LMFDB - Embedded newform 231.2.u.a.20.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.7
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48714 - 0.483201i) q^{2} +(-0.691398 - 1.58807i) q^{3} +(0.360067 + 0.261604i) q^{4} +(0.748085 + 2.30237i) q^{5} +(0.260847 + 2.69577i) q^{6} +(-2.45500 - 0.986383i) q^{7} +(1.42914 + 1.96705i) q^{8} +(-2.04394 + 2.19598i) q^{9} +O(q^{10})$	\(q+(-1.48714 - 0.483201i) q^{2} +(-0.691398 - 1.58807i) q^{3} +(0.360067 + 0.261604i) q^{4} +(0.748085 + 2.30237i) q^{5} +(0.260847 + 2.69577i) q^{6} +(-2.45500 - 0.986383i) q^{7} +(1.42914 + 1.96705i) q^{8} +(-2.04394 + 2.19598i) q^{9} -3.78542i q^{10} +(-3.10579 + 1.16364i) q^{11} +(0.166496 - 0.752684i) q^{12} +(1.61839 + 0.525848i) q^{13} +(3.17431 + 2.65315i) q^{14} +(3.13910 - 2.77986i) q^{15} +(-1.44992 - 4.46240i) q^{16} +(1.11832 + 3.44183i) q^{17} +(4.10072 - 2.27809i) q^{18} +(4.47759 + 6.16288i) q^{19} +(-0.332948 + 1.02471i) q^{20} +(0.130939 + 4.58070i) q^{21} +(5.18102 - 0.229776i) q^{22} -1.12952i q^{23} +(2.13570 - 3.62959i) q^{24} +(-0.696187 + 0.505809i) q^{25} +(-2.15269 - 1.56402i) q^{26} +(4.90054 + 1.72763i) q^{27} +(-0.625924 - 0.997403i) q^{28} +(-3.27295 + 4.50482i) q^{29} +(-6.01151 + 2.61723i) q^{30} +(-3.75680 - 1.22066i) q^{31} +2.47401i q^{32} +(3.99528 + 4.12768i) q^{33} -5.65886i q^{34} +(0.434465 - 6.39023i) q^{35} +(-1.31043 + 0.255996i) q^{36} +(3.18409 + 2.31338i) q^{37} +(-3.68090 - 11.3286i) q^{38} +(-0.283870 - 2.93370i) q^{39} +(-3.45975 + 4.76193i) q^{40} +(-8.91487 + 6.47703i) q^{41} +(2.01868 - 6.87542i) q^{42} -11.1893 q^{43} +(-1.42271 - 0.393498i) q^{44} +(-6.58499 - 3.06312i) q^{45} +(-0.545784 + 1.67975i) q^{46} +(4.43097 - 3.21929i) q^{47} +(-6.08414 + 5.38788i) q^{48} +(5.05410 + 4.84315i) q^{49} +(1.27973 - 0.415811i) q^{50} +(4.69267 - 4.15564i) q^{51} +(0.445166 + 0.612719i) q^{52} +(0.848876 + 0.275816i) q^{53} +(-6.45300 - 4.93717i) q^{54} +(-5.00253 - 6.28017i) q^{55} +(-1.56829 - 6.23879i) q^{56} +(6.69129 - 11.3717i) q^{57} +(7.04406 - 5.11781i) q^{58} +(-5.89051 - 4.27971i) q^{59} +(1.85751 - 0.179736i) q^{60} +(-6.69200 + 2.17436i) q^{61} +(4.99706 + 3.63057i) q^{62} +(7.18395 - 3.37503i) q^{63} +(-1.70440 + 5.24560i) q^{64} +4.11952i q^{65} +(-3.94704 - 8.06896i) q^{66} +3.92237 q^{67} +(-0.497727 + 1.53185i) q^{68} +(-1.79375 + 0.780945i) q^{69} +(-3.73387 + 9.29322i) q^{70} +(-2.03268 + 0.660459i) q^{71} +(-7.24067 - 0.882158i) q^{72} +(3.05072 - 4.19895i) q^{73} +(-3.61737 - 4.97888i) q^{74} +(1.28460 + 0.755879i) q^{75} +3.39040i q^{76} +(8.77253 + 0.206754i) q^{77} +(-0.995411 + 4.49998i) q^{78} +(-0.603371 + 1.85698i) q^{79} +(9.18944 - 6.67652i) q^{80} +(-0.644628 - 8.97688i) q^{81} +(16.3874 - 5.32458i) q^{82} +(4.13806 + 12.7356i) q^{83} +(-1.15118 + 1.68361i) q^{84} +(-7.08777 + 5.14957i) q^{85} +(16.6401 + 5.40669i) q^{86} +(9.41689 + 2.08305i) q^{87} +(-6.72756 - 4.44623i) q^{88} -12.4453 q^{89} +(8.31269 + 7.73717i) q^{90} +(-3.45448 - 2.88732i) q^{91} +(0.295486 - 0.406702i) q^{92} +(0.658949 + 6.81002i) q^{93} +(-8.14503 + 2.64648i) q^{94} +(-10.8396 + 14.9194i) q^{95} +(3.92891 - 1.71053i) q^{96} +(9.26137 + 3.00920i) q^{97} +(-5.17594 - 9.64458i) q^{98} +(3.79272 - 9.19866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.48714	−	0.483201i	−1.05157	−	0.341675i	−0.268283	−	0.963340i	$-0.586456\pi$
$2$	−1.48714	−	0.483201i	−1.05157	−	0.341675i	−0.783283	+	0.621665i	$0.786456\pi$
$3$	−0.691398	−	1.58807i	−0.399179	−	0.916873i
$3$	−0.691398	−	1.58807i	−0.399179	−	0.916873i
$4$	0.360067	+	0.261604i	0.180033	+	0.130802i
$5$	0.748085	+	2.30237i	0.334554	+	1.02965i	0.966941	+	0.254999i	$0.0820750\pi$
$5$	0.748085	+	2.30237i	0.334554	+	1.02965i	−0.632388	+	0.774652i	$0.717925\pi$
$6$	0.260847	+	2.69577i	0.106490	+	1.10054i
$7$	−2.45500	−	0.986383i	−0.927905	−	0.372818i
$7$	−2.45500	−	0.986383i	−0.927905	−	0.372818i
$8$	1.42914	+	1.96705i	0.505278	+	0.695456i
$9$	−2.04394	+	2.19598i	−0.681313	+	0.731992i
$10$		−	3.78542i		−	1.19705i
$11$	−3.10579	+	1.16364i	−0.936431	+	0.350851i
$11$	−3.10579	+	1.16364i	−0.936431	+	0.350851i
$12$	0.166496	−	0.752684i	0.0480633	−	0.217281i
$13$	1.61839	+	0.525848i	0.448862	+	0.145844i	0.524721	−	0.851274i	$-0.324170\pi$
$13$	1.61839	+	0.525848i	0.448862	+	0.145844i	−0.0758587	+	0.997119i	$0.524170\pi$
$14$	3.17431	+	2.65315i	0.848371	+	0.709084i
$15$	3.13910	−	2.77986i	0.810512	−	0.717758i
$16$	−1.44992	−	4.46240i	−0.362481	−	1.11560i
$17$	1.11832	+	3.44183i	0.271232	+	0.834767i	0.990192	+	0.139715i	$0.0446186\pi$
$17$	1.11832	+	3.44183i	0.271232	+	0.834767i	−0.718960	+	0.695052i	$0.755381\pi$
$18$	4.10072	−	2.27809i	0.966549	−	0.536951i
$19$	4.47759	+	6.16288i	1.02723	+	1.41386i	0.907008	+	0.421114i	$0.138361\pi$
$19$	4.47759	+	6.16288i	1.02723	+	1.41386i	0.120223	+	0.992747i	$0.461639\pi$
$20$	−0.332948	+	1.02471i	−0.0744494	+	0.229132i
$21$	0.130939	+	4.58070i	0.0285731	+	0.999592i
$22$	5.18102	−	0.229776i	1.10460	−	0.0489883i
$23$		−	1.12952i		−	0.235521i	−0.993042	−	0.117760i	$-0.962429\pi$
$23$		−	1.12952i		−	0.235521i	0.993042	−	0.117760i	$-0.0375714\pi$
$24$	2.13570	−	3.62959i	0.435949	−	0.740887i
$25$	−0.696187	+	0.505809i	−0.139237	+	0.101162i
$26$	−2.15269	−	1.56402i	−0.422177	−	0.306730i
$27$	4.90054	+	1.72763i	0.943110	+	0.332482i
$28$	−0.625924	−	0.997403i	−0.118289	−	0.188491i
$29$	−3.27295	+	4.50482i	−0.607771	+	0.836525i	−0.996392	−	0.0848729i	$-0.972952\pi$
$29$	−3.27295	+	4.50482i	−0.607771	+	0.836525i	0.388621	+	0.921398i	$0.372952\pi$
$30$	−6.01151	+	2.61723i	−1.09755	+	0.477839i
$31$	−3.75680	−	1.22066i	−0.674740	−	0.219236i	−0.0484491	−	0.998826i	$-0.515428\pi$
$31$	−3.75680	−	1.22066i	−0.674740	−	0.219236i	−0.626291	+	0.779589i	$0.715428\pi$
$32$			2.47401i			0.437348i
$33$	3.99528	+	4.12768i	0.695489	+	0.718537i
$34$		−	5.65886i		−	0.970486i
$35$	0.434465	−	6.39023i	0.0734379	−	1.08015i
$36$	−1.31043	+	0.255996i	−0.218405	+	0.0426660i
$37$	3.18409	+	2.31338i	0.523462	+	0.380317i	0.817906	−	0.575351i	$-0.195135\pi$
$37$	3.18409	+	2.31338i	0.523462	+	0.380317i	−0.294445	+	0.955669i	$0.595135\pi$
$38$	−3.68090	−	11.3286i	−0.597120	−	1.83775i
$39$	−0.283870	−	2.93370i	−0.0454555	−	0.469767i
$40$	−3.45975	+	4.76193i	−0.547034	+	0.752928i
$41$	−8.91487	+	6.47703i	−1.39227	+	1.01154i	−0.396657	+	0.917967i	$0.629830\pi$
$41$	−8.91487	+	6.47703i	−1.39227	+	1.01154i	−0.995612	+	0.0935754i	$0.970170\pi$
$42$	2.01868	−	6.87542i	0.311489	−	1.06090i
$43$	−11.1893			−1.70636			−0.853178	−	0.521620i	$-0.825328\pi$
$43$	−11.1893			−1.70636			−0.853178	+	0.521620i	$0.825328\pi$
$44$	−1.42271	−	0.393498i	−0.214481	−	0.0593221i
$45$	−6.58499	−	3.06312i	−0.981632	−	0.456624i
$46$	−0.545784	+	1.67975i	−0.0804714	+	0.247666i
$47$	4.43097	−	3.21929i	0.646323	−	0.469581i	−0.215694	−	0.976461i	$-0.569201\pi$
$47$	4.43097	−	3.21929i	0.646323	−	0.469581i	0.862017	+	0.506880i	$0.169201\pi$
$48$	−6.08414	+	5.38788i	−0.878170	+	0.777673i
$49$	5.05410	+	4.84315i	0.722014	+	0.691878i
$50$	1.27973	−	0.415811i	0.180982	−	0.0588046i
$51$	4.69267	−	4.15564i	0.657105	−	0.581906i
$52$	0.445166	+	0.612719i	0.0617335	+	0.0849688i
$53$	0.848876	+	0.275816i	0.116602	+	0.0378863i	0.366737	−	0.930325i	$-0.380475\pi$
$53$	0.848876	+	0.275816i	0.116602	+	0.0378863i	−0.250135	+	0.968211i	$0.580475\pi$
$54$	−6.45300	−	4.93717i	−0.878142	−	0.671864i
$55$	−5.00253	−	6.28017i	−0.674541	−	0.846819i
$56$	−1.56829	−	6.23879i	−0.209572	−	0.833694i
$57$	6.69129	−	11.3717i	0.886283	−	1.50622i
$58$	7.04406	−	5.11781i	0.924931	−	0.672002i
$59$	−5.89051	−	4.27971i	−0.766879	−	0.557170i	0.134133	−	0.990963i	$-0.457175\pi$
$59$	−5.89051	−	4.27971i	−0.766879	−	0.557170i	−0.901013	+	0.433793i	$0.857175\pi$
$60$	1.85751	−	0.179736i	0.239803	−	0.0232038i
$61$	−6.69200	+	2.17436i	−0.856822	+	0.278398i	−0.704301	−	0.709902i	$-0.748739\pi$
$61$	−6.69200	+	2.17436i	−0.856822	+	0.278398i	−0.152522	+	0.988300i	$0.548739\pi$
$62$	4.99706	+	3.63057i	0.634627	+	0.461083i
$63$	7.18395	−	3.37503i	0.905093	−	0.425214i
$64$	−1.70440	+	5.24560i	−0.213050	+	0.655700i
$65$			4.11952i			0.510964i
$66$	−3.94704	−	8.06896i	−0.485847	−	0.993220i
$67$	3.92237			0.479194			0.239597	−	0.970872i	$-0.422985\pi$
$67$	3.92237			0.479194			0.239597	+	0.970872i	$0.422985\pi$
$68$	−0.497727	+	1.53185i	−0.0603583	+	0.185764i
$69$	−1.79375	+	0.780945i	−0.215943	+	0.0940148i
$70$	−3.73387	+	9.29322i	−0.446283	+	1.11075i
$71$	−2.03268	+	0.660459i	−0.241235	+	0.0783821i	−0.427139	−	0.904186i	$-0.640479\pi$
$71$	−2.03268	+	0.660459i	−0.241235	+	0.0783821i	0.185904	+	0.982568i	$0.440479\pi$
$72$	−7.24067	−	0.882158i	−0.853321	−	0.103963i
$73$	3.05072	−	4.19895i	0.357060	−	0.491450i	−0.592267	−	0.805742i	$-0.701767\pi$
$73$	3.05072	−	4.19895i	0.357060	−	0.491450i	0.949327	+	0.314291i	$0.101767\pi$
$74$	−3.61737	−	4.97888i	−0.420510	−	0.578783i
$75$	1.28460	+	0.755879i	0.148333	+	0.0872814i
$76$			3.39040i			0.388906i
$77$	8.77253	+	0.206754i	0.999722	+	0.0235618i
$78$	−0.995411	+	4.49998i	−0.112708	+	0.509523i
