LMFDB - Embedded newform 2898.2.g.j.2575.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2898,2,Mod(2575,2898)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2898, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2898.2575");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2898.g (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:	$23.1406465058$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 326x^{12} + 27081x^{8} + 96196x^{4} + 65536 $ x^16 + 326x^12 + 27081x^8 + 96196*x^4 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 966)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2575.7
Root			$-0.691340 - 0.691340i$ of defining polynomial
Character	$\chi$	$=$	2898.2575
Dual form			2898.2.g.j.2575.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} -0.952834 q^{5} +(0.691340 - 2.55383i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} -0.952834 q^{5} +(0.691340 - 2.55383i) q^{7} -1.00000 q^{8} +0.952834 q^{10} -1.02228i q^{11} +5.28761i q^{13} +(-0.691340 + 2.55383i) q^{14} +1.00000 q^{16} -1.38268 q^{17} +5.99105 q^{19} -0.952834 q^{20} +1.02228i q^{22} +(-3.53113 + 3.24517i) q^{23} -4.09211 q^{25} -5.28761i q^{26} +(0.691340 - 2.55383i) q^{28} -5.57914 q^{29} -1.00000 q^{32} +1.38268 q^{34} +(-0.658732 + 2.43338i) q^{35} +0.429846i q^{37} -5.99105 q^{38} +0.952834 q^{40} -1.28761i q^{41} -4.67781i q^{43} -1.02228i q^{44} +(3.53113 - 3.24517i) q^{46} -7.09211i q^{47} +(-6.04410 - 3.53113i) q^{49} +4.09211 q^{50} +5.28761i q^{52} +8.75641i q^{53} +0.974060i q^{55} +(-0.691340 + 2.55383i) q^{56} +5.57914 q^{58} -1.70848i q^{59} -7.37373 q^{61} +1.00000 q^{64} -5.03822i q^{65} +11.6217i q^{67} -1.38268 q^{68} +(0.658732 - 2.43338i) q^{70} +2.29152 q^{71} -2.19551i q^{73} -0.429846i q^{74} +5.99105 q^{76} +(-2.61072 - 0.706741i) q^{77} +9.77869i q^{79} -0.952834 q^{80} +1.28761i q^{82} +5.46806 q^{83} +1.31746 q^{85} +4.67781i q^{86} +1.02228i q^{88} +8.69375 q^{89} +(13.5037 + 3.65554i) q^{91} +(-3.53113 + 3.24517i) q^{92} +7.09211i q^{94} -5.70848 q^{95} -19.2038 q^{97} +(6.04410 + 3.53113i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} + 36 q^{25} - 20 q^{29} - 16 q^{32} + 16 q^{35} - 8 q^{46} - 36 q^{50} + 20 q^{58} + 16 q^{64} - 16 q^{70} + 48 q^{71} - 20 q^{77} - 32 q^{85} + 8 q^{92} - 80 q^{95}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 + 36 * q^25 - 20 * q^29 - 16 * q^32 + 16 * q^35 - 8 * q^46 - 36 * q^50 + 20 * q^58 + 16 * q^64 - 16 * q^70 + 48 * q^71 - 20 * q^77 - 32 * q^85 + 8 * q^92 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2898\mathbb{Z}\right)^\times$.

$n$	$829$	$1289$	$1891$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.952834			−0.426120			−0.213060	−	0.977039i	$-0.568343\pi$
$5$	−0.952834			−0.426120			−0.213060	+	0.977039i	$0.568343\pi$
$6$		0			0
$7$	0.691340	−	2.55383i	0.261302	−	0.965257i
$7$	0.691340	−	2.55383i	0.261302	−	0.965257i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.952834			0.301313
$11$		−	1.02228i		−	0.308228i	−0.988053	−	0.154114i	$-0.950748\pi$
$11$		−	1.02228i		−	0.308228i	0.988053	−	0.154114i	$-0.0492523\pi$
$12$		0			0
$13$			5.28761i			1.46652i	0.679948	+	0.733260i	$0.262002\pi$
$13$			5.28761i			1.46652i	−0.679948	+	0.733260i	$0.737998\pi$
$14$	−0.691340	+	2.55383i	−0.184768	+	0.682540i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.38268			−0.335349			−0.167675	−	0.985842i	$-0.553626\pi$
$17$	−1.38268			−0.335349			−0.167675	+	0.985842i	$0.553626\pi$
$18$		0			0
$19$	5.99105			1.37444			0.687221	−	0.726449i	$-0.258831\pi$
$19$	5.99105			1.37444			0.687221	+	0.726449i	$0.258831\pi$
$20$	−0.952834			−0.213060
$21$		0			0
$22$			1.02228i			0.217950i
$23$	−3.53113	+	3.24517i	−0.736291	+	0.676665i
$23$	−3.53113	+	3.24517i	−0.736291	+	0.676665i
$24$		0			0
$25$	−4.09211			−0.818422
$26$		−	5.28761i		−	1.03699i
$27$		0			0
$28$	0.691340	−	2.55383i	0.130651	−	0.482629i
$29$	−5.57914			−1.03602			−0.518010	−	0.855375i	$-0.673327\pi$
$29$	−5.57914			−1.03602			−0.518010	+	0.855375i	$0.673327\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.38268			0.237128
$35$	−0.658732	+	2.43338i	−0.111346	+	0.411316i
$36$		0			0
$37$			0.429846i			0.0706662i	0.999376	+	0.0353331i	$0.0112492\pi$
$37$			0.429846i			0.0706662i	−0.999376	+	0.0353331i	$0.988751\pi$
$38$	−5.99105			−0.971877
$39$		0			0
$40$	0.952834			0.150656
$41$		−	1.28761i		−	0.201091i	−0.994932	−	0.100546i	$-0.967941\pi$
$41$		−	1.28761i		−	0.201091i	0.994932	−	0.100546i	$-0.0320589\pi$
$42$		0			0
$43$		−	4.67781i		−	0.713360i	−0.934227	−	0.356680i	$-0.883909\pi$
$43$		−	4.67781i		−	0.713360i	0.934227	−	0.356680i	$-0.116091\pi$
$44$		−	1.02228i		−	0.154114i
$45$		0			0
$46$	3.53113	−	3.24517i	0.520637	−	0.478474i
$47$		−	7.09211i		−	1.03449i	−0.855837	−	0.517245i	$-0.826958\pi$
$47$		−	7.09211i		−	1.03449i	0.855837	−	0.517245i	$-0.173042\pi$
$48$		0			0
$49$	−6.04410	−	3.53113i	−0.863443	−	0.504447i
$50$	4.09211			0.578711
$51$		0			0
$52$			5.28761i			0.733260i
$53$			8.75641i			1.20279i	0.798954	+	0.601393i	$0.205387\pi$
$53$			8.75641i			1.20279i	−0.798954	+	0.601393i	$0.794613\pi$
$54$		0			0
$55$			0.974060i			0.131342i
$56$	−0.691340	+	2.55383i	−0.0923842	+	0.341270i
$57$		0			0
$58$	5.57914			0.732577
$59$		−	1.70848i		−	0.222425i	−0.993797	−	0.111212i	$-0.964527\pi$
$59$		−	1.70848i		−	0.222425i	0.993797	−	0.111212i	$-0.0354734\pi$
$60$		0			0
$61$	−7.37373			−0.944109			−0.472055	−	0.881569i	$-0.656488\pi$
$61$	−7.37373			−0.944109			−0.472055	+	0.881569i	$0.656488\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$		−	5.03822i		−	0.624914i
$66$		0			0
$67$			11.6217i			1.41982i	0.704294	+	0.709908i	$0.251264\pi$
$67$			11.6217i			1.41982i	−0.704294	+	0.709908i	$0.748736\pi$
$68$	−1.38268			−0.167675
$69$		0			0
$70$	0.658732	−	2.43338i	0.0787335	−	0.290844i
$71$	2.29152			0.271954			0.135977	−	0.990712i	$-0.456583\pi$
