LMFDB - Embedded newform 160.2.u.a.123.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(43,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("160.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			123.16
Character	$\chi$	$=$	160.123
Dual form			160.2.u.a.147.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.788198 + 1.17420i) q^{2} +(-1.91488 - 0.793171i) q^{3} +(-0.757489 + 1.85100i) q^{4} +(-2.19539 + 0.424581i) q^{5} +(-0.577967 - 2.87363i) q^{6} +3.99422i q^{7} +(-2.77050 + 0.569513i) q^{8} +(0.916343 + 0.916343i) q^{9} +(-2.22894 - 2.24317i) q^{10} +(-3.60412 - 1.49288i) q^{11} +(2.91867 - 2.94364i) q^{12} +(4.61187 + 1.91030i) q^{13} +(-4.69001 + 3.14824i) q^{14} +(4.54068 + 0.928296i) q^{15} +(-2.85242 - 2.80423i) q^{16} +(2.42403 + 2.42403i) q^{17} +(-0.353710 + 1.79823i) q^{18} +(-2.25621 + 0.934554i) q^{19} +(0.877082 - 4.38529i) q^{20} +(3.16810 - 7.64847i) q^{21} +(-1.08783 - 5.40864i) q^{22} -1.48593i q^{23} +(5.75690 + 1.10693i) q^{24} +(4.63946 - 1.86424i) q^{25} +(1.39199 + 6.92095i) q^{26} +(1.35164 + 3.26315i) q^{27} +(-7.39331 - 3.02558i) q^{28} +(6.67682 - 2.76563i) q^{29} +(2.48895 + 6.06335i) q^{30} +4.27390i q^{31} +(1.04445 - 5.55960i) q^{32} +(5.71737 + 5.71737i) q^{33} +(-0.935678 + 4.75690i) q^{34} +(-1.69587 - 8.76887i) q^{35} +(-2.39027 + 1.00203i) q^{36} +(-7.17496 + 2.97197i) q^{37} +(-2.87570 - 1.91263i) q^{38} +(-7.31600 - 7.31600i) q^{39} +(5.84051 - 2.42660i) q^{40} +(-4.93663 + 4.93663i) q^{41} +(11.4779 - 2.30853i) q^{42} +(1.46010 + 3.52499i) q^{43} +(5.49340 - 5.54040i) q^{44} +(-2.40079 - 1.62267i) q^{45} +(1.74478 - 1.17121i) q^{46} +(-1.16100 + 1.16100i) q^{47} +(3.23783 + 7.63223i) q^{48} -8.95380 q^{49} +(5.84580 + 3.97827i) q^{50} +(-2.71906 - 6.56440i) q^{51} +(-7.02941 + 7.08955i) q^{52} +(-4.27746 + 1.77178i) q^{53} +(-2.76623 + 4.15910i) q^{54} +(8.54630 + 1.74720i) q^{55} +(-2.27476 - 11.0660i) q^{56} +5.06165 q^{57} +(8.51006 + 5.66006i) q^{58} +(4.20594 + 1.74216i) q^{59} +(-5.15779 + 7.70164i) q^{60} +(0.256357 + 0.618901i) q^{61} +(-5.01841 + 3.36868i) q^{62} +(-3.66008 + 3.66008i) q^{63} +(7.35131 - 3.15567i) q^{64} +(-10.9359 - 2.23574i) q^{65} +(-2.20692 + 11.2198i) q^{66} +(-0.333385 + 0.804862i) q^{67} +(-6.32305 + 2.65071i) q^{68} +(-1.17860 + 2.84539i) q^{69} +(8.95972 - 8.90289i) q^{70} +(9.01971 - 9.01971i) q^{71} +(-3.06059 - 2.01686i) q^{72} -2.58617 q^{73} +(-9.14497 - 6.08234i) q^{74} +(-10.3627 - 0.110085i) q^{75} +(-0.0208061 - 4.88417i) q^{76} +(5.96288 - 14.3957i) q^{77} +(2.82399 - 14.3569i) q^{78} -4.01204i q^{79} +(7.45279 + 4.94529i) q^{80} -11.2083i q^{81} +(-9.68763 - 1.90555i) q^{82} +(0.144864 - 0.349732i) q^{83} +(11.7575 + 11.6578i) q^{84} +(-6.35088 - 4.29249i) q^{85} +(-2.98819 + 4.49283i) q^{86} -14.9790 q^{87} +(10.8354 + 2.08341i) q^{88} +(-5.80128 + 5.80128i) q^{89} +(0.0130376 - 4.09799i) q^{90} +(-7.63016 + 18.4208i) q^{91} +(2.75046 + 1.12558i) q^{92} +(3.38993 - 8.18402i) q^{93} +(-2.27835 - 0.448149i) q^{94} +(4.55647 - 3.00966i) q^{95} +(-6.40971 + 9.81756i) q^{96} +(3.39247 - 3.39247i) q^{97} +(-7.05737 - 10.5135i) q^{98} +(-1.93463 - 4.67060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24}+ \cdots - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	0.788198	+	1.17420i	0.557340	+	0.830284i
$2$	0.788198	+	1.17420i	0.557340	+	0.830284i
$3$	−1.91488	−	0.793171i	−1.10556	−	0.457938i	−0.246153	−	0.969231i	$-0.579167\pi$
$3$	−1.91488	−	0.793171i	−1.10556	−	0.457938i	−0.859406	+	0.511293i	$0.829167\pi$
$4$	−0.757489	+	1.85100i	−0.378744	+	0.925501i
$5$	−2.19539	+	0.424581i	−0.981808	+	0.189878i
$5$	−2.19539	+	0.424581i	−0.981808	+	0.189878i
$6$	−0.577967	−	2.87363i	−0.235954	−	1.17316i
$7$			3.99422i			1.50967i	0.655913	+	0.754837i	$0.272284\pi$
$7$			3.99422i			1.50967i	−0.655913	+	0.754837i	$0.727716\pi$
$8$	−2.77050	+	0.569513i	−0.979519	+	0.201353i
$9$	0.916343	+	0.916343i	0.305448	+	0.305448i
$10$	−2.22894	−	2.24317i	−0.704854	−	0.709353i
$11$	−3.60412	−	1.49288i	−1.08668	−	0.450119i	−0.233835	−	0.972276i	$-0.575127\pi$
$11$	−3.60412	−	1.49288i	−1.08668	−	0.450119i	−0.852849	+	0.522157i	$0.825127\pi$
$12$	2.91867	−	2.94364i	0.842546	−	0.849755i
$13$	4.61187	+	1.91030i	1.27910	+	0.529822i	0.915719	−	0.401818i	$-0.131622\pi$
$13$	4.61187	+	1.91030i	1.27910	+	0.529822i	0.363383	+	0.931640i	$0.381622\pi$
$14$	−4.69001	+	3.14824i	−1.25346	+	0.841401i
$15$	4.54068	+	0.928296i	1.17240	+	0.239685i
$16$	−2.85242	−	2.80423i	−0.713105	−	0.701057i
$17$	2.42403	+	2.42403i	0.587913	+	0.587913i	0.937066	−	0.349153i	$-0.113531\pi$
$17$	2.42403	+	2.42403i	0.587913	+	0.587913i	−0.349153	+	0.937066i	$0.613531\pi$
$18$	−0.353710	+	1.79823i	−0.0833702	+	0.423847i
$19$	−2.25621	+	0.934554i	−0.517611	+	0.214401i	−0.626167	−	0.779689i	$-0.715377\pi$
$19$	−2.25621	+	0.934554i	−0.517611	+	0.214401i	0.108556	+	0.994090i	$0.465377\pi$
$20$	0.877082	−	4.38529i	0.196122	−	0.980580i
$21$	3.16810	−	7.64847i	0.691336	−	1.66903i
$22$	−1.08783	−	5.40864i	−0.231925	−	1.15313i
$23$		−	1.48593i		−	0.309838i	−0.987927	−	0.154919i	$-0.950488\pi$
$23$		−	1.48593i		−	0.309838i	0.987927	−	0.154919i	$-0.0495117\pi$
$24$	5.75690	+	1.10693i	1.17512	+	0.225950i
$25$	4.63946	−	1.86424i	0.927892	−	0.372848i
$26$	1.39199	+	6.92095i	0.272992	+	1.35731i
$27$	1.35164	+	3.26315i	0.260123	+	0.627993i
$28$	−7.39331	−	3.02558i	−1.39720	−	0.571780i
$29$	6.67682	−	2.76563i	1.23985	−	0.513565i	0.336185	−	0.941796i	$-0.390863\pi$
$29$	6.67682	−	2.76563i	1.23985	−	0.513565i	0.903669	+	0.428231i	$0.140863\pi$
$30$	2.48895	+	6.06335i	0.454418	+	1.10701i
$31$			4.27390i			0.767615i	0.923413	+	0.383807i	$0.125387\pi$
$31$			4.27390i			0.767615i	−0.923413	+	0.383807i	$0.874613\pi$
$32$	1.04445	−	5.55960i	0.184634	−	0.982807i
$33$	5.71737	+	5.71737i	0.995267	+	0.995267i
$34$	−0.935678	+	4.75690i	−0.160468	+	0.815802i
$35$	−1.69587	−	8.76887i	−0.286654	−	1.48221i
$36$	−2.39027	+	1.00203i	−0.398379	+	0.167006i
$37$	−7.17496	+	2.97197i	−1.17956	+	0.488588i	−0.884340	−	0.466843i	$-0.845391\pi$
$37$	−7.17496	+	2.97197i	−1.17956	+	0.488588i	−0.295216	+	0.955431i	$0.595391\pi$
$38$	−2.87570	−	1.91263i	−0.466500	−	0.310270i
$39$	−7.31600	−	7.31600i	−1.17150	−	1.17150i
$40$	5.84051	−	2.42660i	0.923466	−	0.383680i
$41$	−4.93663	+	4.93663i	−0.770973	+	0.770973i	−0.978277	−	0.207304i	$-0.933531\pi$
$41$	−4.93663	+	4.93663i	−0.770973	+	0.770973i	0.207304	+	0.978277i	$0.433531\pi$
$42$	11.4779	−	2.30853i	1.77108	−	0.356213i
$43$	1.46010	+	3.52499i	0.222663	+	0.537556i	0.995250	−	0.0973533i	$-0.0310377\pi$
$43$	1.46010	+	3.52499i	0.222663	+	0.537556i	−0.772587	+	0.634909i	$0.781038\pi$
$44$	5.49340	−	5.54040i	0.828161	−	0.835247i
$45$	−2.40079	−	1.62267i	−0.357889	−	0.241893i
$46$	1.74478	−	1.17121i	0.257254	−	0.172685i
$47$	−1.16100	+	1.16100i	−0.169350	+	0.169350i	−0.786694	−	0.617344i	$-0.788209\pi$
$47$	−1.16100	+	1.16100i	−0.169350	+	0.169350i	0.617344	+	0.786694i	$0.288209\pi$
$48$	3.23783	+	7.63223i	0.467340	+	1.10162i
$49$	−8.95380			−1.27911
$50$	5.84580	+	3.97827i	0.826721	+	0.562612i
$51$	−2.71906	−	6.56440i	−0.380745	−	0.919200i
$52$	−7.02941	+	7.08955i	−0.974803	+	0.983144i
$53$	−4.27746	+	1.77178i	−0.587554	+	0.243373i	−0.656598	−	0.754241i	$-0.728005\pi$
$53$	−4.27746	+	1.77178i	−0.587554	+	0.243373i	0.0690441	+	0.997614i	$0.478005\pi$
$54$	−2.76623	+	4.15910i	−0.376436	+	0.565982i
$55$	8.54630	+	1.74720i	1.15238	+	0.235593i
$56$	−2.27476	−	11.0660i	−0.303978	−	1.47875i
$57$	5.06165			0.670432
$58$	8.51006	+	5.66006i	1.11743	+	0.743202i
$59$	4.20594	+	1.74216i	0.547567	+	0.226810i	0.639278	−	0.768976i	$-0.279233\pi$
$59$	4.20594	+	1.74216i	0.547567	+	0.226810i	−0.0917106	+	0.995786i	$0.529233\pi$
$60$	−5.15779	+	7.70164i	−0.665868	+	0.994277i
$61$	0.256357	+	0.618901i	0.0328232	+	0.0792422i	0.939441	−	0.342710i	$-0.111345\pi$
$61$	0.256357	+	0.618901i	0.0328232	+	0.0792422i	−0.906618	+	0.421952i	$0.861345\pi$
$62$	−5.01841	+	3.36868i	−0.637339	+	0.427822i
$63$	−3.66008	+	3.66008i	−0.461126	+	0.461126i
$64$	7.35131	−	3.15567i	0.918914	−	0.394459i
$65$	−10.9359	−	2.23574i	−1.35643	−	0.277309i
$66$	−2.20692	+	11.2198i	−0.271653	+	1.38106i
$67$	−0.333385	+	0.804862i	−0.0407294	+	0.0983295i	−0.942935	−	0.332976i	$-0.891947\pi$
$67$	−0.333385	+	0.804862i	−0.0407294	+	0.0983295i	0.902206	+	0.431306i	$0.141947\pi$
$68$	−6.32305	+	2.65071i	−0.766783	+	0.321445i
$69$	−1.17860	+	2.84539i	−0.141887	+	0.342544i
$70$	8.95972	−	8.90289i	1.07089	−	1.06410i
$71$	9.01971	−	9.01971i	1.07044	−	1.07044i	0.0731195	−	0.997323i	$-0.476705\pi$
$71$	9.01971	−	9.01971i	1.07044	−	1.07044i	0.997323	−	0.0731195i	$-0.0232954\pi$
$72$	−3.06059	−	2.01686i	−0.360695	−	0.237689i
$73$	−2.58617			−0.302688			−0.151344	−	0.988481i	$-0.548360\pi$
$73$	−2.58617			−0.302688			−0.151344	+	0.988481i	$0.548360\pi$
$74$	−9.14497	−	6.08234i	−1.06308	−	0.707057i
$75$	−10.3627	−	0.110085i	−1.19658	−	0.0127115i
$76$	−0.0208061	−	4.88417i	−0.00238662	−	0.560253i
$77$	5.96288	−	14.3957i	0.679533	−	1.64054i
$78$	2.82399	−	14.3569i	0.319754	−	1.62560i
