LMFDB - Embedded newform 3024.2.t.i.1873.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(289,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.289"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [10,0,0,0,8,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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:	$\Z[a_1, \ldots, a_{13}]$
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			1873.4
Root			$1.19343 + 2.06709i$ of defining polynomial
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.i.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.92087 q^{5} +(-2.35742 - 1.20106i) q^{7} -1.35371 q^{11} +(-0.733001 + 1.26960i) q^{13} +(-1.65514 + 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +2.62830 q^{23} +3.53146 q^{25} +(-0.521720 - 0.903646i) q^{29} +(1.63729 + 2.83587i) q^{31} +(-6.88572 - 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(0.904289 - 1.56627i) q^{41} +(2.17129 + 3.76078i) q^{43} +(-1.98957 + 3.44604i) q^{47} +(4.11489 + 5.66283i) q^{49} +(3.22743 - 5.59008i) q^{53} -3.95402 q^{55} +(6.10700 + 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +(-2.14100 + 3.70832i) q^{65} +(6.40588 + 11.0953i) q^{67} +12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(3.19128 + 1.62590i) q^{77} +(0.383838 - 0.664827i) q^{79} +(-0.983707 - 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(-3.20356 - 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} +(3.22257 + 5.58166i) q^{95} +(-4.14143 - 7.17316i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59}+ \cdots - 12 q^{97}+O(q^{100}) $ 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	2.92087			1.30625			0.653125	−	0.757250i	$-0.273457\pi$
$5$	2.92087			1.30625			0.653125	+	0.757250i	$0.273457\pi$
$6$		0			0
$7$	−2.35742	−	1.20106i	−0.891022	−	0.453959i
$7$	−2.35742	−	1.20106i	−0.891022	−	0.453959i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.35371			−0.408160			−0.204080	−	0.978954i	$-0.565420\pi$
$11$	−1.35371			−0.408160			−0.204080	+	0.978954i	$0.565420\pi$
$12$		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	−0.993899	−	0.110297i	$-0.964820\pi$
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	0.592469	+	0.805593i	$0.298153\pi$
$18$		0			0
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	0.964381	−	0.264516i	$-0.0852123\pi$
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	−0.711268	+	0.702921i	$0.751879\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.62830			0.548038			0.274019	−	0.961724i	$-0.411647\pi$
$23$	2.62830			0.548038			0.274019	+	0.961724i	$0.411647\pi$
$24$		0			0
$25$	3.53146			0.706292
$26$		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
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	0.974767	−	0.223224i	$-0.0716581\pi$
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	−0.680701	+	0.732561i	$0.738325\pi$
$32$		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	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$		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
$47$	−1.98957	+	3.44604i	−0.290209	+	0.502656i	−0.973859	−	0.227154i	$-0.927058\pi$
$47$	−1.98957	+	3.44604i	−0.290209	+	0.502656i	0.683650	+	0.729810i	$0.260391\pi$
$48$		0			0
$49$	4.11489	+	5.66283i	0.587842	+	0.808976i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.22743	−	5.59008i	0.443322	−	0.767856i	−0.554612	−	0.832109i	$-0.687133\pi$
$53$	3.22743	−	5.59008i	0.443322	−	0.767856i	0.997934	+	0.0642533i	$0.0204666\pi$
$54$		0			0
$55$	−3.95402			−0.533160
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.10700	+	10.5776i	0.795064	+	1.37709i	0.922799	+	0.385283i	$0.125896\pi$
$59$	6.10700	+	10.5776i	0.795064	+	1.37709i	−0.127735	+	0.991808i	$0.540771\pi$
$60$		0			0
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	−0.883386	−	0.468646i	$-0.844742\pi$
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	0.847553	+	0.530711i	$0.178075\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.14100	+	3.70832i	−0.265558	+	0.459960i
$66$		0			0
