LMFDB - Embedded newform 297.2.x.a.272.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(2,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("297.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.x (of order $90$, degree $24$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			272.34
Character	$\chi$	$=$	297.272
Dual form			297.2.x.a.95.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16150 + 2.38143i) q^{2} +(-1.68326 + 0.408194i) q^{3} +(-3.09081 + 3.95605i) q^{4} +(-0.0429102 - 0.613644i) q^{5} +(-2.92720 - 3.53446i) q^{6} +(-1.71414 + 0.0598591i) q^{7} +(-7.82768 - 1.66383i) q^{8} +(2.66675 - 1.37420i) q^{9} +O(q^{10})$	\(q+(1.16150 + 2.38143i) q^{2} +(-1.68326 + 0.408194i) q^{3} +(-3.09081 + 3.95605i) q^{4} +(-0.0429102 - 0.613644i) q^{5} +(-2.92720 - 3.53446i) q^{6} +(-1.71414 + 0.0598591i) q^{7} +(-7.82768 - 1.66383i) q^{8} +(2.66675 - 1.37420i) q^{9} +(1.41151 - 0.814937i) q^{10} +(-2.23807 + 2.44766i) q^{11} +(3.58781 - 7.92073i) q^{12} +(-0.903460 + 0.935560i) q^{13} +(-2.13353 - 4.01258i) q^{14} +(0.322715 + 1.01541i) q^{15} +(-2.70054 - 10.8313i) q^{16} +(-0.0482878 + 0.459428i) q^{17} +(6.37000 + 4.75456i) q^{18} +(0.141343 - 0.664968i) q^{19} +(2.56024 + 1.72690i) q^{20} +(2.86092 - 0.800461i) q^{21} +(-8.42846 - 2.48687i) q^{22} +(-1.57794 + 4.33534i) q^{23} +(13.8552 - 0.394558i) q^{24} +(4.57662 - 0.643202i) q^{25} +(-3.27734 - 1.06487i) q^{26} +(-3.92791 + 3.40169i) q^{27} +(5.06127 - 6.96624i) q^{28} +(9.02279 + 4.79750i) q^{29} +(-2.04329 + 1.94792i) q^{30} +(-4.59403 + 1.31732i) q^{31} +(10.3966 - 8.72380i) q^{32} +(2.76815 - 5.03362i) q^{33} +(-1.15018 + 0.418632i) q^{34} +(0.110286 + 1.04930i) q^{35} +(-2.80603 + 14.7972i) q^{36} +(-7.04556 + 1.49758i) q^{37} +(1.74775 - 0.435762i) q^{38} +(1.13887 - 1.94358i) q^{39} +(-0.685109 + 4.87481i) q^{40} +(-8.34437 + 4.43678i) q^{41} +(5.22920 + 5.88334i) q^{42} +(-3.76508 + 4.48705i) q^{43} +(-2.76560 - 16.4192i) q^{44} +(-0.957699 - 1.57747i) q^{45} +(-12.1571 + 1.27776i) q^{46} +(6.13622 - 4.79414i) q^{47} +(8.96698 + 17.1295i) q^{48} +(-4.04826 + 0.283082i) q^{49} +(6.84750 + 10.1518i) q^{50} +(-0.106255 - 0.793049i) q^{51} +(-0.908705 - 6.46577i) q^{52} +(3.92774 + 5.40607i) q^{53} +(-12.6632 - 5.40299i) q^{54} +(1.59803 + 1.26835i) q^{55} +(13.5173 + 2.38347i) q^{56} +(0.0335180 + 1.17701i) q^{57} +(-0.944938 + 27.0595i) q^{58} +(11.0077 - 4.44742i) q^{59} +(-5.01447 - 1.86176i) q^{60} +(1.57199 - 5.48217i) q^{61} +(-8.47308 - 9.41031i) q^{62} +(-4.48893 + 2.51520i) q^{63} +(12.4553 + 5.54545i) q^{64} +(0.612868 + 0.514258i) q^{65} +(15.2024 + 0.745604i) q^{66} +(0.459764 + 2.60745i) q^{67} +(-1.66827 - 1.61103i) q^{68} +(0.886420 - 7.94163i) q^{69} +(-2.37075 + 1.48141i) q^{70} +(11.1758 + 1.17462i) q^{71} +(-23.1609 + 6.31977i) q^{72} +(11.9371 - 10.7482i) q^{73} +(-11.7498 - 15.0391i) q^{74} +(-7.44111 + 2.95083i) q^{75} +(2.19378 + 2.61445i) q^{76} +(3.68986 - 4.32959i) q^{77} +(5.95131 + 0.454670i) q^{78} +(-1.05828 + 0.516157i) q^{79} +(-6.53066 + 2.12194i) q^{80} +(5.22316 - 7.32930i) q^{81} +(-20.2579 - 14.7182i) q^{82} +(-11.5025 + 11.1078i) q^{83} +(-5.67588 + 13.7920i) q^{84} +(0.283997 + 0.00991741i) q^{85} +(-15.0588 - 3.75457i) q^{86} +(-17.1461 - 4.39241i) q^{87} +(21.5914 - 15.4357i) q^{88} +(11.2798 + 6.51241i) q^{89} +(2.64427 - 4.11293i) q^{90} +(1.49265 - 1.65776i) q^{91} +(-12.2738 - 19.6421i) q^{92} +(7.19525 - 4.09265i) q^{93} +(18.5442 + 9.04459i) q^{94} +(-0.414119 - 0.0582006i) q^{95} +(-13.9393 + 18.9283i) q^{96} +(7.82613 + 0.547257i) q^{97} +(-5.37620 - 9.31185i) q^{98} +(-2.60483 + 9.60286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 30 q^{2} - 18 q^{3} - 18 q^{4} - 21 q^{5} - 30 q^{6} - 30 q^{7} - 45 q^{8} - 36 q^{9}+O(q^{10}) $ 816 * q - 30 * q^2 - 18 * q^3 - 18 * q^4 - 21 * q^5 - 30 * q^6 - 30 * q^7 - 45 * q^8 - 36 * q^9	\( 816 q - 30 q^{2} - 18 q^{3} - 18 q^{4} - 21 q^{5} - 30 q^{6} - 30 q^{7} - 45 q^{8} - 36 q^{9} - 33 q^{11} - 30 q^{12} - 30 q^{13} - 18 q^{14} - 21 q^{15} - 30 q^{16} - 45 q^{17} - 15 q^{19} - 60 q^{20} - 15 q^{22} - 84 q^{23} - 30 q^{24} - 27 q^{25} + 36 q^{27} - 60 q^{28} + 60 q^{29} - 75 q^{30} - 9 q^{31} - 63 q^{33} - 42 q^{34} - 45 q^{35} + 36 q^{36} - 9 q^{37} - 18 q^{38} - 150 q^{39} - 90 q^{40} - 30 q^{41} - 66 q^{42} - 108 q^{44} + 24 q^{45} - 15 q^{46} - 6 q^{47} + 174 q^{48} - 18 q^{49} - 105 q^{50} - 30 q^{51} - 30 q^{52} - 48 q^{55} + 54 q^{56} - 75 q^{57} - 18 q^{58} + 81 q^{59} - 72 q^{60} - 30 q^{61} - 45 q^{62} - 30 q^{63} + 51 q^{64} - 75 q^{66} + 6 q^{67} - 225 q^{68} + 9 q^{69} - 93 q^{70} - 27 q^{71} - 30 q^{72} - 15 q^{73} - 30 q^{74} + 42 q^{75} - 141 q^{77} + 30 q^{78} - 30 q^{79} + 48 q^{81} - 36 q^{82} + 15 q^{83} + 90 q^{84} - 30 q^{85} + 93 q^{86} - 108 q^{88} + 54 q^{89} - 15 q^{90} - 9 q^{91} + 276 q^{92} + 87 q^{93} - 30 q^{94} + 90 q^{95} + 90 q^{96} - 81 q^{97} + 3 q^{99}+O(q^{100}) \) 816 * q - 30 * q^2 - 18 * q^3 - 18 * q^4 - 21 * q^5 - 30 * q^6 - 30 * q^7 - 45 * q^8 - 36 * q^9 - 33 * q^11 - 30 * q^12 - 30 * q^13 - 18 * q^14 - 21 * q^15 - 30 * q^16 - 45 * q^17 - 15 * q^19 - 60 * q^20 - 15 * q^22 - 84 * q^23 - 30 * q^24 - 27 * q^25 + 36 * q^27 - 60 * q^28 + 60 * q^29 - 75 * q^30 - 9 * q^31 - 63 * q^33 - 42 * q^34 - 45 * q^35 + 36 * q^36 - 9 * q^37 - 18 * q^38 - 150 * q^39 - 90 * q^40 - 30 * q^41 - 66 * q^42 - 108 * q^44 + 24 * q^45 - 15 * q^46 - 6 * q^47 + 174 * q^48 - 18 * q^49 - 105 * q^50 - 30 * q^51 - 30 * q^52 - 48 * q^55 + 54 * q^56 - 75 * q^57 - 18 * q^58 + 81 * q^59 - 72 * q^60 - 30 * q^61 - 45 * q^62 - 30 * q^63 + 51 * q^64 - 75 * q^66 + 6 * q^67 - 225 * q^68 + 9 * q^69 - 93 * q^70 - 27 * q^71 - 30 * q^72 - 15 * q^73 - 30 * q^74 + 42 * q^75 - 141 * q^77 + 30 * q^78 - 30 * q^79 + 48 * q^81 - 36 * q^82 + 15 * q^83 + 90 * q^84 - 30 * q^85 + 93 * q^86 - 108 * q^88 + 54 * q^89 - 15 * q^90 - 9 * q^91 + 276 * q^92 + 87 * q^93 - 30 * q^94 + 90 * q^95 + 90 * q^96 - 81 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.16150	+	2.38143i	0.821306	+	1.68393i	0.725182	+	0.688557i	$0.241756\pi$
$2$	1.16150	+	2.38143i	0.821306	+	1.68393i	0.0961241	+	0.995369i	$0.469355\pi$
$3$	−1.68326	+	0.408194i	−0.971833	+	0.235671i
$3$	−1.68326	+	0.408194i	−0.971833	+	0.235671i
$4$	−3.09081	+	3.95605i	−1.54540	+	1.97803i
$5$	−0.0429102	−	0.613644i	−0.0191900	−	0.274430i	−0.997677	−	0.0681216i	$-0.978299\pi$
$5$	−0.0429102	−	0.613644i	−0.0191900	−	0.274430i	0.978487	−	0.206308i	$-0.0661450\pi$
$6$	−2.92720	−	3.53446i	−1.19502	−	1.44294i
$7$	−1.71414	+	0.0598591i	−0.647884	+	0.0226246i	−0.356957	−	0.934121i	$-0.616186\pi$
$7$	−1.71414	+	0.0598591i	−0.647884	+	0.0226246i	−0.290927	+	0.956745i	$0.593964\pi$
$8$	−7.82768	−	1.66383i	−2.76750	−	0.588251i
$9$	2.66675	−	1.37420i	0.888918	−	0.458066i
$10$	1.41151	−	0.814937i	0.446359	−	0.257706i
$11$	−2.23807	+	2.44766i	−0.674805	+	0.737996i
$11$	−2.23807	+	2.44766i	−0.674805	+	0.737996i
$12$	3.58781	−	7.92073i	1.03571	−	2.28652i
$13$	−0.903460	+	0.935560i	−0.250575	+	0.259478i	−0.832831	−	0.553528i	$-0.813281\pi$
$13$	−0.903460	+	0.935560i	−0.250575	+	0.259478i	0.582256	+	0.813005i	$0.302170\pi$
$14$	−2.13353	−	4.01258i	−0.570209	−	1.07241i
$15$	0.322715	+	1.01541i	0.0833247	+	0.262178i
$16$	−2.70054	−	10.8313i	−0.675135	−	2.70782i
$17$	−0.0482878	+	0.459428i	−0.0117115	+	0.111428i	−0.998816	−	0.0486505i	$-0.984508\pi$
$17$	−0.0482878	+	0.459428i	−0.0117115	+	0.111428i	0.987104	+	0.160078i	$0.0511746\pi$
$18$	6.37000	+	4.75456i	1.50142	+	1.12066i
$19$	0.141343	−	0.664968i	0.0324264	−	0.152554i	−0.958956	−	0.283556i	$-0.908486\pi$
$19$	0.141343	−	0.664968i	0.0324264	−	0.152554i	0.991382	+	0.131002i	$0.0418193\pi$
$20$	2.56024	+	1.72690i	0.572486	+	0.386147i
$21$	2.86092	−	0.800461i	0.624303	−	0.174675i
$22$	−8.42846	−	2.48687i	−1.79695	−	0.530202i
$23$	−1.57794	+	4.33534i	−0.329022	+	0.903982i	0.659337	+	0.751847i	$0.270837\pi$
$23$	−1.57794	+	4.33534i	−0.329022	+	0.903982i	−0.988360	+	0.152134i	$0.951385\pi$
$24$	13.8552	−	0.394558i	2.82819	−	0.0805389i
$25$	4.57662	−	0.643202i	0.915325	−	0.128640i
$26$	−3.27734	−	1.06487i	−0.642740	−	0.208839i
$27$	−3.92791	+	3.40169i	−0.755927	+	0.654656i
$28$	5.06127	−	6.96624i	0.956491	−	1.31650i
$29$	9.02279	+	4.79750i	1.67549	+	0.890874i	0.986033	+	0.166547i	$0.0532619\pi$
$29$	9.02279	+	4.79750i	1.67549	+	0.890874i	0.689457	+	0.724327i	$0.257849\pi$
$30$	−2.04329	+	1.94792i	−0.373053	+	0.355641i
$31$	−4.59403	+	1.31732i	−0.825112	+	0.236597i	−0.661517	−	0.749930i	$-0.730087\pi$
$31$	−4.59403	+	1.31732i	−0.825112	+	0.236597i	−0.163596	+	0.986527i	$0.552309\pi$
$32$	10.3966	−	8.72380i	1.83788	−	1.54216i
$33$	2.76815	−	5.03362i	0.481873	−	0.876241i
$34$	−1.15018	+	0.418632i	−0.197255	+	0.0717949i
$35$	0.110286	+	1.04930i	0.0186418	+	0.177365i
$36$	−2.80603	+	14.7972i	−0.467671	+	2.46620i
$37$	−7.04556	+	1.49758i	−1.15828	+	0.246201i	−0.746693	−	0.665168i	$-0.768360\pi$
$37$	−7.04556	+	1.49758i	−1.15828	+	0.246201i	−0.411590	+	0.911369i	$0.635026\pi$
$38$	1.74775	−	0.435762i	0.283522	−	0.0706899i
$39$	1.13887	−	1.94358i	0.182365	−	0.311222i
$40$	−0.685109	+	4.87481i	−0.108325	+	0.770775i
$41$	−8.34437	+	4.43678i	−1.30317	+	0.692909i	−0.968403	−	0.249392i	$-0.919769\pi$
$41$	−8.34437	+	4.43678i	−1.30317	+	0.692909i	−0.334769	+	0.942300i	$0.608658\pi$
$42$	5.22920	+	5.88334i	0.806883	+	0.907819i
$43$	−3.76508	+	4.48705i	−0.574170	+	0.684269i	−0.972481	−	0.232981i	$-0.925152\pi$
$43$	−3.76508	+	4.48705i	−0.574170	+	0.684269i	0.398311	+	0.917250i	$0.369596\pi$
$44$	−2.76560	−	16.4192i	−0.416930	−	2.47528i
$45$	−0.957699	−	1.57747i	−0.142765	−	0.235156i
$46$	−12.1571	+	1.27776i	−1.79247	+	0.188396i
$47$	6.13622	−	4.79414i	0.895060	−	0.699297i	−0.0592096	−	0.998246i	$-0.518858\pi$
$47$	6.13622	−	4.79414i	0.895060	−	0.699297i	0.954269	+	0.298948i	$0.0966358\pi$
$48$	8.96698	+	17.1295i	1.29427	+	2.47244i
$49$	−4.04826	+	0.283082i	−0.578322	+	0.0404402i
$50$	6.84750	+	10.1518i	0.968383	+	1.43569i
$51$	−0.106255	−	0.793049i	−0.0148786	−	0.111049i
