LMFDB - Embedded newform 189.2.be.a.104.7

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			104.7
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.422526 + 1.16088i) q^{2} +(-1.51095 - 0.846773i) q^{3} +(0.362974 + 0.304571i) q^{4} +(0.253991 - 1.44045i) q^{5} +(1.62142 - 1.39625i) q^{6} +(1.07486 + 2.41758i) q^{7} +(-2.64668 + 1.52806i) q^{8} +(1.56595 + 2.55887i) q^{9} +(1.56488 + 0.903482i) q^{10} +(4.32398 - 0.762434i) q^{11} +(-0.290533 - 0.767549i) q^{12} +(1.72073 + 4.72766i) q^{13} +(-3.26067 + 0.226294i) q^{14} +(-1.60351 + 1.96138i) q^{15} +(-0.491047 - 2.78487i) q^{16} +(0.691322 - 1.19740i) q^{17} +(-3.63219 + 0.736695i) q^{18} +(-4.13271 + 2.38602i) q^{19} +(0.530913 - 0.445489i) q^{20} +(0.423079 - 4.56300i) q^{21} +(-0.941898 + 5.34177i) q^{22} +(-3.82383 + 4.55707i) q^{23} +(5.29293 - 0.0676904i) q^{24} +(2.68807 + 0.978376i) q^{25} -6.21530 q^{26} +(-0.199298 - 5.19233i) q^{27} +(-0.346179 + 1.20489i) q^{28} +(1.96611 - 5.40183i) q^{29} +(-1.59941 - 2.69021i) q^{30} +(4.06150 - 4.84031i) q^{31} +(-2.57902 - 0.454750i) q^{32} +(-7.17893 - 2.50943i) q^{33} +(1.09794 + 1.30848i) q^{34} +(3.75541 - 0.934242i) q^{35} +(-0.210958 + 1.40575i) q^{36} +(4.81181 - 8.33429i) q^{37} +(-1.02371 - 5.80574i) q^{38} +(1.40332 - 8.60033i) q^{39} +(1.52887 + 4.20054i) q^{40} +(1.26265 - 0.459567i) q^{41} +(5.11834 + 2.41913i) q^{42} +(-0.613355 - 3.47851i) q^{43} +(1.80171 + 1.04022i) q^{44} +(4.08367 - 1.60575i) q^{45} +(-3.67454 - 6.36449i) q^{46} +(-5.55855 + 4.66418i) q^{47} +(-1.61620 + 4.62361i) q^{48} +(-4.68936 + 5.19711i) q^{49} +(-2.27156 + 2.70713i) q^{50} +(-2.05848 + 1.22383i) q^{51} +(-0.815330 + 2.24010i) q^{52} +0.811158i q^{53} +(6.11188 + 1.96253i) q^{54} -6.42214i q^{55} +(-6.53902 - 4.75611i) q^{56} +(8.26475 - 0.105696i) q^{57} +(5.44015 + 4.56483i) q^{58} +(-0.933219 + 5.29255i) q^{59} +(-1.17941 + 0.223550i) q^{60} +(-5.13083 - 6.11468i) q^{61} +(3.90293 + 6.76007i) q^{62} +(-4.50308 + 6.53623i) q^{63} +(4.44544 - 7.69973i) q^{64} +(7.24703 - 1.27785i) q^{65} +(5.94643 - 7.27358i) q^{66} +(-4.21835 + 1.53535i) q^{67} +(0.615627 - 0.224070i) q^{68} +(9.63643 - 3.64759i) q^{69} +(-0.502216 + 4.75433i) q^{70} +(-11.6889 - 6.74856i) q^{71} +(-8.05469 - 4.37964i) q^{72} +(6.23051 - 3.59719i) q^{73} +(7.64200 + 9.10738i) q^{74} +(-3.23308 - 3.75446i) q^{75} +(-2.22678 - 0.392641i) q^{76} +(6.49091 + 9.63404i) q^{77} +(9.39102 + 5.26295i) q^{78} +(-8.07721 - 2.93986i) q^{79} -4.13619 q^{80} +(-4.09559 + 8.01412i) q^{81} +1.65997i q^{82} +(4.57620 + 1.66560i) q^{83} +(1.54333 - 1.52739i) q^{84} +(-1.54922 - 1.29995i) q^{85} +(4.29729 + 0.757728i) q^{86} +(-7.54482 + 6.49706i) q^{87} +(-10.2791 + 8.62523i) q^{88} +(0.219556 + 0.380281i) q^{89} +(0.138631 + 5.41912i) q^{90} +(-9.57994 + 9.24156i) q^{91} +(-2.77590 + 0.489467i) q^{92} +(-10.2354 + 3.87430i) q^{93} +(-3.06592 - 8.42355i) q^{94} +(2.38728 + 6.55901i) q^{95} +(3.51170 + 2.87095i) q^{96} +(-3.66832 + 0.646825i) q^{97} +(-4.05185 - 7.63969i) q^{98} +(8.72210 + 9.87054i) 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 $

$2$	−0.422526	+	1.16088i	−0.298771	+	0.820866i	0.695935	+	0.718105i	$0.254990\pi$
$2$	−0.422526	+	1.16088i	−0.298771	+	0.820866i	−0.994706	+	0.102762i	$0.967232\pi$
$3$	−1.51095	−	0.846773i	−0.872348	−	0.488885i
$3$	−1.51095	−	0.846773i	−0.872348	−	0.488885i
$4$	0.362974	+	0.304571i	0.181487	+	0.152286i
$5$	0.253991	−	1.44045i	0.113588	−	0.644191i	−0.873851	−	0.486193i	$-0.838385\pi$
$5$	0.253991	−	1.44045i	0.113588	−	0.644191i	0.987440	−	0.157997i	$-0.0505038\pi$
$6$	1.62142	−	1.39625i	0.661941	−	0.570017i
$7$	1.07486	+	2.41758i	0.406258	+	0.913758i
$7$	1.07486	+	2.41758i	0.406258	+	0.913758i
$8$	−2.64668	+	1.52806i	−0.935744	+	0.540252i
$9$	1.56595	+	2.55887i	0.521984	+	0.852955i
$10$	1.56488	+	0.903482i	0.494858	+	0.285706i
$11$	4.32398	−	0.762434i	1.30373	−	0.229882i	0.521702	−	0.853128i	$-0.325297\pi$
$11$	4.32398	−	0.762434i	1.30373	−	0.229882i	0.782026	+	0.623246i	$0.214186\pi$
$12$	−0.290533	−	0.767549i	−0.0838698	−	0.221572i
$13$	1.72073	+	4.72766i	0.477244	+	1.31122i	0.911823	+	0.410583i	$0.134675\pi$
$13$	1.72073	+	4.72766i	0.477244	+	1.31122i	−0.434579	+	0.900634i	$0.643103\pi$
$14$	−3.26067	+	0.226294i	−0.871452	+	0.0604795i
$15$	−1.60351	+	1.96138i	−0.414023	+	0.506427i
$16$	−0.491047	−	2.78487i	−0.122762	−	0.696217i
$17$	0.691322	−	1.19740i	0.167670	−	0.290413i	−0.769930	−	0.638128i	$-0.779709\pi$
$17$	0.691322	−	1.19740i	0.167670	−	0.290413i	0.937600	+	0.347715i	$0.113042\pi$
$18$	−3.63219	+	0.736695i	−0.856116	+	0.173641i
$19$	−4.13271	+	2.38602i	−0.948109	+	0.547391i	−0.892493	−	0.451061i	$-0.851046\pi$
$19$	−4.13271	+	2.38602i	−0.948109	+	0.547391i	−0.0556159	+	0.998452i	$0.517712\pi$
$20$	0.530913	−	0.445489i	0.118716	−	0.0996144i
$21$	0.423079	−	4.56300i	0.0923234	−	0.995729i
$22$	−0.941898	+	5.34177i	−0.200813	+	1.13887i
$23$	−3.82383	+	4.55707i	−0.797324	+	0.950214i	−0.999576	−	0.0291193i	$-0.990730\pi$
$23$	−3.82383	+	4.55707i	−0.797324	+	0.950214i	0.202251	+	0.979334i	$0.435174\pi$
$24$	5.29293	−	0.0676904i	1.08042	−	0.0138172i
$25$	2.68807	+	0.978376i	0.537613	+	0.195675i
$26$	−6.21530			−1.21892
$27$	−0.199298	−	5.19233i	−0.0383550	−	0.999264i
$28$	−0.346179	+	1.20489i	−0.0654217	+	0.227703i
$29$	1.96611	−	5.40183i	0.365097	−	1.00310i	−0.612104	−	0.790777i	$-0.709677\pi$
$29$	1.96611	−	5.40183i	0.365097	−	1.00310i	0.977201	−	0.212318i	$-0.0681012\pi$
$30$	−1.59941	−	2.69021i	−0.292011	−	0.491163i
$31$	4.06150	−	4.84031i	0.729467	−	0.869345i	−0.266047	−	0.963960i	$-0.585718\pi$
$31$	4.06150	−	4.84031i	0.729467	−	0.869345i	0.995514	+	0.0946154i	$0.0301621\pi$
$32$	−2.57902	−	0.454750i	−0.455910	−	0.0803892i
$33$	−7.17893	−	2.50943i	−1.24969	−	0.436835i
$34$	1.09794	+	1.30848i	0.188295	+	0.224402i
$35$	3.75541	−	0.934242i	0.634781	−	0.157916i
$36$	−0.210958	+	1.40575i	−0.0351596	+	0.234291i
$37$	4.81181	−	8.33429i	0.791056	−	1.37015i	−0.134258	−	0.990946i	$-0.542865\pi$
$37$	4.81181	−	8.33429i	0.791056	−	1.37015i	0.925314	−	0.379203i	$-0.123802\pi$
$38$	−1.02371	−	5.80574i	−0.166067	−	0.941815i
$39$	1.40332	−	8.60033i	0.224711	−	1.37716i
$40$	1.52887	+	4.20054i	0.241736	+	0.664164i
$41$	1.26265	−	0.459567i	0.197193	−	0.0717724i	−0.241536	−	0.970392i	$-0.577651\pi$
$41$	1.26265	−	0.459567i	0.197193	−	0.0717724i	0.438729	+	0.898620i	$0.355429\pi$
$42$	5.11834	+	2.41913i	0.789777	+	0.373280i
$43$	−0.613355	−	3.47851i	−0.0935357	−	0.530467i	−0.995186	−	0.0980019i	$-0.968755\pi$
$43$	−0.613355	−	3.47851i	−0.0935357	−	0.530467i	0.901651	−	0.432465i	$-0.142356\pi$
$44$	1.80171	+	1.04022i	0.271617	+	0.156818i
$45$	4.08367	−	1.60575i	0.608757	−	0.239371i
$46$	−3.67454	−	6.36449i	−0.541782	−	0.938393i
$47$	−5.55855	+	4.66418i	−0.810798	+	0.680341i	−0.950798	−	0.309811i	$-0.899734\pi$
$47$	−5.55855	+	4.66418i	−0.810798	+	0.680341i	0.140000	+	0.990152i	$0.455290\pi$
$48$	−1.61620	+	4.62361i	−0.233279	+	0.667360i
$49$	−4.68936	+	5.19711i	−0.669908	+	0.742444i
$50$	−2.27156	+	2.70713i	−0.321246	+	0.382847i
$51$	−2.05848	+	1.22383i	−0.288245	+	0.171370i
$52$	−0.815330	+	2.24010i	−0.113066	+	0.310646i
$53$			0.811158i			0.111421i	0.998447	+	0.0557105i	$0.0177424\pi$
$53$			0.811158i			0.111421i	−0.998447	+	0.0557105i	$0.982258\pi$
$54$	6.11188	+	1.96253i	0.831722	+	0.267067i
$55$		−	6.42214i		−	0.865961i
$56$	−6.53902	−	4.75611i	−0.873813	−	0.635562i
$57$	8.26475	−	0.105696i	1.09469	−	0.0139998i
$58$	5.44015	+	4.56483i	0.714327	+	0.599391i
$59$	−0.933219	+	5.29255i	−0.121495	+	0.689031i	0.861834	+	0.507191i	$0.169316\pi$
$59$	−0.933219	+	5.29255i	−0.121495	+	0.689031i	−0.983328	+	0.181839i	$0.941795\pi$
$60$	−1.17941	+	0.223550i	−0.152261	+	0.0288601i
$61$	−5.13083	−	6.11468i	−0.656935	−	0.782905i	0.330007	−	0.943978i	$-0.392949\pi$
$61$	−5.13083	−	6.11468i	−0.656935	−	0.782905i	−0.986942	+	0.161073i	$0.948504\pi$
$62$	3.90293	+	6.76007i	0.495672	+	0.858530i
$63$	−4.50308	+	6.53623i	−0.567335	+	0.823487i
$64$	4.44544	−	7.69973i	0.555680	−	0.962466i
$65$	7.24703	−	1.27785i	0.898883	−	0.158497i
$66$	5.94643	−	7.27358i	0.731954	−	0.895316i
$67$	−4.21835	+	1.53535i	−0.515353	+	0.187573i	−0.586587	−	0.809886i	$-0.699529\pi$
$67$	−4.21835	+	1.53535i	−0.515353	+	0.187573i	0.0712336	+	0.997460i	$0.477306\pi$
$68$	0.615627	−	0.224070i	0.0746557	−	0.0271725i
$69$	9.63643	−	3.64759i	1.16009	−	0.439118i
$70$	−0.502216	+	4.75433i	−0.0600263	+	0.568251i
$71$	−11.6889	−	6.74856i	−1.38721	−	0.800907i	−0.394211	−	0.919020i	$-0.628982\pi$
$71$	−11.6889	−	6.74856i	−1.38721	−	0.800907i	−0.993000	+	0.118113i	$0.962316\pi$
$72$	−8.05469	−	4.37964i	−0.949254	−	0.516145i
$73$	6.23051	−	3.59719i	0.729226	−	0.421019i	−0.0889127	−	0.996039i	$-0.528339\pi$
$73$	6.23051	−	3.59719i	0.729226	−	0.421019i	0.818139	+	0.575020i	$0.195006\pi$
$74$	7.64200	+	9.10738i	0.888365	+	1.05871i
$75$	−3.23308	−	3.75446i	−0.373324	−	0.433528i
$76$	−2.22678	−	0.392641i	−0.255429	−	0.0450391i
$77$	6.49091	+	9.63404i	0.739707	+	1.09790i
$78$	9.39102	+	5.26295i	1.06332	+	0.595911i
$79$	−8.07721	−	2.93986i	−0.908757	−	0.330760i	−0.155000	−	0.987914i	$-0.549538\pi$
