LMFDB - Embedded newform 1680.2.cz.d.97.8

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			97.8
Root			$-0.944649 + 1.05244i$ of defining polynomial
Character	$\chi$	$=$	1680.97
Dual form			1680.2.cz.d.433.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(1.28999 + 1.82645i) q^{5} +(1.75993 + 1.97552i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(1.28999 + 1.82645i) q^{5} +(1.75993 + 1.97552i) q^{7} +1.00000i q^{9} +2.67187 q^{11} +(-1.22714 - 1.22714i) q^{13} +(-0.379340 + 2.20366i) q^{15} +(4.74624 - 4.74624i) q^{17} +6.01729 q^{19} +(-0.152445 + 2.64136i) q^{21} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +(-0.707107 + 0.707107i) q^{27} -0.304889i q^{29} -7.25379i q^{31} +(1.88930 + 1.88930i) q^{33} +(-1.33791 + 5.76281i) q^{35} +(-0.735441 - 0.735441i) q^{37} -1.73544i q^{39} +7.05736i q^{41} +(-0.304889 + 0.304889i) q^{43} +(-1.82645 + 1.28999i) q^{45} +(0.556866 - 0.556866i) q^{47} +(-0.805321 + 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 + 4.99031i) q^{53} +(3.44668 + 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} -7.98837 q^{59} -5.53409i q^{61} +(-1.97552 + 1.75993i) q^{63} +(0.658323 - 3.82432i) q^{65} +(3.43055 + 3.43055i) q^{67} +0.248455 q^{69} -15.3087 q^{71} +(-10.0208 - 10.0208i) q^{73} +(-4.51422 + 2.14984i) q^{75} +(4.70230 + 5.27832i) q^{77} +11.2973i q^{79} -1.00000 q^{81} +(-4.88941 - 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(0.215589 - 0.215589i) q^{87} -6.91251 q^{89} +(0.264559 - 4.58392i) q^{91} +(5.12921 - 5.12921i) q^{93} +(7.76222 + 10.9903i) q^{95} +(8.84137 - 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.75993	+	1.97552i	0.665189	+	0.746675i
$7$	1.75993	+	1.97552i	0.665189	+	0.746675i
$8$		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	0.516150	−	0.856498i	$-0.327365\pi$
$13$	−1.22714	−	1.22714i	−0.340348	−	0.340348i	−0.856498	+	0.516150i	$0.827365\pi$
$14$		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	$-0.447300\pi$
$17$	4.74624	−	4.74624i	1.15113	−	1.15113i	0.986326	−	0.164807i	$-0.0527002\pi$
$18$		0			0
$19$	6.01729			1.38046			0.690231	−	0.723589i	$-0.257509\pi$
$19$	6.01729			1.38046			0.690231	+	0.723589i	$0.257509\pi$
$20$		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	$-0.774178\pi$
$31$		−	7.25379i		−	1.30282i	0.758726	−	0.651410i	$-0.225822\pi$
$32$		0			0
$33$	1.88930	+	1.88930i	0.328885	+	0.328885i
$34$		0			0
$35$	−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	$0.777247\pi$
$38$		0			0
$39$		−	1.73544i		−	0.277893i
$40$		0			0
$41$			7.05736i			1.10217i	0.834447	+	0.551087i	$0.185787\pi$
$41$			7.05736i			1.10217i	−0.834447	+	0.551087i	$0.814213\pi$
$42$		0			0
$43$	−0.304889	+	0.304889i	−0.0464952	+	0.0464952i	−0.729972	−	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	−0.665326	−	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
$50$		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	$-0.674068\pi$
$59$	−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	$-0.115275\pi$
$62$		0			0
$63$	−1.97552	+	1.75993i	−0.248892	+	0.221730i
$64$		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	$-0.938722\pi$
$73$	−10.0208	−	10.0208i	−1.17285	−	1.17285i	−0.191323	−	0.981527i	$-0.561278\pi$
$74$		0			0
$75$	−4.51422	+	2.14984i	−0.521257	+	0.248242i
$76$		0			0
$77$	4.70230	+	5.27832i	0.535876	+	0.601521i
$78$		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	0.385871	−	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			0
$87$	0.215589	−	0.215589i	0.0231136	−	0.0231136i
$88$		0			0
$89$	−6.91251			−0.732725			−0.366363	−	0.930472i	$-0.619397\pi$
$89$	−6.91251			−0.732725			−0.366363	+	0.930472i	$0.619397\pi$
$90$		0			0
$91$	0.264559	−	4.58392i	0.0277333	−	0.480525i