$79$	−0.603371	+	1.85698i	−0.0678845	+	0.208927i	−0.979244	−	0.202684i	$-0.935034\pi$
$79$	−0.603371	+	1.85698i	−0.0678845	+	0.208927i	0.911360	+	0.411611i	$0.135034\pi$
$80$	9.18944	−	6.67652i	1.02741	−	0.746457i
$81$	−0.644628	−	8.97688i	−0.0716254	−	0.997432i
$82$	16.3874	−	5.32458i	1.80968	−	0.588001i
$83$	4.13806	+	12.7356i	0.454211	+	1.39792i	0.872059	+	0.489401i	$0.162784\pi$
$83$	4.13806	+	12.7356i	0.454211	+	1.39792i	−0.417848	+	0.908517i	$0.637216\pi$
$84$	−1.15118	+	1.68361i	−0.125604	+	0.183697i
$85$	−7.08777	+	5.14957i	−0.768776	+	0.558549i
$86$	16.6401	+	5.40669i	1.79435	+	0.583019i
$87$	9.41689	+	2.08305i	1.00960	+	0.223326i
$88$	−6.72756	−	4.44623i	−0.717160	−	0.473969i
$89$	−12.4453			−1.31920			−0.659600	−	0.751617i	$-0.729274\pi$
$89$	−12.4453			−1.31920			−0.659600	+	0.751617i	$0.729274\pi$
$90$	8.31269	+	7.73717i	0.876235	+	0.815569i
$91$	−3.45448	−	2.88732i	−0.362128	−	0.302673i
$92$	0.295486	−	0.406702i	0.0308066	−	0.0424016i
$93$	0.658949	+	6.81002i	0.0683299	+	0.706166i
$94$	−8.14503	+	2.64648i	−0.840095	+	0.272964i
$95$	−10.8396	+	14.9194i	−1.11212	+	1.53070i
$96$	3.92891	−	1.71053i	0.400993	−	0.174580i
$97$	9.26137	+	3.00920i	0.940350	+	0.305538i	0.738788	−	0.673938i	$-0.235398\pi$
$97$	9.26137	+	3.00920i	0.940350	+	0.305538i	0.201562	+	0.979476i	$0.435398\pi$
$98$	−5.17594	−	9.64458i	−0.522848	−	0.974250i
$99$	3.79272	−	9.19866i	0.381183	−	0.924500i
$100$	−0.382996			−0.0382996
$101$	−0.394049	+	1.21276i	−0.0392093	+	0.120674i	−0.968745	−	0.248058i	$-0.920208\pi$
$101$	−0.394049	+	1.21276i	−0.0392093	+	0.120674i	0.929536	+	0.368731i	$0.120208\pi$
$102$	−8.98667	+	3.91252i	−0.889812	+	0.387397i
$103$	−2.27833	+	3.13585i	−0.224491	+	0.308985i	−0.906374	−	0.422476i	$-0.861161\pi$
$103$	−2.27833	+	3.13585i	−0.224491	+	0.308985i	0.681884	+	0.731461i	$0.261161\pi$
$104$	1.27855	+	3.93497i	0.125372	+	0.385856i
$105$	−10.4485	+	3.72823i	−1.01967	+	0.363838i
$106$	−1.12912	−	0.820355i	−0.109670	−	0.0796799i
$107$	−5.19699	−	7.15304i	−0.502412	−	0.691511i	0.480205	−	0.877156i	$-0.340562\pi$
$107$	−5.19699	−	7.15304i	−0.502412	−	0.691511i	−0.982617	+	0.185646i	$0.940562\pi$
$108$	1.31257	+	1.90406i	0.126302	+	0.183218i
$109$	7.36425			0.705368			0.352684	−	0.935743i	$-0.385269\pi$
$109$	7.36425			0.705368			0.352684	+	0.935743i	$0.385269\pi$
$110$	4.40487	+	11.7567i	0.419988	+	1.12096i
$111$	1.47234	−	6.65603i	0.139748	−	0.631763i
$112$	−0.842070	+	12.3854i	−0.0795682	+	1.17031i
$113$	−5.86402	−	8.07113i	−0.551641	−	0.759268i	0.438593	−	0.898686i	$-0.355477\pi$
$113$	−5.86402	−	8.07113i	−0.551641	−	0.759268i	−0.990234	+	0.139418i	$0.955477\pi$
$114$	−15.4457	+	13.6781i	−1.44662	+	1.28107i
$115$	2.60057	−	0.844975i	0.242504	−	0.0787943i
$116$	−2.35696	+	0.765822i	−0.218838	+	0.0711048i
$117$	−4.46265	+	2.47916i	−0.412572	+	0.229198i
$118$	6.69205	+	9.21082i	0.616054	+	0.847925i
$119$	0.649485	−	9.55280i	0.0595382	−	0.875704i
$120$	9.95435	+	2.20193i	0.908704	+	0.201008i
$121$	8.29188	−	7.22805i	0.753807	−	0.657096i
$122$	11.0026			0.996127
$123$	16.4497	+	9.67924i	1.48322	+	0.872748i
$124$	−1.03337	−	1.42231i	−0.0927993	−	0.127727i
$125$	8.10719	+	5.89022i	0.725129	+	0.526837i
$126$	−12.3144	+	1.54784i	−1.09705	+	0.137893i
$127$	3.62750	+	11.1643i	0.321889	+	0.990671i	0.972826	+	0.231539i	$0.0743762\pi$
$127$	3.62750	+	11.1643i	0.321889	+	0.990671i	−0.650937	+	0.759132i	$0.725624\pi$
$128$	7.97774	−	10.9804i	0.705139	−	0.970541i
$129$	7.73627	+	17.7694i	0.681141	+	1.56451i
$130$	1.99056	−	6.12630i	0.174583	−	0.537312i
$131$	13.4508			1.17520			0.587601	−	0.809151i	$-0.300073\pi$
$131$	13.4508			1.17520			0.587601	+	0.809151i	$0.300073\pi$
$132$	0.358752	+	2.53142i	0.0312253	+	0.220332i
$133$	−4.91356	−	19.5465i	−0.426059	−	1.69490i
$134$	−5.83312	−	1.89530i	−0.503905	−	0.163729i
$135$	−0.311613	+	12.5753i	−0.0268194	+	1.08231i
$136$	−5.17201	+	7.11866i	−0.443496	+	0.610420i
$137$	1.89414	−	0.615444i	0.161828	−	0.0525809i	−0.226983	−	0.973899i	$-0.572886\pi$
$137$	1.89414	−	0.615444i	0.161828	−	0.0525809i	0.388810	+	0.921318i	$0.372886\pi$
$138$	3.04492	−	0.294631i	0.259200	−	0.0250807i
$139$	1.67104	−	2.29999i	0.141736	−	0.195083i	−0.732247	−	0.681039i	$-0.761528\pi$
$139$	1.67104	−	2.29999i	0.141736	−	0.195083i	0.873983	+	0.485956i	$0.161528\pi$
$140$	1.82814	−	2.18725i	0.154506	−	0.184856i
$141$	−8.17601	−	4.81088i	−0.688545	−	0.405149i
$142$	3.34202			0.280456
$143$	−5.63830	+	0.250056i	−0.471498	+	0.0209107i
$144$	12.7629	+	5.93688i	1.06357	+	0.494740i
$145$	−12.8202	−	4.16554i	−1.06466	−	0.345929i
$146$	−6.56578	+	4.77032i	−0.543388	+	0.394795i
$147$	4.19687	−	11.3748i	0.346152	−	0.938178i
$148$	0.541298	+	1.66594i	0.0444944	+	0.136940i
$149$	11.2362	−	3.65087i	0.920506	−	0.299091i	0.189832	−	0.981817i	$-0.439206\pi$
$149$	11.2362	−	3.65087i	0.920506	−	0.299091i	0.730674	+	0.682726i	$0.239206\pi$
$150$	−1.54514	−	1.74482i	−0.126160	−	0.142464i
$151$	5.70902	−	4.14785i	0.464594	−	0.337547i	−0.330737	−	0.943723i	$-0.607297\pi$
$151$	5.70902	−	4.14785i	0.464594	−	0.337547i	0.795331	+	0.606176i	$0.207297\pi$
$152$	−5.72355	+	17.6153i	−0.464241	+	1.42879i
$153$	−9.84396	−	4.57909i	−0.795837	−	0.370198i
$154$	−12.9461	−	4.54637i	−1.04322	−	0.366357i
$155$		−	9.56268i		−	0.768093i
$156$	0.665254	−	1.13059i	0.0532630	−	0.0905195i
$157$	3.84355	+	5.29019i	0.306749	+	0.422203i	0.934364	−	0.356320i	$-0.115969\pi$
$157$	3.84355	+	5.29019i	0.306749	+	0.422203i	−0.627615	+	0.778524i	$0.715969\pi$
$158$	1.79459	−	2.47004i	0.142770	−	0.196506i
$159$	−0.148894	−	1.53877i	−0.0118081	−	0.122033i
$160$	−5.69609	+	1.85077i	−0.450316	+	0.146316i
$161$	−1.11414	+	2.77297i	−0.0878062	+	0.218541i
$162$	−3.37899	+	13.6614i	−0.265478	+	1.07334i
$163$	3.76435	−	11.5855i	0.294847	−	0.907444i	−0.688426	−	0.725306i	$-0.741698\pi$
$163$	3.76435	−	11.5855i	0.294847	−	0.907444i	0.983273	−	0.182138i	$-0.0583018\pi$
$164$	−4.90437			−0.382967
$165$	−6.51463	+	12.2865i	−0.507163	+	0.956500i
$166$		−	20.9392i		−	1.62520i
$167$	3.74441	−	11.5241i	0.289751	−	0.891763i	−0.695183	−	0.718833i	$-0.744677\pi$
$167$	3.74441	−	11.5241i	0.289751	−	0.891763i	0.984934	−	0.172930i	$-0.0553234\pi$
$168$	−8.82333	+	6.80404i	−0.680735	+	0.524943i
$169$	−8.17454	−	5.93915i	−0.628810	−	0.456858i
$170$	13.0288	−	4.23331i	0.999261	−	0.324680i
$171$	−22.6855	−	2.76386i	−1.73480	−	0.211357i
$172$	−4.02891	−	2.92717i	−0.307201	−	0.223195i
$173$	10.4698	−	7.60672i	0.796001	−	0.578328i	−0.113737	−	0.993511i	$-0.536282\pi$
$173$	10.4698	−	7.60672i	0.796001	−	0.578328i	0.909738	+	0.415182i	$0.136282\pi$
$174$	−12.9977	−	7.64803i	−0.985353	−	0.579796i
$175$	2.20806	−	0.555058i	0.166914	−	0.0419584i
$176$	9.69580	+	12.1721i	0.730848	+	0.917507i
$177$	−2.72379	+	12.3135i	−0.204733	+	0.925542i
$178$	18.5079	+	6.01359i	1.38723	+	0.450737i
$179$	−7.99088	−	10.9985i	−0.597266	−	0.822066i	0.398188	−	0.917304i	$-0.369639\pi$
$179$	−7.99088	−	10.9985i	−0.597266	−	0.822066i	−0.995455	+	0.0952372i	$0.969639\pi$
$180$	−1.56971	−	2.82559i	−0.116999	−	0.210607i
$181$	−11.1575	+	3.62529i	−0.829331	+	0.269466i	−0.692764	−	0.721165i	$-0.743607\pi$
$181$	−11.1575	+	3.62529i	−0.829331	+	0.269466i	−0.136567	+	0.990631i	$0.543607\pi$
$182$	3.74214	+	5.96305i	0.277386	+	0.442011i
$183$	8.07987	+	9.12402i	0.597281	+	0.674467i
$184$	2.22181	−	1.61424i	0.163794	−	0.119003i
$185$	−2.94428	+	9.06157i	−0.216468	+	0.666220i
$186$	2.31066	−	10.4458i	0.169426	−	0.765927i
$187$	−7.47832	−	9.38829i	−0.546869	−	0.686540i
$188$	2.43762			0.177782
$189$	−10.3268	−	9.07514i	−0.751161	−	0.660119i
$190$	23.3291	−	16.9496i	1.69247	−	1.22965i
$191$	−3.94455	+	5.42920i	−0.285417	+	0.392843i	−0.927519	−	0.373776i	$-0.878063\pi$
$191$	−3.94455	+	5.42920i	−0.285417	+	0.392843i	0.642101	+	0.766620i	$0.278063\pi$
$192$	9.50881	−	0.920089i	0.686239	−	0.0664017i
$193$	−3.73031	−	11.4807i	−0.268513	−	0.826399i	−0.990863	−	0.134871i	$-0.956938\pi$
$193$	−3.73031	−	11.4807i	−0.268513	−	0.826399i	0.722350	−	0.691528i	$-0.243062\pi$
$194$	−12.3189	−	8.95021i	−0.884446	−	0.642587i
$195$	6.54209	−	2.84823i	0.468489	−	0.203966i
$196$	0.552827	+	3.06603i	0.0394876	+	0.219002i
$197$		−	10.8045i		−	0.769786i	−0.922961	−	0.384893i	$-0.874238\pi$
$197$		−	10.8045i		−	0.769786i	0.922961	−	0.384893i	$-0.125762\pi$
$198$	−10.0851	+	11.8470i	−0.716717	+	0.841933i
$199$			17.3013i			1.22646i	0.789906	+	0.613228i	$0.210129\pi$
$199$			17.3013i			1.22646i	−0.789906	+	0.613228i	$0.789871\pi$
$200$	−1.98990	−	0.646558i	−0.140707	−	0.0457186i
$201$	−2.71192	−	6.22901i	−0.191284	−	0.439360i
$202$	1.17201	−	1.61313i	0.0824624	−	0.113500i
$203$	12.4786	−	7.83099i	0.875825	−	0.549628i
$204$	2.77681	−	0.268689i	0.194415	−	0.0188120i
$205$	−21.5816	−	15.6799i	−1.50732	−	1.09514i
$206$	4.90344	−	3.56256i	0.341639	−	0.248215i
$207$	2.48039	+	2.30866i	0.172399	+	0.160463i
$208$		−	7.98437i		−	0.553617i
$209$	−21.0779	−	13.9303i	−1.45799	−	0.963579i
$210$	17.3399	−	0.495657i	1.19657	−	0.0342036i
$211$	−2.94673	+	9.06911i	−0.202861	+	0.624343i	0.796933	+	0.604068i	$0.206454\pi$
