LMFDB - Embedded newform 425.2.r.a.69.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.12
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38991 + 0.451609i) q^{2} +(1.86675 + 2.56936i) q^{3} +(0.109865 - 0.0798213i) q^{4} +(2.21373 - 0.315251i) q^{5} +(-3.75495 - 2.72813i) q^{6} +0.259005i q^{7} +(1.60137 - 2.20410i) q^{8} +(-2.18980 + 6.73951i) q^{9} +(-2.93452 + 1.43791i) q^{10} +(0.353460 + 1.08784i) q^{11} +(0.410179 + 0.133275i) q^{12} +(0.350179 + 0.113780i) q^{13} +(-0.116969 - 0.359993i) q^{14} +(4.94247 + 5.09938i) q^{15} +(-1.31430 + 4.04499i) q^{16} +(-0.587785 + 0.809017i) q^{17} -10.3562i q^{18} +(2.44657 + 1.77754i) q^{19} +(0.218047 - 0.211338i) q^{20} +(-0.665475 + 0.483496i) q^{21} +(-0.982555 - 1.35237i) q^{22} +(-2.23279 + 0.725476i) q^{23} +8.65246 q^{24} +(4.80123 - 1.39576i) q^{25} -0.538101 q^{26} +(-12.3426 + 4.01036i) q^{27} +(0.0206741 + 0.0284555i) q^{28} +(5.99815 - 4.35791i) q^{29} +(-9.17252 - 4.85561i) q^{30} +(-5.81450 - 4.22448i) q^{31} -0.766902i q^{32} +(-2.13522 + 2.93888i) q^{33} +(0.451609 - 1.38991i) q^{34} +(0.0816516 + 0.573367i) q^{35} +(0.297375 + 0.915226i) q^{36} +(-9.73573 - 3.16333i) q^{37} +(-4.20327 - 1.36572i) q^{38} +(0.361354 + 1.11213i) q^{39} +(2.85016 - 5.38411i) q^{40} +(0.123545 - 0.380232i) q^{41} +(0.706599 - 0.972551i) q^{42} -1.20039i q^{43} +(0.125665 + 0.0913012i) q^{44} +(-2.72299 + 15.6098i) q^{45} +(2.77574 - 2.01669i) q^{46} +(-4.59394 - 6.32301i) q^{47} +(-12.8465 + 4.17408i) q^{48} +6.93292 q^{49} +(-6.04294 + 4.10827i) q^{50} -3.17590 q^{51} +(0.0475543 - 0.0154513i) q^{52} +(5.64170 + 7.76513i) q^{53} +(15.3440 - 11.1481i) q^{54} +(1.12541 + 2.29675i) q^{55} +(0.570871 + 0.414762i) q^{56} +9.60433i q^{57} +(-6.36882 + 8.76593i) q^{58} +(-2.50095 + 7.69712i) q^{59} +(0.950042 + 0.165726i) q^{60} +(-0.665804 - 2.04913i) q^{61} +(9.98945 + 3.24577i) q^{62} +(-1.74556 - 0.567168i) q^{63} +(-2.28226 - 7.02406i) q^{64} +(0.811072 + 0.141484i) q^{65} +(1.64054 - 5.04907i) q^{66} +(7.79166 - 10.7243i) q^{67} +0.135800i q^{68} +(-6.03205 - 4.38254i) q^{69} +(-0.372426 - 0.760054i) q^{70} +(2.00137 - 1.45408i) q^{71} +(11.3478 + 15.6190i) q^{72} +(1.02055 - 0.331597i) q^{73} +14.9604 q^{74} +(12.5489 + 9.73054i) q^{75} +0.410677 q^{76} +(-0.281755 + 0.0915477i) q^{77} +(-1.00450 - 1.38257i) q^{78} +(1.43101 - 1.03969i) q^{79} +(-1.63432 + 9.36887i) q^{80} +(-16.1457 - 11.7305i) q^{81} +0.584282i q^{82} +(-7.49157 + 10.3113i) q^{83} +(-0.0345189 + 0.106238i) q^{84} +(-1.04616 + 1.97625i) q^{85} +(0.542109 + 1.66844i) q^{86} +(22.3941 + 7.27627i) q^{87} +(2.96372 + 0.962970i) q^{88} +(0.317468 + 0.977065i) q^{89} +(-3.26482 - 22.9260i) q^{90} +(-0.0294695 + 0.0906979i) q^{91} +(-0.187396 + 0.257928i) q^{92} -22.8256i q^{93} +(9.24069 + 6.71375i) q^{94} +(5.97643 + 3.16371i) q^{95} +(1.97045 - 1.43161i) q^{96} +(-8.37484 - 11.5270i) q^{97} +(-9.63613 + 3.13097i) q^{98} -8.10550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.38991	+	0.451609i	−0.982815	+	0.319336i	−0.755978	−	0.654597i	$-0.772838\pi$
$2$	−1.38991	+	0.451609i	−0.982815	+	0.319336i	−0.226837	+	0.973933i	$0.572838\pi$
$3$	1.86675	+	2.56936i	1.07777	+	1.48342i	0.861956	+	0.506984i	$0.169240\pi$
$3$	1.86675	+	2.56936i	1.07777	+	1.48342i	0.215811	+	0.976435i	$0.430760\pi$
$4$	0.109865	−	0.0798213i	0.0549323	−	0.0399107i
$5$	2.21373	−	0.315251i	0.990012	−	0.140985i
$5$	2.21373	−	0.315251i	0.990012	−	0.140985i
$6$	−3.75495	−	2.72813i	−1.53295	−	1.11376i
$7$			0.259005i			0.0978946i	0.998801	+	0.0489473i	$0.0155866\pi$
$7$			0.259005i			0.0978946i	−0.998801	+	0.0489473i	$0.984413\pi$
$8$	1.60137	−	2.20410i	0.566169	−	0.779265i
$9$	−2.18980	+	6.73951i	−0.729933	+	2.24650i
$10$	−2.93452	+	1.43791i	−0.927977	+	0.454708i
$11$	0.353460	+	1.08784i	0.106572	+	0.327995i	0.990096	−	0.140390i	$-0.0448358\pi$
$11$	0.353460	+	1.08784i	0.106572	+	0.327995i	−0.883524	+	0.468386i	$0.844836\pi$
$12$	0.410179	+	0.133275i	0.118408	+	0.0384732i
$13$	0.350179	+	0.113780i	0.0971221	+	0.0315569i	0.357175	−	0.934037i	$-0.383740\pi$
$13$	0.350179	+	0.113780i	0.0971221	+	0.0315569i	−0.260053	+	0.965594i	$0.583740\pi$
$14$	−0.116969	−	0.359993i	−0.0312612	−	0.0962122i
$15$	4.94247	+	5.09938i	1.27614	+	1.31665i
$16$	−1.31430	+	4.04499i	−0.328575	+	1.01125i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$		−	10.3562i		−	2.44099i
$19$	2.44657	+	1.77754i	0.561282	+	0.407795i	0.831928	−	0.554884i	$-0.187237\pi$
$19$	2.44657	+	1.77754i	0.561282	+	0.407795i	−0.270646	+	0.962679i	$0.587237\pi$
$20$	0.218047	−	0.211338i	0.0487568	−	0.0472566i
$21$	−0.665475	+	0.483496i	−0.145219	+	0.105508i
$22$	−0.982555	−	1.35237i	−0.209481	−	0.288326i
$23$	−2.23279	+	0.725476i	−0.465568	+	0.151272i	−0.532401	−	0.846492i	$-0.678710\pi$
$23$	−2.23279	+	0.725476i	−0.465568	+	0.151272i	0.0668336	+	0.997764i	$0.478710\pi$
$24$	8.65246			1.76618
$25$	4.80123	−	1.39576i	0.960247	−	0.279153i
$26$	−0.538101			−0.105530
$27$	−12.3426	+	4.01036i	−2.37534	+	0.771794i
$28$	0.0206741	+	0.0284555i	0.00390704	+	0.00537757i
$29$	5.99815	−	4.35791i	1.11383	−	0.809244i	0.130567	−	0.991440i	$-0.458320\pi$
$29$	5.99815	−	4.35791i	1.11383	−	0.809244i	0.983262	+	0.182196i	$0.0583204\pi$
$30$	−9.17252	−	4.85561i	−1.67466	−	0.886509i
$31$	−5.81450	−	4.22448i	−1.04432	−	0.758740i	−0.0731924	−	0.997318i	$-0.523319\pi$
$31$	−5.81450	−	4.22448i	−1.04432	−	0.758740i	−0.971123	+	0.238578i	$0.923319\pi$
$32$		−	0.766902i		−	0.135570i
$33$	−2.13522	+	2.93888i	−0.371695	+	0.511594i
$34$	0.451609	−	1.38991i	0.0774503	−	0.238368i
$35$	0.0816516	+	0.573367i	0.0138016	+	0.0969168i
$36$	0.297375	+	0.915226i	0.0495625	+	0.152538i
$37$	−9.73573	−	3.16333i	−1.60054	−	0.520048i	−0.633302	−	0.773905i	$-0.718301\pi$
$37$	−9.73573	−	3.16333i	−1.60054	−	0.520048i	−0.967242	+	0.253857i	$0.918301\pi$
$38$	−4.20327	−	1.36572i	−0.681860	−	0.221550i
$39$	0.361354	+	1.11213i	0.0578629	+	0.178084i
$40$	2.85016	−	5.38411i	0.450650	−	0.851303i
$41$	0.123545	−	0.380232i	0.0192945	−	0.0593823i	−0.940946	−	0.338558i	$-0.890061\pi$
$41$	0.123545	−	0.380232i	0.0192945	−	0.0593823i	0.960240	+	0.279175i	$0.0900610\pi$
$42$	0.706599	−	0.972551i	0.109031	−	0.150068i
$43$		−	1.20039i		−	0.183058i	−0.995802	−	0.0915292i	$-0.970825\pi$
$43$		−	1.20039i		−	0.183058i	0.995802	−	0.0915292i	$-0.0291755\pi$
$44$	0.125665	+	0.0913012i	0.0189448	+	0.0137642i
$45$	−2.72299	+	15.6098i	−0.405920	+	2.32697i
$46$	2.77574	−	2.01669i	0.409260	−	0.297345i
$47$	−4.59394	−	6.32301i	−0.670095	−	0.922306i	0.329668	−	0.944097i	$-0.393063\pi$
$47$	−4.59394	−	6.32301i	−0.670095	−	0.922306i	−0.999763	+	0.0217908i	$0.993063\pi$
$48$	−12.8465	+	4.17408i	−1.85423	+	0.602476i
$49$	6.93292			0.990417
$50$	−6.04294	+	4.10827i	−0.854601	+	0.580997i
$51$	−3.17590			−0.444715
$52$	0.0475543	−	0.0154513i	0.00659460	−	0.00214272i
$53$	5.64170	+	7.76513i	0.774947	+	1.06662i	0.995822	+	0.0913210i	$0.0291089\pi$
$53$	5.64170	+	7.76513i	0.774947	+	1.06662i	−0.220874	+	0.975302i	$0.570891\pi$
$54$	15.3440	−	11.1481i	2.08806	−	1.51706i