$92$		0			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	−0.0975276	−	0.995233i	$-0.531093\pi$
$97$	8.84137	−	8.84137i	0.897705	−	0.897705i	0.995233	+	0.0975276i	$0.0310934\pi$
$98$		0			0
$99$			2.67187i			0.268533i
$100$		0			0
$101$			7.22962i			0.719374i	0.933073	+	0.359687i	$0.117117\pi$
$101$			7.22962i			0.719374i	−0.933073	+	0.359687i	$0.882883\pi$
$102$		0			0
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	0.276628	−	0.960977i	$-0.410783\pi$
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	−0.960977	+	0.276628i	$0.910783\pi$
$104$		0			0
$105$	−5.02097	+	3.12888i	−0.489996	+	0.305347i
$106$		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	$0.133897\pi$
$131$			9.34764i			0.816707i	−0.912824	+	0.408353i	$0.866103\pi$
$132$		0			0
$133$	10.5900	+	11.8873i	0.918268	+	1.03076i
$134$		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	$-0.392841\pi$
$139$	7.78902			0.660656			0.330328	+	0.943866i	$0.392841\pi$
$140$		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
$147$	−5.48633	+	4.34743i	−0.452505	+	0.358570i
$148$		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	−0.788633	−	0.614864i	$-0.789211\pi$
$157$	−2.17731	+	2.17731i	−0.173768	+	0.173768i	0.614864	+	0.788633i	$0.289211\pi$
$158$		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	−0.905870	−	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
$170$		0			0
$171$			6.01729i			0.460154i
$172$		0			0
$173$	−6.76935	−	6.76935i	−0.514664	−	0.514664i	0.401288	−	0.915952i	$-0.368563\pi$
$173$	−6.76935	−	6.76935i	−0.514664	−	0.514664i	−0.915952	+	0.401288i	$0.868563\pi$
$174$		0			0
$175$	−12.2514	+	4.99032i	−0.926119	+	0.377233i
$176$		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	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		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	$-0.536801\pi$
$199$	−3.25460			−0.230712			−0.115356	+	0.993324i	$0.536801\pi$
$200$		0			0
$201$			4.85153i			0.342201i
$202$		0			0
$203$	0.602314	−	0.536583i	0.0422741	−	0.0376607i
$204$		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
$217$	14.3300	−	12.7661i	0.972782	−	0.866622i
$218$		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	0.536768	−	0.843730i	$-0.319645\pi$
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	−0.843730	+	0.536768i	$0.819645\pi$
$224$		0			0
$225$	−4.71220	−	1.67187i	−0.314147	−	0.111458i
$226$		0			0
$227$	14.1613	−	14.1613i	0.939918	−	0.939918i	−0.0583764	−	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			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	$0.119351\pi$
$241$			11.3707i			0.732454i	−0.930526	+	0.366227i	$0.880649\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−13.7391	+	7.49906i	−0.877762	+	0.479098i
$246$		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	$0.0703944\pi$
$251$			6.95039i			0.438705i	−0.975646	+	0.219352i	$0.929606\pi$
$252$		0			0
$253$	0.469405	−	0.469405i	0.0295112	−	0.0295112i
$254$		0			0
$255$	8.65865	+	12.2595i	0.542226	+	0.767722i
$256$		0			0
$257$	−10.0889	+	10.0889i	−0.629329	+	0.629329i	−0.947899	−	0.318570i	$-0.896797\pi$
$257$	−10.0889	+	10.0889i	−0.629329	+	0.629329i	0.318570	+	0.947899i	$0.396797\pi$
$258$		0			0
$259$	0.158553	−	2.74720i	0.00985202	−	0.170703i
$260$		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	$-0.343212\pi$
$269$	15.5119			0.945775			0.472888	+	0.881123i	$0.343212\pi$
$270$		0			0
$271$			13.3418i			0.810458i	0.914215	+	0.405229i	$0.132808\pi$
$271$			13.3418i			0.810458i	−0.914215	+	0.405229i	$0.867192\pi$
$272$		0			0
$273$	3.42839	−	3.05425i	0.207496	−	0.184852i
$274$		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	0.0338017	−	0.999429i	$-0.489239\pi$
