LMFDB - Embedded newform 189.2.be.a.104.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] 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("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.6
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.681310 + 1.87188i) q^{2} +(0.917364 + 1.46916i) q^{3} +(-1.50768 - 1.26509i) q^{4} +(0.291735 - 1.65451i) q^{5} +(-3.37511 + 0.716242i) q^{6} +(0.496759 + 2.59870i) q^{7} +(-0.0549773 + 0.0317412i) q^{8} +(-1.31689 + 2.69552i) q^{9} +(2.89829 + 1.67333i) q^{10} +(-3.13877 + 0.553450i) q^{11} +(0.475538 - 3.37557i) q^{12} +(0.877617 + 2.41123i) q^{13} +(-5.20291 - 0.840643i) q^{14} +(2.69838 - 1.08918i) q^{15} +(-0.705484 - 4.00100i) q^{16} +(0.934264 - 1.61819i) q^{17} +(-4.14849 - 4.30154i) q^{18} +(5.71942 - 3.30211i) q^{19} +(-2.53295 + 2.12540i) q^{20} +(-3.36220 + 3.11377i) q^{21} +(1.10248 - 6.25248i) q^{22} +(4.62225 - 5.50858i) q^{23} +(-0.0970672 - 0.0516525i) q^{24} +(2.04616 + 0.744740i) q^{25} -5.11148 q^{26} +(-5.16822 + 0.538047i) q^{27} +(2.53864 - 4.54644i) q^{28} +(-3.25414 + 8.94067i) q^{29} +(0.200393 + 5.79312i) q^{30} +(0.942831 - 1.12362i) q^{31} +(7.84502 + 1.38329i) q^{32} +(-3.69250 - 4.10365i) q^{33} +(2.39254 + 2.85132i) q^{34} +(4.44450 - 0.0637627i) q^{35} +(5.39551 - 2.39799i) q^{36} +(-0.322537 + 0.558651i) q^{37} +(2.28447 + 12.9559i) q^{38} +(-2.73740 + 3.50134i) q^{39} +(0.0364774 + 0.100221i) q^{40} +(0.477380 - 0.173752i) q^{41} +(-3.53792 - 8.41510i) q^{42} +(-0.197774 - 1.12163i) q^{43} +(5.43241 + 3.13640i) q^{44} +(4.07559 + 2.96518i) q^{45} +(7.16224 + 12.4054i) q^{46} +(8.83196 - 7.41090i) q^{47} +(5.23094 - 4.70684i) q^{48} +(-6.50646 + 2.58185i) q^{49} +(-2.78813 + 3.32277i) q^{50} +(3.23445 - 0.111884i) q^{51} +(1.72727 - 4.74562i) q^{52} -1.23939i q^{53} +(2.51400 - 10.0409i) q^{54} +5.35460i q^{55} +(-0.109796 - 0.127102i) q^{56} +(10.0981 + 5.37353i) q^{57} +(-14.5188 - 12.1827i) q^{58} +(-0.0973892 + 0.552322i) q^{59} +(-5.44620 - 1.77156i) q^{60} +(-4.58297 - 5.46178i) q^{61} +(1.46093 + 2.53041i) q^{62} +(-7.65901 - 2.08317i) q^{63} +(-3.87153 + 6.70568i) q^{64} +(4.24545 - 0.748587i) q^{65} +(10.1973 - 4.11607i) q^{66} +(8.34610 - 3.03773i) q^{67} +(-3.45573 + 1.25778i) q^{68} +(12.3333 + 1.73747i) q^{69} +(-2.90873 + 8.36303i) q^{70} +(-5.31767 - 3.07016i) q^{71} +(-0.0131599 - 0.189992i) q^{72} +(-5.75058 + 3.32010i) q^{73} +(-0.825982 - 0.984367i) q^{74} +(0.782925 + 3.68934i) q^{75} +(-12.8005 - 2.25707i) q^{76} +(-2.99746 - 7.88178i) q^{77} +(-4.68908 - 7.50960i) q^{78} +(0.814895 + 0.296597i) q^{79} -6.82552 q^{80} +(-5.53162 - 7.09938i) q^{81} +1.01198i q^{82} +(7.67310 + 2.79278i) q^{83} +(9.00832 - 0.441067i) q^{84} +(-2.40476 - 2.01784i) q^{85} +(2.23431 + 0.393970i) q^{86} +(-16.1205 + 3.42098i) q^{87} +(0.154994 - 0.130055i) q^{88} +(3.77720 + 6.54230i) q^{89} +(-8.32722 + 5.60881i) q^{90} +(-5.83010 + 3.47846i) q^{91} +(-13.9377 + 2.45759i) q^{92} +(2.51571 + 0.354403i) q^{93} +(7.85503 + 21.5815i) q^{94} +(-3.79483 - 10.4262i) q^{95} +(5.16446 + 12.7946i) q^{96} +(9.45944 - 1.66796i) q^{97} +(-0.400014 - 13.9384i) q^{98} +(2.64157 - 9.18943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.681310	+	1.87188i	−0.481759	+	1.32362i	0.426225	+	0.904617i	$0.359843\pi$
$2$	−0.681310	+	1.87188i	−0.481759	+	1.32362i	−0.907984	+	0.419005i	$0.862379\pi$
$3$	0.917364	+	1.46916i	0.529640	+	0.848222i
$3$	0.917364	+	1.46916i	0.529640	+	0.848222i
$4$	−1.50768	−	1.26509i	−0.753838	−	0.632545i
$5$	0.291735	−	1.65451i	0.130468	−	0.739921i	−0.847441	−	0.530890i	$-0.821858\pi$
$5$	0.291735	−	1.65451i	0.130468	−	0.739921i	0.977909	−	0.209031i	$-0.0670310\pi$
$6$	−3.37511	+	0.716242i	−1.37788	+	0.292405i
$7$	0.496759	+	2.59870i	0.187757	+	0.982215i
$7$	0.496759	+	2.59870i	0.187757	+	0.982215i
$8$	−0.0549773	+	0.0317412i	−0.0194374	+	0.0112222i
$9$	−1.31689	+	2.69552i	−0.438962	+	0.898505i
$10$	2.89829	+	1.67333i	0.916521	+	0.529154i
$11$	−3.13877	+	0.553450i	−0.946374	+	0.166871i	−0.625477	−	0.780243i	$-0.715096\pi$
$11$	−3.13877	+	0.553450i	−0.946374	+	0.166871i	−0.320897	+	0.947114i	$0.603984\pi$
$12$	0.475538	−	3.37557i	0.137276	−	0.974444i
$13$	0.877617	+	2.41123i	0.243407	+	0.668756i	0.999891	+	0.0147436i	$0.00469320\pi$
$13$	0.877617	+	2.41123i	0.243407	+	0.668756i	−0.756484	+	0.654012i	$0.773085\pi$
$14$	−5.20291	−	0.840643i	−1.39054	−	0.224671i
$15$	2.69838	−	1.08918i	0.696719	−	0.281226i
$16$	−0.705484	−	4.00100i	−0.176371	−	1.00025i
$17$	0.934264	−	1.61819i	0.226592	−	0.392469i	−0.730204	−	0.683229i	$-0.760575\pi$
$17$	0.934264	−	1.61819i	0.226592	−	0.392469i	0.956796	+	0.290760i	$0.0939082\pi$
$18$	−4.14849	−	4.30154i	−0.977807	−	1.01388i
$19$	5.71942	−	3.30211i	1.31213	−	0.757556i	0.329677	−	0.944094i	$-0.393060\pi$
$19$	5.71942	−	3.30211i	1.31213	−	0.757556i	0.982448	+	0.186538i	$0.0597267\pi$
$20$	−2.53295	+	2.12540i	−0.566385	+	0.475254i
$21$	−3.36220	+	3.11377i	−0.733693	+	0.679481i
$22$	1.10248	−	6.25248i	0.235050	−	1.33303i
$23$	4.62225	−	5.50858i	0.963805	−	1.14862i	−0.0250426	−	0.999686i	$-0.507972\pi$
$23$	4.62225	−	5.50858i	0.963805	−	1.14862i	0.988848	−	0.148932i	$-0.0475834\pi$
$24$	−0.0970672	−	0.0516525i	−0.0198138	−	0.0105435i
$25$	2.04616	+	0.744740i	0.409231	+	0.148948i
$26$	−5.11148			−1.00244
$27$	−5.16822	+	0.538047i	−0.994625	+	0.103547i
$28$	2.53864	−	4.54644i	0.479757	−	0.859196i
$29$	−3.25414	+	8.94067i	−0.604278	+	1.66024i	0.138228	+	0.990400i	$0.455859\pi$
$29$	−3.25414	+	8.94067i	−0.604278	+	1.66024i	−0.742506	+	0.669840i	$0.766363\pi$
$30$	0.200393	+	5.79312i	0.0365865	+	1.05767i
$31$	0.942831	−	1.12362i	0.169337	−	0.201809i	−0.674701	−	0.738091i	$-0.735727\pi$
$31$	0.942831	−	1.12362i	0.169337	−	0.201809i	0.844038	+	0.536283i	$0.180172\pi$
$32$	7.84502	+	1.38329i	1.38682	+	0.244533i
$33$	−3.69250	−	4.10365i	−0.642782	−	0.714354i
$34$	2.39254	+	2.85132i	0.410318	+	0.488998i
$35$	4.44450	−	0.0637627i	0.751258	−	0.0107779i
$36$	5.39551	−	2.39799i	0.899252	−	0.399664i
$37$	−0.322537	+	0.558651i	−0.0530248	+	0.0918416i	−0.891319	−	0.453376i	$-0.850220\pi$
$37$	−0.322537	+	0.558651i	−0.0530248	+	0.0918416i	0.838295	+	0.545217i	$0.183553\pi$
$38$	2.28447	+	12.9559i	0.370589	+	2.10172i
$39$	−2.73740	+	3.50134i	−0.438335	+	0.560663i
$40$	0.0364774	+	0.100221i	0.00576758	+	0.0158463i
$41$	0.477380	−	0.173752i	0.0745542	−	0.0271355i	−0.304474	−	0.952521i	$-0.598481\pi$
$41$	0.477380	−	0.173752i	0.0745542	−	0.0271355i	0.379028	+	0.925385i	$0.376258\pi$
$42$	−3.53792	−	8.41510i	−0.545912	−	1.29848i
$43$	−0.197774	−	1.12163i	−0.0301603	−	0.171048i	0.966007	−	0.258516i	$-0.0832334\pi$
$43$	−0.197774	−	1.12163i	−0.0301603	−	0.171048i	−0.996167	+	0.0874683i	$0.972122\pi$
$44$	5.43241	+	3.13640i	0.818967	+	0.472831i
$45$	4.07559	+	2.96518i	0.607553	+	0.442024i
$46$	7.16224	+	12.4054i	1.05601	+	1.82907i
$47$	8.83196	−	7.41090i	1.28827	−	1.08099i	0.296228	−	0.955117i	$-0.404271\pi$
$47$	8.83196	−	7.41090i	1.28827	−	1.08099i	0.992046	−	0.125873i	$-0.0401732\pi$
$48$	5.23094	−	4.70684i	0.755021	−	0.679374i
$49$	−6.50646	+	2.58185i	−0.929494	+	0.368836i
$50$	−2.78813	+	3.32277i	−0.394302	+	0.469911i
$51$	3.23445	−	0.111884i	0.452914	−	0.0156669i
$52$	1.72727	−	4.74562i	0.239529	−	0.658099i
$53$		−	1.23939i		−	0.170243i	−0.996371	−	0.0851215i	$-0.972872\pi$
$53$		−	1.23939i		−	0.170243i	0.996371	−	0.0851215i	$-0.0271278\pi$
$54$	2.51400	−	10.0409i	0.342112	−	1.36639i
$55$			5.35460i			0.722013i
$56$	−0.109796	−	0.127102i	−0.0146721	−	0.0169847i
$57$	10.0981	+	5.37353i	1.33753	+	0.711742i
$58$	−14.5188	−	12.1827i	−1.90641	−	1.59967i
$59$	−0.0973892	+	0.552322i	−0.0126790	+	0.0719062i	−0.990491	−	0.137579i	$-0.956068\pi$
$59$	−0.0973892	+	0.552322i	−0.0126790	+	0.0719062i	0.977812	+	0.209486i	$0.0671789\pi$
$60$	−5.44620	−	1.77156i	−0.703101	−	0.228707i
$61$	−4.58297	−	5.46178i	−0.586790	−	0.699309i	0.388196	−	0.921577i	$-0.373098\pi$
$61$	−4.58297	−	5.46178i	−0.586790	−	0.699309i	−0.974986	+	0.222268i	$0.928654\pi$
$62$	1.46093	+	2.53041i	0.185538	+	0.321362i
$63$	−7.65901	−	2.08317i	−0.964944	−	0.262455i
$64$	−3.87153	+	6.70568i	−0.483941	+	0.838210i
$65$	4.24545	−	0.748587i	0.526583	−	0.0928508i
$66$	10.1973	−	4.11607i	1.25520	−	0.506654i
$67$	8.34610	−	3.03773i	1.01964	−	0.371118i	0.222512	−	0.974930i	$-0.428574\pi$
$67$	8.34610	−	3.03773i	1.01964	−	0.371118i	0.797127	+	0.603812i	$0.206352\pi$
$68$	−3.45573	+	1.25778i	−0.419068	+	0.152528i
$69$	12.3333	+	1.73747i	1.48475	+	0.209166i
$70$	−2.90873	+	8.36303i	−0.347659	+	0.999574i
$71$	−5.31767	−	3.07016i	−0.631092	−	0.364361i	0.150083	−	0.988673i	$-0.452046\pi$
$71$	−5.31767	−	3.07016i	−0.631092	−	0.364361i	−0.781175	+	0.624312i	$0.785379\pi$
$72$	−0.0131599	−	0.189992i	−0.00155091	−	0.0223908i
$73$	−5.75058	+	3.32010i	−0.673055	+	0.388588i	−0.797233	−	0.603671i	$-0.793704\pi$
$73$	−5.75058	+	3.32010i	−0.673055	+	0.388588i	0.124178	+	0.992260i	$0.460371\pi$
$74$	−0.825982	−	0.984367i	−0.0960184	−	0.114430i
$75$	0.782925	+	3.68934i	0.0904044	+	0.426008i
$76$	−12.8005	−	2.25707i	−1.46832	−	0.258904i
$77$	−2.99746	−	7.88178i	−0.341592	−	0.898212i
$78$	−4.68908	−	7.50960i	−0.530934	−	0.850294i
$79$	0.814895	+	0.296597i	0.0916828	+	0.0333698i	0.387454	−	0.921889i	$-0.373354\pi$
