LMFDB - Embedded newform 630.2.ce.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("630.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.22986704741655040229376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 $ x^16 - 31x^12 + 880x^8 - 2511*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.3
Root			$-0.596002 + 2.22431i$ of defining polynomial
Character	$\chi$	$=$	630.107
Dual form			630.2.ce.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.48356 - 1.67303i) q^{5} +(-2.30278 + 1.30278i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.48356 - 1.67303i) q^{5} +(-2.30278 + 1.30278i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.23205 - 1.86603i) q^{10} +(4.43664 - 2.56149i) q^{11} +(1.62250 - 1.62250i) q^{13} +(-1.85439 - 1.88713i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.99813 + 1.87514i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(2.12132 + 0.707107i) q^{20} +(3.62250 + 3.62250i) q^{22} +(7.96406 - 2.13396i) q^{23} +(-0.598076 + 4.96410i) q^{25} +(1.98715 + 1.14728i) q^{26} +(1.34287 - 2.27962i) q^{28} -2.82843 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.965926 + 0.258819i) q^{32} +7.24500i q^{34} +(5.59590 + 1.91987i) q^{35} +(1.88170 - 0.504200i) q^{37} +(0.258819 - 0.965926i) q^{38} +(-0.133975 + 2.23205i) q^{40} -7.95141i q^{41} +(3.00000 - 3.00000i) q^{43} +(-2.56149 + 4.43664i) q^{44} +(4.12250 + 7.14038i) q^{46} +(-2.32937 - 8.69333i) q^{47} +(3.60555 - 6.00000i) q^{49} +(-4.94975 + 0.707107i) q^{50} +(-0.593876 + 2.21637i) q^{52} +(-2.65160 + 9.89591i) q^{53} +(-10.8675 - 3.62250i) q^{55} +(2.54951 + 0.707107i) q^{56} +(-0.732051 - 2.73205i) q^{58} +(-3.00167 - 5.19904i) q^{59} +(-4.62250 + 8.00640i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(-5.12157 - 0.307413i) q^{65} +(-2.56218 + 9.56218i) q^{67} +(-6.99813 + 1.87514i) q^{68} +(-0.406124 + 5.90212i) q^{70} -7.41755i q^{71} +(3.06672 + 0.821726i) q^{73} +(0.974040 + 1.68709i) q^{74} +1.00000 q^{76} +(-6.87953 + 11.6785i) q^{77} +(13.2026 + 7.62250i) q^{79} +(-2.19067 + 0.448288i) q^{80} +(7.68048 - 2.05798i) q^{82} +(2.29456 + 2.29456i) q^{83} +(-7.24500 - 14.4900i) q^{85} +(3.67423 + 2.12132i) q^{86} +(-4.94843 - 1.32593i) q^{88} +(4.94975 - 8.57321i) q^{89} +(-1.62250 + 5.85000i) q^{91} +(-5.83009 + 5.83009i) q^{92} +(7.79423 - 4.50000i) q^{94} +(0.448288 + 2.19067i) q^{95} +(3.24500 + 3.24500i) q^{97} +(6.72874 + 1.92978i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 8 q^{10} - 24 q^{13} + 8 q^{16} + 8 q^{22} + 32 q^{25} + 4 q^{28} - 32 q^{31} + 36 q^{37} - 16 q^{40} + 48 q^{43} + 16 q^{46} - 12 q^{52} - 24 q^{55} + 16 q^{58} - 24 q^{61} + 56 q^{67} - 4 q^{70} - 32 q^{73} + 16 q^{76} + 20 q^{82} - 16 q^{85} - 4 q^{88} + 24 q^{91} - 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 8 * q^10 - 24 * q^13 + 8 * q^16 + 8 * q^22 + 32 * q^25 + 4 * q^28 - 32 * q^31 + 36 * q^37 - 16 * q^40 + 48 * q^43 + 16 * q^46 - 12 * q^52 - 24 * q^55 + 16 * q^58 - 24 * q^61 + 56 * q^67 - 4 * q^70 - 32 * q^73 + 16 * q^76 + 20 * q^82 - 16 * q^85 - 4 * q^88 + 24 * q^91 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.48356	−	1.67303i	−0.663470	−	0.748203i
$5$	−1.48356	−	1.67303i	−0.663470	−	0.748203i
$6$		0			0
$7$	−2.30278	+	1.30278i	−0.870367	+	0.492403i
$7$	−2.30278	+	1.30278i	−0.870367	+	0.492403i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.23205	−	1.86603i	0.389609	−	0.590089i
$11$	4.43664	−	2.56149i	1.33770	−	0.772319i	0.351231	−	0.936289i	$-0.385763\pi$
$11$	4.43664	−	2.56149i	1.33770	−	0.772319i	0.986465	+	0.163969i	$0.0524299\pi$
$12$		0			0
$13$	1.62250	−	1.62250i	0.450000	−	0.450000i	−0.445354	−	0.895354i	$-0.646922\pi$
$13$	1.62250	−	1.62250i	0.450000	−	0.450000i	0.895354	+	0.445354i	$0.146922\pi$
$14$	−1.85439	−	1.88713i	−0.495606	−	0.504356i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.99813	+	1.87514i	1.69730	+	0.454789i	0.972256	−	0.233918i	$-0.0751547\pi$
$17$	6.99813	+	1.87514i	1.69730	+	0.454789i	0.725040	+	0.688707i	$0.241821\pi$
$18$		0			0
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	0.397360	−	0.917663i	$-0.369927\pi$
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	−0.596040	+	0.802955i	$0.703260\pi$
$20$	2.12132	+	0.707107i	0.474342	+	0.158114i
$21$		0			0
$22$	3.62250	+	3.62250i	0.772319	+	0.772319i
$23$	7.96406	−	2.13396i	1.66062	−	0.444962i	0.698062	−	0.716037i	$-0.254046\pi$
$23$	7.96406	−	2.13396i	1.66062	−	0.444962i	0.962558	+	0.271075i	$0.0873792\pi$
$24$		0			0
$25$	−0.598076	+	4.96410i	−0.119615	+	0.992820i
$26$	1.98715	+	1.14728i	0.389712	+	0.225000i
$27$		0			0
$28$	1.34287	−	2.27962i	0.253779	−	0.430809i
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$			7.24500i			1.24251i
$35$	5.59590	+	1.91987i	0.945880	+	0.324517i
$36$		0			0
$37$	1.88170	−	0.504200i	0.309350	−	0.0828900i	−0.100804	−	0.994906i	$-0.532142\pi$
$37$	1.88170	−	0.504200i	0.309350	−	0.0828900i	0.410154	+	0.912016i	$0.365475\pi$
$38$	0.258819	−	0.965926i	0.0419860	−	0.156694i
$39$		0			0
$40$	−0.133975	+	2.23205i	−0.0211832	+	0.352918i
$41$		−	7.95141i		−	1.24180i	−0.783889	−	0.620901i	$-0.786767\pi$
$41$		−	7.95141i		−	1.24180i	0.783889	−	0.620901i	$-0.213233\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$	−2.56149	+	4.43664i	−0.386160	+	0.668848i
$45$		0			0
$46$	4.12250	+	7.14038i	0.607829	+	1.05279i
$47$	−2.32937	−	8.69333i	−0.339774	−	1.26805i	−0.898600	−	0.438768i	$-0.855415\pi$
$47$	−2.32937	−	8.69333i	−0.339774	−	1.26805i	0.558827	−	0.829285i	$-0.311252\pi$
$48$		0			0
$49$	3.60555	−	6.00000i	0.515079	−	0.857143i
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$		0			0
$52$	−0.593876	+	2.21637i	−0.0823558	+	0.307356i
$53$	−2.65160	+	9.89591i	−0.364225	+	1.35931i	0.504243	+	0.863562i	$0.331772\pi$
$53$	−2.65160	+	9.89591i	−0.364225	+	1.35931i	−0.868468	+	0.495745i	$0.834895\pi$
$54$		0			0
$55$	−10.8675	−	3.62250i	−1.46537	−	0.488458i
$56$	2.54951	+	0.707107i	0.340693	+	0.0944911i
$57$		0			0
$58$	−0.732051	−	2.73205i	−0.0961230	−	0.358736i
$59$	−3.00167	−	5.19904i	−0.390784	−	0.676857i	0.601769	−	0.798670i	$-0.294463\pi$
$59$	−3.00167	−	5.19904i	−0.390784	−	0.676857i	−0.992553	+	0.121813i	$0.961129\pi$
$60$		0			0
$61$	−4.62250	+	8.00640i	−0.591850	+	1.02511i	0.402133	+	0.915581i	$0.368269\pi$
$61$	−4.62250	+	8.00640i	−0.591850	+	1.02511i	−0.993983	+	0.109534i	$0.965064\pi$
$62$	2.82843	−	2.82843i	0.359211	−	0.359211i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−5.12157	−	0.307413i	−0.635253	−	0.0381299i
$66$		0			0
$67$	−2.56218	+	9.56218i	−0.313020	+	1.16821i	0.612799	+	0.790239i	$0.290043\pi$
$67$	−2.56218	+	9.56218i	−0.313020	+	1.16821i	−0.925819	+	0.377967i	$0.876623\pi$
$68$	−6.99813	+	1.87514i	−0.848648	+	0.227395i
$69$		0			0
$70$	−0.406124	+	5.90212i	−0.0485411	+	0.705439i
$71$		−	7.41755i		−	0.880301i	−0.897924	−	0.440150i	$-0.854925\pi$
$71$		−	7.41755i		−	0.880301i	0.897924	−	0.440150i	$-0.145075\pi$
$72$		0			0
$73$	3.06672	+	0.821726i	0.358933	+	0.0961758i	0.433779	−	0.901019i	$-0.357180\pi$
$73$	3.06672	+	0.821726i	0.358933	+	0.0961758i	−0.0748460	+	0.997195i	$0.523847\pi$
$74$	0.974040	+	1.68709i	0.113230	+	0.196120i
$75$		0			0
$76$	1.00000			0.114708
$77$	−6.87953	+	11.6785i	−0.783995	+	1.33089i
$78$		0			0
$79$	13.2026	+	7.62250i	1.48540	+	0.857598i	0.999862	−	0.0166154i	$-0.00528910\pi$
$79$	13.2026	+	7.62250i	1.48540	+	0.857598i	0.485542	+	0.874214i	$0.338622\pi$
$80$	−2.19067	+	0.448288i	−0.244924	+	0.0501201i
$81$		0			0
