LMFDB - Embedded newform 4320.2.q.p.1441.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4320,2,Mod(1441,4320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4320, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("4320.1441");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4320 = 2^{5} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4320.q (of order $3$, 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:	$34.4953736732$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 1440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1441.5
Root			$-1.41743 - 0.995434i$ of defining polynomial
Character	$\chi$	$=$	4320.1441
Dual form			4320.2.q.p.2881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +(2.57079 + 4.45273i) q^{11} +(-2.18664 + 3.78737i) q^{13} +1.03644 q^{17} +4.06474 q^{19} +(3.31980 - 5.75006i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.936714 + 1.62244i) q^{29} +(-4.50553 + 7.80381i) q^{31} +4.63960 q^{35} -1.75985 q^{37} +(-1.68664 + 2.92134i) q^{41} +(2.53040 + 4.38278i) q^{43} +(-1.68376 - 2.91635i) q^{47} +(-7.26295 + 12.5798i) q^{49} +8.89657 q^{53} +5.14157 q^{55} +(5.20289 - 9.01167i) q^{59} +(-4.77625 - 8.27272i) q^{61} +(2.18664 + 3.78737i) q^{65} +(1.08585 - 1.88074i) q^{67} -8.47841 q^{71} -5.25606 q^{73} +(-11.9274 + 20.6589i) q^{77} +(-1.92499 - 3.33418i) q^{79} +(-5.99797 - 10.3888i) q^{83} +(0.518221 - 0.897586i) q^{85} +1.48291 q^{89} -20.2903 q^{91} +(2.03237 - 3.52017i) q^{95} +(6.61291 + 11.4539i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{5}+O(q^{10}) $ 10 * q + 5 * q^5	$ 10 q + 5 q^{5} + 9 q^{11} - 4 q^{13} - 6 q^{17} + 14 q^{19} + 10 q^{23} - 5 q^{25} + 2 q^{29} - 8 q^{31} + 16 q^{37} + q^{41} - q^{43} + 10 q^{47} - q^{49} + 20 q^{53} + 18 q^{55} + 13 q^{59} - 14 q^{61} + 4 q^{65} - 15 q^{67} - 32 q^{71} - 14 q^{73} - 12 q^{77} - 18 q^{79} - 8 q^{83} - 3 q^{85} - 28 q^{89} - 36 q^{91} + 7 q^{95} + 17 q^{97}+O(q^{100}) $ 10 * q + 5 * q^5 + 9 * q^11 - 4 * q^13 - 6 * q^17 + 14 * q^19 + 10 * q^23 - 5 * q^25 + 2 * q^29 - 8 * q^31 + 16 * q^37 + q^41 - q^43 + 10 * q^47 - q^49 + 20 * q^53 + 18 * q^55 + 13 * q^59 - 14 * q^61 + 4 * q^65 - 15 * q^67 - 32 * q^71 - 14 * q^73 - 12 * q^77 - 18 * q^79 - 8 * q^83 - 3 * q^85 - 28 * q^89 - 36 * q^91 + 7 * q^95 + 17 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4320\mathbb{Z}\right)^\times$.

$n$	$2081$	$2431$	$3457$	$3781$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.31980	+	4.01801i	0.876802	+	1.51867i	0.854830	+	0.518908i	$0.173661\pi$
$7$	2.31980	+	4.01801i	0.876802	+	1.51867i	0.0219721	+	0.999759i	$0.493005\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.57079	+	4.45273i	0.775121	+	1.34255i	0.934726	+	0.355369i	$0.115645\pi$
$11$	2.57079	+	4.45273i	0.775121	+	1.34255i	−0.159605	+	0.987181i	$0.551022\pi$
$12$		0			0
$13$	−2.18664	+	3.78737i	−0.606464	+	1.05043i	0.385354	+	0.922769i	$0.374079\pi$
$13$	−2.18664	+	3.78737i	−0.606464	+	1.05043i	−0.991818	+	0.127658i	$0.959254\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.03644			0.251374			0.125687	−	0.992070i	$-0.459886\pi$
$17$	1.03644			0.251374			0.125687	+	0.992070i	$0.459886\pi$
$18$		0			0
$19$	4.06474			0.932516			0.466258	−	0.884649i	$-0.345602\pi$
$19$	4.06474			0.932516			0.466258	+	0.884649i	$0.345602\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.31980	−	5.75006i	0.692226	−	1.19897i	−0.278880	−	0.960326i	$-0.589963\pi$
$23$	3.31980	−	5.75006i	0.692226	−	1.19897i	0.971107	−	0.238645i	$-0.0767034\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.936714	+	1.62244i	0.173943	+	0.301279i	0.939795	−	0.341738i	$-0.111016\pi$
$29$	0.936714	+	1.62244i	0.173943	+	0.301279i	−0.765852	+	0.643017i	$0.777682\pi$
$30$		0			0
$31$	−4.50553	+	7.80381i	−0.809217	+	1.40160i	0.104190	+	0.994557i	$0.466775\pi$
$31$	−4.50553	+	7.80381i	−0.809217	+	1.40160i	−0.913407	+	0.407047i	$0.866558\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.63960			0.784236
$36$		0			0
$37$	−1.75985			−0.289318			−0.144659	−	0.989482i	$-0.546209\pi$
$37$	−1.75985			−0.289318			−0.144659	+	0.989482i	$0.546209\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.68664	+	2.92134i	−0.263409	+	0.456237i	−0.967145	−	0.254224i	$-0.918180\pi$
$41$	−1.68664	+	2.92134i	−0.263409	+	0.456237i	0.703737	+	0.710461i	$0.251513\pi$
$42$		0			0
$43$	2.53040	+	4.38278i	0.385883	+	0.668368i	0.991891	−	0.127090i	$-0.0405637\pi$
$43$	2.53040	+	4.38278i	0.385883	+	0.668368i	−0.606009	+	0.795458i	$0.707230\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.68376	−	2.91635i	−0.245601	−	0.425394i	0.716699	−	0.697382i	$-0.245652\pi$
$47$	−1.68376	−	2.91635i	−0.245601	−	0.425394i	−0.962300	+	0.271989i	$0.912319\pi$
$48$		0			0
$49$	−7.26295	+	12.5798i	−1.03756	+	1.79712i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.89657			1.22204			0.611019	−	0.791616i	$-0.290760\pi$
$53$	8.89657			1.22204			0.611019	+	0.791616i	$0.290760\pi$
$54$		0			0
$55$	5.14157			0.693290
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.20289	−	9.01167i	0.677358	−	1.17322i	−0.298415	−	0.954436i	$-0.596458\pi$
$59$	5.20289	−	9.01167i	0.677358	−	1.17322i	0.975774	−	0.218783i	$-0.0702087\pi$
$60$		0			0
$61$	−4.77625	−	8.27272i	−0.611537	−	1.05921i	−0.990982	−	0.133998i	$-0.957218\pi$
$61$	−4.77625	−	8.27272i	−0.611537	−	1.05921i	0.379445	−	0.925214i	$-0.376115\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.18664	+	3.78737i	0.271219	+	0.469765i
$66$		0			0
$67$	1.08585	−	1.88074i	0.132657	−	0.229769i	−0.792043	−	0.610466i	$-0.790982\pi$
$67$	1.08585	−	1.88074i	0.132657	−	0.229769i	0.924700	+	0.380696i	$0.124316\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.47841			−1.00620			−0.503101	−	0.864228i	$-0.667808\pi$
$71$	−8.47841			−1.00620			−0.503101	+	0.864228i	$0.667808\pi$