$79$	−8.07721	−	2.93986i	−0.908757	−	0.330760i	−0.753756	+	0.657154i	$0.771760\pi$
$80$	−4.13619			−0.462441
$81$	−4.09559	+	8.01412i	−0.455066	+	0.890458i
$82$			1.65997i			0.183313i
$83$	4.57620	+	1.66560i	0.502303	+	0.182823i	0.580729	−	0.814097i	$-0.302767\pi$
$83$	4.57620	+	1.66560i	0.502303	+	0.182823i	−0.0784266	+	0.996920i	$0.524990\pi$
$84$	1.54333	−	1.52739i	0.168391	−	0.166652i
$85$	−1.54922	−	1.29995i	−0.168036	−	0.140999i
$86$	4.29729	+	0.757728i	0.463388	+	0.0817079i
$87$	−7.54482	+	6.49706i	−0.808889	+	0.696558i
$88$	−10.2791	+	8.62523i	−1.09576	+	0.919453i
$89$	0.219556	+	0.380281i	0.0232728	+	0.0403097i	0.877427	−	0.479710i	$-0.159258\pi$
$89$	0.219556	+	0.380281i	0.0232728	+	0.0403097i	−0.854154	+	0.520019i	$0.825925\pi$
$90$	0.138631	+	5.41912i	0.0146130	+	0.571225i
$91$	−9.57994	+	9.24156i	−1.00425	+	0.968778i
$92$	−2.77590	+	0.489467i	−0.289408	+	0.0510305i
$93$	−10.2354	+	3.87430i	−1.06136	+	0.401746i
$94$	−3.06592	−	8.42355i	−0.316226	−	0.868823i
$95$	2.38728	+	6.55901i	0.244930	+	0.672940i
$96$	3.51170	+	2.87095i	0.358411	+	0.293015i
$97$	−3.66832	+	0.646825i	−0.372462	+	0.0656751i	−0.356746	−	0.934201i	$-0.616114\pi$
$97$	−3.66832	+	0.646825i	−0.372462	+	0.0656751i	−0.0157159	+	0.999876i	$0.505003\pi$
$98$	−4.05185	−	7.63969i	−0.409298	−	0.771726i
$99$	8.72210	+	9.87054i	0.876604	+	0.992027i
$100$	0.677713	+	1.17383i	0.0677713	+	0.117383i
$101$	12.1379	−	10.1849i	1.20777	−	1.01344i	0.208393	−	0.978045i	$-0.433177\pi$
$101$	12.1379	−	10.1849i	1.20777	−	1.01344i	0.999374	−	0.0353913i	$-0.0112677\pi$
$102$	−0.550955	−	2.90675i	−0.0545527	−	0.287811i
$103$	5.45514	+	0.961888i	0.537511	+	0.0947776i	0.435812	−	0.900038i	$-0.356461\pi$
$103$	5.45514	+	0.961888i	0.537511	+	0.0947776i	0.101698	+	0.994815i	$0.467572\pi$
$104$	−11.7784	−	9.88324i	−1.15497	−	0.969131i
$105$	−6.46534	−	1.76839i	−0.630952	−	0.172577i
$106$	−0.941657	−	0.342735i	−0.0914618	−	0.0332894i
$107$		−	2.86545i		−	0.277014i	−0.990361	−	0.138507i	$-0.955770\pi$
$107$		−	2.86545i		−	0.277014i	0.990361	−	0.138507i	$-0.0442303\pi$
$108$	1.50909	−	1.94538i	0.145213	−	0.187194i
$109$	13.5547			1.29831			0.649154	−	0.760657i	$-0.275123\pi$
$109$	13.5547			1.29831			0.649154	+	0.760657i	$0.275123\pi$
$110$	7.45534	+	2.71352i	0.710838	+	0.258724i
$111$	−14.3277	+	8.51821i	−1.35992	+	0.808512i
$112$	6.20482	−	4.18048i	0.586301	−	0.395019i
$113$	−10.0678	−	1.77523i	−0.947100	−	0.166999i	−0.321295	−	0.946979i	$-0.604118\pi$
$113$	−10.0678	−	1.77523i	−0.947100	−	0.166999i	−0.625805	+	0.779980i	$0.715229\pi$
$114$	−3.36937	+	9.63904i	−0.315570	+	0.902779i
$115$	5.59303	+	6.66551i	0.521552	+	0.621562i
$116$	2.35889	−	1.36191i	0.219017	−	0.126450i
$117$	−9.40287	+	11.8064i	−0.869296	+	1.09150i
$118$	−5.74970	−	3.31959i	−0.529303	−	0.305593i
$119$	3.63789	+	0.384283i	0.333485	+	0.0352272i
$120$	1.24685	−	7.64142i	0.113821	−	0.697563i
$121$	7.77885	−	2.83127i	0.707168	−	0.257388i
$122$	9.26632	−	3.37267i	0.838934	−	0.305347i
$123$	−2.29695	−	0.374794i	−0.207109	−	0.0337941i
$124$	2.94844	−	0.519889i	0.264777	−	0.0466874i
$125$	5.74874	−	9.95711i	0.514183	−	0.890591i
$126$	−5.68511	−	7.98926i	−0.506470	−	0.711740i
$127$	3.57642	+	6.19455i	0.317356	+	0.549677i	0.979936	−	0.199315i	$-0.0638715\pi$
$127$	3.57642	+	6.19455i	0.317356	+	0.549677i	−0.662579	+	0.748992i	$0.730538\pi$
$128$	3.69348	+	4.40172i	0.326461	+	0.389061i
$129$	−2.01876	+	5.77523i	−0.177742	+	0.508481i
$130$	−1.57863	+	8.95285i	−0.138455	+	0.785217i
$131$	11.8367	+	9.93219i	1.03418	+	0.867779i	0.991342	−	0.131303i	$-0.0419160\pi$
$131$	11.8367	+	9.93219i	1.03418	+	0.867779i	0.0428368	+	0.999082i	$0.486360\pi$
$132$	−1.84147	−	3.09735i	−0.160279	−	0.269590i
$133$	−10.2105	−	7.42651i	−0.885360	−	0.643960i
$134$		−	5.54572i		−	0.479077i
$135$	−7.52993	−	1.03172i	−0.648073	−	0.0887967i
$136$			4.22553i			0.362336i
$137$	2.61871	−	7.19484i	0.223731	−	0.614697i	−0.776143	−	0.630557i	$-0.782826\pi$
$137$	2.61871	−	7.19484i	0.223731	−	0.614697i	0.999874	+	0.0158603i	$0.00504871\pi$
$138$	0.162775	+	12.7279i	0.0138564	+	1.08347i
$139$	6.08203	−	7.24828i	0.515871	−	0.614791i	−0.443728	−	0.896161i	$-0.646344\pi$
$139$	6.08203	−	7.24828i	0.515871	−	0.614791i	0.959599	+	0.281370i	$0.0907889\pi$
$140$	1.64766	+	0.804686i	0.139253	+	0.0680083i
$141$	12.3482	−	2.34052i	1.03991	−	0.197107i
$142$	12.7731	−	10.7179i	1.07190	−	0.899428i
$143$	11.0449	+	19.1303i	0.923622	+	1.59976i
$144$	6.35715	−	5.61749i	0.529762	−	0.468124i
$145$	−7.28172	−	4.20410i	−0.604714	−	0.349132i
$146$	1.54335	+	8.75278i	0.127729	+	0.724386i
$147$	11.4862	−	3.88176i	0.947363	−	0.320162i
$148$	4.28495	−	1.55959i	0.352220	−	0.128198i
$149$	6.17318	+	16.9607i	0.505726	+	1.38947i	0.885607	+	0.464436i	$0.153743\pi$
$149$	6.17318	+	16.9607i	0.505726	+	1.38947i	−0.379880	+	0.925036i	$0.624035\pi$
$150$	5.72454	−	2.16686i	0.467407	−	0.176923i
$151$	−1.75618	−	9.95978i	−0.142916	−	0.810515i	−0.969017	−	0.246994i	$-0.920557\pi$
$151$	−1.75618	−	9.95978i	−0.142916	−	0.810515i	0.826101	−	0.563521i	$-0.190554\pi$
$152$	7.29198	−	12.6301i	0.591458	−	1.02444i
$153$	4.14657	−	0.106077i	0.335231	−	0.00857581i
$154$	−13.9265	+	3.46454i	−1.12223	+	0.279180i
$155$	−5.94065	−	7.07980i	−0.477165	−	0.568663i
$156$	3.12878	−	2.69429i	0.250503	−	0.215716i
$157$	−21.0842	−	3.71772i	−1.68270	−	0.296706i	−0.751101	−	0.660187i	$-0.770477\pi$
$157$	−21.0842	−	3.71772i	−1.68270	−	0.296706i	−0.931602	+	0.363481i	$0.881588\pi$
$158$	6.82566	−	8.13450i	0.543020	−	0.647146i
$159$	0.686866	−	1.22562i	0.0544720	−	0.0971980i
$160$	−1.31009	+	3.59945i	−0.103572	+	0.284562i
$161$	−15.1271	−	4.34621i	−1.19219	−	0.342529i
$162$	−7.57294	−	8.14067i	−0.594986	−	0.639591i
$163$	−5.89950			−0.462084			−0.231042	−	0.972944i	$-0.574214\pi$
$163$	−5.89950			−0.462084			−0.231042	+	0.972944i	$0.574214\pi$
$164$	0.598280	+	0.217756i	0.0467179	+	0.0170039i
$165$	−5.43809	+	9.70354i	−0.423355	+	0.755420i
$166$	−3.86712	+	4.60866i	−0.300147	+	0.357701i
$167$	1.77762	−	10.0814i	0.137557	−	0.780123i	−0.835488	−	0.549508i	$-0.814815\pi$
$167$	1.77762	−	10.0814i	0.137557	−	0.780123i	0.973045	−	0.230615i	$-0.0740737\pi$
$168$	5.85280	+	12.7233i	0.451553	+	0.981625i
$169$	−9.43129	+	7.91379i	−0.725483	+	0.608753i
$170$	2.16367	−	1.24919i	0.165946	−	0.0958088i
$171$	−12.5771	−	6.83866i	−0.961797	−	0.522965i
$172$	0.836822	−	1.44942i	0.0638071	−	0.110517i
$173$	−0.404033	−	2.29139i	−0.0307181	−	0.174211i	0.965589	−	0.260073i	$-0.0837466\pi$
$173$	−0.404033	−	2.29139i	−0.0307181	−	0.174211i	−0.996307	+	0.0858621i	$0.972636\pi$
$174$	−4.35443	−	11.5038i	−0.330109	−	0.872101i
$175$	0.523992	+	7.55023i	0.0396101	+	0.570743i
$176$	−4.24655	−	11.6673i	−0.320096	−	0.879457i
$177$	5.89163	−	7.20656i	0.442842	−	0.541678i
$178$	−0.534229	+	0.0941990i	−0.0400422	+	0.00706051i
$179$	−6.11585	−	3.53099i	−0.457120	−	0.263919i	0.253712	−	0.967280i	$-0.418348\pi$
$179$	−6.11585	−	3.53099i	−0.457120	−	0.263919i	−0.710833	+	0.703361i	$0.751682\pi$
$180$	1.97133	+	0.660922i	0.146934	+	0.0492622i
$181$	13.6823	−	7.89950i	1.01700	−	0.587165i	0.103766	−	0.994602i	$-0.466911\pi$
$181$	13.6823	−	7.89950i	1.01700	−	0.587165i	0.913234	+	0.407436i	$0.133577\pi$
$182$	−6.68057	−	15.0260i	−0.495197	−	1.11380i
$183$	2.57469	+	13.5836i	0.190326	+	1.00413i
$184$	3.15699	−	17.9042i	0.232736	−	1.31991i
$185$	−10.7830	−	9.04802i	−0.792783	−	0.665224i
$186$	−0.172892	−	13.5190i	−0.0126771	−	0.991263i
$187$	2.07632	−	5.70464i	0.151835	−	0.417164i
$188$	−3.43819			−0.250756
$189$	12.3386	−	6.06284i	0.897504	−	0.441007i
$190$	−8.62291			−0.625572
$191$	−4.22356	+	11.6041i	−0.305606	+	0.839646i	0.687893	+	0.725812i	$0.258536\pi$
$191$	−4.22356	+	11.6041i	−0.305606	+	0.839646i	−0.993500	+	0.113835i	$0.963687\pi$
$192$	−13.2368	+	7.86964i	−0.955281	+	0.567942i
$193$	−2.51840	−	2.11318i	−0.181278	−	0.152110i	0.547633	−	0.836718i	$-0.315529\pi$
$193$	−2.51840	−	2.11318i	−0.181278	−	0.152110i	−0.728911	+	0.684608i	$0.759973\pi$
$194$	0.799076	−	4.53179i	0.0573703	−	0.325363i
$195$	−12.0320	−	4.20582i	−0.861626	−	0.301185i
$196$	−3.28501	+	0.458171i	−0.234643	+	0.0327265i
$197$	9.63928	−	5.56524i	0.686770	−	0.396507i	−0.115631	−	0.993292i	$-0.536889\pi$
$197$	9.63928	−	5.56524i	0.686770	−	0.396507i	0.802401	+	0.596785i	$0.203556\pi$
$198$	−15.1438	+	5.95476i	−1.07623	+	0.423186i
$199$	8.51003	+	4.91327i	0.603260	+	0.348292i	0.770323	−	0.637654i	$-0.220095\pi$
$199$	8.51003	+	4.91327i	0.603260	+	0.348292i	−0.167063	+	0.985946i	$0.553428\pi$
$200$	−8.60948	+	1.51808i	−0.608782	+	0.107345i
$201$	7.67381	+	1.25214i	0.541269	+	0.0883190i
$202$	6.69488	+	18.3940i	0.471050	+	1.29420i
$203$	15.1726	−	1.05299i	1.06491	−	0.0739057i
$204$	−1.11992	−	0.182737i	−0.0784100	−	0.0127942i
$205$	−0.341284	−	1.93552i	−0.0238363	−	0.135182i
$206$	−3.42157	+	5.92634i	−0.238392	+	0.412908i
$207$	−17.6489	−	2.64853i	−1.22668	−	0.184086i
$208$	12.3209	−	7.11350i	0.854304	−	0.493233i
$209$	−16.0506	+	13.4680i	−1.11024	+	0.931602i
$210$	4.78466	−	6.75829i	0.330173	−	0.466367i
$211$	0.351313	−	1.99239i	0.0241854	−	0.137162i	−0.970324	−	0.241808i	$-0.922260\pi$
$211$	0.351313	−	1.99239i	0.0241854	−	0.137162i	0.994510	+	0.104646i	$0.0333708\pi$
