LMFDB - Embedded newform 315.2.p.e.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(118,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("315.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.p (of order $4$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.2
Root			$0.944649 + 1.05244i$ of defining polynomial
Character	$\chi$	$=$	315.307
Dual form			315.2.p.e.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(1.28999 + 1.82645i) q^{5} +(-1.97552 - 1.75993i) q^{7} +(0.640825 - 0.640825i) q^{8} +O(q^{10})$	\(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(1.28999 + 1.82645i) q^{5} +(-1.97552 - 1.75993i) q^{7} +(0.640825 - 0.640825i) q^{8} +(0.798469 - 4.63845i) q^{10} +2.67187 q^{11} +(1.22714 + 1.22714i) q^{13} +(0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(4.74624 - 4.74624i) q^{17} +6.01729 q^{19} +(-4.43929 + 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} -3.65291i q^{26} +(4.27759 - 4.80159i) q^{28} +0.304889i q^{29} -7.25379i q^{31} +(-5.67761 - 5.67761i) q^{32} -14.1284 q^{34} +(0.666037 - 5.87847i) q^{35} +(-0.735441 - 0.735441i) q^{37} +(-8.95602 - 8.95602i) q^{38} +(1.99709 + 0.343782i) q^{40} +7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(-0.556866 + 0.556866i) q^{47} +(0.805321 + 6.95352i) q^{49} +(9.50193 - 4.52517i) q^{50} +(-2.98263 + 2.98263i) q^{52} +(4.99031 - 4.99031i) q^{53} +(3.44668 + 4.88005i) q^{55} +(-2.39376 + 0.138155i) q^{56} +(0.453791 - 0.453791i) q^{58} +7.98837 q^{59} +5.53409i q^{61} +(-10.7964 + 10.7964i) q^{62} +10.9939i q^{64} +(-0.658323 + 3.82432i) q^{65} +(-3.43055 - 3.43055i) q^{67} +(11.5360 + 11.5360i) q^{68} +(-9.74071 + 7.75808i) q^{70} -15.3087 q^{71} +(10.0208 + 10.0208i) q^{73} +2.18923i q^{74} +14.6253i q^{76} +(-5.27832 - 4.70230i) q^{77} -11.2973i q^{79} +(3.81000 + 5.39447i) q^{80} +(10.5040 - 10.5040i) q^{82} +(4.88941 + 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} -0.907583 q^{86} +(1.71220 - 1.71220i) q^{88} -6.91251 q^{89} +(-0.264559 - 4.58392i) q^{91} +(0.427009 + 0.427009i) q^{92} +1.65766 q^{94} +(7.76222 + 10.9903i) q^{95} +(-8.84137 + 8.84137i) q^{97} +(9.15086 - 11.5481i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) $ 16 * q - 8 * q^7 - 24 * q^8	$ 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.48838	−	1.48838i	−1.05244	−	1.05244i	−0.998546	−	0.0538973i	$-0.982836\pi$
$2$	−1.48838	−	1.48838i	−1.05244	−	1.05244i	−0.0538973	−	0.998546i	$-0.517164\pi$
$3$		0			0
$3$		0			0
$4$			2.43055i			1.21528i
$5$	1.28999	+	1.82645i	0.576899	+	0.816815i
$5$	1.28999	+	1.82645i	0.576899	+	0.816815i
$6$		0			0
$7$	−1.97552	−	1.75993i	−0.746675	−	0.665189i
$7$	−1.97552	−	1.75993i	−0.746675	−	0.665189i
$8$	0.640825	−	0.640825i	0.226566	−	0.226566i
$9$		0			0
$10$	0.798469	−	4.63845i	0.252498	−	1.46681i
$11$	2.67187			0.805600			0.402800	−	0.915288i	$-0.368037\pi$
$11$	2.67187			0.805600			0.402800	+	0.915288i	$0.368037\pi$
$12$		0			0
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	0.856498	−	0.516150i	$-0.172635\pi$
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	−0.516150	+	0.856498i	$0.672635\pi$
$14$	0.320879	+	5.55976i	0.0857585	+	1.48591i
$15$		0			0
$16$	2.95352			0.738380
$17$	4.74624	−	4.74624i	1.15113	−	1.15113i	0.164807	−	0.986326i	$-0.447300\pi$
$17$	4.74624	−	4.74624i	1.15113	−	1.15113i	0.986326	−	0.164807i	$-0.0527002\pi$
$18$		0			0
$19$	6.01729			1.38046			0.690231	−	0.723589i	$-0.257509\pi$
$19$	6.01729			1.38046			0.690231	+	0.723589i	$0.257509\pi$
$20$	−4.43929	+	3.13538i	−0.992656	+	0.701092i
$21$		0			0
$22$	−3.97676	−	3.97676i	−0.847848	−	0.847848i
$23$	0.175684	−	0.175684i	0.0366327	−	0.0366327i	−0.688553	−	0.725186i	$-0.741754\pi$
$23$	0.175684	−	0.175684i	0.0366327	−	0.0366327i	0.725186	+	0.688553i	$0.241754\pi$
$24$		0			0
$25$	−1.67187	+	4.71220i	−0.334374	+	0.942440i
$26$		−	3.65291i		−	0.716394i
$27$		0			0
$28$	4.27759	−	4.80159i	0.808389	−	0.907416i
$29$			0.304889i			0.0566165i	0.999599	+	0.0283083i	$0.00901200\pi$
$29$			0.304889i			0.0566165i	−0.999599	+	0.0283083i	$0.990988\pi$
$30$		0			0
$31$		−	7.25379i		−	1.30282i	−0.758726	−	0.651410i	$-0.774178\pi$
$31$		−	7.25379i		−	1.30282i	0.758726	−	0.651410i	$-0.225822\pi$
$32$	−5.67761	−	5.67761i	−1.00367	−	1.00367i
$33$		0			0
$34$	−14.1284			−2.42301
$35$	0.666037	−	5.87847i	0.112581	−	0.993643i
$36$		0			0
$37$	−0.735441	−	0.735441i	−0.120906	−	0.120906i	0.644065	−	0.764971i	$-0.277247\pi$
$37$	−0.735441	−	0.735441i	−0.120906	−	0.120906i	−0.764971	+	0.644065i	$0.777247\pi$
$38$	−8.95602	−	8.95602i	−1.45286	−	1.45286i
$39$		0			0
$40$	1.99709	+	0.343782i	0.315768	+	0.0543567i
$41$			7.05736i			1.10217i	0.834447	+	0.551087i	$0.185787\pi$
$41$			7.05736i			1.10217i	−0.834447	+	0.551087i	$0.814213\pi$
$42$		0			0
$43$	0.304889	−	0.304889i	0.0464952	−	0.0464952i	−0.683477	−	0.729972i	$-0.739533\pi$
$43$	0.304889	−	0.304889i	0.0464952	−	0.0464952i	0.729972	+	0.683477i	$0.239533\pi$
$44$			6.49412i			0.979026i
$45$		0			0
$46$	−0.522969			−0.0771076
$47$	−0.556866	+	0.556866i	−0.0812273	+	0.0812273i	−0.746553	−	0.665326i	$-0.768293\pi$
$47$	−0.556866	+	0.556866i	−0.0812273	+	0.0812273i	0.665326	+	0.746553i	$0.268293\pi$
$48$		0			0
$49$	0.805321	+	6.95352i	0.115046	+	0.993360i
$50$	9.50193	−	4.52517i	1.34378	−	0.639955i
$51$		0			0
$52$	−2.98263	+	2.98263i	−0.413617	+	0.413617i
$53$	4.99031	−	4.99031i	0.685472	−	0.685472i	−0.275756	−	0.961228i	$-0.588928\pi$
$53$	4.99031	−	4.99031i	0.685472	−	0.685472i	0.961228	+	0.275756i	$0.0889282\pi$
$54$		0			0
$55$	3.44668	+	4.88005i	0.464750	+	0.658026i
$56$	−2.39376	+	0.138155i	−0.319880	+	0.0184617i
$57$		0			0
$58$	0.453791	−	0.453791i	0.0595857	−	0.0595857i
$59$	7.98837			1.04000			0.519999	−	0.854167i	$-0.325932\pi$
$59$	7.98837			1.04000			0.519999	+	0.854167i	$0.325932\pi$
$60$		0			0
$61$			5.53409i			0.708567i	0.935138	+	0.354284i	$0.115275\pi$
$61$			5.53409i			0.708567i	−0.935138	+	0.354284i	$0.884725\pi$
$62$	−10.7964	+	10.7964i	−1.37114	+	1.37114i
$63$		0			0
$64$			10.9939i			1.37423i
$65$	−0.658323	+	3.82432i	−0.0816549	+	0.474348i
$66$		0			0
$67$	−3.43055	−	3.43055i	−0.419109	−	0.419109i	0.465788	−	0.884896i	$-0.345771\pi$
$67$	−3.43055	−	3.43055i	−0.419109	−	0.419109i	−0.884896	+	0.465788i	$0.845771\pi$
$68$	11.5360	+	11.5360i	1.39894	+	1.39894i
$69$		0			0
$70$	−9.74071	+	7.75808i	−1.16424	+	0.927268i
$71$	−15.3087			−1.81681			−0.908407	−	0.418087i	$-0.862701\pi$
$71$	−15.3087			−1.81681			−0.908407	+	0.418087i	$0.862701\pi$
$72$		0			0
$73$	10.0208	+	10.0208i	1.17285	+	1.17285i	0.981527	+	0.191323i	$0.0612778\pi$
$73$	10.0208	+	10.0208i	1.17285	+	1.17285i	0.191323	+	0.981527i	$0.438722\pi$
$74$			2.18923i			0.254493i
$75$		0			0
$76$			14.6253i			1.67764i
$77$	−5.27832	−	4.70230i	−0.601521	−	0.535876i
$78$		0			0
$79$		−	11.2973i		−	1.27104i	−0.772084	−	0.635521i	$-0.780785\pi$
$79$		−	11.2973i		−	1.27104i	0.772084	−	0.635521i	$-0.219215\pi$
$80$	3.81000	+	5.39447i	0.425971	+	0.603120i
$81$		0			0
$82$	10.5040	−	10.5040i	1.15998	−	1.15998i
