LMFDB - Embedded newform 572.2.i.c.133.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 $ x^10 - x^9 + 9x^8 + 6x^7 + 59x^6 + 2x^5 + 47x^4 - 26x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.5
Root			$1.61221 + 2.79242i$ of defining polynomial
Character	$\chi$	$=$	572.133
Dual form			572.2.i.c.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61221 + 2.79242i) q^{3} +3.96894 q^{5} +(0.284141 - 0.492146i) q^{7} +(-3.69842 + 6.40585i) q^{9} +O(q^{10})$	\(q+(1.61221 + 2.79242i) q^{3} +3.96894 q^{5} +(0.284141 - 0.492146i) q^{7} +(-3.69842 + 6.40585i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-3.59052 + 0.328858i) q^{13} +(6.39875 + 11.0830i) q^{15} +(-0.777988 + 1.34751i) q^{17} +(4.32616 - 7.49312i) q^{19} +1.83237 q^{21} +(-2.12583 - 3.68204i) q^{23} +10.7525 q^{25} -14.1772 q^{27} +(-3.83231 - 6.63776i) q^{29} -4.29134 q^{31} +(1.61221 - 2.79242i) q^{33} +(1.12774 - 1.95330i) q^{35} +(1.47401 + 2.55305i) q^{37} +(-6.70697 - 9.49607i) q^{39} +(4.00240 + 6.93236i) q^{41} +(0.484469 - 0.839125i) q^{43} +(-14.6788 + 25.4244i) q^{45} -1.07609 q^{47} +(3.33853 + 5.78250i) q^{49} -5.01711 q^{51} -9.71279 q^{53} +(-1.98447 - 3.43720i) q^{55} +27.8986 q^{57} +(3.35058 - 5.80337i) q^{59} +(-1.59668 + 2.76552i) q^{61} +(2.10174 + 3.64033i) q^{63} +(-14.2506 + 1.30522i) q^{65} +(0.0608121 + 0.105330i) q^{67} +(6.85455 - 11.8724i) q^{69} +(0.209642 - 0.363110i) q^{71} -12.1601 q^{73} +(17.3352 + 30.0255i) q^{75} -0.568282 q^{77} -5.77407 q^{79} +(-11.7614 - 20.3713i) q^{81} -1.11577 q^{83} +(-3.08779 + 5.34820i) q^{85} +(12.3570 - 21.4029i) q^{87} +(6.76670 + 11.7203i) q^{89} +(-0.858368 + 1.86050i) q^{91} +(-6.91852 - 11.9832i) q^{93} +(17.1703 - 29.7397i) q^{95} +(6.57357 - 11.3858i) q^{97} +7.39684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.61221	+	2.79242i	0.930808	+	1.61221i	0.781944	+	0.623349i	$0.214228\pi$
$3$	1.61221	+	2.79242i	0.930808	+	1.61221i	0.148864	+	0.988858i	$0.452438\pi$
$4$		0			0
$5$	3.96894			1.77496			0.887482	−	0.460843i	$-0.152453\pi$
$5$	3.96894			1.77496			0.887482	+	0.460843i	$0.152453\pi$
$6$		0			0
$7$	0.284141	−	0.492146i	0.107395	−	0.186014i	−0.807319	−	0.590115i	$-0.799082\pi$
$7$	0.284141	−	0.492146i	0.107395	−	0.186014i	0.914714	+	0.404101i	$0.132416\pi$
$8$		0			0
$9$	−3.69842	+	6.40585i	−1.23281	+	2.13528i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−3.59052	+	0.328858i	−0.995832	+	0.0912087i
$13$	−3.59052	+	0.328858i	−0.995832	+	0.0912087i
$14$		0			0
$15$	6.39875	+	11.0830i	1.65215	+	2.86161i
$16$		0			0
$17$	−0.777988	+	1.34751i	−0.188690	+	0.326820i	−0.944814	−	0.327608i	$-0.893757\pi$
$17$	−0.777988	+	1.34751i	−0.188690	+	0.326820i	0.756124	+	0.654428i	$0.227091\pi$
$18$		0			0
$19$	4.32616	−	7.49312i	0.992489	−	1.71904i	0.390297	−	0.920689i	$-0.372372\pi$
$19$	4.32616	−	7.49312i	0.992489	−	1.71904i	0.602191	−	0.798352i	$-0.294294\pi$
$20$		0			0
$21$	1.83237			0.399857
$22$		0			0
$23$	−2.12583	−	3.68204i	−0.443266	−	0.767759i	0.554664	−	0.832075i	$-0.312847\pi$
$23$	−2.12583	−	3.68204i	−0.443266	−	0.767759i	−0.997930	+	0.0643154i	$0.979514\pi$
$24$		0			0
$25$	10.7525			2.15049
$26$		0			0
$27$	−14.1772			−2.72841
$28$		0			0
$29$	−3.83231	−	6.63776i	−0.711642	−	1.23260i	−0.964240	−	0.265029i	$-0.914618\pi$
$29$	−3.83231	−	6.63776i	−0.711642	−	1.23260i	0.252598	−	0.967571i	$-0.418715\pi$
$30$		0			0
$31$	−4.29134			−0.770747			−0.385374	−	0.922761i	$-0.625927\pi$
$31$	−4.29134			−0.770747			−0.385374	+	0.922761i	$0.625927\pi$
$32$		0			0
$33$	1.61221	−	2.79242i	0.280649	−	0.486099i
$34$		0			0
$35$	1.12774	−	1.95330i	0.190622	−	0.330168i
$36$		0			0
$37$	1.47401	+	2.55305i	0.242325	+	0.419720i	0.961376	−	0.275238i	$-0.0887566\pi$
$37$	1.47401	+	2.55305i	0.242325	+	0.419720i	−0.719051	+	0.694957i	$0.755423\pi$
$38$		0			0
$39$	−6.70697	−	9.49607i	−1.07398	−	1.52059i
$40$		0			0
$41$	4.00240	+	6.93236i	0.625070	+	1.08265i	0.988527	+	0.151042i	$0.0482629\pi$
$41$	4.00240	+	6.93236i	0.625070	+	1.08265i	−0.363457	+	0.931611i	$0.618404\pi$
$42$		0			0
$43$	0.484469	−	0.839125i	0.0738808	−	0.127965i	−0.826718	−	0.562616i	$-0.809795\pi$
$43$	0.484469	−	0.839125i	0.0738808	−	0.127965i	0.900599	+	0.434651i	$0.143128\pi$
$44$		0			0
$45$	−14.6788	+	25.4244i	−2.18819	+	3.79005i
$46$		0			0
$47$	−1.07609			−0.156963			−0.0784817	−	0.996916i	$-0.525007\pi$
$47$	−1.07609			−0.156963			−0.0784817	+	0.996916i	$0.525007\pi$
$48$		0			0
$49$	3.33853	+	5.78250i	0.476933	+	0.826071i
$50$		0			0
$51$	−5.01711			−0.702536
$52$		0			0
$53$	−9.71279			−1.33415			−0.667077	−	0.744989i	$-0.732455\pi$
$53$	−9.71279			−1.33415			−0.667077	+	0.744989i	$0.732455\pi$
$54$		0			0
$55$	−1.98447	−	3.43720i	−0.267586	−	0.463472i
$56$		0			0
$57$	27.8986			3.69526
$58$		0			0
$59$	3.35058	−	5.80337i	0.436208	−	0.755535i	−0.561185	−	0.827690i	$-0.689654\pi$
$59$	3.35058	−	5.80337i	0.436208	−	0.755535i	0.997393	+	0.0721555i	$0.0229878\pi$
$60$		0			0
$61$	−1.59668	+	2.76552i	−0.204433	+	0.354089i	−0.949952	−	0.312396i	$-0.898869\pi$
$61$	−1.59668	+	2.76552i	−0.204433	+	0.354089i	0.745519	+	0.666485i	$0.232202\pi$
$62$		0			0
$63$	2.10174	+	3.64033i	0.264795	+	0.458638i
$64$		0			0
$65$	−14.2506	+	1.30522i	−1.76756	+	0.161892i
$66$		0			0
$67$	0.0608121	+	0.105330i	0.00742939	+	0.0128681i	0.869716	−	0.493552i	$-0.164302\pi$
$67$	0.0608121	+	0.105330i	0.00742939	+	0.0128681i	−0.862287	+	0.506420i	$0.830968\pi$
$68$		0			0
$69$	6.85455	−	11.8724i	0.825191	−	1.42927i
$70$		0			0
$71$	0.209642	−	0.363110i	0.0248799	−	0.0430932i	−0.853317	−	0.521392i	$-0.825413\pi$
$71$	0.209642	−	0.363110i	0.0248799	−	0.0430932i	0.878197	+	0.478299i	$0.158746\pi$
$72$		0			0
$73$	−12.1601			−1.42323			−0.711617	−	0.702567i	$-0.752037\pi$
$73$	−12.1601			−1.42323			−0.711617	+	0.702567i	$0.752037\pi$
$74$		0			0
$75$	17.3352	+	30.0255i	2.00170	+	3.46704i
$76$		0			0
$77$	−0.568282			−0.0647617
$78$		0			0
$79$	−5.77407			−0.649633			−0.324817	−	0.945777i	$-0.605303\pi$
$79$	−5.77407			−0.649633			−0.324817	+	0.945777i	$0.605303\pi$
$80$		0			0
$81$	−11.7614	−	20.3713i	−1.30682	−	2.26348i
$82$		0			0
$83$	−1.11577			−0.122471			−0.0612357	−	0.998123i	$-0.519504\pi$
