LMFDB - Embedded newform 234.2.z.a.137.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] 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("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.6
Character	$\chi$	$=$	234.137
Dual form			234.2.z.a.41.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.60665 + 0.647043i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.84756 + 0.763001i) q^{5} +(-1.38444 - 1.04083i) q^{6} +(-1.37958 + 1.37958i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.16267 + 2.07915i) q^{9} +(-2.55305 - 1.47400i) q^{10} +(0.207457 - 0.774238i) q^{11} +(1.06788 + 1.36368i) q^{12} +(-3.58657 + 0.369493i) q^{13} +(1.68964 - 0.975511i) q^{14} +(4.08135 + 3.06837i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-4.02058 - 6.96385i) q^{17} +(-1.55086 - 2.56804i) q^{18} +(-1.18319 + 4.41574i) q^{19} +(2.08456 + 2.08456i) q^{20} +(-3.10916 + 1.32386i) q^{21} +(-0.400775 + 0.694163i) q^{22} +6.99376 q^{23} +(-0.678548 - 1.59360i) q^{24} +(3.19629 + 1.84538i) q^{25} +(3.55999 + 0.571370i) q^{26} +(2.12937 + 4.73981i) q^{27} +(-1.88454 + 0.504962i) q^{28} +(6.82146 - 3.93837i) q^{29} +(-3.14812 - 4.02015i) q^{30} +(0.619046 - 2.31031i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.834276 - 1.10970i) q^{33} +(2.08121 + 7.76717i) q^{34} +(-4.98106 + 2.87582i) q^{35} +(0.833356 + 2.88193i) q^{36} +(-2.09658 - 7.82455i) q^{37} +(2.28576 - 3.95904i) q^{38} +(-6.00145 - 1.72702i) q^{39} +(-1.47400 - 2.55305i) q^{40} +(-3.66359 + 3.66359i) q^{41} +(3.34586 - 0.474043i) q^{42} -2.33382i q^{43} +(0.566782 - 0.566782i) q^{44} +(4.57194 + 7.57061i) q^{45} +(-6.75546 - 1.81012i) q^{46} +(-5.14869 + 1.37959i) q^{47} +(0.242972 + 1.71492i) q^{48} +3.19351i q^{49} +(-2.60976 - 2.60976i) q^{50} +(-1.95377 - 13.7900i) q^{51} +(-3.29081 - 1.47329i) q^{52} -8.27924i q^{53} +(-0.830059 - 5.12943i) q^{54} +(1.18149 - 2.04640i) q^{55} +1.95102 q^{56} +(-4.75815 + 6.32899i) q^{57} +(-7.60835 + 2.03865i) q^{58} +(-8.52709 + 2.28483i) q^{59} +(2.00036 + 4.69796i) q^{60} -4.93917 q^{61} +(-1.19590 + 2.07137i) q^{62} +(-5.85193 + 0.115230i) q^{63} +1.00000i q^{64} +(-10.4949 - 1.68440i) q^{65} +(-1.09306 + 0.855961i) q^{66} +(0.549015 + 0.549015i) q^{67} -8.04117i q^{68} +(11.2366 + 4.52526i) q^{69} +(5.55565 - 1.48863i) q^{70} +(-2.57304 - 0.689443i) q^{71} +(-0.0590613 - 2.99942i) q^{72} +(5.68293 - 5.68293i) q^{73} +8.10057i q^{74} +(3.94129 + 5.03302i) q^{75} +(-3.23255 + 3.23255i) q^{76} +(0.781921 + 1.35433i) q^{77} +(5.34997 + 3.22146i) q^{78} +(0.554497 - 0.960416i) q^{79} +(0.763001 + 2.84756i) q^{80} +(0.354299 + 8.99302i) q^{81} +(4.48696 - 2.59055i) q^{82} +(0.614312 + 2.29264i) q^{83} +(-3.35454 - 0.408081i) q^{84} +(-6.13542 - 22.8977i) q^{85} +(-0.604036 + 2.25429i) q^{86} +(13.5080 - 1.91382i) q^{87} +(-0.694163 + 0.400775i) q^{88} +(-2.84070 + 0.761164i) q^{89} +(-2.45674 - 8.49595i) q^{90} +(4.43822 - 5.45771i) q^{91} +(6.05678 + 3.49688i) q^{92} +(2.48946 - 3.31132i) q^{93} +5.33031 q^{94} +(-6.73843 + 11.6713i) q^{95} +(0.209163 - 1.71938i) q^{96} +(2.59780 + 2.59780i) q^{97} +(0.826542 - 3.08469i) q^{98} +(2.05842 - 1.24309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	1.60665	+	0.647043i	0.927602	+	0.373570i
$3$	1.60665	+	0.647043i	0.927602	+	0.373570i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.84756	+	0.763001i	1.27347	+	0.341224i	0.831358	−	0.555737i	$-0.187564\pi$
$5$	2.84756	+	0.763001i	1.27347	+	0.341224i	0.442109	+	0.896962i	$0.354231\pi$
$6$	−1.38444	−	1.04083i	−0.565196	−	0.424916i
$7$	−1.37958	+	1.37958i	−0.521433	+	0.521433i	−0.918004	−	0.396571i	$-0.870200\pi$
$7$	−1.37958	+	1.37958i	−0.521433	+	0.521433i	0.396571	+	0.918004i	$0.370200\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.16267	+	2.07915i	0.720891	+	0.693049i
$10$	−2.55305	−	1.47400i	−0.807345	−	0.466121i
$11$	0.207457	−	0.774238i	0.0625505	−	0.233442i	−0.927572	−	0.373643i	$-0.878108\pi$
$11$	0.207457	−	0.774238i	0.0625505	−	0.233442i	0.990123	+	0.140202i	$0.0447751\pi$
$12$	1.06788	+	1.36368i	0.308271	+	0.393661i
$13$	−3.58657	+	0.369493i	−0.994735	+	0.102479i
$13$	−3.58657	+	0.369493i	−0.994735	+	0.102479i
$14$	1.68964	−	0.975511i	0.451574	−	0.260716i
$15$	4.08135	+	3.06837i	1.05380	+	0.792250i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.02058	−	6.96385i	−0.975135	−	1.68898i	−0.679490	−	0.733685i	$-0.737799\pi$
$17$	−4.02058	−	6.96385i	−0.975135	−	1.68898i	−0.295645	−	0.955298i	$-0.595535\pi$
$18$	−1.55086	−	2.56804i	−0.365541	−	0.605293i
$19$	−1.18319	+	4.41574i	−0.271443	+	1.01304i	0.686744	+	0.726899i	$0.259039\pi$
$19$	−1.18319	+	4.41574i	−0.271443	+	1.01304i	−0.958188	+	0.286141i	$0.907627\pi$
$20$	2.08456	+	2.08456i	0.466121	+	0.466121i
$21$	−3.10916	+	1.32386i	−0.678474	+	0.288890i
$22$	−0.400775	+	0.694163i	−0.0854456	+	0.147996i
$23$	6.99376			1.45830			0.729150	−	0.684354i	$-0.239916\pi$
$23$	6.99376			1.45830			0.729150	+	0.684354i	$0.239916\pi$
$24$	−0.678548	−	1.59360i	−0.138508	−	0.325293i
$25$	3.19629	+	1.84538i	0.639258	+	0.369076i
$26$	3.55999	+	0.571370i	0.698172	+	0.112055i
$27$	2.12937	+	4.73981i	0.409797	+	0.912177i
$28$	−1.88454	+	0.504962i	−0.356145	+	0.0954288i
$29$	6.82146	−	3.93837i	1.26671	−	0.731337i	0.292348	−	0.956312i	$-0.405563\pi$
$29$	6.82146	−	3.93837i	1.26671	−	0.731337i	0.974365	+	0.224975i	$0.0722300\pi$
$30$	−3.14812	−	4.02015i	−0.574766	−	0.733975i
$31$	0.619046	−	2.31031i	0.111184	−	0.414944i	−0.887789	−	0.460250i	$-0.847760\pi$
$31$	0.619046	−	2.31031i	0.111184	−	0.414944i	0.998973	+	0.0453062i	$0.0144263\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.834276	−	1.10970i	0.145229	−	0.193174i
$34$	2.08121	+	7.76717i	0.356924	+	1.33206i
$35$	−4.98106	+	2.87582i	−0.841953	+	0.486102i
$36$	0.833356	+	2.88193i	0.138893	+	0.480322i
$37$	−2.09658	−	7.82455i	−0.344676	−	1.28635i	−0.892990	−	0.450076i	$-0.851397\pi$
$37$	−2.09658	−	7.82455i	−0.344676	−	1.28635i	0.548314	−	0.836272i	$-0.315270\pi$
$38$	2.28576	−	3.95904i	0.370798	−	0.642242i
$39$	−6.00145	−	1.72702i	−0.961001	−	0.276544i
$40$	−1.47400	−	2.55305i	−0.233061	−	0.403673i
$41$	−3.66359	+	3.66359i	−0.572156	+	0.572156i	−0.932730	−	0.360574i	$-0.882581\pi$
$41$	−3.66359	+	3.66359i	−0.572156	+	0.572156i	0.360574	+	0.932730i	$0.382581\pi$
$42$	3.34586	−	0.474043i	0.516277	−	0.0731464i
$43$		−	2.33382i		−	0.355904i	−0.984039	−	0.177952i	$-0.943053\pi$
$43$		−	2.33382i		−	0.355904i	0.984039	−	0.177952i	$-0.0569471\pi$
$44$	0.566782	−	0.566782i	0.0854456	−	0.0854456i
$45$	4.57194	+	7.57061i	0.681545	+	1.12856i
$46$	−6.75546	−	1.81012i	−0.996038	−	0.266887i
$47$	−5.14869	+	1.37959i	−0.751013	+	0.201233i	−0.613968	−	0.789331i	$-0.710427\pi$
$47$	−5.14869	+	1.37959i	−0.751013	+	0.201233i	−0.137046	+	0.990565i	$0.543761\pi$
$48$	0.242972	+	1.71492i	0.0350699	+	0.247528i
$49$			3.19351i			0.456216i
$50$	−2.60976	−	2.60976i	−0.369076	−	0.369076i
$51$	−1.95377	−	13.7900i	−0.273583	−	1.93099i
$52$	−3.29081	−	1.47329i	−0.456353	−	0.204309i
$53$		−	8.27924i		−	1.13724i	−0.822600	−	0.568620i	$-0.807477\pi$
$53$		−	8.27924i		−	1.13724i	0.822600	−	0.568620i	$-0.192523\pi$
$54$	−0.830059	−	5.12943i	−0.112957	−	0.698026i
$55$	1.18149	−	2.04640i	0.159312	−	0.275936i
$56$	1.95102			0.260716
$57$	−4.75815	+	6.32899i	−0.630233	+	0.838295i
$58$	−7.60835	+	2.03865i	−0.999025	+	0.267688i
$59$	−8.52709	+	2.28483i	−1.11013	+	0.297459i	−0.766884	−	0.641786i	$-0.778194\pi$
$59$	−8.52709	+	2.28483i	−1.11013	+	0.297459i	−0.343248	+	0.939245i	$0.611527\pi$
$60$	2.00036	+	4.69796i	0.258246	+	0.606504i
$61$	−4.93917			−0.632396			−0.316198	−	0.948693i	$-0.602406\pi$
$61$	−4.93917			−0.632396			−0.316198	+	0.948693i	$0.602406\pi$
$62$	−1.19590	+	2.07137i	−0.151880	+	0.263064i
$63$	−5.85193	+	0.115230i	−0.737274	+	0.0145176i
$64$			1.00000i			0.125000i
$65$	−10.4949	−	1.68440i	−1.30173	−	0.208924i
$66$	−1.09306	+	0.855961i	−0.134546	+	0.105362i
$67$	0.549015	+	0.549015i	0.0670729	+	0.0670729i	0.739847	−	0.672775i	$-0.234898\pi$
$67$	0.549015	+	0.549015i	0.0670729	+	0.0670729i	−0.672775	+	0.739847i	$0.734898\pi$
$68$		−	8.04117i		−	0.975135i
$69$	11.2366	+	4.52526i	1.35272	+	0.544777i
$70$	5.55565	−	1.48863i	0.664027	−	0.177926i
$71$	−2.57304	−	0.689443i	−0.305363	−	0.0818218i	0.102884	−	0.994693i	$-0.467193\pi$
$71$	−2.57304	−	0.689443i	−0.305363	−	0.0818218i	−0.408247	+	0.912872i	$0.633860\pi$
$72$	−0.0590613	−	2.99942i	−0.00696045	−	0.353485i
$73$	5.68293	−	5.68293i	0.665137	−	0.665137i	−0.291449	−	0.956586i	$-0.594137\pi$
$73$	5.68293	−	5.68293i	0.665137	−	0.665137i	0.956586	+	0.291449i	$0.0941375\pi$
$74$			8.10057i			0.941672i
$75$	3.94129	+	5.03302i	0.455101	+	0.581163i
$76$	−3.23255	+	3.23255i	−0.370798	+	0.370798i
$77$	0.781921	+	1.35433i	0.0891082	+	0.154340i
$78$	5.34997	+	3.22146i	0.605765	+	0.364758i
$79$	0.554497	−	0.960416i	0.0623857	−	0.108055i	−0.833146	−	0.553054i	$-0.813462\pi$
$79$	0.554497	−	0.960416i	0.0623857	−	0.108055i	0.895531	+	0.444998i	$0.146796\pi$
$80$	0.763001	+	2.84756i	0.0853061	+	0.318367i
