LMFDB - Embedded newform 140.2.w.b.123.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(23,140)] 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("140.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$140 = 2^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	140.w (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			123.9
Character	$\chi$	$=$	140.123
Dual form			140.2.w.b.107.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0671791 + 1.41262i) q^{2} +(0.638980 + 2.38471i) q^{3} +(-1.99097 + 0.189797i) q^{4} +(2.14503 + 0.631526i) q^{5} +(-3.32575 + 1.06284i) q^{6} +(1.60796 - 2.10106i) q^{7} +(-0.401862 - 2.79973i) q^{8} +(-2.68045 + 1.54756i) q^{9} +(-0.748003 + 3.07254i) q^{10} +(-4.09588 - 2.36476i) q^{11} +(-1.72480 - 4.62661i) q^{12} +(0.0592655 + 0.0592655i) q^{13} +(3.07602 + 2.13028i) q^{14} +(-0.135370 + 5.51881i) q^{15} +(3.92795 - 0.755761i) q^{16} +(-1.27942 - 4.77484i) q^{17} +(-2.36618 - 3.68249i) q^{18} +(1.31544 + 2.27842i) q^{19} +(-4.39057 - 0.850232i) q^{20} +(6.03788 + 2.49197i) q^{21} +(3.06534 - 5.94478i) q^{22} +(-1.09265 - 0.292774i) q^{23} +(6.41976 - 2.74730i) q^{24} +(4.20235 + 2.70929i) q^{25} +(-0.0797380 + 0.0877008i) q^{26} +(-0.166053 - 0.166053i) q^{27} +(-2.80263 + 4.48835i) q^{28} +7.27332i q^{29} +(-7.80506 + 0.179523i) q^{30} +(-4.01558 - 2.31840i) q^{31} +(1.33148 + 5.49792i) q^{32} +(3.02207 - 11.2785i) q^{33} +(6.65908 - 2.12809i) q^{34} +(4.77600 - 3.49139i) q^{35} +(5.04299 - 3.58989i) q^{36} +(2.22779 + 0.596933i) q^{37} +(-3.13016 + 2.01128i) q^{38} +(-0.103461 + 0.179200i) q^{39} +(0.906097 - 6.25931i) q^{40} -5.71767 q^{41} +(-3.11458 + 8.69661i) q^{42} +(1.57302 - 1.57302i) q^{43} +(8.60362 + 3.93079i) q^{44} +(-6.72699 + 1.62679i) q^{45} +(0.340174 - 1.56316i) q^{46} +(0.716679 - 2.67468i) q^{47} +(4.31215 + 8.88410i) q^{48} +(-1.82895 - 6.75684i) q^{49} +(-3.54488 + 6.11832i) q^{50} +(10.5691 - 6.10206i) q^{51} +(-0.129244 - 0.106748i) q^{52} +(-9.12265 + 2.44441i) q^{53} +(0.223414 - 0.245724i) q^{54} +(-7.29241 - 7.65915i) q^{55} +(-6.52860 - 3.65751i) q^{56} +(-4.59281 + 4.59281i) q^{57} +(-10.2744 + 0.488615i) q^{58} +(1.67748 - 2.90547i) q^{59} +(-0.777934 - 11.0135i) q^{60} +(-0.978771 - 1.69528i) q^{61} +(3.00524 - 5.82822i) q^{62} +(-1.05853 + 8.12021i) q^{63} +(-7.67701 + 2.25021i) q^{64} +(0.0896988 + 0.164554i) q^{65} +(16.1352 + 3.51135i) q^{66} +(-0.491893 + 0.131802i) q^{67} +(3.45353 + 9.26376i) q^{68} -2.79272i q^{69} +(5.25285 + 6.51211i) q^{70} +14.4625i q^{71} +(5.40993 + 6.88265i) q^{72} +(9.26507 - 2.48257i) q^{73} +(-0.693578 + 3.18711i) q^{74} +(-3.77565 + 11.7526i) q^{75} +(-3.05145 - 4.28660i) q^{76} +(-11.5545 + 4.80329i) q^{77} +(-0.260092 - 0.134113i) q^{78} +(-3.05204 - 5.28630i) q^{79} +(8.90288 + 0.859474i) q^{80} +(-4.35280 + 7.53927i) q^{81} +(-0.384108 - 8.07688i) q^{82} +(5.62620 - 5.62620i) q^{83} +(-12.4942 - 3.81547i) q^{84} +(0.271049 - 11.0502i) q^{85} +(2.32775 + 2.11640i) q^{86} +(-17.3447 + 4.64751i) q^{87} +(-4.97472 + 12.4177i) q^{88} +(-14.4482 + 8.34169i) q^{89} +(-2.74995 - 9.39337i) q^{90} +(0.219817 - 0.0292243i) q^{91} +(2.23100 + 0.375524i) q^{92} +(2.96282 - 11.0574i) q^{93} +(3.82645 + 0.832711i) q^{94} +(1.38279 + 5.71802i) q^{95} +(-12.2601 + 6.68825i) q^{96} +(5.81505 - 5.81505i) q^{97} +(9.42197 - 3.03752i) q^{98} +14.6384 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100})$ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$ .

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.0671791	+	1.41262i	0.0475028	+	0.998871i
$2$	0.0671791	+	1.41262i	0.0475028	+	0.998871i
$3$	0.638980	+	2.38471i	0.368915	+	1.37681i	0.862035	+	0.506849i	$0.169190\pi$
$3$	0.638980	+	2.38471i	0.368915	+	1.37681i	−0.493119	+	0.869962i	$0.664143\pi$
$4$	−1.99097	+	0.189797i	−0.995487	+	0.0948984i
$5$	2.14503	+	0.631526i	0.959289	+	0.282427i
$5$	2.14503	+	0.631526i	0.959289	+	0.282427i
$6$	−3.32575	+	1.06284i	−1.35773	+	0.433901i
$7$	1.60796	−	2.10106i	0.607751	−	0.794128i
$7$	1.60796	−	2.10106i	0.607751	−	0.794128i
$8$	−0.401862	−	2.79973i	−0.142080	−	0.989855i
$9$	−2.68045	+	1.54756i	−0.893484	+	0.515853i
$10$	−0.748003	+	3.07254i	−0.236539	+	0.971622i
$11$	−4.09588	−	2.36476i	−1.23496	−	0.713002i	−0.266897	−	0.963725i	$-0.585998\pi$
$11$	−4.09588	−	2.36476i	−1.23496	−	0.713002i	−0.968059	+	0.250723i	$0.919332\pi$
$12$	−1.72480	−	4.62661i	−0.497908	−	1.33559i
$13$	0.0592655	+	0.0592655i	0.0164373	+	0.0164373i	0.715278	−	0.698840i	$-0.246300\pi$
$13$	0.0592655	+	0.0592655i	0.0164373	+	0.0164373i	−0.698840	+	0.715278i	$0.746300\pi$
$14$	3.07602	+	2.13028i	0.822101	+	0.569341i
$15$	−0.135370	+	5.51881i	−0.0349524	+	1.42495i
$16$	3.92795	−	0.755761i	0.981989	−	0.188940i
$17$	−1.27942	−	4.77484i	−0.310304	−	1.15807i	−0.928283	−	0.371875i	$-0.878715\pi$
$17$	−1.27942	−	4.77484i	−0.310304	−	1.15807i	0.617979	−	0.786195i	$-0.287952\pi$
$18$	−2.36618	−	3.68249i	−0.557714	−	0.867971i
$19$	1.31544	+	2.27842i	0.301784	+	0.522705i	0.976540	−	0.215336i	$-0.0690846\pi$
$19$	1.31544	+	2.27842i	0.301784	+	0.522705i	−0.674756	+	0.738041i	$0.735751\pi$
$20$	−4.39057	−	0.850232i	−0.981761	−	0.190118i
$21$	6.03788	+	2.49197i	1.31757	+	0.543792i
$22$	3.06534	−	5.94478i	0.653533	−	1.26743i
$23$	−1.09265	−	0.292774i	−0.227832	−	0.0610475i	0.143097	−	0.989709i	$-0.454294\pi$
$23$	−1.09265	−	0.292774i	−0.227832	−	0.0610475i	−0.370929	+	0.928661i	$0.620961\pi$
$24$	6.41976	−	2.74730i	1.31043	−	0.560790i
$25$	4.20235	+	2.70929i	0.840470	+	0.541858i
$26$	−0.0797380	+	0.0877008i	−0.0156379	+	0.0171995i
$27$	−0.166053	−	0.166053i	−0.0319568	−	0.0319568i
$28$	−2.80263	+	4.48835i	−0.529646	+	0.848219i
$29$			7.27332i			1.35062i	0.737533	+	0.675311i	$0.235991\pi$
$29$			7.27332i			1.35062i	−0.737533	+	0.675311i	$0.764009\pi$
$30$	−7.80506	+	0.179523i	−1.42500	+	0.0327762i
$31$	−4.01558	−	2.31840i	−0.721219	−	0.416396i	0.0939821	−	0.995574i	$-0.470040\pi$
$31$	−4.01558	−	2.31840i	−0.721219	−	0.416396i	−0.815201	+	0.579178i	$0.803374\pi$
$32$	1.33148	+	5.49792i	0.235374	+	0.971905i
$33$	3.02207	−	11.2785i	0.526075	−	1.96334i
$34$	6.65908	−	2.12809i	1.14202	−	0.364965i
$35$	4.77600	−	3.49139i	0.807292	−	0.590153i
$36$	5.04299	−	3.58989i	0.840498	−	0.598315i
$37$	2.22779	+	0.596933i	0.366246	+	0.0981352i	0.437248	−	0.899341i	$-0.355953\pi$
$37$	2.22779	+	0.596933i	0.366246	+	0.0981352i	−0.0710024	+	0.997476i	$0.522620\pi$
$38$	−3.13016	+	2.01128i	−0.507779	+	0.326273i
$39$	−0.103461	+	0.179200i	−0.0165671	+	0.0286950i
$40$	0.906097	−	6.25931i	0.143267	−	0.989684i
$41$	−5.71767			−0.892950			−0.446475	−	0.894796i	$-0.647321\pi$
$41$	−5.71767			−0.892950			−0.446475	+	0.894796i	$0.647321\pi$
$42$	−3.11458	+	8.69661i	−0.480589	+	1.34192i
$43$	1.57302	−	1.57302i	0.239883	−	0.239883i	−0.576918	−	0.816802i	$-0.695745\pi$
$43$	1.57302	−	1.57302i	0.239883	−	0.239883i	0.816802	+	0.576918i	$0.195745\pi$
$44$	8.60362	+	3.93079i	1.29704	+	0.592589i
$45$	−6.72699	+	1.62679i	−1.00280	+	0.242508i
$46$	0.340174	−	1.56316i	0.0501559	−	0.230475i
$47$	0.716679	−	2.67468i	0.104538	−	0.390143i	−0.893754	−	0.448558i	$-0.851938\pi$
$47$	0.716679	−	2.67468i	0.104538	−	0.390143i	0.998292	+	0.0584148i	$0.0186046\pi$
$48$	4.31215	+	8.88410i	0.622406	+	1.28231i
$49$	−1.82895	−	6.75684i	−0.261278	−	0.965264i
$50$	−3.54488	+	6.11832i	−0.501322	+	0.865261i
$51$	10.5691	−	6.10206i	1.47997	−	0.854459i
$52$	−0.129244	−	0.106748i	−0.0179230	−	0.0148032i
$53$	−9.12265	+	2.44441i	−1.25309	+	0.335765i	−0.823530	−	0.567272i	$-0.807999\pi$
$53$	−9.12265	+	2.44441i	−1.25309	+	0.335765i	−0.429562	+	0.903037i	$0.641332\pi$
$54$	0.223414	−	0.245724i	0.0304027	−	0.0334388i
$55$	−7.29241	−	7.65915i	−0.983308	−	1.03276i
$56$	−6.52860	−	3.65751i	−0.872421	−	0.488756i
$57$	−4.59281	+	4.59281i	−0.608333	+	0.608333i
$58$	−10.2744	+	0.488615i	−1.34910	+	0.0641584i
$59$	1.67748	−	2.90547i	0.218389	−	0.378260i	−0.735927	−	0.677061i	$-0.763253\pi$
$59$	1.67748	−	2.90547i	0.218389	−	0.378260i	0.954315	+	0.298801i	$0.0965866\pi$
$60$	−0.777934	−	11.0135i	−0.100431	−	1.42184i
$61$	−0.978771	−	1.69528i	−0.125319	−	0.217058i	0.796539	−	0.604587i	$-0.206662\pi$
$61$	−0.978771	−	1.69528i	−0.125319	−	0.217058i	−0.921857	+	0.387529i	$0.873329\pi$
$62$	3.00524	−	5.82822i	0.381666	−	0.740185i
$63$	−1.05853	+	8.12021i	−0.133362	+	1.02305i
$64$	−7.67701	+	2.25021i	−0.959627	+	0.281277i
$65$	0.0896988	+	0.164554i	0.0111258	+	0.0204104i
$66$	16.1352	+	3.51135i	1.98611	+	0.432217i
$67$	−0.491893	+	0.131802i	−0.0600943	+	0.0161022i	−0.288741	−	0.957407i	$-0.593237\pi$
$67$	−0.491893	+	0.131802i	−0.0600943	+	0.0161022i	0.228647	+	0.973509i	$0.426570\pi$
$68$	3.45353	+	9.26376i	0.418802	+	1.12340i
$69$		−	2.79272i		−	0.336204i
$70$	5.25285	+	6.51211i	0.627835	+	0.778346i
$71$			14.4625i			1.71638i	0.513329	+	0.858192i	$0.328412\pi$
$71$			14.4625i			1.71638i	−0.513329	+	0.858192i	$0.671588\pi$
$72$	5.40993	+	6.88265i	0.637566	+	0.811128i
$73$	9.26507	−	2.48257i	1.08439	−	0.290563i	0.327999	−	0.944678i	$-0.393626\pi$
$73$	9.26507	−	2.48257i	1.08439	−	0.290563i	0.756395	+	0.654115i	$0.226959\pi$
