+	0.0267212i	$0.00850663\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.34204	−	10.9847i	0.432523	−	0.749153i
$216$		0			0
$217$	−0.453726	+	8.65184i	−0.0308010	+	0.587325i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.85287			0.326439
$222$		0			0
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	0.777082	−	0.629399i	$-0.216699\pi$
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	−0.933617	+	0.358273i	$0.883366\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.85631	+	17.0716i	−0.654187	+	1.13308i	0.327910	+	0.944709i	$0.393656\pi$
$227$	−9.85631	+	17.0716i	−0.654187	+	1.13308i	−0.982097	+	0.188376i	$0.939678\pi$
$228$		0			0
$229$	−14.0364	−	24.3118i	−0.927552	−	1.60657i	−0.787404	−	0.616437i	$-0.788575\pi$
$229$	−14.0364	−	24.3118i	−0.927552	−	1.60657i	−0.140148	−	0.990131i	$-0.544758\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.90113	−	11.9531i	0.452108	−	0.783074i	−0.546409	−	0.837518i	$-0.684006\pi$
$233$	6.90113	−	11.9531i	0.452108	−	0.783074i	0.998517	+	0.0544448i	$0.0173389\pi$
$234$		0			0
$235$	−5.81127	−	10.0654i	−0.379085	−	0.656595i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5.53069	−	9.57944i	0.357751	−	0.619642i	−0.629834	−	0.776730i	$-0.716877\pi$
$239$	5.53069	−	9.57944i	0.357751	−	0.619642i	0.987585	+	0.157087i	$0.0502104\pi$
$240$		0			0
$241$	11.5849	−	20.0656i	0.746247	−	1.29254i	−0.203362	−	0.979104i	$-0.565187\pi$
$241$	11.5849	−	20.0656i	0.746247	−	1.29254i	0.949610	−	0.313435i	$-0.101480\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.31486	+	18.6790i	0.531217	+	1.19336i
$246$		0			0
$247$	1.61743	+	2.80147i	0.102915	+	0.178253i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.78402			−0.491323			−0.245662	−	0.969356i	$-0.579005\pi$
$251$	−7.78402			−0.491323			−0.245662	+	0.969356i	$0.579005\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.18798	+	8.98585i	0.323618	+	0.560522i	0.981232	−	0.192833i	$-0.0617676\pi$
$257$	5.18798	+	8.98585i	0.323618	+	0.560522i	−0.657614	+	0.753355i	$0.728434\pi$
$258$		0			0
$259$	−24.1311	−	15.6721i	−1.49944	−	0.973820i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.56654	−	16.5697i	0.589898	−	1.02173i	−0.404347	−	0.914605i	$-0.632501\pi$
$263$	9.56654	−	16.5697i	0.589898	−	1.02173i	0.994245	−	0.107128i	$-0.0341653\pi$
$264$		0			0
$265$	9.42689	−	16.3279i	0.579090	−	1.00301i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.41840	+	7.65290i	0.269395	+	0.466605i	0.968706	−	0.248212i	$-0.0798430\pi$
$269$	4.41840	+	7.65290i	0.269395	+	0.466605i	−0.699311	+	0.714818i	$0.746510\pi$
$270$		0			0
$271$	9.16955	−	15.8821i	0.557010	−	0.964770i	−0.440734	−	0.897638i	$-0.645282\pi$
$271$	9.16955	−	15.8821i	0.557010	−	0.964770i	0.997744	−	0.0671321i	$-0.0213849\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.39029	+	4.14011i	0.144140	+	0.249658i
$276$		0			0
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	−0.932460	−	0.361272i	$-0.882343\pi$
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	0.779101	+	0.626899i	$0.215676\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.853180	+	1.47775i	0.0508964	+	0.0881552i	0.890351	−	0.455274i	$-0.150459\pi$
$281$	0.853180	+	1.47775i	0.0508964	+	0.0881552i	−0.839455	+	0.543430i	$0.817125\pi$
$282$		0			0
$283$	12.4883			0.742352			0.371176	−	0.928562i	$-0.378955\pi$
$283$	12.4883			0.742352			0.371176	+	0.928562i	$0.378955\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.01299	−	2.60626i	−0.236879	−	0.153843i
$288$		0			0
$289$	3.02104	−	5.23260i	0.177708	−	0.307800i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.60202	−	4.50684i	0.152012	−	0.263292i	−0.779955	−	0.625835i	$-0.784758\pi$
$293$	2.60202	−	4.50684i	0.152012	−	0.263292i	0.931967	+	0.362543i	$0.118091\pi$
$294$		0			0
$295$	17.8377	+	30.8959i	1.03855	+	1.79883i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.85309			0.222830
$300$		0			0
$301$	10.2373	−	5.21571i	0.590067	−	0.300628i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.817453	−	1.41587i	−0.0468072	−	0.0810725i
$306$		0			0
$307$	−5.00136			−0.285442			−0.142721	−	0.989763i	$-0.545585\pi$
$307$	−5.00136			−0.285442			−0.142721	+	0.989763i	$0.545585\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−32.3968			−1.83706			−0.918528	−	0.395355i	$-0.870621\pi$
$311$	−32.3968			−1.83706			−0.918528	+	0.395355i	$0.870621\pi$
$312$		0			0
$313$	1.51907			0.0858629			0.0429315	−	0.999078i	$-0.486330\pi$