$212$	−0.247055	+	0.294429i	−0.0169678	+	0.0202215i
$213$	11.9468	+	20.0946i	0.818581	+	1.37686i
$214$	3.32644	+	1.21073i	0.227391	+	0.0827636i
$215$	−5.16642			−0.352347
$216$	8.46169	+	13.4379i	0.575745	+	0.914334i
$217$	16.0674	+	4.61634i	1.09072	+	0.313378i
$218$	−5.72723	+	15.7354i	−0.387897	+	1.06574i
$219$	−12.4600	+	0.159349i	−0.841969	+	0.0107678i
$220$	1.95600	−	2.33107i	0.131873	−	0.157161i
$221$	6.85050	+	1.20793i	0.460814	+	0.0812540i
$222$	−3.83481	−	20.2319i	−0.257376	−	1.35787i
$223$	−14.1148	−	16.8214i	−0.945198	−	1.12644i	−0.991835	−	0.127531i	$-0.959295\pi$
$223$	−14.1148	−	16.8214i	−0.945198	−	1.12644i	0.0466367	−	0.998912i	$-0.485150\pi$
$224$	−1.67268	−	6.72376i	−0.111761	−	0.449250i
$225$	1.70585	+	8.41049i	0.113723	+	0.560700i
$226$	6.31473	−	10.9374i	0.420050	−	0.727548i
$227$	−1.17595	−	6.66915i	−0.0780506	−	0.442647i	−0.998641	−	0.0521174i	$-0.983403\pi$
$227$	−1.17595	−	6.66915i	−0.0780506	−	0.442647i	0.920590	−	0.390530i	$-0.127708\pi$
$228$	3.03208	+	2.47884i	0.200804	+	0.164165i
$229$	2.81930	+	7.74596i	0.186304	+	0.511867i	0.997320	−	0.0731567i	$-0.0233073\pi$
$229$	2.81930	+	7.74596i	0.186304	+	0.511867i	−0.811016	+	0.585024i	$0.801085\pi$
$230$	−10.1011	+	3.67648i	−0.666044	+	0.242420i
$231$	−1.64961	−	20.0529i	−0.108536	−	1.31938i
$232$	3.05068	+	17.3013i	0.200287	+	1.13588i
$233$	7.87577	+	4.54708i	0.515959	+	0.297889i	0.735280	−	0.677764i	$-0.237051\pi$
$233$	7.87577	+	4.54708i	0.515959	+	0.297889i	−0.219321	+	0.975653i	$0.570384\pi$
$234$	−9.73285	−	15.9041i	−0.636257	−	1.03968i
$235$	5.30672	+	9.19150i	0.346172	+	0.599587i
$236$	−1.95069	+	1.63682i	−0.126979	+	0.106548i
$237$	9.71487	+	11.2815i	0.631049	+	0.732815i
$238$	−1.98321	+	4.06079i	−0.128552	+	0.263222i
$239$	2.30552	−	2.74761i	0.149132	−	0.177728i	−0.686307	−	0.727312i	$-0.740769\pi$
$239$	2.30552	−	2.74761i	0.149132	−	0.177728i	0.835439	+	0.549584i	$0.185214\pi$
$240$	6.24959	+	3.50242i	0.403409	+	0.226080i
$241$	−4.59174	+	12.6157i	−0.295780	+	0.812649i	0.699413	+	0.714718i	$0.253445\pi$
$241$	−4.59174	+	12.6157i	−0.295780	+	0.812649i	−0.995193	+	0.0979312i	$0.968777\pi$
$242$			10.2266i			0.657391i
$243$	12.9744	−	8.64091i	0.832307	−	0.554315i
$244$		−	3.78218i		−	0.242129i
$245$	6.29514	+	8.07482i	0.402182	+	0.515881i
$246$	1.40561	−	2.50813i	0.0896187	−	0.159912i
$247$	−18.3916	−	15.4324i	−1.17023	−	0.981937i
$248$	−3.35321	+	19.0170i	−0.212929	+	1.20758i
$249$	−5.50403	−	6.39164i	−0.348804	−	0.405054i
$250$	9.13002	+	10.8807i	0.577433	+	0.688158i
$251$	6.38510	+	11.0593i	0.403024	+	0.698057i	0.994089	−	0.108566i	$-0.0346259\pi$
$251$	6.38510	+	11.0593i	0.403024	+	0.698057i	−0.591066	+	0.806624i	$0.701293\pi$
$252$	−3.62525	+	1.00097i	−0.228369	+	0.0630553i
$253$	−13.0597	+	22.6201i	−0.821057	+	1.42211i
$254$	−8.70226	+	1.53444i	−0.546028	+	0.0962795i
$255$	1.24003	+	3.27599i	0.0776538	+	0.205151i
$256$	10.0389	−	3.65387i	0.627433	−	0.228367i
$257$	−8.05762	+	2.93273i	−0.502620	+	0.182939i	−0.580872	−	0.813995i	$-0.697288\pi$
$257$	−8.05762	+	2.93273i	−0.502620	+	0.182939i	0.0782518	+	0.996934i	$0.475066\pi$
$258$	−5.85137	−	4.78372i	−0.364291	−	0.297821i
$259$	25.3208	+	2.67472i	1.57336	+	0.166199i
$260$	3.01968	+	1.74341i	0.187272	+	0.108122i
$261$	16.9014	−	3.42800i	1.04617	−	0.212188i
$262$	−16.5314	+	9.54441i	−1.02131	+	0.589656i
$263$	2.26452	+	2.69875i	0.139636	+	0.166412i	0.831330	−	0.555779i	$-0.187580\pi$
$263$	2.26452	+	2.69875i	0.139636	+	0.166412i	−0.691694	+	0.722191i	$0.743135\pi$
$264$	22.8349	−	4.32820i	1.40539	−	0.266382i
$265$	1.16844	+	0.206027i	0.0717764	+	0.0126561i
$266$	12.9355	−	8.71524i	0.793125	−	0.534366i
$267$	−0.00972590	−	0.760501i	−0.000595216	−	0.0465419i
$268$	−1.99877	−	0.727494i	−0.122095	−	0.0444388i
$269$	−32.0022			−1.95121			−0.975604	−	0.219536i	$-0.929546\pi$
$269$	−32.0022			−1.95121			−0.975604	+	0.219536i	$0.929546\pi$
$270$	4.37930	−	8.30542i	0.266516	−	0.505452i
$271$		−	12.5643i		−	0.763225i	−0.924322	−	0.381612i	$-0.875369\pi$
$271$		−	12.5643i		−	0.763225i	0.924322	−	0.381612i	$-0.124631\pi$
$272$	−3.67408	−	1.33726i	−0.222774	−	0.0810831i
$273$	22.3003	−	5.85151i	1.34968	−	0.354150i
$274$	7.24588	+	6.08001i	0.437739	+	0.367307i
$275$	12.3691	+	2.18100i	0.745884	+	0.131519i
$276$	4.60873	+	1.61100i	0.277413	+	0.0969708i
$277$	11.1823	−	9.38308i	0.671880	−	0.563774i	−0.241741	−	0.970341i	$-0.577718\pi$
$277$	11.1823	−	9.38308i	0.671880	−	0.563774i	0.913621	+	0.406566i	$0.133274\pi$
$278$	5.84457	+	10.1231i	0.350534	+	0.607143i
$279$	18.7458	+	2.81315i	1.12228	+	0.168419i
$280$	−8.51181	+	8.21115i	−0.508678	+	0.490710i
$281$	−3.55531	+	0.626897i	−0.212092	+	0.0373975i	−0.278684	−	0.960383i	$-0.589898\pi$
$281$	−3.55531	+	0.626897i	−0.212092	+	0.0373975i	0.0665925	+	0.997780i	$0.478787\pi$
$282$	−2.50038	+	15.3237i	−0.148895	+	0.912514i
$283$	−7.18235	−	19.7333i	−0.426946	−	1.17303i	−0.947656	−	0.319292i	$-0.896555\pi$
$283$	−7.18235	−	19.7333i	−0.426946	−	1.17303i	0.520710	−	0.853733i	$-0.325667\pi$
$284$	−2.18733	−	6.00964i	−0.129794	−	0.356607i
$285$	1.94692	−	11.9318i	0.115326	−	0.706781i
$286$	−26.8748	+	4.73875i	−1.58914	+	0.280208i
$287$	2.46821	+	2.55859i	0.145694	+	0.151029i
$288$	−2.87497	−	7.31147i	−0.169409	−	0.430833i
$289$	7.54415	+	13.0668i	0.443773	+	0.768638i
$290$	7.95717	−	6.67686i	0.467261	−	0.392079i
$291$	6.09038	+	2.12892i	0.357024	+	0.124799i
$292$	3.35711	+	0.591950i	0.196460	+	0.0346412i
$293$	−4.25738	−	3.57236i	−0.248719	−	0.208700i	0.509902	−	0.860233i	$-0.329682\pi$
$293$	−4.25738	−	3.57236i	−0.248719	−	0.208700i	−0.758620	+	0.651533i	$0.774126\pi$
$294$	−0.346943	+	14.9742i	−0.0202342	+	0.873313i
$295$	7.38664	+	2.68852i	0.430067	+	0.156532i
$296$			29.4110i			1.70948i
$297$	−4.82057	−	22.2996i	−0.279718	−	1.29395i
$298$	−22.2976			−1.29167
$299$	−28.1240	−	10.2363i	−1.62646	−	0.591981i
$300$	−0.0300214	−	2.34747i	−0.00173329	−	0.135532i
$301$	7.75029	−	5.22174i	0.446719	−	0.300976i
$302$	12.3041	+	2.16955i	0.708024	+	0.124844i
$303$	−26.9641	+	5.11086i	−1.54905	+	0.293611i
$304$	8.67411	+	10.3374i	0.497494	+	0.592891i
$305$	−10.1111	+	5.83765i	−0.578960	+	0.334263i
$306$	−1.62889	+	4.85850i	−0.0931176	+	0.277742i
$307$	26.1410	+	15.0925i	1.49195	+	0.861375i	0.999957	−	0.00922626i	$-0.00293685\pi$
$307$	26.1410	+	15.0925i	1.49195	+	0.861375i	0.491989	+	0.870602i	$0.336270\pi$
$308$	−0.578222	+	5.47385i	−0.0329472	+	0.311902i
$309$	−7.42795	−	6.07263i	−0.422561	−	0.345460i
$310$	10.7289	−	3.90499i	0.609359	−	0.221789i
$311$	−24.1028	+	8.77272i	−1.36675	+	0.497455i	−0.918134	−	0.396271i	$-0.870304\pi$
$311$	−24.1028	+	8.77272i	−1.36675	+	0.497455i	−0.448613	+	0.893726i	$0.648082\pi$
$312$	9.42771	+	24.9067i	0.533739	+	1.41006i
$313$	−1.77245	+	0.312531i	−0.100185	+	0.0176653i	−0.223516	−	0.974700i	$-0.571753\pi$
$313$	−1.77245	+	0.312531i	−0.100185	+	0.0176653i	0.123331	+	0.992366i	$0.460642\pi$
$314$	13.2244	−	22.9054i	0.746299	−	1.29263i
$315$	8.27139	+	8.14662i	0.466040	+	0.459010i
$316$	−2.03642	−	3.52718i	−0.114557	−	0.198419i
$317$	−3.17281	−	3.78121i	−0.178203	−	0.212374i	0.669548	−	0.742769i	$-0.266488\pi$
$317$	−3.17281	−	3.78121i	−0.178203	−	0.212374i	−0.847751	+	0.530395i	$0.822044\pi$
$318$	1.13258	+	1.31523i	0.0635119	+	0.0737542i
$319$	4.38286	−	24.8564i	0.245393	−	1.39169i
$320$	−9.96200	−	8.35911i	−0.556893	−	0.467289i
$321$	−2.42639	+	4.32956i	−0.135428	+	0.241652i
$322$	11.4370	−	15.7244i	0.637361	−	0.876287i
$323$			6.59804i			0.367124i
$324$	−3.92747	+	1.66152i	−0.218193	+	0.0923065i
$325$			14.3918i			0.798313i
$326$	2.49269	−	6.84861i	0.138057	−	0.379310i
$327$	−20.4806	−	11.4778i	−1.13258	−	0.634723i
$328$	−2.63959	+	3.14574i	−0.145747	+	0.173694i
$329$	−17.2507	−	8.42490i	−0.951061	−	0.464480i
$330$	−8.96692	−	10.4130i	−0.493613	−	0.573215i
$331$	10.3974	−	8.72442i	0.571491	−	0.479538i	−0.310650	−	0.950525i	$-0.600547\pi$
$331$	10.3974	−	8.72442i	0.571491	−	0.479538i	0.882140	+	0.470987i	$0.156102\pi$
$332$	1.15375	+	1.99835i	0.0633201	+	0.109674i
$333$	28.8614	−	0.738327i	1.58159	−	0.0404601i
$334$	10.9522	+	6.32326i	0.599278	+	0.345994i
$335$	1.14018	+	6.46630i	0.0622949	+	0.353292i
$336$	−12.9151	+	1.06243i	−0.704577	+	0.0579604i
$337$	−21.7478	+	7.91556i	−1.18468	+	0.431188i	−0.857853	−	0.513896i	$-0.828202\pi$
$337$	−21.7478	+	7.91556i	−1.18468	+	0.431188i	−0.326827	+	0.945084i	$0.605980\pi$
$338$	−5.20200	−	14.2924i	−0.282951	−	0.777403i
$339$	13.7088	+	11.2074i	0.744558	+	0.608704i
$340$	−0.166399	−	0.943694i	−0.00902424	−	0.0511790i
$341$	13.8714	−	24.0260i	0.751179	−	1.30108i
$342$	13.2530	−	11.7110i	0.716642	−	0.633260i
$343$	−17.6048	−	5.75073i	−0.950570	−	0.310510i
$344$	6.93873	+	8.26926i	0.374111	+	0.445849i
$345$	−2.80662	−	14.8073i	−0.151103	−	0.797198i
$346$	2.83074	+	0.499136i	0.152182	+	0.0268337i
$347$	−14.4789	+	17.2552i	−0.777266	+	0.926310i	−0.998807	−	0.0488415i	$-0.984447\pi$
$347$	−14.4789	+	17.2552i	−0.777266	+	0.926310i	0.221540	+	0.975151i	$0.428892\pi$
$348$	−4.71739	+	0.0603299i	−0.252879	+	0.00323402i
$349$	−10.9711	+	30.1428i	−0.587269	+	1.61351i	0.188206	+	0.982130i	$0.439733\pi$
$349$	−10.9711	+	30.1428i	−0.587269	+	1.61351i	−0.775475	+	0.631378i	$0.782489\pi$