$67$	6.40588	+	11.0953i	0.782603	+	1.35551i	0.930420	+	0.366494i	$0.119442\pi$
$67$	6.40588	+	11.0953i	0.782603	+	1.35551i	−0.147817	+	0.989015i	$0.547225\pi$
$68$		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	−0.379069	−	0.925368i	$-0.623756\pi$
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	0.990927	−	0.134401i	$-0.0429109\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.19128	+	1.62590i	0.363680	+	0.185288i
$78$		0			0
$79$	0.383838	−	0.664827i	0.0431852	−	0.0747989i	−0.843625	−	0.536933i	$-0.819583\pi$
$79$	0.383838	−	0.664827i	0.0431852	−	0.0747989i	0.886810	+	0.462134i	$0.152916\pi$
$80$		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	0.644777	−	0.764371i	$-0.276950\pi$
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	−0.984353	+	0.176208i	$0.943617\pi$
$90$		0			0
$91$	3.25286	−	2.11259i	0.340992	−	0.221460i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.22257	+	5.58166i	0.330629	+	0.572666i
$96$		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
$101$	16.2266			1.61461			0.807305	−	0.590134i	$-0.200925\pi$
$101$	16.2266			1.61461			0.807305	+	0.590134i	$0.200925\pi$
$102$		0			0
$103$	2.22683			0.219416			0.109708	−	0.993964i	$-0.465008\pi$
$103$	2.22683			0.219416			0.109708	+	0.993964i	$0.465008\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.75403	−	15.1624i	−0.846284	−	1.46581i	−0.884501	−	0.466537i	$-0.845501\pi$
$107$	−8.75403	−	15.1624i	−0.846284	−	1.46581i	0.0382175	−	0.999269i	$-0.487832\pi$
$108$		0			0
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$		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
$115$	7.67690			0.715875
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.34505	−	4.77029i	0.673319	−	0.437292i
$120$		0			0
$121$	−9.16746			−0.833405
$122$		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
$131$	5.32863			0.465565			0.232782	−	0.972529i	$-0.425217\pi$
$131$	5.32863			0.465565			0.232782	+	0.972529i	$0.425217\pi$
$132$		0			0
$133$	−0.305745	−	5.83007i	−0.0265115	−	0.505531i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.49543			0.640378			0.320189	−	0.947354i	$-0.396254\pi$
$137$	7.49543			0.640378			0.320189	+	0.947354i	$0.396254\pi$
$138$		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
$149$	−2.17971			−0.178569			−0.0892846	−	0.996006i	$-0.528458\pi$
$149$	−2.17971			−0.178569			−0.0892846	+	0.996006i	$0.528458\pi$
$150$		0			0
$151$	−14.0277			−1.14156			−0.570781	−	0.821102i	$-0.693359\pi$
$151$	−14.0277			−1.14156			−0.570781	+	0.821102i	$0.693359\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.78231	+	8.28320i	0.384124	+	0.665322i
$156$		0			0
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	0.800755	−	0.598993i	$-0.204432\pi$
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	−0.919120	+	0.393978i	$0.871099\pi$
$158$		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	0.873534	−	0.486764i	$-0.161823\pi$
$163$	0.194278	+	0.336499i	0.0152170	+	0.0263566i	−0.858317	+	0.513120i	$0.828489\pi$
$164$		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
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	−0.932750	−	0.360525i	$-0.882598\pi$
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	0.778598	+	0.627522i	$0.215931\pi$
$174$		0			0
$175$	−8.32514	−	4.24151i	−0.629322	−	0.320628i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.29243	−	9.16675i	0.395575	−	0.685155i	−0.597600	−	0.801795i	$-0.703879\pi$
$179$	5.29243	−	9.16675i	0.395575	−	0.685155i	0.993174	+	0.116639i	$0.0372121\pi$
$180$		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
$185$	15.8829	+	27.5099i	1.16773	+	2.02257i
$186$		0			0
$187$	2.24058	−	3.88081i	0.163848	−	0.283793i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.14357	+	7.17688i	−0.299818	+	0.519301i	−0.976094	−	0.217348i	$-0.930259\pi$
$191$	−4.14357	+	7.17688i	−0.299818	+	0.519301i	0.676276	+	0.736648i	$0.263593\pi$
$192$		0			0
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	0.976152	+	0.217090i	$0.0696566\pi$
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	−0.300070	+	0.953917i	$0.597010\pi$