$81$	0.354299	+	8.99302i	0.0393666	+	0.999225i
$82$	4.48696	−	2.59055i	0.495502	−	0.286078i
$83$	0.614312	+	2.29264i	0.0674295	+	0.251650i	0.991410	−	0.130789i	$-0.0417509\pi$
$83$	0.614312	+	2.29264i	0.0674295	+	0.251650i	−0.923981	+	0.382439i	$0.875084\pi$
$84$	−3.35454	−	0.408081i	−0.366010	−	0.0445253i
$85$	−6.13542	−	22.8977i	−0.665479	−	2.48360i
$86$	−0.604036	+	2.25429i	−0.0651349	+	0.243087i
$87$	13.5080	−	1.91382i	1.44821	−	0.205183i
$88$	−0.694163	+	0.400775i	−0.0739980	+	0.0427228i
$89$	−2.84070	+	0.761164i	−0.301114	+	0.0806832i	−0.406213	−	0.913779i	$-0.633151\pi$
$89$	−2.84070	+	0.761164i	−0.301114	+	0.0806832i	0.105099	+	0.994462i	$0.466484\pi$
$90$	−2.45674	−	8.49595i	−0.258963	−	0.895552i
$91$	4.43822	−	5.45771i	0.465252	−	0.572123i
$92$	6.05678	+	3.49688i	0.631463	+	0.364575i
$93$	2.48946	−	3.31132i	0.258145	−	0.343368i
$94$	5.33031			0.549780
$95$	−6.73843	+	11.6713i	−0.691348	+	1.19745i
$96$	0.209163	−	1.71938i	0.0213476	−	0.175483i
$97$	2.59780	+	2.59780i	0.263767	+	0.263767i	0.826582	−	0.562816i	$-0.190282\pi$
$97$	2.59780	+	2.59780i	0.263767	+	0.263767i	−0.562816	+	0.826582i	$0.690282\pi$
$98$	0.826542	−	3.08469i	0.0834933	−	0.311601i
$99$	2.05842	−	1.24309i	0.206878	−	0.124935i
$100$	1.84538	+	3.19629i	0.184538	+	0.319629i
$101$	−6.82190	−	11.8159i	−0.678804	−	1.17572i	−0.975341	−	0.220702i	$-0.929165\pi$
$101$	−6.82190	−	11.8159i	−0.678804	−	1.17572i	0.296537	−	0.955021i	$-0.404168\pi$
$102$	−1.68191	+	13.8258i	−0.166534	+	1.36896i
$103$	−11.6669	+	6.73592i	−1.14958	+	0.663710i	−0.948785	−	0.315924i	$-0.897686\pi$
$103$	−11.6669	+	6.73592i	−1.14958	+	0.663710i	−0.200794	+	0.979633i	$0.564352\pi$
$104$	2.79736	+	2.27482i	0.274304	+	0.223064i
$105$	−9.86361	+	1.39748i	−0.962590	+	0.136380i
$106$	−2.14282	+	7.99713i	−0.208129	+	0.776750i
$107$	16.0522	+	9.26775i	1.55183	+	0.895947i	0.997993	+	0.0633192i	$0.0201686\pi$
$107$	16.0522	+	9.26775i	1.55183	+	0.895947i	0.553833	+	0.832628i	$0.313165\pi$
$108$	−0.525817	+	5.16948i	−0.0505968	+	0.497433i
$109$	4.23071	+	4.23071i	0.405229	+	0.405229i	0.880071	−	0.474842i	$-0.157495\pi$
$109$	4.23071	+	4.23071i	0.405229	+	0.405229i	−0.474842	+	0.880071i	$0.657495\pi$
$110$	−1.67088	+	1.67088i	−0.159312	+	0.159312i
$111$	1.69434	−	13.9279i	0.160819	−	1.32198i
$112$	−1.88454	−	0.504962i	−0.178073	−	0.0477144i
$113$	−5.17811	−	2.98958i	−0.487116	−	0.281236i	0.236261	−	0.971690i	$-0.424078\pi$
$113$	−5.17811	−	2.98958i	−0.487116	−	0.281236i	−0.723377	+	0.690453i	$0.757411\pi$
$114$	6.23409	−	4.88183i	0.583876	−	0.457225i
$115$	19.9151	+	5.33625i	1.85710	+	0.497608i
$116$	7.87674			0.731337
$117$	−8.52480	−	6.65791i	−0.788118	−	0.615524i
$118$	8.82789			0.812673
$119$	15.1539	+	4.06048i	1.38916	+	0.372224i
$120$	−0.716282	−	5.05561i	−0.0653873	−	0.461512i
$121$	8.96987	+	5.17876i	0.815443	+	0.470796i
$122$	4.77087	+	1.27835i	0.431935	+	0.115737i
$123$	−8.25661	+	3.51562i	−0.744474	+	0.316993i
$124$	1.69127	−	1.69127i	0.151880	−	0.151880i
$125$	−2.72919	−	2.72919i	−0.244106	−	0.244106i
$126$	5.68236	+	1.40329i	0.506225	+	0.125015i
$127$	1.93815	+	1.11899i	0.171983	+	0.0992946i	0.583521	−	0.812098i	$-0.301675\pi$
$127$	1.93815	+	1.11899i	0.171983	+	0.0992946i	−0.411537	+	0.911393i	$0.635008\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	1.51008	−	3.74963i	0.132955	−	0.330137i
$130$	9.70133	+	4.34328i	0.850863	+	0.380931i
$131$	7.37842	−	4.25993i	0.644656	−	0.372192i	−0.141750	−	0.989903i	$-0.545273\pi$
$131$	7.37842	−	4.25993i	0.644656	−	0.372192i	0.786406	+	0.617710i	$0.211940\pi$
$132$	1.27735	−	0.543890i	0.111179	−	0.0473395i
$133$	−4.45956	−	7.72418i	−0.386693	−	0.669772i
$134$	−0.388212	−	0.672403i	−0.0335364	−	0.0580868i
$135$	2.44702	+	15.1216i	0.210606	+	1.30146i
$136$	−2.08121	+	7.76717i	−0.178462	+	0.666029i
$137$	8.21858	+	8.21858i	0.702161	+	0.702161i	0.964874	−	0.262713i	$-0.0846173\pi$
$137$	8.21858	+	8.21858i	0.702161	+	0.702161i	−0.262713	+	0.964874i	$0.584617\pi$
$138$	−9.68245	−	7.27930i	−0.824225	−	0.619655i
$139$	−11.4143	+	19.7701i	−0.968147	+	1.67688i	−0.267238	+	0.963631i	$0.586111\pi$
$139$	−11.4143	+	19.7701i	−0.968147	+	1.67688i	−0.700910	+	0.713250i	$0.747222\pi$
$140$	−5.75163			−0.486102
$141$	−9.16481	−	1.11490i	−0.771816	−	0.0938917i
$142$	2.30692	+	1.33190i	0.193593	+	0.111771i
$143$	−0.457981	+	2.85351i	−0.0382983	+	0.238623i
$144$	−0.719258	+	2.91250i	−0.0599381	+	0.242709i
$145$	22.4295	−	6.00996i	1.86267	−	0.499100i
$146$	−6.96014	+	4.01844i	−0.576026	+	0.332568i
$147$	−2.06634	+	5.13087i	−0.170429	+	0.423187i
$148$	2.09658	−	7.82455i	0.172338	−	0.643174i
$149$	2.01425	+	7.51729i	0.165014	+	0.615840i	0.998038	+	0.0626041i	$0.0199405\pi$
$149$	2.01425	+	7.51729i	0.165014	+	0.615840i	−0.833025	+	0.553236i	$0.813393\pi$
$150$	−2.50435	−	5.88160i	−0.204480	−	0.480231i
$151$	2.05706	+	7.67704i	0.167401	+	0.624748i	0.997722	+	0.0674629i	$0.0214904\pi$
$151$	2.05706	+	7.67704i	0.167401	+	0.624748i	−0.830321	+	0.557285i	$0.811843\pi$
$152$	3.95904	−	2.28576i	0.321121	−	0.185399i
$153$	5.78367	−	23.4199i	0.467582	−	1.89339i
$154$	−0.404752	−	1.51056i	−0.0326159	−	0.121724i
$155$	3.52554	−	6.10641i	0.283178	−	0.490479i
$156$	−4.33390	−	4.49636i	−0.346990	−	0.359997i
$157$	1.97021	+	3.41251i	0.157240	+	0.272348i	0.933872	−	0.357606i	$-0.116407\pi$
$157$	1.97021	+	3.41251i	0.157240	+	0.272348i	−0.776632	+	0.629954i	$0.783074\pi$
$158$	−0.784177	+	0.784177i	−0.0623857	+	0.0623857i
$159$	5.35702	−	13.3019i	0.424839	−	1.05491i
$160$		−	2.94801i		−	0.233061i
$161$	−9.64846	+	9.64846i	−0.760405	+	0.760405i
$162$	1.98534	−	8.77829i	0.155983	−	0.689688i
$163$	−19.9290	−	5.33996i	−1.56096	−	0.418258i	−0.627992	−	0.778220i	$-0.716123\pi$
$163$	−19.9290	−	5.33996i	−1.56096	−	0.418258i	−0.932967	+	0.359962i	$0.882790\pi$
$164$	−5.00455	+	1.34097i	−0.390790	+	0.104712i
$165$	3.22235	−	2.52338i	0.250860	−	0.196445i
$166$		−	2.37352i		−	0.184221i
$167$	−3.99041	−	3.99041i	−0.308787	−	0.308787i	0.535652	−	0.844439i	$-0.320066\pi$
$167$	−3.99041	−	3.99041i	−0.308787	−	0.308787i	−0.844439	+	0.535652i	$0.820066\pi$
$168$	3.13462	+	1.26239i	0.241841	+	0.0973959i
$169$	12.7269	−	2.65042i	0.978996	−	0.203879i
$170$			23.7054i			1.81812i
$171$	−11.7398	+	7.08976i	−0.897767	+	0.542168i
$172$	1.16691	−	2.02114i	0.0889759	−	0.154111i
$173$	−16.4329			−1.24937			−0.624687	−	0.780876i	$-0.714773\pi$
$173$	−16.4329			−1.24937			−0.624687	+	0.780876i	$0.714773\pi$
$174$	−13.5431	−	1.64752i	−1.02670	−	0.124898i
$175$	−6.95539	+	1.86369i	−0.525778	+	0.140882i
$176$	0.774238	−	0.207457i	0.0583604	−	0.0156376i
$177$	−15.1785	−	1.84646i	−1.14088	−	0.138789i
$178$	2.94091			0.220431
$179$	−3.02863	+	5.24575i	−0.226371	+	0.392085i	−0.956730	−	0.290978i	$-0.906019\pi$
$179$	−3.02863	+	5.24575i	−0.226371	+	0.392085i	0.730359	+	0.683063i	$0.239353\pi$
$180$	0.174113	+	8.84231i	0.0129776	+	0.659067i
$181$		−	12.2487i		−	0.910436i	−0.890380	−	0.455218i	$-0.849561\pi$
$181$		−	12.2487i		−	0.910436i	0.890380	−	0.455218i	$-0.150439\pi$
$182$	−5.69955	+	4.12305i	−0.422479	+	0.305621i
$183$	−7.93554	−	3.19585i	−0.586612	−	0.236244i
$184$	−4.94534	−	4.94534i	−0.364575	−	0.364575i
$185$		−	23.8806i		−	1.75573i
$186$	−3.26167	+	2.55417i	−0.239157	+	0.187281i
$187$	−6.22578	+	1.66819i	−0.455274	+	0.121990i
$188$	−5.14869	−	1.37959i	−0.375507	−	0.100617i
$189$	−9.47659	−	3.60132i	−0.689320	−	0.261957i
$190$	9.52957	−	9.52957i	0.691348	−	0.691348i
$191$		−	0.420709i		−	0.0304415i	−0.999884	−	0.0152207i	$-0.995155\pi$
$191$		−	0.420709i		−	0.0304415i	0.999884	−	0.0152207i	$-0.00484510\pi$
$192$	−0.647043	+	1.60665i	−0.0466963	+	0.115950i
$193$	−9.60907	+	9.60907i	−0.691676	+	0.691676i	−0.962601	−	0.270924i	$-0.912671\pi$
$193$	−9.60907	+	9.60907i	−0.691676	+	0.691676i	0.270924	+	0.962601i	$0.412671\pi$
$194$	−1.83692	−	3.18164i	−0.131883	−	0.228429i
$195$	−15.7718	−	9.49689i	−1.12944	−	0.680086i
$196$	−1.59676	+	2.76566i	−0.114054	+	0.197547i
$197$	0.239457	+	0.893667i	0.0170606	+	0.0636712i	0.973931	−	0.226843i	$-0.0728404\pi$
$197$	0.239457	+	0.893667i	0.0170606	+	0.0636712i	−0.956871	+	0.290514i	$0.906174\pi$
$198$	−2.31001	+	0.667976i	−0.164165	+	0.0474710i
$199$	11.1074	−	6.41286i	0.787382	−	0.454595i	−0.0516579	−	0.998665i	$-0.516451\pi$
$199$	11.1074	−	6.41286i	0.787382	−	0.454595i	0.839040	+	0.544070i	$0.183117\pi$
$200$	−0.955238	−	3.56500i	−0.0675455	−	0.252083i
$201$	0.526841	+	1.23731i	0.0371605	+	0.0872733i
$202$	3.53128	+	13.1789i	0.248460	+	0.927264i
$203$	−3.97745	+	14.8441i	−0.279162	+	1.04185i
$204$	5.20298	−	12.9194i	0.364281	−	0.904537i
$205$	−13.2276	+	7.63696i	−0.923855	+	0.533388i
$206$	13.0128	−	3.48677i	0.906644	−	0.242935i
$207$	15.1252	+	14.5411i	1.05127	+	1.01067i
$208$	−2.11327	−	2.92131i	−0.146529	−	0.202557i
$209$	3.17337	+	1.83215i	0.219507	+	0.126732i
$210$	9.88921	+	1.20303i	0.682421	+	0.0830167i
$211$	6.84606			0.471302			0.235651	−	0.971838i	$-0.424278\pi$
$211$	6.84606			0.471302			0.235651	+	0.971838i	$0.424278\pi$
$212$	4.13962	−	7.17003i	0.284310	−	0.492440i
