LMFDB - Embedded newform 4320.2.q.o.2881.1

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			2881.1
Root			$-1.41743 + 0.995434i$ of defining polynomial
Character	$\chi$	$=$	4320.2881
Dual form			4320.2.q.o.1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{5} +(-2.31980 + 4.01801i) q^{7} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{5} +(-2.31980 + 4.01801i) q^{7} +(-2.57079 + 4.45273i) q^{11} +(-2.18664 - 3.78737i) q^{13} +1.03644 q^{17} -4.06474 q^{19} +(-3.31980 - 5.75006i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.936714 - 1.62244i) q^{29} +(4.50553 + 7.80381i) q^{31} -4.63960 q^{35} -1.75985 q^{37} +(-1.68664 - 2.92134i) q^{41} +(-2.53040 + 4.38278i) q^{43} +(1.68376 - 2.91635i) q^{47} +(-7.26295 - 12.5798i) q^{49} +8.89657 q^{53} -5.14157 q^{55} +(-5.20289 - 9.01167i) q^{59} +(-4.77625 + 8.27272i) q^{61} +(2.18664 - 3.78737i) q^{65} +(-1.08585 - 1.88074i) q^{67} +8.47841 q^{71} -5.25606 q^{73} +(-11.9274 - 20.6589i) q^{77} +(1.92499 - 3.33418i) q^{79} +(5.99797 - 10.3888i) q^{83} +(0.518221 + 0.897586i) q^{85} +1.48291 q^{89} +20.2903 q^{91} +(-2.03237 - 3.52017i) q^{95} +(6.61291 - 11.4539i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/4320\mathbb{Z}\right)^\times$.

$n$	$2081$	$2431$	$3457$	$3781$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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	−0.0219721	+	0.999759i	$0.506995\pi$
$7$	−2.31980	+	4.01801i	−0.876802	+	1.51867i	−0.854830	+	0.518908i	$0.826339\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.57079	+	4.45273i	−0.775121	+	1.34255i	0.159605	+	0.987181i	$0.448978\pi$
$11$	−2.57079	+	4.45273i	−0.775121	+	1.34255i	−0.934726	+	0.355369i	$0.884355\pi$
$12$		0			0
$13$	−2.18664	−	3.78737i	−0.606464	−	1.05043i	−0.991818	−	0.127658i	$-0.959254\pi$
$13$	−2.18664	−	3.78737i	−0.606464	−	1.05043i	0.385354	−	0.922769i	$-0.374079\pi$
$14$		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	$-0.654398\pi$
$19$	−4.06474			−0.932516			−0.466258	+	0.884649i	$0.654398\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.31980	−	5.75006i	−0.692226	−	1.19897i	−0.971107	−	0.238645i	$-0.923297\pi$
$23$	−3.31980	−	5.75006i	−0.692226	−	1.19897i	0.278880	−	0.960326i	$-0.410037\pi$
$24$		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	−0.765852	−	0.643017i	$-0.777682\pi$
$29$	0.936714	−	1.62244i	0.173943	−	0.301279i	0.939795	+	0.341738i	$0.111016\pi$
$30$		0			0
$31$	4.50553	+	7.80381i	0.809217	+	1.40160i	0.913407	+	0.407047i	$0.133442\pi$
$31$	4.50553	+	7.80381i	0.809217	+	1.40160i	−0.104190	+	0.994557i	$0.533225\pi$
$32$		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	0.703737	−	0.710461i	$-0.251513\pi$
$41$	−1.68664	−	2.92134i	−0.263409	−	0.456237i	−0.967145	+	0.254224i	$0.918180\pi$
$42$		0			0
$43$	−2.53040	+	4.38278i	−0.385883	+	0.668368i	−0.991891	−	0.127090i	$-0.959436\pi$
$43$	−2.53040	+	4.38278i	−0.385883	+	0.668368i	0.606009	+	0.795458i	$0.292770\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.68376	−	2.91635i	0.245601	−	0.425394i	−0.716699	−	0.697382i	$-0.754348\pi$
$47$	1.68376	−	2.91635i	0.245601	−	0.425394i	0.962300	+	0.271989i	$0.0876813\pi$
$48$		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	−0.975774	−	0.218783i	$-0.929791\pi$
