LMFDB - Embedded newform 640.2.bm.a.101.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] 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("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.30
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.132875 - 1.40796i) q^{2} +(-0.101646 + 0.0543310i) q^{3} +(-1.96469 + 0.374166i) q^{4} +(0.634393 + 0.773010i) q^{5} +(0.0900020 + 0.135894i) q^{6} +(4.25848 - 2.84543i) q^{7} +(0.787868 + 2.71648i) q^{8} +(-1.65933 + 2.48336i) q^{9} +(1.00407 - 0.995913i) q^{10} +(-0.967235 + 0.293407i) q^{11} +(0.179374 - 0.144776i) q^{12} +(3.93989 + 3.23338i) q^{13} +(-4.57209 - 5.61768i) q^{14} +(-0.106482 - 0.0441063i) q^{15} +(3.72000 - 1.47024i) q^{16} +(-3.30544 + 1.36916i) q^{17} +(3.71695 + 2.00629i) q^{18} +(0.465837 + 4.72972i) q^{19} +(-1.53562 - 1.28136i) q^{20} +(-0.278264 + 0.520595i) q^{21} +(0.541627 + 1.32284i) q^{22} +(7.46690 - 1.48526i) q^{23} +(-0.227673 - 0.233314i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(4.02895 - 5.97683i) q^{26} +(0.0676320 - 0.686679i) q^{27} +(-7.30193 + 7.18376i) q^{28} +(1.78745 - 5.89243i) q^{29} +(-0.0479510 + 0.155783i) q^{30} +(-1.50797 - 1.50797i) q^{31} +(-2.56433 - 5.04224i) q^{32} +(0.0823746 - 0.0823746i) q^{33} +(2.36693 + 4.47199i) q^{34} +(4.90110 + 1.48673i) q^{35} +(2.33088 - 5.49990i) q^{36} +(2.42192 + 0.238539i) q^{37} +(6.59735 - 1.28434i) q^{38} +(-0.576148 - 0.114603i) q^{39} +(-1.60005 + 2.33235i) q^{40} +(-0.0260567 - 0.130996i) q^{41} +(0.769950 + 0.322609i) q^{42} +(4.40481 + 2.35442i) q^{43} +(1.79053 - 0.938360i) q^{44} +(-2.97233 + 0.292749i) q^{45} +(-3.08335 - 10.3157i) q^{46} +(-2.85662 - 6.89648i) q^{47} +(-0.298244 + 0.351555i) q^{48} +(7.35945 - 17.7673i) q^{49} +(1.40683 + 0.144357i) q^{50} +(0.261598 - 0.318757i) q^{51} +(-8.95047 - 4.87842i) q^{52} +(-1.77257 - 5.84337i) q^{53} +(-0.975801 - 0.00398025i) q^{54} +(-0.840414 - 0.561547i) q^{55} +(11.0847 + 9.32627i) q^{56} +(-0.304321 - 0.455449i) q^{57} +(-8.53379 - 1.73369i) q^{58} +(3.28406 - 2.69516i) q^{59} +(0.225707 + 0.0468133i) q^{60} +(4.85170 + 9.07689i) q^{61} +(-1.92278 + 2.32353i) q^{62} +15.2969i q^{63} +(-6.75853 + 4.28045i) q^{64} +5.09681i q^{65} +(-0.126925 - 0.105034i) q^{66} +(3.55151 + 6.64440i) q^{67} +(5.98186 - 3.92675i) q^{68} +(-0.678286 + 0.556655i) q^{69} +(1.44202 - 7.09809i) q^{70} +(2.96894 + 4.44333i) q^{71} +(-8.05334 - 2.55098i) q^{72} +(-10.9776 - 7.33497i) q^{73} +(0.0140384 - 3.44166i) q^{74} +(-0.0334569 - 0.110293i) q^{75} +(-2.68492 - 9.11813i) q^{76} +(-3.28408 + 4.00167i) q^{77} +(-0.0848002 + 0.826419i) q^{78} +(-4.75184 + 11.4720i) q^{79} +(3.49645 + 1.94289i) q^{80} +(-3.39847 - 8.20463i) q^{81} +(-0.180974 + 0.0540928i) q^{82} +(-11.4765 + 1.13034i) q^{83} +(0.351913 - 1.12692i) q^{84} +(-3.15532 - 1.68655i) q^{85} +(2.72963 - 6.51463i) q^{86} +(0.138454 + 0.696056i) q^{87} +(-1.55909 - 2.39631i) q^{88} +(-6.45769 - 1.28451i) q^{89} +(0.807129 + 4.14602i) q^{90} +(25.9783 + 2.55864i) q^{91} +(-14.1144 + 5.71192i) q^{92} +(0.235209 + 0.0713498i) q^{93} +(-9.33038 + 4.93837i) q^{94} +(-3.36060 + 3.36060i) q^{95} +(0.534604 + 0.373202i) q^{96} +(5.06752 + 5.06752i) q^{97} +(-25.9935 - 8.00095i) q^{98} +(0.876325 - 2.88886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.132875	−	1.40796i	−0.0939570	−	0.995576i
$2$	−0.132875	−	1.40796i	−0.0939570	−	0.995576i
$3$	−0.101646	+	0.0543310i	−0.0586855	+	0.0313680i	−0.500478	−	0.865749i	$-0.666843\pi$
$3$	−0.101646	+	0.0543310i	−0.0586855	+	0.0313680i	0.441793	+	0.897117i	$0.354343\pi$
$4$	−1.96469	+	0.374166i	−0.982344	+	0.187083i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	0.0900020	+	0.135894i	0.0367432	+	0.0554786i
$7$	4.25848	−	2.84543i	1.60956	−	1.07547i	0.665140	−	0.746719i	$-0.268372\pi$
$7$	4.25848	−	2.84543i	1.60956	−	1.07547i	0.944416	−	0.328752i	$-0.106628\pi$
$8$	0.787868	+	2.71648i	0.278553	+	0.960421i
$9$	−1.65933	+	2.48336i	−0.553110	+	0.827788i
$10$	1.00407	−	0.995913i	0.317515	−	0.314935i
$11$	−0.967235	+	0.293407i	−0.291632	+	0.0884657i	−0.432711	−	0.901533i	$-0.642443\pi$
$11$	−0.967235	+	0.293407i	−0.291632	+	0.0884657i	0.141079	+	0.989998i	$0.454943\pi$
$12$	0.179374	−	0.144776i	0.0517809	−	0.0417932i
$13$	3.93989	+	3.23338i	1.09273	+	0.896779i	0.995142	−	0.0984479i	$-0.0313878\pi$
$13$	3.93989	+	3.23338i	1.09273	+	0.896779i	0.0975864	+	0.995227i	$0.468888\pi$
$14$	−4.57209	−	5.61768i	−1.22194	−	1.50139i
$15$	−0.106482	−	0.0441063i	−0.0274936	−	0.0113882i
$16$	3.72000	−	1.47024i	0.930000	−	0.367559i
$17$	−3.30544	+	1.36916i	−0.801687	+	0.332069i	−0.745632	−	0.666358i	$-0.767852\pi$
$17$	−3.30544	+	1.36916i	−0.801687	+	0.332069i	−0.0560548	+	0.998428i	$0.517852\pi$
$18$	3.71695	+	2.00629i	0.876095	+	0.472887i
$19$	0.465837	+	4.72972i	0.106870	+	1.08507i	0.887729	+	0.460366i	$0.152282\pi$
$19$	0.465837	+	4.72972i	0.106870	+	1.08507i	−0.780859	+	0.624707i	$0.785218\pi$
$20$	−1.53562	−	1.28136i	−0.343375	−	0.286520i
$21$	−0.278264	+	0.520595i	−0.0607221	+	0.113603i
$22$	0.541627	+	1.32284i	0.115475	+	0.282030i
$23$	7.46690	−	1.48526i	1.55696	−	0.309698i	0.659810	−	0.751433i	$-0.270637\pi$
$23$	7.46690	−	1.48526i	1.55696	−	0.309698i	0.897146	+	0.441735i	$0.145637\pi$
$24$	−0.227673	−	0.233314i	−0.0464735	−	0.0476251i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	4.02895	−	5.97683i	0.790143	−	1.17215i
$27$	0.0676320	−	0.686679i	0.0130158	−	0.132151i
$28$	−7.30193	+	7.18376i	−1.37994	+	1.35760i
$29$	1.78745	−	5.89243i	0.331921	−	1.09420i	−0.619163	−	0.785262i	$-0.712528\pi$
$29$	1.78745	−	5.89243i	0.331921	−	1.09420i	0.951084	−	0.308933i	$-0.0999720\pi$
$30$	−0.0479510	+	0.155783i	−0.00875461	+	0.0284419i
$31$	−1.50797	−	1.50797i	−0.270839	−	0.270839i	0.558599	−	0.829438i	$-0.311339\pi$
$31$	−1.50797	−	1.50797i	−0.270839	−	0.270839i	−0.829438	+	0.558599i	$0.811339\pi$
$32$	−2.56433	−	5.04224i	−0.453313	−	0.891351i
$33$	0.0823746	−	0.0823746i	0.0143396	−	0.0143396i
$34$	2.36693	+	4.47199i	0.405925	+	0.766940i
$35$	4.90110	+	1.48673i	0.828437	+	0.251304i
$36$	2.33088	−	5.49990i	0.388480	−	0.916650i
$37$	2.42192	+	0.238539i	0.398162	+	0.0392155i	0.295117	−	0.955461i	$-0.404641\pi$
$37$	2.42192	+	0.238539i	0.398162	+	0.0392155i	0.103045	+	0.994677i	$0.467141\pi$
$38$	6.59735	−	1.28434i	1.07023	−	0.208348i
$39$	−0.576148	−	0.114603i	−0.0922575	−	0.0183512i
$40$	−1.60005	+	2.33235i	−0.252990	+	0.368776i
$41$	−0.0260567	−	0.130996i	−0.00406937	−	0.0204581i	0.978697	−	0.205309i	$-0.0658199\pi$
$41$	−0.0260567	−	0.130996i	−0.00406937	−	0.0204581i	−0.982767	+	0.184851i	$0.940820\pi$
$42$	0.769950	+	0.322609i	0.118806	+	0.0497797i
$43$	4.40481	+	2.35442i	0.671727	+	0.359046i	0.771738	−	0.635941i	$-0.219388\pi$
$43$	4.40481	+	2.35442i	0.671727	+	0.359046i	−0.100011	+	0.994986i	$0.531888\pi$
$44$	1.79053	−	0.938360i	0.269933	−	0.141463i
$45$	−2.97233	+	0.292749i	−0.443089	+	0.0436405i
$46$	−3.08335	−	10.3157i	−0.454615	−	1.52097i
$47$	−2.85662	−	6.89648i	−0.416680	−	1.00596i	−0.983303	−	0.181978i	$-0.941750\pi$
$47$	−2.85662	−	6.89648i	−0.416680	−	1.00596i	0.566622	−	0.823978i	$-0.308250\pi$
$48$	−0.298244	+	0.351555i	−0.0430479	+	0.0507427i
$49$	7.35945	−	17.7673i	1.05135	−	2.53818i
$50$	1.40683	+	0.144357i	0.198955	+	0.0204151i
$51$	0.261598	−	0.318757i	0.0366310	−	0.0446350i
$52$	−8.95047	−	4.87842i	−1.24121	−	0.676515i
$53$	−1.77257	−	5.84337i	−0.243481	−	0.802649i	−0.990460	−	0.137801i	$-0.955996\pi$
$53$	−1.77257	−	5.84337i	−0.243481	−	0.802649i	0.746979	−	0.664848i	$-0.231504\pi$
$54$	−0.975801	−	0.00398025i	−0.132790	−	0.000541643i
$55$	−0.840414	−	0.561547i	−0.113321	−	0.0757190i
$56$	11.0847	+	9.32627i	1.48125	+	1.24627i
$57$	−0.304321	−	0.455449i	−0.0403083	−	0.0603257i
$58$	−8.53379	−	1.73369i	−1.12054	−	0.227645i
$59$	3.28406	−	2.69516i	0.427548	−	0.350879i	−0.395878	−	0.918303i	$-0.629560\pi$
$59$	3.28406	−	2.69516i	0.427548	−	0.350879i	0.823426	+	0.567424i	$0.192060\pi$
$60$	0.225707	+	0.0468133i	0.0291387	+	0.00604357i
$61$	4.85170	+	9.07689i	0.621196	+	1.16218i	0.974015	+	0.226485i	$0.0727233\pi$
$61$	4.85170	+	9.07689i	0.621196	+	1.16218i	−0.352818	+	0.935692i	$0.614777\pi$
$62$	−1.92278	+	2.32353i	−0.244194	+	0.295088i
$63$			15.2969i			1.92722i
$64$	−6.75853	+	4.28045i	−0.844816	+	0.535057i
$65$			5.09681i			0.632182i
$66$	−0.126925	−	0.105034i	−0.0156234	−	0.0129288i
$67$	3.55151	+	6.64440i	0.433885	+	0.811743i	0.999920	−	0.0126388i	$-0.00402316\pi$
$67$	3.55151	+	6.64440i	0.433885	+	0.811743i	−0.566035	+	0.824381i	$0.691523\pi$
$68$	5.98186	−	3.92675i	0.725408	−	0.476188i
$69$	−0.678286	+	0.556655i	−0.0816560	+	0.0670134i
$70$	1.44202	−	7.09809i	0.172354	−	0.848384i
$71$	2.96894	+	4.44333i	0.352349	+	0.527327i	0.964732	−	0.263234i	$-0.0847891\pi$
$71$	2.96894	+	4.44333i	0.352349	+	0.527327i	−0.612383	+	0.790561i	$0.709789\pi$
$72$	−8.05334	−	2.55098i	−0.949095	−	0.300635i
$73$	−10.9776	−	7.33497i	−1.28483	−	0.858493i	−0.289701	−	0.957117i	$-0.593556\pi$
$73$	−10.9776	−	7.33497i	−1.28483	−	0.858493i	−0.995125	+	0.0986245i	$0.968556\pi$
$74$	0.0140384	−	3.44166i	0.00163193	−	0.400085i
$75$	−0.0334569	−	0.110293i	−0.00386327	−	0.0127355i
$76$	−2.68492	−	9.11813i	−0.307982	−	1.04592i
$77$	−3.28408	+	4.00167i	−0.374256	+	0.456032i
$78$	−0.0848002	+	0.826419i	−0.00960173	+	0.0935736i
$79$	−4.75184	+	11.4720i	−0.534624	+	1.29070i	0.393808	+	0.919193i	$0.371157\pi$
