LMFDB - Embedded newform 484.2.g.j.475.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(215,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("484.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.g (of order $10$, degree $4$, not 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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			475.2
Root			$-0.544389 - 1.30524i$ of defining polynomial
Character	$\chi$	$=$	484.475
Dual form			484.2.g.j.215.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.326779 - 1.37594i) q^{2} +(-0.435358 - 0.599219i) q^{3} +(-1.78643 + 0.899257i) q^{4} +(-0.416683 - 1.28242i) q^{5} +(-0.682225 + 0.794840i) q^{6} +(-1.31738 - 0.957131i) q^{7} +(1.82109 + 2.16417i) q^{8} +(0.757524 - 2.33142i) q^{9} +(-1.62837 + 0.992398i) q^{10} +(1.31659 + 0.678965i) q^{12} +(-3.38313 - 1.09925i) q^{13} +(-0.886465 + 2.12541i) q^{14} +(-0.587043 + 0.807995i) q^{15} +(2.38267 - 3.21292i) q^{16} +(-0.0665412 + 0.0216205i) q^{17} +(-3.45544 - 0.280450i) q^{18} +(-6.43293 + 4.67380i) q^{19} +(1.89760 + 1.91625i) q^{20} +1.20609i q^{21} +5.30988i q^{23} +(0.503982 - 2.03342i) q^{24} +(2.57411 - 1.87020i) q^{25} +(-0.406962 + 5.01420i) q^{26} +(-3.84010 + 1.24772i) q^{27} +(3.21411 + 0.525187i) q^{28} +(-2.31370 + 3.18453i) q^{29} +(1.30359 + 0.543701i) q^{30} +(-3.51309 - 1.14147i) q^{31} +(-5.19940 - 2.22850i) q^{32} +(0.0514928 + 0.0844916i) q^{34} +(-0.678513 + 2.08825i) q^{35} +(0.743282 + 4.84613i) q^{36} +(5.56491 + 4.04314i) q^{37} +(8.53302 + 7.32404i) q^{38} +(0.814185 + 2.50580i) q^{39} +(2.01655 - 3.23717i) q^{40} +(-3.40107 - 4.68117i) q^{41} +(1.65951 - 0.394126i) q^{42} +1.89516 q^{43} -3.30550 q^{45} +(7.30608 - 1.73516i) q^{46} +(-5.76344 - 7.93270i) q^{47} +(-2.96256 - 0.0289704i) q^{48} +(-1.34373 - 4.13559i) q^{49} +(-3.41446 - 2.93069i) q^{50} +(0.0419247 + 0.0304601i) q^{51} +(7.03224 - 1.07858i) q^{52} +(-1.20135 + 3.69738i) q^{53} +(2.97166 + 4.87602i) q^{54} +(-0.327678 - 4.59405i) q^{56} +(5.60126 + 1.81996i) q^{57} +(5.13780 + 2.14287i) q^{58} +(2.85758 - 3.93312i) q^{59} +(0.322116 - 1.97133i) q^{60} +(1.28015 - 0.415944i) q^{61} +(-0.422596 + 5.20682i) q^{62} +(-3.22942 + 2.34631i) q^{63} +(-1.36723 + 7.88230i) q^{64} +4.79662i q^{65} -4.91303i q^{67} +(0.0994288 - 0.0984612i) q^{68} +(3.18178 - 2.31170i) q^{69} +(3.09503 + 0.251199i) q^{70} +(-6.63416 + 2.15557i) q^{71} +(6.42510 - 2.60633i) q^{72} +(5.94967 - 8.18902i) q^{73} +(3.74464 - 8.97821i) q^{74} +(-2.24132 - 0.728250i) q^{75} +(7.28904 - 14.1343i) q^{76} +(3.18178 - 1.93911i) q^{78} +(-1.85551 + 5.71067i) q^{79} +(-5.11313 - 1.71681i) q^{80} +(-3.53019 - 2.56484i) q^{81} +(-5.32962 + 6.20939i) q^{82} +(-1.11615 - 3.43515i) q^{83} +(-1.08459 - 2.15460i) q^{84} +(0.0554531 + 0.0763247i) q^{85} +(-0.619298 - 2.60763i) q^{86} +2.91552 q^{87} -5.39711 q^{89} +(1.08017 + 4.54818i) q^{90} +(3.40474 + 4.68622i) q^{91} +(-4.77495 - 9.48573i) q^{92} +(0.845462 + 2.60206i) q^{93} +(-9.03156 + 10.5224i) q^{94} +(8.67425 + 6.30221i) q^{95} +(0.928241 + 4.08578i) q^{96} +(2.26393 - 6.96767i) q^{97} +(-5.25122 + 3.20032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - q^{4} + 4 q^{5} - 10 q^{6} + 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} + 10 q^{17} + 15 q^{18} - 24 q^{20} - 40 q^{24} - 4 q^{25} + 16 q^{26} + 30 q^{28} - 40 q^{29} - 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q + 5 * q^2 - q^4 + 4 * q^5 - 10 * q^6 + 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 + 10 * q^17 + 15 * q^18 - 24 * q^20 - 40 * q^24 - 4 * q^25 + 16 * q^26 + 30 * q^28 - 40 * q^29 - 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 + 50 * q^41 + 24 * q^42 + 40 * q^45 + 40 * q^46 - q^48 + 16 * q^49 - 25 * q^50 + 20 * q^52 - 12 * q^53 - 12 * q^56 + 50 * q^57 - 48 * q^60 - 20 * q^61 + 30 * q^62 - 37 * q^64 - 35 * q^68 + 4 * q^69 + 22 * q^70 + 10 * q^72 + 30 * q^73 - 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 + 10 * q^84 - 60 * q^85 + 46 * q^86 - 36 * q^89 + 40 * q^90 - 54 * q^92 + 2 * q^93 - 60 * q^94 + 55 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.326779	−	1.37594i	−0.231068	−	0.972938i
$2$	−0.326779	−	1.37594i	−0.231068	−	0.972938i
$3$	−0.435358	−	0.599219i	−0.251354	−	0.345959i	0.664631	−	0.747172i	$-0.268589\pi$
$3$	−0.435358	−	0.599219i	−0.251354	−	0.345959i	−0.915985	+	0.401213i	$0.868589\pi$
$4$	−1.78643	+	0.899257i	−0.893216	+	0.449629i
$5$	−0.416683	−	1.28242i	−0.186346	−	0.573515i	0.813623	−	0.581393i	$-0.197492\pi$
$5$	−0.416683	−	1.28242i	−0.186346	−	0.573515i	−0.999969	+	0.00787847i	$0.997492\pi$
$6$	−0.682225	+	0.794840i	−0.278517	+	0.324492i
$7$	−1.31738	−	0.957131i	−0.497922	−	0.361762i	0.310301	−	0.950638i	$-0.399570\pi$
$7$	−1.31738	−	0.957131i	−0.497922	−	0.361762i	−0.808223	+	0.588877i	$0.799570\pi$
$8$	1.82109	+	2.16417i	0.643854	+	0.765148i
$9$	0.757524	−	2.33142i	0.252508	−	0.777140i
$10$	−1.62837	+	0.992398i	−0.514936	+	0.313824i
$11$		0			0
$11$		0			0
$12$	1.31659	+	0.678965i	0.380067	+	0.196000i
$13$	−3.38313	−	1.09925i	−0.938312	−	0.304876i	−0.200354	−	0.979723i	$-0.564209\pi$
$13$	−3.38313	−	1.09925i	−0.938312	−	0.304876i	−0.737957	+	0.674848i	$0.764209\pi$
$14$	−0.886465	+	2.12541i	−0.236918	+	0.568039i
$15$	−0.587043	+	0.807995i	−0.151574	+	0.208624i
$16$	2.38267	−	3.21292i	0.595668	−	0.803231i
$17$	−0.0665412	+	0.0216205i	−0.0161386	+	0.00524375i	−0.317075	−	0.948400i	$-0.602701\pi$
$17$	−0.0665412	+	0.0216205i	−0.0161386	+	0.00524375i	0.300937	+	0.953644i	$0.402701\pi$
$18$	−3.45544	−	0.280450i	−0.814455	−	0.0661028i
$19$	−6.43293	+	4.67380i	−1.47582	+	1.07224i	−0.496940	+	0.867785i	$0.665543\pi$
$19$	−6.43293	+	4.67380i	−1.47582	+	1.07224i	−0.978875	+	0.204458i	$0.934457\pi$
$20$	1.89760	+	1.91625i	0.424316	+	0.428486i
$21$			1.20609i			0.263191i
$22$		0			0
$23$			5.30988i			1.10719i	0.832787	+	0.553593i	$0.186744\pi$
$23$			5.30988i			1.10719i	−0.832787	+	0.553593i	$0.813256\pi$
$24$	0.503982	−	2.03342i	0.102875	−	0.415071i
$25$	2.57411	−	1.87020i	0.514823	−	0.374041i
$26$	−0.406962	+	5.01420i	−0.0798119	+	0.983366i
$27$	−3.84010	+	1.24772i	−0.739027	+	0.240125i
$28$	3.21411	+	0.525187i	0.607410	+	0.0992510i
$29$	−2.31370	+	3.18453i	−0.429643	+	0.591353i	−0.967871	−	0.251446i	$-0.919094\pi$
$29$	−2.31370	+	3.18453i	−0.429643	+	0.591353i	0.538228	+	0.842799i	$0.319094\pi$
$30$	1.30359	+	0.543701i	0.238002	+	0.0992658i
$31$	−3.51309	−	1.14147i	−0.630970	−	0.205015i	−0.0239654	−	0.999713i	$-0.507629\pi$
$31$	−3.51309	−	1.14147i	−0.630970	−	0.205015i	−0.607005	+	0.794698i	$0.707629\pi$
$32$	−5.19940	−	2.22850i	−0.919133	−	0.393947i
$33$		0			0
$34$	0.0514928	+	0.0844916i	0.00883095	+	0.0144902i
$35$	−0.678513	+	2.08825i	−0.114690	+	0.352979i
$36$	0.743282	+	4.84613i	0.123880	+	0.807688i
$37$	5.56491	+	4.04314i	0.914866	+	0.664689i	0.942241	−	0.334936i	$-0.108715\pi$
$37$	5.56491	+	4.04314i	0.914866	+	0.664689i	−0.0273751	+	0.999625i	$0.508715\pi$
$38$	8.53302	+	7.32404i	1.38424	+	1.18812i
$39$	0.814185	+	2.50580i	0.130374	+	0.401250i
$40$	2.01655	−	3.23717i	0.318844	−	0.511842i
$41$	−3.40107	−	4.68117i	−0.531158	−	0.731076i	0.456148	−	0.889904i	$-0.349229\pi$
$41$	−3.40107	−	4.68117i	−0.531158	−	0.731076i	−0.987306	+	0.158827i	$0.949229\pi$
$42$	1.65951	−	0.394126i	0.256069	−	0.0608149i
$43$	1.89516			0.289009			0.144505	−	0.989504i	$-0.453841\pi$
$43$	1.89516			0.289009			0.144505	+	0.989504i	$0.453841\pi$
$44$		0			0
$45$	−3.30550			−0.492755
$46$	7.30608	−	1.73516i	1.07722	−	0.255835i
$47$	−5.76344	−	7.93270i	−0.840685	−	1.15710i	−0.985839	−	0.167694i	$-0.946368\pi$
$47$	−5.76344	−	7.93270i	−0.840685	−	1.15710i	0.145154	−	0.989409i	$-0.453632\pi$
$48$	−2.96256	−	0.0289704i	−0.427609	−	0.00418152i
$49$	−1.34373	−	4.13559i	−0.191962	−	0.590798i
$50$	−3.41446	−	2.93069i	−0.482877	−	0.414462i
$51$	0.0419247	+	0.0304601i	0.00587063	+	0.00426526i
$52$	7.03224	−	1.07858i	0.975196	−	0.149572i
$53$	−1.20135	+	3.69738i	−0.165018	+	0.507874i	−0.999038	−	0.0438612i	$-0.986034\pi$
$53$	−1.20135	+	3.69738i	−0.165018	+	0.507874i	0.834019	+	0.551735i	$0.186034\pi$
$54$	2.97166	+	4.87602i	0.404391	+	0.663543i
$55$		0			0
$56$	−0.327678	−	4.59405i	−0.0437878	−	0.613906i
$57$	5.60126	+	1.81996i	0.741905	+	0.241059i
$58$	5.13780	+	2.14287i	0.674626	+	0.281373i
$59$	2.85758	−	3.93312i	0.372025	−	0.512049i	−0.581425	−	0.813600i	$-0.697504\pi$
$59$	2.85758	−	3.93312i	0.372025	−	0.512049i	0.953450	+	0.301551i	$0.0975045\pi$
$60$	0.322116	−	1.97133i	0.0415850	−	0.254498i
$61$	1.28015	−	0.415944i	0.163906	−	0.0532562i	−0.225915	−	0.974147i	$-0.572537\pi$
$61$	1.28015	−	0.415944i	0.163906	−	0.0532562i	0.389820	+	0.920891i	$0.372537\pi$
$62$	−0.422596	+	5.20682i	−0.0536697	+	0.661267i
$63$	−3.22942	+	2.34631i	−0.406869	+	0.295607i
$64$	−1.36723	+	7.88230i	−0.170904	+	0.985288i
$65$			4.79662i			0.594948i
$66$		0			0
$67$		−	4.91303i		−	0.600223i	−0.953904	−	0.300111i	$-0.902976\pi$
$67$		−	4.91303i		−	0.600223i	0.953904	−	0.300111i	$-0.0970238\pi$
$68$	0.0994288	−	0.0984612i	0.0120575	−	0.0119402i
$69$	3.18178	−	2.31170i	0.383041	−	0.278296i
