LMFDB - Embedded newform 88.2.k.b.35.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(19,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("88.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.k (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:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.6
Character	$\chi$	$=$	88.35
Dual form			88.2.k.b.83.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.612688 - 1.27460i) q^{2} +(-0.903665 + 0.656551i) q^{3} +(-1.24923 - 1.56187i) q^{4} +(3.74056 - 1.21538i) q^{5} +(0.283177 + 1.55407i) q^{6} +(-2.25832 - 1.64076i) q^{7} +(-2.75615 + 0.635331i) q^{8} +(-0.541500 + 1.66657i) q^{9} +(0.742666 - 5.51238i) q^{10} +(3.00002 + 1.41418i) q^{11} +(2.15433 + 0.591224i) q^{12} +(-0.653051 + 2.00988i) q^{13} +(-3.47497 + 1.87318i) q^{14} +(-2.58225 + 3.55416i) q^{15} +(-0.878863 + 3.90226i) q^{16} +(-4.42965 + 1.43928i) q^{17} +(1.79244 + 1.71128i) q^{18} +(2.18382 + 3.00577i) q^{19} +(-6.57107 - 4.32397i) q^{20} +3.11801 q^{21} +(3.64059 - 2.95738i) q^{22} +0.854640i q^{23} +(2.07351 - 2.38368i) q^{24} +(8.46953 - 6.15347i) q^{25} +(2.16169 + 2.06381i) q^{26} +(-1.64036 - 5.04850i) q^{27} +(0.258495 + 5.57688i) q^{28} +(-4.36210 - 3.16925i) q^{29} +(2.94803 + 5.46894i) q^{30} +(-0.796872 - 0.258919i) q^{31} +(4.43536 + 3.51107i) q^{32} +(-3.63949 + 0.691723i) q^{33} +(-0.879482 + 6.52788i) q^{34} +(-10.4415 - 3.39265i) q^{35} +(3.27941 - 1.23617i) q^{36} +(2.13456 - 2.93797i) q^{37} +(5.16916 - 0.941903i) q^{38} +(-0.729452 - 2.24502i) q^{39} +(-9.53736 + 5.72626i) q^{40} +(-2.17890 - 2.99900i) q^{41} +(1.91036 - 3.97422i) q^{42} -1.38448i q^{43} +(-1.53895 - 6.45226i) q^{44} +6.89201i q^{45} +(1.08933 + 0.523628i) q^{46} +(-0.799046 - 1.09979i) q^{47} +(-1.76783 - 4.10335i) q^{48} +(0.244772 + 0.753330i) q^{49} +(-2.65406 - 14.5655i) q^{50} +(3.05796 - 4.20892i) q^{51} +(3.95498 - 1.49082i) q^{52} +(-4.01470 - 1.30446i) q^{53} +(-7.43987 - 1.00235i) q^{54} +(12.9405 + 1.64365i) q^{55} +(7.26668 + 3.08741i) q^{56} +(-3.94688 - 1.28242i) q^{57} +(-6.71215 + 3.61819i) q^{58} +(6.80468 + 4.94389i) q^{59} +(8.77695 - 0.406822i) q^{60} +(0.970728 + 2.98759i) q^{61} +(-0.818253 + 0.857059i) q^{62} +(3.95732 - 2.87516i) q^{63} +(7.19271 - 3.50213i) q^{64} +8.31179i q^{65} +(-1.34820 + 5.06271i) q^{66} +3.45851 q^{67} +(7.78161 + 5.12054i) q^{68} +(-0.561115 - 0.772308i) q^{69} +(-10.7217 + 11.2302i) q^{70} +(-11.7395 + 3.81439i) q^{71} +(0.433633 - 4.93733i) q^{72} +(1.90829 - 2.62654i) q^{73} +(-2.43693 - 4.52077i) q^{74} +(-3.61355 + 11.1214i) q^{75} +(1.96653 - 7.16572i) q^{76} +(-4.45466 - 8.11598i) q^{77} +(-3.30844 - 0.445736i) q^{78} +(3.59997 - 11.0796i) q^{79} +(1.45529 + 15.6648i) q^{80} +(0.543938 + 0.395194i) q^{81} +(-5.15752 + 0.939783i) q^{82} +(0.870974 - 0.282997i) q^{83} +(-3.89510 - 4.86991i) q^{84} +(-14.8201 + 10.7674i) q^{85} +(-1.76466 - 0.848252i) q^{86} +6.02266 q^{87} +(-9.16696 - 1.99168i) q^{88} +7.98458 q^{89} +(8.78458 + 4.22265i) q^{90} +(4.77254 - 3.46745i) q^{91} +(1.33483 - 1.06764i) q^{92} +(0.890099 - 0.289211i) q^{93} +(-1.89137 + 0.344637i) q^{94} +(11.8218 + 8.58907i) q^{95} +(-6.31327 - 0.260789i) q^{96} +(-3.44331 + 10.5974i) q^{97} +(1.11017 + 0.149569i) q^{98} +(-3.98133 + 4.23395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9} - 18 q^{11} - 18 q^{12} + 8 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} - 30 q^{20} + 17 q^{22} + 5 q^{24} + 6 q^{25} - 4 q^{26} - 32 q^{27}+ \cdots + 122 q^{99}+O(q^{100}) $ 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9 - 18 * q^11 - 18 * q^12 + 8 * q^14 - q^16 - 10 * q^17 - 20 * q^18 - 30 * q^20 + 17 * q^22 + 5 * q^24 + 6 * q^25 - 4 * q^26 - 32 * q^27 - 30 * q^28 + 30 * q^30 + 32 * q^33 - 14 * q^34 - 10 * q^35 + 16 * q^36 + 28 * q^38 + 30 * q^40 - 10 * q^41 + 64 * q^42 - 38 * q^44 + 40 * q^46 + 26 * q^48 - 18 * q^49 + 5 * q^50 + 60 * q^51 + 40 * q^52 + 76 * q^56 - 80 * q^57 - 56 * q^58 + 28 * q^59 + 34 * q^60 - 80 * q^62 + 55 * q^64 - 30 * q^66 - 28 * q^67 + 60 * q^68 - 44 * q^70 + 45 * q^72 - 10 * q^73 - 100 * q^74 + 4 * q^75 - 80 * q^78 - 76 * q^80 + 28 * q^81 + 13 * q^82 - 50 * q^84 - 39 * q^86 - 69 * q^88 + 20 * q^89 - 30 * q^90 + 78 * q^91 + 6 * q^92 - 30 * q^94 - 110 * q^96 - 52 * q^97 + 122 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.612688	−	1.27460i	0.433236	−	0.901281i
$2$	0.612688	−	1.27460i	0.433236	−	0.901281i
$3$	−0.903665	+	0.656551i	−0.521731	+	0.379060i	−0.817256	−	0.576275i	$-0.804506\pi$
$3$	−0.903665	+	0.656551i	−0.521731	+	0.379060i	0.295525	+	0.955335i	$0.404506\pi$
$4$	−1.24923	−	1.56187i	−0.624614	−	0.780934i
$5$	3.74056	−	1.21538i	1.67283	−	0.543535i	0.689329	−	0.724448i	$-0.257905\pi$
$5$	3.74056	−	1.21538i	1.67283	−	0.543535i	0.983499	+	0.180914i	$0.0579055\pi$
$6$	0.283177	+	1.55407i	0.115607	+	0.634448i
$7$	−2.25832	−	1.64076i	−0.853564	−	0.620150i	0.0725628	−	0.997364i	$-0.476882\pi$
$7$	−2.25832	−	1.64076i	−0.853564	−	0.620150i	−0.926126	+	0.377214i	$0.876882\pi$
$8$	−2.75615	+	0.635331i	−0.974446	+	0.224624i
$9$	−0.541500	+	1.66657i	−0.180500	+	0.555522i
$10$	0.742666	−	5.51238i	0.234852	−	1.74317i
$11$	3.00002	+	1.41418i	0.904539	+	0.426390i
$11$	3.00002	+	1.41418i	0.904539	+	0.426390i
$12$	2.15433	+	0.591224i	0.621901	+	0.170672i
$13$	−0.653051	+	2.00988i	−0.181124	+	0.557441i	−0.999860	−	0.0167282i	$-0.994675\pi$
$13$	−0.653051	+	2.00988i	−0.181124	+	0.557441i	0.818736	+	0.574170i	$0.194675\pi$
$14$	−3.47497	+	1.87318i	−0.928724	+	0.500629i
$15$	−2.58225	+	3.55416i	−0.666734	+	0.917681i
$16$	−0.878863	+	3.90226i	−0.219716	+	0.975564i
$17$	−4.42965	+	1.43928i	−1.07435	+	0.349077i	−0.792180	−	0.610288i	$-0.791054\pi$
$17$	−4.42965	+	1.43928i	−1.07435	+	0.349077i	−0.282169	+	0.959365i	$0.591054\pi$
$18$	1.79244	+	1.71128i	0.422482	+	0.403353i
$19$	2.18382	+	3.00577i	0.501002	+	0.689570i	0.982370	−	0.186949i	$-0.0598599\pi$
$19$	2.18382	+	3.00577i	0.501002	+	0.689570i	−0.481368	+	0.876519i	$0.659860\pi$
$20$	−6.57107	−	4.32397i	−1.46934	−	0.966869i
$21$	3.11801			0.680405
$22$	3.64059	−	2.95738i	0.776176	−	0.630516i
$23$			0.854640i			0.178205i	0.996022	+	0.0891024i	$0.0283998\pi$
$23$			0.854640i			0.178205i	−0.996022	+	0.0891024i	$0.971600\pi$
$24$	2.07351	−	2.38368i	0.423253	−	0.486566i
$25$	8.46953	−	6.15347i	1.69391	−	1.23069i
$26$	2.16169	+	2.06381i	0.423942	+	0.404747i
$27$	−1.64036	−	5.04850i	−0.315687	−	0.971585i
$28$	0.258495	+	5.57688i	0.0488510	+	1.05393i
$29$	−4.36210	−	3.16925i	−0.810022	−	0.588516i	0.103815	−	0.994597i	$-0.466895\pi$
$29$	−4.36210	−	3.16925i	−0.810022	−	0.588516i	−0.913837	+	0.406081i	$0.866895\pi$
$30$	2.94803	+	5.46894i	0.538235	+	0.998487i
$31$	−0.796872	−	0.258919i	−0.143122	−	0.0465033i	0.236580	−	0.971612i	$-0.423974\pi$
$31$	−0.796872	−	0.258919i	−0.143122	−	0.0465033i	−0.379702	+	0.925109i	$0.623974\pi$
$32$	4.43536	+	3.51107i	0.784068	+	0.620675i
$33$	−3.63949	+	0.691723i	−0.633554	+	0.120413i
$34$	−0.879482	+	6.52788i	−0.150830	+	1.11952i
$35$	−10.4415	−	3.39265i	−1.76494	−	0.573463i
$36$	3.27941	−	1.23617i	0.546569	−	0.206028i
$37$	2.13456	−	2.93797i	0.350919	−	0.482999i	−0.596671	−	0.802486i	$-0.703510\pi$
$37$	2.13456	−	2.93797i	0.350919	−	0.482999i	0.947591	+	0.319487i	$0.103510\pi$
$38$	5.16916	−	0.941903i	0.838548	−	0.152797i
$39$	−0.729452	−	2.24502i	−0.116806	−	0.359491i
$40$	−9.53736	+	5.72626i	−1.50799	+	0.905402i
$41$	−2.17890	−	2.99900i	−0.340287	−	0.468365i	0.604238	−	0.796804i	$-0.293478\pi$
$41$	−2.17890	−	2.99900i	−0.340287	−	0.468365i	−0.944525	+	0.328439i	$0.893478\pi$
$42$	1.91036	−	3.97422i	0.294776	−	0.613236i
$43$		−	1.38448i		−	0.211131i	−0.994412	−	0.105565i	$-0.966335\pi$
$43$		−	1.38448i		−	0.211131i	0.994412	−	0.105565i	$-0.0336652\pi$
$44$	−1.53895	−	6.45226i	−0.232005	−	0.972715i
$45$			6.89201i			1.02740i
$46$	1.08933	+	0.523628i	0.160612	+	0.0772047i
$47$	−0.799046	−	1.09979i	−0.116553	−	0.160421i	0.746754	−	0.665100i	$-0.231611\pi$
$47$	−0.799046	−	1.09979i	−0.116553	−	0.160421i	−0.863307	+	0.504679i	$0.831611\pi$
$48$	−1.76783	−	4.10335i	−0.255165	−	0.592268i
$49$	0.244772	+	0.753330i	0.0349674	+	0.107619i
$50$	−2.65406	−	14.5655i	−0.375341	−	2.05987i
$51$	3.05796	−	4.20892i	0.428200	−	0.589367i
$52$	3.95498	−	1.49082i	0.548457	−	0.206740i
$53$	−4.01470	−	1.30446i	−0.551462	−	0.179181i	0.0200141	−	0.999800i	$-0.493629\pi$
$53$	−4.01470	−	1.30446i	−0.551462	−	0.179181i	−0.571476	+	0.820619i	$0.693629\pi$
$54$	−7.43987	−	1.00235i	−1.01244	−	0.136403i
$55$	12.9405	+	1.64365i	1.74490	+	0.221629i
$56$	7.26668	+	3.08741i	0.971052	+	0.412572i
$57$	−3.94688	−	1.28242i	−0.522776	−	0.169860i
$58$	−6.71215	+	3.61819i	−0.881349	+	0.475091i
$59$	6.80468	+	4.94389i	0.885894	+	0.643640i	0.934804	−	0.355164i	$-0.115575\pi$
$59$	6.80468	+	4.94389i	0.885894	+	0.643640i	−0.0489102	+	0.998803i	$0.515575\pi$
$60$	8.77695	−	0.406822i	1.13310	−	0.0525205i
$61$	0.970728	+	2.98759i	0.124289	+	0.382522i	0.993771	−	0.111443i	$-0.0355471\pi$
$61$	0.970728	+	2.98759i	0.124289	+	0.382522i	−0.869482	+	0.493965i	$0.835547\pi$
$62$	−0.818253	+	0.857059i	−0.103918	+	0.108847i
$63$	3.95732	−	2.87516i	0.498575	−	0.362236i
$64$	7.19271	−	3.50213i	0.899089	−	0.437767i
$65$			8.31179i			1.03095i
$66$	−1.34820	+	5.06271i	−0.165952	+	0.623177i
$67$	3.45851			0.422524			0.211262	−	0.977429i	$-0.432243\pi$
$67$	3.45851			0.422524			0.211262	+	0.977429i	$0.432243\pi$
$68$	7.78161	+	5.12054i	0.943659	+	0.620957i
$69$	−0.561115	−	0.772308i	−0.0675503	−	0.0929750i
$70$	−10.7217	+	11.2302i	−1.28149	+	1.34226i