$82$	7.68048	−	2.05798i	0.848167	−	0.227266i
$83$	2.29456	+	2.29456i	0.251861	+	0.251861i	0.821733	−	0.569872i	$-0.193007\pi$
$83$	2.29456	+	2.29456i	0.251861	+	0.251861i	−0.569872	+	0.821733i	$0.693007\pi$
$84$		0			0
$85$	−7.24500	−	14.4900i	−0.785830	−	1.57166i
$86$	3.67423	+	2.12132i	0.396203	+	0.228748i
$87$		0			0
$88$	−4.94843	−	1.32593i	−0.527504	−	0.141344i
$89$	4.94975	−	8.57321i	0.524672	−	0.908759i	−0.474915	−	0.880032i	$-0.657521\pi$
$89$	4.94975	−	8.57321i	0.524672	−	0.908759i	0.999587	−	0.0287273i	$-0.00914543\pi$
$90$		0			0
$91$	−1.62250	+	5.85000i	−0.170084	+	0.613247i
$92$	−5.83009	+	5.83009i	−0.607829	+	0.607829i
$93$		0			0
$94$	7.79423	−	4.50000i	0.803913	−	0.464140i
$95$	0.448288	+	2.19067i	0.0459934	+	0.224758i
$96$		0			0
$97$	3.24500	+	3.24500i	0.329480	+	0.329480i	0.852389	−	0.522909i	$-0.175153\pi$
$97$	3.24500	+	3.24500i	0.329480	+	0.329480i	−0.522909	+	0.852389i	$0.675153\pi$
$98$	6.72874	+	1.92978i	0.679705	+	0.194937i
$99$		0			0
$100$	−1.96410	−	4.59808i	−0.196410	−	0.459808i
$101$	−13.7723	+	7.95141i	−1.37039	+	0.791195i	−0.990977	−	0.134032i	$-0.957208\pi$
$101$	−13.7723	+	7.95141i	−1.37039	+	0.791195i	−0.379413	+	0.925227i	$0.623874\pi$
$102$		0			0
$103$	−3.01788	−	11.2629i	−0.297360	−	1.10976i	−0.939325	−	0.343030i	$-0.888547\pi$
$103$	−3.01788	−	11.2629i	−0.297360	−	1.10976i	0.641964	−	0.766735i	$-0.278120\pi$
$104$	−2.29456			−0.225000
$105$		0			0
$106$	−10.2450			−0.995082
$107$	1.35751	+	5.06628i	0.131235	+	0.489776i	0.999985	−	0.00547518i	$-0.00174281\pi$
$107$	1.35751	+	5.06628i	0.131235	+	0.489776i	−0.868750	+	0.495251i	$0.835076\pi$
$108$		0			0
$109$	−3.46410	+	2.00000i	−0.331801	+	0.191565i	−0.656640	−	0.754204i	$-0.728023\pi$
$109$	−3.46410	+	2.00000i	−0.331801	+	0.191565i	0.324840	+	0.945769i	$0.394690\pi$
$110$	0.686350	−	11.4348i	0.0654409	−	1.09026i
$111$		0			0
$112$	−0.0231510	+	2.64565i	−0.00218757	+	0.249990i
$113$	10.2460	+	10.2460i	0.963860	+	0.963860i	0.999369	−	0.0355092i	$-0.0113053\pi$
$113$	10.2460	+	10.2460i	0.963860	+	0.963860i	−0.0355092	+	0.999369i	$0.511305\pi$
$114$		0			0
$115$	−15.3854	−	10.1583i	−1.43469	−	0.947262i
$116$	2.44949	−	1.41421i	0.227429	−	0.131306i
$117$		0			0
$118$	4.24500	−	4.24500i	0.390784	−	0.390784i
$119$	−18.5580	+	4.79896i	−1.70121	+	0.439920i
$120$		0			0
$121$	7.62250	−	13.2026i	0.692954	−	1.20023i
$122$	−8.92998	−	2.39278i	−0.808483	−	0.216632i
$123$		0			0
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$	9.19239	−	6.36396i	0.822192	−	0.569210i
$126$		0			0
$127$	−8.37750	−	8.37750i	−0.743383	−	0.743383i	0.229844	−	0.973227i	$-0.426178\pi$
$127$	−8.37750	−	8.37750i	−0.743383	−	0.743383i	−0.973227	+	0.229844i	$0.926178\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	−1.02862	−	5.02663i	−0.0902162	−	0.440864i
$131$	−8.11087	−	4.68281i	−0.708650	−	0.409139i	0.101911	−	0.994794i	$-0.467504\pi$
$131$	−8.11087	−	4.68281i	−0.708650	−	0.409139i	−0.810561	+	0.585654i	$0.800838\pi$
$132$		0			0
$133$	2.64565	+	0.0231510i	0.229407	+	0.00200745i
$134$	−9.89949			−0.855186
$135$		0			0
$136$	−3.62250	−	6.27435i	−0.310627	−	0.538021i
$137$	8.45668	+	2.26596i	0.722503	+	0.193594i	0.601288	−	0.799032i	$-0.294654\pi$
$137$	8.45668	+	2.26596i	0.722503	+	0.193594i	0.121215	+	0.992626i	$0.461321\pi$
$138$		0			0
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$	−5.80613	+	1.13530i	−0.490707	+	0.0959500i
$141$		0			0
$142$	7.16480	−	1.91980i	0.601257	−	0.161106i
$143$	3.04242	−	11.3545i	0.254420	−	0.949508i
$144$		0			0
$145$	4.19615	+	4.73205i	0.348471	+	0.392975i
$146$			3.17491i			0.262757i
$147$		0			0
$148$	−1.37750	+	1.37750i	−0.113230	+	0.113230i
$149$	4.41588	−	7.64853i	0.361763	−	0.626592i	−0.626488	−	0.779431i	$-0.715508\pi$
$149$	4.41588	−	7.64853i	0.361763	−	0.626592i	0.988251	+	0.152839i	$0.0488416\pi$
$150$		0			0
$151$	−5.24500	−	9.08460i	−0.426832	−	0.739295i	0.569758	−	0.821813i	$-0.307037\pi$
$151$	−5.24500	−	9.08460i	−0.426832	−	0.739295i	−0.996590	+	0.0825182i	$0.973704\pi$
$152$	0.258819	+	0.965926i	0.0209930	+	0.0783469i
$153$		0			0
$154$	−13.0611	−	3.62250i	−1.05249	−	0.291909i
$155$	−2.82843	+	8.48528i	−0.227185	+	0.681554i
$156$		0			0
$157$	−0.504200	+	1.88170i	−0.0402396	+	0.150176i	−0.983123	−	0.182948i	$-0.941436\pi$
$157$	−0.504200	+	1.88170i	−0.0402396	+	0.150176i	0.942883	+	0.333124i	$0.108103\pi$
$158$	−3.94570	+	14.7255i	−0.313903	+	1.17150i
$159$		0			0
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$	−15.5594	+	15.2894i	−1.22625	+	1.20497i
$162$		0			0
$163$	−2.65185	−	9.89685i	−0.207709	−	0.775181i	−0.988607	−	0.150522i	$-0.951905\pi$
$163$	−2.65185	−	9.89685i	−0.207709	−	0.775181i	0.780897	−	0.624659i	$-0.214762\pi$
$164$	3.97571	+	6.88613i	0.310451	+	0.537716i
$165$		0			0
$166$	−1.62250	+	2.81025i	−0.125930	+	0.218118i
$167$	−1.58745	+	1.58745i	−0.122841	+	0.122841i	−0.765855	−	0.643014i	$-0.777684\pi$
$167$	−1.58745	+	1.58745i	−0.122841	+	0.122841i	0.643014	+	0.765855i	$0.277684\pi$
$168$		0			0
$169$			7.73499i			0.595000i
$170$	12.1211	−	10.7484i	0.929647	−	0.824366i
$171$		0			0
$172$	−1.09808	+	4.09808i	−0.0837275	+	0.312475i
$173$	19.5552	−	5.23979i	1.48675	−	0.398374i	0.578113	−	0.815957i	$-0.303789\pi$
$173$	19.5552	−	5.23979i	1.48675	−	0.398374i	0.908639	+	0.417583i	$0.137123\pi$
$174$		0			0
$175$	−5.08988	−	12.2104i	−0.384758	−	0.923017i
$176$		−	5.12299i		−	0.386160i
$177$		0			0
$178$	9.56218	+	2.56218i	0.716716	+	0.192043i
$179$	3.80247	+	6.58607i	0.284210	+	0.492266i	0.972417	−	0.233248i	$-0.0749355\pi$
$179$	3.80247	+	6.58607i	0.284210	+	0.492266i	−0.688207	+	0.725514i	$0.741602\pi$
$180$		0			0
$181$	−1.24500			−0.0925400			−0.0462700	−	0.998929i	$-0.514733\pi$
$181$	−1.24500			−0.0925400			−0.0462700	+	0.998929i	$0.514733\pi$
$182$	−6.07060	−	0.0531214i	−0.449983	−	0.00393762i
$183$		0			0
$184$	−7.14038	−	4.12250i	−0.526396	−	0.303915i
$185$	−3.63517	−	2.40013i	−0.267263	−	0.176461i
$186$		0			0
$187$	35.8513	−	9.60634i	2.62171	−	0.702485i
$188$	6.36396	+	6.36396i	0.464140	+	0.464140i
$189$		0			0
$190$	−2.00000	+	1.00000i	−0.145095	+	0.0725476i
$191$	−5.19904	−	3.00167i	−0.376189	−	0.217193i	0.299970	−	0.953949i	$-0.403023\pi$
$191$	−5.19904	−	3.00167i	−0.376189	−	0.217193i	−0.676159	+	0.736756i	$0.736357\pi$
$192$		0			0
$193$	17.0617	+	4.57166i	1.22812	+	0.329075i	0.813849	−	0.581076i	$-0.197368\pi$
$193$	17.0617	+	4.57166i	1.22812	+	0.329075i	0.414276	+	0.910151i	$0.364035\pi$
$194$	−2.29456	+	3.97429i	−0.164740	+	0.285338i
$195$		0			0
$196$	−0.122499	+	6.99893i	−0.00874993	+	0.499923i
$197$	−10.9531	+	10.9531i	−0.780375	+	0.780375i	−0.979894	−	0.199519i	$-0.936062\pi$
$197$	−10.9531	+	10.9531i	−0.780375	+	0.780375i	0.199519	+	0.979894i	$0.436062\pi$
$198$		0			0
$199$	−8.00640	+	4.62250i	−0.567559	+	0.327680i	−0.756174	−	0.654371i	$-0.772934\pi$
$199$	−8.00640	+	4.62250i	−0.567559	+	0.327680i	0.188615	+	0.982051i	$0.439600\pi$
$200$	3.93305	−	3.08725i	0.278109	−	0.218301i
$201$		0			0
$202$	−11.2450	−	11.2450i	−0.791195	−	0.791195i
$203$	6.51323	−	3.68481i	0.457139	−	0.258623i
$204$		0			0
$205$	−13.3030	+	11.7964i	−0.929120	+	0.823899i
$206$	10.0980	−	5.83009i	0.703562	−	0.406202i
$207$		0			0
$208$	−0.593876	−	2.21637i	−0.0411779	−	0.153678i
$209$	−5.12299			−0.354364
$210$		0			0
$211$	−15.7550			−1.08462			−0.542310	−	0.840179i	$-0.682450\pi$
$211$	−15.7550			−1.08462			−0.542310	+	0.840179i	$0.682450\pi$
$212$	−2.65160	−	9.89591i	−0.182113	−	0.679654i
$213$		0			0