$283$	−16.2444	−	16.2444i	−0.965627	−	0.965627i	−0.999429	+	0.0338017i	$0.989239\pi$
$284$		0			0
$285$	−2.28260	+	13.2600i	−0.135210	+	0.785457i
$286$		0			0
$287$	−13.9419	+	12.4204i	−0.822966	+	0.733155i
$288$		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	0.774192	−	0.632951i	$-0.218157\pi$
$293$	2.41765	+	2.41765i	0.141240	+	0.141240i	−0.632951	+	0.774192i	$0.718157\pi$
$294$		0			0
$295$	−10.3049	−	14.5904i	−0.599974	−	0.849486i
$296$		0			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	−0.470652	−	0.882319i	$-0.655981\pi$
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	0.882319	+	0.470652i	$0.155981\pi$
$308$		0			0
$309$		−	9.82225i		−	0.558768i
$310$		0			0
$311$			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	$-0.594418\pi$
$314$		0			0
$315$	−5.76281	−	1.33791i	−0.324698	−	0.0753826i
$316$		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
$343$	−15.1541	+	10.6468i	−0.818244	+	0.574871i
$344$		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	$-0.476368\pi$
$349$	2.77139			0.148349			0.0741746	+	0.997245i	$0.476368\pi$
$350$		0			0
$351$	1.73544			0.0926310
$352$		0			0
$353$	0.970568	+	0.970568i	0.0516581	+	0.0516581i	0.732464	−	0.680806i	$-0.238370\pi$
$353$	0.970568	+	0.970568i	0.0516581	+	0.0516581i	−0.680806	+	0.732464i	$0.738370\pi$
$354$		0			0
$355$	−19.7481	−	27.9607i	−1.04812	−	1.48400i
$356$		0			0
$357$	11.8130	+	13.2601i	0.625209	+	0.701797i
$358$		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	−0.280948	−	0.959723i	$-0.590649\pi$
$367$	13.0035	−	13.0035i	0.678776	−	0.678776i	0.959723	+	0.280948i	$0.0906487\pi$
$368$		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	0.697063	−	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
$386$		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	−0.130109	−	0.991500i	$-0.541533\pi$
$397$	17.1631	−	17.1631i	0.861391	−	0.861391i	0.991500	+	0.130109i	$0.0415327\pi$
$398$		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	$-0.479187\pi$
$409$	2.64278			0.130677			0.0653386	+	0.997863i	$0.479187\pi$
$410$		0			0
$411$			10.6341i			0.524540i
$412$		0			0
$413$	−14.0589	−	15.7812i	−0.691795	−	0.776540i
$414$		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	$-0.421211\pi$
$419$	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	$0.724927\pi$
$422$		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
$427$	10.9327	−	9.73958i	0.529069	−	0.471332i
$428$		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	0.304935	−	0.952373i	$-0.401365\pi$
$433$	−13.4723	−	13.4723i	−0.647438	−	0.647438i	−0.952373	+	0.304935i	$0.901365\pi$
$434$		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	$-0.290045\pi$
$439$	25.6790			1.22559			0.612795	+	0.790242i	$0.290045\pi$
$440$		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
$455$	8.71359	−	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	$0.629064\pi$
$458$		0			0
$459$			6.71220i			0.313299i
$460$		0			0
$461$			29.9845i			1.39652i	0.715846	+	0.698259i	$0.246041\pi$
$461$			29.9845i			1.39652i	−0.715846	+	0.698259i	$0.753959\pi$
$462$		0			0
$463$	−7.70220	+	7.70220i	−0.357951	+	0.357951i	−0.863057	−	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	−0.663997	−	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
$470$		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	$-0.470181\pi$
$479$	4.09455			0.187085			0.0935425	+	0.995615i	$0.470181\pi$
$480$		0			0
$481$			1.80498i			0.0823001i
$482$		0			0
$483$	0.437262	+	0.490826i	0.0198961	+	0.0223334i
$484$		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
$497$	−26.9423	−	30.2427i	−1.20853	−	1.35657i