$71$	−11.7395	+	3.81439i	−1.39322	+	0.452684i	−0.906992	−	0.421148i	$-0.861627\pi$
$71$	−11.7395	+	3.81439i	−1.39322	+	0.452684i	−0.486227	+	0.873832i	$0.661627\pi$
$72$	0.433633	−	4.93733i	0.0511041	−	0.581870i
$73$	1.90829	−	2.62654i	0.223349	−	0.307413i	−0.682607	−	0.730786i	$-0.739154\pi$
$73$	1.90829	−	2.62654i	0.223349	−	0.307413i	0.905956	+	0.423373i	$0.139154\pi$
$74$	−2.43693	−	4.52077i	−0.283287	−	0.525529i
$75$	−3.61355	+	11.1214i	−0.417257	+	1.28418i
$76$	1.96653	−	7.16572i	0.225576	−	0.821964i
$77$	−4.45466	−	8.11598i	−0.507656	−	0.924901i
$78$	−3.30844	−	0.445736i	−0.374607	−	0.0504697i
$79$	3.59997	−	11.0796i	0.405029	−	1.24655i	−0.515843	−	0.856683i	$-0.672521\pi$
$79$	3.59997	−	11.0796i	0.405029	−	1.24655i	0.920871	−	0.389867i	$-0.127479\pi$
$80$	1.45529	+	15.6648i	0.162706	+	1.75137i
$81$	0.543938	+	0.395194i	0.0604376	+	0.0439105i
$82$	−5.15752	+	0.939783i	−0.569553	+	0.103782i
$83$	0.870974	−	0.282997i	0.0956018	−	0.0310629i	−0.260826	−	0.965386i	$-0.583995\pi$
$83$	0.870974	−	0.282997i	0.0956018	−	0.0310629i	0.356427	+	0.934323i	$0.383995\pi$
$84$	−3.89510	−	4.86991i	−0.424990	−	0.531351i
$85$	−14.8201	+	10.7674i	−1.60746	+	1.16789i
$86$	−1.76466	−	0.848252i	−0.190288	−	0.0914694i
$87$	6.02266			0.645697
$88$	−9.16696	−	1.99168i	−0.977202	−	0.212313i
$89$	7.98458			0.846363			0.423182	−	0.906045i	$-0.360913\pi$
$89$	7.98458			0.846363			0.423182	+	0.906045i	$0.360913\pi$
$90$	8.78458	+	4.22265i	0.925976	+	0.445107i
$91$	4.77254	−	3.46745i	0.500298	−	0.363488i
$92$	1.33483	−	1.06764i	0.139166	−	0.111309i
$93$	0.890099	−	0.289211i	0.0922990	−	0.0299898i
$94$	−1.89137	+	0.344637i	−0.195080	+	0.0355466i
$95$	11.8218	+	8.58907i	1.21289	+	0.881220i
$96$	−6.31327	−	0.260789i	−0.644346	−	0.0266166i
$97$	−3.44331	+	10.5974i	−0.349615	+	1.07600i	0.609451	+	0.792824i	$0.291390\pi$
$97$	−3.44331	+	10.5974i	−0.349615	+	1.07600i	−0.959066	+	0.283181i	$0.908610\pi$
$98$	1.11017	+	0.149569i	0.112144	+	0.0151088i
$99$	−3.98133	+	4.23395i	−0.400138	+	0.425528i
$100$	−20.1913	−	5.54120i	−2.01913	−	0.554120i
$101$	−1.65660	+	5.09849i	−0.164838	+	0.507319i	−0.999024	−	0.0441635i	$-0.985938\pi$
$101$	−1.65660	+	5.09849i	−0.164838	+	0.507319i	0.834186	+	0.551483i	$0.185938\pi$
$102$	−3.49113	−	6.47644i	−0.345673	−	0.641263i
$103$	−3.62026	+	4.98285i	−0.356714	+	0.490975i	−0.949230	−	0.314584i	$-0.898135\pi$
$103$	−3.62026	+	4.98285i	−0.356714	+	0.490975i	0.592515	+	0.805559i	$0.298135\pi$
$104$	0.522963	−	5.95444i	0.0512807	−	0.583881i
$105$	11.6631	−	3.78956i	1.13820	−	0.369824i
$106$	−4.12242	+	4.31793i	−0.400405	+	0.419394i
$107$	−9.02248	−	12.4184i	−0.872236	−	1.20053i	−0.978511	−	0.206193i	$-0.933893\pi$
$107$	−9.02248	−	12.4184i	−0.872236	−	1.20053i	0.106275	−	0.994337i	$-0.466107\pi$
$108$	−5.83592	+	8.86875i	−0.561561	+	0.853396i
$109$	2.86723			0.274631			0.137315	−	0.990527i	$-0.456153\pi$
$109$	2.86723			0.274631			0.137315	+	0.990527i	$0.456153\pi$
$110$	10.0235	−	15.4870i	0.955702	−	1.47662i
$111$			4.05639i			0.385015i
$112$	8.38743	−	7.37052i	0.792538	−	0.696449i
$113$	−8.25780	+	5.99964i	−0.776828	+	0.564399i	−0.904025	−	0.427479i	$-0.859402\pi$
$113$	−8.25780	+	5.99964i	−0.776828	+	0.564399i	0.127197	+	0.991877i	$0.459402\pi$
$114$	−4.05278	+	4.24498i	−0.379577	+	0.397579i
$115$	1.03871	+	3.19683i	0.0968605	+	0.298106i
$116$	0.499302	+	10.7721i	0.0463590	+	1.00017i
$117$	−2.99598	−	2.17670i	−0.276978	−	0.201236i
$118$	10.4706	−	5.64421i	0.963901	−	0.519591i
$119$	12.3651	+	4.01766i	1.13350	+	0.368298i
$120$	4.85899	−	11.4364i	0.443563	−	1.04399i
$121$	7.00021	+	8.48511i	0.636383	+	0.771374i
$122$	4.40275	+	0.593170i	0.398606	+	0.0537030i
$123$	3.93799	+	1.27953i	0.355077	+	0.115371i
$124$	0.591076	+	1.56806i	0.0530802	+	0.140816i
$125$	12.6430	−	17.4016i	1.13082	−	1.55645i
$126$	−1.24009	−	6.80559i	−0.110476	−	0.606290i
$127$	−3.94256	−	12.1339i	−0.349845	−	1.07671i	−0.958938	−	0.283614i	$-0.908467\pi$
$127$	−3.94256	−	12.1339i	−0.349845	−	1.07671i	0.609093	−	0.793099i	$-0.291533\pi$
$128$	−0.0569472	−	11.3136i	−0.00503347	−	0.999987i
$129$	0.908979	+	1.25110i	0.0800312	+	0.110153i
$130$	10.5942	+	5.09253i	0.929176	+	0.446645i
$131$			10.8120i			0.944646i	0.881426	+	0.472323i	$0.156584\pi$
$131$			10.8120i			0.944646i	−0.881426	+	0.472323i	$0.843416\pi$
$132$	5.62693	+	4.82028i	0.489761	+	0.419552i
$133$		−	10.3711i		−	0.899288i
$134$	2.11899	−	4.40823i	0.183053	−	0.380813i
$135$	−12.2717	−	16.8906i	−1.05618	−	1.45371i
$136$	11.2944	−	6.78117i	0.968483	−	0.581480i
$137$	−6.64424	−	20.4489i	−0.567656	−	1.74707i	−0.659925	−	0.751332i	$-0.729412\pi$
$137$	−6.64424	−	20.4489i	−0.567656	−	1.74707i	0.0922685	−	0.995734i	$-0.470588\pi$
$138$	−1.32817	+	0.242015i	−0.113062	+	0.0206017i
$139$	4.01113	−	5.52085i	0.340220	−	0.468273i	−0.604286	−	0.796768i	$-0.706541\pi$
$139$	4.01113	−	5.52085i	0.340220	−	0.468273i	0.944506	+	0.328495i	$0.106541\pi$
$140$	7.74495	+	20.5465i	0.654567	+	1.73649i
$141$	1.44414	+	0.469230i	0.121619	+	0.0395163i
$142$	−2.33080	+	17.3002i	−0.195597	+	1.45180i
$143$	−4.80149	+	5.10616i	−0.401521	+	0.426998i
$144$	−6.02746	−	3.57775i	−0.502288	−	0.298146i
$145$	−20.1686	−	6.55316i	−1.67491	−	0.544210i
$146$	−2.17861	−	4.04156i	−0.180303	−	0.334482i
$147$	−0.715792	−	0.520053i	−0.0590375	−	0.0428932i
$148$	−7.25527	+	0.336290i	−0.596379	+	0.0276429i
$149$	3.50314	+	10.7816i	0.286989	+	0.883260i	0.985796	+	0.167950i	$0.0537147\pi$
$149$	3.50314	+	10.7816i	0.286989	+	0.883260i	−0.698807	+	0.715310i	$0.746285\pi$
$150$	11.9613	+	11.4198i	0.976639	+	0.932420i
$151$	−1.11632	+	0.811053i	−0.0908447	+	0.0660026i	−0.632280	−	0.774740i	$-0.717881\pi$
$151$	−1.11632	+	0.811053i	−0.0908447	+	0.0660026i	0.541436	+	0.840742i	$0.317881\pi$
$152$	−7.92858	−	6.89689i	−0.643093	−	0.559411i
$153$		−	8.16168i		−	0.659832i
$154$	−13.0740	+	0.705364i	−1.05353	+	0.0568399i
$155$	−3.29543			−0.264695
$156$	−2.59518	+	3.94385i	−0.207780	+	0.315761i
$157$	11.3001	+	15.5532i	0.901843	+	1.24128i	0.969876	+	0.243598i	$0.0783277\pi$
$157$	11.3001	+	15.5532i	0.901843	+	1.24128i	−0.0680330	+	0.997683i	$0.521672\pi$
$158$	−11.9164	−	11.3769i	−0.948019	−	0.905095i
$159$	4.48439	−	1.45707i	0.355635	−	0.115553i
$160$	20.8580	+	7.74270i	1.64897	+	0.612114i
$161$	1.40226	−	1.93005i	0.110514	−	0.152109i
$162$	0.836980	−	0.451175i	0.0657594	−	0.0354476i
$163$	3.44315	−	10.5969i	0.269689	−	0.830016i	−0.720887	−	0.693052i	$-0.756266\pi$
$163$	3.44315	−	10.5969i	0.269689	−	0.830016i	0.990576	−	0.136964i	$-0.0437345\pi$
$164$	−1.96210	+	7.14959i	−0.153214	+	0.558289i
$165$	−12.7730	+	7.01079i	−0.994378	+	0.545789i
$166$	0.172927	−	1.28353i	0.0134217	−	0.0996216i
$167$	−6.27006	+	19.2973i	−0.485192	+	1.49327i	0.346510	+	0.938046i	$0.387367\pi$
$167$	−6.27006	+	19.2973i	−0.485192	+	1.49327i	−0.831702	+	0.555222i	$0.812633\pi$
$168$	−8.59369	+	1.98097i	−0.663017	+	0.152835i
$169$	6.90406	+	5.01610i	0.531082	+	0.385854i
$170$	4.64411	+	25.4868i	0.356187	+	1.95475i
$171$	−6.19184	+	2.01185i	−0.473502	+	0.153850i
$172$	−2.16237	+	1.72953i	−0.164879	+	0.131875i
$173$	12.6022	−	9.15603i	0.958127	−	0.696120i	0.00541199	−	0.999985i	$-0.498277\pi$
$173$	12.6022	−	9.15603i	0.958127	−	0.696120i	0.952715	+	0.303865i	$0.0982773\pi$
$174$	3.69001	−	7.67650i	0.279739	−	0.581954i
$175$	−29.2233			−2.20907
$176$	−8.15508	+	10.4640i	−0.614713	+	0.788751i
$177$	−9.39507			−0.706176
$178$	4.89205	−	10.1772i	0.366675	−	0.762811i
$179$	13.7239	−	9.97097i	1.02577	−	0.745265i	0.0583123	−	0.998298i	$-0.481428\pi$
$179$	13.7239	−	9.97097i	1.02577	−	0.745265i	0.967458	+	0.253033i	$0.0814281\pi$
$180$	10.7644	−	8.60969i	0.802332	−	0.641728i
$181$	12.6430	−	4.10796i	0.939746	−	0.305342i	0.201204	−	0.979549i	$-0.435515\pi$
$181$	12.6430	−	4.10796i	0.939746	−	0.305342i	0.738542	+	0.674207i	$0.235515\pi$
$182$	−1.49555	−	8.20756i	−0.110857	−	0.608385i
$183$	−2.83872	−	2.06245i	−0.209844	−	0.152461i
$184$	−0.542980	−	2.35551i	−0.0400290	−	0.173651i
$185$	4.41369	−	13.5839i	0.324501	−	0.998711i
$186$	0.176724	−	1.31172i	0.0129580	−	0.0961799i
$187$	−15.3244	−	1.94644i	−1.12063	−	0.142338i
$188$	−0.719541	+	2.62190i	−0.0524779	+	0.191221i
$189$	−4.57895	+	14.0926i	−0.333070	+	1.02508i
$190$	18.1908	−	9.80574i	1.31970	−	0.711383i
$191$	−14.8778	+	20.4775i	−1.07652	+	1.48170i	−0.213224	+	0.977003i	$0.568397\pi$
$191$	−14.8778	+	20.4775i	−1.07652	+	1.48170i	−0.863295	+	0.504699i	$0.831603\pi$
$192$	−4.20047	+	7.88714i	−0.303143	+	0.569205i
$193$	6.00552	−	1.95131i	0.432287	−	0.140458i	−0.0847876	−	0.996399i	$-0.527021\pi$
$193$	6.00552	−	1.95131i	0.432287	−	0.140458i	0.517074	+	0.855941i	$0.327021\pi$
$194$	11.3978	+	10.8818i	0.818317	+	0.781265i
$195$	−5.45711	−	7.51107i	−0.390792	−	0.537879i
$196$	0.870827	−	1.32338i	0.0622019	−	0.0945273i
$197$	10.8725			0.774631			0.387316	−	0.921947i	$-0.373402\pi$
$197$	10.8725			0.774631			0.387316	+	0.921947i	$0.373402\pi$
$198$	2.95729	+	7.66870i	0.210166	+	0.544991i
$199$		−	22.1838i		−	1.57257i	−0.617866	−	0.786283i	$-0.712003\pi$
$199$		−	22.1838i		−	1.57257i	0.617866	−	0.786283i	$-0.287997\pi$
$200$	−19.4338	+	22.3408i	−1.37418	+	1.57974i
$201$	−3.12533	+	2.27069i	−0.220444	+	0.160162i
$202$	5.48358	+	5.23530i	0.385823	+	0.368354i
$203$	4.65102	+	14.3144i	0.326437	+	1.00467i
$204$	−10.3939	+	0.481768i	−0.727716	+	0.0337305i
$205$	−11.7952	−	8.56973i	−0.823814	−	0.598536i
$206$	4.13308	+	7.66732i	0.287965	+	0.534208i
$207$	−1.42431	−	0.462788i	−0.0989966	−	0.0321660i
$208$	−7.26914	−	4.31478i	−0.504024	−	0.299176i