$52$	−0.908705	−	6.46577i	−0.126015	−	0.896641i
$53$	3.92774	+	5.40607i	0.539517	+	0.742581i	0.988543	−	0.150938i	$-0.0482292\pi$
$53$	3.92774	+	5.40607i	0.539517	+	0.742581i	−0.449027	+	0.893518i	$0.648229\pi$
$54$	−12.6632	−	5.40299i	−1.72324	−	0.735253i
$55$	1.59803	+	1.26835i	0.215478	+	0.171025i
$56$	13.5173	+	2.38347i	1.80633	+	0.318505i
$57$	0.0335180	+	1.17701i	0.00443957	+	0.155899i
$58$	−0.944938	+	27.0595i	−0.124076	+	3.55308i
$59$	11.0077	−	4.44742i	1.43309	−	0.579004i	0.478807	−	0.877920i	$-0.341069\pi$
$59$	11.0077	−	4.44742i	1.43309	−	0.579004i	0.954279	+	0.298916i	$0.0966250\pi$
$60$	−5.01447	−	1.86176i	−0.647365	−	0.240352i
$61$	1.57199	−	5.48217i	0.201272	−	0.701920i	−0.794267	−	0.607569i	$-0.792145\pi$
$61$	1.57199	−	5.48217i	0.201272	−	0.701920i	0.995539	−	0.0943506i	$-0.0300775\pi$
$62$	−8.47308	−	9.41031i	−1.07608	−	1.19511i
$63$	−4.48893	+	2.51520i	−0.565552	+	0.316885i
$64$	12.4553	+	5.54545i	1.55691	+	0.693181i
$65$	0.612868	+	0.514258i	0.0760170	+	0.0637858i
$66$	15.2024	+	0.745604i	1.87129	+	0.0917775i
$67$	0.459764	+	2.60745i	0.0561691	+	0.318551i	0.999927	−	0.0120867i	$-0.00384742\pi$
$67$	0.459764	+	2.60745i	0.0561691	+	0.318551i	−0.943758	+	0.330637i	$0.892736\pi$
$68$	−1.66827	−	1.61103i	−0.202308	−	0.195366i
$69$	0.886420	−	7.94163i	0.106712	−	0.956060i
$70$	−2.37075	+	1.48141i	−0.283358	+	0.177062i
$71$	11.1758	+	1.17462i	1.32632	+	0.139402i	0.741058	−	0.671441i	$-0.234324\pi$
$71$	11.1758	+	1.17462i	1.32632	+	0.139402i	0.585264	+	0.810843i	$0.300991\pi$
$72$	−23.1609	+	6.31977i	−2.72954	+	0.744792i
$73$	11.9371	−	10.7482i	1.39713	−	1.25799i	0.470305	−	0.882504i	$-0.344144\pi$
$73$	11.9371	−	10.7482i	1.39713	−	1.25799i	0.926830	−	0.375482i	$-0.122523\pi$
$74$	−11.7498	−	15.0391i	−1.36589	−	1.74826i
$75$	−7.44111	+	2.95083i	−0.859226	+	0.340733i
$76$	2.19378	+	2.61445i	0.251644	+	0.299898i
$77$	3.68986	−	4.32959i	0.420498	−	0.493403i
$78$	5.95131	+	0.454670i	0.673853	+	0.0514812i
$79$	−1.05828	+	0.516157i	−0.119066	+	0.0580722i	−0.496941	−	0.867784i	$-0.665544\pi$
$79$	−1.05828	+	0.516157i	−0.119066	+	0.0580722i	0.377876	+	0.925856i	$0.376655\pi$
$80$	−6.53066	+	2.12194i	−0.730151	+	0.237240i
$81$	5.22316	−	7.32930i	0.580351	−	0.814366i
$82$	−20.2579	−	14.7182i	−2.23711	−	1.62536i
$83$	−11.5025	+	11.1078i	−1.26256	+	1.21924i	−0.298248	+	0.954488i	$0.596402\pi$
$83$	−11.5025	+	11.1078i	−1.26256	+	1.21924i	−0.964316	+	0.264755i	$0.914709\pi$
$84$	−5.67588	+	13.7920i	−0.619289	+	1.50483i
$85$	0.283997	+	0.00991741i	0.0308038	+	0.00107569i
$86$	−15.0588	−	3.75457i	−1.62383	−	0.404866i
$87$	−17.1461	−	4.39241i	−1.83825	−	0.470916i
$88$	21.5914	−	15.4357i	2.30165	−	1.64545i
$89$	11.2798	+	6.51241i	1.19566	+	0.690314i	0.959584	−	0.281422i	$-0.0908059\pi$
$89$	11.2798	+	6.51241i	1.19566	+	0.690314i	0.236074	+	0.971735i	$0.424139\pi$
$90$	2.64427	−	4.11293i	0.278731	−	0.433541i
$91$	1.49265	−	1.65776i	0.156473	−	0.173781i
$92$	−12.2738	−	19.6421i	−1.27963	−	2.04783i
$93$	7.19525	−	4.09265i	0.746112	−	0.424388i
$94$	18.5442	+	9.04459i	1.91268	+	0.932878i
$95$	−0.414119	−	0.0582006i	−0.0424877	−	0.00597125i
$96$	−13.9393	+	18.9283i	−1.42267	+	1.93186i
$97$	7.82613	+	0.547257i	0.794623	+	0.0555655i	0.461297	−	0.887246i	$-0.347384\pi$
$97$	7.82613	+	0.547257i	0.794623	+	0.0555655i	0.333327	+	0.942811i	$0.391829\pi$
$98$	−5.37620	−	9.31185i	−0.543078	−	0.940639i
$99$	−2.60483	+	9.60286i	−0.261796	+	0.965123i
$100$	−11.6009	+	20.0934i	−1.16009	+	2.00934i
$101$	0.804559	−	1.19281i	0.0800566	−	0.118689i	−0.786883	−	0.617103i	$-0.788306\pi$
$101$	0.804559	−	1.19281i	0.0800566	−	0.118689i	0.866939	+	0.498414i	$0.166084\pi$
$102$	1.76518	−	1.17417i	0.174779	−	0.116260i
$103$	−2.17721	−	5.38878i	−0.214527	−	0.530972i	0.781099	−	0.624407i	$-0.214660\pi$
$103$	−2.17721	−	5.38878i	−0.214527	−	0.530972i	−0.995625	+	0.0934357i	$0.970215\pi$
$104$	8.62860	−	5.82007i	0.846104	−	0.570705i
$105$	−0.613960	−	1.72124i	−0.0599164	−	0.167975i
$106$	−8.31211	+	15.6328i	−0.807344	+	1.51839i
$107$	3.36033	+	10.3420i	0.324856	+	0.999803i	0.971506	+	0.237016i	$0.0761694\pi$
$107$	3.36033	+	10.3420i	0.324856	+	0.999803i	−0.646650	+	0.762787i	$0.723831\pi$
$108$	−1.31685	−	26.0530i	−0.126714	−	2.50695i
$109$			8.12587i			0.778318i	0.921171	+	0.389159i	$0.127234\pi$
$109$			8.12587i			0.778318i	−0.921171	+	0.389159i	$0.872766\pi$
$110$	−1.16438	+	5.27878i	−0.111020	+	0.503312i
$111$	11.2482	−	5.39678i	1.06764	−	0.512240i
$112$	5.27745	+	18.4047i	0.498672	+	1.73908i
$113$	−2.93048	+	4.68975i	−0.275676	+	0.441174i	−0.956695	−	0.291091i	$-0.905982\pi$
$113$	−2.93048	+	4.68975i	−0.275676	+	0.441174i	0.681019	+	0.732266i	$0.261537\pi$
$114$	−2.76404	+	1.44692i	−0.258876	+	0.135517i
$115$	2.72807	+	0.782261i	0.254394	+	0.0729462i
$116$	−46.8669	+	20.8665i	−4.35148	+	1.93741i
$117$	−1.12366	+	3.73644i	−0.103883	+	0.345434i
$118$	23.3767	+	21.0485i	2.15200	+	1.93767i
$119$	0.0552712	−	0.790414i	0.00506670	−	0.0724572i
$120$	−0.836648	−	8.48524i	−0.0763752	−	0.774593i
$121$	−0.982042	−	10.9561i	−0.0892765	−	0.996007i
$122$	14.8813	−	2.62397i	1.34729	−	0.237563i
$123$	12.2347	−	10.8744i	1.10317	−	0.980511i
$124$	8.98789	−	22.2458i	0.807137	−	1.99773i
$125$	−1.23056	−	5.78932i	−0.110064	−	0.517812i
$126$	−11.2037	−	7.76868i	−0.998103	−	0.692089i
$127$	−5.80393	−	13.0358i	−0.515016	−	1.15674i	−0.964651	−	0.263532i	$-0.915113\pi$
$127$	−5.80393	−	13.0358i	−0.515016	−	1.15674i	0.449635	−	0.893212i	$-0.351554\pi$
$128$	0.313426	+	8.97535i	0.0277032	+	0.793317i
$129$	4.50604	−	9.08978i	0.396735	−	0.800310i
$130$	−0.512822	+	2.05682i	−0.0449774	+	0.180395i
$131$	14.2204	+	5.17580i	1.24244	+	0.452211i	0.877841	−	0.478953i	$-0.158984\pi$
$131$	14.2204	+	5.17580i	1.24244	+	0.452211i	0.364600	+	0.931164i	$0.381206\pi$
$132$	11.3575	+	26.5089i	0.988539	+	2.30730i
$133$	−0.202478	+	1.14831i	−0.0175570	+	0.0995710i
$134$	−5.67545	+	4.12345i	−0.490284	+	0.356212i
$135$	2.25598	+	2.26437i	0.194163	+	0.194886i
$136$	1.14239	−	3.51591i	0.0979591	−	0.301487i
$137$	−14.3100	−	14.8184i	−1.22258	−	1.26602i	−0.952974	−	0.303053i	$-0.901994\pi$
$137$	−14.3100	−	14.8184i	−1.22258	−	1.26602i	−0.269610	−	0.962970i	$-0.586895\pi$
$138$	19.9420	−	7.11327i	1.69758	−	0.605522i
$139$	−0.0165610	−	0.0129389i	−0.00140468	−	0.00109746i	0.614959	−	0.788559i	$-0.289173\pi$
$139$	−0.0165610	−	0.0129389i	−0.00140468	−	0.00109746i	−0.616364	+	0.787462i	$0.711395\pi$
$140$	−4.49197	−	2.80690i	−0.379641	−	0.237226i
$141$	−8.37194	+	10.5746i	−0.705044	+	0.890540i
$142$	10.1834	+	27.9787i	0.854574	+	2.34792i
$143$	−0.267919	−	4.30521i	−0.0224045	−	0.360020i
$144$	−22.0860	−	25.1733i	−1.84050	−	2.09777i
$145$	2.55679	−	5.74265i	0.212330	−	0.476901i
$146$	39.4612	+	15.9434i	3.26583	+	1.31948i
$147$	6.69873	−	2.12898i	0.552502	−	0.175595i
$148$	15.8520	−	32.5014i	1.30302	−	2.67160i
$149$	4.26774	−	8.75017i	0.349627	−	0.716841i	−0.649423	−	0.760428i	$-0.724989\pi$
$149$	4.26774	−	8.75017i	0.349627	−	0.716841i	0.999050	+	0.0435861i	$0.0138783\pi$
$150$	−15.6701	−	14.2931i	−1.27946	−	1.16703i
$151$	0.230911	+	0.0932943i	0.0187913	+	0.00759218i	0.383983	−	0.923340i	$-0.374552\pi$
$151$	0.230911	+	0.0932943i	0.0187913	+	0.00759218i	−0.365192	+	0.930932i	$0.618997\pi$
$152$	−2.21278	+	4.96999i	−0.179480	+	0.403119i
$153$	0.502573	+	1.29154i	0.0406306	+	0.104415i
$154$	14.5964	+	3.75832i	1.17621	+	0.302854i
$155$	1.00549	+	2.76257i	0.0807633	+	0.221895i
$156$	4.16888	+	10.5127i	0.333778	+	0.841687i
$157$	3.70800	+	2.31702i	0.295931	+	0.184918i	0.669756	−	0.742581i	$-0.266399\pi$
$157$	3.70800	+	2.31702i	0.295931	+	0.184918i	−0.373825	+	0.927499i	$0.621954\pi$
$158$	−2.45838	−	1.92070i	−0.195579	−	0.152803i
$159$	−8.81815	−	7.49656i	−0.699325	−	0.594516i
$160$	−5.79943	−	6.00549i	−0.458485	−	0.474775i
$161$	2.44529	−	7.52584i	0.192716	−	0.593119i
$162$	23.5209	+	3.92562i	1.84798	+	0.308426i
$163$	0.657814	−	0.477930i	0.0515240	−	0.0374343i	−0.561725	−	0.827324i	$-0.689862\pi$
$163$	0.657814	−	0.477930i	0.0515240	−	0.0374343i	0.613249	+	0.789890i	$0.289862\pi$
$164$	8.23871	−	46.7240i	0.643335	−	3.64853i
$165$	−3.20763	−	1.48267i	−0.249714	−	0.115425i
$166$	−39.8127	−	14.4907i	−3.09007	−	1.12469i
$167$	−1.86802	+	7.49220i	−0.144551	+	0.579764i	0.853706	+	0.520755i	$0.174350\pi$
$167$	−1.86802	+	7.49220i	−0.144551	+	0.579764i	−0.998257	+	0.0590088i	$0.981206\pi$
$168$	−23.7262	+	1.50569i	−1.83051	+	0.116166i
$169$	0.394661	+	11.3016i	0.0303585	+	0.869354i
$170$	0.306246	+	0.687839i	0.0234880	+	0.0527549i
$171$	−0.536869	−	1.96754i	−0.0410554	−	0.150461i
$172$	−6.11387	−	28.7635i	−0.466178	−	2.19320i
$173$	0.816902	−	2.02190i	0.0621079	−	0.153722i	−0.892939	−	0.450178i	$-0.851360\pi$
$173$	0.816902	−	2.02190i	0.0621079	−	0.153722i	0.955047	+	0.296456i	$0.0958048\pi$
$174$	−9.45494	−	45.9340i	−0.716777	−	3.48224i
$175$	−7.80647	+	1.37649i	−0.590114	+	0.104053i
$176$	32.5552	+	17.6312i	2.45394	+	1.32900i
$177$	−16.7135	+	11.9795i	−1.25627	+	0.900433i
$178$	−2.40732	+	34.4263i	−0.180436	+	2.58036i
$179$	1.52670	+	1.37465i	0.114111	+	0.102746i	0.724211	−	0.689578i	$-0.242204\pi$
$179$	1.52670	+	1.37465i	0.114111	+	0.102746i	−0.610100	+	0.792324i	$0.708871\pi$
$180$	9.20063	+	1.08695i	0.685774	+	0.0810166i
$181$	−0.885886	+	0.394422i	−0.0658474	+	0.0293171i	−0.439396	−	0.898293i	$-0.644808\pi$
$181$	−0.885886	+	0.394422i	−0.0658474	+	0.0293171i	0.373549	+	0.927611i	$0.378141\pi$
$182$	5.68157	+	1.62916i	0.421146	+	0.120762i
$183$	−0.408278	+	9.86961i	−0.0301808	+	0.729583i
$184$	19.5648	−	31.3103i	1.44234	−	2.30823i
$185$	1.22131	+	4.25921i	0.0897924	+	0.313143i
$186$	18.1037	+	12.3814i	1.32742	+	0.907846i
$187$	−1.01645	−	1.14643i	−0.0743302	−	0.0838350i
$188$			39.0930i			2.85115i
$189$	6.52937	−	6.06610i	0.474942	−	0.441244i
$190$	−0.342399	−	1.05380i	−0.0248402	−	0.0764503i
$191$	3.76263	−	7.07647i	0.272254	−	0.512036i	−0.708888	−	0.705321i	$-0.750803\pi$
$191$	3.76263	−	7.07647i	0.272254	−	0.512036i	0.981143	+	0.193285i	$0.0619142\pi$
$192$	−23.2292	−	4.25028i	−1.67642	−	0.306738i