$350$	−8.98631	−	2.58187i	−0.480338	−	0.138007i
$351$	24.2046	−	9.87680i	1.29195	−	0.527184i
$352$	−11.4983			−0.612863
$353$	−1.94119	−	0.706536i	−0.103319	−	0.0376051i	0.289843	−	0.957074i	$-0.406397\pi$
$353$	−1.94119	−	0.706536i	−0.103319	−	0.0376051i	−0.393163	+	0.919469i	$0.628619\pi$
$354$	5.87658	+	9.88444i	0.312337	+	0.525352i
$355$	−12.6899	+	15.1232i	−0.673508	+	0.802655i
$356$	−0.0361299	+	0.204903i	−0.00191488	+	0.0108598i
$357$	−5.17128	−	3.66110i	−0.273693	−	0.193766i
$358$	6.68316	−	5.60784i	0.353216	−	0.296384i
$359$	5.58124	−	3.22233i	0.294567	−	0.170068i	−0.345433	−	0.938443i	$-0.612268\pi$
$359$	5.58124	−	3.22233i	0.294567	−	0.170068i	0.639999	+	0.768375i	$0.278935\pi$
$360$	−8.35448	+	10.4900i	−0.440320	+	0.552872i
$361$	1.88620	−	3.26699i	0.0992736	−	0.171947i
$362$	3.38923	+	19.2213i	0.178134	+	1.01025i
$363$	−14.1509	−	2.30901i	−0.742730	−	0.121191i
$364$	−6.29198	+	0.436669i	−0.329790	+	0.0228877i
$365$	−3.59909	−	9.88842i	−0.188385	−	0.517584i
$366$	−16.8569	−	2.75054i	−0.881122	−	0.143773i
$367$	13.8164	−	2.43620i	0.721208	−	0.127168i	0.199016	−	0.979996i	$-0.436225\pi$
$367$	13.8164	−	2.43620i	0.721208	−	0.127168i	0.522192	+	0.852828i	$0.325114\pi$
$368$	14.5685	+	8.41113i	0.759436	+	0.438461i
$369$	3.15322	+	2.51129i	0.164150	+	0.130733i
$370$	15.0598	−	8.69476i	0.782920	−	0.452019i
$371$	−1.96104	+	0.871880i	−0.101812	+	0.0452657i
$372$	−4.89517	−	1.71113i	−0.253803	−	0.0887179i
$373$	−3.27412	+	18.5684i	−0.169527	+	0.961437i	0.774745	+	0.632273i	$0.217878\pi$
$373$	−3.27412	+	18.5684i	−0.169527	+	0.961437i	−0.944273	+	0.329164i	$0.893233\pi$
$374$	5.74510	+	4.82071i	0.297072	+	0.249273i
$375$	−17.1175	+	10.1768i	−0.883943	+	0.525529i
$376$	7.58457	−	20.8384i	0.391144	−	1.07466i
$377$	28.9212			1.48952
$378$	1.82484	+	16.8854i	0.0938595	+	0.868491i
$379$	1.19709			0.0614903			0.0307452	−	0.999527i	$-0.490212\pi$
$379$	1.19709			0.0614903			0.0307452	+	0.999527i	$0.490212\pi$
$380$	−1.13116	+	3.10785i	−0.0580275	+	0.159429i
$381$	−0.158429	−	12.3881i	−0.00811656	−	0.634661i
$382$	−11.6865	−	9.80610i	−0.597931	−	0.501724i
$383$	−0.200482	+	1.13699i	−0.0102442	+	0.0580975i	−0.989501	−	0.144524i	$-0.953835\pi$
$383$	−0.200482	+	1.13699i	−0.0102442	+	0.0580975i	0.979257	+	0.202621i	$0.0649461\pi$
$384$	−1.85342	−	9.77833i	−0.0945817	−	0.498998i
$385$	15.5260	−	6.90289i	0.791279	−	0.351804i
$386$	3.51724	−	2.03068i	0.179023	−	0.103359i
$387$	7.94055	−	7.01666i	0.403641	−	0.356677i
$388$	−1.52851	−	0.882486i	−0.0775984	−	0.0448014i
$389$	−33.3699	+	5.88401i	−1.69192	+	0.298331i	−0.934860	−	0.355016i	$-0.884475\pi$
$389$	−33.3699	+	5.88401i	−1.69192	+	0.298331i	−0.757059	+	0.653347i	$0.773364\pi$
$390$	9.96627	−	12.1906i	0.504661	−	0.617294i
$391$	2.81315	+	7.72908i	0.142267	+	0.390876i
$392$	4.46973	−	20.9207i	0.225756	−	1.05666i
$393$	−9.47441	−	25.0301i	−0.477921	−	1.26260i
$394$	2.38773	+	13.5415i	0.120292	+	0.682211i
$395$	−6.28627	+	10.8881i	−0.316297	+	0.547842i
$396$	0.159611	+	6.23925i	0.00802078	+	0.313534i
$397$	−20.5615	+	11.8712i	−1.03195	+	0.595798i	−0.917543	−	0.397636i	$-0.869831\pi$
$397$	−20.5615	+	11.8712i	−1.03195	+	0.595798i	−0.114409	+	0.993434i	$0.536497\pi$
$398$	−9.29942	+	7.80314i	−0.466138	+	0.391136i
$399$	9.13896	+	19.8671i	0.457520	+	0.994597i
$400$	1.40468	−	7.96634i	0.0702340	−	0.398317i
$401$	14.6379	−	17.4448i	0.730984	−	0.871152i	−0.264665	−	0.964340i	$-0.585261\pi$
$401$	14.6379	−	17.4448i	0.730984	−	0.871152i	0.995649	+	0.0931880i	$0.0297058\pi$
$402$	−4.69597	+	8.37932i	−0.234214	+	0.417922i
$403$	29.8721	+	10.8725i	1.48803	+	0.541600i
$404$	7.50778			0.373526
$405$	10.5037	+	7.93503i	0.521934	+	0.394295i
$406$	−5.18843	+	18.0585i	−0.257497	+	0.896230i
$407$	14.4518	−	39.7060i	0.716349	−	1.96815i
$408$	3.57807	−	6.38458i	0.177141	−	0.316084i
$409$	−15.1400	+	18.0432i	−0.748625	+	0.892177i	−0.997072	−	0.0764689i	$-0.975635\pi$
$409$	−15.1400	+	18.0432i	−0.748625	+	0.892177i	0.248447	+	0.968646i	$0.420080\pi$
$410$	2.39110	+	0.421616i	0.118088	+	0.0208221i
$411$	−10.0491	+	8.65361i	−0.495687	+	0.426851i
$412$	1.68711	+	2.01062i	0.0831179	+	0.0990561i
$413$	−13.7982	+	3.43261i	−0.678966	+	0.168908i
$414$	10.5317	−	19.3691i	0.517606	−	0.951942i
$415$	3.56153	−	6.16875i	0.174829	−	0.302812i
$416$	−2.28788	−	12.9752i	−0.112173	−	0.636162i
$417$	−15.3273	+	5.80171i	−0.750581	+	0.284111i
$418$	−8.85298	−	24.3234i	−0.433013	−	1.18969i
$419$	−24.7436	+	9.00593i	−1.20880	+	0.439968i	−0.866289	−	0.499544i	$-0.833501\pi$
$419$	−24.7436	+	9.00593i	−1.20880	+	0.439968i	−0.342515	+	0.939512i	$0.611279\pi$
$420$	−1.80815	−	2.61104i	−0.0882287	−	0.127405i
$421$	−1.75667	−	9.96255i	−0.0856147	−	0.485545i	−0.997222	−	0.0744834i	$-0.976269\pi$
$421$	−1.75667	−	9.96255i	−0.0856147	−	0.485545i	0.911608	−	0.411062i	$-0.134842\pi$
$422$	2.16449	+	1.24967i	0.105366	+	0.0608330i
$423$	−20.6394	−	6.91972i	−1.00352	−	0.336448i
$424$	−1.23950	−	2.14688i	−0.0601954	−	0.104262i
$425$	3.02983	−	2.54233i	0.146968	−	0.123321i
$426$	−28.3752	+	5.37833i	−1.37478	+	0.260581i
$427$	9.26780	−	18.9766i	0.448500	−	0.918342i
$428$	0.872734	−	1.04008i	0.0421852	−	0.0502744i
$429$	−0.489269	−	38.2576i	−0.0236221	−	1.84709i
$430$	2.18294	−	5.99759i	0.105271	−	0.289229i
$431$		−	3.21277i		−	0.154754i	−0.997002	−	0.0773769i	$-0.975346\pi$
$431$		−	3.21277i		−	0.154754i	0.997002	−	0.0773769i	$-0.0246545\pi$
$432$	−14.3621	+	3.10470i	−0.690996	+	0.149375i
$433$		−	15.4984i		−	0.744805i	−0.928071	−	0.372403i	$-0.878534\pi$
$433$		−	15.4984i		−	0.744805i	0.928071	−	0.372403i	$-0.121466\pi$
$434$	−12.1479	+	16.7017i	−0.583117	+	0.801709i
$435$	7.44241	+	12.5182i	0.356836	+	0.600200i
$436$	4.92002	+	4.12839i	0.235626	+	0.197714i
$437$	4.92954	−	27.9568i	0.235812	−	1.33735i
$438$	5.07969	−	14.5319i	0.242717	−	0.694361i
$439$	−15.7258	−	18.7413i	−0.750551	−	0.894472i	0.246660	−	0.969102i	$-0.420667\pi$
$439$	−15.7258	−	18.7413i	−0.750551	−	0.894472i	−0.997211	+	0.0746301i	$0.976222\pi$
$440$	9.81344	+	16.9974i	0.467837	+	0.810318i
$441$	−20.6420	−	3.86102i	−0.982953	−	0.183858i
$442$	−4.29677	+	7.44223i	−0.204377	+	0.353991i
$443$	33.6606	−	5.93527i	1.59926	−	0.281993i	0.698272	−	0.715832i	$-0.253952\pi$
$443$	33.6606	−	5.93527i	1.59926	−	0.281993i	0.900990	+	0.433839i	$0.142841\pi$
$444$	−7.79497	−	1.27191i	−0.369933	−	0.0603620i
$445$	0.603543	−	0.219672i	0.0286107	−	0.0104134i
$446$	25.4915	−	9.27814i	1.20706	−	0.439333i
$447$	5.03446	−	30.8540i	0.238122	−	1.45935i
$448$	23.3929	+	2.47107i	1.10521	+	0.116747i
$449$	9.72152	+	5.61272i	0.458787	+	0.264881i	0.711534	−	0.702652i	$-0.248001\pi$
$449$	9.72152	+	5.61272i	0.458787	+	0.264881i	−0.252747	+	0.967532i	$0.581334\pi$
$450$	−10.4843	−	1.57337i	−0.494237	−	0.0741692i
$451$	5.10928	−	2.94985i	0.240587	−	0.138903i
$452$	−3.11367	−	3.71073i	−0.146455	−	0.174538i
$453$	−5.78017	+	16.5358i	−0.271576	+	0.776921i
$454$	8.23896	+	1.45275i	0.386673	+	0.0681809i
$455$	10.8788	+	16.1467i	0.510007	+	0.756971i
$456$	−21.7127	+	12.9088i	−1.01679	+	0.604510i
$457$	24.0852	+	8.76630i	1.12666	+	0.410070i	0.837078	−	0.547083i	$-0.184262\pi$
$457$	24.0852	+	8.76630i	1.12666	+	0.410070i	0.289581	+	0.957154i	$0.406484\pi$
$458$	−10.1834			−0.475837
$459$	−6.35510	−	3.35093i	−0.296631	−	0.156408i
$460$			4.12288i			0.192230i
$461$	18.4071	+	6.69964i	0.857305	+	0.312033i	0.733015	−	0.680213i	$-0.238113\pi$
$461$	18.4071	+	6.69964i	0.857305	+	0.312033i	0.124290	+	0.992246i	$0.460335\pi$
$462$	23.9760	+	6.55787i	1.11546	+	0.305100i
$463$	−5.40665	−	4.53671i	−0.251268	−	0.210839i	0.508450	−	0.861092i	$-0.330219\pi$
$463$	−5.40665	−	4.53671i	−0.251268	−	0.210839i	−0.759718	+	0.650252i	$0.774663\pi$
$464$	−16.0088	−	2.82279i	−0.743192	−	0.131045i
$465$	2.98106	+	15.7276i	0.138243	+	0.729351i
$466$	−8.60633	+	7.22156i	−0.398680	+	0.334533i
$467$	−6.73186	−	11.6599i	−0.311513	−	0.539557i	0.667177	−	0.744899i	$-0.267502\pi$
$467$	−6.73186	−	11.6599i	−0.311513	−	0.539557i	−0.978690	+	0.205343i	$0.934169\pi$
$468$	−7.00889	+	1.42157i	−0.323986	+	0.0657120i
$469$	−8.24596	−	8.54789i	−0.380763	−	0.394705i
$470$	−12.9125	+	2.27681i	−0.595607	+	0.105022i
$471$	28.7092	+	23.4708i	1.32285	+	1.08148i
$472$	−5.61741	−	15.4337i	−0.258562	−	0.710394i
$473$	−5.30426	−	14.5733i	−0.243890	−	0.670083i
$474$	−17.2013	+	6.51106i	−0.790082	+	0.299063i
$475$	−13.4434	+	2.37044i	−0.616827	+	0.108763i
$476$	1.20342	+	1.24748i	0.0551586	+	0.0571782i
$477$	−2.07564	+	1.27023i	−0.0950372	+	0.0581600i
$478$	2.21551	+	3.83737i	0.101335	+	0.175517i
$479$	19.6234	−	16.4660i	0.896614	−	0.752349i	−0.0729114	−	0.997338i	$-0.523229\pi$
$479$	19.6234	−	16.4660i	0.896614	−	0.752349i	0.969526	+	0.244990i	$0.0787846\pi$
$480$	5.02741	−	4.32925i	0.229469	−	0.197602i
$481$	47.6815	+	8.40753i	2.17409	+	0.383351i
$482$	−12.7052	−	10.6609i	−0.578706	−	0.485592i
$483$	19.1761	+	19.3762i	0.872544	+	0.881646i
$484$	3.68584	+	1.34154i	0.167538	+	0.0609790i
$485$			5.44834i			0.247396i
$486$	4.54905	+	18.7127i	0.206349	+	0.848826i
$487$	−7.30424			−0.330987			−0.165493	−	0.986211i	$-0.552922\pi$
$487$	−7.30424			−0.330987			−0.165493	+	0.986211i	$0.552922\pi$
