LMFDB - Embedded newform 1620.3.o.f.1241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,3,Mod(701,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1620.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1620.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:	$44.1418028264$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1241.1
Root			$-1.40294 - 1.01575i$ of defining polynomial
Character	$\chi$	$=$	1620.1241
Dual form			1620.3.o.f.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93649 + 1.11803i) q^{5} +(-2.74342 + 4.75174i) q^{7} +O(q^{10})$	$q+(-1.93649 + 1.11803i) q^{5} +(-2.74342 + 4.75174i) q^{7} +(7.94472 + 4.58688i) q^{11} +(-5.74342 - 9.94789i) q^{13} -16.9706i q^{17} +26.9737 q^{19} +(-4.27048 + 2.46556i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-17.7749 - 10.2624i) q^{29} +(-10.4868 - 18.1637i) q^{31} -12.2689i q^{35} -62.4605 q^{37} +(35.4531 - 20.4689i) q^{41} +(-0.513167 + 0.888831i) q^{43} +(74.6772 + 43.1149i) q^{47} +(9.44733 + 16.3633i) q^{49} +96.0920i q^{53} -20.5132 q^{55} +(97.3188 - 56.1871i) q^{59} +(33.4605 - 57.9553i) q^{61} +(22.2442 + 12.8427i) q^{65} +(38.0000 + 65.8179i) q^{67} +24.0789i q^{71} -18.9210 q^{73} +(-43.5913 + 25.1675i) q^{77} +(-53.4605 + 92.5963i) q^{79} +(39.1273 + 22.5902i) q^{83} +(18.9737 + 32.8634i) q^{85} +115.928i q^{89} +63.0263 q^{91} +(-52.2343 + 30.1575i) q^{95} +(43.5132 - 75.3670i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7}+O(q^{10}) $ 8 * q + 16 * q^7	$ 8 q + 16 q^{7} - 8 q^{13} + 64 q^{19} + 20 q^{25} - 8 q^{31} - 272 q^{37} - 80 q^{43} - 228 q^{49} - 240 q^{55} + 40 q^{61} + 304 q^{67} + 304 q^{73} - 200 q^{79} + 656 q^{91} + 424 q^{97}+O(q^{100}) $ 8 * q + 16 * q^7 - 8 * q^13 + 64 * q^19 + 20 * q^25 - 8 * q^31 - 272 * q^37 - 80 * q^43 - 228 * q^49 - 240 * q^55 + 40 * q^61 + 304 * q^67 + 304 * q^73 - 200 * q^79 + 656 * q^91 + 424 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	−2.74342	+	4.75174i	−0.391917	+	0.678820i	−0.992702	−	0.120591i	$-0.961521\pi$
$7$	−2.74342	+	4.75174i	−0.391917	+	0.678820i	0.600786	+	0.799410i	$0.294855\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	7.94472	+	4.58688i	0.722247	+	0.416989i	0.815579	−	0.578646i	$-0.196419\pi$
$11$	7.94472	+	4.58688i	0.722247	+	0.416989i	−0.0933322	+	0.995635i	$0.529752\pi$
$12$		0			0
$13$	−5.74342	−	9.94789i	−0.441801	−	0.765222i	0.556022	−	0.831168i	$-0.312327\pi$
$13$	−5.74342	−	9.94789i	−0.441801	−	0.765222i	−0.997823	+	0.0659454i	$0.978994\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	16.9706i		−	0.998268i	−0.866525	−	0.499134i	$-0.833651\pi$
$17$		−	16.9706i		−	0.998268i	0.866525	−	0.499134i	$-0.166349\pi$
$18$		0			0
$19$	26.9737			1.41967			0.709833	−	0.704370i	$-0.248770\pi$
$19$	26.9737			1.41967			0.709833	+	0.704370i	$0.248770\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.27048	+	2.46556i	−0.185673	+	0.107198i	−0.589955	−	0.807436i	$-0.700855\pi$
$23$	−4.27048	+	2.46556i	−0.185673	+	0.107198i	0.404282	+	0.914634i	$0.367521\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−17.7749	−	10.2624i	−0.612929	−	0.353874i	0.161182	−	0.986925i	$-0.448469\pi$
$29$	−17.7749	−	10.2624i	−0.612929	−	0.353874i	−0.774111	+	0.633050i	$0.781803\pi$
$30$		0			0
$31$	−10.4868	−	18.1637i	−0.338285	−	0.585927i	0.645825	−	0.763485i	$-0.276513\pi$
$31$	−10.4868	−	18.1637i	−0.338285	−	0.585927i	−0.984110	+	0.177559i	$0.943180\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	12.2689i		−	0.350541i
$36$		0			0
$37$	−62.4605			−1.68812			−0.844061	−	0.536247i	$-0.819841\pi$
$37$	−62.4605			−1.68812			−0.844061	+	0.536247i	$0.819841\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	35.4531	−	20.4689i	0.864710	−	0.499240i	−0.000876936	−	1.00000i	$-0.500279\pi$
$41$	35.4531	−	20.4689i	0.864710	−	0.499240i	0.865587	+	0.500759i	$0.166946\pi$
$42$		0			0
$43$	−0.513167	+	0.888831i	−0.0119341	+	0.0206705i	−0.871931	−	0.489629i	$-0.837132\pi$
$43$	−0.513167	+	0.888831i	−0.0119341	+	0.0206705i	0.859997	+	0.510300i	$0.170466\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	74.6772	+	43.1149i	1.58888	+	0.917338i	0.993493	+	0.113897i	$0.0363333\pi$
$47$	74.6772	+	43.1149i	1.58888	+	0.917338i	0.595384	+	0.803442i	$0.297000\pi$
$48$		0			0
$49$	9.44733	+	16.3633i	0.192803	+	0.333944i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			96.0920i			1.81306i	0.422144	+	0.906529i	$0.361278\pi$
$53$			96.0920i			1.81306i	−0.422144	+	0.906529i	$0.638722\pi$
$54$		0			0
$55$	−20.5132			−0.372967
$56$		0			0
$57$		0			0
$58$		0			0
$59$	97.3188	−	56.1871i	1.64947	−	0.952323i	0.672190	−	0.740379i	$-0.265354\pi$
$59$	97.3188	−	56.1871i	1.64947	−	0.952323i	0.977282	−	0.211944i	$-0.0679796\pi$
$60$		0			0
$61$	33.4605	−	57.9553i	0.548533	−	0.950087i	−0.449843	−	0.893108i	$-0.648520\pi$
$61$	33.4605	−	57.9553i	0.548533	−	0.950087i	0.998375	−	0.0569788i	$-0.0181467\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	22.2442	+	12.8427i	0.342218	+	0.197580i
$66$		0			0
$67$	38.0000	+	65.8179i	0.567164	+	0.982357i	0.996845	+	0.0793762i	$0.0252928\pi$
$67$	38.0000	+	65.8179i	0.567164	+	0.982357i	−0.429681	+	0.902981i	$0.641374\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			24.0789i			0.339139i	0.985518	+	0.169570i	$0.0542377\pi$
$71$			24.0789i			0.339139i	−0.985518	+	0.169570i	$0.945762\pi$
$72$		0			0
$73$	−18.9210			−0.259192			−0.129596	−	0.991567i	$-0.541368\pi$
$73$	−18.9210			−0.259192			−0.129596	+	0.991567i	$0.541368\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−43.5913	+	25.1675i	−0.566121	+	0.326850i
$78$		0			0
$79$	−53.4605	+	92.5963i	−0.676715	+	1.17211i	0.299249	+	0.954175i	$0.403264\pi$
$79$	−53.4605	+	92.5963i	−0.676715	+	1.17211i	−0.975964	+	0.217930i	$0.930070\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	39.1273	+	22.5902i	0.471414	+	0.272171i	0.716831	−	0.697247i	$-0.245592\pi$