$193$	−7.45071	+	5.02557i	−0.536314	+	0.361748i	−0.797290	−	0.603597i	$-0.793734\pi$
$193$	−7.45071	+	5.02557i	−0.536314	+	0.361748i	0.260976	+	0.965345i	$0.415956\pi$
$194$	7.78682	+	19.2730i	0.559061	+	1.38372i
$195$	−1.24154	−	0.615462i	−0.0889083	−	0.0440741i
$196$	11.3925	−	16.8901i	0.813750	−	1.20643i
$197$	−9.22560	+	15.9792i	−0.657297	+	1.13847i	0.324016	+	0.946052i	$0.394967\pi$
$197$	−9.22560	+	15.9792i	−0.657297	+	1.13847i	−0.981313	+	0.192420i	$0.938366\pi$
$198$	−25.8941	+	4.95050i	−1.84021	+	0.351817i
$199$	0.564555	+	0.977838i	0.0400202	+	0.0693171i	0.885342	−	0.464941i	$-0.153924\pi$
$199$	0.564555	+	0.977838i	0.0400202	+	0.0693171i	−0.845321	+	0.534258i	$0.820591\pi$
$200$	−36.8945	−	2.57992i	−2.60884	−	0.182428i
$201$	−1.83825	−	4.20135i	−0.129660	−	0.296341i
$202$	3.77509	+	0.530554i	0.265614	+	0.0373296i
$203$	−15.7535	−	7.68350i	−1.10568	−	0.539276i
$204$	3.46576	+	2.03081i	0.242652	+	0.142185i
$205$	3.08066	+	4.93009i	0.215163	+	0.344332i
$206$	10.3042	−	11.4439i	0.717926	−	0.797337i
$207$	1.74965	+	13.7297i	0.121609	+	0.954280i
$208$	12.5731	+	7.25910i	0.871790	+	0.503328i
$209$	1.31128	+	1.83421i	0.0907028	+	0.126875i
$210$	3.38589	−	3.46132i	0.233649	−	0.238854i
$211$	−11.4729	−	2.86052i	−0.789828	−	0.196926i	−0.173936	−	0.984757i	$-0.555649\pi$
$211$	−11.4729	−	2.86052i	−0.789828	−	0.196926i	−0.615892	+	0.787831i	$0.711204\pi$
$212$	−33.5266	−	1.17077i	−2.30262	−	0.0804091i
$213$	−19.2913	+	2.58469i	−1.32182	+	0.177100i
$214$	−20.7258	+	20.0147i	−1.41679	+	1.36818i
$215$	2.91501	+	2.11788i	0.198802	+	0.144438i
$216$	36.4063	−	20.0920i	2.47713	−	1.36709i
$217$	7.79596	−	2.53306i	0.529224	−	0.171955i
$218$	−19.3512	+	9.43822i	−1.31063	+	0.639237i
$219$	−15.7060	+	22.9648i	−1.06131	+	1.55182i
$220$	−9.95686	+	2.40164i	−0.671292	+	0.161919i
$221$	−0.386196	−	0.460251i	−0.0259784	−	0.0309598i
$222$	25.9169	+	20.5185i	1.73943	+	1.37711i
$223$	−16.6479	−	21.3083i	−1.11483	−	1.42691i	−0.891990	−	0.452056i	$-0.850691\pi$
$223$	−16.6479	−	21.3083i	−1.11483	−	1.42691i	−0.222836	−	0.974856i	$-0.571532\pi$
$224$	−17.2991	+	15.5761i	−1.15584	+	1.04073i
$225$	11.3208	−	8.00445i	0.754723	−	0.533630i
$226$	−14.5721	−	1.53159i	−0.969320	−	0.101880i
$227$	−10.5251	+	6.57679i	−0.698573	+	0.436517i	−0.832171	−	0.554519i	$-0.812902\pi$
$227$	−10.5251	+	6.57679i	−0.698573	+	0.436517i	0.133598	+	0.991036i	$0.457347\pi$
$228$	−4.75992	−	3.50532i	−0.315233	−	0.232145i
$229$	−13.7313	−	13.2601i	−0.907388	−	0.876254i	0.0853746	−	0.996349i	$-0.472791\pi$
$229$	−13.7313	−	13.2601i	−0.907388	−	0.876254i	−0.992762	+	0.120095i	$0.961680\pi$
$230$	1.30576	+	7.40531i	0.0860989	+	0.488291i
$231$	−4.44369	+	8.79403i	−0.292373	+	0.578605i
$232$	−62.6453	−	52.5657i	−4.11287	−	3.45111i
$233$	5.09708	+	2.26936i	0.333921	+	0.148671i	0.566846	−	0.823823i	$-0.308163\pi$
$233$	5.09708	+	2.26936i	0.333921	+	0.148671i	−0.232926	+	0.972494i	$0.574830\pi$
$234$	−10.2032	+	1.66396i	−0.667005	+	0.108776i
$235$	−3.20520	−	3.55974i	−0.209084	−	0.232212i
$236$	−16.4286	+	57.2934i	−1.06941	+	3.72948i
$237$	1.57067	−	1.30081i	0.102026	−	0.0844967i
$238$	1.94652	−	0.786443i	0.126174	−	0.0509775i
$239$	−0.220192	+	6.30547i	−0.0142430	+	0.407867i	0.971241	+	0.238099i	$0.0765241\pi$
$239$	−0.220192	+	6.30547i	−0.0142430	+	0.407867i	−0.985484	+	0.169768i	$0.945698\pi$
$240$	10.1267	−	6.23757i	0.653674	−	0.402633i
$241$	−4.00179	−	0.705624i	−0.257778	−	0.0454532i	0.0432656	−	0.999064i	$-0.486224\pi$
$241$	−4.00179	−	0.705624i	−0.257778	−	0.0454532i	−0.301044	+	0.953610i	$0.597335\pi$
$242$	24.9505	−	15.0642i	1.60388	−	0.968361i
$243$	−5.80019	+	14.4692i	−0.372082	+	0.928200i
$244$	16.8290	+	23.1632i	1.07737	+	1.48287i
$245$	0.347423	+	2.47204i	0.0221960	+	0.157933i
$246$	40.1073	+	16.5055i	2.55715	+	1.05235i
$247$	0.494419	+	0.733006i	0.0314591	+	0.0466401i
$248$	38.1524	−	2.66788i	2.42268	−	0.169410i
$249$	14.8276	−	23.3927i	0.939660	−	1.48245i
$250$	12.3576	−	9.65479i	0.781562	−	0.610623i
$251$	19.4501	−	2.04429i	1.22768	−	0.129034i	0.531597	−	0.846997i	$-0.321592\pi$
$251$	19.4501	−	2.04429i	1.22768	−	0.129034i	0.696081	+	0.717963i	$0.254925\pi$
$252$	3.92418	−	25.5325i	0.247200	−	1.60839i
$253$	−7.07989	−	13.5651i	−0.445109	−	0.852829i
$254$	24.3027	−	28.9628i	1.52489	−	1.81729i
$255$	−0.482091	+	0.0992325i	−0.0301897	+	0.00621418i
$256$	3.06608	−	1.63026i	0.191630	−	0.101892i
$257$	−0.0244987	+	0.174317i	−0.00152819	+	0.0108736i	−0.991017	−	0.133734i	$-0.957303\pi$
$257$	−0.0244987	+	0.174317i	−0.00152819	+	0.0108736i	0.989489	+	0.144608i	$0.0461920\pi$
$258$	26.8805	+	0.173033i	1.67350	+	0.0107726i
$259$	11.9874	−	2.98880i	0.744863	−	0.185715i
$260$	−3.92869	+	0.835069i	−0.243647	+	0.0517888i
$261$	30.6543	+	0.394668i	1.89745	+	0.0244294i
$262$	4.19120	+	39.8766i	0.258933	+	2.46358i
$263$	−14.6793	+	5.34285i	−0.905167	+	0.329454i	−0.752322	−	0.658796i	$-0.771066\pi$
$263$	−14.6793	+	5.34285i	−0.905167	+	0.329454i	−0.152846	+	0.988250i	$0.548844\pi$
$264$	−30.0433	+	34.7959i	−1.84904	+	2.14154i
$265$	3.14886	−	2.64221i	0.193433	−	0.162310i
$266$	−2.96980	+	0.851575i	−0.182090	+	0.0522134i
$267$	−21.6452	−	6.35774i	−1.32467	−	0.389087i
$268$	−11.7363	−	6.24028i	−0.716906	−	0.381186i
$269$	−3.43294	+	4.72504i	−0.209310	+	0.288091i	−0.900745	−	0.434348i	$-0.856979\pi$
$269$	−3.43294	+	4.72504i	−0.209310	+	0.288091i	0.691435	+	0.722439i	$0.256979\pi$
$270$	−2.77213	+	8.00253i	−0.168707	+	0.487018i
$271$	−0.0396553	−	0.0128848i	−0.00240889	−	0.000782695i	0.307812	−	0.951447i	$-0.400403\pi$
$271$	−0.0396553	−	0.0128848i	−0.00240889	−	0.000782695i	−0.310221	+	0.950664i	$0.600403\pi$
$272$	5.10659	−	0.717685i	0.309633	−	0.0435160i
$273$	−1.83584	+	3.39974i	−0.111110	+	0.205762i
$274$	18.6680	−	51.2898i	1.12777	−	3.09853i
$275$	−8.66849	+	12.6415i	−0.522729	+	0.762313i
$276$	28.6778	+	28.0528i	1.72620	+	1.68858i
$277$	5.64882	+	3.81017i	0.339404	+	0.228931i	0.717054	−	0.697017i	$-0.245490\pi$
$277$	5.64882	+	3.81017i	0.339404	+	0.228931i	−0.377650	+	0.925948i	$0.623268\pi$
$278$	0.0115774	−	0.0544674i	0.000694366	−	0.00326674i
$279$	−10.4409	+	9.82607i	−0.625080	+	0.588271i
$280$	0.882572	−	8.39711i	0.0527438	−	0.501823i
$281$	−6.45631	−	25.8948i	−0.385151	−	1.54476i	−0.779862	−	0.625951i	$-0.784711\pi$
$281$	−6.45631	−	25.8948i	−0.385151	−	1.54476i	0.394712	−	0.918805i	$-0.370845\pi$
$282$	−34.9067	−	7.65481i	−2.07866	−	0.455837i
$283$	9.12847	+	17.1681i	0.542631	+	1.02054i	0.991885	+	0.127137i	$0.0405786\pi$
$283$	9.12847	+	17.1681i	0.542631	+	1.02054i	−0.449254	+	0.893404i	$0.648310\pi$
$284$	−39.1891	+	40.5815i	−2.32545	+	2.40807i
$285$	0.720828	−	0.0710739i	0.0426982	−	0.00421006i
$286$	9.94138	−	5.63854i	0.587846	−	0.333414i
$287$	14.0378	−	8.10475i	0.828627	−	0.478408i
$288$	15.7370	−	37.5513i	0.927313	−	2.21273i
$289$	16.4198	+	3.49013i	0.965869	+	0.205302i
$290$	16.6454	−	0.581271i	0.977454	−	0.0341334i
$291$	−13.3968	+	2.27341i	−0.785336	+	0.133269i
$292$	5.62524	+	80.4447i	0.329192	+	4.70767i
$293$	−11.7668	+	15.0608i	−0.687424	+	0.879862i	−0.997487	−	0.0708537i	$-0.977428\pi$
$293$	−11.7668	+	15.0608i	−0.687424	+	0.879862i	0.310063	+	0.950716i	$0.399650\pi$
$294$	12.8506	+	13.4798i	0.749462	+	0.786156i
$295$	−3.20148	−	6.56400i	−0.186397	−	0.382171i
$296$	57.6422			3.35038
$297$	0.464793	−	17.2274i	0.0269700	−	0.999636i
$298$	25.7949			1.49426
$299$	−2.63037	−	5.39306i	−0.152118	−	0.311889i
$300$	11.3254	−	38.5579i	0.653873	−	2.22614i
$301$	6.18529	−	7.91681i	0.356514	−	0.456317i
$302$	0.0460301	+	0.658261i	0.00264874	+	0.0378787i
$303$	−0.867388	+	2.33623i	−0.0498301	+	0.134213i
$304$	−7.58415	+	0.264844i	−0.434981	+	0.0151899i
$305$	−3.43155	−	0.729399i	−0.196490	−	0.0417653i
$306$	−2.49197	+	2.69697i	−0.142457	+	0.154175i
$307$	−0.669905	+	0.386770i	−0.0382335	+	0.0220741i	−0.518995	−	0.854777i	$-0.673694\pi$
$307$	−0.669905	+	0.386770i	−0.0382335	+	0.0220741i	0.480761	+	0.876851i	$0.340360\pi$
$308$	5.72346	+	27.9792i	0.326125	+	1.59426i
$309$	5.86448	+	8.18201i	0.333619	+	0.465458i
$310$	−5.41100	+	5.60325i	−0.307324	+	0.318243i
$311$	−7.61699	−	14.3255i	−0.431920	−	0.812324i	0.568023	−	0.823013i	$-0.307709\pi$
$311$	−7.61699	−	14.3255i	−0.431920	−	0.812324i	−0.999943	+	0.0106893i	$0.996597\pi$
$312$	−12.1485	+	13.3189i	−0.687773	+	0.754032i
$313$	3.47635	+	13.9429i	0.196495	+	0.788099i	0.984926	+	0.172976i	$0.0553382\pi$
$313$	3.47635	+	13.9429i	0.196495	+	0.788099i	−0.788431	+	0.615123i	$0.789106\pi$
$314$	−1.21097	+	11.5216i	−0.0683388	+	0.650200i
$315$	1.73606	+	2.64668i	0.0978157	+	0.149124i
$316$	1.22899	−	5.78195i	0.0691361	−	0.325260i
$317$	−18.1355	−	12.2325i	−1.01859	−	0.687047i	−0.0680598	−	0.997681i	$-0.521681\pi$
$317$	−18.1355	−	12.2325i	−1.01859	−	0.687047i	−0.950530	+	0.310634i	$0.899459\pi$
$318$	7.61025	−	29.7071i	0.426762	−	1.66589i
$319$	−31.9363	+	11.3475i	−1.78809	+	0.635339i
$320$	2.86847	−	7.88107i	0.160353	−	0.440565i
$321$	−9.87789	−	16.0367i	−0.551330	−	0.895082i
$322$	20.7625	−	2.91798i	1.15705	−	0.162613i
$323$	0.298680	+	0.0970469i	0.0166190	+	0.00539983i
$324$	12.8513	+	43.3166i	0.713961	+	2.40648i
$325$	−3.53304	+	4.86281i	−0.195978	+	0.269740i
$326$	1.90221	+	1.01142i	0.105354	+	0.0560175i
$327$	−3.31694	−	13.6780i	−0.183427	−	0.756395i
$328$	72.6991	−	20.8461i	4.01414	−	1.15104i
$329$	−10.2314	+	8.58514i	−0.564074	+	0.473314i
$330$	−0.194804	−	9.36088i	−0.0107236	−	0.515300i
$331$	8.23558	−	2.99751i	0.452668	−	0.164758i	−0.105617	−	0.994407i	$-0.533682\pi$
$331$	8.23558	−	2.99751i	0.452668	−	0.164758i	0.558285	+	0.829649i	$0.311459\pi$
$332$	−8.39118	−	79.8367i	−0.460526	−	4.38161i
$333$	−16.7308	+	13.6757i	−0.916843	+	0.749422i
$334$	−20.0119	+	4.25365i	−1.09500	+	0.232750i
$335$	1.58032	−	0.394017i	0.0863420	−	0.0215275i
$336$	−16.3960	−	28.8257i	−0.894476	−	1.57257i
$337$	−4.41711	+	31.4293i	−0.240615	+	1.71207i	0.377526	+	0.925999i	$0.376775\pi$
$337$	−4.41711	+	31.4293i	−0.240615	+	1.71207i	−0.618141	+	0.786067i	$0.712114\pi$
$338$	−26.4556	+	14.0667i	−1.43899	+	0.765127i