$211$	−2.94673	+	9.06911i	−0.202861	+	0.624343i	−0.999794	+	0.0202755i	$0.993546\pi$
$212$	0.233497	+	0.321381i	0.0160367	+	0.0220726i
$213$	2.45425	+	2.77141i	0.168162	+	0.189894i
$214$	4.27229	+	13.1488i	0.292048	+	0.898831i
$215$	−8.37057	−	25.7620i	−0.570868	−	1.75695i
$216$	3.60525	+	12.1086i	0.245306	+	0.823887i
$217$	8.01892	+	6.70236i	0.544359	+	0.454986i
$218$	−10.9517	−	3.55841i	−0.741741	−	0.241006i
$219$	−8.77750	−	1.94161i	−0.593128	−	0.131202i
$220$	−0.158326	−	3.56996i	−0.0106743	−	0.240687i
$221$			6.15831i			0.414253i
$222$	−5.40577	+	9.18702i	−0.362812	+	0.616592i
$223$	7.81278	+	10.7534i	0.523182	+	0.720099i	0.986072	−	0.166317i	$-0.0531875\pi$
$223$	7.81278	+	10.7534i	0.523182	+	0.720099i	−0.462890	+	0.886416i	$0.653187\pi$
$224$	2.44033	−	6.07372i	0.163051	−	0.405817i
$225$	0.312218	−	2.56265i	0.0208145	−	0.170844i
$226$	4.82064	+	14.8364i	0.320664	+	0.986902i
$227$	1.59380	+	1.15797i	0.105784	+	0.0768569i	0.639420	−	0.768858i	$-0.279175\pi$
$227$	1.59380	+	1.15797i	0.105784	+	0.0768569i	−0.533636	+	0.845715i	$0.679175\pi$
$228$	5.38420	−	2.34412i	0.356578	−	0.155243i
$229$	26.7975	+	8.70702i	1.77083	+	0.575376i	0.998227	−	0.0595189i	$-0.0189567\pi$
$229$	26.7975	+	8.70702i	1.77083	+	0.575376i	0.772598	+	0.634895i	$0.218957\pi$
$230$	−4.27570			−0.281931
$231$	−5.73696	−	14.0743i	−0.377465	−	0.926024i
$232$	−13.5387			−0.888860
$233$	−22.2143	−	7.21786i	−1.45531	−	0.472858i	−0.528674	−	0.848825i	$-0.677310\pi$
$233$	−22.2143	−	7.21786i	−1.45531	−	0.472858i	−0.926633	+	0.375967i	$0.877310\pi$
$234$	7.83451	−	1.53049i	0.512158	−	0.100051i
$235$	10.7267	+	7.79342i	0.699734	+	0.508387i
$236$	−1.00139	−	3.08196i	−0.0651849	−	0.200619i
$237$	3.36619	−	0.325719i	0.218658	−	0.0211577i
$238$	−5.58180	+	13.8925i	−0.361814	+	0.900518i
$239$	16.6319	+	22.8918i	1.07583	+	1.48075i	0.864034	+	0.503434i	$0.167930\pi$
$239$	16.6319	+	22.8918i	1.07583	+	1.48075i	0.211793	+	0.977315i	$0.432070\pi$
$240$	−16.9563	−	9.97735i	−1.09453	−	0.644035i
$241$			6.53642i			0.421048i	0.977589	+	0.210524i	$0.0675170\pi$
$241$			6.53642i			0.421048i	−0.977589	+	0.210524i	$0.932483\pi$
$242$	−15.8238	+	6.74248i	−1.01719	+	0.433423i
$243$	−13.8102	+	7.23031i	−0.885927	+	0.463825i
$244$	−2.97839	−	0.967737i	−0.190672	−	0.0619530i
$245$	−7.36982	+	15.2595i	−0.470841	+	0.974893i
$246$	−19.7860	−	22.3429i	−1.26151	−	1.42453i
$247$	4.00577	+	12.3285i	0.254881	+	0.784444i
$248$	−2.96791	−	9.13428i	−0.188462	−	0.580028i
$249$	17.3641	−	15.3769i	1.10040	−	0.974473i
$250$	−9.21037	−	12.6770i	−0.582515	−	0.801763i
$251$	8.90275	−	27.3999i	0.561937	−	1.72946i	−0.114945	−	0.993372i	$-0.536669\pi$
$251$	8.90275	−	27.3999i	0.561937	−	1.72946i	0.676882	−	0.736092i	$-0.263331\pi$
$252$	3.46962	+	0.664114i	0.218566	+	0.0418353i
$253$	1.31435	+	3.50804i	0.0826326	+	0.220549i
$254$		−	18.3557i		−	1.15174i
$255$	13.0783	+	7.69548i	0.818997	+	0.481910i
$256$	−8.24541	+	5.99064i	−0.515338	+	0.374415i
$257$	8.33663	+	6.05692i	0.520025	+	0.377820i	0.816613	−	0.577185i	$-0.195849\pi$
$257$	8.33663	+	6.05692i	0.520025	+	0.377820i	−0.296589	+	0.955005i	$0.595849\pi$
$258$	−2.91871	−	30.1638i	−0.181711	−	1.87792i
$259$	−5.53509	−	8.82010i	−0.343934	−	0.548054i
$260$	−1.07768	+	1.48330i	−0.0668350	+	0.0919905i
$261$	−3.20279	−	16.3949i	−0.198248	−	1.01482i
$262$	−20.0032	−	6.49944i	−1.23580	−	0.401537i
$263$			22.5682i			1.39161i	0.718229	+	0.695807i	$0.244953\pi$
$263$			22.5682i			1.39161i	−0.718229	+	0.695807i	$0.755047\pi$
$264$	−2.40951	+	13.7579i	−0.148295	+	0.846743i
$265$			2.16076i			0.132734i
$266$	−2.13775	+	31.4426i	−0.131074	+	1.92787i
$267$	8.60466	+	19.7640i	0.526596	+	1.20954i
$268$	1.41232	+	1.02611i	0.0862710	+	0.0626795i
$269$	6.32242	+	19.4584i	0.385485	+	1.18640i	0.936128	+	0.351660i	$0.114383\pi$
$269$	6.32242	+	19.4584i	0.385485	+	1.18640i	−0.550643	+	0.834741i	$0.685617\pi$
$270$	6.53979	−	18.5506i	0.397999	−	1.12895i
$271$	−7.50466	+	10.3293i	−0.455875	+	0.627459i	−0.973647	−	0.228060i	$-0.926762\pi$
$271$	−7.50466	+	10.3293i	−0.455875	+	0.627459i	0.517772	+	0.855519i	$0.326762\pi$
$272$	13.7374	−	9.98078i	0.832950	−	0.605174i
$273$	−2.19685	+	7.48224i	−0.132959	+	0.452846i
$274$	−3.11424			−0.188138
$275$	1.57363	−	2.38105i	0.0948935	−	0.143583i
$276$	−0.850169	−	0.188060i	−0.0511742	−	0.0113199i
$277$	−3.20939	+	9.87750i	−0.192834	+	0.593481i	0.807161	+	0.590331i	$0.201003\pi$
$277$	−3.20939	+	9.87750i	−0.192834	+	0.593481i	−0.999995	+	0.00315035i	$0.998997\pi$
$278$	−3.59643	+	2.61296i	−0.215700	+	0.156715i
$279$	10.3592	−	5.75489i	0.620189	−	0.344536i
$280$	13.1908	−	8.27793i	0.788300	−	0.494701i
$281$	14.9766	−	4.86621i	0.893432	−	0.290294i	0.173908	−	0.984762i	$-0.444360\pi$
$281$	14.9766	−	4.86621i	0.893432	−	0.290294i	0.719523	+	0.694468i	$0.244360\pi$
$282$	9.83425	+	11.1051i	0.585621	+	0.661300i
$283$	−2.53735	−	3.49237i	−0.150830	−	0.207600i	0.726915	−	0.686727i	$-0.240953\pi$
$283$	−2.53735	−	3.49237i	−0.150830	−	0.207600i	−0.877745	+	0.479127i	$0.840953\pi$
$284$	−0.904681	−	0.293949i	−0.0536829	−	0.0174426i
$285$	31.1876	+	6.89880i	1.84739	+	0.408649i
$286$	8.50576	+	2.35256i	0.502956	+	0.139110i
$287$	28.2749	−	7.10767i	1.66901	−	0.419553i
$288$	−5.43288	−	5.05673i	−0.320135	−	0.297971i
$289$	3.15772	−	2.29422i	0.185748	−	0.134954i
$290$	17.0526	+	12.3895i	1.00137	+	0.727535i
$291$	−1.62446	−	16.7883i	−0.0952277	−	0.984146i
$292$	2.19693	−	0.713824i	0.128565	−	0.0417734i
$293$	−3.79557	−	2.75764i	−0.221740	−	0.161103i	0.471370	−	0.881936i	$-0.343760\pi$
$293$	−3.79557	−	2.75764i	−0.221740	−	0.161103i	−0.693109	+	0.720832i	$0.743760\pi$
$294$	−11.7377	+	14.8880i	−0.684554	+	0.868285i
$295$	5.44686	−	16.7637i	0.317129	−	0.976021i
$296$			9.56941i			0.556211i
$297$	−17.2304	+	0.336823i	−0.999809	+	0.0195445i
$298$	−18.4739			−1.07017
$299$	0.593955	−	1.82800i	0.0343493	−	0.105716i
$300$	0.264802	+	0.608224i	0.0152884	+	0.0351158i
$301$	27.4698	+	11.0370i	1.58334	+	0.636160i
$302$	−10.4944	+	3.40982i	−0.603882	+	0.196213i
$303$	2.19839	−	0.212720i	0.126294	−	0.0122204i
$304$	21.0091	−	28.9165i	1.20495	−	1.65848i
$305$	−10.0124	−	13.7808i	−0.573306	−	0.789089i
$306$	12.4267	+	11.5664i	0.710388	+	0.661205i
$307$			1.68567i			0.0962065i	0.998842	+	0.0481032i	$0.0153176\pi$
$307$			1.68567i			0.0962065i	−0.998842	+	0.0481032i	$0.984682\pi$
$308$	3.10461	+	2.36937i	0.176902	+	0.135008i
$309$	6.55519	+	1.45003i	0.372912	+	0.0824893i
$310$	−4.62070	+	14.2210i	−0.262438	+	0.807701i
$311$	−18.0106	+	13.0855i	−1.02129	+	0.742008i	−0.966546	−	0.256492i	$-0.917433\pi$
$311$	−18.0106	+	13.0855i	−1.02129	+	0.742008i	−0.0547405	+	0.998501i	$0.517433\pi$
$312$	5.36503	−	4.75106i	0.303735	−	0.268976i
$313$	−9.23979	+	3.00219i	−0.522264	+	0.169694i	−0.558272	−	0.829658i	$-0.688536\pi$
$313$	−9.23979	+	3.00219i	−0.522264	+	0.169694i	0.0360088	+	0.999351i	$0.488536\pi$
$314$	−3.15967	−	9.72446i	−0.178310	−	0.548783i
$315$	13.1448	+	14.0153i	0.740624	+	0.789673i
$316$	−0.703048	+	0.510794i	−0.0395495	+	0.0287344i
$317$	14.0261	+	4.55736i	0.787785	+	0.255967i	0.675161	−	0.737671i	$-0.264074\pi$
$317$	14.0261	+	4.55736i	0.787785	+	0.255967i	0.112624	+	0.993638i	$0.464074\pi$
$318$	−0.522110	+	2.36032i	−0.0292785	+	0.132360i
$319$	4.92309	−	17.7996i	0.275640	−	0.996585i
$320$	−13.3524			−0.746419
$321$	−7.76635	+	13.1988i	−0.433476	+	0.736684i
$322$	2.99678	−	3.58544i	0.167004	−	0.199809i
$323$	−16.2042	+	22.3032i	−0.901627	+	1.24098i
$324$	2.11628	−	3.40092i	0.117571	−	0.188940i
$325$	−1.39268	+	0.452511i	−0.0772522	+	0.0251008i
$326$	−11.1962	+	15.4103i	−0.620101	+	0.853496i
$327$	−5.09163	−	11.6950i	−0.281568	−	0.646733i
$328$	−25.4813	−	8.27936i	−1.40697	−	0.457151i
$329$	−14.0535	+	3.53273i	−0.774794	+	0.194766i
$330$	15.6250	−	15.1238i	0.860128	−	0.832539i
$331$	−0.583023			−0.0320459			−0.0160229	−	0.999872i	$-0.505100\pi$
$331$	−0.583023			−0.0320459			−0.0160229	+	0.999872i	$0.505100\pi$
$332$	−1.84171	+	5.66821i	−0.101077	+	0.311084i
$333$	−11.5882	+	2.26379i	−0.635031	+	0.124055i
$334$	−11.1369	+	15.3287i	−0.609385	+	0.838747i
$335$	2.93427	+	9.03075i	0.160316	+	0.493403i
$336$	20.2511	−	7.22597i	1.10479	−	0.394209i
$337$	−2.38500	−	1.73281i	−0.129919	−	0.0943920i	0.520928	−	0.853601i	$-0.325586\pi$
$337$	−2.38500	−	1.73281i	−0.129919	−	0.0943920i	−0.650847	+	0.759209i	$0.725586\pi$
$338$	9.28687	+	12.7823i	0.505139	+	0.695265i
$339$	−8.76316	+	14.8928i	−0.475949	+	0.808868i
$340$	−3.89922			−0.211465
$341$	13.0882	−	0.580457i	0.708767	−	0.0314335i
$342$	32.4010	+	15.0719i	1.75204	+	0.814994i
$343$	−7.63064	−	16.8752i	−0.412016	−	0.911177i
$344$	−15.9911	−	22.0099i	−0.862185	−	1.18670i
$345$	−3.13990	−	3.54567i	−0.169047	−	0.190892i
$346$	−19.2456	+	6.25326i	−1.03465	+	0.336177i
$347$	−11.2501	+	3.65539i	−0.603939	+	0.196232i	−0.594996	−	0.803728i	$-0.702847\pi$
$347$	−11.2501	+	3.65539i	−0.603939	+	0.196232i	−0.00894248	+	0.999960i	$0.502847\pi$
$348$	2.84578	+	3.21353i	0.152550	+	0.172263i
$349$	−7.24958	−	9.97819i	−0.388061	−	0.534120i	0.569637	−	0.821897i	$-0.307084\pi$
