LMFDB - Embedded newform 531.2.i.b.316.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			316.4
Character	$\chi$	$=$	531.316
Dual form			531.2.i.b.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.992185 + 0.596978i) q^{2} +(-0.308769 - 0.582400i) q^{4} +(0.793835 + 0.0863348i) q^{5} +(-4.18976 - 1.41169i) q^{7} +(0.166703 - 3.07465i) q^{8} +O(q^{10})$	\(q+(0.992185 + 0.596978i) q^{2} +(-0.308769 - 0.582400i) q^{4} +(0.793835 + 0.0863348i) q^{5} +(-4.18976 - 1.41169i) q^{7} +(0.166703 - 3.07465i) q^{8} +(0.736091 + 0.559562i) q^{10} +(-0.744195 - 1.09760i) q^{11} +(2.28411 - 2.16363i) q^{13} +(-3.31426 - 3.90185i) q^{14} +(1.26104 - 1.85990i) q^{16} +(7.48680 - 2.52260i) q^{17} +(0.837472 - 5.10835i) q^{19} +(-0.194830 - 0.488987i) q^{20} +(-0.0831328 - 1.53329i) q^{22} +(-0.662011 + 2.38435i) q^{23} +(-4.26038 - 0.937781i) q^{25} +(3.55790 - 0.783152i) q^{26} +(0.471496 + 2.87600i) q^{28} +(-6.94296 + 4.17744i) q^{29} +(-0.686795 - 4.18927i) q^{31} +(-3.22765 + 1.49327i) q^{32} +(8.93422 + 1.96657i) q^{34} +(-3.20410 - 1.48237i) q^{35} +(0.435953 + 8.04068i) q^{37} +(3.88050 - 4.56848i) q^{38} +(0.397784 - 2.42637i) q^{40} +(1.62041 + 5.83619i) q^{41} +(6.39177 - 9.42715i) q^{43} +(-0.409461 + 0.772325i) q^{44} +(-2.08024 + 1.97051i) q^{46} +(-3.69898 + 0.402288i) q^{47} +(9.98853 + 7.59308i) q^{49} +(-3.66725 - 3.47380i) q^{50} +(-1.96536 - 0.662206i) q^{52} +(1.10424 - 0.839421i) q^{53} +(-0.496006 - 0.935567i) q^{55} +(-5.03891 + 12.6467i) q^{56} -9.38254 q^{58} +(7.67111 - 0.392457i) q^{59} +(8.88976 + 5.34879i) q^{61} +(1.81947 - 4.56653i) q^{62} +(-8.56172 - 0.931143i) q^{64} +(2.00000 - 1.52036i) q^{65} +(-0.0694302 + 1.28056i) q^{67} +(-3.78085 - 3.58141i) q^{68} +(-2.29411 - 3.38356i) q^{70} +(-0.433685 + 0.0471661i) q^{71} +(-1.39656 - 1.64416i) q^{73} +(-4.36756 + 8.23809i) q^{74} +(-3.23369 + 1.08956i) q^{76} +(1.56851 + 5.64927i) q^{77} +(-1.73950 - 4.36581i) q^{79} +(1.16163 - 1.36758i) q^{80} +(-1.87633 + 6.75792i) q^{82} +(3.34065 + 1.54555i) q^{83} +(6.16107 - 1.35615i) q^{85} +(11.9696 - 5.53773i) q^{86} +(-3.49881 + 2.10516i) q^{88} +(5.98712 - 3.60233i) q^{89} +(-12.6243 + 5.84060i) q^{91} +(1.59305 - 0.350658i) q^{92} +(-3.91022 - 1.80906i) q^{94} +(1.10584 - 3.98289i) q^{95} +(-6.66777 + 7.84990i) q^{97} +(5.37756 + 13.4967i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) $ 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8	$ 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29} - 12 q^{31} + 150 q^{32} - 2 q^{34} - 6 q^{35} + 12 q^{37} + 12 q^{38} - 66 q^{40} + 4 q^{41} - 60 q^{43} - 20 q^{44} + 76 q^{46} + 25 q^{47} + 31 q^{49} - 137 q^{50} + 118 q^{52} - 48 q^{53} + 93 q^{55} - 228 q^{56} - 120 q^{58} - 57 q^{59} + 72 q^{61} + 179 q^{62} + 249 q^{64} + 39 q^{65} + 40 q^{67} - 94 q^{68} + 94 q^{70} - 30 q^{71} - 205 q^{73} - 66 q^{74} - 216 q^{76} + 46 q^{77} + 4 q^{79} + 356 q^{80} - 28 q^{82} - 4 q^{83} + 50 q^{85} + 18 q^{86} - 162 q^{88} - 26 q^{89} - 198 q^{91} - 10 q^{92} - 4 q^{94} + 326 q^{95} - 20 q^{97} + 143 q^{98}+O(q^{100}) $ 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8 - 116 * q^10 - 2 * q^11 + 4 * q^13 + 43 * q^14 + 7 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 6 * q^23 - 57 * q^25 - 12 * q^26 - 10 * q^28 + 4 * q^29 - 12 * q^31 + 150 * q^32 - 2 * q^34 - 6 * q^35 + 12 * q^37 + 12 * q^38 - 66 * q^40 + 4 * q^41 - 60 * q^43 - 20 * q^44 + 76 * q^46 + 25 * q^47 + 31 * q^49 - 137 * q^50 + 118 * q^52 - 48 * q^53 + 93 * q^55 - 228 * q^56 - 120 * q^58 - 57 * q^59 + 72 * q^61 + 179 * q^62 + 249 * q^64 + 39 * q^65 + 40 * q^67 - 94 * q^68 + 94 * q^70 - 30 * q^71 - 205 * q^73 - 66 * q^74 - 216 * q^76 + 46 * q^77 + 4 * q^79 + 356 * q^80 - 28 * q^82 - 4 * q^83 + 50 * q^85 + 18 * q^86 - 162 * q^88 - 26 * q^89 - 198 * q^91 - 10 * q^92 - 4 * q^94 + 326 * q^95 - 20 * q^97 + 143 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{5}{29}\right)$

Coefficient data

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

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

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

$2$	0.992185	+	0.596978i	0.701580	+	0.422127i	0.821160	−	0.570698i	$-0.193327\pi$
$2$	0.992185	+	0.596978i	0.701580	+	0.422127i	−0.119580	+	0.992825i	$0.538155\pi$
$3$		0			0
$3$		0			0
$4$	−0.308769	−	0.582400i	−0.154384	−	0.291200i
$5$	0.793835	+	0.0863348i	0.355014	+	0.0386101i	0.283888	−	0.958857i	$-0.408375\pi$
$5$	0.793835	+	0.0863348i	0.355014	+	0.0386101i	0.0711254	+	0.997467i	$0.477341\pi$
$6$		0			0
$7$	−4.18976	−	1.41169i	−1.58358	−	0.533570i	−0.616349	−	0.787473i	$-0.711389\pi$
$7$	−4.18976	−	1.41169i	−1.58358	−	0.533570i	−0.967230	+	0.253903i	$0.918286\pi$
$8$	0.166703	−	3.07465i	0.0589383	−	1.08705i
$9$		0			0
$10$	0.736091	+	0.559562i	0.232772	+	0.176949i
$11$	−0.744195	−	1.09760i	−0.224383	−	0.330940i	0.698789	−	0.715328i	$-0.253723\pi$
$11$	−0.744195	−	1.09760i	−0.224383	−	0.330940i	−0.923172	+	0.384388i	$0.874412\pi$
$12$		0			0
$13$	2.28411	−	2.16363i	0.633499	−	0.600082i	−0.302045	−	0.953294i	$-0.597669\pi$
$13$	2.28411	−	2.16363i	0.633499	−	0.600082i	0.935543	+	0.353212i	$0.114911\pi$
$14$	−3.31426	−	3.90185i	−0.885774	−	1.04281i
$15$		0			0
$16$	1.26104	−	1.85990i	0.315260	−	0.464974i
$17$	7.48680	−	2.52260i	1.81582	−	0.611819i	0.816405	−	0.577480i	$-0.195964\pi$
$17$	7.48680	−	2.52260i	1.81582	−	0.611819i	0.999410	−	0.0343397i	$-0.0109328\pi$
$18$		0			0
$19$	0.837472	−	5.10835i	0.192129	−	1.17194i	−0.697956	−	0.716141i	$-0.745907\pi$
$19$	0.837472	−	5.10835i	0.192129	−	1.17194i	0.890085	−	0.455795i	$-0.150645\pi$
$20$	−0.194830	−	0.488987i	−0.0435654	−	0.109341i
$21$		0			0
$22$	−0.0831328	−	1.53329i	−0.0177240	−	0.326899i
$23$	−0.662011	+	2.38435i	−0.138039	+	0.497171i	−0.999951	−	0.00988634i	$-0.996853\pi$
$23$	−0.662011	+	2.38435i	−0.138039	+	0.497171i	0.861912	+	0.507057i	$0.169267\pi$
$24$		0			0
$25$	−4.26038	−	0.937781i	−0.852076	−	0.187556i
$26$	3.55790	−	0.783152i	0.697761	−	0.153589i
$27$		0			0
$28$	0.471496	+	2.87600i	0.0891045	+	0.543513i
$29$	−6.94296	+	4.17744i	−1.28928	+	0.775732i	−0.984279	−	0.176622i	$-0.943483\pi$
$29$	−6.94296	+	4.17744i	−1.28928	+	0.775732i	−0.304997	+	0.952353i	$0.598655\pi$
$30$		0			0
$31$	−0.686795	−	4.18927i	−0.123352	−	0.752414i	−0.973978	−	0.226643i	$-0.927225\pi$
$31$	−0.686795	−	4.18927i	−0.123352	−	0.752414i	0.850626	−	0.525771i	$-0.176223\pi$
$32$	−3.22765	+	1.49327i	−0.570573	+	0.263975i
$33$		0			0
$34$	8.93422	+	1.96657i	1.53221	+	0.337264i
$35$	−3.20410	−	1.48237i	−0.541591	−	0.250567i
$36$		0			0
$37$	0.435953	+	8.04068i	0.0716702	+	1.32188i	0.784319	+	0.620358i	$0.213013\pi$
$37$	0.435953	+	8.04068i	0.0716702	+	1.32188i	−0.712649	+	0.701521i	$0.752505\pi$
$38$	3.88050	−	4.56848i	0.629500	−	0.741105i
$39$		0			0
$40$	0.397784	−	2.42637i	0.0628951	−	0.383643i
$41$	1.62041	+	5.83619i	0.253065	+	0.911459i	0.975496	+	0.220016i	$0.0706109\pi$
$41$	1.62041	+	5.83619i	0.253065	+	0.911459i	−0.722431	+	0.691443i	$0.756975\pi$
$42$		0			0
$43$	6.39177	−	9.42715i	0.974735	−	1.43763i	0.0770311	−	0.997029i	$-0.475456\pi$
$43$	6.39177	−	9.42715i	0.974735	−	1.43763i	0.897704	−	0.440598i	$-0.145234\pi$
$44$	−0.409461	+	0.772325i	−0.0617286	+	0.116432i
$45$		0			0
$46$	−2.08024	+	1.97051i	−0.306715	+	0.290536i
$47$	−3.69898	+	0.402288i	−0.539551	+	0.0586797i	−0.373837	−	0.927494i	$-0.621958\pi$
$47$	−3.69898	+	0.402288i	−0.539551	+	0.0586797i	−0.165714	+	0.986174i	$0.552993\pi$
$48$		0			0
$49$	9.98853	+	7.59308i	1.42693	+	1.08473i
$50$	−3.66725	−	3.47380i	−0.518628	−	0.491270i
$51$		0			0
$52$	−1.96536	−	0.662206i	−0.272546	−	0.0918315i
$53$	1.10424	−	0.839421i	0.151679	−	0.115303i	−0.526582	−	0.850124i	$-0.676527\pi$
$53$	1.10424	−	0.839421i	0.151679	−	0.115303i	0.678261	+	0.734821i	$0.262734\pi$
$54$		0			0
$55$	−0.496006	−	0.935567i	−0.0668815	−	0.126152i
$56$	−5.03891	+	12.6467i	−0.673352	+	1.68999i
$57$		0			0
$58$	−9.38254			−1.23199
$59$	7.67111	−	0.392457i	0.998694	−	0.0510936i
$59$	7.67111	−	0.392457i	0.998694	−	0.0510936i
