LMFDB - Embedded newform 189.2.be.a.104.8

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			104.8
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.8

$q$-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} +(-2.19420 - 1.47834i) 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} +(2.64328 - 1.92257i) 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} +(-2.06352 - 4.09169i) 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} +(2.68678 - 2.78516i) 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} +(5.62185 - 0.666653i) 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} +(2.62904 + 6.48754i) 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} +(8.06635 + 0.559812i) 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} +(0.346855 - 7.92967i) 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} +(2.09800 + 4.29584i) 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} +(-10.6148 - 4.71936i) 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} +(0.497208 - 2.11366i) 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} +(-3.21345 + 12.9173i) 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} +(-8.64209 + 0.310846i) 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	$0.161615\pi$
$5$	−0.253991	+	1.44045i	−0.113588	+	0.644191i	−0.987440	+	0.157997i	$0.949496\pi$
$6$	−1.62142	+	1.39625i	−0.661941	+	0.570017i
$7$	−2.19420	−	1.47834i	−0.829330	−	0.558759i
$7$	−2.19420	−	1.47834i	−0.829330	−	0.558759i
$8$	−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	$-0.865325\pi$
$13$	−1.72073	−	4.72766i	−0.477244	−	1.31122i	0.434579	−	0.900634i	$-0.356897\pi$
$14$	2.64328	−	1.92257i	0.706446	−	0.513828i
$15$	−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	−0.937600	−	0.347715i	$-0.886958\pi$
$17$	−0.691322	+	1.19740i	−0.167670	+	0.290413i	0.769930	+	0.638128i	$0.220291\pi$
$18$	−3.63219	+	0.736695i	−0.856116	+	0.173641i
$19$	4.13271	−	2.38602i	0.948109	−	0.547391i	0.0556159	−	0.998452i	$-0.482288\pi$
$19$	4.13271	−	2.38602i	0.948109	−	0.547391i	0.892493	+	0.451061i	$0.148954\pi$
$20$	−0.530913	+	0.445489i	−0.118716	+	0.0996144i
$21$	−2.06352	−	4.09169i	−0.450296	−	0.892879i
$22$	−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	−0.995514	−	0.0946154i	$-0.969838\pi$
$31$	−4.06150	+	4.84031i	−0.729467	+	0.869345i	0.266047	+	0.963960i	$0.414282\pi$
$32$	−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
$35$	2.68678	−	2.78516i	0.454149	−	0.470778i
$36$	−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	−0.438729	−	0.898620i	$-0.644571\pi$
$41$	−1.26265	+	0.459567i	−0.197193	+	0.0717724i	0.241536	+	0.970392i	$0.422349\pi$
$42$	5.62185	−	0.666653i	0.867470	−	0.102867i
$43$	−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	−0.140000	−	0.990152i	$-0.544710\pi$
$47$	5.55855	−	4.66418i	0.810798	−	0.680341i	0.950798	+	0.309811i	$0.100266\pi$
$48$	1.61620	−	4.62361i	0.233279	−	0.667360i
$49$	2.62904	+	6.48754i	0.375577	+	0.926791i
$50$	−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
$56$	8.06635	+	0.559812i	1.07791	+	0.0748080i
$57$	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	$-0.830684\pi$
$59$	0.933219	−	5.29255i	0.121495	−	0.689031i	0.983328	−	0.181839i	$-0.0582051\pi$
$60$	−1.17941	+	0.223550i	−0.152261	+	0.0288601i
$61$	5.13083	+	6.11468i	0.656935	+	0.782905i	0.986942	−	0.161073i	$-0.0514956\pi$
$61$	5.13083	+	6.11468i	0.656935	+	0.782905i	−0.330007	+	0.943978i	$0.607051\pi$
$62$	−3.90293	−	6.76007i	−0.495672	−	0.858530i
$63$	0.346855	−	7.92967i	0.0436996	−	0.999045i
$64$	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
$70$	2.09800	+	4.29584i	0.250759	+	0.513451i
$71$	−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	−0.818139	−	0.575020i	$-0.804994\pi$
$73$	−6.23051	+	3.59719i	−0.729226	+	0.421019i	0.0889127	+	0.996039i	$0.471661\pi$