$79$	−4.75184	+	11.4720i	−0.534624	+	1.29070i	−0.928432	+	0.371503i	$0.878843\pi$
$80$	3.49645	+	1.94289i	0.390915	+	0.217222i
$81$	−3.39847	−	8.20463i	−0.377607	−	0.911625i
$82$	−0.180974	+	0.0540928i	−0.0199853	+	0.00597356i
$83$	−11.4765	+	1.13034i	−1.25971	+	0.124070i	−0.705742	−	0.708469i	$-0.749386\pi$
$83$	−11.4765	+	1.13034i	−1.25971	+	0.124070i	−0.553966	+	0.832539i	$0.686886\pi$
$84$	0.351913	−	1.12692i	0.0383968	−	0.122957i
$85$	−3.15532	−	1.68655i	−0.342243	−	0.182932i
$86$	2.72963	−	6.51463i	0.294344	−	0.702491i
$87$	0.138454	+	0.696056i	0.0148439	+	0.0746251i
$88$	−1.55909	−	2.39631i	−0.166199	−	0.255447i
$89$	−6.45769	−	1.28451i	−0.684513	−	0.136158i	−0.159430	−	0.987209i	$-0.550966\pi$
$89$	−6.45769	−	1.28451i	−0.684513	−	0.136158i	−0.525083	+	0.851051i	$0.675966\pi$
$90$	0.807129	+	4.14602i	0.0850788	+	0.437029i
$91$	25.9783	+	2.55864i	2.72327	+	0.268218i
$92$	−14.1144	+	5.71192i	−1.47153	+	0.595509i
$93$	0.235209	+	0.0713498i	0.0243900	+	0.00739863i
$94$	−9.33038	+	4.93837i	−0.962355	+	0.509354i
$95$	−3.36060	+	3.36060i	−0.344790	+	0.344790i
$96$	0.534604	+	0.373202i	0.0545628	+	0.0380898i
$97$	5.06752	+	5.06752i	0.514529	+	0.514529i	0.915911	−	0.401382i	$-0.131470\pi$
$97$	5.06752	+	5.06752i	0.514529	+	0.514529i	−0.401382	+	0.915911i	$0.631470\pi$
$98$	−25.9935	−	8.00095i	−2.62574	−	0.808218i
$99$	0.876325	−	2.88886i	0.0880739	−	0.290341i
$100$	0.0163155	−	1.99993i	0.00163155	−	0.199993i
$101$	−0.927557	+	9.41764i	−0.0922953	+	0.937090i	0.831838	+	0.555019i	$0.187289\pi$
$101$	−0.927557	+	9.41764i	−0.0922953	+	0.937090i	−0.924133	+	0.382071i	$0.875211\pi$
$102$	−0.483557	−	0.325963i	−0.0478793	−	0.0322752i
$103$	0.995063	−	5.00252i	0.0980465	−	0.492913i	−0.900292	−	0.435287i	$-0.856647\pi$
$103$	0.995063	−	5.00252i	0.0980465	−	0.492913i	0.998338	−	0.0576261i	$-0.0183531\pi$
$104$	−5.67931	+	13.2501i	−0.556902	+	1.29928i
$105$	−0.578954	+	0.115161i	−0.0565001	+	0.0112386i
$106$	−7.99169	+	3.27214i	−0.776222	+	0.317818i
$107$	−4.63080	+	8.66362i	−0.447677	+	0.837544i	0.552316	+	0.833635i	$0.313744\pi$
$107$	−4.63080	+	8.66362i	−0.447677	+	0.837544i	−0.999992	+	0.00390910i	$0.998756\pi$
$108$	0.124056	+	1.37442i	0.0119373	+	0.132253i
$109$	−2.02312	−	20.5411i	−0.193780	−	1.96748i	−0.247391	−	0.968916i	$-0.579573\pi$
$109$	−2.02312	−	20.5411i	−0.193780	−	1.96748i	0.0536109	−	0.998562i	$-0.482927\pi$
$110$	−0.678964	+	1.25788i	−0.0647366	+	0.119934i
$111$	−0.259139	+	0.107339i	−0.0245964	+	0.0101882i
$112$	11.6581	−	16.8460i	1.10159	−	1.59180i
$113$	−4.18945	−	1.73533i	−0.394110	−	0.163246i	0.176822	−	0.984243i	$-0.443418\pi$
$113$	−4.18945	−	1.73533i	−0.394110	−	0.163246i	−0.570933	+	0.820997i	$0.693418\pi$
$114$	−0.600816	+	0.488989i	−0.0562716	+	0.0457980i
$115$	5.88507	+	4.82975i	0.548785	+	0.450377i
$116$	−1.30703	+	12.2456i	−0.121355	+	1.13697i
$117$	−14.5672	+	4.41893i	−1.34674	+	0.408530i
$118$	−4.23103	−	4.26569i	−0.389498	−	0.392689i
$119$	−10.1803	+	15.2359i	−0.933228	+	1.39667i
$120$	0.0359201	−	0.324007i	0.00327905	−	0.0295776i
$121$	−8.29671	+	5.54368i	−0.754246	+	0.503971i
$122$	12.1352	−	8.03708i	1.09867	−	0.727643i
$123$	0.00976570	+	0.0118995i	0.000880544	+	0.00107295i
$124$	3.52692	+	2.39846i	0.316727	+	0.215388i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	21.5373	−	2.03258i	1.91870	−	0.181076i
$127$	12.5114			1.11021			0.555105	−	0.831780i	$-0.312678\pi$
$127$	12.5114			1.11021			0.555105	+	0.831780i	$0.312678\pi$
$128$	6.92474	+	8.94695i	0.612066	+	0.790806i
$129$	−0.575650			−0.0506832
$130$	7.17609	−	0.677241i	0.629385	−	0.0593979i
$131$	14.3352	−	7.66234i	1.25247	−	0.669461i	0.294318	−	0.955708i	$-0.404907\pi$
$131$	14.3352	−	7.66234i	1.25247	−	0.669461i	0.958156	+	0.286246i	$0.0924075\pi$
$132$	−0.131019	+	0.192662i	−0.0114037	+	0.0167691i
$133$	15.4418	+	18.8159i	1.33898	+	1.63155i
$134$	8.88313	−	5.88325i	0.767385	−	0.508235i
$135$	0.573715	−	0.383344i	0.0493775	−	0.0329930i
$136$	−6.32354	−	7.90044i	−0.542239	−	0.677457i
$137$	−1.96039	+	2.93394i	−0.167488	+	0.250663i	−0.905713	−	0.423891i	$-0.860664\pi$
$137$	−1.96039	+	2.93394i	−0.167488	+	0.250663i	0.738225	+	0.674554i	$0.235664\pi$
$138$	0.873874	+	0.881032i	0.0743891	+	0.0749984i
$139$	9.93232	−	3.01294i	0.842448	−	0.255554i	0.160574	−	0.987024i	$-0.448665\pi$
$139$	9.93232	−	3.01294i	0.842448	−	0.255554i	0.681874	+	0.731470i	$0.261165\pi$
$140$	−10.1854	−	1.08714i	−0.860825	−	0.0918803i
$141$	0.665057	+	0.545798i	0.0560079	+	0.0459645i
$142$	5.86153	−	4.77055i	0.491888	−	0.400336i
$143$	−4.75950	−	1.97145i	−0.398009	−	0.164861i
$144$	−2.52158	+	11.6777i	−0.210131	+	0.973144i
$145$	5.68885	−	2.35640i	0.472433	−	0.195688i
$146$	−8.86867	+	16.4306i	−0.733977	+	1.35980i
$147$	0.217255	+	2.20582i	0.0179188	+	0.181933i
$148$	−4.84758	+	0.437546i	−0.398468	+	0.0359661i
$149$	−3.43645	+	6.42914i	−0.281525	+	0.526696i	−0.982447	−	0.186542i	$-0.940272\pi$
$149$	−3.43645	+	6.42914i	−0.281525	+	0.526696i	0.700922	+	0.713238i	$0.252772\pi$
$150$	−0.150842	+	0.0617610i	−0.0123162	+	0.00504277i
$151$	1.40571	−	0.279614i	0.114395	−	0.0227547i	−0.137561	−	0.990493i	$-0.543926\pi$
$151$	1.40571	−	0.279614i	0.114395	−	0.0227547i	0.251956	+	0.967739i	$0.418926\pi$
$152$	−12.4812	+	4.99183i	−1.01236	+	0.404891i
$153$	2.08470	−	10.4805i	0.168538	−	0.847297i
$154$	6.07055	+	4.09213i	0.489179	+	0.329753i
$155$	0.209030	−	2.12232i	0.0167897	−	0.170469i
$156$	1.17483	+	0.00958432i	0.0940618	+	0.000767359i
$157$	−3.14399	+	10.3644i	−0.250918	+	0.827165i	0.737492	+	0.675356i	$0.236010\pi$
$157$	−3.14399	+	10.3644i	−0.250918	+	0.827165i	−0.988410	+	0.151809i	$0.951490\pi$
$158$	16.7834	+	5.16605i	1.33522	+	0.410989i
$159$	0.497651	+	0.497651i	0.0394663	+	0.0394663i
$160$	2.27091	−	5.18102i	0.179532	−	0.409595i
$161$	27.5715	−	27.5715i	2.17294	−	2.17294i
$162$	−11.1002	+	5.87509i	−0.872113	+	0.461591i
$163$	−1.08926	−	0.330423i	−0.0853175	−	0.0258808i	0.247337	−	0.968929i	$-0.420444\pi$
$163$	−1.08926	−	0.330423i	−0.0853175	−	0.0258808i	−0.332655	+	0.943049i	$0.607944\pi$
$164$	0.100207	+	0.247617i	0.00782489	+	0.0193356i
$165$	0.115934	+	0.0114185i	0.00902547	+	0.000888932i
$166$	3.11641	+	16.0082i	0.241880	+	1.24248i
$167$	−17.9371	−	3.56791i	−1.38801	−	0.276093i	−0.556154	−	0.831079i	$-0.687724\pi$
$167$	−17.9371	−	3.56791i	−1.38801	−	0.276093i	−0.831860	+	0.554986i	$0.812724\pi$
$168$	−1.63342	−	0.345738i	−0.126021	−	0.0266743i
$169$	2.53178	+	12.7281i	0.194753	+	0.979087i
$170$	−1.95533	+	4.66666i	−0.149967	+	0.357916i
$171$	−12.5186	−	6.69133i	−0.957321	−	0.511699i
$172$	−9.53502	−	2.97757i	−0.727039	−	0.227038i
$173$	−14.9277	+	1.47025i	−1.13493	+	0.111781i	−0.647986	−	0.761652i	$-0.724388\pi$
$173$	−14.9277	+	1.47025i	−1.13493	+	0.111781i	−0.486944	+	0.873433i	$0.661888\pi$
$174$	0.961621	−	0.287426i	0.0729003	−	0.0217897i
$175$	1.95997	+	4.73177i	0.148159	+	0.357689i
$176$	−3.16673	+	2.51354i	−0.238702	+	0.189465i
$177$	−0.187381	+	0.452378i	−0.0140844	+	0.0340028i
$178$	−0.950473	+	9.26283i	−0.0712410	+	0.694278i
$179$	3.15767	−	3.84763i	0.236015	−	0.287585i	−0.641511	−	0.767114i	$-0.721692\pi$
$179$	3.15767	−	3.84763i	0.236015	−	0.287585i	0.877526	+	0.479528i	$0.159192\pi$
$180$	5.73017	−	1.68731i	0.427102	−	0.125764i
$181$	0.243574	+	0.802956i	0.0181047	+	0.0596832i	0.965527	−	0.260302i	$-0.0838221\pi$
$181$	0.243574	+	0.802956i	0.0181047	+	0.0596832i	−0.947423	+	0.319985i	$0.896322\pi$
$182$	0.150580	−	36.9163i	0.0111617	−	2.73642i
$183$	−0.986313	−	0.659033i	−0.0729104	−	0.0487172i
$184$	9.91760	+	19.1135i	0.731135	+	1.40907i
$185$	1.35206	+	2.02350i	0.0994053	+	0.148771i
$186$	0.0692040	−	0.340644i	0.00507429	−	0.0249773i
$187$	2.79541	−	2.29414i	0.204421	−	0.167764i
$188$	8.19279	+	12.4806i	0.597520	+	0.910241i
$189$	−1.66589	−	3.11665i	−0.121175	−	0.226703i
$190$	5.17812	+	4.28504i	0.375661	+	0.310870i
$191$		−	17.9892i		−	1.30165i	−0.759226	−	0.650827i	$-0.774422\pi$
$191$		−	17.9892i		−	1.30165i	0.759226	−	0.650827i	$-0.225578\pi$
$192$	0.454417	−	0.802290i	0.0327947	−	0.0579003i
$193$			19.9233i			1.43411i	0.697016	+	0.717055i	$0.254511\pi$
$193$			19.9233i			1.43411i	−0.697016	+	0.717055i	$0.745489\pi$
$194$	6.46151	−	7.80820i	0.463909	−	0.560596i
$195$	−0.276915	−	0.518072i	−0.0198303	−	0.0370999i
$196$	−7.81111	+	37.6608i	−0.557937	+	2.69006i
$197$	−5.02546	+	4.12429i	−0.358049	+	0.293843i	−0.796170	−	0.605073i	$-0.793144\pi$
$197$	−5.02546	+	4.12429i	−0.358049	+	0.293843i	0.438121	+	0.898916i	$0.355644\pi$
$198$	−4.18383	−	0.849970i	−0.297332	−	0.0604048i
$199$	−10.8309	−	16.2096i	−0.767782	−	1.14907i	−0.984934	−	0.172929i	$-0.944677\pi$
$199$	−10.8309	−	16.2096i	−0.767782	−	1.14907i	0.217153	−	0.976138i	$-0.430323\pi$
$200$	−2.81799	+	0.242770i	−0.199262	+	0.0171664i
$201$	−0.721994	−	0.482421i	−0.0509255	−	0.0340274i
$202$	13.3829	+	0.0545881i	0.941617	+	0.00384081i
$203$	−9.15466	−	30.1789i	−0.642531	−	2.11814i
$204$	−0.394689	+	0.724140i	−0.0276338	+	0.0506999i
$205$	0.0847310	−	0.103245i	0.00591787	−	0.00721094i
$206$	−7.17556	−	0.736295i	−0.499945	−	0.0513001i
$207$	−8.70161	+	21.0076i	−0.604804	+	1.46013i
$208$	19.4102	+	6.23561i	1.34586	+	0.432362i
$209$	−1.83831	−	4.43807i	−0.127159	−	0.306988i
$210$	0.239071	+	0.799840i	0.0164974	+	0.0551942i
$211$	−14.4077	+	1.41904i	−0.991869	+	0.0976905i	−0.580914	−	0.813965i	$-0.697305\pi$
