LMFDB - Embedded newform 3024.2.q.h.2881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.h.2305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84981 - 3.20397i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +O(q^{10})$	$q+(1.84981 - 3.20397i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(0.738550 + 1.27921i) q^{11} +(-1.34981 - 2.33795i) q^{13} +(-3.28799 + 5.69497i) q^{17} +(0.444368 + 0.769668i) q^{19} +(-3.14400 + 5.44556i) q^{23} +(-4.34362 - 7.52338i) q^{25} +(-1.25526 + 2.17417i) q^{29} -6.81089 q^{31} +(-5.19963 + 8.29305i) q^{35} +(-1.38874 - 2.40536i) q^{37} +(2.05563 + 3.56046i) q^{41} +(-0.00618986 + 0.0107211i) q^{43} -6.98762 q^{47} +(6.98143 + 0.509538i) q^{49} +(1.60507 - 2.78007i) q^{53} +5.46472 q^{55} +6.90978 q^{59} -5.73305 q^{61} -9.98762 q^{65} +9.46472 q^{67} -5.46472 q^{71} +(-6.03273 + 10.4490i) q^{73} +(-1.82946 - 3.45338i) q^{77} -11.4523 q^{79} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +(4.43818 + 7.68715i) q^{89} +(3.34362 + 6.31159i) q^{91} +3.28799 q^{95} +(-6.58836 + 11.4114i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q + 5 * q^5 - 4 * q^7	$ 6 q + 5 q^{5} - 4 q^{7} - q^{11} - 2 q^{13} + 4 q^{17} + 3 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 28 q^{31} - 19 q^{35} - 9 q^{37} + 12 q^{41} - 18 q^{43} - 6 q^{47} - 12 q^{49} - 9 q^{53} - 14 q^{55} - 8 q^{59} - 8 q^{61} - 24 q^{65} + 10 q^{67} + 14 q^{71} - 25 q^{73} - 52 q^{77} + 14 q^{79} + 8 q^{83} + 14 q^{85} + 9 q^{89} - 4 q^{91} - 4 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q + 5 * q^5 - 4 * q^7 - q^11 - 2 * q^13 + 4 * q^17 + 3 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 28 * q^31 - 19 * q^35 - 9 * q^37 + 12 * q^41 - 18 * q^43 - 6 * q^47 - 12 * q^49 - 9 * q^53 - 14 * q^55 - 8 * q^59 - 8 * q^61 - 24 * q^65 + 10 * q^67 + 14 * q^71 - 25 * q^73 - 52 * q^77 + 14 * q^79 + 8 * q^83 + 14 * q^85 + 9 * q^89 - 4 * q^91 - 4 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.84981	−	3.20397i	0.827262	−	1.43286i	−0.0729162	−	0.997338i	$-0.523231\pi$
$5$	1.84981	−	3.20397i	0.827262	−	1.43286i	0.900178	−	0.435522i	$-0.143436\pi$
$6$		0			0
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	0.955621	−	0.294598i	$-0.0951858\pi$
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	−0.732940	+	0.680293i	$0.761852\pi$
$12$		0			0
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	0.615862	−	0.787854i	$-0.288808\pi$
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	−0.990233	+	0.139425i	$0.955475\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.28799	+	5.69497i	−0.797455	+	1.38123i	0.123813	+	0.992306i	$0.460488\pi$
$17$	−3.28799	+	5.69497i	−0.797455	+	1.38123i	−0.921268	+	0.388927i	$0.872846\pi$
$18$		0			0
$19$	0.444368	+	0.769668i	0.101945	+	0.176574i	0.912486	−	0.409108i	$-0.134160\pi$
$19$	0.444368	+	0.769668i	0.101945	+	0.176574i	−0.810541	+	0.585682i	$0.800827\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	0.326182	+	0.945307i	$0.394238\pi$
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	−0.981751	+	0.190171i	$0.939096\pi$
$24$		0			0
$25$	−4.34362	−	7.52338i	−0.868725	−	1.50468i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.25526	+	2.17417i	−0.233096	+	0.403734i	−0.958718	−	0.284360i	$-0.908219\pi$
$29$	−1.25526	+	2.17417i	−0.233096	+	0.403734i	0.725622	+	0.688094i	$0.241552\pi$
$30$		0			0
$31$	−6.81089			−1.22327			−0.611636	−	0.791139i	$-0.709488\pi$
$31$	−6.81089			−1.22327			−0.611636	+	0.791139i	$0.709488\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.19963	+	8.29305i	−0.878898	+	1.40178i
$36$		0			0
$37$	−1.38874	−	2.40536i	−0.228307	−	0.395439i	0.729000	−	0.684514i	$-0.239986\pi$
$37$	−1.38874	−	2.40536i	−0.228307	−	0.395439i	−0.957306	+	0.289075i	$0.906652\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.05563	+	3.56046i	0.321036	+	0.556050i	0.980702	−	0.195508i	$-0.0626357\pi$
$41$	2.05563	+	3.56046i	0.321036	+	0.556050i	−0.659666	+	0.751559i	$0.729302\pi$
$42$		0			0
$43$	−0.00618986	+	0.0107211i	−0.000943944	+	0.00163496i	−0.866497	−	0.499182i	$-0.833634\pi$
$43$	−0.00618986	+	0.0107211i	−0.000943944	+	0.00163496i	0.865553	+	0.500817i	$0.166967\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.98762			−1.01925			−0.509625	−	0.860397i	$-0.670216\pi$
$47$	−6.98762			−1.01925			−0.509625	+	0.860397i	$0.670216\pi$
$48$		0			0
$49$	6.98143	+	0.509538i	0.997347	+	0.0727912i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.60507	−	2.78007i	0.220474	−	0.381872i	−0.734478	−	0.678632i	$-0.762573\pi$
$53$	1.60507	−	2.78007i	0.220474	−	0.381872i	0.954952	+	0.296760i	$0.0959063\pi$
$54$		0			0
$55$	5.46472			0.736863
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.90978			0.899576			0.449788	−	0.893135i	$-0.351499\pi$
$59$	6.90978			0.899576			0.449788	+	0.893135i	$0.351499\pi$
$60$		0			0
$61$	−5.73305			−0.734042			−0.367021	−	0.930213i	$-0.619622\pi$
$61$	−5.73305			−0.734042			−0.367021	+	0.930213i	$0.619622\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.98762			−1.23881
$66$		0			0
$67$	9.46472			1.15630			0.578150	−	0.815931i	$-0.303775\pi$
$67$	9.46472			1.15630			0.578150	+	0.815931i	$0.303775\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.46472			−0.648543			−0.324271	−	0.945964i	$-0.605119\pi$
$71$	−5.46472			−0.648543			−0.324271	+	0.945964i	$0.605119\pi$
$72$		0			0
$73$	−6.03273	+	10.4490i	−0.706078	+	1.22296i	0.260223	+	0.965548i	$0.416204\pi$
$73$	−6.03273	+	10.4490i	−0.706078	+	1.22296i	−0.966301	+	0.257414i	$0.917130\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.82946	−	3.45338i	−0.208487	−	0.393549i
$78$		0			0
$79$	−11.4523			−1.28849			−0.644244	−	0.764820i	$-0.722828\pi$
$79$	−11.4523			−1.28849			−0.644244	+	0.764820i	$0.722828\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	−0.716619	−	0.697465i	$-0.754311\pi$
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	0.962332	+	0.271878i	$0.0876447\pi$
$84$		0			0