$214$	−4.54230	+	2.62250i	−0.310505	+	0.179270i
$215$	−9.46979	−	0.568406i	−0.645834	−	0.0387650i
$216$		0			0
$217$	9.11850	+	5.37150i	0.619004	+	0.364641i
$218$	−2.82843	−	2.82843i	−0.191565	−	0.191565i
$219$		0			0
$220$	11.2228	−	2.29657i	0.756640	−	0.154835i
$221$	14.3969	−	8.31204i	0.968439	−	0.559128i
$222$		0			0
$223$	−18.2450	+	18.2450i	−1.22178	+	1.22178i	−0.254775	+	0.967000i	$0.582001\pi$
$223$	−18.2450	+	18.2450i	−1.22178	+	1.22178i	−0.967000	+	0.254775i	$0.917999\pi$
$224$	−2.56149	+	0.662382i	−0.171147	+	0.0442573i
$225$		0			0
$226$	−7.24500	+	12.5487i	−0.481930	+	0.834727i
$227$	−6.99813	−	1.87514i	−0.464482	−	0.124458i	0.0189856	−	0.999820i	$-0.493956\pi$
$227$	−6.99813	−	1.87514i	−0.464482	−	0.124458i	−0.483468	+	0.875362i	$0.660623\pi$
$228$		0			0
$229$	2.81025	+	1.62250i	0.185707	+	0.107218i	0.589971	−	0.807424i	$-0.299139\pi$
$229$	2.81025	+	1.62250i	0.185707	+	0.107218i	−0.404264	+	0.914642i	$0.632472\pi$
$230$	5.83009	−	17.4903i	0.384425	−	1.15328i
$231$		0			0
$232$	2.00000	+	2.00000i	0.131306	+	0.131306i
$233$	−26.3166	+	7.05152i	−1.72406	+	0.461961i	−0.978801	−	0.204813i	$-0.934341\pi$
$233$	−26.3166	+	7.05152i	−1.72406	+	0.461961i	−0.745260	+	0.666774i	$0.767675\pi$
$234$		0			0
$235$	−11.0885	+	16.7942i	−0.723331	+	1.09553i
$236$	5.19904	+	3.00167i	0.338429	+	0.195392i
$237$		0			0
$238$	−9.43861	−	16.6836i	−0.611814	−	1.08144i
$239$	−0.346479			−0.0224119			−0.0112059	−	0.999937i	$-0.503567\pi$
$239$	−0.346479			−0.0224119			−0.0112059	+	0.999937i	$0.503567\pi$
$240$		0			0
$241$	1.12250	+	1.94423i	0.0723065	+	0.125239i	0.899912	−	0.436072i	$-0.143631\pi$
$241$	1.12250	+	1.94423i	0.0723065	+	0.125239i	−0.827605	+	0.561311i	$0.810297\pi$
$242$	14.7255	+	3.94570i	0.946593	+	0.253639i
$243$		0			0
$244$		−	9.24500i		−	0.591850i
$245$	−15.3873	+	2.86918i	−0.983056	+	0.183305i
$246$		0			0
$247$	−2.21637	+	0.593876i	−0.141025	+	0.0377874i
$248$	−1.03528	+	3.86370i	−0.0657401	+	0.245345i
$249$		0			0
$250$	8.52628	+	7.23205i	0.539249	+	0.457395i
$251$		−	6.88368i		−	0.434494i	−0.976117	−	0.217247i	$-0.930292\pi$
$251$		−	6.88368i		−	0.434494i	0.976117	−	0.217247i	$-0.0697077\pi$
$252$		0			0
$253$	29.8675	−	29.8675i	1.87775	−	1.87775i
$254$	5.92379	−	10.2603i	0.371692	−	0.643789i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.322229	+	1.20258i	0.0201001	+	0.0750146i	0.975247	−	0.221117i	$-0.0709701\pi$
$257$	0.322229	+	1.20258i	0.0201001	+	0.0750146i	−0.955147	+	0.296131i	$0.904303\pi$
$258$		0			0
$259$	−3.67628	+	3.61249i	−0.228433	+	0.224470i
$260$	4.58912	−	2.29456i	0.284605	−	0.142303i
$261$		0			0
$262$	2.42400	−	9.04650i	0.149755	−	0.558895i
$263$	0.644458	−	2.40515i	0.0397390	−	0.148308i	−0.943206	−	0.332209i	$-0.892206\pi$
$263$	0.644458	−	2.40515i	0.0397390	−	0.148308i	0.982945	+	0.183901i	$0.0588727\pi$
$264$		0			0
$265$	20.4900	−	10.2450i	1.25869	−	0.629345i
$266$	0.662382	+	2.56149i	0.0406133	+	0.157055i
$267$		0			0
$268$	−2.56218	−	9.56218i	−0.156510	−	0.584103i
$269$	−4.94975	−	8.57321i	−0.301791	−	0.522718i	0.674750	−	0.738046i	$-0.264251\pi$
$269$	−4.94975	−	8.57321i	−0.301791	−	0.522718i	−0.976542	+	0.215328i	$0.930918\pi$
$270$		0			0
$271$	9.24500	−	16.0128i	0.561594	−	0.972709i	−0.435764	−	0.900061i	$-0.643522\pi$
$271$	9.24500	−	16.0128i	0.561594	−	0.972709i	0.997358	−	0.0726478i	$-0.0231449\pi$
$272$	5.12299	−	5.12299i	0.310627	−	0.310627i
$273$		0			0
$274$			8.75500i			0.528909i
$275$	10.0621	+	23.5559i	0.606765	+	1.42047i
$276$		0			0
$277$	−5.66973	+	21.1597i	−0.340661	+	1.27136i	0.556939	+	0.830554i	$0.311976\pi$
$277$	−5.66973	+	21.1597i	−0.340661	+	1.27136i	−0.897600	+	0.440811i	$0.854691\pi$
$278$	−7.72741	+	2.07055i	−0.463459	+	0.124183i
$279$		0			0
$280$	−2.59935	−	5.31445i	−0.155341	−	0.317599i
$281$			10.7798i			0.643071i	0.946897	+	0.321536i	$0.104199\pi$
$281$			10.7798i			0.643071i	−0.946897	+	0.321536i	$0.895801\pi$
$282$		0			0
$283$	13.6603	+	3.66025i	0.812018	+	0.217580i	0.640854	−	0.767663i	$-0.278581\pi$
$283$	13.6603	+	3.66025i	0.812018	+	0.217580i	0.171164	+	0.985243i	$0.445247\pi$
$284$	3.70877	+	6.42378i	0.220075	+	0.381181i
$285$		0			0
$286$	11.7550			0.695088
$287$	10.3589	+	18.3103i	0.611467	+	1.08082i
$288$		0			0
$289$	30.7352	+	17.7450i	1.80796	+	1.04382i
$290$	−3.48477	+	5.27792i	−0.204633	+	0.309930i
$291$		0			0
$292$	−3.06672	+	0.821726i	−0.179466	+	0.0480879i
$293$	2.46780	+	2.46780i	0.144170	+	0.144170i	0.775508	−	0.631338i	$-0.217494\pi$
$293$	2.46780	+	2.46780i	0.144170	+	0.144170i	−0.631338	+	0.775508i	$0.717494\pi$
$294$		0			0
$295$	−4.24500	+	12.7350i	−0.247153	+	0.741460i
$296$	−1.68709	−	0.974040i	−0.0980600	−	0.0566149i
$297$		0			0
$298$	8.53083	+	2.28583i	0.494177	+	0.132414i
$299$	9.45932	−	16.3840i	0.547047	−	0.947513i
$300$		0			0
$301$	−3.00000	+	10.8167i	−0.172917	+	0.623462i
$302$	7.41755	−	7.41755i	0.426832	−	0.426832i
$303$		0			0
$304$	−0.866025	+	0.500000i	−0.0496700	+	0.0286770i
$305$	20.2527	−	4.14442i	1.15967	−	0.237309i
$306$		0			0
$307$	6.24500	+	6.24500i	0.356421	+	0.356421i	0.862492	−	0.506071i	$-0.168903\pi$
$307$	6.24500	+	6.24500i	0.356421	+	0.356421i	−0.506071	+	0.862492i	$0.668903\pi$
$308$	0.118602	−	13.5536i	0.00675800	−	0.772290i
$309$		0			0
$310$	−8.92820	−	0.535898i	−0.507088	−	0.0304370i
$311$	9.17333	−	5.29623i	0.520172	−	0.300321i	−0.216833	−	0.976209i	$-0.569573\pi$
$311$	9.17333	−	5.29623i	0.520172	−	0.300321i	0.737005	+	0.675887i	$0.236239\pi$
$312$		0			0
$313$	3.47358	+	12.9636i	0.196338	+	0.732745i	0.991916	+	0.126893i	$0.0405006\pi$
$313$	3.47358	+	12.9636i	0.196338	+	0.732745i	−0.795578	+	0.605851i	$0.792833\pi$
$314$	−1.94808			−0.109937
$315$		0			0
$316$	−15.2450			−0.857598
$317$	−3.10583	−	11.5911i	−0.174441	−	0.651022i	−0.996646	−	0.0818309i	$-0.973923\pi$
$317$	−3.10583	−	11.5911i	−0.174441	−	0.651022i	0.822206	−	0.569191i	$-0.192743\pi$
$318$		0			0
$319$	−12.5487	+	7.24500i	−0.702593	+	0.405642i
$320$	1.67303	−	1.48356i	0.0935254	−	0.0829337i
$321$		0			0
$322$	−18.7955	−	11.0720i	−1.04743	−	0.617018i
$323$	−5.12299	−	5.12299i	−0.285051	−	0.285051i
$324$		0			0
$325$	7.08387	+	9.02463i	0.392943	+	0.500596i
$326$	8.87327	−	5.12299i	0.491445	−	0.283736i
$327$		0			0
$328$	−5.62250	+	5.62250i	−0.310451	+	0.310451i
$329$	16.6895	+	16.9841i	0.920121	+	0.936366i
$330$		0			0
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	−0.946038	−	0.324057i	$-0.894953\pi$
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	0.753660	+	0.657264i	$0.228286\pi$
$332$	−3.13443	−	0.839867i	−0.172024	−	0.0460937i
$333$		0			0
$334$	−1.94423	−	1.12250i	−0.106383	−	0.0614204i
$335$	19.7990	−	9.89949i	1.08173	−	0.540867i
$336$		0			0
$337$	−6.24500	−	6.24500i	−0.340187	−	0.340187i	0.516251	−	0.856437i	$-0.327327\pi$
$337$	−6.24500	−	6.24500i	−0.340187	−	0.340187i	−0.856437	+	0.516251i	$0.827327\pi$
$338$	−7.47143	+	2.00196i	−0.406392	+	0.108892i
$339$		0			0
$340$	13.5194	+	8.92621i	0.733190	+	0.484091i
$341$	−17.7465	−	10.2460i	−0.961029	−	0.554851i
$342$		0			0
$343$	−0.486122	+	18.5139i	−0.0262481	+	0.999655i
$344$	−4.24264			−0.228748
$345$		0			0
$346$	10.1225	+	17.5327i	0.544189	+	0.942563i
$347$	1.20258	+	0.322229i	0.0645576	+	0.0172982i	0.290953	−	0.956737i	$-0.406028\pi$
$347$	1.20258	+	0.322229i	0.0645576	+	0.0172982i	−0.226396	+	0.974035i	$0.572694\pi$
$348$		0			0
$349$			34.4900i			1.84621i	0.384551	+	0.923104i	$0.374356\pi$
$349$			34.4900i			1.84621i	−0.384551	+	0.923104i	$0.625644\pi$