$211$	−14.4077	+	1.41904i	−0.991869	+	0.0976905i	−0.410955	+	0.911656i	$0.634805\pi$
$212$	5.66893	+	10.8172i	0.389344	+	0.742927i
$213$	−0.543193	−	0.290342i	−0.0372189	−	0.0198939i
$214$	12.8133	+	5.36879i	0.875901	+	0.367003i
$215$	0.974391	+	4.89859i	0.0664529	+	0.334081i
$216$	1.91863	−	0.357291i	0.130547	−	0.0243106i
$217$	−10.7125	−	2.13084i	−0.727210	−	0.144651i
$218$	−28.6521	+	5.57787i	−1.94057	+	0.377781i
$219$	1.51434	+	0.149150i	0.102330	+	0.0100786i
$220$	1.86126	+	0.788810i	0.125486	+	0.0531816i
$221$	−17.4501	−	5.29342i	−1.17382	−	0.356074i
$222$	0.185562	+	0.350594i	0.0124541	+	0.0235304i
$223$	−0.554503	+	0.554503i	−0.0371323	+	0.0371323i	−0.725429	−	0.688297i	$-0.758359\pi$
$223$	−0.554503	+	0.554503i	−0.0371323	+	0.0371323i	0.688297	+	0.725429i	$0.258359\pi$
$224$	−25.2675	−	14.1757i	−1.68826	−	0.947154i
$225$	−2.11193	−	2.11193i	−0.140795	−	0.140795i
$226$	−1.88659	+	6.12915i	−0.125494	+	0.407705i
$227$	0.0359619	−	0.118551i	0.00238688	−	0.00786847i	−0.955739	−	0.294216i	$-0.904941\pi$
$227$	0.0359619	−	0.118551i	0.00238688	−	0.00786847i	0.958126	+	0.286348i	$0.0924413\pi$
$228$	0.768310	+	0.780949i	0.0508825	+	0.0517196i
$229$	1.93816	−	19.6785i	0.128078	−	1.30039i	−0.689378	−	0.724402i	$-0.742116\pi$
$229$	1.93816	−	19.6785i	0.128078	−	1.30039i	0.817456	−	0.575991i	$-0.195384\pi$
$230$	6.01810	−	8.92768i	0.396822	−	0.588674i
$231$	0.116400	−	0.585182i	0.00765855	−	0.0385022i
$232$	17.4149	+	0.213113i	1.14335	+	0.0139916i
$233$	3.71704	−	0.739365i	0.243511	−	0.0484374i	−0.0718255	−	0.997417i	$-0.522882\pi$
$233$	3.71704	−	0.739365i	0.243511	−	0.0484374i	0.315337	+	0.948980i	$0.397882\pi$
$234$	8.15729	+	19.9229i	0.533259	+	1.30240i
$235$	3.51883	−	6.58328i	0.229543	−	0.429446i
$236$	−5.44371	+	6.52392i	−0.354355	+	0.424671i
$237$	−0.140277	−	1.42425i	−0.00911195	−	0.0925152i
$238$	22.8042	+	12.3090i	1.47818	+	0.797873i
$239$	−12.0199	+	4.97879i	−0.777501	+	0.322051i	−0.735907	−	0.677083i	$-0.763244\pi$
$239$	−12.0199	+	4.97879i	−0.777501	+	0.322051i	−0.0415944	+	0.999135i	$0.513244\pi$
$240$	−0.460960	−	0.00752156i	−0.0297549	−	0.000485515i
$241$	−23.0217	−	9.53589i	−1.48296	−	0.614261i	−0.513185	−	0.858278i	$-0.671535\pi$
$241$	−23.0217	−	9.53589i	−1.48296	−	0.614261i	−0.969771	+	0.244017i	$0.921535\pi$
$242$	8.90770	+	10.9448i	0.572609	+	0.703558i
$243$	2.39134	+	1.96252i	0.153405	+	0.125896i
$244$	−12.9283	−	16.0179i	−0.827652	−	1.02544i
$245$	18.4031	−	5.58251i	1.17573	−	0.356654i
$246$	0.0154564	−	0.0153309i	0.000985466	−	0.000977459i
$247$	−13.4577	+	20.1408i	−0.856290	+	1.28153i
$248$	2.90829	−	5.28445i	0.184676	−	0.335563i
$249$	1.10513	−	0.738423i	0.0700347	−	0.0467957i
$250$	0.780892	+	1.17907i	0.0493880	+	0.0745710i
$251$	9.82744	+	11.9748i	0.620303	+	0.755841i	0.984482	−	0.175488i	$-0.0561503\pi$
$251$	9.82744	+	11.9748i	0.620303	+	0.755841i	−0.364179	+	0.931329i	$0.618650\pi$
$252$	−5.72356	−	30.0536i	−0.360551	−	1.89320i
$253$	−6.78645	+	3.62744i	−0.426661	+	0.228055i
$254$	−1.66246	−	17.6156i	−0.104312	−	1.10530i
$255$	0.412359			0.0258229
$256$	11.6768	−	10.9386i	0.729800	−	0.683661i
$257$	−9.36206			−0.583989			−0.291995	−	0.956420i	$-0.594319\pi$
$257$	−9.36206			−0.583989			−0.291995	+	0.956420i	$0.594319\pi$
$258$	0.0764897	+	0.810491i	0.00476204	+	0.0504590i
$259$	10.9925	−	5.87560i	0.683039	−	0.365092i
$260$	−1.90705	−	10.0136i	−0.118270	−	0.621020i
$261$	11.6671	+	14.2164i	0.722173	+	0.879971i
$262$	−12.6930	−	19.1652i	−0.784179	−	1.18403i
$263$	10.1353	−	6.77218i	0.624968	−	0.417590i	−0.202359	−	0.979311i	$-0.564861\pi$
$263$	10.1353	−	6.77218i	0.624968	−	0.417590i	0.827327	+	0.561721i	$0.189861\pi$
$264$	0.288669	+	0.158869i	0.0177664	+	0.00977769i
$265$	3.39248	−	5.07721i	0.208399	−	0.311891i
$266$	24.4402	−	24.2416i	1.49853	−	1.48635i
$267$	0.726188	−	0.220287i	0.0444420	−	0.0134813i
$268$	−9.46371	−	11.7253i	−0.578088	−	0.716238i
$269$	−13.4648	−	11.0503i	−0.820963	−	0.673747i	0.127079	−	0.991893i	$-0.459440\pi$
$269$	−13.4648	−	11.0503i	−0.820963	−	0.673747i	−0.948042	+	0.318146i	$0.896940\pi$
$270$	−0.615965	−	0.756830i	−0.0374864	−	0.0460592i
$271$	16.7479	+	6.93721i	1.01736	+	0.421406i	0.828136	−	0.560528i	$-0.189402\pi$
$271$	16.7479	+	6.93721i	1.01736	+	0.421406i	0.189227	+	0.981933i	$0.439402\pi$
$272$	−10.2832	+	9.95305i	−0.623513	+	0.603492i
$273$	−2.77961	+	1.15135i	−0.168230	+	0.0696830i
$274$	4.39135	+	2.37030i	0.265291	+	0.143195i
$275$	−0.0990716	−	1.00589i	−0.00597424	−	0.0606575i
$276$	1.12434	−	1.34744i	0.0676773	−	0.0811066i
$277$	−3.27821	+	6.13311i	−0.196969	+	0.368503i	−0.960944	−	0.276743i	$-0.910745\pi$
$277$	−3.27821	+	6.13311i	−0.196969	+	0.368503i	0.763975	+	0.645246i	$0.223245\pi$
$278$	−5.56184	−	13.5839i	−0.333577	−	0.814710i
$279$	6.24705	−	1.24262i	0.374001	−	0.0743935i
$280$	−0.177260	+	14.4851i	−0.0105933	+	0.865650i
$281$	1.53852	−	7.73467i	0.0917804	−	0.461411i	−0.907375	−	0.420322i	$-0.861917\pi$
$281$	1.53852	−	7.73467i	0.0917804	−	0.461411i	0.999155	−	0.0410895i	$-0.0130829\pi$
$282$	0.680091	−	1.00890i	0.0404988	−	0.0600788i
$283$	0.407656	−	4.13900i	0.0242326	−	0.246038i	−0.975436	−	0.220284i	$-0.929301\pi$
$283$	0.407656	−	4.13900i	0.0242326	−	0.246038i	0.999668	−	0.0257536i	$-0.00819853\pi$
$284$	−7.49559	−	7.61889i	−0.444781	−	0.452098i
$285$	0.159007	−	0.524177i	0.00941879	−	0.0310496i
$286$	−2.14329	+	6.96312i	−0.126736	+	0.411738i
$287$	−0.483701	−	0.483701i	−0.0285520	−	0.0285520i
$288$	16.7768	+	1.99859i	0.988582	+	0.117768i
$289$	−2.96948	+	2.96948i	−0.174676	+	0.174676i
$290$	−4.07362	−	7.69655i	−0.239211	−	0.451957i
$291$	−0.790418	−	0.239771i	−0.0463351	−	0.0140556i
$292$	24.3120	+	10.3035i	1.42275	+	0.602967i
$293$	12.1041	+	1.19215i	0.707127	+	0.0696460i	0.445186	−	0.895438i	$-0.353137\pi$
$293$	12.1041	+	1.19215i	0.707127	+	0.0696460i	0.261941	+	0.965084i	$0.415637\pi$
$294$	3.07684	−	0.598984i	0.179445	−	0.0349335i
$295$	4.16677	+	0.828821i	0.242598	+	0.0482558i
$296$	1.26017	+	6.76704i	0.0732459	+	0.393326i
$297$	0.136061	+	0.684023i	0.00789504	+	0.0396911i
$298$	9.50858	+	3.98410i	0.550817	+	0.230793i
$299$	34.2212	+	18.2916i	1.97906	+	1.05783i
$300$	0.107000	+	0.204172i	0.00617765	+	0.0117879i
$301$	25.4572	−	2.50731i	1.46733	−	0.144519i
$302$	−0.580469	−	1.94203i	−0.0334023	−	0.111751i
$303$	−0.417387	−	1.00766i	−0.0239783	−	0.0578887i
$304$	8.68673	+	16.9097i	0.498218	+	0.969836i
$305$	−3.93865	+	9.50873i	−0.225526	+	0.544468i
$306$	−15.0331	−	1.54257i	−0.859385	−	0.0881828i
$307$	8.64713	−	10.5366i	0.493518	−	0.601353i	−0.465378	−	0.885112i	$-0.654081\pi$
$307$	8.64713	−	10.5366i	0.493518	−	0.601353i	0.958896	+	0.283759i	$0.0915815\pi$
$308$	4.95492	−	9.09082i	0.282332	−	0.517998i
$309$	0.170648	+	0.562550i	0.00970781	+	0.0320024i
$310$	−3.01591	−	0.0123018i	−0.171292	−	0.000698693i
$311$	−21.4600	−	14.3391i	−1.21689	−	0.813097i	−0.229792	−	0.973240i	$-0.573804\pi$
$311$	−21.4600	−	14.3391i	−1.21689	−	0.813097i	−0.987094	+	0.160143i	$0.948804\pi$
$312$	−0.142612	−	1.65539i	−0.00807380	−	0.0937178i
$313$	−9.53146	−	14.2648i	−0.538750	−	0.806296i	0.457820	−	0.889045i	$-0.348630\pi$
$313$	−9.53146	−	14.2648i	−0.538750	−	0.806296i	−0.996570	+	0.0827483i	$0.973630\pi$
$314$	15.0103	+	3.04944i	0.847082	+	0.172090i
$315$	−11.8246	+	9.70423i	−0.666243	+	0.546772i
$316$	5.04347	−	24.3168i	0.283717	−	1.36793i
$317$	8.76227	+	16.3930i	0.492138	+	0.920725i	0.998300	+	0.0582869i	$0.0185638\pi$
$317$	8.76227	+	16.3930i	0.492138	+	0.920725i	−0.506162	+	0.862438i	$0.668936\pi$
$318$	0.634546	−	0.766798i	0.0355836	−	0.0429999i
$319$			6.22381i			0.348466i
$320$	−7.59640	−	2.50892i	−0.424652	−	0.140253i
$321$		−	1.13222i		−	0.0631944i
$322$	−42.4830	−	35.1559i	−2.36749	−	1.95916i
$323$	−8.01553	−	14.9960i	−0.445996	−	0.834400i
$324$	9.74682	+	14.8479i	0.541490	+	0.824886i
$325$	−3.93989	+	3.23338i	−0.218546	+	0.179356i
$326$	−0.320486	+	1.57754i	−0.0177501	+	0.0873717i
$327$	1.32166	+	1.97800i	0.0730880	+	0.109384i
$328$	0.335318	−	0.173990i	0.0185149	−	0.00960699i
$329$	−31.7883	−	21.2403i	−1.75255	−	1.17101i
$330$	0.000671998	−	0.164748i	3.69923e−5	−	0.00906907i
$331$	9.14439	+	30.1450i	0.502621	+	1.65692i	0.730256	+	0.683174i	$0.239401\pi$
$331$	9.14439	+	30.1450i	0.502621	+	1.65692i	−0.227635	+	0.973747i	$0.573099\pi$
$332$	22.1248	−	6.51486i	1.21426	−	0.357550i
$333$	−4.61115	+	5.61870i	−0.252689	+	0.307903i
$334$	−2.64007	+	25.7288i	−0.144458	+	1.40781i
$335$	−2.88314	+	6.96051i	−0.157523	+	0.380294i
$336$	−0.269743	+	2.34573i	−0.0147157	+	0.127970i
$337$	−12.5071	−	30.1948i	−0.681306	−	1.64482i	−0.761601	−	0.648046i	$-0.775586\pi$
$337$	−12.5071	−	30.1948i	−0.681306	−	1.64482i	0.0802955	−	0.996771i	$-0.474414\pi$
$338$	17.5843	−	5.25590i	0.956458	−	0.285883i
$339$	0.520124	−	0.0512277i	0.0282492	−	0.00278231i
$340$	6.83027	+	2.13294i	0.370424	+	0.115675i
$341$	1.90101	+	1.01611i	0.102945	+	0.0550254i
$342$	−7.75770	+	18.5148i	−0.419488	+	1.00116i
$343$	−12.2211	−	61.4399i	−0.659880	−	3.31744i
$344$	−2.92533	+	13.8206i	−0.157723	+	0.745154i
$345$	−0.860600	−	0.171184i	−0.0463332	−	0.00921624i
$346$	4.05357	+	20.8222i	0.217921	+	1.11941i
$347$	9.66551	+	0.951969i	0.518872	+	0.0511044i	0.354064	−	0.935221i	$-0.384800\pi$
$347$	9.66551	+	0.951969i	0.518872	+	0.0511044i	0.164808	+	0.986326i	$0.447300\pi$
