LMFDB - Embedded newform 3240.2.q.be.2161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3240,2,Mod(1081,3240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3240, 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("3240.1081");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3240 = 2^{3} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3240.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:	$25.8715302549$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2161.1
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	3240.2161
Dual form			3240.2.q.be.1081.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{5} +(-2.13746 + 3.70219i) q^{7} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{5} +(-2.13746 + 3.70219i) q^{7} +(-0.637459 + 1.10411i) q^{11} +(-3.13746 - 5.43424i) q^{13} -2.00000 q^{17} +1.00000 q^{19} +(0.137459 + 0.238085i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.637459 + 1.10411i) q^{29} +(0.637459 + 1.10411i) q^{31} -4.27492 q^{35} +4.54983 q^{37} +(-3.77492 - 6.53835i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(3.13746 - 5.43424i) q^{47} +(-5.63746 - 9.76436i) q^{49} -8.27492 q^{53} -1.27492 q^{55} +(-6.50000 - 11.2583i) q^{59} +(3.27492 - 5.67232i) q^{61} +(3.13746 - 5.43424i) q^{65} +(7.27492 + 12.6005i) q^{67} +0.725083 q^{71} -15.0997 q^{73} +(-2.72508 - 4.71998i) q^{77} +(2.27492 - 3.94027i) q^{79} +(6.27492 - 10.8685i) q^{83} +(-1.00000 - 1.73205i) q^{85} +9.82475 q^{89} +26.8248 q^{91} +(0.500000 + 0.866025i) q^{95} +(-8.00000 + 13.8564i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - q^7	$ 4 q + 2 q^{5} - q^{7} + 5 q^{11} - 5 q^{13} - 8 q^{17} + 4 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 5 q^{31} - 2 q^{35} - 12 q^{37} - 8 q^{43} + 5 q^{47} - 15 q^{49} - 18 q^{53} + 10 q^{55} - 26 q^{59} - 2 q^{61} + 5 q^{65} + 14 q^{67} + 18 q^{71} - 26 q^{77} - 6 q^{79} + 10 q^{83} - 4 q^{85} - 6 q^{89} + 62 q^{91} + 2 q^{95} - 32 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - q^7 + 5 * q^11 - 5 * q^13 - 8 * q^17 + 4 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 5 * q^31 - 2 * q^35 - 12 * q^37 - 8 * q^43 + 5 * q^47 - 15 * q^49 - 18 * q^53 + 10 * q^55 - 26 * q^59 - 2 * q^61 + 5 * q^65 + 14 * q^67 + 18 * q^71 - 26 * q^77 - 6 * q^79 + 10 * q^83 - 4 * q^85 - 6 * q^89 + 62 * q^91 + 2 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times$.

$n$	$1297$	$1621$	$2431$	$3161$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−2.13746	+	3.70219i	−0.807883	+	1.39930i	0.106444	+	0.994319i	$0.466054\pi$
$7$	−2.13746	+	3.70219i	−0.807883	+	1.39930i	−0.914327	+	0.404976i	$0.867280\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.637459	+	1.10411i	−0.192201	+	0.332902i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−0.637459	+	1.10411i	−0.192201	+	0.332902i	0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$	−3.13746	−	5.43424i	−0.870174	−	1.50719i	−0.861816	−	0.507221i	$-0.830673\pi$
$13$	−3.13746	−	5.43424i	−0.870174	−	1.50719i	−0.00835861	−	0.999965i	$-0.502661\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.137459	+	0.238085i	0.0286621	+	0.0496442i	0.880001	−	0.474972i	$-0.157542\pi$
$23$	0.137459	+	0.238085i	0.0286621	+	0.0496442i	−0.851339	+	0.524617i	$0.824209\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.637459	+	1.10411i	−0.118373	+	0.205028i	−0.919123	−	0.393970i	$-0.871101\pi$
$29$	−0.637459	+	1.10411i	−0.118373	+	0.205028i	0.800750	+	0.598999i	$0.204435\pi$
$30$		0			0
$31$	0.637459	+	1.10411i	0.114491	+	0.198304i	0.917576	−	0.397560i	$-0.130143\pi$
$31$	0.637459	+	1.10411i	0.114491	+	0.198304i	−0.803085	+	0.595864i	$0.796810\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.27492			−0.722593
$36$		0			0
$37$	4.54983			0.747988			0.373994	−	0.927431i	$-0.377988\pi$
$37$	4.54983			0.747988			0.373994	+	0.927431i	$0.377988\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.77492	−	6.53835i	−0.589543	−	1.02112i	−0.994292	−	0.106691i	$-0.965975\pi$
$41$	−3.77492	−	6.53835i	−0.589543	−	1.02112i	0.404749	−	0.914428i	$-0.367359\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.13746	−	5.43424i	0.457645	−	0.792665i	−0.541191	−	0.840900i	$-0.682026\pi$
$47$	3.13746	−	5.43424i	0.457645	−	0.792665i	0.998836	+	0.0482349i	$0.0153596\pi$
$48$		0			0
$49$	−5.63746	−	9.76436i	−0.805351	−	1.39491i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.27492			−1.13665			−0.568324	−	0.822805i	$-0.692408\pi$
$53$	−8.27492			−1.13665			−0.568324	+	0.822805i	$0.692408\pi$
$54$		0			0
$55$	−1.27492			−0.171910
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.50000	−	11.2583i	−0.846228	−	1.46571i	−0.884551	−	0.466444i	$-0.845535\pi$
$59$	−6.50000	−	11.2583i	−0.846228	−	1.46571i	0.0383226	−	0.999265i	$-0.487799\pi$
$60$		0			0
$61$	3.27492	−	5.67232i	0.419310	−	0.726267i	−0.576560	−	0.817055i	$-0.695605\pi$
$61$	3.27492	−	5.67232i	0.419310	−	0.726267i	0.995870	+	0.0907882i	$0.0289386\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.13746	−	5.43424i	0.389154	−	0.674034i
$66$		0			0
$67$	7.27492	+	12.6005i	0.888773	+	1.53940i	0.841328	+	0.540525i	$0.181775\pi$
$67$	7.27492	+	12.6005i	0.888773	+	1.53940i	0.0474449	+	0.998874i	$0.484892\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.725083			0.0860515			0.0430257	−	0.999074i	$-0.486300\pi$
$71$	0.725083			0.0860515			0.0430257	+	0.999074i	$0.486300\pi$
$72$		0			0
$73$	−15.0997			−1.76728			−0.883641	−	0.468165i	$-0.844915\pi$