$70$	3.09503	+	0.251199i	0.369927	+	0.0300240i
$71$	−6.63416	+	2.15557i	−0.787330	+	0.255819i	−0.674967	−	0.737848i	$-0.735842\pi$
$71$	−6.63416	+	2.15557i	−0.787330	+	0.255819i	−0.112363	+	0.993667i	$0.535842\pi$
$72$	6.42510	−	2.60633i	0.757206	−	0.307158i
$73$	5.94967	−	8.18902i	0.696356	−	0.958452i	−0.303628	−	0.952791i	$-0.598198\pi$
$73$	5.94967	−	8.18902i	0.696356	−	0.958452i	0.999984	−	0.00566160i	$-0.00180215\pi$
$74$	3.74464	−	8.97821i	0.435305	−	1.04370i
$75$	−2.24132	−	0.728250i	−0.258806	−	0.0840911i
$76$	7.28904	−	14.1343i	0.836110	−	1.62131i
$77$		0			0
$78$	3.18178	−	1.93911i	0.360266	−	0.219561i
$79$	−1.85551	+	5.71067i	−0.208761	+	0.642501i	0.790777	+	0.612105i	$0.209677\pi$
$79$	−1.85551	+	5.71067i	−0.208761	+	0.642501i	−0.999538	+	0.0303963i	$0.990323\pi$
$80$	−5.11313	−	1.71681i	−0.571665	−	0.191945i
$81$	−3.53019	−	2.56484i	−0.392244	−	0.284982i
$82$	−5.32962	+	6.20939i	−0.588558	+	0.685712i
$83$	−1.11615	−	3.43515i	−0.122513	−	0.377057i	0.870927	−	0.491413i	$-0.163519\pi$
$83$	−1.11615	−	3.43515i	−0.122513	−	0.377057i	−0.993440	+	0.114356i	$0.963519\pi$
$84$	−1.08459	−	2.15460i	−0.118338	−	0.235086i
$85$	0.0554531	+	0.0763247i	0.00601473	+	0.00827857i
$86$	−0.619298	−	2.60763i	−0.0667806	−	0.281188i
$87$	2.91552			0.312576
$88$		0			0
$89$	−5.39711			−0.572093			−0.286046	−	0.958216i	$-0.592341\pi$
$89$	−5.39711			−0.572093			−0.286046	+	0.958216i	$0.592341\pi$
$90$	1.08017	+	4.54818i	0.113860	+	0.479420i
$91$	3.40474	+	4.68622i	0.356914	+	0.491250i
$92$	−4.77495	−	9.48573i	−0.497823	−	0.988956i
$93$	0.845462	+	2.60206i	0.0876703	+	0.269821i
$94$	−9.03156	+	10.5224i	−0.931535	+	1.08530i
$95$	8.67425	+	6.30221i	0.889960	+	0.646594i
$96$	0.928241	+	4.08578i	0.0947382	+	0.417003i
$97$	2.26393	−	6.96767i	0.229867	−	0.707459i	−0.767893	−	0.640578i	$-0.778695\pi$
$97$	2.26393	−	6.96767i	0.229867	−	0.707459i	0.997761	−	0.0668817i	$-0.0213050\pi$
$98$	−5.25122	+	3.20032i	−0.530454	+	0.323281i
$99$		0			0
$100$	−2.91668	+	5.65578i	−0.291668	+	0.565578i
$101$	−9.10415	−	2.95812i	−0.905897	−	0.294344i	−0.181228	−	0.983441i	$-0.558007\pi$
$101$	−9.10415	−	2.95812i	−0.905897	−	0.294344i	−0.724669	+	0.689097i	$0.758007\pi$
$102$	0.0282112	−	0.0676396i	0.00279332	−	0.00669732i
$103$	6.06681	−	8.35025i	0.597781	−	0.822775i	−0.397722	−	0.917506i	$-0.630199\pi$
$103$	6.06681	−	8.35025i	0.597781	−	0.822775i	0.995503	+	0.0947311i	$0.0301991\pi$
$104$	−3.78205	−	9.32349i	−0.370860	−	0.914243i
$105$	1.54672	−	0.502558i	0.150944	−	0.0490447i
$106$	5.47995	+	0.444764i	0.532260	+	0.0431993i
$107$	8.96161	−	6.51099i	0.866352	−	0.629441i	−0.0632539	−	0.997997i	$-0.520148\pi$
$107$	8.96161	−	6.51099i	0.866352	−	0.629441i	0.929605	+	0.368556i	$0.120148\pi$
$108$	5.73805	−	5.68221i	0.552144	−	0.546771i
$109$		−	8.95933i		−	0.858149i	−0.903269	−	0.429074i	$-0.858840\pi$
$109$		−	8.95933i		−	0.858149i	0.903269	−	0.429074i	$-0.141160\pi$
$110$		0			0
$111$		−	5.09482i		−	0.483579i
$112$	−6.21407	+	1.95210i	−0.587174	+	0.184457i
$113$	−8.91785	+	6.47920i	−0.838921	+	0.609511i	−0.922069	−	0.387026i	$-0.873502\pi$
$113$	−8.91785	+	6.47920i	−0.838921	+	0.609511i	0.0831484	+	0.996537i	$0.473502\pi$
$114$	0.673785	−	8.30173i	0.0631057	−	0.777528i
$115$	6.80948	−	2.21253i	0.634987	−	0.206320i
$116$	1.26955	−	7.76955i	0.117875	−	0.721385i
$117$	−5.12561	+	7.05479i	−0.473863	+	0.652216i
$118$	−6.34554	−	2.64660i	−0.584155	−	0.243640i
$119$	0.108354	+	0.0352062i	0.00993275	+	0.00322735i
$120$	−2.81770	+	0.200977i	−0.257219	+	0.0183466i
$121$		0			0
$122$	−0.990640	−	1.62548i	−0.0896883	−	0.147164i
$123$	−1.32436	+	4.07597i	−0.119414	+	0.367518i
$124$	7.30238	−	1.12001i	0.655773	−	0.100580i
$125$	−8.92542	−	6.48470i	−0.798314	−	0.580009i
$126$	4.28369	+	3.67677i	0.381622	+	0.327553i
$127$	−3.18051	−	9.78860i	−0.282225	−	0.868598i	−0.987217	−	0.159383i	$-0.949050\pi$
$127$	−3.18051	−	9.78860i	−0.282225	−	0.868598i	0.704992	−	0.709215i	$-0.250950\pi$
$128$	11.2924	−	0.694535i	0.998114	−	0.0613888i
$129$	−0.825073	−	1.13562i	−0.0726436	−	0.0999854i
$130$	6.59988	−	1.56744i	0.578847	−	0.137473i
$131$	1.86768			0.163180			0.0815901	−	0.996666i	$-0.474000\pi$
$131$	1.86768			0.163180			0.0815901	+	0.996666i	$0.474000\pi$
$132$		0			0
$133$	12.9480			1.12274
$134$	−6.76005	+	1.60548i	−0.583979	+	0.138692i
$135$	3.20021	+	4.40471i	0.275430	+	0.379097i
$136$	−0.167968	−	0.104633i	−0.0144031	−	0.00897222i
$137$	−0.387654	−	1.19308i	−0.0331195	−	0.101931i	0.933130	−	0.359539i	$-0.117066\pi$
$137$	−0.387654	−	1.19308i	−0.0331195	−	0.101931i	−0.966250	+	0.257607i	$0.917066\pi$
$138$	−4.22050	−	3.62253i	−0.359273	−	0.308370i
$139$	−5.08964	−	3.69784i	−0.431698	−	0.313647i	0.350630	−	0.936514i	$-0.385968\pi$
$139$	−5.08964	−	3.69784i	−0.431698	−	0.313647i	−0.782327	+	0.622867i	$0.785968\pi$
$140$	−0.665757	−	4.34067i	−0.0562667	−	0.366854i
$141$	−2.24426	+	6.90713i	−0.189001	+	0.581686i
$142$	5.13384	+	8.42382i	0.430822	+	0.706912i
$143$		0			0
$144$	−5.68574	−	7.98888i	−0.473812	−	0.665740i
$145$	5.04798	+	1.64019i	0.419212	+	0.136210i
$146$	−13.2118	−	5.51040i	−1.09342	−	0.456044i
$147$	−1.89312	+	2.60565i	−0.156142	+	0.214911i
$148$	−13.5772	−	2.21851i	−1.11604	−	0.182360i
$149$	−16.3160	+	5.30140i	−1.33666	+	0.434307i	−0.888184	−	0.459487i	$-0.848033\pi$
$149$	−16.3160	+	5.30140i	−1.33666	+	0.434307i	−0.448477	+	0.893795i	$0.648033\pi$
$150$	−0.269612	+	3.32191i	−0.0220138	+	0.271233i
$151$	9.83626	−	7.14646i	0.800464	−	0.581571i	−0.110586	−	0.993867i	$-0.535273\pi$
$151$	9.83626	−	7.14646i	0.800464	−	0.581571i	0.911050	+	0.412295i	$0.135273\pi$
$152$	−21.8298	−	5.41051i	−1.77063	−	0.438850i
$153$			0.171513i			0.0138660i
$154$		0			0
$155$			4.98089i			0.400074i
$156$	−3.70785	−	3.74428i	−0.296865	−	0.299782i
$157$	4.28919	−	3.11628i	0.342315	−	0.248706i	−0.403323	−	0.915058i	$-0.632145\pi$
$157$	4.28919	−	3.11628i	0.342315	−	0.248706i	0.745638	+	0.666351i	$0.232145\pi$
$158$	8.46390	+	0.686946i	0.673351	+	0.0546505i
$159$	2.73856	−	0.889811i	0.217182	−	0.0705666i
$160$	−0.691370	+	7.59638i	−0.0546576	+	0.600547i
$161$	5.08225	−	6.99512i	0.400537	−	0.551292i
$162$	−2.37547	+	5.69547i	−0.186635	+	0.447479i
$163$	9.56530	+	3.10795i	0.749212	+	0.243434i	0.658642	−	0.752456i	$-0.271131\pi$
$163$	9.56530	+	3.10795i	0.749212	+	0.243434i	0.0905700	+	0.995890i	$0.471131\pi$
$164$	10.2854	+	5.30415i	0.803152	+	0.414185i
$165$		0			0
$166$	−4.36183	+	2.65829i	−0.338544	+	0.206323i
$167$	6.76983	−	20.8354i	0.523865	−	1.61229i	−0.242683	−	0.970106i	$-0.578028\pi$
$167$	6.76983	−	20.8354i	0.523865	−	1.61229i	0.766549	−	0.642186i	$-0.221972\pi$
$168$	−2.61019	+	2.19641i	−0.201380	+	0.169457i
$169$	−0.279988	−	0.203423i	−0.0215375	−	0.0156479i
$170$	0.0868974	−	0.101242i	0.00666472	−	0.00776487i
$171$	6.02348	+	18.5384i	0.460627	+	1.41766i
$172$	−3.38557	+	1.70424i	−0.258147	+	0.129947i
$173$	6.95480	+	9.57246i	0.528763	+	0.727780i	0.986941	−	0.161080i	$-0.0514977\pi$
$173$	6.95480	+	9.57246i	0.528763	+	0.727780i	−0.458178	+	0.888861i	$0.651498\pi$
$174$	−0.952730	−	4.01158i	−0.0722263	−	0.304117i
$175$	−5.18111			−0.391655
$176$		0			0
$177$	−3.60087			−0.270658
$178$	1.76366	+	7.42611i	0.132192	+	0.556611i
$179$	−0.548801	−	0.755360i	−0.0410193	−	0.0564582i	0.788015	−	0.615656i	$-0.211109\pi$
$179$	−0.548801	−	0.755360i	−0.0410193	−	0.0564582i	−0.829034	+	0.559198i	$0.811109\pi$
$180$	5.90505	−	2.97250i	0.440137	−	0.221557i
$181$	5.82171	+	17.9174i	0.432725	+	1.33179i	0.895400	+	0.445262i	$0.146889\pi$
$181$	5.82171	+	17.9174i	0.432725	+	1.33179i	−0.462676	+	0.886528i	$0.653111\pi$
$182$	5.33537	−	6.21608i	0.395484	−	0.460767i
$183$	−0.806564	−	0.586003i	−0.0596229	−	0.0433186i
$184$	−11.4915	+	9.66978i	−0.847162	+	0.712866i
$185$	2.86620	−	8.82125i	0.210727	−	0.648551i
$186$	3.30401	−	2.01361i	0.242262	−	0.147645i
$187$		0			0
$188$	17.4295	+	8.98840i	1.27118	+	0.655547i
$189$	6.25310	+	2.03175i	0.454846	+	0.147788i
$190$	5.83692	−	13.9947i	0.423454	−	1.01528i
$191$	−12.0167	+	16.5396i	−0.869501	+	1.19676i	0.109719	+	0.993963i	$0.465005\pi$
$191$	−12.0167	+	16.5396i	−0.869501	+	1.19676i	−0.979220	+	0.202802i	$0.934995\pi$
$192$	5.31846	−	2.61235i	0.383827	−	0.188530i
$193$	16.4922	−	5.35865i	1.18714	−	0.385724i	0.352123	−	0.935954i	$-0.385460\pi$
$193$	16.4922	−	5.35865i	1.18714	−	0.385724i	0.835013	+	0.550230i	$0.185460\pi$
$194$	−10.3269	−	0.838152i	−0.741429	−	0.0601758i
$195$	2.87423	−	2.08825i	0.205828	−	0.149543i
$196$	6.11945	+	6.17958i	0.437103	+	0.441399i
$197$		−	3.49133i		−	0.248747i	−0.992235	−	0.124374i	$-0.960308\pi$
$197$		−	3.49133i		−	0.248747i	0.992235	−	0.124374i	$-0.0396921\pi$
$198$		0			0
$199$		−	11.2660i		−	0.798625i	−0.916815	−	0.399313i	$-0.869249\pi$
$199$		−	11.2660i		−	0.798625i	0.916815	−	0.399313i	$-0.130751\pi$
$200$	8.73513	+	2.16500i	0.617667	+	0.153088i
$201$	−2.94398	+	2.13893i	−0.207653	+	0.150868i
$202$	−1.09515	+	13.4934i	−0.0770547	+	0.949394i
$203$	6.09603	−	1.98072i	0.427857	−	0.139019i
$204$	−0.102287	−	0.0167137i	−0.00716152	−	0.00117019i
