LMFDB - Embedded newform 432.7.q.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,7,Mod(17,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("432.17");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	432.q (of order $6$, 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:	$99.3833641238$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 $ x^10 - x^9 + 75x^8 - 2x^7 + 4610x^6 - 2412x^5 + 66932x^4 - 174032x^3 + 870720x^2 - 1272832x + 1982464
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$-2.32209 + 4.02197i$ of defining polynomial
Character	$\chi$	$=$	432.17
Dual form			432.7.q.a.305.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-80.3236 - 46.3749i) q^{5} +(-60.0074 - 103.936i) q^{7} +O(q^{10})$	$q+(-80.3236 - 46.3749i) q^{5} +(-60.0074 - 103.936i) q^{7} +(-1299.95 + 750.527i) q^{11} +(2142.08 - 3710.18i) q^{13} +940.477i q^{17} +8397.07 q^{19} +(7822.55 + 4516.35i) q^{23} +(-3511.24 - 6081.65i) q^{25} +(11618.5 - 6707.92i) q^{29} +(-6751.04 + 11693.1i) q^{31} +11131.3i q^{35} +39037.3 q^{37} +(-95285.0 - 55012.8i) q^{41} +(5770.09 + 9994.09i) q^{43} +(22839.5 - 13186.4i) q^{47} +(51622.7 - 89413.2i) q^{49} +12963.7i q^{53} +139222. q^{55} +(-160987. - 92945.8i) q^{59} +(48707.2 + 84363.3i) q^{61} +(-344118. + 198677. i) q^{65} +(-48333.5 + 83716.1i) q^{67} +264450. i q^{71} -154006. q^{73} +(156013. + 90074.4i) q^{77} +(-43195.7 - 74817.2i) q^{79} +(-543967. + 314059. i) q^{83} +(43614.5 - 75542.5i) q^{85} -874390. i q^{89} -514162. q^{91} +(-674483. - 389413. i) q^{95} +(95150.6 + 164806. i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 219 q^{5} + 121 q^{7}+O(q^{10}) $ 10 * q + 219 * q^5 + 121 * q^7	$ 10 q + 219 q^{5} + 121 q^{7} + 483 q^{11} - 841 q^{13} - 6176 q^{19} + 53565 q^{23} + 8452 q^{25} + 80679 q^{29} + 24601 q^{31} + 12764 q^{37} - 232251 q^{41} + 93271 q^{43} - 142887 q^{47} + 86238 q^{49} + 419982 q^{55} - 995061 q^{59} - 59305 q^{61} - 1642029 q^{65} - 158513 q^{67} + 933896 q^{73} + 2198883 q^{77} - 468707 q^{79} + 3008337 q^{83} - 1189944 q^{85} + 211778 q^{91} - 2562954 q^{95} + 336029 q^{97}+O(q^{100}) $ 10 * q + 219 * q^5 + 121 * q^7 + 483 * q^11 - 841 * q^13 - 6176 * q^19 + 53565 * q^23 + 8452 * q^25 + 80679 * q^29 + 24601 * q^31 + 12764 * q^37 - 232251 * q^41 + 93271 * q^43 - 142887 * q^47 + 86238 * q^49 + 419982 * q^55 - 995061 * q^59 - 59305 * q^61 - 1642029 * q^65 - 158513 * q^67 + 933896 * q^73 + 2198883 * q^77 - 468707 * q^79 + 3008337 * q^83 - 1189944 * q^85 + 211778 * q^91 - 2562954 * q^95 + 336029 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	−80.3236	−	46.3749i	−0.642589	−	0.370999i	0.143022	−	0.989719i	$-0.454318\pi$
$5$	−80.3236	−	46.3749i	−0.642589	−	0.370999i	−0.785611	+	0.618721i	$0.787651\pi$
$6$		0			0
$7$	−60.0074	−	103.936i	−0.174949	−	0.303020i	0.765195	−	0.643799i	$-0.222643\pi$
$7$	−60.0074	−	103.936i	−0.174949	−	0.303020i	−0.940144	+	0.340779i	$0.889309\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1299.95	+	750.527i	−0.976672	+	0.563882i	−0.901264	−	0.433271i	$-0.857359\pi$
$11$	−1299.95	+	750.527i	−0.976672	+	0.563882i	−0.0754083	+	0.997153i	$0.524026\pi$
$12$		0			0
$13$	2142.08	−	3710.18i	0.975000	−	1.68875i	0.295065	−	0.955477i	$-0.404659\pi$
$13$	2142.08	−	3710.18i	0.975000	−	1.68875i	0.679935	−	0.733273i	$-0.262008\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			940.477i			0.191426i	0.995409	+	0.0957131i	$0.0305131\pi$
$17$			940.477i			0.191426i	−0.995409	+	0.0957131i	$0.969487\pi$
$18$		0			0
$19$	8397.07			1.22424			0.612121	−	0.790764i	$-0.290317\pi$
$19$	8397.07			1.22424			0.612121	+	0.790764i	$0.290317\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7822.55	+	4516.35i	0.642932	+	0.371197i	0.785743	−	0.618553i	$-0.212281\pi$
$23$	7822.55	+	4516.35i	0.642932	+	0.371197i	−0.142811	+	0.989750i	$0.545614\pi$
$24$		0			0
$25$	−3511.24	−	6081.65i	−0.224720	−	0.389226i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	11618.5	−	6707.92i	0.476381	−	0.275039i	−0.242526	−	0.970145i	$-0.577976\pi$
$29$	11618.5	−	6707.92i	0.476381	−	0.275039i	0.718907	+	0.695106i	$0.244643\pi$
$30$		0			0
$31$	−6751.04	+	11693.1i	−0.226613	+	0.392506i	−0.956802	−	0.290740i	$-0.906099\pi$
$31$	−6751.04	+	11693.1i	−0.226613	+	0.392506i	0.730189	+	0.683245i	$0.239432\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			11131.3i			0.259623i
$36$		0			0
$37$	39037.3			0.770681			0.385341	−	0.922774i	$-0.374084\pi$
$37$	39037.3			0.770681			0.385341	+	0.922774i	$0.374084\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−95285.0	−	55012.8i	−1.38253	−	0.798201i	−0.390067	−	0.920786i	$-0.627548\pi$
$41$	−95285.0	−	55012.8i	−1.38253	−	0.798201i	−0.992458	+	0.122585i	$0.960882\pi$
$42$		0			0
$43$	5770.09	+	9994.09i	0.0725734	+	0.125701i	0.900028	−	0.435831i	$-0.143546\pi$
$43$	5770.09	+	9994.09i	0.0725734	+	0.125701i	−0.827455	+	0.561532i	$0.810212\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	22839.5	−	13186.4i	0.219985	−	0.127008i	−0.385959	−	0.922516i	$-0.626129\pi$
$47$	22839.5	−	13186.4i	0.219985	−	0.127008i	0.605943	+	0.795508i	$0.292796\pi$
$48$		0			0
$49$	51622.7	−	89413.2i	0.438786	−	0.759999i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			12963.7i			0.0870766i	0.999052	+	0.0435383i	$0.0138631\pi$
$53$			12963.7i			0.0870766i	−0.999052	+	0.0435383i	$0.986137\pi$
$54$		0			0
$55$	139222.			0.836798
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−160987.	−	92945.8i	−0.783853	−	0.452557i	0.0539413	−	0.998544i	$-0.482822\pi$
$59$	−160987.	−	92945.8i	−0.783853	−	0.452557i	−0.837794	+	0.545987i	$0.816155\pi$
$60$		0			0
$61$	48707.2	+	84363.3i	0.214587	+	0.371676i	0.953145	−	0.302515i	$-0.0978261\pi$
$61$	48707.2	+	84363.3i	0.214587	+	0.371676i	−0.738558	+	0.674190i	$0.764493\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−344118.	+	198677.i	−1.25305	+	0.723448i
$66$		0			0
$67$	−48333.5	+	83716.1i	−0.160703	+	0.278346i	−0.935121	−	0.354329i	$-0.884709\pi$
$67$	−48333.5	+	83716.1i	−0.160703	+	0.278346i	0.774418	+	0.632674i	$0.218043\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			264450.i			0.738871i	0.929256	+	0.369435i	$0.120449\pi$