$209$	2.30080	+	12.1056i	0.159150	+	0.837365i
$210$	2.31564	−	17.1876i	0.159794	−	1.18606i
$211$	4.29344	+	1.39502i	0.295572	+	0.0960373i	0.453050	−	0.891485i	$-0.350336\pi$
$211$	4.29344	+	1.39502i	0.295572	+	0.0960373i	−0.157477	+	0.987523i	$0.550336\pi$
$212$	2.97789	+	7.89999i	0.204522	+	0.542574i
$213$	8.10421	−	11.1545i	0.555291	−	0.764293i
$214$	−21.3565	+	3.89149i	−1.45990	+	0.266017i
$215$	−1.68267	−	5.17871i	−0.114757	−	0.353185i
$216$	7.72854	+	12.8723i	0.525861	+	0.875846i
$217$	1.37476	+	1.89220i	0.0933251	+	0.128451i
$218$	1.75672	−	3.65458i	0.118980	−	0.247519i
$219$			3.62640i			0.245049i
$220$	−13.5985	−	22.2646i	−0.916808	−	1.50108i
$221$		−	9.84301i		−	0.662112i
$222$	5.17028	+	2.48530i	0.347007	+	0.166802i
$223$	9.00750	+	12.3978i	0.603187	+	0.830216i	0.995995	−	0.0894046i	$-0.0284964\pi$
$223$	9.00750	+	12.3978i	0.603187	+	0.830216i	−0.392808	+	0.919620i	$0.628496\pi$
$224$	−4.25562	−	15.2065i	−0.284340	−	1.01603i
$225$	5.66892	+	17.4471i	0.377928	+	1.16314i
$226$	2.58771	+	14.2013i	0.172132	+	0.944658i
$227$	−11.9130	+	16.3968i	−0.790692	+	1.08829i	0.203329	+	0.979110i	$0.434824\pi$
$227$	−11.9130	+	16.3968i	−0.790692	+	1.08829i	−0.994022	+	0.109184i	$0.965176\pi$
$228$	2.92758	+	7.76653i	0.193884	+	0.514351i
$229$	−3.54360	−	1.15138i	−0.234168	−	0.0760856i	0.189583	−	0.981865i	$-0.439287\pi$
$229$	−3.54360	−	1.15138i	−0.234168	−	0.0760856i	−0.423750	+	0.905779i	$0.639287\pi$
$230$	4.71110	+	0.634712i	0.310640	+	0.0418517i
$231$	9.35407	+	4.40941i	0.615453	+	0.290118i
$232$	14.0361	+	5.96355i	0.921517	+	0.391527i
$233$	23.3988	+	7.60272i	1.53290	+	0.498071i	0.949408	−	0.314045i	$-0.101684\pi$
$233$	23.3988	+	7.60272i	1.53290	+	0.498071i	0.583496	+	0.812116i	$0.301684\pi$
$234$	−4.61003	+	2.48504i	−0.301367	+	0.162452i
$235$	−4.32555	−	3.14269i	−0.282168	−	0.205007i
$236$	−0.778888	−	16.8041i	−0.0507013	−	1.09385i
$237$	4.02114	+	12.3758i	0.261201	+	0.803894i
$238$	12.6969	−	13.2990i	0.823015	−	0.862046i
$239$	14.0082	−	10.1775i	0.906113	−	0.658330i	−0.0339157	−	0.999425i	$-0.510798\pi$
$239$	14.0082	−	10.1775i	0.906113	−	0.658330i	0.940029	+	0.341095i	$0.110798\pi$
$240$	−11.5998	−	13.2002i	−0.748764	−	0.852071i
$241$		−	12.0062i		−	0.773387i	−0.922208	−	0.386694i	$-0.873617\pi$
$241$		−	12.0062i		−	0.773387i	0.922208	−	0.386694i	$-0.126383\pi$
$242$	15.1041	−	3.72377i	0.970928	−	0.239373i
$243$	15.1739			0.973408
$244$	3.45357	−	5.24833i	0.221092	−	0.335990i
$245$	1.83117	+	2.52038i	0.116989	+	0.161021i
$246$	4.04365	−	4.23542i	0.257814	−	0.270041i
$247$	−7.46738	+	2.42630i	−0.475138	+	0.154382i
$248$	2.36080	+	0.207343i	0.149911	+	0.0131663i
$249$	−0.601267	+	0.827573i	−0.0381037	+	0.0524453i
$250$	−14.4339	−	26.7765i	−0.912881	−	1.69350i
$251$	0.828764	−	2.55067i	0.0523111	−	0.160997i	−0.921488	−	0.388407i	$-0.873026\pi$
$251$	0.828764	−	2.55067i	0.0523111	−	0.160997i	0.973799	+	0.227410i	$0.0730256\pi$
$252$	−9.43421	−	2.58908i	−0.594299	−	0.163097i
$253$	−1.20861	+	2.56393i	−0.0759848	+	0.161193i
$254$	−17.8815	−	2.40912i	−1.12199	−	0.151162i
$255$	6.32303	−	19.4603i	0.395964	−	1.21865i
$256$	−14.4552	−	6.85910i	−0.903450	−	0.428694i
$257$	−10.9160	−	7.93091i	−0.680919	−	0.494717i	0.192743	−	0.981249i	$-0.438261\pi$
$257$	−10.9160	−	7.93091i	−0.680919	−	0.494717i	−0.873662	+	0.486533i	$0.838261\pi$
$258$	2.15158	−	0.392053i	0.133952	−	0.0244081i
$259$	−9.64102	+	3.13256i	−0.599064	+	0.194648i
$260$	12.9819	−	10.3833i	0.805104	−	0.643946i
$261$	7.64385	−	5.55358i	0.473142	−	0.343758i
$262$	13.7810	+	6.62436i	0.851391	+	0.409254i
$263$	−0.593593			−0.0366025			−0.0183013	−	0.999833i	$-0.505826\pi$
$263$	−0.593593			−0.0366025			−0.0183013	+	0.999833i	$0.505826\pi$
$264$	9.59150	−	4.21877i	0.590316	−	0.259647i
$265$	−16.6026			−1.01989
$266$	−13.2190	−	6.35424i	−0.810511	−	0.389604i
$267$	−7.21538	+	5.24228i	−0.441574	+	0.320822i
$268$	−4.32046	−	5.40174i	−0.263914	−	0.329964i
$269$	−18.5270	+	6.01978i	−1.12961	+	0.367032i	−0.813427	−	0.581666i	$-0.802401\pi$
$269$	−18.5270	+	6.01978i	−1.12961	+	0.367032i	−0.316182	+	0.948699i	$0.602401\pi$
$270$	−29.0475	+	5.29292i	−1.76777	+	0.322117i
$271$	19.8565	+	14.4266i	1.20619	+	0.876351i	0.994880	−	0.101067i	$-0.0322258\pi$
$271$	19.8565	+	14.4266i	1.20619	+	0.876351i	0.211314	+	0.977418i	$0.432226\pi$
$272$	−1.72338	−	18.5506i	−0.104496	−	1.12479i
$273$	−2.03622	+	6.26683i	−0.123237	+	0.379286i
$274$	−30.1351	−	4.06001i	−1.82053	−	0.245274i
$275$	34.1108	−	6.48312i	2.05696	−	0.390947i
$276$	−0.505284	+	1.84118i	−0.0304145	+	0.110826i
$277$	4.54208	−	13.9791i	0.272907	−	0.839921i	−0.716859	−	0.697219i	$-0.754421\pi$
$277$	4.54208	−	13.9791i	0.272907	−	0.839921i	0.989766	−	0.142703i	$-0.0455793\pi$
$278$	−4.57932	−	8.49517i	−0.274650	−	0.509506i
$279$	0.863012	−	1.18783i	0.0516672	−	0.0711138i
$280$	30.9338	+	2.71684i	1.84865	+	0.162362i
$281$	−21.9124	+	7.11976i	−1.30718	+	0.424729i	−0.878075	−	0.478524i	$-0.841172\pi$
$281$	−21.9124	+	7.11976i	−1.30718	+	0.424729i	−0.429108	+	0.903253i	$0.641172\pi$
$282$	1.48289	−	1.55321i	0.0883048	−	0.0924926i
$283$	13.2652	+	18.2581i	0.788537	+	1.08533i	0.994289	+	0.106724i	$0.0340362\pi$
$283$	13.2652	+	18.2581i	0.788537	+	1.08533i	−0.205751	+	0.978604i	$0.565964\pi$
$284$	20.6228	+	13.5705i	1.22374	+	0.805259i
$285$	−16.3221			−0.966840
$286$	3.56651	+	9.24848i	0.210892	+	0.546874i
$287$			10.3477i			0.610808i
$288$	−8.25317	+	5.49057i	−0.486323	+	0.323535i
$289$	3.79700	−	2.75868i	0.223353	−	0.162275i
$290$	−20.7097	+	21.6919i	−1.21612	+	1.27379i
$291$	−3.84615	−	11.8372i	−0.225465	−	0.693910i
$292$	−6.48619	+	0.300643i	−0.379576	+	0.0175938i
$293$	0.181791	+	0.132079i	0.0106203	+	0.00771613i	0.593083	−	0.805142i	$-0.297911\pi$
$293$	0.181791	+	0.132079i	0.0106203	+	0.00771613i	−0.582462	+	0.812858i	$0.697911\pi$
$294$	−1.10142	+	0.593720i	−0.0642360	+	0.0346265i
$295$	31.4620	+	10.2226i	1.83179	+	0.595184i
$296$	−4.01658	+	9.45363i	−0.233459	+	0.549481i
$297$	2.21837	−	17.4654i	0.128723	−	1.01344i
$298$	15.8886	+	2.14062i	0.920399	+	0.124003i
$299$	−1.71773	−	0.558123i	−0.0993387	−	0.0322771i
$300$	21.8842	−	8.24922i	1.26349	−	0.476269i
$301$	−2.27160	+	3.12659i	−0.130933	+	0.180213i
$302$	0.349816	+	1.91979i	0.0201296	+	0.110471i
$303$	−1.85041	−	5.69497i	−0.106303	−	0.327168i
$304$	−13.6485	+	5.88015i	−0.782797	+	0.337250i
$305$	7.26213	+	9.99546i	0.415828	+	0.572339i
$306$	−10.4029	−	5.00056i	−0.594694	−	0.285863i
$307$			7.94263i			0.453310i	0.973975	+	0.226655i	$0.0727790\pi$
$307$			7.94263i			0.453310i	−0.973975	+	0.226655i	$0.927221\pi$
$308$	−7.11120	+	17.0963i	−0.405198	+	0.974152i
$309$		−	6.87971i		−	0.391373i
$310$	−2.01907	+	4.20037i	−0.114676	+	0.238565i
$311$	−18.5030	−	25.4672i	−1.04921	−	1.44411i	−0.889491	−	0.456952i	$-0.848941\pi$
$311$	−18.5030	−	25.4672i	−1.04921	−	1.44411i	−0.159720	−	0.987162i	$-0.551059\pi$
$312$	3.43681	+	5.72417i	0.194571	+	0.324067i
$313$	5.75907	+	17.7246i	0.325522	+	1.00185i	0.971204	+	0.238248i	$0.0765730\pi$
$313$	5.75907	+	17.7246i	0.325522	+	1.00185i	−0.645682	+	0.763606i	$0.723427\pi$
$314$	26.7476	−	4.87384i	1.50945	−	0.275047i
$315$	11.3082	−	15.5643i	0.637143	−	0.876952i
$316$	−21.8020	+	8.21823i	−1.22646	+	0.462311i
$317$	−21.9489	−	7.13164i	−1.23277	−	0.400553i	−0.381056	−	0.924552i	$-0.624439\pi$
$317$	−21.9489	−	7.13164i	−1.23277	−	0.400553i	−0.851719	+	0.523999i	$0.824439\pi$
$318$	0.890349	−	6.60854i	0.0499283	−	0.370588i
$319$	−8.60450	−	15.6766i	−0.481760	−	0.877721i
$320$	22.6483	−	21.8418i	1.26608	−	1.22099i
$321$	16.3066	+	5.29833i	0.910145	+	0.295724i
$322$	−1.60090	−	2.96984i	−0.0892145	−	0.165503i
$323$	−13.9997	−	10.1714i	−0.778963	−	0.565950i
$324$	−0.0622611	−	1.34325i	−0.00345895	−	0.0746248i
$325$	6.83673	+	21.0413i	0.379234	+	1.16716i
$326$	−11.3973	−	10.8813i	−0.631239	−	0.602658i
$327$	−2.59101	+	1.88248i	−0.143283	+	0.104101i
$328$	7.91073	+	6.88136i	0.436797	+	0.379960i
$329$			3.79473i			0.209210i
$330$	1.11011	+	20.5759i	0.0611095	+	1.13267i
$331$	−19.9470			−1.09639			−0.548194	−	0.836351i	$-0.684684\pi$
$331$	−19.9470			−1.09639			−0.548194	+	0.836351i	$0.684684\pi$
$332$	−1.53005	−	1.00682i	−0.0839723	−	0.0552564i
$333$	3.74045	+	5.14829i	0.204976	+	0.282125i
$334$	20.7548	+	19.8151i	1.13565	+	1.08423i
$335$	12.9368	−	4.20341i	0.706810	−	0.229657i
$336$	−2.74030	+	12.1673i	−0.149496	+	0.663778i
$337$	2.52155	−	3.47062i	0.137358	−	0.189056i	−0.734797	−	0.678287i	$-0.762722\pi$
$337$	2.52155	−	3.47062i	0.137358	−	0.189056i	0.872154	+	0.489231i	$0.162722\pi$
$338$	10.6236	−	5.72664i	0.577846	−	0.311488i
$339$	3.52321	−	10.8433i	0.191355	−	0.588929i
$340$	35.3310	+	9.69607i	1.91609	+	0.525843i
$341$	−2.02447	−	1.90368i	−0.109631	−	0.103090i
$342$	−1.22935	+	9.12478i	−0.0664759	+	0.493411i
$343$	−5.35494	+	16.4808i	−0.289139	+	0.889880i
$344$	0.879601	+	3.81582i	0.0474249	+	0.205735i
$345$	−3.03753	−	2.20689i	−0.163535	−	0.118815i
$346$	−3.94909	−	21.6726i	−0.212305	−	1.16513i
$347$	13.9379	−	4.52870i	0.748226	−	0.243113i	0.0900080	−	0.995941i	$-0.471311\pi$
$347$	13.9379	−	4.52870i	0.748226	−	0.243113i	0.658217	+	0.752828i	$0.271311\pi$
$348$	−7.52367	−	9.40660i	−0.403311	−	0.504246i
$349$	−27.4557	+	19.9477i	−1.46967	+	1.06778i	−0.488961	+	0.872306i	$0.662624\pi$
$349$	−27.4557	+	19.9477i	−1.46967	+	1.06778i	−0.980709	+	0.195472i	$0.937376\pi$
$350$	−17.9047	+	37.2481i	−0.957049	+	1.99099i
$351$	11.2181			0.598780
$352$	8.34088	+	16.8056i	0.444571	+	0.895744i
$353$	13.8039			0.734707			0.367353	−	0.930081i	$-0.380264\pi$