$71$	2.29152			0.271954			0.135977	+	0.990712i	$0.456583\pi$
$72$		0			0
$73$		−	2.19551i		−	0.256965i	−0.991712	−	0.128482i	$-0.958989\pi$
$73$		−	2.19551i		−	0.256965i	0.991712	−	0.128482i	$-0.0410105\pi$
$74$		−	0.429846i		−	0.0499685i
$75$		0			0
$76$	5.99105			0.687221
$77$	−2.61072	−	0.706741i	−0.297519	−	0.0805406i
$78$		0			0
$79$			9.77869i			1.10019i	0.835103	+	0.550094i	$0.185408\pi$
$79$			9.77869i			1.10019i	−0.835103	+	0.550094i	$0.814592\pi$
$80$	−0.952834			−0.106530
$81$		0			0
$82$			1.28761i			0.142193i
$83$	5.46806			0.600198			0.300099	−	0.953908i	$-0.402980\pi$
$83$	5.46806			0.600198			0.300099	+	0.953908i	$0.402980\pi$
$84$		0			0
$85$	1.31746			0.142899
$86$			4.67781i			0.504422i
$87$		0			0
$88$			1.02228i			0.108975i
$89$	8.69375			0.921536			0.460768	−	0.887521i	$-0.347574\pi$
$89$	8.69375			0.921536			0.460768	+	0.887521i	$0.347574\pi$
$90$		0			0
$91$	13.5037	+	3.65554i	1.41557	+	0.383204i
$92$	−3.53113	+	3.24517i	−0.368146	+	0.338332i
$93$		0			0
$94$			7.09211i			0.731495i
$95$	−5.70848			−0.585677
$96$		0			0
$97$	−19.2038			−1.94985			−0.974923	−	0.222541i	$-0.928565\pi$
$97$	−19.2038			−1.94985			−0.974923	+	0.222541i	$0.928565\pi$
$98$	6.04410	+	3.53113i	0.610546	+	0.356698i
$99$		0			0
$100$	−4.09211			−0.409211
$101$			15.8927i			1.58138i	0.612216	+	0.790691i	$0.290278\pi$
$101$			15.8927i			1.58138i	−0.612216	+	0.790691i	$0.709722\pi$
$102$		0			0
$103$	1.74987			0.172420			0.0862099	−	0.996277i	$-0.472524\pi$
$103$	1.74987			0.172420			0.0862099	+	0.996277i	$0.472524\pi$
$104$		−	5.28761i		−	0.518493i
$105$		0			0
$106$		−	8.75641i		−	0.850498i
$107$			11.0987i			1.07295i	0.843915	+	0.536476i	$0.180245\pi$
$107$			11.0987i			1.07295i	−0.843915	+	0.536476i	$0.819755\pi$
$108$		0			0
$109$		−	2.33551i		−	0.223702i	−0.993725	−	0.111851i	$-0.964322\pi$
$109$		−	2.33551i		−	0.223702i	0.993725	−	0.111851i	$-0.0356779\pi$
$110$		−	0.974060i		−	0.0928730i
$111$		0			0
$112$	0.691340	−	2.55383i	0.0653255	−	0.241314i
$113$			10.2322i			0.962567i	0.876565	+	0.481284i	$0.159829\pi$
$113$			10.2322i			0.962567i	−0.876565	+	0.481284i	$0.840171\pi$
$114$		0			0
$115$	3.36458	−	3.09211i	0.313749	−	0.288341i
$116$	−5.57914			−0.518010
$117$		0			0
$118$			1.70848i			0.157278i
$119$	−0.955901	+	3.53113i	−0.0876273	+	0.323698i
$120$		0			0
$121$	9.95495			0.904995
$122$	7.37373			0.667586
$123$		0			0
$124$		0			0
$125$	8.66327			0.774866
$126$		0			0
$127$	−16.3499			−1.45082			−0.725408	−	0.688319i	$-0.758349\pi$
$127$	−16.3499			−1.45082			−0.725408	+	0.688319i	$0.758349\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$			5.03822i			0.441881i
$131$			11.1583i			0.974903i	0.873150	+	0.487452i	$0.162073\pi$
$131$			11.1583i			0.974903i	−0.873150	+	0.487452i	$0.837927\pi$
$132$		0			0
$133$	4.14185	−	15.3001i	0.359144	−	1.32669i
$134$		−	11.6217i		−	1.00396i
$135$		0			0
$136$	1.38268			0.118564
$137$			0.155798i			0.0133107i	0.999978	+	0.00665534i	$0.00211848\pi$
$137$			0.155798i			0.0133107i	−0.999978	+	0.00665534i	$0.997882\pi$
$138$		0			0
$139$			2.99609i			0.254125i	0.991895	+	0.127063i	$0.0405549\pi$
$139$			2.99609i			0.254125i	−0.991895	+	0.127063i	$0.959445\pi$
$140$	−0.658732	+	2.43338i	−0.0556730	+	0.205658i
$141$		0			0
$142$	−2.29152			−0.192300
$143$	5.40541			0.452023
$144$		0			0
$145$	5.31599			0.441469
$146$			2.19551i			0.181701i
$147$		0			0
$148$			0.429846i			0.0353331i
$149$		−	2.17972i		−	0.178569i	−0.996006	−	0.0892846i	$-0.971542\pi$
$149$		−	2.17972i		−	0.178569i	0.996006	−	0.0892846i	$-0.0284581\pi$
$150$		0			0
$151$	1.38363			0.112598			0.0562992	−	0.998414i	$-0.482070\pi$
$151$	1.38363			0.112598			0.0562992	+	0.998414i	$0.482070\pi$
$152$	−5.99105			−0.485938
$153$		0			0
$154$	2.61072	+	0.706741i	0.210378	+	0.0569508i
$155$		0			0
$156$		0			0
$157$	−11.1851			−0.892665			−0.446333	−	0.894867i	$-0.647270\pi$
$157$	−11.1851			−0.892665			−0.446333	+	0.894867i	$0.647270\pi$
$158$		−	9.77869i		−	0.777951i
$159$		0			0
$160$	0.952834			0.0753281
$161$	5.84640	+	11.2614i	0.460761	+	0.887524i
$162$		0			0
$163$	7.54929			0.591306			0.295653	−	0.955295i	$-0.404463\pi$
$163$	7.54929			0.591306			0.295653	+	0.955295i	$0.404463\pi$
$164$		−	1.28761i		−	0.100546i
$165$		0			0
$166$	−5.46806			−0.424404
$167$		−	11.9290i		−	0.923094i	−0.887116	−	0.461547i	$-0.847294\pi$
$167$		−	11.9290i		−	0.923094i	0.887116	−	0.461547i	$-0.152706\pi$
$168$		0			0
$169$	−14.9589			−1.15068
$170$	−1.31746			−0.101045
$171$		0			0
$172$		−	4.67781i		−	0.356680i
$173$			18.0882i			1.37522i	0.726080	+	0.687610i	$0.241340\pi$
$173$			18.0882i			1.37522i	−0.726080	+	0.687610i	$0.758660\pi$
$174$		0			0
$175$	−2.82904	+	10.4505i	−0.213855	+	0.789987i
$176$		−	1.02228i		−	0.0770571i
$177$		0			0
$178$	−8.69375			−0.651624
$179$	−1.77464			−0.132643			−0.0663216	−	0.997798i	$-0.521126\pi$
$179$	−1.77464			−0.132643			−0.0663216	+	0.997798i	$0.521126\pi$
$180$		0			0
$181$	−20.4933			−1.52325			−0.761627	−	0.648015i	$-0.775599\pi$
$181$	−20.4933			−1.52325			−0.761627	+	0.648015i	$0.775599\pi$
$182$	−13.5037	−	3.65554i	−1.00096	−	0.270966i
$183$		0			0
$184$	3.53113	−	3.24517i	0.260318	−	0.239237i
$185$		−	0.409572i		−	0.0301123i
$186$		0			0
$187$			1.41348i			0.103364i
$188$		−	7.09211i		−	0.517245i
$189$		0			0
$190$	5.70848			0.414136
$191$		−	1.68043i		−	0.121591i	−0.998150	−	0.0607957i	$-0.980636\pi$
$191$		−	1.68043i		−	0.121591i	0.998150	−	0.0607957i	$-0.0193638\pi$
$192$		0			0
$193$	−4.71239			−0.339205			−0.169602	−	0.985513i	$-0.554248\pi$
$193$	−4.71239			−0.339205			−0.169602	+	0.985513i	$0.554248\pi$
$194$	19.2038			1.37875
$195$		0			0
$196$	−6.04410	−	3.53113i	−0.431721	−	0.252223i
$197$	−24.9251			−1.77584			−0.887920	−	0.459998i	$-0.847850\pi$
$197$	−24.9251			−1.77584			−0.887920	+	0.459998i	$0.847850\pi$
$198$		0			0
$199$	−8.60434			−0.609945			−0.304973	−	0.952361i	$-0.598647\pi$