$79$	0.814895	+	0.296597i	0.0916828	+	0.0333698i	−0.295772	+	0.955259i	$0.595577\pi$
$80$	−6.82552			−0.763117
$81$	−5.53162	−	7.09938i	−0.614624	−	0.788820i
$82$			1.01198i			0.111754i
$83$	7.67310	+	2.79278i	0.842232	+	0.306547i	0.726869	−	0.686776i	$-0.240975\pi$
$83$	7.67310	+	2.79278i	0.842232	+	0.306547i	0.115363	+	0.993323i	$0.463197\pi$
$84$	9.00832	−	0.441067i	0.982888	−	0.0481244i
$85$	−2.40476	−	2.01784i	−0.260833	−	0.218865i
$86$	2.23431	+	0.393970i	0.240932	+	0.0424829i
$87$	−16.1205	+	3.42098i	−1.72830	+	0.366768i
$88$	0.154994	−	0.130055i	0.0165224	−	0.0138639i
$89$	3.77720	+	6.54230i	0.400383	+	0.693483i	0.993772	−	0.111433i	$-0.0355439\pi$
$89$	3.77720	+	6.54230i	0.400383	+	0.693483i	−0.593389	+	0.804915i	$0.702211\pi$
$90$	−8.32722	+	5.60881i	−0.877766	+	0.591221i
$91$	−5.83010	+	3.47846i	−0.611161	+	0.364642i
$92$	−13.9377	+	2.45759i	−1.45311	+	0.256222i
$93$	2.51571	+	0.354403i	0.260867	+	0.0367499i
$94$	7.85503	+	21.5815i	0.810185	+	2.22596i
$95$	−3.79483	−	10.4262i	−0.389341	−	1.06971i
$96$	5.16446	+	12.7946i	0.527096	+	1.30584i
$97$	9.45944	−	1.66796i	0.960461	−	0.169355i	0.328628	−	0.944460i	$-0.393414\pi$
$97$	9.45944	−	1.66796i	0.960461	−	0.169355i	0.631833	+	0.775104i	$0.282303\pi$
$98$	−0.400014	−	13.9384i	−0.0404075	−	1.40799i
$99$	2.64157	−	9.18943i	0.265488	−	0.923573i
$100$	−2.14278	−	3.71140i	−0.214278	−	0.371140i
$101$	−0.579504	+	0.486261i	−0.0576628	+	0.0483848i	−0.671164	−	0.741309i	$-0.734205\pi$
$101$	−0.579504	+	0.486261i	−0.0576628	+	0.0483848i	0.613501	+	0.789694i	$0.289761\pi$
$102$	−1.99423	+	6.13074i	−0.197458	+	0.607034i
$103$	−17.6544	−	3.11294i	−1.73954	−	0.306727i	−0.788324	−	0.615260i	$-0.789051\pi$
$103$	−17.6544	−	3.11294i	−1.73954	−	0.306727i	−0.951214	+	0.308533i	$0.900162\pi$
$104$	−0.124784	−	0.104707i	−0.0122361	−	0.0102673i
$105$	4.17090	+	6.47121i	0.407039	+	0.631526i
$106$	2.31999	+	0.844407i	0.225337	+	0.0820161i
$107$			5.82280i			0.562912i	0.959574	+	0.281456i	$0.0908173\pi$
$107$			5.82280i			0.562912i	−0.959574	+	0.281456i	$0.909183\pi$
$108$	8.47268	+	5.72707i	0.815284	+	0.551087i
$109$	−9.44448			−0.904617			−0.452309	−	0.891861i	$-0.649399\pi$
$109$	−9.44448			−0.904617			−0.452309	+	0.891861i	$0.649399\pi$
$110$	−10.0232	−	3.64814i	−0.955673	−	0.347836i
$111$	−1.11663	+	0.0386260i	−0.105986	+	0.00366622i
$112$	10.0469	−	3.82087i	0.949346	−	0.361039i
$113$	−19.8413	−	3.49856i	−1.86652	−	0.329117i	−0.877812	−	0.479005i	$-0.840998\pi$
$113$	−19.8413	−	3.49856i	−1.86652	−	0.329117i	−0.988703	+	0.149888i	$0.952109\pi$
$114$	−16.9386	+	15.2415i	−1.58644	+	1.42750i
$115$	−7.76554	−	9.25462i	−0.724141	−	0.862997i
$116$	16.2169	−	9.36285i	1.50570	−	0.869319i
$117$	−7.65524	−	0.809690i	−0.707727	−	0.0748558i
$118$	−0.967530	−	0.558604i	−0.0890683	−	0.0514236i
$119$	4.66930	+	1.62402i	0.428034	+	0.148873i
$120$	−0.113778	+	0.145530i	−0.0103864	+	0.0132850i
$121$	−0.791060	+	0.287922i	−0.0719145	+	0.0261748i
$122$	13.3462	−	4.85763i	1.20831	−	0.439789i
$123$	0.693201	+	0.541955i	0.0625038	+	0.0488665i
$124$	−2.84297	+	0.501292i	−0.255306	+	0.0450174i
$125$	6.02921	−	10.4429i	0.539269	−	0.934042i
$126$	9.11761	−	12.9175i	0.812261	−	1.15078i
$127$	−6.79079	−	11.7620i	−0.602585	−	1.04371i	−0.992428	−	0.122827i	$-0.960804\pi$
$127$	−6.79079	−	11.7620i	−0.602585	−	1.04371i	0.389843	−	0.920881i	$-0.372529\pi$
$128$	0.326404	+	0.388993i	0.0288503	+	0.0343824i
$129$	1.46643	−	1.31951i	0.129112	−	0.116176i
$130$	−1.49120	+	8.45701i	−0.130787	+	0.741728i
$131$	2.75723	+	2.31359i	0.240901	+	0.202140i	0.755242	−	0.655446i	$-0.227519\pi$
$131$	2.75723	+	2.31359i	0.240901	+	0.202140i	−0.514342	+	0.857585i	$0.671964\pi$
$132$	0.375606	+	10.8583i	0.0326923	+	0.945096i
$133$	11.4224	+	13.2227i	0.990444	+	1.14655i
$134$			17.6926i			1.52840i
$135$	−0.617547	+	8.70786i	−0.0531500	+	0.749453i
$136$			0.118619i			0.0101715i
$137$	0.743270	−	2.04212i	0.0635018	−	0.174470i	−0.903884	−	0.427778i	$-0.859296\pi$
$137$	0.743270	−	2.04212i	0.0635018	−	0.174470i	0.967386	+	0.253308i	$0.0815187\pi$
$138$	−11.6551	+	21.9027i	−0.992150	+	1.86448i
$139$	13.3535	−	15.9141i	1.13263	−	1.34982i	0.203929	−	0.978986i	$-0.434629\pi$
$139$	13.3535	−	15.9141i	1.13263	−	1.34982i	0.928701	−	0.370830i	$-0.120927\pi$
$140$	−6.78154	−	5.52657i	−0.573145	−	0.467080i
$141$	18.9899	+	6.17711i	1.59924	+	0.520207i
$142$	9.36997	−	7.86234i	0.786310	−	0.659793i
$143$	−4.08913	−	7.08258i	−0.341950	−	0.592275i
$144$	11.7138	+	3.36722i	0.976150	+	0.280602i
$145$	13.8431	+	7.99232i	1.14961	+	0.663726i
$146$	−2.29691	−	13.0264i	−0.190094	−	1.07808i
$147$	−9.76196	−	7.19056i	−0.805153	−	0.593067i
$148$	1.19303	−	0.434226i	0.0980661	−	0.0356931i
$149$	0.460486	+	1.26518i	0.0377245	+	0.103647i	0.957125	−	0.289676i	$-0.0935476\pi$
$149$	0.460486	+	1.26518i	0.0377245	+	0.103647i	−0.919400	+	0.393323i	$0.871325\pi$
$150$	−7.43943	−	1.04804i	−0.607427	−	0.0855720i
$151$	−0.578521	−	3.28095i	−0.0470794	−	0.267000i	0.952178	−	0.305545i	$-0.0988388\pi$
$151$	−0.578521	−	3.28095i	−0.0470794	−	0.267000i	−0.999257	+	0.0385451i	$0.987728\pi$
$152$	−0.209626	+	0.363082i	−0.0170029	+	0.0294499i
$153$	3.13154	+	4.64930i	0.253170	+	0.375874i
$154$	16.7960	−	0.240962i	1.35346	−	0.0194173i
$155$	−1.58399	−	1.88773i	−0.127229	−	0.151626i
$156$	8.55663	−	1.81583i	0.685079	−	0.145382i
$157$	17.2240	+	3.03706i	1.37463	+	0.242384i	0.811676	−	0.584107i	$-0.198555\pi$
$157$	17.2240	+	3.03706i	1.37463	+	0.242384i	0.562950	+	0.826491i	$0.309666\pi$
$158$	−1.11039	+	1.32331i	−0.0883380	+	0.105277i
$159$	1.82086	−	1.13697i	0.144404	−	0.0901676i
$160$	4.57734	−	12.5761i	0.361871	−	0.994231i
$161$	16.6113	+	9.27538i	1.30915	+	0.731003i
$162$	17.0580	−	5.51767i	1.34020	−	0.433509i
$163$	−20.1830			−1.58085			−0.790425	−	0.612558i	$-0.790141\pi$
$163$	−20.1830			−1.58085			−0.790425	+	0.612558i	$0.790141\pi$
$164$	−0.939546	−	0.341967i	−0.0733662	−	0.0267031i
$165$	−7.86678	+	4.91211i	−0.612428	+	0.382407i
$166$	−10.4555	+	12.4604i	−0.811506	+	0.967115i
$167$	−0.218933	+	1.24163i	−0.0169415	+	0.0960802i	−0.992106	−	0.125401i	$-0.959978\pi$
$167$	−0.218933	+	1.24163i	−0.0169415	+	0.0960802i	0.975165	+	0.221482i	$0.0710893\pi$
$168$	0.0860102	−	0.277907i	0.00663583	−	0.0214410i
$169$	4.91475	−	4.12396i	0.378057	−	0.317228i
$170$	5.41554	−	3.12667i	0.415353	−	0.239804i
$171$	1.36906	+	19.7653i	0.104695	+	1.51149i
$172$	−1.12079	+	1.94126i	−0.0854594	+	0.148020i
$173$	−3.14577	−	17.8405i	−0.239168	−	1.35639i	−0.833655	−	0.552286i	$-0.813756\pi$
$173$	−3.14577	−	17.8405i	−0.239168	−	1.35639i	0.594486	−	0.804106i	$-0.297355\pi$
$174$	4.57940	−	32.5065i	0.347163	−	2.46431i
$175$	−0.918908	+	5.68730i	−0.0694629	+	0.429920i
$176$	4.42870	+	12.1678i	0.333826	+	0.917179i
$177$	−0.900793	+	0.363599i	−0.0677077	+	0.0273298i
$178$	−14.8199	+	2.61314i	−1.11080	+	0.195863i
$179$	5.04916	+	2.91514i	0.377392	+	0.217887i	0.676683	−	0.736274i	$-0.263417\pi$
$179$	5.04916	+	2.91514i	0.377392	+	0.217887i	−0.299291	+	0.954162i	$0.596750\pi$
$180$	−2.39344	−	9.62652i	−0.178396	−	0.717519i
$181$	−21.6062	+	12.4743i	−1.60598	+	0.927210i	−0.615717	+	0.787967i	$0.711134\pi$
$181$	−21.6062	+	12.4743i	−1.60598	+	0.927210i	−0.990258	+	0.139243i	$0.955533\pi$
$182$	−2.53917	−	13.2832i	−0.188216	−	0.984615i
$183$	3.81999	−	11.7436i	0.282382	−	0.868110i
$184$	−0.0792700	+	0.449562i	−0.00584386	+	0.0331422i
$185$	0.830200	+	0.696620i	0.0610375	+	0.0512166i
$186$	−2.37738	+	4.46765i	−0.174318	+	0.327584i
$187$	−2.03685	+	5.59620i	−0.148949	+	0.409235i
$188$	−22.6912			−1.65493
$189$	−3.96558	−	13.1634i	−0.288454	−	0.957494i
$190$	22.1021			1.60345
$191$	1.74057	−	4.78218i	0.125943	−	0.346026i	−0.860656	−	0.509186i	$-0.829946\pi$
$191$	1.74057	−	4.78218i	0.125943	−	0.346026i	0.986600	+	0.163160i	$0.0521687\pi$
$192$	−13.4033	+	0.463642i	−0.967303	+	0.0334604i
$193$	−1.96765	−	1.65106i	−0.141635	−	0.118846i	0.569218	−	0.822187i	$-0.307246\pi$
$193$	−1.96765	−	1.65106i	−0.141635	−	0.118846i	−0.710852	+	0.703341i	$0.751691\pi$
$194$	−3.32260	+	18.8434i	−0.238548	+	1.35288i
$195$	4.99442	+	5.55053i	0.357658	+	0.397482i
$196$	13.0759	+	4.33866i	0.933994	+	0.309904i
$197$	−2.15214	+	1.24254i	−0.153334	+	0.0885272i	−0.574704	−	0.818362i	$-0.694883\pi$
$197$	−2.15214	+	1.24254i	−0.153334	+	0.0885272i	0.421370	+	0.906889i	$0.361549\pi$
$198$	15.4018	+	11.2056i	1.09456	+	0.796345i
$199$	−16.9476	−	9.78473i	−1.20139	−	0.693621i	−0.240523	−	0.970643i	$-0.577319\pi$
$199$	−16.9476	−	9.78473i	−1.20139	−	0.693621i	−0.960863	+	0.277023i	$0.910652\pi$
$200$	−0.136131	+	0.0240036i	−0.00962593	+	0.00169731i
$201$	12.1193	+	9.47508i	0.854832	+	0.668321i
$202$	−0.515403	−	1.41606i	−0.0362636	−	0.0996335i
$203$	−24.8506	−	4.01516i	−1.74417	−	0.281809i
$204$	−5.01805	−	3.92319i	−0.351334	−	0.274678i
$205$	−0.148206	−	0.840521i	−0.0103512	−	0.0587045i
$206$	17.8552	−	30.9261i	1.24403	−	2.15472i
$207$	8.76149	+	19.7135i	0.608966	+	1.37018i
$208$	9.02819	−	5.21243i	0.625993	−	0.361417i
$209$	−16.1244	+	13.5300i	−1.11535	+	0.935887i
$210$	−14.9550	+	3.39855i	−1.03200	+	0.234522i
$211$	−4.93177	+	27.9694i	−0.339517	+	1.92550i	0.0375160	+	0.999296i	$0.488055\pi$
