LMFDB - Embedded newform 756.2.cf.a.491.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.19
Character	$\chi$	$=$	756.491
Dual form			756.2.cf.a.659.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18843 + 0.766573i) q^{2} +(1.23300 - 1.21644i) q^{3} +(0.824730 - 1.82204i) q^{4} +(0.0717474 + 0.197124i) q^{5} +(-0.532841 + 2.39083i) q^{6} +(0.984808 - 0.173648i) q^{7} +(0.416592 + 2.79758i) q^{8} +(0.0405601 - 2.99973i) q^{9} +(-0.236377 - 0.179269i) q^{10} +(-5.85555 - 2.13125i) q^{11} +(-1.19950 - 3.24980i) q^{12} +(-3.71117 - 3.11405i) q^{13} +(-1.03726 + 0.961296i) q^{14} +(0.328254 + 0.155777i) q^{15} +(-2.63964 - 3.00538i) q^{16} +(-4.41652 - 2.54988i) q^{17} +(2.25131 + 3.59606i) q^{18} +(-5.39829 + 3.11670i) q^{19} +(0.418340 + 0.0318480i) q^{20} +(1.00303 - 1.41206i) q^{21} +(8.59267 - 1.95587i) q^{22} +(-1.34858 + 7.64816i) q^{23} +(3.91674 + 2.94265i) q^{24} +(3.79651 - 3.18565i) q^{25} +(6.79761 + 0.855936i) q^{26} +(-3.59897 - 3.74799i) q^{27} +(0.495807 - 1.93757i) q^{28} +(0.785750 + 0.936421i) q^{29} +(-0.509521 + 0.0665001i) q^{30} +(6.62883 + 1.16884i) q^{31} +(5.44087 + 1.54820i) q^{32} +(-9.81240 + 4.49509i) q^{33} +(7.20339 - 0.355235i) q^{34} +(0.104888 + 0.181671i) q^{35} +(-5.43216 - 2.54787i) q^{36} +(0.533310 - 0.923721i) q^{37} +(4.02630 - 7.84217i) q^{38} +(-8.36391 + 0.674805i) q^{39} +(-0.521582 + 0.282839i) q^{40} +(0.152505 - 0.181749i) q^{41} +(-0.109582 + 2.44704i) q^{42} +(1.44134 - 3.96006i) q^{43} +(-8.71246 + 8.91133i) q^{44} +(0.594229 - 0.207227i) q^{45} +(-4.26019 - 10.1231i) q^{46} +(0.716624 + 4.06418i) q^{47} +(-6.91052 - 0.494664i) q^{48} +(0.939693 - 0.342020i) q^{49} +(-2.06985 + 6.69623i) q^{50} +(-8.54732 + 2.22843i) q^{51} +(-8.73462 + 4.19365i) q^{52} -11.4415i q^{53} +(7.15023 + 1.69535i) q^{54} -1.30718i q^{55} +(0.896057 + 2.68274i) q^{56} +(-2.86480 + 10.4096i) q^{57} +(-1.65164 - 0.510535i) q^{58} +(-2.24509 + 0.817148i) q^{59} +(0.554553 - 0.469616i) q^{60} +(-0.920073 - 5.21799i) q^{61} +(-8.77390 + 3.69240i) q^{62} +(-0.480953 - 2.96120i) q^{63} +(-7.65290 + 2.33090i) q^{64} +(0.347587 - 0.954987i) q^{65} +(8.21553 - 12.8640i) q^{66} +(0.575651 - 0.686034i) q^{67} +(-8.28841 + 5.94410i) q^{68} +(7.64072 + 11.0706i) q^{69} +(-0.263916 - 0.135499i) q^{70} +(-0.384935 + 0.666726i) q^{71} +(8.40887 - 1.13619i) q^{72} +(4.12103 + 7.13783i) q^{73} +(0.0742979 + 1.50660i) q^{74} +(0.805940 - 8.54612i) q^{75} +(1.22662 + 12.4063i) q^{76} +(-6.13668 - 1.08206i) q^{77} +(9.42263 - 7.21351i) q^{78} +(-9.20396 - 10.9688i) q^{79} +(0.403046 - 0.735965i) q^{80} +(-8.99671 - 0.243339i) q^{81} +(-0.0419181 + 0.332903i) q^{82} +(9.07476 - 7.61463i) q^{83} +(-1.74560 - 2.99213i) q^{84} +(0.185769 - 1.05355i) q^{85} +(1.32274 + 5.81114i) q^{86} +(2.10792 + 0.198787i) q^{87} +(3.52296 - 17.2692i) q^{88} +(6.48916 - 3.74652i) q^{89} +(-0.547345 + 0.701795i) q^{90} +(-4.19554 - 2.42230i) q^{91} +(12.8230 + 8.76483i) q^{92} +(9.59514 - 6.62237i) q^{93} +(-3.96715 - 4.28064i) q^{94} +(-1.00169 - 0.840519i) q^{95} +(8.59187 - 4.70955i) q^{96} +(4.22718 + 1.53857i) q^{97} +(-0.854575 + 1.12681i) q^{98} +(-6.63065 + 17.4786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	−1.18843	+	0.766573i	−0.840347	+	0.542049i
$2$	−1.18843	+	0.766573i	−0.840347	+	0.542049i
$3$	1.23300	−	1.21644i	0.711871	−	0.702310i
$3$	1.23300	−	1.21644i	0.711871	−	0.702310i
$4$	0.824730	−	1.82204i	0.412365	−	0.911019i
$5$	0.0717474	+	0.197124i	0.0320864	+	0.0881567i	0.954701	−	0.297565i	$-0.0961746\pi$
$5$	0.0717474	+	0.197124i	0.0320864	+	0.0881567i	−0.922615	+	0.385722i	$0.873952\pi$
$6$	−0.532841	+	2.39083i	−0.217531	+	0.976053i
$7$	0.984808	−	0.173648i	0.372222	−	0.0656328i
$7$	0.984808	−	0.173648i	0.372222	−	0.0656328i
$8$	0.416592	+	2.79758i	0.147287	+	0.989094i
$9$	0.0405601	−	2.99973i	0.0135200	−	0.999909i
$10$	−0.236377	−	0.179269i	−0.0747490	−	0.0566898i
$11$	−5.85555	−	2.13125i	−1.76551	−	0.642595i	−0.765515	−	0.643418i	$-0.777516\pi$
$11$	−5.85555	−	2.13125i	−1.76551	−	0.642595i	−1.00000		0.000823427i	$0.999738\pi$
$12$	−1.19950	−	3.24980i	−0.346267	−	0.938136i
$13$	−3.71117	−	3.11405i	−1.02929	−	0.863681i	−0.0385277	−	0.999258i	$-0.512267\pi$
$13$	−3.71117	−	3.11405i	−1.02929	−	0.863681i	−0.990767	+	0.135577i	$0.956711\pi$
$14$	−1.03726	+	0.961296i	−0.277220	+	0.256917i
$15$	0.328254	+	0.155777i	0.0847547	+	0.0402215i
$16$	−2.63964	−	3.00538i	−0.659910	−	0.751345i
$17$	−4.41652	−	2.54988i	−1.07116	−	0.618436i	−0.142664	−	0.989771i	$-0.545567\pi$
$17$	−4.41652	−	2.54988i	−1.07116	−	0.618436i	−0.928499	+	0.371335i	$0.878900\pi$
$18$	2.25131	+	3.59606i	0.530638	+	0.847598i
$19$	−5.39829	+	3.11670i	−1.23845	+	0.715021i	−0.968778	−	0.247931i	$-0.920249\pi$
$19$	−5.39829	+	3.11670i	−1.23845	+	0.715021i	−0.269675	+	0.962952i	$0.586916\pi$
$20$	0.418340	+	0.0318480i	0.0935437	+	0.00712142i
$21$	1.00303	−	1.41206i	0.218880	−	0.308138i
$22$	8.59267	−	1.95587i	1.83196	−	0.416994i
$23$	−1.34858	+	7.64816i	−0.281198	+	1.59475i	0.437362	+	0.899286i	$0.355913\pi$
$23$	−1.34858	+	7.64816i	−0.281198	+	1.59475i	−0.718559	+	0.695466i	$0.755198\pi$
$24$	3.91674	+	2.94265i	0.799500	+	0.600665i
$25$	3.79651	−	3.18565i	0.759302	−	0.637130i
$26$	6.79761	+	0.855936i	1.33312	+	0.167863i
$27$	−3.59897	−	3.74799i	−0.692622	−	0.721301i
$28$	0.495807	−	1.93757i	0.0936988	−	0.366166i
$29$	0.785750	+	0.936421i	0.145910	+	0.173889i	0.834050	−	0.551690i	$-0.186017\pi$
$29$	0.785750	+	0.936421i	0.145910	+	0.173889i	−0.688139	+	0.725579i	$0.741572\pi$
$30$	−0.509521	+	0.0665001i	−0.0930254	+	0.0121412i
$31$	6.62883	+	1.16884i	1.19057	+	0.209930i	0.733619	−	0.679561i	$-0.237830\pi$
$31$	6.62883	+	1.16884i	1.19057	+	0.209930i	0.456953	+	0.889491i	$0.348941\pi$
$32$	5.44087	+	1.54820i	0.961819	+	0.273686i
$33$	−9.81240	+	4.49509i	−1.70812	+	0.782495i
$34$	7.20339	−	0.355235i	1.23537	−	0.0609223i
$35$	0.104888	+	0.181671i	0.0177292	+	0.0307080i
$36$	−5.43216	−	2.54787i	−0.905360	−	0.424644i
$37$	0.533310	−	0.923721i	0.0876757	−	0.151859i	−0.818853	−	0.574004i	$-0.805389\pi$
$37$	0.533310	−	0.923721i	0.0876757	−	0.151859i	0.906528	+	0.422145i	$0.138723\pi$
$38$	4.02630	−	7.84217i	0.653153	−	1.27217i
$39$	−8.36391	+	0.674805i	−1.33930	+	0.108055i
$40$	−0.521582	+	0.282839i	−0.0824693	+	0.0447208i
$41$	0.152505	−	0.181749i	0.0238174	−	0.0283844i	−0.754004	−	0.656869i	$-0.771880\pi$
$41$	0.152505	−	0.181749i	0.0238174	−	0.0283844i	0.777822	+	0.628485i	$0.216325\pi$
$42$	−0.109582	+	2.44704i	−0.0169089	+	0.377586i
$43$	1.44134	−	3.96006i	0.219803	−	0.603903i	−0.779957	−	0.625833i	$-0.784759\pi$
$43$	1.44134	−	3.96006i	0.219803	−	0.603903i	0.999760	+	0.0219304i	$0.00698121\pi$
$44$	−8.71246	+	8.91133i	−1.31345	+	1.34343i
$45$	0.594229	−	0.207227i	0.0885824	−	0.0308916i
$46$	−4.26019	−	10.1231i	−0.628130	−	1.49257i
$47$	0.716624	+	4.06418i	0.104530	+	0.592821i	0.991407	+	0.130815i	$0.0417592\pi$
$47$	0.716624	+	4.06418i	0.104530	+	0.592821i	−0.886876	+	0.462007i	$0.847130\pi$
$48$	−6.91052	−	0.494664i	−0.997448	−	0.0713986i
$49$	0.939693	−	0.342020i	0.134242	−	0.0488600i
$50$	−2.06985	+	6.69623i	−0.292721	+	0.946990i
$51$	−8.54732	+	2.22843i	−1.19686	+	0.312042i
$52$	−8.73462	+	4.19365i	−1.21127	+	0.581555i
$53$		−	11.4415i		−	1.57162i	−0.618470	−	0.785808i	$-0.712247\pi$
$53$		−	11.4415i		−	1.57162i	0.618470	−	0.785808i	$-0.287753\pi$
$54$	7.15023	+	1.69535i	0.973023	+	0.230708i
$55$		−	1.30718i		−	0.176260i
$56$	0.896057	+	2.68274i	0.119741	+	0.358496i
$57$	−2.86480	+	10.4096i	−0.379451	+	1.37878i
$58$	−1.65164	−	0.510535i	−0.216871	−	0.0670365i
$59$	−2.24509	+	0.817148i	−0.292286	+	0.106384i	−0.484002	−	0.875067i	$-0.660817\pi$
$59$	−2.24509	+	0.817148i	−0.292286	+	0.106384i	0.191715	+	0.981451i	$0.438595\pi$
$60$	0.554553	−	0.469616i	0.0715925	−	0.0606272i
$61$	−0.920073	−	5.21799i	−0.117803	−	0.668096i	−0.985324	−	0.170695i	$-0.945399\pi$
$61$	−0.920073	−	5.21799i	−0.117803	−	0.668096i	0.867521	−	0.497401i	$-0.165712\pi$
$62$	−8.77390	+	3.69240i	−1.11429	+	0.468935i
$63$	−0.480953	−	2.96120i	−0.0605944	−	0.373076i
$64$	−7.65290	+	2.33090i	−0.956613	+	0.291362i
$65$	0.347587	−	0.954987i	0.0431129	−	0.118452i
$66$	8.21553	−	12.8640i	1.01126	−	1.58345i
$67$	0.575651	−	0.686034i	0.0703269	−	0.0838124i	−0.729734	−	0.683731i	$-0.760356\pi$
$67$	0.575651	−	0.686034i	0.0703269	−	0.0838124i	0.800061	+	0.599919i	$0.204800\pi$
$68$	−8.28841	+	5.94410i	−1.00512	+	0.720828i
$69$	7.64072	+	11.0706i	0.919834	+	1.33275i
$70$	−0.263916	−	0.135499i	−0.0315439	−	0.0161952i
$71$	−0.384935	+	0.666726i	−0.0456833	+	0.0791258i	−0.887963	−	0.459915i	$-0.847880\pi$
$71$	−0.384935	+	0.666726i	−0.0456833	+	0.0791258i	0.842280	+	0.539041i	$0.181213\pi$
$72$	8.40887	−	1.13619i	0.990995	−	0.133901i
$73$	4.12103	+	7.13783i	0.482330	+	0.835420i	0.999794	−	0.0202848i	$-0.00645729\pi$
$73$	4.12103	+	7.13783i	0.482330	+	0.835420i	−0.517464	+	0.855705i	$0.673124\pi$
$74$	0.0742979	+	1.50660i	0.00863695	+	0.175139i
$75$	0.805940	−	8.54612i	0.0930619	−	0.986820i
$76$	1.22662	+	12.4063i	0.140703	+	1.42310i
$77$	−6.13668	−	1.08206i	−0.699339	−	0.123312i
$78$	9.42263	−	7.21351i	1.06690	−	0.816769i
$79$	−9.20396	−	10.9688i	−1.03553	−	1.23409i	−0.971722	−	0.236129i	$-0.924121\pi$
