LMFDB - Embedded newform 1680.2.cz.d.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(97,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1680.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.cz (of order $4$, degree $2$, not 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:	$13.4148675396$
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			97.1
Root			$0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	1680.97
Dual form			1680.2.cz.d.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(-1.28999 - 1.82645i) q^{5} +(1.97552 + 1.75993i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.28999 - 1.82645i) q^{5} +(1.97552 + 1.75993i) q^{7} +1.00000i q^{9} +2.67187 q^{11} +(1.22714 + 1.22714i) q^{13} +(-0.379340 + 2.20366i) q^{15} +(-4.74624 + 4.74624i) q^{17} -6.01729 q^{19} +(-0.152445 - 2.64136i) q^{21} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +(0.707107 - 0.707107i) q^{27} -0.304889i q^{29} +7.25379i q^{31} +(-1.88930 - 1.88930i) q^{33} +(0.666037 - 5.87847i) q^{35} +(-0.735441 - 0.735441i) q^{37} -1.73544i q^{39} -7.05736i q^{41} +(-0.304889 + 0.304889i) q^{43} +(1.82645 - 1.28999i) q^{45} +(-0.556866 + 0.556866i) q^{47} +(0.805321 + 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 + 4.99031i) q^{53} +(-3.44668 - 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} +7.98837 q^{59} +5.53409i q^{61} +(-1.75993 + 1.97552i) q^{63} +(0.658323 - 3.82432i) q^{65} +(3.43055 + 3.43055i) q^{67} -0.248455 q^{69} -15.3087 q^{71} +(10.0208 + 10.0208i) q^{73} +(4.51422 - 2.14984i) q^{75} +(5.27832 + 4.70230i) q^{77} +11.2973i q^{79} -1.00000 q^{81} +(4.88941 + 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(-0.215589 + 0.215589i) q^{87} +6.91251 q^{89} +(0.264559 + 4.58392i) q^{91} +(5.12921 - 5.12921i) q^{93} +(7.76222 + 10.9903i) q^{95} +(-8.84137 + 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) $ 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−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			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	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			0
$15$	−0.379340	+	2.20366i	−0.0979452	+	0.568982i
$16$		0			0
$17$	−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	$0.742491\pi$
$20$		0			0
$21$	−0.152445	−	2.64136i	−0.0332662	−	0.576391i
$22$		0			0
$23$	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
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	0.304889i		−	0.0566165i	−0.999599	−	0.0283083i	$-0.990988\pi$
$29$		−	0.304889i		−	0.0566165i	0.999599	−	0.0283083i	$-0.00901200\pi$
$30$		0			0
$31$			7.25379i			1.30282i	0.758726	+	0.651410i	$0.225822\pi$
$31$			7.25379i			1.30282i	−0.758726	+	0.651410i	$0.774178\pi$
$32$		0			0
$33$	−1.88930	−	1.88930i	−0.328885	−	0.328885i
$34$		0			0
$35$	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	$0.777247\pi$
$38$		0			0
$39$		−	1.73544i		−	0.277893i
$40$		0			0
$41$		−	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	−0.729972	−	0.683477i	$-0.760467\pi$
$43$	−0.304889	+	0.304889i	−0.0464952	+	0.0464952i	0.683477	+	0.729972i	$0.260467\pi$
$44$		0			0
$45$	1.82645	−	1.28999i	0.272272	−	0.192300i
$46$		0			0
$47$	−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
$50$		0			0
$51$	6.71220			0.939896
$52$		0			0
$53$	−4.99031	+	4.99031i	−0.685472	+	0.685472i	−0.961228	−	0.275756i	$-0.911072\pi$
$53$	−4.99031	+	4.99031i	−0.685472	+	0.685472i	0.275756	+	0.961228i	$0.411072\pi$
$54$		0			0
$55$	−3.44668	−	4.88005i	−0.464750	−	0.658026i
$56$		0			0
$57$	4.25487	+	4.25487i	0.563571	+	0.563571i
$58$		0			0
$59$	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	$0.884725\pi$
$62$		0			0
$63$	−1.75993	+	1.97552i	−0.221730	+	0.248892i
$64$		0			0
$65$	0.658323	−	3.82432i	0.0816549	−	0.474348i
$66$		0			0
$67$	3.43055	+	3.43055i	0.419109	+	0.419109i	0.884896	−	0.465788i	$-0.154229\pi$
$67$	3.43055	+	3.43055i	0.419109	+	0.419109i	−0.465788	+	0.884896i	$0.654229\pi$
$68$		0			0
$69$	−0.248455			−0.0299104
$70$		0			0
$71$	−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	$0.438722\pi$
$74$		0			0
$75$	4.51422	−	2.14984i	0.521257	−	0.248242i
$76$		0			0
$77$	5.27832	+	4.70230i	0.601521	+	0.535876i
$78$		0			0
$79$			11.2973i			1.27104i	0.772084	+	0.635521i	$0.219215\pi$
$79$			11.2973i			1.27104i	−0.772084	+	0.635521i	$0.780785\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	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			0
