LMFDB - Embedded newform 252.2.bm.a.173.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.01223013094$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.2
Root			$-0.213160 + 1.71888i$ of defining polynomial
Character	$\chi$	$=$	252.173
Dual form			252.2.bm.a.185.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44376 - 0.956855i) q^{3} +2.86804 q^{5} +(-1.83240 - 1.90848i) q^{7} +(1.16886 + 2.76293i) q^{9} +O(q^{10})$	\(q+(-1.44376 - 0.956855i) q^{3} +2.86804 q^{5} +(-1.83240 - 1.90848i) q^{7} +(1.16886 + 2.76293i) q^{9} -2.71286i q^{11} +(3.18987 - 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +(-3.22192 - 5.58052i) q^{17} +(2.73867 + 1.58117i) q^{19} +(0.819404 + 4.50872i) q^{21} -2.99146i q^{23} +3.22563 q^{25} +(0.956179 - 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +(8.26739 + 4.77318i) q^{31} +(-2.59581 + 3.91671i) q^{33} +(-5.25540 - 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(-6.36761 - 0.393320i) q^{39} +(0.794538 + 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(3.35232 + 7.92418i) q^{45} +(5.65372 + 9.79254i) q^{47} +(-0.284592 + 6.99421i) q^{49} +(-0.688093 + 11.1398i) q^{51} +(-2.16419 + 1.24950i) q^{53} -7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} +(-4.33680 + 7.51156i) q^{59} +(-0.566915 + 0.327308i) q^{61} +(3.13118 - 7.29354i) q^{63} +(9.14867 - 5.28199i) q^{65} +(-3.86146 + 6.68825i) q^{67} +(-2.86240 + 4.31894i) q^{69} -7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(-4.65702 - 3.08646i) q^{75} +(-5.17744 + 4.97106i) q^{77} +(-2.59566 - 4.49581i) q^{79} +(-6.26755 + 6.45894i) q^{81} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(2.21342 + 4.44616i) q^{87} +(-3.14826 + 5.45295i) q^{89} +(-9.35993 - 2.71312i) q^{91} +(-7.36885 - 14.8020i) q^{93} +(7.85460 + 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−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	$-0.865885\pi$
$11$		−	2.71286i		−	0.817958i	0.912544	−	0.408979i	$-0.134115\pi$
$12$		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	0.780091	−	0.625666i	$-0.215173\pi$
$19$	2.73867	+	1.58117i	0.628294	+	0.362746i	−0.151797	+	0.988412i	$0.548506\pi$
$20$		0			0
$21$	0.819404	+	4.50872i	0.178809	+	0.983884i
$22$		0			0
$23$		−	2.99146i		−	0.623763i	−0.950121	−	0.311882i	$-0.899041\pi$
$23$		−	2.99146i		−	0.623763i	0.950121	−	0.311882i	$-0.100959\pi$
$24$		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	0.999852	−	0.0172169i	$-0.00548059\pi$
$31$	8.26739	+	4.77318i	1.48487	+	0.857289i	0.485016	+	0.874506i	$0.338814\pi$
$32$		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	$0.419526\pi$
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	−0.963562	+	0.267487i	$0.913807\pi$
$44$		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	$0.141978\pi$
$47$	5.65372	+	9.79254i	0.824680	+	1.42839i	−0.0774831	+	0.996994i	$0.524688\pi$
$48$		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	$0.357638\pi$
$59$	−4.33680	+	7.51156i	−0.564604	+	0.977922i	−0.997086	+	0.0762801i	$0.975696\pi$
$60$		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	−0.999478	−	0.0323159i	$-0.989712\pi$
$67$	−3.86146	+	6.68825i	−0.471752	+	0.817099i	0.527725	+	0.849415i	$0.323045\pi$
$68$		0			0
$69$	−2.86240	+	4.31894i	−0.344592	+	0.519939i
$70$		0			0
$71$		−	7.86582i		−	0.933501i	−0.884389	−	0.466750i	$-0.845425\pi$
$71$		−	7.86582i		−	0.933501i	0.884389	−	0.466750i	$-0.154575\pi$
$72$		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	0.682256	−	0.731113i	$-0.260999\pi$
$79$	−2.59566	−	4.49581i	−0.292034	−	0.505819i	−0.974291	+	0.225295i	$0.927666\pi$