$213$	−3.68788	−	2.77256i	−0.252689	−	0.189973i
$214$	−13.1066	−	13.1066i	−0.895947	−	0.895947i
$215$	1.78070	−	6.64568i	0.121443	−	0.453231i
$216$	1.84586	−	4.85724i	0.125595	−	0.330493i
$217$	2.33324	+	4.04129i	0.158390	+	0.274340i
$218$	−2.99156	−	5.18154i	−0.202614	−	0.350938i
$219$	12.8076	−	5.45341i	0.865458	−	0.368507i
$220$	2.04640	−	1.18149i	0.137968	−	0.0796560i
$221$	16.9932	+	23.4908i	1.14309	+	1.58016i
$222$	−5.24141	+	13.0148i	−0.351781	+	0.873497i
$223$	4.57899	−	17.0890i	0.306632	−	1.14436i	−0.624900	−	0.780705i	$-0.714860\pi$
$223$	4.57899	−	17.0890i	0.306632	−	1.14436i	0.931532	−	0.363660i	$-0.118473\pi$
$224$	1.68964	+	0.975511i	0.112893	+	0.0651791i
$225$	3.07571	+	10.6365i	0.205047	+	0.709100i
$226$	4.22791	+	4.22791i	0.281236	+	0.281236i
$227$	13.6942	−	13.6942i	0.908916	−	0.908916i	−0.0872689	−	0.996185i	$-0.527814\pi$
$227$	13.6942	−	13.6942i	0.908916	−	0.908916i	0.996185	+	0.0872689i	$0.0278139\pi$
$228$	−7.28518	+	3.10199i	−0.482473	+	0.205434i
$229$	25.0861	+	6.72179i	1.65773	+	0.444188i	0.961763	−	0.273882i	$-0.0883077\pi$
$229$	25.0861	+	6.72179i	1.65773	+	0.444188i	0.695971	+	0.718070i	$0.254974\pi$
$230$	−17.8554	−	10.3088i	−1.17735	−	0.679745i
$231$	0.379969	+	2.68187i	0.0250001	+	0.176454i
$232$	−7.60835	−	2.03865i	−0.499512	−	0.133844i
$233$	−11.9090			−0.780184			−0.390092	−	0.920776i	$-0.627557\pi$
$233$	−11.9090			−0.780184			−0.390092	+	0.920776i	$0.627557\pi$
$234$	6.51113	+	8.63743i	0.425646	+	0.564646i
$235$	−15.7138			−1.02506
$236$	−8.52709	−	2.28483i	−0.555066	−	0.148730i
$237$	1.51231	−	1.18427i	0.0982354	−	0.0769268i
$238$	−13.5866	−	7.84425i	−0.880691	−	0.508467i
$239$	8.96480	+	2.40211i	0.579885	+	0.155380i	0.536826	−	0.843693i	$-0.319623\pi$
$239$	8.96480	+	2.40211i	0.579885	+	0.155380i	0.0430587	+	0.999073i	$0.486290\pi$
$240$	−0.616613	+	5.06873i	−0.0398022	+	0.327185i
$241$	−6.92428	+	6.92428i	−0.446032	+	0.446032i	−0.894033	−	0.448001i	$-0.852136\pi$
$241$	−6.92428	+	6.92428i	−0.446032	+	0.446032i	0.448001	+	0.894033i	$0.352136\pi$
$242$	−7.32387	−	7.32387i	−0.470796	−	0.470796i
$243$	−5.24963	+	14.6779i	−0.336764	+	0.941589i
$244$	−4.27745	−	2.46959i	−0.273836	−	0.158099i
$245$	−2.43665	+	9.09371i	−0.155672	+	0.580976i
$246$	8.88518	−	1.25886i	0.566499	−	0.0802619i
$247$	2.61202	−	16.2745i	0.166199	−	1.03552i
$248$	−2.07137	+	1.19590i	−0.131532	+	0.0759400i
$249$	−0.496451	+	4.08097i	−0.0314613	+	0.258621i
$250$	1.92983	+	3.34257i	0.122053	+	0.211402i
$251$	7.05445	+	12.2187i	0.445273	+	0.771235i	0.998071	−	0.0620799i	$-0.0197734\pi$
$251$	7.05445	+	12.2187i	0.445273	+	0.771235i	−0.552798	+	0.833315i	$0.686440\pi$
$252$	−5.12554	−	2.82617i	−0.322879	−	0.178032i
$253$	1.45090	−	5.41484i	0.0912174	−	0.340428i
$254$	−1.58250	−	1.58250i	−0.0992946	−	0.0992946i
$255$	4.95829	−	40.7585i	0.310500	−	2.55240i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.11976			−0.319362			−0.159681	−	0.987169i	$-0.551047\pi$
$257$	−5.11976			−0.319362			−0.159681	+	0.987169i	$0.551047\pi$
$258$	−2.42910	+	3.23103i	−0.151229	+	0.201155i
$259$	13.6870	+	7.90220i	0.850469	+	0.491019i
$260$	−8.24664	−	6.70618i	−0.511435	−	0.415900i
$261$	22.9410	+	5.66541i	1.42001	+	0.350680i
$262$	−8.22956	+	2.20510i	−0.508424	+	0.136232i
$263$	12.4904	−	7.21136i	0.770194	−	0.444671i	−0.0627501	−	0.998029i	$-0.519987\pi$
$263$	12.4904	−	7.21136i	0.770194	−	0.444671i	0.832944	+	0.553358i	$0.186654\pi$
$264$	−1.37460	+	0.194754i	−0.0846007	+	0.0119863i
$265$	6.31706	−	23.5756i	0.388054	−	1.44824i
$266$	2.30844	+	8.61521i	0.141539	+	0.528232i
$267$	−5.05653	−	0.615128i	−0.309455	−	0.0376452i
$268$	0.200953	+	0.749969i	0.0122752	+	0.0458116i
$269$	−10.3656	+	5.98459i	−0.632002	+	0.364887i	−0.781527	−	0.623871i	$-0.785559\pi$
$269$	−10.3656	+	5.98459i	−0.632002	+	0.364887i	0.149525	+	0.988758i	$0.452226\pi$
$270$	1.55011	−	15.2397i	0.0943370	−	0.927457i
$271$	6.16812	+	23.0197i	0.374687	+	1.39835i	0.853802	+	0.520598i	$0.174291\pi$
$271$	6.16812	+	23.0197i	0.374687	+	1.39835i	−0.479115	+	0.877752i	$0.659042\pi$
$272$	4.02058	−	6.96385i	0.243784	−	0.422246i
$273$	10.6620	−	5.89693i	0.645296	−	0.356899i
$274$	−5.81141	−	10.0657i	−0.351080	−	0.608089i
$275$	2.09185	−	2.09185i	0.126143	−	0.126143i
$276$	7.46851	+	9.53727i	0.449551	+	0.574076i
$277$			9.44410i			0.567441i	0.958907	+	0.283721i	$0.0915688\pi$
$277$			9.44410i			0.567441i	−0.958907	+	0.283721i	$0.908431\pi$
$278$	16.1422	−	16.1422i	0.968147	−	0.968147i
$279$	6.14227	−	3.70936i	0.367728	−	0.222073i
$280$	5.55565	+	1.48863i	0.332014	+	0.0889628i
$281$	18.8382	−	5.04768i	1.12379	−	0.301119i	0.351376	−	0.936235i	$-0.385714\pi$
$281$	18.8382	−	5.04768i	1.12379	−	0.301119i	0.772417	+	0.635115i	$0.219047\pi$
$282$	8.56397	+	3.44894i	0.509977	+	0.205381i
$283$			20.7236i			1.23189i	0.787789	+	0.615946i	$0.211226\pi$
$283$			20.7236i			1.23189i	−0.787789	+	0.615946i	$0.788774\pi$
$284$	−1.88359	−	1.88359i	−0.111771	−	0.111771i
$285$	−18.3781	+	14.3917i	−1.08863	+	0.852490i
$286$	1.18092	−	2.63775i	0.0698292	−	0.155973i
$287$		−	10.1084i		−	0.596682i
$288$	1.44856	−	2.62710i	0.0853573	−	0.154804i
$289$	−23.8302	+	41.2751i	−1.40178	+	2.42795i
$290$	−23.2207			−1.36357
$291$	2.49288	+	5.85465i	0.146135	+	0.343206i
$292$	7.76303	−	2.08010i	0.454297	−	0.121729i
$293$	18.6486	−	4.99688i	1.08946	−	0.291921i	0.330996	−	0.943632i	$-0.392615\pi$
$293$	18.6486	−	4.99688i	1.08946	−	0.291921i	0.758467	+	0.651711i	$0.225949\pi$
$294$	3.32389	−	4.42123i	0.193853	−	0.257851i
$295$	−26.0247			−1.51522
$296$	−4.05028	+	7.01530i	−0.235418	+	0.407756i
$297$	4.11149	−	0.665334i	0.238573	−	0.0386066i
$298$		−	7.78247i		−	0.450826i
$299$	−25.0836	+	2.58415i	−1.45062	+	0.149445i
$300$	0.896749	+	6.32937i	0.0517738	+	0.365426i
$301$	3.21969	+	3.21969i	0.185580	+	0.185580i
$302$		−	7.94785i		−	0.457348i
$303$	−3.31506	−	23.3981i	−0.190445	−	1.34418i
$304$	−4.41574	+	1.18319i	−0.253260	+	0.0678608i
$305$	−14.0646	−	3.76859i	−0.805335	−	0.215789i
$306$	−11.6481	+	21.1250i	−0.665879	+	1.20763i
$307$	−15.5762	+	15.5762i	−0.888978	+	0.888978i	−0.994425	−	0.105447i	$-0.966373\pi$
$307$	−15.5762	+	15.5762i	−0.888978	+	0.888978i	0.105447	+	0.994425i	$0.466373\pi$
$308$			1.56384i			0.0891082i
$309$	−23.1032	+	3.27327i	−1.31429	+	0.186210i
$310$	−4.98586	+	4.98586i	−0.283178	+	0.283178i
$311$	−4.85889	−	8.41584i	−0.275522	−	0.477218i	0.694745	−	0.719257i	$-0.255517\pi$
$311$	−4.85889	−	8.41584i	−0.275522	−	0.477218i	−0.970267	+	0.242038i	$0.922184\pi$
$312$	3.02248	+	5.46485i	0.171114	+	0.309386i
$313$	2.74916	−	4.76168i	0.155392	−	0.269146i	−0.777810	−	0.628500i	$-0.783669\pi$
$313$	2.74916	−	4.76168i	0.155392	−	0.269146i	0.933202	+	0.359353i	$0.117003\pi$
$314$	−1.01986	−	3.80616i	−0.0575539	−	0.214794i
$315$	−16.7516	−	4.13691i	−0.943848	−	0.233088i
$316$	0.960416	−	0.554497i	0.0540276	−	0.0311929i
$317$	0.270848	+	1.01082i	0.0152123	+	0.0567731i	0.973115	−	0.230321i	$-0.0739775\pi$
$317$	0.270848	+	1.01082i	0.0152123	+	0.0567731i	−0.957902	+	0.287094i	$0.907311\pi$
$318$	−8.61726	+	11.4621i	−0.483232	+	0.642764i
$319$	−1.63408	−	6.09847i	−0.0914910	−	0.341449i
$320$	−0.763001	+	2.84756i	−0.0426530	+	0.159183i
$321$	19.7937	+	25.2765i	1.10478	+	1.41080i
$322$	11.8169	−	6.82249i	0.658530	−	0.380203i
$323$	35.5077	−	9.51426i	1.97570	−	0.529388i
$324$	−4.18968	+	7.96534i	−0.232760	+	0.442519i
$325$	−12.1456	−	5.43757i	−0.673715	−	0.301622i
$326$	17.8678	+	10.3160i	0.989609	+	0.571351i
$327$	4.05984	+	9.53474i	0.224509	+	0.527272i
$328$	5.18109			0.286078
$329$	5.19978	−	9.00629i	0.286673	−	0.496533i
$330$	−3.76565	+	1.60339i	−0.207292	+	0.0882639i
$331$	−8.72945	−	8.72945i	−0.479814	−	0.479814i	0.425258	−	0.905072i	$-0.360183\pi$
$331$	−8.72945	−	8.72945i	−0.479814	−	0.479814i	−0.905072	+	0.425258i	$0.860183\pi$
$332$	−0.614312	+	2.29264i	−0.0337147	+	0.125825i
$333$	11.7342	−	21.2810i	0.643028	−	1.16619i
$334$	2.82165	+	4.88724i	0.154394	+	0.267418i
$335$	1.14445	+	1.98225i	0.0625282	+	0.108302i
$336$	−2.70108	−	2.03068i	−0.147356	−	0.110783i
$337$	18.3428	−	10.5902i	0.999195	−	0.576886i	0.0911852	−	0.995834i	$-0.470934\pi$
$337$	18.3428	−	10.5902i	0.999195	−	0.576886i	0.908010	+	0.418948i	$0.137601\pi$
$338$	−12.9793	−	0.733864i	−0.705979	−	0.0399170i
$339$	−6.38504	−	8.15368i	−0.346788	−	0.442847i
$340$	6.13542	−	22.8977i	0.332740	−	1.24180i
$341$	−1.66031	−	0.958578i	−0.0899106	−	0.0519099i
$342$	13.1748	−	3.80969i	0.712410	−	0.206005i
$343$	−14.0628	−	14.0628i	−0.759319	−	0.759319i
$344$	−1.65026	+	1.65026i	−0.0889759	+	0.0889759i
$345$	28.5440	+	21.4594i	1.53676	+	1.15534i
$346$	15.8730	+	4.25316i	0.853338	+	0.228651i
$347$	−2.17991	−	1.25857i	−0.117024	−	0.0675636i	0.440346	−	0.897828i	$-0.354856\pi$
$347$	−2.17991	−	1.25857i	−0.117024	−	0.0675636i	−0.557369	+	0.830265i	$0.688189\pi$
$348$	12.6552	+	5.09659i	0.678390	+	0.273206i
$349$	17.1855	+	4.60485i	0.919921	+	0.246492i	0.687552	−	0.726136i	$-0.258686\pi$
$349$	17.1855	+	4.60485i	0.919921	+	0.246492i	0.232369	+	0.972628i	$0.425352\pi$
$350$	7.20075			0.384896