$83$	39.1273	+	22.5902i	0.471414	+	0.272171i	−0.245418	+	0.969417i	$0.578925\pi$
$84$		0			0
$85$	18.9737	+	32.8634i	0.223220	+	0.386628i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			115.928i			1.30256i	0.758835	+	0.651282i	$0.225769\pi$
$89$			115.928i			1.30256i	−0.758835	+	0.651282i	$0.774231\pi$
$90$		0			0
$91$	63.0263			0.692597
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−52.2343	+	30.1575i	−0.549835	+	0.317447i
$96$		0			0
$97$	43.5132	−	75.3670i	0.448589	−	0.776980i	−0.549705	−	0.835359i	$-0.685260\pi$
$97$	43.5132	−	75.3670i	0.448589	−	0.776980i	0.998294	+	0.0583792i	$0.0185933\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	111.919	+	64.6165i	1.10811	+	0.639767i	0.938339	−	0.345717i	$-0.112364\pi$
$101$	111.919	+	64.6165i	1.10811	+	0.639767i	0.169770	+	0.985484i	$0.445697\pi$
$102$		0			0
$103$	−57.1512	−	98.9889i	−0.554866	−	0.961057i	−0.997914	−	0.0645588i	$-0.979436\pi$
$103$	−57.1512	−	98.9889i	−0.554866	−	0.961057i	0.443047	−	0.896498i	$-0.353897\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	93.3381i		−	0.872319i	−0.899869	−	0.436159i	$-0.856338\pi$
$107$		−	93.3381i		−	0.872319i	0.899869	−	0.436159i	$-0.143662\pi$
$108$		0			0
$109$	120.868			1.10888			0.554442	−	0.832222i	$-0.312932\pi$
$109$	120.868			1.10888			0.554442	+	0.832222i	$0.312932\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	95.5301	−	55.1543i	0.845399	−	0.488091i	−0.0136967	−	0.999906i	$-0.504360\pi$
$113$	95.5301	−	55.1543i	0.845399	−	0.488091i	0.859096	+	0.511815i	$0.171027\pi$
$114$		0			0
$115$	5.51317	−	9.54909i	0.0479406	−	0.0830355i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	80.6396	+	46.5573i	0.677644	+	0.391238i
$120$		0			0
$121$	−18.4210	−	31.9061i	−0.152240	−	0.263687i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	105.381			0.829776			0.414888	−	0.909873i	$-0.363821\pi$
$127$	105.381			0.829776			0.414888	+	0.909873i	$0.363821\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	121.749	−	70.2920i	0.929383	−	0.536580i	0.0427669	−	0.999085i	$-0.486383\pi$
$131$	121.749	−	70.2920i	0.929383	−	0.536580i	0.886617	+	0.462505i	$0.153049\pi$
$132$		0			0
$133$	−74.0000	+	128.172i	−0.556391	+	0.963697i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	231.187	+	133.476i	1.68749	+	0.974274i	0.956429	+	0.291965i	$0.0943092\pi$
$137$	231.187	+	133.476i	1.68749	+	0.974274i	0.731064	+	0.682309i	$0.239024\pi$
$138$		0			0
$139$	7.92100	+	13.7196i	0.0569856	+	0.0987019i	0.893111	−	0.449837i	$-0.148518\pi$
$139$	7.92100	+	13.7196i	0.0569856	+	0.0987019i	−0.836125	+	0.548538i	$0.815184\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	105.378i		−	0.736906i
$144$		0			0
$145$	45.8947			0.316515
$146$		0			0
$147$		0			0
$148$		0			0
$149$	36.0493	−	20.8131i	0.241942	−	0.139685i	−0.374127	−	0.927377i	$-0.622058\pi$
$149$	36.0493	−	20.8131i	0.241942	−	0.139685i	0.616069	+	0.787692i	$0.288724\pi$
$150$		0			0
$151$	−51.9210	+	89.9298i	−0.343848	+	0.595562i	−0.985144	−	0.171732i	$-0.945064\pi$
$151$	−51.9210	+	89.9298i	−0.343848	+	0.595562i	0.641296	+	0.767294i	$0.278397\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	40.6153	+	23.4493i	0.262034	+	0.151286i
$156$		0			0
$157$	6.25658	+	10.8367i	0.0398509	+	0.0690237i	0.885263	−	0.465091i	$-0.153978\pi$
$157$	6.25658	+	10.8367i	0.0398509	+	0.0690237i	−0.845412	+	0.534115i	$0.820645\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	27.0563i		−	0.168051i
$162$		0			0
$163$	−290.868			−1.78447			−0.892234	−	0.451573i	$-0.850863\pi$
$163$	−290.868			−1.78447			−0.892234	+	0.451573i	$0.850863\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	151.240	−	87.3184i	0.905628	−	0.522865i	0.0266061	−	0.999646i	$-0.491530\pi$
$167$	151.240	−	87.3184i	0.905628	−	0.522865i	0.879022	+	0.476781i	$0.158197\pi$
$168$		0			0
$169$	18.5263	−	32.0886i	0.109623	−	0.189873i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	37.7413	+	21.7900i	0.218158	+	0.125954i	0.605097	−	0.796152i	$-0.293134\pi$
$173$	37.7413	+	21.7900i	0.218158	+	0.125954i	−0.386939	+	0.922105i	$0.626468\pi$
$174$		0			0
$175$	13.7171	+	23.7587i	0.0783833	+	0.135764i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			88.2952i			0.493270i	0.969109	+	0.246635i	$0.0793248\pi$
$179$			88.2952i			0.493270i	−0.969109	+	0.246635i	$0.920675\pi$
$180$		0			0
$181$	−56.8683			−0.314190			−0.157095	−	0.987584i	$-0.550213\pi$
$181$	−56.8683			−0.314190			−0.157095	+	0.987584i	$0.550213\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	120.954	−	69.8330i	0.653807	−	0.377475i
$186$		0			0
$187$	77.8420	−	134.826i	0.416267	−	0.720996i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−49.0543	−	28.3215i	−0.256829	−	0.148280i	0.366058	−	0.930592i	$-0.380707\pi$
$191$	−49.0543	−	28.3215i	−0.256829	−	0.148280i	−0.622887	+	0.782312i	$0.714040\pi$
$192$		0			0
$193$	−55.0000	−	95.2628i	−0.284974	−	0.493590i	0.687629	−	0.726062i	$-0.258652\pi$
$193$	−55.0000	−	95.2628i	−0.284974	−	0.493590i	−0.972603	+	0.232473i	$0.925318\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			245.049i			1.24391i	0.783055	+	0.621953i	$0.213661\pi$
$197$			245.049i			1.24391i	−0.783055	+	0.621953i	$0.786339\pi$
$198$		0			0
$199$	−169.895			−0.853742			−0.426871	−	0.904313i	$-0.640384\pi$
$199$	−169.895			−0.853742			−0.426871	+	0.904313i	$0.640384\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	97.5281	−	56.3078i	0.480434	−	0.277379i
$204$		0			0
$205$	−45.7698	+	79.2755i	−0.223267	+	0.386710i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	214.298	+	123.725i	1.02535	+	0.591986i
$210$		0			0
$211$	132.789	+	229.998i	0.629333	+	1.09004i	0.987686	+	0.156451i	$0.0500053\pi$
$211$	132.789	+	229.998i	0.629333	+	1.09004i	−0.358352	+	0.933586i	$0.616661\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	2.29495i		−	0.0106742i
$216$		0			0
$217$	115.079			0.530318
