LMFDB - Embedded newform 504.2.i.b.125.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(125,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.i (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.16
Character	$\chi$	$=$	504.125
Dual form			504.2.i.b.125.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 + 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +1.88325i q^{5} +(-0.347296 + 2.62286i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(0.483690 + 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +1.88325i q^{5} +(-0.347296 + 2.62286i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-2.50270 + 0.910909i) q^{10} +3.41687 q^{11} -4.08044 q^{13} +(-3.65357 + 0.807118i) q^{14} +(0.694593 - 3.93923i) q^{16} +3.26189 q^{17} -7.66872 q^{19} +(-2.42106 - 2.88531i) q^{20} +(1.65270 + 4.54077i) q^{22} -0.261336i q^{23} +1.45336 q^{25} +(-1.97367 - 5.42261i) q^{26} +(-2.83979 - 4.46493i) q^{28} -6.08565 q^{29} +8.03690i q^{31} +(5.57091 - 0.982302i) q^{32} +(1.57774 + 4.33481i) q^{34} +(-4.93950 - 0.654046i) q^{35} -1.84321i q^{37} +(-3.70928 - 10.1912i) q^{38} +(2.66332 - 4.61301i) q^{40} +8.10401 q^{41} +7.40333i q^{43} +(-5.23495 + 4.39264i) q^{44} +(0.347296 - 0.126406i) q^{46} -2.57644 q^{47} +(-6.75877 - 1.82182i) q^{49} +(0.702977 + 1.93141i) q^{50} +(6.25160 - 5.24572i) q^{52} +11.6566 q^{53} +6.43482i q^{55} +(4.55998 - 5.93351i) q^{56} +(-2.94356 - 8.08737i) q^{58} +5.77062i q^{59} +8.59369 q^{61} +(-10.6805 + 3.88737i) q^{62} +(4.00000 + 6.92820i) q^{64} -7.68450i q^{65} -4.35705i q^{67} +(-4.99750 + 4.19340i) q^{68} +(-1.52001 - 6.88059i) q^{70} +7.76432i q^{71} -4.61301i q^{73} +(2.44949 - 0.891541i) q^{74} +(11.7492 - 9.85872i) q^{76} +(-1.18667 + 8.96196i) q^{77} +11.1925 q^{79} +(7.41856 + 1.30809i) q^{80} +(3.91983 + 10.7696i) q^{82} -7.07871i q^{83} +6.14296i q^{85} +(-9.83848 + 3.58091i) q^{86} +(-8.36959 - 4.83218i) q^{88} +13.2569 q^{89} +(1.41712 - 10.7024i) q^{91} +(0.335967 + 0.400390i) q^{92} +(-1.24620 - 3.42390i) q^{94} -14.4421i q^{95} -15.1044i q^{97} +(-0.848085 - 9.86310i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{22} - 72 q^{25} - 24 q^{28} - 72 q^{49} + 48 q^{58} + 96 q^{64} - 24 q^{70} + 48 q^{79} - 144 q^{88}+O(q^{100}) $ 24 * q + 48 * q^22 - 72 * q^25 - 24 * q^28 - 72 * q^49 + 48 * q^58 + 96 * q^64 - 24 * q^70 + 48 * q^79 - 144 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.483690	+	1.32893i	0.342020	+	0.939693i
$2$	0.483690	+	1.32893i	0.342020	+	0.939693i
$3$		0			0
$3$		0			0
$4$	−1.53209	+	1.28558i	−0.766044	+	0.642788i
$5$			1.88325i			0.842216i	0.907011	+	0.421108i	$0.138359\pi$
$5$			1.88325i			0.842216i	−0.907011	+	0.421108i	$0.861641\pi$
$6$		0			0
$7$	−0.347296	+	2.62286i	−0.131266	+	0.991347i
$7$	−0.347296	+	2.62286i	−0.131266	+	0.991347i
$8$	−2.44949	−	1.41421i	−0.866025	−	0.500000i
$9$		0			0
$10$	−2.50270	+	0.910909i	−0.791424	+	0.288055i
$11$	3.41687			1.03022			0.515112	−	0.857123i	$-0.327750\pi$
$11$	3.41687			1.03022			0.515112	+	0.857123i	$0.327750\pi$
$12$		0			0
$13$	−4.08044			−1.13171			−0.565856	−	0.824504i	$-0.691454\pi$
$13$	−4.08044			−1.13171			−0.565856	+	0.824504i	$0.691454\pi$
$14$	−3.65357	+	0.807118i	−0.976457	+	0.215711i
$15$		0			0
$16$	0.694593	−	3.93923i	0.173648	−	0.984808i
$17$	3.26189			0.791124			0.395562	−	0.918439i	$-0.370550\pi$
$17$	3.26189			0.791124			0.395562	+	0.918439i	$0.370550\pi$
$18$		0			0
$19$	−7.66872			−1.75933			−0.879663	−	0.475597i	$-0.842232\pi$
$19$	−7.66872			−1.75933			−0.879663	+	0.475597i	$0.842232\pi$
$20$	−2.42106	−	2.88531i	−0.541366	−	0.645175i
$21$		0			0
$22$	1.65270	+	4.54077i	0.352358	+	0.968095i
$23$		−	0.261336i		−	0.0544923i	−0.999629	−	0.0272462i	$-0.991326\pi$
$23$		−	0.261336i		−	0.0544923i	0.999629	−	0.0272462i	$-0.00867380\pi$
$24$		0			0
$25$	1.45336			0.290673
$26$	−1.97367	−	5.42261i	−0.387068	−	1.06346i
$27$		0			0
$28$	−2.83979	−	4.46493i	−0.536670	−	0.843792i
$29$	−6.08565			−1.13008			−0.565038	−	0.825065i	$-0.691139\pi$
$29$	−6.08565			−1.13008			−0.565038	+	0.825065i	$0.691139\pi$
$30$		0			0
$31$			8.03690i			1.44347i	0.692169	+	0.721735i	$0.256655\pi$
$31$			8.03690i			1.44347i	−0.692169	+	0.721735i	$0.743345\pi$
$32$	5.57091	−	0.982302i	0.984808	−	0.173648i
$33$		0			0
$34$	1.57774	+	4.33481i	0.270580	+	0.743413i
$35$	−4.93950	−	0.654046i	−0.834928	−	0.110554i
$36$		0			0
$37$		−	1.84321i		−	0.303022i	−0.988456	−	0.151511i	$-0.951586\pi$
$37$		−	1.84321i		−	0.303022i	0.988456	−	0.151511i	$-0.0484139\pi$
$38$	−3.70928	−	10.1912i	−0.601725	−	1.65323i
$39$		0			0
$40$	2.66332	−	4.61301i	0.421108	−	0.729380i
$41$	8.10401			1.26563			0.632817	−	0.774301i	$-0.281899\pi$
$41$	8.10401			1.26563			0.632817	+	0.774301i	$0.281899\pi$
$42$		0			0
$43$			7.40333i			1.12900i	0.825434	+	0.564499i	$0.190931\pi$
$43$			7.40333i			1.12900i	−0.825434	+	0.564499i	$0.809069\pi$
$44$	−5.23495	+	4.39264i	−0.789198	+	0.662216i
$45$		0			0
$46$	0.347296	−	0.126406i	0.0512061	−	0.0186375i
$47$	−2.57644			−0.375812			−0.187906	−	0.982187i	$-0.560170\pi$
$47$	−2.57644			−0.375812			−0.187906	+	0.982187i	$0.560170\pi$
$48$		0			0
$49$	−6.75877	−	1.82182i	−0.965539	−	0.260260i
$50$	0.702977	+	1.93141i	0.0994159	+	0.273143i
$51$		0			0
$52$	6.25160	−	5.24572i	0.866941	−	0.727450i
$53$	11.6566			1.60115			0.800576	−	0.599232i	$-0.204527\pi$
$53$	11.6566			1.60115			0.800576	+	0.599232i	$0.204527\pi$
$54$		0			0
$55$			6.43482i			0.867671i
$56$	4.55998	−	5.93351i	0.609353	−	0.792899i
$57$		0			0
$58$	−2.94356	−	8.08737i	−0.386509	−	1.06192i
$59$			5.77062i			0.751270i	0.926768	+	0.375635i	$0.122575\pi$
$59$			5.77062i			0.751270i	−0.926768	+	0.375635i	$0.877425\pi$
$60$		0			0
$61$	8.59369			1.10031			0.550154	−	0.835063i	$-0.314569\pi$
$61$	8.59369			1.10031			0.550154	+	0.835063i	$0.314569\pi$
$62$	−10.6805	+	3.88737i	−1.35642	+	0.493696i
$63$		0			0
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$		−	7.68450i		−	0.953145i
$66$		0			0
$67$		−	4.35705i		−	0.532299i	−0.963932	−	0.266149i	$-0.914249\pi$
$67$		−	4.35705i		−	0.532299i	0.963932	−	0.266149i	$-0.0857514\pi$
$68$	−4.99750	+	4.19340i	−0.606036	+	0.508525i
$69$		0			0
$70$	−1.52001	−	6.88059i	−0.181675	−	0.822388i
$71$			7.76432i			0.921455i	0.887542	+	0.460727i	$0.152411\pi$
$71$			7.76432i			0.921455i	−0.887542	+	0.460727i	$0.847589\pi$
$72$		0			0
$73$		−	4.61301i		−	0.539911i	−0.962873	−	0.269956i	$-0.912991\pi$
$73$		−	4.61301i		−	0.539911i	0.962873	−	0.269956i	$-0.0870091\pi$
$74$	2.44949	−	0.891541i	0.284747	−	0.103640i
$75$		0			0
$76$	11.7492	−	9.85872i	1.34772	−	1.13087i
$77$	−1.18667	+	8.96196i	−0.135233	+	1.02131i
$78$		0			0
$79$	11.1925			1.25926			0.629629	−	0.776896i	$-0.283207\pi$