$313$	1.51907			0.0858629			0.0429315	+	0.999078i	$0.486330\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.5089			1.20806			0.604029	−	0.796962i	$-0.293561\pi$
$317$	21.5089			1.20806			0.604029	+	0.796962i	$0.293561\pi$
$318$		0			0
$319$	−1.41252			−0.0790860
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.30441			−0.406428
$324$		0			0
$325$	−2.58856	−	4.48352i	−0.143588	−	0.248701i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.551350	−	10.5134i	0.0303969	−	0.579621i
$330$		0			0
$331$	−19.4780			−1.07061			−0.535305	−	0.844659i	$-0.679803\pi$
$331$	−19.4780			−1.07061			−0.535305	+	0.844659i	$0.679803\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	18.7107	+	32.4079i	1.02228	+	1.77063i
$336$		0			0
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	−0.703260	−	0.710933i	$-0.748273\pi$
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	0.967316	+	0.253575i	$0.0816063\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.21642	+	3.83896i	−0.120026	+	0.207891i
$342$		0			0
$343$	−2.89912	+	18.2919i	−0.156538	+	0.987672i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.02604			0.108763			0.0543817	−	0.998520i	$-0.482681\pi$
$347$	2.02604			0.108763			0.0543817	+	0.998520i	$0.482681\pi$
$348$		0			0
$349$	8.14577	+	14.1089i	0.436033	+	0.755231i	0.997379	−	0.0723497i	$-0.0230498\pi$
$349$	8.14577	+	14.1089i	0.436033	+	0.755231i	−0.561346	+	0.827581i	$0.689716\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.53072	−	14.7756i	0.454045	−	0.786428i	−0.544588	−	0.838704i	$-0.683314\pi$
$353$	8.53072	−	14.7756i	0.454045	−	0.786428i	0.998633	+	0.0522753i	$0.0166473\pi$
$354$		0			0
$355$	−18.8655	−	32.6759i	−1.00127	−	1.73426i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.48363	−	2.56972i	0.0783030	−	0.135625i	−0.824215	−	0.566277i	$-0.808383\pi$
$359$	1.48363	−	2.56972i	0.0783030	−	0.135625i	0.902518	+	0.430652i	$0.141717\pi$
$360$		0			0
$361$	7.06549	+	12.2378i	0.371868	+	0.644094i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.2695	−	26.4475i	0.799240	−	1.38432i
$366$		0			0
$367$	−5.07874	+	8.79664i	−0.265108	+	0.459181i	−0.967592	−	0.252519i	$-0.918741\pi$
$367$	−5.07874	+	8.79664i	−0.265108	+	0.459181i	0.702484	+	0.711700i	$0.252074\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	15.2168	−	7.75270i	0.790019	−	0.402500i
$372$		0			0
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	0.980675	+	0.195645i	$0.0626799\pi$
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	−0.320904	+	0.947112i	$0.603987\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.52969			0.0787829
$378$		0			0
$379$	−9.85497			−0.506216			−0.253108	−	0.967438i	$-0.581453\pi$
$379$	−9.85497			−0.506216			−0.253108	+	0.967438i	$0.581453\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	13.6563	+	23.6535i	0.697806	+	1.20864i	0.969225	+	0.246175i	$0.0791737\pi$
$383$	13.6563	+	23.6535i	0.697806	+	1.20864i	−0.271419	+	0.962461i	$0.587493\pi$
$384$		0			0
$385$	−0.547870	+	10.4470i	−0.0279220	+	0.532428i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.09223	−	3.62385i	0.106080	−	0.183736i	−0.808099	−	0.589047i	$-0.799503\pi$
$389$	2.09223	−	3.62385i	0.106080	−	0.183736i	0.914179	+	0.405311i	$0.132837\pi$
$390$		0			0
$391$	−4.35019	+	7.53475i	−0.219999	+	0.381049i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.12114	+	1.94187i	0.0564107	+	0.0977062i
$396$		0			0
$397$	15.3354	−	26.5618i	0.769664	−	1.33310i	−0.168082	−	0.985773i	$-0.553757\pi$
$397$	15.3354	−	26.5618i	0.769664	−	1.33310i	0.937745	−	0.347323i	$-0.112909\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.42402	−	5.93057i	−0.170987	−	0.296158i	0.767778	−	0.640716i	$-0.221362\pi$
$401$	−3.42402	−	5.93057i	−0.170987	−	0.296158i	−0.938765	+	0.344557i	$0.888029\pi$
$402$		0			0
$403$	2.40027	−	4.15739i	0.119566	−	0.207095i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.36113	−	12.7499i	−0.364878	−	0.631987i
$408$		0			0
$409$	−18.2698			−0.903384			−0.451692	−	0.892174i	$-0.649179\pi$
$409$	−18.2698			−0.903384			−0.451692	+	0.892174i	$0.649179\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.69237	+	32.2709i	−0.0832763	+	1.58795i
$414$		0			0
$415$	−2.87328	+	4.97666i	−0.141044	+	0.244295i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.2310	−	19.4526i	0.548669	−	0.950322i	−0.449698	−	0.893181i	$-0.648468\pi$
$419$	11.2310	−	19.4526i	0.548669	−	0.950322i	0.998366	−	0.0571410i	$-0.0181984\pi$
$420$		0			0
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	0.999960	+	0.00894684i	$0.00284791\pi$