$79$		−	4.01204i		−	0.451389i	−0.974198	−	0.225695i	$-0.927535\pi$
$79$		−	4.01204i		−	0.451389i	0.974198	−	0.225695i	$-0.0724652\pi$
$80$	7.45279	+	4.94529i	0.833248	+	0.552900i
$81$		−	11.2083i		−	1.24537i
$82$	−9.68763	−	1.90555i	−1.06982	−	0.210433i
$83$	0.144864	−	0.349732i	0.0159009	−	0.0383881i	−0.915730	−	0.401795i	$-0.868386\pi$
$83$	0.144864	−	0.349732i	0.0159009	−	0.0383881i	0.931631	+	0.363407i	$0.118386\pi$
$84$	11.7575	+	11.6578i	1.28285	+	1.27197i
$85$	−6.35088	−	4.29249i	−0.688849	−	0.465585i
$86$	−2.98819	+	4.49283i	−0.322225	+	0.484475i
$87$	−14.9790			−1.60591
$88$	10.8354	+	2.08341i	1.15506	+	0.222093i
$89$	−5.80128	+	5.80128i	−0.614935	+	0.614935i	−0.944228	−	0.329293i	$-0.893190\pi$
$89$	−5.80128	+	5.80128i	−0.614935	+	0.614935i	0.329293	+	0.944228i	$0.393190\pi$
$90$	0.0130376	−	4.09799i	0.00137429	−	0.431966i
$91$	−7.63016	+	18.4208i	−0.799858	+	1.93103i
$92$	2.75046	+	1.12558i	0.286756	+	0.117349i
$93$	3.38993	−	8.18402i	0.351520	−	0.848644i
$94$	−2.27835	−	0.448149i	−0.234994	−	0.0462231i
$95$	4.55647	−	3.00966i	0.467484	−	0.308784i
$96$	−6.40971	+	9.81756i	−0.654189	+	1.00200i
$97$	3.39247	−	3.39247i	0.344453	−	0.344453i	−0.513585	−	0.858039i	$-0.671683\pi$
$97$	3.39247	−	3.39247i	0.344453	−	0.344453i	0.858039	+	0.513585i	$0.171683\pi$
$98$	−7.05737	−	10.5135i	−0.712902	−	1.06203i
$99$	−1.93463	−	4.67060i	−0.194437	−	0.469413i
$100$	−0.0636288	+	9.99980i	−0.00636288	+	0.999980i
$101$	10.5478	+	4.36906i	1.04955	+	0.434738i	0.839731	−	0.543002i	$-0.182713\pi$
$101$	10.5478	+	4.36906i	1.04955	+	0.434738i	0.209819	+	0.977740i	$0.432713\pi$
$102$	5.56476	−	8.36677i	0.550993	−	0.828433i
$103$	13.1171			1.29247			0.646233	−	0.763140i	$-0.276344\pi$
$103$	13.1171			1.29247			0.646233	+	0.763140i	$0.276344\pi$
$104$	−13.8651	−	2.66596i	−1.35959	−	0.261419i
$105$	−3.70782	+	18.1365i	−0.361846	+	1.76994i
$106$	−5.45190	−	3.62607i	−0.529536	−	0.352195i
$107$	−14.4975	+	6.00506i	−1.40153	+	0.580531i	−0.950147	−	0.311802i	$-0.899068\pi$
$107$	−14.4975	+	6.00506i	−1.40153	+	0.580531i	−0.451378	+	0.892333i	$0.649068\pi$
$108$	−7.06395	+	0.0300917i	−0.679728	+	0.00289558i
$109$	1.75193	+	4.22953i	0.167805	+	0.405116i	0.985303	−	0.170815i	$-0.0546399\pi$
$109$	1.75193	+	4.22953i	0.167805	+	0.405116i	−0.817499	+	0.575930i	$0.804640\pi$
$110$	4.68461	+	11.4122i	0.446660	+	1.08811i
$111$	16.0965			1.52781
$112$	11.2007	−	11.3932i	1.05837	−	1.07656i
$113$	0.140699	−	0.140699i	0.0132359	−	0.0132359i	−0.700458	−	0.713694i	$-0.747021\pi$
$113$	0.140699	−	0.140699i	0.0132359	−	0.0132359i	0.713694	+	0.700458i	$0.247021\pi$
$114$	3.98958	+	5.94339i	0.373659	+	0.556649i
$115$	0.630898	+	3.26220i	0.0588315	+	0.304201i
$116$	0.0615715	+	14.4537i	0.00571677	+	1.34200i
$117$	2.47556	+	5.97654i	0.228866	+	0.552531i
$118$	1.26947	+	6.31178i	0.116864	+	0.581047i
$119$	−9.68210	+	9.68210i	−0.887556	+	0.887556i
$120$	−13.1086	+	0.0141365i	−1.19665	+	0.00129048i
$121$	2.98284	+	2.98284i	0.271168	+	0.271168i
$122$	−0.524653	+	0.788831i	−0.0474999	+	0.0714174i
$123$	13.3687	−	5.53749i	1.20541	−	0.499298i
$124$	−7.91100	−	3.23743i	−0.710429	−	0.290730i
$125$	−9.39390	+	6.06256i	−0.840216	+	0.542251i
$126$	−7.18252	−	1.41280i	−0.639870	−	0.125862i
$127$	12.6658	+	12.6658i	1.12391	+	1.12391i	0.991148	+	0.132762i	$0.0423846\pi$
$127$	12.6658	+	12.6658i	1.12391	+	1.12391i	0.132762	+	0.991148i	$0.457615\pi$
$128$	9.49967	+	6.14461i	0.839660	+	0.543112i
$129$		−	7.90805i		−	0.696265i
$130$	−5.99447	−	14.6032i	−0.525749	−	1.28078i
$131$	2.28695	−	0.947286i	0.199812	−	0.0827647i	−0.280534	−	0.959844i	$-0.590511\pi$
$131$	2.28695	−	0.947286i	0.199812	−	0.0827647i	0.480345	+	0.877080i	$0.340511\pi$
$132$	−14.9137	+	6.25203i	−1.29807	+	0.544169i
$133$	−3.73282	−	9.01182i	−0.323676	−	0.781424i
$134$	−1.20784	+	0.242930i	−0.104342	+	0.0209860i
$135$	−4.35284	−	6.59000i	−0.374633	−	0.567176i
$136$	−8.09627	−	5.33524i	−0.694250	−	0.457493i
$137$		−	6.36015i		−	0.543384i	−0.962384	−	0.271692i	$-0.912417\pi$
$137$		−	6.36015i		−	0.543384i	0.962384	−	0.271692i	$-0.0875832\pi$
$138$	−4.27002	+	0.858819i	−0.363488	+	0.0731075i
$139$	6.65088	−	16.0566i	0.564120	−	1.36191i	−0.342324	−	0.939582i	$-0.611214\pi$
$139$	6.65088	−	16.0566i	0.564120	−	1.36191i	0.906445	−	0.422325i	$-0.138786\pi$
$140$	17.5158	+	3.50326i	1.48036	+	0.296080i
$141$	3.14406	−	1.30231i	0.264778	−	0.109675i
$142$	17.7003	+	3.48162i	1.48537	+	0.292171i
$143$	−13.7699	−	13.7699i	−1.15150	−	1.15150i
$144$	−0.0441626	−	5.18343i	−0.00368022	−	0.431952i
$145$	−13.4840	+	8.90648i	−1.11978	+	0.739643i
$146$	−2.03841	−	3.03668i	−0.168700	−	0.251317i
$147$	17.1455	+	7.10190i	1.41414	+	0.585755i
$148$	−0.0661652	−	15.5321i	−0.00543875	−	1.27673i
$149$	18.8116	+	7.79203i	1.54111	+	0.638348i	0.981681	−	0.190532i	$-0.0610212\pi$
$149$	18.8116	+	7.79203i	1.54111	+	0.638348i	0.559427	+	0.828880i	$0.311021\pi$
$150$	−8.03859	−	12.2546i	−0.656348	−	1.00059i
$151$	−3.65234	−	3.65234i	−0.297223	−	0.297223i	0.542702	−	0.839925i	$-0.317401\pi$
$151$	−3.65234	−	3.65234i	−0.297223	−	0.297223i	−0.839925	+	0.542702i	$0.817401\pi$
$152$	5.71859	−	3.87412i	0.463839	−	0.314233i
$153$			4.44248i			0.359153i
$154$	21.6033	−	4.34502i	1.74084	−	0.350132i
$155$	−1.81461	−	9.38287i	−0.145753	−	0.753650i
$156$	19.0837	−	8.00015i	1.52792	−	0.640525i
$157$	14.2011	+	5.88227i	1.13337	+	0.469456i	0.868925	−	0.494945i	$-0.164812\pi$
$157$	14.2011	+	5.88227i	1.13337	+	0.469456i	0.264444	+	0.964401i	$0.414812\pi$
$158$	4.71093	−	3.16228i	0.374782	−	0.251577i
$159$	9.59616			0.761025
$160$	0.0675243	+	12.6489i	0.00533827	+	0.999986i
$161$	5.93514			0.467754
$162$	13.1608	−	8.83439i	1.03401	−	0.694095i
$163$	16.7827	+	6.95162i	1.31452	+	0.544493i	0.926201	−	0.377031i	$-0.123055\pi$
$163$	16.7827	+	6.95162i	1.31452	+	0.544493i	0.388322	+	0.921524i	$0.373055\pi$
$164$	−5.39828	−	12.8772i	−0.421535	−	1.00554i
$165$	−14.9793	−	10.1244i	−1.16614	−	0.788181i
$166$	0.524837	−	0.105559i	0.0407352	−	0.00819298i
$167$			5.24280i			0.405700i	0.979210	+	0.202850i	$0.0650203\pi$
$167$			5.24280i			0.405700i	−0.979210	+	0.202850i	$0.934980\pi$
$168$	−4.42131	+	22.9943i	−0.341111	+	1.77405i
$169$	8.42771	+	8.42771i	0.648285	+	0.648285i
$170$	0.0344888	−	10.8405i	0.00264517	−	0.831430i
$171$	−2.92384	−	1.21109i	−0.223591	−	0.0926146i
$172$	−7.63077	+	0.0325063i	−0.581841	+	0.00247858i
$173$	−19.2443	−	7.97123i	−1.46311	−	0.606042i	−0.497837	−	0.867270i	$-0.665872\pi$
$173$	−19.2443	−	7.97123i	−1.46311	−	0.606042i	−0.965277	+	0.261229i	$0.915872\pi$
$174$	−11.8064	−	17.5883i	−0.895040	−	1.33336i
$175$	7.44618	+	18.5310i	0.562879	+	1.40081i
$176$	6.09411	+	14.3651i	0.459361	+	1.08281i
$177$	−6.67207	−	6.67207i	−0.501503	−	0.501503i
$178$	−11.3844	−	2.23931i	−0.853299	−	0.167843i
$179$	0.468304	−	0.193978i	0.0350027	−	0.0144986i	−0.365113	−	0.930963i	$-0.618970\pi$
$179$	0.468304	−	0.193978i	0.0350027	−	0.0144986i	0.400116	+	0.916464i	$0.368970\pi$
$180$	4.82213	−	3.21472i	0.359421	−	0.239611i
$181$	−0.0254869	+	0.0615309i	−0.00189443	+	0.00457355i	−0.924824	−	0.380395i	$-0.875788\pi$
$181$	−0.0254869	+	0.0615309i	−0.00189443	+	0.00457355i	0.922929	+	0.384969i	$0.125788\pi$
$182$	−27.6438	+	5.55993i	−2.04909	+	0.412129i
$183$		−	1.38846i		−	0.102638i
$184$	0.846258	+	4.11677i	0.0623869	+	0.303492i
$185$	14.4900	−	9.57097i	1.06532	−	0.703672i
$186$	12.2816	−	2.47017i	0.900532	−	0.181122i
$187$	−5.11772	−	12.3553i	−0.374245	−	0.903506i
$188$	−1.26957	−	3.02847i	−0.0925932	−	0.220874i
$189$	−13.0337	+	5.39875i	−0.948064	+	0.392701i
$190$	7.12534	+	2.97800i	0.516926	+	0.216047i
$191$		−	1.68378i		−	0.121834i	−0.998143	−	0.0609170i	$-0.980597\pi$
$191$		−	1.68378i		−	0.121834i	0.998143	−	0.0609170i	$-0.0194025\pi$
$192$	−16.5799	+	0.211896i	−1.19655	+	0.0152923i
$193$	−10.4183	−	10.4183i	−0.749926	−	0.749926i	0.224539	−	0.974465i	$-0.427912\pi$
$193$	−10.4183	−	10.4183i	−0.749926	−	0.749926i	−0.974465	+	0.224539i	$0.927912\pi$
$194$	6.65738	+	1.30950i	0.477972	+	0.0940166i
$195$	19.1677	+	12.9552i	1.37263	+	0.927744i
$196$	6.78240	−	16.5735i	0.484457	−	1.18382i
$197$	−22.4597	+	9.30310i	−1.60018	+	0.662818i	−0.991442	−	0.130549i	$-0.958326\pi$
$197$	−22.4597	+	9.30310i	−1.60018	+	0.662818i	−0.608743	+	0.793367i	$0.708326\pi$
$198$	3.95935	−	5.95299i	0.281379	−	0.423061i
$199$	4.09536	+	4.09536i	0.290313	+	0.290313i	0.837204	−	0.546891i	$-0.184189\pi$
$199$	4.09536	+	4.09536i	0.290313	+	0.290313i	−0.546891	+	0.837204i	$0.684189\pi$
$200$	−11.7919	+	7.80710i	−0.833814	+	0.552046i
$201$	1.27679	−	1.27679i	0.0900576	−	0.0900576i
$202$	3.18364	+	15.8290i	0.224000	+	1.11372i
$203$	11.0465	+	26.6687i	0.775315	+	1.87178i
$204$	14.2104	−	0.0605348i	0.994926	−	0.00423829i
$205$	8.74183	−	12.9338i	0.610556	−	0.903338i
$206$	10.3389	+	15.4021i	0.720343	+	1.07311i
$207$	1.36162	−	1.36162i	0.0946393	−	0.0946393i
$208$	−7.79808	−	18.3817i	−0.540700	−	1.27454i
$209$	9.52685			0.658986
$210$	−24.2183	+	9.94142i	−1.67122	+	0.686023i
$211$	−6.01257	−	14.5156i	−0.413922	−	0.999297i	−0.984074	−	0.177758i	$-0.943116\pi$