$199$	−8.60434			−0.609945			−0.304973	+	0.952361i	$0.598647\pi$
$200$	4.09211			0.289356
$201$		0			0
$202$		−	15.8927i		−	1.11821i
$203$	−3.85708	+	14.2482i	−0.270714	+	1.00003i
$204$		0			0
$205$			1.22688i			0.0856892i
$206$	−1.74987			−0.121919
$207$		0			0
$208$			5.28761i			0.366630i
$209$		−	6.12452i		−	0.423642i
$210$		0			0
$211$	−19.3460			−1.33183			−0.665915	−	0.746027i	$-0.731959\pi$
$211$	−19.3460			−1.33183			−0.665915	+	0.746027i	$0.731959\pi$
$212$			8.75641i			0.601393i
$213$		0			0
$214$		−	11.0987i		−	0.758692i
$215$			4.45718i			0.303977i
$216$		0			0
$217$		0			0
$218$			2.33551i			0.158181i
$219$		0			0
$220$			0.974060i			0.0656711i
$221$		−	7.31108i		−	0.491796i
$222$		0			0
$223$			17.7335i			1.18752i	0.804641	+	0.593762i	$0.202358\pi$
$223$			17.7335i			1.18752i	−0.804641	+	0.593762i	$0.797642\pi$
$224$	−0.691340	+	2.55383i	−0.0461921	+	0.170635i
$225$		0			0
$226$		−	10.2322i		−	0.680638i
$227$	9.92436			0.658703			0.329352	−	0.944207i	$-0.393170\pi$
$227$	9.92436			0.658703			0.329352	+	0.944207i	$0.393170\pi$
$228$		0			0
$229$	15.8223			1.04557			0.522783	−	0.852466i	$-0.324894\pi$
$229$	15.8223			1.04557			0.522783	+	0.852466i	$0.324894\pi$
$230$	−3.36458	+	3.09211i	−0.221854	+	0.203888i
$231$		0			0
$232$	5.57914			0.366288
$233$	−13.0259			−0.853358			−0.426679	−	0.904403i	$-0.640317\pi$
$233$	−13.0259			−0.853358			−0.426679	+	0.904403i	$0.640317\pi$
$234$		0			0
$235$			6.75760i			0.440817i
$236$		−	1.70848i		−	0.111212i
$237$		0			0
$238$	0.955901	−	3.53113i	0.0619619	−	0.228889i
$239$	−10.6712			−0.690266			−0.345133	−	0.938554i	$-0.612166\pi$
$239$	−10.6712			−0.690266			−0.345133	+	0.938554i	$0.612166\pi$
$240$		0			0
$241$	19.2038			1.23702			0.618511	−	0.785776i	$-0.287736\pi$
$241$	19.2038			1.23702			0.618511	+	0.785776i	$0.287736\pi$
$242$	−9.95495			−0.639928
$243$		0			0
$244$	−7.37373			−0.472055
$245$	5.75902	+	3.36458i	0.367930	+	0.214955i
$246$		0			0
$247$			31.6784i			2.01565i
$248$		0			0
$249$		0			0
$250$	−8.66327			−0.547913
$251$	−0.429846			−0.0271316			−0.0135658	−	0.999908i	$-0.504318\pi$
$251$	−0.429846			−0.0271316			−0.0135658	+	0.999908i	$0.504318\pi$
$252$		0			0
$253$	3.31746	+	3.60979i	0.208567	+	0.226946i
$254$	16.3499			1.02588
$255$		0			0
$256$	1.00000			0.0625000
$257$			21.2465i			1.32532i	0.748921	+	0.662659i	$0.230572\pi$
$257$			21.2465i			1.32532i	−0.748921	+	0.662659i	$0.769428\pi$
$258$		0			0
$259$	1.09775	+	0.297169i	0.0682111	+	0.0184652i
$260$		−	5.03822i		−	0.312457i
$261$		0			0
$262$		−	11.1583i		−	0.689361i
$263$			18.1188i			1.11725i	0.829419	+	0.558627i	$0.188672\pi$
$263$			18.1188i			1.11725i	−0.829419	+	0.558627i	$0.811328\pi$
$264$		0			0
$265$		−	8.34340i		−	0.512531i
$266$	−4.14185	+	15.3001i	−0.253953	+	0.938111i
$267$		0			0
$268$			11.6217i			0.709908i
$269$			3.44198i			0.209861i	0.994480	+	0.104931i	$0.0334620\pi$
$269$			3.44198i			0.209861i	−0.994480	+	0.104931i	$0.966538\pi$
$270$		0			0
$271$		−	2.57523i		−	0.156434i	−0.996936	−	0.0782170i	$-0.975077\pi$
$271$		−	2.57523i		−	0.156434i	0.996936	−	0.0782170i	$-0.0249227\pi$
$272$	−1.38268			−0.0838373
$273$		0			0
$274$		−	0.155798i		−	0.00941208i
$275$			4.18327i			0.252261i
$276$		0			0
$277$	−15.7335			−0.945335			−0.472667	−	0.881241i	$-0.656709\pi$
$277$	−15.7335			−0.945335			−0.472667	+	0.881241i	$0.656709\pi$
$278$		−	2.99609i		−	0.179694i
$279$		0			0
$280$	0.658732	−	2.43338i	0.0393668	−	0.145422i
$281$		−	24.2115i		−	1.44434i	−0.691717	−	0.722168i	$-0.743146\pi$
$281$		−	24.2115i		−	1.44434i	0.691717	−	0.722168i	$-0.256854\pi$
$282$		0			0
$283$	24.2383			1.44081			0.720407	−	0.693551i	$-0.243955\pi$
$283$	24.2383			1.44081			0.720407	+	0.693551i	$0.243955\pi$
$284$	2.29152			0.135977
$285$		0			0
$286$	−5.40541			−0.319628
$287$	−3.28835	−	0.890179i	−0.194105	−	0.0525456i
$288$		0			0
$289$	−15.0882			−0.887541
$290$	−5.31599			−0.312166
$291$		0			0
$292$		−	2.19551i		−	0.128482i
$293$	27.2814			1.59380			0.796898	−	0.604114i	$-0.206473\pi$
$293$	27.2814			1.59380			0.796898	+	0.604114i	$0.206473\pi$
$294$		0			0
$295$			1.62789i			0.0947796i
$296$		−	0.429846i		−	0.0249843i
$297$		0			0
$298$			2.17972i			0.126268i
$299$	−17.1592	−	18.6712i	−0.992343	−	1.07979i
$300$		0			0
$301$	−11.9463	−	3.23396i	−0.688576	−	0.186402i
$302$	−1.38363			−0.0796191
$303$		0			0
$304$	5.99105			0.343610
$305$	7.02594			0.402304
$306$		0			0
$307$			25.1206i			1.43371i	0.697223	+	0.716854i	$0.254419\pi$
$307$			25.1206i			1.43371i	−0.697223	+	0.716854i	$0.745581\pi$
$308$	−2.61072	−	0.706741i	−0.148760	−	0.0402703i
$309$		0			0
$310$		0			0
$311$		−	10.6712i		−	0.605111i	−0.953132	−	0.302555i	$-0.902160\pi$
$311$		−	10.6712i		−	0.605111i	0.953132	−	0.302555i	$-0.0978397\pi$
$312$		0			0
$313$	9.21674			0.520961			0.260481	−	0.965479i	$-0.416119\pi$
$313$	9.21674			0.520961			0.260481	+	0.965479i	$0.416119\pi$
$314$	11.1851			0.631210
$315$		0			0
$316$			9.77869i			0.550094i
$317$	25.3048			1.42126			0.710630	−	0.703566i	$-0.248410\pi$
$317$	25.3048			1.42126			0.710630	+	0.703566i	$0.248410\pi$
$318$		0			0
$319$			5.70343i			0.319331i
$320$	−0.952834			−0.0532650
$321$		0			0
$322$	−5.84640	−	11.2614i	−0.325807	−	0.627574i
$323$	−8.28370			−0.460918
$324$		0			0
$325$		−	21.6375i		−	1.20023i
$326$	−7.54929			−0.418116
$327$		0			0
$328$			1.28761i			0.0710966i
$329$	−18.1120	−	4.90306i	−0.998549	−	0.270314i
$330$		0			0
$331$	−0.830434			−0.0456448			−0.0228224	−	0.999740i	$-0.507265\pi$
$331$	−0.830434			−0.0456448			−0.0228224	+	0.999740i	$0.507265\pi$
$332$	5.46806			0.300099
$333$		0			0
$334$			11.9290i			0.652726i
$335$		−	11.0735i		−	0.605013i
$336$		0			0
$337$		−	7.58885i		−	0.413391i	−0.978405	−	0.206695i	$-0.933729\pi$
$337$		−	7.58885i		−	0.413391i	0.978405	−	0.206695i	$-0.0662709\pi$
$338$	14.9589			0.813655
$339$		0			0
$340$	1.31746			0.0714495
$341$		0			0
$342$		0			0