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	−0.492232	+	0.870464i	$0.663819\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	11.6901			0.567053
$426$		0			0
$427$	0.0775568	−	1.47888i	0.00375324	−	0.0715682i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.1213	−	17.5307i	−0.487527	−	0.844422i	0.512370	−	0.858765i	$-0.328768\pi$
$431$	−10.1213	−	17.5307i	−0.487527	−	0.844422i	−0.999897	+	0.0143427i	$0.995434\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.79956			−0.277431
$438$		0			0
$439$	35.4781			1.69328			0.846639	−	0.532168i	$-0.178623\pi$
$439$	35.4781			1.69328			0.846639	+	0.532168i	$0.178623\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.2063			−0.912517			−0.456258	−	0.889847i	$-0.650811\pi$
$443$	−19.2063			−0.912517			−0.456258	+	0.889847i	$0.650811\pi$
$444$		0			0
$445$	18.7143			0.887144
$446$		0			0
$447$		0			0
$448$		0			0
$449$	29.6082			1.39730			0.698648	−	0.715465i	$-0.253785\pi$
$449$	29.6082			1.39730			0.698648	+	0.715465i	$0.253785\pi$
$450$		0			0
$451$	−1.22415	−	2.12029i	−0.0576429	−	0.0998405i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.593314	−	11.3136i	0.0278150	−	0.530388i
$456$		0			0
$457$	−9.56196			−0.447290			−0.223645	−	0.974671i	$-0.571796\pi$
$457$	−9.56196			−0.447290			−0.223645	+	0.974671i	$0.571796\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.9187	−	18.9118i	−0.508536	−	0.880809i	−0.999951	−	0.00988416i	$-0.996854\pi$
$461$	−10.9187	−	18.9118i	−0.508536	−	0.880809i	0.491416	−	0.870925i	$-0.336480\pi$
$462$		0			0
$463$	−13.0744	+	22.6456i	−0.607621	+	1.05243i	0.384010	+	0.923329i	$0.374543\pi$
$463$	−13.0744	+	22.6456i	−0.607621	+	1.05243i	−0.991631	+	0.129102i	$0.958791\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.4764	+	30.2699i	−0.808709	+	1.40073i	0.105049	+	0.994467i	$0.466500\pi$
$467$	−17.4764	+	30.2699i	−0.808709	+	1.40073i	−0.913758	+	0.406258i	$0.866833\pi$
$468$		0			0
$469$	−1.77520	+	33.8502i	−0.0819711	+	1.56306i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.87861			0.270299
$474$		0			0
$475$	3.89623	+	6.74848i	0.178771	+	0.309641i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.9054	−	25.8170i	0.681047	−	1.17961i	−0.293615	−	0.955924i	$-0.594858\pi$
$479$	14.9054	−	25.8170i	0.681047	−	1.17961i	0.974662	−	0.223684i	$-0.0718083\pi$
$480$		0			0
$481$	7.97172	+	13.8074i	0.363479	+	0.629565i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−12.0965	+	20.9518i	−0.549276	+	0.951374i
$486$		0			0
$487$	11.2253	+	19.4428i	0.508667	+	0.881037i	0.999950	+	0.0100365i	$0.00319477\pi$
$487$	11.2253	+	19.4428i	0.508667	+	0.881037i	−0.491283	+	0.871000i	$0.663472\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.5222	−	30.3494i	0.790767	−	1.36965i	−0.134726	−	0.990883i	$-0.543016\pi$
$491$	17.5222	−	30.3494i	0.790767	−	1.36965i	0.925493	−	0.378765i	$-0.123651\pi$
$492$		0			0
$493$	−1.72704	+	2.99132i	−0.0777819	+	0.134722i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.78988	−	34.1302i	0.0802871	−	1.53095i
$498$		0			0
$499$	−4.46760	−	7.73811i	−0.199997	−	0.346405i	0.748530	−	0.663101i	$-0.230760\pi$
$499$	−4.46760	−	7.73811i	−0.199997	−	0.346405i	−0.948527	+	0.316696i	$0.897427\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.6403			−0.563603			−0.281802	−	0.959473i	$-0.590932\pi$
$503$	−12.6403			−0.563603			−0.281802	+	0.959473i	$0.590932\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.0555	−	24.3449i	−0.623000	−	1.07907i	−0.988924	−	0.148423i	$-0.952580\pi$
$509$	−14.0555	−	24.3449i	−0.623000	−	1.07907i	0.365924	−	0.930645i	$-0.380753\pi$
$510$		0			0
$511$	24.6479	−	12.5576i	1.09036	−	0.555517i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.25214	+	5.63287i	−0.143306	+	0.248214i
$516$		0			0
$517$	2.69331	−	4.66495i	0.118452	−	0.205164i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.23768	−	7.33988i	−0.185656	−	0.321566i	0.758141	−	0.652090i	$-0.226108\pi$
$521$	−4.23768	−	7.33988i	−0.185656	−	0.321566i	−0.943797	+	0.330524i	$0.892774\pi$
$522$		0			0
$523$	−16.7236	+	28.9662i	−0.731273	+	1.26660i	0.225066	+	0.974344i	$0.427740\pi$
$523$	−16.7236	+	28.9662i	−0.731273	+	1.26660i	−0.956339	+	0.292259i	$0.905593\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.41988	+	9.38751i	0.236094	+	0.408926i
$528$		0			0
$529$	8.04603	−	13.9361i	0.349827	−	0.605919i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.32569	+	2.29616i	0.0574220	+	0.0994579i
$534$		0			0