$79$	−9.20396	−	10.9688i	−1.03553	−	1.23409i	−0.0638044	−	0.997962i	$-0.520323\pi$
$80$	0.403046	−	0.735965i	0.0450619	−	0.0822834i
$81$	−8.99671	−	0.243339i	−0.999634	−	0.0270376i
$82$	−0.0419181	+	0.332903i	−0.00462908	+	0.0367629i
$83$	9.07476	−	7.61463i	0.996085	−	0.835814i	0.00964762	−	0.999953i	$-0.496929\pi$
$83$	9.07476	−	7.61463i	0.996085	−	0.835814i	0.986437	+	0.164139i	$0.0524846\pi$
$84$	−1.74560	−	2.99213i	−0.190461	−	0.326469i
$85$	0.185769	−	1.05355i	0.0201495	−	0.114274i
$86$	1.32274	+	5.81114i	0.142635	+	0.626632i
$87$	2.10792	+	0.198787i	0.225993	+	0.0213122i
$88$	3.52296	−	17.2692i	0.375548	−	1.84091i
$89$	6.48916	−	3.74652i	0.687849	−	0.397130i	−0.114957	−	0.993371i	$-0.536673\pi$
$89$	6.48916	−	3.74652i	0.687849	−	0.397130i	0.802806	+	0.596241i	$0.203340\pi$
$90$	−0.547345	+	0.701795i	−0.0576952	+	0.0739757i
$91$	−4.19554	−	2.42230i	−0.439812	−	0.253926i
$92$	12.8230	+	8.76483i	1.33689	+	0.913796i
$93$	9.59514	−	6.62237i	0.994970	−	0.686708i
$94$	−3.96715	−	4.28064i	−0.409180	−	0.441515i
$95$	−1.00169	−	0.840519i	−0.102771	−	0.0862354i
$96$	8.59187	−	4.70955i	0.876904	−	0.480666i
$97$	4.22718	+	1.53857i	0.429205	+	0.156218i	0.547584	−	0.836751i	$-0.315548\pi$
$97$	4.22718	+	1.53857i	0.429205	+	0.156218i	−0.118379	+	0.992968i	$0.537770\pi$
$98$	−0.854575	+	1.12681i	−0.0863251	+	0.113825i
$99$	−6.63065	+	17.4786i	−0.666406	+	1.75667i
$100$	−2.67328	−	9.54469i	−0.267328	−	0.954469i
$101$	−2.40817	+	0.424626i	−0.239622	+	0.0422519i	−0.292169	−	0.956367i	$-0.594377\pi$
$101$	−2.40817	+	0.424626i	−0.239622	+	0.0422519i	0.0525471	+	0.998618i	$0.483266\pi$
$102$	8.44963	−	9.20048i	0.836639	−	0.910983i
$103$	−5.73157	−	15.7474i	−0.564749	−	1.55163i	−0.812591	−	0.582834i	$-0.801944\pi$
$103$	−5.73157	−	15.7474i	−0.564749	−	1.55163i	0.247842	−	0.968800i	$-0.420279\pi$
$104$	7.16574	−	11.6796i	0.702659	−	1.14528i
$105$	0.350317	+	0.0964101i	0.0341875	+	0.00940866i
$106$	8.77078	+	13.5975i	0.851894	+	1.32070i
$107$	1.48660			0.143715			0.0718576	−	0.997415i	$-0.477107\pi$
$107$	1.48660			0.143715			0.0718576	+	0.997415i	$0.477107\pi$
$108$	−9.79716	+	3.46637i	−0.942732	+	0.333552i
$109$	−3.72833			−0.357109			−0.178555	−	0.983930i	$-0.557142\pi$
$109$	−3.72833			−0.357109			−0.178555	+	0.983930i	$0.557142\pi$
$110$	1.00205	+	1.55349i	0.0955418	+	0.148120i
$111$	−0.466079	−	1.78768i	−0.0442382	−	0.169679i
$112$	−3.12142	−	2.50135i	−0.294946	−	0.236355i
$113$	2.48695	+	6.83284i	0.233952	+	0.642779i	1.00000		4.78492e-6i	$-1.52309e-6\pi$
$113$	2.48695	+	6.83284i	0.233952	+	0.642779i	−0.766048	+	0.642784i	$0.777779\pi$
$114$	−4.57509	−	14.5671i	−0.428496	−	1.36433i
$115$	−1.60439	+	0.282898i	−0.149611	+	0.0263804i
$116$	2.35423	−	0.659372i	0.218584	−	0.0612211i
$117$	−9.49181	+	11.0062i	−0.877518	+	1.01752i
$118$	2.04173	−	2.69215i	0.187957	−	0.247833i
$119$	−4.79220	−	1.74422i	−0.439301	−	0.159892i
$120$	−0.299052	+	0.983211i	−0.0272996	+	0.0897545i
$121$	21.3188	+	17.8886i	1.93807	+	1.62623i
$122$	5.09342	+	5.49592i	0.461136	+	0.497577i
$123$	−0.0330475	−	0.409609i	−0.00297979	−	0.0369332i
$124$	7.59666	−	11.1140i	0.682201	−	0.998066i
$125$	1.80871	+	1.04426i	0.161776	+	0.0934015i
$126$	2.84155	+	3.15049i	0.253146	+	0.280668i
$127$	12.3817	−	7.14855i	1.09869	−	0.634332i	0.162817	−	0.986656i	$-0.447942\pi$
$127$	12.3817	−	7.14855i	1.09869	−	0.634332i	0.935878	+	0.352325i	$0.114609\pi$
$128$	7.30813	−	8.63662i	0.645954	−	0.763376i
$129$	−3.03999	−	6.63604i	−0.267656	−	0.584271i
$130$	0.318985	+	1.40139i	0.0279769	+	0.122910i
$131$	0.185325	−	1.05103i	0.0161919	−	0.0918289i	−0.975641	−	0.219374i	$-0.929599\pi$
$131$	0.185325	−	1.05103i	0.0161919	−	0.0918289i	0.991833	+	0.127545i	$0.0407097\pi$
$132$	0.0976422	+	21.5858i	0.00849866	+	1.87880i
$133$	−4.77507	+	4.00676i	−0.414051	+	0.347430i
$134$	−0.158225	+	1.25658i	−0.0136686	+	0.108552i
$135$	0.480603	−	0.978353i	0.0413638	−	0.0842032i
$136$	5.29360	−	13.4178i	0.453923	−	1.15057i
$137$	−9.13164	−	10.8827i	−0.780168	−	0.929768i	0.218773	−	0.975776i	$-0.429795\pi$
$137$	−9.13164	−	10.8827i	−0.780168	−	0.929768i	−0.998941	+	0.0460075i	$0.985350\pi$
$138$	−17.5669	−	7.29947i	−1.49539	−	0.621372i
$139$	−9.99320	−	1.76207i	−0.847613	−	0.149457i	−0.267060	−	0.963680i	$-0.586052\pi$
$139$	−9.99320	−	1.76207i	−0.847613	−	0.149457i	−0.580552	+	0.814223i	$0.697163\pi$
$140$	0.417515	−	0.0412799i	0.0352864	−	0.00348879i
$141$	5.82741	+	4.13939i	0.490757	+	0.348599i
$142$	−0.0536270	−	1.08744i	−0.00450028	−	0.0912558i
$143$	15.0942	+	26.1439i	1.26224	+	2.18626i
$144$	−9.12238	+	7.79630i	−0.760198	+	0.649691i
$145$	−0.128216	+	0.222076i	−0.0106477	+	0.0184424i
$146$	−10.3692	−	5.32374i	−0.858163	−	0.440596i
$147$	0.742592	−	1.56479i	0.0612479	−	0.129061i
$148$	−1.24322	−	1.73353i	−0.102192	−	0.142495i
$149$	4.56683	−	5.44254i	0.374129	−	0.445870i	−0.545823	−	0.837901i	$-0.683783\pi$
$149$	4.56683	−	5.44254i	0.374129	−	0.445870i	0.919952	+	0.392031i	$0.128227\pi$
$150$	5.59342	+	10.7743i	0.456701	+	0.879715i
$151$	3.88873	−	10.6842i	0.316460	−	0.869467i	−0.674854	−	0.737951i	$-0.735793\pi$
$151$	3.88873	−	10.6842i	0.316460	−	0.869467i	0.991314	−	0.131516i	$-0.0419844\pi$
$152$	−10.9681	−	13.8037i	−0.889631	−	1.11963i
$153$	−7.82807	+	13.1449i	−0.632862	+	1.06270i
$154$	8.12249	−	3.41826i	0.654529	−	0.275451i
$155$	0.245194	+	1.39056i	0.0196945	+	0.111693i
$156$	−5.66845	+	15.7959i	−0.453839	+	1.26468i
$157$	−1.63189	+	0.593959i	−0.130239	+	0.0474031i	−0.406317	−	0.913732i	$-0.633187\pi$
$157$	−1.63189	+	0.593959i	−0.130239	+	0.0474031i	0.276078	+	0.961135i	$0.410965\pi$
$158$	19.3467	+	5.98020i	1.53914	+	0.475759i
$159$	−13.9179	−	14.1074i	−1.10376	−	1.11879i
$160$	0.0851797	+	1.18361i	0.00673405	+	0.0935724i
$161$			7.76614i			0.612058i
$162$	10.8785	−	6.60745i	0.854695	−	0.519130i
$163$		−	1.64783i		−	0.129068i	−0.997916	−	0.0645340i	$-0.979444\pi$
$163$		−	1.64783i		−	0.129068i	0.997916	−	0.0645340i	$-0.0205561\pi$
$164$	−0.205378	−	0.427765i	−0.0160373	−	0.0334028i
$165$	−1.59011	−	1.61175i	−0.123790	−	0.125475i
$166$	−4.94755	+	16.0059i	−0.384004	+	1.24230i
$167$	−17.5610	+	6.39168i	−1.35891	+	0.494603i	−0.915717	−	0.401823i	$-0.868377\pi$
$167$	−17.5610	+	6.39168i	−1.35891	+	0.494603i	−0.443193	+	0.896426i	$0.646155\pi$
$168$	4.36822	+	2.21781i	0.337015	+	0.171108i
$169$	1.81811	+	10.3110i	0.139855	+	0.793156i
$170$	0.586850	+	1.39448i	0.0450093	+	0.106951i
$171$	9.13030	+	16.3198i	0.698212	+	1.24801i
$172$	−6.02665	−	5.89216i	−0.459528	−	0.449273i
$173$	4.03284	−	11.0801i	0.306611	−	0.842406i	−0.686701	−	0.726940i	$-0.740942\pi$
$173$	4.03284	−	11.0801i	0.306611	−	0.842406i	0.993311	−	0.115466i	$-0.0368361\pi$
$174$	−2.65750	+	1.37963i	−0.201465	+	0.104590i
$175$	3.18565	−	3.79651i	0.240813	−	0.286989i
$176$	9.05134	+	23.2239i	0.682271	+	1.75056i
$177$	−1.77418	+	3.73856i	−0.133356	+	0.281007i
$178$	−4.83993	+	9.42689i	−0.362768	+	0.706575i
$179$	−5.20055	+	9.00762i	−0.388707	+	0.673261i	−0.992276	−	0.124050i	$-0.960412\pi$
$179$	−5.20055	+	9.00762i	−0.388707	+	0.673261i	0.603569	+	0.797311i	$0.293745\pi$
$180$	0.112503	−	1.25361i	0.00838549	−	0.0934389i
$181$	4.19189	+	7.26056i	0.311581	+	0.539673i	0.978705	−	0.205273i	$-0.0658083\pi$
$181$	4.19189	+	7.26056i	0.311581	+	0.539673i	−0.667124	+	0.744947i	$0.732475\pi$
$182$	6.84297	−	0.337461i	0.507235	−	0.0250143i
$183$	−7.48181	−	5.31456i	−0.553071	−	0.392863i
$184$	−21.9581	−	0.586592i	−1.61878	−	0.0432442i
$185$	0.220351	+	0.0388539i	0.0162006	+	0.00285660i
$186$	−6.32661	+	15.2256i	−0.463890	+	1.11640i
$187$	20.4267	+	24.3436i	1.49375	+	1.78018i
$188$	7.99610	+	2.04613i	0.583176	+	0.149230i
$189$	−4.19512	−	3.06610i	−0.305150	−	0.223026i
$190$	1.83476	+	0.231027i	0.133107	+	0.0167605i
$191$	16.8136	−	14.1083i	1.21659	−	1.02084i	0.217593	−	0.976040i	$-0.430179\pi$
$191$	16.8136	−	14.1083i	1.21659	−	1.02084i	0.998996	−	0.0447997i	$-0.0142650\pi$
$192$	−6.60061	+	12.1833i	−0.476358	+	0.879251i
$193$	−1.31791	+	7.47424i	−0.0948652	+	0.538007i	0.899923	+	0.436048i	$0.143622\pi$
$193$	−1.31791	+	7.47424i	−0.0948652	+	0.538007i	−0.994789	+	0.101959i	$0.967489\pi$
$194$	−6.20313	+	1.41196i	−0.445359	+	0.101373i
$195$	−0.733109	−	1.60031i	−0.0524990	−	0.114601i
$196$	0.151819	−	1.99423i	0.0108442	−	0.142445i
$197$	4.99172	−	2.88197i	0.355645	−	0.205332i	−0.311524	−	0.950238i	$-0.600839\pi$
$197$	4.99172	−	2.88197i	0.355645	−	0.205332i	0.667169	+	0.744907i	$0.267506\pi$
$198$	−5.51856	−	25.8550i	−0.392187	−	1.83743i
$199$	11.6784	+	6.74251i	0.827858	+	0.477964i	0.853119	−	0.521717i	$-0.174708\pi$
$199$	11.6784	+	6.74251i	0.827858	+	0.477964i	−0.0252608	+	0.999681i	$0.508042\pi$
$200$	10.4937	+	9.29393i	0.742017	+	0.657180i
$201$	−0.124742	−	1.54612i	−0.00879862	−	0.109055i
$202$	2.53644	−	2.35068i	0.178463	−	0.165393i
$203$	0.936421	+	0.785750i	0.0657238	+	0.0551488i
$204$	−2.98895	+	17.4114i	−0.209269	+	1.21904i
$205$	0.0467690	+	0.0170225i	0.00326649	+	0.00118890i
$206$	18.8831	+	14.3210i	1.31565	+	0.997789i
$207$	22.8877	+	4.35557i	1.59080	+	0.302733i
$208$	0.437280	+	19.3734i	0.0303199	+	1.34331i
$209$	38.2524	−	6.74493i	2.64597	−	0.466557i
$210$	−0.490233	+	0.153967i	−0.0338293	+	0.0106247i
$211$	8.34201	+	22.9195i	0.574288	+	1.57784i	0.797659	+	0.603109i	$0.206071\pi$
