LMFDB - Embedded newform 1008.2.df.d.929.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			929.7
Root			$-0.213160 - 1.71888i$ of defining polynomial
Character	$\chi$	$=$	1008.929
Dual form			1008.2.df.d.689.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.44376 + 0.956855i) q^{3} +2.86804 q^{5} +(1.83240 + 1.90848i) q^{7} +(1.16886 + 2.76293i) q^{9} +2.71286i q^{11} +(3.18987 - 1.84167i) q^{13} +(4.14074 + 2.74429i) q^{15} +(-3.22192 - 5.58052i) q^{17} +(-2.73867 - 1.58117i) q^{19} +(0.819404 + 4.50872i) q^{21} +2.99146i q^{23} +3.22563 q^{25} +(-0.956179 + 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +(-8.26739 - 4.77318i) q^{31} +(-2.59581 + 3.91671i) q^{33} +(5.25540 + 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(6.36761 + 0.393320i) q^{39} +(0.794538 + 1.37618i) q^{41} +(4.67828 - 8.10302i) q^{43} +(3.35232 + 7.92418i) q^{45} +(-5.65372 - 9.79254i) q^{47} +(-0.284592 + 6.99421i) q^{49} +(0.688093 - 11.1398i) q^{51} +(-2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} +(4.33680 - 7.51156i) q^{59} +(-0.566915 + 0.327308i) q^{61} +(-3.13118 + 7.29354i) q^{63} +(9.14867 - 5.28199i) q^{65} +(3.86146 - 6.68825i) q^{67} +(-2.86240 + 4.31894i) q^{69} +7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(4.65702 + 3.08646i) q^{75} +(-5.17744 + 4.97106i) q^{77} +(2.59566 + 4.49581i) q^{79} +(-6.26755 + 6.45894i) q^{81} +(-7.92948 + 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-2.21342 - 4.44616i) q^{87} +(-3.14826 + 5.45295i) q^{89} +(9.35993 + 2.71312i) q^{91} +(-7.36885 - 14.8020i) q^{93} +(-7.85460 - 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +(-7.49544 + 3.17095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) $ 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.44376	+	0.956855i	0.833552	+	0.552440i
$3$	1.44376	+	0.956855i	0.833552	+	0.552440i
$4$		0			0
$5$	2.86804			1.28262			0.641312	−	0.767280i	$-0.278390\pi$
$5$	2.86804			1.28262			0.641312	+	0.767280i	$0.278390\pi$
$6$		0			0
$7$	1.83240	+	1.90848i	0.692584	+	0.721338i
$7$	1.83240	+	1.90848i	0.692584	+	0.721338i
$8$		0			0
$9$	1.16886	+	2.76293i	0.389619	+	0.920976i
$10$		0			0
$11$			2.71286i			0.817958i	0.912544	+	0.408979i	$0.134115\pi$
$11$			2.71286i			0.817958i	−0.912544	+	0.408979i	$0.865885\pi$
$12$		0			0
$13$	3.18987	−	1.84167i	0.884712	−	0.510789i	0.0125026	−	0.999922i	$-0.496020\pi$
$13$	3.18987	−	1.84167i	0.884712	−	0.510789i	0.872209	+	0.489133i	$0.162687\pi$
$14$		0			0
$15$	4.14074	+	2.74429i	1.06913	+	0.708574i
$16$		0			0
$17$	−3.22192	−	5.58052i	−0.781429	−	1.35348i	−0.931109	−	0.364741i	$-0.881158\pi$
$17$	−3.22192	−	5.58052i	−0.781429	−	1.35348i	0.149680	−	0.988735i	$-0.452176\pi$
$18$		0			0
$19$	−2.73867	−	1.58117i	−0.628294	−	0.362746i	0.151797	−	0.988412i	$-0.451494\pi$
$19$	−2.73867	−	1.58117i	−0.628294	−	0.362746i	−0.780091	+	0.625666i	$0.784827\pi$
$20$		0			0
$21$	0.819404	+	4.50872i	0.178809	+	0.983884i
$22$		0			0
$23$			2.99146i			0.623763i	0.950121	+	0.311882i	$0.100959\pi$
$23$			2.99146i			0.623763i	−0.950121	+	0.311882i	$0.899041\pi$
$24$		0			0
$25$	3.22563			0.645126
$26$		0			0
$27$	−0.956179	+	5.10742i	−0.184017	+	0.982923i
$28$		0			0
$29$	−2.48332	−	1.43375i	−0.461142	−	0.266240i	0.251383	−	0.967888i	$-0.419115\pi$
$29$	−2.48332	−	1.43375i	−0.461142	−	0.266240i	−0.712524	+	0.701648i	$0.752448\pi$
$30$		0			0
$31$	−8.26739	−	4.77318i	−1.48487	−	0.857289i	−0.485016	−	0.874506i	$-0.661186\pi$
$31$	−8.26739	−	4.77318i	−1.48487	−	0.857289i	−0.999852	+	0.0172169i	$0.994519\pi$
$32$		0			0
$33$	−2.59581	+	3.91671i	−0.451873	+	0.681811i
$34$		0			0
$35$	5.25540	+	5.47359i	0.888325	+	0.925205i
$36$		0			0
$37$	−1.70640	+	2.95556i	−0.280530	+	0.485892i	−0.971515	−	0.236977i	$-0.923843\pi$
$37$	−1.70640	+	2.95556i	−0.280530	+	0.485892i	0.690986	+	0.722868i	$0.257177\pi$
$38$		0			0
$39$	6.36761	+	0.393320i	1.01963	+	0.0629816i
$40$		0			0
$41$	0.794538	+	1.37618i	0.124086	+	0.214923i	0.921375	−	0.388674i	$-0.127067\pi$
$41$	0.794538	+	1.37618i	0.124086	+	0.214923i	−0.797289	+	0.603597i	$0.793733\pi$
$42$		0			0
$43$	4.67828	−	8.10302i	0.713431	−	1.23570i	−0.250131	−	0.968212i	$-0.580474\pi$
$43$	4.67828	−	8.10302i	0.713431	−	1.23570i	0.963562	−	0.267487i	$-0.0861931\pi$
$44$		0			0
$45$	3.35232	+	7.92418i	0.499735	+	1.18127i
$46$		0			0
$47$	−5.65372	−	9.79254i	−0.824680	−	1.42839i	−0.902163	−	0.431394i	$-0.858022\pi$
$47$	−5.65372	−	9.79254i	−0.824680	−	1.42839i	0.0774831	−	0.996994i	$-0.475312\pi$
$48$		0			0
$49$	−0.284592	+	6.99421i	−0.0406560	+	0.999173i
$50$		0			0
$51$	0.688093	−	11.1398i	0.0963523	−	1.55989i
$52$		0			0
$53$	−2.16419	+	1.24950i	−0.297275	+	0.171632i	−0.641218	−	0.767359i	$-0.721571\pi$
$53$	−2.16419	+	1.24950i	−0.297275	+	0.171632i	0.343943	+	0.938990i	$0.388237\pi$
$54$		0			0
$55$			7.78058i			1.04913i
$56$		0			0
$57$	−2.44102	−	4.90333i	−0.323320	−	0.649462i
$58$		0			0
$59$	4.33680	−	7.51156i	0.564604	−	0.977922i	−0.432483	−	0.901642i	$-0.642362\pi$
$59$	4.33680	−	7.51156i	0.564604	−	0.977922i	0.997086	−	0.0762801i	$-0.0243043\pi$
$60$		0			0
$61$	−0.566915	+	0.327308i	−0.0725860	+	0.0419075i	−0.535854	−	0.844311i	$-0.680010\pi$
$61$	−0.566915	+	0.327308i	−0.0725860	+	0.0419075i	0.463268	+	0.886218i	$0.346677\pi$
$62$		0			0
$63$	−3.13118	+	7.29354i	−0.394491	+	0.918900i
$64$		0			0
$65$	9.14867	−	5.28199i	1.13475	−	0.655150i
$66$		0			0
$67$	3.86146	−	6.68825i	0.471752	−	0.817099i	−0.527725	−	0.849415i	$-0.676955\pi$
$67$	3.86146	−	6.68825i	0.471752	−	0.817099i	0.999478	+	0.0323159i	$0.0102883\pi$
$68$		0			0
$69$	−2.86240	+	4.31894i	−0.344592	+	0.519939i
$70$		0			0
$71$			7.86582i			0.933501i	0.884389	+	0.466750i	$0.154575\pi$
$71$			7.86582i			0.933501i	−0.884389	+	0.466750i	$0.845425\pi$
$72$		0			0
$73$	11.0769	−	6.39527i	1.29646	−	0.748510i	0.316667	−	0.948537i	$-0.397436\pi$
$73$	11.0769	−	6.39527i	1.29646	−	0.748510i	0.979790	+	0.200027i	$0.0641028\pi$
$74$		0			0
$75$	4.65702	+	3.08646i	0.537746	+	0.356394i
$76$		0			0
$77$	−5.17744	+	4.97106i	−0.590024	+	0.566504i
$78$		0			0
$79$	2.59566	+	4.49581i	0.292034	+	0.505819i	0.974291	−	0.225295i	$-0.0723345\pi$
$79$	2.59566	+	4.49581i	0.292034	+	0.505819i	−0.682256	+	0.731113i	$0.739001\pi$
$80$		0			0
$81$	−6.26755	+	6.45894i	−0.696394	+	0.717660i
$82$		0			0
$83$	−7.92948	+	13.7343i	−0.870373	+	1.50753i	−0.00876173	+	0.999962i	$0.502789\pi$
$83$	−7.92948	+	13.7343i	−0.870373	+	1.50753i	−0.861611	+	0.507569i	$0.830544\pi$
$84$		0			0
$85$	−9.24057	−	16.0051i	−1.00228	−	1.73600i
$86$		0			0
$87$	−2.21342	−	4.44616i	−0.237304	−	0.476678i
$88$		0			0
$89$	−3.14826	+	5.45295i	−0.333715	+	0.578012i	−0.983237	−	0.182331i	$-0.941636\pi$
$89$	−3.14826	+	5.45295i	−0.333715	+	0.578012i	0.649522	+	0.760343i	$0.274969\pi$