$535$	51.1387			2.21092
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.57039	+	7.66586i	−0.239934	+	0.330192i
$540$		0			0
$541$	−9.12929	+	15.8124i	−0.392499	+	0.679828i	−0.992778	−	0.119962i	$-0.961723\pi$
$541$	−9.12929	+	15.8124i	−0.392499	+	0.679828i	0.600280	+	0.799790i	$0.295056\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−22.7803	+	39.4567i	−0.975802	+	1.69014i
$546$		0			0
$547$	2.88599	+	4.99869i	0.123396	+	0.213728i	0.921105	−	0.389315i	$-0.127288\pi$
$547$	2.88599	+	4.99869i	0.123396	+	0.213728i	−0.797709	+	0.603043i	$0.793955\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.30244			−0.0980874
$552$		0			0
$553$	−0.106369	+	2.02829i	−0.00452329	+	0.0862518i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.6911	−	28.9098i	−0.707223	−	1.22495i	−0.965883	−	0.258977i	$-0.916614\pi$
$557$	−16.6911	−	28.9098i	−0.707223	−	1.22495i	0.258661	−	0.965968i	$-0.416719\pi$
$558$		0			0
$559$	−6.36623			−0.269263
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.19131			0.0923528			0.0461764	−	0.998933i	$-0.485296\pi$
$563$	2.19131			0.0923528			0.0461764	+	0.998933i	$0.485296\pi$
$564$		0			0
$565$	−4.93367			−0.207561
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.9860			−0.795936			−0.397968	−	0.917399i	$-0.630284\pi$
$569$	−18.9860			−0.795936			−0.397968	+	0.917399i	$0.630284\pi$
$570$		0			0
$571$	21.7380			0.909709			0.454854	−	0.890566i	$-0.349691\pi$
$571$	21.7380			0.909709			0.454854	+	0.890566i	$0.349691\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.28172			0.387074
$576$		0			0
$577$	−15.4516	−	26.7629i	−0.643258	−	1.11416i	−0.984701	−	0.174253i	$-0.944249\pi$
$577$	−15.4516	−	26.7629i	−0.643258	−	1.11416i	0.341443	−	0.939903i	$-0.389084\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.63803	+	2.36299i	−0.192418	+	0.0980333i
$582$		0			0
$583$	8.73804			0.361893
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.18332	−	15.9060i	−0.379036	−	0.656510i	0.611886	−	0.790946i	$-0.290411\pi$
$587$	−9.18332	−	15.9060i	−0.379036	−	0.656510i	−0.990922	+	0.134436i	$0.957078\pi$
$588$		0			0
$589$	−3.61282	+	6.25759i	−0.148864	+	0.257840i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.8775	+	24.0365i	−0.569880	+	0.987061i	0.426698	+	0.904394i	$0.359677\pi$
$593$	−13.8775	+	24.0365i	−0.569880	+	0.987061i	−0.996577	+	0.0826662i	$0.973656\pi$
$594$		0			0
$595$	21.4539	+	13.9334i	0.879524	+	0.571213i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.402823			0.0164589			0.00822945	−	0.999966i	$-0.497380\pi$
$599$	0.402823			0.0164589			0.00822945	+	0.999966i	$0.497380\pi$
$600$		0			0
$601$	12.3733	+	21.4312i	0.504717	+	0.874196i	0.999985	+	0.00545577i	$0.00173663\pi$
$601$	12.3733	+	21.4312i	0.504717	+	0.874196i	−0.495268	+	0.868740i	$0.664930\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	13.3885	−	23.1895i	0.544318	−	0.942787i
$606$		0			0
$607$	12.0348	+	20.8449i	0.488479	+	0.846070i	0.999912	−	0.0132531i	$-0.00421872\pi$
$607$	12.0348	+	20.8449i	0.488479	+	0.846070i	−0.511434	+	0.859323i	$0.670885\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.91672	+	5.05190i	−0.117998	+	0.204378i
$612$		0			0
$613$	10.1907	+	17.6509i	0.411600	+	0.712912i	0.995065	−	0.0992261i	$-0.0316367\pi$
$613$	10.1907	+	17.6509i	0.411600	+	0.712912i	−0.583465	+	0.812138i	$0.698303\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.9315	−	36.2544i	0.842669	−	1.45955i	−0.0449604	−	0.998989i	$-0.514316\pi$
$617$	20.9315	−	36.2544i	0.842669	−	1.45955i	0.887630	−	0.460558i	$-0.152350\pi$
$618$		0			0
$619$	7.41095	−	12.8361i	0.297871	−	0.515928i	−0.677777	−	0.735267i	$-0.737057\pi$
$619$	7.41095	−	12.8361i	0.297871	−	0.515928i	0.975649	+	0.219339i	$0.0703900\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.2165	+	9.23301i	0.569572	+	0.369913i
$624$		0			0
$625$	15.0930	+	26.1419i	0.603722	+	1.04568i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−36.0007			−1.43544
$630$		0			0
$631$	21.0294			0.837169			0.418585	−	0.908178i	$-0.362526\pi$
$631$	21.0294			0.837169			0.418585	+	0.908178i	$0.362526\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.79673	−	10.0402i	−0.230036	−	0.398434i
$636$		0			0
$637$	6.03244	−	8.30173i	0.239014	−	0.328926i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.96592	−	10.3333i	0.235640	−	0.408140i	−0.723819	−	0.689990i	$-0.757615\pi$
$641$	5.96592	−	10.3333i	0.235640	−	0.408140i	0.959458	+	0.281850i	$0.0909481\pi$
$642$		0			0