$87$	−0.215589	+	0.215589i	−0.0231136	+	0.0231136i
$88$		0			0
$89$	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			0
$93$	5.12921	−	5.12921i	0.531874	−	0.531874i
$94$		0			0
$95$	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	$0.468907\pi$
$98$		0			0
$99$			2.67187i			0.268533i
$100$		0			0
$101$		−	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	$0.589217\pi$
$104$		0			0
$105$	−4.62766	+	3.68575i	−0.451614	+	0.359692i
$106$		0			0
$107$	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	$-0.0920341\pi$
$110$		0			0
$111$			1.04007i			0.0987192i
$112$		0			0
$113$	6.99031	−	6.99031i	0.657593	−	0.657593i	−0.297217	−	0.954810i	$-0.596058\pi$
$113$	6.99031	−	6.99031i	0.657593	−	0.657593i	0.954810	+	0.297217i	$0.0960585\pi$
$114$		0			0
$115$	−0.547509	−	0.0942489i	−0.0510555	−	0.00878876i
$116$		0			0
$117$	−1.22714	+	1.22714i	−0.113449	+	0.113449i
$118$		0			0
$119$	−17.7293	+	1.02324i	−1.62524	+	0.0938002i
$120$		0			0
$121$	−3.86110			−0.351009
$122$		0			0
$123$	−4.99031	+	4.99031i	−0.449961	+	0.449961i
$124$		0			0
$125$	10.7633	−	3.02508i	0.962700	−	0.270571i
$126$		0			0
$127$	−2.86110	−	2.86110i	−0.253882	−	0.253882i	0.568678	−	0.822560i	$-0.307455\pi$
$127$	−2.86110	−	2.86110i	−0.253882	−	0.253882i	−0.822560	+	0.568678i	$0.807455\pi$
$128$		0			0
$129$	0.431179			0.0379632
$130$		0			0
$131$		−	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
$134$		0			0
$135$	−2.20366	−	0.379340i	−0.189661	−	0.0326484i
$136$		0			0
$137$	7.51943	+	7.51943i	0.642428	+	0.642428i	0.951152	−	0.308724i	$-0.0999019\pi$
$137$	7.51943	+	7.51943i	0.642428	+	0.642428i	−0.308724	+	0.951152i	$0.599902\pi$
$138$		0			0
$139$	−7.78902			−0.660656			−0.330328	−	0.943866i	$-0.607159\pi$
$139$	−7.78902			−0.660656			−0.330328	+	0.943866i	$0.607159\pi$
$140$		0			0
$141$	0.787528			0.0663218
$142$		0			0
$143$	3.27877	+	3.27877i	0.274184	+	0.274184i
$144$		0			0
$145$	−0.556866	+	0.393303i	−0.0462452	+	0.0326620i
$146$		0			0
$147$	4.34743	−	5.48633i	0.358570	−	0.452505i
$148$		0			0
$149$			14.2855i			1.17031i	0.810920	+	0.585157i	$0.198967\pi$
$149$			14.2855i			1.17031i	−0.810920	+	0.585157i	$0.801033\pi$
$150$		0			0
$151$	−9.77990			−0.795877			−0.397939	−	0.917412i	$-0.630274\pi$
$151$	−9.77990			−0.795877			−0.397939	+	0.917412i	$0.630274\pi$
$152$		0			0
$153$	−4.74624	−	4.74624i	−0.383711	−	0.383711i
$154$		0			0
$155$	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	$0.210789\pi$
$158$		0			0
$159$	7.05736			0.559685
$160$		0			0
$161$	0.656257	−	0.0378756i	0.0517203	−	0.00298502i
$162$		0			0
$163$	13.6757	−	13.6757i	1.07117	−	1.07117i	0.0739001	−	0.997266i	$-0.476455\pi$
$163$	13.6757	−	13.6757i	1.07117	−	1.07117i	0.997266	−	0.0739001i	$-0.0235446\pi$
$164$		0			0
$165$	−1.01355	+	5.88789i	−0.0789046	+	0.458371i
$166$		0			0
$167$	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
$170$		0			0
$171$		−	6.01729i		−	0.460154i
$172$		0			0
$173$	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
$175$	−11.5959	+	6.36666i	−0.876570	+	0.481274i
$176$		0			0
$177$	−5.64863	−	5.64863i	−0.424577	−	0.424577i
$178$		0			0
$179$		−	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	$0.897877\pi$
$182$		0			0
$183$	3.91319	−	3.91319i	0.289271	−	0.289271i
$184$		0			0
$185$	−0.394541	+	2.29196i	−0.0290072	+	0.168508i
$186$		0			0
$187$	−12.6814	+	12.6814i	−0.927352	+	0.927352i
$188$		0			0
$189$	2.64136	−	0.152445i	0.192130	−	0.0110887i
$190$		0			0
$191$	−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	$0.380444\pi$
$194$		0			0
$195$	−3.16970	+	2.23870i	−0.226987	+	0.160316i
$196$		0			0
$197$	−8.50767	−	8.50767i	−0.606146	−	0.606146i	0.335790	−	0.941937i	$-0.390997\pi$
$197$	−8.50767	−	8.50767i	−0.606146	−	0.606146i	−0.941937	+	0.335790i	$0.890997\pi$
$198$		0			0
$199$	3.25460			0.230712			0.115356	−	0.993324i	$-0.463199\pi$
$199$	3.25460			0.230712			0.115356	+	0.993324i	$0.463199\pi$
$200$		0			0
$201$		−	4.85153i		−	0.342201i
$202$		0			0
$203$	0.536583	−	0.602314i	0.0376607	−	0.0422741i
$204$		0			0
$205$	−12.8900	+	9.10390i	−0.900273	+	0.635844i
$206$		0			0
$207$	0.175684	+	0.175684i	0.0122109	+	0.0122109i
$208$		0			0
$209$	−16.0774			−1.11210
$210$		0			0
$211$	17.2508			1.18759			0.593797	−	0.804615i	$-0.297628\pi$
$211$	17.2508			1.18759			0.593797	+	0.804615i	$0.297628\pi$
$212$		0			0
$213$	10.8249	+	10.8249i	0.741711	+	0.741711i