$211$	−4.93177	+	27.9694i	−0.339517	+	1.92550i	−0.377033	+	0.926200i	$0.623056\pi$
$212$	−1.56794	+	1.86860i	−0.107686	+	0.128336i
$213$	−0.367673	−	10.6290i	−0.0251925	−	0.728287i
$214$	−10.8996	−	3.96713i	−0.745082	−	0.271188i
$215$	−1.91346			−0.130497
$216$	0.267057	−	0.193626i	0.0181709	−	0.0131746i
$217$	3.38832	+	1.89196i	0.230014	+	0.128435i
$218$	6.43462	−	17.6790i	0.435807	−	1.19737i
$219$	−10.1532	−	5.40281i	−0.686087	−	0.365088i
$220$	6.77405	−	8.07300i	0.456706	−	0.544281i
$221$	4.72176	+	0.832574i	0.317620	+	0.0560050i
$222$	0.688470	−	2.11653i	0.0462071	−	0.142052i
$223$	−8.91266	−	10.6217i	−0.596836	−	0.711281i	0.380069	−	0.924958i	$-0.375900\pi$
$223$	−8.91266	−	10.6217i	−0.596836	−	0.711281i	−0.976904	+	0.213677i	$0.931456\pi$
$224$	0.302336	+	21.0740i	0.0202007	+	1.40807i
$225$	−4.70202	+	4.53471i	−0.313468	+	0.302314i
$226$	20.0670	−	34.7571i	1.33484	−	2.31200i
$227$	3.16640	+	17.9575i	0.210161	+	1.19188i	0.889109	+	0.457696i	$0.151325\pi$
$227$	3.16640	+	17.9575i	0.210161	+	1.19188i	−0.678947	+	0.734187i	$0.737564\pi$
$228$	−8.42671	−	20.8766i	−0.558072	−	1.38259i
$229$	−2.80126	−	7.69640i	−0.185113	−	0.508593i	0.812074	−	0.583555i	$-0.198339\pi$
$229$	−2.80126	−	7.69640i	−0.185113	−	0.508593i	−0.997186	+	0.0749621i	$0.976116\pi$
$230$	22.6143	−	8.23093i	1.49114	−	0.542732i
$231$	8.82987	−	11.6342i	0.580962	−	0.765475i
$232$	−0.104884	−	0.594824i	−0.00688594	−	0.0390521i
$233$	7.85946	+	4.53766i	0.514890	+	0.297272i	0.734841	−	0.678239i	$-0.237257\pi$
$233$	7.85946	+	4.53766i	0.514890	+	0.297272i	−0.219951	+	0.975511i	$0.570590\pi$
$234$	6.73123	−	13.7781i	0.440035	−	0.900700i
$235$	−9.68483	−	16.7746i	−0.631769	−	1.09426i
$236$	0.845569	−	0.709516i	0.0550418	−	0.0461856i
$237$	0.311805	+	1.46930i	0.0202539	+	0.0954414i
$238$	−6.22121	+	7.63392i	−0.403261	+	0.494834i
$239$	12.1412	−	14.4693i	0.785349	−	0.935943i	−0.213813	−	0.976875i	$-0.568588\pi$
$239$	12.1412	−	14.4693i	0.785349	−	0.935943i	0.999162	+	0.0409317i	$0.0130326\pi$
$240$	−6.26149	−	10.0278i	−0.404177	−	0.647293i
$241$	3.70352	−	10.1753i	0.238565	−	0.655452i	−0.761409	−	0.648271i	$-0.775492\pi$
$241$	3.70352	−	10.1753i	0.238565	−	0.655452i	0.999974	−	0.00718031i	$-0.00228558\pi$
$242$		−	1.67694i		−	0.107798i
$243$	5.35565	−	14.6396i	0.343565	−	0.939129i
$244$			14.0325i			0.898337i
$245$	2.37355	+	11.5182i	0.151640	+	0.735874i
$246$	−1.48676	+	0.928352i	−0.0947925	+	0.0591896i
$247$	12.9816	+	10.8929i	0.826000	+	0.693097i
$248$	−0.0161692	+	0.0917003i	−0.00102675	+	0.00582298i
$249$	2.93597	+	13.8350i	0.186060	+	0.876760i
$250$	15.4401	+	18.4008i	0.976520	+	1.16377i
$251$	6.39471	+	11.0760i	0.403630	+	0.699108i	0.994161	−	0.107907i	$-0.0344148\pi$
$251$	6.39471	+	11.0760i	0.403630	+	0.699108i	−0.590531	+	0.807015i	$0.701081\pi$
$252$	8.91191	+	12.8301i	0.561397	+	0.808219i
$253$	−11.4594	+	19.8483i	−0.720449	+	1.24785i
$254$	26.6437	−	4.69800i	1.67177	−	0.294779i
$255$	0.758489	−	5.38408i	0.0474984	−	0.337164i
$256$	−15.5027	+	5.64253i	−0.968920	+	0.352658i
$257$	−15.5948	+	5.67604i	−0.972777	+	0.354062i	−0.779028	−	0.626989i	$-0.784287\pi$
$257$	−15.5948	+	5.67604i	−0.972777	+	0.354062i	−0.193749	+	0.981051i	$0.562065\pi$
$258$	1.47087	+	3.64399i	0.0915725	+	0.226865i
$259$	−1.61199	−	0.560662i	−0.100164	−	0.0348378i
$260$	−7.34779	−	4.24225i	−0.455691	−	0.263093i
$261$	−19.8144	−	20.5454i	−1.22648	−	1.27173i
$262$	−6.20931	+	3.58495i	−0.383613	+	0.221479i
$263$	10.7230	+	12.7791i	0.661206	+	0.787995i	0.987558	−	0.157254i	$-0.0502640\pi$
$263$	10.7230	+	12.7791i	0.661206	+	0.787995i	−0.326352	+	0.945248i	$0.605820\pi$
$264$	0.333259	+	0.108403i	0.0205106	+	0.00667177i
$265$	−2.05058	−	0.361573i	−0.125966	−	0.0222113i
$266$	−32.5335	+	12.3726i	−1.99476	+	0.758611i
$267$	−6.14665	+	11.5510i	−0.376169	+	0.706910i
$268$	−16.4262	−	5.97866i	−1.00339	−	0.365205i
$269$	−27.3326			−1.66650			−0.833250	−	0.552896i	$-0.813523\pi$
$269$	−27.3326			−1.66650			−0.833250	+	0.552896i	$0.813523\pi$
$270$	−15.8794	−	7.08873i	−0.966387	−	0.431406i
$271$		−	18.1849i		−	1.10465i	−0.833628	−	0.552326i	$-0.813740\pi$
$271$		−	18.1849i		−	1.10465i	0.833628	−	0.552326i	$-0.186260\pi$
$272$	−7.13349	−	2.59638i	−0.432532	−	0.157429i
$273$	−10.4588	−	5.37436i	−0.632993	−	0.325271i
$274$	3.31621	+	2.78263i	0.200339	+	0.168105i
$275$	−6.83459	−	1.20512i	−0.412141	−	0.0726716i
$276$	−16.3966	−	18.2223i	−0.986956	−	1.09685i
$277$	2.33912	−	1.96275i	0.140544	−	0.117930i	−0.569805	−	0.821780i	$-0.692981\pi$
$277$	2.33912	−	1.96275i	0.140544	−	0.117930i	0.710349	+	0.703849i	$0.248537\pi$
$278$	20.6915	+	35.8386i	1.24099	+	2.14946i
$279$	1.78714	+	4.02110i	0.106993	+	0.240737i
$280$	−0.242323	+	0.144579i	−0.0144816	+	0.00864026i
$281$	−1.31210	+	0.231358i	−0.0782732	+	0.0138017i	−0.212648	−	0.977129i	$-0.568209\pi$
$281$	−1.31210	+	0.231358i	−0.0782732	+	0.0138017i	0.134374	+	0.990931i	$0.457098\pi$
$282$	−24.5009	+	31.3384i	−1.45901	+	1.86618i
$283$	0.815020	+	2.23925i	0.0484479	+	0.133110i	0.961557	−	0.274606i	$-0.0885476\pi$
$283$	0.815020	+	2.23925i	0.0484479	+	0.133110i	−0.913109	+	0.407716i	$0.866325\pi$
$284$	4.13330	+	11.3561i	0.245266	+	0.673863i
$285$	11.8366	−	15.1398i	0.701138	−	0.896807i
$286$	16.0437	−	2.82894i	0.948686	−	0.167279i
$287$	0.688672	+	1.15425i	0.0406510	+	0.0681334i
$288$	−14.0597	+	19.3248i	−0.828475	+	1.13872i
$289$	6.75430	+	11.6988i	0.397312	+	0.688164i
$290$	−24.3921	+	20.4674i	−1.43236	+	1.20189i
$291$	11.1283	+	12.3674i	0.652350	+	0.724987i
$292$	12.8702	+	2.26937i	0.753174	+	0.132805i
$293$	19.4216	+	16.2967i	1.13462	+	0.952061i	0.999250	−	0.0387342i	$-0.0123326\pi$
$293$	19.4216	+	16.2967i	1.13462	+	0.952061i	0.135372	+	0.990795i	$0.456777\pi$
$294$	20.1108	−	13.3743i	1.17289	−	0.780002i
$295$	0.885412	+	0.322264i	0.0515507	+	0.0187629i
$296$		−	0.0409508i		−	0.00238022i
$297$	15.9241	−	4.54915i	0.924008	−	0.263969i
$298$	−2.68200			−0.155364
$299$	17.3390	+	6.31089i	1.00274	+	0.364968i
$300$	3.48695	−	6.55280i	0.201319	−	0.378326i
$301$	2.81654	−	1.07114i	0.162343	−	0.0617394i
$302$	6.53572	+	1.15242i	0.376088	+	0.0663145i
$303$	−1.24601	−	0.405307i	−0.0715816	−	0.0232843i
$304$	−17.2467	−	20.5538i	−0.989166	−	1.17884i
$305$	−10.3736	+	5.98920i	−0.593991	+	0.342941i
$306$	−10.8365	+	2.69427i	−0.619481	+	0.154021i
$307$	9.17503	+	5.29721i	0.523647	+	0.302328i	0.738425	−	0.674335i	$-0.235570\pi$
$307$	9.17503	+	5.29721i	0.523647	+	0.302328i	−0.214779	+	0.976663i	$0.568903\pi$
$308$	−5.45197	+	15.6752i	−0.310655	+	0.893179i
$309$	−11.6221	−	28.7929i	−0.661156	−	1.63797i
$310$	4.61280	−	1.67892i	0.261989	−	0.0953563i
$311$	5.82677	−	2.12077i	0.330406	−	0.120258i	−0.171490	−	0.985186i	$-0.554858\pi$
$311$	5.82677	−	2.12077i	0.330406	−	0.120258i	0.501896	+	0.864928i	$0.332636\pi$
$312$	0.0393584	−	0.279383i	0.00222823	−	0.0158169i
$313$	14.4632	−	2.55024i	0.817506	−	0.144148i	0.250769	−	0.968047i	$-0.419317\pi$
$313$	14.4632	−	2.55024i	0.817506	−	0.144148i	0.566737	+	0.823899i	$0.308206\pi$
$314$	−17.4199	+	30.1722i	−0.983063	+	1.70271i
$315$	−5.68103	+	12.0642i	−0.320090	+	0.679741i
$316$	−0.853375	−	1.47809i	−0.0480061	−	0.0831490i
$317$	7.18858	+	8.56702i	0.403751	+	0.481172i	0.929160	−	0.369678i	$-0.120532\pi$
$317$	7.18858	+	8.56702i	0.403751	+	0.481172i	−0.525409	+	0.850850i	$0.676088\pi$
$318$	0.887702	+	4.18307i	0.0497799	+	0.234575i
$319$	5.26577	−	29.8637i	0.294827	−	1.67205i
$320$	9.96518	+	8.36178i	0.557070	+	0.467438i
$321$	−8.55465	+	5.34163i	−0.477474	+	0.298141i
$322$	−28.6799	+	24.7750i	−1.59827	+	1.38065i
$323$		−	12.3402i		−	0.686625i
$324$	−0.641470	+	17.7016i	−0.0356372	+	0.983420i
$325$			5.58736i			0.309931i
$326$	13.7508	−	37.7801i	0.761589	−	2.09245i
$327$	−8.66403	−	13.8755i	−0.479122	−	0.767317i
$328$	−0.0207300	+	0.0247050i	−0.00114462	+	0.00136411i
$329$	23.6460	+	19.2702i	1.30365	+	1.06240i
$330$	−3.83519	−	18.0724i	−0.211120	−	0.994851i
$331$	−21.2397	+	17.8222i	−1.16744	+	0.979598i	−0.999980	−	0.00628050i	$-0.998001\pi$
$331$	−21.2397	+	17.8222i	−1.16744	+	0.979598i	−0.167460	+	0.985879i	$0.553556\pi$
$332$	−8.03543	−	13.9178i	−0.441002	−	0.763837i
$333$	−1.08111	−	1.60508i	−0.0592443	−	0.0879581i
$334$	−2.17503	−	1.25575i	−0.119012	−	0.0687117i
$335$	−2.59112	−	14.6949i	−0.141568	−	0.802871i
$336$	14.8302	+	11.2555i	0.809053	+	0.614036i
$337$	19.3322	−	7.03635i	1.05309	−	0.383294i	0.243264	−	0.969960i	$-0.421782\pi$
$337$	19.3322	−	7.03635i	1.05309	−	0.383294i	0.809829	+	0.586666i	$0.199560\pi$
$338$	4.37111	+	12.0095i	0.237757	+	0.653232i
$339$	−13.0618	−	32.3596i	−0.709417	−	1.75753i
$340$	1.07286	+	6.08449i	0.0581840	+	0.329978i
$341$	−2.33746	+	4.04860i	−0.126581	+	0.219244i
$342$	−37.9311	−	10.9036i	−2.05108	−	0.589598i
$343$	−9.94160	−	15.6258i	−0.536796	−	0.843712i
$344$	0.0464751	+	0.0553869i	0.00250577	+	0.00298626i
$345$	6.47272	−	19.8987i	0.348480	−	1.07131i
$346$	35.5387	+	6.26643i	1.91057	+	0.336885i
$347$	−11.8767	+	14.1541i	−0.637575	+	0.759832i	−0.983985	−	0.178251i	$-0.942956\pi$
$347$	−11.8767	+	14.1541i	−0.637575	+	0.759832i	0.346410	+	0.938083i	$0.387401\pi$
$348$	28.6324	+	15.2362i	1.53486	+	0.816746i
$349$	−2.33201	+	6.40713i	−0.124829	+	0.342966i	−0.986328	−	0.164794i	$-0.947304\pi$