$353$	13.8039			0.734707			0.367353	+	0.930081i	$0.380264\pi$
$354$	−5.75624	+	11.9750i	−0.305941	+	0.636463i
$355$	−39.2762	+	28.5359i	−2.08457	+	1.51453i
$356$	−9.97455	−	12.4709i	−0.528650	−	0.660954i
$357$	−13.8117	+	4.48769i	−0.730992	+	0.237514i
$358$	−4.30059	−	23.6016i	−0.227293	−	1.24738i
$359$	13.6648	+	9.92802i	0.721198	+	0.523981i	0.886767	−	0.462217i	$-0.152946\pi$
$359$	13.6648	+	9.92802i	0.721198	+	0.523981i	−0.165569	+	0.986198i	$0.552946\pi$
$360$	−4.37871	−	18.9954i	−0.230778	−	1.00115i
$361$	1.60575	−	4.94200i	0.0845133	−	0.260105i
$362$	2.51019	−	18.6317i	0.131933	−	0.979260i
$363$	−11.8967	−	3.07170i	−0.624417	−	0.161222i
$364$	−11.3777	−	3.12244i	−0.596353	−	0.163660i
$365$	3.94583	−	12.1440i	0.206534	−	0.635646i
$366$	−4.36806	+	2.35460i	−0.228322	+	0.123077i
$367$	−0.132390	+	0.182219i	−0.00691070	+	0.00951176i	−0.812458	−	0.583019i	$-0.801871\pi$
$367$	−0.132390	+	0.182219i	−0.00691070	+	0.00951176i	0.805548	+	0.592531i	$0.201871\pi$
$368$	−3.33502	−	0.751112i	−0.173850	−	0.0391544i
$369$	6.17790	−	2.00732i	0.321609	−	0.104497i
$370$	−14.6099	−	13.9484i	−0.759534	−	0.725144i
$371$	6.92616	+	9.53305i	0.359589	+	0.494931i
$372$	−1.56364	−	1.02893i	−0.0810712	−	0.0533474i
$373$	11.3347			0.586890			0.293445	−	0.955976i	$-0.405198\pi$
$373$	11.3347			0.586890			0.293445	+	0.955976i	$0.405198\pi$
$374$	−11.8700	+	18.3400i	−0.613785	+	0.948339i
$375$			24.0260i			1.24070i
$376$	2.90102	+	2.52353i	0.149609	+	0.130141i
$377$	9.21851	−	6.69764i	0.474777	−	0.344946i
$378$	15.1570	+	14.4707i	0.779590	+	0.744292i
$379$	−1.61104	−	4.95826i	−0.0827534	−	0.254689i	0.901116	−	0.433579i	$-0.142749\pi$
$379$	−1.61104	−	4.95826i	−0.0827534	−	0.254689i	−0.983869	+	0.178890i	$0.942749\pi$
$380$	−1.35317	−	29.1938i	−0.0694161	−	1.49761i
$381$	11.5293	+	8.37652i	0.590664	+	0.429142i
$382$	16.9853	+	31.5096i	0.869043	+	1.61217i
$383$	−31.4132	−	10.2068i	−1.60514	−	0.521541i	−0.636768	−	0.771056i	$-0.719729\pi$
$383$	−31.4132	−	10.2068i	−1.60514	−	0.521541i	−0.968371	+	0.249514i	$0.919729\pi$
$384$	7.47939	+	10.1863i	0.381681	+	0.519817i
$385$	−26.5269	−	24.9442i	−1.35194	−	1.27127i
$386$	1.19236	−	8.85020i	0.0606895	−	0.450463i
$387$	2.30732	+	0.749694i	0.117288	+	0.0381091i
$388$	20.8532	−	7.86059i	1.05866	−	0.399061i
$389$	−4.37628	+	6.02343i	−0.221886	+	0.305400i	−0.905418	−	0.424520i	$-0.860443\pi$
$389$	−4.37628	+	6.02343i	−0.221886	+	0.305400i	0.683532	+	0.729920i	$0.260443\pi$
$390$	−12.9171	+	2.35371i	−0.654085	+	0.119185i
$391$	−1.23007	−	3.78576i	−0.0622072	−	0.191454i
$392$	−1.15324	−	1.92078i	−0.0582475	−	0.0970140i
$393$	−7.09860	−	9.77039i	−0.358077	−	0.492851i
$394$	6.66143	−	13.8581i	0.335598	−	0.698160i
$395$		−	45.8191i		−	2.30541i
$396$	11.5865	+	0.929144i	0.582241	+	0.0466913i
$397$			12.5755i			0.631147i	0.948901	+	0.315573i	$0.102197\pi$
$397$			12.5755i			0.631147i	−0.948901	+	0.315573i	$0.897803\pi$
$398$	−28.2755	−	13.5917i	−1.41732	−	0.681292i
$399$	6.80915	+	9.37199i	0.340884	+	0.469187i
$400$	16.5689	+	38.4583i	0.828444	+	1.92292i
$401$	−4.30402	−	13.2464i	−0.214933	−	0.661494i	−0.999158	−	0.0410189i	$-0.986940\pi$
$401$	−4.30402	−	13.2464i	−0.214933	−	0.661494i	0.784226	−	0.620476i	$-0.213060\pi$
$402$	0.979372	+	5.37478i	0.0488466	+	0.268070i
$403$	1.04080	−	1.43253i	0.0518457	−	0.0713595i
$404$	10.0326	−	3.78178i	0.499143	−	0.188151i
$405$	2.51494	+	0.817155i	0.124969	+	0.0406047i
$406$	21.0948	+	2.84203i	1.04692	+	0.141048i
$407$	10.5585	−	5.79531i	0.523366	−	0.287263i
$408$	−5.75413	+	13.5432i	−0.284872	+	0.670490i
$409$	−1.47362	−	0.478807i	−0.0728657	−	0.0236755i	0.272357	−	0.962196i	$-0.412197\pi$
$409$	−1.47362	−	0.478807i	−0.0728657	−	0.0236755i	−0.345223	+	0.938521i	$0.612197\pi$
$410$	−18.1498	+	9.78366i	−0.896355	+	0.483181i
$411$	19.4299	+	14.1167i	0.958406	+	0.696323i
$412$	12.3051	−	0.570355i	0.606228	−	0.0280994i
$413$	−7.25537	−	22.3297i	−0.357014	−	1.09877i
$414$	−1.46253	+	1.53189i	−0.0718794	+	0.0752883i
$415$	2.91398	−	2.11713i	0.143042	−	0.103926i
$416$	−9.95335	+	6.62165i	−0.488003	+	0.324653i
$417$			7.62252i			0.373276i
$418$	16.8396	+	4.48437i	0.823651	+	0.219338i
$419$	−18.4122			−0.899496			−0.449748	−	0.893155i	$-0.648486\pi$
$419$	−18.4122			−0.899496			−0.449748	+	0.893155i	$0.648486\pi$
$420$	−20.4886	−	13.4822i	−0.999743	−	0.657862i
$421$	−16.4415	−	22.6298i	−0.801311	−	1.10291i	−0.992606	−	0.121378i	$-0.961269\pi$
$421$	−16.4415	−	22.6298i	−0.801311	−	1.10291i	0.191295	−	0.981533i	$-0.438731\pi$
$422$	4.40864	−	4.61772i	0.214609	−	0.224787i
$423$	2.26556	−	0.736125i	0.110155	−	0.0357916i
$424$	11.8939	+	1.04461i	0.577618	+	0.0507306i
$425$	−28.6605	+	39.4478i	−1.39024	+	1.91350i
$426$	−9.25220	−	17.1639i	−0.448270	−	0.831592i
$427$	2.70972	−	8.33967i	0.131133	−	0.403585i
$428$	−8.12474	+	29.6053i	−0.392724	+	1.43103i
$429$	0.986489	−	7.76668i	0.0476282	−	0.374979i
$430$	−7.63175	−	1.02820i	−0.368036	−	0.0495844i
$431$	9.07766	−	27.9382i	0.437256	−	1.34573i	−0.453502	−	0.891255i	$-0.649825\pi$
$431$	9.07766	−	27.9382i	0.437256	−	1.34573i	0.890758	−	0.454479i	$-0.150175\pi$
$432$	21.1422	−	1.96415i	1.01720	−	0.0945003i
$433$	−14.9096	−	10.8325i	−0.716509	−	0.520575i	0.168758	−	0.985658i	$-0.446024\pi$
$433$	−14.9096	−	10.8325i	−0.716509	−	0.520575i	−0.885267	+	0.465083i	$0.846024\pi$
$434$	3.25411	−	0.592951i	0.156202	−	0.0284625i
$435$	22.5281	−	7.31982i	1.08014	−	0.350959i
$436$	−3.58182	−	4.47823i	−0.171538	−	0.214468i
$437$	−2.56885	+	1.86638i	−0.122885	+	0.0892809i
$438$	4.62222	+	2.22185i	0.220858	+	0.106164i
$439$	−2.97316			−0.141901			−0.0709506	−	0.997480i	$-0.522603\pi$
$439$	−2.97316			−0.141901			−0.0709506	+	0.997480i	$0.522603\pi$
$440$	−36.7102	+	3.69137i	−1.75009	+	0.175979i
$441$	−1.38802			−0.0660961
$442$	−12.5459	−	6.03069i	−0.596749	−	0.286851i
$443$	−0.965497	+	0.701475i	−0.0458722	+	0.0333281i	−0.610485	−	0.792028i	$-0.709025\pi$
$443$	−0.965497	+	0.701475i	−0.0458722	+	0.0333281i	0.564613	+	0.825356i	$0.309025\pi$
$444$	6.33554	−	5.06735i	0.300671	−	0.240486i
$445$	29.8668	−	9.70430i	1.41582	−	0.460028i
$446$	21.3210	−	3.88503i	1.00958	−	0.183962i
$447$	−10.2443	−	7.44293i	−0.484540	−	0.352039i
$448$	−21.9896	−	3.89260i	−1.03891	−	0.183908i
$449$	5.69852	−	17.5383i	0.268930	−	0.827681i	−0.721832	−	0.692068i	$-0.756700\pi$
$449$	5.69852	−	17.5383i	0.268930	−	0.827681i	0.990762	−	0.135613i	$-0.0433003\pi$
$450$	25.7115	+	3.46403i	1.21205	+	0.163296i
$451$	−2.29562	−	12.0784i	−0.108097	−	0.568750i
$452$	19.6865	+	5.40268i	0.925976	+	0.254120i
$453$	0.476280	−	1.46584i	0.0223776	−	0.0688712i
$454$	13.6005	+	25.2305i	0.638303	+	1.18412i
$455$	13.6377	−	18.7707i	0.639344	−	0.879982i
$456$	11.6929	+	1.02696i	0.547572	+	0.0480918i
$457$	0.304061	−	0.0987953i	0.0142234	−	0.00462145i	−0.301897	−	0.953341i	$-0.597620\pi$
$457$	0.304061	−	0.0987953i	0.0142234	−	0.00462145i	0.316120	+	0.948719i	$0.397620\pi$
$458$	−3.63868	+	3.81124i	−0.170024	+	0.178088i
$459$	14.5324	+	20.0022i	0.678316	+	0.933622i
$460$	3.69544	−	5.61590i	0.172301	−	0.261843i
$461$	14.6804			0.683735			0.341868	−	0.939748i	$-0.388941\pi$
$461$	14.6804			0.683735			0.341868	+	0.939748i	$0.388941\pi$
$462$	11.3514	−	9.22114i	0.528114	−	0.429006i
$463$			16.1267i			0.749471i	0.927132	+	0.374735i	$0.122266\pi$
$463$			16.1267i			0.749471i	−0.927132	+	0.374735i	$0.877734\pi$
$464$	16.2009	−	14.2367i	0.752110	−	0.660922i
$465$	2.97797	−	2.16362i	0.138100	−	0.100335i
$466$	24.0266	−	25.1661i	1.11301	−	1.16579i
$467$	−1.71292	−	5.27183i	−0.0792645	−	0.243951i	0.903570	−	0.428441i	$-0.140937\pi$
$467$	−1.71292	−	5.27183i	−0.0792645	−	0.243951i	−0.982834	+	0.184489i	$0.940937\pi$
$468$	0.342930	+	7.39852i	0.0158519	+	0.341997i
$469$	−7.81041	−	5.67460i	−0.360651	−	0.262028i
$470$	−6.65590	+	3.58787i	−0.307014	+	0.165496i
$471$	−20.4229	−	6.63582i	−0.941040	−	0.305762i
$472$	−21.8957	−	9.30287i	−1.00783	−	0.428199i
$473$	1.95789	−	4.15345i	0.0900241	−	0.190976i
$474$	18.2379	+	2.45714i	0.837696	+	0.112860i
$475$	36.9918	+	12.0194i	1.69730	+	0.551486i
$476$	−9.17174	−	24.3316i	−0.420386	−	1.11524i
$477$	4.34792	−	5.98440i	0.199078	−	0.274007i
$478$	−4.38968	−	24.0905i	−0.200779	−	1.10187i
$479$	1.04517	+	3.21671i	0.0477551	+	0.146975i	0.972091	−	0.234606i	$-0.0753799\pi$
$479$	1.04517	+	3.21671i	0.0477551	+	0.146975i	−0.924336	+	0.381581i	$0.875380\pi$
$480$	−23.9321	+	6.69753i	−1.09235	+	0.305699i
$481$	4.51100	+	6.20886i	0.205684	+	0.283100i
$482$	−15.3031	−	7.35605i	−0.697039	−	0.335059i
$483$			2.66477i			0.121251i
$484$	4.50777	−	21.5332i	0.204899	−	0.978783i
$485$			43.8252i			1.99000i
$486$	9.29688	−	19.3407i	0.421715	−	0.877314i
$487$	17.9182	+	24.6623i	0.811952	+	1.11756i	0.991019	+	0.133719i	$0.0426919\pi$
$487$	17.9182	+	24.6623i	0.811952	+	1.11756i	−0.179068	+	0.983837i	$0.557308\pi$
$488$	−4.57358	−	7.61752i	−0.207036	−	0.344829i
$489$	3.84597	+	11.8367i	0.173921	+	0.535273i
$490$	4.33442	−	0.789802i	0.195809	−	0.0356796i
$491$	−19.3196	+	26.5912i	−0.871882	+	1.20004i	0.106721	+	0.994289i	$0.465965\pi$
$491$	−19.3196	+	26.5912i	−0.871882	+	1.20004i	−0.978604	+	0.205754i	$0.934035\pi$
$492$	−2.92099	−	7.74905i	−0.131688	−	0.349354i
$493$	23.8841	+	7.76040i	1.07568	+	0.349511i
$494$	−1.48260	+	11.0045i	−0.0667055	+	0.495116i
$495$	−9.74652	+	20.6762i	−0.438074	+	0.929324i
$496$	1.71071	−	2.88204i	0.0768132	−	0.129408i
$497$	32.7700	+	10.6476i	1.46993	+	0.477610i
$498$	0.686438	+	1.27342i	0.0307600	+	0.0570633i
$499$	−8.74683	−	6.35494i	−0.391562	−	0.284486i	0.374533	−	0.927213i	$-0.377803\pi$
