LMFDB - Embedded newform 425.2.q.a.84.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

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([7, 5]))

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

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

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (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:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.9
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14277 + 1.57289i) q^{2} +(-0.782761 - 2.40909i) q^{3} +(-0.550027 - 1.69281i) q^{4} +(1.07788 + 1.95913i) q^{5} +(4.68376 + 1.52185i) q^{6} +3.64131 q^{7} +(-0.406932 - 0.132220i) q^{8} +(-2.76396 + 2.00813i) q^{9} +(-4.31327 - 0.543447i) q^{10} +(-1.43874 + 1.98025i) q^{11} +(-3.64759 + 2.65013i) q^{12} +(-1.60261 - 2.20580i) q^{13} +(-4.16119 + 5.72739i) q^{14} +(3.87599 - 4.13024i) q^{15} +(3.55298 - 2.58139i) q^{16} +(3.51182 - 2.16036i) q^{17} -6.64225i q^{18} +(-0.374938 + 1.15394i) q^{19} +(2.72356 - 2.90222i) q^{20} +(-2.85028 - 8.77225i) q^{21} +(-1.47057 - 4.52595i) q^{22} +(7.60100 + 5.52245i) q^{23} +1.08383i q^{24} +(-2.67635 + 4.22341i) q^{25} +5.30091 q^{26} +(0.853404 + 0.620035i) q^{27} +(-2.00282 - 6.16404i) q^{28} +(-3.09952 + 1.00709i) q^{29} +(2.06705 + 10.8164i) q^{30} +(7.54089 + 2.45019i) q^{31} +7.68265i q^{32} +(5.89679 + 1.91598i) q^{33} +(-0.615200 + 7.99251i) q^{34} +(3.92490 + 7.13379i) q^{35} +(4.91963 + 3.57432i) q^{36} +(8.00851 - 5.81853i) q^{37} +(-1.38656 - 1.90843i) q^{38} +(-4.05952 + 5.58744i) q^{39} +(-0.179588 - 0.939748i) q^{40} +(2.97251 + 4.09130i) q^{41} +(17.0550 + 5.54152i) q^{42} -0.892274i q^{43} +(4.14352 + 1.34631i) q^{44} +(-6.91340 - 3.25041i) q^{45} +(-17.3725 + 5.64465i) q^{46} +(2.81477 - 0.914573i) q^{47} +(-8.99993 - 6.53883i) q^{48} +6.25914 q^{49} +(-3.58451 - 9.03601i) q^{50} +(-7.95341 - 6.76924i) q^{51} +(-2.85252 + 3.92616i) q^{52} +(11.5809 - 3.76285i) q^{53} +(-1.95050 + 0.633754i) q^{54} +(-5.43034 - 0.684192i) q^{55} +(-1.48176 - 0.481455i) q^{56} +3.07344 q^{57} +(1.95800 - 6.02609i) q^{58} +(-8.37777 + 6.08680i) q^{59} +(-9.12360 - 4.28957i) q^{60} +(1.74201 - 2.39767i) q^{61} +(-12.4714 + 9.06101i) q^{62} +(-10.0644 + 7.31223i) q^{63} +(-4.97803 - 3.61675i) q^{64} +(2.59402 - 5.51730i) q^{65} +(-9.75233 + 7.08548i) q^{66} +(-11.2277 - 3.64809i) q^{67} +(-5.58866 - 4.75658i) q^{68} +(7.35432 - 22.6343i) q^{69} +(-15.7059 - 1.97886i) q^{70} +(-3.57649 + 1.16207i) q^{71} +(1.39026 - 0.451722i) q^{72} +(2.32787 + 1.69130i) q^{73} +19.2458i q^{74} +(12.2695 + 3.14165i) q^{75} +2.15963 q^{76} +(-5.23888 + 7.21070i) q^{77} +(-4.14934 - 12.7704i) q^{78} +(7.12162 - 2.31396i) q^{79} +(8.88695 + 4.17830i) q^{80} +(-2.34150 + 7.20641i) q^{81} -9.83208 q^{82} +(-1.51987 - 0.493836i) q^{83} +(-13.2820 + 9.64994i) q^{84} +(8.01773 + 4.55148i) q^{85} +(1.40345 + 1.01967i) q^{86} +(4.85237 + 6.67871i) q^{87} +(0.847296 - 0.615597i) q^{88} +(-6.62169 - 4.81094i) q^{89} +(13.0130 - 7.15955i) q^{90} +(-5.83559 - 8.03200i) q^{91} +(5.16770 - 15.9045i) q^{92} -20.0846i q^{93} +(-1.77811 + 5.47248i) q^{94} +(-2.66485 + 0.509259i) q^{95} +(18.5082 - 6.01368i) q^{96} +(0.0876674 + 0.269813i) q^{97} +(-7.15278 + 9.84496i) q^{98} -8.36249i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−1.14277	+	1.57289i	−0.808063	+	1.11220i	0.183556	+	0.983009i	$0.441239\pi$
$2$	−1.14277	+	1.57289i	−0.808063	+	1.11220i	−0.991619	+	0.129194i	$0.958761\pi$
$3$	−0.782761	−	2.40909i	−0.451927	−	1.39089i	−0.874705	−	0.484656i	$-0.838945\pi$
$3$	−0.782761	−	2.40909i	−0.451927	−	1.39089i	0.422777	−	0.906234i	$-0.361055\pi$
$4$	−0.550027	−	1.69281i	−0.275013	−	0.846404i
$5$	1.07788	+	1.95913i	0.482043	+	0.876148i
$5$	1.07788	+	1.95913i	0.482043	+	0.876148i
$6$	4.68376	+	1.52185i	1.91214	+	0.621291i
$7$	3.64131			1.37629			0.688143	−	0.725575i	$-0.258426\pi$
$7$	3.64131			1.37629			0.688143	+	0.725575i	$0.258426\pi$
$8$	−0.406932	−	0.132220i	−0.143872	−	0.0467469i
$9$	−2.76396	+	2.00813i	−0.921319	+	0.669377i
$10$	−4.31327	−	0.543447i	−1.36398	−	0.171853i
$11$	−1.43874	+	1.98025i	−0.433795	+	0.597068i	−0.968819	−	0.247769i	$-0.920303\pi$
$11$	−1.43874	+	1.98025i	−0.433795	+	0.597068i	0.535024	+	0.844837i	$0.320303\pi$
$12$	−3.64759	+	2.65013i	−1.05297	+	0.765026i
$13$	−1.60261	−	2.20580i	−0.444483	−	0.611779i	0.526718	−	0.850040i	$-0.323423\pi$
$13$	−1.60261	−	2.20580i	−0.444483	−	0.611779i	−0.971201	+	0.238261i	$0.923423\pi$
$14$	−4.16119	+	5.72739i	−1.11213	+	1.53071i
$15$	3.87599	−	4.13024i	1.00078	−	1.06642i
$16$	3.55298	−	2.58139i	0.888244	−	0.645347i
$17$	3.51182	−	2.16036i	0.851741	−	0.523964i
$17$	3.51182	−	2.16036i	0.851741	−	0.523964i
$18$		−	6.64225i		−	1.56559i
$19$	−0.374938	+	1.15394i	−0.0860167	+	0.264732i	−0.984809	−	0.173643i	$-0.944446\pi$
$19$	−0.374938	+	1.15394i	−0.0860167	+	0.264732i	0.898792	+	0.438376i	$0.144446\pi$
$20$	2.72356	−	2.90222i	0.609007	−	0.648955i
$21$	−2.85028	−	8.77225i	−0.621981	−	1.91426i
$22$	−1.47057	−	4.52595i	−0.313527	−	0.964937i
$23$	7.60100	+	5.52245i	1.58492	+	1.15151i	0.910769	+	0.412917i	$0.135490\pi$
$23$	7.60100	+	5.52245i	1.58492	+	1.15151i	0.674150	+	0.738594i	$0.264510\pi$
$24$			1.08383i			0.221236i
$25$	−2.67635	+	4.22341i	−0.535270	+	0.844681i
$26$	5.30091			1.03959
$27$	0.853404	+	0.620035i	0.164238	+	0.119326i
$28$	−2.00282	−	6.16404i	−0.378497	−	1.16489i
$29$	−3.09952	+	1.00709i	−0.575566	+	0.187013i	−0.582313	−	0.812964i	$-0.697852\pi$
$29$	−3.09952	+	1.00709i	−0.575566	+	0.187013i	0.00674718	+	0.999977i	$0.497852\pi$
$30$	2.06705	+	10.8164i	0.377389	+	1.97480i
$31$	7.54089	+	2.45019i	1.35438	+	0.440066i	0.894165	−	0.447739i	$-0.147770\pi$
$31$	7.54089	+	2.45019i	1.35438	+	0.440066i	0.460220	+	0.887805i	$0.347770\pi$
$32$			7.68265i			1.35811i
$33$	5.89679	+	1.91598i	1.02650	+	0.333530i
$34$	−0.615200	+	7.99251i	−0.105506	+	1.37070i
$35$	3.92490	+	7.13379i	0.663429	+	1.20583i
$36$	4.91963	+	3.57432i	0.819938	+	0.595720i
$37$	8.00851	−	5.81853i	1.31659	−	0.956560i	0.316624	−	0.948551i	$-0.397451\pi$
$37$	8.00851	−	5.81853i	1.31659	−	0.956560i	0.999968	−	0.00800840i	$-0.00254918\pi$
$38$	−1.38656	−	1.90843i	−0.224929	−	0.309588i
$39$	−4.05952	+	5.58744i	−0.650043	+	0.894707i
$40$	−0.179588	−	0.939748i	−0.0283953	−	0.148587i
$41$	2.97251	+	4.09130i	0.464227	+	0.638954i	0.975379	−	0.220537i	$-0.0707808\pi$
$41$	2.97251	+	4.09130i	0.464227	+	0.638954i	−0.511151	+	0.859491i	$0.670781\pi$
$42$	17.0550	+	5.54152i	2.63165	+	0.855074i
$43$		−	0.892274i		−	0.136070i	−0.997683	−	0.0680352i	$-0.978327\pi$
$43$		−	0.892274i		−	0.136070i	0.997683	−	0.0680352i	$-0.0216730\pi$
$44$	4.14352	+	1.34631i	0.624660	+	0.202964i
$45$	−6.91340	−	3.25041i	−1.03059	−	0.484543i
$46$	−17.3725	+	5.64465i	−2.56143	+	0.832259i
$47$	2.81477	−	0.914573i	0.410576	−	0.133404i	−0.0964443	−	0.995338i	$-0.530747\pi$
$47$	2.81477	−	0.914573i	0.410576	−	0.133404i	0.507020	+	0.861934i	$0.330747\pi$
$48$	−8.99993	−	6.53883i	−1.29903	−	0.943799i
$49$	6.25914			0.894163
$50$	−3.58451	−	9.03601i	−0.506926	−	1.27788i