$74$	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
$77$	−10.6148	−	4.71936i	−1.20967	−	0.537821i
$78$	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	0.0784266	−	0.996920i	$-0.475010\pi$
$83$	−4.57620	−	1.66560i	−0.502303	−	0.182823i	−0.580729	+	0.814097i	$0.697233\pi$
$84$	0.497208	−	2.11366i	0.0542498	−	0.230620i
$85$	−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	0.854154	−	0.520019i	$-0.174075\pi$
$89$	−0.219556	−	0.380281i	−0.0232728	−	0.0403097i	−0.877427	+	0.479710i	$0.840742\pi$
$90$	−0.138631	−	5.41912i	−0.0146130	−	0.571225i
$91$	−3.21345	+	12.9173i	−0.336861	+	1.35410i
$92$	−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	0.0157159	−	0.999876i	$-0.494997\pi$
$97$	3.66832	−	0.646825i	0.372462	−	0.0656751i	0.356746	+	0.934201i	$0.383886\pi$
$98$	−8.64209	+	0.310846i	−0.872983	+	0.0314002i
$99$	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	$0.566823\pi$
$101$	−12.1379	+	10.1849i	−1.20777	+	1.01344i	−0.999374	+	0.0353913i	$0.988732\pi$
$102$	−0.550955	−	2.90675i	−0.0545527	−	0.287811i
$103$	−5.45514	−	0.961888i	−0.537511	−	0.0947776i	−0.101698	−	0.994815i	$-0.532428\pi$
$103$	−5.45514	−	0.961888i	−0.537511	−	0.0947776i	−0.435812	+	0.900038i	$0.643539\pi$
$104$	11.7784	+	9.88324i	1.15497	+	0.969131i
$105$	6.41800	−	1.93315i	0.626333	−	0.188656i
$106$	−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
$112$	−3.03952	+	6.83649i	−0.287207	+	0.645988i
$113$	−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
$119$	3.28707	−	1.60534i	0.301325	−	0.147161i
$120$	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
$126$	9.05884	+	3.75315i	0.807026	+	0.334357i
$127$	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	−0.0428368	−	0.999082i	$-0.513640\pi$
$131$	−11.8367	−	9.93219i	−1.03418	−	0.867779i	−0.991342	+	0.131303i	$0.958084\pi$
$132$	1.84147	+	3.09735i	0.160279	+	0.269590i
$133$	−12.5953	−	0.874128i	−1.09215	−	0.0757965i
$134$		−	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	−0.959599	−	0.281370i	$-0.909211\pi$
$139$	−6.08203	+	7.24828i	−0.515871	+	0.614791i	0.443728	+	0.896161i	$0.353656\pi$
$140$	1.82351	−	0.192624i	0.154115	−	0.0162797i
$141$	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
$147$	−1.52112	+	12.0286i	−0.125460	+	0.992099i
$148$	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
$154$	9.96365	−	10.3285i	0.802893	−	0.832292i
$155$	−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	0.931602	−	0.363481i	$-0.118412\pi$
$157$	21.0842	+	3.71772i	1.68270	+	0.296706i	0.751101	+	0.660187i	$0.229523\pi$
$158$	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	$0.185185\pi$
$167$	−1.77762	+	10.0814i	−0.137557	+	0.780123i	−0.973045	+	0.230615i	$0.925926\pi$
$168$	11.7138	+	7.67621i	0.903742	+	0.592233i
$169$	−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	0.996307	−	0.0858621i	$-0.0273645\pi$
$173$	0.404033	+	2.29139i	0.0307181	+	0.174211i	−0.965589	+	0.260073i	$0.916253\pi$
$174$	4.35443	+	11.5038i	0.330109	+	0.872101i
$175$	−4.45179	−	6.12062i	−0.336524	−	0.462676i
$176$	−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	−0.913234	−	0.407436i	$-0.866423\pi$
$181$	−13.6823	+	7.89950i	−1.01700	+	0.587165i	−0.103766	+	0.994602i	$0.533089\pi$
$182$	−13.6376	−	9.18831i	−1.01089	−	0.681083i
$183$	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
$189$	7.23871	−	11.6876i	0.526539	−	0.850151i
$190$	−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
$196$	−1.02165	+	3.15554i	−0.0729747	+	0.225396i
$197$	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	0.167063	−	0.985946i	$-0.446572\pi$
$199$	−8.51003	−	4.91327i	−0.603260	−	0.348292i	−0.770323	+	0.637654i	$0.779905\pi$
$200$	−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
$203$	−12.2998	+	8.94614i	−0.863274	+	0.627896i
$204$	−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
