LMFDB - Embedded newform 961.2.d.m.388.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} - x^{9} + 36x^{8} + 18x^{7} + 217x^{6} + 72x^{5} + 1284x^{4} + 215x^{3} + 36x^{2} + 6x + 1 $ x^12 + 6x^10 - x^9 + 36x^8 + 18x^7 + 217x^6 + 72x^5 + 1284x^4 + 215x^3 + 36x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{5}]$

Embedding invariants

Embedding label			388.3
Root			$0.729734 - 2.24589i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.m.374.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.91047 - 1.38804i) q^{2} +(1.10521 - 3.40149i) q^{4} +3.93800 q^{5} +(-0.242558 + 0.746517i) q^{7} +(-1.15045 - 3.54072i) q^{8} +(-0.927051 - 2.85317i) q^{9} +(7.52343 - 5.46609i) q^{10} +(0.572793 + 1.76288i) q^{14} +(-1.32560 - 0.963104i) q^{16} +(-5.73141 - 4.16411i) q^{18} +(-7.00685 + 5.09077i) q^{19} +(4.35232 - 13.3951i) q^{20} +10.5079 q^{25} +(2.27119 + 1.65012i) q^{28} +3.57653 q^{32} +(-0.955194 + 2.93979i) q^{35} -10.7296 q^{36} +(-6.32018 + 19.4515i) q^{38} +(-4.53048 - 13.9434i) q^{40} +(-1.91586 + 1.39196i) q^{41} +(-3.65073 - 11.2358i) q^{45} +(-6.47214 - 4.70228i) q^{47} +(5.16467 + 3.75235i) q^{49} +(20.0750 - 14.5853i) q^{50} +2.92226 q^{56} +(-8.27690 - 6.01352i) q^{59} +2.35480 q^{63} +(9.48406 - 6.89057i) q^{64} -12.0000 q^{67} +(2.25566 + 6.94221i) q^{70} +(5.11020 + 15.7276i) q^{71} +(-9.03576 + 6.56486i) q^{72} +(9.57216 + 29.4601i) q^{76} +(-5.22022 - 3.79271i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-1.72811 + 5.31857i) q^{82} +(-22.5703 - 16.3983i) q^{90} -18.8918 q^{94} +(-27.5930 + 20.0475i) q^{95} +(3.16561 - 9.74276i) q^{97} +15.0753 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{4} - 3 q^{8} + 9 q^{9} + 9 q^{10} - 15 q^{14} - 12 q^{16} - 21 q^{20} + 60 q^{25} - 27 q^{28} + 24 q^{32} - 12 q^{35} - 72 q^{36} + 33 q^{38} + 18 q^{40} - 24 q^{47} - 21 q^{49} + 39 q^{50}+ \cdots + 228 q^{98}+O(q^{100}) $ 12 * q - 6 * q^4 - 3 * q^8 + 9 * q^9 + 9 * q^10 - 15 * q^14 - 12 * q^16 - 21 * q^20 + 60 * q^25 - 27 * q^28 + 24 * q^32 - 12 * q^35 - 72 * q^36 + 33 * q^38 + 18 * q^40 - 24 * q^47 - 21 * q^49 + 39 * q^50 + 120 * q^56 + 21 * q^64 - 144 * q^67 - 3 * q^70 + 9 * q^72 - 15 * q^76 + 9 * q^80 - 27 * q^81 - 21 * q^82 - 27 * q^90 - 48 * q^95 + 228 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.91047	−	1.38804i	1.35091	−	0.981490i	0.351939	−	0.936023i	$-0.385522\pi$
$2$	1.91047	−	1.38804i	1.35091	−	0.981490i	0.998966	−	0.0454672i	$-0.0144777\pi$
$3$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$3$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$4$	1.10521	−	3.40149i	0.552605	−	1.70074i
$5$	3.93800			1.76113			0.880564	−	0.473927i	$-0.157164\pi$
$5$	3.93800			1.76113			0.880564	+	0.473927i	$0.157164\pi$
$6$		0			0
$7$	−0.242558	+	0.746517i	−0.0916783	+	0.282157i	−0.986374	−	0.164520i	$-0.947393\pi$
$7$	−0.242558	+	0.746517i	−0.0916783	+	0.282157i	0.894695	+	0.446677i	$0.147393\pi$
$8$	−1.15045	−	3.54072i	−0.406746	−	1.25183i
$9$	−0.927051	−	2.85317i	−0.309017	−	0.951057i
$10$	7.52343	−	5.46609i	2.37912	−	1.72853i
$11$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$11$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$12$		0			0
$13$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$13$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$14$	0.572793	+	1.76288i	0.153085	+	0.471148i
$15$		0			0
$16$	−1.32560	−	0.963104i	−0.331400	−	0.240776i
$17$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$17$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$18$	−5.73141	−	4.16411i	−1.35091	−	0.981490i
$19$	−7.00685	+	5.09077i	−1.60748	+	1.16790i	−0.736719	+	0.676199i	$0.763626\pi$
$19$	−7.00685	+	5.09077i	−1.60748	+	1.16790i	−0.870762	+	0.491705i	$0.836374\pi$
$20$	4.35232	−	13.3951i	0.973209	−	2.99523i
$21$		0			0
$22$		0			0
$23$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$23$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$24$		0			0
$25$	10.5079			2.10157
$26$		0			0
$27$		0			0
$28$	2.27119	+	1.65012i	0.429214	+	0.311842i
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$		0			0
$31$		0			0
$31$		0			0
$32$	3.57653			0.632248
$33$		0			0
$34$		0			0
$35$	−0.955194	+	2.93979i	−0.161457	+	0.496914i
$36$	−10.7296			−1.78827
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	−6.32018	+	19.4515i	−1.02527	+	3.15545i
$39$		0			0
$40$	−4.53048	−	13.9434i	−0.716332	−	2.20464i
$41$	−1.91586	+	1.39196i	−0.299207	+	0.217387i	−0.727252	−	0.686371i	$-0.759203\pi$
$41$	−1.91586	+	1.39196i	−0.299207	+	0.217387i	0.428044	+	0.903758i	$0.359203\pi$
$42$		0			0
$43$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$43$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$44$		0			0
$45$	−3.65073	−	11.2358i	−0.544219	−	1.67493i
$46$		0			0
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	0.00533600	−	0.999986i	$-0.498301\pi$
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	−0.949394	+	0.314087i	$0.898301\pi$
$48$		0			0
$49$	5.16467	+	3.75235i	0.737809	+	0.536050i
$50$	20.0750	−	14.5853i	2.83903	−	2.06267i
$51$		0			0
$52$		0			0
$53$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$53$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$54$		0			0
$55$		0			0
$56$	2.92226			0.390503
$57$		0			0
$58$		0			0
$59$	−8.27690	−	6.01352i	−1.07756	−	0.782893i	−0.100304	−	0.994957i	$-0.531982\pi$