$211$	8.34201	+	22.9195i	0.574288	+	1.57784i	−0.223372	+	0.974733i	$0.571706\pi$
$212$	−20.8469	−	9.43618i	−1.43177	−	0.648080i
$213$	0.336408	+	1.29032i	0.0230503	+	0.0884113i
$214$	−1.76672	+	1.13959i	−0.120771	+	0.0779007i
$215$	0.884036			0.0602908
$216$	8.98600	−	11.6298i	0.611420	−	0.791306i
$217$	6.73109			0.456936
$218$	4.43086	−	2.85804i	0.300096	−	0.193571i
$219$	13.7639	+	3.78795i	0.930081	+	0.255966i
$220$	−2.38174	−	1.07807i	−0.160577	−	0.0726837i
$221$	8.45004	+	23.2163i	0.568411	+	1.56170i
$222$	1.92429	+	1.76725i	0.129150	+	0.118610i
$223$	−18.6823	+	3.29419i	−1.25106	+	0.220595i	−0.759648	−	0.650334i	$-0.774629\pi$
$223$	−18.6823	+	3.29419i	−1.25106	+	0.220595i	−0.491409	+	0.870929i	$0.663518\pi$
$224$	5.62705	+	0.579885i	0.375973	+	0.0387452i
$225$	−9.40209	−	11.5177i	−0.626806	−	0.767847i
$226$	−8.19343	−	6.21392i	−0.545019	−	0.413344i
$227$	−27.0870	−	9.85886i	−1.79783	−	0.654355i	−0.998575	−	0.0533578i	$-0.983008\pi$
$227$	−27.0870	−	9.85886i	−1.79783	−	0.654355i	−0.799251	−	0.600998i	$-0.794770\pi$
$228$	16.6039	+	13.8048i	1.09962	+	0.914248i
$229$	13.7251	+	11.5168i	0.906982	+	0.761049i	0.971543	−	0.236865i	$-0.0761200\pi$
$229$	13.7251	+	11.5168i	0.906982	+	0.761049i	−0.0645601	+	0.997914i	$0.520564\pi$
$230$	1.68985	−	1.56609i	0.111425	−	0.103265i
$231$	−8.88276	+	6.13071i	−0.584443	+	0.403371i
$232$	−2.29237	+	2.58830i	−0.150502	+	0.169930i
$233$	−13.9351	−	8.04542i	−0.912917	−	0.527073i	−0.0315484	−	0.999502i	$-0.510044\pi$
$233$	−13.9351	−	8.04542i	−0.912917	−	0.527073i	−0.881369	+	0.472429i	$0.843377\pi$
$234$	2.84328	−	20.3563i	0.185871	−	1.33073i
$235$	−0.749732	+	0.432858i	−0.0489071	+	0.0282365i
$236$	−0.362724	+	4.76457i	−0.0236113	+	0.310147i
$237$	−24.6914	−	2.32851i	−1.60388	−	0.151253i
$238$	7.03227	−	1.60069i	0.455834	−	0.103758i
$239$	3.65297	−	20.7170i	0.236291	−	1.34007i	−0.603586	−	0.797298i	$-0.706262\pi$
$239$	3.65297	−	20.7170i	0.236291	−	1.34007i	0.839878	−	0.542776i	$-0.182627\pi$
$240$	−0.398302	−	1.39772i	−0.0257103	−	0.0902226i
$241$	−16.9436	+	14.2174i	−1.09143	+	0.915821i	−0.996819	−	0.0796926i	$-0.974606\pi$
$241$	−16.9436	+	14.2174i	−1.09143	+	0.915821i	−0.0946140	+	0.995514i	$0.530162\pi$
$242$	−39.0487	−	4.91690i	−2.51015	−	0.316071i
$243$	−11.3889	+	10.6439i	−0.730599	+	0.682806i
$244$	−10.2662	−	2.62703i	−0.657226	−	0.168178i
$245$	0.134841	+	0.160697i	0.00861467	+	0.0102666i
$246$	0.353270	+	0.461458i	0.0225237	+	0.0294215i
$247$	29.7395	+	5.24388i	1.89228	+	0.333660i
$248$	−0.508412	+	19.0316i	−0.0322842	+	1.20851i
$249$	1.92643	−	20.4277i	0.122082	−	1.29455i
$250$	−2.95003	+	0.145481i	−0.186576	+	0.00920101i
$251$	4.12931	+	7.15217i	0.260640	+	0.451441i	0.966412	−	0.256998i	$-0.0827332\pi$
$251$	4.12931	+	7.15217i	0.260640	+	0.451441i	−0.705772	+	0.708439i	$0.749400\pi$
$252$	−5.79207	−	1.56587i	−0.364866	−	0.0986408i
$253$	24.1968	−	41.9100i	1.52124	−	2.63486i
$254$	−9.23484	+	17.9870i	−0.579445	+	1.12861i
$255$	−1.05253	−	1.52500i	−0.0659117	−	0.0954992i
$256$	−2.06460	+	15.8662i	−0.129038	+	0.991640i
$257$	−0.0582263	+	0.0693914i	−0.00363206	+	0.00432852i	−0.767857	−	0.640621i	$-0.778677\pi$
$257$	−0.0582263	+	0.0693914i	−0.00363206	+	0.00432852i	0.764225	+	0.644949i	$0.223122\pi$
$258$	8.69983	+	5.55609i	0.541628	+	0.345907i
$259$	0.364806	−	1.00230i	0.0226679	−	0.0622796i
$260$	−1.45336	−	1.42092i	−0.0901334	−	0.0881219i
$261$	2.84087	−	2.31905i	0.175846	−	0.143546i
$262$	0.585446	+	1.39114i	0.0361690	+	0.0859450i
$263$	−0.676321	−	3.83561i	−0.0417037	−	0.236514i	0.956830	−	0.290648i	$-0.0938710\pi$
$263$	−0.676321	−	3.83561i	−0.0417037	−	0.236514i	−0.998534	+	0.0541349i	$0.982760\pi$
$264$	−16.6631	−	25.5783i	−1.02555	−	1.57424i
$265$	2.25541	−	0.820901i	0.138548	−	0.0504275i
$266$	2.60336	−	8.42219i	0.159622	−	0.516397i
$267$	3.44370	−	12.5131i	0.210751	−	0.765789i
$268$	−0.775223	−	1.61465i	−0.0473543	−	0.0986304i
$269$		−	28.3156i		−	1.72643i	−0.504834	−	0.863217i	$-0.668446\pi$
$269$		−	28.3156i		−	1.72643i	0.504834	−	0.863217i	$-0.331554\pi$
$270$	0.178816	+	1.53112i	0.0108824	+	0.0931811i
$271$			16.1786i			0.982781i	0.870939	+	0.491390i	$0.163511\pi$
$271$			16.1786i			0.982781i	−0.870939	+	0.491390i	$0.836489\pi$
$272$	3.99467	+	20.0041i	0.242212	+	1.21293i
$273$	−8.11966	+	2.11693i	−0.491424	+	0.128122i
$274$	19.1947	+	5.93321i	1.15959	+	0.358438i
$275$	−29.0201	+	10.5624i	−1.74998	+	0.636939i
$276$	26.4726	−	4.79140i	1.59346	−	0.288409i
$277$	−0.191326	−	1.08506i	−0.0114956	−	0.0651951i	0.978520	−	0.206151i	$-0.0660937\pi$
$277$	−0.191326	−	1.08506i	−0.0114956	−	0.0651951i	−0.990016	+	0.140955i	$0.954983\pi$
$278$	13.2270	−	5.56643i	0.793301	−	0.333852i
$279$	3.77507	−	19.8373i	0.226007	−	1.18763i
$280$	−0.464543	+	0.369114i	−0.0277618	+	0.0220588i
$281$	4.66580	−	12.8192i	0.278338	−	0.764728i	−0.719213	−	0.694789i	$-0.755498\pi$
$281$	4.66580	−	12.8192i	0.278338	−	0.764728i	0.997551	−	0.0699382i	$-0.0222802\pi$
$282$	−10.0986	−	0.452231i	−0.601364	−	0.0269300i
$283$	−2.63433	+	3.13947i	−0.156595	+	0.186622i	−0.838637	−	0.544690i	$-0.816647\pi$
$283$	−2.63433	+	3.13947i	−0.156595	+	0.186622i	0.682043	+	0.731312i	$0.261092\pi$
$284$	0.897333	+	1.25123i	0.0532469	+	0.0742471i
$285$	−2.25752	+	0.182138i	−0.133724	+	0.0107889i
$286$	−37.9796	−	19.4994i	−2.24578	−	1.15302i
$287$	0.118628	−	0.205470i	0.00700240	−	0.0121285i
$288$	4.86487	−	16.2583i	0.286665	−	0.958031i
$289$	4.50376	+	7.80074i	0.264927	+	0.458867i
$290$	−0.0178623	−	0.362209i	−0.00104891	−	0.0212696i
$291$	7.08367	−	3.24505i	0.415252	−	0.190228i
$292$	16.4041	−	1.62188i	0.959979	−	0.0949135i
$293$	−12.3857	−	2.18393i	−0.723581	−	0.127587i	−0.200285	−	0.979738i	$-0.564187\pi$
$293$	−12.3857	−	2.18393i	−0.723581	−	0.127587i	−0.523296	+	0.852151i	$0.675298\pi$
$294$	0.317006	+	2.42889i	0.0184882	+	0.141656i
$295$	−0.322159	−	0.383935i	−0.0187568	−	0.0223535i
$296$	2.80635	+	1.10716i	0.163116	+	0.0643526i
$297$	13.0860	+	29.6168i	0.759330	+	1.71854i
$298$	−1.25525	+	9.96889i	−0.0727149	+	0.577482i
$299$	28.8215	−	24.1841i	1.66679	−	1.39860i
$300$	−14.9067	−	8.51669i	−0.860636	−	0.491711i
$301$	0.731789	−	4.15018i	0.0421796	−	0.239212i
$302$	3.56874	+	15.6784i	0.205358	+	0.902191i
$303$	−2.45274	+	3.45296i	−0.140906	+	0.198367i
$304$	23.6164	+	7.99693i	1.35449	+	0.458655i
$305$	0.962581	−	0.555746i	0.0551172	−	0.0318219i
$306$	−0.773437	−	21.6226i	−0.0442145	−	1.23608i
$307$	−22.0800	−	12.7479i	−1.26017	−	0.727562i	−0.287066	−	0.957911i	$-0.592680\pi$
$307$	−22.0800	−	12.7479i	−1.26017	−	0.727562i	−0.973108	+	0.230349i	$0.926013\pi$
$308$	−7.03266	+	10.2888i	−0.400723	+	0.586261i
$309$	−26.2227	−	12.4444i	−1.49176	−	0.707934i
$310$	−1.35737	−	1.46463i	−0.0770932	−	0.0831853i
$311$	10.3068	+	8.64842i	0.584444	+	0.490407i	0.886403	−	0.462914i	$-0.153196\pi$
$311$	10.3068	+	8.64842i	0.584444	+	0.490407i	−0.301959	+	0.953321i	$0.597641\pi$
$312$	−5.37215	−	23.1176i	−0.304138	−	1.30877i
$313$	−27.7439	−	10.0980i	−1.56818	−	0.570771i	−0.595588	−	0.803290i	$-0.703081\pi$
$313$	−27.7439	−	10.0980i	−1.56818	−	0.570771i	−0.972592	+	0.232519i	$0.925303\pi$
$314$	1.48407	−	1.95684i	0.0837510	−	0.110431i
$315$	0.549217	−	0.307266i	0.0309449	−	0.0173125i
$316$	−27.5764	+	7.72361i	−1.55130	+	0.434487i
$317$	1.03874	−	0.183159i	0.0583417	−	0.0102872i	−0.144401	−	0.989519i	$-0.546126\pi$
$317$	1.03874	−	0.183159i	0.0583417	−	0.0102872i	0.202743	+	0.979232i	$0.435014\pi$
$318$	27.3548	+	6.09652i	1.53398	+	0.341876i
$319$	−2.60526	−	7.15788i	−0.145866	−	0.400765i
$320$	−1.00855	−	1.34134i	−0.0563798	−	0.0749830i
$321$	1.83297	−	1.80836i	0.102307	−	0.100933i
$322$	−5.95332	−	9.22952i	−0.331766	−	0.514341i
$323$	31.7889			1.76878
$324$	−7.86323	+	16.1917i	−0.436846	+	0.899536i
$325$	−24.0098			−1.33182
$326$	1.26318	+	1.95833i	0.0699613	+	0.108462i
$327$	−4.59702	+	4.53528i	−0.254216	+	0.250802i
$328$	0.571990	+	0.350931i	0.0315828	+	0.0193769i
$329$	1.41147	+	3.87799i	0.0778171	+	0.213801i
$330$	3.12525	+	0.696520i	0.172040	+	0.0383422i
$331$	19.7283	−	3.47864i	1.08437	−	0.191203i	0.397222	−	0.917723i	$-0.369974\pi$
$331$	19.7283	−	3.47864i	1.08437	−	0.191203i	0.687146	+	0.726519i	$0.258863\pi$
$332$	−6.38991	−	22.8146i	−0.350692	−	1.25211i
$333$	−2.74928	−	1.63725i	−0.150659	−	0.0897208i
$334$	15.9703	−	21.0579i	0.873857	−	1.15223i
$335$	0.176535	+	0.0642536i	0.00964516	+	0.00351055i
$336$	−6.89143	+	0.712851i	−0.375958	+	0.0388892i
$337$	13.4342	+	11.2726i	0.731807	+	0.614059i	0.930624	−	0.365978i	$-0.119265\pi$
$337$	13.4342	+	11.2726i	0.731807	+	0.614059i	−0.198817	+	0.980037i	$0.563710\pi$
$338$	−10.0649	−	10.8602i	−0.547456	−	0.590718i
$339$	11.3781	+	5.39964i	0.617974	+	0.293268i
$340$	−1.76640	−	1.20737i	−0.0957964	−	0.0654790i
$341$	−36.3243	−	20.9719i	−1.96707	−	1.13569i
$342$	−23.3610	−	12.3959i	−1.26322	−	0.670293i
$343$	0.866025	−	0.500000i	0.0467610	−	0.0269975i
$344$	11.6790	+	2.38255i	0.629691	+	0.128458i
$345$	−1.63409	+	2.30046i	−0.0879762	+	0.123853i
$346$	3.70099	+	16.2594i	0.198966	+	0.874112i
$347$	−5.31242	+	30.1282i	−0.285186	+	1.61737i	0.419435	+	0.907785i	$0.362228\pi$
$347$	−5.31242	+	30.1282i	−0.285186	+	1.61737i	−0.704621	+	0.709584i	$0.748883\pi$
$348$	2.10067	−	3.67677i	0.112608	−	0.197096i