$74$	−0.693578	+	3.18711i	−0.0806268	+	0.370494i
$75$	−3.77565	+	11.7526i	−0.435974	+	1.35707i
$76$	−3.05145	−	4.28660i	−0.350026	−	0.491707i
$77$	−11.5545	+	4.80329i	−1.31676	+	0.547385i
$78$	−0.260092	−	0.134113i	−0.0294496	−	0.0151853i
$79$	−3.05204	−	5.28630i	−0.343382	−	0.594755i	0.641677	−	0.766975i	$-0.278239\pi$
$79$	−3.05204	−	5.28630i	−0.343382	−	0.594755i	−0.985058	+	0.172221i	$0.944906\pi$
$80$	8.90288	+	0.859474i	0.995372	+	0.0960921i
$81$	−4.35280	+	7.53927i	−0.483644	+	0.837696i
$82$	−0.384108	−	8.07688i	−0.0424176	−	0.891942i
$83$	5.62620	−	5.62620i	0.617555	−	0.617555i	−0.327348	−	0.944904i	$-0.606155\pi$
$83$	5.62620	−	5.62620i	0.617555	−	0.617555i	0.944904	+	0.327348i	$0.106155\pi$
$84$	−12.4942	−	3.81547i	−1.36323	−	0.416302i
$85$	0.271049	−	11.0502i	0.0293994	−	1.19856i
$86$	2.32775	+	2.11640i	0.251008	+	0.228217i
$87$	−17.3447	+	4.64751i	−1.85955	+	0.498265i
$88$	−4.97472	+	12.4177i	−0.530307	+	1.32373i
$89$	−14.4482	+	8.34169i	−1.53151	+	0.884218i	−0.532217	+	0.846608i	$0.678641\pi$
$89$	−14.4482	+	8.34169i	−1.53151	+	0.884218i	−0.999292	+	0.0376100i	$0.988026\pi$
$90$	−2.74995	−	9.39337i	−0.289870	−	0.990148i
$91$	0.219817	−	0.0292243i	0.0230431	−	0.00306354i
$92$	2.23100	+	0.375524i	0.232598	+	0.0391511i
$93$	2.96282	−	11.0574i	0.307230	−	1.14660i
$94$	3.82645	+	0.832711i	0.394668	+	0.0858875i
$95$	1.38279	+	5.71802i	0.141872	+	0.586657i
$96$	−12.2601	+	6.68825i	−1.25130	+	0.682616i
$97$	5.81505	−	5.81505i	0.590429	−	0.590429i	−0.347318	−	0.937747i	$-0.612908\pi$
$97$	5.81505	−	5.81505i	0.590429	−	0.590429i	0.937747	+	0.347318i	$0.112908\pi$
$98$	9.42197	−	3.03752i	0.951762	−	0.306836i
$99$	14.6384			1.47122
$100$	−8.88098	−	4.59654i	−0.888098	−	0.459654i
$101$	4.28723	−	7.42571i	0.426596	−	0.738885i	−0.569972	−	0.821664i	$-0.693046\pi$
$101$	4.28723	−	7.42571i	0.426596	−	0.738885i	0.996568	+	0.0827785i	$0.0263794\pi$
$102$	9.32990	+	14.5201i	0.923798	+	1.43771i
$103$	3.15482	+	0.845330i	0.310853	+	0.0832929i	0.410873	−	0.911693i	$-0.365224\pi$
$103$	3.15482	+	0.845330i	0.310853	+	0.0832929i	−0.100020	+	0.994985i	$0.531891\pi$
$104$	0.142111	−	0.189744i	0.0139351	−	0.0186059i
$105$	11.3777	+	9.15843i	1.11035	+	0.893772i
$106$	−4.06586	−	12.7226i	−0.394911	−	1.23573i
$107$	1.75796	−	6.56081i	0.169949	−	0.634257i	−0.827408	−	0.561601i	$-0.810186\pi$
$107$	1.75796	−	6.56081i	0.169949	−	0.634257i	0.997357	−	0.0726563i	$-0.0231476\pi$
$108$	0.362123	+	0.299090i	0.0348453	+	0.0287800i
$109$	3.39423	+	1.95966i	0.325108	+	0.187701i	0.653667	−	0.756782i	$-0.273230\pi$
$109$	3.39423	+	1.95966i	0.325108	+	0.187701i	−0.328559	+	0.944483i	$0.606563\pi$
$110$	10.3296	−	10.8159i	0.984884	−	1.03126i
$111$			5.69404i			0.540455i
$112$	4.72808	−	9.46812i	0.446762	−	0.894653i
$113$	−0.0280186	−	0.0280186i	−0.00263577	−	0.00263577i	0.705788	−	0.708423i	$-0.250593\pi$
$113$	−0.0280186	−	0.0280186i	−0.00263577	−	0.00263577i	−0.708423	+	0.705788i	$0.750593\pi$
$114$	−6.79643	−	6.17935i	−0.636544	−	0.578749i
$115$	−2.15887	−	1.31804i	−0.201316	−	0.122908i
$116$	−1.38045	−	14.4810i	−0.128172	−	1.34453i
$117$	−0.250575	−	0.0671414i	−0.0231657	−	0.00620723i
$118$	4.21701	+	2.17444i	0.388207	+	0.200174i
$119$	−12.0895	−	4.98961i	−1.10824	−	0.457397i
$120$	15.5056	−	1.83880i	1.41546	−	0.167859i
$121$	5.68418	+	9.84529i	0.516744	+	0.895026i
$122$	2.32903	−	1.49652i	0.210860	−	0.135488i
$123$	−3.65348	−	13.6350i	−0.329423	−	1.22942i
$124$	8.43494	+	3.85372i	0.757480	+	0.346074i
$125$	7.30320	+	8.46542i	0.653218	+	0.757170i
$126$	−11.5419	−	0.949787i	−1.02823	−	0.0846137i
$127$	6.53450	+	6.53450i	0.579843	+	0.579843i	0.934860	−	0.355017i	$-0.115525\pi$
$127$	6.53450	+	6.53450i	0.579843	+	0.579843i	−0.355017	+	0.934860i	$0.615525\pi$
$128$	−3.69442	−	10.6935i	−0.326544	−	0.945182i
$129$	4.75632	+	2.74606i	0.418770	+	0.241777i
$130$	−0.226426	+	0.137765i	−0.0198589	+	0.0120828i
$131$	3.19588	−	1.84514i	0.279225	−	0.161211i	−0.353847	−	0.935303i	$-0.615127\pi$
$131$	3.19588	−	1.84514i	0.279225	−	0.161211i	0.633073	+	0.774092i	$0.281793\pi$
$132$	−3.87624	+	23.0288i	−0.337383	+	2.00440i
$133$	6.90228	+	0.899762i	0.598504	+	0.0780193i
$134$	−0.219231	−	0.686002i	−0.0189387	−	0.0592616i
$135$	−0.251322	−	0.461055i	−0.0216304	−	0.0396813i
$136$	−12.8541	+	5.50085i	−1.10223	+	0.471694i
$137$	−5.13977	−	19.1819i	−0.439120	−	1.63882i	−0.731010	−	0.682366i	$-0.760951\pi$
$137$	−5.13977	−	19.1819i	−0.439120	−	1.63882i	0.291890	−	0.956452i	$-0.405716\pi$
$138$	3.94504	−	0.187612i	0.335824	−	0.0159706i
$139$	−1.15593			−0.0980447			−0.0490223	−	0.998798i	$-0.515611\pi$
$139$	−1.15593			−0.0980447			−0.0490223	+	0.998798i	$0.515611\pi$
$140$	−8.84624	+	7.85774i	−0.747644	+	0.664100i
$141$	6.83628			0.575719
$142$	−20.4300	+	0.971579i	−1.71445	+	0.0815331i
$143$	−0.102596	−	0.382893i	−0.00857950	−	0.0320191i
$144$	−9.35911	+	8.10452i	−0.779926	+	0.675377i
$145$	−4.59330	+	15.6015i	−0.381452	+	1.29564i
$146$	4.12934	+	12.9212i	0.341746	+	1.06937i
$147$	14.9444	−	8.67899i	1.23260	−	0.715831i
$148$	−4.54876	−	0.765652i	−0.373906	−	0.0629362i
$149$	5.37045	−	3.10063i	0.439965	−	0.254014i	−0.263618	−	0.964627i	$-0.584916\pi$
$149$	5.37045	−	3.10063i	0.439965	−	0.254014i	0.703583	+	0.710613i	$0.251582\pi$
$150$	−16.8555	−	4.54402i	−1.37625	−	0.371018i
$151$	8.72300	+	5.03623i	0.709868	+	0.409842i	0.811012	−	0.585029i	$-0.198917\pi$
$151$	8.72300	+	5.03623i	0.709868	+	0.409842i	−0.101144	+	0.994872i	$0.532250\pi$
$152$	5.85033	−	4.59850i	0.474525	−	0.372988i
$153$	10.8188	+	10.8188i	0.874646	+	0.874646i
$154$	−7.56143	−	15.9994i	−0.609317	−	1.28927i
$155$	−7.14943	−	7.50898i	−0.574256	−	0.603136i
$156$	0.171977	−	0.376420i	0.0137692	−	0.0301377i
$157$	3.77089	+	14.0732i	0.300950	+	1.12316i	0.936376	+	0.350999i	$0.114158\pi$
$157$	3.77089	+	14.0732i	0.300950	+	1.12316i	−0.635426	+	0.772162i	$0.719175\pi$
$158$	7.26248	−	4.66650i	0.577772	−	0.371247i
$159$	−11.6584	−	20.1929i	−0.924570	−	1.60140i
$160$	−0.616019	+	12.6341i	−0.0487006	+	0.998813i
$161$	−2.37206	+	1.82495i	−0.186945	+	0.143826i
$162$	−10.9425	−	5.64235i	−0.859725	−	0.443305i
$163$	−2.85106	−	0.763938i	−0.223312	−	0.0598363i	0.145428	−	0.989369i	$-0.453544\pi$
$163$	−2.85106	−	0.763938i	−0.223312	−	0.0598363i	−0.368740	+	0.929533i	$0.620211\pi$
$164$	11.3837	−	1.08519i	0.888920	−	0.0847395i
$165$	13.6051	−	22.2843i	1.05916	−	1.73483i
$166$	8.32562	+	7.56970i	0.646194	+	0.587522i
$167$	6.13096	+	6.13096i	0.474428	+	0.474428i	0.903344	−	0.428916i	$-0.141105\pi$
$167$	6.13096	+	6.13096i	0.474428	+	0.474428i	−0.428916	+	0.903344i	$0.641105\pi$
$168$	4.55045	−	17.9059i	0.351075	−	1.38147i
$169$		−	12.9930i		−	0.999460i
$170$	15.6279	−	0.359454i	1.19861	−	0.0275689i
$171$	−7.05197	−	4.07146i	−0.539278	−	0.311352i
$172$	−2.83329	+	3.43039i	−0.216036	+	0.261565i
$173$	−0.464708	+	1.73431i	−0.0353311	+	0.131857i	−0.981339	−	0.192287i	$-0.938410\pi$
$173$	−0.464708	+	1.73431i	−0.0353311	+	0.131857i	0.946008	+	0.324144i	$0.105076\pi$
$174$	−7.73035	−	24.1893i	−0.586037	−	1.83378i
$175$	12.4496	−	4.47298i	0.941101	−	0.338126i
$176$	−17.8756	−	6.19316i	−1.34743	−	0.466827i
$177$	8.00057	+	2.14375i	0.601360	+	0.161134i
$178$	−12.7542	−	19.8494i	−0.955971	−	1.48778i
$179$	−10.7713	+	18.6564i	−0.805084	+	1.39445i	0.111150	+	0.993804i	$0.464547\pi$
$179$	−10.7713	+	18.6564i	−0.805084	+	1.39445i	−0.916234	+	0.400643i	$0.868787\pi$
$180$	13.0845	−	4.51566i	0.975261	−	0.336578i
$181$	−16.2122			−1.20504			−0.602520	−	0.798104i	$-0.705837\pi$
$181$	−16.2122			−1.20504			−0.602520	+	0.798104i	$0.705837\pi$
$182$	0.0560498	+	0.308554i	0.00415469	+	0.0228715i
$183$	3.41733	−	3.41733i	0.252616	−	0.252616i
$184$	−0.380595	+	3.17677i	−0.0280578	+	0.234195i
$185$	4.40170	+	2.68735i	0.323619	+	0.197578i
$186$	15.8189	+	3.44250i	1.15990	+	0.252416i
$187$	−6.05102	+	22.5827i	−0.442495	+	1.65141i
$188$	−0.919244	+	5.46125i	−0.0670427	+	0.398303i
$189$	−0.615893	+	0.0818818i	−0.0447996	+	0.00595603i
$190$	−7.98448	+	2.33749i	−0.579255	+	0.169579i
$191$	−14.2331	+	8.21746i	−1.02987	+	0.594595i	−0.916947	−	0.399009i	$-0.869354\pi$
$191$	−14.2331	+	8.21746i	−1.02987	+	0.594595i	−0.112921	+	0.993604i	$0.536021\pi$
$192$	−10.2716	−	16.8696i	−0.741286	−	1.21746i
$193$	−4.79080	+	1.28369i	−0.344849	+	0.0924021i	−0.427087	−	0.904211i	$-0.640460\pi$
$193$	−4.79080	+	1.28369i	−0.344849	+	0.0924021i	0.0822374	+	0.996613i	$0.473793\pi$
$194$	8.60509	+	7.82379i	0.617810	+	0.561716i
$195$	−0.335098	+	0.319052i	−0.0239968	+	0.0228478i
$196$	4.92381	+	13.1056i	0.351701	+	0.936112i
$197$	−3.89922	+	3.89922i	−0.277808	+	0.277808i	−0.832233	−	0.554425i	$-0.812938\pi$
$197$	−3.89922	+	3.89922i	−0.277808	+	0.277808i	0.554425	+	0.832233i	$0.312938\pi$
$198$	0.983397	+	20.6785i	0.0698870	+	1.46956i
$199$	−9.44788	+	16.3642i	−0.669743	+	1.16003i	0.308233	+	0.951311i	$0.400262\pi$
$199$	−9.44788	+	16.3642i	−0.669743	+	1.16003i	−0.977976	+	0.208717i	$0.933071\pi$
$200$	5.89653	−	12.8542i	0.416948	−	0.908930i
$201$	−0.628620	−	1.08880i	−0.0443394	−	0.0767981i
$202$	10.7777	+	5.55737i	0.758316	+	0.391015i