$194$		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	0.489221	+	0.872160i	$0.337281\pi$
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	−0.999923	+	0.0124022i	$0.996052\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.144579	+	2.75690i	0.0101475	+	0.193496i
$204$		0			0
$205$	2.64131	−	4.57488i	0.184477	−	0.319523i
$206$		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
$221$	−2.42644	−	4.20271i	−0.163220	−	0.282705i
$222$		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
$227$	19.7126			1.30837			0.654187	−	0.756333i	$-0.273011\pi$
$227$	19.7126			1.30837			0.654187	+	0.756333i	$0.273011\pi$
$228$		0			0
$229$	28.0728			1.85510			0.927552	−	0.373694i	$-0.121909\pi$
$229$	28.0728			1.85510			0.927552	+	0.373694i	$0.121909\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.90113	+	11.9531i	0.452108	+	0.783074i	0.998517	−	0.0544448i	$-0.0173389\pi$
$233$	6.90113	+	11.9531i	0.452108	+	0.783074i	−0.546409	+	0.837518i	$0.684006\pi$
$234$		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
$241$	−23.1697			−1.49249			−0.746247	−	0.665669i	$-0.768146\pi$
$241$	−23.1697			−1.49249			−0.746247	+	0.665669i	$0.768146\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.0190	+	16.5404i	0.767869	+	1.05673i
$246$		0			0
$247$	−3.23486			−0.205829
$248$		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
$257$	−10.3760			−0.647235			−0.323618	−	0.946188i	$-0.604899\pi$
$257$	−10.3760			−0.647235			−0.323618	+	0.946188i	$0.604899\pi$
$258$		0			0
$259$	−1.50690	−	28.7343i	−0.0936345	−	1.78546i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.1331			−1.17980			−0.589898	−	0.807478i	$-0.700832\pi$
$263$	−19.1331			−1.17980			−0.589898	+	0.807478i	$0.700832\pi$
$264$		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	−0.699311	−	0.714818i	$-0.746510\pi$
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	0.968706	+	0.248212i	$0.0798430\pi$
$270$		0			0
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	0.997744	+	0.0671321i	$0.0213849\pi$
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	−0.440734	+	0.897638i	$0.645282\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.78059			−0.288280
$276$		0			0
$277$	5.10482			0.306719			0.153360	−	0.988170i	$-0.450991\pi$
$277$	5.10482			0.306719			0.153360	+	0.988170i	$0.450991\pi$
$278$		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
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	0.618571	−	0.785729i	$-0.287712\pi$
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	−0.989747	+	0.142833i	$0.954379\pi$
$284$		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
$299$	−1.92654	+	3.33687i	−0.111415	+	0.192976i
$300$		0			0
$301$	−0.601708	−	11.4736i	−0.0346819	−	0.661328i
$302$		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
$311$	16.1984	+	28.0565i	0.918528	+	1.59094i	0.801652	+	0.597791i	$0.203955\pi$
$311$	16.1984	+	28.0565i	0.918528	+	1.59094i	0.116876	+	0.993146i	$0.462712\pi$
$312$		0			0
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	−0.886693	−	0.462359i	$-0.847003\pi$
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	0.843761	+	0.536719i	$0.180336\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.7544	+	18.6272i	−0.604029	+	1.04621i	0.388175	+	0.921586i	$0.373106\pi$
$317$	−10.7544	+	18.6272i	−0.604029	+	1.04621i	−0.992204	+	0.124623i	$0.960228\pi$
$318$		0			0
$319$	0.706261	+	1.22328i	0.0395430	+	0.0684905i
$320$		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
$329$	8.82917	−	5.73417i	0.486768	−	0.316135i
$330$		0			0
$331$	9.73902	−	16.8685i	0.535305	−	0.927175i	−0.463844	−	0.885917i	$-0.653530\pi$
$331$	9.73902	−	16.8685i	0.535305	−	0.927175i	0.999149	−	0.0412580i	$-0.0131366\pi$
$332$		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
$347$	−1.01302	−	1.75460i	−0.0543817	−	0.0941919i	0.837553	−	0.546356i	$-0.183985\pi$
$347$	−1.01302	−	1.75460i	−0.0543817	−	0.0941919i	−0.891935	+	0.452164i	$0.850652\pi$
$348$		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
