LMFDB - Embedded newform 1728.3.o.g.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1728.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.o (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:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-0.523926 + 1.93016i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.g.1279.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.03104 - 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +O(q^{10})$	$q+(-4.03104 - 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(3.25842 + 1.88125i) q^{11} +(3.52605 + 6.10730i) q^{13} -0.517890 q^{17} +16.4164i q^{19} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(9.48394 - 16.4267i) q^{29} +(-13.1355 + 7.58377i) q^{31} +36.3299i q^{35} -0.592061 q^{37} +(-12.3766 - 21.4369i) q^{41} +(-27.8686 - 16.0900i) q^{43} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} -0.664765 q^{53} -30.3336i q^{55} +(-30.5921 + 17.6623i) q^{59} +(-33.7750 + 58.5000i) q^{61} +(28.4273 - 49.2376i) q^{65} +(74.4692 - 42.9948i) q^{67} +56.4434i q^{71} +131.921 q^{73} +(-8.47743 - 14.6833i) q^{77} +(126.869 + 73.2481i) q^{79} +(87.1029 + 50.2889i) q^{83} +(2.08764 + 3.61589i) q^{85} +25.8362 q^{89} -31.7786i q^{91} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5}+O(q^{10}) $ 16 * q + 6 * q^5	$ 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−4.03104	−	6.98197i	−0.806209	−	1.39639i	−0.915472	−	0.402382i	$-0.868182\pi$
$5$	−4.03104	−	6.98197i	−0.806209	−	1.39639i	0.109263	−	0.994013i	$-0.465151\pi$
$6$		0			0
$7$	−3.90254	−	2.25313i	−0.557506	−	0.321876i	0.194638	−	0.980875i	$-0.437647\pi$
$7$	−3.90254	−	2.25313i	−0.557506	−	0.321876i	−0.752144	+	0.658999i	$0.770980\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.25842	+	1.88125i	0.296220	+	0.171023i	0.640744	−	0.767755i	$-0.278626\pi$
$11$	3.25842	+	1.88125i	0.296220	+	0.171023i	−0.344523	+	0.938778i	$0.611959\pi$
$12$		0			0
$13$	3.52605	+	6.10730i	0.271235	+	0.469792i	0.969178	−	0.246361i	$-0.0792348\pi$
$13$	3.52605	+	6.10730i	0.271235	+	0.469792i	−0.697944	+	0.716153i	$0.745901\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.517890			−0.0304641			−0.0152321	−	0.999884i	$-0.504849\pi$
$17$	−0.517890			−0.0304641			−0.0152321	+	0.999884i	$0.504849\pi$
$18$		0			0
$19$			16.4164i			0.864023i	0.901868	+	0.432012i	$0.142196\pi$
$19$			16.4164i			0.864023i	−0.901868	+	0.432012i	$0.857804\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−27.7049	+	15.9954i	−1.20456	+	0.695454i	−0.961566	−	0.274573i	$-0.911463\pi$
$23$	−27.7049	+	15.9954i	−1.20456	+	0.695454i	−0.242996	+	0.970027i	$0.578130\pi$
$24$		0			0
$25$	−19.9986	+	34.6387i	−0.799946	+	1.38555i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	9.48394	−	16.4267i	0.327032	−	0.566437i	−0.654889	−	0.755725i	$-0.727285\pi$
$29$	9.48394	−	16.4267i	0.327032	−	0.566437i	0.981922	+	0.189288i	$0.0606180\pi$
$30$		0			0
$31$	−13.1355	+	7.58377i	−0.423725	+	0.244638i	−0.696670	−	0.717392i	$-0.745336\pi$
$31$	−13.1355	+	7.58377i	−0.423725	+	0.244638i	0.272945	+	0.962030i	$0.412002\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			36.3299i			1.03800i
$36$		0			0
$37$	−0.592061			−0.0160017			−0.00800083	−	0.999968i	$-0.502547\pi$
$37$	−0.592061			−0.0160017			−0.00800083	+	0.999968i	$0.502547\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−12.3766	−	21.4369i	−0.301868	−	0.522850i	0.674691	−	0.738100i	$-0.264277\pi$
$41$	−12.3766	−	21.4369i	−0.301868	−	0.522850i	−0.976559	+	0.215250i	$0.930943\pi$
$42$		0			0
$43$	−27.8686	−	16.0900i	−0.648107	−	0.374185i	0.139623	−	0.990205i	$-0.455411\pi$
$43$	−27.8686	−	16.0900i	−0.648107	−	0.374185i	−0.787731	+	0.616020i	$0.788744\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	52.4682	+	30.2925i	1.11634	+	0.644521i	0.940465	−	0.339890i	$-0.110390\pi$
$47$	52.4682	+	30.2925i	1.11634	+	0.644521i	0.175879	+	0.984412i	$0.443723\pi$
$48$		0			0
$49$	−14.3468	−	24.8493i	−0.292791	−	0.507129i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.664765			−0.0125427			−0.00627137	−	0.999980i	$-0.501996\pi$
$53$	−0.664765			−0.0125427			−0.00627137	+	0.999980i	$0.501996\pi$
$54$		0			0
$55$		−	30.3336i		−	0.551521i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−30.5921	+	17.6623i	−0.518510	+	0.299362i	−0.736325	−	0.676628i	$-0.763440\pi$
$59$	−30.5921	+	17.6623i	−0.518510	+	0.299362i	0.217815	+	0.975990i	$0.430107\pi$
$60$		0			0
$61$	−33.7750	+	58.5000i	−0.553688	+	0.959016i	0.444316	+	0.895870i	$0.353447\pi$
$61$	−33.7750	+	58.5000i	−0.553688	+	0.959016i	−0.998004	+	0.0631460i	$0.979887\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	28.4273	−	49.2376i	0.437343	−	0.757501i
$66$		0			0
$67$	74.4692	−	42.9948i	1.11148	−	0.641714i	0.172269	−	0.985050i	$-0.444890\pi$
$67$	74.4692	−	42.9948i	1.11148	−	0.641714i	0.939213	+	0.343336i	$0.111557\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			56.4434i			0.794977i	0.917607	+	0.397489i	$0.130118\pi$
$71$			56.4434i			0.794977i	−0.917607	+	0.397489i	$0.869882\pi$
$72$		0			0
$73$	131.921			1.80713			0.903567	−	0.428447i	$-0.140939\pi$
$73$	131.921			1.80713			0.903567	+	0.428447i	$0.140939\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.47743	−	14.6833i	−0.110096	−	0.190693i
$78$		0			0
$79$	126.869	+	73.2481i	1.60594	+	0.927191i	0.990265	+	0.139192i	$0.0444505\pi$
$79$	126.869	+	73.2481i	1.60594	+	0.927191i	0.615677	+	0.787999i	$0.288883\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	87.1029	+	50.2889i	1.04943	+	0.605890i	0.922491	−	0.386020i	$-0.126150\pi$
$83$	87.1029	+	50.2889i	1.04943	+	0.605890i	0.126942	+	0.991910i	$0.459484\pi$
$84$		0			0
$85$	2.08764	+	3.61589i	0.0245604	+	0.0425399i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	25.8362			0.290295			0.145147	−	0.989410i	$-0.453634\pi$