$90$		0			0
$91$	9.35993	+	2.71312i	0.981188	+	0.284412i
$92$		0			0
$93$	−7.36885	−	14.8020i	−0.764114	−	1.53490i
$94$		0			0
$95$	−7.85460	−	4.53486i	−0.805865	−	0.465267i
$96$		0			0
$97$	13.2065	+	7.62477i	1.34092	+	0.774178i	0.986942	−	0.161077i	$-0.0514967\pi$
$97$	13.2065	+	7.62477i	1.34092	+	0.774178i	0.353974	+	0.935255i	$0.384830\pi$
$98$		0			0
$99$	−7.49544	+	3.17095i	−0.753320	+	0.318692i
$100$		0			0
$101$	−3.48902			−0.347170			−0.173585	−	0.984819i	$-0.555535\pi$
$101$	−3.48902			−0.347170			−0.173585	+	0.984819i	$0.555535\pi$
$102$		0			0
$103$			3.33894i			0.328996i	0.986377	+	0.164498i	$0.0526004\pi$
$103$			3.33894i			0.328996i	−0.986377	+	0.164498i	$0.947400\pi$
$104$		0			0
$105$	2.35008	+	12.9312i	0.229344	+	1.26195i
$106$		0			0
$107$	−3.10776	−	1.79427i	−0.300439	−	0.173458i	0.342201	−	0.939627i	$-0.388828\pi$
$107$	−3.10776	−	1.79427i	−0.300439	−	0.173458i	−0.642640	+	0.766168i	$0.722161\pi$
$108$		0			0
$109$	6.89673	+	11.9455i	0.660587	+	1.14417i	0.980462	+	0.196710i	$0.0630258\pi$
$109$	6.89673	+	11.9455i	0.660587	+	1.14417i	−0.319875	+	0.947460i	$0.603641\pi$
$110$		0			0
$111$	−5.29166	+	2.63434i	−0.502262	+	0.250040i
$112$		0			0
$113$	−5.28607	+	3.05191i	−0.497271	+	0.287100i	−0.727586	−	0.686016i	$-0.759358\pi$
$113$	−5.28607	+	3.05191i	−0.497271	+	0.287100i	0.230315	+	0.973116i	$0.426024\pi$
$114$		0			0
$115$			8.57963i			0.800054i
$116$		0			0
$117$	8.81692	+	6.66074i	0.815125	+	0.615785i
$118$		0			0
$119$	4.74646	−	16.3747i	0.435108	−	1.50107i
$120$		0			0
$121$	3.64039			0.330945
$122$		0			0
$123$	−0.169687	+	2.74712i	−0.0153001	+	0.247700i
$124$		0			0
$125$	−5.08895			−0.455170
$126$		0			0
$127$	13.3819			1.18745			0.593727	−	0.804666i	$-0.297656\pi$
$127$	13.3819			1.18745			0.593727	+	0.804666i	$0.297656\pi$
$128$		0			0
$129$	14.5077	−	7.22234i	1.27733	−	0.635891i
$130$		0			0
$131$	0.777928			0.0679679			0.0339839	−	0.999422i	$-0.489180\pi$
$131$	0.777928			0.0679679			0.0339839	+	0.999422i	$0.489180\pi$
$132$		0			0
$133$	−2.00071	−	8.12404i	−0.173484	−	0.704444i
$134$		0			0
$135$	−2.74235	+	14.6483i	−0.236024	+	1.26072i
$136$		0			0
$137$		−	16.5217i		−	1.41154i	−0.708440	−	0.705771i	$-0.750601\pi$
$137$		−	16.5217i		−	1.41154i	0.708440	−	0.705771i	$-0.249399\pi$
$138$		0			0
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	−0.0164348	−	0.999865i	$-0.505232\pi$
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	0.857691	+	0.514165i	$0.171898\pi$
$140$		0			0
$141$	1.20745	−	19.5478i	0.101685	−	1.64622i
$142$		0			0
$143$	4.99620	+	8.65368i	0.417804	+	0.723657i
$144$		0			0
$145$	−7.12226	−	4.11204i	−0.591472	−	0.341486i
$146$		0			0
$147$	−7.10333	+	9.82562i	−0.585873	+	0.810403i
$148$		0			0
$149$			4.90494i			0.401829i	0.979609	+	0.200914i	$0.0643913\pi$
$149$			4.90494i			0.401829i	−0.979609	+	0.200914i	$0.935609\pi$
$150$		0			0
$151$	−9.85629			−0.802093			−0.401047	−	0.916058i	$-0.631353\pi$
$151$	−9.85629			−0.802093			−0.401047	+	0.916058i	$0.631353\pi$
$152$		0			0
$153$	11.6526	−	15.4248i	0.942059	−	1.24702i
$154$		0			0
$155$	−23.7112	−	13.6897i	−1.90453	−	1.09958i
$156$		0			0
$157$	−13.3514	−	7.70843i	−1.06556	−	0.615200i	−0.138593	−	0.990349i	$-0.544258\pi$
$157$	−13.3514	−	7.70843i	−1.06556	−	0.615200i	−0.926964	+	0.375149i	$0.877591\pi$
$158$		0			0
$159$	−4.32015	−	0.266851i	−0.342610	−	0.0211626i
$160$		0			0
$161$	−5.70915	+	5.48157i	−0.449944	+	0.432008i
$162$		0			0
$163$	5.72053	−	9.90825i	0.448066	−	0.776074i	−0.550194	−	0.835037i	$-0.685446\pi$
$163$	5.72053	−	9.90825i	0.448066	−	0.776074i	0.998260	+	0.0589632i	$0.0187795\pi$
$164$		0			0
$165$	−7.44489	+	11.2333i	−0.579584	+	0.874508i
$166$		0			0
$167$	−6.49103	−	11.2428i	−0.502291	−	0.869993i	−0.999996	−	0.00264735i	$-0.999157\pi$
$167$	−6.49103	−	11.2428i	−0.502291	−	0.869993i	0.497706	−	0.867346i	$-0.334176\pi$
$168$		0			0
$169$	0.283528	−	0.491084i	0.0218098	−	0.0377757i
$170$		0			0
$171$	1.16755	−	9.41491i	0.0892848	−	0.719976i
$172$		0			0
$173$	−9.79984	−	16.9738i	−0.745068	−	1.29050i	−0.950163	−	0.311754i	$-0.899084\pi$
$173$	−9.79984	−	16.9738i	−0.745068	−	1.29050i	0.205095	−	0.978742i	$-0.434250\pi$
$174$		0			0
$175$	5.91066	+	6.15605i	0.446804	+	0.465354i
$176$		0			0
$177$	13.4488	−	6.69517i	1.01087	−	0.503239i
$178$		0			0
$179$	−16.2630	+	9.38942i	−1.21555	+	0.701799i	−0.963963	−	0.266036i	$-0.914286\pi$
$179$	−16.2630	+	9.38942i	−1.21555	+	0.701799i	−0.251588	+	0.967835i	$0.580953\pi$
$180$		0			0
$181$			4.47775i			0.332829i	0.986056	+	0.166414i	$0.0532190\pi$
$181$			4.47775i			0.332829i	−0.986056	+	0.166414i	$0.946781\pi$
$182$		0			0
$183$	−1.13167	−	0.0699021i	−0.0836556	−	0.00516731i
$184$		0			0
$185$	−4.89400	+	8.47666i	−0.359814	+	0.623217i
$186$		0			0
$187$	15.1392	−	8.74061i	1.10709	−	0.639177i
$188$		0			0
$189$	−11.4995	+	7.53401i	−0.836466	+	0.548018i
$190$		0			0
$191$	5.90050	−	3.40665i	0.426945	−	0.246497i	−0.271099	−	0.962551i	$-0.587387\pi$
$191$	5.90050	−	3.40665i	0.426945	−	0.246497i	0.698044	+	0.716055i	$0.254054\pi$
$192$		0			0
$193$	7.97694	−	13.8165i	0.574193	−	0.994531i	−0.421936	−	0.906626i	$-0.638649\pi$
$193$	7.97694	−	13.8165i	0.574193	−	0.994531i	0.996129	−	0.0879053i	$-0.0280173\pi$
$194$		0			0
$195$	18.2625	+	1.12806i	1.30781	+	0.0807817i
$196$		0			0
$197$			25.9511i			1.84894i	0.381254	+	0.924470i	$0.375492\pi$
$197$			25.9511i			1.84894i	−0.381254	+	0.924470i	$0.624508\pi$
$198$		0			0
$199$	−2.75706	+	1.59179i	−0.195443	+	0.112839i	−0.594528	−	0.804075i	$-0.702661\pi$
$199$	−2.75706	+	1.59179i	−0.195443	+	0.112839i	0.399085	+	0.916914i	$0.369328\pi$
$200$		0			0
$201$	11.9747	−	5.96133i	0.844629	−	0.420480i
$202$		0			0
$203$	−1.81417	−	7.36658i	−0.127330	−	0.517032i
$204$		0			0
$205$	2.27876	+	3.94693i	0.159156	+	0.275666i
$206$		0			0
$207$	−8.26520	+	3.49659i	−0.574471	+	0.243030i
$208$		0			0
$209$	4.28950	−	7.42963i	0.296711	−	0.513918i
$210$		0			0
$211$	0.0552411	+	0.0956804i	0.00380295	+	0.00658691i	0.867921	−	0.496703i	$-0.165456\pi$
$211$	0.0552411	+	0.0956804i	0.00380295	+	0.00658691i	−0.864118	+	0.503290i	$0.832123\pi$
$212$		0			0
$213$	−7.52645	+	11.3563i	−0.515704	+	0.778122i
$214$		0			0
$215$	13.4175	−	23.2397i	0.915064	−	1.58494i
$216$		0			0
$217$	−6.03968	−	24.5245i	−0.410000	−	1.66483i
$218$		0			0
$219$	22.1117	+	1.36582i	1.49417	+	0.0922933i
$220$		0			0
$221$	−20.5550	−	11.8674i	−1.38268	−	0.798290i
$222$		0			0
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	0.828265	−	0.560336i	$-0.189328\pi$
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	−0.0711331	+	0.997467i	$0.522661\pi$
$224$		0			0
$225$	3.77030	+	8.91219i	0.251353	+	0.594146i