$353$	−17.0614			−0.908089			−0.454045	−	0.890979i	$-0.650019\pi$
$353$	−17.0614			−0.908089			−0.454045	+	0.890979i	$0.650019\pi$
$354$		0			0
$355$	37.7309			2.00255
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.48363	+	2.56972i	0.0783030	+	0.135625i	0.902518	−	0.430652i	$-0.141717\pi$
$359$	1.48363	+	2.56972i	0.0783030	+	0.135625i	−0.824215	+	0.566277i	$0.808383\pi$
$360$		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
$367$	10.1575			0.530216			0.265108	−	0.964219i	$-0.414592\pi$
$367$	10.1575			0.530216			0.265108	+	0.964219i	$0.414592\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−14.3225	+	9.30182i	−0.743585	+	0.482927i
$372$		0			0
$373$	−25.4846			−1.31954			−0.659771	−	0.751467i	$-0.729347\pi$
$373$	−25.4846			−1.31954			−0.659771	+	0.751467i	$0.729347\pi$
$374$		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
$383$	−27.3127			−1.39561			−0.697806	−	0.716286i	$-0.745840\pi$
$383$	−27.3127			−1.39561			−0.697806	+	0.716286i	$0.745840\pi$
$384$		0			0
$385$	9.32130	+	4.74903i	0.475057	+	0.242033i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.18446			−0.212161			−0.106080	−	0.994358i	$-0.533830\pi$
$389$	−4.18446			−0.212161			−0.106080	+	0.994358i	$0.533830\pi$
$390$		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	0.937745	+	0.347323i	$0.112909\pi$
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	−0.168082	+	0.985773i	$0.553757\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.84803			0.341974			0.170987	−	0.985273i	$-0.445304\pi$
$401$	6.84803			0.341974			0.170987	+	0.985273i	$0.445304\pi$
$402$		0			0
$403$	−4.80055			−0.239132
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.36113	−	12.7499i	−0.364878	−	0.631987i
$408$		0			0
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	0.998491	−	0.0549104i	$-0.0174873\pi$
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	−0.546799	+	0.837264i	$0.684154\pi$
$410$		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
$425$	−5.84505	+	10.1239i	−0.283526	+	0.491082i
$426$		0			0
$427$	1.24197	−	0.806608i	0.0601033	−	0.0390345i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.1213	+	17.5307i	−0.487527	+	0.844422i	−0.999897	−	0.0143427i	$-0.995434\pi$
$431$	−10.1213	+	17.5307i	−0.487527	+	0.844422i	0.512370	+	0.858765i	$0.328768\pi$
$432$		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
$437$	2.89978	+	5.02257i	0.138715	+	0.240262i
$438$		0			0
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	0.0375520	+	0.999295i	$0.488044\pi$
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	−0.884191	+	0.467126i	$0.845289\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.60313	−	16.6331i	0.456258	−	0.790263i	−0.542501	−	0.840055i	$-0.682523\pi$
$443$	9.60313	−	16.6331i	0.456258	−	0.790263i	0.998760	+	0.0497923i	$0.0158559\pi$
$444$		0			0
$445$	−9.35716	−	16.2071i	−0.443572	−	0.768289i
$446$		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
$455$	9.50117	−	6.17060i	0.445422	−	0.289282i
$456$		0			0
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	−0.732267	−	0.681017i	$-0.761538\pi$
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	0.955912	+	0.293653i	$0.0948711\pi$
$458$		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	−0.913758	−	0.406258i	$-0.866833\pi$
$467$	−17.4764	−	30.2699i	−0.808709	−	1.40073i	0.105049	−	0.994467i	$-0.466500\pi$
$468$		0			0
$469$	−1.77520	−	33.8502i	−0.0819711	−	1.56306i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.93930	−	5.09102i	−0.135149	−	0.234086i
$474$		0			0
$475$	3.89623	+	6.74848i	0.178771	+	0.309641i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−29.8109			−1.36209			−0.681047	−	0.732240i	$-0.738475\pi$
$479$	−29.8109			−1.36209			−0.681047	+	0.732240i	$0.738475\pi$
$480$		0			0
$481$	−15.9434			−0.726959
$482$		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	−0.491283	−	0.871000i	$-0.663472\pi$
$487$	11.2253	−	19.4428i	0.508667	−	0.881037i	0.999950	−	0.0100365i	$-0.00319477\pi$
