LMFDB - Embedded newform 315.2.p.e.307.1

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			307.1
Root			$-0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	315.307
Dual form			315.2.p.e.118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +(-1.75993 - 1.97552i) q^{7} +(0.640825 - 0.640825i) q^{8} +O(q^{10})$	\(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +(-1.75993 - 1.97552i) q^{7} +(0.640825 - 0.640825i) q^{8} +(-0.798469 + 4.63845i) q^{10} +2.67187 q^{11} +(-1.22714 - 1.22714i) q^{13} +(-0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(-4.74624 + 4.74624i) q^{17} -6.01729 q^{19} +(4.43929 - 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +3.65291i q^{26} +(4.80159 - 4.27759i) q^{28} +0.304889i q^{29} +7.25379i q^{31} +(-5.67761 - 5.67761i) q^{32} +14.1284 q^{34} +(-1.33791 + 5.76281i) q^{35} +(-0.735441 - 0.735441i) q^{37} +(8.95602 + 8.95602i) q^{38} +(-1.99709 - 0.343782i) q^{40} -7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(0.556866 - 0.556866i) q^{47} +(-0.805321 + 6.95352i) q^{49} +(9.50193 - 4.52517i) q^{50} +(2.98263 - 2.98263i) q^{52} +(4.99031 - 4.99031i) q^{53} +(-3.44668 - 4.88005i) q^{55} +(-2.39376 - 0.138155i) q^{56} +(0.453791 - 0.453791i) q^{58} -7.98837 q^{59} -5.53409i q^{61} +(10.7964 - 10.7964i) q^{62} +10.9939i q^{64} +(-0.658323 + 3.82432i) q^{65} +(-3.43055 - 3.43055i) q^{67} +(-11.5360 - 11.5360i) q^{68} +(10.5686 - 6.58594i) q^{70} -15.3087 q^{71} +(-10.0208 - 10.0208i) q^{73} +2.18923i q^{74} -14.6253i q^{76} +(-4.70230 - 5.27832i) q^{77} -11.2973i q^{79} +(-3.81000 - 5.39447i) q^{80} +(-10.5040 + 10.5040i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} -0.907583 q^{86} +(1.71220 - 1.71220i) q^{88} +6.91251 q^{89} +(-0.264559 + 4.58392i) q^{91} +(0.427009 + 0.427009i) q^{92} -1.65766 q^{94} +(7.76222 + 10.9903i) q^{95} +(8.84137 - 8.84137i) q^{97} +(11.5481 - 9.15086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−1.75993	−	1.97552i	−0.665189	−	0.746675i
$7$	−1.75993	−	1.97552i	−0.665189	−	0.746675i
$8$	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	0.516150	−	0.856498i	$-0.327365\pi$
$13$	−1.22714	−	1.22714i	−0.340348	−	0.340348i	−0.856498	+	0.516150i	$0.827365\pi$
$14$	−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	$0.552700\pi$
$17$	−4.74624	+	4.74624i	−1.15113	+	1.15113i	−0.986326	+	0.164807i	$0.947300\pi$
$18$		0			0
$19$	−6.01729			−1.38046			−0.690231	−	0.723589i	$-0.742491\pi$
$19$	−6.01729			−1.38046			−0.690231	+	0.723589i	$0.742491\pi$
$20$	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
$28$	4.80159	−	4.27759i	0.907416	−	0.808389i
$29$			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	$0.225822\pi$
$31$			7.25379i			1.30282i	−0.758726	+	0.651410i	$0.774178\pi$
$32$	−5.67761	−	5.67761i	−1.00367	−	1.00367i
$33$		0			0
$34$	14.1284			2.42301
$35$	−1.33791	+	5.76281i	−0.226148	+	0.974093i
$36$		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	$-0.814213\pi$
$41$		−	7.05736i		−	1.10217i	0.834447	−	0.551087i	$-0.185787\pi$
$42$		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	−0.665326	−	0.746553i	$-0.731707\pi$
$47$	0.556866	−	0.556866i	0.0812273	−	0.0812273i	0.746553	+	0.665326i	$0.231707\pi$
$48$		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	$-0.674068\pi$
$59$	−7.98837			−1.04000			−0.519999	+	0.854167i	$0.674068\pi$
$60$		0			0
$61$		−	5.53409i		−	0.708567i	−0.935138	−	0.354284i	$-0.884725\pi$