$339$	3.01844	−	9.09029i	0.163939	−	0.493717i
$340$	−0.917015	+	1.09286i	−0.0497321	+	0.0592684i
$341$	7.05745	−	14.1929i	0.382182	−	0.768587i
$342$	4.06199	−	3.56382i	0.219647	−	0.192709i
$343$	18.8629	−	1.98257i	1.01850	−	0.107048i
$344$	36.9376	−	28.8588i	1.99154	−	1.55596i
$345$	−4.91137	−	0.203170i	−0.264419	−	0.0109383i
$346$	5.76386	−	0.403048i	0.309867	−	0.0216680i
$347$	1.51013	+	2.23885i	0.0810678	+	0.120188i	0.867391	−	0.497628i	$-0.165795\pi$
$347$	1.51013	+	2.23885i	0.0810678	+	0.120188i	−0.786323	+	0.617816i	$0.788018\pi$
$348$	70.3718	−	54.2546i	3.77232	−	2.90835i
$349$	2.45334	+	17.4564i	0.131324	+	0.934421i	0.938786	+	0.344501i	$0.111952\pi$
$349$	2.45334	+	17.4564i	0.131324	+	0.934421i	−0.807462	+	0.589920i	$0.799159\pi$
$350$	−12.3453	−	16.9918i	−0.659881	−	0.908249i
$351$	0.366225	−	6.74809i	0.0195476	−	0.360186i
$352$	−1.91555	+	44.9719i	−0.102099	+	2.39701i
$353$	7.87364	+	1.38833i	0.419071	+	0.0738936i	0.379208	−	0.925312i	$-0.376197\pi$
$353$	7.87364	+	1.38833i	0.419071	+	0.0738936i	0.0398636	+	0.999205i	$0.487308\pi$
$354$	−47.9411	−	25.8879i	−2.54804	−	1.37593i
$355$	0.241245	−	6.90836i	0.0128040	−	0.366658i
$356$	−60.6272	+	24.4950i	−3.21323	+	1.29823i
$357$	0.229607	+	1.35304i	0.0121521	+	0.0716103i
$358$	−1.50036	+	5.23239i	−0.0792966	+	0.276540i
$359$	21.2953	+	23.6509i	1.12393	+	1.24825i	0.965367	+	0.260896i	$0.0840179\pi$
$359$	21.2953	+	23.6509i	1.12393	+	1.24825i	0.158558	+	0.987350i	$0.449315\pi$
$360$	4.87193	+	13.9414i	0.256773	+	0.734776i
$361$	16.9352	+	7.54002i	0.891324	+	0.396843i
$362$	−1.96825	−	1.65156i	−0.103449	−	0.0868038i
$363$	6.12524	+	18.0411i	0.321492	+	0.946912i
$364$	1.94468	+	11.0288i	0.101929	+	0.578068i
$365$	−7.10782	−	6.86394i	−0.372040	−	0.359275i
$366$	−23.9780	+	10.4913i	−1.25335	+	0.548388i
$367$	11.2294	−	7.01691i	0.586170	−	0.366280i	−0.204182	−	0.978933i	$-0.565453\pi$
$367$	11.2294	−	7.01691i	0.586170	−	0.366280i	0.790352	+	0.612653i	$0.209898\pi$
$368$	51.2186	+	5.38329i	2.66995	+	0.280623i
$369$	−16.1554	+	23.2986i	−0.841015	+	1.21288i
$370$	−8.72446	+	7.85554i	−0.453563	+	0.408390i
$371$	−7.05630	−	9.03165i	−0.366345	−	0.468900i
$372$	−6.04838	+	41.1144i	−0.313594	+	2.13168i
$373$	20.1696	+	24.0372i	1.04434	+	1.24460i	0.968901	+	0.247448i	$0.0795918\pi$
$373$	20.1696	+	24.0372i	1.04434	+	1.24460i	0.0754405	+	0.997150i	$0.475964\pi$
$374$	1.54953	−	3.75218i	0.0801242	−	0.194021i
$375$	4.43452	+	9.24264i	0.228998	+	0.477288i
$376$	−56.0090	+	27.3174i	−2.88844	+	1.40879i
$377$	−12.6401	+	4.10701i	−0.650997	+	0.211522i
$378$	22.0299	+	8.50347i	1.13309	+	0.437371i
$379$	14.3649	+	10.4367i	0.737874	+	0.536097i	0.892045	−	0.451947i	$-0.149270\pi$
$379$	14.3649	+	10.4367i	0.737874	+	0.536097i	−0.154170	+	0.988044i	$0.549270\pi$
$380$	1.51021	−	1.45839i	0.0774719	−	0.0748138i
$381$	15.0907	+	19.5736i	0.773121	+	1.00279i
$382$	21.2224	+	0.741104i	1.08583	+	0.0379182i
$383$	−3.56203	−	0.888113i	−0.182011	−	0.0453805i	0.149850	−	0.988709i	$-0.452121\pi$
$383$	−3.56203	−	0.888113i	−0.182011	−	0.0453805i	−0.331861	+	0.943328i	$0.607677\pi$
$384$	−4.19127	−	14.9799i	−0.213885	−	0.764442i
$385$	−2.81516	−	2.07848i	−0.143474	−	0.105929i
$386$	−20.6221	−	11.9062i	−1.04964	−	0.606007i
$387$	−3.87446	+	17.1398i	−0.196950	+	0.871267i
$388$	−26.3541	+	29.2691i	−1.33792	+	1.48592i
$389$	−1.39217	−	2.22793i	−0.0705856	−	0.112961i	0.810872	−	0.585223i	$-0.198993\pi$
$389$	−1.39217	−	2.22793i	−0.0705856	−	0.112961i	−0.881458	+	0.472262i	$0.843437\pi$
$390$	0.0236339	−	3.67149i	0.00119675	−	0.185913i
$391$	−1.91558	−	0.934292i	−0.0968752	−	0.0472492i
$392$	32.1595	+	4.51972i	1.62430	+	0.228280i
$393$	−26.0494	−	2.90755i	−1.31402	−	0.146667i
$394$	−48.7689	−	3.41026i	−2.45694	−	0.171806i
$395$	0.362147	+	0.627258i	0.0182216	+	0.0315608i
$396$	−29.9384	−	39.9855i	−1.50446	−	2.00934i
$397$	10.4449	−	18.0911i	0.524215	−	0.907968i	−0.475387	−	0.879777i	$-0.657692\pi$
$397$	10.4449	−	18.0911i	0.524215	−	0.907968i	0.999603	−	0.0281909i	$-0.00897464\pi$
$398$	−1.67292	+	2.48021i	−0.0838560	+	0.124322i
$399$	−0.127909	−	2.01556i	−0.00640348	−	0.100904i
$400$	−19.3260	−	47.8336i	−0.966302	−	2.39168i
$401$	21.0885	−	14.2244i	1.05311	−	0.710330i	0.0946346	−	0.995512i	$-0.469832\pi$
$401$	21.0885	−	14.2244i	1.05311	−	0.710330i	0.958473	+	0.285182i	$0.0920539\pi$
$402$	7.87010	−	9.25754i	0.392525	−	0.461724i
$403$	2.91809	−	5.48813i	0.145361	−	0.273383i
$404$	2.23207	+	6.86962i	0.111050	+	0.341776i
$405$	−4.72171	−	2.89066i	−0.234623	−	0.143638i
$406$		−	46.4403i		−	2.30479i
$407$	12.1029	−	20.5968i	0.599920	−	1.02095i
$408$	−0.487767	+	6.38453i	−0.0241481	+	0.316081i
$409$	−7.92108	−	27.6241i	−0.391672	−	1.36592i	−0.872288	−	0.488992i	$-0.837365\pi$
$409$	−7.92108	−	27.6241i	−0.391672	−	1.36592i	0.480616	−	0.876931i	$-0.340413\pi$
$410$	−8.16248	+	13.0627i	−0.403116	+	0.645121i
$411$	30.1363	+	19.1020i	1.48651	+	0.942235i
$412$	28.0476	+	8.04253i	1.38181	+	0.396227i
$413$	−18.6026	+	8.28241i	−0.915374	+	0.407551i
$414$	−30.6641	+	20.1137i	−1.50706	+	0.988536i
$415$	7.30983	+	6.58180i	0.358826	+	0.323088i
$416$	−1.23129	+	17.6083i	−0.0603689	+	0.863316i
$417$	0.0331581	+	0.0150194i	0.00162376	+	0.000735504i
$418$	−2.84499	+	5.25315i	−0.139153	+	0.256940i
$419$	−16.4329	+	2.89757i	−0.802802	+	0.141556i	−0.559970	−	0.828513i	$-0.689187\pi$
$419$	−16.4329	+	2.89757i	−0.802802	+	0.141556i	−0.242832	+	0.970068i	$0.578076\pi$
$420$	8.70694	+	2.89115i	0.424855	+	0.141074i
$421$	12.1380	−	30.0427i	0.591572	−	1.46419i	−0.273165	−	0.961967i	$-0.588071\pi$
$421$	12.1380	−	30.0427i	0.591572	−	1.46419i	0.864737	−	0.502225i	$-0.167485\pi$
$422$	−6.51368	−	30.6445i	−0.317081	−	1.49175i
$423$	9.77570	−	21.2172i	0.475311	−	1.03161i
$424$	−21.7503	−	48.8521i	−1.05629	−	2.37247i
$425$	0.0745100	+	2.13369i	0.00361427	+	0.103499i
$426$	−28.5621	−	42.9388i	−1.38384	−	2.08039i
$427$	−2.36645	+	9.49130i	−0.114520	+	0.459316i
$428$	−51.2998	−	18.6716i	−2.47967	−	0.902526i
$429$	2.20834	+	7.13744i	0.106620	+	0.344599i
$430$	−1.65780	+	9.40183i	−0.0799460	+	0.453396i
$431$	−7.69080	+	5.58769i	−0.370453	+	0.269150i	−0.757399	−	0.652953i	$-0.773530\pi$
$431$	−7.69080	+	5.58769i	−0.370453	+	0.269150i	0.386946	+	0.922102i	$0.373530\pi$
$432$	47.4521	+	33.3579i	2.28304	+	1.60493i
$433$	−7.09353	+	21.8317i	−0.340894	+	1.04916i	0.622852	+	0.782340i	$0.285974\pi$
$433$	−7.09353	+	21.8317i	−0.340894	+	1.04916i	−0.963746	+	0.266823i	$0.914026\pi$
$434$	15.0873	+	15.6234i	0.724215	+	0.749947i
$435$	−1.95964	+	10.7101i	−0.0939574	+	0.513508i
$436$	−32.1464	−	25.1155i	−1.53953	−	1.20282i
$437$	2.65983	+	1.66205i	0.127237	+	0.0795065i
$438$	−72.9316	−	10.7290i	−3.48481	−	0.512653i
$439$	−1.91262	−	5.25489i	−0.0912845	−	0.250802i	0.885645	−	0.464362i	$-0.153716\pi$
$439$	−1.91262	−	5.25489i	−0.0912845	−	0.250802i	−0.976930	+	0.213560i	$0.931494\pi$
$440$	−10.3985	−	12.5871i	−0.495730	−	0.600066i
$441$	−10.4067	+	6.31801i	−0.495557	+	0.300858i
$442$	0.647488	−	1.45428i	0.0307979	−	0.0691732i
$443$	10.5824	+	4.27557i	0.502786	+	0.203139i	0.611967	−	0.790883i	$-0.290378\pi$
$443$	10.5824	+	4.27557i	0.502786	+	0.203139i	−0.109181	+	0.994022i	$0.534823\pi$
$444$	−13.4162	+	61.1791i	−0.636704	+	2.90343i
$445$	3.51228	−	7.20124i	0.166498	−	0.341372i
$446$	31.4078	−	64.3955i	1.48720	−	3.04922i
$447$	−3.61197	+	16.4709i	−0.170840	+	0.779047i
$448$	−21.6820	−	8.76012i	−1.02438	−	0.413877i
$449$	−5.47523	+	12.2976i	−0.258392	+	0.580358i	−0.995430	−	0.0954934i	$-0.969557\pi$
$449$	−5.47523	+	12.2976i	−0.258392	+	0.580358i	0.737038	+	0.675851i	$0.236224\pi$
$450$	32.2112	+	17.6626i	1.51845	+	0.832625i
$451$	7.81561	−	30.3540i	0.368023	−	1.42931i
$452$	−9.49535	−	26.0883i	−0.446624	−	1.22709i
$453$	−0.426767	−	0.0627822i	−0.0200513	−	0.00294976i
$454$	−27.8871	−	17.4258i	−1.30880	−	0.817832i
$455$	−1.08133	−	0.844824i	−0.0506933	−	0.0396060i
$456$	1.69597	−	9.26904i	0.0794212	−	0.434063i
$457$	−1.72165	−	1.78282i	−0.0805353	−	0.0833967i	0.677863	−	0.735189i	$-0.262906\pi$
$457$	−1.72165	−	1.78282i	−0.0805353	−	0.0833967i	−0.758398	+	0.651792i	$0.774018\pi$
$458$	15.6292	−	48.1018i	0.730305	−	2.24765i
$459$	−1.37316	−	1.96885i	−0.0640937	−	0.0918982i
$460$	−11.5266	+	8.37457i	−0.537431	+	0.390466i
$461$	−2.24987	+	12.7596i	−0.104787	+	0.594275i	0.886519	+	0.462693i	$0.153117\pi$
$461$	−2.24987	+	12.7596i	−0.104787	+	0.594275i	−0.991305	+	0.131582i	$0.957994\pi$
$462$	−26.1037	−	0.368065i	−1.21446	−	0.0171239i
$463$	9.89023	+	3.59975i	0.459638	+	0.167294i	0.561453	−	0.827509i	$-0.310243\pi$
$463$	9.89023	+	3.59975i	0.459638	+	0.167294i	−0.101815	+	0.994803i	$0.532465\pi$
$464$	27.5967	−	110.684i	1.28114	−	5.13838i
$465$	−2.82018	−	4.23970i	−0.130783	−	0.196612i
$466$	0.515927	+	14.7742i	0.0238998	+	0.684402i
$467$	−5.59457	−	12.5656i	−0.258886	−	0.581467i	0.736605	−	0.676323i	$-0.236428\pi$
$467$	−5.59457	−	12.5656i	−0.258886	−	0.581467i	−0.995491	+	0.0948559i	$0.969761\pi$
$468$	−11.3085	−	15.9939i	−0.522737	−	0.739318i
$469$	−0.944179	−	4.44201i	−0.0435981	−	0.205113i
$470$	4.75443	−	11.7676i	0.219305	−	0.542800i
$471$	−7.18734	−	2.38657i	−0.331175	−	0.109967i
$472$	−93.5649	+	16.4980i	−4.30667	+	0.759382i
$473$	−2.55622	−	19.2580i	−0.117535	−	0.885483i
$474$	4.92213	+	2.22955i	0.226081	+	0.102406i
$475$	0.219166	−	3.13422i	0.0100560	−	0.143808i
$476$	2.95609	+	2.66168i	0.135492	+	0.121998i
$477$	17.9033	+	9.01917i	0.819737	+	0.412960i
$478$	−15.2718	+	6.79944i	−0.698516	+	0.310999i
$479$	5.01079	+	1.43682i	0.228949	+	0.0656500i	0.388150	−	0.921596i	$-0.373114\pi$
$479$	5.01079	+	1.43682i	0.228949	+	0.0656500i	−0.159201	+	0.987246i	$0.550892\pi$
$480$	12.2134	+	7.74152i	0.557462	+	0.353351i
$481$	4.96431	−	7.94455i	0.226353	−	0.362240i
$482$	−2.96769	−	10.3496i	−0.135175	−	0.471410i
$483$	−1.04407	+	13.6661i	−0.0475068	+	0.621830i
$484$	46.3781	+	29.9781i	2.10810	+	1.36264i
$485$		−	4.82594i		−	0.219135i
$486$	−41.1944	+	2.99326i	−1.86861	+	0.135777i
$487$	−6.05340	−	18.6304i	−0.274306	−	0.844226i	−0.989402	−	0.145200i	$-0.953617\pi$