$343$	−13.1964	+	12.9944i	−0.712540	+	0.701631i
$344$			4.67781i			0.252211i
$345$		0			0
$346$		−	18.0882i		−	0.972428i
$347$	−30.1431			−1.61817			−0.809083	−	0.587695i	$-0.800035\pi$
$347$	−30.1431			−1.61817			−0.809083	+	0.587695i	$0.800035\pi$
$348$		0			0
$349$			22.6115i			1.21037i	0.796086	+	0.605184i	$0.206901\pi$
$349$			22.6115i			1.21037i	−0.796086	+	0.605184i	$0.793099\pi$
$350$	2.82904	−	10.4505i	0.151218	−	0.558605i
$351$		0			0
$352$			1.02228i			0.0544876i
$353$			8.44589i			0.449529i	0.974413	+	0.224765i	$0.0721613\pi$
$353$			8.44589i			0.449529i	−0.974413	+	0.224765i	$0.927839\pi$
$354$		0			0
$355$	−2.18344			−0.115885
$356$	8.69375			0.460768
$357$		0			0
$358$	1.77464			0.0937928
$359$			18.7007i			0.986988i	0.869749	+	0.493494i	$0.164280\pi$
$359$			18.7007i			0.986988i	−0.869749	+	0.493494i	$0.835720\pi$
$360$		0			0
$361$	16.8927			0.889089
$362$	20.4933			1.07710
$363$		0			0
$364$	13.5037	+	3.65554i	0.707785	+	0.191602i
$365$			2.09195i			0.109498i
$366$		0			0
$367$	27.7112			1.44651			0.723257	−	0.690579i	$-0.242644\pi$
$367$	27.7112			1.44651			0.723257	+	0.690579i	$0.242644\pi$
$368$	−3.53113	+	3.24517i	−0.184073	+	0.169166i
$369$		0			0
$370$			0.409572i			0.0212926i
$371$	22.3624	+	6.05365i	1.16100	+	0.314290i
$372$		0			0
$373$			31.6157i			1.63700i	0.574507	+	0.818500i	$0.305194\pi$
$373$			31.6157i			1.63700i	−0.574507	+	0.818500i	$0.694806\pi$
$374$		−	1.41348i		−	0.0730894i
$375$		0			0
$376$			7.09211i			0.365748i
$377$		−	29.5003i		−	1.51934i
$378$		0			0
$379$		−	31.2347i		−	1.60442i	−0.597044	−	0.802209i	$-0.703658\pi$
$379$		−	31.2347i		−	1.60442i	0.597044	−	0.802209i	$-0.296342\pi$
$380$	−5.70848			−0.292839
$381$		0			0
$382$			1.68043i			0.0859781i
$383$	−10.3880			−0.530804			−0.265402	−	0.964138i	$-0.585505\pi$
$383$	−10.3880			−0.530804			−0.265402	+	0.964138i	$0.585505\pi$
$384$		0			0
$385$	2.48758	+	0.673407i	0.126779	+	0.0343200i
$386$	4.71239			0.239854
$387$		0			0
$388$	−19.2038			−0.974923
$389$		−	11.7081i		−	0.593622i	−0.954936	−	0.296811i	$-0.904077\pi$
$389$		−	11.7081i		−	0.593622i	0.954936	−	0.296811i	$-0.0959231\pi$
$390$		0			0
$391$	4.88242	−	4.48703i	0.246915	−	0.226919i
$392$	6.04410	+	3.53113i	0.305273	+	0.178349i
$393$		0			0
$394$	24.9251			1.25571
$395$		−	9.31746i		−	0.468812i
$396$		0			0
$397$		−	5.35378i		−	0.268699i	−0.990934	−	0.134349i	$-0.957106\pi$
$397$		−	5.35378i		−	0.268699i	0.990934	−	0.134349i	$-0.0428944\pi$
$398$	8.60434			0.431297
$399$		0			0
$400$	−4.09211			−0.204605
$401$			34.9329i			1.74447i	0.489091	+	0.872233i	$0.337329\pi$
$401$			34.9329i			1.74447i	−0.489091	+	0.872233i	$0.662671\pi$
$402$		0			0
$403$		0			0
$404$			15.8927i			0.790691i
$405$		0			0
$406$	3.85708	−	14.2482i	0.191424	−	0.707125i
$407$	0.439422			0.0217813
$408$		0			0
$409$			22.1479i			1.09514i	0.836759	+	0.547572i	$0.184448\pi$
$409$			22.1479i			1.09514i	−0.836759	+	0.547572i	$0.815552\pi$
$410$		−	1.22688i		−	0.0605914i
$411$		0			0
$412$	1.74987			0.0862099
$413$	−4.36316	−	1.18114i	−0.214697	−	0.0581200i
$414$		0			0
$415$	−5.21016			−0.255756
$416$		−	5.28761i		−	0.259247i
$417$		0			0
$418$			6.12452i			0.299560i
$419$	0.215119			0.0105092			0.00525462	−	0.999986i	$-0.498327\pi$
$419$	0.215119			0.0105092			0.00525462	+	0.999986i	$0.498327\pi$
$420$		0			0
$421$			16.3757i			0.798105i	0.916928	+	0.399053i	$0.130661\pi$
$421$			16.3757i			0.798105i	−0.916928	+	0.399053i	$0.869339\pi$
$422$	19.3460			0.941747
$423$		0			0
$424$		−	8.75641i		−	0.425249i
$425$	5.65807			0.274457
$426$		0			0
$427$	−5.09775	+	18.8313i	−0.246698	+	0.911308i
$428$			11.0987i			0.536476i
$429$		0			0
$430$		−	4.45718i		−	0.214944i
$431$		−	17.1982i		−	0.828406i	−0.910184	−	0.414203i	$-0.864060\pi$
$431$		−	17.1982i		−	0.828406i	0.910184	−	0.414203i	$-0.135940\pi$
$432$		0			0
$433$	−3.99224			−0.191855			−0.0959274	−	0.995388i	$-0.530582\pi$
$433$	−3.99224			−0.191855			−0.0959274	+	0.995388i	$0.530582\pi$
$434$		0			0
$435$		0			0
$436$		−	2.33551i		−	0.111851i
$437$	−21.1552	+	19.4420i	−1.01199	+	0.930036i
$438$		0			0
$439$		−	2.76726i		−	0.132074i	−0.997817	−	0.0660371i	$-0.978964\pi$
$439$		−	2.76726i		−	0.132074i	0.997817	−	0.0660371i	$-0.0210356\pi$
$440$		−	0.974060i		−	0.0464365i
$441$		0			0
$442$			7.31108i			0.347752i
$443$	13.6673			0.649355			0.324677	−	0.945825i	$-0.394744\pi$
$443$	13.6673			0.649355			0.324677	+	0.945825i	$0.394744\pi$
$444$		0			0
$445$	−8.28370			−0.392685
$446$		−	17.7335i		−	0.839706i
$447$		0			0
$448$	0.691340	−	2.55383i	0.0326627	−	0.120657i
$449$	11.6012			0.547493			0.273746	−	0.961802i	$-0.411737\pi$
$449$	11.6012			0.547493			0.273746	+	0.961802i	$0.411737\pi$
$450$		0			0
$451$	−1.31630			−0.0619821
$452$			10.2322i			0.481284i
$453$		0			0
$454$	−9.92436			−0.465773
$455$	−12.8668	−	3.48312i	−0.603203	−	0.163291i
$456$		0			0
$457$		−	26.1476i		−	1.22314i	−0.791192	−	0.611568i	$-0.790539\pi$
$457$		−	26.1476i		−	1.22314i	0.791192	−	0.611568i	$-0.209461\pi$
$458$	−15.8223			−0.739326
$459$		0			0
$460$	3.36458	−	3.09211i	0.156874	−	0.144170i
$461$		−	5.44980i		−	0.253822i	−0.991914	−	0.126911i	$-0.959494\pi$
$461$		−	5.44980i		−	0.253822i	0.991914	−	0.126911i	$-0.0405063\pi$
$462$		0			0
$463$	−34.0834			−1.58399			−0.791994	−	0.610528i	$-0.790957\pi$
$463$	−34.0834			−1.58399			−0.791994	+	0.610528i	$0.790957\pi$
$464$	−5.57914			−0.259005
$465$		0			0
$466$	13.0259			0.603415
$467$	−28.7609			−1.33090			−0.665449	−	0.746444i	$-0.731760\pi$
$467$	−28.7609			−1.33090			−0.665449	+	0.746444i	$0.731760\pi$
$468$		0			0
$469$	29.6798	+	8.03454i	1.37049	+	0.371001i
$470$		−	6.75760i		−	0.311705i
$471$		0			0
$472$			1.70848i			0.0786390i
$473$	−4.78202			−0.219878
$474$		0			0
$475$	−24.5160			−1.12487
$476$	−0.955901	+	3.53113i	−0.0438137	+	0.161849i
$477$		0			0
$478$	10.6712			0.488091
$479$	−39.5714			−1.80806			−0.904031	−	0.427468i	$-0.859406\pi$