$73$	−15.0997			−1.76728			−0.883641	+	0.468165i	$0.844915\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.72508	−	4.71998i	−0.310552	−	0.537892i
$78$		0			0
$79$	2.27492	−	3.94027i	0.255948	−	0.443315i	−0.709204	−	0.705003i	$-0.750946\pi$
$79$	2.27492	−	3.94027i	0.255948	−	0.443315i	0.965153	+	0.261688i	$0.0842790\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.27492	−	10.8685i	0.688762	−	1.19297i	−0.283477	−	0.958979i	$-0.591488\pi$
$83$	6.27492	−	10.8685i	0.688762	−	1.19297i	0.972239	−	0.233991i	$-0.0751787\pi$
$84$		0			0
$85$	−1.00000	−	1.73205i	−0.108465	−	0.187867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.82475			1.04142			0.520711	−	0.853733i	$-0.325667\pi$
$89$	9.82475			1.04142			0.520711	+	0.853733i	$0.325667\pi$
$90$		0			0
$91$	26.8248			2.81200
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$		0			0
$97$	−8.00000	+	13.8564i	−0.812277	+	1.40690i	0.0989899	+	0.995088i	$0.468439\pi$
$97$	−8.00000	+	13.8564i	−0.812277	+	1.40690i	−0.911267	+	0.411816i	$0.864894\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.63746	−	14.9605i	0.859459	−	1.48863i	−0.0129862	−	0.999916i	$-0.504134\pi$
$101$	8.63746	−	14.9605i	0.859459	−	1.48863i	0.872445	−	0.488711i	$-0.162533\pi$
$102$		0			0
$103$	−8.41238	−	14.5707i	−0.828896	−	1.43569i	−0.898905	−	0.438144i	$-0.855636\pi$
$103$	−8.41238	−	14.5707i	−0.828896	−	1.43569i	0.0700089	−	0.997546i	$-0.477697\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.0997			1.45974			0.729870	−	0.683586i	$-0.239581\pi$
$107$	15.0997			1.45974			0.729870	+	0.683586i	$0.239581\pi$
$108$		0			0
$109$	1.27492			0.122115			0.0610575	−	0.998134i	$-0.480553\pi$
$109$	1.27492			0.122115			0.0610575	+	0.998134i	$0.480553\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		0			0
$115$	−0.137459	+	0.238085i	−0.0128181	+	0.0222016i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.27492	−	7.40437i	0.391881	−	0.678758i
$120$		0			0
$121$	4.68729	+	8.11863i	0.426118	+	0.738057i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.72508			0.330548			0.165274	−	0.986248i	$-0.447149\pi$
$127$	3.72508			0.330548			0.165274	+	0.986248i	$0.447149\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.77492	−	11.7345i	−0.591927	−	1.02525i	−0.993973	−	0.109628i	$-0.965034\pi$
$131$	−6.77492	−	11.7345i	−0.591927	−	1.02525i	0.402045	−	0.915620i	$-0.368299\pi$
$132$		0			0
$133$	−2.13746	+	3.70219i	−0.185341	+	0.321020i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.274917	+	0.476171i	−0.0234878	+	0.0406820i	−0.877530	−	0.479521i	$-0.840810\pi$
$137$	−0.274917	+	0.476171i	−0.0234878	+	0.0406820i	0.854043	+	0.520203i	$0.174144\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.00000			0.668994
$144$		0			0
$145$	−1.27492			−0.105876
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$		0			0
$151$	2.36254	−	4.09204i	0.192261	−	0.333006i	−0.753738	−	0.657175i	$-0.771751\pi$
$151$	2.36254	−	4.09204i	0.192261	−	0.333006i	0.945999	+	0.324169i	$0.105085\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.637459	+	1.10411i	−0.0512019	+	0.0886843i
$156$		0			0
$157$	−9.13746	−	15.8265i	−0.729249	−	1.26310i	−0.957201	−	0.289423i	$-0.906536\pi$
$157$	−9.13746	−	15.8265i	−0.729249	−	1.26310i	0.227953	−	0.973672i	$-0.426797\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.17525			−0.0926225
$162$		0			0
$163$	5.45017			0.426890			0.213445	−	0.976955i	$-0.431532\pi$
$163$	5.45017			0.426890			0.213445	+	0.976955i	$0.431532\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.2749	−	19.5287i	−0.872479	−	1.51118i	−0.859424	−	0.511264i	$-0.829178\pi$
$167$	−11.2749	−	19.5287i	−0.872479	−	1.51118i	−0.0130554	−	0.999915i	$-0.504156\pi$
$168$		0			0
$169$	−13.1873	+	22.8411i	−1.01441	+	1.75700i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.13746	−	14.0945i	0.618680	−	1.07158i	−0.371047	−	0.928614i	$-0.621001\pi$
$173$	8.13746	−	14.0945i	0.618680	−	1.07158i	0.989727	−	0.142970i	$-0.0456654\pi$
$174$		0			0
$175$	−2.13746	−	3.70219i	−0.161577	−	0.279859i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.54983			−0.265327			−0.132664	−	0.991161i	$-0.542353\pi$
$179$	−3.54983			−0.265327			−0.132664	+	0.991161i	$0.542353\pi$
$180$		0			0
$181$	8.72508			0.648530			0.324265	−	0.945966i	$-0.394883\pi$
$181$	8.72508			0.648530			0.324265	+	0.945966i	$0.394883\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.27492	+	3.94027i	0.167255	+	0.289695i
$186$		0			0
$187$	1.27492	−	2.20822i	0.0932312	−	0.161481i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.18729	+	15.9129i	−0.664769	+	1.15141i	0.314579	+	0.949231i	$0.398137\pi$
$191$	−9.18729	+	15.9129i	−0.664769	+	1.15141i	−0.979348	+	0.202183i	$0.935197\pi$
$192$		0			0
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.3746			−1.09539			−0.547697	−	0.836677i	$-0.684495\pi$
$197$	−15.3746			−1.09539			−0.547697	+	0.836677i	$0.684495\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.72508	−	4.71998i	−0.191263	−	0.331278i
$204$		0			0
$205$	3.77492	−	6.53835i	0.263652	−	0.456658i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.637459	+	1.10411i	−0.0440939	+	0.0763729i
$210$		0			0
$211$	−7.04983	−	12.2107i	−0.485331	−	0.840617i	0.514527	−	0.857474i	$-0.327967\pi$
$211$	−7.04983	−	12.2107i	−0.485331	−	0.840617i	−0.999858	+	0.0168567i	$0.994634\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.00000			−0.272798
$216$		0			0
$217$	−5.45017			−0.369981
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.27492	+	10.8685i	0.422097	+	0.731093i
$222$		0			0