$59$	−8.27690	−	6.01352i	−1.07756	−	0.782893i	−0.977256	+	0.212063i	$0.931982\pi$
$60$		0			0
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$		0			0
$63$	2.35480			0.296677
$64$	9.48406	−	6.89057i	1.18551	−	0.861321i
$65$		0			0
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$		0			0
$70$	2.25566	+	6.94221i	0.269603	+	0.829753i
$71$	5.11020	+	15.7276i	0.606469	+	1.86652i	0.486360	+	0.873759i	$0.338325\pi$
$71$	5.11020	+	15.7276i	0.606469	+	1.86652i	0.120109	+	0.992761i	$0.461675\pi$
$72$	−9.03576	+	6.56486i	−1.06487	+	0.773677i
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$		0			0
$75$		0			0
$76$	9.57216	+	29.4601i	1.09800	+	3.37930i
$77$		0			0
$78$		0			0
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$	−5.22022	−	3.79271i	−0.583638	−	0.424038i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$	−1.72811	+	5.31857i	−0.190838	+	0.587338i
$83$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$83$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$89$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$90$	−22.5703	−	16.3983i	−2.37912	−	1.72853i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−18.8918			−1.94854
$95$	−27.5930	+	20.0475i	−2.83098	+	2.05683i
$96$		0			0
$97$	3.16561	−	9.74276i	0.321419	−	0.989227i	−0.651612	−	0.758553i	$-0.725907\pi$
$97$	3.16561	−	9.74276i	0.321419	−	0.989227i	0.973031	−	0.230674i	$-0.0740932\pi$
$98$	15.0753			1.52284
$99$		0			0
$100$	11.6134	−	35.7424i	1.16134	−	3.57424i
$101$	2.18714	+	6.73133i	0.217629	+	0.669792i	0.998957	+	0.0456715i	$0.0145427\pi$
$101$	2.18714	+	6.73133i	0.217629	+	0.669792i	−0.781328	+	0.624121i	$0.785457\pi$
$102$		0			0
$103$	12.1086	−	8.79743i	1.19310	−	0.866836i	0.199510	−	0.979896i	$-0.436065\pi$
$103$	12.1086	−	8.79743i	1.19310	−	0.866836i	0.993588	+	0.113059i	$0.0360650\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.70615	+	5.25098i	0.164939	+	0.507631i	0.999032	−	0.0439935i	$-0.0140081\pi$
$107$	1.70615	+	5.25098i	0.164939	+	0.507631i	−0.834092	+	0.551625i	$0.814008\pi$
$108$		0			0
$109$	−12.0978	−	8.78959i	−1.15876	−	0.841890i	−0.169141	−	0.985592i	$-0.554099\pi$
$109$	−12.0978	−	8.78959i	−1.15876	−	0.841890i	−0.989621	+	0.143702i	$0.954099\pi$
$110$		0			0
$111$		0			0
$112$	1.04051	−	0.755973i	0.0983188	−	0.0714328i
$113$	−6.56967	+	20.2194i	−0.618022	+	1.90208i	−0.303133	+	0.952948i	$0.598033\pi$
$113$	−6.56967	+	20.2194i	−0.618022	+	1.90208i	−0.314889	+	0.949128i	$0.601967\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−24.1597			−2.22408
$119$		0			0
$120$		0			0
$121$	8.89919	+	6.46564i	0.809017	+	0.587785i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	21.6900			1.94001
$126$	4.49877	−	3.26855i	0.400783	−	0.291186i
$127$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$127$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$128$	6.34421	−	19.5255i	0.560754	−	1.72582i
$129$		0			0
$130$		0			0
$131$	6.18034	−	19.0211i	0.539979	−	1.66188i	−0.192659	−	0.981266i	$-0.561711\pi$
$131$	6.18034	−	19.0211i	0.539979	−	1.66188i	0.732638	−	0.680618i	$-0.238289\pi$
$132$		0			0
$133$	−2.10078	−	6.46554i	−0.182161	−	0.560633i
$134$	−22.9256	+	16.6564i	−1.98047	+	1.43890i
$135$		0			0
$136$		0			0
$137$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$137$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$138$		0			0
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$	8.94395	+	6.49816i	0.755902	+	0.549195i
$141$		0			0
$142$	31.5933	+	22.9539i	2.65125	+	1.92625i
$143$		0			0
$144$	−1.51900	+	4.67501i	−0.126583	+	0.389584i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$151$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$152$	26.0861	+	18.9526i	2.11586	+	1.53726i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	18.4697	−	13.4190i	1.47404	−	1.07095i	0.494621	−	0.869109i	$-0.335307\pi$
$157$	18.4697	−	13.4190i	1.47404	−	1.07095i	0.979418	−	0.201844i	$-0.0646933\pi$
$158$		0			0
$159$		0			0
$160$	14.0844			1.11347
$161$		0			0
$162$	−6.56761	+	20.2130i	−0.516000	+	1.58808i
$163$	7.54402	+	23.2181i	0.590893	+	1.81858i	0.574191	+	0.818721i	$0.305317\pi$
$163$	7.54402	+	23.2181i	0.590893	+	1.81858i	0.0167022	+	0.999861i	$0.494683\pi$
$164$	2.61729	+	8.05518i	0.204376	+	0.629004i
$165$		0			0
$166$		0			0
$167$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$167$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$	21.0205	+	15.2723i	1.60748	+	1.16790i
$172$		0			0
$173$	−11.3262	−	8.22899i	−0.861118	−	0.625639i	0.0670709	−	0.997748i	$-0.478635\pi$
$173$	−11.3262	−	8.22899i	−0.861118	−	0.625639i	−0.928189	+	0.372109i	$0.878635\pi$
$174$		0			0
$175$	−2.54877	+	7.84430i	−0.192669	+	0.592973i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$179$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$180$	−42.2532			−3.14937
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−23.1478	+	16.8179i	−1.68823	+	1.22657i
$189$		0			0
$190$	−24.8889	+	76.6002i	−1.80563	+	5.55716i
$191$	−13.3972			−0.969388			−0.484694	−	0.874684i	$-0.661069\pi$
$191$	−13.3972			−0.969388			−0.484694	+	0.874684i	$0.661069\pi$
$192$		0			0
$193$	−5.59943	+	17.2333i	−0.403056	+	1.24048i	0.519451	+	0.854500i	$0.326136\pi$
$193$	−5.59943	+	17.2333i	−0.403056	+	1.24048i	−0.922508	+	0.385979i	$0.873864\pi$
$194$	−7.47550	−	23.0072i	−0.536710	−	1.65182i
$195$		0			0