$488$	22.9233	+	8.34340i	1.03769	+	0.377688i
$489$	8.91386	+	4.99554i	0.403099	+	0.225906i
$490$	−12.0338	+	3.89608i	−0.543630	+	0.176007i
$491$	21.2089	+	3.73971i	0.957146	+	0.168771i	0.630339	−	0.776320i	$-0.282916\pi$
$491$	21.2089	+	3.73971i	0.957146	+	0.168771i	0.326807	+	0.945091i	$0.394027\pi$
$492$	−0.719583	−	0.835627i	−0.0324413	−	0.0376730i
$493$	−5.10897	−	6.08863i	−0.230096	−	0.274218i
$494$	25.6860	−	14.8298i	1.15567	−	0.667226i
$495$	16.4334	−	10.0568i	0.738626	−	0.452018i
$496$	−15.4740	−	8.93392i	−0.694803	−	0.401145i
$497$	3.75130	−	35.5125i	0.168269	−	1.59295i
$498$	9.74552	−	3.68888i	0.436707	−	0.165303i
$499$	−26.2483	+	9.55359i	−1.17503	+	0.427678i	−0.854446	−	0.519541i	$-0.826103\pi$
$499$	−26.2483	+	9.55359i	−1.17503	+	0.427678i	−0.320589	+	0.947218i	$0.603881\pi$
$500$	5.11929	−	1.86327i	0.228942	−	0.0833280i
$501$	−11.2226	+	13.7273i	−0.501387	+	0.613289i
$502$	−15.5364	+	2.73949i	−0.693424	+	0.122269i
$503$	6.80712	−	11.7903i	0.303514	−	0.525702i	−0.673415	−	0.739265i	$-0.735173\pi$
$503$	6.80712	−	11.7903i	0.303514	−	0.525702i	0.976929	+	0.213562i	$0.0685066\pi$
$504$	1.93046	−	24.1803i	0.0859894	−	1.07708i
$505$	−11.5880	−	20.0710i	−0.515658	−	0.893146i
$506$	−20.7411	−	24.7183i	−0.922056	−	1.09886i
$507$	20.9514	−	3.97120i	0.930484	−	0.176367i
$508$	−0.588533	+	3.33774i	−0.0261119	+	0.148088i
$509$	−1.52700	−	1.28130i	−0.0676830	−	0.0567928i	0.608319	−	0.793693i	$-0.291844\pi$
$509$	−1.52700	−	1.28130i	−0.0676830	−	0.0567928i	−0.676002	+	0.736900i	$0.736289\pi$
$510$	−4.32698	+	0.0553370i	−0.191602	+	0.00245036i
$511$	15.3934	+	11.1963i	0.680964	+	0.495294i
$512$			24.6899i			1.09115i
$513$	13.2127	+	20.9829i	0.583353	+	0.926416i
$514$		−	10.5931i		−	0.467241i
$515$	2.77111	−	7.61356i	0.122110	−	0.335494i
$516$	−2.49173	+	1.48140i	−0.109692	+	0.0652151i
$517$	−20.4789	+	24.4058i	−0.900662	+	1.07337i
$518$	−13.8037	+	28.2643i	−0.606501	+	1.24186i
$519$	−1.32981	+	3.80430i	−0.0583722	+	0.166990i
$520$	−17.2279	+	14.4560i	−0.755495	+	0.633936i
$521$	3.88589	+	6.73055i	0.170244	+	0.294871i	0.938505	−	0.345266i	$-0.112211\pi$
$521$	3.88589	+	6.73055i	0.170244	+	0.294871i	−0.768261	+	0.640136i	$0.778878\pi$
$522$	−3.16178	+	21.0689i	−0.138387	+	0.922161i
$523$	−17.4428	−	10.0706i	−0.762720	−	0.440356i	0.0675518	−	0.997716i	$-0.478481\pi$
$523$	−17.4428	−	10.0706i	−0.762720	−	0.440356i	−0.830271	+	0.557359i	$0.811815\pi$
$524$	1.27136	+	7.21025i	0.0555397	+	0.314981i
$525$	5.60160	−	11.8517i	0.244474	−	0.517252i
$526$	−4.08975	+	1.48855i	−0.178321	+	0.0649037i
$527$	−2.98800	−	8.20947i	−0.130159	−	0.357610i
$528$	−3.46322	+	21.2246i	−0.150717	+	0.923683i
$529$	−2.15125	−	12.2004i	−0.0935327	−	0.530451i
$530$	−0.732866	+	1.26936i	−0.0318337	+	0.0551375i
$531$	−15.0043	+	5.89989i	−0.651131	+	0.256033i
$532$	−1.44423	−	5.80545i	−0.0626155	−	0.251698i
$533$	4.34536	+	5.17859i	0.188218	+	0.224310i
$534$	0.886960	+	0.310041i	0.0383825	+	0.0134168i
$535$	−4.12755	−	0.727798i	−0.178450	−	0.0314655i
$536$	8.81851	−	10.5095i	0.380902	−	0.453941i
$537$	6.25081	+	10.5139i	0.269743	+	0.453708i
$538$	13.5218	−	37.1507i	0.582964	−	1.60168i
$539$	−16.3142	+	26.0475i	−0.702703	+	1.12195i
$540$	−2.41894	−	2.66789i	−0.104094	−	0.114808i
$541$	−33.5967			−1.44444			−0.722219	−	0.691665i	$-0.756877\pi$
$541$	−33.5967			−1.44444			−0.722219	+	0.691665i	$0.756877\pi$
$542$	14.5856	+	5.30873i	0.626506	+	0.228029i
$543$	−27.3624	+	0.349933i	−1.17423	+	0.0150171i
$544$	−2.32745	+	2.77375i	−0.0997886	+	0.118923i
$545$	3.44278	−	19.5250i	0.147473	−	0.836358i
$546$	−2.62956	+	28.3604i	−0.112535	+	1.21371i
$547$	−8.29582	+	6.96102i	−0.354704	+	0.297632i	−0.802675	−	0.596416i	$-0.796591\pi$
$547$	−8.29582	+	6.96102i	−0.354704	+	0.297632i	0.447972	+	0.894048i	$0.352146\pi$
$548$	3.14187	−	1.81396i	0.134214	−	0.0774884i
$549$	7.61203	−	22.7044i	0.324874	−	0.969000i
$550$	−7.75814	+	13.4375i	−0.330808	+	0.572977i
$551$	4.76354	+	27.0154i	0.202934	+	1.15089i
$552$	−19.9308	+	24.3791i	−0.848312	+	1.03764i
$553$	−1.57451	−	22.6872i	−0.0669550	−	0.964758i
$554$	6.16781	+	16.9459i	0.262045	+	0.719963i
$555$	8.63099	+	22.8019i	0.366365	+	0.967886i
$556$	4.41524	−	0.778525i	0.187248	−	0.0330168i
$557$	−2.65395	−	1.53226i	−0.112451	−	0.0649239i	0.442719	−	0.896660i	$-0.354014\pi$
$557$	−2.65395	−	1.53226i	−0.112451	−	0.0649239i	−0.555171	+	0.831736i	$0.687347\pi$
$558$	−11.1863	+	20.5730i	−0.473555	+	0.870925i
$559$	15.3898	−	8.88529i	0.650918	−	0.375808i
$560$	−4.44583	−	9.99957i	−0.187870	−	0.422559i
$561$	−7.96775	+	6.86126i	−0.336399	+	0.289683i
$562$	0.774458	−	4.39217i	0.0326685	−	0.185272i
$563$	35.1445	+	29.4898i	1.48117	+	1.24285i	0.904929	+	0.425563i	$0.139924\pi$
$563$	35.1445	+	29.4898i	1.48117	+	1.24285i	0.576237	+	0.817283i	$0.304521\pi$
$564$	5.19493	+	2.91136i	0.218746	+	0.122591i
$565$	−5.11426	+	14.0513i	−0.215159	+	0.591144i
$566$	25.9428			1.09046
$567$	−23.7769	−	1.28737i	−0.998537	−	0.0540643i
$568$	41.2489			1.73077
$569$	−9.66650	+	26.5585i	−0.405241	+	1.11339i	0.554422	+	0.832236i	$0.312939\pi$
$569$	−9.66650	+	26.5585i	−0.405241	+	1.11339i	−0.959663	+	0.281154i	$0.909283\pi$
$570$	13.0288	+	7.30165i	0.545717	+	0.305832i
$571$	31.2950	+	26.2596i	1.30966	+	1.09893i	0.988389	+	0.151943i	$0.0485529\pi$
$571$	31.2950	+	26.2596i	1.30966	+	1.09893i	0.321266	+	0.946989i	$0.395892\pi$
$572$	−1.81754	+	10.3078i	−0.0759952	+	0.430990i
$573$	16.2077	−	13.9569i	0.677085	−	0.583058i
$574$	−4.01309	+	1.78423i	−0.167503	+	0.0744723i
$575$	−14.7372	+	8.50855i	−0.614586	+	0.354831i
$576$	26.6639	−	0.682112i	1.11100	−	0.0284213i
$577$	0.564874	+	0.326130i	0.0235160	+	0.0135770i	0.511712	−	0.859157i	$-0.329012\pi$
$577$	0.564874	+	0.326130i	0.0235160	+	0.0135770i	−0.488196	+	0.872734i	$0.662345\pi$
$578$	−18.3566	+	3.23677i	−0.763536	+	0.134632i
$579$	2.01579	+	5.32543i	0.0837732	+	0.221317i
$580$	−1.36263	−	3.74378i	−0.0565799	−	0.155452i
$581$	0.892050	+	12.8536i	0.0370085	+	0.533257i
$582$	−5.04476	+	6.17067i	−0.209112	+	0.255783i
$583$	0.618454	+	3.50743i	0.0256137	+	0.145263i
$584$	−10.9935	+	19.0412i	−0.454913	+	0.787932i
$585$	14.6183	+	16.5431i	0.604393	+	0.683974i
$586$	5.94594	−	3.43289i	0.245624	−	0.141811i
$587$	−3.87979	+	3.25553i	−0.160136	+	0.134370i	−0.719335	−	0.694664i	$-0.755553\pi$
$587$	−3.87979	+	3.25553i	−0.160136	+	0.134370i	0.559199	+	0.829034i	$0.311109\pi$
$588$	5.35145	+	2.08938i	0.220690	+	0.0861645i
$589$	−5.23593	+	29.6944i	−0.215743	+	1.22354i
$590$	−6.24209	+	7.43904i	−0.256983	+	0.306260i
$591$	−19.2770	+	0.246530i	−0.792949	+	0.0101409i
$592$	−25.5727	−	9.30771i	−1.05103	−	0.382544i
$593$	1.95836			0.0804204			0.0402102	−	0.999191i	$-0.487197\pi$
$593$	1.95836			0.0804204			0.0402102	+	0.999191i	$0.487197\pi$
$594$	27.9239	+	3.82604i	1.14573	+	0.156984i
$595$	1.47753	−	5.14261i	0.0605729	−	0.210826i
$596$	−2.92503	+	8.03645i	−0.119814	+	0.329186i
$597$	−8.69782	−	14.6298i	−0.355978	−	0.598757i
$598$	23.7663	−	28.3235i	0.971875	−	1.15824i
$599$	−28.4407	−	5.01487i	−1.16206	−	0.204902i	−0.440823	−	0.897594i	$-0.645313\pi$
$599$	−28.4407	−	5.01487i	−1.16206	−	0.204902i	−0.721234	+	0.692692i	$0.756425\pi$
$600$	14.2940	+	4.99652i	0.583549	+	0.203982i
$601$	−5.22977	−	6.23259i	−0.213327	−	0.254233i	0.648761	−	0.760992i	$-0.275288\pi$
$601$	−5.22977	−	6.23259i	−0.213327	−	0.254233i	−0.862087	+	0.506760i	$0.830843\pi$
$602$	2.78711	+	11.2035i	0.113594	+	0.456620i
$603$	−10.5345	−	8.38990i	−0.428997	−	0.341663i
$604$	2.39602	−	4.15002i	0.0974925	−	0.168862i
$605$	−2.10256	−	11.9242i	−0.0854811	−	0.484787i
$606$	5.45993	−	33.4616i	0.221794	−	1.35928i
$607$	6.22814	+	17.1117i	0.252792	+	0.694542i	0.999566	+	0.0294631i	$0.00937975\pi$
$607$	6.22814	+	17.1117i	0.252792	+	0.694542i	−0.746773	+	0.665079i	$0.768398\pi$
$608$	11.7434	−	4.27424i	0.476257	−	0.173343i
$609$	−23.8168	−	11.2568i	−0.965104	−	0.456147i
$610$	−2.50461	−	14.2043i	−0.101409	−	0.575117i
$611$	−31.6154	−	18.2532i	−1.27902	−	0.738444i
$612$	1.53741	+	1.22442i	0.0621460	+	0.0494944i
$613$	4.24675	+	7.35559i	0.171525	+	0.297089i	0.938953	−	0.344045i	$-0.111797\pi$
$613$	4.24675	+	7.35559i	0.171525	+	0.297089i	−0.767428	+	0.641135i	$0.778464\pi$
$614$	−28.5659	+	23.9696i	−1.15282	+	0.967334i
$615$	−1.12328	+	3.21346i	−0.0452950	+	0.129579i
$616$	−31.9008	−	15.5797i	−1.28532	−	0.627725i
$617$	4.56438	−	5.43962i	0.183755	−	0.218991i	−0.666301	−	0.745683i	$-0.732123\pi$
$617$	4.56438	−	5.43962i	0.183755	−	0.218991i	0.850056	+	0.526692i	$0.176568\pi$
$618$	10.1881	−	6.05712i	0.409825	−	0.243653i
$619$	7.83037	−	21.5138i	0.314729	−	0.864711i	−0.676956	−	0.736023i	$-0.736701\pi$
$619$	7.83037	−	21.5138i	0.314729	−	0.864711i	0.991685	−	0.128688i	$-0.0410764\pi$
$620$		−	4.37914i		−	0.175870i
$621$	24.4239	+	18.9464i	0.980096	+	0.760292i
$622$		−	31.6872i		−	1.27054i
$623$	−0.683368	+	0.939541i	−0.0273786	+	0.0376419i
$624$	−24.6399	+	0.315115i	−0.986385	+	0.0126147i
$625$	−1.92597	−	1.61608i	−0.0770387	−	0.0646431i
$626$	0.386095	−	2.18966i	0.0154315	−	0.0875163i
$627$	35.6560	−	6.75835i	1.42396	−	0.269902i
$628$	−6.52071	−	7.77108i	−0.260205	−	0.310100i
$629$	−6.65301	−	11.5234i	−0.265273	−	0.459466i