$55$	1.12541	+	2.29675i	0.151750	+	0.309694i
$56$	0.570871	+	0.414762i	0.0762858	+	0.0554249i
$57$			9.60433i			1.27212i
$58$	−6.36882	+	8.76593i	−0.836267	+	1.15102i
$59$	−2.50095	+	7.69712i	−0.325595	+	1.00208i	0.645576	+	0.763696i	$0.276617\pi$
$59$	−2.50095	+	7.69712i	−0.325595	+	1.00208i	−0.971171	+	0.238383i	$0.923383\pi$
$60$	0.950042	+	0.165726i	0.122650	+	0.0213952i
$61$	−0.665804	−	2.04913i	−0.0852474	−	0.262365i	0.899342	−	0.437246i	$-0.144046\pi$
$61$	−0.665804	−	2.04913i	−0.0852474	−	0.262365i	−0.984590	+	0.174881i	$0.944046\pi$
$62$	9.98945	+	3.24577i	1.26866	+	0.412213i
$63$	−1.74556	−	0.567168i	−0.219920	−	0.0714565i
$64$	−2.28226	−	7.02406i	−0.285282	−	0.878008i
$65$	0.811072	+	0.141484i	0.100601	+	0.0175490i
$66$	1.64054	−	5.04907i	0.201937	−	0.621497i
$67$	7.79166	−	10.7243i	0.951902	−	1.31018i	0.00122494	−	0.999999i	$-0.499610\pi$
$67$	7.79166	−	10.7243i	0.951902	−	1.31018i	0.950677	−	0.310182i	$-0.100390\pi$
$68$			0.135800i			0.0164682i
$69$	−6.03205	−	4.38254i	−0.726174	−	0.527596i
$70$	−0.372426	−	0.760054i	−0.0445134	−	0.0908439i
$71$	2.00137	−	1.45408i	0.237519	−	0.172568i	−0.462658	−	0.886537i	$-0.653104\pi$
$71$	2.00137	−	1.45408i	0.237519	−	0.172568i	0.700177	+	0.713969i	$0.253104\pi$
$72$	11.3478	+	15.6190i	1.33736	+	1.84071i
$73$	1.02055	−	0.331597i	0.119446	−	0.0388104i	−0.248684	−	0.968585i	$-0.579998\pi$
$73$	1.02055	−	0.331597i	0.119446	−	0.0388104i	0.368130	+	0.929774i	$0.379998\pi$
$74$	14.9604			1.73911
$75$	12.5489	+	9.73054i	1.44902	+	1.12359i
$76$	0.410677			0.0471079
$77$	−0.281755	+	0.0915477i	−0.0321090	+	0.0104328i
$78$	−1.00450	−	1.38257i	−0.113737	−	0.156546i
$79$	1.43101	−	1.03969i	0.161002	−	0.116975i	−0.504367	−	0.863489i	$-0.668274\pi$
$79$	1.43101	−	1.03969i	0.161002	−	0.116975i	0.665369	+	0.746515i	$0.268274\pi$
$80$	−1.63432	+	9.36887i	−0.182722	+	1.04747i
$81$	−16.1457	−	11.7305i	−1.79397	−	1.30339i
$82$			0.584282i			0.0645232i
$83$	−7.49157	+	10.3113i	−0.822307	+	1.13181i	0.166999	+	0.985957i	$0.446592\pi$
$83$	−7.49157	+	10.3113i	−0.822307	+	1.13181i	−0.989306	+	0.145852i	$0.953408\pi$
$84$	−0.0345189	+	0.106238i	−0.00376632	+	0.0115915i
$85$	−1.04616	+	1.97625i	−0.113472	+	0.214354i
$86$	0.542109	+	1.66844i	0.0584571	+	0.179912i
$87$	22.3941	+	7.27627i	2.40090	+	0.780098i
$88$	2.96372	+	0.962970i	0.315933	+	0.102653i
$89$	0.317468	+	0.977065i	0.0336515	+	0.103569i	0.966471	−	0.256774i	$-0.0826597\pi$
$89$	0.317468	+	0.977065i	0.0336515	+	0.103569i	−0.932820	+	0.360343i	$0.882660\pi$
$90$	−3.26482	−	22.9260i	−0.344142	−	2.41661i
$91$	−0.0294695	+	0.0906979i	−0.00308925	+	0.00950773i
$92$	−0.187396	+	0.257928i	−0.0195373	+	0.0268909i
$93$		−	22.8256i		−	2.36690i
$94$	9.24069	+	6.71375i	0.953104	+	0.692471i
$95$	5.97643	+	3.16371i	0.613169	+	0.324590i
$96$	1.97045	−	1.43161i	0.201108	−	0.146113i
$97$	−8.37484	−	11.5270i	−0.850336	−	1.17039i	−0.983789	−	0.179332i	$-0.942607\pi$
$97$	−8.37484	−	11.5270i	−0.850336	−	1.17039i	0.133453	−	0.991055i	$-0.457393\pi$
$98$	−9.63613	+	3.13097i	−0.973396	+	0.316276i
$99$	−8.10550			−0.814633
$100$	0.416074	−	0.536586i	0.0416074	−	0.0536586i
$101$	17.7828			1.76946			0.884730	−	0.466104i	$-0.154343\pi$
$101$	17.7828			1.76946			0.884730	+	0.466104i	$0.154343\pi$
$102$	4.41421	−	1.43427i	0.437072	−	0.142013i
$103$	−7.29047	−	10.0345i	−0.718352	−	0.988726i	−0.999577	−	0.0290845i	$-0.990741\pi$
$103$	−7.29047	−	10.0345i	−0.718352	−	0.988726i	0.281225	−	0.959642i	$-0.409259\pi$
$104$	0.811547	−	0.589624i	0.0795788	−	0.0578174i
$105$	−1.32076	+	1.28012i	−0.128893	+	0.124927i
$106$	−11.3483	−	8.24499i	−1.10224	−	0.800825i
$107$			5.23562i			0.506146i	0.967447	+	0.253073i	$0.0814413\pi$
$107$			5.23562i			0.506146i	−0.967447	+	0.253073i	$0.918559\pi$
$108$	−1.03591	+	1.42580i	−0.0996800	+	0.137198i
$109$	5.18707	−	15.9642i	0.496831	−	1.52909i	−0.317253	−	0.948341i	$-0.602760\pi$
$109$	5.18707	−	15.9642i	0.496831	−	1.52909i	0.814084	−	0.580747i	$-0.197240\pi$
$110$	−2.60145	−	2.68404i	−0.248039	−	0.255913i
$111$	−10.0464	−	30.9197i	−0.953564	−	2.93477i
$112$	−1.04767	−	0.340409i	−0.0989957	−	0.0321657i
$113$	8.27551	+	2.68888i	0.778494	+	0.252948i	0.671197	−	0.741279i	$-0.265780\pi$
$113$	8.27551	+	2.68888i	0.778494	+	0.252948i	0.107297	+	0.994227i	$0.465780\pi$
$114$	−4.33740	−	13.3491i	−0.406235	−	1.25026i
$115$	−4.71408	+	2.30990i	−0.439591	+	0.215399i
$116$	0.311130	−	0.957561i	0.0288877	−	0.0889073i
$117$	−1.53364	+	2.11088i	−0.141785	+	0.195151i
$118$		−	11.8278i		−	1.08883i
$119$	−0.209539	−	0.152239i	−0.0192084	−	0.0139557i
$120$	19.1542	−	2.72770i	1.74853	−	0.249004i
$121$	7.84073	−	5.69662i	0.712794	−	0.517875i
$122$	1.85081	+	2.54743i	0.167565	+	0.230633i
$123$	1.20758	−	0.392366i	0.108884	−	0.0353785i
$124$	−0.976012			−0.0876485
$125$	10.1886	−	4.60345i	0.911299	−	0.411745i
$126$	2.68231			0.238960
$127$	−6.74357	+	2.19112i	−0.598395	+	0.194430i	−0.592524	−	0.805552i	$-0.701869\pi$
$127$	−6.74357	+	2.19112i	−0.598395	+	0.194430i	−0.00587048	+	0.999983i	$0.501869\pi$
$128$	7.24581	+	9.97300i	0.640445	+	0.881497i
$129$	3.08424	−	2.24083i	0.271552	−	0.197294i
$130$	−1.19121	+	0.169637i	−0.104476	+	0.0148782i
$131$	17.7804	+	12.9182i	1.55348	+	1.12867i	0.941108	+	0.338107i	$0.109786\pi$
$131$	17.7804	+	12.9182i	1.55348	+	1.12867i	0.612377	+	0.790566i	$0.290214\pi$
$132$			0.493315i			0.0429376i
$133$	−0.460391	+	0.633673i	−0.0399209	+	0.0549464i
$134$	−5.98651	+	18.4246i	−0.517156	+	1.59164i
$135$	−26.0590	+	12.7689i	−2.24280	+	1.09897i
$136$	0.841890	+	2.59107i	0.0721914	+	0.222182i
$137$	5.95869	+	1.93610i	0.509085	+	0.165412i	0.552286	−	0.833655i	$-0.313756\pi$
$137$	5.95869	+	1.93610i	0.509085	+	0.165412i	−0.0432009	+	0.999066i	$0.513756\pi$
$138$	10.3632	+	3.36721i	0.882174	+	0.286636i
$139$	4.24912	+	13.0774i	0.360405	+	1.10921i	0.952808	+	0.303572i	$0.0981793\pi$
$139$	4.24912	+	13.0774i	0.360405	+	1.10921i	−0.592403	+	0.805642i	$0.701821\pi$
$140$	0.0547376	+	0.0564753i	0.00462617	+	0.00477303i
$141$	7.67036	−	23.6069i	0.645960	−	1.98806i
$142$	−2.12505	+	2.92488i	−0.178330	+	0.245450i
$143$			0.421154i			0.0352187i
$144$	−24.3832	−	17.7154i	−2.03194	−	1.47629i
$145$	11.9045	−	11.5382i	0.988613	−	0.958194i
$146$	−1.26872	+	0.921779i	−0.105000	+	0.0762870i
$147$	12.9420	+	17.8131i	1.06744	+	1.46920i
$148$	−1.32211	+	0.429581i	−0.108677	+	0.0353113i
$149$	−3.46162			−0.283587			−0.141794	−	0.989896i	$-0.545287\pi$
$149$	−3.46162			−0.283587			−0.141794	+	0.989896i	$0.545287\pi$
$150$	−21.8362	−	7.85737i	−1.78292	−	0.641552i
$151$	−7.41033			−0.603044			−0.301522	−	0.953459i	$-0.597495\pi$
$151$	−7.41033			−0.603044			−0.301522	+	0.953459i	$0.597495\pi$
$152$	7.83573	−	2.54598i	0.635561	−	0.206506i
$153$	−4.16524	−	5.73297i	−0.336740	−	0.463483i
$154$	0.350270	−	0.254486i	0.0282256	−	0.0205071i
$155$	−14.2035	−	7.51885i	−1.14086	−	0.603929i
$156$	0.128472	+	0.0933403i	0.0102860	+	0.00747321i
$157$			14.2668i			1.13861i	0.822126	+	0.569306i	$0.192788\pi$
$157$			14.2668i			1.13861i	−0.822126	+	0.569306i	$0.807212\pi$
$158$	−1.51945	+	2.09134i	−0.120881	+	0.166378i