$80$		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	$-0.497211\pi$
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.861611	−	0.507569i	$-0.169456\pi$
$84$		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	$-0.947400\pi$
$103$		−	3.33894i		−	0.328996i	0.986377	−	0.164498i	$-0.0526004\pi$
$104$		0			0
$105$	2.35008	+	12.9312i	0.229344	+	1.26195i
$106$		0			0
$107$	3.10776	+	1.79427i	0.300439	+	0.173458i	0.642640	−	0.766168i	$-0.277839\pi$
$107$	3.10776	+	1.79427i	0.300439	+	0.173458i	−0.342201	+	0.939627i	$0.611172\pi$
$108$		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	$-0.702344\pi$
$127$	−13.3819			−1.18745			−0.593727	+	0.804666i	$0.702344\pi$
$128$		0			0
$129$	14.5077	−	7.22234i	1.27733	−	0.635891i
$130$		0			0
$131$	−0.777928			−0.0679679			−0.0339839	−	0.999422i	$-0.510820\pi$
$131$	−0.777928			−0.0679679			−0.0339839	+	0.999422i	$0.510820\pi$
$132$		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	−0.857691	−	0.514165i	$-0.828102\pi$
$139$	−9.91826	+	5.72631i	−0.841256	+	0.485699i	0.0164348	+	0.999865i	$0.494768\pi$
$140$		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	$-0.368647\pi$
$151$	9.85629			0.802093			0.401047	+	0.916058i	$0.368647\pi$
$152$		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	−0.998260	−	0.0589632i	$-0.981221\pi$
$163$	−5.72053	+	9.90825i	−0.448066	+	0.776074i	0.550194	+	0.835037i	$0.314554\pi$
$164$		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	$0.000842678\pi$
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	−0.497706	+	0.867346i	$0.665824\pi$
$168$		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	0.251588	−	0.967835i	$-0.419047\pi$
$179$	16.2630	−	9.38942i	1.21555	−	0.701799i	0.963963	+	0.266036i	$0.0857140\pi$
$180$		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	−0.698044	−	0.716055i	$-0.745946\pi$
$191$	−5.90050	+	3.40665i	−0.426945	+	0.246497i	0.271099	+	0.962551i	$0.412613\pi$
$192$		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	−0.399085	−	0.916914i	$-0.630672\pi$
$199$	2.75706	−	1.59179i	0.195443	−	0.112839i	0.594528	+	0.804075i	$0.297339\pi$
$200$		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	0.864118	−	0.503290i	$-0.167877\pi$
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	−0.867921	+	0.496703i	$0.834544\pi$
$212$		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	0.0711331	−	0.997467i	$-0.477339\pi$
$223$	−11.3064	−	6.52775i	−0.757132	−	0.437130i	−0.828265	+	0.560336i	$0.810672\pi$
$224$		0			0
$225$	3.77030	+	8.91219i	0.251353	+	0.594146i
$226$		0			0
$227$	9.26784			0.615128			0.307564	−	0.951527i	$-0.400486\pi$
$227$	9.26784			0.615128			0.307564	+	0.951527i	$0.400486\pi$
$228$		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	−0.728810	−	0.684716i	$-0.759926\pi$
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	0.228577	+	0.973526i	$0.426593\pi$
$240$		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	$-0.435960\pi$
$251$	6.33194			0.399669			0.199834	+	0.979830i	$0.435960\pi$
$252$		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	$-0.878463\pi$
$263$		−	12.0854i		−	0.745217i	0.927989	−	0.372609i	$-0.121537\pi$
$264$		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	0.494048	−	0.869435i	$-0.335517\pi$
$271$	−0.195591	−	0.112924i	−0.0118813	−	0.00685967i	−0.505929	+	0.862575i	$0.668850\pi$
$272$		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	0.809608	−	0.586971i	$-0.199680\pi$
$283$	11.8781	+	6.85783i	0.706080	+	0.407656i	−0.103528	+	0.994627i	$0.533013\pi$