$196$	18.4716	−	13.4204i	1.31940	−	0.958601i
$197$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$197$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$198$		0			0
$199$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$199$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$200$	−12.0888	−	37.2055i	−0.854807	−	2.63082i
$201$		0			0
$202$	13.5218	+	9.82416i	0.951390	+	0.691226i
$203$		0			0
$204$		0			0
$205$	−7.54467	+	5.48152i	−0.526943	+	0.382846i
$206$	10.9220	−	33.6144i	0.760971	−	2.34203i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	22.8431			1.57258			0.786291	−	0.617856i	$-0.211998\pi$
$211$	22.8431			1.57258			0.786291	+	0.617856i	$0.211998\pi$
$212$		0			0
$213$		0			0
$214$	10.5481	+	7.66363i	0.721052	+	0.523875i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−35.3128			−2.39168
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$	−0.867517	+	2.66994i	−0.0579634	+	0.178393i
$225$	−9.74133	−	29.9807i	−0.649422	−	1.99872i
$226$	15.5141	+	47.7474i	1.03198	+	3.17611i
$227$	−22.6525	+	16.4580i	−1.50350	+	1.09235i	−0.534535	+	0.845146i	$0.679513\pi$
$227$	−22.6525	+	16.4580i	−1.50350	+	1.09235i	−0.968962	+	0.247209i	$0.920487\pi$
$228$		0			0
$229$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$229$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.99606	+	5.08294i	0.458327	+	0.332994i	0.792875	−	0.609385i	$-0.208583\pi$
$233$	6.99606	+	5.08294i	0.458327	+	0.332994i	−0.334547	+	0.942379i	$0.608583\pi$
$234$		0			0
$235$	−25.4873	−	18.5176i	−1.66261	−	1.20796i
$236$	−29.6026	+	21.5076i	−1.92697	+	1.40002i
$237$		0			0
$238$		0			0
$239$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$239$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$240$		0			0
$241$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$241$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$242$	25.9762			1.66981
$243$		0			0
$244$		0			0
$245$	20.3385	+	14.7768i	1.29938	+	0.944053i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	41.4381	−	30.1065i	2.62078	−	1.90410i
$251$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$251$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$252$	2.60255	−	8.00983i	0.163945	−	0.504572i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−7.73647	−	23.8104i	−0.483529	−	1.48815i
$257$	−7.53990	−	23.2054i	−0.470326	−	1.44751i	−0.852159	−	0.523283i	$-0.824707\pi$
$257$	−7.53990	−	23.2054i	−0.470326	−	1.44751i	0.381833	−	0.924231i	$-0.375293\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−14.5947	−	44.9178i	−0.901662	−	2.77503i
$263$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$263$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$264$		0			0
$265$		0			0
$266$	−12.9879	−	9.43624i	−0.796338	−	0.578573i
$267$		0			0
$268$	−13.2625	+	40.8178i	−0.810137	+	2.49335i
$269$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$269$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$270$		0			0
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$277$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$278$		0			0
$279$		0			0
$280$	11.5079			0.687727
$281$	−0.624238	+	0.453536i	−0.0372389	+	0.0270557i	−0.606249	−	0.795275i	$-0.707327\pi$
$281$	−0.624238	+	0.453536i	−0.0372389	+	0.0270557i	0.569010	+	0.822331i	$0.307327\pi$
$282$		0			0
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	−0.907573	−	0.419894i	$-0.862067\pi$
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	0.981050	+	0.193756i	$0.0620672\pi$
$284$	59.1450			3.50961
$285$		0			0
$286$		0			0
$287$	−0.574410	−	1.76785i	−0.0339064	−	0.104353i
$288$	−3.31563	−	10.2045i	−0.195375	−	0.601304i
$289$	13.7533	−	9.99235i	0.809017	−	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.03444	−	24.7275i	−0.469377	−	1.44459i	−0.853393	−	0.521268i	$-0.825459\pi$
$293$	−8.03444	−	24.7275i	−0.469377	−	1.44459i	0.384016	−	0.923326i	$-0.374541\pi$
$294$		0			0
$295$	−32.5945	−	23.6813i	−1.89772	−	1.37878i
$296$		0			0
$297$		0			0
$298$	19.1047	−	13.8804i	1.10670	−	0.804068i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	14.1912			0.813922
$305$		0			0
$306$		0			0
$307$	10.8170	+	7.85901i	0.617359	+	0.448537i	0.851998	−	0.523545i	$-0.175391\pi$
$307$	10.8170	+	7.85901i	0.617359	+	0.448537i	−0.234639	+	0.972083i	$0.575391\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−21.2466			−1.20478			−0.602391	−	0.798201i	$-0.705785\pi$
$311$	−21.2466			−1.20478			−0.602391	+	0.798201i	$0.705785\pi$
$312$		0			0
$313$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$313$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$314$	16.6596	−	51.2731i	0.940158	−	2.89351i
$315$	9.27322			0.522487
$316$		0			0
$317$	5.11432	−	15.7403i	0.287249	−	0.884061i	−0.698467	−	0.715642i	$-0.746134\pi$
$317$	5.11432	−	15.7403i	0.287249	−	0.884061i	0.985716	−	0.168418i	$-0.0538659\pi$
$318$		0			0
$319$		0			0
$320$	37.3482	−	27.1351i	2.08783	−	1.51690i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	9.94689	+	30.6134i	0.552605	+	1.70074i
$325$		0			0
$326$	46.6402	+	33.8861i	2.58316	+	1.87678i
$327$		0			0
$328$	7.13263	+	5.18216i	0.393834	+	0.286137i
$329$	5.08020	−	3.69098i	0.280080	−	0.203490i
$330$		0			0
$331$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$331$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−47.2560			−2.58187
$336$		0			0