$350$	10.4770	−	8.07672i	0.560017	−	0.431719i
$351$		0			0
$352$	4.94843	−	1.32593i	0.263752	−	0.0706721i
$353$	4.78556	−	17.8600i	0.254710	−	0.950590i	−0.713542	−	0.700613i	$-0.752910\pi$
$353$	4.78556	−	17.8600i	0.254710	−	0.950590i	0.968252	−	0.249977i	$-0.0804232\pi$
$354$		0			0
$355$	−12.4098	+	11.0044i	−0.658644	+	0.584053i
$356$			9.89949i			0.524672i
$357$		0			0
$358$	−5.37750	+	5.37750i	−0.284210	+	0.284210i
$359$	−5.65685	+	9.79796i	−0.298557	+	0.517116i	−0.975806	−	0.218638i	$-0.929839\pi$
$359$	−5.65685	+	9.79796i	−0.298557	+	0.517116i	0.677249	+	0.735754i	$0.263172\pi$
$360$		0			0
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	−0.322229	−	1.20258i	−0.0169360	−	0.0632060i
$363$		0			0
$364$	−1.51988	−	5.87750i	−0.0796632	−	0.308065i
$365$	−3.17491	−	6.34981i	−0.166182	−	0.332364i
$366$		0			0
$367$	−6.53996	+	24.4075i	−0.341383	+	1.27406i	0.555398	+	0.831585i	$0.312566\pi$
$367$	−6.53996	+	24.4075i	−0.341383	+	1.27406i	−0.896781	+	0.442474i	$0.854101\pi$
$368$	2.13396	−	7.96406i	0.111240	−	0.415155i
$369$		0			0
$370$	1.37750	−	4.13250i	0.0716129	−	0.214839i
$371$	−6.78611	−	26.2425i	−0.352317	−	1.36244i
$372$		0			0
$373$	1.55378	+	5.79878i	0.0804515	+	0.300249i	0.994414	−	0.105549i	$-0.0336601\pi$
$373$	1.55378	+	5.79878i	0.0804515	+	0.300249i	−0.913963	+	0.405799i	$0.866993\pi$
$374$	18.5580	+	32.1434i	0.959612	+	1.66210i
$375$		0			0
$376$	−4.50000	+	7.79423i	−0.232070	+	0.401957i
$377$	−4.58912	+	4.58912i	−0.236352	+	0.236352i
$378$		0			0
$379$		−	32.7350i		−	1.68148i	−0.541436	−	0.840742i	$-0.682119\pi$
$379$		−	32.7350i		−	1.68148i	0.541436	−	0.840742i	$-0.317881\pi$
$380$	−1.48356	−	1.67303i	−0.0761052	−	0.0858248i
$381$		0			0
$382$	1.55378	−	5.79878i	0.0794982	−	0.296691i
$383$	27.0266	−	7.24175i	1.38099	−	0.370036i	0.509512	−	0.860463i	$-0.329826\pi$
$383$	27.0266	−	7.24175i	1.38099	−	0.370036i	0.871482	+	0.490427i	$0.163159\pi$
$384$		0			0
$385$	29.7447	−	5.81611i	1.51593	−	0.296416i
$386$			17.6635i			0.899050i
$387$		0			0
$388$	−4.43275	−	1.18775i	−0.225039	−	0.0602990i
$389$	17.3170	+	29.9940i	0.878009	+	1.52076i	0.853523	+	0.521056i	$0.174462\pi$
$389$	17.3170	+	29.9940i	0.878009	+	1.52076i	0.0244863	+	0.999700i	$0.492205\pi$
$390$		0			0
$391$	59.7350			3.02093
$392$	−6.79215	+	1.69313i	−0.343055	+	0.0855160i
$393$		0			0
$394$	−13.4147	−	7.74500i	−0.675824	−	0.390187i
$395$	−6.83415	−	33.3968i	−0.343863	−	1.68037i
$396$		0			0
$397$	−31.0566	+	8.32159i	−1.55869	+	0.417648i	−0.932247	−	0.361823i	$-0.882155\pi$
$397$	−31.0566	+	8.32159i	−1.55869	+	0.417648i	−0.626438	+	0.779471i	$0.715488\pi$
$398$	−6.53720	−	6.53720i	−0.327680	−	0.327680i
$399$		0			0
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$	9.63568	+	5.56316i	0.481183	+	0.277811i	0.720909	−	0.693029i	$-0.243724\pi$
$401$	9.63568	+	5.56316i	0.481183	+	0.277811i	−0.239727	+	0.970840i	$0.577058\pi$
$402$		0			0
$403$	−8.86550	−	2.37550i	−0.441622	−	0.118332i
$404$	7.95141	−	13.7723i	0.395598	−	0.685195i
$405$		0			0
$406$	5.24500	+	5.33760i	0.260305	+	0.264901i
$407$	7.05692	−	7.05692i	0.349799	−	0.349799i
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$	−14.8375	−	9.79655i	−0.732774	−	0.483817i
$411$		0			0
$412$	8.24500	+	8.24500i	0.406202	+	0.406202i
$413$	13.6853	+	8.06172i	0.673412	+	0.396691i
$414$		0			0
$415$	0.434747	−	7.24300i	0.0213409	−	0.355545i
$416$	1.98715	−	1.14728i	0.0974279	−	0.0562500i
$417$		0			0
$418$	−1.32593	−	4.94843i	−0.0648532	−	0.242035i
$419$	−31.9930			−1.56296			−0.781481	−	0.623929i	$-0.785536\pi$
$419$	−31.9930			−1.56296			−0.781481	+	0.623929i	$0.785536\pi$
$420$		0			0
$421$	17.2450			0.840470			0.420235	−	0.907415i	$-0.361948\pi$
$421$	17.2450			0.840470			0.420235	+	0.907415i	$0.361948\pi$
$422$	−4.07769	−	15.2182i	−0.198499	−	0.740809i
$423$		0			0
$424$	8.87243	−	5.12250i	0.430883	−	0.248771i
$425$	−13.4938	+	33.6180i	−0.654546	+	1.63071i
$426$		0			0
$427$	0.214031	−	24.4590i	0.0103577	−	1.18366i
$428$	−3.70877	−	3.70877i	−0.179270	−	0.179270i
$429$		0			0
$430$	−1.90192	−	9.29423i	−0.0917189	−	0.448208i
$431$	−5.19904	+	3.00167i	−0.250429	+	0.144585i	−0.619961	−	0.784633i	$-0.712851\pi$
$431$	−5.19904	+	3.00167i	−0.250429	+	0.144585i	0.369532	+	0.929218i	$0.379518\pi$
$432$		0			0
$433$	−6.75500	+	6.75500i	−0.324625	+	0.324625i	−0.850538	−	0.525913i	$-0.823724\pi$
$433$	−6.75500	+	6.75500i	−0.324625	+	0.324625i	0.525913	+	0.850538i	$0.323724\pi$
$434$	−2.82843	+	10.1980i	−0.135769	+	0.489522i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	−7.96406	−	2.13396i	−0.380972	−	0.102081i
$438$		0			0
$439$	−17.3205	−	10.0000i	−0.826663	−	0.477274i	0.0260459	−	0.999661i	$-0.491708\pi$
$439$	−17.3205	−	10.0000i	−0.826663	−	0.477274i	−0.852709	+	0.522387i	$0.825042\pi$
$440$	5.12299	+	10.2460i	0.244229	+	0.488458i
$441$		0			0
$442$	11.7550	+	11.7550i	0.559128	+	0.559128i
$443$	−2.18783	+	0.586227i	−0.103947	+	0.0278525i	−0.310418	−	0.950600i	$-0.600469\pi$
$443$	−2.18783	+	0.586227i	−0.103947	+	0.0278525i	0.206471	+	0.978453i	$0.433802\pi$
$444$		0			0
$445$	−21.6865	+	4.43782i	−1.02804	+	0.210373i
$446$	−22.3455	−	12.9012i	−1.05809	−	0.610888i
$447$		0			0
$448$	−1.30278	−	2.30278i	−0.0615504	−	0.108796i
$449$	16.7832			0.792047			0.396024	−	0.918240i	$-0.370390\pi$
$449$	16.7832			0.792047			0.396024	+	0.918240i	$0.370390\pi$
$450$		0			0
$451$	−20.3675	−	35.2775i	−0.959068	−	1.66115i
$452$	−13.9963	−	3.75029i	−0.658329	−	0.176399i
$453$		0			0
$454$		−	7.24500i		−	0.340025i
$455$	12.1943	−	5.96436i	0.571679	−	0.279614i
$456$		0			0
$457$	0.669347	−	0.179351i	0.0313107	−	0.00838969i	−0.243130	−	0.969994i	$-0.578174\pi$
$457$	0.669347	−	0.179351i	0.0313107	−	0.00838969i	0.274440	+	0.961604i	$0.411507\pi$
$458$	−0.839867	+	3.13443i	−0.0392444	+	0.146462i
$459$		0			0
$460$	18.4033	+	1.10462i	0.858056	+	0.0515032i
$461$			24.3881i			1.13587i	0.823074	+	0.567934i	$0.192257\pi$
$461$			24.3881i			1.13587i	−0.823074	+	0.567934i	$0.807743\pi$
$462$		0			0
$463$	−5.86750	+	5.86750i	−0.272686	+	0.272686i	−0.830180	−	0.557495i	$-0.811763\pi$
$463$	−5.86750	+	5.86750i	−0.272686	+	0.272686i	0.557495	+	0.830180i	$0.311763\pi$
$464$	−1.41421	+	2.44949i	−0.0656532	+	0.113715i
$465$		0			0
$466$	−13.6225	−	23.5949i	−0.631050	−	1.09301i
$467$	1.35751	+	5.06628i	0.0628179	+	0.234439i	0.990196	−	0.139686i	$-0.0446095\pi$
$467$	1.35751	+	5.06628i	0.0628179	+	0.234439i	−0.927378	+	0.374126i	$0.877943\pi$
$468$		0			0
$469$	−6.55725	−	25.3575i	−0.302786	−	1.17090i
$470$	−19.0919	−	6.36396i	−0.880643	−	0.293548i
$471$		0			0
$472$	−1.55378	+	5.79878i	−0.0715184	+	0.266910i
$473$	5.62543	−	20.9944i	0.258658	−	0.965323i
$474$		0			0
$475$	3.00000	−	4.00000i	0.137649	−	0.183533i
$476$	13.6722	−	13.4350i	0.626666	−	0.615794i
$477$		0			0
$478$	−0.0896755	−	0.334673i	−0.00410166	−	0.0153076i
$479$	8.12465	+	14.0723i	0.371225	+	0.642980i	0.989754	−	0.142781i	$-0.0456045\pi$
$479$	8.12465	+	14.0723i	0.371225	+	0.642980i	−0.618529	+	0.785762i	$0.712271\pi$
$480$		0			0
$481$	2.23499	−	3.87112i	0.101907	−	0.176508i
$482$	−1.58745	+	1.58745i	−0.0723065	+	0.0723065i
$483$		0			0
$484$			15.2450i			0.692954i
$485$	0.614826	−	10.2431i	0.0279178	−	0.465117i
$486$		0			0
$487$	3.47358	−	12.9636i	0.157403	−	0.587436i	−0.841485	−	0.540281i	$-0.818318\pi$
$487$	3.47358	−	12.9636i	0.157403	−	0.587436i	0.998888	−	0.0471547i	$-0.0150154\pi$
$488$	8.92998	−	2.39278i	0.404241	−	0.108316i
$489$		0			0