$51$	−7.95341	−	6.76924i	−1.11370	−	0.947884i
$52$	−2.85252	+	3.92616i	−0.395573	+	0.544460i
$53$	11.5809	−	3.76285i	1.59075	−	0.516868i	0.625956	−	0.779858i	$-0.284709\pi$
$53$	11.5809	−	3.76285i	1.59075	−	0.516868i	0.964798	+	0.262990i	$0.0847088\pi$
$54$	−1.95050	+	0.633754i	−0.265429	+	0.0862431i
$55$	−5.43034	−	0.684192i	−0.732227	−	0.0922564i
$56$	−1.48176	−	0.481455i	−0.198009	−	0.0643371i
$57$	3.07344			0.407087
$58$	1.95800	−	6.02609i	0.257097	−	0.791265i
$59$	−8.37777	+	6.08680i	−1.09069	+	0.792434i	−0.979516	−	0.201366i	$-0.935462\pi$
$59$	−8.37777	+	6.08680i	−1.09069	+	0.792434i	−0.111176	+	0.993801i	$0.535462\pi$
$60$	−9.12360	−	4.28957i	−1.17785	−	0.553780i
$61$	1.74201	−	2.39767i	0.223042	−	0.306991i	−0.682801	−	0.730604i	$-0.739238\pi$
$61$	1.74201	−	2.39767i	0.223042	−	0.306991i	0.905843	+	0.423613i	$0.139238\pi$
$62$	−12.4714	+	9.06101i	−1.58387	+	1.15075i
$63$	−10.0644	+	7.31223i	−1.26800	+	0.921255i
$64$	−4.97803	−	3.61675i	−0.622253	−	0.452094i
$65$	2.59402	−	5.51730i	0.321749	−	0.684337i
$66$	−9.75233	+	7.08548i	−1.20043	+	0.872163i
$67$	−11.2277	−	3.64809i	−1.37168	−	0.445685i	−0.471754	−	0.881730i	$-0.656379\pi$
$67$	−11.2277	−	3.64809i	−1.37168	−	0.445685i	−0.899925	+	0.436045i	$0.856379\pi$
$68$	−5.58866	−	4.75658i	−0.677725	−	0.576820i
$69$	7.35432	−	22.6343i	0.885357	−	2.72485i
$70$	−15.7059	−	1.97886i	−1.87722	−	0.236519i
$71$	−3.57649	+	1.16207i	−0.424451	+	0.137912i	−0.513450	−	0.858119i	$-0.671633\pi$
$71$	−3.57649	+	1.16207i	−0.424451	+	0.137912i	0.0889996	+	0.996032i	$0.471633\pi$
$72$	1.39026	−	0.451722i	0.163843	−	0.0532359i
$73$	2.32787	+	1.69130i	0.272457	+	0.197951i	0.715620	−	0.698489i	$-0.246144\pi$
$73$	2.32787	+	1.69130i	0.272457	+	0.197951i	−0.443164	+	0.896441i	$0.646144\pi$
$74$			19.2458i			2.23728i
$75$	12.2695	+	3.14165i	1.41676	+	0.362766i
$76$	2.15963			0.247726
$77$	−5.23888	+	7.21070i	−0.597026	+	0.821736i
$78$	−4.14934	−	12.7704i	−0.469821	−	1.44596i
$79$	7.12162	−	2.31396i	0.801245	−	0.260340i	0.120360	−	0.992730i	$-0.461595\pi$
$79$	7.12162	−	2.31396i	0.801245	−	0.260340i	0.680885	+	0.732390i	$0.261595\pi$
$80$	8.88695	+	4.17830i	0.993591	+	0.467148i
$81$	−2.34150	+	7.20641i	−0.260167	+	0.800712i
$82$	−9.83208			−1.08577
$83$	−1.51987	−	0.493836i	−0.166828	−	0.0542056i	0.224412	−	0.974494i	$-0.427954\pi$
$83$	−1.51987	−	0.493836i	−0.166828	−	0.0542056i	−0.391240	+	0.920289i	$0.627954\pi$
$84$	−13.2820	+	9.64994i	−1.44919	+	1.05290i
$85$	8.01773	+	4.55148i	0.869645	+	0.493678i
$86$	1.40345	+	1.01967i	0.151338	+	0.109953i
$87$	4.85237	+	6.67871i	0.520228	+	0.716033i
$88$	0.847296	−	0.615597i	0.0903221	−	0.0656228i
$89$	−6.62169	−	4.81094i	−0.701898	−	0.509958i	0.178652	−	0.983912i	$-0.442826\pi$
$89$	−6.62169	−	4.81094i	−0.701898	−	0.509958i	−0.880550	+	0.473954i	$0.842826\pi$
$90$	13.0130	−	7.15955i	1.37169	−	0.754683i
$91$	−5.83559	−	8.03200i	−0.611736	−	0.841983i
$92$	5.16770	−	15.9045i	0.538770	−	1.65816i
$93$		−	20.0846i		−	2.08268i
$94$	−1.77811	+	5.47248i	−0.183399	+	0.564443i
$95$	−2.66485	+	0.509259i	−0.273408	+	0.0522489i
$96$	18.5082	−	6.01368i	1.88898	−	0.613768i
$97$	0.0876674	+	0.269813i	0.00890128	+	0.0273953i	0.955409	−	0.295287i	$-0.0954154\pi$
$97$	0.0876674	+	0.269813i	0.00890128	+	0.0273953i	−0.946507	+	0.322683i	$0.895415\pi$
$98$	−7.15278	+	9.84496i	−0.722540	+	0.994491i
$99$		−	8.36249i		−	0.840462i
$100$	8.62148	+	2.20756i	0.862148	+	0.220756i
$101$	9.06965			0.902464			0.451232	−	0.892407i	$-0.350985\pi$
$101$	9.06965			0.902464			0.451232	+	0.892407i	$0.350985\pi$
$102$	19.7362	−	4.77416i	1.95418	−	0.472712i
$103$	−6.81149	+	2.21319i	−0.671156	+	0.218072i	−0.624719	−	0.780849i	$-0.714787\pi$
$103$	−6.81149	+	2.21319i	−0.671156	+	0.218072i	−0.0464370	+	0.998921i	$0.514787\pi$
$104$	0.360501	+	1.10951i	0.0353500	+	0.108796i
$105$	14.1137	−	15.0395i	1.37735	−	1.46770i
$106$	−7.31575	+	22.5156i	−0.710568	+	2.18690i
$107$	−9.00721			−0.870760			−0.435380	−	0.900247i	$-0.643386\pi$
$107$	−9.00721			−0.870760			−0.435380	+	0.900247i	$0.643386\pi$
$108$	0.580204	−	1.78568i	0.0558302	−	0.171828i
$109$	−9.15874	−	12.6059i	−0.877248	−	1.20743i	−0.977175	−	0.212434i	$-0.931861\pi$
$109$	−9.15874	−	12.6059i	−0.877248	−	1.20743i	0.0999270	−	0.994995i	$-0.468139\pi$
$110$	7.28181	−	7.75947i	0.694294	−	0.739837i
$111$	−20.2861	−	14.7387i	−1.92547	−	1.39894i
$112$	12.9375	−	9.39964i	1.22248	−	0.888182i
$113$	−8.68084	+	6.30700i	−0.816625	+	0.593313i	−0.915744	−	0.401763i	$-0.868398\pi$
$113$	−8.68084	+	6.30700i	−0.816625	+	0.593313i	0.0991186	+	0.995076i	$0.468398\pi$
$114$	−3.51224	+	4.83419i	−0.328952	+	0.452763i
$115$	−2.62621	+	20.8439i	−0.244895	+	1.94370i
$116$	3.40964	+	4.69296i	0.316577	+	0.435730i
$117$	8.85908	+	2.87849i	0.819022	+	0.266116i
$118$		−	20.1332i		−	1.85341i
$119$	12.7876	−	7.86653i	1.17224	−	0.721124i
$120$	−2.12336	+	1.16824i	−0.193836	+	0.106645i
$121$	1.54776	+	4.76351i	0.140705	+	0.433046i
$122$	1.78056	+	5.48000i	0.161204	+	0.496136i
$123$	7.52956	−	10.3636i	0.678918	−	0.934450i
$124$		−	14.1130i		−	1.26738i
$125$	−11.1590	−	0.690976i	−0.998088	−	0.0618028i
$126$		−	24.1865i		−	2.15470i
$127$	−2.95917	+	4.07295i	−0.262584	+	0.361416i	−0.919869	−	0.392227i	$-0.871705\pi$
$127$	−2.95917	+	4.07295i	−0.262584	+	0.361416i	0.657285	+	0.753642i	$0.271705\pi$
$128$	−3.23574	+	1.05136i	−0.286002	+	0.0929277i
$129$	−2.14957	+	0.698437i	−0.189259	+	0.0614940i
$130$	5.71374	+	10.3851i	0.501128	+	0.910837i
$131$	10.6495	+	3.46022i	0.930449	+	0.302321i	0.734746	−	0.678342i	$-0.237301\pi$
$131$	10.6495	+	3.46022i	0.930449	+	0.302321i	0.195703	+	0.980663i	$0.437301\pi$
$132$		−	11.0360i		−	0.960558i
$133$	−1.36527	+	4.20186i	−0.118384	+	0.364347i
$134$	18.5687	−	13.4910i	1.60410	−	1.16544i
$135$	−0.294858	+	2.34025i	−0.0253773	+	0.201417i
$136$	−1.71471	+	0.414785i	−0.147035	+	0.0355675i
$137$	−10.8041	−	14.8706i	−0.923058	−	1.27048i	−0.962507	−	0.271259i	$-0.912560\pi$
$137$	−10.8041	−	14.8706i	−0.923058	−	1.27048i	0.0394486	−	0.999222i	$-0.487440\pi$
$138$	27.1970	+	37.4334i	2.31516	+	3.18654i
$139$	3.65495	−	5.03060i	0.310009	−	0.426690i	−0.625375	−	0.780324i	$-0.715054\pi$
$139$	3.65495	−	5.03060i	0.310009	−	0.426690i	0.935384	+	0.353634i	$0.115054\pi$
$140$	9.91733	−	10.5679i	0.838167	−	0.893148i
$141$	−4.40658	−	6.06514i	−0.371101	−	0.510777i
$142$	2.25930	−	6.95341i	0.189596	−	0.583518i
$143$	6.67376			0.558088
$144$	−4.63650	+	14.2697i	−0.386375	+	1.18914i
$145$	−5.31393	−	4.98682i	−0.441298	−	0.414133i
$146$	−5.32046	+	1.72872i	−0.440324	+	0.143070i
$147$	−4.89942	−	15.0788i	−0.404097	−	1.24368i
$148$	−14.2545	−	10.3565i	−1.17172	−	0.851302i
$149$	−8.65283			−0.708867			−0.354434	−	0.935081i	$-0.615326\pi$
$149$	−8.65283			−0.708867			−0.354434	+	0.935081i	$0.615326\pi$
$150$	−18.9628	+	15.7084i	−1.54830	+	1.28259i
$151$	−18.3478			−1.49312			−0.746559	−	0.665319i	$-0.768296\pi$
$151$	−18.3478			−1.49312			−0.746559	+	0.665319i	$0.768296\pi$
$152$	0.305148	−	0.420001i	0.0247508	−	0.0340666i
$153$	−5.36822	+	13.0233i	−0.433995	+	1.05287i