$349$	−7.24958	−	9.97819i	−0.388061	−	0.534120i	−0.957698	+	0.287777i	$0.907084\pi$
$350$	−3.55190	−	0.241490i	−0.189857	−	0.0129082i
$351$	7.02254	+	5.37292i	0.374836	+	0.286785i
$352$	−2.87887	−	7.68377i	−0.153444	−	0.409546i
$353$	−10.0973			−0.537423			−0.268712	−	0.963221i	$-0.586598\pi$
$353$	−10.0973			−0.537423			−0.268712	+	0.963221i	$0.586598\pi$
$354$	10.0006	−	16.9958i	0.531524	−	0.903317i
$355$	−3.04124	−	4.18591i	−0.161412	−	0.222165i
$356$	−4.48114	−	3.25574i	−0.237500	−	0.172554i
$357$	−15.6196	+	5.57336i	−0.826676	+	0.294973i
$358$	6.56907	+	20.2175i	0.347186	+	1.06853i
$359$	5.44335	−	7.49213i	0.287289	−	0.395419i	−0.640842	−	0.767673i	$-0.721415\pi$
$359$	5.44335	−	7.49213i	0.287289	−	0.395419i	0.928131	+	0.372253i	$0.121415\pi$
$360$	−3.38558	−	17.3306i	−0.178436	−	0.913404i
$361$	−12.0609	+	37.1197i	−0.634785	+	1.95367i
$362$	18.3445			0.964166
$363$	−17.2116	−	8.17063i	−0.903377	−	0.428847i
$364$	−0.488510	−	1.94333i	−0.0256049	−	0.101858i
$365$	11.9497	+	3.88271i	0.625478	+	0.203230i
$366$	−7.60716	−	17.4729i	−0.397633	−	0.913323i
$367$	16.9513	−	23.3314i	0.884850	−	1.21789i	−0.0902045	−	0.995923i	$-0.528752\pi$
$367$	16.9513	−	23.3314i	0.884850	−	1.21789i	0.975054	−	0.221968i	$-0.0712479\pi$
$368$	−5.04036	+	1.63771i	−0.262747	+	0.0853717i
$369$	3.99804	−	32.8155i	0.208129	−	1.70831i
$370$	8.75711	−	12.0531i	0.455261	−	0.626613i
$371$	−1.81193	−	1.51445i	−0.0940709	−	0.0786262i
$372$	−1.54426	+	2.62444i	−0.0800662	+	0.136071i
$373$	8.06208			0.417438			0.208719	−	0.977976i	$-0.433071\pi$
$373$	8.06208			0.417438			0.208719	+	0.977976i	$0.433071\pi$
$374$	6.58488	+	17.5752i	0.340496	+	0.908793i
$375$	3.74879	−	16.9473i	0.193587	−	0.875154i
$376$	12.6650	+	4.11510i	0.653146	+	0.212220i
$377$	−7.66577	+	5.56951i	−0.394807	+	0.286844i
$378$	10.9722	+	18.4859i	0.564349	+	0.950812i
$379$	2.62990	+	8.09399i	0.135089	+	0.415760i	0.995604	−	0.0936646i	$-0.0298581\pi$
$379$	2.62990	+	8.09399i	0.135089	+	0.415760i	−0.860515	+	0.509425i	$0.829858\pi$
$380$	−7.80596	+	2.53631i	−0.400437	+	0.130110i
$381$	15.2217	−	13.4797i	0.779829	−	0.690586i
$382$	8.48949	−	6.16797i	0.434360	−	0.315581i
$383$	−7.01286	+	21.5834i	−0.358340	+	1.10286i	0.595707	+	0.803202i	$0.296872\pi$
$383$	−7.01286	+	21.5834i	−0.358340	+	1.10286i	−0.954047	+	0.299656i	$0.903128\pi$
$384$	−22.9535	−	5.07738i	−1.17134	−	0.259104i
$385$	6.08657	+	20.3523i	0.310200	+	1.03725i
$386$			18.8759i			0.960758i
$387$	22.8703	−	24.5715i	1.16256	−	1.24904i
$388$	2.54749	+	3.50632i	0.129329	+	0.178007i
$389$	−4.58070	+	6.30480i	−0.232251	+	0.319666i	−0.909197	−	0.416367i	$-0.863303\pi$
$389$	−4.58070	+	6.30480i	−0.232251	+	0.319666i	0.676946	+	0.736033i	$0.263303\pi$
$390$	−11.1053	+	1.07457i	−0.562337	+	0.0544128i
$391$	3.88761	−	1.26316i	0.196605	−	0.0638808i
$392$	−2.30367	+	16.8632i	−0.116353	+	0.851720i
$393$	−9.29985	−	21.3608i	−0.469115	−	1.07751i
$394$	−5.22072	+	16.0677i	−0.263016	+	0.809481i
$395$	−4.72683			−0.237833
$396$	3.77204	−	2.31994i	0.189552	−	0.116581i
$397$		−	6.58697i		−	0.330590i	−0.986244	−	0.165295i	$-0.947142\pi$
$397$		−	6.58697i		−	0.330590i	0.986244	−	0.165295i	$-0.0528577\pi$
$398$	8.36000	−	25.7294i	0.419049	−	1.28970i
$399$	−27.6440	+	21.3175i	−1.38393	+	1.06721i
$400$	3.26654	+	2.37328i	0.163327	+	0.118664i
$401$	−22.4718	+	7.30152i	−1.12219	+	0.364621i	−0.810602	−	0.585598i	$-0.800860\pi$
$401$	−22.4718	+	7.30152i	−1.12219	+	0.364621i	−0.311585	+	0.950218i	$0.600860\pi$
$402$	1.02314	+	10.5738i	0.0510296	+	0.527374i
$403$	−5.43810	−	3.95101i	−0.270891	−	0.196814i
$404$	−0.459146	+	0.333589i	−0.0228434	+	0.0165967i
$405$	20.1859	−	8.19965i	1.00304	−	0.407444i
$406$	−22.3413	+	5.61611i	−1.10878	+	0.278723i
$407$	−12.5811	−	3.47973i	−0.623621	−	0.172484i
$408$	14.8808	+	3.29169i	0.736711	+	0.162963i
$409$	−7.55980	−	2.45633i	−0.373808	−	0.121458i	0.116087	−	0.993239i	$-0.462965\pi$
$409$	−7.55980	−	2.45633i	−0.373808	−	0.121458i	−0.489895	+	0.871781i	$0.662965\pi$
$410$	24.5183	+	33.7465i	1.21087	+	1.66662i
$411$	−2.28697	−	2.58252i	−0.112808	−	0.127386i
$412$	−1.64070	+	0.533097i	−0.0808316	+	0.0262638i
$413$	10.2398	+	16.3170i	0.503868	+	0.802907i
$414$	−2.57314	−	4.63183i	−0.126463	−	0.227642i
$415$	−26.2265	+	19.0547i	−1.28741	+	0.935357i
$416$	−1.30096	+	4.00393i	−0.0637846	+	0.196309i
$417$	−4.80791	−	1.06352i	−0.235444	−	0.0520810i
$418$	24.6146	+	30.9011i	1.20394	+	1.51142i
$419$	14.4830			0.707543			0.353771	−	0.935332i	$-0.384899\pi$
$419$	14.4830			0.707543			0.353771	+	0.935332i	$0.384899\pi$
$420$	−4.73748	−	1.39096i	−0.231166	−	0.0678720i
$421$	18.5517	−	13.4786i	0.904156	−	0.656908i	−0.0353738	−	0.999374i	$-0.511262\pi$
$421$	18.5517	−	13.4786i	0.904156	−	0.656908i	0.939530	+	0.342466i	$0.111262\pi$
$422$	8.76440	−	12.0632i	0.426644	−	0.587226i
$423$	−1.98715	+	16.3103i	−0.0966184	+	0.793035i
$424$	0.670621	+	2.06396i	0.0325682	+	0.100235i
$425$	−2.51947	−	1.83050i	−0.122212	−	0.0887924i
$426$	−2.31066	−	5.30736i	−0.111952	−	0.257143i
$427$	18.5736	+	1.26280i	0.898841	+	0.0611113i
$428$		−	3.93513i		−	0.190212i
$429$	4.29541	+	8.78113i	0.207384	+	0.423957i
$430$			42.3563i			2.04260i
$431$	−25.8047	−	8.38445i	−1.24297	−	0.403865i	−0.387572	−	0.921839i	$-0.626686\pi$
$431$	−25.8047	−	8.38445i	−1.24297	−	0.403865i	−0.855396	+	0.517975i	$0.826686\pi$
$432$	0.603962	−	24.3731i	0.0290581	−	1.17265i
$433$	3.19563	−	4.39840i	0.153572	−	0.211374i	−0.725298	−	0.688435i	$-0.758298\pi$
$433$	3.19563	−	4.39840i	0.153572	−	0.211374i	0.878870	+	0.477061i	$0.158298\pi$
$434$	−8.68666	−	13.8421i	−0.416973	−	0.664441i
$435$	2.24869	+	23.2394i	0.107816	+	1.11425i
$436$	2.65162	+	1.92652i	0.126990	+	0.0922634i
$437$	6.96108	−	5.05752i	0.332993	−	0.241934i
$438$	12.1152	+	7.12874i	0.578885	+	0.340624i
$439$			12.5681i			0.599843i	0.953964	+	0.299921i	$0.0969604\pi$
$439$			12.5681i			0.599843i	−0.953964	+	0.299921i	$0.903040\pi$
$440$	5.20407	−	18.8155i	0.248094	−	0.896993i
$441$	−20.9657	+	1.19958i	−0.998367	+	0.0571230i
$442$	2.97570	−	9.15826i	0.141540	−	0.435614i
$443$	−5.40454	−	7.43871i	−0.256777	−	0.353424i	0.661093	−	0.750304i	$-0.270093\pi$
$443$	−5.40454	−	7.43871i	−0.256777	−	0.353424i	−0.917870	+	0.396880i	$0.870093\pi$
$444$	2.27138	−	2.01145i	0.107795	−	0.0954591i
$445$	−9.31015	−	28.6537i	−0.441343	−	1.35832i
$446$	−6.42266	−	19.7669i	−0.304122	−	0.935990i
$447$	−13.5665	−	15.3197i	−0.641674	−	0.724597i
$448$	9.35848	−	11.1968i	0.442147	−	0.528999i
$449$	27.2749	+	8.86215i	1.28718	+	0.418231i	0.871104	−	0.491099i	$-0.163405\pi$
$449$	27.2749	+	8.86215i	1.28718	+	0.418231i	0.416077	+	0.909329i	$0.363405\pi$
$450$	−1.70259	+	3.66016i	−0.0802608	+	0.172542i
$451$	20.1508	−	30.4900i	0.948863	−	1.43572i
$452$		−	4.44020i		−	0.208849i
$453$	−10.5343	−	6.19852i	−0.494944	−	0.291232i
$454$	−1.81068	−	2.49218i	−0.0849793	−	0.116964i
$455$	4.06342	−	10.1134i	0.190496	−	0.474126i
$456$	31.9316	−	3.08975i	1.49533	−	0.144691i
$457$	2.42684	+	7.46905i	0.113523	+	0.349387i	0.991636	−	0.129066i	$-0.0411978\pi$
$457$	2.42684	+	7.46905i	0.113523	+	0.349387i	−0.878113	+	0.478453i	$0.841198\pi$
$458$	−35.6443	−	25.8971i	−1.66555	−	1.21009i
$459$	−0.465833	+	18.7989i	−0.0217432	+	0.877456i
$460$	1.15743	+	0.376071i	0.0539653	+	0.0175344i
$461$	−6.43738			−0.299819			−0.149909	−	0.988700i	$-0.547898\pi$
$461$	−6.43738			−0.299819			−0.149909	+	0.988700i	$0.547898\pi$
$462$	1.73093	+	23.7026i	0.0805301	+	1.10275i
$463$	−21.3802			−0.993624			−0.496812	−	0.867858i	$-0.665496\pi$
$463$	−21.3802			−0.993624			−0.496812	+	0.867858i	$0.665496\pi$
$464$	24.8479	+	8.07356i	1.15353	+	0.374806i
$465$	−15.1862	+	6.61162i	−0.704244	+	0.306606i
$466$	29.5481	+	21.4679i	1.36879	+	0.994483i
$467$	2.44127	+	7.51345i	0.112968	+	0.347681i	0.991518	−	0.129970i	$-0.0414882\pi$
$467$	2.44127	+	7.51345i	0.112968	+	0.347681i	−0.878549	+	0.477651i	$0.841488\pi$
$468$	−2.25541	−	0.274785i	−0.104256	−	0.0127019i
$469$	−9.62945	−	3.86896i	−0.444647	−	0.178652i
$470$	−12.1863	−	16.7731i	−0.562114	−	0.773684i
$471$	5.74378	−	9.76146i	0.264660	−	0.449784i
$472$		−	17.7032i		−	0.814857i
$473$	34.7517	−	13.0204i	1.59789	−	0.598677i
$474$	−5.16338	−	1.14216i	−0.237162	−	0.0524610i
$475$	−6.23448	−	2.02571i	−0.286058	−	0.0929458i
$476$	2.73291	−	3.26974i	0.125263	−	0.149868i
$477$	−2.34074	+	1.30036i	−0.107175	+	0.0595394i
$478$	−13.6726	−	42.0799i	−0.625369	−	1.92469i
$479$	4.18337	+	12.8751i	0.191143	+	0.588278i	1.00000		0.000272461i	$8.67269e-5\pi$
$479$	4.18337	+	12.8751i	0.191143	+	0.588278i	−0.808857	+	0.588006i	$0.799913\pi$
$480$	6.87743	+	7.76618i	0.313910	+	0.354476i
$481$	3.93664	+	5.41831i	0.179495	+	0.247054i
$482$	3.15840	−	9.72057i	0.143861	−	0.442760i
$483$	5.17398	−	0.147897i	0.235424	−	0.00672956i
$484$	4.87652	−	0.433395i	0.221660	−	0.0196998i
$485$			23.5742i			1.07045i
$486$	24.0314	−	4.07936i	1.09009	−	0.185044i
$487$	23.9925	−	17.4316i	1.08720	−	0.789901i	0.108280	−	0.994120i	$-0.465466\pi$
$487$	23.9925	−	17.4316i	1.08720	−	0.789901i	0.978925	+	0.204220i	$0.0654658\pi$
$488$	−13.8409	−	10.0560i	−0.626548	−	0.455214i
