LMFDB - Embedded newform 504.2.i.b.125.12

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			125.12
Character	$\chi$	$=$	504.125
Dual form			504.2.i.b.125.9

$q$-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	$-0.672250\pi$
$11$	−3.41687			−1.03022			−0.515112	+	0.857123i	$0.672250\pi$
$12$		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	$-0.629450\pi$
$17$	−3.26189			−0.791124			−0.395562	+	0.918439i	$0.629450\pi$
$18$		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	$-0.308861\pi$
$29$	6.08565			1.13008			0.565038	+	0.825065i	$0.308861\pi$
$30$		0			0
$31$		−	8.03690i		−	1.44347i	−0.692169	−	0.721735i	$-0.743345\pi$
$31$		−	8.03690i		−	1.44347i	0.692169	−	0.721735i	$-0.256655\pi$
$32$	−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	$0.0484139\pi$
$37$			1.84321i			0.303022i	−0.988456	+	0.151511i	$0.951586\pi$
$38$	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	$-0.718101\pi$
$41$	−8.10401			−1.26563			−0.632817	+	0.774301i	$0.718101\pi$
$42$		0			0
$43$		−	7.40333i		−	1.12900i	−0.825434	−	0.564499i	$-0.809069\pi$
$43$		−	7.40333i		−	1.12900i	0.825434	−	0.564499i	$-0.190931\pi$
$44$	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	$-0.439830\pi$
$47$	2.57644			0.375812			0.187906	+	0.982187i	$0.439830\pi$
$48$		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	$-0.795473\pi$
$53$	−11.6566			−1.60115			−0.800576	+	0.599232i	$0.795473\pi$
$54$		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	$0.0857514\pi$
$67$			4.35705i			0.532299i	−0.963932	+	0.266149i	$0.914249\pi$
$68$	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	$0.0870091\pi$
$73$			4.61301i			0.539911i	−0.962873	+	0.269956i	$0.912991\pi$
$74$	−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	$-0.747984\pi$
$89$	−13.2569			−1.40523			−0.702614	+	0.711571i	$0.747984\pi$
$90$		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	$0.278158\pi$
$97$			15.1044i			1.53362i	−0.641872	+	0.766812i	$0.721842\pi$
$98$	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	$-0.870415\pi$
$103$		−	8.03690i		−	0.791900i	0.918272	−	0.395950i	$-0.129585\pi$
$104$	−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	$-0.519225\pi$
$107$	−1.24875			−0.120721			−0.0603606	+	0.998177i	$0.519225\pi$
$108$		0			0
$109$		−	7.15052i		−	0.684896i	−0.939537	−	0.342448i	$-0.888744\pi$
$109$		−	7.15052i		−	0.684896i	0.939537	−	0.342448i	$-0.111256\pi$
$110$	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	$-0.572262\pi$
$149$	−5.49476			−0.450148			−0.225074	+	0.974342i	$0.572262\pi$
$150$		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	$-0.745157\pi$
$163$		−	18.3281i		−	1.43557i	0.696267	−	0.717783i	$-0.254843\pi$
$164$	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	$-0.451194\pi$
$167$	3.94734			0.305454			0.152727	+	0.988268i	$0.451194\pi$
$168$		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	$-0.759164\pi$
$179$	−19.4577			−1.45433			−0.727167	+	0.686460i	$0.759164\pi$
$180$		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	$-0.290841\pi$
$197$	17.1464			1.22163			0.610816	+	0.791772i	$0.290841\pi$
$198$		0			0
$199$			10.8281i			0.767583i	0.923420	+	0.383792i	$0.125382\pi$
$199$			10.8281i			0.767583i	−0.923420	+	0.383792i	$0.874618\pi$
$200$	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	$0.0725875\pi$
$211$			6.56769i			0.452138i	−0.974111	+	0.226069i	$0.927412\pi$
$212$	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	$0.0425478\pi$
$223$			3.98029i			0.266540i	−0.991080	+	0.133270i	$0.957452\pi$
$224$	−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	$0.0606320\pi$
$241$			5.87843i			0.378663i	−0.981913	+	0.189331i	$0.939368\pi$
$242$	−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	$-0.246192\pi$
$257$	22.9411			1.43103			0.715514	+	0.698598i	$0.246192\pi$
$258$		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	$0.115441\pi$
$271$			11.6805i			0.709542i	−0.934953	+	0.354771i	$0.884559\pi$
$272$	−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	$0.191434\pi$
$277$			18.8337i			1.13161i	−0.824540	+	0.565804i	$0.808566\pi$
$278$	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	$-0.669325\pi$
$311$	−17.8897			−1.01443			−0.507215	+	0.861819i	$0.669325\pi$