$337$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$337$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$338$	−24.8361	−	18.0445i	−1.35091	−	0.981490i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	61.3576			3.31784
$343$	−8.49910	+	6.17496i	−0.458908	+	0.333416i
$344$		0			0
$345$		0			0
$346$	−33.0606			−1.77735
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$	−9.27051	−	28.5317i	−0.496239	−	1.52727i	−0.815017	−	0.579437i	$-0.803272\pi$
$349$	−9.27051	−	28.5317i	−0.496239	−	1.52727i	0.318778	−	0.947829i	$-0.396728\pi$
$350$	6.01884	+	18.5241i	0.321720	+	0.990153i
$351$		0			0
$352$		0			0
$353$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$353$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$354$		0			0
$355$	20.1240	+	61.9352i	1.06807	+	3.28718i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.8523	+	18.0562i	1.31165	+	0.952971i	0.999996	+	0.00277654i	$0.000883801\pi$
$359$	24.8523	+	18.0562i	1.31165	+	0.952971i	0.311656	+	0.950195i	$0.399116\pi$
$360$	−35.5829	+	25.8525i	−1.87538	+	1.36254i
$361$	17.3086	−	53.2705i	0.910980	−	2.80371i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$		0			0
$369$	5.74759	+	4.17587i	0.299207	+	0.217387i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−38.5818			−1.99769			−0.998844	−	0.0480672i	$-0.984694\pi$
$373$	−38.5818			−1.99769			−0.998844	+	0.0480672i	$0.984694\pi$
$374$		0			0
$375$		0			0
$376$	−9.20361	+	28.3258i	−0.474640	+	1.46079i
$377$		0			0
$378$		0			0
$379$	6.18034	−	19.0211i	0.317463	−	0.977050i	−0.657266	−	0.753659i	$-0.728287\pi$
$379$	6.18034	−	19.0211i	0.317463	−	0.977050i	0.974729	−	0.223391i	$-0.0717128\pi$
$380$	37.6952	+	116.014i	1.93372	+	5.95139i
$381$		0			0
$382$	−25.5949	+	18.5958i	−1.30955	+	0.951445i
$383$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$383$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$384$		0			0
$385$		0			0
$386$	13.2229	+	40.6959i	0.673027	+	2.07137i
$387$		0			0
$388$	−29.6412	−	21.5356i	−1.50480	−	1.09330i
$389$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$389$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$390$		0			0
$391$		0			0
$392$	7.34434	−	22.6036i	0.370945	−	1.14165i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−18.0935			−0.908086			−0.454043	−	0.890980i	$-0.650019\pi$
$397$	−18.0935			−0.908086			−0.454043	+	0.890980i	$0.650019\pi$
$398$		0			0
$399$		0			0
$400$	−13.9292	−	10.1202i	−0.696462	−	0.506009i
$401$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$401$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$402$		0			0
$403$		0			0
$404$	25.3138			1.25941
$405$	−28.6732	+	20.8323i	−1.42478	+	1.03517i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$	−6.80530	+	20.9446i	−0.336090	+	1.03438i
$411$		0			0
$412$	−16.5418	−	50.9103i	−0.814954	−	2.50817i
$413$	6.49682	−	4.72022i	0.319688	−	0.232267i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.92665	+	1.39979i	0.0941229	+	0.0683843i	0.633851	−	0.773455i	$-0.281473\pi$
$419$	1.92665	+	1.39979i	0.0941229	+	0.0683843i	−0.539728	+	0.841839i	$0.681473\pi$
$420$		0			0
$421$	−8.26611	−	6.00568i	−0.402866	−	0.292699i	0.367842	−	0.929888i	$-0.380097\pi$
$421$	−8.26611	−	6.00568i	−0.402866	−	0.292699i	−0.770707	+	0.637189i	$0.780097\pi$
$422$	43.6410	−	31.7070i	2.12441	−	1.54347i
$423$	−7.41641	+	22.8254i	−0.360598	+	1.10981i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	19.7468			0.954497
$429$		0			0
$430$		0			0
$431$	−32.3607	−	23.5114i	−1.55876	−	1.13250i	−0.937018	−	0.349282i	$-0.886425\pi$
$431$	−32.3607	−	23.5114i	−1.55876	−	1.13250i	−0.621742	−	0.783222i	$-0.713575\pi$
$432$		0			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$	−43.2683	+	31.4363i	−2.07218	+	1.50552i
$437$		0			0
$438$		0			0
$439$	−36.9986			−1.76585			−0.882923	−	0.469519i	$-0.844428\pi$
$439$	−36.9986			−1.76585			−0.882923	+	0.469519i	$0.844428\pi$
$440$		0			0
$441$	5.91818	−	18.2143i	0.281818	−	0.867347i
$442$		0			0
$443$	−12.8968	−	39.6922i	−0.612744	−	1.88583i	−0.430538	−	0.902572i	$-0.641676\pi$
$443$	−12.8968	−	39.6922i	−0.612744	−	1.88583i	−0.182206	−	0.983260i	$-0.558324\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	2.84349	+	8.75137i	0.134342	+	0.413463i
$449$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$449$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$450$	−60.2249	−	43.7559i	−2.83903	−	2.06267i
$451$		0			0
$452$	61.5150	+	44.6933i	2.89342	+	2.10219i
$453$		0			0
$454$	−20.4326	+	62.8849i	−0.958947	+	2.95134i
$455$		0			0
$456$		0			0
$457$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$457$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$461$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$462$		0			0
$463$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$463$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$464$		0			0
$465$		0			0
$466$	20.4211			0.945987
$467$	32.4941	−	23.6084i	1.50365	−	1.09247i	0.534750	−	0.845010i	$-0.320406\pi$
$467$	32.4941	−	23.6084i	1.50365	−	1.09247i	0.968899	−	0.247455i	$-0.0795943\pi$
$468$		0			0
$469$	2.91070	−	8.95820i	0.134403	−	0.413651i
$470$	−74.3958			−3.43162
$471$		0			0
$472$	−11.7700	+	36.2245i	−0.541760	+	1.66737i
$473$		0			0
$474$		0			0
$475$	−73.6271	+	53.4932i	−3.37824	+	2.45444i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.00761	−	27.7226i	−0.411568	−	1.26668i	−0.915285	−	0.402807i	$-0.868034\pi$