$203$	15.2817	+	11.6952i	1.07257	+	0.820842i
$204$	−19.8846	+	14.1550i	−1.39220	+	0.991050i
$205$	−12.2646	−	3.61086i	−0.856597	−	0.252193i
$206$	−0.982190	+	4.51334i	−0.0684324	+	0.314459i
$207$	3.38187	−	0.906169i	0.235056	−	0.0629831i
$208$	0.277583	+	0.188002i	0.0192469	+	0.0130356i
$209$		−	12.4428i		−	0.860690i
$210$	−12.1730	+	16.6876i	−0.840018	+	1.15155i
$211$			10.9795i			0.755859i	0.925834	+	0.377929i	$0.123364\pi$
$211$			10.9795i			0.755859i	−0.925834	+	0.377929i	$0.876636\pi$
$212$	17.6990	−	6.59820i	1.21557	−	0.453166i
$213$	−34.4888	+	9.24126i	−2.36314	+	0.633201i
$214$	9.38600	+	2.04258i	0.641614	+	0.139628i
$215$	4.36758	−	2.38078i	0.297867	−	0.162368i
$216$	−0.398173	+	0.531633i	−0.0270922	+	0.0361731i
$217$	−11.3280	+	4.70911i	−0.768993	+	0.319675i
$218$	−2.54022	+	4.92639i	−0.172046	+	0.333657i
$219$	11.8404	+	20.5082i	0.800099	+	1.38581i
$220$	15.9727	+	13.8651i	1.07688	+	0.934785i
$221$	0.207158	−	0.358809i	0.0139350	−	0.0241361i
$222$	−8.04350	+	0.382521i	−0.539845	+	0.0256731i
$223$	−13.6990	+	13.6990i	−0.917356	+	0.917356i	−0.996836	−	0.0794806i	$-0.974674\pi$
$223$	−13.6990	+	13.6990i	−0.917356	+	0.917356i	0.0794806	+	0.996836i	$0.474674\pi$
$224$	13.6925	+	6.04291i	0.914866	+	0.403759i
$225$	−15.4570	−	0.758741i	−1.03047	−	0.0505828i
$226$	0.0376973	−	0.0414618i	0.00250759	−	0.00275800i
$227$	22.1724	−	5.94107i	1.47163	−	0.394322i	0.568141	−	0.822931i	$-0.307663\pi$
$227$	22.1724	−	5.94107i	1.47163	−	0.394322i	0.903490	+	0.428609i	$0.140996\pi$
$228$	8.27247	−	10.0159i	0.547858	−	0.663317i
$229$	10.3396	−	5.96955i	0.683258	−	0.394479i	−0.117824	−	0.993035i	$-0.537592\pi$
$229$	10.3396	−	5.96955i	0.683258	−	0.394479i	0.801081	+	0.598556i	$0.204258\pi$
$230$	1.71686	−	3.13820i	0.113206	−	0.206927i
$231$	−18.8375	−	24.4849i	−1.23942	−	1.61099i
$232$	20.3634	−	2.92287i	1.33692	−	0.191896i
$233$	−6.15761	+	22.9805i	−0.403399	+	1.50550i	0.403592	+	0.914939i	$0.367762\pi$
$233$	−6.15761	+	22.9805i	−0.403399	+	1.50550i	−0.806990	+	0.590565i	$0.798905\pi$
$234$	0.0780117	−	0.358477i	0.00509978	−	0.0234344i
$235$	3.22644	−	5.28469i	0.210469	−	0.344735i
$236$	−2.78836	+	6.10310i	−0.181507	+	0.397278i
$237$	10.6561	−	10.6561i	0.692186	−	0.692186i
$238$	6.23625	−	17.4130i	0.404236	−	1.12872i
$239$	−1.50749			−0.0975113			−0.0487556	−	0.998811i	$-0.515526\pi$
$239$	−1.50749			−0.0975113			−0.0487556	+	0.998811i	$0.515526\pi$
$240$	3.63917	+	21.7799i	0.234908	+	1.40589i
$241$	9.26556	−	16.0484i	0.596847	−	1.03377i	−0.396436	−	0.918062i	$-0.629753\pi$
$241$	9.26556	−	16.0484i	0.596847	−	1.03377i	0.993283	−	0.115708i	$-0.0369136\pi$
$242$	−13.5258	+	8.69097i	−0.869469	+	0.558676i
$243$	−21.4408	−	5.74504i	−1.37543	−	0.368544i
$244$	2.27047	+	3.18949i	0.145352	+	0.204186i
$245$	0.343969	−	15.6487i	0.0219754	−	0.999759i
$246$	19.0155	−	6.07695i	1.21239	−	0.387452i
$247$	−0.0570710	+	0.212992i	−0.00363134	+	0.0135524i
$248$	−4.87718	+	12.1742i	−0.309701	+	0.773064i
$249$	17.0119	+	9.82180i	1.07808	+	0.622431i
$250$	−11.4678	+	10.8853i	−0.725286	+	0.688448i
$251$		−	18.0219i		−	1.13753i	−0.822500	−	0.568765i	$-0.807421\pi$
$251$		−	18.0219i		−	1.13753i	0.822500	−	0.568765i	$-0.192579\pi$
$252$	0.566313	−	16.3680i	0.0356743	−	1.03109i
$253$	3.78301	+	3.78301i	0.237836	+	0.237836i
$254$	−8.79176	+	9.66973i	−0.551644	+	0.606733i
$255$	26.5247	−	6.41448i	1.66104	−	0.401690i
$256$	14.8577	−	5.93719i	0.928603	−	0.371074i
$257$	14.4032	+	3.85933i	0.898448	+	0.240738i	0.678350	−	0.734739i	$-0.262696\pi$
$257$	14.4032	+	3.85933i	0.898448	+	0.240738i	0.220098	+	0.975478i	$0.429362\pi$
$258$	−3.55961	+	6.90333i	−0.221611	+	0.429783i
$259$	4.83638	−	3.72088i	0.300518	−	0.231204i
$260$	−0.209820	−	0.310599i	−0.0130125	−	0.0192625i
$261$	−11.2559	−	19.4958i	−0.696723	−	1.20676i
$262$	2.82117	+	4.39060i	0.174293	+	0.271252i
$263$	−1.83499	−	6.84826i	−0.113150	−	0.422282i	0.885992	−	0.463701i	$-0.153479\pi$
$263$	−1.83499	−	6.84826i	−0.113150	−	0.422282i	−0.999142	+	0.0414191i	$0.986812\pi$
$264$	−32.7913	−	3.92858i	−2.01816	−	0.241787i
$265$	−21.1121	−	0.517856i	−1.29691	−	0.0318117i
$266$	−0.807330	+	9.81073i	−0.0495006	+	0.601534i
$267$	−29.1246	−	29.1246i	−1.78240	−	1.78240i
$268$	0.954331	−	0.355775i	0.0582950	−	0.0217324i
$269$	−5.23463	−	3.02221i	−0.319161	−	0.184268i	0.331858	−	0.943329i	$-0.392325\pi$
$269$	−5.23463	−	3.02221i	−0.319161	−	0.184268i	−0.651019	+	0.759062i	$0.725658\pi$
$270$	0.634411	−	0.385995i	0.0386090	−	0.0234909i
$271$	20.3476	−	11.7477i	1.23603	−	0.713622i	0.267750	−	0.963488i	$-0.413720\pi$
$271$	20.3476	−	11.7477i	1.23603	−	0.713622i	0.968280	+	0.249866i	$0.0803866\pi$
$272$	−8.63413	−	17.7884i	−0.523521	−	1.07858i
$273$	0.210150	+	0.505525i	0.0127189	+	0.0305958i
$274$	26.7514	−	8.54914i	1.61611	−	0.516473i
$275$	−10.8055	−	21.0345i	−0.651597	−	1.26843i
$276$	0.530048	+	5.56023i	0.0319052	+	0.334686i
$277$	6.03684	+	22.5298i	0.362719	+	1.35369i	0.870487	+	0.492191i	$0.163804\pi$
$277$	6.03684	+	22.5298i	0.362719	+	1.35369i	−0.507768	+	0.861494i	$0.669529\pi$
$278$	−0.0776543	−	1.63289i	−0.00465740	−	0.0979340i
$279$	14.3514			0.859197
$280$	−11.6943	−	11.9685i	−0.698865	−	0.715253i
$281$	−19.3011			−1.15141			−0.575703	−	0.817659i	$-0.695272\pi$
$281$	−19.3011			−1.15141			−0.575703	+	0.817659i	$0.695272\pi$
$282$	0.459255	+	9.65704i	0.0273483	+	0.575069i
$283$	1.84508	+	6.88593i	0.109679	+	0.409326i	0.998834	−	0.0482794i	$-0.0153738\pi$
$283$	1.84508	+	6.88593i	0.109679	+	0.409326i	−0.889155	+	0.457606i	$0.848707\pi$
$284$	−2.74494	−	28.7945i	−0.162882	−	1.70864i
$285$	−12.7522	+	6.95126i	−0.755377	+	0.411757i
$286$	0.533989	−	0.170651i	0.0315754	−	0.0100908i
$287$	−9.19377	+	12.0132i	−0.542691	+	0.709116i
$288$	−12.0773	−	12.6764i	−0.711663	−	0.746963i
$289$	−6.43980	+	3.71802i	−0.378812	+	0.218707i
$290$	−22.3476	−	5.44047i	−1.31229	−	0.319475i
$291$	17.5829	+	10.1515i	1.03073	+	0.595091i
$292$	−17.9753	+	6.70121i	−1.05193	+	0.392159i
$293$	1.29442	+	1.29442i	0.0756208	+	0.0756208i	0.743906	−	0.668285i	$-0.232971\pi$
$293$	1.29442	+	1.29442i	0.0756208	+	0.0756208i	−0.668285	+	0.743906i	$0.732971\pi$
$294$	13.2640	+	20.5277i	0.773575	+	1.19720i
$295$	5.43312	−	5.17297i	0.316329	−	0.301182i
$296$	0.775992	−	6.47709i	0.0451036	−	0.376473i
$297$	0.287458	+	1.07281i	0.0166800	+	0.0622506i
$298$	4.74079	+	7.37810i	0.274627	+	0.427402i
$299$	−0.0474048	−	0.0821076i	−0.00274149	−	0.00474840i
$300$	5.28662	−	24.1156i	0.305223	−	1.39232i
$301$	−0.775668	−	5.83436i	−0.0447088	−	0.336287i
$302$	−6.52826	+	12.6606i	−0.375659	+	0.728535i
$303$	20.4476	+	5.47891i	1.17468	+	0.314755i
$304$	6.88895	+	7.95536i	0.395108	+	0.456271i
$305$	−1.02888	−	4.25456i	−0.0589137	−	0.243615i
$306$	−14.5560	+	16.0096i	−0.832110	+	0.915206i
$307$	−3.86175	−	3.86175i	−0.220402	−	0.220402i	0.588266	−	0.808667i	$-0.299811\pi$
$307$	−3.86175	−	3.86175i	−0.220402	−	0.220402i	−0.808667	+	0.588266i	$0.799811\pi$
$308$	22.0931	−	11.7562i	1.25887	−	0.669873i
$309$			8.06346i			0.458714i
$310$	10.1270	−	10.6039i	0.575176	−	0.602258i
$311$	−17.7808	−	10.2657i	−1.00826	−	0.582116i	−0.0975749	−	0.995228i	$-0.531109\pi$
$311$	−17.7808	−	10.2657i	−1.00826	−	0.582116i	−0.910680	+	0.413112i	$0.864442\pi$
$312$	0.543290	+	0.217650i	0.0307577	+	0.0123220i
$313$	7.22385	−	26.9598i	0.408316	−	1.52386i	−0.389540	−	0.921009i	$-0.627366\pi$
$313$	7.22385	−	26.9598i	0.408316	−	1.52386i	0.797856	−	0.602847i	$-0.205967\pi$
$314$	−19.6267	+	6.27225i	−1.10760	+	0.353964i
$315$	−7.39871	+	16.7497i	−0.416870	+	0.943736i
$316$	7.07986	+	9.94561i	0.398273	+	0.559484i
$317$	12.5169	+	3.35388i	0.703016	+	0.188373i	0.592581	−	0.805511i	$-0.298109\pi$
$317$	12.5169	+	3.35388i	0.703016	+	0.188373i	0.110435	+	0.993883i	$0.464776\pi$
$318$	27.7417	−	17.8254i	1.55567	−	0.999597i
$319$	17.1997	−	29.7907i	0.962996	−	1.66796i
$320$	−17.8885	−	0.0214515i	−0.999999	−	0.00119917i
$321$	16.7689			0.935949
$322$	−2.73731	−	3.22822i	−0.152544	−	0.179902i
$323$	9.19609	−	9.19609i	0.511684	−	0.511684i
$324$	7.23538	−	15.8366i	0.401965	−	0.879813i
$325$	0.0884867	+	0.409622i	0.00490836	+	0.0227217i
$326$	0.887621	−	4.07877i	0.0491608	−	0.225902i
$327$	−2.50436	+	9.34642i	−0.138492	+	0.516858i
$328$	2.29771	+	16.0079i	0.126870	+	0.883891i
$329$	−4.46729	−	5.80657i	−0.246290	−	0.320126i
$330$	32.3932	+	17.7218i	1.78318	+	0.975552i
$331$	−6.41324	+	3.70269i	−0.352504	+	0.203518i	−0.665787	−	0.746142i	$-0.731904\pi$
$331$	−6.41324	+	3.70269i	−0.352504	+	0.203518i	0.313284	+	0.949660i	$0.398571\pi$
$332$	−10.1338	+	12.2694i	−0.556163	+	0.673373i
$333$	−6.89526	+	1.84758i	−0.377858	+	0.101247i
$334$	−8.24882	+	9.07257i	−0.451356	+	0.496429i
$335$	−1.13836	−	0.0279228i	−0.0621955	−	0.00152559i
$336$	25.5998	+	5.22514i	1.39659	+	0.285055i
$337$	−5.81990	+	5.81990i	−0.317030	+	0.317030i	−0.847625	−	0.530595i	$-0.821968\pi$
$337$	−5.81990	+	5.81990i	−0.317030	+	0.317030i	0.530595	+	0.847625i	$0.321968\pi$
$338$	18.3541	−	0.872857i	0.998331	−	0.0474771i
$339$	0.0489128	−	0.0847195i	0.00265658	−	0.00460133i
$340$	1.55764	+	22.0521i	0.0844749	+	1.19594i