$214$		0			0
$215$	0.950169	+	0.163563i	0.0648010	+	0.0111549i
$216$		0			0
$217$	−12.7661	+	14.3300i	−0.866622	+	0.972782i
$218$		0			0
$219$		−	14.1716i		−	0.957628i
$220$		0			0
$221$	−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	$0.680355\pi$
$224$		0			0
$225$	−4.71220	−	1.67187i	−0.314147	−	0.111458i
$226$		0			0
$227$	−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			0
$231$	−0.407313	−	7.05736i	−0.0267992	−	0.464340i
$232$		0			0
$233$	−4.78546	+	4.78546i	−0.313506	+	0.313506i	−0.846266	−	0.532760i	$-0.821155\pi$
$233$	−4.78546	+	4.78546i	−0.313506	+	0.313506i	0.532760	+	0.846266i	$0.321155\pi$
$234$		0			0
$235$	1.73544	+	0.298741i	0.113208	+	0.0194877i
$236$		0			0
$237$	7.98837	−	7.98837i	0.518901	−	0.518901i
$238$		0			0
$239$		−	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	$-0.119351\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	11.6614	−	10.4408i	0.745022	−	0.667040i
$246$		0			0
$247$	−7.38407	−	7.38407i	−0.469837	−	0.469837i
$248$		0			0
$249$		−	6.91467i		−	0.438199i
$250$		0			0
$251$		−	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
$254$		0			0
$255$	−8.65865	−	12.2595i	−0.542226	−	0.767722i
$256$		0			0
$257$	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
$260$		0			0
$261$	0.304889			0.0188722
$262$		0			0
$263$	−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
$266$		0			0
$267$	−4.88789	−	4.88789i	−0.299134	−	0.299134i
$268$		0			0
$269$	−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	$-0.132808\pi$
$272$		0			0
$273$	3.05425	−	3.42839i	0.184852	−	0.207496i
$274$		0			0
$275$	−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	$0.777156\pi$
$278$		0			0
$279$	−7.25379			−0.434273
$280$		0			0
$281$	13.5557			0.808664			0.404332	−	0.914612i	$-0.367504\pi$
$281$	13.5557			0.808664			0.404332	+	0.914612i	$0.367504\pi$
$282$		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	$0.510761\pi$
$284$		0			0
$285$	2.28260	−	13.2600i	0.135210	−	0.785457i
$286$		0			0
$287$	12.4204	−	13.9419i	0.733155	−	0.822966i
$288$		0			0
$289$		−	28.0537i		−	1.65021i
$290$		0			0
$291$	12.5036			0.732973
$292$		0			0
$293$	−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			0
$297$	1.88930	−	1.88930i	0.109628	−	0.109628i
$298$		0			0
$299$	0.431179			0.0249357
$300$		0			0
$301$	−1.13890	+	0.0657309i	−0.0656449	+	0.00378867i
$302$		0			0
$303$	−5.11211	+	5.11211i	−0.293683	+	0.293683i
$304$		0			0
$305$	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	$0.344019\pi$
$308$		0			0
$309$		−	9.82225i		−	0.558768i
$310$		0			0
$311$		−	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	$0.405582\pi$
$314$		0			0
$315$	5.87847	+	0.666037i	0.331214	+	0.0375269i
$316$		0			0
$317$	−12.2563	−	12.2563i	−0.688385	−	0.688385i	0.273490	−	0.961875i	$-0.411822\pi$
$317$	−12.2563	−	12.2563i	−0.688385	−	0.688385i	−0.961875	+	0.273490i	$0.911822\pi$
$318$		0			0
$319$		−	0.814625i		−	0.0456102i
$320$		0			0
$321$		−	10.5683i		−	0.589867i
$322$		0			0
$323$	28.5595	−	28.5595i	1.58909	−	1.58909i
$324$		0			0
$325$	−7.83417	+	3.73092i	−0.434561	+	0.206954i
$326$		0			0
$327$	−4.20978	+	4.20978i	−0.232801	+	0.232801i
$328$		0			0
$329$	−2.08014	+	0.120054i	−0.114682	+	0.00661882i
$330$		0			0
$331$	−1.26308			−0.0694252			−0.0347126	−	0.999397i	$-0.511052\pi$
$331$	−1.26308			−0.0694252			−0.0347126	+	0.999397i	$0.511052\pi$
$332$		0			0
$333$	0.735441	−	0.735441i	0.0403019	−	0.0403019i
$334$		0			0
$335$	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	$0.869989\pi$
$338$		0			0
$339$	−9.88579			−0.536922
$340$		0			0
$341$			19.3812i			1.04955i
$342$		0			0
$343$	−10.6468	+	15.1541i	−0.574871	+	0.818244i
$344$		0			0
$345$	0.320503	+	0.453791i	0.0172553	+	0.0244313i
$346$		0			0
$347$	−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	$0.523632\pi$
$350$		0			0
$351$	1.73544			0.0926310
$352$		0			0
$353$	−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
$356$		0			0
$357$	13.2601	+	11.8130i	0.701797	+	0.625209i
$358$		0			0
$359$			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
$362$		0			0
$363$	2.73021	+	2.73021i	0.143299	+	0.143299i
$364$		0			0
$365$	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			0
$369$	7.05736			0.367392
$370$		0			0
$371$	−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	$-0.0233320\pi$
$374$		0			0
$375$	−9.74986	−	5.47176i	−0.503481	−	0.282560i
$376$		0			0