$79$	11.1925			1.25926			0.629629	+	0.776896i	$0.283207\pi$
$80$	7.41856	+	1.30809i	0.829421	+	0.146249i
$81$		0			0
$82$	3.91983	+	10.7696i	0.432872	+	1.18931i
$83$		−	7.07871i		−	0.776989i	−0.921451	−	0.388495i	$-0.872995\pi$
$83$		−	7.07871i		−	0.776989i	0.921451	−	0.388495i	$-0.127005\pi$
$84$		0			0
$85$			6.14296i			0.666297i
$86$	−9.83848	+	3.58091i	−1.06091	+	0.386140i
$87$		0			0
$88$	−8.36959	−	4.83218i	−0.892201	−	0.515112i
$89$	13.2569			1.40523			0.702614	−	0.711571i	$-0.252016\pi$
$89$	13.2569			1.40523			0.702614	+	0.711571i	$0.252016\pi$
$90$		0			0
$91$	1.41712	−	10.7024i	0.148555	−	1.12192i
$92$	0.335967	+	0.400390i	0.0350270	+	0.0417436i
$93$		0			0
$94$	−1.24620	−	3.42390i	−0.128535	−	0.353148i
$95$		−	14.4421i		−	1.48173i
$96$		0			0
$97$		−	15.1044i		−	1.53362i	−0.641872	−	0.766812i	$-0.721842\pi$
$97$		−	15.1044i		−	1.53362i	0.641872	−	0.766812i	$-0.278158\pi$
$98$	−0.848085	−	9.86310i	−0.0856695	−	0.996324i
$99$		0			0
$100$	−2.22668	+	1.86841i	−0.222668	+	0.186841i
$101$			1.88325i			0.187391i	0.995601	+	0.0936953i	$0.0298679\pi$
$101$			1.88325i			0.187391i	−0.995601	+	0.0936953i	$0.970132\pi$
$102$		0			0
$103$			8.03690i			0.791900i	0.918272	+	0.395950i	$0.129585\pi$
$103$			8.03690i			0.791900i	−0.918272	+	0.395950i	$0.870415\pi$
$104$	9.99500	+	5.77062i	0.980091	+	0.565856i
$105$		0			0
$106$	5.63816	+	15.4907i	0.547626	+	1.50459i
$107$	1.24875			0.120721			0.0603606	−	0.998177i	$-0.480775\pi$
$107$	1.24875			0.120721			0.0603606	+	0.998177i	$0.480775\pi$
$108$		0			0
$109$			7.15052i			0.684896i	0.939537	+	0.342448i	$0.111256\pi$
$109$			7.15052i			0.684896i	−0.939537	+	0.342448i	$0.888744\pi$
$110$	−8.55140	+	3.11246i	−0.815344	+	0.296761i
$111$		0			0
$112$	10.0908	+	3.18990i	0.953492	+	0.301417i
$113$			11.0633i			1.04075i	0.853938	+	0.520375i	$0.174208\pi$
$113$			11.0633i			1.04075i	−0.853938	+	0.520375i	$0.825792\pi$
$114$		0			0
$115$	0.492162			0.0458943
$116$	9.32375	−	7.82356i	0.865688	−	0.726399i
$117$		0			0
$118$	−7.66872	+	2.79119i	−0.705963	+	0.256950i
$119$	−1.13284	+	8.55547i	−0.103847	+	0.784279i
$120$		0			0
$121$	0.674992			0.0613629
$122$	4.15668	+	11.4204i	0.376328	+	1.03395i
$123$		0			0
$124$	−10.3320	−	12.3133i	−0.927845	−	1.10576i
$125$			12.1533i			1.08702i
$126$		0			0
$127$	−0.581719			−0.0516192			−0.0258096	−	0.999667i	$-0.508216\pi$
$127$	−0.581719			−0.0516192			−0.0258096	+	0.999667i	$0.508216\pi$
$128$	−7.27231	+	8.66680i	−0.642788	+	0.766044i
$129$		0			0
$130$	10.2121	−	3.71691i	0.895663	−	0.325995i
$131$			9.08283i			0.793570i	0.917912	+	0.396785i	$0.129874\pi$
$131$			9.08283i			0.793570i	−0.917912	+	0.396785i	$0.870126\pi$
$132$		0			0
$133$	2.66332	−	20.1140i	0.230939	−	1.74410i
$134$	5.79020	−	2.10746i	0.500197	−	0.182057i
$135$		0			0
$136$	−7.98996	−	4.61301i	−0.685133	−	0.395562i
$137$			0.0907611i			0.00775424i	0.999992	+	0.00387712i	$0.00123413\pi$
$137$			0.0907611i			0.00775424i	−0.999992	+	0.00387712i	$0.998766\pi$
$138$		0			0
$139$	−5.32664			−0.451800			−0.225900	−	0.974151i	$-0.572532\pi$
$139$	−5.32664			−0.451800			−0.225900	+	0.974151i	$0.572532\pi$
$140$	8.40858	−	5.34804i	0.710655	−	0.451992i
$141$		0			0
$142$	−10.3182	+	3.75552i	−0.865884	+	0.315156i
$143$	−13.9423			−1.16592
$144$		0			0
$145$		−	11.4608i		−	0.951768i
$146$	6.13034	−	2.23126i	0.507351	−	0.184661i
$147$		0			0
$148$	2.36959	+	2.82396i	0.194779	+	0.232128i
$149$	5.49476			0.450148			0.225074	−	0.974342i	$-0.427738\pi$
$149$	5.49476			0.450148			0.225074	+	0.974342i	$0.427738\pi$
$150$		0			0
$151$	−19.7297			−1.60558			−0.802789	−	0.596263i	$-0.796652\pi$
$151$	−19.7297			−1.60558			−0.802789	+	0.596263i	$0.796652\pi$
$152$	18.7845	+	10.8452i	1.52362	+	0.879663i
$153$		0			0
$154$	−12.4838	+	2.75782i	−1.00597	+	0.222231i
$155$	−15.1355			−1.21571
$156$		0			0
$157$	8.59369			0.685851			0.342925	−	0.939363i	$-0.388582\pi$
$157$	8.59369			0.685851			0.342925	+	0.939363i	$0.388582\pi$
$158$	5.41371	+	14.8740i	0.430692	+	1.18332i
$159$		0			0
$160$	1.84992	+	10.4914i	0.146249	+	0.829421i
$161$	0.685448	+	0.0907611i	0.0540208	+	0.00715297i
$162$		0			0
$163$			18.3281i			1.43557i	0.696267	+	0.717783i	$0.254843\pi$
$163$			18.3281i			1.43557i	−0.696267	+	0.717783i	$0.745157\pi$
$164$	−12.4161	+	10.4183i	−0.969532	+	0.813534i
$165$		0			0
$166$	9.40708	−	3.42390i	0.730131	−	0.265746i
$167$	−3.94734			−0.305454			−0.152727	−	0.988268i	$-0.548806\pi$
$167$	−3.94734			−0.305454			−0.152727	+	0.988268i	$0.548806\pi$
$168$		0			0
$169$	3.65002			0.280770
$170$	−8.16353	+	2.97128i	−0.626114	+	0.227887i
$171$		0			0
$172$	−9.51754	−	11.3426i	−0.725706	−	0.864862i
$173$		−	25.5778i		−	1.94464i	−0.233646	−	0.972322i	$-0.575066\pi$
$173$		−	25.5778i		−	1.94464i	0.233646	−	0.972322i	$-0.424934\pi$
$174$		0			0
$175$	−0.504748	+	3.81197i	−0.0381553	+	0.288158i
$176$	2.37333	−	13.4598i	0.178897	−	1.01457i
$177$		0			0
$178$	6.41222	+	17.6174i	0.480616	+	1.32048i
$179$	19.4577			1.45433			0.727167	−	0.686460i	$-0.240836\pi$
$179$	19.4577			1.45433			0.727167	+	0.686460i	$0.240836\pi$
$180$		0			0
$181$	9.40708			0.699223			0.349611	−	0.936895i	$-0.386314\pi$
$181$	9.40708			0.699223			0.349611	+	0.936895i	$0.386314\pi$
$182$	14.9082	−	3.29340i	1.10507	−	0.244123i
$183$		0			0
$184$	−0.369585	+	0.640140i	−0.0272462	+	0.0471918i
$185$	3.47123			0.255210
$186$		0			0
$187$	11.1454			0.815035
$188$	3.94734	−	3.31221i	0.287889	−	0.241568i
$189$		0			0
$190$	19.1925	−	6.98551i	1.39237	−	0.506782i
$191$		−	3.61244i		−	0.261387i	−0.991423	−	0.130693i	$-0.958280\pi$
$191$		−	3.61244i		−	0.261387i	0.991423	−	0.130693i	$-0.0417203\pi$
$192$		0			0
$193$	14.0993			1.01489			0.507443	−	0.861685i	$-0.330591\pi$
$193$	14.0993			1.01489			0.507443	+	0.861685i	$0.330591\pi$
$194$	20.0727	−	7.30586i	1.44113	−	0.524530i
$195$		0			0
$196$	12.6971	−	5.89772i	0.906937	−	0.421266i
$197$	−17.1464			−1.22163			−0.610816	−	0.791772i	$-0.709159\pi$
$197$	−17.1464			−1.22163			−0.610816	+	0.791772i	$0.709159\pi$
$198$		0			0
$199$		−	10.8281i		−	0.767583i	−0.923420	−	0.383792i	$-0.874618\pi$
$199$		−	10.8281i		−	0.767583i	0.923420	−	0.383792i	$-0.125382\pi$
$200$	−3.56000	−	2.05537i	−0.251730	−	0.145336i
$201$		0			0
$202$	−2.50270	+	0.910909i	−0.176090	+	0.0640913i
$203$	2.11352	−	15.9618i	0.148340	−	1.12030i
$204$		0			0
$205$			15.2619i			1.06594i
$206$	−10.6805	+	3.88737i	−0.744142	+	0.270846i
$207$		0			0
$208$	−2.83425	+	16.0738i	−0.196520	+	1.11452i
$209$	−26.2030			−1.81250
$210$		0			0
$211$		−	6.56769i		−	0.452138i	−0.974111	−	0.226069i	$-0.927412\pi$
$211$		−	6.56769i		−	0.452138i	0.974111	−	0.226069i	$-0.0725875\pi$