$341$	10.9649	+	18.9918i	0.593782	+	1.02846i
$342$	5.27767	−	10.2353i	0.285384	−	0.553459i
$343$	−17.1374	−	7.02198i	−0.925335	−	0.379151i
$344$	−5.03617	−	3.77190i	−0.271532	−	0.203367i
$345$	1.76367	−	5.99047i	0.0949530	−	0.322516i
$346$	−2.48114	−	0.539944i	−0.133387	−	0.0290276i
$347$	−10.6671	+	2.85823i	−0.572638	+	0.153438i	−0.533506	−	0.845796i	$-0.679126\pi$
$347$	−10.6671	+	2.85823i	−0.572638	+	0.153438i	−0.0391317	+	0.999234i	$0.512459\pi$
$348$	33.6508	−	12.5450i	1.80387	−	0.672485i
$349$			10.3995i			0.556672i	0.960484	+	0.278336i	$0.0897829\pi$
$349$			10.3995i			0.556672i	−0.960484	+	0.278336i	$0.910217\pi$
$350$	7.15496	+	17.2860i	0.382449	+	0.923977i
$351$		−	0.0196824i		−	0.00105057i
$352$	7.54769	−	25.6675i	0.402293	−	1.36808i
$353$	7.28892	−	1.95306i	0.387950	−	0.103951i	−0.0595714	−	0.998224i	$-0.518973\pi$
$353$	7.28892	−	1.95306i	0.387950	−	0.103951i	0.447522	+	0.894273i	$0.352307\pi$
$354$	−2.49082	+	11.4458i	−0.132386	+	0.608335i
$355$	−9.13346	+	31.0226i	−0.484754	+	1.64651i
$356$	27.1828	−	19.3503i	1.44069	−	1.02556i
$357$	4.17380	−	32.0182i	0.220901	−	1.69458i
$358$	−27.0780	−	13.9624i	−1.43112	−	0.737935i
$359$	5.74179	+	9.94507i	0.303040	+	0.524881i	0.976823	−	0.214049i	$-0.0686651\pi$
$359$	5.74179	+	9.94507i	0.303040	+	0.524881i	−0.673783	+	0.738929i	$0.735332\pi$
$360$	7.25791	+	18.1800i	0.382525	+	0.958172i
$361$	6.03921	−	10.4602i	0.317853	−	0.550538i
$362$	−1.08912	−	22.9016i	−0.0572428	−	1.20368i
$363$	−19.8460	+	19.8460i	−1.04165	+	1.04165i
$364$	−0.432103	+	0.0999053i	−0.0226484	+	0.00523646i
$365$	21.4417	+	0.525941i	1.12231	+	0.0275290i
$366$	5.05695	+	4.59781i	0.264331	+	0.240331i
$367$	12.2312	−	3.27735i	0.638465	−	0.171076i	0.0749570	−	0.997187i	$-0.476118\pi$
$367$	12.2312	−	3.27735i	0.638465	−	0.171076i	0.563508	+	0.826111i	$0.309451\pi$
$368$	−4.51313	−	0.324222i	−0.235263	−	0.0169013i
$369$	15.3259	−	8.84843i	0.797836	−	0.460631i
$370$	−3.50049	+	6.39845i	−0.181982	+	0.332639i
$371$	−9.53297	+	23.0978i	−0.494927	+	1.19918i
$372$	−3.80024	+	22.5773i	−0.197033	+	1.17058i
$373$	−6.44552	+	24.0550i	−0.333737	+	1.24552i	0.571496	+	0.820605i	$0.306363\pi$
$373$	−6.44552	+	24.0550i	−0.333737	+	1.24552i	−0.905232	+	0.424917i	$0.860303\pi$
$374$	−32.3072	−	7.03069i	−1.67057	−	0.363548i
$375$	−15.5209	+	22.8252i	−0.801498	+	1.17869i
$376$	−7.77641	−	0.931657i	−0.401038	−	0.0480466i
$377$	−0.431057	+	0.431057i	−0.0222006	+	0.0222006i
$378$	−0.157043	−	0.864520i	−0.00807741	−	0.0444661i
$379$	−4.18354			−0.214894			−0.107447	−	0.994211i	$-0.534268\pi$
$379$	−4.18354			−0.214894			−0.107447	+	0.994211i	$0.534268\pi$
$380$	−3.83837	−	11.1220i	−0.196904	−	0.570546i
$381$	−11.4074	+	19.7583i	−0.584421	+	1.01225i
$382$	−12.5643	−	19.5538i	−0.642845	−	1.00046i
$383$	12.9702	+	3.47535i	0.662745	+	0.177582i	0.574484	−	0.818515i	$-0.305203\pi$
$383$	12.9702	+	3.47535i	0.662745	+	0.177582i	0.0882604	+	0.996097i	$0.471869\pi$
$384$	23.1402	−	15.6431i	1.18087	−	0.798282i
$385$	−27.8183	+	3.00623i	−1.41775	+	0.153212i
$386$	−2.13521	−	6.68133i	−0.108679	−	0.340071i
$387$	−1.78206	+	6.65075i	−0.0905873	+	0.338076i
$388$	−10.4739	+	12.6813i	−0.531734	+	0.643795i
$389$	15.5106	+	8.95506i	0.786419	+	0.454039i	0.838700	−	0.544593i	$-0.183316\pi$
$389$	15.5106	+	8.95506i	0.786419	+	0.454039i	−0.0522811	+	0.998632i	$0.516649\pi$
$390$	−0.473210	−	0.451931i	−0.0239619	−	0.0228844i
$391$			5.59179i			0.282789i
$392$	−18.1824	+	7.83589i	−0.918349	+	0.395772i
$393$	6.44222	+	6.44222i	0.324967	+	0.324967i
$394$	−5.77005	−	5.24616i	−0.290691	−	0.264298i
$395$	−3.20831	−	13.2667i	−0.161427	−	0.667522i
$396$	−29.1447	+	2.77833i	−1.46458	+	0.139616i
$397$	5.90626	+	1.58258i	0.296427	+	0.0794273i	0.403967	−	0.914773i	$-0.367631\pi$
$397$	5.90626	+	1.58258i	0.296427	+	0.0794273i	−0.107541	+	0.994201i	$0.534298\pi$
$398$	−23.7511	−	12.2469i	−1.19053	−	0.613882i
$399$	2.26475	+	17.0348i	0.113379	+	0.852809i
$400$	18.5542	+	7.46601i	0.927711	+	0.373300i
$401$	−9.81777	−	17.0049i	−0.490276	−	0.849183i	0.509662	−	0.860375i	$-0.329771\pi$
$401$	−9.81777	−	17.0049i	−0.490276	−	0.849183i	−0.999937	+	0.0111923i	$0.996437\pi$
$402$	1.49583	−	0.961144i	0.0746052	−	0.0479375i
$403$	−0.100584	−	0.375386i	−0.00501046	−	0.0186993i
$404$	−7.12640	+	15.5981i	−0.354551	+	0.776034i
$405$	−14.0981	+	13.4231i	−0.700542	+	0.666998i
$406$	−15.4942	+	22.3729i	−0.768965	+	1.11035i
$407$	−7.71315	−	7.71315i	−0.382327	−	0.382327i
$408$	−21.3315	−	27.1384i	−1.05606	−	1.34355i
$409$	−8.70611	−	5.02647i	−0.430489	−	0.248543i	0.269066	−	0.963122i	$-0.413285\pi$
$409$	−8.70611	−	5.02647i	−0.430489	−	0.248543i	−0.699555	+	0.714579i	$0.746618\pi$
$410$	4.27684	−	17.5678i	0.211218	−	0.867610i
$411$	42.4589	−	24.5137i	2.09434	−	1.20917i
$412$	−6.44160	−	1.08426i	−0.317355	−	0.0534175i
$413$	−3.40728	−	8.19636i	−0.167661	−	0.403316i
$414$	1.50726	+	4.71641i	0.0740779	+	0.231799i
$415$	15.6215	−	8.51529i	0.766828	−	0.417999i
$416$	−0.246926	+	0.404748i	−0.0121066	+	0.0198444i
$417$	−0.738616	−	2.75655i	−0.0361702	−	0.134989i
$418$	17.5770	−	0.835899i	0.859718	−	0.0408852i
$419$	17.7853			0.868870			0.434435	−	0.900703i	$-0.356948\pi$
$419$	17.7853			0.868870			0.434435	+	0.900703i	$0.356948\pi$
$420$	−24.3910	−	16.0747i	−1.19016	−	0.784367i
$421$	39.6482			1.93234			0.966168	−	0.257913i	$-0.0830348\pi$
$421$	39.6482			1.93234			0.966168	+	0.257913i	$0.0830348\pi$
$422$	−15.5098	+	0.737592i	−0.755006	+	0.0359054i
$423$	2.21821	+	8.27847i	0.107853	+	0.402513i
$424$	10.5097	+	24.5587i	0.510398	+	1.19267i
$425$	7.55990	−	23.5319i	0.366709	−	1.14146i
$426$	−15.3713	−	48.0987i	−0.744741	−	2.33039i
$427$	−5.13572	−	0.669478i	−0.248535	−	0.0323983i
$428$	−2.25484	+	13.3960i	−0.108992	+	0.647522i
$429$	0.847531	−	0.489322i	0.0409192	−	0.0236247i
$430$	3.65654	+	6.00979i	0.176334	+	0.289818i
$431$	21.7939	+	12.5827i	1.04977	+	0.606087i	0.922586	−	0.385792i	$-0.126072\pi$
$431$	21.7939	+	12.5827i	1.04977	+	0.606087i	0.127187	+	0.991879i	$0.459405\pi$
$432$	−0.777743	−	0.526751i	−0.0374192	−	0.0253433i
$433$	9.19231	+	9.19231i	0.441754	+	0.441754i	0.892601	−	0.450847i	$-0.148878\pi$
$433$	9.19231	+	9.19231i	0.441754	+	0.441754i	−0.450847	+	0.892601i	$0.648878\pi$
$434$	−7.41317	−	15.6857i	−0.355844	−	0.752940i
$435$	−40.1401	−	0.984591i	−1.92457	−	0.0472075i
$436$	−7.12975	−	3.25741i	−0.341453	−	0.156002i
$437$	−0.770255	−	2.87463i	−0.0368463	−	0.137512i
$438$	−28.1747	+	18.1037i	−1.34624	+	0.865026i
$439$	−14.8997	−	25.8071i	−0.711125	−	1.23170i	−0.964435	−	0.264320i	$-0.914853\pi$
$439$	−14.8997	−	25.8071i	−0.711125	−	1.23170i	0.253310	−	0.967385i	$-0.418481\pi$
$440$	−18.5130	+	23.4947i	−0.882575	+	1.12007i
$441$	15.3590	+	15.2810i	0.731382	+	0.727666i
$442$	0.520776	+	0.268531i	0.0247708	+	0.0127727i
$443$	−39.4412	−	10.5682i	−1.87391	−	0.502112i	−0.999868	−	0.0162556i	$-0.994825\pi$
$443$	−39.4412	−	10.5682i	−1.87391	−	0.502112i	−0.874039	−	0.485856i	$-0.838508\pi$
$444$	−1.08071	−	11.3367i	−0.0512883	−	0.538016i
$445$	−36.2600	+	8.76878i	−1.71889	+	0.415680i
$446$	−20.2718	−	18.4312i	−0.959897	−	0.872743i
$447$	10.8257	+	10.8257i	0.512039	+	0.512039i
$448$	−7.61647	+	19.7482i	−0.359844	+	0.933012i
$449$			20.7052i			0.977139i	0.872525	+	0.488570i	$0.162481\pi$
$449$			20.7052i			0.977139i	−0.872525	+	0.488570i	$0.837519\pi$
$450$	0.0334243	−	21.8858i	0.00157563	−	1.03171i
$451$	23.4189	+	13.5209i	1.10275	+	0.636675i
$452$	0.0611021	+	0.0504665i	0.00287400	+	0.00237374i
$453$	−6.43610	+	24.0199i	−0.302394	+	1.12855i
$454$	9.88197	+	30.9219i	0.463784	+	1.45124i
$455$	0.489971	+	0.0761331i	0.0229702	+	0.00356918i
$456$	14.7043	+	11.0130i	0.688593	+	0.515730i
$457$	−3.61891	−	0.969683i	−0.169285	−	0.0453599i	0.173181	−	0.984890i	$-0.444596\pi$
$457$	−3.61891	−	0.969683i	−0.169285	−	0.0453599i	−0.342466	+	0.939530i	$0.611262\pi$
$458$	9.12729	+	14.2048i	0.426490	+	0.663748i
$459$	−0.580425	+	1.00533i	−0.0270919	+	0.0469246i
$460$	4.54841	+	2.21445i	0.212071	+	0.103249i
$461$	−6.66823			−0.310570			−0.155285	−	0.987870i	$-0.549630\pi$
$461$	−6.66823			−0.310570			−0.155285	+	0.987870i	$0.549630\pi$
$462$	33.3223	−	28.2551i	1.55030	−	1.31455i
$463$	14.7884	−	14.7884i	0.687277	−	0.687277i	−0.274353	−	0.961629i	$-0.588464\pi$
$463$	14.7884	−	14.7884i	0.687277	−	0.687277i	0.961629	+	0.274353i	$0.0884635\pi$
$464$	5.49689	+	28.5693i	0.255187	+	1.32630i
$465$	13.3384	−	21.8474i	0.618552	−	1.01315i
$466$	−32.8763	−	7.15454i	−1.52297	−	0.331428i
$467$	7.26895	−	27.1281i	0.336367	−	1.25534i	−0.566013	−	0.824396i	$-0.691515\pi$
$467$	7.26895	−	27.1281i	0.336367	−	1.25534i	0.902380	−	0.430941i	$-0.141818\pi$
$468$	0.511632	+	0.0861184i	0.0236502	+	0.00398083i
$469$	−0.514018	+	1.24543i	−0.0237351	+	0.0575087i
$470$	7.68199	+	4.20270i	0.354344	+	0.193856i
$471$	−31.1509	+	17.9850i	−1.43536	+	0.828703i
$472$	−8.80866	−	3.52888i	−0.405451	−	0.162430i
$473$	−10.1627	+	2.72309i	−0.467282	+	0.125208i
$474$	15.7688	+	14.3371i	0.724285	+	0.658524i
$475$	−0.644940	+	13.1386i	−0.0295919	+	0.602842i
$476$	25.0169	+	7.63963i	1.14665	+	0.350162i