$60$		0			0
$61$	8.88976	+	5.34879i	1.13822	+	0.684843i	0.954522	−	0.298140i	$-0.0963664\pi$
$61$	8.88976	+	5.34879i	1.13822	+	0.684843i	0.183696	+	0.982983i	$0.441194\pi$
$62$	1.81947	−	4.56653i	0.231073	−	0.579949i
$63$		0			0
$64$	−8.56172	−	0.931143i	−1.07021	−	0.116393i
$65$	2.00000	−	1.52036i	0.248070	−	0.188578i
$66$		0			0
$67$	−0.0694302	+	1.28056i	−0.00848225	+	0.156446i	0.991224	+	0.132195i	$0.0422027\pi$
$67$	−0.0694302	+	1.28056i	−0.00848225	+	0.156446i	−0.999706	+	0.0242504i	$0.992280\pi$
$68$	−3.78085	−	3.58141i	−0.458495	−	0.434310i
$69$		0			0
$70$	−2.29411	−	3.38356i	−0.274199	−	0.404413i
$71$	−0.433685	+	0.0471661i	−0.0514689	+	0.00559758i	−0.133817	−	0.991006i	$-0.542724\pi$
$71$	−0.433685	+	0.0471661i	−0.0514689	+	0.00559758i	0.0823483	+	0.996604i	$0.473758\pi$
$72$		0			0
$73$	−1.39656	−	1.64416i	−0.163455	−	0.192434i	0.674337	−	0.738424i	$-0.264430\pi$
$73$	−1.39656	−	1.64416i	−0.163455	−	0.192434i	−0.837792	+	0.545990i	$0.816154\pi$
$74$	−4.36756	+	8.23809i	−0.507718	+	0.957659i
$75$		0			0
$76$	−3.23369	+	1.08956i	−0.370930	+	0.124981i
$77$	1.56851	+	5.64927i	0.178749	+	0.643794i
$78$		0			0
$79$	−1.73950	−	4.36581i	−0.195709	−	0.491191i	0.798070	−	0.602565i	$-0.205854\pi$
$79$	−1.73950	−	4.36581i	−0.195709	−	0.491191i	−0.993779	+	0.111373i	$0.964475\pi$
$80$	1.16163	−	1.36758i	0.129875	−	0.152900i
$81$		0			0
$82$	−1.87633	+	6.75792i	−0.207206	+	0.746288i
$83$	3.34065	+	1.54555i	0.366684	+	0.169646i	0.594574	−	0.804041i	$-0.297321\pi$
$83$	3.34065	+	1.54555i	0.366684	+	0.169646i	−0.227890	+	0.973687i	$0.573183\pi$
$84$		0			0
$85$	6.16107	−	1.35615i	0.668262	−	0.147096i
$86$	11.9696	−	5.53773i	1.29072	−	0.597149i
$87$		0			0
$88$	−3.49881	+	2.10516i	−0.372974	+	0.224411i
$89$	5.98712	−	3.60233i	0.634634	−	0.381846i	−0.161582	−	0.986859i	$-0.551660\pi$
$89$	5.98712	−	3.60233i	0.634634	−	0.381846i	0.796216	+	0.605013i	$0.206832\pi$
$90$		0			0
$91$	−12.6243	+	5.84060i	−1.32338	+	0.612261i
$92$	1.59305	−	0.350658i	0.166087	−	0.0365586i
$93$		0			0
$94$	−3.91022	−	1.80906i	−0.403309	−	0.186590i
$95$	1.10584	−	3.98289i	0.113457	−	0.408635i
$96$		0			0
$97$	−6.66777	+	7.84990i	−0.677009	+	0.797037i	−0.988177	−	0.153318i	$-0.951004\pi$
$97$	−6.66777	+	7.84990i	−0.677009	+	0.797037i	0.311167	+	0.950355i	$0.399280\pi$
$98$	5.37756	+	13.4967i	0.543216	+	1.36337i
$99$		0			0
$100$	0.769310	+	2.77080i	0.0769310	+	0.277080i
$101$	−0.188243	+	0.0634265i	−0.0187309	+	0.00631117i	−0.328651	−	0.944451i	$-0.606594\pi$
$101$	−0.188243	+	0.0634265i	−0.0187309	+	0.00631117i	0.309920	+	0.950762i	$0.399698\pi$
$102$		0			0
$103$	−2.88236	+	5.43671i	−0.284008	+	0.535695i	−0.983937	−	0.178517i	$-0.942870\pi$
$103$	−2.88236	+	5.43671i	−0.284008	+	0.535695i	0.699929	+	0.714212i	$0.253215\pi$
$104$	−6.27162	−	7.38353i	−0.614983	−	0.724014i
$105$		0			0
$106$	1.59672	−	0.173654i	0.155088	−	0.0168668i
$107$	5.57926	+	8.22880i	0.539368	+	0.795508i	0.995536	−	0.0943857i	$-0.0300887\pi$
$107$	5.57926	+	8.22880i	0.539368	+	0.795508i	−0.456168	+	0.889894i	$0.650778\pi$
$108$		0			0
$109$	3.79341	+	3.59331i	0.363343	+	0.344177i	0.847491	−	0.530809i	$-0.178112\pi$
$109$	3.79341	+	3.59331i	0.363343	+	0.344177i	−0.484148	+	0.874986i	$0.660871\pi$
$110$	0.0663829	−	1.22436i	0.00632936	−	0.116738i
$111$		0			0
$112$	−7.90906	+	6.01231i	−0.747336	+	0.568110i
$113$	7.13771	+	0.776273i	0.671459	+	0.0730256i	0.437497	−	0.899220i	$-0.355865\pi$
$113$	7.13771	+	0.776273i	0.671459	+	0.0730256i	0.233963	+	0.972246i	$0.424831\pi$
$114$		0			0
$115$	−0.731380	+	1.83563i	−0.0682015	+	0.171173i
$116$	4.57671	+	2.75372i	0.424937	+	0.255676i
$117$		0			0
$118$	7.84545	+	4.19009i	0.722232	+	0.385729i
$119$	−34.9290			−3.20194
$120$		0			0
$121$	3.42061	−	8.58508i	0.310964	−	0.780462i
$122$	5.62718	+	10.6140i	0.509461	+	0.960945i
$123$		0			0
$124$	−2.22777	+	1.69350i	−0.200059	+	0.152081i
$125$	−7.08466	−	2.38710i	−0.633671	−	0.213509i
$126$		0			0
$127$	11.3503	+	10.7516i	1.00718	+	0.954049i	0.998945	−	0.0459172i	$-0.0146210\pi$
$127$	11.3503	+	10.7516i	1.00718	+	0.954049i	0.00823195	+	0.999966i	$0.497380\pi$
$128$	−2.27658	−	1.73061i	−0.201223	−	0.152966i
$129$		0			0
$130$	2.89200	−	0.314524i	0.253645	−	0.0275856i
$131$	−6.01093	+	5.69385i	−0.525177	+	0.497474i	−0.903728	−	0.428106i	$-0.859181\pi$
$131$	−6.01093	+	5.69385i	−0.525177	+	0.497474i	0.378551	+	0.925580i	$0.376422\pi$
$132$		0			0
$133$	−10.7202	+	20.2205i	−0.929562	+	1.75334i
$134$	−0.833356	+	1.22911i	−0.0719910	+	0.106179i
$135$		0			0
$136$	−6.50803	−	23.4398i	−0.558059	−	2.00995i
$137$	1.85540	−	11.3174i	0.158518	−	0.966914i	−0.781029	−	0.624494i	$-0.785305\pi$
$137$	1.85540	−	11.3174i	0.158518	−	0.966914i	0.939547	−	0.342420i	$-0.111247\pi$
$138$		0			0
$139$	12.1020	−	14.2476i	1.02648	−	1.20847i	0.0487070	−	0.998813i	$-0.484490\pi$
$139$	12.1020	−	14.2476i	1.02648	−	1.20847i	0.977775	−	0.209655i	$-0.0672342\pi$
$140$	0.125992	+	2.32378i	0.0106482	+	0.196395i
$141$		0			0
$142$	−0.458453	−	0.212103i	−0.0384725	−	0.0177993i
$143$	−4.07463	−	0.896894i	−0.340738	−	0.0750020i
$144$		0			0
$145$	−5.87223	+	2.71678i	−0.487662	+	0.225616i
$146$	−0.404120	−	2.46502i	−0.0334452	−	0.204007i
$147$		0			0
$148$	4.54828	−	2.73661i	0.373866	−	0.224948i
$149$	−2.87916	−	17.5621i	−0.235870	−	1.43874i	−0.793458	−	0.608625i	$-0.791722\pi$
$149$	−2.87916	−	17.5621i	−0.235870	−	1.43874i	0.557588	−	0.830118i	$-0.311727\pi$
$150$		0			0
$151$	12.4650	−	2.74375i	1.01439	−	0.223283i	0.323485	−	0.946233i	$-0.395145\pi$
$151$	12.4650	−	2.74375i	1.01439	−	0.223283i	0.690900	+	0.722950i	$0.257214\pi$
$152$	−15.5668	−	3.42651i	−1.26263	−	0.277926i
$153$		0			0
$154$	−1.81623	+	6.54149i	−0.146356	+	0.527128i
$155$	−0.183523	−	3.38488i	−0.0147409	−	0.271880i
$156$		0			0
$157$	−7.26263	−	18.2278i	−0.579621	−	1.45474i	−0.867678	−	0.497126i	$-0.834389\pi$
$157$	−7.26263	−	18.2278i	−0.579621	−	1.45474i	0.288057	−	0.957613i	$-0.406991\pi$
$158$	0.880387	−	5.37013i	0.0700399	−	0.427224i
$159$		0			0
$160$	−2.69114	+	0.906750i	−0.212753	+	0.0716849i
$161$	6.13964	−	9.05528i	0.483871	−	0.713656i
$162$		0			0
$163$	−7.48651	−	8.81380i	−0.586388	−	0.690350i	0.386324	−	0.922363i	$-0.373745\pi$
$163$	−7.48651	−	8.81380i	−0.586388	−	0.690350i	−0.972713	+	0.232013i	$0.925469\pi$
$164$	2.89866	−	2.74576i	0.226347	−	0.214408i
$165$		0			0
$166$	2.39188	+	3.52777i	0.185646	+	0.273808i
$167$	3.21429	+	2.44344i	0.248729	+	0.189079i	0.722109	−	0.691780i	$-0.243173\pi$
$167$	3.21429	+	2.44344i	0.248729	+	0.189079i	−0.473380	+	0.880858i	$0.656966\pi$
$168$		0			0
$169$	−0.167915	+	3.09700i	−0.0129165	+	0.238231i
$170$	6.92251	+	2.33247i	0.530933	+	0.178892i
$171$		0			0
$172$	−7.46395	−	0.811754i	−0.569121	−	0.0618956i
$173$	3.10214	+	5.85125i	0.235851	+	0.444862i	0.972980	−	0.230890i	$-0.0741638\pi$
$173$	3.10214	+	5.85125i	0.235851	+	0.444862i	−0.737129	+	0.675752i	$0.763819\pi$
$174$		0			0
$175$	16.5261	+	9.94343i	1.24926	+	0.751652i
$176$	−2.97989			−0.224618
$177$		0			0
$178$	8.09084			0.606434
$179$	−7.43790	−	4.47524i	−0.555935	−	0.334495i	0.209705	−	0.977765i	$-0.432750\pi$
$179$	−7.43790	−	4.47524i	−0.555935	−	0.334495i	−0.765639	+	0.643270i	$0.777577\pi$
$180$		0			0
$181$	3.00529	+	5.66857i	0.223381	+	0.421341i	0.969718	−	0.244227i	$-0.0785341\pi$
$181$	3.00529	+	5.66857i	0.223381	+	0.421341i	−0.746337	+	0.665568i	$0.768189\pi$
$182$	−16.0123	−	1.74144i	−1.18691	−	0.129084i
$183$		0			0
$184$	7.22068	+	2.43293i	0.532315	+	0.179358i
$185$	−0.348115	+	6.42061i	−0.0255940	+	0.472053i
$186$		0			0
$187$	−8.34045	−	6.34024i	−0.609914	−	0.463645i
$188$	1.37642	+	2.03007i	0.100386	+	0.148058i
$189$		0			0
$190$	3.47489	−	3.29159i	0.252095	−	0.238797i
$191$	16.4433	+	19.3585i	1.18979	+	1.40073i	0.895526	+	0.445009i	$0.146799\pi$
$191$	16.4433	+	19.3585i	1.18979	+	1.40073i	0.294266	+	0.955723i	$0.404925\pi$
$192$		0			0
$193$	0.407806	−	0.601468i	0.0293545	−	0.0432946i	−0.812729	−	0.582642i	$-0.802019\pi$
$193$	0.407806	−	0.601468i	0.0293545	−	0.0432946i	0.842083	+	0.539348i	$0.181329\pi$