$498$		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	0.182786	−	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
$506$		0			0
$507$	7.06275	−	7.06275i	0.313668	−	0.313668i
$508$		0			0
$509$	−16.8977			−0.748979			−0.374489	−	0.927231i	$-0.622182\pi$
$509$	−16.8977			−0.748979			−0.374489	+	0.927231i	$0.622182\pi$
$510$		0			0
$511$	2.16039	−	37.4322i	0.0955698	−	1.65590i
$512$		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	$0.0552552\pi$
$521$			7.88477i			0.345438i	−0.984971	+	0.172719i	$0.944745\pi$
$522$		0			0
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	0.679669	−	0.733519i	$-0.262123\pi$
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	−0.733519	+	0.679669i	$0.762123\pi$
$524$		0			0
$525$	−12.1917	−	5.13436i	−0.532091	−	0.224082i
$526$		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
$553$	−22.3179	+	19.8823i	−0.949054	+	0.845483i
$554$		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	$0.000328032\pi$
$563$	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
$566$		0			0
$567$	−1.75993	−	1.97552i	−0.0739099	−	0.0829638i
$568$		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	$0.586569\pi$
$577$	−29.5905	+	29.5905i	−1.23187	+	1.23187i	−0.963245	+	0.268625i	$0.913431\pi$
$578$		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	$-0.466396\pi$
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.994433	−	0.105375i	$-0.0336041\pi$
$588$		0			0
$589$		−	43.6482i		−	1.79849i
$590$		0			0
$591$		−	12.0317i		−	0.494916i
$592$		0			0
$593$	−15.1889	−	15.1889i	−0.623733	−	0.623733i	0.322751	−	0.946484i	$-0.395392\pi$
$593$	−15.1889	−	15.1889i	−0.623733	−	0.623733i	−0.946484	+	0.322751i	$0.895392\pi$
$594$		0			0
$595$	21.0017	+	33.7017i	0.860985	+	1.38164i
$596$		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	$-0.849371\pi$
$601$		−	22.3458i		−	0.911503i	0.890107	−	0.455752i	$-0.150629\pi$
$602$		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	−0.718700	−	0.695320i	$-0.755263\pi$
$607$	−0.576027	+	0.576027i	−0.0233802	+	0.0233802i	0.695320	+	0.718700i	$0.255263\pi$
$608$		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	$-0.795984\pi$
$619$	−39.8840			−1.60307			−0.801536	+	0.597946i	$0.795984\pi$
$620$		0			0
$621$			0.248455i			0.00997015i
$622$		0			0
$623$	−12.1655	−	13.6558i	−0.487401	−	0.547107i
$624$		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
$637$	9.52120	−	7.54472i	0.377244	−	0.298933i
$638$		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	$0.103039\pi$
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.318082	+	0.948063i	$0.396961\pi$
$644$		0			0
$645$	−0.556214	−	0.787528i	−0.0219009	−	0.0310089i
$646$		0			0
$647$	12.9277	−	12.9277i	0.508241	−	0.508241i	−0.405745	−	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
$650$		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	$0.186878\pi$
$661$			28.4837i			1.10789i	−0.832554	+	0.553943i	$0.813122\pi$
$662$		0			0
$663$	−8.23683	−	8.23683i	−0.319892	−	0.319892i
$664$		0			0
$665$	−8.05059	+	34.6765i	−0.312188	+	1.34470i
$666$		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	−0.683731	−	0.729734i	$-0.739644\pi$
$677$	1.19694	−	1.19694i	0.0460022	−	0.0460022i	0.729734	+	0.683731i	$0.239644\pi$
$678$		0			0
$679$	33.0264	+	1.90611i	1.26744	+	0.0731496i
$680$		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	$0.291276\pi$
$691$			41.6703i			1.58521i	−0.609735	+	0.792606i	$0.708724\pi$
$692$		0			0
$693$	−5.27832	+	4.70230i	−0.200507	+	0.178625i
$694$		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
$707$	−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	$0.846668\pi$
$710$		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	$-0.688338\pi$