$71$			264450.i			0.738871i	−0.929256	+	0.369435i	$0.879551\pi$
$72$		0			0
$73$	−154006.			−0.395885			−0.197942	−	0.980214i	$-0.563426\pi$
$73$	−154006.			−0.395885			−0.197942	+	0.980214i	$0.563426\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	156013.	+	90074.4i	0.341735	+	0.197301i
$78$		0			0
$79$	−43195.7	−	74817.2i	−0.0876112	−	0.151747i	0.818890	−	0.573951i	$-0.194590\pi$
$79$	−43195.7	−	74817.2i	−0.0876112	−	0.151747i	−0.906501	+	0.422204i	$0.861257\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−543967.	+	314059.i	−0.951345	+	0.549259i	−0.893499	−	0.449066i	$-0.851757\pi$
$83$	−543967.	+	314059.i	−0.951345	+	0.549259i	−0.0578467	+	0.998325i	$0.518423\pi$
$84$		0			0
$85$	43614.5	−	75542.5i	0.0710189	−	0.123008i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	874390.i		−	1.24032i	−0.784474	−	0.620162i	$-0.787067\pi$
$89$		−	874390.i		−	1.24032i	0.784474	−	0.620162i	$-0.212933\pi$
$90$		0			0
$91$	−514162.			−0.682300
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−674483.	−	389413.i	−0.786684	−	0.454192i
$96$		0			0
$97$	95150.6	+	164806.i	0.104255	+	0.180575i	0.913434	−	0.406988i	$-0.133421\pi$
$97$	95150.6	+	164806.i	0.104255	+	0.180575i	−0.809179	+	0.587563i	$0.800088\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−983657.	+	567915.i	−0.954728	+	0.551213i	−0.894547	−	0.446975i	$-0.852501\pi$
$101$	−983657.	+	567915.i	−0.954728	+	0.551213i	−0.0601817	+	0.998187i	$0.519168\pi$
$102$		0			0
$103$	555871.	−	962798.i	0.508701	−	0.881096i	−0.491248	−	0.871020i	$-0.663459\pi$
$103$	555871.	−	962798.i	0.508701	−	0.881096i	0.999949	−	0.0100765i	$-0.00320751\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.27312e6i		−	1.03924i	−0.854396	−	0.519622i	$-0.826073\pi$
$107$		−	1.27312e6i		−	1.03924i	0.854396	−	0.519622i	$-0.173927\pi$
$108$		0			0
$109$	−1.87984e6			−1.45158			−0.725792	−	0.687915i	$-0.758526\pi$
$109$	−1.87984e6			−1.45158			−0.725792	+	0.687915i	$0.758526\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.21138e6	+	699388.i	0.839544	+	0.484711i	0.857109	−	0.515135i	$-0.172258\pi$
$113$	1.21138e6	+	699388.i	0.839544	+	0.484711i	−0.0175650	+	0.999846i	$0.505591\pi$
$114$		0			0
$115$	−418890.	−	725539.i	−0.275427	−	0.477054i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	97749.4	−	56435.6i	0.0580060	−	0.0334898i
$120$		0			0
$121$	240800.	−	417079.i	0.135926	−	0.235430i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.10055e6i			1.07548i
$126$		0			0
$127$	−2.84521e6			−1.38900			−0.694501	−	0.719491i	$-0.744375\pi$
$127$	−2.84521e6			−1.38900			−0.694501	+	0.719491i	$0.744375\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.24280e6	+	717533.i	0.552827	+	0.319175i	0.750261	−	0.661141i	$-0.229928\pi$
$131$	1.24280e6	+	717533.i	0.552827	+	0.319175i	−0.197435	+	0.980316i	$0.563261\pi$
$132$		0			0
$133$	−503887.	−	872757.i	−0.214180	−	0.370970i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	485772.	−	280461.i	0.188917	−	0.109071i	−0.402558	−	0.915394i	$-0.631879\pi$
$137$	485772.	−	280461.i	0.188917	−	0.109071i	0.591475	+	0.806323i	$0.298546\pi$
$138$		0			0
$139$	409282.	−	708898.i	0.152398	−	0.263961i	−0.779711	−	0.626140i	$-0.784634\pi$
$139$	409282.	−	708898.i	0.152398	−	0.263961i	0.932108	+	0.362179i	$0.117967\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			6.43074e6i			2.19914i
$144$		0			0
$145$	−1.24432e6			−0.408156
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.45815e6	−	1.41921e6i	−0.743104	−	0.429032i	0.0800926	−	0.996787i	$-0.474478\pi$
$149$	−2.45815e6	−	1.41921e6i	−0.743104	−	0.429032i	−0.823197	+	0.567756i	$0.807812\pi$
$150$		0			0
$151$	−881580.	−	1.52694e6i	−0.256054	−	0.443498i	0.709127	−	0.705080i	$-0.249089\pi$
$151$	−881580.	−	1.52694e6i	−0.256054	−	0.443498i	−0.965181	+	0.261582i	$0.915756\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.08454e6	−	626157.i	0.291238	−	0.168147i
$156$		0			0
$157$	215379.	−	373048.i	0.0556551	−	0.0963974i	−0.836856	−	0.547424i	$-0.815609\pi$
$157$	215379.	−	373048.i	0.0556551	−	0.0963974i	0.892511	+	0.451026i	$0.148942\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	1.08406e6i		−	0.259762i
$162$		0			0
$163$	−4.87338e6			−1.12530			−0.562649	−	0.826696i	$-0.690218\pi$
$163$	−4.87338e6			−1.12530			−0.562649	+	0.826696i	$0.690218\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.72564e6	−	3.88305e6i	−1.44406	−	0.833726i	−0.445939	−	0.895063i	$-0.647130\pi$
$167$	−6.72564e6	−	3.88305e6i	−1.44406	−	0.833726i	−0.998117	+	0.0613369i	$0.980464\pi$
$168$		0			0
$169$	−6.76357e6	−	1.17148e7i	−1.40125	−	2.42704i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.09924e6	+	3.52140e6i	−1.17798	+	0.680106i	−0.955546	−	0.294842i	$-0.904733\pi$
$173$	−6.09924e6	+	3.52140e6i	−1.17798	+	0.680106i	−0.222432	+	0.974948i	$0.571400\pi$
$174$		0			0
$175$	−421401.	+	729889.i	−0.0786289	+	0.136189i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			352194.i			0.0614077i	0.999529	+	0.0307039i	$0.00977488\pi$
$179$			352194.i			0.0614077i	−0.999529	+	0.0307039i	$0.990225\pi$
$180$		0			0
$181$	−503263.			−0.0848710			−0.0424355	−	0.999099i	$-0.513512\pi$
$181$	−503263.			−0.0848710			−0.0424355	+	0.999099i	$0.513512\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.13562e6	−	1.81035e6i	−0.495231	−	0.285922i
$186$		0			0
$187$	−705853.	−	1.22257e6i	−0.107942	−	0.186961i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.51607e6	+	3.18470e6i	−0.791643	+	0.457055i	−0.840541	−	0.541749i	$-0.817763\pi$
$191$	−5.51607e6	+	3.18470e6i	−0.791643	+	0.457055i	0.0488977	+	0.998804i	$0.484429\pi$
$192$		0			0
$193$	−1.35056e6	+	2.33925e6i	−0.187864	+	0.325390i	−0.944538	−	0.328403i	$-0.893490\pi$
$193$	−1.35056e6	+	2.33925e6i	−0.187864	+	0.325390i	0.756674	+	0.653792i	$0.226823\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.74167e6i		−	0.750999i	−0.926823	−	0.375499i	$-0.877471\pi$
$197$		−	5.74167e6i		−	0.750999i	0.926823	−	0.375499i	$-0.122529\pi$
$198$		0			0
$199$	7.52739e6			0.955180			0.477590	−	0.878583i	$-0.341510\pi$
