LMFDB - Embedded newform 425.2.q.a.84.10

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			84.10
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.10

$q$-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} +(1.57129 + 3.81196i) 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} +(-7.79144 - 1.88473i) 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} +(5.77444 - 7.18720i) 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	$0.161055\pi$
$3$	0.782761	+	2.40909i	0.451927	+	1.39089i	−0.422777	+	0.906234i	$0.638945\pi$
$4$	−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	$-0.741574\pi$
$7$	−3.64131			−1.37629			−0.688143	+	0.725575i	$0.741574\pi$
$8$	−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	−0.535024	−	0.844837i	$-0.679697\pi$
$11$	1.43874	−	1.98025i	0.433795	−	0.597068i	0.968819	+	0.247769i	$0.0796974\pi$
$12$	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
$17$	1.57129	+	3.81196i	0.381094	+	0.924536i
$17$	1.57129	+	3.81196i	0.381094	+	0.924536i
$18$		−	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	$-0.864510\pi$
$23$	−7.60100	−	5.52245i	−1.58492	−	1.15151i	−0.674150	−	0.738594i	$-0.735490\pi$
$24$		−	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	−0.00674718	−	0.999977i	$-0.502148\pi$
$29$	3.09952	−	1.00709i	0.575566	−	0.187013i	0.582313	+	0.812964i	$0.302148\pi$
$30$	2.06705	+	10.8164i	0.377389	+	1.97480i
$31$	−7.54089	−	2.45019i	−1.35438	−	0.440066i	−0.460220	−	0.887805i	$-0.652230\pi$
$31$	−7.54089	−	2.45019i	−1.35438	−	0.440066i	−0.894165	+	0.447739i	$0.852230\pi$
$32$			7.68265i			1.35811i
$33$	5.89679	+	1.91598i	1.02650	+	0.333530i
$34$	−7.79144	−	1.88473i	−1.33622	−	0.323229i
$35$	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	$0.602549\pi$
$37$	−8.00851	+	5.81853i	−1.31659	+	0.956560i	−0.999968	+	0.00800840i	$0.997451\pi$
$38$	−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	0.511151	−	0.859491i	$-0.329219\pi$
$41$	−2.97251	−	4.09130i	−0.464227	−	0.638954i	−0.975379	+	0.220537i	$0.929219\pi$
$42$	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	−0.905843	−	0.423613i	$-0.860762\pi$
$61$	−1.74201	+	2.39767i	−0.223042	+	0.306991i	0.682801	+	0.730604i	$0.260762\pi$
$62$	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	−0.0889996	−	0.996032i	$-0.528367\pi$
$71$	3.57649	−	1.16207i	0.424451	−	0.137912i	0.513450	+	0.858119i	$0.328367\pi$
$72$	1.39026	−	0.451722i	0.163843	−	0.0532359i
$73$	−2.32787	−	1.69130i	−0.272457	−	0.197951i	0.443164	−	0.896441i	$-0.353856\pi$
$73$	−2.32787	−	1.69130i	−0.272457	−	0.197951i	−0.715620	+	0.698489i	$0.753856\pi$
$74$		−	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	−0.680885	−	0.732390i	$-0.738405\pi$
$79$	−7.12162	+	2.31396i	−0.801245	+	0.260340i	−0.120360	+	0.992730i	$0.538405\pi$
$80$	−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
$85$	5.77444	−	7.18720i	0.626326	−	0.779561i
$86$	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	0.946507	−	0.322683i	$-0.104585\pi$
$97$	−0.0876674	−	0.269813i	−0.00890128	−	0.0273953i	−0.955409	+	0.295287i	$0.904585\pi$
$98$	−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	$0.350985\pi$
$102$	−1.55834	−	20.2456i	−0.154299	−	2.00461i
$103$	−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	$-0.356614\pi$
$107$	9.00721			0.870760			0.435380	+	0.900247i	$0.356614\pi$
$108$	−0.580204	+	1.78568i	−0.0558302	+	0.171828i