$61$		−	5.53409i		−	0.708567i	0.935138	−	0.354284i	$-0.115275\pi$
$62$	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
$70$	10.5686	−	6.58594i	1.26319	−	0.787170i
$71$	−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	$-0.938722\pi$
$73$	−10.0208	−	10.0208i	−1.17285	−	1.17285i	−0.191323	−	0.981527i	$-0.561278\pi$
$74$			2.18923i			0.254493i
$75$		0			0
$76$		−	14.6253i		−	1.67764i
$77$	−4.70230	−	5.27832i	−0.535876	−	0.601521i
$78$		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	0.385871	−	0.922553i	$-0.373901\pi$
$83$	−4.88941	−	4.88941i	−0.536682	−	0.536682i	−0.922553	+	0.385871i	$0.873901\pi$
$84$		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	$-0.380603\pi$
$89$	6.91251			0.732725			0.366363	+	0.930472i	$0.380603\pi$
$90$		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	−0.0975276	−	0.995233i	$-0.531093\pi$
$97$	8.84137	−	8.84137i	0.897705	−	0.897705i	0.995233	+	0.0975276i	$0.0310934\pi$
$98$	11.5481	−	9.15086i	1.16654	−	0.924376i
$99$		0			0
$100$	−11.4533	−	4.06357i	−1.14533	−	0.406357i
$101$		−	7.22962i		−	0.719374i	−0.933073	−	0.359687i	$-0.882883\pi$
$101$		−	7.22962i		−	0.719374i	0.933073	−	0.359687i	$-0.117117\pi$
$102$		0			0
$103$	6.94538	+	6.94538i	0.684349	+	0.684349i	0.960977	−	0.276628i	$-0.0892171\pi$
$103$	6.94538	+	6.94538i	0.684349	+	0.684349i	−0.276628	+	0.960977i	$0.589217\pi$
$104$	−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
$112$	−5.19798	−	5.83473i	−0.491163	−	0.551330i
$113$	−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	$0.133897\pi$
$131$			9.34764i			0.816707i	−0.912824	+	0.408353i	$0.866103\pi$
$132$		0			0
$133$	10.5900	+	11.8873i	0.918268	+	1.03076i
$134$			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	$-0.607159\pi$
$139$	−7.78902			−0.660656			−0.330328	+	0.943866i	$0.607159\pi$
$140$	−14.0068	−	3.25186i	−1.18379	−	0.274832i
$141$		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	−0.788633	−	0.614864i	$-0.789211\pi$
$157$	−2.17731	+	2.17731i	−0.173768	+	0.173768i	0.614864	+	0.788633i	$0.289211\pi$
$158$	−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	−0.905870	−	0.423555i	$-0.860782\pi$
$167$	−6.23288	+	6.23288i	−0.482315	+	0.482315i	0.423555	+	0.905870i	$0.360782\pi$
$168$		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	0.915952	−	0.401288i	$-0.131437\pi$
$173$	6.76935	+	6.76935i	0.514664	+	0.514664i	−0.401288	+	0.915952i	$0.631437\pi$
$174$		0			0
$175$	12.2514	−	4.99032i	0.926119	−	0.377233i
$176$	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	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	7.21638	−	6.42885i	0.534913	−	0.476538i
$183$		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	$-0.463199\pi$
$199$	3.25460			0.230712			0.115356	+	0.993324i	$0.463199\pi$
$200$	1.94832	+	4.09107i	0.137767	+	0.289283i
$201$		0			0
$202$	−10.7604	+	10.7604i	−0.757101	+	0.757101i
$203$	0.602314	−	0.536583i	0.0422741	−	0.0376607i
$204$		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
$217$	14.3300	−	12.7661i	0.972782	−	0.866622i
$218$	−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	0.843730	−	0.536768i	$-0.180355\pi$
$223$	4.58392	+	4.58392i	0.306962	+	0.306962i	−0.536768	+	0.843730i	$0.680355\pi$
$224$	−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	−0.0583764	−	0.998295i	$-0.518592\pi$
$227$	14.1613	−	14.1613i	0.939918	−	0.939918i	0.998295	+	0.0583764i	$0.0185924\pi$
$228$		0			0
$229$	28.9307			1.91180			0.955898	−	0.293699i	$-0.0948864\pi$
