LMFDB - Embedded newform 700.2.bj.a.323.56

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(127,700)] 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("700.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			323.56
Character	$\chi$	$=$	700.323
Dual form			700.2.bj.a.687.56

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.527914 + 1.31199i) q^{2} +(-1.24589 - 2.44519i) q^{3} +(-1.44261 + 1.38523i) q^{4} +(-1.65605 - 1.50250i) q^{5} +(2.55034 - 2.92544i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.57898 - 1.16141i) q^{8} +(-2.66338 + 3.66583i) q^{9} +(1.09701 - 2.96590i) q^{10} +(-2.05862 - 2.83344i) q^{11} +(5.18450 + 1.80163i) q^{12} +(0.978870 + 6.18034i) q^{13} +(0.554423 - 1.30101i) q^{14} +(-1.61066 + 5.92130i) q^{15} +(0.162271 - 3.99671i) q^{16} +(2.62303 + 1.33650i) q^{17} +(-6.21555 - 1.55908i) q^{18} +(1.98500 + 6.10921i) q^{19} +(4.47035 - 0.126473i) q^{20} +(-0.848037 + 2.60999i) q^{21} +(2.63067 - 4.19669i) q^{22} +(-0.192546 + 1.21569i) q^{23} +(0.373256 + 7.75309i) q^{24} +(0.484971 + 4.97642i) q^{25} +(-7.59176 + 4.54695i) q^{26} +(4.15038 + 0.657356i) q^{27} +(1.99959 + 0.0405761i) q^{28} +(-2.17885 - 0.707951i) q^{29} +(-8.61896 + 1.01277i) q^{30} +(8.96116 - 2.91166i) q^{31} +(5.32929 - 1.89702i) q^{32} +(-4.36351 + 8.56387i) q^{33} +(-0.368736 + 4.14693i) q^{34} +(0.108571 + 2.23343i) q^{35} +(-1.23579 - 8.97777i) q^{36} +(-9.22506 + 1.46111i) q^{37} +(-6.96728 + 5.82943i) q^{38} +(13.8926 - 10.0935i) q^{39} +(2.52589 + 5.79827i) q^{40} +(2.24507 + 1.63114i) q^{41} +(-3.87196 + 0.265237i) q^{42} +(1.19017 - 1.19017i) q^{43} +(6.89476 + 1.23591i) q^{44} +(9.91860 - 2.06904i) q^{45} +(-1.69661 + 0.389161i) q^{46} +(-6.22666 + 3.17264i) q^{47} +(-9.97490 + 4.58267i) q^{48} +1.00000i q^{49} +(-6.27298 + 3.26340i) q^{50} -8.07894i q^{51} +(-9.97333 - 7.55989i) q^{52} +(-8.46224 + 4.31173i) q^{53} +(1.32860 + 5.79227i) q^{54} +(-0.848093 + 7.78539i) q^{55} +(1.00238 + 2.64485i) q^{56} +(12.4651 - 12.4651i) q^{57} +(-0.221423 - 3.23236i) q^{58} +(-5.93237 - 4.31012i) q^{59} +(-5.87881 - 10.7733i) q^{60} +(-3.53233 + 2.56639i) q^{61} +(8.55078 + 10.2198i) q^{62} +(4.47543 - 0.708838i) q^{63} +(5.30227 + 5.99049i) q^{64} +(7.66493 - 11.7057i) q^{65} +(-13.5392 - 1.20388i) q^{66} +(-4.51785 + 8.86679i) q^{67} +(-5.63538 + 1.70545i) q^{68} +(3.21249 - 1.04380i) q^{69} +(-2.87291 + 1.32150i) q^{70} +(-5.52173 - 1.79412i) q^{71} +(11.1263 - 6.36083i) q^{72} +(-1.32532 - 0.209909i) q^{73} +(-6.78699 - 11.3318i) q^{74} +(11.5641 - 7.38592i) q^{75} +(-11.3263 - 6.06354i) q^{76} +(-0.547885 + 3.45921i) q^{77} +(20.5767 + 12.8983i) q^{78} +(-2.06946 + 6.36915i) q^{79} +(-6.27379 + 6.37492i) q^{80} +(0.637113 + 1.96083i) q^{81} +(-0.954829 + 3.80660i) q^{82} +(-1.66794 - 0.849858i) q^{83} +(-2.39205 - 4.93994i) q^{84} +(-2.33576 - 6.15441i) q^{85} +(2.18980 + 0.933182i) q^{86} +(0.983526 + 6.20974i) q^{87} +(2.01835 + 9.69828i) q^{88} +(5.37994 + 7.40486i) q^{89} +(7.95072 + 11.9208i) q^{90} +(3.67800 - 5.06233i) q^{91} +(-1.40624 - 2.02049i) q^{92} +(-18.2842 - 18.2842i) q^{93} +(-7.44960 - 6.49441i) q^{94} +(5.89185 - 13.0996i) q^{95} +(-11.2783 - 10.6677i) q^{96} +(4.85444 + 9.52738i) q^{97} +(-1.31199 + 0.527914i) q^{98} +15.8698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.527914	+	1.31199i	0.373291	+	0.927714i
$2$	0.527914	+	1.31199i	0.373291	+	0.927714i
$3$	−1.24589	−	2.44519i	−0.719314	−	1.41173i	−0.903389	−	0.428821i	$-0.858929\pi$
$3$	−1.24589	−	2.44519i	−0.719314	−	1.41173i	0.184075	−	0.982912i	$-0.441071\pi$
$4$	−1.44261	+	1.38523i	−0.721307	+	0.692615i
$5$	−1.65605	−	1.50250i	−0.740606	−	0.671940i
$5$	−1.65605	−	1.50250i	−0.740606	−	0.671940i
$6$	2.55034	−	2.92544i	1.04117	−	1.19431i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−2.57898	−	1.16141i	−0.911807	−	0.410619i
$9$	−2.66338	+	3.66583i	−0.887794	+	1.22194i
$10$	1.09701	−	2.96590i	0.346906	−	0.937900i
$11$	−2.05862	−	2.83344i	−0.620696	−	0.854315i	0.376707	−	0.926332i	$-0.377056\pi$
$11$	−2.05862	−	2.83344i	−0.620696	−	0.854315i	−0.997403	+	0.0720172i	$0.977056\pi$
$12$	5.18450	+	1.80163i	1.49663	+	0.520085i
$13$	0.978870	+	6.18034i	0.271490	+	1.71412i	0.626639	+	0.779309i	$0.284430\pi$
$13$	0.978870	+	6.18034i	0.271490	+	1.71412i	−0.355150	+	0.934809i	$0.615570\pi$
$14$	0.554423	−	1.30101i	0.148176	−	0.347708i
$15$	−1.61066	+	5.92130i	−0.415871	+	1.52887i
$16$	0.162271	−	3.99671i	0.0405677	−	0.999177i
$17$	2.62303	+	1.33650i	0.636178	+	0.324149i	0.742163	−	0.670219i	$-0.233800\pi$
$17$	2.62303	+	1.33650i	0.636178	+	0.324149i	−0.105986	+	0.994368i	$0.533800\pi$
$18$	−6.21555	−	1.55908i	−1.46502	−	0.367478i
$19$	1.98500	+	6.10921i	0.455390	+	1.40155i	0.870676	+	0.491857i	$0.163682\pi$
$19$	1.98500	+	6.10921i	0.455390	+	1.40155i	−0.415286	+	0.909691i	$0.636318\pi$
$20$	4.47035	−	0.126473i	0.999600	−	0.0282803i
$21$	−0.848037	+	2.60999i	−0.185057	+	0.569546i
$22$	2.63067	−	4.19669i	0.560860	−	0.894737i
$23$	−0.192546	+	1.21569i	−0.0401486	+	0.253489i	−0.999597	−	0.0283968i	$-0.990960\pi$
$23$	−0.192546	+	1.21569i	−0.0401486	+	0.253489i	0.959448	+	0.281885i	$0.0909598\pi$
$24$	0.373256	+	7.75309i	0.0761905	+	1.58259i
$25$	0.484971	+	4.97642i	0.0969942	+	0.995285i
$26$	−7.59176	+	4.54695i	−1.48887	+	0.891731i
$27$	4.15038	+	0.657356i	0.798742	+	0.126508i
$28$	1.99959	+	0.0405761i	0.377887	+	0.00766815i
$29$	−2.17885	−	0.707951i	−0.404602	−	0.131463i	0.0996440	−	0.995023i	$-0.468230\pi$
$29$	−2.17885	−	0.707951i	−0.404602	−	0.131463i	−0.504246	+	0.863560i	$0.668230\pi$
$30$	−8.61896	+	1.01277i	−1.57360	+	0.184906i
$31$	8.96116	−	2.91166i	1.60947	−	0.522949i	0.640047	−	0.768336i	$-0.278915\pi$
$31$	8.96116	−	2.91166i	1.60947	−	0.522949i	0.969425	+	0.245386i	$0.0789148\pi$
$32$	5.32929	−	1.89702i	0.942094	−	0.335349i
$33$	−4.36351	+	8.56387i	−0.759590	+	1.49078i
$34$	−0.368736	+	4.14693i	−0.0632377	+	0.711193i
$35$	0.108571	+	2.23343i	0.0183518	+	0.377519i
$36$	−1.23579	−	8.97777i	−0.205965	−	1.49630i
$37$	−9.22506	+	1.46111i	−1.51659	+	0.240204i	−0.858531	−	0.512762i	$-0.828622\pi$
$37$	−9.22506	+	1.46111i	−1.51659	+	0.240204i	−0.658059	+	0.752966i	$0.728622\pi$
$38$	−6.96728	+	5.82943i	−1.13024	+	0.945658i
$39$	13.8926	−	10.0935i	2.22459	−	1.61626i
$40$	2.52589	+	5.79827i	0.399378	+	0.916786i
$41$	2.24507	+	1.63114i	0.350621	+	0.254741i	0.749130	−	0.662423i	$-0.230472\pi$
$41$	2.24507	+	1.63114i	0.350621	+	0.254741i	−0.398508	+	0.917165i	$0.630472\pi$
$42$	−3.87196	+	0.265237i	−0.597456	+	0.0409269i
$43$	1.19017	−	1.19017i	0.181500	−	0.181500i	−0.610509	−	0.792009i	$-0.709035\pi$
$43$	1.19017	−	1.19017i	0.181500	−	0.181500i	0.792009	+	0.610509i	$0.209035\pi$
$44$	6.89476	+	1.23591i	1.03942	+	0.186320i
$45$	9.91860	−	2.06904i	1.47858	−	0.308435i
$46$	−1.69661	+	0.389161i	−0.250152	+	0.0573786i
$47$	−6.22666	+	3.17264i	−0.908252	+	0.462777i	−0.844724	−	0.535203i	$-0.820235\pi$
$47$	−6.22666	+	3.17264i	−0.908252	+	0.462777i	−0.0635281	+	0.997980i	$0.520235\pi$
$48$	−9.97490	+	4.58267i	−1.43975	+	0.661451i
$49$			1.00000i			0.142857i
$50$	−6.27298	+	3.26340i	−0.887133	+	0.461514i
$51$		−	8.07894i		−	1.13128i
$52$	−9.97333	−	7.55989i	−1.38305	−	1.04837i
$53$	−8.46224	+	4.31173i	−1.16238	+	0.592261i	−0.925302	−	0.379230i	$-0.876189\pi$
$53$	−8.46224	+	4.31173i	−1.16238	+	0.592261i	−0.237076	+	0.971491i	$0.576189\pi$
$54$	1.32860	+	5.79227i	0.180800	+	0.788229i
$55$	−0.848093	+	7.78539i	−0.114357	+	1.04978i
$56$	1.00238	+	2.64485i	0.133948	+	0.353433i
$57$	12.4651	−	12.4651i	1.65104	−	1.65104i
$58$	−0.221423	−	3.23236i	−0.0290742	−	0.424429i
$59$	−5.93237	−	4.31012i	−0.772329	−	0.561130i	0.130338	−	0.991470i	$-0.458394\pi$
$59$	−5.93237	−	4.31012i	−0.772329	−	0.561130i	−0.902667	+	0.430339i	$0.858394\pi$
$60$	−5.87881	−	10.7733i	−0.758951	−	1.39083i
$61$	−3.53233	+	2.56639i	−0.452269	+	0.328592i	−0.790491	−	0.612474i	$-0.790174\pi$
$61$	−3.53233	+	2.56639i	−0.452269	+	0.328592i	0.338222	+	0.941066i	$0.390174\pi$
$62$	8.55078	+	10.2198i	1.08595	+	1.29792i
$63$	4.47543	−	0.708838i	0.563851	−	0.0893052i
$64$	5.30227	+	5.99049i	0.662783	+	0.748811i
$65$	7.66493	−	11.7057i	0.950717	−	1.45191i
$66$	−13.5392	−	1.20388i	−1.66657	−	0.148187i
$67$	−4.51785	+	8.86679i	−0.551944	+	1.08325i	0.431513	+	0.902107i	$0.357980\pi$
$67$	−4.51785	+	8.86679i	−0.551944	+	1.08325i	−0.983457	+	0.181144i	$0.942020\pi$
$68$	−5.63538	+	1.70545i	−0.683390	+	0.206816i
$69$	3.21249	−	1.04380i	0.386738	−	0.125659i
$70$	−2.87291	+	1.32150i	−0.343379	+	0.157950i
$71$	−5.52173	−	1.79412i	−0.655308	−	0.212923i	−0.0375550	−	0.999295i	$-0.511957\pi$
$71$	−5.52173	−	1.79412i	−0.655308	−	0.212923i	−0.617753	+	0.786372i	$0.711957\pi$
$72$	11.1263	−	6.36083i	1.31125	−	0.749631i
$73$	−1.32532	−	0.209909i	−0.155116	−	0.0245680i	0.0783932	−	0.996923i	$-0.475021\pi$
$73$	−1.32532	−	0.209909i	−0.155116	−	0.0245680i	−0.233510	+	0.972354i	$0.575021\pi$
$74$	−6.78699	−	11.3318i	−0.788971	−	1.31730i
$75$	11.5641	−	7.38592i	1.33531	−	0.852853i
$76$	−11.3263	−	6.06354i	−1.29921	−	0.695536i
$77$	−0.547885	+	3.45921i	−0.0624373	+	0.394213i
$78$	20.5767	+	12.8983i	2.32985	+	1.46045i
