LMFDB - Embedded newform 531.2.i.b.163.4

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			163.4
Character	$\chi$	$=$	531.163
Dual form			531.2.i.b.316.4

$q$-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 $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{24}{29}\right)$

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	−0.119580	−	0.992825i	$-0.538155\pi$
$2$	0.992185	−	0.596978i	0.701580	−	0.422127i	0.821160	+	0.570698i	$0.193327\pi$
$3$		0			0
$3$		0			0
$4$	−0.308769	+	0.582400i	−0.154384	+	0.291200i
$5$	0.793835	−	0.0863348i	0.355014	−	0.0386101i	0.0711254	−	0.997467i	$-0.477341\pi$
$5$	0.793835	−	0.0863348i	0.355014	−	0.0386101i	0.283888	+	0.958857i	$0.408375\pi$
$6$		0			0
$7$	−4.18976	+	1.41169i	−1.58358	+	0.533570i	−0.967230	−	0.253903i	$-0.918286\pi$
$7$	−4.18976	+	1.41169i	−1.58358	+	0.533570i	−0.616349	+	0.787473i	$0.711389\pi$
$8$	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	−0.923172	−	0.384388i	$-0.874412\pi$
$11$	−0.744195	+	1.09760i	−0.224383	+	0.330940i	0.698789	+	0.715328i	$0.253723\pi$
$12$		0			0
$13$	2.28411	+	2.16363i	0.633499	+	0.600082i	0.935543	−	0.353212i	$-0.114911\pi$
$13$	2.28411	+	2.16363i	0.633499	+	0.600082i	−0.302045	+	0.953294i	$0.597669\pi$
$14$	−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	0.999410	+	0.0343397i	$0.0109328\pi$
$17$	7.48680	+	2.52260i	1.81582	+	0.611819i	0.816405	+	0.577480i	$0.195964\pi$
$18$		0			0
$19$	0.837472	+	5.10835i	0.192129	+	1.17194i	0.890085	+	0.455795i	$0.150645\pi$
$19$	0.837472	+	5.10835i	0.192129	+	1.17194i	−0.697956	+	0.716141i	$0.745907\pi$
$20$	−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	0.861912	−	0.507057i	$-0.169267\pi$
$23$	−0.662011	−	2.38435i	−0.138039	−	0.497171i	−0.999951	+	0.00988634i	$0.996853\pi$
$24$		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	−0.304997	−	0.952353i	$-0.598655\pi$
$29$	−6.94296	−	4.17744i	−1.28928	−	0.775732i	−0.984279	+	0.176622i	$0.943483\pi$
$30$		0			0
$31$	−0.686795	+	4.18927i	−0.123352	+	0.752414i	0.850626	+	0.525771i	$0.176223\pi$
$31$	−0.686795	+	4.18927i	−0.123352	+	0.752414i	−0.973978	+	0.226643i	$0.927225\pi$
$32$	−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	−0.712649	−	0.701521i	$-0.752505\pi$
$37$	0.435953	−	8.04068i	0.0716702	−	1.32188i	0.784319	−	0.620358i	$-0.213013\pi$
$38$	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	−0.722431	−	0.691443i	$-0.756975\pi$
$41$	1.62041	−	5.83619i	0.253065	−	0.911459i	0.975496	−	0.220016i	$-0.0706109\pi$
$42$		0			0
$43$	6.39177	+	9.42715i	0.974735	+	1.43763i	0.897704	+	0.440598i	$0.145234\pi$
$43$	6.39177	+	9.42715i	0.974735	+	1.43763i	0.0770311	+	0.997029i	$0.475456\pi$
$44$	−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	−0.165714	−	0.986174i	$-0.552993\pi$
$47$	−3.69898	−	0.402288i	−0.539551	−	0.0586797i	−0.373837	+	0.927494i	$0.621958\pi$
$48$		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	0.678261	−	0.734821i	$-0.262734\pi$
$53$	1.10424	+	0.839421i	0.151679	+	0.115303i	−0.526582	+	0.850124i	$0.676527\pi$
$54$		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	0.183696	−	0.982983i	$-0.441194\pi$
$61$	8.88976	−	5.34879i	1.13822	−	0.684843i	0.954522	+	0.298140i	$0.0963664\pi$
$62$	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	−0.999706	−	0.0242504i	$-0.992280\pi$
$67$	−0.0694302	−	1.28056i	−0.00848225	−	0.156446i	0.991224	−	0.132195i	$-0.0422027\pi$
$68$	−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	0.0823483	−	0.996604i	$-0.473758\pi$
$71$	−0.433685	−	0.0471661i	−0.0514689	−	0.00559758i	−0.133817	+	0.991006i	$0.542724\pi$
$72$		0			0
$73$	−1.39656	+	1.64416i	−0.163455	+	0.192434i	−0.837792	−	0.545990i	$-0.816154\pi$
$73$	−1.39656	+	1.64416i	−0.163455	+	0.192434i	0.674337	+	0.738424i	$0.264430\pi$