$226$		0			0
$227$	−9.26784			−0.615128			−0.307564	−	0.951527i	$-0.599514\pi$
$227$	−9.26784			−0.615128			−0.307564	+	0.951527i	$0.599514\pi$
$228$		0			0
$229$			13.4180i			0.886689i	0.896351	+	0.443344i	$0.146208\pi$
$229$			13.4180i			0.886689i	−0.896351	+	0.443344i	$0.853792\pi$
$230$		0			0
$231$	−12.2315	+	2.22293i	−0.804776	+	0.146258i
$232$		0			0
$233$	18.3415	+	10.5895i	1.20159	+	0.693738i	0.960909	−	0.276866i	$-0.0892958\pi$
$233$	18.3415	+	10.5895i	1.20159	+	0.693738i	0.240681	+	0.970604i	$0.422629\pi$
$234$		0			0
$235$	−16.2151	−	28.0853i	−1.05776	−	1.83209i
$236$		0			0
$237$	−0.554346	+	8.97452i	−0.0360086	+	0.582958i
$238$		0			0
$239$	7.73342	−	4.46489i	0.500233	−	0.288810i	−0.228577	−	0.973526i	$-0.573407\pi$
$239$	7.73342	−	4.46489i	0.500233	−	0.288810i	0.728810	+	0.684716i	$0.240074\pi$
$240$		0			0
$241$		−	18.4094i		−	1.18585i	−0.805257	−	0.592926i	$-0.797973\pi$
$241$		−	18.4094i		−	1.18585i	0.805257	−	0.592926i	$-0.202027\pi$
$242$		0			0
$243$	−15.2291	+	3.32799i	−0.976945	+	0.213491i
$244$		0			0
$245$	−0.816219	+	20.0597i	−0.0521463	+	1.28156i
$246$		0			0
$247$	−11.6480			−0.741145
$248$		0			0
$249$	−24.5899	+	12.2415i	−1.55832	+	0.775776i
$250$		0			0
$251$	−6.33194			−0.399669			−0.199834	−	0.979830i	$-0.564040\pi$
$251$	−6.33194			−0.399669			−0.199834	+	0.979830i	$0.564040\pi$
$252$		0			0
$253$	−8.11542			−0.510212
$254$		0			0
$255$	1.97348	−	31.9494i	0.123584	−	2.00075i
$256$		0			0
$257$	16.3857			1.02211			0.511054	−	0.859548i	$-0.329255\pi$
$257$	16.3857			1.02211			0.511054	+	0.859548i	$0.329255\pi$
$258$		0			0
$259$	−8.76744	+	2.15916i	−0.544782	+	0.134164i
$260$		0			0
$261$	1.05869	−	8.53709i	0.0655313	−	0.528433i
$262$		0			0
$263$			12.0854i			0.745217i	0.927989	+	0.372609i	$0.121537\pi$
$263$			12.0854i			0.745217i	−0.927989	+	0.372609i	$0.878463\pi$
$264$		0			0
$265$	−6.20698	+	3.58360i	−0.381292	+	0.220139i
$266$		0			0
$267$	−9.76300	+	4.86029i	−0.597486	+	0.297445i
$268$		0			0
$269$	−12.6652	−	21.9368i	−0.772212	−	1.33751i	−0.936348	−	0.351072i	$-0.885817\pi$
$269$	−12.6652	−	21.9368i	−0.772212	−	1.33751i	0.164136	−	0.986438i	$-0.447516\pi$
$270$		0			0
$271$	0.195591	+	0.112924i	0.0118813	+	0.00685967i	0.505929	−	0.862575i	$-0.331150\pi$
$271$	0.195591	+	0.112924i	0.0118813	+	0.00685967i	−0.494048	+	0.869435i	$0.664483\pi$
$272$		0			0
$273$	10.9174	+	12.8732i	0.660751	+	0.779120i
$274$		0			0
$275$			8.75069i			0.527686i
$276$		0			0
$277$	−20.4339			−1.22776			−0.613878	−	0.789401i	$-0.710391\pi$
$277$	−20.4339			−1.22776			−0.613878	+	0.789401i	$0.710391\pi$
$278$		0			0
$279$	3.52456	−	28.4214i	0.211010	−	1.70154i
$280$		0			0
$281$	8.96635	+	5.17672i	0.534887	+	0.308817i	0.743004	−	0.669287i	$-0.233400\pi$
$281$	8.96635	+	5.17672i	0.534887	+	0.308817i	−0.208117	+	0.978104i	$0.566733\pi$
$282$		0			0
$283$	−11.8781	−	6.85783i	−0.706080	−	0.407656i	0.103528	−	0.994627i	$-0.466987\pi$
$283$	−11.8781	−	6.85783i	−0.706080	−	0.407656i	−0.809608	+	0.586971i	$0.800320\pi$
$284$		0			0
$285$	−7.00092	−	14.0629i	−0.414699	−	0.833017i
$286$		0			0
$287$	−1.17050	+	4.03808i	−0.0690923	+	0.238360i
$288$		0			0
$289$	−12.2615	+	21.2375i	−0.721264	+	1.24927i
$290$		0			0
$291$	11.7711	+	23.6450i	0.690036	+	1.38609i
$292$		0			0
$293$	−4.21527	−	7.30105i	−0.246258	−	0.426532i	0.716226	−	0.697868i	$-0.245868\pi$
$293$	−4.21527	−	7.30105i	−0.246258	−	0.426532i	−0.962485	+	0.271336i	$0.912535\pi$
$294$		0			0
$295$	12.4381	−	21.5434i	0.724175	−	1.25431i
$296$		0			0
$297$	−13.8557	−	2.59398i	−0.803990	−	0.150518i
$298$		0			0
$299$	5.50930	+	9.54239i	0.318611	+	0.551851i
$300$		0			0
$301$	24.0369	−	5.91960i	1.38547	−	0.341200i
$302$		0			0
$303$	−5.03729	−	3.33849i	−0.289385	−	0.191791i
$304$		0			0
$305$	−1.62593	+	0.938732i	−0.0931006	+	0.0537516i
$306$		0			0
$307$			5.34345i			0.304967i	0.988306	+	0.152484i	$0.0487271\pi$
$307$			5.34345i			0.304967i	−0.988306	+	0.152484i	$0.951273\pi$
$308$		0			0
$309$	−3.19488	+	4.82061i	−0.181751	+	0.274235i
$310$		0			0
$311$	4.70867	−	8.15565i	0.267004	−	0.462465i	−0.701083	−	0.713080i	$-0.747300\pi$
$311$	4.70867	−	8.15565i	0.267004	−	0.462465i	0.968087	+	0.250615i	$0.0806329\pi$
$312$		0			0
$313$	14.3347	−	8.27614i	0.810245	−	0.467795i	−0.0367961	−	0.999323i	$-0.511715\pi$
$313$	14.3347	−	8.27614i	0.810245	−	0.467795i	0.847041	+	0.531528i	$0.178382\pi$
$314$		0			0
$315$	−8.98032	+	20.9181i	−0.505984	+	1.17860i
$316$		0			0
$317$	−22.9725	+	13.2632i	−1.29026	+	0.744934i	−0.978701	−	0.205291i	$-0.934186\pi$
$317$	−22.9725	+	13.2632i	−1.29026	+	0.744934i	−0.311563	+	0.950225i	$0.600853\pi$
$318$		0			0
$319$	3.88956	−	6.73691i	0.217773	−	0.377194i
$320$		0			0
$321$	−2.76999	−	5.56416i	−0.154606	−	0.310561i
$322$		0			0
$323$			20.3776i			1.13384i
$324$		0			0
$325$	10.2894	−	5.94056i	0.570751	−	0.329523i
$326$		0			0
$327$	−1.47291	+	23.8455i	−0.0814521	+	1.31866i
$328$		0			0
$329$	8.32895	−	28.7339i	0.459190	−	1.58415i
$330$		0			0
$331$	−8.82000	−	15.2767i	−0.484791	−	0.839682i	0.515056	−	0.857156i	$-0.327771\pi$
$331$	−8.82000	−	15.2767i	−0.484791	−	0.839682i	−0.999847	+	0.0174739i	$0.994438\pi$
$332$		0			0
$333$	−10.1605	−	1.26002i	−0.556794	−	0.0690485i
$334$		0			0
$335$	11.0748	−	19.1821i	0.605081	−	1.04803i
$336$		0			0
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	0.993515	−	0.113697i	$-0.0362694\pi$
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	−0.595222	+	0.803561i	$0.702936\pi$
$338$		0			0
$339$	−10.5520	−	0.651786i	−0.573107	−	0.0354002i
$340$		0			0
$341$	12.9490	−	22.4283i	0.701226	−	1.21456i
$342$		0			0
$343$	−13.8698	+	12.2731i	−0.748899	+	0.662684i
$344$		0			0
$345$	−8.20946	+	12.3869i	−0.441982	+	0.666887i
$346$		0			0
$347$	−1.05563	−	0.609467i	−0.0566691	−	0.0327179i	0.471398	−	0.881921i	$-0.343750\pi$
$347$	−1.05563	−	0.609467i	−0.0566691	−	0.0327179i	−0.528067	+	0.849203i	$0.677083\pi$
$348$		0			0
$349$	10.6857	+	6.16942i	0.571995	+	0.330241i	0.757946	−	0.652318i	$-0.226203\pi$
$349$	10.6857	+	6.16942i	0.571995	+	0.330241i	−0.185951	+	0.982559i	$0.559537\pi$
$350$		0			0
$351$	6.35611	+	18.0530i	0.339264	+	0.963597i
$352$		0			0
$353$	−22.2969			−1.18674			−0.593372	−	0.804928i	$-0.702204\pi$
$353$	−22.2969			−1.18674			−0.593372	+	0.804928i	$0.702204\pi$
$354$		0			0
$355$			22.5595i			1.19733i
$356$		0			0
$357$	22.5210	−	19.0994i	1.19194	−	1.01085i
$358$		0			0
$359$	10.4819	+	6.05173i	0.553214	+	0.319398i	0.750417	−	0.660965i	$-0.229853\pi$
$359$	10.4819	+	6.05173i	0.553214	+	0.319398i	−0.197204	+	0.980363i	$0.563186\pi$
$360$		0			0
$361$	−4.49979	−	7.79387i	−0.236831	−	0.410204i
$362$		0			0
$363$	5.25583	+	3.48333i	0.275860	+	0.182827i
$364$		0			0
$365$	31.7691	−	18.3419i	1.66287	−	0.960058i