$210$	−0.467616	+	8.26734i	−0.0322686	+	0.570500i
$211$	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	$0.0407053\pi$
$223$	14.1148	+	16.8214i	0.945198	+	1.12644i	−0.0466367	+	0.998912i	$0.514850\pi$
$224$	4.98661	+	4.81047i	0.333182	+	0.321413i
$225$	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	$0.0165970\pi$
$227$	1.17595	+	6.66915i	0.0780506	+	0.442647i	−0.920590	+	0.390530i	$0.872292\pi$
$228$	3.03208	+	2.47884i	0.200804	+	0.164165i
$229$	−2.81930	−	7.74596i	−0.186304	−	0.511867i	0.811016	−	0.585024i	$-0.198915\pi$
$229$	−2.81930	−	7.74596i	−0.186304	−	0.511867i	−0.997320	+	0.0731567i	$0.976693\pi$
$230$	10.1011	−	3.67648i	0.666044	−	0.242420i
$231$	−12.0422	−	16.1191i	−0.792321	−	1.06056i
$232$	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
$238$	0.474737	+	4.49419i	0.0307726	+	0.291315i
$239$	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	$-0.746555\pi$
$241$	4.59174	−	12.6157i	0.295780	−	0.812649i	0.995193	−	0.0979312i	$-0.0312225\pi$
$242$			10.2266i			0.657391i
$243$	−12.9744	+	8.64091i	−0.832307	+	0.554315i
$244$			3.78218i			0.242129i
$245$	−10.0128	+	2.13923i	−0.639691	+	0.136671i
$246$	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	0.591066	−	0.806624i	$-0.298707\pi$
$251$	−6.38510	−	11.0593i	−0.403024	−	0.698057i	−0.994089	+	0.108566i	$0.965374\pi$
$252$	2.54105	−	2.77262i	0.160071	−	0.174659i
$253$	−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	−0.0782518	−	0.996934i	$-0.524934\pi$
$257$	8.05762	−	2.93273i	0.502620	−	0.182939i	0.580872	+	0.813995i	$0.302712\pi$
$258$	5.85137	+	4.78372i	0.364291	+	0.297821i
$259$	−22.8790	+	11.1736i	−1.42163	+	0.694296i
$260$	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
$266$	6.33662	−	14.2523i	0.388523	−	0.873867i
$267$	−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	$-0.0704544\pi$
$269$	32.0022			1.95121			0.975604	+	0.219536i	$0.0704544\pi$
$270$	4.37930	−	8.30542i	0.266516	−	0.505452i
$271$			12.5643i			0.763225i	0.924322	+	0.381612i	$0.124631\pi$
$271$			12.5643i			0.763225i	−0.924322	+	0.381612i	$0.875369\pi$
$272$	3.67408	+	1.33726i	0.222774	+	0.0810831i
$273$	−15.7934	+	16.7963i	−0.955857	+	1.01656i
$274$	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
$280$	−2.85516	+	11.4770i	−0.170629	+	0.685883i
$281$	−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	$0.103445\pi$
$283$	7.18235	+	19.7333i	0.426946	+	1.17303i	−0.520710	+	0.853733i	$0.674333\pi$
$284$	−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
$287$	3.44991	+	0.858240i	0.203641	+	0.0506603i
$288$	−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	0.758620	−	0.651533i	$-0.225874\pi$
$293$	4.25738	+	3.57236i	0.248719	+	0.208700i	−0.509902	+	0.860233i	$0.670318\pi$
$294$	−13.3210	−	6.84822i	−0.776897	−	0.399396i
$295$	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
$301$	−3.79658	+	8.53929i	−0.218831	+	0.492196i
$302$	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	−0.491989	−	0.870602i	$-0.663730\pi$
$307$	−26.1410	−	15.0925i	−1.49195	−	0.861375i	−0.999957	+	0.00922626i	$0.997063\pi$
$308$	−2.41552	−	4.94597i	−0.137637	−	0.281823i
$309$	−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	0.448613	−	0.893726i	$-0.351918\pi$
$311$	24.1028	−	8.77272i	1.36675	−	0.497455i	0.918134	+	0.396271i	$0.129696\pi$
$312$	9.42771	+	24.9067i	0.533739	+	1.41006i
$313$	1.77245	−	0.312531i	0.100185	−	0.0176653i	−0.123331	−	0.992366i	$-0.539358\pi$
$313$	1.77245	−	0.312531i	0.100185	−	0.0176653i	0.223516	+	0.974700i	$0.428247\pi$
$314$	−13.2244	+	22.9054i	−0.746299	+	1.29263i
$315$	11.3342	+	2.51369i	0.638611	+	0.141631i
$316$	−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
$322$	−1.34618	+	19.3972i	−0.0750198	+	1.08096i
$323$			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
$329$	−19.0918	+	2.01673i	−1.05257	+	0.111186i