$199$	7.52739e6			0.955180			0.477590	+	0.878583i	$0.341510\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.39439e6	−	805050.i	−0.166685	−	0.0962354i
$204$		0			0
$205$	5.10243e6	+	8.83766e6i	0.592264	+	1.02583i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.09158e7	+	6.30223e6i	−1.19568	+	0.690328i
$210$		0			0
$211$	−6.34178e6	+	1.09843e7i	−0.675094	+	1.16930i	0.301348	+	0.953514i	$0.402563\pi$
$211$	−6.34178e6	+	1.09843e7i	−0.675094	+	1.16930i	−0.976441	+	0.215782i	$0.930770\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	1.07035e6i		−	0.107699i
$216$		0			0
$217$	1.62045e6			0.158583
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.48934e6	+	2.01457e6i	0.323271	+	0.186641i
$222$		0			0
$223$	−6.60263e6	−	1.14361e7i	−0.595392	−	1.03125i	−0.993491	−	0.113906i	$-0.963664\pi$
$223$	−6.60263e6	−	1.14361e7i	−0.595392	−	1.03125i	0.398100	−	0.917342i	$-0.369670\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.37632e7	+	7.94620e6i	−1.17664	+	0.679332i	−0.955234	−	0.295851i	$-0.904397\pi$
$227$	−1.37632e7	+	7.94620e6i	−1.17664	+	0.679332i	−0.221403	+	0.975182i	$0.571064\pi$
$228$		0			0
$229$	1.57241e6	−	2.72350e6i	0.130936	−	0.226788i	−0.793102	−	0.609089i	$-0.791535\pi$
$229$	1.57241e6	−	2.72350e6i	0.130936	−	0.226788i	0.924038	+	0.382301i	$0.124868\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			6.95409e6i			0.549759i	0.961479	+	0.274880i	$0.0886380\pi$
$233$			6.95409e6i			0.549759i	−0.961479	+	0.274880i	$0.911362\pi$
$234$		0			0
$235$	−2.44606e6			−0.188480
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.35289e6	+	1.35844e6i	0.172349	+	0.0995057i	0.583693	−	0.811974i	$-0.301607\pi$
$239$	2.35289e6	+	1.35844e6i	0.172349	+	0.0995057i	−0.411344	+	0.911480i	$0.634941\pi$
$240$		0			0
$241$	1.35533e6	+	2.34750e6i	0.0968266	+	0.167709i	0.910369	−	0.413796i	$-0.135797\pi$
$241$	1.35533e6	+	2.34750e6i	0.0968266	+	0.167709i	−0.813543	+	0.581505i	$0.802464\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.29305e6	+	4.78799e6i	−0.563918	+	0.325578i
$246$		0			0
$247$	1.79872e7	−	3.11547e7i	1.19364	−	2.06744i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	2.84107e7i		−	1.79664i	−0.439342	−	0.898320i	$-0.644788\pi$
$251$		−	2.84107e7i		−	1.79664i	0.439342	−	0.898320i	$-0.355212\pi$
$252$		0			0
$253$	−1.35586e7			−0.837244
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.70883e6	−	5.60539e6i	−0.571962	−	0.330223i	0.185970	−	0.982555i	$-0.440457\pi$
$257$	−9.70883e6	−	5.60539e6i	−0.571962	−	0.330223i	−0.757933	+	0.652333i	$0.773790\pi$
$258$		0			0
$259$	−2.34253e6	−	4.05738e6i	−0.134830	−	0.233532i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.41287e7	+	1.39307e7i	−1.32638	+	0.765784i	−0.984737	−	0.174047i	$-0.944315\pi$
$263$	−2.41287e7	+	1.39307e7i	−1.32638	+	0.765784i	−0.341639	+	0.939831i	$0.610982\pi$
$264$		0			0
$265$	601190.	−	1.04129e6i	0.0323053	−	0.0559545i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			7.85279e6i			0.403429i	0.979444	+	0.201714i	$0.0646513\pi$
$269$			7.85279e6i			0.403429i	−0.979444	+	0.201714i	$0.935349\pi$
$270$		0			0
$271$	−2.02821e6			−0.101907			−0.0509535	−	0.998701i	$-0.516226\pi$
$271$	−2.02821e6			−0.101907			−0.0509535	+	0.998701i	$0.516226\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.12889e6	+	5.27056e6i	0.438955	+	0.253431i
$276$		0			0
$277$	−1.40017e7	−	2.42517e7i	−0.658782	−	1.14104i	−0.980931	−	0.194355i	$-0.937739\pi$
$277$	−1.40017e7	−	2.42517e7i	−0.658782	−	1.14104i	0.322149	−	0.946689i	$-0.395595\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.01460e7	−	1.74048e7i	1.35866	−	0.784423i	0.369217	−	0.929343i	$-0.379626\pi$
$281$	3.01460e7	−	1.74048e7i	1.35866	−	0.784423i	0.989443	+	0.144921i	$0.0462926\pi$
$282$		0			0
$283$	−1.54784e7	+	2.68093e7i	−0.682914	+	1.18284i	0.291174	+	0.956670i	$0.405954\pi$
$283$	−1.54784e7	+	2.68093e7i	−0.682914	+	1.18284i	−0.974088	+	0.226171i	$0.927379\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			1.32047e7i			0.558578i
$288$		0			0
$289$	2.32531e7			0.963356
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.14339e7	+	1.23749e7i	0.852116	+	0.491969i	0.861364	−	0.507988i	$-0.169611\pi$
$293$	2.14339e7	+	1.23749e7i	0.852116	+	0.491969i	−0.00924835	+	0.999957i	$0.502944\pi$
$294$		0			0
$295$	8.62070e6	+	1.49315e7i	0.335797	+	0.581617i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.35130e7	−	1.93487e7i	1.25372	−	0.723834i
$300$		0			0
$301$	692497.	−	1.19944e6i	0.0253932	−	0.0439824i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	9.03516e6i		−	0.318446i
$306$		0			0
$307$	1.90164e7			0.657222			0.328611	−	0.944465i	$-0.393419\pi$
$307$	1.90164e7			0.657222			0.328611	+	0.944465i	$0.393419\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.49630e7	+	1.44124e7i	0.829879	+	0.479131i	0.853811	−	0.520583i	$-0.174285\pi$
$311$	2.49630e7	+	1.44124e7i	0.829879	+	0.479131i	−0.0239322	+	0.999714i	$0.507619\pi$
$312$		0			0
$313$	2.40307e7	+	4.16225e7i	0.783672	+	1.35736i	0.929789	+	0.368092i	$0.119989\pi$
$313$	2.40307e7	+	4.16225e7i	0.783672	+	1.35736i	−0.146118	+	0.989267i	$0.546678\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.07478e6	−	1.77522e6i	0.0965242	−	0.0557282i	−0.450961	−	0.892544i	$-0.648919\pi$
$317$	3.07478e6	−	1.77522e6i	0.0965242	−	0.0557282i	0.547485	+	0.836815i	$0.315585\pi$
$318$		0			0
$319$	−1.00689e7	+	1.74399e7i	−0.310179	+	0.537245i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			7.89725e6i			0.234352i
$324$		0			0
$325$	−3.00854e7			−0.876406
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.74107e6	−	1.58256e6i	−0.0769721	−	0.0444398i
$330$		0			0
$331$	−4.51963e6	−	7.82823e6i	−0.124629	−	0.215864i	0.796959	−	0.604034i	$-0.206441\pi$
$331$	−4.51963e6	−	7.82823e6i	−0.124629	−	0.215864i	−0.921588	+	0.388170i	$0.873107\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.76465e6	−	4.48292e6i	0.206532	−	0.119241i
$336$		0			0
$337$	82154.7	−	142296.i	0.00214656	−	0.00371795i	−0.864950	−	0.501858i	$-0.832650\pi$
$337$	82154.7	−	142296.i	0.00214656	−	0.00371795i	0.867097	+	0.498140i	$0.165983\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	2.02673e7i		−	0.511132i