$212$	−17.8589	+	14.9854i	−1.22655	+	1.02920i
$213$		0			0
$214$	0.604007	+	1.65950i	0.0412891	+	0.113441i
$215$	−13.9423			−0.950860
$216$		0			0
$217$	−21.0797	−	2.79119i	−1.43098	−	0.189478i
$218$	−9.50251	+	3.45863i	−0.643591	+	0.234248i
$219$		0			0
$220$	−8.27245	−	9.85872i	−0.557728	−	0.664675i
$221$	−13.3099			−0.895324
$222$		0			0
$223$		−	3.98029i		−	0.266540i	−0.991080	−	0.133270i	$-0.957452\pi$
$223$		−	3.98029i		−	0.266540i	0.991080	−	0.133270i	$-0.0425478\pi$
$224$	0.641682	+	14.9529i	0.0428742	+	0.999080i
$225$		0			0
$226$	−14.7023	+	5.35121i	−0.977985	+	0.355957i
$227$		−	21.0784i		−	1.39902i	−0.714623	−	0.699510i	$-0.753402\pi$
$227$		−	21.0784i		−	1.39902i	0.714623	−	0.699510i	$-0.246598\pi$
$228$		0			0
$229$	−11.2570			−0.743884			−0.371942	−	0.928256i	$-0.621308\pi$
$229$	−11.2570			−0.743884			−0.371942	+	0.928256i	$0.621308\pi$
$230$	0.238053	+	0.654046i	0.0156968	+	0.0431265i
$231$		0			0
$232$	14.9067	+	8.60640i	0.978675	+	0.565038i
$233$		−	27.9927i		−	1.83387i	−0.399042	−	0.916933i	$-0.630657\pi$
$233$		−	27.9927i		−	1.83387i	0.399042	−	0.916933i	$-0.369343\pi$
$234$		0			0
$235$		−	4.85208i		−	0.316515i
$236$	−7.41856	−	8.84110i	−0.482907	−	0.575507i
$237$		0			0
$238$	−11.9175	+	2.63273i	−0.772499	+	0.170654i
$239$			10.5516i			0.682526i	0.939968	+	0.341263i	$0.110855\pi$
$239$			10.5516i			0.682526i	−0.939968	+	0.341263i	$0.889145\pi$
$240$		0			0
$241$		−	5.87843i		−	0.378663i	−0.981913	−	0.189331i	$-0.939368\pi$
$241$		−	5.87843i		−	0.378663i	0.981913	−	0.189331i	$-0.0606320\pi$
$242$	0.326487	+	0.897015i	0.0209874	+	0.0576623i
$243$		0			0
$244$	−13.1663	+	11.0478i	−0.842885	+	0.707265i
$245$	3.43094	−	12.7285i	0.219195	−	0.813192i
$246$		0			0
$247$	31.2918			1.99105
$248$	11.3659	−	19.6863i	0.721735	−	1.25008i
$249$		0			0
$250$	−16.1508	+	5.87843i	−1.02147	+	0.371784i
$251$		−	8.84110i		−	0.558045i	−0.960285	−	0.279023i	$-0.909990\pi$
$251$		−	8.84110i		−	0.558045i	0.960285	−	0.279023i	$-0.0900104\pi$
$252$		0			0
$253$		−	0.892951i		−	0.0561394i
$254$	−0.281371	−	0.773061i	−0.0176548	−	0.0485062i
$255$		0			0
$256$	−15.0351	−	5.47232i	−0.939693	−	0.342020i
$257$	−22.9411			−1.43103			−0.715514	−	0.698598i	$-0.753808\pi$
$257$	−22.9411			−1.43103			−0.715514	+	0.698598i	$0.753808\pi$
$258$		0			0
$259$	4.83448	+	0.640140i	0.300400	+	0.0397764i
$260$	9.87900	+	11.7733i	0.612670	+	0.730151i
$261$		0			0
$262$	−12.0704	+	4.39327i	−0.745712	+	0.271417i
$263$		−	9.91044i		−	0.611104i	−0.952175	−	0.305552i	$-0.901159\pi$
$263$		−	9.91044i		−	0.611104i	0.952175	−	0.305552i	$-0.0988410\pi$
$264$		0			0
$265$			21.9522i			1.34852i
$266$	28.0182	−	6.18956i	1.71791	−	0.379507i
$267$		0			0
$268$	5.60132	+	6.67539i	0.342155	+	0.407764i
$269$		−	7.65387i		−	0.466665i	−0.972397	−	0.233332i	$-0.925037\pi$
$269$		−	7.65387i		−	0.466665i	0.972397	−	0.233332i	$-0.0749630\pi$
$270$		0			0
$271$		−	11.6805i		−	0.709542i	−0.934953	−	0.354771i	$-0.884559\pi$
$271$		−	11.6805i		−	0.709542i	0.934953	−	0.354771i	$-0.115441\pi$
$272$	2.26568	−	12.8493i	0.137377	−	0.779105i
$273$		0			0
$274$	−0.120615	+	0.0439002i	−0.00728660	+	0.00265211i
$275$	4.96595			0.299458
$276$		0			0
$277$		−	18.8337i		−	1.13161i	−0.824540	−	0.565804i	$-0.808566\pi$
$277$		−	18.8337i		−	1.13161i	0.824540	−	0.565804i	$-0.191434\pi$
$278$	−2.57644	−	7.07871i	−0.154525	−	0.424553i
$279$		0			0
$280$	11.1743	+	8.58759i	0.667792	+	0.513207i
$281$			26.2508i			1.56599i	0.622027	+	0.782996i	$0.286309\pi$
$281$			26.2508i			1.56599i	−0.622027	+	0.782996i	$0.713691\pi$
$282$		0			0
$283$	−18.6639			−1.10945			−0.554726	−	0.832033i	$-0.687177\pi$
$283$	−18.6639			−1.10945			−0.554726	+	0.832033i	$0.687177\pi$
$284$	−9.98161	−	11.8956i	−0.592300	−	0.705875i
$285$		0			0
$286$	−6.74376	−	18.5283i	−0.398767	−	1.09560i
$287$	−2.81449	+	21.2557i	−0.166134	+	1.25468i
$288$		0			0
$289$	−6.36009			−0.374123
$290$	15.2306	−	5.54347i	0.894369	−	0.325524i
$291$		0			0
$292$	5.93037	+	7.06753i	0.347048	+	0.413596i
$293$		−	17.8031i		−	1.04007i	−0.854146	−	0.520033i	$-0.825920\pi$
$293$		−	17.8031i		−	1.04007i	0.854146	−	0.520033i	$-0.174080\pi$
$294$		0			0
$295$	−10.8675			−0.632732
$296$	−2.60669	+	4.51492i	−0.151511	+	0.262425i
$297$		0			0
$298$	2.65776	+	7.30212i	0.153960	+	0.423001i
$299$			1.06637i			0.0616696i
$300$		0			0
$301$	−19.4179	−	2.57115i	−1.11923	−	0.148199i
$302$	−9.54304	−	26.2193i	−0.549140	−	1.50875i
$303$		0			0
$304$	−5.32664	+	30.2089i	−0.305504	+	1.73260i
$305$			16.1841i			0.926697i
$306$		0			0
$307$	26.4829			1.51146			0.755729	−	0.654884i	$-0.227283\pi$
$307$	26.4829			1.51146			0.755729	+	0.654884i	$0.227283\pi$
$308$	−9.70320	−	15.2561i	−0.552891	−	0.869295i
$309$		0			0
$310$	−7.32089	−	20.1140i	−0.415799	−	1.14240i
$311$	17.8897			1.01443			0.507215	−	0.861819i	$-0.330675\pi$
$311$	17.8897			1.01443			0.507215	+	0.861819i	$0.330675\pi$
$312$		0			0
$313$			20.9829i			1.18602i	0.805194	+	0.593011i	$0.202061\pi$
$313$			20.9829i			1.18602i	−0.805194	+	0.593011i	$0.797939\pi$
$314$	4.15668	+	11.4204i	0.234575	+	0.644489i
$315$		0			0
$316$	−17.1480	+	14.3888i	−0.964648	+	0.809436i
$317$	31.3335			1.75987			0.879933	−	0.475098i	$-0.157587\pi$
$317$	31.3335			1.75987			0.879933	+	0.475098i	$0.157587\pi$
$318$		0			0
$319$	−20.7939			−1.16423
$320$	−13.0476	+	7.53301i	−0.729380	+	0.421108i
$321$		0			0
$322$	0.210929	+	0.954809i	0.0117546	+	0.0532094i
$323$	−25.0145			−1.39184
$324$		0			0
$325$	−5.93037			−0.328958
$326$	−24.3567	+	8.86510i	−1.34899	+	0.490992i
$327$		0			0
$328$	−19.8507	−	11.4608i	−1.09607	−	0.632817i
$329$	0.894788	−	6.75764i	0.0493313	−	0.372561i
$330$		0			0
$331$			18.0180i			0.990356i	0.868791	+	0.495178i	$0.164897\pi$
$331$			18.0180i			0.990356i	−0.868791	+	0.495178i	$0.835103\pi$
$332$	9.10022	+	10.8452i	0.499439	+	0.595208i
$333$		0			0
$334$	−1.90928	−	5.24572i	−0.104471	−	0.287033i
$335$	8.20543			0.448310
$336$		0			0
$337$	−2.77837			−0.151348			−0.0756738	−	0.997133i	$-0.524111\pi$
$337$	−2.77837			−0.151348			−0.0756738	+	0.997133i	$0.524111\pi$
$338$	1.76547	+	4.85060i	0.0960291	+	0.263838i
$339$		0			0
$340$	−7.89723	−	9.41155i	−0.428287	−	0.510413i
$341$			27.4610i			1.48710i
$342$		0			0
$343$	7.12567	−	17.0946i	0.384750	−	0.923021i
$344$	10.4699	−	18.1344i	0.564499	−	0.977741i
$345$		0			0
$346$	33.9910	−	12.3717i	1.82737	−	0.665107i
$347$	−2.51157			−0.134828			−0.0674142	−	0.997725i	$-0.521475\pi$
$347$	−2.51157			−0.134828			−0.0674142	+	0.997725i	$0.521475\pi$
$348$		0			0
$349$	−5.75944			−0.308296			−0.154148	−	0.988048i	$-0.549263\pi$
$349$	−5.75944			−0.308296			−0.154148	+	0.988048i	$0.549263\pi$
$350$	−5.30996	+	1.17304i	−0.283829	+	0.0627014i