$477$	20.6700	−	20.6700i	0.946413	−	0.946413i
$478$	−0.101272	−	2.12950i	−0.00463206	−	0.0974012i
$479$	5.27141	−	9.13034i	0.240857	−	0.417176i	−0.720102	−	0.693868i	$-0.755905\pi$
$479$	5.27141	−	9.13034i	0.240857	−	0.417176i	0.960959	+	0.276692i	$0.0892383\pi$
$480$	−30.5222	+	6.60391i	−1.39314	+	0.301426i
$481$	0.0966532	+	0.167408i	0.00440701	+	0.00763316i
$482$	23.2927	+	12.0106i	1.06096	+	0.547067i
$483$	−5.86768	−	4.49057i	−0.266989	−	0.204328i
$484$	−13.1857	−	18.5229i	−0.599348	−	0.841949i
$485$	16.1459	−	8.80113i	0.733145	−	0.399639i
$486$	6.67517	−	30.6736i	0.302792	−	1.39138i
$487$	−36.7636	+	9.85078i	−1.66592	+	0.446381i	−0.964006	−	0.265882i	$-0.914337\pi$
$487$	−36.7636	+	9.85078i	−1.66592	+	0.446381i	−0.701913	+	0.712263i	$0.747670\pi$
$488$	−4.35300	+	3.42157i	−0.197051	+	0.154887i
$489$		−	7.28707i		−	0.329533i
$490$	22.1287	−	0.565370i	0.999674	−	0.0255408i
$491$		−	3.59770i		−	0.162362i	−0.996699	−	0.0811809i	$-0.974131\pi$
$491$		−	3.59770i		−	0.162362i	0.996699	−	0.0811809i	$-0.0258691\pi$
$492$	9.86185	+	26.4534i	0.444606	+	1.19261i
$493$	34.7290	−	9.30560i	1.56411	−	0.419103i
$494$	−0.304710	−	0.0663109i	−0.0137096	−	0.00298347i
$495$	31.3999	+	9.24455i	1.41132	+	0.415512i
$496$	−17.5252	−	6.07173i	−0.786903	−	0.272629i
$497$	30.3867	+	23.2551i	1.36303	+	1.04313i
$498$	−12.7316	+	24.6910i	−0.570516	+	1.10643i
$499$	5.11616	+	8.86145i	0.229031	+	0.396693i	0.957521	−	0.288363i	$-0.0931110\pi$
$499$	5.11616	+	8.86145i	0.229031	+	0.396693i	−0.728490	+	0.685056i	$0.759778\pi$
$500$	−16.1472	−	15.4683i	−0.722124	−	0.691764i
$501$	−10.7030	+	18.5381i	−0.478174	+	0.828221i
$502$	25.4580	−	1.21069i	1.13625	−	0.0540359i
$503$	30.0943	−	30.0943i	1.34184	−	1.34184i	0.447605	−	0.894231i	$-0.352277\pi$
$503$	30.0943	−	30.0943i	1.34184	−	1.34184i	0.894231	−	0.447605i	$-0.147723\pi$
$504$	23.1598	−	0.299608i	1.03162	−	0.0133456i
$505$	13.8858	−	13.2209i	0.617910	−	0.588322i
$506$	−5.08981	+	5.59809i	−0.226270	+	0.248865i
$507$	30.9844	−	8.30225i	1.37607	−	0.368716i
$508$	−14.2502	−	11.7698i	−0.632252	−	0.522200i
$509$	−0.0145211	+	0.00838376i	−0.000643637	+	0.000371604i	−0.500322	−	0.865840i	$-0.666785\pi$
$509$	−0.0145211	+	0.00838376i	−0.000643637	+	0.000371604i	0.499678	+	0.866211i	$0.333452\pi$
$510$	10.8431	+	37.0383i	0.480141	+	1.64008i
$511$	9.68180	−	23.4584i	0.428298	−	1.03774i
$512$	9.38510	+	20.5893i	0.414767	+	0.909928i
$513$	0.159904	−	0.596770i	0.00705994	−	0.0263481i
$514$	−4.48416	+	20.6055i	−0.197788	+	0.908869i
$515$	6.23334	+	3.80561i	0.274674	+	0.167695i
$516$	−9.99090	−	4.56460i	−0.439825	−	0.200945i
$517$	−9.26042	+	9.26042i	−0.407273	+	0.407273i
$518$	5.58108	+	6.58199i	0.245219	+	0.289196i
$519$	−4.43276			−0.194577
$520$	0.424661	−	0.317261i	0.0186226	−	0.0139128i
$521$	0.00830997	−	0.0143933i	0.000364066	−	0.000630582i	−0.865843	−	0.500315i	$-0.833217\pi$
$521$	0.00830997	−	0.0143933i	0.000364066	−	0.000630582i	0.866207	+	0.499685i	$0.166551\pi$
$522$	26.7839	−	17.2100i	1.17230	−	0.753261i
$523$	−29.8717	−	8.00409i	−1.30620	−	0.349994i	−0.462407	−	0.886668i	$-0.653014\pi$
$523$	−29.8717	−	8.00409i	−1.30620	−	0.349994i	−0.843790	+	0.536674i	$0.819681\pi$
$524$	−6.01271	+	4.28019i	−0.262666	+	0.186981i
$525$	18.6218	+	26.8305i	0.812722	+	1.17098i
$526$	9.55070	−	3.05219i	0.416430	−	0.133082i
$527$	−5.93238	+	22.1400i	−0.258419	+	0.964432i
$528$	3.34669	−	46.5855i	0.145646	−	2.02737i
$529$	−18.8104	−	10.8602i	−0.817845	−	0.472183i
$530$	−0.686760	−	29.8581i	−0.0298310	−	1.29695i
$531$			10.3840i			0.450626i
$532$	−13.9130	−	0.481373i	−0.603207	−	0.0208702i
$533$	−0.338860	−	0.338860i	−0.0146777	−	0.0146777i
$534$	39.1854	−	43.0985i	1.69572	−	1.86505i
$535$	7.91421	−	12.9630i	0.342161	−	0.560438i
$536$	0.566685	+	1.32420i	0.0244771	+	0.0571969i
$537$	−51.3727	−	13.7653i	−2.21690	−	0.594016i
$538$	3.91757	−	7.59756i	0.168899	−	0.327554i
$539$	−8.48716	+	32.0003i	−0.365568	+	1.37835i
$540$	0.587882	+	0.870249i	0.0252984	+	0.0374496i
$541$	−14.5885	−	25.2681i	−0.627211	−	1.08636i	−0.988109	−	0.153756i	$-0.950863\pi$
$541$	−14.5885	−	25.2681i	−0.627211	−	1.08636i	0.360898	−	0.932605i	$-0.382470\pi$
$542$	17.9619	+	27.9542i	0.771532	+	1.20074i
$543$	−10.3592	−	38.6612i	−0.444558	−	1.65911i
$544$	24.5482	−	13.3917i	1.05250	−	0.574166i
$545$	6.04316	+	6.34708i	0.258860	+	0.271879i
$546$	−0.699996	+	0.330822i	−0.0299571	+	0.0141579i
$547$	−0.913792	−	0.913792i	−0.0390709	−	0.0390709i	0.687301	−	0.726372i	$-0.258795\pi$
$547$	−0.913792	−	0.913792i	−0.0390709	−	0.0390709i	−0.726372	+	0.687301i	$0.758795\pi$
$548$	13.8738	+	37.2151i	0.592659	+	1.58975i
$549$	5.24710	+	3.02941i	0.223941	+	0.129292i
$550$	28.9878	−	16.6771i	1.23604	−	0.711115i
$551$	−16.5717	+	9.56766i	−0.705977	+	0.407596i
$552$	−7.81886	+	1.12229i	−0.332793	+	0.0477677i
$553$	−16.0144	−	2.08759i	−0.681002	−	0.0887735i
$554$	−31.4204	+	10.0413i	−1.33493	+	0.426613i
$555$	−3.59594	+	12.2139i	−0.152639	+	0.518452i
$556$	2.30143	−	0.219392i	0.0976022	−	0.00930428i
$557$	0.744970	+	2.78027i	0.0315654	+	0.117804i	0.979911	−	0.199436i	$-0.0639109\pi$
$557$	0.744970	+	2.78027i	0.0315654	+	0.117804i	−0.948346	+	0.317239i	$0.897244\pi$
$558$	0.964116	+	20.2731i	0.0408143	+	0.858227i
$559$	0.186452			0.00788606
$560$	16.1213	−	17.3235i	0.681248	−	0.732053i
$561$	−57.7196			−2.43693
$562$	−1.29663	−	27.2651i	−0.0546951	−	1.15011i
$563$	7.23315	+	26.9945i	0.304841	+	1.13768i	0.933082	+	0.359663i	$0.117108\pi$
$563$	7.23315	+	26.9945i	0.304841	+	1.13768i	−0.628241	+	0.778018i	$0.716225\pi$
$564$	−13.6109	+	1.29750i	−0.573120	+	0.0546348i
$565$	−0.0424064	−	0.0777954i	−0.00178405	−	0.00327288i
$566$	−9.60324	+	3.06898i	−0.403654	+	0.128999i
$567$	8.84138	+	21.2683i	0.371303	+	0.893186i
$568$	40.4912	−	5.81193i	1.69897	−	0.243863i
$569$	31.8950	−	18.4146i	1.33711	−	0.771981i	0.350732	−	0.936476i	$-0.385933\pi$
$569$	31.8950	−	18.4146i	1.33711	−	0.771981i	0.986378	+	0.164495i	$0.0525996\pi$
$570$	−10.6762	−	17.5470i	−0.447175	−	0.734964i
$571$	−35.5147	−	20.5044i	−1.48624	−	0.858084i	−0.486367	−	0.873754i	$-0.661678\pi$
$571$	−35.5147	−	20.5044i	−1.48624	−	0.858084i	−0.999877	+	0.0156706i	$0.995012\pi$
$572$	0.276938	+	0.742858i	0.0115793	+	0.0310605i
$573$	−28.6909	−	28.6909i	−1.19858	−	1.19858i
$574$	−17.5877	−	12.1802i	−0.734095	−	0.508393i
$575$	−3.79847	−	4.19063i	−0.158407	−	0.174762i
$576$	17.0955	−	17.9122i	0.712314	−	0.746343i
$577$	5.52692	+	20.6267i	0.230089	+	0.858703i	0.980302	+	0.197506i	$0.0632843\pi$
$577$	5.52692	+	20.6267i	0.230089	+	0.858703i	−0.750213	+	0.661196i	$0.770049\pi$
$578$	−5.68476	−	8.84720i	−0.236455	−	0.367995i
$579$	−6.12245	−	10.6044i	−0.254440	−	0.440704i
$580$	6.18401	−	31.9340i	0.256777	−	1.32599i
$581$	−2.77432	−	20.8677i	−0.115098	−	0.865737i
$582$	−13.1590	+	25.5199i	−0.545457	+	1.05783i
$583$	43.1458	+	11.5609i	1.78691	+	0.478802i
$584$	−10.6738	−	24.9421i	−0.441685	−	1.03211i
$585$	−0.495091	−	0.302265i	−0.0204695	−	0.0124971i
$586$	−1.74156	+	1.91548i	−0.0719432	+	0.0791276i
$587$	0.870374	+	0.870374i	0.0359242	+	0.0359242i	0.724841	−	0.688917i	$-0.241913\pi$
$587$	0.870374	+	0.870374i	0.0359242	+	0.0359242i	−0.688917	+	0.724841i	$0.741913\pi$
$588$	−28.1067	+	20.1161i	−1.15910	+	0.829572i
$589$		−	12.1989i		−	0.502646i
$590$	7.67242	+	7.32741i	0.315868	+	0.301665i
$591$	−11.7900	−	6.80697i	−0.484977	−	0.280001i
$592$	9.20178	+	0.661054i	0.378191	+	0.0271692i
$593$	0.547190	−	2.04214i	0.0224704	−	0.0838607i	−0.953780	−	0.300505i	$-0.902845\pi$
$593$	0.547190	−	2.04214i	0.0224704	−	0.0838607i	0.976251	+	0.216645i	$0.0695113\pi$
$594$	−1.49615	+	0.478138i	−0.0613880	+	0.0196182i
$595$	−22.7813	−	18.3377i	−0.933944	−	0.751774i
$596$	−10.1039	+	7.19257i	−0.413874	+	0.294619i
$597$	−45.0608	−	12.0740i	−1.84422	−	0.494157i
$598$	0.112802	−	0.0724808i	0.00461281	−	0.00296396i
$599$	12.9248	−	22.3864i	0.528092	−	0.914683i	−0.471371	−	0.881935i	$-0.656241\pi$
$599$	12.9248	−	22.3864i	0.528092	−	0.914683i	0.999464	−	0.0327479i	$-0.0104258\pi$
$600$	34.4213	+	5.84790i	1.40524	+	0.238740i
$601$	20.5570			0.838537			0.419269	−	0.907862i	$-0.362287\pi$
$601$	20.5570			0.838537			0.419269	+	0.907862i	$0.362287\pi$
$602$	8.18961	−	1.48767i	0.333784	−	0.0606329i
$603$	1.11452	−	1.11452i	0.0453869	−	0.0453869i
$604$	−18.3231	−	8.37140i	−0.745558	−	0.340627i
$605$	5.97520	+	24.7082i	0.242927	+	1.00453i
$606$	−6.36596	+	29.2527i	−0.258599	+	1.18831i
$607$	5.79881	−	21.6414i	0.235366	−	0.878399i	−0.742617	−	0.669716i	$-0.766416\pi$
$607$	5.79881	−	21.6414i	0.235366	−	0.878399i	0.977983	−	0.208683i	$-0.0669177\pi$
$608$	−10.7751	+	10.2659i	−0.436987	+	0.416336i
$609$	−18.1249	+	43.9154i	−0.734457	+	1.77954i
$610$	5.94094	−	1.73923i	0.240542	−	0.0704196i
$611$	0.200991	−	0.116042i	0.00813122	−	0.00469456i
$612$	−23.5933	−	19.4865i	−0.953701	−	0.787696i
$613$	31.9774	−	8.56832i	1.29156	−	0.346071i	0.453304	−	0.891356i	$-0.350245\pi$
$613$	31.9774	−	8.56832i	1.29156	−	0.346071i	0.838251	+	0.545285i	$0.183578\pi$
$614$	5.19574	−	5.71460i	0.209683	−	0.230622i