$159$	−9.41977	+	28.9911i	−0.747037	+	2.29914i
$160$	−0.241767	−	1.69772i	−0.0191134	−	0.134216i
$161$	−0.187902	−	0.578302i	−0.0148087	−	0.0455766i
$162$	27.7387	+	9.01284i	2.17936	+	0.708116i
$163$	10.3695	+	3.36925i	0.812201	+	0.263900i	0.685530	−	0.728045i	$-0.259571\pi$
$163$	10.3695	+	3.36925i	0.812201	+	0.263900i	0.126671	+	0.991945i	$0.459571\pi$
$164$	−0.0167774	−	0.0516356i	−0.00131010	−	0.00403206i
$165$	−3.80033	+	7.17903i	−0.295855	+	0.558887i
$166$	5.75595	−	17.7150i	0.446748	−	1.37495i
$167$	12.3594	−	17.0112i	0.956396	−	1.31637i	0.00776920	−	0.999970i	$-0.497527\pi$
$167$	12.3594	−	17.0112i	0.956396	−	1.31637i	0.948627	−	0.316397i	$-0.102473\pi$
$168$			2.24103i			0.172899i
$169$	−10.4075	−	7.56152i	−0.800580	−	0.581656i
$170$	0.561571	−	3.21926i	0.0430706	−	0.246906i
$171$	−17.3372	+	12.5962i	−1.32581	+	0.963258i
$172$	−0.0958171	−	0.131881i	−0.00730598	−	0.0100558i
$173$	−17.9554	+	5.83405i	−1.36512	+	0.443555i	−0.897749	−	0.440507i	$-0.854799\pi$
$173$	−17.9554	+	5.83405i	−1.36512	+	0.443555i	−0.467371	+	0.884061i	$0.654799\pi$
$174$	−34.4118			−2.60875
$175$	0.361510	+	1.24354i	0.0273276	+	0.0940029i
$176$	−4.86485			−0.366702
$177$	−24.4453	+	7.94275i	−1.83742	+	0.597014i
$178$	−0.882502	−	1.21466i	−0.0661464	−	0.0910426i
$179$	−8.39092	+	6.09636i	−0.627167	+	0.455663i	−0.855418	−	0.517939i	$-0.826699\pi$
$179$	−8.39092	+	6.09636i	−0.627167	+	0.455663i	0.228251	+	0.973602i	$0.426699\pi$
$180$	0.946835	+	1.93232i	0.0705729	+	0.144027i
$181$	5.83050	+	4.23611i	0.433378	+	0.314867i	0.782998	−	0.622024i	$-0.213689\pi$
$181$	5.83050	+	4.23611i	0.433378	+	0.314867i	−0.349620	+	0.936891i	$0.613689\pi$
$182$		−	0.139371i		−	0.0103308i
$183$	4.02207	−	5.53590i	0.297320	−	0.409226i
$184$	−1.97650	+	6.08303i	−0.145709	+	0.448447i
$185$	−22.5495	−	3.93357i	−1.65788	−	0.289202i
$186$	10.3082	+	31.7255i	0.755837	+	2.32623i
$187$	−1.08784	−	0.353460i	−0.0795506	−	0.0258475i
$188$	−1.00942	−	0.327981i	−0.0736197	−	0.0239205i
$189$	−1.03870	−	3.19680i	−0.0755544	−	0.232533i
$190$	−9.73546	−	1.69826i	−0.706284	−	0.123205i
$191$	−0.0778776	+	0.239683i	−0.00563502	+	0.0173428i	−0.953834	−	0.300333i	$-0.902902\pi$
$191$	−0.0778776	+	0.239683i	−0.00563502	+	0.0173428i	0.948199	+	0.317676i	$0.102902\pi$
$192$	13.7869	−	18.9761i	0.994986	−	1.36948i
$193$			16.8794i			1.21501i	0.794316	+	0.607504i	$0.207829\pi$
$193$			16.8794i			1.21501i	−0.794316	+	0.607504i	$0.792171\pi$
$194$	16.8460	+	12.2393i	1.20947	+	0.878731i
$195$	1.15054	+	2.34805i	0.0823921	+	0.168147i
$196$	0.761682	−	0.553395i	0.0544059	−	0.0395282i
$197$	−12.0232	−	16.5485i	−0.856615	−	1.17903i	−0.982366	−	0.186967i	$-0.940134\pi$
$197$	−12.0232	−	16.5485i	−0.856615	−	1.17903i	0.125752	−	0.992062i	$-0.459866\pi$
$198$	11.2659	−	3.66052i	0.800633	−	0.260142i
$199$	10.2139			0.724042			0.362021	−	0.932170i	$-0.382087\pi$
$199$	10.2139			0.724042			0.362021	+	0.932170i	$0.382087\pi$
$200$	4.61215	−	12.8175i	0.326128	−	0.906335i
$201$	42.0996			2.96948
$202$	−24.7166	+	8.03090i	−1.73905	+	0.565052i
$203$	1.12872	+	1.55355i	0.0792206	+	0.109038i
$204$	−0.348919	+	0.253505i	−0.0244292	+	0.0177489i
$205$	0.153627	−	0.880680i	0.0107298	−	0.0615094i
$206$	14.6648	+	10.6546i	1.02174	+	0.742339i
$207$		−	16.6365i		−	1.15632i
$208$	−0.920479	+	1.26693i	−0.0638237	+	0.0878458i
$209$	−1.06891	+	3.28976i	−0.0739379	+	0.227557i
$210$	1.25763	−	2.37572i	0.0867844	−	0.163941i
$211$	1.64807	+	5.07225i	0.113458	+	0.349188i	0.991622	−	0.129171i	$-0.0412317\pi$
$211$	1.64807	+	5.07225i	0.113458	+	0.349188i	−0.878164	+	0.478359i	$0.841232\pi$
$212$	1.23965	+	0.402786i	0.0851393	+	0.0276634i
$213$	7.47211	+	2.42783i	0.511980	+	0.166352i
$214$	−2.36445	−	7.27704i	−0.161631	−	0.497448i
$215$	−0.378426	−	2.65735i	−0.0258084	−	0.181230i
$216$	−10.9259	+	33.6264i	−0.743412	+	2.28799i
$217$	1.09416	−	1.50598i	0.0742765	−	0.102233i
$218$			24.5313i			1.66147i
$219$	2.75710	+	2.00315i	0.186307	+	0.135360i
$220$	0.306972	+	0.162500i	0.0206961	+	0.0109558i
$221$	−0.297880	+	0.216422i	−0.0200376	+	0.0145581i
$222$	27.9272	+	38.4385i	1.87435	+	2.57983i
$223$	−24.3194	+	7.90184i	−1.62855	+	0.529147i	−0.973936	−	0.226821i	$-0.927167\pi$
$223$	−24.3194	+	7.90184i	−1.62855	+	0.529147i	−0.654609	+	0.755967i	$0.727167\pi$
$224$	0.198631			0.0132716
$225$	−1.10697	+	35.4144i	−0.0737977	+	2.36096i
$226$	−12.7165			−0.845891
$227$	−13.6979	+	4.45071i	−0.909161	+	0.295404i	−0.726013	−	0.687681i	$-0.758629\pi$
$227$	−13.6979	+	4.45071i	−0.909161	+	0.295404i	−0.183148	+	0.983085i	$0.558629\pi$
$228$	0.766630	+	1.05518i	0.0507713	+	0.0698807i
$229$	20.5739	−	14.9478i	1.35956	−	0.987779i	0.361088	−	0.932532i	$-0.382405\pi$
$229$	20.5739	−	14.9478i	1.35956	−	0.987779i	0.998473	−	0.0552473i	$-0.0175947\pi$
$230$	5.50898	−	5.33947i	0.363251	−	0.352075i
$231$	−0.761184	−	0.553033i	−0.0500822	−	0.0363869i
$232$		−	20.1991i		−	1.32614i
$233$	6.52152	−	8.97610i	0.427239	−	0.588044i	−0.540078	−	0.841615i	$-0.681605\pi$
$233$	6.52152	−	8.97610i	0.427239	−	0.588044i	0.967317	+	0.253571i	$0.0816052\pi$
$234$	1.17833	−	3.62654i	0.0770300	−	0.237074i
$235$	−12.1631	−	12.5492i	−0.793433	−	0.818621i
$236$	0.339629	+	1.04527i	0.0221079	+	0.0680413i
$237$	5.34268	+	1.73594i	0.347044	+	0.112762i
$238$	0.359993	+	0.116969i	0.0233349	+	0.00758196i
$239$	1.63488	+	5.03164i	0.105752	+	0.325470i	0.989906	−	0.141725i	$-0.0452648\pi$
$239$	1.63488	+	5.03164i	0.105752	+	0.325470i	−0.884155	+	0.467194i	$0.845265\pi$
$240$	−27.1228	+	13.2902i	−1.75077	+	0.857877i
$241$	0.0681714	−	0.209810i	0.00439130	−	0.0135150i	−0.948837	−	0.315767i	$-0.897738\pi$
$241$	0.0681714	−	0.209810i	0.00439130	−	0.0135150i	0.953228	+	0.302252i	$0.0977383\pi$
$242$	−8.32526	+	11.4587i	−0.535168	+	0.736596i
$243$		−	24.4486i		−	1.56838i
$244$	−0.236713	−	0.171982i	−0.0151540	−	0.0110100i
$245$	15.3476	−	2.18561i	0.980524	−	0.139634i
$246$	−1.50123	+	1.09071i	−0.0957149	+	0.0695410i
$247$	0.654489	+	0.900827i	0.0416441	+	0.0573182i
$248$	−18.6223	+	6.05076i	−1.18252	+	0.384224i
$249$	−40.4782			−2.56520
$250$	−12.0823	+	10.9997i	−0.764153	+	0.695679i
$251$	−7.69008			−0.485393			−0.242697	−	0.970102i	$-0.578032\pi$
$251$	−7.69008			−0.485393			−0.242697	+	0.970102i	$0.578032\pi$
$252$	−0.237048	+	0.0770215i	−0.0149326	+	0.00485190i
$253$	−1.57840	−	2.17248i	−0.0992331	−	0.136583i
$254$	8.38342	−	6.09091i	0.526023	−	0.382178i
$255$	−7.03060	+	1.00121i	−0.440273	+	0.0626980i
$256$	−2.62487	−	1.90708i	−0.164054	−	0.119192i
$257$		−	18.7288i		−	1.16827i	−0.811657	−	0.584135i	$-0.801434\pi$
$257$		−	18.7288i		−	1.16827i	0.811657	−	0.584135i	$-0.198566\pi$
$258$	−3.27484	+	4.50743i	−0.203882	+	0.280620i
$259$	0.819317	−	2.52160i	0.0509099	−	0.156685i
$260$	0.100402	−	0.0491967i	0.00622664	−	0.00305105i
$261$	16.2354	+	49.9675i	1.00495	+	3.09291i
$262$	−30.5472	−	9.92539i	−1.88721	−	0.613193i
$263$	−10.6989	−	3.47627i	−0.659720	−	0.214356i	−0.0400249	−	0.999199i	$-0.512744\pi$
$263$	−10.6989	−	3.47627i	−0.659720	−	0.214356i	−0.619695	+	0.784843i	$0.712744\pi$
$264$	3.05830	+	9.41247i	0.188225	+	0.579297i