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	−0.140072	−	0.990141i	$-0.544733\pi$
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	0.927524	−	0.373765i	$-0.121933\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.494477	+	0.856459i	0.0194399	+	0.0336709i	0.875582	−	0.483070i	$-0.160478\pi$
$647$	0.494477	+	0.856459i	0.0194399	+	0.0336709i	−0.856142	+	0.516741i	$0.827145\pi$
$648$		0			0
$649$	−8.26714	+	14.3191i	−0.324514	+	0.562074i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.3573	+	19.6715i	0.444447	+	0.769804i	0.998014	−	0.0630004i	$-0.0200669\pi$
$653$	11.3573	+	19.6715i	0.444447	+	0.769804i	−0.553567	+	0.832805i	$0.686734\pi$
$654$		0			0
$655$	−7.78211	+	13.4790i	−0.304072	+	0.526668i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.1943	−	33.2454i	−0.747702	−	1.29506i	−0.948922	−	0.315512i	$-0.897824\pi$
$659$	−19.1943	−	33.2454i	−0.747702	−	1.29506i	0.201220	−	0.979546i	$-0.435509\pi$
$660$		0			0
$661$	33.9258			1.31956			0.659780	−	0.751459i	$-0.270649\pi$
$661$	33.9258			1.31956			0.659780	+	0.751459i	$0.270649\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.893040	+	17.0288i	−0.0346306	+	0.660350i
$666$		0			0
$667$	−1.37124	+	2.37505i	−0.0530944	+	0.0919623i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.378860	−	0.656205i	0.0146257	−	0.0253325i
$672$		0			0
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	−0.989351	−	0.145549i	$-0.953505\pi$
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	0.368626	−	0.929578i	$-0.379828\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	37.9684			1.45924			0.729622	−	0.683850i	$-0.239696\pi$
$677$	37.9684			1.45924			0.729622	+	0.683850i	$0.239696\pi$
$678$		0			0
$679$	−19.5262	+	9.94823i	−0.749346	+	0.381778i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.59357	+	13.1525i	0.290560	+	0.503265i	0.973942	−	0.226796i	$-0.0728251\pi$
$683$	7.59357	+	13.1525i	0.290560	+	0.503265i	−0.683382	+	0.730061i	$0.739492\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.46285			−0.360506
$690$		0			0
$691$	−2.69148			−0.102389			−0.0511943	−	0.998689i	$-0.516303\pi$
$691$	−2.69148			−0.102389			−0.0511943	+	0.998689i	$0.516303\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	41.0840			1.55841
$696$		0			0
$697$	−5.98689			−0.226770
$698$		0			0
$699$		0			0
$700$		0			0
$701$	11.8515			0.447625			0.223813	−	0.974632i	$-0.428150\pi$
$701$	11.8515			0.447625			0.223813	+	0.974632i	$0.428150\pi$
$702$		0			0
$703$	−11.9988	−	20.7826i	−0.452544	−	0.783829i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	36.0047	+	23.3835i	1.35410	+	0.879427i
$708$		0			0
$709$	−41.0333			−1.54104			−0.770520	−	0.637416i	$-0.780003\pi$
$709$	−41.0333			−1.54104			−0.770520	+	0.637416i	$0.780003\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.30328	+	7.45351i	0.161159	+	0.279136i
$714$		0			0
$715$	2.89830	−	5.02001i	0.108390	−	0.187738i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.4555	−	18.1094i	0.389923	−	0.675366i	−0.602516	−	0.798107i	$-0.705835\pi$
$719$	10.4555	−	18.1094i	0.389923	−	0.675366i	0.992439	+	0.122741i	$0.0391685\pi$
$720$		0			0
$721$	−5.24958	+	2.67457i	−0.195505	+	0.0996060i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.68487			0.136853
$726$		0			0
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	0.840476	−	0.541849i	$-0.182276\pi$
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	−0.889493	+	0.456949i	$0.848942\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.18756	−	12.4492i	0.265841	−	0.460451i
$732$		0			0
$733$	−7.07446	−	12.2533i	−0.261301	−	0.452587i	0.705287	−	0.708922i	$-0.250818\pi$
$733$	−7.07446	−	12.2533i	−0.261301	−	0.452587i	−0.966588	+	0.256335i	$0.917485\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.67174	+	15.0199i	−0.319428	+	0.553265i
$738$		0			0
$739$	7.85905	+	13.6123i	0.289100	+	0.500736i	0.973595	−	0.228282i	$-0.0733107\pi$
$739$	7.85905	+	13.6123i	0.289100	+	0.500736i	−0.684495	+	0.729017i	$0.739977\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.5496	−	18.2724i	0.387026	−	0.670348i	−0.605022	−	0.796208i	$-0.706836\pi$
$743$	10.5496	−	18.2724i	0.387026	−	0.670348i	0.992048	+	0.125861i	$0.0401692\pi$
$744$		0			0
$745$	3.18333	−	5.51368i	0.116628	−	0.202006i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	38.8480	+	25.2301i	1.41947	+	0.921888i
$750$		0			0
$751$	6.51848	+	11.2903i	0.237863	+	0.411990i	0.960101	−	0.279654i	$-0.0902199\pi$