$205$	−4.58605	+	6.31216i	−0.320304	+	0.440860i
$206$	−13.4720	−	5.61890i	−0.938637	−	0.391487i
$207$	12.3796	+	4.02236i	0.860438	+	0.279573i
$208$	−11.5927	+	8.25060i	−0.803808	+	0.572076i
$209$		0			0
$210$	−1.19693	−	1.96397i	−0.0825957	−	0.135526i
$211$	0.847619	−	2.60870i	0.0583525	−	0.179590i	−0.917632	−	0.397432i	$-0.869902\pi$
$211$	0.847619	−	2.60870i	0.0583525	−	0.179590i	0.975984	+	0.217841i	$0.0699015\pi$
$212$	−1.17876	−	7.68544i	−0.0809579	−	0.527838i
$213$	4.17989	+	3.03687i	0.286402	+	0.208083i
$214$	−11.8872	−	10.2030i	−0.812593	−	0.697463i
$215$	−0.789680	−	2.43039i	−0.0538558	−	0.165751i
$216$	−9.69346	−	6.03839i	−0.659557	−	0.410861i
$217$	3.53553	+	4.86624i	0.240008	+	0.330342i
$218$	−12.3275	+	2.92772i	−0.834925	+	0.198290i
$219$	−7.49726			−0.506618
$220$		0			0
$221$	0.248884			0.0167417
$222$	−7.01017	+	1.66488i	−0.470492	+	0.111739i
$223$	13.9457	+	19.1946i	0.933871	+	1.28536i	0.958330	+	0.285662i	$0.0922134\pi$
$223$	13.9457	+	19.1946i	0.933871	+	1.28536i	−0.0244597	+	0.999701i	$0.507787\pi$
$224$	4.71661	+	7.91229i	0.315142	+	0.528662i
$225$	−2.41027	−	7.41806i	−0.160685	−	0.494538i
$226$	11.8292	+	10.1532i	0.786864	+	0.675379i
$227$	−0.647893	−	0.470721i	−0.0430021	−	0.0312429i	0.566077	−	0.824353i	$-0.308461\pi$
$227$	−0.647893	−	0.470721i	−0.0430021	−	0.0312429i	−0.609079	+	0.793110i	$0.708461\pi$
$228$	−11.6429	+	1.78574i	−0.771068	+	0.118264i
$229$	−7.28939	+	22.4344i	−0.481696	+	1.48251i	0.355013	+	0.934861i	$0.384476\pi$
$229$	−7.28939	+	22.4344i	−0.481696	+	1.48251i	−0.836709	+	0.547647i	$0.815524\pi$
$230$	−5.26951	−	8.64644i	−0.347461	−	0.570129i
$231$		0			0
$232$	−11.1053	+	0.792103i	−0.729100	+	0.0520041i
$233$	16.6354	+	5.40517i	1.08982	+	0.354105i	0.798178	−	0.602422i	$-0.205798\pi$
$233$	16.6354	+	5.40517i	1.08982	+	0.354105i	0.291644	+	0.956527i	$0.405798\pi$
$234$	11.3819	+	4.74718i	0.744060	+	0.310333i
$235$	−7.77151	+	10.6966i	−0.506957	+	0.697767i
$236$	−1.56798	+	9.59595i	−0.102067	+	0.624643i
$237$	4.22976	−	1.37433i	0.274752	−	0.0892724i
$238$	0.0130340	−	0.160593i	0.000844871	−	0.0104097i
$239$	5.40825	−	3.92933i	0.349831	−	0.254167i	−0.398967	−	0.916965i	$-0.630631\pi$
$239$	5.40825	−	3.92933i	0.349831	−	0.254167i	0.748798	+	0.662798i	$0.230631\pi$
$240$	1.19730	+	3.81131i	0.0772851	+	0.246019i
$241$			4.28655i			0.276121i	0.990424	+	0.138061i	$0.0440868\pi$
$241$			4.28655i			0.276121i	−0.990424	+	0.138061i	$0.955913\pi$
$242$		0			0
$243$			15.3451i			0.984391i
$244$	−1.91285	+	1.89424i	−0.122458	+	0.121266i
$245$	−4.74364	+	3.44646i	−0.303060	+	0.220186i
$246$	6.04108	+	0.490306i	0.385165	+	0.0312607i
$247$	26.9011	−	8.74070i	1.71168	−	0.556157i
$248$	−3.92734	−	9.68165i	−0.249386	−	0.614785i
$249$	−1.57248	+	2.16434i	−0.0996521	+	0.137159i
$250$	−6.00593	+	14.3999i	−0.379848	+	0.910731i
$251$	−4.65797	−	1.51346i	−0.294008	−	0.0955291i	0.158299	−	0.987391i	$-0.449399\pi$
$251$	−4.65797	−	1.51346i	−0.294008	−	0.0955291i	−0.452307	+	0.891862i	$0.649399\pi$
$252$	3.65920	−	7.09560i	0.230508	−	0.446981i
$253$		0			0
$254$	−12.4292	+	7.57491i	−0.779879	+	0.475292i
$255$	0.0215932	−	0.0664571i	0.00135222	−	0.00416171i
$256$	−4.64575	−	15.3107i	−0.290359	−	0.956918i
$257$	10.0191	+	7.27931i	0.624975	+	0.454071i	0.854656	−	0.519195i	$-0.173768\pi$
$257$	10.0191	+	7.27931i	0.624975	+	0.454071i	−0.229681	+	0.973266i	$0.573768\pi$
$258$	−1.29292	+	1.50635i	−0.0804940	+	0.0937811i
$259$	−3.46127	−	10.6527i	−0.215073	−	0.661927i
$260$	−4.31340	−	8.56884i	−0.267506	−	0.531417i
$261$	5.67180	+	7.80656i	0.351075	+	0.483214i
$262$	−0.610320	−	2.56982i	−0.0377057	−	0.158764i
$263$	−16.9489			−1.04511			−0.522556	−	0.852605i	$-0.675021\pi$
$263$	−16.9489			−1.04511			−0.522556	+	0.852605i	$0.675021\pi$
$264$		0			0
$265$	5.24217			0.322024
$266$	−4.23115	−	17.8157i	−0.259428	−	1.09235i
$267$	2.34968	+	3.23405i	0.143798	+	0.197921i
$268$	4.41808	+	8.77680i	0.269877	+	0.536128i
$269$	1.22209	+	3.76120i	0.0745120	+	0.229324i	0.981375	−	0.192101i	$-0.0615300\pi$
$269$	1.22209	+	3.76120i	0.0745120	+	0.229324i	−0.906863	+	0.421425i	$0.861530\pi$
$270$	5.01486	−	5.84266i	0.305195	−	0.355573i
$271$	−19.2040	−	13.9525i	−1.16656	−	0.847556i	−0.175968	−	0.984396i	$-0.556305\pi$
$271$	−19.2040	−	13.9525i	−1.16656	−	0.847556i	−0.990593	+	0.136840i	$0.956305\pi$
$272$	−0.0890806	+	0.265306i	−0.00540131	+	0.0160866i
$273$	1.32579	−	4.08037i	0.0802406	−	0.246955i
$274$	−1.51493	+	0.923261i	−0.0915200	+	0.0557763i
$275$		0			0
$276$	−3.60522	+	6.99093i	−0.217009	+	0.420804i
$277$	−14.2764	−	4.63868i	−0.857784	−	0.278711i	−0.153081	−	0.988214i	$-0.548920\pi$
$277$	−14.2764	−	4.63868i	−0.857784	−	0.278711i	−0.704703	+	0.709503i	$0.748920\pi$
$278$	−3.42483	+	8.21143i	−0.205407	+	0.492489i
$279$	−5.32251	+	7.32580i	−0.318650	+	0.438584i
$280$	−5.75496	+	2.33448i	−0.343924	+	0.139512i
$281$	5.46035	−	1.77417i	0.325737	−	0.105838i	−0.141584	−	0.989926i	$-0.545219\pi$
$281$	5.46035	−	1.77417i	0.325737	−	0.105838i	0.467321	+	0.884088i	$0.345219\pi$
$282$	10.2372	+	0.830870i	0.609616	+	0.0494776i
$283$	−9.05676	+	6.58012i	−0.538369	+	0.391148i	−0.823479	−	0.567347i	$-0.807970\pi$
$283$	−9.05676	+	6.58012i	−0.538369	+	0.391148i	0.285110	+	0.958495i	$0.407970\pi$
$284$	9.91306	−	9.81660i	0.588232	−	0.582508i
$285$		−	7.94150i		−	0.470414i
$286$		0			0
$287$			9.42215i			0.556172i
$288$	−9.13425	+	10.4338i	−0.538241	+	0.614820i
$289$	−13.7493	+	9.98947i	−0.808784	+	0.587616i
$290$	0.607230	−	7.48170i	0.0356577	−	0.439341i
$291$	−5.16078	+	1.67684i	−0.302530	+	0.0982981i
$292$	−3.26464	+	19.9794i	−0.191049	+	1.16921i
$293$	−3.11697	+	4.29014i	−0.182095	+	0.250632i	−0.890300	−	0.455375i	$-0.849505\pi$
$293$	−3.11697	+	4.29014i	−0.182095	+	0.250632i	0.708205	+	0.706007i	$0.249505\pi$
$294$	4.20386	+	1.75335i	0.245174	+	0.102257i
$295$	−6.23461	−	2.02575i	−0.362993	−	0.117944i
$296$	1.38419	+	19.4063i	0.0804542	+	1.12797i
$297$		0			0
$298$	12.6261	+	20.7175i	0.731413	+	1.20013i
$299$	5.83686	−	17.9640i	0.337554	−	1.03889i
$300$	4.65885	−	0.714558i	0.268979	−	0.0412550i
$301$	−2.49664	−	1.81392i	−0.143904	−	0.104552i
$302$	−13.0474	−	11.1988i	−0.750794	−	0.644419i
$303$	2.19101	+	6.74322i	0.125870	+	0.387388i
$304$	−0.311012	+	31.8046i	−0.0178378	+	1.82412i
$305$	−1.06683	−	1.46836i	−0.0610865	−	0.0840783i
$306$	0.235992	−	0.0560470i	0.0134908	−	0.00320399i
$307$	−2.27014			−0.129564			−0.0647820	−	0.997899i	$-0.520635\pi$
$307$	−2.27014			−0.129564			−0.0647820	+	0.997899i	$0.520635\pi$
$308$		0			0
$309$	−7.64487			−0.434901
$310$	6.85341	−	1.62765i	0.389248	−	0.0924442i
$311$	−11.8536	−	16.3151i	−0.672155	−	0.925143i	0.327651	−	0.944799i	$-0.393743\pi$
$311$	−11.8536	−	16.3151i	−0.672155	−	0.925143i	−0.999807	+	0.0196560i	$0.993743\pi$
$312$	−3.94027	+	6.32533i	−0.223074	+	0.358101i
$313$	0.476468	+	1.46642i	0.0269316	+	0.0828869i	0.963619	−	0.267280i	$-0.0861249\pi$
$313$	0.476468	+	1.46642i	0.0269316	+	0.0828869i	−0.936687	+	0.350167i	$0.886125\pi$
$314$	−5.68944	−	4.88334i	−0.321073	−	0.275583i
$315$	4.35460	+	3.16380i	0.245354	+	0.178260i
$316$	−1.82062	−	11.8703i	−0.102418	−	0.667757i
$317$	−5.21071	+	16.0369i	−0.292663	+	0.900723i	0.691334	+	0.722536i	$0.257023\pi$
$317$	−5.21071	+	16.0369i	−0.292663	+	0.900723i	−0.983997	+	0.178188i	$0.942977\pi$
$318$	−2.11923	−	3.47732i	−0.118841	−	0.194999i
$319$		0			0
$320$	10.6781	−	1.53105i	0.596924	−	0.0855885i
$321$	−7.80302	−	2.53535i	−0.435522	−	0.141510i
$322$	−11.2856	−	4.70702i	−0.628924	−	0.262312i
$323$	0.327005	−	0.450083i	0.0181950	−	0.0250433i
$324$	8.61290	+	1.40735i	0.478494	+	0.0781861i
$325$	−10.7644	+	3.49756i	−0.597100	+	0.194010i
$326$	1.15063	−	14.1769i	0.0637273	−	0.785186i
$327$	−5.36860	+	3.90052i	−0.296885	+	0.215699i
$328$	3.93717	−	15.8853i	0.217394	−	0.877121i
$329$			15.9667i			0.880275i
$330$		0			0
$331$		−	33.9735i		−	1.86735i	−0.358115	−	0.933677i	$-0.616581\pi$
$331$		−	33.9735i		−	1.86735i	0.358115	−	0.933677i	$-0.383419\pi$
$332$	5.08300	+	5.13295i	0.278966	+	0.281707i
$333$	13.6418	−	9.91136i	0.747567	−	0.543139i
$334$	−30.8805	−	2.50632i	−1.68971	−	0.137140i
$335$	−6.30056	+	2.04718i	−0.344237	+	0.111849i
$336$	3.87508	+	2.87372i	0.211403	+	0.156775i
$337$	10.0486	−	13.8307i	0.547382	−	0.753407i	−0.442272	−	0.896881i	$-0.645827\pi$
$337$	10.0486	−	13.8307i	0.547382	−	0.753407i	0.989654	+	0.143474i	$0.0458274\pi$
$338$	−0.188404	+	0.451722i	−0.0102478	+	0.0245704i
$339$	7.76492	+	2.52297i	0.421732	+	0.137029i
$340$	−0.167699	−	0.0864821i	−0.00909474	−	0.00469015i
$341$		0			0
$342$	23.5394	−	14.3459i	1.27286	−	0.775738i
$343$	−5.71045	+	17.5750i	−0.308335	+	0.948959i
$344$	3.45126	+	4.10144i	0.186080	+	0.221135i
$345$	−4.29036	−	3.11713i	−0.230985	−	0.167820i
$346$	10.8985	−	12.6975i	0.585905	−	0.682620i
$347$	0.772260	+	2.37677i	0.0414571	+	0.127592i	0.969643	−	0.244525i	$-0.0786321\pi$
$347$	0.772260	+	2.37677i	0.0414571	+	0.127592i	−0.928186	+	0.372117i	$0.878632\pi$
$348$	−5.20837	+	2.62180i	−0.279198	+	0.140543i
$349$	4.12112	+	5.67223i	0.220598	+	0.303628i	0.904944	−	0.425530i	$-0.139912\pi$