$229$	28.9307			1.91180			0.955898	+	0.293699i	$0.0948864\pi$
$230$	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
$238$	−24.8650	−	27.9109i	−1.61176	−	1.80920i
$239$		−	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	$0.119351\pi$
$241$			11.3707i			0.732454i	−0.930526	+	0.366227i	$0.880649\pi$
$242$	5.74679	+	5.74679i	0.369418	+	0.369418i
$243$		0			0
$244$	13.4509			0.861105
$245$	13.7391	−	7.49906i	0.877762	−	0.479098i
$246$		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	$0.0703944\pi$
$251$			6.95039i			0.438705i	−0.975646	+	0.219352i	$0.929606\pi$
$252$		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	−0.318570	−	0.947899i	$-0.603203\pi$
$257$	10.0889	−	10.0889i	0.629329	−	0.629329i	0.947899	+	0.318570i	$0.103203\pi$
$258$		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	$-0.656788\pi$
$269$	−15.5119			−0.945775			−0.472888	+	0.881123i	$0.656788\pi$
$270$		0			0
$271$		−	13.3418i		−	0.810458i	−0.914215	−	0.405229i	$-0.867192\pi$
$271$		−	13.3418i		−	0.810458i	0.914215	−	0.405229i	$-0.132808\pi$
$272$	−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
$280$	2.83559	+	4.55032i	0.169459	+	0.271934i
$281$	−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	0.999429	−	0.0338017i	$-0.0107615\pi$
$283$	16.2444	+	16.2444i	0.965627	+	0.965627i	−0.0338017	+	0.999429i	$0.510761\pi$
$284$		−	37.2087i		−	2.20793i
$285$		0			0
$286$			9.76010i			0.577127i
$287$	−13.9419	+	12.4204i	−0.822966	+	0.733155i
$288$		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	0.632951	−	0.774192i	$-0.281843\pi$
$293$	−2.41765	−	2.41765i	−0.141240	−	0.141240i	−0.774192	+	0.632951i	$0.781843\pi$
$294$		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	−0.882319	−	0.470652i	$-0.844019\pi$
$307$	−7.21300	+	7.21300i	−0.411667	+	0.411667i	0.470652	+	0.882319i	$0.344019\pi$
$308$	12.8292	−	11.4292i	0.731014	−	0.651238i
$309$		0			0
$310$	−33.6463	−	5.79193i	−1.91098	−	0.328959i
$311$			10.2542i			0.581460i	0.956805	+	0.290730i	$0.0938981\pi$
$311$			10.2542i			0.581460i	−0.956805	+	0.290730i	$0.906102\pi$
$312$		0			0
$313$	−22.0904	−	22.0904i	−1.24862	−	1.24862i	−0.956329	−	0.292293i	$-0.905582\pi$
$313$	−22.0904	−	22.0904i	−1.24862	−	1.24862i	−0.292293	−	0.956329i	$-0.594418\pi$
$314$	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
$322$	0.920387	+	1.03313i	0.0512912	+	0.0575743i
$323$	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
$343$	15.1541	−	10.6468i	0.818244	−	0.574871i
$344$		−	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	$-0.476368\pi$
$349$	2.77139			0.148349			0.0741746	+	0.997245i	$0.476368\pi$
$350$	−25.6622	−	10.8072i	−1.37170	−	0.577672i
$351$		0			0
$352$	−15.1699	−	15.1699i	−0.808556	−	0.808556i
$353$	−0.970568	−	0.970568i	−0.0516581	−	0.0516581i	0.680806	−	0.732464i	$-0.261630\pi$
$353$	−0.970568	−	0.970568i	−0.0516581	−	0.0516581i	−0.732464	+	0.680806i	$0.761630\pi$
$354$		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	−0.959723	−	0.280948i	$-0.909351\pi$
$367$	−13.0035	+	13.0035i	−0.678776	+	0.678776i	0.280948	+	0.959723i	$0.409351\pi$
$368$	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	0.697063	−	0.717010i	$-0.254490\pi$
$383$	−0.390382	−	0.390382i	−0.0199476	−	0.0199476i	−0.717010	+	0.697063i	$0.754490\pi$
$384$		0			0
$385$	−3.57472	+	15.3975i	−0.182185	+	0.784729i
$386$	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
$392$	3.93992	+	4.97206i	0.198996	+	0.251127i