$351$	−9.38845	−	16.2129i	−0.501118	−	0.865379i
$352$	−0.801550			−0.0427228
$353$	−3.01498	−	0.807861i	−0.160471	−	0.0429981i	0.177689	−	0.984087i	$-0.443138\pi$
$353$	−3.01498	−	0.807861i	−0.160471	−	0.0429981i	−0.338160	+	0.941089i	$0.609805\pi$
$354$	14.1834	+	5.71202i	0.753837	+	0.303590i
$355$	−6.80082	−	3.92646i	−0.360950	−	0.208395i
$356$	−2.84070	−	0.761164i	−0.150557	−	0.0403416i
$357$	21.7198	+	16.3290i	1.14953	+	0.864224i
$358$	4.28313	−	4.28313i	0.226371	−	0.226371i
$359$	14.3618	+	14.3618i	0.757986	+	0.757986i	0.975956	−	0.217970i	$-0.0699434\pi$
$359$	14.3618	+	14.3618i	0.757986	+	0.757986i	−0.217970	+	0.975956i	$0.569943\pi$
$360$	2.12038	−	8.58608i	0.111754	−	0.452526i
$361$	−1.64433	−	0.949354i	−0.0865436	−	0.0499660i
$362$	−3.17019	+	11.8313i	−0.166621	+	0.621839i
$363$	11.0606	+	14.1244i	0.580531	+	0.741337i
$364$	6.57246	−	2.50741i	0.344491	−	0.131424i
$365$	20.5186	−	11.8464i	1.07399	−	0.620069i
$366$	6.83799	+	5.14083i	0.357428	+	0.268715i
$367$	−11.6102	−	20.1095i	−0.606049	−	1.04971i	−0.991885	−	0.127141i	$-0.959420\pi$
$367$	−11.6102	−	20.1095i	−0.606049	−	1.04971i	0.385835	−	0.922568i	$-0.373913\pi$
$368$	3.49688	+	6.05678i	0.182288	+	0.315731i
$369$	−15.5403	+	0.306002i	−0.808994	+	0.0159298i
$370$	−6.18074	+	23.0668i	−0.321321	+	1.19919i
$371$	11.4219	+	11.4219i	0.592994	+	0.592994i
$372$	3.81160	−	1.62296i	0.197622	−	0.0841464i
$373$	−12.6570	+	21.9226i	−0.655355	+	1.13511i	0.326450	+	0.945214i	$0.394148\pi$
$373$	−12.6570	+	21.9226i	−0.655355	+	1.13511i	−0.981805	+	0.189893i	$0.939186\pi$
$374$	6.44540			0.333284
$375$	−2.61896	−	6.15077i	−0.135243	−	0.317624i
$376$	4.61619	+	2.66516i	0.238062	+	0.137445i
$377$	−23.0104	+	16.6457i	−1.18510	+	0.857298i
$378$	8.22159	+	5.93132i	0.422873	+	0.305074i
$379$	−22.2862	+	5.97156i	−1.14476	+	0.306738i	−0.780865	−	0.624700i	$-0.785221\pi$
$379$	−22.2862	+	5.97156i	−1.14476	+	0.306738i	−0.363898	+	0.931439i	$0.618554\pi$
$380$	−11.6713	+	6.73843i	−0.598725	+	0.345674i
$381$	2.38991	+	3.05190i	0.122439	+	0.156354i
$382$	−0.108888	+	0.406374i	−0.00557117	+	0.0207919i
$383$	−6.17345	−	23.0396i	−0.315448	−	1.17727i	−0.923571	−	0.383426i	$-0.874744\pi$
$383$	−6.17345	−	23.0396i	−0.315448	−	1.17727i	0.608123	−	0.793843i	$-0.291923\pi$
$384$	1.04083	−	1.38444i	0.0531145	−	0.0706495i
$385$	1.19321	+	4.45313i	0.0608118	+	0.226953i
$386$	11.7687	−	6.79464i	0.599009	−	0.345838i
$387$	4.85235	−	5.04728i	0.246659	−	0.256568i
$388$	0.950861	+	3.54866i	0.0482726	+	0.180156i
$389$	−12.4984	+	21.6479i	−0.633694	+	1.09759i	0.353096	+	0.935587i	$0.385129\pi$
$389$	−12.4984	+	21.6479i	−0.633694	+	1.09759i	−0.986790	+	0.162004i	$0.948204\pi$
$390$	12.7764	+	13.2553i	0.646957	+	0.671209i
$391$	−28.1190	−	48.7035i	−1.42204	−	2.46304i
$392$	2.25815	−	2.25815i	0.114054	−	0.114054i
$393$	14.6109	−	2.07009i	0.737024	−	0.104422i
$394$		−	0.925192i		−	0.0466105i
$395$	2.31176	−	2.31176i	0.116317	−	0.116317i
$396$	2.40419	−	0.0473406i	0.120815	−	0.00237896i
$397$	20.3908	+	5.46370i	1.02338	+	0.274215i	0.731212	−	0.682150i	$-0.238955\pi$
$397$	20.3908	+	5.46370i	1.02338	+	0.274215i	0.292173	+	0.956366i	$0.405622\pi$
$398$	−12.3887	+	3.31954i	−0.620989	+	0.166393i
$399$	−2.16709	−	15.2956i	−0.108490	−	0.765738i
$400$			3.69076i			0.184538i
$401$	−12.5004	−	12.5004i	−0.624242	−	0.624242i	0.322371	−	0.946613i	$-0.395520\pi$
$401$	−12.5004	−	12.5004i	−0.624242	−	0.624242i	−0.946613	+	0.322371i	$0.895520\pi$
$402$	−0.188649	−	1.33151i	−0.00940896	−	0.0664096i
$403$	−1.36661	+	8.51482i	−0.0680756	+	0.424154i
$404$		−	13.6438i		−	0.678804i
$405$	−5.85280	+	25.8785i	−0.290828	+	1.28591i
$406$	7.68385	−	13.3088i	0.381343	−	0.660506i
$407$	−6.49301			−0.321847
$408$	−8.36947	+	11.1325i	−0.414350	+	0.551142i
$409$	20.2046	−	5.41382i	0.999055	−	0.267696i	0.278005	−	0.960580i	$-0.410327\pi$
$409$	20.2046	−	5.41382i	0.999055	−	0.267696i	0.721050	+	0.692884i	$0.243660\pi$
$410$	14.7535	−	3.95318i	0.728622	−	0.195234i
$411$	7.88664	+	18.5222i	0.389019	+	0.913632i
$412$	−13.4718			−0.663710
$413$	8.61171	−	14.9159i	0.423754	−	0.733964i
$414$	−10.8463	−	17.9603i	−0.533068	−	0.882699i
$415$			6.99715i			0.343477i
$416$	1.28518	+	3.36873i	0.0630109	+	0.165165i
$417$	−31.1309	+	24.3782i	−1.52449	+	1.19381i
$418$	−2.59105	−	2.59105i	−0.126732	−	0.126732i
$419$			17.8998i			0.874462i	0.899349	+	0.437231i	$0.144041\pi$
$419$			17.8998i			0.874462i	−0.899349	+	0.437231i	$0.855959\pi$
$420$	−9.24088	−	3.72155i	−0.450909	−	0.181593i
$421$	0.922884	−	0.247286i	0.0449786	−	0.0120520i	−0.236260	−	0.971690i	$-0.575922\pi$
$421$	0.922884	−	0.247286i	0.0449786	−	0.0120520i	0.281238	+	0.959638i	$0.409255\pi$
$422$	−6.61278	−	1.77189i	−0.321905	−	0.0862542i
$423$	−14.0033	−	7.72128i	−0.680863	−	0.375422i
$424$	−5.85430	+	5.85430i	−0.284310	+	0.284310i
$425$		−	29.6780i		−	1.43959i
$426$	2.84463	+	3.63258i	0.137823	+	0.175999i
$427$	6.81399	−	6.81399i	0.329752	−	0.329752i
$428$	9.26775	+	16.0522i	0.447974	+	0.775913i
$429$	−2.58216	+	4.28827i	−0.124668	+	0.207040i
$430$	−3.44006	+	5.95835i	−0.165894	+	0.287337i
$431$	−10.1624	−	37.9267i	−0.489507	−	1.82687i	−0.558845	−	0.829272i	$-0.688755\pi$
$431$	−10.1624	−	37.9267i	−0.489507	−	1.82687i	0.0693375	−	0.997593i	$-0.477911\pi$
$432$	−3.04011	+	4.21399i	−0.146267	+	0.202746i
$433$	9.53436	−	5.50467i	0.458192	−	0.264537i	−0.253092	−	0.967442i	$-0.581447\pi$
$433$	9.53436	−	5.50467i	0.458192	−	0.264537i	0.711284	+	0.702905i	$0.248114\pi$
$434$	−1.20777	−	4.50747i	−0.0579749	−	0.216365i
$435$	39.9251	+	4.85690i	1.91426	+	0.232871i
$436$	1.54855	+	5.77926i	0.0741620	+	0.276776i
$437$	−8.27498	+	30.8826i	−0.395846	+	1.47732i
$438$	−13.7826	+	1.95273i	−0.658560	+	0.0933052i
$439$	3.69190	−	2.13152i	0.176205	−	0.101732i	−0.409304	−	0.912398i	$-0.634228\pi$
$439$	3.69190	−	2.13152i	0.176205	−	0.101732i	0.585508	+	0.810666i	$0.300895\pi$
$440$	−2.28246	+	0.611584i	−0.108812	+	0.0291561i
$441$	−6.63978	+	6.90652i	−0.316180	+	0.328882i
$442$	−10.3343	−	27.0885i	−0.491553	−	1.28847i
$443$	24.9846	+	14.4249i	1.18705	+	0.685346i	0.957636	−	0.287981i	$-0.0929841\pi$
$443$	24.9846	+	14.4249i	1.18705	+	0.685346i	0.229419	+	0.973328i	$0.426317\pi$
$444$	8.43130	−	11.2148i	0.400132	−	0.532229i
$445$	−8.66983			−0.410989
$446$	−8.84592	+	15.3216i	−0.418866	+	0.725498i
$447$	−1.62780	+	13.3810i	−0.0769923	+	0.632899i
$448$	−1.37958	−	1.37958i	−0.0651791	−	0.0651791i
$449$	6.56424	−	24.4981i	0.309786	−	1.15614i	−0.618961	−	0.785421i	$-0.712446\pi$
$449$	6.56424	−	24.4981i	0.309786	−	1.15614i	0.928747	−	0.370714i	$-0.120887\pi$
$450$	−0.217981	−	11.0701i	−0.0102757	−	0.521851i
$451$	2.07645	+	3.59652i	0.0977764	+	0.169354i
$452$	−2.98958	−	5.17811i	−0.140618	−	0.243558i
$453$	−1.66239	+	13.6653i	−0.0781060	+	0.642054i
$454$	−16.7719	+	9.68326i	−0.787144	+	0.454458i
$455$	16.8023	−	12.1548i	0.787705	−	0.569825i
$456$	7.83979	−	1.11075i	0.367132	−	0.0520155i
$457$	−7.44528	+	27.7862i	−0.348275	+	1.29978i	0.540463	+	0.841368i	$0.318249\pi$
$457$	−7.44528	+	27.7862i	−0.348275	+	1.29978i	−0.888739	+	0.458414i	$0.848418\pi$
$458$	−22.4916	−	12.9855i	−1.05096	−	0.606773i
$459$	24.4460	−	33.8854i	1.14104	−	1.58164i
$460$	14.5789	+	14.5789i	0.679745	+	0.679745i
$461$	26.1642	−	26.1642i	1.21859	−	1.21859i	0.250464	−	0.968126i	$-0.419417\pi$
$461$	26.1642	−	26.1642i	1.21859	−	1.21859i	0.968126	−	0.250464i	$-0.0805832\pi$
$462$	0.327097	−	2.68883i	0.0152179	−	0.125096i
$463$	−2.40613	−	0.644720i	−0.111822	−	0.0299627i	0.202474	−	0.979288i	$-0.435102\pi$
$463$	−2.40613	−	0.644720i	−0.111822	−	0.0299627i	−0.314296	+	0.949325i	$0.601769\pi$
$464$	6.82146	+	3.93837i	0.316678	+	0.182834i
$465$	9.61543	−	7.52972i	0.445905	−	0.349182i
$466$	11.5032	+	3.08227i	0.532875	+	0.142784i
$467$	−31.2741			−1.44719			−0.723596	−	0.690223i	$-0.757512\pi$
$467$	−31.2741			−1.44719			−0.723596	+	0.690223i	$0.757512\pi$
$468$	−4.05374	−	10.0283i	−0.187384	−	0.463559i
$469$	−1.51482			−0.0699480
$470$	15.1784	+	4.06703i	0.700126	+	0.187598i
$471$	0.957412	+	6.75753i	0.0441152	+	0.311371i
$472$	7.64518	+	4.41394i	0.351898	+	0.203168i
$473$	−1.80693	−	0.484165i	−0.0830827	−	0.0222619i
$474$	−1.76730	+	0.752505i	−0.0811746	+	0.0345637i
$475$	−11.9305	+	11.9305i	−0.547411	+	0.547411i
$476$	11.0934	+	11.0934i	0.508467	+	0.508467i
$477$	17.2137	−	17.9053i	0.788163	−	0.819826i
$478$	−8.03762	−	4.64052i	−0.367632	−	0.212253i
$479$	1.43340	−	5.34951i	0.0654936	−	0.244426i	−0.925416	−	0.378952i	$-0.876285\pi$
$479$	1.43340	−	5.34951i	0.0654936	−	0.244426i	0.990910	+	0.134526i	$0.0429513\pi$
$480$	1.90749	−	4.73643i	0.0870645	−	0.216187i
$481$	10.4107	+	27.2886i	0.474685	+	1.24425i
$482$	8.48048	−	4.89621i	0.386275	−	0.223016i
$483$	−21.7447	+	9.25877i	−0.989418	+	0.421289i
$484$	5.17876	+	8.96987i	0.235398	+	0.407721i
$485$	5.41526	+	9.37951i	0.245894	+	0.425902i
$486$	8.86968	−	12.8191i	0.402337	−	0.581485i
$487$	−0.759319	+	2.83382i	−0.0344080	+	0.128412i	−0.980994	−	0.194040i	$-0.937841\pi$
$487$	−0.759319	+	2.83382i	−0.0344080	+	0.128412i	0.946586	+	0.322453i	$0.104507\pi$