$342$		0			0
$343$	−2.65106e7			−0.656958
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.59533e7	+	1.49841e7i	0.621160	+	0.358627i	0.777321	−	0.629105i	$-0.216578\pi$
$347$	2.59533e7	+	1.49841e7i	0.621160	+	0.358627i	−0.156160	+	0.987732i	$0.549912\pi$
$348$		0			0
$349$	−1.24435e7	−	2.15528e7i	−0.292729	−	0.507022i	0.681725	−	0.731609i	$-0.261230\pi$
$349$	−1.24435e7	−	2.15528e7i	−0.292729	−	0.507022i	−0.974454	+	0.224587i	$0.927897\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.88005e7	+	1.08545e7i	−0.427410	+	0.246765i	−0.698243	−	0.715861i	$-0.746034\pi$
$353$	−1.88005e7	+	1.08545e7i	−0.427410	+	0.246765i	0.270833	+	0.962626i	$0.412701\pi$
$354$		0			0
$355$	1.22638e7	−	2.12416e7i	0.274120	−	0.474790i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	7.81560e7i		−	1.68919i	−0.535404	−	0.844596i	$-0.679841\pi$
$359$		−	7.81560e7i		−	1.68919i	0.535404	−	0.844596i	$-0.320159\pi$
$360$		0			0
$361$	2.34649e7			0.498767
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.23703e7	+	7.14200e6i	0.254391	+	0.146873i
$366$		0			0
$367$	2.43155e7	+	4.21157e7i	0.491910	+	0.852012i	0.999957	−	0.00931702i	$-0.00296574\pi$
$367$	2.43155e7	+	4.21157e7i	0.491910	+	0.852012i	−0.508047	+	0.861329i	$0.669632\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.34739e6	−	777919.i	0.0263860	−	0.0152339i
$372$		0			0
$373$	−2.28561e7	+	3.95878e7i	−0.440428	+	0.762843i	−0.997721	−	0.0674723i	$-0.978507\pi$
$373$	−2.28561e7	+	3.95878e7i	−0.440428	+	0.762843i	0.557293	+	0.830316i	$0.311840\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	5.74755e7i		−	1.07265i
$378$		0			0
$379$	−2.09916e7			−0.385593			−0.192796	−	0.981239i	$-0.561756\pi$
$379$	−2.09916e7			−0.385593			−0.192796	+	0.981239i	$0.561756\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.34458e7	+	3.08569e7i	0.951299	+	0.549233i	0.893484	−	0.449095i	$-0.148253\pi$
$383$	5.34458e7	+	3.08569e7i	0.951299	+	0.549233i	0.0578149	+	0.998327i	$0.481587\pi$
$384$		0			0
$385$	−8.35438e6	−	1.44702e7i	−0.146397	−	0.253567i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.24081e7	−	7.16380e6i	0.210793	−	0.121701i	−0.390887	−	0.920439i	$-0.627832\pi$
$389$	1.24081e7	−	7.16380e6i	0.210793	−	0.121701i	0.601680	+	0.798737i	$0.294498\pi$
$390$		0			0
$391$	−4.24752e6	+	7.35693e6i	−0.0710568	+	0.123074i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			8.01278e6i			0.130015i
$396$		0			0
$397$	7.70168e7			1.23088			0.615438	−	0.788186i	$-0.288979\pi$
$397$	7.70168e7			1.23088			0.615438	+	0.788186i	$0.288979\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.57065e7	+	4.37092e7i	1.17409	+	0.677859i	0.954639	−	0.297765i	$-0.0962411\pi$
$401$	7.57065e7	+	4.37092e7i	1.17409	+	0.677859i	0.219448	+	0.975624i	$0.429574\pi$
$402$		0			0
$403$	2.89225e7	+	5.00952e7i	0.441896	+	0.765386i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.07466e7	+	2.92985e7i	−0.752703	+	0.434573i
$408$		0			0
$409$	2.56830e7	−	4.44842e7i	0.375384	−	0.650183i	−0.615001	−	0.788526i	$-0.710844\pi$
$409$	2.56830e7	−	4.44842e7i	0.375384	−	0.650183i	0.990384	+	0.138343i	$0.0441777\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			2.23098e7i			0.316698i
$414$		0			0
$415$	5.82579e7			0.815099
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.15800e7	+	6.68574e6i	0.157423	+	0.0908881i	0.576642	−	0.816997i	$-0.304363\pi$
$419$	1.15800e7	+	6.68574e6i	0.157423	+	0.0908881i	−0.419219	+	0.907885i	$0.637696\pi$
$420$		0			0
$421$	5.48660e7	+	9.50307e7i	0.735287	+	1.27355i	0.954597	+	0.297899i	$0.0962860\pi$
$421$	5.48660e7	+	9.50307e7i	0.735287	+	1.27355i	−0.219310	+	0.975655i	$0.570381\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.71965e6	−	3.30224e6i	0.0745080	−	0.0430172i
$426$		0			0
$427$	5.84559e6	−	1.01249e7i	0.0750835	−	0.130048i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	6.35161e7i		−	0.793327i	−0.917964	−	0.396664i	$-0.870168\pi$
$431$		−	6.35161e7i		−	0.793327i	0.917964	−	0.396664i	$-0.129832\pi$
$432$		0			0
$433$	−1.45827e7			−0.179628			−0.0898142	−	0.995959i	$-0.528627\pi$
$433$	−1.45827e7			−0.179628			−0.0898142	+	0.995959i	$0.528627\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.56865e7	+	3.79241e7i	0.787103	+	0.454434i
$438$		0			0
$439$	2.80070e7	+	4.85095e7i	0.331034	+	0.573367i	0.982715	−	0.185126i	$-0.0592692\pi$
$439$	2.80070e7	+	4.85095e7i	0.331034	+	0.573367i	−0.651681	+	0.758493i	$0.725936\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.15568e7	+	6.67232e6i	−0.132931	+	0.0767478i	−0.564991	−	0.825097i	$-0.691120\pi$
$443$	−1.15568e7	+	6.67232e6i	−0.132931	+	0.0767478i	0.432060	+	0.901845i	$0.357787\pi$
$444$		0			0
$445$	−4.05497e7	+	7.02341e7i	−0.460159	+	0.797018i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	9.37897e7i		−	1.03613i	−0.855340	−	0.518067i	$-0.826652\pi$
$449$		−	9.37897e7i		−	1.03613i	0.855340	−	0.518067i	$-0.173348\pi$
$450$		0			0
$451$	1.65154e8			1.80037
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.12993e7	+	2.38442e7i	0.438439	+	0.253133i
$456$		0			0
$457$	5.76767e7	+	9.98990e7i	0.604299	+	1.04668i	0.992162	+	0.124959i	$0.0398800\pi$
$457$	5.76767e7	+	9.98990e7i	0.604299	+	1.04668i	−0.387863	+	0.921717i	$0.626787\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.60801e7	+	9.28384e6i	−0.164129	+	0.0947600i	−0.579815	−	0.814748i	$-0.696875\pi$
$461$	−1.60801e7	+	9.28384e6i	−0.164129	+	0.0947600i	0.415686	+	0.909508i	$0.363542\pi$
$462$		0			0
$463$	3.53162e7	−	6.11695e7i	0.355821	−	0.616300i	−0.631437	−	0.775427i	$-0.717535\pi$
$463$	3.53162e7	−	6.11695e7i	0.355821	−	0.616300i	0.987258	+	0.159127i	$0.0508680\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	8.13433e7i		−	0.798677i	−0.916804	−	0.399338i	$-0.869240\pi$
$467$		−	8.13433e7i		−	0.798677i	0.916804	−	0.399338i	$-0.130760\pi$
$468$		0			0
$469$	1.16015e7			0.112459
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.50017e7	−	8.66121e6i	−0.141761	−	0.0818456i
$474$		0			0
$475$	−2.94842e7	−	5.10681e7i	−0.275111	−	0.476506i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.72480e7	−	5.61461e7i	0.884859	−	0.510874i	0.0126015	−	0.999921i	$-0.495989\pi$