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.2749	+	19.5287i	−0.748343	+	1.29617i	0.200274	+	0.979740i	$0.435817\pi$
$227$	−11.2749	+	19.5287i	−0.748343	+	1.29617i	−0.948617	+	0.316427i	$0.897517\pi$
$228$		0			0
$229$	3.27492	+	5.67232i	0.216413	+	0.374838i	0.953709	−	0.300732i	$-0.0972310\pi$
$229$	3.27492	+	5.67232i	0.216413	+	0.374838i	−0.737296	+	0.675570i	$0.763898\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−21.0997			−1.38229			−0.691143	−	0.722718i	$-0.742892\pi$
$233$	−21.0997			−1.38229			−0.691143	+	0.722718i	$0.742892\pi$
$234$		0			0
$235$	6.27492			0.409330
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.2749	−	24.7249i	−0.923368	−	1.59932i	−0.794166	−	0.607701i	$-0.792092\pi$
$239$	−14.2749	−	24.7249i	−0.923368	−	1.59932i	−0.129202	−	0.991618i	$-0.541242\pi$
$240$		0			0
$241$	8.36254	−	14.4843i	0.538679	−	0.933019i	−0.460297	−	0.887765i	$-0.652257\pi$
$241$	8.36254	−	14.4843i	0.538679	−	0.933019i	0.998976	−	0.0452537i	$-0.0144096\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.63746	−	9.76436i	0.360164	−	0.623822i
$246$		0			0
$247$	−3.13746	−	5.43424i	−0.199632	−	0.345772i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.2749			−1.65846			−0.829229	−	0.558909i	$-0.811220\pi$
$251$	−26.2749			−1.65846			−0.829229	+	0.558909i	$0.811220\pi$
$252$		0			0
$253$	−0.350497			−0.0220355
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.5498	−	23.4690i	−0.845215	−	1.46396i	−0.885434	−	0.464765i	$-0.846139\pi$
$257$	−13.5498	−	23.4690i	−0.845215	−	1.46396i	0.0402185	−	0.999191i	$-0.487195\pi$
$258$		0			0
$259$	−9.72508	+	16.8443i	−0.604287	+	1.04666i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.13746	+	7.16629i	−0.255127	+	0.441892i	−0.964930	−	0.262508i	$-0.915450\pi$
$263$	−4.13746	+	7.16629i	−0.255127	+	0.441892i	0.709803	+	0.704400i	$0.248784\pi$
$264$		0			0
$265$	−4.13746	−	7.16629i	−0.254162	−	0.440222i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−26.9244			−1.64161			−0.820805	−	0.571208i	$-0.806475\pi$
$269$	−26.9244			−1.64161			−0.820805	+	0.571208i	$0.806475\pi$
$270$		0			0
$271$	28.5498			1.73428			0.867139	−	0.498065i	$-0.165956\pi$
$271$	28.5498			1.73428			0.867139	+	0.498065i	$0.165956\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.637459	−	1.10411i	−0.0384402	−	0.0665804i
$276$		0			0
$277$	−8.86254	+	15.3504i	−0.532499	+	0.922314i	0.466781	+	0.884373i	$0.345413\pi$
$277$	−8.86254	+	15.3504i	−0.532499	+	0.922314i	−0.999280	+	0.0379418i	$0.987920\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.4124	−	24.9630i	0.859770	−	1.48917i	−0.0123776	−	0.999923i	$-0.503940\pi$
$281$	14.4124	−	24.9630i	0.859770	−	1.48917i	0.872148	−	0.489242i	$-0.162727\pi$
$282$		0			0
$283$	13.2749	+	22.9928i	0.789112	+	1.36678i	0.926512	+	0.376266i	$0.122792\pi$
$283$	13.2749	+	22.9928i	0.789112	+	1.36678i	−0.137400	+	0.990516i	$0.543874\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	32.2749			1.90513
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.13746	+	15.8265i	0.533816	+	0.924596i	0.999220	+	0.0394979i	$0.0125759\pi$
$293$	9.13746	+	15.8265i	0.533816	+	0.924596i	−0.465404	+	0.885099i	$0.654091\pi$
$294$		0			0
$295$	6.50000	−	11.2583i	0.378445	−	0.655485i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.862541	−	1.49397i	0.0498821	−	0.0863983i
$300$		0			0
$301$	−8.54983	−	14.8087i	−0.492804	−	0.853562i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.54983			0.375042
$306$		0			0
$307$	−29.0997			−1.66081			−0.830403	−	0.557163i	$-0.811890\pi$
$307$	−29.0997			−1.66081			−0.830403	+	0.557163i	$0.811890\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.4622	+	23.3172i	0.763372	+	1.32220i	0.941103	+	0.338120i	$0.109791\pi$
$311$	13.4622	+	23.3172i	0.763372	+	1.32220i	−0.177731	+	0.984079i	$0.556876\pi$
$312$		0			0
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	−0.956647	−	0.291250i	$-0.905929\pi$
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	0.730554	+	0.682855i	$0.239262\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.13746	+	1.97014i	−0.0638860	+	0.110654i	−0.896199	−	0.443652i	$-0.853683\pi$
$317$	−1.13746	+	1.97014i	−0.0638860	+	0.110654i	0.832313	+	0.554306i	$0.187016\pi$
$318$		0			0
$319$	−0.812707	−	1.40765i	−0.0455029	−	0.0788133i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.00000			−0.111283
$324$		0			0
$325$	6.27492			0.348070
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.4124	+	23.2309i	0.739448	+	1.28076i
$330$		0			0
$331$	−1.91238	+	3.31233i	−0.105114	+	0.182062i	−0.913785	−	0.406199i	$-0.866854\pi$
$331$	−1.91238	+	3.31233i	−0.105114	+	0.182062i	0.808671	+	0.588261i	$0.200187\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.27492	+	12.6005i	−0.397471	+	0.688440i
$336$		0			0
$337$	−10.2749	−	17.7967i	−0.559710	−	0.969447i	−0.997520	−	0.0703793i	$-0.977579\pi$
$337$	−10.2749	−	17.7967i	−0.559710	−	0.969447i	0.437810	−	0.899068i	$-0.355754\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.62541			−0.0880211
$342$		0			0
$343$	18.2749			0.986753
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.00000	+	12.1244i	0.375780	+	0.650870i	0.990443	−	0.137920i	$-0.0440416\pi$
$347$	7.00000	+	12.1244i	0.375780	+	0.650870i	−0.614664	+	0.788789i	$0.710708\pi$
$348$		0			0
$349$	4.91238	−	8.50848i	0.262953	−	0.455449i	−0.704072	−	0.710129i	$-0.748637\pi$
$349$	4.91238	−	8.50848i	0.262953	−	0.455449i	0.967025	+	0.254680i	$0.0819701\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.27492	+	7.40437i	−0.227531	+	0.394095i	−0.957076	−	0.289838i	$-0.906399\pi$