$59$	−5.20289	−	9.01167i	−0.677358	−	1.17322i	0.298415	−	0.954436i	$-0.403542\pi$
$60$		0			0
$61$	−4.77625	+	8.27272i	−0.611537	+	1.05921i	0.379445	+	0.925214i	$0.376115\pi$
$61$	−4.77625	+	8.27272i	−0.611537	+	1.05921i	−0.990982	+	0.133998i	$0.957218\pi$
$62$		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	$-0.209018\pi$
$67$	−1.08585	−	1.88074i	−0.132657	−	0.229769i	−0.924700	+	0.380696i	$0.875684\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.47841			1.00620			0.503101	−	0.864228i	$-0.332192\pi$
$71$	8.47841			1.00620			0.503101	+	0.864228i	$0.332192\pi$
$72$		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	$-0.763844\pi$
$79$	1.92499	−	3.33418i	0.216578	−	0.375125i	0.953760	+	0.300570i	$0.0971770\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.99797	−	10.3888i	0.658363	−	1.14032i	−0.322677	−	0.946509i	$-0.604583\pi$
$83$	5.99797	−	10.3888i	0.658363	−	1.14032i	0.981039	−	0.193808i	$-0.0620840\pi$
$84$		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	−0.306057	−	0.952013i	$-0.599010\pi$
$97$	6.61291	−	11.4539i	0.671439	−	1.16297i	0.977496	−	0.210954i	$-0.0676570\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.40790	+	11.0988i	−0.637610	+	1.10437i	0.348346	+	0.937366i	$0.386743\pi$
$101$	−6.40790	+	11.0988i	−0.637610	+	1.10437i	−0.985956	+	0.167007i	$0.946590\pi$
$102$		0			0
$103$	8.60854	+	14.9104i	0.848224	+	1.46917i	0.882791	+	0.469765i	$0.155661\pi$
$103$	8.60854	+	14.9104i	0.848224	+	1.46917i	−0.0345670	+	0.999402i	$0.511005\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.4323			1.29855			0.649273	−	0.760556i	$-0.275073\pi$
$107$	13.4323			1.29855			0.649273	+	0.760556i	$0.275073\pi$
$108$		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	−0.999986	−	0.00521530i	$-0.998340\pi$
$113$	−5.36301	−	9.28901i	−0.504510	−	0.873837i	0.495477	−	0.868621i	$-0.334993\pi$
$114$		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	$-0.489185\pi$
$127$	0.765616			0.0679374			0.0339687	+	0.999423i	$0.489185\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.961434	+	1.66525i	0.0840009	+	0.145494i	0.904965	−	0.425486i	$-0.139897\pi$
$131$	0.961434	+	1.66525i	0.0840009	+	0.145494i	−0.820964	+	0.570980i	$0.806563\pi$
$132$		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	−0.798009	−	0.602646i	$-0.794113\pi$
$137$	1.43853	−	2.49161i	0.122902	−	0.212873i	0.920911	+	0.389773i	$0.127447\pi$
$138$		0			0
$139$	−7.67948	−	13.3012i	−0.651365	−	1.12820i	−0.982792	−	0.184716i	$-0.940864\pi$
$139$	−7.67948	−	13.3012i	−0.651365	−	1.12820i	0.331427	−	0.943481i	$-0.392470\pi$
$140$		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	0.953456	−	0.301533i	$-0.0974983\pi$
$149$	2.63164	+	4.55814i	0.215593	+	0.373418i	−0.737863	+	0.674950i	$0.764165\pi$
$150$		0			0
$151$	6.80830	−	11.7923i	0.554051	−	0.959645i	−0.443925	−	0.896064i	$-0.646414\pi$
$151$	6.80830	−	11.7923i	0.554051	−	0.959645i	0.997977	−	0.0635814i	$-0.0202523\pi$
$152$		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	0.994111	+	0.108362i	$0.0345606\pi$
$157$	7.40396	+	12.8240i	0.590900	+	1.02347i	−0.403211	+	0.915107i	$0.632106\pi$
$158$		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	$-0.742199\pi$