$74$	−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	−0.993779	−	0.111373i	$-0.964475\pi$
$79$	−1.73950	+	4.36581i	−0.195709	+	0.491191i	0.798070	+	0.602565i	$0.205854\pi$
$80$	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	−0.227890	−	0.973687i	$-0.573183\pi$
$83$	3.34065	−	1.54555i	0.366684	−	0.169646i	0.594574	+	0.804041i	$0.297321\pi$
$84$		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	0.796216	−	0.605013i	$-0.206832\pi$
$89$	5.98712	+	3.60233i	0.634634	+	0.381846i	−0.161582	+	0.986859i	$0.551660\pi$
$90$		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	0.311167	−	0.950355i	$-0.399280\pi$
$97$	−6.66777	−	7.84990i	−0.677009	−	0.797037i	−0.988177	+	0.153318i	$0.951004\pi$
$98$	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	0.309920	−	0.950762i	$-0.399698\pi$
$101$	−0.188243	−	0.0634265i	−0.0187309	−	0.00631117i	−0.328651	+	0.944451i	$0.606594\pi$
$102$		0			0
$103$	−2.88236	−	5.43671i	−0.284008	−	0.535695i	0.699929	−	0.714212i	$-0.253215\pi$
$103$	−2.88236	−	5.43671i	−0.284008	−	0.535695i	−0.983937	+	0.178517i	$0.942870\pi$
$104$	−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	−0.456168	−	0.889894i	$-0.650778\pi$
$107$	5.57926	−	8.22880i	0.539368	−	0.795508i	0.995536	+	0.0943857i	$0.0300887\pi$
$108$		0			0
$109$	3.79341	−	3.59331i	0.363343	−	0.344177i	−0.484148	−	0.874986i	$-0.660871\pi$
$109$	3.79341	−	3.59331i	0.363343	−	0.344177i	0.847491	+	0.530809i	$0.178112\pi$
$110$	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	0.233963	−	0.972246i	$-0.424831\pi$
$113$	7.13771	−	0.776273i	0.671459	−	0.0730256i	0.437497	+	0.899220i	$0.355865\pi$
$114$		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	0.00823195	−	0.999966i	$-0.497380\pi$
$127$	11.3503	−	10.7516i	1.00718	−	0.954049i	0.998945	+	0.0459172i	$0.0146210\pi$
$128$	−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	0.378551	−	0.925580i	$-0.376422\pi$
$131$	−6.01093	−	5.69385i	−0.525177	−	0.497474i	−0.903728	+	0.428106i	$0.859181\pi$
$132$		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	0.939547	+	0.342420i	$0.111247\pi$
$137$	1.85540	+	11.3174i	0.158518	+	0.966914i	−0.781029	+	0.624494i	$0.785305\pi$
$138$		0			0
$139$	12.1020	+	14.2476i	1.02648	+	1.20847i	0.977775	+	0.209655i	$0.0672342\pi$
$139$	12.1020	+	14.2476i	1.02648	+	1.20847i	0.0487070	+	0.998813i	$0.484490\pi$
$140$	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	0.557588	+	0.830118i	$0.311727\pi$
$149$	−2.87916	+	17.5621i	−0.235870	+	1.43874i	−0.793458	+	0.608625i	$0.791722\pi$
$150$		0			0
$151$	12.4650	+	2.74375i	1.01439	+	0.223283i	0.690900	−	0.722950i	$-0.257214\pi$
$151$	12.4650	+	2.74375i	1.01439	+	0.223283i	0.323485	+	0.946233i	$0.395145\pi$
$152$	−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	0.288057	+	0.957613i	$0.406991\pi$
$157$	−7.26263	+	18.2278i	−0.579621	+	1.45474i	−0.867678	+	0.497126i	$0.834389\pi$
$158$	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	−0.972713	−	0.232013i	$-0.925469\pi$
$163$	−7.48651	+	8.81380i	−0.586388	+	0.690350i	0.386324	+	0.922363i	$0.373745\pi$
$164$	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	−0.473380	−	0.880858i	$-0.656966\pi$
$167$	3.21429	−	2.44344i	0.248729	−	0.189079i	0.722109	+	0.691780i	$0.243173\pi$
$168$		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	−0.737129	−	0.675752i	$-0.763819\pi$
$173$	3.10214	−	5.85125i	0.235851	−	0.444862i	0.972980	+	0.230890i	$0.0741638\pi$
$174$		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	−0.765639	−	0.643270i	$-0.777577\pi$
$179$	−7.43790	+	4.47524i	−0.555935	+	0.334495i	0.209705	+	0.977765i	$0.432750\pi$
$180$		0			0
$181$	3.00529	−	5.66857i	0.223381	−	0.421341i	−0.746337	−	0.665568i	$-0.768189\pi$
$181$	3.00529	−	5.66857i	0.223381	−	0.421341i	0.969718	+	0.244227i	$0.0785341\pi$
$182$	−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	0.294266	−	0.955723i	$-0.404925\pi$
