LMFDB - Embedded newform 4410.2.d.b.4409.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4410,2,Mod(4409,4410)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4410, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("4410.4409");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4410.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:	$35.2140272914$
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} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4409.1
Root			$0.948234 + 2.02506i$ of defining polynomial
Character	$\chi$	$=$	4410.4409
Dual form			4410.2.d.b.4409.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-2.22787 - 0.191334i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.22787 - 0.191334i) q^{5} +1.00000 q^{8} +(-2.22787 - 0.191334i) q^{10} +2.39690i q^{11} -5.67714 q^{13} +1.00000 q^{16} -2.07192i q^{17} +5.91397i q^{19} +(-2.22787 - 0.191334i) q^{20} +2.39690i q^{22} +1.86175 q^{23} +(4.92678 + 0.852531i) q^{25} -5.67714 q^{26} -4.88913i q^{29} -4.52651i q^{31} +1.00000 q^{32} -2.07192i q^{34} -2.96911i q^{37} +5.91397i q^{38} +(-2.22787 - 0.191334i) q^{40} +7.04428 q^{41} -8.55956i q^{43} +2.39690i q^{44} +1.86175 q^{46} -5.57882i q^{47} +(4.92678 + 0.852531i) q^{50} -5.67714 q^{52} +4.19077 q^{53} +(0.458606 - 5.33996i) q^{55} -4.88913i q^{58} -2.00624 q^{59} -12.4548i q^{61} -4.52651i q^{62} +1.00000 q^{64} +(12.6479 + 1.08623i) q^{65} +7.62222i q^{67} -2.07192i q^{68} -9.14126i q^{71} -1.08235 q^{73} -2.96911i q^{74} +5.91397i q^{76} -16.7678 q^{79} +(-2.22787 - 0.191334i) q^{80} +7.04428 q^{82} -13.6122i q^{83} +(-0.396428 + 4.61597i) q^{85} -8.55956i q^{86} +2.39690i q^{88} +13.2626 q^{89} +1.86175 q^{92} -5.57882i q^{94} +(1.13154 - 13.1755i) q^{95} -12.8260 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 16 q^{23} + 12 q^{25} + 16 q^{32} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{64} + 40 q^{65} - 8 q^{79} + 64 q^{85} + 16 q^{92} + 24 q^{95}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 16 * q^16 + 16 * q^23 + 12 * q^25 + 16 * q^32 + 16 * q^46 + 12 * q^50 - 32 * q^53 + 16 * q^64 + 40 * q^65 - 8 * q^79 + 64 * q^85 + 16 * q^92 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times$.

$n$	$1081$	$2647$	$3431$
$\chi(n)$	$-1$	$-1$	$-1$

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
$5$	−2.22787	−	0.191334i	−0.996332	−	0.0855670i
$5$	−2.22787	−	0.191334i	−0.996332	−	0.0855670i
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.22787	−	0.191334i	−0.704513	−	0.0605050i
$11$			2.39690i			0.722691i	0.932432	+	0.361346i	$0.117683\pi$
$11$			2.39690i			0.722691i	−0.932432	+	0.361346i	$0.882317\pi$
$12$		0			0
$13$	−5.67714			−1.57455			−0.787277	−	0.616599i	$-0.788510\pi$
$13$	−5.67714			−1.57455			−0.787277	+	0.616599i	$0.788510\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$		−	2.07192i		−	0.502515i	−0.967920	−	0.251258i	$-0.919156\pi$
$17$		−	2.07192i		−	0.502515i	0.967920	−	0.251258i	$-0.0808441\pi$
$18$		0			0
$19$			5.91397i			1.35676i	0.734713	+	0.678378i	$0.237317\pi$
$19$			5.91397i			1.35676i	−0.734713	+	0.678378i	$0.762683\pi$
$20$	−2.22787	−	0.191334i	−0.498166	−	0.0427835i
$21$		0			0
$22$			2.39690i			0.511020i
$23$	1.86175			0.388203			0.194101	−	0.980981i	$-0.437821\pi$
$23$	1.86175			0.388203			0.194101	+	0.980981i	$0.437821\pi$
$24$		0			0
$25$	4.92678	+	0.852531i	0.985357	+	0.170506i
$26$	−5.67714			−1.11338
$27$		0			0
$28$		0			0
$29$		−	4.88913i		−	0.907889i	−0.891030	−	0.453944i	$-0.850016\pi$
$29$		−	4.88913i		−	0.907889i	0.891030	−	0.453944i	$-0.149984\pi$
$30$		0			0
$31$		−	4.52651i		−	0.812986i	−0.913654	−	0.406493i	$-0.866752\pi$
$31$		−	4.52651i		−	0.812986i	0.913654	−	0.406493i	$-0.133248\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$		−	2.07192i		−	0.355332i
$35$		0			0
$36$		0			0
$37$		−	2.96911i		−	0.488119i	−0.969760	−	0.244059i	$-0.921521\pi$
$37$		−	2.96911i		−	0.488119i	0.969760	−	0.244059i	$-0.0784792\pi$
$38$			5.91397i			0.959372i
$39$		0			0
$40$	−2.22787	−	0.191334i	−0.352257	−	0.0302525i
$41$	7.04428			1.10013			0.550066	−	0.835121i	$-0.314603\pi$
$41$	7.04428			1.10013			0.550066	+	0.835121i	$0.314603\pi$
$42$		0			0
$43$		−	8.55956i		−	1.30532i	−0.757651	−	0.652660i	$-0.773653\pi$
$43$		−	8.55956i		−	1.30532i	0.757651	−	0.652660i	$-0.226347\pi$
$44$			2.39690i			0.361346i
$45$		0			0
$46$	1.86175			0.274501
$47$		−	5.57882i		−	0.813754i	−0.913483	−	0.406877i	$-0.866618\pi$
$47$		−	5.57882i		−	0.813754i	0.913483	−	0.406877i	$-0.133382\pi$
$48$		0			0
$49$		0			0
$50$	4.92678	+	0.852531i	0.696752	+	0.120566i
$51$		0			0
$52$	−5.67714			−0.787277
$53$	4.19077			0.575646			0.287823	−	0.957684i	$-0.407068\pi$
$53$	4.19077			0.575646			0.287823	+	0.957684i	$0.407068\pi$
$54$		0			0
$55$	0.458606	−	5.33996i	0.0618385	−	0.720041i
$56$		0			0
$57$		0			0
$58$		−	4.88913i		−	0.641974i
$59$	−2.00624			−0.261191			−0.130595	−	0.991436i	$-0.541689\pi$
$59$	−2.00624			−0.261191			−0.130595	+	0.991436i	$0.541689\pi$
$60$		0			0
$61$		−	12.4548i		−	1.59467i	−0.603537	−	0.797335i	$-0.706242\pi$
$61$		−	12.4548i		−	1.59467i	0.603537	−	0.797335i	$-0.293758\pi$
$62$		−	4.52651i		−	0.574868i
$63$		0			0
$64$	1.00000			0.125000
$65$	12.6479	+	1.08623i	1.56878	+	0.134730i
$66$		0			0
$67$			7.62222i			0.931202i	0.884995	+	0.465601i	$0.154162\pi$
$67$			7.62222i			0.931202i	−0.884995	+	0.465601i	$0.845838\pi$
$68$		−	2.07192i		−	0.251258i
$69$		0			0
$70$		0			0
$71$		−	9.14126i		−	1.08487i	−0.840099	−	0.542434i	$-0.817503\pi$
$71$		−	9.14126i		−	1.08487i	0.840099	−	0.542434i	$-0.182497\pi$
$72$		0			0
$73$	−1.08235			−0.126679			−0.0633395	−	0.997992i	$-0.520175\pi$
$73$	−1.08235			−0.126679			−0.0633395	+	0.997992i	$0.520175\pi$
$74$		−	2.96911i		−	0.345152i
$75$		0			0
$76$			5.91397i			0.678378i
$77$		0			0
$78$		0			0