$479$	9.72480e7	−	5.61461e7i	0.884859	−	0.510874i	0.872257	+	0.489047i	$0.162655\pi$
$480$		0			0
$481$	8.36208e7	−	1.44836e8i	0.751414	−	1.30149i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	1.76504e7i		−	0.154714i
$486$		0			0
$487$	−1.17703e8			−1.01907			−0.509533	−	0.860451i	$-0.670182\pi$
$487$	−1.17703e8			−1.01907			−0.509533	+	0.860451i	$0.670182\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.17596e8	−	6.78940e7i	−0.993453	−	0.573571i	−0.0871486	−	0.996195i	$-0.527775\pi$
$491$	−1.17596e8	−	6.78940e7i	−0.993453	−	0.573571i	−0.906305	+	0.422625i	$0.861109\pi$
$492$		0			0
$493$	6.30865e6	+	1.09269e7i	0.0526496	+	0.0911918i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.74859e7	−	1.58690e7i	0.223893	−	0.129265i
$498$		0			0
$499$	2.40967e7	−	4.17367e7i	0.193935	−	0.335905i	−0.752616	−	0.658460i	$-0.771208\pi$
$499$	2.40967e7	−	4.17367e7i	0.193935	−	0.335905i	0.946551	+	0.322555i	$0.104542\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			1.99031e7i			0.156393i	0.996938	+	0.0781963i	$0.0249161\pi$
$503$			1.99031e7i			0.156393i	−0.996938	+	0.0781963i	$0.975084\pi$
$504$		0			0
$505$	1.05348e8			0.817997
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.74516e7	+	2.73962e7i	0.359830	+	0.207748i	0.669006	−	0.743257i	$-0.266720\pi$
$509$	4.74516e7	+	2.73962e7i	0.359830	+	0.207748i	−0.309176	+	0.951005i	$0.600053\pi$
$510$		0			0
$511$	9.24150e6	+	1.60067e7i	0.0692595	+	0.119961i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.92992e7	+	5.15569e7i	−0.653772	+	0.377455i
$516$		0			0
$517$	−1.97934e7	+	3.42832e7i	−0.143235	+	0.248091i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	2.09737e8i		−	1.48307i	−0.670912	−	0.741537i	$-0.734097\pi$
$521$		−	2.09737e8i		−	1.48307i	0.670912	−	0.741537i	$-0.265903\pi$
$522$		0			0
$523$	−1.69217e7			−0.118287			−0.0591436	−	0.998249i	$-0.518837\pi$
$523$	−1.69217e7			−0.118287			−0.0591436	+	0.998249i	$0.518837\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.09971e7	−	6.34919e6i	−0.0751359	−	0.0433797i
$528$		0			0
$529$	−3.32231e7	−	5.75441e7i	−0.224426	−	0.388717i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.08215e8	+	2.35683e8i	−2.69592	+	1.55649i
$534$		0			0
$535$	−5.90407e7	+	1.02262e8i	−0.385559	+	0.667807i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			1.54977e8i			0.989694i
$540$		0			0
$541$	−2.96138e8			−1.87026			−0.935132	−	0.354299i	$-0.884719\pi$
$541$	−2.96138e8			−1.87026			−0.935132	+	0.354299i	$0.884719\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.50996e8	+	8.71775e7i	0.932772	+	0.538536i
$546$		0			0
$547$	−2.32052e7	−	4.01926e7i	−0.141783	−	0.245575i	0.786385	−	0.617736i	$-0.211950\pi$
$547$	−2.32052e7	−	4.01926e7i	−0.141783	−	0.245575i	−0.928168	+	0.372161i	$0.878617\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.75610e7	−	5.63269e7i	0.583205	−	0.336714i
$552$		0			0
$553$	−5.18413e6	+	8.97917e6i	−0.0306549	+	0.0530959i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.93358e8i			1.11892i	0.828859	+	0.559458i	$0.188991\pi$
$557$			1.93358e8i			1.11892i	−0.828859	+	0.559458i	$0.811009\pi$
$558$		0			0
$559$	4.94399e7			0.283036
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.78735e8	+	1.60928e8i	1.56195	+	0.901790i	0.997060	+	0.0766203i	$0.0244129\pi$
$563$	2.78735e8	+	1.60928e8i	1.56195	+	0.901790i	0.564885	+	0.825169i	$0.308920\pi$
$564$		0			0
$565$	−6.48681e7	−	1.12355e8i	−0.359655	−	0.622940i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.32578e8	−	7.65442e7i	0.719674	−	0.415504i	−0.0949586	−	0.995481i	$-0.530272\pi$
$569$	1.32578e8	−	7.65442e7i	0.719674	−	0.415504i	0.814633	+	0.579977i	$0.196939\pi$
$570$		0			0
$571$	−1.23735e8	+	2.14315e8i	−0.664635	+	1.15118i	0.314749	+	0.949175i	$0.398080\pi$
$571$	−1.23735e8	+	2.14315e8i	−0.664635	+	1.15118i	−0.979384	+	0.202007i	$0.935254\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	6.34320e7i		−	0.333661i
$576$		0			0
$577$	1.55274e8			0.808296			0.404148	−	0.914694i	$-0.367568\pi$
$577$	1.55274e8			0.808296			0.404148	+	0.914694i	$0.367568\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.52841e7	+	3.76918e7i	0.332873	+	0.192185i
$582$		0			0
$583$	−9.72960e6	−	1.68522e7i	−0.0491009	−	0.0850453i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.78742e8	+	1.60932e8i	−1.37812	+	0.795659i	−0.991933	−	0.126760i	$-0.959542\pi$
$587$	−2.78742e8	+	1.60932e8i	−1.37812	+	0.795659i	−0.386189	+	0.922420i	$0.626209\pi$
$588$		0			0
$589$	−5.66889e7	+	9.81881e7i	−0.277429	+	0.480522i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	3.82156e8i		−	1.83264i	−0.400448	−	0.916319i	$-0.631146\pi$
$593$		−	3.82156e8i		−	1.83264i	0.400448	−	0.916319i	$-0.368854\pi$
$594$		0			0
$595$	−1.04688e7			−0.0496987
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.30381e7	−	4.21685e7i	−0.339835	−	0.196204i	0.320364	−	0.947295i	$-0.396195\pi$
$599$	−7.30381e7	−	4.21685e7i	−0.339835	−	0.196204i	−0.660199	+	0.751090i	$0.729528\pi$
$600$		0			0
$601$	−4.80447e7	−	8.32159e7i	−0.221321	−	0.383339i	0.733889	−	0.679270i	$-0.237703\pi$
$601$	−4.80447e7	−	8.32159e7i	−0.221321	−	0.383339i	−0.955209	+	0.295931i	$0.904370\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.86839e7	+	2.23342e7i	−0.174689	+	0.100857i
$606$		0			0
$607$	−4.97861e7	+	8.62320e7i	−0.222609	+	0.385569i	−0.955599	−	0.294669i	$-0.904791\pi$
$607$	−4.97861e7	+	8.62320e7i	−0.222609	+	0.385569i	0.732991	+	0.680239i	$0.238124\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	1.12985e8i		−	0.495332i
$612$		0			0
$613$	−2.79460e8			−1.21322			−0.606609	−	0.795000i	$-0.707471\pi$
$613$	−2.79460e8			−1.21322			−0.606609	+	0.795000i	$0.707471\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.17031e8	−	1.83038e8i	−1.34973	−	0.779265i	−0.361516	−	0.932366i	$-0.617741\pi$
$617$	−3.17031e8	−	1.83038e8i	−1.34973	−	0.779265i	−0.988211	+	0.153101i	$0.951074\pi$
$618$		0			0
$619$	−1.53497e8	−	2.65865e8i	−0.647186	−	1.12096i	−0.983792	−	0.179313i	$-0.942613\pi$