$284$		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	$-0.951273\pi$
$307$		−	5.34345i		−	0.304967i	0.988306	−	0.152484i	$-0.0487271\pi$
$308$		0			0
$309$	−3.19488	+	4.82061i	−0.181751	+	0.274235i
$310$		0			0
$311$	−4.70867	+	8.15565i	−0.267004	+	0.462465i	−0.968087	−	0.250615i	$-0.919367\pi$
$311$	−4.70867	+	8.15565i	−0.267004	+	0.462465i	0.701083	+	0.713080i	$0.252700\pi$
$312$		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	0.999847	−	0.0174739i	$-0.00556238\pi$
$331$	8.82000	+	15.2767i	0.484791	+	0.839682i	−0.515056	+	0.857156i	$0.672229\pi$
$332$		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	0.528067	−	0.849203i	$-0.322917\pi$
$347$	1.05563	+	0.609467i	0.0566691	+	0.0327179i	−0.471398	+	0.881921i	$0.656250\pi$
$348$		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	0.197204	−	0.980363i	$-0.436814\pi$
$359$	−10.4819	−	6.05173i	−0.553214	−	0.319398i	−0.750417	+	0.660965i	$0.770147\pi$
$360$		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	$-0.874414\pi$
$367$		−	14.7275i		−	0.768769i	0.923173	−	0.384385i	$-0.125586\pi$
$368$		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	$-0.316435\pi$
$379$	21.2298			1.09050			0.545250	+	0.838273i	$0.316435\pi$
$380$		0			0
$381$	19.3202	+	12.8046i	0.989806	+	0.655998i
$382$		0			0
$383$	6.70454			0.342586			0.171293	−	0.985220i	$-0.445206\pi$
$383$	6.70454			0.342586			0.171293	+	0.985220i	$0.445206\pi$
$384$		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	$-0.992094\pi$
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	0.478339	−	0.878176i	$-0.341239\pi$
$420$		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	0.346333	−	0.938112i	$-0.387427\pi$
$431$	27.6515	−	15.9646i	1.33193	−	0.768989i	0.985595	+	0.169123i	$0.0540934\pi$
$432$		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	−0.456352	−	0.889799i	$-0.650844\pi$
$439$	1.80316	−	1.04106i	0.0860603	−	0.0496869i	0.542413	+	0.840112i	$0.317511\pi$
$440$		0			0
$441$	−19.6572	+	7.38893i	−0.936055	+	0.351854i
$442$		0			0
$443$	2.13895	−	1.23493i	0.101625	−	0.0586731i	−0.448326	−	0.893870i	$-0.647980\pi$
$443$	2.13895	−	1.23493i	0.101625	−	0.0586731i	0.549951	+	0.835197i	$0.314646\pi$
$444$		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	0.957057	−	0.289901i	$-0.0936225\pi$
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	−0.729590	+	0.683885i	$0.760289\pi$
$464$		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	$0.392557\pi$
$467$	−14.0806	+	24.3883i	−0.651572	+	1.12856i	−0.982741	+	0.184985i	$0.940776\pi$
$468$		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	$-0.736491\pi$
$479$	−29.6105			−1.35294			−0.676470	+	0.736470i	$0.736491\pi$
$480$		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	$-0.935198\pi$
$487$	−14.6701	−	25.4094i	−0.664767	−	1.15141i	0.314582	−	0.949230i	$-0.398136\pi$
$488$		0			0
$489$	17.7398	−	8.83136i	0.802221	−	0.399368i
$490$		0			0
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	−0.682075	−	0.731283i	$-0.738922\pi$
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	0.292272	+	0.956335i	$0.405589\pi$
$492$		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	$-0.644530\pi$
$499$	−19.5957			−0.877223			−0.438611	+	0.898677i	$0.644530\pi$
$500$		0			0
$501$	1.38627	−	22.4428i	0.0619338	−	1.00267i
$502$		0			0
$503$	−21.2907			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$503$	−21.2907			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$504$		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	$-0.993445\pi$