$194$	−11.3019	+	3.80805i	−0.811427	+	0.273402i
$195$		0			0
$196$	1.33806	−	8.16183i	0.0955760	−	0.582988i
$197$	0.971271	+	2.43771i	0.0692002	+	0.173679i	0.959509	−	0.281678i	$-0.0908909\pi$
$197$	0.971271	+	2.43771i	0.0692002	+	0.173679i	−0.890309	+	0.455357i	$0.849512\pi$
$198$		0			0
$199$	0.0527440	+	0.972806i	0.00373892	+	0.0689604i	0.999807	−	0.0196264i	$-0.00624769\pi$
$199$	0.0527440	+	0.972806i	0.00373892	+	0.0689604i	−0.996068	+	0.0885868i	$0.971765\pi$
$200$	−3.59356	+	12.9429i	−0.254103	+	0.915198i
$201$		0			0
$202$	−0.224636	−	0.0494461i	−0.0158053	−	0.00347902i
$203$	34.9866	−	7.70113i	2.45558	−	0.540513i
$204$		0			0
$205$	0.782472	+	4.77287i	0.0546502	+	0.333351i
$206$	−6.10543	+	3.67352i	−0.425386	+	0.255946i
$207$		0			0
$208$	−1.14376	−	6.97664i	−0.0793056	−	0.483743i
$209$	−6.23019	+	2.88239i	−0.430951	+	0.199379i
$210$		0			0
$211$	−3.55199	−	0.781851i	−0.244529	−	0.0538248i	0.0910148	−	0.995850i	$-0.470989\pi$
$211$	−3.55199	−	0.781851i	−0.244529	−	0.0538248i	−0.335544	+	0.942025i	$0.608920\pi$
$212$	−0.829833	−	0.383922i	−0.0569932	−	0.0263679i
$213$		0			0
$214$	0.623251	+	11.4952i	0.0426045	+	0.785795i
$215$	5.88790	−	6.93177i	0.401551	−	0.472743i
$216$		0			0
$217$	−3.03645	+	18.5215i	−0.206128	+	1.25732i
$218$	1.61864	+	5.82981i	0.109628	+	0.394845i
$219$		0			0
$220$	−0.391723	+	0.577748i	−0.0264100	+	0.0389518i
$221$	11.6427	−	21.9605i	0.783175	−	1.47722i
$222$		0			0
$223$	3.70796	−	3.51237i	0.248304	−	0.235206i	−0.553417	−	0.832904i	$-0.686677\pi$
$223$	3.70796	−	3.51237i	0.248304	−	0.235206i	0.801721	+	0.597698i	$0.203918\pi$
$224$	15.6311	−	1.69998i	1.04440	−	0.113585i
$225$		0			0
$226$	6.61851	+	5.03126i	0.440257	+	0.334674i
$227$	−9.29992	−	8.80935i	−0.617257	−	0.584697i	0.313836	−	0.949477i	$-0.398386\pi$
$227$	−9.29992	−	8.80935i	−0.617257	−	0.584697i	−0.931094	+	0.364780i	$0.881144\pi$
$228$		0			0
$229$	20.8942	+	7.04007i	1.38073	+	0.465221i	0.909100	−	0.416578i	$-0.136771\pi$
$229$	20.8942	+	7.04007i	1.38073	+	0.465221i	0.471626	+	0.881799i	$0.343667\pi$
$230$	−1.82149	+	1.38466i	−0.120106	+	0.0913019i
$231$		0			0
$232$	11.6868	+	22.0436i	0.767273	+	1.44723i
$233$	−4.30895	+	10.8147i	−0.282289	+	0.708492i	0.717638	+	0.696416i	$0.245223\pi$
$233$	−4.30895	+	10.8147i	−0.282289	+	0.708492i	−0.999927	+	0.0120755i	$0.996156\pi$
$234$		0			0
$235$	−2.97111			−0.193814
$236$	−2.59717	−	4.34648i	−0.169061	−	0.282932i
$237$		0			0
$238$	−34.6560	−	20.8518i	−2.24642	−	1.35162i
$239$	4.80006	−	12.0472i	0.310490	−	0.779271i	−0.688071	−	0.725643i	$-0.741542\pi$
$239$	4.80006	−	12.0472i	0.310490	−	0.779271i	0.998561	−	0.0536279i	$-0.0170785\pi$
$240$		0			0
$241$	−14.3385	−	1.55941i	−0.923624	−	0.100450i	−0.366066	−	0.930589i	$-0.619296\pi$
$241$	−14.3385	−	1.55941i	−0.923624	−	0.100450i	−0.557557	+	0.830139i	$0.688261\pi$
$242$	8.51898	−	6.47596i	0.547621	−	0.416290i
$243$		0			0
$244$	0.370254	−	6.82894i	0.0237031	−	0.437178i
$245$	7.27370	+	6.89001i	0.464699	+	0.440187i
$246$		0			0
$247$	−9.13968	−	13.4800i	−0.581544	−	0.857713i
$248$	−12.9950	+	1.41329i	−0.825184	+	0.0897442i
$249$		0			0
$250$	−5.60424	−	6.59783i	−0.354444	−	0.417283i
$251$	−3.75643	+	7.08538i	−0.237104	+	0.447225i	−0.973298	−	0.229545i	$-0.926276\pi$
$251$	−3.75643	+	7.08538i	−0.237104	+	0.447225i	0.736194	+	0.676770i	$0.236621\pi$
$252$		0			0
$253$	3.10974	−	1.04779i	0.195508	−	0.0658742i
$254$	4.84315	+	17.4434i	0.303886	+	1.09450i
$255$		0			0
$256$	5.14976	+	12.9249i	0.321860	+	0.807807i
$257$	−16.5510	+	19.4853i	−1.03242	+	1.21546i	−0.0562614	+	0.998416i	$0.517918\pi$
$257$	−16.5510	+	19.4853i	−1.03242	+	1.21546i	−0.976161	+	0.217046i	$0.930358\pi$
$258$		0			0
$259$	9.52443	−	34.3039i	0.591820	−	2.13154i
$260$	−1.50300	−	0.695362i	−0.0932121	−	0.0431245i
$261$		0			0
$262$	−9.36305	+	2.06096i	−0.578451	+	0.127327i
$263$	−20.8210	+	9.63280i	−1.28388	+	0.593984i	−0.938758	−	0.344576i	$-0.888023\pi$
$263$	−20.8210	+	9.63280i	−1.28388	+	0.593984i	−0.345117	+	0.938560i	$0.612161\pi$
$264$		0			0
$265$	0.949055	−	0.571027i	0.0583000	−	0.0350779i
$266$	−22.7076	+	13.6627i	−1.39229	+	0.837715i
$267$		0			0
$268$	0.767238	−	0.354962i	0.0468665	−	0.0216828i
$269$	29.4845	−	6.49003i	1.79770	−	0.395704i	0.814787	−	0.579760i	$-0.196854\pi$
$269$	29.4845	−	6.49003i	1.79770	−	0.395704i	0.982916	+	0.184056i	$0.0589226\pi$
$270$		0			0
$271$	6.39160	+	2.95707i	0.388262	+	0.179629i	0.604302	−	0.796755i	$-0.293452\pi$
$271$	6.39160	+	2.95707i	0.388262	+	0.179629i	−0.216040	+	0.976384i	$0.569314\pi$
$272$	4.74940	−	17.1058i	0.287974	−	1.03719i
$273$		0			0
$274$	8.59716	−	10.1214i	0.519373	−	0.611454i
$275$	2.14124	+	5.37411i	0.129122	+	0.324071i
$276$		0			0
$277$	−4.24669	−	15.2952i	−0.255159	−	0.919000i	−0.974508	−	0.224351i	$-0.927974\pi$
$277$	−4.24669	−	15.2952i	−0.255159	−	0.919000i	0.719349	−	0.694649i	$-0.244440\pi$
$278$	20.5130	−	6.91163i	1.23029	−	0.414532i
$279$		0			0
$280$	−5.09191	+	9.60436i	−0.304300	+	0.573970i
$281$	−6.91504	−	8.14101i	−0.412517	−	0.485652i	0.516187	−	0.856476i	$-0.327351\pi$
$281$	−6.91504	−	8.14101i	−0.412517	−	0.485652i	−0.928703	+	0.370824i	$0.879075\pi$
$282$		0			0
$283$	−4.66278	+	0.507108i	−0.277174	+	0.0301445i	−0.245650	−	0.969359i	$-0.579001\pi$
$283$	−4.66278	+	0.507108i	−0.277174	+	0.0301445i	−0.0315236	+	0.999503i	$0.510036\pi$
$284$	0.161378	+	0.238015i	0.00957602	+	0.0141236i
$285$		0			0
$286$	−3.50736	−	3.32235i	−0.207395	−	0.196455i
$287$	1.44979	−	26.7397i	0.0855781	−	1.57840i
$288$		0			0
$289$	36.1551	−	27.4844i	2.12677	−	1.61673i
$290$	−7.44819	−	0.810040i	−0.437373	−	0.0475672i
$291$		0			0
$292$	−0.526342	+	1.32102i	−0.0308019	+	0.0773068i
$293$	8.14496	+	4.90066i	0.475834	+	0.286300i	0.733198	−	0.680015i	$-0.238027\pi$
$293$	8.14496	+	4.90066i	0.475834	+	0.286300i	−0.257365	+	0.966314i	$0.582854\pi$
$294$		0			0
$295$	6.12348	+	0.350737i	0.356523	+	0.0204207i
$296$	24.7949			1.44118
$297$		0			0
$298$	7.62752	−	19.1436i	0.441850	−	1.10896i
$299$	3.64673	+	6.87847i	0.210896	+	0.397792i
$300$		0			0
$301$	−40.0882	+	30.4743i	−2.31065	+	1.75651i
$302$	14.0055	+	4.71901i	0.805927	+	0.271548i
$303$		0			0
$304$	−8.44492	−	7.99946i	−0.484350	−	0.458800i
$305$	6.59522	+	5.01356i	0.377641	+	0.287075i
$306$		0			0
$307$	−9.36164	+	1.01814i	−0.534297	+	0.0581083i	−0.371291	−	0.928517i	$-0.621085\pi$
$307$	−9.36164	+	1.01814i	−0.534297	+	0.0581083i	−0.163006	+	0.986625i	$0.552119\pi$
$308$	2.80583	−	2.65782i	0.159877	−	0.151443i
$309$		0			0
$310$	1.83861	−	3.46799i	0.104426	−	0.196968i
$311$	−10.1967	+	15.0390i	−0.578203	+	0.852785i	−0.998508	−	0.0545974i	$-0.982612\pi$
$311$	−10.1967	+	15.0390i	−0.578203	+	0.852785i	0.420306	+	0.907383i	$0.361923\pi$
$312$		0			0
$313$	−5.64119	−	20.3177i	−0.318859	−	1.14843i	−0.933192	−	0.359379i	$-0.882989\pi$
$313$	−5.64119	−	20.3177i	−0.318859	−	1.14843i	0.614333	−	0.789047i	$-0.289425\pi$
$314$	3.67574	−	22.4210i	0.207434	−	1.26529i
$315$		0			0
$316$	−2.00554	+	2.36111i	−0.112821	+	0.132823i
$317$	0.181796	+	3.35302i	0.0102107	+	0.188324i	0.999189	+	0.0402646i	$0.0128201\pi$
$317$	0.181796	+	3.35302i	0.0102107	+	0.188324i	−0.988978	+	0.148060i	$0.952697\pi$
$318$		0			0
$319$	9.75210	+	4.51180i	0.546013	+	0.252612i
$320$	−6.71620	−	1.47835i	−0.375447	−	0.0826422i
$321$		0			0
$322$	11.4975	−	5.31929i	0.640728	−	0.296432i
$323$	−6.61633	−	40.3578i	−0.368142	−	2.24557i
$324$		0			0
$325$	−11.7602	+	7.07588i	−0.652338	+	0.392499i
$326$	−2.16636	−	13.2142i	−0.119983	−	0.731866i
$327$		0			0
$328$	18.2143	−	4.00928i	1.00572	−	0.221376i
$329$	16.0657	+	3.53633i	0.885731	+	0.194964i
$330$		0			0
$331$	−2.94133	+	10.5937i	−0.161670	+	0.582282i	0.837678	+	0.546165i	$0.183913\pi$
$331$	−2.94133	+	10.5937i	−0.161670	+	0.582282i	−0.999348	+	0.0361174i	$0.988501\pi$
$332$	−0.131361	−	2.42281i	−0.00720938	−	0.132969i
$333$		0			0
$334$	1.73049	+	4.34320i	0.0946881	+	0.237649i
$335$	−0.165673	+	1.01056i	−0.00905170	+	0.0552129i
$336$		0			0
$337$	25.2273	−	8.50006i	1.37422	−	0.463028i	0.467212	−	0.884146i	$-0.345259\pi$