$499$	−8.74683	−	6.35494i	−0.391562	−	0.284486i	−0.766095	+	0.642727i	$0.777803\pi$
$500$	−42.9730	+	1.99185i	−1.92181	+	0.0890781i
$501$	−7.00361	−	21.5549i	−0.312898	−	0.963001i
$502$	−2.74332	−	2.61911i	−0.122441	−	0.116897i
$503$	−20.9779	+	15.2413i	−0.935357	+	0.679577i	−0.947299	−	0.320352i	$-0.896199\pi$
$503$	−20.9779	+	15.2413i	−0.935357	+	0.679577i	0.0119412	+	0.999929i	$0.496199\pi$
$504$	−9.08028	+	10.4386i	−0.404468	+	0.464971i
$505$			21.0846i			0.938253i
$506$	2.52750	+	3.11139i	0.112361	+	0.138318i
$507$	−9.53228			−0.423344
$508$	−14.0265	+	21.3158i	−0.622324	+	0.945735i
$509$	15.4298	+	21.2373i	0.683914	+	0.941327i	0.999973	−	0.00741265i	$-0.00235954\pi$
$509$	15.4298	+	21.2373i	0.683914	+	0.941327i	−0.316058	+	0.948740i	$0.602360\pi$
$510$	−20.9301	−	19.9824i	−0.926801	−	0.884837i
$511$	−8.61905	+	2.80050i	−0.381284	+	0.123887i
$512$	−17.5992	+	14.2222i	−0.777780	+	0.628536i
$513$	11.5924	−	15.9555i	0.511816	−	0.704454i
$514$	−16.7968	+	9.05435i	−0.740877	+	0.399370i
$515$	−7.48571	+	23.0386i	−0.329860	+	1.01520i
$516$	0.818536	−	2.98262i	0.0360340	−	0.131302i
$517$	−0.841852	−	4.42939i	−0.0370246	−	0.194804i
$518$	−1.91417	+	14.2078i	−0.0841037	+	0.624253i
$519$	−5.37676	+	16.5480i	−0.236014	+	0.726375i
$520$	−5.28074	−	22.9085i	−0.231576	−	1.00461i
$521$	9.15472	+	6.65129i	0.401076	+	0.291399i	0.769979	−	0.638069i	$-0.220267\pi$
$521$	9.15472	+	6.65129i	0.401076	+	0.291399i	−0.368903	+	0.929468i	$0.620267\pi$
$522$	−2.39532	−	13.1455i	−0.104840	−	0.575362i
$523$	−21.7647	+	7.07178i	−0.951704	+	0.309227i	−0.743408	−	0.668838i	$-0.766792\pi$
$523$	−21.7647	+	7.07178i	−0.951704	+	0.309227i	−0.208296	+	0.978066i	$0.566792\pi$
$524$	16.8869	−	13.5066i	0.737706	−	0.590038i
$525$	26.4080	−	19.1866i	1.15254	−	0.837371i
$526$	−0.363687	+	0.756596i	−0.0158575	+	0.0329891i
$527$	3.90252			0.169997
$528$	0.499336	−	14.8101i	0.0217308	−	0.644529i
$529$	22.2696			0.968243
$530$	−10.1722	+	21.1618i	−0.441853	+	0.919208i
$531$	−11.9241	+	8.66333i	−0.517460	+	0.375957i
$532$	−16.1983	+	12.9559i	−0.702285	+	0.561707i
$533$	7.45057	−	2.42084i	0.322720	−	0.104858i
$534$	2.26105	+	12.4086i	0.0978453	+	0.536974i
$535$	−48.8421	−	35.4859i	−2.11163	−	1.53419i
$536$	−9.53217	+	2.19730i	−0.411727	+	0.0949089i
$537$	−5.85532	+	18.0208i	−0.252676	+	0.777656i
$538$	−3.67842	+	27.3028i	−0.158588	+	1.17711i
$539$	−0.331022	+	2.60616i	−0.0142581	+	0.112255i
$540$	−11.0507	+	40.2669i	−0.475545	+	1.73281i
$541$	5.01194	−	15.4252i	0.215480	−	0.663180i	−0.783639	−	0.621217i	$-0.786639\pi$
$541$	5.01194	−	15.4252i	0.215480	−	0.663180i	0.999119	−	0.0419633i	$-0.0133613\pi$
$542$	30.5539	−	16.4701i	1.31240	−	0.707452i
$543$	−8.72795	+	12.0130i	−0.374552	+	0.515527i
$544$	−24.7005	−	9.16908i	−1.05903	−	0.393121i
$545$	10.7250	−	3.48477i	0.459410	−	0.149271i
$546$	6.74016	+	6.43498i	0.288452	+	0.275392i
$547$	−6.35466	−	8.74643i	−0.271705	−	0.373970i	0.651259	−	0.758855i	$-0.274241\pi$
$547$	−6.35466	−	8.74643i	−0.271705	−	0.373970i	−0.922965	+	0.384885i	$0.874241\pi$
$548$	−23.6383	+	35.9227i	−1.00978	+	1.53454i
$549$	−5.50467			−0.234934
$550$	12.6359	−	47.4499i	0.538796	−	2.02327i
$551$		−	20.0325i		−	0.853415i
$552$	2.03719	+	1.77210i	0.0867084	+	0.0754257i
$553$	−26.3088	+	19.1145i	−1.11877	+	0.812831i
$554$	−15.0349	−	14.3542i	−0.638772	−	0.609850i
$555$	4.93005	+	15.1731i	0.209269	+	0.644064i
$556$	−13.6337	+	0.631936i	−0.578196	+	0.0268001i
$557$	−3.64856	−	2.65084i	−0.154595	−	0.112320i	0.507799	−	0.861476i	$-0.330459\pi$
$557$	−3.64856	−	2.65084i	−0.154595	−	0.112320i	−0.662394	+	0.749156i	$0.730459\pi$
$558$	−0.985261	−	1.82777i	−0.0417094	−	0.0773757i
$559$	2.78264	+	0.904133i	0.117693	+	0.0382408i
$560$	22.4157	−	37.7638i	0.947235	−	1.59581i
$561$	15.1261	−	8.30234i	0.638624	−	0.350525i
$562$	−4.35057	+	32.2918i	−0.183518	+	1.36215i
$563$	−0.590824	−	0.191970i	−0.0249003	−	0.00809058i	0.296540	−	0.955020i	$-0.404167\pi$
$563$	−0.590824	−	0.191970i	−0.0249003	−	0.00809058i	−0.321441	+	0.946930i	$0.604167\pi$
$564$	−1.07118	−	2.84173i	−0.0451050	−	0.119658i
$565$	−23.5969	+	32.4784i	−0.992730	+	1.36638i
$566$	31.3992	−	5.72144i	1.31981	−	0.240490i
$567$	−0.579965	−	1.78495i	−0.0243562	−	0.0749607i
$568$	29.9323	−	17.9715i	1.25593	−	0.754066i
$569$	−11.6083	−	15.9774i	−0.486644	−	0.669807i	0.493121	−	0.869961i	$-0.335856\pi$
$569$	−11.6083	−	15.9774i	−0.486644	−	0.669807i	−0.979765	+	0.200153i	$0.935856\pi$
$570$	−10.0004	+	20.8043i	−0.418870	+	0.871394i
$571$		−	28.2428i		−	1.18193i	−0.806699	−	0.590963i	$-0.798748\pi$
$571$		−	28.2428i		−	1.18193i	0.806699	−	0.590963i	$-0.201252\pi$
$572$	13.9733	+	1.12055i	0.584253	+	0.0468526i
$573$		−	28.2729i		−	1.18112i
$574$	13.1893	+	6.33994i	0.550510	+	0.264624i
$575$	5.25901	+	7.23840i	0.219316	+	0.301862i
$576$	1.94169	+	13.8835i	0.0809036	+	0.578480i
$577$	4.23700	+	13.0402i	0.176389	+	0.542869i	0.999694	−	0.0247297i	$-0.00787253\pi$
$577$	4.23700	+	13.0402i	0.176389	+	0.542869i	−0.823305	+	0.567599i	$0.807873\pi$
$578$	−1.18985	−	6.52987i	−0.0494912	−	0.271607i
$579$	−4.14584	+	5.70626i	−0.172295	+	0.237144i
$580$	14.9599	+	39.6870i	0.621177	+	1.64791i
$581$	−2.43126	−	0.789966i	−0.100866	−	0.0327733i
$582$	−17.4443	−	2.35021i	−0.723088	−	0.0974194i
$583$	−10.1994	−	9.59089i	−0.422418	−	0.397214i
$584$	−3.59081	+	8.45152i	−0.148589	+	0.349726i
$585$	−13.8521	−	4.50083i	−0.572716	−	0.186087i
$586$	0.279729	−	0.150788i	0.0115555	−	0.00622900i
$587$	27.8108	+	20.2057i	1.14788	+	0.833981i	0.988197	−	0.153188i	$-0.0489542\pi$
$587$	27.8108	+	20.2057i	1.14788	+	0.833981i	0.159679	+	0.987169i	$0.448954\pi$
$588$	0.0819320	+	1.76764i	0.00337882	+	0.0728961i
$589$	−0.961971	−	2.96064i	−0.0396373	−	0.121991i
$590$	32.3062	−	33.8383i	1.33002	−	1.39310i
$591$	−9.82507	+	7.13833i	−0.404149	+	0.293632i
$592$	9.58872	+	10.9117i	0.394094	+	0.448467i
$593$		−	18.6125i		−	0.764323i	−0.924096	−	0.382161i	$-0.875180\pi$
$593$		−	18.6125i		−	0.764323i	0.924096	−	0.382161i	$-0.124820\pi$
$594$	−20.9022	−	13.5284i	−0.857629	−	0.555075i
$595$	51.1353			2.09634
$596$	12.4632	−	18.9401i	0.510511	−	0.775816i
$597$	14.5648	+	20.0467i	0.596097	+	0.820457i
$598$	−1.76382	+	1.84746i	−0.0721278	+	0.0755485i
$599$	14.6710	−	4.76689i	0.599440	−	0.194770i	0.00644913	−	0.999979i	$-0.497947\pi$
$599$	14.6710	−	4.76689i	0.599440	−	0.194770i	0.592990	+	0.805209i	$0.297947\pi$
$600$	2.89373	−	32.9479i	0.118136	−	1.34509i
$601$	−6.78408	+	9.33748i	−0.276728	+	0.380884i	−0.924647	−	0.380826i	$-0.875640\pi$
$601$	−6.78408	+	9.33748i	−0.276728	+	0.380884i	0.647919	+	0.761710i	$0.275640\pi$
$602$	2.59338	+	4.81101i	0.105698	+	0.196082i
$603$	−1.87278	+	5.76383i	−0.0762656	+	0.234721i
$604$	2.66129	+	0.730353i	0.108286	+	0.0297176i
$605$	36.4973	+	23.2311i	1.48383	+	0.944479i
$606$	−8.39255	−	1.13070i	−0.340924	−	0.0459317i
$607$	0.811344	−	2.49706i	0.0329314	−	0.101353i	−0.933240	−	0.359254i	$-0.883031\pi$
$607$	0.811344	−	2.49706i	0.0329314	−	0.101353i	0.966171	+	0.257902i	$0.0830311\pi$
$608$	−0.867434	+	20.9992i	−0.0351791	+	0.851629i
$609$	−13.6011	−	9.88175i	−0.551143	−	0.400429i
$610$	17.1897	−	3.13223i	0.695989	−	0.126820i
$611$	2.73227	−	0.887770i	0.110536	−	0.0359153i
$612$	−12.7475	+	10.1958i	−0.515286	+	0.412140i
$613$	23.6605	−	17.1903i	0.955638	−	0.694311i	0.00350423	−	0.999994i	$-0.498885\pi$
$613$	23.6605	−	17.1903i	0.955638	−	0.694311i	0.952134	+	0.305682i	$0.0988846\pi$
$614$	10.1237	+	4.86635i	0.408559	+	0.196390i
$615$	16.2854			0.656691
$616$	17.4340	+	19.5387i	0.702437	+	0.787235i
$617$	−18.7736			−0.755798			−0.377899	−	0.925847i	$-0.623353\pi$
$617$	−18.7736			−0.755798			−0.377899	+	0.925847i	$0.623353\pi$
$618$	−8.76890	−	4.21512i	−0.352737	−	0.169557i
$619$	35.7686	−	25.9874i	1.43766	−	1.04452i	0.449139	−	0.893462i	$-0.351731\pi$
$619$	35.7686	−	25.9874i	1.43766	−	1.04452i	0.988524	−	0.151061i	$-0.0482690\pi$
$620$	4.11674	+	5.14703i	0.165332	+	0.206710i
$621$	4.31465	−	1.40192i	0.173141	−	0.0562569i
$622$	−43.7972	+	7.98056i	−1.75611	+	0.319991i
$623$	−18.0317	−	13.1008i	−0.722425	−	0.524872i
$624$	9.40174	−	0.873440i	0.376371	−	0.0349656i
$625$	9.96692	−	30.6750i	0.398677	−	1.22700i
$626$	26.1204	+	3.51912i	1.04398	+	0.140652i
$627$	−10.0271	−	9.42885i	−0.400445	−	0.376552i
$628$	10.1757	−	37.0787i	0.406055	−	1.47960i
$629$	−5.22679	+	16.0864i	−0.208406	+	0.641407i
$630$	−12.9100	−	23.9495i	−0.514347	−	0.954171i
$631$	−3.44264	+	4.73839i	−0.137049	+	0.188632i	−0.872025	−	0.489461i	$-0.837194\pi$
$631$	−3.44264	+	4.73839i	−0.137049	+	0.188632i	0.734976	+	0.678093i	$0.237194\pi$
$632$	−2.88286	+	32.8241i	−0.114674	+	1.30567i
$633$	−4.79573	+	1.55823i	−0.190613	+	0.0619340i
$634$	−22.5379	+	23.6067i	−0.895093	+	0.937542i
$635$	−29.4947	−	40.5960i	−1.17046	−	1.61100i
$636$	−7.87776	−	5.18381i	−0.312373	−	0.205552i
$637$	−1.67395			−0.0663245
$638$	−25.2533	+	1.36246i	−0.999789	+	0.0539404i
$639$		−	21.6301i		−	0.855673i
$640$	−13.9633	−	42.2498i	−0.551948	−	1.67007i
$641$	−15.9169	+	11.5643i	−0.628680	+	0.456763i	−0.855943	−	0.517071i	$-0.827022\pi$
$641$	−15.9169	+	11.5643i	−0.628680	+	0.456763i	0.227263	+	0.973833i	$0.427022\pi$
$642$	16.7441	−	17.5382i	0.660838	−	0.692178i
$643$	3.22855	+	9.93645i	0.127322	+	0.391855i	0.994317	−	0.106461i	$-0.0339519\pi$
$643$	3.22855	+	9.93645i	0.127322	+	0.391855i	−0.866995	+	0.498316i	$0.833952\pi$
$644$	−4.76622	+	0.220920i	−0.187816	+	0.00870547i
$645$	4.92065	+	3.57506i	0.193751	+	0.140768i
$646$	−21.5419	+	11.6122i	−0.847555	+	0.456875i