$83$	−1.11577			−0.122471			−0.0612357	+	0.998123i	$0.519504\pi$
$84$		0			0
$85$	−3.08779	+	5.34820i	−0.334917	+	0.580094i
$86$		0			0
$87$	12.3570	−	21.4029i	1.32480	−	2.29463i
$88$		0			0
$89$	6.76670	+	11.7203i	0.717269	+	1.24235i	0.962078	+	0.272775i	$0.0879414\pi$
$89$	6.76670	+	11.7203i	0.717269	+	1.24235i	−0.244809	+	0.969571i	$0.578725\pi$
$90$		0			0
$91$	−0.858368	+	1.86050i	−0.0899814	+	0.195034i
$92$		0			0
$93$	−6.91852	−	11.9832i	−0.717418	−	1.24260i
$94$		0			0
$95$	17.1703	−	29.7397i	1.76163	−	3.05123i
$96$		0			0
$97$	6.57357	−	11.3858i	0.667445	−	1.15605i	−0.311171	−	0.950354i	$-0.600721\pi$
$97$	6.57357	−	11.3858i	0.667445	−	1.15605i	0.978616	−	0.205695i	$-0.0659454\pi$
$98$		0			0
$99$	7.39684			0.743410
$100$		0			0
$101$	7.05515	+	12.2199i	0.702014	+	1.21592i	0.967758	+	0.251880i	$0.0810489\pi$
$101$	7.05515	+	12.2199i	0.702014	+	1.21592i	−0.265745	+	0.964043i	$0.585618\pi$
$102$		0			0
$103$	1.47772			0.145604			0.0728020	−	0.997346i	$-0.476806\pi$
$103$	1.47772			0.145604			0.0728020	+	0.997346i	$0.476806\pi$
$104$		0			0
$105$	7.27258			0.709731
$106$		0			0
$107$	1.23215	+	2.13415i	0.119117	+	0.206316i	0.919418	−	0.393282i	$-0.128660\pi$
$107$	1.23215	+	2.13415i	0.119117	+	0.206316i	−0.800301	+	0.599598i	$0.795327\pi$
$108$		0			0
$109$	8.63305			0.826896			0.413448	−	0.910528i	$-0.364324\pi$
$109$	8.63305			0.826896			0.413448	+	0.910528i	$0.364324\pi$
$110$		0			0
$111$	−4.75281	+	8.23210i	−0.451116	+	0.781357i
$112$		0			0
$113$	0.845441	−	1.46435i	0.0795324	−	0.137754i	−0.823516	−	0.567293i	$-0.807991\pi$
$113$	0.845441	−	1.46435i	0.0795324	−	0.137754i	0.903048	+	0.429539i	$0.141324\pi$
$114$		0			0
$115$	−8.43728	−	14.6138i	−0.786781	−	1.36274i
$116$		0			0
$117$	11.1726	−	24.2166i	1.03291	−	2.23883i
$118$		0			0
$119$	0.442116	+	0.765768i	0.0405287	+	0.0701978i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−12.9054	+	22.3528i	−1.16364	+	2.01548i
$124$		0			0
$125$	22.8312			2.04208
$126$		0			0
$127$	−6.07631	−	10.5245i	−0.539185	−	0.933896i	−0.998948	−	0.0458544i	$-0.985399\pi$
$127$	−6.07631	−	10.5245i	−0.539185	−	0.933896i	0.459763	−	0.888042i	$-0.347934\pi$
$128$		0			0
$129$	3.12426			0.275076
$130$		0			0
$131$	19.2762			1.68417			0.842085	−	0.539345i	$-0.181328\pi$
$131$	19.2762			1.68417			0.842085	+	0.539345i	$0.181328\pi$
$132$		0			0
$133$	−2.45848	−	4.25821i	−0.213177	−	0.369233i
$134$		0			0
$135$	−56.2685			−4.84283
$136$		0			0
$137$	−2.14998	+	3.72387i	−0.183685	+	0.318152i	−0.943133	−	0.332417i	$-0.892136\pi$
$137$	−2.14998	+	3.72387i	−0.183685	+	0.318152i	0.759448	+	0.650568i	$0.225469\pi$
$138$		0			0
$139$	−4.14833	+	7.18511i	−0.351856	+	0.609433i	−0.986575	−	0.163310i	$-0.947783\pi$
$139$	−4.14833	+	7.18511i	−0.351856	+	0.609433i	0.634718	+	0.772744i	$0.281116\pi$
$140$		0			0
$141$	−1.73488	−	3.00489i	−0.146103	−	0.253058i
$142$		0			0
$143$	2.08006	+	2.94505i	0.173943	+	0.246278i
$144$		0			0
$145$	−15.2102	−	26.3448i	−1.26314	−	2.18782i
$146$		0			0
$147$	−10.7648	+	18.6452i	−0.887865	+	1.53783i
$148$		0			0
$149$	−3.03962	+	5.26477i	−0.249015	+	0.431307i	−0.963253	−	0.268596i	$-0.913440\pi$
$149$	−3.03962	+	5.26477i	−0.249015	+	0.431307i	0.714238	+	0.699903i	$0.246774\pi$
$150$		0			0
$151$	−11.5014			−0.935967			−0.467984	−	0.883737i	$-0.655019\pi$
$151$	−11.5014			−0.935967			−0.467984	+	0.883737i	$0.655019\pi$
$152$		0			0
$153$	−5.75465	−	9.96735i	−0.465236	−	0.805812i
$154$		0			0
$155$	−17.0321			−1.36805
$156$		0			0
$157$	−2.81091			−0.224335			−0.112167	−	0.993689i	$-0.535779\pi$
$157$	−2.81091			−0.224335			−0.112167	+	0.993689i	$0.535779\pi$
$158$		0			0
$159$	−15.6590	−	27.1222i	−1.24184	−	2.15093i
$160$		0			0
$161$	−2.41614			−0.190418
$162$		0			0
$163$	−5.47749	+	9.48729i	−0.429030	+	0.743102i	−0.996787	−	0.0800939i	$-0.974478\pi$
$163$	−5.47749	+	9.48729i	−0.429030	+	0.743102i	0.567757	+	0.823196i	$0.307811\pi$
$164$		0			0
$165$	6.39875	−	11.0830i	0.498142	−	0.862807i
$166$		0			0
$167$	4.67597	+	8.09902i	0.361838	+	0.626721i	0.988263	−	0.152760i	$-0.0488162\pi$
$167$	4.67597	+	8.09902i	0.361838	+	0.626721i	−0.626426	+	0.779481i	$0.715483\pi$
$168$		0			0
$169$	12.7837	−	2.36154i	0.983362	−	0.181657i
$170$		0			0
$171$	31.9999	+	55.4254i	2.44709	+	4.23849i
$172$		0			0
$173$	6.41543	−	11.1118i	0.487756	−	0.844818i	−0.512145	−	0.858899i	$-0.671149\pi$
$173$	6.41543	−	11.1118i	0.487756	−	0.844818i	0.999901	+	0.0140810i	$0.00448226\pi$
$174$		0			0
$175$	3.05522	−	5.29179i	0.230953	−	0.400022i
$176$		0			0
$177$	21.6073			1.62410
$178$		0			0
$179$	3.20540	+	5.55191i	0.239583	+	0.414969i	0.960595	−	0.277953i	$-0.0896561\pi$
$179$	3.20540	+	5.55191i	0.239583	+	0.414969i	−0.721012	+	0.692923i	$0.756323\pi$
$180$		0			0
$181$	10.1419			0.753840			0.376920	−	0.926246i	$-0.376983\pi$
$181$	10.1419			0.753840			0.376920	+	0.926246i	$0.376983\pi$
$182$		0			0
$183$	−10.2967			−0.761153
$184$		0			0
$185$	5.85024	+	10.1329i	0.430118	+	0.744987i
$186$		0			0
$187$	1.55598			0.113784
$188$		0			0
$189$	−4.02833	+	6.97727i	−0.293018	+	0.507522i
$190$		0			0
$191$	1.18382	−	2.05043i	0.0856580	−	0.148364i	−0.820013	−	0.572344i	$-0.806034\pi$
$191$	1.18382	−	2.05043i	0.0856580	−	0.148364i	0.905671	+	0.423980i	$0.139367\pi$
$192$		0			0
$193$	−8.97493	−	15.5450i	−0.646029	−	1.11896i	−0.984063	−	0.177822i	$-0.943095\pi$
$193$	−8.97493	−	15.5450i	−0.646029	−	1.11896i	0.338033	−	0.941134i	$-0.390238\pi$
$194$		0			0
$195$	−26.6196	−	37.6893i	−1.90627	−	2.69899i
$196$		0			0
$197$	−5.68887	−	9.85342i	−0.405316	−	0.702027i	0.589043	−	0.808102i	$-0.299505\pi$
$197$	−5.68887	−	9.85342i	−0.405316	−	0.702027i	−0.994358	+	0.106075i	$0.966172\pi$
$198$		0			0
$199$	2.66778	−	4.62073i	0.189114	−	0.327555i	−0.755841	−	0.654755i	$-0.772772\pi$
$199$	2.66778	−	4.62073i	0.189114	−	0.327555i	0.944955	+	0.327200i	$0.106105\pi$
$200$		0			0
$201$	−0.196083	+	0.339627i	−0.0138307	+	0.0239554i
$202$		0			0
$203$	−4.35566			−0.305708
$204$		0			0
$205$	15.8853	+	27.5141i	1.10948	+	1.92167i
$206$		0			0
$207$	31.4488			2.18585
$208$		0			0
$209$	−8.65231			−0.598493
$210$		0			0
$211$	−4.83711	−	8.37812i	−0.333000	−	0.576773i	0.650098	−	0.759850i	$-0.274728\pi$