$337$	25.2273	−	8.50006i	1.37422	−	0.463028i	0.907006	+	0.421118i	$0.138362\pi$
$338$	−2.01544	+	2.97256i	−0.109626	+	0.161686i
$339$		0			0
$340$	−2.69217	−	3.16947i	−0.146004	−	0.171889i
$341$	−4.08705	+	3.87146i	−0.221326	+	0.209651i
$342$		0			0
$343$	−13.7626	−	20.2983i	−0.743110	−	1.09601i
$344$	−27.9197	−	21.2240i	−1.50533	−	1.14432i
$345$		0			0
$346$	−0.415173	+	7.65742i	−0.0223199	+	0.411666i
$347$	8.50773	+	2.86659i	0.456719	+	0.153886i	0.538252	−	0.842784i	$-0.319085\pi$
$347$	8.50773	+	2.86659i	0.456719	+	0.153886i	−0.0815329	+	0.996671i	$0.525982\pi$
$348$		0			0
$349$	21.2727	+	2.31354i	1.13870	+	0.123841i	0.657982	−	0.753034i	$-0.271410\pi$
$349$	21.2727	+	2.31354i	1.13870	+	0.123841i	0.480718	+	0.876875i	$0.340376\pi$
$350$	10.4609	+	19.7314i	0.559161	+	1.05469i
$351$		0			0
$352$	4.04101	+	2.43140i	0.215387	+	0.129594i
$353$	−8.75208			−0.465826			−0.232913	−	0.972498i	$-0.574826\pi$
$353$	−8.75208			−0.465826			−0.232913	+	0.972498i	$0.574826\pi$
$354$		0			0
$355$	−0.348346			−0.0184883
$356$	−3.94664	−	2.37461i	−0.209171	−	0.125854i
$357$		0			0
$358$	−4.70815	−	8.88052i	−0.248834	−	0.469350i
$359$	−1.85696	−	0.201956i	−0.0980065	−	0.0106588i	0.0589844	−	0.998259i	$-0.481214\pi$
$359$	−1.85696	−	0.201956i	−0.0980065	−	0.0106588i	−0.156991	+	0.987600i	$0.550179\pi$
$360$		0			0
$361$	−7.38848	−	2.48947i	−0.388868	−	0.131025i
$362$	−0.402212	+	7.41836i	−0.0211398	+	0.389900i
$363$		0			0
$364$	7.29954	+	5.54897i	0.382600	+	0.290845i
$365$	−0.966689	−	1.42576i	−0.0505988	−	0.0746277i
$366$		0			0
$367$	−8.22928	+	7.79518i	−0.429565	+	0.406905i	−0.871698	−	0.490044i	$-0.836981\pi$
$367$	−8.22928	+	7.79518i	−0.429565	+	0.406905i	0.442133	+	0.896950i	$0.354222\pi$
$368$	3.59982	+	4.23804i	0.187654	+	0.220923i
$369$		0			0
$370$	−4.17836	+	6.16261i	−0.217222	+	0.320379i
$371$	−5.81150	+	1.95812i	−0.301718	+	0.101661i
$372$		0			0
$373$	−2.72783	+	16.6390i	−0.141242	+	0.861537i	0.817222	+	0.576323i	$0.195513\pi$
$373$	−2.72783	+	16.6390i	−0.141242	+	0.861537i	−0.958464	+	0.285214i	$0.907935\pi$
$374$	−4.49028	−	11.2698i	−0.232187	−	0.582745i
$375$		0			0
$376$	0.620265	+	11.4401i	0.0319877	+	0.589979i
$377$	−6.82008	+	24.5637i	−0.351252	+	1.26510i
$378$		0			0
$379$	7.93556	+	1.74675i	0.407622	+	0.0897244i	0.414048	−	0.910255i	$-0.364114\pi$
$379$	7.93556	+	1.74675i	0.407622	+	0.0897244i	−0.00642610	+	0.999979i	$0.502046\pi$
$380$	−2.66108	+	0.585749i	−0.136511	+	0.0300483i
$381$		0			0
$382$	4.75816	+	29.0235i	0.243448	+	1.48497i
$383$	−24.6615	+	14.8383i	−1.26014	+	0.758204i	−0.979468	−	0.201599i	$-0.935386\pi$
$383$	−24.6615	+	14.8383i	−1.26014	+	0.758204i	−0.280676	+	0.959802i	$0.590559\pi$
$384$		0			0
$385$	0.757412	+	4.62001i	0.0386013	+	0.235457i
$386$	0.763682	−	0.353317i	0.0388704	−	0.0179833i
$387$		0			0
$388$	6.63058	+	1.45950i	0.336617	+	0.0740950i
$389$	3.20473	+	1.48267i	0.162486	+	0.0751742i	0.499447	−	0.866345i	$-0.333537\pi$
$389$	3.20473	+	1.48267i	0.162486	+	0.0751742i	−0.336960	+	0.941519i	$0.609399\pi$
$390$		0			0
$391$	1.05840	+	19.5211i	0.0535258	+	0.987226i
$392$	25.0112	−	29.4454i	1.26326	−	1.48722i
$393$		0			0
$394$	−0.491576	+	2.99848i	−0.0247652	+	0.151061i
$395$	−1.00395	−	3.61591i	−0.0505143	−	0.181936i
$396$		0			0
$397$	−4.77515	+	7.04282i	−0.239658	+	0.353469i	−0.928429	−	0.371510i	$-0.878840\pi$
$397$	−4.77515	+	7.04282i	−0.239658	+	0.353469i	0.688771	+	0.724979i	$0.258151\pi$
$398$	−0.528412	+	0.996690i	−0.0264869	+	0.0499595i
$399$		0			0
$400$	−7.11670	+	6.74129i	−0.355835	+	0.337065i
$401$	−24.9046	+	2.70854i	−1.24368	+	0.135258i	−0.706195	−	0.708017i	$-0.749590\pi$
$401$	−24.9046	+	2.70854i	−1.24368	+	0.135258i	−0.537482	+	0.843275i	$0.680624\pi$
$402$		0			0
$403$	−10.6327	−	8.08278i	−0.529654	−	0.402632i
$404$	0.0950632	+	0.0900486i	0.00472957	+	0.00448009i
$405$		0			0
$406$	39.3106	+	13.2453i	1.95095	+	0.657352i
$407$	8.50105	−	6.46233i	0.421382	−	0.320326i
$408$		0			0
$409$	−7.67640	−	14.4792i	−0.379574	−	0.715952i	0.617955	−	0.786214i	$-0.287961\pi$
$409$	−7.67640	−	14.4792i	−0.379574	−	0.715952i	−0.997529	+	0.0702616i	$0.977617\pi$
$410$	−2.07294	+	5.20268i	−0.102375	+	0.256942i
$411$		0			0
$412$	4.05633			0.199841
$413$	−32.6941	−	9.18496i	−1.60877	−	0.451962i
$414$		0			0
$415$	2.51849	+	1.51533i	0.123628	+	0.0743845i
$416$	−4.14143	+	10.3942i	−0.203050	+	0.509618i
$417$		0			0
$418$	−7.90223	−	0.859419i	−0.386511	−	0.0420356i
$419$	17.9264	−	13.6273i	0.875760	−	0.665735i	−0.0675257	−	0.997718i	$-0.521510\pi$
$419$	17.9264	−	13.6273i	0.875760	−	0.665735i	0.943286	+	0.331982i	$0.107717\pi$
$420$		0			0
$421$	1.51998	−	28.0343i	0.0740791	−	1.36631i	−0.691225	−	0.722640i	$-0.742928\pi$
$421$	1.51998	−	28.0343i	0.0740791	−	1.36631i	0.765304	−	0.643669i	$-0.222589\pi$
$422$	−3.05748	−	2.89620i	−0.148836	−	0.140985i
$423$		0			0
$424$	−2.39684	−	3.53508i	−0.116401	−	0.171679i
$425$	−34.2623	+	3.72625i	−1.66196	+	0.180749i
$426$		0			0
$427$	−29.6951	−	34.9598i	−1.43705	−	1.69182i
$428$	3.06975	−	5.79016i	0.148382	−	0.279878i
$429$		0			0
$430$	9.98000	−	3.36265i	0.481278	−	0.162162i
$431$	3.64968	+	13.1450i	0.175799	+	0.633170i	0.997956	+	0.0639092i	$0.0203568\pi$
$431$	3.64968	+	13.1450i	0.175799	+	0.633170i	−0.822157	+	0.569261i	$0.807229\pi$
$432$		0			0
$433$	−1.95391	−	4.90393i	−0.0938987	−	0.235668i	0.874524	−	0.484982i	$-0.161174\pi$
$433$	−1.95391	−	4.90393i	−0.0938987	−	0.235668i	−0.968423	+	0.249314i	$0.919795\pi$
$434$	−14.0697	+	16.5641i	−0.675366	+	0.795102i
$435$		0			0
$436$	0.921456	−	3.31879i	0.0441298	−	0.158941i
$437$	11.6257	+	5.37861i	0.556132	+	0.257294i
$438$		0			0
$439$	−29.8771	+	6.57644i	−1.42595	+	0.313876i	−0.859888	−	0.510484i	$-0.829466\pi$
$439$	−29.8771	+	6.57644i	−1.42595	+	0.313876i	−0.566066	+	0.824360i	$0.691535\pi$
$440$	−2.95923	+	1.36908i	−0.141076	+	0.0652685i
$441$		0			0
$442$	24.6617	−	14.8384i	1.17304	−	0.705793i
$443$	13.4066	−	8.06647i	0.636966	−	0.383250i	−0.160135	−	0.987095i	$-0.551193\pi$
$443$	13.4066	−	8.06647i	0.636966	−	0.383250i	0.797102	+	0.603845i	$0.206366\pi$
$444$		0			0
$445$	5.06379	−	2.34276i	0.240047	−	0.111058i
$446$	5.77579	−	1.27135i	0.273492	−	0.0602001i
$447$		0			0
$448$	34.5570	+	15.9878i	1.63267	+	0.755352i
$449$	9.31068	−	33.5340i	0.439398	−	1.58257i	−0.330117	−	0.943940i	$-0.607088\pi$
$449$	9.31068	−	33.5340i	0.439398	−	1.58257i	0.769515	−	0.638629i	$-0.220498\pi$
$450$		0			0
$451$	5.19993	−	6.12183i	0.244855	−	0.288266i
$452$	−1.75180	−	4.39669i	−0.0823978	−	0.206803i
$453$		0			0
$454$	−3.96825	−	14.2923i	−0.186239	−	0.670773i
$455$	−10.5258	+	3.54656i	−0.493458	+	0.166265i
$456$		0			0
$457$	−3.79277	+	7.15393i	−0.177418	+	0.334647i	−0.956232	−	0.292608i	$-0.905477\pi$
$457$	−3.79277	+	7.15393i	−0.177418	+	0.334647i	0.778814	+	0.627255i	$0.215822\pi$
$458$	16.5281	+	19.4584i	0.772308	+	0.909231i
$459$		0			0
$460$	1.29490	−	0.140828i	0.0603748	−	0.00656616i
$461$	−3.00186	−	4.42741i	−0.139811	−	0.206205i	0.751337	−	0.659919i	$-0.229409\pi$
$461$	−3.00186	−	4.42741i	−0.139811	−	0.206205i	−0.891148	+	0.453714i	$0.850099\pi$
$462$		0			0
$463$	−2.09195	−	1.98160i	−0.0972214	−	0.0920930i	0.637545	−	0.770413i	$-0.279950\pi$
$463$	−2.09195	−	1.98160i	−0.0972214	−	0.0920930i	−0.734767	+	0.678320i	$0.762708\pi$
$464$	−0.985752	+	18.1811i	−0.0457624	+	0.844038i
$465$		0			0
$466$	−10.7314	+	8.15779i	−0.497122	+	0.377902i
$467$	−10.0330	−	1.09115i	−0.464272	−	0.0504926i	−0.127006	−	0.991902i	$-0.540537\pi$
$467$	−10.0330	−	1.09115i	−0.464272	−	0.0504926i	−0.337266	+	0.941409i	$0.609502\pi$
$468$		0			0
$469$	2.09866	−	5.26724i	0.0969071	−	0.243218i
$470$	−2.94789	−	1.77369i	−0.135976	−	0.0818140i
$471$		0			0
$472$	0.0721257	−	23.6514i	0.00331986	−	1.08864i
$473$	−15.1040			−0.694483
$474$		0			0
$475$	−8.35846	+	20.9782i	−0.383513	+	0.962544i
$476$	10.7850	+	20.3426i	0.494329	+	0.932404i
$477$		0			0
$478$	11.9545	−	9.08756i	0.546785	−	0.415655i
$479$	37.0448	+	12.4818i	1.69262	+	0.570310i	0.989976	−	0.141234i	$-0.0451069\pi$