$79$	−2.06946	+	6.36915i	−0.232833	+	0.716586i	0.764569	+	0.644542i	$0.222952\pi$
$79$	−2.06946	+	6.36915i	−0.232833	+	0.716586i	−0.997401	+	0.0720434i	$0.977048\pi$
$80$	−6.27379	+	6.37492i	−0.701431	+	0.712737i
$81$	0.637113	+	1.96083i	0.0707903	+	0.217870i
$82$	−0.954829	+	3.80660i	−0.105443	+	0.420369i
$83$	−1.66794	−	0.849858i	−0.183080	−	0.0932840i	0.360048	−	0.932934i	$-0.382760\pi$
$83$	−1.66794	−	0.849858i	−0.183080	−	0.0932840i	−0.543128	+	0.839650i	$0.682760\pi$
$84$	−2.39205	−	4.93994i	−0.260994	−	0.538991i
$85$	−2.33576	−	6.15441i	−0.253349	−	0.667539i
$86$	2.18980	+	0.933182i	0.236132	+	0.100628i
$87$	0.983526	+	6.20974i	0.105445	+	0.665754i
$88$	2.01835	+	9.69828i	0.215157	+	1.03384i
$89$	5.37994	+	7.40486i	0.570273	+	0.784913i	0.992587	−	0.121536i	$-0.0387821\pi$
$89$	5.37994	+	7.40486i	0.570273	+	0.784913i	−0.422314	+	0.906450i	$0.638782\pi$
$90$	7.95072	+	11.9208i	0.838079	+	1.25656i
$91$	3.67800	−	5.06233i	0.385559	−	0.530676i
$92$	−1.40624	−	2.02049i	−0.146611	−	0.210651i
$93$	−18.2842	−	18.2842i	−1.89598	−	1.89598i
$94$	−7.44960	−	6.49441i	−0.768368	−	0.669847i
$95$	5.89185	−	13.0996i	0.604491	−	1.34399i
$96$	−11.2783	−	10.6677i	−1.15108	−	1.08876i
$97$	4.85444	+	9.52738i	0.492894	+	0.967358i	0.994743	+	0.102403i	$0.0326532\pi$
$97$	4.85444	+	9.52738i	0.492894	+	0.967358i	−0.501849	+	0.864955i	$0.667347\pi$
$98$	−1.31199	+	0.527914i	−0.132531	+	0.0533273i
$99$	15.8698			1.59498
$100$	−7.59312	−	6.50726i	−0.759312	−	0.650726i
$101$	8.49428			0.845212			0.422606	−	0.906313i	$-0.361115\pi$
$101$	8.49428			0.845212			0.422606	+	0.906313i	$0.361115\pi$
$102$	10.5995	−	4.26498i	1.04950	−	0.422296i
$103$	−5.52064	−	10.8349i	−0.543965	−	1.06759i	−0.985393	−	0.170295i	$-0.945528\pi$
$103$	−5.52064	−	10.8349i	−0.543965	−	1.06759i	0.441428	−	0.897297i	$-0.354472\pi$
$104$	4.65341	−	17.0758i	0.456304	−	1.67442i
$105$	5.32590	−	3.04808i	0.519755	−	0.297462i
$106$	−10.1243	−	8.82612i	−0.983355	−	0.857269i
$107$	−1.41463	−	1.41463i	−0.136757	−	0.136757i	0.635414	−	0.772171i	$-0.280829\pi$
$107$	−1.41463	−	1.41463i	−0.136757	−	0.136757i	−0.772171	+	0.635414i	$0.780829\pi$
$108$	−6.89799	+	4.80093i	−0.663760	+	0.461970i
$109$	4.63789	−	6.38351i	0.444230	−	0.611430i	−0.526916	−	0.849917i	$-0.676652\pi$
$109$	4.63789	−	6.38351i	0.444230	−	0.611430i	0.971146	+	0.238488i	$0.0766517\pi$
$110$	−10.6620	+	2.99733i	−1.01659	+	0.285784i
$111$	15.0661	+	20.7367i	1.43001	+	1.96824i
$112$	−2.94084	+	2.71136i	−0.277883	+	0.256199i
$113$	−1.17754	−	7.43468i	−0.110773	−	0.699396i	−0.979096	−	0.203397i	$-0.934802\pi$
$113$	−1.17754	−	7.43468i	−0.110773	−	0.699396i	0.868323	−	0.495999i	$-0.165198\pi$
$114$	22.9345	+	9.77354i	2.14802	+	0.915376i
$115$	2.14544	−	1.72393i	0.200063	−	0.160758i
$116$	4.12392	−	1.99691i	0.382896	−	0.185408i
$117$	−25.2632	−	12.8722i	−2.33558	−	1.19004i
$118$	2.52304	−	10.0586i	0.232264	−	0.925966i
$119$	−0.909713	−	2.79981i	−0.0833932	−	0.256658i
$120$	11.0309	−	13.4003i	1.00698	−	1.22327i
$121$	−0.391310	+	1.20433i	−0.0355736	+	0.109484i
$122$	−5.23183	−	3.27954i	−0.473668	−	0.296915i
$123$	1.19135	−	7.52186i	0.107420	−	0.678223i
$124$	−8.89418	+	16.6137i	−0.798721	+	1.49195i
$125$	6.67396	−	8.96985i	0.596937	−	0.802288i
$126$	3.29263	+	5.49749i	0.293330	+	0.489756i
$127$	−2.50634	−	0.396965i	−0.222402	−	0.0352250i	0.0442390	−	0.999021i	$-0.485914\pi$
$127$	−2.50634	−	0.396965i	−0.222402	−	0.0352250i	−0.266641	+	0.963796i	$0.585914\pi$
$128$	−5.06030	+	10.1190i	−0.447271	+	0.894398i
$129$	−4.39303	−	1.42738i	−0.386785	−	0.125674i
$130$	19.4041	+	3.87669i	1.70185	+	0.340008i
$131$	−2.50358	+	0.813463i	−0.218739	+	0.0710726i	−0.416336	−	0.909211i	$-0.636686\pi$
$131$	−2.50358	+	0.813463i	−0.218739	+	0.0710726i	0.197597	+	0.980283i	$0.436686\pi$
$132$	−5.56808	−	18.3988i	−0.484639	−	1.60141i
$133$	2.91625	−	5.72347i	0.252871	−	0.496288i
$134$	−14.0181	−	1.24646i	−1.21098	−	0.107678i
$135$	−5.88554	−	7.32458i	−0.506547	−	0.630399i
$136$	−5.21251	−	6.49321i	−0.446969	−	0.556788i
$137$	12.5553	−	1.98856i	1.07267	−	0.169894i	0.404973	−	0.914329i	$-0.367281\pi$
$137$	12.5553	−	1.98856i	1.07267	−	0.169894i	0.667695	+	0.744435i	$0.267281\pi$
$138$	3.06537	+	3.66370i	0.260941	+	0.311875i
$139$	10.8625	−	7.89209i	0.921348	−	0.669398i	−0.0225114	−	0.999747i	$-0.507166\pi$
$139$	10.8625	−	7.89209i	0.921348	−	0.669398i	0.943859	+	0.330348i	$0.107166\pi$
$140$	−3.25044	−	3.07158i	−0.274713	−	0.259596i
$141$	15.5155	+	11.2726i	1.30664	+	0.949327i
$142$	−0.561138	−	8.19157i	−0.0470897	−	0.687421i
$143$	15.4965	−	15.4965i	1.29589	−	1.29589i
$144$	14.2191	+	11.2396i	1.18492	+	0.936634i
$145$	2.54458	+	4.44613i	0.211315	+	0.369231i
$146$	−0.424254	−	1.84961i	−0.0351115	−	0.153075i
$147$	2.44519	−	1.24589i	0.201676	−	0.102759i
$148$	11.2842	−	14.8866i	0.927558	−	1.22367i
$149$			10.7188i			0.878120i	0.898458	+	0.439060i	$0.144688\pi$
$149$			10.7188i			0.878120i	−0.898458	+	0.439060i	$0.855312\pi$
$150$	15.7951	+	11.2728i	1.28966	+	0.920421i
$151$			12.7336i			1.03624i	0.855307	+	0.518121i	$0.173368\pi$
$151$			12.7336i			1.03624i	−0.855307	+	0.518121i	$0.826632\pi$
$152$	1.97600	−	18.0609i	0.160274	−	1.46493i
$153$	−11.8855	+	6.05596i	−0.960886	+	0.489596i
$154$	−4.82767	+	1.10735i	−0.389025	+	0.0892326i
$155$	−19.2149	−	8.64234i	−1.54338	−	0.694169i
$156$	−6.05973	+	33.8055i	−0.485167	+	2.70661i
$157$	−15.3611	+	15.3611i	−1.22595	+	1.22595i	−0.260470	+	0.965482i	$0.583877\pi$
$157$	−15.3611	+	15.3611i	−1.22595	+	1.22595i	−0.965482	+	0.260470i	$0.916123\pi$
$158$	−9.44874	+	0.647257i	−0.751701	+	0.0514930i
$159$	21.0860	+	15.3199i	1.67223	+	1.21495i
$160$	−11.6758	−	4.86572i	−0.923055	−	0.384669i
$161$	0.995772	−	0.723471i	0.0784778	−	0.0570175i
$162$	−2.23624	+	1.87103i	−0.175696	+	0.147002i
$163$	−21.5993	+	3.42100i	−1.69179	+	0.267953i	−0.926654	−	0.375916i	$-0.877328\pi$
$163$	−21.5993	+	3.42100i	−1.69179	+	0.267953i	−0.765136	+	0.643869i	$0.777328\pi$
$164$	−5.49828	+	0.756837i	−0.429343	+	0.0590990i
$165$	20.0934	−	7.62597i	1.56427	−	0.593681i
$166$	0.234473	−	2.63697i	0.0181986	−	0.204668i
$167$	−9.62003	+	18.8804i	−0.744420	+	1.46101i	0.137944	+	0.990440i	$0.455951\pi$
$167$	−9.62003	+	18.8804i	−0.744420	+	1.46101i	−0.882364	+	0.470567i	$0.844049\pi$
$168$	5.21833	−	5.74619i	0.402603	−	0.443328i
$169$	−24.8747	+	8.08229i	−1.91344	+	0.621714i
$170$	6.84142	−	6.31348i	0.524713	−	0.484222i
$171$	−27.6821	−	8.99447i	−2.11690	−	0.687824i
$172$	−0.0682960	+	3.36563i	−0.00520752	+	0.256627i
$173$	20.0959	+	3.18287i	1.52786	+	0.241989i	0.863086	−	0.505056i	$-0.168528\pi$
$173$	20.0959	+	3.18287i	1.52786	+	0.241989i	0.664773	+	0.747045i	$0.268528\pi$
$174$	−7.62787	+	4.56858i	−0.578268	+	0.346343i
$175$	3.17594	−	3.86179i	0.240078	−	0.291924i
$176$	−11.6585	+	7.76790i	−0.878792	+	0.585528i
$177$	−3.14801	+	19.8757i	−0.236619	+	1.49395i
$178$	−6.87492	+	10.9675i	−0.515297	+	0.822052i
$179$	−2.93877	+	9.04461i	−0.219654	+	0.676026i	0.779136	+	0.626855i	$0.215658\pi$
$179$	−2.93877	+	9.04461i	−0.219654	+	0.676026i	−0.998790	+	0.0491712i	$0.984342\pi$
$180$	−11.4426	+	16.7244i	−0.852882	+	1.24656i
$181$	−7.40333	−	22.7851i	−0.550285	−	1.69360i	−0.708080	−	0.706132i	$-0.750438\pi$
$181$	−7.40333	−	22.7851i	−0.550285	−	1.69360i	0.157795	−	0.987472i	$-0.449562\pi$
$182$	8.58337	+	2.15301i	0.636242	+	0.159592i
$183$	10.6762	+	5.43980i	0.789208	+	0.402122i
$184$	1.90848	−	2.91161i	0.140695	−	0.214647i
$185$	17.4724	+	11.4410i	1.28460	+	0.841160i
$186$	14.3361	−	33.6411i	1.05118	−	2.46668i
$187$	−1.61291	−	10.1835i	−0.117948	−	0.744694i
$188$	4.58783	−	13.2023i	0.334602	−	0.962874i
$189$	−2.46994	−	3.39959i	−0.179662	−	0.247284i
$190$	20.2969	+	0.814565i	1.47249	+	0.0590948i
$191$	−8.29249	+	11.4136i	−0.600024	+	0.825862i	−0.995710	−	0.0925237i	$-0.970507\pi$
$191$	−8.29249	+	11.4136i	−0.600024	+	0.825862i	0.395687	+	0.918386i	$0.370507\pi$
$192$	8.04187	−	20.4286i	0.580372	−	1.47430i
$193$	−3.79394	−	3.79394i	−0.273094	−	0.273094i	0.557251	−	0.830344i	$-0.311856\pi$
$193$	−3.79394	−	3.79394i	−0.273094	−	0.273094i	−0.830344	+	0.557251i	$0.811856\pi$
$194$	−9.93706	+	11.3986i	−0.713439	+	0.818371i
$195$	−38.1723	−	4.15826i	−2.73358	−	0.297779i
$196$	−1.38523	−	1.44261i	−0.0989451	−	0.103044i
$197$	−4.02740	−	7.90421i	−0.286940	−	0.563152i	0.701875	−	0.712300i	$-0.252347\pi$
$197$	−4.02740	−	7.90421i	−0.286940	−	0.563152i	−0.988815	+	0.149149i	$0.952347\pi$
$198$	8.37789	+	20.8210i	0.595390	+	1.47968i
$199$	−21.4292			−1.51907			−0.759537	−	0.650464i	$-0.774575\pi$
$199$	−21.4292			−1.51907			−0.759537	+	0.650464i	$0.774575\pi$
$200$	4.52892	−	13.3973i	0.320243	−	0.947335i
$201$	27.3098			1.92628
$202$	4.48425	+	11.1444i	0.315511	+	0.784116i
$203$	1.04008	+	2.04128i	0.0729995	+	0.143270i
$204$	11.1912	+	11.6548i	0.783541	+	0.815999i
$205$	−1.26715	−	6.07447i	−0.0885014	−	0.424259i
$206$	11.3008	−	12.9629i	0.787363	−	0.903167i
$207$	−3.94368	−	3.94368i	−0.274105	−	0.274105i
$208$	24.8599	−	2.90937i	1.72372	−	0.201728i
$209$	13.2237	−	18.2009i	0.914705	−	1.25898i
$210$	6.81066	+	5.37839i	0.469980	+	0.371144i
$211$	6.82854	+	9.39868i	0.470096	+	0.647032i	0.976564	−	0.215227i	$-0.0690491\pi$