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−168.821	+	97.4690i	−0.763897	+	0.441036i
$222$		0			0
$223$	93.6644	−	162.232i	0.420020	−	0.727496i	−0.575921	−	0.817505i	$-0.695356\pi$
$223$	93.6644	−	162.232i	0.420020	−	0.727496i	0.995941	+	0.0900097i	$0.0286898\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−364.651	−	210.532i	−1.60639	−	0.927452i	−0.990168	−	0.139883i	$-0.955327\pi$
$227$	−364.651	−	210.532i	−1.60639	−	0.927452i	−0.616226	−	0.787569i	$-0.711339\pi$
$228$		0			0
$229$	51.0527	+	88.4258i	0.222937	+	0.386139i	0.955699	−	0.294347i	$-0.0951021\pi$
$229$	51.0527	+	88.4258i	0.222937	+	0.386139i	−0.732761	+	0.680486i	$0.761769\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			99.0694i			0.425191i	0.977140	+	0.212595i	$0.0681916\pi$
$233$			99.0694i			0.425191i	−0.977140	+	0.212595i	$0.931808\pi$
$234$		0			0
$235$	−192.816			−0.820492
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−67.5222	+	38.9840i	−0.282520	+	0.163113i	−0.634564	−	0.772871i	$-0.718820\pi$
$239$	−67.5222	+	38.9840i	−0.282520	+	0.163113i	0.352044	+	0.935984i	$0.385487\pi$
$240$		0			0
$241$	128.974	−	223.389i	0.535160	−	0.926925i	−0.463995	−	0.885838i	$-0.653584\pi$
$241$	128.974	−	223.389i	0.535160	−	0.926925i	0.999156	−	0.0410873i	$-0.0130822\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−36.5894	−	21.1249i	−0.149344	−	0.0862240i
$246$		0			0
$247$	−154.921	−	268.331i	−0.627211	−	1.08636i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			274.971i			1.09550i	0.836641	+	0.547752i	$0.184516\pi$
$251$			274.971i			1.09550i	−0.836641	+	0.547752i	$0.815484\pi$
$252$		0			0
$253$	−45.2370			−0.178802
$254$		0			0
$255$		0			0
$256$		0			0
$257$	113.998	−	65.8168i	0.443572	−	0.256096i	−0.261540	−	0.965193i	$-0.584230\pi$
$257$	113.998	−	65.8168i	0.443572	−	0.256096i	0.705112	+	0.709096i	$0.250897\pi$
$258$		0			0
$259$	171.355	−	296.796i	0.661603	−	1.14593i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	397.317	+	229.391i	1.51071	+	0.872209i	0.999922	+	0.0125026i	$0.00397982\pi$
$263$	397.317	+	229.391i	1.51071	+	0.872209i	0.510789	+	0.859706i	$0.329354\pi$
$264$		0			0
$265$	−107.434	−	186.081i	−0.405412	−	0.702194i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	301.916i		−	1.12236i	−0.827692	−	0.561182i	$-0.810347\pi$
$269$		−	301.916i		−	1.12236i	0.827692	−	0.561182i	$-0.189653\pi$
$270$		0			0
$271$	475.842			1.75587			0.877937	−	0.478776i	$-0.158919\pi$
$271$	475.842			1.75587			0.877937	+	0.478776i	$0.158919\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	39.7236	−	22.9344i	0.144449	−	0.0833979i
$276$		0			0
$277$	−161.020	+	278.894i	−0.581298	+	1.00684i	0.414028	+	0.910264i	$0.364122\pi$
$277$	−161.020	+	278.894i	−0.581298	+	1.00684i	−0.995326	+	0.0965736i	$0.969212\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	304.961	+	176.070i	1.08527	+	0.626582i	0.932314	−	0.361650i	$-0.117787\pi$
$281$	304.961	+	176.070i	1.08527	+	0.626582i	0.152958	+	0.988233i	$0.451120\pi$
$282$		0			0
$283$	140.816	+	243.900i	0.497582	+	0.861837i	0.999996	−	0.00279000i	$-0.000888086\pi$
$283$	140.816	+	243.900i	0.497582	+	0.861837i	−0.502414	+	0.864627i	$0.667555\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			224.618i			0.782642i
$288$		0			0
$289$	1.00000			0.00346021
$290$		0			0
$291$		0			0
$292$		0			0
$293$	55.7098	−	32.1640i	0.190136	−	0.109775i	−0.401910	−	0.915679i	$-0.631654\pi$
$293$	55.7098	−	32.1640i	0.190136	−	0.109775i	0.592046	+	0.805904i	$0.298320\pi$
$294$		0			0
$295$	−125.638	+	217.612i	−0.425892	+	0.737666i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	49.0543	+	28.3215i	0.164061	+	0.0947208i
$300$		0			0
$301$	−2.81566	−	4.87687i	−0.00935436	−	0.0162022i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			149.640i			0.490623i
$306$		0			0
$307$	230.158			0.749700			0.374850	−	0.927085i	$-0.377694\pi$
$307$	230.158			0.749700			0.374850	+	0.927085i	$0.377694\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.34847	−	4.24264i	0.0236285	−	0.0136419i	−0.488139	−	0.872766i	$-0.662324\pi$
$311$	7.34847	−	4.24264i	0.0236285	−	0.0136419i	0.511768	+	0.859124i	$0.328991\pi$
$312$		0			0
$313$	−302.789	+	524.446i	−0.967378	+	1.67555i	−0.264293	+	0.964443i	$0.585138\pi$
$313$	−302.789	+	524.446i	−0.967378	+	1.67555i	−0.703085	+	0.711105i	$0.748195\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	76.1757	+	43.9800i	0.240302	+	0.138738i	0.615315	−	0.788281i	$-0.289029\pi$
$317$	76.1757	+	43.9800i	0.240302	+	0.138738i	−0.375014	+	0.927019i	$0.622362\pi$
$318$		0			0
$319$	−94.1445	−	163.063i	−0.295124	−	0.511169i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	457.758i		−	1.41721i
$324$		0			0
$325$	−57.4342			−0.176721
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−409.741	+	236.564i	−1.24541	+	0.719040i
$330$		0			0
$331$	24.6185	−	42.6405i	0.0743761	−	0.128823i	−0.826439	−	0.563027i	$-0.809637\pi$
$331$	24.6185	−	42.6405i	0.0743761	−	0.128823i	0.900815	+	0.434204i	$0.142970\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−147.173	−	84.9706i	−0.439323	−	0.253644i
$336$		0			0
$337$	1.35516	+	2.34721i	0.00402125	+	0.00696502i	0.868029	−	0.496513i	$-0.165387\pi$
$337$	1.35516	+	2.34721i	0.00402125	+	0.00696502i	−0.864008	+	0.503478i	$0.832053\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	192.408i		−	0.564245i
$342$		0			0
$343$	−372.527			−1.08608
$344$		0			0
$345$		0			0
$346$		0			0
$347$	64.9437	−	37.4953i	0.187158	−	0.108056i	−0.403494	−	0.914982i	$-0.632204\pi$
$347$	64.9437	−	37.4953i	0.187158	−	0.108056i	0.590651	+	0.806927i	$0.298871\pi$
$348$		0			0
$349$	75.4605	−	130.701i	0.216219	−	0.374503i	−0.737430	−	0.675424i	$-0.763961\pi$
$349$	75.4605	−	130.701i	0.216219	−	0.374503i	0.953649	+	0.300921i	$0.0972941\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−253.232	−	146.204i	−0.717371	−	0.414174i	0.0964134	−	0.995341i	$-0.469263\pi$