$479$	−9.00761	−	27.7226i	−0.411568	−	1.26668i	0.503717	−	0.863869i	$-0.331966\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	31.8283	−	23.1246i	1.44674	−	1.05112i
$485$	12.4662	−	38.3670i	0.566061	−	1.74216i
$486$		0			0
$487$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$487$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$488$		0			0
$489$		0			0
$490$	59.3667			2.68191
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.9804			−0.582251
$498$		0			0
$499$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$499$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$500$	23.9720	−	73.7783i	1.07206	−	3.29947i
$501$		0			0
$502$		0			0
$503$	7.05066	−	21.6997i	0.314373	−	0.967542i	−0.661638	−	0.749823i	$-0.730138\pi$
$503$	7.05066	−	21.6997i	0.314373	−	0.967542i	0.976012	−	0.217719i	$-0.0698615\pi$
$504$	−2.70908	−	8.33770i	−0.120672	−	0.371391i
$505$	8.61297	+	26.5080i	0.383272	+	1.17959i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$509$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$510$		0			0
$511$		0			0
$512$	−14.6113	−	10.6157i	−0.645734	−	0.469154i
$513$		0			0
$514$	−46.6147	−	33.8676i	−2.05609	−	1.49383i
$515$	47.6838	−	34.6443i	2.10120	−	1.52661i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$		0			0
$523$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$523$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$524$	−57.8695	−	42.0447i	−2.52804	−	1.83673i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	18.6074	−	13.5191i	0.809017	−	0.587785i
$530$		0			0
$531$	−9.48448	+	29.1902i	−0.411591	+	1.26675i
$532$	−24.3142			−1.05416
$533$		0			0
$534$		0			0
$535$	6.71881	+	20.6784i	0.290479	+	0.894004i
$536$	13.8054	+	42.4887i	0.596303	+	1.83523i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	14.3562	+	44.1840i	0.617223	+	1.89962i	0.357316	+	0.933984i	$0.383692\pi$
$541$	14.3562	+	44.1840i	0.617223	+	1.89962i	0.259907	+	0.965634i	$0.416308\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−47.6413	−	34.6134i	−2.04073	−	1.48268i
$546$		0			0
$547$	−11.9265	+	36.7061i	−0.509942	+	1.56944i	0.282358	+	0.959309i	$0.408883\pi$
$547$	−11.9265	+	36.7061i	−0.509942	+	1.56944i	−0.792300	+	0.610131i	$0.791117\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	4.09753	−	2.97703i	0.173152	−	0.125802i
$561$		0			0
$562$	−0.563063	+	1.73293i	−0.0237514	+	0.0730993i
$563$	44.8746			1.89124			0.945619	−	0.325277i	$-0.105457\pi$
$563$	44.8746			1.89124			0.945619	+	0.325277i	$0.105457\pi$
$564$		0			0
$565$	−25.8714	+	79.6239i	−1.08842	+	3.34980i
$566$	−2.91894	−	8.98356i	−0.122692	−	0.377607i
$567$	−2.18302	−	6.71865i	−0.0916783	−	0.282157i
$568$	49.8080	−	36.1876i	2.08990	−	1.51840i
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$571$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$572$		0			0
$573$		0			0
$574$	−3.55124	−	2.58012i	−0.148226	−	0.107692i
$575$		0			0
$576$	−28.4522	−	20.6717i	−1.18551	−	0.861321i
$577$	−14.5623	+	10.5801i	−0.606237	+	0.440457i	−0.848087	−	0.529857i	$-0.822246\pi$
$577$	−14.5623	+	10.5801i	−0.606237	+	0.440457i	0.241850	+	0.970314i	$0.422246\pi$
$578$	12.4055	−	38.1801i	0.516000	−	1.58808i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−49.6722	−	36.0889i	−2.05194	−	1.49082i
$587$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$587$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$588$		0			0
$589$		0			0
$590$	−95.1411			−3.91690
$591$		0			0
$592$		0			0
$593$	−14.8414	+	45.6770i	−0.609462	+	1.87573i	−0.146876	+	0.989155i	$0.546922\pi$
$593$	−14.8414	+	45.6770i	−0.609462	+	1.87573i	−0.462585	+	0.886575i	$0.653078\pi$
$594$		0			0
$595$		0			0
$596$	11.0521	−	34.0149i	0.452712	−	1.39330i
$597$		0			0
$598$		0			0
$599$	31.2025	−	22.6700i	1.27490	−	0.926269i	0.275514	−	0.961297i	$-0.411152\pi$
$599$	31.2025	−	22.6700i	1.27490	−	0.926269i	0.999386	+	0.0350277i	$0.0111520\pi$
$600$		0			0
$601$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$601$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$602$		0			0
$603$	11.1246	+	34.2380i	0.453029	+	1.39428i
$604$		0			0
$605$	35.0450	+	25.4617i	1.42478	+	1.03517i
$606$		0			0
$607$	38.8328	+	28.2137i	1.57618	+	1.14516i	0.920920	+	0.389751i	$0.127439\pi$
$607$	38.8328	+	28.2137i	1.57618	+	1.14516i	0.655255	+	0.755408i	$0.272561\pi$
$608$	−25.0602	+	18.2073i	−1.01633	+	0.738405i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$	31.5741			1.27423
$615$		0			0
$616$		0			0
$617$	17.7984	+	12.9313i	0.716536	+	0.520594i	0.885275	−	0.465067i	$-0.153970\pi$
$617$	17.7984	+	12.9313i	0.716536	+	0.520594i	−0.168740	+	0.985661i	$0.553970\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$	−40.5909	+	29.4910i	−1.62755	+	1.18248i
$623$		0			0
$624$		0			0
$625$	32.8760			1.31504
$626$		0			0
$627$		0			0
$628$	−25.2317	−	77.6551i	−1.00685	−	3.09878i
$629$		0			0
$630$	17.7162	−	12.8716i	0.705830	−	0.512815i
$631$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$631$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$632$		0			0
$633$		0			0
$634$	−12.0773	−	37.1701i	−0.479651	−	1.47621i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	40.1360	−	29.1605i	1.58776	−	1.15357i
$640$	24.9835	−	76.8913i	0.987560	−	3.03940i