$265$	14.9372	+	15.4114i	0.917584	+	0.946714i
$266$	0.353729	−	1.08867i	0.0216885	−	0.0667504i
$267$	−1.91780	+	2.63962i	−0.117367	+	0.161542i
$268$		−	1.80016i		−	0.109962i
$269$	10.9694	+	7.96975i	0.668817	+	0.485924i	0.869629	−	0.493706i	$-0.164358\pi$
$269$	10.9694	+	7.96975i	0.668817	+	0.485924i	−0.200812	+	0.979630i	$0.564358\pi$
$270$	30.4531	−	29.5161i	1.85332	−	1.79629i
$271$	−17.9276	+	13.0251i	−1.08902	+	0.791221i	−0.979234	−	0.202734i	$-0.935017\pi$
$271$	−17.9276	+	13.0251i	−1.08902	+	0.791221i	−0.109788	+	0.993955i	$0.535017\pi$
$272$	−2.49994	−	3.44088i	−0.151581	−	0.208634i
$273$	−0.288048	+	0.0935923i	−0.0174334	+	0.00566446i
$274$	−9.15640			−0.553159
$275$	3.21541	+	4.72961i	0.193896	+	0.285207i
$276$	−1.01253			−0.0609471
$277$	2.37413	−	0.771403i	0.142648	−	0.0463491i	−0.236823	−	0.971553i	$-0.576106\pi$
$277$	2.37413	−	0.771403i	0.142648	−	0.0463491i	0.379471	+	0.925204i	$0.376106\pi$
$278$	−11.8118	−	16.2575i	−0.708423	−	0.975061i
$279$	41.2035	−	29.9361i	2.46679	−	1.79223i
$280$	1.39451	+	0.738205i	0.0833379	+	0.0441162i
$281$	−2.91579	−	2.11845i	−0.173942	−	0.126376i	0.497408	−	0.867517i	$-0.334285\pi$
$281$	−2.91579	−	2.11845i	−0.173942	−	0.126376i	−0.671350	+	0.741141i	$0.734285\pi$
$282$			36.2755i			2.16017i
$283$	18.2516	−	25.1212i	1.08495	−	1.49330i	0.230988	−	0.972956i	$-0.425804\pi$
$283$	18.2516	−	25.1212i	1.08495	−	1.49330i	0.853957	−	0.520343i	$-0.174196\pi$
$284$	0.103813	−	0.319504i	0.00616018	−	0.0189591i
$285$	3.02778	+	21.2614i	0.179350	+	1.25942i
$286$	−0.190197	−	0.585367i	−0.0112466	−	0.0346134i
$287$	0.0984819	+	0.0319987i	0.00581320	+	0.00188882i
$288$	5.16855	+	1.67936i	0.304559	+	0.0989574i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−11.3354	+	21.4132i	−0.665637	+	1.25743i
$291$	13.9832	−	43.0359i	0.819710	−	2.52281i
$292$	0.0856538	−	0.117892i	0.00501251	−	0.00689913i
$293$		−	8.89986i		−	0.519935i	−0.965617	−	0.259968i	$-0.916288\pi$
$293$		−	8.89986i		−	0.519935i	0.965617	−	0.259968i	$-0.0837119\pi$
$294$	−26.0328	−	18.9139i	−1.51826	−	1.10308i
$295$	−3.10990	+	17.8278i	−0.181065	+	1.03797i
$296$	−22.5628	+	16.3928i	−1.31143	+	0.952813i
$297$	−8.72524	−	12.0093i	−0.506290	−	0.696848i
$298$	4.81135	−	1.56330i	0.278714	−	0.0905596i
$299$	−0.864419			−0.0499906
$300$	2.15539	+	0.0673720i	0.124441	+	0.00388972i
$301$	0.310908			0.0179204
$302$	10.2997	−	3.34657i	0.592680	−	0.192574i
$303$	33.1961	+	45.6905i	1.90706	+	2.62485i
$304$	−10.4057	+	7.56015i	−0.596805	+	0.433604i
$305$	−2.11990	−	4.32634i	−0.121385	−	0.247725i
$306$	8.37838	+	6.08725i	0.478960	+	0.347985i
$307$		−	13.8368i		−	0.789709i	−0.918744	−	0.394855i	$-0.870795\pi$
$307$		−	13.8368i		−	0.789709i	0.918744	−	0.394855i	$-0.129205\pi$
$308$	−0.0236474	+	0.0325479i	−0.00134744	+	0.00185459i
$309$	12.1727	−	37.4637i	0.692480	−	2.13123i
$310$	23.1372	+	4.03608i	1.31411	+	0.229234i
$311$	−9.08306	−	27.9548i	−0.515053	−	1.58517i	−0.783186	−	0.621788i	$-0.786407\pi$
$311$	−9.08306	−	27.9548i	−0.515053	−	1.58517i	0.268133	−	0.963382i	$-0.413593\pi$
$312$	3.02991	+	0.984477i	0.171535	+	0.0557350i
$313$	−33.4875	−	10.8808i	−1.89283	−	0.615017i	−0.976912	−	0.213643i	$-0.931467\pi$
$313$	−33.4875	−	10.8808i	−1.89283	−	0.615017i	−0.915915	−	0.401373i	$-0.868533\pi$
$314$	−6.44300	−	19.8295i	−0.363600	−	1.11904i
$315$	−4.04301	−	0.705268i	−0.227798	−	0.0397373i
$316$	0.0742282	−	0.228451i	0.00417566	−	0.0128514i
$317$	2.45777	−	3.38283i	0.138042	−	0.189998i	−0.734399	−	0.678718i	$-0.762536\pi$
$317$	2.45777	−	3.38283i	0.138042	−	0.189998i	0.872441	+	0.488720i	$0.162536\pi$
$318$		−	44.5490i		−	2.49819i
$319$	6.86081	+	4.98467i	0.384131	+	0.279088i
$320$	−7.26665	−	14.8299i	−0.406218	−	0.829018i
$321$	−13.4522	+	9.77357i	−0.750827	+	0.545508i
$322$	0.522333	+	0.718929i	0.0291085	+	0.0400644i
$323$	−2.87612	+	0.934507i	−0.160031	+	0.0519974i
$324$	−2.71019			−0.150566
$325$	1.84010	+	0.0575170i	0.102070	+	0.00319047i
$326$	−15.9342			−0.882515
$327$	50.7005	−	16.4736i	2.80375	−	0.910992i
$328$	−0.640227	−	0.881197i	−0.0353506	−	0.0486560i
$329$	1.63769	−	1.18985i	0.0902887	−	0.0655986i
$330$	2.04000	−	11.6945i	0.112298	−	0.643759i
$331$	4.62835	+	3.36269i	0.254397	+	0.184830i	0.707673	−	0.706540i	$-0.249745\pi$
$331$	4.62835	+	3.36269i	0.254397	+	0.184830i	−0.453276	+	0.891370i	$0.649745\pi$
$332$			1.73083i			0.0949917i
$333$	42.6386	−	58.6869i	2.33658	−	3.21603i
$334$	−9.49599	+	29.2256i	−0.519597	+	1.59916i
$335$	13.8678	−	26.1971i	0.757679	−	1.43130i
$336$	−1.08111	−	3.32730i	−0.0589792	−	0.181519i
$337$	−18.2081	−	5.91619i	−0.991861	−	0.322275i	−0.232252	−	0.972656i	$-0.574610\pi$
$337$	−18.2081	−	5.91619i	−0.991861	−	0.322275i	−0.759609	+	0.650380i	$0.774610\pi$
$338$	17.8804	+	5.80969i	0.972565	+	0.316006i
$339$	8.53960	+	26.2822i	0.463807	+	1.42745i
$340$	0.0428112	+	0.300625i	0.00232176	+	0.0163037i
$341$	2.54036	−	7.81842i	0.137568	−	0.423391i
$342$	18.4086	−	25.3373i	0.995424	−	1.37008i
$343$			3.60869i			0.194851i
$344$	−2.64578	−	1.92227i	−0.142651	−	0.103642i
$345$	−14.7350	−	7.80017i	−0.793303	−	0.419947i
$346$	22.3216	−	16.2176i	1.20002	−	0.871864i
$347$	7.54035	+	10.3784i	0.404787	+	0.557141i	0.961937	−	0.273270i	$-0.0881053\pi$
$347$	7.54035	+	10.3784i	0.404787	+	0.557141i	−0.557150	+	0.830412i	$0.688105\pi$
$348$	3.04112	−	0.988119i	0.163021	−	0.0529687i
$349$	−22.0051			−1.17791			−0.588953	−	0.808167i	$-0.700460\pi$
$349$	−22.0051			−1.17791			−0.588953	+	0.808167i	$0.700460\pi$
$350$	−1.06406	−	1.56515i	−0.0568764	−	0.0836608i
$351$	−4.77842			−0.255053
$352$	0.834265	−	0.271069i	0.0444665	−	0.0144480i
$353$	−9.69068	−	13.3381i	−0.515783	−	0.709914i	0.469098	−	0.883146i	$-0.344579\pi$
$353$	−9.69068	−	13.3381i	−0.515783	−	0.709914i	−0.984881	+	0.173232i	$0.944579\pi$
$354$	30.3897	−	22.0794i	1.61519	−	1.17351i
$355$	3.97210	−	3.84988i	0.210817	−	0.204331i
$356$	0.112869	+	0.0820042i	0.00598205	+	0.00434621i
$357$		−	0.822573i		−	0.0435352i
$358$	8.90945	−	12.2628i	0.470879	−	0.648110i
$359$	5.10134	−	15.7003i	0.269239	−	0.828631i	−0.721448	−	0.692469i	$-0.756523\pi$
$359$	5.10134	−	15.7003i	0.269239	−	0.828631i	0.990687	−	0.136163i	$-0.0434769\pi$
$360$	30.0450	+	30.9988i	1.58351	+	1.63378i
$361$	−3.04525	−	9.37233i	−0.160277	−	0.493280i
$362$	−10.0169	−	3.25470i	−0.526478	−	0.171063i
$363$	29.2733	+	9.51148i	1.53645	+	0.499223i
$364$	0.00400197	+	0.0123168i	0.000209760	+	0.000645575i
$365$	2.15469	−	1.05580i	0.112782	−	0.0552629i
$366$	−3.09025	+	9.51080i	−0.161530	+	0.497138i
$367$	−7.35972	+	10.1298i	−0.384174	+	0.528770i	−0.956684	−	0.291127i	$-0.905970\pi$
$367$	−7.35972	+	10.1298i	−0.384174	+	0.528770i	0.572510	+	0.819898i	$0.305970\pi$
$368$		−	9.98509i		−	0.520509i
$369$	2.29204	+	1.66526i	0.119319	+	0.0866902i
$370$	33.1183	−	4.71628i	1.72174	−	0.245188i
$371$	−2.01121	+	1.46123i	−0.104417	+	0.0758631i
$372$	−1.82197	−	2.50772i	−0.0944646	−	0.130019i
$373$	11.5376	−	3.74878i	0.597392	−	0.194104i	0.00531507	−	0.999986i	$-0.498308\pi$
$373$	11.5376	−	3.74878i	0.597392	−	0.194104i	0.592077	+	0.805881i	$0.298308\pi$