$490$	−6.75393	−	14.1204i	−0.305111	−	0.637893i
$491$			15.1816i			0.685135i	0.939493	+	0.342567i	$0.111297\pi$
$491$			15.1816i			0.685135i	−0.939493	+	0.342567i	$0.888703\pi$
$492$		0			0
$493$	−19.7937	−	5.30371i	−0.891464	−	0.238867i
$494$	−1.14728	−	1.98715i	−0.0516186	−	0.0894060i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	9.66340	+	17.0809i	0.433463	+	0.766185i
$498$		0			0
$499$	−7.35255	−	4.24500i	−0.329145	−	0.190032i	0.326316	−	0.945261i	$-0.394193\pi$
$499$	−7.35255	−	4.24500i	−0.329145	−	0.190032i	−0.655462	+	0.755228i	$0.727526\pi$
$500$	−4.77886	+	10.1075i	−0.213717	+	0.452023i
$501$		0			0
$502$	6.64912	−	1.78163i	0.296765	−	0.0795179i
$503$	−4.93560	−	4.93560i	−0.220068	−	0.220068i	0.588459	−	0.808527i	$-0.299735\pi$
$503$	−4.93560	−	4.93560i	−0.220068	−	0.220068i	−0.808527	+	0.588459i	$0.799735\pi$
$504$		0			0
$505$	33.7350	+	11.2450i	1.50119	+	0.500396i
$506$	36.5801	+	21.1195i	1.62618	+	0.938877i
$507$		0			0
$508$	11.4439	+	3.06638i	0.507740	+	0.136049i
$509$	16.7832	−	29.0693i	0.743901	−	1.28847i	−0.206805	−	0.978382i	$-0.566307\pi$
$509$	16.7832	−	29.0693i	0.743901	−	1.28847i	0.950706	−	0.310092i	$-0.100360\pi$
$510$		0			0
$511$	−8.13250	+	2.10300i	−0.359761	+	0.0930313i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−1.07820	+	0.622499i	−0.0475574	+	0.0274573i
$515$	−14.3659	+	21.7582i	−0.633039	+	0.958781i
$516$		0			0
$517$	−32.6025	−	32.6025i	−1.43386	−	1.43386i
$518$	−4.44089	−	2.61603i	−0.195122	−	0.114942i
$519$		0			0
$520$	3.40413	+	3.83887i	0.149281	+	0.168346i
$521$	−35.9554	+	20.7589i	−1.57524	+	0.909463i	−0.579726	+	0.814812i	$0.696840\pi$
$521$	−35.9554	+	20.7589i	−1.57524	+	0.909463i	−0.995510	+	0.0946516i	$0.969826\pi$
$522$		0			0
$523$	−4.30263	−	16.0576i	−0.188141	−	0.702151i	−0.993936	−	0.109957i	$-0.964929\pi$
$523$	−4.30263	−	16.0576i	−0.188141	−	0.702151i	0.805795	−	0.592194i	$-0.201738\pi$
$524$	9.36563			0.409139
$525$		0			0
$526$	2.49000			0.108569
$527$	−7.50057	−	27.9925i	−0.326730	−	1.21937i
$528$		0			0
$529$	38.9538	−	22.4900i	1.69364	−	0.977826i
$530$	15.1991	+	17.1402i	0.660207	+	0.744523i
$531$		0			0
$532$	−2.30278	+	1.30278i	−0.0998380	+	0.0564825i
$533$	−12.9012	−	12.9012i	−0.558811	−	0.558811i
$534$		0			0
$535$	6.46210	−	9.78730i	0.279381	−	0.423142i
$536$	8.57321	−	4.94975i	0.370306	−	0.213797i
$537$		0			0
$538$	7.00000	−	7.00000i	0.301791	−	0.301791i
$539$	0.627561	−	35.8554i	0.0270310	−	1.54440i
$540$		0			0
$541$	−9.62250	+	16.6667i	−0.413704	+	0.716556i	−0.995291	−	0.0969280i	$-0.969098\pi$
$541$	−9.62250	+	16.6667i	−0.413704	+	0.716556i	0.581588	+	0.813484i	$0.302432\pi$
$542$	17.8600	+	4.78556i	0.767151	+	0.205558i
$543$		0			0
$544$	6.27435	+	3.62250i	0.269011	+	0.155313i
$545$	8.48528	+	2.82843i	0.363470	+	0.121157i
$546$		0			0
$547$	−6.24500	−	6.24500i	−0.267017	−	0.267017i	0.560880	−	0.827897i	$-0.310463\pi$
$547$	−6.24500	−	6.24500i	−0.267017	−	0.267017i	−0.827897	+	0.560880i	$0.810463\pi$
$548$	−8.45668	+	2.26596i	−0.361252	+	0.0967971i
$549$		0			0
$550$	−20.1490	+	15.8159i	−0.859156	+	0.674393i
$551$	2.44949	+	1.41421i	0.104352	+	0.0602475i
$552$		0			0
$553$	−40.3329	−	0.352937i	−1.71513	−	0.0150084i
$554$	−21.9062			−0.930704
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	−29.2144	−	7.82798i	−1.23785	−	0.331682i	−0.420222	−	0.907422i	$-0.638048\pi$
$557$	−29.2144	−	7.82798i	−1.23785	−	0.331682i	−0.817633	+	0.575739i	$0.804714\pi$
$558$		0			0
$559$		−	9.73499i		−	0.411746i
$560$	4.46060	−	3.88626i	0.188495	−	0.164224i
$561$		0			0
$562$	−10.4125	+	2.79003i	−0.439226	+	0.117690i
$563$	−1.67973	+	6.26885i	−0.0707924	+	0.264201i	−0.992246	−	0.124287i	$-0.960336\pi$
$563$	−1.67973	+	6.26885i	−0.0707924	+	0.264201i	0.921454	+	0.388488i	$0.127002\pi$
$564$		0			0
$565$	1.94129	−	32.3424i	0.0816707	−	1.36066i
$566$			14.1421i			0.594438i
$567$		0			0
$568$	−5.24500	+	5.24500i	−0.220075	+	0.220075i
$569$	1.50791	−	2.61177i	0.0632148	−	0.109491i	−0.832686	−	0.553746i	$-0.813198\pi$
$569$	1.50791	−	2.61177i	0.0632148	−	0.109491i	0.895901	+	0.444254i	$0.146531\pi$
$570$		0			0
$571$	2.49000	+	4.31280i	0.104203	+	0.180485i	0.913412	−	0.407035i	$-0.133437\pi$
$571$	2.49000	+	4.31280i	0.104203	+	0.180485i	−0.809209	+	0.587521i	$0.800104\pi$
$572$	3.04242	+	11.3545i	0.127210	+	0.474754i
$573$		0			0
$574$	−15.0053	+	14.7450i	−0.626310	+	0.615444i
$575$	5.83009	+	40.8107i	0.243132	+	1.70192i
$576$		0			0
$577$	0.545376	−	2.03537i	0.0227043	−	0.0847337i	−0.953644	−	0.300937i	$-0.902701\pi$
$577$	0.545376	−	2.03537i	0.0227043	−	0.0847337i	0.976348	+	0.216203i	$0.0693673\pi$
$578$	−9.18549	+	34.2807i	−0.382066	+	1.42589i
$579$		0			0
$580$	−6.00000	−	2.00000i	−0.249136	−	0.0830455i
$581$	−8.27315	−	2.29456i	−0.343228	−	0.0951944i
$582$		0			0
$583$	13.5841	+	50.6966i	0.562597	+	2.09964i
$584$	−1.58745	−	2.74955i	−0.0656893	−	0.113777i
$585$		0			0
$586$	−1.74500	+	3.02243i	−0.0720852	+	0.124855i
$587$	4.93560	−	4.93560i	0.203714	−	0.203714i	−0.597875	−	0.801589i	$-0.703988\pi$
$587$	4.93560	−	4.93560i	0.203714	−	0.203714i	0.801589	+	0.597875i	$0.203988\pi$
$588$		0			0
$589$			4.00000i			0.164817i
$590$	−13.3997	−	0.804294i	−0.551659	−	0.0331123i
$591$		0			0
$592$	0.504200	−	1.88170i	0.0207225	−	0.0773374i
$593$	−31.1270	+	8.34044i	−1.27823	+	0.342501i	−0.833179	−	0.553004i	$-0.813481\pi$
$593$	−31.1270	+	8.34044i	−1.27823	+	0.342501i	−0.445052	+	0.895505i	$0.646815\pi$
$594$		0			0
$595$	35.5608	+	23.9286i	1.45785	+	0.980977i
$596$			8.83176i			0.361763i
$597$		0			0
$598$	18.2740	+	4.89651i	0.747280	+	0.200233i
$599$	−22.2668	−	38.5672i	−0.909796	−	1.57581i	−0.814346	−	0.580379i	$-0.802904\pi$
$599$	−22.2668	−	38.5672i	−0.909796	−	1.57581i	−0.0954501	−	0.995434i	$-0.530429\pi$
$600$		0			0
$601$	−10.9800			−0.447883			−0.223942	−	0.974603i	$-0.571892\pi$
$601$	−10.9800			−0.447883			−0.223942	+	0.974603i	$0.571892\pi$
$602$	−11.2245	−	0.0982215i	−0.457478	−	0.00400321i
$603$		0			0
$604$	9.08460	+	5.24500i	0.369647	+	0.213416i
$605$	−33.3968	+	6.83415i	−1.35777	+	0.277848i
$606$		0			0
$607$	14.5106	−	3.88810i	0.588967	−	0.157813i	0.0479861	−	0.998848i	$-0.484720\pi$
$607$	14.5106	−	3.88810i	0.588967	−	0.157813i	0.540981	+	0.841035i	$0.318053\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$		0			0
$610$	9.24500	+	18.4900i	0.374319	+	0.748638i
$611$	−17.8843	−	10.3255i	−0.723522	−	0.417726i
$612$		0			0
$613$	−15.1800	−	4.06746i	−0.613112	−	0.164283i	−0.0611177	−	0.998131i	$-0.519466\pi$
$613$	−15.1800	−	4.06746i	−0.613112	−	0.164283i	−0.551995	+	0.833848i	$0.686133\pi$
$614$	−4.41588	+	7.64853i	−0.178210	+	0.308670i
$615$		0			0
$616$	13.1225	−	3.39338i	0.528721	−	0.136723i
$617$	1.94808	−	1.94808i	0.0784268	−	0.0784268i	−0.666805	−	0.745232i	$-0.732339\pi$
$617$	1.94808	−	1.94808i	0.0784268	−	0.0784268i	0.745232	+	0.666805i	$0.232339\pi$
$618$		0			0
$619$	11.4532	−	6.61249i	0.460342	−	0.265779i	−0.251846	−	0.967767i	$-0.581038\pi$
$619$	11.4532	−	6.61249i	0.460342	−	0.265779i	0.712188	+	0.701989i	$0.247704\pi$
$620$	−1.79315	−	8.76268i	−0.0720147	−	0.351918i
$621$		0			0
$622$	7.49000	+	7.49000i	0.300321	+	0.300321i
$623$	−0.229183	+	26.1906i	−0.00918204	+	1.04930i
$624$		0			0
$625$	−24.2846	−	5.93782i	−0.971384	−	0.237513i
$626$	−11.6228	+	6.71044i	−0.464541	+	0.268203i
$627$		0			0
$628$	−0.504200	−	1.88170i	−0.0201198	−	0.0750881i
$629$	14.1138			0.562756
$630$		0			0
$631$	−14.9800			−0.596344			−0.298172	−	0.954512i	$-0.596377\pi$