$79$	−16.7678			−1.88653			−0.943265	−	0.332042i	$-0.892263\pi$
$79$	−16.7678			−1.88653			−0.943265	+	0.332042i	$0.892263\pi$
$80$	−2.22787	−	0.191334i	−0.249083	−	0.0213917i
$81$		0			0
$82$	7.04428			0.777911
$83$		−	13.6122i		−	1.49414i	−0.664747	−	0.747068i	$-0.731461\pi$
$83$		−	13.6122i		−	1.49414i	0.664747	−	0.747068i	$-0.268539\pi$
$84$		0			0
$85$	−0.396428	+	4.61597i	−0.0429987	+	0.500672i
$86$		−	8.55956i		−	0.923001i
$87$		0			0
$88$			2.39690i			0.255510i
$89$	13.2626			1.40583			0.702916	−	0.711273i	$-0.251881\pi$
$89$	13.2626			1.40583			0.702916	+	0.711273i	$0.251881\pi$
$90$		0			0
$91$		0			0
$92$	1.86175			0.194101
$93$		0			0
$94$		−	5.57882i		−	0.575411i
$95$	1.13154	−	13.1755i	0.116094	−	1.35178i
$96$		0			0
$97$	−12.8260			−1.30229			−0.651143	−	0.758955i	$-0.725710\pi$
$97$	−12.8260			−1.30229			−0.651143	+	0.758955i	$0.725710\pi$
$98$		0			0
$99$		0			0
$100$	4.92678	+	0.852531i	0.492678	+	0.0852531i
$101$	−8.91147			−0.886724			−0.443362	−	0.896343i	$-0.646214\pi$
$101$	−8.91147			−0.886724			−0.443362	+	0.896343i	$0.646214\pi$
$102$		0			0
$103$	−10.8198			−1.06611			−0.533053	−	0.846082i	$-0.678955\pi$
$103$	−10.8198			−1.06611			−0.533053	+	0.846082i	$0.678955\pi$
$104$	−5.67714			−0.556689
$105$		0			0
$106$	4.19077			0.407043
$107$	5.57707			0.539156			0.269578	−	0.962979i	$-0.413116\pi$
$107$	5.57707			0.539156			0.269578	+	0.962979i	$0.413116\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	0.458606	−	5.33996i	0.0437264	−	0.509146i
$111$		0			0
$112$		0			0
$113$	14.5030			1.36432			0.682161	−	0.731202i	$-0.261040\pi$
$113$	14.5030			1.36432			0.682161	+	0.731202i	$0.261040\pi$
$114$		0			0
$115$	−4.14774	−	0.356216i	−0.386779	−	0.0332173i
$116$		−	4.88913i		−	0.453944i
$117$		0			0
$118$	−2.00624			−0.184690
$119$		0			0
$120$		0			0
$121$	5.25489			0.477717
$122$		−	12.4548i		−	1.12760i
$123$		0			0
$124$		−	4.52651i		−	0.406493i
$125$	−10.8131	−	2.84199i	−0.967153	−	0.254195i
$126$		0			0
$127$		−	19.2462i		−	1.70783i	−0.520416	−	0.853913i	$-0.674223\pi$
$127$		−	19.2462i		−	1.70783i	0.520416	−	0.853913i	$-0.325777\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	12.6479	+	1.08623i	1.10929	+	0.0952684i
$131$	4.69940			0.410589			0.205294	−	0.978700i	$-0.434185\pi$
$131$	4.69940			0.410589			0.205294	+	0.978700i	$0.434185\pi$
$132$		0			0
$133$		0			0
$134$			7.62222i			0.658459i
$135$		0			0
$136$		−	2.07192i		−	0.177666i
$137$	−22.8845			−1.95515			−0.977577	−	0.210579i	$-0.932465\pi$
$137$	−22.8845			−1.95515			−0.977577	+	0.210579i	$0.932465\pi$
$138$		0			0
$139$			9.13862i			0.775127i	0.921843	+	0.387564i	$0.126683\pi$
$139$			9.13862i			0.775127i	−0.921843	+	0.387564i	$0.873317\pi$
$140$		0			0
$141$		0			0
$142$		−	9.14126i		−	0.767117i
$143$		−	13.6075i		−	1.13792i
$144$		0			0
$145$	−0.935455	+	10.8923i	−0.0776853	+	0.904559i
$146$	−1.08235			−0.0895756
$147$		0			0
$148$		−	2.96911i		−	0.244059i
$149$			10.4506i			0.856150i	0.903743	+	0.428075i	$0.140808\pi$
$149$			10.4506i			0.856150i	−0.903743	+	0.428075i	$0.859192\pi$
$150$		0			0
$151$	−17.7187			−1.44193			−0.720965	−	0.692971i	$-0.756301\pi$
$151$	−17.7187			−1.44193			−0.720965	+	0.692971i	$0.756301\pi$
$152$			5.91397i			0.479686i
$153$		0			0
$154$		0			0
$155$	−0.866074	+	10.0845i	−0.0695647	+	0.810004i
$156$		0			0
$157$	6.08297			0.485474			0.242737	−	0.970092i	$-0.421955\pi$
$157$	6.08297			0.485474			0.242737	+	0.970092i	$0.421955\pi$
$158$	−16.7678			−1.33398
$159$		0			0
$160$	−2.22787	−	0.191334i	−0.176128	−	0.0151262i
$161$		0			0
$162$		0			0
$163$			0.937339i			0.0734181i	0.999326	+	0.0367090i	$0.0116875\pi$
$163$			0.937339i			0.0734181i	−0.999326	+	0.0367090i	$0.988313\pi$
$164$	7.04428			0.550066
$165$		0			0
$166$		−	13.6122i		−	1.05651i
$167$		−	17.2101i		−	1.33176i	−0.746060	−	0.665879i	$-0.768057\pi$
$167$		−	17.2101i		−	1.33176i	0.746060	−	0.665879i	$-0.231943\pi$
$168$		0			0
$169$	19.2299			1.47922
$170$	−0.396428	+	4.61597i	−0.0304047	+	0.354029i
$171$		0			0
$172$		−	8.55956i		−	0.652660i
$173$			1.97623i			0.150250i	0.997174	+	0.0751249i	$0.0239355\pi$
$173$			1.97623i			0.150250i	−0.997174	+	0.0751249i	$0.976064\pi$
$174$		0			0
$175$		0			0
$176$			2.39690i			0.180673i
$177$		0			0
$178$	13.2626			0.994073
$179$		−	0.887342i		−	0.0663231i	−0.999450	−	0.0331615i	$-0.989442\pi$
$179$		−	0.887342i		−	0.0663231i	0.999450	−	0.0331615i	$-0.0105576\pi$
$180$		0			0
$181$			4.89973i			0.364194i	0.983281	+	0.182097i	$0.0582885\pi$
$181$			4.89973i			0.364194i	−0.983281	+	0.182097i	$0.941712\pi$
$182$		0			0
$183$		0			0
$184$	1.86175			0.137250
$185$	−0.568090	+	6.61478i	−0.0417668	+	0.486328i
$186$		0			0
$187$	4.96618			0.363163
$188$		−	5.57882i		−	0.406877i
$189$		0			0
$190$	1.13154	−	13.1755i	0.0820905	−	0.955853i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$		0			0
$193$		−	19.4966i		−	1.40339i	−0.712476	−	0.701697i	$-0.752426\pi$
$193$		−	19.4966i		−	1.40339i	0.712476	−	0.701697i	$-0.247574\pi$
$194$	−12.8260			−0.920855
$195$		0			0
$196$		0			0
$197$	27.1576			1.93490			0.967448	−	0.253069i	$-0.0814401\pi$
$197$	27.1576			1.93490			0.967448	+	0.253069i	$0.0814401\pi$
$198$		0			0
$199$		−	3.46410i		−	0.245564i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$		−	3.46410i		−	0.245564i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$	4.92678	+	0.852531i	0.348376	+	0.0602831i
$201$		0			0
$202$	−8.91147			−0.627009
$203$		0			0
$204$		0			0
$205$	−15.6937	−	1.34781i	−1.09610	−	0.0941349i
$206$	−10.8198			−0.753850
$207$		0			0
$208$	−5.67714			−0.393639
$209$	−14.1752			−0.980516
$210$		0			0
$211$	−4.06071			−0.279551			−0.139775	−	0.990183i	$-0.544638\pi$
$211$	−4.06071			−0.279551			−0.139775	+	0.990183i	$0.544638\pi$
$212$	4.19077			0.287823
$213$		0			0
$214$	5.57707			0.381241
$215$	−1.63773	+	19.0696i	−0.111692	+	1.30053i