$330$	−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
$336$	−10.3815	+	7.75583i	−0.566358	+	0.423115i
$337$	−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
$343$	3.82213	−	18.1216i	0.206376	−	0.978473i
$344$	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	$-0.560267\pi$
$349$	10.9711	−	30.1428i	0.587269	−	1.61351i	0.775475	−	0.631378i	$-0.217511\pi$
$350$	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	0.393163	−	0.919469i	$-0.371381\pi$
$353$	1.94119	+	0.706536i	0.103319	+	0.0376051i	−0.289843	+	0.957074i	$0.593603\pi$
$354$	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
$357$	6.32596	+	0.357808i	0.334805	+	0.0189372i
$358$	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
$364$	−5.10062	+	3.70990i	−0.267345	+	0.194452i
$365$	−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	−0.522192	−	0.852828i	$-0.674886\pi$
$367$	−13.8164	+	2.43620i	−0.721208	+	0.127168i	−0.199016	+	0.979996i	$0.563775\pi$
$368$	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
$371$	1.19916	−	1.77984i	0.0622575	−	0.0924048i
$372$	−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
$378$	10.5094	+	13.3416i	0.540546	+	0.686218i
$379$	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	−0.979257	−	0.202621i	$-0.935054\pi$
$383$	0.200482	−	1.13699i	0.0102442	−	0.0580975i	0.989501	+	0.144524i	$0.0461651\pi$
$384$	1.85342	+	9.77833i	0.0945817	+	0.498998i
$385$	9.49409	−	14.0915i	0.483864	−	0.718168i
$386$	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
$392$	−16.8716	−	13.1531i	−0.852144	−	0.664333i
$393$	−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	0.114409	−	0.993434i	$-0.463503\pi$
$397$	20.5615	−	11.8712i	1.03195	−	0.595798i	0.917543	+	0.397636i	$0.130169\pi$
$398$	9.29942	−	7.80314i	0.466138	−	0.391136i
$399$	−18.2908	−	11.9862i	−0.915684	−	0.600059i
$400$	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	−0.248447	−	0.968646i	$-0.579920\pi$
$409$	15.1400	−	18.0432i	0.748625	−	0.892177i	0.997072	+	0.0764689i	$0.0243646\pi$
$410$	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
$413$	−9.87184	+	10.2333i	−0.485761	+	0.503548i
$414$	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	0.342515	−	0.939512i	$-0.388721\pi$
$419$	24.7436	−	9.00593i	1.20880	−	0.439968i	0.866289	+	0.499544i	$0.166499\pi$
$420$	2.91835	+	1.25306i	0.142401	+	0.0611429i
$421$	−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
$427$	−2.21851	−	21.0019i	−0.107361	−	1.01636i
$428$	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	$0.121466\pi$
$433$			15.4984i			0.744805i	−0.928071	+	0.372403i	$0.878534\pi$
$434$	−1.42985	+	20.6028i	−0.0686351	+	0.988966i
$435$	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	0.997211	−	0.0746301i	$-0.0237776\pi$
$439$	15.7258	+	18.7413i	0.750551	+	0.894472i	−0.246660	+	0.969102i	$0.579333\pi$
$440$	−9.81344	−	16.9974i	−0.467837	−	0.810318i
$441$	−12.4838	+	16.8865i	−0.594467	+	0.804120i
$442$	−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
$448$	−21.1370	+	10.3229i	−0.998629	+	0.487711i
$449$	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
$455$	−17.7905	−	7.90969i	−0.834032	−	0.370812i
$456$	−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	−0.124290	−	0.992246i	$-0.539665\pi$
$461$	−18.4071	−	6.69964i	−0.857305	−	0.312033i	−0.733015	+	0.680213i	$0.761887\pi$
$462$	23.8005	−	7.16888i	1.10730	−	0.333526i
$463$	−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	0.978690	−	0.205343i	$-0.0658309\pi$
$467$	6.73186	+	11.6599i	0.311513	+	0.539557i	−0.667177	+	0.744899i	$0.732498\pi$
$468$	7.00889	−	1.42157i	0.323986	−	0.0657120i
$469$	11.5257	+	2.86727i	0.532206	+	0.132398i
$470$	−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
$476$	1.68206	+	0.418450i	0.0770971	+	0.0191796i
$477$	−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	−0.969526	−	0.244990i	$-0.921215\pi$