$719$	−29.9117			−1.11552			−0.557758	+	0.830003i	$0.688338\pi$
$720$		0			0
$721$	1.49735	−	25.9441i	0.0557642	−	0.966207i
$722$		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	$0.536203\pi$
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.993539	+	0.113491i	$0.963797\pi$
$728$		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	0.774908	−	0.632074i	$-0.217796\pi$
$733$	3.86707	+	3.86707i	0.142834	+	0.142834i	−0.632074	+	0.774908i	$0.717796\pi$
$734$		0			0
$735$	−15.0177	−	4.41240i	−0.553935	−	0.162754i
$736$		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	$0.199078\pi$
$761$			32.3002i			1.17088i	−0.810716	+	0.585440i	$0.800922\pi$
$762$		0			0
$763$	11.7613	−	10.4778i	0.425787	−	0.379320i
$764$		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	$-0.607831\pi$
$769$	−18.4310			−0.664640			−0.332320	+	0.943167i	$0.607831\pi$
$770$		0			0
$771$	−14.2679			−0.513845
$772$		0			0
$773$	−17.7963	−	17.7963i	−0.640088	−	0.640088i	0.310489	−	0.950577i	$-0.399507\pi$
$773$	−17.7963	−	17.7963i	−0.640088	−	0.640088i	−0.950577	+	0.310489i	$0.899507\pi$
$774$		0			0
$775$	34.1813	+	12.1274i	1.22783	+	0.435629i
$776$		0			0
$777$	2.05468	−	1.83045i	0.0737111	−	0.0656670i
$778$		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	−0.932890	−	0.360160i	$-0.882722\pi$
$787$	−16.0671	+	16.0671i	−0.572730	+	0.572730i	0.360160	+	0.932890i	$0.382722\pi$
$788$		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	−0.0913664	−	0.995817i	$-0.529123\pi$
$797$	25.5337	−	25.5337i	0.904451	−	0.904451i	0.995817	+	0.0913664i	$0.0291235\pi$
$798$		0			0
$799$		−	5.28605i		−	0.187007i
$800$		0			0
$801$		−	6.91251i		−	0.244242i
$802$		0			0
$803$	−26.7744	−	26.7744i	−0.944847	−	0.944847i
$804$		0			0
$805$	0.777385	+	1.24748i	0.0273992	+	0.0439680i
$806$		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	$-0.794602\pi$
$811$		−	34.2545i		−	1.20284i	0.798933	−	0.601420i	$-0.205398\pi$
$812$		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	$-0.336150\pi$
$829$	28.3500			0.984636			0.492318	+	0.870415i	$0.336150\pi$
$830$		0			0
$831$		−	2.83636i		−	0.0983922i
$832$		0			0
$833$	29.1809	+	36.8254i	1.01106	+	1.27592i
$834$		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	$-0.308350\pi$
$839$	32.8100			1.13273			0.566364	+	0.824156i	$0.308350\pi$
$840$		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
$847$	−6.79526	−	7.62767i	−0.233488	−	0.262090i
$848$		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	0.920737	−	0.390184i	$-0.127589\pi$
$853$	15.4954	+	15.4954i	0.530553	+	0.530553i	−0.390184	+	0.920737i	$0.627589\pi$
$854$		0			0
$855$	−10.9903	+	7.76222i	−0.375861	+	0.265462i
$856$		0			0
$857$	17.8346	−	17.8346i	0.609218	−	0.609218i	−0.333523	−	0.942742i	$-0.608238\pi$
$857$	17.8346	−	17.8346i	0.609218	−	0.609218i	0.942742	+	0.333523i	$0.108238\pi$
$858$		0			0
$859$	17.2711			0.589283			0.294641	−	0.955608i	$-0.404800\pi$
$859$	17.2711			0.589283			0.294641	+	0.955608i	$0.404800\pi$
$860$		0			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
$875$	−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	$0.815035\pi$
$878$		0			0
$879$			3.41907i			0.115322i
$880$		0			0
$881$		−	35.7762i		−	1.20533i	−0.797994	−	0.602665i	$-0.794106\pi$
$881$		−	35.7762i		−	1.20533i	0.797994	−	0.602665i	$-0.205894\pi$
$882$		0			0
$883$	−24.6278	+	24.6278i	−0.828791	+	0.828791i	−0.987350	−	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	−0.694703	−	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
$890$		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
$903$	−0.758842	−	0.851800i	−0.0252527	−	0.0283461i
$904$		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
$917$	−18.4664	+	16.4512i	−0.609814	+	0.543265i