$353$	−253.232	−	146.204i	−0.717371	−	0.414174i	−0.813784	+	0.581167i	$0.802596\pi$
$354$		0			0
$355$	−26.9210	−	46.6285i	−0.0758338	−	0.131348i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	576.776i		−	1.60662i	−0.595563	−	0.803309i	$-0.703071\pi$
$359$		−	576.776i		−	1.60662i	0.595563	−	0.803309i	$-0.296929\pi$
$360$		0			0
$361$	366.579			1.01545
$362$		0			0
$363$		0			0
$364$		0			0
$365$	36.6404	−	21.1543i	0.100385	−	0.0579570i
$366$		0			0
$367$	−121.770	+	210.911i	−0.331798	+	0.574690i	−0.982864	−	0.184330i	$-0.940988\pi$
$367$	−121.770	+	210.911i	−0.331798	+	0.574690i	0.651067	+	0.759021i	$0.274322\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−456.604	−	263.620i	−1.23074	−	0.710567i
$372$		0			0
$373$	−57.9541	−	100.379i	−0.155373	−	0.269114i	0.777822	−	0.628485i	$-0.216325\pi$
$373$	−57.9541	−	100.379i	−0.155373	−	0.269114i	−0.933195	+	0.359371i	$0.882991\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			235.764i			0.625369i
$378$		0			0
$379$	30.2107			0.0797115			0.0398558	−	0.999205i	$-0.487310\pi$
$379$	30.2107			0.0797115			0.0398558	+	0.999205i	$0.487310\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−564.059	+	325.660i	−1.47274	+	0.850286i	−0.999530	−	0.0306636i	$-0.990238\pi$
$383$	−564.059	+	325.660i	−1.47274	+	0.850286i	−0.473209	+	0.880950i	$0.656905\pi$
$384$		0			0
$385$	56.2762	−	97.4732i	0.146172	−	0.253177i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−178.055	−	102.800i	−0.457726	−	0.264268i	0.253362	−	0.967372i	$-0.418464\pi$
$389$	−178.055	−	102.800i	−0.457726	−	0.264268i	−0.711087	+	0.703104i	$0.751797\pi$
$390$		0			0
$391$	41.8420	+	72.4725i	0.107013	+	0.185352i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	239.083i		−	0.605272i
$396$		0			0
$397$	118.355			0.298124			0.149062	−	0.988828i	$-0.452375\pi$
$397$	118.355			0.298124			0.149062	+	0.988828i	$0.452375\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−148.065	+	85.4854i	−0.369240	+	0.213181i	−0.673126	−	0.739528i	$-0.735049\pi$
$401$	−148.065	+	85.4854i	−0.369240	+	0.213181i	0.303887	+	0.952708i	$0.401716\pi$
$402$		0			0
$403$	−120.460	+	208.644i	−0.298909	+	0.517726i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−496.231	−	286.499i	−1.21924	−	0.703929i
$408$		0			0
$409$	167.974	+	290.939i	0.410694	+	0.711342i	0.994966	−	0.100216i	$-0.0319533\pi$
$409$	167.974	+	290.939i	0.410694	+	0.711342i	−0.584272	+	0.811558i	$0.698620\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			616.578i			1.49292i
$414$		0			0
$415$	−101.026			−0.243437
$416$		0			0
$417$		0			0
$418$		0			0
$419$	352.936	−	203.768i	0.842329	−	0.486319i	−0.0157264	−	0.999876i	$-0.505006\pi$
$419$	352.936	−	203.768i	0.842329	−	0.486319i	0.858055	+	0.513558i	$0.171673\pi$
$420$		0			0
$421$	385.605	−	667.887i	0.915926	−	1.58643i	0.110387	−	0.993889i	$-0.464791\pi$
$421$	385.605	−	667.887i	0.915926	−	1.58643i	0.805539	−	0.592542i	$-0.201876\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−73.4847	−	42.4264i	−0.172905	−	0.0998268i
$426$		0			0
$427$	183.592	+	317.991i	0.429958	+	0.744710i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	436.210i		−	1.01209i	−0.862508	−	0.506044i	$-0.831107\pi$
$431$		−	436.210i		−	1.01209i	0.862508	−	0.506044i	$-0.168893\pi$
$432$		0			0
$433$	−838.500			−1.93649			−0.968244	−	0.250006i	$-0.919568\pi$
$433$	−838.500			−1.93649			−0.968244	+	0.250006i	$0.919568\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−115.191	+	66.5053i	−0.263594	+	0.152186i
$438$		0			0
$439$	−25.0000	+	43.3013i	−0.0569476	+	0.0986362i	−0.893094	−	0.449871i	$-0.851470\pi$
$439$	−25.0000	+	43.3013i	−0.0569476	+	0.0986362i	0.836146	+	0.548507i	$0.184803\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−426.823	−	246.426i	−0.963483	−	0.556267i	−0.0662400	−	0.997804i	$-0.521100\pi$
$443$	−426.823	−	246.426i	−0.963483	−	0.556267i	−0.897243	+	0.441536i	$0.854434\pi$
$444$		0			0
$445$	−129.612	−	224.494i	−0.291262	−	0.504481i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			483.102i			1.07595i	0.842960	+	0.537976i	$0.180811\pi$
$449$			483.102i			1.07595i	−0.842960	+	0.537976i	$0.819189\pi$
$450$		0			0
$451$	375.553			0.832712
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−122.050	+	70.4656i	−0.268242	+	0.154869i
$456$		0			0
$457$	273.460	−	473.647i	0.598382	−	1.03643i	−0.394678	−	0.918819i	$-0.629144\pi$
$457$	273.460	−	473.647i	0.598382	−	1.03643i	0.993060	−	0.117608i	$-0.0375227\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−112.918	−	65.1932i	−0.244941	−	0.141417i	0.372504	−	0.928030i	$-0.378499\pi$
$461$	−112.918	−	65.1932i	−0.244941	−	0.141417i	−0.617446	+	0.786613i	$0.711833\pi$
$462$		0			0
$463$	−12.3883	−	21.4571i	−0.0267565	−	0.0463436i	0.852337	−	0.522993i	$-0.175185\pi$
$463$	−12.3883	−	21.4571i	−0.0267565	−	0.0463436i	−0.879094	+	0.476649i	$0.841851\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	671.491i		−	1.43788i	−0.695071	−	0.718941i	$-0.744627\pi$
$467$		−	671.491i		−	1.43788i	0.695071	−	0.718941i	$-0.255373\pi$
$468$		0			0
$469$	−416.999			−0.889124
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.15393	+	4.70767i	−0.0172388	+	0.00995280i
$474$		0			0
$475$	67.4342	−	116.799i	0.141967	−	0.245893i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−466.144	−	269.128i	−0.973161	−	0.561855i	−0.0729624	−	0.997335i	$-0.523245\pi$
$479$	−466.144	−	269.128i	−0.973161	−	0.561855i	−0.900198	+	0.435480i	$0.856579\pi$
$480$		0			0
$481$	358.737	+	621.350i	0.745814	+	1.29179i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			194.597i			0.401231i
$486$		0			0
$487$	608.250			1.24897			0.624486	−	0.781036i	$-0.285308\pi$
$487$	608.250			1.24897			0.624486	+	0.781036i	$0.285308\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	124.328	−	71.7806i	0.253213	−	0.146193i	−0.368021	−	0.929817i	$-0.619965\pi$