$211$	−6.01257	−	14.5156i	−0.413922	−	0.999297i	0.570152	−	0.821539i	$-0.306884\pi$
$212$	−0.0394454	−	9.25969i	−0.00270912	−	0.635958i
$213$	−24.4259	+	10.1175i	−1.67363	+	0.693242i
$214$	−18.4780	−	12.2898i	−1.26313	−	0.840112i
$215$	−4.70212	−	7.11879i	−0.320682	−	0.485497i
$216$	−5.60312	−	8.27076i	−0.381244	−	0.562754i
$217$	−17.0709			−1.15885
$218$	−3.58545	+	5.39083i	−0.242837	+	0.365113i
$219$	4.95222	+	2.05128i	0.334640	+	0.138612i
$220$	−9.70780	+	14.4957i	−0.654500	+	0.977302i
$221$	6.54868	+	15.8099i	0.440512	+	1.06349i
$222$	12.6872	+	18.9005i	0.851511	+	1.26852i
$223$	10.4731	−	10.4731i	0.701333	−	0.701333i	−0.263363	−	0.964697i	$-0.584832\pi$
$223$	10.4731	−	10.4731i	0.701333	−	0.701333i	0.964697	+	0.263363i	$0.0848318\pi$
$224$	22.2063	+	4.17176i	1.48372	+	0.278738i
$225$	5.95962	+	2.54306i	0.397308	+	0.169537i
$226$	0.276108	+	0.0543102i	0.0183664	+	0.00361266i
$227$	4.44058	−	10.7205i	0.294732	−	0.711545i	−0.705265	−	0.708944i	$-0.749172\pi$
$227$	4.44058	−	10.7205i	0.294732	−	0.711545i	0.999997	−	0.00260114i	$-0.000827971\pi$
$228$	−3.83414	+	9.36913i	−0.253922	+	0.620486i
$229$	−0.986786	+	2.38231i	−0.0652087	+	0.157428i	−0.953125	−	0.302578i	$-0.902153\pi$
$229$	−0.986786	+	2.38231i	−0.0652087	+	0.157428i	0.887916	+	0.460006i	$0.152153\pi$
$230$	−3.33320	+	3.31206i	−0.219785	+	0.218390i
$231$	−22.8365	+	22.8365i	−1.50253	+	1.50253i
$232$	−16.9231	+	11.4647i	−1.11105	+	0.752695i
$233$	11.6838			0.765432			0.382716	−	0.923866i	$-0.374989\pi$
$233$	11.6838			0.765432			0.382716	+	0.923866i	$0.374989\pi$
$234$	−5.06642	+	7.61750i	−0.331202	+	0.497972i
$235$	2.05591	−	3.04179i	0.134113	−	0.198425i
$236$	−6.41069	+	6.46555i	−0.417301	+	0.420871i
$237$	−3.18223	+	7.68259i	−0.206708	+	0.499038i
$238$	−19.0001	−	3.73731i	−1.23159	−	0.242254i
$239$		−	10.9778i		−	0.710092i	−0.934849	−	0.355046i	$-0.884465\pi$
$239$		−	10.9778i		−	0.710092i	0.934849	−	0.355046i	$-0.115535\pi$
$240$	−10.3488	−	15.3810i	−0.668011	−	0.992839i
$241$			8.52834i			0.549359i	0.961536	+	0.274679i	$0.0885717\pi$
$241$			8.52834i			0.549359i	−0.961536	+	0.274679i	$0.911428\pi$
$242$	−1.15138	+	5.85353i	−0.0740137	+	0.376279i
$243$	−4.83522	+	11.6732i	−0.310179	+	0.748839i
$244$	−1.33978	+	0.00570731i	−0.0857703	+	0.000365373i
$245$	19.6571	−	3.80161i	1.25584	−	0.242876i
$246$	17.0393	+	11.3329i	1.08638	+	0.722557i
$247$	−12.1906			−0.775672
$248$	−2.43404	−	11.8408i	−0.154562	−	0.751893i
$249$	−0.554795	+	0.554795i	−0.0351587	+	0.0351587i
$250$	−14.5229	−	6.25182i	−0.918509	−	0.395400i
$251$	−1.70754	+	4.12236i	−0.107779	+	0.260201i	−0.968563	−	0.248769i	$-0.919974\pi$
$251$	−1.70754	+	4.12236i	−0.107779	+	0.260201i	0.860784	+	0.508971i	$0.169974\pi$
$252$	−4.00234	−	9.54728i	−0.252124	−	0.601422i
$253$	−2.21831	+	5.35548i	−0.139464	+	0.336696i
$254$	−4.88903	+	24.8554i	−0.306765	+	1.55956i
$255$	8.75652	+	13.2569i	0.548354	+	0.830182i
$256$	0.272619	+	15.9977i	0.0170387	+	0.999855i
$257$	6.23845	−	6.23845i	0.389144	−	0.389144i	−0.485238	−	0.874382i	$-0.661267\pi$
$257$	6.23845	−	6.23845i	0.389144	−	0.389144i	0.874382	+	0.485238i	$0.161267\pi$
$258$	9.28563	−	6.23311i	0.578098	−	0.388056i
$259$	−11.8707	−	28.6584i	−0.737609	−	1.78074i
$260$	12.4222	−	18.5489i	0.770392	−	1.15035i
$261$	8.65252	+	3.58399i	0.535578	+	0.221844i
$262$	2.91487	+	1.93869i	0.180081	+	0.119772i
$263$	−3.58504			−0.221063			−0.110531	−	0.993873i	$-0.535255\pi$
$263$	−3.58504			−0.221063			−0.110531	+	0.993873i	$0.535255\pi$
$264$	−19.0961	−	12.5838i	−1.17528	−	0.774482i
$265$	8.63841	−	5.70587i	0.530654	−	0.350509i
$266$	7.63947	−	11.4862i	0.468406	−	0.704262i
$267$	15.7102	−	6.50738i	0.961449	−	0.398245i
$268$	−1.23727	−	1.22677i	−0.0755781	−	0.0749369i
$269$	8.68237	+	20.9611i	0.529374	+	1.27802i	0.931934	+	0.362627i	$0.118120\pi$
$269$	8.68237	+	20.9611i	0.529374	+	1.27802i	−0.402561	+	0.915393i	$0.631880\pi$
$270$	4.30707	−	10.3053i	0.262120	−	0.627162i
$271$	−17.4129			−1.05776			−0.528880	−	0.848697i	$-0.677388\pi$
$271$	−17.4129			−1.05776			−0.528880	+	0.848697i	$0.677388\pi$
$272$	−0.116825	−	13.7119i	−0.00708353	−	0.831404i
$273$	29.2217	−	29.2217i	1.76858	−	1.76858i
$274$	7.46808	−	5.01305i	0.451163	−	0.302850i
$275$	−19.5043	−	0.207198i	−1.17615	−	0.0124945i
$276$	−4.37404	−	4.33694i	−0.263287	−	0.261053i
$277$	3.47469	+	8.38863i	0.208774	+	0.504024i	0.993231	−	0.116159i	$-0.0370582\pi$
$277$	3.47469	+	8.38863i	0.208774	+	0.504024i	−0.784457	+	0.620183i	$0.787058\pi$
$278$	24.0959	−	4.84635i	1.44518	−	0.290665i
$279$	−3.91636	+	3.91636i	−0.234466	+	0.234466i
$280$	9.69239	+	23.3283i	0.579231	+	1.39413i
$281$	−21.0092	−	21.0092i	−1.25330	−	1.25330i	−0.954230	−	0.299074i	$-0.903322\pi$
$281$	−21.0092	−	21.0092i	−1.25330	−	1.25330i	−0.299074	−	0.954230i	$-0.596678\pi$
$282$	4.00732	+	2.66528i	0.238632	+	0.158715i
$283$	−29.5272	+	12.2306i	−1.75521	+	0.727032i	−0.758012	+	0.652241i	$0.773829\pi$
$283$	−29.5272	+	12.2306i	−1.75521	+	0.727032i	−0.997199	+	0.0747917i	$0.976171\pi$
$284$	9.86318	+	23.5278i	0.585272	+	1.39612i
$285$	−11.1123	+	2.14908i	−0.658235	+	0.127300i
$286$	5.31521	−	27.0220i	0.314295	−	1.59785i
$287$	−19.7180	−	19.7180i	−1.16392	−	1.16392i
$288$	6.05157	−	4.13742i	0.356592	−	0.243800i
$289$		−	5.24819i		−	0.308717i
$290$	−21.0860	−	8.81282i	−1.23821	−	0.517507i
$291$	−9.18701	+	3.80538i	−0.538552	+	0.223075i
$292$	1.95900	−	4.78701i	0.114642	−	0.280139i
$293$	5.27232	+	12.7285i	0.308012	+	0.743608i	0.999769	+	0.0214772i	$0.00683694\pi$
$293$	5.27232	+	12.7285i	0.308012	+	0.743608i	−0.691757	+	0.722130i	$0.743163\pi$
$294$	5.17500	+	25.7299i	0.301812	+	1.50060i
$295$	−9.97337	−	2.03895i	−0.580672	−	0.118712i
$296$	18.1856	−	12.3201i	1.05702	−	0.716089i
$297$		−	13.7786i		−	0.799516i
$298$	5.67788	+	28.2303i	0.328911	+	1.63533i
$299$	2.83857	−	6.85292i	0.164159	−	0.396315i
$300$	8.05339	−	19.0980i	0.464963	−	1.10262i
$301$	−14.0796	+	5.83195i	−0.811533	+	0.336148i
$302$	1.40981	−	7.16734i	0.0811254	−	0.412434i
$303$	−16.7325	−	16.7325i	−0.961257	−	0.961257i
$304$	9.05638	+	3.66119i	0.519419	+	0.209984i
$305$	−0.825577	−	1.24988i	−0.0472724	−	0.0715682i
$306$	−5.21636	+	3.50155i	−0.298199	+	0.200170i
$307$	18.5558	+	7.68608i	1.05904	+	0.438668i	0.843110	−	0.537742i	$-0.180722\pi$
$307$	18.5558	+	7.68608i	1.05904	+	0.438668i	0.215928	+	0.976409i	$0.430722\pi$
$308$	22.1296	+	21.9419i	1.26095	+	1.25025i
$309$	−25.1177	−	10.4041i	−1.42890	−	0.591869i
$310$	9.58708	−	9.52628i	0.544510	−	0.541056i
$311$	1.22618	+	1.22618i	0.0695303	+	0.0695303i	0.741017	−	0.671486i	$-0.234344\pi$
$311$	1.22618	+	1.22618i	0.0695303	+	0.0695303i	−0.671486	+	0.741017i	$0.734344\pi$
$312$	24.4355	+	16.1024i	1.38339	+	0.911619i
$313$			18.9123i			1.06898i	0.845174	+	0.534492i	$0.179497\pi$
$313$			18.9123i			1.06898i	−0.845174	+	0.534492i	$0.820503\pi$
$314$	4.28628	+	21.3113i	0.241889	+	1.20266i
$315$	6.48129	−	9.58929i	0.365179	−	0.540295i
$316$	7.42629	+	3.03907i	0.417761	+	0.170961i
$317$	6.91362	+	2.86372i	0.388308	+	0.160842i	0.568292	−	0.822827i	$-0.307605\pi$
$317$	6.91362	+	2.86372i	0.388308	+	0.160842i	−0.179984	+	0.983670i	$0.557605\pi$
$318$	7.56367	+	11.2678i	0.424150	+	0.631867i
$319$	−28.1928			−1.57850
$320$	−14.7991	+	10.0491i	−0.827297	+	0.561764i
$321$	32.5241			1.81532
$322$	4.67806	+	6.96904i	0.260698	+	0.388369i
$323$	−7.73451	−	3.20374i	−0.430360	−	0.178261i
$324$	20.7467	+	8.49019i	1.15259	+	0.471677i
$325$	24.9578	+	0.265132i	1.38441	+	0.0147069i
$326$	5.06549	+	25.1855i	0.280552	+	1.39490i
$327$		−	9.48865i		−	0.524724i
$328$	10.8655	−	16.4884i	0.599944	−	0.910420i
$329$	−4.63731	−	4.63731i	−0.255663	−	0.255663i
$330$	0.0813462	−	25.5687i	0.00447796	−	1.40751i
$331$	13.9660	+	5.78490i	0.767640	+	0.317967i	0.731916	−	0.681395i	$-0.238626\pi$
$331$	13.9660	+	5.78490i	0.767640	+	0.317967i	0.0357242	+	0.999362i	$0.488626\pi$
$332$	0.537623	+	0.533062i	0.0295059	+	0.0292556i
$333$	−9.29806	−	3.85138i	−0.509531	−	0.211054i
$334$	−6.15609	+	4.13236i	−0.336846	+	0.226113i
$335$	0.390180	−	1.90853i	0.0213178	−	0.104274i
$336$	−30.4848	+	12.9326i	−1.66308	+	0.705531i
$337$	−24.0981	−	24.0981i	−1.31271	−	1.31271i	−0.919412	−	0.393295i	$-0.871335\pi$
$337$	−24.0981	−	24.0981i	−1.31271	−	1.31271i	−0.393295	−	0.919412i	$-0.628665\pi$
$338$	−3.25311	+	16.5385i	−0.176946	+	0.899576i
$339$	−0.381022	+	0.157824i	−0.0206943	+	0.00857184i
$340$	12.7561	−	8.50398i	0.691798	−	0.461193i
$341$	6.38040	−	15.4037i	0.345518	−	0.834155i
$342$	−0.882497	−	4.38775i	−0.0477200	−	0.237262i
$343$		−	7.80392i		−	0.421372i
$344$	−6.05272	−	8.93442i	−0.326341	−	0.481712i
$345$	1.37938	−	6.74714i	0.0742635	−	0.363254i
$346$	−5.80846	−	28.8795i	−0.312265	−	1.55257i
$347$	1.10173	+	2.65981i	0.0591439	+	0.142786i	0.950689	−	0.310146i	$-0.100378\pi$
$347$	1.10173	+	2.65981i	0.0591439	+	0.142786i	−0.891545	+	0.452932i	$0.850378\pi$
$348$	11.3464	−	27.7261i	0.608231	−	1.48627i
$349$	27.5386	−	11.4069i	1.47411	−	0.610595i	0.506316	−	0.862348i	$-0.331007\pi$
$349$	27.5386	−	11.4069i	1.47411	−	0.610595i	0.967791	+	0.251753i	$0.0810071\pi$