$488$	3.49252	+	3.49252i	0.158099	+	0.158099i
$489$	−28.5638	−	21.4744i	−1.29170	−	0.971105i
$490$	4.70725	−	8.15320i	0.212652	−	0.368324i
$491$	−35.6988			−1.61106			−0.805531	−	0.592553i	$-0.798120\pi$
$491$	−35.6988			−1.61106			−0.805531	+	0.592553i	$0.798120\pi$
$492$	−8.90824	−	1.08369i	−0.401615	−	0.0488566i
$493$	−54.8525	−	31.6691i	−2.47043	−	1.42630i
$494$	−6.73518	+	15.0440i	−0.303030	+	0.676860i
$495$	6.80994	−	1.96920i	0.306084	−	0.0885090i
$496$	2.31031	−	0.619046i	0.103736	−	0.0277960i
$497$	4.50085	−	2.59857i	0.201891	−	0.116562i
$498$	1.53577	−	3.81342i	0.0688194	−	0.170883i
$499$	4.71922	−	17.6124i	0.211261	−	0.788438i	−0.776188	−	0.630502i	$-0.782849\pi$
$499$	4.71922	−	17.6124i	0.211261	−	0.788438i	0.987449	−	0.157936i	$-0.0504841\pi$
$500$	−0.998954	−	3.72815i	−0.0446746	−	0.166728i
$501$	−3.82924	−	8.99318i	−0.171078	−	0.401786i
$502$	−3.65165	−	13.6281i	−0.162981	−	0.608254i
$503$	20.2816	−	11.7096i	0.904310	−	0.522104i	0.0257142	−	0.999669i	$-0.491814\pi$
$503$	20.2816	−	11.7096i	0.904310	−	0.522104i	0.878596	+	0.477565i	$0.158481\pi$
$504$	4.21942	+	4.05646i	0.187948	+	0.180689i
$505$	−10.4102	−	38.8515i	−0.463249	−	1.72887i
$506$	−2.80293	+	4.85481i	−0.124605	+	0.215823i
$507$	22.1627	+	3.97657i	0.984282	+	0.176605i
$508$	1.11899	+	1.93815i	0.0496473	+	0.0859917i
$509$	2.33968	−	2.33968i	0.103705	−	0.103705i	−0.653351	−	0.757055i	$-0.726637\pi$
$509$	2.33968	−	2.33968i	0.103705	−	0.103705i	0.757055	+	0.653351i	$0.226637\pi$
$510$	−15.3384	+	38.0864i	−0.679197	+	1.68649i
$511$			15.6801i			0.693648i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−23.4492	+	3.79462i	−1.03531	+	0.167537i
$514$	4.94531	+	1.32509i	0.218128	+	0.0584473i
$515$	−38.3618	+	10.2790i	−1.69042	+	0.452948i
$516$	3.18258	−	2.49224i	0.140105	−	0.109715i
$517$			4.27252i			0.187905i
$518$	−11.1754	−	11.1754i	−0.491019	−	0.491019i
$519$	−26.4020	−	10.6328i	−1.15892	−	0.466729i
$520$	6.22995	+	8.61206i	0.273201	+	0.377664i
$521$			7.00178i			0.306754i	0.988168	+	0.153377i	$0.0490148\pi$
$521$			7.00178i			0.306754i	−0.988168	+	0.153377i	$0.950985\pi$
$522$	−20.6930	−	11.4099i	−0.905709	−	0.499399i
$523$	−21.4957	+	37.2316i	−0.939940	+	1.62802i	−0.174360	+	0.984682i	$0.555786\pi$
$523$	−21.4957	+	37.2316i	−0.939940	+	1.62802i	−0.765580	+	0.643341i	$0.777548\pi$
$524$	8.51987			0.372192
$525$	−12.3808	−	1.50613i	−0.540342	−	0.0657328i
$526$	−13.9313	+	3.73287i	−0.607433	+	0.162761i
$527$	−18.5776	+	4.97785i	−0.809253	+	0.216839i
$528$	1.37817	+	0.167654i	0.0599770	+	0.00729622i
$529$	25.9127			1.12664
$530$	−12.2036	+	21.1373i	−0.530092	+	0.918146i
$531$	−23.1918	−	12.7877i	−1.00644	−	0.554940i
$532$		−	8.91912i		−	0.386693i
$533$	11.7860	−	14.4934i	0.510510	−	0.627778i
$534$	4.72503	+	1.90289i	0.204472	+	0.0823463i
$535$	38.6383	+	38.6383i	1.67048	+	1.67048i
$536$		−	0.776425i		−	0.0335364i
$537$	−8.26018	+	6.46844i	−0.356453	+	0.279134i
$538$	11.5613	−	3.09785i	0.498445	−	0.133558i
$539$	2.47254	+	0.662515i	0.106500	+	0.0285365i
$540$	−5.44161	+	14.3192i	−0.234170	+	0.616200i
$541$	8.12664	−	8.12664i	0.349391	−	0.349391i	−0.510491	−	0.859883i	$-0.670536\pi$
$541$	8.12664	−	8.12664i	0.349391	−	0.349391i	0.859883	+	0.510491i	$0.170536\pi$
$542$		−	23.8318i		−	1.02366i
$543$	7.92540	−	19.6794i	0.340112	−	0.844522i
$544$	−5.68596	+	5.68596i	−0.243784	+	0.243784i
$545$	8.81916	+	15.2752i	0.377771	+	0.654319i
$546$	−11.8250	+	2.93646i	−0.506063	+	0.125669i
$547$	2.01972	−	3.49826i	0.0863570	−	0.149575i	−0.819612	−	0.572919i	$-0.805811\pi$
$547$	2.01972	−	3.49826i	0.0863570	−	0.149575i	0.905969	+	0.423345i	$0.139144\pi$
$548$	3.00821	+	11.2268i	0.128504	+	0.479585i
$549$	−10.6818	−	10.2693i	−0.455888	−	0.438281i
$550$	−2.56199	+	1.47916i	−0.109243	+	0.0630717i
$551$	9.31971	+	34.7816i	0.397033	+	1.48175i
$552$	−4.74560	−	11.1453i	−0.201986	−	0.474375i
$553$	0.559999	+	2.08995i	0.0238136	+	0.0888735i
$554$	2.44431	−	9.12230i	0.103849	−	0.387570i
$555$	15.4517	−	38.3678i	0.655890	−	1.62862i
$556$	−19.7701	+	11.4143i	−0.838440	+	0.484074i
$557$	−22.2275	+	5.95584i	−0.941810	+	0.252357i	−0.696883	−	0.717185i	$-0.745430\pi$
$557$	−22.2275	+	5.95584i	−0.941810	+	0.252357i	−0.244926	+	0.969542i	$0.578764\pi$
$558$	−6.89303	+	1.99323i	−0.291805	+	0.0843801i
$559$	0.862329	+	8.37039i	0.0364726	+	0.354030i
$560$	−4.98106	−	2.87582i	−0.210488	−	0.121525i
$561$	−11.0821	−	1.34814i	−0.467885	−	0.0569184i
$562$	−19.5027			−0.822674
$563$	2.44455	−	4.23408i	0.103025	−	0.178445i	−0.809904	−	0.586562i	$-0.800481\pi$
$563$	2.44455	−	4.23408i	0.103025	−	0.178445i	0.912930	+	0.408117i	$0.133814\pi$
$564$	−7.37951	−	5.54794i	−0.310733	−	0.233610i
$565$	−12.4639	−	12.4639i	−0.524361	−	0.524361i
$566$	5.36367	−	20.0175i	0.225452	−	0.841397i
$567$	−12.8954	−	11.9178i	−0.541556	−	0.500501i
$568$	1.33190	+	2.30692i	0.0558853	+	0.0967963i
$569$	−10.6832	−	18.5038i	−0.447863	−	0.775721i	0.550384	−	0.834912i	$-0.314481\pi$
$569$	−10.6832	−	18.5038i	−0.447863	−	0.775721i	−0.998247	+	0.0591908i	$0.981148\pi$
$570$	21.4768	−	9.14469i	0.899563	−	0.383029i
$571$	21.5820	−	12.4604i	0.903179	−	0.521451i	0.0249486	−	0.999689i	$-0.492058\pi$
$571$	21.5820	−	12.4604i	0.903179	−	0.521451i	0.878230	+	0.478238i	$0.158724\pi$
$572$	−1.82338	+	2.24222i	−0.0762393	+	0.0937521i
$573$	0.272217	−	0.675934i	0.0113720	−	0.0282376i
$574$	−2.61625	+	9.76399i	−0.109200	+	0.407541i
$575$	22.3541	+	12.9061i	0.932230	+	0.538223i
$576$	−2.07915	+	2.16267i	−0.0866311	+	0.0901113i
$577$	−4.11164	−	4.11164i	−0.171170	−	0.171170i	0.616323	−	0.787493i	$-0.288621\pi$
$577$	−4.11164	−	4.11164i	−0.171170	−	0.171170i	−0.787493	+	0.616323i	$0.788621\pi$
$578$	33.7010	−	33.7010i	1.40178	−	1.40178i
$579$	−21.6559	+	9.22097i	−0.899990	+	0.383211i
$580$	22.4295	+	6.00996i	0.931333	+	0.249550i
$581$	−4.01038	−	2.31539i	−0.166379	−	0.0960587i
$582$	−0.892639	−	6.30036i	−0.0370011	−	0.261158i
$583$	−6.41010	−	1.71758i	−0.265479	−	0.0711350i
$584$	−8.03688			−0.332568
$585$	−19.1949	−	25.4632i	−0.793610	−	1.05277i
$586$	−19.3065			−0.797542
$587$	−17.3963	−	4.66134i	−0.718024	−	0.192394i	−0.118734	−	0.992926i	$-0.537884\pi$
$587$	−17.3963	−	4.66134i	−0.718024	−	0.192394i	−0.599290	+	0.800532i	$0.704550\pi$
$588$	−4.35493	+	3.41029i	−0.179594	+	0.140638i
$589$	9.46928	+	5.46709i	0.390175	+	0.225268i
$590$	25.1379	+	6.73569i	1.03491	+	0.277304i
$591$	−0.193516	+	1.59075i	−0.00796017	+	0.0654348i
$592$	5.72797	−	5.72797i	0.235418	−	0.235418i
$593$	8.08152	+	8.08152i	0.331868	+	0.331868i	0.853296	−	0.521427i	$-0.174600\pi$
$593$	8.08152	+	8.08152i	0.331868	+	0.331868i	−0.521427	+	0.853296i	$0.674600\pi$
$594$	−4.14360	−	0.421469i	−0.170014	−	0.0172931i
$595$	40.0535	+	23.1249i	1.64203	+	0.948029i
$596$	−2.01425	+	7.51729i	−0.0825069	+	0.307920i
$597$	21.9951	−	3.11628i	0.900201	−	0.127541i
$598$	24.8977	+	3.99602i	1.01814	+	0.163410i
$599$	−0.103217	+	0.0595921i	−0.00421731	+	0.00243487i	−0.502107	−	0.864805i	$-0.667442\pi$
$599$	−0.103217	+	0.0595921i	−0.00421731	+	0.00243487i	0.497890	+	0.867240i	$0.334108\pi$
$600$	0.771968	−	6.34580i	0.0315155	−	0.259066i
$601$	−13.5435	−	23.4581i	−0.552452	−	0.956875i	−0.998097	−	0.0616651i	$-0.980359\pi$
$601$	−13.5435	−	23.4581i	−0.552452	−	0.956875i	0.445645	−	0.895210i	$-0.352974\pi$
$602$	−2.27666	−	3.94330i	−0.0927899	−	0.160717i
$603$	0.0458567	+	2.32882i	0.00186743	+	0.0948370i
$604$	−2.05706	+	7.67704i	−0.0837004	+	0.312374i
$605$	21.5908	+	21.5908i	0.877792	+	0.877792i
$606$	−2.85377	+	23.4588i	−0.115927	+	0.952949i
$607$	9.24915	−	16.0200i	0.375412	−	0.650232i	−0.614977	−	0.788545i	$-0.710835\pi$
$607$	9.24915	−	16.0200i	0.375412	−	0.650232i	0.990389	+	0.138313i	$0.0441680\pi$
$608$	4.57151			0.185399
$609$	−15.9951	+	21.2757i	−0.648155	+	0.862134i
$610$	12.6100	+	7.28036i	0.510562	+	0.294773i
$611$	17.9564	−	6.85039i	0.726437	−	0.277137i
$612$	16.7188	−	17.3904i	0.675816	−	0.702965i
$613$	−21.0392	+	5.63743i	−0.849764	+	0.227694i	−0.657317	−	0.753614i	$-0.728309\pi$
$613$	−21.0392	+	5.63743i	−0.849764	+	0.227694i	−0.192447	+	0.981307i	$0.561642\pi$
$614$	19.0768	−	11.0140i	0.769878	−	0.444489i
$615$	−26.1936	+	3.71113i	−1.05623	+	0.149647i
$616$	0.404752	−	1.51056i	0.0163079	−	0.0608620i
$617$	0.679941	+	2.53758i	0.0273734	+	0.102159i	0.978261	−	0.207377i	$-0.0664928\pi$
$617$	0.679941	+	2.53758i	0.0273734	+	0.102159i	−0.950888	+	0.309536i	$0.899826\pi$
$618$	23.1631	+	2.81780i	0.931758	+	0.113349i
$619$	−3.69004	−	13.7714i	−0.148315	−	0.553520i	−0.999585	−	0.0287923i	$-0.990834\pi$
$619$	−3.69004	−	13.7714i	−0.148315	−	0.553520i	0.851270	−	0.524728i	$-0.175833\pi$
$620$	6.10641	−	3.52554i	0.245239	−	0.141589i
$621$	14.8923	+	33.1491i	0.597607	+	1.33023i
$622$	2.51514	+	9.38665i	0.100848	+	0.376370i
$623$	2.86889	−	4.96907i	0.114940	−	0.199081i
$624$	−1.50509	−	6.06092i	−0.0602517	−	0.242631i
$625$	−14.9160	−	25.8354i	−0.596642	−	1.03341i
$626$	−3.88790	+	3.88790i	−0.155392	+	0.155392i
$627$	3.91303	+	4.99693i	0.156272	+	0.199558i
$628$			3.94043i			0.157240i