$211$	−4.83711	−	8.37812i	−0.333000	−	0.576773i	−0.983099	+	0.183077i	$0.941394\pi$
$212$		0			0
$213$	1.35194			0.0926336
$214$		0			0
$215$	1.92283	−	3.33044i	0.131136	−	0.227134i
$216$		0			0
$217$	−1.21934	+	2.11197i	−0.0827745	+	0.143370i
$218$		0			0
$219$	−19.6046	−	33.9562i	−1.32476	−	2.29455i
$220$		0			0
$221$	2.35024	−	5.09413i	0.158094	−	0.342668i
$222$		0			0
$223$	−3.10408	−	5.37643i	−0.207865	−	0.360032i	0.743177	−	0.669095i	$-0.233318\pi$
$223$	−3.10408	−	5.37643i	−0.207865	−	0.360032i	−0.951042	+	0.309063i	$0.899985\pi$
$224$		0			0
$225$	−39.7672	+	68.8787i	−2.65114	+	4.59192i
$226$		0			0
$227$	−0.235147	+	0.407287i	−0.0156073	+	0.0270326i	−0.873724	−	0.486423i	$-0.838301\pi$
$227$	−0.235147	+	0.407287i	−0.0156073	+	0.0270326i	0.858116	+	0.513455i	$0.171635\pi$
$228$		0			0
$229$	−18.5497			−1.22580			−0.612898	−	0.790162i	$-0.709996\pi$
$229$	−18.5497			−1.22580			−0.612898	+	0.790162i	$0.709996\pi$
$230$		0			0
$231$	−0.916187	−	1.58688i	−0.0602807	−	0.104409i
$232$		0			0
$233$	6.92361			0.453581			0.226790	−	0.973944i	$-0.427177\pi$
$233$	6.92361			0.453581			0.226790	+	0.973944i	$0.427177\pi$
$234$		0			0
$235$	−4.27092			−0.278604
$236$		0			0
$237$	−9.30899	−	16.1236i	−0.604684	−	1.04734i
$238$		0			0
$239$	11.3351			0.733210			0.366605	−	0.930377i	$-0.380520\pi$
$239$	11.3351			0.733210			0.366605	+	0.930377i	$0.380520\pi$
$240$		0			0
$241$	−1.51286	+	2.62036i	−0.0974521	+	0.168792i	−0.910629	−	0.413224i	$-0.864403\pi$
$241$	−1.51286	+	2.62036i	−0.0974521	+	0.168792i	0.813177	+	0.582016i	$0.197736\pi$
$242$		0			0
$243$	16.6576	−	28.8519i	1.06859	−	1.85085i
$244$		0			0
$245$	13.2504	+	22.9504i	0.846538	+	1.46625i
$246$		0			0
$247$	−13.0690	+	28.3269i	−0.831560	+	1.80240i
$248$		0			0
$249$	−1.79885	−	3.11570i	−0.113997	−	0.197449i
$250$		0			0
$251$	4.52544	−	7.83829i	0.285643	−	0.494749i	−0.687122	−	0.726542i	$-0.741126\pi$
$251$	4.52544	−	7.83829i	0.285643	−	0.494749i	0.972765	+	0.231794i	$0.0744594\pi$
$252$		0			0
$253$	−2.12583	+	3.68204i	−0.133650	+	0.231488i
$254$		0			0
$255$	−19.9126			−1.24697
$256$		0			0
$257$	10.8601	+	18.8103i	0.677435	+	1.17335i	0.975751	+	0.218885i	$0.0702419\pi$
$257$	10.8601	+	18.8103i	0.677435	+	1.17335i	−0.298315	+	0.954467i	$0.596425\pi$
$258$		0			0
$259$	1.67530			0.104098
$260$		0			0
$261$	56.6940			3.50927
$262$		0			0
$263$	7.82317	+	13.5501i	0.482397	+	0.835537i	0.999796	−	0.0202079i	$-0.00643282\pi$
$263$	7.82317	+	13.5501i	0.482397	+	0.835537i	−0.517398	+	0.855745i	$0.673099\pi$
$264$		0			0
$265$	−38.5495			−2.36807
$266$		0			0
$267$	−21.8186	+	37.7910i	−1.33528	+	2.31277i
$268$		0			0
$269$	14.5782	−	25.2501i	0.888846	−	1.53953i	0.0476041	−	0.998866i	$-0.484841\pi$
$269$	14.5782	−	25.2501i	0.888846	−	1.53953i	0.841242	−	0.540659i	$-0.181825\pi$
$270$		0			0
$271$	15.0864	+	26.1304i	0.916432	+	1.58731i	0.804792	+	0.593558i	$0.202277\pi$
$271$	15.0864	+	26.1304i	0.916432	+	1.58731i	0.111640	+	0.993749i	$0.464390\pi$
$272$		0			0
$273$	−6.57918	+	0.602590i	−0.398190	+	0.0364704i
$274$		0			0
$275$	−5.37624	−	9.31191i	−0.324199	−	0.561529i
$276$		0			0
$277$	−10.0862	+	17.4698i	−0.606022	+	1.04966i	0.385867	+	0.922554i	$0.373902\pi$
$277$	−10.0862	+	17.4698i	−0.606022	+	1.04966i	−0.991889	+	0.127106i	$0.959431\pi$
$278$		0			0
$279$	15.8712	−	27.4897i	0.950182	−	1.64576i
$280$		0			0
$281$	−15.1895			−0.906127			−0.453063	−	0.891478i	$-0.649669\pi$
$281$	−15.1895			−0.906127			−0.453063	+	0.891478i	$0.649669\pi$
$282$		0			0
$283$	−11.2618	−	19.5060i	−0.669444	−	1.15951i	−0.978060	−	0.208324i	$-0.933199\pi$
$283$	−11.2618	−	19.5060i	−0.669444	−	1.15951i	0.308616	−	0.951187i	$-0.400134\pi$
$284$		0			0
$285$	110.728			6.55896
$286$		0			0
$287$	4.54898			0.268518
$288$		0			0
$289$	7.28947	+	12.6257i	0.428792	+	0.742690i
$290$		0			0
$291$	42.3918			2.48505
$292$		0			0
$293$	0.931702	−	1.61375i	0.0544306	−	0.0942766i	−0.837526	−	0.546397i	$-0.815999\pi$
$293$	0.931702	−	1.61375i	0.0544306	−	0.0942766i	0.891957	+	0.452120i	$0.149332\pi$
$294$		0			0
$295$	13.2982	−	23.0332i	0.774253	−	1.34105i
$296$		0			0
$297$	7.08861	+	12.2778i	0.411323	+	0.712433i
$298$		0			0
$299$	8.84371	+	12.5214i	0.511445	+	0.724129i
$300$		0			0
$301$	−0.275315	−	0.476859i	−0.0158689	−	0.0274857i
$302$		0			0
$303$	−22.7487	+	39.4019i	−1.30688	+	2.26358i
$304$		0			0
$305$	−6.33711	+	10.9762i	−0.362862	+	0.628495i
$306$		0			0
$307$	−17.1746			−0.980206			−0.490103	−	0.871665i	$-0.663041\pi$
$307$	−17.1746			−0.980206			−0.490103	+	0.871665i	$0.663041\pi$
$308$		0			0
$309$	2.38239	+	4.12642i	0.135529	+	0.234744i
$310$		0			0
$311$	7.99432			0.453316			0.226658	−	0.973974i	$-0.427220\pi$
$311$	7.99432			0.453316			0.226658	+	0.973974i	$0.427220\pi$
$312$		0			0
$313$	−4.81574			−0.272202			−0.136101	−	0.990695i	$-0.543457\pi$
$313$	−4.81574			−0.272202			−0.136101	+	0.990695i	$0.543457\pi$
$314$		0			0
$315$	8.34169	+	14.4482i	0.470001	+	0.814066i
$316$		0			0
$317$	12.8226			0.720187			0.360094	−	0.932916i	$-0.382745\pi$
$317$	12.8226			0.720187			0.360094	+	0.932916i	$0.382745\pi$
$318$		0			0
$319$	−3.83231	+	6.63776i	−0.214568	+	0.371643i
$320$		0			0
$321$	−3.97298	+	6.88140i	−0.221750	+	0.384082i
$322$		0			0
$323$	6.73140	+	11.6591i	0.374545	+	0.648731i
$324$		0			0
$325$	−38.6070	+	3.53603i	−2.14153	+	0.196144i
$326$		0			0
$327$	13.9183	+	24.1071i	0.769681	+	1.33313i
$328$		0			0
$329$	−0.305760	+	0.529593i	−0.0168571	+	0.0291974i
$330$		0			0
$331$	3.28871	−	5.69621i	0.180764	−	0.313092i	−0.761377	−	0.648309i	$-0.775476\pi$
$331$	3.28871	−	5.69621i	0.180764	−	0.313092i	0.942141	+	0.335217i	$0.108810\pi$
$332$		0			0
$333$	−21.8060			−1.19496
$334$		0			0
$335$	0.241360	+	0.418047i	0.0131869	+	0.0228404i
$336$		0			0
$337$	−24.6670			−1.34370			−0.671849	−	0.740688i	$-0.734500\pi$
$337$	−24.6670			−1.34370			−0.671849	+	0.740688i	$0.734500\pi$
$338$		0			0
$339$	5.45210			0.296117
$340$		0			0
$341$	2.14567	+	3.71641i	0.116195	+	0.201255i
$342$		0			0
$343$	7.77242			0.419671
$344$		0			0
$345$	27.2053	−	47.1209i	1.46468	−	2.53691i
$346$		0			0
$347$	−8.53494	+	14.7829i	−0.458179	+	0.793590i	−0.998865	−	0.0476349i	$-0.984832\pi$
$347$	−8.53494	+	14.7829i	−0.458179	+	0.793590i	0.540685	+	0.841225i	$0.318165\pi$