$83$	4.88941	+	4.88941i	0.536682	+	0.536682i	0.922553	−	0.385871i	$-0.126099\pi$
$83$	4.88941	+	4.88941i	0.536682	+	0.536682i	−0.385871	+	0.922553i	$0.626099\pi$
$84$		0			0
$85$	14.7914	+	2.54621i	1.60435	+	0.276175i
$86$	−0.907583			−0.0978671
$87$		0			0
$88$	1.71220	−	1.71220i	0.182521	−	0.182521i
$89$	−6.91251			−0.732725			−0.366363	−	0.930472i	$-0.619397\pi$
$89$	−6.91251			−0.732725			−0.366363	+	0.930472i	$0.619397\pi$
$90$		0			0
$91$	−0.264559	−	4.58392i	−0.0277333	−	0.480525i
$92$	0.427009	+	0.427009i	0.0445188	+	0.0445188i
$93$		0			0
$94$	1.65766			0.170974
$95$	7.76222	+	10.9903i	0.796387	+	1.12758i
$96$		0			0
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	−0.995233	−	0.0975276i	$-0.968907\pi$
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	0.0975276	+	0.995233i	$0.468907\pi$
$98$	9.15086	−	11.5481i	0.924376	−	1.16654i
$99$		0			0
$100$	−11.4533	−	4.06357i	−1.14533	−	0.406357i
$101$			7.22962i			0.719374i	0.933073	+	0.359687i	$0.117117\pi$
$101$			7.22962i			0.719374i	−0.933073	+	0.359687i	$0.882883\pi$
$102$		0			0
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	0.276628	−	0.960977i	$-0.410783\pi$
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	−0.960977	+	0.276628i	$0.910783\pi$
$104$	1.57277			0.154222
$105$		0			0
$106$	−14.8550			−1.44284
$107$	7.47295	+	7.47295i	0.722437	+	0.722437i	0.969101	−	0.246664i	$-0.0793344\pi$
$107$	7.47295	+	7.47295i	0.722437	+	0.722437i	−0.246664	+	0.969101i	$0.579334\pi$
$108$		0			0
$109$		−	5.95352i		−	0.570244i	−0.958491	−	0.285122i	$-0.907966\pi$
$109$		−	5.95352i		−	0.570244i	0.958491	−	0.285122i	$-0.0920341\pi$
$110$	2.13341	−	12.3933i	0.203412	−	1.18166i
$111$		0			0
$112$	−5.83473	−	5.19798i	−0.551330	−	0.491163i
$113$	−6.99031	+	6.99031i	−0.657593	+	0.657593i	−0.954810	−	0.297217i	$-0.903942\pi$
$113$	−6.99031	+	6.99031i	−0.657593	+	0.657593i	0.297217	+	0.954810i	$0.403942\pi$
$114$		0			0
$115$	0.547509	+	0.0942489i	0.0510555	+	0.00878876i
$116$	−0.741049			−0.0688047
$117$		0			0
$118$	−11.8897	−	11.8897i	−1.09454	−	1.09454i
$119$	−17.7293	+	1.02324i	−1.62524	+	0.0938002i
$120$		0			0
$121$	−3.86110			−0.351009
$122$	8.23683	−	8.23683i	0.745727	−	0.745727i
$123$		0			0
$124$	17.6307			1.58329
$125$	−10.7633	+	3.02508i	−0.962700	+	0.270571i
$126$		0			0
$127$	2.86110	+	2.86110i	0.253882	+	0.253882i	0.822560	−	0.568678i	$-0.192545\pi$
$127$	2.86110	+	2.86110i	0.253882	+	0.253882i	−0.568678	+	0.822560i	$0.692545\pi$
$128$	5.00781	−	5.00781i	0.442632	−	0.442632i
$129$		0			0
$130$	6.67187	−	4.71220i	0.585162	−	0.413287i
$131$		−	9.34764i		−	0.816707i	−0.912824	−	0.408353i	$-0.866103\pi$
$131$		−	9.34764i		−	0.816707i	0.912824	−	0.408353i	$-0.133897\pi$
$132$		0			0
$133$	−11.8873	−	10.5900i	−1.03076	−	0.918268i
$134$			10.2119i			0.882177i
$135$		0			0
$136$		−	6.08302i		−	0.521615i
$137$	−7.51943	−	7.51943i	−0.642428	−	0.642428i	0.308724	−	0.951152i	$-0.400098\pi$
$137$	−7.51943	−	7.51943i	−0.642428	−	0.642428i	−0.951152	+	0.308724i	$0.900098\pi$
$138$		0			0
$139$	7.78902			0.660656			0.330328	−	0.943866i	$-0.392841\pi$
$139$	7.78902			0.660656			0.330328	+	0.943866i	$0.392841\pi$
$140$	14.2879	+	1.61884i	1.20755	+	0.136817i
$141$		0			0
$142$	22.7852	+	22.7852i	1.91209	+	1.91209i
$143$	3.27877	+	3.27877i	0.274184	+	0.274184i
$144$		0			0
$145$	−0.556866	+	0.393303i	−0.0462452	+	0.0326620i
$146$		−	29.8296i		−	2.46872i
$147$		0			0
$148$	1.78753	−	1.78753i	0.146934	−	0.146934i
$149$		−	14.2855i		−	1.17031i	−0.810920	−	0.585157i	$-0.801033\pi$
$149$		−	14.2855i		−	1.17031i	0.810920	−	0.585157i	$-0.198967\pi$
$150$		0			0
$151$	9.77990			0.795877			0.397939	−	0.917412i	$-0.369726\pi$
$151$	9.77990			0.795877			0.397939	+	0.917412i	$0.369726\pi$
$152$	3.85603	−	3.85603i	0.312765	−	0.312765i
$153$		0			0
$154$	0.857347	+	14.8550i	0.0690870	+	1.19705i
$155$	13.2487	−	9.35729i	1.06416	−	0.751596i
$156$		0			0
$157$	2.17731	−	2.17731i	0.173768	−	0.173768i	−0.614864	−	0.788633i	$-0.710789\pi$
$157$	2.17731	−	2.17731i	0.173768	−	0.173768i	0.788633	+	0.614864i	$0.210789\pi$
$158$	−16.8146	+	16.8146i	−1.33770	+	1.33770i
$159$		0			0
$160$	3.04586	−	17.6939i	0.240796	−	1.39883i
$161$	−0.656257	+	0.0378756i	−0.0517203	+	0.00298502i
$162$		0			0
$163$	−13.6757	+	13.6757i	−1.07117	+	1.07117i	−0.0739001	+	0.997266i	$0.523545\pi$
$163$	−13.6757	+	13.6757i	−1.07117	+	1.07117i	−0.997266	+	0.0739001i	$0.976455\pi$
$164$	−17.1533			−1.33945
$165$		0			0
$166$		−	14.5546i		−	1.12966i
$167$	6.23288	−	6.23288i	0.482315	−	0.482315i	−0.423555	−	0.905870i	$-0.639218\pi$
$167$	6.23288	−	6.23288i	0.482315	−	0.482315i	0.905870	+	0.423555i	$0.139218\pi$
$168$		0			0
$169$		−	9.98824i		−	0.768326i
$170$	−18.2255	−	25.8049i	−1.39783	−	1.97915i
$171$		0			0
$172$	0.741049	+	0.741049i	0.0565045	+	0.0565045i
$173$	−6.76935	−	6.76935i	−0.514664	−	0.514664i	0.401288	−	0.915952i	$-0.368563\pi$
$173$	−6.76935	−	6.76935i	−0.514664	−	0.514664i	−0.915952	+	0.401288i	$0.868563\pi$
$174$		0			0
$175$	11.5959	−	6.36666i	0.876570	−	0.481274i
$176$	7.89143			0.594839
$177$		0			0
$178$	10.2885	+	10.2885i	0.771152	+	0.771152i
$179$		−	1.30103i		−	0.0972437i	−0.998817	−	0.0486218i	$-0.984517\pi$
$179$		−	1.30103i		−	0.0972437i	0.998817	−	0.0486218i	$-0.0154829\pi$
$180$		0			0
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	−6.42885	+	7.21638i	−0.476538	+	0.534913i
$183$		0			0
$184$		−	0.225165i		−	0.0165994i
$185$	0.394541	−	2.29196i	0.0290072	−	0.168508i
$186$		0			0
$187$	12.6814	−	12.6814i	0.927352	−	0.927352i
$188$	−1.35349	−	1.35349i	−0.0987136	−	0.0987136i
$189$		0			0
$190$	4.80462	−	27.9109i	0.348564	−	2.02487i
$191$	−1.93791			−0.140222			−0.0701110	−	0.997539i	$-0.522335\pi$
$191$	−1.93791			−0.140222			−0.0701110	+	0.997539i	$0.522335\pi$
$192$		0			0
$193$	−7.82786	+	7.82786i	−0.563462	+	0.563462i	−0.930289	−	0.366827i	$-0.880444\pi$
$193$	−7.82786	+	7.82786i	−0.563462	+	0.563462i	0.366827	+	0.930289i	$0.380444\pi$
$194$	26.3186			1.88957
$195$		0			0
$196$	−16.9009	+	1.95738i	−1.20721	+	0.139813i
$197$	8.50767	+	8.50767i	0.606146	+	0.606146i	0.941937	−	0.335790i	$-0.109003\pi$
$197$	8.50767	+	8.50767i	0.606146	+	0.606146i	−0.335790	+	0.941937i	$0.609003\pi$
$198$		0			0
$199$	−3.25460			−0.230712			−0.115356	−	0.993324i	$-0.536801\pi$
$199$	−3.25460			−0.230712			−0.115356	+	0.993324i	$0.536801\pi$
$200$	1.94832	+	4.09107i	0.137767	+	0.289283i
$201$		0			0
$202$	10.7604	−	10.7604i	0.757101	−	0.757101i
$203$	0.536583	−	0.602314i	0.0376607	−	0.0422741i
$204$		0			0
$205$	−12.8900	+	9.10390i	−0.900273	+	0.635844i
$206$			20.6747i			1.44048i
$207$		0			0
$208$	3.62439	+	3.62439i	0.251306	+	0.251306i
$209$	16.0774			1.11210
$210$		0			0
$211$	−17.2508			−1.18759			−0.593797	−	0.804615i	$-0.702372\pi$
$211$	−17.2508			−1.18759			−0.593797	+	0.804615i	$0.702372\pi$
$212$	12.1292	+	12.1292i	0.833037	+	0.833037i
$213$		0			0
$214$		−	22.2452i		−	1.52065i
$215$	0.950169	+	0.163563i	0.0648010	+	0.0111549i
$216$		0			0
$217$	−12.7661	+	14.3300i	−0.866622	+	0.972782i
$218$	−8.86110	+	8.86110i	−0.600150	+	0.600150i