$489$	−21.0012	+	2.03212i	−0.949708	+	0.0918954i
$490$	18.3334	−	19.1319i	0.828216	−	0.864290i
$491$	8.95704	−	12.3283i	0.404226	−	0.556369i	−0.557573	−	0.830128i	$-0.688267\pi$
$491$	8.95704	−	12.3283i	0.404226	−	0.556369i	0.961798	+	0.273759i	$0.0882672\pi$
$492$	3.39087	+	7.78848i	0.152872	+	0.351132i
$493$	−19.1650	−	6.22710i	−0.863150	−	0.280454i
$494$		−	20.2698i		−	0.911982i
$495$	24.0160	+	1.85086i	1.07944	+	0.0831899i
$496$			18.5342i			0.832210i
$497$	5.64171	+	0.383574i	0.253065	+	0.0172057i
$498$	−33.2529	+	14.4773i	−1.49010	+	0.648743i
$499$	6.35906	+	4.62013i	0.284671	+	0.206825i	0.720952	−	0.692985i	$-0.243705\pi$
$499$	6.35906	+	4.62013i	0.284671	+	0.206825i	−0.436281	+	0.899810i	$0.643705\pi$
$500$	1.37823	+	4.24175i	0.0616362	+	0.189697i
$501$	−20.8900	+	2.02135i	−0.933296	+	0.0903074i
$502$	−26.4793	+	36.4456i	−1.18183	+	1.62665i
$503$	−19.4703	+	14.1460i	−0.868139	+	0.630740i	−0.930087	−	0.367340i	$-0.880269\pi$
$503$	−19.4703	+	14.1460i	−0.868139	+	0.630740i	0.0619481	+	0.998079i	$0.480269\pi$
$504$	16.9057	+	9.30777i	0.753041	+	0.414601i
$505$	−3.08700			−0.137370
$506$	−0.259536	−	5.85205i	−0.0115378	−	0.260155i
$507$	−3.77993	+	17.0881i	−0.167873	+	0.758907i
$508$	−1.61448	+	4.96886i	−0.0716310	+	0.220458i
$509$	33.3855	−	24.2560i	1.47979	−	1.07513i	0.502161	−	0.864774i	$-0.332538\pi$
$509$	33.3855	−	24.2560i	1.47979	−	1.07513i	0.977625	−	0.210354i	$-0.0674617\pi$
$510$	−15.7309	−	17.7637i	−0.696574	−	0.786591i
$511$	−11.6313	+	7.29928i	−0.514539	+	0.322901i
$512$	−10.6598	+	3.46357i	−0.471099	+	0.153069i
$513$	11.2955	+	37.9371i	0.498708	+	1.67496i
$514$	−9.47102	−	13.0357i	−0.417749	−	0.574982i
$515$	−8.92428	−	2.89967i	−0.393251	−	0.127775i
$516$	−1.86298	+	8.42203i	−0.0820131	+	0.370759i
$517$	−10.0156	+	15.1545i	−0.440484	+	0.666493i
$518$	3.96957	+	15.7913i	0.174413	+	0.693829i
$519$	−19.3188	−	11.3674i	−0.848000	−	0.498975i
$520$	−8.10329	+	5.88739i	−0.355353	+	0.258179i
$521$	−22.4687	−	16.3245i	−0.984372	−	0.715188i	−0.0256903	−	0.999670i	$-0.508178\pi$
$521$	−22.4687	−	16.3245i	−0.984372	−	0.715188i	−0.958681	+	0.284482i	$0.908178\pi$
$522$	−3.15904	+	25.9291i	−0.138267	+	1.13489i
$523$	22.0175	−	7.15393i	0.962760	−	0.312820i	0.214870	−	0.976643i	$-0.431067\pi$
$523$	22.0175	−	7.15393i	0.962760	−	0.312820i	0.747890	+	0.663823i	$0.231067\pi$
$524$	4.84319	+	3.51878i	0.211576	+	0.153719i
$525$	−2.40812	−	3.12280i	−0.105099	−	0.136290i
$526$	10.9050	−	33.5621i	0.475479	−	1.46338i
$527$		−	14.2953i		−	0.622715i
$528$	12.6265	−	23.8134i	0.549499	−	1.03634i
$529$	21.7242			0.944530
$530$	1.04408	−	3.21335i	0.0453520	−	0.139579i
$531$	21.4380	−	4.18797i	0.930329	−	0.181742i
$532$	3.34424	−	8.32346i	0.144991	−	0.360868i
$533$	−17.8337	+	5.79453i	−0.772464	+	0.250989i
$534$	−3.24633	−	33.5497i	−0.140482	−	1.45184i
$535$	12.5812	−	17.3165i	0.543931	−	0.748656i
$536$	5.60564	+	7.71549i	0.242127	+	0.333259i
$537$	−11.9415	+	20.2944i	−0.515315	+	0.875769i
$538$		−	31.9924i		−	1.37929i
$539$	−21.3327	−	9.16065i	−0.918863	−	0.394577i
$540$	−3.40194	+	4.44642i	−0.146396	+	0.191343i
$541$	−3.00532	+	9.24943i	−0.129209	+	0.397664i	−0.994644	−	0.103356i	$-0.967042\pi$
$541$	−3.00532	+	9.24943i	−0.129209	+	0.397664i	0.865436	+	0.501020i	$0.167042\pi$
$542$	16.1516	−	11.7348i	0.693770	−	0.504053i
$543$	13.4715	+	15.2124i	0.578117	+	0.652826i
$544$	−8.51514	+	2.76674i	−0.365084	+	0.118623i
$545$	5.50909	+	16.9552i	0.235983	+	0.726282i
$546$	6.88244	−	10.0656i	0.294541	−	0.430769i
$547$	1.63089	−	1.18491i	0.0697316	−	0.0506630i	−0.552373	−	0.833597i	$-0.686278\pi$
$547$	1.63089	−	1.18491i	0.0697316	−	0.0506630i	0.622105	+	0.782934i	$0.286278\pi$
$548$	0.843020	+	0.273914i	0.0360120	+	0.0117010i
$549$	8.90319	−	19.1397i	0.379979	−	0.816864i
$550$	−3.49073	+	2.78057i	−0.148845	+	0.118564i
$551$	−42.4176			−1.80705
$552$	−4.09969	−	2.41231i	−0.174494	−	0.102675i
$553$	3.31297	−	3.96375i	0.140882	−	0.168556i
$554$	9.54563	−	13.1384i	0.405555	−	0.558199i
$555$	16.4261	−	1.58942i	0.697248	−	0.0674670i
$556$	1.20337	−	0.391000i	0.0510344	−	0.0165821i
$557$	21.8652	−	30.0949i	0.926459	−	1.27516i	−0.0347659	−	0.999395i	$-0.511069\pi$
$557$	21.8652	−	30.0949i	0.926459	−	1.27516i	0.961225	−	0.275766i	$-0.0889314\pi$
$558$	−18.1863	+	3.55275i	−0.769889	+	0.150400i
$559$	−18.1087	−	5.88389i	−0.765918	−	0.248862i
$560$	−29.1457	+	7.32658i	−1.23163	+	0.309604i
$561$	−9.73877	+	18.3671i	−0.411171	+	0.775461i
$562$	−24.6237			−1.03869
$563$	0.767081	−	2.36083i	0.0323286	−	0.0994972i	−0.933590	−	0.358343i	$-0.883342\pi$
$563$	0.767081	−	2.36083i	0.0323286	−	0.0994972i	0.965919	+	0.258845i	$0.0833420\pi$
$564$	−1.68537	−	3.87112i	−0.0709667	−	0.163003i
$565$	14.1959	−	19.5390i	0.597227	−	0.822013i
$566$	2.08588	+	6.41969i	0.0876762	+	0.269840i
$567$	−7.27208	+	22.6741i	−0.305399	+	0.952225i
$568$	−4.20415	−	3.05449i	−0.176402	−	0.128164i
$569$	9.71819	+	13.3759i	0.407408	+	0.560749i	0.962584	−	0.270984i	$-0.0873491\pi$
$569$	9.71819	+	13.3759i	0.407408	+	0.560749i	−0.555176	+	0.831733i	$0.687349\pi$
$570$	−43.0468	−	25.3293i	−1.80303	−	1.06093i
$571$	−36.0650			−1.50927			−0.754636	−	0.656143i	$-0.772187\pi$
$571$	−36.0650			−1.50927			−0.754636	+	0.656143i	$0.772187\pi$
$572$	−2.09558	−	1.38496i	−0.0876205	−	0.0579082i
$573$	11.3492	+	2.51048i	0.474120	+	0.104877i
$574$	−45.4831	−	3.09235i	−1.89843	−	0.129072i
$575$	0.571320	+	0.786355i	0.0238257	+	0.0327933i
$576$	−8.03553	−	14.4645i	−0.334814	−	0.602688i
$577$	−35.7475	+	11.6151i	−1.48819	+	0.483542i	−0.936548	−	0.350540i	$-0.885998\pi$
$577$	−35.7475	+	11.6151i	−1.48819	+	0.483542i	−0.551641	+	0.834082i	$0.685998\pi$
$578$	−5.80454	+	1.88601i	−0.241437	+	0.0784477i
$579$	−15.6530	+	13.8617i	−0.650518	+	0.576074i
$580$	−3.52641	−	4.85369i	−0.146426	−	0.201538i
$581$	2.40326	−	35.3478i	0.0997039	−	1.46647i
$582$	−5.69630	+	25.7514i	−0.236119	+	1.06743i
$583$	−2.95738	+	0.131158i	−0.122482	+	0.00543203i
$584$	12.6195			0.522197
$585$	−9.04637	−	8.42005i	−0.374022	−	0.348126i
$586$	4.31205	+	5.93502i	0.178129	+	0.245174i
$587$	2.77191	+	2.01391i	0.114409	+	0.0831229i	0.643518	−	0.765431i	$-0.277474\pi$
$587$	2.77191	+	2.01391i	0.114409	+	0.0831229i	−0.529110	+	0.848553i	$0.677474\pi$
$588$	4.48685	−	2.99777i	0.185035	−	0.123626i
$589$	−9.29864	−	28.6183i	−0.383144	−	1.17920i
$590$	−16.2005	+	22.2981i	−0.666964	+	0.917997i
$591$	−17.1582	+	7.47017i	−0.705796	+	0.307282i
$592$	5.70655	−	17.5629i	0.234538	−	0.721832i
$593$	31.0208			1.27387			0.636937	−	0.770916i	$-0.280201\pi$
$593$	31.0208			1.27387			0.636937	+	0.770916i	$0.280201\pi$
$594$	25.7868	+	7.82484i	1.05804	+	0.321057i
$595$	22.4799	−	5.65096i	0.921588	−	0.231667i
$596$	5.00087	+	1.62488i	0.204843	+	0.0665577i
$597$	27.4757	−	11.9621i	1.12450	−	0.489575i
$598$	−1.76659	+	2.43150i	−0.0722411	+	0.0994314i
$599$	5.14503	−	1.67172i	0.210220	−	0.0683048i	−0.202014	−	0.979383i	$-0.564749\pi$
$599$	5.14503	−	1.67172i	0.210220	−	0.0683048i	0.412234	+	0.911078i	$0.364749\pi$
$600$	0.349033	+	3.60713i	0.0142492	+	0.147261i
$601$	12.6605	−	17.4257i	0.516433	−	0.710810i	−0.468554	−	0.883435i	$-0.655225\pi$
$601$	12.6605	−	17.4257i	0.516433	−	0.710810i	0.984988	+	0.172625i	$0.0552249\pi$
$602$	−35.5184	−	29.6870i	−1.44762	−	1.20995i
$603$	−8.01709	+	8.61344i	−0.326481	+	0.350767i
$604$	3.14072			0.127794
$605$	22.8447	+	13.6838i	0.928768	+	0.556324i
$606$	−3.37210	−	0.745919i	−0.136982	−	0.0303009i
$607$	−45.1530	−	14.6711i	−1.83270	−	0.595482i	−0.999068	−	0.0431689i	$-0.986255\pi$
$607$	−45.1530	−	14.6711i	−1.83270	−	0.595482i	−0.833637	−	0.552313i	$-0.813745\pi$
$608$	−15.2471	+	11.0776i	−0.618350	+	0.449257i
$609$	−21.0638	−	14.4025i	−0.853549	−	0.583621i
$610$	8.23087	+	25.3320i	0.333258	+	1.02566i
$611$	8.86391	−	2.88006i	0.358595	−	0.116515i
$612$	−2.34657	−	4.22400i	−0.0948547	−	0.170745i
$613$	6.22409	−	4.52207i	0.251389	−	0.182645i	−0.454953	−	0.890515i	$-0.650344\pi$
$613$	6.22409	−	4.52207i	0.251389	−	0.182645i	0.706342	+	0.707871i	$0.250344\pi$
$614$	0.814519	−	2.50683i	0.0328713	−	0.101168i
$615$	−9.97941	+	45.1142i	−0.402409	+	1.81918i
$616$	12.1305	+	17.5515i	0.488752	+	0.707168i
$617$		−	9.75410i		−	0.392685i	−0.980535	−	0.196343i	$-0.937094\pi$
$617$		−	9.75410i		−	0.392685i	0.980535	−	0.196343i	$-0.0629065\pi$
$618$	−9.04782	−	5.32387i	−0.363957	−	0.214157i
$619$	24.3094	+	33.4590i	0.977077	+	1.34483i	0.938389	+	0.345579i	$0.112318\pi$
$619$	24.3094	+	33.4590i	0.977077	+	1.34483i	0.0386873	+	0.999251i	$0.487682\pi$
$620$	2.50164	−	3.44321i	0.100468	−	0.138282i
$621$	1.95138	−	5.53525i	0.0783063	−	0.222122i
$622$	33.1072	−	10.7572i	1.32748	−	0.431323i
$623$	30.5533	+	12.2758i	1.22409	+	0.491821i
$624$	−12.6797	+	5.52037i	−0.507596	+	0.220992i
$625$	−8.82619	+	27.1642i	−0.353048	+	1.08657i
$626$	15.1915			0.607175
$627$	−7.54913	+	43.1045i	−0.301483	+	1.72143i
$628$			2.91031i			0.116134i
$629$	−4.40143	+	13.5462i	−0.175497	+	0.540123i
$630$	−12.7759	−	27.1943i	−0.509004	−	1.08345i
$631$	4.01833	+	2.91949i	0.159967	+	0.116223i	0.664889	−	0.746942i	$-0.268479\pi$