$918$		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	$-0.364616\pi$
$929$	25.1526			0.825229			0.412615	+	0.910906i	$0.364616\pi$
$930$		0			0
$931$	−4.84585	+	41.8414i	−0.158816	+	1.37130i
$932$		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	−0.997464	−	0.0711778i	$-0.977324\pi$
$937$	−28.3540	+	28.3540i	−0.926286	+	0.926286i	0.0711778	+	0.997464i	$0.477324\pi$
$938$		0			0
$939$		−	31.2405i		−	1.01950i
$940$		0			0
$941$		−	0.106973i		−	0.00348721i	−0.999998	−	0.00174360i	$-0.999445\pi$
$941$		−	0.106973i		−	0.00348721i	0.999998	−	0.00174360i	$-0.000555007\pi$
$942$		0			0
$943$	1.23987	+	1.23987i	0.0403756	+	0.0403756i
$944$		0			0
$945$	−3.12888	−	5.02097i	−0.101782	−	0.163332i
$946$		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	$0.334813\pi$
$971$			54.1165i			1.73668i	−0.495969	+	0.868340i	$0.665187\pi$
$972$		0			0
$973$	13.7081	+	15.3873i	0.439462	+	0.493295i
$974$		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	0.687161	−	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
$986$		0			0
$987$	1.38599	+	1.55577i	0.0441166	+	0.0495208i
$988$		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	−0.870940	−	0.491389i	$-0.836489\pi$
$997$	−11.9844	+	11.9844i	−0.379551	+	0.379551i	0.491389	+	0.870940i	$0.336489\pi$
$998$		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.97.8		16
4.3	odd	2		105.2.m.a.97.7	yes	16
5.3	odd	4	inner	1680.2.cz.d.433.1		16
7.6	odd	2	inner	1680.2.cz.d.97.1		16
12.11	even	2		315.2.p.e.307.1		16
20.3	even	4		105.2.m.a.13.8	yes	16
20.7	even	4		525.2.m.b.118.1		16
20.19	odd	2		525.2.m.b.307.2		16
28.3	even	6		735.2.v.a.607.2		32
28.11	odd	6		735.2.v.a.607.1		32
28.19	even	6		735.2.v.a.472.7		32
28.23	odd	6		735.2.v.a.472.8		32
28.27	even	2		105.2.m.a.97.8	yes	16
35.13	even	4	inner	1680.2.cz.d.433.8		16
60.23	odd	4		315.2.p.e.118.2		16
84.83	odd	2		315.2.p.e.307.2		16
140.3	odd	12		735.2.v.a.313.8		32
140.23	even	12		735.2.v.a.178.2		32
140.27	odd	4		525.2.m.b.118.2		16
140.83	odd	4		105.2.m.a.13.7	✓	16
140.103	odd	12		735.2.v.a.178.1		32
140.123	even	12		735.2.v.a.313.7		32
140.139	even	2		525.2.m.b.307.1		16
420.83	even	4		315.2.p.e.118.1		16

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.28999 + 1.82645i) q^{5} +(1.75993 + 1.97552i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.28999 + 1.82645i) q^{5} +(1.75993 + 1.97552i) q^{7} +1.00000i q^{9} +2.67187 q^{11} +(-1.22714 - 1.22714i) q^{13} +(-0.379340 + 2.20366i) q^{15} +(4.74624 - 4.74624i) q^{17} +6.01729 q^{19} +(-0.152445 + 2.64136i) q^{21} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +(-0.707107 + 0.707107i) q^{27} -0.304889i q^{29} -7.25379i q^{31} +(1.88930 + 1.88930i) q^{33} +(-1.33791 + 5.76281i) q^{35} +(-0.735441 - 0.735441i) q^{37} -1.73544i q^{39} +7.05736i q^{41} +(-0.304889 + 0.304889i) q^{43} +(-1.82645 + 1.28999i) q^{45} +(0.556866 - 0.556866i) q^{47} +(-0.805321 + 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 + 4.99031i) q^{53} +(3.44668 + 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} -7.98837 q^{59} -5.53409i q^{61} +(-1.97552 + 1.75993i) q^{63} +(0.658323 - 3.82432i) q^{65} +(3.43055 + 3.43055i) q^{67} +0.248455 q^{69} -15.3087 q^{71} +(-10.0208 - 10.0208i) q^{73} +(-4.51422 + 2.14984i) q^{75} +(4.70230 + 5.27832i) q^{77} +11.2973i q^{79} -1.00000 q^{81} +(-4.88941 - 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(0.215589 - 0.215589i) q^{87} -6.91251 q^{89} +(0.264559 - 4.58392i) q^{91} +(5.12921 - 5.12921i) q^{93} +(7.76222 + 10.9903i) q^{95} +(8.84137 - 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 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

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