$629$	−46.0595	+	46.0595i	−1.83651	+	1.83651i
$630$	15.1101	+	8.33159i	0.602002	+	0.331938i
$631$	34.0030	+	9.11109i	1.35364	+	0.362707i	0.861477	−	0.507797i	$-0.169540\pi$
$631$	34.0030	+	9.11109i	1.35364	+	0.362707i	0.492163	+	0.870503i	$0.336206\pi$
$632$	−1.07121	+	0.287029i	−0.0426103	+	0.0114174i
$633$	10.9992	+	4.42969i	0.437181	+	0.176064i
$634$		−	1.04647i		−	0.0415608i
$635$	4.66521	+	4.66521i	0.185133	+	0.185133i
$636$	11.2902	−	8.84124i	0.447687	−	0.350578i
$637$	−1.17998	−	11.4537i	−0.0467525	−	0.453814i
$638$			6.31360i			0.249958i
$639$	−4.13118	−	6.84076i	−0.163427	−	0.270616i
$640$	1.47400	−	2.55305i	0.0582651	−	0.100918i
$641$	5.81916			0.229843			0.114922	−	0.993375i	$-0.463338\pi$
$641$	5.81916			0.229843			0.114922	+	0.993375i	$0.463338\pi$
$642$	−12.5772	−	29.5382i	−0.496383	−	1.16578i
$643$	5.74185	−	1.53852i	0.226436	−	0.0606735i	−0.143817	−	0.989604i	$-0.545938\pi$
$643$	5.74185	−	1.53852i	0.226436	−	0.0606735i	0.370253	+	0.928931i	$0.379271\pi$
$644$	−13.1800	+	3.53158i	−0.519367	+	0.139164i
$645$	7.16101	−	9.52511i	0.281964	−	0.375051i
$646$	−36.7603			−1.44631
$647$	−2.47586	+	4.28832i	−0.0973362	+	0.168591i	−0.910581	−	0.413330i	$-0.864366\pi$
$647$	−2.47586	+	4.28832i	−0.0973362	+	0.168591i	0.813245	+	0.581921i	$0.197699\pi$
$648$	6.10850	−	6.60956i	0.239965	−	0.259648i
$649$			7.07600i			0.277757i
$650$	10.3244	+	8.39579i	0.404955	+	0.329310i
$651$	1.13382	+	8.00265i	0.0444379	+	0.313649i
$652$	−14.5890	−	14.5890i	−0.571351	−	0.571351i
$653$			20.4897i			0.801824i	0.916117	+	0.400912i	$0.131307\pi$
$653$			20.4897i			0.801824i	−0.916117	+	0.400912i	$0.868693\pi$
$654$	−1.45373	−	10.2606i	−0.0568453	−	0.401222i
$655$	24.2608	−	6.50067i	0.947949	−	0.254002i
$656$	−5.00455	−	1.34097i	−0.195395	−	0.0523559i
$657$	24.1060	−	0.474669i	0.940463	−	0.0185186i
$658$	−7.35360	+	7.35360i	−0.286673	+	0.286673i
$659$		−	4.80810i		−	0.187297i	−0.995605	−	0.0936484i	$-0.970147\pi$
$659$		−	4.80810i		−	0.187297i	0.995605	−	0.0936484i	$-0.0298530\pi$
$660$	4.05233	−	0.574136i	0.157737	−	0.0223482i
$661$	−28.8974	+	28.8974i	−1.12398	+	1.12398i	−0.132839	+	0.991138i	$0.542409\pi$
$661$	−28.8974	+	28.8974i	−1.12398	+	1.12398i	−0.991138	+	0.132839i	$0.957591\pi$
$662$	6.17265	+	10.6913i	0.239907	+	0.415531i
$663$	12.1027	+	48.7368i	0.470028	+	1.89278i
$664$	1.18676	−	2.05553i	0.0460552	−	0.0797699i
$665$	−6.80530	−	25.3977i	−0.263898	−	0.984881i
$666$	−16.8423	+	17.5189i	−0.652625	+	0.678843i
$667$	47.7077	−	27.5440i	1.84725	−	1.06651i
$668$	−1.46059	−	5.45101i	−0.0565120	−	0.210906i
$669$	18.4142	−	24.4933i	0.711932	−	0.946966i
$670$	−0.592413	−	2.21091i	−0.0228869	−	0.0854151i
$671$	−1.02466	+	3.82410i	−0.0395567	+	0.147628i
$672$	2.08346	+	2.66057i	0.0803713	+	0.102634i
$673$	22.6393	−	13.0708i	0.872680	−	0.503842i	0.00444195	−	0.999990i	$-0.498586\pi$
$673$	22.6393	−	13.0708i	0.872680	−	0.503842i	0.868238	+	0.496148i	$0.165253\pi$
$674$	−20.4587	+	5.48190i	−0.788040	+	0.211155i
$675$	−1.94066	+	19.0793i	−0.0746962	+	0.734362i
$676$	12.3471	+	4.06814i	0.474887	+	0.156467i
$677$	−34.5645	−	19.9558i	−1.32842	−	0.766964i	−0.343365	−	0.939202i	$-0.611567\pi$
$677$	−34.5645	−	19.9558i	−1.32842	−	0.766964i	−0.985055	+	0.172238i	$0.944900\pi$
$678$	4.05715	+	9.52842i	0.155814	+	0.365937i
$679$	−7.16775			−0.275073
$680$	−11.8527	+	20.5295i	−0.454531	+	0.787271i
$681$	30.8626	−	13.1411i	1.18266	−	0.503568i
$682$	1.35563	+	1.35563i	0.0519099	+	0.0519099i
$683$	−9.69531	+	36.1834i	−0.370981	+	1.38452i	0.488148	+	0.872761i	$0.337673\pi$
$683$	−9.69531	+	36.1834i	−0.370981	+	1.38452i	−0.859129	+	0.511759i	$0.828994\pi$
$684$	−13.7119	+	0.270000i	−0.524287	+	0.0103237i
$685$	17.1321	+	29.6737i	0.654584	+	1.13377i
$686$	9.94388	+	17.2233i	0.379659	+	0.657589i
$687$	35.9553	+	27.0313i	1.37178	+	1.03131i
$688$	2.02114	−	1.16691i	0.0770554	−	0.0444880i
$689$	3.05912	+	29.6941i	0.116543	+	1.13125i
$690$	−22.0172	−	28.1160i	−0.838182	−	1.07036i
$691$	12.0361	−	44.9193i	0.457875	−	1.70881i	−0.221621	−	0.975133i	$-0.571135\pi$
$691$	12.0361	−	44.9193i	0.457875	−	1.70881i	0.679496	−	0.733679i	$-0.262199\pi$
$692$	−14.2313	−	8.21647i	−0.540994	−	0.312343i
$693$	−1.12481	+	4.55470i	−0.0427279	+	0.173019i
$694$	1.77989	+	1.77989i	0.0675636	+	0.0675636i
$695$	−47.5875	+	47.5875i	−1.80510	+	1.80510i
$696$	−10.9049	−	8.19833i	−0.413349	−	0.310757i
$697$	40.2424	+	10.7829i	1.52429	+	0.408433i
$698$	−15.4081	−	8.89589i	−0.583206	−	0.336714i
$699$	−19.1336	−	7.70562i	−0.723700	−	0.291453i
$700$	−6.95539	−	1.86369i	−0.262889	−	0.0704409i
$701$	27.1053			1.02375			0.511876	−	0.859059i	$-0.328951\pi$
$701$	27.1053			1.02375			0.511876	+	0.859059i	$0.328951\pi$
$702$	4.87235	+	18.0903i	0.183895	+	0.682776i
$703$	37.0318			1.39668
$704$	0.774238	+	0.207457i	0.0291802	+	0.00781881i
$705$	−25.2467	−	10.1675i	−0.950844	−	0.382930i
$706$	2.70316	+	1.56067i	0.101735	+	0.0587365i
$707$	25.7123	+	6.88960i	0.967012	+	0.259110i
$708$	−12.2217	−	9.18831i	−0.459319	−	0.345318i
$709$	32.1360	−	32.1360i	1.20689	−	1.20689i	0.234865	−	0.972028i	$-0.424535\pi$
$709$	32.1360	−	32.1360i	1.20689	−	1.20689i	0.972028	−	0.234865i	$-0.0754647\pi$
$710$	5.55285	+	5.55285i	0.208395	+	0.208395i
$711$	3.19604	−	0.924186i	0.119861	−	0.0346597i
$712$	2.54690	+	1.47046i	0.0954492	+	0.0551076i
$713$	4.32946	−	16.1578i	0.162140	−	0.605113i
$714$	−16.7535	−	21.3941i	−0.626982	−	0.800655i
$715$	−3.48136	+	7.77610i	−0.130196	+	0.290810i
$716$	−5.24575	+	3.02863i	−0.196043	+	0.113185i
$717$	12.8491	+	9.65997i	0.479857	+	0.360758i
$718$	−10.1553	−	17.5895i	−0.378993	−	0.656435i
$719$	−10.2199	−	17.7014i	−0.381138	−	0.660150i	0.610087	−	0.792334i	$-0.291134\pi$
$719$	−10.2199	−	17.7014i	−0.381138	−	0.660150i	−0.991225	+	0.132184i	$0.957801\pi$
$720$	−4.27037	+	7.74472i	−0.159147	+	0.288629i
$721$	6.80276	−	25.3882i	0.253348	−	0.945508i
$722$	1.34259	+	1.34259i	0.0499660	+	0.0499660i
$723$	−15.6052	+	6.64462i	−0.580365	+	0.247116i
$724$	6.12433	−	10.6077i	0.227609	−	0.394230i
$725$	29.0711			1.07967
$726$	−7.02807	−	16.5058i	−0.260836	−	0.612587i
$727$	25.7087	+	14.8430i	0.953485	+	0.550495i	0.894162	−	0.447744i	$-0.147773\pi$
$727$	25.7087	+	14.8430i	0.953485	+	0.550495i	0.0593229	+	0.998239i	$0.481106\pi$
$728$	−6.99748	+	0.720889i	−0.259344	+	0.0267179i
$729$	−17.9316	+	20.1856i	−0.664133	+	0.747615i
$730$	−22.8855	+	6.13215i	−0.847030	+	0.226961i
$731$	−16.2524	+	9.38330i	−0.601115	+	0.347054i
$732$	−5.27445	−	6.73546i	−0.194949	−	0.248950i
$733$	−0.441496	+	1.64769i	−0.0163070	+	0.0608587i	−0.973600	−	0.228261i	$-0.926696\pi$
$733$	−0.441496	+	1.64769i	−0.0163070	+	0.0608587i	0.957293	+	0.289120i	$0.0933626\pi$
$734$	6.00990	+	22.4293i	0.221829	+	0.827879i
$735$	−9.79887	+	13.0338i	−0.361437	+	0.480760i
$736$	−1.81012	−	6.75546i	−0.0667219	−	0.249009i
$737$	0.538965	−	0.311172i	0.0198530	−	0.0114622i
$738$	15.0899	+	3.72654i	0.555469	+	0.137176i
$739$	−12.2243	−	45.6218i	−0.449679	−	1.67822i	−0.703279	−	0.710914i	$-0.748281\pi$
$739$	−12.2243	−	45.6218i	−0.449679	−	1.67822i	0.253600	−	0.967309i	$-0.418385\pi$
$740$	11.9403	−	20.6812i	0.438933	−	0.760255i
$741$	14.7269	−	24.4575i	0.541007	−	0.898467i
$742$	−8.07649	−	13.9889i	−0.296497	−	0.513548i
$743$	−22.8373	+	22.8373i	−0.837819	+	0.837819i	−0.988571	−	0.150753i	$-0.951830\pi$
$743$	−22.8373	+	22.8373i	−0.837819	+	0.837819i	0.150753	+	0.988571i	$0.451830\pi$
$744$	−4.10177	+	0.581142i	−0.150378	+	0.0213057i
$745$			22.9428i			0.840558i
$746$	17.8997	−	17.8997i	0.655355	−	0.655355i
$747$	−3.43818	+	6.23548i	−0.125797	+	0.228144i
$748$	−6.22578	−	1.66819i	−0.227637	−	0.0609952i
$749$	−34.9309	+	9.35972i	−1.27635	+	0.341997i
$750$	0.937788	+	6.61903i	0.0342432	+	0.241693i
$751$			36.8858i			1.34598i	0.739651	+	0.672991i	$0.234991\pi$
$751$			36.8858i			1.34598i	−0.739651	+	0.672991i	$0.765009\pi$
$752$	−3.76910	−	3.76910i	−0.137445	−	0.137445i
$753$	3.42806	+	24.1957i	0.124925	+	0.881740i
$754$	26.5346	−	10.1230i	0.966333	−	0.368658i
$755$			23.4303i			0.852717i
$756$	−6.40631	−	7.85712i	−0.232995	−	0.285761i
$757$	−6.73813	+	11.6708i	−0.244902	+	0.424182i	−0.962104	−	0.272683i	$-0.912089\pi$
$757$	−6.73813	+	11.6708i	−0.244902	+	0.424182i	0.717202	+	0.696865i	$0.245422\pi$
$758$	23.0723			0.838025
$759$	5.83473	−	7.76097i	0.211787	−	0.281706i
$760$	13.0176	−	3.48807i	0.472199	−	0.126525i
$761$	−39.5762	+	10.6044i	−1.43463	+	0.384409i	−0.890651	−	0.454687i	$-0.849751\pi$
$761$	−39.5762	+	10.6044i	−1.43463	+	0.384409i	−0.543983	+	0.839096i	$0.683085\pi$
$762$	−1.51858	−	3.56647i	−0.0550124	−	0.129199i
$763$	−11.6732			−0.422599
$764$	0.210355	−	0.364345i	0.00761037	−	0.0131815i
$765$	34.3388	−	62.2766i	1.24152	−	2.25162i
$766$			23.8524i			0.861821i
$767$	29.7388	−	11.3454i	1.07380	−	0.409658i
$768$	−1.36368	+	1.06788i	−0.0492076	+	0.0385339i
$769$	−15.4846	−	15.4846i	−0.558390	−	0.558390i	0.370459	−	0.928849i	$-0.379200\pi$
$769$	−15.4846	−	15.4846i	−0.558390	−	0.558390i	−0.928849	+	0.370459i	$0.879200\pi$
$770$		−	4.61022i		−	0.166141i