$211$	6.82854	+	9.39868i	0.470096	+	0.647032i	−0.506468	+	0.862259i	$0.669049\pi$
$212$	6.23501	−	17.9423i	0.428222	−	1.23228i
$213$	2.49249	+	15.7370i	0.170783	+	1.07828i
$214$	1.10917	−	2.60277i	0.0758213	−	0.177922i
$215$	−3.75922	+	0.182742i	−0.256377	+	0.0124629i
$216$	−9.94030	−	6.51559i	−0.676352	−	0.443330i
$217$	−8.39535	−	4.27765i	−0.569914	−	0.290386i
$218$	10.8235	+	2.71491i	0.733059	+	0.183877i
$219$	1.13793	+	3.50218i	0.0768939	+	0.236655i
$220$	−9.56109	−	12.4061i	−0.644608	−	0.836420i
$221$	−5.69242	+	17.5195i	−0.382914	+	1.17849i
$222$	−19.2526	+	30.7137i	−1.29215	+	2.06137i
$223$	−0.836806	+	5.28338i	−0.0560367	+	0.353802i	0.943699	+	0.330806i	$0.107320\pi$
$223$	−0.836806	+	5.28338i	−0.0560367	+	0.353802i	−0.999736	+	0.0229959i	$0.992680\pi$
$224$	−5.10977	−	2.42698i	−0.341411	−	0.162159i
$225$	−19.5344	−	11.4763i	−1.30229	−	0.765086i
$226$	9.13256	−	5.46979i	0.607489	−	0.363845i
$227$	3.15449	+	0.499622i	0.209371	+	0.0331611i	0.260239	−	0.965544i	$-0.416199\pi$
$227$	3.15449	+	0.499622i	0.209371	+	0.0331611i	−0.0508678	+	0.998705i	$0.516199\pi$
$228$	−0.715288	+	35.2494i	−0.0473711	+	2.33445i
$229$	12.3849	+	4.02411i	0.818420	+	0.265921i	0.688160	−	0.725559i	$-0.258419\pi$
$229$	12.3849	+	4.02411i	0.818420	+	0.265921i	0.130260	+	0.991480i	$0.458419\pi$
$230$	3.39438	+	1.90470i	0.223819	+	0.125592i
$231$	9.14104	−	2.97010i	0.601436	−	0.195419i
$232$	4.79699	+	4.35632i	0.314938	+	0.286007i
$233$	−4.62740	+	9.08179i	−0.303151	+	0.594968i	−0.991454	−	0.130455i	$-0.958356\pi$
$233$	−4.62740	+	9.08179i	−0.303151	+	0.594968i	0.688303	+	0.725423i	$0.258356\pi$
$234$	3.55141	−	39.9404i	0.232163	−	2.61098i
$235$	15.0785	+	4.10154i	0.983615	+	0.267555i
$236$	14.5286	−	1.99987i	0.945734	−	0.130180i
$237$	18.1521	−	2.87502i	1.17911	−	0.186752i
$238$	3.19306	−	2.67159i	0.206975	−	0.173173i
$239$	13.4935	−	9.80357i	0.872819	−	0.634140i	−0.0585227	−	0.998286i	$-0.518639\pi$
$239$	13.4935	−	9.80357i	0.872819	−	0.634140i	0.931342	+	0.364146i	$0.118639\pi$
$240$	23.4044	+	7.39820i	1.51074	+	0.477552i
$241$	11.9328	+	8.66967i	0.768657	+	0.558462i	0.901553	−	0.432668i	$-0.142428\pi$
$241$	11.9328	+	8.66967i	0.768657	+	0.558462i	−0.132896	+	0.991130i	$0.542428\pi$
$242$	−1.78664	+	0.122388i	−0.114850	+	0.00786742i
$243$	12.9149	−	12.9149i	0.828490	−	0.828490i
$244$	1.54075	−	8.59540i	0.0986364	−	0.550264i
$245$	1.50250	−	1.65605i	0.0959914	−	0.105801i
$246$	10.4975	−	2.40786i	0.669296	−	0.153520i
$247$	−35.8139	+	18.2481i	−2.27879	+	1.16110i
$248$	−26.4923	−	2.89845i	−1.68226	−	0.184052i
$249$			5.13727i			0.325561i
$250$	15.2916	+	4.02083i	0.967126	+	0.254300i
$251$		−	2.08327i		−	0.131495i	−0.997836	−	0.0657474i	$-0.979057\pi$
$251$		−	2.08327i		−	0.131495i	0.997836	−	0.0657474i	$-0.0209432\pi$
$252$	−5.47441	+	7.22208i	−0.344855	+	0.454948i
$253$	3.84096	−	1.95707i	0.241479	−	0.123040i
$254$	−0.802319	−	3.49785i	−0.0503420	−	0.219474i
$255$	−12.1386	+	13.3791i	−0.760150	+	0.837831i
$256$	−15.9473	−	1.29710i	−0.996709	−	0.0810686i
$257$	5.88803	−	5.88803i	0.367285	−	0.367285i	−0.499201	−	0.866486i	$-0.666373\pi$
$257$	5.88803	−	5.88803i	0.367285	−	0.367285i	0.866486	+	0.499201i	$0.166373\pi$
$258$	−0.446436	−	6.51713i	−0.0277939	−	0.405739i
$259$	7.55626	+	5.48994i	0.469523	+	0.341128i
$260$	5.15754	+	27.5045i	0.319857	+	1.70576i
$261$	8.39834	−	6.10175i	0.519844	−	0.377689i
$262$	−2.38893	−	2.85523i	−0.147588	−	0.176396i
$263$	−10.4688	+	1.65810i	−0.645534	+	0.102243i	−0.470613	−	0.882340i	$-0.655967\pi$
$263$	−10.4688	+	1.65810i	−0.645534	+	0.102243i	−0.174921	+	0.984582i	$0.555967\pi$
$264$	21.1995	−	17.0182i	1.30474	−	1.04740i
$265$	20.4922	+	5.57412i	1.25883	+	0.342416i
$266$	9.04864	+	0.804585i	0.554808	+	0.0493323i
$267$	11.4035	−	22.3806i	0.697883	−	1.36967i
$268$	−5.76503	−	19.0496i	−0.352155	−	1.16364i
$269$	−17.8761	+	5.80828i	−1.08992	+	0.354137i	−0.798216	−	0.602371i	$-0.794223\pi$
$269$	−17.8761	+	5.80828i	−1.08992	+	0.354137i	−0.291706	+	0.956508i	$0.594223\pi$
$270$	6.50268	−	11.5885i	0.395741	−	0.705253i
$271$	6.73128	+	2.18713i	0.408896	+	0.132858i	0.506241	−	0.862392i	$-0.331035\pi$
$271$	6.73128	+	2.18713i	0.408896	+	0.132858i	−0.0973443	+	0.995251i	$0.531035\pi$
$272$	5.76724	−	10.2666i	0.349690	−	0.622504i
$273$	−16.9608	−	2.68632i	−1.02651	−	0.162583i
$274$	9.23705	+	15.4225i	0.558031	+	0.931709i
$275$	13.1020	−	11.6187i	0.790083	−	0.700633i
$276$	−3.18847	+	5.95583i	−0.191924	+	0.358499i
$277$	−0.576361	+	3.63900i	−0.0346301	+	0.218646i	−0.998935	−	0.0461502i	$-0.985305\pi$
$277$	−0.576361	+	3.63900i	−0.0346301	+	0.218646i	0.964304	+	0.264796i	$0.0853047\pi$
$278$	16.0888	+	10.0851i	0.964941	+	0.604867i
$279$	−13.1933	+	40.6050i	−0.789865	+	2.43096i
$280$	2.31392	−	5.88607i	0.138283	−	0.351760i
$281$	−5.75471	−	17.7112i	−0.343297	−	1.05656i	−0.962489	−	0.271320i	$-0.912540\pi$
$281$	−5.75471	−	17.7112i	−0.343297	−	1.05656i	0.619192	−	0.785240i	$-0.287460\pi$
$282$	−6.59872	+	26.3070i	−0.392948	+	1.56656i
$283$	9.85897	+	5.02340i	0.586055	+	0.298610i	0.721764	−	0.692139i	$-0.243331\pi$
$283$	9.85897	+	5.02340i	0.586055	+	0.298610i	−0.135709	+	0.990749i	$0.543331\pi$
$284$	10.4510	−	5.06065i	0.620152	−	0.300294i
$285$	−39.3716	+	1.91392i	−2.33217	+	0.113371i
$286$	28.5121	+	12.1504i	1.68595	+	0.718468i
$287$	−0.434115	−	2.74090i	−0.0256250	−	0.161790i
$288$	−7.23977	+	24.5887i	−0.426608	+	1.44891i
$289$	−4.89831	−	6.74194i	−0.288136	−	0.396585i
$290$	−4.48994	+	5.68562i	−0.263658	+	0.333871i
$291$	17.2482	−	23.7401i	1.01111	−	1.39167i
$292$	2.20269	−	1.53305i	0.128903	−	0.0897149i
$293$	2.97227	+	2.97227i	0.173642	+	0.173642i	0.788577	−	0.614936i	$-0.210818\pi$
$293$	2.97227	+	2.97227i	0.173642	+	0.173642i	−0.614936	+	0.788577i	$0.710818\pi$
$294$	2.92544	+	2.55034i	0.170615	+	0.148739i
$295$	3.34831	+	16.0512i	0.194946	+	0.934535i
$296$	25.4882	+	6.94588i	1.48147	+	0.403721i
$297$	−6.68147	−	13.1131i	−0.387698	−	0.760901i
$298$	−14.0629	+	5.65861i	−0.814644	+	0.327795i
$299$	−7.70185			−0.445409
$300$	−6.45134	+	26.6740i	−0.372468	+	1.54002i
$301$	−1.68316			−0.0970157
$302$	−16.7062	+	6.72222i	−0.961336	+	0.386820i
$303$	−10.5829	−	20.7702i	−0.607973	−	1.19321i
$304$	24.7388	−	6.94212i	1.41887	−	0.398158i
$305$	9.70571	+	1.05728i	0.555747	+	0.0605398i
$306$	−14.2199	−	12.3966i	−0.812895	−	0.708665i
$307$	−20.8285	−	20.8285i	−1.18875	−	1.18875i	−0.977414	−	0.211332i	$-0.932220\pi$
$307$	−20.8285	−	20.8285i	−1.18875	−	1.18875i	−0.211332	−	0.977414i	$-0.567780\pi$
$308$	−4.00142	−	5.74925i	−0.228002	−	0.327594i
$309$	−19.6153	+	26.9981i	−1.11587	+	1.53587i
$310$	1.19483	−	29.7720i	0.0678617	−	1.69094i
$311$	−16.0105	−	22.0366i	−0.907873	−	1.24958i	−0.967888	−	0.251382i	$-0.919115\pi$
$311$	−16.0105	−	22.0366i	−0.907873	−	1.24958i	0.0600152	−	0.998197i	$-0.480885\pi$
$312$	−47.5514	+	9.89612i	−2.69207	+	0.560257i
$313$	2.86597	+	18.0950i	0.161994	+	1.02279i	0.925984	+	0.377563i	$0.123238\pi$
$313$	2.86597	+	18.0950i	0.161994	+	1.02279i	−0.763989	+	0.645229i	$0.776762\pi$
$314$	−28.2629	−	12.0442i	−1.59497	−	0.679696i
$315$	−8.47654	−	5.55047i	−0.477599	−	0.312734i
$316$	−5.83731	−	12.0549i	−0.328374	−	0.678142i
$317$	−29.0696	−	14.8117i	−1.63271	−	0.831909i	−0.998261	−	0.0589462i	$-0.981226\pi$
$317$	−29.0696	−	14.8117i	−1.63271	−	0.831909i	−0.634452	−	0.772963i	$-0.718774\pi$
$318$	−8.96788	+	35.7521i	−0.502894	+	2.00488i
$319$	2.47948	+	7.63105i	0.138824	+	0.427257i
$320$	0.219930	−	17.8872i	0.0122945	−	0.999924i
$321$	−1.69657	+	5.22150i	−0.0946933	+	0.291436i
$322$	1.47487	+	0.924509i	0.0821910	+	0.0515209i
$323$	−2.95824	+	18.6776i	−0.164601	+	1.03925i
$324$	−3.63531	−	1.94618i	−0.201962	−	0.108121i
$325$	−30.2813	+	7.86856i	−1.67970	+	0.436469i
$326$	−15.8909	−	26.5320i	−0.880114	−	1.46947i
$327$	−21.3872	−	3.38740i	−1.18272	−	0.187324i
$328$	−3.89558	−	6.81412i	−0.215097	−	0.376247i
$329$	6.64631	+	2.15952i	0.366423	+	0.119058i
$330$	20.6128	+	22.3364i	1.13470	+	1.22958i
$331$	11.8021	−	3.83475i	0.648704	−	0.210777i	0.0338613	−	0.999427i	$-0.489220\pi$
$331$	11.8021	−	3.83475i	0.648704	−	0.210777i	0.614843	+	0.788650i	$0.289220\pi$
$332$	3.58344	−	1.08447i	0.196667	−	0.0595178i
$333$	19.2137	−	37.7090i	1.05290	−	2.06644i
$334$	−29.8493	−	2.65414i	−1.63328	−	0.145228i
$335$	20.8041	−	7.89571i	1.13665	−	0.431389i
$336$	10.2938	+	3.81288i	0.561570	+	0.208010i
$337$	−18.5719	+	2.94150i	−1.01168	+	0.160234i	−0.640200	−	0.768209i	$-0.721148\pi$
$337$	−18.5719	+	2.94150i	−1.01168	+	0.160234i	−0.371476	+	0.928442i	$0.621148\pi$
$338$	−23.7355	−	28.3685i	−1.29104	−	1.54304i
$339$	−16.7122	+	12.1421i	−0.907680	+	0.659468i
$340$	11.8949	+	5.64287i	0.645090	+	0.306028i
$341$	−26.6976	−	19.3970i	−1.44576	−	1.05040i
$342$	−2.81316	−	41.0669i	−0.152118	−	2.22064i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−4.45171	+	1.68716i	−0.240020	+	0.0909654i
$345$	−6.88833	−	3.09819i	−0.370855	−	0.166801i
$346$	6.43300	+	28.0458i	0.345840	+	1.50775i
$347$	−6.18805	+	3.15297i	−0.332192	+	0.169260i	−0.612129	−	0.790758i	$-0.709687\pi$
$347$	−6.18805	+	3.15297i	−0.332192	+	0.169260i	0.279937	+	0.960019i	$0.409687\pi$
$348$	−10.0208	−	7.59585i	−0.537170	−	0.407180i