$219$		0			0
$220$	−11.8612	+	8.37733i	−0.799683	+	0.564799i
$221$	11.6486			0.783572
$222$		0			0
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	0.536768	−	0.843730i	$-0.319645\pi$
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	−0.843730	+	0.536768i	$0.819645\pi$
$224$	1.22403	+	21.2084i	0.0817841	+	1.41705i
$225$		0			0
$226$	20.8085			1.38416
$227$	−14.1613	+	14.1613i	−0.939918	+	0.939918i	−0.998295	−	0.0583764i	$-0.981408\pi$
$227$	−14.1613	+	14.1613i	−0.939918	+	0.939918i	0.0583764	+	0.998295i	$0.481408\pi$
$228$		0			0
$229$	−28.9307			−1.91180			−0.955898	−	0.293699i	$-0.905114\pi$
$229$	−28.9307			−1.91180			−0.955898	+	0.293699i	$0.905114\pi$
$230$	−0.674623	−	0.955180i	−0.0444833	−	0.0629827i
$231$		0			0
$232$	0.195381	+	0.195381i	0.0128274	+	0.0128274i
$233$	4.78546	−	4.78546i	0.313506	−	0.313506i	−0.532760	−	0.846266i	$-0.678845\pi$
$233$	4.78546	−	4.78546i	0.313506	−	0.313506i	0.846266	+	0.532760i	$0.178845\pi$
$234$		0			0
$235$	−1.73544	−	0.298741i	−0.113208	−	0.0194877i
$236$			19.4162i			1.26388i
$237$		0			0
$238$	27.9109	+	24.8650i	1.80920	+	1.61176i
$239$		−	16.1769i		−	1.04640i	−0.852210	−	0.523200i	$-0.824738\pi$
$239$		−	16.1769i		−	1.04640i	0.852210	−	0.523200i	$-0.175262\pi$
$240$		0			0
$241$		−	11.3707i		−	0.732454i	−0.930526	−	0.366227i	$-0.880649\pi$
$241$		−	11.3707i		−	0.732454i	0.930526	−	0.366227i	$-0.119351\pi$
$242$	5.74679	+	5.74679i	0.369418	+	0.369418i
$243$		0			0
$244$	−13.4509			−0.861105
$245$	−11.6614	+	10.4408i	−0.745022	+	0.667040i
$246$		0			0
$247$	7.38407	+	7.38407i	0.469837	+	0.469837i
$248$	−4.64841	−	4.64841i	−0.295174	−	0.295174i
$249$		0			0
$250$	20.5224	+	11.5174i	1.29795	+	0.728427i
$251$		−	6.95039i		−	0.438705i	−0.975646	−	0.219352i	$-0.929606\pi$
$251$		−	6.95039i		−	0.438705i	0.975646	−	0.219352i	$-0.0703944\pi$
$252$		0			0
$253$	0.469405	−	0.469405i	0.0295112	−	0.0295112i
$254$		−	8.51682i		−	0.534393i
$255$		0			0
$256$	7.08066			0.442541
$257$	−10.0889	+	10.0889i	−0.629329	+	0.629329i	−0.947899	−	0.318570i	$-0.896797\pi$
$257$	−10.0889	+	10.0889i	−0.629329	+	0.629329i	0.318570	+	0.947899i	$0.396797\pi$
$258$		0			0
$259$	0.158553	+	2.74720i	0.00985202	+	0.170703i
$260$	−9.29520	−	1.60009i	−0.576464	−	0.0992332i
$261$		0			0
$262$	−13.9128	+	13.9128i	−0.859538	+	0.859538i
$263$	−18.1984	+	18.1984i	−1.12216	+	1.12216i	−0.130744	+	0.991416i	$0.541737\pi$
$263$	−18.1984	+	18.1984i	−1.12216	+	1.12216i	−0.991416	+	0.130744i	$0.958263\pi$
$264$		0			0
$265$	15.5520	+	2.67714i	0.955352	+	0.164456i
$266$	1.93082	+	33.4547i	0.118386	+	2.05124i
$267$		0			0
$268$	8.33813	−	8.33813i	0.509333	−	0.509333i
$269$	15.5119			0.945775			0.472888	−	0.881123i	$-0.343212\pi$
$269$	15.5119			0.945775			0.472888	+	0.881123i	$0.343212\pi$
$270$		0			0
$271$			13.3418i			0.810458i	0.914215	+	0.405229i	$0.132808\pi$
$271$			13.3418i			0.810458i	−0.914215	+	0.405229i	$0.867192\pi$
$272$	14.0181	−	14.0181i	0.849974	−	0.849974i
$273$		0			0
$274$			22.3835i			1.35224i
$275$	−4.46702	+	12.5904i	−0.269372	+	0.759229i
$276$		0			0
$277$	−2.00561	−	2.00561i	−0.120505	−	0.120505i	0.644282	−	0.764788i	$-0.277156\pi$
$277$	−2.00561	−	2.00561i	−0.120505	−	0.120505i	−0.764788	+	0.644282i	$0.777156\pi$
$278$	−11.5930	−	11.5930i	−0.695304	−	0.695304i
$279$		0			0
$280$	−3.34026	−	4.19388i	−0.199619	−	0.250632i
$281$	−13.5557			−0.808664			−0.404332	−	0.914612i	$-0.632496\pi$
$281$	−13.5557			−0.808664			−0.404332	+	0.914612i	$0.632496\pi$
$282$		0			0
$283$	−16.2444	−	16.2444i	−0.965627	−	0.965627i	0.0338017	−	0.999429i	$-0.489239\pi$
$283$	−16.2444	−	16.2444i	−0.965627	−	0.965627i	−0.999429	+	0.0338017i	$0.989239\pi$
$284$		−	37.2087i		−	2.20793i
$285$		0			0
$286$		−	9.76010i		−	0.577127i
$287$	12.4204	−	13.9419i	0.733155	−	0.822966i
$288$		0			0
$289$		−	28.0537i		−	1.65021i
$290$	1.41421	+	0.243445i	0.0830455	+	0.0142956i
$291$		0			0
$292$	−24.3562	+	24.3562i	−1.42534	+	1.42534i
$293$	2.41765	+	2.41765i	0.141240	+	0.141240i	0.774192	−	0.632951i	$-0.218157\pi$
$293$	2.41765	+	2.41765i	0.141240	+	0.141240i	−0.632951	+	0.774192i	$0.718157\pi$
$294$		0			0
$295$	10.3049	+	14.5904i	0.599974	+	0.849486i
$296$	−0.942578			−0.0547862
$297$		0			0
$298$	−21.2623	+	21.2623i	−1.23169	+	1.23169i
$299$	0.431179			0.0249357
$300$		0			0
$301$	−1.13890	+	0.0657309i	−0.0656449	+	0.00378867i
$302$	−14.5562	−	14.5562i	−0.837616	−	0.837616i
$303$		0			0
$304$	17.7722			1.01931
$305$	−10.1078	+	7.13890i	−0.578769	+	0.408772i
$306$		0			0
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	−0.470652	−	0.882319i	$-0.655981\pi$
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	0.882319	+	0.470652i	$0.155981\pi$
$308$	11.4292	−	12.8292i	0.651238	−	0.731014i
$309$		0			0
$310$	−33.6463	−	5.79193i	−1.91098	−	0.328959i
$311$		−	10.2542i		−	0.581460i	−0.956805	−	0.290730i	$-0.906102\pi$
$311$		−	10.2542i		−	0.581460i	0.956805	−	0.290730i	$-0.0938981\pi$
$312$		0			0
$313$	22.0904	+	22.0904i	1.24862	+	1.24862i	0.956329	+	0.292293i	$0.0944182\pi$
$313$	22.0904	+	22.0904i	1.24862	+	1.24862i	0.292293	+	0.956329i	$0.405582\pi$
$314$	−6.48134			−0.365763
$315$		0			0
$316$	27.4586			1.54467
$317$	12.2563	+	12.2563i	0.688385	+	0.688385i	0.961875	−	0.273490i	$-0.0881780\pi$
$317$	12.2563	+	12.2563i	0.688385	+	0.688385i	−0.273490	+	0.961875i	$0.588178\pi$
$318$		0			0
$319$			0.814625i			0.0456102i
$320$	−20.0798	+	14.1819i	−1.12249	+	0.792793i
$321$		0			0
$322$	1.03313	+	0.920387i	0.0575743	+	0.0512912i
$323$	28.5595	−	28.5595i	1.58909	−	1.58909i
$324$		0			0
$325$	−7.83417	+	3.73092i	−0.434561	+	0.206954i
$326$	40.7094			2.25468
$327$		0			0
$328$	4.52253	+	4.52253i	0.249715	+	0.249715i
$329$	2.08014	−	0.120054i	0.114682	−	0.00661882i
$330$		0			0
$331$	1.26308			0.0694252			0.0347126	−	0.999397i	$-0.488948\pi$
$331$	1.26308			0.0694252			0.0347126	+	0.999397i	$0.488948\pi$
$332$	−11.8840	+	11.8840i	−0.652217	+	0.652217i
$333$		0			0
$334$	−18.5538			−1.01522
$335$	1.84038	−	10.6911i	0.100551	−	0.584118i
$336$		0			0
$337$	−9.55621	−	9.55621i	−0.520560	−	0.520560i	0.397180	−	0.917741i	$-0.369989\pi$
$337$	−9.55621	−	9.55621i	−0.520560	−	0.520560i	−0.917741	+	0.397180i	$0.869989\pi$
$338$	−14.8663	+	14.8663i	−0.808620	+	0.808620i
$339$		0			0
$340$	−6.18869	+	35.9512i	−0.335629	+	1.94973i
$341$		−	19.3812i		−	1.04955i
$342$		0			0
$343$	10.6468	−	15.1541i	0.574871	−	0.818244i
$344$		−	0.390761i		−	0.0210684i
$345$		0			0
$346$			20.1507i			1.08331i
$347$	−6.54975	−	6.54975i	−0.351609	−	0.351609i	0.509099	−	0.860708i	$-0.329979\pi$
$347$	−6.54975	−	6.54975i	−0.351609	−	0.351609i	−0.860708	+	0.509099i	$0.829979\pi$
$348$		0			0
$349$	−2.77139			−0.148349			−0.0741746	−	0.997245i	$-0.523632\pi$
$349$	−2.77139			−0.148349			−0.0741746	+	0.997245i	$0.523632\pi$
$350$	−26.7352	−	7.78315i	−1.42905	−	0.416027i
$351$		0			0
$352$	−15.1699	−	15.1699i	−0.808556	−	0.808556i
$353$	0.970568	+	0.970568i	0.0516581	+	0.0516581i	0.732464	−	0.680806i	$-0.238370\pi$
$353$	0.970568	+	0.970568i	0.0516581	+	0.0516581i	−0.680806	+	0.732464i	$0.738370\pi$