$631$	−14.9800			−0.596344			−0.298172	+	0.954512i	$0.596377\pi$
$632$	−3.94570	−	14.7255i	−0.156951	−	0.585750i
$633$		0			0
$634$	10.3923	−	6.00000i	0.412731	−	0.238290i
$635$	−1.58727	+	26.4444i	−0.0629891	+	1.04941i
$636$		0			0
$637$	−3.88499	−	15.5850i	−0.153929	−	0.617500i
$638$	−10.2460	−	10.2460i	−0.405642	−	0.405642i
$639$		0			0
$640$	1.86603	+	1.23205i	0.0737611	+	0.0487011i
$641$	13.6345	−	7.87187i	0.538529	−	0.310920i	−0.205953	−	0.978562i	$-0.566030\pi$
$641$	13.6345	−	7.87187i	0.538529	−	0.310920i	0.744483	+	0.667642i	$0.232696\pi$
$642$		0			0
$643$	−27.7350	+	27.7350i	−1.09376	+	1.09376i	−0.0986380	+	0.995123i	$0.531449\pi$
$643$	−27.7350	+	27.7350i	−1.09376	+	1.09376i	−0.995123	+	0.0986380i	$0.968551\pi$
$644$	5.83009	−	21.0207i	0.229738	−	0.828332i
$645$		0			0
$646$	3.62250	−	6.27435i	0.142525	−	0.246861i
$647$	34.2807	+	9.18549i	1.34771	+	0.361119i	0.859290	−	0.511488i	$-0.170906\pi$
$647$	34.2807	+	9.18549i	1.34771	+	0.361119i	0.488423	+	0.872607i	$0.337572\pi$
$648$		0			0
$649$	−26.6346	−	15.3775i	−1.04550	−	0.603620i
$650$	−6.88368	+	9.17824i	−0.270000	+	0.360000i
$651$		0			0
$652$	7.24500	+	7.24500i	0.283736	+	0.283736i
$653$	−26.5533	+	7.11493i	−1.03911	+	0.278429i	−0.737745	−	0.675080i	$-0.764109\pi$
$653$	−26.5533	+	7.11493i	−1.03911	+	0.278429i	−0.301366	+	0.953509i	$0.597443\pi$
$654$		0			0
$655$	4.19850	+	20.5170i	0.164049	+	0.801666i
$656$	−6.88613	−	3.97571i	−0.268858	−	0.155225i
$657$		0			0
$658$	−12.0859	+	20.5166i	−0.471156	+	0.799821i
$659$	32.5269			1.26707			0.633534	−	0.773715i	$-0.281604\pi$
$659$	32.5269			1.26707			0.633534	+	0.773715i	$0.281604\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−6.76148	−	1.81173i	−0.262792	−	0.0704150i
$663$		0			0
$664$		−	3.24500i		−	0.125930i
$665$	−3.88626	−	4.46060i	−0.150703	−	0.172975i
$666$		0			0
$667$	−22.5258	+	6.03576i	−0.872201	+	0.233705i
$668$	0.581048	−	2.16850i	0.0224814	−	0.0839018i
$669$		0			0
$670$	14.6865	+	16.5622i	0.567390	+	0.639853i
$671$			47.3620i			1.82839i
$672$		0			0
$673$	18.7550	−	18.7550i	0.722952	−	0.722952i	−0.246253	−	0.969206i	$-0.579200\pi$
$673$	18.7550	−	18.7550i	0.722952	−	0.722952i	0.969206	+	0.246253i	$0.0791995\pi$
$674$	4.41588	−	7.64853i	0.170093	−	0.294610i
$675$		0			0
$676$	−3.86750	−	6.69870i	−0.148750	−	0.257642i
$677$	−9.82995	−	36.6859i	−0.377795	−	1.40995i	−0.849217	−	0.528044i	$-0.822926\pi$
$677$	−9.82995	−	36.6859i	−0.377795	−	1.40995i	0.471422	−	0.881908i	$-0.343741\pi$
$678$		0			0
$679$	−11.7000	−	3.24500i	−0.449005	−	0.124532i
$680$	−5.12299	+	15.3690i	−0.196458	+	0.589373i
$681$		0			0
$682$	5.30371	−	19.7937i	0.203089	−	0.757940i
$683$	−9.57113	+	35.7199i	−0.366229	+	1.36679i	0.499518	+	0.866303i	$0.333510\pi$
$683$	−9.57113	+	35.7199i	−0.366229	+	1.36679i	−0.865747	+	0.500482i	$0.833156\pi$
$684$		0			0
$685$	−8.75500	−	17.5100i	−0.334511	−	0.669023i
$686$	−18.0089	+	4.32219i	−0.687581	+	0.165022i
$687$		0			0
$688$	−1.09808	−	4.09808i	−0.0418638	−	0.156238i
$689$	11.7539	+	20.3583i	0.447787	+	0.775590i
$690$		0			0
$691$	−12.4900	+	21.6333i	−0.475142	+	0.822970i	−0.999595	−	0.0284697i	$-0.990937\pi$
$691$	−12.4900	+	21.6333i	−0.475142	+	0.822970i	0.524453	+	0.851440i	$0.324270\pi$
$692$	−14.3154	+	14.3154i	−0.544189	+	0.544189i
$693$		0			0
$694$			1.24500i			0.0472595i
$695$	13.3843	−	11.8685i	0.507694	−	0.450198i
$696$		0			0
$697$	14.9100	−	55.6450i	0.564758	−	2.10771i
$698$	−33.3148	+	8.92667i	−1.26098	+	0.337879i
$699$		0			0
$700$	10.5131	+	8.02955i	0.397360	+	0.303489i
$701$		−	49.4692i		−	1.86843i	−0.356717	−	0.934213i	$-0.616104\pi$
$701$		−	49.4692i		−	1.86843i	0.356717	−	0.934213i	$-0.383896\pi$
$702$		0			0
$703$	−1.88170	−	0.504200i	−0.0709697	−	0.0190163i
$704$	2.56149	+	4.43664i	0.0965399	+	0.167212i
$705$		0			0
$706$	18.4900			0.695880
$707$	21.3555	−	36.2525i	0.803156	−	1.36341i
$708$		0			0
$709$	−25.5218	−	14.7350i	−0.958490	−	0.553384i	−0.0627819	−	0.998027i	$-0.519997\pi$
$709$	−25.5218	−	14.7350i	−0.958490	−	0.553384i	−0.895708	+	0.444643i	$0.853331\pi$
$710$	−13.8413	−	9.13880i	−0.519456	−	0.342973i
$711$		0			0
$712$	−9.56218	+	2.56218i	−0.358358	+	0.0960217i
$713$	−23.3204	−	23.3204i	−0.873355	−	0.873355i
$714$		0			0
$715$	−23.5100	+	11.7550i	−0.879224	+	0.439612i
$716$	−6.58607	−	3.80247i	−0.246133	−	0.142105i
$717$		0			0
$718$	−10.9282	−	2.92820i	−0.407837	−	0.109280i
$719$	−15.5563	+	26.9444i	−0.580154	+	1.00486i	0.415307	+	0.909681i	$0.363674\pi$
$719$	−15.5563	+	26.9444i	−0.580154	+	1.00486i	−0.995461	+	0.0951746i	$0.969659\pi$
$720$		0			0
$721$	21.6225	+	22.0043i	0.805264	+	0.819481i
$722$	12.7279	−	12.7279i	0.473684	−	0.473684i
$723$		0			0
$724$	1.07820	−	0.622499i	0.0400710	−	0.0231350i
$725$	1.69161	−	14.0406i	0.0628250	−	0.521455i
$726$		0			0
$727$	−16.6225	−	16.6225i	−0.616494	−	0.616494i	0.328136	−	0.944630i	$-0.393580\pi$
$727$	−16.6225	−	16.6225i	−0.616494	−	0.616494i	−0.944630	+	0.328136i	$0.893580\pi$
$728$	5.28386	−	2.98930i	0.195833	−	0.110791i
$729$		0			0
$730$	5.31172	−	4.71018i	0.196596	−	0.174331i
$731$	26.6198	−	15.3690i	0.984570	−	0.568442i
$732$		0			0
$733$	8.73611	+	32.6036i	0.322676	+	1.20424i	0.916628	+	0.399741i	$0.130900\pi$
$733$	8.73611	+	32.6036i	0.322676	+	1.20424i	−0.593952	+	0.804500i	$0.702433\pi$
$734$	−25.2685			−0.932676
$735$		0			0
$736$	8.24500			0.303915
$737$	13.1260	+	48.9869i	0.483503	+	1.80446i
$738$		0			0
$739$	25.9634	−	14.9900i	0.955080	−	0.551416i	0.0604250	−	0.998173i	$-0.480754\pi$
$739$	25.9634	−	14.9900i	0.955080	−	0.551416i	0.894655	+	0.446757i	$0.147421\pi$
$740$	4.34821	+	0.260993i	0.159844	+	0.00959430i
$741$		0			0
$742$	23.5919	−	13.3469i	0.866087	−	0.489981i
$743$	−5.29623	−	5.29623i	−0.194300	−	0.194300i	0.603251	−	0.797551i	$-0.293872\pi$
$743$	−5.29623	−	5.29623i	−0.194300	−	0.194300i	−0.797551	+	0.603251i	$0.793872\pi$
$744$		0			0
$745$	−19.3475	+	3.95917i	−0.708837	+	0.145053i
$746$	−5.19904	+	3.00167i	−0.190350	+	0.109899i
$747$		0			0
$748$	−26.2450	+	26.2450i	−0.959612	+	0.959612i
$749$	−9.72626	−	9.89798i	−0.355390	−	0.361664i
$750$		0			0
$751$	25.8675	−	44.8038i	0.943918	−	1.63491i	0.186016	−	0.982547i	$-0.440442\pi$
$751$	25.8675	−	44.8038i	0.943918	−	1.63491i	0.757903	−	0.652368i	$-0.226224\pi$
$752$	−8.69333	−	2.32937i	−0.317013	−	0.0849434i
$753$		0			0
$754$	−5.62050	−	3.24500i	−0.204687	−	0.118176i
$755$	−7.41755	+	22.2526i	−0.269952	+	0.809857i
$756$		0			0
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	0.851487	−	0.524376i	$-0.175701\pi$
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	−0.524376	+	0.851487i	$0.675701\pi$
$758$	31.6196	−	8.47244i	1.14847	−	0.307733i
$759$		0			0
$760$	1.23205	−	1.86603i	0.0446912	−	0.0676879i
$761$	37.1802	+	21.4660i	1.34778	+	0.778141i	0.987935	−	0.154870i	$-0.0494960\pi$
$761$	37.1802	+	21.4660i	1.34778	+	0.778141i	0.359846	+	0.933012i	$0.382829\pi$
$762$		0			0
$763$	5.37150	−	9.11850i	0.194461	−	0.330112i
$764$	6.00333			0.217193
$765$		0			0
$766$	13.9900	+	24.2314i	0.505479	+	0.875515i
$767$	−13.3056	−	3.56523i	−0.480439	−	0.128733i
$768$		0			0
$769$			14.7350i			0.531357i	0.964062	+	0.265679i	$0.0855960\pi$
$769$			14.7350i			0.531357i	−0.964062	+	0.265679i	$0.914404\pi$
$770$	13.3164	+	27.2259i	0.479891	+	0.981152i
$771$		0			0
$772$	−17.0617	+	4.57166i	−0.614062	+	0.164537i
$773$	4.13593	−	15.4355i	0.148759	−	0.555176i	−0.850800	−	0.525489i	$-0.823882\pi$
$773$	4.13593	−	15.4355i	0.148759	−	0.555176i	0.999559	−	0.0296868i	$-0.00945098\pi$