$216$		0			0
$217$		0			0
$218$	2.00000			0.135457
$219$		0			0
$220$	0.458606	−	5.33996i	0.0309192	−	0.360020i
$221$			11.7626i			0.791238i
$222$		0			0
$223$	16.1486			1.08139			0.540696	−	0.841218i	$-0.318161\pi$
$223$	16.1486			1.08139			0.540696	+	0.841218i	$0.318161\pi$
$224$		0			0
$225$		0			0
$226$	14.5030			0.964722
$227$			1.67980i			0.111492i	0.998445	+	0.0557462i	$0.0177538\pi$
$227$			1.67980i			0.111492i	−0.998445	+	0.0557462i	$0.982246\pi$
$228$		0			0
$229$			12.6027i			0.832811i	0.909179	+	0.416406i	$0.136710\pi$
$229$			12.6027i			0.832811i	−0.909179	+	0.416406i	$0.863290\pi$
$230$	−4.14774	−	0.356216i	−0.273494	−	0.0234882i
$231$		0			0
$232$		−	4.88913i		−	0.320987i
$233$	14.5164			0.950999			0.475499	−	0.879716i	$-0.342267\pi$
$233$	14.5164			0.950999			0.475499	+	0.879716i	$0.342267\pi$
$234$		0			0
$235$	−1.06742	+	12.4289i	−0.0696305	+	0.810770i
$236$	−2.00624			−0.130595
$237$		0			0
$238$		0			0
$239$			0.207089i			0.0133955i	0.999978	+	0.00669774i	$0.00213197\pi$
$239$			0.207089i			0.0133955i	−0.999978	+	0.00669774i	$0.997868\pi$
$240$		0			0
$241$			10.4405i			0.672530i	0.941767	+	0.336265i	$0.109164\pi$
$241$			10.4405i			0.672530i	−0.941767	+	0.336265i	$0.890836\pi$
$242$	5.25489			0.337797
$243$		0			0
$244$		−	12.4548i		−	0.797335i
$245$		0			0
$246$		0			0
$247$		−	33.5744i		−	2.13629i
$248$		−	4.52651i		−	0.287434i
$249$		0			0
$250$	−10.8131	−	2.84199i	−0.683880	−	0.179743i
$251$	28.6464			1.80815			0.904074	−	0.427377i	$-0.140562\pi$
$251$	28.6464			1.80815			0.904074	+	0.427377i	$0.140562\pi$
$252$		0			0
$253$			4.46243i			0.280551i
$254$		−	19.2462i		−	1.20762i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	24.9190i		−	1.55440i	−0.629251	−	0.777202i	$-0.716638\pi$
$257$		−	24.9190i		−	1.55440i	0.629251	−	0.777202i	$-0.283362\pi$
$258$		0			0
$259$		0			0
$260$	12.6479	+	1.08623i	0.784390	+	0.0673649i
$261$		0			0
$262$	4.69940			0.290330
$263$	−19.1908			−1.18335			−0.591677	−	0.806175i	$-0.701534\pi$
$263$	−19.1908			−1.18335			−0.591677	+	0.806175i	$0.701534\pi$
$264$		0			0
$265$	−9.33647	−	0.801834i	−0.573535	−	0.0492563i
$266$		0			0
$267$		0			0
$268$			7.62222i			0.465601i
$269$	−4.85489			−0.296008			−0.148004	−	0.988987i	$-0.547285\pi$
$269$	−4.85489			−0.296008			−0.148004	+	0.988987i	$0.547285\pi$
$270$		0			0
$271$			13.6651i			0.830098i	0.909799	+	0.415049i	$0.136236\pi$
$271$			13.6651i			0.830098i	−0.909799	+	0.415049i	$0.863764\pi$
$272$		−	2.07192i		−	0.125629i
$273$		0			0
$274$	−22.8845			−1.38250
$275$	−2.04343	+	11.8090i	−0.123223	+	0.712109i
$276$		0			0
$277$			12.1298i			0.728810i	0.931241	+	0.364405i	$0.118728\pi$
$277$			12.1298i			0.728810i	−0.931241	+	0.364405i	$0.881272\pi$
$278$			9.13862i			0.548098i
$279$		0			0
$280$		0			0
$281$		−	32.6206i		−	1.94598i	−0.230839	−	0.972992i	$-0.574147\pi$
$281$		−	32.6206i		−	1.94598i	0.230839	−	0.972992i	$-0.425853\pi$
$282$		0			0
$283$	−12.6609			−0.752612			−0.376306	−	0.926495i	$-0.622806\pi$
$283$	−12.6609			−0.752612			−0.376306	+	0.926495i	$0.622806\pi$
$284$		−	9.14126i		−	0.542434i
$285$		0			0
$286$		−	13.6075i		−	0.804628i
$287$		0			0
$288$		0			0
$289$	12.7071			0.747478
$290$	−0.935455	+	10.8923i	−0.0549318	+	0.639620i
$291$		0			0
$292$	−1.08235			−0.0633395
$293$		−	25.1151i		−	1.46724i	−0.679559	−	0.733621i	$-0.737829\pi$
$293$		−	25.1151i		−	1.46724i	0.679559	−	0.733621i	$-0.262171\pi$
$294$		0			0
$295$	4.46965	+	0.383862i	0.260233	+	0.0223493i
$296$		−	2.96911i		−	0.172576i
$297$		0			0
$298$			10.4506i			0.605390i
$299$	−10.5694			−0.611246
$300$		0			0
$301$		0			0
$302$	−17.7187			−1.01960
$303$		0			0
$304$			5.91397i			0.339189i
$305$	−2.38302	+	27.7476i	−0.136451	+	1.58882i
$306$		0			0
$307$	−18.5674			−1.05970			−0.529849	−	0.848092i	$-0.677751\pi$
$307$	−18.5674			−1.05970			−0.529849	+	0.848092i	$0.677751\pi$
$308$		0			0
$309$		0			0
$310$	−0.866074	+	10.0845i	−0.0491897	+	0.572760i
$311$	12.4366			0.705216			0.352608	−	0.935771i	$-0.385295\pi$
$311$	12.4366			0.705216			0.352608	+	0.935771i	$0.385295\pi$
$312$		0			0
$313$	12.4135			0.701653			0.350826	−	0.936441i	$-0.385901\pi$
$313$	12.4135			0.701653			0.350826	+	0.936441i	$0.385901\pi$
$314$	6.08297			0.343282
$315$		0			0
$316$	−16.7678			−0.943265
$317$	−24.6464			−1.38428			−0.692141	−	0.721763i	$-0.743332\pi$
$317$	−24.6464			−1.38428			−0.692141	+	0.721763i	$0.743332\pi$
$318$		0			0
$319$	11.7187			0.656123
$320$	−2.22787	−	0.191334i	−0.124542	−	0.0106959i
$321$		0			0
$322$		0			0
$323$	12.2533			0.681791
$324$		0			0
$325$	−27.9700	−	4.83994i	−1.55150	−	0.268471i
$326$			0.937339i			0.0519144i
$327$		0			0
$328$	7.04428			0.388955
$329$		0			0
$330$		0			0
$331$	−25.1576			−1.38278			−0.691392	−	0.722479i	$-0.743002\pi$
$331$	−25.1576			−1.38278			−0.691392	+	0.722479i	$0.743002\pi$
$332$		−	13.6122i		−	0.747068i
$333$		0			0
$334$		−	17.2101i		−	0.941694i
$335$	1.45839	−	16.9813i	0.0796801	−	0.927787i
$336$		0			0
$337$		−	14.4214i		−	0.785584i	−0.919627	−	0.392792i	$-0.871509\pi$
$337$		−	14.4214i		−	0.785584i	0.919627	−	0.392792i	$-0.128491\pi$
$338$	19.2299			1.04597
$339$		0			0
$340$	−0.396428	+	4.61597i	−0.0214994	+	0.250336i
$341$	10.8496			0.587538
$342$		0			0
$343$		0			0
$344$		−	8.55956i		−	0.461500i
$345$		0			0
$346$			1.97623i			0.106243i
$347$	14.4866			0.777680			0.388840	−	0.921305i	$-0.372876\pi$
$347$	14.4866			0.777680			0.388840	+	0.921305i	$0.372876\pi$
$348$		0			0
$349$		−	2.12483i		−	0.113739i	−0.998382	−	0.0568697i	$-0.981888\pi$
$349$		−	2.12483i		−	0.113739i	0.998382	−	0.0568697i	$-0.0181119\pi$
$350$		0			0
$351$		0			0
$352$			2.39690i			0.127755i
$353$		−	14.5267i		−	0.773178i	−0.922252	−	0.386589i	$-0.873653\pi$
$353$		−	14.5267i		−	0.773178i	0.922252	−	0.386589i	$-0.126347\pi$
$354$		0			0