$85$	12.1643	+	21.0693i	1.31941	+	2.28528i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.43818	+	7.68715i	0.470446	+	0.814836i	0.999429	−	0.0337963i	$-0.0107597\pi$
$89$	4.43818	+	7.68715i	0.470446	+	0.814836i	−0.528983	+	0.848633i	$0.677426\pi$
$90$		0			0
$91$	3.34362	+	6.31159i	0.350507	+	0.661634i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.28799			0.337341
$96$		0			0
$97$	−6.58836	+	11.4114i	−0.668947	+	1.15865i	0.309252	+	0.950980i	$0.399921\pi$
$97$	−6.58836	+	11.4114i	−0.668947	+	1.15865i	−0.978199	+	0.207670i	$0.933412\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.62729	+	4.55059i	0.261425	+	0.452801i	0.966621	−	0.256212i	$-0.0824744\pi$
$101$	2.62729	+	4.55059i	0.261425	+	0.452801i	−0.705196	+	0.709012i	$0.749141\pi$
$102$		0			0
$103$	0.833104	−	1.44298i	0.0820882	−	0.142181i	−0.822059	−	0.569403i	$-0.807174\pi$
$103$	0.833104	−	1.44298i	0.0820882	−	0.142181i	0.904147	+	0.427222i	$0.140508\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.38255	−	9.32284i	−0.520350	−	0.901273i	−0.999720	−	0.0236602i	$-0.992468\pi$
$107$	−5.38255	−	9.32284i	−0.520350	−	0.901273i	0.479370	−	0.877613i	$-0.340865\pi$
$108$		0			0
$109$	−0.0945538	+	0.163772i	−0.00905662	+	0.0156865i	−0.870518	−	0.492136i	$-0.836216\pi$
$109$	−0.0945538	+	0.163772i	−0.00905662	+	0.0156865i	0.861462	+	0.507823i	$0.169550\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.78180	+	11.7464i	0.637978	+	1.10501i	0.985876	+	0.167478i	$0.0535624\pi$
$113$	6.78180	+	11.7464i	0.637978	+	1.10501i	−0.347897	+	0.937533i	$0.613104\pi$
$114$		0			0
$115$	11.6316	+	20.1466i	1.08465	+	1.87868i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.24219	−	14.7407i	0.847230	−	1.35127i
$120$		0			0
$121$	4.40909	−	7.63676i	0.400826	−	0.694251i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−13.6414			−1.22013
$126$		0			0
$127$	2.85669			0.253490			0.126745	−	0.991935i	$-0.459547\pi$
$127$	2.85669			0.253490			0.126745	+	0.991935i	$0.459547\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	−0.869406	−	0.494098i	$-0.835498\pi$
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	0.862605	+	0.505878i	$0.168832\pi$
$132$		0			0
$133$	−1.10074	−	2.07782i	−0.0954466	−	0.180170i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.70582	−	2.95456i	−0.145738	−	0.252425i	0.783910	−	0.620874i	$-0.213222\pi$
$137$	−1.70582	−	2.95456i	−0.145738	−	0.252425i	−0.929648	+	0.368449i	$0.879889\pi$
$138$		0			0
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	0.996259	+	0.0864229i	$0.0275436\pi$
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	−0.423285	+	0.905997i	$0.639123\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.99381	−	3.45338i	0.166731	−	0.288786i
$144$		0			0
$145$	4.64400	+	8.04364i	0.385663	+	0.667988i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.166896	−	0.289073i	0.0136727	−	0.0236818i	−0.859108	−	0.511794i	$-0.828981\pi$
$149$	0.166896	−	0.289073i	0.0136727	−	0.0236818i	0.872781	+	0.488112i	$0.162314\pi$
$150$		0			0
$151$	−9.95489	−	17.2424i	−0.810117	−	1.40316i	−0.912781	−	0.408448i	$-0.866070\pi$
$151$	−9.95489	−	17.2424i	−0.810117	−	1.40316i	0.102664	−	0.994716i	$-0.467263\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.5989	+	21.8219i	−1.01197	+	1.75278i
$156$		0			0
$157$	−6.96286			−0.555697			−0.277848	−	0.960625i	$-0.589621\pi$
$157$	−6.96286			−0.555697			−0.277848	+	0.960625i	$0.589621\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.83743	−	14.0951i	0.696487	−	1.11085i
$162$		0			0
$163$	−4.03706	−	6.99240i	−0.316207	−	0.547687i	0.663486	−	0.748189i	$-0.269076\pi$
$163$	−4.03706	−	6.99240i	−0.316207	−	0.547687i	−0.979693	+	0.200502i	$0.935743\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	0.945906	+	0.324440i	$0.105176\pi$
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	−0.191979	+	0.981399i	$0.561491\pi$
$168$		0			0
$169$	2.85600	−	4.94674i	0.219693	−	0.380519i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−22.5636			−1.71548			−0.857740	−	0.514085i	$-0.828132\pi$
$173$	−22.5636			−1.71548			−0.857740	+	0.514085i	$0.828132\pi$
$174$		0			0
$175$	10.7596	+	20.3103i	0.813349	+	1.53532i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.166896	−	0.289073i	0.0124744	−	0.0216063i	−0.859721	−	0.510764i	$-0.829363\pi$
$179$	0.166896	−	0.289073i	0.0124744	−	0.0216063i	0.872195	+	0.489158i	$0.162696\pi$
$180$		0			0
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.2756			−0.755478
$186$		0			0
$187$	−9.71339			−0.710313
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.3214			−1.18098			−0.590488	−	0.807046i	$-0.701065\pi$
$191$	−16.3214			−1.18098			−0.590488	+	0.807046i	$0.701065\pi$
$192$		0			0
$193$	−14.3214			−1.03088			−0.515439	−	0.856926i	$-0.672371\pi$
$193$	−14.3214			−1.03088			−0.515439	+	0.856926i	$0.672371\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.42402			−0.172704			−0.0863520	−	0.996265i	$-0.527521\pi$
$197$	−2.42402			−0.172704			−0.0863520	+	0.996265i	$0.527521\pi$
$198$		0			0
$199$	3.05563	−	5.29251i	0.216608	−	0.375176i	−0.737161	−	0.675717i	$-0.763834\pi$
$199$	3.05563	−	5.29251i	0.216608	−	0.375176i	0.953769	+	0.300541i	$0.0971673\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.52840	−	5.62755i	0.247645	−	0.394977i
$204$		0			0
$205$	15.2101			1.06232
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.656376	+	1.13688i	−0.0454025	+	0.0786394i
$210$		0			0
$211$	−5.72253	−	9.91171i	−0.393955	−	0.682350i	0.599012	−	0.800740i	$-0.295560\pi$
$211$	−5.72253	−	9.91171i	−0.393955	−	0.682350i	−0.992967	+	0.118390i	$0.962227\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0229002	+	0.0396643i	0.00156178	+	0.00270508i
$216$		0			0
$217$	18.0080	+	0.656281i	1.22246	+	0.0445513i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.7527			1.19418
$222$		0			0
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	−0.719407	−	0.694589i	$-0.755586\pi$