$647$	−6.43578	−	2.09111i	−0.253017	−	0.0822101i	0.179763	−	0.983710i	$-0.442467\pi$
$647$	−6.43578	−	2.09111i	−0.253017	−	0.0822101i	−0.432779	+	0.901500i	$0.642467\pi$
$648$	−1.75025	−	0.743633i	−0.0687565	−	0.0292127i
$649$	13.4226	+	24.4548i	0.526884	+	0.959934i
$650$	31.0081	+	4.17763i	1.21624	+	0.163860i
$651$	−2.48465	−	0.807312i	−0.0973812	−	0.0316411i
$652$	−20.8523	+	7.86023i	−0.816639	+	0.307830i
$653$	−20.1960	+	27.7974i	−0.790332	+	1.08780i	0.203735	+	0.979026i	$0.434692\pi$
$653$	−20.1960	+	27.7974i	−0.790332	+	1.08780i	−0.994067	+	0.108772i	$0.965308\pi$
$654$	0.811935	+	4.45589i	0.0317492	+	0.174239i
$655$	13.1406	+	40.4428i	0.513448	+	1.58023i
$656$	13.6178	−	5.86692i	0.531686	−	0.229065i
$657$	3.34396	+	4.60256i	0.130460	+	0.179563i
$658$	4.83677	+	2.32498i	0.188557	+	0.0906373i
$659$			34.5518i			1.34595i	0.739667	+	0.672973i	$0.234983\pi$
$659$			34.5518i			1.34595i	−0.739667	+	0.672973i	$0.765017\pi$
$660$	26.9063	+	11.1917i	1.04733	+	0.435636i
$661$		−	17.3103i		−	0.673292i	−0.941631	−	0.336646i	$-0.890707\pi$
$661$		−	17.3103i		−	0.673292i	0.941631	−	0.336646i	$-0.109293\pi$
$662$	−12.2213	+	25.4245i	−0.474994	+	0.988152i
$663$	6.46244	+	8.89478i	0.250980	+	0.345445i
$664$	−2.22074	+	1.33334i	−0.0861813	+	0.0517435i
$665$	−12.6048	−	38.7937i	−0.488794	−	1.50435i
$666$	8.85376	−	1.61330i	0.343076	−	0.0625140i
$667$	2.70857	−	3.72803i	0.104876	−	0.144350i
$668$	37.9725	−	14.3137i	1.46920	−	0.553812i
$669$	−16.2795	−	5.28954i	−0.629403	−	0.204505i
$670$	2.56852	−	19.0646i	0.0992305	−	0.736530i
$671$	−1.31278	+	10.3356i	−0.0506795	+	0.399002i
$672$	13.8295	+	10.9475i	0.533484	+	0.422310i
$673$	−25.9975	−	8.44710i	−1.00213	−	0.325612i	−0.238413	−	0.971164i	$-0.576627\pi$
$673$	−25.9975	−	8.44710i	−1.00213	−	0.325612i	−0.763716	+	0.645552i	$0.776627\pi$
$674$	−2.87873	−	5.34038i	−0.110885	−	0.205704i
$675$	−44.9589	−	32.6646i	−1.73047	−	1.25726i
$676$	−0.790264	−	17.0495i	−0.0303948	−	0.655749i
$677$	−8.46763	−	26.0607i	−0.325438	−	1.00159i	−0.971243	−	0.238091i	$-0.923478\pi$
$677$	−8.46763	−	26.0607i	−0.325438	−	1.00159i	0.645805	−	0.763502i	$-0.276522\pi$
$678$	−11.6623	−	11.1343i	−0.447888	−	0.427609i
$679$	25.1639	−	18.2827i	0.965703	−	0.701625i
$680$	34.0055	−	39.0923i	1.30405	−	1.49912i
$681$		−	22.6387i		−	0.867517i
$682$	−3.66681	+	1.41404i	−0.140409	+	0.0541463i
$683$	−19.0093			−0.727370			−0.363685	−	0.931522i	$-0.618482\pi$
$683$	−19.0093			−0.727370			−0.363685	+	0.931522i	$0.618482\pi$
$684$	10.8773	+	7.15758i	0.415903	+	0.273677i
$685$	−49.7064	−	68.4149i	−1.89918	−	2.61400i
$686$	17.7256	+	16.9230i	0.676766	+	0.646123i
$687$	3.95817	−	1.28609i	0.151013	−	0.0490673i
$688$	5.40258	+	1.21677i	0.205971	+	0.0463888i
$689$	5.24361	−	7.21721i	0.199766	−	0.274954i
$690$	−4.67397	+	2.51951i	−0.177935	+	0.0959160i
$691$	10.0374	−	30.8919i	0.381840	−	1.17518i	−0.556907	−	0.830575i	$-0.688012\pi$
$691$	10.0374	−	30.8919i	0.381840	−	1.17518i	0.938747	−	0.344607i	$-0.111988\pi$
$692$	−30.0435	−	8.24500i	−1.14208	−	0.313428i
$693$	15.9380	−	3.02918i	0.605435	−	0.115069i
$694$	2.76729	−	20.5400i	0.105045	−	0.779686i
$695$	8.29394	−	25.5261i	0.314607	−	0.968261i
$696$	−16.5993	+	3.82638i	−0.629196	+	0.145039i
$697$	13.9682	+	10.1485i	0.529082	+	0.384401i
$698$	8.60367	+	47.2169i	0.325654	+	1.78719i
$699$	−26.1362	+	8.49217i	−0.988563	+	0.321203i
$700$	36.5065	+	45.6429i	1.37982	+	1.72514i
$701$	−34.5883	+	25.1299i	−1.30638	+	0.949142i	−0.999996	−	0.00276567i	$-0.999120\pi$
$701$	−34.5883	+	25.1299i	−1.30638	+	0.949142i	−0.306386	+	0.951908i	$0.599120\pi$
$702$	6.87322	−	14.2987i	0.259413	−	0.539669i
$703$	13.4923			0.508873
$704$	26.5309	−	0.334705i	0.999920	−	0.0126147i
$705$	5.97218			0.224925
$706$	8.45747	−	17.5945i	0.318301	−	0.662177i
$707$	12.1066	−	8.79593i	0.455314	−	0.330805i
$708$	11.7366	+	14.6739i	0.441087	+	0.551477i
$709$	−6.59283	+	2.14214i	−0.247599	+	0.0804498i	−0.430187	−	0.902740i	$-0.641552\pi$
$709$	−6.59283	+	2.14214i	−0.247599	+	0.0804498i	0.182588	+	0.983189i	$0.441552\pi$
$710$	12.3078	+	67.5452i	0.461904	+	2.53493i
$711$	16.5155	+	11.9992i	0.619378	+	0.450005i
$712$	−22.0067	+	5.07285i	−0.824735	+	0.190113i
$713$	0.221283	−	0.681039i	0.00828711	−	0.0255051i
$714$	−2.74223	+	20.3540i	−0.102625	+	0.761728i
$715$	−11.7543	+	24.9355i	−0.439587	+	0.932535i
$716$	−32.7176	−	8.97886i	−1.22271	−	0.335556i
$717$	−5.97662	+	18.3942i	−0.223201	+	0.686942i
$718$	21.0265	−	11.3344i	0.784703	−	0.422994i
$719$	29.1465	−	40.1168i	1.08698	−	1.49610i	0.235388	−	0.971901i	$-0.424364\pi$
$719$	29.1465	−	40.1168i	1.08698	−	1.49610i	0.851594	−	0.524202i	$-0.175636\pi$
$720$	−26.8944	−	6.05714i	−1.00229	−	0.225736i
$721$	16.3514	−	5.31288i	0.608957	−	0.197862i
$722$	−5.31526	−	5.07460i	−0.197813	−	0.188857i
$723$	7.88268	+	10.8496i	0.293160	+	0.403500i
$724$	−22.2101	−	14.6149i	−0.825430	−	0.543159i
$725$	−56.4469			−2.09639
$726$	−11.2042	+	13.2816i	−0.415827	+	0.492928i
$727$			20.0972i			0.745365i	0.927959	+	0.372683i	$0.121562\pi$
$727$			20.0972i			0.745365i	−0.927959	+	0.372683i	$0.878438\pi$
$728$	−10.9508	+	12.5890i	−0.405865	+	0.466578i
$729$	−15.3440	+	11.1480i	−0.568295	+	0.412890i
$730$	−13.0612	−	12.4699i	−0.483418	−	0.461530i
$731$	1.99265	+	6.13275i	0.0737008	+	0.226828i
$732$	0.324930	+	7.01018i	0.0120098	+	0.259104i
$733$	38.5016	+	27.9731i	1.42209	+	1.03321i	0.991422	+	0.130699i	$0.0417222\pi$
$733$	38.5016	+	27.9731i	1.42209	+	1.03321i	0.430669	+	0.902510i	$0.358278\pi$
$734$	0.151143	+	0.280388i	0.00557881	+	0.0103493i
$735$	−3.30952	−	1.07533i	−0.122074	−	0.0396641i
$736$	−3.00070	+	3.79064i	−0.110607	+	0.139725i
$737$	10.3756	+	4.89094i	0.382190	+	0.180160i
$738$	1.22659	−	9.10424i	0.0451513	−	0.335132i
$739$	−47.1991	−	15.3359i	−1.73625	−	0.564140i	−0.741917	−	0.670492i	$-0.766083\pi$
$739$	−47.1991	−	15.3359i	−1.73625	−	0.564140i	−0.994329	+	0.106351i	$0.966083\pi$
$740$	−26.7300	+	10.0758i	−0.982615	+	0.370395i
$741$	5.15502	−	7.09528i	0.189374	−	0.260651i
$742$	16.3944	−	2.98733i	0.601859	−	0.109668i
$743$	11.3841	+	35.0366i	0.417642	+	1.28537i	0.909866	+	0.414901i	$0.136184\pi$
$743$	11.3841	+	35.0366i	0.417642	+	1.28537i	−0.492225	+	0.870468i	$0.663816\pi$
$744$	−2.26950	+	1.36262i	−0.0832039	+	0.0499559i
$745$	26.2074	+	36.0714i	0.960166	+	1.32155i
$746$	6.94465	−	14.4473i	0.254262	−	0.528953i
$747$			1.60478i			0.0587157i
$748$	16.1036	+	26.3663i	0.588806	+	0.964047i
$749$			42.8484i			1.56565i
$750$	30.6236	+	14.7204i	1.11822	+	0.537514i
$751$	3.19001	+	4.39067i	0.116405	+	0.160218i	0.863244	−	0.504788i	$-0.168429\pi$
$751$	3.19001	+	4.39067i	0.116405	+	0.160218i	−0.746839	+	0.665005i	$0.768429\pi$
$752$	4.99393	−	2.15152i	0.182110	−	0.0784577i
$753$	0.925722	+	2.84908i	0.0337352	+	0.103826i
$754$	−2.88876	−	15.8535i	−0.105203	−	0.577350i
$755$	−3.18992	+	4.39054i	−0.116093	+	0.159788i
$756$	27.7309	−	10.4531i	1.00856	−	0.380175i
$757$	18.5263	+	6.01955i	0.673348	+	0.218784i	0.625681	−	0.780079i	$-0.284821\pi$
$757$	18.5263	+	6.01955i	0.673348	+	0.218784i	0.0476675	+	0.998863i	$0.484821\pi$
$758$	−7.30688	−	0.984433i	−0.265398	−	0.0357562i
$759$	−0.591174	−	3.11045i	−0.0214582	−	0.112902i
$760$	−38.0396	−	16.1620i	−1.37984	−	0.586256i
$761$	−11.3571	−	3.69015i	−0.411695	−	0.133768i	0.0958447	−	0.995396i	$-0.469445\pi$
$761$	−11.3571	−	3.69015i	−0.411695	−	0.133768i	−0.507539	+	0.861629i	$0.669445\pi$
$762$	17.7406	−	9.56308i	0.642674	−	0.346434i
$763$	−6.47511	−	4.70444i	−0.234415	−	0.170312i
$764$	50.5690	−	2.34393i	1.82952	−	0.0848004i
$765$	−9.91954	−	30.5292i	−0.358642	−	1.10379i
$766$	−32.2561	+	33.7858i	−1.16546	+	1.22073i
$767$	−14.3804	+	10.4480i	−0.519248	+	0.377256i
$768$	17.5660	−	3.29225i	0.633859	−	0.118799i
$769$		−	42.9323i		−	1.54818i	−0.633077	−	0.774089i	$-0.718208\pi$
$769$		−	42.9323i		−	1.54818i	0.633077	−	0.774089i	$-0.281792\pi$
$770$	−48.0466	+	18.5283i	−1.73148	+	0.667714i
$771$	15.0714			0.542784
$772$	−10.5499	−	6.94219i	−0.379701	−	0.249855i
$773$	−5.52701	−	7.60728i	−0.198793	−	0.273615i	0.697969	−	0.716128i	$-0.254087\pi$
$773$	−5.52701	−	7.60728i	−0.198793	−	0.273615i	−0.896762	+	0.442513i	$0.854087\pi$
$774$	2.36923	−	2.48159i	0.0851602	−	0.0891989i
$775$	−8.34239	+	2.71061i	−0.299667	+	0.0973678i
$776$	2.75740	−	31.3957i	0.0989850	−	1.12704i
$777$	6.65557	−	9.16060i	0.238767	−	0.328635i
$778$	4.99619	+	9.26850i	0.179122	+	0.332292i
$779$	4.25597	−	13.0985i	0.152486	−	0.469303i
$780$	−4.91413	+	17.9063i	−0.175954	+	0.641149i
$781$	−40.6128	−	5.15846i	−1.45324	−	0.184584i
$782$	−5.57899	−	0.751640i	−0.199504	−	0.0268786i
$783$	−8.84458	+	27.2208i	−0.316079	+	0.972793i
$784$	−3.15481	+	0.293088i	−0.112672	+	0.0104674i
$785$	61.1716	+	44.4438i	2.18331	+	1.58627i
$786$	−16.8026	+	3.06170i	−0.599329	+	0.109207i
$787$	48.8038	−	15.8573i	1.73967	−	0.565252i	0.744878	−	0.667200i	$-0.232507\pi$
$787$	48.8038	−	15.8573i	1.73967	−	0.565252i	0.994790	+	0.101948i	$0.0325074\pi$
$788$	−13.5822	−	16.9814i	−0.483845	−	0.604936i
$789$	0.536409	−	0.389724i	0.0190967	−	0.0138745i
$790$	−58.4012	−	28.0728i	−2.07782	−	0.998786i
$791$	28.4927			1.01308
$792$	8.28317	−	14.1989i	0.294330	−	0.504534i
$793$	−6.63865			−0.235745
$794$	16.0288	+	7.70486i	0.568840	+	0.273435i
$795$	15.0032	−	10.9005i	0.532109	−	0.386600i
$796$	−34.6481	+	27.7126i	−1.22807	+	0.982246i
$797$	−20.8890	+	6.78723i	−0.739925	+	0.240416i	−0.654640	−	0.755941i	$-0.727180\pi$
$797$	−20.8890	+	6.78723i	−0.739925	+	0.240416i	−0.0852843	+	0.996357i	$0.527180\pi$