$154$	−5.35481	−	16.4804i	−0.431503	−	1.32803i
$155$	3.32796	+	17.4146i	0.267308	+	1.39877i
$156$	11.6913	+	3.79874i	0.936054	+	0.304142i
$157$		−	10.8626i		−	0.866928i	−0.901171	−	0.433464i	$-0.857291\pi$
$157$		−	10.8626i		−	0.866928i	0.901171	−	0.433464i	$-0.142709\pi$
$158$	−4.49880	+	13.8459i	−0.357905	+	1.10152i
$159$	−18.1301	−	24.9540i	−1.43781	−	1.97898i
$160$	−15.0513	+	8.28097i	−1.18991	+	0.654668i
$161$	27.6776	+	20.1090i	2.18130	+	1.58481i
$162$	−8.65910	−	11.9182i	−0.680323	−	0.936384i
$163$	−3.35738	+	2.43928i	−0.262970	+	0.191059i	−0.711455	−	0.702731i	$-0.751964\pi$
$163$	−3.35738	+	2.43928i	−0.262970	+	0.191059i	0.448485	+	0.893790i	$0.351964\pi$
$164$	5.29083	−	7.28221i	0.413145	−	0.568645i
$165$	2.60238	+	13.6178i	0.202595	+	1.06014i
$166$	2.51362	−	1.82625i	0.195095	−	0.141745i
$167$	1.15853	−	3.56559i	0.0896497	−	0.275914i	−0.896173	−	0.443705i	$-0.853664\pi$
$167$	1.15853	−	3.56559i	0.0896497	−	0.275914i	0.985822	+	0.167792i	$0.0536637\pi$
$168$			3.94657i			0.304485i
$169$	1.72002	−	5.29367i	0.132309	−	0.407205i
$170$	−16.3214	+	7.40972i	−1.25180	+	0.568299i
$171$	−1.28095	−	3.94237i	−0.0979569	−	0.301480i
$172$	−1.51045	+	0.490774i	−0.115171	+	0.0374212i
$173$	0.970668	+	0.705231i	0.0737985	+	0.0536177i	0.624073	−	0.781366i	$-0.285477\pi$
$173$	0.970668	+	0.705231i	0.0737985	+	0.0536177i	−0.550274	+	0.834984i	$0.685477\pi$
$174$	−16.0500			−1.21675
$175$	−9.74541	+	15.3787i	−0.736684	+	1.16252i
$176$			10.7497i			0.810290i
$177$	21.2215	+	15.4183i	1.59510	+	1.15891i
$178$	15.1342	−	4.91739i	1.13435	−	0.368574i
$179$	3.36940	+	10.3699i	0.251841	+	0.775086i	0.994436	+	0.105345i	$0.0335948\pi$
$179$	3.36940	+	10.3699i	0.251841	+	0.775086i	−0.742595	+	0.669741i	$0.766405\pi$
$180$	−1.69977	+	13.4909i	−0.126693	+	1.00555i
$181$	13.9066	+	4.51854i	1.03367	+	0.335861i	0.776241	−	0.630436i	$-0.217124\pi$
$181$	13.9066	+	4.51854i	1.03367	+	0.335861i	0.257432	+	0.966297i	$0.417124\pi$
$182$	19.3022			1.43078
$183$	−7.13980	−	2.31986i	−0.527789	−	0.171489i
$184$	−2.36291	−	3.25227i	−0.174196	−	0.239760i
$185$	20.0314	+	9.41801i	1.47274	+	0.692426i
$186$	31.5910	+	22.9522i	2.31636	+	1.68293i
$187$	−0.774527	+	10.0625i	−0.0566391	+	0.735840i
$188$	−3.09639	−	4.26182i	−0.225828	−	0.310825i
$189$	3.10751	+	2.25774i	0.226038	+	0.164226i
$190$	2.24431	−	4.77350i	0.162820	−	0.346306i
$191$	5.89647	−	4.28404i	0.426654	−	0.309982i	−0.353656	−	0.935376i	$-0.615062\pi$
$191$	5.89647	−	4.28404i	0.426654	−	0.309982i	0.780309	+	0.625394i	$0.215062\pi$
$192$	−4.81647	+	14.8236i	−0.347599	+	1.06980i
$193$	−18.0772			−1.30123			−0.650614	−	0.759409i	$-0.725488\pi$
$193$	−18.0772			−1.30123			−0.650614	+	0.759409i	$0.725488\pi$
$194$	−0.524570	−	0.170443i	−0.0376620	−	0.0122371i
$195$	−15.3222	−	1.93051i	−1.09724	−	0.138246i
$196$	−3.44270	−	10.5955i	−0.245907	−	0.756823i
$197$	−4.20410	−	12.9389i	−0.299530	−	0.921857i	−0.981662	−	0.190629i	$-0.938947\pi$
$197$	−4.20410	−	12.9389i	−0.299530	−	0.921857i	0.682133	−	0.731229i	$-0.261053\pi$
$198$	13.1533	+	9.55644i	0.934765	+	0.679146i
$199$			12.8687i			0.912237i	0.889919	+	0.456118i	$0.150761\pi$
$199$			12.8687i			0.912237i	−0.889919	+	0.456118i	$0.849239\pi$
$200$	1.64751	−	1.36477i	0.116497	−	0.0965039i
$201$			29.9041i			2.10927i
$202$	−10.3646	+	14.2656i	−0.729248	+	1.00372i
$203$	−11.2863	+	3.66714i	−0.792144	+	0.257383i
$204$	−7.08444	+	17.1869i	−0.496010	+	1.20332i
$205$	−4.81137	+	10.2334i	−0.336041	+	0.714735i
$206$	4.30289	−	13.2429i	0.299796	−	0.922678i
$207$	−32.0987			−2.23101
$208$	−11.3881	−	3.70020i	−0.789619	−	0.256563i
$209$	−1.74565	−	2.40269i	−0.120749	−	0.166197i
$210$	7.52676	+	39.3860i	0.519396	+	2.71790i
$211$	−7.95391	+	10.9476i	−0.547570	+	0.753665i	−0.989680	−	0.143295i	$-0.954230\pi$
$211$	−7.95391	+	10.9476i	−0.547570	+	0.753665i	0.442110	+	0.896961i	$0.354230\pi$
$212$	−12.7396	−	17.5345i	−0.874957	−	1.20428i
$213$	5.59907	+	7.70646i	0.383642	+	0.528038i
$214$	10.2932	−	14.1674i	0.703629	−	0.968462i
$215$	1.74808	−	0.961764i	0.119218	−	0.0655918i
$216$	−0.265296	−	0.365149i	−0.0180511	−	0.0248452i
$217$	27.4587	+	8.92189i	1.86402	+	0.605657i
$218$	30.2941			2.05178
$219$	2.25232	−	6.93193i	0.152198	−	0.468417i
$220$	1.82863	+	9.56885i	0.123286	+	0.645132i
$221$	−10.3934	−	4.28416i	−0.699135	−	0.288184i
$222$	46.3649	−	15.0649i	3.11181	−	1.01109i
$223$	−4.80664	+	6.61577i	−0.321876	+	0.443025i	−0.939039	−	0.343811i	$-0.888282\pi$
$223$	−4.80664	+	6.61577i	−0.321876	+	0.443025i	0.617163	+	0.786836i	$0.288282\pi$
$224$			27.9749i			1.86915i
$225$	−1.08385	−	17.0478i	−0.0722565	−	1.13652i
$226$		−	20.8615i		−	1.38769i
$227$	−16.7077	−	12.1389i	−1.10893	−	0.805684i	−0.126435	−	0.991975i	$-0.540353\pi$
$227$	−16.7077	−	12.1389i	−1.10893	−	0.805684i	−0.982495	+	0.186291i	$0.940353\pi$
$228$	−1.69047	−	5.20274i	−0.111954	−	0.344560i
$229$	6.62974	+	20.4042i	0.438105	+	1.34835i	0.889871	+	0.456213i	$0.150794\pi$
$229$	6.62974	+	20.4042i	0.438105	+	1.34835i	−0.451765	+	0.892137i	$0.649206\pi$
$230$	−29.7840	−	27.9506i	−1.96390	−	1.84301i
$231$	21.4720	+	6.97669i	1.41276	+	0.459032i
$232$	1.39445			0.0915502
$233$	5.87182	−	18.0716i	0.384676	−	1.18391i	−0.552039	−	0.833818i	$-0.686150\pi$
$233$	5.87182	−	18.0716i	0.384676	−	1.18391i	0.936715	−	0.350093i	$-0.113850\pi$
$234$	−14.6515	+	10.6449i	−0.957797	+	0.695880i
$235$	4.82574	+	4.52868i	0.314797	+	0.295419i
$236$	14.9118	+	10.8340i	0.970674	+	0.705236i
$237$	−11.1491	−	15.3454i	−0.724209	−	0.996789i
$238$	−2.24013	+	29.1032i	−0.145206	+	1.88648i
$239$	−5.60576	−	4.07282i	−0.362607	−	0.263449i	0.391532	−	0.920165i	$-0.371945\pi$
$239$	−5.60576	−	4.07282i	−0.362607	−	0.263449i	−0.754138	+	0.656715i	$0.771945\pi$
$240$	3.10955	−	24.6801i	0.200720	−	1.59309i
$241$	−18.2044	−	25.0562i	−1.17265	−	1.61401i	−0.643348	−	0.765574i	$-0.722455\pi$
$241$	−18.2044	−	25.0562i	−1.17265	−	1.61401i	−0.529299	−	0.848435i	$-0.677545\pi$
$242$	−9.26123	−	3.00916i	−0.595334	−	0.193436i
$243$	22.3583			1.43429
$244$	−5.01696	−	1.63011i	−0.321178	−	0.104357i
$245$	6.74661	+	12.2624i	0.431025	+	0.783419i
$246$	7.69617	+	23.6864i	0.490690	+	1.51019i
$247$	3.14624	−	1.02228i	0.200191	−	0.0650459i
$248$	−2.74467	−	1.99412i	−0.174286	−	0.126627i
$249$			4.04807i			0.256536i
$250$	13.8390	−	16.7622i	0.875255	−	1.06014i
$251$	−3.86587			−0.244011			−0.122006	−	0.992529i	$-0.538933\pi$
$251$	−3.86587			−0.244011			−0.122006	+	0.992529i	$0.538933\pi$
$252$	17.9139	+	13.0152i	1.12847	+	0.819881i
$253$	−21.8717	+	7.10654i	−1.37506	+	0.446784i
$254$	−3.02465	−	9.30891i	−0.189783	−	0.584093i
$255$	4.68897	−	22.8782i	0.293635	−	1.43269i
$256$	5.84693	−	17.9950i	0.365433	−	1.12469i
$257$		−	1.89460i		−	0.118182i	−0.998253	−	0.0590909i	$-0.981180\pi$
$257$		−	1.89460i		−	0.118182i	0.998253	−	0.0590909i	$-0.0188202\pi$
$258$	1.35790	−	4.17920i	0.0845394	−	0.260185i
$259$	29.1615	−	21.1871i	1.81201	−	1.31650i
$260$	−10.7665	−	1.35652i	−0.667710	−	0.0841277i
$261$	6.54455	−	9.00781i	0.405098	−	0.557569i
$262$	−17.6125	+	12.7962i	−1.08810	+	0.790554i
