LMFDB - Embedded newform 2790.2.d.i.559.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(559,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("2790.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.d (of order $2$, degree $1$, 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:	$22.2782621639$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 930)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.4
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2790.559
Dual form			2790.2.d.i.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +0.828427i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +0.828427i q^{7} -1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} +0.828427 q^{11} -4.82843i q^{13} -0.828427 q^{14} +1.00000 q^{16} -0.828427i q^{17} +(2.00000 - 1.00000i) q^{20} +0.828427i q^{22} +8.48528i q^{23} +(3.00000 - 4.00000i) q^{25} +4.82843 q^{26} -0.828427i q^{28} +9.65685 q^{29} +1.00000 q^{31} +1.00000i q^{32} +0.828427 q^{34} +(-0.828427 - 1.65685i) q^{35} -10.4853i q^{37} +(1.00000 + 2.00000i) q^{40} -7.65685 q^{41} +9.65685i q^{43} -0.828427 q^{44} -8.48528 q^{46} +5.65685i q^{47} +6.31371 q^{49} +(4.00000 + 3.00000i) q^{50} +4.82843i q^{52} +0.343146i q^{53} +(-1.65685 + 0.828427i) q^{55} +0.828427 q^{56} +9.65685i q^{58} +3.17157 q^{59} +0.828427 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(4.82843 + 9.65685i) q^{65} +9.17157i q^{67} +0.828427i q^{68} +(1.65685 - 0.828427i) q^{70} +2.82843 q^{71} +13.6569i q^{73} +10.4853 q^{74} +0.686292i q^{77} -11.3137 q^{79} +(-2.00000 + 1.00000i) q^{80} -7.65685i q^{82} -1.65685i q^{83} +(0.828427 + 1.65685i) q^{85} -9.65685 q^{86} -0.828427i q^{88} +4.82843 q^{89} +4.00000 q^{91} -8.48528i q^{92} -5.65685 q^{94} -11.3137i q^{97} +6.31371i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 8 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 - 8 * q^5	$ 4 q - 4 q^{4} - 8 q^{5} - 4 q^{10} - 8 q^{11} + 8 q^{14} + 4 q^{16} + 8 q^{20} + 12 q^{25} + 8 q^{26} + 16 q^{29} + 4 q^{31} - 8 q^{34} + 8 q^{35} + 4 q^{40} - 8 q^{41} + 8 q^{44} - 20 q^{49} + 16 q^{50} + 16 q^{55} - 8 q^{56} + 24 q^{59} - 8 q^{61} - 4 q^{64} + 8 q^{65} - 16 q^{70} + 8 q^{74} - 8 q^{80} - 8 q^{85} - 16 q^{86} + 8 q^{89} + 16 q^{91}+O(q^{100}) $ 4 * q - 4 * q^4 - 8 * q^5 - 4 * q^10 - 8 * q^11 + 8 * q^14 + 4 * q^16 + 8 * q^20 + 12 * q^25 + 8 * q^26 + 16 * q^29 + 4 * q^31 - 8 * q^34 + 8 * q^35 + 4 * q^40 - 8 * q^41 + 8 * q^44 - 20 * q^49 + 16 * q^50 + 16 * q^55 - 8 * q^56 + 24 * q^59 - 8 * q^61 - 4 * q^64 + 8 * q^65 - 16 * q^70 + 8 * q^74 - 8 * q^80 - 8 * q^85 - 16 * q^86 + 8 * q^89 + 16 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times$.

$n$	$1117$	$1801$	$2171$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		0			0
$7$			0.828427i			0.313116i	0.987669	+	0.156558i	$0.0500398\pi$
$7$			0.828427i			0.313116i	−0.987669	+	0.156558i	$0.949960\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	0.828427			0.249780			0.124890	−	0.992171i	$-0.460142\pi$
$11$	0.828427			0.249780			0.124890	+	0.992171i	$0.460142\pi$
$12$		0			0
$13$		−	4.82843i		−	1.33916i	−0.742738	−	0.669582i	$-0.766473\pi$
$13$		−	4.82843i		−	1.33916i	0.742738	−	0.669582i	$-0.233527\pi$
$14$	−0.828427			−0.221406
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.828427i		−	0.200923i	−0.994941	−	0.100462i	$-0.967968\pi$
$17$		−	0.828427i		−	0.200923i	0.994941	−	0.100462i	$-0.0320319\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$		0			0
$22$			0.828427i			0.176621i
$23$			8.48528i			1.76930i	0.466252	+	0.884652i	$0.345604\pi$
$23$			8.48528i			1.76930i	−0.466252	+	0.884652i	$0.654396\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	4.82843			0.946932
$27$		0			0
$28$		−	0.828427i		−	0.156558i
$29$	9.65685			1.79323			0.896616	−	0.442808i	$-0.146018\pi$
$29$	9.65685			1.79323			0.896616	+	0.442808i	$0.146018\pi$
$30$		0			0
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.828427			0.142074
$35$	−0.828427	−	1.65685i	−0.140030	−	0.280059i
$36$		0			0
$37$		−	10.4853i		−	1.72377i	−0.507104	−	0.861885i	$-0.669284\pi$
$37$		−	10.4853i		−	1.72377i	0.507104	−	0.861885i	$-0.330716\pi$
$38$		0			0
$39$		0			0
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	−7.65685			−1.19580			−0.597900	−	0.801571i	$-0.703998\pi$
$41$	−7.65685			−1.19580			−0.597900	+	0.801571i	$0.703998\pi$
$42$		0			0
$43$			9.65685i			1.47266i	0.676625	+	0.736328i	$0.263442\pi$
$43$			9.65685i			1.47266i	−0.676625	+	0.736328i	$0.736558\pi$
$44$	−0.828427			−0.124890
$45$		0			0
$46$	−8.48528			−1.25109
$47$			5.65685i			0.825137i	0.910927	+	0.412568i	$0.135368\pi$
$47$			5.65685i			0.825137i	−0.910927	+	0.412568i	$0.864632\pi$
$48$		0			0
$49$	6.31371			0.901958
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$		0			0
$52$			4.82843i			0.669582i
$53$			0.343146i			0.0471347i	0.999722	+	0.0235673i	$0.00750241\pi$
$53$			0.343146i			0.0471347i	−0.999722	+	0.0235673i	$0.992498\pi$
$54$		0			0
$55$	−1.65685	+	0.828427i	−0.223410	+	0.111705i
$56$	0.828427			0.110703
$57$		0			0
$58$			9.65685i			1.26801i
$59$	3.17157			0.412904			0.206452	−	0.978457i	$-0.433808\pi$
$59$	3.17157			0.412904			0.206452	+	0.978457i	$0.433808\pi$
$60$		0			0
$61$	0.828427			0.106069			0.0530346	−	0.998593i	$-0.483111\pi$
$61$	0.828427			0.106069			0.0530346	+	0.998593i	$0.483111\pi$
$62$			1.00000i			0.127000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.82843	+	9.65685i	0.598893	+	1.19779i
$66$		0			0
$67$			9.17157i			1.12049i	0.828328	+	0.560243i	$0.189292\pi$
$67$			9.17157i			1.12049i	−0.828328	+	0.560243i	$0.810708\pi$
$68$			0.828427i			0.100462i
$69$		0			0
$70$	1.65685	−	0.828427i	0.198032	−	0.0990160i
$71$	2.82843			0.335673			0.167836	−	0.985815i	$-0.446322\pi$
$71$	2.82843			0.335673			0.167836	+	0.985815i	$0.446322\pi$