$374$	1.67162			0.0864375
$375$	30.8475	+	17.5848i	1.59296	+	0.908073i
$376$	−21.2931			−1.09811
$377$	2.59627	−	0.843579i	0.133715	−	0.0434465i
$378$	2.88740	+	3.97417i	0.148512	+	0.204409i
$379$	−25.1263	+	18.2553i	−1.29065	+	0.937711i	−0.999818	−	0.0190631i	$-0.993932\pi$
$379$	−25.1263	+	18.2553i	−1.29065	+	0.937711i	−0.290831	+	0.956775i	$0.593932\pi$
$380$	0.909130	−	0.129466i	0.0466374	−	0.00664149i
$381$	−18.2183	−	13.2364i	−0.933352	−	0.678120i
$382$		−	0.368307i		−	0.0188442i
$383$	−20.9647	+	28.8554i	−1.07125	+	1.47444i	−0.202436	+	0.979295i	$0.564886\pi$
$383$	−20.9647	+	28.8554i	−1.07125	+	1.47444i	−0.868809	+	0.495147i	$0.835114\pi$
$384$	−12.0981	+	37.2341i	−0.617379	+	1.90010i
$385$	−0.594870	+	0.291486i	−0.0303174	+	0.0148555i
$386$	−7.62291	−	23.4609i	−0.387996	−	1.19413i
$387$	8.09007	+	2.62862i	0.411241	+	0.133620i
$388$	−1.84020	−	0.597916i	−0.0934218	−	0.0303546i
$389$	2.48426	+	7.64577i	0.125957	+	0.387656i	0.994074	−	0.108703i	$-0.0346699\pi$
$389$	2.48426	+	7.64577i	0.125957	+	0.387656i	−0.868117	+	0.496359i	$0.834670\pi$
$390$	−2.65955	−	2.74398i	−0.134672	−	0.138947i
$391$	0.725476	−	2.23279i	0.0366889	−	0.112917i
$392$	11.1022	−	15.2808i	0.560744	−	0.771797i
$393$			69.7994i			3.52091i
$394$	24.1845	+	17.5711i	1.21840	+	0.885219i
$395$	2.84012	−	2.75273i	0.142902	−	0.138505i
$396$	−0.890507	+	0.646991i	−0.0447497	+	0.0325125i
$397$	−19.5469	−	26.9040i	−0.981032	−	1.35028i	−0.936271	−	0.351277i	$-0.885747\pi$
$397$	−19.5469	−	26.9040i	−0.981032	−	1.35028i	−0.0447610	−	0.998998i	$-0.514253\pi$
$398$	−14.1963	+	4.61267i	−0.711599	+	0.231212i
$399$	−2.48757			−0.124534
$400$	−0.664391	+	21.2554i	−0.0332196	+	1.06277i
$401$	−20.6693			−1.03218			−0.516088	−	0.856536i	$-0.672612\pi$
$401$	−20.6693			−1.03218			−0.516088	+	0.856536i	$0.672612\pi$
$402$	−58.5146	+	19.0126i	−2.91844	+	0.948260i
$403$	−1.55545	−	2.14090i	−0.0774827	−	0.106646i
$404$	1.95371	−	1.41945i	0.0972005	−	0.0706203i
$405$	−39.4403	−	20.8783i	−1.95981	−	1.03745i
$406$	−2.27042	−	1.64955i	−0.112679	−	0.0818660i
$407$		−	11.7090i		−	0.580394i
$408$	−5.08579	+	6.99999i	−0.251784	+	0.346551i
$409$	4.46704	−	13.7481i	0.220881	−	0.679801i	−0.777803	−	0.628508i	$-0.783666\pi$
$409$	4.46704	−	13.7481i	0.220881	−	0.679801i	0.998684	−	0.0512929i	$-0.0163342\pi$
$410$	0.184196	+	1.29345i	0.00909678	+	0.0638787i
$411$	6.14885	+	18.9242i	0.303300	+	0.933462i
$412$	−1.60193	−	0.520499i	−0.0789214	−	0.0256431i
$413$	−1.99359	−	0.647756i	−0.0980981	−	0.0318740i
$414$	7.51320	+	23.1233i	0.369254	+	1.13645i
$415$	−13.3337	+	25.1881i	−0.654526	+	1.23644i
$416$	0.0872582	−	0.268553i	0.00427818	−	0.0131669i
$417$	−25.6686	+	35.3298i	−1.25700	+	1.73011i
$418$		−	5.05520i		−	0.247258i
$419$	−13.9728	−	10.1518i	−0.682615	−	0.495949i	0.191609	−	0.981471i	$-0.438629\pi$
$419$	−13.9728	−	10.1518i	−0.682615	−	0.495949i	−0.874224	+	0.485523i	$0.838629\pi$
$420$	−0.0429239	+	0.246065i	−0.00209447	+	0.0120068i
$421$	−20.9181	+	15.1979i	−1.01949	+	0.740700i	−0.966178	−	0.257878i	$-0.916977\pi$
$421$	−20.9181	+	15.1979i	−1.01949	+	0.740700i	−0.0533091	+	0.998578i	$0.516977\pi$
$422$	−4.58135	−	6.30568i	−0.223016	−	0.306956i
$423$	52.6738	−	17.1148i	2.56109	−	0.832148i
$424$	26.1495			1.26993
$425$	−1.69290	+	4.70469i	−0.0821175	+	0.228211i
$426$	−11.4820			−0.556304
$427$	0.530735	−	0.172446i	0.0256841	−	0.00834526i
$428$	0.417914	+	0.575209i	0.0202006	+	0.0278038i
$429$	−1.08210	+	0.786188i	−0.0522441	+	0.0379575i
$430$	1.72606	+	3.52258i	0.0832381	+	0.169874i
$431$	28.9533	+	21.0358i	1.39463	+	1.01326i	0.995339	+	0.0964371i	$0.0307447\pi$
$431$	28.9533	+	21.0358i	1.39463	+	1.01326i	0.399294	+	0.916823i	$0.369255\pi$
$432$		−	55.1966i		−	2.65565i
$433$	6.97062	−	9.59424i	0.334987	−	0.461070i	−0.607982	−	0.793951i	$-0.708021\pi$
$433$	6.97062	−	9.59424i	0.334987	−	0.461070i	0.942969	+	0.332881i	$0.108021\pi$
$434$	−0.840669	+	2.58731i	−0.0403534	+	0.124195i
$435$	51.8683	+	9.04797i	2.48690	+	0.433817i
$436$	−0.704405	−	2.16793i	−0.0337349	−	0.103825i
$437$	−6.75223	−	2.19393i	−0.323003	−	0.104950i
$438$	−4.73676	−	1.53907i	−0.226331	−	0.0735394i
$439$	−5.91506	−	18.2047i	−0.282310	−	0.868862i	−0.987192	−	0.159537i	$-0.949000\pi$
$439$	−5.91506	−	18.2047i	−0.282310	−	0.868862i	0.704882	−	0.709325i	$-0.251000\pi$
$440$	6.86446	+	1.19744i	0.327250	+	0.0570859i
$441$	−15.1817	+	46.7244i	−0.722938	+	2.22497i
$442$	0.316288	−	0.435333i	0.0150443	−	0.0207067i
$443$		−	4.12083i		−	0.195787i	−0.995197	−	0.0978933i	$-0.968790\pi$
$443$		−	4.12083i		−	0.195787i	0.995197	−	0.0978933i	$-0.0312104\pi$
$444$	−3.57180	−	2.59506i	−0.169510	−	0.123156i
$445$	1.01081	+	2.06288i	0.0479170	+	0.0977898i
$446$	30.2332	−	21.9657i	1.43158	−	1.04011i
$447$	−6.46198	−	8.89415i	−0.305641	−	0.420679i
$448$	1.81927	−	0.591115i	0.0859522	−	0.0279276i
$449$	−6.32711			−0.298595			−0.149297	−	0.988792i	$-0.547701\pi$
$449$	−6.32711			−0.298595			−0.149297	+	0.988792i	$0.547701\pi$
$450$	−14.4549	−	49.7227i	−0.681410	−	2.34395i
$451$	0.457299			0.0215334
$452$	1.12382	−	0.365150i	0.0528598	−	0.0171752i
$453$	−13.8332	−	19.0398i	−0.649941	−	0.894567i
$454$	17.0289	−	12.3722i	0.799204	−	0.580655i
$455$	−0.0366451	+	0.210071i	−0.00171795	+	0.00984830i
$456$	21.1689	+	15.3801i	0.991322	+	0.720238i
$457$			27.7724i			1.29914i	0.760304	+	0.649568i	$0.225050\pi$
$457$			27.7724i			1.29914i	−0.760304	+	0.649568i	$0.774950\pi$
$458$	−21.8453	+	30.0675i	−1.02076	+	1.40496i
$459$	4.01036	−	12.3426i	0.187188	−	0.576104i
$460$	−0.333532	+	0.630061i	−0.0155510	+	0.0293767i
$461$	8.08848	+	24.8938i	0.376718	+	1.15942i	0.942312	+	0.334735i	$0.108647\pi$
$461$	8.08848	+	24.8938i	0.376718	+	1.15942i	−0.565594	+	0.824684i	$0.691353\pi$
$462$	1.30773	+	0.424908i	0.0608412	+	0.0197685i
$463$	22.9019	+	7.44127i	1.06434	+	0.345825i	0.788281	−	0.615316i	$-0.210971\pi$
$463$	22.9019	+	7.44127i	1.06434	+	0.345825i	0.276059	+	0.961141i	$0.410971\pi$
$464$	9.74437	+	29.9901i	0.452371	+	1.39225i
$465$	−7.19579	−	50.5297i	−0.333697	−	2.34326i
$466$	−5.01063	+	15.4211i	−0.232113	+	0.714371i
$467$	−4.72904	+	6.50896i	−0.218834	+	0.301199i	−0.904293	−	0.426912i	$-0.859601\pi$
$467$	−4.72904	+	6.50896i	−0.218834	+	0.301199i	0.685459	+	0.728111i	$0.259601\pi$
$468$			0.354328i			0.0163788i
$469$	2.77764	+	2.01807i	0.128260	+	0.0931860i
$470$	22.5729	+	11.9493i	1.04121	+	0.551181i
$471$	−36.6564	+	26.6324i	−1.68904	+	1.22716i
$472$	12.9602	+	17.8383i	0.596544	+	0.821072i
$473$	1.30583	−	0.424291i	0.0600423	−	0.0195089i
$474$	−8.20981			−0.377089
$475$	14.2276	+	5.11954i	0.652806	+	0.234900i
$476$	−0.0351729			−0.00161215
$477$	−64.6874	+	21.0182i	−2.96183	+	0.962357i
$478$	−4.54467	−	6.25520i	−0.207868	−	0.286106i
$479$	2.62811	−	1.90943i	0.120081	−	0.0872443i	−0.526124	−	0.850408i	$-0.676355\pi$
$479$	2.62811	−	1.90943i	0.120081	−	0.0872443i	0.646205	+	0.763164i	$0.276355\pi$
$480$	3.91072	−	3.79040i	0.178499	−	0.173007i
$481$	−3.04932	−	2.21546i	−0.139037	−	0.101016i
$482$			0.322404i			0.0146851i