$491$	124.328	−	71.7806i	0.253213	−	0.146193i	0.621235	+	0.783625i	$0.286631\pi$
$492$		0			0
$493$	−174.158	+	301.651i	−0.353262	+	0.611867i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−114.416	−	66.0584i	−0.230214	−	0.132914i
$498$		0			0
$499$	−308.302	−	533.996i	−0.617841	−	1.07013i	−0.989879	−	0.141914i	$-0.954674\pi$
$499$	−308.302	−	533.996i	−0.617841	−	1.07013i	0.372038	−	0.928217i	$-0.378659\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	374.729i		−	0.744989i	−0.928034	−	0.372494i	$-0.878503\pi$
$503$		−	374.729i		−	0.744989i	0.928034	−	0.372494i	$-0.121497\pi$
$504$		0			0
$505$	−288.974			−0.572225
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−149.854	+	86.5182i	−0.294408	+	0.169977i	−0.639928	−	0.768435i	$-0.721036\pi$
$509$	−149.854	+	86.5182i	−0.294408	+	0.169977i	0.345520	+	0.938411i	$0.387703\pi$
$510$		0			0
$511$	51.9082	−	89.9076i	0.101582	−	0.175944i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	221.346	+	127.794i	0.429798	+	0.248144i
$516$		0			0
$517$	395.526	+	685.071i	0.765041	+	1.32509i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			455.116i			0.873543i	0.899572	+	0.436772i	$0.143878\pi$
$521$			455.116i			0.873543i	−0.899572	+	0.436772i	$0.856122\pi$
$522$		0			0
$523$	−295.395			−0.564809			−0.282404	−	0.959295i	$-0.591132\pi$
$523$	−295.395			−0.564809			−0.282404	+	0.959295i	$0.591132\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−308.249	+	177.967i	−0.584912	+	0.337699i
$528$		0			0
$529$	−252.342	+	437.069i	−0.477017	+	0.826218i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−407.244	−	235.122i	−0.764060	−	0.441130i
$534$		0			0
$535$	104.355	+	180.748i	0.195056	+	0.337848i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			173.335i			0.321587i
$540$		0			0
$541$	906.394			1.67541			0.837703	−	0.546127i	$-0.183898\pi$
$541$	906.394			1.67541			0.837703	+	0.546127i	$0.183898\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−234.061	+	135.135i	−0.429469	+	0.247954i
$546$		0			0
$547$	336.460	−	582.767i	0.615101	−	1.06539i	−0.375265	−	0.926917i	$-0.622448\pi$
$547$	336.460	−	582.767i	0.615101	−	1.06539i	0.990367	−	0.138470i	$-0.0442183\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−479.455	−	276.813i	−0.870154	−	0.502384i
$552$		0			0
$553$	−293.329	−	508.060i	−0.530432	−	0.918735i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	870.336i		−	1.56254i	−0.624192	−	0.781271i	$-0.714572\pi$
$557$		−	870.336i		−	1.56254i	0.624192	−	0.781271i	$-0.285428\pi$
$558$		0			0
$559$	11.7893			0.0210900
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−20.4659	+	11.8160i	−0.0363515	+	0.0209875i	−0.518066	−	0.855341i	$-0.673348\pi$
$563$	−20.4659	+	11.8160i	−0.0363515	+	0.0209875i	0.481714	+	0.876328i	$0.340014\pi$
$564$		0			0
$565$	−123.329	+	213.612i	−0.218281	+	0.378074i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−255.714	−	147.636i	−0.449409	−	0.259466i	0.258172	−	0.966099i	$-0.416880\pi$
$569$	−255.714	−	147.636i	−0.449409	−	0.259466i	−0.707581	+	0.706633i	$0.750213\pi$
$570$		0			0
$571$	−446.960	−	774.158i	−0.782767	−	1.35579i	−0.930324	−	0.366739i	$-0.880474\pi$
$571$	−446.960	−	774.158i	−0.782767	−	1.35579i	0.147556	−	0.989054i	$-0.452859\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			24.6556i			0.0428794i
$576$		0			0
$577$	−264.763			−0.458861			−0.229431	−	0.973325i	$-0.573686\pi$
$577$	−264.763			−0.458861			−0.229431	+	0.973325i	$0.573686\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−214.685	+	123.949i	−0.369510	+	0.213337i
$582$		0			0
$583$	−440.763	+	763.424i	−0.756026	+	1.30947i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	685.793	+	395.943i	1.16830	+	0.674519i	0.953279	−	0.302090i	$-0.0976845\pi$
$587$	685.793	+	395.943i	1.16830	+	0.674519i	0.215022	+	0.976609i	$0.431018\pi$
$588$		0			0
$589$	−282.868	−	489.942i	−0.480252	−	0.831821i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.82388i			0.00307567i	0.999999	+	0.00153784i	$0.000489509\pi$
$593$			1.82388i			0.00307567i	−0.999999	+	0.00153784i	$0.999510\pi$
$594$		0			0
$595$	−208.211			−0.349934
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−656.624	+	379.102i	−1.09620	+	0.632891i	−0.935220	−	0.354067i	$-0.884799\pi$
$599$	−656.624	+	379.102i	−1.09620	+	0.632891i	−0.160980	+	0.986958i	$0.551465\pi$
$600$		0			0
$601$	141.789	−	245.586i	0.235922	−	0.408629i	−0.723618	−	0.690201i	$-0.757522\pi$
$601$	141.789	−	245.586i	0.235922	−	0.408629i	0.959540	+	0.281571i	$0.0908556\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	71.3442	+	41.1906i	0.117924	+	0.0680836i
$606$		0			0
$607$	−83.9142	−	145.344i	−0.138244	−	0.239446i	0.788588	−	0.614922i	$-0.210813\pi$
$607$	−83.9142	−	145.344i	−0.138244	−	0.239446i	−0.926832	+	0.375476i	$0.877479\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	990.507i		−	1.62112i
$612$		0			0
$613$	−395.698			−0.645510			−0.322755	−	0.946483i	$-0.604609\pi$
$613$	−395.698			−0.645510			−0.322755	+	0.946483i	$0.604609\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−740.616	+	427.595i	−1.20035	+	0.693022i	−0.960633	−	0.277821i	$-0.910388\pi$
$617$	−740.616	+	427.595i	−1.20035	+	0.693022i	−0.239717	+	0.970843i	$0.577055\pi$
$618$		0			0
$619$	−154.079	+	266.873i	−0.248916	+	0.431135i	−0.963225	−	0.268695i	$-0.913408\pi$
$619$	−154.079	+	266.873i	−0.248916	+	0.431135i	0.714309	+	0.699830i	$0.246741\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−550.861	−	318.040i	−0.884206	−	0.510497i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1059.99i			1.68520i
$630$		0			0
$631$	344.974			0.546709			0.273355	−	0.961913i	$-0.411867\pi$
$631$	344.974			0.546709			0.273355	+	0.961913i	$0.411867\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−204.070	+	117.820i	−0.321371	+	0.185543i
$636$		0			0