$487$	−6.05340	−	18.6304i	−0.274306	−	0.844226i	0.715097	−	0.699025i	$-0.246383\pi$
$488$	−21.4264	+	40.2972i	−0.969927	+	1.82417i
$489$	−0.912186	+	1.07300i	−0.0412505	+	0.0485226i
$490$	−5.48347	+	3.69864i	−0.247718	+	0.167088i
$491$	−1.21113	−	2.99765i	−0.0546574	−	0.135282i	0.897385	−	0.441249i	$-0.145465\pi$
$491$	−1.21113	−	2.99765i	−0.0546574	−	0.135282i	−0.952042	+	0.305967i	$0.901020\pi$
$492$	5.20456	+	82.0118i	0.234640	+	3.69738i
$493$	−2.63980	+	3.91366i	−0.118891	+	0.176262i
$494$	−1.17134	+	2.02881i	−0.0527009	+	0.0912807i
$495$	6.00451	+	1.18638i	0.269883	+	0.0533239i
$496$	26.6746	+	46.2017i	1.19772	+	2.07452i
$497$	−19.2272	−	1.34450i	−0.862457	−	0.0603089i
$498$	72.9303	+	8.14026i	3.26809	+	0.364774i
$499$	−25.4225	−	3.57290i	−1.13807	−	0.159945i	−0.455131	−	0.890424i	$-0.650408\pi$
$499$	−25.4225	−	3.57290i	−1.13807	−	0.159945i	−0.682935	+	0.730480i	$0.739297\pi$
$500$	26.7063	+	13.0255i	1.19434	+	0.582519i
$501$	0.0860895	−	13.3739i	0.00384619	−	0.597500i
$502$	27.4596	+	43.9446i	1.22558	+	1.96134i
$503$	−1.88123	+	2.08931i	−0.0838797	+	0.0931579i	−0.783624	−	0.621236i	$-0.786631\pi$
$503$	−1.88123	+	2.08931i	−0.0838797	+	0.0931579i	0.699744	+	0.714394i	$0.253297\pi$
$504$	39.3228	−	12.2194i	1.75158	−	0.544293i
$505$	−0.766483	−	0.442529i	−0.0341081	−	0.0196923i
$506$	24.0810	−	32.6161i	1.07053	−	1.44996i
$507$	−5.27757	−	18.8625i	−0.234385	−	0.837712i
$508$	69.5094	+	17.3306i	3.08398	+	0.768923i
$509$	5.99218	+	0.209251i	0.265599	+	0.00927490i	0.167389	−	0.985891i	$-0.446466\pi$
$509$	5.99218	+	0.209251i	0.265599	+	0.00927490i	0.0982092	+	0.995166i	$0.468689\pi$
$510$	−0.796265	−	1.03281i	−0.0352592	−	0.0457335i
$511$	−19.8185	+	19.1385i	−0.876720	+	0.846638i
$512$	21.9749	+	15.9657i	0.971163	+	0.705591i
$513$	1.70683	+	3.09274i	0.0753584	+	0.136548i
$514$	−0.443580	+	0.144128i	−0.0195655	+	0.00635720i
$515$	−3.21337	+	1.56726i	−0.141598	+	0.0690619i
$516$	22.0324	+	45.9209i	0.969920	+	2.02156i
$517$	−1.99891	+	25.7490i	−0.0879121	+	1.13244i
$518$	21.0411	+	25.0758i	0.924491	+	1.10177i
$519$	−0.549732	+	3.73685i	−0.0241306	+	0.164030i
$520$	−3.94170	−	5.04515i	−0.172855	−	0.221245i
$521$	4.20469	−	3.78592i	0.184211	−	0.165864i	−0.571866	−	0.820347i	$-0.693780\pi$
$521$	4.20469	−	3.78592i	0.184211	−	0.165864i	0.756077	+	0.654483i	$0.227114\pi$
$522$	34.6651	+	73.4595i	1.51725	+	3.21524i
$523$	36.1307	+	3.79748i	1.57988	+	0.166052i	0.853446	−	0.521181i	$-0.174508\pi$
$523$	36.1307	+	3.79748i	1.57988	+	0.166052i	0.726437	+	0.687233i	$0.241175\pi$
$524$	−64.4282	+	40.2592i	−2.81456	+	1.75873i
$525$	12.5785	−	5.50355i	0.548970	−	0.240195i
$526$	−29.7737	−	28.7521i	−1.29820	−	1.25365i
$527$	−0.383377	−	2.17424i	−0.0167001	−	0.0947112i
$528$	−61.9960	−	16.3891i	−2.69803	−	0.713244i
$529$	1.31370	+	1.10232i	0.0571173	+	0.0479271i
$530$	9.94965	+	4.42987i	0.432185	+	0.192421i
$531$	23.2433	−	26.9870i	1.00867	−	1.17114i
$532$	−3.91695	−	4.35021i	−0.169821	−	0.188606i
$533$	3.38793	−	11.8151i	0.146747	−	0.511769i
$534$	−10.0005	−	58.9312i	−0.432762	−	2.55020i
$535$	6.20214	−	2.50583i	0.268142	−	0.108336i
$536$	0.739456	−	21.1753i	0.0319396	−	0.914632i
$537$	−3.13096	−	1.69070i	−0.135111	−	0.0729592i
$538$	−15.2397	−	2.68717i	−0.657031	−	0.115852i
$539$	8.36741	−	10.5423i	0.360410	−	0.454089i
$540$	−15.9308	+	1.92602i	−0.685551	+	0.0828825i
$541$	−1.17931	−	1.62318i	−0.0507024	−	0.0697858i	0.782913	−	0.622131i	$-0.213733\pi$
$541$	−1.17931	−	1.62318i	−0.0507024	−	0.0697858i	−0.833615	+	0.552345i	$0.813733\pi$
$542$	−0.0153755	−	0.109402i	−0.000660433	−	0.00469922i
$543$	1.33018	−	1.02553i	0.0570834	−	0.0440097i
$544$	3.50593	+	5.19775i	0.150315	+	0.222852i
$545$	4.98640	−	0.348683i	0.213594	−	0.0149359i
$546$	−10.2286	−	0.423128i	−0.437743	−	0.0181082i
$547$	−15.6652	+	12.2390i	−0.669797	+	0.523303i	−0.892193	−	0.451654i	$-0.850834\pi$
$547$	−15.6652	+	12.2390i	−0.669797	+	0.523303i	0.222396	+	0.974956i	$0.428612\pi$
$548$	102.852	−	10.8102i	4.39361	−	0.461787i
$549$	−3.34148	−	16.7798i	−0.142611	−	0.716145i
$550$	−40.1734	−	5.96024i	−1.71300	−	0.254146i
$551$	4.46550	−	5.32177i	0.190236	−	0.226715i
$552$	−20.1521	+	60.6897i	−0.857731	+	2.58313i
$553$	1.78314	−	0.948112i	0.0758268	−	0.0403178i
$554$	−2.51256	+	17.8778i	−0.106748	+	0.759555i
$555$	−3.79437	−	6.67084i	−0.161062	−	0.283161i
$556$	0.102374	−	0.0255246i	0.00434161	−	0.00108249i
$557$	3.37720	−	0.717846i	0.143096	−	0.0304161i	−0.135807	−	0.990735i	$-0.543363\pi$
$557$	3.37720	−	0.717846i	0.143096	−	0.0304161i	0.278903	+	0.960319i	$0.410029\pi$
$558$	−35.5272	−	13.4513i	−1.50399	−	0.569439i
$559$	−0.796304	−	7.57633i	−0.0336801	−	0.320445i
$560$	11.0675	−	4.02822i	0.467685	−	0.170224i
$561$	2.17892	+	1.51483i	0.0919940	+	0.0639561i
$562$	54.1678	−	45.4521i	2.28493	−	1.91728i
$563$	42.8798	−	12.2956i	1.80717	−	0.518197i	0.809542	−	0.587062i	$-0.199715\pi$
$563$	42.8798	−	12.2956i	1.80717	−	0.518197i	0.997626	+	0.0688645i	$0.0219376\pi$
$564$	−15.9575	−	65.8038i	−0.671934	−	2.77084i
$565$	3.00358	+	1.59703i	0.126362	+	0.0671877i
$566$	−30.2820	+	41.6797i	−1.27285	+	1.75193i
$567$	−8.51451	+	12.8761i	−0.357576	+	0.540745i
$568$	−85.5262	−	27.7891i	−3.58860	−	1.16601i
$569$	1.97756	−	0.277927i	0.0829035	−	0.0116513i	−0.0975994	−	0.995226i	$-0.531116\pi$
$569$	1.97756	−	0.277927i	0.0829035	−	0.0116513i	0.180503	+	0.983574i	$0.442227\pi$
$570$	1.00650	+	1.63405i	0.0421577	+	0.0684428i
$571$	1.41619	−	3.89096i	0.0592658	−	0.162832i	−0.906526	−	0.422150i	$-0.861276\pi$
$571$	1.41619	−	3.89096i	0.0592658	−	0.162832i	0.965792	+	0.259318i	$0.0834978\pi$
$572$	17.8597	+	12.2467i	0.746753	+	0.512060i
$573$	−3.44492	+	13.4475i	−0.143914	+	0.561776i
$574$	35.6059	+	24.0165i	1.48616	+	1.00243i
$575$	−4.43311	+	20.8562i	−0.184874	+	0.869762i
$576$	40.8357	−	2.32766i	1.70149	−	0.0969860i
$577$	3.52513	−	33.5394i	0.146753	−	1.39626i	−0.634921	−	0.772577i	$-0.718968\pi$
$577$	3.52513	−	33.5394i	0.146753	−	1.39626i	0.781675	−	0.623687i	$-0.214366\pi$
$578$	10.7601	+	43.1564i	0.447561	+	1.79507i
$579$	10.4901	−	11.5007i	0.435954	−	0.477953i
$580$	14.8157	+	27.8642i	0.615187	+	1.15700i
$581$	19.0520	−	19.7289i	0.790410	−	0.818493i
$582$	−20.9744	−	29.2631i	−0.869417	−	1.21299i
$583$	−22.0228	−	2.48543i	−0.912090	−	0.102936i
$584$	−111.323	+	64.2725i	−4.60659	+	2.65961i
$585$	2.34106	+	0.529197i	0.0967910	+	0.0218796i
$586$	−49.5335	−	10.5287i	−2.04621	−	0.434935i
$587$	20.9856	−	0.732832i	0.866167	−	0.0302472i	0.401631	−	0.915801i	$-0.368443\pi$
$587$	20.9856	−	0.732832i	0.866167	−	0.0302472i	0.464536	+	0.885554i	$0.346221\pi$
$588$	−12.2821	+	33.0808i	−0.506507	+	1.36423i
$589$	0.226638	+	3.24108i	0.00933846	+	0.133546i
$590$	11.9132	−	15.2482i	0.490458	−	0.627758i
$591$	9.00650	−	30.6631i	0.370478	−	1.26131i
$592$	35.2475	+	72.2681i	1.44866	+	2.97020i
$593$	−6.44646			−0.264724			−0.132362	−	0.991201i	$-0.542256\pi$
$593$	−6.44646			−0.264724			−0.132362	+	0.991201i	$0.542256\pi$
$594$	41.5658	−	18.9028i	1.70546	−	0.775592i
$595$	−0.487405			−0.0199816
$596$	21.4254	+	43.9285i	0.877617	+	1.79938i
$597$	−1.34944	−	1.41551i	−0.0552290	−	0.0579330i
$598$	9.78803	−	12.5281i	0.400262	−	0.512312i
$599$	−2.75006	−	39.3277i	−0.112365	−	1.60689i	−0.647462	−	0.762098i	$-0.724170\pi$
$599$	−2.75006	−	39.3277i	−0.112365	−	1.60689i	0.535098	−	0.844790i	$-0.320275\pi$
$600$	63.1563	−	10.7175i	2.57835	−	0.437538i
$601$	3.79706	−	0.132596i	0.154885	−	0.00540872i	0.0426482	−	0.999090i	$-0.486421\pi$
$601$	3.79706	−	0.132596i	0.154885	−	0.00540872i	0.112237	+	0.993681i	$0.464198\pi$
$602$	26.0376	+	5.53446i	1.06121	+	0.225568i
$603$	4.80923	+	6.32162i	0.195847	+	0.257436i
$604$	−1.08278	+	0.625144i	−0.0440577	+	0.0254367i
$605$	−6.68099	+	1.07275i	−0.271621	+	0.0436135i
$606$	−6.57104	+	0.647907i	−0.266930	+	0.0263194i
$607$	22.8286	−	23.6397i	0.926585	−	0.959507i	−0.0726984	−	0.997354i	$-0.523161\pi$
$607$	22.8286	−	23.6397i	0.926585	−	0.959507i	0.999284	+	0.0378470i	$0.0120499\pi$
$608$	−4.33155	−	8.14647i	−0.175668	−	0.330383i
$609$	29.6537	+	6.50286i	1.20163	+	0.263509i
$610$	−2.24874	−	9.01921i	−0.0910489	−	0.365177i
$611$	−1.05862	+	10.0721i	−0.0428273	+	0.407474i
$612$	−6.66275	−	2.00369i	−0.269326	−	0.0809945i
$613$	−6.72557	+	31.6413i	−0.271643	+	1.27798i	0.604762	+	0.796407i	$0.293268\pi$
$613$	−6.72557	+	31.6413i	−0.271643	+	1.27798i	−0.876405	+	0.481575i	$0.840065\pi$
$614$	−1.69916	−	1.14610i	−0.0685726	−	0.0462528i
$615$	−7.19800	−	7.04113i	−0.290251	−	0.283926i
$616$	−36.0867	+	27.7514i	−1.45398	+	1.11814i
$617$	1.50850	−	4.14458i	0.0607301	−	0.166855i	−0.905617	−	0.424097i	$-0.860592\pi$
$617$	1.50850	−	4.14458i	0.0607301	−	0.166855i	0.966347	+	0.257242i	$0.0828138\pi$
$618$	−12.6733	+	23.4693i	−0.509794	+	0.944073i
$619$	35.7108	−	5.01882i	1.43534	−	0.201724i	0.621773	−	0.783198i	$-0.286413\pi$
$619$	35.7108	−	5.01882i	1.43534	−	0.201724i	0.813565	+	0.581474i	$0.197524\pi$
$620$	−14.0367	−	4.56080i	−0.563727	−	0.183166i
$621$	−8.54951	−	22.3965i	−0.343080	−	0.898741i
$622$	25.2680	−	34.7784i	1.01315	−	1.39449i
$623$	−19.7250	−	10.4880i	−0.790266	−	0.420192i
$624$	−24.1270	−	7.08670i	−0.965854	−	0.283695i
$625$	18.7131	−	5.36588i	0.748522	−	0.214635i
$626$	−29.1663	+	24.4734i	−1.16572	+	0.978154i
$627$	−2.95594	−	2.55220i	−0.118049	−	0.101925i
$628$	−20.6270	+	7.50761i	−0.823106	+	0.299586i
$629$	−0.347816	−	3.30924i	−0.0138683	−	0.131948i
$630$	−4.28645	+	7.20842i	−0.170776	+	0.287190i
$631$	8.30642	−	1.76558i	0.330673	−	0.0702868i	−0.0395834	−	0.999216i	$-0.512603\pi$
$631$	8.30642	−	1.76558i	0.330673	−	0.0702868i	0.370257	+	0.928929i	$0.379270\pi$
$632$	9.14266	−	2.27952i	0.363675	−	0.0906745i
$633$	20.4796	+	0.131830i	0.813991	+	0.00523977i
$634$	8.06655	−	57.3965i	0.320364	−	2.27951i
$635$	−7.75032	+	4.12092i	−0.307562	+	0.163534i
$636$	56.9120	−	11.7146i	2.25671	−	0.464516i
$637$	3.39260	−	4.04314i	0.134420	−	0.160195i
$638$	−64.1175	−	62.8740i	−2.53843	−	2.48921i
$639$	31.4173	−	12.2253i	1.24285	−	0.483626i