$483$	1.13510	−	1.56233i	0.0516488	−	0.0710884i
$484$	0.406707	−	1.25171i	0.0184867	−	0.0568961i
$485$	−22.1735	−	22.8775i	−1.00685	−	1.03881i
$486$	11.0412	+	33.9813i	0.500839	+	1.54142i
$487$	16.1794	+	5.25700i	0.733158	+	0.238218i	0.651719	−	0.758461i	$-0.274048\pi$
$487$	16.1794	+	5.25700i	0.733158	+	0.238218i	0.0814395	+	0.996678i	$0.474048\pi$
$488$	−5.58268	−	1.81392i	−0.252716	−	0.0821125i
$489$	10.7004	+	32.9324i	0.483889	+	1.48926i
$490$	−20.3448	+	9.96893i	−0.919084	+	0.450350i
$491$	−1.79091	+	5.51185i	−0.0808226	+	0.248746i	−0.983300	−	0.181990i	$-0.941746\pi$
$491$	−1.79091	+	5.51185i	−0.0808226	+	0.248746i	0.902478	+	0.430736i	$0.141746\pi$
$492$	0.101351	−	0.139498i	0.00456926	−	0.00628904i
$493$			7.41412i			0.333915i
$494$	−1.31650	−	0.956495i	−0.0592322	−	0.0430347i
$495$	−17.9434	+	2.55527i	−0.806496	+	0.114851i
$496$	24.7300	−	17.9674i	1.11041	−	0.806760i
$497$	0.376614	+	0.518364i	0.0168934	+	0.0232518i
$498$	56.2610	−	18.2803i	2.52112	−	0.819161i
$499$	−0.286848			−0.0128411			−0.00642055	−	0.999979i	$-0.502044\pi$
$499$	−0.286848			−0.0128411			−0.00642055	+	0.999979i	$0.502044\pi$
$500$	0.751917	−	1.31903i	0.0336268	−	0.0589887i
$501$	66.7797			2.98349
$502$	10.6885	−	3.47291i	0.477052	−	0.155003i
$503$	9.12512	+	12.5597i	0.406869	+	0.560007i	0.962451	−	0.271454i	$-0.0875046\pi$
$503$	9.12512	+	12.5597i	0.406869	+	0.560007i	−0.555582	+	0.831462i	$0.687505\pi$
$504$	−4.04538	+	2.93914i	−0.180196	+	0.130920i
$505$	39.3665	−	5.60607i	1.75179	−	0.249467i
$506$	3.17495	+	2.30673i	0.141144	+	0.102547i
$507$		−	40.8561i		−	1.81448i
$508$	−0.565982	+	0.779007i	−0.0251114	+	0.0345628i
$509$	−0.104840	+	0.322664i	−0.00464694	+	0.0143018i	−0.953353	−	0.301857i	$-0.902393\pi$
$509$	−0.104840	+	0.322664i	−0.00464694	+	0.0143018i	0.948706	+	0.316159i	$0.102393\pi$
$510$	9.31974	−	4.56667i	0.412685	−	0.202215i
$511$	0.0858851	+	0.264327i	0.00379933	+	0.0116931i
$512$	−18.9383	−	6.15344i	−0.836965	−	0.271946i
$513$	−37.3257	−	12.1278i	−1.64797	−	0.535457i
$514$	8.45809	+	26.0313i	0.373070	+	1.14819i
$515$	−19.3025	−	19.9153i	−0.850572	−	0.877574i
$516$	0.159983	−	0.492376i	0.00704285	−	0.0216757i
$517$	5.25464	−	7.23239i	0.231099	−	0.318080i
$518$			3.87481i			0.170249i
$519$	−48.5079	−	35.2430i	−2.12926	−	1.54700i
$520$	1.61067	−	1.56111i	0.0706326	−	0.0684593i
$521$	9.46116	−	6.87394i	0.414501	−	0.301153i	−0.360920	−	0.932597i	$-0.617537\pi$
$521$	9.46116	−	6.87394i	0.414501	−	0.301153i	0.775422	+	0.631444i	$0.217537\pi$
$522$	−45.1316	−	62.1183i	−1.97536	−	2.71884i
$523$	31.8360	−	10.3442i	1.39209	−	0.452318i	0.485467	−	0.874255i	$-0.338650\pi$
$523$	31.8360	−	10.3442i	1.39209	−	0.452318i	0.906625	+	0.421937i	$0.138650\pi$
$524$	2.98459			0.130383
$525$	−2.52026	+	3.25022i	−0.109993	+	0.141851i
$526$	16.4404			0.716834
$527$	6.83536	−	2.22094i	0.297753	−	0.0967458i
$528$	−9.08144	−	12.4995i	−0.395219	−	0.543972i
$529$	−14.1484	+	10.2794i	−0.615147	+	0.446930i
$530$	−27.7213	−	14.6747i	−1.20414	−	0.637427i
$531$	−46.3982	−	33.7103i	−2.01351	−	1.46290i
$532$			0.106367i			0.00461161i
$533$	0.0865256	−	0.119092i	0.00374784	−	0.00515846i
$534$	1.47349	−	4.53493i	0.0637640	−	0.196245i
$535$	1.65054	+	11.5903i	0.0713589	+	0.501091i
$536$	−11.1601	−	34.3471i	−0.482041	−	1.48357i
$537$	−31.3275	−	10.1789i	−1.35188	−	0.439252i
$538$	−18.8457	−	6.12334i	−0.812496	−	0.263996i
$539$	2.45051	+	7.54189i	0.105551	+	0.324852i
$540$	−1.84373	+	3.48291i	−0.0793416	+	0.149881i
$541$	−1.82888	+	5.62872i	−0.0786298	+	0.241998i	−0.982643	−	0.185507i	$-0.940607\pi$
$541$	−1.82888	+	5.62872i	−0.0786298	+	0.241998i	0.904013	+	0.427505i	$0.140607\pi$
$542$	19.0354	−	26.2000i	0.817641	−	1.12539i
$543$			22.8884i			0.982234i
$544$	0.620437	+	0.450774i	0.0266010	+	0.0193268i
$545$	6.45007	−	36.9756i	0.276290	−	1.58386i
$546$	0.358093	−	0.260170i	0.0153250	−	0.0111342i
$547$	−12.0797	−	16.6263i	−0.516492	−	0.710890i	0.468505	−	0.883461i	$-0.344793\pi$
$547$	−12.0797	−	16.6263i	−0.516492	−	0.710890i	−0.984997	+	0.172571i	$0.944793\pi$
$548$	0.809191	−	0.262922i	0.0345669	−	0.0112315i
$549$	15.2681			0.651628
$550$	−6.60507	−	5.12163i	−0.281641	−	0.218387i
$551$	22.4213			0.955178
$552$	−19.3191	+	6.27715i	−0.822275	+	0.267173i
$553$	0.269285	+	0.370639i	0.0114512	+	0.0157612i
$554$	−2.95146	+	2.14436i	−0.125396	+	0.0911052i
$555$	−31.9876	−	65.2808i	−1.35780	−	2.77102i
$556$	1.51069	+	1.09758i	0.0640674	+	0.0465477i
$557$		−	0.761791i		−	0.0322781i	−0.999870	−	0.0161391i	$-0.994863\pi$
$557$		−	0.761791i		−	0.0322781i	0.999870	−	0.0161391i	$-0.00513744\pi$
$558$	−43.7498	+	60.2164i	−1.85208	+	2.54916i
$559$	0.136581	−	0.420353i	0.00577675	−	0.0177790i
$560$	−2.42658	−	0.423296i	−0.102542	−	0.0178875i
$561$	−1.12255	−	3.45486i	−0.0473942	−	0.145864i
$562$	5.00940	+	1.62765i	0.211309	+	0.0686583i
$563$	16.7006	+	5.42637i	0.703848	+	0.228694i	0.639006	−	0.769201i	$-0.279346\pi$
$563$	16.7006	+	5.42637i	0.703848	+	0.228694i	0.0648419	+	0.997896i	$0.479346\pi$
$564$	−1.04164	−	3.20582i	−0.0438608	−	0.134990i
$565$	19.1674	+	3.34359i	0.806381	+	0.140666i
$566$	−14.0231	+	43.1588i	−0.589436	+	1.81410i
$567$	3.03826	−	4.18181i	0.127595	−	0.175619i
$568$		−	6.73973i		−	0.282793i
$569$	6.44807	+	4.68480i	0.270317	+	0.196397i	0.714683	−	0.699448i	$-0.246571\pi$
$569$	6.44807	+	4.68480i	0.270317	+	0.196397i	−0.444366	+	0.895845i	$0.646571\pi$
$570$	−13.8102	−	28.1841i	−0.578445	−	1.18050i
$571$	−13.6029	+	9.88312i	−0.569266	+	0.413596i	−0.834838	−	0.550495i	$-0.814439\pi$
$571$	−13.6029	+	9.88312i	−0.569266	+	0.413596i	0.265573	+	0.964091i	$0.414439\pi$
$572$	0.0336171	+	0.0462700i	0.00140560	+	0.00193464i
$573$	−0.761208	+	0.247331i	−0.0317999	+	0.0103324i
$574$	−0.151332			−0.00631647
$575$	−9.70753	+	6.59962i	−0.404832	+	0.275223i
$576$	52.3364			2.18068
$577$	−20.6419	+	6.70697i	−0.859334	+	0.279215i	−0.705351	−	0.708859i	$-0.749210\pi$
$577$	−20.6419	+	6.70697i	−0.859334	+	0.279215i	−0.153984	+	0.988073i	$0.549210\pi$
$578$	0.859012	+	1.18233i	0.0357302	+	0.0491784i
$579$	−43.3693	+	31.5096i	−1.80237	+	1.30950i
$580$	0.386887	−	2.21787i	0.0160646	−	0.0920920i
$581$	−2.67067	−	1.94035i	−0.110798	−	0.0804994i
$582$			66.1309i			2.74122i
$583$	−6.45309	+	8.88192i	−0.267260	+	0.367851i
$584$	0.903406	−	2.78040i	0.0373832	−	0.115054i
$585$	−2.72962	+	5.15640i	−0.112856	+	0.213191i
$586$	4.01926	+	12.3700i	0.166034	+	0.511000i
$587$	−1.58879	−	0.516230i	−0.0655764	−	0.0213071i	0.276045	−	0.961145i	$-0.410976\pi$
$587$	−1.58879	−	0.516230i	−0.0655764	−	0.0213071i	−0.341622	+	0.939838i	$0.610976\pi$
$588$	2.84374	+	0.923986i	0.117274	+	0.0381045i
$589$	−6.71642	−	20.6710i	−0.276745	−	0.851734i
$590$	−3.72871	−	26.1835i	−0.153509	−	1.07796i
$591$	20.0747	−	61.7836i	0.825763	−	2.54144i
$592$	25.5913	−	35.2234i	1.05180	−	1.44767i
$593$		−	9.01124i		−	0.370047i	−0.982734	−	0.185024i	$-0.940764\pi$
$593$		−	9.01124i		−	0.370047i	0.982734	−	0.185024i	$-0.0592362\pi$
$594$	17.5508	+	12.7514i	0.720118	+	0.523196i
$595$	−0.511857	−	0.270959i	−0.0209841	−	0.0111083i
$596$	−0.380310	+	0.276311i	−0.0155781	+	0.0113182i