$349$			22.8335i			1.22225i	0.791535	+	0.611124i	$0.209282\pi$
$349$			22.8335i			1.22225i	−0.791535	+	0.611124i	$0.790718\pi$
$350$	6.74324	+	2.12809i	0.360441	+	0.113751i
$351$			26.2943i			1.40348i
$352$	−16.3461	−	11.1950i	−0.871248	−	0.596695i
$353$	27.5538	−	14.0393i	1.46654	−	0.747239i	0.475363	−	0.879790i	$-0.342317\pi$
$353$	27.5538	−	14.0393i	1.46654	−	0.747239i	0.991176	+	0.132551i	$0.0423168\pi$
$354$	−27.7386	+	6.36254i	−1.47429	+	0.338165i
$355$	6.44856	+	11.2675i	0.342254	+	0.598019i
$356$	−18.0186	−	3.22989i	−0.954985	−	0.171184i
$357$	−5.71267	+	5.71267i	−0.302347	+	0.302347i
$358$	−13.4178	+	0.919147i	−0.709154	+	0.0485784i
$359$	−3.88631	−	2.82357i	−0.205111	−	0.149022i	0.480488	−	0.877001i	$-0.340460\pi$
$359$	−3.88631	−	2.82357i	−0.205111	−	0.149022i	−0.685599	+	0.727979i	$0.740460\pi$
$360$	−27.9829	−	6.18351i	−1.47483	−	0.325900i
$361$	−18.0108	+	13.0856i	−0.947939	+	0.688718i
$362$	25.9854	−	21.7416i	1.36576	−	1.14272i
$363$	3.43234	−	0.543630i	0.180151	−	0.0285332i
$364$	1.70656	+	12.3979i	0.0894482	+	0.649824i
$365$	1.87939	+	2.33891i	0.0983719	+	0.122424i
$366$	−1.50082	+	16.8788i	−0.0784493	+	0.882268i
$367$	−12.9419	+	25.3999i	−0.675563	+	1.32587i	0.257544	+	0.966267i	$0.417087\pi$
$367$	−12.9419	+	25.3999i	−0.675563	+	1.32587i	−0.933107	+	0.359600i	$0.882913\pi$
$368$	4.82751	+	0.966821i	0.251651	+	0.0503990i
$369$	−11.9590	+	3.88570i	−0.622559	+	0.202282i
$370$	−5.78652	+	28.9635i	−0.300827	+	1.50574i
$371$	9.03256	+	2.93486i	0.468947	+	0.152370i
$372$	51.7048	+	1.04921i	2.68077	+	0.0543988i
$373$	36.4902	+	5.77947i	1.88939	+	0.299250i	0.990347	−	0.138613i	$-0.0442643\pi$
$373$	36.4902	+	5.77947i	1.88939	+	0.299250i	0.899042	+	0.437862i	$0.144264\pi$
$374$	12.5092	−	7.49215i	0.646834	−	0.387410i
$375$	−30.2480	−	5.14368i	−1.56200	−	0.265619i
$376$	19.7432	−	0.950491i	1.01818	−	0.0490179i
$377$	2.24257	−	14.1590i	0.115498	−	0.729227i
$378$	3.15629	−	5.03522i	0.162342	−	0.258984i
$379$	5.15429	−	15.8633i	0.264758	−	0.814842i	−0.726991	−	0.686647i	$-0.759082\pi$
$379$	5.15429	−	15.8633i	0.264758	−	0.814842i	0.991749	−	0.128195i	$-0.0409183\pi$
$380$	9.64630	+	27.0592i	0.494845	+	1.38811i
$381$	2.15196	+	6.62306i	0.110248	+	0.339310i
$382$	−19.3523	−	4.85422i	−0.990147	−	0.248363i
$383$	−5.04327	−	2.56968i	−0.257699	−	0.131304i	0.320369	−	0.947293i	$-0.396193\pi$
$383$	−5.04327	−	2.56968i	−0.257699	−	0.131304i	−0.578068	+	0.815989i	$0.696193\pi$
$384$	31.0474	−	0.233693i	1.58438	−	0.0119256i
$385$	6.10479	−	4.90541i	0.311129	−	0.250003i
$386$	2.97472	−	6.98047i	0.151409	−	0.355297i
$387$	1.19309	+	7.53286i	0.0606481	+	0.382917i
$388$	−20.2007	−	7.01981i	−1.02554	−	0.356377i
$389$	0.0838455	+	0.115403i	0.00425114	+	0.00585119i	0.811137	−	0.584856i	$-0.198849\pi$
$389$	0.0838455	+	0.115403i	0.00425114	+	0.00585119i	−0.806886	+	0.590707i	$0.798849\pi$
$390$	−14.6961	−	52.2767i	−0.744166	−	2.64714i
$391$	−2.12982	+	2.93145i	−0.107710	+	0.148250i
$392$	1.16141	−	2.57898i	0.0586599	−	0.130258i
$393$	5.10826	+	5.10826i	0.257678	+	0.257678i
$394$	8.24409	−	9.45663i	0.415331	−	0.476418i
$395$	12.9968	−	7.43823i	0.653940	−	0.374258i
$396$	−22.8940	+	21.9833i	−1.15047	+	1.10470i
$397$	−8.93016	−	17.5264i	−0.448192	−	0.879627i	−0.998988	−	0.0449863i	$-0.985676\pi$
$397$	−8.93016	−	17.5264i	−0.448192	−	0.879627i	0.550795	−	0.834640i	$-0.314324\pi$
$398$	−11.3128	−	28.1148i	−0.567058	−	1.40927i
$399$	−17.6283			−0.882520
$400$	19.9680	−	1.13076i	0.998400	−	0.0565380i
$401$	−0.873032			−0.0435972			−0.0217986	−	0.999762i	$-0.506939\pi$
$401$	−0.873032			−0.0435972			−0.0217986	+	0.999762i	$0.506939\pi$
$402$	14.4172	+	35.8300i	0.719065	+	1.78704i
$403$	26.7669	+	52.5329i	1.33335	+	2.61685i
$404$	−12.2540	+	11.7665i	−0.609658	+	0.585407i
$405$	1.89107	−	4.20449i	0.0939679	−	0.208923i
$406$	−2.12905	+	2.44219i	−0.105663	+	0.121204i
$407$	23.1308	+	23.1308i	1.14655	+	1.14655i
$408$	−9.38294	+	20.8354i	−0.464525	+	1.03151i
$409$	12.5553	−	17.2809i	0.620821	−	0.854487i	−0.376591	−	0.926380i	$-0.622904\pi$
$409$	12.5553	−	17.2809i	0.620821	−	0.854487i	0.997412	+	0.0718922i	$0.0229038\pi$
$410$	7.30067	−	4.86928i	0.360555	−	0.240476i
$411$	−20.5049	−	28.2225i	−1.01143	−	1.39211i
$412$	22.9730	+	7.98318i	1.13180	+	0.393303i
$413$	1.14711	+	7.24254i	0.0564454	+	0.356382i
$414$	3.09213	−	7.25598i	0.151970	−	0.356612i
$415$	1.48527	+	3.91349i	0.0729090	+	0.192106i
$416$	16.9409	+	31.0799i	0.830597	+	1.52382i
$417$	−32.8312	−	16.7283i	−1.60775	−	0.819190i
$418$	30.8603	+	7.74084i	1.50943	+	0.378617i
$419$	−1.93348	−	5.95063i	−0.0944566	−	0.290708i	0.892655	−	0.450740i	$-0.148840\pi$
$419$	−1.93348	−	5.95063i	−0.0944566	−	0.290708i	−0.987112	+	0.160033i	$0.948840\pi$
$420$	−3.46093	+	11.7748i	−0.168876	+	0.574552i
$421$	−7.71567	+	23.7464i	−0.376039	+	1.15733i	0.566736	+	0.823899i	$0.308206\pi$
$421$	−7.71567	+	23.7464i	−0.376039	+	1.15733i	−0.942775	+	0.333429i	$0.891794\pi$
$422$	−8.72606	+	13.9206i	−0.424778	+	0.677646i
$423$	4.95360	−	31.2758i	0.240853	−	1.52068i
$424$	26.8316	−	1.29175i	1.30306	−	0.0627329i
$425$	−5.37889	+	13.7015i	−0.260915	+	0.664618i
$426$	−19.3309	+	11.5779i	−0.936583	+	0.560950i
$427$	4.31245	+	0.683025i	0.208694	+	0.0330539i
$428$	4.00035	+	0.0811758i	0.193364	+	0.00392378i
$429$	−57.1990	−	18.5851i	−2.76159	−	0.897296i
$430$	−2.22430	−	4.83557i	−0.107265	−	0.233192i
$431$	17.0669	−	5.54537i	0.822083	−	0.267111i	0.132376	−	0.991200i	$-0.457739\pi$
$431$	17.0669	−	5.54537i	0.822083	−	0.267111i	0.689707	+	0.724088i	$0.257739\pi$
$432$	3.30075	−	16.4812i	0.158807	−	0.792952i
$433$	−1.48754	+	2.91947i	−0.0714868	+	0.140301i	−0.923984	−	0.382431i	$-0.875087\pi$
$433$	−1.48754	+	2.91947i	−0.0714868	+	0.140301i	0.852497	+	0.522732i	$0.175087\pi$
$434$	1.18019	−	13.2728i	0.0566509	−	0.637115i
$435$	7.70139	−	11.7614i	0.369253	−	0.563914i
$436$	2.15195	+	15.6335i	0.103060	+	0.748709i
$437$	−7.80909	+	1.23684i	−0.373560	+	0.0591660i
$438$	−3.99408	+	3.34179i	−0.190845	+	0.159677i
$439$	−1.57305	+	1.14289i	−0.0750775	+	0.0545470i	−0.624691	−	0.780872i	$-0.714775\pi$
$439$	−1.57305	+	1.14289i	−0.0750775	+	0.0545470i	0.549613	+	0.835419i	$0.314775\pi$
$440$	11.2292	−	19.0934i	0.535332	−	0.910241i
$441$	−3.66583	−	2.66338i	−0.174563	−	0.126828i
$442$	−25.9904	+	1.78039i	−1.23624	+	0.0846847i
$443$	8.19976	−	8.19976i	0.389583	−	0.389583i	−0.484956	−	0.874539i	$-0.661164\pi$
$443$	8.19976	−	8.19976i	0.389583	−	0.389583i	0.874539	+	0.484956i	$0.161164\pi$
$444$	−50.4596	−	9.04503i	−2.39471	−	0.429258i
$445$	2.21639	−	20.3462i	0.105067	−	0.964500i
$446$	−7.37349	+	1.69129i	−0.349145	+	0.0800851i
$447$	26.2096	−	13.3545i	1.23967	−	0.631644i
$448$	0.486646	−	7.98518i	0.0229918	−	0.377265i
$449$		−	34.9172i		−	1.64784i	−0.566703	−	0.823922i	$-0.691781\pi$
$449$		−	34.9172i		−	1.64784i	0.566703	−	0.823922i	$-0.308219\pi$
$450$	4.74426	−	31.6873i	0.223647	−	1.49376i
$451$		−	9.71918i		−	0.457658i
$452$	11.9975	+	9.09422i	0.564314	+	0.427756i
$453$	31.1360	−	15.8646i	1.46290	−	0.745384i
$454$	1.00980	+	4.40241i	0.0473924	+	0.206615i
$455$	−13.6971	+	2.85724i	−0.642129	+	0.133950i
$456$	−46.6243	+	17.6702i	−2.18338	+	0.827482i
$457$	14.0117	−	14.0117i	0.655440	−	0.655440i	−0.298858	−	0.954298i	$-0.596606\pi$
$457$	14.0117	−	14.0117i	0.655440	−	0.655440i	0.954298	+	0.298858i	$0.0966057\pi$
$458$	1.25860	+	18.3732i	0.0588107	+	0.858525i
$459$	10.0080	+	7.27125i	0.467134	+	0.339393i
$460$	−0.706996	+	5.45890i	−0.0329639	+	0.254523i
$461$	5.57896	−	4.05335i	0.259838	−	0.188783i	−0.450238	−	0.892909i	$-0.648661\pi$
$461$	5.57896	−	4.05335i	0.259838	−	0.188783i	0.710076	+	0.704125i	$0.248661\pi$
$462$	8.72242	+	10.4250i	0.405804	+	0.485013i
$463$	−20.7517	+	3.28675i	−0.964415	+	0.152748i	−0.618731	−	0.785603i	$-0.712353\pi$
$463$	−20.7517	+	3.28675i	−0.964415	+	0.152748i	−0.345684	+	0.938351i	$0.612353\pi$
$464$	−3.18304	+	8.59334i	−0.147769	+	0.398936i
$465$	2.80740	+	57.7515i	0.130190	+	2.67816i
$466$	−14.3581	−	1.27669i	−0.665124	−	0.0591413i
$467$	−14.3779	+	28.2182i	−0.665330	+	1.30578i	0.273656	+	0.961828i	$0.411767\pi$
$467$	−14.3779	+	28.2182i	−0.665330	+	1.30578i	−0.938986	+	0.343955i	$0.888233\pi$
$468$	54.2760	−	16.4257i	2.50891	−	0.759277i
$469$	9.46437	−	3.07516i	0.437024	−	0.141998i
$470$	2.57901	+	21.9481i	0.118961	+	1.01239i
$471$	56.6992	+	18.4227i	2.61256	+	0.848873i
$472$	10.2937	+	18.0056i	0.473804	+	0.828776i
$473$	−5.82240	−	0.922178i	−0.267714	−	0.0424018i
$474$	13.3547	+	22.2976i	0.613404	+	1.02416i
$475$	−29.4393	+	12.8410i	−1.35077	+	0.589185i
$476$	5.19074	+	2.77888i	0.237917	+	0.127370i
$477$	6.73211	−	42.5049i	0.308242	−	1.94617i
$478$	19.9855	+	12.5278i	0.914117	+	0.573008i
$479$	−10.2194	+	31.4521i	−0.466936	+	1.43708i	0.389595	+	0.920986i	$0.372615\pi$
$479$	−10.2194	+	31.4521i	−0.466936	+	1.43708i	−0.856531	+	0.516096i	$0.827385\pi$
$480$	2.64914	+	34.6118i	0.120916	+	1.57981i
$481$	−18.0603	−	55.5838i	−0.823477	−	2.53440i
$482$	−5.07500	+	20.2325i	−0.231160	+	0.921563i
$483$	−3.00965	−	1.53349i	−0.136944	−	0.0697763i
$484$	−1.10376	−	2.27944i	−0.0501711	−	0.103611i
$485$	6.27574	−	23.0716i	0.284966	−	1.04763i
$486$	23.7621	+	10.1262i	1.07787	+	0.459334i