$488$		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
$493$	3.45407			0.155564
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−30.4525	−	15.5150i	−1.36598	−	0.695943i
$498$		0			0
$499$	8.93520			0.399994			0.199997	−	0.979796i	$-0.435907\pi$
$499$	8.93520			0.399994			0.199997	+	0.979796i	$0.435907\pi$
$500$		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
$509$	28.1110			1.24600			0.623000	−	0.782222i	$-0.285914\pi$
$509$	28.1110			1.24600			0.623000	+	0.782222i	$0.285914\pi$
$510$		0			0
$511$	−23.1992	+	15.0669i	−1.02627	+	0.666519i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.50427			0.286613
$516$		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	−0.943797	−	0.330524i	$-0.892774\pi$
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	0.758141	+	0.652090i	$0.226108\pi$
$522$		0			0
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	−0.956339	−	0.292259i	$-0.905593\pi$
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	0.225066	−	0.974344i	$-0.427740\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.8398			−0.472187
$528$		0			0
$529$	−16.0921			−0.699655
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.32569	+	2.29616i	0.0574220	+	0.0994579i
$534$		0			0
$535$	−25.5693	−	44.2874i	−1.10546	−	1.91471i
$536$		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	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$		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
$551$	1.15122	−	1.99397i	0.0490437	−	0.0849461i
$552$		0			0
$553$	−1.70337	+	1.10627i	−0.0724346	+	0.0470432i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.6911	+	28.9098i	−0.707223	+	1.22495i	0.258661	+	0.965968i	$0.416719\pi$
$557$	−16.6911	+	28.9098i	−0.707223	+	1.22495i	−0.965883	+	0.258977i	$0.916614\pi$
$558$		0			0
$559$	−6.36623			−0.269263
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.09566	−	1.89773i	−0.0461764	−	0.0799799i	0.842013	−	0.539457i	$-0.181370\pi$
$563$	−1.09566	−	1.89773i	−0.0461764	−	0.0799799i	−0.888190	+	0.459477i	$0.848037\pi$
$564$		0			0
$565$	2.46683	−	4.27268i	0.103780	−	0.179753i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.49302	−	16.4424i	0.397968	−	0.689301i	−0.595507	−	0.803350i	$-0.703049\pi$
$569$	9.49302	−	16.4424i	0.397968	−	0.689301i	0.993475	+	0.114049i	$0.0363822\pi$
$570$		0			0
$571$	−10.8690	−	18.8257i	−0.454854	−	0.787831i	0.543825	−	0.839198i	$-0.316975\pi$
$571$	−10.8690	−	18.8257i	−0.454854	−	0.787831i	−0.998680	+	0.0513674i	$0.983642\pi$
$572$		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	0.341443	+	0.939903i	$0.389084\pi$
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	−0.984701	+	0.174253i	$0.944249\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.272605	+	5.19815i	0.0113096	+	0.215655i
$582$		0			0
$583$	−4.36902	+	7.56737i	−0.180946	+	0.313408i
$584$		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	−0.996577	−	0.0826662i	$-0.973656\pi$
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	0.426698	−	0.904394i	$-0.359677\pi$
$594$		0			0
$595$	21.4539	−	13.9334i	0.879524	−	0.571213i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.201412	−	0.348855i	−0.00822945	−	0.0142538i	0.861881	−	0.507110i	$-0.169286\pi$
$599$	−0.201412	−	0.348855i	−0.00822945	−	0.0142538i	−0.870111	+	0.492856i	$0.835953\pi$
$600$		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
$605$	−26.7769			−1.08864
$606$		0			0
$607$	−24.0697			−0.976957			−0.488479	−	0.872576i	$-0.662448\pi$
$607$	−24.0697			−0.976957			−0.488479	+	0.872576i	$0.662448\pi$
$608$		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	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$		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
$619$	−14.8219			−0.595743			−0.297871	−	0.954606i	$-0.596277\pi$
$619$	−14.8219			−0.595743			−0.297871	+	0.954606i	$0.596277\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.887770	+	16.9284i	0.0355678	+	0.678221i
$624$		0			0
$625$	−30.1861			−1.20744
$626$		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
$635$	11.5935			0.460072