$366$		0			0
$367$			14.7275i			0.768769i	0.923173	+	0.384385i	$0.125586\pi$
$367$			14.7275i			0.768769i	−0.923173	+	0.384385i	$0.874414\pi$
$368$		0			0
$369$	−2.87358	+	3.80381i	−0.149593	+	0.198018i
$370$		0			0
$371$	−6.35032	−	1.84073i	−0.329692	−	0.0955662i
$372$		0			0
$373$	−9.08558			−0.470433			−0.235217	−	0.971943i	$-0.575580\pi$
$373$	−9.08558			−0.470433			−0.235217	+	0.971943i	$0.575580\pi$
$374$		0			0
$375$	−7.34720	−	4.86939i	−0.379408	−	0.251454i
$376$		0			0
$377$	−10.5620			−0.543970
$378$		0			0
$379$	−21.2298			−1.09050			−0.545250	−	0.838273i	$-0.683565\pi$
$379$	−21.2298			−1.09050			−0.545250	+	0.838273i	$0.683565\pi$
$380$		0			0
$381$	19.3202	+	12.8046i	0.989806	+	0.655998i
$382$		0			0
$383$	−6.70454			−0.342586			−0.171293	−	0.985220i	$-0.554794\pi$
$383$	−6.70454			−0.342586			−0.171293	+	0.985220i	$0.554794\pi$
$384$		0			0
$385$	−14.8491	+	14.2572i	−0.756779	+	0.726613i
$386$		0			0
$387$	27.8563	+	3.45448i	1.41602	+	0.175601i
$388$		0			0
$389$		−	7.69794i		−	0.390301i	−0.980773	−	0.195151i	$-0.937480\pi$
$389$		−	7.69794i		−	0.390301i	0.980773	−	0.195151i	$-0.0625195\pi$
$390$		0			0
$391$	16.6939	−	9.63825i	0.844249	−	0.487427i
$392$		0			0
$393$	1.12314	+	0.744364i	0.0566548	+	0.0375482i
$394$		0			0
$395$	7.44444	+	12.8942i	0.374571	+	0.648775i
$396$		0			0
$397$	−0.0428112	−	0.0247170i	−0.00214863	−	0.00124051i	0.498925	−	0.866645i	$-0.333728\pi$
$397$	−0.0428112	−	0.0247170i	−0.00214863	−	0.00124051i	−0.501074	+	0.865404i	$0.667062\pi$
$398$		0			0
$399$	4.88499	−	13.6435i	0.244555	−	0.683030i
$400$		0			0
$401$		−	20.3272i		−	1.01509i	−0.861625	−	0.507546i	$-0.830553\pi$
$401$		−	20.3272i		−	1.01509i	0.861625	−	0.507546i	$-0.169447\pi$
$402$		0			0
$403$	−35.1626			−1.75157
$404$		0			0
$405$	−17.9755	+	18.5245i	−0.893212	+	0.920488i
$406$		0			0
$407$	−8.01803	−	4.62921i	−0.397439	−	0.229461i
$408$		0			0
$409$	12.1144	+	6.99428i	0.599021	+	0.345845i	0.768656	−	0.639662i	$-0.220926\pi$
$409$	12.1144	+	6.99428i	0.599021	+	0.345845i	−0.169636	+	0.985507i	$0.554259\pi$
$410$		0			0
$411$	15.8088	−	23.8532i	0.779792	−	1.17659i
$412$		0			0
$413$	22.2824	−	5.48752i	1.09645	−	0.270023i
$414$		0			0
$415$	−22.7420	+	39.3903i	−1.11636	+	1.93360i
$416$		0			0
$417$	19.7988	+	1.22295i	0.969551	+	0.0598880i
$418$		0			0
$419$	10.6718	+	18.4842i	0.521353	+	0.903010i	0.999692	+	0.0248344i	$0.00790585\pi$
$419$	10.6718	+	18.4842i	0.521353	+	0.903010i	−0.478339	+	0.878176i	$0.658761\pi$
$420$		0			0
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	−0.752823	−	0.658223i	$-0.771309\pi$
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	0.946449	+	0.322853i	$0.104642\pi$
$422$		0			0
$423$	20.4477	−	27.0669i	0.994200	−	1.31604i
$424$		0			0
$425$	−10.3927	−	18.0007i	−0.504121	−	0.873163i
$426$		0			0
$427$	−1.66348	−	0.482184i	−0.0805013	−	0.0233345i
$428$		0			0
$429$	−1.06702	+	17.2744i	−0.0515163	+	0.834018i
$430$		0			0
$431$	−27.6515	+	15.9646i	−1.33193	+	0.768989i	−0.985595	−	0.169123i	$-0.945907\pi$
$431$	−27.6515	+	15.9646i	−1.33193	+	0.768989i	−0.346333	+	0.938112i	$0.612573\pi$
$432$		0			0
$433$			18.5300i			0.890493i	0.895408	+	0.445247i	$0.146884\pi$
$433$			18.5300i			0.890493i	−0.895408	+	0.445247i	$0.853116\pi$
$434$		0			0
$435$	−6.34817	−	12.7517i	−0.304372	−	0.611400i
$436$		0			0
$437$	4.73002	−	8.19263i	0.226267	−	0.391907i
$438$		0			0
$439$	−1.80316	+	1.04106i	−0.0860603	+	0.0496869i	−0.542413	−	0.840112i	$-0.682489\pi$
$439$	−1.80316	+	1.04106i	−0.0860603	+	0.0496869i	0.456352	+	0.889799i	$0.349156\pi$
$440$		0			0
$441$	−19.6572	+	7.38893i	−0.936055	+	0.351854i
$442$		0			0
$443$	−2.13895	+	1.23493i	−0.101625	+	0.0586731i	−0.549951	−	0.835197i	$-0.685354\pi$
$443$	−2.13895	+	1.23493i	−0.101625	+	0.0586731i	0.448326	+	0.893870i	$0.352020\pi$
$444$		0			0
$445$	−9.02933	+	15.6393i	−0.428031	+	0.741372i
$446$		0			0
$447$	−4.69332	+	7.08154i	−0.221986	+	0.334945i
$448$		0			0
$449$			37.5094i			1.77018i	0.465424	+	0.885088i	$0.345902\pi$
$449$			37.5094i			1.77018i	−0.465424	+	0.885088i	$0.654098\pi$
$450$		0			0
$451$	−3.73338	+	2.15547i	−0.175798	+	0.101497i
$452$		0			0
$453$	−14.2301	−	9.43104i	−0.668587	−	0.443109i
$454$		0			0
$455$	26.8446	+	7.78132i	1.25850	+	0.364794i
$456$		0			0
$457$	−2.92345	−	5.06356i	−0.136753	−	0.236864i	0.789513	−	0.613734i	$-0.210333\pi$
$457$	−2.92345	−	5.06356i	−0.136753	−	0.236864i	−0.926266	+	0.376871i	$0.877000\pi$
$458$		0			0
$459$	31.5828	−	11.1197i	1.47416	−	0.519023i
$460$		0			0
$461$	−3.82830	+	6.63081i	−0.178302	+	0.308827i	−0.941299	−	0.337574i	$-0.890394\pi$
$461$	−3.82830	+	6.63081i	−0.178302	+	0.308827i	0.762997	+	0.646402i	$0.223727\pi$
$462$		0			0
$463$	−4.89449	−	8.47751i	−0.227466	−	0.393983i	0.729590	−	0.683885i	$-0.239711\pi$
$463$	−4.89449	−	8.47751i	−0.227466	−	0.393983i	−0.957057	+	0.289901i	$0.906378\pi$
$464$		0			0
$465$	−21.1341	−	42.4527i	−0.980071	−	1.96870i
$466$		0			0
$467$	14.0806	−	24.3883i	0.651572	−	1.12856i	−0.331169	−	0.943571i	$-0.607443\pi$
$467$	14.0806	−	24.3883i	0.651572	−	1.12856i	0.982741	−	0.184985i	$-0.0592235\pi$
$468$		0			0
$469$	19.8401	−	4.88605i	0.916132	−	0.225617i
$470$		0			0
$471$	−11.9003	−	23.9044i	−0.548337	−	1.10146i
$472$		0			0
$473$	21.9824	+	12.6915i	1.01075	+	0.583557i
$474$		0			0
$475$	−8.83394	−	5.10028i	−0.405329	−	0.234017i
$476$		0			0
$477$	−5.98190	−	4.51903i	−0.273893	−	0.206912i
$478$		0			0
$479$	29.6105			1.35294			0.676470	−	0.736470i	$-0.263509\pi$
$479$	29.6105			1.35294			0.676470	+	0.736470i	$0.263509\pi$
$480$		0			0
$481$			12.5705i			0.573165i
$482$		0			0
$483$	−13.4877	+	2.45122i	−0.613711	+	0.111534i
$484$		0			0
$485$	37.8767	+	21.8681i	1.71989	+	0.992980i
$486$		0			0
$487$	14.6701	+	25.4094i	0.664767	+	1.15141i	0.979348	+	0.202180i	$0.0648025\pi$
$487$	14.6701	+	25.4094i	0.664767	+	1.15141i	−0.314582	+	0.949230i	$0.601864\pi$
$488$		0			0
$489$	17.7398	−	8.83136i	0.802221	−	0.399368i
$490$		0			0
$491$	8.63745	−	4.98683i	0.389803	−	0.225053i	−0.292272	−	0.956335i	$-0.594411\pi$
$491$	8.63745	−	4.98683i	0.389803	−	0.225053i	0.682075	+	0.731283i	$0.261078\pi$
$492$		0			0
$493$			18.4777i			0.832192i
$494$		0			0
$495$	−21.4972	+	9.09439i	−0.966227	+	0.408762i
$496$		0			0
$497$	−15.0118	+	14.4134i	−0.673369	+	0.646527i
$498$		0			0
$499$	19.5957			0.877223			0.438611	−	0.898677i	$-0.355470\pi$
$499$	19.5957			0.877223			0.438611	+	0.898677i	$0.355470\pi$
$500$		0			0
$501$	1.38627	−	22.4428i	0.0619338	−	1.00267i
$502$		0			0
$503$	21.2907			0.949304			0.474652	−	0.880174i	$-0.342574\pi$
$503$	21.2907			0.949304			0.474652	+	0.880174i	$0.342574\pi$
$504$		0			0
$505$	−10.0066			−0.445289
$506$		0			0