$355$	−1.74903	+	20.3655i	−0.0928288	+	1.08089i
$356$	13.2626			0.702916
$357$		0			0
$358$		−	0.887342i		−	0.0468975i
$359$		−	3.94970i		−	0.208457i	−0.994553	−	0.104228i	$-0.966763\pi$
$359$		−	3.94970i		−	0.208457i	0.994553	−	0.104228i	$-0.0332373\pi$
$360$		0			0
$361$	−15.9750			−0.840789
$362$			4.89973i			0.257524i
$363$		0			0
$364$		0			0
$365$	2.41132	+	0.207089i	0.126214	+	0.0108395i
$366$		0			0
$367$	27.6927			1.44555			0.722775	−	0.691084i	$-0.242866\pi$
$367$	27.6927			1.44555			0.722775	+	0.691084i	$0.242866\pi$
$368$	1.86175			0.0970506
$369$		0			0
$370$	−0.568090	+	6.61478i	−0.0295336	+	0.343886i
$371$		0			0
$372$		0			0
$373$		−	12.1298i		−	0.628058i	−0.949413	−	0.314029i	$-0.898321\pi$
$373$		−	12.1298i		−	0.628058i	0.949413	−	0.314029i	$-0.101679\pi$
$374$	4.96618			0.256795
$375$		0			0
$376$		−	5.57882i		−	0.287706i
$377$			27.7563i			1.42952i
$378$		0			0
$379$	−18.6821			−0.959636			−0.479818	−	0.877368i	$-0.659297\pi$
$379$	−18.6821			−0.959636			−0.479818	+	0.877368i	$0.659297\pi$
$380$	1.13154	−	13.1755i	0.0580468	−	0.675890i
$381$		0			0
$382$			2.82843i			0.144715i
$383$			11.0293i			0.563569i	0.959478	+	0.281784i	$0.0909263\pi$
$383$			11.0293i			0.563569i	−0.959478	+	0.281784i	$0.909074\pi$
$384$		0			0
$385$		0			0
$386$		−	19.4966i		−	0.992349i
$387$		0			0
$388$	−12.8260			−0.651143
$389$			34.3710i			1.74268i	0.490679	+	0.871341i	$0.336749\pi$
$389$			34.3710i			1.74268i	−0.490679	+	0.871341i	$0.663251\pi$
$390$		0			0
$391$		−	3.85741i		−	0.195078i
$392$		0			0
$393$		0			0
$394$	27.1576			1.36818
$395$	37.3565	+	3.20825i	1.87961	+	0.161425i
$396$		0			0
$397$	31.0107			1.55638			0.778191	−	0.628027i	$-0.216137\pi$
$397$	31.0107			1.55638			0.778191	+	0.628027i	$0.216137\pi$
$398$		−	3.46410i		−	0.173640i
$399$		0			0
$400$	4.92678	+	0.852531i	0.246339	+	0.0426266i
$401$		−	9.47745i		−	0.473281i	−0.971597	−	0.236641i	$-0.923954\pi$
$401$		−	9.47745i		−	0.473281i	0.971597	−	0.236641i	$-0.0760464\pi$
$402$		0			0
$403$			25.6976i			1.28009i
$404$	−8.91147			−0.443362
$405$		0			0
$406$		0			0
$407$	7.11665			0.352759
$408$		0			0
$409$			9.47784i			0.468649i	0.972158	+	0.234324i	$0.0752878\pi$
$409$			9.47784i			0.468649i	−0.972158	+	0.234324i	$0.924712\pi$
$410$	−15.6937	−	1.34781i	−0.775058	−	0.0665634i
$411$		0			0
$412$	−10.8198			−0.533053
$413$		0			0
$414$		0			0
$415$	−2.60448	+	30.3262i	−0.127849	+	1.48866i
$416$	−5.67714			−0.278345
$417$		0			0
$418$	−14.1752			−0.693330
$419$	−2.54445			−0.124305			−0.0621523	−	0.998067i	$-0.519796\pi$
$419$	−2.54445			−0.124305			−0.0621523	+	0.998067i	$0.519796\pi$
$420$		0			0
$421$	−5.08573			−0.247863			−0.123932	−	0.992291i	$-0.539550\pi$
$421$	−5.08573			−0.247863			−0.123932	+	0.992291i	$0.539550\pi$
$422$	−4.06071			−0.197672
$423$		0			0
$424$	4.19077			0.203522
$425$	1.76638	−	10.2079i	0.0856820	−	0.495157i
$426$		0			0
$427$		0			0
$428$	5.57707			0.269578
$429$		0			0
$430$	−1.63773	+	19.0696i	−0.0789784	+	0.919616i
$431$		−	13.2980i		−	0.640544i	−0.947326	−	0.320272i	$-0.896226\pi$
$431$		−	13.2980i		−	0.640544i	0.947326	−	0.320272i	$-0.103774\pi$
$432$		0			0
$433$	−12.7895			−0.614626			−0.307313	−	0.951608i	$-0.599430\pi$
$433$	−12.7895			−0.614626			−0.307313	+	0.951608i	$0.599430\pi$
$434$		0			0
$435$		0			0
$436$	2.00000			0.0957826
$437$			11.0103i			0.526696i
$438$		0			0
$439$		−	0.373212i		−	0.0178125i	−0.999960	−	0.00890623i	$-0.997165\pi$
$439$		−	0.373212i		−	0.0178125i	0.999960	−	0.00890623i	$-0.00283498\pi$
$440$	0.458606	−	5.33996i	0.0218632	−	0.254573i
$441$		0			0
$442$			11.7626i			0.559490i
$443$	24.6330			1.17035			0.585175	−	0.810907i	$-0.301026\pi$
$443$	24.6330			1.17035			0.585175	+	0.810907i	$0.301026\pi$
$444$		0			0
$445$	−29.5473	−	2.53758i	−1.40068	−	0.120293i
$446$	16.1486			0.764660
$447$		0			0
$448$		0			0
$449$			40.6223i			1.91708i	0.284950	+	0.958542i	$0.408023\pi$
$449$			40.6223i			1.91708i	−0.284950	+	0.958542i	$0.591977\pi$
$450$		0			0
$451$			16.8844i			0.795056i
$452$	14.5030			0.682161
$453$		0			0
$454$			1.67980i			0.0788370i
$455$		0			0
$456$		0			0
$457$			0.990551i			0.0463360i	0.999732	+	0.0231680i	$0.00737527\pi$
$457$			0.990551i			0.0463360i	−0.999732	+	0.0231680i	$0.992625\pi$
$458$			12.6027i			0.588886i
$459$		0			0
$460$	−4.14774	−	0.356216i	−0.193389	−	0.0166087i
$461$	−20.7397			−0.965945			−0.482972	−	0.875636i	$-0.660443\pi$
$461$	−20.7397			−0.965945			−0.482972	+	0.875636i	$0.660443\pi$
$462$		0			0
$463$			1.46421i			0.0680476i	0.999421	+	0.0340238i	$0.0108322\pi$
$463$			1.46421i			0.0680476i	−0.999421	+	0.0340238i	$0.989168\pi$
$464$		−	4.88913i		−	0.226972i
$465$		0			0
$466$	14.5164			0.672458
$467$		−	36.2680i		−	1.67828i	−0.543912	−	0.839142i	$-0.683057\pi$
$467$		−	36.2680i		−	1.67828i	0.543912	−	0.839142i	$-0.316943\pi$
$468$		0			0
$469$		0			0
$470$	−1.06742	+	12.4289i	−0.0492362	+	0.573301i
$471$		0			0
$472$	−2.00624			−0.0923449
$473$	20.5164			0.943343
$474$		0			0
$475$	−5.04184	+	29.1368i	−0.231336	+	1.33689i
$476$		0			0
$477$		0			0
$478$			0.207089i			0.00947203i
$479$	10.3258			0.471796			0.235898	−	0.971778i	$-0.424197\pi$
$479$	10.3258			0.471796			0.235898	+	0.971778i	$0.424197\pi$
$480$		0			0
$481$			16.8560i			0.768569i
$482$			10.4405i			0.475551i
$483$		0			0
$484$	5.25489			0.238859
$485$	28.5747	+	2.45405i	1.29751	+	0.111433i
$486$		0			0
$487$		−	20.3291i		−	0.921198i	−0.887608	−	0.460599i	$-0.847635\pi$
$487$		−	20.3291i		−	0.921198i	0.887608	−	0.460599i	$-0.152365\pi$
$488$		−	12.4548i		−	0.563801i
$489$		0			0
$490$		0			0
$491$			34.6034i			1.56163i	0.624764	+	0.780814i	$0.285195\pi$
$491$			34.6034i			1.56163i	−0.624764	+	0.780814i	$0.714805\pi$
$492$		0			0
$493$	−10.1299			−0.456228
$494$		−	33.5744i		−	1.51058i
$495$		0			0
$496$		−	4.52651i		−	0.203247i
$497$		0			0
$498$		0			0