$349$	−2.33201	+	6.40713i	−0.124829	+	0.342966i	0.861499	+	0.507760i	$0.169526\pi$
$350$	−10.0199	−	5.59490i	−0.535586	−	0.299060i
$351$	−5.83307	−	11.9896i	−0.311346	−	0.639957i
$352$	−25.3893			−1.35325
$353$	1.67606	+	0.610036i	0.0892077	+	0.0324689i	0.386238	−	0.922399i	$-0.373774\pi$
$353$	1.67606	+	0.610036i	0.0892077	+	0.0324689i	−0.297031	+	0.954868i	$0.595996\pi$
$354$	−0.0668966	−	1.93390i	−0.00355551	−	0.102786i
$355$	−6.63098	+	7.90249i	−0.351936	+	0.419421i
$356$	2.58181	−	14.6422i	0.136836	−	0.776034i
$357$	1.89750	+	8.34978i	0.100426	+	0.441917i
$358$	−8.89684	+	7.46533i	−0.470213	+	0.394555i
$359$	20.9229	−	12.0799i	1.10427	−	0.637550i	0.166930	−	0.985969i	$-0.446614\pi$
$359$	20.9229	−	12.0799i	1.10427	−	0.637550i	0.937339	+	0.348418i	$0.113281\pi$
$360$	−0.318183	−	0.0336540i	−0.0167697	−	0.00177372i
$361$	12.3079	−	21.3178i	0.647782	−	1.12199i
$362$	−8.63000	−	48.9432i	−0.453583	−	2.57240i
$363$	−1.14870	−	0.898067i	−0.0602909	−	0.0471363i
$364$	13.1905	+	2.13121i	0.691369	+	0.111706i
$365$	3.81550	+	10.4830i	0.199713	+	0.548706i
$366$	19.3800	+	15.1516i	1.01301	+	0.791987i
$367$	12.6882	−	2.23726i	0.662316	−	0.116784i	0.167622	−	0.985851i	$-0.446391\pi$
$367$	12.6882	−	2.23726i	0.662316	−	0.116784i	0.494694	+	0.869067i	$0.335280\pi$
$368$	−25.3007	−	14.6074i	−1.31889	−	0.761463i
$369$	−0.160304	+	1.51560i	−0.00834507	+	0.0788988i
$370$	−1.86962	+	1.07942i	−0.0971967	+	0.0561165i
$371$	3.22079	−	0.615677i	0.167215	−	0.0319644i
$372$	−3.34452	−	3.71692i	−0.173405	−	0.192713i
$373$	3.00218	−	17.0262i	0.155447	−	0.881585i	−0.802929	−	0.596075i	$-0.796726\pi$
$373$	3.00218	−	17.0262i	0.155447	−	0.881585i	0.958376	−	0.285510i	$-0.0921629\pi$
$374$	−9.08771	−	7.62549i	−0.469914	−	0.394305i
$375$	20.8733	−	0.722039i	1.07789	−	0.0372859i
$376$	−0.250327	+	0.687768i	−0.0129096	+	0.0354689i
$377$	−24.4139			−1.25738
$378$	27.3421	+	1.54522i	1.40632	+	0.0794777i
$379$	22.4692			1.15416			0.577082	−	0.816687i	$-0.304191\pi$
$379$	22.4692			1.15416			0.577082	+	0.816687i	$0.304191\pi$
$380$	−7.46872	+	20.5201i	−0.383137	+	1.05266i
$381$	11.0507	−	20.7668i	0.566143	−	1.06392i
$382$	7.76581	+	6.51629i	0.397333	+	0.333402i
$383$	3.13629	−	17.7868i	0.160257	−	0.908864i	−0.793564	−	0.608487i	$-0.791777\pi$
$383$	3.13629	−	17.7868i	0.160257	−	0.908864i	0.953821	−	0.300376i	$-0.0971123\pi$
$384$	−0.272063	+	0.836389i	−0.0138837	+	0.0426818i
$385$	−13.9150	+	2.65994i	−0.709173	+	0.135563i
$386$	4.43116	−	2.55833i	0.225540	−	0.130216i
$387$	3.28383	+	0.943961i	0.166926	+	0.0479842i
$388$	−16.3719	−	9.45232i	−0.831157	−	0.479869i
$389$	−19.1153	+	3.37054i	−0.969184	+	0.170893i	−0.635762	−	0.771885i	$-0.719314\pi$
$389$	−19.1153	+	3.37054i	−0.969184	+	0.170893i	−0.333421	+	0.942778i	$0.608203\pi$
$390$	−13.7927	+	5.56734i	−0.698421	+	0.281913i
$391$	−4.59554	−	12.6261i	−0.232407	−	0.638532i
$392$	0.275757	−	0.348466i	0.0139278	−	0.0176002i
$393$	−0.869663	+	6.17324i	−0.0438687	+	0.311399i
$394$	−0.859613	−	4.87511i	−0.0433067	−	0.245604i
$395$	0.728458	−	1.26173i	0.0366527	−	0.0634844i
$396$	−15.6081	+	10.5129i	−0.784336	+	0.528291i
$397$	11.5666	−	6.67796i	0.580509	−	0.335157i	−0.180826	−	0.983515i	$-0.557877\pi$
$397$	11.5666	−	6.67796i	0.580509	−	0.335157i	0.761336	+	0.648358i	$0.224544\pi$
$398$	29.8625	−	25.0576i	1.49687	−	1.25602i
$399$	−8.94785	+	28.9113i	−0.447953	+	1.44738i
$400$	1.53617	−	8.71208i	0.0768087	−	0.435604i
$401$	2.35877	−	2.81108i	0.117792	−	0.140379i	−0.703926	−	0.710273i	$-0.748571\pi$
$401$	2.35877	−	2.81108i	0.117792	−	0.140379i	0.821718	+	0.569894i	$0.193016\pi$
$402$	−25.9933	+	16.2305i	−1.29643	+	0.809505i
$403$	3.53676	+	1.28728i	0.176179	+	0.0641238i
$404$	1.48887			0.0740740
$405$	−13.3598	+	7.08100i	−0.663853	+	0.351858i
$406$	24.4469	−	43.7819i	1.21328	−	2.17286i
$407$	0.703185	−	1.93198i	0.0348556	−	0.0957649i
$408$	−0.174270	+	0.108816i	−0.00862765	+	0.00538721i
$409$	−1.06836	+	1.27322i	−0.0528271	+	0.0629569i	−0.791811	−	0.610766i	$-0.790862\pi$
$409$	−1.06836	+	1.27322i	−0.0528271	+	0.0629569i	0.738984	+	0.673723i	$0.235306\pi$
$410$	1.67433	+	0.295230i	0.0826893	+	0.0145804i
$411$	3.68205	−	0.781379i	0.181622	−	0.0385426i
$412$	22.6789	+	27.0277i	1.11731	+	1.33156i
$413$	−1.48370	+	0.0212857i	−0.0730079	+	0.00104740i
$414$	−42.8707	+	2.96947i	−2.10698	+	0.145942i
$415$	6.85921	−	11.8805i	0.336705	−	0.583191i
$416$	3.54949	+	20.1302i	0.174028	+	0.986963i
$417$	35.6304	+	5.01948i	1.74483	+	0.245805i
$418$	−14.3408	−	39.4011i	−0.701432	−	1.92717i
$419$	0.883387	−	0.321527i	0.0431563	−	0.0157076i	−0.320352	−	0.947299i	$-0.603801\pi$
$419$	0.883387	−	0.321527i	0.0431563	−	0.0157076i	0.363508	+	0.931591i	$0.381579\pi$
$420$	1.89829	−	15.0331i	0.0926273	−	0.733538i
$421$	6.25816	+	35.4918i	0.305004	+	1.72976i	0.623486	+	0.781835i	$0.285716\pi$
$421$	6.25816	+	35.4918i	0.305004	+	1.72976i	−0.318482	+	0.947929i	$0.603173\pi$
$422$	−48.9955	−	28.2876i	−2.38506	−	1.37702i
$423$	8.34550	+	33.5660i	0.405772	+	1.63204i
$424$	0.0393396	+	0.0681382i	0.00191050	+	0.00330908i
$425$	3.11678	−	2.61529i	0.151186	−	0.126860i
$426$	20.1467	+	6.55340i	0.976113	+	0.317513i
$427$	11.9169	−	14.6230i	0.576698	−	0.707654i
$428$	7.36637	−	8.77890i	0.356067	−	0.424344i
$429$	6.65426	−	12.5049i	0.321270	−	0.603743i
$430$	1.30366	−	3.58177i	0.0628679	−	0.172728i
$431$			25.0083i			1.20461i	0.798268	+	0.602303i	$0.205750\pi$
$431$			25.0083i			1.20461i	−0.798268	+	0.602303i	$0.794250\pi$
$432$	5.79882	+	20.2985i	0.278996	+	0.976610i
$433$			28.5219i			1.37068i	0.728225	+	0.685338i	$0.240346\pi$
$433$			28.5219i			1.37068i	−0.728225	+	0.685338i	$0.759654\pi$
$434$	−5.85003	+	5.05352i	−0.280810	+	0.242577i
$435$	0.957135	+	27.6697i	0.0458911	+	1.32666i
$436$	14.2392	+	11.9481i	0.681935	+	0.572211i
$437$	8.24664	−	46.7690i	0.394490	−	2.23727i
$438$	17.0309	−	15.3245i	0.813767	−	0.732234i
$439$	18.7971	+	22.4015i	0.897136	+	1.06917i	0.997244	+	0.0741886i	$0.0236367\pi$
$439$	18.7971	+	22.4015i	0.897136	+	1.06917i	−0.100108	+	0.994977i	$0.531919\pi$
$440$	−0.169961	−	0.294381i	−0.00810258	−	0.0140341i
$441$	1.60884	−	20.9383i	0.0766116	−	0.997061i
$442$	−4.77547	+	8.27135i	−0.227146	+	0.393428i
$443$	−2.26061	+	0.398607i	−0.107405	+	0.0189384i	−0.227092	−	0.973873i	$-0.572922\pi$
$443$	−2.26061	+	0.398607i	−0.107405	+	0.0189384i	0.119687	+	0.992812i	$0.461811\pi$
$444$	1.73239	+	1.35441i	0.0822155	+	0.0642773i
$445$	11.9263	−	4.34081i	0.565360	−	0.205774i
$446$	25.9549	−	9.44680i	1.22900	−	0.447319i
$447$	−1.43632	+	1.83716i	−0.0679355	+	0.0868945i
$448$	−19.3493	−	6.72982i	−0.914166	−	0.317954i
$449$	−18.7877	−	10.8471i	−0.886646	−	0.511905i	−0.0138018	−	0.999905i	$-0.504393\pi$
$449$	−18.7877	−	10.8471i	−0.886646	−	0.511905i	−0.872844	+	0.488000i	$0.837727\pi$
$450$	−5.28492	−	11.8912i	−0.249134	−	0.560555i
$451$	−1.40222	+	0.809573i	−0.0660280	+	0.0381213i
$452$	25.4883	+	30.3758i	1.19887	+	1.42876i
$453$	4.28955	−	3.85977i	0.201540	−	0.181348i
$454$	−35.7717	−	6.30752i	−1.67885	−	0.296026i
$455$	4.05432	+	10.6608i	0.190069	+	0.499785i
$456$	−0.725730	+	0.0251041i	−0.0339854	+	0.00117561i
$457$	0.112432	+	0.0409217i	0.00525933	+	0.00191424i	0.344648	−	0.938732i	$-0.387998\pi$
$457$	0.112432	+	0.0409217i	0.00525933	+	0.00191424i	−0.339389	+	0.940646i	$0.610220\pi$
$458$	16.3153			0.762364
$459$	−3.95782	+	8.86585i	−0.184735	+	0.413823i
$460$			23.7771i			1.10861i
$461$	−32.1671	−	11.7079i	−1.49817	−	0.545289i	−0.542584	−	0.840001i	$-0.682554\pi$
$461$	−32.1671	−	11.7079i	−1.49817	−	0.545289i	−0.955586	+	0.294712i	$0.904776\pi$
$462$	15.7620	+	24.4550i	0.733316	+	1.13775i
$463$	11.1529	+	9.35842i	0.518321	+	0.434923i	0.864046	−	0.503413i	$-0.167923\pi$
$463$	11.1529	+	9.35842i	0.518321	+	0.434923i	−0.345725	+	0.938336i	$0.612367\pi$
$464$	38.0673	+	6.71230i	1.76723	+	0.311611i
$465$	1.32029	−	4.05888i	0.0612268	−	0.188226i
$466$	−13.8487	+	11.6204i	−0.641528	+	0.538306i
$467$	−9.08585	−	15.7372i	−0.420443	−	0.728229i	0.575540	−	0.817774i	$-0.304792\pi$
$467$	−9.08585	−	15.7372i	−0.420443	−	0.728229i	−0.995983	+	0.0895452i	$0.971459\pi$
$468$	10.5173	+	10.9053i	0.486162	+	0.504099i
$469$	12.0401	+	20.1800i	0.555962	+	0.931824i
$470$	37.9985	−	6.70016i	1.75274	−	0.309056i
$471$	11.3388	+	28.0910i	0.522462	+	1.29436i
$472$	−0.0121771	−	0.0334564i	−0.000560498	−	0.00153996i
$473$	1.24154	+	3.41109i	0.0570859	+	0.156842i
$474$	−2.96280	−	0.417388i	−0.136086	−	0.0191713i
$475$	14.1621	−	2.49715i	0.649799	−	0.114577i
$476$	−4.98526	−	8.35558i	−0.228499	−	0.382977i
$477$	3.34079	+	1.63213i	0.152964	+	0.0747303i
$478$	18.8130	+	32.5850i	0.860485	+	1.49040i
$479$	−6.32713	+	5.30910i	−0.289094	+	0.242579i	−0.775788	−	0.630994i	$-0.782647\pi$
$479$	−6.32713	+	5.30910i	−0.289094	+	0.242579i	0.486694	+	0.873573i	$0.338203\pi$
$480$	22.6755	−	4.81203i	1.03499	−	0.219638i
$481$	−1.63010	−	0.287431i	−0.0743262	−	0.0131057i
$482$	16.5238	+	13.8651i	0.752639	+	0.631539i
$483$	1.61152	+	32.9136i	0.0733268	+	1.49762i
$484$	1.55691	+	0.566669i	0.0707686	+	0.0257577i
$485$		−	16.1374i		−	0.732761i
$486$	23.7547	+	19.9992i	1.07754	+	0.907184i
$487$	11.6289			0.526957			0.263478	−	0.964665i	$-0.415130\pi$
$487$	11.6289			0.526957			0.263478	+	0.964665i	$0.415130\pi$