$479$	−19.6234	+	16.4660i	−0.896614	+	0.752349i	0.0729114	+	0.997338i	$0.476771\pi$
$480$	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
$483$	26.5366	+	6.24234i	1.20746	+	0.284036i
$484$	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
$490$	1.74725	−	12.5275i	0.0789328	−	0.565934i
$491$	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
$497$	15.6710	+	32.0878i	0.702942	+	1.43933i
$498$	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	−0.976929	−	0.213562i	$-0.931493\pi$
$503$	−6.80712	+	11.7903i	−0.303514	+	0.525702i	0.673415	+	0.739265i	$0.264827\pi$
$504$	11.1990	+	21.5173i	0.498844	+	0.958459i
$505$	−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	0.676002	−	0.736900i	$-0.263711\pi$
$509$	1.52700	+	1.28130i	0.0676830	+	0.0567928i	−0.608319	+	0.793693i	$0.708156\pi$
$510$	4.32698	−	0.0553370i	0.191602	−	0.00245036i
$511$	18.9889	+	1.31784i	0.840018	+	0.0582979i
$512$			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
$518$	−3.30431	−	31.2809i	−0.145183	−	1.37440i
$519$	−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	0.768261	−	0.640136i	$-0.221122\pi$
$521$	−3.88589	−	6.73055i	−0.170244	−	0.294871i	−0.938505	+	0.345266i	$0.887789\pi$
$522$	−3.16178	+	21.0689i	−0.138387	+	0.922161i
$523$	17.4428	+	10.0706i	0.762720	+	0.440356i	0.830271	−	0.557359i	$-0.188185\pi$
$523$	17.4428	+	10.0706i	0.762720	+	0.440356i	−0.0675518	+	0.997716i	$0.521519\pi$
$524$	−1.27136	−	7.21025i	−0.0555397	−	0.314981i
$525$	−1.54366	−	13.0176i	−0.0673709	−	0.568136i
$526$	−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
$532$	−4.30555	−	4.15347i	−0.186669	−	0.180076i
$533$	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
$546$	−12.8254	−	25.4311i	−0.548875	−	1.08835i
$547$	−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
$553$	13.3769	+	18.3915i	0.568844	+	0.782085i
$554$	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
$560$	−9.07564	−	6.11469i	−0.383516	−	0.258393i
$561$	−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	$-0.860076\pi$
$563$	−35.1445	−	29.4898i	−1.48117	−	1.24285i	−0.576237	−	0.817283i	$-0.695479\pi$
$564$	5.19493	+	2.91136i	0.218746	+	0.122591i
$565$	5.11426	−	14.0513i	0.215159	−	0.591144i
$566$	−25.9428			−1.09046
$567$	20.8341	−	11.5299i	0.874951	−	0.484211i
$568$	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
$574$	−2.45399	+	3.64230i	−0.102428	+	0.152027i
$575$	−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	0.488196	−	0.872734i	$-0.337655\pi$
$577$	−0.564874	−	0.326130i	−0.0235160	−	0.0135770i	−0.511712	+	0.859157i	$0.670988\pi$
$578$	−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
$581$	7.57878	+	10.4198i	0.314421	+	0.432287i
$582$	−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	−0.559199	−	0.829034i	$-0.688891\pi$
$587$	3.87979	−	3.25553i	0.160136	−	0.134370i	0.719335	+	0.694664i	$0.244447\pi$
$588$	−4.21568	+	3.90276i	−0.173852	+	0.160947i
$589$	−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	$-0.512803\pi$
$593$	−1.95836			−0.0804204			−0.0402102	+	0.999191i	$0.512803\pi$
$594$	−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	0.862087	−	0.506760i	$-0.169157\pi$
$601$	5.22977	+	6.23259i	0.213327	+	0.254233i	−0.648761	+	0.760992i	$0.724712\pi$
$602$	−8.30894	−	8.01545i	−0.338647	−	0.326685i
$603$	−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	$-0.990620\pi$
$607$	−6.22814	−	17.1117i	−0.252792	−	0.694542i	0.746773	−	0.665079i	$-0.231602\pi$
$608$	−11.7434	+	4.27424i	−0.476257	+	0.173343i
$609$	−26.1597	+	3.10208i	−1.06004	+	0.125703i
$610$	−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
$616$	35.3055	−	3.72944i	1.42250	−	0.150264i
$617$	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	$0.263299\pi$
$619$	−7.83037	+	21.5138i	−0.314729	+	0.864711i	−0.991685	+	0.128688i	$0.958924\pi$