$479$	37.0448	+	12.4818i	1.69262	+	0.570310i	0.702642	+	0.711543i	$0.252003\pi$
$480$		0			0
$481$	18.3928	+	17.4226i	0.838639	+	0.794401i
$482$	−13.2955	−	10.1070i	−0.605594	−	0.460360i
$483$		0			0
$484$	−6.05613	+	0.658644i	−0.275279	+	0.0299383i
$485$	−5.97083	+	5.65587i	−0.271121	+	0.256820i
$486$		0			0
$487$	−8.04378	+	15.1722i	−0.364498	+	0.687517i	−0.996143	−	0.0877408i	$-0.972035\pi$
$487$	−8.04378	+	15.1722i	−0.364498	+	0.687517i	0.631645	+	0.775258i	$0.282380\pi$
$488$	17.9276	−	26.4412i	0.811545	−	1.19694i
$489$		0			0
$490$	3.10367	+	11.1784i	0.140209	+	0.504989i
$491$	−5.31911	+	32.4451i	−0.240048	+	1.46423i	0.541668	+	0.840593i	$0.317793\pi$
$491$	−5.31911	+	32.4451i	−0.240048	+	1.46423i	−0.781716	+	0.623635i	$0.785655\pi$
$492$		0			0
$493$	−41.4426	+	48.7900i	−1.86648	+	2.19739i
$494$	−1.02098	−	18.8309i	−0.0459360	−	0.847240i
$495$		0			0
$496$	−8.65768	−	4.00547i	−0.388741	−	0.179851i
$497$	1.88362	+	0.414616i	0.0844918	+	0.0185981i
$498$		0			0
$499$	−38.9781	+	18.0332i	−1.74490	+	0.807277i	−0.756765	+	0.653687i	$0.773221\pi$
$499$	−38.9781	+	18.0332i	−1.74490	+	0.807277i	−0.988135	+	0.153589i	$0.950917\pi$
$500$	0.797276	+	4.86317i	0.0356553	+	0.217487i
$501$		0			0
$502$	−7.95689	+	4.78750i	−0.355133	+	0.213677i
$503$	−3.93390	−	23.9957i	−0.175404	−	1.06992i	−0.916946	−	0.399010i	$-0.869354\pi$
$503$	−3.93390	−	23.9957i	−0.175404	−	1.06992i	0.741543	−	0.670906i	$-0.234095\pi$
$504$		0			0
$505$	−0.154910	+	0.0340982i	−0.00689340	+	0.00151735i
$506$	3.71094	+	0.816840i	0.164972	+	0.0363130i
$507$		0			0
$508$	2.75710	−	9.93018i	0.122327	−	0.440580i
$509$	2.07068	+	38.1914i	0.0917813	+	1.69281i	0.575674	+	0.817679i	$0.304740\pi$
$509$	2.07068	+	38.1914i	0.0917813	+	1.69281i	−0.483893	+	0.875127i	$0.660778\pi$
$510$		0			0
$511$	3.53020	+	8.86012i	0.156167	+	0.391949i
$512$	−3.53167	+	21.5422i	−0.156079	+	0.952041i
$513$		0			0
$514$	−28.0540	+	9.45248i	−1.23741	+	0.416931i
$515$	−2.75750	+	4.06701i	−0.121510	+	0.179214i
$516$		0			0
$517$	3.19431	+	3.76063i	0.140486	+	0.165392i
$518$	29.9287	−	28.3499i	1.31499	−	1.24562i
$519$		0			0
$520$	−4.34118	−	6.40276i	−0.190373	−	0.280780i
$521$	33.7434	+	25.6510i	1.47832	+	1.12379i	0.963903	+	0.266254i	$0.0857860\pi$
$521$	33.7434	+	25.6510i	1.47832	+	1.12379i	0.514420	+	0.857538i	$0.328007\pi$
$522$		0			0
$523$	0.484092	−	8.92856i	0.0211679	−	0.390419i	−0.968682	−	0.248304i	$-0.920127\pi$
$523$	0.484092	−	8.92856i	0.0211679	−	0.390419i	0.989850	−	0.142115i	$-0.0453903\pi$
$524$	5.17209	+	1.74268i	0.225944	+	0.0761293i
$525$		0			0
$526$	−26.4088	−	2.87213i	−1.15148	−	0.125231i
$527$	−15.7097	−	29.6317i	−0.684326	−	1.29078i
$528$		0			0
$529$	14.4609	+	8.70081i	0.628733	+	0.378296i
$530$	1.28253			0.0557095
$531$		0			0
$532$	15.0865			0.654082
$533$	16.3285	+	9.82454i	0.707267	+	0.425548i
$534$		0			0
$535$	3.71858	+	7.01399i	0.160768	+	0.303241i
$536$	3.92571	+	0.426947i	0.169565	+	0.0184413i
$537$		0			0
$538$	33.1285	+	11.1623i	1.42827	+	0.481240i
$539$	0.900795	−	16.6142i	0.0388000	−	0.715624i
$540$		0			0
$541$	−3.00212	−	2.28215i	−0.129071	−	0.0981174i	0.538647	−	0.842532i	$-0.318936\pi$
$541$	−3.00212	−	2.28215i	−0.129071	−	0.0981174i	−0.667718	+	0.744414i	$0.732729\pi$
$542$	4.57634	+	6.74960i	0.196571	+	0.289920i
$543$		0			0
$544$	−20.3978	+	19.3218i	−0.874549	+	0.828417i
$545$	2.70112	+	3.18000i	0.115703	+	0.136216i
$546$		0			0
$547$	−13.9910	+	20.6352i	−0.598214	+	0.882300i	−0.999433	−	0.0336828i	$-0.989276\pi$
$547$	−13.9910	+	20.6352i	−0.598214	+	0.882300i	0.401219	+	0.915982i	$0.368587\pi$
$548$	−7.16417	+	2.41389i	−0.306038	+	0.103116i
$549$		0			0
$550$	−1.08372	+	6.61038i	−0.0462098	+	0.281868i
$551$	15.5253	+	38.9656i	0.661400	+	1.65999i
$552$		0			0
$553$	1.12489	+	20.7473i	0.0478350	+	0.882265i
$554$	4.91739	−	17.7109i	0.208920	−	0.752462i
$555$		0			0
$556$	−12.0346	−	2.64901i	−0.510379	−	0.112343i
$557$	−36.6543	+	8.06823i	−1.55309	+	0.341862i	−0.906912	−	0.421321i	$-0.861567\pi$
$557$	−36.6543	+	8.06823i	−1.55309	+	0.341862i	−0.646183	+	0.763183i	$0.723636\pi$
$558$		0			0
$559$	−5.79732	−	35.3621i	−0.245200	−	1.49566i
$560$	−6.79756	+	4.08996i	−0.287250	+	0.172832i
$561$		0			0
$562$	−2.00099	−	12.2055i	−0.0844067	−	0.514858i
$563$	3.18405	−	1.47310i	0.134192	−	0.0620837i	−0.351644	−	0.936134i	$-0.614377\pi$
$563$	3.18405	−	1.47310i	0.134192	−	0.0620837i	0.485836	+	0.874050i	$0.338515\pi$
$564$		0			0
$565$	5.59914	+	1.23246i	0.235558	+	0.0518502i
$566$	−4.92908	−	2.28043i	−0.207184	−	0.0958537i
$567$		0			0
$568$	0.0727227	+	1.34129i	0.00305138	+	0.0562793i
$569$	9.96616	−	11.7331i	0.417803	−	0.491876i	−0.512490	−	0.858693i	$-0.671277\pi$
$569$	9.96616	−	11.7331i	0.417803	−	0.491876i	0.930293	+	0.366817i	$0.119553\pi$
$570$		0			0
$571$	−5.59746	+	34.1430i	−0.234246	+	1.42884i	0.563635	+	0.826024i	$0.309402\pi$
$571$	−5.59746	+	34.1430i	−0.234246	+	1.42884i	−0.797881	+	0.602815i	$0.794046\pi$
$572$	0.735768	+	2.65000i	0.0307640	+	0.110802i
$573$		0			0
$574$	17.4015	−	25.6652i	0.726323	−	1.07125i
$575$	5.05642	−	9.53742i	0.210867	−	0.397738i
$576$		0			0
$577$	−7.20125	+	6.82139i	−0.299792	+	0.283978i	−0.822778	−	0.568363i	$-0.807577\pi$
$577$	−7.20125	+	6.82139i	−0.299792	+	0.283978i	0.522986	+	0.852342i	$0.324818\pi$
$578$	52.2801	−	5.68580i	2.17456	−	0.236498i
$579$		0			0
$580$	3.39541	+	2.58113i	0.140987	+	0.107175i
$581$	−11.8147	−	11.1915i	−0.490155	−	0.464300i
$582$		0			0
$583$	−1.74312	−	0.587326i	−0.0721927	−	0.0243245i
$584$	−5.28801	+	4.01984i	−0.218819	+	0.166342i
$585$		0			0
$586$	5.15572	+	9.72472i	0.212981	+	0.401724i
$587$	−10.6872	+	26.8227i	−0.441106	+	1.10709i	0.525493	+	0.850798i	$0.323881\pi$
$587$	−10.6872	+	26.8227i	−0.441106	+	1.10709i	−0.966599	+	0.256295i	$0.917498\pi$
$588$		0			0
$589$	−21.9754			−0.905481
$590$	5.86624	+	4.00358i	0.241509	+	0.164825i
$591$		0			0
$592$	15.5046	+	9.32880i	0.637235	+	0.383411i
$593$	0.0333929	−	0.0838098i	0.00137128	−	0.00344166i	−0.928289	−	0.371858i	$-0.878721\pi$
$593$	0.0333929	−	0.0838098i	0.00137128	−	0.00344166i	0.929661	+	0.368417i	$0.120100\pi$
$594$		0			0
$595$	−27.7279	−	3.01559i	−1.13673	−	0.123627i
$596$	−9.33916	+	7.09945i	−0.382547	+	0.290805i
$597$		0			0
$598$	−0.488059	+	9.00173i	−0.0199582	+	0.368108i
$599$	−4.53741	−	4.29806i	−0.185393	−	0.175614i	0.589374	−	0.807860i	$-0.299374\pi$
$599$	−4.53741	−	4.29806i	−0.185393	−	0.175614i	−0.774767	+	0.632246i	$0.782133\pi$
$600$		0			0
$601$	−0.938158	−	1.38368i	−0.0382683	−	0.0564415i	0.808074	−	0.589082i	$-0.200510\pi$
$601$	−0.938158	−	1.38368i	−0.0382683	−	0.0564415i	−0.846342	+	0.532640i	$0.821200\pi$
$602$	−57.9673	+	6.30433i	−2.36257	+	0.256945i
$603$		0			0
$604$	−5.44676	−	6.41242i	−0.221625	−	0.260918i
$605$	3.45659	−	6.51982i	0.140530	−	0.265068i
$606$		0			0
$607$	0.934319	−	0.314809i	0.0379228	−	0.0127777i	−0.300276	−	0.953852i	$-0.597079\pi$
$607$	0.934319	−	0.314809i	0.0379228	−	0.0127777i	0.338199	+	0.941075i	$0.390182\pi$
$608$	4.92507	+	17.7385i	0.199738	+	0.719392i
$609$		0			0
$610$	3.55069	+	8.91157i	0.143763	+	0.360819i
$611$	−7.57847	+	8.92207i	−0.306592	+	0.360948i
$612$		0			0
$613$	5.47497	−	19.7190i	0.221132	−	0.796445i	−0.766844	−	0.641834i	$-0.778174\pi$
$613$	5.47497	−	19.7190i	0.221132	−	0.796445i	0.987975	−	0.154611i	$-0.0494123\pi$
$614$	−9.89628	−	4.57851i	−0.399381	−	0.184774i
$615$		0			0
$616$	17.6310	−	3.88088i	0.710373	−	0.156365i
$617$	7.96916	−	3.68693i	0.320826	−	0.148430i	−0.252865	−	0.967502i	$-0.581373\pi$
$617$	7.96916	−	3.68693i	0.320826	−	0.148430i	0.573692	+	0.819071i	$0.305511\pi$
$618$		0			0
$619$	8.28427	−	4.98448i	0.332973	−	0.200343i	−0.339242	−	0.940699i	$-0.610171\pi$
$619$	8.28427	−	4.98448i	0.332973	−	0.200343i	0.672215	+	0.740356i	$0.265343\pi$
$620$	−1.91469	+	1.15203i	−0.0768957	+	0.0462666i
$621$		0			0
$622$	−19.0950	+	8.83428i	−0.765639	+	0.354222i
$623$	−30.1700	+	6.64091i	−1.20873	+	0.266063i
$624$		0			0
$625$	14.3779	+	6.65195i	0.575118	+	0.266078i