$354$		0			0
$355$	−19.7481	−	27.9607i	−1.04812	−	1.48400i
$356$		−	16.8012i		−	0.890463i
$357$		0			0
$358$	−1.93643	+	1.93643i	−0.102344	+	0.102344i
$359$			9.32813i			0.492320i	0.969229	+	0.246160i	$0.0791688\pi$
$359$			9.32813i			0.492320i	−0.969229	+	0.246160i	$0.920831\pi$
$360$		0			0
$361$	17.2078			0.905674
$362$	12.6293	−	12.6293i	0.663783	−	0.663783i
$363$		0			0
$364$	11.1415	−	0.643024i	0.583971	−	0.0337036i
$365$	−5.37586	+	31.2293i	−0.281385	+	1.63462i
$366$		0			0
$367$	13.0035	−	13.0035i	0.678776	−	0.678776i	−0.280948	−	0.959723i	$-0.590649\pi$
$367$	13.0035	−	13.0035i	0.678776	−	0.678776i	0.959723	+	0.280948i	$0.0906487\pi$
$368$	0.518887	−	0.518887i	0.0270488	−	0.0270488i
$369$		0			0
$370$	−3.99853	+	2.82408i	−0.207874	+	0.146817i
$371$	−18.6410	+	1.07586i	−0.967793	+	0.0558557i
$372$		0			0
$373$	20.6757	−	20.6757i	1.07055	−	1.07055i	0.0732339	−	0.997315i	$-0.476668\pi$
$373$	20.6757	−	20.6757i	1.07055	−	1.07055i	0.997315	−	0.0732339i	$-0.0233320\pi$
$374$	−37.7493			−1.95197
$375$		0			0
$376$			0.713708i			0.0368067i
$377$	−0.374143	+	0.374143i	−0.0192693	+	0.0192693i
$378$		0			0
$379$			22.0077i			1.13046i	0.824933	+	0.565230i	$0.191213\pi$
$379$			22.0077i			1.13046i	−0.824933	+	0.565230i	$0.808787\pi$
$380$	−26.7125	+	18.8665i	−1.37032	+	0.967830i
$381$		0			0
$382$	2.88434	+	2.88434i	0.147576	+	0.147576i
$383$	0.390382	+	0.390382i	0.0199476	+	0.0199476i	0.717010	−	0.697063i	$-0.245510\pi$
$383$	0.390382	+	0.390382i	0.0199476	+	0.0199476i	−0.697063	+	0.717010i	$0.745510\pi$
$384$		0			0
$385$	1.77957	−	15.7065i	0.0906950	−	0.800478i
$386$	23.3017			1.18602
$387$		0			0
$388$	−21.4894	−	21.4894i	−1.09096	−	1.09096i
$389$		−	25.9300i		−	1.31470i	−0.753584	−	0.657352i	$-0.771677\pi$
$389$		−	25.9300i		−	1.31470i	0.753584	−	0.657352i	$-0.228323\pi$
$390$		0			0
$391$		−	1.66768i		−	0.0843381i
$392$	4.97206	+	3.93992i	0.251127	+	0.198996i
$393$		0			0
$394$		−	25.3253i		−	1.27587i
$395$	20.6339	−	14.5733i	1.03821	−	0.733263i
$396$		0			0
$397$	−17.1631	+	17.1631i	−0.861391	+	0.861391i	−0.991500	−	0.130109i	$-0.958467\pi$
$397$	−17.1631	+	17.1631i	−0.861391	+	0.861391i	0.130109	+	0.991500i	$0.458467\pi$
$398$	4.84408	+	4.84408i	0.242812	+	0.242812i
$399$		0			0
$400$	−4.93791	+	13.9176i	−0.246895	+	0.695879i
$401$	12.9418			0.646281			0.323140	−	0.946351i	$-0.395261\pi$
$401$	12.9418			0.646281			0.323140	+	0.946351i	$0.395261\pi$
$402$		0			0
$403$	8.90143	−	8.90143i	0.443412	−	0.443412i
$404$	−17.5720			−0.874238
$405$		0			0
$406$	−1.69511	+	0.0978326i	−0.0841269	+	0.00485535i
$407$	−1.96500	−	1.96500i	−0.0974016	−	0.0974016i
$408$		0			0
$409$	−2.64278			−0.130677			−0.0653386	−	0.997863i	$-0.520813\pi$
$409$	−2.64278			−0.130677			−0.0653386	+	0.997863i	$0.520813\pi$
$410$	32.7352	+	5.63508i	1.61668	+	0.278297i
$411$		0			0
$412$	16.8811	−	16.8811i	0.831672	−	0.831672i
$413$	−15.7812	−	14.0589i	−0.776540	−	0.691795i
$414$		0			0
$415$	−2.62301	+	15.2376i	−0.128759	+	0.747982i
$416$		−	13.9345i		−	0.683194i
$417$		0			0
$418$	−23.9293	−	23.9293i	−1.17042	−	1.17042i
$419$	−10.0302			−0.490007			−0.245003	−	0.969522i	$-0.578789\pi$
$419$	−10.0302			−0.490007			−0.245003	+	0.969522i	$0.578789\pi$
$420$		0			0
$421$	−26.6440			−1.29855			−0.649274	−	0.760555i	$-0.724927\pi$
$421$	−26.6440			−1.29855			−0.649274	+	0.760555i	$0.724927\pi$
$422$	25.6757	+	25.6757i	1.24987	+	1.24987i
$423$		0			0
$424$		−	6.39583i		−	0.310609i
$425$	14.4301	+	30.3004i	0.699965	+	1.46978i
$426$		0			0
$427$	9.73958	−	10.9327i	0.471332	−	0.529069i
$428$	−18.1634	+	18.1634i	−0.877960	+	0.877960i
$429$		0			0
$430$	−1.17077	−	1.65766i	−0.0564595	−	0.0799394i
$431$	−22.3747			−1.07775			−0.538876	−	0.842385i	$-0.681151\pi$
$431$	−22.3747			−1.07775			−0.538876	+	0.842385i	$0.681151\pi$
$432$		0			0
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	0.952373	−	0.304935i	$-0.0986349\pi$
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	−0.304935	+	0.952373i	$0.598635\pi$
$434$	40.3293	−	2.32759i	1.93587	−	0.111728i
$435$		0			0
$436$	14.4703			0.693004
$437$	1.05714	−	1.05714i	0.0505700	−	0.0505700i
$438$		0			0
$439$	25.6790			1.22559			0.612795	−	0.790242i	$-0.290045\pi$
$439$	25.6790			1.22559			0.612795	+	0.790242i	$0.290045\pi$
$440$	5.33598	+	0.918542i	0.254383	+	0.0437898i
$441$		0			0
$442$	−17.3376	−	17.3376i	−0.824665	−	0.824665i
$443$	15.6351	−	15.6351i	0.742845	−	0.742845i	−0.230279	−	0.973125i	$-0.573964\pi$
$443$	15.6351	−	15.6351i	0.742845	−	0.742845i	0.973125	+	0.230279i	$0.0739640\pi$
$444$		0			0
$445$	−8.91705	−	12.6254i	−0.422709	−	0.598501i
$446$			13.6452i			0.646120i
$447$		0			0
$448$	19.3484	−	21.7185i	0.914124	−	1.02610i
$449$			7.01947i			0.331269i	0.986187	+	0.165635i	$0.0529673\pi$
$449$			7.01947i			0.331269i	−0.986187	+	0.165635i	$0.947033\pi$
$450$		0			0
$451$			18.8564i			0.887912i
$452$	−16.9903	−	16.9903i	−0.799157	−	0.799157i
$453$		0			0
$454$	42.1548			1.97842
$455$	8.03104	−	6.39640i	0.376501	−	0.299868i
$456$		0			0
$457$	11.2119	+	11.2119i	0.524472	+	0.524472i	0.918919	−	0.394447i	$-0.129064\pi$
$457$	11.2119	+	11.2119i	0.524472	+	0.524472i	−0.394447	+	0.918919i	$0.629064\pi$
$458$	43.0599	+	43.0599i	2.01206	+	2.01206i
$459$		0			0
$460$	−0.229077	+	1.33075i	−0.0106808	+	0.0620465i
$461$			29.9845i			1.39652i	0.715846	+	0.698259i	$0.246041\pi$
$461$			29.9845i			1.39652i	−0.715846	+	0.698259i	$0.753959\pi$
$462$		0			0
$463$	7.70220	−	7.70220i	0.357951	−	0.357951i	−0.505106	−	0.863057i	$-0.668547\pi$
$463$	7.70220	−	7.70220i	0.357951	−	0.357951i	0.863057	+	0.505106i	$0.168547\pi$
$464$			0.900497i			0.0418045i
$465$		0			0
$466$	−14.2452			−0.659895
$467$	−1.80961	+	1.80961i	−0.0837386	+	0.0837386i	−0.747735	−	0.663997i	$-0.768859\pi$
$467$	−1.80961	+	1.80961i	−0.0837386	+	0.0837386i	0.663997	+	0.747735i	$0.268859\pi$
$468$		0			0
$469$	0.739590	+	12.8146i	0.0341511	+	0.591724i
$470$	2.13836	+	3.02764i	0.0986350	+	0.139654i
$471$		0			0
$472$	5.11915	−	5.11915i	0.235628	−	0.235628i
$473$	0.814625	−	0.814625i	0.0374565	−	0.0374565i
$474$		0			0
$475$	−10.0601	+	28.3547i	−0.461591	+	1.30100i
$476$	−2.48704	−	43.0920i	−0.113993	−	1.97512i
$477$		0			0
$478$	−24.0774	+	24.0774i	−1.10128	+	1.10128i
$479$	−4.09455			−0.187085			−0.0935425	−	0.995615i	$-0.529819\pi$
$479$	−4.09455			−0.187085			−0.0935425	+	0.995615i	$0.529819\pi$
$480$		0			0
$481$		−	1.80498i		−	0.0823001i
$482$	−16.9240	+	16.9240i	−0.770867	+	0.770867i
$483$		0			0
$484$		−	9.38461i		−	0.426573i
$485$	−27.5536	−	4.74311i	−1.25114	−	0.215374i
$486$		0			0
$487$	−10.3049	−	10.3049i	−0.466959	−	0.466959i	0.433969	−	0.900928i	$-0.357113\pi$
$487$	−10.3049	−	10.3049i	−0.466959	−	0.466959i	−0.900928	+	0.433969i	$0.857113\pi$
$488$	3.54638	+	3.54638i	0.160537	+	0.160537i
$489$		0			0
$490$	32.8966	+	1.81673i	1.48612	+	0.0820714i
$491$	8.55953			0.386286			0.193143	−	0.981171i	$-0.438132\pi$
$491$	8.55953			0.386286			0.193143	+	0.981171i	$0.438132\pi$
$492$		0			0