$72$		0			0
$73$			13.6569i			1.59841i	0.601056	+	0.799207i	$0.294747\pi$
$73$			13.6569i			1.59841i	−0.601056	+	0.799207i	$0.705253\pi$
$74$	10.4853			1.21889
$75$		0			0
$76$		0			0
$77$			0.686292i			0.0782102i
$78$		0			0
$79$	−11.3137			−1.27289			−0.636446	−	0.771321i	$-0.719596\pi$
$79$	−11.3137			−1.27289			−0.636446	+	0.771321i	$0.719596\pi$
$80$	−2.00000	+	1.00000i	−0.223607	+	0.111803i
$81$		0			0
$82$		−	7.65685i		−	0.845558i
$83$		−	1.65685i		−	0.181863i	−0.995857	−	0.0909317i	$-0.971016\pi$
$83$		−	1.65685i		−	0.181863i	0.995857	−	0.0909317i	$-0.0289845\pi$
$84$		0			0
$85$	0.828427	+	1.65685i	0.0898555	+	0.179711i
$86$	−9.65685			−1.04133
$87$		0			0
$88$		−	0.828427i		−	0.0883106i
$89$	4.82843			0.511812			0.255906	−	0.966702i	$-0.417626\pi$
$89$	4.82843			0.511812			0.255906	+	0.966702i	$0.417626\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$		−	8.48528i		−	0.884652i
$93$		0			0
$94$	−5.65685			−0.583460
$95$		0			0
$96$		0			0
$97$		−	11.3137i		−	1.14873i	−0.818598	−	0.574367i	$-0.805248\pi$
$97$		−	11.3137i		−	1.14873i	0.818598	−	0.574367i	$-0.194752\pi$
$98$			6.31371i			0.637781i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−11.3137			−1.12576			−0.562878	−	0.826540i	$-0.690306\pi$
$101$	−11.3137			−1.12576			−0.562878	+	0.826540i	$0.690306\pi$
$102$		0			0
$103$			1.51472i			0.149250i	0.997212	+	0.0746248i	$0.0237759\pi$
$103$			1.51472i			0.149250i	−0.997212	+	0.0746248i	$0.976224\pi$
$104$	−4.82843			−0.473466
$105$		0			0
$106$	−0.343146			−0.0333293
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$		0			0
$109$	11.6569			1.11652			0.558262	−	0.829665i	$-0.311468\pi$
$109$	11.6569			1.11652			0.558262	+	0.829665i	$0.311468\pi$
$110$	−0.828427	−	1.65685i	−0.0789874	−	0.157975i
$111$		0			0
$112$			0.828427i			0.0782790i
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	−8.48528	−	16.9706i	−0.791257	−	1.58251i
$116$	−9.65685			−0.896616
$117$		0			0
$118$			3.17157i			0.291967i
$119$	0.686292			0.0629122
$120$		0			0
$121$	−10.3137			−0.937610
$122$			0.828427i			0.0750023i
$123$		0			0
$124$	−1.00000			−0.0898027
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$			16.1421i			1.43238i	0.697904	+	0.716191i	$0.254116\pi$
$127$			16.1421i			1.43238i	−0.697904	+	0.716191i	$0.745884\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−9.65685	+	4.82843i	−0.846962	+	0.423481i
$131$	−18.4853			−1.61507			−0.807533	−	0.589822i	$-0.799198\pi$
$131$	−18.4853			−1.61507			−0.807533	+	0.589822i	$0.799198\pi$
$132$		0			0
$133$		0			0
$134$	−9.17157			−0.792303
$135$		0			0
$136$	−0.828427			−0.0710370
$137$			6.48528i			0.554075i	0.960859	+	0.277037i	$0.0893526\pi$
$137$			6.48528i			0.554075i	−0.960859	+	0.277037i	$0.910647\pi$
$138$		0			0
$139$	14.1421			1.19952			0.599760	−	0.800180i	$-0.295263\pi$
$139$	14.1421			1.19952			0.599760	+	0.800180i	$0.295263\pi$
$140$	0.828427	+	1.65685i	0.0700149	+	0.140030i
$141$		0			0
$142$			2.82843i			0.237356i
$143$		−	4.00000i		−	0.334497i
$144$		0			0
$145$	−19.3137	+	9.65685i	−1.60392	+	0.801958i
$146$	−13.6569			−1.13025
$147$		0			0
$148$			10.4853i			0.861885i
$149$	−0.686292			−0.0562232			−0.0281116	−	0.999605i	$-0.508949\pi$
$149$	−0.686292			−0.0562232			−0.0281116	+	0.999605i	$0.508949\pi$
$150$		0			0
$151$	21.6569			1.76241			0.881205	−	0.472735i	$-0.156733\pi$
$151$	21.6569			1.76241			0.881205	+	0.472735i	$0.156733\pi$
$152$		0			0
$153$		0			0
$154$	−0.686292			−0.0553029
$155$	−2.00000	+	1.00000i	−0.160644	+	0.0803219i
$156$		0			0
$157$			17.3137i			1.38178i	0.722958	+	0.690892i	$0.242782\pi$
$157$			17.3137i			1.38178i	−0.722958	+	0.690892i	$0.757218\pi$
$158$		−	11.3137i		−	0.900070i
$159$		0			0
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$	−7.02944			−0.553997
$162$		0			0
$163$			14.8284i			1.16145i	0.814099	+	0.580726i	$0.197231\pi$
$163$			14.8284i			1.16145i	−0.814099	+	0.580726i	$0.802769\pi$
$164$	7.65685			0.597900
$165$		0			0
$166$	1.65685			0.128597
$167$			0.485281i			0.0375522i	0.999824	+	0.0187761i	$0.00597697\pi$
$167$			0.485281i			0.0375522i	−0.999824	+	0.0187761i	$0.994023\pi$
$168$		0			0
$169$	−10.3137			−0.793362
$170$	−1.65685	+	0.828427i	−0.127075	+	0.0635375i
$171$		0			0
$172$		−	9.65685i		−	0.736328i
$173$		−	1.31371i		−	0.0998794i	−0.998752	−	0.0499397i	$-0.984097\pi$
$173$		−	1.31371i		−	0.0998794i	0.998752	−	0.0499397i	$-0.0159029\pi$
$174$		0			0
$175$	3.31371	+	2.48528i	0.250493	+	0.187870i
$176$	0.828427			0.0624450
$177$		0			0
$178$			4.82843i			0.361906i
$179$	−11.1716			−0.835003			−0.417501	−	0.908676i	$-0.637094\pi$
$179$	−11.1716			−0.835003			−0.417501	+	0.908676i	$0.637094\pi$
$180$		0			0
$181$	24.8284			1.84548			0.922741	−	0.385420i	$-0.125943\pi$
$181$	24.8284			1.84548			0.922741	+	0.385420i	$0.125943\pi$
$182$			4.00000i			0.296500i
$183$		0			0
$184$	8.48528			0.625543
$185$	10.4853	+	20.9706i	0.770893	+	1.54179i
$186$		0			0
$187$		−	0.686292i		−	0.0501866i
$188$		−	5.65685i		−	0.412568i
$189$		0			0
$190$		0			0
$191$	0.485281			0.0351137			0.0175569	−	0.999846i	$-0.494411\pi$
$191$	0.485281			0.0351137			0.0175569	+	0.999846i	$0.494411\pi$
$192$		0			0
$193$		−	15.3137i		−	1.10230i	−0.834405	−	0.551152i	$-0.814188\pi$
$193$		−	15.3137i		−	1.10230i	0.834405	−	0.551152i	$-0.185812\pi$
$194$	11.3137			0.812277
$195$		0			0
$196$	−6.31371			−0.450979
$197$			26.9706i			1.92157i	0.277289	+	0.960787i	$0.410564\pi$
$197$			26.9706i			1.92157i	−0.277289	+	0.960787i	$0.589436\pi$
$198$		0			0
$199$	−13.6569			−0.968109			−0.484054	−	0.875038i	$-0.660836\pi$
$199$	−13.6569			−0.968109			−0.484054	+	0.875038i	$0.660836\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$		0			0
$202$		−	11.3137i		−	0.796030i
$203$			8.00000i			0.561490i
$204$		0			0
$205$	15.3137	−	7.65685i	1.06956	−	0.534778i