$163$	−17.6076			−1.37913			−0.689567	+	0.724222i	$0.742199\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.788888	+	1.36639i	0.0610459	+	0.105735i	0.894933	−	0.446200i	$-0.147223\pi$
$167$	0.788888	+	1.36639i	0.0610459	+	0.105735i	−0.833887	+	0.551935i	$0.813890\pi$
$168$		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	−0.0941297	−	0.995560i	$-0.530007\pi$
$173$	10.7212	−	18.5696i	0.815115	−	1.41182i	0.909245	−	0.416261i	$-0.136660\pi$
$174$		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	$-0.724631\pi$
$179$	−17.3544			−1.29713			−0.648566	+	0.761158i	$0.724631\pi$
$180$		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	$-0.899022\pi$
$191$	−2.83186	+	4.90493i	−0.204906	+	0.354908i	0.745197	+	0.666845i	$0.232356\pi$
$192$		0			0
$193$	3.09520	+	5.36105i	0.222797	+	0.385897i	0.955656	−	0.294484i	$-0.0951478\pi$
$193$	3.09520	+	5.36105i	0.222797	+	0.385897i	−0.732859	+	0.680381i	$0.761814\pi$
$194$		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	$-0.696214\pi$
$199$	−16.3108			−1.15624			−0.578121	+	0.815951i	$0.696214\pi$
$200$		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	−0.916659	−	0.399670i	$-0.869125\pi$
$211$	−11.6854	−	20.2396i	−0.804454	−	1.39335i	0.112205	−	0.993685i	$-0.464209\pi$
$212$		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	$-0.857250\pi$
$223$	−1.12098	+	1.94160i	−0.0750666	+	0.130019i	0.826049	+	0.563599i	$0.190584\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.48880	−	2.57867i	0.0988150	−	0.171153i	−0.812379	−	0.583129i	$-0.801828\pi$
$227$	1.48880	−	2.57867i	0.0988150	−	0.171153i	0.911194	+	0.411977i	$0.135161\pi$
$228$		0			0
$229$	−13.5205	−	23.4182i	−0.893460	−	1.54752i	−0.835699	−	0.549188i	$-0.814937\pi$
$229$	−13.5205	−	23.4182i	−0.893460	−	1.54752i	−0.0577615	−	0.998330i	$-0.518396\pi$
$230$		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	$-0.0599186\pi$
$239$	5.08789	+	8.81248i	0.329108	+	0.570032i	−0.653227	+	0.757162i	$0.726585\pi$
$240$		0			0
$241$	6.56639	−	11.3733i	0.422978	−	0.732620i	−0.573251	−	0.819380i	$-0.694318\pi$
$241$	6.56639	−	11.3733i	0.422978	−	0.732620i	0.996229	+	0.0867601i	$0.0276514\pi$
$242$		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	$-0.692061\pi$
$251$	−17.9795			−1.13486			−0.567428	+	0.823423i	$0.692061\pi$
$252$		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	0.802888	+	0.596130i	$0.203296\pi$
$257$	14.7120	+	25.4819i	0.917708	+	1.58952i	0.114820	+	0.993386i	$0.463371\pi$
$258$		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	0.344963	+	0.938616i	$0.387891\pi$
$263$	−10.3853	+	17.9878i	−0.640384	+	1.10918i	−0.985347	+	0.170561i	$0.945442\pi$
$264$		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	$-0.373423\pi$
$271$	12.7500			0.774509			0.387255	+	0.921973i	$0.373423\pi$
$272$		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	−0.797179	−	0.603742i	$-0.793676\pi$
$277$	2.06821	−	3.58224i	0.124267	−	0.215236i	0.921446	+	0.388506i	$0.127009\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.784699	−	1.35914i	0.0468112	−	0.0810794i	−0.841670	−	0.539992i	$-0.818427\pi$
$281$	0.784699	−	1.35914i	0.0468112	−	0.0810794i	0.888482	+	0.458912i	$0.151761\pi$
$282$		0			0
$283$	1.78533	+	3.09228i	0.106127	+	0.183817i	0.914198	−	0.405268i	$-0.132822\pi$