$620$		−	4.37914i		−	0.175870i
$621$	−24.4239	−	18.9464i	−0.980096	−	0.760292i
$622$			31.6872i			1.27054i
$623$	−0.0804350	+	1.15899i	−0.00322256	+	0.0464340i
$624$	−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
$630$	−7.70710	+	12.0956i	−0.307058	+	0.481900i
$631$	−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
$637$	26.1470	−	23.5925i	1.03598	−	0.934768i
$638$	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	0.0309184	−	0.999522i	$-0.490157\pi$
$643$	−7.14787	−	1.26036i	−0.281884	−	0.0497038i	−0.312803	+	0.949818i	$0.601268\pi$
$644$	6.81449	+	3.02973i	0.268529	+	0.119388i
$645$	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	$-0.704381\pi$
$647$	−30.4657			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$648$	−1.40634	−	27.4692i	−0.0552464	−	1.07909i
$649$		−	23.5964i		−	0.926238i
$650$	16.7071	+	6.08090i	0.655308	+	0.238513i
$651$	28.1860	+	6.63033i	1.10470	+	0.259863i
$652$	−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
$658$	5.72560	−	23.0154i	0.223207	−	0.897235i
$659$	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	$0.167798\pi$
$661$	13.5122	+	37.1245i	0.525564	+	1.44398i	−0.338679	+	0.940902i	$0.609980\pi$
$662$	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
$665$	4.45824	−	17.9210i	0.172883	−	0.694946i
$666$	−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
$672$	3.46115	+	11.4909i	0.133517	+	0.443271i
$673$	−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	0.573822	−	0.818980i	$-0.305460\pi$
$677$	12.6704	+	4.61166i	0.486965	+	0.177241i	−0.0868572	+	0.996221i	$0.527682\pi$
$678$	18.8028	−	11.1788i	0.722117	−	0.429319i
$679$	−9.00527	−	4.00376i	−0.345590	−	0.153650i
$680$	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
$686$	19.4220	+	12.0939i	0.741536	+	0.461746i
$687$	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	−0.502140	−	0.864787i	$-0.667454\pi$
$691$	−17.8283	+	3.14362i	−0.678222	+	0.119589i	−0.176083	+	0.984375i	$0.556343\pi$
$692$	−0.551237	+	0.954771i	−0.0209549	+	0.0362949i
$693$	−4.54606	−	34.5522i	−0.172690	−	1.31253i
$694$	−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
$700$	0.248283	−	3.57752i	0.00938420	−	0.135217i
$701$		−	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
$707$	41.6897	−	4.40383i	1.56790	−	0.165623i
$708$	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
$714$	−3.08825	+	7.19250i	−0.115575	+	0.269172i
$715$	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	$-0.506616\pi$
$719$	22.9381	−	39.7300i	0.855447	−	1.48168i	0.876230	−	0.481894i	$-0.160051\pi$
$720$	6.47708	+	10.5840i	0.241386	+	0.394441i
$721$	10.5477	+	10.1751i	0.392816	+	0.378941i
$722$	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	−0.870896	−	0.491467i	$-0.836461\pi$
$727$	3.02410	−	8.30865i	0.112158	−	0.308151i	0.983054	+	0.183316i	$0.0586831\pi$
$728$	−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	−0.813808	−	0.581134i	$-0.802609\pi$
$733$	−2.71245	+	3.23257i	−0.100187	+	0.119398i	0.713621	+	0.700532i	$0.247054\pi$
$734$	3.00964	−	17.0685i	0.111088	−	0.630009i
$735$	−16.9402	−	5.24625i	−0.624850	−	0.193511i
$736$	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
$742$	1.55951	+	2.14412i	0.0572513	+	0.0787130i
$743$	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
$749$	−4.23610	+	6.28737i	−0.154784	+	0.229736i
$750$	−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
$756$	6.18719	−	2.03761i	0.225026	−	0.0741070i
$757$	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	−0.981655	−	0.190663i	$-0.938936\pi$
$761$	0.165785	−	0.940211i	0.00600969	−	0.0340826i	0.987665	+	0.156581i	$0.0500472\pi$
$762$	−14.4480	−	5.05037i	−0.523397	−	0.182956i
$763$	−29.7418	−	20.0385i	−1.07673	−	0.725442i
$764$	−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	$-0.804369\pi$