$637$	108.520	−	187.962i	0.170361	−	0.295074i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	175.492	+	101.321i	0.273779	+	0.158066i	0.630604	−	0.776105i	$-0.282807\pi$
$641$	175.492	+	101.321i	0.273779	+	0.158066i	−0.356825	+	0.934171i	$0.616141\pi$
$642$		0			0
$643$	−362.302	−	627.526i	−0.563456	−	0.975935i	−0.997191	−	0.0748947i	$-0.976138\pi$
$643$	−362.302	−	627.526i	−0.563456	−	0.975935i	0.433735	−	0.901040i	$-0.357195\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	125.679i		−	0.194249i	−0.995272	−	0.0971243i	$-0.969036\pi$
$647$		−	125.679i		−	0.194249i	0.995272	−	0.0971243i	$-0.0309644\pi$
$648$		0			0
$649$	1030.89			1.58843
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−477.376	+	275.613i	−0.731050	+	0.422072i	−0.818806	−	0.574070i	$-0.805364\pi$
$653$	−477.376	+	275.613i	−0.731050	+	0.422072i	0.0877559	+	0.996142i	$0.472030\pi$
$654$		0			0
$655$	−157.178	+	272.240i	−0.239966	+	0.415633i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−694.349	−	400.883i	−1.05364	−	0.608320i	−0.129974	−	0.991517i	$-0.541490\pi$
$659$	−694.349	−	400.883i	−1.05364	−	0.608320i	−0.923666	+	0.383198i	$0.874823\pi$
$660$		0			0
$661$	264.540	+	458.196i	0.400211	+	0.693186i	0.993751	−	0.111619i	$-0.0356035\pi$
$661$	264.540	+	458.196i	0.400211	+	0.693186i	−0.593540	+	0.804804i	$0.702270\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	330.938i		−	0.497651i
$666$		0			0
$667$	101.210			0.151739
$668$		0			0
$669$		0			0
$670$		0			0
$671$	531.668	−	306.959i	0.792352	−	0.457465i
$672$		0			0
$673$	−206.698	+	358.011i	−0.307129	+	0.531962i	−0.977733	−	0.209853i	$-0.932701\pi$
$673$	−206.698	+	358.011i	−0.307129	+	0.531962i	0.670604	+	0.741815i	$0.266035\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	311.714	+	179.968i	0.460434	+	0.265832i	0.712227	−	0.701950i	$-0.247687\pi$
$677$	311.714	+	179.968i	0.460434	+	0.265832i	−0.251793	+	0.967781i	$0.581020\pi$
$678$		0			0
$679$	238.749	+	413.526i	0.351619	+	0.609022i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			21.5484i			0.0315496i	0.999876	+	0.0157748i	$0.00502148\pi$
$683$			21.5484i			0.0315496i	−0.999876	+	0.0157748i	$0.994979\pi$
$684$		0			0
$685$	−596.921			−0.871418
$686$		0			0
$687$		0			0
$688$		0			0
$689$	955.913	−	551.897i	1.38739	−	0.801011i
$690$		0			0
$691$	192.460	−	333.351i	0.278525	−	0.482419i	−0.692494	−	0.721424i	$-0.743488\pi$
$691$	192.460	−	333.351i	0.278525	−	0.482419i	0.971018	+	0.239005i	$0.0768213\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−30.6779	−	17.7119i	−0.0441409	−	0.0254847i
$696$		0			0
$697$	−347.368	−	601.659i	−0.498376	−	0.863212i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			439.057i			0.626330i	0.949699	+	0.313165i	$0.101389\pi$
$701$			439.057i			0.626330i	−0.949699	+	0.313165i	$0.898611\pi$
$702$		0			0
$703$	−1684.79			−2.39657
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−614.081	+	354.540i	−0.868573	+	0.501471i
$708$		0			0
$709$	63.2107	−	109.484i	0.0891547	−	0.154420i	−0.817999	−	0.575219i	$-0.804917\pi$
$709$	63.2107	−	109.484i	0.0891547	−	0.154420i	0.907154	+	0.420799i	$0.138250\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	89.5676	+	51.7119i	0.125621	+	0.0725272i
$714$		0			0
$715$	117.816	+	204.063i	0.164777	+	0.285402i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	571.715i		−	0.795153i	−0.917569	−	0.397576i	$-0.869851\pi$
$719$		−	571.715i		−	0.795153i	0.917569	−	0.397576i	$-0.130149\pi$
$720$		0			0
$721$	627.159			0.869846
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−88.8746	+	51.3118i	−0.122586	+	0.0707749i
$726$		0			0
$727$	420.519	−	728.361i	0.578431	−	1.00187i	−0.417229	−	0.908802i	$-0.636999\pi$
$727$	420.519	−	728.361i	0.578431	−	1.00187i	0.995660	−	0.0930701i	$-0.0296681\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.0840	+	8.70873i	0.0206347	+	0.0119135i
$732$		0			0
$733$	−247.375	−	428.466i	−0.337483	−	0.584537i	0.646476	−	0.762934i	$-0.276242\pi$
$733$	−247.375	−	428.466i	−0.337483	−	0.584537i	−0.983959	+	0.178397i	$0.942909\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			697.206i			0.946006i
$738$		0			0
$739$	1263.97			1.71038			0.855191	−	0.518312i	$-0.173439\pi$
$739$	1263.97			1.71038			0.855191	+	0.518312i	$0.173439\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	828.217	−	478.171i	1.11469	−	0.643568i	0.174652	−	0.984630i	$-0.444120\pi$
$743$	828.217	−	478.171i	1.11469	−	0.643568i	0.940041	+	0.341062i	$0.110787\pi$
$744$		0			0
$745$	−46.5395	+	80.6088i	−0.0624691	+	0.108200i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	443.518	+	256.065i	0.592147	+	0.341876i
$750$		0			0
$751$	560.828	+	971.383i	0.746776	+	1.29345i	0.949361	+	0.314189i	$0.101732\pi$
$751$	560.828	+	971.383i	0.746776	+	1.29345i	−0.202585	+	0.979265i	$0.564934\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	232.198i		−	0.307547i
$756$		0			0
$757$	−466.433			−0.616160			−0.308080	−	0.951360i	$-0.599687\pi$
$757$	−466.433			−0.616160			−0.308080	+	0.951360i	$0.599687\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1059.50	+	611.703i	−1.39225	+	0.803814i	−0.993564	−	0.113274i	$-0.963866\pi$
$761$	−1059.50	+	611.703i	−1.39225	+	0.803814i	−0.398684	+	0.917089i	$0.630533\pi$
$762$		0			0
$763$	−331.592	+	574.334i	−0.434590	+	0.752732i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1117.89	−	645.411i	−1.45748	−	0.841475i
$768$		0			0
$769$	645.315	+	1117.72i	0.839162	+	1.45347i	0.890597	+	0.454794i	$0.150287\pi$
$769$	645.315	+	1117.72i	0.839162	+	1.45347i	−0.0514349	+	0.998676i	$0.516379\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			329.455i			0.426204i	0.977030	+	0.213102i	$0.0683566\pi$
$773$			329.455i			0.426204i	−0.977030	+	0.213102i	$0.931643\pi$
$774$		0			0
$775$	−104.868			−0.135314
$776$		0			0
$777$		0			0
$778$		0			0
$779$	956.300	−	552.120i	1.22760	−	0.708755i
$780$		0			0
$781$	−110.447	+	191.300i	−0.141417	+	0.244942i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−24.2316	−	13.9901i	−0.0308683	−	0.0178218i