$350$	−15.8901	+	23.3494i	−0.849360	+	1.24808i
$351$			17.6312i			0.941086i
$352$	−12.0641	+	18.4782i	−0.643020	+	0.984893i
$353$	0.168967	+	0.168967i	0.00899322	+	0.00899322i	0.711589	−	0.702596i	$-0.247976\pi$
$353$	0.168967	+	0.168967i	0.00899322	+	0.00899322i	−0.702596	+	0.711589i	$0.747976\pi$
$354$	2.57543	−	13.0932i	0.136883	−	0.695898i
$355$	−15.9722	+	23.6314i	−0.847715	+	1.25422i
$356$	−6.34378	−	15.1326i	−0.336220	−	0.802026i
$357$	26.2197	−	10.8605i	1.38769	−	0.574801i
$358$	0.596885	+	0.396989i	0.0315463	+	0.0209815i
$359$	3.65935	+	3.65935i	0.193133	+	0.193133i	0.797048	−	0.603915i	$-0.206394\pi$
$359$	3.65935	+	3.65935i	0.193133	+	0.193133i	−0.603915	+	0.797048i	$0.706394\pi$
$360$	7.57551	+	3.12831i	0.399265	+	0.164877i
$361$	−9.21792	+	9.21792i	−0.485154	+	0.485154i
$362$	−0.0923383	+	0.0185718i	−0.00485319	+	0.000976110i
$363$	−3.34590	−	8.07771i	−0.175614	−	0.423970i
$364$	−28.3172	−	28.0770i	−1.48423	−	1.47163i
$365$	5.67765	−	1.09804i	0.297182	−	0.0574739i
$366$	1.63033	−	1.09438i	0.0852187	−	0.0572042i
$367$	−8.89181	+	8.89181i	−0.464148	+	0.464148i	−0.900013	−	0.435864i	$-0.856443\pi$
$367$	−8.89181	+	8.89181i	−0.464148	+	0.464148i	0.435864	+	0.900013i	$0.356443\pi$
$368$	−4.16689	+	4.23850i	−0.217214	+	0.220947i
$369$	−9.04730			−0.470983
$370$	22.6592	+	9.47032i	1.17800	+	0.492338i
$371$	−7.07688	−	17.0851i	−0.367413	−	0.887014i
$372$	12.5808	+	12.4741i	0.652285	+	0.646751i
$373$	4.57910	−	1.89672i	0.237097	−	0.0982086i	−0.260972	−	0.965346i	$-0.584043\pi$
$373$	4.57910	−	1.89672i	0.237097	−	0.0982086i	0.498068	+	0.867138i	$0.334043\pi$
$374$	10.4738	−	15.7476i	0.541586	−	0.814289i
$375$	22.7969	−	4.15812i	1.17723	−	0.214724i
$376$	2.55535	−	3.87776i	0.131782	−	0.199980i
$377$	36.0758			1.85800
$378$	−16.6124	−	11.0489i	−0.854448	−	0.568295i
$379$	4.79165	+	1.98477i	0.246130	+	0.101951i	0.502338	−	0.864671i	$-0.332473\pi$
$379$	4.79165	+	1.98477i	0.246130	+	0.101951i	−0.256208	+	0.966622i	$0.582473\pi$
$380$	2.11940	+	10.7138i	0.108723	+	0.549608i
$381$	−14.2074	−	34.2998i	−0.727868	−	1.75723i
$382$	1.97709	−	1.32715i	0.101157	−	0.0679030i
$383$	2.52572	−	2.52572i	0.129058	−	0.129058i	−0.639627	−	0.768685i	$-0.720911\pi$
$383$	2.52572	−	2.52572i	0.129058	−	0.129058i	0.768685	+	0.639627i	$0.220911\pi$
$384$	−13.3170	−	19.3011i	−0.679583	−	0.984955i
$385$	−6.97872	+	34.1358i	−0.355668	+	1.73972i
$386$	4.02148	−	20.4449i	0.204688	−	1.04062i
$387$	−1.89215	+	4.56805i	−0.0961832	+	0.232207i
$388$	3.70972	+	8.84924i	0.188332	+	0.449252i
$389$	6.04264	−	14.5882i	0.306374	−	0.739652i	−0.693443	−	0.720512i	$-0.743907\pi$
$389$	6.04264	−	14.5882i	0.306374	−	0.739652i	0.999817	−	0.0191406i	$-0.00609302\pi$
$390$	−0.104091	+	32.7180i	−0.00527087	+	1.65674i
$391$	3.60194	−	3.60194i	0.182158	−	0.182158i
$392$	24.8065	−	5.09931i	1.25292	−	0.257554i
$393$	−5.13060			−0.258805
$394$	−28.6263	−	19.0394i	−1.44217	−	0.959193i
$395$	1.70343	+	8.80798i	0.0857090	+	0.443178i
$396$	10.1107	−	0.0430708i	0.508084	−	0.00216439i
$397$	6.54490	−	15.8008i	0.328479	−	0.793019i	−0.670226	−	0.742157i	$-0.733803\pi$
$397$	6.54490	−	15.8008i	0.328479	−	0.793019i	0.998706	−	0.0508624i	$-0.0161970\pi$
$398$	−1.58082	+	8.03673i	−0.0792392	+	0.402845i
$399$			20.2174i			1.01213i
$400$	−18.4615	−	7.69251i	−0.923073	−	0.384626i
$401$			29.8120i			1.48874i	0.667767	+	0.744370i	$0.267250\pi$
$401$			29.8120i			1.48874i	−0.667767	+	0.744370i	$0.732750\pi$
$402$	2.50556	+	0.492842i	0.124966	+	0.0245807i
$403$	−8.16442	+	19.7107i	−0.406699	+	0.981858i
$404$	−16.0770	+	16.2146i	−0.799862	+	0.806706i
$405$	4.75885	+	24.6067i	0.236469	+	1.22272i
$406$	−22.6075	+	33.9910i	−1.12199	+	1.68695i
$407$	30.2962			1.50173
$408$	11.2717	+	16.6381i	0.558031	+	0.823709i
$409$	−15.1414	+	15.1414i	−0.748693	+	0.748693i	−0.974234	−	0.225541i	$-0.927585\pi$
$409$	−15.1414	+	15.1414i	−0.748693	+	0.748693i	0.225541	+	0.974234i	$0.427585\pi$
$410$	22.0772	+	0.0702379i	1.09031	+	0.00346880i
$411$	−5.04469	+	12.1790i	−0.248836	+	0.600743i
$412$	−9.93605	+	24.2798i	−0.489514	+	1.19618i
$413$	−6.95857	+	16.7995i	−0.342409	+	0.826648i
$414$	2.67204	+	0.525589i	0.131324	+	0.0258313i
$415$	−0.169543	+	0.829305i	−0.00832254	+	0.0407090i
$416$	15.4374	−	23.6449i	0.756879	−	1.15929i
$417$	−25.4713	+	25.4713i	−1.24734	+	1.24734i
$418$	7.50904	+	11.1864i	0.367279	+	0.547146i
$419$	5.28993	+	12.7710i	0.258430	+	0.623905i	0.998835	−	0.0482556i	$-0.0153662\pi$
$419$	5.28993	+	12.7710i	0.258430	+	0.623905i	−0.740405	+	0.672161i	$0.765366\pi$
$420$	−30.7621	−	20.6014i	−1.50103	−	1.00524i
$421$	−12.0311	−	4.98346i	−0.586361	−	0.242879i	0.0697230	−	0.997566i	$-0.477788\pi$
$421$	−12.0311	−	4.98346i	−0.586361	−	0.242879i	−0.656084	+	0.754688i	$0.727788\pi$
$422$	12.3051	−	18.5011i	0.599005	−	0.900621i
$423$	−2.12775			−0.103455
$424$	10.8416	−	7.34478i	0.526516	−	0.356694i
$425$	15.7651	+	6.72721i	0.764722	+	0.326318i
$426$	−31.1324	−	20.7062i	−1.50837	−	1.00322i
$427$	−2.47203	+	1.02395i	−0.119630	+	0.0495523i
$428$	−0.133691	−	31.3837i	−0.00646221	−	1.51699i
$429$	15.4459	+	37.2897i	0.745734	+	1.80036i
$430$	4.65267	−	11.1322i	0.224372	−	0.536844i
$431$	0.344781			0.0166075			0.00830377	−	0.999966i	$-0.497357\pi$
$431$	0.344781			0.0166075			0.00830377	+	0.999966i	$0.497357\pi$
$432$	5.29516	−	13.0982i	0.254763	−	0.630186i
$433$	18.9759	−	18.9759i	0.911923	−	0.911923i	−0.0845001	−	0.996423i	$-0.526929\pi$
$433$	18.9759	−	18.9759i	0.911923	−	0.911923i	0.996423	+	0.0845001i	$0.0269293\pi$
$434$	−13.4552	−	20.0446i	−0.645872	−	0.962173i
$435$	32.8846	−	6.35978i	1.57670	−	0.304928i
$436$	−9.15595	+	0.0390034i	−0.438490	+	0.00186793i
$437$	1.38868	+	3.35258i	0.0664298	+	0.160376i
$438$	1.49472	+	7.43170i	0.0714205	+	0.355101i
$439$	11.4173	−	11.4173i	0.544919	−	0.544919i	−0.380048	−	0.924967i	$-0.624092\pi$
$439$	11.4173	−	11.4173i	0.544919	−	0.544919i	0.924967	+	0.380048i	$0.124092\pi$
$440$	−24.6725	+	0.0266072i	−1.17622	+	0.00126845i
$441$	−8.20475	−	8.20475i	−0.390702	−	0.390702i
$442$	−13.4023	+	20.1508i	−0.637484	+	0.958475i
$443$	32.2485	−	13.3578i	1.53217	−	0.634647i	0.552188	−	0.833720i	$-0.313793\pi$
$443$	32.2485	−	13.3578i	1.53217	−	0.634647i	0.979985	+	0.199073i	$0.0637931\pi$
$444$	−12.1929	+	29.7947i	−0.578650	+	1.41399i
$445$	10.2730	−	15.1992i	0.486985	−	0.720511i
$446$	20.5525	+	4.04265i	0.973187	+	0.191425i
$447$	−29.8417	−	29.8417i	−1.41146	−	1.41146i
$448$	12.6044	+	29.3628i	0.595504	+	1.38726i
$449$			22.9968i			1.08529i	0.839963	+	0.542644i	$0.182577\pi$
$449$			22.9968i			1.08529i	−0.839963	+	0.542644i	$0.817423\pi$
$450$	1.71130	+	9.00221i	0.0806716	+	0.424368i
$451$	25.1620	−	10.4224i	1.18483	−	0.490774i
$452$	0.153857	+	0.367013i	0.00723681	+	0.0172628i
$453$	4.09688	+	9.89074i	0.192488	+	0.464707i
$454$	16.0881	−	3.23575i	0.755050	−	0.151861i
$455$	8.93003	−	43.6805i	0.418646	−	2.04777i
$456$	−14.0233	+	2.88268i	−0.656701	+	0.134994i
$457$		−	38.4239i		−	1.79739i	−0.438570	−	0.898697i	$-0.644515\pi$
$457$		−	38.4239i		−	1.79739i	0.438570	−	0.898697i	$-0.355485\pi$
$458$	−3.57509	+	0.719049i	−0.167053	+	0.0335990i
$459$	−4.63354	+	11.1864i	−0.216275	+	0.522135i
$460$	−6.51623	−	1.30328i	−0.303821	−	0.0607659i
$461$	−29.2007	+	12.0953i	−1.36001	+	0.563336i	−0.939062	−	0.343748i	$-0.888303\pi$
$461$	−29.2007	+	12.0953i	−1.36001	+	0.563336i	−0.420951	+	0.907084i	$0.638303\pi$
$462$	−44.8142	−	8.81491i	−2.08494	−	0.410107i
$463$	8.54250	+	8.54250i	0.397004	+	0.397004i	0.877175	−	0.480171i	$-0.159425\pi$
$463$	8.54250	+	8.54250i	0.397004	+	0.397004i	−0.480171	+	0.877175i	$0.659425\pi$
$464$	−26.8006	−	10.8346i	−1.24418	−	0.502983i
$465$	−3.96744	+	19.4064i	−0.183986	+	0.899951i
$466$	9.20915	+	13.7191i	0.426606	+	0.635526i
$467$	0.834121	+	0.345504i	0.0385985	+	0.0159880i	0.401899	−	0.915684i	$-0.368350\pi$
$467$	0.834121	+	0.345504i	0.0385985	+	0.0159880i	−0.363301	+	0.931672i	$0.618350\pi$
$468$	−12.9378	+	0.0551138i	−0.598050	+	0.00254764i
$469$	−3.21480	−	1.33161i	−0.148446	−	0.0614881i
$470$	5.19214	+	0.0165187i	0.239496	+	0.000761949i
$471$	−22.5277	−	22.5277i	−1.03802	−	1.03802i
$472$	−12.6447	−	2.43131i	−0.582021	−	0.111910i
$473$		−	14.8842i		−	0.684378i
$474$	−11.5291	+	2.31882i	−0.529550	+	0.106507i
$475$	−8.72539	+	8.54195i	−0.400348	+	0.391932i
$476$	−10.5875	−	25.2557i	−0.485278	−	1.15759i
$477$	−5.54317	−	2.29606i	−0.253804	−	0.105129i
$478$	12.8901	−	8.65264i	0.589578	−	0.395762i
$479$	−3.43571			−0.156982			−0.0784908	−	0.996915i	$-0.525010\pi$
$479$	−3.43571			−0.156982			−0.0784908	+	0.996915i	$0.525010\pi$
$480$	9.90347	−	24.2748i	0.452029	−	1.10799i
$481$	−38.7673			−1.76764
$482$	−10.0140	+	6.72202i	−0.456124	+	0.306180i
$483$	−11.3651	−	4.70758i	−0.517130	−	0.214202i
$484$	−7.78072	+	3.26178i	−0.353669	+	0.148263i
$485$	−6.00742	+	8.88817i	−0.272783	+	0.403591i
$486$	−17.5178	+	3.52332i	−0.794625	+	0.159821i
$487$			19.9807i			0.905412i	0.891660	+	0.452706i	$0.149541\pi$
$487$			19.9807i			0.905412i	−0.891660	+	0.452706i	$0.850459\pi$