$206$	−1.51472			−0.105535
$207$		0			0
$208$		−	4.82843i		−	0.334791i
$209$		0			0
$210$		0			0
$211$	23.3137			1.60498			0.802491	−	0.596664i	$-0.203508\pi$
$211$	23.3137			1.60498			0.802491	+	0.596664i	$0.203508\pi$
$212$		−	0.343146i		−	0.0235673i
$213$		0			0
$214$	4.00000			0.273434
$215$	−9.65685	−	19.3137i	−0.658592	−	1.31718i
$216$		0			0
$217$			0.828427i			0.0562373i
$218$			11.6569i			0.789502i
$219$		0			0
$220$	1.65685	−	0.828427i	0.111705	−	0.0558525i
$221$	−4.00000			−0.269069
$222$		0			0
$223$			17.7990i			1.19191i	0.803018	+	0.595954i	$0.203226\pi$
$223$			17.7990i			1.19191i	−0.803018	+	0.595954i	$0.796774\pi$
$224$	−0.828427			−0.0553516
$225$		0			0
$226$	−14.0000			−0.931266
$227$		−	17.6569i		−	1.17193i	−0.810338	−	0.585963i	$-0.800716\pi$
$227$		−	17.6569i		−	1.17193i	0.810338	−	0.585963i	$-0.199284\pi$
$228$		0			0
$229$	−18.4853			−1.22154			−0.610771	−	0.791807i	$-0.709140\pi$
$229$	−18.4853			−1.22154			−0.610771	+	0.791807i	$0.709140\pi$
$230$	16.9706	−	8.48528i	1.11901	−	0.559503i
$231$		0			0
$232$		−	9.65685i		−	0.634004i
$233$		−	6.97056i		−	0.456657i	−0.973584	−	0.228328i	$-0.926674\pi$
$233$		−	6.97056i		−	0.456657i	0.973584	−	0.228328i	$-0.0733260\pi$
$234$		0			0
$235$	−5.65685	−	11.3137i	−0.369012	−	0.738025i
$236$	−3.17157			−0.206452
$237$		0			0
$238$			0.686292i			0.0444857i
$239$	0.686292			0.0443925			0.0221963	−	0.999754i	$-0.492934\pi$
$239$	0.686292			0.0443925			0.0221963	+	0.999754i	$0.492934\pi$
$240$		0			0
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$		−	10.3137i		−	0.662990i
$243$		0			0
$244$	−0.828427			−0.0530346
$245$	−12.6274	+	6.31371i	−0.806736	+	0.403368i
$246$		0			0
$247$		0			0
$248$		−	1.00000i		−	0.0635001i
$249$		0			0
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−3.17157			−0.200188			−0.100094	−	0.994978i	$-0.531914\pi$
$251$	−3.17157			−0.200188			−0.100094	+	0.994978i	$0.531914\pi$
$252$		0			0
$253$			7.02944i			0.441937i
$254$	−16.1421			−1.01285
$255$		0			0
$256$	1.00000			0.0625000
$257$			15.6569i			0.976648i	0.872662	+	0.488324i	$0.162392\pi$
$257$			15.6569i			0.976648i	−0.872662	+	0.488324i	$0.837608\pi$
$258$		0			0
$259$	8.68629			0.539740
$260$	−4.82843	−	9.65685i	−0.299446	−	0.598893i
$261$		0			0
$262$		−	18.4853i		−	1.14202i
$263$			24.4853i			1.50983i	0.655824	+	0.754914i	$0.272321\pi$
$263$			24.4853i			1.50983i	−0.655824	+	0.754914i	$0.727679\pi$
$264$		0			0
$265$	−0.343146	−	0.686292i	−0.0210793	−	0.0421586i
$266$		0			0
$267$		0			0
$268$		−	9.17157i		−	0.560243i
$269$	−4.97056			−0.303061			−0.151530	−	0.988453i	$-0.548420\pi$
$269$	−4.97056			−0.303061			−0.151530	+	0.988453i	$0.548420\pi$
$270$		0			0
$271$	−13.6569			−0.829595			−0.414797	−	0.909914i	$-0.636148\pi$
$271$	−13.6569			−0.829595			−0.414797	+	0.909914i	$0.636148\pi$
$272$		−	0.828427i		−	0.0502308i
$273$		0			0
$274$	−6.48528			−0.391790
$275$	2.48528	−	3.31371i	0.149868	−	0.199824i
$276$		0			0
$277$			4.14214i			0.248877i	0.992227	+	0.124438i	$0.0397129\pi$
$277$			4.14214i			0.248877i	−0.992227	+	0.124438i	$0.960287\pi$
$278$			14.1421i			0.848189i
$279$		0			0
$280$	−1.65685	+	0.828427i	−0.0990160	+	0.0495080i
$281$	21.3137			1.27147			0.635735	−	0.771908i	$-0.280697\pi$
$281$	21.3137			1.27147			0.635735	+	0.771908i	$0.280697\pi$
$282$		0			0
$283$			14.8284i			0.881458i	0.897640	+	0.440729i	$0.145280\pi$
$283$			14.8284i			0.881458i	−0.897640	+	0.440729i	$0.854720\pi$
$284$	−2.82843			−0.167836
$285$		0			0
$286$	4.00000			0.236525
$287$		−	6.34315i		−	0.374424i
$288$		0			0
$289$	16.3137			0.959630
$290$	−9.65685	−	19.3137i	−0.567070	−	1.13414i
$291$		0			0
$292$		−	13.6569i		−	0.799207i
$293$		−	2.00000i		−	0.116841i	−0.998292	−	0.0584206i	$-0.981394\pi$
$293$		−	2.00000i		−	0.116841i	0.998292	−	0.0584206i	$-0.0186065\pi$
$294$		0			0
$295$	−6.34315	+	3.17157i	−0.369312	+	0.184656i
$296$	−10.4853			−0.609445
$297$		0			0
$298$		−	0.686292i		−	0.0397558i
$299$	40.9706			2.36939
$300$		0			0
$301$	−8.00000			−0.461112
$302$			21.6569i			1.24621i
$303$		0			0
$304$		0			0
$305$	−1.65685	+	0.828427i	−0.0948712	+	0.0474356i
$306$		0			0
$307$		−	0.485281i		−	0.0276965i	−0.999904	−	0.0138482i	$-0.995592\pi$
$307$		−	0.485281i		−	0.0276965i	0.999904	−	0.0138482i	$-0.00440817\pi$
$308$		−	0.686292i		−	0.0391051i
$309$		0			0
$310$	−1.00000	−	2.00000i	−0.0567962	−	0.113592i
$311$	16.4853			0.934795			0.467397	−	0.884047i	$-0.345192\pi$
$311$	16.4853			0.934795			0.467397	+	0.884047i	$0.345192\pi$
$312$		0			0
$313$		−	0.970563i		−	0.0548595i	−0.999624	−	0.0274297i	$-0.991268\pi$
$313$		−	0.970563i		−	0.0548595i	0.999624	−	0.0274297i	$-0.00873225\pi$
$314$	−17.3137			−0.977069
$315$		0			0
$316$	11.3137			0.636446
$317$		−	13.3137i		−	0.747772i	−0.927475	−	0.373886i	$-0.878025\pi$
$317$		−	13.3137i		−	0.747772i	0.927475	−	0.373886i	$-0.121975\pi$
$318$		0			0
$319$	8.00000			0.447914
$320$	2.00000	−	1.00000i	0.111803	−	0.0559017i
$321$		0			0
$322$		−	7.02944i		−	0.391735i
$323$		0			0
$324$		0			0
$325$	−19.3137	−	14.4853i	−1.07133	−	0.803499i
$326$	−14.8284			−0.821271
$327$		0			0
$328$			7.65685i			0.422779i
$329$	−4.68629			−0.258364
$330$		0			0
$331$	12.4853			0.686253			0.343127	−	0.939289i	$-0.388514\pi$
$331$	12.4853			0.686253			0.343127	+	0.939289i	$0.388514\pi$
$332$			1.65685i			0.0909317i
$333$		0			0
$334$	−0.485281			−0.0265534
$335$	−9.17157	−	18.3431i	−0.501097	−	1.00219i
$336$		0			0
$337$		−	5.65685i		−	0.308148i	−0.988059	−	0.154074i	$-0.950761\pi$
$337$		−	5.65685i		−	0.308148i	0.988059	−	0.154074i	$-0.0492395\pi$
$338$		−	10.3137i		−	0.560992i
$339$		0			0
$340$	−0.828427	−	1.65685i	−0.0449278	−	0.0898555i
$341$	0.828427			0.0448618
$342$		0			0
$343$			11.0294i			0.595534i
$344$	9.65685			0.520663
$345$		0			0
$346$	1.31371			0.0706254