$393$		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	−0.130109	−	0.991500i	$-0.541533\pi$
$397$	17.1631	−	17.1631i	0.861391	−	0.861391i	0.991500	+	0.130109i	$0.0415327\pi$
$398$	−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	$-0.479187\pi$
$409$	2.64278			0.130677			0.0653386	+	0.997863i	$0.479187\pi$
$410$	32.7352	+	5.63508i	1.61668	+	0.278297i
$411$		0			0
$412$	−16.8811	+	16.8811i	−0.831672	+	0.831672i
$413$	14.0589	+	15.7812i	0.691795	+	0.776540i
$414$		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	$-0.421211\pi$
$419$	10.0302			0.490007			0.245003	+	0.969522i	$0.421211\pi$
$420$		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
$427$	−10.9327	+	9.73958i	−0.529069	+	0.471332i
$428$	−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	0.304935	−	0.952373i	$-0.401365\pi$
$433$	−13.4723	−	13.4723i	−0.647438	−	0.647438i	−0.952373	+	0.304935i	$0.901365\pi$
$434$	−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	$-0.709955\pi$
$439$	−25.6790			−1.22559			−0.612795	+	0.790242i	$0.709955\pi$
$440$	−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
$448$	21.7185	−	19.3484i	1.02610	−	0.914124i
$449$			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
$455$	8.71359	−	5.42999i	0.408500	−	0.254562i
$456$		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	$-0.753959\pi$
$461$		−	29.9845i		−	1.39652i	0.715846	−	0.698259i	$-0.246041\pi$
$462$		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	−0.663997	−	0.747735i	$-0.731141\pi$
$467$	1.80961	−	1.80961i	0.0837386	−	0.0837386i	0.747735	+	0.663997i	$0.231141\pi$
$468$		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	$-0.470181\pi$
$479$	4.09455			0.187085			0.0935425	+	0.995615i	$0.470181\pi$
$480$		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
$490$	−31.6105	−	9.28761i	−1.42802	−	0.419571i
$491$	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
$497$	26.9423	+	30.2427i	1.20853	+	1.35657i
$498$		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	0.182786	−	0.983153i	$-0.441489\pi$
$503$	−17.9504	−	17.9504i	−0.800367	−	0.800367i	−0.983153	+	0.182786i	$0.941489\pi$
$504$		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	$-0.377818\pi$
$509$	16.8977			0.748979			0.374489	+	0.927231i	$0.377818\pi$
$510$		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
$518$	4.32486	−	3.85289i	0.190024	−	0.169286i
$519$		0			0
$520$	2.02885	+	2.87259i	0.0889708	+	0.125971i
$521$		−	7.88477i		−	0.345438i	−0.984971	−	0.172719i	$-0.944745\pi$
$521$		−	7.88477i		−	0.345438i	0.984971	−	0.172719i	$-0.0552552\pi$
$522$		0			0
$523$	1.23149	+	1.23149i	0.0538493	+	0.0538493i	0.733519	−	0.679669i	$-0.237877\pi$
$523$	1.23149	+	1.23149i	0.0538493	+	0.0538493i	−0.679669	+	0.733519i	$0.737877\pi$
$524$	−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
$532$	−28.8926	+	25.7395i	−1.25265	+	1.11595i
$533$	−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
$553$	−22.3179	+	19.8823i	−0.949054	+	0.845483i
$554$			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
$560$	−3.95154	+	17.0206i	−0.166983	+	0.719251i
$561$		0			0
$562$	20.1760	+	20.1760i	0.851073	+	0.851073i
$563$	23.7521	+	23.7521i	1.00103	+	1.00103i	0.999999	+	0.00103054i	$0.000328032\pi$
$563$	23.7521	+	23.7521i	1.00103	+	1.00103i	0.00103054	+	0.999999i	$0.499672\pi$
$564$		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	$0.586569\pi$
$577$	−29.5905	+	29.5905i	−1.23187	+	1.23187i	−0.963245	+	0.268625i	$0.913431\pi$