$615$	0.774002	−	31.5547i	0.0312108	−	1.27241i
$616$	18.0912	+	30.4193i	0.728917	+	1.22563i
$617$	27.2948	−	27.2948i	1.09885	−	1.09885i	0.104300	−	0.994546i	$-0.466740\pi$
$617$	27.2948	−	27.2948i	1.09885	−	1.09885i	0.994546	−	0.104300i	$-0.0332603\pi$
$618$	−11.3906	+	0.541696i	−0.458196	+	0.0217902i
$619$	−18.1903	+	31.5065i	−0.731130	+	1.26635i	0.225270	+	0.974296i	$0.427674\pi$
$619$	−18.1903	+	31.5065i	−0.731130	+	1.26635i	−0.956400	+	0.292059i	$0.905660\pi$
$620$	15.6595	+	13.5932i	0.628901	+	0.545918i
$621$	0.132821	+	0.230053i	0.00532992	+	0.00923169i
$622$	13.3071	−	25.8071i	0.533564	−	1.03477i
$623$	−5.70571	+	43.7698i	−0.228594	+	1.75360i
$624$	−0.270959	+	0.782082i	−0.0108470	+	0.0313083i
$625$	10.3195	+	22.7708i	0.412779	+	0.910831i
$626$	38.5691	+	8.39340i	1.54153	+	0.335468i
$627$	29.6725	−	7.95073i	1.18501	−	0.317522i
$628$	−10.1788	−	27.3036i	−0.406178	−	1.08953i
$629$		−	11.4011i		−	0.454590i
$630$	−24.1579	−	9.32632i	−0.962473	−	0.371569i
$631$			10.6984i			0.425897i	0.977063	+	0.212949i	$0.0683067\pi$
$631$			10.6984i			0.425897i	−0.977063	+	0.212949i	$0.931693\pi$
$632$	−13.5737	+	10.6693i	−0.539934	+	0.424401i
$633$	−26.1828	+	7.01567i	−1.04067	+	0.278848i
$634$	−3.89688	+	17.9068i	−0.154765	+	0.711171i
$635$	9.89002	+	18.1434i	0.392473	+	0.720000i
$636$	27.0441	+	37.9908i	1.07237	+	1.50643i
$637$	0.292054	−	0.508841i	0.0115716	−	0.0201610i
$638$	43.2383	+	22.2952i	1.71182	+	0.882676i
$639$	−22.3816	−	38.7661i	−0.885402	−	1.53356i
$640$	−1.17143	−	25.2711i	−0.0463050	−	0.998927i
$641$	−2.64450	+	4.58042i	−0.104452	+	0.180916i	−0.913514	−	0.406807i	$-0.866642\pi$
$641$	−2.64450	+	4.58042i	−0.104452	+	0.180916i	0.809062	+	0.587723i	$0.199975\pi$
$642$	1.12652	+	23.6880i	0.0444602	+	0.934892i
$643$	6.36844	−	6.36844i	0.251147	−	0.251147i	−0.570294	−	0.821441i	$-0.693171\pi$
$643$	6.36844	−	6.36844i	0.251147	−	0.251147i	0.821441	+	0.570294i	$0.193171\pi$
$644$	4.37635	−	4.08364i	0.172452	−	0.160918i
$645$	8.46826	+	8.89414i	0.333437	+	0.350206i
$646$	13.6083	+	12.3728i	0.535413	+	0.486800i
$647$	5.91812	−	1.58576i	0.232665	−	0.0623425i	−0.140602	−	0.990066i	$-0.544904\pi$
$647$	5.91812	−	1.58576i	0.232665	−	0.0623425i	0.373268	+	0.927724i	$0.378237\pi$
$648$	22.8572	+	9.15693i	0.897914	+	0.359718i
$649$	−13.7415	+	7.93365i	−0.539401	+	0.311423i
$650$	−0.572694	+	0.152516i	−0.0224629	+	0.00598217i
$651$	−18.4682	−	24.0049i	−0.723826	−	0.940825i
$652$	5.82137	+	0.979860i	0.227983	+	0.0383743i
$653$	10.1250	−	37.7871i	0.396223	−	1.47872i	−0.423464	−	0.905913i	$-0.639186\pi$
$653$	10.1250	−	37.7871i	0.396223	−	1.47872i	0.819687	−	0.572812i	$-0.194147\pi$
$654$	−13.3711	−	2.90982i	−0.522853	−	0.113783i
$655$	8.02052	−	1.93961i	0.313388	−	0.0757869i
$656$	−22.4587	+	4.32119i	−0.876867	+	0.168714i
$657$	−20.9927	+	20.9927i	−0.819001	+	0.819001i
$658$	7.90235	−	6.70066i	0.308066	−	0.261219i
$659$	7.96382			0.310226			0.155113	−	0.987897i	$-0.450426\pi$
$659$	7.96382			0.310226			0.155113	+	0.987897i	$0.450426\pi$
$660$	−22.8580	+	46.9497i	−0.889745	+	1.82751i
$661$	−17.8362	+	30.8932i	−0.693748	+	1.20161i	0.276854	+	0.960912i	$0.410708\pi$
$661$	−17.8362	+	30.8932i	−0.693748	+	1.20161i	−0.970601	+	0.240694i	$0.922625\pi$
$662$	−5.66131	−	8.81071i	−0.220033	−	0.342438i
$663$	0.988023	+	0.264740i	0.0383716	+	0.0102817i
$664$	−18.0128	−	13.4909i	−0.699032	−	0.523548i
$665$	14.2374	+	6.28899i	0.552103	+	0.243877i
$666$	−3.07314	−	9.61625i	−0.119082	−	0.372622i
$667$	2.12944	−	7.94717i	0.0824521	−	0.307716i
$668$	−13.3702	−	11.0429i	−0.517309	−	0.427264i
$669$	−41.4216	−	23.9148i	−1.60145	−	0.924599i
$670$	−0.0370301	−	1.60995i	−0.00143060	−	0.0621978i
$671$			9.25823i			0.357410i
$672$	−5.66135	+	36.5138i	−0.218391	+	1.40855i
$673$	−29.4853	−	29.4853i	−1.13657	−	1.13657i	−0.989060	−	0.147515i	$-0.952873\pi$
$673$	−29.4853	−	29.4853i	−1.13657	−	1.13657i	−0.147515	−	0.989060i	$-0.547127\pi$
$674$	−8.61226	−	7.83031i	−0.331732	−	0.301612i
$675$	−0.247926	−	1.14770i	−0.00954268	−	0.0441748i
$676$	2.46602	+	25.8687i	0.0948471	+	0.994949i
$677$	−44.5308	−	11.9320i	−1.71146	−	0.458584i	−0.735676	−	0.677333i	$-0.763136\pi$
$677$	−44.5308	−	11.9320i	−1.71146	−	0.458584i	−0.975781	+	0.218750i	$0.929802\pi$
$678$	0.122962	+	0.0634037i	0.00472233	+	0.00243500i
$679$	−2.86745	−	21.5682i	−0.110043	−	0.827710i
$680$	−31.0465	+	3.68179i	−1.19058	+	0.141190i
$681$	28.3354	+	49.0783i	1.08581	+	1.88069i
$682$	−26.0915	+	16.7650i	−0.999094	+	0.641967i
$683$	10.7522	+	40.1276i	0.411420	+	1.53544i	0.791899	+	0.610652i	$0.209093\pi$
$683$	10.7522	+	40.1276i	0.411420	+	1.53544i	−0.380479	+	0.924790i	$0.624241\pi$
$684$	14.8130	+	6.76773i	0.566391	+	0.258771i
$685$	1.08888	−	44.3917i	0.0416039	−	1.69612i
$686$	8.76809	−	24.6804i	0.334767	−	0.942301i
$687$	20.8424	+	20.8424i	0.795187	+	0.795187i
$688$	4.98992	−	7.36758i	0.190239	−	0.280886i
$689$	−0.685527	−	0.395789i	−0.0261165	−	0.0150784i
$690$	8.58073	+	2.08896i	0.326663	+	0.0795254i
$691$	15.8798	−	9.16821i	0.604096	−	0.348775i	−0.166555	−	0.986032i	$-0.553264\pi$
$691$	15.8798	−	9.16821i	0.604096	−	0.348775i	0.770651	+	0.637257i	$0.219931\pi$
$692$	0.596054	−	3.54117i	0.0226586	−	0.134615i
$693$	23.5380	−	30.7563i	0.894133	−	1.16833i
$694$	−4.75419	−	14.8765i	−0.180466	−	0.564703i
$695$	−2.47951	−	0.730000i	−0.0940532	−	0.0276905i
$696$	19.9820	+	46.6930i	0.757415	+	1.76989i
$697$	7.31528	+	27.3010i	0.277086	+	1.03410i
$698$	−14.6905	+	0.698628i	−0.556043	+	0.0264435i
$699$	−58.7364			−2.22161
$700$	−23.9379	+	11.2685i	−0.904766	+	0.425909i
$701$	3.42628			0.129409			0.0647045	−	0.997904i	$-0.479390\pi$
$701$	3.42628			0.129409			0.0647045	+	0.997904i	$0.479390\pi$
$702$	0.0278037	−	0.00132224i	0.00104938	−	4.99049e-5i
$703$	1.57047	+	5.86106i	0.0592312	+	0.221054i
$704$	36.7654	+	8.93768i	1.38565	+	0.336852i
$705$	14.6641	+	4.31729i	0.552280	+	0.162599i
$706$	3.24859	+	10.1653i	0.122262	+	0.382574i
$707$	−8.70820	−	20.9480i	−0.327506	−	0.787830i
$708$	−16.3358	−	2.74966i	−0.613937	−	0.103339i
$709$	−26.8261	+	15.4881i	−1.00748	+	0.581667i	−0.910452	−	0.413615i	$-0.864266\pi$
$709$	−26.8261	+	15.4881i	−1.00748	+	0.581667i	−0.0970248	+	0.995282i	$0.530933\pi$
$710$	−44.4366	−	10.8180i	−1.66768	−	0.405993i
$711$	16.3617	+	9.44644i	0.613612	+	0.354269i
$712$	29.1607	+	37.0990i	1.09284	+	1.39034i
$713$	3.70884	+	3.70884i	0.138897	+	0.138897i
$714$	45.5098	+	3.74503i	1.70316	+	0.140154i
$715$	0.0217353	−	0.886111i	0.000812854	−	0.0331387i
$716$	17.9044	−	39.1888i	0.669120	−	1.46456i
$717$	−0.963255	−	3.59492i	−0.0359734	−	0.134255i
$718$	−13.6628	+	8.77905i	−0.509893	+	0.327631i
$719$	21.3674	+	37.0094i	0.796869	+	1.38022i	0.921646	+	0.388033i	$0.126845\pi$
$719$	21.3674	+	37.0094i	0.796869	+	1.38022i	−0.124777	+	0.992185i	$0.539821\pi$
$720$	−25.1938	+	11.4740i	−0.938919	+	0.427609i
$721$	6.84890	−	5.26922i	0.255066	−	0.196236i
$722$	15.1820	+	7.82838i	0.565015	+	0.291342i
$723$	44.1913	+	11.8410i	1.64349	+	0.440372i
$724$	32.2780	−	3.07701i	1.19960	−	0.114356i
$725$	−19.7056	+	30.5650i	−0.731846	+	1.13516i
$726$	−29.3681	−	26.7016i	−1.08995	−	0.990990i
$727$	−21.7303	−	21.7303i	−0.805931	−	0.805931i	0.178084	−	0.984015i	$-0.443010\pi$
$727$	−21.7303	−	21.7303i	−0.805931	−	0.805931i	−0.984015	+	0.178084i	$0.943010\pi$
$728$	−0.170156	−	0.603685i	−0.00630641	−	0.0223740i
$729$		−	28.6841i		−	1.06238i
$730$	0.697482	+	30.3242i	0.0258150	+	1.12235i
$731$	−9.52347	−	5.49838i	−0.352238	−	0.203365i
$732$	−6.15522	+	7.45242i	−0.227503	+	0.275449i
$733$	0.986629	−	3.68215i	0.0364420	−	0.136003i	−0.945308	−	0.326179i	$-0.894239\pi$
$733$	0.986629	−	3.68215i	0.0364420	−	0.136003i	0.981750	+	0.190175i	$0.0609056\pi$
$734$	5.45132	+	17.0579i	0.201212	+	0.629618i
$735$	37.5373	−	9.17894i	1.38459	−	0.338570i
$736$	0.154814	−	6.39711i	0.00570652	−	0.235800i
$737$	2.32642	+	0.623362i	0.0856947	+	0.0229618i
$738$	13.5290	+	21.0553i	0.498011	+	0.775054i
$739$	−6.00177	+	10.3954i	−0.220779	+	0.382400i	−0.955045	−	0.296462i	$-0.904193\pi$
$739$	−6.00177	+	10.3954i	−0.220779	+	0.382400i	0.734266	+	0.678862i	$0.237526\pi$
$740$	−9.27372	−	4.51501i	−0.340909	−	0.165975i
$741$	−0.544391			−0.0199987
$742$	−33.2687	−	11.9148i	−1.22133	−	0.437404i
$743$	7.86007	−	7.86007i	0.288358	−	0.288358i	−0.548073	−	0.836431i	$-0.684638\pi$
$743$	7.86007	−	7.86007i	0.288358	−	0.288358i	0.836431	+	0.548073i	$0.184638\pi$
$744$	−32.1484	−	3.85156i	−1.17862	−	0.141205i
$745$	13.4779	−	3.25938i	0.493794	−	0.119415i
$746$	−34.4135	−	7.48906i	−1.25997	−	0.274194i
$747$	−6.37387	+	23.7876i	−0.233208	+	0.870344i
$748$	7.76130	−	46.1101i	0.283781	−	1.68595i
$749$	−10.9580	−	14.2431i	−0.400395	−	0.520431i
$750$	−33.2860	−	20.3918i	−1.21543	−	0.744602i
$751$	1.00430	−	0.579834i	0.0366475	−	0.0211584i	−0.481564	−	0.876411i	$-0.659931\pi$
$751$	1.00430	−	0.579834i	0.0366475	−	0.0211584i	0.518212	+	0.855252i	$0.326598\pi$
$752$	0.793663	−	11.0477i	0.0289419	−	0.402867i
$753$	42.9769	−	11.5156i	1.56616	−	0.419653i
$754$	−0.637876	−	0.579960i	−0.0232301	−	0.0211209i
$755$	15.5306	+	16.3117i	0.565218	+	0.593643i