$487$	3.51481	+	22.1916i	0.159271	+	1.00560i	0.929765	+	0.368152i	$0.120010\pi$
$487$	3.51481	+	22.1916i	0.159271	+	1.00560i	−0.770494	+	0.637447i	$0.779990\pi$
$488$	12.0904	−	2.51619i	0.547308	−	0.113903i
$489$	35.2754	+	48.5524i	1.59521	+	2.19561i
$490$	2.96590	+	1.09701i	0.133986	+	0.0495580i
$491$	5.70304	−	7.84956i	0.257375	−	0.354246i	−0.660702	−	0.750648i	$-0.729741\pi$
$491$	5.70304	−	7.84956i	0.257375	−	0.354246i	0.918077	+	0.396402i	$0.129741\pi$
$492$	8.70086	+	12.5014i	0.392265	+	0.563608i
$493$	−4.76901	−	4.76901i	−0.214785	−	0.214785i
$494$	−42.8479	−	37.3539i	−1.92782	−	1.68063i
$495$	−26.2811	−	23.8444i	−1.18125	−	1.07173i
$496$	−10.1829	−	36.2876i	−0.457226	−	1.62936i
$497$	2.63582	+	5.17308i	0.118233	+	0.232044i
$498$	−6.74002	+	2.71203i	−0.302028	+	0.121529i
$499$	−6.31485			−0.282691			−0.141346	−	0.989960i	$-0.545143\pi$
$499$	−6.31485			−0.282691			−0.141346	+	0.989960i	$0.545143\pi$
$500$	2.79737	+	22.1850i	0.125102	+	0.992144i
$501$	58.1517			2.59802
$502$	2.73322	−	1.09979i	0.121990	−	0.0490859i
$503$	−9.82592	−	19.2845i	−0.438116	−	0.859851i	−0.999479	−	0.0322815i	$-0.989723\pi$
$503$	−9.82592	−	19.2845i	−0.438116	−	0.859851i	0.561363	−	0.827570i	$-0.310277\pi$
$504$	−12.3653	−	3.36971i	−0.550794	−	0.150099i
$505$	−14.0669	−	12.7627i	−0.625969	−	0.567932i
$506$	4.59534	+	4.00613i	0.204288	+	0.178094i
$507$	50.7539	+	50.7539i	2.25406	+	2.25406i
$508$	4.16557	−	2.89919i	0.184817	−	0.128631i
$509$	5.83488	−	8.03103i	0.258627	−	0.355969i	−0.659883	−	0.751369i	$-0.729394\pi$
$509$	5.83488	−	8.03103i	0.258627	−	0.355969i	0.918509	+	0.395400i	$0.129394\pi$
$510$	−23.9613	−	8.86271i	−1.06103	−	0.392447i
$511$	0.788711	+	1.08557i	0.0348905	+	0.0480227i
$512$	−6.71704	−	21.6074i	−0.296854	−	0.954923i
$513$	4.22259	+	26.6604i	0.186432	+	1.17709i
$514$	10.8334	+	4.61664i	0.477840	+	0.203631i
$515$	−7.13699	+	26.2378i	−0.314493	+	1.15618i
$516$	8.31470	−	4.02620i	0.366034	−	0.177244i
$517$	21.8078	+	11.1116i	0.959106	+	0.488689i
$518$	−3.21368	+	12.8119i	−0.141201	+	0.562924i
$519$	−17.2545	−	53.1038i	−0.757387	−	2.33100i
$520$	−33.3628	+	21.2866i	−1.46305	+	0.933480i
$521$	−1.38716	+	4.26925i	−0.0607728	+	0.187039i	−0.976834	−	0.214000i	$-0.931351\pi$
$521$	−1.38716	+	4.26925i	−0.0607728	+	0.187039i	0.916061	+	0.401039i	$0.131351\pi$
$522$	12.4390	+	7.79730i	0.544440	+	0.341279i
$523$	3.44257	−	21.7355i	0.150533	−	0.950429i	−0.790585	−	0.612352i	$-0.790224\pi$
$523$	3.44257	−	21.7355i	0.150533	−	0.950429i	0.941119	−	0.338077i	$-0.109776\pi$
$524$	2.48487	−	4.64155i	0.108552	−	0.202767i
$525$	−13.3997	−	2.95442i	−0.584810	−	0.128942i
$526$	−7.70203	−	12.8596i	−0.335824	−	0.560705i
$527$	27.3968	+	4.33923i	1.19342	+	0.189020i
$528$	33.5192	+	18.8293i	1.45874	+	0.819442i
$529$	20.4335	+	6.63924i	0.888412	+	0.288663i
$530$	3.50496	+	29.8282i	0.152246	+	1.29565i
$531$	31.6003	−	10.2676i	1.37134	−	0.445575i
$532$	3.72130	+	12.2964i	0.161339	+	0.533118i
$533$	−7.88337	+	15.4720i	−0.341467	+	0.670166i
$534$	35.3831	+	3.14619i	1.53118	+	0.136149i
$535$	0.217205	+	4.46817i	0.00939060	+	0.193176i
$536$	21.9494	−	17.6202i	0.948070	−	0.761077i
$537$	25.7772	−	4.08271i	1.11237	−	0.176182i
$538$	−17.0574	−	20.3869i	−0.735397	−	0.878940i
$539$	2.83344	−	2.05862i	0.122045	−	0.0886709i
$540$	18.6368	+	2.41370i	0.802000	+	0.103869i
$541$	−10.8000	−	7.84665i	−0.464328	−	0.337354i	0.330899	−	0.943666i	$-0.392648\pi$
$541$	−10.8000	−	7.84665i	−0.464328	−	0.337354i	−0.795227	+	0.606312i	$0.792648\pi$
$542$	0.684058	+	9.98596i	0.0293828	+	0.428934i
$543$	−46.4903	+	46.4903i	−1.99509	+	1.99509i
$544$	16.5142	+	2.14666i	0.708042	+	0.0920371i
$545$	−17.2718	+	3.60294i	−0.739843	+	0.154333i
$546$	−5.42940	−	23.6704i	−0.232357	−	1.01300i
$547$	31.4731	−	16.0363i	1.34569	−	0.685664i	0.375233	−	0.926930i	$-0.377563\pi$
$547$	31.4731	−	16.0363i	1.34569	−	0.685664i	0.970459	+	0.241266i	$0.0775627\pi$
$548$	−15.3578	+	20.2606i	−0.656052	+	0.865492i
$549$		−	19.7842i		−	0.844369i
$550$	22.1603	+	11.0560i	0.944919	+	0.471431i
$551$		−	14.7163i		−	0.626937i
$552$	−9.49721	−	1.03906i	−0.404228	−	0.0442255i
$553$	5.96700	−	3.04034i	0.253743	−	0.129288i
$554$	−5.07858	+	1.16490i	−0.215768	+	0.0494919i
$555$	6.20681	−	56.9777i	0.263464	−	2.41857i
$556$	−4.73807	+	26.4323i	−0.200939	+	1.12098i
$557$	−3.39122	+	3.39122i	−0.143690	+	0.143690i	−0.775293	−	0.631602i	$-0.782398\pi$
$557$	−3.39122	+	3.39122i	−0.143690	+	0.143690i	0.631602	+	0.775293i	$0.282398\pi$
$558$	−60.2381	+	4.12643i	−2.55008	+	0.174686i
$559$	8.52071	+	6.19066i	0.360388	+	0.261837i
$560$	8.94399	−	0.0715055i	0.377952	−	0.00302166i
$561$	−22.8912	+	16.6314i	−0.966468	+	0.702180i
$562$	20.1988	−	16.9001i	0.852035	−	0.712886i
$563$	−6.07889	+	0.962802i	−0.256195	+	0.0405773i	−0.283211	−	0.959058i	$-0.591400\pi$
$563$	−6.07889	+	0.962802i	−0.256195	+	0.0405773i	0.0270159	+	0.999635i	$0.491400\pi$
$564$	−37.9980	+	5.23042i	−1.60001	+	0.220240i
$565$	−9.22058	+	14.0814i	−0.387913	+	0.592410i
$566$	−1.38594	+	15.5868i	−0.0582554	+	0.655160i
$567$	0.936011	−	1.83702i	0.0393088	−	0.0771478i
$568$	12.1567	+	11.0400i	0.510084	+	0.463227i
$569$	24.8960	−	8.08921i	1.04370	−	0.339117i	0.263504	−	0.964658i	$-0.415122\pi$
$569$	24.8960	−	8.08921i	1.04370	−	0.339117i	0.780191	+	0.625541i	$0.215122\pi$
$570$	−23.2959	−	50.6446i	−0.975756	−	2.12127i
$571$	−2.36730	−	0.769182i	−0.0990684	−	0.0321893i	0.259063	−	0.965860i	$-0.416586\pi$
$571$	−2.36730	−	0.769182i	−0.0990684	−	0.0321893i	−0.358132	+	0.933671i	$0.616586\pi$
$572$	−0.889241	+	43.8218i	−0.0371810	+	1.83228i
$573$	38.2401	+	6.05663i	1.59750	+	0.253020i
$574$	3.36684	−	2.01651i	0.140529	−	0.0841675i
$575$	−6.14316	−	0.368617i	−0.256187	−	0.0153724i
$576$	−36.0821	+	3.48226i	−1.50342	+	0.145094i
$577$	1.95888	−	12.3679i	0.0815493	−	0.514882i	−0.912773	−	0.408468i	$-0.866063\pi$
$577$	1.95888	−	12.3679i	0.0815493	−	0.514882i	0.994322	−	0.106414i	$-0.0339369\pi$
$578$	6.25945	−	9.98567i	0.260359	−	0.415349i
$579$	−4.55010	+	14.0038i	−0.189096	+	0.581976i
$580$	−9.82975	−	2.88922i	−0.408158	−	0.119968i
$581$	0.578471	+	1.78035i	0.0239990	+	0.0738614i
$582$	40.2522	+	10.0967i	1.66851	+	0.418520i
$583$	29.6375	+	15.1011i	1.22746	+	0.625423i
$584$	3.17417	+	2.08058i	0.131348	+	0.0860951i
$585$	22.4964	+	59.2750i	0.930112	+	2.45072i
$586$	−2.33047	+	5.46868i	−0.0962710	+	0.225909i
$587$	−0.883506	−	5.57824i	−0.0364662	−	0.230238i	0.962723	−	0.270488i	$-0.0871849\pi$
$587$	−0.883506	−	5.57824i	−0.0364662	−	0.230238i	−0.999190	+	0.0402490i	$0.987185\pi$
$588$	−1.80163	+	5.18450i	−0.0742979	+	0.213805i
$589$	35.5758	+	48.9659i	1.46588	+	2.01761i
$590$	−19.2913	+	12.8666i	−0.794210	+	0.529708i
$591$	−14.3096	+	19.6955i	−0.588620	+	0.810166i
$592$	4.34265	+	37.1070i	0.178482	+	1.52509i
$593$	−5.35511	−	5.35511i	−0.219908	−	0.219908i	0.588552	−	0.808460i	$-0.299698\pi$
$593$	−5.35511	−	5.35511i	−0.219908	−	0.219908i	−0.808460	+	0.588552i	$0.799698\pi$
$594$	13.6770	−	15.6886i	0.561174	−	0.643711i
$595$	−2.70019	+	6.00345i	−0.110697	+	0.246118i
$596$	−14.8480	−	15.4631i	−0.608199	−	0.633394i
$597$	26.6984	+	52.3985i	1.09269	+	2.14453i
$598$	−4.06591	−	10.1047i	−0.166267	−	0.413213i
$599$	31.3193			1.27967			0.639837	−	0.768511i	$-0.279002\pi$
$599$	31.3193			1.27967			0.639837	+	0.768511i	$0.279002\pi$
$600$	−38.4016	+	5.61750i	−1.56774	+	0.229334i
$601$	−16.6777			−0.680297			−0.340149	−	0.940372i	$-0.610477\pi$
$601$	−16.6777			−0.680297			−0.340149	+	0.940372i	$0.610477\pi$
$602$	−0.888563	−	2.20828i	−0.0362151	−	0.0900029i
$603$	−20.4714	−	40.1773i	−0.833658	−	1.63615i
$604$	−17.6389	−	18.3696i	−0.717717	−	0.747449i
$605$	2.45753	−	1.40648i	0.0999129	−	0.0571814i
$606$	21.6633	−	24.8495i	0.880011	−	1.00944i
$607$	−8.54366	−	8.54366i	−0.346777	−	0.346777i	0.512131	−	0.858907i	$-0.328856\pi$
$607$	−8.54366	−	8.54366i	−0.346777	−	0.346777i	−0.858907	+	0.512131i	$0.828856\pi$
$608$	22.1679	+	28.7921i	0.899028	+	1.16768i
$609$	3.69549	−	5.08641i	0.149749	−	0.206112i
$610$	3.73664	+	13.2919i	0.151292	+	0.538174i
$611$	−25.7031	−	35.3773i	−1.03984	−	1.43121i
$612$	8.75728	−	25.2006i	0.353992	−	1.01867i
$613$	5.17503	+	32.6738i	0.209017	+	1.31968i	0.839449	+	0.543439i	$0.182878\pi$
$613$	5.17503	+	32.6738i	0.209017	+	1.31968i	−0.630431	+	0.776245i	$0.717122\pi$
$614$	16.3311	−	38.3224i	0.659068	−	1.54657i
$615$	−13.2745	+	10.6665i	−0.535281	+	0.430116i
$616$	5.43053	−	8.28491i	0.218802	−	0.333809i
$617$	38.6185	+	19.6771i	1.55472	+	0.792170i	0.999226	−	0.0393485i	$-0.0125282\pi$
$617$	38.6185	+	19.6771i	1.55472	+	0.792170i	0.555496	+	0.831519i	$0.312528\pi$
$618$	−45.7763	−	11.4823i	−1.84139	−	0.461885i
$619$	−0.422073	−	1.29901i	−0.0169646	−	0.0522115i	0.942216	−	0.335006i	$-0.108738\pi$
$619$	−0.422073	−	1.29901i	−0.0169646	−	0.0522115i	−0.959180	+	0.282795i	$0.908738\pi$
$620$	39.6913	−	14.1495i	1.59404	−	0.568257i
$621$	−1.59828	+	4.91900i	−0.0641368	+	0.197393i
$622$	20.4595	−	32.6390i	0.820352	−	1.30870i
$623$	1.43183	−	9.04022i	0.0573651	−	0.362189i
$624$	−38.0866	−	57.1624i	−1.52468	−	2.28833i
$625$	−24.5296	+	4.82685i	−0.981184	+	0.193074i
$626$	−22.2275	+	13.3127i	−0.888388	+	0.532084i