$89$	25.8362			0.290295			0.145147	+	0.989410i	$0.453634\pi$
$90$		0			0
$91$		−	31.7786i		−	0.349216i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	114.619	−	66.1754i	1.20652	−	0.696583i
$96$		0			0
$97$	−48.2534	+	83.5773i	−0.497457	+	0.861621i	−0.999996	−	0.00293363i	$-0.999066\pi$
$97$	−48.2534	+	83.5773i	−0.497457	+	0.861621i	0.502538	+	0.864555i	$0.332400\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−21.6600	+	37.5163i	−0.214456	+	0.371448i	−0.953104	−	0.302643i	$-0.902131\pi$
$101$	−21.6600	+	37.5163i	−0.214456	+	0.371448i	0.738648	+	0.674091i	$0.235464\pi$
$102$		0			0
$103$	125.439	−	72.4223i	1.21786	−	0.703129i	0.253397	−	0.967362i	$-0.418452\pi$
$103$	125.439	−	72.4223i	1.21786	−	0.703129i	0.964459	+	0.264233i	$0.0851189\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	54.9861i		−	0.513889i	−0.966426	−	0.256944i	$-0.917284\pi$
$107$		−	54.9861i		−	0.513889i	0.966426	−	0.256944i	$-0.0827158\pi$
$108$		0			0
$109$	63.9235			0.586454			0.293227	−	0.956043i	$-0.405271\pi$
$109$	63.9235			0.586454			0.293227	+	0.956043i	$0.405271\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−17.8239	−	30.8720i	−0.157734	−	0.273203i	0.776317	−	0.630342i	$-0.217086\pi$
$113$	−17.8239	−	30.8720i	−0.157734	−	0.273203i	−0.934051	+	0.357139i	$0.883752\pi$
$114$		0			0
$115$	223.360	+	128.957i	1.94226	+	1.12136i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.02109	+	1.16688i	0.0169839	+	0.00980568i
$120$		0			0
$121$	−53.4218	−	92.5292i	−0.441502	−	0.764704i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	120.909			0.967276
$126$		0			0
$127$			9.81219i			0.0772613i	0.999254	+	0.0386307i	$0.0122996\pi$
$127$			9.81219i			0.0772613i	−0.999254	+	0.0386307i	$0.987700\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	101.561	−	58.6365i	0.775278	−	0.447607i	−0.0594761	−	0.998230i	$-0.518943\pi$
$131$	101.561	−	58.6365i	0.775278	−	0.447607i	0.834754	+	0.550623i	$0.185610\pi$
$132$		0			0
$133$	36.9884	−	64.0659i	0.278109	−	0.481698i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−125.606	+	217.556i	−0.916831	+	1.58800i	−0.112634	+	0.993637i	$0.535929\pi$
$137$	−125.606	+	217.556i	−0.916831	+	1.58800i	−0.804198	+	0.594362i	$0.797405\pi$
$138$		0			0
$139$	133.073	−	76.8298i	0.957361	−	0.552732i	0.0620009	−	0.998076i	$-0.480252\pi$
$139$	133.073	−	76.8298i	0.957361	−	0.552732i	0.895360	+	0.445344i	$0.146919\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			26.5335i			0.185549i
$144$		0			0
$145$	−152.921			−1.05463
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−45.8643	−	79.4393i	−0.307814	−	0.533150i	0.670070	−	0.742298i	$-0.266264\pi$
$149$	−45.8643	−	79.4393i	−0.307814	−	0.533150i	−0.977884	+	0.209148i	$0.932931\pi$
$150$		0			0
$151$	36.0215	+	20.7970i	0.238553	+	0.137729i	0.614512	−	0.788908i	$-0.289353\pi$
$151$	36.0215	+	20.7970i	0.238553	+	0.137729i	−0.375958	+	0.926637i	$0.622686\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	105.899	+	61.1410i	0.683222	+	0.394458i
$156$		0			0
$157$	−112.909	−	195.565i	−0.719167	−	1.24563i	−0.961330	−	0.275399i	$-0.911190\pi$
$157$	−112.909	−	195.565i	−0.719167	−	1.24563i	0.242163	−	0.970236i	$-0.422143\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	144.160			0.895401
$162$		0			0
$163$			125.175i			0.767945i	0.923344	+	0.383973i	$0.125444\pi$
$163$			125.175i			0.767945i	−0.923344	+	0.383973i	$0.874556\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−154.373	+	89.1274i	−0.924390	+	0.533697i	−0.885033	−	0.465528i	$-0.845864\pi$
$167$	−154.373	+	89.1274i	−0.924390	+	0.533697i	−0.0393573	+	0.999225i	$0.512531\pi$
$168$		0			0
$169$	59.6340	−	103.289i	0.352864	−	0.611178i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−75.5904	+	130.926i	−0.436939	+	0.756800i	−0.997452	−	0.0713455i	$-0.977271\pi$
$173$	−75.5904	+	130.926i	−0.436939	+	0.756800i	0.560513	+	0.828146i	$0.310604\pi$
$174$		0			0
$175$	156.091	−	90.1193i	0.891949	−	0.514967i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			276.827i			1.54652i	0.634088	+	0.773261i	$0.281376\pi$
$179$			276.827i			1.54652i	−0.634088	+	0.773261i	$0.718624\pi$
$180$		0			0
$181$	104.729			0.578612			0.289306	−	0.957237i	$-0.406575\pi$
$181$	104.729			0.578612			0.289306	+	0.957237i	$0.406575\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.38663	+	4.13376i	0.0129007	+	0.0223446i
$186$		0			0
$187$	−1.68751	−	0.974282i	−0.00902409	−	0.00521006i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	192.972	+	111.413i	1.01033	+	0.583312i	0.911287	−	0.411772i	$-0.135090\pi$
$191$	192.972	+	111.413i	1.01033	+	0.583312i	0.0990389	+	0.995084i	$0.468423\pi$
$192$		0			0
$193$	56.6790	+	98.1709i	0.293674	+	0.508657i	0.974675	−	0.223624i	$-0.0717888\pi$
$193$	56.6790	+	98.1709i	0.293674	+	0.508657i	−0.681002	+	0.732282i	$0.738455\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−120.998			−0.614201			−0.307100	−	0.951677i	$-0.599359\pi$
$197$	−120.998			−0.614201			−0.307100	+	0.951677i	$0.599359\pi$
$198$		0			0
$199$			82.2364i			0.413248i	0.978420	+	0.206624i	$0.0662477\pi$
$199$			82.2364i			0.413248i	−0.978420	+	0.206624i	$0.933752\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−74.0230	+	42.7372i	−0.364645	+	0.210528i
$204$		0			0
$205$	−99.7811	+	172.826i	−0.486737	+	0.843053i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−30.8835	+	53.4917i	−0.147768	+	0.255941i
$210$		0			0
$211$	−93.5819	+	54.0295i	−0.443516	+	0.256064i	−0.705088	−	0.709120i	$-0.749093\pi$
$211$	−93.5819	+	54.0295i	−0.443516	+	0.256064i	0.261572	+	0.965184i	$0.415759\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			259.437i			1.20668i
$216$		0			0
$217$	68.3490			0.314972
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.82611	−	3.16291i	−0.00826292	−	0.0143118i