$191$	16.4433	−	19.3585i	1.18979	−	1.40073i	0.895526	−	0.445009i	$-0.146799\pi$
$192$		0			0
$193$	0.407806	+	0.601468i	0.0293545	+	0.0432946i	0.842083	−	0.539348i	$-0.181329\pi$
$193$	0.407806	+	0.601468i	0.0293545	+	0.0432946i	−0.812729	+	0.582642i	$0.802019\pi$
$194$	−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	−0.890309	−	0.455357i	$-0.849512\pi$
$197$	0.971271	−	2.43771i	0.0692002	−	0.173679i	0.959509	+	0.281678i	$0.0908909\pi$
$198$		0			0
$199$	0.0527440	−	0.972806i	0.00373892	−	0.0689604i	−0.996068	−	0.0885868i	$-0.971765\pi$
$199$	0.0527440	−	0.972806i	0.00373892	−	0.0689604i	0.999807	+	0.0196264i	$0.00624769\pi$
$200$	−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	−0.335544	−	0.942025i	$-0.608920\pi$
$211$	−3.55199	+	0.781851i	−0.244529	+	0.0538248i	0.0910148	+	0.995850i	$0.470989\pi$
$212$	−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	0.801721	−	0.597698i	$-0.203918\pi$
$223$	3.70796	+	3.51237i	0.248304	+	0.235206i	−0.553417	+	0.832904i	$0.686677\pi$
$224$	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	−0.931094	−	0.364780i	$-0.881144\pi$
$227$	−9.29992	+	8.80935i	−0.617257	+	0.584697i	0.313836	+	0.949477i	$0.398386\pi$
$228$		0			0
$229$	20.8942	−	7.04007i	1.38073	−	0.465221i	0.471626	−	0.881799i	$-0.343667\pi$
$229$	20.8942	−	7.04007i	1.38073	−	0.465221i	0.909100	+	0.416578i	$0.136771\pi$
$230$	−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	−0.999927	−	0.0120755i	$-0.996156\pi$
$233$	−4.30895	−	10.8147i	−0.282289	−	0.708492i	0.717638	−	0.696416i	$-0.245223\pi$
$234$		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	0.998561	+	0.0536279i	$0.0170785\pi$
$239$	4.80006	+	12.0472i	0.310490	+	0.779271i	−0.688071	+	0.725643i	$0.741542\pi$
$240$		0			0
$241$	−14.3385	+	1.55941i	−0.923624	+	0.100450i	−0.557557	−	0.830139i	$-0.688261\pi$
$241$	−14.3385	+	1.55941i	−0.923624	+	0.100450i	−0.366066	+	0.930589i	$0.619296\pi$
$242$	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	0.736194	−	0.676770i	$-0.236621\pi$
$251$	−3.75643	−	7.08538i	−0.237104	−	0.447225i	−0.973298	+	0.229545i	$0.926276\pi$
$252$		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	−0.976161	−	0.217046i	$-0.930358\pi$
$257$	−16.5510	−	19.4853i	−1.03242	−	1.21546i	−0.0562614	−	0.998416i	$-0.517918\pi$
$258$		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	−0.345117	−	0.938560i	$-0.612161\pi$
$263$	−20.8210	−	9.63280i	−1.28388	−	0.593984i	−0.938758	+	0.344576i	$0.888023\pi$
$264$		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	0.982916	−	0.184056i	$-0.0589226\pi$
$269$	29.4845	+	6.49003i	1.79770	+	0.395704i	0.814787	+	0.579760i	$0.196854\pi$
$270$		0			0
$271$	6.39160	−	2.95707i	0.388262	−	0.179629i	−0.216040	−	0.976384i	$-0.569314\pi$
$271$	6.39160	−	2.95707i	0.388262	−	0.179629i	0.604302	+	0.796755i	$0.293452\pi$
$272$	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	0.719349	+	0.694649i	$0.244440\pi$
$277$	−4.24669	+	15.2952i	−0.255159	+	0.919000i	−0.974508	+	0.224351i	$0.927974\pi$
$278$	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	−0.928703	−	0.370824i	$-0.879075\pi$
$281$	−6.91504	+	8.14101i	−0.412517	+	0.485652i	0.516187	+	0.856476i	$0.327351\pi$
$282$		0			0
$283$	−4.66278	−	0.507108i	−0.277174	−	0.0301445i	−0.0315236	−	0.999503i	$-0.510036\pi$
$283$	−4.66278	−	0.507108i	−0.277174	−	0.0301445i	−0.245650	+	0.969359i	$0.579001\pi$
$284$	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	−0.257365	−	0.966314i	$-0.582854\pi$
$293$	8.14496	−	4.90066i	0.475834	−	0.286300i	0.733198	+	0.680015i	$0.238027\pi$
$294$		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	−0.163006	−	0.986625i	$-0.552119\pi$
$307$	−9.36164	−	1.01814i	−0.534297	−	0.0581083i	−0.371291	+	0.928517i	$0.621085\pi$