$349$	−0.266906	+	0.223960i	−0.0142871	+	0.0119883i	−0.649903	−	0.760017i	$-0.725191\pi$
$349$	−0.266906	+	0.223960i	−0.0142871	+	0.0119883i	0.635616	+	0.772005i	$0.280746\pi$
$350$	−0.875618	+	6.95392i	−0.0468037	+	0.371703i
$351$	1.68499	+	25.1168i	0.0899381	+	1.34064i
$352$	−28.5597	−	20.6614i	−1.52224	−	1.10126i
$353$	−5.54325	−	6.60619i	−0.295038	−	0.351612i	0.598079	−	0.801437i	$-0.295931\pi$
$353$	−5.54325	−	6.60619i	−0.295038	−	0.351612i	−0.893117	+	0.449825i	$0.851486\pi$
$354$	−0.757385	−	5.80305i	−0.0402546	−	0.308429i
$355$	−0.159046	−	0.0280441i	−0.00844129	−	0.00148843i
$356$	−1.47449	−	14.9134i	−0.0781478	−	0.790406i
$357$	−8.03050	+	3.67880i	−0.425019	+	0.194703i
$358$	−0.724512	−	14.6915i	−0.0382917	−	0.776471i
$359$	−11.3409	−	19.6431i	−0.598551	−	1.03672i	−0.993035	−	0.117818i	$-0.962410\pi$
$359$	−11.3409	−	19.6431i	−0.598551	−	1.03672i	0.394484	−	0.918903i	$-0.370923\pi$
$360$	0.827285	+	1.57607i	0.0436017	+	0.0830664i
$361$	9.92768	−	17.1952i	0.522509	−	0.905013i
$362$	−10.5475	−	5.41528i	−0.554365	−	0.284621i
$363$	48.0463	−	3.87640i	2.52178	−	0.203458i
$364$	−7.87371	+	5.64669i	−0.412694	+	0.295967i
$365$	−1.11137	+	1.32448i	−0.0581716	+	0.0693262i
$366$	12.9656	+	0.580620i	0.677723	+	0.0303495i
$367$	0.638598	−	1.75453i	0.0333346	−	0.0915860i	−0.921909	−	0.387407i	$-0.873371\pi$
$367$	0.638598	−	1.75453i	0.0333346	−	0.0915860i	0.955243	+	0.295821i	$0.0955931\pi$
$368$	26.5454	−	16.1354i	1.38377	−	0.841116i
$369$	−0.539011	−	0.464846i	−0.0280598	−	0.0241989i
$370$	−0.291657	+	0.122740i	−0.0151625	+	0.00638097i
$371$	−1.98680	−	11.2677i	−0.103150	−	0.584991i
$372$	−4.15281	−	22.9444i	−0.215313	−	1.18961i
$373$	−4.16063	+	1.51435i	−0.215429	+	0.0784099i	−0.447480	−	0.894294i	$-0.647679\pi$
$373$	−4.16063	+	1.51435i	−0.215429	+	0.0784099i	0.232051	+	0.972704i	$0.425456\pi$
$374$	−42.9369	−	13.2721i	−2.22021	−	0.686284i
$375$	3.50041	−	0.912616i	0.180761	−	0.0471273i
$376$	−11.0713	+	3.69791i	−0.570960	+	0.190705i
$377$		−	5.92208i		−	0.305003i
$378$	7.33600	+	0.427968i	0.377323	+	0.0220123i
$379$			20.3144i			1.04348i	0.853105	+	0.521739i	$0.174717\pi$
$379$			20.3144i			1.04348i	−0.853105	+	0.521739i	$0.825283\pi$
$380$	−2.35758	+	1.13192i	−0.120941	+	0.0580661i
$381$	6.57077	−	23.8757i	0.336631	−	1.22319i
$382$	−9.16674	+	29.6556i	−0.469011	+	1.51731i
$383$	0.481384	−	0.175209i	0.0245975	−	0.00895278i	−0.329692	−	0.944089i	$-0.606945\pi$
$383$	0.481384	−	0.175209i	0.0245975	−	0.00895278i	0.354290	+	0.935136i	$0.384723\pi$
$384$	−1.49500	−	19.5388i	−0.0762916	−	0.997086i
$385$	−0.226990	−	1.28732i	−0.0115685	−	0.0656081i
$386$	−4.16331	−	9.89288i	−0.211907	−	0.503534i
$387$	−11.8206	−	4.48425i	−0.600876	−	0.227947i
$388$	6.28961	−	6.43318i	0.319307	−	0.326595i
$389$	−3.75915	+	10.3282i	−0.190596	+	0.523659i	−0.997777	−	0.0666458i	$-0.978770\pi$
$389$	−3.75915	+	10.3282i	−0.190596	+	0.523659i	0.807180	+	0.590305i	$0.200992\pi$
$390$	2.09801	+	1.33988i	0.106237	+	0.0678474i
$391$	25.4579	−	30.3395i	1.28746	−	1.53434i
$392$	1.34830	+	2.48638i	0.0680993	+	0.125581i
$393$	−1.05001	−	1.52135i	−0.0529659	−	0.0767421i
$394$	−3.72306	+	7.25153i	−0.187565	+	0.365327i
$395$	1.50187	−	2.60131i	0.0755671	−	0.130886i
$396$	26.3782	+	26.4964i	1.32555	+	1.33150i
$397$	8.55345	+	14.8150i	0.429285	+	0.743544i	0.996810	−	0.0798123i	$-0.0254321\pi$
$397$	8.55345	+	14.8150i	0.429285	+	0.743544i	−0.567524	+	0.823357i	$0.692099\pi$
$398$	−19.0476	+	0.939330i	−0.954768	+	0.0470843i
$399$	−1.01367	+	10.7489i	−0.0507470	+	0.538117i
$400$	−19.5955	−	3.00098i	−0.979776	−	0.150049i
$401$	32.5873	+	5.74601i	1.62733	+	0.286942i	0.911490	−	0.411322i	$-0.134933\pi$
$401$	32.5873	+	5.74601i	1.62733	+	0.286942i	0.715840	+	0.698264i	$0.246044\pi$
$402$	1.33346	+	1.74183i	0.0665070	+	0.0868747i
$403$	−20.9609	−	24.9802i	−1.04414	−	1.24435i
$404$	−1.21241	+	4.73799i	−0.0603196	+	0.235724i
$405$	−0.597522	−	1.79093i	−0.0296911	−	0.0889920i
$406$	−1.71521	−	0.215974i	−0.0851242	−	0.0107186i
$407$	−5.09150	+	4.27228i	−0.252376	+	0.211769i
$408$	−9.79495	−	22.9835i	−0.484922	−	1.13785i
$409$	−3.79995	+	21.5506i	−0.187895	+	1.06561i	0.734283	+	0.678843i	$0.237518\pi$
$409$	−3.79995	+	21.5506i	−0.187895	+	1.06561i	−0.922179	+	0.386764i	$0.873593\pi$
$410$	−0.0686307	+	0.0156218i	−0.00338943	+	0.000771506i
$411$	−24.4973	−	2.31022i	−1.20837	−	0.113955i
$412$	−33.4193	−	2.54419i	−1.64645	−	0.125343i
$413$	−2.06909	+	1.19459i	−0.101813	+	0.0587819i
$414$	−30.5393	+	12.3688i	−1.50092	+	0.607893i
$415$	2.15212	+	1.24253i	0.105643	+	0.0609932i
$416$	−15.3708	−	22.6888i	−0.753618	−	1.11241i
$417$	−14.4650	+	9.98348i	−0.708356	+	0.488893i
$418$	−40.2898	+	37.3392i	−1.97064	+	1.82632i
$419$	11.1970	+	9.39541i	0.547010	+	0.458996i	0.873927	−	0.486057i	$-0.161565\pi$
$419$	11.1970	+	9.39541i	0.547010	+	0.458996i	−0.326917	+	0.945053i	$0.606010\pi$
$420$	0.464580	−	0.558779i	0.0226692	−	0.0272656i
$421$	28.7248	+	10.4550i	1.39996	+	0.509544i	0.928167	−	0.372165i	$-0.121384\pi$
$421$	28.7248	+	10.4550i	1.39996	+	0.509544i	0.471794	+	0.881709i	$0.343607\pi$
$422$	−27.4834	−	20.8434i	−1.33787	−	1.01464i
$423$	12.2205	−	1.98483i	0.594180	−	0.0965058i
$424$	32.0086	−	4.76645i	1.55448	−	0.231479i
$425$	−24.8904	+	4.38885i	−1.20736	+	0.212890i
$426$	−1.38892	−	1.27557i	−0.0672935	−	0.0618017i
$427$	−1.81219	−	4.97895i	−0.0876980	−	0.240948i
$428$	1.22604	−	2.70864i	0.0592631	−	0.130927i
$429$	50.4134	+	13.8742i	2.43398	+	0.669852i
$430$	−1.05061	+	0.677679i	−0.0506651	+	0.0326806i
$431$	17.2184			0.829381			0.414690	−	0.909963i	$-0.363890\pi$
$431$	17.2184			0.829381			0.414690	+	0.909963i	$0.363890\pi$
$432$	−1.76415	+	20.7096i	−0.0848776	+	0.996391i
$433$	20.8058			0.999863			0.499932	−	0.866065i	$-0.333358\pi$
$433$	20.8058			0.999863			0.499932	+	0.866065i	$0.333358\pi$
$434$	−7.99942	+	5.15987i	−0.383985	+	0.247682i
$435$	0.112052	+	0.429786i	0.00537249	+	0.0206066i
$436$	−3.07487	+	6.79316i	−0.147259	+	0.325333i
$437$	−16.5570	−	45.4901i	−0.792030	−	2.17609i
$438$	−19.2612	+	6.04936i	−0.920336	+	0.289050i
$439$	−29.9194	+	5.27560i	−1.42797	+	0.251790i	−0.833587	−	0.552388i	$-0.813717\pi$
$439$	−29.9194	+	5.27560i	−1.42797	+	0.251790i	−0.594388	+	0.804179i	$0.702605\pi$
$440$	3.65695	−	0.544561i	0.174338	−	0.0259609i
$441$	−0.987853	−	2.83269i	−0.0470406	−	0.134890i
$442$	−27.8393	−	21.1133i	−1.32418	−	1.00426i
$443$	−6.59829	−	2.40158i	−0.313494	−	0.114103i	0.180481	−	0.983578i	$-0.442234\pi$
$443$	−6.59829	−	2.40158i	−0.313494	−	0.114103i	−0.493975	+	0.869476i	$0.664457\pi$
$444$	−3.64161	−	0.625144i	−0.172823	−	0.0296680i
$445$	1.20411	+	1.01037i	0.0570803	+	0.0478960i
$446$	19.6773	−	18.2362i	0.931748	−	0.863511i
$447$	−0.989620	−	12.2659i	−0.0468074	−	0.580157i
$448$	−7.13188	+	3.62440i	−0.336950	+	0.171237i
$449$	22.3368	+	12.8962i	1.05414	+	0.608607i	0.923805	−	0.382863i	$-0.125062\pi$
$449$	22.3368	+	12.8962i	1.05414	+	0.608607i	0.130333	+	0.991470i	$0.458395\pi$
$450$	20.0029	+	6.48059i	0.942946	+	0.305498i
$451$	−1.28036	+	0.739213i	−0.0602896	+	0.0348082i
$452$	14.5007	+	1.10393i	0.682058	+	0.0519246i
$453$	−8.20186	−	17.9040i	−0.385357	−	0.841202i
$454$	39.7485	−	9.04761i	1.86549	−	0.424625i
$455$	0.176475	−	1.00084i	0.00827325	−	0.0469199i
$456$	−30.3150	−	3.67796i	−1.41963	−	0.172236i
$457$	2.59144	−	2.17448i	0.121222	−	0.101718i	−0.580161	−	0.814502i	$-0.697010\pi$
$457$	2.59144	−	2.17448i	0.121222	−	0.101718i	0.701384	+	0.712784i	$0.252566\pi$
$458$	−25.1398	−	3.16553i	−1.17471	−	0.147915i
$459$	6.33799	+	25.7300i	0.295832	+	1.20097i
$460$	−0.807742	+	3.15658i	−0.0376612	+	0.147176i
$461$	5.61926	+	6.69677i	0.261715	+	0.311900i	0.880860	−	0.473377i	$-0.156965\pi$
$461$	5.61926	+	6.69677i	0.261715	+	0.311900i	−0.619145	+	0.785277i	$0.712521\pi$
$462$	5.85690	−	14.0952i	0.272488	−	0.655768i
$463$	7.08211	+	1.24877i	0.329134	+	0.0580351i	0.335773	−	0.941943i	$-0.391002\pi$
$463$	7.08211	+	1.24877i	0.329134	+	0.0580351i	−0.00663971	+	0.999978i	$0.502114\pi$
$464$	0.740201	−	4.83329i	0.0343630	−	0.224380i
$465$	1.99386	+	1.41630i	0.0924629	+	0.0656792i
$466$	22.7283	−	1.12084i	1.05287	−	0.0519221i
$467$	−13.9994	−	24.2476i	−0.647813	−	1.12205i	−0.983644	−	0.180123i	$-0.942350\pi$
$467$	−13.9994	−	24.2476i	−0.647813	−	1.12205i	0.335831	−	0.941922i	$-0.390983\pi$
$468$	12.2255	+	26.3716i	0.565125	+	1.21903i
$469$	0.447777	−	0.775572i	0.0206764	−	0.0358126i
$470$	0.559186	−	1.08915i	0.0257933	−	0.0502386i
$471$	−1.28960	+	2.71744i	−0.0594216	+	0.125213i
$472$	−3.22132	−	5.94041i	−0.148273	−	0.273430i
$473$	−16.8797	+	20.1165i	−0.776130	+	0.924956i
$474$	31.1289	−	16.1605i	1.42980	−	0.742275i
$475$	−10.5659	+	29.0297i	−0.484798	+	1.33197i
$476$	−7.13031	+	7.29306i	−0.326817	+	0.334277i
$477$	−34.3215	−	0.464070i	−1.57147	−	0.0212483i
$478$	11.5398	+	27.4210i	0.527819	+	1.25421i
$479$	0.954702	+	5.41439i	0.0436215	+	0.247390i	0.998819	−	0.0485782i	$-0.0154690\pi$
$479$	0.954702	+	5.41439i	0.0436215	+	0.247390i	−0.955198	+	0.295968i	$0.904358\pi$
$480$	1.54481	+	1.35577i	0.0705106	+	0.0618820i
$481$	−4.85572	+	1.76734i	−0.221402	+	0.0805836i
$482$	9.23762	−	29.8849i	0.420762	−	1.36122i
$483$	9.44703	+	9.57563i	0.429855	+	0.435706i
$484$	50.1759	−	24.0903i	2.28072	−	1.09502i
$485$			0.943668i			0.0428498i