$493$	1.44708	+	1.44708i	0.0651732	+	0.0651732i
$494$		−	21.9806i		−	0.988955i
$495$		0			0
$496$		−	21.4242i		−	0.961976i
$497$	30.2427	+	26.9423i	1.35657	+	1.20853i
$498$		0			0
$499$			23.7564i			1.06348i	0.846907	+	0.531741i	$0.178462\pi$
$499$			23.7564i			1.06348i	−0.846907	+	0.531741i	$0.821538\pi$
$500$	−7.35261	−	26.1608i	−0.328819	−	1.16995i
$501$		0			0
$502$	−10.3448	+	10.3448i	−0.461712	+	0.461712i
$503$	17.9504	+	17.9504i	0.800367	+	0.800367i	0.983153	−	0.182786i	$-0.0585115\pi$
$503$	17.9504	+	17.9504i	0.800367	+	0.800367i	−0.182786	+	0.983153i	$0.558511\pi$
$504$		0			0
$505$	−13.2046	+	9.32611i	−0.587596	+	0.415007i
$506$	−1.39731			−0.0621179
$507$		0			0
$508$	−6.95406	+	6.95406i	−0.308537	+	0.308537i
$509$	−16.8977			−0.748979			−0.374489	−	0.927231i	$-0.622182\pi$
$509$	−16.8977			−0.748979			−0.374489	+	0.927231i	$0.622182\pi$
$510$		0			0
$511$	−2.16039	−	37.4322i	−0.0955698	−	1.65590i
$512$	−20.5543	−	20.5543i	−0.908382	−	0.908382i
$513$		0			0
$514$	30.0323			1.32467
$515$	3.72598	−	21.6449i	0.164186	−	0.953787i
$516$		0			0
$517$	−1.48788	+	1.48788i	−0.0654367	+	0.0654367i
$518$	3.85289	−	4.32486i	0.169286	−	0.190024i
$519$		0			0
$520$	2.02885	+	2.87259i	0.0889708	+	0.125971i
$521$			7.88477i			0.345438i	0.984971	+	0.172719i	$0.0552552\pi$
$521$			7.88477i			0.345438i	−0.984971	+	0.172719i	$0.944745\pi$
$522$		0			0
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	0.679669	−	0.733519i	$-0.262123\pi$
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	−0.733519	+	0.679669i	$0.762123\pi$
$524$	22.7199			0.992524
$525$		0			0
$526$	54.1722			2.36202
$527$	−34.4283	−	34.4283i	−1.49972	−	1.49972i
$528$		0			0
$529$			22.9383i			0.997316i
$530$	−19.1627	−	27.1319i	−0.832374	−	1.17853i
$531$		0			0
$532$	25.7395	−	28.8926i	1.11595	−	1.25265i
$533$	−8.66039	+	8.66039i	−0.375123	+	0.375123i
$534$		0			0
$535$	−4.00900	+	23.2890i	−0.173324	+	1.00687i
$536$	−4.39677			−0.189911
$537$		0			0
$538$	−23.0876	−	23.0876i	−0.995375	−	0.995375i
$539$	2.15171	+	18.5789i	0.0926809	+	0.800250i
$540$		0			0
$541$	34.9495			1.50260			0.751298	−	0.659963i	$-0.229428\pi$
$541$	34.9495			1.50260			0.751298	+	0.659963i	$0.229428\pi$
$542$	19.8577	−	19.8577i	0.852962	−	0.852962i
$543$		0			0
$544$	−53.8947			−2.31071
$545$	10.8738	−	7.67996i	0.465784	−	0.328973i
$546$		0			0
$547$	3.83548	+	3.83548i	0.163993	+	0.163993i	0.784333	−	0.620340i	$-0.213005\pi$
$547$	3.83548	+	3.83548i	0.163993	+	0.163993i	−0.620340	+	0.784333i	$0.713005\pi$
$548$	18.2764	−	18.2764i	0.780727	−	0.780727i
$549$		0			0
$550$	25.3879	−	12.0907i	1.08255	−	0.515548i
$551$			1.83461i			0.0781569i
$552$		0			0
$553$	−19.8823	+	22.3179i	−0.845483	+	0.949054i
$554$			5.97022i			0.253650i
$555$		0			0
$556$			18.9316i			0.802880i
$557$	16.3147	+	16.3147i	0.691275	+	0.691275i	0.962512	−	0.271238i	$-0.0874329\pi$
$557$	16.3147	+	16.3147i	0.691275	+	0.691275i	−0.271238	+	0.962512i	$0.587433\pi$
$558$		0			0
$559$	0.748285			0.0316491
$560$	1.96715	−	17.3622i	0.0831275	−	0.733686i
$561$		0			0
$562$	20.1760	+	20.1760i	0.851073	+	0.851073i
$563$	−23.7521	−	23.7521i	−1.00103	−	1.00103i	−0.999999	−	0.00103054i	$-0.999672\pi$
$563$	−23.7521	−	23.7521i	−1.00103	−	1.00103i	−0.00103054	−	0.999999i	$-0.500328\pi$
$564$		0			0
$565$	−21.7849	−	3.75008i	−0.916497	−	0.157767i
$566$			48.3556i			2.03254i
$567$		0			0
$568$	−9.81023	+	9.81023i	−0.411628	+	0.411628i
$569$			0.277792i			0.0116457i	0.999983	+	0.00582283i	$0.00185348\pi$
$569$			0.277792i			0.0116457i	−0.999983	+	0.00582283i	$0.998147\pi$
$570$		0			0
$571$	−3.11538			−0.130375			−0.0651874	−	0.997873i	$-0.520765\pi$
$571$	−3.11538			−0.130375			−0.0651874	+	0.997873i	$0.520765\pi$
$572$	−7.96921	+	7.96921i	−0.333209	+	0.333209i
$573$		0			0
$574$	−39.2372	+	2.26456i	−1.63773	+	0.0945209i
$575$	0.534138	+	1.12158i	0.0222751	+	0.0467731i
$576$		0			0
$577$	29.5905	−	29.5905i	1.23187	−	1.23187i	0.268625	−	0.963245i	$-0.413431\pi$
$577$	29.5905	−	29.5905i	1.23187	−	1.23187i	0.963245	−	0.268625i	$-0.0865693\pi$
$578$	−41.7545	+	41.7545i	−1.73676	+	1.73676i
$579$		0			0
$580$	−0.955943	−	1.35349i	−0.0396934	−	0.0562007i
$581$	−1.05410	−	18.2641i	−0.0437316	−	0.757722i
$582$		0			0
$583$	13.3335	−	13.3335i	0.552216	−	0.552216i
$584$	12.8432			0.531456
$585$		0			0
$586$		−	7.19676i		−	0.297295i
$587$	−26.6462	+	26.6462i	−1.09981	+	1.09981i	−0.105375	+	0.994433i	$0.533604\pi$
$587$	−26.6462	+	26.6462i	−1.09981	+	1.09981i	−0.994433	+	0.105375i	$0.966396\pi$
$588$		0			0
$589$		−	43.6482i		−	1.79849i
$590$	6.37847	−	37.0537i	0.262597	−	1.52547i
$591$		0			0
$592$	−2.17214	−	2.17214i	−0.0892745	−	0.0892745i
$593$	−15.1889	−	15.1889i	−0.623733	−	0.623733i	0.322751	−	0.946484i	$-0.395392\pi$
$593$	−15.1889	−	15.1889i	−0.623733	−	0.623733i	−0.946484	+	0.322751i	$0.895392\pi$
$594$		0			0
$595$	−24.7395	−	31.0618i	−1.01422	−	1.27341i
$596$	34.7217			1.42225
$597$		0			0
$598$	−0.641758	−	0.641758i	−0.0262434	−	0.0262434i
$599$			22.2776i			0.910238i	0.890431	+	0.455119i	$0.150403\pi$
$599$			22.2776i			0.910238i	−0.890431	+	0.455119i	$0.849597\pi$
$600$		0			0
$601$			22.3458i			0.911503i	0.890107	+	0.455752i	$0.150629\pi$
$601$			22.3458i			0.911503i	−0.890107	+	0.455752i	$0.849371\pi$
$602$	1.79294	+	1.59728i	0.0730749	+	0.0651002i
$603$		0			0
$604$			23.7706i			0.967210i
$605$	−4.98077	−	7.05213i	−0.202497	−	0.286710i
$606$		0			0
$607$	−0.576027	+	0.576027i	−0.0233802	+	0.0233802i	−0.718700	−	0.695320i	$-0.755263\pi$
$607$	−0.576027	+	0.576027i	−0.0233802	+	0.0233802i	0.695320	+	0.718700i	$0.255263\pi$
$608$	−34.1639	−	34.1639i	−1.38553	−	1.38553i
$609$		0			0
$610$	25.6696	+	4.41880i	1.03933	+	0.178912i
$611$	−1.36671			−0.0552911
$612$		0			0
$613$	−16.4709	+	16.4709i	−0.665253	+	0.665253i	−0.956613	−	0.291361i	$-0.905892\pi$
$613$	−16.4709	+	16.4709i	−0.665253	+	0.665253i	0.291361	+	0.956613i	$0.405892\pi$
$614$	−21.4714			−0.866514
$615$		0			0
$616$	−6.39583	+	0.369132i	−0.257695	+	0.0148728i
$617$	3.70013	+	3.70013i	0.148962	+	0.148962i	0.777654	−	0.628692i	$-0.216410\pi$
$617$	3.70013	+	3.70013i	0.148962	+	0.148962i	−0.628692	+	0.777654i	$0.716410\pi$
$618$		0			0
$619$	−39.8840			−1.60307			−0.801536	−	0.597946i	$-0.795984\pi$
$619$	−39.8840			−1.60307			−0.801536	+	0.597946i	$0.795984\pi$
$620$	22.7434	+	32.2017i	0.913396	+	1.29325i
$621$		0			0
$622$	−15.2621	+	15.2621i	−0.611954	+	0.611954i
$623$	13.6558	+	12.1655i	0.547107	+	0.487401i
$624$		0			0
$625$	−19.4097	−	15.7564i	−0.776388	−	0.630256i
$626$		−	65.7578i		−	2.62821i
$627$		0			0
$628$	5.29207	+	5.29207i	0.211177	+	0.211177i
$629$	−6.98117			−0.278357
$630$		0			0
$631$	−33.9725			−1.35242			−0.676211	−	0.736708i	$-0.736379\pi$
$631$	−33.9725			−1.35242			−0.676211	+	0.736708i	$0.736379\pi$
$632$	−7.23957	−	7.23957i	−0.287975	−	0.287975i
$633$		0			0
$634$		−	36.4842i		−	1.44897i
$635$	−1.53489	+	8.91646i	−0.0609103	+	0.353839i
$636$		0			0
$637$	−7.54472	+	9.52120i	−0.298933	+	0.377244i
$638$	1.21247	−	1.21247i	0.0480022	−	0.0480022i
$639$		0			0