$353$	−4.27492	+	7.40437i	−0.227531	+	0.394095i	0.729545	+	0.683933i	$0.239732\pi$
$354$		0			0
$355$	0.362541	+	0.627940i	0.0192417	+	0.0333276i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	21.8248			1.15187			0.575933	−	0.817497i	$-0.304639\pi$
$359$	21.8248			1.15187			0.575933	+	0.817497i	$0.304639\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.54983	−	13.0767i	−0.395176	−	0.684466i
$366$		0			0
$367$	1.27492	−	2.20822i	0.0665501	−	0.115268i	−0.830830	−	0.556526i	$-0.812134\pi$
$367$	1.27492	−	2.20822i	0.0665501	−	0.115268i	0.897381	+	0.441257i	$0.145467\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	17.6873	−	30.6353i	0.918279	−	1.59051i
$372$		0			0
$373$	−0.450166	−	0.779710i	−0.0233087	−	0.0403718i	0.854136	−	0.520050i	$-0.174087\pi$
$373$	−0.450166	−	0.779710i	−0.0233087	−	0.0403718i	−0.877444	+	0.479678i	$0.840753\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	1.72508			0.0886116			0.0443058	−	0.999018i	$-0.485892\pi$
$379$	1.72508			0.0886116			0.0443058	+	0.999018i	$0.485892\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.6873	−	30.6353i	−0.903778	−	1.56539i	−0.822549	−	0.568695i	$-0.807449\pi$
$383$	−17.6873	−	30.6353i	−0.903778	−	1.56539i	−0.0812298	−	0.996695i	$-0.525885\pi$
$384$		0			0
$385$	2.72508	−	4.71998i	0.138883	−	0.240553i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.725083	+	1.25588i	−0.0367632	+	0.0636757i	−0.883822	−	0.467824i	$-0.845038\pi$
$389$	−0.725083	+	1.25588i	−0.0367632	+	0.0636757i	0.847058	+	0.531500i	$0.178371\pi$
$390$		0			0
$391$	−0.274917	−	0.476171i	−0.0139032	−	0.0240810i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.54983			0.228927
$396$		0			0
$397$	−23.0997			−1.15934			−0.579670	−	0.814852i	$-0.696818\pi$
$397$	−23.0997			−1.15934			−0.579670	+	0.814852i	$0.696818\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.86254	+	13.6183i	0.392637	+	0.680067i	0.992796	−	0.119814i	$-0.0382297\pi$
$401$	7.86254	+	13.6183i	0.392637	+	0.680067i	−0.600160	+	0.799880i	$0.704896\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.90033	+	5.02352i	−0.143764	+	0.249007i
$408$		0			0
$409$	3.58762	+	6.21395i	0.177397	+	0.307260i	0.940988	−	0.338440i	$-0.109899\pi$
$409$	3.58762	+	6.21395i	0.177397	+	0.307260i	−0.763591	+	0.645700i	$0.776566\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	55.5739			2.73461
$414$		0			0
$415$	12.5498			0.616047
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.5498	+	18.2728i	0.515393	+	0.892687i	0.999840	+	0.0178666i	$0.00568743\pi$
$419$	10.5498	+	18.2728i	0.515393	+	0.892687i	−0.484447	+	0.874820i	$0.660979\pi$
$420$		0			0
$421$	12.3625	−	21.4125i	0.602513	−	1.04358i	−0.389926	−	0.920846i	$-0.627499\pi$
$421$	12.3625	−	21.4125i	0.602513	−	1.04358i	0.992439	−	0.122738i	$-0.0391673\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	14.0000	+	24.2487i	0.677507	+	1.17348i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.27492			−0.0614106			−0.0307053	−	0.999528i	$-0.509775\pi$
$431$	−1.27492			−0.0614106			−0.0307053	+	0.999528i	$0.509775\pi$
$432$		0			0
$433$	−2.54983			−0.122537			−0.0612686	−	0.998121i	$-0.519515\pi$
$433$	−2.54983			−0.122537			−0.0612686	+	0.998121i	$0.519515\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.137459	+	0.238085i	0.00657554	+	0.0113892i
$438$		0			0
$439$	−6.18729	+	10.7167i	−0.295303	+	0.511480i	−0.975055	−	0.221962i	$-0.928754\pi$
$439$	−6.18729	+	10.7167i	−0.295303	+	0.511480i	0.679752	+	0.733442i	$0.262087\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.27492	+	3.94027i	−0.108085	+	0.187208i	−0.914994	−	0.403467i	$-0.867805\pi$
$443$	−2.27492	+	3.94027i	−0.108085	+	0.187208i	0.806910	+	0.590675i	$0.201138\pi$
$444$		0			0
$445$	4.91238	+	8.50848i	0.232869	+	0.403341i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	13.5498			0.639456			0.319728	−	0.947509i	$-0.396408\pi$
$449$	13.5498			0.639456			0.319728	+	0.947509i	$0.396408\pi$
$450$		0			0
$451$	9.62541			0.453243
$452$		0			0
$453$		0			0
$454$		0			0
$455$	13.4124	+	23.2309i	0.628782	+	1.08908i
$456$		0			0
$457$	−8.00000	+	13.8564i	−0.374224	+	0.648175i	−0.990211	−	0.139581i	$-0.955424\pi$
$457$	−8.00000	+	13.8564i	−0.374224	+	0.648175i	0.615986	+	0.787757i	$0.288758\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.18729	−	12.4488i	0.334746	−	0.579796i	−0.648690	−	0.761052i	$-0.724683\pi$
$461$	7.18729	−	12.4488i	0.334746	−	0.579796i	0.983436	+	0.181256i	$0.0580163\pi$
$462$		0			0
$463$	13.2371	+	22.9274i	0.615181	+	1.06553i	0.990353	+	0.138570i	$0.0442506\pi$
$463$	13.2371	+	22.9274i	0.615181	+	1.06553i	−0.375171	+	0.926956i	$0.622416\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.1993			−0.934714			−0.467357	−	0.884069i	$-0.654794\pi$
$467$	−20.1993			−0.934714			−0.467357	+	0.884069i	$0.654794\pi$
$468$		0			0
$469$	−62.1993			−2.87210
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.54983	−	4.41644i	−0.117242	−	0.203068i
$474$		0			0
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.63746	−	2.83616i	0.0748174	−	0.129588i	−0.826189	−	0.563392i	$-0.809496\pi$
$479$	1.63746	−	2.83616i	0.0748174	−	0.129588i	0.901007	+	0.433805i	$0.142829\pi$
$480$		0			0
$481$	−14.2749	−	24.7249i	−0.650880	−	1.12736i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.0000			−0.726523
$486$		0			0
$487$	−29.7251			−1.34697			−0.673486	−	0.739200i	$-0.735204\pi$
$487$	−29.7251			−1.34697			−0.673486	+	0.739200i	$0.735204\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$		0			0