$641$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$641$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$642$		0			0
$643$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$643$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$647$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$648$	27.1073	+	19.6946i	1.06487	+	0.773677i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	87.3138			3.41947
$653$	37.2148	−	27.0381i	1.45633	−	1.05808i	0.472026	−	0.881585i	$-0.343523\pi$
$653$	37.2148	−	27.0381i	1.45633	−	1.05808i	0.984301	−	0.176499i	$-0.0564772\pi$
$654$		0			0
$655$	24.3382	−	74.9053i	0.950972	−	2.92679i
$656$	3.88026			0.151499
$657$		0			0
$658$	4.58234	−	14.1030i	0.178638	−	0.549792i
$659$	0.250798	+	0.771878i	0.00976972	+	0.0300681i	0.955823	−	0.293944i	$-0.0949680\pi$
$659$	0.250798	+	0.771878i	0.00976972	+	0.0300681i	−0.946053	+	0.324012i	$0.894968\pi$
$660$		0			0
$661$	26.1331	−	18.9868i	1.01646	−	0.738501i	0.0509058	−	0.998703i	$-0.483789\pi$
$661$	26.1331	−	18.9868i	1.01646	−	0.738501i	0.965554	+	0.260202i	$0.0837892\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.27288	−	25.4613i	−0.320809	−	0.987347i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−90.2812	+	65.5931i	−3.48787	+	2.53408i
$671$		0			0
$672$		0			0
$673$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$673$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$674$		0			0
$675$		0			0
$676$	−46.4950			−1.78827
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$	6.50529	+	4.72637i	0.249650	+	0.181381i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	37.0252			1.41673			0.708366	−	0.705846i	$-0.249433\pi$
$683$	37.0252			1.41673			0.708366	+	0.705846i	$0.249433\pi$
$684$	75.1807	−	54.6220i	2.87461	−	2.08852i
$685$		0			0
$686$	−7.66619	+	23.5941i	−0.292697	+	0.900827i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−5.60355	−	17.2460i	−0.213169	−	0.656068i	−0.999279	−	0.0379799i	$-0.987908\pi$
$691$	−5.60355	−	17.2460i	−0.213169	−	0.656068i	0.786109	−	0.618088i	$-0.212092\pi$
$692$	−40.5087	+	29.4313i	−1.53991	+	1.11881i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−57.3141	−	41.6411i	−2.16937	−	1.57614i
$699$		0			0
$700$	23.8654	+	17.3392i	0.902026	+	0.655360i
$701$	−40.1252	+	29.1527i	−1.51551	+	1.10108i	−0.551851	+	0.833943i	$0.686078\pi$
$701$	−40.1252	+	29.1527i	−1.51551	+	1.10108i	−0.963658	+	0.267139i	$0.913922\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.55556			−0.208938
$708$		0			0
$709$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$709$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$710$	124.415	+	90.3925i	4.66920	+	3.39237i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	72.5422			2.70725
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−5.98184	+	18.4102i	−0.222930	+	0.686107i
$721$	3.63038	+	11.1732i	0.135203	+	0.416111i
$722$	−40.8738	−	125.797i	−1.52116	−	4.68166i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−16.3008	−	50.1688i	−0.604564	−	1.86066i	−0.499759	−	0.866164i	$-0.666578\pi$
$727$	−16.3008	−	50.1688i	−0.604564	−	1.86066i	−0.104805	−	0.994493i	$-0.533422\pi$
$728$		0			0
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	4.14409	−	12.7542i	0.153065	−	0.471087i	−0.844894	−	0.534933i	$-0.820337\pi$
$733$	4.14409	−	12.7542i	0.153065	−	0.471087i	0.997960	+	0.0638465i	$0.0203368\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	16.7768			0.617564
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	39.3800			1.44277
$746$	−73.7092	+	53.5529i	−2.69869	+	1.96071i
$747$		0			0
$748$		0			0
$749$	−4.33378			−0.158353
$750$		0			0
$751$	−7.53578	+	23.1927i	−0.274984	+	0.846315i	0.714239	+	0.699902i	$0.246773\pi$
$751$	−7.53578	+	23.1927i	−0.274984	+	0.846315i	−0.989224	+	0.146413i	$0.953227\pi$
$752$	4.05067	+	12.4667i	0.147713	+	0.454613i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$757$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$758$	−14.5947	−	44.9178i	−0.530103	−	1.63149i
$759$		0			0
$760$	102.727	+	74.6355i	3.72630	+	2.70732i
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$	9.49600	−	6.89925i	0.343778	−	0.249770i
$764$	−14.8067	+	45.5704i	−0.535689	+	1.64868i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−52.7639			−1.90272			−0.951358	−	0.308089i	$-0.900311\pi$
$769$	−52.7639			−1.90272			−0.951358	+	0.308089i	$0.900311\pi$
$770$		0			0
$771$		0			0
$772$	52.4302	+	38.0928i	1.88701	+	1.37099i
$773$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$773$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$774$		0			0
$775$		0			0
$776$	−38.1383			−1.36909
$777$		0			0
$778$		0			0
$779$	6.33803	−	19.5064i	0.227083	−	0.698891i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−3.23237	−	9.94823i	−0.115442	−	0.355294i
$785$	72.7336	−	52.8440i	2.59597	−	1.88608i
$786$		0			0
$787$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$787$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−13.5006	−	9.80873i	−0.480025	−	0.348758i
$792$		0			0
$793$		0			0
$794$	−34.5670	+	25.1144i	−1.22674	+	0.891277i
$795$		0			0
$796$		0			0
$797$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$797$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$798$		0			0
$799$		0			0
$800$	37.5818			1.32872
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	21.3176	−	15.4881i	0.749950	−	0.544871i
