LMFDB - Embedded newform 432.6.s.b.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,6,Mod(143,432)]

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([3, 0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("432.143");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	432.s (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:	$69.2858101592$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 12929 x^{18} + 122470 x^{17} + 67551337 x^{16} - 634332392 x^{15} + \cdots + 12\!\cdots\!83 $ x^20 - 8x^19 - 12929x^18 + 122470x^17 + 67551337x^16 - 634332392x^15 - 188739189566x^14 + 1465408138900x^13 + 318666777232513x^12 - 1659822095888928x^11 - 342482041534942599x^10 + 771926315021092530x^9 + 235755127534409726427x^8 + 153250066227088305288x^7 - 100256545026170218824966x^6 - 307587004828158415060260x^5 + 24024188188277080735469283x^4 + 105469820000699659948031832x^3 - 2717384790950355201449127129x^2 - 8852858122961343064388762610*x + 128982324636807574943959790283
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{39} $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.4
Root			$30.2198 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	432.143
Dual form			432.6.s.b.287.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-49.0797 + 28.3362i) q^{5} +(-75.4185 - 43.5429i) q^{7} +O(q^{10})$	$q+(-49.0797 + 28.3362i) q^{5} +(-75.4185 - 43.5429i) q^{7} +(159.302 - 275.919i) q^{11} +(377.472 + 653.801i) q^{13} +332.298i q^{17} +69.0437i q^{19} +(1013.77 + 1755.90i) q^{23} +(43.3805 - 75.1372i) q^{25} +(6016.97 + 3473.90i) q^{29} +(-5599.59 + 3232.93i) q^{31} +4935.36 q^{35} -10060.5 q^{37} +(-3454.97 + 1994.73i) q^{41} +(-13143.7 - 7588.53i) q^{43} +(8608.06 - 14909.6i) q^{47} +(-4611.53 - 7987.41i) q^{49} -13095.4i q^{53} +18056.0i q^{55} +(-10216.6 - 17695.6i) q^{59} +(13312.7 - 23058.2i) q^{61} +(-37052.4 - 21392.2i) q^{65} +(32423.3 - 18719.6i) q^{67} +74248.6 q^{71} -57615.2 q^{73} +(-24028.6 + 13872.9i) q^{77} +(-27339.3 - 15784.4i) q^{79} +(-12160.6 + 21062.8i) q^{83} +(-9416.07 - 16309.1i) q^{85} -87035.9i q^{89} -65744.9i q^{91} +(-1956.44 - 3388.64i) q^{95} +(-89837.0 + 155602. i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 87 q^{5} + 87 q^{7}+O(q^{10}) $ 20 * q - 87 * q^5 + 87 * q^7	$ 20 q - 87 q^{5} + 87 q^{7} + 570 q^{11} - 181 q^{13} + 99 q^{23} + 7903 q^{25} - 13191 q^{29} + 6651 q^{31} + 10830 q^{35} - 4856 q^{37} - 846 q^{41} - 15315 q^{47} + 17891 q^{49} + 13308 q^{59} - 24773 q^{61} + 48255 q^{65} - 6402 q^{67} - 43188 q^{71} - 11614 q^{73} + 79317 q^{77} - 171897 q^{79} - 43347 q^{83} - 8850 q^{85} - 210684 q^{95} + 66332 q^{97}+O(q^{100}) $ 20 * q - 87 * q^5 + 87 * q^7 + 570 * q^11 - 181 * q^13 + 99 * q^23 + 7903 * q^25 - 13191 * q^29 + 6651 * q^31 + 10830 * q^35 - 4856 * q^37 - 846 * q^41 - 15315 * q^47 + 17891 * q^49 + 13308 * q^59 - 24773 * q^61 + 48255 * q^65 - 6402 * q^67 - 43188 * q^71 - 11614 * q^73 + 79317 * q^77 - 171897 * q^79 - 43347 * q^83 - 8850 * q^85 - 210684 * q^95 + 66332 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−49.0797	+	28.3362i	−0.877965	+	0.506893i	−0.869987	−	0.493075i	$-0.835873\pi$
$5$	−49.0797	+	28.3362i	−0.877965	+	0.506893i	−0.00797815	+	0.999968i	$0.502540\pi$
$6$		0			0
$7$	−75.4185	−	43.5429i	−0.581745	−	0.335871i	0.180081	−	0.983652i	$-0.442364\pi$
$7$	−75.4185	−	43.5429i	−0.581745	−	0.335871i	−0.761827	+	0.647781i	$0.775697\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	159.302	−	275.919i	0.396952	−	0.687542i	−0.596396	−	0.802691i	$-0.703401\pi$
$11$	159.302	−	275.919i	0.396952	−	0.687542i	0.993348	+	0.115149i	$0.0367344\pi$
$12$		0			0
$13$	377.472	+	653.801i	0.619479	+	1.07297i	0.989581	+	0.143977i	$0.0459892\pi$
$13$	377.472	+	653.801i	0.619479	+	1.07297i	−0.370102	+	0.928991i	$0.620677\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			332.298i			0.278873i	0.990231	+	0.139436i	$0.0445290\pi$
$17$			332.298i			0.278873i	−0.990231	+	0.139436i	$0.955471\pi$
$18$		0			0
$19$			69.0437i			0.0438773i	0.999759	+	0.0219386i	$0.00698385\pi$
$19$			69.0437i			0.0438773i	−0.999759	+	0.0219386i	$0.993016\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1013.77	+	1755.90i	0.399594	+	0.692117i	0.993676	−	0.112287i	$-0.0358177\pi$
$23$	1013.77	+	1755.90i	0.399594	+	0.692117i	−0.594082	+	0.804405i	$0.702484\pi$
$24$		0			0
$25$	43.3805	−	75.1372i	0.0138818	−	0.0240439i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6016.97	+	3473.90i	1.32857	+	0.767048i	0.985078	−	0.172109i	$-0.0550583\pi$
$29$	6016.97	+	3473.90i	1.32857	+	0.767048i	0.343488	+	0.939157i	$0.388392\pi$
$30$		0			0
$31$	−5599.59	+	3232.93i	−1.04653	+	0.604215i	−0.921676	−	0.387960i	$-0.873180\pi$
$31$	−5599.59	+	3232.93i	−1.04653	+	0.604215i	−0.124855	+	0.992175i	$0.539847\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4935.36			0.681003
$36$		0			0
$37$	−10060.5			−1.20814			−0.604070	−	0.796931i	$-0.706455\pi$
$37$	−10060.5			−1.20814			−0.604070	+	0.796931i	$0.706455\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3454.97	+	1994.73i	−0.320985	+	0.185321i	−0.651832	−	0.758364i	$-0.725999\pi$
$41$	−3454.97	+	1994.73i	−0.320985	+	0.185321i	0.330847	+	0.943685i	$0.392666\pi$
$42$		0			0
$43$	−13143.7	−	7588.53i	−1.08404	−	0.625873i	−0.152060	−	0.988371i	$-0.548591\pi$
$43$	−13143.7	−	7588.53i	−1.08404	−	0.625873i	−0.931985	+	0.362498i	$0.881924\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8608.06	−	14909.6i	0.568409	−	0.984513i	−0.428315	−	0.903630i	$-0.640893\pi$
$47$	8608.06	−	14909.6i	0.568409	−	0.984513i	0.996724	−	0.0808833i	$-0.0257741\pi$
$48$		0			0
$49$	−4611.53	−	7987.41i	−0.274382	−	0.475243i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	13095.4i		−	0.640369i	−0.947355	−	0.320184i	$-0.896255\pi$
$53$		−	13095.4i		−	0.640369i	0.947355	−	0.320184i	$-0.103745\pi$
$54$		0			0
$55$			18056.0i			0.804850i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−10216.6	−	17695.6i	−0.382099	−	0.661814i	0.609263	−	0.792968i	$-0.291465\pi$
$59$	−10216.6	−	17695.6i	−0.382099	−	0.661814i	−0.991362	+	0.131154i	$0.958132\pi$
$60$		0			0