$349$	4.12112	+	5.67223i	0.220598	+	0.303628i	−0.684346	+	0.729157i	$0.739912\pi$
$350$	1.69308	+	7.12891i	0.0904988	+	0.381056i
$351$	14.3631			0.766646
$352$		0			0
$353$	17.9431			0.955017			0.477509	−	0.878627i	$-0.341540\pi$
$353$	17.9431			0.955017			0.477509	+	0.878627i	$0.341540\pi$
$354$	1.17669	+	4.95459i	0.0625403	+	0.263334i
$355$	5.52868	+	7.60958i	0.293432	+	0.403874i
$356$	9.64157	−	4.85339i	0.511002	−	0.257229i
$357$	−0.0260764	−	0.0802548i	−0.00138011	−	0.00424754i
$358$	−0.859995	+	1.00195i	−0.0454521	+	0.0529549i
$359$	7.83085	+	5.68945i	0.413297	+	0.300278i	0.774935	−	0.632041i	$-0.217783\pi$
$359$	7.83085	+	5.68945i	0.413297	+	0.300278i	−0.361638	+	0.932318i	$0.617783\pi$
$360$	−6.01963	−	7.15366i	−0.317262	−	0.377031i
$361$	13.6669	−	42.0624i	0.719310	−	2.21381i
$362$	22.7509	−	13.8654i	1.19576	−	0.728748i
$363$		0			0
$364$	−10.2965	−	5.30988i	−0.539681	−	0.278313i
$365$	−12.9809	−	4.21774i	−0.679450	−	0.220767i
$366$	−0.542738	+	1.30128i	−0.0283693	+	0.0680189i
$367$	18.1903	−	25.0368i	0.949524	−	1.30691i	−0.00221435	−	0.999998i	$-0.500705\pi$
$367$	18.1903	−	25.0368i	0.949524	−	1.30691i	0.951738	−	0.306910i	$-0.0992952\pi$
$368$	17.0602	+	12.6517i	0.889326	+	0.659515i
$369$	−13.4902	+	4.38322i	−0.702270	+	0.228181i
$370$	−13.0741	−	1.06112i	−0.679692	−	0.0551651i
$371$	5.12151	−	3.72100i	0.265896	−	0.193184i
$372$	−3.85028	−	3.88812i	−0.199628	−	0.201590i
$373$			4.92658i			0.255088i	0.991833	+	0.127544i	$0.0407095\pi$
$373$			4.92658i			0.255088i	−0.991833	+	0.127544i	$0.959291\pi$
$374$		0			0
$375$			8.17145i			0.421972i
$376$	6.67191	−	26.9192i	0.344078	−	1.38825i
$377$	11.3281	−	8.23036i	0.583428	−	0.423885i
$378$	0.752195	−	9.26783i	0.0386888	−	0.476686i
$379$	−3.82815	+	1.24384i	−0.196639	+	0.0638918i	−0.405681	−	0.914015i	$-0.632965\pi$
$379$	−3.82815	+	1.24384i	−0.196639	+	0.0638918i	0.209042	+	0.977907i	$0.432965\pi$
$380$	−21.1633	−	3.45808i	−1.08565	−	0.177396i
$381$	−4.48086	+	6.16737i	−0.229561	+	0.315964i
$382$	26.6844	+	11.1295i	1.36529	+	0.569436i
$383$	−11.4021	−	3.70477i	−0.582621	−	0.189305i	0.00285329	−	0.999996i	$-0.499092\pi$
$383$	−11.4021	−	3.70477i	−0.582621	−	0.189305i	−0.585474	+	0.810691i	$0.699092\pi$
$384$	−5.33240	−	6.46423i	−0.272118	−	0.329877i
$385$		0			0
$386$	−12.7625	−	20.9412i	−0.649594	−	1.06588i
$387$	1.43563	−	4.41841i	0.0729771	−	0.224600i
$388$	2.22137	+	14.4831i	0.112773	+	0.735269i
$389$	−11.1135	−	8.07444i	−0.563477	−	0.409390i	0.269253	−	0.963070i	$-0.413223\pi$
$389$	−11.1135	−	8.07444i	−0.563477	−	0.409390i	−0.832730	+	0.553679i	$0.813223\pi$
$390$	−3.81255	−	3.27238i	−0.193056	−	0.165703i
$391$	−0.114802	−	0.353325i	−0.00580580	−	0.0178684i
$392$	6.50304	−	10.4394i	0.328453	−	0.527267i
$393$	−0.813111	−	1.11915i	−0.0410160	−	0.0564537i
$394$	−4.80387	+	1.14089i	−0.242015	+	0.0574774i
$395$	8.09663			0.407386
$396$		0			0
$397$	−12.1547			−0.610027			−0.305014	−	0.952348i	$-0.598661\pi$
$397$	−12.1547			−0.610027			−0.305014	+	0.952348i	$0.598661\pi$
$398$	−15.5014	+	3.68149i	−0.777013	+	0.184536i
$399$	−5.63704	−	7.75871i	−0.282205	−	0.388422i
$400$	0.124450	−	12.7265i	0.00622252	−	0.636326i
$401$	−8.89366	−	27.3719i	−0.444128	−	1.36689i	−0.883437	−	0.468550i	$-0.844777\pi$
$401$	−8.89366	−	27.3719i	−0.444128	−	1.36689i	0.439309	−	0.898336i	$-0.355223\pi$
$402$	3.90507	+	3.35179i	0.194767	+	0.167172i
$403$	10.6305	+	7.72351i	0.529543	+	0.384735i
$404$	18.9240	−	2.90250i	0.941507	−	0.144405i
$405$	−1.81822	+	5.59591i	−0.0903481	+	0.278063i
$406$	−4.71741	−	7.74052i	−0.234121	−	0.384156i
$407$		0			0
$408$	0.0104281	+	0.146203i	0.000516269	+	0.00723811i
$409$	18.0275	+	5.85749i	0.891402	+	0.289634i	0.718684	−	0.695337i	$-0.244745\pi$
$409$	18.0275	+	5.85749i	0.891402	+	0.289634i	0.172718	+	0.984971i	$0.444745\pi$
$410$	10.1838	+	4.24746i	0.502942	+	0.209767i
$411$	−0.546146	+	0.751705i	−0.0269394	+	0.0370789i
$412$	−3.32892	+	20.3728i	−0.164004	+	1.00369i
$413$	−7.52903	+	2.44633i	−0.370479	+	0.120376i
$414$	1.48916	−	18.3480i	0.0731881	−	0.901753i
$415$	−3.94022	+	2.86274i	−0.193418	+	0.140526i
$416$	15.1406	+	13.2547i	0.742328	+	0.649867i
$417$			4.65970i			0.228186i
$418$		0			0
$419$			15.3705i			0.750898i	0.926843	+	0.375449i	$0.122512\pi$
$419$			15.3705i			0.750898i	−0.926843	+	0.375449i	$0.877488\pi$
$420$	−2.31117	+	2.28868i	−0.112774	+	0.111676i
$421$	−15.6309	+	11.3565i	−0.761803	+	0.553482i	−0.899463	−	0.436997i	$-0.856042\pi$
$421$	−15.6309	+	11.3565i	−0.761803	+	0.553482i	0.137660	+	0.990480i	$0.456042\pi$
$422$	−3.86641	−	0.313805i	−0.188214	−	0.0152758i
$423$	−22.8604	+	7.42780i	−1.11151	+	0.361152i
$424$	−10.1895	+	4.13335i	−0.494847	+	0.200733i
$425$	−0.130850	+	0.180099i	−0.00634714	+	0.00873609i
$426$	2.81266	−	6.74368i	0.136274	−	0.326732i
$427$	−2.08455	−	0.677311i	−0.100878	−	0.0327774i
$428$	−10.1542	+	19.6902i	−0.490824	+	0.951763i
$429$		0			0
$430$	−3.08602	+	1.88075i	−0.148821	+	0.0906980i
$431$	−8.37559	+	25.7774i	−0.403438	+	1.24165i	0.518754	+	0.854923i	$0.326396\pi$
$431$	−8.37559	+	25.7774i	−0.403438	+	1.24165i	−0.922192	+	0.386732i	$0.873604\pi$
$432$	−5.14086	+	15.3109i	−0.247340	+	0.736644i
$433$	−3.52419	−	2.56048i	−0.169362	−	0.123049i	0.499876	−	0.866097i	$-0.333379\pi$
$433$	−3.52419	−	2.56048i	−0.169362	−	0.123049i	−0.669237	+	0.743049i	$0.733379\pi$
$434$	5.54033	−	6.45487i	0.265944	−	0.309844i
$435$	−1.21485	−	3.73891i	−0.0582474	−	0.179267i
$436$	8.05675	+	16.0052i	0.385848	+	0.766512i
$437$	−24.8173	−	34.1581i	−1.18717	−	1.63400i
$438$	2.44995	+	10.3158i	0.117063	+	0.492907i
$439$	24.0996			1.15021			0.575105	−	0.818080i	$-0.304961\pi$
$439$	24.0996			1.15021			0.575105	+	0.818080i	$0.304961\pi$
$440$		0			0
$441$	−10.6597			−0.507605
$442$	−0.0813299	−	0.342449i	−0.00386847	−	0.0162887i
$443$	−13.5454	−	18.6436i	−0.643561	−	0.885786i	0.355238	−	0.934776i	$-0.384400\pi$
$443$	−13.5454	−	18.6436i	−0.643561	−	0.885786i	−0.998799	+	0.0489896i	$0.984400\pi$
$444$	4.58155	+	9.10154i	0.217431	+	0.431940i
$445$	2.24888	+	6.92135i	0.106607	+	0.328104i
$446$	21.8534	−	25.4608i	1.03479	−	1.20560i
$447$	10.2800	+	7.46887i	0.486228	+	0.353265i
$448$	9.34556	−	9.07535i	0.441536	−	0.428770i
$449$	−1.16607	+	3.58880i	−0.0550303	+	0.169366i	−0.974794	−	0.223107i	$-0.928380\pi$
$449$	−1.16607	+	3.58880i	−0.0550303	+	0.169366i	0.919764	+	0.392473i	$0.128380\pi$
$450$	−9.41920	+	5.74046i	−0.444025	+	0.270608i
$451$		0			0
$452$	10.1047	−	19.5941i	0.475283	−	0.921628i
$453$	−8.56460	−	2.78281i	−0.402400	−	0.130748i
$454$	−0.435968	+	1.04528i	−0.0204610	+	0.0490576i
$455$	4.59100	−	6.31897i	0.215229	−	0.296238i
$456$	6.26172	+	15.4364i	0.293232	+	0.722874i
$457$	33.5315	−	10.8950i	1.56854	−	0.509649i	0.609466	−	0.792812i	$-0.291384\pi$
$457$	33.5315	−	10.8950i	1.56854	−	0.509649i	0.959072	+	0.283164i	$0.0913840\pi$
$458$	33.2505	+	2.69867i	1.55369	+	0.126101i
$459$	0.228548	−	0.166050i	0.0106677	−	0.00775055i
$460$	−10.1750	+	10.0760i	−0.474413	+	0.469797i
$461$		−	38.5074i		−	1.79347i	−0.442571	−	0.896734i	$-0.645933\pi$
$461$		−	38.5074i		−	1.79347i	0.442571	−	0.896734i	$-0.354067\pi$
$462$		0			0
$463$			10.7672i			0.500394i	0.968195	+	0.250197i	$0.0804954\pi$
$463$			10.7672i			0.500394i	−0.968195	+	0.250197i	$0.919505\pi$
$464$	4.71887	+	15.0214i	0.219068	+	0.697352i
$465$	2.98464	−	2.16847i	0.138409	−	0.100560i
$466$	2.00110	−	24.6557i	0.0926992	−	1.14215i
$467$	−19.6677	+	6.39043i	−0.910114	+	0.295714i	−0.726405	−	0.687267i	$-0.758810\pi$
$467$	−19.6677	+	6.39043i	−0.910114	+	0.295714i	−0.183709	+	0.982981i	$0.558810\pi$
$468$	2.81247	−	17.2121i	0.130006	−	0.795631i
$469$	−4.70242	+	6.47232i	−0.217138	+	0.298864i
$470$	17.2574	+	7.19773i	0.796025	+	0.332007i
$471$	−3.73467	−	1.21347i	−0.172084	−	0.0559136i
$472$	13.7159	−	0.978304i	0.631323	−	0.0450301i
$473$		0			0
$474$	−3.27320	−	5.37080i	−0.150343	−	0.246689i
$475$	−7.81814	+	24.0618i	−0.358721	+	1.10403i
$476$	−0.225226	+	0.0345443i	−0.0103232	+	0.00158333i
$477$	7.71009	+	5.60171i	0.353021	+	0.256485i
$478$	−7.17383	−	6.15742i	−0.328123	−	0.281634i
$479$	3.52707	+	10.8552i	0.161156	+	0.495986i	0.998732	−	0.0503333i	$-0.0160284\pi$
$479$	3.52707	+	10.8552i	0.161156	+	0.495986i	−0.837577	+	0.546320i	$0.816028\pi$
$480$	4.85289	−	2.89287i	0.221503	−	0.132041i
$481$	−14.3824	−	19.7957i	−0.655781	−	0.902606i
$482$	5.89804	−	1.40075i	0.268649	−	0.0638026i
$483$	−6.40421			−0.291401
$484$		0			0
$485$	−9.87880			−0.448573
$486$	21.1140	−	5.01447i	0.957751	−	0.227461i
$487$	−2.35405	−	3.24008i	−0.106672	−	0.146822i	0.752343	−	0.658771i	$-0.228924\pi$
$487$	−2.35405	−	3.24008i	−0.106672	−	0.146822i	−0.859016	+	0.511949i	$0.828924\pi$
$488$	3.23144	+	2.01297i	0.146280	+	0.0911230i
$489$	−2.30199	−	7.08479i	−0.104099	−	0.320385i
$490$	6.29225	+	5.40074i	0.284255	+	0.243981i
$491$	9.05615	+	6.57968i	0.408698	+	0.296937i	0.773075	−	0.634315i	$-0.218718\pi$
$491$	9.05615	+	6.57968i	0.408698	+	0.296937i	−0.364376	+	0.931252i	$0.618718\pi$
$492$	−1.29946	−	8.47239i	−0.0585844	−	0.381965i
$493$	0.0851048	−	0.261926i	0.00383293	−	0.0117965i