$786$		0			0
$787$	753.065	+	1304.35i	0.956881	+	1.65737i	0.730003	+	0.683444i	$0.239518\pi$
$787$	753.065	+	1304.35i	0.956881	+	1.65737i	0.226878	+	0.973923i	$0.427148\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			605.245i			0.765165i
$792$		0			0
$793$	−768.710			−0.969370
$794$		0			0
$795$		0			0
$796$		0			0
$797$	217.264	−	125.437i	0.272602	−	0.157387i	−0.357468	−	0.933926i	$-0.616360\pi$
$797$	217.264	−	125.437i	0.272602	−	0.157387i	0.630069	+	0.776539i	$0.283026\pi$
$798$		0			0
$799$	731.684	−	1267.31i	0.915750	−	1.58612i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−150.322	−	86.7884i	−0.187200	−	0.108080i
$804$		0			0
$805$	30.2498	+	52.3942i	0.0375774	+	0.0650860i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	1097.02i		−	1.35602i	−0.735053	−	0.678010i	$-0.762843\pi$
$809$		−	1097.02i		−	1.35602i	0.735053	−	0.678010i	$-0.237157\pi$
$810$		0			0
$811$	−221.473			−0.273087			−0.136543	−	0.990634i	$-0.543599\pi$
$811$	−221.473			−0.273087			−0.136543	+	0.990634i	$0.543599\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	563.264	−	325.201i	0.691122	−	0.399019i
$816$		0			0
$817$	−13.8420	+	23.9750i	−0.0169425	+	0.0293452i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−869.423	−	501.962i	−1.05898	−	0.611403i	−0.133831	−	0.991004i	$-0.542728\pi$
$821$	−869.423	−	501.962i	−1.05898	−	0.611403i	−0.925150	+	0.379601i	$0.876061\pi$
$822$		0			0
$823$	−167.506	−	290.130i	−0.203531	−	0.352527i	0.746132	−	0.665798i	$-0.231909\pi$
$823$	−167.506	−	290.130i	−0.203531	−	0.352527i	−0.949664	+	0.313271i	$0.898575\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1004.72i		−	1.21490i	−0.794357	−	0.607451i	$-0.792192\pi$
$827$		−	1004.72i		−	1.21490i	0.794357	−	0.607451i	$-0.207808\pi$
$828$		0			0
$829$	676.763			0.816361			0.408180	−	0.912901i	$-0.366163\pi$
$829$	676.763			0.816361			0.408180	+	0.912901i	$0.366163\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	277.694	−	160.327i	0.333366	−	0.192469i
$834$		0			0
$835$	−195.250	+	338.183i	−0.233832	+	0.405009i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−538.049	−	310.643i	−0.641298	−	0.370254i	0.143816	−	0.989604i	$-0.454063\pi$
$839$	−538.049	−	310.643i	−0.641298	−	0.370254i	−0.785114	+	0.619351i	$0.787396\pi$
$840$		0			0
$841$	−209.868	−	363.502i	−0.249546	−	0.432226i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			82.8523i			0.0980500i
$846$		0			0
$847$	202.146			0.238661
$848$		0			0
$849$		0			0
$850$		0			0
$851$	266.736	−	154.000i	0.313439	−	0.180964i
$852$		0			0
$853$	272.296	−	471.630i	0.319221	−	0.552907i	−0.661105	−	0.750294i	$-0.729912\pi$
$853$	272.296	−	471.630i	0.319221	−	0.552907i	0.980326	+	0.197386i	$0.0632454\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	313.631	+	181.075i	0.365963	+	0.211289i	0.671693	−	0.740829i	$-0.265567\pi$
$857$	313.631	+	181.075i	0.365963	+	0.211289i	−0.305730	+	0.952118i	$0.598901\pi$
$858$		0			0
$859$	10.8420	+	18.7789i	0.0126216	+	0.0218613i	0.872267	−	0.489030i	$-0.162649\pi$
$859$	10.8420	+	18.7789i	0.0126216	+	0.0218613i	−0.859646	+	0.510891i	$0.829316\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	220.300i		−	0.255273i	−0.991821	−	0.127636i	$-0.959261\pi$
$863$		−	220.300i		−	0.255273i	0.991821	−	0.127636i	$-0.0407390\pi$
$864$		0			0
$865$	−97.4477			−0.112656
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−849.457	+	490.434i	−0.977511	+	0.564366i
$870$		0			0
$871$	436.500	−	756.040i	0.501148	−	0.868013i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−53.1260	−	30.6723i	−0.0607155	−	0.0350541i
$876$		0			0
$877$	−568.204	−	984.158i	−0.647895	−	1.12219i	−0.983625	−	0.180229i	$-0.942316\pi$
$877$	−568.204	−	984.158i	−0.647895	−	1.12219i	0.335730	−	0.941958i	$-0.391017\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			711.758i			0.807898i	0.914782	+	0.403949i	$0.132363\pi$
$881$			711.758i			0.807898i	−0.914782	+	0.403949i	$0.867637\pi$
$882$		0			0
$883$	−536.394			−0.607468			−0.303734	−	0.952757i	$-0.598233\pi$
$883$	−536.394			−0.607468			−0.303734	+	0.952757i	$0.598233\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1267.82	−	731.976i	1.42934	−	0.825227i	0.432267	−	0.901746i	$-0.357714\pi$
$887$	1267.82	−	731.976i	1.42934	−	0.825227i	0.997068	+	0.0765188i	$0.0243805\pi$
$888$		0			0
$889$	−289.105	+	500.745i	−0.325203	+	0.563268i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2014.32	+	1162.97i	2.25567	+	1.30231i
$894$		0			0
$895$	−98.7171	−	170.983i	−0.110298	−	0.191042i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			430.479i			0.478842i
$900$		0			0
$901$	1630.74			1.80992
$902$		0			0
$903$		0			0
$904$		0			0
$905$	110.125	−	63.5807i	0.121685	−	0.0702549i
$906$		0			0
$907$	−427.828	+	741.021i	−0.471696	+	0.817002i	−0.999476	−	0.0323796i	$-0.989691\pi$
$907$	−427.828	+	741.021i	−0.471696	+	0.817002i	0.527779	+	0.849381i	$0.323025\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1369.20	+	790.508i	1.50296	+	0.867737i	0.999994	+	0.00343281i	$0.00109270\pi$
$911$	1369.20	+	790.508i	1.50296	+	0.867737i	0.502970	+	0.864304i	$0.332241\pi$
$912$		0			0
$913$	207.237	+	358.945i	0.226985	+	0.393149i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			771.360i			0.841178i
$918$		0			0
$919$	−1489.08			−1.62033			−0.810163	−	0.586205i	$-0.800621\pi$
$919$	−1489.08			−1.62033			−0.810163	+	0.586205i	$0.800621\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	239.534	−	138.295i	0.259517	−	0.149832i
$924$		0			0
$925$	−156.151	+	270.462i	−0.168812	+	0.292391i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	638.252	+	368.495i	0.687032	+	0.396658i	0.802499	−	0.596653i	$-0.203503\pi$
$929$	638.252	+	368.495i	0.687032	+	0.396658i	−0.115467	+	0.993311i	$0.536837\pi$
$930$		0			0