$61$	13312.7	−	23058.2i	0.458080	−	0.793417i	−0.540780	−	0.841164i	$-0.681871\pi$
$61$	13312.7	−	23058.2i	0.458080	−	0.793417i	0.998859	+	0.0477470i	$0.0152041\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−37052.4	−	21392.2i	−1.08776	−	0.628019i
$66$		0			0
$67$	32423.3	−	18719.6i	0.882410	−	0.509460i	0.0109577	−	0.999940i	$-0.496512\pi$
$67$	32423.3	−	18719.6i	0.882410	−	0.509460i	0.871452	+	0.490480i	$0.163179\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	74248.6			1.74800			0.874002	−	0.485922i	$-0.161516\pi$
$71$	74248.6			1.74800			0.874002	+	0.485922i	$0.161516\pi$
$72$		0			0
$73$	−57615.2			−1.26541			−0.632703	−	0.774394i	$-0.718055\pi$
$73$	−57615.2			−1.26541			−0.632703	+	0.774394i	$0.718055\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−24028.6	+	13872.9i	−0.461850	+	0.266649i
$78$		0			0
$79$	−27339.3	−	15784.4i	−0.492856	−	0.284551i	0.232903	−	0.972500i	$-0.425178\pi$
$79$	−27339.3	−	15784.4i	−0.492856	−	0.284551i	−0.725759	+	0.687950i	$0.758511\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−12160.6	+	21062.8i	−0.193758	+	0.335598i	−0.946493	−	0.322725i	$-0.895401\pi$
$83$	−12160.6	+	21062.8i	−0.193758	+	0.335598i	0.752735	+	0.658324i	$0.228734\pi$
$84$		0			0
$85$	−9416.07	−	16309.1i	−0.141359	−	0.244840i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	87035.9i		−	1.16473i	−0.812929	−	0.582363i	$-0.802128\pi$
$89$		−	87035.9i		−	1.16473i	0.812929	−	0.582363i	$-0.197872\pi$
$90$		0			0
$91$		−	65744.9i		−	0.832259i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1956.44	−	3388.64i	−0.0222411	−	0.0385227i
$96$		0			0
$97$	−89837.0	+	155602.i	−0.969451	+	1.67914i	−0.272301	+	0.962212i	$0.587785\pi$
$97$	−89837.0	+	155602.i	−0.969451	+	1.67914i	−0.697150	+	0.716926i	$0.745549\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−92093.8	−	53170.4i	−0.898312	−	0.518640i	−0.0216596	−	0.999765i	$-0.506895\pi$
$101$	−92093.8	−	53170.4i	−0.898312	−	0.518640i	−0.876652	+	0.481125i	$0.840228\pi$
$102$		0			0
$103$	160588.	−	92715.5i	1.49149	−	0.861112i	0.491536	−	0.870857i	$-0.336435\pi$
$103$	160588.	−	92715.5i	1.49149	−	0.861112i	0.999953	+	0.00974553i	$0.00310215\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−122692.			−1.03599			−0.517995	−	0.855384i	$-0.673321\pi$
$107$	−122692.			−1.03599			−0.517995	+	0.855384i	$0.673321\pi$
$108$		0			0
$109$	−119948.			−0.966997			−0.483499	−	0.875345i	$-0.660634\pi$
$109$	−119948.			−0.966997			−0.483499	+	0.875345i	$0.660634\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	138127.	−	79747.5i	1.01761	−	0.587518i	0.104200	−	0.994556i	$-0.466772\pi$
$113$	138127.	−	79747.5i	1.01761	−	0.587518i	0.913411	+	0.407039i	$0.133439\pi$
$114$		0			0
$115$	−99511.0	−	57452.7i	−0.701659	−	0.405103i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14469.2	−	25061.4i	0.0936651	−	0.162233i
$120$		0			0
$121$	29771.5	+	51565.7i	0.184857	+	0.320182i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	172184.i		−	0.985640i
$126$		0			0
$127$		−	61771.8i		−	0.339845i	−0.985457	−	0.169923i	$-0.945648\pi$
$127$		−	61771.8i		−	0.339845i	0.985457	−	0.169923i	$-0.0543517\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	12343.8	+	21380.1i	0.0628449	+	0.108851i	0.895736	−	0.444586i	$-0.146649\pi$
$131$	12343.8	+	21380.1i	0.0628449	+	0.108851i	−0.832891	+	0.553437i	$0.813316\pi$
$132$		0			0
$133$	3006.36	−	5207.17i	0.0147371	−	0.0255254i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−325739.	−	188066.i	−1.48275	−	0.856068i	−0.482945	−	0.875651i	$-0.660433\pi$
$137$	−325739.	−	188066.i	−1.48275	−	0.856068i	−0.999808	+	0.0195831i	$0.993766\pi$
$138$		0			0
$139$	−112288.	+	64829.3i	−0.492941	+	0.284599i	−0.725794	−	0.687913i	$-0.758527\pi$
$139$	−112288.	+	64829.3i	−0.492941	+	0.284599i	0.232853	+	0.972512i	$0.425194\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	240528.			0.983614
$144$		0			0
$145$	−393749.			−1.55525
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−223759.	+	129187.i	−0.825685	+	0.476709i	−0.852373	−	0.522934i	$-0.824837\pi$
$149$	−223759.	+	129187.i	−0.825685	+	0.476709i	0.0266881	+	0.999644i	$0.491504\pi$
$150$		0			0
$151$	92287.3	+	53282.1i	0.329382	+	0.190169i	0.655567	−	0.755137i	$-0.272430\pi$
$151$	92287.3	+	53282.1i	0.329382	+	0.190169i	−0.326185	+	0.945306i	$0.605763\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	183218.	−	317342.i	0.612545	−	1.06096i
$156$		0			0
$157$	−155176.	−	268772.i	−0.502428	−	0.870231i	−0.999996	−	0.00280627i	$-0.999107\pi$
$157$	−155176.	−	268772.i	−0.502428	−	0.870231i	0.497568	−	0.867425i	$-0.334227\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	176570.i		−	0.536848i
$162$		0			0
$163$		−	498750.i		−	1.47033i	−0.677890	−	0.735163i	$-0.737105\pi$
$163$		−	498750.i		−	1.47033i	0.677890	−	0.735163i	$-0.262895\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−55474.5	−	96084.6i	−0.153923	−	0.266602i	0.778744	−	0.627342i	$-0.215857\pi$
$167$	−55474.5	−	96084.6i	−0.153923	−	0.266602i	−0.932666	+	0.360741i	$0.882524\pi$
$168$		0			0
$169$	−99323.6	+	172034.i	−0.267507	+	0.463336i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−320045.	−	184778.i	−0.813011	−	0.469392i	0.0349895	−	0.999388i	$-0.488860\pi$
$173$	−320045.	−	184778.i	−0.813011	−	0.469392i	−0.848000	+	0.529996i	$0.822194\pi$
$174$		0			0
$175$	−6543.39	+	3777.83i	−0.0161513	+	0.00932496i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	715607.			1.66933			0.834664	−	0.550759i	$-0.185662\pi$
$179$	715607.			1.66933			0.834664	+	0.550759i	$0.185662\pi$
$180$		0			0
$181$	−246891.			−0.560155			−0.280077	−	0.959977i	$-0.590360\pi$
$181$	−246891.			−0.560155			−0.280077	+	0.959977i	$0.590360\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	493769.	−	285078.i	1.06070	−	0.612398i
$186$		0			0
$187$	91687.3	+	52935.7i	0.191737	+	0.110699i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−62758.7	+	108701.i	−0.124477	+	0.215601i	−0.921529	−	0.388311i	$-0.873059\pi$
$191$	−62758.7	+	108701.i	−0.124477	+	0.215601i	0.797051	+	0.603912i	$0.206392\pi$
$192$		0			0