$523$	−34.7043	−	20.0365i	−1.51751	−	0.876137i	−0.517726	−	0.855547i	$-0.673221\pi$
$524$		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	−0.915162	−	0.403086i	$-0.867938\pi$
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	0.806664	+	0.591011i	$0.201271\pi$
$548$		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	−0.951825	−	0.306641i	$-0.900795\pi$
$563$	−4.99118	+	8.64498i	−0.210353	+	0.364343i	0.741472	+	0.670984i	$0.234128\pi$
$564$		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	−0.703244	−	0.710948i	$-0.748266\pi$
$571$	6.31028	−	10.9297i	0.264077	−	0.457395i	0.967321	+	0.253553i	$0.0815994\pi$
$572$		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	−0.953925	−	0.300044i	$-0.902999\pi$
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	0.736809	+	0.676101i	$0.236332\pi$
$588$		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	0.347516	−	0.937674i	$-0.387025\pi$
$599$	−7.11658	−	4.10876i	−0.290776	−	0.167879i	−0.638292	+	0.769795i	$0.720359\pi$
$600$		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	$-0.742796\pi$
$607$		−	35.6221i		−	1.44586i	0.690923	−	0.722929i	$-0.257204\pi$
$608$		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	$0.0677888\pi$
$619$			10.5171i			0.422717i	−0.977409	+	0.211359i	$0.932211\pi$
$620$		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	$-0.512855\pi$
$631$	−2.02836			−0.0807477			−0.0403739	+	0.999185i	$0.512855\pi$
$632$		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	−0.236635	−	0.971599i	$-0.576044\pi$
$643$	12.3358	−	7.12209i	0.486477	−	0.280868i	0.723112	+	0.690731i	$0.242711\pi$
$644$		0			0
$645$	41.6086	−	20.7139i	1.63834	−	0.815610i
$646$		0			0
$647$	10.1910	+	17.6513i	0.400649	+	0.693945i	0.993804	−	0.111143i	$-0.0354512\pi$
$647$	10.1910	+	17.6513i	0.400649	+	0.693945i	−0.593155	+	0.805088i	$0.702118\pi$
$648$		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	0.136864	−	0.990590i	$-0.456298\pi$
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	−0.789444	+	0.613822i	$0.789631\pi$
$660$		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	−0.327148	−	0.944973i	$-0.606088\pi$
$683$	8.56287	−	4.94377i	0.327649	−	0.189168i	0.654797	+	0.755805i	$0.272754\pi$
$684$		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	0.444587	−	0.895736i	$-0.353351\pi$
$691$	37.9217	−	21.8941i	1.44261	−	0.832891i	0.998023	+	0.0628444i	$0.0200172\pi$
$692$		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	−0.882480	−	0.470349i	$-0.844128\pi$
$719$	−0.909148	+	1.57469i	−0.0339055	+	0.0587261i	0.848575	+	0.529076i	$0.177461\pi$
$720$		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	0.0382766	−	0.999267i	$-0.487813\pi$
$727$	−21.7854	−	12.5778i	−0.807976	−	0.466485i	−0.846252	+	0.532782i	$0.821147\pi$
$728$		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	0.652358	−	0.757911i	$-0.273780\pi$
$739$	−8.97608	−	15.5470i	−0.330191	−	0.571907i	−0.982549	+	0.186004i	$0.940446\pi$
$740$		0			0
$741$	−16.8169	−	11.1455i	−0.617783	−	0.409439i
$742$		0			0
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.949106	−	0.314956i	$-0.898010\pi$
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.201793	+	0.979428i	$0.564677\pi$
$744$		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	$-0.429952\pi$
$751$	11.9642			0.436580			0.218290	+	0.975884i	$0.429952\pi$
$752$		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	0.471335	−	0.881954i	$-0.343772\pi$
$787$	−1.59324	−	0.919855i	−0.0567927	−	0.0327893i	−0.528128	+	0.849165i	$0.677106\pi$