$640$	15.6065	+	2.68653i	0.616902	+	0.106194i
$641$	18.1113			0.715352			0.357676	−	0.933846i	$-0.383569\pi$
$641$	18.1113			0.715352			0.357676	+	0.933846i	$0.383569\pi$
$642$		0			0
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.948063	+	0.318082i	$0.103039\pi$
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.318082	+	0.948063i	$0.396961\pi$
$644$	−0.0920586	−	1.59507i	−0.00362762	−	0.0628545i
$645$		0			0
$646$	−85.0149			−3.34487
$647$	−12.9277	+	12.9277i	−0.508241	+	0.508241i	−0.913986	−	0.405745i	$-0.867012\pi$
$647$	−12.9277	+	12.9277i	−0.508241	+	0.508241i	0.405745	+	0.913986i	$0.367012\pi$
$648$		0			0
$649$	21.3439			0.837821
$650$	17.2132	+	6.10719i	0.675159	+	0.239544i
$651$		0			0
$652$	−33.2396	−	33.2396i	−1.30176	−	1.30176i
$653$	9.39937	−	9.39937i	0.367826	−	0.367826i	−0.498858	−	0.866684i	$-0.666247\pi$
$653$	9.39937	−	9.39937i	0.367826	−	0.367826i	0.866684	+	0.498858i	$0.166247\pi$
$654$		0			0
$655$	17.0730	−	12.0583i	0.667099	−	0.471158i
$656$			20.8441i			0.813824i
$657$		0			0
$658$	−3.27473	−	2.91736i	−0.127662	−	0.113730i
$659$			9.13808i			0.355969i	0.984033	+	0.177985i	$0.0569577\pi$
$659$			9.13808i			0.355969i	−0.984033	+	0.177985i	$0.943042\pi$
$660$		0			0
$661$		−	28.4837i		−	1.10789i	−0.832554	−	0.553943i	$-0.813122\pi$
$661$		−	28.4837i		−	1.10789i	0.832554	−	0.553943i	$-0.186878\pi$
$662$	−1.87995	−	1.87995i	−0.0730662	−	0.0730662i
$663$		0			0
$664$	6.26651			0.243188
$665$	4.00774	−	35.3725i	0.155413	−	1.37169i
$666$		0			0
$667$	0.0535642	+	0.0535642i	0.00207401	+	0.00207401i
$668$	15.1493	+	15.1493i	0.586146	+	0.586146i
$669$		0			0
$670$	−18.6516	+	13.1733i	−0.720575	+	0.508927i
$671$			14.7864i			0.570821i
$672$		0			0
$673$	26.8815	−	26.8815i	1.03621	−	1.03621i	0.0368867	−	0.999319i	$-0.488256\pi$
$673$	26.8815	−	26.8815i	1.03621	−	1.03621i	0.999319	−	0.0368867i	$-0.0117441\pi$
$674$			28.4466i			1.09572i
$675$		0			0
$676$	24.2769			0.933729
$677$	1.19694	−	1.19694i	0.0460022	−	0.0460022i	−0.683731	−	0.729734i	$-0.739644\pi$
$677$	1.19694	−	1.19694i	0.0460022	−	0.0460022i	0.729734	+	0.683731i	$0.239644\pi$
$678$		0			0
$679$	33.0264	−	1.90611i	1.26744	−	0.0731496i
$680$	11.1104	−	7.84702i	0.426063	−	0.300919i
$681$		0			0
$682$	−28.8466	+	28.8466i	−1.10459	+	1.10459i
$683$	−2.41553	+	2.41553i	−0.0924275	+	0.0924275i	−0.751809	−	0.659381i	$-0.770818\pi$
$683$	−2.41553	+	2.41553i	−0.0924275	+	0.0924275i	0.659381	+	0.751809i	$0.270818\pi$
$684$		0			0
$685$	4.03393	−	23.4338i	0.154129	−	0.895361i
$686$	−38.4015	+	6.70863i	−1.46618	+	0.256137i
$687$		0			0
$688$	0.900497	−	0.900497i	0.0343311	−	0.0343311i
$689$	12.2476			0.466598
$690$		0			0
$691$			41.6703i			1.58521i	0.609735	+	0.792606i	$0.291276\pi$
$691$			41.6703i			1.58521i	−0.609735	+	0.792606i	$0.708724\pi$
$692$	16.4533	−	16.4533i	0.625459	−	0.625459i
$693$		0			0
$694$			19.4970i			0.740098i
$695$	10.0477	+	14.2263i	0.381132	+	0.539634i
$696$		0			0
$697$	33.4960	+	33.4960i	1.26875	+	1.26875i
$698$	4.12488	+	4.12488i	0.156129	+	0.156129i
$699$		0			0
$700$	15.4745	+	28.1845i	0.584881	+	1.06527i
$701$	−13.7870			−0.520727			−0.260364	−	0.965511i	$-0.583842\pi$
$701$	−13.7870			−0.520727			−0.260364	+	0.965511i	$0.583842\pi$
$702$		0			0
$703$	−4.42536	−	4.42536i	−0.166906	−	0.166906i
$704$			29.3742i			1.10708i
$705$		0			0
$706$		−	2.88915i		−	0.108735i
$707$	12.7236	−	14.2822i	0.478520	−	0.537138i
$708$		0			0
$709$			24.6722i			0.926585i	0.886205	+	0.463293i	$0.153332\pi$
$709$			24.6722i			0.926585i	−0.886205	+	0.463293i	$0.846668\pi$
$710$	−12.2236	+	71.0088i	−0.458742	+	2.66491i
$711$		0			0
$712$	−4.42971	+	4.42971i	−0.166010	+	0.166010i
$713$	−1.27438	−	1.27438i	−0.0477257	−	0.0477257i
$714$		0			0
$715$	−1.75895	+	10.2181i	−0.0657811	+	0.382135i
$716$	3.16223			0.118178
$717$		0			0
$718$	13.8838	−	13.8838i	0.518139	−	0.518139i
$719$	29.9117			1.11552			0.557758	−	0.830003i	$-0.311662\pi$
$719$	29.9117			1.11552			0.557758	+	0.830003i	$0.311662\pi$
$720$		0			0
$721$	1.49735	+	25.9441i	0.0557642	+	0.966207i
$722$	−25.6118	−	25.6118i	−0.953171	−	0.953171i
$723$		0			0
$724$	−20.6239			−0.766482
$725$	−1.43670	−	0.509736i	−0.0533577	−	0.0189311i
$726$		0			0
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.113491	+	0.993539i	$0.536203\pi$
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.993539	+	0.113491i	$0.963797\pi$
$728$	−3.10702	−	2.76795i	−0.115154	−	0.102587i
$729$		0			0
$730$	54.4825	−	38.4798i	2.01649	−	1.42420i
$731$		−	2.89416i		−	0.107044i
$732$		0			0
$733$	−3.86707	−	3.86707i	−0.142834	−	0.142834i	0.632074	−	0.774908i	$-0.282204\pi$
$733$	−3.86707	−	3.86707i	−0.142834	−	0.142834i	−0.774908	+	0.632074i	$0.782204\pi$
$734$	−38.7082			−1.42875
$735$		0			0
$736$	−1.99493			−0.0735342
$737$	−9.16599	−	9.16599i	−0.337634	−	0.337634i
$738$		0			0
$739$		−	11.9735i		−	0.440454i	−0.975449	−	0.220227i	$-0.929320\pi$
$739$		−	11.9735i		−	0.440454i	0.975449	−	0.220227i	$-0.0706797\pi$
$740$	5.57073	+	0.958952i	0.204784	+	0.0352518i
$741$		0			0
$742$	29.3462	+	26.1436i	1.07733	+	0.959763i
$743$	12.0406	−	12.0406i	0.441728	−	0.441728i	−0.450864	−	0.892593i	$-0.648884\pi$
$743$	12.0406	−	12.0406i	0.441728	−	0.441728i	0.892593	+	0.450864i	$0.148884\pi$
$744$		0			0
$745$	26.0918	−	18.4281i	0.955931	−	0.675154i
$746$	−61.5467			−2.25338
$747$		0			0
$748$	30.8227	+	30.8227i	1.12699	+	1.12699i
$749$	−1.61109	−	27.9148i	−0.0588679	−	1.01998i
$750$		0			0
$751$	−24.1119			−0.879855			−0.439928	−	0.898033i	$-0.644996\pi$
$751$	−24.1119			−0.879855			−0.439928	+	0.898033i	$0.644996\pi$
$752$	−1.64472	+	1.64472i	−0.0599767	+	0.0599767i
$753$		0			0
$754$	1.11373			0.0405598
$755$	12.6159	+	17.8625i	0.459141	+	0.650085i
$756$		0			0
$757$	29.2896	+	29.2896i	1.06455	+	1.06455i	0.997768	+	0.0667825i	$0.0212733\pi$
$757$	29.2896	+	29.2896i	1.06455	+	1.06455i	0.0667825	+	0.997768i	$0.478727\pi$
$758$	32.7558	−	32.7558i	1.18975	−	1.18975i
$759$		0			0
$760$	12.0171	+	2.06864i	0.435906	+	0.0750374i
$761$			32.3002i			1.17088i	0.810716	+	0.585440i	$0.199078\pi$
$761$			32.3002i			1.17088i	−0.810716	+	0.585440i	$0.800922\pi$
$762$		0			0
$763$	−10.4778	+	11.7613i	−0.379320	+	0.425787i
$764$		−	4.71018i		−	0.170408i
$765$		0			0
$766$		−	1.16207i		−	0.0419874i
$767$	9.80287	+	9.80287i	0.353961	+	0.353961i
$768$		0			0
$769$	18.4310			0.664640			0.332320	−	0.943167i	$-0.392169\pi$
$769$	18.4310			0.664640			0.332320	+	0.943167i	$0.392169\pi$
$770$	−26.0259	+	20.7286i	−0.937910	+	0.747007i
$771$		0			0
$772$	−19.0260	−	19.0260i	−0.684761	−	0.684761i
$773$	−17.7963	−	17.7963i	−0.640088	−	0.640088i	0.310489	−	0.950577i	$-0.399507\pi$
$773$	−17.7963	−	17.7963i	−0.640088	−	0.640088i	−0.950577	+	0.310489i	$0.899507\pi$
$774$		0			0
$775$	34.1813	+	12.1274i	1.22783	+	0.435629i
$776$			11.3315i			0.406779i
$777$		0			0
$778$	−38.5937	+	38.5937i	−1.38365	+	1.38365i
$779$			42.4662i			1.52151i
$780$		0			0
$781$	−40.9030			−1.46362
$782$	−2.48214	+	2.48214i	−0.0887611	+	0.0887611i
$783$		0			0
$784$	2.37853	+	20.5374i	0.0849476	+	0.733478i