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	0.961235	+	0.275730i	$0.0889196\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	0.545417	−	0.838165i	$-0.316371\pi$
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	−0.998581	+	0.0532622i	$0.983038\pi$
$228$		0			0
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	0.422073	+	0.906562i	$0.361303\pi$
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	−0.996142	+	0.0877555i	$0.972031\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.62110	−	13.2001i	−0.499275	−	0.864769i	0.500725	−	0.865606i	$-0.333067\pi$
$233$	−7.62110	−	13.2001i	−0.499275	−	0.864769i	−1.00000		0.000837426i	$0.999733\pi$
$234$		0			0
$235$	−12.9258	+	22.3881i	−0.843186	+	1.46044i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	0.990749	+	0.135710i	$0.0433314\pi$
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	−0.377846	+	0.925868i	$0.623335\pi$
$240$		0			0
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	0.926417	+	0.376500i	$0.122872\pi$
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	−0.137150	+	0.990550i	$0.543794\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	14.5469	−	21.4258i	0.929367	−	1.36884i
$246$		0			0
$247$	1.19963	−	2.07782i	0.0763305	−	0.132208i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.10439	+	7.10900i	−0.256025	+	0.443448i	−0.965173	−	0.261611i	$-0.915746\pi$
$257$	−4.10439	+	7.10900i	−0.256025	+	0.443448i	0.709149	+	0.705059i	$0.249079\pi$
$258$		0			0
$259$	3.44004	+	6.49358i	0.213754	+	0.403491i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	0.936595	−	0.350414i	$-0.113959\pi$
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	−0.771765	+	0.635908i	$0.780626\pi$
$264$		0			0
$265$	−5.93818	−	10.2852i	−0.364779	−	0.631816i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.24219	+	16.0079i	−0.563506	+	0.976022i	0.433681	+	0.901067i	$0.357215\pi$
$269$	−9.24219	+	16.0079i	−0.563506	+	0.976022i	−0.997187	+	0.0749550i	$0.976119\pi$
$270$		0			0
$271$	3.67742	+	6.36947i	0.223387	+	0.386918i	0.955834	−	0.293906i	$-0.0949552\pi$
$271$	3.67742	+	6.36947i	0.223387	+	0.386918i	−0.732447	+	0.680824i	$0.761622\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.41597	−	11.1128i	0.386897	−	0.670126i
$276$		0			0
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	0.969717	−	0.244230i	$-0.0785351\pi$
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	−0.696368	+	0.717685i	$0.745202\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00433	+	10.3998i	−0.358188	+	0.620400i	−0.987658	−	0.156624i	$-0.949939\pi$
$281$	−6.00433	+	10.3998i	−0.358188	+	0.620400i	0.629470	+	0.777025i	$0.283272\pi$
$282$		0			0
$283$	−9.84294			−0.585102			−0.292551	−	0.956250i	$-0.594504\pi$
$283$	−9.84294			−0.585102			−0.292551	+	0.956250i	$0.594504\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.09201	−	9.61192i	−0.300572	−	0.567373i
$288$		0			0
$289$	−13.1218	−	22.7276i	−0.771870	−	1.33692i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.7101	−	18.5505i	−0.625694	−	1.08373i	−0.988406	−	0.151832i	$-0.951483\pi$
$293$	−10.7101	−	18.5505i	−0.625694	−	1.08373i	0.362713	−	0.931901i	$-0.381851\pi$
$294$		0			0
$295$	12.7818	−	22.1387i	0.744185	−	1.28897i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.9752			0.981704
$300$		0			0
$301$	0.0173990	−	0.0277502i	0.00100286	−	0.00159950i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.6051	+	18.3685i	−0.607245	+	1.05178i
$306$		0			0
$307$	5.68725			0.324588			0.162294	−	0.986742i	$-0.448111\pi$
$307$	5.68725			0.324588			0.162294	+	0.986742i	$0.448111\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.7207			−0.664618			−0.332309	−	0.943171i	$-0.607828\pi$
$311$	−11.7207			−0.664618			−0.332309	+	0.943171i	$0.607828\pi$
$312$		0			0
$313$	−26.7738			−1.51334			−0.756671	−	0.653796i	$-0.773176\pi$
$313$	−26.7738			−1.51334			−0.756671	+	0.653796i	$0.773176\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.90249			−0.106855			−0.0534273	−	0.998572i	$-0.517015\pi$
$317$	−1.90249			−0.106855			−0.0534273	+	0.998572i	$0.517015\pi$
$318$		0			0
$319$	−3.70829			−0.207624
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.84431			−0.325186
$324$		0			0
$325$	−11.7262	+	20.3103i	−0.650451	+	1.12661i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	18.4752	+	0.673310i	1.01857	+	0.0371208i
$330$		0			0
$331$	−5.56732			−0.306008			−0.153004	−	0.988226i	$-0.548895\pi$
$331$	−5.56732			−0.306008			−0.153004	+	0.988226i	$0.548895\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.5080	−	30.3247i	0.956563	−	1.65682i
$336$		0			0
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.799585	−	0.600553i	$-0.794947\pi$
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.120302	−	0.992737i	$-0.538386\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.03018	−	8.71253i	−0.272400	−	0.471810i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−30.4065			−1.63231			−0.816154	−	0.577834i	$-0.803898\pi$
$347$	−30.4065			−1.63231			−0.816154	+	0.577834i	$0.803898\pi$
$348$		0			0
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	−0.983889	−	0.178782i	$-0.942784\pi$
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	0.646774	+	0.762682i	$0.276118\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.76578	−	6.52252i	−0.200432	−	0.347159i	0.748235	−	0.663433i	$-0.230901\pi$
$353$	−3.76578	−	6.52252i	−0.200432	−	0.347159i	−0.948668	+	0.316274i	$0.897568\pi$
$354$		0			0
$355$	−10.1087	+	17.5088i	−0.536515	+	0.929271i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.44801	−	5.97213i	−0.181979	−	0.315197i	0.760575	−	0.649250i	$-0.224917\pi$
$359$	−3.44801	−	5.97213i	−0.181979	−	0.315197i	−0.942554	+	0.334053i	$0.891584\pi$
$360$		0			0
$361$	9.10507	−	15.7705i	0.479214	−	0.830024i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	22.3189	+	38.6574i	1.16822	+	2.02342i
$366$		0			0