$774$		0			0
$775$	18.3923	−	7.85641i	0.660671	−	0.282210i
$776$		−	4.58912i		−	0.164740i
$777$		0			0
$778$	−24.4900	+	24.4900i	−0.878009	+	0.878009i
$779$	−3.97571	+	6.88613i	−0.142444	+	0.246721i
$780$		0			0
$781$	−19.0000	−	32.9090i	−0.679873	−	1.17758i
$782$	15.4606	+	57.6996i	0.552868	+	2.06333i
$783$		0			0
$784$	−3.39338	−	6.12250i	−0.121192	−	0.218661i
$785$	3.89616	−	1.94808i	0.139060	−	0.0695300i
$786$		0			0
$787$	−12.9006	+	48.1456i	−0.459855	+	1.71620i	0.213551	+	0.976932i	$0.431497\pi$
$787$	−12.9006	+	48.1456i	−0.459855	+	1.71620i	−0.673407	+	0.739272i	$0.735170\pi$
$788$	4.00911	−	14.9622i	0.142818	−	0.533006i
$789$		0			0
$790$	30.4900	−	15.2450i	1.08479	−	0.542393i
$791$	−36.9424	−	10.2460i	−1.31352	−	0.364305i
$792$		0			0
$793$	5.49038	+	20.4904i	0.194969	+	0.727635i
$794$	−16.0761	−	27.8446i	−0.570518	−	0.988167i
$795$		0			0
$796$	4.62250	−	8.00640i	0.163840	−	0.283779i
$797$	21.9062	−	21.9062i	0.775956	−	0.775956i	−0.203184	−	0.979140i	$-0.565129\pi$
$797$	21.9062	−	21.9062i	0.775956	−	0.775956i	0.979140	+	0.203184i	$0.0651291\pi$
$798$		0			0
$799$		−	65.2050i		−	2.30679i
$800$	−1.86250	+	4.64016i	−0.0658494	+	0.164054i
$801$		0			0
$802$	−2.87970	+	10.7472i	−0.101686	+	0.379497i
$803$	15.7108	−	4.20969i	0.554422	−	0.148557i
$804$		0			0
$805$	48.6630	+	3.34849i	1.71515	+	0.118019i
$806$		−	9.17824i		−	0.323290i
$807$		0			0
$808$	15.3610	+	4.11595i	0.540396	+	0.144799i
$809$	−21.9999	−	38.1049i	−0.773474	−	1.33970i	−0.935648	−	0.352934i	$-0.885184\pi$
$809$	−21.9999	−	38.1049i	−0.773474	−	1.33970i	0.162175	−	0.986762i	$-0.448149\pi$
$810$		0			0
$811$	45.2250			1.58806			0.794032	−	0.607876i	$-0.207978\pi$
$811$	45.2250			1.58806			0.794032	+	0.607876i	$0.207978\pi$
$812$	−3.79822	+	6.44775i	−0.133291	+	0.226272i
$813$		0			0
$814$	8.64293	+	4.99000i	0.302934	+	0.174899i
$815$	−12.6236	+	19.1192i	−0.442184	+	0.669718i
$816$		0			0
$817$	−4.09808	+	1.09808i	−0.143374	+	0.0384168i
$818$		0			0
$819$		0			0
$820$	5.62250	−	16.8675i	0.196346	−	0.589039i
$821$	31.5188	+	18.1974i	1.10001	+	0.635093i	0.936225	−	0.351402i	$-0.114295\pi$
$821$	31.5188	+	18.1974i	1.10001	+	0.635093i	0.163789	+	0.986495i	$0.447628\pi$
$822$		0			0
$823$	42.3468	+	11.3468i	1.47612	+	0.395524i	0.905024	−	0.425361i	$-0.139853\pi$
$823$	42.3468	+	11.3468i	1.47612	+	0.395524i	0.571093	+	0.820886i	$0.306520\pi$
$824$	−5.83009	+	10.0980i	−0.203101	+	0.351781i
$825$		0			0
$826$	−4.24500	+	15.3056i	−0.147702	+	0.532548i
$827$	25.4558	−	25.4558i	0.885186	−	0.885186i	−0.108870	−	0.994056i	$-0.534723\pi$
$827$	25.4558	−	25.4558i	0.885186	−	0.885186i	0.994056	+	0.108870i	$0.0347231\pi$
$828$		0			0
$829$	−43.0718	+	24.8675i	−1.49594	+	0.863684i	−0.999989	−	0.00466423i	$-0.998515\pi$
$829$	−43.0718	+	24.8675i	−1.49594	+	0.863684i	−0.495955	+	0.868348i	$0.665182\pi$
$830$	7.10872	−	1.45469i	0.246747	−	0.0504931i
$831$		0			0
$832$	1.62250	+	1.62250i	0.0562500	+	0.0562500i
$833$	36.4830	−	35.2279i	1.26406	−	1.22057i
$834$		0			0
$835$	5.01095	+	0.300773i	0.173411	+	0.0104087i
$836$	4.43664	−	2.56149i	0.153444	−	0.0885911i
$837$		0			0
$838$	−8.28041	−	30.9029i	−0.286042	−	1.06752i
$839$	−18.3848			−0.634713			−0.317356	−	0.948306i	$-0.602795\pi$
$839$	−18.3848			−0.634713			−0.317356	+	0.948306i	$0.602795\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	4.46333	+	16.6574i	0.153817	+	0.574052i
$843$		0			0
$844$	13.6442	−	7.87750i	0.469654	−	0.271155i
$845$	12.9409	−	11.4754i	0.445180	−	0.394764i
$846$		0			0
$847$	−0.352937	+	40.3329i	−0.0121271	+	1.38586i
$848$	7.24431	+	7.24431i	0.248771	+	0.248771i
$849$		0			0
$850$	−35.9649	−	4.33306i	−1.23359	−	0.148623i
$851$	13.9100	−	8.03096i	0.476830	−	0.275298i
$852$		0			0
$853$	−12.1325	+	12.1325i	−0.415409	+	0.415409i	−0.883618	−	0.468209i	$-0.844899\pi$
$853$	−12.1325	+	12.1325i	−0.415409	+	0.415409i	0.468209	+	0.883618i	$0.344899\pi$
$854$	23.6810	−	6.12372i	0.810347	−	0.209550i
$855$		0			0
$856$	2.62250	−	4.54230i	0.0896352	−	0.155253i
$857$	14.7255	+	3.94570i	0.503015	+	0.134782i	0.501399	−	0.865216i	$-0.332819\pi$
$857$	14.7255	+	3.94570i	0.503015	+	0.134782i	0.00161596	+	0.999999i	$0.499486\pi$
$858$		0			0
$859$	−2.15640	−	1.24500i	−0.0735754	−	0.0424788i	0.462761	−	0.886483i	$-0.346859\pi$
$859$	−2.15640	−	1.24500i	−0.0735754	−	0.0424788i	−0.536336	+	0.844004i	$0.680192\pi$
$860$	8.48528	−	4.24264i	0.289346	−	0.144673i
$861$		0			0
$862$	−4.24500	−	4.24500i	−0.144585	−	0.144585i
$863$	−33.5514	+	8.99008i	−1.14210	+	0.306026i	−0.779797	−	0.626033i	$-0.784678\pi$
$863$	−33.5514	+	8.99008i	−1.14210	+	0.306026i	−0.362307	+	0.932059i	$0.618011\pi$
$864$		0			0
$865$	−37.7777	−	24.9429i	−1.28448	−	0.848083i
$866$	−8.27315	−	4.77651i	−0.281133	−	0.162312i
$867$		0			0
$868$	−10.5826	−	0.0926041i	−0.359197	−	0.00314319i
$869$	78.0999			2.64936
$870$		0			0
$871$	11.3575	+	19.6718i	0.384834	+	0.666552i
$872$	3.86370	+	1.03528i	0.130842	+	0.0350589i
$873$		0			0
$874$		−	8.24500i		−	0.278891i
$875$	−12.8772	+	26.6304i	−0.435329	+	0.900272i
$876$		0			0
$877$	−2.21637	+	0.593876i	−0.0748417	+	0.0200538i	−0.296046	−	0.955174i	$-0.595668\pi$
$877$	−2.21637	+	0.593876i	−0.0748417	+	0.0200538i	0.221204	+	0.975228i	$0.429001\pi$
$878$	5.17638	−	19.3185i	0.174694	−	0.651968i
$879$		0			0
$880$	−8.57092	+	7.60028i	−0.288926	+	0.256205i
$881$			10.0586i			0.338882i	0.985540	+	0.169441i	$0.0541963\pi$
$881$			10.0586i			0.338882i	−0.985540	+	0.169441i	$0.945804\pi$
$882$		0			0
$883$	−8.73499	+	8.73499i	−0.293956	+	0.293956i	−0.838641	−	0.544685i	$-0.816649\pi$
$883$	−8.73499	+	8.73499i	−0.293956	+	0.293956i	0.544685	+	0.838641i	$0.316649\pi$
$884$	−8.31204	+	14.3969i	−0.279564	+	0.484219i
$885$		0			0
$886$	−1.13250	−	1.96155i	−0.0380472	−	0.0658997i
$887$	9.44431	+	35.2466i	0.317109	+	1.18347i	0.922010	+	0.387166i	$0.126546\pi$
$887$	9.44431	+	35.2466i	0.317109	+	1.18347i	−0.604901	+	0.796300i	$0.706787\pi$
$888$		0			0
$889$	30.2055	+	8.37750i	1.01306	+	0.280972i
$890$	−9.89949	−	19.7990i	−0.331832	−	0.663664i
$891$		0			0
$892$	6.67813	−	24.9231i	0.223600	−	0.834488i
$893$	−2.32937	+	8.69333i	−0.0779494	+	0.290911i
$894$		0			0
$895$	5.37750	−	16.1325i	0.179750	−	0.539250i
$896$	1.88713	−	1.85439i	0.0630445	−	0.0619507i
$897$		0			0
$898$	4.34381	+	16.2113i	0.144955	+	0.540978i
$899$	5.65685	+	9.79796i	0.188667	+	0.326780i
$900$		0			0
$901$	−37.1125	+	64.2807i	−1.23640	+	2.14150i
$902$	28.8040	−	28.8040i	0.959068	−	0.959068i
$903$		0			0
$904$		−	14.4900i		−	0.481930i
$905$	1.84703	+	2.08292i	0.0613975	+	0.0692387i
$906$		0			0
$907$	−8.59794	+	32.0879i	−0.285490	+	1.06546i	0.662991	+	0.748627i	$0.269287\pi$
$907$	−8.59794	+	32.0879i	−0.285490	+	1.06546i	−0.948481	+	0.316835i	$0.897380\pi$
$908$	6.99813	−	1.87514i	0.232241	−	0.0622288i
$909$		0			0
$910$	8.91725	+	10.2351i	0.295604	+	0.339291i
$911$		−	49.8440i		−	1.65140i	−0.564107	−	0.825702i	$-0.690779\pi$
$911$		−	49.8440i		−	1.65140i	0.564107	−	0.825702i	$-0.309221\pi$
$912$		0			0
$913$	16.0576	+	4.30263i	0.531430	+	0.142396i
$914$	0.346479	+	0.600120i	0.0114605	+	0.0198502i
$915$		0			0
$916$	−3.24500			−0.107218
$917$	24.7782	+	0.216824i	0.818247	+	0.00716015i
$918$		0			0
$919$	24.6731	+	14.2450i	0.813889	+	0.469899i	0.848305	−	0.529508i	$-0.177624\pi$
$919$	24.6731	+	14.2450i	0.813889	+	0.469899i	−0.0344155	+	0.999408i	$0.510957\pi$
$920$	3.69613	+	18.0621i	0.121858	+	0.595489i
$921$		0			0
$922$	−23.5571	+	6.31211i	−0.775812	+	0.207878i