$193$	−375743.	−	650805.i	−0.726101	−	1.25764i	−0.958519	−	0.285028i	$-0.907997\pi$
$193$	−375743.	−	650805.i	−0.726101	−	1.25764i	0.232418	−	0.972616i	$-0.425336\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			547772.i			1.00562i	0.864397	+	0.502811i	$0.167701\pi$
$197$			547772.i			1.00562i	−0.864397	+	0.502811i	$0.832299\pi$
$198$		0			0
$199$		−	90612.6i		−	0.162202i	−0.996706	−	0.0811009i	$-0.974156\pi$
$199$		−	90612.6i		−	0.162202i	0.996706	−	0.0811009i	$-0.0258436\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−302527.	−	523993.i	−0.515258	−	0.892453i
$204$		0			0
$205$	113046.	−	195801.i	0.187876	−	0.325410i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	19050.4	+	10998.8i	0.0301675	+	0.0174172i
$210$		0			0
$211$	−723942.	+	417968.i	−1.11943	+	0.646304i	−0.941256	−	0.337694i	$-0.890353\pi$
$211$	−723942.	+	417968.i	−1.11943	+	0.646304i	−0.178176	+	0.983999i	$0.557020\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	860120.			1.26900
$216$		0			0
$217$	563084.			0.811753
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−217257.	+	125433.i	−0.299221	+	0.172756i
$222$		0			0
$223$	−437025.	−	252317.i	−0.588497	−	0.339769i	0.176006	−	0.984389i	$-0.443682\pi$
$223$	−437025.	−	252317.i	−0.588497	−	0.339769i	−0.764503	+	0.644620i	$0.777016\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−372929.	+	645931.i	−0.480354	+	0.831997i	−0.999746	−	0.0225389i	$-0.992825\pi$
$227$	−372929.	+	645931.i	−0.480354	+	0.831997i	0.519392	+	0.854536i	$0.326158\pi$
$228$		0			0
$229$	289677.	+	501735.i	0.365027	+	0.632245i	0.988780	−	0.149376i	$-0.0477265\pi$
$229$	289677.	+	501735.i	0.365027	+	0.632245i	−0.623754	+	0.781621i	$0.714393\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	247422.i		−	0.298572i	−0.988794	−	0.149286i	$-0.952303\pi$
$233$		−	247422.i		−	0.298572i	0.988794	−	0.149286i	$-0.0476975\pi$
$234$		0			0
$235$			975679.i			1.15249i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−285864.	−	495131.i	−0.323716	−	0.560693i	0.657536	−	0.753424i	$-0.271599\pi$
$239$	−285864.	−	495131.i	−0.323716	−	0.560693i	−0.981252	+	0.192731i	$0.938266\pi$
$240$		0			0
$241$	−697541.	+	1.20818e6i	−0.773619	+	1.33995i	0.161949	+	0.986799i	$0.448222\pi$
$241$	−697541.	+	1.20818e6i	−0.773619	+	1.33995i	−0.935567	+	0.353148i	$0.885111\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	452666.	+	261347.i	0.481795	+	0.278165i
$246$		0			0
$247$	−45140.8	+	26062.0i	−0.0470789	+	0.0271810i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.24063e6			−1.24296			−0.621482	−	0.783428i	$-0.713469\pi$
$251$	−1.24063e6			−1.24296			−0.621482	+	0.783428i	$0.713469\pi$
$252$		0			0
$253$	645980.			0.634480
$254$		0			0
$255$		0			0
$256$		0			0
$257$	130654.	−	75433.1i	0.123393	−	0.0712409i	−0.437033	−	0.899445i	$-0.643971\pi$
$257$	130654.	−	75433.1i	0.123393	−	0.0712409i	0.560426	+	0.828205i	$0.310637\pi$
$258$		0			0
$259$	758751.	+	438065.i	0.702830	+	0.405779i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−893985.	+	1.54843e6i	−0.796968	+	1.38039i	0.124614	+	0.992205i	$0.460231\pi$
$263$	−893985.	+	1.54843e6i	−0.796968	+	1.38039i	−0.921582	+	0.388183i	$0.873103\pi$
$264$		0			0
$265$	371075.	+	642720.i	0.324599	+	0.562221i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			1.01794e6i			0.857710i	0.903373	+	0.428855i	$0.141083\pi$
$269$			1.01794e6i			0.857710i	−0.903373	+	0.428855i	$0.858917\pi$
$270$		0			0
$271$		−	1.47206e6i		−	1.21759i	−0.793326	−	0.608797i	$-0.791652\pi$
$271$		−	1.47206e6i		−	1.21759i	0.793326	−	0.608797i	$-0.208348\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13821.2	−	23939.0i	−0.0110208	−	0.0190886i
$276$		0			0
$277$	878713.	−	1.52197e6i	0.688093	−	1.19181i	−0.284360	−	0.958717i	$-0.591781\pi$
$277$	878713.	−	1.52197e6i	0.688093	−	1.19181i	0.972454	−	0.233095i	$-0.0748854\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.07123e6	+	618476.i	0.809315	+	0.467258i	0.846718	−	0.532042i	$-0.178575\pi$
$281$	1.07123e6	+	618476.i	0.809315	+	0.467258i	−0.0374032	+	0.999300i	$0.511909\pi$
$282$		0			0
$283$	1.29827e6	−	749559.i	0.963608	−	0.556339i	0.0663264	−	0.997798i	$-0.478872\pi$
$283$	1.29827e6	−	749559.i	0.963608	−	0.556339i	0.897282	+	0.441459i	$0.145539\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	347425.			0.248975
$288$		0			0
$289$	1.30943e6			0.922230
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.38201e6	−	797904.i	0.940465	−	0.542978i	0.0503587	−	0.998731i	$-0.483964\pi$
$293$	1.38201e6	−	797904.i	0.940465	−	0.542978i	0.890106	+	0.455754i	$0.150630\pi$
$294$		0			0
$295$	1.00285e6	+	578998.i	0.670939	+	0.387367i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−765338.	+	1.32560e6i	−0.495080	+	0.857504i
$300$		0			0
$301$	660853.	+	1.14463e6i	0.420425	+	0.728197i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.50892e6i			0.928790i
$306$		0			0
$307$			2.51933e6i			1.52559i	0.646638	+	0.762797i	$0.276174\pi$
$307$			2.51933e6i			1.52559i	−0.646638	+	0.762797i	$0.723826\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−349799.	−	605869.i	−0.205077	−	0.355204i	0.745080	−	0.666975i	$-0.232411\pi$
$311$	−349799.	−	605869.i	−0.205077	−	0.355204i	−0.950157	+	0.311771i	$0.899078\pi$
$312$		0			0
$313$	928393.	−	1.60802e6i	0.535638	−	0.927752i	−0.463494	−	0.886100i	$-0.653405\pi$
$313$	928393.	−	1.60802e6i	0.535638	−	0.927752i	0.999132	−	0.0416519i	$-0.0132621\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.46403e6	−	845260.i	−0.818281	−	0.472435i	0.0315422	−	0.999502i	$-0.489958\pi$
$317$	−1.46403e6	−	845260.i	−0.818281	−	0.472435i	−0.849823	+	0.527068i	$0.823291\pi$
$318$		0			0
$319$	1.91703e6	−	1.10680e6i	1.05475	−	0.608963i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−22943.1			−0.0122362
$324$		0			0
$325$	65499.7			0.0343978
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.29841e6	+	749640.i	−0.661338	+	0.381824i
$330$		0			0
$331$	−1.36973e6	−	790813.i	−0.687170	−	0.396738i	0.115381	−	0.993321i	$-0.463191\pi$
$331$	−1.36973e6	−	790813.i	−0.687170	−	0.396738i	−0.802551	+	0.596583i	$0.796525\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.06089e6	+	1.83751e6i	−0.516483	+	0.894575i