$377$	0.374143	−	0.374143i	0.0192693	−	0.0192693i
$378$		0			0
$379$		−	22.0077i		−	1.13046i	−0.824933	−	0.565230i	$-0.808787\pi$
$379$		−	22.0077i		−	1.13046i	0.824933	−	0.565230i	$-0.191213\pi$
$380$		0			0
$381$			4.04621i			0.207294i
$382$		0			0
$383$	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
$386$		0			0
$387$	−0.304889	−	0.304889i	−0.0154984	−	0.0154984i
$388$		0			0
$389$			25.9300i			1.31470i	0.753584	+	0.657352i	$0.228323\pi$
$389$			25.9300i			1.31470i	−0.753584	+	0.657352i	$0.771677\pi$
$390$		0			0
$391$			1.66768i			0.0843381i
$392$		0			0
$393$	−6.60978	+	6.60978i	−0.333419	+	0.333419i
$394$		0			0
$395$	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	$0.458467\pi$
$398$		0			0
$399$	0.917304	+	15.8938i	0.0459226	+	0.795686i
$400$		0			0
$401$	−12.9418			−0.646281			−0.323140	−	0.946351i	$-0.604739\pi$
$401$	−12.9418			−0.646281			−0.323140	+	0.946351i	$0.604739\pi$
$402$		0			0
$403$	−8.90143	+	8.90143i	−0.443412	+	0.443412i
$404$		0			0
$405$	1.28999	+	1.82645i	0.0640999	+	0.0907572i
$406$		0			0
$407$	−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	$0.520813\pi$
$410$		0			0
$411$		−	10.6341i		−	0.524540i
$412$		0			0
$413$	15.7812	+	14.0589i	0.776540	+	0.691795i
$414$		0			0
$415$	2.62301	−	15.2376i	0.128759	−	0.747982i
$416$		0			0
$417$	5.50767	+	5.50767i	0.269712	+	0.269712i
$418$		0			0
$419$	−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	$0.724927\pi$
$422$		0			0
$423$	−0.556866	−	0.556866i	−0.0270758	−	0.0270758i
$424$		0			0
$425$	−14.4301	−	30.3004i	−0.699965	−	1.46978i
$426$		0			0
$427$	−9.73958	+	10.9327i	−0.471332	+	0.529069i
$428$		0			0
$429$		−	4.63688i		−	0.223870i
$430$		0			0
$431$	−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	$0.598635\pi$
$434$		0			0
$435$	0.671871	+	0.115657i	0.0322138	+	0.00554532i
$436$		0			0
$437$	−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	$0.709955\pi$
$440$		0			0
$441$	−6.95352	+	0.805321i	−0.331120	+	0.0383486i
$442$		0			0
$443$	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
$446$		0			0
$447$	10.1014	−	10.1014i	0.477779	−	0.477779i
$448$		0			0
$449$		−	7.01947i		−	0.331269i	−0.986187	−	0.165635i	$-0.947033\pi$
$449$		−	7.01947i		−	0.331269i	0.986187	−	0.165635i	$-0.0529673\pi$
$450$		0			0
$451$		−	18.8564i		−	0.887912i
$452$		0			0
$453$	6.91544	+	6.91544i	0.324916	+	0.324916i
$454$		0			0
$455$	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	$0.629064\pi$
$458$		0			0
$459$			6.71220i			0.313299i
$460$		0			0
$461$		−	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	−0.863057	−	0.505106i	$-0.831453\pi$
$463$	−7.70220	+	7.70220i	−0.357951	+	0.357951i	0.505106	+	0.863057i	$0.331453\pi$
$464$		0			0
$465$	−15.9849	−	2.75166i	−0.741280	−	0.127605i
$466$		0			0
$467$	−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
$470$		0			0
$471$	−3.07918			−0.141881
$472$		0			0
$473$	−0.814625	+	0.814625i	−0.0374565	+	0.0374565i
$474$		0			0
$475$	10.0601	−	28.3547i	0.461591	−	1.30100i
$476$		0			0
$477$	−4.99031	−	4.99031i	−0.228491	−	0.228491i
$478$		0			0
$479$	−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
$482$		0			0
$483$	−0.490826	−	0.437262i	−0.0223334	−	0.0198961i
$484$		0			0
$485$	27.5536	+	4.74311i	1.25114	+	0.215374i
$486$		0			0
$487$	10.3049	+	10.3049i	0.466959	+	0.466959i	0.900928	−	0.433969i	$-0.142887\pi$
$487$	10.3049	+	10.3049i	0.466959	+	0.466959i	−0.433969	+	0.900928i	$0.642887\pi$
$488$		0			0
$489$	−19.3404			−0.874603
$490$		0			0
$491$	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
$494$		0			0
$495$	4.88005	−	3.44668i	0.219342	−	0.154917i
$496$		0			0
$497$	−30.2427	−	26.9423i	−1.35657	−	1.20853i
$498$		0			0
$499$		−	23.7564i		−	1.06348i	−0.846907	−	0.531741i	$-0.821538\pi$
$499$		−	23.7564i		−	1.06348i	0.846907	−	0.531741i	$-0.178462\pi$
$500$		0			0
$501$	−8.81463			−0.393808
$502$		0			0
$503$	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
$506$		0			0
$507$	−7.06275	+	7.06275i	−0.313668	+	0.313668i
$508$		0			0
$509$	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
$512$		0			0
$513$	−4.25487	+	4.25487i	−0.187857	+	0.187857i
$514$		0			0
$515$	3.72598	−	21.6449i	0.164186	−	0.953787i
$516$		0			0
$517$	−1.48788	+	1.48788i	−0.0654367	+	0.0654367i
$518$		0			0
$519$		−	9.57331i		−	0.420221i
$520$		0			0
$521$		−	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	$0.737877\pi$
$524$		0			0
$525$	12.7015	+	3.69766i	0.554338	+	0.161379i