$312$		0			0
$313$		−	20.9829i		−	1.18602i	−0.805194	−	0.593011i	$-0.797939\pi$
$313$		−	20.9829i		−	1.18602i	0.805194	−	0.593011i	$-0.202061\pi$
$314$	−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	$-0.842413\pi$
$317$	−31.3335			−1.75987			−0.879933	+	0.475098i	$0.842413\pi$
$318$		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	$-0.835103\pi$
$331$		−	18.0180i		−	0.990356i	0.868791	−	0.495178i	$-0.164897\pi$
$332$	−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	$-0.478525\pi$
$347$	2.51157			0.134828			0.0674142	+	0.997725i	$0.478525\pi$
$348$		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	$-0.231184\pi$
$353$	28.0940			1.49529			0.747647	+	0.664097i	$0.231184\pi$
$354$		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	$0.102219\pi$
$367$			12.0935i			0.631276i	−0.948880	+	0.315638i	$0.897781\pi$
$368$	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	$-0.893440\pi$
$373$		−	12.6907i		−	0.657102i	0.944486	−	0.328551i	$-0.106560\pi$
$374$	−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	$0.184977\pi$
$379$			21.3744i			1.09793i	−0.835846	+	0.548963i	$0.815023\pi$
$380$	−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	$-0.662222\pi$
$383$	−19.0952			−0.975720			−0.487860	+	0.872922i	$0.662222\pi$
$384$		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	$-0.385323\pi$
$389$	13.9057			0.705048			0.352524	+	0.935803i	$0.385323\pi$
$390$		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	$-0.600059\pi$
$409$		−	38.4655i		−	1.90200i	0.309195	−	0.950999i	$-0.399941\pi$
$410$	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	$-0.870386\pi$
$421$		−	16.2520i		−	0.792072i	0.918235	−	0.396036i	$-0.129614\pi$
$422$	−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	$-0.928844\pi$
$433$		−	9.22601i		−	0.443374i	0.975118	−	0.221687i	$-0.0711563\pi$
$434$	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	$0.169897\pi$
$439$			21.3195i			1.01753i	−0.860907	+	0.508763i	$0.830103\pi$
$440$	−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	$-0.783639\pi$
$443$	−32.7395			−1.55550			−0.777750	+	0.628574i	$0.783639\pi$
$444$		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	$-0.809935\pi$
$479$	−36.1980			−1.65393			−0.826965	+	0.562253i	$0.809935\pi$
$480$		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	$-0.605931\pi$
$491$	−14.4777			−0.653367			−0.326684	+	0.945134i	$0.605931\pi$
$492$		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	$-0.971127\pi$
$499$		−	4.04693i		−	0.181166i	0.995889	−	0.0905828i	$-0.0288730\pi$
$500$	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	$-0.444875\pi$
$503$	7.72932			0.344633			0.172317	+	0.985042i	$0.444875\pi$
$504$		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	$-0.852408\pi$
$521$	−40.8308			−1.78883			−0.894415	+	0.447238i	$0.852408\pi$
$522$		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	$0.371843\pi$
$541$			42.7991i			1.84008i	−0.391828	+	0.920039i	$0.628157\pi$
$542$	−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	$-0.934108\pi$
$547$		−	9.61397i		−	0.411064i	0.978650	−	0.205532i	$-0.0658924\pi$
$548$	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	$-0.451643\pi$
$557$	7.14326			0.302669			0.151335	+	0.988483i	$0.451643\pi$
$558$		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	$-0.955574\pi$
$571$		−	6.64858i		−	0.278234i	0.990276	−	0.139117i	$-0.0444265\pi$
$572$	−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	$0.161642\pi$
$577$			23.3611i			0.972535i	−0.873810	+	0.486267i	$0.838358\pi$
$578$	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	$-0.432810\pi$
$593$	10.2043			0.419042			0.209521	+	0.977804i	$0.432810\pi$
$594$		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	$-0.881888\pi$
$601$		−	17.7787i		−	0.725209i	0.931943	−	0.362604i	$-0.118112\pi$
$602$	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	$-0.845239\pi$
$607$		−	23.0244i		−	0.934532i	0.884117	−	0.467266i	$-0.154761\pi$
$608$	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	$-0.734701\pi$
$613$		−	36.6561i		−	1.48053i	0.672316	−	0.740264i	$-0.265299\pi$
$614$	−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	$-0.266183\pi$