$72$		0			0
$73$	−5.25606			−0.615176			−0.307588	−	0.951520i	$-0.599522\pi$
$73$	−5.25606			−0.615176			−0.307588	+	0.951520i	$0.599522\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.9274	+	20.6589i	−1.35926	+	2.35430i
$78$		0			0
$79$	−1.92499	−	3.33418i	−0.216578	−	0.375125i	0.737181	−	0.675695i	$-0.236156\pi$
$79$	−1.92499	−	3.33418i	−0.216578	−	0.375125i	−0.953760	+	0.300570i	$0.902823\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.99797	−	10.3888i	−0.658363	−	1.14032i	−0.981039	−	0.193808i	$-0.937916\pi$
$83$	−5.99797	−	10.3888i	−0.658363	−	1.14032i	0.322677	−	0.946509i	$-0.395417\pi$
$84$		0			0
$85$	0.518221	−	0.897586i	0.0562090	−	0.0973569i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.48291			0.157188			0.0785940	−	0.996907i	$-0.474957\pi$
$89$	1.48291			0.157188			0.0785940	+	0.996907i	$0.474957\pi$
$90$		0			0
$91$	−20.2903			−2.12700
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.03237	−	3.52017i	0.208517	−	0.361162i
$96$		0			0
$97$	6.61291	+	11.4539i	0.671439	+	1.16297i	0.977496	+	0.210954i	$0.0676570\pi$
$97$	6.61291	+	11.4539i	0.671439	+	1.16297i	−0.306057	+	0.952013i	$0.599010\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.40790	−	11.0988i	−0.637610	−	1.10437i	−0.985956	−	0.167007i	$-0.946590\pi$
$101$	−6.40790	−	11.0988i	−0.637610	−	1.10437i	0.348346	−	0.937366i	$-0.386743\pi$
$102$		0			0
$103$	−8.60854	+	14.9104i	−0.848224	+	1.46917i	0.0345670	+	0.999402i	$0.488995\pi$
$103$	−8.60854	+	14.9104i	−0.848224	+	1.46917i	−0.882791	+	0.469765i	$0.844339\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.4323			−1.29855			−0.649273	−	0.760556i	$-0.724927\pi$
$107$	−13.4323			−1.29855			−0.649273	+	0.760556i	$0.724927\pi$
$108$		0			0
$109$	7.64592			0.732347			0.366173	−	0.930547i	$-0.380668\pi$
$109$	7.64592			0.732347			0.366173	+	0.930547i	$0.380668\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.36301	+	9.28901i	−0.504510	+	0.873837i	0.495477	+	0.868621i	$0.334993\pi$
$113$	−5.36301	+	9.28901i	−0.504510	+	0.873837i	−0.999986	+	0.00521530i	$0.998340\pi$
$114$		0			0
$115$	−3.31980	−	5.75006i	−0.309573	−	0.536196i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.40434	+	4.16444i	0.220406	+	0.381754i
$120$		0			0
$121$	−7.71789	+	13.3678i	−0.701626	+	1.21525i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.765616			−0.0679374			−0.0339687	−	0.999423i	$-0.510815\pi$
$127$	−0.765616			−0.0679374			−0.0339687	+	0.999423i	$0.510815\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.961434	+	1.66525i	−0.0840009	+	0.145494i	−0.904965	−	0.425486i	$-0.860103\pi$
$131$	−0.961434	+	1.66525i	−0.0840009	+	0.145494i	0.820964	+	0.570980i	$0.193437\pi$
$132$		0			0
$133$	9.42940	+	16.3322i	0.817633	+	1.41618i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.43853	+	2.49161i	0.122902	+	0.212873i	0.920911	−	0.389773i	$-0.127447\pi$
$137$	1.43853	+	2.49161i	0.122902	+	0.212873i	−0.798009	+	0.602646i	$0.794113\pi$
$138$		0			0
$139$	7.67948	−	13.3012i	0.651365	−	1.12820i	−0.331427	−	0.943481i	$-0.607530\pi$
$139$	7.67948	−	13.3012i	0.651365	−	1.12820i	0.982792	−	0.184716i	$-0.0591365\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−22.4855			−1.88033
$144$		0			0
$145$	1.87343			0.155580
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.63164	−	4.55814i	0.215593	−	0.373418i	−0.737863	−	0.674950i	$-0.764165\pi$
$149$	2.63164	−	4.55814i	0.215593	−	0.373418i	0.953456	+	0.301533i	$0.0974983\pi$
$150$		0			0
$151$	−6.80830	−	11.7923i	−0.554051	−	0.959645i	−0.997977	−	0.0635814i	$-0.979748\pi$
$151$	−6.80830	−	11.7923i	−0.554051	−	0.959645i	0.443925	−	0.896064i	$-0.353586\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.50553	+	7.80381i	0.361893	+	0.626817i
$156$		0			0
$157$	7.40396	−	12.8240i	0.590900	−	1.02347i	−0.403211	−	0.915107i	$-0.632106\pi$
$157$	7.40396	−	12.8240i	0.590900	−	1.02347i	0.994111	−	0.108362i	$-0.0345606\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	30.8051			2.42778
$162$		0			0
$163$	17.6076			1.37913			0.689567	−	0.724222i	$-0.257801\pi$
$163$	17.6076			1.37913			0.689567	+	0.724222i	$0.257801\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.788888	+	1.36639i	−0.0610459	+	0.105735i	−0.894933	−	0.446200i	$-0.852777\pi$
$167$	−0.788888	+	1.36639i	−0.0610459	+	0.105735i	0.833887	+	0.551935i	$0.186110\pi$
$168$		0			0
$169$	−3.06277	−	5.30488i	−0.235598	−	0.408068i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.7212	+	18.5696i	0.815115	+	1.41182i	0.909245	+	0.416261i	$0.136660\pi$
$173$	10.7212	+	18.5696i	0.815115	+	1.41182i	−0.0941297	+	0.995560i	$0.530007\pi$
$174$		0			0
$175$	2.31980	−	4.01801i	0.175360	−	0.303733i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	17.3544			1.29713			0.648566	−	0.761158i	$-0.275369\pi$
$179$	17.3544			1.29713			0.648566	+	0.761158i	$0.275369\pi$
$180$		0			0
$181$	−24.0323			−1.78631			−0.893154	−	0.449751i	$-0.851513\pi$
$181$	−24.0323			−1.78631			−0.893154	+	0.449751i	$0.851513\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.879927	+	1.52408i	−0.0646935	+	0.112052i
$186$		0			0
$187$	2.66447	+	4.61500i	0.194846	+	0.337483i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.83186	+	4.90493i	0.204906	+	0.354908i	0.950103	−	0.311937i	$-0.100978\pi$
$191$	2.83186	+	4.90493i	0.204906	+	0.354908i	−0.745197	+	0.666845i	$0.767644\pi$
$192$		0			0
$193$	3.09520	−	5.36105i	0.222797	−	0.385897i	−0.732859	−	0.680381i	$-0.761814\pi$
$193$	3.09520	−	5.36105i	0.222797	−	0.385897i	0.955656	+	0.294484i	$0.0951478\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.28709			0.519184			0.259592	−	0.965718i	$-0.416412\pi$
$197$	7.28709			0.519184			0.259592	+	0.965718i	$0.416412\pi$
$198$		0			0
$199$	16.3108			1.15624			0.578121	−	0.815951i	$-0.303786\pi$