$636$		0			0
$637$	−10.2057	+	1.07339i	−0.404366	+	0.0425291i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.9318			−0.471279			−0.235640	−	0.971840i	$-0.575719\pi$
$641$	−11.9318			−0.471279			−0.235640	+	0.971840i	$0.575719\pi$
$642$		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	−0.856142	−	0.516741i	$-0.827145\pi$
$647$	0.494477	−	0.856459i	0.0194399	−	0.0336709i	0.875582	+	0.483070i	$0.160478\pi$
$648$		0			0
$649$	−8.26714	−	14.3191i	−0.324514	−	0.562074i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.7147			−0.888894			−0.444447	−	0.895805i	$-0.646600\pi$
$653$	−22.7147			−0.888894			−0.444447	+	0.895805i	$0.646600\pi$
$654$		0			0
$655$	15.5642			0.608144
$656$		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
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	−0.980672	−	0.195657i	$-0.937316\pi$
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	0.320892	−	0.947116i	$-0.396017\pi$
$662$		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
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	0.227421	+	0.973797i	$0.426971\pi$
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	−0.957043	+	0.289946i	$0.906363\pi$
$678$		0			0
$679$	1.14767	+	21.8843i	0.0440436	+	0.839842i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.59357	−	13.1525i	0.290560	−	0.503265i	−0.683382	−	0.730061i	$-0.739492\pi$
$683$	7.59357	−	13.1525i	0.290560	−	0.503265i	0.973942	+	0.226796i	$0.0728251\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.73142	+	8.19507i	0.180253	+	0.312207i
$690$		0			0
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	−0.839293	−	0.543680i	$-0.817031\pi$
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	0.890487	+	0.455009i	$0.150364\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−20.5420	+	35.5798i	−0.779203	+	1.34962i
$696$		0			0
$697$	2.99344	+	5.18480i	0.113385	+	0.196388i
$698$		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
$707$	−38.2530	−	19.4892i	−1.43865	−	0.732967i
$708$		0			0
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	−0.166759	−	0.985998i	$-0.553330\pi$
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	0.937278	−	0.348582i	$-0.113337\pi$
$710$		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	0.992439	−	0.122741i	$-0.0391685\pi$
$719$	10.4555	+	18.1094i	0.389923	+	0.675366i	−0.602516	+	0.798107i	$0.705835\pi$
$720$		0			0
$721$	−5.24958	−	2.67457i	−0.195505	−	0.0996060i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.84243	−	3.19119i	−0.0684263	−	0.118518i
$726$		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
$731$	−14.3751			−0.531683
$732$		0			0
$733$	14.1489			0.522602			0.261301	−	0.965257i	$-0.415848\pi$
$733$	14.1489			0.522602			0.261301	+	0.965257i	$0.415848\pi$
$734$		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	−0.684495	−	0.729017i	$-0.739977\pi$
$739$	7.85905	−	13.6123i	0.289100	−	0.500736i	0.973595	+	0.228282i	$0.0733107\pi$
$740$		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
$745$	−6.36665			−0.233256
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.42592	+	46.2584i	0.0886412	+	1.69025i
$750$		0			0
$751$	−13.0370			−0.475725			−0.237863	−	0.971299i	$-0.576447\pi$
$751$	−13.0370			−0.475725			−0.237863	+	0.971299i	$0.576447\pi$
$752$		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
$761$	6.04077			0.218978			0.109489	−	0.993988i	$-0.465079\pi$
$761$	6.04077			0.218978			0.109489	+	0.993988i	$0.465079\pi$
$762$		0			0
$763$	34.6106	−	22.4781i	1.25299	−	0.813761i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.9058			−0.646540
$768$		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	0.299316	+	0.954154i	$0.403241\pi$
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	−0.975980	+	0.217861i	$0.930092\pi$
$774$		0			0
$775$	5.78202	+	10.0148i	0.207696	+	0.359741i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.99078			0.142985
$780$		0			0
$781$	−17.4869			−0.625730
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.33198	−	7.50321i	−0.154615	−	0.267801i