$493$	1.27492	−	2.20822i	0.0574194	−	0.0994533i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.54983	+	2.68439i	−0.0695196	+	0.120411i
$498$		0			0
$499$	7.22508	+	12.5142i	0.323439	+	0.560213i	0.981195	−	0.193018i	$-0.0618276\pi$
$499$	7.22508	+	12.5142i	0.323439	+	0.560213i	−0.657756	+	0.753231i	$0.728494\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	17.2749			0.768724
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.0997	−	27.8854i	−0.713605	−	1.23600i	−0.963495	−	0.267726i	$-0.913728\pi$
$509$	−16.0997	−	27.8854i	−0.713605	−	1.23600i	0.249890	−	0.968274i	$-0.419606\pi$
$510$		0			0
$511$	32.2749	−	55.9018i	1.42776	−	2.47295i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.41238	−	14.5707i	0.370694	−	0.642060i
$516$		0			0
$517$	4.00000	+	6.92820i	0.175920	+	0.304702i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−25.9244			−1.13577			−0.567885	−	0.823108i	$-0.692238\pi$
$521$	−25.9244			−1.13577			−0.567885	+	0.823108i	$0.692238\pi$
$522$		0			0
$523$	5.64950			0.247036			0.123518	−	0.992342i	$-0.460582\pi$
$523$	5.64950			0.247036			0.123518	+	0.992342i	$0.460582\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.27492	−	2.20822i	−0.0555363	−	0.0961916i
$528$		0			0
$529$	11.4622	−	19.8531i	0.498357	−	0.863180i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.6873	+	41.0276i	−1.02601	+	1.77710i
$534$		0			0
$535$	7.54983	+	13.0767i	0.326408	+	0.565355i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	14.3746			0.619157
$540$		0			0
$541$	−8.92442			−0.383691			−0.191845	−	0.981425i	$-0.561447\pi$
$541$	−8.92442			−0.383691			−0.191845	+	0.981425i	$0.561447\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.637459	+	1.10411i	0.0273057	+	0.0472949i
$546$		0			0
$547$	−10.0000	+	17.3205i	−0.427569	+	0.740571i	−0.996657	−	0.0817056i	$-0.973963\pi$
$547$	−10.0000	+	17.3205i	−0.427569	+	0.740571i	0.569087	+	0.822277i	$0.307297\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.637459	+	1.10411i	−0.0271566	+	0.0470367i
$552$		0			0
$553$	9.72508	+	16.8443i	0.413553	+	0.716294i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.9244			0.844225			0.422112	−	0.906544i	$-0.361289\pi$
$557$	19.9244			0.844225			0.422112	+	0.906544i	$0.361289\pi$
$558$		0			0
$559$	25.0997			1.06160
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.45017	+	5.97586i	0.145407	+	0.251853i	0.929525	−	0.368760i	$-0.120217\pi$
$563$	3.45017	+	5.97586i	0.145407	+	0.251853i	−0.784118	+	0.620612i	$0.786884\pi$
$564$		0			0
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.7749	+	35.9832i	−0.870930	+	1.50849i	−0.00989364	+	0.999951i	$0.503149\pi$
$569$	−20.7749	+	35.9832i	−0.870930	+	1.50849i	−0.861036	+	0.508544i	$0.830184\pi$
$570$		0			0
$571$	11.9124	+	20.6328i	0.498517	+	0.863457i	0.999999	−	0.00171110i	$-0.000544660\pi$
$571$	11.9124	+	20.6328i	0.498517	+	0.863457i	−0.501481	+	0.865169i	$0.667211\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.274917			−0.0114648
$576$		0			0
$577$	−26.5498			−1.10528			−0.552642	−	0.833419i	$-0.686380\pi$
$577$	−26.5498			−1.10528			−0.552642	+	0.833419i	$0.686380\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	26.8248	+	46.4618i	1.11288	+	1.92756i
$582$		0			0
$583$	5.27492	−	9.13642i	0.218465	−	0.378392i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.72508	+	16.8443i	−0.401397	+	0.695240i	−0.993895	−	0.110332i	$-0.964809\pi$
$587$	−9.72508	+	16.8443i	−0.401397	+	0.695240i	0.592498	+	0.805572i	$0.298142\pi$
$588$		0			0
$589$	0.637459	+	1.10411i	0.0262660	+	0.0454941i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.1993			−0.500967			−0.250483	−	0.968121i	$-0.580590\pi$
$593$	−12.1993			−0.500967			−0.250483	+	0.968121i	$0.580590\pi$
$594$		0			0
$595$	8.54983			0.350509
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11.6375	−	20.1567i	−0.475494	−	0.823579i	0.524112	−	0.851649i	$-0.324397\pi$
$599$	−11.6375	−	20.1567i	−0.475494	−	0.823579i	−0.999606	+	0.0280700i	$0.991064\pi$
$600$		0			0
$601$	16.0498	−	27.7991i	0.654686	−	1.13395i	−0.327286	−	0.944925i	$-0.606134\pi$
$601$	16.0498	−	27.7991i	0.654686	−	1.13395i	0.981972	−	0.189025i	$-0.0605326\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.68729	+	8.11863i	−0.190566	+	0.330069i
$606$		0			0
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	0.999889	−	0.0148722i	$-0.00473415\pi$
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	−0.512824	+	0.858494i	$0.671401\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−39.3746			−1.59293
$612$		0			0
$613$	37.0241			1.49539			0.747694	−	0.664043i	$-0.231161\pi$
$613$	37.0241			1.49539			0.747694	+	0.664043i	$0.231161\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.824752	+	1.42851i	0.0332033	+	0.0575097i	0.882150	−	0.470969i	$-0.156096\pi$
$617$	0.824752	+	1.42851i	0.0332033	+	0.0575097i	−0.848946	+	0.528479i	$0.822762\pi$
$618$		0			0
$619$	−9.68729	+	16.7789i	−0.389365	+	0.674400i	−0.992364	−	0.123342i	$-0.960639\pi$
$619$	−9.68729	+	16.7789i	−0.389365	+	0.674400i	0.602999	+	0.797742i	$0.293972\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.0000	+	36.3731i	−0.841347	+	1.45726i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.09967			−0.362828
$630$		0			0
$631$	−43.4743			−1.73068			−0.865341	−	0.501183i	$-0.832898\pi$
$631$	−43.4743			−1.73068			−0.865341	+	0.501183i	$0.832898\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.86254	+	3.22602i	0.0739127	+	0.128021i
$636$		0			0