$627$	−60.9800	−	9.65829i	−2.43531	−	0.385715i
$628$	0.881471	−	43.4389i	0.0351745	−	1.73340i
$629$	−26.1503	−	8.49676i	−1.04268	−	0.338788i
$630$	2.80726	−	14.0513i	0.111844	−	0.559816i
$631$	23.1322	−	7.51610i	0.920877	−	0.299211i	0.190051	−	0.981774i	$-0.439135\pi$
$631$	23.1322	−	7.51610i	0.920877	−	0.299211i	0.730827	+	0.682563i	$0.239135\pi$
$632$	12.7343	−	14.0224i	0.506542	−	0.557782i
$633$	14.4740	−	28.4068i	0.575290	−	1.12907i
$634$	4.08650	−	45.9582i	0.162296	−	1.82524i
$635$	3.55417	+	4.42318i	0.141043	+	0.175528i
$636$	−51.6406	+	7.10832i	−2.04768	+	0.281863i
$637$	−6.18034	+	0.978870i	−0.244874	+	0.0387842i
$638$	−8.70288	+	7.28158i	−0.344550	+	0.288280i
$639$	21.2834	−	15.4633i	0.841958	−	0.611718i
$640$	23.5838	−	9.15435i	0.932233	−	0.361857i
$641$	−21.6222	−	15.7095i	−0.854026	−	0.620486i	0.0722273	−	0.997388i	$-0.476989\pi$
$641$	−21.6222	−	15.7095i	−0.854026	−	0.620486i	−0.926253	+	0.376902i	$0.876989\pi$
$642$	−7.74618	+	0.530629i	−0.305717	+	0.0209422i
$643$	−5.52715	+	5.52715i	−0.217970	+	0.217970i	−0.807642	−	0.589673i	$-0.799257\pi$
$643$	−5.52715	+	5.52715i	−0.217970	+	0.217970i	0.589673	+	0.807642i	$0.299257\pi$
$644$	−0.434341	+	2.42306i	−0.0171154	+	0.0954821i
$645$	5.13041	+	8.96435i	0.202010	+	0.352971i
$646$	−26.0664	+	5.97898i	−1.02557	+	0.235240i
$647$	24.6154	−	12.5422i	0.967730	−	0.493083i	0.102650	−	0.994718i	$-0.467268\pi$
$647$	24.6154	−	12.5422i	0.967730	−	0.493083i	0.865080	+	0.501635i	$0.167268\pi$
$648$	0.634223	−	5.79689i	0.0249146	−	0.227723i
$649$			25.6819i			1.00810i
$650$	−26.3094	−	35.5747i	−1.03194	−	1.39535i
$651$			25.8577i			1.01344i
$652$	26.4206	−	34.8552i	1.03471	−	1.36504i
$653$	−23.3346	+	11.8896i	−0.913153	+	0.465275i	−0.846432	−	0.532497i	$-0.821254\pi$
$653$	−23.3346	+	11.8896i	−0.913153	+	0.465275i	−0.0667214	+	0.997772i	$0.521254\pi$
$654$	−6.84639	−	29.8480i	−0.267715	−	1.16715i
$655$	5.36828	+	2.41451i	0.209756	+	0.0943426i
$656$	6.88350	−	8.70821i	0.268756	−	0.339998i
$657$	4.29931	−	4.29931i	0.167732	−	0.167732i
$658$	0.675423	+	9.85991i	0.0263307	+	0.384379i
$659$	4.33391	+	3.14877i	0.168825	+	0.122659i	0.668990	−	0.743272i	$-0.266727\pi$
$659$	4.33391	+	3.14877i	0.168825	+	0.122659i	−0.500164	+	0.865930i	$0.666727\pi$
$660$	−18.4233	+	38.8354i	−0.717126	+	1.51166i
$661$	−8.20998	+	5.96490i	−0.319331	+	0.232008i	−0.735890	−	0.677101i	$-0.763236\pi$
$661$	−8.20998	+	5.96490i	−0.319331	+	0.232008i	0.416559	+	0.909109i	$0.363236\pi$
$662$	11.2616	+	13.4598i	0.437696	+	0.523131i
$663$	49.9306	−	7.90823i	1.93914	−	0.307130i
$664$	3.31455	+	4.12892i	0.128630	+	0.160233i
$665$	−13.4290	+	5.09664i	−0.520753	+	0.197639i
$666$	59.6168	+	5.30099i	2.31010	+	0.205409i
$667$	1.28018	−	2.51249i	0.0495687	−	0.0972840i
$668$	−12.2757	−	40.5631i	−0.474960	−	1.56943i
$669$	13.9615	−	4.53636i	0.539782	−	0.175386i
$670$	21.3419	+	23.1265i	0.824508	+	0.893454i
$671$	14.5434	+	4.72545i	0.561443	+	0.182424i
$672$	0.431768	+	15.5181i	0.0166558	+	0.598625i
$673$	8.25987	+	1.30823i	0.318395	+	0.0504287i	0.313586	−	0.949560i	$-0.398469\pi$
$673$	8.25987	+	1.30823i	0.318395	+	0.0504287i	0.00480823	+	0.999988i	$0.498469\pi$
$674$	−13.6636	−	22.8132i	−0.526301	−	0.878732i
$675$	−1.25847	+	20.9729i	−0.0484384	+	0.807246i
$676$	24.6888	−	46.1168i	0.949569	−	1.77372i
$677$	−6.45882	+	40.7794i	−0.248233	+	1.56728i	0.477081	+	0.878859i	$0.341695\pi$
$677$	−6.45882	+	40.7794i	−0.248233	+	1.56728i	−0.725313	+	0.688419i	$0.758305\pi$
$678$	−24.7528	−	15.5161i	−0.950627	−	0.595894i
$679$	3.30426	−	10.1695i	0.126806	−	0.390269i
$680$	−1.12390	+	18.5849i	−0.0430996	+	0.712697i
$681$	−2.70847	−	8.33582i	−0.103789	−	0.319429i
$682$	11.3545	−	45.2668i	0.434786	−	1.73336i
$683$	13.4179	+	6.83678i	0.513423	+	0.261602i	0.691451	−	0.722423i	$-0.256972\pi$
$683$	13.4179	+	6.83678i	0.513423	+	0.261602i	−0.178028	+	0.984025i	$0.556972\pi$
$684$	52.3940	−	25.3706i	2.00334	−	0.970068i
$685$	−23.7799	−	15.5712i	−0.908583	−	0.594944i
$686$	1.30101	+	0.554423i	0.0496726	+	0.0211680i
$687$	−5.59052	−	35.2972i	−0.213292	−	1.34667i
$688$	−4.56365	−	4.94991i	−0.173987	−	0.188713i
$689$	−34.9314	−	48.0789i	−1.33078	−	1.83166i
$690$	0.428334	−	10.6730i	0.0163064	−	0.406313i
$691$	5.16938	−	7.11504i	0.196653	−	0.270669i	−0.699291	−	0.714837i	$-0.746501\pi$
$691$	5.16938	−	7.11504i	0.196653	−	0.270669i	0.895943	+	0.444168i	$0.146501\pi$
$692$	−33.3996	+	23.2457i	−1.26966	+	0.883670i
$693$	−11.2216	−	11.2216i	−0.426275	−	0.426275i
$694$	−7.40341	−	6.45414i	−0.281030	−	0.244996i
$695$	−29.8467	−	3.25132i	−1.13215	−	0.123330i
$696$	4.67554	−	17.1571i	0.177226	−	0.650337i
$697$	3.70887	+	7.27906i	0.140483	+	0.275714i
$698$	−29.9572	+	12.0541i	−1.13390	+	0.456254i
$699$	27.9720			1.05800
$700$	0.767819	+	9.97048i	0.0290208	+	0.376849i
$701$	−38.8213			−1.46626			−0.733131	−	0.680088i	$-0.761942\pi$
$701$	−38.8213			−1.46626			−0.733131	+	0.680088i	$0.761942\pi$
$702$	−34.4977	+	13.8811i	−1.30203	+	0.523909i
$703$	−27.2379	−	53.4575i	−1.02730	−	2.01619i
$704$	6.05837	−	27.3558i	0.228333	−	1.03101i
$705$	−8.75712	−	41.9800i	−0.329812	−	1.58106i
$706$	32.9654	+	28.7386i	1.24067	+	1.08159i
$707$	−6.00636	−	6.00636i	−0.225893	−	0.225893i
$708$	−22.9911	−	33.0337i	−0.864060	−	1.24148i
$709$	−0.543494	+	0.748056i	−0.0204114	+	0.0280938i	−0.819101	−	0.573650i	$-0.805527\pi$
$709$	−0.543494	+	0.748056i	−0.0204114	+	0.0280938i	0.798689	+	0.601744i	$0.205527\pi$
$710$	−11.3786	+	14.4087i	−0.427030	+	0.540749i
$711$	−17.8365	−	24.5498i	−0.668919	−	0.920689i
$712$	−5.27471	−	25.3453i	−0.197678	−	0.949854i
$713$	1.81423	+	11.4546i	0.0679435	+	0.428979i
$714$	−10.5107	−	4.47915i	−0.393355	−	0.167628i
$715$	−48.9465	+	2.37938i	−1.83050	+	0.0889836i
$716$	−8.28936	−	17.1188i	−0.309788	−	0.639758i
$717$	−40.7830	−	20.7800i	−1.52307	−	0.776042i
$718$	1.65285	−	6.58938i	0.0616836	−	0.245913i
$719$	1.97439	+	6.07655i	0.0736323	+	0.226617i	0.981099	−	0.193508i	$-0.0619864\pi$
$719$	1.97439	+	6.07655i	0.0736323	+	0.226617i	−0.907466	+	0.420125i	$0.861986\pi$
$720$	−6.65986	−	39.9775i	−0.248198	−	1.48987i
$721$	−3.75773	+	11.5651i	−0.139945	+	0.430707i
$722$	−26.6763	−	16.7219i	−0.992791	−	0.622324i
$723$	6.33211	−	39.9794i	0.235494	−	1.48685i
$724$	42.2428	+	22.6148i	1.56994	+	0.840472i
$725$	2.46639	−	11.1862i	0.0915993	−	0.415446i
$726$	2.52522	+	4.21620i	0.0937196	+	0.156478i
$727$	11.6439	+	1.84421i	0.431847	+	0.0683979i	0.368574	−	0.929598i	$-0.379846\pi$
$727$	11.6439	+	1.84421i	0.431847	+	0.0683979i	0.0632731	+	0.997996i	$0.479846\pi$
$728$	−15.3649	+	8.78399i	−0.569461	+	0.325556i
$729$	−41.7874	−	13.5776i	−1.54768	−	0.502872i
$730$	−2.07646	+	3.70048i	−0.0768532	+	0.136961i
$731$	4.71252	−	1.53119i	0.174299	−	0.0566332i
$732$	−22.9370	+	6.94148i	−0.847777	+	0.256565i
$733$	18.7558	−	36.8104i	0.692762	−	1.35962i	−0.229596	−	0.973286i	$-0.573740\pi$
$733$	18.7558	−	36.8104i	0.692762	−	1.35962i	0.922358	−	0.386336i	$-0.126260\pi$
$734$	−40.1566	−	3.57063i	−1.48221	−	0.131794i
$735$	−5.92130	−	1.61066i	−0.218411	−	0.0594102i
$736$	1.28005	+	6.84402i	0.0471833	+	0.252274i
$737$	34.4241	−	5.45224i	1.26803	−	0.200836i
$738$	−11.4113	−	13.6387i	−0.420055	−	0.502047i
$739$	0.169955	−	0.123479i	0.00625188	−	0.00454226i	−0.584655	−	0.811282i	$-0.698770\pi$
$739$	0.169955	−	0.123479i	0.00625188	−	0.00454226i	0.590907	+	0.806740i	$0.298770\pi$
$740$	−41.0544	+	7.69837i	−1.50919	+	0.282998i
$741$	89.2403	+	64.8369i	3.27833	+	2.38184i
$742$	0.917922	+	13.3999i	0.0336980	+	0.491927i
$743$	−6.37037	+	6.37037i	−0.233706	+	0.233706i	−0.814238	−	0.580532i	$-0.802845\pi$
$743$	−6.37037	+	6.37037i	−0.233706	+	0.233706i	0.580532	+	0.814238i	$0.302845\pi$
$744$	25.9192	+	68.3899i	0.950242	+	2.50730i
$745$	16.1051	−	17.7509i	0.590044	−	0.650341i
$746$	11.6811	+	50.9256i	0.427674	+	1.86452i
$747$	7.55779	−	3.85089i	0.276525	−	0.140897i
$748$	16.4334	+	12.4567i	0.600863	+	0.455461i
$749$			2.00058i			0.0730998i
$750$	−9.21992	−	42.4004i	−0.336664	−	1.54824i
$751$		−	9.62682i		−	0.351288i	−0.984454	−	0.175644i	$-0.943799\pi$
$751$		−	9.62682i		−	0.351288i	0.984454	−	0.175644i	$-0.0562007\pi$
$752$	11.6697	+	25.4010i	0.425551	+	0.926278i
$753$	−5.09400	+	2.59552i	−0.185636	+	0.0945861i
$754$	19.7603	−	4.53253i	0.719629	−	0.165065i
$755$	19.1322	−	21.0873i	0.696292	−	0.767447i
$756$	8.27239	+	1.48285i	0.300864	+	0.0539307i
$757$	5.28091	−	5.28091i	0.191938	−	0.191938i	−0.604595	−	0.796533i	$-0.706665\pi$
$757$	5.28091	−	5.28091i	0.191938	−	0.191938i	0.796533	+	0.604595i	$0.206665\pi$
$758$	23.5334	−	1.61209i	0.854772	−	0.0585536i
$759$	−9.57082	−	6.95361i	−0.347399	−	0.252400i
$760$	−30.4089	+	26.9407i	−1.10305	+	0.977243i
$761$	−37.2743	+	27.0814i	−1.35119	+	0.981700i	−0.352243	+	0.935909i	$0.614581\pi$
$761$	−37.2743	+	27.0814i	−1.35119	+	0.981700i	−0.998951	+	0.0457909i	$0.985419\pi$
$762$	−7.55332	+	6.31975i	−0.273628	+	0.228941i
$763$	−7.79331	+	1.23434i	−0.282137	+	0.0446861i
$764$	−3.84766	−	27.9525i	−0.139203	−	1.01129i
$765$	28.7820	+	7.82904i	1.04062	+	0.283060i
$766$	0.708965	−	7.97327i	0.0256160	−	0.288086i
$767$	20.8310	−	40.8832i	0.752164	−	1.47621i
$768$	16.6970	+	40.6104i	0.602499	+	1.46540i