$199$	16.3108			1.15624			0.578121	+	0.815951i	$0.303786\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.34598	+	7.52746i	−0.305028	+	0.528324i
$204$		0			0
$205$	1.68664	+	2.92134i	0.117800	+	0.204035i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.4496	+	18.0992i	0.722813	+	1.25195i
$210$		0			0
$211$	11.6854	−	20.2396i	0.804454	−	1.39335i	−0.112205	−	0.993685i	$-0.535791\pi$
$211$	11.6854	−	20.2396i	0.804454	−	1.39335i	0.916659	−	0.399670i	$-0.130875\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.06080			0.345144
$216$		0			0
$217$	−41.8077			−2.83809
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.26633	+	3.92539i	−0.152450	+	0.264050i
$222$		0			0
$223$	1.12098	+	1.94160i	0.0750666	+	0.130019i	0.901115	−	0.433580i	$-0.142750\pi$
$223$	1.12098	+	1.94160i	0.0750666	+	0.130019i	−0.826049	+	0.563599i	$0.809416\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.48880	−	2.57867i	−0.0988150	−	0.171153i	0.812379	−	0.583129i	$-0.198172\pi$
$227$	−1.48880	−	2.57867i	−0.0988150	−	0.171153i	−0.911194	+	0.411977i	$0.864839\pi$
$228$		0			0
$229$	−13.5205	+	23.4182i	−0.893460	+	1.54752i	−0.0577615	+	0.998330i	$0.518396\pi$
$229$	−13.5205	+	23.4182i	−0.893460	+	1.54752i	−0.835699	+	0.549188i	$0.814937\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.913026			−0.0598143			−0.0299072	−	0.999553i	$-0.509521\pi$
$233$	−0.913026			−0.0598143			−0.0299072	+	0.999553i	$0.509521\pi$
$234$		0			0
$235$	−3.36751			−0.219672
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.08789	+	8.81248i	−0.329108	+	0.570032i	−0.982335	−	0.187130i	$-0.940081\pi$
$239$	−5.08789	+	8.81248i	−0.329108	+	0.570032i	0.653227	+	0.757162i	$0.273415\pi$
$240$		0			0
$241$	6.56639	+	11.3733i	0.422978	+	0.732620i	0.996229	−	0.0867601i	$-0.0276514\pi$
$241$	6.56639	+	11.3733i	0.422978	+	0.732620i	−0.573251	+	0.819380i	$0.694318\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.26295	+	12.5798i	0.464013	+	0.803694i
$246$		0			0
$247$	−8.88813	+	15.3947i	−0.565538	+	0.979540i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	17.9795			1.13486			0.567428	−	0.823423i	$-0.307939\pi$
$251$	17.9795			1.13486			0.567428	+	0.823423i	$0.307939\pi$
$252$		0			0
$253$	34.1380			2.14624
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.7120	−	25.4819i	0.917708	−	1.58952i	0.114820	−	0.993386i	$-0.463371\pi$
$257$	14.7120	−	25.4819i	0.917708	−	1.58952i	0.802888	−	0.596130i	$-0.203296\pi$
$258$		0			0
$259$	−4.08251	−	7.07111i	−0.253675	−	0.439378i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.3853	+	17.9878i	0.640384	+	1.10918i	0.985347	+	0.170561i	$0.0545580\pi$
$263$	10.3853	+	17.9878i	0.640384	+	1.10918i	−0.344963	+	0.938616i	$0.612109\pi$
$264$		0			0
$265$	4.44829	−	7.70466i	0.273256	−	0.473293i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.16593			−0.497886			−0.248943	−	0.968518i	$-0.580083\pi$
$269$	−8.16593			−0.497886			−0.248943	+	0.968518i	$0.580083\pi$
$270$		0			0
$271$	−12.7500			−0.774509			−0.387255	−	0.921973i	$-0.626577\pi$
$271$	−12.7500			−0.774509			−0.387255	+	0.921973i	$0.626577\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.57079	−	4.45273i	0.155024	−	0.268510i
$276$		0			0
$277$	2.06821	+	3.58224i	0.124267	+	0.215236i	0.921446	−	0.388506i	$-0.127009\pi$
$277$	2.06821	+	3.58224i	0.124267	+	0.215236i	−0.797179	+	0.603742i	$0.793676\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.784699	+	1.35914i	0.0468112	+	0.0810794i	0.888482	−	0.458912i	$-0.151761\pi$
$281$	0.784699	+	1.35914i	0.0468112	+	0.0810794i	−0.841670	+	0.539992i	$0.818427\pi$
$282$		0			0
$283$	−1.78533	+	3.09228i	−0.106127	+	0.183817i	−0.914198	−	0.405268i	$-0.867178\pi$
$283$	−1.78533	+	3.09228i	−0.106127	+	0.183817i	0.808071	+	0.589085i	$0.200512\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−15.6507			−0.923829
$288$		0			0
$289$	−15.9258			−0.936811
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−11.1568	+	19.3241i	−0.651784	+	1.12892i	0.330905	+	0.943664i	$0.392646\pi$
$293$	−11.1568	+	19.3241i	−0.651784	+	1.12892i	−0.982690	+	0.185260i	$0.940687\pi$
$294$		0			0
$295$	−5.20289	−	9.01167i	−0.302924	−	0.524680i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	14.5184	+	25.1466i	0.839621	+	1.45427i
$300$		0			0
$301$	−11.7401	+	20.3344i	−0.676685	+	1.17205i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.55251			−0.546975
$306$		0			0
$307$	17.1543			0.979050			0.489525	−	0.871989i	$-0.337170\pi$
$307$	17.1543			0.979050			0.489525	+	0.871989i	$0.337170\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.24224	−	9.07983i	0.297260	−	0.514870i	−0.678248	−	0.734833i	$-0.737260\pi$
$311$	5.24224	−	9.07983i	0.297260	−	0.514870i	0.975508	+	0.219963i	$0.0705938\pi$
$312$		0			0
$313$	−8.49522	−	14.7141i	−0.480178	−	0.831693i	0.519563	−	0.854432i	$-0.326095\pi$
$313$	−8.49522	−	14.7141i	−0.480178	−	0.831693i	−0.999741	+	0.0227392i	$0.992761\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.28206	+	10.8809i	0.352836	+	0.611130i	0.986745	−	0.162278i	$-0.0518841\pi$
$317$	6.28206	+	10.8809i	0.352836	+	0.611130i	−0.633909	+	0.773407i	$0.718551\pi$
$318$		0			0
$319$	−4.81618	+	8.34188i	−0.269655	+	0.467055i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.21288			0.234411
$324$		0			0
$325$	4.37328			0.242586
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.81196	−	13.5307i	0.430687	−	0.745972i
$330$		0			0
$331$	12.5854	+	21.7985i	0.691754	+	1.19815i	0.971263	+	0.238010i	$0.0764950\pi$
$331$	12.5854	+	21.7985i	0.691754	+	1.19815i	−0.279509	+	0.960143i	$0.590172\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.08585	−	1.88074i	−0.0593262	−	0.102756i
$336$		0			0
$337$	−3.72618	+	6.45394i	−0.202978	+	0.351568i	−0.949487	−	0.313807i	$-0.898395\pi$