$578$	−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	$-0.466396\pi$
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.994433	−	0.105375i	$-0.0336041\pi$
$588$		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	0.946484	−	0.322751i	$-0.104608\pi$
$593$	15.1889	+	15.1889i	0.623733	+	0.623733i	−0.322751	+	0.946484i	$0.604608\pi$
$594$		0			0
$595$	−21.0017	−	33.7017i	−0.860985	−	1.38164i
$596$	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	$-0.849371\pi$
$601$		−	22.3458i		−	0.911503i	0.890107	−	0.455752i	$-0.150629\pi$
$602$	1.59728	+	1.79294i	0.0651002	+	0.0730749i
$603$		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	−0.695320	−	0.718700i	$-0.744737\pi$
$607$	0.576027	−	0.576027i	0.0233802	−	0.0233802i	0.718700	+	0.695320i	$0.244737\pi$
$608$	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	$-0.204016\pi$
$619$	39.8840			1.60307			0.801536	+	0.597946i	$0.204016\pi$
$620$	22.7434	+	32.2017i	0.913396	+	1.29325i
$621$		0			0
$622$	15.2621	−	15.2621i	0.611954	−	0.611954i
$623$	−12.1655	−	13.6558i	−0.487401	−	0.547107i
$624$		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
$637$	9.52120	−	7.54472i	0.377244	−	0.298933i
$638$	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	$-0.896961\pi$
$643$	−32.1062	−	32.1062i	−1.26614	−	1.26614i	−0.318082	−	0.948063i	$-0.603039\pi$
$644$	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	−0.405745	−	0.913986i	$-0.632988\pi$
$647$	12.9277	−	12.9277i	0.508241	−	0.508241i	0.913986	+	0.405745i	$0.132988\pi$
$648$		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
$658$	2.91736	+	3.27473i	0.113730	+	0.127662i
$659$			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	$0.186878\pi$
$661$			28.4837i			1.10789i	−0.832554	+	0.553943i	$0.813122\pi$
$662$	−1.87995	−	1.87995i	−0.0730662	−	0.0730662i
$663$		0			0
$664$	−6.26651			−0.243188
$665$	8.05059	−	34.6765i	0.312188	−	1.34470i
$666$		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	−0.729734	−	0.683731i	$-0.760356\pi$
$677$	−1.19694	+	1.19694i	−0.0460022	+	0.0460022i	0.683731	+	0.729734i	$0.260356\pi$
$678$		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	$-0.708724\pi$
$691$		−	41.6703i		−	1.58521i	0.609735	−	0.792606i	$-0.291276\pi$
$692$	−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
$700$	12.1292	+	29.7777i	0.458442	+	1.12549i
$701$	−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
$707$	−14.2822	+	12.7236i	−0.537138	+	0.478520i
$708$		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	$-0.688338\pi$
$719$	−29.9117			−1.11552			−0.557758	+	0.830003i	$0.688338\pi$
$720$		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	$-0.463797\pi$
$727$	29.8488	−	29.8488i	1.10703	−	1.10703i	0.993539	−	0.113491i	$-0.0362034\pi$
$728$	2.76795	+	3.10702i	0.102587	+	0.115154i
$729$		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	0.774908	−	0.632074i	$-0.217796\pi$
$733$	3.86707	+	3.86707i	0.142834	+	0.142834i	−0.632074	+	0.774908i	$0.717796\pi$
$734$	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
$742$	26.1436	+	29.3462i	0.959763	+	1.07733i
$743$	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	$-0.800922\pi$
$761$		−	32.3002i		−	1.17088i	0.810716	−	0.585440i	$-0.199078\pi$
$762$		0			0
$763$	−11.7613	+	10.4778i	−0.425787	+	0.379320i
$764$		−	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	$-0.607831\pi$
$769$	−18.4310			−0.664640			−0.332320	+	0.943167i	$0.607831\pi$