$809$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$809$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$810$	−25.8633	+	79.5989i	−0.908742	+	2.79682i
$811$	−12.0000			−0.421377			−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000			−0.421377			−0.210688	+	0.977553i	$0.567571\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	29.7084	+	91.4330i	1.04064	+	3.20276i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	10.3069	+	31.7213i	0.359932	+	1.10776i
$821$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$821$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$822$		0			0
$823$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$823$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$824$	−45.0796	−	32.7523i	−1.57042	−	1.14098i
$825$		0			0
$826$	5.86014	−	18.0356i	0.203900	−	0.627540i
$827$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$827$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$828$		0			0
$829$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$829$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	5.62376			0.194270
$839$	−12.9443	+	9.40456i	−0.446886	+	0.324682i	−0.788365	−	0.615208i	$-0.789072\pi$
$839$	−12.9443	+	9.40456i	−0.446886	+	0.324682i	0.341479	+	0.939889i	$0.389072\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$	−24.1282			−0.831514
$843$		0			0
$844$	25.2464	−	77.7005i	0.869017	−	2.67456i
$845$	−15.8198	−	48.6884i	−0.544219	−	1.67493i
$846$	17.5136	+	53.9014i	0.602131	+	1.85317i
$847$	−6.98527	+	5.07510i	−0.240017	+	0.174382i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	43.6869	+	31.7404i	1.49581	+	1.08677i	0.972013	+	0.234929i	$0.0754857\pi$
$853$	43.6869	+	31.7404i	1.49581	+	1.08677i	0.523799	+	0.851842i	$0.324514\pi$
$854$		0			0
$855$	82.7790	+	60.1425i	2.83098	+	2.05683i
$856$	16.6294	−	12.0820i	0.568382	−	0.412954i
$857$	11.7426	−	36.1401i	0.401121	−	1.23452i	−0.522970	−	0.852351i	$-0.675176\pi$
$857$	11.7426	−	36.1401i	0.401121	−	1.23452i	0.924091	−	0.382173i	$-0.124824\pi$
$858$		0			0
$859$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$859$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$860$		0			0
$861$		0			0
$862$	−94.4588			−3.21728
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−44.6028	−	32.4058i	−1.51654	−	1.10183i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−17.2036	+	52.9471i	−0.582586	+	1.79301i
$873$	−30.7324			−1.04014
$874$		0			0
$875$	−5.26109	+	16.1920i	−0.177857	+	0.547388i
$876$		0			0
$877$	17.7603	+	54.6606i	0.599723	+	1.84576i	0.529654	+	0.848214i	$0.322322\pi$
$877$	17.7603	+	54.6606i	0.599723	+	1.84576i	0.0700687	+	0.997542i	$0.477678\pi$
$878$	−70.6846	+	51.3554i	−2.38549	+	1.73316i
$879$		0			0
$880$		0			0
$881$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$881$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$882$	−13.9756	−	43.0125i	−0.470583	−	1.44831i
$883$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$883$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$884$		0			0
$885$		0			0
$886$	−79.7331	−	57.9295i	−2.67869	−	1.94618i
$887$	21.0421	−	15.2880i	0.706525	−	0.513321i	−0.175526	−	0.984475i	$-0.556162\pi$
$887$	21.0421	−	15.2880i	0.706525	−	0.513321i	0.882051	+	0.471154i	$0.156162\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	69.2875			2.31862
$894$		0			0
$895$		0			0
$896$	13.0372	+	9.47211i	0.435544	+	0.316441i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−112.745			−3.75818
$901$		0			0
$902$		0			0
$903$		0			0
$904$	79.1492			2.63246
$905$		0			0
$906$		0			0
$907$	14.8372	+	45.6643i	0.492662	+	1.51626i	0.820568	+	0.571549i	$0.193657\pi$
$907$	14.8372	+	45.6643i	0.492662	+	1.51626i	−0.327906	+	0.944710i	$0.606343\pi$
$908$	30.9459	+	95.2416i	1.02698	+	3.16070i
$909$	17.1780	−	12.4806i	0.569759	−	0.413954i
$910$		0			0
$911$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$911$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.7005	+	9.22745i	0.419407	+	0.304717i
$918$		0			0
$919$	−7.41641	+	22.8254i	−0.244645	+	0.752939i	0.751050	+	0.660245i	$0.229548\pi$
$919$	−7.41641	+	22.8254i	−0.244645	+	0.752939i	−0.995695	+	0.0926936i	$0.970452\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−36.3259	−	26.3923i	−1.19310	−	0.866836i
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	−55.2904			−1.81207
$932$	25.0217	−	18.1793i	0.819612	−	0.595483i
$933$		0			0
$934$	29.3097	−	90.2061i	0.959044	−	2.95163i
$935$		0			0
$936$		0			0
$937$	−12.9787	+	39.9444i	−0.423996	+	1.30493i	0.479956	+	0.877292i	$0.340653\pi$
$937$	−12.9787	+	39.9444i	−0.423996	+	1.30493i	−0.903952	+	0.427633i	$0.859347\pi$
$938$	−6.87352	−	21.1545i	−0.224428	−	0.690719i
$939$		0			0
$940$	−91.1562	+	66.2289i	−2.97319	+	2.16015i
$941$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$941$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$942$		0			0
$943$		0			0
$944$	5.18021	+	15.9430i	0.168601	+	0.518902i
$945$		0			0
$946$		0			0
$947$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$947$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$948$		0			0
$949$		0			0
$950$	−66.4117	+	204.394i	−2.15468	+	6.63142i
$951$		0			0
$952$		0			0
$953$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$953$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$954$		0			0
$955$	−52.7583			−1.70722
$956$		0			0
$957$		0			0