$507$	0.879241	−	0.437711i	0.0390485	−	0.0194394i
$508$		0			0
$509$	43.6614			1.93526			0.967630	−	0.252375i	$-0.0812115\pi$
$509$	43.6614			1.93526			0.967630	+	0.252375i	$0.0812115\pi$
$510$		0			0
$511$	32.5027	+	9.42139i	1.43783	+	0.416778i
$512$		0			0
$513$	10.6944	−	12.4756i	0.472168	−	0.550813i
$514$		0			0
$515$			9.57621i			0.421978i
$516$		0			0
$517$	26.5658	−	15.3378i	1.16836	−	0.674554i
$518$		0			0
$519$	2.09292	−	33.8831i	0.0918689	−	1.48730i
$520$		0			0
$521$	−2.60043	−	4.50408i	−0.113927	−	0.197327i	0.803423	−	0.595408i	$-0.203010\pi$
$521$	−2.60043	−	4.50408i	−0.113927	−	0.197327i	−0.917350	+	0.398081i	$0.869676\pi$
$522$		0			0
$523$	34.7043	+	20.0365i	1.51751	+	0.876137i	0.999788	+	0.0205902i	$0.00655454\pi$
$523$	34.7043	+	20.0365i	1.51751	+	0.876137i	0.517726	+	0.855547i	$0.326779\pi$
$524$		0			0
$525$	2.64309	+	14.5435i	0.115354	+	0.634729i
$526$		0			0
$527$			61.5152i			2.67964i
$528$		0			0
$529$	14.0511			0.610919
$530$		0			0
$531$	25.8230	+	3.20233i	1.12062	+	0.138969i
$532$		0			0
$533$	5.06895	+	2.92656i	0.219561	+	0.126763i
$534$		0			0
$535$	−8.91317	−	5.14602i	−0.385350	−	0.222482i
$536$		0			0
$537$	−32.4640	−	2.00527i	−1.40093	−	0.0865336i
$538$		0			0
$539$	−18.9743	−	0.772057i	−0.817282	−	0.0332549i
$540$		0			0
$541$	−4.12096	+	7.13771i	−0.177174	+	0.306874i	−0.940911	−	0.338653i	$-0.890029\pi$
$541$	−4.12096	+	7.13771i	−0.177174	+	0.306874i	0.763738	+	0.645527i	$0.223362\pi$
$542$		0			0
$543$	−4.28456	+	6.46478i	−0.183868	+	0.277430i
$544$		0			0
$545$	19.7801	+	34.2601i	0.847285	+	1.46754i
$546$		0			0
$547$	2.53756	−	4.39518i	0.108498	−	0.187925i	−0.806664	−	0.591011i	$-0.798729\pi$
$547$	2.53756	−	4.39518i	0.108498	−	0.187925i	0.915162	+	0.403086i	$0.132062\pi$
$548$		0			0
$549$	−1.56697	−	1.18377i	−0.0668767	−	0.0505220i
$550$		0			0
$551$	4.53400	+	7.85312i	0.193155	+	0.334554i
$552$		0			0
$553$	−3.82387	+	13.1919i	−0.162608	+	0.560977i
$554$		0			0
$555$	−15.1767	+	7.55537i	−0.644214	+	0.320708i
$556$		0			0
$557$	−37.6102	+	21.7142i	−1.59359	+	0.920062i	−0.600910	+	0.799316i	$0.705195\pi$
$557$	−37.6102	+	21.7142i	−1.59359	+	0.920062i	−0.992684	+	0.120745i	$0.961472\pi$
$558$		0			0
$559$		−	34.4635i		−	1.45765i
$560$		0			0
$561$	30.2208	+	1.86670i	1.27592	+	0.0788122i
$562$		0			0
$563$	4.99118	−	8.64498i	0.210353	−	0.364343i	−0.741472	−	0.670984i	$-0.765872\pi$
$563$	4.99118	−	8.64498i	0.210353	−	0.364343i	0.951825	+	0.306641i	$0.0992052\pi$
$564$		0			0
$565$	−15.1606	+	8.75300i	−0.637813	+	0.368241i
$566$		0			0
$567$	−23.8114	−	0.126106i	−0.999986	−	0.00529593i
$568$		0			0
$569$	−14.0597	+	8.11739i	−0.589415	+	0.340299i	−0.764866	−	0.644189i	$-0.777195\pi$
$569$	−14.0597	+	8.11739i	−0.589415	+	0.340299i	0.175451	+	0.984488i	$0.443862\pi$
$570$		0			0
$571$	−6.31028	+	10.9297i	−0.264077	+	0.457395i	−0.967321	−	0.253553i	$-0.918401\pi$
$571$	−6.31028	+	10.9297i	−0.264077	+	0.457395i	0.703244	+	0.710948i	$0.251734\pi$
$572$		0			0
$573$	11.7785	+	0.727547i	0.492056	+	0.0303937i
$574$		0			0
$575$			9.64936i			0.402406i
$576$		0			0
$577$	−4.18012	+	2.41339i	−0.174020	+	0.100471i	−0.584480	−	0.811408i	$-0.698702\pi$
$577$	−4.18012	+	2.41339i	−0.174020	+	0.100471i	0.410460	+	0.911879i	$0.365368\pi$
$578$		0			0
$579$	24.7371	−	12.3148i	1.02804	−	0.511786i
$580$		0			0
$581$	−40.7416	+	10.0335i	−1.69024	+	0.416258i
$582$		0			0
$583$	−3.38971	−	5.87115i	−0.140387	−	0.243158i
$584$		0			0
$585$	25.2872	+	19.1032i	1.04550	+	0.789822i
$586$		0			0
$587$	5.26032	−	9.11114i	0.217117	−	0.376057i	−0.736809	−	0.676101i	$-0.763668\pi$
$587$	5.26032	−	9.11114i	0.217117	−	0.376057i	0.953925	+	0.300044i	$0.0970015\pi$
$588$		0			0
$589$	15.0944	+	26.1443i	0.621955	+	1.07726i
$590$		0			0
$591$	−24.8315	+	37.4671i	−1.02143	+	1.54119i
$592$		0			0
$593$	−14.7342	+	25.5205i	−0.605063	+	1.04800i	0.386979	+	0.922089i	$0.373519\pi$
$593$	−14.7342	+	25.5205i	−0.605063	+	1.04800i	−0.992042	+	0.125911i	$0.959815\pi$
$594$		0			0
$595$	13.6130	−	46.9633i	0.558080	−	1.92531i
$596$		0			0
$597$	−5.50362	−	0.339952i	−0.225248	−	0.0139133i
$598$		0			0
$599$	7.11658	+	4.10876i	0.290776	+	0.167879i	0.638292	−	0.769795i	$-0.279641\pi$
$599$	7.11658	+	4.10876i	0.290776	+	0.167879i	−0.347516	+	0.937674i	$0.612975\pi$
$600$		0			0
$601$	−32.7131	−	18.8869i	−1.33439	−	0.770413i	−0.348425	−	0.937337i	$-0.613283\pi$
$601$	−32.7131	−	18.8869i	−1.33439	−	0.770413i	−0.985970	+	0.166924i	$0.946617\pi$
$602$		0			0
$603$	22.9926	+	2.85133i	0.936333	+	0.116115i
$604$		0			0
$605$	10.4408			0.424478
$606$		0			0
$607$			35.6221i			1.44586i	0.690923	+	0.722929i	$0.257204\pi$
$607$			35.6221i			1.44586i	−0.690923	+	0.722929i	$0.742796\pi$
$608$		0			0
$609$	4.42952	−	12.3714i	0.179493	−	0.501316i
$610$		0			0
$611$	−36.0693	−	20.8246i	−1.45921	−	0.842474i
$612$		0			0
$613$	11.9660	+	20.7256i	0.483301	+	0.837101i	0.999816	−	0.0191767i	$-0.00610451\pi$
$613$	11.9660	+	20.7256i	0.483301	+	0.837101i	−0.516516	+	0.856278i	$0.672771\pi$
$614$		0			0
$615$	−0.486667	+	7.87885i	−0.0196243	+	0.317706i
$616$		0			0
$617$	−1.98622	+	1.14675i	−0.0799623	+	0.0461663i	−0.539448	−	0.842019i	$-0.681367\pi$
$617$	−1.98622	+	1.14675i	−0.0799623	+	0.0461663i	0.459486	+	0.888185i	$0.348034\pi$
$618$		0			0
$619$		−	10.5171i		−	0.422717i	−0.977409	−	0.211359i	$-0.932211\pi$
$619$		−	10.5171i		−	0.422717i	0.977409	−	0.211359i	$-0.0677888\pi$
$620$		0			0
$621$	−15.2787	−	2.86037i	−0.613112	−	0.114783i
$622$		0			0
$623$	−16.1757	+	3.98361i	−0.648067	+	0.159600i
$624$		0			0
$625$	−30.7235			−1.22894
$626$		0			0
$627$	13.3021	−	6.62214i	0.531233	−	0.264463i
$628$		0			0
$629$	21.9914			0.876856
$630$		0			0
$631$	2.02836			0.0807477			0.0403739	−	0.999185i	$-0.487145\pi$
$631$	2.02836			0.0807477			0.0403739	+	0.999185i	$0.487145\pi$
$632$		0			0
$633$	−0.0117976	+	0.190997i	−0.000468914	+	0.00759144i
$634$		0			0
$635$	38.3799			1.52306
$636$		0			0
$637$	11.9732	+	22.8348i	0.474397	+	0.904747i
$638$		0			0
$639$	−21.7327	+	9.19402i	−0.859732	+	0.363710i
$640$		0			0
$641$			12.4451i			0.491553i	0.969326	+	0.245777i	$0.0790430\pi$
$641$			12.4451i			0.491553i	−0.969326	+	0.245777i	$0.920957\pi$
$642$		0			0
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	−0.723112	−	0.690731i	$-0.757289\pi$
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	0.236635	+	0.971599i	$0.423956\pi$
$644$		0			0
$645$	41.6086	−	20.7139i	1.63834	−	0.815610i
$646$		0			0
$647$	−10.1910	−	17.6513i	−0.400649	−	0.693945i	0.593155	−	0.805088i	$-0.297882\pi$
$647$	−10.1910	−	17.6513i	−0.400649	−	0.693945i	−0.993804	+	0.111143i	$0.964549\pi$
$648$		0			0
$649$	20.3778	+	11.7651i	0.799899	+	0.461822i
$650$		0			0
$651$	14.7466	−	41.1865i	0.577965	−	1.61423i