$367$	11.5618	+	20.0257i	0.603522	+	1.04533i	0.992283	+	0.123992i	$0.0395699\pi$
$367$	11.5618	+	20.0257i	0.603522	+	1.04533i	−0.388761	+	0.921339i	$0.627097\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.51169	+	7.19583i	−0.234235	+	0.373589i
$372$		0			0
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	0.190320	+	0.981722i	$0.439047\pi$
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	−0.945356	+	0.326039i	$0.894286\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.77747			0.349058
$378$		0			0
$379$	13.5622			0.696645			0.348322	−	0.937375i	$-0.386751\pi$
$379$	13.5622			0.696645			0.348322	+	0.937375i	$0.386751\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	−0.827526	−	0.561428i	$-0.810252\pi$
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	0.899973	+	0.435945i	$0.143586\pi$
$384$		0			0
$385$	−14.4487	−	0.526567i	−0.736374	−	0.0268364i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.30401	−	16.1150i	−0.471732	−	0.817064i	0.527745	−	0.849403i	$-0.323038\pi$
$389$	−9.30401	−	16.1150i	−0.471732	−	0.817064i	−0.999477	+	0.0323388i	$0.989704\pi$
$390$		0			0
$391$	−20.6749	−	35.8099i	−1.04557	−	1.81099i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−21.1847	+	36.6930i	−1.06592	+	1.84622i
$396$		0			0
$397$	−10.2880	−	17.8193i	−0.516340	−	0.894326i	−0.999820	−	0.0189712i	$-0.993961\pi$
$397$	−10.2880	−	17.8193i	−0.516340	−	0.894326i	0.483481	−	0.875355i	$-0.339372\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.37704	+	5.84921i	−0.168642	+	0.292096i	−0.937942	−	0.346791i	$-0.887271\pi$
$401$	−3.37704	+	5.84921i	−0.168642	+	0.292096i	0.769301	+	0.638887i	$0.220605\pi$
$402$		0			0
$403$	9.19344	+	15.9235i	0.457958	+	0.793206i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.05130	−	3.55296i	0.101679	−	0.176114i
$408$		0			0
$409$	15.3214			0.757595			0.378798	−	0.925480i	$-0.376338\pi$
$409$	15.3214			0.757595			0.378798	+	0.925480i	$0.376338\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−18.2694	−	0.665809i	−0.898980	−	0.0327623i
$414$		0			0
$415$	−8.28180	−	14.3445i	−0.406538	−	0.704144i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	0.740949	−	0.671561i	$-0.234376\pi$
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	−0.952064	+	0.305900i	$0.901043\pi$
$420$		0			0
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.0834618	−	0.996511i	$-0.473402\pi$
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.821273	−	0.570536i	$-0.193264\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	57.1272			2.77108
$426$		0			0
$427$	15.1582	+	0.552423i	0.733555	+	0.0267336i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.71015	+	8.15822i	−0.226880	+	0.392967i	−0.956882	−	0.290478i	$-0.906186\pi$
$431$	−4.71015	+	8.15822i	−0.226880	+	0.392967i	0.730002	+	0.683445i	$0.239519\pi$
$432$		0			0
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.58836			−0.267328
$438$		0			0
$439$	9.96796			0.475745			0.237872	−	0.971296i	$-0.423550\pi$
$439$	9.96796			0.475745			0.237872	+	0.971296i	$0.423550\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.6996			−0.745912			−0.372956	−	0.927849i	$-0.621656\pi$
$443$	−15.6996			−0.745912			−0.372956	+	0.927849i	$0.621656\pi$
$444$		0			0
$445$	32.8392			1.55673
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.6253			−1.58688			−0.793439	−	0.608650i	$-0.791712\pi$
$449$	−33.6253			−1.58688			−0.793439	+	0.608650i	$0.791712\pi$
$450$		0			0
$451$	−3.03637	+	5.25915i	−0.142977	+	0.247644i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	26.4072	+	0.962383i	1.23799	+	0.0451172i
$456$		0			0
$457$	32.7083			1.53003			0.765015	−	0.644013i	$-0.222732\pi$
$457$	32.7083			1.53003			0.765015	+	0.644013i	$0.222732\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.07165	−	3.58821i	0.0964865	−	0.167120i	−0.813742	−	0.581227i	$-0.802573\pi$
$461$	2.07165	−	3.58821i	0.0964865	−	0.167120i	0.910228	+	0.414107i	$0.135906\pi$
$462$		0			0
$463$	8.34176	+	14.4484i	0.387675	+	0.671472i	0.992136	−	0.125162i	$-0.0399451\pi$
$463$	8.34176	+	14.4484i	0.387675	+	0.671472i	−0.604462	+	0.796634i	$0.706612\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.9585	+	25.9089i	0.692198	+	1.19892i	0.971116	+	0.238608i	$0.0766909\pi$
$467$	14.9585	+	25.9089i	0.692198	+	1.19892i	−0.278918	+	0.960315i	$0.589976\pi$
$468$		0			0
$469$	−25.0247	−	0.911998i	−1.15553	−	0.0421121i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.0182861			−0.000840794
$474$		0			0
$475$	3.86033	−	6.68630i	0.177124	−	0.306788i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	0.897847	−	0.440307i	$-0.145130\pi$
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	−0.830241	+	0.557405i	$0.811797\pi$
$480$		0			0
$481$	−3.74907	+	6.49358i	−0.170943	+	0.296082i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	24.3745	+	42.2179i	1.10679	+	1.91701i
$486$		0			0
$487$	14.0309	−	24.3022i	0.635800	−	1.10124i	−0.350546	−	0.936546i	$-0.614004\pi$
$487$	14.0309	−	24.3022i	0.635800	−	1.10124i	0.986345	−	0.164691i	$-0.0526628\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.0734	+	29.5721i	0.770513	+	1.33457i	0.937282	+	0.348572i	$0.113333\pi$
$491$	17.0734	+	29.5721i	0.770513	+	1.33457i	−0.166769	+	0.985996i	$0.553333\pi$
$492$		0			0
$493$	−8.25457	−	14.2973i	−0.371767	−	0.643920i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.4487	+	0.526567i	0.648113	+	0.0236198i
$498$		0			0
$499$	−1.14035	+	1.97515i	−0.0510493	+	0.0884199i	−0.890421	−	0.455138i	$-0.849590\pi$
$499$	−1.14035	+	1.97515i	−0.0510493	+	0.0884199i	0.839372	+	0.543558i	$0.182923\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.8090	−	22.1859i	0.567750	−	0.983373i	−0.429038	−	0.903287i	$-0.641147\pi$
$509$	12.8090	−	22.1859i	0.567750	−	0.983373i	0.996788	−	0.0800859i	$-0.0255195\pi$
$510$		0			0
$511$	16.9574	−	27.0458i	0.750149	−	1.19644i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.08217	−	5.33848i	−0.135817	−	0.235242i
$516$		0			0