$109$	9.15874	+	12.6059i	0.877248	+	1.20743i	0.977175	+	0.212434i	$0.0681391\pi$
$109$	9.15874	+	12.6059i	0.877248	+	1.20743i	−0.0999270	+	0.994995i	$0.531861\pi$
$110$	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	−0.0991186	−	0.995076i	$-0.531602\pi$
$113$	8.68084	−	6.30700i	0.816625	−	0.593313i	0.915744	+	0.401763i	$0.131602\pi$
$114$	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
$119$	−5.72156	−	13.8805i	−0.524495	−	1.27243i
$120$	−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	−0.195703	−	0.980663i	$-0.562699\pi$
$131$	−10.6495	−	3.46022i	−0.930449	−	0.302321i	−0.734746	+	0.678342i	$0.762699\pi$
$132$		−	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
$136$	−0.135391	−	1.75896i	−0.0116097	−	0.150830i
$137$	−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	−0.935384	−	0.353634i	$-0.884946\pi$
$139$	−3.65495	+	5.03060i	−0.310009	+	0.426690i	0.625375	+	0.780324i	$0.284946\pi$
$140$	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
$153$	−11.9979	−	7.38073i	−0.969973	−	0.596697i
$154$	−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	−0.448485	−	0.893790i	$-0.648036\pi$
$163$	3.35738	−	2.43928i	0.262970	−	0.191059i	0.711455	+	0.702731i	$0.248036\pi$
$164$	−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	−0.985822	−	0.167792i	$-0.946336\pi$
$167$	−1.15853	+	3.56559i	−0.0896497	+	0.275914i	0.896173	+	0.443705i	$0.146336\pi$
$168$			3.94657i			0.304485i
$169$	1.72002	−	5.29367i	0.132309	−	0.407205i
$170$	4.70581	+	17.2959i	0.360919	+	1.32654i
$171$	−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	0.550274	−	0.834984i	$-0.314523\pi$
$173$	−0.970668	−	0.705231i	−0.0737985	−	0.0536177i	−0.624073	+	0.781366i	$0.714523\pi$
$174$	−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	−0.257432	−	0.966297i	$-0.582876\pi$
$181$	−13.9066	−	4.51854i	−1.03367	−	0.335861i	−0.776241	+	0.630436i	$0.782876\pi$
$182$	−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
$187$	9.80931	+	2.37285i	0.717328	+	0.173520i
$188$	−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	$-0.274512\pi$
$193$	18.0772			1.30123			0.650614	+	0.759409i	$0.274512\pi$
$194$	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	$0.0610527\pi$
$197$	4.20410	+	12.9389i	0.299530	+	0.921857i	−0.682133	+	0.731229i	$0.738947\pi$
$198$	−13.1533	−	9.55644i	−0.934765	−	0.679146i
$199$		−	12.8687i		−	0.912237i	−0.889919	−	0.456118i	$-0.849239\pi$
$199$		−	12.8687i		−	0.912237i	0.889919	−	0.456118i	$-0.150761\pi$
$200$	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
$204$	15.8336	+	9.74034i	1.10857	+	0.681960i
$205$	−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	−0.442110	−	0.896961i	$-0.645770\pi$
$211$	7.95391	−	10.9476i	0.547570	−	0.753665i	0.989680	+	0.143295i	$0.0457699\pi$
$212$	−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
$221$	5.89026	−	9.57503i	0.396222	−	0.644087i
$222$	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	0.982495	−	0.186291i	$-0.0596466\pi$
$227$	16.7077	+	12.1389i	1.10893	+	0.805684i	0.126435	+	0.991975i	$0.459647\pi$
$228$	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	$0.313850\pi$
$233$	−5.87182	+	18.0716i	−0.384676	+	1.18391i	−0.936715	+	0.350093i	$0.886150\pi$
$234$	−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
$238$	28.3710	+	6.86290i	1.83902	+	0.444855i
$239$	−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	$0.277545\pi$
$241$	18.2044	+	25.0562i	1.17265	+	1.61401i	0.529299	+	0.848435i	$0.322455\pi$