$770$	28.2379	−	17.5968i	1.01762	−	0.634144i
$771$		0			0
$772$	−19.0260	−	19.0260i	−0.684761	−	0.684761i
$773$	17.7963	+	17.7963i	0.640088	+	0.640088i	0.950577	−	0.310489i	$-0.100493\pi$
$773$	17.7963	+	17.7963i	0.640088	+	0.640088i	−0.310489	+	0.950577i	$0.600493\pi$
$774$		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	−0.360160	−	0.932890i	$-0.617278\pi$
$787$	16.0671	−	16.0671i	0.572730	−	0.572730i	0.932890	+	0.360160i	$0.117278\pi$
$788$	−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	−0.995817	−	0.0913664i	$-0.970877\pi$
$797$	−25.5337	+	25.5337i	−0.904451	+	0.904451i	0.0913664	+	0.995817i	$0.470877\pi$
$798$		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
$805$	0.777385	+	1.24748i	0.0273992	+	0.0439680i
$806$	−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	$0.205398\pi$
$811$			34.2545i			1.20284i	−0.798933	+	0.601420i	$0.794602\pi$
$812$	1.30419	+	1.46395i	0.0457682	+	0.0513747i
$813$		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	$-0.336150\pi$
$829$	28.3500			0.984636			0.492318	+	0.870415i	$0.336150\pi$
$830$	26.5833	−	18.7752i	0.922720	−	0.651698i
$831$		0			0
$832$	13.4910	−	13.4910i	0.467717	−	0.467717i
$833$	−29.1809	−	36.8254i	−1.01106	−	1.27592i
$834$		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	$-0.308350\pi$
$839$	32.8100			1.13273			0.566364	+	0.824156i	$0.308350\pi$
$840$		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
$847$	6.79526	+	7.62767i	0.233488	+	0.262090i
$848$	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	0.920737	−	0.390184i	$-0.127589\pi$
$853$	15.4954	+	15.4954i	0.530553	+	0.530553i	−0.390184	+	0.920737i	$0.627589\pi$
$854$	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	−0.942742	−	0.333523i	$-0.891762\pi$
$857$	−17.8346	+	17.8346i	−0.609218	+	0.609218i	0.333523	+	0.942742i	$0.391762\pi$
$858$		0			0
$859$	−17.2711			−0.589283			−0.294641	−	0.955608i	$-0.595200\pi$
$859$	−17.2711			−0.589283			−0.294641	+	0.955608i	$0.595200\pi$
$860$	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
$868$	31.0288	+	34.8298i	1.05318	+	1.18220i
$869$		−	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
$875$	−24.9187	−	15.9392i	−0.842407	−	0.538842i
$876$		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	$0.205894\pi$
$881$			35.7762i			1.20533i	−0.797994	+	0.602665i	$0.794106\pi$
$882$		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	−0.694703	−	0.719297i	$-0.744464\pi$
$887$	0.732491	−	0.732491i	0.0245946	−	0.0245946i	0.719297	+	0.694703i	$0.244464\pi$
$888$		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
$910$	−21.0510	−	4.88726i	−0.697835	−	0.162011i
$911$	−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
$917$	18.4664	−	16.4512i	0.609814	−	0.543265i
$918$		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	$-0.635384\pi$
$929$	−25.1526			−0.825229			−0.412615	+	0.910906i	$0.635384\pi$
$930$		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	−0.997464	−	0.0711778i	$-0.977324\pi$
$937$	−28.3540	+	28.3540i	−0.926286	+	0.926286i	0.0711778	+	0.997464i	$0.477324\pi$
$938$	20.1738	−	17.9722i	0.658699	−	0.586815i
$939$		0			0
$940$	0.726106	−	4.21808i	0.0236830	−	0.137579i
$941$			0.106973i			0.00348721i	0.999998	+	0.00174360i	$0.000555007\pi$
$941$			0.106973i			0.00348721i	−0.999998	+	0.00174360i	$0.999445\pi$
$942$		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
$952$	12.0171	−	10.7057i	0.389477	−	0.346973i