$785$	6.78546	+	1.16806i	0.242184	+	0.0416898i
$786$		0			0
$787$	−16.0671	+	16.0671i	−0.572730	+	0.572730i	−0.932890	−	0.360160i	$-0.882722\pi$
$787$	−16.0671	+	16.0671i	−0.572730	+	0.572730i	0.360160	+	0.932890i	$0.382722\pi$
$788$	−20.6783	+	20.6783i	−0.736635	+	0.736635i
$789$		0			0
$790$	−52.4018	−	9.02051i	−1.86437	−	0.320935i
$791$	26.1119	−	1.50704i	0.928432	−	0.0535840i
$792$		0			0
$793$	−6.79111	+	6.79111i	−0.241159	+	0.241159i
$794$	51.0904			1.81313
$795$		0			0
$796$		−	7.91046i		−	0.280379i
$797$	25.5337	−	25.5337i	0.904451	−	0.904451i	−0.0913664	−	0.995817i	$-0.529123\pi$
$797$	25.5337	−	25.5337i	0.904451	−	0.904451i	0.995817	+	0.0913664i	$0.0291235\pi$
$798$		0			0
$799$			5.28605i			0.187007i
$800$	36.2463	−	17.2618i	1.28150	−	0.610297i
$801$		0			0
$802$	−19.2623	−	19.2623i	−0.680174	−	0.680174i
$803$	26.7744	+	26.7744i	0.944847	+	0.944847i
$804$		0			0
$805$	−0.915741	−	1.14977i	−0.0322756	−	0.0405239i
$806$	−26.4974			−0.933332
$807$		0			0
$808$	4.63292	+	4.63292i	0.162986	+	0.162986i
$809$		−	27.5404i		−	0.968270i	−0.874993	−	0.484135i	$-0.839134\pi$
$809$		−	27.5404i		−	0.968270i	0.874993	−	0.484135i	$-0.160866\pi$
$810$		0			0
$811$		−	34.2545i		−	1.20284i	−0.798933	−	0.601420i	$-0.794602\pi$
$811$		−	34.2545i		−	1.20284i	0.798933	−	0.601420i	$-0.205398\pi$
$812$	1.46395	+	1.30419i	0.0513747	+	0.0457682i
$813$		0			0
$814$			5.84935i			0.205020i
$815$	−42.6196	−	7.33659i	−1.49290	−	0.256990i
$816$		0			0
$817$	1.83461	−	1.83461i	0.0641848	−	0.0641848i
$818$	3.93347	+	3.93347i	0.137530	+	0.137530i
$819$		0			0
$820$	−22.1275	−	31.3297i	−0.772726	−	1.09408i
$821$	−49.7482			−1.73623			−0.868113	−	0.496367i	$-0.834667\pi$
$821$	−49.7482			−1.73623			−0.868113	+	0.496367i	$0.834667\pi$
$822$		0			0
$823$	−6.10417	+	6.10417i	−0.212778	+	0.212778i	−0.805447	−	0.592668i	$-0.798074\pi$
$823$	−6.10417	+	6.10417i	−0.212778	+	0.212778i	0.592668	+	0.805447i	$0.298074\pi$
$824$	−8.90155			−0.310100
$825$		0			0
$826$	2.56330	+	44.4134i	0.0891886	+	1.54534i
$827$	4.96734	+	4.96734i	0.172731	+	0.172731i	0.788178	−	0.615447i	$-0.211024\pi$
$827$	4.96734	+	4.96734i	0.172731	+	0.172731i	−0.615447	+	0.788178i	$0.711024\pi$
$828$		0			0
$829$	−28.3500			−0.984636			−0.492318	−	0.870415i	$-0.663850\pi$
$829$	−28.3500			−0.984636			−0.492318	+	0.870415i	$0.663850\pi$
$830$	26.5833	−	18.7752i	0.922720	−	0.651698i
$831$		0			0
$832$	−13.4910	+	13.4910i	−0.467717	+	0.467717i
$833$	36.8254	+	29.1809i	1.27592	+	1.01106i
$834$		0			0
$835$	19.4244	+	3.34374i	0.672209	+	0.115715i
$836$			39.0770i			1.35151i
$837$		0			0
$838$	14.9287	+	14.9287i	0.515705	+	0.515705i
$839$	−32.8100			−1.13273			−0.566364	−	0.824156i	$-0.691650\pi$
$839$	−32.8100			−1.13273			−0.566364	+	0.824156i	$0.691650\pi$
$840$		0			0
$841$	28.9070			0.996795
$842$	39.6563	+	39.6563i	1.36665	+	1.36665i
$843$		0			0
$844$		−	41.9289i		−	1.44325i
$845$	18.2431	−	12.8847i	0.627581	−	0.443247i
$846$		0			0
$847$	7.62767	+	6.79526i	0.262090	+	0.233488i
$848$	14.7390	−	14.7390i	0.506139	−	0.506139i
$849$		0			0
$850$	23.6209	−	66.5760i	0.810191	−	2.28354i
$851$	−0.258411			−0.00885820
$852$		0			0
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	0.390184	−	0.920737i	$-0.372411\pi$
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	−0.920737	+	0.390184i	$0.872411\pi$
$854$	−30.7682	+	1.77577i	−1.05287	+	0.0607657i
$855$		0			0
$856$	9.57770			0.327359
$857$	17.8346	−	17.8346i	0.609218	−	0.609218i	−0.333523	−	0.942742i	$-0.608238\pi$
$857$	17.8346	−	17.8346i	0.609218	−	0.609218i	0.942742	+	0.333523i	$0.108238\pi$
$858$		0			0
$859$	17.2711			0.589283			0.294641	−	0.955608i	$-0.404800\pi$
$859$	17.2711			0.589283			0.294641	+	0.955608i	$0.404800\pi$
$860$	−0.397549	+	2.30944i	−0.0135563	+	0.0787511i
$861$		0			0
$862$	33.3021	+	33.3021i	1.13427	+	1.13427i
$863$	−2.94383	+	2.94383i	−0.100209	+	0.100209i	−0.755434	−	0.655225i	$-0.772574\pi$
$863$	−2.94383	+	2.94383i	−0.100209	+	0.100209i	0.655225	+	0.755434i	$0.272574\pi$
$864$		0			0
$865$	3.63154	−	21.0963i	0.123476	−	0.717295i
$866$		−	40.1038i		−	1.36278i
$867$		0			0
$868$	−34.8298	−	31.0288i	−1.18220	−	1.05318i
$869$		−	30.1848i		−	1.02395i
$870$		0			0
$871$		−	8.41955i		−	0.285286i
$872$	−3.81517	−	3.81517i	−0.129198	−	0.129198i
$873$		0			0
$874$	−3.14686			−0.106444
$875$	26.5870	+	12.9665i	0.898805	+	0.438349i
$876$		0			0
$877$	−8.49735	−	8.49735i	−0.286935	−	0.286935i	0.548932	−	0.835867i	$-0.315035\pi$
$877$	−8.49735	−	8.49735i	−0.286935	−	0.286935i	−0.835867	+	0.548932i	$0.815035\pi$
$878$	−38.2201	−	38.2201i	−1.28987	−	1.28987i
$879$		0			0
$880$	10.1798	+	14.4133i	0.343162	+	0.485873i
$881$		−	35.7762i		−	1.20533i	−0.797994	−	0.602665i	$-0.794106\pi$
$881$		−	35.7762i		−	1.20533i	0.797994	−	0.602665i	$-0.205894\pi$
$882$		0			0
$883$	24.6278	−	24.6278i	0.828791	−	0.828791i	−0.158559	−	0.987350i	$-0.550685\pi$
$883$	24.6278	−	24.6278i	0.828791	−	0.828791i	0.987350	+	0.158559i	$0.0506848\pi$
$884$			28.3126i			0.952256i
$885$		0			0
$886$	−46.5419			−1.56361
$887$	−0.732491	+	0.732491i	−0.0245946	+	0.0245946i	−0.719297	−	0.694703i	$-0.755536\pi$
$887$	−0.732491	+	0.732491i	−0.0245946	+	0.0245946i	0.694703	+	0.719297i	$0.255536\pi$
$888$		0			0
$889$	−0.616823	−	10.6875i	−0.0206876	−	0.358447i
$890$	−5.51943	+	32.0633i	−0.185012	+	1.07477i
$891$		0			0
$892$	11.1415	−	11.1415i	0.373043	−	0.373043i
$893$	−3.35083	+	3.35083i	−0.112131	+	0.112131i
$894$		0			0
$895$	2.37628	−	1.67831i	0.0794301	−	0.0560998i
$896$	−18.7064	+	1.07963i	−0.624936	+	0.0360679i
$897$		0			0
$898$	10.4476	−	10.4476i	0.348642	−	0.348642i
$899$	2.21160			0.0737611
$900$		0			0
$901$		−	47.3704i		−	1.57814i
$902$	28.0654	−	28.0654i	0.934477	−	0.934477i
$903$		0			0
$904$			8.95913i			0.297976i
$905$	−15.4980	+	10.9459i	−0.515170	+	0.363854i
$906$		0			0
$907$	−22.8743	−	22.8743i	−0.759530	−	0.759530i	0.216707	−	0.976237i	$-0.430468\pi$
$907$	−22.8743	−	22.8743i	−0.759530	−	0.759530i	−0.976237	+	0.216707i	$0.930468\pi$
$908$	−34.4198	−	34.4198i	−1.14226	−	1.14226i
$909$		0			0
$910$	−21.4735	−	2.43297i	−0.711840	−	0.0806523i
$911$	−24.7867			−0.821220			−0.410610	−	0.911811i	$-0.634684\pi$
$911$	−24.7867			−0.821220			−0.410610	+	0.911811i	$0.634684\pi$
$912$		0			0
$913$	13.0639	+	13.0639i	0.432351	+	0.432351i
$914$		−	33.3752i		−	1.10395i
$915$		0			0
$916$		−	70.3176i		−	2.32336i
$917$	−16.4512	+	18.4664i	−0.543265	+	0.609814i
$918$		0			0
$919$			14.5898i			0.481272i	0.970615	+	0.240636i	$0.0773560\pi$
$919$			14.5898i			0.481272i	−0.970615	+	0.240636i	$0.922644\pi$
$920$	0.411254	−	0.290460i	0.0135587	−	0.00957619i
$921$		0			0
$922$	44.6283	−	44.6283i	1.46976	−	1.46976i
$923$	−18.7860	−	18.7860i	−0.618349	−	0.618349i
$924$		0			0
$925$	4.69511	−	2.23598i	0.154374	−	0.0735187i
$926$	−22.9276			−0.753447
$927$		0			0
$928$	1.73104	−	1.73104i	0.0568243	−	0.0568243i
$929$	25.1526			0.825229			0.412615	−	0.910906i	$-0.364616\pi$
$929$	25.1526			0.825229			0.412615	+	0.910906i	$0.364616\pi$
$930$		0			0