$337$	−3.72618	+	6.45394i	−0.202978	+	0.351568i	0.746509	+	0.665376i	$0.231729\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−46.3310			−2.50897
$342$		0			0
$343$	−34.9172			−1.88535
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.90762	−	17.1605i	0.531869	−	0.921224i	−0.467439	−	0.884025i	$-0.654823\pi$
$347$	9.90762	−	17.1605i	0.531869	−	0.921224i	0.999308	−	0.0371987i	$-0.0118434\pi$
$348$		0			0
$349$	−3.25642	−	5.64029i	−0.174312	−	0.301918i	0.765611	−	0.643304i	$-0.222437\pi$
$349$	−3.25642	−	5.64029i	−0.174312	−	0.301918i	−0.939923	+	0.341386i	$0.889104\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.5162	+	18.2145i	0.559719	+	0.969461i	0.997520	+	0.0703891i	$0.0224241\pi$
$353$	10.5162	+	18.2145i	0.559719	+	0.969461i	−0.437801	+	0.899072i	$0.644243\pi$
$354$		0			0
$355$	−4.23920	+	7.34252i	−0.224994	+	0.389700i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−34.3505			−1.81295			−0.906475	−	0.422259i	$-0.861237\pi$
$359$	−34.3505			−1.81295			−0.906475	+	0.422259i	$0.861237\pi$
$360$		0			0
$361$	−2.47785			−0.130413
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.62803	+	4.55188i	−0.137557	+	0.238256i
$366$		0			0
$367$	9.46211	+	16.3889i	0.493918	+	0.855491i	0.999975	−	0.00700874i	$-0.00223097\pi$
$367$	9.46211	+	16.3889i	0.493918	+	0.855491i	−0.506057	+	0.862500i	$0.668898\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	20.6383	+	35.7465i	1.07149	+	1.85587i
$372$		0			0
$373$	−14.9604	+	25.9122i	−0.774621	+	1.34168i	0.160387	+	0.987054i	$0.448726\pi$
$373$	−14.9604	+	25.9122i	−0.774621	+	1.34168i	−0.935007	+	0.354628i	$0.884608\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.19302			−0.421962
$378$		0			0
$379$	20.9258			1.07489			0.537443	−	0.843300i	$-0.319390\pi$
$379$	20.9258			1.07489			0.537443	+	0.843300i	$0.319390\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.52065	−	7.82999i	0.230994	−	0.400094i	−0.727107	−	0.686525i	$-0.759135\pi$
$383$	4.52065	−	7.82999i	0.230994	−	0.400094i	0.958101	+	0.286431i	$0.0924688\pi$
$384$		0			0
$385$	11.9274	+	20.6589i	0.607878	+	1.05288i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.29213	+	5.70214i	0.166918	+	0.289110i	0.937335	−	0.348431i	$-0.113285\pi$
$389$	3.29213	+	5.70214i	0.166918	+	0.289110i	−0.770417	+	0.637540i	$0.779952\pi$
$390$		0			0
$391$	3.44078	−	5.95961i	0.174008	−	0.301391i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.84998			−0.193714
$396$		0			0
$397$	−26.7100			−1.34054			−0.670269	−	0.742119i	$-0.733821\pi$
$397$	−26.7100			−1.34054			−0.670269	+	0.742119i	$0.733821\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.44698	+	5.97034i	−0.172134	+	0.298145i	−0.939166	−	0.343464i	$-0.888399\pi$
$401$	−3.44698	+	5.97034i	−0.172134	+	0.298145i	0.767032	+	0.641609i	$0.221733\pi$
$402$		0			0
$403$	−19.7039	−	34.1282i	−0.981522	−	1.70005i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.52421	−	7.83616i	−0.224257	−	0.388424i
$408$		0			0
$409$	19.7484	−	34.2053i	0.976496	−	1.69134i	0.301591	−	0.953437i	$-0.402482\pi$
$409$	19.7484	−	34.2053i	0.976496	−	1.69134i	0.674906	−	0.737904i	$-0.264184\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	48.2787			2.37564
$414$		0			0
$415$	−11.9959			−0.588857
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.7772	−	32.5231i	0.917326	−	1.58886i	0.113866	−	0.993496i	$-0.463676\pi$
$419$	18.7772	−	32.5231i	0.917326	−	1.58886i	0.803460	−	0.595359i	$-0.202990\pi$
$420$		0			0
$421$	−11.5064	−	19.9297i	−0.560788	−	0.971313i	−0.997428	−	0.0716768i	$-0.977165\pi$
$421$	−11.5064	−	19.9297i	−0.560788	−	0.971313i	0.436640	−	0.899636i	$-0.356168\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.518221	−	0.897586i	−0.0251374	−	0.0435393i
$426$		0			0
$427$	22.1599	−	38.3821i	1.07239	−	1.85744i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.7109			0.515924			0.257962	−	0.966155i	$-0.416949\pi$
$431$	10.7109			0.515924			0.257962	+	0.966155i	$0.416949\pi$
$432$		0			0
$433$	32.1104			1.54313			0.771563	−	0.636153i	$-0.219475\pi$
$433$	32.1104			1.54313			0.771563	+	0.636153i	$0.219475\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.4941	−	23.3725i	0.645512	−	1.11806i
$438$		0			0
$439$	9.46116	+	16.3872i	0.451557	+	0.782119i	0.998483	−	0.0550616i	$-0.0175355\pi$
$439$	9.46116	+	16.3872i	0.451557	+	0.782119i	−0.546926	+	0.837181i	$0.684202\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.9593	+	22.4461i	0.615714	+	1.06645i	0.990259	+	0.139239i	$0.0444656\pi$
$443$	12.9593	+	22.4461i	0.615714	+	1.06645i	−0.374545	+	0.927209i	$0.622201\pi$
$444$		0			0
$445$	0.741454	−	1.28424i	0.0351483	−	0.0608786i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−32.4821			−1.53292			−0.766462	−	0.642290i	$-0.777984\pi$
$449$	−32.4821			−1.53292			−0.766462	+	0.642290i	$0.777984\pi$
$450$		0			0
$451$	−17.3439			−0.816695
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−10.1451	+	17.5719i	−0.475611	+	0.823783i
$456$		0			0
$457$	20.5099	+	35.5242i	0.959413	+	1.66175i	0.723929	+	0.689874i	$0.242334\pi$
$457$	20.5099	+	35.5242i	0.959413	+	1.66175i	0.235484	+	0.971878i	$0.424332\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.378678	−	0.655890i	−0.0176368	−	0.0305478i	0.857072	−	0.515196i	$-0.172281\pi$
$461$	−0.378678	−	0.655890i	−0.0176368	−	0.0305478i	−0.874709	+	0.484648i	$0.838948\pi$
$462$		0			0
$463$	15.1949	−	26.3183i	0.706166	−	1.22311i	−0.260103	−	0.965581i	$-0.583757\pi$
$463$	15.1949	−	26.3183i	0.706166	−	1.22311i	0.966269	−	0.257534i	$-0.0829100\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.41191			−0.111610			−0.0558049	−	0.998442i	$-0.517772\pi$
$467$	−2.41191			−0.111610			−0.0558049	+	0.998442i	$0.517772\pi$
$468$		0			0
$469$	10.0758			0.465257
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−13.0102	+	22.5344i	−0.598212	+	1.03613i
$474$		0			0