$619$	−1.53497e8	−	2.65865e8i	−0.647186	−	1.12096i	0.336606	−	0.941645i	$-0.390721\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.08805e7	+	5.24699e7i	−0.375843	+	0.216993i
$624$		0			0
$625$	4.25495e7	−	7.36978e7i	0.174283	−	0.301866i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			3.67137e7i			0.147529i
$630$		0			0
$631$	−4.69076e8			−1.86705			−0.933523	−	0.358518i	$-0.883282\pi$
$631$	−4.69076e8			−1.86705			−0.933523	+	0.358518i	$0.883282\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.28538e8	+	1.31946e8i	0.892558	+	0.515319i
$636$		0			0
$637$	−2.21159e8	−	3.83059e8i	−0.855632	−	1.48200i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.78248e8	+	1.02911e8i	−0.676784	+	0.390742i	−0.798642	−	0.601806i	$-0.794448\pi$
$641$	−1.78248e8	+	1.02911e8i	−0.676784	+	0.390742i	0.121858	+	0.992548i	$0.461115\pi$
$642$		0			0
$643$	1.50649e8	−	2.60932e8i	0.566676	−	0.981511i	−0.430216	−	0.902726i	$-0.641563\pi$
$643$	1.50649e8	−	2.60932e8i	0.566676	−	0.981511i	0.996892	−	0.0787851i	$-0.0251041\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1.33959e8i		−	0.494604i	−0.968938	−	0.247302i	$-0.920456\pi$
$647$		−	1.33959e8i		−	0.494604i	0.968938	−	0.247302i	$-0.0795440\pi$
$648$		0			0
$649$	2.79033e8			1.02076
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.13278e8	+	1.80871e8i	1.12510	+	0.649576i	0.942698	−	0.333649i	$-0.108280\pi$
$653$	3.13278e8	+	1.80871e8i	1.12510	+	0.649576i	0.182401	+	0.983224i	$0.441613\pi$
$654$		0			0
$655$	−6.65510e7	−	1.15270e8i	−0.236827	−	0.410196i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.64863e8	+	2.10654e8i	−1.27489	+	0.736060i	−0.975905	−	0.218196i	$-0.929983\pi$
$659$	−3.64863e8	+	2.10654e8i	−1.27489	+	0.736060i	−0.298989	+	0.954257i	$0.596649\pi$
$660$		0			0
$661$	−1.67487e8	+	2.90095e8i	−0.579930	+	1.00447i	0.415557	+	0.909567i	$0.363587\pi$
$661$	−1.67487e8	+	2.90095e8i	−0.579930	+	1.00447i	−0.995487	+	0.0949012i	$0.969746\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			9.34707e7i			0.317842i
$666$		0			0
$667$	1.21181e8			0.408374
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.26634e8	−	7.31121e7i	−0.419162	−	0.242003i
$672$		0			0
$673$	−1.42359e8	−	2.46572e8i	−0.467024	−	0.808908i	0.532267	−	0.846577i	$-0.321340\pi$
$673$	−1.42359e8	−	2.46572e8i	−0.467024	−	0.808908i	−0.999290	+	0.0376682i	$0.988007\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.29812e8	+	7.49471e7i	−0.418359	+	0.241540i	−0.694375	−	0.719613i	$-0.744319\pi$
$677$	−1.29812e8	+	7.49471e7i	−0.418359	+	0.241540i	0.276016	+	0.961153i	$0.410986\pi$
$678$		0			0
$679$	1.14195e7	−	1.97791e7i	0.0364785	−	0.0631826i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	5.60477e8i		−	1.75912i	−0.475787	−	0.879560i	$-0.657837\pi$
$683$		−	5.60477e8i		−	1.75912i	0.475787	−	0.879560i	$-0.342163\pi$
$684$		0			0
$685$	−5.20253e7			−0.161861
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.80977e7	+	2.77692e7i	0.147051	+	0.0848997i
$690$		0			0
$691$	8.08334e6	+	1.40008e7i	0.0244995	+	0.0424343i	0.878015	−	0.478633i	$-0.158867\pi$
$691$	8.08334e6	+	1.40008e7i	0.0244995	+	0.0424343i	−0.853516	+	0.521067i	$0.825534\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.57501e7	+	3.79608e7i	−0.195858	+	0.113079i
$696$		0			0
$697$	5.17383e7	−	8.96134e7i	0.152797	−	0.264652i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			5.37669e8i			1.56085i	0.625249	+	0.780425i	$0.284997\pi$
$701$			5.37669e8i			1.56085i	−0.625249	+	0.780425i	$0.715003\pi$
$702$		0			0
$703$	3.27799e8			0.943500
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.18054e8	+	6.81582e7i	0.334057	+	0.192868i
$708$		0			0
$709$	2.93468e8	+	5.08302e8i	0.823422	+	1.42621i	0.903119	+	0.429390i	$0.141271\pi$
$709$	2.93468e8	+	5.08302e8i	0.823422	+	1.42621i	−0.0796974	+	0.996819i	$0.525395\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.05621e8	+	6.09801e7i	−0.291394	+	0.168236i
$714$		0			0
$715$	2.98225e8	−	5.16540e8i	0.815878	−	1.41314i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			4.52832e8i			1.21829i	0.793059	+	0.609144i	$0.208487\pi$
$719$			4.52832e8i			1.21829i	−0.793059	+	0.609144i	$0.791513\pi$
$720$		0			0
$721$	−1.33426e8			−0.355987
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.15905e7	−	4.71063e7i	−0.214104	−	0.123613i
$726$		0			0
$727$	−8.62458e7	−	1.49382e8i	−0.224458	−	0.388772i	0.731699	−	0.681628i	$-0.238728\pi$
$727$	−8.62458e7	−	1.49382e8i	−0.224458	−	0.388772i	−0.956157	+	0.292856i	$0.905394\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.39921e6	+	5.42664e6i	−0.0240624	+	0.0138924i
$732$		0			0
$733$	8.58050e7	−	1.48619e8i	0.217872	−	0.377365i	−0.736285	−	0.676671i	$-0.763422\pi$
$733$	8.58050e7	−	1.48619e8i	0.217872	−	0.377365i	0.954157	+	0.299306i	$0.0967552\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1.45102e8i		−	0.362470i
$738$		0			0
$739$	−5.61249e8			−1.39066			−0.695332	−	0.718688i	$-0.744743\pi$
$739$	−5.61249e8			−1.39066			−0.695332	+	0.718688i	$0.744743\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.02996e8	−	5.94646e7i	−0.251103	−	0.144975i	0.369166	−	0.929363i	$-0.379643\pi$
$743$	−1.02996e8	−	5.94646e7i	−0.251103	−	0.144975i	−0.620269	+	0.784389i	$0.712977\pi$
$744$		0			0
$745$	1.31632e8	+	2.27993e8i	0.318340	+	0.551382i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.32323e8	+	7.63966e7i	−0.314912	+	0.181815i
$750$		0			0
$751$	1.22156e7	−	2.11581e7i	0.0288400	−	0.0499524i	−0.851245	−	0.524768i	$-0.824152\pi$
$751$	1.22156e7	−	2.11581e7i	0.0288400	−	0.0499524i	0.880085	+	0.474816i	$0.157485\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1.63533e8i			0.379983i
$756$		0			0
$757$	−2.95715e8			−0.681688			−0.340844	−	0.940120i	$-0.610713\pi$
$757$	−2.95715e8			−0.681688			−0.340844	+	0.940120i	$0.610713\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.26182e8	−	1.30586e8i	−0.513220	−	0.296308i	0.220936	−	0.975288i	$-0.429089\pi$
$761$	−2.26182e8	−	1.30586e8i	−0.513220	−	0.296308i	−0.734156	+	0.678981i	$0.762422\pi$
$762$		0			0
$763$	1.12805e8	+	1.95383e8i	0.253953	+	0.439859i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.89692e8	+	3.98194e8i	−1.52851	+	0.882487i
$768$		0			0