$931$	254.829	+	441.377i	0.273716	+	0.474089i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			348.120i			0.372321i
$936$		0			0
$937$	1550.05			1.65427			0.827135	−	0.562003i	$-0.189969\pi$
$937$	1550.05			1.65427			0.827135	+	0.562003i	$0.189969\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	544.480	−	314.356i	0.578618	−	0.334065i	−0.181966	−	0.983305i	$-0.558246\pi$
$941$	544.480	−	314.356i	0.578618	−	0.334065i	0.760584	+	0.649239i	$0.224913\pi$
$942$		0			0
$943$	−100.935	+	174.824i	−0.107036	+	0.185391i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1297.94	+	749.365i	1.37058	+	0.791304i	0.991001	−	0.133855i	$-0.0427358\pi$
$947$	1297.94	+	749.365i	1.37058	+	0.791304i	0.379578	+	0.925160i	$0.376069\pi$
$948$		0			0
$949$	108.671	+	188.224i	0.114511	+	0.198339i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	224.748i		−	0.235832i	−0.993024	−	0.117916i	$-0.962379\pi$
$953$		−	224.748i		−	0.235832i	0.993024	−	0.117916i	$-0.0376214\pi$
$954$		0			0
$955$	126.658			0.132626
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1268.48	+	732.358i	−1.32271	+	0.763669i
$960$		0			0
$961$	260.553	−	451.290i	0.271127	−	0.469605i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	213.014	+	122.984i	0.220740	+	0.127444i
$966$		0			0
$967$	−116.993	−	202.638i	−0.120986	−	0.209554i	0.799171	−	0.601104i	$-0.205272\pi$
$967$	−116.993	−	202.638i	−0.120986	−	0.209554i	−0.920157	+	0.391550i	$0.871939\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	691.940i		−	0.712606i	−0.934371	−	0.356303i	$-0.884037\pi$
$971$		−	691.940i		−	0.712606i	0.934371	−	0.356303i	$-0.115963\pi$
$972$		0			0
$973$	−86.9224			−0.0893344
$974$		0			0
$975$		0			0
$976$		0			0
$977$	342.575	−	197.786i	0.350639	−	0.202442i	−0.314327	−	0.949315i	$-0.601779\pi$
$977$	342.575	−	197.786i	0.350639	−	0.202442i	0.664967	+	0.746873i	$0.268446\pi$
$978$		0			0
$979$	−531.749	+	921.017i	−0.543156	+	0.940773i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.57952	+	0.911938i	0.00160684	+	0.000927709i	0.500803	−	0.865561i	$-0.333038\pi$
$983$	1.57952	+	0.911938i	0.00160684	+	0.000927709i	−0.499196	+	0.866489i	$0.666371\pi$
$984$		0			0
$985$	−273.974	−	474.536i	−0.278146	−	0.481763i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	5.06098i		−	0.00511727i
$990$		0			0
$991$	506.316			0.510914			0.255457	−	0.966820i	$-0.417774\pi$
$991$	506.316			0.510914			0.255457	+	0.966820i	$0.417774\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	329.000	−	189.948i	0.330653	−	0.190903i
$996$		0			0
$997$	147.835	−	256.058i	0.148280	−	0.256829i	−0.782312	−	0.622887i	$-0.785960\pi$
$997$	147.835	−	256.058i	0.148280	−	0.256829i	0.930592	+	0.366058i	$0.119293\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.3.o.f.1241.1		8
3.2	odd	2	inner	1620.3.o.f.1241.3		8
9.2	odd	6		180.3.g.a.161.4	yes	4
9.4	even	3	inner	1620.3.o.f.701.3		8
9.5	odd	6	inner	1620.3.o.f.701.1		8
9.7	even	3		180.3.g.a.161.2	✓	4
36.7	odd	6		720.3.l.c.161.1		4
36.11	even	6		720.3.l.c.161.3		4
45.2	even	12		900.3.b.b.449.6		8
45.7	odd	12		900.3.b.b.449.5		8
45.29	odd	6		900.3.g.d.701.2		4
45.34	even	6		900.3.g.d.701.1		4
45.38	even	12		900.3.b.b.449.4		8
45.43	odd	12		900.3.b.b.449.3		8
72.11	even	6		2880.3.l.f.1601.1		4
72.29	odd	6		2880.3.l.b.1601.2		4
72.43	odd	6		2880.3.l.f.1601.3		4
72.61	even	6		2880.3.l.b.1601.4		4
180.7	even	12		3600.3.c.k.449.4		8
180.43	even	12		3600.3.c.k.449.6		8
180.47	odd	12		3600.3.c.k.449.3		8
180.79	odd	6		3600.3.l.n.1601.4		4
180.83	odd	12		3600.3.c.k.449.5		8
180.119	even	6		3600.3.l.n.1601.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.g.a.161.2	✓	4	9.7	even	3
180.3.g.a.161.4	yes	4	9.2	odd	6
720.3.l.c.161.1		4	36.7	odd	6
720.3.l.c.161.3		4	36.11	even	6
900.3.b.b.449.3		8	45.43	odd	12
900.3.b.b.449.4		8	45.38	even	12
900.3.b.b.449.5		8	45.7	odd	12
900.3.b.b.449.6		8	45.2	even	12
900.3.g.d.701.1		4	45.34	even	6
900.3.g.d.701.2		4	45.29	odd	6
1620.3.o.f.701.1		8	9.5	odd	6	inner
1620.3.o.f.701.3		8	9.4	even	3	inner
1620.3.o.f.1241.1		8	1.1	even	1	trivial
1620.3.o.f.1241.3		8	3.2	odd	2	inner
2880.3.l.b.1601.2		4	72.29	odd	6
2880.3.l.b.1601.4		4	72.61	even	6
2880.3.l.f.1601.1		4	72.11	even	6
2880.3.l.f.1601.3		4	72.43	odd	6
3600.3.c.k.449.3		8	180.47	odd	12
3600.3.c.k.449.4		8	180.7	even	12
3600.3.c.k.449.5		8	180.83	odd	12
3600.3.c.k.449.6		8	180.43	even	12
3600.3.l.n.1601.3		4	180.119	even	6
3600.3.l.n.1601.4		4	180.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93649 + 1.11803i) q^{5} +(-2.74342 + 4.75174i) q^{7} +O(q^{10})\)	\(q+(-1.93649 + 1.11803i) q^{5} +(-2.74342 + 4.75174i) q^{7} +(7.94472 + 4.58688i) q^{11} +(-5.74342 - 9.94789i) q^{13} -16.9706i q^{17} +26.9737 q^{19} +(-4.27048 + 2.46556i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-17.7749 - 10.2624i) q^{29} +(-10.4868 - 18.1637i) q^{31} -12.2689i q^{35} -62.4605 q^{37} +(35.4531 - 20.4689i) q^{41} +(-0.513167 + 0.888831i) q^{43} +(74.6772 + 43.1149i) q^{47} +(9.44733 + 16.3633i) q^{49} +96.0920i q^{53} -20.5132 q^{55} +(97.3188 - 56.1871i) q^{59} +(33.4605 - 57.9553i) q^{61} +(22.2442 + 12.8427i) q^{65} +(38.0000 + 65.8179i) q^{67} +24.0789i q^{71} -18.9210 q^{73} +(-43.5913 + 25.1675i) q^{77} +(-53.4605 + 92.5963i) q^{79} +(39.1273 + 22.5902i) q^{83} +(18.9737 + 32.8634i) q^{85} +115.928i q^{89} +63.0263 q^{91} +(-52.2343 + 30.1575i) q^{95} +(43.5132 - 75.3670i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7}+O(q^{10}) \) 8 * q + 16 * q^7	\( 8 q + 16 q^{7} - 8 q^{13} + 64 q^{19} + 20 q^{25} - 8 q^{31} - 272 q^{37} - 80 q^{43} - 228 q^{49} - 240 q^{55} + 40 q^{61} + 304 q^{67} + 304 q^{73} - 200 q^{79} + 656 q^{91} + 424 q^{97}+O(q^{100}) \) 8 * q + 16 * q^7 - 8 * q^13 + 64 * q^19 + 20 * q^25 - 8 * q^31 - 272 * q^37 - 80 * q^43 - 228 * q^49 - 240 * q^55 + 40 * q^61 + 304 * q^67 + 304 * q^73 - 200 * q^79 + 656 * q^91 + 424 * q^97

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