$499$	2.95089			0.132100			0.0660501	−	0.997816i	$-0.478960\pi$
$499$	2.95089			0.132100			0.0660501	+	0.997816i	$0.478960\pi$
$500$	−10.8131	−	2.84199i	−0.483577	−	0.127097i
$501$		0			0
$502$	28.6464			1.27855
$503$			31.8907i			1.42193i	0.703225	+	0.710967i	$0.251742\pi$
$503$			31.8907i			1.42193i	−0.703225	+	0.710967i	$0.748258\pi$
$504$		0			0
$505$	19.8536	+	1.70506i	0.883472	+	0.0758743i
$506$			4.46243i			0.198379i
$507$		0			0
$508$		−	19.2462i		−	0.853913i
$509$	−0.842398			−0.0373386			−0.0186693	−	0.999826i	$-0.505943\pi$
$509$	−0.842398			−0.0373386			−0.0186693	+	0.999826i	$0.505943\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	24.9190i		−	1.09913i
$515$	24.1050	+	2.07019i	1.06220	+	0.0912234i
$516$		0			0
$517$	13.3718			0.588093
$518$		0			0
$519$		0			0
$520$	12.6479	+	1.08623i	0.554647	+	0.0476342i
$521$	5.62999			0.246654			0.123327	−	0.992366i	$-0.460644\pi$
$521$	5.62999			0.246654			0.123327	+	0.992366i	$0.460644\pi$
$522$		0			0
$523$	−17.8380			−0.780001			−0.390000	−	0.920815i	$-0.627525\pi$
$523$	−17.8380			−0.780001			−0.390000	+	0.920815i	$0.627525\pi$
$524$	4.69940			0.205294
$525$		0			0
$526$	−19.1908			−0.836757
$527$	−9.37859			−0.408538
$528$		0			0
$529$	−19.5339			−0.849299
$530$	−9.33647	−	0.801834i	−0.405550	−	0.0348295i
$531$		0			0
$532$		0			0
$533$	−39.9913			−1.73222
$534$		0			0
$535$	−12.4250	−	1.06708i	−0.537179	−	0.0461339i
$536$			7.62222i			0.329230i
$537$		0			0
$538$	−4.85489			−0.209309
$539$		0			0
$540$		0			0
$541$	−25.4241			−1.09307			−0.546533	−	0.837438i	$-0.684053\pi$
$541$	−25.4241			−1.09307			−0.546533	+	0.837438i	$0.684053\pi$
$542$			13.6651i			0.586968i
$543$		0			0
$544$		−	2.07192i		−	0.0888330i
$545$	−4.45573	−	0.382667i	−0.190863	−	0.0163917i
$546$		0			0
$547$			12.1182i			0.518138i	0.965859	+	0.259069i	$0.0834158\pi$
$547$			12.1182i			0.518138i	−0.965859	+	0.259069i	$0.916584\pi$
$548$	−22.8845			−0.977577
$549$		0			0
$550$	−2.04343	+	11.8090i	−0.0871321	+	0.503537i
$551$	28.9141			1.23178
$552$		0			0
$553$		0			0
$554$			12.1298i			0.515346i
$555$		0			0
$556$			9.13862i			0.387564i
$557$	−1.53957			−0.0652338			−0.0326169	−	0.999468i	$-0.510384\pi$
$557$	−1.53957			−0.0652338			−0.0326169	+	0.999468i	$0.510384\pi$
$558$		0			0
$559$			48.5938i			2.05530i
$560$		0			0
$561$		0			0
$562$		−	32.6206i		−	1.37602i
$563$			22.4644i			0.946762i	0.880858	+	0.473381i	$0.156967\pi$
$563$			22.4644i			0.946762i	−0.880858	+	0.473381i	$0.843033\pi$
$564$		0			0
$565$	−32.3106	−	2.77490i	−1.35932	−	0.116741i
$566$	−12.6609			−0.532177
$567$		0			0
$568$		−	9.14126i		−	0.383559i
$569$			10.8058i			0.453003i	0.974011	+	0.226501i	$0.0727288\pi$
$569$			10.8058i			0.453003i	−0.974011	+	0.226501i	$0.927271\pi$
$570$		0			0
$571$	−7.96338			−0.333257			−0.166629	−	0.986020i	$-0.553288\pi$
$571$	−7.96338			−0.333257			−0.166629	+	0.986020i	$0.553288\pi$
$572$		−	13.6075i		−	0.568958i
$573$		0			0
$574$		0			0
$575$	9.17246	+	1.58720i	0.382518	+	0.0661910i
$576$		0			0
$577$	24.5928			1.02381			0.511906	−	0.859041i	$-0.328939\pi$
$577$	24.5928			1.02381			0.511906	+	0.859041i	$0.328939\pi$
$578$	12.7071			0.528547
$579$		0			0
$580$	−0.935455	+	10.8923i	−0.0388426	+	0.452280i
$581$		0			0
$582$		0			0
$583$			10.0448i			0.416014i
$584$	−1.08235			−0.0447878
$585$		0			0
$586$		−	25.1151i		−	1.03750i
$587$			12.8469i			0.530248i	0.964214	+	0.265124i	$0.0854129\pi$
$587$			12.8469i			0.530248i	−0.964214	+	0.265124i	$0.914587\pi$
$588$		0			0
$589$	26.7696			1.10302
$590$	4.46965	+	0.383862i	0.184012	+	0.0158033i
$591$		0			0
$592$		−	2.96911i		−	0.122030i
$593$			17.1631i			0.704804i	0.935849	+	0.352402i	$0.114635\pi$
$593$			17.1631i			0.704804i	−0.935849	+	0.352402i	$0.885365\pi$
$594$		0			0
$595$		0			0
$596$			10.4506i			0.428075i
$597$		0			0
$598$	−10.5694			−0.432216
$599$			19.6083i			0.801174i	0.916259	+	0.400587i	$0.131194\pi$
$599$			19.6083i			0.801174i	−0.916259	+	0.400587i	$0.868806\pi$
$600$		0			0
$601$		−	28.2340i		−	1.15169i	−0.817560	−	0.575844i	$-0.804674\pi$
$601$		−	28.2340i		−	1.15169i	0.817560	−	0.575844i	$-0.195326\pi$
$602$		0			0
$603$		0			0
$604$	−17.7187			−0.720965
$605$	−11.7072	−	1.00544i	−0.475965	−	0.0408768i
$606$		0			0
$607$	−9.65314			−0.391809			−0.195904	−	0.980623i	$-0.562764\pi$
$607$	−9.65314			−0.391809			−0.195904	+	0.980623i	$0.562764\pi$
$608$			5.91397i			0.239843i
$609$		0			0
$610$	−2.38302	+	27.7476i	−0.0964855	+	1.12347i
$611$			31.6717i			1.28130i
$612$		0			0
$613$			9.05588i			0.365764i	0.983135	+	0.182882i	$0.0585426\pi$
$613$			9.05588i			0.365764i	−0.983135	+	0.182882i	$0.941457\pi$
$614$	−18.5674			−0.749320
$615$		0			0
$616$		0			0
$617$	−25.3122			−1.01903			−0.509515	−	0.860462i	$-0.670175\pi$
$617$	−25.3122			−1.01903			−0.509515	+	0.860462i	$0.670175\pi$
$618$		0			0
$619$			38.8711i			1.56236i	0.624305	+	0.781181i	$0.285382\pi$
$619$			38.8711i			1.56236i	−0.624305	+	0.781181i	$0.714618\pi$
$620$	−0.866074	+	10.0845i	−0.0347824	+	0.405002i
$621$		0			0
$622$	12.4366			0.498663
$623$		0			0
$624$		0			0
$625$	23.5464	+	8.40047i	0.941855	+	0.336019i
$626$	12.4135			0.496143
$627$		0			0
$628$	6.08297			0.242737
$629$	−6.15177			−0.245287
$630$		0			0
$631$	−23.8670			−0.950129			−0.475065	−	0.879951i	$-0.657575\pi$
$631$	−23.8670			−0.950129			−0.475065	+	0.879951i	$0.657575\pi$
$632$	−16.7678			−0.666989
$633$		0			0
$634$	−24.6464			−0.978834
$635$	−3.68245	+	42.8780i	−0.146133	+	1.70156i
$636$		0			0
$637$		0			0
$638$	11.7187			0.463949
$639$		0			0
$640$	−2.22787	−	0.191334i	−0.0880642	−	0.00756312i
$641$		−	34.8796i		−	1.37766i	−0.724923	−	0.688830i	$-0.758124\pi$
$641$		−	34.8796i		−	1.37766i	0.724923	−	0.688830i	$-0.241876\pi$
$642$		0			0
$643$	−6.25944			−0.246848			−0.123424	−	0.992354i	$-0.539388\pi$