$336$		0			0
$337$	514647.	+	891394.i	0.246851	+	0.427558i	0.962650	−	0.270748i	$-0.0872709\pi$
$337$	514647.	+	891394.i	0.246851	+	0.427558i	−0.715800	+	0.698306i	$0.753938\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			2.06004e6i			0.959379i
$342$		0			0
$343$			2.26685e6i			1.04037i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.03935e6	−	3.53226e6i	−0.909219	−	1.57481i	−0.815152	−	0.579247i	$-0.803347\pi$
$347$	−2.03935e6	−	3.53226e6i	−0.909219	−	1.57481i	−0.0940669	−	0.995566i	$-0.529987\pi$
$348$		0			0
$349$	729214.	−	1.26304e6i	0.320473	−	0.555076i	−0.660113	−	0.751167i	$-0.729491\pi$
$349$	729214.	−	1.26304e6i	0.320473	−	0.555076i	0.980586	+	0.196091i	$0.0628248\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.25781e6	−	726195.i	−0.537251	−	0.310182i	0.206713	−	0.978402i	$-0.433723\pi$
$353$	−1.25781e6	−	726195.i	−0.537251	−	0.310182i	−0.743964	+	0.668220i	$0.767057\pi$
$354$		0			0
$355$	−3.64410e6	+	2.10392e6i	−1.53469	+	0.886052i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.33155e6			0.954793			0.477396	−	0.878688i	$-0.341581\pi$
$359$	2.33155e6			0.954793			0.477396	+	0.878688i	$0.341581\pi$
$360$		0			0
$361$	2.47133e6			0.998075
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.82774e6	−	1.63260e6i	1.11098	−	0.641426i
$366$		0			0
$367$	1.61177e6	+	930558.i	0.624653	+	0.360644i	0.778678	−	0.627423i	$-0.215890\pi$
$367$	1.61177e6	+	930558.i	0.624653	+	0.360644i	−0.154025	+	0.988067i	$0.549224\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−570213.	+	987638.i	−0.215081	+	0.372531i
$372$		0			0
$373$	232428.	+	402576.i	0.0864999	+	0.149822i	0.906029	−	0.423215i	$-0.139098\pi$
$373$	232428.	+	402576.i	0.0864999	+	0.149822i	−0.819529	+	0.573037i	$0.805765\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.24520e6i			1.90068i
$378$		0			0
$379$			1.43544e6i			0.513320i	0.966502	+	0.256660i	$0.0826220\pi$
$379$			1.43544e6i			0.513320i	−0.966502	+	0.256660i	$0.917378\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	272349.	+	471722.i	0.0948700	+	0.164320i	0.909554	−	0.415585i	$-0.136423\pi$
$383$	272349.	+	471722.i	0.0948700	+	0.164320i	−0.814684	+	0.579905i	$0.803090\pi$
$384$		0			0
$385$	786211.	−	1.36176e6i	0.270326	−	0.468218i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.01371e6	+	2.31732e6i	1.34484	+	0.776446i	0.987514	−	0.157532i	$-0.0503537\pi$
$389$	4.01371e6	+	2.31732e6i	1.34484	+	0.776446i	0.357330	+	0.933978i	$0.383687\pi$
$390$		0			0
$391$	−583482.	+	336873.i	−0.193013	+	0.111436i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.78908e6			0.576947
$396$		0			0
$397$	−544504.			−0.173390			−0.0866951	−	0.996235i	$-0.527631\pi$
$397$	−544504.			−0.173390			−0.0866951	+	0.996235i	$0.527631\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.13163e6	−	2.38540e6i	1.28310	−	0.740798i	0.305686	−	0.952132i	$-0.401114\pi$
$401$	4.13163e6	−	2.38540e6i	1.28310	−	0.740798i	0.977414	+	0.211334i	$0.0677808\pi$
$402$		0			0
$403$	−4.22738e6	−	2.44068e6i	−1.29661	−	0.748597i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.60266e6	+	2.77589e6i	−0.479574	+	0.830647i
$408$		0			0
$409$	−1.41683e6	−	2.45402e6i	−0.418802	−	0.725386i	0.577017	−	0.816732i	$-0.304217\pi$
$409$	−1.41683e6	−	2.45402e6i	−0.418802	−	0.725386i	−0.995819	+	0.0913456i	$0.970883\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			1.77944e6i			0.513343i
$414$		0			0
$415$		−	1.37834e6i		−	0.392858i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.96751e6	−	3.40783e6i	−0.547497	−	0.948293i	−0.998445	−	0.0557425i	$-0.982247\pi$
$419$	−1.96751e6	−	3.40783e6i	−0.547497	−	0.948293i	0.450948	−	0.892550i	$-0.351086\pi$
$420$		0			0
$421$	−1.57203e6	+	2.72283e6i	−0.432270	+	0.748713i	−0.997068	−	0.0765157i	$-0.975620\pi$
$421$	−1.57203e6	+	2.72283e6i	−0.432270	+	0.748713i	0.564799	+	0.825229i	$0.308954\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	24968.0	+	14415.3i	0.00670519	+	0.00387124i
$426$		0			0
$427$	−2.00804e6	+	1.15935e6i	−0.532971	+	0.307711i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.92623e6			1.79599			0.897995	−	0.440006i	$-0.145024\pi$
$431$	6.92623e6			1.79599			0.897995	+	0.440006i	$0.145024\pi$
$432$		0			0
$433$	−271898.			−0.0696925			−0.0348463	−	0.999393i	$-0.511094\pi$
$433$	−271898.			−0.0696925			−0.0348463	+	0.999393i	$0.511094\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−121234.	+	69994.3i	−0.0303682	+	0.0175331i
$438$		0			0
$439$	1.29341e6	+	746752.i	0.320314	+	0.184933i	0.651533	−	0.758621i	$-0.274126\pi$
$439$	1.29341e6	+	746752.i	0.320314	+	0.184933i	−0.331219	+	0.943554i	$0.607460\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.00244e6	+	1.73627e6i	−0.242688	+	0.420347i	−0.961479	−	0.274879i	$-0.911362\pi$
$443$	−1.00244e6	+	1.73627e6i	−0.242688	+	0.420347i	0.718791	+	0.695226i	$0.244696\pi$
$444$		0			0
$445$	2.46627e6	+	4.27170e6i	0.590392	+	1.02259i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.31263e6i			0.775455i	0.921774	+	0.387728i	$0.126740\pi$
$449$			3.31263e6i			0.775455i	−0.921774	+	0.387728i	$0.873260\pi$
$450$		0			0
$451$			1.27105e6i			0.294254i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.86296e6	+	3.22674e6i	0.421866	+	0.730694i
$456$		0			0
$457$	−1.05272e6	+	1.82336e6i	−0.235788	+	0.408397i	−0.959501	−	0.281704i	$-0.909100\pi$
$457$	−1.05272e6	+	1.82336e6i	−0.235788	+	0.408397i	0.723713	+	0.690101i	$0.242434\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.15181e6	−	2.97440e6i	−1.12903	−	0.651849i	−0.185343	−	0.982674i	$-0.559340\pi$
$461$	−5.15181e6	−	2.97440e6i	−1.12903	−	0.651849i	−0.943692	+	0.330825i	$0.892673\pi$
$462$		0			0
$463$	5.43951e6	−	3.14050e6i	1.17925	−	0.680843i	0.223412	−	0.974724i	$-0.428280\pi$
$463$	5.43951e6	−	3.14050e6i	1.17925	−	0.680843i	0.955842	+	0.293881i	$0.0949470\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.97537e6			−1.05568			−0.527841	−	0.849343i	$-0.676998\pi$
$467$	−4.97537e6			−1.05568			−0.527841	+	0.849343i	$0.676998\pi$
$468$		0			0
$469$	−3.26042e6			−0.684450