$348$	−0.532460	−	1.31573i	−0.0285428	−	0.0705305i
$349$	−0.669110	−	0.202972i	−0.0358166	−	0.0108649i	0.272326	−	0.962205i	$-0.412207\pi$
$349$	−0.669110	−	0.202972i	−0.0358166	−	0.0108649i	−0.308142	+	0.951340i	$0.599707\pi$
$350$	6.40171	−	3.38828i	0.342186	−	0.181111i
$351$	2.48676	−	2.48676i	0.132733	−	0.132733i
$352$	3.95974	+	4.12464i	0.211055	+	0.219844i
$353$	−8.29927	−	8.29927i	−0.441726	−	0.441726i	0.450866	−	0.892592i	$-0.351115\pi$
$353$	−8.29927	−	8.29927i	−0.441726	−	0.441726i	−0.892592	+	0.450866i	$0.851115\pi$
$354$	0.661828	+	0.203715i	0.0351758	+	0.0108273i
$355$	−1.55127	+	5.11384i	−0.0823327	+	0.271415i
$356$	13.1680	+	0.107425i	0.697901	+	0.00569350i
$357$	0.207007	−	2.10178i	0.0109560	−	0.111238i
$358$	−5.83687	−	3.93461i	−0.308488	−	0.207950i
$359$	−0.285302	+	1.43431i	−0.0150576	+	0.0756999i	−0.987583	−	0.157095i	$-0.949787\pi$
$359$	−0.285302	+	1.43431i	−0.0150576	+	0.0756999i	0.972526	+	0.232795i	$0.0747871\pi$
$360$	−3.13705	−	7.84364i	−0.165337	−	0.413396i
$361$	−3.51835	+	0.699843i	−0.185176	+	0.0368338i
$362$	1.09816	−	0.449635i	0.0577181	−	0.0236323i
$363$	0.542135	−	1.01426i	0.0284547	−	0.0532350i
$364$	−51.9967	+	4.69326i	−2.72537	+	0.245994i
$365$	−1.29408	−	13.1390i	−0.0677352	−	0.687728i
$366$	−0.796834	+	1.47626i	−0.0416512	+	0.0771652i
$367$	1.69335	−	0.701409i	0.0883922	−	0.0366133i	−0.338049	−	0.941128i	$-0.609767\pi$
$367$	1.69335	−	0.701409i	0.0883922	−	0.0366133i	0.426441	+	0.904515i	$0.359767\pi$
$368$	25.5932	−	16.5033i	1.33414	−	0.860293i
$369$	0.368547	+	0.152657i	0.0191858	+	0.00794702i
$370$	2.66934	−	2.17251i	0.138773	−	0.112944i
$371$	−24.1754	−	19.8402i	−1.25512	−	1.03005i
$372$	−0.488808	−	0.0521731i	−0.0253435	−	0.00270505i
$373$	36.0150	−	10.9250i	1.86479	−	0.565677i	0.867066	−	0.498193i	$-0.166003\pi$
$373$	36.0150	−	10.9250i	1.86479	−	0.565677i	0.997720	−	0.0674838i	$-0.0214971\pi$
$374$	−3.60149	−	3.63099i	−0.186229	−	0.187754i
$375$	0.0640325	−	0.0958314i	0.00330662	−	0.00494871i
$376$	16.4835	−	13.1935i	0.850073	−	0.680401i
$377$	26.0948	−	17.4360i	1.34395	−	0.898000i
$378$	−4.16676	+	2.75962i	−0.214315	+	0.141940i
$379$	−21.6778	−	26.4145i	−1.11352	−	1.35682i	−0.927303	−	0.374313i	$-0.877879\pi$
$379$	−21.6778	−	26.4145i	−1.11352	−	1.35682i	−0.186213	−	0.982509i	$-0.559621\pi$
$380$	5.34511	−	7.85995i	0.274198	−	0.403207i
$381$	−1.27174	+	0.679759i	−0.0651532	+	0.0348251i
$382$	−25.3281	+	2.39032i	−1.29590	+	0.122300i
$383$	18.4547			0.942992			0.471496	−	0.881868i	$-0.343714\pi$
$383$	18.4547			0.942992			0.471496	+	0.881868i	$0.343714\pi$
$384$	−1.18997	−	0.533196i	−0.0607254	−	0.0272095i
$385$	−5.17673			−0.263831
$386$	28.0512	−	2.64732i	1.42777	−	0.134745i
$387$	−13.1559	+	7.03198i	−0.668753	+	0.357456i
$388$	−11.8522	−	8.06001i	−0.601704	−	0.409185i
$389$	7.69134	+	9.37192i	0.389966	+	0.475175i	0.930576	−	0.366098i	$-0.119307\pi$
$389$	7.69134	+	9.37192i	0.389966	+	0.475175i	−0.540610	+	0.841273i	$0.681807\pi$
$390$	−0.692628	+	0.458723i	−0.0350726	+	0.0232284i
$391$	−22.6478	+	15.1328i	−1.14535	+	0.765298i
$392$	54.0627	+	5.99352i	2.73058	+	0.302719i
$393$	−1.04082	+	1.55769i	−0.0525023	+	0.0785753i
$394$	6.47458	+	6.52761i	0.326185	+	0.328856i
$395$	−11.8825	+	3.60451i	−0.597872	+	0.181363i
$396$	−0.640794	+	6.00359i	−0.0322011	+	0.301692i
$397$	−7.36658	−	6.04560i	−0.369718	−	0.303420i	0.431127	−	0.902291i	$-0.358116\pi$
$397$	−7.36658	−	6.04560i	−0.369718	−	0.303420i	−0.800845	+	0.598871i	$0.795616\pi$
$398$	−21.3832	+	17.4033i	−1.07184	+	0.872348i
$399$	−2.59189	−	1.07360i	−0.129757	−	0.0537471i
$400$	0.716251	+	3.93535i	0.0358126	+	0.196768i
$401$	3.95273	−	1.63728i	0.197390	−	0.0817617i	−0.281799	−	0.959474i	$-0.590931\pi$
$401$	3.95273	−	1.63728i	0.197390	−	0.0817617i	0.479189	+	0.877712i	$0.340931\pi$
$402$	−0.583293	+	1.08064i	−0.0290920	+	0.0538974i
$403$	−1.06539	−	10.8171i	−0.0530708	−	0.538837i
$404$	−1.70140	−	18.8498i	−0.0846477	−	0.937812i
$405$	4.18630	−	7.83201i	0.208019	−	0.389176i
$406$	−41.2741	+	16.8994i	−2.04840	+	0.838703i
$407$	−2.41256	+	0.479887i	−0.119586	+	0.0237871i
$408$	1.07200	+	0.459486i	0.0530720	+	0.0227479i
$409$	4.81623	−	24.2128i	0.238147	−	1.19725i	−0.657837	−	0.753160i	$-0.728528\pi$
$409$	4.81623	−	24.2128i	0.238147	−	1.19725i	0.895984	−	0.444086i	$-0.146472\pi$
$410$	−0.156623	−	0.105579i	−0.00773507	−	0.00521417i
$411$	0.0398628	−	0.404734i	0.00196629	−	0.0199641i
$412$	−0.0832178	+	10.2007i	−0.00409985	+	0.502553i
$413$	6.31623	−	20.8218i	0.310801	−	1.02457i
$414$	30.7340	+	9.46012i	1.51049	+	0.464939i
$415$	−8.15437	−	8.15437i	−0.400282	−	0.400282i
$416$	6.20034	−	28.1573i	0.303997	−	1.38053i
$417$	−0.845886	+	0.845886i	−0.0414232	+	0.0414232i
$418$	−6.00435	+	3.17797i	−0.293682	+	0.155440i
$419$	−14.7252	−	4.46685i	−0.719375	−	0.218220i	−0.0906890	−	0.995879i	$-0.528907\pi$
$419$	−14.7252	−	4.46685i	−0.719375	−	0.218220i	−0.628686	+	0.777659i	$0.716407\pi$
$420$	1.09437	−	0.442880i	0.0534000	−	0.0216103i
$421$	−5.60643	−	0.552186i	−0.273241	−	0.0269119i	−0.0395313	−	0.999218i	$-0.512586\pi$
$421$	−5.60643	−	0.552186i	−0.273241	−	0.0269119i	−0.233710	+	0.972306i	$0.575086\pi$
$422$	3.91237	+	20.0969i	0.190451	+	0.978302i
$423$	21.8665	+	4.34953i	1.06319	+	0.211481i
$424$	14.4769	−	9.41895i	0.703059	−	0.457425i
$425$	−0.697990	−	3.50903i	−0.0338575	−	0.170213i
$426$	−0.336613	+	0.803371i	−0.0163090	+	0.0389235i
$427$	46.4885	+	24.8486i	2.24974	+	1.20251i
$428$	5.85646	−	18.7540i	0.283082	−	0.906509i
$429$	0.590895	−	0.0581981i	0.0285287	−	0.00280983i
$430$	6.76754	−	2.02280i	0.326360	−	0.0975482i
$431$	−4.44991	−	10.7430i	−0.214344	−	0.517473i	0.779737	−	0.626107i	$-0.215353\pi$
$431$	−4.44991	−	10.7430i	−0.214344	−	0.517473i	−0.994082	+	0.108633i	$0.965353\pi$
$432$	−0.757990	−	2.65388i	−0.0364688	−	0.127685i
$433$	−4.35310	+	10.5093i	−0.209197	+	0.505046i	−0.993297	−	0.115588i	$-0.963125\pi$
$433$	−4.35310	+	10.5093i	−0.209197	+	0.505046i	0.784100	+	0.620634i	$0.213125\pi$
$434$	−1.57671	+	15.3658i	−0.0756847	+	0.737584i
$435$	−0.450224	+	0.548600i	−0.0215866	+	0.0263034i
$436$	11.6606	+	39.5998i	0.558440	+	1.89649i
$437$	10.5032	+	34.6245i	0.502437	+	1.65631i
$438$	0.00877769	−	2.15195i	0.000419414	−	0.102824i
$439$	−16.4647	−	11.0014i	−0.785819	−	0.525067i	0.0967173	−	0.995312i	$-0.469166\pi$
$439$	−16.4647	−	11.0014i	−0.785819	−	0.525067i	−0.882536	+	0.470245i	$0.844166\pi$
$440$	0.863295	−	2.72539i	0.0411560	−	0.129928i
$441$	31.9108	+	47.7580i	1.51956	+	2.27419i
$442$	−5.13423	+	25.2723i	−0.244210	+	1.20208i
$443$	16.0081	−	13.1375i	0.760570	−	0.624183i	−0.172032	−	0.985091i	$-0.555033\pi$
$443$	16.0081	−	13.1375i	0.760570	−	0.624183i	0.932601	+	0.360908i	$0.117533\pi$
$444$	0.468965	−	0.307849i	0.0222561	−	0.0146099i
$445$	−3.10377	−	5.80675i	−0.147133	−	0.275266i
$446$	0.854397	+	0.707037i	0.0404569	+	0.0334792i
$447$		−	0.840203i		−	0.0397403i
$448$	−16.6014	+	37.4592i	−0.784341	+	1.76978i
$449$		−	7.17984i		−	0.338837i	−0.985544	−	0.169419i	$-0.945811\pi$
$449$		−	7.17984i		−	0.338837i	0.985544	−	0.169419i	$-0.0541890\pi$
$450$	−2.69288	+	3.25413i	−0.126944	+	0.153401i
$451$	0.0636381	+	0.119059i	0.00299660	+	0.00560625i
$452$	8.88026	+	1.84183i	0.417692	+	0.0866323i
$453$	−0.127694	+	0.104796i	−0.00599958	+	0.00492373i
$454$	−0.171693	−	0.0348804i	−0.00805793	−	0.00163702i
$455$	14.5026	+	21.7047i	0.679893	+	1.01753i
$456$	0.997453	−	1.18552i	0.0467100	−	0.0555169i
$457$	26.3959	+	17.6372i	1.23475	+	0.825032i	0.989515	−	0.144432i	$-0.0461354\pi$
$457$	26.3959	+	17.6372i	1.23475	+	0.825032i	0.245233	+	0.969464i	$0.421135\pi$
$458$	−27.9640	−	0.114064i	−1.30667	−	0.00532986i
$459$	0.716618	+	2.36237i	0.0334489	+	0.110266i
$460$	−13.3695	−	7.28696i	−0.623354	−	0.339756i
$461$	−24.9417	+	30.3915i	−1.16165	+	1.41547i	−0.269933	+	0.962879i	$0.587002\pi$
$461$	−24.9417	+	30.3915i	−1.16165	+	1.41547i	−0.891716	+	0.452595i	$0.850498\pi$
$462$	−0.839378	−	0.0861299i	−0.0390514	−	0.00400713i
$463$	−13.5212	+	32.6430i	−0.628382	+	1.51705i	0.213250	+	0.976998i	$0.431595\pi$
$463$	−13.5212	+	32.6430i	−0.628382	+	1.51705i	−0.841632	+	0.540051i	$0.818405\pi$
$464$	−2.01396	−	24.5478i	−0.0934957	−	1.13960i
$465$	0.0940607	+	0.227083i	0.00436196	+	0.0105307i
$466$	−1.53490	−	5.13519i	−0.0711028	−	0.237883i
$467$	−40.5561	+	3.99443i	−1.87671	+	0.184840i	−0.971004	−	0.239062i	$-0.923160\pi$
$467$	−40.5561	+	3.99443i	−1.87671	+	0.184840i	−0.905708	+	0.423902i	$0.860660\pi$
$468$	26.9667	−	14.1324i	1.24654	−	0.653269i
$469$	34.0302	+	18.1895i	1.57137	+	0.839914i
$470$	−9.73654	−	4.07961i	−0.449113	−	0.188179i
$471$	−0.243531	−	1.22431i	−0.0112213	−	0.0564134i
$472$	9.90874	+	6.79765i	0.456087	+	0.312887i
$473$	−4.95129	−	0.984873i	−0.227661	−	0.0452845i
$474$	−1.98665	+	0.386752i	−0.0912498	+	0.0177641i
$475$	−4.72972	−	0.465837i	−0.217015	−	0.0213741i
$476$	14.3004	−	33.7430i	0.655458	−	1.54661i
$477$	17.4525	+	5.29416i	0.799095	+	0.242403i
$478$	8.60708	+	16.2619i	0.393678	+	0.743803i
$479$	23.9182	−	23.9182i	1.09285	−	1.09285i	0.0976294	−	0.995223i	$-0.468874\pi$
$479$	23.9182	−	23.9182i	1.09285	−	1.09285i	0.995223	−	0.0976294i	$-0.0311260\pi$
$480$	0.0506602	+	0.650012i	0.00231231	+	0.0296688i
$481$	8.77082	+	8.77082i	0.399915	+	0.399915i
$482$	−10.3671	+	33.6806i	−0.472209	+	1.53411i
$483$	−1.30455	+	4.30052i	−0.0593590	+	0.195680i