$769$	−10.7597	+	3.49605i	−0.388006	+	0.126071i	−0.496522	−	0.868024i	$-0.665390\pi$
$769$	−10.7597	+	3.49605i	−0.388006	+	0.126071i	0.108517	+	0.994095i	$0.465390\pi$
$770$	9.65863	+	5.41977i	0.348073	+	0.195315i
$771$	−21.7332	−	7.06155i	−0.782702	−	0.254315i
$772$	10.7287	+	0.217709i	0.386134	+	0.00783550i
$773$	32.2287	+	5.10452i	1.15919	+	0.183597i	0.706261	−	0.707952i	$-0.250381\pi$
$773$	32.2287	+	5.10452i	1.15919	+	0.183597i	0.452925	+	0.891549i	$0.350381\pi$
$774$	−9.25316	+	5.54201i	−0.332598	+	0.199204i
$775$	18.8356	+	43.1825i	0.676593	+	1.55116i
$776$	−1.45434	−	30.2089i	−0.0522078	−	1.08444i
$777$	4.00972	−	25.3164i	0.143848	−	0.908220i
$778$	−0.107145	+	0.170927i	−0.00384132	+	0.00612804i
$779$	−5.50850	+	16.9534i	−0.197363	+	0.607419i
$780$	60.8281	−	46.8787i	2.17799	−	1.67853i
$781$	6.28359	+	19.3389i	0.224844	+	0.692000i
$782$	−4.97038	−	1.24674i	−0.177740	−	0.0445834i
$783$	−8.57769	−	4.37055i	−0.306542	−	0.156191i
$784$	3.99671	+	0.162271i	0.142740	+	0.00579539i
$785$	48.5189	−	2.35859i	1.73171	−	0.0841815i
$786$	−4.00525	+	9.39869i	−0.142862	+	0.335240i
$787$	−0.699834	−	4.41858i	−0.0249464	−	0.157505i	0.972070	−	0.234689i	$-0.0754072\pi$
$787$	−0.699834	−	4.41858i	−0.0249464	−	0.157505i	−0.997017	+	0.0771837i	$0.975407\pi$
$788$	16.7591	+	5.82385i	0.597019	+	0.207466i
$789$	17.0973	+	23.5325i	0.608681	+	0.837778i
$790$	16.6200	+	13.1249i	0.591314	+	0.466962i
$791$	−4.42447	+	6.08976i	−0.157316	+	0.216527i
$792$	−40.9279	−	18.4313i	−1.45431	−	0.654928i
$793$	−19.3189	−	19.3189i	−0.686033	−	0.686033i
$794$	18.2801	−	20.9687i	0.648736	−	0.744151i
$795$	−11.9012	−	57.0522i	−0.422093	−	2.02343i
$796$	30.9141	−	29.6844i	1.09572	−	1.05213i
$797$	13.6962	+	26.8803i	0.485145	+	0.952150i	0.995729	+	0.0923226i	$0.0294291\pi$
$797$	13.6962	+	26.8803i	0.485145	+	0.952150i	−0.510584	+	0.859828i	$0.670571\pi$
$798$	−9.30623	−	23.1281i	−0.329437	−	0.818726i
$799$	−20.5729			−0.727818
$800$	12.0249	+	25.6008i	0.425145	+	0.905125i
$801$	−41.4738			−1.46540
$802$	−0.460886	−	1.14541i	−0.0162744	−	0.0404457i
$803$	2.13355	+	4.18733i	0.0752914	+	0.147768i
$804$	−39.3975	+	37.8303i	−1.38944	+	1.33417i
$805$	−2.73606	−	0.298050i	−0.0964335	−	0.0105049i
$806$	−54.7919	+	62.8506i	−1.92996	+	2.21382i
$807$	36.4739	+	36.4739i	1.28394	+	1.28394i
$808$	−21.9066	−	9.86532i	−0.770670	−	0.347061i
$809$	−6.84882	+	9.42660i	−0.240792	+	0.331421i	−0.912260	−	0.409612i	$-0.865664\pi$
$809$	−6.84882	+	9.42660i	−0.240792	+	0.331421i	0.671468	+	0.741034i	$0.265664\pi$
$810$	6.51455	+	0.261446i	0.228898	+	0.00918627i
$811$	29.7039	+	40.8840i	1.04305	+	1.43563i	0.894685	+	0.446697i	$0.147400\pi$
$811$	29.7039	+	40.8840i	1.04305	+	1.43563i	0.148361	+	0.988933i	$0.452600\pi$
$812$	−4.32808	−	1.50402i	−0.151886	−	0.0527808i
$813$	−3.03848	−	19.1842i	−0.106564	−	0.672820i
$814$	−18.1362	+	42.5584i	−0.635675	+	1.49167i
$815$	40.9095	+	26.7877i	1.43300	+	0.938333i
$816$	−32.2892	−	1.31098i	−1.13035	−	0.0458934i
$817$	9.63351	+	4.90852i	0.337034	+	0.171727i
$818$	29.3005	+	7.34958i	1.02447	+	0.256972i
$819$	8.76172	+	26.9658i	0.306159	+	0.942262i
$820$	10.2425	+	7.00782i	0.357685	+	0.244724i
$821$	2.09954	−	6.46173i	0.0732746	−	0.225516i	−0.907711	−	0.419595i	$-0.862172\pi$
$821$	2.09954	−	6.46173i	0.0732746	−	0.225516i	0.980986	+	0.194079i	$0.0621720\pi$
$822$	26.2027	−	41.8011i	0.913926	−	1.45798i
$823$	−4.90213	+	30.9508i	−0.170877	+	1.07888i	0.741927	+	0.670481i	$0.233912\pi$
$823$	−4.90213	+	30.9508i	−0.170877	+	1.07888i	−0.912804	+	0.408397i	$0.866088\pi$
$824$	1.65393	+	34.3546i	0.0576173	+	1.19680i
$825$	−44.7337	−	17.5615i	−1.55743	−	0.611411i
$826$	−8.89654	+	5.32842i	−0.309550	+	0.185400i
$827$	−42.0678	−	6.66288i	−1.46284	−	0.231691i	−0.626294	−	0.779587i	$-0.715429\pi$
$827$	−42.0678	−	6.66288i	−1.46284	−	0.231691i	−0.836547	+	0.547896i	$0.815429\pi$
$828$	11.1521	+	0.226301i	0.387563	+	0.00786451i
$829$	36.4466	+	11.8422i	1.26584	+	0.411297i	0.863573	−	0.504224i	$-0.168221\pi$
$829$	36.4466	+	11.8422i	1.26584	+	0.411297i	0.402270	+	0.915521i	$0.368221\pi$
$830$	−4.35035	+	4.01464i	−0.151003	+	0.139350i
$831$	9.61614	−	3.12447i	0.333580	−	0.108387i
$832$	−31.8330	+	38.6337i	−1.10361	+	1.33938i
$833$	−1.33650	+	2.62303i	−0.0463069	+	0.0908825i
$834$	4.61529	−	51.9052i	0.159815	−	1.79733i
$835$	44.2990	−	16.8126i	1.53303	−	0.581825i
$836$	6.13571	+	44.5748i	0.212208	+	1.54165i
$837$	39.1063	−	6.19383i	1.35171	−	0.214090i
$838$	6.78644	−	5.67812i	0.234434	−	0.196147i
$839$	−23.9962	+	17.4343i	−0.828442	+	0.601898i	−0.919118	−	0.393982i	$-0.871097\pi$
$839$	−23.9962	+	17.4343i	−0.828442	+	0.601898i	0.0906761	+	0.995880i	$0.471097\pi$
$840$	−17.2755	+	1.67540i	−0.596060	+	0.0578068i
$841$	−19.2153	−	13.9607i	−0.662597	−	0.481405i
$842$	−35.2282	+	2.41320i	−1.21404	+	0.0831643i
$843$	−36.1375	+	36.1375i	−1.24464	+	1.24464i
$844$	−22.8703	−	4.09956i	−0.787228	−	0.141113i
$845$	53.3373	+	23.9897i	1.83486	+	0.825271i
$846$	43.6485	−	10.0119i	1.50067	−	0.344216i
$847$	1.12829	−	0.574891i	0.0387684	−	0.0197535i
$848$	15.8595	+	34.5208i	0.544619	+	1.18545i
$849$		−	30.3657i		−	1.04215i
$850$	−20.8157	+	0.176156i	−0.713973	+	0.00604210i
$851$		−	11.4961i		−	0.394082i
$852$	−25.3950	−	19.2497i	−0.870019	−	0.659484i
$853$	44.8557	−	22.8551i	1.53583	−	0.782544i	0.537668	−	0.843157i	$-0.319306\pi$
$853$	44.8557	−	22.8551i	1.53583	−	0.782544i	0.998161	+	0.0606131i	$0.0193056\pi$
$854$	1.38048	+	6.01845i	0.0472391	+	0.205947i
$855$	32.3286	+	56.4877i	1.10562	+	1.93184i
$856$	2.00534	+	5.29125i	0.0685410	+	0.180851i
$857$	−21.3548	+	21.3548i	−0.729465	+	0.729465i	−0.970513	−	0.241049i	$-0.922509\pi$
$857$	−21.3548	+	21.3548i	−0.729465	+	0.729465i	0.241049	+	0.970513i	$0.422509\pi$
$858$	−5.81277	−	84.8556i	−0.198445	−	2.89692i
$859$	31.6989	+	23.0306i	1.08155	+	0.785794i	0.977953	−	0.208825i	$-0.0669640\pi$
$859$	31.6989	+	23.0306i	1.08155	+	0.785794i	0.103599	+	0.994619i	$0.466964\pi$
$860$	5.16996	−	5.47102i	0.176294	−	0.186560i
$861$	−6.16116	+	4.47635i	−0.209972	+	0.152554i
$862$	16.2853	+	19.4641i	0.554679	+	0.662948i
$863$	6.78813	−	1.07513i	0.231071	−	0.0365980i	−0.0398252	−	0.999207i	$-0.512680\pi$
$863$	6.78813	−	1.07513i	0.231071	−	0.0365980i	0.270896	+	0.962609i	$0.412680\pi$
$864$	23.3656	−	4.37012i	0.794914	−	0.148675i
$865$	−28.4974	−	35.4650i	−0.968940	−	1.20585i
$866$	−4.61560	−	0.410409i	−0.156844	−	0.0139463i
$867$	−10.3826	+	20.3770i	−0.352612	+	0.692040i
$868$	18.0368	−	5.45851i	0.612208	−	0.185274i
$869$	22.3069	−	7.24794i	0.756709	−	0.245870i
$870$	19.4964	+	3.89513i	0.660990	+	0.132057i
$871$	−59.2222	−	19.2425i	−2.00667	−	0.652006i
$872$	−19.3749	+	11.0765i	−0.656117	+	0.375097i
$873$	−47.8550	−	7.57948i	−1.61964	−	0.256527i
$874$	−5.74524	−	9.59248i	−0.194336	−	0.324470i
$875$	−11.0618	+	1.62344i	−0.373959	+	0.0548824i
$876$	−6.49291	−	3.47600i	−0.219375	−	0.117443i
$877$	0.0979650	−	0.618526i	0.00330804	−	0.0208862i	−0.985979	−	0.166869i	$-0.946634\pi$
$877$	0.0979650	−	0.618526i	0.00330804	−	0.0208862i	0.989287	+	0.145983i	$0.0466344\pi$
$878$	−2.32989	−	1.46047i	−0.0786298	−	0.0492885i
$879$	3.56466	−	10.9709i	0.120233	−	0.370039i
$880$	30.9783	+	4.65292i	1.04428	+	0.156850i
$881$	−3.35433	−	10.3236i	−0.113010	−	0.347809i	0.878517	−	0.477712i	$-0.158534\pi$
$881$	−3.35433	−	10.3236i	−0.113010	−	0.347809i	−0.991527	+	0.129902i	$0.958534\pi$
$882$	1.55908	−	6.21555i	0.0524968	−	0.209289i
$883$	−3.18347	−	1.62206i	−0.107132	−	0.0545867i	0.399603	−	0.916688i	$-0.369148\pi$
$883$	−3.18347	−	1.62206i	−0.107132	−	0.0545867i	−0.506736	+	0.862102i	$0.669148\pi$
$884$	−16.0565	−	33.1591i	−0.540040	−	1.11526i
$885$	35.0766	−	28.1852i	1.17909	−	0.947436i
$886$	15.0867	+	6.42921i	0.506849	+	0.215993i
$887$	0.440232	+	2.77951i	0.0147815	+	0.0933270i	0.993976	−	0.109596i	$-0.0349558\pi$
$887$	0.440232	+	2.77951i	0.0147815	+	0.0933270i	−0.979195	+	0.202923i	$0.934956\pi$
$888$	−14.7714	−	70.9773i	−0.495695	−	2.38184i
$889$	1.49155	+	2.05295i	0.0500251	+	0.0688536i
$890$	27.8639	−	7.83315i	0.934001	−	0.262568i
$891$	4.24433	−	5.84183i	0.142191	−	0.195709i
$892$	−6.11152	−	8.78105i	−0.204629	−	0.294011i
$893$	−31.7423	−	31.7423i	−1.06221	−	1.06221i
$894$	31.3573	+	27.3366i	1.04874	+	0.914273i
$895$	18.4563	−	10.5628i	0.616926	−	0.353074i
$896$	10.7334	−	3.57702i	0.358576	−	0.119500i
$897$	9.59565	+	18.8325i	0.320389	+	0.628799i
$898$	45.8109	−	18.4333i	1.52873	−	0.615126i
$899$	−21.5863			−0.719945
$900$	44.0779	−	10.5038i	1.46926	−	0.350126i
$901$	−27.9593			−0.931460
$902$	12.7514	−	5.13089i	0.424576	−	0.170840i
$903$	2.09703	+	4.11565i	0.0697848	+	0.136960i
$904$	−5.59785	+	20.5415i	−0.186182	+	0.683200i
$905$	−21.9744	+	48.8567i	−0.730455	+	1.62405i
$906$	37.2513	+	32.4749i	1.23759	+	1.07891i
$907$	−20.6296	−	20.6296i	−0.684995	−	0.684995i	0.276126	−	0.961121i	$-0.410949\pi$
$907$	−20.6296	−	20.6296i	−0.684995	−	0.684995i	−0.961121	+	0.276126i	$0.910949\pi$
$908$	−5.24281	+	3.64894i	−0.173989	+	0.121094i
$909$	−22.6235	+	31.1386i	−0.750374	+	1.03280i
$910$	−10.9795	−	16.4620i	−0.363968	−	0.545710i
$911$	−1.58981	−	2.18818i	−0.0526727	−	0.0724978i	0.781868	−	0.623444i	$-0.214267\pi$