$640$	5.49422	−	0.577466i	0.217178	−	0.0228264i
$641$	−19.5614	+	15.2830i	−0.772628	+	0.603643i	−0.922917	−	0.384999i	$-0.874202\pi$
$641$	−19.5614	+	15.2830i	−0.772628	+	0.603643i	0.150289	+	0.988642i	$0.451980\pi$
$642$	26.7172	−	42.1502i	1.05444	−	1.66354i
$643$	2.59631	−	0.181552i	0.102388	−	0.00715969i	−0.0184704	−	0.999829i	$-0.505880\pi$
$643$	2.59631	−	0.181552i	0.102388	−	0.00715969i	0.120859	+	0.992670i	$0.461435\pi$
$644$	22.2147	+	32.9346i	0.875382	+	1.29781i
$645$	−5.77124	−	2.37506i	−0.227243	−	0.0935179i
$646$	0.115806	+	0.824005i	0.00455634	+	0.0324201i
$647$	−17.8579	−	24.5794i	−0.702068	−	0.966314i	−0.999931	−	0.0117056i	$-0.996274\pi$
$647$	−17.8579	−	24.5794i	−0.702068	−	0.966314i	0.297863	−	0.954609i	$-0.403726\pi$
$648$	−53.0799	+	48.6810i	−2.08518	+	1.91237i
$649$	−13.7504	+	36.8968i	−0.539751	+	1.44833i
$650$	−15.6841	−	2.76553i	−0.615181	−	0.108473i
$651$	−12.0887	+	7.44607i	−0.473793	+	0.291835i
$652$	−0.142461	+	4.07954i	−0.00557919	+	0.159767i
$653$	−28.1383	+	11.3686i	−1.10114	+	0.444888i	−0.851980	−	0.523575i	$-0.824598\pi$
$653$	−28.1383	+	11.3686i	−1.10114	+	0.444888i	−0.249157	+	0.968463i	$0.580154\pi$
$654$	28.7206	−	23.7861i	1.12306	−	0.930109i
$655$	2.56590	−	8.94835i	0.100258	−	0.349641i
$656$	70.5903	+	78.3984i	2.75609	+	3.06094i
$657$	17.0632	−	45.0669i	0.665698	−	1.75823i
$658$	−32.3287	−	14.3937i	−1.26030	−	0.561123i
$659$	4.92089	+	4.12912i	0.191691	+	0.160848i	0.733582	−	0.679601i	$-0.237847\pi$
$659$	4.92089	+	4.12912i	0.191691	+	0.160848i	−0.541891	+	0.840449i	$0.682292\pi$
$660$	15.7797	−	8.10694i	0.614224	−	0.315562i
$661$	7.94027	+	45.0315i	0.308841	+	1.75152i	0.604853	+	0.796338i	$0.293232\pi$
$661$	7.94027	+	45.0315i	0.308841	+	1.75152i	−0.296012	+	0.955184i	$0.595657\pi$
$662$	16.7040	+	16.1309i	0.649219	+	0.626944i
$663$	0.837942	+	0.617080i	0.0325430	+	0.0239654i
$664$	108.519	−	67.8105i	4.21137	−	2.63156i
$665$	0.713341	+	0.0749752i	0.0276622	+	0.00290741i
$666$	−52.0006	−	23.9590i	−2.01498	−	0.928392i
$667$	−35.0362	+	31.5468i	−1.35661	+	1.22150i
$668$	−23.8659	−	30.5469i	−0.923399	−	1.18190i
$669$	36.7208	+	29.0720i	1.41971	+	1.12399i
$670$	2.77387	+	3.30577i	0.107164	+	0.127713i
$671$	9.90024	+	16.1172i	0.382195	+	0.622197i
$672$	22.7608	−	33.2801i	0.878017	−	1.28381i
$673$	28.8329	−	14.0627i	1.11143	−	0.542078i	0.211174	−	0.977449i	$-0.432271\pi$
$673$	28.8329	−	14.0627i	1.11143	−	0.542078i	0.900252	+	0.435370i	$0.143382\pi$
$674$	−79.9773	+	25.9862i	−3.08061	+	1.00095i
$675$	−15.7886	+	18.0947i	−0.607703	+	0.696465i
$676$	−45.9296	−	33.3698i	−1.76652	−	1.28345i
$677$	−16.0542	+	15.5034i	−0.617013	+	0.595843i	−0.936036	−	0.351904i	$-0.885534\pi$
$677$	−16.0542	+	15.5034i	−0.617013	+	0.595843i	0.319023	+	0.947747i	$0.396645\pi$
$678$	25.1538	−	3.37017i	0.966027	−	0.129431i
$679$	−13.4478	−	0.469609i	−0.516081	−	0.0180219i
$680$	−2.20654	−	0.550152i	−0.0846170	−	0.0210974i
$681$	15.0318	−	15.3667i	0.576022	−	0.588855i
$682$	41.9966	+	0.321789i	1.60813	+	0.0123219i
$683$	−0.999916	−	0.577302i	−0.0382607	−	0.0220898i	0.480748	−	0.876859i	$-0.340365\pi$
$683$	−0.999916	−	0.577302i	−0.0382607	−	0.0220898i	−0.519008	+	0.854769i	$0.673699\pi$
$684$	9.44305	+	3.95740i	0.361064	+	0.151315i
$685$	−8.47919	+	9.41709i	−0.323973	+	0.359809i
$686$	26.6306	+	42.6178i	1.01676	+	1.62716i
$687$	28.5261	+	16.7153i	1.08834	+	0.637728i
$688$	58.7682	+	28.6632i	2.24052	+	1.09277i
$689$	−8.60626	−	1.20953i	−0.327872	−	0.0460794i
$690$	−5.22073	−	11.9321i	−0.198750	−	0.454247i
$691$	−3.32814	−	0.232726i	−0.126608	−	0.00885333i	0.00631165	−	0.999980i	$-0.497991\pi$
$691$	−3.32814	−	0.232726i	−0.126608	−	0.00885333i	−0.132920	+	0.991127i	$0.542435\pi$
$692$	5.47387	+	9.48103i	0.208085	+	0.360415i
$693$	3.89023	−	16.6166i	0.147778	−	0.631211i
$694$	−3.57766	+	6.19669i	−0.135806	+	0.235223i
$695$	−0.00722922	+	0.0107178i	−0.000274220	+	0.000406548i
$696$	126.906	+	62.9105i	4.81035	+	2.38461i
$697$	−1.63545	−	4.04788i	−0.0619471	−	0.153324i
$698$	−38.7217	+	26.1181i	−1.46564	+	0.988586i
$699$	−9.50607	−	1.73934i	−0.359552	−	0.0657880i
$700$	18.6828	−	35.1373i	0.706145	−	1.32806i
$701$	5.28920	+	16.2785i	0.199770	+	0.614829i	0.999888	+	0.0149862i	$0.00477042\pi$
$701$	5.28920	+	16.2785i	0.199770	+	0.614829i	−0.800118	+	0.599843i	$0.795230\pi$
$702$	16.4955	−	6.96578i	0.622582	−	0.262906i
$703$			4.89674i			0.184684i
$704$	−41.4492	+	18.0751i	−1.56218	+	0.681232i
$705$	6.84827	+	4.68363i	0.257921	+	0.176396i
$706$	5.83902	+	20.3631i	0.219754	+	0.766375i
$707$	−1.30773	+	2.09280i	−0.0491821	+	0.0787078i
$708$	4.26686	−	103.146i	0.160358	−	3.87646i
$709$	−15.7050	−	4.50333i	−0.589812	−	0.169126i	−0.0325609	−	0.999470i	$-0.510366\pi$
$709$	−15.7050	−	4.50333i	−0.589812	−	0.169126i	−0.557251	+	0.830344i	$0.688144\pi$
$710$	16.7320	−	7.44957i	0.627941	−	0.279577i
$711$	−2.11287	+	2.83075i	−0.0792387	+	0.106161i
$712$	−77.4593	−	69.7447i	−2.90291	−	2.61379i
$713$	1.53806	−	21.9953i	0.0576010	−	0.823732i
$714$	−2.95548	+	2.11835i	−0.110606	+	0.0792772i
$715$	−2.63037	+	0.349144i	−0.0983703	+	0.0130572i
$716$	−10.1569	+	1.79094i	−0.379582	+	0.0669305i
$717$	−2.20321	−	10.7036i	−0.0822806	−	0.399735i
$718$	−31.5884	+	78.1839i	−1.17887	+	2.91780i
$719$	−4.90386	−	23.0709i	−0.182883	−	0.860398i	−0.969907	−	0.243475i	$-0.921712\pi$
$719$	−4.90386	−	23.0709i	−0.182883	−	0.860398i	0.787024	−	0.616923i	$-0.211621\pi$
$720$	−14.4997	+	14.6331i	−0.540372	+	0.545344i
$721$	4.05460	+	9.10679i	0.151001	+	0.339155i
$722$	1.71418	+	49.0877i	0.0637952	+	1.82685i
$723$	7.02410	−	0.445757i	0.261229	−	0.0165779i
$724$	1.17775	−	4.72370i	0.0437707	−	0.175555i
$725$	44.3797	+	16.1529i	1.64822	+	0.599903i
$726$	−35.8492	+	35.5416i	−1.33049	+	1.31907i
$727$	5.17861	−	29.3693i	0.192064	−	1.08925i	−0.724474	−	0.689302i	$-0.757917\pi$
$727$	5.17861	−	29.3693i	0.192064	−	1.08925i	0.916538	−	0.399947i	$-0.130971\pi$
$728$	−14.4423	+	10.4929i	−0.535265	+	0.388893i
$729$	3.85700	−	26.7231i	0.142852	−	0.989744i
$730$	8.09026	−	24.8993i	0.299434	−	0.921563i
$731$	−1.87967	−	1.94645i	−0.0695221	−	0.0719922i
$732$	−37.7828	−	32.1203i	−1.39649	−	1.18720i
$733$	−21.2340	−	16.5898i	−0.784294	−	0.612758i	0.141867	−	0.989886i	$-0.454689\pi$
$733$	−21.2340	−	16.5898i	−0.784294	−	0.612758i	−0.926161	+	0.377128i	$0.876912\pi$
$734$	29.7533	+	18.5919i	1.09821	+	0.686240i
$735$	−1.59388	−	4.01928i	−0.0587911	−	0.148253i
$736$	21.4155	+	58.8385i	0.789385	+	2.16882i
$737$	−7.41112	−	4.71032i	−0.272992	−	0.173507i
$738$	−74.2486	−	11.4115i	−2.73313	−	0.420065i
$739$	−3.53467	+	7.93899i	−0.130025	+	0.292040i	−0.966812	−	0.255487i	$-0.917764\pi$
$739$	−3.53467	+	7.93899i	−0.130025	+	0.292040i	0.836788	+	0.547527i	$0.184431\pi$
$740$	−20.6245	−	8.33283i	−0.758171	−	0.306321i
$741$	−1.13145	−	1.03202i	−0.0415647	−	0.0379124i
$742$	13.3124	−	27.2944i	0.488712	−	1.00201i
$743$	3.14790	−	6.45414i	0.115485	−	0.236780i	−0.833220	−	0.552941i	$-0.813505\pi$
$743$	3.14790	−	6.45414i	0.115485	−	0.236780i	0.948705	+	0.316162i	$0.102394\pi$
$744$	−63.1316	+	20.0643i	−2.31452	+	0.735594i
$745$	−5.55262	−	2.24340i	−0.203432	−	0.0821919i
$746$	−33.8159	+	75.9517i	−1.23809	+	2.78079i
$747$	−15.4100	+	45.4286i	−0.563822	+	1.66215i
$748$	7.67698	−	0.477748i	0.280698	−	0.0174682i
$749$	−6.37914	−	17.5266i	−0.233089	−	0.640406i
$750$	−16.8600	+	21.2959i	−0.615641	+	0.777615i
$751$	4.01958	+	2.51171i	0.146676	+	0.0916536i	0.601272	−	0.799044i	$-0.294661\pi$
$751$	4.01958	+	2.51171i	0.146676	+	0.0916536i	−0.454596	+	0.890698i	$0.650216\pi$
$752$	−68.4977	−	53.5163i	−2.49786	−	1.95154i
$753$	−31.9052	+	11.3805i	−1.16269	+	0.414728i
$754$	−24.4620	−	25.3312i	−0.890855	−	0.922508i
$755$	0.0473410	−	0.145701i	0.00172292	−	0.00530259i
$756$	3.81677	+	44.5797i	0.138815	+	1.62135i
$757$	−8.61542	+	6.25947i	−0.313133	+	0.227504i	−0.733240	−	0.679970i	$-0.761993\pi$
$757$	−8.61542	+	6.25947i	−0.313133	+	0.227504i	0.420107	+	0.907475i	$0.361993\pi$
$758$	−8.16944	+	46.3312i	−0.296728	+	1.68283i
$759$	17.4545	+	19.9436i	0.633559	+	0.723908i
$760$	3.14475	+	1.14460i	0.114072	+	0.0415189i
$761$	−8.79388	+	35.2703i	−0.318778	+	1.27855i	0.570544	+	0.821267i	$0.306732\pi$
$761$	−8.79388	+	35.2703i	−0.318778	+	1.27855i	−0.889322	+	0.457282i	$0.848823\pi$
$762$	−29.0854	+	58.6723i	−1.05365	+	2.12547i
$763$	−0.486407	−	13.9289i	−0.0176091	−	0.504260i
$764$	16.3654	+	36.7572i	0.592078	+	1.32983i
$765$	0.770980	−	0.363821i	0.0278748	−	0.0131540i
$766$	−2.02232	−	9.51427i	−0.0730694	−	0.343765i
$767$	−5.78423	+	14.3165i	−0.208856	+	0.516938i
$768$	−4.49556	+	3.99572i	−0.162220	+	0.144183i
$769$	−21.4421	+	3.78082i	−0.773221	+	0.136340i	−0.546318	−	0.837578i	$-0.683971\pi$
$769$	−21.4421	+	3.78082i	−0.773221	+	0.136340i	−0.226903	+	0.973917i	$0.572860\pi$
$770$	1.67993	−	9.11827i	0.0605406	−	0.328600i
$771$	−0.0299175	−	0.303422i	−0.00107745	−	0.0109275i
$772$	3.14730	−	45.0085i	0.113274	−	1.61989i
$773$	38.6493	+	34.8000i	1.39012	+	1.25167i	0.931845	+	0.362857i	$0.118199\pi$
$773$	38.6493	+	34.8000i	1.39012	+	1.25167i	0.458273	+	0.888811i	$0.348468\pi$
$774$	−45.3175	+	10.6812i	−1.62891	+	0.383927i
$775$	−20.1778	+	8.98376i	−0.724810	+	0.322706i
$776$	−60.3500	−	17.3051i	−2.16644	−	0.621216i
$777$	−18.9580	+	9.92415i	−0.680115	+	0.356027i
$778$	3.68866	−	5.90310i	0.132245	−	0.211636i
$779$	1.77089	+	6.17584i	0.0634489	+	0.221273i
$780$	6.27215	−	3.00931i	0.224579	−	0.107751i
$781$	−27.8873	+	24.7256i	−0.997887	+	0.884752i
$782$		−	5.64701i		−	0.201937i
$783$	−51.7604	+	11.8486i	−1.84976	+	0.423434i
$784$	13.9986	+	43.0833i	0.499950	+	1.53869i
$785$	1.26271	−	2.37482i	0.0450682	−	0.0847609i
$786$	−23.3323	−	65.4120i	−0.832235	−	2.33317i
$787$	−27.8041	+	18.7541i	−0.991108	+	0.668511i	−0.943851	−	0.330372i	$-0.892826\pi$
$787$	−27.8041	+	18.7541i	−0.991108	+	0.668511i	−0.0472574	+	0.998883i	$0.515048\pi$
$788$	−34.7001	−	85.8856i	−1.23614	−	3.05955i
$789$	22.5283	−	14.9854i	0.802029	−	0.533496i
$790$	−1.07314	+	1.59099i	−0.0381805	+	0.0566049i