$494$	−20.8174	−	34.1581i	−0.936619	−	1.53684i
$495$		0			0
$496$	−12.0380	+	8.56754i	−0.540523	+	0.384694i
$497$	10.8029	+	3.51006i	0.484575	+	0.157448i
$498$	3.49186	+	1.45639i	0.156474	+	0.0652622i
$499$	23.1385	−	31.8474i	1.03582	−	1.42569i	0.135336	−	0.990800i	$-0.456789\pi$
$499$	23.1385	−	31.8474i	1.03582	−	1.42569i	0.900485	−	0.434886i	$-0.143211\pi$
$500$	21.7761	+	3.55821i	0.973855	+	0.159128i
$501$	−15.4323	+	5.01425i	−0.689463	+	0.224020i
$502$	−0.560314	+	6.90366i	−0.0250081	+	0.308125i
$503$	−15.6439	+	11.3660i	−0.697527	+	0.506783i	−0.879126	−	0.476589i	$-0.841873\pi$
$503$	−15.6439	+	11.3660i	−0.697527	+	0.506783i	0.181599	+	0.983373i	$0.441873\pi$
$504$	−10.9589	−	2.71615i	−0.488148	−	0.120987i
$505$			12.9079i			0.574395i
$506$		0			0
$507$			0.256336i			0.0113843i
$508$	14.4842	+	14.6266i	0.642634	+	0.648949i
$509$	34.7849	−	25.2727i	1.54181	−	1.12019i	0.592628	−	0.805476i	$-0.298090\pi$
$509$	34.7849	−	25.2727i	1.54181	−	1.12019i	0.949186	−	0.314717i	$-0.101910\pi$
$510$	−0.0984974	−	0.00799424i	−0.00436154	−	0.000353991i
$511$	−15.6759	+	5.09342i	−0.693463	+	0.225320i
$512$	−19.5485	+	11.3955i	−0.863929	+	0.503614i
$513$	18.8715	−	25.9744i	0.833196	−	1.14680i
$514$	6.74187	−	16.1644i	0.297371	−	0.712982i
$515$	−13.2365	−	4.30078i	−0.583268	−	0.189515i
$516$	2.49515	+	1.28675i	0.109843	+	0.0566458i
$517$		0			0
$518$	−13.5264	+	8.24359i	−0.594317	+	0.362202i
$519$	2.70817	−	8.33490i	0.118876	−	0.365861i
$520$	−10.3807	+	8.73510i	−0.455224	+	0.383060i
$521$	11.9178	+	8.65882i	0.522130	+	0.379350i	0.817406	−	0.576062i	$-0.195411\pi$
$521$	11.9178	+	8.65882i	0.522130	+	0.379350i	−0.295275	+	0.955412i	$0.595411\pi$
$522$	8.88795	−	10.3551i	0.389015	−	0.453230i
$523$	−12.5006	−	38.4729i	−0.546614	−	1.68230i	−0.717122	−	0.696948i	$-0.754541\pi$
$523$	−12.5006	−	38.4729i	−0.546614	−	1.68230i	0.170508	−	0.985356i	$-0.445459\pi$
$524$	−3.33649	+	1.67953i	−0.145755	+	0.0733705i
$525$	2.25564	+	3.10462i	0.0984442	+	0.135497i
$526$	5.53853	+	23.3206i	0.241491	+	1.01683i
$527$	0.258445			0.0112580
$528$		0			0
$529$	−5.19479			−0.225860
$530$	−1.71303	−	7.21292i	−0.0744093	−	0.313309i
$531$	−7.00507	−	9.64165i	−0.303994	−	0.418412i
$532$	−23.1308	+	11.6436i	−1.00285	+	0.504815i
$533$	6.36051	+	19.5756i	0.275504	+	0.847915i
$534$	3.68204	−	4.28984i	0.159338	−	0.185639i
$535$	−12.0840	−	8.77951i	−0.522435	−	0.379571i
$536$	10.6326	−	8.94710i	0.459259	−	0.386456i
$537$	−0.213701	+	0.657704i	−0.00922188	+	0.0283820i
$538$	4.77584	−	2.91060i	0.205901	−	0.125485i
$539$		0			0
$540$	−9.67791	−	4.99089i	−0.416471	−	0.214774i
$541$	−15.9160	−	5.17141i	−0.684281	−	0.222336i	−0.0538123	−	0.998551i	$-0.517137\pi$
$541$	−15.9160	−	5.17141i	−0.684281	−	0.222336i	−0.630469	+	0.776215i	$0.717137\pi$
$542$	−12.9224	+	30.9830i	−0.555065	+	1.33083i
$543$	8.20192	−	11.2890i	0.351978	−	0.484456i
$544$	0.394156	+	0.0358733i	0.0168993	+	0.00153805i
$545$	−11.4896	+	3.73320i	−0.492161	+	0.159913i
$546$	−6.04759	−	0.490835i	−0.258813	−	0.0210058i
$547$	−7.51580	+	5.46055i	−0.321352	+	0.233476i	−0.736752	−	0.676163i	$-0.763642\pi$
$547$	−7.51580	+	5.46055i	−0.321352	+	0.233476i	0.415400	+	0.909639i	$0.363642\pi$
$548$	1.76540	+	1.78275i	0.0754141	+	0.0761552i
$549$		−	3.29964i		−	0.140825i
$550$		0			0
$551$		−	31.2996i		−	1.33341i
$552$	10.7972	+	2.67608i	0.459560	+	0.113902i
$553$	7.91027	−	5.74715i	0.336379	−	0.244394i
$554$	−1.71733	+	21.1593i	−0.0729623	+	0.898972i
$555$	−6.53368	+	2.12292i	−0.277339	+	0.0901131i
$556$	12.4176	+	2.02904i	0.526624	+	0.0860505i
$557$	−7.79519	+	10.7292i	−0.330293	+	0.454609i	−0.941575	−	0.336804i	$-0.890654\pi$
$557$	−7.79519	+	10.7292i	−0.330293	+	0.454609i	0.611282	+	0.791413i	$0.290654\pi$
$558$	11.8192	+	4.92954i	0.500345	+	0.208684i
$559$	−6.41157	−	2.08325i	−0.271181	−	0.0881119i
$560$	5.09271	+	7.15563i	0.215206	+	0.302380i
$561$		0			0
$562$	−4.22549	−	6.93336i	−0.178241	−	0.292466i
$563$	−7.26327	+	22.3541i	−0.306110	+	0.942111i	0.673150	+	0.739506i	$0.264941\pi$
$563$	−7.26327	+	22.3541i	−0.306110	+	0.942111i	−0.979260	+	0.202605i	$0.935059\pi$
$564$	−2.20207	−	14.3573i	−0.0927238	−	0.604551i
$565$	12.0250	+	8.73664i	0.505893	+	0.367553i
$566$	12.0134	+	10.3113i	0.504962	+	0.433418i
$567$	2.19572	+	6.75772i	0.0922114	+	0.283797i
$568$	−16.7464	−	10.4319i	−0.702665	−	0.437714i
$569$	7.57056	+	10.4200i	0.317374	+	0.436828i	0.937663	−	0.347545i	$-0.112985\pi$
$569$	7.57056	+	10.4200i	0.317374	+	0.436828i	−0.620289	+	0.784373i	$0.712985\pi$
$570$	−10.9270	+	2.59511i	−0.457683	+	0.108697i
$571$	20.4261			0.854806			0.427403	−	0.904061i	$-0.359429\pi$
$571$	20.4261			0.854806			0.427403	+	0.904061i	$0.359429\pi$
$572$		0			0
$573$	15.1424			0.632585
$574$	12.9643	−	3.07896i	0.541121	−	0.128513i
$575$	9.93055	+	13.6682i	0.414132	+	0.570004i
$576$	17.3412	+	9.15863i	0.722552	+	0.381610i
$577$	2.11524	+	6.51003i	0.0880585	+	0.271016i	0.985383	−	0.170356i	$-0.0544918\pi$
$577$	2.11524	+	6.51003i	0.0880585	+	0.271016i	−0.897324	+	0.441372i	$0.854492\pi$
$578$	18.2379	+	15.6539i	0.758598	+	0.651117i
$579$	−10.3910	−	7.54952i	−0.431836	−	0.313747i
$580$	−10.4928	+	1.60935i	−0.435690	+	0.0668246i
$581$	−1.81750	+	5.59369i	−0.0754026	+	0.232065i
$582$	3.99367	+	6.55298i	0.165543	+	0.271630i
$583$		0			0
$584$	28.5573	−	2.03689i	1.18171	−	0.0842873i
$585$	11.1829	+	3.63356i	0.462358	+	0.150229i
$586$	6.92154	+	2.88684i	0.285926	+	0.119254i
$587$	0.375476	−	0.516798i	0.0154975	−	0.0213305i	−0.801198	−	0.598399i	$-0.795804\pi$
$587$	0.375476	−	0.516798i	0.0154975	−	0.0213305i	0.816695	+	0.577069i	$0.195804\pi$
$588$	1.03877	−	6.35722i	0.0428382	−	0.262167i
$589$	27.9345	−	9.07647i	1.15102	−	0.373989i
$590$	−0.749972	+	9.24043i	−0.0308758	+	0.380423i
$591$	−2.09207	+	1.51998i	−0.0860564	+	0.0625236i
$592$	26.2497	−	8.24614i	1.07885	−	0.338914i
$593$			17.0480i			0.700077i	0.936735	+	0.350039i	$0.113832\pi$
$593$			17.0480i			0.700077i	−0.936735	+	0.350039i	$0.886168\pi$
$594$		0			0
$595$		−	0.153624i		−	0.00629799i
$596$	24.3801	−	24.1429i	0.998649	−	0.988931i
$597$	−6.75080	+	4.90474i	−0.276292	+	0.200738i
$598$	−26.6248	−	2.16092i	−1.08877	−	0.0883666i
$599$	−1.88754	+	0.613298i	−0.0771227	+	0.0250587i	−0.347324	−	0.937745i	$-0.612910\pi$
$599$	−1.88754	+	0.613298i	−0.0771227	+	0.0250587i	0.270202	+	0.962804i	$0.412910\pi$
$600$	−2.50561	−	6.17681i	−0.102291	−	0.252167i
$601$	−9.67660	+	13.3187i	−0.394717	+	0.543281i	−0.959408	−	0.282021i	$-0.908995\pi$
$601$	−9.67660	+	13.3187i	−0.394717	+	0.543281i	0.564692	+	0.825302i	$0.308995\pi$
$602$	−1.67999	+	4.02798i	−0.0684714	+	0.164168i
$603$	−11.4543	−	3.72174i	−0.466457	−	0.151561i
$604$	−11.1453	+	21.6120i	−0.453496	+	0.879380i
$605$		0			0
$606$	8.56231	−	5.21824i	0.347820	−	0.211976i
$607$	8.87509	−	27.3147i	0.360229	−	1.10867i	−0.592686	−	0.805433i	$-0.701933\pi$
$607$	8.87509	−	27.3147i	0.360229	−	1.10867i	0.952915	−	0.303237i	$-0.0980674\pi$
$608$	43.8630	−	9.96515i	1.77888	−	0.404140i
$609$	−3.84084	−	2.79053i	−0.155639	−	0.113078i
$610$	−1.67177	+	1.94773i	−0.0676878	+	0.0788611i
$611$	10.7785	+	33.1728i	0.436051	+	1.34203i
$612$	−0.154235	−	0.306397i	−0.00623457	−	0.0123854i
$613$	−3.91099	−	5.38302i	−0.157964	−	0.217418i	0.722698	−	0.691164i	$-0.242902\pi$
$613$	−3.91099	−	5.38302i	−0.157964	−	0.217418i	−0.880662	+	0.473745i	$0.842902\pi$
$614$	0.741835	+	3.12359i	0.0299380	+	0.126058i
$615$	5.77894			0.233029
$616$		0			0
$617$	−17.8948			−0.720416			−0.360208	−	0.932872i	$-0.617294\pi$
$617$	−17.8948			−0.720416			−0.360208	+	0.932872i	$0.617294\pi$
$618$	2.49818	+	10.5189i	0.100492	+	0.423132i
$619$	−13.6588	−	18.7998i	−0.548995	−	0.755627i	0.440880	−	0.897566i	$-0.354666\pi$
$619$	−13.6588	−	18.7998i	−0.548995	−	0.755627i	−0.989875	+	0.141939i	$0.954666\pi$
$620$	−4.47910	−	8.89801i	−0.179885	−	0.357353i
$621$	−6.62526	−	20.3904i	−0.265862	−	0.818241i
$622$	−18.5751	+	21.6413i	−0.744793	+	0.867736i
$623$	7.11004	+	5.16574i	0.284858	+	0.206961i
$624$	9.99088	+	3.35459i	0.399955	+	0.134291i
$625$	0.319097	−	0.982080i	0.0127639	−	0.0392832i
$626$	1.86201	−	1.13479i	0.0744208	−	0.0453552i
$627$		0			0
$628$	−4.86001	+	9.42411i	−0.193935	+	0.376063i
$629$	−0.457710	−	0.148719i	−0.0182501	−	0.00592982i
$630$	2.93021	−	7.02553i	0.116742	−	0.279904i
$631$	−27.2272	+	37.4750i	−1.08390	+	1.49186i	−0.228739	+	0.973488i	$0.573460\pi$
$631$	−27.2272	+	37.4750i	−1.08390	+	1.49186i	−0.855158	+	0.518368i	$0.826540\pi$
$632$	−15.7379	+	6.38404i	−0.626020	+	0.253943i
$633$	−1.93220	+	0.627811i	−0.0767981	+	0.0249532i
$634$	23.7686	+	1.92911i	0.943972	+	0.0766147i
$635$	−11.2278	+	8.15749i	−0.445562	+	0.323720i
$636$	−4.09208	+	4.05226i	−0.162261	+	0.160682i
$637$			15.4683i			0.612877i
$638$		0			0
$639$			17.0999i			0.676462i
$640$	−5.59602	−	14.1921i	−0.221202	−	0.560993i
$641$	−21.9856	+	15.9734i	−0.868377	+	0.630913i	−0.930151	−	0.367177i	$-0.880324\pi$
$641$	−21.9856	+	15.9734i	−0.868377	+	0.630913i	0.0617738	+	0.998090i	$0.480324\pi$
$642$	−0.938638	+	11.5650i	−0.0370451	+	0.456434i