$484$	14.2262	−	13.9960i	0.646645	−	0.636180i
$485$	−0.702445	+	7.13205i	−0.0318964	+	0.323850i
$486$	2.44540	−	3.62768i	0.110926	−	0.164555i
$487$	4.18565	−	21.0427i	0.189670	−	0.953535i	−0.762272	−	0.647257i	$-0.775916\pi$
$487$	4.18565	−	21.0427i	0.189670	−	0.953535i	0.951942	−	0.306279i	$-0.0990839\pi$
$488$	−20.8347	+	20.3309i	−0.943142	+	0.920338i
$489$	0.128671	−	0.0255943i	0.00581872	−	0.00115742i
$490$	−10.3053	−	25.1690i	−0.465544	−	1.13702i
$491$	1.89229	−	3.54022i	0.0853978	−	0.159768i	−0.835597	−	0.549343i	$-0.814878\pi$
$491$	1.89229	−	3.54022i	0.0853978	−	0.159768i	0.920995	+	0.389575i	$0.127378\pi$
$492$	−0.0236390	−	0.0197249i	−0.00106573	−	0.000889267i
$493$	2.15936	+	21.9243i	0.0972527	+	0.987423i
$494$	30.1456	+	16.2716i	1.35631	+	0.732094i
$495$	2.78905	−	1.15526i	0.125358	−	0.0519252i
$496$	−7.82671	−	3.39257i	−0.351430	−	0.152331i
$497$	25.2864	+	10.4740i	1.13425	+	0.469821i
$498$	−1.18651	−	1.45786i	−0.0531689	−	0.0653281i
$499$	−3.29420	−	2.70348i	−0.147468	−	0.121024i	0.557766	−	0.829998i	$-0.311658\pi$
$499$	−3.29420	−	2.70348i	−0.147468	−	0.121024i	−0.705235	+	0.708974i	$0.749158\pi$
$500$	1.55632	−	1.25613i	0.0696007	−	0.0561759i
$501$	2.01709	−	0.611876i	0.0901168	−	0.0273366i
$502$	15.5541	−	15.4278i	0.694215	−	0.688575i
$503$	10.7417	−	16.0761i	0.478948	−	0.716797i	−0.510787	−	0.859707i	$-0.670646\pi$
$503$	10.7417	−	16.0761i	0.478948	−	0.716797i	0.989736	+	0.142910i	$0.0456461\pi$
$504$	−41.5537	+	12.0519i	−1.85095	+	0.536835i
$505$	−7.86837	+	5.25748i	−0.350138	+	0.233955i
$506$	6.00903	+	9.07304i	0.267134	+	0.403346i
$507$	−0.948879	−	1.15621i	−0.0421412	−	0.0513492i
$508$	−24.5811	+	4.68135i	−1.09061	+	0.207701i
$509$	−1.67887	+	0.897377i	−0.0744148	+	0.0397755i	−0.508184	−	0.861248i	$-0.669683\pi$
$509$	−1.67887	+	0.897377i	−0.0744148	+	0.0397755i	0.433770	+	0.901024i	$0.357183\pi$
$510$	−0.0547923	−	0.580583i	−0.00242624	−	0.0257087i
$511$	−67.6189			−2.99128
$512$	−16.9526	−	14.9870i	−0.749206	−	0.662337i
$513$	3.27931			0.144785
$514$	1.24399	+	13.1814i	0.0548699	+	0.581406i
$515$	4.49826	−	2.40437i	0.198217	−	0.105949i
$516$	1.13097	−	0.215389i	0.0497883	−	0.00948195i
$517$	4.78650	+	5.83236i	0.210510	+	0.256507i
$518$	−9.73322	−	14.6962i	−0.427653	−	0.645714i
$519$	1.43746	−	0.960481i	0.0630976	−	0.0421604i
$520$	−13.8454	+	4.01561i	−0.607160	+	0.176096i
$521$	−17.3727	+	26.0001i	−0.761113	+	1.13909i	0.225218	+	0.974308i	$0.427691\pi$
$521$	−17.3727	+	26.0001i	−0.761113	+	1.13909i	−0.986331	+	0.164778i	$0.947309\pi$
$522$	18.4658	−	18.3157i	0.808225	−	0.801658i
$523$	−5.82672	+	1.76752i	−0.254785	+	0.0772881i	−0.415093	−	0.909779i	$-0.636251\pi$
$523$	−5.82672	+	1.76752i	−0.254785	+	0.0772881i	0.160309	+	0.987067i	$0.448751\pi$
$524$	−25.2973	+	20.4178i	−1.10512	+	0.891958i
$525$	−0.456305	−	0.374480i	−0.0199148	−	0.0163436i
$526$	−10.8817	−	13.3702i	−0.474463	−	0.582968i
$527$	7.04914	+	2.91985i	0.307065	+	0.127191i
$528$	0.185323	−	0.427544i	0.00806516	−	0.0186065i
$529$	32.2993	−	13.3788i	1.40432	−	0.581688i
$530$	−7.59928	−	4.10184i	−0.330091	−	0.178172i
$531$	1.24372	+	12.6277i	0.0539727	+	0.547994i
$532$	−37.3787	−	31.1897i	−1.62057	−	1.35224i
$533$	0.320899	−	0.600360i	0.0138997	−	0.0260045i
$534$	−0.406647	−	0.993172i	−0.0175973	−	0.0429787i
$535$	−9.63482	+	1.91649i	−0.416550	+	0.0828569i
$536$	−15.2513	+	14.8825i	−0.658754	+	0.642826i
$537$	−0.111919	+	0.562656i	−0.00482967	+	0.0242804i
$538$	−13.7692	+	20.4262i	−0.593631	+	0.880634i
$539$	−1.90526	+	19.3444i	−0.0820654	+	0.833224i
$540$	−0.983737	+	0.967817i	−0.0423333	+	0.0416482i
$541$	−2.75389	+	9.07834i	−0.118399	+	0.390309i	−0.996029	−	0.0890299i	$-0.971623\pi$
$541$	−2.75389	+	9.07834i	−0.118399	+	0.390309i	0.877630	+	0.479338i	$0.159123\pi$
$542$	7.54191	−	24.5021i	0.323953	−	1.05246i
$543$	−0.0683838	−	0.0683838i	−0.00293463	−	0.00293463i
$544$	15.3799	+	13.1559i	0.659406	+	0.564053i
$545$	14.5950	−	14.5950i	0.625182	−	0.625182i
$546$	1.99040	+	3.76059i	0.0851811	+	0.160938i
$547$	−16.7597	−	5.08399i	−0.716591	−	0.217376i	−0.0891262	−	0.996020i	$-0.528407\pi$
$547$	−16.7597	−	5.08399i	−0.716591	−	0.217376i	−0.627465	+	0.778645i	$0.715907\pi$
$548$	2.75379	−	6.49779i	0.117636	−	0.277572i
$549$	−30.5918	−	3.01303i	−1.30563	−	0.128593i
$550$	−1.40309	+	0.273147i	−0.0598278	+	0.0116470i
$551$	28.7022	+	5.70922i	1.22275	+	0.243221i
$552$	−2.04654	−	1.40398i	−0.0871066	−	0.0597574i
$553$	12.4070	+	62.3742i	0.527599	+	2.65242i
$554$	9.07075	+	3.80065i	0.385379	+	0.161474i
$555$	−0.247370	−	0.132222i	−0.0105003	−	0.00561252i
$556$	−18.3866	+	9.63581i	−0.779764	+	0.408649i
$557$	−17.4658	+	1.72024i	−0.740052	+	0.0728887i	−0.461016	−	0.887392i	$-0.652515\pi$
$557$	−17.4658	+	1.72024i	−0.740052	+	0.0728887i	−0.279036	+	0.960281i	$0.590015\pi$
$558$	−2.57963	−	8.63047i	−0.109204	−	0.365357i
$559$	9.74172	+	23.5186i	0.412031	+	0.994731i
$560$	20.4179	−	1.67514i	0.862816	−	0.0707875i
$561$	−0.159500	+	0.385068i	−0.00673411	+	0.0162576i
$562$	−11.0945	−	1.13843i	−0.467994	−	0.0480216i
$563$	5.65405	−	6.88948i	0.238290	−	0.290357i	−0.640110	−	0.768283i	$-0.721111\pi$
$563$	5.65405	−	6.88948i	0.238290	−	0.290357i	0.878400	+	0.477926i	$0.158611\pi$
$564$	−1.51085	−	0.823482i	−0.0636182	−	0.0346748i
$565$	−1.31633	−	4.33937i	−0.0553785	−	0.182559i
$566$	−5.88170	−	0.0239912i	−0.247226	−	0.00100842i
$567$	−37.8180	−	25.2692i	−1.58821	−	1.06121i
$568$	−9.73110	+	11.5658i	−0.408308	+	0.485291i
$569$	−6.24081	−	9.34004i	−0.261628	−	0.391555i	0.677278	−	0.735727i	$-0.263159\pi$
$569$	−6.24081	−	9.34004i	−0.261628	−	0.391555i	−0.938906	+	0.344173i	$0.888159\pi$
$570$	−0.759147	−	0.154225i	−0.0317972	−	0.00645979i
$571$	19.5445	−	16.0397i	0.817911	−	0.671242i	−0.129388	−	0.991594i	$-0.541301\pi$
$571$	19.5445	−	16.0397i	0.817911	−	0.671242i	0.947299	+	0.320352i	$0.103801\pi$
$572$	10.0886	+	2.09244i	0.421824	+	0.0874893i
$573$	0.977373	+	1.82854i	0.0408303	+	0.0763882i
$574$	−0.616759	+	0.745303i	−0.0257430	+	0.0311083i
$575$			7.61318i			0.317492i
$576$	0.584706	−	23.8866i	0.0243628	−	0.995274i
$577$			9.07670i			0.377868i	0.981990	+	0.188934i	$0.0605032\pi$
$577$			9.07670i			0.377868i	−0.981990	+	0.188934i	$0.939497\pi$
$578$	4.57548	+	3.78634i	0.190315	+	0.157491i
$579$	−1.08245	−	2.02513i	−0.0449852	−	0.0841615i
$580$	−10.2951	+	6.75816i	−0.427482	+	0.280617i
$581$	−45.6562	+	37.4690i	−1.89414	+	1.55448i
$582$	−0.232560	+	1.14473i	−0.00963992	+	0.0474508i
$583$	3.42898	+	5.13183i	0.142014	+	0.212539i
$584$	11.2764	−	35.5993i	0.466622	−	1.47311i
$585$	−12.6572	−	8.45730i	−0.523312	−	0.349666i
$586$	0.0701597	−	17.2004i	0.00289827	−	0.710543i
$587$	9.98425	+	32.9137i	0.412094	+	1.35849i	0.880109	+	0.474772i	$0.157469\pi$
$587$	9.98425	+	32.9137i	0.412094	+	1.35849i	−0.468015	+	0.883721i	$0.655031\pi$
$588$	−1.25218	−	4.25246i	−0.0516390	−	0.175369i
$589$	6.42980	−	7.83474i	0.264935	−	0.322825i
$590$	0.613285	−	5.97676i	0.0252485	−	0.246059i
$591$	0.286742	−	0.692256i	0.0117950	−	0.0284756i
$592$	9.36026	−	2.67344i	0.384704	−	0.109878i
$593$	17.1433	+	41.3876i	0.703991	+	1.69958i	0.714496	+	0.699640i	$0.246656\pi$
$593$	17.1433	+	41.3876i	0.703991	+	1.69958i	−0.0105048	+	0.999945i	$0.503344\pi$
$594$	0.944997	−	0.282458i	0.0387737	−	0.0115894i
$595$	−18.2359	+	1.79608i	−0.747597	+	0.0736319i
$596$	4.34598	−	13.9171i	0.178018	−	0.570065i
$597$	1.98160	+	1.05919i	0.0811016	+	0.0433497i
$598$	21.2066	−	50.6124i	0.867203	−	2.06970i
$599$	−0.139602	−	0.701827i	−0.00570398	−	0.0286759i	0.977828	−	0.209407i	$-0.0671535\pi$
$599$	−0.139602	−	0.701827i	−0.00570398	−	0.0286759i	−0.983532	+	0.180732i	$0.942153\pi$
$600$	0.273248	−	0.177781i	0.0111553	−	0.00725788i
$601$	12.4944	+	2.48528i	0.509656	+	0.101377i	0.443218	−	0.896414i	$-0.353837\pi$
$601$	12.4944	+	2.48528i	0.509656	+	0.101377i	0.0664376	+	0.997791i	$0.478837\pi$
$602$	−6.91281	−	35.5094i	−0.281745	−	1.44726i
$603$	−22.3936	−	2.20558i	−0.911937	−	0.0898180i
$604$	−2.65717	+	1.07532i	−0.108119	+	0.0437543i
$605$	−9.54870	−	2.89657i	−0.388210	−	0.117762i
$606$	−1.36329	+	0.721557i	−0.0553797	+	0.0293113i
$607$	−17.3840	+	17.3840i	−0.705596	+	0.705596i	−0.965606	−	0.260010i	$-0.916274\pi$
$607$	−17.3840	+	17.3840i	−0.705596	+	0.705596i	0.260010	+	0.965606i	$0.416274\pi$
$608$	22.6539	−	14.4774i	0.918735	−	0.587137i
$609$	2.57018	+	2.57018i	0.104149	+	0.104149i
$610$	13.9112	+	4.28197i	0.563249	+	0.173372i
$611$	11.0442	−	36.4079i	0.446801	−	1.47291i
$612$	−0.174345	+	21.3709i	−0.00704747	+	0.863868i
$613$	−0.917735	+	9.31792i	−0.0370670	+	0.376347i	0.958699	+	0.284423i	$0.0918019\pi$
$613$	−0.917735	+	9.31792i	−0.0370670	+	0.376347i	−0.995766	+	0.0919247i	$0.970698\pi$
$614$	−15.9840	−	10.7747i	−0.645063	−	0.434833i
$615$	−0.00300318	+	0.0150980i	−0.000121100	+	0.000608809i
$616$	−13.4579	−	5.76836i	−0.542233	−	0.232414i
$617$	−38.2718	+	7.61273i	−1.54076	+	0.306477i	−0.891122	−	0.453764i	$-0.850081\pi$
$617$	−38.2718	+	7.61273i	−1.54076	+	0.306477i	−0.649641	+	0.760241i	$0.725081\pi$
$618$	0.769372	−	0.315014i	0.0309487	−	0.0126717i
$619$	−7.84226	+	14.6718i	−0.315207	+	0.589711i	−0.988775	−	0.149415i	$-0.952261\pi$
$619$	−7.84226	+	14.6718i	−0.315207	+	0.589711i	0.673568	+	0.739126i	$0.264761\pi$
$620$	0.383420	+	4.24791i	0.0153985	+	0.170600i
$621$	−0.514894	−	5.22781i	−0.0206620	−	0.209785i
$622$	−17.3374	+	32.1201i	−0.695165	+	1.28790i