$911$	−1.58981	−	2.18818i	−0.0526727	−	0.0724978i	−0.834541	+	0.550946i	$0.814267\pi$
$912$	−47.7966	−	51.8421i	−1.58271	−	1.71666i
$913$	1.02563	+	6.47555i	0.0339433	+	0.214309i
$914$	25.7801	+	10.9862i	0.852731	+	0.363391i
$915$	−9.50697	−	25.0496i	−0.314291	−	0.828114i
$916$	−23.4410	+	11.3508i	−0.774513	+	0.375040i
$917$	2.34551	+	1.19509i	0.0774554	+	0.0394655i
$918$	−4.25641	+	16.9690i	−0.140482	+	0.560059i
$919$	12.0484	+	37.0811i	0.397439	+	1.22319i	0.927046	+	0.374948i	$0.122339\pi$
$919$	12.0484	+	37.0811i	0.397439	+	1.22319i	−0.529607	+	0.848243i	$0.677661\pi$
$920$	−7.53523	+	1.95426i	−0.248429	+	0.0644301i
$921$	−24.9798	+	76.8798i	−0.823111	+	2.53328i
$922$	8.26314	+	5.17969i	0.272132	+	0.170584i
$923$	5.68321	−	35.8824i	0.187065	−	1.18108i
$924$	−9.07272	+	16.9472i	−0.298470	+	0.557521i
$925$	−11.7450	−	45.1992i	−0.386172	−	1.48614i
$926$	−15.2673	−	25.4909i	−0.501715	−	0.837682i
$927$	54.4224	+	8.61966i	1.78747	+	0.283107i
$928$	−12.9547	+	0.360445i	−0.425259	+	0.0118322i
$929$	−44.8303	−	14.5663i	−1.47084	−	0.477903i	−0.539475	−	0.842002i	$-0.681377\pi$
$929$	−44.8303	−	14.5663i	−1.47084	−	0.477903i	−0.931361	+	0.364098i	$0.881377\pi$
$930$	−74.2871	+	34.1711i	−2.43597	+	1.12051i
$931$	−6.10921	+	1.98500i	−0.200221	+	0.0650558i
$932$	−5.90482	−	19.5115i	−0.193419	−	0.639122i
$933$	−33.9364	+	66.6039i	−1.11103	+	2.18051i
$934$	−44.6122	−	3.96682i	−1.45976	−	0.129798i
$935$	−12.6297	+	19.2878i	−0.413037	+	0.630779i
$936$	50.2033	+	62.5381i	1.64095	+	2.04412i
$937$	−12.6689	+	2.00656i	−0.413876	+	0.0655515i	−0.359900	−	0.932991i	$-0.617189\pi$
$937$	−12.6689	+	2.00656i	−0.413876	+	0.0655515i	−0.0539756	+	0.998542i	$0.517189\pi$
$938$	9.03094	+	10.7937i	0.294871	+	0.352427i
$939$	40.6752	−	29.5523i	1.32739	−	0.964402i
$940$	−27.4341	+	14.9703i	−0.894801	+	0.488278i
$941$	39.5139	+	28.7086i	1.28812	+	0.935872i	0.999766	−	0.0216520i	$-0.00689260\pi$
$941$	39.5139	+	28.7086i	1.28812	+	0.935872i	0.288352	+	0.957524i	$0.406893\pi$
$942$	5.76198	+	84.1142i	0.187736	+	2.74059i
$943$	−2.41524	+	2.41524i	−0.0786510	+	0.0786510i
$944$	−18.1889	+	23.0106i	−0.592000	+	0.748930i
$945$	−1.01755	+	9.34097i	−0.0331009	+	0.303862i
$946$	−1.86384	−	8.12574i	−0.0605987	−	0.264191i
$947$	3.79704	−	1.93469i	0.123387	−	0.0628690i	−0.391207	−	0.920303i	$-0.627942\pi$
$947$	3.79704	−	1.93469i	0.123387	−	0.0628690i	0.514595	+	0.857434i	$0.327942\pi$
$948$	−22.2040	+	29.2924i	−0.721151	+	0.951374i
$949$		−	8.39638i		−	0.272558i
$950$	−32.3886	−	31.8450i	−1.05083	−	1.03319i
$951$			89.5346i			2.90336i
$952$	−0.905586	+	8.27719i	−0.0293502	+	0.268265i
$953$	−2.88107	+	1.46798i	−0.0933269	+	0.0475524i	−0.500031	−	0.866008i	$-0.666678\pi$
$953$	−2.88107	+	1.46798i	−0.0933269	+	0.0475524i	0.406704	+	0.913560i	$0.366678\pi$
$954$	59.3198	−	13.6065i	1.92055	−	0.440526i
$955$	30.8818	−	6.44201i	0.999310	−	0.208458i
$956$	−5.88564	+	32.8343i	−0.190355	+	1.06194i
$957$	15.5702	−	15.5702i	0.503314	−	0.503314i
$958$	−46.6597	+	3.19628i	−1.50750	+	0.103267i
$959$	−10.2840	−	7.47178i	−0.332089	−	0.241276i
$960$	−44.0117	+	21.7477i	−1.42047	+	0.701903i
$961$	46.7452	−	33.9624i	1.50791	−	1.09556i
$962$	63.3909	−	53.0383i	2.04380	−	1.71002i
$963$	8.95347	−	1.41809i	0.288522	−	0.0456973i
$964$	−29.2239	+	4.02266i	−0.941238	+	0.129561i
$965$	0.582531	+	11.9833i	0.0187523	+	0.385758i
$966$	0.423086	−	4.75817i	0.0136126	−	0.153092i
$967$	20.1372	−	39.5214i	0.647567	−	1.27092i	−0.300781	−	0.953693i	$-0.597247\pi$
$967$	20.1372	−	39.5214i	0.647567	−	1.27092i	0.948349	−	0.317230i	$-0.102753\pi$
$968$	2.40790	−	2.65147i	0.0773927	−	0.0852214i
$969$	49.3559	−	16.0367i	1.58554	−	0.515173i
$970$	33.5826	−	3.94613i	1.07827	−	0.126702i
$971$	23.5147	+	7.64039i	0.754623	+	0.245192i	0.660969	−	0.750413i	$-0.270145\pi$
$971$	23.5147	+	7.64039i	0.754623	+	0.245192i	0.0936536	+	0.995605i	$0.470145\pi$
$972$	−0.741098	+	36.5213i	−0.0237707	+	1.17142i
$973$	−13.2615	−	2.10042i	−0.425145	−	0.0673363i
$974$	−27.2596	+	16.3267i	−0.873454	+	0.523140i
$975$	56.9673	+	64.2403i	1.82441	+	2.05734i
$976$	9.68391	+	14.5341i	0.309974	+	0.465227i
$977$	−1.81751	+	11.4753i	−0.0581472	+	0.367127i	0.941407	+	0.337272i	$0.109504\pi$
$977$	−1.81751	+	11.4753i	−0.0581472	+	0.367127i	−0.999554	+	0.0298543i	$0.990496\pi$
$978$	−45.0777	+	71.9122i	−1.44142	+	2.29950i
$979$	9.90600	−	30.4875i	0.316597	−	0.974386i
$980$	0.126473	+	4.47035i	0.00404004	+	0.142800i
$981$	11.0484	+	34.0035i	0.352748	+	1.08565i
$982$	13.3092	+	3.33842i	0.424715	+	0.106533i
$983$	29.9788	+	15.2750i	0.956175	+	0.487196i	0.861190	−	0.508283i	$-0.169720\pi$
$983$	29.9788	+	15.2750i	0.956175	+	0.487196i	0.0949852	+	0.995479i	$0.469720\pi$
$984$	−11.8084	+	18.0151i	−0.376438	+	0.574300i
$985$	−5.20655	+	19.1409i	−0.165894	+	0.609880i
$986$	3.73924	−	8.77449i	0.119082	−	0.279437i
$987$	−3.00012	−	18.9420i	−0.0954950	−	0.602932i
$988$	26.3878	−	75.9355i	0.839509	−	2.41583i
$989$	1.21772	+	1.67604i	0.0387211	+	0.0532951i
$990$	17.4094	−	47.0682i	0.553307	−	1.49593i
$991$	−29.4258	+	40.5011i	−0.934740	+	1.28656i	0.0232410	+	0.999730i	$0.492601\pi$
$991$	−29.4258	+	40.5011i	−0.934740	+	1.28656i	−0.957982	+	0.286830i	$0.907399\pi$
$992$	42.2332	−	32.5166i	1.34090	−	1.03240i
$993$	−24.0808	−	24.0808i	−0.764182	−	0.764182i
$994$	−5.39553	+	6.18910i	−0.171136	+	0.196306i
$995$	35.4877	+	32.1974i	1.12504	+	1.02073i
$996$	−7.11630	−	7.41109i	−0.225489	−	0.234829i
$997$	−7.34384	−	14.4131i	−0.232582	−	0.456467i	0.744988	−	0.667077i	$-0.232455\pi$
$997$	−7.34384	−	14.4131i	−0.232582	−	0.456467i	−0.977570	+	0.210610i	$0.932455\pi$
$998$	−3.33369	−	8.28499i	−0.105526	−	0.262257i
$999$	−39.2480			−1.24175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.323.56	yes	720
4.3	odd	2	inner	700.2.bj.a.323.27	✓	720
25.12	odd	20	inner	700.2.bj.a.687.27	yes	720
100.87	even	20	inner	700.2.bj.a.687.56	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.27	✓	720	4.3	odd	2	inner
700.2.bj.a.323.56	yes	720	1.1	even	1	trivial
700.2.bj.a.687.27	yes	720	25.12	odd	20	inner
700.2.bj.a.687.56	yes	720	100.87	even	20	inner

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.527914 + 1.31199i) q^{2} +(-1.24589 - 2.44519i) q^{3} +(-1.44261 + 1.38523i) q^{4} +(-1.65605 - 1.50250i) q^{5} +(2.55034 - 2.92544i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.57898 - 1.16141i) q^{8} +(-2.66338 + 3.66583i) q^{9} +(1.09701 - 2.96590i) q^{10} +(-2.05862 - 2.83344i) q^{11} +(5.18450 + 1.80163i) q^{12} +(0.978870 + 6.18034i) q^{13} +(0.554423 - 1.30101i) q^{14} +(-1.61066 + 5.92130i) q^{15} +(0.162271 - 3.99671i) q^{16} +(2.62303 + 1.33650i) q^{17} +(-6.21555 - 1.55908i) q^{18} +(1.98500 + 6.10921i) q^{19} +(4.47035 - 0.126473i) q^{20} +(-0.848037 + 2.60999i) q^{21} +(2.63067 - 4.19669i) q^{22} +(-0.192546 + 1.21569i) q^{23} +(0.373256 + 7.75309i) q^{24} +(0.484971 + 4.97642i) q^{25} +(-7.59176 + 4.54695i) q^{26} +(4.15038 + 0.657356i) q^{27} +(1.99959 + 0.0405761i) q^{28} +(-2.17885 - 0.707951i) q^{29} +(-8.61896 + 1.01277i) q^{30} +(8.96116 - 2.91166i) q^{31} +(5.32929 - 1.89702i) q^{32} +(-4.36351 + 8.56387i) q^{33} +(-0.368736 + 4.14693i) q^{34} +(0.108571 + 2.23343i) q^{35} +(-1.23579 - 8.97777i) q^{36} +(-9.22506 + 1.46111i) q^{37} +(-6.96728 + 5.82943i) q^{38} +(13.8926 - 10.0935i) q^{39} +(2.52589 + 5.79827i) q^{40} +(2.24507 + 1.63114i) q^{41} +(-3.87196 + 0.265237i) q^{42} +(1.19017 - 1.19017i) q^{43} +(6.89476 + 1.23591i) q^{44} +(9.91860 - 2.06904i) q^{45} +(-1.69661 + 0.389161i) q^{46} +(-6.22666 + 3.17264i) q^{47} +(-9.97490 + 4.58267i) q^{48} +1.00000i q^{49} +(-6.27298 + 3.26340i) q^{50} -8.07894i q^{51} +(-9.97333 - 7.55989i) q^{52} +(-8.46224 + 4.31173i) q^{53} +(1.32860 + 5.79227i) q^{54} +(-0.848093 + 7.78539i) q^{55} +(1.00238 + 2.64485i) q^{56} +(12.4651 - 12.4651i) q^{57} +(-0.221423 - 3.23236i) q^{58} +(-5.93237 - 4.31012i) q^{59} +(-5.87881 - 10.7733i) q^{60} +(-3.53233 + 2.56639i) q^{61} +(8.55078 + 10.2198i) q^{62} +(4.47543 - 0.708838i) q^{63} +(5.30227 + 5.99049i) q^{64} +(7.66493 - 11.7057i) q^{65} +(-13.5392 - 1.20388i) q^{66} +(-4.51785 + 8.86679i) q^{67} +(-5.63538 + 1.70545i) q^{68} +(3.21249 - 1.04380i) q^{69} +(-2.87291 + 1.32150i) q^{70} +(-5.52173 - 1.79412i) q^{71} +(11.1263 - 6.36083i) q^{72} +(-1.32532 - 0.209909i) q^{73} +(-6.78699 - 11.3318i) q^{74} +(11.5641 - 7.38592i) q^{75} +(-11.3263 - 6.06354i) q^{76} +(-0.547885 + 3.45921i) q^{77} +(20.5767 + 12.8983i) q^{78} +(-2.06946 + 6.36915i) q^{79} +(-6.27379 + 6.37492i) q^{80} +(0.637113 + 1.96083i) q^{81} +(-0.954829 + 3.80660i) q^{82} +(-1.66794 - 0.849858i) q^{83} +(-2.39205 - 4.93994i) q^{84} +(-2.33576 - 6.15441i) q^{85} +(2.18980 + 0.933182i) q^{86} +(0.983526 + 6.20974i) q^{87} +(2.01835 + 9.69828i) q^{88} +(5.37994 + 7.40486i) q^{89} +(7.95072 + 11.9208i) q^{90} +(3.67800 - 5.06233i) q^{91} +(-1.40624 - 2.02049i) q^{92} +(-18.2842 - 18.2842i) q^{93} +(-7.44960 - 6.49441i) q^{94} +(5.89185 - 13.0996i) q^{95} +(-11.2783 - 10.6677i) q^{96} +(4.85444 + 9.52738i) q^{97} +(-1.31199 + 0.527914i) q^{98} +15.8698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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