$751$	6.51848	+	11.2903i	0.237863	+	0.411990i	−0.722238	+	0.691644i	$0.756887\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−40.9732			−1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.02038	−	5.23146i	−0.109489	−	0.189640i	0.806074	−	0.591814i	$-0.201588\pi$
$761$	−3.02038	−	5.23146i	−0.109489	−	0.189640i	−0.915563	+	0.402174i	$0.868255\pi$
$762$		0			0
$763$	−36.7719	+	18.7346i	−1.33123	+	0.678238i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.95288	−	15.5068i	0.323270	−	0.559920i
$768$		0			0
$769$	0.108129	−	0.187285i	0.00389924	−	0.00675368i	−0.864069	−	0.503373i	$-0.832092\pi$
$769$	0.108129	−	0.187285i	0.00389924	−	0.00675368i	0.867968	+	0.496619i	$0.165425\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.8132	−	32.5854i	−0.676663	−	1.17202i	−0.975980	−	0.217861i	$-0.930092\pi$
$773$	−18.8132	−	32.5854i	−0.676663	−	1.17202i	0.299316	−	0.954154i	$-0.403241\pi$
$774$		0			0
$775$	5.78202	−	10.0148i	0.207696	−	0.359741i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.99539	−	3.45612i	−0.0714923	−	0.123828i
$780$		0			0
$781$	8.74345	−	15.1441i	0.312865	−	0.541898i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.33198	−	7.50321i	−0.154615	−	0.267801i
$786$		0			0
$787$	−30.8135			−1.09838			−0.549191	−	0.835697i	$-0.685064\pi$
$787$	−30.8135			−1.09838			−0.549191	+	0.835697i	$0.685064\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.74791	−	2.43410i	−0.133260	−	0.0865468i
$792$		0			0
$793$	−0.410286	+	0.710636i	−0.0145697	+	0.0252354i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.9792	−	31.1408i	0.636855	−	1.10306i	−0.349264	−	0.937024i	$-0.613569\pi$
$797$	17.9792	−	31.1408i	0.636855	−	1.10306i	0.986119	−	0.166040i	$-0.0530981\pi$
$798$		0			0
$799$	−6.58602	−	11.4073i	−0.232997	−	0.403562i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	14.1537			0.499472
$804$		0			0
$805$	17.0340	+	11.0628i	0.600369	+	0.389914i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.4818	+	33.7435i	0.684943	+	1.18636i	0.973455	+	0.228880i	$0.0735065\pi$
$809$	19.4818	+	33.7435i	0.684943	+	1.18636i	−0.288511	+	0.957477i	$0.593160\pi$
$810$		0			0
$811$	28.2811			0.993082			0.496541	−	0.868013i	$-0.334603\pi$
$811$	28.2811			0.993082			0.496541	+	0.868013i	$0.334603\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.13492			−0.0397544
$816$		0			0
$817$	9.58227			0.335241
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−41.5834			−1.45127			−0.725635	−	0.688080i	$-0.758454\pi$
$821$	−41.5834			−1.45127			−0.725635	+	0.688080i	$0.758454\pi$
$822$		0			0
$823$	−8.45998			−0.294896			−0.147448	−	0.989070i	$-0.547106\pi$
$823$	−8.45998			−0.294896			−0.147448	+	0.989070i	$0.547106\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	44.2823			1.53985			0.769923	−	0.638137i	$-0.220294\pi$
$827$	44.2823			1.53985			0.769923	+	0.638137i	$0.220294\pi$
$828$		0			0
$829$	−8.31637	−	14.4044i	−0.288839	−	0.500284i	0.684694	−	0.728831i	$-0.259936\pi$
$829$	−8.31637	−	14.4044i	−0.288839	−	0.500284i	−0.973533	+	0.228547i	$0.926603\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.42339	+	21.1693i	0.326501	+	0.733471i
$834$		0			0
$835$	−21.3158			−0.737665
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.8006	+	25.6354i	0.510974	+	0.885033i	0.999919	+	0.0127182i	$0.00404843\pi$
$839$	14.8006	+	25.6354i	0.510974	+	0.885033i	−0.488945	+	0.872314i	$0.662618\pi$
$840$		0			0
$841$	13.9556	−	24.1718i	0.481228	−	0.833512i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	15.8469	−	27.4477i	0.545151	−	0.944228i
$846$		0			0
$847$	21.6116	−	11.0107i	0.742583	−	0.378332i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−28.5839			−0.979844
$852$		0			0
$853$	−15.0619	−	26.0880i	−0.515710	−	0.893236i	−0.999834	−	0.0182366i	$-0.994195\pi$
$853$	−15.0619	−	26.0880i	−0.515710	−	0.893236i	0.484124	−	0.875000i	$-0.339139\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	18.5447	−	32.1204i	0.633475	−	1.09721i	−0.353361	−	0.935487i	$-0.614961\pi$
$857$	18.5447	−	32.1204i	0.633475	−	1.09721i	0.986836	−	0.161724i	$-0.0517053\pi$
$858$		0			0
$859$	−1.89166	−	3.27646i	−0.0645427	−	0.111791i	0.831948	−	0.554853i	$-0.187226\pi$
$859$	−1.89166	−	3.27646i	−0.0645427	−	0.111791i	−0.896491	+	0.443062i	$0.853892\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.213559	−	0.369895i	0.00726963	−	0.0125914i	−0.862368	−	0.506282i	$-0.831019\pi$
$863$	0.213559	−	0.369895i	0.00726963	−	0.0125914i	0.869637	+	0.493691i	$0.164353\pi$
$864$		0			0