$222$		0			0
$223$	−141.400	−	81.6371i	−0.634079	−	0.366086i	0.148251	−	0.988950i	$-0.452636\pi$
$223$	−141.400	−	81.6371i	−0.634079	−	0.366086i	−0.782330	+	0.622864i	$0.785969\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.56722	+	5.52364i	0.0421463	+	0.0243332i	0.520925	−	0.853602i	$-0.325587\pi$
$227$	9.56722	+	5.52364i	0.0421463	+	0.0243332i	−0.478779	+	0.877936i	$0.658920\pi$
$228$		0			0
$229$	16.1725	+	28.0116i	0.0706222	+	0.122321i	0.899174	−	0.437591i	$-0.144168\pi$
$229$	16.1725	+	28.0116i	0.0706222	+	0.122321i	−0.828552	+	0.559912i	$0.810835\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−181.049			−0.777036			−0.388518	−	0.921441i	$-0.627013\pi$
$233$	−181.049			−0.777036			−0.388518	+	0.921441i	$0.627013\pi$
$234$		0			0
$235$		−	488.442i		−	2.07848i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	39.6432	−	22.8880i	0.165871	−	0.0957658i	−0.414766	−	0.909928i	$-0.636137\pi$
$239$	39.6432	−	22.8880i	0.165871	−	0.0957658i	0.580638	+	0.814162i	$0.302803\pi$
$240$		0			0
$241$	169.216	−	293.090i	0.702140	−	1.21614i	−0.265573	−	0.964091i	$-0.585561\pi$
$241$	169.216	−	293.090i	0.702140	−	1.21614i	0.967714	−	0.252052i	$-0.0811054\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−115.665	+	200.338i	−0.472102	+	0.817704i
$246$		0			0
$247$	−100.260	+	57.8852i	−0.405911	+	0.234353i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			282.587i			1.12585i	0.826510	+	0.562923i	$0.190323\pi$
$251$			282.587i			1.12585i	−0.826510	+	0.562923i	$0.809677\pi$
$252$		0			0
$253$	−120.366			−0.475754
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−38.8897	−	67.3589i	−0.151322	−	0.262097i	0.780392	−	0.625291i	$-0.215020\pi$
$257$	−38.8897	−	67.3589i	−0.151322	−	0.262097i	−0.931714	+	0.363194i	$0.881686\pi$
$258$		0			0
$259$	2.31055	+	1.33399i	0.00892102	+	0.00515056i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	195.201	+	112.700i	0.742211	+	0.428516i	0.822873	−	0.568226i	$-0.192370\pi$
$263$	195.201	+	112.700i	0.742211	+	0.428516i	−0.0806619	+	0.996742i	$0.525703\pi$
$264$		0			0
$265$	2.67970	+	4.64138i	0.0101121	+	0.0175146i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	425.808			1.58293			0.791465	−	0.611214i	$-0.209319\pi$
$269$	425.808			1.58293			0.791465	+	0.611214i	$0.209319\pi$
$270$		0			0
$271$		−	56.3665i		−	0.207995i	−0.994578	−	0.103997i	$-0.966837\pi$
$271$		−	56.3665i		−	0.207995i	0.994578	−	0.103997i	$-0.0331633\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−130.328	+	75.2450i	−0.473920	+	0.273618i
$276$		0			0
$277$	209.641	−	363.109i	0.756828	−	1.31086i	−0.187633	−	0.982239i	$-0.560082\pi$
$277$	209.641	−	363.109i	0.756828	−	1.31086i	0.944461	−	0.328625i	$-0.106585\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	73.9638	−	128.109i	0.263216	−	0.455904i	−0.703878	−	0.710320i	$-0.748550\pi$
$281$	73.9638	−	128.109i	0.263216	−	0.455904i	0.967095	+	0.254416i	$0.0818833\pi$
$282$		0			0
$283$	−229.852	+	132.705i	−0.812198	+	0.468923i	−0.847719	−	0.530446i	$-0.822024\pi$
$283$	−229.852	+	132.705i	−0.812198	+	0.468923i	0.0355207	+	0.999369i	$0.488691\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			111.544i			0.388656i
$288$		0			0
$289$	−288.732			−0.999072
$290$		0			0
$291$		0			0
$292$		0			0
$293$	124.844	+	216.236i	0.426088	+	0.738006i	0.996521	−	0.0833379i	$-0.0265581\pi$
$293$	124.844	+	216.236i	0.426088	+	0.738006i	−0.570433	+	0.821344i	$0.693225\pi$
$294$		0			0
$295$	246.636	+	142.395i	0.836054	+	0.482696i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−195.378	−	112.801i	−0.653438	−	0.377262i
$300$		0			0
$301$	72.5056	+	125.583i	0.240883	+	0.417221i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	544.594			1.78555
$306$		0			0
$307$			259.968i			0.846801i	0.905943	+	0.423401i	$0.139164\pi$
$307$			259.968i			0.846801i	−0.905943	+	0.423401i	$0.860836\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	16.5959	−	9.58164i	0.0533630	−	0.0308091i	−0.473081	−	0.881019i	$-0.656858\pi$
$311$	16.5959	−	9.58164i	0.0533630	−	0.0308091i	0.526444	+	0.850210i	$0.323525\pi$
$312$		0			0
$313$	−21.9358	+	37.9939i	−0.0700823	+	0.121386i	−0.898937	−	0.438078i	$-0.855660\pi$
$313$	−21.9358	+	37.9939i	−0.0700823	+	0.121386i	0.828855	+	0.559464i	$0.188993\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	68.9690	−	119.458i	0.217568	−	0.376838i	−0.736496	−	0.676442i	$-0.763521\pi$
$317$	68.9690	−	119.458i	0.217568	−	0.376838i	0.954064	+	0.299603i	$0.0968544\pi$
$318$		0			0
$319$	61.8054	−	35.6834i	0.193747	−	0.111860i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	8.50191i		−	0.0263217i
$324$		0			0
$325$	−282.065			−0.867892
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−136.506	−	236.436i	−0.414912	−	0.718649i
$330$		0			0
$331$	51.7490	+	29.8773i	0.156341	+	0.0902638i	0.576130	−	0.817358i	$-0.304562\pi$
$331$	51.7490	+	29.8773i	0.156341	+	0.0902638i	−0.419788	+	0.907622i	$0.637896\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−600.378	−	346.628i	−1.79217	−	1.03471i
$336$		0			0
$337$	224.356	+	388.595i	0.665743	+	1.15310i	0.979083	+	0.203460i	$0.0652188\pi$
$337$	224.356	+	388.595i	0.665743	+	1.15310i	−0.313340	+	0.949641i	$0.601448\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−57.0679			−0.167355
$342$		0			0
$343$			350.108i			1.02072i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	500.441	−	288.930i	1.44219	−	0.832651i	0.444198	−	0.895929i	$-0.353489\pi$
$347$	500.441	−	288.930i	1.44219	−	0.832651i	0.997996	+	0.0632779i	$0.0201555\pi$
$348$		0			0
$349$	−66.1311	+	114.542i	−0.189487	+	0.328202i	−0.945079	−	0.326841i	$-0.894016\pi$
$349$	−66.1311	+	114.542i	−0.189487	+	0.328202i	0.755592	+	0.655042i	$0.227349\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−270.562	+	468.628i	−0.766465	+	1.32756i	0.173003	+	0.984921i	$0.444653\pi$