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.18763e6	+	2.41773e6i	−0.860628	+	0.496884i
$474$		0			0
$475$	5187.75	+	2995.15i	0.00105498	+	0.000609094i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.46449e6	−	6.00068e6i	0.689924	−	1.19498i	−0.281939	−	0.959432i	$-0.590977\pi$
$479$	3.46449e6	−	6.00068e6i	0.689924	−	1.19498i	0.971862	−	0.235550i	$-0.0756892\pi$
$480$		0			0
$481$	−3.79757e6	−	6.57759e6i	−0.748417	−	1.29630i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	1.01826e7i		−	1.96563i
$486$		0			0
$487$		−	3.30201e6i		−	0.630894i	−0.948943	−	0.315447i	$-0.897846\pi$
$487$		−	3.30201e6i		−	0.630894i	0.948943	−	0.315447i	$-0.102154\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.64921e6	−	6.32061e6i	−0.683116	−	1.18319i	−0.974025	−	0.226441i	$-0.927291\pi$
$491$	−3.64921e6	−	6.32061e6i	−0.683116	−	1.18319i	0.290908	−	0.956751i	$-0.406043\pi$
$492$		0			0
$493$	−1.15437e6	+	1.99943e6i	−0.213909	+	0.370500i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.59972e6	−	3.23300e6i	−1.01689	−	0.587104i
$498$		0			0
$499$	−4.72456e6	+	2.72772e6i	−0.849395	+	0.490398i	−0.860447	−	0.509540i	$-0.829815\pi$
$499$	−4.72456e6	+	2.72772e6i	−0.849395	+	0.490398i	0.0110516	+	0.999939i	$0.496482\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.08959e7			1.92018			0.960090	−	0.279691i	$-0.0902321\pi$
$503$	1.08959e7			1.92018			0.960090	+	0.279691i	$0.0902321\pi$
$504$		0			0
$505$	6.02659e6			1.05158
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.54763e6	+	893524.i	−0.264772	+	0.152866i	−0.626510	−	0.779414i	$-0.715517\pi$
$509$	−1.54763e6	+	893524.i	−0.264772	+	0.152866i	0.361737	+	0.932280i	$0.382184\pi$
$510$		0			0
$511$	4.34525e6	+	2.50873e6i	0.736144	+	0.425013i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.25441e6	+	9.10091e6i	−0.872983	+	1.51205i
$516$		0			0
$517$	−2.74256e6	−	4.75025e6i	−0.451263	−	0.781610i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	7.93525e6i		−	1.28076i	−0.768060	−	0.640378i	$-0.778778\pi$
$521$		−	7.93525e6i		−	1.28076i	0.768060	−	0.640378i	$-0.221222\pi$
$522$		0			0
$523$		−	9.05176e6i		−	1.44703i	−0.690307	−	0.723517i	$-0.742524\pi$
$523$		−	9.05176e6i		−	1.44703i	0.690307	−	0.723517i	$-0.257476\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.07430e6	−	1.86074e6i	−0.168499	−	0.291849i
$528$		0			0
$529$	1.16272e6	−	2.01389e6i	0.180649	−	0.312893i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.60831e6	−	1.50591e6i	−0.397687	−	0.229604i
$534$		0			0
$535$	6.02167e6	−	3.47661e6i	0.909562	−	0.525136i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.93850e6			−0.435666
$540$		0			0
$541$	−9.38544e6			−1.37867			−0.689337	−	0.724441i	$-0.742098\pi$
$541$	−9.38544e6			−1.37867			−0.689337	+	0.724441i	$0.742098\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.88700e6	−	3.39886e6i	0.848990	−	0.490165i
$546$		0			0
$547$	5.69374e6	+	3.28728e6i	0.813635	+	0.469752i	0.848217	−	0.529649i	$-0.177677\pi$
$547$	5.69374e6	+	3.28728e6i	0.813635	+	0.469752i	−0.0345816	+	0.999402i	$0.511010\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−239851.	+	415434.i	−0.0336560	+	0.0582939i
$552$		0			0
$553$	1.37459e6	+	2.38087e6i	0.191144	+	0.331072i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	3.72122e6i		−	0.508215i	−0.967176	−	0.254108i	$-0.918218\pi$
$557$		−	3.72122e6i		−	0.508215i	0.967176	−	0.254108i	$-0.0817817\pi$
$558$		0			0
$559$		−	1.14578e7i		−	1.55086i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.09208e6	−	1.22838e7i	−0.942981	−	1.63329i	−0.759745	−	0.650221i	$-0.774676\pi$
$563$	−7.09208e6	−	1.22838e7i	−0.942981	−	1.63329i	−0.183236	−	0.983069i	$-0.558657\pi$
$564$		0			0
$565$	−4.51948e6	+	7.82797e6i	−0.595618	+	1.03164i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.12005e7	−	6.46660e6i	−1.45029	−	0.837328i	−0.451796	−	0.892121i	$-0.649217\pi$
$569$	−1.12005e7	−	6.46660e6i	−1.45029	−	0.837328i	−0.998498	+	0.0547934i	$0.982550\pi$
$570$		0			0
$571$	38289.0	−	22106.2i	0.00491455	−	0.00283742i	−0.497541	−	0.867441i	$-0.665763\pi$
$571$	38289.0	−	22106.2i	0.00491455	−	0.00283742i	0.502455	+	0.864603i	$0.332430\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	175911.			0.0221883
$576$		0			0
$577$	−1.58754e7			−1.98512			−0.992558	−	0.121769i	$-0.961143\pi$
$577$	−1.58754e7			−1.98512			−0.992558	+	0.121769i	$0.961143\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.83427e6	−	1.05901e6i	0.225435	−	0.130155i
$582$		0			0
$583$	−3.61327e6	−	2.08612e6i	−0.440280	−	0.254196i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	630254.	−	1.09163e6i	0.0754953	−	0.130762i	−0.825806	−	0.563954i	$-0.809280\pi$
$587$	630254.	−	1.09163e6i	0.0754953	−	0.130762i	0.901302	+	0.433192i	$0.142613\pi$
$588$		0			0
$589$	−223213.	−	386616.i	−0.0265113	−	0.0459190i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			6.92056e6i			0.808174i	0.914721	+	0.404087i	$0.132411\pi$
$593$			6.92056e6i			0.808174i	−0.914721	+	0.404087i	$0.867589\pi$
$594$		0			0
$595$			1.64001e6i			0.189913i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.77898e6	+	1.17415e7i	0.771965	+	1.33708i	0.936485	+	0.350708i	$0.114059\pi$
$599$	6.77898e6	+	1.17415e7i	0.771965	+	1.33708i	−0.164520	+	0.986374i	$0.552608\pi$
$600$		0			0
$601$	−3.38948e6	+	5.87074e6i	−0.382778	+	0.662990i	−0.991458	−	0.130425i	$-0.958366\pi$
$601$	−3.38948e6	+	5.87074e6i	−0.382778	+	0.662990i	0.608681	+	0.793415i	$0.291699\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.92235e6	−	1.68722e6i	−0.324597	−	0.187406i
$606$		0			0
$607$	−390111.	+	225231.i	−0.0429750	+	0.0248117i	−0.521334	−	0.853353i	$-0.674565\pi$
$607$	−390111.	+	225231.i	−0.0429750	+	0.0248117i	0.478359	+	0.878165i	$0.341232\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.29972e7			1.40847
$612$		0			0
$613$	2.35062e6			0.252657			0.126329	−	0.991988i	$-0.459681\pi$
$613$	2.35062e6			0.252657			0.126329	+	0.991988i	$0.459681\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.23165e6	−	1.86579e6i	0.341752	−	0.197311i	−0.319294	−	0.947656i	$-0.603446\pi$