$283$	1.78533	+	3.09228i	0.106127	+	0.183817i	−0.808071	+	0.589085i	$0.799488\pi$
$284$		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	−0.982690	−	0.185260i	$-0.940687\pi$
$293$	−11.1568	−	19.3241i	−0.651784	−	1.12892i	0.330905	−	0.943664i	$-0.392646\pi$
$294$		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	$-0.662830\pi$
$307$	−17.1543			−0.979050			−0.489525	+	0.871989i	$0.662830\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.24224	−	9.07983i	−0.297260	−	0.514870i	0.678248	−	0.734833i	$-0.262740\pi$
$311$	−5.24224	−	9.07983i	−0.297260	−	0.514870i	−0.975508	+	0.219963i	$0.929406\pi$
$312$		0			0
$313$	−8.49522	+	14.7141i	−0.480178	+	0.831693i	−0.999741	−	0.0227392i	$-0.992761\pi$
$313$	−8.49522	+	14.7141i	−0.480178	+	0.831693i	0.519563	+	0.854432i	$0.326095\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.28206	−	10.8809i	0.352836	−	0.611130i	−0.633909	−	0.773407i	$-0.718551\pi$
$317$	6.28206	−	10.8809i	0.352836	−	0.611130i	0.986745	+	0.162278i	$0.0518841\pi$
$318$		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	0.279509	+	0.960143i	$0.409828\pi$
$331$	−12.5854	+	21.7985i	−0.691754	+	1.19815i	−0.971263	+	0.238010i	$0.923505\pi$
$332$		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	0.746509	−	0.665376i	$-0.231729\pi$
$337$	−3.72618	−	6.45394i	−0.202978	−	0.351568i	−0.949487	+	0.313807i	$0.898395\pi$
$338$		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	−0.999308	−	0.0371987i	$-0.988157\pi$
$347$	−9.90762	−	17.1605i	−0.531869	−	0.921224i	0.467439	−	0.884025i	$-0.345177\pi$
$348$		0			0
$349$	−3.25642	+	5.64029i	−0.174312	+	0.301918i	−0.939923	−	0.341386i	$-0.889104\pi$
$349$	−3.25642	+	5.64029i	−0.174312	+	0.301918i	0.765611	+	0.643304i	$0.222437\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.5162	−	18.2145i	0.559719	−	0.969461i	−0.437801	−	0.899072i	$-0.644243\pi$
$353$	10.5162	−	18.2145i	0.559719	−	0.969461i	0.997520	−	0.0703891i	$-0.0224241\pi$
$354$		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	$-0.138763\pi$
$359$	34.3505			1.81295			0.906475	+	0.422259i	$0.138763\pi$
$360$		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	$-0.997769\pi$
$367$	−9.46211	+	16.3889i	−0.493918	+	0.855491i	0.506057	+	0.862500i	$0.331102\pi$
$368$		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	−0.935007	−	0.354628i	$-0.884608\pi$
$373$	−14.9604	−	25.9122i	−0.774621	−	1.34168i	0.160387	−	0.987054i	$-0.448726\pi$
$374$		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	$-0.680610\pi$
$379$	−20.9258			−1.07489			−0.537443	+	0.843300i	$0.680610\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.52065	−	7.82999i	−0.230994	−	0.400094i	0.727107	−	0.686525i	$-0.240865\pi$
$383$	−4.52065	−	7.82999i	−0.230994	−	0.400094i	−0.958101	+	0.286431i	$0.907531\pi$
$384$		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	−0.770417	−	0.637540i	$-0.779952\pi$
$389$	3.29213	−	5.70214i	0.166918	−	0.289110i	0.937335	+	0.348431i	$0.113285\pi$
$390$		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	0.767032	−	0.641609i	$-0.221733\pi$
$401$	−3.44698	−	5.97034i	−0.172134	−	0.298145i	−0.939166	+	0.343464i	$0.888399\pi$
$402$		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	0.674906	+	0.737904i	$0.264184\pi$