$756$	1.21069	−	0.279919i	0.0440322	−	0.0101806i
$757$	−15.7431	+	15.7431i	−0.572192	+	0.572192i	−0.932740	−	0.360549i	$-0.882590\pi$
$757$	−15.7431	+	15.7431i	−0.572192	+	0.572192i	0.360549	+	0.932740i	$0.382590\pi$
$758$	−0.281047	−	5.90974i	−0.0102081	−	0.214652i
$759$	−6.60410	+	11.4386i	−0.239714	+	0.415196i
$760$	15.4532	−	6.16931i	0.560548	−	0.223784i
$761$	9.62047	+	16.6631i	0.348742	+	0.604039i	0.986026	−	0.166590i	$-0.0532757\pi$
$761$	9.62047	+	16.6631i	0.348742	+	0.604039i	−0.637284	+	0.770629i	$0.719942\pi$
$762$	−28.6772	−	14.7870i	−1.03887	−	0.535677i
$763$	9.57514	−	3.98044i	0.346643	−	0.144102i
$764$	26.7780	−	19.0621i	0.968794	−	0.689644i
$765$	16.3743	+	30.0390i	0.592014	+	1.08606i
$766$	−4.03801	+	18.5554i	−0.145899	+	0.670432i
$767$	0.271611	−	0.0727778i	0.00980729	−	0.00262786i
$768$	23.6522	+	31.6374i	0.853475	+	1.14162i
$769$			30.8833i			1.11368i	0.830620	+	0.556840i	$0.187986\pi$
$769$			30.8833i			1.11368i	−0.830620	+	0.556840i	$0.812014\pi$
$770$	−6.11546	−	39.0946i	−0.220386	−	1.40887i
$771$			36.8135i			1.32580i
$772$	9.29472	−	3.46507i	0.334524	−	0.124711i
$773$	15.6699	−	4.19873i	0.563607	−	0.151018i	0.0342438	−	0.999414i	$-0.489098\pi$
$773$	15.6699	−	4.19873i	0.563607	−	0.151018i	0.529363	+	0.848396i	$0.322431\pi$
$774$	−9.51467	−	2.07058i	−0.341998	−	0.0744254i
$775$	−10.5937	−	20.6221i	−0.380535	−	0.740767i
$776$	−18.6174	−	13.9437i	−0.668327	−	0.500551i
$777$	11.9636	+	9.15578i	0.429190	+	0.328462i
$778$	−11.6081	+	22.5122i	−0.416170	+	0.807100i
$779$	−7.52128	−	13.0272i	−0.269478	−	0.466749i
$780$	0.606616	−	0.698825i	0.0217203	−	0.0250220i
$781$	34.2004	−	59.2368i	1.22379	−	2.11966i
$782$	−7.89906	+	0.375652i	−0.282470	+	0.0134333i
$783$	1.20775	−	1.20775i	0.0431616	−	0.0431616i
$784$	−12.2906	−	25.1583i	−0.438949	−	0.898512i
$785$	−0.798877	+	32.5689i	−0.0285132	+	1.16243i
$786$	−8.66761	+	9.53317i	−0.309163	+	0.340037i
$787$	−40.5750	+	10.8721i	−1.44634	+	0.387547i	−0.894751	−	0.446566i	$-0.852647\pi$
$787$	−40.5750	+	10.8721i	−1.44634	+	0.387547i	−0.551594	+	0.834113i	$0.685980\pi$
$788$	7.02319	−	8.50331i	0.250191	−	0.302918i
$789$	15.1586	−	8.75180i	0.539659	−	0.311572i
$790$	18.5253	−	5.42336i	0.659100	−	0.192954i
$791$	−0.103922	+	0.0138162i	−0.00369503	+	0.000491247i
$792$	−5.88263	−	40.9837i	−0.209030	−	1.45629i
$793$	0.0424643	−	0.158479i	0.00150795	−	0.00562775i
$794$	−1.83880	+	8.44960i	−0.0652565	+	0.299865i
$795$	−12.2553	−	50.6771i	−0.434650	−	1.79733i
$796$	15.7046	−	34.3739i	0.556635	−	1.21835i
$797$	5.01705	−	5.01705i	0.177713	−	0.177713i	−0.612645	−	0.790358i	$-0.709894\pi$
$797$	5.01705	−	5.01705i	0.177713	−	0.177713i	0.790358	+	0.612645i	$0.209894\pi$
$798$	−23.9116	+	4.34361i	−0.846460	+	0.153762i
$799$	−13.6881			−0.484251
$800$	−9.30015	+	26.7116i	−0.328810	+	0.944396i
$801$	25.8185	−	44.7190i	0.912253	−	1.58007i
$802$	23.3618	−	15.0111i	0.824935	−	0.530061i
$803$	−43.8193	−	11.7414i	−1.54635	−	0.414343i
$804$	1.45822	+	2.04847i	0.0514273	+	0.0722438i
$805$	−6.24067	+	2.41657i	−0.219955	+	0.0851728i
$806$	0.523519	−	0.167305i	0.0184402	−	0.00589308i
$807$	3.86227	−	14.4142i	0.135958	−	0.507403i
$808$	−22.5129	−	9.01900i	−0.792000	−	0.317287i
$809$	16.3576	+	9.44409i	0.575104	+	0.332036i	0.759185	−	0.650875i	$-0.225598\pi$
$809$	16.3576	+	9.44409i	0.575104	+	0.332036i	−0.184081	+	0.982911i	$0.558931\pi$
$810$	−19.9088	−	19.0135i	−0.699523	−	0.668067i
$811$			21.4189i			0.752118i	0.926596	+	0.376059i	$0.122721\pi$
$811$			21.4189i			0.752118i	−0.926596	+	0.376059i	$0.877279\pi$
$812$	−32.6452	−	20.3844i	−1.14562	−	0.715352i
$813$	41.0166	+	41.0166i	1.43851	+	1.43851i
$814$	10.3776	−	11.4139i	0.363733	−	0.400057i
$815$	−5.63317	−	3.43919i	−0.197321	−	0.120470i
$816$	36.9032	−	31.9563i	1.29187	−	1.11869i
$817$	5.65322	+	1.51477i	0.197781	+	0.0529953i
$818$	6.51561	−	12.6361i	0.227813	−	0.441810i
$819$	−0.543983	+	0.418514i	−0.0190083	+	0.0146241i
$820$	25.1038	+	4.86134i	0.876664	+	0.169765i
$821$	20.8528	+	36.1180i	0.727766	+	1.26053i	0.957825	+	0.287351i	$0.0927747\pi$
$821$	20.8528	+	36.1180i	0.727766	+	1.26053i	−0.230059	+	0.973177i	$0.573892\pi$
$822$	37.4808	+	58.3314i	1.30729	+	2.03454i
$823$	10.4750	+	39.0933i	0.365136	+	1.36271i	0.867236	+	0.497897i	$0.165894\pi$
$823$	10.4750	+	39.0933i	0.365136	+	1.36271i	−0.502100	+	0.864809i	$0.667439\pi$
$824$	1.09890	−	9.17235i	0.0382820	−	0.319534i
$825$	43.2566	−	39.2086i	1.50600	−	1.36507i
$826$	11.3494	−	5.36380i	0.394897	−	0.186631i
$827$	30.7849	+	30.7849i	1.07050	+	1.07050i	0.997319	+	0.0731766i	$0.0233137\pi$
$827$	30.7849	+	30.7849i	1.07050	+	1.07050i	0.0731766	+	0.997319i	$0.476686\pi$
$828$	−6.56123	+	2.44603i	−0.228018	+	0.0850053i
$829$	−36.1486	−	20.8704i	−1.25549	−	0.724859i	−0.283298	−	0.959032i	$-0.591429\pi$
$829$	−36.1486	−	20.8704i	−1.25549	−	0.724859i	−0.972195	+	0.234172i	$0.924762\pi$
$830$	13.0783	+	21.4951i	0.453954	+	0.746106i
$831$	−49.8696	+	28.7922i	−1.72996	+	0.998790i
$832$	−0.588342	−	0.321622i	−0.0203971	−	0.0111502i
$833$	−29.9229	+	17.3778i	−1.03677	+	0.602104i
$834$	3.84433	−	1.22856i	0.133118	−	0.0425417i
$835$	9.27926	+	17.0230i	0.321122	+	0.589105i
$836$	2.36161	+	24.7734i	0.0816780	+	0.856805i
$837$	0.281822	+	1.05177i	0.00974118	+	0.0363546i
$838$	1.19480	+	25.1239i	0.0412738	+	0.867889i
$839$	20.9842			0.724456			0.362228	−	0.932090i	$-0.382016\pi$
$839$	20.9842			0.724456			0.362228	+	0.932090i	$0.382016\pi$
$840$	21.0689	−	35.5350i	0.726946	−	1.22607i
$841$	−23.9012			−0.824180
$842$	2.66353	+	56.0078i	0.0917914	+	1.93015i
$843$	−12.3330	−	46.0274i	−0.424772	−	1.58527i
$844$	−2.08387	−	21.8599i	−0.0717298	−	0.752448i
$845$	8.20541	−	27.8704i	0.282275	−	0.958770i
$846$	−11.5453	+	3.68962i	−0.396935	+	0.126852i
$847$	29.8255	+	3.88797i	1.02482	+	0.133592i
$848$	−33.9860	+	16.4961i	−1.16708	+	0.566477i
$849$	−15.2420	+	8.79995i	−0.523103	+	0.302014i
$850$	33.7494	+	9.09839i	1.15759	+	0.312072i
$851$	−2.25941	−	1.30447i	−0.0774517	−	0.0447168i
$852$	66.9124	−	24.9450i	2.29238	−	0.854601i
$853$	19.9509	+	19.9509i	0.683106	+	0.683106i	0.960699	−	0.277593i	$-0.0895367\pi$
$853$	19.9509	+	19.9509i	0.683106	+	0.683106i	−0.277593	+	0.960699i	$0.589537\pi$
$854$	0.600703	−	7.29978i	0.0205556	−	0.249793i
$855$	−12.5555	−	13.1869i	−0.429389	−	0.450983i
$856$	−19.0750	−	2.28529i	−0.651969	−	0.0781095i
$857$	−9.92835	−	37.0531i	−0.339146	−	1.26571i	−0.899304	−	0.437324i	$-0.855926\pi$
$857$	−9.92835	−	37.0531i	−0.339146	−	1.26571i	0.560158	−	0.828386i	$-0.310740\pi$
$858$	0.748161	+	1.16436i	0.0255418	+	0.0397507i
$859$	−3.51740	−	6.09232i	−0.120012	−	0.207867i	0.799760	−	0.600320i	$-0.204960\pi$
$859$	−3.51740	−	6.09232i	−0.120012	−	0.207867i	−0.919772	+	0.392453i	$0.871627\pi$
$860$	−8.24388	+	5.56902i	−0.281114	+	0.189902i
$861$	−34.5226	−	14.2482i	−1.17653	−	0.485579i
$862$	−16.3104	+	31.6317i	−0.555536	+	1.07738i
$863$	−43.2762	−	11.5958i	−1.47314	−	0.394726i	−0.569132	−	0.822246i	$-0.692721\pi$
$863$	−43.2762	−	11.5958i	−1.47314	−	0.394726i	−0.904006	+	0.427520i	$0.859387\pi$
$864$	0.691849	−	1.13404i	0.0235372	−	0.0385808i
$865$	−2.09208	+	3.42669i	−0.0711328	+	0.116511i
$866$	−12.3677	+	13.6027i	−0.420271	+	0.462240i
$867$	−12.9813	−	12.9813i	−0.440868	−	0.440868i
$868$	21.6599	−	11.5257i	0.735186	−	0.391209i
$869$			28.8694i			0.979328i
$870$	−1.30573	−	56.7687i	−0.0442683	−	1.92464i
$871$	−0.0369636	−	0.0213410i	−0.00125246	−	0.000723111i
$872$	4.12251	−	10.2904i	0.139606	−	0.348478i
$873$	−6.58783	+	24.5861i	−0.222964	+	0.832114i
$874$	4.00901	−	1.28119i	0.135607	−	0.0433369i
$875$	29.5296	−	1.73246i	0.998283	−	0.0585677i
$876$	−27.4663	−	38.5839i	−0.928000	−	1.30363i
$877$	−5.54663	−	1.48622i	−0.187297	−	0.0501860i	0.163951	−	0.986468i	$-0.447576\pi$
$877$	−5.54663	−	1.48622i	−0.187297	−	0.0501860i	−0.351248	+	0.936282i	$0.614243\pi$
$878$	35.4546	−	22.7813i	1.19653	−	0.768832i
$879$	−2.25970	+	3.91392i	−0.0762179	+	0.132013i
$880$	−34.4327	−	24.5735i	−1.16073	−	0.828372i
$881$	3.68416			0.124122			0.0620612	−	0.998072i	$-0.480233\pi$
$881$	3.68416			0.124122			0.0620612	+	0.998072i	$0.480233\pi$
$882$	−20.5544	+	22.7230i	−0.692102	+	0.765123i
$883$	10.4605	−	10.4605i	0.352023	−	0.352023i	−0.508839	−	0.860862i	$-0.669925\pi$
$883$	10.4605	−	10.4605i	0.352023	−	0.352023i	0.860862	+	0.508839i	$0.169925\pi$
$884$	−0.344346	+	0.753697i	−0.0115816	+	0.0253496i
$885$	15.8077	+	9.65098i	0.531369	+	0.324414i
$886$	12.2792	−	56.4252i	0.412529	−	1.89564i
$887$	−8.27950	+	30.8995i	−0.277998	+	1.03750i	0.675807	+	0.737079i	$0.263795\pi$
$887$	−8.27950	+	30.8995i	−0.277998	+	1.03750i	−0.953805	+	0.300426i	$0.902871\pi$
$888$	15.9418	−	2.28822i	0.534972	−	0.0767876i
$889$	24.2366	−	3.22221i	0.812869	−	0.108070i
$890$	−14.8228	−	50.6324i	−0.496863	−	1.69720i
$891$	35.6571	−	20.5866i	1.19456	−	0.689678i
$892$	24.6744	−	29.8745i	0.826160	−	1.00027i
$893$	7.03680	−	1.88550i	0.235477	−	0.0630960i
$894$	−14.5653	+	16.0198i	−0.487137	+	0.535784i
$895$	−34.8868	+	33.2163i	−1.16614	+	1.11030i
$896$	−28.4082	−	9.43249i	−0.949053	−	0.315117i