$623$	−31.1550	+	12.9048i	−1.24820	+	0.517020i
$624$	−2.31176	+	0.420751i	−0.0925446	+	0.0168435i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−18.8178	+	15.3153i	−0.752110	+	0.612124i
$627$	0.427982	+	0.351236i	0.0170920	+	0.0140270i
$628$	2.29898	−	21.5391i	0.0917393	−	0.859504i
$629$	−8.33211	+	2.52752i	−0.332223	+	0.100779i
$630$	15.2344	+	15.3591i	0.606951	+	0.611923i
$631$	19.9469	−	29.8527i	0.794075	−	1.18842i	−0.184561	−	0.982821i	$-0.559086\pi$
$631$	19.9469	−	29.8527i	0.794075	−	1.18842i	0.978637	−	0.205597i	$-0.0659136\pi$
$632$	−34.9072	−	3.86989i	−1.38853	−	0.153936i
$633$	1.38739	−	0.927026i	0.0551439	−	0.0368460i
$634$	21.9164	−	14.5151i	0.870412	−	0.576469i
$635$	7.93717	+	9.67146i	0.314977	+	0.383800i
$636$	−1.16393	−	0.791526i	−0.0461530	−	0.0313860i
$637$	86.4438	−	46.2052i	3.42503	−	1.83072i
$638$	8.76286	−	0.826991i	0.346925	−	0.0327409i
$639$	−15.9609			−0.631402
$640$	−2.52308	+	11.0288i	−0.0997335	+	0.435951i
$641$	28.0974			1.10978			0.554890	−	0.831924i	$-0.312760\pi$
$641$	28.0974			1.10978			0.554890	+	0.831924i	$0.312760\pi$
$642$	−1.59412	+	0.150444i	−0.0629148	+	0.00593756i
$643$	−1.05163	+	0.562107i	−0.0414721	+	0.0221673i	−0.492002	−	0.870594i	$-0.663735\pi$
$643$	−1.05163	+	0.562107i	−0.0414721	+	0.0221673i	0.450530	+	0.892761i	$0.351235\pi$
$644$	−43.8530	+	64.4856i	−1.72805	+	2.54109i
$645$	−0.365189	−	0.444984i	−0.0143793	−	0.0175212i
$646$	−20.0487	+	13.2781i	−0.788804	+	0.522421i
$647$	10.7562	−	7.18708i	0.422871	−	0.282553i	−0.325872	−	0.945414i	$-0.605658\pi$
$647$	10.7562	−	7.18708i	0.422871	−	0.282553i	0.748743	+	0.662861i	$0.230658\pi$
$648$	19.6102	−	15.6960i	0.770360	−	0.616598i
$649$	−2.38567	+	3.57041i	−0.0936459	+	0.140151i
$650$	5.07598	+	5.11756i	0.199096	+	0.200727i
$651$	1.20465	−	0.365428i	0.0472141	−	0.0143222i
$652$	2.26369	+	0.241615i	0.0886529	+	0.00946239i
$653$	−31.1864	−	25.5940i	−1.22042	−	1.00157i	−0.999656	−	0.0262417i	$-0.991646\pi$
$653$	−31.1864	−	25.5940i	−1.22042	−	1.00157i	−0.220761	−	0.975328i	$-0.570854\pi$
$654$	2.60933	−	2.12367i	0.102033	−	0.0830420i
$655$	15.0172	+	6.22034i	0.586772	+	0.243049i
$656$	−0.289526	−	0.448995i	−0.0113041	−	0.0175303i
$657$	36.4308	−	15.0901i	1.42130	−	0.588722i
$658$	−25.6815	+	47.5789i	−1.00117	+	1.85482i
$659$	3.19881	+	32.4781i	0.124608	+	1.26517i	0.830569	+	0.556915i	$0.188015\pi$
$659$	3.19881	+	32.4781i	0.124608	+	1.26517i	−0.705961	+	0.708250i	$0.749485\pi$
$660$	−0.232047	+	0.0209448i	−0.00903243	+	0.000815274i
$661$	7.88645	−	14.7545i	0.306747	−	0.573884i	−0.680563	−	0.732690i	$-0.738265\pi$
$661$	7.88645	−	14.7545i	0.306747	−	0.573884i	0.987310	+	0.158806i	$0.0507645\pi$
$662$	41.2278	−	16.8804i	1.60237	−	0.656077i
$663$	2.06133	−	0.410024i	0.0800554	−	0.0159240i
$664$	−12.1125	−	30.2851i	−0.470056	−	1.17529i
$665$	−4.74872	+	23.8734i	−0.184147	+	0.925771i
$666$	8.52360	+	5.74571i	0.330283	+	0.222642i
$667$	4.59491	−	46.6529i	0.177916	−	1.80641i
$668$	36.5758	+	0.298387i	1.41516	+	0.0115449i
$669$	0.0262364	−	0.0864899i	0.00101436	−	0.00334389i
$670$	10.1832	+	3.13446i	0.393412	+	0.121095i
$671$	−7.35596	−	7.35596i	−0.283974	−	0.283974i
$672$	3.33853	+	0.0680975i	0.128786	+	0.00262692i
$673$	8.89264	−	8.89264i	0.342786	−	0.342786i	−0.514628	−	0.857414i	$-0.672070\pi$
$673$	8.89264	−	8.89264i	0.342786	−	0.342786i	0.857414	+	0.514628i	$0.172070\pi$
$674$	−40.8512	+	21.6216i	−1.57353	+	0.832834i
$675$	0.660290	+	0.200297i	0.0254146	+	0.00770943i
$676$	−9.73660	−	24.0595i	−0.374484	−	0.925366i
$677$	−1.54049	−	0.151725i	−0.0592057	−	0.00583125i	0.0683709	−	0.997660i	$-0.478220\pi$
$677$	−1.54049	−	0.151725i	−0.0592057	−	0.00583125i	−0.127577	+	0.991829i	$0.540720\pi$
$678$	−0.141238	−	0.725505i	−0.00542421	−	0.0278629i
$679$	35.9992	+	7.16069i	1.38152	+	0.274802i
$680$	2.09551	−	9.90015i	0.0803593	−	0.379653i
$681$	0.00278558	+	0.0140041i	0.000106744	+	0.000536637i
$682$	1.17804	−	2.81155i	0.0451096	−	0.107660i
$683$	20.8019	+	11.1188i	0.795962	+	0.425451i	0.818651	−	0.574292i	$-0.194723\pi$
$683$	20.8019	+	11.1188i	0.795962	+	0.425451i	−0.0226885	+	0.999743i	$0.507223\pi$
$684$	27.0988	+	8.46235i	1.03615	+	0.323566i
$685$	−3.51163	+	0.345865i	−0.134172	+	0.0132148i
$686$	−84.8808	+	25.3707i	−3.24076	+	0.968658i
$687$	0.872147	+	2.10555i	0.0332745	+	0.0803317i
$688$	19.8475	+	2.28233i	0.756677	+	0.0870128i
$689$	11.9101	−	28.7536i	0.453741	−	1.09543i
$690$	−0.126667	+	1.23443i	−0.00482214	+	0.0469941i
$691$	−4.35306	+	5.30422i	−0.165598	+	0.201782i	−0.849197	−	0.528076i	$-0.822914\pi$
$691$	−4.35306	+	5.30422i	−0.165598	+	0.201782i	0.683599	+	0.729858i	$0.260414\pi$
$692$	28.7781	−	8.47400i	1.09398	−	0.322133i
$693$	−4.48822	−	14.7957i	−0.170493	−	0.562041i
$694$	0.0560249	−	13.7351i	0.00212667	−	0.521378i
$695$	8.63003	+	5.76640i	0.327356	+	0.218732i
$696$	−1.78174	+	0.924509i	−0.0675367	+	0.0350434i
$697$	0.265483	+	0.397323i	0.0100559	+	0.0150497i
$698$	−0.196868	+	0.969048i	−0.00745157	+	0.0366790i
$699$	−0.337652	+	0.277104i	−0.0127712	+	0.0104810i
$700$	−5.62119	−	8.56311i	−0.212461	−	0.323655i
$701$	−24.4837	−	45.8057i	−0.924736	−	1.73006i	−0.634150	−	0.773210i	$-0.718650\pi$
$701$	−24.4837	−	45.8057i	−0.924736	−	1.73006i	−0.290586	−	0.956849i	$-0.593850\pi$
$702$	−3.83168	−	3.17082i	−0.144617	−	0.119675i
$703$			11.5661i			0.436225i
$704$	5.28117	−	6.12321i	0.199041	−	0.230777i
$705$			0.860347i			0.0324025i
$706$	−10.5823	+	12.7878i	−0.398268	+	0.481275i
$707$	22.8472	+	42.7442i	0.859259	+	1.60756i
$708$	0.198881	−	0.958894i	0.00747442	−	0.0360374i
$709$	7.00882	−	5.75199i	0.263222	−	0.216021i	−0.493520	−	0.869734i	$-0.664290\pi$
$709$	7.00882	−	5.75199i	0.263222	−	0.216021i	0.756742	+	0.653714i	$0.226790\pi$
$710$	7.40620	+	1.50462i	0.277950	+	0.0564672i
$711$	−20.6042	−	30.8363i	−0.772716	−	1.15645i
$712$	−1.59845	−	18.5542i	−0.0599044	−	0.695348i
$713$	−13.4996	−	9.02012i	−0.505563	−	0.337806i
$714$	−2.98672	−	0.0121827i	−0.111775	−	0.000455926i
$715$	−1.49544	−	4.92981i	−0.0559264	−	0.184365i
$716$	−4.76418	+	8.74088i	−0.178046	+	0.326662i
$717$	0.951271	−	1.15913i	0.0355259	−	0.0432884i
$718$	2.05736	+	0.211108i	0.0767798	+	0.00787850i
$719$	7.03526	−	16.9846i	0.262371	−	0.633420i	−0.736713	−	0.676205i	$-0.763623\pi$
$719$	7.03526	−	16.9846i	0.262371	−	0.633420i	0.999084	+	0.0427856i	$0.0136232\pi$
$720$	−10.6267	+	5.45907i	−0.396033	+	0.203447i
$721$	−9.99686	−	24.1345i	−0.372302	−	0.898817i
$722$	1.45285	+	4.86069i	0.0540695	+	0.180896i
$723$	2.85816	−	0.281504i	0.106296	−	0.0104693i
$724$	−0.778985	−	1.48642i	−0.0289508	−	0.0552424i
$725$	5.43049	+	2.90266i	0.201683	+	0.107802i
$726$	−1.50008	−	0.628532i	−0.0556730	−	0.0233270i
$727$	2.91082	+	14.6337i	0.107956	+	0.542733i	0.996475	+	0.0838922i	$0.0267351\pi$
$727$	2.91082	+	14.6337i	0.107956	+	0.542733i	−0.888519	+	0.458841i	$0.848265\pi$
$728$	13.5170	+	72.5855i	0.500973	+	2.69020i
$729$	25.7803	+	5.12801i	0.954824	+	0.189926i
$730$	−18.3272	+	3.56786i	−0.678321	+	0.132052i
$731$	−17.7834	−	1.75151i	−0.657743	−	0.0647820i
$732$	2.18439	+	0.925751i	0.0807372	+	0.0342167i
$733$	14.8896	+	4.51672i	0.549961	+	0.166829i	0.553022	−	0.833166i	$-0.313474\pi$
$733$	14.8896	+	4.51672i	0.549961	+	0.166829i	−0.00306121	+	0.999995i	$0.500974\pi$
$734$	−1.21256	−	2.29097i	−0.0447564	−	0.0845611i
$735$	−1.56730	+	1.56730i	−0.0578107	+	0.0578107i
$736$	−26.6366	−	33.8412i	−0.981838	−	1.24740i
$737$	−5.38466	−	5.38466i	−0.198346	−	0.198346i
$738$	0.165964	−	0.539183i	0.00610922	−	0.0198476i
$739$	−10.1743	+	33.5403i	−0.374269	+	1.23380i	0.544418	+	0.838814i	$0.316751\pi$
$739$	−10.1743	+	33.5403i	−0.374269	+	1.23380i	−0.918687	+	0.394986i	$0.870749\pi$
$740$	−3.41350	−	3.46965i	−0.125483	−	0.127547i
$741$	0.273649	−	2.77841i	0.0100527	−	0.102067i
$742$	−24.7219	+	36.6742i	−0.907568	+	1.34635i
$743$	−4.41022	+	22.1717i	−0.161795	+	0.813400i	0.811590	+	0.584227i	$0.198602\pi$
$743$	−4.41022	+	22.1717i	−0.161795	+	0.813400i	−0.973386	+	0.229173i	$0.926398\pi$
$744$	−0.00850687	+	0.695154i	−0.000311877	+	0.0254856i
$745$	−7.14985	+	1.42219i	−0.261950	+	0.0521052i
$746$	−20.1675	−	49.2559i	−0.738384	−	1.80339i
$747$	16.2363	−	30.3759i	0.594053	−	1.11140i
$748$	−4.63373	+	5.55321i	−0.169426	+	0.203046i
$749$	4.93152	+	50.0705i	0.180194	+	1.82954i
$750$	−0.143435	−	0.0774214i	−0.00523750	−	0.00282703i
$751$	0.620040	−	0.256829i	0.0226256	−	0.00937182i	−0.371342	−	0.928496i	$-0.621102\pi$
$751$	0.620040	−	0.256829i	0.0226256	−	0.00937182i	0.393968	+	0.919124i	$0.371102\pi$
$752$	−20.7661	−	21.4550i	−0.757261	−	0.782384i
$753$	−1.64952	−	0.683255i	−0.0601120	−	0.0248992i
$754$	−28.0165	−	34.4236i	−1.02030	−	1.25363i
$755$	1.10792	+	0.909247i	0.0403213	+	0.0330909i
$756$	4.43909	+	5.49994i	0.161448	+	0.200031i
$757$	−36.7266	+	11.1409i	−1.33485	+	0.404923i	−0.875451	−	0.483306i	$-0.839436\pi$
$757$	−36.7266	+	11.1409i	−1.33485	+	0.404923i	−0.459401	+	0.888229i	$0.651936\pi$
$758$	−34.3101	+	34.0313i	−1.24620	+	1.23607i
$759$	0.492735	−	0.737430i	0.0178851	−	0.0267670i
$760$	−11.7767	−	6.48130i	−0.427186	−	0.235101i
$761$	4.41458	−	2.94973i	0.160028	−	0.106927i	−0.472978	−	0.881074i	$-0.656821\pi$
$761$	4.41458	−	2.94973i	0.160028	−	0.106927i	0.633006	+	0.774147i	$0.281821\pi$
$762$	1.12605	+	1.70023i	0.0407926	+	0.0615929i
$763$	−67.0636	−	81.7172i	−2.42786	−	2.95836i