$488$	0.425323	+	0.154805i	0.0192535	+	0.00700769i
$489$	−18.5151	−	29.6521i	−0.837282	−	1.34091i
$490$	−23.1779	−	3.40449i	−1.04707	−	0.153799i
$491$	−23.9209	−	4.21791i	−1.07954	−	0.190351i	−0.394526	−	0.918885i	$-0.629091\pi$
$491$	−23.9209	−	4.21791i	−1.07954	−	0.190351i	−0.685010	+	0.728533i	$0.740202\pi$
$492$	−0.359500	−	1.69406i	−0.0162075	−	0.0763739i
$493$	11.4275	+	13.6188i	0.514669	+	0.613358i
$494$	−29.2347	+	16.8787i	−1.31533	+	0.759406i
$495$	−14.4334	−	7.05140i	−0.648733	−	0.316937i
$496$	−5.16077	−	2.97957i	−0.231725	−	0.133787i
$497$	5.33682	−	15.3442i	0.239389	−	0.688280i
$498$	−27.8979	−	3.93015i	−1.25013	−	0.176114i
$499$	−15.5923	+	5.67512i	−0.698006	+	0.254053i	−0.666559	−	0.745452i	$-0.732234\pi$
$499$	−15.5923	+	5.67512i	−0.698006	+	0.254053i	−0.0314466	+	0.999505i	$0.510011\pi$
$500$	−22.3013	+	8.11702i	−0.997345	+	0.363004i
$501$	−2.02500	+	0.817378i	−0.0904703	+	0.0365178i
$502$	−25.0897	+	4.42399i	−1.11981	+	0.197452i
$503$	2.75453	−	4.77099i	0.122819	−	0.212728i	−0.798060	−	0.602579i	$-0.794140\pi$
$503$	2.75453	−	4.77099i	0.122819	−	0.212728i	0.920878	+	0.389851i	$0.127473\pi$
$504$	0.487194	−	0.128579i	0.0217013	−	0.00572736i
$505$	0.635464	+	1.10066i	0.0282778	+	0.0489786i
$506$	−29.3463	−	34.9736i	−1.30460	−	1.55477i
$507$	10.5674	+	3.43740i	0.469314	+	0.152660i
$508$	−4.64167	+	26.3242i	−0.205941	+	1.16795i
$509$	−28.4889	−	23.9050i	−1.26275	−	1.05957i	−0.995384	−	0.0959772i	$-0.969402\pi$
$509$	−28.4889	−	23.9050i	−1.26275	−	1.05957i	−0.267366	−	0.963595i	$-0.586153\pi$
$510$	9.56161	+	5.08803i	0.423395	+	0.225302i
$511$	−11.4846	−	13.2947i	−0.508049	−	0.588125i
$512$		−	31.8480i		−	1.40750i
$513$	−27.7825	+	20.1433i	−1.22663	+	0.889350i
$514$		−	33.0588i		−	1.45816i
$515$	−10.3008	+	28.3013i	−0.453908	+	1.24710i
$516$	−3.88021	+	0.134222i	−0.170817	+	0.00590880i
$517$	−23.6199	+	28.1491i	−1.03880	+	1.23800i
$518$	2.14776	−	2.63547i	0.0943670	−	0.115796i
$519$	23.3249	−	20.9879i	1.02385	−	0.921268i
$520$	−0.209642	+	0.175911i	−0.00919343	+	0.00771420i
$521$	4.68325	+	8.11162i	0.205177	+	0.355376i	0.950189	−	0.311674i	$-0.100890\pi$
$521$	4.68325	+	8.11162i	0.205177	+	0.355376i	−0.745012	+	0.667051i	$0.767556\pi$
$522$	51.9584	−	23.0924i	2.27416	−	1.01073i
$523$	−8.64692	−	4.99230i	−0.378104	−	0.218298i	0.298889	−	0.954288i	$-0.403384\pi$
$523$	−8.64692	−	4.99230i	−0.378104	−	0.218298i	−0.676993	+	0.735990i	$0.736717\pi$
$524$	−1.23011	−	6.97630i	−0.0537376	−	0.304761i
$525$	−9.19855	+	3.86730i	−0.401458	+	0.168783i
$526$	−31.2267	+	11.3656i	−1.36155	+	0.495563i
$527$	−0.937384	−	2.57544i	−0.0408331	−	0.112188i
$528$	−13.8137	+	17.6688i	−0.601164	+	0.768934i
$529$	−4.98537	−	28.2734i	−0.216755	−	1.22928i
$530$	2.07391	−	3.59211i	0.0900847	−	0.156031i
$531$	−1.36054	−	0.989860i	−0.0590425	−	0.0429562i
$532$	−0.493314	−	34.3859i	−0.0213879	−	1.49082i
$533$	0.837913	+	0.998586i	0.0362940	+	0.0432535i
$534$	−17.4344	−	19.3756i	−0.754458	−	0.838465i
$535$	9.63391	+	1.69872i	0.416510	+	0.0734420i
$536$	−0.362425	+	0.431921i	−0.0156544	+	0.0186562i
$537$	0.349107	+	10.0923i	0.0150651	+	0.435514i
$538$	18.6220	−	51.1635i	0.802851	−	2.20582i
$539$	18.9933	−	11.7048i	0.818101	−	0.504163i
$540$	11.9473	−	12.3474i	0.514130	−	0.531347i
$541$	−6.07091			−0.261009			−0.130504	−	0.991448i	$-0.541660\pi$
$541$	−6.07091			−0.261009			−0.130504	+	0.991448i	$0.541660\pi$
$542$	34.0400	+	12.3895i	1.46214	+	0.532176i
$543$	−38.1476	−	20.2995i	−1.63707	−	0.871136i
$544$	9.56775	−	11.4024i	0.410214	−	0.488874i
$545$	−2.75529	+	15.6260i	−0.118024	+	0.669345i
$546$	17.1858	−	15.9160i	0.735486	−	0.681141i
$547$	−23.6417	+	19.8377i	−1.01084	+	0.848199i	−0.988450	−	0.151550i	$-0.951574\pi$
$547$	−23.6417	+	19.8377i	−1.01084	+	0.848199i	−0.0223949	+	0.999749i	$0.507129\pi$
$548$	−3.70407	+	2.13855i	−0.158230	+	0.0913542i
$549$	20.7576	−	5.16094i	0.885911	−	0.220264i
$550$	6.91232	−	11.9725i	0.294742	−	0.510509i
$551$	10.9113	+	61.8810i	0.464836	+	2.63622i
$552$	−0.733200	+	0.295952i	−0.0312071	+	0.0125965i
$553$	−0.365961	+	2.26500i	−0.0155622	+	0.0963177i
$554$	2.08038	+	5.71580i	0.0883869	+	0.242841i
$555$	−0.261854	+	1.85875i	−0.0111151	+	0.0788997i
$556$	−40.2655	+	7.09990i	−1.70764	+	0.301103i
$557$	0.0926294	+	0.0534796i	0.00392483	+	0.00226600i	0.501961	−	0.864890i	$-0.332612\pi$
$557$	0.0926294	+	0.0534796i	0.00392483	+	0.00226600i	−0.498036	+	0.867156i	$0.665945\pi$
$558$	−8.74463	+	0.605704i	−0.370190	+	0.0256415i
$559$	2.53095	−	1.46124i	0.107048	−	0.0618041i
$560$	−3.39064	−	17.7375i	−0.143281	−	0.749545i
$561$	−10.0903	+	2.14128i	−0.426011	+	0.0904051i
$562$	0.460870	−	2.61372i	0.0194406	−	0.110253i
$563$	16.8629	+	14.1497i	0.710687	+	0.596337i	0.924792	−	0.380474i	$-0.124239\pi$
$563$	16.8629	+	14.1497i	0.710687	+	0.596337i	−0.214105	+	0.976811i	$0.568683\pi$
$564$	−20.8161	−	33.3371i	−0.876515	−	1.40374i
$565$	−11.5768	+	31.8071i	−0.487041	+	1.33813i
$566$	−4.74689			−0.199527
$567$	15.7013	−	17.9017i	0.659391	−	0.751800i
$568$	0.389802			0.0163557
$569$	3.90300	−	10.7234i	0.163622	−	0.449549i	−0.830603	−	0.556866i	$-0.812004\pi$
$569$	3.90300	−	10.7234i	0.163622	−	0.449549i	0.994225	+	0.107317i	$0.0342260\pi$
$570$	20.2757	+	32.4716i	0.849254	+	1.36009i
$571$	−4.28570	−	3.59613i	−0.179351	−	0.150493i	0.548693	−	0.836024i	$-0.315126\pi$
$571$	−4.28570	−	3.59613i	−0.179351	−	0.150493i	−0.728044	+	0.685531i	$0.759570\pi$
$572$	−2.79502	+	15.8514i	−0.116866	+	0.662779i
$573$	8.62254	−	1.82981i	0.360212	−	0.0764416i
$574$	−2.62983	+	0.502709i	−0.109767	+	0.0209827i
$575$	13.5603	−	7.82905i	0.565504	−	0.326494i
$576$	−12.9769	−	19.2664i	−0.540705	−	0.802766i
$577$	−1.56687	−	0.904634i	−0.0652297	−	0.0376604i	0.467030	−	0.884241i	$-0.345324\pi$
$577$	−1.56687	−	0.904634i	−0.0652297	−	0.0376604i	−0.532260	+	0.846581i	$0.678657\pi$
$578$	−26.5006	+	4.67276i	−1.10228	+	0.194361i
$579$	0.620619	−	4.40542i	0.0257921	−	0.183083i
$580$	−10.7599	−	29.5626i	−0.446781	−	1.22752i
$581$	−3.44591	+	21.3274i	−0.142960	+	0.884810i
$582$	−30.7320	+	12.4048i	−1.27388	+	0.514195i
$583$	0.685939	+	3.89015i	0.0284087	+	0.161114i
$584$	0.210768	−	0.365061i	0.00872164	−	0.0151063i
$585$	−3.57295	+	12.4295i	−0.147723	+	0.513896i
$586$	−43.7376	+	25.2519i	−1.80678	+	1.04315i
$587$	24.7393	−	20.7587i	1.02110	−	0.856804i	0.0313339	−	0.999509i	$-0.490024\pi$
$587$	24.7393	−	20.7587i	1.02110	−	0.856804i	0.989765	+	0.142705i	$0.0455800\pi$
$588$	5.62117	+	23.1908i	0.231813	+	0.956372i
$589$	1.68212	−	9.53980i	0.0693107	−	0.393081i
$590$	−1.20648	+	1.43783i	−0.0496700	+	0.0591944i
$591$	−3.79979	−	2.02199i	−0.156302	−	0.0831734i
$592$	2.46271	+	0.896352i	0.101217	+	0.0368398i
$593$	−6.02328			−0.247347			−0.123673	−	0.992323i	$-0.539467\pi$
$593$	−6.02328			−0.247347			−0.123673	+	0.992323i	$0.539467\pi$
$594$	−2.33374	+	32.9074i	−0.0957544	+	1.35021i
$595$	4.04916	−	7.25163i	0.165999	−	0.297288i
$596$	0.906298	−	2.49003i	0.0371234	−	0.101996i
$597$	−1.17179	−	33.8750i	−0.0479581	−	1.38641i
$598$	−23.6265	+	28.1570i	−0.966159	+	1.15142i
$599$	−8.19802	−	1.44553i	−0.334962	−	0.0590629i	0.00363751	−	0.999993i	$-0.498842\pi$
$599$	−8.19802	−	1.44553i	−0.334962	−	0.0590629i	−0.338600	+	0.940931i	$0.609953\pi$
$600$	−0.160147	−	0.177979i	−0.00653798	−	0.00726596i
$601$	−13.5043	−	16.0938i	−0.550851	−	0.656479i	0.416733	−	0.909029i	$-0.363175\pi$
$601$	−13.5043	−	16.0938i	−0.550851	−	0.656479i	−0.967584	+	0.252550i	$0.918731\pi$
$602$	0.0861074	+	6.00202i	0.00350947	+	0.244624i
$603$	−2.80261	+	26.4974i	−0.114131	+	1.07906i
$604$	−3.27848	+	5.67850i	−0.133400	+	0.231055i
$605$	0.245591	+	1.39282i	0.00998470	+	0.0566260i
$606$	1.60761	−	2.05625i	0.0653047	−	0.0835295i
$607$	−13.9808	−	38.4119i	−0.567463	−	1.55909i	−0.808452	−	0.588563i	$-0.799694\pi$
$607$	−13.9808	−	38.4119i	−0.567463	−	1.55909i	0.240989	−	0.970528i	$-0.422528\pi$
$608$	49.4368	−	17.9935i	2.00493	−	0.729733i
$609$	−16.8981	−	40.1930i	−0.684747	−	1.62870i
$610$	−4.14345	−	23.4987i	−0.167763	−	0.951433i
$611$	25.6205	+	14.7920i	1.03649	+	0.598420i
$612$	1.16043	−	10.9713i	0.0469076	−	0.443490i
$613$	7.05243	+	12.2152i	0.284845	+	0.493366i	0.972572	−	0.232604i	$-0.0747245\pi$
$613$	7.05243	+	12.2152i	0.284845	+	0.493366i	−0.687727	+	0.725970i	$0.741391\pi$
$614$	−16.1668	+	13.5656i	−0.652439	+	0.547461i
$615$	1.09890	−	0.988803i	0.0443121	−	0.0398724i
$616$	0.414969	+	0.338176i	0.0167196	+	0.0136255i
$617$	19.9970	−	23.8315i	0.805051	−	0.959422i	−0.194720	−	0.980859i	$-0.562380\pi$
$617$	19.9970	−	23.8315i	0.805051	−	0.959422i	0.999770	+	0.0214370i	$0.00682414\pi$
$618$	61.8152	−	2.13828i	2.48657	−	0.0860141i
$619$	−15.2211	+	41.8197i	−0.611789	+	1.68088i	0.114446	+	0.993429i	$0.463491\pi$
$619$	−15.2211	+	41.8197i	−0.611789	+	1.68088i	−0.726235	+	0.687446i	$0.758732\pi$
$620$			4.84998i			0.194780i
$621$	−20.9249	+	30.9565i	−0.839688	+	1.24224i
$622$			12.3519i			0.495267i
$623$	−15.1251	+	13.0658i	−0.605975	+	0.523468i
$624$	15.9401	+	8.48220i	0.638113	+	0.339560i
$625$	−7.17877	−	6.02371i	−0.287151	−	0.240948i
$626$	−5.08013	+	28.8108i	−0.203043	+	1.15151i
$627$	−34.6697	−	11.2775i	−1.38457	−	0.450379i
$628$	−22.1261	−	26.3688i	−0.882927	−	1.05223i