$263$	−4.19849	−	5.77873i	−0.258890	−	0.356332i	0.659710	−	0.751521i	$-0.270679\pi$
$263$	−4.19849	−	5.77873i	−0.258890	−	0.356332i	−0.918600	+	0.395189i	$0.870679\pi$
$264$	−2.14626	−	1.55935i	−0.132093	−	0.0959713i
$265$	19.8547	+	18.6325i	1.21966	+	1.14458i
$266$	−5.04888	−	6.94919i	−0.309567	−	0.426082i
$267$	−6.40679	+	19.7181i	−0.392089	+	1.20673i
$268$			21.0128i			1.28356i
$269$	5.13522	+	1.66854i	0.313100	+	0.101732i	0.461352	−	0.887217i	$-0.347365\pi$
$269$	5.13522	+	1.66854i	0.313100	+	0.101732i	−0.148252	+	0.988950i	$0.547365\pi$
$270$	−3.34401	−	3.13816i	−0.203510	−	0.190982i
$271$	5.53687	+	17.0407i	0.336341	+	1.03515i	0.966058	+	0.258326i	$0.0831707\pi$
$271$	5.53687	+	17.0407i	0.336341	+	1.03515i	−0.629717	+	0.776824i	$0.716829\pi$
$272$	6.90068	−	16.7411i	0.418415	−	1.01508i
$273$	−14.7820	+	20.3456i	−0.894645	+	1.23137i
$274$	35.7365			2.15892
$275$	−4.51284	−	11.3762i	−0.272135	−	0.686011i
$276$	−42.3606			−2.54981
$277$	−1.67467	−	1.21672i	−0.100621	−	0.0731054i	0.536337	−	0.844004i	$-0.319808\pi$
$277$	−1.67467	−	1.21672i	−0.100621	−	0.0731054i	−0.636958	+	0.770898i	$0.719808\pi$
$278$	3.73582	+	11.4977i	0.224060	+	0.689585i
$279$	−25.7630	+	8.37091i	−1.54239	+	0.501153i
$280$	−0.653935	−	3.42191i	−0.0390801	−	0.204498i
$281$	0.837843	−	2.57862i	0.0499815	−	0.153827i	−0.922951	−	0.384918i	$-0.874230\pi$
$281$	0.837843	−	2.57862i	0.0499815	−	0.153827i	0.972932	+	0.231091i	$0.0742296\pi$
$282$	14.5755			0.867960
$283$	−3.86447	+	11.8936i	−0.229719	+	0.707003i	0.768059	+	0.640379i	$0.221223\pi$
$283$	−3.86447	+	11.8936i	−0.229719	+	0.707003i	−0.997778	+	0.0666239i	$0.978777\pi$
$284$	3.93433	+	5.41513i	0.233459	+	0.321329i
$285$	3.31280	+	6.02125i	0.196233	+	0.356668i
$286$	−7.62660	+	10.4971i	−0.450970	+	0.620707i
$287$	10.8238	+	14.8977i	0.638910	+	0.879384i
$288$	−15.4278	−	21.2345i	−0.909090	−	1.25125i
$289$	7.66571	−	15.1736i	0.450924	−	0.892562i
$290$	13.9164	−	2.65945i	0.817197	−	0.156168i
$291$	0.581381	−	0.422398i	0.0340811	−	0.0247614i
$292$	1.58265	−	4.87089i	0.0926175	−	0.285047i
$293$			7.59155i			0.443503i	0.975103	+	0.221751i	$0.0711774\pi$
$293$			7.59155i			0.443503i	−0.975103	+	0.221751i	$0.928823\pi$
$294$	29.3163	+	9.52546i	1.70976	+	0.555536i
$295$	−20.9550	−	9.85225i	−1.22005	−	0.573620i
$296$	−4.02824	+	1.30886i	−0.234137	+	0.0760757i
$297$	−2.45565	+	0.797888i	−0.142491	+	0.0462981i
$298$	9.88822	−	13.6100i	0.572809	−	0.788404i
$299$		−	25.6166i		−	1.48145i
$300$	−1.43035	−	22.4979i	−0.0825814	−	1.29892i
$301$		−	3.24905i		−	0.187272i
$302$	20.9673	−	28.8590i	1.20653	−	1.66065i
$303$	−7.09937	−	21.8496i	−0.407848	−	1.25523i
$304$	1.64662	+	5.06778i	0.0944403	+	0.290657i
$305$	6.57503	+	0.828416i	0.376485	+	0.0474349i
$306$	−14.3496	−	23.3264i	−0.820314	−	1.33348i
$307$			18.2629i			1.04232i	0.853460	+	0.521158i	$0.174500\pi$
$307$			18.2629i			1.04232i	−0.853460	+	0.521158i	$0.825500\pi$
$308$	15.0879	+	4.90234i	0.859711	+	0.279337i
$309$	10.6635	+	14.6771i	0.606628	+	0.834952i
$310$	−31.1944	−	14.6664i	−1.77172	−	0.832995i
$311$	8.42375	−	11.5943i	0.477667	−	0.657452i	−0.500387	−	0.865802i	$-0.666809\pi$
$311$	8.42375	−	11.5943i	0.477667	−	0.657452i	0.978054	+	0.208349i	$0.0668091\pi$
$312$	2.39072	−	1.73696i	0.135348	−	0.0983359i
$313$	−3.94388	+	2.86540i	−0.222921	+	0.161962i	−0.693641	−	0.720321i	$-0.743994\pi$
$313$	−3.94388	+	2.86540i	−0.222921	+	0.161962i	0.470719	+	0.882283i	$0.343994\pi$
$314$	17.0857	+	12.4135i	0.964200	+	0.700532i
$315$	−25.1738	−	11.8358i	−1.41838	−	0.666870i
$316$	−7.83416	−	10.7828i	−0.440706	−	0.606580i
$317$	0.0771171	−	0.237342i	0.00433133	−	0.0133305i	−0.948867	−	0.315675i	$-0.897769\pi$
$317$	0.0771171	−	0.237342i	0.00433133	−	0.0133305i	0.953199	+	0.302344i	$0.0977692\pi$
$318$	59.9685			3.36287
$319$	2.46509	−	7.58676i	0.138018	−	0.424777i
$320$	1.71995	−	13.6510i	0.0961480	−	0.763114i
$321$	7.05050	+	21.6992i	0.393520	+	1.21113i
$322$	−63.2585	+	20.5539i	−3.52526	+	1.14543i
$323$	1.17621	+	4.86243i	0.0654461	+	0.270553i
$324$	13.4870			0.749275
$325$	13.6051	−	0.864974i	0.754677	−	0.0479801i
$326$		−	8.06834i		−	0.446864i
$327$	−23.1997	+	31.9317i	−1.28295	+	1.76583i
$328$	−0.668654	−	2.05791i	−0.0369202	−	0.113629i
$329$	10.2494	−	3.33024i	0.565070	−	0.183602i
$330$	−24.3932	−	11.4687i	−1.34280	−	0.631333i
$331$	11.0922	−	34.1382i	0.609680	−	1.87640i	0.148999	−	0.988837i	$-0.452395\pi$
$331$	11.0922	−	34.1382i	0.609680	−	1.87640i	0.460681	−	0.887566i	$-0.347605\pi$
$332$			2.84447i			0.156111i
$333$	−10.4508	+	32.1643i	−0.572701	+	1.76259i
$334$	4.28435	+	5.89690i	0.234429	+	0.322664i
$335$	−4.95502	−	25.9286i	−0.270721	−	1.41663i
$336$	−32.7715	−	23.8099i	−1.78783	−	1.29894i
$337$	23.5022	−	17.0753i	1.28024	−	0.930152i	0.280684	−	0.959800i	$-0.409439\pi$
$337$	23.5022	−	17.0753i	1.28024	−	0.930152i	0.999560	+	0.0296487i	$0.00943885\pi$
$338$	6.36078	+	8.75487i	0.345981	+	0.476202i
$339$	21.9892	+	15.9761i	1.19429	+	0.867701i
$340$	3.29482	−	16.0759i	0.178687	−	0.871839i
$341$	−15.7013	+	11.4077i	−0.850275	+	0.617761i
$342$	7.66476	+	2.49043i	0.414463	+	0.134667i
$343$	−2.69769			−0.145662
$344$	−0.117977	+	0.363094i	−0.00636087	+	0.0195767i
$345$	52.2705	−	9.98900i	2.81415	−	0.537790i
$346$	−2.21851	+	0.720836i	−0.119268	+	0.0387524i
$347$	4.64306	+	14.2899i	0.249253	+	0.767120i	0.994908	+	0.100789i	$0.0321366\pi$
$347$	4.64306	+	14.2899i	0.249253	+	0.767120i	−0.745655	+	0.666332i	$0.767863\pi$
$348$	8.63684	−	11.8876i	0.462983	−	0.637242i
$349$	5.83459			0.312318			0.156159	−	0.987732i	$-0.450089\pi$
$349$	5.83459			0.312318			0.156159	+	0.987732i	$0.450089\pi$
$350$	−13.0523	−	32.9029i	−0.697675	−	1.75873i
$351$		−	2.87611i		−	0.153515i
$352$	−15.2136	−	11.0533i	−0.810885	−	0.589143i
$353$	−28.2252	+	9.17094i	−1.50228	+	0.488120i	−0.940681	−	0.339291i	$-0.889813\pi$
$353$	−28.2252	+	9.17094i	−1.50228	+	0.488120i	−0.561597	+	0.827411i	$0.689813\pi$
$354$	−48.5026	+	15.7595i	−2.57789	+	0.837606i
$355$	−6.13167	−	5.75421i	−0.325435	−	0.305402i
$356$	−4.50189	+	13.8554i	−0.238600	+	0.734334i
$357$	−28.9609	−	24.6489i	−1.53277	−	1.30456i
$358$	−20.1613	−	6.55080i	−1.06556	−	0.346220i
$359$	1.94441	−	1.41270i	0.102622	−	0.0745593i	−0.535291	−	0.844668i	$-0.679798\pi$
$359$	1.94441	−	1.41270i	0.102622	−	0.0745593i	0.637913	+	0.770109i	$0.279798\pi$
$360$	2.38351	+	2.23679i	0.125622	+	0.117889i
$361$	14.1803	+	10.3026i	0.746333	+	0.542242i
$362$	−22.9993	+	16.7100i	−1.20882	+	0.878258i
$363$	10.2642	−	7.45738i	0.538731	−	0.391411i
$364$	−10.3869	+	14.2964i	−0.544422	+	0.749332i
$365$	−0.804297	+	6.38360i	−0.0420989	+	0.334133i
$366$	11.8081	−	8.57906i	0.617217	−	0.448435i
$367$	−1.46103	+	4.49658i	−0.0762650	+	0.234720i	−0.981920	−	0.189295i	$-0.939380\pi$
$367$	−1.46103	+	4.49658i	−0.0762650	+	0.234720i	0.905655	+	0.424015i	$0.139380\pi$
$368$	41.2618			2.15092
$369$	−16.4317	−	5.33900i	−0.855403	−	0.277937i
$370$	−37.7049	+	20.7447i	−1.96019	+	1.07846i
$371$	42.1695	−	13.7017i	2.18933	−	0.711358i