$630$	−12.9521	+	6.15994i	−0.516025	+	0.245418i
$631$	−21.5784	+	37.3748i	−0.859021	+	1.48787i	0.0138420	+	0.999904i	$0.495594\pi$
$631$	−21.5784	+	37.3748i	−0.859021	+	1.48787i	−0.872863	+	0.487965i	$0.837740\pi$
$632$	25.8701	−	4.56160i	1.02906	−	0.181451i
$633$	−2.21792	+	2.71293i	−0.0881545	+	0.107829i
$634$	5.73013	−	2.08560i	0.227572	−	0.0828296i
$635$	9.83134	−	3.57832i	0.390145	−	0.142001i
$636$	0.622603	−	0.235668i	0.0246878	−	0.00934486i
$637$	−32.6393	−	13.2269i	−1.29321	−	0.524068i
$638$	27.0035	+	15.5905i	1.06908	+	0.617232i
$639$	−1.03550	−	40.4781i	−0.0409639	−	1.60129i
$640$	7.27859	−	4.20229i	0.287711	−	0.166110i
$641$	27.2005	+	32.4163i	1.07436	+	1.28037i	0.957878	+	0.287175i	$0.0927161\pi$
$641$	27.2005	+	32.4163i	1.07436	+	1.28037i	0.116478	+	0.993193i	$0.462839\pi$
$642$	−4.00089	−	4.64609i	−0.157902	−	0.183367i
$643$	7.14787	+	1.26036i	0.281884	+	0.0497038i	0.312803	−	0.949818i	$-0.398732\pi$
$643$	7.14787	+	1.26036i	0.281884	+	0.0497038i	−0.0309184	+	0.999522i	$0.509843\pi$
$644$	−4.16703	−	6.18486i	−0.164204	−	0.243717i
$645$	7.80620	+	4.37478i	0.307369	+	0.172257i
$646$	−7.65953	−	2.78784i	−0.301360	−	0.109686i
$647$	30.4657			1.19773			0.598865	−	0.800850i	$-0.295619\pi$
$647$	30.4657			1.19773			0.598865	+	0.800850i	$0.295619\pi$
$648$	−1.40634	−	27.4692i	−0.0552464	−	1.07909i
$649$			23.5964i			0.926238i
$650$	−16.7071	−	6.08090i	−0.655308	−	0.238513i
$651$	−20.3680	−	20.5805i	−0.798285	−	0.806612i
$652$	−2.14136	−	1.79682i	−0.0838623	−	0.0703688i
$653$	−14.6823	−	2.58888i	−0.574561	−	0.101311i	−0.121185	−	0.992630i	$-0.538669\pi$
$653$	−14.6823	−	2.58888i	−0.574561	−	0.101311i	−0.453376	+	0.891319i	$0.649781\pi$
$654$	21.9779	−	18.9258i	0.859404	−	0.740058i
$655$	17.3133	−	14.5276i	0.676486	−	0.567639i
$656$	−1.89986	−	3.29065i	−0.0741769	−	0.128478i
$657$	18.9614	+	10.3100i	0.739755	+	0.402232i
$658$	17.0692	−	16.4662i	0.665425	−	0.641921i
$659$	15.1310	−	2.66800i	0.589420	−	0.103931i	0.129019	−	0.991642i	$-0.458817\pi$
$659$	15.1310	−	2.66800i	0.589420	−	0.103931i	0.460400	+	0.887711i	$0.347706\pi$
$660$	−4.92931	+	1.86585i	−0.191873	+	0.0726280i
$661$	−13.5122	−	37.1245i	−0.525564	−	1.44398i	−0.864244	−	0.503074i	$-0.832202\pi$
$661$	−13.5122	−	37.1245i	−0.525564	−	1.44398i	0.338679	−	0.940902i	$-0.390020\pi$
$662$	5.73485	+	15.7564i	0.222891	+	0.612389i
$663$	−9.32793	−	7.62594i	−0.362267	−	0.296167i
$664$	−14.6569	+	2.58440i	−0.568797	+	0.100294i
$665$	−13.2909	+	12.8214i	−0.515399	+	0.497194i
$666$	−11.3376	+	33.8166i	−0.439322	+	1.31037i
$667$	17.0985	+	29.6154i	0.662055	+	1.14671i
$668$	3.71574	−	3.11788i	0.143766	−	0.120634i
$669$	7.08292	+	37.3683i	0.273841	+	1.44474i
$670$	−7.98836	−	1.40856i	−0.308617	−	0.0544175i
$671$	−26.8476	−	22.5278i	−1.03644	−	0.869677i
$672$	−3.16615	+	11.5757i	−0.122137	+	0.446541i
$673$	−17.0901	−	6.22029i	−0.658776	−	0.239775i	−0.00906796	−	0.999959i	$-0.502886\pi$
$673$	−17.0901	−	6.22029i	−0.658776	−	0.239775i	−0.649708	+	0.760184i	$0.725109\pi$
$674$		−	28.5912i		−	1.10129i
$675$	4.54432	−	14.1523i	0.174911	−	0.544723i
$676$	−5.83362			−0.224370
$677$	−12.6704	−	4.61166i	−0.486965	−	0.177241i	0.0868572	−	0.996221i	$-0.472318\pi$
$677$	−12.6704	−	4.61166i	−0.486965	−	0.177241i	−0.573822	+	0.818980i	$0.694540\pi$
$678$	−18.8028	+	11.1788i	−0.722117	+	0.429319i
$679$	−5.50668	−	8.17321i	−0.211327	−	0.313659i
$680$	6.08669	+	1.07325i	0.233414	+	0.0411571i
$681$	−3.87045	+	11.0725i	−0.148316	+	0.424300i
$682$	22.0303	+	26.2547i	0.843583	+	1.00534i
$683$	1.56791	−	0.905232i	0.0599943	−	0.0346377i	−0.469703	−	0.882825i	$-0.655639\pi$
$683$	1.56791	−	0.905232i	0.0599943	−	0.0346377i	0.529697	+	0.848187i	$0.322306\pi$
$684$	−2.48231	−	6.31289i	−0.0949136	−	0.241379i
$685$	−9.69871	−	5.59955i	−0.370569	−	0.213948i
$686$	14.1144	−	18.0072i	0.538890	−	0.687520i
$687$	2.29924	−	14.0911i	0.0877216	−	0.537608i
$688$	−9.38599	+	3.41622i	−0.357838	+	0.130242i
$689$	−3.83488	+	1.39578i	−0.146097	+	0.0531750i
$690$	18.3754	+	2.99831i	0.699538	+	0.114144i
$691$	17.8283	−	3.14362i	0.678222	−	0.119589i	0.176083	−	0.984375i	$-0.443657\pi$
$691$	17.8283	−	3.14362i	0.678222	−	0.119589i	0.502140	+	0.864787i	$0.332546\pi$
$692$	0.551237	−	0.954771i	0.0209549	−	0.0362949i
$693$	−14.4878	+	31.6958i	−0.550345	+	1.20402i
$694$	−13.9136	−	24.0990i	−0.528152	−	0.914786i
$695$	−8.89603	−	10.6019i	−0.337446	−	0.402152i
$696$	10.0408	−	28.7246i	0.380596	−	1.08880i
$697$	0.322610	−	1.82961i	0.0122197	−	0.0693015i
$698$	−30.3566	−	25.4722i	−1.14902	−	0.964139i
$699$	−8.04956	−	13.5394i	−0.304462	−	0.512107i
$700$	−2.10939	+	2.90013i	−0.0797273	+	0.109615i
$701$		−	44.5178i		−	1.68141i	−0.541490	−	0.840707i	$-0.682140\pi$
$701$		−	44.5178i		−	1.68141i	0.541490	−	0.840707i	$-0.317860\pi$
$702$	1.23870	+	32.2719i	0.0467516	+	1.21802i
$703$			45.9243i			1.73207i
$704$	13.3514	−	36.6828i	0.503201	−	1.38253i
$705$	−0.235078	−	18.3815i	−0.00885354	−	0.692287i
$706$	1.64041	−	1.95496i	0.0617375	−	0.0735759i
$707$	37.6693	+	18.3970i	1.41670	+	0.691889i
$708$	4.33342	−	0.821371i	0.162860	−	0.0308690i
$709$	−28.5175	+	23.9291i	−1.07100	+	0.898675i	−0.995143	−	0.0984439i	$-0.968614\pi$
$709$	−28.5175	+	23.9291i	−1.07100	+	0.898675i	−0.0758564	+	0.997119i	$0.524169\pi$
$710$	−12.1944	−	21.1213i	−0.457648	−	0.792670i
$711$	−5.12579	−	25.2722i	−0.192232	−	0.947780i
$712$	−1.16219	−	0.670989i	−0.0435548	−	0.0251464i
$713$	6.52711	+	37.0171i	0.244442	+	1.38630i
$714$	6.43510	−	4.45632i	0.240827	−	0.166774i
$715$	30.3617	−	11.0508i	1.13546	−	0.413275i
$716$	−1.14446	−	3.14437i	−0.0427704	−	0.117511i
$717$	−5.81014	+	2.19926i	−0.216984	+	0.0821328i
$718$	1.38252	+	7.84067i	0.0515952	+	0.292611i
$719$	−22.9381	+	39.7300i	−0.855447	+	1.48168i	0.0207825	+	0.999784i	$0.493384\pi$
$719$	−22.9381	+	39.7300i	−0.855447	+	1.48168i	−0.876230	+	0.481894i	$0.839949\pi$
$720$	−6.47708	−	10.5840i	−0.241386	−	0.394441i
$721$	3.53806	+	14.2221i	0.131764	+	0.529659i
$722$	2.99562	+	3.57004i	0.111485	+	0.132863i
$723$	17.6205	−	15.1736i	0.655315	−	0.564311i
$724$	7.37229	+	1.29993i	0.273989	+	0.0483117i
$725$	10.5701	−	12.5969i	0.392562	−	0.467837i
$726$	8.65960	−	15.4519i	0.321388	−	0.573474i
$727$	−3.02410	+	8.30865i	−0.112158	+	0.308151i	−0.983054	−	0.183316i	$-0.941317\pi$
$727$	−3.02410	+	8.30865i	−0.112158	+	0.308151i	0.870896	+	0.491467i	$0.163539\pi$
$728$	11.2334	−	39.0982i	0.416337	−	1.44908i
$729$	−26.9206	+	2.06964i	−0.997058	+	0.0766535i
$730$	13.0000			0.481151
$731$	−4.58920	−	1.67033i	−0.169738	−	0.0617795i
$732$	−3.20264	+	5.71468i	−0.118373	+	0.211221i
$733$	2.71245	−	3.23257i	0.100187	−	0.119398i	−0.713621	−	0.700532i	$-0.752946\pi$
$733$	2.71245	−	3.23257i	0.100187	−	0.119398i	0.813808	+	0.581134i	$0.197391\pi$
$734$	−3.00964	+	17.0685i	−0.111088	+	0.630009i
$735$	−2.67411	−	17.5312i	−0.0986362	−	0.646649i
$736$	11.9341	−	10.0139i	0.439895	−	0.369116i
$737$	−17.0694	+	9.85504i	−0.628760	+	0.363015i
$738$	−4.24763	+	2.59943i	−0.156357	+	0.0956862i
$739$	23.4859	−	40.6787i	0.863941	−	1.49639i	−0.00415394	−	0.999991i	$-0.501322\pi$
$739$	23.4859	−	40.6787i	0.863941	−	1.49639i	0.868095	−	0.496398i	$-0.165344\pi$
$740$	−1.15818	−	6.56839i	−0.0425757	−	0.241459i
$741$	14.7211	+	38.8910i	0.540792	+	1.42870i
$742$	−0.183560	−	2.64492i	−0.00673869	−	0.0970981i
$743$	7.59281	+	20.8611i	0.278553	+	0.765319i	0.997527	+	0.0702816i	$0.0223898\pi$
$743$	7.59281	+	20.8611i	0.278553	+	0.765319i	−0.718974	+	0.695037i	$0.755388\pi$
$744$	21.1696	−	25.8943i	0.776115	−	0.949333i
$745$	25.9990	−	4.58432i	0.952529	−	0.167957i
$746$	−20.1723	−	11.6465i	−0.738562	−	0.426409i
$747$	2.90405	+	14.3181i	0.106254	+	0.523873i
$748$	2.49112	−	1.43825i	0.0910843	−	0.0525875i
$749$	6.92745	−	3.07995i	0.253123	−	0.112539i
$750$	−4.58151	−	24.1713i	−0.167293	−	0.882612i
$751$	−1.64819	+	9.34735i	−0.0601433	+	0.341090i	−1.00000		0.000479731i	$-0.999847\pi$
$751$	−1.64819	+	9.34735i	−0.0601433	+	0.341090i	0.939857	+	0.341569i	$0.110958\pi$
$752$	15.7186	+	13.1895i	0.573200	+	0.480972i
$753$	−0.282848	−	22.1168i	−0.0103076	−	0.805981i
$754$	−12.2199	+	33.5740i	−0.445024	+	1.22269i
$755$	−14.7927			−0.538360
$756$	6.32517	+	1.55734i	0.230044	+	0.0566400i
$757$	39.9101			1.45056			0.725279	−	0.688456i	$-0.241711\pi$
$757$	39.9101			1.45056			0.725279	+	0.688456i	$0.241711\pi$
$758$	−0.505801	+	1.38968i	−0.0183715	+	0.0504753i
$759$	38.8867	−	23.1192i	1.41150	−	0.839175i
$760$	−16.3410	−	13.7117i	−0.592749	−	0.497375i
$761$	−0.165785	+	0.940211i	−0.00600969	+	0.0340826i	−0.987665	−	0.156581i	$-0.949953\pi$
$761$	−0.165785	+	0.940211i	−0.00600969	+	0.0340826i	0.981655	+	0.190663i	$0.0610639\pi$
$762$	14.4480	+	5.05037i	0.523397	+	0.182956i
$763$	14.5694	+	32.7696i	0.527449	+	1.18634i
$764$	−5.06733	+	2.92563i	−0.183330	+	0.105845i
$765$	0.900393	−	5.99989i	0.0325538	−	0.216927i
$766$	−1.23520	−	0.713143i	−0.0446296	−	0.0257669i
$767$	−26.6272	+	4.69509i	−0.961451	+	0.169530i
$768$	−18.2623	−	2.97987i	−0.658985	−	0.107527i
$769$	15.5790	+	42.8029i	0.561792	+	1.54351i	0.817008	+	0.576627i	$0.195631\pi$
$769$	15.5790	+	42.8029i	0.561792	+	1.54351i	−0.255216	+	0.966884i	$0.582146\pi$