$953$	−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	$0.334813\pi$
$971$			54.1165i			1.73668i	−0.495969	+	0.868340i	$0.665187\pi$
$972$		0			0
$973$	13.7081	+	15.3873i	0.439462	+	0.493295i
$974$			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
$980$	18.2269	+	33.3937i	0.582236	+	1.06672i
$981$		0			0
$982$	−12.7398	−	12.7398i	−0.406545	−	0.406545i
$983$	−1.23358	−	1.23358i	−0.0393451	−	0.0393451i	0.687161	−	0.726506i	$-0.258857\pi$
$983$	−1.23358	−	1.23358i	−0.0393451	−	0.0393451i	−0.726506	+	0.687161i	$0.758857\pi$
$984$		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	−0.870940	−	0.491389i	$-0.836489\pi$
$997$	−11.9844	+	11.9844i	−0.379551	+	0.379551i	0.491389	+	0.870940i	$0.336489\pi$
$998$	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.307.1		16
3.2	odd	2		105.2.m.a.97.7	yes	16
5.3	odd	4	inner	315.2.p.e.118.2		16
7.6	odd	2	inner	315.2.p.e.307.2		16
12.11	even	2		1680.2.cz.d.97.8		16
15.2	even	4		525.2.m.b.118.1		16
15.8	even	4		105.2.m.a.13.8	yes	16
15.14	odd	2		525.2.m.b.307.2		16
21.2	odd	6		735.2.v.a.472.8		32
21.5	even	6		735.2.v.a.472.7		32
21.11	odd	6		735.2.v.a.607.1		32
21.17	even	6		735.2.v.a.607.2		32
21.20	even	2		105.2.m.a.97.8	yes	16
35.13	even	4	inner	315.2.p.e.118.1		16
60.23	odd	4		1680.2.cz.d.433.1		16
84.83	odd	2		1680.2.cz.d.97.1		16
105.23	even	12		735.2.v.a.178.2		32
105.38	odd	12		735.2.v.a.313.8		32
105.53	even	12		735.2.v.a.313.7		32
105.62	odd	4		525.2.m.b.118.2		16
105.68	odd	12		735.2.v.a.178.1		32
105.83	odd	4		105.2.m.a.13.7	✓	16
105.104	even	2		525.2.m.b.307.1		16
420.83	even	4		1680.2.cz.d.433.8		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +(-1.75993 - 1.97552i) q^{7} +(0.640825 - 0.640825i) q^{8} +O(q^{10})\)	\(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(-1.28999 - 1.82645i) q^{5} +(-1.75993 - 1.97552i) q^{7} +(0.640825 - 0.640825i) q^{8} +(-0.798469 + 4.63845i) q^{10} +2.67187 q^{11} +(-1.22714 - 1.22714i) q^{13} +(-0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(-4.74624 + 4.74624i) q^{17} -6.01729 q^{19} +(4.43929 - 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +3.65291i q^{26} +(4.80159 - 4.27759i) q^{28} +0.304889i q^{29} +7.25379i q^{31} +(-5.67761 - 5.67761i) q^{32} +14.1284 q^{34} +(-1.33791 + 5.76281i) q^{35} +(-0.735441 - 0.735441i) q^{37} +(8.95602 + 8.95602i) q^{38} +(-1.99709 - 0.343782i) q^{40} -7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(0.556866 - 0.556866i) q^{47} +(-0.805321 + 6.95352i) q^{49} +(9.50193 - 4.52517i) q^{50} +(2.98263 - 2.98263i) q^{52} +(4.99031 - 4.99031i) q^{53} +(-3.44668 - 4.88005i) q^{55} +(-2.39376 - 0.138155i) q^{56} +(0.453791 - 0.453791i) q^{58} -7.98837 q^{59} -5.53409i q^{61} +(10.7964 - 10.7964i) q^{62} +10.9939i q^{64} +(-0.658323 + 3.82432i) q^{65} +(-3.43055 - 3.43055i) q^{67} +(-11.5360 - 11.5360i) q^{68} +(10.5686 - 6.58594i) q^{70} -15.3087 q^{71} +(-10.0208 - 10.0208i) q^{73} +2.18923i q^{74} -14.6253i q^{76} +(-4.70230 - 5.27832i) q^{77} -11.2973i q^{79} +(-3.81000 - 5.39447i) q^{80} +(-10.5040 + 10.5040i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} -0.907583 q^{86} +(1.71220 - 1.71220i) q^{88} +6.91251 q^{89} +(-0.264559 + 4.58392i) q^{91} +(0.427009 + 0.427009i) q^{92} -1.65766 q^{94} +(7.76222 + 10.9903i) q^{95} +(8.84137 - 8.84137i) q^{97} +(11.5481 - 9.15086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 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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