$348$		0			0
$349$	−0.119189	−	0.206441i	−0.00638002	−	0.0110505i	0.862818	−	0.505515i	$-0.168698\pi$
$349$	−0.119189	−	0.206441i	−0.00638002	−	0.0110505i	−0.869198	+	0.494465i	$0.835364\pi$
$350$		0			0
$351$	50.9037	−	4.66229i	2.71704	−	0.248855i
$352$		0			0
$353$	−1.52294	−	2.63781i	−0.0810580	−	0.140397i	0.822647	−	0.568553i	$-0.192497\pi$
$353$	−1.52294	−	2.63781i	−0.0810580	−	0.140397i	−0.903705	+	0.428156i	$0.859163\pi$
$354$		0			0
$355$	0.832055	−	1.44116i	0.0441609	−	0.0764889i
$356$		0			0
$357$	−1.42557	+	2.46915i	−0.0754489	+	0.130681i
$358$		0			0
$359$	−2.05263			−0.108333			−0.0541667	−	0.998532i	$-0.517250\pi$
$359$	−2.05263			−0.108333			−0.0541667	+	0.998532i	$0.517250\pi$
$360$		0			0
$361$	−27.9313	−	48.3784i	−1.47007	−	2.54623i
$362$		0			0
$363$	−3.22441			−0.169238
$364$		0			0
$365$	−48.2628			−2.52619
$366$		0			0
$367$	−18.1052	−	31.3592i	−0.945086	−	1.63694i	−0.755580	−	0.655057i	$-0.772645\pi$
$367$	−18.1052	−	31.3592i	−0.945086	−	1.63694i	−0.189506	−	0.981880i	$-0.560689\pi$
$368$		0			0
$369$	−59.2102			−3.08236
$370$		0			0
$371$	−2.75980	+	4.78011i	−0.143282	+	0.248171i
$372$		0			0
$373$	−16.0119	+	27.7334i	−0.829063	+	1.43598i	0.0697102	+	0.997567i	$0.477793\pi$
$373$	−16.0119	+	27.7334i	−0.829063	+	1.43598i	−0.898774	+	0.438413i	$0.855541\pi$
$374$		0			0
$375$	36.8086	+	63.7544i	1.90079	+	3.29226i
$376$		0			0
$377$	15.9429	+	22.5727i	0.821100	+	1.16255i
$378$		0			0
$379$	12.7854	+	22.1449i	0.656741	+	1.13751i	0.981454	+	0.191696i	$0.0613988\pi$
$379$	12.7854	+	22.1449i	0.656741	+	1.13751i	−0.324713	+	0.945812i	$0.605268\pi$
$380$		0			0
$381$	19.5925	−	33.9353i	1.00376	−	1.73856i
$382$		0			0
$383$	−13.9898	+	24.2310i	−0.714844	+	1.23815i	0.248176	+	0.968715i	$0.420169\pi$
$383$	−13.9898	+	24.2310i	−0.714844	+	1.23815i	−0.963020	+	0.269430i	$0.913165\pi$
$384$		0			0
$385$	−2.25547			−0.114950
$386$		0			0
$387$	3.58354	+	6.20687i	0.182162	+	0.315513i
$388$		0			0
$389$	−21.9235			−1.11156			−0.555782	−	0.831328i	$-0.687581\pi$
$389$	−21.9235			−1.11156			−0.555782	+	0.831328i	$0.687581\pi$
$390$		0			0
$391$	6.61548			0.334559
$392$		0			0
$393$	31.0772	+	53.8273i	1.56764	+	2.71523i
$394$		0			0
$395$	−22.9169			−1.15308
$396$		0			0
$397$	3.94959	−	6.84088i	0.198224	−	0.343334i	−0.749729	−	0.661745i	$-0.769816\pi$
$397$	3.94959	−	6.84088i	0.198224	−	0.343334i	0.947953	+	0.318411i	$0.103149\pi$
$398$		0			0
$399$	7.92714	−	13.7302i	0.396853	−	0.687370i
$400$		0			0
$401$	14.1109	+	24.4408i	0.704664	+	1.22051i	0.966812	+	0.255487i	$0.0822358\pi$
$401$	14.1109	+	24.4408i	0.704664	+	1.22051i	−0.262148	+	0.965028i	$0.584431\pi$
$402$		0			0
$403$	15.4081	−	1.41124i	0.767535	−	0.0702988i
$404$		0			0
$405$	−46.6801	−	80.8523i	−2.31955	−	4.01758i
$406$		0			0
$407$	1.47401	−	2.55305i	0.0730638	−	0.126550i
$408$		0			0
$409$	−11.5705	+	20.0407i	−0.572125	+	0.990950i	0.424222	+	0.905558i	$0.360548\pi$
$409$	−11.5705	+	20.0407i	−0.572125	+	0.990950i	−0.996347	+	0.0853917i	$0.972786\pi$
$410$		0			0
$411$	−13.8648			−0.683902
$412$		0			0
$413$	−1.90407	−	3.29795i	−0.0936933	−	0.162282i
$414$		0			0
$415$	−4.42841			−0.217382
$416$		0			0
$417$	−26.7518			−1.31004
$418$		0			0
$419$	−19.2040	−	33.2623i	−0.938176	−	1.62497i	−0.768870	−	0.639405i	$-0.779181\pi$
$419$	−19.2040	−	33.2623i	−0.938176	−	1.62497i	−0.169306	−	0.985563i	$-0.554153\pi$
$420$		0			0
$421$	−9.42324			−0.459261			−0.229630	−	0.973278i	$-0.573752\pi$
$421$	−9.42324			−0.459261			−0.229630	+	0.973278i	$0.573752\pi$
$422$		0			0
$423$	3.97982	−	6.89326i	0.193506	−	0.335162i
$424$		0			0
$425$	−8.36529	+	14.4891i	−0.405776	+	0.702825i
$426$		0			0
$427$	0.907362	+	1.57160i	0.0439103	+	0.0760549i
$428$		0			0
$429$	−4.87035	+	10.5564i	−0.235143	+	0.509670i
$430$		0			0
$431$	−5.62479	−	9.74242i	−0.270937	−	0.469276i	0.698165	−	0.715937i	$-0.254000\pi$
$431$	−5.62479	−	9.74242i	−0.270937	−	0.469276i	−0.969102	+	0.246661i	$0.920667\pi$
$432$		0			0
$433$	7.58686	−	13.1408i	0.364601	−	0.631508i	−0.624111	−	0.781336i	$-0.714539\pi$
$433$	7.58686	−	13.1408i	0.364601	−	0.631508i	0.988712	+	0.149828i	$0.0478720\pi$
$434$		0			0
$435$	49.0440	−	84.9467i	2.35148	−	4.07288i
$436$		0			0
$437$	−36.7867			−1.75975
$438$		0			0
$439$	−8.31935	−	14.4095i	−0.397061	−	0.687730i	0.596301	−	0.802761i	$-0.296636\pi$
$439$	−8.31935	−	14.4095i	−0.397061	−	0.687730i	−0.993362	+	0.115031i	$0.963303\pi$
$440$		0			0
$441$	−49.3891			−2.35186
$442$		0			0
$443$	20.3775			0.968165			0.484082	−	0.875022i	$-0.339154\pi$
$443$	20.3775			0.968165			0.484082	+	0.875022i	$0.339154\pi$
$444$		0			0
$445$	26.8566	+	46.5170i	1.27313	+	2.20512i
$446$		0			0
$447$	−19.6020			−0.927141
$448$		0			0
$449$	4.08493	−	7.07530i	0.192780	−	0.333904i	−0.753391	−	0.657573i	$-0.771583\pi$
$449$	4.08493	−	7.07530i	0.192780	−	0.333904i	0.946170	+	0.323669i	$0.104916\pi$
$450$		0			0
$451$	4.00240	−	6.93236i	0.188466	−	0.326432i
$452$		0			0
$453$	−18.5426	−	32.1167i	−0.871206	−	1.50897i
$454$		0			0
$455$	−3.40681	+	7.38423i	−0.159714	+	0.346178i
$456$		0			0
$457$	5.97912	+	10.3561i	0.279691	+	0.484440i	0.971308	−	0.237825i	$-0.0764345\pi$
$457$	5.97912	+	10.3561i	0.279691	+	0.484440i	−0.691617	+	0.722265i	$0.743101\pi$
$458$		0			0
$459$	11.0297	−	19.1040i	0.514823	−	0.891699i
$460$		0			0
$461$	12.6945	−	21.9875i	0.591241	−	1.02406i	−0.402824	−	0.915277i	$-0.631971\pi$
$461$	12.6945	−	21.9875i	0.591241	−	1.02406i	0.994066	−	0.108783i	$-0.0346952\pi$
$462$		0			0
$463$	−23.8729			−1.10947			−0.554734	−	0.832028i	$-0.687180\pi$
$463$	−23.8729			−1.10947			−0.554734	+	0.832028i	$0.687180\pi$
$464$		0			0
$465$	−27.4592	−	47.5607i	−1.27339	−	2.20558i
$466$		0			0
$467$	−29.5442			−1.36714			−0.683571	−	0.729884i	$-0.739574\pi$
$467$	−29.5442			−1.36714			−0.683571	+	0.729884i	$0.739574\pi$
$468$		0			0
$469$	0.0691169			0.00319152
$470$		0			0
$471$	−4.53176	−	7.84924i	−0.208813	−	0.361674i
$472$		0			0
$473$	−0.968938			−0.0445518
$474$		0			0
$475$	46.5169	−	80.5696i	2.13434	−	3.69679i
$476$		0			0
$477$	35.9220	−	62.2187i	1.64475	−	2.84880i
$478$		0			0
$479$	8.84844	+	15.3259i	0.404295	+	0.700260i	0.994239	−	0.107184i	$-0.0341834\pi$