$791$	4.74253	−	8.21430i	0.168625	−	0.292067i
$792$	36.3673	−	70.8341i	1.29226	−	2.51698i
$793$	3.70867	+	6.42361i	0.131699	+	0.228109i
$794$	55.2146	+	3.86098i	1.95949	+	0.137021i
$795$	−4.22183	+	5.73288i	−0.149733	+	0.203324i
$796$	−5.61331	−	0.788899i	−0.198959	−	0.0279618i
$797$	−35.0878	−	17.1134i	−1.24287	−	0.606189i	−0.304730	−	0.952439i	$-0.598566\pi$
$797$	−35.0878	−	17.1134i	−1.24287	−	0.606189i	−0.938142	+	0.346250i	$0.887455\pi$
$798$	4.65134	−	2.64568i	0.164656	−	0.0936561i
$799$	1.90626	+	3.05065i	0.0674386	+	0.107924i
$800$	41.9702	−	46.6127i	1.48387	−	1.64801i
$801$	39.0298	+	1.86629i	1.37905	+	0.0659422i
$802$	58.3686	+	33.6991i	2.06107	+	1.18996i
$803$	−0.408194	+	53.2733i	−0.0144049	+	1.87997i
$804$	22.3025	+	5.71336i	0.786547	+	0.201495i
$805$	−4.72312	−	1.17760i	−0.166468	−	0.0415051i
$806$	16.4590	+	0.574761i	0.579743	+	0.0202451i
$807$	3.84981	−	9.35479i	0.135520	−	0.329304i
$808$	−8.28246	+	7.99828i	−0.291376	+	0.281378i
$809$	2.83436	+	2.05928i	0.0996507	+	0.0724004i	0.636495	−	0.771281i	$-0.280384\pi$
$809$	2.83436	+	2.05928i	0.0996507	+	0.0724004i	−0.536844	+	0.843681i	$0.680384\pi$
$810$	1.39964	−	14.6019i	0.0491785	−	0.513060i
$811$	9.72074	−	3.15846i	0.341342	−	0.110909i	−0.133330	−	0.991072i	$-0.542567\pi$
$811$	9.72074	−	3.15846i	0.341342	−	0.110909i	0.474671	+	0.880163i	$0.342567\pi$
$812$	79.0874	−	38.5735i	2.77542	−	1.35366i
$813$	0.0720098	+	0.00550143i	0.00252549	+	0.000192944i
$814$	63.1075	+	4.89908i	2.21192	+	0.171713i
$815$	−0.321506	−	0.383156i	−0.0112619	−	0.0134214i
$816$	−8.30279	+	3.29253i	−0.290656	+	0.115262i
$817$	2.45158	+	3.13787i	0.0857698	+	0.109780i
$818$	56.5845	−	50.9489i	1.97843	−	1.78139i
$819$	1.70245	−	6.47204i	0.0594885	−	0.226151i
$820$	−29.0254	−	3.05070i	−1.01361	−	0.106535i
$821$	8.02414	−	5.01404i	0.280045	−	0.174991i	−0.382624	−	0.923904i	$-0.624979\pi$
$821$	8.02414	−	5.01404i	0.280045	−	0.174991i	0.662668	+	0.748913i	$0.269424\pi$
$822$	−10.4869	+	93.9545i	−0.365773	+	3.27704i
$823$	−11.5290	−	11.1335i	−0.401877	−	0.388088i	0.466068	−	0.884749i	$-0.345670\pi$
$823$	−11.5290	−	11.1335i	−0.401877	−	0.388088i	−0.867945	+	0.496661i	$0.834559\pi$
$824$	8.07650	+	45.8041i	0.281358	+	1.59566i
$825$	9.43115	−	24.8175i	0.328350	−	0.864033i
$826$	−41.3309	−	34.6808i	−1.43809	−	1.20670i
$827$	20.6736	+	9.20447i	0.718890	+	0.320071i	0.733375	−	0.679824i	$-0.237944\pi$
$827$	20.6736	+	9.20447i	0.718890	+	0.320071i	−0.0144845	+	0.999895i	$0.504611\pi$
$828$	−59.7233	−	35.5142i	−2.07553	−	1.23420i
$829$	−9.49949	−	10.5503i	−0.329931	−	0.366426i	0.555241	−	0.831690i	$-0.312626\pi$
$829$	−9.49949	−	10.5503i	−0.329931	−	0.366426i	−0.885172	+	0.465264i	$0.845959\pi$
$830$	−7.18373	+	25.0527i	−0.249351	+	0.869590i
$831$	−11.0637	−	4.10771i	−0.383797	−	0.142495i
$832$	−16.4409	+	6.64257i	−0.569987	+	0.230290i
$833$	0.0654259	−	1.87355i	0.00226687	−	0.0649147i
$834$	0.00274546	+	0.0964088i	9.50673e−5	+	0.00333836i
$835$	4.67770	+	0.824805i	0.161879	+	0.0285436i
$836$	−11.3091	−	0.481706i	−0.391134	−	0.0166601i
$837$	13.5638	−	20.8018i	0.468835	−	0.719015i
$838$	−25.9873	−	35.7684i	−0.897716	−	1.23560i
$839$	0.192329	+	1.36849i	0.00663994	+	0.0472456i	0.993306	−	0.115511i	$-0.0368505\pi$
$839$	0.192329	+	1.36849i	0.00663994	+	0.0472456i	−0.986666	+	0.162756i	$0.947962\pi$
$840$	1.94205	+	14.4948i	0.0670071	+	0.500119i
$841$	42.1781	+	62.5317i	1.45442	+	2.15626i
$842$	85.6430	−	5.98874i	2.95145	−	0.206386i
$843$	21.4378	+	40.9524i	0.738357	+	1.41048i
$844$	46.7769	−	36.5462i	1.61013	−	1.25797i
$845$	6.91823	−	0.727135i	0.237994	−	0.0250142i
$846$	61.8818	−	1.36363i	2.12754	−	0.0468825i
$847$	2.33918	+	18.7215i	0.0803751	+	0.643277i
$848$	47.9476	−	57.1417i	1.64653	−	1.96225i
$849$	−22.3736	−	25.1723i	−0.767859	−	0.863912i
$850$	−4.99469	+	2.65572i	−0.171316	+	0.0910905i
$851$	4.62492	−	32.9080i	0.158540	−	1.12807i
$852$	49.4005	−	84.3062i	1.69243	−	2.88828i
$853$	−25.9349	+	6.46631i	−0.887995	+	0.221402i	−0.659106	−	0.752050i	$-0.729065\pi$
$853$	−25.9349	+	6.46631i	−0.887995	+	0.221402i	−0.228890	+	0.973452i	$0.573510\pi$
$854$	−25.3515	+	5.38863i	−0.867511	+	0.184395i
$855$	−1.18433	+	0.413874i	−0.0405033	+	0.0141542i
$856$	−9.09627	−	86.5452i	−0.310904	−	2.95805i
$857$	15.8178	−	5.75720i	0.540325	−	0.196662i	−0.0574176	−	0.998350i	$-0.518287\pi$
$857$	15.8178	−	5.75720i	0.540325	−	0.196662i	0.597743	+	0.801688i	$0.296064\pi$
$858$	−14.4323	+	13.5492i	−0.492712	+	0.462561i
$859$	−14.7210	+	12.3524i	−0.502275	+	0.421459i	−0.858401	−	0.512979i	$-0.828542\pi$
$859$	−14.7210	+	12.3524i	−0.502275	+	0.421459i	0.356126	+	0.934438i	$0.384097\pi$
$860$	−17.3882	+	4.98599i	−0.592933	+	0.170021i
$861$	−20.3211	+	19.3726i	−0.692540	+	0.660216i
$862$	−22.2396	−	11.8250i	−0.757484	−	0.402761i
$863$	27.5578	−	37.9300i	0.938078	−	1.29115i	−0.0185466	−	0.999828i	$-0.505904\pi$
$863$	27.5578	−	37.9300i	0.938078	−	1.29115i	0.956624	−	0.291325i	$-0.0940961\pi$
$864$	−11.1613	+	69.6324i	−0.379717	+	2.36894i
$865$	−1.27578	−	0.414527i	−0.0433779	−	0.0140943i
$866$	−60.2298	+	8.46474i	−2.04669	+	0.287644i
$867$	−29.0635	+	0.827646i	−0.987047	+	0.0281083i
$868$	−14.0749	+	38.6704i	−0.477733	+	1.31256i
$869$	1.10513	−	3.74550i	0.0374890	−	0.127057i
$870$	−27.7814	+	7.77300i	−0.941877	+	0.263530i
$871$	−2.85480	−	1.92559i	−0.0967313	−	0.0652461i
$872$	13.5200	−	63.6068i	0.457846	−	2.15400i
$873$	21.6224	−	9.29525i	0.731808	−	0.314597i
$874$	−0.868653	+	8.26468i	−0.0293826	+	0.279557i
$875$	2.45589	+	9.85004i	0.0830243	+	0.332992i
$876$	−42.3058	−	133.113i	−1.42938	−	4.49748i
$877$	−0.876208	−	1.64791i	−0.0295875	−	0.0556459i	0.867715	−	0.497061i	$-0.165588\pi$
$877$	−0.876208	−	1.64791i	−0.0295875	−	0.0556459i	−0.897303	+	0.441415i	$0.854477\pi$
$878$	10.2926	−	10.6583i	0.347360	−	0.359702i
$879$	13.6589	−	30.1545i	0.460703	−	1.01709i
$880$	9.42233	−	20.7339i	0.317627	−	0.698939i
$881$	−44.4271	+	25.6500i	−1.49679	+	0.864171i	−0.999993	−	0.00369717i	$-0.998823\pi$
$881$	−44.4271	+	25.6500i	−1.49679	+	0.864171i	−0.496795	+	0.867868i	$0.665490\pi$
$882$	−27.1333	−	17.4445i	−0.913626	−	0.587385i
$883$	9.86183	+	2.09620i	0.331877	+	0.0705427i	0.370837	−	0.928698i	$-0.379071\pi$
$883$	9.86183	+	2.09620i	0.331877	+	0.0705427i	−0.0389595	+	0.999241i	$0.512404\pi$
$884$	3.01444	−	0.105266i	0.101386	−	0.00354049i
$885$	8.06832	+	9.74212i	0.271213	+	0.327478i
$886$	2.10951	+	30.1674i	0.0708704	+	1.01349i
$887$	32.1134	−	41.1033i	1.07826	−	1.38011i	0.158629	−	0.987338i	$-0.449292\pi$
$887$	32.1134	−	41.1033i	1.07826	−	1.38011i	0.919634	−	0.392776i	$-0.128485\pi$
$888$	−97.0270	+	23.5292i	−3.25601	+	0.789588i
$889$	10.7291	+	21.9978i	0.359841	+	0.737784i
$890$	21.2288			0.711591
$891$	6.24977	+	29.1880i	0.209375	+	0.977835i
$892$	135.752			4.54533
$893$	−2.32064	−	4.75801i	−0.0776571	−	0.159221i
$894$	−43.4196	+	10.5293i	−1.45217	+	0.352154i
$895$	0.778033	−	0.995836i	0.0260068	−	0.0332871i
$896$	−1.07451	−	15.3662i	−0.0358970	−	0.513350i
$897$	6.62903	+	8.00424i	0.221337	+	0.267254i
$898$	−35.6453	+	1.24476i	−1.18950	+	0.0415382i
$899$	−47.7708	−	10.1540i	−1.59325	−	0.338655i
$900$	−3.32453	+	69.5261i	−0.110818	+	2.31754i
$901$	−2.67336	+	1.54347i	−0.0890626	+	0.0514203i
$902$	81.3638	−	16.6439i	2.70912	−	0.554180i
$903$	−7.17988	+	15.8509i	−0.238931	+	0.527484i
$904$	30.7418	−	31.8341i	1.02246	−	1.05878i
$905$	0.280048	+	0.526694i	0.00930911	+	0.0175079i
$906$	−0.346179	−	1.08924i	−0.0115010	−	0.0361875i
$907$	3.78945	+	15.1986i	0.125826	+	0.504662i	0.999825	+	0.0187330i	$0.00596325\pi$
$907$	3.78945	+	15.1986i	0.125826	+	0.504662i	−0.873998	+	0.485929i	$0.838481\pi$
$908$	6.51282	−	61.9653i	0.216135	−	2.05639i
$909$	0.506408	−	4.28655i	0.0167965	−	0.142176i
$910$	0.755929	−	3.55637i	0.0250588	−	0.117892i
$911$	32.7721	+	22.1051i	1.08579	+	0.732374i	0.965510	−	0.260366i	$-0.0838431\pi$
$911$	32.7721	+	22.1051i	1.08579	+	0.732374i	0.120280	+	0.992740i	$0.461621\pi$
$912$	12.6580	−	3.54161i	0.419149	−	0.117274i
$913$	−1.44471	−	53.0143i	−0.0478128	−	1.75452i
$914$	2.24596	−	6.17073i	0.0742899	−	0.204110i
$915$	6.07395	−	0.172969i	0.200799	−	0.00571819i
$916$	94.8985	−	13.3371i	3.13554	−	0.440671i
$917$	−24.6855	−	8.02082i	−0.815188	−	0.264871i
$918$	3.09376	−	5.55692i	0.102109	−	0.183406i
$919$	−12.2576	+	16.8711i	−0.404340	+	0.556527i	−0.961827	−	0.273659i	$-0.911766\pi$
$919$	−12.2576	+	16.8711i	−0.404340	+	0.556527i	0.557486	+	0.830186i	$0.311766\pi$
$920$	−20.0529	−	10.6623i	−0.661125	−	0.351526i
$921$	0.969750	−	0.924488i	0.0319544	−	0.0304629i
$922$	−32.9994	+	9.46243i	−1.08678	+	0.311628i
$923$	−11.1958	+	9.39440i	−0.368514	+	0.309220i
$924$	−21.0551	−	44.7601i	−0.692661	−	1.47250i
$925$	−31.2816	+	11.3856i	−1.02853	+	0.374356i
$926$	2.91496	+	27.7340i	0.0957916	+	0.911396i
$927$	−13.2113	−	11.3786i	−0.433917	−	0.373723i
$928$	135.659	−	28.8352i	4.45323	−	0.946562i
$929$	−50.7865	+	12.6625i	−1.66625	+	0.415443i	−0.957134	−	0.289646i	$-0.906462\pi$
$929$	−50.7865	+	12.6625i	−1.66625	+	0.415443i	−0.709118	+	0.705089i	$0.750907\pi$
$930$	6.82092	−	11.6405i	0.223667	−	0.381707i
$931$	−0.383953	+	2.73197i	−0.0125836	+	0.0895367i
$932$	−24.7318	+	13.1501i	−0.810118	+	0.430747i
$933$	18.6690	+	21.0044i	0.611195	+	0.687652i
$934$	23.4260	−	27.9181i	0.766524	−	0.913507i
$935$	−0.659882	+	0.672932i	−0.0215804	+	0.0220072i
$936$	15.0125	−	27.3781i	0.490697	−	0.894881i
$937$	−39.6658	+	4.16905i	−1.29583	+	0.136197i	−0.727215	−	0.686409i	$-0.759186\pi$
$937$	−39.6658	+	4.16905i	−1.29583	+	0.136197i	−0.568611	+	0.822606i	$0.692519\pi$
$938$	9.48168	−	7.40790i	0.309588	−	0.241877i
$939$	−11.5430	−	22.0505i	−0.376693	−	0.719592i
$940$	23.9892	−	1.67749i	0.782441	−	0.0547136i
$941$	−23.5683	−	34.9415i	−0.768306	−	1.13906i	−0.986597	−	0.163176i	$-0.947826\pi$
$941$	−23.5683	−	34.9415i	−0.768306	−	1.13906i	0.218291	−	0.975884i	$-0.429952\pi$
$942$	−2.66467	−	19.8882i	−0.0868195	−	0.647992i
$943$	−6.06809	−	43.1767i	−0.197604	−	1.40603i
$944$	−77.8980	−	107.217i	−2.53536	−	3.48963i