$488$	−1.06271	−	1.56867i	−0.0481066	−	0.0710101i
$489$	−26.6231	−	26.6231i	−1.20394	−	1.20394i
$490$	19.9575	+	20.0849i	0.901589	+	0.907344i
$491$	11.5483	+	4.78347i	0.521168	+	0.215875i	0.627730	−	0.778431i	$-0.283984\pi$
$491$	11.5483	+	4.78347i	0.521168	+	0.215875i	−0.106562	+	0.994306i	$0.533984\pi$
$492$	0.123282	+	28.9400i	0.00555797	+	1.30472i
$493$	22.8888	+	9.48083i	1.03086	+	0.426995i
$494$	−9.60864	−	14.3142i	−0.432313	−	0.644028i
$495$	6.23030	+	9.43237i	0.280031	+	0.423954i
$496$	11.9850	−	12.1910i	0.538142	−	0.547390i
$497$	36.0267	+	36.0267i	1.61602	+	1.61602i
$498$	−1.08873	−	0.214152i	−0.0487871	−	0.00959638i
$499$	−19.6637	+	8.14498i	−0.880269	+	0.364619i	−0.776601	−	0.629993i	$-0.783058\pi$
$499$	−19.6637	+	8.14498i	−0.880269	+	0.364619i	−0.103668	+	0.994612i	$0.533058\pi$
$500$	−4.10603	−	21.9805i	−0.183627	−	0.982996i
$501$	4.15843	−	10.0393i	0.185785	−	0.448525i
$502$	−6.18635	+	1.24425i	−0.276111	+	0.0555334i
$503$			34.6943i			1.54694i	0.633831	+	0.773472i	$0.281482\pi$
$503$			34.6943i			1.54694i	−0.633831	+	0.773472i	$0.718518\pi$
$504$	8.05577	−	12.2247i	0.358832	−	0.544531i
$505$	−25.0116	−	5.11338i	−1.11300	−	0.227542i
$506$	−8.03687	+	1.61644i	−0.357282	+	0.0718593i
$507$	−9.45347	−	22.8227i	−0.419843	−	1.01359i
$508$	−33.0387	+	13.8503i	−1.46585	+	0.614506i
$509$	−2.79710	+	1.15860i	−0.123979	+	0.0513539i	−0.443811	−	0.896121i	$-0.646374\pi$
$509$	−2.79710	+	1.15860i	−0.123979	+	0.0513539i	0.319831	+	0.947474i	$0.396374\pi$
$510$	−8.66443	+	20.7310i	−0.383667	+	0.917984i
$511$		−	10.3297i		−	0.456961i
$512$	−18.5696	+	12.9294i	−0.820668	+	0.571406i
$513$	−6.09918	−	6.09918i	−0.269285	−	0.269285i
$514$	12.2423	+	2.40805i	0.539986	+	0.106215i
$515$	−28.7971	+	5.56926i	−1.26895	+	0.245411i
$516$	14.6378	+	5.99026i	0.644394	+	0.263707i
$517$	5.91764	−	2.45116i	0.260257	−	0.107802i
$518$	24.2942	−	36.5270i	1.06743	−	1.60491i
$519$	30.5280	+	30.5280i	1.34003	+	1.34003i
$520$	31.5712	−	0.0340469i	1.38449	−	0.00149305i
$521$	7.05795	−	7.05795i	0.309214	−	0.309214i	−0.535390	−	0.844605i	$-0.679836\pi$
$521$	7.05795	−	7.05795i	0.309214	−	0.309214i	0.844605	+	0.535390i	$0.179836\pi$
$522$	2.61158	+	12.9847i	0.114306	+	0.568324i
$523$	−15.7272	−	37.9688i	−0.687702	−	1.66026i	−0.749361	−	0.662161i	$-0.769639\pi$
$523$	−15.7272	−	37.9688i	−0.687702	−	1.66026i	0.0616596	−	0.998097i	$-0.480361\pi$
$524$	0.0210895	+	4.95071i	0.000921300	+	0.216273i
$525$	0.439704	−	41.3909i	0.0191902	−	1.80645i
$526$	−2.82572	−	4.20955i	−0.123207	−	0.183545i
$527$	−10.3600	+	10.3600i	−0.451291	+	0.451291i
$528$	−0.275545	−	32.3412i	−0.0119916	−	1.40747i
$529$	20.7920			0.904000
$530$	13.5086	+	5.64587i	0.586776	+	0.245241i
$531$	2.25767	+	5.45050i	0.0979746	+	0.236532i
$532$	19.5085	−	0.0831042i	0.845799	−	0.00360302i
$533$	−32.1975	+	13.3367i	−1.39463	+	0.577675i
$534$	20.0237	+	13.3178i	0.866511	+	0.576318i
$535$	29.2780	−	19.3388i	1.26580	−	0.836089i
$536$	0.465262	−	2.41973i	0.0200963	−	0.104517i
$537$	−1.05061			−0.0453370
$538$	−17.7691	+	26.7163i	−0.766080	+	1.15182i
$539$	32.2706	+	13.3669i	1.38999	+	0.575754i
$540$	15.4953	−	3.06528i	0.666813	−	0.131909i
$541$	2.84743	+	6.87431i	0.122421	+	0.295550i	0.973195	−	0.229982i	$-0.0738666\pi$
$541$	2.84743	+	6.87431i	0.122421	+	0.295550i	−0.850774	+	0.525531i	$0.823867\pi$
$542$	−13.7248	−	20.4462i	−0.589532	−	0.878241i
$543$	0.0976091	−	0.0976091i	0.00418881	−	0.00418881i
$544$	16.0084	−	10.9448i	0.686354	−	0.469256i
$545$	−5.64195	−	8.54164i	−0.241674	−	0.365884i
$546$	57.3447	+	11.2796i	2.45412	+	0.482724i
$547$	0.448550	−	1.08290i	0.0191786	−	0.0463013i	−0.914000	−	0.405714i	$-0.867023\pi$
$547$	0.448550	−	1.08290i	0.0191786	−	0.0463013i	0.933179	+	0.359413i	$0.117023\pi$
$548$	11.7727	+	4.81774i	0.502903	+	0.205804i
$549$	−0.332215	+	0.802037i	−0.0141786	+	0.0342301i
$550$	−15.1299	−	23.0652i	−0.645142	−	0.983504i
$551$	−12.4797	+	12.4797i	−0.531653	+	0.531653i
$552$	1.64482	−	8.55436i	0.0700081	−	0.364098i
$553$	16.0250			0.681451
$554$	−7.11119	+	10.6919i	−0.302126	+	0.454254i
$555$	−35.3381	+	6.83426i	−1.50002	+	0.290098i
$556$	24.6829	+	24.4735i	1.04679	+	1.03791i
$557$	−13.0854	+	31.5908i	−0.554444	+	1.33855i	0.359666	+	0.933081i	$0.382891\pi$
$557$	−13.0854	+	31.5908i	−0.554444	+	1.33855i	−0.914110	+	0.405466i	$0.867109\pi$
$558$	−7.68545	−	1.51172i	−0.325351	−	0.0639962i
$559$			19.0460i			0.805560i
$560$	−19.7526	+	29.7681i	−0.834698	+	1.25793i
$561$			27.7181i			1.17026i
$562$	8.10959	−	41.2284i	0.342082	−	1.73912i
$563$	−12.6767	+	30.6043i	−0.534261	+	1.28982i	0.394417	+	0.918932i	$0.370947\pi$
$563$	−12.6767	+	30.6043i	−0.534261	+	1.28982i	−0.928678	+	0.370888i	$0.879053\pi$
$564$	0.0289936	+	6.80616i	0.00122085	+	0.286591i
$565$	−0.249151	+	0.368628i	−0.0104819	+	0.0155083i
$566$	−37.6344	−	25.0307i	−1.58189	−	1.05212i
$567$	44.7686			1.88010
$568$	−19.8522	+	30.1259i	−0.832981	+	1.26406i
$569$	25.6590	−	25.6590i	1.07568	−	1.07568i	0.0787904	−	0.996891i	$-0.474894\pi$
$569$	25.6590	−	25.6590i	1.07568	−	1.07568i	0.996891	−	0.0787904i	$-0.0251058\pi$
$570$	−11.2821	−	11.3541i	−0.472556	−	0.475573i
$571$	15.9694	−	38.5535i	0.668299	−	1.61342i	−0.116157	−	0.993231i	$-0.537058\pi$
$571$	15.9694	−	38.5535i	0.668299	−	1.61342i	0.784456	−	0.620185i	$-0.212942\pi$
$572$	35.9187	−	15.0576i	1.50183	−	0.629589i
$573$	−1.33553	+	3.22425i	−0.0557924	+	0.134695i
$574$	7.61118	−	38.6946i	0.317685	−	1.61508i
$575$	−2.77013	−	6.89392i	−0.115522	−	0.287496i
$576$	9.62799	+	3.84464i	0.401166	+	0.160194i
$577$	−1.99052	+	1.99052i	−0.0828663	+	0.0828663i	−0.747325	−	0.664459i	$-0.768662\pi$
$577$	−1.99052	+	1.99052i	−0.0828663	+	0.0828663i	0.664459	+	0.747325i	$0.268662\pi$
$578$	6.16242	−	4.13661i	0.256323	−	0.172060i
$579$	11.6864	+	28.2134i	0.485668	+	1.17251i
$580$	−6.27196	−	31.7054i	−0.260429	−	1.31650i
$581$	1.39691	+	0.578618i	0.0579535	+	0.0240051i
$582$	−11.7095	−	7.78798i	−0.485373	−	0.322822i
$583$	18.0615			0.748032
$584$	7.16498	−	1.47286i	0.296489	−	0.0609473i
$585$	−7.97235	−	12.0698i	−0.329616	−	0.499023i
$586$	−10.7902	+	16.2233i	−0.445738	+	0.670180i
$587$	15.7565	−	6.52654i	0.650339	−	0.269379i	−0.0330280	−	0.999454i	$-0.510515\pi$
$587$	15.7565	−	6.52654i	0.650339	−	0.269379i	0.683367	+	0.730075i	$0.260515\pi$
$588$	−26.1332	+	26.3568i	−1.07771	+	1.08693i
$589$	−3.99419	−	9.64283i	−0.164578	−	0.397326i
$590$	−5.46685	−	13.3178i	−0.225067	−	0.548286i
$591$	50.3866			2.07263
$592$	28.8001	+	11.6429i	1.18368	+	0.478521i
$593$	−29.9937	+	29.9937i	−1.23169	+	1.23169i	−0.268380	+	0.963313i	$0.586488\pi$
$593$	−29.9937	+	29.9937i	−1.23169	+	1.23169i	−0.963313	+	0.268380i	$0.913512\pi$
$594$	16.1788	−	10.8603i	0.663826	−	0.445602i
$595$	17.1451	−	25.3668i	0.702882	−	1.03994i
$596$	−28.6727	+	28.9180i	−1.17448	+	1.18453i
$597$	−4.59383	−	11.0905i	−0.188013	−	0.453903i
$598$	10.2841	−	2.06841i	0.420546	−	0.0845834i
$599$	−22.3788	+	22.3788i	−0.914371	+	0.914371i	−0.996612	−	0.0822411i	$-0.973792\pi$
$599$	−22.3788	+	22.3788i	−0.914371	+	0.914371i	0.0822411	+	0.996612i	$0.473792\pi$
$600$	28.7725	−	5.59670i	1.17463	−	0.228484i
$601$	21.1686	+	21.1686i	0.863486	+	0.863486i	0.991741	−	0.128255i	$-0.0409376\pi$
$601$	21.1686	+	21.1686i	0.863486	+	0.863486i	−0.128255	+	0.991741i	$0.540938\pi$
$602$	−17.9454	−	11.9355i	−0.731399	−	0.486455i
$603$	−1.04302	+	0.432035i	−0.0424752	+	0.0175938i
$604$	9.52710	−	3.99388i	0.387652	−	0.162509i
$605$	−7.81496	−	5.28204i	−0.317723	−	0.214746i
$606$	6.45877	−	32.8358i	0.262370	−	1.33386i
$607$	11.2244	+	11.2244i	0.455586	+	0.455586i	0.897203	−	0.441617i	$-0.145595\pi$
$607$	11.2244	+	11.2244i	0.455586	+	0.455586i	−0.441617	+	0.897203i	$0.645595\pi$
$608$	2.83924	+	13.5197i	0.115147	+	0.548298i
$609$		−	59.8293i		−	2.42440i
$610$	0.816895	−	1.95455i	0.0330751	−	0.0791374i
$611$	−7.57226	+	3.13653i	−0.306341	+	0.126891i
$612$	−8.22304	−	3.36513i	−0.332397	−	0.136027i
$613$	−13.1276	−	31.6928i	−0.530218	−	1.28006i	−0.931379	−	0.364051i	$-0.881393\pi$
$613$	−13.1276	−	31.6928i	−0.530218	−	1.28006i	0.401161	−	0.916008i	$-0.368607\pi$
$614$	5.60068	+	27.8464i	0.226025	+	1.12379i
$615$	−26.9983	+	17.8330i	−1.08868	+	0.719097i
$616$	−8.32162	+	43.2791i	−0.335288	+	1.74376i
$617$			14.2086i			0.572018i	0.958227	+	0.286009i	$0.0923288\pi$
$617$			14.2086i			0.572018i	−0.958227	+	0.286009i	$0.907671\pi$
$618$	−7.58124	−	37.6937i	−0.304962	−	1.51626i
$619$	−0.266695	+	0.643860i	−0.0107194	+	0.0258789i	−0.929149	−	0.369706i	$-0.879458\pi$
$619$	−0.266695	+	0.643860i	−0.0107194	+	0.0258789i	0.918429	+	0.395585i	$0.129458\pi$
$620$	18.7423	+	3.74856i	0.752708	+	0.150546i
$621$	4.84881	−	2.00844i	0.194576	−	0.0805961i
$622$	−0.473308	+	2.40625i	−0.0189779	+	0.0964820i
$623$	−23.1716	−	23.1716i	−0.928351	−	0.928351i
$624$	0.352591	+	41.3841i	0.0141149	+	1.65669i
$625$	18.0492	−	17.2981i	0.721969	−	0.691925i
$626$	−22.2068	+	14.9066i	−0.887561	+	0.595787i
$627$	−18.2428	−	7.55642i	−0.728548	−	0.301774i
$628$	−21.6452	+	21.8304i	−0.863739	+	0.871130i
$629$	−24.5964	−	10.1882i	−0.980723	−	0.406229i