$629$	0.602670	+	1.04385i	0.0240300	+	0.0416212i
$630$	−18.7122	−	18.8537i	−0.745513	−	0.751149i
$631$	4.05881	−	7.03007i	0.161579	−	0.279862i	−0.773856	−	0.633361i	$-0.781675\pi$
$631$	4.05881	−	7.03007i	0.161579	−	0.279862i	0.935435	+	0.353499i	$0.115008\pi$
$632$	−0.0542151	+	0.00955958i	−0.00215656	+	0.000380260i
$633$	−45.6159	+	18.4126i	−1.81307	+	0.731834i
$634$	−20.9341	+	7.61940i	−0.831400	+	0.302605i
$635$	−21.4415	+	7.80406i	−0.850879	+	0.309695i
$636$	−4.18364	−	0.589376i	−0.165892	−	0.0233703i
$637$	−11.9356	−	13.4227i	−0.472907	−	0.531827i
$638$	52.3137	+	30.2033i	2.07112	+	1.19576i
$639$	15.2784	−	10.2908i	0.604406	−	0.407099i
$640$	0.738818	−	0.426557i	0.0292043	−	0.0168611i
$641$	−12.1403	−	14.4683i	−0.479514	−	0.571462i	0.471005	−	0.882131i	$-0.343892\pi$
$641$	−12.1403	−	14.4683i	−0.479514	−	0.571462i	−0.950518	+	0.310669i	$0.899447\pi$
$642$	−4.17054	−	19.6526i	−0.164598	−	0.775627i
$643$	25.9951	+	4.58364i	1.02515	+	0.180761i	0.660847	−	0.750521i	$-0.270197\pi$
$643$	25.9951	+	4.58364i	1.02515	+	0.180761i	0.364300	+	0.931282i	$0.381308\pi$
$644$	−13.3102	−	34.9990i	−0.524496	−	1.37916i
$645$	−1.75534	−	2.81118i	−0.0691163	−	0.110690i
$646$	23.0993	+	8.40748i	0.908832	+	0.330788i
$647$	25.0360			0.984267			0.492133	−	0.870520i	$-0.336217\pi$
$647$	25.0360			0.984267			0.492133	+	0.870520i	$0.336217\pi$
$648$	0.529456	+	0.214725i	0.0207990	+	0.00843519i
$649$		−	1.78751i		−	0.0701659i
$650$	−10.4589	−	3.80672i	−0.410231	−	0.149312i
$651$	0.328713	+	6.71361i	0.0128833	+	0.263127i
$652$	30.4294	+	25.5333i	1.19171	+	0.999960i
$653$	−24.9911	−	4.40660i	−0.977977	−	0.172444i	−0.338259	−	0.941053i	$-0.609838\pi$
$653$	−24.9911	−	4.40660i	−0.977977	−	0.172444i	−0.639718	+	0.768609i	$0.720949\pi$
$654$	31.8762	−	6.76454i	1.24646	−	0.264514i
$655$	4.63226	−	3.88693i	0.180997	−	0.151875i
$656$	−1.03197	−	1.78742i	−0.0402915	−	0.0697869i
$657$	−1.37652	−	19.8730i	−0.0537031	−	0.775319i
$658$	−52.1818	+	31.1337i	−2.03426	+	1.21372i
$659$	−28.7214	+	5.06437i	−1.11883	+	0.197280i	−0.702326	−	0.711855i	$-0.747855\pi$
$659$	−28.7214	+	5.06437i	−1.11883	+	0.197280i	−0.416502	+	0.909135i	$0.636744\pi$
$660$	18.0748	+	2.54631i	0.703562	+	0.0991151i
$661$	1.91283	+	5.25546i	0.0744005	+	0.204414i	0.971318	−	0.237784i	$-0.0764211\pi$
$661$	1.91283	+	5.25546i	0.0744005	+	0.204414i	−0.896917	+	0.442198i	$0.854199\pi$
$662$	−18.8903	−	51.9007i	−0.734193	−	2.01718i
$663$	3.10839	+	7.70082i	0.120720	+	0.299075i
$664$	−0.510493	+	0.0900136i	−0.0198110	+	0.00349321i
$665$	25.2094	−	15.0409i	0.977580	−	0.583262i
$666$	3.74110	−	0.930148i	0.144965	−	0.0360425i
$667$	34.2089	+	59.2516i	1.32458	+	2.29423i
$668$	1.90085	−	1.59501i	0.0735463	−	0.0617126i
$669$	7.42886	−	22.8381i	0.287216	−	0.882973i
$670$	29.2726	+	5.16155i	1.13090	+	0.199408i
$671$	17.4077	+	14.6068i	0.672017	+	0.563889i
$672$	−30.6838	+	19.7767i	−1.18365	+	0.762903i
$673$	21.3185	+	7.75929i	0.821767	+	0.299099i	0.718475	−	0.695552i	$-0.244840\pi$
$673$	21.3185	+	7.75929i	0.821767	+	0.299099i	0.103292	+	0.994651i	$0.467063\pi$
$674$			40.9816i			1.57855i
$675$	−10.9757	−	2.74805i	−0.422455	−	0.105773i
$676$	−12.6270			−0.485655
$677$	−7.76681	−	2.82689i	−0.298503	−	0.108646i	0.188427	−	0.982087i	$-0.439661\pi$
$677$	−7.76681	−	2.82689i	−0.298503	−	0.108646i	−0.486930	+	0.873441i	$0.661883\pi$
$678$	69.4726	−	2.40316i	2.66808	−	0.0922927i
$679$	9.03358	+	23.7537i	0.346677	+	0.911582i
$680$	0.196256	+	0.0346052i	0.00752607	+	0.00132705i
$681$	−23.4778	+	21.1256i	−0.899672	+	0.809533i
$682$	−5.98597	−	7.13381i	−0.229215	−	0.273168i
$683$	23.0002	−	13.2792i	0.880080	−	0.508114i	0.00939496	−	0.999956i	$-0.497009\pi$
$683$	23.0002	−	13.2792i	0.880080	−	0.508114i	0.870685	+	0.491842i	$0.163676\pi$
$684$	22.9408	−	31.5317i	0.877163	−	1.20564i
$685$	−3.16187	−	1.82551i	−0.120809	−	0.0697491i
$686$	36.0229	−	7.96353i	1.37536	−	0.304049i
$687$	8.73750	−	11.1759i	0.333357	−	0.426388i
$688$	−4.34813	+	1.58259i	−0.165771	+	0.0603357i
$689$	2.98845	−	1.08771i	0.113851	−	0.0414384i
$690$	32.8381	+	25.6734i	1.25013	+	0.977368i
$691$	37.5870	−	6.62760i	1.42988	−	0.252126i	0.595515	−	0.803344i	$-0.296948\pi$
$691$	37.5870	−	6.62760i	1.42988	−	0.252126i	0.834361	+	0.551218i	$0.185837\pi$
$692$	−17.8271	+	30.8774i	−0.677685	+	1.17378i
$693$	25.1928	+	2.29971i	0.956995	+	0.0873587i
$694$	−18.4031	−	31.8751i	−0.698573	−	1.20996i
$695$	−22.4344	−	26.7363i	−0.850985	−	1.01416i
$696$	0.777678	−	0.699761i	0.0294778	−	0.0265244i
$697$	0.164834	−	0.934822i	0.00624355	−	0.0354089i
$698$	−10.4046	−	8.73049i	−0.393820	−	0.330454i
$699$	0.543415	+	15.7095i	0.0205539	+	0.594188i
$700$	8.58037	−	7.41211i	0.324307	−	0.280151i
$701$			12.5706i			0.474787i	0.971414	+	0.237393i	$0.0762930\pi$
$701$			12.5706i			0.474787i	−0.971414	+	0.237393i	$0.923707\pi$
$702$	26.4172	−	2.75021i	0.997054	−	0.103800i
$703$			4.26021i			0.160677i
$704$	8.44057	−	23.1903i	0.318116	−	0.874016i
$705$	15.7602	−	29.6170i	0.593562	−	1.11544i
$706$	−2.28383	+	2.72177i	−0.0859532	+	0.102435i
$707$	−1.55152	−	1.26440i	−0.0583509	−	0.0475527i
$708$	1.81809	+	0.591394i	0.0683280	+	0.0222260i
$709$	14.2522	−	11.9590i	0.535254	−	0.449131i	−0.334657	−	0.942340i	$-0.608620\pi$
$709$	14.2522	−	11.9590i	0.535254	−	0.449131i	0.869911	+	0.493209i	$0.164176\pi$
$710$	−10.2748	−	17.7965i	−0.385606	−	0.667889i
$711$	−1.87261	+	1.80598i	−0.0702283	+	0.0677294i
$712$	−0.415321	−	0.239786i	−0.0155648	−	0.00898634i
$713$	−1.83156	−	10.3873i	−0.0685926	−	0.389008i
$714$	−16.9226	−	2.13689i	−0.633312	−	0.0799713i
$715$	−12.9112	+	4.69928i	−0.482851	+	0.175743i
$716$	−3.92459	−	10.7827i	−0.146669	−	0.402969i
$717$	32.3957	+	4.56379i	1.20984	+	0.170438i
$718$	8.35709	+	47.3954i	0.311884	+	1.76878i
$719$	−5.19387	+	8.99605i	−0.193699	+	0.335496i	−0.946473	−	0.322783i	$-0.895382\pi$
$719$	−5.19387	+	8.99605i	−0.193699	+	0.335496i	0.752774	+	0.658278i	$0.228715\pi$
$720$	8.98844	−	18.3983i	0.334979	−	0.685664i
$721$	−0.680375	−	47.4248i	−0.0253385	−	1.76619i
$722$	31.5190	+	37.5629i	1.17302	+	1.39795i
$723$	18.3467	−	3.89341i	0.682322	−	0.144798i
$724$	48.3563	+	8.52652i	1.79715	+	0.316886i
$725$	−13.3170	+	15.8705i	−0.494579	+	0.589417i
$726$	2.46370	−	1.53836i	0.0914363	−	0.0570939i
$727$	1.63424	−	4.49002i	0.0606104	−	0.166526i	−0.905691	−	0.423938i	$-0.860648\pi$
$727$	1.63424	−	4.49002i	0.0606104	−	0.166526i	0.966302	+	0.257412i	$0.0828697\pi$
$728$	0.210113	−	0.376291i	0.00778730	−	0.0139463i
$729$	26.4210	−	5.56149i	0.978556	−	0.205981i
$730$	−22.2225			−0.822492
$731$	−1.99979	−	0.727865i	−0.0739650	−	0.0269211i
$732$	−20.6160	+	12.8729i	−0.761989	+	0.475795i
$733$	−26.9708	+	32.1426i	−0.996189	+	1.18721i	−0.0138884	+	0.999904i	$0.504421\pi$
$733$	−26.9708	+	32.1426i	−0.996189	+	1.18721i	−0.982301	+	0.187309i	$0.940023\pi$
$734$	−4.45667	+	25.2750i	−0.164499	+	0.932918i
$735$	−14.7448	+	14.0536i	−0.543870	+	0.518373i
$736$	43.8816	−	36.8210i	1.61750	−	1.35724i
$737$	−24.5152	+	14.1539i	−0.903030	+	0.521365i
$738$	−2.72780	−	1.33266i	−0.100412	−	0.0490559i
$739$	8.69080	−	15.0529i	0.319696	−	0.553730i	−0.660728	−	0.750625i	$-0.729752\pi$
$739$	8.69080	−	15.0529i	0.319696	−	0.553730i	0.980425	+	0.196895i	$0.0630858\pi$
$740$	−0.370385	−	2.10056i	−0.0136156	−	0.0772180i
$741$	−4.09455	+	29.0648i	−0.150417	+	1.06772i
$742$	−1.04188	+	6.44842i	−0.0382487	+	0.236729i
$743$	2.40577	+	6.60980i	0.0882591	+	0.242490i	0.975967	−	0.217916i	$-0.0699260\pi$
$743$	2.40577	+	6.60980i	0.0882591	+	0.242490i	−0.887708	+	0.460406i	$0.847704\pi$
$744$	−0.149556	+	0.0603673i	−0.00548299	+	0.00221317i
$745$	2.22759	−	0.392784i	0.0816126	−	0.0143905i
$746$	29.8257	+	17.2199i	1.09200	+	0.630465i
$747$	−17.6326	+	17.0052i	−0.645143	+	0.622187i
$748$	10.1506	−	5.86046i	0.371143	−	0.214279i
$749$	−15.1317	+	2.89253i	−0.552901	+	0.105691i
$750$	−12.8696	+	39.5644i	−0.469932	+	1.44469i
$751$	−3.67514	+	20.8427i	−0.134108	+	0.760562i	0.841369	+	0.540461i	$0.181750\pi$
$751$	−3.67514	+	20.8427i	−0.134108	+	0.760562i	−0.975477	+	0.220102i	$0.929361\pi$
$752$	−35.8818	−	30.1084i	−1.30847	−	1.09794i
$753$	−10.4061	+	19.5556i	−0.379220	+	0.712644i
$754$	16.6334	−	45.7000i	0.605754	−	1.66430i
$755$	−5.59716			−0.203701
$756$	−10.6740	+	24.8629i	−0.388211	+	0.904255i
$757$	−13.1453			−0.477773			−0.238886	−	0.971048i	$-0.576782\pi$
$757$	−13.1453			−0.477773			−0.238886	+	0.971048i	$0.576782\pi$
$758$	−15.3085	+	42.0596i	−0.556028	+	1.52768i
$759$	−39.6729	+	1.37235i	−1.44004	+	0.0498130i
$760$	0.539569	+	0.452752i	0.0195722	+	0.0164231i
$761$	4.65271	−	26.3869i	0.168661	−	0.956523i	−0.776548	−	0.630058i	$-0.783031\pi$
$761$	4.65271	−	26.3869i	0.168661	−	0.956523i	0.945209	−	0.326465i	$-0.105858\pi$
$762$	31.3441	+	34.8342i	1.13548	+	1.26191i
$763$	−4.69163	−	24.5434i	−0.169849	−	0.888529i
$764$	−8.67410	+	5.00800i	−0.313818	+	0.181183i
$765$	8.60591	−	3.82482i	0.311147	−	0.138287i
$766$	31.1581	+	17.9891i	1.12579	+	0.649973i
$767$	−1.41725	+	0.249899i	−0.0511738	+	0.00902332i
$768$	−22.5114	−	17.5998i	−0.812311	−	0.635077i
$769$	4.19859	+	11.5355i	0.151405	+	0.415982i	0.992088	−	0.125546i	$-0.0400683\pi$
$769$	4.19859	+	11.5355i	0.151405	+	0.415982i	−0.840683	+	0.541528i	$0.817846\pi$