$643$	−6.25944			−0.246848			−0.123424	+	0.992354i	$0.539388\pi$
$644$		0			0
$645$		0			0
$646$	12.2533			0.482099
$647$		−	37.5022i		−	1.47436i	−0.675695	−	0.737181i	$-0.736156\pi$
$647$		−	37.5022i		−	1.47436i	0.675695	−	0.737181i	$-0.263844\pi$
$648$		0			0
$649$		−	4.80876i		−	0.188760i
$650$	−27.9700	−	4.83994i	−1.09707	−	0.189838i
$651$		0			0
$652$			0.937339i			0.0367090i
$653$	−26.4516			−1.03513			−0.517565	−	0.855644i	$-0.673161\pi$
$653$	−26.4516			−1.03513			−0.517565	+	0.855644i	$0.673161\pi$
$654$		0			0
$655$	−10.4696	−	0.899153i	−0.409083	−	0.0351328i
$656$	7.04428			0.275033
$657$		0			0
$658$		0			0
$659$		−	19.9524i		−	0.777234i	−0.921399	−	0.388617i	$-0.872953\pi$
$659$		−	19.9524i		−	0.777234i	0.921399	−	0.388617i	$-0.127047\pi$
$660$		0			0
$661$			5.44098i			0.211630i	0.994386	+	0.105815i	$0.0337451\pi$
$661$			5.44098i			0.211630i	−0.994386	+	0.105815i	$0.966255\pi$
$662$	−25.1576			−0.977776
$663$		0			0
$664$		−	13.6122i		−	0.528257i
$665$		0			0
$666$		0			0
$667$		−	9.10236i		−	0.352445i
$668$		−	17.2101i		−	0.665879i
$669$		0			0
$670$	1.45839	−	16.9813i	0.0563424	−	0.656044i
$671$	29.8528			1.15245
$672$		0			0
$673$			8.50635i			0.327896i	0.986469	+	0.163948i	$0.0524228\pi$
$673$			8.50635i			0.327896i	−0.986469	+	0.163948i	$0.947577\pi$
$674$		−	14.4214i		−	0.555492i
$675$		0			0
$676$	19.2299			0.739611
$677$			5.08639i			0.195486i	0.995212	+	0.0977430i	$0.0311623\pi$
$677$			5.08639i			0.195486i	−0.995212	+	0.0977430i	$0.968838\pi$
$678$		0			0
$679$		0			0
$680$	−0.396428	+	4.61597i	−0.0152023	+	0.177014i
$681$		0			0
$682$	10.8496			0.415452
$683$	−21.0145			−0.804099			−0.402050	−	0.915618i	$-0.631702\pi$
$683$	−21.0145			−0.804099			−0.402050	+	0.915618i	$0.631702\pi$
$684$		0			0
$685$	50.9836	+	4.37857i	1.94798	+	0.167297i
$686$		0			0
$687$		0			0
$688$		−	8.55956i		−	0.326330i
$689$	−23.7916			−0.906386
$690$		0			0
$691$			24.9095i			0.947604i	0.880631	+	0.473802i	$0.157119\pi$
$691$			24.9095i			0.947604i	−0.880631	+	0.473802i	$0.842881\pi$
$692$			1.97623i			0.0751249i
$693$		0			0
$694$	14.4866			0.549903
$695$	1.74852	−	20.3596i	0.0663253	−	0.772285i
$696$		0			0
$697$		−	14.5952i		−	0.552833i
$698$		−	2.12483i		−	0.0804259i
$699$		0			0
$700$		0			0
$701$		−	22.5321i		−	0.851025i	−0.904953	−	0.425512i	$-0.860094\pi$
$701$		−	22.5321i		−	0.851025i	0.904953	−	0.425512i	$-0.139906\pi$
$702$		0			0
$703$	17.5592			0.662258
$704$			2.39690i			0.0903364i
$705$		0			0
$706$		−	14.5267i		−	0.546719i
$707$		0			0
$708$		0			0
$709$	24.9009			0.935172			0.467586	−	0.883948i	$-0.345124\pi$
$709$	24.9009			0.935172			0.467586	+	0.883948i	$0.345124\pi$
$710$	−1.74903	+	20.3655i	−0.0656399	+	0.764304i
$711$		0			0
$712$	13.2626			0.497037
$713$		−	8.42726i		−	0.315603i
$714$		0			0
$715$	−2.60357	+	30.3157i	−0.0973681	+	1.13374i
$716$		−	0.887342i		−	0.0331615i
$717$		0			0
$718$		−	3.94970i		−	0.147401i
$719$	39.8483			1.48609			0.743045	−	0.669241i	$-0.233381\pi$
$719$	39.8483			1.48609			0.743045	+	0.669241i	$0.233381\pi$
$720$		0			0
$721$		0			0
$722$	−15.9750			−0.594527
$723$		0			0
$724$			4.89973i			0.182097i
$725$	4.16814	−	24.0877i	0.154801	−	0.894594i
$726$		0			0
$727$	0.124004			0.00459906			0.00229953	−	0.999997i	$-0.499268\pi$
$727$	0.124004			0.00459906			0.00229953	+	0.999997i	$0.499268\pi$
$728$		0			0
$729$		0			0
$730$	2.41132	+	0.207089i	0.0892471	+	0.00766471i
$731$	−17.7348			−0.655943
$732$		0			0
$733$	−28.5478			−1.05444			−0.527218	−	0.849730i	$-0.676765\pi$
$733$	−28.5478			−1.05444			−0.527218	+	0.849730i	$0.676765\pi$
$734$	27.6927			1.02216
$735$		0			0
$736$	1.86175			0.0686252
$737$	−18.2697			−0.672972
$738$		0			0
$739$	−19.0361			−0.700256			−0.350128	−	0.936702i	$-0.613862\pi$
$739$	−19.0361			−0.700256			−0.350128	+	0.936702i	$0.613862\pi$
$740$	−0.568090	+	6.61478i	−0.0208834	+	0.243164i
$741$		0			0
$742$		0			0
$743$	−17.0800			−0.626605			−0.313303	−	0.949653i	$-0.601435\pi$
$743$	−17.0800			−0.626605			−0.313303	+	0.949653i	$0.601435\pi$
$744$		0			0
$745$	1.99956	−	23.2826i	0.0732582	−	0.853010i
$746$		−	12.1298i		−	0.444104i
$747$		0			0
$748$	4.96618			0.181582
$749$		0			0
$750$		0			0
$751$	−16.8893			−0.616298			−0.308149	−	0.951338i	$-0.599709\pi$
$751$	−16.8893			−0.616298			−0.308149	+	0.951338i	$0.599709\pi$
$752$		−	5.57882i		−	0.203439i
$753$		0			0
$754$			27.7563i			1.01082i
$755$	39.4750	+	3.39019i	1.43664	+	0.123382i
$756$		0			0
$757$		−	33.4057i		−	1.21415i	−0.794644	−	0.607076i	$-0.792342\pi$
$757$		−	33.4057i		−	1.21415i	0.794644	−	0.607076i	$-0.207658\pi$
$758$	−18.6821			−0.678565
$759$		0			0
$760$	1.13154	−	13.1755i	0.0410453	−	0.477927i
$761$	32.6148			1.18229			0.591143	−	0.806566i	$-0.298677\pi$
$761$	32.6148			1.18229			0.591143	+	0.806566i	$0.298677\pi$
$762$		0			0
$763$		0			0
$764$			2.82843i			0.102329i
$765$		0			0
$766$			11.0293i			0.398503i
$767$	11.3897			0.411259
$768$		0			0
$769$		−	22.4396i		−	0.809192i	−0.914495	−	0.404596i	$-0.867412\pi$
$769$		−	22.4396i		−	0.809192i	0.914495	−	0.404596i	$-0.132588\pi$
$770$		0			0
$771$		0			0
$772$		−	19.4966i		−	0.701697i
$773$			39.8331i			1.43270i	0.697743	+	0.716348i	$0.254188\pi$
$773$			39.8331i			1.43270i	−0.697743	+	0.716348i	$0.745812\pi$
$774$		0			0
$775$	3.85900	−	22.3012i	0.138619	−	0.801081i
$776$	−12.8260			−0.460428
$777$		0			0
$778$			34.3710i			1.23226i
$779$			41.6596i			1.49261i
$780$		0			0
$781$	21.9106			0.784024
$782$		−	3.85741i		−	0.137941i
$783$		0			0
$784$		0			0
$785$	−13.5521	−	1.16388i	−0.483694	−	0.0415405i
$786$		0			0
$787$	16.7330			0.596466			0.298233	−	0.954493i	$-0.403603\pi$
$787$	16.7330			0.596466			0.298233	+	0.954493i	$0.403603\pi$
$788$	27.1576			0.967448
$789$		0			0
$790$	37.3565	+	3.20825i	1.32909	+	0.114144i
$791$		0			0
$792$		0			0
$793$			70.7074i			2.51090i
$794$	31.0107			1.10053