$788$		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	$0.229122\pi$
$811$			37.5478i			1.31848i	−0.751933	+	0.659240i	$0.770878\pi$
$812$		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	$0.514342\pi$
$823$	−25.4654	+	44.1073i	−0.887667	+	1.53748i	−0.842626	+	0.538499i	$0.818992\pi$
$824$		0			0
$825$	−8.37314	+	12.6338i	−0.291515	+	0.439854i
$826$		0			0
$827$			16.9198i			0.588360i	0.955750	+	0.294180i	$0.0950465\pi$
$827$			16.9198i			0.588360i	−0.955750	+	0.294180i	$0.904954\pi$
$828$		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	−0.585026	−	0.811014i	$-0.698916\pi$
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	0.994872	+	0.101140i	$0.0322492\pi$
$840$		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	$0.232591\pi$
$859$			39.1210i			1.33479i	−0.744704	+	0.667395i	$0.767409\pi$
$860$		0			0
$861$	−5.55376	+	4.71000i	−0.189272	+	0.160516i
$862$		0			0
$863$	−39.2319	−	22.6506i	−1.33547	−	0.771034i	−0.349338	−	0.936997i	$-0.613593\pi$
$863$	−39.2319	−	22.6506i	−1.33547	−	0.771034i	−0.986132	+	0.165963i	$0.946927\pi$
$864$		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	$-0.372827\pi$
$883$	23.1175			0.777965			0.388982	+	0.921245i	$0.372827\pi$
$884$		0			0
$885$	38.5715	−	19.2020i	1.29657	−	0.645467i
$886$		0			0
$887$	25.5636			0.858342			0.429171	−	0.903223i	$-0.358806\pi$
$887$	25.5636			0.858342			0.429171	+	0.903223i	$0.358806\pi$
$888$		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	$-0.710641\pi$
$907$	−37.0130			−1.22900			−0.614498	+	0.788918i	$0.710641\pi$
$908$		0			0
$909$	−4.07817	−	9.63991i	−0.135264	−	0.319736i
$910$		0			0
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	0.551476	−	0.834191i	$-0.314065\pi$
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	−0.446692	+	0.894688i	$0.647398\pi$
$912$		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	$-0.638742\pi$
$919$	17.3994	−	30.1367i	0.573954	−	0.994117i	0.996154	−	0.0876145i	$-0.0279244\pi$
$920$		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	$0.734379\pi$
$947$	−50.7461	+	29.2983i	−1.64903	+	0.952067i	−0.977459	+	0.211125i	$0.932287\pi$
$948$		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	0.969829	−	0.243787i	$-0.0783898\pi$
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	−0.696040	+	0.718003i	$0.745057\pi$
$968$		0			0
$969$	−19.4984	+	29.4203i	−0.626379	+	0.945115i
$970$		0			0
$971$	−13.5651	+	23.4955i	−0.435325	+	0.754006i	−0.997322	−	0.0731339i	$-0.976700\pi$
$971$	−13.5651	+	23.4955i	−0.435325	+	0.754006i	0.561997	+	0.827139i	$0.310033\pi$
$972$		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	$-0.396852\pi$
$983$	19.9660			0.636817			0.318408	+	0.947954i	$0.396852\pi$
$984$		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	0.949469	−	0.313861i	$-0.101623\pi$
$991$	6.38803	+	11.0644i	0.202922	+	0.351472i	−0.746546	+	0.665333i	$0.768289\pi$
$992$		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	252.2.bm.a.173.2	yes	16
3.2	odd	2		756.2.bm.a.89.1		16
4.3	odd	2		1008.2.df.d.929.7		16
7.2	even	3		1764.2.x.b.1469.8		16
7.3	odd	6		252.2.w.a.101.5	yes	16
7.4	even	3		1764.2.w.b.1109.4		16
7.5	odd	6		1764.2.x.a.1469.1		16
7.6	odd	2		1764.2.bm.a.1685.7		16
9.2	odd	6		2268.2.t.b.2105.8		16
9.4	even	3		756.2.w.a.341.1		16
9.5	odd	6		252.2.w.a.5.5	✓	16
9.7	even	3		2268.2.t.a.2105.1		16
12.11	even	2		3024.2.df.d.1601.1		16
21.2	odd	6		5292.2.x.b.4409.8		16
21.5	even	6		5292.2.x.a.4409.1		16
21.11	odd	6		5292.2.w.b.521.8		16
21.17	even	6		756.2.w.a.521.1		16
21.20	even	2		5292.2.bm.a.4625.8		16
28.3	even	6		1008.2.ca.d.353.4		16