$626$	6.53213	−	23.5266i	0.261076	−	0.940312i
$627$		0			0
$628$	−8.37342	+	9.85795i	−0.334136	+	0.393375i
$629$	23.5473	+	59.0992i	0.938891	+	2.35644i
$630$		0			0
$631$	−2.67131	−	9.62119i	−0.106343	−	0.383014i	0.891156	−	0.453698i	$-0.149896\pi$
$631$	−2.67131	−	9.62119i	−0.106343	−	0.383014i	−0.997499	+	0.0706843i	$0.977482\pi$
$632$	−13.7133	+	4.62055i	−0.545486	+	0.183796i
$633$		0			0
$634$	−1.82130	+	3.43534i	−0.0723332	+	0.136435i
$635$	8.08204	+	9.51491i	0.320726	+	0.377588i
$636$		0			0
$637$	39.2435	−	4.26799i	1.55488	−	0.169104i
$638$	6.98244	+	10.2983i	0.276437	+	0.407714i
$639$		0			0
$640$	−1.65782	−	1.57037i	−0.0655310	−	0.0620742i
$641$	1.42450	−	26.2733i	0.0562642	−	1.03773i	−0.825008	−	0.565122i	$-0.808829\pi$
$641$	1.42450	−	26.2733i	0.0562642	−	1.03773i	0.881272	−	0.472610i	$-0.156688\pi$
$642$		0			0
$643$	4.57009	−	3.47409i	0.180227	−	0.137005i	−0.511171	−	0.859479i	$-0.670788\pi$
$643$	4.57009	−	3.47409i	0.180227	−	0.137005i	0.691398	+	0.722474i	$0.256995\pi$
$644$	−7.16953	−	0.779733i	−0.282519	−	0.0307258i
$645$		0			0
$646$	17.5281	−	43.9922i	0.689633	−	1.73085i
$647$	−1.57126	−	0.945395i	−0.0617726	−	0.0371673i	0.484333	−	0.874884i	$-0.339062\pi$
$647$	−1.57126	−	0.945395i	−0.0617726	−	0.0371673i	−0.546105	+	0.837717i	$0.683890\pi$
$648$		0			0
$649$	−6.13956	−	8.12779i	−0.240999	−	0.319044i
$650$	−15.8924			−0.623352
$651$		0			0
$652$	−2.82155	+	7.08157i	−0.110501	+	0.277336i
$653$	−16.4492	−	31.0265i	−0.643707	−	1.21416i	−0.963763	−	0.266762i	$-0.914046\pi$
$653$	−16.4492	−	31.0265i	−0.643707	−	1.21416i	0.320056	−	0.947399i	$-0.396298\pi$
$654$		0			0
$655$	−5.26326	+	4.00103i	−0.205653	+	0.156333i
$656$	12.8981	+	4.34588i	0.503587	+	0.169678i
$657$		0			0
$658$	13.8290	+	13.0996i	0.539112	+	0.510674i
$659$	12.7676	+	9.70566i	0.497354	+	0.378079i	0.823568	−	0.567217i	$-0.191980\pi$
$659$	12.7676	+	9.70566i	0.497354	+	0.378079i	−0.326214	+	0.945296i	$0.605773\pi$
$660$		0			0
$661$	16.0604	−	1.74667i	0.624677	−	0.0679377i	0.209694	−	0.977767i	$-0.432753\pi$
$661$	16.0604	−	1.74667i	0.624677	−	0.0679377i	0.414983	+	0.909829i	$0.363788\pi$
$662$	−9.24254	+	8.75500i	−0.359222	+	0.340273i
$663$		0			0
$664$	5.30892	−	10.0137i	0.206026	−	0.388606i
$665$	−10.2558	+	15.1262i	−0.397704	+	0.586569i
$666$		0			0
$667$	−5.36416	−	19.3200i	−0.207701	−	0.748072i
$668$	0.430586	−	2.62646i	0.0166599	−	0.101621i
$669$		0			0
$670$	−0.767662	+	0.903761i	−0.0296574	+	0.0349153i
$671$	−0.744852	−	13.7380i	−0.0287547	−	0.530349i
$672$		0			0
$673$	31.4438	+	14.5475i	1.21207	+	0.560763i	0.918594	−	0.395203i	$-0.129326\pi$
$673$	31.4438	+	14.5475i	1.21207	+	0.560763i	0.293476	+	0.955966i	$0.405188\pi$
$674$	30.1045	+	6.62649i	1.15958	+	0.255243i
$675$		0			0
$676$	1.85554	−	0.858465i	0.0713670	−	0.0330179i
$677$	5.73680	+	34.9929i	0.220483	+	1.34489i	0.832492	+	0.554037i	$0.186913\pi$
$677$	5.73680	+	34.9929i	0.220483	+	1.34489i	−0.612009	+	0.790851i	$0.709638\pi$
$678$		0			0
$679$	39.0180	−	23.4763i	1.49737	−	0.900939i
$680$	−3.14263	−	19.1692i	−0.120514	−	0.735106i
$681$		0			0
$682$	−6.36628	+	1.40132i	−0.243777	+	0.0536595i
$683$	−48.6714	−	10.7134i	−1.86236	−	0.409936i	−0.866370	−	0.499403i	$-0.833553\pi$
$683$	−48.6714	−	10.7134i	−1.86236	−	0.409936i	−0.995990	+	0.0894664i	$0.971484\pi$
$684$		0			0
$685$	2.44997	−	8.82400i	0.0936086	−	0.337148i
$686$	−1.53740	−	28.3556i	−0.0586981	−	1.08262i
$687$		0			0
$688$	−9.47325	−	23.7761i	−0.361164	−	0.906454i
$689$	0.706013	−	4.30649i	0.0268970	−	0.164064i
$690$		0			0
$691$	−28.1356	+	9.47999i	−1.07033	+	0.360636i	−0.798677	−	0.601760i	$-0.794466\pi$
$691$	−28.1356	+	9.47999i	−1.07033	+	0.360636i	−0.271652	+	0.962396i	$0.587570\pi$
$692$	2.44992	−	3.61337i	0.0931321	−	0.137360i
$693$		0			0
$694$	6.72995	+	7.92311i	0.255465	+	0.300757i
$695$	10.8371	−	10.2654i	0.411075	−	0.389391i
$696$		0			0
$697$	26.8540	+	39.6067i	1.01717	+	1.50021i
$698$	19.7253	+	14.9948i	0.746613	+	0.567560i
$699$		0			0
$700$	0.688304	−	12.6950i	0.0260155	−	0.479827i
$701$	−25.8068	−	8.69531i	−0.974708	−	0.328417i	−0.213513	−	0.976940i	$-0.568490\pi$
$701$	−25.8068	−	8.69531i	−0.974708	−	0.328417i	−0.761195	+	0.648523i	$0.775387\pi$
$702$		0			0
$703$	41.4397	+	4.50684i	1.56293	+	0.169979i
$704$	5.34956	+	10.0903i	0.201619	+	0.380294i
$705$		0			0
$706$	−8.68368	−	5.22479i	−0.326814	−	0.196638i
$707$	0.878231			0.0330293
$708$		0			0
$709$	26.0629			0.978812			0.489406	−	0.872056i	$-0.337214\pi$
$709$	26.0629			0.978812			0.489406	+	0.872056i	$0.337214\pi$
$710$	−0.345624	−	0.207955i	−0.0129710	−	0.00780441i
$711$		0			0
$712$	−10.0778	−	19.0088i	−0.377683	−	0.712386i
$713$	10.4433	+	1.13578i	0.391106	+	0.0425353i
$714$		0			0
$715$	−3.15715	−	1.06377i	−0.118071	−	0.0397827i
$716$	−0.309785	+	5.71365i	−0.0115772	+	0.213529i
$717$		0			0
$718$	−1.72188	−	1.30894i	−0.0642600	−	0.0488492i
$719$	−24.8663	−	36.6750i	−0.927356	−	1.36775i	−0.929924	−	0.367752i	$-0.880128\pi$
$719$	−24.8663	−	36.6750i	−0.927356	−	1.36775i	0.00256756	−	0.999997i	$-0.499183\pi$
$720$		0			0
$721$	19.7514	−	18.7095i	0.735579	−	0.696778i
$722$	−5.84458	−	6.88077i	−0.217513	−	0.256076i
$723$		0			0
$724$	2.37344	−	3.50056i	0.0882081	−	0.130097i
$725$	33.4972	−	11.2865i	1.24405	−	0.419171i
$726$		0			0
$727$	2.96185	−	18.0665i	0.109849	−	0.670049i	−0.873292	−	0.487198i	$-0.838019\pi$
$727$	2.96185	−	18.0665i	0.109849	−	0.670049i	0.983141	−	0.182851i	$-0.0585326\pi$
$728$	15.8533	+	39.7888i	0.587562	+	1.47467i
$729$		0			0
$730$	−0.107987	−	1.99171i	−0.00399679	−	0.0737165i
$731$	24.0730	−	86.7030i	0.890371	−	3.20683i
$732$		0			0
$733$	−32.1939	−	7.08642i	−1.18911	−	0.261743i	−0.424012	−	0.905657i	$-0.639378\pi$
$733$	−32.1939	−	7.08642i	−1.18911	−	0.261743i	−0.765098	+	0.643914i	$0.777309\pi$
$734$	−12.8185	+	2.82157i	−0.473140	+	0.104146i
$735$		0			0
$736$	−1.42373	−	8.68439i	−0.0524795	−	0.320111i
$737$	1.45722	−	0.876782i	0.0536775	−	0.0322967i
$738$		0			0
$739$	−3.02035	−	18.4233i	−0.111106	−	0.677714i	−0.982377	−	0.186912i	$-0.940152\pi$
$739$	−3.02035	−	18.4233i	−0.111106	−	0.677714i	0.871271	−	0.490802i	$-0.163296\pi$
$740$	3.84685	−	1.77974i	0.141413	−	0.0654246i
$741$		0			0
$742$	−6.93503	−	1.52652i	−0.254593	−	0.0560402i
$743$	−42.5593	−	19.6900i	−1.56135	−	0.722357i	−0.566531	−	0.824040i	$-0.691715\pi$
$743$	−42.5593	−	19.6900i	−1.56135	−	0.722357i	−0.994817	+	0.101683i	$0.967577\pi$
$744$		0			0
$745$	−0.769358	−	14.1900i	−0.0281871	−	0.519880i
$746$	−12.6397	+	14.8805i	−0.462771	+	0.544816i
$747$		0			0
$748$	−1.11729	+	6.81515i	−0.0408520	+	0.249186i
$749$	−11.7592	−	42.3529i	−0.429672	−	1.54754i
$750$		0			0
$751$	0.750798	−	1.10734i	0.0273970	−	0.0404075i	−0.813744	−	0.581224i	$-0.802574\pi$
$751$	0.750798	−	1.10734i	0.0273970	−	0.0404075i	0.841141	+	0.540816i	$0.181885\pi$
$752$	−3.91635	+	7.38702i	−0.142815	+	0.269377i
$753$		0			0
$754$	−21.4308	+	20.3003i	−0.780463	+	0.739294i
$755$	10.1320	−	1.10192i	0.368742	−	0.0401031i
$756$		0			0
$757$	18.7522	+	14.2551i	0.681561	+	0.518109i	0.887705	−	0.460413i	$-0.152299\pi$
$757$	18.7522	+	14.2551i	0.681561	+	0.518109i	−0.206144	+	0.978522i	$0.566092\pi$
$758$	6.83077	+	6.47045i	0.248105	+	0.235017i
$759$		0			0
$760$	−12.0616	−	4.06404i	−0.437521	−	0.147418i
$761$	36.4550	−	27.7124i	1.32149	−	1.00457i	0.323191	−	0.946334i	$-0.395244\pi$
$761$	36.4550	−	27.7124i	1.32149	−	1.00457i	0.998303	−	0.0582398i	$-0.0185488\pi$
$762$		0			0
$763$	−10.8208	−	20.4102i	−0.391740	−	0.738900i
$764$	6.19722	−	15.5539i	0.224208	−	0.562719i
$765$		0			0
$766$	−33.3269			−1.20415
$767$	16.6726	−	17.4938i	0.602011	−	0.631666i
$768$		0			0
$769$	6.84073	+	4.11593i	0.246683	+	0.148424i	0.633526	−	0.773721i	$-0.281607\pi$
$769$	6.84073	+	4.11593i	0.246683	+	0.148424i	−0.386843	+	0.922146i	$0.626434\pi$
$770$	−2.00655	+	5.03606i	−0.0723110	+	0.181487i
$771$		0			0
$772$	−0.476213	−	0.0517913i	−0.0171393	−	0.00186401i
$773$	−32.9287	+	25.0317i	−1.18436	+	0.900328i	−0.996641	−	0.0818941i	$-0.973903\pi$
$773$	−32.9287	+	25.0317i	−1.18436	+	0.900328i	−0.187721	+	0.982222i	$0.560110\pi$