$630$	16.3683	+	0.0520752i	0.652128	+	0.00207473i
$631$	25.7027	+	25.7027i	1.02321	+	1.02321i	0.999724	+	0.0234841i	$0.00747591\pi$
$631$	25.7027	+	25.7027i	1.02321	+	1.02321i	0.0234841	+	0.999724i	$0.492524\pi$
$632$	2.28491	+	11.1153i	0.0908888	+	0.442144i
$633$			32.5647i			1.29433i
$634$	2.08673	+	10.3751i	0.0828745	+	0.412050i
$635$	−33.1841	−	22.4287i	−1.31687	−	0.890057i
$636$	−7.26898	+	17.7625i	−0.288234	+	0.704330i
$637$	−41.2938	−	17.1044i	−1.63612	−	0.677702i
$638$	−22.2215	−	33.1040i	−0.879758	−	1.31060i
$639$	16.5303			0.653928
$640$	−23.4644	−	9.45643i	−0.927510	−	0.373798i
$641$	28.2602			1.11621			0.558106	−	0.829769i	$-0.311528\pi$
$641$	28.2602			1.11621			0.558106	+	0.829769i	$0.311528\pi$
$642$	25.6354	+	38.1897i	1.01175	+	1.50723i
$643$	−10.8688	−	4.50200i	−0.428623	−	0.177542i	0.157933	−	0.987450i	$-0.449517\pi$
$643$	−10.8688	−	4.50200i	−0.428623	−	0.177542i	−0.586557	+	0.809908i	$0.699517\pi$
$644$	−4.49580	+	10.9860i	−0.177159	+	0.432907i
$645$	3.35761	+	17.3612i	0.132206	+	0.683598i
$646$	−2.33449	−	11.6070i	−0.0918494	−	0.456673i
$647$		−	20.8638i		−	0.820239i	−0.912032	−	0.410119i	$-0.865487\pi$
$647$		−	20.8638i		−	0.820239i	0.912032	−	0.410119i	$-0.134513\pi$
$648$	6.38330	+	31.0527i	0.250760	+	1.21986i
$649$	−12.5579	−	12.5579i	−0.492941	−	0.492941i
$650$	19.3604	+	29.5145i	0.759377	+	1.15765i
$651$	32.6888	+	13.5401i	1.28118	+	0.530680i
$652$	−25.5802	+	25.7990i	−1.00180	+	1.01037i
$653$	15.1610	+	6.27991i	0.593297	+	0.245752i	0.659068	−	0.752083i	$-0.270951\pi$
$653$	15.1610	+	6.27991i	0.593297	+	0.245752i	−0.0657711	+	0.997835i	$0.520951\pi$
$654$	11.1416	−	7.47893i	0.435670	−	0.292449i
$655$	−4.61854	+	3.05065i	−0.180461	+	0.119199i
$656$	27.9248	−	0.237918i	1.09028	−	0.00928914i
$657$	−2.36982	−	2.36982i	−0.0924554	−	0.0924554i
$658$	1.79001	−	9.10024i	0.0697818	−	0.354764i
$659$	14.4411	−	5.98169i	0.562545	−	0.233014i	−0.0832448	−	0.996529i	$-0.526528\pi$
$659$	14.4411	−	5.98169i	0.562545	−	0.233014i	0.645790	+	0.763515i	$0.276528\pi$
$660$	30.0869	−	20.0577i	1.17113	−	0.780745i
$661$	14.2613	−	34.4299i	0.554702	−	1.33917i	−0.359210	−	0.933257i	$-0.616954\pi$
$661$	14.2613	−	34.4299i	0.554702	−	1.33917i	0.913912	−	0.405912i	$-0.133046\pi$
$662$	4.21533	+	20.9585i	0.163834	+	0.814576i
$663$		−	35.4684i		−	1.37748i
$664$	−0.202168	+	1.05143i	−0.00784563	+	0.0408036i
$665$	12.0212	+	18.1996i	0.466163	+	0.705749i
$666$	−2.80642	−	13.9534i	−0.108747	−	0.540684i
$667$	−4.10954	−	9.92130i	−0.159122	−	0.384154i
$668$	−9.70443	−	3.97136i	−0.375476	−	0.153656i
$669$	−28.3618	+	11.7479i	−1.09653	+	0.454199i
$670$	2.54854	−	1.04615i	0.0984586	−	0.0404164i
$671$		−	2.61331i		−	0.100886i
$672$	−39.2135	−	25.6018i	−1.51269	−	0.987611i
$673$	17.8153	+	17.8153i	0.686728	+	0.686728i	0.961507	−	0.274779i	$-0.0886047\pi$
$673$	17.8153	+	17.8153i	0.686728	+	0.686728i	−0.274779	+	0.961507i	$0.588605\pi$
$674$	9.30191	−	47.2901i	0.358296	−	1.82154i
$675$	12.3542	+	12.6195i	0.475512	+	0.485724i
$676$	−21.9836	+	9.21581i	−0.845523	+	0.354454i
$677$	15.5644	−	6.44700i	0.598190	−	0.247778i	−0.0629799	−	0.998015i	$-0.520060\pi$
$677$	15.5644	−	6.44700i	0.598190	−	0.247778i	0.661170	+	0.750237i	$0.270060\pi$
$678$	−0.485638	−	0.322999i	−0.0186508	−	0.0124047i
$679$	13.5503	+	13.5503i	0.520012	+	0.520012i
$680$	20.0397	+	8.27541i	0.768488	+	0.317348i
$681$	−17.0064	+	17.0064i	−0.651686	+	0.651686i
$682$	23.1160	−	4.64926i	0.885157	−	0.178029i
$683$	−16.0034	−	38.6356i	−0.612353	−	1.47835i	−0.860409	−	0.509605i	$-0.829792\pi$
$683$	−16.0034	−	38.6356i	−0.612353	−	1.47835i	0.248056	−	0.968746i	$-0.420208\pi$
$684$	4.45651	−	4.49464i	0.170399	−	0.171857i
$685$	2.70040	+	13.9630i	0.103177	+	0.533499i
$686$	9.16336	−	6.15103i	0.349859	−	0.234847i
$687$	3.77916	−	3.77916i	0.144184	−	0.144184i
$688$	5.72005	−	14.1492i	0.218075	−	0.539433i
$689$	−23.1117			−0.880485
$690$	9.00972	−	3.69841i	0.342994	−	0.140796i
$691$	−18.9490	−	45.7470i	−0.720855	−	1.74030i	−0.670902	−	0.741546i	$-0.734093\pi$
$691$	−18.9490	−	45.7470i	−0.720855	−	1.74030i	−0.0499527	−	0.998752i	$-0.515907\pi$
$692$	29.3321	−	29.5831i	1.11504	−	1.12458i
$693$	18.6554	−	7.72732i	0.708660	−	0.293537i
$694$	−2.25477	+	3.39010i	−0.0855897	+	0.128687i
$695$	−7.78392	+	38.0744i	−0.295261	+	1.44424i
$696$	41.4992	−	8.53072i	1.57302	−	0.323356i
$697$	−23.9331			−0.906529
$698$	35.0998	+	23.3449i	1.32855	+	0.883619i
$699$	−22.3732	−	9.26726i	−0.846230	−	0.350520i
$700$	−39.9414	−	0.254148i	−1.50964	−	0.00960587i
$701$	−6.57906	−	15.8833i	−0.248488	−	0.599902i	0.749588	−	0.661904i	$-0.230251\pi$
$701$	−6.57906	−	15.8833i	−0.248488	−	0.599902i	−0.998076	+	0.0620020i	$0.980251\pi$
$702$	−20.7026	+	13.8969i	−0.781369	+	0.524505i
$703$	13.4108	−	13.4108i	0.505797	−	0.505797i
$704$	−31.2060	+	0.398823i	−1.17612	+	0.0150312i
$705$	−6.34950	+	4.19399i	−0.239136	+	0.157955i
$706$	−0.0652216	+	0.331581i	−0.00245465	+	0.0124792i
$707$	−17.4510	+	42.1304i	−0.656312	+	1.58448i
$708$	17.4040	−	7.29600i	0.654083	−	0.274200i
$709$	16.5931	−	40.0592i	0.623166	−	1.50446i	−0.224800	−	0.974405i	$-0.572173\pi$
$709$	16.5931	−	40.0592i	0.623166	−	1.50446i	0.847966	−	0.530050i	$-0.177827\pi$
$710$	−40.3372	−	0.128332i	−1.51383	−	0.00481620i
$711$	3.67640	−	3.67640i	0.137876	−	0.137876i
$712$	12.7685	−	19.3763i	0.478521	−	0.726159i
$713$	6.35072			0.237836
$714$	33.4187	+	22.2269i	1.25066	+	0.831819i
$715$	36.0767	+	24.3838i	1.34919	+	0.911904i
$716$	0.00431855	+	1.01377i	0.000161392	+	0.0378863i
$717$	−8.70724	+	21.0211i	−0.325178	+	0.785048i
$718$	−1.41251	+	7.18109i	−0.0527146	+	0.267996i
$719$		−	23.8913i		−	0.890995i	−0.895283	−	0.445498i	$-0.853027\pi$
$719$		−	23.8913i		−	0.890995i	0.895283	−	0.445498i	$-0.146973\pi$
$720$	2.29774	+	11.3609i	0.0856316	+	0.423395i
$721$			52.3926i			1.95120i
$722$	−18.0892	−	3.55813i	−0.673211	−	0.132420i
$723$	6.76444	−	16.3308i	0.251572	−	0.607349i
$724$	−0.0945878	−	0.0937853i	−0.00351533	−	0.00348550i
$725$	25.8211	−	25.2782i	0.958970	−	0.938810i
$726$	6.84761	−	10.2956i	0.254139	−	0.382105i
$727$	−35.8816			−1.33078			−0.665388	−	0.746498i	$-0.731734\pi$
$727$	−35.8816			−1.33078			−0.665388	+	0.746498i	$0.731734\pi$
$728$	10.6484	−	55.3803i	0.394657	−	2.05253i
$729$	−5.25872	+	5.25872i	−0.194767	+	0.194767i
$730$	5.76443	+	5.80122i	0.213351	+	0.214713i
$731$	−5.00535	+	12.0840i	−0.185129	+	0.446942i
$732$	2.57004	+	1.05174i	0.0949915	+	0.0388735i
$733$	8.53556	−	20.6067i	0.315268	−	0.761125i	−0.684224	−	0.729272i	$-0.739859\pi$
$733$	8.53556	−	20.6067i	0.315268	−	0.761125i	0.999493	−	0.0318532i	$-0.0101409\pi$
$734$	−17.4493	−	3.43225i	−0.644064	−	0.126687i
$735$	−40.6564	−	8.31178i	−1.49963	−	0.306585i
$736$	−8.26118	−	1.55198i	−0.304511	−	0.0572068i
$737$	2.40312	−	2.40312i	0.0885200	−	0.0885200i
$738$	−7.13106	−	10.6233i	−0.262498	−	0.391050i
$739$	−5.39403	−	13.0223i	−0.198423	−	0.479034i	0.793081	−	0.609117i	$-0.208476\pi$
$739$	−5.39403	−	13.0223i	−0.198423	−	0.479034i	−0.991503	+	0.130082i	$0.958476\pi$
$740$	6.73989	+	34.0709i	0.247763	+	1.25247i
$741$	23.3437	+	9.66927i	0.857551	+	0.355209i
$742$	14.4833	−	21.7761i	0.531700	−	0.799426i
$743$	−11.4383			−0.419629			−0.209814	−	0.977741i	$-0.567286\pi$
$743$	−11.4383			−0.419629			−0.209814	+	0.977741i	$0.567286\pi$
$744$	−4.73089	+	24.6044i	−0.173443	+	0.902042i
$745$	−44.6072	−	9.11948i	−1.63428	−	0.334112i
$746$	5.83636	+	3.88178i	0.213684	+	0.142122i
$747$	0.453220	−	0.187730i	0.0165824	−	0.00686867i
$748$	26.7462	−	0.113936i	0.977939	−	0.00416593i
$749$	−23.9855	−	57.9062i	−0.876412	−	2.11585i
$750$	22.8509	+	23.4907i	0.834398	+	0.857758i
$751$	40.8048			1.48899			0.744494	−	0.667629i	$-0.232691\pi$
$751$	40.8048			1.48899			0.744494	+	0.667629i	$0.232691\pi$
$752$	6.56739	−	0.0559539i	0.239488	−	0.00204043i
$753$	6.53948	−	6.53948i	0.238312	−	0.238312i
$754$	28.4349	+	42.3602i	1.03554	+	1.54267i
$755$	9.56902	+	6.46759i	0.348252	+	0.235380i
$756$	−0.120193	−	28.2150i	−0.00437138	−	1.02617i
$757$	17.9768	+	43.3999i	0.653378	+	1.57739i	0.807844	+	0.589396i	$0.200634\pi$
$757$	17.9768	+	43.3999i	0.653378	+	1.57739i	−0.154466	+	0.987998i	$0.549366\pi$
$758$	1.44626	+	7.19074i	0.0525304	+	0.261179i
$759$	8.49562	−	8.49562i	0.308372	−	0.308372i
$760$	−10.9097	+	10.9332i	−0.395735	+	0.396589i
$761$	−29.1500	−	29.1500i	−1.05669	−	1.05669i	−0.998294	−	0.0583945i	$-0.981402\pi$
$761$	−29.1500	−	29.1500i	−1.05669	−	1.05669i	−0.0583945	−	0.998294i	$-0.518598\pi$
$762$	29.0765	−	43.7173i	1.05333	−	1.58371i
$763$	−16.8937	+	6.99760i	−0.611593	+	0.253330i
$764$	3.11668	+	1.27544i	0.112758	+	0.0461440i
$765$	−1.88619	−	9.75297i	−0.0681954	−	0.352619i
$766$	4.95647	+	0.974933i	0.179085	+	0.0352258i
$767$	16.0692	+	16.0692i	0.580226	+	0.580226i
$768$	12.1669	−	30.8499i	0.439034	−	1.11320i
$769$		−	16.3064i		−	0.588022i	−0.955802	−	0.294011i	$-0.905010\pi$
$769$		−	16.3064i		−	0.588022i	0.955802	−	0.294011i	$-0.0949903\pi$
$770$	−45.5828	+	18.7114i	−1.64269	+	0.674310i
$771$	−16.8941	+	6.99776i	−0.608425	+	0.252018i