$308$	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	0.420306	−	0.907383i	$-0.361923\pi$
$311$	−10.1967	−	15.0390i	−0.578203	−	0.852785i	−0.998508	+	0.0545974i	$0.982612\pi$
$312$		0			0
$313$	−5.64119	+	20.3177i	−0.318859	+	1.14843i	0.614333	+	0.789047i	$0.289425\pi$
$313$	−5.64119	+	20.3177i	−0.318859	+	1.14843i	−0.933192	+	0.359379i	$0.882989\pi$
$314$	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	−0.988978	−	0.148060i	$-0.952697\pi$
$317$	0.181796	−	3.35302i	0.0102107	−	0.188324i	0.999189	−	0.0402646i	$-0.0128201\pi$
$318$		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	−0.999348	−	0.0361174i	$-0.988501\pi$
$331$	−2.94133	−	10.5937i	−0.161670	−	0.582282i	0.837678	−	0.546165i	$-0.183913\pi$
$332$	−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	0.907006	−	0.421118i	$-0.138362\pi$
$337$	25.2273	+	8.50006i	1.37422	+	0.463028i	0.467212	+	0.884146i	$0.345259\pi$
$338$	−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	−0.0815329	−	0.996671i	$-0.525982\pi$
$347$	8.50773	−	2.86659i	0.456719	−	0.153886i	0.538252	+	0.842784i	$0.319085\pi$
$348$		0			0
$349$	21.2727	−	2.31354i	1.13870	−	0.123841i	0.480718	−	0.876875i	$-0.340376\pi$
$349$	21.2727	−	2.31354i	1.13870	−	0.123841i	0.657982	+	0.753034i	$0.271410\pi$
$350$	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	−0.156991	−	0.987600i	$-0.550179\pi$
$359$	−1.85696	+	0.201956i	−0.0980065	+	0.0106588i	0.0589844	+	0.998259i	$0.481214\pi$
$360$		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	0.442133	−	0.896950i	$-0.354222\pi$
$367$	−8.22928	−	7.79518i	−0.429565	−	0.406905i	−0.871698	+	0.490044i	$0.836981\pi$
$368$	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	−0.958464	−	0.285214i	$-0.907935\pi$
$373$	−2.72783	−	16.6390i	−0.141242	−	0.861537i	0.817222	−	0.576323i	$-0.195513\pi$
$374$	−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	−0.00642610	−	0.999979i	$-0.502046\pi$
$379$	7.93556	−	1.74675i	0.407622	−	0.0897244i	0.414048	+	0.910255i	$0.364114\pi$
$380$	−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	−0.280676	−	0.959802i	$-0.590559\pi$
$383$	−24.6615	−	14.8383i	−1.26014	−	0.758204i	−0.979468	+	0.201599i	$0.935386\pi$
$384$		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	−0.336960	−	0.941519i	$-0.609399\pi$
$389$	3.20473	−	1.48267i	0.162486	−	0.0751742i	0.499447	+	0.866345i	$0.333537\pi$
$390$		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	0.688771	−	0.724979i	$-0.258151\pi$
$397$	−4.77515	−	7.04282i	−0.239658	−	0.353469i	−0.928429	+	0.371510i	$0.878840\pi$
$398$	−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	−0.537482	−	0.843275i	$-0.680624\pi$
$401$	−24.9046	−	2.70854i	−1.24368	−	0.135258i	−0.706195	+	0.708017i	$0.749590\pi$
$402$		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	−0.997529	−	0.0702616i	$-0.977617\pi$
$409$	−7.67640	+	14.4792i	−0.379574	+	0.715952i	0.617955	+	0.786214i	$0.287961\pi$
$410$	−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	0.943286	−	0.331982i	$-0.107717\pi$
$419$	17.9264	+	13.6273i	0.875760	+	0.665735i	−0.0675257	+	0.997718i	$0.521510\pi$
$420$		0			0
$421$	1.51998	+	28.0343i	0.0740791	+	1.36631i	0.765304	+	0.643669i	$0.222589\pi$
$421$	1.51998	+	28.0343i	0.0740791	+	1.36631i	−0.691225	+	0.722640i	$0.742928\pi$
$422$	−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	−0.822157	−	0.569261i	$-0.807229\pi$
$431$	3.64968	−	13.1450i	0.175799	−	0.633170i	0.997956	−	0.0639092i	$-0.0203568\pi$
$432$		0			0
$433$	−1.95391	+	4.90393i	−0.0938987	+	0.235668i	−0.968423	−	0.249314i	$-0.919795\pi$
$433$	−1.95391	+	4.90393i	−0.0938987	+	0.235668i	0.874524	+	0.484982i	$0.161174\pi$
$434$	−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	−0.566066	−	0.824360i	$-0.691535\pi$
$439$	−29.8771	−	6.57644i	−1.42595	−	0.313876i	−0.859888	+	0.510484i	$0.829466\pi$