$517$	−5.16071	−	8.93861i	−0.226968	−	0.393119i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.9127	−	36.2219i	0.916203	−	1.58691i	0.111073	−	0.993812i	$-0.464571\pi$
$521$	20.9127	−	36.2219i	0.916203	−	1.58691i	0.805130	−	0.593099i	$-0.202096\pi$
$522$		0			0
$523$	−7.88323	−	13.6542i	−0.344710	−	0.597055i	0.640591	−	0.767882i	$-0.278689\pi$
$523$	−7.88323	−	13.6542i	−0.344710	−	0.597055i	−0.985301	+	0.170827i	$0.945356\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	22.3942	−	38.7878i	0.975505	−	1.68962i
$528$		0			0
$529$	−8.26942	−	14.3231i	−0.359540	−	0.622742i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.54944	−	9.61192i	0.240373	−	0.416338i
$534$		0			0
$535$	−39.8268			−1.72186
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.50433	+	9.30701i	0.194015	+	0.400881i
$540$		0			0
$541$	−21.0963	−	36.5399i	−0.907002	−	1.57097i	−0.818207	−	0.574924i	$-0.805031\pi$
$541$	−21.0963	−	36.5399i	−0.907002	−	1.57097i	−0.0887957	−	0.996050i	$-0.528302\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.349814	+	0.605896i	0.0149844	+	0.0259537i
$546$		0			0
$547$	−20.3356	+	35.2222i	−0.869486	+	1.50599i	−0.00696400	+	0.999976i	$0.502217\pi$
$547$	−20.3356	+	35.2222i	−0.869486	+	1.50599i	−0.862522	+	0.506019i	$0.831117\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.23119			−0.0950519
$552$		0			0
$553$	30.2799	+	1.10352i	1.28763	+	0.0469264i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.68794	+	11.5838i	−0.283377	+	0.490823i	−0.972214	−	0.234093i	$-0.924788\pi$
$557$	−6.68794	+	11.5838i	−0.283377	+	0.490823i	0.688837	+	0.724916i	$0.258121\pi$
$558$		0			0
$559$	0.0334206			0.00141354
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−32.7614			−1.38073			−0.690364	−	0.723463i	$-0.742549\pi$
$563$	−32.7614			−1.38073			−0.690364	+	0.723463i	$0.742549\pi$
$564$		0			0
$565$	50.1803			2.11110
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.7280			0.701272			0.350636	−	0.936512i	$-0.385965\pi$
$569$	16.7280			0.701272			0.350636	+	0.936512i	$0.385965\pi$
$570$		0			0
$571$	27.4734			1.14973			0.574863	−	0.818250i	$-0.305055\pi$
$571$	27.4734			1.14973			0.574863	+	0.818250i	$0.305055\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	54.6253			2.27803
$576$		0			0
$577$	1.41714	−	2.45455i	0.0589962	−	0.102184i	−0.835019	−	0.550221i	$-0.814543\pi$
$577$	1.41714	−	2.45455i	0.0589962	−	0.102184i	0.894015	+	0.448037i	$0.147877\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.29232	+	10.0358i	−0.261050	+	0.416356i
$582$		0			0
$583$	4.74171			0.196382
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	−0.910404	−	0.413720i	$-0.864229\pi$
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	0.813494	+	0.581573i	$0.197563\pi$
$588$		0			0
$589$	−3.02654	−	5.24212i	−0.124706	−	0.215998i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.636024	−	1.10163i	−0.0261184	−	0.0452383i	0.852671	−	0.522449i	$-0.174981\pi$
$593$	−0.636024	−	1.10163i	−0.0261184	−	0.0452383i	−0.878789	+	0.477210i	$0.841648\pi$
$594$		0			0
$595$	−30.1323	−	56.8792i	−1.23530	−	2.33182i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	43.8516			1.79173			0.895864	−	0.444329i	$-0.146558\pi$
$599$	43.8516			1.79173			0.895864	+	0.444329i	$0.146558\pi$
$600$		0			0
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	−0.969874	−	0.243609i	$-0.921669\pi$
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	0.695908	+	0.718131i	$0.255002\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−16.3120	−	28.2532i	−0.663177	−	1.14866i
$606$		0			0
$607$	−2.29232	+	3.97042i	−0.0930425	+	0.161154i	−0.908790	−	0.417254i	$-0.862993\pi$
$607$	−2.29232	+	3.97042i	−0.0930425	+	0.161154i	0.815747	+	0.578408i	$0.196326\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.43199	+	16.3367i	0.381577	+	0.660911i
$612$		0			0
$613$	−11.0538	+	19.1457i	−0.446458	+	0.773287i	−0.998152	−	0.0607587i	$-0.980648\pi$
$613$	−11.0538	+	19.1457i	−0.446458	+	0.773287i	0.551695	+	0.834046i	$0.313981\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00433	−	10.3998i	−0.241725	−	0.418680i	0.719481	−	0.694513i	$-0.244380\pi$
$617$	−6.00433	−	10.3998i	−0.241725	−	0.418680i	−0.961206	+	0.275832i	$0.911047\pi$
$618$		0			0
$619$	−8.78180	−	15.2105i	−0.352970	−	0.611363i	0.633798	−	0.773499i	$-0.281495\pi$
$619$	−8.78180	−	15.2105i	−0.352970	−	0.611363i	−0.986768	+	0.162136i	$0.948162\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−10.9938	−	20.7524i	−0.440458	−	0.831429i
$624$		0			0
$625$	−3.51602	+	6.08993i	−0.140641	+	0.243597i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.2646			0.728258
$630$		0			0
$631$	44.9381			1.78896			0.894479	−	0.447110i	$-0.147547\pi$
$631$	44.9381			1.78896			0.894479	+	0.447110i	$0.147547\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.28435	−	9.15276i	0.209703	−	0.363216i
$636$		0			0
$637$	−8.23236	−	17.0100i	−0.326178	−	0.673960i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.4920	−	25.1008i	−0.572398	−	0.991422i	−0.996319	−	0.0857228i	$-0.972680\pi$
$641$	−14.4920	−	25.1008i	−0.572398	−	0.991422i	0.423921	−	0.905699i	$-0.360653\pi$
$642$		0			0
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	0.722258	−	0.691623i	$-0.243104\pi$
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	−0.960093	+	0.279682i	$0.909771\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.8825	−	32.7055i	0.742349	−	1.28579i	−0.209073	−	0.977900i	$-0.567045\pi$
$647$	18.8825	−	32.7055i	0.742349	−	1.28579i	0.951423	−	0.307887i	$-0.0996219\pi$
$648$		0			0
$649$	5.10322	+	8.83903i	0.200319	+	0.346962i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.7040	−	32.3962i	0.731942	−	1.26776i	−0.224109	−	0.974564i	$-0.571947\pi$
$653$	18.7040	−	32.3962i	0.731942	−	1.26776i	0.956052	−	0.293198i	$-0.0947194\pi$
$654$		0			0
$655$	0.287992	+	0.498817i	0.0112528	+	0.0194904i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	−0.413455	−	0.910524i	$-0.635678\pi$