$409$	19.7484	+	34.2053i	0.976496	+	1.69134i	0.301591	+	0.953437i	$0.402482\pi$
$410$		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	−0.803460	−	0.595359i	$-0.797010\pi$
$419$	−18.7772	−	32.5231i	−0.917326	−	1.58886i	−0.113866	−	0.993496i	$-0.536324\pi$
$420$		0			0
$421$	−11.5064	+	19.9297i	−0.560788	+	0.971313i	0.436640	+	0.899636i	$0.356168\pi$
$421$	−11.5064	+	19.9297i	−0.560788	+	0.971313i	−0.997428	+	0.0716768i	$0.977165\pi$
$422$		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	$-0.583051\pi$
$431$	−10.7109			−0.515924			−0.257962	+	0.966155i	$0.583051\pi$
$432$		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	$-0.982464\pi$
$439$	−9.46116	+	16.3872i	−0.451557	+	0.782119i	0.546926	+	0.837181i	$0.315798\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.9593	+	22.4461i	−0.615714	+	1.06645i	0.374545	+	0.927209i	$0.377799\pi$
$443$	−12.9593	+	22.4461i	−0.615714	+	1.06645i	−0.990259	+	0.139239i	$0.955534\pi$
$444$		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	0.235484	−	0.971878i	$-0.424332\pi$
$457$	20.5099	−	35.5242i	0.959413	−	1.66175i	0.723929	−	0.689874i	$-0.242334\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.378678	+	0.655890i	−0.0176368	+	0.0305478i	−0.874709	−	0.484648i	$-0.838948\pi$
$461$	−0.378678	+	0.655890i	−0.0176368	+	0.0305478i	0.857072	+	0.515196i	$0.172281\pi$
$462$		0			0
$463$	−15.1949	−	26.3183i	−0.706166	−	1.22311i	−0.966269	−	0.257534i	$-0.917090\pi$
$463$	−15.1949	−	26.3183i	−0.706166	−	1.22311i	0.260103	−	0.965581i	$-0.416243\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.41191			0.111610			0.0558049	−	0.998442i	$-0.482228\pi$
$467$	2.41191			0.111610			0.0558049	+	0.998442i	$0.482228\pi$
$468$		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	−0.142436	−	0.989804i	$-0.545494\pi$
$479$	17.2020	−	29.7947i	0.785977	−	1.36135i	0.928413	−	0.371549i	$-0.121173\pi$
$480$		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	$-0.625266\pi$
$487$	−16.9242			−0.766909			−0.383455	+	0.923560i	$0.625266\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.41686	−	11.1143i	−0.289589	−	0.501582i	0.684123	−	0.729367i	$-0.260185\pi$
$491$	−6.41686	−	11.1143i	−0.289589	−	0.501582i	−0.973712	+	0.227784i	$0.926852\pi$
$492$		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	$-0.0295511\pi$
$499$	9.32764	+	16.1559i	0.417563	+	0.723240i	−0.578131	+	0.815944i	$0.696218\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	25.4535			1.13492			0.567458	−	0.823402i	$-0.307927\pi$
$503$	25.4535			1.13492			0.567458	+	0.823402i	$0.307927\pi$
$504$		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	0.963650	−	0.267168i	$-0.0860880\pi$
$509$	5.65042	+	9.78681i	0.250450	+	0.433793i	−0.713199	+	0.700961i	$0.752755\pi$
$510$		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	$-0.476003\pi$
$523$	3.44488			0.150634			0.0753171	+	0.997160i	$0.476003\pi$
$524$		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	$-0.812197\pi$
$547$	1.55190	−	2.68797i	0.0663544	−	0.114929i	0.897294	+	0.441434i	$0.145530\pi$
$548$		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	$-0.195899\pi$
$563$	−2.17598	−	3.76890i	−0.0917065	−	0.158840i	−0.908229	+	0.418473i	$0.862565\pi$
$564$		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	−0.445928	−	0.895069i	$-0.647126\pi$