$526$		0			0
$527$	−34.4283	−	34.4283i	−1.49972	−	1.49972i
$528$		0			0
$529$			22.9383i			0.997316i
$530$		0			0
$531$			7.98837i			0.346666i
$532$		0			0
$533$	8.66039	−	8.66039i	0.375123	−	0.375123i
$534$		0			0
$535$	4.00900	−	23.2890i	0.173324	−	1.00687i
$536$		0			0
$537$	−0.919968	+	0.919968i	−0.0396996	+	0.0396996i
$538$		0			0
$539$	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	$0.229428\pi$
$542$		0			0
$543$	6.00000	−	6.00000i	0.257485	−	0.257485i
$544$		0			0
$545$	−10.8738	+	7.67996i	−0.465784	+	0.328973i
$546$		0			0
$547$	−3.83548	−	3.83548i	−0.163993	−	0.163993i	0.620340	−	0.784333i	$-0.286995\pi$
$547$	−3.83548	−	3.83548i	−0.163993	−	0.163993i	−0.784333	+	0.620340i	$0.786995\pi$
$548$		0			0
$549$	−5.53409			−0.236189
$550$		0			0
$551$			1.83461i			0.0781569i
$552$		0			0
$553$	−19.8823	+	22.3179i	−0.845483	+	0.949054i
$554$		0			0
$555$	1.89964	−	1.34168i	0.0806353	−	0.0569510i
$556$		0			0
$557$	−16.3147	−	16.3147i	−0.691275	−	0.691275i	0.271238	−	0.962512i	$-0.412567\pi$
$557$	−16.3147	−	16.3147i	−0.691275	−	0.691275i	−0.962512	+	0.271238i	$0.912567\pi$
$558$		0			0
$559$	−0.748285			−0.0316491
$560$		0			0
$561$	17.9341			0.757180
$562$		0			0
$563$	−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
$566$		0			0
$567$	−1.97552	−	1.75993i	−0.0829638	−	0.0739099i
$568$		0			0
$569$		−	0.277792i		−	0.0116457i	−0.999983	−	0.00582283i	$-0.998147\pi$
$569$		−	0.277792i		−	0.0116457i	0.999983	−	0.00582283i	$-0.00185348\pi$
$570$		0			0
$571$	3.11538			0.130375			0.0651874	−	0.997873i	$-0.479235\pi$
$571$	3.11538			0.130375			0.0651874	+	0.997873i	$0.479235\pi$
$572$		0			0
$573$	1.37031	+	1.37031i	0.0572454	+	0.0572454i
$574$		0			0
$575$	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	$-0.0865693\pi$
$578$		0			0
$579$	11.0703			0.460064
$580$		0			0
$581$	1.05410	+	18.2641i	0.0437316	+	0.757722i
$582$		0			0
$583$	−13.3335	+	13.3335i	−0.552216	+	0.552216i
$584$		0			0
$585$	3.82432	+	0.658323i	0.158116	+	0.0272183i
$586$		0			0
$587$	−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
$590$		0			0
$591$			12.0317i			0.494916i
$592$		0			0
$593$	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
$595$	24.7395	+	31.0618i	1.01422	+	1.27341i
$596$		0			0
$597$	−2.30135	−	2.30135i	−0.0941878	−	0.0941878i
$598$		0			0
$599$			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	$0.849371\pi$
$602$		0			0
$603$	−3.43055	+	3.43055i	−0.139703	+	0.139703i
$604$		0			0
$605$	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	$0.244737\pi$
$608$		0			0
$609$	−0.805321	+	0.0464788i	−0.0326333	+	0.00188341i
$610$		0			0
$611$	−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	$0.405892\pi$
$614$		0			0
$615$	15.5520	+	2.67714i	0.627117	+	0.107953i
$616$		0			0
$617$	−3.70013	−	3.70013i	−0.148962	−	0.148962i	0.628692	−	0.777654i	$-0.283590\pi$
$617$	−3.70013	−	3.70013i	−0.148962	−	0.148962i	−0.777654	+	0.628692i	$0.783590\pi$
$618$		0			0
$619$	39.8840			1.60307			0.801536	−	0.597946i	$-0.204016\pi$
$619$	39.8840			1.60307			0.801536	+	0.597946i	$0.204016\pi$
$620$		0			0
$621$		−	0.248455i		−	0.00997015i
$622$		0			0
$623$	13.6558	+	12.1655i	0.547107	+	0.487401i
$624$		0			0
$625$	−19.4097	−	15.7564i	−0.776388	−	0.630256i
$626$		0			0
$627$	11.3685	+	11.3685i	0.454013	+	0.454013i
$628$		0			0
$629$	6.98117			0.278357
$630$		0			0
$631$	33.9725			1.35242			0.676211	−	0.736708i	$-0.263621\pi$
$631$	33.9725			1.35242			0.676211	+	0.736708i	$0.263621\pi$
$632$		0			0
$633$	−12.1981	−	12.1981i	−0.484833	−	0.484833i
$634$		0			0
$635$	−1.53489	+	8.91646i	−0.0609103	+	0.353839i
$636$		0			0
$637$	−7.54472	+	9.52120i	−0.298933	+	0.377244i
$638$		0			0
$639$		−	15.3087i		−	0.605605i
$640$		0			0
$641$	−18.1113			−0.715352			−0.357676	−	0.933846i	$-0.616431\pi$
$641$	−18.1113			−0.715352			−0.357676	+	0.933846i	$0.616431\pi$
$642$		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			0
$645$	−0.556214	−	0.787528i	−0.0219009	−	0.0310089i
$646$		0			0
$647$	−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
$650$		0			0
$651$	19.1598	−	1.10580i	0.750934	−	0.0433398i
$652$		0			0
$653$	−9.39937	+	9.39937i	−0.367826	+	0.367826i	−0.866684	−	0.498858i	$-0.833753\pi$
$653$	−9.39937	+	9.39937i	−0.367826	+	0.367826i	0.498858	+	0.866684i	$0.333753\pi$
$654$		0			0
$655$	−17.0730	+	12.0583i	−0.667099	+	0.471158i
$656$		0			0
$657$	−10.0208	+	10.0208i	−0.390950	+	0.390950i