$647$	34.0977			1.34052			0.670259	+	0.742127i	$0.266183\pi$
$648$		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	$-0.413517\pi$
$653$	13.7155			0.536728			0.268364	+	0.963318i	$0.413517\pi$
$654$		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	$-0.739957\pi$
$659$	−35.1410			−1.36890			−0.684449	+	0.729061i	$0.739957\pi$
$660$		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	$-0.588549\pi$
$683$	−14.3535			−0.549221			−0.274610	+	0.961556i	$0.588549\pi$
$684$		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	$-0.596190\pi$
$701$	−15.7594			−0.595226			−0.297613	+	0.954687i	$0.596190\pi$
$702$		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	$-0.895915\pi$
$709$		−	17.1051i		−	0.642396i	0.947012	−	0.321198i	$-0.104085\pi$
$710$	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	$-0.303484\pi$
$719$	31.0451			1.15779			0.578894	+	0.815403i	$0.303484\pi$
$720$		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	$-0.992980\pi$
$727$		−	1.18911i		−	0.0441016i	0.999757	−	0.0220508i	$-0.00701955\pi$
$728$	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	$-0.585409\pi$
$739$		−	52.4237i		−	1.92844i	0.265111	−	0.964218i	$-0.414591\pi$
$740$	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	$-0.984790\pi$
$757$		−	2.62846i		−	0.0955329i	0.998859	−	0.0477665i	$-0.0152103\pi$
$758$	−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	$-0.606390\pi$
$761$	−18.0990			−0.656089			−0.328044	+	0.944662i	$0.606390\pi$
$762$		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	$0.143642\pi$
$769$			24.1870i			0.872206i	−0.899897	+	0.436103i	$0.856358\pi$
$770$	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	$-0.376883\pi$
$821$	21.6166			0.754425			0.377212	+	0.926127i	$0.376883\pi$
$822$		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	$-0.624671\pi$
$827$	−21.9552			−0.763456			−0.381728	+	0.924275i	$0.624671\pi$
$828$		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	$-0.540875\pi$
$839$	−7.41856			−0.256117			−0.128059	+	0.991767i	$0.540875\pi$
$840$		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	$-0.610322\pi$
$857$	−19.8886			−0.679381			−0.339691	+	0.940537i	$0.610322\pi$
$858$		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	$0.0545959\pi$
$877$			10.1090i			0.341357i	−0.985327	+	0.170678i	$0.945404\pi$
$878$	−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	$-0.588592\pi$
$881$	−16.3094			−0.549479			−0.274739	+	0.961519i	$0.588592\pi$
$882$		0			0
$883$			33.6603i			1.13276i	0.824145	+	0.566379i	$0.191656\pi$
$883$			33.6603i			1.13276i	−0.824145	+	0.566379i	$0.808344\pi$
$884$	−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	$-0.254522\pi$
$887$	41.5163			1.39398			0.696990	+	0.717081i	$0.254522\pi$
$888$		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	$0.320165\pi$
$907$			50.8731i			1.68921i	−0.535388	+	0.844606i	$0.679835\pi$
$908$	−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	$-0.307761\pi$
$929$	34.6178			1.13577			0.567886	+	0.823107i	$0.307761\pi$
$930$		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	$0.262970\pi$
$937$			45.0173i			1.47065i	−0.677715	+	0.735325i	$0.737030\pi$
$938$	−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	$-0.390256\pi$
$947$	20.8015			0.675959			0.337980	+	0.941153i	$0.390256\pi$
$948$		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	$-0.520051\pi$
$983$	−3.94734			−0.125900			−0.0629502	+	0.998017i	$0.520051\pi$
$984$		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.125.12	yes	24
3.2	odd	2	inner	504.2.i.b.125.13	yes	24
4.3	odd	2		2016.2.i.b.881.24		24
7.6	odd	2	inner	504.2.i.b.125.11	yes	24
8.3	odd	2		2016.2.i.b.881.1		24
8.5	even	2	inner	504.2.i.b.125.15	yes	24
12.11	even	2		2016.2.i.b.881.11		24
21.20	even	2	inner	504.2.i.b.125.14	yes	24
24.5	odd	2	inner	504.2.i.b.125.10	yes	24
24.11	even	2		2016.2.i.b.881.14		24
28.27	even	2		2016.2.i.b.881.13		24
56.13	odd	2	inner	504.2.i.b.125.16	yes	24
56.27	even	2		2016.2.i.b.881.12		24
84.83	odd	2		2016.2.i.b.881.2		24
168.83	odd	2		2016.2.i.b.881.23		24
168.125	even	2	inner	504.2.i.b.125.9	✓	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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