$569$	13.1717	−	22.8141i	0.552188	−	0.956418i	0.998116	−	0.0613492i	$-0.0195403\pi$
$570$		0			0
$571$	−1.85712	−	3.21662i	−0.0777180	−	0.134612i	0.824547	−	0.565793i	$-0.191430\pi$
$571$	−1.85712	−	3.21662i	−0.0777180	−	0.134612i	−0.902265	+	0.431182i	$0.858097\pi$
$572$		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	$-0.921960\pi$
$587$	−6.65897	+	11.5337i	−0.274845	+	0.476045i	0.695251	+	0.718767i	$0.255293\pi$
$588$		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	$-0.103710\pi$
$599$	4.80917	+	8.32974i	0.196498	+	0.340344i	−0.750893	+	0.660424i	$0.770377\pi$
$600$		0			0
$601$	−2.33420	+	4.04295i	−0.0952139	+	0.164915i	−0.909698	−	0.415271i	$-0.863687\pi$
$601$	−2.33420	+	4.04295i	−0.0952139	+	0.164915i	0.814484	+	0.580186i	$0.197020\pi$
$602$		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	$-0.124917\pi$
$607$	3.22217	+	5.58096i	0.130784	+	0.226524i	−0.793195	+	0.608968i	$0.791584\pi$
$608$		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	0.802542	−	0.596595i	$-0.203480\pi$
$617$	−2.86636	−	4.96468i	−0.115395	−	0.199870i	−0.917938	+	0.396725i	$0.870147\pi$
$618$		0			0
$619$	9.08484	−	15.7354i	0.365151	−	0.632459i	−0.623650	−	0.781704i	$-0.714351\pi$
$619$	9.08484	−	15.7354i	0.365151	−	0.632459i	0.988800	+	0.149244i	$0.0476841\pi$
$620$		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	$-0.638589\pi$
$631$	−21.1892			−0.843528			−0.421764	+	0.906706i	$0.638589\pi$
$632$		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	−0.0851952	+	0.996364i	$0.527151\pi$
$641$	−22.9248	+	39.7069i	−0.905474	+	1.56833i	−0.820279	+	0.571963i	$0.806182\pi$
$642$		0			0
$643$	−14.2494	−	24.6807i	−0.561942	−	0.973311i	−0.997327	−	0.0730672i	$-0.976721\pi$
$643$	−14.2494	−	24.6807i	−0.561942	−	0.973311i	0.435385	−	0.900244i	$-0.356612\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	32.9396			1.29499			0.647494	−	0.762070i	$-0.275817\pi$
$647$	32.9396			1.29499			0.647494	+	0.762070i	$0.275817\pi$
$648$		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	0.913685	−	0.406424i	$-0.133224\pi$
$653$	2.67981	+	4.64157i	0.104869	+	0.181639i	−0.808816	+	0.588062i	$0.799891\pi$
$654$		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	$-0.738042\pi$
$659$	7.57080	−	13.1130i	0.294916	−	0.510810i	0.974965	+	0.222357i	$0.0713749\pi$
$660$		0			0
$661$	−2.15422	−	3.73121i	−0.0837893	−	0.145127i	0.821085	−	0.570805i	$-0.193369\pi$
$661$	−2.15422	−	3.73121i	−0.0837893	−	0.145127i	−0.904875	+	0.425678i	$0.860036\pi$
$662$		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	−0.605618	−	0.795756i	$-0.707074\pi$
$673$	10.0224	−	17.3593i	0.386336	−	0.669153i	0.991954	+	0.126603i	$0.0404073\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.3326	+	23.0928i	−0.512415	+	0.887529i	0.487481	+	0.873134i	$0.337916\pi$
$677$	−13.3326	+	23.0928i	−0.512415	+	0.887529i	−0.999896	+	0.0143957i	$0.995418\pi$
$678$		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	$-0.660150\pi$
$683$	−25.2021			−0.964331			−0.482166	+	0.876080i	$0.660150\pi$
$684$		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	$-0.744105\pi$
$691$	7.27258	−	12.5965i	0.276662	−	0.479193i	0.970553	+	0.240887i	$0.0774384\pi$