$242$	−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
$255$	21.8346	+	8.28531i	1.36734	+	0.518846i
$256$	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	0.148252	−	0.988950i	$-0.452635\pi$
$269$	−5.13522	−	1.66854i	−0.313100	−	0.101732i	−0.461352	+	0.887217i	$0.652635\pi$
$270$	−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	$0.716829\pi$
$272$	15.4229	+	9.48769i	0.935151	+	0.575275i
$273$	−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	0.636958	−	0.770898i	$-0.280192\pi$
$277$	1.67467	+	1.21672i	0.100621	+	0.0731054i	−0.536337	+	0.844004i	$0.680192\pi$
$278$	−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	$-0.778777\pi$
$283$	3.86447	−	11.8936i	0.229719	−	0.707003i	0.997778	−	0.0666239i	$-0.0212228\pi$
$284$	−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
$289$	−12.0621	+	11.9794i	−0.709534	+	0.704671i
$290$	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
$306$	25.3200	−	10.4369i	1.44745	−	0.596639i
$307$			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	−0.978054	−	0.208349i	$-0.933191\pi$
$311$	−8.42375	+	11.5943i	−0.477667	+	0.657452i	0.500387	+	0.865802i	$0.333191\pi$
$312$	−2.39072	+	1.73696i	−0.135348	+	0.0983359i
$313$	3.94388	−	2.86540i	0.222921	−	0.161962i	−0.470719	−	0.882283i	$-0.656006\pi$
$313$	3.94388	−	2.86540i	0.222921	−	0.161962i	0.693641	+	0.720321i	$0.256006\pi$
$314$	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	−0.953199	−	0.302344i	$-0.902231\pi$
$317$	−0.0771171	+	0.237342i	−0.00433133	+	0.0133305i	0.948867	+	0.315675i	$0.102231\pi$
$318$	−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
$323$	−4.98791	+	0.383930i	−0.277535	+	0.0213624i
$324$	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	−0.999560	−	0.0296487i	$-0.990561\pi$
$337$	−23.5022	+	17.0753i	−1.28024	+	0.930152i	−0.280684	+	0.959800i	$0.590561\pi$
$338$	6.36078	+	8.75487i	0.345981	+	0.476202i
$339$	21.9892	+	15.9761i	1.19429	+	0.867701i
$340$	−15.3426	−	5.82187i	−0.832072	−	0.315735i
$341$	−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	$-0.967863\pi$
$347$	−4.64306	−	14.2899i	−0.249253	−	0.767120i	0.745655	−	0.666332i	$-0.232137\pi$
$348$	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	−0.905655	−	0.424015i	$-0.860620\pi$
$367$	1.46103	−	4.49658i	0.0762650	−	0.234720i	0.981920	+	0.189295i	$0.0606204\pi$
$368$	−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	−0.769062	−	0.639175i	$-0.779276\pi$
$379$	−19.7706	+	6.42386i	−1.01555	+	0.329972i	−0.246487	+	0.969146i	$0.579276\pi$
$380$	−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
$391$	9.10797	−	37.6521i	0.460610	−	1.90415i
$392$	−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	$-0.773778\pi$
$397$	−10.5242	−	32.3903i	−0.528197	−	1.62562i	0.229710	−	0.973259i	$-0.426222\pi$
$398$	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	$-0.768590\pi$
$401$		−	26.6184i		−	1.32926i	0.747173	−	0.664629i	$-0.231410\pi$
$402$	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
$408$	4.13153	−	1.70302i	0.204541	−	0.0843120i
$409$	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	0.403281	−	0.915076i	$-0.367870\pi$
$419$	3.92349	+	1.27482i	0.191675	+	0.0622790i	−0.211607	+	0.977355i	$0.567870\pi$
$420$	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
$425$	−20.3048	−	3.56592i	−0.984927	−	0.172973i
$426$	−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	0.701389	−	0.712779i	$-0.252564\pi$