$479$	−39.5714			−1.80806			−0.904031	+	0.427468i	$0.859406\pi$
$480$		0			0
$481$	−2.27286			−0.103633
$482$	−19.2038			−0.874707
$483$		0			0
$484$	9.95495			0.452498
$485$	18.2980			0.830869
$486$		0			0
$487$	−12.8006			−0.580050			−0.290025	−	0.957019i	$-0.593664\pi$
$487$	−12.8006			−0.580050			−0.290025	+	0.957019i	$0.593664\pi$
$488$	7.37373			0.333793
$489$		0			0
$490$	−5.75902	−	3.36458i	−0.260166	−	0.151996i
$491$	−39.4670			−1.78112			−0.890561	−	0.454865i	$-0.849688\pi$
$491$	−39.4670			−1.78112			−0.890561	+	0.454865i	$0.849688\pi$
$492$		0			0
$493$	7.71416			0.347428
$494$		−	31.6784i		−	1.42528i
$495$		0			0
$496$		0			0
$497$	1.58422	−	5.85216i	0.0710621	−	0.262505i
$498$		0			0
$499$	−8.58305			−0.384230			−0.192115	−	0.981372i	$-0.561535\pi$
$499$	−8.58305			−0.384230			−0.192115	+	0.981372i	$0.561535\pi$
$500$	8.66327			0.387433
$501$		0			0
$502$	0.429846			0.0191850
$503$	25.3794			1.13161			0.565807	−	0.824538i	$-0.308565\pi$
$503$	25.3794			1.13161			0.565807	+	0.824538i	$0.308565\pi$
$504$		0			0
$505$		−	15.1431i		−	0.673859i
$506$	−3.31746	−	3.60979i	−0.147479	−	0.160475i
$507$		0			0
$508$	−16.3499			−0.725408
$509$		−	19.0623i		−	0.844920i	−0.906382	−	0.422460i	$-0.861167\pi$
$509$		−	19.0623i		−	0.844920i	0.906382	−	0.422460i	$-0.138833\pi$
$510$		0			0
$511$	−5.60695	−	1.51784i	−0.248037	−	0.0671453i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	21.2465i		−	0.937142i
$515$	−1.66734			−0.0734716
$516$		0			0
$517$	−7.25010			−0.318859
$518$	−1.09775	−	0.297169i	−0.0482325	−	0.0130569i
$519$		0			0
$520$			5.03822i			0.220940i
$521$	26.9484			1.18063			0.590316	−	0.807173i	$-0.299003\pi$
$521$	26.9484			1.18063			0.590316	+	0.807173i	$0.299003\pi$
$522$		0			0
$523$	−8.04918			−0.351966			−0.175983	−	0.984393i	$-0.556310\pi$
$523$	−8.04918			−0.351966			−0.175983	+	0.984393i	$0.556310\pi$
$524$			11.1583i			0.487452i
$525$		0			0
$526$		−	18.1188i		−	0.790018i
$527$		0			0
$528$		0			0
$529$	1.93774	−	22.9182i	0.0842497	−	0.996445i
$530$			8.34340i			0.362414i
$531$		0			0
$532$	4.14185	−	15.3001i	0.179572	−	0.663345i
$533$	6.80840			0.294905
$534$		0			0
$535$		−	10.5752i		−	0.457207i
$536$		−	11.6217i		−	0.501981i
$537$		0			0
$538$		−	3.44198i		−	0.148394i
$539$	−3.60979	+	6.17875i	−0.155485	+	0.266137i
$540$		0			0
$541$	45.6184			1.96129			0.980644	−	0.195802i	$-0.0627308\pi$
$541$	45.6184			1.96129			0.980644	+	0.195802i	$0.0627308\pi$
$542$			2.57523i			0.110615i
$543$		0			0
$544$	1.38268			0.0592819
$545$			2.22536i			0.0953238i
$546$		0			0
$547$	16.7707			0.717065			0.358532	−	0.933517i	$-0.383277\pi$
$547$	16.7707			0.717065			0.358532	+	0.933517i	$0.383277\pi$
$548$			0.155798i			0.00665534i
$549$		0			0
$550$		−	4.18327i		−	0.178375i
$551$	−33.4249			−1.42395
$552$		0			0
$553$	24.9731	+	6.76040i	1.06196	+	0.287481i
$554$	15.7335			0.668453
$555$		0			0
$556$			2.99609i			0.127063i
$557$		−	18.0646i		−	0.765423i	−0.923868	−	0.382712i	$-0.874990\pi$
$557$		−	18.0646i		−	0.765423i	0.923868	−	0.382712i	$-0.125010\pi$
$558$		0			0
$559$	24.7345			1.04616
$560$	−0.658732	+	2.43338i	−0.0278365	+	0.102829i
$561$		0			0
$562$			24.2115i			1.02130i
$563$	5.55748			0.234220			0.117110	−	0.993119i	$-0.462637\pi$
$563$	5.55748			0.234220			0.117110	+	0.993119i	$0.462637\pi$
$564$		0			0
$565$		−	9.74962i		−	0.410169i
$566$	−24.2383			−1.01881
$567$		0			0
$568$	−2.29152			−0.0961502
$569$			4.66769i			0.195680i	0.995202	+	0.0978399i	$0.0311933\pi$
$569$			4.66769i			0.195680i	−0.995202	+	0.0978399i	$0.968807\pi$
$570$		0			0
$571$		−	25.3232i		−	1.05974i	−0.848078	−	0.529871i	$-0.822240\pi$
$571$		−	25.3232i		−	1.05974i	0.848078	−	0.529871i	$-0.177760\pi$
$572$	5.40541			0.226011
$573$		0			0
$574$	3.28835	+	0.890179i	0.137253	+	0.0371553i
$575$	14.4498	−	13.2796i	0.602597	−	0.553797i
$576$		0			0
$577$		−	7.44198i		−	0.309814i	−0.987929	−	0.154907i	$-0.950492\pi$
$577$		−	7.44198i		−	0.309814i	0.987929	−	0.154907i	$-0.0495077\pi$
$578$	15.0882			0.627586
$579$		0			0
$580$	5.31599			0.220735
$581$	3.78029	−	13.9645i	0.156833	−	0.579345i
$582$		0			0
$583$	8.95148			0.370732
$584$			2.19551i			0.0908507i
$585$		0			0
$586$	−27.2814			−1.12698
$587$		−	13.6012i		−	0.561380i	−0.959798	−	0.280690i	$-0.909437\pi$
$587$		−	13.6012i		−	0.561380i	0.959798	−	0.280690i	$-0.0905633\pi$
$588$		0			0
$589$		0			0
$590$		−	1.62789i		−	0.0670193i
$591$		0			0
$592$			0.429846i			0.0176665i
$593$		−	25.9147i		−	1.06419i	−0.846685	−	0.532095i	$-0.821405\pi$
$593$		−	25.9147i		−	1.06419i	0.846685	−	0.532095i	$-0.178595\pi$
$594$		0			0
$595$	0.910815	−	3.36458i	0.0373398	−	0.137934i
$596$		−	2.17972i		−	0.0892846i
$597$		0			0
$598$	17.1592	+	18.6712i	0.701692	+	0.763524i
$599$	−8.09602			−0.330794			−0.165397	−	0.986227i	$-0.552891\pi$
$599$	−8.09602			−0.330794			−0.165397	+	0.986227i	$0.552891\pi$
$600$		0			0
$601$			44.5924i			1.81896i	0.415744	+	0.909482i	$0.363521\pi$
$601$			44.5924i			1.81896i	−0.415744	+	0.909482i	$0.636479\pi$
$602$	11.9463	+	3.23396i	0.486897	+	0.131806i
$603$		0			0
$604$	1.38363			0.0562992
$605$	−9.48541			−0.385637
$606$		0			0
$607$		−	4.30873i		−	0.174886i	−0.996170	−	0.0874430i	$-0.972130\pi$
$607$		−	4.30873i		−	0.174886i	0.996170	−	0.0874430i	$-0.0278696\pi$
$608$	−5.99105			−0.242969
$609$		0			0
$610$	−7.02594			−0.284472
$611$	37.5003			1.51710
$612$		0			0
$613$		−	3.10372i		−	0.125358i	−0.998034	−	0.0626789i	$-0.980036\pi$
$613$		−	3.10372i		−	0.125358i	0.998034	−	0.0626789i	$-0.0199644\pi$
$614$		−	25.1206i		−	1.01379i
$615$		0			0
$616$	2.61072	+	0.706741i	0.105189	+	0.0284754i
$617$		−	27.8081i		−	1.11951i	−0.828658	−	0.559756i	$-0.810895\pi$
$617$		−	27.8081i		−	1.11951i	0.828658	−	0.559756i	$-0.189105\pi$
$618$		0			0
$619$	45.5624			1.83131			0.915654	−	0.401968i	$-0.131674\pi$
$619$	45.5624			1.83131			0.915654	+	0.401968i	$0.131674\pi$
$620$		0			0