36.23	even	6		1008.2.ca.d.257.4		16
36.31	odd	6		3024.2.ca.d.2609.1		16
63.4	even	3		5292.2.bm.a.2285.8		16
63.5	even	6		1764.2.x.b.293.8		16
63.13	odd	6		5292.2.w.b.1097.8		16
63.23	odd	6		1764.2.x.a.293.1		16
63.31	odd	6		756.2.bm.a.17.1		16
63.32	odd	6		1764.2.bm.a.1697.7		16
63.38	even	6		2268.2.t.a.1781.1		16
63.40	odd	6		5292.2.x.b.881.8		16
63.41	even	6		1764.2.w.b.509.4		16
63.52	odd	6		2268.2.t.b.1781.8		16
63.58	even	3		5292.2.x.a.881.1		16
63.59	even	6	inner	252.2.bm.a.185.2	yes	16
84.59	odd	6		3024.2.ca.d.2033.1		16
252.31	even	6		3024.2.df.d.17.1		16
252.59	odd	6		1008.2.df.d.689.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	9.5	odd	6
252.2.w.a.101.5	yes	16	7.3	odd	6
252.2.bm.a.173.2	yes	16	1.1	even	1	trivial
252.2.bm.a.185.2	yes	16	63.59	even	6	inner
756.2.w.a.341.1		16	9.4	even	3
756.2.w.a.521.1		16	21.17	even	6
756.2.bm.a.17.1		16	63.31	odd	6
756.2.bm.a.89.1		16	3.2	odd	2
1008.2.ca.d.257.4		16	36.23	even	6
1008.2.ca.d.353.4		16	28.3	even	6
1008.2.df.d.689.7		16	252.59	odd	6
1008.2.df.d.929.7		16	4.3	odd	2
1764.2.w.b.509.4		16	63.41	even	6
1764.2.w.b.1109.4		16	7.4	even	3
1764.2.x.a.293.1		16	63.23	odd	6
1764.2.x.a.1469.1		16	7.5	odd	6
1764.2.x.b.293.8		16	63.5	even	6
1764.2.x.b.1469.8		16	7.2	even	3
1764.2.bm.a.1685.7		16	7.6	odd	2
1764.2.bm.a.1697.7		16	63.32	odd	6
2268.2.t.a.1781.1		16	63.38	even	6
2268.2.t.a.2105.1		16	9.7	even	3
2268.2.t.b.1781.8		16	63.52	odd	6
2268.2.t.b.2105.8		16	9.2	odd	6
3024.2.ca.d.2033.1		16	84.59	odd	6
3024.2.ca.d.2609.1		16	36.31	odd	6
3024.2.df.d.17.1		16	252.31	even	6
3024.2.df.d.1601.1		16	12.11	even	2
5292.2.w.b.521.8		16	21.11	odd	6
5292.2.w.b.1097.8		16	63.13	odd	6
5292.2.x.a.881.1		16	63.58	even	3
5292.2.x.a.4409.1		16	21.5	even	6
5292.2.x.b.881.8		16	63.40	odd	6
5292.2.x.b.4409.8		16	21.2	odd	6
5292.2.bm.a.2285.8		16	63.4	even	3
5292.2.bm.a.4625.8		16	21.20	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44376 - 0.956855i) q^{3} +2.86804 q^{5} +(-1.83240 - 1.90848i) q^{7} +(1.16886 + 2.76293i) q^{9} +O(q^{10})\)	\(q+(-1.44376 - 0.956855i) q^{3} +2.86804 q^{5} +(-1.83240 - 1.90848i) q^{7} +(1.16886 + 2.76293i) q^{9} -2.71286i q^{11} +(3.18987 - 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +(-3.22192 - 5.58052i) q^{17} +(2.73867 + 1.58117i) q^{19} +(0.819404 + 4.50872i) q^{21} -2.99146i q^{23} +3.22563 q^{25} +(0.956179 - 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +(8.26739 + 4.77318i) q^{31} +(-2.59581 + 3.91671i) q^{33} +(-5.25540 - 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(-6.36761 - 0.393320i) q^{39} +(0.794538 + 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(3.35232 + 7.92418i) q^{45} +(5.65372 + 9.79254i) q^{47} +(-0.284592 + 6.99421i) q^{49} +(-0.688093 + 11.1398i) q^{51} +(-2.16419 + 1.24950i) q^{53} -7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} +(-4.33680 + 7.51156i) q^{59} +(-0.566915 + 0.327308i) q^{61} +(3.13118 - 7.29354i) q^{63} +(9.14867 - 5.28199i) q^{65} +(-3.86146 + 6.68825i) q^{67} +(-2.86240 + 4.31894i) q^{69} -7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(-4.65702 - 3.08646i) q^{75} +(-5.17744 + 4.97106i) q^{77} +(-2.59566 - 4.49581i) q^{79} +(-6.26755 + 6.45894i) q^{81} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(2.21342 + 4.44616i) q^{87} +(-3.14826 + 5.45295i) q^{89} +(-9.35993 - 2.71312i) q^{91} +(-7.36885 - 14.8020i) q^{93} +(7.85460 + 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 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

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