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	0.995265	−	0.0971993i	$-0.0309884\pi$
$660$		0			0
$661$	5.60803			0.218127			0.109063	−	0.994035i	$-0.465215\pi$
$661$	5.60803			0.218127			0.109063	+	0.994035i	$0.465215\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.69344	−	0.316823i	−0.337117	−	0.0122859i
$666$		0			0
$667$	−7.89307	−	13.6712i	−0.305621	−	0.529351i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.23414	−	7.33375i	−0.163457	−	0.283116i
$672$		0			0
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	−0.942575	−	0.333994i	$-0.891603\pi$
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.0617			−0.425137			−0.212569	−	0.977146i	$-0.568183\pi$
$677$	−11.0617			−0.425137			−0.212569	+	0.977146i	$0.568183\pi$
$678$		0			0
$679$	18.5192	−	29.5368i	0.710701	−	1.13352i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.41961	+	7.65499i	−0.169112	+	0.292910i	−0.938108	−	0.346343i	$-0.887423\pi$
$683$	−4.41961	+	7.65499i	−0.169112	+	0.292910i	0.768996	+	0.639253i	$0.220757\pi$
$684$		0			0
$685$	−12.6218			−0.482254
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.66621			−0.330156
$690$		0			0
$691$	−25.0617			−0.953394			−0.476697	−	0.879068i	$-0.658166\pi$
$691$	−25.0617			−0.953394			−0.476697	+	0.879068i	$0.658166\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	49.9839			1.89600
$696$		0			0
$697$	−27.0356			−1.02405
$698$		0			0
$699$		0			0
$700$		0			0
$701$	43.4858			1.64243			0.821217	−	0.570616i	$-0.193295\pi$
$701$	43.4858			1.64243			0.821217	+	0.570616i	$0.193295\pi$
$702$		0			0
$703$	1.23422	−	2.13773i	0.0465495	−	0.0806260i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.50805	−	12.2849i	−0.244760	−	0.462021i
$708$		0			0
$709$	−22.7403			−0.854031			−0.427016	−	0.904244i	$-0.640435\pi$
$709$	−22.7403			−0.854031			−0.427016	+	0.904244i	$0.640435\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	21.4134	−	37.0891i	0.801939	−	1.38900i
$714$		0			0
$715$	−7.37636	−	12.7762i	−0.275860	−	0.477804i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.06182	+	10.4994i	0.226068	+	0.391561i	0.956639	−	0.291275i	$-0.0940796\pi$
$719$	6.06182	+	10.4994i	0.226068	+	0.391561i	−0.730571	+	0.682836i	$0.760746\pi$
$720$		0			0
$721$	−2.34176	+	3.73495i	−0.0872119	+	0.139097i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	21.8095			0.809985
$726$		0			0
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	0.0189562	+	0.999820i	$0.493966\pi$
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	−0.875348	+	0.483494i	$0.839368\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.0407044	−	0.0705021i	−0.00150551	−	0.00260761i
$732$		0			0
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	−0.313785	−	0.949494i	$-0.601597\pi$
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	0.979178	−	0.203002i	$-0.0650696\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.99017	+	12.1073i	0.257486	+	0.445979i
$738$		0			0
$739$	−23.2119	+	40.2042i	−0.853865	+	1.47894i	0.0238296	+	0.999716i	$0.492414\pi$
$739$	−23.2119	+	40.2042i	−0.853865	+	1.47894i	−0.877694	+	0.479221i	$0.840919\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.598884	+	1.03730i	0.0219709	+	0.0380548i	0.876802	−	0.480852i	$-0.159673\pi$
$743$	0.598884	+	1.03730i	0.0219709	+	0.0380548i	−0.854831	+	0.518907i	$0.826339\pi$
$744$		0			0
$745$	−0.617454	−	1.06946i	−0.0226218	−	0.0391820i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13.3331	+	25.1682i	0.487181	+	0.919626i
$750$		0			0
$751$	24.0600	−	41.6731i	0.877961	−	1.52067i	0.0243853	−	0.999703i	$-0.492237\pi$
$751$	24.0600	−	41.6731i	0.877961	−	1.52067i	0.853575	−	0.520970i	$-0.174430\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−73.6588			−2.68072
$756$		0			0
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.7701	+	32.5108i	−0.680416	+	1.17852i	0.294438	+	0.955671i	$0.404868\pi$
$761$	−18.7701	+	32.5108i	−0.680416	+	1.17852i	−0.974854	+	0.222845i	$0.928466\pi$
$762$		0			0
$763$	0.265781	−	0.423902i	0.00962191	−	0.0153463i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.32691	−	16.1547i	−0.336775	−	0.583312i
$768$		0			0
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	0.514506	−	0.857486i	$-0.327975\pi$
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	−0.999858	+	0.0168324i	$0.994642\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.1130	+	43.4971i	−0.903254	+	1.56448i	−0.0800089	+	0.996794i	$0.525495\pi$
$773$	−25.1130	+	43.4971i	−0.903254	+	1.56448i	−0.823245	+	0.567687i	$0.807838\pi$
$774$		0			0
$775$	29.5840	+	51.2409i	1.06269	+	1.84063i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.82691	+	3.16431i	−0.0654560	+	0.113373i
$780$		0			0
$781$	−4.03597	−	6.99050i	−0.144418	−	0.250140i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.8800	+	22.3088i	−0.459707	+	0.796236i
$786$		0			0
$787$	1.65892			0.0591342			0.0295671	−	0.999563i	$-0.490587\pi$
$787$	1.65892			0.0591342			0.0295671	+	0.999563i	$0.490587\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−16.7992	−	31.7110i	−0.597311	−	1.12751i
$792$		0			0
$793$	7.73855	+	13.4036i	0.274804	+	0.475974i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.3702	+	26.6219i	0.544439	+	0.942996i	0.998642	+	0.0520981i	$0.0165908\pi$
$797$	15.3702	+	26.6219i	0.544439	+	0.942996i	−0.454203	+	0.890898i	$0.650076\pi$
$798$		0			0
$799$	22.9752	−	39.7943i	0.812806	−	1.40782i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.8219			−0.628921
$804$		0			0
$805$	−28.8127	−	54.3882i	−1.01551	−	1.91693i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.44251	−	2.49850i	0.0507159	−	0.0878425i	−0.839553	−	0.543278i	$-0.817183\pi$
$809$	1.44251	−	2.49850i	0.0507159	−	0.0878425i	0.890269	+	0.455435i	$0.150516\pi$
$810$		0			0
$811$	−28.5461			−1.00239			−0.501195	−	0.865334i	$-0.667106\pi$
$811$	−28.5461			−1.00239			−0.501195	+	0.865334i	$0.667106\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−29.8713			−1.04634