$431$	17.6436	+	5.73276i	0.849864	+	0.276138i	0.148475	+	0.988916i	$0.452564\pi$
$432$	−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	−0.833452	−	0.552592i	$-0.813639\pi$
$439$	−1.05506	+	1.45217i	−0.0503553	+	0.0693082i	0.783097	+	0.621900i	$0.213639\pi$
$440$	2.11931	+	0.996420i	0.101034	+	0.0475025i
$441$	−17.3000	+	12.5692i	−0.823809	+	0.598533i
$442$	8.32927	+	20.2068i	0.396183	+	0.961141i
$443$			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	$-0.847817\pi$
$449$		−	19.4983i		−	0.920181i	0.887872	−	0.460091i	$-0.152183\pi$
$450$	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
$459$	1.02260	−	4.22740i	0.0477308	−	0.197318i
$460$	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	−0.0300454	−	0.999549i	$-0.509565\pi$
$479$	11.6689	−	3.79147i	0.533167	−	0.173237i	0.563213	+	0.826312i	$0.309565\pi$
$480$	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	−0.725103	−	0.688640i	$-0.758208\pi$
$487$	−6.49323	+	4.71761i	−0.294236	+	0.213775i	0.430867	+	0.902416i	$0.358208\pi$
$488$	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	$0.0376899\pi$
$499$			5.27764i			0.236260i	−0.992998	+	0.118130i	$0.962310\pi$
$500$	−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	$0.113311\pi$
$503$	8.60899	+	26.4957i	0.383856	+	1.18139i	−0.553451	+	0.832882i	$0.686689\pi$
$504$	−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	$0.397405\pi$
$510$	−37.9839	+	24.8753i	−1.68196	+	1.10150i
$511$	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	0.663059	−	0.748567i	$-0.269258\pi$
$521$	37.4219	−	12.1591i	1.63948	−	0.532700i	0.976423	+	0.215867i	$0.0692576\pi$
$522$	−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
$527$	−2.50894	−	32.5955i	−0.109291	−	1.41988i
$528$	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	0.420288	−	0.907391i	$-0.361929\pi$
$541$	−13.3176	−	18.3301i	−0.572568	−	0.788073i	−0.992856	+	0.119318i	$0.961929\pi$
$542$	−33.1306	−	10.7648i	−1.42308	−	0.462387i
$543$		−	37.0393i		−	1.58951i
$544$	−29.2859	+	12.0717i	−1.25562	+	0.517569i
$545$	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	$-0.962903\pi$
$547$	−6.03495	−	18.5737i	−0.258036	−	0.794152i	0.735181	−	0.677871i	$-0.237097\pi$
$548$	−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
$561$	1.96193	+	25.4889i	0.0828328	+	1.07614i
$562$	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	−0.0470452	−	0.998893i	$-0.514980\pi$
$571$	11.9963	−	3.89783i	0.502029	−	0.163119i	0.549074	+	0.835774i	$0.314980\pi$
$572$	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	$-0.0524669\pi$
$578$	−5.05810	−	32.6621i	−0.210389	−	1.35856i
$579$	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
$595$	−21.0265	+	26.1708i	−0.862004	+	1.07290i
$596$	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	$-0.945120\pi$
$601$		−	8.41153i		−	0.343113i	0.985174	−	0.171557i	$-0.0548797\pi$
$602$	−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	$-0.661900\pi$
$607$	−23.9956			−0.973951			−0.486976	+	0.873416i	$0.661900\pi$
$608$	−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
$612$	−5.89499	+	24.3697i	−0.238291	+	0.985088i
$613$	−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	$0.219156\pi$
$617$	−5.61346	+	17.2764i	−0.225989	+	0.695523i	−0.998190	+	0.0601444i	$0.980844\pi$
$618$	35.2716			1.41883
$619$	0.361074	+	0.117320i	0.0145128	+	0.00471549i	0.316264	−	0.948671i	$-0.397571\pi$