$692$		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	0.410215	+	0.911989i	$0.365454\pi$
$709$	−15.5688	+	26.9659i	−0.584698	+	1.01273i	−0.994913	+	0.100738i	$0.967880\pi$
$710$		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	$-0.695592\pi$
$719$	−30.9181			−1.15305			−0.576525	+	0.817080i	$0.695592\pi$
$720$		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	$-0.938640\pi$
$727$	−8.75834	+	15.1699i	−0.324829	+	0.562620i	0.656649	+	0.754197i	$0.271973\pi$
$728$		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	0.991163	+	0.132652i	$0.0423492\pi$
$733$	16.5276	+	28.6267i	0.610461	+	1.05735i	−0.380701	+	0.924698i	$0.624317\pi$
$734$		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	$-0.405431\pi$
$739$	15.9164			0.585493			0.292747	+	0.956190i	$0.405431\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.97902	−	13.8201i	−0.292722	−	0.507009i	0.681730	−	0.731604i	$-0.261228\pi$
$743$	−7.97902	−	13.8201i	−0.292722	−	0.507009i	−0.974452	+	0.224594i	$0.927894\pi$
$744$		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	$-0.259367\pi$
$751$	−7.86854	−	13.6287i	−0.287127	−	0.497319i	−0.973123	+	0.230287i	$0.926034\pi$
$752$		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	0.969217	−	0.246207i	$-0.0791844\pi$
$761$	7.48654	+	12.9671i	0.271387	+	0.470056i	−0.697830	+	0.716263i	$0.745851\pi$
$762$		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	0.854517	−	0.519424i	$-0.173854\pi$
$769$	−0.626060	−	1.08437i	−0.0225763	−	0.0391033i	−0.877093	+	0.480321i	$0.840520\pi$
$770$		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	$-0.178201\pi$
$787$	−1.01630	−	1.76028i	−0.0362272	−	0.0627473i	−0.883571	+	0.468298i	$0.844867\pi$
$788$		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	0.737351	−	0.675510i	$-0.236076\pi$
$797$	−6.10733	−	10.5782i	−0.216333	−	0.374699i	−0.953684	+	0.300810i	$0.902743\pi$
$798$		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	$-0.551881\pi$
$811$	−9.24210			−0.324534			−0.162267	+	0.986747i	$0.551881\pi$
$812$		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	−0.973065	−	0.230532i	$-0.925953\pi$
$821$	−8.22018	+	14.2378i	−0.286886	+	0.496901i	0.686179	+	0.727433i	$0.259287\pi$
$822$		0			0
$823$	−20.8503	−	36.1138i	−0.726796	−	1.25885i	−0.958231	−	0.285996i	$-0.907675\pi$
$823$	−20.8503	−	36.1138i	−0.726796	−	1.25885i	0.231435	−	0.972850i	$-0.425658\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.03875			0.209988			0.104994	−	0.994473i	$-0.466518\pi$
$827$	6.03875			0.209988			0.104994	+	0.994473i	$0.466518\pi$
$828$		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	$-0.865109\pi$
$839$	−2.88669	+	4.99990i	−0.0996597	+	0.172616i	0.811884	+	0.583819i	$0.198442\pi$
$840$		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	−0.928774	−	0.370646i	$-0.879136\pi$
$853$	−4.18810	+	7.25401i	−0.143398	+	0.248372i	0.785376	+	0.619019i	$0.212470\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.04677	+	7.00920i	−0.138235	+	0.239430i	−0.926829	−	0.375485i	$-0.877476\pi$
$857$	−4.04677	+	7.00920i	−0.138235	+	0.239430i	0.788594	+	0.614915i	$0.210810\pi$
$858$		0			0
$859$	19.8503	+	34.3817i	0.677283	+	1.17309i	0.975796	+	0.218683i	$0.0701762\pi$