$643$	29.5052	−	9.58683i	1.16357	−	0.378068i	0.337333	−	0.941386i	$-0.390475\pi$
$643$	29.5052	−	9.58683i	1.16357	−	0.378068i	0.826240	+	0.563318i	$0.190475\pi$
$644$	−2.78868	+	17.0665i	−0.109889	+	0.672516i
$645$	−1.11254	+	1.53128i	−0.0438062	+	0.0602941i
$646$	−0.726147	−	0.302862i	−0.0285699	−	0.0119159i
$647$	40.1073	+	13.0317i	1.57678	+	0.512327i	0.961225	−	0.275765i	$-0.0889313\pi$
$647$	40.1073	+	13.0317i	1.57678	+	0.512327i	0.615557	+	0.788093i	$0.288931\pi$
$648$	−0.878082	−	12.3107i	−0.0344943	−	0.483611i
$649$		0			0
$650$	8.33001	+	13.6682i	0.326730	+	0.536112i
$651$	1.37672	−	4.23712i	0.0539580	−	0.166066i
$652$	−19.8826	+	3.04952i	−0.778663	+	0.119428i
$653$	3.27455	+	2.37910i	0.128143	+	0.0931015i	0.650011	−	0.759925i	$-0.274764\pi$
$653$	3.27455	+	2.37910i	0.128143	+	0.0931015i	−0.521867	+	0.853027i	$0.674764\pi$
$654$	7.12123	+	6.11228i	0.278462	+	0.239009i
$655$	−0.778232	−	2.39515i	−0.0304080	−	0.0935863i
$656$	−23.1439	−	0.226320i	−0.903617	−	0.00883632i
$657$	−14.5850	−	20.0746i	−0.569016	−	0.783183i
$658$	21.9693	−	5.21759i	0.856453	−	0.203403i
$659$	−6.46292			−0.251760			−0.125880	−	0.992045i	$-0.540175\pi$
$659$	−6.46292			−0.251760			−0.125880	+	0.992045i	$0.540175\pi$
$660$		0			0
$661$	26.6232			1.03552			0.517761	−	0.855525i	$-0.326766\pi$
$661$	26.6232			1.03552			0.517761	+	0.855525i	$0.326766\pi$
$662$	−46.7456	+	11.1018i	−1.81682	+	0.431485i
$663$	−0.108354	−	0.149136i	−0.00420810	−	0.00579196i
$664$	5.40163	−	8.67126i	0.209624	−	0.336510i
$665$	−5.39523	−	16.6048i	−0.209218	−	0.643907i
$666$	−18.0953	−	15.5315i	−0.701179	−	0.601834i
$667$	−16.9095	−	12.2854i	−0.654737	−	0.475694i
$668$	6.64255	+	43.3088i	0.257008	+	1.67567i
$669$	5.43039	−	16.7130i	0.209951	−	0.646163i
$670$	4.87569	+	8.00023i	0.188364	+	0.309076i
$671$		0			0
$672$	2.68778	−	6.27096i	0.103683	−	0.241908i
$673$	−7.91272	−	2.57100i	−0.305013	−	0.0991047i	0.152512	−	0.988302i	$-0.451264\pi$
$673$	−7.91272	−	2.57100i	−0.305013	−	0.0991047i	−0.457525	+	0.889197i	$0.651264\pi$
$674$	−22.3139	−	9.30670i	−0.859500	−	0.358481i
$675$	−7.55135	+	10.3935i	−0.290652	+	0.400048i
$676$	0.683109	+	0.111620i	0.0262734	+	0.00429309i
$677$	−14.5159	+	4.71650i	−0.557891	+	0.181270i	−0.574372	−	0.818594i	$-0.694754\pi$
$677$	−14.5159	+	4.71650i	−0.557891	+	0.181270i	0.0164808	+	0.999864i	$0.494754\pi$
$678$	0.934055	−	11.5085i	0.0358721	−	0.441982i
$679$	−9.65143	+	7.01217i	−0.370388	+	0.269102i
$680$	−0.0641940	+	0.259004i	−0.00246173	+	0.00993236i
$681$			0.593162i			0.0227300i
$682$		0			0
$683$			32.9156i			1.25948i	0.776806	+	0.629740i	$0.216839\pi$
$683$			32.9156i			1.25948i	−0.776806	+	0.629740i	$0.783161\pi$
$684$	−27.4313	−	27.7009i	−1.04886	−	1.05917i
$685$	−1.36849	+	0.994269i	−0.0522875	+	0.0379891i
$686$	26.0482	+	2.11412i	0.994524	+	0.0807175i
$687$	16.6166	−	5.39907i	0.633964	−	0.205987i
$688$	4.51554	−	6.08900i	0.172153	−	0.232141i
$689$	8.12866	−	11.1881i	0.309677	−	0.426234i
$690$	−2.88699	+	6.92189i	−0.109906	+	0.263512i
$691$	−43.2897	−	14.0657i	−1.64682	−	0.535083i	−0.668771	−	0.743469i	$-0.733179\pi$
$691$	−43.2897	−	14.0657i	−1.64682	−	0.535083i	−0.978047	+	0.208385i	$0.933179\pi$
$692$	−21.0324	−	10.8464i	−0.799531	−	0.412318i
$693$		0			0
$694$	3.01794	−	1.83926i	0.114559	−	0.0698175i
$695$	−2.62141	+	8.06787i	−0.0994358	+	0.306032i
$696$	5.30943	+	6.30967i	0.201254	+	0.239167i
$697$	0.327521	+	0.237958i	0.0124057	+	0.00901329i
$698$	6.45797	−	7.52398i	0.244438	−	0.284787i
$699$	−4.00348	−	12.3214i	−0.151426	−	0.466040i
$700$	9.25570	−	4.65915i	0.349833	−	0.176099i
$701$	29.4388	+	40.5191i	1.11189	+	1.53038i	0.818604	+	0.574359i	$0.194748\pi$
$701$	29.4388	+	40.5191i	1.11189	+	1.53038i	0.293285	+	0.956025i	$0.405252\pi$
$702$	−4.69356	−	19.7628i	−0.177147	−	0.745899i
$703$	−54.6955			−2.06288
$704$		0			0
$705$	9.79298			0.368825
$706$	−5.86344	−	24.6887i	−0.220674	−	0.929172i
$707$	9.16230	+	12.6108i	0.344584	+	0.474279i
$708$	6.43271	−	3.23811i	0.241756	−	0.121696i
$709$	−2.62623	−	8.08270i	−0.0986301	−	0.303552i	0.889553	−	0.456833i	$-0.151016\pi$
$709$	−2.62623	−	8.08270i	−0.0986301	−	0.303552i	−0.988183	+	0.153280i	$0.951016\pi$
$710$	8.66368	−	10.0938i	0.325142	−	0.378813i
$711$	11.9084	+	8.65195i	0.446599	+	0.324473i
$712$	−9.82865	−	11.6802i	−0.368344	−	0.437736i
$713$	6.06108	−	18.6541i	0.226989	−	0.698601i
$714$	−0.101905	+	0.0621052i	−0.00381369	+	0.00232423i
$715$		0			0
$716$	1.65966	+	0.855885i	0.0620243	+	0.0319859i
$717$	−4.70905	−	1.53006i	−0.175863	−	0.0571413i
$718$	5.26939	−	12.6340i	0.196652	−	0.471496i
$719$	−4.28927	+	5.90368i	−0.159963	+	0.220170i	−0.881474	−	0.472233i	$-0.843448\pi$
$719$	−4.28927	+	5.90368i	−0.159963	+	0.220170i	0.721511	+	0.692403i	$0.243448\pi$
$720$	−7.87593	+	10.6203i	−0.293518	+	0.395796i
$721$	−15.9846	+	5.19370i	−0.595297	+	0.193424i
$722$	−62.3414	−	5.05975i	−2.32011	−	0.188304i
$723$	2.56858	−	1.86619i	0.0955266	−	0.0694042i
$724$	−26.5124	−	26.7730i	−0.985327	−	0.995010i
$725$			12.5244i			0.465146i
$726$		0			0
$727$			1.85004i			0.0686140i	0.999411	+	0.0343070i	$0.0109224\pi$
$727$			1.85004i			0.0686140i	−0.999411	+	0.0343070i	$0.989078\pi$
$728$	−3.94142	+	15.9025i	−0.146079	+	0.589385i
$729$	−1.39548	+	1.01388i	−0.0516845	+	0.0375510i
$730$	−1.56149	+	19.2392i	−0.0577934	+	0.712075i
$731$	−0.126106	+	0.0409743i	−0.00466420	+	0.00151549i
$732$	1.96784	+	0.321545i	0.0727334	+	0.0118847i
$733$	−11.1055	+	15.2854i	−0.410190	+	0.564578i	−0.963265	−	0.268554i	$-0.913454\pi$
$733$	−11.1055	+	15.2854i	−0.410190	+	0.564578i	0.553075	+	0.833132i	$0.313454\pi$
$734$	−40.3933	−	16.8473i	−1.49094	−	0.621844i
$735$	4.13037	+	1.34204i	0.152351	+	0.0495018i
$736$	11.8331	−	27.6082i	0.436173	−	1.01765i
$737$		0			0
$738$	10.4394	+	17.1293i	0.384278	+	0.630540i
$739$	4.85731	−	14.9493i	0.178679	−	0.549918i	−0.821103	−	0.570780i	$-0.806641\pi$
$739$	4.85731	−	14.9493i	0.178679	−	0.549918i	0.999782	+	0.0208619i	$0.00664102\pi$
$740$	2.81231	+	18.3360i	0.103383	+	0.674045i
$741$	−16.9492	−	12.3143i	−0.622645	−	0.452378i
$742$	−6.79347	−	5.83096i	−0.249396	−	0.214061i
$743$	1.79427	+	5.52219i	0.0658253	+	0.202590i	0.978559	−	0.205964i	$-0.0660331\pi$
$743$	1.79427	+	5.52219i	0.0658253	+	0.202590i	−0.912734	+	0.408554i	$0.866033\pi$
$744$	−4.09163	+	6.56832i	−0.150007	+	0.240806i
$745$	13.5972	+	18.7150i	0.498163	+	0.685663i
$746$	6.77868	−	1.60990i	0.248185	−	0.0589427i
$747$	−8.85428			−0.323961
$748$		0			0
$749$	−18.0377			−0.659083
$750$	11.2434	−	2.67026i	0.410552	−	0.0975040i
$751$	1.76537	+	2.42982i	0.0644193	+	0.0886655i	0.840011	−	0.542569i	$-0.182548\pi$
$751$	1.76537	+	2.42982i	0.0644193	+	0.0886655i	−0.775592	+	0.631235i	$0.782548\pi$
$752$	−39.2196	−	0.383522i	−1.43019	−	0.0139856i
$753$	1.12099	+	3.45004i	0.0408510	+	0.125727i
$754$	−15.0263	−	12.8973i	−0.547225	−	0.469693i
$755$	−13.2634	−	9.63639i	−0.482703	−	0.350704i
$756$	−12.9978	+	1.99356i	−0.472725	+	0.0725049i
$757$	−8.06136	+	24.8103i	−0.292995	+	0.901746i	0.690892	+	0.722958i	$0.257218\pi$
$757$	−8.06136	+	24.8103i	−0.292995	+	0.901746i	−0.983888	+	0.178789i	$0.942782\pi$
$758$	2.96241	+	4.86085i	0.107600	+	0.176554i
$759$		0			0
$760$	2.15759	+	30.2495i	0.0782639	+	1.09726i
$761$	−30.3887	−	9.87389i	−1.10159	−	0.357928i	−0.298876	−	0.954292i	$-0.596612\pi$
$761$	−30.3887	−	9.87389i	−1.10159	−	0.357928i	−0.802714	+	0.596364i	$0.796612\pi$
$762$	9.95019	+	4.15003i	0.360457	+	0.150340i
$763$	−8.57526	+	11.8028i	−0.310445	+	0.427291i
$764$	6.59370	−	40.3530i	0.238552	−	1.45992i
$765$	0.219952	−	0.0714667i	0.00795238	−	0.00258388i
$766$	−1.37158	+	16.8993i	−0.0495572	+	0.610596i
$767$	−13.9910	+	10.1651i	−0.505187	+	0.367040i
$768$	−7.15189	+	9.44945i	−0.258072	+	0.340978i
$769$		−	22.3560i		−	0.806176i	−0.915161	−	0.403088i	$-0.867937\pi$
$769$		−	22.3560i		−	0.806176i	0.915161	−	0.403088i	$-0.132063\pi$
$770$		0			0
$771$		−	9.17275i		−	0.330348i
$772$	−24.6434	+	24.4036i	−0.886936	+	0.878305i
$773$	−4.10741	+	2.98421i	−0.147733	+	0.107335i	−0.659197	−	0.751970i	$-0.729104\pi$
$773$	−4.10741	+	2.98421i	−0.147733	+	0.107335i	0.511463	+	0.859305i	$0.329104\pi$
$774$	−6.54861	−	0.531498i	−0.235385	−	0.0191043i
$775$	−11.1779	+	3.63192i	−0.401522	+	0.130462i
$776$	19.2020	−	7.78925i	0.689312	−	0.279618i
$777$	−4.87641	+	6.71180i	−0.174940	+	0.240785i
$778$	−7.47830	+	17.9301i	−0.268110	+	0.642825i
$779$	43.7577	+	14.2177i	1.56778	+	0.509404i
$780$	−3.25674	+	6.31519i	−0.116610	+	0.226120i
$781$		0			0
$782$	−0.448640	+	0.273421i	−0.0160433	+	0.00977750i
$783$	4.91141	−	15.1158i	0.175519	−	0.540193i
$784$	−16.4890	−	5.53644i	−0.588893	−	0.197730i
$785$	−5.78361	−	4.20204i	−0.206426	−	0.149977i
$786$	−1.27418	+	1.48451i	−0.0454485	+	0.0529507i
$787$	0.909670	+	2.79968i	0.0324262	+	0.0997977i	0.965960	−	0.258693i	$-0.0832916\pi$
$787$	0.909670	+	2.79968i	0.0324262	+	0.0997977i	−0.933533	+	0.358490i	$0.883292\pi$
$788$	3.13961	+	6.23702i	0.111844	+	0.222185i
$789$	7.37882	+	10.1561i	0.262693	+	0.361566i
$790$	−2.64581	−	11.1405i	−0.0941336	−	0.396361i
$791$	17.9496			0.638215