$372$	−33.9994	+	11.0471i	−1.76279	+	0.572764i
$373$	17.7124	−	24.3791i	0.917114	−	1.26230i	−0.0475637	−	0.998868i	$-0.515146\pi$
$373$	17.7124	−	24.3791i	0.917114	−	1.26230i	0.964678	−	0.263432i	$-0.0848543\pi$
$374$	−14.9421	−	12.7174i	−0.772635	−	0.657599i
$375$	7.07018	+	27.4238i	0.365103	+	1.41616i
$376$	−1.26634			−0.0653066
$377$	7.18876	+	5.22294i	0.370240	+	0.268995i
$378$	−7.10236	+	2.30770i	−0.365306	+	0.118695i
$379$	19.7706	−	6.42386i	1.01555	−	0.329972i	0.246487	−	0.969146i	$-0.420724\pi$
$379$	19.7706	−	6.42386i	1.01555	−	0.329972i	0.769062	+	0.639175i	$0.220724\pi$
$380$	2.32782	+	4.23098i	0.119415	+	0.217045i
$381$	12.1284	+	3.94077i	0.621358	+	0.201892i
$382$			14.1702i			0.725011i
$383$	20.6427	+	6.70722i	1.05479	+	0.342723i	0.784547	−	0.620069i	$-0.212895\pi$
$383$	20.6427	+	6.70722i	1.05479	+	0.342723i	0.270245	+	0.962792i	$0.412895\pi$
$384$	5.06563	+	6.97224i	0.258504	+	0.355801i
$385$	−19.7736	−	2.49136i	−1.00775	−	0.126971i
$386$	20.6582	−	28.4336i	1.05147	−	1.44723i
$387$	1.79180	+	2.46620i	0.0910825	+	0.125364i
$388$	0.408521	−	0.296808i	0.0207395	−	0.0150682i
$389$	−30.7362	−	22.3312i	−1.55839	−	1.13223i	−0.937316	−	0.348481i	$-0.886698\pi$
$389$	−30.7362	−	22.3312i	−1.55839	−	1.13223i	−0.621072	−	0.783754i	$-0.713302\pi$
$390$	20.5463	−	21.8940i	1.04040	−	1.10865i
$391$	38.6238	+	2.97295i	1.95329	+	0.150349i
$392$	−2.54704	−	0.827585i	−0.128645	−	0.0417993i
$393$		−	28.3641i		−	1.43078i
$394$	25.1558	+	8.17362i	1.26733	+	0.411781i
$395$	12.2096	+	11.4580i	0.614331	+	0.576514i
$396$	−14.1561	+	4.59959i	−0.711371	+	0.231138i
$397$	10.5242	+	32.3903i	0.528197	+	1.62562i	0.757907	+	0.652363i	$0.226222\pi$
$397$	10.5242	+	32.3903i	0.528197	+	1.62562i	−0.229710	+	0.973259i	$0.573778\pi$
$398$	−20.2411	−	14.7060i	−1.01459	−	0.737145i
$399$	11.1913			0.560268
$400$	1.39325	+	21.9144i	0.0696625	+	1.09572i
$401$			26.6184i			1.32926i	0.747173	+	0.664629i	$0.231410\pi$
$401$			26.6184i			1.32926i	−0.747173	+	0.664629i	$0.768590\pi$
$402$	−47.0359	−	34.1736i	−2.34594	−	1.70442i
$403$	−6.68048	−	20.5604i	−0.332778	−	1.02419i
$404$	−4.98855	−	15.3532i	−0.248190	−	0.763849i
$405$	−16.6421	+	3.18034i	−0.826954	+	0.158033i
$406$	7.12967	−	21.9429i	0.353840	−	1.08901i
$407$			24.2302i			1.20105i
$408$	2.34147	+	3.80622i	0.115920	+	0.188436i
$409$	11.5051	−	8.35897i	0.568893	−	0.413325i	−0.265810	−	0.964025i	$-0.585639\pi$
$409$	11.5051	−	8.35897i	0.568893	−	0.413325i	0.834703	+	0.550701i	$0.185639\pi$
$410$	−10.5978	−	19.2623i	−0.523388	−	0.951296i
$411$	−27.3676	+	37.6682i	−1.34994	+	1.85804i
$412$	7.49301	+	10.3132i	0.369154	+	0.508097i
$413$	−30.5060	+	22.1639i	−1.50110	+	1.09062i
$414$	36.6815	−	50.4878i	1.80280	−	2.48134i
$415$	−0.670753	−	3.50992i	−0.0329259	−	0.172295i
$416$	16.9464	−	12.3123i	0.830865	−	0.603659i
$417$	−14.9801	−	4.86734i	−0.733581	−	0.238355i
$418$	5.77406			0.282418
$419$	−3.92349	−	1.27482i	−0.191675	−	0.0622790i	0.211607	−	0.977355i	$-0.432130\pi$
$419$	−3.92349	−	1.27482i	−0.191675	−	0.0622790i	−0.403281	+	0.915076i	$0.632130\pi$
$420$	−33.2219	−	15.6196i	−1.62106	−	0.762160i
$421$	−4.17147	−	12.8385i	−0.203305	−	0.625709i	−0.999779	−	0.0210357i	$-0.993304\pi$
$421$	−4.17147	−	12.8385i	−0.203305	−	0.625709i	0.796474	−	0.604673i	$-0.206696\pi$
$422$	−8.12992	−	25.0213i	−0.395758	−	1.21802i
$423$	−5.94331	+	8.18026i	−0.288973	+	0.397738i
$424$	−5.21015			−0.253027
$425$	−0.274774	+	20.6137i	−0.0133285	+	0.999911i
$426$	−18.5199			−0.897292
$427$	6.34321	−	8.73068i	0.306969	−	0.422507i
$428$	4.95421	+	15.2475i	0.239471	+	0.737015i
$429$	−5.22396	−	16.0777i	−0.252215	−	0.776239i
$430$	−0.484903	+	3.84862i	−0.0233841	+	0.185597i
$431$	−17.6436	−	5.73276i	−0.849864	−	0.276138i	−0.148475	−	0.988916i	$-0.547436\pi$
$431$	−17.6436	−	5.73276i	−0.849864	−	0.276138i	−0.701389	+	0.712779i	$0.747436\pi$
$432$	4.63267			0.222890
$433$	−1.15281	−	0.374569i	−0.0554003	−	0.0180007i	0.281186	−	0.959653i	$-0.409272\pi$
$433$	−1.15281	−	0.374569i	−0.0554003	−	0.0180007i	−0.336586	+	0.941653i	$0.609272\pi$
$434$	−45.4123	+	32.9940i	−2.17986	+	1.58376i
$435$	−7.85416	+	16.7052i	−0.376578	+	0.800955i
$436$	−16.3019	+	22.4376i	−0.780718	+	1.07457i
$437$	−9.22249	+	6.70053i	−0.441172	+	0.320530i
$438$	8.32929	+	11.4643i	0.397989	+	0.547785i
$439$	1.05506	−	1.45217i	0.0503553	−	0.0693082i	−0.783097	−	0.621900i	$-0.786361\pi$
$439$	1.05506	−	1.45217i	0.0503553	−	0.0693082i	0.833452	+	0.552592i	$0.186361\pi$
$440$	2.11931	+	0.996420i	0.101034	+	0.0475025i
$441$	−17.3000	+	12.5692i	−0.823809	+	0.598533i
$442$	18.6158	−	11.4519i	0.885464	−	0.544709i
$443$			17.5649i			0.834531i	0.908785	+	0.417266i	$0.137012\pi$
$443$			17.5649i			0.834531i	−0.908785	+	0.417266i	$0.862988\pi$
$444$	−13.7919	+	42.4472i	−0.654536	+	2.01445i
$445$	2.28785	−	18.1583i	0.108454	−	0.860788i
$446$	−4.91300	−	15.1206i	−0.232637	−	0.715983i
$447$	6.77310	+	20.8455i	0.320357	+	0.985956i
$448$	−18.1265	−	13.1697i	−0.856399	−	0.622210i
$449$			19.4983i			0.920181i	0.887872	+	0.460091i	$0.152183\pi$
$449$			19.4983i			0.920181i	−0.887872	+	0.460091i	$0.847817\pi$
$450$	28.0529	+	17.7770i	1.32243	+	0.838014i
$451$	−12.3784			−0.582878
$452$	15.4512	+	11.2260i	0.726765	+	0.528026i
$453$	14.3619	+	44.2014i	0.674781	+	2.07676i
$454$	38.1862	−	12.4075i	1.79217	−	0.582311i
$455$	9.44564	−	20.0902i	0.442818	−	0.941843i
$456$	−1.25068	−	0.406370i	−0.0585684	−	0.0190300i
$457$		−	17.8148i		−	0.833343i	−0.909057	−	0.416671i	$-0.863197\pi$
$457$		−	17.8148i		−	0.833343i	0.909057	−	0.416671i	$-0.136803\pi$
$458$	−39.6700	−	12.8896i	−1.85366	−	0.602289i
$459$	4.33650	+	0.333789i	0.202410	+	0.0155799i
$460$	36.7291	−	7.01902i	1.71251	−	0.327263i
$461$	−9.87570	−	7.17511i	−0.459957	−	0.334178i	0.333557	−	0.942730i	$-0.391751\pi$
$461$	−9.87570	−	7.17511i	−0.459957	−	0.334178i	−0.793514	+	0.608551i	$0.791751\pi$
$462$	−35.5113	+	25.8004i	−1.65213	+	1.20035i
$463$	0.147699	+	0.203290i	0.00686415	+	0.00944769i	0.812435	−	0.583051i	$-0.198141\pi$
$463$	0.147699	+	0.203290i	0.00686415	+	0.00944769i	−0.805571	+	0.592499i	$0.798141\pi$
$464$	−8.41281	+	11.5792i	−0.390555	+	0.537553i
$465$	39.3483	−	21.6488i	1.82473	−	1.00394i
$466$	21.7145	+	29.8875i	1.00591	+	1.38451i
$467$	−16.9801	−	5.51718i	−0.785747	−	0.255305i	−0.111455	−	0.993770i	$-0.535551\pi$
$467$	−16.9801	−	5.51718i	−0.785747	−	0.255305i	−0.674292	+	0.738465i	$0.735551\pi$
$468$		−	16.5800i		−	0.766409i
$469$	−40.8834	−	13.2838i	−1.88782	−	0.613391i
$470$	−12.6379	+	2.41512i	−0.582941	+	0.111401i
$471$	−26.1689	+	8.50280i	−1.20580	+	0.391789i
$472$	4.21398	−	1.36920i	0.193964	−	0.0630227i
$473$	1.76692	+	1.28375i	0.0812433	+	0.0590267i
$474$	36.8775			1.69384
$475$	−3.87010	−	4.67186i	−0.177572	−	0.214360i
$476$	−20.3501	−	17.3202i	−0.932743	−	0.793869i
$477$	−24.4527	+	33.6563i	−1.11961	+	1.54101i
$478$	12.8122	−	4.16295i	0.586018	−	0.190409i
$479$	−11.6689	+	3.79147i	−0.533167	+	0.173237i	−0.563213	−	0.826312i	$-0.690435\pi$
$479$	−11.6689	+	3.79147i	−0.533167	+	0.173237i	0.0300454	+	0.999549i	$0.490435\pi$