$770$	4.50130	−	27.8595i	0.162216	−	1.00399i
$771$	−22.6451	−	17.7043i	−0.815545	−	0.637606i
$772$	0.877846	+	4.97851i	0.0315944	+	0.179181i
$773$	5.69422	−	9.86268i	0.204807	−	0.354736i	−0.745264	−	0.666769i	$-0.767677\pi$
$773$	5.69422	−	9.86268i	0.204807	−	0.354736i	0.950071	+	0.312033i	$0.101010\pi$
$774$	−4.00429	+	5.50382i	−0.143931	+	0.197831i
$775$	2.76599	−	1.59694i	0.0993572	−	0.0573639i
$776$	−0.467112	+	0.391954i	−0.0167683	+	0.0140703i
$777$	−0.655075	−	2.88261i	−0.0235007	−	0.103413i
$778$	6.71418	−	38.0780i	0.240715	−	1.36516i
$779$	2.15659	−	2.57012i	0.0772678	−	0.0920841i
$780$	−0.508038	−	14.6868i	−0.0181907	−	0.525872i
$781$	18.3901	+	6.69346i	0.658050	+	0.239511i
$782$	26.7657			0.957138
$783$	12.0076	−	47.9582i	0.429117	−	1.71389i
$784$	14.9202	+	24.2109i	0.532864	+	0.864675i
$785$	10.0497	−	27.6113i	0.358690	−	0.985491i
$786$	−10.9631	−	5.83380i	−0.391040	−	0.208085i
$787$	22.4585	−	26.7650i	0.800558	−	0.954068i	−0.199106	−	0.979978i	$-0.563804\pi$
$787$	22.4585	−	26.7650i	0.800558	−	0.954068i	0.999664	+	0.0259096i	$0.00824820\pi$
$788$	4.81665	+	0.849306i	0.171586	+	0.0302553i
$789$	−8.93778	+	27.4769i	−0.318193	+	0.978203i
$790$	1.86550	+	2.22322i	0.0663715	+	0.0790985i
$791$	−0.764657	−	53.2996i	−0.0271881	−	1.89511i
$792$	0.146457	+	0.589057i	0.00520412	+	0.0209312i
$793$	9.14752	−	15.8440i	0.324838	−	0.562636i
$794$	4.61995	+	26.2010i	0.163956	+	0.929840i
$795$	−1.34992	−	3.34434i	−0.0478768	−	0.118611i
$796$	13.1730	+	36.1925i	0.466904	+	1.28281i
$797$	−21.0051	+	7.64522i	−0.744038	+	0.270808i	−0.686095	−	0.727512i	$-0.740676\pi$
$797$	−21.0051	+	7.64522i	−0.744038	+	0.270808i	−0.0579433	+	0.998320i	$0.518454\pi$
$798$	−48.0224	−	36.4469i	−1.69997	−	1.29021i
$799$	−3.74087	−	21.2155i	−0.132343	−	0.750552i
$800$	15.0220	+	8.67293i	0.531107	+	0.306634i
$801$	−22.6090	+	1.56603i	−0.798851	+	0.0553331i
$802$	3.65495	+	6.33057i	0.129061	+	0.223540i
$803$	16.2122	−	13.6037i	0.572118	−	0.480064i
$804$	−6.28520	−	29.6174i	−0.221662	−	1.04453i
$805$	20.1923	−	24.7776i	0.711687	−	0.873296i
$806$	−4.81926	+	5.74337i	−0.169751	+	0.202302i
$807$	−25.0740	−	40.1561i	−0.882646	−	1.41356i
$808$	0.0164251	−	0.0451275i	0.000577831	−	0.00158758i
$809$		−	7.66333i		−	0.269428i	−0.990884	−	0.134714i	$-0.956988\pi$
$809$		−	7.66333i		−	0.269428i	0.990884	−	0.134714i	$-0.0430116\pi$
$810$	−4.15265	−	29.8323i	−0.145909	−	1.04820i
$811$		−	4.98733i		−	0.175129i	−0.996159	−	0.0875644i	$-0.972092\pi$
$811$		−	4.98733i		−	0.175129i	0.996159	−	0.0875644i	$-0.0279084\pi$
$812$	32.3871	+	37.4918i	1.13657	+	1.31571i
$813$	26.7166	−	16.6822i	0.936991	−	0.585069i
$814$	3.13736	+	2.63256i	0.109964	+	0.0922712i
$815$	−5.88808	+	33.3930i	−0.206251	+	1.16970i
$816$	−2.72950	−	12.8621i	−0.0955517	−	0.450264i
$817$	−4.83491	−	5.76202i	−0.169152	−	0.201588i
$818$	−1.65544	−	2.86731i	−0.0578812	−	0.100253i
$819$	−1.69867	−	20.2959i	−0.0593564	−	0.709195i
$820$	−0.839888	+	1.45473i	−0.0293301	+	0.0508013i
$821$	−7.38627	+	1.30240i	−0.257782	+	0.0454540i	−0.301046	−	0.953610i	$-0.597336\pi$
$821$	−7.38627	+	1.30240i	−0.257782	+	0.0454540i	0.0432633	+	0.999064i	$0.486225\pi$
$822$	−1.04597	+	7.42474i	−0.0364824	+	0.258967i
$823$	−11.9501	+	4.34947i	−0.416553	+	0.151613i	−0.541790	−	0.840514i	$-0.682253\pi$
$823$	−11.9501	+	4.34947i	−0.416553	+	0.151613i	0.125237	+	0.992127i	$0.460031\pi$
$824$	1.06940	−	0.389229i	0.0372543	−	0.0135595i
$825$	−4.49928	−	11.1467i	−0.156645	−	0.388077i
$826$	0.971013	−	2.79181i	0.0337859	−	0.0971395i
$827$	10.6649	+	6.15737i	0.370854	+	0.214113i	0.673832	−	0.738885i	$-0.264647\pi$
$827$	10.6649	+	6.15737i	0.370854	+	0.214113i	−0.302977	+	0.952998i	$0.597981\pi$
$828$	11.7299	−	40.8057i	0.407642	−	1.41810i
$829$	10.1850	−	5.88032i	0.353740	−	0.204232i	−0.312591	−	0.949888i	$-0.601197\pi$
$829$	10.1850	−	5.88032i	0.353740	−	0.204232i	0.666331	+	0.745656i	$0.267864\pi$
$830$	17.5657	+	20.9339i	0.609713	+	0.726628i
$831$	5.02943	+	1.63599i	0.174469	+	0.0567518i
$832$	−19.5667	−	3.45013i	−0.678352	−	0.119612i
$833$	−1.90081	+	12.9408i	−0.0658593	+	0.448373i
$834$	−33.6713	+	63.2762i	−1.16594	+	2.19108i
$835$	1.99042	+	0.724455i	0.0688814	+	0.0250708i
$836$	41.4270			1.43278
$837$	−4.26820	+	6.31442i	−0.147531	+	0.218258i
$838$			1.87266i			0.0646899i
$839$	−37.4037	−	13.6138i	−1.29132	−	0.470002i	−0.397160	−	0.917749i	$-0.630004\pi$
$839$	−37.4037	−	13.6138i	−1.29132	−	0.470002i	−0.894160	+	0.447747i	$0.852226\pi$
$840$	−0.434709	−	0.223380i	−0.0149989	−	0.00770736i
$841$	−47.1308	−	39.5475i	−1.62520	−	1.36371i
$842$	−70.7002	−	12.4664i	−2.43649	−	0.429619i
$843$	−1.54357	−	1.71545i	−0.0531635	−	0.0590831i
$844$	42.8194	−	35.9297i	1.47390	−	1.23675i
$845$	−5.38935	−	9.33462i	−0.185399	−	0.321121i
$846$	−68.5175	−	7.24706i	−2.35568	−	0.249159i
$847$	−1.14119	−	1.91270i	−0.0392117	−	0.0657211i
$848$	−4.95879	+	0.874368i	−0.170286	+	0.0300259i
$849$	−2.54215	+	3.25160i	−0.0872465	+	0.111595i
$850$	2.77203	+	7.61608i	0.0950797	+	0.261229i
$851$	1.58653	+	4.35894i	0.0543854	+	0.149423i
$852$	−12.8923	+	16.4902i	−0.441683	+	0.564946i
$853$	20.0361	−	3.53291i	0.686023	−	0.120964i	0.180237	−	0.983623i	$-0.442314\pi$
$853$	20.0361	−	3.53291i	0.686023	−	0.120964i	0.505786	+	0.862659i	$0.331202\pi$
$854$	19.2534	+	32.2698i	0.658837	+	1.10425i
$855$	33.1014	+	3.50111i	1.13204	+	0.119735i
$856$	−0.184823	−	0.320122i	−0.00631711	−	0.0109416i
$857$	−3.25940	+	2.73496i	−0.111339	+	0.0934245i	−0.696758	−	0.717307i	$-0.745375\pi$
$857$	−3.25940	+	2.73496i	−0.111339	+	0.0934245i	0.585419	+	0.810731i	$0.300930\pi$
$858$	18.8741	+	20.9757i	0.644352	+	0.716099i
$859$	−16.4971	−	2.90888i	−0.562872	−	0.0992495i	−0.115030	−	0.993362i	$-0.536696\pi$
$859$	−16.4971	−	2.90888i	−0.562872	−	0.0992495i	−0.447842	+	0.894113i	$0.647807\pi$
$860$	2.88487	+	2.42070i	0.0983734	+	0.0825450i
$861$	−1.06402	+	2.07064i	−0.0362618	+	0.0705673i
$862$	−46.8126	−	17.0384i	−1.59444	−	0.580329i
$863$		−	21.7088i		−	0.738977i	−0.929235	−	0.369488i	$-0.879533\pi$
$863$		−	21.7088i		−	0.738977i	0.929235	−	0.369488i	$-0.120467\pi$
$864$	−41.2891	−	2.92816i	−1.40468	−	0.0996179i
$865$	−30.4352			−1.03483
$866$	−53.3897	−	19.4323i	−1.81426	−	0.660335i
$867$	−10.9913	+	20.6552i	−0.373284	+	0.701488i
$868$	−2.71498	−	7.13900i	−0.0921523	−	0.242313i
$869$	−2.72192	−	0.479948i	−0.0923347	−	0.0162811i
$870$	−52.4465	−	17.0600i	−1.77810	−	0.578387i
$871$	14.6494	+	17.4584i	0.496374	+	0.591556i
$872$	0.519232	−	0.299779i	0.0175834	−	0.0101518i
$873$	−7.96102	+	27.6946i	−0.269440	+	0.937320i
$874$	81.9277	+	47.3010i	2.77125	+	1.59998i
$875$	30.1330	+	10.4805i	1.01868	+	0.354305i
$876$	8.47262	+	20.9903i	0.286263	+	0.709198i
$877$	35.8799	−	13.0592i	1.21158	−	0.440978i	0.344327	−	0.938850i	$-0.388107\pi$
$877$	35.8799	−	13.0592i	1.21158	−	0.440978i	0.867251	+	0.497872i	$0.165885\pi$
$878$	−54.7396	+	19.9236i	−1.84737	+	0.672389i
$879$	−6.12579	+	43.4835i	−0.206618	+	1.46666i
$880$	21.4237	−	3.77758i	0.722194	−	0.127342i
$881$	−19.9609	+	34.5734i	−0.672501	+	1.16481i	0.304692	+	0.952451i	$0.401447\pi$
$881$	−19.9609	+	34.5734i	−0.672501	+	1.16481i	−0.977193	+	0.212355i	$0.931887\pi$
$882$	38.0979	+	17.2770i	1.28282	+	0.581748i
$883$	−15.2724	−	26.4525i	−0.513957	−	0.890199i	−0.999869	−	0.0161915i	$-0.994846\pi$
$883$	−15.2724	−	26.4525i	−0.513957	−	0.890199i	0.485912	−	0.874008i	$-0.338487\pi$
$884$	−6.06561	−	7.22871i	−0.204008	−	0.243128i
$885$	0.338787	+	1.59645i	0.0113882	+	0.0536640i
$886$	0.794032	−	4.50318i	0.0266760	−	0.151287i
$887$	3.33017	+	2.79434i	0.111816	+	0.0938248i	0.696981	−	0.717089i	$-0.254526\pi$
$887$	3.33017	+	2.79434i	0.111816	+	0.0938248i	−0.585165	+	0.810914i	$0.698970\pi$
$888$	0.0601635	−	0.0375668i	0.00201896	−	0.00126066i
$889$	27.1925	−	23.4901i	0.912006	−	0.787832i
$890$			25.2820i			0.847456i
$891$	21.2916	+	19.2218i	0.713296	+	0.643956i
$892$			27.2894i			0.913717i
$893$	26.0421	−	71.5501i	0.871466	−	2.39433i
$894$	−2.46037	−	3.94029i	−0.0822870	−	0.131783i
$895$	6.29615	−	7.50346i	0.210457	−	0.250813i
$896$	−0.848731	+	1.04146i	−0.0283541	+	0.0347928i
$897$	6.63446	+	31.2633i	0.221518	+	1.04385i
$898$	33.1047	−	27.7781i	1.10472	−	0.926968i
$899$	6.97783	+	12.0860i	0.232724	+	0.403089i
$900$	12.8259	−	0.888400i	0.427531	−	0.0296133i
$901$	−2.00557	−	1.15791i	−0.0668151	−	0.0385757i
$902$	−0.560079	−	3.17636i	−0.0186486	−	0.105761i
$903$	4.15747	+	3.15534i	0.138352	+	0.105003i
$904$	1.20187	−	0.437446i	0.0399737	−	0.0145492i
$905$	14.3357	+	39.3869i	0.476534	+	1.30927i
$906$	4.30253	+	10.6592i	0.142942	+	0.354129i
$907$	−1.87379	−	10.6268i	−0.0622180	−	0.352856i	−0.999984	−	0.00558913i	$-0.998221\pi$
$907$	−1.87379	−	10.6268i	−0.0622180	−	0.352856i	0.937766	−	0.347267i	$-0.112890\pi$
$908$	17.9440	−	31.0799i	0.595493	−	1.03142i
$909$	−0.547585	−	2.20241i	−0.0181622	−	0.0730494i
$910$	−22.7180	+	0.325921i	−0.753093	+	0.0108042i
$911$	−17.8805	−	21.3091i	−0.592407	−	0.706003i	0.383660	−	0.923474i	$-0.374663\pi$
$911$	−17.8805	−	21.3091i	−0.592407	−	0.706003i	−0.976067	+	0.217472i	$0.930219\pi$
$912$	14.3754	−	44.1936i	0.476018	−	1.46339i
$913$	−25.6297	−	4.51922i	−0.848221	−	0.149564i
$914$	−0.153201	+	0.182578i	−0.00506745	+	0.00603916i