$652$		0			0
$653$		−	8.72186i		−	0.341313i	−0.985331	−	0.170656i	$-0.945411\pi$
$653$		−	8.72186i		−	0.341313i	0.985331	−	0.170656i	$-0.0545888\pi$
$654$		0			0
$655$	2.23113			0.0871773
$656$		0			0
$657$	30.6170	+	23.1296i	1.19448	+	0.902373i
$658$		0			0
$659$	16.7524	+	9.67200i	0.652581	+	0.376768i	0.789444	−	0.613822i	$-0.210369\pi$
$659$	16.7524	+	9.67200i	0.652581	+	0.376768i	−0.136864	+	0.990590i	$0.543702\pi$
$660$		0			0
$661$	−31.8948	−	18.4145i	−1.24056	−	0.716240i	−0.271355	−	0.962479i	$-0.587472\pi$
$661$	−31.8948	−	18.4145i	−1.24056	−	0.716240i	−0.969209	+	0.246239i	$0.920805\pi$
$662$		0			0
$663$	−18.3210	−	36.8018i	−0.711528	−	1.42926i
$664$		0			0
$665$	−5.73812	−	23.3000i	−0.222515	−	0.903537i
$666$		0			0
$667$	4.28900	−	7.42877i	0.166071	−	0.287643i
$668$		0			0
$669$	10.0776	+	20.2430i	0.389621	+	0.782641i
$670$		0			0
$671$	−0.887942	−	1.53796i	−0.0342786	−	0.0593723i
$672$		0			0
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	−0.645319	−	0.763913i	$-0.723276\pi$
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	0.984228	+	0.176907i	$0.0566091\pi$
$674$		0			0
$675$	−3.08428	+	16.4746i	−0.118714	+	0.634110i
$676$		0			0
$677$	20.4146	+	35.3590i	0.784595	+	1.35896i	0.929241	+	0.369475i	$0.120462\pi$
$677$	20.4146	+	35.3590i	0.784595	+	1.35896i	−0.144646	+	0.989484i	$0.546204\pi$
$678$		0			0
$679$	9.64790	+	39.1760i	0.370253	+	1.50344i
$680$		0			0
$681$	−13.3805	−	8.86797i	−0.512741	−	0.339822i
$682$		0			0
$683$	−8.56287	+	4.94377i	−0.327649	+	0.189168i	−0.654797	−	0.755805i	$-0.727246\pi$
$683$	−8.56287	+	4.94377i	−0.327649	+	0.189168i	0.327148	+	0.944973i	$0.393912\pi$
$684$		0			0
$685$		−	47.3847i		−	1.81048i
$686$		0			0
$687$	−12.8391	+	19.3724i	−0.489843	+	0.739102i
$688$		0			0
$689$	−4.60233	+	7.97148i	−0.175335	+	0.303689i
$690$		0			0
$691$	−37.9217	+	21.8941i	−1.44261	+	0.832891i	−0.998023	−	0.0628444i	$-0.979983\pi$
$691$	−37.9217	+	21.8941i	−1.44261	+	0.832891i	−0.444587	+	0.895736i	$0.646649\pi$
$692$		0			0
$693$	−19.7864	−	8.49444i	−0.751622	−	0.322677i
$694$		0			0
$695$	28.4459	−	16.4233i	1.07902	−	0.622970i
$696$		0			0
$697$	5.11987	−	8.86787i	0.193929	−	0.335894i
$698$		0			0
$699$	16.3480	+	32.8387i	0.618339	+	1.24207i
$700$		0			0
$701$		−	29.6742i		−	1.12078i	−0.828229	−	0.560389i	$-0.810651\pi$
$701$		−	29.6742i		−	1.12078i	0.828229	−	0.560389i	$-0.189349\pi$
$702$		0			0
$703$	9.34651	−	5.39621i	0.352510	−	0.203522i
$704$		0			0
$705$	3.46300	−	56.0638i	0.130424	−	2.11149i
$706$		0			0
$707$	−6.39329	−	6.65872i	−0.240445	−	0.250427i
$708$		0			0
$709$	−23.5269	−	40.7498i	−0.883572	−	1.53039i	−0.847342	−	0.531048i	$-0.821799\pi$
$709$	−23.5269	−	40.7498i	−0.883572	−	1.53039i	−0.0362296	−	0.999343i	$-0.511535\pi$
$710$		0			0
$711$	−9.38766	+	12.4266i	−0.352065	+	0.466033i
$712$		0			0
$713$	14.2788	−	24.7316i	0.534745	−	0.926206i
$714$		0			0
$715$	14.3293	+	24.8191i	0.535885	+	0.928180i
$716$		0			0
$717$	15.4374	+	0.953551i	0.576521	+	0.0356110i
$718$		0			0
$719$	0.909148	−	1.57469i	0.0339055	−	0.0587261i	−0.848575	−	0.529076i	$-0.822539\pi$
$719$	0.909148	−	1.57469i	0.0339055	−	0.0587261i	0.882480	+	0.470349i	$0.155872\pi$
$720$		0			0
$721$	−6.37230	+	6.11829i	−0.237317	+	0.227857i
$722$		0			0
$723$	17.6151	−	26.5786i	0.655113	−	0.988470i
$724$		0			0
$725$	−8.01029	−	4.62474i	−0.297495	−	0.171759i
$726$		0			0
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	0.846252	−	0.532782i	$-0.178853\pi$
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	−0.0382766	+	0.999267i	$0.512187\pi$
$728$		0			0
$729$	−25.1714	−	9.76721i	−0.932276	−	0.361748i
$730$		0			0
$731$	−60.2921			−2.22998
$732$		0			0
$733$		−	4.44032i		−	0.164007i	−0.996632	−	0.0820034i	$-0.973868\pi$
$733$		−	4.44032i		−	0.164007i	0.996632	−	0.0820034i	$-0.0261319\pi$
$734$		0			0
$735$	−20.3726	+	28.1802i	−0.751455	+	1.03944i
$736$		0			0
$737$	18.1443	+	10.4756i	0.668353	+	0.385874i
$738$		0			0
$739$	8.97608	+	15.5470i	0.330191	+	0.571907i	0.982549	−	0.186004i	$-0.0595536\pi$
$739$	8.97608	+	15.5470i	0.330191	+	0.571907i	−0.652358	+	0.757911i	$0.726220\pi$
$740$		0			0
$741$	−16.8169	−	11.1455i	−0.617783	−	0.409439i
$742$		0			0
$743$	31.3712	−	18.1122i	1.15090	−	0.664472i	0.201793	−	0.979428i	$-0.435323\pi$
$743$	31.3712	−	18.1122i	1.15090	−	0.664472i	0.949106	+	0.314956i	$0.101990\pi$
$744$		0			0
$745$			14.0676i			0.515395i
$746$		0			0
$747$	−47.2152	−	5.85519i	−1.72751	−	0.214230i
$748$		0			0
$749$	−2.27035	−	9.21892i	−0.0829568	−	0.336852i
$750$		0			0
$751$	−11.9642			−0.436580			−0.218290	−	0.975884i	$-0.570048\pi$
$751$	−11.9642			−0.436580			−0.218290	+	0.975884i	$0.570048\pi$
$752$		0			0
$753$	−9.14177	−	6.05875i	−0.333145	−	0.220793i
$754$		0			0
$755$	−28.2682			−1.02878
$756$		0			0
$757$	−49.4440			−1.79707			−0.898537	−	0.438898i	$-0.855369\pi$
$757$	−49.4440			−1.79707			−0.898537	+	0.438898i	$0.855369\pi$
$758$		0			0
$759$	−11.7167	−	7.76528i	−0.425289	−	0.281862i
$760$		0			0
$761$	29.2384			1.05989			0.529945	−	0.848032i	$-0.322212\pi$
$761$	29.2384			1.05989			0.529945	+	0.848032i	$0.322212\pi$
$762$		0			0
$763$	−10.1601	+	35.0512i	−0.367821	+	1.26894i
$764$		0			0
$765$	33.4201	−	44.2388i	1.20831	−	1.59946i
$766$		0			0
$767$		−	31.9479i		−	1.15357i
$768$		0			0
$769$	4.54689	−	2.62515i	0.163965	−	0.0946653i	−0.415772	−	0.909469i	$-0.636489\pi$
$769$	4.54689	−	2.62515i	0.163965	−	0.0946653i	0.579737	+	0.814804i	$0.303155\pi$
$770$		0			0
$771$	23.6569	+	15.6787i	0.851981	+	0.564654i
$772$		0			0
$773$	15.6829	+	27.1635i	0.564073	+	0.977003i	0.997135	+	0.0756393i	$0.0240997\pi$
$773$	15.6829	+	27.1635i	0.564073	+	0.977003i	−0.433062	+	0.901364i	$0.642567\pi$
$774$		0			0
$775$	−26.6676	−	15.3965i	−0.957927	−	0.553059i
$776$		0			0
$777$	−14.7240	−	5.27186i	−0.528222	−	0.189127i
$778$		0			0
$779$		−	5.02520i		−	0.180047i
$780$		0			0
$781$	−21.3389			−0.763565
$782$		0			0
$783$	9.69725	−	11.3125i	0.346551	−	0.404274i
$784$		0			0
$785$	−38.2923	−	22.1081i	−1.36671	−	0.789071i
$786$		0			0
$787$	1.59324	+	0.919855i	0.0567927	+	0.0327893i	0.528128	−	0.849165i	$-0.322894\pi$
$787$	1.59324	+	0.919855i	0.0567927	+	0.0327893i	−0.471335	+	0.881954i	$0.656228\pi$
$788$		0			0
$789$	−11.5640	+	17.4483i	−0.411688	+	0.621178i
$790$		0			0
$791$	−15.5107	−	4.49602i	−0.551498	−	0.159860i
$792$		0			0
$793$	−1.20559	+	2.08814i	−0.0428118	+	0.0741522i
$794$		0			0
$795$	−12.3904	−	0.765337i	−0.439440	−	0.0271437i
$796$		0			0
$797$	6.39659	+	11.0792i	0.226579	+	0.392446i	0.956792	−	0.290773i	$-0.0939126\pi$
$797$	6.39659	+	11.0792i	0.226579	+	0.392446i	−0.730213	+	0.683219i	$0.760579\pi$
$798$		0			0
$799$	−36.4316	+	63.1015i	−1.28886	+	2.23237i