$786$		0			0
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	0.998330	+	0.0577648i	$0.0183973\pi$
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	−0.449139	+	0.893462i	$0.648269\pi$
$788$		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
$803$	−7.07684	+	12.2574i	−0.249736	+	0.432556i
$804$		0			0
$805$	−18.0977	−	9.22045i	−0.637860	−	0.324978i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.4818	−	33.7435i	0.684943	−	1.18636i	−0.288511	−	0.957477i	$-0.593160\pi$
$809$	19.4818	−	33.7435i	0.684943	−	1.18636i	0.973455	−	0.228880i	$-0.0735065\pi$
$810$		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
$815$	0.567459	+	0.982867i	0.0198772	+	0.0344283i
$816$		0			0
$817$	−4.79113	+	8.29849i	−0.167621	+	0.290327i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.7917	−	36.0123i	0.725635	−	1.25684i	−0.233077	−	0.972458i	$-0.574879\pi$
$821$	20.7917	−	36.0123i	0.725635	−	1.25684i	0.958712	−	0.284378i	$-0.0917872\pi$
$822$		0			0
$823$	4.22999	+	7.32656i	0.147448	+	0.255388i	0.930284	−	0.366841i	$-0.119561\pi$
$823$	4.22999	+	7.32656i	0.147448	+	0.255388i	−0.782835	+	0.622229i	$0.786227\pi$
$824$		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	−0.973533	−	0.228547i	$-0.926603\pi$
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	0.684694	+	0.728831i	$0.259936\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−23.0448	+	2.42373i	−0.798455	+	0.0839774i
$834$		0			0
$835$	10.6579	−	18.4601i	0.368832	−	0.638836i
$836$		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
$851$	14.2920	+	24.7544i	0.489922	+	0.848570i
$852$		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
$857$	−37.0894			−1.26695			−0.633475	−	0.773763i	$-0.718372\pi$
$857$	−37.0894			−1.26695			−0.633475	+	0.773763i	$0.718372\pi$
$858$		0			0
$859$	3.78333			0.129085			0.0645427	−	0.997915i	$-0.479441\pi$
$859$	3.78333			0.129085			0.0645427	+	0.997915i	$0.479441\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.213559	+	0.369895i	0.00726963	+	0.0125914i	0.869637	−	0.493691i	$-0.164353\pi$
$863$	0.213559	+	0.369895i	0.00726963	+	0.0125914i	−0.862368	+	0.506282i	$0.831019\pi$
$864$		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
$871$	−18.7821			−0.636407
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.1120	+	5.15186i	0.341847	+	0.174165i
$876$		0			0
$877$	11.2608			0.380249			0.190124	−	0.981760i	$-0.439111\pi$
$877$	11.2608			0.380249			0.190124	+	0.981760i	$0.439111\pi$
$878$		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
$887$	57.5664			1.93289			0.966446	−	0.256870i	$-0.0826913\pi$
$887$	57.5664			1.93289			0.966446	+	0.256870i	$0.0826913\pi$
$888$		0			0
$889$	−9.35705	−	4.76724i	−0.313825	−	0.159888i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.78032			−0.293822
$894$		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
$905$	−57.3400			−1.90605
$906$		0			0
$907$	−20.8972			−0.693879			−0.346939	−	0.937888i	$-0.612779\pi$
$907$	−20.8972			−0.693879			−0.346939	+	0.937888i	$0.612779\pi$
$908$		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
$913$	1.33166	+	2.30650i	0.0440715	+	0.0763340i
$914$		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	−0.990339	−	0.138664i	$-0.955719\pi$
$919$	−18.6515	−	32.3054i	−0.615257	−	1.06566i	0.375083	−	0.926991i	$-0.377614\pi$
$920$		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
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	−0.815791	−	0.578347i	$-0.803698\pi$
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	0.908759	+	0.417322i	$0.137031\pi$
$930$		0			0
$931$	−6.28151	+	14.1112i	−0.205868	+	0.462475i
$932$		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
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	0.983178	−	0.182650i	$-0.0584674\pi$
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	−0.649768	+	0.760132i	$0.725134\pi$
$942$		0			0
$943$	2.37674	−	4.11663i	0.0773973	−	0.134056i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.38343	−	4.12823i	0.0774512	−	0.134149i	−0.824698	−	0.565573i	$-0.808655\pi$