$351$		0			0
$352$	19.0351	−	3.35640i	1.01457	−	0.178897i
$353$	−28.0940			−1.49529			−0.747647	−	0.664097i	$-0.768816\pi$
$353$	−28.0940			−1.49529			−0.747647	+	0.664097i	$0.768816\pi$
$354$		0			0
$355$	−14.6222			−0.776064
$356$	−20.3107	+	17.0427i	−1.07647	+	0.903263i
$357$		0			0
$358$	9.41147	+	25.8578i	0.497412	+	1.36663i
$359$		−	15.9084i		−	0.839616i	−0.907613	−	0.419808i	$-0.862097\pi$
$359$		−	15.9084i		−	0.839616i	0.907613	−	0.419808i	$-0.137903\pi$
$360$		0			0
$361$	39.8093			2.09523
$362$	4.55011	+	12.5013i	0.239148	+	0.657055i
$363$		0			0
$364$	11.5876	+	18.2189i	0.607356	+	0.954929i
$365$	8.68745			0.454722
$366$		0			0
$367$		−	12.0935i		−	0.631276i	−0.948880	−	0.315638i	$-0.897781\pi$
$367$		−	12.0935i		−	0.631276i	0.948880	−	0.315638i	$-0.102219\pi$
$368$	−1.02946	−	0.181522i	−0.0536645	−	0.00946250i
$369$		0			0
$370$	1.67900	+	4.61301i	0.0872869	+	0.239819i
$371$	−4.04828	+	30.5735i	−0.210176	+	1.58730i
$372$		0			0
$373$			12.6907i			0.657102i	0.944486	+	0.328551i	$0.106560\pi$
$373$			12.6907i			0.657102i	−0.944486	+	0.328551i	$0.893440\pi$
$374$	5.39093	+	14.8115i	0.278759	+	0.765883i
$375$		0			0
$376$	6.31096	+	3.64364i	0.325463	+	0.187906i
$377$	24.8321			1.27892
$378$		0			0
$379$		−	21.3744i		−	1.09793i	−0.835846	−	0.548963i	$-0.815023\pi$
$379$		−	21.3744i		−	1.09793i	0.835846	−	0.548963i	$-0.184977\pi$
$380$	18.5665	+	22.1266i	0.952439	+	1.13507i
$381$		0			0
$382$	4.80066	−	1.74730i	0.245623	−	0.0893995i
$383$	19.0952			0.975720			0.487860	−	0.872922i	$-0.337778\pi$
$383$	19.0952			0.975720			0.487860	+	0.872922i	$0.337778\pi$
$384$		0			0
$385$	−16.8776	−	2.23479i	−0.860164	−	0.113895i
$386$	6.81966	+	18.7369i	0.347112	+	0.953682i
$387$		0			0
$388$	19.4179	+	23.1413i	0.985794	+	1.17482i
$389$	−13.9057			−0.705048			−0.352524	−	0.935803i	$-0.614677\pi$
$389$	−13.9057			−0.705048			−0.352524	+	0.935803i	$0.614677\pi$
$390$		0			0
$391$		−	0.852449i		−	0.0431102i
$392$	13.9791	+	14.0209i	0.706051	+	0.708161i
$393$		0			0
$394$	−8.29355	−	22.7863i	−0.417823	−	1.14796i
$395$			21.0784i			1.06057i
$396$		0			0
$397$	14.9046			0.748043			0.374021	−	0.927420i	$-0.377979\pi$
$397$	14.9046			0.748043			0.374021	+	0.927420i	$0.377979\pi$
$398$	14.3897	−	5.23743i	0.721292	−	0.262529i
$399$		0			0
$400$	1.00950	−	5.72513i	0.0504748	−	0.286257i
$401$		−	22.3989i		−	1.11855i	−0.828983	−	0.559274i	$-0.811080\pi$
$401$		−	22.3989i		−	1.11855i	0.828983	−	0.559274i	$-0.188920\pi$
$402$		0			0
$403$		−	32.7941i		−	1.63359i
$404$	−2.42106	−	2.88531i	−0.120452	−	0.143549i
$405$		0			0
$406$	22.2343	−	4.91183i	1.10347	−	0.243770i
$407$		−	6.29801i		−	0.312181i
$408$		0			0
$409$			38.4655i			1.90200i	0.309195	+	0.950999i	$0.399941\pi$
$409$			38.4655i			1.90200i	−0.309195	+	0.950999i	$0.600059\pi$
$410$	−20.2819	+	7.38202i	−1.00165	+	0.364572i
$411$		0			0
$412$	−10.3320	−	12.3133i	−0.509023	−	0.606630i
$413$	−15.1355	−	2.00411i	−0.744770	−	0.0986160i
$414$		0			0
$415$	13.3310			0.654393
$416$	−22.7318	+	4.00823i	−1.11452	+	0.196520i
$417$		0			0
$418$	−12.6741	−	34.8219i	−0.619912	−	1.70319i
$419$			35.6061i			1.73947i	0.493516	+	0.869736i	$0.335711\pi$
$419$			35.6061i			1.73947i	−0.493516	+	0.869736i	$0.664289\pi$
$420$		0			0
$421$			16.2520i			0.792072i	0.918235	+	0.396036i	$0.129614\pi$
$421$			16.2520i			0.792072i	−0.918235	+	0.396036i	$0.870386\pi$
$422$	8.72797	−	3.17672i	0.424871	−	0.154640i
$423$		0			0
$424$	−28.5526	−	16.4849i	−1.38664	−	0.800576i
$425$	4.74071			0.229958
$426$		0			0
$427$	−2.98456	+	22.5400i	−0.144433	+	1.09079i
$428$	−1.91320	+	1.60536i	−0.0924778	+	0.0775981i
$429$		0			0
$430$	−6.74376	−	18.5283i	−0.325213	−	0.893516i
$431$		−	31.3959i		−	1.51229i	−0.654405	−	0.756144i	$-0.727081\pi$
$431$		−	31.3959i		−	1.51229i	0.654405	−	0.756144i	$-0.272919\pi$
$432$		0			0
$433$			9.22601i			0.443374i	0.975118	+	0.221687i	$0.0711563\pi$
$433$			9.22601i			0.443374i	−0.975118	+	0.221687i	$0.928844\pi$
$434$	−6.48673	−	29.3634i	−0.311373	−	1.40949i
$435$		0			0
$436$	−9.19253	−	10.9552i	−0.440243	−	0.524661i
$437$			2.00411i			0.0958698i
$438$		0			0
$439$		−	21.3195i		−	1.01753i	−0.860907	−	0.508763i	$-0.830103\pi$
$439$		−	21.3195i		−	1.01753i	0.860907	−	0.508763i	$-0.169897\pi$
$440$	9.10022	−	15.7620i	0.433836	−	0.751426i
$441$		0			0
$442$	−6.43788	−	17.6879i	−0.306219	−	0.841329i
$443$	32.7395			1.55550			0.777750	−	0.628574i	$-0.216361\pi$
$443$	32.7395			1.55550			0.777750	+	0.628574i	$0.216361\pi$
$444$		0			0
$445$			24.9661i			1.18350i
$446$	5.28952	−	1.92523i	0.250466	−	0.0911621i
$447$		0			0
$448$	−19.5609	+	8.08529i	−0.924165	+	0.381994i
$449$			10.1995i			0.481344i	0.970607	+	0.240672i	$0.0773678\pi$
$449$			10.1995i			0.481344i	−0.970607	+	0.240672i	$0.922632\pi$
$450$		0			0
$451$	27.6903			1.30389
$452$	−14.2227	−	16.9500i	−0.668981	−	0.797260i
$453$		0			0
$454$	28.0116	−	10.1954i	1.31465	−	0.478493i
$455$	20.1554	+	2.66880i	0.944898	+	0.125115i
$456$		0			0
$457$	−4.00000			−0.187112			−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000			−0.187112			−0.0935561	+	0.995614i	$0.529823\pi$
$458$	−5.44490	−	14.9597i	−0.254423	−	0.699022i
$459$		0			0
$460$	−0.754035	+	0.632711i	−0.0351571	+	0.0295003i
$461$			10.8083i			0.503393i	0.967806	+	0.251696i	$0.0809884\pi$
$461$			10.8083i			0.503393i	−0.967806	+	0.251696i	$0.919012\pi$
$462$		0			0
$463$	−23.3601			−1.08564			−0.542818	−	0.839851i	$-0.682643\pi$
$463$	−23.3601			−1.08564			−0.542818	+	0.839851i	$0.682643\pi$
$464$	−4.22705	+	23.9728i	−0.196236	+	1.11291i
$465$		0			0
$466$	37.2003	−	13.5398i	1.72327	−	0.627219i
$467$		−	18.9903i		−	0.878766i	−0.898300	−	0.439383i	$-0.855197\pi$
$467$		−	18.9903i		−	0.878766i	0.898300	−	0.439383i	$-0.144803\pi$
$468$		0			0
$469$	11.4279	+	1.51319i	0.527693	+	0.0698726i
$470$	6.44806	−	2.34690i	0.297427	−	0.108255i
$471$		0			0
$472$	8.16089	−	14.1351i	0.375635	−	0.650619i
$473$			25.2962i			1.16312i
$474$		0			0
$475$	−11.1454			−0.511388
$476$	−9.26308	−	14.5641i	−0.424573	−	0.667544i
$477$		0			0
$478$	−14.0223	+	5.10370i	−0.641365	+	0.233438i
$479$	36.1980			1.65393			0.826965	−	0.562253i	$-0.190065\pi$
$479$	36.1980			1.65393			0.826965	+	0.562253i	$0.190065\pi$
$480$		0			0
$481$			7.52111i			0.342933i
$482$	7.81200	−	2.84333i	0.355827	−	0.129510i
$483$		0			0
$484$	−1.03415	+	0.867753i	−0.0470067	+	0.0394433i
$485$	28.4455			1.29164
$486$		0			0
$487$	−25.1189			−1.13824			−0.569122	−	0.822253i	$-0.692717\pi$
$487$	−25.1189			−1.13824			−0.569122	+	0.822253i	$0.692717\pi$
$488$	−21.0501	−	12.1533i	−0.952895	−	0.550154i
$489$		0			0
$490$	18.5747	−	1.59716i	0.839119	−	0.0721522i
$491$	14.4777			0.653367			0.326684	−	0.945134i	$-0.394069\pi$