$771$	−8.22568	−	3.31270i	−0.296241	−	0.119304i
$772$	−13.1262	+	3.51716i	−0.472424	+	0.126586i
$773$	34.2518	+	9.17773i	1.23195	+	0.330100i	0.815338	−	0.578985i	$-0.196551\pi$
$773$	34.2518	+	9.17773i	1.23195	+	0.330100i	0.416611	+	0.909085i	$0.363218\pi$
$774$	−5.99334	+	3.61942i	−0.215426	+	0.130097i
$775$	6.24205	−	6.24205i	0.224221	−	0.224221i
$776$		−	3.67384i		−	0.131883i
$777$	16.8772	+	21.5522i	0.605467	+	0.773180i
$778$	17.6754	−	17.6754i	0.633694	−	0.633694i
$779$	−11.8427	−	20.5122i	−0.424309	−	0.734925i
$780$	−8.91031	−	16.1104i	−0.319040	−	0.576846i
$781$	−1.06759	+	1.84911i	−0.0382012	+	0.0661665i
$782$	14.5555	+	54.3217i	0.520502	+	1.94254i
$783$	33.1925	+	23.9462i	1.18620	+	0.855766i
$784$	−2.76566	+	1.59676i	−0.0987736	+	0.0570270i
$785$	3.00655	+	11.2206i	0.107308	+	0.400480i
$786$	−14.6489	−	1.78204i	−0.522507	−	0.0635632i
$787$	−1.37584	−	5.13469i	−0.0490432	−	0.183032i	0.937059	−	0.349171i	$-0.113537\pi$
$787$	−1.37584	−	5.13469i	−0.0490432	−	0.183032i	−0.986102	+	0.166139i	$0.946870\pi$
$788$	−0.239457	+	0.893667i	−0.00853032	+	0.0318356i
$789$	24.7339	−	3.50431i	0.880549	−	0.124757i
$790$	−2.83132	+	1.63466i	−0.100734	+	0.0581586i
$791$	11.2680	−	3.01925i	0.400644	−	0.107352i
$792$	−2.33452	−	0.576521i	−0.0829535	−	0.0204858i
$793$	17.7147	−	1.82499i	0.629067	−	0.0648073i
$794$	−18.2819	−	10.5551i	−0.648800	−	0.374585i
$795$	25.4038	−	33.7904i	0.900978	−	1.19842i
$796$	12.8257			0.454595
$797$	−2.55627	+	4.42759i	−0.0905478	+	0.156833i	−0.907742	−	0.419529i	$-0.862195\pi$
$797$	−2.55627	+	4.42759i	−0.0905478	+	0.156833i	0.817194	+	0.576363i	$0.195528\pi$
$798$	−1.86555	+	15.3353i	−0.0660396	+	0.542864i
$799$	30.3080	+	30.3080i	1.07222	+	1.07222i
$800$	0.955238	−	3.56500i	0.0337728	−	0.126042i
$801$	−7.72608	−	4.26009i	−0.272988	−	0.150523i
$802$	8.83914	+	15.3098i	0.312121	+	0.540609i
$803$	−3.22098	−	5.57891i	−0.113666	−	0.196875i
$804$	−0.162399	+	1.33497i	−0.00572737	+	0.0470806i
$805$	−34.8363	+	20.1128i	−1.22782	+	0.708882i
$806$	3.52384	−	7.87098i	0.124122	−	0.277244i
$807$	−20.5262	+	2.90817i	−0.722558	+	0.102372i
$808$	−3.53128	+	13.1789i	−0.124230	+	0.463632i
$809$	−12.6443	−	7.30018i	−0.444549	−	0.256661i	0.260976	−	0.965345i	$-0.415956\pi$
$809$	−12.6443	−	7.30018i	−0.444549	−	0.256661i	−0.705525	+	0.708685i	$0.749289\pi$
$810$	12.3512	−	23.4819i	0.433977	−	0.825069i
$811$	−20.1306	−	20.1306i	−0.706880	−	0.706880i	0.258998	−	0.965878i	$-0.416608\pi$
$811$	−20.1306	−	20.1306i	−0.706880	−	0.706880i	−0.965878	+	0.258998i	$0.916608\pi$
$812$	−10.8666	+	10.8666i	−0.381343	+	0.381343i
$813$	−4.98472	+	40.9758i	−0.174822	+	1.43708i
$814$	6.27177	+	1.68052i	0.219825	+	0.0589021i
$815$	−52.6746	−	30.4117i	−1.84511	−	1.06527i
$816$	10.9656	−	8.58701i	0.383873	−	0.300606i
$817$	10.3055	+	2.76136i	0.360545	+	0.0966077i
$818$	−20.9174			−0.731359
$819$	20.9458	−	2.57553i	0.731905	−	0.0899962i
$820$	−15.2739			−0.533388
$821$	4.87897	+	1.30731i	0.170277	+	0.0456256i	0.342950	−	0.939354i	$-0.388574\pi$
$821$	4.87897	+	1.30731i	0.170277	+	0.0456256i	−0.172673	+	0.984979i	$0.555240\pi$
$822$	−2.82402	−	19.9323i	−0.0984989	−	0.695218i
$823$	−38.3390	−	22.1350i	−1.33641	−	0.771579i	−0.350140	−	0.936697i	$-0.613866\pi$
$823$	−38.3390	−	22.1350i	−1.33641	−	0.771579i	−0.986274	+	0.165118i	$0.947199\pi$
$824$	13.0128	+	3.48677i	0.453322	+	0.121467i
$825$	4.71440	−	2.00737i	0.164134	−	0.0698875i
$826$	−12.1788	+	12.1788i	−0.423754	+	0.423754i
$827$	−14.3305	−	14.3305i	−0.498320	−	0.498320i	0.412595	−	0.910915i	$-0.364623\pi$
$827$	−14.3305	−	14.3305i	−0.498320	−	0.498320i	−0.910915	+	0.412595i	$0.864623\pi$
$828$	5.82829	+	20.1555i	0.202547	+	0.700453i
$829$	18.5330	+	10.7000i	0.643677	+	0.371627i	0.786030	−	0.618189i	$-0.212133\pi$
$829$	18.5330	+	10.7000i	0.643677	+	0.371627i	−0.142352	+	0.989816i	$0.545467\pi$
$830$	1.81100	−	6.75873i	0.0628606	−	0.234599i
$831$	−6.11074	+	15.1734i	−0.211979	+	0.526360i
$832$	−0.369493	−	3.58657i	−0.0128099	−	0.124342i
$833$	22.2391	−	12.8398i	0.770541	−	0.444872i
$834$	36.3797	−	15.4903i	1.25973	−	0.536384i
$835$	−8.31824	−	14.4076i	−0.287865	−	0.498596i
$836$	1.83215	+	3.17337i	0.0633662	+	0.109753i
$837$	12.2686	−	1.98534i	0.424065	−	0.0686235i
$838$	4.63281	−	17.2899i	0.160038	−	0.597269i
$839$	34.4148	+	34.4148i	1.18813	+	1.18813i	0.977583	+	0.210549i	$0.0675252\pi$
$839$	34.4148	+	34.4148i	1.18813	+	1.18813i	0.210549	+	0.977583i	$0.432475\pi$
$840$	7.96280	+	5.98646i	0.274743	+	0.206552i
$841$	16.5215	−	28.6161i	0.569708	−	0.986763i
$842$	−0.955439			−0.0329266
$843$	33.5325	+	4.07924i	1.15492	+	0.140497i
$844$	5.92886	+	3.42303i	0.204080	+	0.117825i
$845$	38.2630	+	2.16344i	1.31629	+	0.0744246i
$846$	11.5277	+	11.0825i	0.396331	+	0.381024i
$847$	−19.5192	+	5.23015i	−0.670687	+	0.179710i
$848$	7.17003	−	4.13962i	0.246220	−	0.142155i
$849$	−13.4091	+	33.2957i	−0.460198	+	1.14270i
$850$	−7.68123	+	28.6667i	−0.263464	+	0.983261i
$851$	−14.6630	−	54.7230i	−0.502641	−	1.87588i
$852$	−1.80752	−	4.24505i	−0.0619245	−	0.145433i
$853$	−0.430304	−	1.60592i	−0.0147333	−	0.0549855i	0.958168	−	0.286207i	$-0.0923945\pi$
$853$	−0.430304	−	1.60592i	−0.0147333	−	0.0549855i	−0.972901	+	0.231221i	$0.925728\pi$
$854$	−8.34540	+	4.81822i	−0.285574	+	0.164876i
$855$	−38.8393	+	11.2310i	−1.32828	+	0.384092i
$856$	−4.79734	−	17.9039i	−0.163970	−	0.611943i
$857$	6.29501	−	10.9033i	0.215033	−	0.372449i	−0.738249	−	0.674528i	$-0.764347\pi$
$857$	6.29501	−	10.9033i	0.215033	−	0.372449i	0.953283	+	0.302079i	$0.0976806\pi$
$858$	3.60406	−	3.47384i	0.123041	−	0.118595i
$859$	11.6155	+	20.1186i	0.396315	+	0.686438i	0.993268	−	0.115838i	$-0.0369554\pi$
$859$	11.6155	+	20.1186i	0.396315	+	0.686438i	−0.596953	+	0.802276i	$0.703622\pi$
$860$	4.86497	−	4.86497i	0.165894	−	0.165894i
$861$	6.54059	−	16.2407i	0.222903	−	0.553483i
$862$			39.2646i			1.33736i
$863$	21.8752	−	21.8752i	0.744642	−	0.744642i	−0.228826	−	0.973467i	$-0.573489\pi$
$863$	21.8752	−	21.8752i	0.744642	−	0.744642i	0.973467	+	0.228826i	$0.0734885\pi$
$864$	4.02718	−	3.28356i	0.137008	−	0.111709i
$865$	−46.7937	−	12.5383i	−1.59103	−	0.426316i
$866$	−10.6342	+	2.84942i	−0.361365	+	0.0968274i
$867$	−64.9936	+	50.8956i	−2.20730	+	1.72851i
$868$			4.66648i			0.158390i
$869$	−0.628557	−	0.628557i	−0.0213223	−	0.0213223i
$870$	−37.3076	−	15.0248i	−1.26485	−	0.509388i
$871$	−2.17194	−	1.76622i	−0.0735933	−	0.0598462i
$872$		−	5.98313i		−	0.202614i
$873$	0.216982	+	11.0194i	0.00734373	+	0.372950i
$874$	15.9860	−	27.6886i	0.540735	−	0.936581i
$875$	7.53029			0.254570
$876$	13.8184	+	1.68101i	0.466881	+	0.0567962i
$877$	−25.8463	+	6.92550i	−0.872769	+	0.233858i	−0.667285	−	0.744803i	$-0.732544\pi$
$877$	−25.8463	+	6.92550i	−0.872769	+	0.233858i	−0.205484	+	0.978660i	$0.565877\pi$
$878$	−4.11778	+	1.10336i	−0.138968	+	0.0372364i
$879$	33.1950	+	4.03819i	1.11964	+	0.136205i
$880$	2.36298			0.0796560
$881$	11.3559	−	19.6690i	0.382589	−	0.662664i	−0.608842	−	0.793291i	$-0.708366\pi$
$881$	11.3559	−	19.6690i	0.382589	−	0.662664i	0.991432	+	0.130627i	$0.0416990\pi$
$882$	8.20107	−	4.95268i	0.276144	−	0.166765i
$883$		−	11.3387i		−	0.381577i	−0.981631	−	0.190789i	$-0.938895\pi$
$883$		−	11.3387i		−	0.381577i	0.981631	−	0.190789i	$-0.0611045\pi$
$884$	2.97115	+	28.8402i	0.0999307	+	0.970001i
$885$	−41.8127	−	16.8391i	−1.40552	−	0.566040i
$886$	−20.3999	−	20.3999i	−0.685346	−	0.685346i
$887$		−	17.8989i		−	0.600985i	−0.953784	−	0.300492i	$-0.902849\pi$
$887$		−	17.8989i		−	0.600985i	0.953784	−	0.300492i	$-0.0971510\pi$
$888$	−11.0466	+	8.65045i	−0.370700	+	0.290290i
$889$	−4.21758	+	1.13010i	−0.141453	+	0.0379023i
$890$	8.37441	+	2.24392i	0.280711	+	0.0752163i
$891$	7.03624	+	1.59135i	0.235723	+	0.0533122i
$892$	12.5100	−	12.5100i	0.418866	−	0.418866i
$893$		−	24.3676i		−	0.815430i
$894$	5.03559	−	12.5037i	0.168415	−	0.418187i
$895$	−12.6267	+	12.6267i	−0.422065	+	0.422065i
$896$	0.975511	+	1.68964i	0.0325895	+	0.0564467i
$897$	−41.9727	−	12.0783i	−1.40143	−	0.403284i
$898$	−12.6811	+	21.9644i	−0.423175	+	0.732961i
$899$	−4.87606	−	18.1977i	−0.162626	−	0.606928i
$900$	−2.65461	+	10.7493i	−0.0884868	+	0.358311i
$901$	−57.6554	+	33.2874i	−1.92078	+	1.10896i
$902$	−1.07485	−	4.01140i	−0.0357886	−	0.133565i
$903$	3.08965	+	7.25620i	0.102817	+	0.241471i
$904$	1.54752	+	5.77543i	0.0514698	+	0.192088i
$905$	9.34574	−	34.8788i	0.310663	−	1.15941i
$906$	5.14260	−	12.7694i	0.170851	−	0.424236i
$907$	−42.4694	+	24.5197i	−1.41017	+	0.814165i	−0.995404	−	0.0957617i	$-0.969471\pi$
$907$	−42.4694	+	24.5197i	−1.41017	+	0.814165i	−0.414770	+	0.909926i	$0.636138\pi$
$908$	18.7066	−	5.01242i	0.620801	−	0.166343i
$909$	9.81341	−	39.7376i	0.325490	−	1.31801i
$910$	−19.3757	+	7.39185i	−0.642298	+	0.245038i
$911$	−49.7924	−	28.7477i	−1.64970	−	0.952453i	−0.977191	−	0.212362i	$-0.931885\pi$
$911$	−49.7924	−	28.7477i	−1.64970	−	0.952453i	−0.672506	−	0.740092i	$-0.734782\pi$
$912$	−7.86014	−	0.956189i	−0.260275	−	0.0316626i
$913$	1.90249			0.0629634
$914$	14.3832	−	24.9124i	0.475753	−	0.824029i