$475$	−2.03237	−	3.52017i	−0.0932516	−	0.161517i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.2020	−	29.7947i	−0.785977	−	1.36135i	−0.928413	−	0.371549i	$-0.878827\pi$
$479$	−17.2020	−	29.7947i	−0.785977	−	1.36135i	0.142436	−	0.989804i	$-0.454506\pi$
$480$		0			0
$481$	3.84816	−	6.66521i	0.175461	−	0.303908i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.2258			0.600554
$486$		0			0
$487$	16.9242			0.766909			0.383455	−	0.923560i	$-0.374734\pi$
$487$	16.9242			0.766909			0.383455	+	0.923560i	$0.374734\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.41686	−	11.1143i	0.289589	−	0.501582i	−0.684123	−	0.729367i	$-0.739815\pi$
$491$	6.41686	−	11.1143i	0.289589	−	0.501582i	0.973712	+	0.227784i	$0.0731482\pi$
$492$		0			0
$493$	0.970851	+	1.68156i	0.0437249	+	0.0757338i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.6682	−	34.0664i	−0.882240	−	1.52808i
$498$		0			0
$499$	−9.32764	+	16.1559i	−0.417563	+	0.723240i	−0.995694	−	0.0927043i	$-0.970449\pi$
$499$	−9.32764	+	16.1559i	−0.417563	+	0.723240i	0.578131	+	0.815944i	$0.303782\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−25.4535			−1.13492			−0.567458	−	0.823402i	$-0.692073\pi$
$503$	−25.4535			−1.13492			−0.567458	+	0.823402i	$0.692073\pi$
$504$		0			0
$505$	−12.8158			−0.570296
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.65042	−	9.78681i	0.250450	−	0.433793i	−0.713199	−	0.700961i	$-0.752755\pi$
$509$	5.65042	−	9.78681i	0.250450	−	0.433793i	0.963650	+	0.267168i	$0.0860880\pi$
$510$		0			0
$511$	−12.1930	−	21.1189i	−0.539387	−	0.934246i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.60854	+	14.9104i	0.379337	+	0.657032i
$516$		0			0
$517$	8.65716	−	14.9946i	0.380741	−	0.659464i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−30.8279			−1.35059			−0.675297	−	0.737546i	$-0.735985\pi$
$521$	−30.8279			−1.35059			−0.675297	+	0.737546i	$0.735985\pi$
$522$		0			0
$523$	−3.44488			−0.150634			−0.0753171	−	0.997160i	$-0.523997\pi$
$523$	−3.44488			−0.150634			−0.0753171	+	0.997160i	$0.523997\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.66972	+	8.08820i	−0.203416	+	0.352328i
$528$		0			0
$529$	−10.5422	−	18.2596i	−0.458355	−	0.793894i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.37614	−	12.7758i	−0.319496	−	0.553383i
$534$		0			0
$535$	−6.71613	+	11.6327i	−0.290364	+	0.502924i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−74.6860			−3.21696
$540$		0			0
$541$	12.7479			0.548074			0.274037	−	0.961719i	$-0.411641\pi$
$541$	12.7479			0.548074			0.274037	+	0.961719i	$0.411641\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.82296	−	6.62156i	0.163758	−	0.283637i
$546$		0			0
$547$	−1.55190	−	2.68797i	−0.0663544	−	0.114929i	0.830940	−	0.556363i	$-0.187803\pi$
$547$	−1.55190	−	2.68797i	−0.0663544	−	0.114929i	−0.897294	+	0.441434i	$0.854470\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.80750	+	6.59479i	0.162205	+	0.280947i
$552$		0			0
$553$	8.93119	−	15.4693i	0.379793	−	0.657821i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.5905			−0.702960			−0.351480	−	0.936195i	$-0.614322\pi$
$557$	−16.5905			−0.702960			−0.351480	+	0.936195i	$0.614322\pi$
$558$		0			0
$559$	−22.1323			−0.936096
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.17598	−	3.76890i	0.0917065	−	0.158840i	−0.816523	−	0.577313i	$-0.804101\pi$
$563$	2.17598	−	3.76890i	0.0917065	−	0.158840i	0.908229	+	0.418473i	$0.137435\pi$
$564$		0			0
$565$	5.36301	+	9.28901i	0.225624	+	0.390792i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13.1717	+	22.8141i	0.552188	+	0.956418i	0.998116	+	0.0613492i	$0.0195403\pi$
$569$	13.1717	+	22.8141i	0.552188	+	0.956418i	−0.445928	+	0.895069i	$0.647126\pi$
$570$		0			0
$571$	1.85712	−	3.21662i	0.0777180	−	0.134612i	−0.824547	−	0.565793i	$-0.808570\pi$
$571$	1.85712	−	3.21662i	0.0777180	−	0.134612i	0.902265	+	0.431182i	$0.141903\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.63960			−0.276891
$576$		0			0
$577$	6.77213			0.281927			0.140964	−	0.990015i	$-0.454980\pi$
$577$	6.77213			0.281927			0.140964	+	0.990015i	$0.454980\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	27.8282	−	48.1998i	1.15451	−	1.99967i
$582$		0			0
$583$	22.8712	+	39.6141i	0.947228	+	1.64065i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.65897	+	11.5337i	0.274845	+	0.476045i	0.970096	−	0.242722i	$-0.0780401\pi$
$587$	6.65897	+	11.5337i	0.274845	+	0.476045i	−0.695251	+	0.718767i	$0.744707\pi$
$588$		0			0
$589$	−18.3138	+	31.7205i	−0.754608	+	1.30702i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.3373			−0.547696			−0.273848	−	0.961773i	$-0.588297\pi$
$593$	−13.3373			−0.547696			−0.273848	+	0.961773i	$0.588297\pi$
$594$		0			0
$595$	4.80868			0.197137
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.80917	+	8.32974i	−0.196498	+	0.340344i	−0.947390	−	0.320080i	$-0.896290\pi$
$599$	−4.80917	+	8.32974i	−0.196498	+	0.340344i	0.750893	+	0.660424i	$0.229623\pi$
$600$		0			0
$601$	−2.33420	−	4.04295i	−0.0952139	−	0.164915i	0.814484	−	0.580186i	$-0.197020\pi$
$601$	−2.33420	−	4.04295i	−0.0952139	−	0.164915i	−0.909698	+	0.415271i	$0.863687\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.71789	+	13.3678i	0.313777	+	0.543477i
$606$		0			0
$607$	−3.22217	+	5.58096i	−0.130784	+	0.226524i	−0.923979	−	0.382443i	$-0.875083\pi$
$607$	−3.22217	+	5.58096i	−0.130784	+	0.226524i	0.793195	+	0.608968i	$0.208416\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14.7271			0.595793
$612$		0			0
$613$	20.1411			0.813493			0.406746	−	0.913541i	$-0.366663\pi$
$613$	20.1411			0.813493			0.406746	+	0.913541i	$0.366663\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.86636	+	4.96468i	−0.115395	+	0.199870i	−0.917938	−	0.396725i	$-0.870147\pi$
$617$	−2.86636	+	4.96468i	−0.115395	+	0.199870i	0.802542	+	0.596595i	$0.203480\pi$
$618$		0			0