$658$		0			0
$659$			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	$-0.186878\pi$
$662$		0			0
$663$	8.23683	+	8.23683i	0.319892	+	0.319892i
$664$		0			0
$665$	−4.00774	+	35.3725i	−0.155413	+	1.37169i
$666$		0			0
$667$	−0.0535642	−	0.0535642i	−0.00207401	−	0.00207401i
$668$		0			0
$669$		−	6.48264i		−	0.250633i
$670$		0			0
$671$			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	$-0.0117441\pi$
$674$		0			0
$675$	2.14984	+	4.51422i	0.0827473	+	0.173752i
$676$		0			0
$677$	−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
$680$		0			0
$681$	20.0271			0.767440
$682$		0			0
$683$	−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
$686$		0			0
$687$	20.4571	+	20.4571i	0.780487	+	0.780487i
$688$		0			0
$689$	−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	$-0.291276\pi$
$692$		0			0
$693$	−4.70230	+	5.27832i	−0.178625	+	0.200507i
$694$		0			0
$695$	10.0477	+	14.2263i	0.381132	+	0.539634i
$696$		0			0
$697$	33.4960	+	33.4960i	1.26875	+	1.26875i
$698$		0			0
$699$	6.76767			0.255977
$700$		0			0
$701$	13.7870			0.520727			0.260364	−	0.965511i	$-0.416158\pi$
$701$	13.7870			0.520727			0.260364	+	0.965511i	$0.416158\pi$
$702$		0			0
$703$	4.42536	+	4.42536i	0.166906	+	0.166906i
$704$		0			0
$705$	−1.01590	−	1.43838i	−0.0382610	−	0.0541727i
$706$		0			0
$707$	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	$0.846668\pi$
$710$		0			0
$711$	−11.2973			−0.423680
$712$		0			0
$713$	1.27438	+	1.27438i	0.0477257	+	0.0477257i
$714$		0			0
$715$	1.75895	−	10.2181i	0.0657811	−	0.382135i
$716$		0			0
$717$	−11.4388	+	11.4388i	−0.427191	+	0.427191i
$718$		0			0
$719$	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
$722$		0			0
$723$	−8.04033	+	8.04033i	−0.299023	+	0.299023i
$724$		0			0
$725$	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	$-0.0362034\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	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	$0.782204\pi$
$734$		0			0
$735$	−15.6287	−	0.863100i	−0.576472	−	0.0318359i
$736$		0			0
$737$	9.16599	+	9.16599i	0.337634	+	0.337634i
$738$		0			0
$739$			11.9735i			0.440454i	0.975449	+	0.220227i	$0.0706797\pi$
$739$			11.9735i			0.440454i	−0.975449	+	0.220227i	$0.929320\pi$
$740$		0			0
$741$			10.4427i			0.383621i
$742$		0			0
$743$	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
$746$		0			0
$747$	−4.88941	+	4.88941i	−0.178894	+	0.178894i
$748$		0			0
$749$	1.61109	+	27.9148i	0.0588679	+	1.01998i
$750$		0			0
$751$	24.1119			0.879855			0.439928	−	0.898033i	$-0.355004\pi$
$751$	24.1119			0.879855			0.439928	+	0.898033i	$0.355004\pi$
$752$		0			0
$753$	−4.91467	+	4.91467i	−0.179100	+	0.179100i
$754$		0			0
$755$	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	$0.478727\pi$
$758$		0			0
$759$	−0.663839			−0.0240958
$760$		0			0
$761$		−	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
$763$	10.4778	−	11.7613i	0.379320	−	0.425787i
$764$		0			0
$765$	−2.54621	+	14.7914i	−0.0920584	+	0.534784i
$766$		0			0
$767$	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	$0.392169\pi$
$770$		0			0
$771$	−14.2679			−0.513845
$772$		0			0
$773$	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
$776$		0			0
$777$	−1.83045	+	2.05468i	−0.0656670	+	0.0737111i
$778$		0			0
$779$			42.4662i			1.52151i
$780$		0			0
$781$	−40.9030			−1.46362
$782$		0			0
$783$	−0.215589	−	0.215589i	−0.00770453	−	0.00770453i
$784$		0			0
$785$	−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	$0.117278\pi$
$788$		0			0
$789$	25.7364			0.916240
$790$		0			0
$791$	26.1119	−	1.50704i	0.928432	−	0.0535840i
$792$		0			0
$793$	−6.79111	+	6.79111i	−0.241159	+	0.241159i
$794$		0			0
$795$	−9.10390	−	12.8900i	−0.322882	−	0.457159i
$796$		0			0
$797$	−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
$800$		0			0
$801$			6.91251i			0.244242i
$802$		0			0
$803$	26.7744	+	26.7744i	0.944847	+	0.944847i
$804$		0			0
$805$	−0.915741	−	1.14977i	−0.0322756	−	0.0405239i
$806$		0			0
$807$	10.9685	+	10.9685i	0.386111	+	0.386111i
$808$		0			0
$809$			27.5404i			0.968270i	0.874993	+	0.484135i	$0.160866\pi$
$809$			27.5404i			0.968270i	−0.874993	+	0.484135i	$0.839134\pi$
$810$		0			0
$811$			34.2545i			1.20284i	0.798933	+	0.601420i	$0.205398\pi$
$811$			34.2545i			1.20284i	−0.798933	+	0.601420i	$0.794602\pi$
$812$		0			0
$813$	−9.43409	+	9.43409i	−0.330868	+	0.330868i
$814$		0			0
$815$	−42.6196	−	7.33659i	−1.49290	−	0.256990i