$480$	31.7312	+	29.7779i	1.44832	+	1.35917i
$481$	−25.6690	−	8.34037i	−1.17041	−	0.380288i
$482$	60.2141			2.74268
$483$	26.7794	−	82.4184i	1.21850	−	3.75017i
$484$	7.21240	−	5.24012i	0.327836	−	0.238187i
$485$	−0.434102	+	0.462577i	−0.0197115	+	0.0210045i
$486$	−25.5505	+	35.1673i	−1.15899	+	1.59522i
$487$	6.49323	−	4.71761i	0.294236	−	0.213775i	−0.430867	−	0.902416i	$-0.641792\pi$
$487$	6.49323	−	4.71761i	0.294236	−	0.213775i	0.725103	+	0.688640i	$0.241792\pi$
$488$	−1.02590	+	0.745361i	−0.0464404	+	0.0337409i
$489$	8.50447	+	6.17886i	0.384586	+	0.279418i
$490$	−26.9974	−	3.40151i	−1.21962	−	0.153665i
$491$	−20.9655	+	15.2323i	−0.946160	+	0.687425i	−0.949896	−	0.312568i	$-0.898811\pi$
$491$	−20.9655	+	15.2323i	−0.946160	+	0.687425i	0.00373564	+	0.999993i	$0.498811\pi$
$492$	−21.6850	−	7.04587i	−0.977633	−	0.317652i
$493$	−8.70925	+	10.2328i	−0.392245	+	0.460862i
$494$	−1.98751	+	6.11693i	−0.0894224	+	0.275214i
$495$	16.3832	−	9.01377i	0.736369	−	0.405139i
$496$	33.1175	−	10.7605i	1.48702	−	0.483162i
$497$	−13.0231	+	4.23146i	−0.584166	+	0.189807i
$498$	−6.36718	−	4.62602i	−0.285320	−	0.207297i
$499$		−	5.27764i		−	0.236260i	−0.992998	−	0.118130i	$-0.962310\pi$
$499$		−	5.27764i		−	0.236260i	0.992998	−	0.118130i	$-0.0376899\pi$
$500$	4.96804	+	19.2700i	0.222177	+	0.861782i
$501$	−9.49668			−0.424280
$502$	4.41781	−	6.08059i	0.197177	−	0.271390i
$503$	−8.60899	−	26.4957i	−0.383856	−	1.18139i	−0.937307	−	0.348505i	$-0.886689\pi$
$503$	−8.60899	−	26.4957i	−0.383856	−	1.18139i	0.553451	−	0.832882i	$-0.313311\pi$
$504$	5.06236	−	1.64486i	0.225495	−	0.0732679i
$505$	9.77600	+	17.7686i	0.435026	+	0.790692i
$506$	13.8165	−	42.5230i	0.614220	−	1.89038i
$507$	−14.0993			−0.626172
$508$	8.52234	+	2.76908i	0.378118	+	0.122858i
$509$	−10.9971	+	7.98988i	−0.487439	+	0.354145i	−0.804199	−	0.594361i	$-0.797405\pi$
$509$	−10.9971	+	7.98988i	−0.487439	+	0.354145i	0.316760	+	0.948506i	$0.397405\pi$
$510$	30.6265	+	33.5198i	1.35616	+	1.48428i
$511$	8.47650	+	6.15854i	0.374978	+	0.272438i
$512$	17.6229	+	24.2558i	0.778828	+	1.07197i
$513$	−1.03546	+	0.752303i	−0.0457165	+	0.0332150i
$514$	2.98000	+	2.16510i	0.131442	+	0.0954984i
$515$	−11.6779	−	10.9590i	−0.514589	−	0.482912i
$516$	2.36464	+	3.25465i	0.104097	+	0.143278i
$517$	−2.23862	+	6.88977i	−0.0984544	+	0.303012i
$518$			70.0799i			3.07913i
$519$	0.939166	−	2.89045i	0.0412248	−	0.126877i
$520$	−1.78509	+	1.90218i	−0.0782813	+	0.0834162i
$521$	−37.4219	+	12.1591i	−1.63948	+	0.532700i	−0.976423	−	0.215867i	$-0.930742\pi$
$521$	−37.4219	+	12.1591i	−1.63948	+	0.532700i	−0.663059	+	0.748567i	$0.730742\pi$
$522$	6.68937	+	20.5878i	0.292786	+	0.901102i
$523$	0.967592	−	1.33178i	0.0423098	−	0.0582345i	−0.787338	−	0.616522i	$-0.788541\pi$
$523$	0.967592	−	1.33178i	0.0423098	−	0.0582345i	0.829648	+	0.558287i	$0.188541\pi$
$524$		−	19.9307i		−	0.870678i
$525$	44.6771	+	11.4397i	1.94987	+	0.499270i
$526$	13.8873			0.605513
$527$	31.7755	−	7.68643i	1.38416	−	0.334826i
$528$	25.8970	−	8.41446i	1.12702	−	0.366192i
$529$	20.1704	+	62.0781i	0.876974	+	2.69905i
$530$	−51.9963	+	9.93660i	−2.25858	+	0.431619i
$531$	10.9327	−	33.6473i	0.474438	−	1.46017i
$532$	7.86387			0.340942
$533$	4.26084	−	13.1135i	0.184557	−	0.568009i
$534$	−23.6929	−	32.6105i	−1.02529	−	1.41119i
$535$	−9.70870	−	17.6463i	−0.419744	−	0.762914i
$536$	4.08655	+	2.96905i	0.176512	+	0.128243i
$537$	22.3447	−	16.2344i	0.964246	−	0.700565i
$538$	−8.49282	+	6.17040i	−0.366152	+	0.266025i
$539$	−9.00525	+	12.3947i	−0.387884	+	0.533876i
$540$	4.12377	−	0.788062i	0.177459	−	0.0339128i
$541$	13.3176	+	18.3301i	0.572568	+	0.788073i	0.992856	−	0.119318i	$-0.0380709\pi$
$541$	13.3176	+	18.3301i	0.572568	+	0.788073i	−0.420288	+	0.907391i	$0.638071\pi$
$542$	−33.1306	−	10.7648i	−1.42308	−	0.462387i
$543$		−	37.0393i		−	1.58951i
$544$	16.5973	+	26.9800i	0.711602	+	1.15676i
$545$	14.8246	−	31.5308i	0.635015	−	1.35063i
$546$	−15.1090	−	46.5009i	−0.646608	−	1.99005i
$547$	6.03495	+	18.5737i	0.258036	+	0.794152i	0.993216	+	0.116281i	$0.0370974\pi$
$547$	6.03495	+	18.5737i	0.258036	+	0.794152i	−0.735181	+	0.677871i	$0.762903\pi$
$548$	−19.2305	+	26.4685i	−0.821486	+	1.13068i
$549$			10.1253i			0.432136i
$550$	23.0507	+	5.90221i	0.982885	+	0.251671i
$551$		−	3.95426i		−	0.168457i
$552$	−5.98542	+	8.23822i	−0.254756	+	0.350642i
$553$	25.9320	−	8.42583i	1.10274	−	0.358303i
$554$	3.82753	−	1.24364i	0.162616	−	0.0528372i
$555$	7.00901	−	55.6296i	0.297516	−	2.36135i
$556$	−10.5262	−	3.42016i	−0.446409	−	0.145047i
$557$		−	4.45768i		−	0.188878i	−0.995531	−	0.0944389i	$-0.969894\pi$
$557$		−	4.45768i		−	0.188878i	0.995531	−	0.0944389i	$-0.0301057\pi$
$558$	16.2747	−	50.0885i	0.688965	−	2.12041i
$559$	−1.96818	+	1.42996i	−0.0832450	+	0.0604811i
$560$	32.3601	+	15.2145i	1.36747	+	0.642929i
$561$	24.8476	−	6.01059i	1.04907	−	0.253767i
$562$	3.09842	+	4.26461i	0.130699	+	0.179892i
$563$	−11.4057	−	15.6986i	−0.480693	−	0.661617i	0.497945	−	0.867209i	$-0.334088\pi$
$563$	−11.4057	−	15.6986i	−0.480693	−	0.661617i	−0.978638	+	0.205592i	$0.934088\pi$
$564$	−7.84337	+	10.7955i	−0.330266	+	0.454572i
$565$	−21.7131	−	10.2087i	−0.913478	−	0.429482i
$566$	−14.2912	−	19.6701i	−0.600703	−	0.826797i
$567$	−8.52614	+	26.2408i	−0.358064	+	1.10201i
$568$	1.60904			0.0675136
$569$	−1.60492	+	4.93943i	−0.0672817	+	0.207072i	−0.979045	−	0.203645i	$-0.934721\pi$
$569$	−1.60492	+	4.93943i	−0.0672817	+	0.207072i	0.911763	+	0.410716i	$0.134721\pi$
$570$	−13.2566	−	1.67025i	−0.555256	−	0.0699591i
$571$	−11.9963	+	3.89783i	−0.502029	+	0.163119i	−0.549074	−	0.835774i	$-0.685020\pi$
$571$	−11.9963	+	3.89783i	−0.502029	+	0.163119i	0.0470452	+	0.998893i	$0.485020\pi$
$572$	−3.67075	−	11.2974i	−0.153482	−	0.472368i
$573$	−14.9362	−	10.8518i	−0.623967	−	0.453339i
$574$	−35.8017			−1.49433
$575$	−43.6665	+	17.3221i	−1.82102	+	0.722383i
$576$	21.0220			0.875915
$577$	20.1215	−	27.6949i	0.837671	−	1.15296i	−0.148775	−	0.988871i	$-0.547533\pi$
$577$	20.1215	−	27.6949i	0.837671	−	1.15296i	0.986446	−	0.164084i	$-0.0524669\pi$
$578$	15.1062	+	29.3973i	0.628336	+	1.22277i
$579$	14.1502	+	43.5497i	0.588061	+	1.80986i
$580$	−5.51892	+	11.7384i	−0.229161	+	0.487409i
$581$	−5.53433	−	1.79821i	−0.229603	−	0.0746024i
$582$			1.39715i			0.0579139i
$583$	−9.21042	+	28.3468i	−0.381457	+	1.17400i
$584$	−0.723661	−	0.996033i	−0.0299453	−	0.0412162i
$585$	3.90970	+	20.4587i	0.161646	+	0.845864i
$586$	−11.9407	−	8.67542i	−0.493265	−	0.358378i
$587$	−18.9177	−	26.0380i	−0.780818	−	1.07470i	−0.995191	−	0.0979515i	$-0.968771\pi$
$587$	−18.9177	−	26.0380i	−0.780818	−	1.07470i	0.214374	−	0.976752i	$-0.431229\pi$
$588$	−22.8308	+	16.5875i	−0.941526	+	0.684058i
$589$	−5.65474	+	7.78308i	−0.232999	+	0.320696i
$590$	39.4434	−	21.7011i	1.62386	−	0.893422i
$591$	−27.8802	+	20.2561i	−1.14684	+	0.833225i
$592$	13.4342	−	41.3462i	0.552141	−	1.69932i
$593$		−	44.6097i		−	1.83190i	−0.401289	−	0.915951i	$-0.631438\pi$
$593$		−	44.6097i		−	1.83190i	0.401289	−	0.915951i	$-0.368562\pi$
$594$	1.55126	−	4.77427i	0.0636488	−	0.195891i