$486$	5.37560	−	21.3800i	0.243842	−	0.969815i
$487$			33.0451i			1.49742i	0.662899	+	0.748709i	$0.269326\pi$
$487$			33.0451i			1.49742i	−0.662899	+	0.748709i	$0.730674\pi$
$488$	14.2145	−	4.74775i	0.643458	−	0.214921i
$489$	−2.00448	−	2.03177i	−0.0906459	−	0.0918798i
$490$	−0.283435	−	0.0876118i	−0.0128043	−	0.00395790i
$491$	11.2412	−	4.09145i	0.507306	−	0.184644i	−0.0756710	−	0.997133i	$-0.524110\pi$
$491$	11.2412	−	4.09145i	0.507306	−	0.184644i	0.582977	+	0.812488i	$0.301888\pi$
$492$	−0.773579	−	0.277603i	−0.0348756	−	0.0125153i
$493$	−1.08252	−	6.13929i	−0.0487543	−	0.276500i
$494$	−39.3632	+	16.5656i	−1.77103	+	0.745320i
$495$	−3.92119	−	0.0530195i	−0.176244	−	0.00238305i
$496$	−13.9849	−	23.0074i	−0.627941	−	1.03306i
$497$	−0.263311	+	0.723440i	−0.0118111	+	0.0324507i
$498$	13.3699	+	25.7536i	0.599120	+	1.15405i
$499$	22.4074	−	26.7041i	1.00309	−	1.19544i	0.0224289	−	0.999748i	$-0.492860\pi$
$499$	22.4074	−	26.7041i	1.00309	−	1.19544i	0.980665	−	0.195693i	$-0.0626955\pi$
$500$	3.39438	−	2.43431i	0.151801	−	0.108866i
$501$	−13.8776	+	29.2428i	−0.620004	+	1.30647i
$502$	−10.3901	−	5.33443i	−0.463731	−	0.238087i
$503$	1.32060	−	2.28734i	0.0588825	−	0.101988i	−0.835082	−	0.550126i	$-0.814580\pi$
$503$	1.32060	−	2.28734i	0.0588825	−	0.101988i	0.893964	+	0.448139i	$0.147913\pi$
$504$	8.08382	−	2.57911i	0.360082	−	0.114883i
$505$	−0.256484	−	0.444244i	−0.0114134	−	0.0197686i
$506$	3.37096	+	68.3557i	0.149857	+	3.03878i
$507$	14.7844	+	10.5018i	0.656600	+	0.466403i
$508$	−2.81340	−	28.4555i	−0.124825	−	1.26251i
$509$	−4.76193	−	0.839657i	−0.211069	−	0.0372172i	0.0671138	−	0.997745i	$-0.478621\pi$
$509$	−4.76193	−	0.839657i	−0.211069	−	0.0372172i	−0.278183	+	0.960528i	$0.589732\pi$
$510$	2.41988	+	1.00552i	0.107154	+	0.0445251i
$511$	5.29789	+	6.31378i	0.234365	+	0.279305i
$512$	−9.70900	−	20.4386i	−0.429081	−	0.903266i
$513$	31.1096	+	9.01582i	1.37352	+	0.398058i
$514$	0.0160043	−	0.127102i	0.000705918	−	0.00560621i
$515$	2.69296	−	2.25967i	0.118666	−	0.0995728i
$516$	−14.5983	+	0.0660346i	−0.642654	+	0.00290701i
$517$	4.46553	−	25.3253i	0.196394	−	1.11381i
$518$	0.334787	+	1.47081i	0.0147097	+	0.0646236i
$519$	−8.50581	−	18.5674i	−0.373364	−	0.815021i
$520$	2.81645	+	0.574562i	0.123510	+	0.0251962i
$521$	−12.1791	+	7.03158i	−0.533574	+	0.308059i	−0.742471	−	0.669879i	$-0.766346\pi$
$521$	−12.1791	+	7.03158i	−0.533574	+	0.308059i	0.208897	+	0.977938i	$0.433013\pi$
$522$	−1.59846	+	4.93377i	−0.0699625	+	0.215945i
$523$	17.9477	+	10.3621i	0.784797	+	0.453103i	0.838128	−	0.545474i	$-0.183650\pi$
$523$	17.9477	+	10.3621i	0.784797	+	0.453103i	−0.0533307	+	0.998577i	$0.516984\pi$
$524$	−1.76217	−	1.20449i	−0.0769809	−	0.0526182i
$525$	−0.690322	−	8.55623i	−0.0301281	−	0.373425i
$526$	3.74403	+	4.03990i	0.163248	+	0.176148i
$527$	−26.2959	−	22.0649i	−1.14547	−	0.961162i
$528$	39.4106	+	17.6245i	1.71513	+	0.767010i
$529$	−35.0627	−	12.7618i	−1.52447	−	0.554861i
$530$	−2.05111	+	2.70452i	−0.0890946	+	0.117477i
$531$	2.36016	+	6.76781i	0.102422	+	0.293698i
$532$	3.36232	+	12.0048i	0.145775	+	0.520476i
$533$	−1.13195	+	0.199593i	−0.0490301	+	0.00864534i
$534$	5.49961	+	17.5108i	0.237991	+	0.757766i
$535$	0.106660	+	0.293045i	0.00461130	+	0.0126694i
$536$	2.15905	+	1.32463i	0.0932566	+	0.0572154i
$537$	4.54494	+	17.4325i	0.196129	+	0.752268i
$538$	21.7060	+	33.6511i	0.935812	+	1.45080i
$539$	−6.23135			−0.268403
$540$	−1.38623	−	1.68255i	−0.0596537	−	0.0724056i
$541$	3.89562			0.167486			0.0837430	−	0.996487i	$-0.473313\pi$
$541$	3.89562			0.167486			0.0837430	+	0.996487i	$0.473313\pi$
$542$	−12.4021	−	19.2271i	−0.532716	−	0.825877i
$543$	14.0006	+	3.85308i	0.600823	+	0.165351i
$544$	−20.0820	−	20.7112i	−0.861008	−	0.887987i
$545$	−0.267498	−	0.734945i	−0.0114584	−	0.0314816i
$546$	8.02686	−	8.74014i	0.343518	−	0.374043i
$547$	−44.3088	+	7.81284i	−1.89451	+	0.334053i	−0.994750	−	0.102335i	$-0.967369\pi$
$547$	−44.3088	+	7.81284i	−1.89451	+	0.334053i	−0.899758	+	0.436388i	$0.856257\pi$
$548$	−27.3597	+	7.66292i	−1.16875	+	0.327344i
$549$	−15.6899	+	2.54832i	−0.669627	+	0.108760i
$550$	26.3914	−	34.7987i	1.12533	−	1.48382i
$551$	−7.16025	−	2.60612i	−0.305037	−	0.111024i
$552$	−27.7879	+	25.9874i	−1.18273	+	1.10610i
$553$	−10.9688	−	9.20396i	−0.466443	−	0.391392i
$554$	1.05916	+	1.14285i	0.0449993	+	0.0485552i
$555$	0.318956	−	0.220137i	0.0135389	−	0.00934430i
$556$	−11.4523	+	16.7548i	−0.485684	+	0.710560i
$557$	33.8499	+	19.5433i	1.43427	+	0.828074i	0.997443	−	0.0714729i	$-0.0227699\pi$
$557$	33.8499	+	19.5433i	1.43427	+	0.828074i	0.436824	+	0.899547i	$0.356103\pi$
$558$	10.7203	+	26.4690i	0.453827	+	1.12052i
$559$	−17.6809	+	10.2081i	−0.747821	+	0.431755i
$560$	0.269124	−	0.794772i	0.0113726	−	0.0335853i
$561$	54.7986	+	5.16777i	2.31360	+	0.218183i
$562$	4.28186	+	18.8114i	0.180620	+	0.793509i
$563$	4.15488	−	23.5635i	0.175107	−	0.993084i	−0.762912	−	0.646502i	$-0.776231\pi$
$563$	4.15488	−	23.5635i	0.175107	−	0.993084i	0.938020	−	0.346582i	$-0.112658\pi$
$564$	12.3482	−	7.20388i	0.519951	−	0.303338i
$565$	−1.16849	+	0.980476i	−0.0491586	+	0.0412489i
$566$	0.724079	−	5.75044i	0.0304353	−	0.241709i
$567$	−8.90228	+	1.32262i	−0.373861	+	0.0555448i
$568$	−2.02558	−	0.799133i	−0.0849915	−	0.0335309i
$569$	19.9126	+	23.7309i	0.834780	+	0.994852i	0.999963	+	0.00858886i	$0.00273395\pi$
$569$	19.9126	+	23.7309i	0.834780	+	0.994852i	−0.165183	+	0.986263i	$0.552822\pi$
$570$	2.54328	−	1.94701i	0.106526	−	0.0815514i
$571$	−32.9922	−	5.81741i	−1.38068	−	0.243451i	−0.566499	−	0.824062i	$-0.691703\pi$
$571$	−32.9922	−	5.81741i	−1.38068	−	0.243451i	−0.814181	+	0.580611i	$0.802814\pi$
$572$	60.0837	−	5.94050i	2.51223	−	0.248385i
$573$	3.56926	−	37.8481i	0.149108	−	1.58113i
$574$	0.0165266	+	0.335124i	0.000689808	+	0.0139878i
$575$	19.2445	+	33.3324i	0.802550	+	1.39006i
$576$	6.68165	+	23.0512i	0.278402	+	0.960465i
$577$	2.18324	−	3.78147i	0.0908893	−	0.157425i	−0.816996	−	0.576643i	$-0.804362\pi$
$577$	2.18324	−	3.78147i	0.0908893	−	0.157425i	0.907886	+	0.419218i	$0.137696\pi$
$578$	−11.3322	−	5.81817i	−0.471359	−	0.242004i
$579$	7.46696	+	10.8189i	0.310316	+	0.449617i
$580$	0.298888	+	0.416767i	0.0124106	+	0.0173053i
$581$	7.61463	−	9.07476i	0.315908	−	0.376485i
$582$	−5.93087	+	9.28667i	−0.245843	+	0.384945i
$583$	−24.3847	+	66.9965i	−1.00991	+	2.77471i
$584$	−18.2519	+	14.5025i	−0.755268	+	0.600116i
$585$	−2.85060	−	1.08140i	−0.117858	−	0.0447104i
$586$	16.3937	−	6.89910i	0.677217	−	0.284999i
$587$	1.19273	+	6.76431i	0.0492292	+	0.279193i	0.999478	−	0.0322984i	$-0.0102827\pi$
$587$	1.19273	+	6.76431i	0.0492292	+	0.279193i	−0.950249	+	0.311491i	$0.899172\pi$
$588$	−2.23866	−	2.64356i	−0.0923209	−	0.109018i
$589$	−39.4272	+	14.3503i	−1.62457	+	0.591296i
$590$	0.677178	+	0.209320i	0.0278790	+	0.00861758i
$591$	2.64903	−	9.62557i	0.108967	−	0.395943i
$592$	−4.18388	+	0.835491i	−0.171956	+	0.0343385i
$593$			22.9784i			0.943608i	0.881704	+	0.471804i	$0.156397\pi$
$593$			22.9784i			0.943608i	−0.881704	+	0.471804i	$0.843603\pi$
$594$	−38.2553	−	25.1661i	−1.56963	−	1.03258i
$595$		−	1.06980i		−	0.0438577i
$596$	−6.15010	−	12.8096i	−0.251918	−	0.524700i
$597$	22.6012	−	5.89252i	0.925007	−	0.241165i
$598$	−15.7134	+	50.8349i	−0.642570	+	2.07880i
$599$	−0.655424	+	0.238555i	−0.0267799	+	0.00974708i	−0.355375	−	0.934724i	$-0.615647\pi$
$599$	−0.655424	+	0.238555i	−0.0267799	+	0.00974708i	0.328595	+	0.944471i	$0.393425\pi$
$600$	24.2442	−	1.30556i	0.989765	−	0.0532993i
$601$	2.67161	+	15.1514i	0.108977	+	0.618040i	0.989557	+	0.144142i	$0.0460423\pi$
$601$	2.67161	+	15.1514i	0.108977	+	0.618040i	−0.880580	+	0.473898i	$0.842847\pi$
$602$	2.31174	+	5.49317i	0.0942195	+	0.223885i
$603$	−2.03456	−	1.75462i	−0.0828539	−	0.0714536i
$604$	−16.2598	−	15.8970i	−0.661604	−	0.646839i
$605$	−1.99671	+	5.48590i	−0.0811776	+	0.223034i
$606$	0.267964	−	5.98380i	0.0108853	−	0.243075i
$607$	0.924959	−	1.10232i	0.0375429	−	0.0447419i	−0.746946	−	0.664884i	$-0.768481\pi$
$607$	0.924959	−	1.10232i	0.0375429	−	0.0447419i	0.784489	+	0.620142i	$0.212925\pi$
$608$	−34.1967	+	8.59993i	−1.38686	+	0.348773i
$609$	2.11042	−	0.170270i	0.0855185	−	0.00689968i
$610$	−0.717939	+	1.39835i	−0.0290685	+	0.0566177i
$611$	9.99651	−	17.3145i	0.404416	−	0.700468i
$612$	17.4945	+	25.1041i	0.707173	+	1.01477i
$613$	4.62706	+	8.01431i	0.186885	+	0.323695i	0.944210	−	0.329343i	$-0.106827\pi$
$613$	4.62706	+	8.01431i	0.186885	+	0.323695i	−0.757325	+	0.653038i	$0.773494\pi$
$614$	36.0128	−	1.77597i	1.45336	−	0.0716723i
$615$	0.0783729	−	0.0359029i	0.00316030	−	0.00144774i
$616$	0.470666	−	17.6186i	0.0189637	−	0.709874i
$617$	−39.7124	−	7.00237i	−1.59876	−	0.281905i	−0.697961	−	0.716136i	$-0.745909\pi$
$617$	−39.7124	−	7.00237i	−1.59876	−	0.281905i	−0.900801	+	0.434231i	$0.857020\pi$
$618$	40.7033	−	5.31239i	1.63733	−	0.213696i
$619$	−26.4482	−	31.5197i	−1.06304	−	1.26689i	−0.962305	−	0.271972i	$-0.912324\pi$
$619$	−26.4482	−	31.5197i	−1.06304	−	1.26689i	−0.100738	−	0.994913i	$-0.532120\pi$
$620$	2.73588	+	0.700088i	0.109876	+	0.0281162i
$621$	33.5187	−	22.4710i	1.34506	−	0.901731i
$622$	−18.8785	−	2.37713i	−0.756961	−	0.0953143i
$623$	5.74000	−	4.81643i	0.229968	−	0.192966i
$624$	24.1057	+	23.3555i	0.965002	+	0.934967i
$625$	4.22692	−	23.9720i	0.169077	−	0.958882i