$347$		−	17.6569i		−	0.947870i	−0.880560	−	0.473935i	$-0.842833\pi$
$347$		−	17.6569i		−	0.947870i	0.880560	−	0.473935i	$-0.157167\pi$
$348$		0			0
$349$	25.3137			1.35501			0.677506	−	0.735517i	$-0.263061\pi$
$349$	25.3137			1.35501			0.677506	+	0.735517i	$0.263061\pi$
$350$	−2.48528	+	3.31371i	−0.132844	+	0.177125i
$351$		0			0
$352$			0.828427i			0.0441553i
$353$		−	23.1716i		−	1.23330i	−0.787238	−	0.616649i	$-0.788490\pi$
$353$		−	23.1716i		−	1.23330i	0.787238	−	0.616649i	$-0.211510\pi$
$354$		0			0
$355$	−5.65685	+	2.82843i	−0.300235	+	0.150117i
$356$	−4.82843			−0.255906
$357$		0			0
$358$		−	11.1716i		−	0.590436i
$359$	10.1421			0.535281			0.267641	−	0.963519i	$-0.413756\pi$
$359$	10.1421			0.535281			0.267641	+	0.963519i	$0.413756\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$			24.8284i			1.30495i
$363$		0			0
$364$	−4.00000			−0.209657
$365$	−13.6569	−	27.3137i	−0.714832	−	1.42966i
$366$		0			0
$367$		−	28.1421i		−	1.46901i	−0.678605	−	0.734504i	$-0.737415\pi$
$367$		−	28.1421i		−	1.46901i	0.678605	−	0.734504i	$-0.262585\pi$
$368$			8.48528i			0.442326i
$369$		0			0
$370$	−20.9706	+	10.4853i	−1.09021	+	0.545104i
$371$	−0.284271			−0.0147586
$372$		0			0
$373$		−	0.343146i		−	0.0177674i	−0.999961	−	0.00888371i	$-0.997172\pi$
$373$		−	0.343146i		−	0.0177674i	0.999961	−	0.00888371i	$-0.00282781\pi$
$374$	0.686292			0.0354873
$375$		0			0
$376$	5.65685			0.291730
$377$		−	46.6274i		−	2.40143i
$378$		0			0
$379$	9.65685			0.496039			0.248020	−	0.968755i	$-0.420220\pi$
$379$	9.65685			0.496039			0.248020	+	0.968755i	$0.420220\pi$
$380$		0			0
$381$		0			0
$382$			0.485281i			0.0248292i
$383$			11.5147i			0.588375i	0.955748	+	0.294187i	$0.0950490\pi$
$383$			11.5147i			0.588375i	−0.955748	+	0.294187i	$0.904951\pi$
$384$		0			0
$385$	−0.686292	−	1.37258i	−0.0349767	−	0.0699533i
$386$	15.3137			0.779447
$387$		0			0
$388$			11.3137i			0.574367i
$389$	12.6863			0.643221			0.321610	−	0.946872i	$-0.395776\pi$
$389$	12.6863			0.643221			0.321610	+	0.946872i	$0.395776\pi$
$390$		0			0
$391$	7.02944			0.355494
$392$		−	6.31371i		−	0.318890i
$393$		0			0
$394$	−26.9706			−1.35876
$395$	22.6274	−	11.3137i	1.13851	−	0.569254i
$396$		0			0
$397$			15.6569i			0.785795i	0.919582	+	0.392897i	$0.128527\pi$
$397$			15.6569i			0.785795i	−0.919582	+	0.392897i	$0.871473\pi$
$398$		−	13.6569i		−	0.684556i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−2.48528			−0.124109			−0.0620545	−	0.998073i	$-0.519765\pi$
$401$	−2.48528			−0.124109			−0.0620545	+	0.998073i	$0.519765\pi$
$402$		0			0
$403$		−	4.82843i		−	0.240521i
$404$	11.3137			0.562878
$405$		0			0
$406$	−8.00000			−0.397033
$407$		−	8.68629i		−	0.430563i
$408$		0			0
$409$	−33.3137			−1.64726			−0.823628	−	0.567130i	$-0.808054\pi$
$409$	−33.3137			−1.64726			−0.823628	+	0.567130i	$0.808054\pi$
$410$	7.65685	+	15.3137i	0.378145	+	0.756290i
$411$		0			0
$412$		−	1.51472i		−	0.0746248i
$413$			2.62742i			0.129287i
$414$		0			0
$415$	1.65685	+	3.31371i	0.0813318	+	0.162664i
$416$	4.82843			0.236733
$417$		0			0
$418$		0			0
$419$	−9.79899			−0.478712			−0.239356	−	0.970932i	$-0.576936\pi$
$419$	−9.79899			−0.478712			−0.239356	+	0.970932i	$0.576936\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$			23.3137i			1.13489i
$423$		0			0
$424$	0.343146			0.0166646
$425$	−3.31371	−	2.48528i	−0.160738	−	0.120554i
$426$		0			0
$427$			0.686292i			0.0332120i
$428$			4.00000i			0.193347i
$429$		0			0
$430$	19.3137	−	9.65685i	0.931390	−	0.465695i
$431$	1.17157			0.0564327			0.0282163	−	0.999602i	$-0.491017\pi$
$431$	1.17157			0.0564327			0.0282163	+	0.999602i	$0.491017\pi$
$432$		0			0
$433$			13.6569i			0.656307i	0.944624	+	0.328153i	$0.106426\pi$
$433$			13.6569i			0.656307i	−0.944624	+	0.328153i	$0.893574\pi$
$434$	−0.828427			−0.0397658
$435$		0			0
$436$	−11.6569			−0.558262
$437$		0			0
$438$		0			0
$439$	0.970563			0.0463224			0.0231612	−	0.999732i	$-0.492627\pi$
$439$	0.970563			0.0463224			0.0231612	+	0.999732i	$0.492627\pi$
$440$	0.828427	+	1.65685i	0.0394937	+	0.0789874i
$441$		0			0
$442$		−	4.00000i		−	0.190261i
$443$			6.34315i			0.301372i	0.988582	+	0.150686i	$0.0481482\pi$
$443$			6.34315i			0.301372i	−0.988582	+	0.150686i	$0.951852\pi$
$444$		0			0
$445$	−9.65685	+	4.82843i	−0.457779	+	0.228889i
$446$	−17.7990			−0.842807
$447$		0			0
$448$		−	0.828427i		−	0.0391395i
$449$	−12.1421			−0.573023			−0.286511	−	0.958077i	$-0.592496\pi$
$449$	−12.1421			−0.573023			−0.286511	+	0.958077i	$0.592496\pi$
$450$		0			0
$451$	−6.34315			−0.298687
$452$		−	14.0000i		−	0.658505i
$453$		0			0
$454$	17.6569			0.828677
$455$	−8.00000	+	4.00000i	−0.375046	+	0.187523i
$456$		0			0
$457$		−	31.3137i		−	1.46479i	−0.680878	−	0.732397i	$-0.738402\pi$
$457$		−	31.3137i		−	1.46479i	0.680878	−	0.732397i	$-0.261598\pi$
$458$		−	18.4853i		−	0.863760i
$459$		0			0
$460$	8.48528	+	16.9706i	0.395628	+	0.791257i
$461$	19.3137			0.899529			0.449765	−	0.893147i	$-0.351508\pi$
$461$	19.3137			0.899529			0.449765	+	0.893147i	$0.351508\pi$
$462$		0			0
$463$		−	3.17157i		−	0.147395i	−0.997281	−	0.0736977i	$-0.976520\pi$
$463$		−	3.17157i		−	0.147395i	0.997281	−	0.0736977i	$-0.0234800\pi$
$464$	9.65685			0.448308
$465$		0			0
$466$	6.97056			0.322905
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		0			0
$469$	−7.59798			−0.350842
$470$	11.3137	−	5.65685i	0.521862	−	0.260931i
$471$		0			0
$472$		−	3.17157i		−	0.145983i
$473$			8.00000i			0.367840i
$474$		0			0
$475$		0			0
$476$	−0.686292			−0.0314561
$477$		0			0
$478$			0.686292i			0.0313902i
$479$	21.1716			0.967354			0.483677	−	0.875247i	$-0.339301\pi$
$479$	21.1716			0.967354			0.483677	+	0.875247i	$0.339301\pi$
$480$		0			0
$481$	−50.6274			−2.30841
$482$			22.0000i			1.00207i
$483$		0			0
$484$	10.3137			0.468805
$485$	11.3137	+	22.6274i	0.513729	+	1.02746i