$619$	0.361074	+	0.117320i	0.0145128	+	0.00471549i	−0.301752	+	0.953387i	$0.597571\pi$
$620$	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
$629$	−34.7637	−	21.3855i	−1.38612	−	0.852697i
$630$	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	0.995907	−	0.0903846i	$-0.0288096\pi$
$641$	15.2463	+	20.9848i	0.602194	+	0.828849i	−0.393713	+	0.919233i	$0.628810\pi$
$642$	−42.1876	−	13.7076i	−1.66501	−	0.540996i
$643$	−2.88423			−0.113743			−0.0568715	−	0.998382i	$-0.518113\pi$
$643$	−2.88423			−0.113743			−0.0568715	+	0.998382i	$0.518113\pi$
$644$	18.8172	−	57.9134i	0.741501	−	2.28211i
$645$	−3.68530	−	3.45844i	−0.145109	−	0.136176i
$646$	5.09618	−	8.28420i	0.200506	−	0.325937i
$647$	−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	0.904938	−	0.425542i	$-0.139917\pi$
$653$	−1.97531	−	6.07937i	−0.0772997	−	0.237904i	−0.982238	+	0.187638i	$0.939917\pi$
$654$	−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
$663$	27.6778	+	6.69520i	1.07492	+	0.260020i
$664$	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	0.693464	−	0.720492i	$-0.256084\pi$
$673$	5.77286	+	4.19423i	0.222527	+	0.161676i	−0.470936	+	0.882167i	$0.656084\pi$
$674$		−	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	$-0.982982\pi$
$677$	−35.3333	−	25.6712i	−1.35797	−	0.986623i	−0.359399	−	0.933184i	$-0.617018\pi$
$678$	−50.2573	+	16.3296i	−1.93012	+	0.627134i
$679$	0.319224	+	0.982471i	0.0122507	+	0.0377038i
$680$	−3.30010	+	2.16120i	−0.126553	+	0.0828783i
$681$	−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	$-0.615814\pi$
$683$	12.5795	−	38.7158i	0.481343	−	1.48142i	0.837209	−	0.546884i	$-0.184186\pi$
$684$	−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	0.545861	−	0.837876i	$-0.316203\pi$
$691$	−11.0323	−	15.1846i	−0.419687	−	0.577649i	−0.965548	+	0.260227i	$0.916203\pi$
$692$	−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
$697$	10.9252	−	17.7597i	0.413822	−	0.672697i
$698$	−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	0.952953	−	0.303119i	$-0.0980281\pi$
$709$	9.85708	+	13.5671i	0.370190	+	0.509523i	−0.582762	+	0.812643i	$0.698028\pi$
$710$	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
$714$	5.67441	+	73.7204i	0.212359	+	2.75892i
$715$	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	0.447183	−	0.894443i	$-0.352427\pi$
$719$	7.59434	+	2.46755i	0.283221	+	0.0920241i	−0.163962	+	0.986467i	$0.552427\pi$
$720$	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
$731$	3.40131	−	1.40202i	0.125802	−	0.0518557i
$732$			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	$-0.485394\pi$
$743$	2.50059			0.0917378			0.0458689	+	0.998947i	$0.485394\pi$
$744$	−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
$748$	−1.37860	−	17.9104i	−0.0504066	−	0.654869i
$749$	−32.7981			−1.19841
$750$	−51.2144	−	20.2186i	−1.87009	−	0.738279i
$751$		−	9.21941i		−	0.336421i	−0.985751	−	0.168210i	$-0.946201\pi$
$751$		−	9.21941i		−	0.336421i	0.985751	−	0.168210i	$-0.0537988\pi$
$752$	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
$765$	−1.52747	+	31.4609i	−0.0552259	+	1.13747i
$766$	−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} +(1.57129 + 3.81196i) 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} +(-7.79144 - 1.88473i) 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} +(5.77444 - 7.18720i) 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

Groups

Database

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