$440$	−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	0.797102	−	0.603845i	$-0.206366\pi$
$443$	13.4066	+	8.06647i	0.636966	+	0.383250i	−0.160135	+	0.987095i	$0.551193\pi$
$444$		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	0.769515	+	0.638629i	$0.220498\pi$
$449$	9.31068	+	33.5340i	0.439398	+	1.58257i	−0.330117	+	0.943940i	$0.607088\pi$
$450$		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	0.778814	−	0.627255i	$-0.215822\pi$
$457$	−3.79277	−	7.15393i	−0.177418	−	0.334647i	−0.956232	+	0.292608i	$0.905477\pi$
$458$	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	−0.891148	−	0.453714i	$-0.850099\pi$
$461$	−3.00186	+	4.42741i	−0.139811	+	0.206205i	0.751337	+	0.659919i	$0.229409\pi$
$462$		0			0
$463$	−2.09195	+	1.98160i	−0.0972214	+	0.0920930i	−0.734767	−	0.678320i	$-0.762708\pi$
$463$	−2.09195	+	1.98160i	−0.0972214	+	0.0920930i	0.637545	+	0.770413i	$0.279950\pi$
$464$	−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	−0.337266	−	0.941409i	$-0.609502\pi$
$467$	−10.0330	+	1.09115i	−0.464272	+	0.0504926i	−0.127006	+	0.991902i	$0.540537\pi$
$468$		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	0.702642	−	0.711543i	$-0.252003\pi$
$479$	37.0448	−	12.4818i	1.69262	−	0.570310i	0.989976	+	0.141234i	$0.0451069\pi$
$480$		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	0.631645	−	0.775258i	$-0.282380\pi$
$487$	−8.04378	−	15.1722i	−0.364498	−	0.687517i	−0.996143	+	0.0877408i	$0.972035\pi$
$488$	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	−0.781716	−	0.623635i	$-0.785655\pi$
$491$	−5.31911	−	32.4451i	−0.240048	−	1.46423i	0.541668	−	0.840593i	$-0.317793\pi$
$492$		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	−0.988135	−	0.153589i	$-0.950917\pi$
$499$	−38.9781	−	18.0332i	−1.74490	−	0.807277i	−0.756765	−	0.653687i	$-0.773221\pi$
$500$	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	0.741543	+	0.670906i	$0.234095\pi$
$503$	−3.93390	+	23.9957i	−0.175404	+	1.06992i	−0.916946	+	0.399010i	$0.869354\pi$
$504$		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	−0.483893	−	0.875127i	$-0.660778\pi$
$509$	2.07068	−	38.1914i	0.0917813	−	1.69281i	0.575674	−	0.817679i	$-0.304740\pi$
$510$		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	0.514420	−	0.857538i	$-0.328007\pi$
$521$	33.7434	−	25.6510i	1.47832	−	1.12379i	0.963903	−	0.266254i	$-0.0857860\pi$
$522$		0			0
$523$	0.484092	+	8.92856i	0.0211679	+	0.390419i	0.989850	+	0.142115i	$0.0453903\pi$
$523$	0.484092	+	8.92856i	0.0211679	+	0.390419i	−0.968682	+	0.248304i	$0.920127\pi$
$524$	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	−0.667718	−	0.744414i	$-0.732729\pi$
$541$	−3.00212	+	2.28215i	−0.129071	+	0.0981174i	0.538647	+	0.842532i	$0.318936\pi$
$542$	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	0.401219	−	0.915982i	$-0.368587\pi$
$547$	−13.9910	−	20.6352i	−0.598214	−	0.882300i	−0.999433	+	0.0336828i	$0.989276\pi$
$548$	−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	−0.646183	−	0.763183i	$-0.723636\pi$
$557$	−36.6543	−	8.06823i	−1.55309	−	0.341862i	−0.906912	+	0.421321i	$0.861567\pi$
$558$		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	0.485836	−	0.874050i	$-0.338515\pi$
$563$	3.18405	+	1.47310i	0.134192	+	0.0620837i	−0.351644	+	0.936134i	$0.614377\pi$
$564$		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	0.930293	−	0.366817i	$-0.119553\pi$
$569$	9.96616	+	11.7331i	0.417803	+	0.491876i	−0.512490	+	0.858693i	$0.671277\pi$
$570$		0			0
$571$	−5.59746	−	34.1430i	−0.234246	−	1.42884i	−0.797881	−	0.602815i	$-0.794046\pi$
$571$	−5.59746	−	34.1430i	−0.234246	−	1.42884i	0.563635	−	0.826024i	$-0.309402\pi$
$572$	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	0.522986	−	0.852342i	$-0.324818\pi$
$577$	−7.20125	−	6.82139i	−0.299792	−	0.283978i	−0.822778	+	0.568363i	$0.807577\pi$