$816$		0			0
$817$	1.83461	−	1.83461i	0.0641848	−	0.0641848i
$818$		0			0
$819$	−4.58392	+	0.264559i	−0.160175	+	0.00924443i
$820$		0			0
$821$	49.7482			1.73623			0.868113	−	0.496367i	$-0.165333\pi$
$821$	49.7482			1.73623			0.868113	+	0.496367i	$0.165333\pi$
$822$		0			0
$823$	6.10417	−	6.10417i	0.212778	−	0.212778i	−0.592668	−	0.805447i	$-0.701926\pi$
$823$	6.10417	−	6.10417i	0.212778	−	0.212778i	0.805447	+	0.592668i	$0.201926\pi$
$824$		0			0
$825$	12.0614	−	5.74409i	0.419925	−	0.199984i
$826$		0			0
$827$	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	$0.663850\pi$
$830$		0			0
$831$			2.83636i			0.0983922i
$832$		0			0
$833$	−36.8254	−	29.1809i	−1.27592	−	1.01106i
$834$		0			0
$835$	−19.4244	−	3.34374i	−0.672209	−	0.115715i
$836$		0			0
$837$	5.12921	+	5.12921i	0.177291	+	0.177291i
$838$		0			0
$839$	−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
$842$		0			0
$843$	−9.58531	−	9.58531i	−0.330136	−	0.330136i
$844$		0			0
$845$	−18.2431	+	12.8847i	−0.627581	+	0.443247i
$846$		0			0
$847$	−7.62767	−	6.79526i	−0.262090	−	0.233488i
$848$		0			0
$849$		−	22.9730i		−	0.788431i
$850$		0			0
$851$	−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	$0.872411\pi$
$854$		0			0
$855$	−10.9903	+	7.76222i	−0.375861	+	0.265462i
$856$		0			0
$857$	−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			0
$861$	−18.6410	+	1.07586i	−0.635284	+	0.0366651i
$862$		0			0
$863$	−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
$866$		0			0
$867$	−19.8369	+	19.8369i	−0.673697	+	0.673697i
$868$		0			0
$869$			30.1848i			1.02395i
$870$		0			0
$871$			8.41955i			0.285286i
$872$		0			0
$873$	−8.84137	−	8.84137i	−0.299235	−	0.299235i
$874$		0			0
$875$	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	$0.815035\pi$
$878$		0			0
$879$			3.41907i			0.115322i
$880$		0			0
$881$			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	−0.987350	−	0.158559i	$-0.949315\pi$
$883$	−24.6278	+	24.6278i	−0.828791	+	0.828791i	0.158559	+	0.987350i	$0.449315\pi$
$884$		0			0
$885$	−3.03031	+	17.6036i	−0.101863	+	0.591739i
$886$		0			0
$887$	−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
$890$		0			0
$891$	−2.67187			−0.0895111
$892$		0			0
$893$	3.35083	−	3.35083i	0.112131	−	0.112131i
$894$		0			0
$895$	−2.37628	+	1.67831i	−0.0794301	+	0.0560998i
$896$		0			0
$897$	−0.304889	−	0.304889i	−0.0101800	−	0.0101800i
$898$		0			0
$899$	2.21160			0.0737611
$900$		0			0
$901$		−	47.3704i		−	1.57814i
$902$		0			0
$903$	0.851800	+	0.758842i	0.0283461	+	0.0252527i
$904$		0			0
$905$	15.4980	−	10.9459i	0.515170	−	0.363854i
$906$		0			0
$907$	22.8743	+	22.8743i	0.759530	+	0.759530i	0.976237	−	0.216707i	$-0.0695316\pi$
$907$	22.8743	+	22.8743i	0.759530	+	0.759530i	−0.216707	+	0.976237i	$0.569532\pi$
$908$		0			0
$909$	7.22962			0.239791
$910$		0			0
$911$	−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
$914$		0			0
$915$	−12.1952	−	2.09930i	−0.403162	−	0.0694008i
$916$		0			0
$917$	16.4512	−	18.4664i	0.543265	−	0.609814i
$918$		0			0
$919$		−	14.5898i		−	0.481272i	−0.970615	−	0.240636i	$-0.922644\pi$
$919$		−	14.5898i		−	0.481272i	0.970615	−	0.240636i	$-0.0773560\pi$
$920$		0			0
$921$	10.2007			0.336125
$922$		0			0
$923$	−18.7860	−	18.7860i	−0.618349	−	0.618349i
$924$		0			0
$925$	4.69511	−	2.23598i	0.154374	−	0.0735187i
$926$		0			0
$927$	−6.94538	+	6.94538i	−0.228116	+	0.228116i
$928$		0			0
$929$	−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
$932$		0			0
$933$	−7.25079	+	7.25079i	−0.237380	+	0.237380i
$934$		0			0
$935$	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	$0.0226758\pi$
$938$		0			0
$939$		−	31.2405i		−	1.01950i
$940$		0			0
$941$			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
$944$		0			0
$945$	−3.68575	−	4.62766i	−0.119897	−	0.150538i
$946$		0			0
$947$	−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
$950$		0			0
$951$			17.3331i			0.562064i
$952$		0			0
$953$	31.8008	−	31.8008i	1.03013	−	1.03013i	0.0305973	−	0.999532i	$-0.490259\pi$
$953$	31.8008	−	31.8008i	1.03013	−	1.03013i	0.999532	−	0.0305973i	$-0.00974093\pi$
$954$		0			0
$955$	2.49987	+	3.53950i	0.0808940	+	0.114536i
$956$		0			0
$957$	−0.576027	+	0.576027i	−0.0186203	+	0.0186203i
$958$		0			0
$959$	1.62111	+	28.0884i	0.0523483	+	0.907021i
$960$		0			0
$961$	−21.6175			−0.697339
$962$		0			0
$963$	−7.47295	+	7.47295i	−0.240812	+	0.240812i
$964$		0			0
$965$	24.3951	+	4.19940i	0.785305	+	0.135183i