$897$	0.165512	−	0.165512i	0.00552627	−	0.00552627i
$898$	−29.2485	+	1.39096i	−0.976036	+	0.0464169i
$899$	16.8624	−	29.2066i	0.562394	−	0.974095i
$900$	30.9185	−	1.42305i	1.03062	−	0.0474350i
$901$	23.3433	+	40.4318i	0.777679	+	1.34698i
$902$	−17.5266	+	33.9903i	−0.583572	+	1.13175i
$903$	13.4176	−	5.57778i	0.446510	−	0.185617i
$904$	−0.0671850	+	0.0897042i	−0.00223454	+	0.00298352i
$905$	−34.7756	−	10.2384i	−1.15598	−	0.340336i
$906$	−34.3632	−	7.47811i	−1.14164	−	0.248444i
$907$	13.3895	−	3.58771i	0.444592	−	0.119128i	−0.0295760	−	0.999563i	$-0.509416\pi$
$907$	13.3895	−	3.58771i	0.444592	−	0.119128i	0.474168	+	0.880435i	$0.342749\pi$
$908$	−43.0170	+	16.0368i	−1.42757	+	0.532198i
$909$			26.5390i			0.880243i
$910$	−0.0746311	+	0.697256i	−0.00247400	+	0.0231138i
$911$		−	47.8573i		−	1.58558i	−0.609494	−	0.792791i	$-0.708627\pi$
$911$		−	47.8573i		−	1.58558i	0.609494	−	0.792791i	$-0.291373\pi$
$912$	−14.5693	+	21.5114i	−0.482437	+	0.712315i
$913$	−36.3488	+	9.73964i	−1.20297	+	0.322335i
$914$	1.12668	−	5.17727i	0.0372671	−	0.171249i
$915$	9.48843	−	5.17216i	0.313678	−	0.170986i
$916$	−19.4528	+	13.8476i	−0.642739	+	0.457539i
$917$	1.26207	−	9.68165i	0.0416773	−	0.319716i
$918$	−1.45913	−	0.752382i	−0.0481586	−	0.0248323i
$919$	3.56719	+	6.17855i	0.117671	+	0.203812i	0.918844	−	0.394620i	$-0.129124\pi$
$919$	3.56719	+	6.17855i	0.117671	+	0.203812i	−0.801173	+	0.598432i	$0.795791\pi$
$920$	−2.82261	+	6.57393i	−0.0930585	+	0.216736i
$921$	6.74155	−	11.6767i	0.222142	−	0.384761i
$922$	−0.447966	−	9.41965i	−0.0147530	−	0.310220i
$923$	−0.857128	+	0.857128i	−0.0282127	+	0.0282127i
$924$	42.1522	+	45.1736i	1.38671	+	1.48610i
$925$	7.74467	+	8.54424i	0.254643	+	0.280933i
$926$	21.8839	+	19.8969i	0.719148	+	0.653853i
$927$	−9.76453	+	2.61640i	−0.320709	+	0.0859338i
$928$	−39.9882	+	9.68426i	−1.31268	+	0.317902i
$929$	22.9712	−	13.2625i	0.753662	−	0.435127i	−0.0733534	−	0.997306i	$-0.523370\pi$
$929$	22.9712	−	13.2625i	0.753662	−	0.435127i	0.827016	+	0.562179i	$0.190037\pi$
$930$	31.7580	+	17.3743i	1.04139	+	0.569727i
$931$	12.9890	−	13.0554i	0.425698	−	0.427872i
$932$	7.89802	−	46.9223i	0.258708	−	1.53699i
$933$	13.1192	−	48.9615i	0.429503	−	1.60293i
$934$	38.8099	+	8.44580i	1.26990	+	0.276355i
$935$	−27.2412	+	44.6193i	−0.890884	+	1.45921i
$936$	−0.0872814	+	0.728525i	−0.00285288	+	0.0238126i
$937$	4.34151	−	4.34151i	0.141831	−	0.141831i	−0.632626	−	0.774457i	$-0.718023\pi$
$937$	4.34151	−	4.34151i	0.141831	−	0.141831i	0.774457	+	0.632626i	$0.218023\pi$
$938$	−1.79385	−	0.642443i	−0.0585713	−	0.0209765i
$939$	68.9071			2.24870
$940$	−5.42073	+	11.1340i	−0.176805	+	0.363152i
$941$	−12.9331	+	22.4008i	−0.421607	+	0.730245i	−0.996097	−	0.0882670i	$-0.971867\pi$
$941$	−12.9331	+	22.4008i	−0.421607	+	0.730245i	0.574490	+	0.818512i	$0.305200\pi$
$942$	−27.4985	−	42.7960i	−0.895951	−	1.39437i
$943$	6.24739	+	1.67398i	0.203443	+	0.0545124i
$944$	4.39320	−	12.6803i	0.142987	−	0.412710i
$945$	−1.37282	−	0.213313i	−0.0446579	−	0.00693908i
$946$	−4.52941	−	14.1731i	−0.147264	−	0.460807i
$947$	7.68227	−	28.6706i	0.249640	−	0.931670i	−0.721354	−	0.692567i	$-0.756480\pi$
$947$	7.68227	−	28.6706i	0.249640	−	0.931670i	0.970994	−	0.239103i	$-0.0768535\pi$
$948$	−19.1935	+	23.2384i	−0.623375	+	0.754750i
$949$	0.696229	+	0.401968i	0.0226006	+	0.0130484i
$950$	−18.6032	−	0.0284110i	−0.603567	−	0.000921776i
$951$			31.9921i			1.03741i
$952$	−9.11126	+	35.8525i	−0.295298	+	1.16199i
$953$	−33.9836	−	33.9836i	−1.10084	−	1.10084i	−0.994310	−	0.106528i	$-0.966027\pi$
$953$	−33.9836	−	33.9836i	−1.10084	−	1.10084i	−0.106528	−	0.994310i	$-0.533973\pi$
$954$	30.5873	+	27.8102i	0.990301	+	0.900387i
$955$	−35.7200	+	8.63819i	−1.15587	+	0.279525i
$956$	3.00137	−	0.286116i	0.0970712	−	0.00925366i
$957$	82.0323	+	21.9805i	2.65173	+	0.710528i
$958$	13.2518	+	6.83311i	0.428146	+	0.220768i
$959$	−48.5669	−	20.0446i	−1.56831	−	0.647275i
$960$	−11.3793	−	42.6726i	−0.367264	−	1.37725i
$961$	−4.75009	−	8.22739i	−0.153229	−	0.265400i
$962$	−0.229991	+	0.147780i	−0.00741520	+	0.00476463i
$963$	5.44110	+	20.3065i	0.175337	+	0.654367i
$964$	−15.4016	+	33.7106i	−0.496051	+	1.08574i
$965$	−11.0871	−	0.271955i	−0.356907	−	0.00875453i
$966$	5.94927	−	8.59046i	0.191415	−	0.276393i
$967$	−26.2766	−	26.2766i	−0.844999	−	0.844999i	0.144505	−	0.989504i	$-0.453841\pi$
$967$	−26.2766	−	26.2766i	−0.844999	−	0.844999i	−0.989504	+	0.144505i	$0.953841\pi$
$968$	25.2799	−	19.8706i	0.812527	−	0.638666i
$969$	27.8061	+	16.0539i	0.893260	+	0.515724i
$970$	13.5173	+	22.2167i	0.434014	+	0.713334i
$971$	40.7412	−	23.5219i	1.30745	−	0.754855i	0.325778	−	0.945446i	$-0.394374\pi$
$971$	40.7412	−	23.5219i	1.30745	−	0.754855i	0.981670	+	0.190591i	$0.0610404\pi$
$972$	43.7784	+	7.36883i	1.40419	+	0.236355i
$973$	−1.85869	+	2.42868i	−0.0595867	+	0.0778600i
$974$	−16.3851	−	51.2711i	−0.525013	−	1.64283i
$975$	−0.920286	+	0.472755i	−0.0294727	+	0.0151403i
$976$	−5.12579	−	5.91927i	−0.164073	−	0.189471i
$977$	−5.73007	−	21.3849i	−0.183321	−	0.684163i	−0.994984	−	0.100037i	$-0.968104\pi$
$977$	−5.73007	−	21.3849i	−0.183321	−	0.684163i	0.811663	−	0.584126i	$-0.198563\pi$
$978$	10.2938	−	0.489539i	0.329161	−	0.0156537i
$979$	78.9044			2.52180
$980$	2.28524	+	31.2214i	0.0729993	+	0.997332i
$981$	−12.1307			−0.387305
$982$	5.08217	−	0.241690i	0.162178	−	0.00771264i
$983$	−4.57305	−	17.0668i	−0.145858	−	0.544348i	−0.999716	−	0.0238421i	$-0.992410\pi$
$983$	−4.57305	−	17.0668i	−0.145858	−	0.544348i	0.853858	−	0.520506i	$-0.174257\pi$
$984$	−36.7061	+	15.7081i	−1.17015	+	0.500757i
$985$	−10.8264	+	5.90150i	−0.344959	+	0.188038i
$986$	15.4783	+	48.4336i	0.492930	+	1.54244i
$987$	10.9924	−	14.3635i	0.349893	−	0.457194i
$988$	0.0732017	−	0.434893i	0.00232886	−	0.0138358i
$989$	−2.17929	+	1.25821i	−0.0692975	+	0.0400089i
$990$	−10.9496	+	44.9771i	−0.348001	+	1.42947i
$991$	−3.59673	−	2.07657i	−0.114254	−	0.0659645i	0.441784	−	0.897121i	$-0.354346\pi$
$991$	−3.59673	−	2.07657i	−0.114254	−	0.0659645i	−0.556038	+	0.831157i	$0.687679\pi$
$992$	7.39971	−	25.1642i	0.234941	−	0.798965i
$993$	−12.9278	−	12.9278i	−0.410250	−	0.410250i
$994$	−30.8092	+	44.4870i	−0.977208	+	1.41104i
$995$	−30.6005	+	29.1352i	−0.970100	+	0.923649i
$996$	−35.7343	−	16.3261i	−1.13228	−	0.517314i
$997$	−6.26677	−	23.3879i	−0.198471	−	0.740702i	−0.991341	−	0.131312i	$-0.958081\pi$
$997$	−6.26677	−	23.3879i	−0.198471	−	0.740702i	0.792870	−	0.609390i	$-0.208586\pi$
$998$	−12.1741	+	7.82248i	−0.385366	+	0.247616i
$999$	−0.270807	−	0.469052i	−0.00856796	−	0.0148401i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.123.9	yes	72
4.3	odd	2	inner	140.2.w.b.123.12	yes	72
5.2	odd	4	inner	140.2.w.b.67.1	yes	72
5.3	odd	4		700.2.be.e.207.18		72
5.4	even	2		700.2.be.e.543.10		72
7.2	even	3	inner	140.2.w.b.23.15	yes	72
7.3	odd	6		980.2.k.j.883.4		36
7.4	even	3		980.2.k.k.883.4		36
7.5	odd	6		980.2.x.m.863.15		72
7.6	odd	2		980.2.x.m.263.9		72
20.3	even	4		700.2.be.e.207.4		72
20.7	even	4	inner	140.2.w.b.67.15	yes	72
20.19	odd	2		700.2.be.e.543.7		72
28.3	even	6		980.2.k.j.883.14		36
28.11	odd	6		980.2.k.k.883.14		36
28.19	even	6		980.2.x.m.863.1		72
28.23	odd	6	inner	140.2.w.b.23.1	✓	72
28.27	even	2		980.2.x.m.263.12		72
35.2	odd	12	inner	140.2.w.b.107.12	yes	72
35.9	even	6		700.2.be.e.443.4		72
35.12	even	12		980.2.x.m.667.12		72
35.17	even	12		980.2.k.j.687.14		36
35.23	odd	12		700.2.be.e.107.7		72
35.27	even	4		980.2.x.m.67.1		72
35.32	odd	12		980.2.k.k.687.14		36
140.23	even	12		700.2.be.e.107.10		72
140.27	odd	4		980.2.x.m.67.15		72
140.47	odd	12		980.2.x.m.667.9		72
140.67	even	12		980.2.k.k.687.4		36
140.79	odd	6		700.2.be.e.443.18		72
140.87	odd	12		980.2.k.j.687.4		36
140.107	even	12	inner	140.2.w.b.107.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.1	✓	72	28.23	odd	6	inner
140.2.w.b.23.15	yes	72	7.2	even	3	inner
140.2.w.b.67.1	yes	72	5.2	odd	4	inner
140.2.w.b.67.15	yes	72	20.7	even	4	inner
140.2.w.b.107.9	yes	72	140.107	even	12	inner
140.2.w.b.107.12	yes	72	35.2	odd	12	inner
140.2.w.b.123.9	yes	72	1.1	even	1	trivial
140.2.w.b.123.12	yes	72	4.3	odd	2	inner
700.2.be.e.107.7		72	35.23	odd	12
700.2.be.e.107.10		72	140.23	even	12
700.2.be.e.207.4		72	20.3	even	4
700.2.be.e.207.18		72	5.3	odd	4
700.2.be.e.443.4		72	35.9	even	6
700.2.be.e.443.18		72	140.79	odd	6
700.2.be.e.543.7		72	20.19	odd	2
700.2.be.e.543.10		72	5.4	even	2
980.2.k.j.687.4		36	140.87	odd	12
980.2.k.j.687.14		36	35.17	even	12
980.2.k.j.883.4		36	7.3	odd	6
980.2.k.j.883.14		36	28.3	even	6
980.2.k.k.687.4		36	140.67	even	12
980.2.k.k.687.14		36	35.32	odd	12
980.2.k.k.883.4		36	7.4	even	3
980.2.k.k.883.14		36	28.11	odd	6
980.2.x.m.67.1		72	35.27	even	4
980.2.x.m.67.15		72	140.27	odd	4
980.2.x.m.263.9		72	7.6	odd	2
980.2.x.m.263.12		72	28.27	even	2
980.2.x.m.667.9		72	140.47	odd	12
980.2.x.m.667.12		72	35.12	even	12
980.2.x.m.863.1		72	28.19	even	6
980.2.x.m.863.15		72	7.5	odd	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	140.2.w.b.123.9

Level	$140$
Weight	$2$
Character	140.123
Analytic conductor	$1.118$
Analytic rank	$0$
Dimension	$72$
Inner twists	$8$