$578$	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	−0.966599	−	0.256295i	$-0.917498\pi$
$587$	−10.6872	−	26.8227i	−0.441106	−	1.10709i	0.525493	−	0.850798i	$-0.323881\pi$
$588$		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	0.929661	−	0.368417i	$-0.120100\pi$
$593$	0.0333929	+	0.0838098i	0.00137128	+	0.00344166i	−0.928289	+	0.371858i	$0.878721\pi$
$594$		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	−0.774767	−	0.632246i	$-0.782133\pi$
$599$	−4.53741	+	4.29806i	−0.185393	+	0.175614i	0.589374	+	0.807860i	$0.299374\pi$
$600$		0			0
$601$	−0.938158	+	1.38368i	−0.0382683	+	0.0564415i	−0.846342	−	0.532640i	$-0.821200\pi$
$601$	−0.938158	+	1.38368i	−0.0382683	+	0.0564415i	0.808074	+	0.589082i	$0.200510\pi$
$602$	−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	0.338199	−	0.941075i	$-0.390182\pi$
$607$	0.934319	+	0.314809i	0.0379228	+	0.0127777i	−0.300276	+	0.953852i	$0.597079\pi$
$608$	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	0.987975	+	0.154611i	$0.0494123\pi$
$613$	5.47497	+	19.7190i	0.221132	+	0.796445i	−0.766844	+	0.641834i	$0.778174\pi$
$614$	−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	0.573692	−	0.819071i	$-0.305511\pi$
$617$	7.96916	+	3.68693i	0.320826	+	0.148430i	−0.252865	+	0.967502i	$0.581373\pi$
$618$		0			0
$619$	8.28427	+	4.98448i	0.332973	+	0.200343i	0.672215	−	0.740356i	$-0.265343\pi$
$619$	8.28427	+	4.98448i	0.332973	+	0.200343i	−0.339242	+	0.940699i	$0.610171\pi$
$620$	−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	−0.997499	−	0.0706843i	$-0.977482\pi$
$631$	−2.67131	+	9.62119i	−0.106343	+	0.383014i	0.891156	+	0.453698i	$0.149896\pi$
$632$	−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	0.881272	+	0.472610i	$0.156688\pi$
$641$	1.42450	+	26.2733i	0.0562642	+	1.03773i	−0.825008	+	0.565122i	$0.808829\pi$
$642$		0			0
$643$	4.57009	+	3.47409i	0.180227	+	0.137005i	0.691398	−	0.722474i	$-0.256995\pi$
$643$	4.57009	+	3.47409i	0.180227	+	0.137005i	−0.511171	+	0.859479i	$0.670788\pi$
$644$	−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	−0.546105	−	0.837717i	$-0.683890\pi$
$647$	−1.57126	+	0.945395i	−0.0617726	+	0.0371673i	0.484333	+	0.874884i	$0.339062\pi$
$648$		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	0.320056	+	0.947399i	$0.396298\pi$
$653$	−16.4492	+	31.0265i	−0.643707	+	1.21416i	−0.963763	+	0.266762i	$0.914046\pi$
$654$		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	−0.326214	−	0.945296i	$-0.605773\pi$
$659$	12.7676	−	9.70566i	0.497354	−	0.378079i	0.823568	+	0.567217i	$0.191980\pi$
$660$		0			0
$661$	16.0604	+	1.74667i	0.624677	+	0.0679377i	0.414983	−	0.909829i	$-0.363788\pi$
$661$	16.0604	+	1.74667i	0.624677	+	0.0679377i	0.209694	+	0.977767i	$0.432753\pi$
$662$	−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	0.293476	−	0.955966i	$-0.405188\pi$
$673$	31.4438	−	14.5475i	1.21207	−	0.560763i	0.918594	+	0.395203i	$0.129326\pi$
$674$	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	−0.612009	−	0.790851i	$-0.709638\pi$
$677$	5.73680	−	34.9929i	0.220483	−	1.34489i	0.832492	−	0.554037i	$-0.186913\pi$
$678$		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	−0.995990	−	0.0894664i	$-0.971484\pi$
$683$	−48.6714	+	10.7134i	−1.86236	+	0.409936i	−0.866370	+	0.499403i	$0.833553\pi$
$684$		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	−0.271652	−	0.962396i	$-0.587570\pi$
$691$	−28.1356	−	9.47999i	−1.07033	−	0.360636i	−0.798677	+	0.601760i	$0.794466\pi$
$692$	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	−0.761195	−	0.648523i	$-0.775387\pi$
$701$	−25.8068	+	8.69531i	−0.974708	+	0.328417i	−0.213513	+	0.976940i	$0.568490\pi$
$702$		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	0.00256756	+	0.999997i	$0.499183\pi$
$719$	−24.8663	+	36.6750i	−0.927356	+	1.36775i	−0.929924	+	0.367752i	$0.880128\pi$