$795$		0			0
$796$		−	3.46410i		−	0.122782i
$797$			2.68812i			0.0952182i	0.998866	+	0.0476091i	$0.0151602\pi$
$797$			2.68812i			0.0952182i	−0.998866	+	0.0476091i	$0.984840\pi$
$798$		0			0
$799$	−11.5589			−0.408924
$800$	4.92678	+	0.852531i	0.174188	+	0.0301415i
$801$		0			0
$802$		−	9.47745i		−	0.334660i
$803$		−	2.59427i		−	0.0915498i
$804$		0			0
$805$		0			0
$806$			25.6976i			0.905161i
$807$		0			0
$808$	−8.91147			−0.313504
$809$			31.4325i			1.10511i	0.833477	+	0.552554i	$0.186347\pi$
$809$			31.4325i			1.10511i	−0.833477	+	0.552554i	$0.813653\pi$
$810$		0			0
$811$		−	49.3830i		−	1.73407i	−0.498246	−	0.867036i	$-0.666022\pi$
$811$		−	49.3830i		−	1.73407i	0.498246	−	0.867036i	$-0.333978\pi$
$812$		0			0
$813$		0			0
$814$	7.11665			0.249438
$815$	0.179344	−	2.08827i	0.00628216	−	0.0731488i
$816$		0			0
$817$	50.6209			1.77100
$818$			9.47784i			0.331385i
$819$		0			0
$820$	−15.6937	−	1.34781i	−0.548048	−	0.0470675i
$821$		−	44.7263i		−	1.56096i	−0.625181	−	0.780480i	$-0.714975\pi$
$821$		−	44.7263i		−	1.56096i	0.625181	−	0.780480i	$-0.285025\pi$
$822$		0			0
$823$		−	13.1414i		−	0.458081i	−0.973417	−	0.229041i	$-0.926441\pi$
$823$		−	13.1414i		−	0.458081i	0.973417	−	0.229041i	$-0.0735589\pi$
$824$	−10.8198			−0.376925
$825$		0			0
$826$		0			0
$827$	−47.4125			−1.64869			−0.824346	−	0.566086i	$-0.808457\pi$
$827$	−47.4125			−1.64869			−0.824346	+	0.566086i	$0.808457\pi$
$828$		0			0
$829$			8.21588i			0.285349i	0.989770	+	0.142675i	$0.0455703\pi$
$829$			8.21588i			0.285349i	−0.989770	+	0.142675i	$0.954430\pi$
$830$	−2.60448	+	30.3262i	−0.0904027	+	1.05264i
$831$		0			0
$832$	−5.67714			−0.196819
$833$		0			0
$834$		0			0
$835$	−3.29287	+	38.3418i	−0.113954	+	1.32687i
$836$	−14.1752			−0.490258
$837$		0			0
$838$	−2.54445			−0.0878967
$839$	−17.6943			−0.610875			−0.305437	−	0.952212i	$-0.598803\pi$
$839$	−17.6943			−0.610875			−0.305437	+	0.952212i	$0.598803\pi$
$840$		0			0
$841$	5.09640			0.175738
$842$	−5.08573			−0.175266
$843$		0			0
$844$	−4.06071			−0.139775
$845$	−42.8416	−	3.67932i	−1.47380	−	0.126572i
$846$		0			0
$847$		0			0
$848$	4.19077			0.143912
$849$		0			0
$850$	1.76638	−	10.2079i	0.0605863	−	0.350129i
$851$		−	5.52775i		−	0.189489i
$852$		0			0
$853$	40.1129			1.37344			0.686720	−	0.726922i	$-0.259050\pi$
$853$	40.1129			1.37344			0.686720	+	0.726922i	$0.259050\pi$
$854$		0			0
$855$		0			0
$856$	5.57707			0.190620
$857$		−	44.1308i		−	1.50748i	−0.657173	−	0.753740i	$-0.728248\pi$
$857$		−	44.1308i		−	1.50748i	0.657173	−	0.753740i	$-0.271752\pi$
$858$		0			0
$859$			14.3575i			0.489870i	0.969539	+	0.244935i	$0.0787667\pi$
$859$			14.3575i			0.489870i	−0.969539	+	0.244935i	$0.921233\pi$
$860$	−1.63773	+	19.0696i	−0.0558461	+	0.650266i
$861$		0			0
$862$		−	13.2980i		−	0.452933i
$863$	−12.8029			−0.435814			−0.217907	−	0.975970i	$-0.569923\pi$
$863$	−12.8029			−0.435814			−0.217907	+	0.975970i	$0.569923\pi$
$864$		0			0
$865$	0.378119	−	4.40277i	0.0128564	−	0.149699i
$866$	−12.7895			−0.434606
$867$		0			0
$868$		0			0
$869$		−	40.1908i		−	1.36338i
$870$		0			0
$871$		−	43.2724i		−	1.46623i
$872$	2.00000			0.0677285
$873$		0			0
$874$			11.0103i			0.372431i
$875$		0			0
$876$		0			0
$877$		−	58.2720i		−	1.96771i	−0.178980	−	0.983853i	$-0.557280\pi$
$877$		−	58.2720i		−	1.96771i	0.178980	−	0.983853i	$-0.442720\pi$
$878$		−	0.373212i		−	0.0125953i
$879$		0			0
$880$	0.458606	−	5.33996i	0.0154596	−	0.180010i
$881$	1.80667			0.0608682			0.0304341	−	0.999537i	$-0.490311\pi$
$881$	1.80667			0.0608682			0.0304341	+	0.999537i	$0.490311\pi$
$882$		0			0
$883$			13.8997i			0.467761i	0.972265	+	0.233881i	$0.0751425\pi$
$883$			13.8997i			0.467761i	−0.972265	+	0.233881i	$0.924858\pi$
$884$			11.7626i			0.395619i
$885$		0			0
$886$	24.6330			0.827562
$887$		−	26.4918i		−	0.889508i	−0.895653	−	0.444754i	$-0.853291\pi$
$887$		−	26.4918i		−	0.889508i	0.895653	−	0.444754i	$-0.146709\pi$
$888$		0			0
$889$		0			0
$890$	−29.5473	−	2.53758i	−0.990427	−	0.0850598i
$891$		0			0
$892$	16.1486			0.540696
$893$	32.9929			1.10407
$894$		0			0
$895$	−0.169778	+	1.97688i	−0.00567506	+	0.0660798i
$896$		0			0
$897$		0			0
$898$			40.6223i			1.35558i
$899$	−22.1307			−0.738101
$900$		0			0
$901$		−	8.68295i		−	0.289271i
$902$			16.8844i			0.562189i
$903$		0			0
$904$	14.5030			0.482361
$905$	0.937482	−	10.9159i	0.0311630	−	0.362858i
$906$		0			0
$907$		−	36.7300i		−	1.21960i	−0.792556	−	0.609800i	$-0.791250\pi$
$907$		−	36.7300i		−	1.21960i	0.792556	−	0.609800i	$-0.208750\pi$
$908$			1.67980i			0.0557462i
$909$		0			0
$910$		0			0
$911$		−	39.8018i		−	1.31869i	−0.751839	−	0.659347i	$-0.770833\pi$
$911$		−	39.8018i		−	1.31869i	0.751839	−	0.659347i	$-0.229167\pi$
$912$		0			0
$913$	32.6271			1.07980
$914$			0.990551i			0.0327645i
$915$		0			0
$916$			12.6027i			0.416406i
$917$		0			0
$918$		0			0
$919$	−60.3383			−1.99038			−0.995189	−	0.0979740i	$-0.968764\pi$
$919$	−60.3383			−1.99038			−0.995189	+	0.0979740i	$0.968764\pi$
$920$	−4.14774	−	0.356216i	−0.136747	−	0.0117441i
$921$		0			0
$922$	−20.7397			−0.683026
$923$			51.8962i			1.70818i
$924$		0			0
$925$	2.53126	−	14.6282i	0.0832273	−	0.480971i
$926$			1.46421i			0.0481169i
$927$		0			0
$928$		−	4.88913i		−	0.160494i
$929$	−44.3497			−1.45507			−0.727533	−	0.686072i	$-0.759333\pi$
$929$	−44.3497			−1.45507			−0.727533	+	0.686072i	$0.759333\pi$
$930$		0			0
$931$		0			0
$932$	14.5164			0.475499
$933$		0			0
$934$		−	36.2680i		−	1.18673i
$935$	−11.0640	−	0.950198i	−0.361831	−	0.0310748i
$936$		0			0
$937$	−2.54073			−0.0830021			−0.0415010	−	0.999138i	$-0.513214\pi$
$937$	−2.54073			−0.0830021			−0.0415010	+	0.999138i	$0.513214\pi$
$938$		0			0
$939$		0			0
$940$	−1.06742	+	12.4289i	−0.0348152	+	0.405385i
$941$	33.8977			1.10503			0.552516	−	0.833502i	$-0.313668\pi$
$941$	33.8977			1.10503			0.552516	+	0.833502i	$0.313668\pi$