$621$		0			0
$622$			10.6712i			0.427878i
$623$	6.01034	−	22.2024i	0.240799	−	0.889519i
$624$		0			0
$625$	12.2059			0.488235
$626$	−9.21674			−0.368375
$627$		0			0
$628$	−11.1851			−0.446333
$629$		−	0.594339i		−	0.0236978i
$630$		0			0
$631$		−	9.09170i		−	0.361935i	−0.983489	−	0.180968i	$-0.942077\pi$
$631$		−	9.09170i		−	0.361935i	0.983489	−	0.180968i	$-0.0579229\pi$
$632$		−	9.77869i		−	0.388975i
$633$		0			0
$634$	−25.3048			−1.00498
$635$	15.5787			0.618222
$636$		0			0
$637$	18.6712	−	31.9589i	0.739782	−	1.26626i
$638$		−	5.70343i		−	0.225801i
$639$		0			0
$640$	0.952834			0.0376641
$641$		−	45.7219i		−	1.80591i	−0.429738	−	0.902954i	$-0.641394\pi$
$641$		−	45.7219i		−	1.80591i	0.429738	−	0.902954i	$-0.358606\pi$
$642$		0			0
$643$	33.7328			1.33029			0.665145	−	0.746714i	$-0.268370\pi$
$643$	33.7328			1.33029			0.665145	+	0.746714i	$0.268370\pi$
$644$	5.84640	+	11.2614i	0.230381	+	0.443762i
$645$		0			0
$646$	8.28370			0.325918
$647$			18.6712i			0.734042i	0.930213	+	0.367021i	$0.119622\pi$
$647$			18.6712i			0.734042i	−0.930213	+	0.367021i	$0.880378\pi$
$648$		0			0
$649$	−1.74654			−0.0685575
$650$			21.6375i			0.848692i
$651$		0			0
$652$	7.54929			0.295653
$653$	25.3161			0.990696			0.495348	−	0.868695i	$-0.335041\pi$
$653$	25.3161			0.990696			0.495348	+	0.868695i	$0.335041\pi$
$654$		0			0
$655$		−	10.6320i		−	0.415426i
$656$		−	1.28761i		−	0.0502729i
$657$		0			0
$658$	18.1120	+	4.90306i	0.706081	+	0.191141i
$659$		−	42.9498i		−	1.67309i	−0.547901	−	0.836543i	$-0.684573\pi$
$659$		−	42.9498i		−	1.67309i	0.547901	−	0.836543i	$-0.315427\pi$
$660$		0			0
$661$	−43.2862			−1.68364			−0.841819	−	0.539759i	$-0.818515\pi$
$661$	−43.2862			−1.68364			−0.841819	+	0.539759i	$0.818515\pi$
$662$	0.830434			0.0322757
$663$		0			0
$664$	−5.46806			−0.212202
$665$	−3.94650	+	14.5785i	−0.153039	+	0.565329i
$666$		0			0
$667$	19.7007	−	18.1053i	0.762812	−	0.701038i
$668$		−	11.9290i		−	0.461547i
$669$		0			0
$670$			11.0735i			0.427808i
$671$			7.53800i			0.291001i
$672$		0			0
$673$	−3.66734			−0.141365			−0.0706827	−	0.997499i	$-0.522518\pi$
$673$	−3.66734			−0.141365			−0.0706827	+	0.997499i	$0.522518\pi$
$674$			7.58885i			0.292312i
$675$		0			0
$676$	−14.9589			−0.575341
$677$	9.06801			0.348512			0.174256	−	0.984700i	$-0.444248\pi$
$677$	9.06801			0.348512			0.174256	+	0.984700i	$0.444248\pi$
$678$		0			0
$679$	−13.2763	+	49.0431i	−0.509499	+	1.88210i
$680$	−1.31746			−0.0505224
$681$		0			0
$682$		0			0
$683$	−19.3823			−0.741642			−0.370821	−	0.928704i	$-0.620924\pi$
$683$	−19.3823			−0.741642			−0.370821	+	0.928704i	$0.620924\pi$
$684$		0			0
$685$		−	0.148449i		−	0.00567195i
$686$	13.1964	−	12.9944i	0.503842	−	0.496128i
$687$		0			0
$688$		−	4.67781i		−	0.178340i
$689$	−46.3005			−1.76391
$690$		0			0
$691$		−	0.800584i		−	0.0304556i	−0.999884	−	0.0152278i	$-0.995153\pi$
$691$		−	0.800584i		−	0.0304556i	0.999884	−	0.0152278i	$-0.00484735\pi$
$692$			18.0882i			0.687610i
$693$		0			0
$694$	30.1431			1.14422
$695$		−	2.85478i		−	0.108288i
$696$		0			0
$697$			1.78036i			0.0674358i
$698$		−	22.6115i		−	0.855860i
$699$		0			0
$700$	−2.82904	+	10.4505i	−0.106928	+	0.394994i
$701$		−	43.0748i		−	1.62691i	−0.581625	−	0.813457i	$-0.697583\pi$
$701$		−	43.0748i		−	1.62691i	0.581625	−	0.813457i	$-0.302417\pi$
$702$		0			0
$703$			2.57523i			0.0971265i
$704$		−	1.02228i		−	0.0385285i
$705$		0			0
$706$		−	8.44589i		−	0.317865i
$707$	40.5872	+	10.9872i	1.52644	+	0.413218i
$708$		0			0
$709$			3.01430i			0.113204i	0.998397	+	0.0566022i	$0.0180267\pi$
$709$			3.01430i			0.113204i	−0.998397	+	0.0566022i	$0.981973\pi$
$710$	2.18344			0.0819431
$711$		0			0
$712$	−8.69375			−0.325812
$713$		0			0
$714$		0			0
$715$	−5.15046			−0.192616
$716$	−1.77464			−0.0663216
$717$		0			0
$718$		−	18.7007i		−	0.697906i
$719$		−	6.84472i		−	0.255265i	−0.991822	−	0.127633i	$-0.959262\pi$
$719$		−	6.84472i		−	0.255265i	0.991822	−	0.127633i	$-0.0407378\pi$
$720$		0			0
$721$	1.20975	−	4.46887i	0.0450536	−	0.166429i
$722$	−16.8927			−0.628681
$723$		0			0
$724$	−20.4933			−0.761627
$725$	22.8304			0.847901
$726$		0			0
$727$	10.8772			0.403413			0.201706	−	0.979446i	$-0.435351\pi$
$727$	10.8772			0.403413			0.201706	+	0.979446i	$0.435351\pi$
$728$	−13.5037	−	3.65554i	−0.500479	−	0.135483i
$729$		0			0
$730$		−	2.09195i		−	0.0774266i
$731$			6.46792i			0.239225i
$732$		0			0
$733$	−0.0626552			−0.00231422			−0.00115711	−	0.999999i	$-0.500368\pi$
$733$	−0.0626552			−0.00231422			−0.00115711	+	0.999999i	$0.500368\pi$
$734$	−27.7112			−1.02284
$735$		0			0
$736$	3.53113	−	3.24517i	0.130159	−	0.119619i
$737$	11.8806			0.437628
$738$		0			0
$739$	38.9549			1.43298			0.716490	−	0.697597i	$-0.245747\pi$
$739$	38.9549			1.43298			0.716490	+	0.697597i	$0.245747\pi$
$740$		−	0.409572i		−	0.0150561i
$741$		0			0
$742$	−22.3624	−	6.05365i	−0.820949	−	0.222237i
$743$			5.61707i			0.206070i	0.994678	+	0.103035i	$0.0328554\pi$
$743$			5.61707i			0.206070i	−0.994678	+	0.103035i	$0.967145\pi$
$744$		0			0
$745$			2.07691i			0.0760920i
$746$		−	31.6157i		−	1.15753i
$747$		0			0
$748$			1.41348i			0.0516820i
$749$	28.3442	+	7.67298i	1.03568	+	0.280365i
$750$		0			0
$751$			20.8401i			0.760467i	0.924891	+	0.380233i	$0.124156\pi$
$751$			20.8401i			0.760467i	−0.924891	+	0.380233i	$0.875844\pi$
$752$		−	7.09211i		−	0.258623i
$753$		0			0
$754$			29.5003i			1.07434i
$755$	−1.31837			−0.0479804
$756$		0			0
$757$		−	42.0037i		−	1.52665i	−0.646014	−	0.763326i	$-0.723565\pi$
$757$		−	42.0037i		−	1.52665i	0.646014	−	0.763326i	$-0.276435\pi$
$758$			31.2347i			1.13449i
$759$		0			0
$760$	5.70848			0.207068
$761$			2.34687i			0.0850741i	0.999095	+	0.0425370i	$0.0135440\pi$
$761$			2.34687i			0.0850741i	−0.999095	+	0.0425370i	$0.986456\pi$
$762$		0			0
$763$	−5.96450	−	1.61463i	−0.215930	−	0.0584536i
$764$		−	1.68043i		−	0.0607957i
$765$		0			0
$766$	10.3880			0.375335