$479$	8.84844	+	15.3259i	0.404295	+	0.700260i	−0.589944	+	0.807444i	$0.700850\pi$
$480$		0			0
$481$	−6.13205	−	8.68206i	−0.279597	−	0.395868i
$482$		0			0
$483$	−3.89532	−	6.74689i	−0.177243	−	0.306994i
$484$		0			0
$485$	26.0901	−	45.1894i	1.18469	−	2.05194i
$486$		0			0
$487$	10.0231	−	17.3604i	0.454188	−	0.786677i	−0.544453	−	0.838791i	$-0.683263\pi$
$487$	10.0231	−	17.3604i	0.454188	−	0.786677i	0.998641	+	0.0521147i	$0.0165961\pi$
$488$		0			0
$489$	−35.3234			−1.59738
$490$		0			0
$491$	9.95334	+	17.2397i	0.449188	+	0.778017i	0.998333	−	0.0577103i	$-0.0183800\pi$
$491$	9.95334	+	17.2397i	0.449188	+	0.778017i	−0.549145	+	0.835727i	$0.685047\pi$
$492$		0			0
$493$	11.9260			0.537118
$494$		0			0
$495$	29.3576			1.31953
$496$		0			0
$497$	−0.119136	−	0.206349i	−0.00534396	−	0.00925601i
$498$		0			0
$499$	29.3516			1.31396			0.656980	−	0.753908i	$-0.271834\pi$
$499$	29.3516			1.31396			0.656980	+	0.753908i	$0.271834\pi$
$500$		0			0
$501$	−15.0773	+	26.1146i	−0.673602	+	1.16671i
$502$		0			0
$503$	8.05978	−	13.9599i	0.359368	−	0.622443i	−0.628487	−	0.777820i	$-0.716326\pi$
$503$	8.05978	−	13.9599i	0.359368	−	0.622443i	0.987855	+	0.155376i	$0.0496590\pi$
$504$		0			0
$505$	28.0015	+	48.5000i	1.24605	+	2.15822i
$506$		0			0
$507$	27.2044	+	31.8902i	1.20819	+	1.41629i
$508$		0			0
$509$	−2.40987	−	4.17401i	−0.106815	−	0.185010i	0.807663	−	0.589644i	$-0.200732\pi$
$509$	−2.40987	−	4.17401i	−0.106815	−	0.185010i	−0.914478	+	0.404635i	$0.867399\pi$
$510$		0			0
$511$	−3.45519	+	5.98456i	−0.152848	+	0.264741i
$512$		0			0
$513$	−61.3329	+	106.232i	−2.70791	+	4.69025i
$514$		0			0
$515$	5.86498			0.258442
$516$		0			0
$517$	0.538044	+	0.931919i	0.0236631	+	0.0409858i
$518$		0			0
$519$	41.3720			1.81603
$520$		0			0
$521$	−6.69841			−0.293463			−0.146731	−	0.989176i	$-0.546875\pi$
$521$	−6.69841			−0.293463			−0.146731	+	0.989176i	$0.546875\pi$
$522$		0			0
$523$	12.4147	+	21.5029i	0.542858	+	0.940257i	0.998738	+	0.0502161i	$0.0159910\pi$
$523$	12.4147	+	21.5029i	0.542858	+	0.940257i	−0.455881	+	0.890041i	$0.650676\pi$
$524$		0			0
$525$	19.7026			0.859890
$526$		0			0
$527$	3.33861	−	5.78264i	0.145432	−	0.251896i
$528$		0			0
$529$	2.46170	−	4.26379i	0.107030	−	0.185382i
$530$		0			0
$531$	24.7837	+	42.9266i	1.07552	+	1.86286i
$532$		0			0
$533$	−16.6505	−	23.5746i	−0.721212	−	1.02113i
$534$		0			0
$535$	4.89035	+	8.47033i	0.211428	+	0.366204i
$536$		0			0
$537$	−10.3355	+	17.9017i	−0.446011	+	0.772513i
$538$		0			0
$539$	3.33853	−	5.78250i	0.143801	−	0.249070i
$540$		0			0
$541$	11.0147			0.473560			0.236780	−	0.971563i	$-0.423908\pi$
$541$	11.0147			0.473560			0.236780	+	0.971563i	$0.423908\pi$
$542$		0			0
$543$	16.3508	+	28.3204i	0.701680	+	1.21535i
$544$		0			0
$545$	34.2640			1.46771
$546$		0			0
$547$	−39.7209			−1.69834			−0.849171	−	0.528118i	$-0.822898\pi$
$547$	−39.7209			−1.69834			−0.849171	+	0.528118i	$0.822898\pi$
$548$		0			0
$549$	−11.8104	−	20.4561i	−0.504054	−	0.873047i
$550$		0			0
$551$	−66.3167			−2.82519
$552$		0			0
$553$	−1.64065	+	2.84169i	−0.0697675	+	0.120841i
$554$		0			0
$555$	−18.8636	+	32.6727i	−0.800715	+	1.38688i
$556$		0			0
$557$	0.830419	+	1.43833i	0.0351860	+	0.0609439i	0.883082	−	0.469218i	$-0.155464\pi$
$557$	0.830419	+	1.43833i	0.0351860	+	0.0609439i	−0.847896	+	0.530162i	$0.822131\pi$
$558$		0			0
$559$	−1.46354	+	3.17222i	−0.0619013	+	0.134171i
$560$		0			0
$561$	2.50855	+	4.34494i	0.105911	+	0.183444i
$562$		0			0
$563$	−6.30203	+	10.9154i	−0.265599	+	0.460031i	−0.967720	−	0.252026i	$-0.918903\pi$
$563$	−6.30203	+	10.9154i	−0.265599	+	0.460031i	0.702121	+	0.712057i	$0.252236\pi$
$564$		0			0
$565$	3.35550	−	5.81190i	0.141167	−	0.244508i
$566$		0			0
$567$	−13.3675			−0.561384
$568$		0			0
$569$	−6.53937	−	11.3265i	−0.274144	−	0.474832i	0.695774	−	0.718260i	$-0.255061\pi$
$569$	−6.53937	−	11.3265i	−0.274144	−	0.474832i	−0.969919	+	0.243428i	$0.921728\pi$
$570$		0			0
$571$	−6.58938			−0.275757			−0.137878	−	0.990449i	$-0.544028\pi$
$571$	−6.58938			−0.275757			−0.137878	+	0.990449i	$0.544028\pi$
$572$		0			0
$573$	7.63423			0.318925
$574$		0			0
$575$	−22.8579	−	39.5911i	−0.953241	−	1.65106i
$576$		0			0
$577$	6.77295			0.281962			0.140981	−	0.990012i	$-0.454974\pi$
$577$	6.77295			0.281962			0.140981	+	0.990012i	$0.454974\pi$
$578$		0			0
$579$	28.9389	−	50.1236i	1.20266	−	2.08307i
$580$		0			0
$581$	−0.317035	+	0.549121i	−0.0131528	+	0.0227814i
$582$		0			0
$583$	4.85640	+	8.41152i	0.201131	+	0.348370i
$584$		0			0
$585$	44.3435	−	96.1142i	1.83338	−	3.97383i
$586$		0			0
$587$	17.5807	+	30.4507i	0.725634	+	1.25683i	0.958713	+	0.284376i	$0.0917866\pi$
$587$	17.5807	+	30.4507i	0.725634	+	1.25683i	−0.233079	+	0.972458i	$0.574880\pi$
$588$		0			0
$589$	−18.5650	+	32.1555i	−0.764958	+	1.32495i
$590$		0			0
$591$	18.3433	−	31.7715i	0.754542	−	1.30690i
$592$		0			0
$593$	28.5003			1.17037			0.585184	−	0.810901i	$-0.301022\pi$
$593$	28.5003			1.17037			0.585184	+	0.810901i	$0.301022\pi$
$594$		0			0
$595$	1.75473	+	3.03928i	0.0719370	+	0.124599i
$596$		0			0
$597$	17.2041			0.704115
$598$		0			0
$599$	−28.7782			−1.17584			−0.587922	−	0.808918i	$-0.700054\pi$
$599$	−28.7782			−1.17584			−0.587922	+	0.808918i	$0.700054\pi$
$600$		0			0
$601$	17.3688	+	30.0837i	0.708489	+	1.22714i	0.965418	+	0.260708i	$0.0839561\pi$
$601$	17.3688	+	30.0837i	0.708489	+	1.22714i	−0.256929	+	0.966430i	$0.582711\pi$
$602$		0			0
$603$	−0.899635			−0.0366360
$604$		0			0
$605$	−1.98447	+	3.43720i	−0.0806801	+	0.139742i
$606$		0			0
$607$	−5.58277	+	9.66965i	−0.226598	+	0.392479i	−0.956798	−	0.290755i	$-0.906094\pi$
$607$	−5.58277	+	9.66965i	−0.226598	+	0.392479i	0.730200	+	0.683234i	$0.239427\pi$
$608$		0			0
$609$	−7.02223	−	12.1629i	−0.284555	−	0.492864i
$610$		0			0
$611$	3.86372	−	0.353880i	0.156309	−	0.0143164i
$612$		0			0
$613$	−5.10234	−	8.83751i	−0.206081	−	0.356943i	0.744395	−	0.667739i	$-0.232738\pi$
$613$	−5.10234	−	8.83751i	−0.206081	−	0.356943i	−0.950477	+	0.310796i	$0.899405\pi$
$614$		0			0
$615$	−51.2207	+	88.7169i	−2.06542	+	3.57741i
$616$		0			0
$617$	−1.89447	+	3.28133i	−0.0762686	+	0.132101i	−0.901637	−	0.432493i	$-0.857634\pi$