$491$	14.4777			0.653367			0.326684	+	0.945134i	$0.394069\pi$
$492$		0			0
$493$	−19.8507			−0.894030
$494$	15.1355	+	41.5845i	0.680979	+	1.87097i
$495$		0			0
$496$	31.6592	+	5.58237i	1.42154	+	0.250656i
$497$	−20.3647	−	2.69652i	−0.913482	−	0.120955i
$498$		0			0
$499$			4.04693i			0.181166i	0.995889	+	0.0905828i	$0.0288730\pi$
$499$			4.04693i			0.181166i	−0.995889	+	0.0905828i	$0.971127\pi$
$500$	−15.6240	−	18.6199i	−0.698726	−	0.832709i
$501$		0			0
$502$	11.7492	−	4.27635i	0.524391	−	0.190863i
$503$	−7.72932			−0.344633			−0.172317	−	0.985042i	$-0.555125\pi$
$503$	−7.72932			−0.344633			−0.172317	+	0.985042i	$0.555125\pi$
$504$		0			0
$505$	−3.54664			−0.157823
$506$	1.18667	−	0.431911i	0.0527537	−	0.0192008i
$507$		0			0
$508$	0.891245	−	0.747843i	0.0395426	−	0.0331802i
$509$			17.4327i			0.772692i	0.922354	+	0.386346i	$0.126263\pi$
$509$			17.4327i			0.772692i	−0.922354	+	0.386346i	$0.873737\pi$
$510$		0			0
$511$	12.0993	+	1.60208i	0.535240	+	0.0708718i
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$	−11.0964	−	30.4871i	−0.489441	−	1.34473i
$515$	−15.1355			−0.666950
$516$		0			0
$517$	−8.80336			−0.387171
$518$	1.48769	+	6.73429i	0.0653652	+	0.295888i
$519$		0			0
$520$	−10.8675	+	18.8231i	−0.476573	+	0.825448i
$521$	40.8308			1.78883			0.894415	−	0.447238i	$-0.147592\pi$
$521$	40.8308			1.78883			0.894415	+	0.447238i	$0.147592\pi$
$522$		0			0
$523$	31.3174			1.36941			0.684706	−	0.728819i	$-0.259930\pi$
$523$	31.3174			1.36941			0.684706	+	0.728819i	$0.259930\pi$
$524$	−11.6767	−	13.9157i	−0.510097	−	0.607910i
$525$		0			0
$526$	13.1702	−	4.79358i	0.574250	−	0.209010i
$527$			26.2155i			1.14196i
$528$		0			0
$529$	22.9317			0.997031
$530$	−29.1729	+	10.6181i	−1.26719	+	0.461219i
$531$		0			0
$532$	21.7776	+	34.2403i	0.944178	+	1.48451i
$533$	−33.0680			−1.43233
$534$		0			0
$535$			2.35171i			0.101673i
$536$	−6.16180	+	10.6726i	−0.266149	+	0.460984i
$537$		0			0
$538$	10.1714	−	3.70210i	0.438521	−	0.159609i
$539$	−23.0938	−	6.22491i	−0.994722	−	0.268126i
$540$		0			0
$541$		−	42.7991i		−	1.84008i	−0.391828	−	0.920039i	$-0.628157\pi$
$541$		−	42.7991i		−	1.84008i	0.391828	−	0.920039i	$-0.371843\pi$
$542$	15.5226	−	5.64975i	0.666752	−	0.242678i
$543$		0			0
$544$	18.1717	−	3.20416i	0.779105	−	0.137377i
$545$	−13.4662			−0.576830
$546$		0			0
$547$			9.61397i			0.411064i	0.978650	+	0.205532i	$0.0658924\pi$
$547$			9.61397i			0.411064i	−0.978650	+	0.205532i	$0.934108\pi$
$548$	−0.116680	−	0.139054i	−0.00498433	−	0.00594009i
$549$		0			0
$550$	2.40198	+	6.59938i	0.102421	+	0.281399i
$551$	46.6691			1.98817
$552$		0			0
$553$	−3.88713	+	29.3564i	−0.165297	+	1.24836i
$554$	25.0286	−	9.10966i	1.06336	−	0.387032i
$555$		0			0
$556$	8.16089	−	6.84780i	0.346099	−	0.290411i
$557$	−7.14326			−0.302669			−0.151335	−	0.988483i	$-0.548357\pi$
$557$	−7.14326			−0.302669			−0.151335	+	0.988483i	$0.548357\pi$
$558$		0			0
$559$		−	30.2089i		−	1.27770i
$560$	−6.00738	+	19.0035i	−0.253858	+	0.803046i
$561$		0			0
$562$	−34.8854	+	12.6972i	−1.47155	+	0.535601i
$563$			3.07048i			0.129405i	0.997905	+	0.0647027i	$0.0206099\pi$
$563$			3.07048i			0.129405i	−0.997905	+	0.0647027i	$0.979390\pi$
$564$		0			0
$565$	−20.8350			−0.876536
$566$	−9.02751	−	24.8029i	−0.379455	−	1.04254i
$567$		0			0
$568$	10.9804	−	19.0186i	0.460727	−	0.798003i
$569$		−	22.1544i		−	0.928759i	−0.885636	−	0.464380i	$-0.846277\pi$
$569$		−	22.1544i		−	0.928759i	0.885636	−	0.464380i	$-0.153723\pi$
$570$		0			0
$571$			6.64858i			0.278234i	0.990276	+	0.139117i	$0.0444265\pi$
$571$			6.64858i			0.278234i	−0.990276	+	0.139117i	$0.955574\pi$
$572$	21.3609	−	17.9239i	0.893144	−	0.749437i
$573$		0			0
$574$	−29.6086	+	6.54089i	−1.23584	+	0.273012i
$575$		−	0.379816i		−	0.0158394i
$576$		0			0
$577$		−	23.3611i		−	0.972535i	−0.873810	−	0.486267i	$-0.838358\pi$
$577$		−	23.3611i		−	0.972535i	0.873810	−	0.486267i	$-0.161642\pi$
$578$	−3.07631	−	8.45209i	−0.127958	−	0.351561i
$579$		0			0
$580$	14.7337	+	17.5590i	0.611785	+	0.729096i
$581$	18.5665	+	2.45841i	0.770266	+	0.101992i
$582$		0			0
$583$	39.8289			1.64955
$584$	−6.52378	+	11.2995i	−0.269956	+	0.467577i
$585$		0			0
$586$	23.6590	−	8.61115i	0.977342	−	0.355724i
$587$			17.4696i			0.721049i	0.932750	+	0.360524i	$0.117402\pi$
$587$			17.4696i			0.721049i	−0.932750	+	0.360524i	$0.882598\pi$
$588$		0			0
$589$		−	61.6328i		−	2.53954i
$590$	−5.25651	−	14.4421i	−0.216407	−	0.594573i
$591$		0			0
$592$	−7.26083	−	1.28028i	−0.298418	−	0.0526192i
$593$	−10.2043			−0.419042			−0.209521	−	0.977804i	$-0.567190\pi$
$593$	−10.2043			−0.419042			−0.209521	+	0.977804i	$0.567190\pi$
$594$		0			0
$595$	−16.1121	−	2.13343i	−0.660532	−	0.0874619i
$596$	−8.41846	+	7.06392i	−0.344833	+	0.289350i
$597$		0			0
$598$	−1.41712	+	0.515791i	−0.0579505	+	0.0210922i
$599$		−	11.3743i		−	0.464740i	−0.972627	−	0.232370i	$-0.925352\pi$
$599$		−	11.3743i		−	0.464740i	0.972627	−	0.232370i	$-0.0746480\pi$
$600$		0			0
$601$			17.7787i			0.725209i	0.931943	+	0.362604i	$0.118112\pi$
$601$			17.7787i			0.725209i	−0.931943	+	0.362604i	$0.881888\pi$
$602$	−5.97536	−	27.0486i	−0.243538	−	1.10242i
$603$		0			0
$604$	30.2276	−	25.3640i	1.22994	−	1.03205i
$605$			1.27118i			0.0516808i
$606$		0			0
$607$			23.0244i			0.934532i	0.884117	+	0.467266i	$0.154761\pi$
$607$			23.0244i			0.934532i	−0.884117	+	0.467266i	$0.845239\pi$
$608$	−42.7218	+	7.53301i	−1.73260	+	0.305504i
$609$		0			0
$610$	−21.5074	+	7.82807i	−0.870811	+	0.316949i
$611$	10.5130			0.425311
$612$		0			0
$613$			36.6561i			1.48053i	0.672316	+	0.740264i	$0.265299\pi$
$613$			36.6561i			1.48053i	−0.672316	+	0.740264i	$0.734701\pi$
$614$	12.8095	+	35.1938i	0.516949	+	1.42031i
$615$		0			0
$616$	15.5809	−	20.2740i	0.627771	−	0.816864i
$617$		−	29.4758i		−	1.18665i	−0.804962	−	0.593326i	$-0.797815\pi$
$617$		−	29.4758i		−	1.18665i	0.804962	−	0.593326i	$-0.202185\pi$
$618$		0			0
$619$	22.5140			0.904915			0.452457	−	0.891786i	$-0.350548\pi$
$619$	22.5140			0.904915			0.452457	+	0.891786i	$0.350548\pi$
$620$	23.1890	−	19.4578i	0.931291	−	0.781446i
$621$		0			0
$622$	8.65305	+	23.7741i	0.346956	+	0.953253i
$623$	−4.60407	+	34.7709i	−0.184458	+	1.39307i
$624$		0			0
$625$	−15.6209			−0.624837
$626$	−27.8847	+	10.1492i	−1.11450	+	0.405643i
$627$		0			0
$628$	−13.1663	+	11.0478i	−0.525392	+	0.440856i
$629$		−	6.01234i		−	0.239728i
$630$		0			0
$631$	−19.8425			−0.789919			−0.394960	−	0.918698i	$-0.629241\pi$
$631$	−19.8425			−0.789919			−0.394960	+	0.918698i	$0.629241\pi$
$632$	−27.4160	−	15.8286i	−1.09055	−	0.629629i
$633$		0			0
$634$	15.1557	+	41.6399i	0.601910	+	1.65373i
$635$		−	1.09552i		−	0.0434745i
$636$		0			0