$619$	−9.08484	−	15.7354i	−0.365151	−	0.632459i	0.623650	−	0.781704i	$-0.285649\pi$
$619$	−9.08484	−	15.7354i	−0.365151	−	0.632459i	−0.988800	+	0.149244i	$0.952316\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.44005	+	5.95835i	0.137823	+	0.238716i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.82399			−0.0727271
$630$		0			0
$631$	21.1892			0.843528			0.421764	−	0.906706i	$-0.361411\pi$
$631$	21.1892			0.843528			0.421764	+	0.906706i	$0.361411\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.382808	+	0.663043i	−0.0151913	+	0.0263121i
$636$		0			0
$637$	−31.7629	−	55.0150i	−1.25849	−	2.17977i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−22.9248	−	39.7069i	−0.905474	−	1.56833i	−0.820279	−	0.571963i	$-0.806182\pi$
$641$	−22.9248	−	39.7069i	−0.905474	−	1.56833i	−0.0851952	−	0.996364i	$-0.527151\pi$
$642$		0			0
$643$	14.2494	−	24.6807i	0.561942	−	0.973311i	−0.435385	−	0.900244i	$-0.643388\pi$
$643$	14.2494	−	24.6807i	0.561942	−	0.973311i	0.997327	−	0.0730672i	$-0.0232788\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.9396			−1.29499			−0.647494	−	0.762070i	$-0.724183\pi$
$647$	−32.9396			−1.29499			−0.647494	+	0.762070i	$0.724183\pi$
$648$		0			0
$649$	53.5021			2.10014
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.67981	−	4.64157i	0.104869	−	0.181639i	−0.808816	−	0.588062i	$-0.799891\pi$
$653$	2.67981	−	4.64157i	0.104869	−	0.181639i	0.913685	+	0.406424i	$0.133224\pi$
$654$		0			0
$655$	0.961434	+	1.66525i	0.0375663	+	0.0650668i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.57080	−	13.1130i	−0.294916	−	0.510810i	0.680049	−	0.733167i	$-0.261958\pi$
$659$	−7.57080	−	13.1130i	−0.294916	−	0.510810i	−0.974965	+	0.222357i	$0.928625\pi$
$660$		0			0
$661$	−2.15422	+	3.73121i	−0.0837893	+	0.145127i	−0.904875	−	0.425678i	$-0.860036\pi$
$661$	−2.15422	+	3.73121i	−0.0837893	+	0.145127i	0.821085	+	0.570805i	$0.193369\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	18.8588			0.731313
$666$		0			0
$667$	12.4388			0.481633
$668$		0			0
$669$		0			0
$670$		0			0
$671$	24.5575	−	42.5348i	0.948030	−	1.64204i
$672$		0			0
$673$	10.0224	+	17.3593i	0.386336	+	0.669153i	0.991954	−	0.126603i	$-0.0404073\pi$
$673$	10.0224	+	17.3593i	0.386336	+	0.669153i	−0.605618	+	0.795756i	$0.707074\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.3326	−	23.0928i	−0.512415	−	0.887529i	−0.999896	−	0.0143957i	$-0.995418\pi$
$677$	−13.3326	−	23.0928i	−0.512415	−	0.887529i	0.487481	−	0.873134i	$-0.337916\pi$
$678$		0			0
$679$	−30.6813	+	53.1415i	−1.17744	+	2.03938i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	25.2021			0.964331			0.482166	−	0.876080i	$-0.339850\pi$
$683$	25.2021			0.964331			0.482166	+	0.876080i	$0.339850\pi$
$684$		0			0
$685$	2.87707			0.109927
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.4536	+	33.6946i	−0.741122	+	1.28366i
$690$		0			0
$691$	−7.27258	−	12.5965i	−0.276662	−	0.479193i	0.693891	−	0.720080i	$-0.255895\pi$
$691$	−7.27258	−	12.5965i	−0.276662	−	0.479193i	−0.970553	+	0.240887i	$0.922562\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.67948	−	13.3012i	−0.291299	−	0.504545i
$696$		0			0
$697$	−1.74810	+	3.02781i	−0.0662142	+	0.114686i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	16.0567			0.606455			0.303227	−	0.952918i	$-0.401936\pi$
$701$	16.0567			0.606455			0.303227	+	0.952918i	$0.401936\pi$
$702$		0			0
$703$	−7.15335			−0.269794
$704$		0			0
$705$		0			0
$706$		0			0
$707$	29.7301	−	51.4941i	1.11812	−	1.93663i
$708$		0			0
$709$	−15.5688	−	26.9659i	−0.584698	−	1.01273i	−0.994913	−	0.100738i	$-0.967880\pi$
$709$	−15.5688	−	26.9659i	−0.584698	−	1.01273i	0.410215	−	0.911989i	$-0.365454\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.9149	+	51.8142i	1.12032	+	1.94046i
$714$		0			0
$715$	−11.2428	+	19.4730i	−0.420455	+	0.728250i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	30.9181			1.15305			0.576525	−	0.817080i	$-0.304408\pi$
$719$	30.9181			1.15305			0.576525	+	0.817080i	$0.304408\pi$
$720$		0			0
$721$	−79.8804			−2.97490
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.936714	−	1.62244i	0.0347887	−	0.0602558i
$726$		0			0
$727$	8.75834	+	15.1699i	0.324829	+	0.562620i	0.981478	−	0.191576i	$-0.0613599\pi$
$727$	8.75834	+	15.1699i	0.324829	+	0.562620i	−0.656649	+	0.754197i	$0.728027\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.62262	+	4.54250i	0.0970010	+	0.168011i
$732$		0			0
$733$	16.5276	−	28.6267i	0.610461	−	1.05735i	−0.380701	−	0.924698i	$-0.624317\pi$
$733$	16.5276	−	28.6267i	0.610461	−	1.05735i	0.991163	−	0.132652i	$-0.0423492\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.1659			0.411302
$738$		0			0
$739$	−15.9164			−0.585493			−0.292747	−	0.956190i	$-0.594569\pi$
$739$	−15.9164			−0.585493			−0.292747	+	0.956190i	$0.594569\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.97902	−	13.8201i	0.292722	−	0.507009i	−0.681730	−	0.731604i	$-0.738772\pi$
$743$	7.97902	−	13.8201i	0.292722	−	0.507009i	0.974452	+	0.224594i	$0.0721056\pi$
$744$		0			0
$745$	−2.63164	−	4.55814i	−0.0964160	−	0.166997i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−31.1602	−	53.9710i	−1.13857	−	1.97206i
$750$		0			0
$751$	7.86854	−	13.6287i	0.287127	−	0.497319i	−0.685996	−	0.727606i	$-0.740633\pi$
$751$	7.86854	−	13.6287i	0.287127	−	0.497319i	0.973123	+	0.230287i	$0.0739664\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13.6166			−0.495559
$756$		0			0
$757$	−9.11012			−0.331113			−0.165556	−	0.986200i	$-0.552942\pi$
$757$	−9.11012			−0.331113			−0.165556	+	0.986200i	$0.552942\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.48654	−	12.9671i	0.271387	−	0.470056i	−0.697830	−	0.716263i	$-0.745851\pi$
$761$	7.48654	−	12.9671i	0.271387	−	0.470056i	0.969217	+	0.246207i	$0.0791844\pi$
$762$		0			0