$958$	−55.6887	−	40.4602i	−1.79922	−	1.30721i
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	13.4002	−	9.73585i	0.431817	−	0.313733i
$964$		0			0
$965$	−22.0506	+	67.8647i	−0.709834	+	2.18464i
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	12.6550	−	38.9480i	0.406746	−	1.25183i
$969$		0			0
$970$	−29.4385	−	90.6025i	−0.945215	−	2.90907i
$971$	−22.6525	+	16.4580i	−0.726953	+	0.528162i	−0.888598	−	0.458687i	$-0.848320\pi$
$971$	−22.6525	+	16.4580i	−0.726953	+	0.528162i	0.161645	+	0.986849i	$0.448320\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−40.1468	−	29.1684i	−1.28441	−	0.933179i	−0.284733	−	0.958607i	$-0.591905\pi$
$977$	−40.1468	−	29.1684i	−1.28441	−	0.933179i	−0.999677	+	0.0254283i	$0.991905\pi$
$978$		0			0
$979$		0			0
$980$	72.7413	−	52.8496i	2.32363	−	1.68822i
$981$	−13.8629	+	42.6656i	−0.442608	+	1.36221i
$982$		0			0
$983$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$983$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		0			0
$993$		0			0
$994$	−24.7987	+	18.0173i	−0.786566	+	0.571474i
$995$		0			0
$996$		0			0
$997$	62.2098			1.97020			0.985102	−	0.171972i	$-0.0550138\pi$
$997$	62.2098			1.97020			0.985102	+	0.171972i	$0.0550138\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.m.388.3		12
31.2	even	5	inner	961.2.d.m.374.3		12
31.3	odd	30		961.2.g.u.547.1		24
31.4	even	5	inner	961.2.d.m.628.1		12
31.5	even	3		961.2.g.u.338.3		24
31.6	odd	6		961.2.g.u.235.3		24
31.7	even	15		961.2.g.u.846.1		24
31.8	even	5		961.2.a.g.1.1	✓	3
31.9	even	15		961.2.c.g.521.1		6
31.10	even	15		961.2.g.u.732.3		24
31.11	odd	30		961.2.g.u.448.1		24
31.12	odd	30		961.2.g.u.816.3		24
31.13	odd	30		961.2.g.u.844.1		24
31.14	even	15		961.2.c.g.439.1		6
31.15	odd	10	inner	961.2.d.m.531.1		12
31.16	even	5	inner	961.2.d.m.531.1		12
31.17	odd	30		961.2.c.g.439.1		6
31.18	even	15		961.2.g.u.844.1		24
31.19	even	15		961.2.g.u.816.3		24
31.20	even	15		961.2.g.u.448.1		24
31.21	odd	30		961.2.g.u.732.3		24
31.22	odd	30		961.2.c.g.521.1		6
31.23	odd	10		961.2.a.g.1.1	✓	3
31.24	odd	30		961.2.g.u.846.1		24
31.25	even	3		961.2.g.u.235.3		24
31.26	odd	6		961.2.g.u.338.3		24
31.27	odd	10	inner	961.2.d.m.628.1		12
31.28	even	15		961.2.g.u.547.1		24
31.29	odd	10	inner	961.2.d.m.374.3		12
31.30	odd	2	CM	961.2.d.m.388.3		12
93.8	odd	10		8649.2.a.q.1.3		3
93.23	even	10		8649.2.a.q.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.g.1.1	✓	3	31.8	even	5
961.2.a.g.1.1	✓	3	31.23	odd	10
961.2.c.g.439.1		6	31.14	even	15
961.2.c.g.439.1		6	31.17	odd	30
961.2.c.g.521.1		6	31.9	even	15
961.2.c.g.521.1		6	31.22	odd	30
961.2.d.m.374.3		12	31.2	even	5	inner
961.2.d.m.374.3		12	31.29	odd	10	inner
961.2.d.m.388.3		12	1.1	even	1	trivial
961.2.d.m.388.3		12	31.30	odd	2	CM
961.2.d.m.531.1		12	31.15	odd	10	inner
961.2.d.m.531.1		12	31.16	even	5	inner
961.2.d.m.628.1		12	31.4	even	5	inner
961.2.d.m.628.1		12	31.27	odd	10	inner
961.2.g.u.235.3		24	31.6	odd	6
961.2.g.u.235.3		24	31.25	even	3
961.2.g.u.338.3		24	31.5	even	3
961.2.g.u.338.3		24	31.26	odd	6
961.2.g.u.448.1		24	31.11	odd	30
961.2.g.u.448.1		24	31.20	even	15
961.2.g.u.547.1		24	31.3	odd	30
961.2.g.u.547.1		24	31.28	even	15
961.2.g.u.732.3		24	31.10	even	15
961.2.g.u.732.3		24	31.21	odd	30
961.2.g.u.816.3		24	31.12	odd	30
961.2.g.u.816.3		24	31.19	even	15
961.2.g.u.844.1		24	31.13	odd	30
961.2.g.u.844.1		24	31.18	even	15
961.2.g.u.846.1		24	31.7	even	15
961.2.g.u.846.1		24	31.24	odd	30
8649.2.a.q.1.3		3	93.8	odd	10
8649.2.a.q.1.3		3	93.23	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.91047 - 1.38804i) q^{2} +(1.10521 - 3.40149i) q^{4} +3.93800 q^{5} +(-0.242558 + 0.746517i) q^{7} +(-1.15045 - 3.54072i) q^{8} +(-0.927051 - 2.85317i) q^{9} +(7.52343 - 5.46609i) q^{10} +(0.572793 + 1.76288i) q^{14} +(-1.32560 - 0.963104i) q^{16} +(-5.73141 - 4.16411i) q^{18} +(-7.00685 + 5.09077i) q^{19} +(4.35232 - 13.3951i) q^{20} +10.5079 q^{25} +(2.27119 + 1.65012i) q^{28} +3.57653 q^{32} +(-0.955194 + 2.93979i) q^{35} -10.7296 q^{36} +(-6.32018 + 19.4515i) q^{38} +(-4.53048 - 13.9434i) q^{40} +(-1.91586 + 1.39196i) q^{41} +(-3.65073 - 11.2358i) q^{45} +(-6.47214 - 4.70228i) q^{47} +(5.16467 + 3.75235i) q^{49} +(20.0750 - 14.5853i) q^{50} +2.92226 q^{56} +(-8.27690 - 6.01352i) q^{59} +2.35480 q^{63} +(9.48406 - 6.89057i) q^{64} -12.0000 q^{67} +(2.25566 + 6.94221i) q^{70} +(5.11020 + 15.7276i) q^{71} +(-9.03576 + 6.56486i) q^{72} +(9.57216 + 29.4601i) q^{76} +(-5.22022 - 3.79271i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-1.72811 + 5.31857i) q^{82} +(-22.5703 - 16.3983i) q^{90} -18.8918 q^{94} +(-27.5930 + 20.0475i) q^{95} +(3.16561 - 9.74276i) q^{97} +15.0753 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{4} - 3 q^{8} + 9 q^{9} + 9 q^{10} - 15 q^{14} - 12 q^{16} - 21 q^{20} + 60 q^{25} - 27 q^{28} + 24 q^{32} - 12 q^{35} - 72 q^{36} + 33 q^{38} + 18 q^{40} - 24 q^{47} - 21 q^{49} + 39 q^{50}+ \cdots + 228 q^{98}+O(q^{100}) \) 12 * q - 6 * q^4 - 3 * q^8 + 9 * q^9 + 9 * q^10 - 15 * q^14 - 12 * q^16 - 21 * q^20 + 60 * q^25 - 27 * q^28 + 24 * q^32 - 12 * q^35 - 72 * q^36 + 33 * q^38 + 18 * q^40 - 24 * q^47 - 21 * q^49 + 39 * q^50 + 120 * q^56 + 21 * q^64 - 144 * q^67 - 3 * q^70 + 9 * q^72 - 15 * q^76 + 9 * q^80 - 27 * q^81 - 21 * q^82 - 27 * q^90 - 48 * q^95 + 228 * q^98

Introduction

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