$637$	−35.3746	+	61.2706i	−1.40159	+	2.42763i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.46221	+	16.3890i	−0.373735	+	0.647328i	−0.990137	−	0.140104i	$-0.955256\pi$
$641$	−9.46221	+	16.3890i	−0.373735	+	0.647328i	0.616402	+	0.787432i	$0.288590\pi$
$642$		0			0
$643$	1.45017	+	2.51176i	0.0571889	+	0.0990542i	0.893203	−	0.449655i	$-0.148453\pi$
$643$	1.45017	+	2.51176i	0.0571889	+	0.0990542i	−0.836014	+	0.548709i	$0.815120\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.4502			0.528781			0.264390	−	0.964416i	$-0.414829\pi$
$647$	13.4502			0.528781			0.264390	+	0.964416i	$0.414829\pi$
$648$		0			0
$649$	16.5739			0.650583
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.2749	+	21.2608i	0.480355	+	0.831999i	0.999746	−	0.0225379i	$-0.00717463\pi$
$653$	12.2749	+	21.2608i	0.480355	+	0.831999i	−0.519391	+	0.854536i	$0.673841\pi$
$654$		0			0
$655$	6.77492	−	11.7345i	0.264718	−	0.458505i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.86254	+	8.42217i	−0.189418	+	0.328081i	−0.945056	−	0.326908i	$-0.893993\pi$
$659$	−4.86254	+	8.42217i	−0.189418	+	0.328081i	0.755639	+	0.654989i	$0.227327\pi$
$660$		0			0
$661$	−6.46221	−	11.1929i	−0.251351	−	0.435352i	0.712547	−	0.701624i	$-0.247541\pi$
$661$	−6.46221	−	11.1929i	−0.251351	−	0.435352i	−0.963898	+	0.266272i	$0.914208\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.27492			−0.165774
$666$		0			0
$667$	−0.350497			−0.0135713
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.17525	+	7.23174i	0.161184	+	0.279178i
$672$		0			0
$673$	19.5498	−	33.8613i	0.753591	−	1.30526i	−0.192481	−	0.981301i	$-0.561653\pi$
$673$	19.5498	−	33.8613i	0.753591	−	1.30526i	0.946072	−	0.323957i	$-0.105013\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.9622	−	22.4512i	0.498178	−	0.862870i	−0.501820	−	0.864972i	$-0.667336\pi$
$677$	12.9622	−	22.4512i	0.498178	−	0.862870i	0.999998	+	0.00210235i	$0.000669198\pi$
$678$		0			0
$679$	−34.1993	−	59.2350i	−1.31245	−	2.27323i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.5498			0.633262			0.316631	−	0.948549i	$-0.397448\pi$
$683$	16.5498			0.633262			0.316631	+	0.948549i	$0.397448\pi$
$684$		0			0
$685$	−0.549834			−0.0210081
$686$		0			0
$687$		0			0
$688$		0			0
$689$	25.9622	+	44.9679i	0.989081	+	1.71314i
$690$		0			0
$691$	−7.41238	+	12.8386i	−0.281980	+	0.488404i	−0.971872	−	0.235508i	$-0.924325\pi$
$691$	−7.41238	+	12.8386i	−0.281980	+	0.488404i	0.689892	+	0.723912i	$0.257658\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.50000	+	7.79423i	−0.170695	+	0.295652i
$696$		0			0
$697$	7.54983	+	13.0767i	0.285970	+	0.495315i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.37459			−0.165226			−0.0826129	−	0.996582i	$-0.526327\pi$
$701$	−4.37459			−0.165226			−0.0826129	+	0.996582i	$0.526327\pi$
$702$		0			0
$703$	4.54983			0.171600
$704$		0			0
$705$		0			0
$706$		0			0
$707$	36.9244	+	63.9550i	1.38869	+	2.40527i
$708$		0			0
$709$	15.5498	−	26.9331i	0.583986	−	1.01149i	−0.411015	−	0.911629i	$-0.634826\pi$
$709$	15.5498	−	26.9331i	0.583986	−	1.01149i	0.995001	−	0.0998652i	$-0.0318412\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.175248	+	0.303539i	−0.00656310	+	0.0113676i
$714$		0			0
$715$	4.00000	+	6.92820i	0.149592	+	0.259100i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.1752			0.826997			0.413499	−	0.910505i	$-0.364307\pi$
$719$	22.1752			0.826997			0.413499	+	0.910505i	$0.364307\pi$
$720$		0			0
$721$	71.9244			2.67861
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.637459	−	1.10411i	−0.0236746	−	0.0410056i
$726$		0			0
$727$	−3.68729	+	6.38658i	−0.136754	+	0.236865i	−0.926266	−	0.376870i	$-0.877000\pi$
$727$	−3.68729	+	6.38658i	−0.136754	+	0.236865i	0.789512	+	0.613735i	$0.210334\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.5498			−0.683292
$738$		0			0
$739$	−36.9244			−1.35829			−0.679143	−	0.734006i	$-0.737649\pi$
$739$	−36.9244			−1.35829			−0.679143	+	0.734006i	$0.737649\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.72508	−	11.6482i	−0.246719	−	0.427330i	0.715894	−	0.698209i	$-0.246019\pi$
$743$	−6.72508	−	11.6482i	−0.246719	−	0.427330i	−0.962614	+	0.270878i	$0.912686\pi$
$744$		0			0
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−32.2749	+	55.9018i	−1.17930	+	2.04261i
$750$		0			0
$751$	−9.72508	−	16.8443i	−0.354873	−	0.614659i	0.632223	−	0.774787i	$-0.282143\pi$
$751$	−9.72508	−	16.8443i	−0.354873	−	0.614659i	−0.987096	+	0.160128i	$0.948809\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.72508			0.171963
$756$		0			0
$757$	−3.37459			−0.122651			−0.0613257	−	0.998118i	$-0.519533\pi$
$757$	−3.37459			−0.122651			−0.0613257	+	0.998118i	$0.519533\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.2251	+	29.8347i	0.624409	+	1.08151i	0.988655	+	0.150205i	$0.0479934\pi$
$761$	17.2251	+	29.8347i	0.624409	+	1.08151i	−0.364246	+	0.931303i	$0.618673\pi$
$762$		0			0
$763$	−2.72508	+	4.71998i	−0.0986546	+	0.170875i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−40.7870	+	70.6451i	−1.47273	+	2.55085i
$768$		0			0
$769$	4.36254	+	7.55614i	0.157317	+	0.272481i	0.933900	−	0.357533i	$-0.116382\pi$
$769$	4.36254	+	7.55614i	0.157317	+	0.272481i	−0.776583	+	0.630015i	$0.783049\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.6495			0.490939			0.245469	−	0.969404i	$-0.421058\pi$
$773$	13.6495			0.490939			0.245469	+	0.969404i	$0.421058\pi$
$774$		0			0
$775$	−1.27492			−0.0457964
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.77492	−	6.53835i	−0.135250	−	0.234261i
$780$		0			0