$720$		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	0.983141	+	0.182851i	$0.0585326\pi$
$727$	2.96185	+	18.0665i	0.109849	+	0.670049i	−0.873292	+	0.487198i	$0.838019\pi$
$728$	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	−0.765098	−	0.643914i	$-0.777309\pi$
$733$	−32.1939	+	7.08642i	−1.18911	+	0.261743i	−0.424012	+	0.905657i	$0.639378\pi$
$734$	−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	0.871271	+	0.490802i	$0.163296\pi$
$739$	−3.02035	+	18.4233i	−0.111106	+	0.677714i	−0.982377	+	0.186912i	$0.940152\pi$
$740$	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	−0.994817	−	0.101683i	$-0.967577\pi$
$743$	−42.5593	+	19.6900i	−1.56135	+	0.722357i	−0.566531	+	0.824040i	$0.691715\pi$
$744$		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	0.841141	−	0.540816i	$-0.181885\pi$
$751$	0.750798	+	1.10734i	0.0273970	+	0.0404075i	−0.813744	+	0.581224i	$0.802574\pi$
$752$	−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	−0.206144	−	0.978522i	$-0.566092\pi$
$757$	18.7522	−	14.2551i	0.681561	−	0.518109i	0.887705	+	0.460413i	$0.152299\pi$
$758$	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	0.998303	+	0.0582398i	$0.0185488\pi$
$761$	36.4550	+	27.7124i	1.32149	+	1.00457i	0.323191	+	0.946334i	$0.395244\pi$
$762$		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	−0.386843	−	0.922146i	$-0.626434\pi$
$769$	6.84073	−	4.11593i	0.246683	−	0.148424i	0.633526	+	0.773721i	$0.281607\pi$
$770$	−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	−0.187721	−	0.982222i	$-0.560110\pi$
$773$	−32.9287	−	25.0317i	−1.18436	−	0.900328i	−0.996641	+	0.0818941i	$0.973903\pi$
$774$		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	−0.831779	−	0.555106i	$-0.812678\pi$
$787$	4.31562	−	10.8314i	0.153835	−	0.386097i	0.985614	+	0.169009i	$0.0540568\pi$
$788$	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	−0.951526	−	0.307570i	$-0.900484\pi$
$797$	−47.1170	−	28.3494i	−1.66897	−	1.00419i	−0.717444	−	0.696616i	$-0.754688\pi$
$798$		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	−0.234256	−	0.972175i	$-0.575265\pi$
$809$	−28.7012	−	9.67056i	−1.00908	−	0.339999i	−0.774825	+	0.632176i	$0.782162\pi$
$810$		0			0
$811$	7.12872	+	13.4462i	0.250323	+	0.472160i	0.976549	−	0.215297i	$-0.0690720\pi$
$811$	7.12872	+	13.4462i	0.250323	+	0.472160i	−0.726225	+	0.687457i	$0.758727\pi$
$812$	−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	−0.184876	−	0.982762i	$-0.559188\pi$
$821$	−4.41732	+	0.480413i	−0.154166	+	0.0167665i	0.0307107	+	0.999528i	$0.490223\pi$
$822$		0			0
$823$	6.28245	+	15.7678i	0.218992	+	0.549629i	0.996894	−	0.0787568i	$-0.0250951\pi$
$823$	6.28245	+	15.7678i	0.218992	+	0.549629i	−0.777901	+	0.628386i	$0.783716\pi$
$824$	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	−0.998824	−	0.0484870i	$-0.984560\pi$
$829$	−8.84002	−	22.1868i	−0.307027	−	0.770579i	0.691797	−	0.722092i	$-0.256819\pi$
$830$	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	0.843767	−	0.536710i	$-0.180333\pi$
$839$	10.2400	+	9.69986i	0.353525	+	0.334876i	−0.490242	+	0.871586i	$0.663092\pi$
$840$		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	0.341347	−	0.939937i	$-0.389117\pi$
$853$	−4.49931	−	2.08160i	−0.154053	−	0.0712727i	−0.495401	+	0.868664i	$0.664979\pi$
$854$	−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	−0.580519	−	0.814247i	$-0.697150\pi$
$857$	6.72149	−	40.9993i	0.229602	−	1.40051i	0.810121	−	0.586263i	$-0.199401\pi$
$858$		0			0
$859$	−42.6648	−	9.39122i	−1.45570	−	0.320424i	−0.584519	−	0.811380i	$-0.698717\pi$
$859$	−42.6648	−	9.39122i	−1.45570	−	0.320424i	−0.871184	+	0.490956i	$0.836648\pi$
$860$	−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	0.949093	+	0.314997i	$0.102004\pi$
$863$	−0.837052	+	15.4385i	−0.0284936	+	0.525533i	−0.977586	+	0.210536i	$0.932479\pi$