$764$	6.73095	+	35.3432i	0.243517	+	1.27867i
$765$	9.42405	−	5.03726i	0.340727	−	0.182122i
$766$	−2.45218	−	25.9835i	−0.0886007	−	0.938820i
$767$	21.6533			0.781855
$768$	−0.592599	+	1.74628i	−0.0213836	+	0.0630133i
$769$	33.0296			1.19108			0.595538	−	0.803327i	$-0.296939\pi$
$769$	33.0296			1.19108			0.595538	+	0.803327i	$0.296939\pi$
$770$	0.687860	+	7.28862i	0.0247888	+	0.262664i
$771$	0.951618	−	0.508650i	0.0342717	−	0.0183186i
$772$	−7.45462	−	39.1431i	−0.268297	−	1.40879i
$773$	−1.06718	−	1.30036i	−0.0383838	−	0.0467708i	0.753465	−	0.657488i	$-0.228381\pi$
$773$	−1.06718	−	1.30036i	−0.0383838	−	0.0467708i	−0.791849	+	0.610718i	$0.790881\pi$
$774$	11.6488	+	17.5886i	0.418709	+	0.632209i
$775$	1.77318	−	1.18480i	0.0636946	−	0.0425594i
$776$	−9.77328	+	17.7584i	−0.350840	+	0.637488i
$777$	−0.798115	+	1.19446i	−0.0286322	+	0.0428512i
$778$	12.1733	−	12.0744i	0.436433	−	0.432887i
$779$	0.607436	−	0.184264i	0.0217636	−	0.00660193i
$780$	0.737896	+	0.914237i	0.0264209	+	0.0327349i
$781$	−4.17537	−	3.42664i	−0.149407	−	0.122615i
$782$	24.3157	+	29.8764i	0.869526	+	1.06838i
$783$	−3.92532	−	1.62592i	−0.140279	−	0.0581056i
$784$	1.25502	−	76.9144i	0.0448223	−	2.74694i
$785$	−10.0063	+	4.14474i	−0.357139	+	0.147932i
$786$	2.33147	+	1.25845i	0.0831607	+	0.0448874i
$787$	−3.73028	−	37.8741i	−0.132970	−	1.35007i	−0.797732	−	0.603012i	$-0.793967\pi$
$787$	−3.73028	−	37.8741i	−0.132970	−	1.35007i	0.664762	−	0.747055i	$-0.268533\pi$
$788$	8.33029	−	9.98329i	0.296754	−	0.355640i
$789$	−0.662273	+	1.23903i	−0.0235776	+	0.0441105i
$790$	6.65388	+	16.2511i	0.236735	+	0.578187i
$791$	−22.7785	+	4.53092i	−0.809909	+	0.161101i
$792$	8.53795	+	0.104482i	0.303383	+	0.00371261i
$793$	−10.2339	+	51.4493i	−0.363417	+	1.82702i
$794$	−7.53311	+	11.1751i	−0.267340	+	0.396591i
$795$	−0.0689830	+	0.700396i	−0.00244658	+	0.0248405i
$796$	27.3444	+	27.7942i	0.969196	+	0.985140i
$797$	−13.7699	+	45.3934i	−0.487756	+	1.60792i	0.275146	+	0.961402i	$0.411274\pi$
$797$	−13.7699	+	45.3934i	−0.487756	+	1.60792i	−0.762902	+	0.646514i	$0.776226\pi$
$798$	−1.16718	+	3.79193i	−0.0413178	+	0.134233i
$799$	18.8847	+	18.8847i	0.668094	+	0.668094i
$800$	5.44563	−	1.53136i	0.192532	−	0.0541418i
$801$	13.9054	−	13.9054i	0.491322	−	0.491322i
$802$	−2.83044	−	5.34773i	−0.0999462	−	0.188835i
$803$	12.7700	+	3.87374i	0.450644	+	0.136701i
$804$	1.59900	+	0.677662i	0.0563923	+	0.0238993i
$805$	38.8042	+	3.82188i	1.36767	+	0.134704i
$806$	−15.0884	+	2.93734i	−0.531466	+	0.103463i
$807$	1.96902	+	0.391662i	0.0693127	+	0.0137872i
$808$	−26.3136	+	4.90017i	−0.925710	+	0.172387i
$809$	−2.90841	−	14.6216i	−0.102254	−	0.514067i	−0.997633	−	0.0687619i	$-0.978095\pi$
$809$	−2.90841	−	14.6216i	−0.102254	−	0.514067i	0.895379	−	0.445305i	$-0.146905\pi$
$810$	−11.5834	−	4.85345i	−0.406999	−	0.170533i
$811$	−9.43886	−	5.04518i	−0.331443	−	0.177160i	0.297278	−	0.954791i	$-0.403921\pi$
$811$	−9.43886	−	5.04518i	−0.331443	−	0.177160i	−0.628721	+	0.777631i	$0.716421\pi$
$812$	29.2779	+	55.8667i	1.02745	+	1.96054i
$813$	−2.07927	+	0.204790i	−0.0729231	+	0.00718230i
$814$	0.996230	+	3.33301i	0.0349179	+	0.116822i
$815$	−0.435599	−	1.05163i	−0.0152584	−	0.0368369i
$816$	0.504494	−	1.57039i	0.0176608	−	0.0549746i
$817$	−9.08383	+	21.9303i	−0.317803	+	0.767244i
$818$	−34.7306	−	3.56376i	−1.21433	−	0.124604i
$819$	−49.4607	+	60.2680i	−1.72830	+	2.10593i
$820$	−0.127839	+	0.234548i	−0.00446434	+	0.00819076i
$821$	−7.52486	−	24.8062i	−0.262620	−	0.865741i	−0.984749	−	0.173982i	$-0.944336\pi$
$821$	−7.52486	−	24.8062i	−0.262620	−	0.865741i	0.722129	−	0.691758i	$-0.243164\pi$
$822$	−0.575145	−	0.00234599i	−0.0200605	−	8.18257e-5i
$823$	24.4684	+	16.3493i	0.852916	+	0.569900i	0.903387	−	0.428825i	$-0.141072\pi$
$823$	24.4684	+	16.3493i	0.852916	+	0.569900i	−0.0504717	+	0.998725i	$0.516072\pi$
$824$	14.3732	−	1.23826i	0.500715	−	0.0431367i
$825$	0.0647213	+	0.0968623i	0.00225331	+	0.00337231i
$826$	−30.1555	−	6.12628i	−1.04924	−	0.213160i
$827$	26.8106	−	22.0029i	0.932296	−	0.765116i	−0.0399192	−	0.999203i	$-0.512710\pi$
$827$	26.8106	−	22.0029i	0.932296	−	0.765116i	0.972216	+	0.234087i	$0.0752101\pi$
$828$	9.23565	−	44.5291i	0.320961	−	1.54749i
$829$	4.63397	+	8.66955i	0.160944	+	0.301106i	0.949448	−	0.313924i	$-0.101644\pi$
$829$	4.63397	+	8.66955i	0.160944	+	0.301106i	−0.788504	+	0.615030i	$0.789144\pi$
$830$	−10.3975	+	12.5645i	−0.360902	+	0.436121i
$831$		−	0.801516i		−	0.0278043i
$832$	−40.4682	−	4.98840i	−1.40298	−	0.172942i
$833$			68.8049i			2.38395i
$834$	1.30337	+	1.07857i	0.0451320	+	0.0373480i
$835$	−8.62114	−	16.1290i	−0.298347	−	0.558168i
$836$	5.27228	+	8.03159i	0.182346	+	0.277778i
$837$	−1.13748	+	0.933503i	−0.0393170	+	0.0322666i
$838$	−4.33252	+	21.3260i	−0.149664	+	0.736696i
$839$	15.3781	+	23.0149i	0.530910	+	0.794562i	0.995872	−	0.0907680i	$-0.0289322\pi$
$839$	15.3781	+	23.0149i	0.530910	+	0.794562i	−0.464962	+	0.885330i	$0.653932\pi$
$840$	−0.768972	−	1.48199i	−0.0265321	−	0.0511333i
$841$	−7.41309	−	4.95327i	−0.255624	−	0.170802i
$842$	−0.0324970	+	7.96699i	−0.00111992	+	0.274561i
$843$	0.263848	+	0.869789i	0.00908739	+	0.0299571i
$844$	27.7757	−	8.17884i	0.956080	−	0.281527i
$845$	−8.23283	+	10.0317i	−0.283218	+	0.345102i
$846$	3.21842	−	31.3651i	0.110652	−	1.07835i
$847$	−19.5573	+	47.2154i	−0.671995	+	1.62234i
$848$	−15.1851	−	19.1313i	−0.521459	−	0.656970i
$849$	0.183439	+	0.442862i	0.00629562	+	0.0151990i
$850$	−4.84783	+	1.44900i	−0.166279	+	0.0497005i
$851$	18.4385	−	1.81604i	0.632065	−	0.0622530i
$852$	1.17584	+	0.367188i	0.0402836	+	0.0125797i
$853$	1.87929	+	1.00450i	0.0643458	+	0.0343935i	0.503256	−	0.864137i	$-0.332135\pi$
$853$	1.87929	+	1.00450i	0.0643458	+	0.0343935i	−0.438910	+	0.898531i	$0.644635\pi$
$854$	28.8086	−	68.7556i	0.985811	−	2.35277i
$855$	−2.76925	−	13.9219i	−0.0947062	−	0.476120i
$856$	−27.1830	−	5.75369i	−0.929097	−	0.196657i
$857$	−41.1036	−	8.17601i	−1.40407	−	0.279287i	−0.565801	−	0.824542i	$-0.691433\pi$
$857$	−41.1036	−	8.17601i	−1.40407	−	0.279287i	−0.838270	+	0.545255i	$0.816433\pi$
$858$	−0.160456	−	0.824223i	−0.00547787	−	0.0281385i
$859$	4.73151	+	0.466013i	0.161437	+	0.0159001i	0.178413	−	0.983956i	$-0.442904\pi$
$859$	4.73151	+	0.466013i	0.161437	+	0.0159001i	−0.0169758	+	0.999856i	$0.505404\pi$
$860$	−3.74726	−	9.25962i	−0.127780	−	0.315751i
$861$	0.0754464	+	0.0228864i	0.00257121	+	0.000779967i
$862$	−14.5344	+	7.69276i	−0.495045	+	0.262017i
$863$	38.8767	−	38.8767i	1.32338	−	1.32338i	0.412355	−	0.911023i	$-0.364706\pi$
$863$	38.8767	−	38.8767i	1.32338	−	1.32338i	0.911023	−	0.412355i	$-0.135294\pi$
$864$	−3.63583	+	1.41985i	−0.123694	+	0.0483044i
$865$	−10.6065	−	10.6065i	−0.360633	−	0.360633i
$866$	15.3751	+	4.73255i	0.522467	+	0.160819i
$867$	0.140502	−	0.463172i	0.00477169	−	0.0157301i
$868$	21.8440	+	0.178204i	0.741433	+	0.00604863i
$869$	1.23019	−	12.4903i	0.0417312	−	0.423704i
$870$	0.832229	+	0.561001i	0.0282152	+	0.0190197i
$871$	−7.49135	+	37.6616i	−0.253835	+	1.27611i
$872$	54.2055	−	21.6794i	1.83563	−	0.734158i
$873$	−20.9932	+	4.17581i	−0.710512	+	0.141330i
$874$	47.3541	−	19.3888i	1.60178	−	0.655836i
$875$	−2.41432	+	4.51688i	−0.0816190	+	0.152698i
$876$	−3.03102	+	0.273582i	−0.102409	+	0.00924349i
$877$	−1.18985	−	12.0808i	−0.0401784	−	0.407938i	−0.994147	−	0.108033i	$-0.965545\pi$
$877$	−1.18985	−	12.0808i	−0.0401784	−	0.407938i	0.953969	−	0.299906i	$-0.0969552\pi$
$878$	−13.3017	+	24.6435i	−0.448911	+	0.831676i
$879$	−1.29510	+	0.536449i	−0.0436827	+	0.0180940i
$880$	−3.95195	−	0.853346i	−0.133220	−	0.0287663i
$881$	−12.3783	−	5.12728i	−0.417037	−	0.172742i	0.164291	−	0.986412i	$-0.447467\pi$
$881$	−12.3783	−	5.12728i	−0.417037	−	0.172742i	−0.581328	+	0.813670i	$0.697467\pi$
$882$	63.0010	−	51.2750i	2.12135	−	1.72652i
$883$	−25.6613	−	21.0597i	−0.863573	−	0.708716i	0.0944124	−	0.995533i	$-0.469903\pi$
$883$	−25.6613	−	21.0597i	−0.863573	−	0.708716i	−0.957985	+	0.286817i	$0.907403\pi$
$884$	36.2646	+	3.87071i	1.21971	+	0.130186i
$885$	−0.468567	+	0.142138i	−0.0157507	+	0.00477792i
$886$	−20.6242	−	20.7931i	−0.692883	−	0.698559i
$887$	16.2081	−	24.2571i	0.544213	−	0.814473i	−0.452807	−	0.891608i	$-0.649577\pi$
$887$	16.2081	−	24.2571i	0.544213	−	0.814473i	0.997021	+	0.0771355i	$0.0245774\pi$
$888$	−0.495752	−	0.619378i	−0.0166363	−	0.0207850i
$889$	53.2797	−	35.6004i	1.78694	−	1.19400i
$890$	−7.76324	+	5.14155i	−0.260224	+	0.172345i
$891$	5.69441	+	6.93866i	0.190770	+	0.232454i
$892$	0.881950	−	1.29690i	0.0295299	−	0.0434235i
$893$	31.2877	−	16.7236i	1.04700	−	0.559635i
$894$	−1.18297	+	0.111642i	−0.0395645	+	0.00373388i
$895$	4.97746			0.166378
$896$	54.9468	+	18.3966i	1.83564	+	0.614588i
$897$	−4.47225			−0.149324
$898$	−10.1089	+	0.954023i	−0.337339	+	0.0318362i
$899$	−11.5810	+	6.19018i	−0.386248	+	0.206454i
$900$	4.93949	+	3.35907i	0.164650	+	0.111969i
$901$	13.8596	+	16.8880i	0.461731	+	0.562621i
$902$	0.159173	−	0.105420i	0.00529989	−	0.00351009i
$903$	−2.45140	+	1.63797i	−0.0815774	+	0.0545083i
$904$	1.41325	−	12.7478i	0.0470039	−	0.423984i
$905$	−0.466171	+	0.697675i	−0.0154961	+	0.0231915i
$906$	0.164515	+	0.165863i	0.00546565	+	0.00551042i
$907$	−24.1952	+	7.33953i	−0.803388	+	0.243705i	−0.665165	−	0.746696i	$-0.731639\pi$
$907$	−24.1952	+	7.33953i	−0.803388	+	0.243705i	−0.138222	+	0.990401i	$0.544139\pi$