$767$	9.03376			0.326190
$768$		0			0
$769$	−0.553475			−0.0199588			−0.00997941	−	0.999950i	$-0.503177\pi$
$769$	−0.553475			−0.0199588			−0.00997941	+	0.999950i	$0.503177\pi$
$770$	−2.48758	−	0.673407i	−0.0896463	−	0.0242679i
$771$		0			0
$772$	−4.71239			−0.169602
$773$	−24.1488			−0.868573			−0.434287	−	0.900775i	$-0.642999\pi$
$773$	−24.1488			−0.868573			−0.434287	+	0.900775i	$0.642999\pi$
$774$		0			0
$775$		0			0
$776$	19.2038			0.689375
$777$		0			0
$778$			11.7081i			0.419754i
$779$		−	7.71416i		−	0.276388i
$780$		0			0
$781$		−	2.34257i		−	0.0838239i
$782$	−4.88242	+	4.48703i	−0.174595	+	0.160456i
$783$		0			0
$784$	−6.04410	−	3.53113i	−0.215861	−	0.126112i
$785$	10.6575			0.380383
$786$		0			0
$787$	−25.2842			−0.901285			−0.450643	−	0.892704i	$-0.648805\pi$
$787$	−25.2842			−0.901285			−0.450643	+	0.892704i	$0.648805\pi$
$788$	−24.9251			−0.887920
$789$		0			0
$790$			9.31746i			0.331500i
$791$	26.1314	+	7.07395i	0.929125	+	0.251521i
$792$		0			0
$793$		−	38.9894i		−	1.38456i
$794$			5.35378i			0.189999i
$795$		0			0
$796$	−8.60434			−0.304973
$797$	48.5161			1.71853			0.859265	−	0.511531i	$-0.170922\pi$
$797$	48.5161			1.71853			0.859265	+	0.511531i	$0.170922\pi$
$798$		0			0
$799$			9.80611i			0.346915i
$800$	4.09211			0.144678
$801$		0			0
$802$		−	34.9329i		−	1.23352i
$803$	−2.24442			−0.0792037
$804$		0			0
$805$	−5.57065	−	10.7303i	−0.196340	−	0.378192i
$806$		0			0
$807$		0			0
$808$		−	15.8927i		−	0.559103i
$809$	−19.6738			−0.691694			−0.345847	−	0.938291i	$-0.612408\pi$
$809$	−19.6738			−0.691694			−0.345847	+	0.938291i	$0.612408\pi$
$810$		0			0
$811$		−	53.0496i		−	1.86282i	−0.363967	−	0.931412i	$-0.618578\pi$
$811$		−	53.0496i		−	1.86282i	0.363967	−	0.931412i	$-0.381422\pi$
$812$	−3.85708	+	14.2482i	−0.135357	+	0.500013i
$813$		0			0
$814$	−0.439422			−0.0154017
$815$	−7.19322			−0.251967
$816$		0			0
$817$		−	28.0250i		−	0.980472i
$818$		−	22.1479i		−	0.774383i
$819$		0			0
$820$			1.22688i			0.0428446i
$821$	21.8080			0.761103			0.380552	−	0.924760i	$-0.375734\pi$
$821$	21.8080			0.761103			0.380552	+	0.924760i	$0.375734\pi$
$822$		0			0
$823$	−22.8084			−0.795051			−0.397525	−	0.917591i	$-0.630131\pi$
$823$	−22.8084			−0.795051			−0.397525	+	0.917591i	$0.630131\pi$
$824$	−1.74987			−0.0609596
$825$		0			0
$826$	4.36316	+	1.18114i	0.151814	+	0.0410970i
$827$			19.9503i			0.693741i	0.937913	+	0.346871i	$0.112756\pi$
$827$			19.9503i			0.693741i	−0.937913	+	0.346871i	$0.887244\pi$
$828$		0			0
$829$		−	18.2205i		−	0.632825i	−0.948622	−	0.316413i	$-0.897522\pi$
$829$		−	18.2205i		−	0.632825i	0.948622	−	0.316413i	$-0.102478\pi$
$830$	5.21016			0.180847
$831$		0			0
$832$			5.28761i			0.183315i
$833$	8.35705	+	4.88242i	0.289555	+	0.169166i
$834$		0			0
$835$			11.3664i			0.393349i
$836$		−	6.12452i		−	0.211821i
$837$		0			0
$838$	−0.215119			−0.00743116
$839$	−22.1838			−0.765871			−0.382936	−	0.923775i	$-0.625087\pi$
$839$	−22.1838			−0.765871			−0.382936	+	0.923775i	$0.625087\pi$
$840$		0			0
$841$	2.12678			0.0733372
$842$		−	16.3757i		−	0.564345i
$843$		0			0
$844$	−19.3460			−0.665915
$845$	14.2533			0.490329
$846$		0			0
$847$	6.88225	−	25.4233i	0.236477	−	0.873553i
$848$			8.75641i			0.300696i
$849$		0			0
$850$	−5.65807			−0.194070
$851$	−1.39492	−	1.51784i	−0.0478173	−	0.0520309i
$852$		0			0
$853$		−	51.9476i		−	1.77865i	−0.457275	−	0.889325i	$-0.651174\pi$
$853$		−	51.9476i		−	1.77865i	0.457275	−	0.889325i	$-0.348826\pi$
$854$	5.09775	−	18.8313i	0.174442	−	0.644392i
$855$		0			0
$856$		−	11.0987i		−	0.379346i
$857$			35.7806i			1.22224i	0.791538	+	0.611120i	$0.209281\pi$
$857$			35.7806i			1.22224i	−0.791538	+	0.611120i	$0.790719\pi$
$858$		0			0
$859$		−	6.28506i		−	0.214443i	−0.994235	−	0.107222i	$-0.965805\pi$
$859$		−	6.28506i		−	0.214443i	0.994235	−	0.107222i	$-0.0341955\pi$
$860$			4.45718i			0.151989i
$861$		0			0
$862$			17.1982i			0.585772i
$863$	−20.4507			−0.696150			−0.348075	−	0.937467i	$-0.613165\pi$
$863$	−20.4507			−0.696150			−0.348075	+	0.937467i	$0.613165\pi$
$864$		0			0
$865$		−	17.2350i		−	0.586009i
$866$	3.99224			0.135662
$867$		0			0
$868$		0			0
$869$	9.99653			0.339109
$870$		0			0
$871$	−61.4511			−2.08219
$872$			2.33551i			0.0790905i
$873$		0			0
$874$	21.1552	−	19.4420i	0.715584	−	0.657635i
$875$	5.98926	−	22.1245i	0.202474	−	0.747945i
$876$		0			0
$877$	16.8840			0.570131			0.285065	−	0.958508i	$-0.407985\pi$
$877$	16.8840			0.570131			0.285065	+	0.958508i	$0.407985\pi$
$878$			2.76726i			0.0933906i
$879$		0			0
$880$			0.974060i			0.0328356i
$881$	−54.6901			−1.84256			−0.921279	−	0.388903i	$-0.872854\pi$
$881$	−54.6901			−1.84256			−0.921279	+	0.388903i	$0.872854\pi$
$882$		0			0
$883$	13.2811			0.446946			0.223473	−	0.974710i	$-0.428261\pi$
$883$	13.2811			0.446946			0.223473	+	0.974710i	$0.428261\pi$
$884$		−	7.31108i		−	0.245898i
$885$		0			0
$886$	−13.6673			−0.459163
$887$			50.9913i			1.71212i	0.516877	+	0.856060i	$0.327094\pi$
$887$			50.9913i			1.71212i	−0.516877	+	0.856060i	$0.672906\pi$
$888$		0			0
$889$	−11.3033	+	41.7548i	−0.379101	+	1.40041i
$890$	8.28370			0.277670
$891$		0			0
$892$			17.7335i			0.593762i
$893$		−	42.4892i		−	1.42185i
$894$		0			0
$895$	1.69094			0.0565219
$896$	−0.691340	+	2.55383i	−0.0230960	+	0.0853175i
$897$		0			0
$898$	−11.6012			−0.387136
$899$		0			0
$900$		0			0
$901$		−	12.1073i		−	0.403353i
$902$	1.31630			0.0438279
$903$		0			0
$904$		−	10.2322i		−	0.340319i
$905$	19.5267			0.649090
$906$		0			0
$907$			54.9286i			1.82387i	0.410332	+	0.911936i	$0.365413\pi$
$907$			54.9286i			1.82387i	−0.410332	+	0.911936i	$0.634587\pi$
$908$	9.92436			0.329352
$909$		0			0
$910$	12.8668	+	3.48312i	0.426529	+	0.115464i
$911$		−	0.862754i		−	0.0285843i	−0.999898	−	0.0142922i	$-0.995451\pi$
$911$		−	0.862754i		−	0.0285843i	0.999898	−	0.0142922i	$-0.00454949\pi$
$912$		0			0
$913$		−	5.58988i		−	0.184998i
$914$			26.1476i			0.864887i
$915$		0			0