$617$	−1.89447	+	3.28133i	−0.0762686	+	0.132101i	0.825369	+	0.564594i	$0.190967\pi$
$618$		0			0
$619$	−15.4522			−0.621077			−0.310538	−	0.950561i	$-0.600509\pi$
$619$	−15.4522			−0.621077			−0.310538	+	0.950561i	$0.600509\pi$
$620$		0			0
$621$	30.1384	+	52.2012i	1.20941	+	2.09476i
$622$		0			0
$623$	7.69079			0.308125
$624$		0			0
$625$	36.8533			1.47413
$626$		0			0
$627$	−13.9493	−	24.1609i	−0.557082	−	0.964895i
$628$		0			0
$629$	−4.58704			−0.182897
$630$		0			0
$631$	14.9772	−	25.9413i	0.596235	−	1.03271i	−0.397137	−	0.917759i	$-0.629996\pi$
$631$	14.9772	−	25.9413i	0.596235	−	1.03271i	0.993371	−	0.114949i	$-0.0366705\pi$
$632$		0			0
$633$	15.5968	−	27.0145i	0.619918	−	1.07373i
$634$		0			0
$635$	−24.1165	−	41.7710i	−0.957034	−	1.65763i
$636$		0			0
$637$	−13.8887	−	19.6643i	−0.550290	−	0.779128i
$638$		0			0
$639$	1.55069	+	2.68587i	0.0613442	+	0.106251i
$640$		0			0
$641$	−12.3532	+	21.3964i	−0.487922	+	0.845106i	−0.999904	−	0.0138907i	$-0.995578\pi$
$641$	−12.3532	+	21.3964i	−0.487922	+	0.845106i	0.511981	+	0.858997i	$0.328912\pi$
$642$		0			0
$643$	−6.59416	+	11.4214i	−0.260048	+	0.450417i	−0.966254	−	0.257589i	$-0.917072\pi$
$643$	−6.59416	+	11.4214i	−0.260048	+	0.450417i	0.706206	+	0.708006i	$0.250405\pi$
$644$		0			0
$645$	12.4000			0.488249
$646$		0			0
$647$	−0.762341	−	1.32041i	−0.0299707	−	0.0519108i	0.850651	−	0.525731i	$-0.176208\pi$
$647$	−0.762341	−	1.32041i	−0.0299707	−	0.0519108i	−0.880622	+	0.473820i	$0.842875\pi$
$648$		0			0
$649$	−6.70116			−0.263043
$650$		0			0
$651$	−7.86334			−0.308189
$652$		0			0
$653$	17.7204	+	30.6927i	0.693453	+	1.20110i	0.970699	+	0.240298i	$0.0772450\pi$
$653$	17.7204	+	30.6927i	0.693453	+	1.20110i	−0.277246	+	0.960799i	$0.589422\pi$
$654$		0			0
$655$	76.5061			2.98934
$656$		0			0
$657$	44.9732	−	77.8959i	1.75457	−	3.03901i
$658$		0			0
$659$	4.68223	−	8.10987i	0.182394	−	0.315916i	−0.760301	−	0.649571i	$-0.774949\pi$
$659$	4.68223	−	8.10987i	0.182394	−	0.315916i	0.942695	+	0.333655i	$0.108282\pi$
$660$		0			0
$661$	−14.1592	−	24.5245i	−0.550730	−	0.953893i	−0.998222	−	0.0596048i	$-0.981016\pi$
$661$	−14.1592	−	24.5245i	−0.550730	−	0.953893i	0.447492	−	0.894288i	$-0.352317\pi$
$662$		0			0
$663$	18.0140	−	1.64991i	0.699607	−	0.0640774i
$664$		0			0
$665$	−9.75754	−	16.9006i	−0.378381	−	0.655375i
$666$		0			0
$667$	−16.2937	+	28.2215i	−0.630894	+	1.09274i
$668$		0			0
$669$	10.0088	−	17.3358i	0.386964	−	0.670241i
$670$		0			0
$671$	3.19335			0.123278
$672$		0			0
$673$	−10.7038	−	18.5396i	−0.412602	−	0.714648i	0.582571	−	0.812780i	$-0.302047\pi$
$673$	−10.7038	−	18.5396i	−0.412602	−	0.714648i	−0.995173	+	0.0981317i	$0.968713\pi$
$674$		0			0
$675$	−152.440			−5.86743
$676$		0			0
$677$	37.6052			1.44529			0.722643	−	0.691221i	$-0.242927\pi$
$677$	37.6052			1.44529			0.722643	+	0.691221i	$0.242927\pi$
$678$		0			0
$679$	−3.73564	−	6.47032i	−0.143361	−	0.248308i
$680$		0			0
$681$	−1.51642			−0.0581095
$682$		0			0
$683$	13.9613	−	24.1816i	0.534213	−	0.925284i	−0.464988	−	0.885317i	$-0.653941\pi$
$683$	13.9613	−	24.1816i	0.534213	−	0.925284i	0.999201	−	0.0399671i	$-0.0127253\pi$
$684$		0			0
$685$	−8.53313	+	14.7798i	−0.326034	+	0.564708i
$686$		0			0
$687$	−29.9059	−	51.7985i	−1.14098	−	1.97624i
$688$		0			0
$689$	34.8740	−	3.19413i	1.32859	−	0.121686i
$690$		0			0
$691$	19.1842	+	33.2280i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$691$	19.1842	+	33.2280i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$692$		0			0
$693$	2.10174	−	3.64033i	0.0798387	−	0.138285i
$694$		0			0
$695$	−16.4644	+	28.5173i	−0.624532	+	1.08172i
$696$		0			0
$697$	−12.4553			−0.471777
$698$		0			0
$699$	11.1623	+	19.3337i	0.422197	+	0.731266i
$700$		0			0
$701$	−44.1698			−1.66827			−0.834135	−	0.551560i	$-0.814033\pi$
$701$	−44.1698			−1.66827			−0.834135	+	0.551560i	$0.814033\pi$
$702$		0			0
$703$	25.5071			0.962020
$704$		0			0
$705$	−6.88561	−	11.9262i	−0.259327	−	0.449168i
$706$		0			0
$707$	8.01863			0.301572
$708$		0			0
$709$	5.16288	−	8.94237i	0.193896	−	0.335838i	−0.752642	−	0.658430i	$-0.771221\pi$
$709$	5.16288	−	8.94237i	0.193896	−	0.335838i	0.946538	+	0.322592i	$0.104554\pi$
$710$		0			0
$711$	21.3549	−	36.9878i	0.800872	−	1.38715i
$712$		0			0
$713$	9.12265	+	15.8009i	0.341646	+	0.591748i
$714$		0			0
$715$	8.25563	+	11.6887i	0.308743	+	0.437134i
$716$		0			0
$717$	18.2746	+	31.6525i	0.682477	+	1.18209i
$718$		0			0
$719$	3.38601	−	5.86475i	0.126277	−	0.218718i	−0.795954	−	0.605357i	$-0.793031\pi$
$719$	3.38601	−	5.86475i	0.126277	−	0.218718i	0.922231	+	0.386638i	$0.126364\pi$
$720$		0			0
$721$	0.419880	−	0.727254i	0.0156372	−	0.0270844i
$722$		0			0
$723$	−9.75619			−0.362837
$724$		0			0
$725$	−41.2068	−	71.3723i	−1.53038	−	2.65070i
$726$		0			0
$727$	−12.1064			−0.449001			−0.224501	−	0.974474i	$-0.572075\pi$
$727$	−12.1064			−0.449001			−0.224501	+	0.974474i	$0.572075\pi$
$728$		0			0
$729$	36.8541			1.36497
$730$		0			0
$731$	0.753822	+	1.30566i	0.0278811	+	0.0482915i
$732$		0			0
$733$	39.8476			1.47181			0.735903	−	0.677087i	$-0.236758\pi$
$733$	39.8476			1.47181			0.735903	+	0.677087i	$0.236758\pi$
$734$		0			0
$735$	−42.7248	+	74.0015i	−1.57593	+	2.72959i
$736$		0			0
$737$	0.0608121	−	0.105330i	0.00224004	−	0.00387987i
$738$		0			0
$739$	−23.4687	−	40.6489i	−0.863309	−	1.49530i	−0.868716	−	0.495310i	$-0.835054\pi$
$739$	−23.4687	−	40.6489i	−0.863309	−	1.49530i	0.00540705	−	0.999985i	$-0.498279\pi$
$740$		0			0
$741$	−100.171	+	9.17468i	−3.67986	+	0.337040i
$742$		0			0
$743$	−15.3305	−	26.5531i	−0.562420	−	0.974140i	−0.997285	−	0.0736439i	$-0.976537\pi$
$743$	−15.3305	−	26.5531i	−0.562420	−	0.974140i	0.434865	−	0.900496i	$-0.356796\pi$
$744$		0			0
$745$	−12.0640	+	20.8955i	−0.441992	+	0.765553i
$746$		0			0
$747$	4.12658	−	7.14744i	0.150984	−	0.261511i
$748$		0			0
$749$	1.40042			0.0511703
$750$		0			0
$751$	−7.74068	−	13.4072i	−0.282461	−	0.489237i	0.689529	−	0.724258i	$-0.257818\pi$
$751$	−7.74068	−	13.4072i	−0.282461	−	0.489237i	−0.971990	+	0.235021i	$0.924484\pi$
$752$		0			0
$753$	29.1838			1.06352
$754$		0			0
$755$	−45.6482			−1.66131
$756$		0			0
$757$	8.19784	+	14.1991i	0.297956	+	0.516074i	0.975668	−	0.219253i	$-0.0703619\pi$