$945$	−4.00260	−	3.74641i	−0.130205	−	0.121871i
$946$	42.8925	−	28.4557i	1.39456	−	0.925173i
$947$	32.7602	+	5.77651i	1.06456	+	0.187711i	0.678381	−	0.734711i	$-0.262682\pi$
$947$	32.7602	+	5.77651i	1.06456	+	0.187711i	0.386183	+	0.922422i	$0.373793\pi$
$948$	0.291442	+	10.2342i	0.00946559	+	0.332392i
$949$	−0.729093	+	20.8785i	−0.0236674	+	0.677744i
$950$	7.71849	−	3.11847i	0.250421	−	0.101177i
$951$	35.5200	+	13.1878i	1.15182	+	0.427643i
$952$	−1.74776	+	6.09515i	−0.0566451	+	0.197545i
$953$	16.3034	+	18.1067i	0.528119	+	0.586535i	0.946890	−	0.321556i	$-0.104206\pi$
$953$	16.3034	+	18.1067i	0.528119	+	0.586535i	−0.418772	+	0.908091i	$0.637539\pi$
$954$	−0.683799	+	53.1113i	−0.0221388	+	1.71954i
$955$	−4.50389	−	2.00526i	−0.145743	−	0.0648887i
$956$	−24.2642	−	20.3601i	−0.784760	−	0.658492i
$957$	49.1253	−	32.1371i	1.58799	−	1.03884i
$958$	2.39835	+	13.6017i	0.0774872	+	0.439452i
$959$	25.4163	+	24.5442i	0.820736	+	0.792575i
$960$	−1.61139	+	14.4368i	−0.0520075	+	0.465946i
$961$	−6.91969	+	4.32391i	−0.223216	+	0.139481i
$962$	24.6855	+	2.59455i	0.795891	+	0.0836515i
$963$	23.1732	+	22.9619i	0.746745	+	0.739938i
$964$	15.1603	−	13.6504i	0.488279	−	0.439648i
$965$	3.40362	+	4.35644i	0.109566	+	0.140239i
$966$	−33.7576	+	13.3869i	−1.08613	+	0.430715i
$967$	−27.4619	−	32.7278i	−0.883115	−	1.05246i	−0.998252	−	0.0591061i	$-0.981175\pi$
$967$	−27.4619	−	32.7278i	−0.883115	−	1.05246i	0.115136	−	0.993350i	$-0.463269\pi$
$968$	−10.5419	+	87.3946i	−0.338829	+	2.80897i
$969$	−0.542371	−	0.0414362i	−0.0174235	−	0.00133112i
$970$	11.4927	−	5.60534i	0.369007	−	0.179977i
$971$	30.4399	−	9.89052i	0.976863	−	0.317402i	0.223280	−	0.974754i	$-0.428324\pi$
$971$	30.4399	−	9.89052i	0.976863	−	0.317402i	0.753583	+	0.657352i	$0.228324\pi$
$972$	−39.3137	−	67.6674i	−1.26099	−	2.17043i
$973$	0.0291624	+	0.0211877i	0.000934902	+	0.000679246i
$974$	37.3361	−	36.0550i	1.19633	−	1.15528i
$975$	3.96207	−	9.62756i	0.126888	−	0.308329i
$976$	−63.6241	−	2.22180i	−2.03656	−	0.0711181i
$977$	32.9925	+	8.22596i	1.05552	+	0.263172i	0.730768	−	0.682626i	$-0.239162\pi$
$977$	32.9925	+	8.22596i	1.05552	+	0.263172i	0.324756	+	0.945798i	$0.394718\pi$
$978$	−3.61478	−	0.926020i	−0.115588	−	0.0296109i
$979$	−41.1852	+	13.0339i	−1.31628	+	0.416564i
$980$	−10.8533	−	6.26618i	−0.346697	−	0.200166i
$981$	11.1666	+	21.6697i	0.356521	+	0.691861i
$982$	5.73196	−	6.36599i	0.182914	−	0.203147i
$983$	18.8007	+	30.0874i	0.599650	+	0.959640i	0.999080	+	0.0428768i	$0.0136523\pi$
$983$	18.8007	+	30.0874i	0.599650	+	0.959640i	−0.399431	+	0.916763i	$0.630792\pi$
$984$	−113.863	+	64.7649i	−3.62980	+	2.06463i
$985$	10.2014	+	4.97556i	0.325044	+	0.158535i
$986$	−12.3863	−	1.74077i	−0.394459	−	0.0554375i
$987$	13.7177	−	18.6274i	0.436639	−	0.592918i
$988$	−4.42797	−	0.309634i	−0.140872	−	0.00985076i
$989$	−13.5119	−	23.4032i	−0.429652	−	0.744179i
$990$	4.14896	+	15.6773i	0.131863	+	0.498258i
$991$	24.1598	−	41.8460i	0.767461	−	1.32928i	−0.171475	−	0.985189i	$-0.554853\pi$
$991$	24.1598	−	41.8460i	0.767461	−	1.32928i	0.938936	−	0.344093i	$-0.111813\pi$
$992$	−36.2704	+	53.7731i	−1.15159	+	1.70730i
$993$	−12.6391	+	8.40731i	−0.401089	+	0.266798i
$994$	−19.1306	−	47.3499i	−0.606785	−	1.50185i
$995$	0.575819	−	0.388395i	0.0182547	−	0.0123129i
$996$	46.7135	+	130.961i	1.48017	+	4.14966i
$997$	3.77724	−	7.10395i	0.119626	−	0.224984i	−0.815939	−	0.578138i	$-0.803780\pi$
$997$	3.77724	−	7.10395i	0.119626	−	0.224984i	0.935565	+	0.353154i	$0.114891\pi$
$998$	−21.0196	−	64.6918i	−0.665365	−	2.04778i
$999$	22.5801	−	29.8492i	0.714401	−	0.944387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.x.a.272.34	yes	816
3.2	odd	2		891.2.bb.a.8.1		816
11.7	odd	10	inner	297.2.x.a.29.34	✓	816
27.13	even	9		891.2.bb.a.800.1		816
27.14	odd	18	inner	297.2.x.a.41.34	yes	816
33.29	even	10		891.2.bb.a.656.1		816
297.40	odd	90		891.2.bb.a.557.1		816
297.95	even	90	inner	297.2.x.a.95.34	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.29.34	✓	816	11.7	odd	10	inner
297.2.x.a.41.34	yes	816	27.14	odd	18	inner
297.2.x.a.95.34	yes	816	297.95	even	90	inner
297.2.x.a.272.34	yes	816	1.1	even	1	trivial
891.2.bb.a.8.1		816	3.2	odd	2
891.2.bb.a.557.1		816	297.40	odd	90
891.2.bb.a.656.1		816	33.29	even	10
891.2.bb.a.800.1		816	27.13	even	9

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.x (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16150 + 2.38143i) q^{2} +(-1.68326 + 0.408194i) q^{3} +(-3.09081 + 3.95605i) q^{4} +(-0.0429102 - 0.613644i) q^{5} +(-2.92720 - 3.53446i) q^{6} +(-1.71414 + 0.0598591i) q^{7} +(-7.82768 - 1.66383i) q^{8} +(2.66675 - 1.37420i) q^{9} +O(q^{10})\)	\(q+(1.16150 + 2.38143i) q^{2} +(-1.68326 + 0.408194i) q^{3} +(-3.09081 + 3.95605i) q^{4} +(-0.0429102 - 0.613644i) q^{5} +(-2.92720 - 3.53446i) q^{6} +(-1.71414 + 0.0598591i) q^{7} +(-7.82768 - 1.66383i) q^{8} +(2.66675 - 1.37420i) q^{9} +(1.41151 - 0.814937i) q^{10} +(-2.23807 + 2.44766i) q^{11} +(3.58781 - 7.92073i) q^{12} +(-0.903460 + 0.935560i) q^{13} +(-2.13353 - 4.01258i) q^{14} +(0.322715 + 1.01541i) q^{15} +(-2.70054 - 10.8313i) q^{16} +(-0.0482878 + 0.459428i) q^{17} +(6.37000 + 4.75456i) q^{18} +(0.141343 - 0.664968i) q^{19} +(2.56024 + 1.72690i) q^{20} +(2.86092 - 0.800461i) q^{21} +(-8.42846 - 2.48687i) q^{22} +(-1.57794 + 4.33534i) q^{23} +(13.8552 - 0.394558i) q^{24} +(4.57662 - 0.643202i) q^{25} +(-3.27734 - 1.06487i) q^{26} +(-3.92791 + 3.40169i) q^{27} +(5.06127 - 6.96624i) q^{28} +(9.02279 + 4.79750i) q^{29} +(-2.04329 + 1.94792i) q^{30} +(-4.59403 + 1.31732i) q^{31} +(10.3966 - 8.72380i) q^{32} +(2.76815 - 5.03362i) q^{33} +(-1.15018 + 0.418632i) q^{34} +(0.110286 + 1.04930i) q^{35} +(-2.80603 + 14.7972i) q^{36} +(-7.04556 + 1.49758i) q^{37} +(1.74775 - 0.435762i) q^{38} +(1.13887 - 1.94358i) q^{39} +(-0.685109 + 4.87481i) q^{40} +(-8.34437 + 4.43678i) q^{41} +(5.22920 + 5.88334i) q^{42} +(-3.76508 + 4.48705i) q^{43} +(-2.76560 - 16.4192i) q^{44} +(-0.957699 - 1.57747i) q^{45} +(-12.1571 + 1.27776i) q^{46} +(6.13622 - 4.79414i) q^{47} +(8.96698 + 17.1295i) q^{48} +(-4.04826 + 0.283082i) q^{49} +(6.84750 + 10.1518i) q^{50} +(-0.106255 - 0.793049i) q^{51} +(-0.908705 - 6.46577i) q^{52} +(3.92774 + 5.40607i) q^{53} +(-12.6632 - 5.40299i) q^{54} +(1.59803 + 1.26835i) q^{55} +(13.5173 + 2.38347i) q^{56} +(0.0335180 + 1.17701i) q^{57} +(-0.944938 + 27.0595i) q^{58} +(11.0077 - 4.44742i) q^{59} +(-5.01447 - 1.86176i) q^{60} +(1.57199 - 5.48217i) q^{61} +(-8.47308 - 9.41031i) q^{62} +(-4.48893 + 2.51520i) q^{63} +(12.4553 + 5.54545i) q^{64} +(0.612868 + 0.514258i) q^{65} +(15.2024 + 0.745604i) q^{66} +(0.459764 + 2.60745i) q^{67} +(-1.66827 - 1.61103i) q^{68} +(0.886420 - 7.94163i) q^{69} +(-2.37075 + 1.48141i) q^{70} +(11.1758 + 1.17462i) q^{71} +(-23.1609 + 6.31977i) q^{72} +(11.9371 - 10.7482i) q^{73} +(-11.7498 - 15.0391i) q^{74} +(-7.44111 + 2.95083i) q^{75} +(2.19378 + 2.61445i) q^{76} +(3.68986 - 4.32959i) q^{77} +(5.95131 + 0.454670i) q^{78} +(-1.05828 + 0.516157i) q^{79} +(-6.53066 + 2.12194i) q^{80} +(5.22316 - 7.32930i) q^{81} +(-20.2579 - 14.7182i) q^{82} +(-11.5025 + 11.1078i) q^{83} +(-5.67588 + 13.7920i) q^{84} +(0.283997 + 0.00991741i) q^{85} +(-15.0588 - 3.75457i) q^{86} +(-17.1461 - 4.39241i) q^{87} +(21.5914 - 15.4357i) q^{88} +(11.2798 + 6.51241i) q^{89} +(2.64427 - 4.11293i) q^{90} +(1.49265 - 1.65776i) q^{91} +(-12.2738 - 19.6421i) q^{92} +(7.19525 - 4.09265i) q^{93} +(18.5442 + 9.04459i) q^{94} +(-0.414119 - 0.0582006i) q^{95} +(-13.9393 + 18.9283i) q^{96} +(7.82613 + 0.547257i) q^{97} +(-5.37620 - 9.31185i) q^{98} +(-2.60483 + 9.60286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 30 q^{2} - 18 q^{3} - 18 q^{4} - 21 q^{5} - 30 q^{6} - 30 q^{7} - 45 q^{8} - 36 q^{9}+O(q^{10}) \) 816 * q - 30 * q^2 - 18 * q^3 - 18 * q^4 - 21 * q^5 - 30 * q^6 - 30 * q^7 - 45 * q^8 - 36 * q^9	\( 816 q - 30 q^{2} - 18 q^{3} - 18 q^{4} - 21 q^{5} - 30 q^{6} - 30 q^{7} - 45 q^{8} - 36 q^{9} - 33 q^{11} - 30 q^{12} - 30 q^{13} - 18 q^{14} - 21 q^{15} - 30 q^{16} - 45 q^{17} - 15 q^{19} - 60 q^{20} - 15 q^{22} - 84 q^{23} - 30 q^{24} - 27 q^{25} + 36 q^{27} - 60 q^{28} + 60 q^{29} - 75 q^{30} - 9 q^{31} - 63 q^{33} - 42 q^{34} - 45 q^{35} + 36 q^{36} - 9 q^{37} - 18 q^{38} - 150 q^{39} - 90 q^{40} - 30 q^{41} - 66 q^{42} - 108 q^{44} + 24 q^{45} - 15 q^{46} - 6 q^{47} + 174 q^{48} - 18 q^{49} - 105 q^{50} - 30 q^{51} - 30 q^{52} - 48 q^{55} + 54 q^{56} - 75 q^{57} - 18 q^{58} + 81 q^{59} - 72 q^{60} - 30 q^{61} - 45 q^{62} - 30 q^{63} + 51 q^{64} - 75 q^{66} + 6 q^{67} - 225 q^{68} + 9 q^{69} - 93 q^{70} - 27 q^{71} - 30 q^{72} - 15 q^{73} - 30 q^{74} + 42 q^{75} - 141 q^{77} + 30 q^{78} - 30 q^{79} + 48 q^{81} - 36 q^{82} + 15 q^{83} + 90 q^{84} - 30 q^{85} + 93 q^{86} - 108 q^{88} + 54 q^{89} - 15 q^{90} - 9 q^{91} + 276 q^{92} + 87 q^{93} - 30 q^{94} + 90 q^{95} + 90 q^{96} - 81 q^{97} + 3 q^{99}+O(q^{100}) \) 816 * q - 30 * q^2 - 18 * q^3 - 18 * q^4 - 21 * q^5 - 30 * q^6 - 30 * q^7 - 45 * q^8 - 36 * q^9 - 33 * q^11 - 30 * q^12 - 30 * q^13 - 18 * q^14 - 21 * q^15 - 30 * q^16 - 45 * q^17 - 15 * q^19 - 60 * q^20 - 15 * q^22 - 84 * q^23 - 30 * q^24 - 27 * q^25 + 36 * q^27 - 60 * q^28 + 60 * q^29 - 75 * q^30 - 9 * q^31 - 63 * q^33 - 42 * q^34 - 45 * q^35 + 36 * q^36 - 9 * q^37 - 18 * q^38 - 150 * q^39 - 90 * q^40 - 30 * q^41 - 66 * q^42 - 108 * q^44 + 24 * q^45 - 15 * q^46 - 6 * q^47 + 174 * q^48 - 18 * q^49 - 105 * q^50 - 30 * q^51 - 30 * q^52 - 48 * q^55 + 54 * q^56 - 75 * q^57 - 18 * q^58 + 81 * q^59 - 72 * q^60 - 30 * q^61 - 45 * q^62 - 30 * q^63 + 51 * q^64 - 75 * q^66 + 6 * q^67 - 225 * q^68 + 9 * q^69 - 93 * q^70 - 27 * q^71 - 30 * q^72 - 15 * q^73 - 30 * q^74 + 42 * q^75 - 141 * q^77 + 30 * q^78 - 30 * q^79 + 48 * q^81 - 36 * q^82 + 15 * q^83 + 90 * q^84 - 30 * q^85 + 93 * q^86 - 108 * q^88 + 54 * q^89 - 15 * q^90 - 9 * q^91 + 276 * q^92 + 87 * q^93 - 30 * q^94 + 90 * q^95 + 90 * q^96 - 81 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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