$769$	2.50506e8	−	4.33889e8i	0.550857	−	0.954112i	−0.447356	−	0.894356i	$-0.647634\pi$
$769$	2.50506e8	−	4.33889e8i	0.550857	−	0.954112i	0.998213	−	0.0597559i	$-0.0190322\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	4.17209e8i		−	0.903265i	−0.892204	−	0.451633i	$-0.850842\pi$
$773$		−	4.17209e8i		−	0.903265i	0.892204	−	0.451633i	$-0.149158\pi$
$774$		0			0
$775$	9.48181e7			0.203698
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.00115e8	−	4.61947e8i	−1.69254	−	0.977191i
$780$		0			0
$781$	−1.98477e8	−	3.43772e8i	−0.416636	−	0.721635i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.46001e7	+	1.99764e7i	−0.0715267	+	0.0412959i
$786$		0			0
$787$	−4.21601e8	+	7.30234e8i	−0.864922	+	1.49809i	0.00220161	+	0.999998i	$0.499299\pi$
$787$	−4.21601e8	+	7.30234e8i	−0.864922	+	1.49809i	−0.867124	+	0.498092i	$0.834034\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	1.67874e8i		−	0.339199i
$792$		0			0
$793$	4.17338e8			0.836889
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.47167e8	−	3.73642e8i	−1.27833	−	0.738042i	−0.301786	−	0.953376i	$-0.597583\pi$
$797$	−6.47167e8	−	3.73642e8i	−1.27833	−	0.738042i	−0.976540	+	0.215334i	$0.930916\pi$
$798$		0			0
$799$	1.24015e7	+	2.14800e7i	0.0243127	+	0.0421108i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.00200e8	−	1.15586e8i	0.386649	−	0.223232i
$804$		0			0
$805$	−5.02731e7	+	8.70755e7i	−0.0963713	+	0.166920i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	4.29916e8i		−	0.811967i	−0.913880	−	0.405984i	$-0.866929\pi$
$809$		−	4.29916e8i		−	0.811967i	0.913880	−	0.405984i	$-0.133071\pi$
$810$		0			0
$811$	2.17167e8			0.407128			0.203564	−	0.979062i	$-0.434748\pi$
$811$	2.17167e8			0.407128			0.203564	+	0.979062i	$0.434748\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.91448e8	+	2.26002e8i	0.723104	+	0.417484i
$816$		0			0
$817$	4.84519e7	+	8.39211e7i	0.0888473	+	0.153888i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.93226e7	+	5.73439e7i	−0.179481	+	0.103623i	−0.587049	−	0.809552i	$-0.699710\pi$
$821$	−9.93226e7	+	5.73439e7i	−0.179481	+	0.103623i	0.407568	+	0.913175i	$0.366377\pi$
$822$		0			0
$823$	3.31550e8	−	5.74262e8i	0.594771	−	1.03017i	−0.398808	−	0.917034i	$-0.630576\pi$
$823$	3.31550e8	−	5.74262e8i	0.594771	−	1.03017i	0.993579	−	0.113139i	$-0.0360905\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	7.09882e7i		−	0.125508i	−0.998029	−	0.0627538i	$-0.980012\pi$
$827$		−	7.09882e7i		−	0.125508i	0.998029	−	0.0627538i	$-0.0199883\pi$
$828$		0			0
$829$	−9.23151e8			−1.62035			−0.810176	−	0.586187i	$-0.800629\pi$
$829$	−9.23151e8			−1.62035			−0.810176	+	0.586187i	$0.800629\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.40910e7	+	4.85500e7i	0.145484	+	0.0839951i
$834$		0			0
$835$	3.60152e8	+	6.23801e8i	0.618623	+	1.07149i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.54532e8	−	3.20159e8i	0.938946	−	0.542101i	0.0493163	−	0.998783i	$-0.484296\pi$
$839$	5.54532e8	−	3.20159e8i	0.938946	−	0.542101i	0.889630	+	0.456682i	$0.150962\pi$
$840$		0			0
$841$	−2.07419e8	+	3.59261e8i	−0.348707	+	0.603979i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.25464e9i			2.07945i
$846$		0			0
$847$	−5.77993e7			−0.0951201
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.05371e8	+	1.76306e8i	0.495495	+	0.286074i
$852$		0			0
$853$	1.17026e8	+	2.02694e8i	0.188553	+	0.326584i	0.944768	−	0.327740i	$-0.106287\pi$
$853$	1.17026e8	+	2.02694e8i	0.188553	+	0.326584i	−0.756215	+	0.654323i	$0.772954\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.81860e8	−	4.51407e8i	1.24219	−	0.717177i	0.272647	−	0.962114i	$-0.412101\pi$
$857$	7.81860e8	−	4.51407e8i	1.24219	−	0.717177i	0.969539	+	0.244937i	$0.0787674\pi$
$858$		0			0
$859$	−3.87666e8	+	6.71458e8i	−0.611616	+	1.05935i	0.379352	+	0.925252i	$0.376147\pi$
$859$	−3.87666e8	+	6.71458e8i	−0.611616	+	1.05935i	−0.990968	+	0.134097i	$0.957186\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1.80225e6i		−	0.00280402i	−0.999999	−	0.00140201i	$-0.999554\pi$
$863$		−	1.80225e6i		−	0.00280402i	0.999999	−	0.00140201i	$-0.000446274\pi$
$864$		0			0
$865$	6.53217e8			1.00927
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.12305e8	+	6.48391e7i	0.171135	+	0.0988047i
$870$		0			0
$871$	2.07068e8	+	3.58652e8i	0.313371	+	0.542774i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.18322e8	−	1.26049e8i	0.325892	−	0.188154i
$876$		0			0
$877$	1.32637e8	−	2.29734e8i	0.196637	−	0.340585i	−0.750799	−	0.660531i	$-0.770331\pi$
$877$	1.32637e8	−	2.29734e8i	0.196637	−	0.340585i	0.947436	+	0.319945i	$0.103665\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1.59497e6i		−	0.00233251i	−0.999999	−	0.00116626i	$-0.999629\pi$
$881$		−	1.59497e6i		−	0.00233251i	0.999999	−	0.00116626i	$-0.000371231\pi$
$882$		0			0
$883$	−7.55655e8			−1.09759			−0.548796	−	0.835956i	$-0.684914\pi$
$883$	−7.55655e8			−1.09759			−0.548796	+	0.835956i	$0.684914\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.65191e8	+	2.10843e8i	0.523298	+	0.302127i	0.738283	−	0.674491i	$-0.235637\pi$
$887$	3.65191e8	+	2.10843e8i	0.523298	+	0.302127i	−0.214985	+	0.976617i	$0.568970\pi$
$888$		0			0
$889$	1.70734e8	+	2.95720e8i	0.243004	+	0.420896i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.91785e8	−	1.10727e8i	0.269314	−	0.155489i
$894$		0			0
$895$	1.63330e7	−	2.82895e7i	0.0227822	−	0.0394599i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1.81142e8i			0.249310i
$900$		0			0
$901$	−1.21921e7			−0.0166687
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.04239e7	+	2.33388e7i	0.0545372	+	0.0314870i
$906$		0			0
$907$	−5.00053e8	−	8.66117e8i	−0.670184	−	1.16079i	−0.977852	−	0.209299i	$-0.932882\pi$
$907$	−5.00053e8	−	8.66117e8i	−0.670184	−	1.16079i	0.307668	−	0.951494i	$-0.400451\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.24689e8	+	7.19891e7i	−0.164920	+	0.0952164i	−0.580188	−	0.814482i	$-0.697021\pi$
$911$	−1.24689e8	+	7.19891e7i	−0.164920	+	0.0952164i	0.415268	+	0.909699i	$0.363688\pi$
$912$		0			0
$913$	4.71420e8	−	8.16523e8i	0.619435	−	1.07289i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1.72229e8i		−	0.223357i