$631$	4.01833	+	2.91949i	0.159967	+	0.116223i	−0.504922	+	0.863165i	$0.668479\pi$
$632$	−4.51508	+	1.46704i	−0.179600	+	0.0583556i
$633$	16.4397	−	1.59074i	0.653421	−	0.0632262i
$634$	−18.6567	−	13.5549i	−0.740951	−	0.538332i
$635$	−22.9907	+	16.7037i	−0.912356	+	0.662866i
$636$	0.348937	−	0.593013i	0.0138363	−	0.0235145i
$637$	5.63276	+	10.4958i	0.223178	+	0.415859i
$638$	−15.9221	+	24.0916i	−0.630362	+	0.953796i
$639$	2.70433	−	5.81366i	0.106982	−	0.229985i
$640$	31.2490	+	10.1534i	1.23523	+	0.401349i
$641$	13.4792	+	18.5525i	0.532396	+	0.732781i	0.987493	−	0.157661i	$-0.0503954\pi$
$641$	13.4792	+	18.5525i	0.532396	+	0.732781i	−0.455097	+	0.890442i	$0.650395\pi$
$642$	17.9273	−	15.8757i	0.707535	−	0.626565i
$643$	18.6976	−	6.07523i	0.737363	−	0.239584i	0.0838280	−	0.996480i	$-0.473285\pi$
$643$	18.6976	−	6.07523i	0.737363	−	0.239584i	0.653535	+	0.756897i	$0.273285\pi$
$644$	−1.12658	+	0.706992i	−0.0443936	+	0.0278594i
$645$	−35.1244	+	31.1048i	−1.38302	+	1.22475i
$646$	34.8748	−	25.3381i	1.37213	−	0.996913i
$647$	−8.27933	+	25.4812i	−0.325494	+	1.00177i	0.645723	+	0.763572i	$0.276556\pi$
$647$	−8.27933	+	25.4812i	−0.325494	+	1.00177i	−0.971217	+	0.238196i	$0.923444\pi$
$648$	16.7367	−	14.0973i	0.657479	−	0.553793i
$649$	23.2747	+	6.43744i	0.913614	+	0.252691i
$650$	2.28977			0.0898122
$651$	5.09956	−	17.3686i	0.199867	−	0.680729i
$652$	4.38622	−	3.18678i	0.171778	−	0.124804i
$653$	20.8925	−	28.7560i	0.817586	−	1.12531i	−0.172522	−	0.985006i	$-0.555192\pi$
$653$	20.8925	−	28.7560i	0.817586	−	1.12531i	0.990108	−	0.140305i	$-0.0448084\pi$
$654$	1.92095	+	19.8523i	0.0751149	+	0.776287i
$655$	10.0623	+	30.9687i	0.393168	+	1.21005i
$656$	41.8290	+	30.3906i	1.63315	+	1.18655i
$657$	2.98532	+	15.2817i	0.116469	+	0.596196i
$658$	22.6065	+	1.53699i	0.881294	+	0.0599182i
$659$		−	21.2490i		−	0.827744i	−0.910335	−	0.413872i	$-0.864176\pi$
$659$		−	21.2490i		−	0.827744i	0.910335	−	0.413872i	$-0.135824\pi$
$660$	−5.55989	+	2.71970i	−0.216418	+	0.105864i
$661$			30.5091i			1.18666i	0.804958	+	0.593332i	$0.202188\pi$
$661$			30.5091i			1.18666i	−0.804958	+	0.593332i	$0.797812\pi$
$662$	0.867037	+	0.281717i	0.0336983	+	0.0109493i
$663$	9.77983	−	4.25784i	0.379817	−	0.165361i
$664$	−19.1377	+	26.3408i	−0.742687	+	1.02222i
$665$	41.3275	−	25.9353i	1.60261	−	1.00573i
$666$	18.3272	+	2.23287i	0.710163	+	0.0865219i
$667$	5.08828	+	3.69685i	0.197019	+	0.143143i
$668$	4.36299	−	3.16990i	0.168809	−	0.122647i
$669$	11.6754	−	19.8421i	0.451396	−	0.767140i
$670$		−	14.8478i		−	0.573622i
$671$	18.2538	−	14.5402i	0.704679	−	0.561318i
$672$	−11.3327	+	0.323944i	−0.437170	+	0.0124964i
$673$	0.965070	−	2.97018i	0.0372007	−	0.114492i	−0.930732	−	0.365703i	$-0.880829\pi$
$673$	0.965070	−	2.97018i	0.0372007	−	0.114492i	0.967932	+	0.251211i	$0.0808287\pi$
$674$	2.70954	+	3.72936i	0.104368	+	0.143650i
$675$	−4.28554	+	1.27599i	−0.164951	+	0.0491128i
$676$	−1.38968	−	4.27698i	−0.0534490	−	0.164499i
$677$	2.15657	+	6.63726i	0.0828839	+	0.255090i	0.983907	−	0.178680i	$-0.0571828\pi$
$677$	2.15657	+	6.63726i	0.0828839	+	0.255090i	−0.901023	+	0.433771i	$0.857183\pi$
$678$	20.2283	−	17.9134i	0.776862	−	0.687959i
$679$	−19.7685	−	16.5229i	−0.758645	−	0.634089i
$680$	−20.2589	−	6.58251i	−0.776892	−	0.252428i
$681$	0.736980	−	3.33169i	0.0282411	−	0.127671i
$682$	−19.7445	−	5.46102i	−0.756056	−	0.209113i
$683$		−	8.24938i		−	0.315654i	−0.987467	−	0.157827i	$-0.949551\pi$
$683$		−	8.24938i		−	0.315654i	0.987467	−	0.157827i	$-0.0504488\pi$
$684$	−7.44525	−	6.92978i	−0.284676	−	0.264967i
$685$	2.83396	+	3.90061i	0.108280	+	0.149035i
$686$	3.19370	+	28.7830i	0.121936	+	1.09894i
$687$	−4.70033	−	48.5763i	−0.179329	−	1.85330i
$688$	16.2237	+	49.9313i	0.618521	+	1.90361i
$689$	1.22878	+	0.892760i	0.0468127	+	0.0340114i
$690$	2.95621	+	6.79011i	0.112541	+	0.258495i
$691$	20.1356	+	6.54244i	0.765993	+	0.248886i	0.665849	−	0.746087i	$-0.268070\pi$
$691$	20.1356	+	6.54244i	0.765993	+	0.248886i	0.100144	+	0.994973i	$0.468070\pi$
$692$	5.75976			0.218953
$693$	−18.3845	+	18.8417i	−0.698371	+	0.715736i
$694$	18.4968			0.702129
$695$	6.54551	+	2.12677i	0.248285	+	0.0806728i
$696$	9.36063	+	21.5004i	0.354814	+	0.814972i
$697$	−32.2625	−	23.4401i	−1.22203	−	0.887857i
$698$	5.95966	+	18.3420i	0.225577	+	0.694253i
$699$	3.89643	+	40.2683i	0.147377	+	1.52309i
$700$	0.940256	+	0.377780i	0.0355383	+	0.0142787i
$701$	18.0945	+	24.9049i	0.683420	+	0.940647i	0.999969	−	0.00792951i	$-0.00252407\pi$
$701$	18.0945	+	24.9049i	0.683420	+	0.940647i	−0.316549	+	0.948576i	$0.602524\pi$
$702$	−7.84730	−	11.3836i	−0.296177	−	0.429646i
$703$			29.9816i			1.13078i
$704$	−0.810490	−	18.2751i	−0.0305465	−	0.688767i
$705$	4.96007	−	22.4231i	0.186807	−	0.844505i
$706$	15.0160	+	4.87901i	0.565136	+	0.183624i
$707$	2.16363	−	2.58864i	0.0813718	−	0.0973559i
$708$	−4.20202	+	3.72114i	−0.157921	+	0.139849i
$709$	4.04296	+	12.4429i	0.151836	+	0.467305i	0.997827	−	0.0658938i	$-0.0209899\pi$
$709$	4.04296	+	12.4429i	0.151836	+	0.467305i	−0.845990	+	0.533199i	$0.820990\pi$
$710$	2.50011	+	7.69456i	0.0938276	+	0.288772i
$711$	−2.84464	−	5.12055i	−0.106682	−	0.192036i
$712$	−17.7861	−	24.4805i	−0.666563	−	0.917446i
$713$	−1.37875	+	4.24336i	−0.0516347	+	0.158915i
$714$	25.9215	−	0.740963i	0.970090	−	0.0277298i
$715$	−4.79364	−	12.7944i	−0.179272	−	0.478482i
$716$		−	6.05064i		−	0.226123i
$717$	24.8546	−	42.2399i	0.928211	−	1.57748i
$718$	−11.7152	+	8.51161i	−0.437208	+	0.317650i
$719$	−12.4746	−	9.06336i	−0.465226	−	0.338006i	0.330352	−	0.943858i	$-0.392833\pi$
$719$	−12.4746	−	9.06336i	−0.465226	−	0.338006i	−0.795578	+	0.605852i	$0.792833\pi$
$720$	−4.12117	+	33.8262i	−0.153587	+	1.26063i
$721$	8.68646	−	5.45123i	0.323501	−	0.203014i
$722$	35.8725	−	49.3743i	1.33504	−	1.83752i
$723$	10.3803	−	4.51926i	0.386047	−	0.168073i
$724$	−4.96584	−	1.61350i	−0.184554	−	0.0599652i
$725$		−	4.79169i		−	0.177959i
$726$	21.6481	+	20.4676i	0.803435	+	0.759622i
$727$			35.7566i			1.32614i	0.748558	+	0.663069i	$0.230747\pi$
$727$			35.7566i			1.32614i	−0.748558	+	0.663069i	$0.769253\pi$
$728$	0.742542	−	10.9215i	0.0275204	−	0.404778i
$729$	21.0306	+	16.9326i	0.778912	+	0.627134i
$730$	−15.8948	−	11.5483i	−0.588293	−	0.427420i
$731$	−12.5132	−	38.5118i	−0.462819	−	1.42441i
$732$	0.522415	+	5.39898i	0.0193090	+	0.199552i
$733$	17.8551	−	24.5754i	0.659492	−	0.907713i	−0.339972	−	0.940436i	$-0.610418\pi$
$733$	17.8551	−	24.5754i	0.659492	−	0.907713i	0.999464	+	0.0327221i	$0.0104176\pi$
$734$	−36.4827	+	26.5062i	−1.34660	+	0.978363i
$735$	29.3286	+	1.15343i	1.08180	+	0.0425448i
$736$	2.79444			0.103004
$737$	−12.1821	+	4.56424i	−0.448733	+	0.168126i
$738$	−21.8021	+	46.8694i	−0.802547	+	1.72529i
$739$	−15.5519	+	47.8638i	−0.572086	+	1.76070i	0.0738079	+	0.997272i	$0.476485\pi$
$739$	−15.5519	+	47.8638i	−0.572086	+	1.76070i	−0.645894	+	0.763427i	$0.723515\pi$
$740$	−3.43068	+	2.49253i	−0.126114	+	0.0916274i
$741$	16.8090	−	14.8854i	0.617493	−	0.546827i
$742$	1.96282	+	3.12772i	0.0720572	+	0.114822i
$743$	8.04010	−	2.61239i	0.294963	−	0.0958392i	−0.157798	−	0.987471i	$-0.550439\pi$
$743$	8.04010	−	2.61239i	0.294963	−	0.0958392i	0.452760	+	0.891632i	$0.350439\pi$
$744$	−12.4539	+	11.0287i	−0.456582	+	0.404331i
$745$	16.8113	+	23.1387i	0.615918	+	0.847738i
$746$	−11.9894	−	3.89560i	−0.438964	−	0.142628i
$747$	−36.4251	−	16.9438i	−1.33272	−	0.619940i
$748$	−0.236683	−	5.33677i	−0.00865399	−	0.195132i
$749$	5.70300	+	22.6870i	0.208383	+	0.828964i
$750$	−13.7639	+	23.3916i	−0.502587	+	0.854139i
$751$	−32.6330	+	23.7093i	−1.19079	+	0.865163i	−0.993348	−	0.115150i	$-0.963265\pi$
$751$	−32.6330	+	23.7093i	−1.19079	+	0.865163i	−0.197447	+	0.980314i	$0.563265\pi$
$752$	−20.7903	−	15.1050i	−0.758145	−	0.550824i
$753$	−49.6683	+	4.80599i	−1.81001	+	0.175140i
$754$	14.0913	−	4.57853i	0.513174	−	0.166740i
$755$	13.8207	+	10.0413i	0.502987	+	0.365442i
$756$	−1.34423	−	5.96918i	−0.0488891	−	0.217097i
$757$	−12.9897	+	39.9783i	−0.472120	+	1.45304i	0.377683	+	0.925935i	$0.376721\pi$
$757$	−12.9897	+	39.9783i	−0.472120	+	1.45304i	−0.849803	+	0.527100i	$0.823279\pi$
$758$		−	13.3077i		−	0.483356i
$759$	4.66228	−	4.51274i	0.169230	−	0.163802i
$760$	−44.8386			−1.62647
$761$	−5.49052	+	16.8981i	−0.199031	+	0.612555i	0.800875	+	0.598832i	$0.204368\pi$
$761$	−5.49052	+	16.8981i	−0.199031	+	0.612555i	−0.999906	+	0.0137231i	$0.995632\pi$
$762$	−29.1501	+	12.6911i	−1.05600	+	0.459749i
$763$	−18.0793	−	7.26397i	−0.654514	−	0.262973i
$764$	−2.84060	+	0.922967i	−0.102769	+	0.0333918i
$765$	3.17864	−	26.0900i	0.114924	−	0.943285i
$766$	20.8582	−	28.7088i	0.753637	−	1.03729i
$767$	−7.28270	−	10.0238i	−0.262963	−	0.361937i
$768$	15.2144	+	8.95238i	0.549003	+	0.323041i
$769$			29.3448i			1.05820i	0.848559	+	0.529101i	$0.177471\pi$
$769$			29.3448i			1.05820i	−0.848559	+	0.529101i	$0.822529\pi$
$770$	0.782651	−	33.2077i	0.0282048	−	1.19672i
$771$	3.85489	−	17.4269i	0.138830	−	0.627614i
$772$	1.66024	−	5.10968i	0.0597532	−	0.183902i