$595$	29.1950	+	16.5734i	1.19688	+	0.679442i
$596$	4.75928	+	14.6476i	0.194948	+	0.599988i
$597$	31.0018	−	10.0731i	1.26882	−	0.412265i
$598$	40.2922	+	29.2740i	1.64767	+	1.19710i
$599$	25.7955			1.05397			0.526987	−	0.849873i	$-0.323321\pi$
$599$	25.7955			1.05397			0.526987	+	0.849873i	$0.323321\pi$
$600$	−4.57747	−	2.90071i	−0.186874	−	0.118421i
$601$			8.41153i			0.343113i	0.985174	+	0.171557i	$0.0548797\pi$
$601$			8.41153i			0.343113i	−0.985174	+	0.171557i	$0.945120\pi$
$602$	5.11040	+	3.71292i	0.208284	+	0.151327i
$603$	38.3586	−	12.4635i	1.56208	−	0.507552i
$604$	10.0918	+	31.0592i	0.410628	+	1.26378i
$605$	−7.66402	+	8.16675i	−0.311587	+	0.332026i
$606$	42.4801	+	13.8026i	1.72564	+	0.560693i
$607$	23.9956			0.973951			0.486976	−	0.873416i	$-0.338100\pi$
$607$	23.9956			0.973951			0.486976	+	0.873416i	$0.338100\pi$
$608$	−8.86532	−	2.88052i	−0.359536	−	0.116820i
$609$	17.6690	+	24.3193i	0.715983	+	0.985466i
$610$	−8.81678	+	9.39512i	−0.356981	+	0.380397i
$611$	−6.52833	−	4.74311i	−0.264108	−	0.191886i
$612$	24.9987	+	1.92420i	1.01051	+	0.0777810i
$613$	−12.9690	−	17.8503i	−0.523813	−	0.720967i	0.462358	−	0.886693i	$-0.347003\pi$
$613$	−12.9690	−	17.8503i	−0.523813	−	0.720967i	−0.986172	+	0.165726i	$0.947003\pi$
$614$	−28.7255	−	20.8703i	−1.15927	−	0.842257i
$615$	28.4195	+	3.58069i	1.14598	+	0.144387i
$616$	3.08527	−	2.24158i	0.124309	−	0.0903158i
$617$	5.61346	−	17.2764i	0.225989	−	0.695523i	−0.772200	−	0.635379i	$-0.780844\pi$
$617$	5.61346	−	17.2764i	0.225989	−	0.695523i	0.998190	−	0.0601444i	$-0.0191561\pi$
$618$	−35.2716			−1.41883
$619$	−0.361074	−	0.117320i	−0.0145128	−	0.00471549i	0.301752	−	0.953387i	$-0.402429\pi$
$619$	−0.361074	−	0.117320i	−0.0145128	−	0.00471549i	−0.316264	+	0.948671i	$0.602429\pi$
$620$	27.6491	−	15.2121i	1.11041	−	0.610932i
$621$	3.06262	+	9.42577i	0.122899	+	0.378243i
$622$	8.61015	+	26.4993i	0.345235	+	1.06253i
$623$	−24.1116	−	17.5181i	−0.966012	−	0.701849i
$624$			30.3312i			1.21422i
$625$	−10.6743	−	22.6066i	−0.426973	−	0.904264i
$626$		−	9.47781i		−	0.378809i
$627$	−4.42186	+	6.08617i	−0.176592	+	0.243058i
$628$	−18.3883	+	5.97471i	−0.733771	+	0.238417i
$629$	15.5543	−	37.7348i	0.620192	−	1.50459i
$630$	47.3844	−	26.0701i	1.88784	−	1.03866i
$631$	−6.50075	+	20.0072i	−0.258791	+	0.796476i	0.734268	+	0.678859i	$0.237525\pi$
$631$	−6.50075	+	20.0072i	−0.258791	+	0.796476i	−0.993059	+	0.117617i	$0.962475\pi$
$632$	−3.20397			−0.127447
$633$	32.5998	+	10.5923i	1.29573	+	0.421007i
$634$	0.285186	+	0.392525i	0.0113262	+	0.0155892i
$635$	−11.1690	−	1.40724i	−0.443230	−	0.0558445i
$636$	−32.2702	+	44.4161i	−1.27960	+	1.76121i
$637$	−10.0310	−	13.8064i	−0.397441	−	0.547030i
$638$	9.11613	+	12.5473i	0.360911	+	0.496751i
$639$	7.55166	−	10.3940i	0.298739	−	0.411179i
$640$	−5.54749	−	5.20599i	−0.219284	−	0.205785i
$641$	−15.2463	−	20.9848i	−0.602194	−	0.828849i	0.393713	−	0.919233i	$-0.371190\pi$
$641$	−15.2463	−	20.9848i	−0.602194	−	0.828849i	−0.995907	+	0.0903846i	$0.971190\pi$
$642$	−42.1876	−	13.7076i	−1.66501	−	0.540996i
$643$	2.88423			0.113743			0.0568715	−	0.998382i	$-0.481887\pi$
$643$	2.88423			0.113743			0.0568715	+	0.998382i	$0.481887\pi$
$644$	18.8172	−	57.9134i	0.741501	−	2.28211i
$645$	−3.68530	−	3.45844i	−0.145109	−	0.136176i
$646$	−8.99222	−	3.70660i	−0.353794	−	0.145834i
$647$	−23.2854	+	7.56588i	−0.915443	+	0.297445i	−0.728596	−	0.684944i	$-0.759827\pi$
$647$	−23.2854	+	7.56588i	−0.915443	+	0.297445i	−0.186847	+	0.982389i	$0.559827\pi$
$648$	1.90566	−	2.62292i	0.0748616	−	0.103038i
$649$		−	25.3474i		−	0.994971i
$650$	−14.1871	+	22.3879i	−0.556463	+	0.878125i
$651$		−	73.1343i		−	2.86636i
$652$	5.97588	+	4.34173i	0.234033	+	0.170035i
$653$	1.97531	+	6.07937i	0.0772997	+	0.237904i	0.982238	−	0.187638i	$-0.0600833\pi$
$653$	1.97531	+	6.07937i	0.0772997	+	0.237904i	−0.904938	+	0.425542i	$0.860083\pi$
$654$	−23.7131	−	72.9814i	−0.927255	−	2.85380i
$655$	4.69985	+	24.5934i	0.183638	+	0.960943i
$656$	21.1225	+	6.86311i	0.824694	+	0.267959i
$657$	−9.83048			−0.383523
$658$	−6.47467	+	19.9270i	−0.252409	+	0.776835i
$659$	21.2942	−	15.4711i	0.829504	−	0.602670i	−0.0899150	−	0.995949i	$-0.528660\pi$
$659$	21.2942	−	15.4711i	0.829504	−	0.602670i	0.919419	+	0.393280i	$0.128660\pi$
$660$	21.6209	−	11.8955i	0.841591	−	0.463030i
$661$	−14.4712	−	10.5140i	−0.562866	−	0.408946i	0.269641	−	0.962961i	$-0.413095\pi$
$661$	−14.4712	−	10.5140i	−0.562866	−	0.408946i	−0.832507	+	0.554015i	$0.813095\pi$
$662$	41.0198	+	56.4590i	1.59428	+	2.19434i
$663$	−2.18540	+	28.3921i	−0.0848737	+	1.10266i
$664$	0.553189	+	0.401915i	0.0214679	+	0.0155973i
$665$	−9.70356	+	1.85437i	−0.376288	+	0.0719094i
$666$	−38.6481	−	53.1945i	−1.49758	−	2.06125i
$667$	−29.1211	−	9.46201i	−1.12757	−	0.366371i
$668$	−6.67308			−0.258189
$669$	19.7004	+	6.40106i	0.761663	+	0.247479i
$670$	46.4454	+	21.8368i	1.79434	+	0.843631i
$671$	2.24170	+	6.89924i	0.0865398	+	0.266342i
$672$	67.3941	−	21.8977i	2.59978	−	0.844721i
$673$	−5.77286	−	4.19423i	−0.222527	−	0.161676i	0.470936	−	0.882167i	$-0.343916\pi$
$673$	−5.77286	−	4.19423i	−0.222527	−	0.161676i	−0.693464	+	0.720492i	$0.743916\pi$
$674$			56.4796i			2.17551i
$675$	−4.90266	+	1.94484i	−0.188704	+	0.0748571i
$676$	−9.90722			−0.381047
$677$	35.3333	+	25.6712i	1.35797	+	0.986623i	0.998571	+	0.0534394i	$0.0170184\pi$
$677$	35.3333	+	25.6712i	1.35797	+	0.986623i	0.359399	+	0.933184i	$0.382982\pi$
$678$	−50.2573	+	16.3296i	−1.93012	+	0.627134i
$679$	0.319224	+	0.982471i	0.0122507	+	0.0377038i
$680$	−2.66087	−	2.91225i	−0.102040	−	0.111680i
$681$	−16.1655	+	49.7522i	−0.619462	+	1.90651i
$682$		−	37.7329i		−	1.44487i
$683$	−12.5795	+	38.7158i	−0.481343	+	1.48142i	0.355866	+	0.934537i	$0.384186\pi$
$683$	−12.5795	+	38.7158i	−0.481343	+	1.48142i	−0.837209	+	0.546884i	$0.815814\pi$
$684$	−5.96911	+	4.33681i	−0.228235	+	0.165822i
$685$	17.4878	−	37.1953i	0.668175	−	1.42116i
$686$	3.08285	−	4.24318i	0.117704	−	0.162005i
$687$	43.9662	−	31.9433i	1.67741	−	1.21871i
$688$	−2.30330	−	3.17023i	−0.0878126	−	0.120864i
$689$	−26.8597	−	19.5147i	−1.02327	−	0.743451i
$690$	−44.0217	+	93.6310i	−1.67588	+	3.56447i
$691$	11.0323	+	15.1846i	0.419687	+	0.577649i	0.965548	−	0.260227i	$-0.0837973\pi$
$691$	11.0323	+	15.1846i	0.419687	+	0.577649i	−0.545861	+	0.837876i	$0.683797\pi$
$692$	0.659928	−	2.03105i	0.0250867	−	0.0772089i
$693$		−	30.4504i		−	1.15672i
$694$	−27.7824	−	9.02705i	−1.05461	−	0.342662i
$695$	13.7952	+	1.73811i	0.523281	+	0.0659304i
$696$	−1.09152	−	3.35936i	−0.0413740	−	0.127336i
$697$	19.2776	+	7.94623i	0.730190	+	0.300985i
$698$	−6.66761	+	9.17718i	−0.252373	+	0.347361i
$699$	−48.1324			−1.82053
$700$	31.3935	+	8.03840i	1.18656	+	0.303823i
$701$	−28.0466			−1.05931			−0.529654	−	0.848214i	$-0.677678\pi$
$701$	−28.0466			−1.05931			−0.529654	+	0.848214i	$0.677678\pi$
$702$	4.52382	+	3.28674i	0.170740	+	0.124050i
$703$	3.71154	+	11.4229i	0.139983	+	0.430824i
$704$	14.3241	−	4.65419i	0.539861	−	0.175411i
$705$	7.13260	−	15.1705i	0.268629	−	0.571355i
$706$	17.8302	−	54.8756i	0.671047	−	2.06527i