$617$	3.23165e6	−	1.86579e6i	0.341752	−	0.197311i	0.661047	+	0.750345i	$0.270113\pi$
$618$		0			0
$619$	−1.02772e7	−	5.93355e6i	−1.07807	−	0.622426i	−0.147697	−	0.989033i	$-0.547186\pi$
$619$	−1.02772e7	−	5.93355e6i	−1.07807	−	0.622426i	−0.930376	+	0.366607i	$0.880519\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.78980e6	+	6.56412e6i	−0.391197	+	0.677574i
$624$		0			0
$625$	5.01461e6	+	8.68556e6i	0.513496	+	0.889402i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	3.34310e6i		−	0.336917i
$630$		0			0
$631$			2.06573e6i			0.206538i	0.994653	+	0.103269i	$0.0329302\pi$
$631$			2.06573e6i			0.206538i	−0.994653	+	0.103269i	$0.967070\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.75038e6	+	3.03174e6i	0.172265	+	0.298372i
$636$		0			0
$637$	3.48145e6	−	6.03005e6i	0.339947	−	0.588806i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.86538e6	+	3.96373e6i	0.659963	+	0.381030i	0.792263	−	0.610180i	$-0.208903\pi$
$641$	6.86538e6	+	3.96373e6i	0.659963	+	0.381030i	−0.132300	+	0.991210i	$0.542236\pi$
$642$		0			0
$643$	−6.46543e6	+	3.73282e6i	−0.616694	+	0.356049i	−0.775581	−	0.631248i	$-0.782543\pi$
$643$	−6.46543e6	+	3.73282e6i	−0.616694	+	0.356049i	0.158886	+	0.987297i	$0.449210\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.70028e6			0.911011			0.455505	−	0.890233i	$-0.349459\pi$
$647$	9.70028e6			0.911011			0.455505	+	0.890233i	$0.349459\pi$
$648$		0			0
$649$	−6.51007e6			−0.606700
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.53756e6	+	5.50651e6i	−0.875295	+	0.505352i	−0.869104	−	0.494629i	$-0.835304\pi$
$653$	−9.53756e6	+	5.50651e6i	−0.875295	+	0.505352i	−0.00619069	+	0.999981i	$0.501971\pi$
$654$		0			0
$655$	−1.21166e6	−	699552.i	−0.110351	−	0.0637114i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.00677e7	−	1.74377e7i	0.903056	−	1.56414i	0.0795504	−	0.996831i	$-0.474652\pi$
$659$	1.00677e7	−	1.74377e7i	0.903056	−	1.56414i	0.823506	−	0.567308i	$-0.192015\pi$
$660$		0			0
$661$	−7.60566e6	−	1.31734e7i	−0.677069	−	1.17272i	−0.975859	−	0.218400i	$-0.929916\pi$
$661$	−7.60566e6	−	1.31734e7i	−0.677069	−	1.17272i	0.298790	−	0.954319i	$-0.403417\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			340755.i			0.0298805i
$666$		0			0
$667$			1.40869e7i			1.22603i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.24146e6	−	7.34643e6i	−0.363672	−	0.629898i
$672$		0			0
$673$	−2.10176e6	+	3.64035e6i	−0.178873	+	0.309817i	−0.941495	−	0.337028i	$-0.890578\pi$
$673$	−2.10176e6	+	3.64035e6i	−0.178873	+	0.309817i	0.762622	+	0.646845i	$0.223912\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.50662e6	+	3.17925e6i	0.461757	+	0.266596i	0.712783	−	0.701385i	$-0.247435\pi$
$677$	5.50662e6	+	3.17925e6i	0.461757	+	0.266596i	−0.251026	+	0.967980i	$0.580768\pi$
$678$		0			0
$679$	1.35507e7	−	7.82352e6i	1.12795	−	0.651220i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.62892e6			−0.707790			−0.353895	−	0.935285i	$-0.615143\pi$
$683$	−8.62892e6			−0.707790			−0.353895	+	0.935285i	$0.615143\pi$
$684$		0			0
$685$	2.13163e7			1.73574
$686$		0			0
$687$		0			0
$688$		0			0
$689$	8.56180e6	−	4.94316e6i	0.687095	−	0.396695i
$690$		0			0
$691$	−6.72909e6	−	3.88504e6i	−0.536119	−	0.309528i	0.207386	−	0.978259i	$-0.433504\pi$
$691$	−6.72909e6	−	3.88504e6i	−0.536119	−	0.309528i	−0.743504	+	0.668731i	$0.766838\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.67403e6	−	6.36361e6i	0.288523	−	0.499737i
$696$		0			0
$697$	−662845.	−	1.14808e6i	−0.0516809	−	0.0895139i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			9.88824e6i			0.760018i	0.924983	+	0.380009i	$0.124079\pi$
$701$			9.88824e6i			0.760018i	−0.924983	+	0.380009i	$0.875921\pi$
$702$		0			0
$703$		−	694617.i		−	0.0530099i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.63038e6	+	8.02006e6i	0.348392	+	0.603433i
$708$		0			0
$709$	407942.	−	706576.i	0.0304777	−	0.0527890i	−0.850384	−	0.526162i	$-0.823630\pi$
$709$	407942.	−	706576.i	0.0304777	−	0.0527890i	0.880862	+	0.473373i	$0.156964\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.13534e7	−	6.55488e6i	−0.836376	−	0.482882i
$714$		0			0
$715$	−1.18050e7	+	6.81564e6i	−0.863579	+	0.498588i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.31549e7			−0.948998			−0.474499	−	0.880256i	$-0.657371\pi$
$719$	−1.31549e7			−0.948998			−0.474499	+	0.880256i	$0.657371\pi$
$720$		0			0
$721$	−1.61484e7			−1.15689
$722$		0			0
$723$		0			0
$724$		0			0
$725$	522039.	−	301399.i	0.0368857	−	0.0212960i
$726$		0			0
$727$	−7.16360e6	−	4.13591e6i	−0.502684	−	0.290225i	0.227137	−	0.973863i	$-0.427063\pi$
$727$	−7.16360e6	−	4.13591e6i	−0.502684	−	0.290225i	−0.729821	+	0.683638i	$0.760397\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.52165e6	−	4.36763e6i	0.174539	−	0.302310i
$732$		0			0
$733$	−2.10778e6	−	3.65078e6i	−0.144899	−	0.250972i	0.784436	−	0.620209i	$-0.212952\pi$
$733$	−2.10778e6	−	3.65078e6i	−0.144899	−	0.250972i	−0.929335	+	0.369237i	$0.879619\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1.19283e7i		−	0.808925i
$738$		0			0
$739$			1.00932e7i			0.679858i	0.940451	+	0.339929i	$0.110403\pi$
$739$			1.00932e7i			0.679858i	−0.940451	+	0.339929i	$0.889597\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.86469e6	+	8.42589e6i	0.323283	+	0.559943i	0.981163	−	0.193180i	$-0.0618800\pi$
$743$	4.86469e6	+	8.42589e6i	0.323283	+	0.559943i	−0.657880	+	0.753123i	$0.728547\pi$
$744$		0			0
$745$	7.32135e6	−	1.26809e7i	0.483282	−	0.837068i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.25321e6	+	5.34234e6i	0.602682	+	0.347958i
$750$		0			0
$751$	1.70727e6	−	985694.i	0.110459	−	0.0637738i	−0.443752	−	0.896149i	$-0.646353\pi$
$751$	1.70727e6	−	985694.i	0.110459	−	0.0637738i	0.554212	+	0.832376i	$0.313020\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.03925e6			−0.385581
$756$		0			0
$757$	−1.08135e7			−0.685844			−0.342922	−	0.939364i	$-0.611417\pi$
$757$	−1.08135e7			−0.685844			−0.342922	+	0.939364i	$0.611417\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.37745e6	+	5.41407e6i	−0.586980	+	0.338893i	−0.763902	−	0.645332i	$-0.776719\pi$