$792$		0			0
$793$	−4.78812			−0.170031
$794$	3.97190	+	16.7242i	0.140958	+	0.593519i
$795$	−2.28222	−	3.14121i	−0.0809420	−	0.111407i
$796$	10.1310	+	20.1259i	0.359085	+	0.713345i
$797$	2.31514	+	7.12526i	0.0820064	+	0.252390i	0.983650	−	0.180090i	$-0.0576388\pi$
$797$	2.31514	+	7.12526i	0.0820064	+	0.252390i	−0.901644	+	0.432479i	$0.857639\pi$
$798$	−8.83347	+	10.2916i	−0.312702	+	0.364319i
$799$	0.555015	+	0.403242i	0.0196350	+	0.0142657i
$800$	−17.5516	+	3.98752i	−0.620543	+	0.140980i
$801$	−4.08844	+	12.5829i	−0.144458	+	0.444596i
$802$	−34.7558	+	21.1817i	−1.22727	+	0.747952i
$803$		0			0
$804$	3.33578	−	6.46845i	0.117644	−	0.228125i
$805$	−11.0883	−	3.60282i	−0.390813	−	0.126983i
$806$	7.15327	−	17.1508i	0.251963	−	0.604112i
$807$	1.72174	−	2.36977i	0.0606080	−	0.0834197i
$808$	−10.1777	−	25.0899i	−0.358049	−	0.882660i
$809$	37.8768	−	12.3069i	1.33168	−	0.432688i	0.445188	−	0.895437i	$-0.353137\pi$
$809$	37.8768	−	12.3069i	1.33168	−	0.432688i	0.886489	+	0.462749i	$0.153137\pi$
$810$	8.29380	+	0.673141i	0.291414	+	0.0236518i
$811$	34.5030	−	25.0679i	1.21157	−	0.880254i	0.216193	−	0.976351i	$-0.430636\pi$
$811$	34.5030	−	25.0679i	1.21157	−	0.880254i	0.995372	+	0.0960970i	$0.0306359\pi$
$812$	−9.10896	+	9.02032i	−0.319662	+	0.316551i
$813$			17.5818i			0.616619i
$814$		0			0
$815$		−	13.5617i		−	0.475047i
$816$	0.197759	−	0.0621244i	0.00692293	−	0.00217479i
$817$	−12.1914	+	8.85759i	−0.426524	+	0.309888i
$818$	2.16856	−	26.7189i	0.0758218	−	0.934204i
$819$	13.5047	−	4.38795i	0.471893	−	0.153327i
$820$	2.51641	−	15.4003i	0.0878769	−	0.537801i
$821$	11.3507	−	15.6229i	0.396142	−	0.545243i	−0.563628	−	0.826029i	$-0.690595\pi$
$821$	11.3507	−	15.6229i	0.396142	−	0.545243i	0.959771	+	0.280785i	$0.0905949\pi$
$822$	1.21277	+	0.505823i	0.0423003	+	0.0176426i
$823$	9.43380	+	3.06523i	0.328842	+	0.106847i	0.468785	−	0.883312i	$-0.344692\pi$
$823$	9.43380	+	3.06523i	0.328842	+	0.106847i	−0.139943	+	0.990160i	$0.544692\pi$
$824$	29.1196	−	2.07700i	1.01443	−	0.0723557i
$825$		0			0
$826$	5.82633	+	9.56010i	0.202724	+	0.332638i
$827$	13.4827	−	41.4953i	0.468838	−	1.44293i	−0.385253	−	0.922811i	$-0.625886\pi$
$827$	13.4827	−	41.4953i	0.468838	−	1.44293i	0.854091	−	0.520124i	$-0.174114\pi$
$828$	−25.7324	+	3.94673i	−0.894261	+	0.137159i
$829$	22.7735	+	16.5459i	0.790957	+	0.574664i	0.908247	−	0.418434i	$-0.137421\pi$
$829$	22.7735	+	16.5459i	0.790957	+	0.574664i	−0.117290	+	0.993098i	$0.537421\pi$
$830$	5.22654	+	4.48603i	0.181416	+	0.155712i
$831$	3.43575	+	10.5742i	0.119185	+	0.366814i
$832$	13.2901	−	25.1639i	0.460752	−	0.872402i
$833$	0.178827	+	0.246135i	0.00619600	+	0.00852806i
$834$	6.41147	−	1.52269i	0.222011	−	0.0527265i
$835$	−29.5406			−1.02229
$836$		0			0
$837$	14.9149			0.515533
$838$	21.1489	−	5.02276i	0.730577	−	0.173508i
$839$	20.5447	+	28.2774i	0.709283	+	0.976244i	0.999812	+	0.0193779i	$0.00616858\pi$
$839$	20.5447	+	28.2774i	0.709283	+	0.976244i	−0.290529	+	0.956866i	$0.593831\pi$
$840$	3.90433	+	2.43214i	0.134712	+	0.0839170i
$841$	4.17345	+	12.8446i	0.143912	+	0.442916i
$842$	20.7337	+	17.7961i	0.714532	+	0.613295i
$843$	−3.44033	−	2.49954i	−0.118491	−	0.0860889i
$844$	0.831683	+	5.42249i	0.0286277	+	0.186650i
$845$	−0.144207	+	0.443825i	−0.00496089	+	0.0152680i
$846$	17.6905	+	29.0273i	0.608212	+	0.997980i
$847$		0			0
$848$	9.01697	+	12.6695i	0.309644	+	0.435072i
$849$	7.88587	+	2.56227i	0.270642	+	0.0879371i
$850$	0.290565	+	0.121189i	0.00996629	+	0.00415675i
$851$	−21.4686	+	29.5490i	−0.735934	+	1.01293i
$852$	−10.1980	−	1.66636i	−0.349379	−	0.0570885i
$853$	−25.8841	+	8.41026i	−0.886255	+	0.287962i	−0.716552	−	0.697533i	$-0.754281\pi$
$853$	−25.8841	+	8.41026i	−0.886255	+	0.287962i	−0.169703	+	0.985495i	$0.554281\pi$
$854$	−0.250754	+	3.08955i	−0.00858062	+	0.105722i
$855$	21.2641	−	15.4492i	0.727216	−	0.528353i
$856$	30.4108	+	7.53729i	1.03942	+	0.257619i
$857$		−	37.5541i		−	1.28282i	−0.767197	−	0.641412i	$-0.778349\pi$
$857$		−	37.5541i		−	1.28282i	0.767197	−	0.641412i	$-0.221651\pi$
$858$		0			0
$859$		−	4.50293i		−	0.153638i	−0.997045	−	0.0768190i	$-0.975524\pi$
$859$		−	4.50293i		−	0.153638i	0.997045	−	0.0768190i	$-0.0244764\pi$
$860$	3.59625	+	3.63159i	0.122631	+	0.123836i
$861$	5.64593	−	4.10201i	0.192413	−	0.139796i
$862$	38.2052	+	3.10081i	1.30127	+	0.105614i
$863$	17.1534	−	5.57348i	0.583908	−	0.189723i	−0.00214238	−	0.999998i	$-0.500682\pi$
$863$	17.1534	−	5.57348i	0.583908	−	0.189723i	0.586051	+	0.810274i	$0.300682\pi$
$864$	22.7468	+	2.07025i	0.773861	+	0.0704314i
$865$	9.37795	−	12.9076i	0.318860	−	0.438873i
$866$	−2.37143	+	5.68579i	−0.0805846	+	0.193211i
$867$	11.9718	+	3.88986i	0.406582	+	0.132107i
$868$	−10.6920	−	5.51386i	−0.362910	−	0.187152i
$869$		0			0
$870$	−4.74754	+	2.89336i	−0.160957	+	0.0980940i
$871$	−5.40063	+	16.6214i	−0.182993	+	0.563196i
$872$	19.3895	−	16.3158i	0.656611	−	0.552522i
$873$	−14.5296	−	10.5564i	−0.491751	−	0.357278i
$874$	−38.8897	+	45.3093i	−1.31547	+	1.53261i
$875$	5.55145	+	17.0856i	0.187673	+	0.577599i
$876$	13.3933	−	6.74196i	0.452519	−	0.227790i
$877$	8.00606	+	11.0194i	0.270345	+	0.372099i	0.922506	−	0.385982i	$-0.126137\pi$
$877$	8.00606	+	11.0194i	0.270345	+	0.372099i	−0.652161	+	0.758081i	$0.726137\pi$
$878$	−7.87523	−	33.1596i	−0.265776	−	1.11908i
$879$	3.92773			0.132479
$880$		0			0
$881$	5.44549			0.183463			0.0917317	−	0.995784i	$-0.470760\pi$
$881$	5.44549			0.183463			0.0917317	+	0.995784i	$0.470760\pi$
$882$	3.48337	+	14.6671i	0.117291	+	0.493868i
$883$	16.5930	+	22.8383i	0.558399	+	0.768570i	0.991122	−	0.132957i	$-0.0424472\pi$
$883$	16.5930	+	22.8383i	0.558399	+	0.768570i	−0.432723	+	0.901527i	$0.642447\pi$
$884$	−0.444614	+	0.223811i	−0.0149540	+	0.00752756i
$885$	1.50042	+	4.61782i	0.0504361	+	0.155226i
$886$	−21.2262	+	24.7300i	−0.713109	+	0.830822i
$887$	−34.3342	−	24.9453i	−1.15283	−	0.837580i	−0.163975	−	0.986464i	$-0.552432\pi$
$887$	−34.3342	−	24.9453i	−1.15283	−	0.837580i	−0.988855	+	0.148885i	$0.952432\pi$
$888$	11.0260	−	9.27814i	0.370009	−	0.311354i
$889$	−5.17904	+	15.9395i	−0.173700	+	0.534592i
$890$	8.78849	−	5.35608i	0.294591	−	0.179536i
$891$		0			0
$892$	−42.1738	−	21.7490i	−1.41208	−	0.728211i
$893$	74.1517	+	24.0933i	2.48139	+	0.806253i
$894$	6.91744	−	16.5854i	0.231354	−	0.554698i
$895$	−0.740011	+	1.01854i	−0.0247358	+	0.0340460i
$896$	−15.5411	−	9.89332i	−0.519191	−	0.330513i
$897$	−13.3055	+	4.32322i	−0.444258	+	0.144348i
$898$	5.31903	+	0.431703i	0.177498	+	0.0144061i
$899$	11.7633	−	8.54653i	0.392328	−	0.285043i
$900$	10.9765	+	11.0844i	0.365885	+	0.369480i
$901$		−	0.272002i		−	0.00906169i
$902$		0			0
$903$			2.28574i			0.0760646i
$904$	−30.2623	−	7.50049i	−1.00651	−	0.249462i
$905$	20.5518	−	14.9317i	0.683164	−	0.496348i
$906$	−1.03025	+	12.6937i	−0.0342277	+	0.421722i
$907$	32.9920	−	10.7198i	1.09548	−	0.355944i	0.295120	−	0.955460i	$-0.404640\pi$
$907$	32.9920	−	10.7198i	1.09548	−	0.355944i	0.800363	+	0.599516i	$0.204640\pi$
$908$	1.58072	+	0.258289i	0.0524579	+	0.00857163i
$909$	−13.7932	+	18.9847i	−0.457492	+	0.629684i
$910$	−10.1948	−	4.25204i	−0.337953	−	0.140954i
$911$	−28.2154	−	9.16772i	−0.934816	−	0.303740i	−0.198286	−	0.980144i	$-0.563537\pi$
$911$	−28.2154	−	9.16772i	−0.934816	−	0.303740i	−0.736531	+	0.676404i	$0.763537\pi$
$912$	19.1933	−	13.6600i	0.635555	−	0.452329i
$913$		0			0
$914$	−25.9483	−	42.5771i	−0.858294	−	1.40833i
$915$	−0.415419	+	1.27853i	−0.0137333	+	0.0422669i
$916$	−7.15234	−	46.6326i	−0.236320	−	1.54078i
$917$	−2.46045	−	1.78762i	−0.0812511	−	0.0590324i
$918$	−0.303160	−	0.260207i	−0.0100058	−	0.00858812i
$919$	−6.67764	−	20.5517i	−0.220275	−	0.677937i	−0.998737	−	0.0502448i	$-0.984000\pi$
$919$	−6.67764	−	20.5517i	−0.220275	−	0.677937i	0.778462	−	0.627692i	$-0.216000\pi$
$920$	17.1890	+	10.7076i	0.566704	+	0.353020i
$921$	0.988326	+	1.36031i	0.0325665	+	0.0448239i
$922$	−52.9839	+	12.5834i	−1.74493	+	0.414412i
$923$	24.8137			0.816754
$924$		0			0
$925$	21.8862			0.719614
$926$	14.8150	−	3.51849i	0.486852	−	0.115625i
$927$	−14.8722	−	20.4698i	−0.488467	−	0.672317i
$928$	19.1266	−	11.4016i	0.627861	−	0.374275i
$929$	14.5920	+	44.9097i	0.478749	+	1.47344i	0.840834	+	0.541293i	$0.182065\pi$
$929$	14.5920	+	44.9097i	0.478749	+	1.47344i	−0.362085	+	0.932145i	$0.617935\pi$
$930$	−3.95901	−	3.39808i	−0.129821	−	0.111428i
$931$	27.9730	+	20.3236i	0.916780	+	0.666079i
$932$	−34.5787	+	5.30355i	−1.13266	+	0.173724i
$933$	−4.61574	+	14.2058i	−0.151113	+	0.465077i
$934$	15.2199	+	24.9734i	0.498009	+	0.817154i
$935$		0			0
$936$	−24.6020	+	1.75477i	−0.804140	+	0.0573565i
$937$	44.1171	+	14.3345i	1.44124	+	0.468289i	0.922285	−	0.386510i	$-0.126320\pi$
$937$	44.1171	+	14.3345i	1.44124	+	0.468289i	0.518959	+	0.854799i	$0.326320\pi$
$938$	10.4422	+	4.35524i	0.340950	+	0.142203i
$939$	0.671272	−	0.923926i	0.0219061	−	0.0301512i
$940$	4.26430	−	26.0973i	0.139086	−	0.851199i
$941$	37.4912	−	12.1816i	1.22218	−	0.397109i	0.374303	−	0.927307i	$-0.377882\pi$
$941$	37.4912	−	12.1816i	1.22218	−	0.397109i	0.847874	+	0.530197i	$0.177882\pi$