$816$		0			0
$817$	−0.0110023			−0.000384922
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.96658			−0.278036			−0.139018	−	0.990290i	$-0.544395\pi$
$821$	−7.96658			−0.278036			−0.139018	+	0.990290i	$0.544395\pi$
$822$		0			0
$823$	−40.5461			−1.41335			−0.706675	−	0.707539i	$-0.749806\pi$
$823$	−40.5461			−1.41335			−0.706675	+	0.707539i	$0.749806\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.22115			0.0424636			0.0212318	−	0.999775i	$-0.493241\pi$
$827$	1.22115			0.0424636			0.0212318	+	0.999775i	$0.493241\pi$
$828$		0			0
$829$	−7.07530	+	12.2548i	−0.245735	+	0.425626i	−0.962338	−	0.271856i	$-0.912363\pi$
$829$	−7.07530	+	12.2548i	−0.245735	+	0.425626i	0.716603	+	0.697481i	$0.245696\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−25.8567	+	38.0837i	−0.895881	+	1.31952i
$834$		0			0
$835$	72.0901			2.49478
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	−0.844642	−	0.535332i	$-0.820187\pi$
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	0.885932	+	0.463815i	$0.153520\pi$
$840$		0			0
$841$	11.3486	+	19.6564i	0.391333	+	0.677808i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.5662	−	18.3011i	−0.363487	−	0.629577i
$846$		0			0
$847$	−12.3935	+	19.7667i	−0.425845	+	0.679193i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.4647			0.598683
$852$		0			0
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	−0.972744	−	0.231883i	$-0.925511\pi$
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	0.687188	+	0.726479i	$0.258845\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.92580	−	11.9958i	−0.236581	−	0.409770i	0.723150	−	0.690691i	$-0.242693\pi$
$857$	−6.92580	−	11.9958i	−0.236581	−	0.409770i	−0.959731	+	0.280921i	$0.909360\pi$
$858$		0			0
$859$	24.2472	−	41.9974i	0.827304	−	1.43293i	−0.0728414	−	0.997344i	$-0.523207\pi$
$859$	24.2472	−	41.9974i	0.827304	−	1.43293i	0.900146	−	0.435589i	$-0.143460\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.96541	+	5.13624i	0.100944	+	0.174840i	0.912074	−	0.410026i	$-0.134480\pi$
$863$	2.96541	+	5.13624i	0.100944	+	0.174840i	−0.811130	+	0.584866i	$0.801147\pi$
$864$		0			0
$865$	−41.7385	+	72.2932i	−1.41915	+	2.45804i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.45813	−	14.6499i	−0.286922	−	0.496964i
$870$		0			0
$871$	−12.7756	−	22.1280i	−0.432885	−	0.749779i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	36.0679	+	1.31446i	1.21932	+	0.0444368i
$876$		0			0
$877$	−1.96472	+	3.40300i	−0.0663439	+	0.114911i	−0.897289	−	0.441443i	$-0.854467\pi$
$877$	−1.96472	+	3.40300i	−0.0663439	+	0.114911i	0.830945	+	0.556354i	$0.187800\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37.6552			−1.26864			−0.634318	−	0.773072i	$-0.718719\pi$
$881$	−37.6552			−1.26864			−0.634318	+	0.773072i	$0.718719\pi$
$882$		0			0
$883$	53.2334			1.79145			0.895723	−	0.444613i	$-0.146659\pi$
$883$	53.2334			1.79145			0.895723	+	0.444613i	$0.146659\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.4938	−	32.0322i	0.620961	−	1.07554i	−0.368346	−	0.929689i	$-0.620076\pi$
$887$	18.4938	−	32.0322i	0.620961	−	1.07554i	0.989307	−	0.145848i	$-0.0465910\pi$
$888$		0			0
$889$	−7.55308	−	0.275264i	−0.253322	−	0.00923206i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.10507	−	5.37815i	−0.103907	−	0.179973i
$894$		0			0
$895$	−0.617454	−	1.06946i	−0.0206392	−	0.0357482i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	8.54944	−	14.8081i	0.285140	−	0.493877i
$900$		0			0
$901$	10.5549	+	18.2817i	0.351636	+	0.609052i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	42.9937	−	74.4673i	1.42916	−	2.47538i
$906$		0			0
$907$	−19.5080	−	33.7888i	−0.647752	−	1.12194i	−0.983659	−	0.180044i	$-0.942376\pi$
$907$	−19.5080	−	33.7888i	−0.647752	−	1.12194i	0.335907	−	0.941895i	$-0.390957\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	−0.996363	−	0.0852158i	$-0.972842\pi$
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	0.571980	+	0.820267i	$0.306175\pi$
$912$		0			0
$913$	6.61312			0.218862
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.218810	−	0.348986i	0.00722574	−	0.0115245i
$918$		0			0
$919$	−10.3367	−	17.9038i	−0.340978	−	0.590591i	0.643637	−	0.765331i	$-0.277425\pi$
$919$	−10.3367	−	17.9038i	−0.340978	−	0.590591i	−0.984615	+	0.174740i	$0.944091\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.37636	+	12.7762i	0.242796	+	0.420535i
$924$		0			0
$925$	−12.0643	+	20.8960i	−0.396672	+	0.687055i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.74033			0.122716			0.0613582	−	0.998116i	$-0.480457\pi$
$929$	3.74033			0.122716			0.0613582	+	0.998116i	$0.480457\pi$
$930$		0			0
$931$	2.71015	+	5.59980i	0.0888215	+	0.183526i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−17.9680	+	31.1214i	−0.587615	+	1.01778i
$936$		0			0
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.32870			−0.206310			−0.103155	−	0.994665i	$-0.532894\pi$
$941$	−6.32870			−0.206310			−0.103155	+	0.994665i	$0.532894\pi$
$942$		0			0
$943$	−25.8516			−0.841844
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.2792			1.01644			0.508218	−	0.861228i	$-0.330304\pi$
$947$	31.2792			1.01644			0.508218	+	0.861228i	$0.330304\pi$
$948$		0			0
$949$	32.5723			1.05734
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−4.28937			−0.138946			−0.0694732	−	0.997584i	$-0.522132\pi$
$953$	−4.28937			−0.138946			−0.0694732	+	0.997584i	$0.522132\pi$
$954$		0			0
$955$	−30.1916	+	52.2933i	−0.976977	+	1.69217i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.22548	+	7.97622i	0.136448	+	0.257566i
$960$		0			0
$961$	15.3883			0.496395
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−26.4920	+	45.8854i	−0.852806	+	1.47710i
$966$		0			0
$967$	7.59201	+	13.1497i	0.244142	+	0.422867i	0.961890	−	0.273436i	$-0.0881602\pi$
$967$	7.59201	+	13.1497i	0.244142	+	0.422867i	−0.717748	+	0.696303i	$0.754827\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.62364	+	2.81223i	0.0521052	+	0.0902489i	0.890902	−	0.454196i	$-0.150074\pi$