$773$	31.1817	−	22.6548i	1.12153	−	0.814837i	0.137087	−	0.990559i	$-0.456226\pi$
$773$	31.1817	−	22.6548i	1.12153	−	0.814837i	0.984440	+	0.175722i	$0.0562261\pi$
$774$	−45.8843	+	25.4903i	−1.64928	+	0.916230i
$775$	3.23285	−	1.05042i	0.116127	−	0.0377321i
$776$	7.31658	+	22.5181i	0.262650	+	0.808354i
$777$	−10.1800	+	14.8883i	−0.365205	+	0.534115i
$778$	9.85863	−	7.16271i	0.353449	−	0.256796i
$779$	−79.8343	−	25.9397i	−2.86036	−	0.929388i
$780$	3.10070	+	0.685885i	0.111023	+	0.0245586i
$781$	5.54455	−	4.41656i	0.198400	−	0.158037i
$782$	−6.39177			−0.228569
$783$	−23.8219	+	16.4216i	−0.851324	+	0.586862i
$784$	14.2840	−	29.5756i	0.510144	−	1.05627i
$785$	−9.30468	+	12.8068i	−0.332098	+	0.457094i
$786$	3.50860	+	36.2602i	0.125148	+	1.29336i
$787$	−33.5130	+	10.8890i	−1.19461	+	0.388152i	−0.837775	−	0.546016i	$-0.816144\pi$
$787$	−33.5130	+	10.8890i	−1.19461	+	0.388152i	−0.356833	+	0.934168i	$0.616144\pi$
$788$	2.82649	−	3.89033i	0.100689	−	0.138587i
$789$	35.8399	−	15.6036i	1.27593	−	0.555503i
$790$	7.02946	+	2.28401i	0.250097	+	0.0812615i
$791$	6.43497	+	25.5988i	0.228801	+	0.910190i
$792$	23.5145	−	5.68574i	0.835552	−	0.202034i
$793$	−11.9737			−0.425198
$794$	−3.18283	+	9.79574i	−0.112954	+	0.347638i
$795$	3.43144	−	1.49394i	0.121701	−	0.0529847i
$796$	−4.52608	+	6.22962i	−0.160423	+	0.220803i
$797$	2.90990	+	8.95574i	0.103074	+	0.317229i	0.989274	−	0.146075i	$-0.0466640\pi$
$797$	2.90990	+	8.95574i	0.103074	+	0.317229i	−0.886200	+	0.463303i	$0.846664\pi$
$798$	51.4112	−	18.3445i	1.81994	−	0.649387i
$799$	16.0355	+	11.6505i	0.567294	+	0.412163i
$800$	−1.25138	−	1.72238i	−0.0442430	−	0.0608952i
$801$	25.4375	−	27.3296i	0.898788	−	0.965644i
$802$	36.9468			1.30464
$803$	−4.58882	+	16.5910i	−0.161936	+	0.585484i
$804$	0.653060	−	2.95231i	0.0230317	−	0.104120i
$805$	−7.21787	−	0.490735i	−0.254396	−	0.0172961i
$806$	6.17808	+	8.50340i	0.217614	+	0.299519i
$807$	26.5300	−	23.4940i	0.933902	−	0.827027i
$808$	−2.94870	+	0.958091i	−0.103735	+	0.0337055i
$809$	4.03656	−	1.31156i	0.141918	−	0.0461119i	−0.237197	−	0.971462i	$-0.576229\pi$
$809$	4.03656	−	1.31156i	0.141918	−	0.0461119i	0.379115	+	0.925350i	$0.376229\pi$
$810$	−33.9813	+	2.44019i	−1.19398	+	0.0857395i
$811$	−16.4940	−	22.7020i	−0.579183	−	0.797176i	0.414423	−	0.910084i	$-0.363983\pi$
$811$	−16.4940	−	22.7020i	−0.579183	−	0.797176i	−0.993605	+	0.112908i	$0.963983\pi$
$812$	6.54174	+	0.444766i	0.229570	+	0.0156082i
$813$	21.5923	+	4.77629i	0.757276	+	0.167512i
$814$	17.0284	+	11.2540i	0.596845	+	0.394454i
$815$	29.4901			1.03299
$816$	−25.3482	−	14.9152i	−0.887363	−	0.522137i
$817$	−50.1013	−	68.9585i	−1.75282	−	2.41255i
$818$	10.0556	+	7.30581i	0.351585	+	0.255442i
$819$	13.4012	−	1.68446i	0.468277	−	0.0588597i
$820$	−3.66888	−	11.2917i	−0.128123	−	0.394322i
$821$	−3.70508	+	5.09960i	−0.129308	+	0.177977i	−0.868762	−	0.495230i	$-0.835084\pi$
$821$	−3.70508	+	5.09960i	−0.129308	+	0.177977i	0.739454	+	0.673207i	$0.235084\pi$
$822$	2.15318	+	4.94563i	0.0751006	+	0.172499i
$823$	10.7693	−	33.1446i	0.375395	−	1.15535i	−0.567817	−	0.823155i	$-0.692212\pi$
$823$	10.7693	−	33.1446i	0.375395	−	1.15535i	0.943212	−	0.332192i	$-0.107788\pi$
$824$	−9.42443			−0.328316
$825$	−4.86928	−	0.852785i	−0.169527	−	0.0296902i
$826$	−7.34363	−	29.2135i	−0.255518	−	1.01647i
$827$	31.4307	+	10.2125i	1.09295	+	0.355122i	0.799387	−	0.600817i	$-0.205158\pi$
$827$	31.4307	+	10.2125i	1.09295	+	0.355122i	0.293566	+	0.955939i	$0.405158\pi$
$828$	0.289152	+	1.48015i	0.0100487	+	0.0514389i
$829$	1.38521	−	1.90657i	0.0481102	−	0.0662180i	−0.784284	−	0.620402i	$-0.786970\pi$
$829$	1.38521	−	1.90657i	0.0481102	−	0.0662180i	0.832394	+	0.554184i	$0.186970\pi$
$830$	48.2097	−	15.6643i	1.67338	−	0.543715i
$831$	17.9051	−	1.73253i	0.621122	−	0.0601009i
$832$	−5.51678	+	7.59320i	−0.191260	+	0.263247i
$833$	−11.0172	+	22.8115i	−0.381724	+	0.790373i
$834$	6.63613	+	3.90479i	0.229790	+	0.135212i
$835$	29.3339			1.01514
$836$	−3.94521	−	10.5299i	−0.136448	−	0.364184i
$837$	−16.3015	−	12.4722i	−0.563462	−	0.431103i
$838$	−21.5383	−	6.99822i	−0.744028	−	0.241749i
$839$	20.5876	−	14.9578i	0.710763	−	0.516400i	−0.172657	−	0.984982i	$-0.555235\pi$
$839$	20.5876	−	14.9578i	0.710763	−	0.516400i	0.883420	+	0.468582i	$0.155235\pi$
$840$	−22.2660	−	15.2246i	−0.768251	−	0.525297i
$841$	−0.619771	−	1.90746i	−0.0213714	−	0.0657744i
$842$	−34.1019	+	11.0804i	−1.17523	+	0.381855i
$843$	−18.0827	−	20.4195i	−0.622801	−	0.703285i
$844$	−3.43353	+	2.49461i	−0.118187	+	0.0858680i
$845$	7.55886	−	23.2638i	0.260033	−	0.800299i
$846$	10.8363	−	23.2955i	0.372561	−	0.800917i
$847$	−27.4862	+	9.56594i	−0.944438	+	0.328690i
$848$		−	4.18794i		−	0.143814i
$849$	−3.79181	+	6.44411i	−0.130135	+	0.221161i
$850$	2.86230	+	3.93962i	0.0981762	+	0.135128i
$851$	2.61300	−	3.59649i	0.0895726	−	0.123286i
$852$	0.158683	+	1.63993i	0.00543638	+	0.0561832i
$853$	−32.0548	+	10.4152i	−1.09753	+	0.356611i	−0.801153	−	0.598459i	$-0.795780\pi$
$853$	−32.0548	+	10.4152i	−1.09753	+	0.356611i	−0.296381	+	0.955070i	$0.595780\pi$
$854$	−27.0114	−	10.8528i	−0.924311	−	0.371374i
$855$	−10.6072	−	54.2979i	−0.362760	−	1.85695i
$856$	6.64313	−	20.4454i	0.227057	−	0.698811i
$857$	−13.3423			−0.455763			−0.227882	−	0.973689i	$-0.573180\pi$
$857$	−13.3423			−0.455763			−0.227882	+	0.973689i	$0.573180\pi$
$858$	−2.14483	−	15.1343i	−0.0732231	−	0.516677i
$859$		−	3.03978i		−	0.103716i	−0.998654	−	0.0518580i	$-0.983486\pi$
$859$		−	3.03978i		−	0.103716i	0.998654	−	0.0518580i	$-0.0165143\pi$
$860$	3.72546	−	11.4658i	0.127037	−	0.390981i
$861$	−30.8367	−	39.9883i	−1.05091	−	1.36280i
$862$	34.3238	+	24.9377i	1.16907	+	0.849381i
$863$	−27.6480	+	8.98339i	−0.941150	+	0.305798i	−0.739114	−	0.673580i	$-0.764756\pi$
$863$	−27.6480	+	8.98339i	−0.941150	+	0.305798i	−0.202036	+	0.979378i	$0.564756\pi$
$864$	−4.27417	+	12.1240i	−0.145410	+	0.412467i
$865$	25.3457	+	18.4148i	0.861781	+	0.626121i
$866$	−6.87765	+	4.99691i	−0.233712	+	0.169802i
$867$	−5.82663	−	3.42847i	−0.197883	−	0.116437i
$868$	1.13398	+	4.51108i	0.0384899	+	0.153116i
$869$	−0.286920	−	6.46951i	−0.00973308	−	0.219463i
$870$	7.88521	−	35.6469i	0.267333	−	1.20854i
$871$	6.34795	+	2.06257i	0.215092	+	0.0698877i
$872$	10.5246	+	14.4858i	0.356407	+	0.490552i
$873$	−25.5378	+	14.1871i	−0.864324	+	0.480162i
$874$	−12.7959	+	4.15764i	−0.432827	+	0.140634i
$875$	−14.0932	−	22.4573i	−0.476437	−	0.759196i
$876$	−2.65255	−	2.99534i	−0.0896214	−	0.101203i
$877$	−3.10313	+	2.25456i	−0.104785	+	0.0761310i	−0.638944	−	0.769253i	$-0.720628\pi$
$877$	−3.10313	+	2.25456i	−0.104785	+	0.0761310i	0.534159	+	0.845384i	$0.320628\pi$
$878$	6.07292	−	18.6905i	0.204951	−	0.630774i
$879$	−1.75509	+	7.93426i	−0.0591975	+	0.267616i
$880$	−20.7714	+	31.4291i	−0.700204	+	1.05947i
$881$	−39.7267			−1.33843			−0.669213	−	0.743071i	$-0.733369\pi$
$881$	−39.7267			−1.33843			−0.669213	+	0.743071i	$0.733369\pi$
$882$	31.7586	+	8.34670i	1.06937	+	0.281048i
$883$	9.12448	−	6.62932i	0.307063	−	0.223095i	−0.423572	−	0.905862i	$-0.639224\pi$
$883$	9.12448	−	6.62932i	0.307063	−	0.223095i	0.730635	+	0.682768i	$0.239224\pi$
$884$	−1.61104	+	2.21740i	−0.0541850	+	0.0745793i
$885$	−30.3879	+	2.94039i	−1.02148	+	0.0988401i
$886$	4.44291	+	13.6739i	0.149263	+	0.459383i
$887$	−39.9041	−	28.9920i	−1.33985	−	0.973456i	−0.999450	−	0.0331749i	$-0.989438\pi$
$887$	−39.9041	−	28.9920i	−1.33985	−	0.973456i	−0.340398	−	0.940281i	$-0.610562\pi$
$888$	15.1969	−	6.61627i	0.509975	−	0.222027i
$889$	2.10674	−	30.9865i	0.0706578	−	1.03925i
$890$			47.1107i			1.57915i
$891$	12.4480	+	27.1302i	0.417022	+	0.908896i
$892$			5.91579i			0.198075i
$893$	39.6801	+	12.8929i	1.32785	+	0.431443i
$894$	12.7728	+	29.3379i	0.427187	+	0.981206i
$895$	19.3447	−	26.6258i	0.646624	−	0.890001i
$896$	−30.4163	+	19.0879i	−1.01614	+	0.637681i
$897$	−3.31366	+	0.320636i	−0.110640	+	0.0107057i
$898$	−36.2794	−	26.3585i	−1.21066	−	0.879595i
$899$	17.7946	−	12.9286i	0.593484	−	0.431192i
$900$	0.782819	−	0.841049i	0.0260940	−	0.0280350i
$901$			3.23014i			0.107611i
$902$	−44.6998	+	35.6060i	−1.48834	+	1.18555i
$903$	−1.46511	−	51.2550i	−0.0487560	−	1.70566i
$904$	7.49577	−	23.0696i	0.249306	−	0.767284i
$905$	−16.6935	−	22.9767i	−0.554912	−	0.763770i
$906$	12.6708	+	14.3082i	0.420960	+	0.475359i
$907$	12.7086	+	39.1129i	0.421981	+	1.29872i	0.905856	+	0.423586i	$0.139229\pi$
$907$	12.7086	+	39.1129i	0.421981	+	1.29872i	−0.483876	+	0.875137i	$0.660771\pi$
$908$	0.270947	+	0.833890i	0.00899170	+	0.0276736i
$909$	−1.85777	−	3.34412i	−0.0616185	−	0.110918i
$910$	−10.9297	+	13.0767i	−0.362316	+	0.433487i
$911$	48.8110	+	15.8597i	1.61718	+	0.525454i	0.971274	−	0.237962i	$-0.0764795\pi$
$911$	48.8110	+	15.8597i	1.61718	+	0.525454i	0.645907	+	0.763416i	$0.276480\pi$
$912$	−60.4471	−	13.3711i	−2.00160	−	0.442762i
$913$	−27.6717	−	34.7390i	−0.915798	−	1.14969i
$914$		−	12.2802i		−	0.406192i
$915$	−14.9624	+	25.4284i	−0.494643	+	0.840637i
$916$	7.37108	+	10.1454i	0.243547	+	0.335214i
$917$	−33.0218	−	13.2676i	−1.09047	−	0.438136i
$918$	9.77639	−	27.7315i	0.322669	−	0.915275i