$761$	−9.37745e6	+	5.41407e6i	−0.586980	+	0.338893i	0.176923	+	0.984225i	$0.443386\pi$
$762$		0			0
$763$	9.04627e6	+	5.22286e6i	0.562546	+	0.324786i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.71295e6	−	1.33592e7i	0.473404	−	0.819960i
$768$		0			0
$769$	2.56286e6	+	4.43901e6i	0.156282	+	0.270689i	0.933525	−	0.358512i	$-0.116716\pi$
$769$	2.56286e6	+	4.43901e6i	0.156282	+	0.270689i	−0.777243	+	0.629201i	$0.783382\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1.62727e7i			0.979514i	0.871859	+	0.489757i	$0.162915\pi$
$773$			1.62727e7i			0.979514i	−0.871859	+	0.489757i	$0.837085\pi$
$774$		0			0
$775$			560984.i			0.0335503i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−137723.	−	238544.i	−0.00813137	−	0.0140840i
$780$		0			0
$781$	1.18279e7	−	2.04866e7i	0.693875	−	1.20183i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.52319e7	+	8.79417e6i	0.882229	+	0.509355i
$786$		0			0
$787$	2.48957e6	−	1.43735e6i	0.143280	−	0.0827230i	−0.426646	−	0.904419i	$-0.640305\pi$
$787$	2.48957e6	−	1.43735e6i	0.143280	−	0.0827230i	0.569927	+	0.821696i	$0.306972\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.38898e7			−0.789320
$792$		0			0
$793$	2.01007e7			1.13508
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.94946e6	+	5.74433e6i	−0.554822	+	0.320327i	−0.751065	−	0.660229i	$-0.770459\pi$
$797$	−9.94946e6	+	5.74433e6i	−0.554822	+	0.320327i	0.196242	+	0.980555i	$0.437126\pi$
$798$		0			0
$799$	4.95443e6	+	2.86044e6i	0.274554	+	0.158514i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.17820e6	+	1.58971e7i	−0.502306	+	0.870020i
$804$		0			0
$805$	5.00331e6	+	8.66599e6i	0.272125	+	0.471334i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	3.78991e6i		−	0.203590i	−0.994805	−	0.101795i	$-0.967541\pi$
$809$		−	3.78991e6i		−	0.203590i	0.994805	−	0.101795i	$-0.0324586\pi$
$810$		0			0
$811$			2.21605e7i			1.18312i	0.806263	+	0.591558i	$0.201487\pi$
$811$			2.21605e7i			1.18312i	−0.806263	+	0.591558i	$0.798513\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.41327e7	+	2.44785e7i	0.745299	+	1.29090i
$816$		0			0
$817$	523940.	−	907490.i	0.0274616	−	0.0475649i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.72408e7	+	9.95399e6i	0.892688	+	0.515394i	0.874821	−	0.484447i	$-0.160979\pi$
$821$	1.72408e7	+	9.95399e6i	0.892688	+	0.515394i	0.0178673	+	0.999840i	$0.494312\pi$
$822$		0			0
$823$	1.47206e7	−	8.49895e6i	0.757576	−	0.437387i	−0.0708485	−	0.997487i	$-0.522571\pi$
$823$	1.47206e7	−	8.49895e6i	0.757576	−	0.437387i	0.828425	+	0.560100i	$0.189237\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.76625e7			−0.898023			−0.449011	−	0.893526i	$-0.648224\pi$
$827$	−1.76625e7			−0.898023			−0.449011	+	0.893526i	$0.648224\pi$
$828$		0			0
$829$	3.46600e7			1.75163			0.875815	−	0.482646i	$-0.160324\pi$
$829$	3.46600e7			1.75163			0.875815	+	0.482646i	$0.160324\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.65420e6	−	1.53240e6i	0.132532	−	0.0765175i
$834$		0			0
$835$	5.44535e6	+	3.14387e6i	0.270277	+	0.156045i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.44675e7	+	2.50584e7i	−0.709558	+	1.22899i	0.255463	+	0.966819i	$0.417772\pi$
$839$	−1.44675e7	+	2.50584e7i	−0.709558	+	1.22899i	−0.965021	+	0.262172i	$0.915561\pi$
$840$		0			0
$841$	1.38804e7	+	2.40416e7i	0.676724	+	1.17212i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	1.12578e7i		−	0.542391i
$846$		0			0
$847$		−	5.18534e6i		−	0.248353i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.01991e7	−	1.76653e7i	−0.482766	−	0.836175i
$852$		0			0
$853$	−7.47233e6	+	1.29424e7i	−0.351628	+	0.609037i	−0.986535	−	0.163551i	$-0.947705\pi$
$853$	−7.47233e6	+	1.29424e7i	−0.351628	+	0.609037i	0.634907	+	0.772589i	$0.281038\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.49021e7	+	8.60372e6i	0.693098	+	0.400160i	0.804772	−	0.593585i	$-0.202288\pi$
$857$	1.49021e7	+	8.60372e6i	0.693098	+	0.400160i	−0.111674	+	0.993745i	$0.535621\pi$
$858$		0			0
$859$	6.94546e6	−	4.00997e6i	0.321158	−	0.185420i	−0.330751	−	0.943718i	$-0.607302\pi$
$859$	6.94546e6	−	4.00997e6i	0.321158	−	0.185420i	0.651908	+	0.758298i	$0.273969\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.17919e6			−0.0996022			−0.0498011	−	0.998759i	$-0.515859\pi$
$863$	−2.17919e6			−0.0996022			−0.0498011	+	0.998759i	$0.515859\pi$
$864$		0			0
$865$	2.09437e7			0.951727
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.71040e6	+	5.02895e6i	−0.391281	+	0.225906i
$870$		0			0
$871$	2.44778e7	+	1.41323e7i	1.09327	+	0.631199i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.49740e6	+	1.29859e7i	−0.331048	+	0.573392i
$876$		0			0
$877$	1.62241e7	+	2.81010e7i	0.712299	+	1.23374i	0.963992	+	0.265931i	$0.0856793\pi$
$877$	1.62241e7	+	2.81010e7i	0.712299	+	1.23374i	−0.251693	+	0.967807i	$0.580987\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			2.57161e7i			1.11626i	0.829753	+	0.558130i	$0.188481\pi$
$881$			2.57161e7i			1.11626i	−0.829753	+	0.558130i	$0.811519\pi$
$882$		0			0
$883$		−	3.35163e7i		−	1.44662i	−0.690524	−	0.723310i	$-0.742620\pi$
$883$		−	3.35163e7i		−	1.44662i	0.690524	−	0.723310i	$-0.257380\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.09787e7	−	1.90157e7i	−0.468536	−	0.811528i	0.530818	−	0.847486i	$-0.321885\pi$
$887$	−1.09787e7	−	1.90157e7i	−0.468536	−	0.811528i	−0.999353	+	0.0359585i	$0.988552\pi$
$888$		0			0
$889$	−2.68972e6	+	4.65874e6i	−0.114144	+	0.197703i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.02941e6	+	594332.i	0.0431978	+	0.0249402i
$894$		0			0
$895$	−3.51218e7	+	2.02776e7i	−1.46561	+	0.846171i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.49235e7			−1.85385
$900$		0			0
$901$	4.35159e6			0.178581
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.21173e7	−	6.99594e6i	0.491796	−	0.283939i
$906$		0			0
$907$	9.46566e6	+	5.46500e6i	0.382061	+	0.220583i	0.678715	−	0.734402i	$-0.262537\pi$
$907$	9.46566e6	+	5.46500e6i	0.382061	+	0.220583i	−0.296654	+	0.954985i	$0.595871\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.77190e6	−	1.69254e7i	0.390107	−	0.675684i	−0.602357	−	0.798227i	$-0.705772\pi$