$757$	8.19784	+	14.1991i	0.297956	+	0.516074i	−0.677713	+	0.735327i	$0.737029\pi$
$758$		0			0
$759$	−13.7091			−0.497609
$760$		0			0
$761$	−21.3328	+	36.9494i	−0.773312	+	1.33942i	0.162426	+	0.986721i	$0.448068\pi$
$761$	−21.3328	+	36.9494i	−0.773312	+	1.33942i	−0.935738	+	0.352695i	$0.885265\pi$
$762$		0			0
$763$	2.45300	−	4.24872i	0.0888046	−	0.153814i
$764$		0			0
$765$	−22.8399	−	39.5598i	−0.825777	−	1.43029i
$766$		0			0
$767$	−10.1218	+	21.9390i	−0.365479	+	0.792171i
$768$		0			0
$769$	−1.38521	−	2.39926i	−0.0499520	−	0.0865195i	0.839968	−	0.542636i	$-0.182574\pi$
$769$	−1.38521	−	2.39926i	−0.0499520	−	0.0865195i	−0.889920	+	0.456116i	$0.849240\pi$
$770$		0			0
$771$	−35.0175	+	60.6521i	−1.26112	+	2.18433i
$772$		0			0
$773$	−12.4976	+	21.6464i	−0.449506	+	0.778568i	−0.998354	−	0.0573547i	$-0.981733\pi$
$773$	−12.4976	+	21.6464i	−0.449506	+	0.778568i	0.548848	+	0.835922i	$0.315067\pi$
$774$		0			0
$775$	−46.1425			−1.65749
$776$		0			0
$777$	2.70093	+	4.67815i	0.0968954	+	0.167828i
$778$		0			0
$779$	69.2601			2.48150
$780$		0			0
$781$	−0.419283			−0.0150031
$782$		0			0
$783$	54.3315	+	94.1050i	1.94165	+	3.36304i
$784$		0			0
$785$	−11.1563			−0.398186
$786$		0			0
$787$	3.62689	−	6.28195i	0.129285	−	0.223927i	−0.794115	−	0.607767i	$-0.792065\pi$
$787$	3.62689	−	6.28195i	0.129285	−	0.223927i	0.923400	+	0.383840i	$0.125399\pi$
$788$		0			0
$789$	−25.2251	+	43.6912i	−0.898038	+	1.55545i
$790$		0			0
$791$	−0.480448	−	0.832161i	−0.0170828	−	0.0295882i
$792$		0			0
$793$	4.82344	−	10.4548i	0.171285	−	0.371259i
$794$		0			0
$795$	−62.1497	−	107.646i	−2.20422	−	3.81783i
$796$		0			0
$797$	19.0551	−	33.0045i	0.674968	−	1.16908i	−0.301511	−	0.953463i	$-0.597491\pi$
$797$	19.0551	−	33.0045i	0.674968	−	1.16908i	0.976478	−	0.215616i	$-0.0691758\pi$
$798$		0			0
$799$	0.837183	−	1.45004i	0.0296174	−	0.0512988i
$800$		0			0
$801$	−100.104			−3.53702
$802$		0			0
$803$	6.08006	+	10.5310i	0.214561	+	0.371630i
$804$		0			0
$805$	−9.58951			−0.337986
$806$		0			0
$807$	94.0120			3.30938
$808$		0			0
$809$	2.70470	+	4.68468i	0.0950922	+	0.164705i	0.909647	−	0.415382i	$-0.136352\pi$
$809$	2.70470	+	4.68468i	0.0950922	+	0.164705i	−0.814555	+	0.580087i	$0.803019\pi$
$810$		0			0
$811$	10.1744			0.357271			0.178636	−	0.983915i	$-0.442832\pi$
$811$	10.1744			0.357271			0.178636	+	0.983915i	$0.442832\pi$
$812$		0			0
$813$	−48.6447	+	84.2551i	−1.70604	+	2.95495i
$814$		0			0
$815$	−21.7398	+	37.6545i	−0.761513	+	1.31898i
$816$		0			0
$817$	−4.19178	−	7.26037i	−0.146652	−	0.254008i
$818$		0			0
$819$	−8.74351	−	12.3795i	−0.305523	−	0.432575i
$820$		0			0
$821$	14.9416	+	25.8795i	0.521464	+	0.903202i	0.999688	+	0.0249645i	$0.00794728\pi$
$821$	14.9416	+	25.8795i	0.521464	+	0.903202i	−0.478224	+	0.878238i	$0.658719\pi$
$822$		0			0
$823$	15.7410	−	27.2643i	0.548698	−	0.950372i	−0.449666	−	0.893197i	$-0.648457\pi$
$823$	15.7410	−	27.2643i	0.548698	−	0.950372i	0.998364	−	0.0571758i	$-0.0182096\pi$
$824$		0			0
$825$	17.3352	−	30.0255i	0.603534	−	1.04535i
$826$		0			0
$827$	55.3898			1.92609			0.963046	−	0.269335i	$-0.0868040\pi$
$827$	55.3898			1.92609			0.963046	+	0.269335i	$0.0868040\pi$
$828$		0			0
$829$	12.3688	+	21.4233i	0.429585	+	0.744063i	0.996836	−	0.0794819i	$-0.0253266\pi$
$829$	12.3688	+	21.4233i	0.429585	+	0.744063i	−0.567252	+	0.823545i	$0.691993\pi$
$830$		0			0
$831$	−65.0442			−2.25636
$832$		0			0
$833$	−10.3893			−0.359969
$834$		0			0
$835$	18.5586	+	32.1445i	0.642248	+	1.11241i
$836$		0			0
$837$	60.8393			2.10291
$838$		0			0
$839$	−1.49844	+	2.59537i	−0.0517318	+	0.0896020i	−0.890732	−	0.454529i	$-0.849807\pi$
$839$	−1.49844	+	2.59537i	−0.0517318	+	0.0896020i	0.839000	+	0.544132i	$0.183141\pi$
$840$		0			0
$841$	−14.8732	+	25.7612i	−0.512869	+	0.888316i
$842$		0			0
$843$	−24.4885	−	42.4154i	−0.843430	−	1.46086i
$844$		0			0
$845$	50.7377	−	9.37281i	1.74543	−	0.322435i
$846$		0			0
$847$	0.284141	+	0.492146i	0.00976319	+	0.0169103i
$848$		0			0
$849$	36.3127	−	62.8954i	1.24625	−	2.15856i
$850$		0			0
$851$	6.26697	−	10.8547i	0.214829	−	0.372095i
$852$		0			0
$853$	21.8608			0.748500			0.374250	−	0.927328i	$-0.377900\pi$
$853$	21.8608			0.748500			0.374250	+	0.927328i	$0.377900\pi$
$854$		0			0
$855$	127.006	+	219.980i	4.34350	+	7.52316i
$856$		0			0
$857$	10.8591			0.370941			0.185470	−	0.982650i	$-0.440619\pi$
$857$	10.8591			0.370941			0.185470	+	0.982650i	$0.440619\pi$
$858$		0			0
$859$	−25.3612			−0.865313			−0.432657	−	0.901559i	$-0.642424\pi$
$859$	−25.3612			−0.865313			−0.432657	+	0.901559i	$0.642424\pi$
$860$		0			0
$861$	7.33390	+	12.7027i	0.249939	+	0.432906i
$862$		0			0
$863$	−25.9524			−0.883428			−0.441714	−	0.897156i	$-0.645629\pi$
$863$	−25.9524			−0.883428			−0.441714	+	0.897156i	$0.645629\pi$
$864$		0			0
$865$	25.4624	−	44.1022i	0.865749	−	1.49952i
$866$		0			0
$867$	−23.5043	+	40.7106i	−0.798247	+	1.38260i
$868$		0			0
$869$	2.88703	+	5.00049i	0.0979359	+	0.169630i
$870$		0			0
$871$	−0.252986	−	0.358190i	−0.00857210	−	0.0121368i
$872$		0			0
$873$	48.6237	+	84.2186i	1.64566	+	2.85037i
$874$		0			0
$875$	6.48728	−	11.2363i	0.219310	−	0.379856i
$876$		0			0
$877$	4.87972	−	8.45192i	0.164776	−	0.285401i	−0.771800	−	0.635866i	$-0.780643\pi$
$877$	4.87972	−	8.45192i	0.164776	−	0.285401i	0.936576	+	0.350465i	$0.113976\pi$
$878$		0			0
$879$	6.00838			0.202658
$880$		0			0
$881$	7.95209	+	13.7734i	0.267913	+	0.464039i	0.968323	−	0.249702i	$-0.0803327\pi$
$881$	7.95209	+	13.7734i	0.267913	+	0.464039i	−0.700410	+	0.713741i	$0.746999\pi$
$882$		0			0
$883$	48.5958			1.63538			0.817690	−	0.575659i	$-0.195254\pi$
$883$	48.5958			1.63538			0.817690	+	0.575659i	$0.195254\pi$
$884$		0			0
$885$	85.7580			2.88272
$886$		0			0
$887$	−2.14868	−	3.72162i	−0.0721456	−	0.124960i	0.827696	−	0.561177i	$-0.189651\pi$
$887$	−2.14868	−	3.72162i	−0.0721456	−	0.124960i	−0.899841	+	0.436217i	$0.856318\pi$
$888$		0			0
$889$	−6.90611			−0.231623
$890$		0			0
$891$	−11.7614	+	20.3713i	−0.394020	+	0.682463i
$892$		0			0
$893$	−4.65532	+	8.06326i	−0.155784	+	0.269827i
$894$		0			0
$895$	12.7220	+	22.0352i	0.425250	+	0.736555i
$896$		0			0
$897$	−20.7071	+	44.8824i	−0.691389	+	1.49858i
$898$		0			0
$899$	16.4457	+	28.4849i	0.548496	+	0.950023i