$769$	−15.5790	−	42.8029i	−0.561792	−	1.54351i	0.255216	−	0.966884i	$-0.417854\pi$
$770$	12.3470	+	16.9755i	0.444955	+	0.611755i
$771$	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	$0.502864\pi$
$773$	−24.2021	+	41.9192i	−0.870488	+	1.50773i	−0.861492	+	0.507771i	$0.830470\pi$
$774$	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
$777$	−44.0305	−	2.49045i	−1.57959	−	0.0893444i
$778$	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	−0.790026	−	0.613074i	$-0.789933\pi$
$787$	−1.37685	+	1.64087i	−0.0490795	+	0.0584906i	0.740946	+	0.671564i	$0.234377\pi$
$788$	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
$791$	19.4664	+	18.7788i	0.692146	+	0.667698i
$792$	−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	−0.348390	−	0.937350i	$-0.613271\pi$
$797$	−0.360086	+	0.131061i	−0.0127549	+	0.00464241i	0.335635	+	0.941992i	$0.391049\pi$
$798$	21.6428	−	16.1689i	0.766148	−	0.572374i
$799$	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
$805$	2.41836	+	22.8939i	0.0852359	+	0.806902i
$806$	−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	$0.0614474\pi$
$811$			10.9268i			0.383692i	−0.981425	+	0.191846i	$0.938553\pi$
$812$	−7.18923	−	0.498939i	−0.252293	−	0.0175093i
$813$	−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
$819$	−38.0856	+	12.0050i	−1.33082	+	0.419488i
$820$	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
$826$	−7.70853	−	15.7839i	−0.268214	−	0.549190i
$827$	−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	0.422160	−	0.906521i	$-0.361272\pi$
$829$	40.8365	−	23.5770i	1.41831	−	0.818862i	0.996150	+	0.0876596i	$0.0279388\pi$
$830$	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
$833$	−9.58572	−	1.33695i	−0.332125	−	0.0463227i
$834$	−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	0.455551	−	0.890209i	$-0.349442\pi$
$839$	6.72893	+	2.44913i	0.232309	+	0.0845534i	−0.223243	+	0.974763i	$0.571664\pi$
$840$	−14.0324	+	14.9235i	−0.484165	+	0.514911i
$841$	−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
$847$	−21.2539	−	5.28739i	−0.730294	−	0.181677i
$848$	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	−0.266301	−	0.963890i	$-0.585801\pi$
$853$	−5.45780	+	0.962357i	−0.186871	+	0.0329505i	0.0794291	+	0.996841i	$0.474690\pi$
$854$	25.3181	+	6.29844i	0.866368	+	0.215528i
$855$	−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	$-0.387091\pi$
$857$	38.9684	−	32.6983i	1.33113	−	1.11695i	0.983811	−	0.179208i	$-0.0573535\pi$
$858$	44.6192	+	15.5968i	1.52327	+	0.532467i
$859$	9.91290	+	1.74791i	0.338224	+	0.0596380i	0.340181	−	0.940360i	$-0.389512\pi$
$859$	9.91290	+	1.74791i	0.338224	+	0.0596380i	−0.00195691	+	0.999998i	$0.500623\pi$
$860$	1.87527	+	1.57354i	0.0639463	+	0.0536573i
$861$	4.48591	+	4.21805i	0.152879	+	0.143751i
$862$	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
$868$	7.23804	+	3.21804i	0.245675	+	0.109227i
$869$	−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
$875$	27.3339	−	13.3493i	0.924053	−	0.451290i
$876$	−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	$-0.414952\pi$
$881$	28.7112	−	49.7293i	0.967306	−	1.67542i	0.703288	−	0.710905i	$-0.251714\pi$
$882$	−14.3285	−	21.6272i	−0.482466	−	0.728225i
$883$	−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	0.441178	−	0.897419i	$-0.354561\pi$
$887$	−10.9003	−	9.14647i	−0.365997	−	0.307108i	−0.807176	+	0.590311i	$0.799005\pi$
$888$	−24.9044	+	44.4386i	−0.835737	+	1.49126i
$889$	1.31024	−	18.8792i	0.0439439	−	0.633190i
$890$			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
$896$	−1.59702	−	15.1185i	−0.0533526	−	0.505073i
$897$	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
$903$	−12.9673	+	9.68761i	−0.431524	+	0.322384i
$904$	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
$910$	16.6992	−	17.3106i	0.553572	−	0.573841i
$911$	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