$353$	−270.562	+	468.628i	−0.766465	+	1.32756i	−0.939468	+	0.342636i	$0.888680\pi$
$354$		0			0
$355$	394.086	−	227.526i	1.11010	−	0.640918i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	292.754i		−	0.815470i	−0.913100	−	0.407735i	$-0.866319\pi$
$359$		−	292.754i		−	0.815470i	0.913100	−	0.407735i	$-0.133681\pi$
$360$		0			0
$361$	91.5006			0.253464
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−531.779	−	921.067i	−1.45693	−	2.52347i
$366$		0			0
$367$	−378.870	−	218.741i	−1.03234	−	0.596024i	−0.114689	−	0.993401i	$-0.536587\pi$
$367$	−378.870	−	218.741i	−1.03234	−	0.596024i	−0.917655	+	0.397377i	$0.869920\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.59428	+	1.49781i	0.00699266	+	0.00403721i
$372$		0			0
$373$	352.979	+	611.377i	0.946323	+	1.63908i	0.753080	+	0.657929i	$0.228567\pi$
$373$	352.979	+	611.377i	0.946323	+	1.63908i	0.193243	+	0.981151i	$0.438099\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	133.763			0.354810
$378$		0			0
$379$			541.432i			1.42858i	0.699850	+	0.714290i	$0.253250\pi$
$379$			541.432i			1.42858i	−0.699850	+	0.714290i	$0.746750\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	311.941	−	180.099i	0.814467	−	0.470233i	−0.0340377	−	0.999421i	$-0.510837\pi$
$383$	311.941	−	180.099i	0.814467	−	0.470233i	0.848505	+	0.529188i	$0.177503\pi$
$384$		0			0
$385$	−68.3458	+	118.378i	−0.177521	+	0.307476i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−43.9057	+	76.0468i	−0.112868	+	0.195493i	−0.916926	−	0.399058i	$-0.869337\pi$
$389$	−43.9057	+	76.0468i	−0.112868	+	0.195493i	0.804057	+	0.594552i	$0.202670\pi$
$390$		0			0
$391$	14.3481	−	8.28388i	0.0366959	−	0.0211864i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	1181.07i		−	2.99004i
$396$		0			0
$397$	48.4128			0.121947			0.0609733	−	0.998139i	$-0.480580\pi$
$397$	48.4128			0.121947			0.0609733	+	0.998139i	$0.480580\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−217.859	−	377.343i	−0.543290	−	0.941005i	−0.998712	−	0.0507299i	$-0.983845\pi$
$401$	−217.859	−	377.343i	−0.543290	−	0.941005i	0.455423	−	0.890275i	$-0.349488\pi$
$402$		0			0
$403$	−92.6326	−	53.4815i	−0.229858	−	0.132708i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.92919	−	1.11382i	−0.00474002	−	0.00273665i
$408$		0			0
$409$	−27.1145	−	46.9636i	−0.0662945	−	0.114825i	0.830973	−	0.556313i	$-0.187784\pi$
$409$	−27.1145	−	46.9636i	−0.0662945	−	0.114825i	−0.897267	+	0.441487i	$0.854451\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	159.182			0.385430
$414$		0			0
$415$		−	810.867i		−	1.95390i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−552.029	+	318.714i	−1.31749	+	0.760655i	−0.983325	−	0.181859i	$-0.941789\pi$
$419$	−552.029	+	318.714i	−1.31749	+	0.760655i	−0.334168	+	0.942514i	$0.608455\pi$
$420$		0			0
$421$	95.7757	−	165.888i	0.227496	−	0.394034i	−0.729570	−	0.683907i	$-0.760280\pi$
$421$	95.7757	−	165.888i	0.227496	−	0.394034i	0.957065	+	0.289873i	$0.0936129\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.3571	−	17.9390i	0.0243696	−	0.0422095i
$426$		0			0
$427$	263.617	−	152.199i	0.617369	−	0.356438i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	481.190i		−	1.11645i	−0.829689	−	0.558225i	$-0.811482\pi$
$431$		−	481.190i		−	1.11645i	0.829689	−	0.558225i	$-0.188518\pi$
$432$		0			0
$433$	−360.347			−0.832209			−0.416105	−	0.909317i	$-0.636605\pi$
$433$	−360.347			−0.832209			−0.416105	+	0.909317i	$0.636605\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−262.588	−	454.816i	−0.600888	−	1.04077i
$438$		0			0
$439$	488.267	+	281.901i	1.11223	+	0.642144i	0.939405	−	0.342809i	$-0.111378\pi$
$439$	488.267	+	281.901i	1.11223	+	0.642144i	0.172821	+	0.984953i	$0.444712\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	569.917	+	329.042i	1.28649	+	0.742757i	0.978027	−	0.208478i	$-0.0668509\pi$
$443$	569.917	+	329.042i	1.28649	+	0.742757i	0.308467	+	0.951235i	$0.400184\pi$
$444$		0			0
$445$	−104.147	−	180.388i	−0.234038	−	0.405366i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−227.569			−0.506836			−0.253418	−	0.967357i	$-0.581555\pi$
$449$	−227.569			−0.506836			−0.253418	+	0.967357i	$0.581555\pi$
$450$		0			0
$451$		−	93.1339i		−	0.206505i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−221.878	+	128.101i	−0.487643	+	0.281541i
$456$		0			0
$457$	−358.879	+	621.596i	−0.785292	+	1.36017i	0.143532	+	0.989646i	$0.454154\pi$
$457$	−358.879	+	621.596i	−0.785292	+	1.36017i	−0.928824	+	0.370520i	$0.879179\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−200.873	+	347.922i	−0.435733	+	0.754712i	−0.997355	−	0.0726819i	$-0.976844\pi$
$461$	−200.873	+	347.922i	−0.435733	+	0.754712i	0.561622	+	0.827394i	$0.310178\pi$
$462$		0			0
$463$	−396.754	+	229.066i	−0.856920	+	0.494743i	−0.862980	−	0.505239i	$-0.831405\pi$
$463$	−396.754	+	229.066i	−0.856920	+	0.494743i	0.00605956	+	0.999982i	$0.498071\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			204.395i			0.437677i	0.975761	+	0.218838i	$0.0702267\pi$
$467$			204.395i			0.437677i	−0.975761	+	0.218838i	$0.929773\pi$
$468$		0			0
$469$	−387.493			−0.826210
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−60.5385	−	104.856i	−0.127988	−	0.221682i
$474$		0			0
$475$	−568.643	−	328.306i	−1.19714	−	0.691172i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−78.4548	−	45.2959i	−0.163789	−	0.0945634i	0.415865	−	0.909426i	$-0.363479\pi$
$479$	−78.4548	−	45.2959i	−0.163789	−	0.0945634i	−0.579654	+	0.814863i	$0.696812\pi$
$480$		0			0
$481$	−2.08764	−	3.61589i	−0.00434020	−	0.00751745i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	778.046			1.60422
$486$		0			0
$487$			301.289i			0.618663i	0.950954	+	0.309332i	$0.100105\pi$