$486$		0			0
$487$			20.1421i			0.912727i	0.889793	+	0.456364i	$0.150848\pi$
$487$			20.1421i			0.912727i	−0.889793	+	0.456364i	$0.849152\pi$
$488$		−	0.828427i		−	0.0375011i
$489$		0			0
$490$	−6.31371	−	12.6274i	−0.285224	−	0.570449i
$491$	43.4558			1.96113			0.980567	−	0.196183i	$-0.0628545\pi$
$491$	43.4558			1.96113			0.980567	+	0.196183i	$0.0628545\pi$
$492$		0			0
$493$		−	8.00000i		−	0.360302i
$494$		0			0
$495$		0			0
$496$	1.00000			0.0449013
$497$			2.34315i			0.105104i
$498$		0			0
$499$	−18.1421			−0.812154			−0.406077	−	0.913839i	$-0.633103\pi$
$499$	−18.1421			−0.812154			−0.406077	+	0.913839i	$0.633103\pi$
$500$	2.00000	−	11.0000i	0.0894427	−	0.491935i
$501$		0			0
$502$		−	3.17157i		−	0.141554i
$503$			12.6863i			0.565654i	0.959171	+	0.282827i	$0.0912722\pi$
$503$			12.6863i			0.565654i	−0.959171	+	0.282827i	$0.908728\pi$
$504$		0			0
$505$	22.6274	−	11.3137i	1.00691	−	0.503453i
$506$	−7.02944			−0.312497
$507$		0			0
$508$		−	16.1421i		−	0.716191i
$509$	20.9706			0.929504			0.464752	−	0.885441i	$-0.346144\pi$
$509$	20.9706			0.929504			0.464752	+	0.885441i	$0.346144\pi$
$510$		0			0
$511$	−11.3137			−0.500489
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−15.6569			−0.690594
$515$	−1.51472	−	3.02944i	−0.0667465	−	0.133493i
$516$		0			0
$517$			4.68629i			0.206103i
$518$			8.68629i			0.381654i
$519$		0			0
$520$	9.65685	−	4.82843i	0.423481	−	0.211741i
$521$	−34.2843			−1.50202			−0.751011	−	0.660290i	$-0.770433\pi$
$521$	−34.2843			−1.50202			−0.751011	+	0.660290i	$0.770433\pi$
$522$		0			0
$523$		−	22.6274i		−	0.989428i	−0.869056	−	0.494714i	$-0.835273\pi$
$523$		−	22.6274i		−	0.989428i	0.869056	−	0.494714i	$-0.164727\pi$
$524$	18.4853			0.807533
$525$		0			0
$526$	−24.4853			−1.06761
$527$		−	0.828427i		−	0.0360869i
$528$		0			0
$529$	−49.0000			−2.13043
$530$	0.686292	−	0.343146i	0.0298106	−	0.0149053i
$531$		0			0
$532$		0			0
$533$			36.9706i			1.60137i
$534$		0			0
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$	9.17157			0.396152
$537$		0			0
$538$		−	4.97056i		−	0.214296i
$539$	5.23045			0.225291
$540$		0			0
$541$	22.2843			0.958076			0.479038	−	0.877794i	$-0.340986\pi$
$541$	22.2843			0.958076			0.479038	+	0.877794i	$0.340986\pi$
$542$		−	13.6569i		−	0.586612i
$543$		0			0
$544$	0.828427			0.0355185
$545$	−23.3137	+	11.6569i	−0.998650	+	0.499325i
$546$		0			0
$547$			9.85786i			0.421492i	0.977541	+	0.210746i	$0.0675893\pi$
$547$			9.85786i			0.421492i	−0.977541	+	0.210746i	$0.932411\pi$
$548$		−	6.48528i		−	0.277037i
$549$		0			0
$550$	3.31371	+	2.48528i	0.141297	+	0.105973i
$551$		0			0
$552$		0			0
$553$		−	9.37258i		−	0.398563i
$554$	−4.14214			−0.175982
$555$		0			0
$556$	−14.1421			−0.599760
$557$		−	17.3137i		−	0.733605i	−0.930299	−	0.366803i	$-0.880452\pi$
$557$		−	17.3137i		−	0.733605i	0.930299	−	0.366803i	$-0.119548\pi$
$558$		0			0
$559$	46.6274			1.97213
$560$	−0.828427	−	1.65685i	−0.0350074	−	0.0700149i
$561$		0			0
$562$			21.3137i			0.899065i
$563$			4.97056i			0.209484i	0.994499	+	0.104742i	$0.0334017\pi$
$563$			4.97056i			0.209484i	−0.994499	+	0.104742i	$0.966598\pi$
$564$		0			0
$565$	−14.0000	−	28.0000i	−0.588984	−	1.17797i
$566$	−14.8284			−0.623285
$567$		0			0
$568$		−	2.82843i		−	0.118678i
$569$	−19.1716			−0.803714			−0.401857	−	0.915702i	$-0.631635\pi$
$569$	−19.1716			−0.803714			−0.401857	+	0.915702i	$0.631635\pi$
$570$		0			0
$571$	−33.1716			−1.38819			−0.694094	−	0.719885i	$-0.744195\pi$
$571$	−33.1716			−1.38819			−0.694094	+	0.719885i	$0.744195\pi$
$572$			4.00000i			0.167248i
$573$		0			0
$574$	6.34315			0.264758
$575$	33.9411	+	25.4558i	1.41544	+	1.06158i
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$			16.3137i			0.678561i
$579$		0			0
$580$	19.3137	−	9.65685i	0.801958	−	0.400979i
$581$	1.37258			0.0569443
$582$		0			0
$583$			0.284271i			0.0117733i
$584$	13.6569			0.565125
$585$		0			0
$586$	2.00000			0.0826192
$587$			7.31371i			0.301869i	0.988544	+	0.150935i	$0.0482283\pi$
$587$			7.31371i			0.301869i	−0.988544	+	0.150935i	$0.951772\pi$
$588$		0			0
$589$		0			0
$590$	−3.17157	−	6.34315i	−0.130572	−	0.261143i
$591$		0			0
$592$		−	10.4853i		−	0.430942i
$593$		−	26.9706i		−	1.10755i	−0.832667	−	0.553774i	$-0.813187\pi$
$593$		−	26.9706i		−	1.10755i	0.832667	−	0.553774i	$-0.186813\pi$
$594$		0			0
$595$	−1.37258	+	0.686292i	−0.0562704	+	0.0281352i
$596$	0.686292			0.0281116
$597$		0			0
$598$			40.9706i			1.67541i
$599$	21.4558			0.876662			0.438331	−	0.898814i	$-0.355570\pi$
$599$	21.4558			0.876662			0.438331	+	0.898814i	$0.355570\pi$
$600$		0			0
$601$	18.0000			0.734235			0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000			0.734235			0.367118	+	0.930175i	$0.380345\pi$
$602$		−	8.00000i		−	0.326056i
$603$		0			0
$604$	−21.6569			−0.881205
$605$	20.6274	−	10.3137i	0.838624	−	0.419312i
$606$		0			0
$607$		−	9.79899i		−	0.397729i	−0.980027	−	0.198864i	$-0.936275\pi$
$607$		−	9.79899i		−	0.397729i	0.980027	−	0.198864i	$-0.0637253\pi$
$608$		0			0
$609$		0			0
$610$	−0.828427	−	1.65685i	−0.0335420	−	0.0670841i
$611$	27.3137			1.10499
$612$		0			0
$613$			49.1127i			1.98364i	0.127632	+	0.991822i	$0.459262\pi$
$613$			49.1127i			1.98364i	−0.127632	+	0.991822i	$0.540738\pi$
$614$	0.485281			0.0195844
$615$		0			0
$616$	0.686292			0.0276515
$617$		−	41.5980i		−	1.67467i	−0.546689	−	0.837336i	$-0.684112\pi$
$617$		−	41.5980i		−	1.67467i	0.546689	−	0.837336i	$-0.315888\pi$
$618$		0			0
$619$	15.5147			0.623589			0.311795	−	0.950150i	$-0.399070\pi$
$619$	15.5147			0.623589			0.311795	+	0.950150i	$0.399070\pi$
$620$	2.00000	−	1.00000i	0.0803219	−	0.0401610i
$621$		0			0
$622$			16.4853i			0.661000i
$623$			4.00000i			0.160257i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	0.970563			0.0387915
$627$		0			0
$628$		−	17.3137i		−	0.690892i