$865$	−5.92218	−	10.2575i	−0.201360	−	0.348766i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.519608	+	0.899987i	−0.0176265	+	0.0305300i
$870$		0			0
$871$	9.39105	−	16.2658i	0.318203	−	0.551145i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.594342	+	11.3332i	−0.0200924	+	0.383130i
$876$		0			0
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	0.755167	−	0.655532i	$-0.227556\pi$
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	−0.945291	+	0.326228i	$0.894222\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	35.4810			1.19538			0.597692	−	0.801726i	$-0.296084\pi$
$881$	35.4810			1.19538			0.597692	+	0.801726i	$0.296084\pi$
$882$		0			0
$883$	5.30092			0.178390			0.0891952	−	0.996014i	$-0.471571\pi$
$883$	5.30092			0.178390			0.0891952	+	0.996014i	$0.471571\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−28.7832	−	49.8540i	−0.966446	−	1.67393i	−0.705679	−	0.708532i	$-0.749358\pi$
$887$	−28.7832	−	49.8540i	−0.966446	−	1.67393i	−0.260767	−	0.965402i	$-0.583975\pi$
$888$		0			0
$889$	0.549971	−	10.4871i	0.0184454	−	0.351725i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.39016	−	7.60398i	0.146911	−	0.254458i
$894$		0			0
$895$	15.4585	−	26.7749i	0.516720	−	0.894985i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.70842	+	2.95906i	0.0569788	+	0.0986903i
$900$		0			0
$901$	10.6837	−	18.5047i	0.355925	−	0.616480i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	28.6700	+	49.6579i	0.953023	+	1.65068i
$906$		0			0
$907$	10.4486	−	18.0975i	0.346939	−	0.600917i	−0.638765	−	0.769402i	$-0.720554\pi$
$907$	10.4486	−	18.0975i	0.346939	−	0.600917i	0.985704	+	0.168485i	$0.0538876\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.3819	+	19.7141i	0.377101	+	0.653157i	0.990639	−	0.136508i	$-0.0435878\pi$
$911$	11.3819	+	19.7141i	0.377101	+	0.653157i	−0.613539	+	0.789665i	$0.710254\pi$
$912$		0			0
$913$	−2.66332			−0.0881430
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.5618	+	6.40002i	−0.414828	+	0.211347i
$918$		0			0
$919$	−18.6515	+	32.3054i	−0.615257	+	1.06566i	0.375083	+	0.926991i	$0.377614\pi$
$919$	−18.6515	+	32.3054i	−0.615257	+	1.06566i	−0.990339	+	0.138664i	$0.955719\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.46870	+	16.4003i	−0.311666	+	0.539822i
$924$		0			0
$925$	19.2031	+	33.2607i	0.631394	+	1.09361i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.66725			−0.185937			−0.0929683	−	0.995669i	$-0.529636\pi$
$929$	−5.66725			−0.185937			−0.0929683	+	0.995669i	$0.529636\pi$
$930$		0			0
$931$	−9.07987	+	12.4955i	−0.297581	+	0.409524i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.54444	+	11.3353i	0.214026	+	0.370704i
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−20.4552			−0.666819			−0.333410	−	0.942782i	$-0.608199\pi$
$941$	−20.4552			−0.666819			−0.333410	+	0.942782i	$0.608199\pi$
$942$		0			0
$943$	−4.75348			−0.154795
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.76687			−0.154902			−0.0774512	−	0.996996i	$-0.524678\pi$
$947$	−4.76687			−0.154902			−0.0774512	+	0.996996i	$0.524678\pi$
$948$		0			0
$949$	−15.3277			−0.497558
$950$		0			0
$951$		0			0
$952$		0			0
$953$	48.9412			1.58536			0.792680	−	0.609638i	$-0.208685\pi$
$953$	48.9412			1.58536			0.792680	+	0.609638i	$0.208685\pi$
$954$		0			0
$955$	−12.1028	−	20.9627i	−0.391638	−	0.678337i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.6313	+	10.8013i	0.537054	+	0.348794i
$960$		0			0
$961$	−20.2771			−0.654101
$962$		0			0
$963$		0			0
$964$		0			0
$965$	27.4340	+	47.5171i	0.883132	+	1.52963i
$966$		0			0
$967$	2.95856	−	5.12438i	0.0951409	−	0.164789i	−0.814526	−	0.580126i	$-0.803003\pi$
$967$	2.95856	−	5.12438i	0.0951409	−	0.164789i	0.909667	+	0.415337i	$0.136336\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.4888	−	25.0953i	0.464966	−	0.805345i	−0.534234	−	0.845337i	$-0.679400\pi$
$971$	14.4888	−	25.0953i	0.464966	−	0.805345i	0.999200	+	0.0399914i	$0.0127331\pi$
$972$		0			0
$973$	31.2099	+	20.2695i	1.00054	+	0.649809i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.8455			−0.730893			−0.365447	−	0.930832i	$-0.619084\pi$
$977$	−22.8455			−0.730893			−0.365447	+	0.930832i	$0.619084\pi$
$978$		0			0
$979$	4.33670	+	7.51139i	0.138602	+	0.240065i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	15.6351	−	27.0809i	0.498684	−	0.863745i	−0.501315	−	0.865265i	$-0.667150\pi$
$983$	15.6351	−	27.0809i	0.498684	−	0.863745i	0.999999	+	0.00151933i	$0.000483619\pi$
$984$		0			0