$781$	−0.462210	+	0.800572i	−0.0165392	+	0.0286467i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9.13746	−	15.8265i	0.326130	−	0.564874i
$786$		0			0
$787$	17.0000	+	29.4449i	0.605985	+	1.04960i	0.991895	+	0.127060i	$0.0405540\pi$
$787$	17.0000	+	29.4449i	0.605985	+	1.04960i	−0.385911	+	0.922536i	$0.626113\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	25.6495			0.911991
$792$		0			0
$793$	−41.0997			−1.45949
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−20.2749	−	35.1172i	−0.718174	−	1.24391i	−0.961722	−	0.274026i	$-0.911645\pi$
$797$	−20.2749	−	35.1172i	−0.718174	−	1.24391i	0.243548	−	0.969889i	$-0.421689\pi$
$798$		0			0
$799$	−6.27492	+	10.8685i	−0.221991	+	0.384499i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.62541	−	16.6717i	0.339673	−	0.588332i
$804$		0			0
$805$	−0.587624	−	1.01779i	−0.0207110	−	0.0358726i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	28.6495			1.00726			0.503631	−	0.863919i	$-0.331997\pi$
$809$	28.6495			1.00726			0.503631	+	0.863919i	$0.331997\pi$
$810$		0			0
$811$	35.8248			1.25798			0.628989	−	0.777415i	$-0.283469\pi$
$811$	35.8248			1.25798			0.628989	+	0.777415i	$0.283469\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.72508	+	4.71998i	0.0954555	+	0.165334i
$816$		0			0
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.91238	+	15.4367i	−0.311044	+	0.538744i	−0.978589	−	0.205826i	$-0.934012\pi$
$821$	−8.91238	+	15.4367i	−0.311044	+	0.538744i	0.667545	+	0.744570i	$0.267345\pi$
$822$		0			0
$823$	−19.2749	−	33.3851i	−0.671881	−	1.16373i	−0.977370	−	0.211537i	$-0.932153\pi$
$823$	−19.2749	−	33.3851i	−0.671881	−	1.16373i	0.305489	−	0.952196i	$-0.401180\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	9.09967			0.316426			0.158213	−	0.987405i	$-0.449427\pi$
$827$	9.09967			0.316426			0.158213	+	0.987405i	$0.449427\pi$
$828$		0			0
$829$	−35.8248			−1.24425			−0.622123	−	0.782920i	$-0.713729\pi$
$829$	−35.8248			−1.24425			−0.622123	+	0.782920i	$0.713729\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	11.2749	+	19.5287i	0.390653	+	0.676630i
$834$		0			0
$835$	11.2749	−	19.5287i	0.390185	−	0.675820i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.73713	+	13.4011i	−0.267115	+	0.462657i	−0.968116	−	0.250504i	$-0.919404\pi$
$839$	−7.73713	+	13.4011i	−0.267115	+	0.462657i	0.701000	+	0.713161i	$0.252737\pi$
$840$		0			0
$841$	13.6873	+	23.7071i	0.471976	+	0.817486i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−26.3746			−0.907313
$846$		0			0
$847$	−40.0756			−1.37701
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.625414	+	1.08325i	0.0214389	+	0.0371333i
$852$		0			0
$853$	−20.6495	+	35.7660i	−0.707026	+	1.22460i	0.258930	+	0.965896i	$0.416630\pi$
$853$	−20.6495	+	35.7660i	−0.707026	+	1.22460i	−0.965956	+	0.258708i	$0.916703\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.3746	−	19.7014i	0.388548	−	0.672986i	−0.603706	−	0.797207i	$-0.706310\pi$
$857$	11.3746	−	19.7014i	0.388548	−	0.672986i	0.992255	+	0.124221i	$0.0396433\pi$
$858$		0			0
$859$	7.73713	+	13.4011i	0.263987	+	0.457240i	0.967298	−	0.253643i	$-0.0816289\pi$
$859$	7.73713	+	13.4011i	0.263987	+	0.457240i	−0.703310	+	0.710883i	$0.748296\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.7251			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$863$	−15.7251			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$864$		0			0
$865$	16.2749			0.553364
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.90033	+	5.02352i	0.0983870	+	0.170411i
$870$		0			0
$871$	45.6495	−	79.0673i	1.54677	−	2.67909i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.13746	−	3.70219i	0.0722593	−	0.125157i
$876$		0			0
$877$	2.86254	+	4.95807i	0.0966612	+	0.167422i	0.910301	−	0.413948i	$-0.135850\pi$
$877$	2.86254	+	4.95807i	0.0966612	+	0.167422i	−0.813640	+	0.581370i	$0.802517\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−56.3746			−1.89931			−0.949654	−	0.313301i	$-0.898565\pi$
$881$	−56.3746			−1.89931			−0.949654	+	0.313301i	$0.898565\pi$
$882$		0			0
$883$	−28.1993			−0.948983			−0.474492	−	0.880260i	$-0.657368\pi$
$883$	−28.1993			−0.948983			−0.474492	+	0.880260i	$0.657368\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.4124	+	19.7668i	0.383190	+	0.663705i	0.991516	−	0.129982i	$-0.0414921\pi$
$887$	11.4124	+	19.7668i	0.383190	+	0.663705i	−0.608326	+	0.793687i	$0.708159\pi$
$888$		0			0
$889$	−7.96221	+	13.7910i	−0.267044	+	0.462534i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.13746	−	5.43424i	0.104991	−	0.181850i
$894$		0			0
$895$	−1.77492	−	3.07425i	−0.0593289	−	0.102761i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.62541			−0.0542106
$900$		0			0
$901$	16.5498			0.551355
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.36254	+	7.55614i	0.145016	+	0.251175i
$906$		0			0
$907$	−10.4502	+	18.1002i	−0.346992	+	0.601008i	−0.985714	−	0.168430i	$-0.946130\pi$
$907$	−10.4502	+	18.1002i	−0.346992	+	0.601008i	0.638722	+	0.769438i	$0.279464\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	28.0120	−	48.5183i	0.928080	−	1.60748i	0.141550	−	0.989931i	$-0.454791\pi$
$911$	28.0120	−	48.5183i	0.928080	−	1.60748i	0.786531	−	0.617551i	$-0.211875\pi$
$912$		0			0
$913$	8.00000	+	13.8564i	0.264761	+	0.458580i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	57.9244			1.91283
$918$		0			0
$919$	−40.9244			−1.34997			−0.674986	−	0.737831i	$-0.735850\pi$
$919$	−40.9244			−1.34997			−0.674986	+	0.737831i	$0.735850\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.27492	−	3.94027i	−0.0748798	−	0.129696i