$931$	4.84585	+	41.8414i	0.158816	+	1.37130i
$932$	11.6313	+	11.6313i	0.380996	+	0.380996i
$933$		0			0
$934$	5.38676			0.176260
$935$	39.5207	+	6.80314i	1.29246	+	0.222487i
$936$		0			0
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	−0.0711778	−	0.997464i	$-0.522676\pi$
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	0.997464	+	0.0711778i	$0.0226758\pi$
$938$	17.9722	−	20.1738i	0.586815	−	0.658699i
$939$		0			0
$940$	0.726106	−	4.21808i	0.0236830	−	0.137579i
$941$		−	0.106973i		−	0.00348721i	−0.999998	−	0.00174360i	$-0.999445\pi$
$941$		−	0.106973i		−	0.00348721i	0.999998	−	0.00174360i	$-0.000555007\pi$
$942$		0			0
$943$	1.23987	+	1.23987i	0.0403756	+	0.0403756i
$944$	23.5938			0.767914
$945$		0			0
$946$	−2.42494			−0.0788417
$947$	−17.9671	−	17.9671i	−0.583851	−	0.583851i	0.352108	−	0.935959i	$-0.385465\pi$
$947$	−17.9671	−	17.9671i	−0.583851	−	0.583851i	−0.935959	+	0.352108i	$0.885465\pi$
$948$		0			0
$949$			24.5940i			0.798354i
$950$	57.1759	−	27.2293i	1.85503	−	0.883434i
$951$		0			0
$952$	−10.7057	+	12.0171i	−0.346973	+	0.389477i
$953$	−31.8008	+	31.8008i	−1.03013	+	1.03013i	−0.0305973	+	0.999532i	$0.509741\pi$
$953$	−31.8008	+	31.8008i	−1.03013	+	1.03013i	−0.999532	+	0.0305973i	$0.990259\pi$
$954$		0			0
$955$	−2.49987	−	3.53950i	−0.0808940	−	0.114536i
$956$	39.3189			1.27166
$957$		0			0
$958$	6.09425	+	6.09425i	0.196896	+	0.196896i
$959$	1.62111	+	28.0884i	0.0523483	+	0.907021i
$960$		0			0
$961$	−21.6175			−0.697339
$962$	−2.68650	+	2.68650i	−0.0866162	+	0.0866162i
$963$		0			0
$964$	27.6372			0.890134
$965$	−24.3951	−	4.19940i	−0.785305	−	0.135183i
$966$		0			0
$967$	0.210995	+	0.210995i	0.00678513	+	0.00678513i	0.710491	−	0.703706i	$-0.248473\pi$
$967$	0.210995	+	0.210995i	0.00678513	+	0.00678513i	−0.703706	+	0.710491i	$0.748473\pi$
$968$	−2.47429	+	2.47429i	−0.0795267	+	0.0795267i
$969$		0			0
$970$	33.9507	+	48.0698i	1.09009	+	1.54343i
$971$		−	54.1165i		−	1.73668i	−0.495969	−	0.868340i	$-0.665187\pi$
$971$		−	54.1165i		−	1.73668i	0.495969	−	0.868340i	$-0.334813\pi$
$972$		0			0
$973$	−15.3873	−	13.7081i	−0.493295	−	0.439462i
$974$			30.6752i			0.982896i
$975$		0			0
$976$			16.3450i			0.523192i
$977$	−25.0981	−	25.0981i	−0.802958	−	0.802958i	0.180599	−	0.983557i	$-0.442197\pi$
$977$	−25.0981	−	25.0981i	−0.802958	−	0.802958i	−0.983557	+	0.180599i	$0.942197\pi$
$978$		0			0
$979$	−18.4693			−0.590283
$980$	−25.3770	−	28.3437i	−0.810638	−	0.905407i
$981$		0			0
$982$	−12.7398	−	12.7398i	−0.406545	−	0.406545i
$983$	1.23358	+	1.23358i	0.0393451	+	0.0393451i	0.726506	−	0.687161i	$-0.241143\pi$
$983$	1.23358	+	1.23358i	0.0393451	+	0.0393451i	−0.687161	+	0.726506i	$0.741143\pi$
$984$		0			0
$985$	−4.56409	+	26.5136i	−0.145424	+	0.844795i
$986$		−	4.30761i		−	0.137182i
$987$		0			0
$988$	−17.9474	+	17.9474i	−0.570982	+	0.570982i
$989$		−	0.107128i		−	0.00340648i
$990$		0			0
$991$	48.9637			1.55538			0.777691	−	0.628647i	$-0.216391\pi$
$991$	48.9637			1.55538			0.777691	+	0.628647i	$0.216391\pi$
$992$	−41.1842	+	41.1842i	−1.30760	+	1.30760i
$993$		0			0
$994$	−4.91225	−	85.1129i	−0.155807	−	2.69962i
$995$	−4.19838	−	5.94437i	−0.133098	−	0.188449i
$996$		0			0
$997$	11.9844	−	11.9844i	0.379551	−	0.379551i	−0.491389	−	0.870940i	$-0.663511\pi$
$997$	11.9844	−	11.9844i	0.379551	−	0.379551i	0.870940	+	0.491389i	$0.163511\pi$
$998$	35.3585	−	35.3585i	1.11926	−	1.11926i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.e.307.2		16
3.2	odd	2		105.2.m.a.97.8	yes	16
5.3	odd	4	inner	315.2.p.e.118.1		16
7.6	odd	2	inner	315.2.p.e.307.1		16
12.11	even	2		1680.2.cz.d.97.1		16
15.2	even	4		525.2.m.b.118.2		16
15.8	even	4		105.2.m.a.13.7	✓	16
15.14	odd	2		525.2.m.b.307.1		16
21.2	odd	6		735.2.v.a.472.7		32
21.5	even	6		735.2.v.a.472.8		32
21.11	odd	6		735.2.v.a.607.2		32
21.17	even	6		735.2.v.a.607.1		32
21.20	even	2		105.2.m.a.97.7	yes	16
35.13	even	4	inner	315.2.p.e.118.2		16
60.23	odd	4		1680.2.cz.d.433.8		16
84.83	odd	2		1680.2.cz.d.97.8		16
105.23	even	12		735.2.v.a.178.1		32
105.38	odd	12		735.2.v.a.313.7		32
105.53	even	12		735.2.v.a.313.8		32
105.62	odd	4		525.2.m.b.118.1		16
105.68	odd	12		735.2.v.a.178.2		32
105.83	odd	4		105.2.m.a.13.8	yes	16
105.104	even	2		525.2.m.b.307.2		16
420.83	even	4		1680.2.cz.d.433.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	15.8	even	4
105.2.m.a.13.8	yes	16	105.83	odd	4
105.2.m.a.97.7	yes	16	21.20	even	2
105.2.m.a.97.8	yes	16	3.2	odd	2
315.2.p.e.118.1		16	5.3	odd	4	inner
315.2.p.e.118.2		16	35.13	even	4	inner
315.2.p.e.307.1		16	7.6	odd	2	inner
315.2.p.e.307.2		16	1.1	even	1	trivial
525.2.m.b.118.1		16	105.62	odd	4
525.2.m.b.118.2		16	15.2	even	4
525.2.m.b.307.1		16	15.14	odd	2
525.2.m.b.307.2		16	105.104	even	2
735.2.v.a.178.1		32	105.23	even	12
735.2.v.a.178.2		32	105.68	odd	12
735.2.v.a.313.7		32	105.38	odd	12
735.2.v.a.313.8		32	105.53	even	12
735.2.v.a.472.7		32	21.2	odd	6
735.2.v.a.472.8		32	21.5	even	6
735.2.v.a.607.1		32	21.17	even	6
735.2.v.a.607.2		32	21.11	odd	6
1680.2.cz.d.97.1		16	12.11	even	2
1680.2.cz.d.97.8		16	84.83	odd	2
1680.2.cz.d.433.1		16	420.83	even	4
1680.2.cz.d.433.8		16	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(1.28999 + 1.82645i) q^{5} +(-1.97552 - 1.75993i) q^{7} +(0.640825 - 0.640825i) q^{8} +O(q^{10})\)	\(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(1.28999 + 1.82645i) q^{5} +(-1.97552 - 1.75993i) q^{7} +(0.640825 - 0.640825i) q^{8} +(0.798469 - 4.63845i) q^{10} +2.67187 q^{11} +(1.22714 + 1.22714i) q^{13} +(0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(4.74624 - 4.74624i) q^{17} +6.01729 q^{19} +(-4.43929 + 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} -3.65291i q^{26} +(4.27759 - 4.80159i) q^{28} +0.304889i q^{29} -7.25379i q^{31} +(-5.67761 - 5.67761i) q^{32} -14.1284 q^{34} +(0.666037 - 5.87847i) q^{35} +(-0.735441 - 0.735441i) q^{37} +(-8.95602 - 8.95602i) q^{38} +(1.99709 + 0.343782i) q^{40} +7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(-0.556866 + 0.556866i) q^{47} +(0.805321 + 6.95352i) q^{49} +(9.50193 - 4.52517i) q^{50} +(-2.98263 + 2.98263i) q^{52} +(4.99031 - 4.99031i) q^{53} +(3.44668 + 4.88005i) q^{55} +(-2.39376 + 0.138155i) q^{56} +(0.453791 - 0.453791i) q^{58} +7.98837 q^{59} +5.53409i q^{61} +(-10.7964 + 10.7964i) q^{62} +10.9939i q^{64} +(-0.658323 + 3.82432i) q^{65} +(-3.43055 - 3.43055i) q^{67} +(11.5360 + 11.5360i) q^{68} +(-9.74071 + 7.75808i) q^{70} -15.3087 q^{71} +(10.0208 + 10.0208i) q^{73} +2.18923i q^{74} +14.6253i q^{76} +(-5.27832 - 4.70230i) q^{77} -11.2973i q^{79} +(3.81000 + 5.39447i) q^{80} +(10.5040 - 10.5040i) q^{82} +(4.88941 + 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} -0.907583 q^{86} +(1.71220 - 1.71220i) q^{88} -6.91251 q^{89} +(-0.264559 - 4.58392i) q^{91} +(0.427009 + 0.427009i) q^{92} +1.65766 q^{94} +(7.76222 + 10.9903i) q^{95} +(-8.84137 + 8.84137i) q^{97} +(9.15086 - 11.5481i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 - 24 * q^8	\( 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

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