$985$	8.75726	+	15.1680i	0.279029	+	0.483293i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.70679	−	9.88444i	0.181465	−	0.314307i
$990$		0			0
$991$	−3.50732	−	6.07485i	−0.111414	−	0.192974i	0.804927	−	0.593374i	$-0.202204\pi$
$991$	−3.50732	−	6.07485i	−0.111414	−	0.192974i	−0.916340	+	0.400400i	$0.868871\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−21.0429	+	36.4474i	−0.667105	+	1.15546i
$996$		0			0
$997$	10.6439	−	18.4358i	0.337095	−	0.583866i	−0.646790	−	0.762668i	$-0.723889\pi$
$997$	10.6439	−	18.4358i	0.337095	−	0.583866i	0.983885	+	0.178802i	$0.0572222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.i.2305.2		10
3.2	odd	2		1008.2.q.i.625.4		10
4.3	odd	2		189.2.h.b.37.5		10
7.4	even	3		3024.2.t.i.1873.4		10
9.2	odd	6		1008.2.t.i.961.3		10
9.7	even	3		3024.2.t.i.289.4		10
12.11	even	2		63.2.h.b.58.1	yes	10
21.11	odd	6		1008.2.t.i.193.3		10
28.3	even	6		1323.2.g.f.361.1		10
28.11	odd	6		189.2.g.b.172.1		10
28.19	even	6		1323.2.f.f.442.1		10
28.23	odd	6		1323.2.f.e.442.1		10
28.27	even	2		1323.2.h.f.226.5		10
36.7	odd	6		189.2.g.b.100.1		10
36.11	even	6		63.2.g.b.16.5	yes	10
36.23	even	6		567.2.e.f.163.5		10
36.31	odd	6		567.2.e.e.163.1		10
63.11	odd	6		1008.2.q.i.529.4		10
63.25	even	3	inner	3024.2.q.i.2881.2		10
84.11	even	6		63.2.g.b.4.5	✓	10
84.23	even	6		441.2.f.e.148.5		10
84.47	odd	6		441.2.f.f.148.5		10
84.59	odd	6		441.2.g.f.67.5		10
84.83	odd	2		441.2.h.f.373.1		10
252.11	even	6		63.2.h.b.25.1	yes	10
252.23	even	6		3969.2.a.z.1.1		5
252.47	odd	6		441.2.f.f.295.5		10
252.67	odd	6		567.2.e.e.487.1		10
252.79	odd	6		1323.2.f.e.883.1		10
252.83	odd	6		441.2.g.f.79.5		10
252.95	even	6		567.2.e.f.487.5		10
252.103	even	6		3969.2.a.bb.1.5		5
252.115	even	6		1323.2.h.f.802.5		10
252.131	odd	6		3969.2.a.ba.1.1		5
252.151	odd	6		189.2.h.b.46.5		10
252.187	even	6		1323.2.f.f.883.1		10
252.191	even	6		441.2.f.e.295.5		10
252.223	even	6		1323.2.g.f.667.1		10
252.227	odd	6		441.2.h.f.214.1		10
252.247	odd	6		3969.2.a.bc.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	84.11	even	6
63.2.g.b.16.5	yes	10	36.11	even	6
63.2.h.b.25.1	yes	10	252.11	even	6
63.2.h.b.58.1	yes	10	12.11	even	2
189.2.g.b.100.1		10	36.7	odd	6
189.2.g.b.172.1		10	28.11	odd	6
189.2.h.b.37.5		10	4.3	odd	2
189.2.h.b.46.5		10	252.151	odd	6
441.2.f.e.148.5		10	84.23	even	6
441.2.f.e.295.5		10	252.191	even	6
441.2.f.f.148.5		10	84.47	odd	6
441.2.f.f.295.5		10	252.47	odd	6
441.2.g.f.67.5		10	84.59	odd	6
441.2.g.f.79.5		10	252.83	odd	6
441.2.h.f.214.1		10	252.227	odd	6
441.2.h.f.373.1		10	84.83	odd	2
567.2.e.e.163.1		10	36.31	odd	6
567.2.e.e.487.1		10	252.67	odd	6
567.2.e.f.163.5		10	36.23	even	6
567.2.e.f.487.5		10	252.95	even	6
1008.2.q.i.529.4		10	63.11	odd	6
1008.2.q.i.625.4		10	3.2	odd	2
1008.2.t.i.193.3		10	21.11	odd	6
1008.2.t.i.961.3		10	9.2	odd	6
1323.2.f.e.442.1		10	28.23	odd	6
1323.2.f.e.883.1		10	252.79	odd	6
1323.2.f.f.442.1		10	28.19	even	6
1323.2.f.f.883.1		10	252.187	even	6
1323.2.g.f.361.1		10	28.3	even	6
1323.2.g.f.667.1		10	252.223	even	6
1323.2.h.f.226.5		10	28.27	even	2
1323.2.h.f.802.5		10	252.115	even	6
3024.2.q.i.2305.2		10	1.1	even	1	trivial
3024.2.q.i.2881.2		10	63.25	even	3	inner
3024.2.t.i.289.4		10	9.7	even	3
3024.2.t.i.1873.4		10	7.4	even	3
3969.2.a.z.1.1		5	252.23	even	6
3969.2.a.ba.1.1		5	252.131	odd	6
3969.2.a.bb.1.5		5	252.103	even	6
3969.2.a.bc.1.5		5	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)

\(f(q)\)	\(=\)	\(q+(-1.46043 - 2.52954i) q^{5} +(0.138560 - 2.64212i) q^{7} +O(q^{10})\)	\(q+(-1.46043 - 2.52954i) q^{5} +(0.138560 - 2.64212i) q^{7} +(0.676857 - 1.17235i) q^{11} +(-0.733001 + 1.26960i) q^{13} +(-1.65514 - 2.86678i) q^{17} +(1.10329 - 1.91096i) q^{19} +(-1.31415 - 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +(-0.521720 - 0.903646i) q^{29} -3.27458 q^{31} +(-6.88572 + 3.50815i) q^{35} +(5.43773 - 9.41842i) q^{37} +(0.904289 - 1.56627i) q^{41} +(2.17129 + 3.76078i) q^{43} +3.97914 q^{47} +(-6.96160 - 0.732185i) q^{49} +(3.22743 + 5.59008i) q^{53} -3.95402 q^{55} -12.2140 q^{59} +0.559734 q^{61} +4.28200 q^{65} -12.8118 q^{67} +12.9177 q^{71} +(5.22772 + 9.05467i) q^{73} +(-3.00371 - 1.95078i) q^{77} -0.767677 q^{79} +(-0.983707 - 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(-3.20356 + 5.54872i) q^{89} +(3.25286 + 2.11259i) q^{91} -6.44514 q^{95} +(-4.14143 - 7.17316i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 10 * q - 4 * q^5 + 4 * q^7	\( 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

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