$629$	−8.68629			−0.346345
$630$		0			0
$631$	14.6274			0.582308			0.291154	−	0.956676i	$-0.405961\pi$
$631$	14.6274			0.582308			0.291154	+	0.956676i	$0.405961\pi$
$632$			11.3137i			0.450035i
$633$		0			0
$634$	13.3137			0.528755
$635$	−16.1421	−	32.2843i	−0.640581	−	1.28116i
$636$		0			0
$637$		−	30.4853i		−	1.20787i
$638$			8.00000i			0.316723i
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	19.4558			0.768460			0.384230	−	0.923237i	$-0.374467\pi$
$641$	19.4558			0.768460			0.384230	+	0.923237i	$0.374467\pi$
$642$		0			0
$643$			8.00000i			0.315489i	0.987480	+	0.157745i	$0.0504223\pi$
$643$			8.00000i			0.315489i	−0.987480	+	0.157745i	$0.949578\pi$
$644$	7.02944			0.276999
$645$		0			0
$646$		0			0
$647$		−	18.1421i		−	0.713241i	−0.934249	−	0.356620i	$-0.883929\pi$
$647$		−	18.1421i		−	0.713241i	0.934249	−	0.356620i	$-0.116071\pi$
$648$		0			0
$649$	2.62742			0.103135
$650$	14.4853	−	19.3137i	0.568159	−	0.757546i
$651$		0			0
$652$		−	14.8284i		−	0.580726i
$653$		−	14.0000i		−	0.547862i	−0.961749	−	0.273931i	$-0.911676\pi$
$653$		−	14.0000i		−	0.547862i	0.961749	−	0.273931i	$-0.0883240\pi$
$654$		0			0
$655$	36.9706	−	18.4853i	1.44456	−	0.722280i
$656$	−7.65685			−0.298950
$657$		0			0
$658$		−	4.68629i		−	0.182691i
$659$	−11.1716			−0.435183			−0.217591	−	0.976040i	$-0.569820\pi$
$659$	−11.1716			−0.435183			−0.217591	+	0.976040i	$0.569820\pi$
$660$		0			0
$661$	24.6274			0.957896			0.478948	−	0.877843i	$-0.341018\pi$
$661$	24.6274			0.957896			0.478948	+	0.877843i	$0.341018\pi$
$662$			12.4853i			0.485254i
$663$		0			0
$664$	−1.65685			−0.0642984
$665$		0			0
$666$		0			0
$667$			81.9411i			3.17277i
$668$		−	0.485281i		−	0.0187761i
$669$		0			0
$670$	18.3431	−	9.17157i	0.708658	−	0.354329i
$671$	0.686292			0.0264940
$672$		0			0
$673$		−	7.02944i		−	0.270965i	−0.990780	−	0.135482i	$-0.956742\pi$
$673$		−	7.02944i		−	0.270965i	0.990780	−	0.135482i	$-0.0432584\pi$
$674$	5.65685			0.217894
$675$		0			0
$676$	10.3137			0.396681
$677$			38.0000i			1.46046i	0.683202	+	0.730229i	$0.260587\pi$
$677$			38.0000i			1.46046i	−0.683202	+	0.730229i	$0.739413\pi$
$678$		0			0
$679$	9.37258			0.359687
$680$	1.65685	−	0.828427i	0.0635375	−	0.0317687i
$681$		0			0
$682$			0.828427i			0.0317221i
$683$			24.2843i			0.929212i	0.885518	+	0.464606i	$0.153804\pi$
$683$			24.2843i			0.929212i	−0.885518	+	0.464606i	$0.846196\pi$
$684$		0			0
$685$	−6.48528	−	12.9706i	−0.247790	−	0.495580i
$686$	−11.0294			−0.421106
$687$		0			0
$688$			9.65685i			0.368164i
$689$	1.65685			0.0631211
$690$		0			0
$691$	−44.2843			−1.68465			−0.842327	−	0.538968i	$-0.818815\pi$
$691$	−44.2843			−1.68465			−0.842327	+	0.538968i	$0.818815\pi$
$692$			1.31371i			0.0499397i
$693$		0			0
$694$	17.6569			0.670245
$695$	−28.2843	+	14.1421i	−1.07288	+	0.536442i
$696$		0			0
$697$			6.34315i			0.240264i
$698$			25.3137i			0.958138i
$699$		0			0
$700$	−3.31371	−	2.48528i	−0.125246	−	0.0939348i
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$		0			0
$703$		0			0
$704$	−0.828427			−0.0312225
$705$		0			0
$706$	23.1716			0.872074
$707$		−	9.37258i		−	0.352492i
$708$		0			0
$709$	40.8284			1.53334			0.766672	−	0.642039i	$-0.221911\pi$
$709$	40.8284			1.53334			0.766672	+	0.642039i	$0.221911\pi$
$710$	−2.82843	−	5.65685i	−0.106149	−	0.212298i
$711$		0			0
$712$		−	4.82843i		−	0.180953i
$713$			8.48528i			0.317776i
$714$		0			0
$715$	4.00000	+	8.00000i	0.149592	+	0.299183i
$716$	11.1716			0.417501
$717$		0			0
$718$			10.1421i			0.378501i
$719$	−35.3137			−1.31698			−0.658490	−	0.752590i	$-0.728804\pi$
$719$	−35.3137			−1.31698			−0.658490	+	0.752590i	$0.728804\pi$
$720$		0			0
$721$	−1.25483			−0.0467325
$722$		−	19.0000i		−	0.707107i
$723$		0			0
$724$	−24.8284			−0.922741
$725$	28.9706	−	38.6274i	1.07594	−	1.43459i
$726$		0			0
$727$		−	29.5147i		−	1.09464i	−0.836923	−	0.547320i	$-0.815648\pi$
$727$		−	29.5147i		−	1.09464i	0.836923	−	0.547320i	$-0.184352\pi$
$728$		−	4.00000i		−	0.148250i
$729$		0			0
$730$	27.3137	−	13.6569i	1.01093	−	0.505463i
$731$	8.00000			0.295891
$732$		0			0
$733$			16.3431i			0.603648i	0.953364	+	0.301824i	$0.0975955\pi$
$733$			16.3431i			0.603648i	−0.953364	+	0.301824i	$0.902405\pi$
$734$	28.1421			1.03875
$735$		0			0
$736$	−8.48528			−0.312772
$737$			7.59798i			0.279875i
$738$		0			0
$739$	3.51472			0.129291			0.0646455	−	0.997908i	$-0.479408\pi$
$739$	3.51472			0.129291			0.0646455	+	0.997908i	$0.479408\pi$
$740$	−10.4853	−	20.9706i	−0.385447	−	0.770893i
$741$		0			0
$742$		−	0.284271i		−	0.0104359i
$743$		−	21.4558i		−	0.787139i	−0.919295	−	0.393569i	$-0.871240\pi$
$743$		−	21.4558i		−	0.787139i	0.919295	−	0.393569i	$-0.128760\pi$
$744$		0			0
$745$	1.37258	−	0.686292i	0.0502876	−	0.0251438i
$746$	0.343146			0.0125635
$747$		0			0
$748$			0.686292i			0.0250933i
$749$	3.31371			0.121080
$750$		0			0
$751$	−4.28427			−0.156335			−0.0781676	−	0.996940i	$-0.524907\pi$
$751$	−4.28427			−0.156335			−0.0781676	+	0.996940i	$0.524907\pi$
$752$			5.65685i			0.206284i
$753$		0			0
$754$	46.6274			1.69807
$755$	−43.3137	+	21.6569i	−1.57635	+	0.788174i
$756$		0			0
$757$		−	9.51472i		−	0.345818i	−0.984938	−	0.172909i	$-0.944683\pi$
$757$		−	9.51472i		−	0.345818i	0.984938	−	0.172909i	$-0.0553167\pi$
$758$			9.65685i			0.350753i
$759$		0			0
$760$		0			0
$761$	−33.1127			−1.20033			−0.600167	−	0.799875i	$-0.704899\pi$
$761$	−33.1127			−1.20033			−0.600167	+	0.799875i	$0.704899\pi$
$762$		0			0
$763$			9.65685i			0.349602i
$764$	−0.485281			−0.0175569
$765$		0			0
$766$	−11.5147			−0.416044
$767$		−	15.3137i		−	0.552946i
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$	1.37258	−	0.686292i	0.0494645	−	0.0247322i
$771$		0			0
$772$			15.3137i			0.551152i
$773$		−	0.343146i		−	0.0123421i	−0.999981	−	0.00617105i	$-0.998036\pi$
$773$		−	0.343146i		−	0.0123421i	0.999981	−	0.00617105i	$-0.00196432\pi$