$947$	2.38343	−	4.12823i	0.0774512	−	0.134149i	0.902150	+	0.431423i	$0.141988\pi$
$948$		0			0
$949$	7.66385	+	13.2742i	0.248779	+	0.430898i
$950$		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
$959$	−17.6699	−	9.00249i	−0.570591	−	0.290706i
$960$		0			0
$961$	10.1386	−	17.5605i	0.327050	−	0.566468i
$962$		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	0.999200	−	0.0399914i	$-0.0127331\pi$
$971$	14.4888	+	25.0953i	0.464966	+	0.805345i	−0.534234	+	0.845337i	$0.679400\pi$
$972$		0			0
$973$	31.2099	−	20.2695i	1.00054	−	0.649809i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.4228	+	19.7848i	0.365447	+	0.632972i	0.988848	−	0.148930i	$-0.0475830\pi$
$977$	11.4228	+	19.7848i	0.365447	+	0.632972i	−0.623401	+	0.781902i	$0.714250\pi$
$978$		0			0
$979$	4.33670	+	7.51139i	0.138602	+	0.240065i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−31.2703			−0.997367			−0.498684	−	0.866784i	$-0.666183\pi$
$983$	−31.2703			−0.997367			−0.498684	+	0.866784i	$0.666183\pi$
$984$		0			0
$985$	−17.5145			−0.558059
$986$		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	−0.916340	−	0.400400i	$-0.868871\pi$
$991$	−3.50732	+	6.07485i	−0.111414	+	0.192974i	0.804927	+	0.593374i	$0.202204\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−21.0429	+	36.4474i	−0.667105	+	1.15546i
$996$		0			0
$997$	−21.2878			−0.674191			−0.337095	−	0.941470i	$-0.609445\pi$
$997$	−21.2878			−0.674191			−0.337095	+	0.941470i	$0.609445\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	12.11	even	2
63.2.g.b.16.5	yes	10	252.191	even	6
63.2.h.b.25.1	yes	10	36.11	even	6
63.2.h.b.58.1	yes	10	84.23	even	6
189.2.g.b.100.1		10	252.79	odd	6
189.2.g.b.172.1		10	4.3	odd	2
189.2.h.b.37.5		10	28.23	odd	6
189.2.h.b.46.5		10	36.7	odd	6
441.2.f.e.148.5		10	84.11	even	6
441.2.f.e.295.5		10	252.11	even	6
441.2.f.f.148.5		10	84.59	odd	6
441.2.f.f.295.5		10	252.227	odd	6
441.2.g.f.67.5		10	84.83	odd	2
441.2.g.f.79.5		10	252.47	odd	6
441.2.h.f.214.1		10	252.83	odd	6
441.2.h.f.373.1		10	84.47	odd	6
567.2.e.e.163.1		10	252.247	odd	6
567.2.e.e.487.1		10	36.31	odd	6
567.2.e.f.163.5		10	252.23	even	6
567.2.e.f.487.5		10	36.23	even	6
1008.2.q.i.529.4		10	9.2	odd	6
1008.2.q.i.625.4		10	21.2	odd	6
1008.2.t.i.193.3		10	3.2	odd	2
1008.2.t.i.961.3		10	63.2	odd	6
1323.2.f.e.442.1		10	28.11	odd	6
1323.2.f.e.883.1		10	252.151	odd	6
1323.2.f.f.442.1		10	28.3	even	6
1323.2.f.f.883.1		10	252.115	even	6
1323.2.g.f.361.1		10	28.27	even	2
1323.2.g.f.667.1		10	252.187	even	6
1323.2.h.f.226.5		10	28.19	even	6
1323.2.h.f.802.5		10	252.223	even	6
3024.2.q.i.2305.2		10	7.2	even	3
3024.2.q.i.2881.2		10	9.7	even	3
3024.2.t.i.289.4		10	63.16	even	3	inner
3024.2.t.i.1873.4		10	1.1	even	1	trivial
3969.2.a.z.1.1		5	252.95	even	6
3969.2.a.ba.1.1		5	252.59	odd	6
3969.2.a.bb.1.5		5	252.31	even	6
3969.2.a.bc.1.5		5	252.67	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+2.92087 q^{5} +(-2.35742 - 1.20106i) q^{7} -1.35371 q^{11} +(-0.733001 + 1.26960i) q^{13} +(-1.65514 + 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +2.62830 q^{23} +3.53146 q^{25} +(-0.521720 - 0.903646i) q^{29} +(1.63729 + 2.83587i) q^{31} +(-6.88572 - 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(0.904289 - 1.56627i) q^{41} +(2.17129 + 3.76078i) q^{43} +(-1.98957 + 3.44604i) q^{47} +(4.11489 + 5.66283i) q^{49} +(3.22743 - 5.59008i) q^{53} -3.95402 q^{55} +(6.10700 + 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +(-2.14100 + 3.70832i) q^{65} +(6.40588 + 11.0953i) q^{67} +12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(3.19128 + 1.62590i) q^{77} +(0.383838 - 0.664827i) q^{79} +(-0.983707 - 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(-3.20356 - 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} +(3.22257 + 5.58166i) q^{95} +(-4.14143 - 7.17316i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59}+ \cdots - 12 q^{97}+O(q^{100}) \) 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

Introduction

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