$942$	−0.449250	+	5.53522i	−0.0146373	+	0.180347i
$943$	24.8565	−	18.0593i	0.809438	−	0.588091i
$944$	−5.82814	−	18.5525i	−0.189690	−	0.603833i
$945$		−	8.86568i		−	0.288401i
$946$		0			0
$947$		−	24.9488i		−	0.810725i	−0.914156	−	0.405363i	$-0.867145\pi$
$947$		−	24.9488i		−	0.810725i	0.914156	−	0.405363i	$-0.132855\pi$
$948$	−6.32029	+	6.25879i	−0.205274	+	0.203276i
$949$	−29.1303	+	21.1644i	−0.945608	+	0.687025i
$950$	35.6624	+	2.89443i	1.15704	+	0.0939077i
$951$	11.8782	−	3.85945i	0.385176	−	0.125151i
$952$	0.121130	+	0.298609i	0.00392584	+	0.00967797i
$953$	−24.0471	+	33.0979i	−0.778961	+	1.07215i	0.216435	+	0.976297i	$0.430557\pi$
$953$	−24.0471	+	33.0979i	−0.778961	+	1.07215i	−0.995396	+	0.0958506i	$0.969443\pi$
$954$	5.18813	−	12.4392i	0.167972	−	0.402732i
$955$	26.2179	+	8.51870i	0.848391	+	0.275659i
$956$	−6.12800	+	11.8829i	−0.198194	+	0.384320i
$957$		0			0
$958$	13.7835	−	8.40029i	0.445326	−	0.271401i
$959$	−0.631244	+	1.94277i	−0.0203839	+	0.0627353i
$960$	−5.56624	−	5.73197i	−0.179650	−	0.184999i
$961$	−14.0407	−	10.2011i	−0.452924	−	0.329069i
$962$	−22.5378	+	26.2582i	−0.726649	+	0.846597i
$963$	−8.39122	−	25.8255i	−0.270403	−	0.832215i
$964$	−3.85471	−	7.65763i	−0.124152	−	0.246636i
$965$	−13.7440	−	18.9171i	−0.442437	−	0.608962i
$966$	2.09276	+	8.81181i	0.0673334	+	0.283515i
$967$	23.6696			0.761164			0.380582	−	0.924747i	$-0.375724\pi$
$967$	23.6696			0.761164			0.380582	+	0.924747i	$0.375724\pi$
$968$		0			0
$969$	−0.412063			−0.0132374
$970$	3.22818	+	13.5927i	0.103651	+	0.436434i
$971$	31.7005	+	43.6320i	1.01732	+	1.40022i	0.914067	+	0.405563i	$0.132924\pi$
$971$	31.7005	+	43.6320i	1.01732	+	1.40022i	0.103251	+	0.994655i	$0.467076\pi$
$972$	−13.7992	−	27.4130i	−0.442610	−	0.879273i
$973$	3.16566	+	9.74291i	0.101487	+	0.312343i
$974$	−3.68890	+	4.29783i	−0.118200	+	0.137711i
$975$	6.78216	+	4.92753i	0.217203	+	0.157807i
$976$	1.71377	−	5.10407i	0.0548564	−	0.163377i
$977$	−2.96528	+	9.12620i	−0.0948678	+	0.291973i	−0.987219	−	0.159368i	$-0.949054\pi$
$977$	−2.96528	+	9.12620i	−0.0948678	+	0.291973i	0.892351	+	0.451341i	$0.149054\pi$
$978$	−8.99601	+	5.48256i	−0.287661	+	0.175313i
$979$		0			0
$980$	5.37494	−	10.4226i	0.171696	−	0.332938i
$981$	−20.8880	−	6.78691i	−0.666901	−	0.216689i
$982$	6.09389	−	14.6108i	0.194464	−	0.466250i
$983$	20.7503	−	28.5603i	0.661831	−	0.910932i	−0.337709	−	0.941250i	$-0.609652\pi$
$983$	20.7503	−	28.5603i	0.661831	−	0.910932i	0.999540	+	0.0303182i	$0.00965206\pi$
$984$	−11.2329	+	4.55659i	−0.358091	+	0.145259i
$985$	−4.47735	+	1.45478i	−0.142660	+	0.0463531i
$986$	−0.388205	−	0.0315075i	−0.0123630	−	0.00100340i
$987$	9.56758	−	6.95125i	0.304539	−	0.221261i
$988$	−40.1968	+	39.8057i	−1.27883	+	1.26639i
$989$			10.0631i			0.319987i
$990$		0			0
$991$		−	17.8021i		−	0.565502i	−0.959193	−	0.282751i	$-0.908753\pi$
$991$		−	17.8021i		−	0.565502i	0.959193	−	0.282751i	$-0.0912471\pi$
$992$	15.7222	+	13.7639i	0.499181	+	0.437005i
$993$	−20.3576	+	14.7907i	−0.646029	+	0.469367i
$994$	1.29949	−	16.0111i	0.0412175	−	0.507842i
$995$	−14.4477	+	4.69435i	−0.458023	+	0.148821i
$996$	0.862836	−	5.28051i	0.0273400	−	0.167319i
$997$	36.9946	−	50.9188i	1.17163	−	1.61261i	0.519648	−	0.854380i	$-0.326063\pi$
$997$	36.9946	−	50.9188i	1.17163	−	1.61261i	0.651984	−	0.758233i	$-0.273937\pi$
$998$	−51.3814	−	21.4302i	−1.62645	−	0.678360i
$999$	−26.4145	−	8.58260i	−0.835719	−	0.271542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.g.j.475.2		16
4.3	odd	2	inner	484.2.g.j.475.1		16
11.2	odd	10		44.2.g.a.19.3	yes	16
11.3	even	5		44.2.g.a.7.1	✓	16
11.4	even	5		484.2.c.d.483.13		16
11.5	even	5		484.2.g.f.215.4		16
11.6	odd	10	inner	484.2.g.j.215.1		16
11.7	odd	10		484.2.c.d.483.4		16
11.8	odd	10		484.2.g.i.403.4		16
11.9	even	5		484.2.g.i.239.2		16
11.10	odd	2		484.2.g.f.475.3		16
33.2	even	10		396.2.r.a.19.2		16
33.14	odd	10		396.2.r.a.271.4		16
44.3	odd	10		44.2.g.a.7.3	yes	16
44.7	even	10		484.2.c.d.483.14		16
44.15	odd	10		484.2.c.d.483.3		16
44.19	even	10		484.2.g.i.403.2		16
44.27	odd	10		484.2.g.f.215.3		16
44.31	odd	10		484.2.g.i.239.4		16
44.35	even	10		44.2.g.a.19.1	yes	16
44.39	even	10	inner	484.2.g.j.215.2		16
44.43	even	2		484.2.g.f.475.4		16
88.3	odd	10		704.2.u.c.447.3		16
88.13	odd	10		704.2.u.c.63.3		16
88.35	even	10		704.2.u.c.63.2		16
88.69	even	10		704.2.u.c.447.2		16
132.35	odd	10		396.2.r.a.19.4		16
132.47	even	10		396.2.r.a.271.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.7.1	✓	16	11.3	even	5
44.2.g.a.7.3	yes	16	44.3	odd	10
44.2.g.a.19.1	yes	16	44.35	even	10
44.2.g.a.19.3	yes	16	11.2	odd	10
396.2.r.a.19.2		16	33.2	even	10
396.2.r.a.19.4		16	132.35	odd	10
396.2.r.a.271.2		16	132.47	even	10
396.2.r.a.271.4		16	33.14	odd	10
484.2.c.d.483.3		16	44.15	odd	10
484.2.c.d.483.4		16	11.7	odd	10
484.2.c.d.483.13		16	11.4	even	5
484.2.c.d.483.14		16	44.7	even	10
484.2.g.f.215.3		16	44.27	odd	10
484.2.g.f.215.4		16	11.5	even	5
484.2.g.f.475.3		16	11.10	odd	2
484.2.g.f.475.4		16	44.43	even	2
484.2.g.i.239.2		16	11.9	even	5
484.2.g.i.239.4		16	44.31	odd	10
484.2.g.i.403.2		16	44.19	even	10
484.2.g.i.403.4		16	11.8	odd	10
484.2.g.j.215.1		16	11.6	odd	10	inner
484.2.g.j.215.2		16	44.39	even	10	inner
484.2.g.j.475.1		16	4.3	odd	2	inner
484.2.g.j.475.2		16	1.1	even	1	trivial
704.2.u.c.63.2		16	88.35	even	10
704.2.u.c.63.3		16	88.13	odd	10
704.2.u.c.447.2		16	88.69	even	10
704.2.u.c.447.3		16	88.3	odd	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.326779 - 1.37594i) q^{2} +(-0.435358 - 0.599219i) q^{3} +(-1.78643 + 0.899257i) q^{4} +(-0.416683 - 1.28242i) q^{5} +(-0.682225 + 0.794840i) q^{6} +(-1.31738 - 0.957131i) q^{7} +(1.82109 + 2.16417i) q^{8} +(0.757524 - 2.33142i) q^{9} +(-1.62837 + 0.992398i) q^{10} +(1.31659 + 0.678965i) q^{12} +(-3.38313 - 1.09925i) q^{13} +(-0.886465 + 2.12541i) q^{14} +(-0.587043 + 0.807995i) q^{15} +(2.38267 - 3.21292i) q^{16} +(-0.0665412 + 0.0216205i) q^{17} +(-3.45544 - 0.280450i) q^{18} +(-6.43293 + 4.67380i) q^{19} +(1.89760 + 1.91625i) q^{20} +1.20609i q^{21} +5.30988i q^{23} +(0.503982 - 2.03342i) q^{24} +(2.57411 - 1.87020i) q^{25} +(-0.406962 + 5.01420i) q^{26} +(-3.84010 + 1.24772i) q^{27} +(3.21411 + 0.525187i) q^{28} +(-2.31370 + 3.18453i) q^{29} +(1.30359 + 0.543701i) q^{30} +(-3.51309 - 1.14147i) q^{31} +(-5.19940 - 2.22850i) q^{32} +(0.0514928 + 0.0844916i) q^{34} +(-0.678513 + 2.08825i) q^{35} +(0.743282 + 4.84613i) q^{36} +(5.56491 + 4.04314i) q^{37} +(8.53302 + 7.32404i) q^{38} +(0.814185 + 2.50580i) q^{39} +(2.01655 - 3.23717i) q^{40} +(-3.40107 - 4.68117i) q^{41} +(1.65951 - 0.394126i) q^{42} +1.89516 q^{43} -3.30550 q^{45} +(7.30608 - 1.73516i) q^{46} +(-5.76344 - 7.93270i) q^{47} +(-2.96256 - 0.0289704i) q^{48} +(-1.34373 - 4.13559i) q^{49} +(-3.41446 - 2.93069i) q^{50} +(0.0419247 + 0.0304601i) q^{51} +(7.03224 - 1.07858i) q^{52} +(-1.20135 + 3.69738i) q^{53} +(2.97166 + 4.87602i) q^{54} +(-0.327678 - 4.59405i) q^{56} +(5.60126 + 1.81996i) q^{57} +(5.13780 + 2.14287i) q^{58} +(2.85758 - 3.93312i) q^{59} +(0.322116 - 1.97133i) q^{60} +(1.28015 - 0.415944i) q^{61} +(-0.422596 + 5.20682i) q^{62} +(-3.22942 + 2.34631i) q^{63} +(-1.36723 + 7.88230i) q^{64} +4.79662i q^{65} -4.91303i q^{67} +(0.0994288 - 0.0984612i) q^{68} +(3.18178 - 2.31170i) q^{69} +(3.09503 + 0.251199i) q^{70} +(-6.63416 + 2.15557i) q^{71} +(6.42510 - 2.60633i) q^{72} +(5.94967 - 8.18902i) q^{73} +(3.74464 - 8.97821i) q^{74} +(-2.24132 - 0.728250i) q^{75} +(7.28904 - 14.1343i) q^{76} +(3.18178 - 1.93911i) q^{78} +(-1.85551 + 5.71067i) q^{79} +(-5.11313 - 1.71681i) q^{80} +(-3.53019 - 2.56484i) q^{81} +(-5.32962 + 6.20939i) q^{82} +(-1.11615 - 3.43515i) q^{83} +(-1.08459 - 2.15460i) q^{84} +(0.0554531 + 0.0763247i) q^{85} +(-0.619298 - 2.60763i) q^{86} +2.91552 q^{87} -5.39711 q^{89} +(1.08017 + 4.54818i) q^{90} +(3.40474 + 4.68622i) q^{91} +(-4.77495 - 9.48573i) q^{92} +(0.845462 + 2.60206i) q^{93} +(-9.03156 + 10.5224i) q^{94} +(8.67425 + 6.30221i) q^{95} +(0.928241 + 4.08578i) q^{96} +(2.26393 - 6.96767i) q^{97} +(-5.25122 + 3.20032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - q^{4} + 4 q^{5} - 10 q^{6} + 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} + 10 q^{17} + 15 q^{18} - 24 q^{20} - 40 q^{24} - 4 q^{25} + 16 q^{26} + 30 q^{28} - 40 q^{29} - 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q + 5 * q^2 - q^4 + 4 * q^5 - 10 * q^6 + 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 + 10 * q^17 + 15 * q^18 - 24 * q^20 - 40 * q^24 - 4 * q^25 + 16 * q^26 + 30 * q^28 - 40 * q^29 - 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 + 50 * q^41 + 24 * q^42 + 40 * q^45 + 40 * q^46 - q^48 + 16 * q^49 - 25 * q^50 + 20 * q^52 - 12 * q^53 - 12 * q^56 + 50 * q^57 - 48 * q^60 - 20 * q^61 + 30 * q^62 - 37 * q^64 - 35 * q^68 + 4 * q^69 + 22 * q^70 + 10 * q^72 + 30 * q^73 - 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 + 10 * q^84 - 60 * q^85 + 46 * q^86 - 36 * q^89 + 40 * q^90 - 54 * q^92 + 2 * q^93 - 60 * q^94 + 55 * q^96 + 72 * q^97

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