$911$	9.77190e6	−	1.69254e7i	0.390107	−	0.675684i	0.992463	+	0.122543i	$0.0391048\pi$
$912$		0			0
$913$	3.87440e6	+	6.71066e6i	0.153825	+	0.266433i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	2.14994e6i		−	0.0844311i
$918$		0			0
$919$			1.93174e7i			0.754500i	0.926112	+	0.377250i	$0.123130\pi$
$919$			1.93174e7i			0.754500i	−0.926112	+	0.377250i	$0.876870\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.80268e7	+	4.85438e7i	1.08285	+	1.87555i
$924$		0			0
$925$	−436432.	+	755922.i	−0.0167711	+	0.0290484i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.13708e7	+	1.81119e7i	1.19258	+	0.688535i	0.958890	−	0.283777i	$-0.0915877\pi$
$929$	3.13708e7	+	1.81119e7i	1.19258	+	0.688535i	0.233687	+	0.972312i	$0.424921\pi$
$930$		0			0
$931$	551480.	−	318397.i	0.0208524	−	0.0120391i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.99998e6			−0.224451
$936$		0			0
$937$	−188121.			−0.00699984			−0.00349992	−	0.999994i	$-0.501114\pi$
$937$	−188121.			−0.00699984			−0.00349992	+	0.999994i	$0.501114\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.36344e7	+	1.36453e7i	−0.870102	+	0.502353i	−0.867382	−	0.497643i	$-0.834199\pi$
$941$	−2.36344e7	+	1.36453e7i	−0.870102	+	0.502353i	−0.00271966	+	0.999996i	$0.500866\pi$
$942$		0			0
$943$	−7.00508e6	−	4.04438e6i	−0.256527	−	0.148106i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.72890e6	−	1.51189e7i	0.316289	−	0.547829i	−0.663421	−	0.748246i	$-0.730896\pi$
$947$	8.72890e6	−	1.51189e7i	0.316289	−	0.547829i	0.979711	+	0.200417i	$0.0642297\pi$
$948$		0			0
$949$	−2.17481e7	−	3.76689e7i	−0.783892	−	1.35774i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	413139.i		−	0.0147355i	−0.999973	−	0.00736773i	$-0.997655\pi$
$953$		−	413139.i		−	0.0147355i	0.999973	−	0.00736773i	$-0.00234524\pi$
$954$		0			0
$955$		−	7.11337e6i		−	0.252387i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.63778e7	+	2.83673e7i	0.575056	+	0.996027i
$960$		0			0
$961$	6.58906e6	−	1.14126e7i	0.230152	−	0.398635i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.68827e7	+	2.12942e7i	1.27498	+	0.736112i
$966$		0			0
$967$	−2.21949e7	+	1.28143e7i	−0.763287	+	0.440684i	−0.830475	−	0.557057i	$-0.811931\pi$
$967$	−2.21949e7	+	1.28143e7i	−0.763287	+	0.440684i	0.0671879	+	0.997740i	$0.478597\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.41869e7			−0.823252			−0.411626	−	0.911353i	$-0.635039\pi$
$971$	−2.41869e7			−0.823252			−0.411626	+	0.911353i	$0.635039\pi$
$972$		0			0
$973$	1.12914e7			0.382355
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.99179e6	−	2.88201e6i	0.167309	−	0.0965961i	−0.414007	−	0.910274i	$-0.635871\pi$
$977$	4.99179e6	−	2.88201e6i	0.167309	−	0.0965961i	0.581317	+	0.813678i	$0.302538\pi$
$978$		0			0
$979$	−2.40148e7	−	1.38650e7i	−0.800798	−	0.462341i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.91656e6	−	3.31957e6i	0.0632613	−	0.109572i	−0.832660	−	0.553784i	$-0.813183\pi$
$983$	1.91656e6	−	3.31957e6i	0.0632613	−	0.109572i	0.895921	+	0.444213i	$0.146517\pi$
$984$		0			0
$985$	−1.55218e7	−	2.68845e7i	−0.509743	−	0.882900i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	3.07720e7i		−	1.00038i
$990$		0			0
$991$			4.32957e7i			1.40043i	0.713933	+	0.700214i	$0.246912\pi$
$991$			4.32957e7i			1.40043i	−0.713933	+	0.700214i	$0.753088\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.56762e6	+	4.44724e6i	0.0822190	+	0.142408i
$996$		0			0
$997$	3.51917e6	−	6.09538e6i	0.112125	−	0.194206i	−0.804502	−	0.593950i	$-0.797568\pi$
$997$	3.51917e6	−	6.09538e6i	0.112125	−	0.194206i	0.916627	+	0.399744i	$0.130901\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.6.s.b.143.4		20
3.2	odd	2		144.6.s.c.47.2	yes	20
4.3	odd	2		432.6.s.a.143.4		20
9.4	even	3		144.6.s.a.95.9	yes	20
9.5	odd	6		432.6.s.a.287.4		20
12.11	even	2		144.6.s.a.47.9	✓	20
36.23	even	6	inner	432.6.s.b.287.4		20
36.31	odd	6		144.6.s.c.95.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.6.s.a.47.9	✓	20	12.11	even	2
144.6.s.a.95.9	yes	20	9.4	even	3
144.6.s.c.47.2	yes	20	3.2	odd	2
144.6.s.c.95.2	yes	20	36.31	odd	6
432.6.s.a.143.4		20	4.3	odd	2
432.6.s.a.287.4		20	9.5	odd	6
432.6.s.b.143.4		20	1.1	even	1	trivial
432.6.s.b.287.4		20	36.23	even	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	432.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-49.0797 + 28.3362i) q^{5} +(-75.4185 - 43.5429i) q^{7} +O(q^{10})\)	\(q+(-49.0797 + 28.3362i) q^{5} +(-75.4185 - 43.5429i) q^{7} +(159.302 - 275.919i) q^{11} +(377.472 + 653.801i) q^{13} +332.298i q^{17} +69.0437i q^{19} +(1013.77 + 1755.90i) q^{23} +(43.3805 - 75.1372i) q^{25} +(6016.97 + 3473.90i) q^{29} +(-5599.59 + 3232.93i) q^{31} +4935.36 q^{35} -10060.5 q^{37} +(-3454.97 + 1994.73i) q^{41} +(-13143.7 - 7588.53i) q^{43} +(8608.06 - 14909.6i) q^{47} +(-4611.53 - 7987.41i) q^{49} -13095.4i q^{53} +18056.0i q^{55} +(-10216.6 - 17695.6i) q^{59} +(13312.7 - 23058.2i) q^{61} +(-37052.4 - 21392.2i) q^{65} +(32423.3 - 18719.6i) q^{67} +74248.6 q^{71} -57615.2 q^{73} +(-24028.6 + 13872.9i) q^{77} +(-27339.3 - 15784.4i) q^{79} +(-12160.6 + 21062.8i) q^{83} +(-9416.07 - 16309.1i) q^{85} -87035.9i q^{89} -65744.9i q^{91} +(-1956.44 - 3388.64i) q^{95} +(-89837.0 + 155602. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 87 q^{5} + 87 q^{7}+O(q^{10}) \) 20 * q - 87 * q^5 + 87 * q^7	\( 20 q - 87 q^{5} + 87 q^{7} + 570 q^{11} - 181 q^{13} + 99 q^{23} + 7903 q^{25} - 13191 q^{29} + 6651 q^{31} + 10830 q^{35} - 4856 q^{37} - 846 q^{41} - 15315 q^{47} + 17891 q^{49} + 13308 q^{59} - 24773 q^{61} + 48255 q^{65} - 6402 q^{67} - 43188 q^{71} - 11614 q^{73} + 79317 q^{77} - 171897 q^{79} - 43347 q^{83} - 8850 q^{85} - 210684 q^{95} + 66332 q^{97}+O(q^{100}) \) 20 * q - 87 * q^5 + 87 * q^7 + 570 * q^11 - 181 * q^13 + 99 * q^23 + 7903 * q^25 - 13191 * q^29 + 6651 * q^31 + 10830 * q^35 - 4856 * q^37 - 846 * q^41 - 15315 * q^47 + 17891 * q^49 + 13308 * q^59 - 24773 * q^61 + 48255 * q^65 - 6402 * q^67 - 43188 * q^71 - 11614 * q^73 + 79317 * q^77 - 171897 * q^79 - 43347 * q^83 - 8850 * q^85 - 210684 * q^95 + 66332 * q^97

Introduction

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