$774$		0			0
$775$	3.00000	−	4.00000i	0.107763	−	0.143684i
$776$	−11.3137			−0.406138
$777$		0			0
$778$			12.6863i			0.454826i
$779$		0			0
$780$		0			0
$781$	2.34315			0.0838443
$782$			7.02944i			0.251372i
$783$		0			0
$784$	6.31371			0.225490
$785$	−17.3137	−	34.6274i	−0.617953	−	1.23591i
$786$		0			0
$787$		−	24.9706i		−	0.890104i	−0.895505	−	0.445052i	$-0.853185\pi$
$787$		−	24.9706i		−	0.890104i	0.895505	−	0.445052i	$-0.146815\pi$
$788$		−	26.9706i		−	0.960787i
$789$		0			0
$790$	11.3137	+	22.6274i	0.402524	+	0.805047i
$791$	−11.5980			−0.412377
$792$		0			0
$793$		−	4.00000i		−	0.142044i
$794$	−15.6569			−0.555641
$795$		0			0
$796$	13.6569			0.484054
$797$			1.31371i			0.0465339i	0.999729	+	0.0232670i	$0.00740678\pi$
$797$			1.31371i			0.0465339i	−0.999729	+	0.0232670i	$0.992593\pi$
$798$		0			0
$799$	4.68629			0.165789
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$		0			0
$802$		−	2.48528i		−	0.0877583i
$803$			11.3137i			0.399252i
$804$		0			0
$805$	14.0589	−	7.02944i	0.495510	−	0.247755i
$806$	4.82843			0.170074
$807$		0			0
$808$			11.3137i			0.398015i
$809$	−18.4853			−0.649908			−0.324954	−	0.945730i	$-0.605349\pi$
$809$	−18.4853			−0.649908			−0.324954	+	0.945730i	$0.605349\pi$
$810$		0			0
$811$	−20.9706			−0.736376			−0.368188	−	0.929751i	$-0.620022\pi$
$811$	−20.9706			−0.736376			−0.368188	+	0.929751i	$0.620022\pi$
$812$		−	8.00000i		−	0.280745i
$813$		0			0
$814$	8.68629			0.304454
$815$	−14.8284	−	29.6569i	−0.519417	−	1.03883i
$816$		0			0
$817$		0			0
$818$		−	33.3137i		−	1.16479i
$819$		0			0
$820$	−15.3137	+	7.65685i	−0.534778	+	0.267389i
$821$	−25.6569			−0.895430			−0.447715	−	0.894176i	$-0.647762\pi$
$821$	−25.6569			−0.895430			−0.447715	+	0.894176i	$0.647762\pi$
$822$		0			0
$823$			31.1716i			1.08657i	0.839547	+	0.543286i	$0.182820\pi$
$823$			31.1716i			1.08657i	−0.839547	+	0.543286i	$0.817180\pi$
$824$	1.51472			0.0527677
$825$		0			0
$826$	−2.62742			−0.0914195
$827$			39.3137i			1.36707i	0.729917	+	0.683536i	$0.239559\pi$
$827$			39.3137i			1.36707i	−0.729917	+	0.683536i	$0.760441\pi$
$828$		0			0
$829$	−19.1716			−0.665856			−0.332928	−	0.942952i	$-0.608037\pi$
$829$	−19.1716			−0.665856			−0.332928	+	0.942952i	$0.608037\pi$
$830$	−3.31371	+	1.65685i	−0.115021	+	0.0575103i
$831$		0			0
$832$			4.82843i			0.167396i
$833$		−	5.23045i		−	0.181224i
$834$		0			0
$835$	−0.485281	−	0.970563i	−0.0167939	−	0.0335877i
$836$		0			0
$837$		0			0
$838$		−	9.79899i		−	0.338500i
$839$	40.7696			1.40752			0.703761	−	0.710437i	$-0.251503\pi$
$839$	40.7696			1.40752			0.703761	+	0.710437i	$0.251503\pi$
$840$		0			0
$841$	64.2548			2.21568
$842$			14.0000i			0.482472i
$843$		0			0
$844$	−23.3137			−0.802491
$845$	20.6274	−	10.3137i	0.709605	−	0.354802i
$846$		0			0
$847$		−	8.54416i		−	0.293581i
$848$			0.343146i			0.0117837i
$849$		0			0
$850$	2.48528	−	3.31371i	0.0852444	−	0.113659i
$851$	88.9706			3.04987
$852$		0			0
$853$		−	21.3137i		−	0.729767i	−0.931053	−	0.364884i	$-0.881109\pi$
$853$		−	21.3137i		−	0.729767i	0.931053	−	0.364884i	$-0.118891\pi$
$854$	−0.686292			−0.0234844
$855$		0			0
$856$	−4.00000			−0.136717
$857$		−	6.68629i		−	0.228399i	−0.993458	−	0.114200i	$-0.963570\pi$
$857$		−	6.68629i		−	0.228399i	0.993458	−	0.114200i	$-0.0364304\pi$
$858$		0			0
$859$	42.4264			1.44757			0.723785	−	0.690025i	$-0.242401\pi$
$859$	42.4264			1.44757			0.723785	+	0.690025i	$0.242401\pi$
$860$	9.65685	+	19.3137i	0.329296	+	0.658592i
$861$		0			0
$862$			1.17157i			0.0399039i
$863$		−	3.79899i		−	0.129319i	−0.997907	−	0.0646596i	$-0.979404\pi$
$863$		−	3.79899i		−	0.129319i	0.997907	−	0.0646596i	$-0.0205961\pi$
$864$		0			0
$865$	1.31371	+	2.62742i	0.0446674	+	0.0893349i
$866$	−13.6569			−0.464079
$867$		0			0
$868$		−	0.828427i		−	0.0281186i
$869$	−9.37258			−0.317943
$870$		0			0
$871$	44.2843			1.50052
$872$		−	11.6569i		−	0.394751i
$873$		0			0
$874$		0			0
$875$	−9.11270	−	1.65685i	−0.308065	−	0.0560119i
$876$		0			0
$877$		−	23.6569i		−	0.798835i	−0.916769	−	0.399418i	$-0.869212\pi$
$877$		−	23.6569i		−	0.798835i	0.916769	−	0.399418i	$-0.130788\pi$
$878$			0.970563i			0.0327549i
$879$		0			0
$880$	−1.65685	+	0.828427i	−0.0558525	+	0.0279263i
$881$	36.1421			1.21766			0.608830	−	0.793301i	$-0.291639\pi$
$881$	36.1421			1.21766			0.608830	+	0.793301i	$0.291639\pi$
$882$		0			0
$883$		−	0.970563i		−	0.0326620i	−0.999867	−	0.0163310i	$-0.994801\pi$
$883$		−	0.970563i		−	0.0326620i	0.999867	−	0.0163310i	$-0.00519856\pi$
$884$	4.00000			0.134535
$885$		0			0
$886$	−6.34315			−0.213102
$887$			20.0000i			0.671534i	0.941945	+	0.335767i	$0.108996\pi$
$887$			20.0000i			0.671534i	−0.941945	+	0.335767i	$0.891004\pi$
$888$		0			0
$889$	−13.3726			−0.448502
$890$	−4.82843	−	9.65685i	−0.161849	−	0.323698i
$891$		0			0
$892$		−	17.7990i		−	0.595954i
$893$		0			0
$894$		0			0
$895$	22.3431	−	11.1716i	0.746849	−	0.373424i
$896$	0.828427			0.0276758
$897$		0			0
$898$		−	12.1421i		−	0.405188i
$899$	9.65685			0.322074
$900$		0			0
$901$	0.284271			0.00947045
$902$		−	6.34315i		−	0.211204i
$903$		0			0
$904$	14.0000			0.465633
$905$	−49.6569	+	24.8284i	−1.65065	+	0.825325i
$906$		0			0
$907$			38.1421i			1.26649i	0.773952	+	0.633244i	$0.218277\pi$
$907$			38.1421i			1.26649i	−0.773952	+	0.633244i	$0.781723\pi$
$908$			17.6569i			0.585963i
$909$		0			0
$910$	−4.00000	−	8.00000i	−0.132599	−	0.265197i
$911$	49.9411			1.65462			0.827312	−	0.561743i	$-0.189869\pi$
$911$	49.9411			1.65462			0.827312	+	0.561743i	$0.189869\pi$
$912$		0			0
$913$		−	1.37258i		−	0.0454259i
$914$	31.3137			1.03577
$915$		0			0
$916$	18.4853			0.610771
$917$		−	15.3137i		−	0.505703i
$918$		0			0
$919$	16.9706			0.559807			0.279904	−	0.960028i	$-0.409697\pi$
$919$	16.9706			0.559807			0.279904	+	0.960028i	$0.409697\pi$