$626$	40.7126	−	9.26704i	1.62720	−	0.370386i
$627$	38.9603	−	54.8481i	1.55592	−	2.19042i
$628$	−0.263653	+	3.46322i	−0.0105209	+	0.138197i
$629$	−4.71075	+	2.71975i	−0.187830	+	0.108444i
$630$	−0.417164	+	0.786179i	−0.0166202	+	0.0313221i
$631$	15.7004	+	9.06464i	0.625024	+	0.360857i	0.778822	−	0.627245i	$-0.215817\pi$
$631$	15.7004	+	9.06464i	0.625024	+	0.360857i	−0.153799	+	0.988102i	$0.549151\pi$
$632$	26.8519	−	30.3183i	1.06811	−	1.20600i
$633$	38.1658	+	18.1121i	1.51695	+	0.719891i
$634$	−1.09407	+	1.01395i	−0.0434511	+	0.0402689i
$635$	2.29751	+	1.92784i	0.0911737	+	0.0765038i
$636$	−37.1827	+	13.7242i	−1.47439	+	0.544199i
$637$	−4.55243	−	1.65695i	−0.180374	−	0.0656507i
$638$	8.58321	+	6.50952i	0.339812	+	0.257714i
$639$	1.98438	+	1.18174i	0.0785010	+	0.0467489i
$640$	2.22683	+	0.820956i	0.0880231	+	0.0324511i
$641$	16.5242	−	2.91367i	0.652667	−	0.115083i	0.162496	−	0.986709i	$-0.448045\pi$
$641$	16.5242	−	2.91367i	0.652667	−	0.115083i	0.490171	+	0.871626i	$0.336934\pi$
$642$	−0.792122	+	3.55421i	−0.0312626	+	0.140274i
$643$	0.644909	+	1.77187i	0.0254327	+	0.0698759i	0.951759	−	0.306846i	$-0.0992736\pi$
$643$	0.644909	+	1.77187i	0.0254327	+	0.0698759i	−0.926327	+	0.376722i	$0.877051\pi$
$644$	14.1502	+	6.40497i	0.557596	+	0.252391i
$645$	1.09001	−	1.07537i	0.0429192	−	0.0423428i
$646$	−37.7788	+	24.3685i	−1.48639	+	0.958766i
$647$	−18.8928			−0.742752			−0.371376	−	0.928483i	$-0.621114\pi$
$647$	−18.8928			−0.742752			−0.371376	+	0.928483i	$0.621114\pi$
$648$	−3.06719	−	25.2704i	−0.120491	−	0.992714i
$649$	14.8878			0.584397
$650$	28.5339	−	18.4053i	1.11919	−	0.721914i
$651$	8.29940	−	8.18794i	0.325279	−	0.320911i
$652$	−3.00241	−	1.35902i	−0.117583	−	0.0532232i
$653$	−0.364662	−	1.00190i	−0.0142703	−	0.0392074i	0.932353	−	0.361549i	$-0.117752\pi$
$653$	−0.364662	−	1.00190i	−0.0142703	−	0.0392074i	−0.946623	+	0.322342i	$0.895530\pi$
$654$	1.98661	−	8.91381i	0.0776825	−	0.348558i
$655$	0.220480	−	0.0388766i	0.00861487	−	0.00151903i
$656$	−0.948784	+	0.0214151i	−0.0370438	+	0.000836120i
$657$	21.5787	−	12.0724i	0.841865	−	0.470991i
$658$	−4.65020	−	3.52672i	−0.181284	−	0.137486i
$659$	−36.6392	−	13.3356i	−1.42726	−	0.519480i	−0.491115	−	0.871095i	$-0.663410\pi$
$659$	−36.6392	−	13.3356i	−1.42726	−	0.519480i	−0.936145	+	0.351615i	$0.885633\pi$
$660$	−4.24808	+	1.56797i	−0.165356	+	0.0610332i
$661$	−0.881864	−	0.739972i	−0.0343005	−	0.0287816i	0.625476	−	0.780243i	$-0.284905\pi$
$661$	−0.881864	−	0.739972i	−0.0343005	−	0.0287816i	−0.659777	+	0.751462i	$0.729349\pi$
$662$	−20.7791	+	19.2573i	−0.807603	+	0.748458i
$663$	38.6600	+	18.3467i	1.50143	+	0.712525i
$664$	25.0830	+	22.2152i	0.973410	+	0.862116i
$665$	−1.13243	−	0.653807i	−0.0439137	−	0.0253536i
$666$	4.52240	−	0.161765i	0.175239	−	0.00626828i
$667$	−8.22154	+	4.74671i	−0.318339	+	0.183793i
$668$	−2.83721	+	37.2682i	−0.109775	+	1.44195i
$669$	−19.0280	+	26.7875i	−0.735665	+	1.03567i
$670$	−0.259055	+	0.0589664i	−0.0100082	+	0.00227807i
$671$	−5.73329	+	32.5151i	−0.221331	+	1.25523i
$672$	7.64353	−	6.12996i	0.294856	−	0.236468i
$673$	15.9127	−	13.3524i	0.613390	−	0.514695i	−0.282328	−	0.959318i	$-0.591107\pi$
$673$	15.9127	−	13.3524i	0.613390	−	0.514695i	0.895718	+	0.444623i	$0.146662\pi$
$674$	−24.6069	−	3.09843i	−0.947822	−	0.119347i
$675$	−25.6033	−	2.76423i	−0.985472	−	0.106395i
$676$	20.2865	+	5.19115i	0.780251	+	0.199660i
$677$	−5.14585	−	6.13259i	−0.197771	−	0.235694i	0.658040	−	0.752983i	$-0.271386\pi$
$677$	−5.14585	−	6.13259i	−0.197771	−	0.235694i	−0.855811	+	0.517289i	$0.826941\pi$
$678$	−17.6613	+	2.30506i	−0.678279	+	0.0885255i
$679$	4.43013	+	0.781151i	0.170013	+	0.0299778i
$680$	3.02478	+	0.0808044i	0.115995	+	0.00309871i
$681$	−45.3908	+	20.7937i	−1.73938	+	0.796816i
$682$	59.2454	−	2.92168i	2.26862	−	0.111877i
$683$	−4.69599	−	8.13370i	−0.179687	−	0.311227i	0.762086	−	0.647476i	$-0.224175\pi$
$683$	−4.69599	−	8.13370i	−0.179687	−	0.311227i	−0.941773	+	0.336248i	$0.890842\pi$
$684$	37.2653	−	3.17632i	1.42488	−	0.121449i
$685$	1.49007	−	2.58087i	0.0569325	−	0.0986100i
$686$	−0.645924	+	1.25809i	−0.0246615	+	0.0480340i
$687$	30.9325	−	2.49565i	1.18015	−	0.0952150i
$688$	−15.7061	+	6.12134i	−0.598789	+	0.233374i
$689$	−35.6295	+	42.4616i	−1.35737	+	1.61766i
$690$	0.178525	−	3.98658i	0.00679634	−	0.151766i
$691$	9.83836	−	27.0307i	0.374269	−	1.02830i	−0.599424	−	0.800431i	$-0.704604\pi$
$691$	9.83836	−	27.0307i	0.374269	−	1.02830i	0.973693	−	0.227864i	$-0.0731740\pi$
$692$	−16.8624	−	16.4861i	−0.641012	−	0.626707i
$693$	−3.49479	+	18.3645i	−0.132756	+	0.697608i
$694$	−16.7821	−	39.8777i	−0.637039	−	1.51374i
$695$	−0.369639	−	2.09633i	−0.0140212	−	0.0795182i
$696$	0.322020	+	5.97990i	0.0122061	+	0.226667i
$697$	−1.13698	+	0.413827i	−0.0430662	+	0.0156748i
$698$	0.145516	−	0.470764i	0.00550788	−	0.0178187i
$699$	−26.9686	+	7.03117i	−1.02005	+	0.265943i
$700$	−4.29008	−	8.93547i	−0.162150	−	0.337729i
$701$		−	5.26383i		−	0.198812i	−0.995047	−	0.0994060i	$-0.968306\pi$
$701$		−	5.26383i		−	0.198812i	0.995047	−	0.0994060i	$-0.0316943\pi$
$702$	−21.2564	−	28.5579i	−0.802270	−	1.07785i
$703$			6.64868i			0.250760i
$704$	49.7797	+	2.66154i	1.87614	+	0.100311i
$705$	−0.397872	+	1.44571i	−0.0149847	+	0.0544488i
$706$	11.6519	+	3.60168i	0.438525	+	0.135551i
$707$	−2.29785	+	0.836350i	−0.0864197	+	0.0314542i
$708$	5.34857	+	6.31593i	0.201011	+	0.237367i
$709$	−2.26372	−	12.8382i	−0.0850158	−	0.482149i	−0.997353	−	0.0727094i	$-0.976835\pi$
$709$	−2.26372	−	12.8382i	−0.0850158	−	0.482149i	0.912337	−	0.409439i	$-0.134276\pi$
$710$	0.210513	−	0.0885920i	0.00790041	−	0.00332480i
$711$	−33.2768	+	27.1644i	−1.24798	+	1.01875i
$712$	13.1845	+	16.5932i	0.494110	+	0.621855i
$713$	−17.8790	+	49.1220i	−0.669572	+	1.83963i
$714$	6.72362	−	10.5280i	0.251625	−	0.393999i
$715$	−4.07062	+	4.85118i	−0.152233	+	0.181424i
$716$	12.1232	+	16.9045i	0.453064	+	0.631749i
$717$	−20.6969	−	29.9876i	−0.772939	−	1.11991i
$718$	28.5357	+	14.6507i	1.06494	+	0.546761i
$719$	−17.1062	+	29.6289i	−0.637955	+	1.10497i	0.347926	+	0.937522i	$0.386886\pi$
$719$	−17.1062	+	29.6289i	−0.637955	+	1.10497i	−0.985881	+	0.167448i	$0.946447\pi$
$720$	−2.19135	−	1.23888i	−0.0816667	−	0.0461703i
$721$	−8.37900	−	14.5129i	−0.312050	−	0.540487i
$722$	1.38307	+	28.0456i	0.0514725	+	1.04375i
$723$	−3.59686	+	38.1408i	−0.133769	+	1.41847i
$724$	16.6862	−	1.64977i	0.620137	−	0.0613132i
$725$	5.96622	+	1.05201i	0.221580	+	0.0390705i
$726$	−54.1281	+	41.4378i	−2.00888	+	1.53790i
$727$	−14.8972	−	17.7538i	−0.552507	−	0.658452i	0.415436	−	0.909623i	$-0.363629\pi$
$727$	−14.8972	−	17.7538i	−0.552507	−	0.658452i	−0.967943	+	0.251170i	$0.919185\pi$
$728$	5.02874	−	12.7465i	0.186378	−	0.472416i
$729$	−1.09486	+	26.9778i	−0.0405503	+	0.999178i
$730$	0.305474	−	2.42599i	0.0113061	−	0.0897899i
$731$	−16.4634	+	13.8144i	−0.608920	+	0.510945i
$732$	−15.8538	+	9.24906i	−0.585973	+	0.341855i
$733$	1.99363	−	11.3064i	0.0736364	−	0.417613i	−0.925599	−	0.378506i	$-0.876438\pi$
$733$	1.99363	−	11.3064i	0.0736364	−	0.417613i	0.999235	−	0.0391064i	$-0.0124511\pi$
$734$	0.586050	+	2.57467i	0.0216315	+	0.0950329i
$735$	0.361737	+	0.0341135i	0.0133429	+	0.00125829i
$736$	−19.1783	+	39.5248i	−0.706923	+	1.45690i
$737$	−4.83286	+	2.79025i	−0.178021	+	0.102780i
$738$	0.996916	+	0.139245i	0.0366970	+	0.00512569i
$739$	20.8648	+	12.0463i	0.767525	+	0.443130i	0.831991	−	0.554789i	$-0.187201\pi$
$739$	20.8648	+	12.0463i	0.767525	+	0.443130i	−0.0644663	+	0.997920i	$0.520535\pi$
$740$	0.252524	−	0.369445i	0.00928296	−	0.0135811i
$741$	43.0476	−	29.7106i	1.58139	−	1.09145i
$742$	10.9987	+	11.8679i	0.403775	+	0.435683i
$743$	−15.0237	−	12.6064i	−0.551167	−	0.462484i	0.324169	−	0.945999i	$-0.394915\pi$
$743$	−15.0237	−	12.6064i	−0.551167	−	0.462484i	−0.875336	+	0.483515i	$0.839360\pi$
$744$	22.5239	+	24.0843i	0.825765	+	0.882975i
$745$	1.40051	+	0.509746i	0.0513109	+	0.0186756i
$746$	3.78376	−	4.98913i	0.138533	−	0.182665i
$747$	−22.4737	−	27.5307i	−0.822271	−	1.00729i
$748$	61.2015	−	17.1413i	2.23775	−	0.626749i
$749$	1.46402	−	0.258146i	0.0534940	−	0.00943243i
$750$	−3.46041	+	3.76790i	−0.126356	+	0.137584i
$751$	−12.8072	−	35.1876i	−0.467343	−	1.28401i	−0.919856	−	0.392256i	$-0.871695\pi$
$751$	−12.8072	−	35.1876i	−0.467343	−	1.28401i	0.452513	−	0.891758i	$-0.350527\pi$
$752$	10.3228	−	12.8817i	0.376432	−	0.469747i
$753$	13.7916	+	3.79556i	0.502593	+	0.138318i
$754$	4.53971	+	7.03798i	0.165326	+	0.256308i
$755$	2.38512			0.0868034
$756$	−9.04639	+	5.11497i	−0.329014	+	0.186030i
$757$	−19.6606			−0.714575			−0.357288	−	0.933994i	$-0.616298\pi$
$757$	−19.6606			−0.714575			−0.357288	+	0.933994i	$0.616298\pi$
$758$	−15.5724	−	24.1422i	−0.565617	−	0.876883i
$759$	−21.1464	−	81.1088i	−0.767566	−	2.94406i
$760$	1.93412	−	3.15246i	0.0701580	−	0.114352i
$761$	−8.03428	−	22.0740i	−0.291242	−	0.800182i	−0.995886	−	0.0906201i	$-0.971115\pi$
$761$	−8.03428	−	22.0740i	−0.291242	−	0.800182i	0.704643	−	0.709562i	$-0.251107\pi$
$762$	10.4935	+	33.4115i	0.380141	+	1.21037i
$763$	−3.67169	+	0.647418i	−0.132924	+	0.0234381i
$764$	−11.8391	−	42.2705i	−0.428325	−	1.52929i
$765$	−3.15283	−	0.599989i	−0.113991	−	0.0216927i
$766$	−0.437780	+	0.577240i	−0.0158176	+	0.0208565i