$800$		0			0
$801$	−18.7460	−	2.32470i	−0.662357	−	0.0821394i
$802$		0			0
$803$	17.3495	+	30.0502i	0.612250	+	1.06045i
$804$		0			0
$805$	−16.3740	+	15.7213i	−0.577109	+	0.554105i
$806$		0			0
$807$	2.70486	−	43.7901i	0.0952158	−	1.54149i
$808$		0			0
$809$	−12.9217	+	7.46032i	−0.454301	+	0.262291i	−0.709645	−	0.704559i	$-0.751145\pi$
$809$	−12.9217	+	7.46032i	−0.454301	+	0.262291i	0.255344	+	0.966850i	$0.417811\pi$
$810$		0			0
$811$		−	37.5478i		−	1.31848i	−0.751933	−	0.659240i	$-0.770878\pi$
$811$		−	37.5478i		−	1.31848i	0.751933	−	0.659240i	$-0.229122\pi$
$812$		0			0
$813$	0.174333	+	0.350187i	0.00611413	+	0.0122816i
$814$		0			0
$815$	16.4067	−	28.4172i	0.574701	−	0.995411i
$816$		0			0
$817$	−25.6245	+	14.7943i	−0.896489	+	0.517588i
$818$		0			0
$819$	3.44427	+	29.0321i	0.120353	+	1.01446i
$820$		0			0
$821$	−2.88164	+	1.66371i	−0.100570	+	0.0580640i	−0.549441	−	0.835532i	$-0.685159\pi$
$821$	−2.88164	+	1.66371i	−0.100570	+	0.0580640i	0.448872	+	0.893596i	$0.351826\pi$
$822$		0			0
$823$	25.4654	−	44.1073i	0.887667	−	1.53748i	0.0450407	−	0.998985i	$-0.485658\pi$
$823$	25.4654	−	44.1073i	0.887667	−	1.53748i	0.842626	−	0.538499i	$-0.181008\pi$
$824$		0			0
$825$	−8.37314	+	12.6338i	−0.291515	+	0.439854i
$826$		0			0
$827$		−	16.9198i		−	0.588360i	−0.955750	−	0.294180i	$-0.904954\pi$
$827$		−	16.9198i		−	0.588360i	0.955750	−	0.294180i	$-0.0950465\pi$
$828$		0			0
$829$	−4.65467	+	2.68737i	−0.161663	+	0.0933364i	−0.578649	−	0.815577i	$-0.696420\pi$
$829$	−4.65467	+	2.68737i	−0.161663	+	0.0933364i	0.416986	+	0.908913i	$0.363087\pi$
$830$		0			0
$831$	−29.5016	−	19.5523i	−1.02340	−	0.678262i
$832$		0			0
$833$	39.9483	−	20.9466i	1.38413	−	0.725757i
$834$		0			0
$835$	−18.6165	−	32.2447i	−0.644251	−	1.11588i
$836$		0			0
$837$	32.2837	−	37.6610i	1.11589	−	1.30176i
$838$		0			0
$839$	−11.8714	+	20.5618i	−0.409846	+	0.709874i	−0.994872	−	0.101140i	$-0.967751\pi$
$839$	−11.8714	+	20.5618i	−0.409846	+	0.709874i	0.585026	+	0.811014i	$0.301084\pi$
$840$		0			0
$841$	−10.3887	−	17.9938i	−0.358232	−	0.620477i
$842$		0			0
$843$	7.99183	+	16.0534i	0.275253	+	0.552909i
$844$		0			0
$845$	0.813168	−	1.40845i	0.0279738	−	0.0484521i
$846$		0			0
$847$	6.67066	+	6.94761i	0.229207	+	0.238723i
$848$		0			0
$849$	−10.5871	−	21.2667i	−0.363349	−	0.729870i
$850$		0			0
$851$	−8.84146	−	5.10462i	−0.303081	−	0.174984i
$852$		0			0
$853$	10.3810	+	5.99345i	0.355437	+	0.205212i	0.667077	−	0.744988i	$-0.267545\pi$
$853$	10.3810	+	5.99345i	0.355437	+	0.205212i	−0.311640	+	0.950200i	$0.600878\pi$
$854$		0			0
$855$	3.34858	−	27.0023i	0.114519	−	0.923459i
$856$		0			0
$857$	55.0635			1.88093			0.940467	−	0.339885i	$-0.110388\pi$
$857$	55.0635			1.88093			0.940467	+	0.339885i	$0.110388\pi$
$858$		0			0
$859$		−	39.1210i		−	1.33479i	−0.744704	−	0.667395i	$-0.767409\pi$
$859$		−	39.1210i		−	1.33479i	0.744704	−	0.667395i	$-0.232591\pi$
$860$		0			0
$861$	−5.55376	+	4.71000i	−0.189272	+	0.160516i
$862$		0			0
$863$	39.2319	+	22.6506i	1.33547	+	0.771034i	0.986132	−	0.165963i	$-0.0530733\pi$
$863$	39.2319	+	22.6506i	1.33547	+	0.771034i	0.349338	+	0.936997i	$0.386407\pi$
$864$		0			0
$865$	−28.1063	−	48.6815i	−0.955643	−	1.65522i
$866$		0			0
$867$	−38.0238	+	18.9293i	−1.29136	+	0.642873i
$868$		0			0
$869$	−12.1965	+	7.04166i	−0.413738	+	0.238872i
$870$		0			0
$871$		−	28.4462i		−	0.963863i
$872$		0			0
$873$	−5.63020	+	45.4009i	−0.190553	+	1.53659i
$874$		0			0
$875$	−9.32502	−	9.71217i	−0.315243	−	0.328331i
$876$		0			0
$877$	−4.05651			−0.136979			−0.0684893	−	0.997652i	$-0.521818\pi$
$877$	−4.05651			−0.136979			−0.0684893	+	0.997652i	$0.521818\pi$
$878$		0			0
$879$	0.900239	−	14.5743i	0.0303643	−	0.491580i
$880$		0			0
$881$	−54.3727			−1.83186			−0.915931	−	0.401336i	$-0.868546\pi$
$881$	−54.3727			−1.83186			−0.915931	+	0.401336i	$0.868546\pi$
$882$		0			0
$883$	−23.1175			−0.777965			−0.388982	−	0.921245i	$-0.627173\pi$
$883$	−23.1175			−0.777965			−0.388982	+	0.921245i	$0.627173\pi$
$884$		0			0
$885$	38.5715	−	19.2020i	1.29657	−	0.645467i
$886$		0			0
$887$	−25.5636			−0.858342			−0.429171	−	0.903223i	$-0.641194\pi$
$887$	−25.5636			−0.858342			−0.429171	+	0.903223i	$0.641194\pi$
$888$		0			0
$889$	24.5211	+	25.5392i	0.822412	+	0.856556i
$890$		0			0
$891$	−17.5222	−	17.0030i	−0.587016	−	0.569621i
$892$		0			0
$893$			35.7580i			1.19660i
$894$		0			0
$895$	−46.6428	+	26.9292i	−1.55910	+	0.900144i
$896$		0			0
$897$	−1.17660	+	19.0485i	−0.0392856	+	0.636010i
$898$		0			0
$899$	13.6871	+	23.7067i	0.456489	+	0.790663i
$900$		0			0
$901$	13.9457	+	8.05155i	0.464598	+	0.268236i
$902$		0			0
$903$	40.3677	+	14.4534i	1.34335	+	0.480980i
$904$		0			0
$905$			12.8424i			0.426895i
$906$		0			0
$907$	37.0130			1.22900			0.614498	−	0.788918i	$-0.289359\pi$
$907$	37.0130			1.22900			0.614498	+	0.788918i	$0.289359\pi$
$908$		0			0
$909$	−4.07817	−	9.63991i	−0.135264	−	0.319736i
$910$		0			0
$911$	−3.16266	−	1.82596i	−0.104784	−	0.0604969i	0.446692	−	0.894688i	$-0.352602\pi$
$911$	−3.16266	−	1.82596i	−0.104784	−	0.0604969i	−0.551476	+	0.834191i	$0.685935\pi$
$912$		0			0
$913$	−37.2591	−	21.5116i	−1.23310	−	0.711929i
$914$		0			0
$915$	−3.24568	−	0.200482i	−0.107299	−	0.00662772i
$916$		0			0
$917$	1.42548	+	1.48466i	0.0470734	+	0.0490278i
$918$		0			0
$919$	−17.3994	+	30.1367i	−0.573954	+	0.994117i	0.422201	+	0.906502i	$0.361258\pi$
$919$	−17.3994	+	30.1367i	−0.573954	+	0.994117i	−0.996154	+	0.0876145i	$0.972076\pi$
$920$		0			0
$921$	−5.11291	+	7.71464i	−0.168476	+	0.254206i
$922$		0			0
$923$	14.4863	+	25.0910i	0.476822	+	0.825879i
$924$		0			0
$925$	−5.50420	+	9.53356i	−0.180977	+	0.313461i
$926$		0			0
$927$	−9.22526	+	3.90275i	−0.302997	+	0.128183i
$928$		0			0
$929$	−25.1736	−	43.6019i	−0.825917	−	1.43053i	−0.901216	−	0.433370i	$-0.857324\pi$
$929$	−25.1736	−	43.6019i	−0.825917	−	1.43053i	0.0752987	−	0.997161i	$-0.476009\pi$
$930$		0			0
$931$	11.8385	−	18.7048i	0.387990	−	0.613027i
$932$		0			0
$933$	14.6019	−	7.26925i	0.478046	−	0.237985i
$934$		0			0
$935$	43.4197	−	25.0684i	1.41998	−	0.819824i
$936$		0			0
$937$			6.48087i			0.211721i	0.994381	+	0.105860i	$0.0337596\pi$
$937$			6.48087i			0.211721i	−0.994381	+	0.105860i	$0.966240\pi$
$938$		0			0
$939$	28.6148	+	1.76751i	0.933810	+	0.0576804i
$940$		0			0
$941$	0.334024	−	0.578547i	0.0108889	−	0.0188601i	−0.860530	−	0.509400i	$-0.829867\pi$
$941$	0.334024	−	0.578547i	0.0108889	−	0.0188601i	0.871418	+	0.490540i	$0.163201\pi$
$942$		0			0
$943$	−4.11679	+	2.37683i	−0.134061	+	0.0774003i
$944$		0			0
$945$	−32.9810	+	21.6078i	−1.07287	+	0.702902i
$946$		0			0
$947$	50.7461	−	29.2983i	1.64903	−	0.952067i	0.671569	−	0.740942i	$-0.265621\pi$
$947$	50.7461	−	29.2983i	1.64903	−	0.952067i	0.977459	−	0.211125i	$-0.0677127\pi$