$915$	−18.3155	−	9.74624i	−0.605491	−	0.322201i
$916$	−5.51325	+	15.1475i	−0.182163	+	0.500489i
$917$	−4.64265	+	8.31452i	−0.153314	+	0.274570i
$918$	−13.8993	−	13.4490i	−0.458747	−	0.443882i
$919$	−41.7928			−1.37862			−0.689308	−	0.724468i	$-0.742085\pi$
$919$	−41.7928			−1.37862			−0.689308	+	0.724468i	$0.742085\pi$
$920$	0.720681	+	0.262307i	0.0237602	+	0.00864799i
$921$	0.634376	+	18.3391i	0.0209034	+	0.604294i
$922$	43.8315	−	52.2364i	1.44351	−	1.72031i
$923$	2.73599	−	15.5166i	0.0900562	−	0.510734i
$924$	−28.0309	+	6.37006i	−0.922150	+	0.209560i
$925$	−1.07601	+	0.902881i	−0.0353791	+	0.0296866i
$926$	−25.1165	+	14.5010i	−0.825378	+	0.476532i
$927$	31.6398	−	43.4883i	1.03919	−	1.42834i
$928$	−37.8963	+	65.6383i	−1.24401	+	2.15468i
$929$	5.51917	+	31.3007i	0.181078	+	1.02694i	0.930892	+	0.365295i	$0.119032\pi$
$929$	5.51917	+	31.3007i	0.181078	+	1.02694i	−0.749814	+	0.661649i	$0.769857\pi$
$930$	6.69822	+	5.23677i	0.219643	+	0.171721i
$931$	−28.6876	+	36.2518i	−0.940199	+	1.18810i
$932$	−6.10897	−	16.7842i	−0.200106	−	0.549786i
$933$	8.46102	+	6.61496i	0.277001	+	0.216564i
$934$	35.6484	−	6.28577i	1.16645	−	0.205677i
$935$	8.66476	+	5.00260i	0.283368	+	0.163603i
$936$	0.446565	−	0.198472i	0.0145964	−	0.00648725i
$937$	−12.7723	+	7.37411i	−0.417254	+	0.240902i	−0.693902	−	0.720070i	$-0.744110\pi$
$937$	−12.7723	+	7.37411i	−0.417254	+	0.240902i	0.276648	+	0.960971i	$0.410777\pi$
$938$	−45.9776	+	8.78894i	−1.50122	+	0.286969i
$939$	17.0147	+	18.9092i	0.555254	+	0.617080i
$940$	−6.61983	+	37.5429i	−0.215915	+	1.22451i
$941$	22.9309	+	19.2413i	0.747524	+	0.627248i	0.934847	−	0.355051i	$-0.115536\pi$
$941$	22.9309	+	19.2413i	0.747524	+	0.627248i	−0.187322	+	0.982298i	$0.559981\pi$
$942$	−60.3083	+	2.08615i	−1.96495	+	0.0679705i
$943$	1.24944	−	3.43281i	0.0406874	−	0.111788i
$944$	2.27855			0.0741603
$945$	−22.9359	+	2.72089i	−0.746104	+	0.0885105i
$946$	−7.23104			−0.235101
$947$	−15.8287	+	43.4890i	−0.514364	+	1.41320i	0.362283	+	0.932068i	$0.381997\pi$
$947$	−15.8287	+	43.4890i	−0.514364	+	1.41320i	−0.876647	+	0.481135i	$0.840225\pi$
$948$	1.38870	−	2.60969i	0.0451029	−	0.0847589i
$949$	−13.0523	−	10.9522i	−0.423697	−	0.355524i
$950$	−4.97437	+	28.2110i	−0.161390	+	0.915287i
$951$	−5.99181	+	18.4203i	−0.194298	+	0.597319i
$952$	−0.308254	+	0.0589248i	−0.00999056	+	0.00190976i
$953$	−23.3288	+	13.4689i	−0.755694	+	0.436300i	−0.827747	−	0.561101i	$-0.810378\pi$
$953$	−23.3288	+	13.4689i	−0.755694	+	0.436300i	0.0720539	+	0.997401i	$0.477045\pi$
$954$	−5.33128	+	5.14158i	−0.172606	+	0.166465i
$955$	−7.40439	−	4.27493i	−0.239600	−	0.138333i
$956$	−36.6100	+	6.45533i	−1.18405	+	0.208780i
$957$	48.7053	−	19.6596i	1.57442	−	0.635504i
$958$	−5.62727	−	15.4608i	−0.181809	−	0.499516i
$959$	5.67607	+	0.917093i	0.183290	+	0.0296145i
$960$	−3.14313	+	22.3113i	−0.101444	+	0.720093i
$961$	5.00950	+	28.4103i	0.161597	+	0.916460i
$962$	1.64864	−	2.85553i	0.0531543	−	0.0920660i
$963$	−15.6955	−	7.66797i	−0.505779	−	0.247097i
$964$	−18.4565	+	10.6558i	−0.594442	+	0.343201i
$965$	−3.30573	+	2.77383i	−0.106415	+	0.0892929i
$966$	−62.7084	−	19.4078i	−2.01761	−	0.624435i
$967$	−1.68216	+	9.53998i	−0.0540945	+	0.306785i	−0.999836	−	0.0181363i	$-0.994227\pi$
$967$	−1.68216	+	9.53998i	−0.0540945	+	0.306785i	0.945741	+	0.324921i	$0.105338\pi$
$968$	0.0343514	−	0.0409384i	0.00110409	−	0.00131581i
$969$	18.1297	−	11.3204i	0.582411	−	0.363664i
$970$	30.2073	+	10.9946i	0.969898	+	0.353014i
$971$	17.2534			0.553688			0.276844	−	0.960915i	$-0.410711\pi$
$971$	17.2534			0.553688			0.276844	+	0.960915i	$0.410711\pi$
$972$	−26.5950	+	15.2964i	−0.853034	+	0.490631i
$973$	47.9894	+	26.7963i	1.53847	+	0.859049i
$974$	−7.92290	+	21.7680i	−0.253866	+	0.697492i
$975$	−8.20875	+	5.12564i	−0.262890	+	0.164152i
$976$	−18.6193	+	22.1897i	−0.595991	+	0.710274i
$977$	32.3224	+	5.69932i	1.03409	+	0.182337i	0.664833	−	0.746992i	$-0.268503\pi$
$977$	32.3224	+	5.69932i	1.03409	+	0.182337i	0.369253	+	0.929329i	$0.379614\pi$
$978$	68.1198	−	14.4559i	2.17823	−	0.462248i
$979$	−15.4766	−	18.4443i	−0.494634	−	0.589482i
$980$	10.9931	−	20.3685i	0.351161	−	0.650649i
$981$	12.4373	−	25.4578i	0.397093	−	0.812804i
$982$	24.1930	−	41.9035i	0.772030	−	1.33719i
$983$	−6.82161	−	38.6873i	−0.217576	−	1.23393i	−0.876381	−	0.481619i	$-0.840049\pi$
$983$	−6.82161	−	38.6873i	−0.217576	−	1.23393i	0.658805	−	0.752314i	$-0.271062\pi$
$984$	−0.0553126	−	0.00779224i	−0.00176330	−	0.000248407i
$985$	1.42794	+	3.92324i	0.0454980	+	0.125005i
$986$	−33.2784	+	12.1123i	−1.05980	+	0.385736i
$987$	−6.61902	+	52.4177i	−0.210686	+	1.66847i
$988$	−5.79161	−	32.8458i	−0.184256	−	1.04497i
$989$	−7.09277	−	4.09501i	−0.225537	−	0.130214i
$990$	23.0330	−	22.2135i	0.732037	−	0.705990i
$991$	11.3750	+	19.7020i	0.361338	+	0.625856i	0.988181	−	0.153289i	$-0.0489867\pi$
$991$	11.3750	+	19.7020i	0.361338	+	0.625856i	−0.626843	+	0.779145i	$0.715653\pi$
$992$	8.95083	−	7.51064i	0.284189	−	0.238463i
$993$	−45.6683	−	14.8551i	−1.44924	−	0.471414i
$994$	25.0865	+	20.4440i	0.795694	+	0.648445i
$995$	−21.1332	+	25.1856i	−0.669967	+	0.798436i
$996$	13.0761	−	24.5730i	0.414332	−	0.778626i
$997$	−6.82407	+	18.7490i	−0.216120	+	0.593786i	−0.999619	−	0.0276077i	$-0.991211\pi$
$997$	−6.82407	+	18.7490i	−0.216120	+	0.593786i	0.783498	+	0.621394i	$0.213433\pi$
$998$		−	33.0534i		−	1.04629i
$999$	1.36636	−	3.06077i	0.0432298	−	0.0968385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.6	yes	132
3.2	odd	2		567.2.be.a.503.17		132
7.6	odd	2	inner	189.2.be.a.104.5	yes	132
21.20	even	2		567.2.be.a.503.18		132
27.7	even	9		567.2.be.a.62.18		132
27.20	odd	18	inner	189.2.be.a.20.5	✓	132
189.20	even	18	inner	189.2.be.a.20.6	yes	132
189.34	odd	18		567.2.be.a.62.17		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.5	✓	132	27.20	odd	18	inner
189.2.be.a.20.6	yes	132	189.20	even	18	inner
189.2.be.a.104.5	yes	132	7.6	odd	2	inner
189.2.be.a.104.6	yes	132	1.1	even	1	trivial
567.2.be.a.62.17		132	189.34	odd	18
567.2.be.a.62.18		132	27.7	even	9
567.2.be.a.503.17		132	3.2	odd	2
567.2.be.a.503.18		132	21.20	even	2

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.681310 + 1.87188i) q^{2} +(0.917364 + 1.46916i) q^{3} +(-1.50768 - 1.26509i) q^{4} +(0.291735 - 1.65451i) q^{5} +(-3.37511 + 0.716242i) q^{6} +(0.496759 + 2.59870i) q^{7} +(-0.0549773 + 0.0317412i) q^{8} +(-1.31689 + 2.69552i) q^{9} +(2.89829 + 1.67333i) q^{10} +(-3.13877 + 0.553450i) q^{11} +(0.475538 - 3.37557i) q^{12} +(0.877617 + 2.41123i) q^{13} +(-5.20291 - 0.840643i) q^{14} +(2.69838 - 1.08918i) q^{15} +(-0.705484 - 4.00100i) q^{16} +(0.934264 - 1.61819i) q^{17} +(-4.14849 - 4.30154i) q^{18} +(5.71942 - 3.30211i) q^{19} +(-2.53295 + 2.12540i) q^{20} +(-3.36220 + 3.11377i) q^{21} +(1.10248 - 6.25248i) q^{22} +(4.62225 - 5.50858i) q^{23} +(-0.0970672 - 0.0516525i) q^{24} +(2.04616 + 0.744740i) q^{25} -5.11148 q^{26} +(-5.16822 + 0.538047i) q^{27} +(2.53864 - 4.54644i) q^{28} +(-3.25414 + 8.94067i) q^{29} +(0.200393 + 5.79312i) q^{30} +(0.942831 - 1.12362i) q^{31} +(7.84502 + 1.38329i) q^{32} +(-3.69250 - 4.10365i) q^{33} +(2.39254 + 2.85132i) q^{34} +(4.44450 - 0.0637627i) q^{35} +(5.39551 - 2.39799i) q^{36} +(-0.322537 + 0.558651i) q^{37} +(2.28447 + 12.9559i) q^{38} +(-2.73740 + 3.50134i) q^{39} +(0.0364774 + 0.100221i) q^{40} +(0.477380 - 0.173752i) q^{41} +(-3.53792 - 8.41510i) q^{42} +(-0.197774 - 1.12163i) q^{43} +(5.43241 + 3.13640i) q^{44} +(4.07559 + 2.96518i) q^{45} +(7.16224 + 12.4054i) q^{46} +(8.83196 - 7.41090i) q^{47} +(5.23094 - 4.70684i) q^{48} +(-6.50646 + 2.58185i) q^{49} +(-2.78813 + 3.32277i) q^{50} +(3.23445 - 0.111884i) q^{51} +(1.72727 - 4.74562i) q^{52} -1.23939i q^{53} +(2.51400 - 10.0409i) q^{54} +5.35460i q^{55} +(-0.109796 - 0.127102i) q^{56} +(10.0981 + 5.37353i) q^{57} +(-14.5188 - 12.1827i) q^{58} +(-0.0973892 + 0.552322i) q^{59} +(-5.44620 - 1.77156i) q^{60} +(-4.58297 - 5.46178i) q^{61} +(1.46093 + 2.53041i) q^{62} +(-7.65901 - 2.08317i) q^{63} +(-3.87153 + 6.70568i) q^{64} +(4.24545 - 0.748587i) q^{65} +(10.1973 - 4.11607i) q^{66} +(8.34610 - 3.03773i) q^{67} +(-3.45573 + 1.25778i) q^{68} +(12.3333 + 1.73747i) q^{69} +(-2.90873 + 8.36303i) q^{70} +(-5.31767 - 3.07016i) q^{71} +(-0.0131599 - 0.189992i) q^{72} +(-5.75058 + 3.32010i) q^{73} +(-0.825982 - 0.984367i) q^{74} +(0.782925 + 3.68934i) q^{75} +(-12.8005 - 2.25707i) q^{76} +(-2.99746 - 7.88178i) q^{77} +(-4.68908 - 7.50960i) q^{78} +(0.814895 + 0.296597i) q^{79} -6.82552 q^{80} +(-5.53162 - 7.09938i) q^{81} +1.01198i q^{82} +(7.67310 + 2.79278i) q^{83} +(9.00832 - 0.441067i) q^{84} +(-2.40476 - 2.01784i) q^{85} +(2.23431 + 0.393970i) q^{86} +(-16.1205 + 3.42098i) q^{87} +(0.154994 - 0.130055i) q^{88} +(3.77720 + 6.54230i) q^{89} +(-8.32722 + 5.60881i) q^{90} +(-5.83010 + 3.47846i) q^{91} +(-13.9377 + 2.45759i) q^{92} +(2.51571 + 0.354403i) q^{93} +(7.85503 + 21.5815i) q^{94} +(-3.79483 - 10.4262i) q^{95} +(5.16446 + 12.7946i) q^{96} +(9.45944 - 1.66796i) q^{97} +(-0.400014 - 13.9384i) q^{98} +(2.64157 - 9.18943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

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Database

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