$637$	27.5788	+	7.43383i	1.09271	+	0.294539i
$638$	−10.0578	−	27.6335i	−0.398191	−	1.09402i
$639$		0			0
$640$	−16.3218	−	13.6956i	−0.645175	−	0.541366i
$641$			18.3848i			0.726155i	0.931759	+	0.363078i	$0.118274\pi$
$641$			18.3848i			0.726155i	−0.931759	+	0.363078i	$0.881726\pi$
$642$		0			0
$643$	−23.3480			−0.920756			−0.460378	−	0.887723i	$-0.652286\pi$
$643$	−23.3480			−0.920756			−0.460378	+	0.887723i	$0.652286\pi$
$644$	−1.16685	+	0.742140i	−0.0459802	+	0.0292444i
$645$		0			0
$646$	−12.0993	−	33.2424i	−0.476039	−	1.30791i
$647$	−34.0977			−1.34052			−0.670259	−	0.742127i	$-0.733817\pi$
$647$	−34.0977			−1.34052			−0.670259	+	0.742127i	$0.733817\pi$
$648$		0			0
$649$			19.7174i			0.773977i
$650$	−2.86846	−	7.88102i	−0.112510	−	0.309119i
$651$		0			0
$652$	−23.5621	−	28.0802i	−0.922764	−	1.09971i
$653$	−13.7155			−0.536728			−0.268364	−	0.963318i	$-0.586483\pi$
$653$	−13.7155			−0.536728			−0.268364	+	0.963318i	$0.586483\pi$
$654$		0			0
$655$	−17.1052			−0.668357
$656$	5.62899	−	31.9236i	0.219775	−	1.24641i
$657$		0			0
$658$	9.41320	−	2.07949i	0.366965	−	0.0810670i
$659$	35.1410			1.36890			0.684449	−	0.729061i	$-0.260043\pi$
$659$	35.1410			1.36890			0.684449	+	0.729061i	$0.260043\pi$
$660$		0			0
$661$	−7.38623			−0.287291			−0.143646	−	0.989629i	$-0.545883\pi$
$661$	−7.38623			−0.287291			−0.143646	+	0.989629i	$0.545883\pi$
$662$	−23.9445	+	8.71510i	−0.930631	+	0.338722i
$663$		0			0
$664$	−10.0108	+	17.3392i	−0.388495	+	0.672893i
$665$	37.8797	+	5.01570i	1.46891	+	0.194501i
$666$		0			0
$667$			1.59040i			0.0615805i
$668$	6.04767	−	5.07460i	0.233991	−	0.196342i
$669$		0			0
$670$	3.96888	+	10.9044i	0.153331	+	0.421274i
$671$	29.3635			1.13357
$672$		0			0
$673$	0.453363			0.0174759			0.00873793	−	0.999962i	$-0.497219\pi$
$673$	0.453363			0.0174759			0.00873793	+	0.999962i	$0.497219\pi$
$674$	−1.34387	−	3.69225i	−0.0517639	−	0.142220i
$675$		0			0
$676$	−5.59215	+	4.69237i	−0.215083	+	0.180476i
$677$		−	8.80419i		−	0.338372i	−0.985584	−	0.169186i	$-0.945886\pi$
$677$		−	8.80419i		−	0.338372i	0.985584	−	0.169186i	$-0.0541139\pi$
$678$		0			0
$679$	39.6168	+	5.24572i	1.52035	+	0.201312i
$680$	8.68745	−	15.0471i	0.333149	−	0.577030i
$681$		0			0
$682$	−36.4937	+	13.2826i	−1.39742	+	0.508618i
$683$	14.3535			0.549221			0.274610	−	0.961556i	$-0.411451\pi$
$683$	14.3535			0.549221			0.274610	+	0.961556i	$0.411451\pi$
$684$		0			0
$685$	−0.170926			−0.00653074
$686$	26.1641	+	1.20101i	0.998948	+	0.0458549i
$687$		0			0
$688$	29.1634	+	5.14230i	1.11185	+	0.196048i
$689$	−47.5639			−1.81204
$690$		0			0
$691$	−21.3066			−0.810540			−0.405270	−	0.914197i	$-0.632822\pi$
$691$	−21.3066			−0.810540			−0.405270	+	0.914197i	$0.632822\pi$
$692$	32.8822	+	39.1875i	1.24999	+	1.48968i
$693$		0			0
$694$	−1.21482	−	3.33770i	−0.0461140	−	0.126697i
$695$		−	10.0314i		−	0.380513i
$696$		0			0
$697$	26.4344			1.00127
$698$	−2.78578	−	7.65387i	−0.105443	−	0.289703i
$699$		0			0
$700$	−4.12725	−	6.48916i	−0.155995	−	0.245267i
$701$	15.7594			0.595226			0.297613	−	0.954687i	$-0.403810\pi$
$701$	15.7594			0.595226			0.297613	+	0.954687i	$0.403810\pi$
$702$		0			0
$703$			14.1351i			0.533114i
$704$	13.6675	+	23.6728i	0.515112	+	0.892201i
$705$		0			0
$706$	−13.5888	−	37.3349i	−0.511421	−	1.40512i
$707$	−4.93950	−	0.654046i	−0.185769	−	0.0245979i
$708$		0			0
$709$			17.1051i			0.642396i	0.947012	+	0.321198i	$0.104085\pi$
$709$			17.1051i			0.642396i	−0.947012	+	0.321198i	$0.895915\pi$
$710$	−7.07259	−	19.4318i	−0.265429	−	0.729261i
$711$		0			0
$712$	−32.4726	−	18.7481i	−1.21696	−	0.702614i
$713$	2.10033			0.0786581
$714$		0			0
$715$		−	26.2569i		−	0.981954i
$716$	−29.8109	+	25.0143i	−1.11409	+	0.934829i
$717$		0			0
$718$	21.1411	−	7.69475i	0.788981	−	0.287165i
$719$	−31.0451			−1.15779			−0.578894	−	0.815403i	$-0.696516\pi$
$719$	−31.0451			−1.15779			−0.578894	+	0.815403i	$0.696516\pi$
$720$		0			0
$721$	−21.0797	−	2.79119i	−0.785048	−	0.103949i
$722$	19.2554	+	52.9037i	0.716610	+	1.96887i
$723$		0			0
$724$	−14.4125	+	12.0935i	−0.535636	+	0.449452i
$725$	−8.84465			−0.328482
$726$		0			0
$727$			1.18911i			0.0441016i	0.999757	+	0.0220508i	$0.00701955\pi$
$727$			1.18911i			0.0441016i	−0.999757	+	0.0220508i	$0.992980\pi$
$728$	−18.6067	+	24.2114i	−0.689612	+	0.897333i
$729$		0			0
$730$	4.20203	+	11.5450i	0.155524	+	0.427299i
$731$			24.1488i			0.893177i
$732$		0			0
$733$	−47.6004			−1.75816			−0.879080	−	0.476674i	$-0.841842\pi$
$733$	−47.6004			−1.75816			−0.879080	+	0.476674i	$0.841842\pi$
$734$	16.0714	−	5.84951i	0.593206	−	0.215909i
$735$		0			0
$736$	−0.256711	−	1.45588i	−0.00946250	−	0.0536645i
$737$		−	14.8875i		−	0.548387i
$738$		0			0
$739$			52.4237i			1.92844i	0.265111	+	0.964218i	$0.414591\pi$
$739$			52.4237i			1.92844i	−0.265111	+	0.964218i	$0.585409\pi$
$740$	−5.31823	+	4.46252i	−0.195502	+	0.164046i
$741$		0			0
$742$	−42.5880	+	9.40822i	−1.56346	+	0.345387i
$743$		−	3.77206i		−	0.138384i	−0.997603	−	0.0691918i	$-0.977958\pi$
$743$		−	3.77206i		−	0.138384i	0.997603	−	0.0691918i	$-0.0220420\pi$
$744$		0			0
$745$			10.3480i			0.379122i
$746$	−16.8651	+	6.13838i	−0.617474	+	0.224742i
$747$		0			0
$748$	−17.0758	+	14.3283i	−0.624353	+	0.523895i
$749$	−0.433686	+	3.27530i	−0.0158466	+	0.119677i
$750$		0			0
$751$	0.301289			0.0109942			0.00549709	−	0.999985i	$-0.498250\pi$
$751$	0.301289			0.0109942			0.00549709	+	0.999985i	$0.498250\pi$
$752$	−1.78958	+	10.1492i	−0.0652591	+	0.370103i
$753$		0			0
$754$	12.0110	+	33.0001i	0.437416	+	1.20179i
$755$		−	37.1559i		−	1.35224i
$756$		0			0
$757$			2.62846i			0.0955329i	0.998859	+	0.0477665i	$0.0152103\pi$
$757$			2.62846i			0.0955329i	−0.998859	+	0.0477665i	$0.984790\pi$
$758$	28.4049	−	10.3386i	1.03171	−	0.375513i
$759$		0			0
$760$	−20.4243	+	35.3759i	−0.740866	+	1.28322i
$761$	18.0990			0.656089			0.328044	−	0.944662i	$-0.393610\pi$
$761$	18.0990			0.656089			0.328044	+	0.944662i	$0.393610\pi$
$762$		0			0
$763$	−18.7548	−	2.48335i	−0.678970	−	0.0899033i
$764$	4.64406	+	5.53457i	0.168016	+	0.200234i
$765$		0			0
$766$	9.23616	+	25.3761i	0.333716	+	0.916877i
$767$		−	23.5467i		−	0.850221i
$768$		0			0
$769$		−	24.1870i		−	0.872206i	−0.899897	−	0.436103i	$-0.856358\pi$
$769$		−	24.1870i		−	0.872206i	0.899897	−	0.436103i	$-0.143642\pi$
$770$	−5.19366	−	23.5101i	−0.187167	−	0.847244i
$771$		0			0
$772$	−21.6013	+	18.1257i	−0.777448	+	0.652357i
$773$			12.0324i			0.432777i	0.976307	+	0.216388i	$0.0694278\pi$
$773$			12.0324i			0.432777i	−0.976307	+	0.216388i	$0.930572\pi$
$774$		0			0
$775$			11.6805i			0.419577i
$776$	−21.3609	+	36.9982i	−0.766812	+	1.32816i
$777$		0			0
$778$	−6.72605	−	18.4797i	−0.241141	−	0.662529i
$779$	−62.1474			−2.22666