$859$	19.8503	+	34.3817i	0.677283	+	1.17309i	−0.298513	+	0.954406i	$0.596490\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−34.2524			−1.16597			−0.582983	−	0.812484i	$-0.698115\pi$
$863$	−34.2524			−1.16597			−0.582983	+	0.812484i	$0.698115\pi$
$864$		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	−0.960589	−	0.277972i	$-0.910338\pi$
$877$	−21.3526	−	36.9837i	−0.721025	−	1.24885i	0.239564	−	0.970881i	$-0.422995\pi$
$878$		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	$-0.590081\pi$
$883$	−16.5952			−0.558472			−0.279236	+	0.960223i	$0.590081\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.30159	−	5.71852i	−0.110857	−	0.192009i	0.805259	−	0.592923i	$-0.202026\pi$
$887$	−3.30159	−	5.71852i	−0.110857	−	0.192009i	−0.916116	+	0.400914i	$0.868693\pi$
$888$		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	$-0.959676\pi$
$907$	−11.6423	+	20.1651i	−0.386576	+	0.669570i	0.605410	+	0.795914i	$0.293009\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	16.1372	−	27.9505i	0.534650	−	0.926040i	−0.464531	−	0.885557i	$-0.653777\pi$
$911$	16.1372	−	27.9505i	0.534650	−	0.926040i	0.999180	−	0.0404832i	$-0.0128897\pi$
$912$		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	$-0.564928\pi$
$919$	−12.2816			−0.405131			−0.202566	+	0.979269i	$0.564928\pi$
$920$		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	−0.163495	+	0.986544i	$0.552277\pi$
$929$	−28.5325	+	49.4197i	−0.936120	+	1.62141i	−0.772625	+	0.634863i	$0.781057\pi$
$930$		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	0.994111	+	0.108369i	$0.0345627\pi$
$941$	18.1264	+	31.3959i	0.590905	+	1.02348i	−0.403205	+	0.915109i	$0.632104\pi$
$942$		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	−0.160996	−	0.986955i	$-0.551471\pi$
$947$	23.8257	−	41.2673i	0.774230	−	1.34101i	0.935226	−	0.354050i	$-0.115196\pi$
$948$		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	0.707513	+	0.706701i	$0.249817\pi$
$967$	30.0324	+	52.0177i	0.965777	+	1.67278i	0.258265	+	0.966074i	$0.416849\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−21.5189			−0.690575			−0.345288	−	0.938497i	$-0.612219\pi$
$971$	−21.5189			−0.690575			−0.345288	+	0.938497i	$0.612219\pi$
$972$		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	0.996096	+	0.0882751i	$0.0281355\pi$
$977$	17.9570	+	31.1025i	0.574497	+	0.995057i	−0.421600	+	0.906782i	$0.638531\pi$
$978$		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	$-0.954091\pi$
$983$	−11.6111	+	20.1110i	−0.370336	+	0.641441i	0.619281	+	0.785169i	$0.287424\pi$
$984$		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	$-0.599183\pi$
$991$	−19.3020			−0.613149			−0.306575	+	0.951847i	$0.599183\pi$
$992$		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	−0.460731	−	0.887540i	$-0.652413\pi$
$997$	16.9959	−	29.4378i	0.538267	−	0.932305i	0.998998	−	0.0447654i	$-0.0142540\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.o.481.3	✓	10	9.5	odd	6
1440.2.q.o.961.3	yes	10	3.2	odd	2
1440.2.q.p.481.3	yes	10	36.23	even	6
1440.2.q.p.961.3	yes	10	12.11	even	2
4320.2.q.o.1441.1		10	9.4	even	3	inner
4320.2.q.o.2881.1		10	1.1	even	1	trivial
4320.2.q.p.1441.5		10	36.31	odd	6
4320.2.q.p.2881.5		10	4.3	odd	2

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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