$971$	1.62364	+	2.81223i	0.0521052	+	0.0902489i	−0.838796	+	0.544445i	$0.816740\pi$
$972$		0			0
$973$	−16.7335	−	31.5869i	−0.536450	−	1.01263i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.5439			−0.497295			−0.248647	−	0.968594i	$-0.579986\pi$
$977$	−15.5439			−0.497295			−0.248647	+	0.968594i	$0.579986\pi$
$978$		0			0
$979$	−6.55563	+	11.3547i	−0.209519	+	0.362897i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.19158	−	10.7241i	−0.197481	−	0.342047i	0.750230	−	0.661177i	$-0.229943\pi$
$983$	−6.19158	−	10.7241i	−0.197481	−	0.342047i	−0.947711	+	0.319130i	$0.896609\pi$
$984$		0			0
$985$	−4.48398	+	7.76648i	−0.142871	+	0.247461i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.0389218	−	0.0674145i	−0.00123764	−	0.00214366i
$990$		0			0
$991$	3.32760	−	5.76358i	0.105705	−	0.183086i	−0.808321	−	0.588742i	$-0.799623\pi$
$991$	3.32760	−	5.76358i	0.105705	−	0.183086i	0.914026	+	0.405656i	$0.132957\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.3047	−	19.5803i	−0.358383	−	0.620738i
$996$		0			0
$997$	−2.40104	−	4.15872i	−0.0760417	−	0.131708i	0.825497	−	0.564406i	$-0.190895\pi$
$997$	−2.40104	−	4.15872i	−0.0760417	−	0.131708i	−0.901539	+	0.432698i	$0.857562\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.h.2881.3		6
3.2	odd	2		1008.2.q.h.529.3		6
4.3	odd	2		378.2.e.c.235.3		6
7.2	even	3		3024.2.t.g.289.1		6
9.4	even	3		3024.2.t.g.1873.1		6
9.5	odd	6		1008.2.t.g.193.3		6
12.11	even	2		126.2.e.d.25.1	✓	6
21.2	odd	6		1008.2.t.g.961.3		6
28.3	even	6		2646.2.f.n.883.1		6
28.11	odd	6		2646.2.f.o.883.3		6
28.19	even	6		2646.2.h.p.667.3		6
28.23	odd	6		378.2.h.d.289.1		6
28.27	even	2		2646.2.e.o.2125.1		6
36.7	odd	6		1134.2.g.n.487.3		6
36.11	even	6		1134.2.g.k.487.1		6
36.23	even	6		126.2.h.c.67.1	yes	6
36.31	odd	6		378.2.h.d.361.1		6
63.23	odd	6		1008.2.q.h.625.3		6
63.58	even	3	inner	3024.2.q.h.2305.3		6
84.11	even	6		882.2.f.l.295.3		6
84.23	even	6		126.2.h.c.79.1	yes	6
84.47	odd	6		882.2.h.o.79.3		6
84.59	odd	6		882.2.f.m.295.1		6
84.83	odd	2		882.2.e.p.655.3		6
252.11	even	6		7938.2.a.cb.1.3		3
252.23	even	6		126.2.e.d.121.1	yes	6
252.31	even	6		2646.2.f.n.1765.1		6
252.59	odd	6		882.2.f.m.589.1		6
252.67	odd	6		2646.2.f.o.1765.3		6
252.79	odd	6		1134.2.g.n.163.3		6
252.95	even	6		882.2.f.l.589.3		6
252.103	even	6		2646.2.e.o.1549.1		6
252.115	even	6		7938.2.a.bx.1.3		3
252.131	odd	6		882.2.e.p.373.3		6
252.139	even	6		2646.2.h.p.361.3		6
252.151	odd	6		7938.2.a.bu.1.1		3
252.167	odd	6		882.2.h.o.67.3		6
252.191	even	6		1134.2.g.k.163.1		6
252.227	odd	6		7938.2.a.by.1.1		3
252.247	odd	6		378.2.e.c.37.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	12.11	even	2
126.2.e.d.121.1	yes	6	252.23	even	6
126.2.h.c.67.1	yes	6	36.23	even	6
126.2.h.c.79.1	yes	6	84.23	even	6
378.2.e.c.37.3		6	252.247	odd	6
378.2.e.c.235.3		6	4.3	odd	2
378.2.h.d.289.1		6	28.23	odd	6
378.2.h.d.361.1		6	36.31	odd	6
882.2.e.p.373.3		6	252.131	odd	6
882.2.e.p.655.3		6	84.83	odd	2
882.2.f.l.295.3		6	84.11	even	6
882.2.f.l.589.3		6	252.95	even	6
882.2.f.m.295.1		6	84.59	odd	6
882.2.f.m.589.1		6	252.59	odd	6
882.2.h.o.67.3		6	252.167	odd	6
882.2.h.o.79.3		6	84.47	odd	6
1008.2.q.h.529.3		6	3.2	odd	2
1008.2.q.h.625.3		6	63.23	odd	6
1008.2.t.g.193.3		6	9.5	odd	6
1008.2.t.g.961.3		6	21.2	odd	6
1134.2.g.k.163.1		6	252.191	even	6
1134.2.g.k.487.1		6	36.11	even	6
1134.2.g.n.163.3		6	252.79	odd	6
1134.2.g.n.487.3		6	36.7	odd	6
2646.2.e.o.1549.1		6	252.103	even	6
2646.2.e.o.2125.1		6	28.27	even	2
2646.2.f.n.883.1		6	28.3	even	6
2646.2.f.n.1765.1		6	252.31	even	6
2646.2.f.o.883.3		6	28.11	odd	6
2646.2.f.o.1765.3		6	252.67	odd	6
2646.2.h.p.361.3		6	252.139	even	6
2646.2.h.p.667.3		6	28.19	even	6
3024.2.q.h.2305.3		6	63.58	even	3	inner
3024.2.q.h.2881.3		6	1.1	even	1	trivial
3024.2.t.g.289.1		6	7.2	even	3
3024.2.t.g.1873.1		6	9.4	even	3
7938.2.a.bu.1.1		3	252.151	odd	6
7938.2.a.bx.1.3		3	252.115	even	6
7938.2.a.by.1.1		3	252.227	odd	6
7938.2.a.cb.1.3		3	252.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.84981 - 3.20397i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +O(q^{10})\)	\(q+(1.84981 - 3.20397i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(0.738550 + 1.27921i) q^{11} +(-1.34981 - 2.33795i) q^{13} +(-3.28799 + 5.69497i) q^{17} +(0.444368 + 0.769668i) q^{19} +(-3.14400 + 5.44556i) q^{23} +(-4.34362 - 7.52338i) q^{25} +(-1.25526 + 2.17417i) q^{29} -6.81089 q^{31} +(-5.19963 + 8.29305i) q^{35} +(-1.38874 - 2.40536i) q^{37} +(2.05563 + 3.56046i) q^{41} +(-0.00618986 + 0.0107211i) q^{43} -6.98762 q^{47} +(6.98143 + 0.509538i) q^{49} +(1.60507 - 2.78007i) q^{53} +5.46472 q^{55} +6.90978 q^{59} -5.73305 q^{61} -9.98762 q^{65} +9.46472 q^{67} -5.46472 q^{71} +(-6.03273 + 10.4490i) q^{73} +(-1.82946 - 3.45338i) q^{77} -11.4523 q^{79} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +(4.43818 + 7.68715i) q^{89} +(3.34362 + 6.31159i) q^{91} +3.28799 q^{95} +(-6.58836 + 11.4114i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q + 5 * q^5 - 4 * q^7	\( 6 q + 5 q^{5} - 4 q^{7} - q^{11} - 2 q^{13} + 4 q^{17} + 3 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 28 q^{31} - 19 q^{35} - 9 q^{37} + 12 q^{41} - 18 q^{43} - 6 q^{47} - 12 q^{49} - 9 q^{53} - 14 q^{55} - 8 q^{59} - 8 q^{61} - 24 q^{65} + 10 q^{67} + 14 q^{71} - 25 q^{73} - 52 q^{77} + 14 q^{79} + 8 q^{83} + 14 q^{85} + 9 q^{89} - 4 q^{91} - 4 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q + 5 * q^5 - 4 * q^7 - q^11 - 2 * q^13 + 4 * q^17 + 3 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 28 * q^31 - 19 * q^35 - 9 * q^37 + 12 * q^41 - 18 * q^43 - 6 * q^47 - 12 * q^49 - 9 * q^53 - 14 * q^55 - 8 * q^59 - 8 * q^61 - 24 * q^65 + 10 * q^67 + 14 * q^71 - 25 * q^73 - 52 * q^77 + 14 * q^79 + 8 * q^83 + 14 * q^85 + 9 * q^89 - 4 * q^91 - 4 * q^95 - 28 * q^97

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