$924$	0.538385	−	9.51852i	0.0177116	−	0.313136i
$925$	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	$0.334404\pi$
$929$	9.95917	+	56.4812i	0.326750	+	1.85309i	−0.170333	+	0.985387i	$0.554484\pi$
$930$	19.5175	+	3.18467i	0.640003	+	0.104429i
$931$	26.3445	+	20.5382i	0.863405	+	0.673112i
$932$	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	−0.819500	−	0.573080i	$-0.805748\pi$
$937$	−22.4359	+	12.9533i	−0.732948	+	0.423167i	0.0865519	+	0.996247i	$0.472415\pi$
$938$	−8.19845	+	12.1684i	−0.267689	+	0.397313i
$939$	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	0.346593	−	0.938016i	$-0.387339\pi$
$941$	−15.8590	−	13.3072i	−0.516987	−	0.433804i	−0.863580	+	0.504212i	$0.831783\pi$
$942$	−39.3772	+	23.4109i	−1.28298	+	0.762767i
$943$	2.73389	−	7.51129i	0.0890276	−	0.244601i
$944$	−15.1973			−0.494630
$945$	14.9969	+	13.3956i	0.487851	+	0.435758i
$946$	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
$952$	−6.24676	+	9.27167i	−0.202459	+	0.300497i
$953$	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
$959$	−16.3824	+	11.9156i	−0.529014	+	0.384775i
$960$	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
$966$	−18.4590	+	28.1683i	−0.593910	+	0.906300i
$967$	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	$-0.785566\pi$
$971$	−48.7070			−1.56308			−0.781540	+	0.623855i	$0.785566\pi$
$972$	−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
$980$	−4.28592	−	2.27311i	−0.136909	−	0.0726119i
$981$	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	0.953427	−	0.301624i	$-0.0975287\pi$
$983$	−1.43166	−	8.11934i	−0.0456628	−	0.258967i	−0.999090	+	0.0426573i	$0.986418\pi$
$984$	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
$987$	−30.5545	−	13.1192i	−0.972562	−	0.417590i
$988$	−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
$994$	−43.8715	+	4.63430i	−1.39152	+	0.146991i
$995$	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	$0.497092\pi$
$997$	−20.2279	+	55.5756i	−0.640623	+	1.76010i	−0.649760	+	0.760139i	$0.725131\pi$
$998$		−	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.104.8	yes	132
3.2	odd	2		567.2.be.a.503.16		132
7.6	odd	2	inner	189.2.be.a.104.7	yes	132
21.20	even	2		567.2.be.a.503.15		132
27.7	even	9		567.2.be.a.62.15		132
27.20	odd	18	inner	189.2.be.a.20.7	✓	132
189.20	even	18	inner	189.2.be.a.20.8	yes	132
189.34	odd	18		567.2.be.a.62.16		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.7	✓	132	27.20	odd	18	inner
189.2.be.a.20.8	yes	132	189.20	even	18	inner
189.2.be.a.104.7	yes	132	7.6	odd	2	inner
189.2.be.a.104.8	yes	132	1.1	even	1	trivial
567.2.be.a.62.15		132	27.7	even	9
567.2.be.a.62.16		132	189.34	odd	18
567.2.be.a.503.15		132	21.20	even	2
567.2.be.a.503.16		132	3.2	odd	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} +(-2.19420 - 1.47834i) 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} +(2.64328 - 1.92257i) 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} +(-2.06352 - 4.09169i) 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} +(2.68678 - 2.78516i) 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} +(5.62185 - 0.666653i) 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} +(2.62904 + 6.48754i) 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} +(8.06635 + 0.559812i) 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} +(0.346855 - 7.92967i) 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} +(2.09800 + 4.29584i) 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} +(-10.6148 - 4.71936i) 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} +(0.497208 - 2.11366i) 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} +(-3.21345 + 12.9173i) 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} +(-8.64209 + 0.310846i) 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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