$487$			301.289i			0.618663i	−0.950954	+	0.309332i	$0.899895\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	389.556	−	224.911i	0.793394	−	0.458066i	−0.0477620	−	0.998859i	$-0.515209\pi$
$491$	389.556	−	224.911i	0.793394	−	0.458066i	0.841156	+	0.540792i	$0.181876\pi$
$492$		0			0
$493$	−4.91164	+	8.50721i	−0.00996276	+	0.0172560i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	127.175	−	220.273i	0.255884	−	0.443205i
$498$		0			0
$499$	−552.630	+	319.061i	−1.10748	+	0.639401i	−0.938174	−	0.346163i	$-0.887484\pi$
$499$	−552.630	+	319.061i	−1.10748	+	0.639401i	−0.169301	+	0.985564i	$0.554151\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			182.179i			0.362185i	0.983466	+	0.181093i	$0.0579634\pi$
$503$			182.179i			0.362185i	−0.983466	+	0.181093i	$0.942037\pi$
$504$		0			0
$505$	349.250			0.691585
$506$		0			0
$507$		0			0
$508$		0			0
$509$	471.123	+	816.009i	0.925585	+	1.60316i	0.790617	+	0.612311i	$0.209760\pi$
$509$	471.123	+	816.009i	0.925585	+	1.60316i	0.134968	+	0.990850i	$0.456907\pi$
$510$		0			0
$511$	−514.827	−	297.235i	−1.00749	−	0.581674i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1011.30	−	583.875i	−1.96369	−	1.13374i
$516$		0			0
$517$	113.976	+	197.412i	0.220456	+	0.381841i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	634.330			1.21752			0.608762	−	0.793353i	$-0.291666\pi$
$521$	634.330			1.21752			0.608762	+	0.793353i	$0.291666\pi$
$522$		0			0
$523$		−	534.777i		−	1.02252i	−0.859426	−	0.511259i	$-0.829179\pi$
$523$		−	534.777i		−	1.02252i	0.859426	−	0.511259i	$-0.170821\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.80273	−	3.92756i	0.0129084	−	0.00745267i
$528$		0			0
$529$	247.208	−	428.178i	0.467313	−	0.809409i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	87.2809	−	151.175i	0.163754	−	0.283630i
$534$		0			0
$535$	−383.912	+	221.652i	−0.717592	+	0.414302i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	107.960i		−	0.200296i
$540$		0			0
$541$	61.0097			0.112772			0.0563860	−	0.998409i	$-0.482042\pi$
$541$	61.0097			0.112772			0.0563860	+	0.998409i	$0.482042\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−257.678	−	446.312i	−0.472805	−	0.818921i
$546$		0			0
$547$	−104.430	−	60.2925i	−0.190914	−	0.110224i	0.401497	−	0.915861i	$-0.368490\pi$
$547$	−104.430	−	60.2925i	−0.190914	−	0.110224i	−0.592410	+	0.805637i	$0.701823\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	269.667	+	155.693i	0.489415	+	0.282564i
$552$		0			0
$553$	−330.076	−	571.708i	−0.596882	−	1.03383i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−527.461			−0.946968			−0.473484	−	0.880802i	$-0.657004\pi$
$557$	−527.461			−0.946968			−0.473484	+	0.880802i	$0.657004\pi$
$558$		0			0
$559$		−	226.936i		−	0.405967i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−595.478	+	343.800i	−1.05769	+	0.610656i	−0.924792	−	0.380474i	$-0.875761\pi$
$563$	−595.478	+	343.800i	−1.05769	+	0.610656i	−0.132896	+	0.991130i	$0.542428\pi$
$564$		0			0
$565$	−143.698	+	248.893i	−0.254333	+	0.440518i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−293.677	+	508.664i	−0.516128	+	0.893961i	0.483696	+	0.875236i	$0.339294\pi$
$569$	−293.677	+	508.664i	−0.516128	+	0.893961i	−0.999825	+	0.0187248i	$0.994039\pi$
$570$		0			0
$571$	−742.245	+	428.535i	−1.29990	+	0.750500i	−0.980387	−	0.197081i	$-0.936854\pi$
$571$	−742.245	+	428.535i	−1.29990	+	0.750500i	−0.319517	+	0.947581i	$0.603521\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	1279.55i		−	2.22530i
$576$		0			0
$577$	871.732			1.51080			0.755401	−	0.655263i	$-0.227442\pi$
$577$	871.732			1.51080			0.755401	+	0.655263i	$0.227442\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−226.615	−	392.509i	−0.390044	−	0.675575i
$582$		0			0
$583$	−2.16609	−	1.25059i	−0.00371542	−	0.00214510i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−700.071	−	404.186i	−1.19263	−	0.688563i	−0.233725	−	0.972303i	$-0.575091\pi$
$587$	−700.071	−	404.186i	−1.19263	−	0.688563i	−0.958901	+	0.283740i	$0.908425\pi$
$588$		0			0
$589$	−124.498	−	215.638i	−0.211373	−	0.366108i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	445.123			0.750628			0.375314	−	0.926898i	$-0.377535\pi$
$593$	445.123			0.750628			0.375314	+	0.926898i	$0.377535\pi$
$594$		0			0
$595$		−	18.8149i		−	0.0316217i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−684.932	+	395.445i	−1.14346	+	0.660176i	−0.947285	−	0.320393i	$-0.896185\pi$
$599$	−684.932	+	395.445i	−1.14346	+	0.660176i	−0.196174	+	0.980569i	$0.562852\pi$
$600$		0			0
$601$	193.532	−	335.208i	0.322017	−	0.557750i	−0.658887	−	0.752242i	$-0.728972\pi$
$601$	193.532	−	335.208i	0.322017	−	0.557750i	0.980904	+	0.194492i	$0.0623057\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−430.691	+	745.979i	−0.711886	+	1.23302i
$606$		0			0
$607$	−902.512	+	521.066i	−1.48684	+	0.858428i	−0.999887	−	0.0150003i	$-0.995225\pi$
$607$	−902.512	+	521.066i	−1.48684	+	0.858428i	−0.486953	+	0.873428i	$0.661892\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			427.251i			0.699266i
$612$		0			0
$613$	−256.336			−0.418166			−0.209083	−	0.977898i	$-0.567048\pi$
$613$	−256.336			−0.418166			−0.209083	+	0.977898i	$0.567048\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	253.519	+	439.108i	0.410890	+	0.711683i	0.994987	−	0.100001i	$-0.0318846\pi$
$617$	253.519	+	439.108i	0.410890	+	0.711683i	−0.584097	+	0.811684i	$0.698551\pi$
$618$		0			0
$619$	−662.787	−	382.660i	−1.07074	−	0.618191i	−0.142355	−	0.989816i	$-0.545468\pi$
$619$	−662.787	−	382.660i	−1.07074	−	0.618191i	−0.928383	+	0.371624i	$0.878801\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−100.827	−	58.2125i	−0.161841	−	0.0934390i
$624$		0			0
$625$	12.5746	+	21.7799i	0.0201194	+	0.0348479i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.306623			0.000487477
$630$		0			0