$763$	17.7370	+	30.7214i	0.642123	+	1.11219i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	22.7537	+	39.4105i	0.821587	+	1.42303i
$768$		0			0
$769$	−0.626060	+	1.08437i	−0.0225763	+	0.0391033i	−0.877093	−	0.480321i	$-0.840520\pi$
$769$	−0.626060	+	1.08437i	−0.0225763	+	0.0391033i	0.854517	+	0.519424i	$0.173854\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	14.5747			0.524215			0.262108	−	0.965039i	$-0.415582\pi$
$773$	14.5747			0.524215			0.262108	+	0.965039i	$0.415582\pi$
$774$		0			0
$775$	9.01106			0.323687
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.85575	+	11.8745i	−0.245633	+	0.425449i
$780$		0			0
$781$	−21.7962	−	37.7521i	−0.779929	−	1.35088i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.40396	−	12.8240i	−0.264259	−	0.457709i
$786$		0			0
$787$	1.01630	−	1.76028i	0.0362272	−	0.0627473i	−0.847343	−	0.531045i	$-0.821799\pi$
$787$	1.01630	−	1.76028i	0.0362272	−	0.0627473i	0.883571	+	0.468298i	$0.155133\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−49.7645			−1.76942
$792$		0			0
$793$	41.7758			1.48350
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.10733	+	10.5782i	−0.216333	+	0.374699i	−0.953684	−	0.300810i	$-0.902743\pi$
$797$	−6.10733	+	10.5782i	−0.216333	+	0.374699i	0.737351	+	0.675510i	$0.236076\pi$
$798$		0			0
$799$	−1.74512	−	3.02263i	−0.0617378	−	0.106933i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−13.5122	−	23.4038i	−0.476836	−	0.825904i
$804$		0			0
$805$	15.4026	−	26.6780i	0.542869	−	0.940276i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	27.8097			0.977737			0.488869	−	0.872357i	$-0.337410\pi$
$809$	27.8097			0.977737			0.488869	+	0.872357i	$0.337410\pi$
$810$		0			0
$811$	9.24210			0.324534			0.162267	−	0.986747i	$-0.448119\pi$
$811$	9.24210			0.324534			0.162267	+	0.986747i	$0.448119\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.80380	−	15.2486i	0.308384	−	0.534136i
$816$		0			0
$817$	10.2854	+	17.8149i	0.359842	+	0.623264i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.22018	−	14.2378i	−0.286886	−	0.496901i	0.686179	−	0.727433i	$-0.259287\pi$
$821$	−8.22018	−	14.2378i	−0.286886	−	0.496901i	−0.973065	+	0.230532i	$0.925953\pi$
$822$		0			0
$823$	20.8503	−	36.1138i	0.726796	−	1.25885i	−0.231435	−	0.972850i	$-0.574342\pi$
$823$	20.8503	−	36.1138i	0.726796	−	1.25885i	0.958231	−	0.285996i	$-0.0923246\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.03875			−0.209988			−0.104994	−	0.994473i	$-0.533482\pi$
$827$	−6.03875			−0.209988			−0.104994	+	0.994473i	$0.533482\pi$
$828$		0			0
$829$	11.7973			0.409736			0.204868	−	0.978790i	$-0.434324\pi$
$829$	11.7973			0.409736			0.204868	+	0.978790i	$0.434324\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.52764	+	13.0383i	−0.260817	+	0.451749i
$834$		0			0
$835$	0.788888	+	1.36639i	0.0273006	+	0.0472860i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.88669	+	4.99990i	0.0996597	+	0.172616i	0.911544	−	0.411203i	$-0.134891\pi$
$839$	2.88669	+	4.99990i	0.0996597	+	0.172616i	−0.811884	+	0.583819i	$0.801558\pi$
$840$		0			0
$841$	12.7451	−	22.0752i	0.439487	−	0.761214i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.12555			−0.210725
$846$		0			0
$847$	−71.6159			−2.46075
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.84236	+	10.1193i	−0.200274	+	0.346884i
$852$		0			0
$853$	−4.18810	−	7.25401i	−0.143398	−	0.248372i	0.785376	−	0.619019i	$-0.212470\pi$
$853$	−4.18810	−	7.25401i	−0.143398	−	0.248372i	−0.928774	+	0.370646i	$0.879136\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.04677	−	7.00920i	−0.138235	−	0.239430i	0.788594	−	0.614915i	$-0.210810\pi$
$857$	−4.04677	−	7.00920i	−0.138235	−	0.239430i	−0.926829	+	0.375485i	$0.877476\pi$
$858$		0			0
$859$	−19.8503	+	34.3817i	−0.677283	+	1.17309i	0.298513	+	0.954406i	$0.403510\pi$
$859$	−19.8503	+	34.3817i	−0.677283	+	1.17309i	−0.975796	+	0.218683i	$0.929824\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	34.2524			1.16597			0.582983	−	0.812484i	$-0.301885\pi$
$863$	34.2524			1.16597			0.582983	+	0.812484i	$0.301885\pi$
$864$		0			0
$865$	21.4423			0.729061
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.89748	−	17.1429i	0.335749	−	0.581535i
$870$		0			0
$871$	4.74871	+	8.22501i	0.160904	+	0.278694i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.31980	−	4.01801i	−0.0784236	−	0.135834i
$876$		0			0
$877$	−21.3526	+	36.9837i	−0.721025	+	1.24885i	0.239564	+	0.970881i	$0.422995\pi$
$877$	−21.3526	+	36.9837i	−0.721025	+	1.24885i	−0.960589	+	0.277972i	$0.910338\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−8.80329			−0.296590			−0.148295	−	0.988943i	$-0.547379\pi$
$881$	−8.80329			−0.296590			−0.148295	+	0.988943i	$0.547379\pi$
$882$		0			0
$883$	16.5952			0.558472			0.279236	−	0.960223i	$-0.409919\pi$
$883$	16.5952			0.558472			0.279236	+	0.960223i	$0.409919\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.30159	−	5.71852i	0.110857	−	0.192009i	−0.805259	−	0.592923i	$-0.797974\pi$
$887$	3.30159	−	5.71852i	0.110857	−	0.192009i	0.916116	+	0.400914i	$0.131307\pi$
$888$		0			0
$889$	−1.77608	−	3.07626i	−0.0595677	−	0.103174i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.84404	−	11.8542i	−0.229027	−	0.396687i
$894$		0			0
$895$	8.67722	−	15.0294i	0.290048	−	0.502377i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.8816			−0.563032
$900$		0			0
$901$	9.22079			0.307189
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.0162	+	20.8126i	−0.399431	+	0.691834i
$906$		0			0
$907$	11.6423	+	20.1651i	0.386576	+	0.669570i	0.991987	−	0.126344i	$-0.0403243\pi$
$907$	11.6423	+	20.1651i	0.386576	+	0.669570i	−0.605410	+	0.795914i	$0.706991\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.1372	−	27.9505i	−0.534650	−	0.926040i	−0.999180	−	0.0404832i	$-0.987110\pi$
$911$	−16.1372	−	27.9505i	−0.534650	−	0.926040i	0.464531	−	0.885557i	$-0.346223\pi$