$774$		0			0
$775$	−1.00260	+	18.4919i	−0.0360146	+	0.664250i
$776$	23.0242	+	21.8097i	0.826520	+	0.782921i
$777$		0			0
$778$	2.29457	+	3.38423i	0.0822642	+	0.121331i
$779$	31.1703	−	3.38998i	1.11679	−	0.121459i
$780$		0			0
$781$	0.374516	+	0.440914i	0.0134012	+	0.0157771i
$782$	−10.6035	+	20.0004i	−0.379182	+	0.715213i
$783$		0			0
$784$	26.7183	−	9.00245i	0.954225	−	0.321516i
$785$	−4.19164	−	15.0969i	−0.149606	−	0.538832i
$786$		0			0
$787$	4.31562	+	10.8314i	0.153835	+	0.386097i	0.985614	−	0.169009i	$-0.0540568\pi$
$787$	4.31562	+	10.8314i	0.153835	+	0.386097i	−0.831779	+	0.555106i	$0.812678\pi$
$788$	1.11982	−	1.31836i	0.0398920	−	0.0469645i
$789$		0			0
$790$	1.16251	−	4.18699i	0.0413603	−	0.148966i
$791$	−28.8094	−	13.3286i	−1.02434	−	0.473912i
$792$		0			0
$793$	31.8780	−	7.01688i	1.13202	−	0.249177i
$794$	−8.94224	+	4.13712i	−0.317348	+	0.146821i
$795$		0			0
$796$	0.550276	−	0.331090i	0.0195040	−	0.0117352i
$797$	−47.1170	+	28.3494i	−1.66897	+	1.00419i	−0.717444	+	0.696616i	$0.754688\pi$
$797$	−47.1170	+	28.3494i	−1.66897	+	1.00419i	−0.951526	+	0.307570i	$0.900484\pi$
$798$		0			0
$799$	−26.6787	+	12.3429i	−0.943823	+	0.436659i
$800$	15.1514	−	3.33507i	0.535682	−	0.117912i
$801$		0			0
$802$	−26.3269	−	12.1801i	−0.929636	−	0.430095i
$803$	−0.765322	+	2.75644i	−0.0270076	+	0.0972727i
$804$		0			0
$805$	5.65564	−	6.65834i	0.199335	−	0.234676i
$806$	−5.72438	−	14.3671i	−0.201633	−	0.506060i
$807$		0			0
$808$	0.163634	+	0.589355i	0.00575661	+	0.0207334i
$809$	−28.7012	+	9.67056i	−1.00908	+	0.339999i	−0.774825	−	0.632176i	$-0.782162\pi$
$809$	−28.7012	+	9.67056i	−1.00908	+	0.339999i	−0.234256	+	0.972175i	$0.575265\pi$
$810$		0			0
$811$	7.12872	−	13.4462i	0.250323	−	0.472160i	−0.726225	−	0.687457i	$-0.758727\pi$
$811$	7.12872	−	13.4462i	0.250323	−	0.472160i	0.976549	+	0.215297i	$0.0690720\pi$
$812$	−15.2879	−	17.9983i	−0.536500	−	0.631617i
$813$		0			0
$814$	12.2925	−	1.33689i	0.430851	−	0.0468579i
$815$	−5.18211	−	7.64305i	−0.181522	−	0.267724i
$816$		0			0
$817$	−42.8043	−	40.5464i	−1.49753	−	1.41854i
$818$	1.02737	−	18.9487i	0.0359211	−	0.662526i
$819$		0			0
$820$	2.53811	−	1.92942i	0.0886348	−	0.0673784i
$821$	−4.41732	−	0.480413i	−0.154166	−	0.0167665i	0.0307107	−	0.999528i	$-0.490223\pi$
$821$	−4.41732	−	0.480413i	−0.154166	−	0.0167665i	−0.184876	+	0.982762i	$0.559188\pi$
$822$		0			0
$823$	6.28245	−	15.7678i	0.218992	−	0.549629i	−0.777901	−	0.628386i	$-0.783716\pi$
$823$	6.28245	−	15.7678i	0.218992	−	0.549629i	0.996894	+	0.0787568i	$0.0250951\pi$
$824$	16.2355	+	9.76857i	0.565590	+	0.340304i
$825$		0			0
$826$	−26.9554	−	28.6308i	−0.937898	−	0.996194i
$827$	31.3425			1.08988			0.544942	−	0.838474i	$-0.316552\pi$
$827$	31.3425			1.08988			0.544942	+	0.838474i	$0.316552\pi$
$828$		0			0
$829$	−8.84002	+	22.1868i	−0.307027	+	0.770579i	0.691797	+	0.722092i	$0.256819\pi$
$829$	−8.84002	+	22.1868i	−0.307027	+	0.770579i	−0.998824	+	0.0484870i	$0.984560\pi$
$830$	1.59419	+	3.00697i	0.0553353	+	0.104373i
$831$		0			0
$832$	−21.5706	+	16.3975i	−0.747825	+	0.568482i
$833$	93.9364	+	31.6508i	3.25470	+	1.09664i
$834$		0			0
$835$	2.34066	+	2.21719i	0.0810019	+	0.0767291i
$836$	3.60240	+	2.73847i	0.124591	+	0.0947120i
$837$		0			0
$838$	25.9214	−	2.81913i	0.895441	−	0.0973851i
$839$	10.2400	−	9.69986i	0.353525	−	0.334876i	−0.490242	−	0.871586i	$-0.663092\pi$
$839$	10.2400	−	9.69986i	0.353525	−	0.334876i	0.843767	+	0.536710i	$0.180333\pi$
$840$		0			0
$841$	17.1699	−	32.3858i	0.592064	−	1.11675i
$842$	18.2440	−	26.9078i	0.628729	−	0.927305i
$843$		0			0
$844$	0.641393	+	2.31009i	0.0220776	+	0.0795165i
$845$	−0.400676	+	2.44401i	−0.0137837	+	0.0840766i
$846$		0			0
$847$	−26.4510	+	31.1405i	−0.908868	+	1.07000i
$848$	−0.168745	−	3.11232i	−0.00579472	−	0.106877i
$849$		0			0
$850$	−36.2190	−	16.7567i	−1.24230	−	0.574749i
$851$	−19.4604	−	4.28356i	−0.667093	−	0.146838i
$852$		0			0
$853$	−4.49931	+	2.08160i	−0.154053	+	0.0712727i	−0.495401	−	0.868664i	$-0.664979\pi$
$853$	−4.49931	+	2.08160i	−0.154053	+	0.0712727i	0.341347	+	0.939937i	$0.389117\pi$
$854$	−8.59281	−	52.4138i	−0.294040	−	1.79356i
$855$		0			0
$856$	26.2308	−	15.7825i	0.896549	−	0.539435i
$857$	6.72149	+	40.9993i	0.229602	+	1.40051i	0.810121	+	0.586263i	$0.199401\pi$
$857$	6.72149	+	40.9993i	0.229602	+	1.40051i	−0.580519	+	0.814247i	$0.697150\pi$
$858$		0			0
$859$	−42.6648	+	9.39122i	−1.45570	+	0.320424i	−0.871184	−	0.490956i	$-0.836648\pi$
$859$	−42.6648	+	9.39122i	−1.45570	+	0.320424i	−0.584519	+	0.811380i	$0.698717\pi$
$860$	−5.85507	−	1.28880i	−0.199656	−	0.0439476i
$861$		0			0
$862$	−4.22609	+	15.2210i	−0.143941	+	0.518429i
$863$	−0.837052	−	15.4385i	−0.0284936	−	0.525533i	−0.977586	−	0.210536i	$-0.932479\pi$
$863$	−0.837052	−	15.4385i	−0.0284936	−	0.525533i	0.949093	−	0.314997i	$-0.102004\pi$
$864$		0			0
$865$	1.95742	+	4.91275i	0.0665542	+	0.167038i
$866$	0.988904	−	6.03204i	0.0336043	−	0.204977i
$867$		0			0
$868$	11.7245	−	3.95045i	0.397956	−	0.134087i
$869$	−3.49741	+	5.15829i	−0.118641	+	0.174983i
$870$		0			0
$871$	2.61208	+	3.07517i	0.0885068	+	0.104198i
$872$	11.6805	−	11.0644i	0.395553	−	0.374688i
$873$		0			0
$874$	8.32391	+	12.2768i	0.281560	+	0.415270i
$875$	26.3131	+	20.0027i	0.889547	+	0.676216i
$876$		0			0
$877$	−0.906204	+	16.7140i	−0.0306003	+	0.564390i	0.942528	+	0.334127i	$0.108441\pi$
$877$	−0.906204	+	16.7140i	−0.0306003	+	0.564390i	−0.973128	+	0.230263i	$0.926041\pi$
$878$	−33.5695	−	11.3109i	−1.13292	−	0.381724i
$879$		0			0
$880$	−2.36554	−	0.257268i	−0.0797425	−	0.00867252i
$881$	−13.9870	−	26.3823i	−0.471235	−	0.888843i	−0.999216	−	0.0395869i	$-0.987396\pi$
$881$	−13.9870	−	26.3823i	−0.471235	−	0.888843i	0.527982	−	0.849256i	$-0.322949\pi$
$882$		0			0
$883$	35.5740	+	21.4042i	1.19716	+	0.720307i	0.967477	−	0.252958i	$-0.0814036\pi$
$883$	35.5740	+	21.4042i	1.19716	+	0.720307i	0.229683	+	0.973266i	$0.426231\pi$
$884$	−16.3847			−0.551078
$885$		0			0
$886$	18.1173			0.608663
$887$	13.1844	+	7.93278i	0.442688	+	0.266357i	0.719400	−	0.694596i	$-0.244417\pi$
$887$	13.1844	+	7.93278i	0.442688	+	0.266357i	−0.276711	+	0.960953i	$0.589245\pi$
$888$		0			0
$889$	−32.3771	−	61.0697i	−1.08589	−	2.04821i
$890$	6.42280	+	0.698521i	0.215293	+	0.0234145i
$891$		0			0
$892$	−3.19051	−	1.07501i	−0.106826	−	0.0359939i
$893$	−1.04276	+	19.2326i	−0.0348946	+	0.643593i
$894$		0			0
$895$	−5.51810	−	4.19475i	−0.184450	−	0.140215i
$896$	7.09522	+	10.4647i	0.237035	+	0.349600i
$897$		0			0
$898$	29.2570	−	27.7137i	0.976318	−	0.924817i
$899$	22.2688	+	26.2169i	0.742706	+	0.874381i
$900$		0			0
$901$	6.14969	−	9.07012i	0.204876	−	0.302170i
$902$	8.81388	−	2.96974i	0.293470	−	0.0988816i
$903$		0			0
$904$	3.57664	−	21.8165i	0.118957	−	0.725607i
$905$	1.89631	+	4.75937i	0.0630354	+	0.158207i
$906$		0			0
$907$	2.67775	+	49.3882i	0.0889132	+	1.63991i	0.614321	+	0.789057i	$0.289430\pi$
$907$	2.67775	+	49.3882i	0.0889132	+	1.63991i	−0.525407	+	0.850851i	$0.676087\pi$
$908$	−2.25904	+	8.13633i	−0.0749689	+	0.270014i
$909$		0			0
$910$	−12.5608	−	2.76484i	−0.416386	−	0.0916534i
$911$	46.2768	−	10.1863i	1.53322	−	0.337487i	0.633425	−	0.773804i	$-0.281648\pi$
$911$	46.2768	−	10.1863i	1.53322	−	0.337487i	0.899793	+	0.436317i	$0.143717\pi$
$912$		0			0
$913$	−0.789692	−	4.81691i	−0.0261350	−	0.159416i
$914$	−8.03386	+	4.83381i	−0.265737	+	0.159888i
$915$		0			0
$916$	−2.35134	−	14.3425i	−0.0776903	−	0.473890i
$917$	33.2223	−	15.3703i	1.09710	−	0.507571i
$918$		0			0
$919$	12.8102	+	2.81973i	0.422568	+	0.0930143i	0.421163	−	0.906985i	$-0.361622\pi$
$919$	12.8102	+	2.81973i	0.422568	+	0.0930143i	0.00140458	+	0.999999i	$0.499553\pi$
$920$	5.52198	+	2.55474i	0.182054	+	0.0842273i
$921$		0			0
$922$	−0.335333	−	6.18485i	−0.0110436	−	0.203687i
$923$	−0.888535	+	1.04606i	−0.0292465	+	0.0344316i
$924$		0			0
$925$	5.68307	−	34.6652i	0.186858	−	1.13978i
$926$	−0.892631	−	3.21497i	−0.0293337	−	0.105650i
$927$		0			0
$928$	16.1714	−	23.8510i	0.530852	−	0.782948i