$942$		0			0
$943$	13.1147			0.427074
$944$	−2.00624			−0.0652977
$945$		0			0
$946$	20.5164			0.667045
$947$	−49.5089			−1.60882			−0.804411	−	0.594073i	$-0.797519\pi$
$947$	−49.5089			−1.60882			−0.804411	+	0.594073i	$0.797519\pi$
$948$		0			0
$949$	6.14463			0.199463
$950$	−5.04184	+	29.1368i	−0.163579	+	0.945323i
$951$		0			0
$952$		0			0
$953$	−17.0625			−0.552709			−0.276355	−	0.961056i	$-0.589126\pi$
$953$	−17.0625			−0.552709			−0.276355	+	0.961056i	$0.589126\pi$
$954$		0			0
$955$	0.541173	−	6.30136i	0.0175119	−	0.203907i
$956$			0.207089i			0.00669774i
$957$		0			0
$958$	10.3258			0.333610
$959$		0			0
$960$		0			0
$961$	10.5107			0.339054
$962$			16.8560i			0.543461i
$963$		0			0
$964$			10.4405i			0.336265i
$965$	−3.73035	+	43.4357i	−0.120084	+	1.39825i
$966$		0			0
$967$			49.6639i			1.59708i	0.601940	+	0.798541i	$0.294394\pi$
$967$			49.6639i			1.59708i	−0.601940	+	0.798541i	$0.705606\pi$
$968$	5.25489			0.168899
$969$		0			0
$970$	28.5747	+	2.45405i	0.917478	+	0.0787948i
$971$	−28.5859			−0.917366			−0.458683	−	0.888600i	$-0.651679\pi$
$971$	−28.5859			−0.917366			−0.458683	+	0.888600i	$0.651679\pi$
$972$		0			0
$973$		0			0
$974$		−	20.3291i		−	0.651386i
$975$		0			0
$976$		−	12.4548i		−	0.398668i
$977$	−27.7205			−0.886859			−0.443429	−	0.896309i	$-0.646238\pi$
$977$	−27.7205			−0.886859			−0.443429	+	0.896309i	$0.646238\pi$
$978$		0			0
$979$			31.7890i			1.01598i
$980$		0			0
$981$		0			0
$982$			34.6034i			1.10424i
$983$			42.8268i			1.36596i	0.730436	+	0.682982i	$0.239317\pi$
$983$			42.8268i			1.36596i	−0.730436	+	0.682982i	$0.760683\pi$
$984$		0			0
$985$	−60.5034	−	5.19615i	−1.92780	−	0.165563i
$986$	−10.1299			−0.322602
$987$		0			0
$988$		−	33.5744i		−	1.06814i
$989$		−	15.9358i		−	0.506729i
$990$		0			0
$991$	42.7446			1.35783			0.678914	−	0.734218i	$-0.262451\pi$
$991$	42.7446			1.35783			0.678914	+	0.734218i	$0.262451\pi$
$992$		−	4.52651i		−	0.143717i
$993$		0			0
$994$		0			0
$995$	−0.662799	+	7.71756i	−0.0210121	+	0.244663i
$996$		0			0
$997$	32.8719			1.04106			0.520531	−	0.853843i	$-0.325734\pi$
$997$	32.8719			1.04106			0.520531	+	0.853843i	$0.325734\pi$
$998$	2.95089			0.0934089
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4410.2.d.b.4409.1		16
3.2	odd	2		4410.2.d.a.4409.16		16
5.4	even	2		4410.2.d.a.4409.2		16
7.4	even	3		630.2.bo.a.89.7	yes	16
7.5	odd	6		630.2.bo.a.269.4	yes	16
7.6	odd	2	inner	4410.2.d.b.4409.16		16
15.14	odd	2	inner	4410.2.d.b.4409.15		16
21.5	even	6		630.2.bo.b.269.5	yes	16
21.11	odd	6		630.2.bo.b.89.2	yes	16
21.20	even	2		4410.2.d.a.4409.1		16
35.4	even	6		630.2.bo.b.89.5	yes	16
35.12	even	12		3150.2.bf.f.1151.12		32
35.18	odd	12		3150.2.bf.f.1601.11		32
35.19	odd	6		630.2.bo.b.269.2	yes	16
35.32	odd	12		3150.2.bf.f.1601.2		32
35.33	even	12		3150.2.bf.f.1151.1		32
35.34	odd	2		4410.2.d.a.4409.15		16
105.32	even	12		3150.2.bf.f.1601.12		32
105.47	odd	12		3150.2.bf.f.1151.2		32
105.53	even	12		3150.2.bf.f.1601.1		32
105.68	odd	12		3150.2.bf.f.1151.11		32
105.74	odd	6		630.2.bo.a.89.4	✓	16
105.89	even	6		630.2.bo.a.269.7	yes	16
105.104	even	2	inner	4410.2.d.b.4409.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.4	✓	16	105.74	odd	6
630.2.bo.a.89.7	yes	16	7.4	even	3
630.2.bo.a.269.4	yes	16	7.5	odd	6
630.2.bo.a.269.7	yes	16	105.89	even	6
630.2.bo.b.89.2	yes	16	21.11	odd	6
630.2.bo.b.89.5	yes	16	35.4	even	6
630.2.bo.b.269.2	yes	16	35.19	odd	6
630.2.bo.b.269.5	yes	16	21.5	even	6
3150.2.bf.f.1151.1		32	35.33	even	12
3150.2.bf.f.1151.2		32	105.47	odd	12
3150.2.bf.f.1151.11		32	105.68	odd	12
3150.2.bf.f.1151.12		32	35.12	even	12
3150.2.bf.f.1601.1		32	105.53	even	12
3150.2.bf.f.1601.2		32	35.32	odd	12
3150.2.bf.f.1601.11		32	35.18	odd	12
3150.2.bf.f.1601.12		32	105.32	even	12
4410.2.d.a.4409.1		16	21.20	even	2
4410.2.d.a.4409.2		16	5.4	even	2
4410.2.d.a.4409.15		16	35.34	odd	2
4410.2.d.a.4409.16		16	3.2	odd	2
4410.2.d.b.4409.1		16	1.1	even	1	trivial
4410.2.d.b.4409.2		16	105.104	even	2	inner
4410.2.d.b.4409.15		16	15.14	odd	2	inner
4410.2.d.b.4409.16		16	7.6	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:	\( N \)	\(=\)	\( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4410.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.22787 - 0.191334i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.22787 - 0.191334i) q^{5} +1.00000 q^{8} +(-2.22787 - 0.191334i) q^{10} +2.39690i q^{11} -5.67714 q^{13} +1.00000 q^{16} -2.07192i q^{17} +5.91397i q^{19} +(-2.22787 - 0.191334i) q^{20} +2.39690i q^{22} +1.86175 q^{23} +(4.92678 + 0.852531i) q^{25} -5.67714 q^{26} -4.88913i q^{29} -4.52651i q^{31} +1.00000 q^{32} -2.07192i q^{34} -2.96911i q^{37} +5.91397i q^{38} +(-2.22787 - 0.191334i) q^{40} +7.04428 q^{41} -8.55956i q^{43} +2.39690i q^{44} +1.86175 q^{46} -5.57882i q^{47} +(4.92678 + 0.852531i) q^{50} -5.67714 q^{52} +4.19077 q^{53} +(0.458606 - 5.33996i) q^{55} -4.88913i q^{58} -2.00624 q^{59} -12.4548i q^{61} -4.52651i q^{62} +1.00000 q^{64} +(12.6479 + 1.08623i) q^{65} +7.62222i q^{67} -2.07192i q^{68} -9.14126i q^{71} -1.08235 q^{73} -2.96911i q^{74} +5.91397i q^{76} -16.7678 q^{79} +(-2.22787 - 0.191334i) q^{80} +7.04428 q^{82} -13.6122i q^{83} +(-0.396428 + 4.61597i) q^{85} -8.55956i q^{86} +2.39690i q^{88} +13.2626 q^{89} +1.86175 q^{92} -5.57882i q^{94} +(1.13154 - 13.1755i) q^{95} -12.8260 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 16 q^{16} + 16 q^{23} + 12 q^{25} + 16 q^{32} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{64} + 40 q^{65} - 8 q^{79} + 64 q^{85} + 16 q^{92} + 24 q^{95}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 16 * q^16 + 16 * q^23 + 12 * q^25 + 16 * q^32 + 16 * q^46 + 12 * q^50 - 32 * q^53 + 16 * q^64 + 40 * q^65 - 8 * q^79 + 64 * q^85 + 16 * q^92 + 24 * q^95

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