$631$			719.756i			1.14066i	0.821416	+	0.570330i	$0.193185\pi$
$631$			719.756i			1.14066i	−0.821416	+	0.570330i	$0.806815\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	68.5084	−	39.5534i	0.107887	−	0.0622888i
$636$		0			0
$637$	101.175	−	175.240i	0.158830	−	0.275102i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−351.516	+	608.844i	−0.548388	+	0.949835i	0.449998	+	0.893030i	$0.351425\pi$
$641$	−351.516	+	608.844i	−0.548388	+	0.949835i	−0.998385	+	0.0568054i	$0.981909\pi$
$642$		0			0
$643$	−507.224	+	292.846i	−0.788841	+	0.455437i	−0.839554	−	0.543276i	$-0.817184\pi$
$643$	−507.224	+	292.846i	−0.788841	+	0.455437i	0.0507136	+	0.998713i	$0.483850\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			791.553i			1.22342i	0.791082	+	0.611710i	$0.209518\pi$
$647$			791.553i			1.22342i	−0.791082	+	0.611710i	$0.790482\pi$
$648$		0			0
$649$	−132.909			−0.204791
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−196.385	−	340.148i	−0.300742	−	0.520901i	0.675562	−	0.737303i	$-0.263901\pi$
$653$	−196.385	−	340.148i	−0.300742	−	0.520901i	−0.976304	+	0.216402i	$0.930568\pi$
$654$		0			0
$655$	−818.797	−	472.733i	−1.25007	−	0.721730i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	372.557	+	215.096i	0.565337	+	0.326398i	0.755285	−	0.655397i	$-0.227499\pi$
$659$	372.557	+	215.096i	0.565337	+	0.326398i	−0.189948	+	0.981794i	$0.560832\pi$
$660$		0			0
$661$	−453.865	−	786.117i	−0.686633	−	1.18928i	−0.972920	−	0.231140i	$-0.925754\pi$
$661$	−453.865	−	786.117i	−0.686633	−	1.18928i	0.286287	−	0.958144i	$-0.407579\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−596.408			−0.896854
$666$		0			0
$667$			606.799i			0.909744i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−220.106	+	127.078i	−0.328027	+	0.189387i
$672$		0			0
$673$	−34.8528	+	60.3668i	−0.0517872	+	0.0896980i	−0.890757	−	0.454480i	$-0.849825\pi$
$673$	−34.8528	+	60.3668i	−0.0517872	+	0.0896980i	0.838970	+	0.544178i	$0.183158\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−144.502	+	250.285i	−0.213444	+	0.369697i	−0.952790	−	0.303629i	$-0.901802\pi$
$677$	−144.502	+	250.285i	−0.213444	+	0.369697i	0.739346	+	0.673326i	$0.235135\pi$
$678$		0			0
$679$	376.622	−	217.443i	0.554671	−	0.320239i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	522.729i		−	0.765343i	−0.923884	−	0.382672i	$-0.875004\pi$
$683$		−	522.729i		−	0.765343i	0.923884	−	0.382672i	$-0.124996\pi$
$684$		0			0
$685$	2025.29			2.95663
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.34400	−	4.05992i	−0.00340203	−	0.00589248i
$690$		0			0
$691$	485.917	+	280.544i	0.703208	+	0.405997i	0.808541	−	0.588440i	$-0.200258\pi$
$691$	485.917	+	280.544i	0.703208	+	0.405997i	−0.105333	+	0.994437i	$0.533591\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1072.85	−	619.409i	−1.54367	−	0.891236i
$696$		0			0
$697$	6.40971	+	11.1019i	0.00919614	+	0.0159282i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1203.11			1.71627			0.858137	−	0.513421i	$-0.171622\pi$
$701$	1203.11			1.71627			0.858137	+	0.513421i	$0.171622\pi$
$702$		0			0
$703$		−	9.71954i		−	0.0138258i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	169.058	−	97.6059i	0.239121	−	0.138056i
$708$		0			0
$709$	−89.2724	+	154.624i	−0.125913	+	0.218088i	−0.922090	−	0.386977i	$-0.873519\pi$
$709$	−89.2724	+	154.624i	−0.125913	+	0.218088i	0.796176	+	0.605065i	$0.206853\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	242.611	−	420.215i	0.340269	−	0.589362i
$714$		0			0
$715$	185.257	−	106.958i	0.259100	−	0.149591i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	53.0278i		−	0.0737521i	−0.999320	−	0.0368760i	$-0.988259\pi$
$719$		−	53.0278i		−	0.0737521i	0.999320	−	0.0368760i	$-0.0117407\pi$
$720$		0			0
$721$	−652.709			−0.905282
$722$		0			0
$723$		0			0
$724$		0			0
$725$	379.332	+	657.022i	0.523216	+	0.906238i
$726$		0			0
$727$	−436.956	−	252.277i	−0.601041	−	0.347011i	0.168410	−	0.985717i	$-0.446137\pi$
$727$	−436.956	−	252.277i	−0.601041	−	0.347011i	−0.769451	+	0.638706i	$0.779470\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	14.4329	+	8.33283i	0.0197440	+	0.0113992i
$732$		0			0
$733$	−410.964	−	711.811i	−0.560660	−	0.971092i	−0.997439	−	0.0715233i	$-0.977214\pi$
$733$	−410.964	−	711.811i	−0.560660	−	0.971092i	0.436779	−	0.899569i	$-0.356119\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	323.536			0.438991
$738$		0			0
$739$			190.298i			0.257507i	0.991677	+	0.128754i	$0.0410977\pi$
$739$			190.298i			0.257507i	−0.991677	+	0.128754i	$0.958902\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	664.128	−	383.435i	0.893847	−	0.516063i	0.0186481	−	0.999826i	$-0.494064\pi$
$743$	664.128	−	383.435i	0.893847	−	0.516063i	0.875199	+	0.483763i	$0.160730\pi$
$744$		0			0
$745$	−369.762	+	640.447i	−0.496325	+	0.859660i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−123.891	+	214.586i	−0.165409	+	0.286496i
$750$		0			0
$751$	519.601	−	299.992i	0.691879	−	0.399456i	−0.112437	−	0.993659i	$-0.535866\pi$
$751$	519.601	−	299.992i	0.691879	−	0.399456i	0.804315	+	0.594202i	$0.202532\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	335.335i		−	0.444152i
$756$		0			0
$757$	343.082			0.453213			0.226606	−	0.973986i	$-0.427237\pi$
$757$	343.082			0.453213			0.226606	+	0.973986i	$0.427237\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	149.365	+	258.708i	0.196275	+	0.339958i	0.947318	−	0.320295i	$-0.103782\pi$
$761$	149.365	+	258.708i	0.196275	+	0.339958i	−0.751043	+	0.660253i	$0.770449\pi$
$762$		0			0
$763$	−249.464	−	144.028i	−0.326952	−	0.188766i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−215.738	−	124.557i	−0.281275	−	0.162394i
$768$		0			0
$769$	−466.241	−	807.553i	−0.606295	−	1.05013i	−0.991845	−	0.127447i	$-0.959322\pi$