$918$		0			0
$919$	1.25483e9			1.61673			0.808365	−	0.588682i	$-0.200353\pi$
$919$	1.25483e9			1.61673			0.808365	+	0.588682i	$0.200353\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.81158e8	+	5.66472e8i	1.24777	+	0.720399i
$924$		0			0
$925$	−1.37069e8	−	2.37411e8i	−0.173187	−	0.299969i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.98994e7	−	2.30359e7i	0.0497644	−	0.0287315i	−0.474911	−	0.880034i	$-0.657520\pi$
$929$	3.98994e7	−	2.30359e7i	0.0497644	−	0.0287315i	0.524676	+	0.851302i	$0.324187\pi$
$930$		0			0
$931$	4.33480e8	−	7.50809e8i	0.537180	−	0.930423i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1.30935e8i			0.160185i
$936$		0			0
$937$	5.55499e8			0.675250			0.337625	−	0.941281i	$-0.390376\pi$
$937$	5.55499e8			0.675250			0.337625	+	0.941281i	$0.390376\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.36911e8	+	4.25456e8i	0.884394	+	0.510605i	0.872105	−	0.489319i	$-0.162755\pi$
$941$	7.36911e8	+	4.25456e8i	0.884394	+	0.510605i	0.0122896	+	0.999924i	$0.496088\pi$
$942$		0			0
$943$	−4.96914e8	−	8.60681e8i	−0.592579	−	1.02638i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.09931e9	−	6.34686e8i	1.29440	−	0.747325i	0.314973	−	0.949101i	$-0.398005\pi$
$947$	1.09931e9	−	6.34686e8i	1.29440	−	0.747325i	0.979432	+	0.201776i	$0.0646713\pi$
$948$		0			0
$949$	−3.29892e8	+	5.71390e8i	−0.385988	+	0.668550i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.54351e9i		−	1.78333i	−0.452694	−	0.891666i	$-0.649537\pi$
$953$		−	1.54351e9i		−	1.78333i	0.452694	−	0.891666i	$-0.350463\pi$
$954$		0			0
$955$	5.90761e8			0.678268
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.82999e7	−	3.36595e7i	−0.0661016	−	0.0381638i
$960$		0			0
$961$	3.52599e8	+	6.10719e8i	0.397293	+	0.688131i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.16965e8	−	1.25265e8i	0.241439	−	0.139395i
$966$		0			0
$967$	−5.94735e8	+	1.03011e9i	−0.657724	+	1.13921i	0.323479	+	0.946235i	$0.395148\pi$
$967$	−5.94735e8	+	1.03011e9i	−0.657724	+	1.13921i	−0.981203	+	0.192977i	$0.938186\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	8.11000e8i		−	0.885856i	−0.896557	−	0.442928i	$-0.853940\pi$
$971$		−	8.11000e8i		−	0.885856i	0.896557	−	0.442928i	$-0.146060\pi$
$972$		0			0
$973$	−9.82399e7			−0.106647
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.17951e9	+	6.80992e8i	1.26479	+	0.730228i	0.973998	−	0.226558i	$-0.0727474\pi$
$977$	1.17951e9	+	6.80992e8i	1.26479	+	0.730228i	0.290794	+	0.956786i	$0.406081\pi$
$978$		0			0
$979$	6.56253e8	+	1.13666e9i	0.699396	+	1.21139i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.09347e8	+	6.31316e7i	−0.115119	+	0.0664640i	−0.556454	−	0.830878i	$-0.687838\pi$
$983$	−1.09347e8	+	6.31316e7i	−0.115119	+	0.0664640i	0.441335	+	0.897342i	$0.354505\pi$
$984$		0			0
$985$	−2.66269e8	+	4.61191e8i	−0.278620	+	0.482584i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			1.04239e8i			0.107756i
$990$		0			0
$991$	1.97170e8			0.202590			0.101295	−	0.994856i	$-0.467701\pi$
$991$	1.97170e8			0.202590			0.101295	+	0.994856i	$0.467701\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.04627e8	−	3.49082e8i	−0.613788	−	0.354371i
$996$		0			0
$997$	−4.53174e7	−	7.84920e7i	−0.0457277	−	0.0792026i	0.842256	−	0.539078i	$-0.181227\pi$
$997$	−4.53174e7	−	7.84920e7i	−0.0457277	−	0.0792026i	−0.887983	+	0.459876i	$0.847894\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.7.q.a.17.2		10
3.2	odd	2		144.7.q.a.113.4		10
4.3	odd	2		27.7.d.a.17.2		10
9.2	odd	6	inner	432.7.q.a.305.2		10
9.7	even	3		144.7.q.a.65.4		10
12.11	even	2		9.7.d.a.5.4	yes	10
36.7	odd	6		9.7.d.a.2.4	✓	10
36.11	even	6		27.7.d.a.8.2		10
36.23	even	6		81.7.b.a.80.8		10
36.31	odd	6		81.7.b.a.80.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.4	✓	10	36.7	odd	6
9.7.d.a.5.4	yes	10	12.11	even	2
27.7.d.a.8.2		10	36.11	even	6
27.7.d.a.17.2		10	4.3	odd	2
81.7.b.a.80.3		10	36.31	odd	6
81.7.b.a.80.8		10	36.23	even	6
144.7.q.a.65.4		10	9.7	even	3
144.7.q.a.113.4		10	3.2	odd	2
432.7.q.a.17.2		10	1.1	even	1	trivial
432.7.q.a.305.2		10	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	432.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-80.3236 - 46.3749i) q^{5} +(-60.0074 - 103.936i) q^{7} +O(q^{10})\)	\(q+(-80.3236 - 46.3749i) q^{5} +(-60.0074 - 103.936i) q^{7} +(-1299.95 + 750.527i) q^{11} +(2142.08 - 3710.18i) q^{13} +940.477i q^{17} +8397.07 q^{19} +(7822.55 + 4516.35i) q^{23} +(-3511.24 - 6081.65i) q^{25} +(11618.5 - 6707.92i) q^{29} +(-6751.04 + 11693.1i) q^{31} +11131.3i q^{35} +39037.3 q^{37} +(-95285.0 - 55012.8i) q^{41} +(5770.09 + 9994.09i) q^{43} +(22839.5 - 13186.4i) q^{47} +(51622.7 - 89413.2i) q^{49} +12963.7i q^{53} +139222. q^{55} +(-160987. - 92945.8i) q^{59} +(48707.2 + 84363.3i) q^{61} +(-344118. + 198677. i) q^{65} +(-48333.5 + 83716.1i) q^{67} +264450. i q^{71} -154006. q^{73} +(156013. + 90074.4i) q^{77} +(-43195.7 - 74817.2i) q^{79} +(-543967. + 314059. i) q^{83} +(43614.5 - 75542.5i) q^{85} -874390. i q^{89} -514162. q^{91} +(-674483. - 389413. i) q^{95} +(95150.6 + 164806. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 219 q^{5} + 121 q^{7}+O(q^{10}) \) 10 * q + 219 * q^5 + 121 * q^7	\( 10 q + 219 q^{5} + 121 q^{7} + 483 q^{11} - 841 q^{13} - 6176 q^{19} + 53565 q^{23} + 8452 q^{25} + 80679 q^{29} + 24601 q^{31} + 12764 q^{37} - 232251 q^{41} + 93271 q^{43} - 142887 q^{47} + 86238 q^{49} + 419982 q^{55} - 995061 q^{59} - 59305 q^{61} - 1642029 q^{65} - 158513 q^{67} + 933896 q^{73} + 2198883 q^{77} - 468707 q^{79} + 3008337 q^{83} - 1189944 q^{85} + 211778 q^{91} - 2562954 q^{95} + 336029 q^{97}+O(q^{100}) \) 10 * q + 219 * q^5 + 121 * q^7 + 483 * q^11 - 841 * q^13 - 6176 * q^19 + 53565 * q^23 + 8452 * q^25 + 80679 * q^29 + 24601 * q^31 + 12764 * q^37 - 232251 * q^41 + 93271 * q^43 - 142887 * q^47 + 86238 * q^49 + 419982 * q^55 - 995061 * q^59 - 59305 * q^61 - 1642029 * q^65 - 158513 * q^67 + 933896 * q^73 + 2198883 * q^77 - 468707 * q^79 + 3008337 * q^83 - 1189944 * q^85 + 211778 * q^91 - 2562954 * q^95 + 336029 * q^97

Introduction

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