$780$		0			0
$781$			26.5296i			0.949305i
$782$	1.13284	−	0.412321i	0.0405103	−	0.0147446i
$783$		0			0
$784$	−11.8712	+	25.3589i	−0.423970	+	0.905676i
$785$			16.1841i			0.577634i
$786$		0			0
$787$	−31.5405			−1.12430			−0.562149	−	0.827036i	$-0.690025\pi$
$787$	−31.5405			−1.12430			−0.562149	+	0.827036i	$0.690025\pi$
$788$	26.2699	−	22.0430i	0.935825	−	0.785250i
$789$		0			0
$790$	−28.0116	+	10.1954i	−0.996607	+	0.362735i
$791$	−29.0175	−	3.84225i	−1.03174	−	0.136615i
$792$		0			0
$793$	−35.0660			−1.24523
$794$	7.20922	+	19.8072i	0.255846	+	0.702930i
$795$		0			0
$796$	13.9203	+	16.5896i	0.493393	+	0.588003i
$797$		−	52.4268i		−	1.85705i	−0.371268	−	0.928526i	$-0.621077\pi$
$797$		−	52.4268i		−	1.85705i	0.371268	−	0.928526i	$-0.378923\pi$
$798$		0			0
$799$	−8.40406			−0.297314
$800$	8.09656	−	1.42764i	0.286257	−	0.0504748i
$801$		0			0
$802$	29.7665	−	10.8341i	1.05109	−	0.382566i
$803$		−	15.7620i		−	0.556230i
$804$		0			0
$805$	−0.170926	+	1.29087i	−0.00602435	+	0.0454972i
$806$	43.5810	−	15.8622i	1.53507	−	0.558721i
$807$		0			0
$808$	2.66332	−	4.61301i	0.0936953	−	0.162285i
$809$			15.5782i			0.547702i	0.961772	+	0.273851i	$0.0882975\pi$
$809$			15.5782i			0.547702i	−0.961772	+	0.273851i	$0.911703\pi$
$810$		0			0
$811$	−39.4783			−1.38627			−0.693135	−	0.720808i	$-0.743771\pi$
$811$	−39.4783			−1.38627			−0.693135	+	0.720808i	$0.743771\pi$
$812$	17.2820	+	27.1720i	0.606478	+	0.953549i
$813$		0			0
$814$	8.36959	−	3.04628i	0.293354	−	0.106772i
$815$	−34.5164			−1.20906
$816$		0			0
$817$		−	56.7741i		−	1.98627i
$818$	−51.1178	+	18.6054i	−1.78729	+	0.650521i
$819$		0			0
$820$	−19.6203	−	23.3826i	−0.685171	−	0.816555i
$821$	−21.6166			−0.754425			−0.377212	−	0.926127i	$-0.623117\pi$
$821$	−21.6166			−0.754425			−0.377212	+	0.926127i	$0.623117\pi$
$822$		0			0
$823$	−27.4492			−0.956821			−0.478410	−	0.878136i	$-0.658787\pi$
$823$	−27.4492			−0.956821			−0.478410	+	0.878136i	$0.658787\pi$
$824$	11.3659	−	19.6863i	0.395950	−	0.685805i
$825$		0			0
$826$	−4.65757	−	21.0833i	−0.162058	−	0.733583i
$827$	21.9552			0.763456			0.381728	−	0.924275i	$-0.375329\pi$
$827$	21.9552			0.763456			0.381728	+	0.924275i	$0.375329\pi$
$828$		0			0
$829$	4.72291			0.164034			0.0820168	−	0.996631i	$-0.473864\pi$
$829$	4.72291			0.164034			0.0820168	+	0.996631i	$0.473864\pi$
$830$	6.44806	+	17.7159i	0.223816	+	0.614928i
$831$		0			0
$832$	−16.3218	−	28.2701i	−0.565856	−	0.980091i
$833$	−22.0463	−	5.94257i	−0.763861	−	0.205898i
$834$		0			0
$835$		−	7.43383i		−	0.257258i
$836$	40.1454	−	33.6860i	1.38846	−	1.16505i
$837$		0			0
$838$	−47.3179	+	17.2223i	−1.63457	+	0.594935i
$839$	7.41856			0.256117			0.128059	−	0.991767i	$-0.459125\pi$
$839$	7.41856			0.256117			0.128059	+	0.991767i	$0.459125\pi$
$840$		0			0
$841$	8.03508			0.277072
$842$	−21.5976	+	7.86090i	−0.744304	+	0.270905i
$843$		0			0
$844$	8.44326	+	10.0623i	0.290629	+	0.346358i
$845$			6.87390i			0.236469i
$846$		0			0
$847$	−0.234422	+	1.77041i	−0.00805485	+	0.0608320i
$848$	8.09656	−	45.9179i	0.278037	−	1.57683i
$849$		0			0
$850$	2.29303	+	6.30005i	0.0786503	+	0.216090i
$851$	−0.481697			−0.0165124
$852$		0			0
$853$	24.5736			0.841384			0.420692	−	0.907203i	$-0.361787\pi$
$853$	24.5736			0.841384			0.420692	+	0.907203i	$0.361787\pi$
$854$	−31.3976	+	6.93612i	−1.07440	+	0.237349i
$855$		0			0
$856$	−3.05880	−	1.76600i	−0.104548	−	0.0603606i
$857$	19.8886			0.679381			0.339691	−	0.940537i	$-0.389678\pi$
$857$	19.8886			0.679381			0.339691	+	0.940537i	$0.389678\pi$
$858$		0			0
$859$	47.1470			1.60863			0.804317	−	0.594200i	$-0.202531\pi$
$859$	47.1470			1.60863			0.804317	+	0.594200i	$0.202531\pi$
$860$	21.3609	−	17.9239i	0.728401	−	0.611201i
$861$		0			0
$862$	41.7229	−	15.1859i	1.42109	−	0.517233i
$863$			35.9520i			1.22382i	0.790927	+	0.611910i	$0.209599\pi$
$863$			35.9520i			1.22382i	−0.790927	+	0.611910i	$0.790401\pi$
$864$		0			0
$865$	48.1694			1.63781
$866$	−12.2607	+	4.46252i	−0.416635	+	0.151643i
$867$		0			0
$868$	35.8842	−	22.8231i	1.21799	−	0.774668i
$869$	38.2434			1.29732
$870$		0			0
$871$			17.7787i			0.602408i
$872$	10.1124	−	17.5151i	0.342448	−	0.593137i
$873$		0			0
$874$	−2.66332	+	0.969369i	−0.0900881	+	0.0327894i
$875$	−31.8764	−	4.22080i	−1.07762	−	0.142689i
$876$		0			0
$877$		−	10.1090i		−	0.341357i	−0.985327	−	0.170678i	$-0.945404\pi$
$877$		−	10.1090i		−	0.341357i	0.985327	−	0.170678i	$-0.0545959\pi$
$878$	28.3321	−	10.3120i	0.956161	−	0.348014i
$879$		0			0
$880$	25.3483	+	4.46958i	0.854490	+	0.150670i
$881$	16.3094			0.549479			0.274739	−	0.961519i	$-0.411408\pi$
$881$	16.3094			0.549479			0.274739	+	0.961519i	$0.411408\pi$
$882$		0			0
$883$		−	33.6603i		−	1.13276i	−0.824145	−	0.566379i	$-0.808344\pi$
$883$		−	33.6603i		−	1.13276i	0.824145	−	0.566379i	$-0.191656\pi$
$884$	20.3920	−	17.1109i	0.685858	−	0.575503i
$885$		0			0
$886$	15.8357	+	43.5083i	0.532012	+	1.46169i
$887$	−41.5163			−1.39398			−0.696990	−	0.717081i	$-0.745478\pi$
$887$	−41.5163			−1.39398			−0.696990	+	0.717081i	$0.745478\pi$
$888$		0			0
$889$	0.202029	−	1.52577i	0.00677583	−	0.0511725i
$890$	−33.1780	+	12.0758i	−1.11213	+	0.404782i
$891$		0			0
$892$	5.11697	+	6.09817i	0.171329	+	0.204182i
$893$	19.7580			0.661177
$894$		0			0
$895$			36.6437i			1.22486i
$896$	−20.2061	−	22.0842i	−0.675040	−	0.737781i
$897$		0			0
$898$	−13.5544	+	4.93339i	−0.452315	+	0.164629i
$899$		−	48.9097i		−	1.63123i
$900$		0			0
$901$	38.0224			1.26671
$902$	13.3935	+	36.7984i	0.445956	+	1.22525i
$903$		0			0
$904$	15.6459	−	27.0995i	0.520375	−	0.901316i
$905$			17.7159i			0.588897i
$906$		0			0
$907$		−	50.8731i		−	1.68921i	−0.535388	−	0.844606i	$-0.679835\pi$
$907$		−	50.8731i		−	1.68921i	0.535388	−	0.844606i	$-0.320165\pi$
$908$	27.0978	+	32.2939i	0.899273	+	1.07171i
$909$		0			0
$910$	6.20230	+	28.0758i	0.205604	+	0.930705i
$911$		−	46.9388i		−	1.55515i	−0.628788	−	0.777577i	$-0.716449\pi$
$911$		−	46.9388i		−	1.55515i	0.628788	−	0.777577i	$-0.283551\pi$
$912$		0			0
$913$		−	24.1870i		−	0.800474i
$914$	−1.93476	−	5.31570i	−0.0639961	−	0.175828i
$915$		0			0
$916$	17.2467	−	14.4717i	0.569848	−	0.478159i
$917$	−23.8230	−	3.15443i	−0.786704	−	0.104169i
$918$		0			0
$919$	−19.5039			−0.643375			−0.321688	−	0.946846i	$-0.604250\pi$
$919$	−19.5039			−0.643375			−0.321688	+	0.946846i	$0.604250\pi$
$920$	−1.20554	−	0.696022i	−0.0397456	−	0.0229472i
$921$		0			0
$922$	−14.3634	+	5.22786i	−0.473034	+	0.172170i
$923$		−	31.6818i		−	1.04282i
$924$		0			0
$925$		−	2.67885i		−	0.0880802i
$926$	−11.2990	−	31.0438i	−0.371309	−	1.02016i
$927$		0			0
$928$	−33.9026	+	5.97794i	−1.11291	+	0.196236i
$929$	−34.6178			−1.13577			−0.567886	−	0.823107i	$-0.692239\pi$