$772$	27.1761	−	11.3926i	0.978088	−	0.410027i
$773$	1.77348	+	4.28156i	0.0637877	+	0.153997i	0.952559	−	0.304354i	$-0.0984404\pi$
$773$	1.77348	+	4.28156i	0.0637877	+	0.153997i	−0.888771	+	0.458351i	$0.848440\pi$
$774$	−6.85518	+	1.37877i	−0.246404	+	0.0495587i
$775$	7.96757	+	19.8286i	0.286204	+	0.712264i
$776$	−7.46678	+	11.3309i	−0.268042	+	0.406755i
$777$			64.2930i			2.30650i
$778$	21.8923	−	4.40314i	0.784876	−	0.157860i
$779$	6.52455	−	15.7517i	0.233766	−	0.564362i
$780$	−38.4995	+	25.6660i	−1.37850	+	0.918991i
$781$	−45.9735	+	19.0428i	−1.64506	+	0.681406i
$782$	7.06843	+	1.39035i	0.252767	+	0.0497190i
$783$	18.0493	+	18.0493i	0.645030	+	0.645030i
$784$	25.5400	+	25.1085i	0.912144	+	0.896732i
$785$	−33.6744	−	6.88438i	−1.20189	−	0.245714i
$786$	−4.04393	−	6.02435i	−0.144242	−	0.214882i
$787$	−5.30919	−	2.19914i	−0.189252	−	0.0783908i	0.286045	−	0.958216i	$-0.407659\pi$
$787$	−5.30919	−	2.19914i	−0.189252	−	0.0783908i	−0.475297	+	0.879825i	$0.657659\pi$
$788$	−0.207116	−	48.6199i	−0.00737820	−	1.73201i
$789$	6.86494	+	2.84355i	0.244398	+	0.101233i
$790$	−8.99968	+	8.94260i	−0.320194	+	0.318163i
$791$	0.561984	+	0.561984i	0.0199819	+	0.0199819i
$792$	8.01984	+	11.8381i	0.284973	+	0.420648i
$793$			3.34401i			0.118749i
$794$	23.7120	−	4.76913i	0.841506	−	0.169250i
$795$	−21.0673	+	4.07434i	−0.747180	+	0.144502i
$796$	−10.6827	+	4.47834i	−0.378639	+	0.158730i
$797$	−32.0963	−	13.2947i	−1.13691	−	0.470923i	−0.266785	−	0.963756i	$-0.585961\pi$
$797$	−32.0963	−	13.2947i	−1.13691	−	0.470923i	−0.870124	+	0.492833i	$0.835961\pi$
$798$	−23.7392	+	15.9353i	−0.840359	+	0.564103i
$799$	−5.62861			−0.199126
$800$	−5.51873	−	27.7406i	−0.195117	−	0.980780i
$801$	−10.6319			−0.375661
$802$	−35.0052	+	23.4978i	−1.23608	+	0.829735i
$803$	9.32088	+	3.86083i	0.328927	+	0.136246i
$804$	1.39618	+	3.33049i	0.0492396	+	0.117457i
$805$	−13.0299	+	2.51995i	−0.459245	+	0.0888164i
$806$	−29.5794	+	5.94924i	−1.04189	+	0.209553i
$807$		−	47.0247i		−	1.65535i
$808$	−31.7110	−	6.09733i	−1.11559	−	0.214503i
$809$	9.81472	+	9.81472i	0.345067	+	0.345067i	0.858268	−	0.513201i	$-0.171541\pi$
$809$	9.81472	+	9.81472i	0.345067	+	0.345067i	−0.513201	+	0.858268i	$0.671541\pi$
$810$	−25.1422	+	24.9828i	−0.883408	+	0.877805i
$811$	−43.3570	−	17.9591i	−1.52247	−	0.630628i	−0.544386	−	0.838835i	$-0.683237\pi$
$811$	−43.3570	−	17.9591i	−1.52247	−	0.630628i	−0.978085	+	0.208206i	$0.933237\pi$
$812$	−57.7315	+	0.245930i	−2.02598	+	0.00863046i
$813$	33.3437	+	13.8114i	1.16942	+	0.484388i
$814$	23.8794	+	35.5738i	0.836973	+	1.24686i
$815$	−39.7961	−	8.13590i	−1.39400	−	0.284988i
$816$	−10.6522	+	26.3493i	−0.372900	+	0.922410i
$817$	−6.58859	−	6.58859i	−0.230505	−	0.230505i
$818$	−29.7134	−	5.84460i	−1.03890	−	0.204351i
$819$	−23.8716	+	9.88795i	−0.834142	+	0.345513i
$820$	17.3187	+	25.9784i	0.604796	+	0.907204i
$821$	2.93216	−	7.07886i	0.102333	−	0.247054i	−0.864418	−	0.502774i	$-0.832313\pi$
$821$	2.93216	−	7.07886i	0.102333	−	0.247054i	0.966751	+	0.255720i	$0.0823126\pi$
$822$	−18.2767	+	3.67595i	−0.637474	+	0.128214i
$823$			41.5524i			1.44843i	0.689576	+	0.724213i	$0.257797\pi$
$823$			41.5524i			1.44843i	−0.689576	+	0.724213i	$0.742203\pi$
$824$	−36.3409	+	7.47036i	−1.26599	+	0.260242i
$825$	37.1841	+	15.8670i	1.29458	+	0.552418i
$826$	−25.2106	+	5.07056i	−0.877191	+	0.176427i
$827$	11.0325	+	26.6348i	0.383637	+	0.926181i	0.991256	+	0.131953i	$0.0421247\pi$
$827$	11.0325	+	26.6348i	0.383637	+	0.926181i	−0.607619	+	0.794229i	$0.707875\pi$
$828$	1.48895	+	3.55178i	0.0517447	+	0.123433i
$829$	15.5518	−	6.44175i	0.540135	−	0.223731i	−0.0959005	−	0.995391i	$-0.530573\pi$
$829$	15.5518	−	6.44175i	0.540135	−	0.223731i	0.636036	+	0.771660i	$0.280573\pi$
$830$	−1.10740	+	0.454579i	−0.0384385	+	0.0157787i
$831$		−	18.8193i		−	0.652834i
$832$	39.9315	−	0.510338i	1.38438	−	0.0176928i
$833$	−21.7043	−	21.7043i	−0.752008	−	0.752008i
$834$	−49.9849	−	9.83198i	−1.73083	−	0.340454i
$835$	−2.22599	−	11.5100i	−0.0770336	−	0.398319i
$836$	−7.21648	+	17.6342i	−0.249587	+	0.609892i
$837$	−13.9464	+	5.77677i	−0.482057	+	0.199674i
$838$	−10.8262	+	16.2775i	−0.373986	+	0.562298i
$839$	−10.7757	−	10.7757i	−0.372019	−	0.372019i	0.496193	−	0.868212i	$-0.334731\pi$
$839$	−10.7757	−	10.7757i	−0.372019	−	0.372019i	−0.868212	+	0.496193i	$0.834731\pi$
$840$	−0.0564645	−	52.3587i	−0.00194821	−	1.80655i
$841$	16.4251	−	16.4251i	0.566384	−	0.566384i
$842$	−3.63134	−	18.0549i	−0.125144	−	0.622213i
$843$	23.5663	+	56.8941i	0.811667	+	1.95954i
$844$	31.4229	−	0.133859i	1.08162	−	0.00460760i
$845$	−22.0803	−	14.9238i	−0.759586	−	0.513396i
$846$	−1.67709	−	2.49841i	−0.0576596	−	0.0858971i
$847$	−11.9141	+	11.9141i	−0.409375	+	0.409375i
$848$	17.1696	+	6.94109i	0.589606	+	0.238358i
$849$	66.2422			2.27343
$850$	4.52696	+	23.8138i	0.155273	+	0.816807i
$851$	4.41614	+	10.6615i	0.151383	+	0.365471i
$852$	−0.225248	−	52.8763i	−0.00771686	−	1.81151i
$853$	19.6079	−	8.12187i	0.671363	−	0.278088i	−0.0208484	−	0.999783i	$-0.506637\pi$
$853$	19.6079	−	8.12187i	0.671363	−	0.278088i	0.692211	+	0.721695i	$0.256637\pi$
$854$	−3.15077	−	2.09558i	−0.107817	−	0.0717093i
$855$	6.93317	+	1.41742i	0.237109	+	0.0484746i
$856$	36.7453	−	24.8935i	1.25593	−	0.850843i
$857$	−4.25465			−0.145336			−0.0726680	−	0.997356i	$-0.523151\pi$
$857$	−4.25465			−0.145336			−0.0726680	+	0.997356i	$0.523151\pi$
$858$	−31.6111	+	47.5282i	−1.07918	+	1.62259i
$859$	−31.3404	−	12.9816i	−1.06932	−	0.442927i	−0.222570	−	0.974917i	$-0.571444\pi$
$859$	−31.3404	−	12.9816i	−1.06932	−	0.442927i	−0.846751	+	0.531990i	$0.821444\pi$
$860$	16.7387	−	3.31124i	0.570785	−	0.112912i
$861$	22.1180	+	53.3975i	0.753778	+	1.81978i
$862$	0.271756	+	0.404842i	0.00925604	+	0.0137890i
$863$	−7.27680	+	7.27680i	−0.247705	+	0.247705i	−0.820028	−	0.572323i	$-0.806042\pi$
$863$	−7.27680	+	7.27680i	−0.247705	+	0.247705i	0.572323	+	0.820028i	$0.306042\pi$
$864$	19.5535	−	4.10638i	0.665224	−	0.139702i
$865$	45.6331	+	9.32922i	1.55157	+	0.317203i
$866$	37.2382	+	7.32473i	1.26541	+	0.248904i
$867$	−4.16271	+	10.0497i	−0.141373	+	0.341305i
$868$	12.9310	−	31.5983i	0.438907	−	1.07252i
$869$	−5.98947	+	14.4599i	−0.203179	+	0.490518i
$870$	33.3872	+	33.6004i	1.13193	+	1.13916i
$871$	−3.07505	+	3.07505i	−0.104194	+	0.104194i
$872$	−7.26250	−	10.7202i	−0.245939	−	0.363031i
$873$	6.21734			0.210425
$874$	−2.84204	+	4.27309i	−0.0961334	+	0.144539i
$875$	−24.2152	−	37.5213i	−0.818623	−	1.26845i
$876$	−7.54817	+	7.61275i	−0.255029	+	0.257211i
$877$	9.34978	−	22.5724i	0.315720	−	0.762215i	−0.683752	−	0.729714i	$-0.739653\pi$
$877$	9.34978	−	22.5724i	0.315720	−	0.762215i	0.999472	−	0.0325003i	$-0.0103470\pi$
$878$	22.4053	+	4.40711i	0.756143	+	0.148733i
$879$		−	28.5555i		−	0.963153i
$880$	−19.4781	−	28.9495i	−0.656606	−	0.975888i
$881$		−	44.4215i		−	1.49660i	−0.663362	−	0.748299i	$-0.730871\pi$
$881$		−	44.4215i		−	1.49660i	0.663362	−	0.748299i	$-0.269129\pi$
$882$	3.16705	−	16.1010i	0.106640	−	0.542148i
$883$	15.5378	−	37.5117i	0.522890	−	1.26237i	−0.413210	−	0.910636i	$-0.635593\pi$
$883$	15.5378	−	37.5117i	0.522890	−	1.26237i	0.936100	−	0.351733i	$-0.114407\pi$
$884$	−34.2247	+	0.145794i	−1.15110	+	0.00490358i
$885$	17.4806	+	11.8149i	0.587604	+	0.397155i
$886$	41.1029	+	27.3376i	1.38088	+	0.918425i
$887$	42.0020			1.41029			0.705145	−	0.709064i	$-0.250882\pi$
$887$	42.0020			1.41029			0.705145	+	0.709064i	$0.250882\pi$
$888$	−44.5953	+	9.16717i	−1.49652	+	0.307630i
$889$	−50.5901	+	50.5901i	−1.69674	+	1.69674i
$890$	25.9440	+	0.0825401i	0.869645	+	0.00276675i
$891$	−16.7327	+	40.3962i	−0.560566	+	1.35333i
$892$	11.4525	+	27.3191i	0.383459	+	0.914711i
$893$	1.53445	−	3.70449i	0.0513485	−	0.123966i
$894$	11.5189	−	58.5612i	0.385251	−	1.95858i
$895$	−0.945750	+	0.624690i	−0.0316129	+	0.0208811i
$896$	−24.5429	+	37.9438i	−0.819922	+	1.26761i
$897$	−10.8711	+	10.8711i	−0.362975	+	0.362975i
$898$	−27.0029	+	18.1261i	−0.901098	+	0.604874i
$899$	11.8200	+	28.5361i	0.394220	+	0.951731i
$900$	−9.22155	+	9.10494i	−0.307385	+	0.303498i
$901$	−14.6635	−	6.07382i	−0.488512	−	0.202348i
$902$	32.0707	+	21.3303i	1.06784	+	0.710220i
$903$	31.5865			1.05113
$904$	−0.309677	+	0.469937i	−0.0102997	+	0.0156299i
$905$	0.0298289	−	0.145905i	0.000991546	−	0.00485006i
$906$	−8.38455	+	12.6064i	−0.278558	+	0.418820i
$907$	1.02594	−	0.424958i	0.0340657	−	0.0141105i	−0.365586	−	0.930778i	$-0.619131\pi$
$907$	1.02594	−	0.424958i	0.0340657	−	0.0141105i	0.399651	+	0.916667i	$0.369131\pi$
$908$	16.4800	+	16.3402i	0.546908	+	0.542268i
$909$	5.66189	+	13.6690i	0.187793	+	0.453372i
$910$	58.3282	−	23.9432i	1.93356	−	0.793710i
$911$	18.7806			0.622228			0.311114	−	0.950373i	$-0.399298\pi$
$911$	18.7806			0.622228			0.311114	+	0.950373i	$0.399298\pi$
$912$	−14.4380	−	14.1940i	−0.478089	−	0.470011i
$913$	−1.04421	+	1.04421i	−0.0345585	+	0.0345585i
$914$	45.1173	−	30.2856i	1.49235	−	1.00176i
$915$	0.589513	+	3.04821i	0.0194887	+	0.100771i
$916$	−3.66219	−	3.63112i	−0.121002	−	0.119976i
$917$	3.78367	+	9.13458i	0.124948	+	0.301650i
$918$	−16.7872	+	3.37636i	−0.554059	+	0.111437i