$767$	10.8766	+	3.95875i	0.392730	+	0.142942i
$768$	16.7546	+	22.0745i	0.604581	+	0.796544i
$769$	14.9901	+	12.5782i	0.540558	+	0.453582i	0.871729	−	0.489989i	$-0.162999\pi$
$769$	14.9901	+	12.5782i	0.540558	+	0.453582i	−0.331171	+	0.943571i	$0.607444\pi$
$770$	1.25659	+	1.35589i	0.0452843	+	0.0488628i
$771$	0.0126175	+	0.156388i	0.000454408	+	0.00563218i
$772$	12.5314	+	8.56551i	0.451016	+	0.308279i
$773$	−9.48548	−	5.47645i	−0.341169	−	0.196974i	0.319620	−	0.947546i	$-0.396445\pi$
$773$	−9.48548	−	5.47645i	−0.341169	−	0.196974i	−0.660789	+	0.750572i	$0.729778\pi$
$774$	17.4855	−	3.73216i	0.628503	−	0.134150i
$775$	28.8899	−	16.6796i	1.03776	−	0.599149i
$776$	−2.54326	+	12.4668i	−0.0912976	+	0.447533i
$777$	−0.769426	−	1.67959i	−0.0276030	−	0.0602550i
$778$	−3.44982	−	15.1560i	−0.123682	−	0.543368i
$779$	−0.256811	+	1.45645i	−0.00920121	+	0.0521827i
$780$	−3.52045	+	0.0159246i	−0.126052	+	0.000570191i
$781$	3.67496	−	3.08366i	0.131500	−	0.110342i
$782$	−6.99743	+	55.5718i	−0.250228	+	1.98724i
$783$	0.681805	−	6.31513i	0.0243657	−	0.225684i
$784$	−3.50835	−	1.92132i	−0.125298	−	0.0686186i
$785$	−0.234167	−	0.279070i	−0.00835779	−	0.00996043i
$786$	2.41409	+	1.00311i	0.0861077	+	0.0357799i
$787$	−18.8346	−	3.32106i	−0.671383	−	0.118383i	−0.172443	−	0.985020i	$-0.555166\pi$
$787$	−18.8346	−	3.32106i	−0.671383	−	0.118383i	−0.498940	+	0.866637i	$0.666277\pi$
$788$	−1.13424	−	11.4719i	−0.0404055	−	0.408671i
$789$	−5.49968	−	3.90659i	−0.195794	−	0.139078i
$790$	0.209232	+	4.24276i	0.00744413	+	0.150951i
$791$	3.63568	+	6.29718i	0.129270	+	0.223902i
$792$	−51.6600	−	11.2683i	−1.83566	−	0.400403i
$793$	−12.8345	+	22.2300i	−0.455767	+	0.789412i
$794$	−21.5220	−	11.0498i	−0.763786	−	0.392141i
$795$	1.78233	−	3.75573i	0.0632128	−	0.133202i
$796$	21.9166	−	15.7177i	0.776814	−	0.557098i
$797$	13.2392	−	15.7779i	0.468957	−	0.558881i	−0.478780	−	0.877935i	$-0.658921\pi$
$797$	13.2392	−	15.7779i	0.468957	−	0.558881i	0.947737	+	0.319054i	$0.103365\pi$
$798$	−7.03513	−	13.5513i	−0.249041	−	0.479713i
$799$	7.19817	−	19.7768i	0.254653	−	0.699654i
$800$	25.5884	−	11.4549i	0.904685	−	0.404993i
$801$	−10.9753	−	19.6177i	−0.387794	−	0.693156i
$802$	−43.1324	+	18.1518i	−1.52306	+	0.640962i
$803$	−8.91842	−	50.5789i	−0.314724	−	1.78489i
$804$	−2.91997	−	1.04785i	−0.102979	−	0.0369547i
$805$	−1.53090	+	0.557201i	−0.0539570	+	0.0196387i
$806$	44.0597	+	13.6192i	1.55194	+	0.479715i
$807$	−34.4442	−	34.9130i	−1.21249	−	1.22900i
$808$	−2.19115	−	6.56016i	−0.0770844	−	0.230786i
$809$			1.01081i			0.0355380i	0.999842	+	0.0177690i	$0.00565635\pi$
$809$			1.01081i			0.0355380i	−0.999842	+	0.0177690i	$0.994344\pi$
$810$	2.08299	+	1.67035i	0.0731889	+	0.0586901i
$811$		−	11.9078i		−	0.418139i	−0.977901	−	0.209070i	$-0.932956\pi$
$811$		−	11.9078i		−	0.418139i	0.977901	−	0.209070i	$-0.0670435\pi$
$812$	2.20396	−	1.05816i	0.0773438	−	0.0371342i
$813$	19.6803	+	19.9482i	0.690217	+	0.699613i
$814$	2.77588	−	8.98031i	0.0972944	−	0.314760i
$815$	0.324828	−	0.118228i	0.0113782	−	0.00414133i
$816$	29.2591	+	19.8057i	1.02427	+	0.693338i
$817$	4.56154	+	25.8698i	0.159588	+	0.905069i
$818$	−12.0041	−	28.5243i	−0.419714	−	0.997328i
$819$	−7.43640	+	12.4872i	−0.259849	+	0.436339i
$820$	0.0695875	−	0.0711759i	0.00243010	−	0.00248557i
$821$	16.2221	−	44.5699i	0.566155	−	1.55550i	−0.244301	−	0.969699i	$-0.578558\pi$
$821$	16.2221	−	44.5699i	0.566155	−	1.55550i	0.810456	−	0.585799i	$-0.199219\pi$
$822$	30.8843	−	16.0335i	1.07721	−	0.559232i
$823$	13.5903	−	16.1963i	0.473729	−	0.564568i	−0.475273	−	0.879838i	$-0.657651\pi$
$823$	13.5903	−	16.1963i	0.473729	−	0.564568i	0.949002	+	0.315271i	$0.102095\pi$
$824$	41.6668	−	22.5948i	1.45153	−	0.787126i
$825$	−22.9331	+	48.3245i	−0.798428	+	1.68244i
$826$	1.54323	−	3.00580i	0.0536957	−	0.104585i
$827$	22.3496	−	38.7106i	0.777171	−	1.34610i	−0.156395	−	0.987695i	$-0.549987\pi$
$827$	22.3496	−	38.7106i	0.777171	−	1.34610i	0.933566	−	0.358406i	$-0.116680\pi$
$828$	26.8122	−	38.1100i	0.931788	−	1.32442i
$829$	−8.98059	−	15.5548i	−0.311909	−	0.540242i	0.666867	−	0.745177i	$-0.267635\pi$
$829$	−8.98059	−	15.5548i	−0.311909	−	0.540242i	−0.978776	+	0.204935i	$0.934302\pi$
$830$	−3.51013	+	0.173102i	−0.121838	+	0.00600846i
$831$	−1.55581	−	1.10514i	−0.0539706	−	0.0383369i
$832$	35.6598	+	15.1811i	1.23628	+	0.526311i
$833$	−5.02228	−	0.885564i	−0.174012	−	0.0306830i
$834$	9.53761	−	22.9532i	0.330260	−	0.794803i
$835$	−2.51991	−	3.00311i	−0.0872051	−	0.103927i
$836$	19.2584	−	75.2601i	0.666066	−	2.60292i
$837$	−19.4761	−	29.0514i	−0.673193	−	1.00416i
$838$	−20.5091	−	2.58245i	−0.708476	−	0.0892092i
$839$	−10.2211	+	8.57652i	−0.352871	+	0.296094i	−0.801942	−	0.597402i	$-0.796200\pi$
$839$	−10.2211	+	8.57652i	−0.352871	+	0.296094i	0.449070	+	0.893496i	$0.351755\pi$
$840$	−0.123776	+	1.02020i	−0.00427067	+	0.0352004i
$841$	4.77632	−	27.0878i	0.164701	−	0.934063i
$842$	−42.1519	+	9.59466i	−1.45265	+	0.330654i
$843$	−9.84081	−	21.4816i	−0.338935	−	0.739867i
$844$	48.6401	+	3.70294i	1.67426	+	0.127460i
$845$	−1.90211	+	1.09818i	−0.0654345	+	0.0377787i
$846$	−13.0017	+	11.7267i	−0.447006	+	0.403173i
$847$	24.1012	+	13.9148i	0.828127	+	0.478119i
$848$	−34.3862	+	30.2015i	−1.18083	+	1.03713i
$849$	0.570852	+	7.07545i	0.0195916	+	0.242829i
$850$	26.2161	−	24.2962i	0.899205	−	0.833351i
$851$	6.34555	+	5.32455i	0.217523	+	0.182523i
$852$	2.62846	+	0.451218i	0.0900494	+	0.0154585i
$853$	28.8818	+	10.5121i	0.988895	+	0.359928i	0.785292	−	0.619125i	$-0.212513\pi$
$853$	28.8818	+	10.5121i	0.988895	+	0.359928i	0.203602	+	0.979054i	$0.434735\pi$
$854$	5.97039	+	4.52796i	0.204303	+	0.154944i
$855$	−2.56195	+	2.97071i	−0.0876170	+	0.101596i
$856$	0.619305	+	4.15888i	0.0211674	+	0.142148i
$857$	−10.2413	+	1.80582i	−0.349837	+	0.0616856i	−0.345805	−	0.938306i	$-0.612394\pi$
$857$	−10.2413	+	1.80582i	−0.349837	+	0.0616856i	−0.00403118	+	0.999992i	$0.501283\pi$
$858$	−70.5484	+	22.1571i	−2.40848	+	0.756431i
$859$	5.48475	+	15.0692i	0.187137	+	0.514155i	0.997412	−	0.0718945i	$-0.0229045\pi$
$859$	5.48475	+	15.0692i	0.187137	+	0.514155i	−0.810275	+	0.586050i	$0.800682\pi$
$860$	0.729091	−	1.61075i	0.0248618	−	0.0549260i
$861$	−0.103673	−	0.397648i	−0.00353318	−	0.0135518i
$862$	−20.4628	+	13.1992i	−0.696967	+	0.449565i
$863$	−5.13713			−0.174870			−0.0874349	−	0.996170i	$-0.527867\pi$
$863$	−5.13713			−0.174870			−0.0874349	+	0.996170i	$0.527867\pi$
$864$	−13.7789	−	25.9643i	−0.468767	−	0.883322i
$865$	2.47351			0.0841018
$866$	−24.7262	+	15.9492i	−0.840232	+	0.541975i
$867$	15.0422	+	4.13975i	0.510861	+	0.140593i
$868$	5.55133	−	12.2643i	0.188424	−	0.416277i
$869$	30.5169	+	83.8445i	1.03522	+	2.84423i
$870$	−0.462628	−	0.424874i	−0.0156846	−	0.0144046i
$871$	−4.27268	+	0.753389i	−0.144774	+	0.0255276i
$872$	−1.55319	−	10.4303i	−0.0525977	−	0.353215i
$873$	4.78674	−	12.6180i	0.162006	−	0.427054i
$874$	54.5484	+	41.3696i	1.84513	+	1.39935i
$875$	1.96257	+	0.714317i	0.0663469	+	0.0241483i
$876$	18.2533	−	21.9544i	0.616722	−	0.741770i
$877$	−5.87087	−	4.92624i	−0.198245	−	0.166347i	0.538261	−	0.842778i	$-0.319081\pi$
$877$	−5.87087	−	4.92624i	−0.198245	−	0.166347i	−0.736506	+	0.676431i	$0.763526\pi$
$878$	31.5130	−	29.2051i	1.06351	−	0.985624i
$879$	−17.9281	+	12.3737i	−0.604701	+	0.417353i
$880$	−3.92858	+	3.45049i	−0.132432	+	0.116316i
$881$	−26.0106	−	15.0172i	−0.876321	−	0.505944i	−0.00687719	−	0.999976i	$-0.502189\pi$
$881$	−26.0106	−	15.0172i	−0.876321	−	0.505944i	−0.869444	+	0.494032i	$0.835522\pi$
$882$	3.34546	+	2.60919i	0.112648	+	0.0878561i
$883$	4.23339	−	2.44415i	0.142465	−	0.0822521i	−0.427073	−	0.904217i	$-0.640455\pi$
$883$	4.23339	−	2.44415i	0.142465	−	0.0822521i	0.569538	+	0.821965i	$0.307122\pi$
$884$	49.2699	+	3.75089i	1.65713	+	0.126156i
$885$	−0.864254	−	0.0815032i	−0.0290516	−	0.00273970i
$886$	9.68259	−	2.20396i	0.325293	−	0.0740436i
$887$	−5.56560	+	31.5641i	−0.186875	+	1.05982i	0.736648	+	0.676276i	$0.236407\pi$
$887$	−5.56560	+	31.5641i	−0.186875	+	1.05982i	−0.923523	+	0.383543i	$0.874704\pi$
$888$	4.80702	−	2.04863i	0.161313	−	0.0687474i
$889$	10.9522	−	9.19000i	0.367326	−	0.308223i
$890$	−2.20552	−	0.277713i	−0.0739292	−	0.00930895i
$891$	52.1621	+	20.5991i	1.74749	+	0.690095i
$892$	−9.40570	+	36.7566i	−0.314926	+	1.23070i
$893$	−16.5354	−	19.7061i	−0.553335	−	0.659439i
$894$	10.5788	+	13.8185i	0.353808	+	0.462161i
$895$	−2.14875	−	0.378882i	−0.0718247	−	0.0126646i
$896$	5.69737	−	9.77445i	0.190336	−	0.326542i
$897$	6.11835	−	64.8785i	0.204286	−	2.16623i
$898$	−36.4315	+	1.79662i	−1.21574	+	0.0599540i
$899$	4.11407	+	7.12578i	0.137212	+	0.237658i
$900$	−28.7399	+	7.63197i	−0.957996	+	0.254399i
$901$	−29.1745	+	50.5318i	−0.971945	+	1.68346i
$902$	0.954951	−	1.85999i	0.0317964	−	0.0619309i
$903$	−4.14614	−	6.00733i	−0.137975	−	0.199912i
$904$	−18.0794	+	9.80394i	−0.601311	+	0.326074i
$905$	−1.13048	+	1.34725i	−0.0375783	+	0.0447841i
$906$	23.4720	+	14.9903i	0.779806	+	0.498018i
$907$	3.35467	−	9.21688i	0.111390	−	0.306042i	−0.871455	−	0.490476i	$-0.836823\pi$
$907$	3.35467	−	9.21688i	0.111390	−	0.306042i	0.982845	+	0.184434i	$0.0590453\pi$
$908$	−40.3027	+	41.2226i	−1.33749	+	1.36802i
$909$	1.17609	+	7.24109i	0.0390083	+	0.240172i
$910$	0.557487	+	1.32470i	0.0184805	+	0.0439135i