$923$	−12.0350	−	12.0350i	−0.396136	−	0.396136i
$924$		0			0
$925$	1.37750	+	9.64251i	0.0452920	+	0.317044i
$926$	−7.18619	−	4.14895i	−0.236153	−	0.136343i
$927$		0			0
$928$	−2.73205	−	0.732051i	−0.0896840	−	0.0240307i
$929$	−10.1664	+	17.6088i	−0.333550	+	0.577725i	−0.983205	−	0.182504i	$-0.941580\pi$
$929$	−10.1664	+	17.6088i	−0.333550	+	0.577725i	0.649655	+	0.760229i	$0.274913\pi$
$930$		0			0
$931$	−6.12250	+	3.39338i	−0.200657	+	0.111213i
$932$	19.2651	−	19.2651i	0.631050	−	0.631050i
$933$		0			0
$934$	−4.54230	+	2.62250i	−0.148629	+	0.0858108i
$935$	−69.2595	−	45.7288i	−2.26503	−	1.49549i
$936$		0			0
$937$	−17.0000	−	17.0000i	−0.555366	−	0.555366i	0.372619	−	0.927985i	$-0.378460\pi$
$937$	−17.0000	−	17.0000i	−0.555366	−	0.555366i	−0.927985	+	0.372619i	$0.878460\pi$
$938$	22.7963	−	12.8968i	0.744326	−	0.421096i
$939$		0			0
$940$	1.20577	−	20.0885i	0.0393279	−	0.655213i
$941$	33.6682	−	19.4384i	1.09755	−	0.633673i	0.161976	−	0.986795i	$-0.448213\pi$
$941$	33.6682	−	19.4384i	1.09755	−	0.633673i	0.935577	+	0.353122i	$0.114880\pi$
$942$		0			0
$943$	−16.9680	−	63.3255i	−0.552555	−	2.06216i
$944$	−6.00333			−0.195392
$945$		0			0
$946$	21.7350			0.706666
$947$	−4.59015	−	17.1307i	−0.149160	−	0.556673i	−0.999535	−	0.0304954i	$-0.990292\pi$
$947$	−4.59015	−	17.1307i	−0.149160	−	0.556673i	0.850375	−	0.526177i	$-0.176375\pi$
$948$		0			0
$949$	6.30901	−	3.64251i	0.204799	−	0.118241i
$950$	4.64016	+	1.86250i	0.150547	+	0.0604275i
$951$		0			0
$952$	16.5159	+	9.72912i	0.535283	+	0.315323i
$953$	8.13880	+	8.13880i	0.263642	+	0.263642i	0.826532	−	0.562890i	$-0.190311\pi$
$953$	8.13880	+	8.13880i	0.263642	+	0.263642i	−0.562890	+	0.826532i	$0.690311\pi$
$954$		0			0
$955$	2.69122	+	13.1513i	0.0870859	+	0.425567i
$956$	0.300060	−	0.173240i	0.00970464	−	0.00560297i
$957$		0			0
$958$	−11.4900	+	11.4900i	−0.371225	+	0.371225i
$959$	−22.4259	+	5.79916i	−0.724169	+	0.187265i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	4.31768	+	1.15692i	0.139207	+	0.0373005i
$963$		0			0
$964$	−1.94423	−	1.12250i	−0.0626193	−	0.0361533i
$965$	−17.6635	−	35.3270i	−0.568609	−	1.13722i
$966$		0			0
$967$	10.7350	+	10.7350i	0.345214	+	0.345214i	0.858323	−	0.513109i	$-0.171506\pi$
$967$	10.7350	+	10.7350i	0.345214	+	0.345214i	−0.513109	+	0.858323i	$0.671506\pi$
$968$	−14.7255	+	3.94570i	−0.473297	+	0.126819i
$969$		0			0
$970$	10.0533	−	2.05725i	0.322790	−	0.0660542i
$971$	15.4593	+	8.92545i	0.496114	+	0.286431i	0.727107	−	0.686524i	$-0.240864\pi$
$971$	15.4593	+	8.92545i	0.496114	+	0.286431i	−0.230993	+	0.972955i	$0.574198\pi$
$972$		0			0
$973$	−10.4222	−	18.4222i	−0.334121	−	0.590589i
$974$	13.4209			0.430033
$975$		0			0
$976$	4.62250	+	8.00640i	0.147963	+	0.256279i
$977$	−28.5045	−	7.63775i	−0.911939	−	0.244353i	−0.227803	−	0.973707i	$-0.573154\pi$
$977$	−28.5045	−	7.63775i	−0.911939	−	0.244353i	−0.684136	+	0.729354i	$0.739821\pi$
$978$		0			0
$979$		−	50.7150i		−	1.62086i
$980$	11.8912	−	10.1784i	0.379849	−	0.325137i
$981$		0			0
$982$	−14.6643	+	3.92928i	−0.467956	+	0.125388i
$983$	1.29410	−	4.82963i	0.0412752	−	0.154041i	−0.942213	−	0.335016i	$-0.891258\pi$
$983$	1.29410	−	4.82963i	0.0412752	−	0.154041i	0.983488	+	0.180974i	$0.0579251\pi$
$984$		0			0
$985$	34.5745	+	2.07527i	1.10163	+	0.0661235i
$986$		−	20.4919i		−	0.652597i
$987$		0			0
$988$	1.62250	−	1.62250i	0.0516186	−	0.0516186i
$989$	17.4903	−	30.2941i	0.556159	−	0.963295i
$990$		0			0
$991$	18.1125	+	31.3718i	0.575362	+	0.996557i	0.996002	+	0.0893291i	$0.0284723\pi$
$991$	18.1125	+	31.3718i	0.575362	+	0.996557i	−0.420640	+	0.907228i	$0.638194\pi$
$992$	−1.03528	−	3.86370i	−0.0328701	−	0.122673i
$993$		0			0
$994$	−13.9979	+	13.7550i	−0.443985	+	0.436282i
$995$	19.6116	+	6.53720i	0.621730	+	0.207243i
$996$		0			0
$997$	−6.22243	+	23.2224i	−0.197066	+	0.735462i	0.794656	+	0.607060i	$0.207651\pi$
$997$	−6.22243	+	23.2224i	−0.197066	+	0.735462i	−0.991722	+	0.128402i	$0.959015\pi$
$998$	2.19737	−	8.20071i	0.0695566	−	0.259589i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.a.107.3	yes	16
3.2	odd	2	inner	630.2.ce.a.107.1	yes	16
5.3	odd	4	inner	630.2.ce.a.233.4	yes	16
7.4	even	3	inner	630.2.ce.a.557.2	yes	16
15.8	even	4	inner	630.2.ce.a.233.2	yes	16
21.11	odd	6	inner	630.2.ce.a.557.4	yes	16
35.18	odd	12	inner	630.2.ce.a.53.1	✓	16
105.53	even	12	inner	630.2.ce.a.53.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.a.53.1	✓	16	35.18	odd	12	inner
630.2.ce.a.53.3	yes	16	105.53	even	12	inner
630.2.ce.a.107.1	yes	16	3.2	odd	2	inner
630.2.ce.a.107.3	yes	16	1.1	even	1	trivial
630.2.ce.a.233.2	yes	16	15.8	even	4	inner
630.2.ce.a.233.4	yes	16	5.3	odd	4	inner
630.2.ce.a.557.2	yes	16	7.4	even	3	inner
630.2.ce.a.557.4	yes	16	21.11	odd	6	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.48356 - 1.67303i) q^{5} +(-2.30278 + 1.30278i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-1.48356 - 1.67303i) q^{5} +(-2.30278 + 1.30278i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.23205 - 1.86603i) q^{10} +(4.43664 - 2.56149i) q^{11} +(1.62250 - 1.62250i) q^{13} +(-1.85439 - 1.88713i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.99813 + 1.87514i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(2.12132 + 0.707107i) q^{20} +(3.62250 + 3.62250i) q^{22} +(7.96406 - 2.13396i) q^{23} +(-0.598076 + 4.96410i) q^{25} +(1.98715 + 1.14728i) q^{26} +(1.34287 - 2.27962i) q^{28} -2.82843 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.965926 + 0.258819i) q^{32} +7.24500i q^{34} +(5.59590 + 1.91987i) q^{35} +(1.88170 - 0.504200i) q^{37} +(0.258819 - 0.965926i) q^{38} +(-0.133975 + 2.23205i) q^{40} -7.95141i q^{41} +(3.00000 - 3.00000i) q^{43} +(-2.56149 + 4.43664i) q^{44} +(4.12250 + 7.14038i) q^{46} +(-2.32937 - 8.69333i) q^{47} +(3.60555 - 6.00000i) q^{49} +(-4.94975 + 0.707107i) q^{50} +(-0.593876 + 2.21637i) q^{52} +(-2.65160 + 9.89591i) q^{53} +(-10.8675 - 3.62250i) q^{55} +(2.54951 + 0.707107i) q^{56} +(-0.732051 - 2.73205i) q^{58} +(-3.00167 - 5.19904i) q^{59} +(-4.62250 + 8.00640i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(-5.12157 - 0.307413i) q^{65} +(-2.56218 + 9.56218i) q^{67} +(-6.99813 + 1.87514i) q^{68} +(-0.406124 + 5.90212i) q^{70} -7.41755i q^{71} +(3.06672 + 0.821726i) q^{73} +(0.974040 + 1.68709i) q^{74} +1.00000 q^{76} +(-6.87953 + 11.6785i) q^{77} +(13.2026 + 7.62250i) q^{79} +(-2.19067 + 0.448288i) q^{80} +(7.68048 - 2.05798i) q^{82} +(2.29456 + 2.29456i) q^{83} +(-7.24500 - 14.4900i) q^{85} +(3.67423 + 2.12132i) q^{86} +(-4.94843 - 1.32593i) q^{88} +(4.94975 - 8.57321i) q^{89} +(-1.62250 + 5.85000i) q^{91} +(-5.83009 + 5.83009i) q^{92} +(7.79423 - 4.50000i) q^{94} +(0.448288 + 2.19067i) q^{95} +(3.24500 + 3.24500i) q^{97} +(6.72874 + 1.92978i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 8 q^{10} - 24 q^{13} + 8 q^{16} + 8 q^{22} + 32 q^{25} + 4 q^{28} - 32 q^{31} + 36 q^{37} - 16 q^{40} + 48 q^{43} + 16 q^{46} - 12 q^{52} - 24 q^{55} + 16 q^{58} - 24 q^{61} + 56 q^{67} - 4 q^{70} - 32 q^{73} + 16 q^{76} + 20 q^{82} - 16 q^{85} - 4 q^{88} + 24 q^{91} - 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 8 * q^10 - 24 * q^13 + 8 * q^16 + 8 * q^22 + 32 * q^25 + 4 * q^28 - 32 * q^31 + 36 * q^37 - 16 * q^40 + 48 * q^43 + 16 * q^46 - 12 * q^52 - 24 * q^55 + 16 * q^58 - 24 * q^61 + 56 * q^67 - 4 * q^70 - 32 * q^73 + 16 * q^76 + 20 * q^82 - 16 * q^85 - 4 * q^88 + 24 * q^91 - 48 * q^97

Introduction

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