$900$		0			0
$901$	7.55643	−	13.0881i	0.251741	−	0.436029i
$902$		0			0
$903$	0.887729	−	1.53759i	0.0295418	−	0.0511679i
$904$		0			0
$905$	40.2525			1.33804
$906$		0			0
$907$	−21.4411	−	37.1371i	−0.711940	−	1.23312i	−0.964128	−	0.265438i	$-0.914484\pi$
$907$	−21.4411	−	37.1371i	−0.711940	−	1.23312i	0.252188	−	0.967678i	$-0.418850\pi$
$908$		0			0
$909$	−104.372			−3.46179
$910$		0			0
$911$	−50.0422			−1.65797			−0.828987	−	0.559269i	$-0.811082\pi$
$911$	−50.0422			−1.65797			−0.828987	+	0.559269i	$0.811082\pi$
$912$		0			0
$913$	0.557884	+	0.966283i	0.0184633	+	0.0319793i
$914$		0			0
$915$	−40.8669			−1.35102
$916$		0			0
$917$	5.47716	−	9.48671i	0.180872	−	0.313279i
$918$		0			0
$919$	30.2345	−	52.3677i	0.997345	−	1.72745i	0.435602	−	0.900139i	$-0.356535\pi$
$919$	30.2345	−	52.3677i	0.997345	−	1.72745i	0.561742	−	0.827312i	$-0.310131\pi$
$920$		0			0
$921$	−27.6890	−	47.9587i	−0.912383	−	1.58029i
$922$		0			0
$923$	−0.633312	+	1.37270i	−0.0208457	+	0.0451829i
$924$		0			0
$925$	15.8492	+	27.4516i	0.521119	+	0.902605i
$926$		0			0
$927$	−5.46523	+	9.46605i	−0.179502	+	0.310906i
$928$		0			0
$929$	19.9911	−	34.6255i	0.655886	−	1.13603i	−0.325786	−	0.945444i	$-0.605629\pi$
$929$	19.9911	−	34.6255i	0.655886	−	1.13603i	0.981671	−	0.190583i	$-0.0610379\pi$
$930$		0			0
$931$	57.7720			1.89340
$932$		0			0
$933$	12.8885	+	22.3235i	0.421950	+	0.730839i
$934$		0			0
$935$	6.17557			0.201963
$936$		0			0
$937$	−8.89951			−0.290734			−0.145367	−	0.989378i	$-0.546436\pi$
$937$	−8.89951			−0.290734			−0.145367	+	0.989378i	$0.546436\pi$
$938$		0			0
$939$	−7.76397	−	13.4476i	−0.253368	−	0.438846i
$940$		0			0
$941$	48.6867			1.58714			0.793570	−	0.608479i	$-0.208220\pi$
$941$	48.6867			1.58714			0.793570	+	0.608479i	$0.208220\pi$
$942$		0			0
$943$	17.0168	−	29.4740i	0.554145	−	0.959807i
$944$		0			0
$945$	−15.9882	+	27.6924i	−0.520096	+	0.900833i
$946$		0			0
$947$	17.9937	+	31.1660i	0.584716	+	1.01276i	0.994911	+	0.100760i	$0.0321273\pi$
$947$	17.9937	+	31.1660i	0.584716	+	1.01276i	−0.410195	+	0.911998i	$0.634539\pi$
$948$		0			0
$949$	43.6612	−	3.99895i	1.41730	−	0.129811i
$950$		0			0
$951$	20.6726	+	35.8061i	0.670356	+	1.16109i
$952$		0			0
$953$	20.0725	−	34.7666i	0.650213	−	1.12620i	−0.332859	−	0.942977i	$-0.608013\pi$
$953$	20.0725	−	34.7666i	0.650213	−	1.12620i	0.983071	−	0.183224i	$-0.0586535\pi$
$954$		0			0
$955$	4.69850	−	8.13804i	0.152040	−	0.263341i
$956$		0			0
$957$	−24.7139			−0.798887
$958$		0			0
$959$	1.22179	+	2.11621i	0.0394538	+	0.0683359i
$960$		0			0
$961$	−12.5844			−0.405949
$962$		0			0
$963$	−18.2281			−0.587392
$964$		0			0
$965$	−35.6209	−	61.6973i	−1.14668	−	1.98611i
$966$		0			0
$967$	−29.3357			−0.943374			−0.471687	−	0.881766i	$-0.656355\pi$
$967$	−29.3357			−0.943374			−0.471687	+	0.881766i	$0.656355\pi$
$968$		0			0
$969$	−21.7048	+	37.5938i	−0.697259	+	1.20769i
$970$		0			0
$971$	13.6536	−	23.6488i	0.438166	−	0.758926i	−0.559382	−	0.828910i	$-0.688962\pi$
$971$	13.6536	−	23.6488i	0.438166	−	0.758926i	0.997548	+	0.0699841i	$0.0222949\pi$
$972$		0			0
$973$	2.35742	+	4.08317i	0.0755753	+	0.130900i
$974$		0			0
$975$	−72.1165	−	102.106i	−2.30958	−	3.27002i
$976$		0			0
$977$	−14.0438	−	24.3246i	−0.449302	−	0.778213i	0.549039	−	0.835797i	$-0.314994\pi$
$977$	−14.0438	−	24.3246i	−0.449302	−	0.778213i	−0.998341	+	0.0575834i	$0.981660\pi$
$978$		0			0
$979$	6.76670	−	11.7203i	0.216265	−	0.374581i
$980$		0			0
$981$	−31.9286	+	55.3020i	−1.01940	+	1.76566i
$982$		0			0
$983$	21.2655			0.678265			0.339133	−	0.940739i	$-0.389866\pi$
$983$	21.2655			0.678265			0.339133	+	0.940739i	$0.389866\pi$
$984$		0			0
$985$	−22.5788	−	39.1076i	−0.719420	−	1.24607i
$986$		0			0
$987$	−1.97180			−0.0627630
$988$		0			0
$989$	−4.11959			−0.130995
$990$		0			0
$991$	11.9943	+	20.7747i	0.381010	+	0.659929i	0.991207	−	0.132321i	$-0.0422430\pi$
$991$	11.9943	+	20.7747i	0.381010	+	0.659929i	−0.610197	+	0.792250i	$0.708910\pi$
$992$		0			0
$993$	21.2083			0.673025
$994$		0			0
$995$	10.5883	−	18.3394i	0.335670	−	0.581398i
$996$		0			0
$997$	−19.1376	+	33.1474i	−0.606095	+	1.04979i	0.385782	+	0.922590i	$0.373932\pi$
$997$	−19.1376	+	33.1474i	−0.606095	+	1.04979i	−0.991877	+	0.127198i	$0.959402\pi$
$998$		0			0
$999$	−20.8973	−	36.1952i	−0.661162	−	1.14517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.c.133.5	✓	10
13.3	even	3		7436.2.a.r.1.1		5
13.9	even	3	inner	572.2.i.c.529.5	yes	10
13.10	even	6		7436.2.a.q.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.c.133.5	✓	10	1.1	even	1	trivial
572.2.i.c.529.5	yes	10	13.9	even	3	inner
7436.2.a.q.1.1		5	13.10	even	6
7436.2.a.r.1.1		5	13.3	even	3

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61221 + 2.79242i) q^{3} +3.96894 q^{5} +(0.284141 - 0.492146i) q^{7} +(-3.69842 + 6.40585i) q^{9} +O(q^{10})\)	\(q+(1.61221 + 2.79242i) q^{3} +3.96894 q^{5} +(0.284141 - 0.492146i) q^{7} +(-3.69842 + 6.40585i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-3.59052 + 0.328858i) q^{13} +(6.39875 + 11.0830i) q^{15} +(-0.777988 + 1.34751i) q^{17} +(4.32616 - 7.49312i) q^{19} +1.83237 q^{21} +(-2.12583 - 3.68204i) q^{23} +10.7525 q^{25} -14.1772 q^{27} +(-3.83231 - 6.63776i) q^{29} -4.29134 q^{31} +(1.61221 - 2.79242i) q^{33} +(1.12774 - 1.95330i) q^{35} +(1.47401 + 2.55305i) q^{37} +(-6.70697 - 9.49607i) q^{39} +(4.00240 + 6.93236i) q^{41} +(0.484469 - 0.839125i) q^{43} +(-14.6788 + 25.4244i) q^{45} -1.07609 q^{47} +(3.33853 + 5.78250i) q^{49} -5.01711 q^{51} -9.71279 q^{53} +(-1.98447 - 3.43720i) q^{55} +27.8986 q^{57} +(3.35058 - 5.80337i) q^{59} +(-1.59668 + 2.76552i) q^{61} +(2.10174 + 3.64033i) q^{63} +(-14.2506 + 1.30522i) q^{65} +(0.0608121 + 0.105330i) q^{67} +(6.85455 - 11.8724i) q^{69} +(0.209642 - 0.363110i) q^{71} -12.1601 q^{73} +(17.3352 + 30.0255i) q^{75} -0.568282 q^{77} -5.77407 q^{79} +(-11.7614 - 20.3713i) q^{81} -1.11577 q^{83} +(-3.08779 + 5.34820i) q^{85} +(12.3570 - 21.4029i) q^{87} +(6.76670 + 11.7203i) q^{89} +(-0.858368 + 1.86050i) q^{91} +(-6.91852 - 11.9832i) q^{93} +(17.1703 - 29.7397i) q^{95} +(6.57357 - 11.3858i) q^{97} +7.39684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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