$864$		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	−0.973128	−	0.230263i	$-0.926041\pi$
$877$	−0.906204	−	16.7140i	−0.0306003	−	0.564390i	0.942528	−	0.334127i	$-0.108441\pi$
$878$	−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	0.527982	+	0.849256i	$0.322949\pi$
$881$	−13.9870	+	26.3823i	−0.471235	+	0.888843i	−0.999216	+	0.0395869i	$0.987396\pi$
$882$		0			0
$883$	35.5740	−	21.4042i	1.19716	−	0.720307i	0.229683	−	0.973266i	$-0.426231\pi$
$883$	35.5740	−	21.4042i	1.19716	−	0.720307i	0.967477	+	0.252958i	$0.0814036\pi$
$884$	−16.3847			−0.551078
$885$		0			0
$886$	18.1173			0.608663
$887$	13.1844	−	7.93278i	0.442688	−	0.266357i	−0.276711	−	0.960953i	$-0.589245\pi$
$887$	13.1844	−	7.93278i	0.442688	−	0.266357i	0.719400	+	0.694596i	$0.244417\pi$
$888$		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	−0.525407	−	0.850851i	$-0.676087\pi$
$907$	2.67775	−	49.3882i	0.0889132	−	1.63991i	0.614321	−	0.789057i	$-0.289430\pi$
$908$	−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	0.899793	−	0.436317i	$-0.143717\pi$
$911$	46.2768	+	10.1863i	1.53322	+	0.337487i	0.633425	+	0.773804i	$0.281648\pi$
$912$		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	0.00140458	−	0.999999i	$-0.499553\pi$
$919$	12.8102	−	2.81973i	0.422568	−	0.0930143i	0.421163	+	0.906985i	$0.361622\pi$
$920$	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	0.996065	−	0.0886242i	$-0.0282470\pi$
$929$	11.0864	+	20.9112i	0.363733	+	0.686073i	−0.632332	+	0.774697i	$0.717902\pi$
$930$		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	−0.425255	−	0.905074i	$-0.639816\pi$
$937$	−6.61401	+	2.22852i	−0.216070	+	0.0728025i	0.209185	+	0.977876i	$0.432919\pi$
$938$	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	−0.951947	−	0.306264i	$-0.900921\pi$
$941$	−14.4622	−	36.2975i	−0.471455	−	1.18326i	0.480491	−	0.877000i	$-0.340458\pi$
$942$		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	0.958756	+	0.284229i	$0.0917377\pi$
$947$	14.0994	+	35.3867i	0.458168	+	1.14991i	−0.500588	+	0.865685i	$0.666883\pi$
$948$		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	−0.925894	−	0.377784i	$-0.876686\pi$
$953$	−18.4851	+	17.5100i	−0.598790	+	0.567204i	0.327103	+	0.944989i	$0.393928\pi$
$954$		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	0.940677	+	0.339304i	$0.110192\pi$
$967$	9.62691	+	34.6730i	0.309581	+	1.11501i	−0.631096	+	0.775705i	$0.717395\pi$
$968$	−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	−0.0479711	−	0.998849i	$-0.515276\pi$
$971$	−26.1848	−	12.1144i	−0.840312	−	0.388770i	−0.792340	+	0.610079i	$0.791138\pi$
$972$		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	−0.238473	−	0.971149i	$-0.576647\pi$
$977$	−26.9648	−	5.93540i	−0.862680	−	0.189890i	−0.624207	+	0.781259i	$0.714578\pi$
$978$		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	−0.947386	−	0.320092i	$-0.896286\pi$
$983$	−1.23721	+	3.10515i	−0.0394607	+	0.0990390i	0.907926	+	0.419131i	$0.137665\pi$
$984$		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	0.169723	−	0.985492i	$-0.445713\pi$
$991$	3.89177	+	0.423256i	0.123626	+	0.0134452i	−0.0460967	+	0.998937i	$0.514678\pi$
$992$	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	0.850632	−	0.525761i	$-0.176220\pi$
$997$	18.0485	+	13.7201i	0.571603	+	0.434521i	−0.279029	+	0.960283i	$0.590013\pi$
$998$	−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.163.4		140
3.2	odd	2		177.2.e.b.163.2	yes	140
59.21	even	29	inner	531.2.i.b.316.4		140
177.80	odd	58		177.2.e.b.139.2	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.139.2	✓	140	177.80	odd	58
177.2.e.b.163.2	yes	140	3.2	odd	2
531.2.i.b.163.4		140	1.1	even	1	trivial
531.2.i.b.316.4		140	59.21	even	29	inner

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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