$707$	33.0254			1.24205
$708$	14.4278	−	44.4043i	0.542231	−	1.66882i
$709$	−9.85708	−	13.5671i	−0.370190	−	0.509523i	0.582762	−	0.812643i	$-0.301972\pi$
$709$	−9.85708	−	13.5671i	−0.370190	−	0.509523i	−0.952953	+	0.303119i	$0.901972\pi$
$710$	16.0579	−	3.06869i	0.602641	−	0.115166i
$711$	−15.0371	+	20.6968i	−0.563936	+	0.776192i
$712$	2.05847	+	2.83324i	0.0771445	+	0.106180i
$713$	43.7873	+	60.2681i	1.63985	+	2.25706i
$714$	71.8658	−	17.3842i	2.68951	−	0.650587i
$715$	7.19352	+	13.0747i	0.269022	+	0.488968i
$716$	15.7011	−	11.4075i	0.586776	−	0.426318i
$717$	−5.42383	+	16.6928i	−0.202557	+	0.623406i
$718$			4.67274i			0.174385i
$719$	−7.59434	−	2.46755i	−0.283221	−	0.0920241i	0.163962	−	0.986467i	$-0.447573\pi$
$719$	−7.59434	−	2.46755i	−0.283221	−	0.0920241i	−0.447183	+	0.894443i	$0.647573\pi$
$720$	−32.9537	+	6.29752i	−1.22811	+	0.234695i
$721$	−24.8028	+	8.05891i	−0.923703	+	0.300129i
$722$	−32.4098	+	10.5306i	−1.20617	+	0.391908i
$723$	−46.1129	+	63.4690i	−1.71496	+	2.36044i
$724$		−	26.0266i		−	0.967271i
$725$	4.04202	−	15.7859i	0.150117	−	0.586272i
$726$			24.6666i			0.915463i
$727$	−11.4378	+	15.7428i	−0.424204	+	0.583867i	−0.966611	−	0.256249i	$-0.917513\pi$
$727$	−11.4378	+	15.7428i	−0.424204	+	0.583867i	0.542406	+	0.840116i	$0.317513\pi$
$728$	1.31270	+	4.04006i	0.0486517	+	0.149735i
$729$	−10.4767	−	32.2441i	−0.388027	−	1.19422i
$730$	−9.12160	−	8.56009i	−0.337605	−	0.316823i
$731$	−1.92763	−	3.13350i	−0.0712960	−	0.115897i
$732$			13.3623i			0.493885i
$733$	17.5658	+	5.70747i	0.648807	+	0.210810i	0.614888	−	0.788615i	$-0.289201\pi$
$733$	17.5658	+	5.70747i	0.648807	+	0.210810i	0.0339188	+	0.999425i	$0.489201\pi$
$734$	−5.40302	−	7.43661i	−0.199429	−	0.274490i
$735$	24.2604	−	25.8518i	0.894858	−	0.953557i
$736$	−42.4271	+	58.3958i	−1.56388	+	2.15250i
$737$	23.3778	−	16.9850i	0.861132	−	0.625649i
$738$	27.1754	−	19.7441i	1.00034	−	0.726791i
$739$	14.5384	+	10.5628i	0.534805	+	0.388559i	0.822152	−	0.569268i	$-0.192773\pi$
$739$	14.5384	+	10.5628i	0.534805	+	0.388559i	−0.287347	+	0.957827i	$0.592773\pi$
$740$	4.92506	−	39.0895i	0.181049	−	1.43696i
$741$	−4.92551	−	6.77939i	−0.180943	−	0.249047i
$742$	−26.6389	+	81.9861i	−0.977945	+	3.00981i
$743$	−2.50059			−0.0917378			−0.0458689	−	0.998947i	$-0.514606\pi$
$743$	−2.50059			−0.0917378			−0.0458689	+	0.998947i	$0.514606\pi$
$744$	−2.65559	+	8.17307i	−0.0973587	+	0.299639i
$745$	−9.32671	−	16.9520i	−0.341704	−	0.621072i
$746$	18.1044	+	55.7195i	0.662848	+	2.04004i
$747$	5.19255	−	1.68716i	0.189985	−	0.0617300i
$748$	17.4598	−	4.22349i	0.638394	−	0.154426i
$749$	−32.7981			−1.19841
$750$	−51.2144	−	20.2186i	−1.87009	−	0.738279i
$751$			9.21941i			0.336421i	0.985751	+	0.168210i	$0.0537988\pi$
$751$			9.21941i			0.336421i	−0.985751	+	0.168210i	$0.946201\pi$
$752$	7.63993	−	10.5155i	0.278599	−	0.383459i
$753$	3.02605	+	9.31323i	0.110275	+	0.339393i
$754$	−16.4303	+	5.33851i	−0.598355	+	0.194417i
$755$	−19.7767	−	35.9456i	−0.719747	−	1.30819i
$756$	2.11270	−	6.50223i	0.0768383	−	0.236484i
$757$			14.6106i			0.531033i	0.964106	+	0.265517i	$0.0855425\pi$
$757$			14.6106i			0.531033i	−0.964106	+	0.265517i	$0.914458\pi$
$758$	−12.4893	+	38.4381i	−0.453631	+	1.39613i
$759$	34.2406	+	47.1281i	1.24285	+	1.71064i
$760$	1.15175	+	0.145114i	0.0417783	+	0.00526382i
$761$	−3.30469	−	2.40100i	−0.119795	−	0.0870362i	0.526275	−	0.850315i	$-0.323588\pi$
$761$	−3.30469	−	2.40100i	−0.119795	−	0.0870362i	−0.646070	+	0.763279i	$0.723588\pi$
$762$	−20.0585	+	14.5733i	−0.726641	+	0.527936i
$763$	−33.3498	−	45.9021i	−1.20734	−	1.66177i
$764$	−10.4953	−	7.62526i	−0.379706	−	0.275872i
$765$	−31.3006	+	3.52056i	−1.13168	+	0.127286i
$766$	−34.1396	+	24.8039i	−1.23352	+	0.896202i
$767$	26.8525	+	8.72492i	0.969589	+	0.315039i
$768$	−47.9283			−1.72946
$769$	−8.68247	+	26.7219i	−0.313098	+	0.963616i	0.663432	+	0.748236i	$0.269099\pi$
$769$	−8.68247	+	26.7219i	−0.313098	+	0.963616i	−0.976530	+	0.215380i	$0.930901\pi$
$770$	26.5153	−	28.2546i	0.955547	−	1.01823i
$771$	−4.56426	+	1.48302i	−0.164378	+	0.0534096i

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.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14277 + 1.57289i) q^{2} +(-0.782761 - 2.40909i) q^{3} +(-0.550027 - 1.69281i) q^{4} +(1.07788 + 1.95913i) q^{5} +(4.68376 + 1.52185i) q^{6} +3.64131 q^{7} +(-0.406932 - 0.132220i) q^{8} +(-2.76396 + 2.00813i) q^{9} +(-4.31327 - 0.543447i) q^{10} +(-1.43874 + 1.98025i) q^{11} +(-3.64759 + 2.65013i) q^{12} +(-1.60261 - 2.20580i) q^{13} +(-4.16119 + 5.72739i) q^{14} +(3.87599 - 4.13024i) q^{15} +(3.55298 - 2.58139i) q^{16} +(3.51182 - 2.16036i) q^{17} -6.64225i q^{18} +(-0.374938 + 1.15394i) q^{19} +(2.72356 - 2.90222i) q^{20} +(-2.85028 - 8.77225i) q^{21} +(-1.47057 - 4.52595i) q^{22} +(7.60100 + 5.52245i) q^{23} +1.08383i q^{24} +(-2.67635 + 4.22341i) q^{25} +5.30091 q^{26} +(0.853404 + 0.620035i) q^{27} +(-2.00282 - 6.16404i) q^{28} +(-3.09952 + 1.00709i) q^{29} +(2.06705 + 10.8164i) q^{30} +(7.54089 + 2.45019i) q^{31} +7.68265i q^{32} +(5.89679 + 1.91598i) q^{33} +(-0.615200 + 7.99251i) q^{34} +(3.92490 + 7.13379i) q^{35} +(4.91963 + 3.57432i) q^{36} +(8.00851 - 5.81853i) q^{37} +(-1.38656 - 1.90843i) q^{38} +(-4.05952 + 5.58744i) q^{39} +(-0.179588 - 0.939748i) q^{40} +(2.97251 + 4.09130i) q^{41} +(17.0550 + 5.54152i) q^{42} -0.892274i q^{43} +(4.14352 + 1.34631i) q^{44} +(-6.91340 - 3.25041i) q^{45} +(-17.3725 + 5.64465i) q^{46} +(2.81477 - 0.914573i) q^{47} +(-8.99993 - 6.53883i) q^{48} +6.25914 q^{49} +(-3.58451 - 9.03601i) q^{50} +(-7.95341 - 6.76924i) q^{51} +(-2.85252 + 3.92616i) q^{52} +(11.5809 - 3.76285i) q^{53} +(-1.95050 + 0.633754i) q^{54} +(-5.43034 - 0.684192i) q^{55} +(-1.48176 - 0.481455i) q^{56} +3.07344 q^{57} +(1.95800 - 6.02609i) q^{58} +(-8.37777 + 6.08680i) q^{59} +(-9.12360 - 4.28957i) q^{60} +(1.74201 - 2.39767i) q^{61} +(-12.4714 + 9.06101i) q^{62} +(-10.0644 + 7.31223i) q^{63} +(-4.97803 - 3.61675i) q^{64} +(2.59402 - 5.51730i) q^{65} +(-9.75233 + 7.08548i) q^{66} +(-11.2277 - 3.64809i) q^{67} +(-5.58866 - 4.75658i) q^{68} +(7.35432 - 22.6343i) q^{69} +(-15.7059 - 1.97886i) q^{70} +(-3.57649 + 1.16207i) q^{71} +(1.39026 - 0.451722i) q^{72} +(2.32787 + 1.69130i) q^{73} +19.2458i q^{74} +(12.2695 + 3.14165i) q^{75} +2.15963 q^{76} +(-5.23888 + 7.21070i) q^{77} +(-4.14934 - 12.7704i) q^{78} +(7.12162 - 2.31396i) q^{79} +(8.88695 + 4.17830i) q^{80} +(-2.34150 + 7.20641i) q^{81} -9.83208 q^{82} +(-1.51987 - 0.493836i) q^{83} +(-13.2820 + 9.64994i) q^{84} +(8.01773 + 4.55148i) q^{85} +(1.40345 + 1.01967i) q^{86} +(4.85237 + 6.67871i) q^{87} +(0.847296 - 0.615597i) q^{88} +(-6.62169 - 4.81094i) q^{89} +(13.0130 - 7.15955i) q^{90} +(-5.83559 - 8.03200i) q^{91} +(5.16770 - 15.9045i) q^{92} -20.0846i q^{93} +(-1.77811 + 5.47248i) q^{94} +(-2.66485 + 0.509259i) q^{95} +(18.5082 - 6.01368i) q^{96} +(0.0876674 + 0.269813i) q^{97} +(-7.15278 + 9.84496i) q^{98} -8.36249i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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