$919$	−11.1434	−	34.2959i	−0.367587	−	1.13132i	−0.948345	−	0.317240i	$-0.897244\pi$
$919$	−11.1434	−	34.2959i	−0.367587	−	1.13132i	0.580758	−	0.814076i	$-0.302756\pi$
$920$	5.37869	+	3.90784i	0.177330	+	0.128838i
$921$	2.67697	−	1.16547i	0.0882092	−	0.0384036i
$922$	9.57328	+	3.11055i	0.315279	+	0.102440i
$923$	−3.63699			−0.119713
$924$	1.61621	−	6.56852i	0.0531695	−	0.216088i
$925$	−3.38685			−0.111359
$926$	31.7954	+	10.3310i	1.04486	+	0.339496i
$927$	−2.22949	−	11.4127i	−0.0732261	−	0.374841i
$928$	−11.1450	−	8.09732i	−0.365853	−	0.265807i
$929$	−5.31968	−	16.3723i	−0.174533	−	0.537158i	0.825079	−	0.565018i	$-0.191131\pi$
$929$	−5.31968	−	16.3723i	−0.174533	−	0.537158i	−0.999612	+	0.0278601i	$0.991131\pi$
$930$	25.7788	−	2.49440i	0.845319	−	0.0817946i
$931$	−7.21754	+	52.8334i	−0.236545	+	1.73155i
$932$	−6.11041	−	8.41026i	−0.200153	−	0.275487i
$933$	33.2331	+	19.5548i	1.08800	+	0.640197i
$934$		−	12.3532i		−	0.404208i
$935$	16.0209	−	24.2411i	0.523939	−	0.792769i
$936$	−11.2544	−	5.23517i	−0.367861	−	0.171117i
$937$	52.2821	+	16.9875i	1.70798	+	0.554957i	0.989995	−	0.141101i	$-0.0450644\pi$
$937$	52.2821	+	16.9875i	1.70798	+	0.554957i	0.717986	+	0.696058i	$0.245064\pi$
$938$	12.4508	+	10.4066i	0.406535	+	0.339789i
$939$	11.1561	+	12.5977i	0.364064	+	0.411111i
$940$	1.82355	+	5.61230i	0.0594776	+	0.183053i
$941$	−13.8378	−	42.5885i	−0.451101	−	1.38835i	−0.875652	−	0.482942i	$-0.839568\pi$
$941$	−13.8378	−	42.5885i	−0.451101	−	1.38835i	0.424551	−	0.905404i	$-0.360432\pi$
$942$	−13.2586	+	11.7413i	−0.431987	+	0.382551i
$943$	7.31592	+	10.0695i	0.238239	+	0.327908i
$944$	−10.5570	+	32.4911i	−0.343601	+	1.05749i
$945$	13.1690	−	30.5650i	0.428389	−	0.994279i
$946$	−57.9721	+	2.57103i	−1.88484	+	0.0835915i
$947$			19.0889i			0.620305i	0.950687	+	0.310152i	$0.100380\pi$
$947$			19.0889i			0.620305i	−0.950687	+	0.310152i	$0.899620\pi$
$948$	1.29726	+	0.763328i	0.0421331	+	0.0247917i
$949$	7.14528	−	5.19135i	0.231946	−	0.168518i
$950$	8.29273	+	6.02502i	0.269052	+	0.195477i
$951$	−2.46021	−	25.4254i	−0.0797777	−	0.824476i
$952$	19.7190	−	12.3748i	0.639097	−	0.401068i
$953$	31.9656	−	43.9969i	1.03547	−	1.42520i	0.134705	−	0.990886i	$-0.456991\pi$
$953$	31.9656	−	43.9969i	1.03547	−	1.42520i	0.900762	−	0.434313i	$-0.143009\pi$
$954$	4.10934	−	0.802770i	0.133045	−	0.0259906i
$955$	−15.4509	−	5.02030i	−0.499979	−	0.162453i
$956$			12.5935i			0.407304i
$957$	−31.6708	+	4.48837i	−1.02377	+	0.145088i
$958$		−	21.1685i		−	0.683922i
$959$	−5.25719	−	0.357431i	−0.169764	−	0.0115420i
$960$	9.23178	+	21.2045i	0.297955	+	0.684372i
$961$	−12.4560	−	9.04983i	−0.401807	−	0.291930i
$962$	−3.23619	−	9.95997i	−0.104339	−	0.321122i
$963$	26.3302	+	3.20791i	0.848480	+	0.103374i
$964$	−1.70995	+	2.35355i	−0.0550739	+	0.0758027i
$965$	23.6422	−	17.1771i	0.761070	−	0.552950i
$966$	−7.76590	−	2.28013i	−0.249864	−	0.0733620i
$967$	−37.6244			−1.20992			−0.604959	−	0.796256i	$-0.706811\pi$
$967$	−37.6244			−1.20992			−0.604959	+	0.796256i	$0.706811\pi$
$968$	26.0682	+	5.98059i	0.837864	+	0.192223i
$969$	46.6226	+	10.3131i	1.49773	+	0.331304i
$970$	11.3911	−	35.0582i	0.365746	−	1.12565i
$971$	−27.3120	+	19.8433i	−0.876484	+	0.636803i	−0.932319	−	0.361637i	$-0.882218\pi$
$971$	−27.3120	+	19.8433i	−0.876484	+	0.636803i	0.0558347	+	0.998440i	$0.482218\pi$
$972$	−6.86409	−	1.00942i	−0.220166	−	0.0323770i
$973$	−6.37109	+	3.99821i	−0.204248	+	0.128177i
$974$	−44.1032	+	14.3300i	−1.41316	+	0.459163i
$975$	1.68152	+	1.89882i	0.0538517	+	0.0608108i
$976$	19.4058	+	26.7097i	0.621163	+	0.854958i
$977$	−37.0123	−	12.0260i	−1.18413	−	0.384746i	−0.350229	−	0.936664i	$-0.613896\pi$
$977$	−37.0123	−	12.0260i	−1.18413	−	0.384746i	−0.833898	+	0.551918i	$0.813896\pi$
$978$	32.2137	+	7.12577i	1.03008	+	0.227857i
$979$	38.6525	−	14.4819i	1.23534	−	0.462843i
$980$	−6.64557	+	3.56646i	−0.212285	+	0.113926i
$981$	−15.0521	+	16.1717i	−0.480576	+	0.516324i
$982$	−19.2774	+	14.0059i	−0.615167	+	0.446945i
$983$	−9.02020	−	6.55356i	−0.287700	−	0.209026i	0.434569	−	0.900638i	$-0.356901\pi$
$983$	−9.02020	−	6.55356i	−0.287700	−	0.209026i	−0.722269	+	0.691612i	$0.756901\pi$
$984$	4.46946	+	46.1904i	0.142481	+	1.47250i
$985$	24.8758	−	8.08265i	0.792610	−	0.257535i
$986$	25.4922	+	18.5211i	0.811836	+	0.589833i
$987$	15.3268	+	19.8754i	0.487857	+	0.632642i
$988$	−1.78284	+	5.48701i	−0.0567196	+	0.174565i
$989$			12.6385i			0.401882i
$990$	−34.8208	−	14.3570i	−1.10668	−	0.456296i
$991$	44.0922			1.40064			0.700318	−	0.713831i	$-0.253042\pi$
$991$	44.0922			1.40064			0.700318	+	0.713831i	$0.253042\pi$
$992$	3.01992	−	9.29437i	0.0958826	−	0.295096i
$993$	0.403101	+	0.925882i	0.0127920	+	0.0293820i
$994$	−8.20467	−	3.29651i	−0.260236	−	0.104559i
$995$	−39.8339	+	12.9428i	−1.26282	+	0.410315i
$996$	10.2749	−	0.994216i	0.325572	−	0.0315029i
$997$	10.3382	−	14.2293i	0.327414	−	0.450646i	−0.613299	−	0.789851i	$-0.710158\pi$
$997$	10.3382	−	14.2293i	0.327414	−	0.450646i	0.940713	+	0.339205i	$0.110158\pi$
$998$	−7.22436	−	9.94348i	−0.228683	−	0.314755i
$999$	11.6071	+	16.8377i	0.367233	+	0.532723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.7	✓	112
3.2	odd	2	inner	231.2.u.a.20.21	yes	112
7.6	odd	2	inner	231.2.u.a.20.8	yes	112
11.5	even	5	inner	231.2.u.a.104.22	yes	112
21.20	even	2	inner	231.2.u.a.20.22	yes	112
33.5	odd	10	inner	231.2.u.a.104.8	yes	112
77.27	odd	10	inner	231.2.u.a.104.21	yes	112
231.104	even	10	inner	231.2.u.a.104.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.7	✓	112	1.1	even	1	trivial
231.2.u.a.20.8	yes	112	7.6	odd	2	inner
231.2.u.a.20.21	yes	112	3.2	odd	2	inner
231.2.u.a.20.22	yes	112	21.20	even	2	inner
231.2.u.a.104.7	yes	112	231.104	even	10	inner
231.2.u.a.104.8	yes	112	33.5	odd	10	inner
231.2.u.a.104.21	yes	112	77.27	odd	10	inner
231.2.u.a.104.22	yes	112	11.5	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48714 - 0.483201i) q^{2} +(-0.691398 - 1.58807i) q^{3} +(0.360067 + 0.261604i) q^{4} +(0.748085 + 2.30237i) q^{5} +(0.260847 + 2.69577i) q^{6} +(-2.45500 - 0.986383i) q^{7} +(1.42914 + 1.96705i) q^{8} +(-2.04394 + 2.19598i) q^{9} +O(q^{10})\)	\(q+(-1.48714 - 0.483201i) q^{2} +(-0.691398 - 1.58807i) q^{3} +(0.360067 + 0.261604i) q^{4} +(0.748085 + 2.30237i) q^{5} +(0.260847 + 2.69577i) q^{6} +(-2.45500 - 0.986383i) q^{7} +(1.42914 + 1.96705i) q^{8} +(-2.04394 + 2.19598i) q^{9} -3.78542i q^{10} +(-3.10579 + 1.16364i) q^{11} +(0.166496 - 0.752684i) q^{12} +(1.61839 + 0.525848i) q^{13} +(3.17431 + 2.65315i) q^{14} +(3.13910 - 2.77986i) q^{15} +(-1.44992 - 4.46240i) q^{16} +(1.11832 + 3.44183i) q^{17} +(4.10072 - 2.27809i) q^{18} +(4.47759 + 6.16288i) q^{19} +(-0.332948 + 1.02471i) q^{20} +(0.130939 + 4.58070i) q^{21} +(5.18102 - 0.229776i) q^{22} -1.12952i q^{23} +(2.13570 - 3.62959i) q^{24} +(-0.696187 + 0.505809i) q^{25} +(-2.15269 - 1.56402i) q^{26} +(4.90054 + 1.72763i) q^{27} +(-0.625924 - 0.997403i) q^{28} +(-3.27295 + 4.50482i) q^{29} +(-6.01151 + 2.61723i) q^{30} +(-3.75680 - 1.22066i) q^{31} +2.47401i q^{32} +(3.99528 + 4.12768i) q^{33} -5.65886i q^{34} +(0.434465 - 6.39023i) q^{35} +(-1.31043 + 0.255996i) q^{36} +(3.18409 + 2.31338i) q^{37} +(-3.68090 - 11.3286i) q^{38} +(-0.283870 - 2.93370i) q^{39} +(-3.45975 + 4.76193i) q^{40} +(-8.91487 + 6.47703i) q^{41} +(2.01868 - 6.87542i) q^{42} -11.1893 q^{43} +(-1.42271 - 0.393498i) q^{44} +(-6.58499 - 3.06312i) q^{45} +(-0.545784 + 1.67975i) q^{46} +(4.43097 - 3.21929i) q^{47} +(-6.08414 + 5.38788i) q^{48} +(5.05410 + 4.84315i) q^{49} +(1.27973 - 0.415811i) q^{50} +(4.69267 - 4.15564i) q^{51} +(0.445166 + 0.612719i) q^{52} +(0.848876 + 0.275816i) q^{53} +(-6.45300 - 4.93717i) q^{54} +(-5.00253 - 6.28017i) q^{55} +(-1.56829 - 6.23879i) q^{56} +(6.69129 - 11.3717i) q^{57} +(7.04406 - 5.11781i) q^{58} +(-5.89051 - 4.27971i) q^{59} +(1.85751 - 0.179736i) q^{60} +(-6.69200 + 2.17436i) q^{61} +(4.99706 + 3.63057i) q^{62} +(7.18395 - 3.37503i) q^{63} +(-1.70440 + 5.24560i) q^{64} +4.11952i q^{65} +(-3.94704 - 8.06896i) q^{66} +3.92237 q^{67} +(-0.497727 + 1.53185i) q^{68} +(-1.79375 + 0.780945i) q^{69} +(-3.73387 + 9.29322i) q^{70} +(-2.03268 + 0.660459i) q^{71} +(-7.24067 - 0.882158i) q^{72} +(3.05072 - 4.19895i) q^{73} +(-3.61737 - 4.97888i) q^{74} +(1.28460 + 0.755879i) q^{75} +3.39040i q^{76} +(8.77253 + 0.206754i) q^{77} +(-0.995411 + 4.49998i) q^{78} +(-0.603371 + 1.85698i) q^{79} +(9.18944 - 6.67652i) q^{80} +(-0.644628 - 8.97688i) q^{81} +(16.3874 - 5.32458i) q^{82} +(4.13806 + 12.7356i) q^{83} +(-1.15118 + 1.68361i) q^{84} +(-7.08777 + 5.14957i) q^{85} +(16.6401 + 5.40669i) q^{86} +(9.41689 + 2.08305i) q^{87} +(-6.72756 - 4.44623i) q^{88} -12.4453 q^{89} +(8.31269 + 7.73717i) q^{90} +(-3.45448 - 2.88732i) q^{91} +(0.295486 - 0.406702i) q^{92} +(0.658949 + 6.81002i) q^{93} +(-8.14503 + 2.64648i) q^{94} +(-10.8396 + 14.9194i) q^{95} +(3.92891 - 1.71053i) q^{96} +(9.26137 + 3.00920i) q^{97} +(-5.17594 - 9.64458i) q^{98} +(3.79272 - 9.19866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

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