$929$	−34.6178			−1.13577			−0.567886	+	0.823107i	$0.692239\pi$
$930$		0			0
$931$	51.8311	+	13.9710i	1.69870	+	0.457882i
$932$	35.9868	+	42.8874i	1.17879	+	1.40482i
$933$		0			0
$934$	25.2367	−	9.18541i	0.825770	−	0.300556i
$935$			20.9897i			0.686436i
$936$		0			0
$937$		−	45.0173i		−	1.47065i	−0.677715	−	0.735325i	$-0.737030\pi$
$937$		−	45.0173i		−	1.47065i	0.677715	−	0.735325i	$-0.262970\pi$
$938$	3.51666	+	15.9188i	0.114823	+	0.519767i
$939$		0			0
$940$	6.23772	+	7.43383i	0.203452	+	0.242465i
$941$			10.2701i			0.334794i	0.985890	+	0.167397i	$0.0535362\pi$
$941$			10.2701i			0.334794i	−0.985890	+	0.167397i	$0.946464\pi$
$942$		0			0
$943$		−	2.11787i		−	0.0689674i
$944$	22.7318	+	4.00823i	0.739857	+	0.130457i
$945$		0			0
$946$	−33.6168	+	12.2355i	−1.09298	+	0.397811i
$947$	−20.8015			−0.675959			−0.337980	−	0.941153i	$-0.609744\pi$
$947$	−20.8015			−0.675959			−0.337980	+	0.941153i	$0.609744\pi$
$948$		0			0
$949$			18.8231i			0.611024i
$950$	−5.39093	−	14.8115i	−0.174905	−	0.480547i
$951$		0			0
$952$	14.8741	−	19.3545i	0.482074	−	0.627281i
$953$		−	4.88379i		−	0.158202i	−0.996867	−	0.0791008i	$-0.974795\pi$
$953$		−	4.88379i		−	0.158202i	0.996867	−	0.0791008i	$-0.0252049\pi$
$954$		0			0
$955$	6.80313			0.220144
$956$	−13.5649	−	16.1660i	−0.438719	−	0.522845i
$957$		0			0
$958$	17.5086	+	48.1045i	0.565677	+	1.55419i
$959$	−0.238053	−	0.0315210i	−0.00768715	−	0.00101787i
$960$		0			0
$961$	−33.5918			−1.08361
$962$	−9.99500	+	3.63788i	−0.322252	+	0.117290i
$963$		0			0
$964$	7.55716	+	9.00627i	0.243400	+	0.290073i
$965$			26.5525i			0.854754i
$966$		0			0
$967$	−6.62092			−0.212914			−0.106457	−	0.994317i	$-0.533951\pi$
$967$	−6.62092			−0.212914			−0.106457	+	0.994317i	$0.533951\pi$
$968$	−1.65339	−	0.954583i	−0.0531419	−	0.0306815i
$969$		0			0
$970$	13.7588	+	37.8019i	0.441767	+	1.21375i
$971$			6.92094i			0.222103i	0.993815	+	0.111052i	$0.0354219\pi$
$971$			6.92094i			0.222103i	−0.993815	+	0.111052i	$0.964578\pi$
$972$		0			0
$973$	1.84992	−	13.9710i	0.0593058	−	0.447890i
$974$	−12.1497	−	33.3811i	−0.389302	−	1.06960i
$975$		0			0
$976$	5.96911	−	33.8525i	0.191067	−	1.08359i
$977$			39.4468i			1.26202i	0.775777	+	0.631008i	$0.217358\pi$
$977$			39.4468i			1.26202i	−0.775777	+	0.631008i	$0.782642\pi$
$978$		0			0
$979$	45.2971			1.44770
$980$	11.1069	+	23.9119i	0.354797	+	0.763837i
$981$		0			0
$982$	7.00269	+	19.2397i	0.223465	+	0.613964i
$983$	3.94734			0.125900			0.0629502	−	0.998017i	$-0.479949\pi$
$983$	3.94734			0.125900			0.0629502	+	0.998017i	$0.479949\pi$
$984$		0			0
$985$		−	32.2910i		−	1.02888i
$986$	−9.60157	−	26.3801i	−0.305776	−	0.840114i
$987$		0			0
$988$	−47.9418	+	40.2280i	−1.52523	+	1.27982i
$989$	1.93476			0.0615217
$990$		0			0
$991$	43.5621			1.38380			0.691898	−	0.721995i	$-0.256775\pi$
$991$	43.5621			1.38380			0.691898	+	0.721995i	$0.256775\pi$
$992$	7.89467	+	44.7729i	0.250656	+	1.42154i
$993$		0			0
$994$	−6.26672	−	28.3675i	−0.198768	−	0.899761i
$995$	20.3920			0.646471
$996$		0			0
$997$	52.4143			1.65998			0.829988	−	0.557781i	$-0.188347\pi$
$997$	52.4143			1.65998			0.829988	+	0.557781i	$0.188347\pi$
$998$	−5.37808	+	1.95746i	−0.170240	+	0.0619623i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.i.b.125.16	yes	24
3.2	odd	2	inner	504.2.i.b.125.9	✓	24
4.3	odd	2		2016.2.i.b.881.12		24
7.6	odd	2	inner	504.2.i.b.125.15	yes	24
8.3	odd	2		2016.2.i.b.881.13		24
8.5	even	2	inner	504.2.i.b.125.11	yes	24
12.11	even	2		2016.2.i.b.881.23		24
21.20	even	2	inner	504.2.i.b.125.10	yes	24
24.5	odd	2	inner	504.2.i.b.125.14	yes	24
24.11	even	2		2016.2.i.b.881.2		24
28.27	even	2		2016.2.i.b.881.1		24
56.13	odd	2	inner	504.2.i.b.125.12	yes	24
56.27	even	2		2016.2.i.b.881.24		24
84.83	odd	2		2016.2.i.b.881.14		24
168.83	odd	2		2016.2.i.b.881.11		24
168.125	even	2	inner	504.2.i.b.125.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.i.b.125.9	✓	24	3.2	odd	2	inner
504.2.i.b.125.10	yes	24	21.20	even	2	inner
504.2.i.b.125.11	yes	24	8.5	even	2	inner
504.2.i.b.125.12	yes	24	56.13	odd	2	inner
504.2.i.b.125.13	yes	24	168.125	even	2	inner
504.2.i.b.125.14	yes	24	24.5	odd	2	inner
504.2.i.b.125.15	yes	24	7.6	odd	2	inner
504.2.i.b.125.16	yes	24	1.1	even	1	trivial
2016.2.i.b.881.1		24	28.27	even	2
2016.2.i.b.881.2		24	24.11	even	2
2016.2.i.b.881.11		24	168.83	odd	2
2016.2.i.b.881.12		24	4.3	odd	2
2016.2.i.b.881.13		24	8.3	odd	2
2016.2.i.b.881.14		24	84.83	odd	2
2016.2.i.b.881.23		24	12.11	even	2
2016.2.i.b.881.24		24	56.27	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.483690 + 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +1.88325i q^{5} +(-0.347296 + 2.62286i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(0.483690 + 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +1.88325i q^{5} +(-0.347296 + 2.62286i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-2.50270 + 0.910909i) q^{10} +3.41687 q^{11} -4.08044 q^{13} +(-3.65357 + 0.807118i) q^{14} +(0.694593 - 3.93923i) q^{16} +3.26189 q^{17} -7.66872 q^{19} +(-2.42106 - 2.88531i) q^{20} +(1.65270 + 4.54077i) q^{22} -0.261336i q^{23} +1.45336 q^{25} +(-1.97367 - 5.42261i) q^{26} +(-2.83979 - 4.46493i) q^{28} -6.08565 q^{29} +8.03690i q^{31} +(5.57091 - 0.982302i) q^{32} +(1.57774 + 4.33481i) q^{34} +(-4.93950 - 0.654046i) q^{35} -1.84321i q^{37} +(-3.70928 - 10.1912i) q^{38} +(2.66332 - 4.61301i) q^{40} +8.10401 q^{41} +7.40333i q^{43} +(-5.23495 + 4.39264i) q^{44} +(0.347296 - 0.126406i) q^{46} -2.57644 q^{47} +(-6.75877 - 1.82182i) q^{49} +(0.702977 + 1.93141i) q^{50} +(6.25160 - 5.24572i) q^{52} +11.6566 q^{53} +6.43482i q^{55} +(4.55998 - 5.93351i) q^{56} +(-2.94356 - 8.08737i) q^{58} +5.77062i q^{59} +8.59369 q^{61} +(-10.6805 + 3.88737i) q^{62} +(4.00000 + 6.92820i) q^{64} -7.68450i q^{65} -4.35705i q^{67} +(-4.99750 + 4.19340i) q^{68} +(-1.52001 - 6.88059i) q^{70} +7.76432i q^{71} -4.61301i q^{73} +(2.44949 - 0.891541i) q^{74} +(11.7492 - 9.85872i) q^{76} +(-1.18667 + 8.96196i) q^{77} +11.1925 q^{79} +(7.41856 + 1.30809i) q^{80} +(3.91983 + 10.7696i) q^{82} -7.07871i q^{83} +6.14296i q^{85} +(-9.83848 + 3.58091i) q^{86} +(-8.36959 - 4.83218i) q^{88} +13.2569 q^{89} +(1.41712 - 10.7024i) q^{91} +(0.335967 + 0.400390i) q^{92} +(-1.24620 - 3.42390i) q^{94} -14.4421i q^{95} -15.1044i q^{97} +(-0.848085 - 9.86310i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{22} - 72 q^{25} - 24 q^{28} - 72 q^{49} + 48 q^{58} + 96 q^{64} - 24 q^{70} + 48 q^{79} - 144 q^{88}+O(q^{100}) \) 24 * q + 48 * q^22 - 72 * q^25 - 24 * q^28 - 72 * q^49 + 48 * q^58 + 96 * q^64 - 24 * q^70 + 48 * q^79 - 144 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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