$597$	19.0667	+	26.2431i	0.780348	+	1.07406i
$598$	1.20146	−	0.390379i	0.0491315	−	0.0159638i
$599$	−3.99167			−0.163095			−0.0815476	−	0.996669i	$-0.525986\pi$
$599$	−3.99167			−0.163095			−0.0815476	+	0.996669i	$0.525986\pi$
$600$	41.5425	−	12.0768i	1.69596	−	0.493033i
$601$	−46.4077			−1.89301			−0.946505	−	0.322690i	$-0.895413\pi$
$601$	−46.4077			−1.89301			−0.946505	+	0.322690i	$0.895413\pi$
$602$	−0.432134	+	0.140409i	−0.0176125	+	0.00572263i
$603$	55.2143	+	75.9960i	2.24850	+	3.09480i
$604$	−0.814133	+	0.591502i	−0.0331266	+	0.0240679i
$605$	15.5614	−	15.0826i	0.632662	−	0.613195i
$606$	−66.7738	−	48.5140i	−2.71250	−	1.97075i
$607$			29.1889i			1.18474i	0.805666	+	0.592370i	$0.201807\pi$
$607$			29.1889i			1.18474i	−0.805666	+	0.592370i	$0.798193\pi$
$608$	1.36320	−	1.87628i	0.0552850	−	0.0760933i
$609$	−1.88459	+	5.80017i	−0.0763674	+	0.235035i
$610$	4.90029	+	5.05585i	0.198407	+	0.204706i
$611$	−0.889267	−	2.73688i	−0.0359759	−	0.110722i
$612$	−0.915226	−	0.297375i	−0.0369958	−	0.0120207i
$613$	14.6465	+	4.75895i	0.591568	+	0.192212i	0.589476	−	0.807786i	$-0.299334\pi$
$613$	14.6465	+	4.75895i	0.591568	+	0.192212i	0.00209166	+	0.999998i	$0.499334\pi$
$614$	6.24884	+	19.2319i	0.252182	+	0.776138i
$615$	2.54956	−	1.24929i	0.102808	−	0.0503760i
$616$	−0.249414	+	0.767617i	−0.0100492	+	0.0309282i
$617$	−23.7900	+	32.7442i	−0.957750	+	1.31823i	−0.00975291	+	0.999952i	$0.503104\pi$
$617$	−23.7900	+	32.7442i	−0.957750	+	1.31823i	−0.947997	+	0.318278i	$0.896896\pi$
$618$			57.5684i			2.31574i
$619$	−27.0619	−	19.6616i	−1.08771	−	0.790268i	−0.108700	−	0.994075i	$-0.534669\pi$
$619$	−27.0619	−	19.6616i	−1.08771	−	0.790268i	−0.979011	+	0.203807i	$0.934669\pi$
$620$	−2.16063	+	0.307689i	−0.0867730	+	0.0123571i
$621$	24.6490	−	17.9085i	0.989130	−	0.718645i
$622$	25.2493	+	34.7526i	1.01240	+	1.39345i
$623$	−0.253064	+	0.0822256i	−0.0101388	+	0.00329430i
$624$	−4.97350			−0.199099
$625$	21.1037	−	13.4028i	0.844147	−	0.536111i
$626$	51.4585			2.05669
$627$	−10.4479	+	3.39474i	−0.417251	+	0.135573i
$628$	1.13879	+	1.56741i	0.0454428	+	0.0625466i
$629$	8.28170	−	6.01701i	0.330213	−	0.239914i
$630$	5.93793	−	0.845603i	0.236573	−	0.0336896i
$631$	9.97594	+	7.24794i	0.397136	+	0.288536i	0.768373	−	0.640002i	$-0.221066\pi$
$631$	9.97594	+	7.24794i	0.397136	+	0.288536i	−0.371237	+	0.928538i	$0.621066\pi$
$632$		−	4.81902i		−	0.191690i
$633$	−9.95588	+	13.7031i	−0.395711	+	0.544649i
$634$	−1.88836	+	5.81177i	−0.0749963	+	0.230815i
$635$	−14.2377	+	6.97647i	−0.565006	+	0.276853i
$636$	1.27921	+	3.93699i	0.0507238	+	0.156112i
$637$	2.42776	+	0.788827i	0.0961914	+	0.0312545i
$638$	−11.7870	−	3.82984i	−0.466653	−	0.151625i
$639$	5.41719	+	16.6724i	0.214301	+	0.659550i
$640$	19.1843	+	19.7933i	0.758326	+	0.782400i
$641$	7.35223	−	22.6278i	0.290395	−	0.893745i	−0.694334	−	0.719653i	$-0.744301\pi$
$641$	7.35223	−	22.6278i	0.290395	−	0.893745i	0.984729	−	0.174092i	$-0.0556991\pi$
$642$	14.2835	−	19.6595i	0.563724	−	0.775899i
$643$		−	9.81816i		−	0.387190i	−0.981081	−	0.193595i	$-0.937985\pi$
$643$		−	9.81816i		−	0.387190i	0.981081	−	0.193595i	$-0.0620148\pi$
$644$	−0.0668046	−	0.0485363i	−0.00263247	−	0.00191260i
$645$	6.12126	−	5.93292i	0.241024	−	0.233608i
$646$	3.57551	−	2.59776i	0.140677	−	0.102208i
$647$	8.70320	+	11.9789i	0.342158	+	0.470940i	0.945070	−	0.326867i	$-0.105993\pi$
$647$	8.70320	+	11.9789i	0.342158	+	0.470940i	−0.602912	+	0.797808i	$0.705993\pi$
$648$	−51.7104	+	16.8017i	−2.03138	+	0.660034i
$649$	−9.25720			−0.363377
$650$	−2.58355	+	0.751063i	−0.101335	+	0.0294591i
$651$	5.91193			0.231707
$652$	1.40818	−	0.457545i	0.0551485	−	0.0179188i
$653$	−4.13332	−	5.68902i	−0.161749	−	0.222629i	0.720448	−	0.693509i	$-0.243936\pi$
$653$	−4.13332	−	5.68902i	−0.161749	−	0.222629i	−0.882197	+	0.470880i	$0.843936\pi$
$654$	−63.0296	+	45.7937i	−2.46465	+	1.79067i
$655$	43.4337	+	22.9923i	1.69709	+	0.898382i
$656$	1.37566	+	0.999477i	0.0537106	+	0.0390230i
$657$			7.60413i			0.296665i
$658$	−1.73889	+	2.39338i	−0.0677891	+	0.0933037i
$659$	5.53519	−	17.0356i	0.215620	−	0.663612i	−0.783489	−	0.621406i	$-0.786562\pi$
$659$	5.53519	−	17.0356i	0.215620	−	0.663612i	0.999109	−	0.0422052i	$-0.0134383\pi$
$660$	0.155518	+	1.09207i	0.00605354	+	0.0425087i
$661$	5.07381	+	15.6156i	0.197348	+	0.607375i	0.999941	+	0.0108483i	$0.00345319\pi$
$661$	5.07381	+	15.6156i	0.197348	+	0.607375i	−0.802593	+	0.596527i	$0.796547\pi$
$662$	−7.95161	−	2.58363i	−0.309048	−	0.100416i
$663$	−1.11213	−	0.361354i	−0.0431917	−	0.0140338i
$664$	10.7302	+	33.0243i	0.416414	+	1.28159i
$665$	−0.819416	+	1.54792i	−0.0317756	+	0.0600259i
$666$	−32.7602	+	100.826i	−1.26943	+	3.90691i
$667$	−10.2310	+	14.0818i	−0.396147	+	0.545249i
$668$		−	2.85547i		−	0.110481i
$669$	−65.7008	−	47.7344i	−2.54014	−	1.84552i
$670$	−7.44416	+	42.6744i	−0.287593	+	1.64865i
$671$	1.99379	−	1.44857i	0.0769694	−	0.0559215i
$672$	0.370794	+	0.510355i	0.0143037	+	0.0196874i
$673$	22.3012	−	7.24609i	0.859647	−	0.279316i	0.154166	−	0.988045i	$-0.450731\pi$
$673$	22.3012	−	7.24609i	0.859647	−	0.279316i	0.705481	+	0.708729i	$0.250731\pi$
$674$	27.9795			1.07773
$675$	−53.6623	+	36.4821i	−2.06546	+	1.40420i
$676$	−1.74699			−0.0671920
$677$	26.1808	−	8.50665i	1.00621	−	0.326937i	0.240865	−	0.970559i	$-0.422569\pi$
$677$	26.1808	−	8.50665i	1.00621	−	0.326937i	0.765344	+	0.643622i	$0.222569\pi$
$678$	−23.7386	−	32.6733i	−0.911674	−	1.25481i
$679$	2.98554	−	2.16912i	0.114574	−	0.0832432i
$680$	2.68056	+	5.47053i	0.102795	+	0.209785i
$681$	−37.0060	−	26.8864i	−1.41807	−	1.03029i
$682$			12.0142i			0.460046i
$683$	−0.844571	+	1.16245i	−0.0323166	+	0.0444800i	−0.824870	−	0.565323i	$-0.808751\pi$
$683$	−0.844571	+	1.16245i	−0.0323166	+	0.0444800i	0.792553	+	0.609803i	$0.208751\pi$
$684$	−0.899300	+	2.76776i	−0.0343856	+	0.105828i
$685$	13.8013	+	2.40752i	0.527321	+	0.0919865i
$686$	−1.62972	−	5.01575i	−0.0622229	−	0.191502i
$687$	76.8125	+	24.9579i	2.93058	+	0.952203i
$688$	4.85559	+	1.57768i	0.185118	+	0.0601483i
$689$	1.09209	+	3.36110i	0.0416052	+	0.128048i
$690$	24.0029	+	4.18709i	0.913774	+	0.159400i
$691$	6.44952	−	19.8496i	0.245351	−	0.755113i	−0.750227	−	0.661180i	$-0.770056\pi$
$691$	6.44952	−	19.8496i	0.245351	−	0.755113i	0.995578	−	0.0939333i	$-0.0299440\pi$
$692$	−1.50698	+	2.07418i	−0.0572867	+	0.0788483i
$693$		−	2.09936i		−	0.0797481i
$694$	−15.1674	−	11.0197i	−0.575746	−	0.418304i
$695$	13.5291	+	27.6104i	0.513188	+	1.04732i
$696$	51.8988	−	37.7067i	1.96722	−	1.42927i
$697$	0.234996	+	0.323445i	0.00890112	+	0.0122513i
$698$	30.5851	−	9.93771i	1.15766	−	0.376148i
$699$	35.2368			1.33278
$700$	0.138978	+	0.107765i	0.00525288	+	0.00407314i
$701$	−29.3643			−1.10907			−0.554536	−	0.832159i	$-0.687104\pi$
$701$	−29.3643			−1.10907			−0.554536	+	0.832159i	$0.687104\pi$
$702$	6.64158	−	2.15798i	0.250670	−	0.0814477i
$703$	−18.1962	−	25.0449i	−0.686283	−	0.944588i
$704$	6.83435	−	4.96545i	0.257579	−	0.187142i
$705$	9.53801	−	54.6775i	0.359222	−	2.05928i
$706$	19.4928	+	14.1623i	0.733620	+	0.533006i