$919$	−21.4817	+	21.4817i	−0.708616	+	0.708616i	−0.966244	−	0.257628i	$-0.917059\pi$
$919$	−21.4817	+	21.4817i	−0.708616	+	0.708616i	0.257628	+	0.966244i	$0.417059\pi$
$920$	−3.60576	−	8.67860i	−0.118879	−	0.286125i
$921$	−29.4359	−	29.4359i	−0.969946	−	0.969946i
$922$	−37.2183	−	24.7539i	−1.22572	−	0.815228i
$923$	58.8281	−	24.3674i	1.93635	−	0.802062i
$924$	−24.9720	−	59.5687i	−0.821518	−	1.95967i
$925$	−27.7475	+	27.1642i	−0.912332	+	0.893152i
$926$	−3.29742	+	16.7638i	−0.108360	+	0.550892i
$927$	12.0198	+	12.0198i	0.394780	+	0.394780i
$928$	−8.40218	−	40.0090i	−0.275815	−	1.31336i
$929$			23.9733i			0.786539i	0.919423	+	0.393270i	$0.128656\pi$
$929$			23.9733i			0.786539i	−0.919423	+	0.393270i	$0.871344\pi$
$930$	−25.9141	+	10.6375i	−0.849758	+	0.348818i
$931$	20.2017	−	8.36782i	0.662084	−	0.274244i
$932$	−8.85036	+	21.6268i	−0.289903	+	0.708408i
$933$	−1.37542	−	3.32057i	−0.0450293	−	0.108710i
$934$	0.251762	+	1.25175i	0.00823789	+	0.0409585i
$935$	16.4812	+	24.9517i	0.538992	+	0.816008i
$936$	−10.2623	−	15.1481i	−0.335433	−	0.495132i
$937$			34.5342i			1.12818i	0.825712	+	0.564092i	$0.190774\pi$
$937$			34.5342i			1.12818i	−0.825712	+	0.564092i	$0.809226\pi$
$938$	−0.970317	−	4.82439i	−0.0316820	−	0.157522i
$939$	15.0007	−	36.2148i	0.489528	−	1.18182i
$940$	4.07304	+	6.10963i	0.132848	+	0.199274i
$941$	29.0306	−	12.0249i	0.946369	−	0.391999i	0.144504	−	0.989504i	$-0.453841\pi$
$941$	29.0306	−	12.0249i	0.946369	−	0.391999i	0.801865	+	0.597505i	$0.203841\pi$
$942$	8.69575	−	44.2084i	0.283323	−	1.44039i
$943$	7.33550	+	7.33550i	0.238877	+	0.238877i
$944$	−7.11171	−	16.7638i	−0.231467	−	0.545615i
$945$	26.3219	−	17.3862i	0.856251	−	0.565574i
$946$	17.4771	−	11.7317i	0.568228	−	0.381431i
$947$	−4.78647	−	1.98262i	−0.155539	−	0.0644265i	0.303556	−	0.952814i	$-0.401826\pi$
$947$	−4.78647	−	1.98262i	−0.155539	−	0.0644265i	−0.459095	+	0.888387i	$0.651826\pi$
$948$	−11.8100	−	11.7098i	−0.383570	−	0.380316i
$949$	−11.9271	−	4.94036i	−0.387169	−	0.160371i
$950$	−16.9073	−	3.51260i	−0.548545	−	0.113964i
$951$	−10.9674	−	10.9674i	−0.355641	−	0.355641i
$952$	21.3101	−	32.3383i	0.690666	−	1.04809i
$953$		−	32.2417i		−	1.04441i	−0.852820	−	0.522205i	$-0.825109\pi$
$953$		−	32.2417i		−	1.04441i	0.852820	−	0.522205i	$-0.174891\pi$
$954$	−1.67309	−	8.31854i	−0.0541682	−	0.269323i
$955$	0.714901	+	3.69655i	0.0231336	+	0.119618i
$956$	20.3198	+	8.31552i	0.657191	+	0.268943i
$957$	53.9860	+	22.3617i	1.74512	+	0.722852i
$958$	−2.70802	−	4.03421i	−0.0874921	−	0.130339i
$959$	25.4038			0.820333
$960$	36.3093	−	7.50470i	1.17188	−	0.242213i
$961$	12.7338			0.410767
$962$	−30.5563	−	45.5206i	−0.985175	−	1.46764i
$963$	−18.7874	−	7.78198i	−0.605414	−	0.250771i
$964$	−15.7860	−	6.46012i	−0.508432	−	0.208067i
$965$	27.2956	+	18.4488i	0.878678	+	0.593889i
$966$	−3.43031	−	17.0554i	−0.110368	−	0.548749i
$967$		−	21.4034i		−	0.688286i	−0.938917	−	0.344143i	$-0.888169\pi$
$967$		−	21.4034i		−	0.688286i	0.938917	−	0.344143i	$-0.111831\pi$
$968$	−9.96273	−	6.56519i	−0.320214	−	0.211013i
$969$	12.2696	+	12.2696i	0.394156	+	0.394156i
$970$	−15.1715	−	0.0482678i	−0.487128	−	0.00154978i
$971$	22.0598	+	9.13746i	0.707932	+	0.293235i	0.707449	−	0.706765i	$-0.249846\pi$
$971$	22.0598	+	9.13746i	0.707932	+	0.293235i	0.000483467		1.00000i	$0.499846\pi$
$972$	−17.9446	−	17.7924i	−0.575573	−	0.570690i
$973$	64.1338	+	26.5651i	2.05603	+	0.851637i
$974$	−23.4613	+	15.7487i	−0.751749	+	0.504622i
$975$	−47.5811	−	20.3035i	−1.52381	−	0.650234i
$976$	1.00430	−	2.48425i	0.0321469	−	0.0795190i
$977$	−24.5451	−	24.5451i	−0.785266	−	0.785266i	0.195448	−	0.980714i	$-0.437384\pi$
$977$	−24.5451	−	24.5451i	−0.785266	−	0.785266i	−0.980714	+	0.195448i	$0.937384\pi$
$978$	10.2766	−	52.2451i	0.328608	−	1.67061i
$979$	29.5691	−	12.2479i	0.945034	−	0.391446i
$980$	−7.85322	+	39.2650i	−0.250862	+	1.25427i
$981$	−2.27033	+	5.48107i	−0.0724862	+	0.174997i
$982$	3.48561	+	17.3303i	0.111230	+	0.553034i
$983$		−	17.6379i		−	0.562563i	−0.959625	−	0.281281i	$-0.909241\pi$
$983$		−	17.6379i		−	0.562563i	0.959625	−	0.281281i	$-0.0907594\pi$
$984$	−33.8842	+	22.9552i	−1.08019	+	0.731786i
$985$	45.3578	−	29.9599i	1.44522	−	0.954600i
$986$	6.90847	+	34.3487i	0.220011	+	1.09389i
$987$	5.20173	+	12.5581i	0.165573	+	0.399728i
$988$	9.23427	−	22.5649i	0.293781	−	0.717885i
$989$	5.23789	−	2.16960i	0.166555	−	0.0689894i
$990$	−6.16478	+	14.7502i	−0.195930	+	0.468792i
$991$		−	27.9699i		−	0.888493i	−0.895905	−	0.444246i	$-0.853472\pi$
$991$		−	27.9699i		−	0.888493i	0.895905	−	0.444246i	$-0.146528\pi$
$992$	23.7612	+	4.46387i	0.754418	+	0.141728i
$993$	−22.1549	−	22.1549i	−0.703063	−	0.703063i
$994$	−13.9064	+	70.6987i	−0.441083	+	2.24243i
$995$	−10.7297	−	7.25210i	−0.340155	−	0.229907i
$996$	−0.606676	−	1.44718i	−0.0192233	−	0.0458556i
$997$	17.4929	−	7.24580i	0.554006	−	0.229477i	−0.0880748	−	0.996114i	$-0.528071\pi$
$997$	17.4929	−	7.24580i	0.554006	−	0.229477i	0.642081	+	0.766637i	$0.278071\pi$
$998$	−25.0627	−	16.6693i	−0.793347	−	0.527657i
$999$	−19.3959	−	19.3959i	−0.613660	−	0.613660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.123.16	✓	88
4.3	odd	2		640.2.u.a.143.19		88
5.2	odd	4		160.2.ba.a.27.5	yes	88
5.3	odd	4		800.2.bb.b.507.18		88
5.4	even	2		800.2.v.b.443.7		88
20.7	even	4		640.2.ba.a.527.19		88
32.13	even	8		640.2.ba.a.623.19		88
32.19	odd	8		160.2.ba.a.83.5	yes	88
160.19	odd	8		800.2.bb.b.243.18		88
160.77	odd	8		640.2.u.a.367.19		88
160.83	even	8		800.2.v.b.307.7		88
160.147	even	8	inner	160.2.u.a.147.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.123.16	✓	88	1.1	even	1	trivial
160.2.u.a.147.16	yes	88	160.147	even	8	inner
160.2.ba.a.27.5	yes	88	5.2	odd	4
160.2.ba.a.83.5	yes	88	32.19	odd	8
640.2.u.a.143.19		88	4.3	odd	2
640.2.u.a.367.19		88	160.77	odd	8
640.2.ba.a.527.19		88	20.7	even	4
640.2.ba.a.623.19		88	32.13	even	8
800.2.v.b.307.7		88	160.83	even	8
800.2.v.b.443.7		88	5.4	even	2
800.2.bb.b.243.18		88	160.19	odd	8
800.2.bb.b.507.18		88	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.788198 + 1.17420i) q^{2} +(-1.91488 - 0.793171i) q^{3} +(-0.757489 + 1.85100i) q^{4} +(-2.19539 + 0.424581i) q^{5} +(-0.577967 - 2.87363i) q^{6} +3.99422i q^{7} +(-2.77050 + 0.569513i) q^{8} +(0.916343 + 0.916343i) q^{9} +(-2.22894 - 2.24317i) q^{10} +(-3.60412 - 1.49288i) q^{11} +(2.91867 - 2.94364i) q^{12} +(4.61187 + 1.91030i) q^{13} +(-4.69001 + 3.14824i) q^{14} +(4.54068 + 0.928296i) q^{15} +(-2.85242 - 2.80423i) q^{16} +(2.42403 + 2.42403i) q^{17} +(-0.353710 + 1.79823i) q^{18} +(-2.25621 + 0.934554i) q^{19} +(0.877082 - 4.38529i) q^{20} +(3.16810 - 7.64847i) q^{21} +(-1.08783 - 5.40864i) q^{22} -1.48593i q^{23} +(5.75690 + 1.10693i) q^{24} +(4.63946 - 1.86424i) q^{25} +(1.39199 + 6.92095i) q^{26} +(1.35164 + 3.26315i) q^{27} +(-7.39331 - 3.02558i) q^{28} +(6.67682 - 2.76563i) q^{29} +(2.48895 + 6.06335i) q^{30} +4.27390i q^{31} +(1.04445 - 5.55960i) q^{32} +(5.71737 + 5.71737i) q^{33} +(-0.935678 + 4.75690i) q^{34} +(-1.69587 - 8.76887i) q^{35} +(-2.39027 + 1.00203i) q^{36} +(-7.17496 + 2.97197i) q^{37} +(-2.87570 - 1.91263i) q^{38} +(-7.31600 - 7.31600i) q^{39} +(5.84051 - 2.42660i) q^{40} +(-4.93663 + 4.93663i) q^{41} +(11.4779 - 2.30853i) q^{42} +(1.46010 + 3.52499i) q^{43} +(5.49340 - 5.54040i) q^{44} +(-2.40079 - 1.62267i) q^{45} +(1.74478 - 1.17121i) q^{46} +(-1.16100 + 1.16100i) q^{47} +(3.23783 + 7.63223i) q^{48} -8.95380 q^{49} +(5.84580 + 3.97827i) q^{50} +(-2.71906 - 6.56440i) q^{51} +(-7.02941 + 7.08955i) q^{52} +(-4.27746 + 1.77178i) q^{53} +(-2.76623 + 4.15910i) q^{54} +(8.54630 + 1.74720i) q^{55} +(-2.27476 - 11.0660i) q^{56} +5.06165 q^{57} +(8.51006 + 5.66006i) q^{58} +(4.20594 + 1.74216i) q^{59} +(-5.15779 + 7.70164i) q^{60} +(0.256357 + 0.618901i) q^{61} +(-5.01841 + 3.36868i) q^{62} +(-3.66008 + 3.66008i) q^{63} +(7.35131 - 3.15567i) q^{64} +(-10.9359 - 2.23574i) q^{65} +(-2.20692 + 11.2198i) q^{66} +(-0.333385 + 0.804862i) q^{67} +(-6.32305 + 2.65071i) q^{68} +(-1.17860 + 2.84539i) q^{69} +(8.95972 - 8.90289i) q^{70} +(9.01971 - 9.01971i) q^{71} +(-3.06059 - 2.01686i) q^{72} -2.58617 q^{73} +(-9.14497 - 6.08234i) q^{74} +(-10.3627 - 0.110085i) q^{75} +(-0.0208061 - 4.88417i) q^{76} +(5.96288 - 14.3957i) q^{77} +(2.82399 - 14.3569i) q^{78} -4.01204i q^{79} +(7.45279 + 4.94529i) q^{80} -11.2083i q^{81} +(-9.68763 - 1.90555i) q^{82} +(0.144864 - 0.349732i) q^{83} +(11.7575 + 11.6578i) q^{84} +(-6.35088 - 4.29249i) q^{85} +(-2.98819 + 4.49283i) q^{86} -14.9790 q^{87} +(10.8354 + 2.08341i) q^{88} +(-5.80128 + 5.80128i) q^{89} +(0.0130376 - 4.09799i) q^{90} +(-7.63016 + 18.4208i) q^{91} +(2.75046 + 1.12558i) q^{92} +(3.38993 - 8.18402i) q^{93} +(-2.27835 - 0.448149i) q^{94} +(4.55647 - 3.00966i) q^{95} +(-6.40971 + 9.81756i) q^{96} +(3.39247 - 3.39247i) q^{97} +(-7.05737 - 10.5135i) q^{98} +(-1.93463 - 4.67060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24}+ \cdots - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

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