$798$	16.1175	−	2.93686i	0.570552	−	0.103964i
$799$	5.12241	+	3.72165i	0.181218	+	0.131662i
$800$	59.1707	+	2.44422i	2.09200	+	0.0864163i
$801$	−4.32365	+	13.3068i	−0.152769	+	0.470173i
$802$	−19.5209	−	2.63000i	−0.689309	−	0.0928685i
$803$	9.43929	−	5.18100i	0.333105	−	0.182833i
$804$	7.45077	+	2.04475i	0.262768	+	0.0721129i
$805$	2.89950	−	8.92374i	0.102194	−	0.314520i
$806$	−1.18823	−	2.20430i	−0.0418535	−	0.0776430i
$807$	12.7899	−	17.6038i	0.450225	−	0.619682i
$808$	1.32661	−	15.1047i	0.0466698	−	0.531381i
$809$	−44.5044	+	14.4604i	−1.56469	+	0.508399i	−0.958056	−	0.286580i	$-0.907482\pi$
$809$	−44.5044	+	14.4604i	−1.56469	+	0.508399i	−0.606636	+	0.794980i	$0.707482\pi$
$810$	2.58242	−	2.70489i	0.0907371	−	0.0950403i
$811$	−1.59838	−	2.19998i	−0.0561267	−	0.0772518i	0.780031	−	0.625741i	$-0.215203\pi$
$811$	−1.59838	−	2.19998i	−0.0561267	−	0.0772518i	−0.836158	+	0.548489i	$0.815203\pi$
$812$	16.5470	−	25.1462i	0.580685	−	0.882457i
$813$	−27.4153			−0.961498
$814$	−0.917647	−	17.0086i	−0.0321635	−	0.596153i
$815$		−	43.8232i		−	1.53506i
$816$	13.7368	+	15.6320i	0.480883	+	0.547230i
$817$	4.16141	−	3.02344i	0.145589	−	0.105777i
$818$	−1.51316	+	1.58492i	−0.0529063	+	0.0554154i
$819$	3.19441	+	9.83137i	0.111622	+	0.343536i
$820$	1.35012	+	29.1281i	0.0471484	+	1.01720i
$821$	35.2195	+	25.5884i	1.22917	+	0.893043i	0.996828	−	0.0795914i	$-0.0253616\pi$
$821$	35.2195	+	25.5884i	1.22917	+	0.893043i	0.232341	+	0.972634i	$0.425362\pi$
$822$	29.8976	−	16.1163i	1.04280	−	0.562121i
$823$	−18.1038	−	5.88230i	−0.631060	−	0.205044i	−0.0240156	−	0.999712i	$-0.507645\pi$
$823$	−18.1038	−	5.88230i	−0.631060	−	0.205044i	−0.607045	+	0.794668i	$0.707645\pi$
$824$	6.81220	−	16.0335i	0.237314	−	0.558555i
$825$	−26.5683	+	28.2541i	−0.924988	+	0.983680i
$826$	−32.9068	−	4.43344i	−1.14498	−	0.154259i
$827$	36.6382	+	11.9045i	1.27404	+	0.413959i	0.866476	−	0.499220i	$-0.166380\pi$
$827$	36.6382	+	11.9045i	1.27404	+	0.413959i	0.407560	+	0.913179i	$0.366380\pi$
$828$	1.05648	+	2.80272i	0.0367152	+	0.0974011i
$829$	−19.6824	+	27.0905i	−0.683597	+	0.940890i	−0.999970	−	0.00774447i	$-0.997535\pi$
$829$	−19.6824	+	27.0905i	−0.683597	+	0.940890i	0.316373	+	0.948635i	$0.397535\pi$
$830$	−0.913141	−	5.01131i	−0.0316956	−	0.173945i
$831$	5.07346	+	15.6145i	0.175996	+	0.541661i
$832$	2.34168	+	16.7436i	0.0811831	+	0.580479i
$833$	−2.16851	−	2.98470i	−0.0751344	−	0.103414i
$834$	9.71568	+	4.67022i	0.336427	+	0.161717i
$835$			79.8031i			2.76170i
$836$	16.0332	−	18.7163i	0.554520	−	0.647315i
$837$			4.44773i			0.153736i
$838$	−11.2809	+	23.4683i	−0.389694	+	0.810698i
$839$	−3.48024	−	4.79014i	−0.120151	−	0.165374i	0.744705	−	0.667394i	$-0.232590\pi$
$839$	−3.48024	−	4.79014i	−0.120151	−	0.165374i	−0.864856	+	0.502020i	$0.832590\pi$
$840$	−29.7375	+	17.8545i	−1.02604	+	0.616039i
$841$	0.0222891	+	0.0685987i	0.000768589	+	0.00236547i
$842$	−38.9176	+	7.09141i	−1.34119	+	0.244386i
$843$	15.1270	−	20.8205i	0.521000	−	0.717095i
$844$	−3.18464	−	8.44848i	−0.109620	−	0.290809i
$845$	31.9215	+	10.3719i	1.09813	+	0.356805i
$846$	0.449814	−	3.33871i	0.0154649	−	0.114787i
$847$	−1.88663	−	30.6477i	−0.0648255	−	1.05307i
$848$	8.61869	−	14.5200i	0.295967	−	0.498617i
$849$	−23.9747	−	7.78985i	−0.822809	−	0.267347i
$850$	32.7203	+	60.6999i	1.12230	+	2.08199i
$851$	2.51091	+	1.82428i	0.0860727	+	0.0625355i
$852$	−27.5458	+	1.27678i	−0.943705	+	0.0437418i
$853$	−2.67901	−	8.24514i	−0.0917275	−	0.282308i	0.894660	−	0.446749i	$-0.147418\pi$
$853$	−2.67901	−	8.24514i	−0.0917275	−	0.282308i	−0.986387	+	0.164440i	$0.947418\pi$
$854$	−8.96956	−	8.56344i	−0.306932	−	0.293035i
$855$	−20.7158	+	15.0509i	−0.708464	+	0.514730i
$856$	32.7571	+	28.4946i	1.11961	+	0.973926i
$857$			18.5127i			0.632382i	0.948695	+	0.316191i	$0.102404\pi$
$857$			18.5127i			0.632382i	−0.948695	+	0.316191i	$0.897596\pi$
$858$	−9.29502	−	6.01593i	−0.317327	−	0.205381i
$859$	−0.218543			−0.00745661			−0.00372830	−	0.999993i	$-0.501187\pi$
$859$	−0.218543			−0.00745661			−0.00372830	+	0.999993i	$0.501187\pi$
$860$	−5.98643	+	9.09749i	−0.204136	+	0.310222i
$861$	−6.79382	−	9.35090i	−0.231533	−	0.318678i
$862$	−30.0483	−	28.6878i	−1.02345	−	0.977110i
$863$	5.38003	−	1.74808i	0.183138	−	0.0595053i	−0.216012	−	0.976391i	$-0.569305\pi$
$863$	5.38003	−	1.74808i	0.183138	−	0.0595053i	0.399151	+	0.916885i	$0.369305\pi$
$864$	10.4501	−	28.1513i	0.355518	−	0.957728i
$865$	36.0112	−	49.5651i	1.22442	−	1.68526i
$866$	−22.9420	+	12.3669i	−0.779601	+	0.420245i
$867$	−1.62000	+	4.98584i	−0.0550180	+	0.169328i
$868$	1.23797	−	4.51099i	0.0420196	−	0.153113i
$869$	26.4685	−	28.1479i	0.897881	−	0.954853i
$870$	4.47282	−	33.1991i	0.151643	−	1.12556i
$871$	−2.25858	+	6.95120i	−0.0765291	+	0.235532i
$872$	−7.90251	+	1.82164i	−0.267613	+	0.0616885i
$873$	−15.7967	−	11.4770i	−0.534639	−	0.388438i
$874$	0.804988	+	4.41777i	0.0272291	+	0.149433i
$875$	−57.1038	+	18.5541i	−1.93046	+	0.627244i
$876$	5.66396	−	4.53020i	0.191367	−	0.153061i
$877$	28.1771	−	20.4719i	0.951473	−	0.691286i	0.000318228	−	1.00000i	$-0.499899\pi$
$877$	28.1771	−	20.4719i	0.951473	−	0.691286i	0.951155	+	0.308714i	$0.0998987\pi$
$878$	−1.82162	+	3.78960i	−0.0614767	+	0.127893i
$879$	−0.250994			−0.00846583
$880$	−17.7869	+	49.0526i	−0.599595	+	1.65356i
$881$	−29.7384			−1.00191			−0.500957	−	0.865472i	$-0.667018\pi$
$881$	−29.7384			−1.00191			−0.500957	+	0.865472i	$0.667018\pi$
$882$	−0.850422	+	1.76917i	−0.0286352	+	0.0595712i
$883$	16.7903	−	12.1988i	0.565038	−	0.410524i	−0.268262	−	0.963346i	$-0.586449\pi$
$883$	16.7903	−	12.1988i	0.565038	−	0.410524i	0.833299	+	0.552822i	$0.186449\pi$
$884$	−15.3735	+	12.2962i	−0.517066	+	0.413564i
$885$	−35.1428	+	11.4186i	−1.18131	+	0.383831i
$886$	0.302554	+	1.66041i	0.0101645	+	0.0557826i
$887$	21.3255	+	15.4939i	0.716042	+	0.520235i	0.885117	−	0.465368i	$-0.154078\pi$
$887$	21.3255	+	15.4939i	0.716042	+	0.520235i	−0.169075	+	0.985603i	$0.554078\pi$
$888$	−2.57715	−	11.1800i	−0.0864835	−	0.375176i
$889$	−11.0054	+	33.8711i	−0.369109	+	1.13600i
$890$	5.92987	−	44.0140i	0.198770	−	1.47535i
$891$	1.07295	+	1.95481i	0.0359452	+	0.0654887i
$892$	8.11126	−	29.5562i	0.271585	−	0.989613i
$893$	1.56075	−	4.80349i	0.0522285	−	0.160743i
$894$	−15.7634	+	8.49725i	−0.527205	+	0.284190i
$895$	39.2164	−	53.9767i	1.31086	−	1.80424i
$896$	−18.4343	+	25.6431i	−0.615846	+	0.856674i
$897$	1.91869	−	0.623419i	0.0640630	−	0.0208153i
$898$	−18.8629	−	18.0088i	−0.629463	−	0.600962i
$899$	2.65546	+	3.65492i	0.0885645	+	0.121899i
$900$	20.1684	−	30.6495i	0.672279	−	1.02165i
$901$	19.6612			0.655010
$902$	−16.8017	−	4.47428i	−0.559434	−	0.148977i
$903$		−	4.31681i		−	0.143654i
$904$	18.9480	−	21.7823i	0.630200	−	0.724470i
$905$	42.2991	−	30.7321i	1.40607	−	1.02157i
$906$	−1.57655	−	1.50517i	−0.0523775	−	0.0500060i
$907$	2.25055	+	6.92648i	0.0747283	+	0.229990i	0.981443	−	0.191755i	$-0.0614178\pi$
$907$	2.25055	+	6.92648i	0.0747283	+	0.229990i	−0.906715	+	0.421745i	$0.861418\pi$
$908$	40.4917	−	1.87684i	1.34376	−	0.0622850i
$909$	−7.59993	−	5.52167i	−0.252074	−	0.183142i
$910$	−15.5695	−	28.8832i	−0.516124	−	0.957468i
$911$	15.5732	+	5.06005i	0.515964	+	0.167647i	0.555413	−	0.831575i	$-0.312560\pi$
$911$	15.5732	+	5.06005i	0.515964	+	0.167647i	−0.0394488	+	0.999222i	$0.512560\pi$
$912$	8.47309	−	14.2746i	0.280572	−	0.472681i
$913$	3.01314	+	0.382716i	0.0997205	+	0.0126661i
$914$	0.0603695	−	0.448087i	0.00199684	−	0.0148214i
$915$	−13.1251	−	4.26459i	−0.433901	−	0.140983i
$916$	2.62845	+	6.97297i	0.0868463	+	0.230393i
$917$	17.7399	−	24.4168i	0.585822	−	0.806315i
$918$	34.3987	−	6.26799i	1.13533	−	0.206875i
$919$	1.67576	+	5.15747i	0.0552783	+	0.170129i	0.974884	−	0.222714i	$-0.0714916\pi$
$919$	1.67576	+	5.15747i	0.0552783	+	0.170129i	−0.919606	+	0.392843i	$0.871492\pi$
$920$	−4.89389	−	8.15101i	−0.161347	−	0.268731i
$921$	−5.21474	−	7.17748i	−0.171832	−	0.236506i
$922$	8.99452	−	18.7117i	0.296219	−	0.616237i
$923$		−	26.0860i		−	0.858630i
$924$	−4.79844	−	20.1182i	−0.157857	−	0.661840i
$925$		−	38.0182i		−	1.25003i
$926$	20.5551	+	9.88063i	0.675483	+	0.324697i
$927$	−6.34389	−	8.73161i	−0.208361	−	0.286784i
$928$	−8.22003	−	29.3724i	−0.269836	−	0.964197i
$929$	5.92577	+	18.2377i	0.194418	+	0.598358i	0.999983	+	0.00584999i	$0.00186212\pi$
$929$	5.92577	+	18.2377i	0.194418	+	0.598358i	−0.805565	+	0.592508i	$0.798138\pi$
$930$	−0.933192	−	5.12135i	−0.0306006	−	0.167936i
$931$	−1.72980	+	2.38086i	−0.0566918	+	0.0780296i
$932$	−17.3559	−	46.0433i	−0.568512	−	1.50820i
$933$	33.4411	+	10.8657i	1.09481	+	0.355726i
$934$	−7.76897	−	1.04669i	−0.254209	−	0.0342488i
$935$	−59.6876	+	11.3442i	−1.95199	+	0.370996i
$936$	9.64028	+	4.09588i	0.315102	+	0.133878i
$937$	29.5300	+	9.59489i	0.964705	+	0.313452i	0.748676	−	0.662936i	$-0.230690\pi$
$937$	29.5300	+	9.59489i	0.964705	+	0.313452i	0.216028	+	0.976387i	$0.430690\pi$
$938$	−12.0182	+	6.47842i	−0.392408	+	0.211528i
$939$	−16.8414	−	12.2360i	−0.549598	−	0.399306i
$940$	0.495117	+	10.6819i	0.0161489	+	0.348404i
$941$	17.9943	+	55.3808i	0.586598	+	1.80536i	0.592756	+	0.805382i	$0.298040\pi$
$941$	17.9943	+	55.3808i	0.586598	+	1.80536i	−0.00615836	+	0.999981i	$0.501960\pi$
$942$	−20.9709	+	21.9655i	−0.683270	+	0.715674i
$943$	2.56306	−	1.86218i	0.0834649	−	0.0606408i
$944$	−25.2727	+	22.2086i	−0.822557	+	0.722828i
$945$			58.2792i			1.89582i
$946$	−4.09443	−	5.04031i	−0.133121	−	0.163875i
$947$	3.35443			0.109004			0.0545022	−	0.998514i	$-0.482643\pi$
$947$	3.35443			0.109004			0.0545022	+	0.998514i	$0.482643\pi$