$707$			4.60584i			0.173220i
$708$	−2.05167	+	2.82388i	−0.0771065	+	0.106128i
$709$	−0.191889	+	0.590572i	−0.00720653	+	0.0221794i	−0.954595	−	0.297906i	$-0.903712\pi$
$709$	−0.191889	+	0.590572i	−0.00720653	+	0.0221794i	0.947389	+	0.320086i	$0.103712\pi$
$710$	−3.78222	+	7.14483i	−0.141944	+	0.268141i
$711$	3.87338	+	11.9210i	0.145263	+	0.447074i
$712$	2.66193	+	0.864912i	0.0997599	+	0.0324140i
$713$	16.0473	+	5.21408i	0.600976	+	0.195269i
$714$	0.371481	+	1.14330i	0.0139023	+	0.0427870i
$715$	0.132769	+	0.932323i	0.00496530	+	0.0348669i
$716$	−0.435246	+	1.33955i	−0.0162659	+	0.0500613i
$717$	−9.87617	+	13.5934i	−0.368832	+	0.507654i
$718$			24.1258i			0.900369i
$719$	−1.89648	−	1.37787i	−0.0707267	−	0.0513859i	0.551860	−	0.833937i	$-0.313918\pi$
$719$	−1.89648	−	1.37787i	−0.0707267	−	0.0513859i	−0.622587	+	0.782551i	$0.713918\pi$
$720$	−59.5628	−	31.5304i	−2.21977	−	1.17507i
$721$	2.59898	−	1.88827i	0.0967909	−	0.0703227i
$722$	8.46526	+	11.6514i	0.315044	+	0.433621i
$723$	0.666335	−	0.216505i	0.0247813	−	0.00805192i
$724$	0.978697			0.0363730
$725$	22.7159	−	29.2954i	0.843648	−	1.08800i
$726$	−44.9827			−1.66947
$727$	−23.8191	+	7.73931i	−0.883403	+	0.287035i	−0.715370	−	0.698746i	$-0.753742\pi$
$727$	−23.8191	+	7.73931i	−0.883403	+	0.287035i	−0.168033	+	0.985781i	$0.553742\pi$
$728$	0.152715	+	0.210195i	0.00566001	+	0.00779033i
$729$	14.3800	−	10.4477i	0.532594	−	0.386952i
$730$	−2.51802	+	2.44054i	−0.0931959	+	0.0903284i
$731$	0.971139	+	0.705574i	0.0359189	+	0.0260966i
$732$		−	0.929246i		−	0.0343459i
$733$	18.4289	−	25.3652i	0.680687	−	0.936886i	−0.319255	−	0.947669i	$-0.603433\pi$
$733$	18.4289	−	25.3652i	0.680687	−	0.936886i	0.999942	+	0.0107834i	$0.00343252\pi$
$734$	5.65464	−	17.4032i	0.208717	−	0.642364i
$735$	34.2658	+	35.3536i	1.26391	+	1.30404i
$736$	0.556369	+	1.71233i	0.0205080	+	0.0631173i
$737$	14.4203	+	4.68545i	0.531180	+	0.172591i
$738$	−3.93778	−	1.27946i	−0.144952	−	0.0470976i
$739$	8.96697	+	27.5975i	0.329855	+	1.01519i	0.969201	+	0.246271i	$0.0792053\pi$
$739$	8.96697	+	27.5975i	0.329855	+	1.01519i	−0.639346	+	0.768919i	$0.720795\pi$
$740$	−2.79138	+	1.36777i	−0.102613	+	0.0502804i
$741$	−1.09278	+	3.36323i	−0.0401443	+	0.123551i
$742$	2.13549	−	2.93925i	0.0783964	−	0.107903i
$743$			44.1135i			1.61837i	0.587555	+	0.809184i	$0.300091\pi$
$743$			44.1135i			1.61837i	−0.587555	+	0.809184i	$0.699909\pi$
$744$	−50.3098	−	36.5522i	−1.84445	−	1.34007i
$745$	−7.66312	+	1.09128i	−0.280755	+	0.0399815i
$746$	−14.3432	+	10.4209i	−0.525141	+	0.381537i
$747$	−53.0878	−	73.0691i	−1.94238	−	2.67346i
$748$	−0.147729	+	0.0479999i	−0.00540149	+	0.00175505i
$749$	−1.35605			−0.0495490
$750$	−50.8167	−	10.5102i	−1.85556	−	0.383779i
$751$	−24.1661			−0.881834			−0.440917	−	0.897548i	$-0.645347\pi$
$751$	−24.1661			−0.881834			−0.440917	+	0.897548i	$0.645347\pi$
$752$	31.6144	−	10.2721i	1.15286	−	0.374586i
$753$	−14.3554	−	19.7585i	−0.523141	−	0.720041i
$754$	−3.22761	+	2.34500i	−0.117543	+	0.0853998i
$755$	−16.4045	+	2.33612i	−0.597021	+	0.0850200i
$756$	−0.369289	−	0.268304i	−0.0134309	−	0.00975813i
$757$			35.4949i			1.29008i	0.764148	+	0.645041i	$0.223160\pi$
$757$			35.4949i			1.29008i	−0.764148	+	0.645041i	$0.776840\pi$
$758$	26.6790	−	36.7205i	0.969024	−	1.33375i
$759$	2.63541	−	8.11094i	0.0956592	−	0.294409i
$760$	16.5436	−	8.10635i	0.600099	−	0.294048i
$761$	9.17812	+	28.2473i	0.332707	+	1.02397i	0.967841	+	0.251564i	$0.0809448\pi$
$761$	9.17812	+	28.2473i	0.332707	+	1.02397i	−0.635134	+	0.772402i	$0.719055\pi$
$762$	31.2995	+	10.1698i	1.13386	+	0.368413i
$763$	4.13479	+	1.34347i	0.149689	+	0.0486370i
$764$	0.0105758	+	0.0325489i	0.000382619	+	0.00117758i
$765$	−11.0281	−	11.3782i	−0.398721	−	0.411378i
$766$	16.1077	−	49.5743i	0.581993	−	1.79119i
$767$	−1.75156	+	2.41081i	−0.0632450	+	0.0870493i
$768$		−	10.3043i		−	0.371823i
$769$	−2.69518	−	1.95816i	−0.0971907	−	0.0706132i	0.538129	−	0.842863i	$-0.319131\pi$
$769$	−2.69518	−	1.95816i	−0.0971907	−	0.0706132i	−0.635319	+	0.772250i	$0.719131\pi$
$770$	0.695178	−	0.673788i	0.0250525	−	0.0242816i
$771$	48.1209	−	34.9619i	1.73303	−

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38991 + 0.451609i) q^{2} +(1.86675 + 2.56936i) q^{3} +(0.109865 - 0.0798213i) q^{4} +(2.21373 - 0.315251i) q^{5} +(-3.75495 - 2.72813i) q^{6} +0.259005i q^{7} +(1.60137 - 2.20410i) q^{8} +(-2.18980 + 6.73951i) q^{9} +(-2.93452 + 1.43791i) q^{10} +(0.353460 + 1.08784i) q^{11} +(0.410179 + 0.133275i) q^{12} +(0.350179 + 0.113780i) q^{13} +(-0.116969 - 0.359993i) q^{14} +(4.94247 + 5.09938i) q^{15} +(-1.31430 + 4.04499i) q^{16} +(-0.587785 + 0.809017i) q^{17} -10.3562i q^{18} +(2.44657 + 1.77754i) q^{19} +(0.218047 - 0.211338i) q^{20} +(-0.665475 + 0.483496i) q^{21} +(-0.982555 - 1.35237i) q^{22} +(-2.23279 + 0.725476i) q^{23} +8.65246 q^{24} +(4.80123 - 1.39576i) q^{25} -0.538101 q^{26} +(-12.3426 + 4.01036i) q^{27} +(0.0206741 + 0.0284555i) q^{28} +(5.99815 - 4.35791i) q^{29} +(-9.17252 - 4.85561i) q^{30} +(-5.81450 - 4.22448i) q^{31} -0.766902i q^{32} +(-2.13522 + 2.93888i) q^{33} +(0.451609 - 1.38991i) q^{34} +(0.0816516 + 0.573367i) q^{35} +(0.297375 + 0.915226i) q^{36} +(-9.73573 - 3.16333i) q^{37} +(-4.20327 - 1.36572i) q^{38} +(0.361354 + 1.11213i) q^{39} +(2.85016 - 5.38411i) q^{40} +(0.123545 - 0.380232i) q^{41} +(0.706599 - 0.972551i) q^{42} -1.20039i q^{43} +(0.125665 + 0.0913012i) q^{44} +(-2.72299 + 15.6098i) q^{45} +(2.77574 - 2.01669i) q^{46} +(-4.59394 - 6.32301i) q^{47} +(-12.8465 + 4.17408i) q^{48} +6.93292 q^{49} +(-6.04294 + 4.10827i) q^{50} -3.17590 q^{51} +(0.0475543 - 0.0154513i) q^{52} +(5.64170 + 7.76513i) q^{53} +(15.3440 - 11.1481i) q^{54} +(1.12541 + 2.29675i) q^{55} +(0.570871 + 0.414762i) q^{56} +9.60433i q^{57} +(-6.36882 + 8.76593i) q^{58} +(-2.50095 + 7.69712i) q^{59} +(0.950042 + 0.165726i) q^{60} +(-0.665804 - 2.04913i) q^{61} +(9.98945 + 3.24577i) q^{62} +(-1.74556 - 0.567168i) q^{63} +(-2.28226 - 7.02406i) q^{64} +(0.811072 + 0.141484i) q^{65} +(1.64054 - 5.04907i) q^{66} +(7.79166 - 10.7243i) q^{67} +0.135800i q^{68} +(-6.03205 - 4.38254i) q^{69} +(-0.372426 - 0.760054i) q^{70} +(2.00137 - 1.45408i) q^{71} +(11.3478 + 15.6190i) q^{72} +(1.02055 - 0.331597i) q^{73} +14.9604 q^{74} +(12.5489 + 9.73054i) q^{75} +0.410677 q^{76} +(-0.281755 + 0.0915477i) q^{77} +(-1.00450 - 1.38257i) q^{78} +(1.43101 - 1.03969i) q^{79} +(-1.63432 + 9.36887i) q^{80} +(-16.1457 - 11.7305i) q^{81} +0.584282i q^{82} +(-7.49157 + 10.3113i) q^{83} +(-0.0345189 + 0.106238i) q^{84} +(-1.04616 + 1.97625i) q^{85} +(0.542109 + 1.66844i) q^{86} +(22.3941 + 7.27627i) q^{87} +(2.96372 + 0.962970i) q^{88} +(0.317468 + 0.977065i) q^{89} +(-3.26482 - 22.9260i) q^{90} +(-0.0294695 + 0.0906979i) q^{91} +(-0.187396 + 0.257928i) q^{92} -22.8256i q^{93} +(9.24069 + 6.71375i) q^{94} +(5.97643 + 3.16371i) q^{95} +(1.97045 - 1.43161i) q^{96} +(-8.37484 - 11.5270i) q^{97} +(-9.63613 + 3.13097i) q^{98} -8.10550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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