$911$	−2.65313	−	15.0467i	−0.0879022	−	0.498518i	−0.996693	−	0.0812649i	$-0.974104\pi$
$911$	−2.65313	−	15.0467i	−0.0879022	−	0.498518i	0.908790	−	0.417253i	$-0.137007\pi$
$912$	38.8467	−	18.8677i	1.28634	−	0.624772i
$913$	−69.3664	+	25.2473i	−2.29569	+	0.835564i
$914$	−1.41285	+	4.57074i	−0.0467328	+	0.151187i
$915$	0.510828	−	1.85615i	0.0168875	−	0.0613625i
$916$	32.3035	−	15.5095i	1.06734	−	0.512448i
$917$		−	1.06724i		−	0.0352435i
$918$	−27.2562	−	25.7198i	−0.899589	−	0.848879i
$919$		−	13.3298i		−	0.439710i	−0.975533	−	0.219855i	$-0.929442\pi$
$919$		−	13.3298i		−	0.439710i	0.975533	−	0.219855i	$-0.0705584\pi$
$920$	−1.45981	−	4.37057i	−0.0481284	−	0.144093i
$921$	−42.7316	+	11.1408i	−1.40806	+	0.367103i
$922$	−11.8117	−	3.65107i	−0.388996	−	0.120242i
$923$	3.50477	−	1.27563i	0.115361	−	0.0419880i
$924$	3.84449	+	21.2409i	0.126475	+	0.698774i
$925$	−0.917933	−	5.20586i	−0.0301815	−	0.171168i
$926$	−9.37386	+	3.94489i	−0.308044	+	0.129637i
$927$	−47.4703	+	16.5544i	−1.55913	+	0.543719i
$928$	2.82540	+	6.31144i	0.0927481	+	0.207183i
$929$	−9.97212	+	27.3982i	−0.327175	+	0.898905i	0.661649	+	0.749814i	$0.269857\pi$
$929$	−9.97212	+	27.3982i	−0.327175	+	0.898905i	−0.988823	+	0.149091i	$0.952365\pi$
$930$	−3.45525	−	0.154732i	−0.113302	−	0.00507385i
$931$	−4.00676	+	4.77507i	−0.131316	+	0.156496i
$932$	−26.1517	+	18.7549i	−0.856628	+	0.614338i
$933$	23.2285	−	1.87409i	0.760467	−	0.0613549i
$934$	35.2248	+	18.0850i	1.15259	+	0.591760i
$935$	−3.33316	+	5.77320i	−0.109006	+	0.188804i
$936$	−34.7449	−	21.9690i	−1.13567	−	0.718079i
$937$	−23.0016	−	39.8400i	−0.751430	−	1.30152i	−0.947130	−	0.320851i	$-0.896031\pi$
$937$	−23.0016	−	39.8400i	−0.751430	−	1.30152i	0.195699	−	0.980664i	$-0.437302\pi$
$938$	0.0623818	+	1.26497i	0.00203684	+	0.0413026i
$939$	−46.4917	+	21.2980i	−1.51720	+	0.695034i
$940$	0.170357	+	1.72303i	0.00555643	+	0.0561991i
$941$	56.9923	+	10.0493i	1.85790	+	0.327597i	0.986600	−	0.163161i	$-0.0521689\pi$
$941$	56.9923	+	10.0493i	1.85790	+	0.327597i	0.871296	+	0.490758i	$0.163280\pi$
$942$	−0.550519	−	4.21806i	−0.0179369	−	0.137432i
$943$	1.18438	+	1.41149i	0.0385687	+	0.0459644i
$944$	8.38208	+	4.59038i	0.272813	+	0.149404i
$945$	0.303413	−	1.04695i	0.00987002	−	0.0340571i
$946$	4.63961	−	36.8465i	0.150847	−	1.19798i
$947$	19.0467	−	15.9821i	0.618935	−	0.519348i	−0.278534	−	0.960426i	$-0.589848\pi$
$947$	19.0467	−	15.9821i	0.618935	−	0.519348i	0.897468	+	0.441079i	$0.145404\pi$
$948$	−24.6064	+	43.0682i	−0.799177	+	1.39879i
$949$	6.93367	−	39.3228i	0.225077	−	1.27647i
$950$	−9.69650	−	42.5993i	−0.314596	−	1.38210i
$951$	1.05797	−	1.48940i	0.0343069	−	0.0482972i
$952$	2.88320	−	14.1332i	0.0934451	−	0.458060i
$953$	22.8721	−	13.2052i	0.740900	−	0.427759i	−0.0814962	−	0.996674i	$-0.525970\pi$
$953$	22.8721	−	13.2052i	0.740900	−	0.427759i	0.822397	+	0.568915i	$0.192637\pi$
$954$	41.1444	−	25.7584i	1.33210	−	0.833960i
$955$	3.98742	+	2.30214i	0.129030	+	0.0744954i
$956$	−34.7345	−	23.7418i	−1.12339	−	0.767865i
$957$	−11.9194	−	5.65651i	−0.385299	−	0.182849i
$958$	−5.28512	−	5.70277i	−0.170755	−	0.184248i
$959$	−10.8827	−	9.13164i	−0.351419	−	0.294876i
$960$	−2.87519	−	0.427024i	−0.0927965	−	0.0137821i
$961$	13.4447	+	4.89346i	0.433699	+	0.157853i
$962$	4.41588	−	5.82262i	0.142374	−	0.187729i
$963$	0.0602967	−	4.45940i	0.00194304	−	0.143702i
$964$	11.9307	+	42.5974i	0.384261	+	1.37197i
$965$	−1.56791	+	0.276465i	−0.0504728	+	0.00889972i
$966$	−18.5676	−	4.13812i	−0.597401	−	0.133142i
$967$	−6.78026	−	18.6286i	−0.218039	−	0.599056i	0.781658	−	0.623708i	$-0.214374\pi$
$967$	−6.78026	−	18.6286i	−0.218039	−	0.599056i	−0.999696	+	0.0246519i	$0.992152\pi$
$968$	−41.1635	+	67.0932i	−1.32304	+	2.15646i
$969$	39.1956	−	38.6692i	1.25914	−	1.24223i
$970$	−0.723391	−	1.12148i	−0.0232267	−	0.0360087i
$971$	51.3629			1.64831			0.824157	−	0.566361i	$-0.191649\pi$
$971$	51.3629			1.64831			0.824157	+	0.566361i	$0.191649\pi$
$972$	10.0008	+	29.5294i	0.320776	+	0.947155i
$973$	−10.1474			−0.325310
$974$	−25.3315	−	39.2718i	−0.811675	−	1.25835i
$975$	−29.6040	+	29.2064i	−0.948086	+	0.935353i
$976$	−13.2534	+	16.5388i	−0.424231	+	0.529394i
$977$	10.9848	+	30.1806i	0.351436	+	0.965563i	0.981909	+	0.189352i	$0.0606388\pi$
$977$	10.9848	+	30.1806i	0.351436	+	0.965563i	−0.630473	+	0.776211i	$0.717139\pi$
$978$	3.93969	+	0.878032i	0.125977	+	0.0280764i
$979$	−45.9823	+	8.10792i	−1.46960	+	0.259130i
$980$	0.404004	−	0.113153i	0.0129054	−	0.00361455i
$981$	−0.151222	+	11.1840i	−0.00482813	+	0.357077i
$982$	−10.2229	+	13.4796i	−0.326227	+	0.430150i
$983$	−13.8128	−	5.02744i	−0.440559	−	0.160350i	0.112211	−	0.993684i	$-0.464207\pi$
$983$	−13.8128	−	5.02744i	−0.440559	−	0.160350i	−0.552770	+	0.833334i	$0.686429\pi$
$984$	1.13215	−	0.263093i	0.0360915	−	0.00838709i
$985$	0.926249	+	0.777215i	0.0295127	+	0.0247641i
$986$	5.99272	+	6.46628i	0.190847	+	0.205928i
$987$	6.45768	+	3.06458i	0.205550	+	0.0975467i
$988$	34.0817	−	49.8618i	1.08428	−	1.58631i
$989$	28.3434	+	16.3641i	0.901267	+	0.520347i
$990$	4.70070	−	2.94287i	0.149398	−	0.0935305i
$991$	−13.0214	+	7.51788i	−0.413637	+	0.238813i	−0.692351	−	0.721561i	$-0.743425\pi$
$991$	−13.0214	+	7.51788i	−0.413637	+	0.238813i	0.278714	+	0.960374i	$0.410092\pi$
$992$	34.2570	+	16.6223i	1.08766	+	0.527758i
$993$	20.0934	−	28.2874i	0.637646	−	0.897675i
$994$	−0.241644	−	1.06161i	−0.00766448	−	0.0336721i
$995$	−0.491220	+	2.78585i	−0.0155727	+	0.0883173i
$996$	−35.6312	−	20.3574i	−1.12902	−	0.645048i
$997$	−4.73960	+	3.97700i	−0.150105	+	0.125953i	−0.714748	−	0.699383i	$-0.753458\pi$
$997$	−4.73960	+	3.97700i	−0.150105	+	0.125953i	0.564643	+	0.825335i	$0.309014\pi$
$998$	−6.15897	+	48.9129i	−0.194959	+	1.54831i
$999$	−5.38146	+	1.32560i	−0.170262	+	0.0419401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.491.19	✓	648
4.3	odd	2	inner	756.2.cf.a.491.80	yes	648
27.11	odd	18	inner	756.2.cf.a.659.80	yes	648
108.11	even	18	inner	756.2.cf.a.659.19	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.19	✓	648	1.1	even	1	trivial
756.2.cf.a.491.80	yes	648	4.3	odd	2	inner
756.2.cf.a.659.19	yes	648	108.11	even	18	inner
756.2.cf.a.659.80	yes	648	27.11	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18843 + 0.766573i) q^{2} +(1.23300 - 1.21644i) q^{3} +(0.824730 - 1.82204i) q^{4} +(0.0717474 + 0.197124i) q^{5} +(-0.532841 + 2.39083i) q^{6} +(0.984808 - 0.173648i) q^{7} +(0.416592 + 2.79758i) q^{8} +(0.0405601 - 2.99973i) q^{9} +(-0.236377 - 0.179269i) q^{10} +(-5.85555 - 2.13125i) q^{11} +(-1.19950 - 3.24980i) q^{12} +(-3.71117 - 3.11405i) q^{13} +(-1.03726 + 0.961296i) q^{14} +(0.328254 + 0.155777i) q^{15} +(-2.63964 - 3.00538i) q^{16} +(-4.41652 - 2.54988i) q^{17} +(2.25131 + 3.59606i) q^{18} +(-5.39829 + 3.11670i) q^{19} +(0.418340 + 0.0318480i) q^{20} +(1.00303 - 1.41206i) q^{21} +(8.59267 - 1.95587i) q^{22} +(-1.34858 + 7.64816i) q^{23} +(3.91674 + 2.94265i) q^{24} +(3.79651 - 3.18565i) q^{25} +(6.79761 + 0.855936i) q^{26} +(-3.59897 - 3.74799i) q^{27} +(0.495807 - 1.93757i) q^{28} +(0.785750 + 0.936421i) q^{29} +(-0.509521 + 0.0665001i) q^{30} +(6.62883 + 1.16884i) q^{31} +(5.44087 + 1.54820i) q^{32} +(-9.81240 + 4.49509i) q^{33} +(7.20339 - 0.355235i) q^{34} +(0.104888 + 0.181671i) q^{35} +(-5.43216 - 2.54787i) q^{36} +(0.533310 - 0.923721i) q^{37} +(4.02630 - 7.84217i) q^{38} +(-8.36391 + 0.674805i) q^{39} +(-0.521582 + 0.282839i) q^{40} +(0.152505 - 0.181749i) q^{41} +(-0.109582 + 2.44704i) q^{42} +(1.44134 - 3.96006i) q^{43} +(-8.71246 + 8.91133i) q^{44} +(0.594229 - 0.207227i) q^{45} +(-4.26019 - 10.1231i) q^{46} +(0.716624 + 4.06418i) q^{47} +(-6.91052 - 0.494664i) q^{48} +(0.939693 - 0.342020i) q^{49} +(-2.06985 + 6.69623i) q^{50} +(-8.54732 + 2.22843i) q^{51} +(-8.73462 + 4.19365i) q^{52} -11.4415i q^{53} +(7.15023 + 1.69535i) q^{54} -1.30718i q^{55} +(0.896057 + 2.68274i) q^{56} +(-2.86480 + 10.4096i) q^{57} +(-1.65164 - 0.510535i) q^{58} +(-2.24509 + 0.817148i) q^{59} +(0.554553 - 0.469616i) q^{60} +(-0.920073 - 5.21799i) q^{61} +(-8.77390 + 3.69240i) q^{62} +(-0.480953 - 2.96120i) q^{63} +(-7.65290 + 2.33090i) q^{64} +(0.347587 - 0.954987i) q^{65} +(8.21553 - 12.8640i) q^{66} +(0.575651 - 0.686034i) q^{67} +(-8.28841 + 5.94410i) q^{68} +(7.64072 + 11.0706i) q^{69} +(-0.263916 - 0.135499i) q^{70} +(-0.384935 + 0.666726i) q^{71} +(8.40887 - 1.13619i) q^{72} +(4.12103 + 7.13783i) q^{73} +(0.0742979 + 1.50660i) q^{74} +(0.805940 - 8.54612i) q^{75} +(1.22662 + 12.4063i) q^{76} +(-6.13668 - 1.08206i) q^{77} +(9.42263 - 7.21351i) q^{78} +(-9.20396 - 10.9688i) q^{79} +(0.403046 - 0.735965i) q^{80} +(-8.99671 - 0.243339i) q^{81} +(-0.0419181 + 0.332903i) q^{82} +(9.07476 - 7.61463i) q^{83} +(-1.74560 - 2.99213i) q^{84} +(0.185769 - 1.05355i) q^{85} +(1.32274 + 5.81114i) q^{86} +(2.10792 + 0.198787i) q^{87} +(3.52296 - 17.2692i) q^{88} +(6.48916 - 3.74652i) q^{89} +(-0.547345 + 0.701795i) q^{90} +(-4.19554 - 2.42230i) q^{91} +(12.8230 + 8.76483i) q^{92} +(9.59514 - 6.62237i) q^{93} +(-3.96715 - 4.28064i) q^{94} +(-1.00169 - 0.840519i) q^{95} +(8.59187 - 4.70955i) q^{96} +(4.22718 + 1.53857i) q^{97} +(-0.854575 + 1.12681i) q^{98} +(-6.63065 + 17.4786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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