$769$	−466.241	−	807.553i	−0.606295	−	1.05013i	0.385550	−	0.922687i	$-0.374012\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−173.239			−0.224113			−0.112056	−	0.993702i	$-0.535744\pi$
$773$	−173.239			−0.224113			−0.112056	+	0.993702i	$0.535744\pi$
$774$		0			0
$775$		−	606.660i		−	0.782787i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	351.917	−	203.179i	0.451755	−	0.260821i
$780$		0			0
$781$	−106.184	+	183.916i	−0.135959	+	0.235488i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−910.285	+	1576.66i	−1.15960	+	2.00848i
$786$		0			0
$787$	43.1896	−	24.9355i	0.0548788	−	0.0316843i	−0.472310	−	0.881433i	$-0.656580\pi$
$787$	43.1896	−	24.9355i	0.0548788	−	0.0316843i	0.527188	+	0.849748i	$0.323246\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			160.639i			0.203083i
$792$		0			0
$793$	−476.369			−0.600717
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−513.753	−	889.846i	−0.644608	−	1.11649i	−0.984392	−	0.175991i	$-0.943687\pi$
$797$	−513.753	−	889.846i	−0.644608	−	1.11649i	0.339784	−	0.940504i	$-0.389646\pi$
$798$		0			0
$799$	−27.1727	−	15.6882i	−0.0340084	−	0.0196348i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	429.854	+	248.176i	0.535310	+	0.309061i
$804$		0			0
$805$	−581.114	−	1006.52i	−0.721880	−	1.25033i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	637.363			0.787841			0.393920	−	0.919145i	$-0.371119\pi$
$809$	637.363			0.787841			0.393920	+	0.919145i	$0.371119\pi$
$810$		0			0
$811$		−	1486.54i		−	1.83298i	−0.400061	−	0.916489i	$-0.631011\pi$
$811$		−	1486.54i		−	1.83298i	0.400061	−	0.916489i	$-0.368989\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	873.969	−	504.586i	1.07235	−	0.619124i
$816$		0			0
$817$	264.140	−	457.503i	0.323304	−	0.559980i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	517.865	−	896.969i	0.630773	−	1.09253i	−0.356620	−	0.934249i	$-0.616071\pi$
$821$	517.865	−	896.969i	0.630773	−	1.09253i	0.987394	−	0.158282i	$-0.0505956\pi$
$822$		0			0
$823$	−278.230	+	160.636i	−0.338068	+	0.195184i	−0.659417	−	0.751777i	$-0.729197\pi$
$823$	−278.230	+	160.636i	−0.338068	+	0.195184i	0.321349	+	0.946961i	$0.395864\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	119.865i		−	0.144939i	−0.997371	−	0.0724695i	$-0.976912\pi$
$827$		−	119.865i		−	0.144939i	0.997371	−	0.0724695i	$-0.0230880\pi$
$828$		0			0
$829$	−810.947			−0.978223			−0.489112	−	0.872221i	$-0.662679\pi$
$829$	−810.947			−0.978223			−0.489112	+	0.872221i	$0.662679\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.43005	+	12.8692i	0.00891963	+	0.0154492i
$834$		0			0
$835$	1244.57	+	718.553i	1.49050	+	0.860543i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	51.3491	+	29.6464i	0.0612027	+	0.0353354i	0.530289	−	0.847817i	$-0.322083\pi$
$839$	51.3491	+	29.6464i	0.0612027	+	0.0353354i	−0.469086	+	0.883152i	$0.655417\pi$
$840$		0			0
$841$	240.610	+	416.748i	0.286100	+	0.495539i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−961.549			−1.13793
$846$		0			0
$847$			481.466i			0.568437i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	16.4030	−	9.47029i	0.0192750	−	0.0111284i
$852$		0			0
$853$	−547.729	+	948.694i	−0.642121	+	1.11219i	0.342838	+	0.939395i	$0.388612\pi$
$853$	−547.729	+	948.694i	−0.642121	+	1.11219i	−0.984959	+	0.172791i	$0.944722\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	692.162	−	1198.86i	0.807658	−	1.39890i	−0.106825	−	0.994278i	$-0.534068\pi$
$857$	692.162	−	1198.86i	0.807658	−	1.39890i	0.914482	−	0.404626i	$-0.132598\pi$
$858$		0			0
$859$	414.983	−	239.591i	0.483101	−	0.278918i	−0.238607	−	0.971116i	$-0.576691\pi$
$859$	414.983	−	239.591i	0.483101	−	0.278918i	0.721708	+	0.692198i	$0.243357\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			4.93230i			0.00571530i	0.999996	+	0.00285765i	$0.000909619\pi$
$863$			4.93230i			0.00571530i	−0.999996	+	0.00285765i	$0.999090\pi$
$864$		0			0
$865$	1218.83			1.40906
$866$		0			0
$867$		0			0
$868$		0			0
$869$	275.596	+	477.347i	0.317142	+	0.549306i
$870$		0			0
$871$	525.164	+	303.204i	0.602944	+	0.348110i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−471.854	−	272.425i	−0.539262	−	0.311343i
$876$		0			0
$877$	839.494	+	1454.05i	0.957234	+	1.65798i	0.729172	+	0.684331i	$0.239905\pi$
$877$	839.494	+	1454.05i	0.957234	+	1.65798i	0.228062	+	0.973647i	$0.426761\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−830.879			−0.943109			−0.471555	−	0.881837i	$-0.656307\pi$
$881$	−830.879			−0.943109			−0.471555	+	0.881837i	$0.656307\pi$
$882$		0			0
$883$			1228.46i			1.39123i	0.718414	+	0.695615i	$0.244868\pi$
$883$			1228.46i			1.39123i	−0.718414	+	0.695615i	$0.755132\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−660.079	+	381.097i	−0.744170	+	0.429647i	−0.823584	−	0.567195i	$-0.808029\pi$
$887$	−660.079	+	381.097i	−0.744170	+	0.429647i	0.0794134	+	0.996842i	$0.474695\pi$
$888$		0			0
$889$	22.1082	−	38.2925i	0.0248686	−	0.0430737i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−497.295	+	861.340i	−0.556881	+	0.964547i
$894$		0			0
$895$	1932.80	−	1115.90i	2.15955	−	1.24682i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			287.696i			0.320018i
$900$		0			0
$901$	0.344275			0.000382104
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−422.166	−	731.214i	−0.466482	−	0.807971i
$906$		0			0
$907$	−324.076	−	187.106i	−0.357306	−	0.206291i	0.310592	−	0.950543i	$-0.399473\pi$
$907$	−324.076	−	187.106i	−0.357306	−	0.206291i	−0.667898	+	0.744253i	$0.732806\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1265.50	+	730.639i	1.38914	+	0.802018i	0.993218	−	0.116268i	$-0.0370930\pi$
$911$	1265.50	+	730.639i	1.38914	+	0.802018i	0.395918	+	0.918286i	$0.370426\pi$
$912$		0			0
$913$	189.212	+	327.725i	0.207242	+	0.358954i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−528.464			−0.576296
$918$		0			0