$770$	1.45329	+	20.9405i	0.0523729	+	0.754643i
$771$	14.6580	+	2.39175i	0.527896	+	0.0861369i
$772$	−0.270497	−	1.53406i	−0.00973538	−	0.0552121i
$773$	24.2021	−	41.9192i	0.870488	−	1.50773i	0.00899604	−	0.999960i	$-0.497136\pi$
$773$	24.2021	−	41.9192i	0.870488	−	1.50773i	0.861492	−	0.507771i	$-0.169530\pi$
$774$	4.79042	+	12.1828i	0.172188	+	0.437900i
$775$	15.6532	−	9.03739i	0.562280	−	0.324633i
$776$	8.72050	−	7.31737i	0.313048	−	0.262678i
$777$	−35.9936	−	25.4823i	−1.29126	−	0.914174i
$778$	7.26900	−	41.2245i	0.260606	−	1.47797i
$779$	−4.12163	+	4.91197i	−0.147673	+	0.175990i
$780$	−3.08631	−	5.19119i	−0.110508	−	0.185874i
$781$	−55.6877	−	20.2686i	−1.99266	−	0.725269i
$782$	−10.1612			−0.363362
$783$	−28.4399	−	9.13210i	−1.01636	−	0.326354i
$784$	16.7760	+	10.5072i	0.599141	+	0.375258i
$785$	−10.7104	+	29.4266i	−0.382270	+	1.05028i
$786$	33.0601	−	0.422800i	1.17921	−	0.0150808i
$787$	1.37685	−	1.64087i	0.0490795	−	0.0584906i	−0.740946	−	0.671564i	$-0.765623\pi$
$787$	1.37685	−	1.64087i	0.0490795	−	0.0584906i	0.790026	+	0.613074i	$0.210067\pi$
$788$	5.19382	+	0.915811i	0.185022	+	0.0326244i
$789$	−1.13635	−	5.99522i	−0.0404552	−	0.213435i
$790$	−9.98372	−	11.8981i	−0.355205	−	0.423317i
$791$	−6.52973	−	26.2478i	−0.232170	−	0.933265i
$792$	−38.1675	−	12.7963i	−1.35622	−	0.454696i
$793$	20.0794	−	34.7785i	0.713040	−	1.23502i
$794$	−5.09326	−	28.8853i	−0.180753	−	1.02510i
$795$	−1.59099	−	1.30070i	−0.0564267	−	0.0461309i
$796$	1.59248	+	4.37530i	0.0564439	+	0.155078i
$797$	0.360086	−	0.131061i	0.0127549	−	0.00464241i	−0.335635	−	0.941992i	$-0.608951\pi$
$797$	0.360086	−	0.131061i	0.0127549	−	0.00464241i	0.348390	+	0.937350i	$0.386729\pi$
$798$	−26.9247	+	2.21490i	−0.953125	+	0.0784066i
$799$	1.74216	+	9.88029i	0.0616332	+	0.349539i
$800$	−6.48765	−	3.74565i	−0.229373	−	0.132429i
$801$	−0.629276	+	1.15732i	−0.0222344	+	0.0408917i
$802$	14.0664	+	24.3638i	0.496703	+	0.860315i
$803$	24.1980	−	20.3045i	0.853928	−	0.716531i
$804$	2.40403	+	2.79172i	0.0847836	+	0.0984563i
$805$	−10.1027	+	20.6861i	−0.356072	+	0.729088i
$806$	−25.2434	+	30.0839i	−0.889162	+	1.05966i
$807$	48.3538	+	27.0986i	1.70213	+	0.953916i
$808$	−16.5620	+	45.5037i	−0.582649	+	1.60081i
$809$		−	9.37609i		−	0.329646i	−0.986323	−	0.164823i	$-0.947295\pi$
$809$		−	9.37609i		−	0.329646i	0.986323	−	0.164823i	$-0.0527052\pi$
$810$	−13.6497	+	8.84081i	−0.479602	+	0.310635i
$811$		−	10.9268i		−	0.383692i	−0.981425	−	0.191846i	$-0.938553\pi$
$811$		−	10.9268i		−	0.383692i	0.981425	−	0.191846i	$-0.0614474\pi$
$812$	5.82798	+	4.23894i	0.204522	+	0.148758i
$813$	−10.6391	+	18.9840i	−0.373129	+	0.665798i
$814$	39.9876	+	33.5536i	1.40157	+	1.17605i
$815$	−1.49842	+	8.49796i	−0.0524873	+	0.297670i
$816$	4.41901	+	5.13165i	0.154696	+	0.179644i
$817$	10.8346	+	12.9122i	0.379055	+	0.451740i
$818$	−14.5489	−	25.1994i	−0.508690	−	0.881077i
$819$	−38.6496	−	10.0420i	−1.35053	−	0.350895i
$820$	0.465626	−	0.806487i	0.0162604	−	0.0281638i
$821$	−38.4318	+	6.77656i	−1.34128	+	0.236504i	−0.797801	−	0.602920i	$-0.794004\pi$
$821$	−38.4318	+	6.77656i	−1.34128	+	0.236504i	−0.543477	+	0.839424i	$0.682893\pi$
$822$	−5.79978	−	15.3222i	−0.202291	−	0.534424i
$823$	−14.4443	+	5.25731i	−0.503498	+	0.183258i	−0.581267	−	0.813713i	$-0.697443\pi$
$823$	−14.4443	+	5.25731i	−0.503498	+	0.183258i	0.0777686	+	0.996971i	$0.475220\pi$
$824$	−15.9078	+	5.78998i	−0.554176	+	0.201704i
$825$	−16.8423	−	13.7692i	−0.586373	−	0.479382i
$826$	1.84525	−	17.4684i	0.0642045	−	0.607805i
$827$	−21.5267	−	12.4285i	−0.748558	−	0.432180i	0.0766147	−	0.997061i	$-0.475589\pi$
$827$	−21.5267	−	12.4285i	−0.748558	−	0.432180i	−0.825173	+	0.564881i	$0.808922\pi$
$828$	−5.59941	−	6.33669i	−0.194593	−	0.220215i
$829$	−40.8365	+	23.5770i	−1.41831	+	0.818862i	−0.996150	−	0.0876596i	$-0.972061\pi$
$829$	−40.8365	+	23.5770i	−1.41831	+	0.818862i	−0.422160	+	0.906521i	$0.638728\pi$
$830$	5.65634	+	6.74097i	0.196335	+	0.233982i
$831$	−24.8413	+	4.70849i	−0.861734	+	0.163336i
$832$	44.0511	+	7.76739i	1.52720	+	0.269286i
$833$	2.98119	+	9.20793i	0.103292	+	0.319036i
$834$	−0.258904	−	20.2445i	−0.00896510	−	0.701011i
$835$	−14.0703	−	5.12117i	−0.486923	−	0.177225i
$836$	−9.92791			−0.343364
$837$	−25.9419	−	20.1240i	−0.896684	−	0.695586i
$838$		−	32.5296i		−	1.12372i
$839$	−6.72893	−	2.44913i	−0.232309	−	0.0845534i	0.223243	−	0.974763i	$-0.428336\pi$
$839$	−6.72893	−	2.44913i	−0.232309	−	0.0845534i	−0.455551	+	0.890209i	$0.650558\pi$
$840$	19.8139	−	5.19909i	0.683645	−	0.179385i
$841$	−3.09894	−	2.60032i	−0.106860	−	0.0896661i
$842$	12.3076	+	2.17016i	0.424147	+	0.0747885i
$843$	5.90274	+	2.06333i	0.203301	+	0.0710648i
$844$	0.734343	−	0.616187i	0.0252771	−	0.0212100i
$845$	9.00399	+	15.5954i	0.309747	+	0.536497i
$846$	16.7537	−	21.0362i	0.576003	−	0.723238i
$847$	15.2060	+	15.7628i	0.522484	+	0.541615i
$848$	2.25897	−	0.398317i	0.0775732	−	0.0136783i
$849$	−5.85747	+	35.8979i	−0.201028	+	1.23201i
$850$	1.67116	+	4.59147i	0.0573203	+	0.157486i
$851$	19.5804	+	53.7967i	0.671207	+	1.84413i
$852$	−1.78385	+	10.9325i	−0.0611137	+	0.374540i
$853$	5.45780	−	0.962357i	0.186871	−	0.0329505i	−0.0794291	−	0.996841i	$-0.525310\pi$
$853$	5.45780	−	0.962357i	0.186871	−	0.0329505i	0.266301	+	0.963890i	$0.414199\pi$
$854$	18.1137	+	18.7769i	0.619837	+	0.642533i
$855$	−13.0453	+	16.3798i	−0.446138	+	0.560178i
$856$	4.37859	+	7.58394i	0.149657	+	0.259214i
$857$	−38.9684	+	32.6983i	−1.33113	+	1.11695i	−0.347322	+	0.937746i	$0.612909\pi$
$857$	−38.9684	+	32.6983i	−1.33113	+	1.11695i	−0.983811	+	0.179208i	$0.942647\pi$
$858$	44.6192	+	15.5968i	1.52327	+	0.532467i
$859$	−9.91290	−	1.74791i	−0.338224	−	0.0596380i	0.00195691	−	0.999998i	$-0.499377\pi$
$859$	−9.91290	−	1.74791i	−0.338224	−	0.0596380i	−0.340181	+	0.940360i	$0.610488\pi$
$860$	−1.87527	−	1.57354i	−0.0639463	−	0.0536573i
$861$	−1.56281	−	5.95591i	−0.0532603	−	0.202977i
$862$	3.72964	+	1.35748i	0.127032	+	0.0462359i
$863$		−	51.7414i		−	1.76130i	−0.473768	−	0.880649i	$-0.657107\pi$
$863$		−	51.7414i		−	1.76130i	0.473768	−	0.880649i	$-0.342893\pi$
$864$	−1.84722	+	13.4817i	−0.0628437	+	0.458658i
$865$	−3.40326			−0.115714
$866$	17.9918	+	6.54847i	0.611386	+	0.222526i
$867$	−0.334192	−	26.1316i	−0.0113497	−	0.887474i
$868$	4.42603	+	6.56927i	0.150229	+	0.222975i
$869$	−37.1671	−	6.55356i	−1.26081	−	0.222314i
$870$	−17.6767	+	3.35050i	−0.599296	+	0.113592i
$871$	−14.5172	−	17.3010i	−0.491898	−	0.586221i
$872$	−35.8751	+	20.7125i	−1.21488	+	0.701414i
$873$	−7.39955	−	8.37386i	−0.250437	−	0.283412i
$874$	30.3716	+	17.5351i	1.02734	+	0.593133i
$875$	30.2512	+	3.19553i	1.02268	+	0.108029i
$876$	−4.57119	−	3.73712i	−0.154446	−	0.126266i
$877$	−5.63056	+	2.04936i	−0.190131	+	0.0692019i	−0.435331	−	0.900271i	$-0.643369\pi$
$877$	−5.63056	+	2.04936i	−0.190131	+	0.0692019i	0.245200	+	0.969472i	$0.421146\pi$
$878$	28.4009	−	10.3371i	0.958485	−	0.348860i
$879$	3.40771	+	9.00270i	0.114939	+	0.303654i
$880$	−17.8848	+	3.15357i	−0.602897	+	0.106307i
$881$	−28.7112	+	49.7293i	−0.967306	+	1.67542i	−0.264017	+	0.964518i	$0.585048\pi$
$881$	−28.7112	+	49.7293i	−0.967306	+	1.67542i	−0.703288	+	0.710905i	$0.748286\pi$
$882$	13.2040	−	22.3315i	0.444601	−	0.751941i
$883$	−26.5130	−	45.9219i	−0.892235	−	1.54540i	−0.837190	−	0.546912i	$-0.815803\pi$
$883$	−26.5130	−	45.9219i	−0.892235	−	1.54540i	−0.0550448	−	0.998484i	$-0.517530\pi$
$884$	2.11865	+	2.52491i	0.0712580	+	0.0849220i
$885$	−8.88429	−	10.3170i	−0.298642	−	0.346803i
$886$	−7.33233	+	41.5837i	−0.246334	+	1.39703i
$887$	10.9003	+	9.14647i	0.365997	+	0.307108i	0.807176	−	0.590311i	$-0.200995\pi$
$887$	10.9003	+	9.14647i	0.365997	+	0.307108i	−0.441178	+	0.897419i	$0.645439\pi$
$888$	24.9044	−	44.4386i	0.835737	−	1.49126i
$889$	−11.1316	+	15.3045i	−0.373343	+	0.513298i
$890$			0.793458i			0.0265968i
$891$	−11.5990	+	37.7755i	−0.388582	+	1.26553i
$892$		−	10.4047i		−	0.348375i
$893$	11.8431	−	32.5385i	0.396313	−	1.08886i
$894$	33.6906	+	18.8810i	1.12678	+	0.631476i
$895$	−6.63960	+	7.91277i	−0.221937	+	0.264495i
$896$	−6.67153	+	13.6605i	−0.222880	+	0.456365i
$897$	33.8262	+	39.2813i	1.12943	+	1.31156i
$898$	−10.6233	+	8.91400i	−0.354504	+	0.297464i
$899$	−18.1612	−	31.4561i	−0.605709	−	1.04912i
$900$	−1.94242	+	3.57234i	−0.0647472	+	0.119078i
$901$	0.971284	+	0.560771i	0.0323582	+	0.0186820i
$902$	1.26561	+	7.17765i	0.0421403	+	0.238990i
$903$	−16.1319	+	1.32706i	−0.536837	+	0.0441617i
$904$	29.3590	−	10.6858i	0.976464	−	0.355404i
$905$	−7.90368	−	21.7152i	−0.262727	−	0.721837i
$906$	−16.7538	−	13.6969i	−0.556609	−	0.455049i
$907$	7.77690	+	44.1050i	0.258228	+	1.46448i	0.787649	+	0.616124i	$0.211298\pi$
$907$	7.77690	+	44.1050i	0.258228	+	1.46448i	−0.529422	+	0.848359i	$0.677591\pi$
$908$	1.60439	−	2.77889i	0.0532436	−	0.0922207i
$909$	45.0692	+	15.1102i	1.49485	+	0.501174i
$910$	−23.3410	+	5.80659i	−0.773747	+	0.192487i
$911$	24.5858	+	29.3003i	0.814565	+	0.970761i	0.999929	−	0.0119092i	$-0.00379090\pi$
$911$	24.5858	+	29.3003i	0.814565	+	0.970761i	−0.185364	+	0.982670i	$0.559346\pi$
$912$	−4.35273	−	22.9643i	−0.144133	−	0.760425i
$913$	21.0573	+	3.71297i	0.696894	+	0.122881i
$914$	−20.3533	+	24.2561i	−0.673226	+	0.802319i