$920$	−16.9706	+	8.48528i	−0.559503	+	0.279751i
$921$		0			0
$922$			19.3137i			0.636063i
$923$		−	13.6569i		−	0.449521i
$924$		0			0
$925$	−41.9411	−	31.4558i	−1.37902	−	1.03426i
$926$	3.17157			0.104224
$927$		0			0
$928$			9.65685i			0.317002i
$929$	−36.1421			−1.18579			−0.592893	−	0.805282i	$-0.702014\pi$
$929$	−36.1421			−1.18579			−0.592893	+	0.805282i	$0.702014\pi$
$930$		0			0
$931$		0			0
$932$			6.97056i			0.228328i
$933$		0			0
$934$	36.0000			1.17796
$935$	0.686292	+	1.37258i	0.0224441	+	0.0448883i
$936$		0			0
$937$		−	22.6274i		−	0.739205i	−0.929190	−	0.369603i	$-0.879494\pi$
$937$		−	22.6274i		−	0.739205i	0.929190	−	0.369603i	$-0.120506\pi$
$938$		−	7.59798i		−	0.248083i
$939$		0			0
$940$	5.65685	+	11.3137i	0.184506	+	0.369012i
$941$	40.0000			1.30396			0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000			1.30396			0.651981	+	0.758235i	$0.273938\pi$
$942$		0			0
$943$		−	64.9706i		−	2.11573i
$944$	3.17157			0.103226
$945$		0			0
$946$	−8.00000			−0.260102
$947$		−	54.9117i		−	1.78439i	−0.451650	−	0.892195i	$-0.649165\pi$
$947$		−	54.9117i		−	1.78439i	0.451650	−	0.892195i	$-0.350835\pi$
$948$		0			0
$949$	65.9411			2.14054
$950$		0			0
$951$		0			0
$952$		−	0.686292i		−	0.0222428i
$953$			5.79899i			0.187848i	0.995579	+	0.0939239i	$0.0299410\pi$
$953$			5.79899i			0.187848i	−0.995579	+	0.0939239i	$0.970059\pi$
$954$		0			0
$955$	−0.970563	+	0.485281i	−0.0314067	+	0.0157033i
$956$	−0.686292			−0.0221963
$957$		0			0
$958$			21.1716i			0.684022i
$959$	−5.37258			−0.173490
$960$		0			0
$961$	1.00000			0.0322581
$962$		−	50.6274i		−	1.63229i
$963$		0			0
$964$	−22.0000			−0.708572
$965$	15.3137	+	30.6274i	0.492966	+	0.985931i
$966$		0			0
$967$			7.17157i			0.230622i	0.993329	+	0.115311i	$0.0367865\pi$
$967$			7.17157i			0.230622i	−0.993329	+	0.115311i	$0.963213\pi$
$968$			10.3137i			0.331495i
$969$		0			0
$970$	−22.6274	+	11.3137i	−0.726523	+	0.363261i
$971$	7.45584			0.239269			0.119635	−	0.992818i	$-0.461828\pi$
$971$	7.45584			0.239269			0.119635	+	0.992818i	$0.461828\pi$
$972$		0			0
$973$			11.7157i			0.375589i
$974$	−20.1421			−0.645396
$975$		0			0
$976$	0.828427			0.0265173
$977$			27.6569i			0.884821i	0.896813	+	0.442411i	$0.145877\pi$
$977$			27.6569i			0.884821i	−0.896813	+	0.442411i	$0.854123\pi$
$978$		0			0
$979$	4.00000			0.127841
$980$	12.6274	−	6.31371i	0.403368	−	0.201684i
$981$		0			0
$982$			43.4558i			1.38673i
$983$			36.4853i			1.16370i	0.813296	+	0.581850i	$0.197671\pi$
$983$			36.4853i			1.16370i	−0.813296	+	0.581850i	$0.802329\pi$
$984$		0			0
$985$	−26.9706	−	53.9411i	−0.859354	−	1.71871i
$986$	8.00000			0.254772
$987$		0			0
$988$		0			0
$989$	−81.9411			−2.60558
$990$		0			0
$991$	−33.9411			−1.07818			−0.539088	−	0.842250i	$-0.681231\pi$
$991$	−33.9411			−1.07818			−0.539088	+	0.842250i	$0.681231\pi$
$992$			1.00000i			0.0317500i
$993$		0			0
$994$	−2.34315			−0.0743201
$995$	27.3137	−	13.6569i	0.865903	−	0.432951i
$996$		0			0
$997$			10.2843i			0.325706i	0.986650	+	0.162853i	$0.0520697\pi$
$997$			10.2843i			0.325706i	−0.986650	+	0.162853i	$0.947930\pi$
$998$		−	18.1421i		−	0.574279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.d.i.559.4		4
3.2	odd	2		930.2.d.g.559.2	✓	4
5.4	even	2	inner	2790.2.d.i.559.1		4
15.2	even	4		4650.2.a.cf.1.1		2
15.8	even	4		4650.2.a.cc.1.2		2
15.14	odd	2		930.2.d.g.559.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.g.559.2	✓	4	3.2	odd	2
930.2.d.g.559.3	yes	4	15.14	odd	2
2790.2.d.i.559.1		4	5.4	even	2	inner
2790.2.d.i.559.4		4	1.1	even	1	trivial
4650.2.a.cc.1.2		2	15.8	even	4
4650.2.a.cf.1.1		2	15.2	even	4

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:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +0.828427i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +0.828427i q^{7} -1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} +0.828427 q^{11} -4.82843i q^{13} -0.828427 q^{14} +1.00000 q^{16} -0.828427i q^{17} +(2.00000 - 1.00000i) q^{20} +0.828427i q^{22} +8.48528i q^{23} +(3.00000 - 4.00000i) q^{25} +4.82843 q^{26} -0.828427i q^{28} +9.65685 q^{29} +1.00000 q^{31} +1.00000i q^{32} +0.828427 q^{34} +(-0.828427 - 1.65685i) q^{35} -10.4853i q^{37} +(1.00000 + 2.00000i) q^{40} -7.65685 q^{41} +9.65685i q^{43} -0.828427 q^{44} -8.48528 q^{46} +5.65685i q^{47} +6.31371 q^{49} +(4.00000 + 3.00000i) q^{50} +4.82843i q^{52} +0.343146i q^{53} +(-1.65685 + 0.828427i) q^{55} +0.828427 q^{56} +9.65685i q^{58} +3.17157 q^{59} +0.828427 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(4.82843 + 9.65685i) q^{65} +9.17157i q^{67} +0.828427i q^{68} +(1.65685 - 0.828427i) q^{70} +2.82843 q^{71} +13.6569i q^{73} +10.4853 q^{74} +0.686292i q^{77} -11.3137 q^{79} +(-2.00000 + 1.00000i) q^{80} -7.65685i q^{82} -1.65685i q^{83} +(0.828427 + 1.65685i) q^{85} -9.65685 q^{86} -0.828427i q^{88} +4.82843 q^{89} +4.00000 q^{91} -8.48528i q^{92} -5.65685 q^{94} -11.3137i q^{97} +6.31371i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 8 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 8 * q^5	\( 4 q - 4 q^{4} - 8 q^{5} - 4 q^{10} - 8 q^{11} + 8 q^{14} + 4 q^{16} + 8 q^{20} + 12 q^{25} + 8 q^{26} + 16 q^{29} + 4 q^{31} - 8 q^{34} + 8 q^{35} + 4 q^{40} - 8 q^{41} + 8 q^{44} - 20 q^{49} + 16 q^{50} + 16 q^{55} - 8 q^{56} + 24 q^{59} - 8 q^{61} - 4 q^{64} + 8 q^{65} - 16 q^{70} + 8 q^{74} - 8 q^{80} - 8 q^{85} - 16 q^{86} + 8 q^{89} + 16 q^{91}+O(q^{100}) \) 4 * q - 4 * q^4 - 8 * q^5 - 4 * q^10 - 8 * q^11 + 8 * q^14 + 4 * q^16 + 8 * q^20 + 12 * q^25 + 8 * q^26 + 16 * q^29 + 4 * q^31 - 8 * q^34 + 8 * q^35 + 4 * q^40 - 8 * q^41 + 8 * q^44 - 20 * q^49 + 16 * q^50 + 16 * q^55 - 8 * q^56 + 24 * q^59 - 8 * q^61 - 4 * q^64 + 8 * q^65 - 16 * q^70 + 8 * q^74 - 8 * q^80 - 8 * q^85 - 16 * q^86 + 8 * q^89 + 16 * q^91

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