$948$	14.3060	−	21.7407i	0.464639	−	0.706104i
$949$	4.03282	+	5.55070i	0.130911	+	0.180183i
$950$	37.9843	−	39.7858i	1.23238	−	1.29082i
$951$	24.5168	−	7.96598i	0.795010	−	0.258315i
$952$	−36.6325	−	3.21734i	−1.18727	−	0.104275i
$953$	10.8409	−	14.9213i	0.351173	−	0.483348i	−0.596490	−	0.802620i	$-0.703439\pi$
$953$	10.8409	−	14.9213i	0.351173	−	0.483348i	0.947663	+	0.319273i	$0.103439\pi$
$954$	−4.96382	−	9.20844i	−0.160710	−	0.298134i
$955$	−30.7633	+	94.6796i	−0.995476	+	3.06376i
$956$	−33.3953	−	9.16487i	−1.08008	−	0.296413i
$957$	18.0681	+	8.51710i	0.584058	+	0.275319i
$958$	4.74039	+	0.638658i	0.153155	+	0.0206341i
$959$	−18.5470	+	57.0817i	−0.598913	+	1.84326i
$960$	−6.12622	+	34.6074i	−0.197723	+	1.11695i
$961$	−24.5116	−	17.8087i	−0.790696	−	0.574474i
$962$	10.6777	−	1.94564i	0.344262	−	0.0627300i
$963$	25.5817	−	8.31200i	0.824359	−	0.267850i
$964$	−18.7521	+	14.9985i	−0.603964	+	0.483068i
$965$	20.0924	−	14.5980i	0.646797	−	0.469925i
$966$	3.39653	+	1.63267i	0.109281	+	0.0525304i
$967$	−48.1597			−1.54871			−0.774356	−	0.632750i	$-0.781926\pi$
$967$	−48.1597			−1.54871			−0.774356	+	0.632750i	$0.781926\pi$
$968$	−24.6845	−	18.9388i	−0.793389	−	0.608715i
$969$	19.3290			0.620938
$970$	55.8597	+	26.8512i	1.79355	+	0.862139i
$971$	−1.37224	+	0.996990i	−0.0440372	+	0.0319949i	−0.609586	−	0.792720i	$-0.708664\pi$
$971$	−1.37224	+	0.996990i	−0.0440372	+	0.0319949i	0.565549	+	0.824715i	$0.308664\pi$
$972$	−18.9557	−	23.6997i	−0.608004	−	0.760168i
$973$	−18.1168	+	5.88651i	−0.580799	+	0.188713i
$974$	42.4129	−	7.72832i	1.35900	−	0.247631i
$975$	−19.9928	−	14.5256i	−0.640282	−	0.465192i
$976$	−12.5115	+	1.16234i	−0.400483	+	0.0372057i
$977$	−13.9474	+	42.9258i	−0.446218	+	1.37332i	0.434925	+	0.900467i	$0.356775\pi$
$977$	−13.9474	+	42.9258i	−0.446218	+	1.37332i	−0.881143	+	0.472851i	$0.843225\pi$
$978$	17.4435	+	2.35011i	0.557780	+	0.0751481i
$979$	23.9539	+	11.2916i	0.765569	+	0.360881i
$980$	1.64896	−	6.00857i	0.0526743	−	0.191937i
$981$	−1.55260	+	4.77842i	−0.0495708	+	0.152563i
$982$	22.0563	+	40.9169i	0.703845	+	1.30571i
$983$	9.96222	−	13.7118i	0.317745	−	0.437339i	−0.620032	−	0.784577i	$-0.712880\pi$
$983$	9.96222	−	13.7118i	0.317745	−	0.437339i	0.937777	+	0.347238i	$0.112880\pi$
$984$	−11.6666	−	1.02465i	−0.371918	−	0.0326646i
$985$	40.6691	−	13.2142i	1.29582	−	0.421039i
$986$	24.5249	−	25.6880i	0.781032	−	0.818072i
$987$	−2.49143	−	3.42916i	−0.0793031	−	0.109151i
$988$	13.1180	+	8.63206i	0.417340	+	0.274623i
$989$	1.18323			0.0376245
$990$	20.3823	+	25.0910i	0.647793	+	0.797444i
$991$			18.1908i			0.577849i	0.957352	+	0.288925i	$0.0932977\pi$
$991$			18.1908i			0.577849i	−0.957352	+	0.288925i	$0.906702\pi$
$992$	−2.62533	−	3.94627i	−0.0833543	−	0.125294i
$993$	18.0254	−	13.0962i	0.572019	−	0.415596i
$994$	33.6492	−	35.2450i	1.06729	−	1.11790i
$995$	−26.9617	−	82.9797i	−0.854744	−	2.63063i
$996$	2.04368	−	0.0947269i	0.0647564	−	0.00300154i
$997$	−9.00121	−	6.53976i	−0.285071	−	0.207116i	0.436055	−	0.899920i	$-0.356375\pi$
$997$	−9.00121	−	6.53976i	−0.285071	−	0.207116i	−0.721126	+	0.692804i	$0.756375\pi$
$998$	−13.4591	+	7.25514i	−0.426040	+	0.229657i
$999$	−18.3338	−	5.95701i	−0.580055	−	0.188471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.k.b.35.6	yes	32
3.2	odd	2		792.2.bp.b.739.3		32
4.3	odd	2		352.2.s.b.79.6		32
8.3	odd	2	inner	88.2.k.b.35.4	✓	32
8.5	even	2		352.2.s.b.79.5		32
11.2	odd	10		968.2.k.i.723.7		32
11.3	even	5		968.2.k.i.403.3		32
11.4	even	5		968.2.g.e.483.32		32
11.5	even	5		968.2.k.h.699.5		32
11.6	odd	10	inner	88.2.k.b.83.4	yes	32
11.7	odd	10		968.2.g.e.483.1		32
11.8	odd	10		968.2.k.e.403.6		32
11.9	even	5		968.2.k.e.723.2		32
11.10	odd	2		968.2.k.h.475.3		32
24.11	even	2		792.2.bp.b.739.5		32
33.17	even	10		792.2.bp.b.523.5		32
44.7	even	10		3872.2.g.d.1935.14		32
44.15	odd	10		3872.2.g.d.1935.16		32
44.39	even	10		352.2.s.b.303.5		32
88.3	odd	10		968.2.k.i.403.7		32
88.19	even	10		968.2.k.e.403.2		32
88.27	odd	10		968.2.k.h.699.3		32
88.29	odd	10		3872.2.g.d.1935.13		32
88.35	even	10		968.2.k.i.723.3		32
88.37	even	10		3872.2.g.d.1935.15		32
88.43	even	2		968.2.k.h.475.5		32
88.51	even	10		968.2.g.e.483.31		32
88.59	odd	10		968.2.g.e.483.2		32
88.61	odd	10		352.2.s.b.303.6		32
88.75	odd	10		968.2.k.e.723.6		32
88.83	even	10	inner	88.2.k.b.83.6	yes	32
264.83	odd	10		792.2.bp.b.523.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.b.35.4	✓	32	8.3	odd	2	inner
88.2.k.b.35.6	yes	32	1.1	even	1	trivial
88.2.k.b.83.4	yes	32	11.6	odd	10	inner
88.2.k.b.83.6	yes	32	88.83	even	10	inner
352.2.s.b.79.5		32	8.5	even	2
352.2.s.b.79.6		32	4.3	odd	2
352.2.s.b.303.5		32	44.39	even	10
352.2.s.b.303.6		32	88.61	odd	10
792.2.bp.b.523.3		32	264.83	odd	10
792.2.bp.b.523.5		32	33.17	even	10
792.2.bp.b.739.3		32	3.2	odd	2
792.2.bp.b.739.5		32	24.11	even	2
968.2.g.e.483.1		32	11.7	odd	10
968.2.g.e.483.2		32	88.59	odd	10
968.2.g.e.483.31		32	88.51	even	10
968.2.g.e.483.32		32	11.4	even	5
968.2.k.e.403.2		32	88.19	even	10
968.2.k.e.403.6		32	11.8	odd	10
968.2.k.e.723.2		32	11.9	even	5
968.2.k.e.723.6		32	88.75	odd	10
968.2.k.h.475.3		32	11.10	odd	2
968.2.k.h.475.5		32	88.43	even	2
968.2.k.h.699.3		32	88.27	odd	10
968.2.k.h.699.5		32	11.5	even	5
968.2.k.i.403.3		32	11.3	even	5
968.2.k.i.403.7		32	88.3	odd	10
968.2.k.i.723.3		32	88.35	even	10
968.2.k.i.723.7		32	11.2	odd	10
3872.2.g.d.1935.13		32	88.29	odd	10
3872.2.g.d.1935.14		32	44.7	even	10
3872.2.g.d.1935.15		32	88.37	even	10
3872.2.g.d.1935.16		32	44.15	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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.612688 - 1.27460i) q^{2} +(-0.903665 + 0.656551i) q^{3} +(-1.24923 - 1.56187i) q^{4} +(3.74056 - 1.21538i) q^{5} +(0.283177 + 1.55407i) q^{6} +(-2.25832 - 1.64076i) q^{7} +(-2.75615 + 0.635331i) q^{8} +(-0.541500 + 1.66657i) q^{9} +(0.742666 - 5.51238i) q^{10} +(3.00002 + 1.41418i) q^{11} +(2.15433 + 0.591224i) q^{12} +(-0.653051 + 2.00988i) q^{13} +(-3.47497 + 1.87318i) q^{14} +(-2.58225 + 3.55416i) q^{15} +(-0.878863 + 3.90226i) q^{16} +(-4.42965 + 1.43928i) q^{17} +(1.79244 + 1.71128i) q^{18} +(2.18382 + 3.00577i) q^{19} +(-6.57107 - 4.32397i) q^{20} +3.11801 q^{21} +(3.64059 - 2.95738i) q^{22} +0.854640i q^{23} +(2.07351 - 2.38368i) q^{24} +(8.46953 - 6.15347i) q^{25} +(2.16169 + 2.06381i) q^{26} +(-1.64036 - 5.04850i) q^{27} +(0.258495 + 5.57688i) q^{28} +(-4.36210 - 3.16925i) q^{29} +(2.94803 + 5.46894i) q^{30} +(-0.796872 - 0.258919i) q^{31} +(4.43536 + 3.51107i) q^{32} +(-3.63949 + 0.691723i) q^{33} +(-0.879482 + 6.52788i) q^{34} +(-10.4415 - 3.39265i) q^{35} +(3.27941 - 1.23617i) q^{36} +(2.13456 - 2.93797i) q^{37} +(5.16916 - 0.941903i) q^{38} +(-0.729452 - 2.24502i) q^{39} +(-9.53736 + 5.72626i) q^{40} +(-2.17890 - 2.99900i) q^{41} +(1.91036 - 3.97422i) q^{42} -1.38448i q^{43} +(-1.53895 - 6.45226i) q^{44} +6.89201i q^{45} +(1.08933 + 0.523628i) q^{46} +(-0.799046 - 1.09979i) q^{47} +(-1.76783 - 4.10335i) q^{48} +(0.244772 + 0.753330i) q^{49} +(-2.65406 - 14.5655i) q^{50} +(3.05796 - 4.20892i) q^{51} +(3.95498 - 1.49082i) q^{52} +(-4.01470 - 1.30446i) q^{53} +(-7.43987 - 1.00235i) q^{54} +(12.9405 + 1.64365i) q^{55} +(7.26668 + 3.08741i) q^{56} +(-3.94688 - 1.28242i) q^{57} +(-6.71215 + 3.61819i) q^{58} +(6.80468 + 4.94389i) q^{59} +(8.77695 - 0.406822i) q^{60} +(0.970728 + 2.98759i) q^{61} +(-0.818253 + 0.857059i) q^{62} +(3.95732 - 2.87516i) q^{63} +(7.19271 - 3.50213i) q^{64} +8.31179i q^{65} +(-1.34820 + 5.06271i) q^{66} +3.45851 q^{67} +(7.78161 + 5.12054i) q^{68} +(-0.561115 - 0.772308i) q^{69} +(-10.7217 + 11.2302i) q^{70} +(-11.7395 + 3.81439i) q^{71} +(0.433633 - 4.93733i) q^{72} +(1.90829 - 2.62654i) q^{73} +(-2.43693 - 4.52077i) q^{74} +(-3.61355 + 11.1214i) q^{75} +(1.96653 - 7.16572i) q^{76} +(-4.45466 - 8.11598i) q^{77} +(-3.30844 - 0.445736i) q^{78} +(3.59997 - 11.0796i) q^{79} +(1.45529 + 15.6648i) q^{80} +(0.543938 + 0.395194i) q^{81} +(-5.15752 + 0.939783i) q^{82} +(0.870974 - 0.282997i) q^{83} +(-3.89510 - 4.86991i) q^{84} +(-14.8201 + 10.7674i) q^{85} +(-1.76466 - 0.848252i) q^{86} +6.02266 q^{87} +(-9.16696 - 1.99168i) q^{88} +7.98458 q^{89} +(8.78458 + 4.22265i) q^{90} +(4.77254 - 3.46745i) q^{91} +(1.33483 - 1.06764i) q^{92} +(0.890099 - 0.289211i) q^{93} +(-1.89137 + 0.344637i) q^{94} +(11.8218 + 8.58907i) q^{95} +(-6.31327 - 0.260789i) q^{96} +(-3.44331 + 10.5974i) q^{97} +(1.11017 + 0.149569i) q^{98} +(-3.98133 + 4.23395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9} - 18 q^{11} - 18 q^{12} + 8 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} - 30 q^{20} + 17 q^{22} + 5 q^{24} + 6 q^{25} - 4 q^{26} - 32 q^{27}+ \cdots + 122 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9 - 18 * q^11 - 18 * q^12 + 8 * q^14 - q^16 - 10 * q^17 - 20 * q^18 - 30 * q^20 + 17 * q^22 + 5 * q^24 + 6 * q^25 - 4 * q^26 - 32 * q^27 - 30 * q^28 + 30 * q^30 + 32 * q^33 - 14 * q^34 - 10 * q^35 + 16 * q^36 + 28 * q^38 + 30 * q^40 - 10 * q^41 + 64 * q^42 - 38 * q^44 + 40 * q^46 + 26 * q^48 - 18 * q^49 + 5 * q^50 + 60 * q^51 + 40 * q^52 + 76 * q^56 - 80 * q^57 - 56 * q^58 + 28 * q^59 + 34 * q^60 - 80 * q^62 + 55 * q^64 - 30 * q^66 - 28 * q^67 + 60 * q^68 - 44 * q^70 + 45 * q^72 - 10 * q^73 - 100 * q^74 + 4 * q^75 - 80 * q^78 - 76 * q^80 + 28 * q^81 + 13 * q^82 - 50 * q^84 - 39 * q^86 - 69 * q^88 + 20 * q^89 - 30 * q^90 + 78 * q^91 + 6 * q^92 - 30 * q^94 - 110 * q^96 - 52 * q^97 + 122 * q^99

Introduction

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