$915$	20.2206	−	0.258597i	0.668471	−	0.00854895i
$916$	−1.33586	+	3.67026i	−0.0441382	+	0.121269i
$917$	−11.2890	+	39.2919i	−0.372797	+	1.29753i
$918$	6.57522	−	5.96165i	0.217015	−	0.196764i
$919$	−39.5867			−1.30584			−0.652922	−	0.757425i	$-0.726457\pi$
$919$	−39.5867			−1.30584			−0.652922	+	0.757425i	$0.726457\pi$
$920$	−24.9883	−	9.09499i	−0.823840	−	0.299853i
$921$	−26.7179	−	44.9396i	−0.880384	−	1.48081i
$922$	−15.5550	+	18.5377i	−0.512275	+	0.610506i
$923$	11.7916	−	66.8734i	0.388124	−	2.20116i
$924$	5.50877	−	7.78110i	0.181225	−	0.255979i
$925$	21.0885	−	17.6954i	0.693387	−	0.581820i
$926$	7.55103	−	4.35959i	0.248142	−	0.143265i
$927$	6.08114	+	15.4652i	0.199731	+	0.507945i
$928$	−7.52710	+	13.0373i	−0.247089	+	0.427971i
$929$	−9.95917	−	56.4812i	−0.326750	−	1.85309i	−0.497083	−	0.867703i	$-0.665596\pi$
$929$	−9.95917	−	56.4812i	−0.326750	−	1.85309i	0.170333	−	0.985387i	$-0.445516\pi$
$930$	−19.5175	−	3.18467i	−0.640003	−	0.104429i
$931$	6.97935	−	32.6671i	0.228739	−	1.07062i
$932$	1.47379	+	4.04920i	0.0482756	+	0.132636i
$933$	43.8467	+	7.15448i	1.43548	+	0.234227i
$934$	16.3801	−	2.88826i	0.535975	−	0.0945068i
$935$	−7.68990	−	4.43977i	−0.251487	−	0.145196i
$936$	6.84551	−	45.6160i	0.223752	−	1.49100i
$937$	22.4359	−	12.9533i	0.732948	−	0.423167i	−0.0865519	−	0.996247i	$-0.527585\pi$
$937$	22.4359	−	12.9533i	0.732948	−	0.423167i	0.819500	+	0.573080i	$0.194252\pi$
$938$	13.4072	−	5.96087i	0.437761	−	0.194629i
$939$	2.94273	+	1.02864i	0.0960324	+	0.0335685i
$940$	−0.873268	+	4.95255i	−0.0284829	+	0.161534i
$941$	15.8590	+	13.3072i	0.516987	+	0.433804i	0.863580	−	0.504212i	$-0.168217\pi$
$941$	15.8590	+	13.3072i	0.516987	+	0.433804i	−0.346593	+	0.938016i	$0.612661\pi$
$942$	−39.3772	+	23.4109i	−1.28298	+	0.762767i
$943$	−2.73389	+	7.51129i	−0.0890276	+	0.244601i
$944$	15.1973			0.494630
$945$	−5.59934	−	19.3131i	−0.182147	−	0.628257i
$946$	19.1591			0.622916
$947$	8.96478	−	24.6305i	0.291316	−	0.800385i	−0.704558	−	0.709646i	$-0.748855\pi$
$947$	8.96478	−	24.6305i	0.291316	−	0.800385i	0.995875	−	0.0907390i	$-0.0289229\pi$
$948$	0.0902095	+	7.05378i	0.00292987	+	0.229096i
$949$	27.7273	+	23.2660i	0.900066	+	0.755245i
$950$	2.92840	−	16.6078i	0.0950099	−	0.538828i
$951$	1.59214	+	8.39988i	0.0516287	+	0.272385i
$952$	−10.2156	+	4.54185i	−0.331088	+	0.147202i
$953$	30.8895	−	17.8340i	1.00061	−	0.577701i	0.0921795	−	0.995742i	$-0.470617\pi$
$953$	30.8895	−	17.8340i	1.00061	−	0.577701i	0.908428	+	0.418041i	$0.137283\pi$
$954$	−0.597575	−	2.94628i	−0.0193472	−	0.0953893i
$955$	15.6425	+	9.03119i	0.506179	+	0.292243i
$956$	1.67369	−	0.295117i	0.0541310	−	0.00954475i
$957$	−27.6700	+	33.8456i	−0.894445	+	1.09407i
$958$	10.8236	+	29.7377i	0.349695	+	0.960780i
$959$	20.2088	−	1.40251i	0.652577	−	0.0452894i
$960$	7.97384	+	21.0658i	0.257354	+	0.679895i
$961$	−1.54969	−	8.78876i	−0.0499902	−	0.283508i
$962$	−29.9068	+	51.8001i	−0.964234	+	1.67010i
$963$	7.33230	−	4.48716i	0.236280	−	0.144597i
$964$	−5.50906	+	3.18066i	−0.177435	+	0.102442i
$965$	−3.68359	+	3.09090i	−0.118579	+	0.0994997i
$966$	−30.5958	+	14.0743i	−0.984404	+	0.452832i
$967$	3.02065	−	17.1310i	0.0971377	−	0.550895i	−0.896934	−	0.442165i	$-0.854210\pi$
$967$	3.02065	−	17.1310i	0.0971377	−	0.550895i	0.994071	−	0.108730i	$-0.0346784\pi$
$968$	−16.2618	+	19.3800i	−0.522674	+	0.622898i
$969$	5.58704	−	9.96931i	0.179482	−	0.320260i
$970$	−6.32487	−	2.30206i	−0.203079	−	0.0739148i
$971$	48.7070			1.56308			0.781540	−	0.623855i	$-0.214434\pi$
$971$	48.7070			1.56308			0.781540	+	0.623855i	$0.214434\pi$
$972$	7.34114	+	0.815200i	0.235467	+	0.0261475i
$973$	24.0606	+	6.91290i	0.771347	+	0.221617i
$974$	3.08623	−	8.47934i	0.0988891	−	0.271696i
$975$	12.1866	−	21.7453i	0.390283	−	0.696407i
$976$	−14.5091	+	17.2913i	−0.464425	+	0.553480i
$977$	18.0628	+	3.18497i	0.577881	+	0.101896i	0.454947	−	0.890519i	$-0.349658\pi$
$977$	18.0628	+	3.18497i	0.577881	+	0.101896i	0.122935	+	0.992415i	$0.460769\pi$
$978$	−9.56555	+	8.23718i	−0.305873	+	0.263396i
$979$	1.23929	+	1.47693i	0.0396080	+	0.0472029i
$980$	−0.174387	+	4.84827i	−0.00557058	+	0.154872i
$981$	21.2261	+	34.6848i	0.677696	+	1.10740i
$982$	−13.3027	+	23.0409i	−0.424505	+	0.735265i
$983$	1.43166	+	8.11934i	0.0456628	+	0.258967i	0.999090	−	0.0426573i	$-0.0135824\pi$
$983$	1.43166	+	8.11934i	0.0456628	+	0.258967i	−0.953427	+	0.301624i	$0.902471\pi$
$984$	6.65202	−	2.51793i	0.212059	−	0.0802686i
$985$	−5.56819	−	15.2985i	−0.177417	−	0.487450i
$986$	9.22684	−	3.35830i	0.293842	−	0.106950i
$987$	18.9310	+	27.3370i	0.602579	+	0.870147i
$988$	−1.97541	−	11.2031i	−0.0628461	−	0.356418i
$989$	18.1972	+	10.5061i	0.578636	+	0.334076i
$990$	4.73116	+	23.3264i	0.150366	+	0.741363i
$991$	8.03577	+	13.9184i	0.255265	+	0.442131i	0.964967	−	0.262370i	$-0.0845040\pi$
$991$	8.03577	+	13.9184i	0.255265	+	0.442131i	−0.709703	+	0.704501i	$0.751171\pi$
$992$	−12.6758	+	10.6363i	−0.402457	+	0.337702i
$993$	−23.0975	+	4.37798i	−0.732977	+	0.138931i
$994$	39.6407	+	19.3597i	1.25733	+	0.614054i
$995$	9.23880	−	11.0104i	0.292890	−	0.349052i
$996$	−0.0511088	−	3.99637i	−0.00161945	−	0.126630i
$997$	20.2279	−	55.5756i	0.640623	−	1.76010i	−0.00913679	−	0.999958i	$-0.502908\pi$
$997$	20.2279	−	55.5756i	0.640623	−	1.76010i	0.649760	−	0.760139i	$-0.274869\pi$
$998$		−	34.5078i		−	1.09232i
$999$	−44.2334	−	23.3235i	−1.39948	−	0.737922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.7	yes	132
3.2	odd	2		567.2.be.a.503.15		132
7.6	odd	2	inner	189.2.be.a.104.8	yes	132
21.20	even	2		567.2.be.a.503.16		132
27.7	even	9		567.2.be.a.62.16		132
27.20	odd	18	inner	189.2.be.a.20.8	yes	132
189.20	even	18	inner	189.2.be.a.20.7	✓	132
189.34	odd	18		567.2.be.a.62.15		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.7	✓	132	189.20	even	18	inner
189.2.be.a.20.8	yes	132	27.20	odd	18	inner
189.2.be.a.104.7	yes	132	1.1	even	1	trivial
189.2.be.a.104.8	yes	132	7.6	odd	2	inner
567.2.be.a.62.15		132	189.34	odd	18
567.2.be.a.62.16		132	27.7	even	9
567.2.be.a.503.15		132	3.2	odd	2
567.2.be.a.503.16		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+(-0.422526 + 1.16088i) q^{2} +(-1.51095 - 0.846773i) q^{3} +(0.362974 + 0.304571i) q^{4} +(0.253991 - 1.44045i) q^{5} +(1.62142 - 1.39625i) q^{6} +(1.07486 + 2.41758i) q^{7} +(-2.64668 + 1.52806i) q^{8} +(1.56595 + 2.55887i) q^{9} +(1.56488 + 0.903482i) q^{10} +(4.32398 - 0.762434i) q^{11} +(-0.290533 - 0.767549i) q^{12} +(1.72073 + 4.72766i) q^{13} +(-3.26067 + 0.226294i) q^{14} +(-1.60351 + 1.96138i) q^{15} +(-0.491047 - 2.78487i) q^{16} +(0.691322 - 1.19740i) q^{17} +(-3.63219 + 0.736695i) q^{18} +(-4.13271 + 2.38602i) q^{19} +(0.530913 - 0.445489i) q^{20} +(0.423079 - 4.56300i) q^{21} +(-0.941898 + 5.34177i) q^{22} +(-3.82383 + 4.55707i) q^{23} +(5.29293 - 0.0676904i) q^{24} +(2.68807 + 0.978376i) q^{25} -6.21530 q^{26} +(-0.199298 - 5.19233i) q^{27} +(-0.346179 + 1.20489i) q^{28} +(1.96611 - 5.40183i) q^{29} +(-1.59941 - 2.69021i) q^{30} +(4.06150 - 4.84031i) q^{31} +(-2.57902 - 0.454750i) q^{32} +(-7.17893 - 2.50943i) q^{33} +(1.09794 + 1.30848i) q^{34} +(3.75541 - 0.934242i) q^{35} +(-0.210958 + 1.40575i) q^{36} +(4.81181 - 8.33429i) q^{37} +(-1.02371 - 5.80574i) q^{38} +(1.40332 - 8.60033i) q^{39} +(1.52887 + 4.20054i) q^{40} +(1.26265 - 0.459567i) q^{41} +(5.11834 + 2.41913i) q^{42} +(-0.613355 - 3.47851i) q^{43} +(1.80171 + 1.04022i) q^{44} +(4.08367 - 1.60575i) q^{45} +(-3.67454 - 6.36449i) q^{46} +(-5.55855 + 4.66418i) q^{47} +(-1.61620 + 4.62361i) q^{48} +(-4.68936 + 5.19711i) q^{49} +(-2.27156 + 2.70713i) q^{50} +(-2.05848 + 1.22383i) q^{51} +(-0.815330 + 2.24010i) q^{52} +0.811158i q^{53} +(6.11188 + 1.96253i) q^{54} -6.42214i q^{55} +(-6.53902 - 4.75611i) q^{56} +(8.26475 - 0.105696i) q^{57} +(5.44015 + 4.56483i) q^{58} +(-0.933219 + 5.29255i) q^{59} +(-1.17941 + 0.223550i) q^{60} +(-5.13083 - 6.11468i) q^{61} +(3.90293 + 6.76007i) q^{62} +(-4.50308 + 6.53623i) q^{63} +(4.44544 - 7.69973i) q^{64} +(7.24703 - 1.27785i) q^{65} +(5.94643 - 7.27358i) q^{66} +(-4.21835 + 1.53535i) q^{67} +(0.615627 - 0.224070i) q^{68} +(9.63643 - 3.64759i) q^{69} +(-0.502216 + 4.75433i) q^{70} +(-11.6889 - 6.74856i) q^{71} +(-8.05469 - 4.37964i) q^{72} +(6.23051 - 3.59719i) q^{73} +(7.64200 + 9.10738i) q^{74} +(-3.23308 - 3.75446i) q^{75} +(-2.22678 - 0.392641i) q^{76} +(6.49091 + 9.63404i) q^{77} +(9.39102 + 5.26295i) q^{78} +(-8.07721 - 2.93986i) q^{79} -4.13619 q^{80} +(-4.09559 + 8.01412i) q^{81} +1.65997i q^{82} +(4.57620 + 1.66560i) q^{83} +(1.54333 - 1.52739i) q^{84} +(-1.54922 - 1.29995i) q^{85} +(4.29729 + 0.757728i) q^{86} +(-7.54482 + 6.49706i) q^{87} +(-10.2791 + 8.62523i) q^{88} +(0.219556 + 0.380281i) q^{89} +(0.138631 + 5.41912i) q^{90} +(-9.57994 + 9.24156i) q^{91} +(-2.77590 + 0.489467i) q^{92} +(-10.2354 + 3.87430i) q^{93} +(-3.06592 - 8.42355i) q^{94} +(2.38728 + 6.55901i) q^{95} +(3.51170 + 2.87095i) q^{96} +(-3.66832 + 0.646825i) q^{97} +(-4.05185 - 7.63969i) q^{98} +(8.72210 + 9.87054i) 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

Varieties

Fields

Representations

Groups

Database

Properties

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