$912$		0			0
$913$	30.8390	−	53.4147i	1.02062	−	1.76777i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.92134			−0.294609
$918$		0			0
$919$	12.2816			0.405131			0.202566	−	0.979269i	$-0.435072\pi$
$919$	12.2816			0.405131			0.202566	+	0.979269i	$0.435072\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	18.5392	−	32.1109i	0.610226	−	1.05694i
$924$		0			0
$925$	0.879927	+	1.52408i	0.0289318	+	0.0501114i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.5325	−	49.4197i	−0.936120	−	1.62141i	−0.772625	−	0.634863i	$-0.781057\pi$
$929$	−28.5325	−	49.4197i	−0.936120	−	1.62141i	−0.163495	−	0.986544i	$-0.552277\pi$
$930$		0			0
$931$	−29.5221	+	51.1337i	−0.967546	+	1.67584i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.32895			0.174275
$936$		0			0
$937$	22.7487			0.743169			0.371585	−	0.928399i	$-0.378815\pi$
$937$	22.7487			0.743169			0.371585	+	0.928399i	$0.378815\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.1264	−	31.3959i	0.590905	−	1.02348i	−0.403205	−	0.915109i	$-0.632104\pi$
$941$	18.1264	−	31.3959i	0.590905	−	1.02348i	0.994111	−	0.108369i	$-0.0345627\pi$
$942$		0			0
$943$	11.1986	+	19.3966i	0.364677	+	0.631639i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.8257	−	41.2673i	−0.774230	−	1.34101i	−0.935226	−	0.354050i	$-0.884804\pi$
$947$	−23.8257	−	41.2673i	−0.774230	−	1.34101i	0.160996	−	0.986955i	$-0.448529\pi$
$948$		0			0
$949$	11.4931	−	19.9066i	0.373082	−	0.646197i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.4521			0.532935			0.266468	−	0.963844i	$-0.414143\pi$
$953$	16.4521			0.532935			0.266468	+	0.963844i	$0.414143\pi$
$954$		0			0
$955$	5.66372			0.183274
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.67423	+	11.5601i	−0.215522	+	0.373295i
$960$		0			0
$961$	−25.0996	−	43.4738i	−0.809664	−	1.40238i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.09520	−	5.36105i	−0.0996381	−	0.172578i
$966$		0			0
$967$	−30.0324	+	52.0177i	−0.965777	+	1.67278i	−0.258265	+	0.966074i	$0.583151\pi$
$967$	−30.0324	+	52.0177i	−0.965777	+	1.67278i	−0.707513	+	0.706701i	$0.750183\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.5189			0.690575			0.345288	−	0.938497i	$-0.387781\pi$
$971$	21.5189			0.690575			0.345288	+	0.938497i	$0.387781\pi$
$972$		0			0
$973$	71.2594			2.28447
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17.9570	−	31.1025i	0.574497	−	0.995057i	−0.421600	−	0.906782i	$-0.638531\pi$
$977$	17.9570	−	31.1025i	0.574497	−	0.995057i	0.996096	−	0.0882751i	$-0.0281355\pi$
$978$		0			0
$979$	3.81224	+	6.60300i	0.121840	+	0.211033i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.6111	+	20.1110i	0.370336	+	0.641441i	0.989617	−	0.143728i	$-0.0459091\pi$
$983$	11.6111	+	20.1110i	0.370336	+	0.641441i	−0.619281	+	0.785169i	$0.712576\pi$
$984$		0			0
$985$	3.64355	−	6.31081i	0.116093	−	0.201079i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	33.6017			1.06847
$990$		0			0
$991$	19.3020			0.613149			0.306575	−	0.951847i	$-0.400817\pi$
$991$	19.3020			0.613149			0.306575	+	0.951847i	$0.400817\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.15540	−	14.1256i	0.258543	−	0.447810i
$996$		0			0
$997$	16.9959	+	29.4378i	0.538267	+	0.932305i	0.998998	+	0.0447654i	$0.0142540\pi$
$997$	16.9959	+	29.4378i	0.538267	+	0.932305i	−0.460731	+	0.887540i	$0.652413\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4320.2.q.p.1441.5		10
3.2	odd	2		1440.2.q.p.481.3	yes	10
4.3	odd	2		4320.2.q.o.1441.1		10
9.2	odd	6		1440.2.q.p.961.3	yes	10
9.7	even	3	inner	4320.2.q.p.2881.5		10
12.11	even	2		1440.2.q.o.481.3	✓	10
36.7	odd	6		4320.2.q.o.2881.1		10
36.11	even	6		1440.2.q.o.961.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.o.481.3	✓	10	12.11	even	2
1440.2.q.o.961.3	yes	10	36.11	even	6
1440.2.q.p.481.3	yes	10	3.2	odd	2
1440.2.q.p.961.3	yes	10	9.2	odd	6
4320.2.q.o.1441.1		10	4.3	odd	2
4320.2.q.o.2881.1		10	36.7	odd	6
4320.2.q.p.1441.5		10	1.1	even	1	trivial
4320.2.q.p.2881.5		10	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4320 = 2^{5} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4320.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +(2.57079 + 4.45273i) q^{11} +(-2.18664 + 3.78737i) q^{13} +1.03644 q^{17} +4.06474 q^{19} +(3.31980 - 5.75006i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.936714 + 1.62244i) q^{29} +(-4.50553 + 7.80381i) q^{31} +4.63960 q^{35} -1.75985 q^{37} +(-1.68664 + 2.92134i) q^{41} +(2.53040 + 4.38278i) q^{43} +(-1.68376 - 2.91635i) q^{47} +(-7.26295 + 12.5798i) q^{49} +8.89657 q^{53} +5.14157 q^{55} +(5.20289 - 9.01167i) q^{59} +(-4.77625 - 8.27272i) q^{61} +(2.18664 + 3.78737i) q^{65} +(1.08585 - 1.88074i) q^{67} -8.47841 q^{71} -5.25606 q^{73} +(-11.9274 + 20.6589i) q^{77} +(-1.92499 - 3.33418i) q^{79} +(-5.99797 - 10.3888i) q^{83} +(0.518221 - 0.897586i) q^{85} +1.48291 q^{89} -20.2903 q^{91} +(2.03237 - 3.52017i) q^{95} +(6.61291 + 11.4539i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{5}+O(q^{10}) \) 10 * q + 5 * q^5	\( 10 q + 5 q^{5} + 9 q^{11} - 4 q^{13} - 6 q^{17} + 14 q^{19} + 10 q^{23} - 5 q^{25} + 2 q^{29} - 8 q^{31} + 16 q^{37} + q^{41} - q^{43} + 10 q^{47} - q^{49} + 20 q^{53} + 18 q^{55} + 13 q^{59} - 14 q^{61} + 4 q^{65} - 15 q^{67} - 32 q^{71} - 14 q^{73} - 12 q^{77} - 18 q^{79} - 8 q^{83} - 3 q^{85} - 28 q^{89} - 36 q^{91} + 7 q^{95} + 17 q^{97}+O(q^{100}) \) 10 * q + 5 * q^5 + 9 * q^11 - 4 * q^13 - 6 * q^17 + 14 * q^19 + 10 * q^23 - 5 * q^25 + 2 * q^29 - 8 * q^31 + 16 * q^37 + q^41 - q^43 + 10 * q^47 - q^49 + 20 * q^53 + 18 * q^55 + 13 * q^59 - 14 * q^61 + 4 * q^65 - 15 * q^67 - 32 * q^71 - 14 * q^73 - 12 * q^77 - 18 * q^79 - 8 * q^83 - 3 * q^85 - 28 * q^89 - 36 * q^91 + 7 * q^95 + 17 * q^97

Introduction

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