$929$	11.0864	−	20.9112i	0.363733	−	0.686073i	−0.632332	−	0.774697i	$-0.717902\pi$
$929$	11.0864	−	20.9112i	0.363733	−	0.686073i	0.996065	+	0.0886242i	$0.0282470\pi$
$930$		0			0
$931$	47.1532	−	44.6659i	1.54538	−	1.46387i
$932$	7.62893	−	0.829696i	0.249894	−	0.0271776i
$933$		0			0
$934$	−9.30319	−	7.07210i	−0.304410	−	0.231406i
$935$	−6.07356	−	5.75318i	−0.198627	−	0.188149i
$936$		0			0
$937$	−6.61401	−	2.22852i	−0.216070	−	0.0728025i	0.209185	−	0.977876i	$-0.432919\pi$
$937$	−6.61401	−	2.22852i	−0.216070	−	0.0728025i	−0.425255	+	0.905074i	$0.639816\pi$
$938$	5.22668	−	3.97322i	0.170657	−	0.129730i
$939$		0			0
$940$	0.917386	+	1.73037i	0.0299218	+	0.0564386i
$941$	−14.4622	+	36.2975i	−0.471455	+	1.18326i	0.480491	+	0.877000i	$0.340458\pi$
$941$	−14.4622	+	36.2975i	−0.471455	+	1.18326i	−0.951947	+	0.306264i	$0.900921\pi$
$942$		0			0
$943$	−14.9882			−0.488084
$944$	8.94366	−	14.7624i	0.291091	−	0.480475i
$945$		0			0
$946$	−14.9860	−	9.01675i	−0.487236	−	0.293160i
$947$	14.0994	−	35.3867i	0.458168	−	1.14991i	−0.500588	−	0.865685i	$-0.666883\pi$
$947$	14.0994	−	35.3867i	0.458168	−	1.14991i	0.958756	−	0.284229i	$-0.0917377\pi$
$948$		0			0
$949$	−6.74723	−	0.733806i	−0.219025	−	0.0238204i
$950$	−20.8166	+	15.8244i	−0.675381	+	0.513411i
$951$		0			0
$952$	−5.82275	+	107.394i	−0.188717	+	3.48067i
$953$	−18.4851	−	17.5100i	−0.598790	−	0.567204i	0.327103	−	0.944989i	$-0.393928\pi$
$953$	−18.4851	−	17.5100i	−0.598790	−	0.567204i	−0.925894	+	0.377784i	$0.876686\pi$
$954$		0			0
$955$	11.3819	+	16.7871i	0.368310	+	0.543217i
$956$	−8.49842	+	0.924259i	−0.274859	+	0.0298927i
$957$		0			0
$958$	29.3039	+	34.4992i	0.946765	+	1.11462i
$959$	−23.7504	+	44.7981i	−0.766942	+	1.44661i
$960$		0			0
$961$	12.2990	−	4.14401i	0.396742	−	0.133678i
$962$	7.84815	+	28.2665i	0.253035	+	0.911348i
$963$		0			0
$964$	3.51908	+	8.83223i	0.113342	+	0.284467i
$965$	0.375658	−	0.442259i	0.0120929	−	0.0142368i
$966$		0			0
$967$	9.62691	−	34.6730i	0.309581	−	1.11501i	−0.631096	−	0.775705i	$-0.717395\pi$
$967$	9.62691	−	34.6730i	0.309581	−	1.11501i	0.940677	−	0.339304i	$-0.110192\pi$
$968$	−25.8259	−	11.9483i	−0.830075	−	0.384034i
$969$		0			0
$970$	−9.30059	+	2.04722i	−0.298624	+	0.0657321i
$971$	−26.1848	+	12.1144i	−0.840312	+	0.388770i	−0.792340	−	0.610079i	$-0.791138\pi$
$971$	−26.1848	+	12.1144i	−0.840312	+	0.388770i	−0.0479711	+	0.998849i	$0.515276\pi$
$972$		0			0
$973$	−70.8179	+	42.6097i	−2.27032	+	1.36601i
$974$	−17.0384	+	10.2516i	−0.545944	+	0.328484i
$975$		0			0
$976$	21.1586	−	9.78900i	0.677269	−	0.313338i
$977$	−26.9648	+	5.93540i	−0.862680	+	0.189890i	−0.624207	−	0.781259i	$-0.714578\pi$
$977$	−26.9648	+	5.93540i	−0.862680	+	0.189890i	−0.238473	+	0.971149i	$0.576647\pi$
$978$		0			0
$979$	−8.40952	−	3.89066i	−0.268769	−	0.124346i
$980$	1.76685	−	6.36362i	0.0564400	−	0.203278i
$981$		0			0
$982$	−24.6465	+	29.0161i	−0.786503	+	0.925943i
$983$	−1.23721	−	3.10515i	−0.0394607	−	0.0990390i	0.907926	−	0.419131i	$-0.137665\pi$
$983$	−1.23721	−	3.10515i	−0.0394607	−	0.0990390i	−0.947386	+	0.320092i	$0.896286\pi$
$984$		0			0
$985$	0.560570	+	2.01899i	0.0178612	+	0.0643304i
$986$	−70.2452	+	23.6684i	−2.23706	+	0.753754i
$987$		0			0
$988$	−5.02872	+	9.48516i	−0.159985	+	0.301763i
$989$	18.2462	+	21.4811i	0.580195	+	0.683059i
$990$		0			0
$991$	3.89177	−	0.423256i	0.123626	−	0.0134452i	−0.0460967	−	0.998937i	$-0.514678\pi$
$991$	3.89177	−	0.423256i	0.123626	−	0.0134452i	0.169723	+	0.985492i	$0.445713\pi$
$992$	8.47243	+	12.4959i	0.269000	+	0.396745i
$993$		0			0
$994$	1.62138	+	1.53585i	0.0514271	+	0.0487143i
$995$	−0.0421169	+	0.776801i	−0.00133520	+	0.0246262i
$996$		0			0
$997$	18.0485	−	13.7201i	0.571603	−	0.434521i	−0.279029	−	0.960283i	$-0.590013\pi$
$997$	18.0485	−	13.7201i	0.571603	−	0.434521i	0.850632	+	0.525761i	$0.176220\pi$
$998$	−49.4389	−	5.37680i	−1.56496	−	0.170200i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.b.316.4		140
3.2	odd	2		177.2.e.b.139.2	✓	140
59.45	even	29	inner	531.2.i.b.163.4		140
177.104	odd	58		177.2.e.b.163.2	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.139.2	✓	140	3.2	odd	2
177.2.e.b.163.2	yes	140	177.104	odd	58
531.2.i.b.163.4		140	59.45	even	29	inner
531.2.i.b.316.4		140	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.992185 + 0.596978i) q^{2} +(-0.308769 - 0.582400i) q^{4} +(0.793835 + 0.0863348i) q^{5} +(-4.18976 - 1.41169i) q^{7} +(0.166703 - 3.07465i) q^{8} +O(q^{10})\)	\(q+(0.992185 + 0.596978i) q^{2} +(-0.308769 - 0.582400i) q^{4} +(0.793835 + 0.0863348i) q^{5} +(-4.18976 - 1.41169i) q^{7} +(0.166703 - 3.07465i) q^{8} +(0.736091 + 0.559562i) q^{10} +(-0.744195 - 1.09760i) q^{11} +(2.28411 - 2.16363i) q^{13} +(-3.31426 - 3.90185i) q^{14} +(1.26104 - 1.85990i) q^{16} +(7.48680 - 2.52260i) q^{17} +(0.837472 - 5.10835i) q^{19} +(-0.194830 - 0.488987i) q^{20} +(-0.0831328 - 1.53329i) q^{22} +(-0.662011 + 2.38435i) q^{23} +(-4.26038 - 0.937781i) q^{25} +(3.55790 - 0.783152i) q^{26} +(0.471496 + 2.87600i) q^{28} +(-6.94296 + 4.17744i) q^{29} +(-0.686795 - 4.18927i) q^{31} +(-3.22765 + 1.49327i) q^{32} +(8.93422 + 1.96657i) q^{34} +(-3.20410 - 1.48237i) q^{35} +(0.435953 + 8.04068i) q^{37} +(3.88050 - 4.56848i) q^{38} +(0.397784 - 2.42637i) q^{40} +(1.62041 + 5.83619i) q^{41} +(6.39177 - 9.42715i) q^{43} +(-0.409461 + 0.772325i) q^{44} +(-2.08024 + 1.97051i) q^{46} +(-3.69898 + 0.402288i) q^{47} +(9.98853 + 7.59308i) q^{49} +(-3.66725 - 3.47380i) q^{50} +(-1.96536 - 0.662206i) q^{52} +(1.10424 - 0.839421i) q^{53} +(-0.496006 - 0.935567i) q^{55} +(-5.03891 + 12.6467i) q^{56} -9.38254 q^{58} +(7.67111 - 0.392457i) q^{59} +(8.88976 + 5.34879i) q^{61} +(1.81947 - 4.56653i) q^{62} +(-8.56172 - 0.931143i) q^{64} +(2.00000 - 1.52036i) q^{65} +(-0.0694302 + 1.28056i) q^{67} +(-3.78085 - 3.58141i) q^{68} +(-2.29411 - 3.38356i) q^{70} +(-0.433685 + 0.0471661i) q^{71} +(-1.39656 - 1.64416i) q^{73} +(-4.36756 + 8.23809i) q^{74} +(-3.23369 + 1.08956i) q^{76} +(1.56851 + 5.64927i) q^{77} +(-1.73950 - 4.36581i) q^{79} +(1.16163 - 1.36758i) q^{80} +(-1.87633 + 6.75792i) q^{82} +(3.34065 + 1.54555i) q^{83} +(6.16107 - 1.35615i) q^{85} +(11.9696 - 5.53773i) q^{86} +(-3.49881 + 2.10516i) q^{88} +(5.98712 - 3.60233i) q^{89} +(-12.6243 + 5.84060i) q^{91} +(1.59305 - 0.350658i) q^{92} +(-3.91022 - 1.80906i) q^{94} +(1.10584 - 3.98289i) q^{95} +(-6.66777 + 7.84990i) q^{97} +(5.37756 + 13.4967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) \) 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8	\( 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29} - 12 q^{31} + 150 q^{32} - 2 q^{34} - 6 q^{35} + 12 q^{37} + 12 q^{38} - 66 q^{40} + 4 q^{41} - 60 q^{43} - 20 q^{44} + 76 q^{46} + 25 q^{47} + 31 q^{49} - 137 q^{50} + 118 q^{52} - 48 q^{53} + 93 q^{55} - 228 q^{56} - 120 q^{58} - 57 q^{59} + 72 q^{61} + 179 q^{62} + 249 q^{64} + 39 q^{65} + 40 q^{67} - 94 q^{68} + 94 q^{70} - 30 q^{71} - 205 q^{73} - 66 q^{74} - 216 q^{76} + 46 q^{77} + 4 q^{79} + 356 q^{80} - 28 q^{82} - 4 q^{83} + 50 q^{85} + 18 q^{86} - 162 q^{88} - 26 q^{89} - 198 q^{91} - 10 q^{92} - 4 q^{94} + 326 q^{95} - 20 q^{97} + 143 q^{98}+O(q^{100}) \) 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8 - 116 * q^10 - 2 * q^11 + 4 * q^13 + 43 * q^14 + 7 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 6 * q^23 - 57 * q^25 - 12 * q^26 - 10 * q^28 + 4 * q^29 - 12 * q^31 + 150 * q^32 - 2 * q^34 - 6 * q^35 + 12 * q^37 + 12 * q^38 - 66 * q^40 + 4 * q^41 - 60 * q^43 - 20 * q^44 + 76 * q^46 + 25 * q^47 + 31 * q^49 - 137 * q^50 + 118 * q^52 - 48 * q^53 + 93 * q^55 - 228 * q^56 - 120 * q^58 - 57 * q^59 + 72 * q^61 + 179 * q^62 + 249 * q^64 + 39 * q^65 + 40 * q^67 - 94 * q^68 + 94 * q^70 - 30 * q^71 - 205 * q^73 - 66 * q^74 - 216 * q^76 + 46 * q^77 + 4 * q^79 + 356 * q^80 - 28 * q^82 - 4 * q^83 + 50 * q^85 + 18 * q^86 - 162 * q^88 - 26 * q^89 - 198 * q^91 - 10 * q^92 - 4 * q^94 + 326 * q^95 - 20 * q^97 + 143 * q^98

Introduction

L-functions

Modular forms

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