$919$			1112.72i			1.21080i	0.795923	+	0.605398i	$0.206986\pi$
$919$			1112.72i			1.21080i	−0.795923	+	0.605398i	$0.793014\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−344.717	+	199.022i	−0.373474	+	0.215625i
$924$		0			0
$925$	11.8404	−	20.5082i	0.0128005	−	0.0221710i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	508.204	−	880.234i	0.547044	−	0.947507i	−0.451432	−	0.892306i	$-0.649086\pi$
$929$	508.204	−	880.234i	0.547044	−	0.947507i	0.998475	−	0.0552017i	$-0.0175802\pi$
$930$		0			0
$931$	407.938	−	235.523i	0.438171	−	0.252978i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			15.7095i			0.0168016i
$936$		0			0
$937$	170.282			0.181731			0.0908654	−	0.995863i	$-0.471037\pi$
$937$	170.282			0.181731			0.0908654	+	0.995863i	$0.471037\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−150.929	−	261.417i	−0.160392	−	0.277808i	0.774617	−	0.632430i	$-0.217943\pi$
$941$	−150.929	−	261.417i	−0.160392	−	0.277808i	−0.935009	+	0.354623i	$0.884609\pi$
$942$		0			0
$943$	685.784	+	395.938i	0.727237	+	0.419870i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	730.155	+	421.555i	0.771019	+	0.445148i	0.833238	−	0.552914i	$-0.186484\pi$
$947$	730.155	+	421.555i	0.771019	+	0.445148i	−0.0622189	+	0.998063i	$0.519818\pi$
$948$		0			0
$949$	465.159	+	805.679i	0.490157	+	0.848977i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−306.171			−0.321270			−0.160635	−	0.987014i	$-0.551354\pi$
$953$	−306.171			−0.321270			−0.160635	+	0.987014i	$0.551354\pi$
$954$		0			0
$955$		−	1796.44i		−	1.88109i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	980.365	−	566.014i	1.02228	−	0.590213i
$960$		0			0
$961$	−365.473	+	633.018i	−0.380305	+	0.658707i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	456.951	−	791.462i	0.473524	−	0.820168i
$966$		0			0
$967$	−103.822	+	59.9417i	−0.107365	+	0.0619873i	−0.552721	−	0.833366i	$-0.686410\pi$
$967$	−103.822	+	59.9417i	−0.107365	+	0.0619873i	0.445356	+	0.895354i	$0.353077\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			62.7602i			0.0646346i	0.999478	+	0.0323173i	$0.0102887\pi$
$971$			62.7602i			0.0646346i	−0.999478	+	0.0323173i	$0.989711\pi$
$972$		0			0
$973$	−692.431			−0.711646
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−618.115	−	1070.61i	−0.632666	−	1.09581i	−0.987004	−	0.160693i	$-0.948627\pi$
$977$	−618.115	−	1070.61i	−0.632666	−	1.09581i	0.354338	−	0.935117i	$-0.384706\pi$
$978$		0			0
$979$	84.1854	+	48.6045i	0.0859912	+	0.0496471i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−490.618	−	283.258i	−0.499103	−	0.288157i	0.229240	−	0.973370i	$-0.426376\pi$
$983$	−490.618	−	283.258i	−0.499103	−	0.288157i	−0.728343	+	0.685213i	$0.759709\pi$
$984$		0			0
$985$	487.746	+	844.801i	0.495174	+	0.857666i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1029.46			1.04091
$990$		0			0
$991$		−	457.774i		−	0.461931i	−0.972962	−	0.230966i	$-0.925812\pi$
$991$		−	457.774i		−	0.461931i	0.972962	−	0.230966i	$-0.0741885\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	574.172	−	331.498i	0.577057	−	0.333164i
$996$		0			0
$997$	−19.3798	+	33.5667i	−0.0194381	+	0.0336677i	−0.875581	−	0.483072i	$-0.839521\pi$
$997$	−19.3798	+	33.5667i	−0.0194381	+	0.0336677i	0.856143	+	0.516739i	$0.172854\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.g.127.1		16
3.2	odd	2		576.3.o.g.511.8		16
4.3	odd	2	inner	1728.3.o.g.127.2		16
8.3	odd	2		108.3.f.c.19.4		16
8.5	even	2		108.3.f.c.19.8		16
9.4	even	3	inner	1728.3.o.g.1279.2		16
9.5	odd	6		576.3.o.g.319.1		16
12.11	even	2		576.3.o.g.511.1		16
24.5	odd	2		36.3.f.c.7.1	✓	16
24.11	even	2		36.3.f.c.7.5	yes	16
36.23	even	6		576.3.o.g.319.8		16
36.31	odd	6	inner	1728.3.o.g.1279.1		16
72.5	odd	6		36.3.f.c.31.5	yes	16
72.11	even	6		324.3.d.i.163.5		8
72.13	even	6		108.3.f.c.91.4		16
72.29	odd	6		324.3.d.i.163.6		8
72.43	odd	6		324.3.d.g.163.4		8
72.59	even	6		36.3.f.c.31.1	yes	16
72.61	even	6		324.3.d.g.163.3		8
72.67	odd	6		108.3.f.c.91.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.1	✓	16	24.5	odd	2
36.3.f.c.7.5	yes	16	24.11	even	2
36.3.f.c.31.1	yes	16	72.59	even	6
36.3.f.c.31.5	yes	16	72.5	odd	6
108.3.f.c.19.4		16	8.3	odd	2
108.3.f.c.19.8		16	8.5	even	2
108.3.f.c.91.4		16	72.13	even	6
108.3.f.c.91.8		16	72.67	odd	6
324.3.d.g.163.3		8	72.61	even	6
324.3.d.g.163.4		8	72.43	odd	6
324.3.d.i.163.5		8	72.11	even	6
324.3.d.i.163.6		8	72.29	odd	6
576.3.o.g.319.1		16	9.5	odd	6
576.3.o.g.319.8		16	36.23	even	6
576.3.o.g.511.1		16	12.11	even	2
576.3.o.g.511.8		16	3.2	odd	2
1728.3.o.g.127.1		16	1.1	even	1	trivial
1728.3.o.g.127.2		16	4.3	odd	2	inner
1728.3.o.g.1279.1		16	36.31	odd	6	inner
1728.3.o.g.1279.2		16	9.4	even	3	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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.03104 - 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +O(q^{10})\)	\(q+(-4.03104 - 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(3.25842 + 1.88125i) q^{11} +(3.52605 + 6.10730i) q^{13} -0.517890 q^{17} +16.4164i q^{19} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(9.48394 - 16.4267i) q^{29} +(-13.1355 + 7.58377i) q^{31} +36.3299i q^{35} -0.592061 q^{37} +(-12.3766 - 21.4369i) q^{41} +(-27.8686 - 16.0900i) q^{43} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} -0.664765 q^{53} -30.3336i q^{55} +(-30.5921 + 17.6623i) q^{59} +(-33.7750 + 58.5000i) q^{61} +(28.4273 - 49.2376i) q^{65} +(74.4692 - 42.9948i) q^{67} +56.4434i q^{71} +131.921 q^{73} +(-8.47743 - 14.6833i) q^{77} +(126.869 + 73.2481i) q^{79} +(87.1029 + 50.2889i) q^{83} +(2.08764 + 3.61589i) q^{85} +25.8362 q^{89} -31.7786i q^{91} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5}+O(q^{10}) \) 16 * q + 6 * q^5	\( 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

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