$948$		0			0
$949$	23.5560	−	40.8002i	0.764661	−	1.32443i
$950$		0			0
$951$	−45.8576	−	2.83257i	−1.48703	−	0.0918524i
$952$		0			0
$953$		−	48.3707i		−	1.56688i	−0.621467	−	0.783441i	$-0.713463\pi$
$953$		−	48.3707i		−	1.56688i	0.621467	−	0.783441i	$-0.286537\pi$
$954$		0			0
$955$	16.9228	−	9.77041i	0.547610	−	0.316163i
$956$		0			0
$957$	12.0618	−	6.00470i	0.389903	−	0.194105i
$958$		0			0
$959$	31.5313	−	30.2744i	1.01820	−	0.977610i
$960$		0			0
$961$	30.0665	+	52.0767i	0.969887	+	1.67989i
$962$		0			0
$963$	1.32490	−	10.6838i	0.0426944	−	0.344279i
$964$		0			0
$965$	22.8781	−	39.6261i	0.736474	−	1.27561i
$966$		0			0
$967$	−8.51390	−	14.7465i	−0.273788	−	0.474216i	0.696040	−	0.718003i	$-0.254943\pi$
$967$	−8.51390	−	14.7465i	−0.273788	−	0.474216i	−0.969829	+	0.243787i	$0.921610\pi$
$968$		0			0
$969$	−19.4984	+	29.4203i	−0.626379	+	0.945115i
$970$		0			0
$971$	13.5651	−	23.4955i	0.435325	−	0.754006i	−0.561997	−	0.827139i	$-0.689967\pi$
$971$	13.5651	−	23.4955i	0.435325	−	0.754006i	0.997322	+	0.0731339i	$0.0233000\pi$
$972$		0			0
$973$	29.1028	+	8.43589i	0.932994	+	0.270442i
$974$		0			0
$975$	20.5396	+	1.26870i	0.657792	+	0.0406311i
$976$		0			0
$977$	5.49838	+	3.17449i	0.175909	+	0.101561i	0.585369	−	0.810767i	$-0.300950\pi$
$977$	5.49838	+	3.17449i	0.175909	+	0.101561i	−0.409460	+	0.912328i	$0.634283\pi$
$978$		0			0
$979$	−14.7931	−	8.54080i	−0.472789	−	0.272965i
$980$		0			0
$981$	−24.9432	+	33.0177i	−0.796376	+	1.05418i
$982$		0			0
$983$	−19.9660			−0.636817			−0.318408	−	0.947954i	$-0.603148\pi$
$983$	−19.9660			−0.636817			−0.318408	+	0.947954i	$0.603148\pi$
$984$		0			0
$985$			74.4288i			2.37150i
$986$		0			0
$987$	39.5191	−	33.5151i	1.25791	−	1.06680i
$988$		0			0
$989$	24.2399	+	13.9949i	0.770784	+	0.445012i
$990$		0			0
$991$	−6.38803	−	11.0644i	−0.202922	−	0.351472i	0.746546	−	0.665333i	$-0.231711\pi$
$991$	−6.38803	−	11.0644i	−0.202922	−	0.351472i	−0.949469	+	0.313861i	$0.898377\pi$
$992$		0			0
$993$	1.88366	−	30.4952i	0.0597760	−	0.967737i
$994$		0			0
$995$	−7.90734	+	4.56530i	−0.250679	+	0.144730i
$996$		0			0
$997$			20.7669i			0.657694i	0.944383	+	0.328847i	$0.106660\pi$
$997$			20.7669i			0.657694i	−0.944383	+	0.328847i	$0.893340\pi$
$998$		0			0
$999$	−13.4637	−	11.5413i	−0.425972	−	0.365151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.d.929.7		16
3.2	odd	2		3024.2.df.d.1601.1		16
4.3	odd	2		252.2.bm.a.173.2	yes	16
7.3	odd	6		1008.2.ca.d.353.4		16
9.4	even	3		3024.2.ca.d.2609.1		16
9.5	odd	6		1008.2.ca.d.257.4		16
12.11	even	2		756.2.bm.a.89.1		16
21.17	even	6		3024.2.ca.d.2033.1		16
28.3	even	6		252.2.w.a.101.5	yes	16
28.11	odd	6		1764.2.w.b.1109.4		16
28.19	even	6		1764.2.x.a.1469.1		16
28.23	odd	6		1764.2.x.b.1469.8		16
28.27	even	2		1764.2.bm.a.1685.7		16
36.7	odd	6		2268.2.t.a.2105.1		16
36.11	even	6		2268.2.t.b.2105.8		16
36.23	even	6		252.2.w.a.5.5	✓	16
36.31	odd	6		756.2.w.a.341.1		16
63.31	odd	6		3024.2.df.d.17.1		16
63.59	even	6	inner	1008.2.df.d.689.7		16
84.11	even	6		5292.2.w.b.521.8		16
84.23	even	6		5292.2.x.b.4409.8		16
84.47	odd	6		5292.2.x.a.4409.1		16
84.59	odd	6		756.2.w.a.521.1		16
84.83	odd	2		5292.2.bm.a.4625.8		16
252.23	even	6		1764.2.x.a.293.1		16
252.31	even	6		756.2.bm.a.17.1		16
252.59	odd	6		252.2.bm.a.185.2	yes	16
252.67	odd	6		5292.2.bm.a.2285.8		16
252.95	even	6		1764.2.bm.a.1697.7		16
252.103	even	6		5292.2.x.b.881.8		16
252.115	even	6		2268.2.t.b.1781.8		16
252.131	odd	6		1764.2.x.b.293.8		16
252.139	even	6		5292.2.w.b.1097.8		16
252.167	odd	6		1764.2.w.b.509.4		16
252.227	odd	6		2268.2.t.a.1781.1		16
252.247	odd	6		5292.2.x.a.881.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	36.23	even	6
252.2.w.a.101.5	yes	16	28.3	even	6
252.2.bm.a.173.2	yes	16	4.3	odd	2
252.2.bm.a.185.2	yes	16	252.59	odd	6
756.2.w.a.341.1		16	36.31	odd	6
756.2.w.a.521.1		16	84.59	odd	6
756.2.bm.a.17.1		16	252.31	even	6
756.2.bm.a.89.1		16	12.11	even	2
1008.2.ca.d.257.4		16	9.5	odd	6
1008.2.ca.d.353.4		16	7.3	odd	6
1008.2.df.d.689.7		16	63.59	even	6	inner
1008.2.df.d.929.7		16	1.1	even	1	trivial
1764.2.w.b.509.4		16	252.167	odd	6
1764.2.w.b.1109.4		16	28.11	odd	6
1764.2.x.a.293.1		16	252.23	even	6
1764.2.x.a.1469.1		16	28.19	even	6
1764.2.x.b.293.8		16	252.131	odd	6
1764.2.x.b.1469.8		16	28.23	odd	6
1764.2.bm.a.1685.7		16	28.27	even	2
1764.2.bm.a.1697.7		16	252.95	even	6
2268.2.t.a.1781.1		16	252.227	odd	6
2268.2.t.a.2105.1		16	36.7	odd	6
2268.2.t.b.1781.8		16	252.115	even	6
2268.2.t.b.2105.8		16	36.11	even	6
3024.2.ca.d.2033.1		16	21.17	even	6
3024.2.ca.d.2609.1		16	9.4	even	3
3024.2.df.d.17.1		16	63.31	odd	6
3024.2.df.d.1601.1		16	3.2	odd	2
5292.2.w.b.521.8		16	84.11	even	6
5292.2.w.b.1097.8		16	252.139	even	6
5292.2.x.a.881.1		16	252.247	odd	6
5292.2.x.a.4409.1		16	84.47	odd	6
5292.2.x.b.881.8		16	252.103	even	6
5292.2.x.b.4409.8		16	84.23	even	6
5292.2.bm.a.2285.8		16	252.67	odd	6
5292.2.bm.a.4625.8		16	84.83	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.44376 + 0.956855i) q^{3} +2.86804 q^{5} +(1.83240 + 1.90848i) q^{7} +(1.16886 + 2.76293i) q^{9} +2.71286i q^{11} +(3.18987 - 1.84167i) q^{13} +(4.14074 + 2.74429i) q^{15} +(-3.22192 - 5.58052i) q^{17} +(-2.73867 - 1.58117i) q^{19} +(0.819404 + 4.50872i) q^{21} +2.99146i q^{23} +3.22563 q^{25} +(-0.956179 + 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +(-8.26739 - 4.77318i) q^{31} +(-2.59581 + 3.91671i) q^{33} +(5.25540 + 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(6.36761 + 0.393320i) q^{39} +(0.794538 + 1.37618i) q^{41} +(4.67828 - 8.10302i) q^{43} +(3.35232 + 7.92418i) q^{45} +(-5.65372 - 9.79254i) q^{47} +(-0.284592 + 6.99421i) q^{49} +(0.688093 - 11.1398i) q^{51} +(-2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} +(4.33680 - 7.51156i) q^{59} +(-0.566915 + 0.327308i) q^{61} +(-3.13118 + 7.29354i) q^{63} +(9.14867 - 5.28199i) q^{65} +(3.86146 - 6.68825i) q^{67} +(-2.86240 + 4.31894i) q^{69} +7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(4.65702 + 3.08646i) q^{75} +(-5.17744 + 4.97106i) q^{77} +(2.59566 + 4.49581i) q^{79} +(-6.26755 + 6.45894i) q^{81} +(-7.92948 + 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-2.21342 - 4.44616i) q^{87} +(-3.14826 + 5.45295i) q^{89} +(9.35993 + 2.71312i) q^{91} +(-7.36885 - 14.8020i) q^{93} +(-7.85460 - 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +(-7.49544 + 3.17095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) \) 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Introduction

L-functions

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Varieties

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Database

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