$966$		0			0
$967$	−0.210995	−	0.210995i	−0.00678513	−	0.00678513i	0.703706	−	0.710491i	$-0.251527\pi$
$967$	−0.210995	−	0.210995i	−0.00678513	−	0.00678513i	−0.710491	+	0.703706i	$0.751527\pi$
$968$		0			0
$969$	−40.3893			−1.29749
$970$		0			0
$971$		−	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
$974$		0			0
$975$	8.17775	+	2.90143i	0.261898	+	0.0929203i
$976$		0			0
$977$	25.0981	+	25.0981i	0.802958	+	0.802958i	0.983557	−	0.180599i	$-0.0578035\pi$
$977$	25.0981	+	25.0981i	0.802958	+	0.802958i	−0.180599	+	0.983557i	$0.557803\pi$
$978$		0			0
$979$	18.4693			0.590283
$980$		0			0
$981$	5.95352			0.190081
$982$		0			0
$983$	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
$986$		0			0
$987$	1.55577	+	1.38599i	0.0495208	+	0.0441166i
$988$		0			0
$989$			0.107128i			0.00340648i
$990$		0			0
$991$	−48.9637			−1.55538			−0.777691	−	0.628647i	$-0.783609\pi$
$991$	−48.9637			−1.55538			−0.777691	+	0.628647i	$0.783609\pi$
$992$		0			0
$993$	0.893133	+	0.893133i	0.0283427	+	0.0283427i
$994$		0			0
$995$	−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	$0.163511\pi$
$998$		0			0
$999$	−1.04007			−0.0329064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.d.97.1		16
4.3	odd	2		105.2.m.a.97.8	yes	16
5.3	odd	4	inner	1680.2.cz.d.433.8		16
7.6	odd	2	inner	1680.2.cz.d.97.8		16
12.11	even	2		315.2.p.e.307.2		16
20.3	even	4		105.2.m.a.13.7	✓	16
20.7	even	4		525.2.m.b.118.2		16
20.19	odd	2		525.2.m.b.307.1		16
28.3	even	6		735.2.v.a.607.1		32
28.11	odd	6		735.2.v.a.607.2		32
28.19	even	6		735.2.v.a.472.8		32
28.23	odd	6		735.2.v.a.472.7		32
28.27	even	2		105.2.m.a.97.7	yes	16
35.13	even	4	inner	1680.2.cz.d.433.1		16
60.23	odd	4		315.2.p.e.118.1		16
84.83	odd	2		315.2.p.e.307.1		16
140.3	odd	12		735.2.v.a.313.7		32
140.23	even	12		735.2.v.a.178.1		32
140.27	odd	4		525.2.m.b.118.1		16
140.83	odd	4		105.2.m.a.13.8	yes	16
140.103	odd	12		735.2.v.a.178.2		32
140.123	even	12		735.2.v.a.313.8		32
140.139	even	2		525.2.m.b.307.2		16
420.83	even	4		315.2.p.e.118.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	20.3	even	4
105.2.m.a.13.8	yes	16	140.83	odd	4
105.2.m.a.97.7	yes	16	28.27	even	2
105.2.m.a.97.8	yes	16	4.3	odd	2
315.2.p.e.118.1		16	60.23	odd	4
315.2.p.e.118.2		16	420.83	even	4
315.2.p.e.307.1		16	84.83	odd	2
315.2.p.e.307.2		16	12.11	even	2
525.2.m.b.118.1		16	140.27	odd	4
525.2.m.b.118.2		16	20.7	even	4
525.2.m.b.307.1		16	20.19	odd	2
525.2.m.b.307.2		16	140.139	even	2
735.2.v.a.178.1		32	140.23	even	12
735.2.v.a.178.2		32	140.103	odd	12
735.2.v.a.313.7		32	140.3	odd	12
735.2.v.a.313.8		32	140.123	even	12
735.2.v.a.472.7		32	28.23	odd	6
735.2.v.a.472.8		32	28.19	even	6
735.2.v.a.607.1		32	28.3	even	6
735.2.v.a.607.2		32	28.11	odd	6
1680.2.cz.d.97.1		16	1.1	even	1	trivial
1680.2.cz.d.97.8		16	7.6	odd	2	inner
1680.2.cz.d.433.1		16	35.13	even	4	inner
1680.2.cz.d.433.8		16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.28999 - 1.82645i) q^{5} +(1.97552 + 1.75993i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.28999 - 1.82645i) q^{5} +(1.97552 + 1.75993i) q^{7} +1.00000i q^{9} +2.67187 q^{11} +(1.22714 + 1.22714i) q^{13} +(-0.379340 + 2.20366i) q^{15} +(-4.74624 + 4.74624i) q^{17} -6.01729 q^{19} +(-0.152445 - 2.64136i) q^{21} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +(0.707107 - 0.707107i) q^{27} -0.304889i q^{29} +7.25379i q^{31} +(-1.88930 - 1.88930i) q^{33} +(0.666037 - 5.87847i) q^{35} +(-0.735441 - 0.735441i) q^{37} -1.73544i q^{39} -7.05736i q^{41} +(-0.304889 + 0.304889i) q^{43} +(1.82645 - 1.28999i) q^{45} +(-0.556866 + 0.556866i) q^{47} +(0.805321 + 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 + 4.99031i) q^{53} +(-3.44668 - 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} +7.98837 q^{59} +5.53409i q^{61} +(-1.75993 + 1.97552i) q^{63} +(0.658323 - 3.82432i) q^{65} +(3.43055 + 3.43055i) q^{67} -0.248455 q^{69} -15.3087 q^{71} +(10.0208 + 10.0208i) q^{73} +(4.51422 - 2.14984i) q^{75} +(5.27832 + 4.70230i) q^{77} +11.2973i q^{79} -1.00000 q^{81} +(4.88941 + 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(-0.215589 + 0.215589i) q^{87} +6.91251 q^{89} +(0.264559 + 4.58392i) q^{91} +(5.12921 - 5.12921i) q^{93} +(7.76222 + 10.9903i) q^{95} +(-8.84137 + 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) \) 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Introduction

L-functions

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