$908$	−0.0262964	+	0.246371i	−0.000872677	+	0.00817609i
$909$	−21.8483	−	17.9304i	−0.724662	−	0.594715i
$910$	28.6323	−	23.3031i	0.949150	−	0.772490i
$911$	6.60986	+	2.73789i	0.218994	+	0.0907104i	0.489483	−	0.872013i	$-0.337185\pi$
$911$	6.60986	+	2.73789i	0.218994	+	0.0907104i	−0.270489	+	0.962723i	$0.587185\pi$
$912$	−1.80169	−	1.24685i	−0.0596600	−	0.0412872i
$913$	10.7688	−	4.46059i	0.356395	−	0.147624i
$914$	21.3250	−	39.5079i	0.705369	−	1.30680i
$915$	−0.116271	−	1.18052i	−0.00384379	−	0.0390267i
$916$	3.55514	+	39.3873i	0.117465	+	1.30139i
$917$	39.2437	−	73.4198i	1.29594	−	2.42454i
$918$	3.23090	−	1.32287i	0.106636	−	0.0436612i
$919$	44.6159	−	8.87466i	1.47174	−	0.292748i	0.606895	−	0.794782i	$-0.292415\pi$
$919$	44.6159	−	8.87466i	1.47174	−	0.292748i	0.864848	+	0.502034i	$0.167415\pi$
$920$	−8.48327	+	19.7919i	−0.279685	+	0.652519i
$921$	−0.306486	+	1.54081i	−0.0100991	+	0.0507714i
$922$	46.1041	+	31.0785i	1.51836	+	1.02352i
$923$	−2.66971	+	27.1060i	−0.0878744	+	0.892204i
$924$	−0.00973460	+	1.19325i	−0.000320245	+	0.0392551i
$925$	−0.706449	+	2.32885i	−0.0232279	+	0.0765721i
$926$	47.7566	+	14.6998i	1.56938	+	0.483065i
$927$	10.7719	+	10.7719i	0.353797	+	0.353797i
$928$	−34.2946	+	6.09737i	−1.12578	+	0.200156i
$929$	−37.4211	+	37.4211i	−1.22775	+	1.22775i	−0.262933	+	0.964814i	$0.584690\pi$
$929$	−37.4211	+	37.4211i	−1.22775	+	1.22775i	−0.964814	+	0.262933i	$0.915310\pi$
$930$	0.307224	−	0.162607i	0.0100743	−	0.00533210i
$931$	87.4626	+	26.5315i	2.86647	+	0.869534i
$932$	−7.02618	+	2.84341i	−0.230150	+	0.0931390i
$933$	2.96039	+	0.291573i	0.0969187	+	0.00954566i
$934$	11.0129	+	56.5705i	0.360353	+	1.85104i
$935$	3.54678	+	0.705499i	0.115992	+	0.0230723i
$936$	−23.4810	−	36.0901i	−0.767500	−	1.17964i
$937$	2.53786	+	12.7587i	0.0829082	+	0.416808i	0.999842	+	0.0177686i	$0.00565623\pi$
$937$	2.53786	+	12.7587i	0.0829082	+	0.416808i	−0.916934	+	0.399039i	$0.869344\pi$
$938$	21.0883	−	50.3300i	0.688557	−	1.64333i
$939$	1.74386	+	0.932113i	0.0569087	+	0.0304183i
$940$	−4.45018	+	14.2507i	−0.145149	+	0.464807i
$941$	−13.0591	+	1.28621i	−0.425714	+	0.0419292i	−0.308606	−	0.951190i	$-0.599862\pi$
$941$	−13.0591	+	1.28621i	−0.425714	+	0.0419292i	−0.117108	+	0.993119i	$0.537362\pi$
$942$	−1.69142	+	0.505562i	−0.0551095	+	0.0164721i
$943$	−0.389125	−	0.939432i	−0.0126717	−	0.0305921i
$944$	8.25417	−	14.8543i	0.268650	−	0.483467i
$945$	1.35238	−	3.26493i	0.0439929	−	0.106208i
$946$	−0.728755	+	7.10207i	−0.0236939	+	0.230908i
$947$	12.0582	−	14.6930i	0.391839	−	0.477457i	−0.539304	−	0.842111i	$-0.681313\pi$
$947$	12.0582	−	14.6930i	0.391839	−	0.477457i	0.931143	+	0.364654i	$0.118813\pi$
$948$	0.808506	+	2.74573i	0.0262591	+	0.0891770i
$949$	−19.5336	−	64.3936i	−0.634087	−	2.09030i
$950$	−0.0274152	+	6.72115i	−0.000889467	+	0.218063i
$951$	−1.78130	−	1.19023i	−0.0577627	−	0.0385958i
$952$	−49.4088	−	15.6507i	−1.60135	−	0.507243i
$953$	28.6673	+	42.9036i	0.928624	+	1.38978i	0.920893	+	0.389814i	$0.127461\pi$
$953$	28.6673	+	42.9036i	0.928624	+	1.38978i	0.00773078	+	0.999970i	$0.497539\pi$
$954$	5.13494	−	25.2758i	0.166250	−	0.818336i
$955$	13.9059	−	11.4122i	0.449983	−	0.369291i
$956$	21.7524	−	14.2792i	0.703523	−	0.461822i
$957$	−0.338146	−	0.632626i	−0.0109307	−	0.0204499i
$958$	−36.8540	−	30.4977i	−1.19070	−	0.985337i
$959$			18.0723i			0.583585i
$960$	0.908458	−	0.157698i	0.0293203	−	0.00508968i
$961$		−	26.4521i		−	0.853292i
$962$	11.1835	−	13.5144i	0.360571	−	0.435721i
$963$	−13.8309	−	25.8758i	−0.445694	−	0.833836i
$964$	48.7984	+	10.1211i	1.57169	+	0.325980i
$965$	−15.4009	+	12.6392i	−0.495773	+	0.406871i
$966$	6.22829	+	1.26532i	0.200392	+	0.0407109i
$967$	7.92559	+	11.8615i	0.254870	+	0.381440i	0.936736	−	0.350038i	$-0.113831\pi$
$967$	7.92559	+	11.8615i	0.254870	+	0.381440i	−0.681866	+	0.731477i	$0.738831\pi$
$968$	−21.5960	−	18.1702i	−0.694122	−	0.584011i
$969$	1.62950	+	1.08879i	0.0523470	+	0.0349771i
$970$	10.1350	+	0.0413400i	0.325414	+	0.00132735i
$971$	−2.31993	−	7.64780i	−0.0744502	−	0.245430i	0.911814	−	0.410603i	$-0.134682\pi$
$971$	−2.31993	−	7.64780i	−0.0744502	−	0.245430i	−0.986265	+	0.165173i	$0.947182\pi$
$972$	−5.43255	−	2.96099i	−0.174249	−	0.0949738i
$973$	33.7235	−	41.0922i	1.08113	−	1.31736i
$974$	−30.1834	−	3.09716i	−0.967138	−	0.0992396i
$975$	0.224802	−	0.542719i	0.00719942	−	0.0173809i
$976$	31.3935	+	26.6329i	1.00488	+	0.852498i
$977$	14.2877	+	34.4935i	0.457104	+	1.10355i	0.969565	+	0.244835i	$0.0787339\pi$
$977$	14.2877	+	34.4935i	0.457104	+	1.10355i	−0.512461	+	0.858711i	$0.671266\pi$
$978$	−0.0531330	−	0.177763i	−0.00169901	−	0.00568423i
$979$	6.62298	−	0.652307i	0.211672	−	0.0208478i
$980$	−34.0675	+	17.8537i	−1.08825	+	0.570315i
$981$	54.3680	+	29.0603i	1.73584	+	0.927824i
$982$	−5.23592	−	2.19385i	−0.167085	−	0.0700087i
$983$	10.4858	+	52.7158i	0.334446	+	1.68137i	0.672383	+	0.740203i	$0.265271\pi$
$983$	10.4858	+	52.7158i	0.334446	+	1.68137i	−0.337938	+	0.941168i	$0.609729\pi$
$984$	−0.0246308	+	0.0359036i	−0.000785201	+	0.00114457i
$985$	−6.37623	−	1.26831i	−0.203164	−	0.0404118i
$986$	30.5816	−	5.95349i	0.973917	−	0.189598i
$987$	4.38517	+	0.431901i	0.139581	+	0.0137476i
$988$	18.9041	−	44.6058i	0.601420	−	1.41910i
$989$	36.3872	+	11.0379i	1.15705	+	0.350986i
$990$	−1.99716	−	3.77336i	−0.0634738	−	0.119925i
$991$	33.0201	−	33.0201i	1.04892	−	1.04892i	0.0501784	−	0.998740i	$-0.484021\pi$
$991$	33.0201	−	33.0201i	1.04892	−	1.04892i	0.998740	−	0.0501784i	$-0.0159790\pi$
$992$	−3.73662	+	11.4705i	−0.118638	+	0.364188i
$993$	−2.56730	−	2.56730i	−0.0814709	−	0.0814709i
$994$	11.3870	−	36.9939i	0.361172	−	1.17337i
$995$	5.65913	−	18.6556i	0.179406	−	0.591423i
$996$	−1.89494	+	1.86427i	−0.0600435	+	0.0590718i
$997$	−5.17730	+	52.5660i	−0.163967	+	1.66478i	0.463469	+	0.886113i	$0.346605\pi$
$997$	−5.17730	+	52.5660i	−0.163967	+	1.66478i	−0.627436	+	0.778668i	$0.715895\pi$
$998$	−3.36866	+	4.99731i	−0.106633	+	0.158187i
$999$	0.327599	−	1.64695i	0.0103648	−	0.0521072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.30	✓	1024
128.109	even	32	inner	640.2.bm.a.621.30	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.30	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.30	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.132875 - 1.40796i) q^{2} +(-0.101646 + 0.0543310i) q^{3} +(-1.96469 + 0.374166i) q^{4} +(0.634393 + 0.773010i) q^{5} +(0.0900020 + 0.135894i) q^{6} +(4.25848 - 2.84543i) q^{7} +(0.787868 + 2.71648i) q^{8} +(-1.65933 + 2.48336i) q^{9} +(1.00407 - 0.995913i) q^{10} +(-0.967235 + 0.293407i) q^{11} +(0.179374 - 0.144776i) q^{12} +(3.93989 + 3.23338i) q^{13} +(-4.57209 - 5.61768i) q^{14} +(-0.106482 - 0.0441063i) q^{15} +(3.72000 - 1.47024i) q^{16} +(-3.30544 + 1.36916i) q^{17} +(3.71695 + 2.00629i) q^{18} +(0.465837 + 4.72972i) q^{19} +(-1.53562 - 1.28136i) q^{20} +(-0.278264 + 0.520595i) q^{21} +(0.541627 + 1.32284i) q^{22} +(7.46690 - 1.48526i) q^{23} +(-0.227673 - 0.233314i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(4.02895 - 5.97683i) q^{26} +(0.0676320 - 0.686679i) q^{27} +(-7.30193 + 7.18376i) q^{28} +(1.78745 - 5.89243i) q^{29} +(-0.0479510 + 0.155783i) q^{30} +(-1.50797 - 1.50797i) q^{31} +(-2.56433 - 5.04224i) q^{32} +(0.0823746 - 0.0823746i) q^{33} +(2.36693 + 4.47199i) q^{34} +(4.90110 + 1.48673i) q^{35} +(2.33088 - 5.49990i) q^{36} +(2.42192 + 0.238539i) q^{37} +(6.59735 - 1.28434i) q^{38} +(-0.576148 - 0.114603i) q^{39} +(-1.60005 + 2.33235i) q^{40} +(-0.0260567 - 0.130996i) q^{41} +(0.769950 + 0.322609i) q^{42} +(4.40481 + 2.35442i) q^{43} +(1.79053 - 0.938360i) q^{44} +(-2.97233 + 0.292749i) q^{45} +(-3.08335 - 10.3157i) q^{46} +(-2.85662 - 6.89648i) q^{47} +(-0.298244 + 0.351555i) q^{48} +(7.35945 - 17.7673i) q^{49} +(1.40683 + 0.144357i) q^{50} +(0.261598 - 0.318757i) q^{51} +(-8.95047 - 4.87842i) q^{52} +(-1.77257 - 5.84337i) q^{53} +(-0.975801 - 0.00398025i) q^{54} +(-0.840414 - 0.561547i) q^{55} +(11.0847 + 9.32627i) q^{56} +(-0.304321 - 0.455449i) q^{57} +(-8.53379 - 1.73369i) q^{58} +(3.28406 - 2.69516i) q^{59} +(0.225707 + 0.0468133i) q^{60} +(4.85170 + 9.07689i) q^{61} +(-1.92278 + 2.32353i) q^{62} +15.2969i q^{63} +(-6.75853 + 4.28045i) q^{64} +5.09681i q^{65} +(-0.126925 - 0.105034i) q^{66} +(3.55151 + 6.64440i) q^{67} +(5.98186 - 3.92675i) q^{68} +(-0.678286 + 0.556655i) q^{69} +(1.44202 - 7.09809i) q^{70} +(2.96894 + 4.44333i) q^{71} +(-8.05334 - 2.55098i) q^{72} +(-10.9776 - 7.33497i) q^{73} +(0.0140384 - 3.44166i) q^{74} +(-0.0334569 - 0.110293i) q^{75} +(-2.68492 - 9.11813i) q^{76} +(-3.28408 + 4.00167i) q^{77} +(-0.0848002 + 0.826419i) q^{78} +(-4.75184 + 11.4720i) q^{79} +(3.49645 + 1.94289i) q^{80} +(-3.39847 - 8.20463i) q^{81} +(-0.180974 + 0.0540928i) q^{82} +(-11.4765 + 1.13034i) q^{83} +(0.351913 - 1.12692i) q^{84} +(-3.15532 - 1.68655i) q^{85} +(2.72963 - 6.51463i) q^{86} +(0.138454 + 0.696056i) q^{87} +(-1.55909 - 2.39631i) q^{88} +(-6.45769 - 1.28451i) q^{89} +(0.807129 + 4.14602i) q^{90} +(25.9783 + 2.55864i) q^{91} +(-14.1144 + 5.71192i) q^{92} +(0.235209 + 0.0713498i) q^{93} +(-9.33038 + 4.93837i) q^{94} +(-3.36060 + 3.36060i) q^{95} +(0.534604 + 0.373202i) q^{96} +(5.06752 + 5.06752i) q^{97} +(-25.9935 - 8.00095i) q^{98} +(0.876325 - 2.88886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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