$916$	15.8223			0.522783
$917$	28.4963	+	7.71416i	0.941032	+	0.254744i
$918$		0			0
$919$			23.5411i			0.776551i	0.921543	+	0.388275i	$0.126929\pi$
$919$			23.5411i			0.776551i	−0.921543	+	0.388275i	$0.873071\pi$
$920$	−3.36458	+	3.09211i	−0.110927	+	0.101944i
$921$		0			0
$922$			5.44980i			0.179480i
$923$			12.1167i			0.398826i
$924$		0			0
$925$		−	1.75897i		−	0.0578347i
$926$	34.0834			1.12005
$927$		0			0
$928$	5.57914			0.183144
$929$		−	50.0471i		−	1.64199i	−0.570935	−	0.820995i	$-0.693419\pi$
$929$		−	50.0471i		−	1.64199i	0.570935	−	0.820995i	$-0.306581\pi$
$930$		0			0
$931$	−36.2105	−	21.1552i	−1.18675	−	0.693333i
$932$	−13.0259			−0.426679
$933$		0			0
$934$	28.7609			0.941086
$935$		−	1.34681i		−	0.0440455i
$936$		0			0
$937$	−57.6038			−1.88184			−0.940918	−	0.338636i	$-0.890035\pi$
$937$	−57.6038			−1.88184			−0.940918	+	0.338636i	$0.890035\pi$
$938$	−29.6798	−	8.03454i	−0.969081	−	0.262337i
$939$		0			0
$940$			6.75760i			0.220409i
$941$	50.1440			1.63465			0.817324	−	0.576178i	$-0.195457\pi$
$941$	50.1440			1.63465			0.817324	+	0.576178i	$0.195457\pi$
$942$		0			0
$943$	4.17853	+	4.54673i	0.136072	+	0.148062i
$944$		−	1.70848i		−	0.0556062i
$945$		0			0
$946$	4.78202			0.155477
$947$	−21.8187			−0.709013			−0.354506	−	0.935054i	$-0.615351\pi$
$947$	−21.8187			−0.709013			−0.354506	+	0.935054i	$0.615351\pi$
$948$		0			0
$949$	11.6090			0.376844
$950$	24.5160			0.795405
$951$		0			0
$952$	0.955901	−	3.53113i	0.0309809	−	0.114445i
$953$			34.1070i			1.10483i	0.833568	+	0.552417i	$0.186295\pi$
$953$			34.1070i			1.10483i	−0.833568	+	0.552417i	$0.813705\pi$
$954$		0			0
$955$			1.60117i			0.0518126i
$956$	−10.6712			−0.345133
$957$		0			0
$958$	39.5714			1.27849
$959$	0.397881	+	0.107709i	0.0128482	+	0.00347811i
$960$		0			0
$961$	31.0000			1.00000
$962$	2.27286			0.0732799
$963$		0			0
$964$	19.2038			0.618511
$965$	4.49012			0.144542
$966$		0			0
$967$	−16.7820			−0.539674			−0.269837	−	0.962906i	$-0.586970\pi$
$967$	−16.7820			−0.539674			−0.269837	+	0.962906i	$0.586970\pi$
$968$	−9.95495			−0.319964
$969$		0			0
$970$	−18.2980			−0.587513
$971$	55.1233			1.76899			0.884496	−	0.466549i	$-0.154503\pi$
$971$	55.1233			1.76899			0.884496	+	0.466549i	$0.154503\pi$
$972$		0			0
$973$	7.65150	+	2.07132i	0.245296	+	0.0664033i
$974$	12.8006			0.410157
$975$		0			0
$976$	−7.37373			−0.236027
$977$		−	29.0350i		−	0.928911i	−0.885596	−	0.464456i	$-0.846250\pi$
$977$		−	29.0350i		−	0.928911i	0.885596	−	0.464456i	$-0.153750\pi$
$978$		0			0
$979$		−	8.88743i		−	0.284043i
$980$	5.75902	+	3.36458i	0.183965	+	0.107478i
$981$		0			0
$982$	39.4670			1.25944
$983$	46.8899			1.49556			0.747778	−	0.663949i	$-0.231121\pi$
$983$	46.8899			1.49556			0.747778	+	0.663949i	$0.231121\pi$
$984$		0			0
$985$	23.7495			0.756721
$986$	−7.71416			−0.245669
$987$		0			0
$988$			31.6784i			1.00782i
$989$	15.1803	+	16.5180i	0.482706	+	0.525241i
$990$		0			0
$991$	21.9325			0.696708			0.348354	−	0.937363i	$-0.386741\pi$
$991$	21.9325			0.696708			0.348354	+	0.937363i	$0.386741\pi$
$992$		0			0
$993$		0			0
$994$	−1.58422	+	5.85216i	−0.0502485	+	0.185619i
$995$	8.19850			0.259910
$996$		0			0
$997$		−	36.4714i		−	1.15506i	−0.816369	−	0.577530i	$-0.804017\pi$
$997$		−	36.4714i		−	1.15506i	0.816369	−	0.577530i	$-0.195983\pi$
$998$	8.58305			0.271692
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2898.2.g.j.2575.7		16
3.2	odd	2		966.2.g.e.643.13	yes	16
7.6	odd	2	inner	2898.2.g.j.2575.9		16
21.20	even	2		966.2.g.e.643.4	✓	16
23.22	odd	2	inner	2898.2.g.j.2575.10		16
69.68	even	2		966.2.g.e.643.12	yes	16
161.160	even	2	inner	2898.2.g.j.2575.8		16
483.482	odd	2		966.2.g.e.643.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.g.e.643.4	✓	16	21.20	even	2
966.2.g.e.643.5	yes	16	483.482	odd	2
966.2.g.e.643.12	yes	16	69.68	even	2
966.2.g.e.643.13	yes	16	3.2	odd	2
2898.2.g.j.2575.7		16	1.1	even	1	trivial
2898.2.g.j.2575.8		16	161.160	even	2	inner
2898.2.g.j.2575.9		16	7.6	odd	2	inner
2898.2.g.j.2575.10		16	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2898.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} -0.952834 q^{5} +(0.691340 - 2.55383i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} -0.952834 q^{5} +(0.691340 - 2.55383i) q^{7} -1.00000 q^{8} +0.952834 q^{10} -1.02228i q^{11} +5.28761i q^{13} +(-0.691340 + 2.55383i) q^{14} +1.00000 q^{16} -1.38268 q^{17} +5.99105 q^{19} -0.952834 q^{20} +1.02228i q^{22} +(-3.53113 + 3.24517i) q^{23} -4.09211 q^{25} -5.28761i q^{26} +(0.691340 - 2.55383i) q^{28} -5.57914 q^{29} -1.00000 q^{32} +1.38268 q^{34} +(-0.658732 + 2.43338i) q^{35} +0.429846i q^{37} -5.99105 q^{38} +0.952834 q^{40} -1.28761i q^{41} -4.67781i q^{43} -1.02228i q^{44} +(3.53113 - 3.24517i) q^{46} -7.09211i q^{47} +(-6.04410 - 3.53113i) q^{49} +4.09211 q^{50} +5.28761i q^{52} +8.75641i q^{53} +0.974060i q^{55} +(-0.691340 + 2.55383i) q^{56} +5.57914 q^{58} -1.70848i q^{59} -7.37373 q^{61} +1.00000 q^{64} -5.03822i q^{65} +11.6217i q^{67} -1.38268 q^{68} +(0.658732 - 2.43338i) q^{70} +2.29152 q^{71} -2.19551i q^{73} -0.429846i q^{74} +5.99105 q^{76} +(-2.61072 - 0.706741i) q^{77} +9.77869i q^{79} -0.952834 q^{80} +1.28761i q^{82} +5.46806 q^{83} +1.31746 q^{85} +4.67781i q^{86} +1.02228i q^{88} +8.69375 q^{89} +(13.5037 + 3.65554i) q^{91} +(-3.53113 + 3.24517i) q^{92} +7.09211i q^{94} -5.70848 q^{95} -19.2038 q^{97} +(6.04410 + 3.53113i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} + 36 q^{25} - 20 q^{29} - 16 q^{32} + 16 q^{35} - 8 q^{46} - 36 q^{50} + 20 q^{58} + 16 q^{64} - 16 q^{70} + 48 q^{71} - 20 q^{77} - 32 q^{85} + 8 q^{92} - 80 q^{95}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 + 36 * q^25 - 20 * q^29 - 16 * q^32 + 16 * q^35 - 8 * q^46 - 36 * q^50 + 20 * q^58 + 16 * q^64 - 16 * q^70 + 48 * q^71 - 20 * q^77 - 32 * q^85 + 8 * q^92 - 80 * q^95

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