$924$		0			0
$925$	−2.27492	+	3.94027i	−0.0747988	+	0.129555i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.5619	−	46.0065i	0.871467	−	1.50943i	0.0109877	−	0.999940i	$-0.496502\pi$
$929$	26.5619	−	46.0065i	0.871467	−	1.50943i	0.860479	−	0.509485i	$-0.170164\pi$
$930$		0			0
$931$	−5.63746	−	9.76436i	−0.184760	−	0.320014i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.54983			0.0833885
$936$		0			0
$937$	14.5498			0.475322			0.237661	−	0.971348i	$-0.423619\pi$
$937$	14.5498			0.475322			0.237661	+	0.971348i	$0.423619\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.5498	−	20.0049i	−0.376514	−	0.652141i	0.614039	−	0.789276i	$-0.289544\pi$
$941$	−11.5498	−	20.0049i	−0.376514	−	0.652141i	−0.990552	+	0.137135i	$0.956211\pi$
$942$		0			0
$943$	1.03779	−	1.79750i	0.0337951	−	0.0585348i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.2749	+	36.8492i	−0.691342	+	1.19744i	0.280056	+	0.959984i	$0.409647\pi$
$947$	−21.2749	+	36.8492i	−0.691342	+	1.19744i	−0.971398	+	0.237456i	$0.923687\pi$
$948$		0			0
$949$	47.3746	+	82.0552i	1.53784	+	2.66362i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.90033			0.0939509			0.0469755	−	0.998896i	$-0.485042\pi$
$953$	2.90033			0.0939509			0.0469755	+	0.998896i	$0.485042\pi$
$954$		0			0
$955$	−18.3746			−0.594588
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.17525	−	2.03559i	−0.0379507	−	0.0657326i
$960$		0			0
$961$	14.6873	−	25.4391i	0.473784	−	0.820617i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.00000	−	3.46410i	0.0643823	−	0.111513i
$966$		0			0
$967$	−27.8248	−	48.1939i	−0.894784	−	1.54981i	−0.834072	−	0.551655i	$-0.813996\pi$
$967$	−27.8248	−	48.1939i	−0.894784	−	1.54981i	−0.0607116	−	0.998155i	$-0.519337\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.64950			0.277576			0.138788	−	0.990322i	$-0.455679\pi$
$971$	8.64950			0.277576			0.138788	+	0.990322i	$0.455679\pi$
$972$		0			0
$973$	−38.4743			−1.23343
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.8248	−	36.0695i	−0.666243	−	1.15397i	−0.978947	−	0.204116i	$-0.934568\pi$
$977$	−20.8248	−	36.0695i	−0.666243	−	1.15397i	0.312704	−	0.949851i	$-0.398765\pi$
$978$		0			0
$979$	−6.26287	+	10.8476i	−0.200162	+	0.346691i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	14.3746	−	24.8975i	0.458478	−	0.794107i	−0.540403	−	0.841407i	$-0.681728\pi$
$983$	14.3746	−	24.8975i	0.458478	−	0.794107i	0.998881	+	0.0472992i	$0.0150614\pi$
$984$		0			0
$985$	−7.68729	−	13.3148i	−0.244938	−	0.424244i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.09967			−0.0349674
$990$		0			0
$991$	−9.27492			−0.294627			−0.147314	−	0.989090i	$-0.547063\pi$
$991$	−9.27492			−0.294627			−0.147314	+	0.989090i	$0.547063\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.00000	+	6.92820i	0.126809	+	0.219639i
$996$		0			0
$997$	14.6873	−	25.4391i	0.465151	−	0.805666i	−0.534057	−	0.845448i	$-0.679333\pi$
$997$	14.6873	−	25.4391i	0.465151	−	0.805666i	0.999208	+	0.0397828i	$0.0126666\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3240.2.q.be.2161.1		4
3.2	odd	2		3240.2.q.y.2161.1		4
9.2	odd	6		3240.2.a.n.1.2	yes	2
9.4	even	3	inner	3240.2.q.be.1081.1		4
9.5	odd	6		3240.2.q.y.1081.1		4
9.7	even	3		3240.2.a.h.1.2	✓	2
36.7	odd	6		6480.2.a.bf.1.1		2
36.11	even	6		6480.2.a.bm.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3240.2.a.h.1.2	✓	2	9.7	even	3
3240.2.a.n.1.2	yes	2	9.2	odd	6
3240.2.q.y.1081.1		4	9.5	odd	6
3240.2.q.y.2161.1		4	3.2	odd	2
3240.2.q.be.1081.1		4	9.4	even	3	inner
3240.2.q.be.2161.1		4	1.1	even	1	trivial
6480.2.a.bf.1.1		2	36.7	odd	6
6480.2.a.bm.1.1		2	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3240.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{5} +(-2.13746 + 3.70219i) q^{7} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{5} +(-2.13746 + 3.70219i) q^{7} +(-0.637459 + 1.10411i) q^{11} +(-3.13746 - 5.43424i) q^{13} -2.00000 q^{17} +1.00000 q^{19} +(0.137459 + 0.238085i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.637459 + 1.10411i) q^{29} +(0.637459 + 1.10411i) q^{31} -4.27492 q^{35} +4.54983 q^{37} +(-3.77492 - 6.53835i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(3.13746 - 5.43424i) q^{47} +(-5.63746 - 9.76436i) q^{49} -8.27492 q^{53} -1.27492 q^{55} +(-6.50000 - 11.2583i) q^{59} +(3.27492 - 5.67232i) q^{61} +(3.13746 - 5.43424i) q^{65} +(7.27492 + 12.6005i) q^{67} +0.725083 q^{71} -15.0997 q^{73} +(-2.72508 - 4.71998i) q^{77} +(2.27492 - 3.94027i) q^{79} +(6.27492 - 10.8685i) q^{83} +(-1.00000 - 1.73205i) q^{85} +9.82475 q^{89} +26.8248 q^{91} +(0.500000 + 0.866025i) q^{95} +(-8.00000 + 13.8564i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - q^7	\( 4 q + 2 q^{5} - q^{7} + 5 q^{11} - 5 q^{13} - 8 q^{17} + 4 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 5 q^{31} - 2 q^{35} - 12 q^{37} - 8 q^{43} + 5 q^{47} - 15 q^{49} - 18 q^{53} + 10 q^{55} - 26 q^{59} - 2 q^{61} + 5 q^{65} + 14 q^{67} + 18 q^{71} - 26 q^{77} - 6 q^{79} + 10 q^{83} - 4 q^{85} - 6 q^{89} + 62 q^{91} + 2 q^{95} - 32 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - q^7 + 5 * q^11 - 5 * q^13 - 8 * q^17 + 4 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 5 * q^31 - 2 * q^35 - 12 * q^37 - 8 * q^43 + 5 * q^47 - 15 * q^49 - 18 * q^53 + 10 * q^55 - 26 * q^59 - 2 * q^61 + 5 * q^65 + 14 * q^67 + 18 * q^71 - 26 * q^77 - 6 * q^79 + 10 * q^83 - 4 * q^85 - 6 * q^89 + 62 * q^91 + 2 * q^95 - 32 * q^97

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