$915$	−20.1585	−	15.1552i	−0.666418	−	0.501015i
$916$	18.3643	+	18.3643i	0.606773	+	0.606773i
$917$	−4.30221	+	16.0561i	−0.142071	+	0.530218i
$918$	−32.3833	+	26.4037i	−1.06881	+	0.871452i
$919$	−18.6828	−	32.3595i	−0.616288	−	1.06744i	−0.990157	−	0.139961i	$-0.955302\pi$
$919$	−18.6828	−	32.3595i	−0.616288	−	1.06744i	0.373869	−	0.927482i	$-0.378031\pi$
$920$	−10.3088	−	17.8554i	−0.339872	−	0.588676i
$921$	−35.1039	+	14.9470i	−1.15671	+	0.492522i
$922$	−32.0445	+	18.5009i	−1.05533	+	0.609295i
$923$	9.48312	+	1.52202i	0.312141	+	0.0500978i
$924$	−1.01187	+	2.51255i	−0.0332882	+	0.0826570i
$925$	7.73797	−	28.8785i	0.254423	−	0.949519i
$926$	2.15728	+	1.24550i	0.0708925	+	0.0409298i
$927$	−39.2367	−	9.68972i	−1.28870	−	0.318252i
$928$	−5.56970	−	5.56970i	−0.182834	−	0.182834i
$929$	−13.3388	+	13.3388i	−0.437632	+	0.437632i	−0.891214	−	0.453582i	$-0.850146\pi$
$929$	−13.3388	+	13.3388i	−0.437632	+	0.437632i	0.453582	+	0.891214i	$0.350146\pi$
$930$	−11.2366	+	4.78449i	−0.368463	+	0.156890i
$931$	−14.1017	−	3.77854i	−0.462165	−	0.123837i
$932$	−10.3135	−	5.95449i	−0.337830	−	0.195046i
$933$	−2.36114	−	16.6652i	−0.0773003	−	0.545596i
$934$	30.2085	+	8.09433i	0.988451	+	0.264855i
$935$	−19.0011			−0.621402
$936$	1.32009	+	10.7358i	0.0431485	+	0.350911i
$937$	38.9992			1.27405			0.637025	−	0.770843i	$-0.280165\pi$
$937$	38.9992			1.27405			0.637025	+	0.770843i	$0.280165\pi$
$938$	1.46321	+	0.392065i	0.0477754	+	0.0128014i
$939$	7.49796	−	5.87155i	0.244687	−	0.191611i
$940$	−13.6086	−	7.85691i	−0.443862	−	0.256264i
$941$	−52.8136	−	14.1514i	−1.72167	−	0.461321i	−0.743437	−	0.668806i	$-0.766805\pi$
$941$	−52.8136	−	14.1514i	−1.72167	−	0.461321i	−0.978238	+	0.207485i	$0.933472\pi$
$942$	0.824190	−	6.77507i	0.0268536	−	0.220744i
$943$	−25.6223	+	25.6223i	−0.834375	+	0.834375i
$944$	−6.24226	−	6.24226i	−0.203168	−	0.203168i
$945$	−24.2373	−	17.4856i	−0.788440	−	0.568807i
$946$	1.62005	+	0.935336i	0.0526723	+	0.0304104i
$947$	0.410138	−	1.53066i	0.0133277	−	0.0497397i	−0.958942	−	0.283603i	$-0.908470\pi$
$947$	0.410138	−	1.53066i	0.0133277	−	0.0497397i	0.972269	+	0.233863i	$0.0751369\pi$
$948$	1.90184	−	0.269454i	0.0617689	−	0.00875145i
$949$	−18.2824	+	22.4820i	−0.593473	+	0.729798i
$950$	14.6119	−	8.43617i	0.474072	−	0.273705i
$951$	−0.218883	+	1.79928i	−0.00709778	+	0.0583457i
$952$	−7.84425	−	13.5866i	−0.254234	−	0.440345i
$953$	10.7911	+	18.6908i	0.349559	+	0.605454i	0.986171	−	0.165730i	$-0.0529981\pi$
$953$	10.7911	+	18.6908i	0.349559	+	0.605454i	−0.636612	+	0.771184i	$0.719665\pi$
$954$	−21.2614	+	12.8399i	−0.688364	+	0.415708i
$955$	0.321002	−	1.19799i	0.0103874	−	0.0387662i
$956$	6.56269	+	6.56269i	0.212253	+	0.212253i
$957$	1.32057	−	10.8555i	0.0426880	−	0.350907i
$958$	−2.76911	+	4.79624i	−0.0894659	+	0.154960i
$959$	−22.6764			−0.732259
$960$	−3.06837	+	4.08135i	−0.0990312	+	0.131725i
$961$	21.8925	+	12.6396i	0.706209	+	0.407730i
$962$	−2.99310	−	29.0532i	−0.0965015	−	0.936714i
$963$	15.4467	+	53.4180i	0.497762	+	1.72137i
$964$	−9.45875	+	2.53446i	−0.304646	+	0.0816296i
$965$	−34.6941	+	20.0307i	−1.11684	+	0.644810i
$966$	23.4001	−	3.31534i	0.752886	−	0.106669i
$967$	12.5386	−	46.7947i	0.403215	−	1.50482i	−0.404110	−	0.914710i	$-0.632419\pi$
$967$	12.5386	−	46.7947i	0.403215	−	1.50482i	0.807325	−	0.590107i	$-0.200915\pi$
$968$	−2.68072	−	10.0046i	−0.0861617	−	0.321560i
$969$	63.2047	+	7.68887i	2.03043	+	0.247002i
$970$	−2.80315	−	10.4615i	−0.0900036	−	0.335898i
$971$	1.30561	−	0.753792i	0.0418989	−	0.0241903i	−0.478904	−	0.877867i	$-0.658966\pi$
$971$	1.30561	−	0.753792i	0.0418989	−	0.0241903i	0.520803	+	0.853677i	$0.325633\pi$
$972$	−11.8853	+	10.0866i	−0.381220	+	0.323529i
$973$	−11.5276	−	43.0214i	−0.369557	−	1.37920i
$974$	1.46689	−	2.54073i	0.0470022	−	0.0814102i
$975$	−15.9954	−	16.5950i	−0.512262	−	0.531465i
$976$	−2.46959	−	4.27745i	−0.0790495	−	0.136918i
$977$	22.2801	−	22.2801i	0.712804	−	0.712804i	−0.254317	−	0.967121i	$-0.581851\pi$
$977$	22.2801	−	22.2801i	0.712804	−	0.712804i	0.967121	+	0.254317i	$0.0818507\pi$
$978$	22.0325	+	28.1355i	0.704523	+	0.899674i
$979$			2.35729i			0.0753393i
$980$	−6.65706	+	6.65706i	−0.212652	+	0.212652i
$981$	0.353372	+	17.9459i	0.0112823	+	0.572969i
$982$	34.4824	+	9.23952i	1.10038	+	0.294845i
$983$	−13.9059	+	3.72607i	−0.443529	+	0.118843i	−0.473670	−	0.880702i	$-0.657071\pi$
$983$	−13.9059	+	3.72607i	−0.443529	+	0.118843i	0.0301410	+	0.999546i	$0.490404\pi$
$984$	8.32422	+	3.35239i	0.265367	+	0.106870i
$985$			2.72748i			0.0869046i
$986$	44.7869	+	44.7869i	1.42630	+	1.42630i
$987$	14.1817	−	11.1055i	0.451408	−	0.353492i
$988$	10.3993	−	12.7882i	0.330847	−	0.406845i
$989$		−	16.3222i		−	0.519014i
$990$	−7.08756	+	0.139561i	−0.225257	+	0.00443553i
$991$	9.55307	−	16.5464i	0.303463	−	0.525614i	−0.673455	−	0.739229i	$-0.735190\pi$
$991$	9.55307	−	16.5464i	0.303463	−	0.525614i	0.976918	+	0.213615i	$0.0685236\pi$
$992$	−2.39181			−0.0759400
$993$	−8.37687	−	19.6735i	−0.265832	−	0.624320i
$994$	−5.02005	+	1.34512i	−0.159226	+	0.0426646i
$995$	36.5220	−	9.78603i	1.15782	−	0.310238i
$996$	−2.47042	+	3.28600i	−0.0782783	+	0.104121i
$997$	4.95003			0.156769			0.0783845	−	0.996923i	$-0.475024\pi$
$997$	4.95003			0.156769			0.0783845	+	0.996923i	$0.475024\pi$
$998$	−9.11683	+	15.7908i	−0.288588	+	0.499850i
$999$	32.6225	−	26.5987i	1.03213	−	0.841547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.137.6	yes	56
3.2	odd	2		702.2.bc.a.683.9		56
9.4	even	3		702.2.bb.a.449.9		56
9.5	odd	6		234.2.y.a.59.1	✓	56
13.2	odd	12		234.2.y.a.119.1	yes	56
39.2	even	12		702.2.bb.a.197.9		56
117.41	even	12	inner	234.2.z.a.41.6	yes	56
117.67	odd	12		702.2.bc.a.665.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.1	✓	56	9.5	odd	6
234.2.y.a.119.1	yes	56	13.2	odd	12
234.2.z.a.41.6	yes	56	117.41	even	12	inner
234.2.z.a.137.6	yes	56	1.1	even	1	trivial
702.2.bb.a.197.9		56	39.2	even	12
702.2.bb.a.449.9		56	9.4	even	3
702.2.bc.a.665.9		56	117.67	odd	12
702.2.bc.a.683.9		56	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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.60665 + 0.647043i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.84756 + 0.763001i) q^{5} +(-1.38444 - 1.04083i) q^{6} +(-1.37958 + 1.37958i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.16267 + 2.07915i) q^{9} +(-2.55305 - 1.47400i) q^{10} +(0.207457 - 0.774238i) q^{11} +(1.06788 + 1.36368i) q^{12} +(-3.58657 + 0.369493i) q^{13} +(1.68964 - 0.975511i) q^{14} +(4.08135 + 3.06837i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-4.02058 - 6.96385i) q^{17} +(-1.55086 - 2.56804i) q^{18} +(-1.18319 + 4.41574i) q^{19} +(2.08456 + 2.08456i) q^{20} +(-3.10916 + 1.32386i) q^{21} +(-0.400775 + 0.694163i) q^{22} +6.99376 q^{23} +(-0.678548 - 1.59360i) q^{24} +(3.19629 + 1.84538i) q^{25} +(3.55999 + 0.571370i) q^{26} +(2.12937 + 4.73981i) q^{27} +(-1.88454 + 0.504962i) q^{28} +(6.82146 - 3.93837i) q^{29} +(-3.14812 - 4.02015i) q^{30} +(0.619046 - 2.31031i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.834276 - 1.10970i) q^{33} +(2.08121 + 7.76717i) q^{34} +(-4.98106 + 2.87582i) q^{35} +(0.833356 + 2.88193i) q^{36} +(-2.09658 - 7.82455i) q^{37} +(2.28576 - 3.95904i) q^{38} +(-6.00145 - 1.72702i) q^{39} +(-1.47400 - 2.55305i) q^{40} +(-3.66359 + 3.66359i) q^{41} +(3.34586 - 0.474043i) q^{42} -2.33382i q^{43} +(0.566782 - 0.566782i) q^{44} +(4.57194 + 7.57061i) q^{45} +(-6.75546 - 1.81012i) q^{46} +(-5.14869 + 1.37959i) q^{47} +(0.242972 + 1.71492i) q^{48} +3.19351i q^{49} +(-2.60976 - 2.60976i) q^{50} +(-1.95377 - 13.7900i) q^{51} +(-3.29081 - 1.47329i) q^{52} -8.27924i q^{53} +(-0.830059 - 5.12943i) q^{54} +(1.18149 - 2.04640i) q^{55} +1.95102 q^{56} +(-4.75815 + 6.32899i) q^{57} +(-7.60835 + 2.03865i) q^{58} +(-8.52709 + 2.28483i) q^{59} +(2.00036 + 4.69796i) q^{60} -4.93917 q^{61} +(-1.19590 + 2.07137i) q^{62} +(-5.85193 + 0.115230i) q^{63} +1.00000i q^{64} +(-10.4949 - 1.68440i) q^{65} +(-1.09306 + 0.855961i) q^{66} +(0.549015 + 0.549015i) q^{67} -8.04117i q^{68} +(11.2366 + 4.52526i) q^{69} +(5.55565 - 1.48863i) q^{70} +(-2.57304 - 0.689443i) q^{71} +(-0.0590613 - 2.99942i) q^{72} +(5.68293 - 5.68293i) q^{73} +8.10057i q^{74} +(3.94129 + 5.03302i) q^{75} +(-3.23255 + 3.23255i) q^{76} +(0.781921 + 1.35433i) q^{77} +(5.34997 + 3.22146i) q^{78} +(0.554497 - 0.960416i) q^{79} +(0.763001 + 2.84756i) q^{80} +(0.354299 + 8.99302i) q^{81} +(4.48696 - 2.59055i) q^{82} +(0.614312 + 2.29264i) q^{83} +(-3.35454 - 0.408081i) q^{84} +(-6.13542 - 22.8977i) q^{85} +(-0.604036 + 2.25429i) q^{86} +(13.5080 - 1.91382i) q^{87} +(-0.694163 + 0.400775i) q^{88} +(-2.84070 + 0.761164i) q^{89} +(-2.45674 - 8.49595i) q^{90} +(4.43822 - 5.45771i) q^{91} +(6.05678 + 3.49688i) q^{92} +(2.48946 - 3.31132i) q^{93} +5.33031 q^{94} +(-6.73843 + 11.6713i) q^{95} +(0.209163 - 1.71938i) q^{96} +(2.59780 + 2.59780i) q^{97} +(0.826542 - 3.08469i) q^{98} +(2.05842 - 1.24309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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