LMFDB - Embedded newform 384.2.v.a.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			181.2
Character	$\chi$	$=$	384.181
Dual form			384.2.v.a.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39167 + 0.251498i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(1.87350 - 0.700005i) q^{4} +(-2.59468 - 1.38689i) q^{5} +(-0.386695 - 1.36032i) q^{6} +(0.265268 - 1.33359i) q^{7} +(-2.43124 + 1.44536i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(-1.39167 + 0.251498i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(1.87350 - 0.700005i) q^{4} +(-2.59468 - 1.38689i) q^{5} +(-0.386695 - 1.36032i) q^{6} +(0.265268 - 1.33359i) q^{7} +(-2.43124 + 1.44536i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(3.95975 + 1.27753i) q^{10} +(0.533699 + 0.650315i) q^{11} +(0.880269 + 1.79586i) q^{12} +(3.22942 + 6.04181i) q^{13} +(-0.0337699 + 1.92263i) q^{14} +(1.12589 - 2.71813i) q^{15} +(3.01999 - 2.62292i) q^{16} +(0.823388 + 1.98783i) q^{17} +(1.31587 - 0.518167i) q^{18} +(-1.67036 + 5.50644i) q^{19} +(-5.83196 - 0.782037i) q^{20} +(1.35317 + 0.133276i) q^{21} +(-0.906287 - 0.770800i) q^{22} +(4.34114 + 2.90066i) q^{23} +(-1.67670 - 2.27787i) q^{24} +(2.03108 + 3.03972i) q^{25} +(-6.01379 - 7.59602i) q^{26} +(-0.290285 - 0.956940i) q^{27} +(-0.436542 - 2.68417i) q^{28} +(2.85483 + 2.34289i) q^{29} +(-0.883259 + 4.06590i) q^{30} +(-6.18979 - 6.18979i) q^{31} +(-3.54317 + 4.40976i) q^{32} +(-0.594872 + 0.594872i) q^{33} +(-1.64582 - 2.55933i) q^{34} +(-2.53783 + 3.09235i) q^{35} +(-1.70093 + 1.05206i) q^{36} +(2.51667 - 0.763422i) q^{37} +(0.939734 - 8.08325i) q^{38} +(-5.69618 + 3.80607i) q^{39} +(8.31285 - 0.378388i) q^{40} +(-6.09075 + 9.11546i) q^{41} +(-1.91669 + 0.154844i) q^{42} +(-0.874026 + 8.87413i) q^{43} +(1.45511 + 0.844770i) q^{44} +(2.81540 + 0.854041i) q^{45} +(-6.77095 - 2.94497i) q^{46} +(0.833630 - 0.345301i) q^{47} +(2.90630 + 2.74835i) q^{48} +(4.75906 + 1.97127i) q^{49} +(-3.59107 - 3.71948i) q^{50} +(-1.89756 + 1.01426i) q^{51} +(10.2796 + 9.05871i) q^{52} +(10.5951 - 8.69519i) q^{53} +(0.644650 + 1.25874i) q^{54} +(-0.482868 - 2.42754i) q^{55} +(1.28259 + 3.62569i) q^{56} +(-5.64365 - 1.12259i) q^{57} +(-4.56221 - 2.54256i) q^{58} +(-4.50037 + 8.41960i) q^{59} +(0.206639 - 5.88053i) q^{60} +(3.34094 - 0.329054i) q^{61} +(10.1709 + 7.05743i) q^{62} +1.35972i q^{63} +(3.82188 - 7.02803i) q^{64} -20.1554i q^{65} +(0.678257 - 0.977475i) q^{66} +(-3.83692 + 0.377904i) q^{67} +(2.93411 + 3.14783i) q^{68} +(-2.46118 + 4.60455i) q^{69} +(2.75410 - 4.94179i) q^{70} +(-4.72390 - 0.939642i) q^{71} +(2.10255 - 1.89190i) q^{72} +(-0.914367 - 4.59683i) q^{73} +(-3.31037 + 1.69537i) q^{74} +(-2.82600 + 2.31924i) q^{75} +(0.725122 + 11.4856i) q^{76} +(1.00883 - 0.539229i) q^{77} +(6.96999 - 6.72937i) q^{78} +(-5.80215 - 2.40333i) q^{79} +(-11.4736 + 2.61726i) q^{80} +(0.923880 - 0.382683i) q^{81} +(6.18381 - 14.2175i) q^{82} +(1.84959 + 0.561066i) q^{83} +(2.62845 - 0.697535i) q^{84} +(0.620471 - 6.29975i) q^{85} +(-1.01547 - 12.5697i) q^{86} +(-2.05179 + 3.07072i) q^{87} +(-2.23749 - 0.809686i) q^{88} +(8.85921 - 5.91954i) q^{89} +(-4.13290 - 0.480478i) q^{90} +(8.91396 - 2.70402i) q^{91} +(10.1636 + 2.39555i) q^{92} +(5.55328 - 6.76669i) q^{93} +(-1.07330 + 0.690201i) q^{94} +(11.9709 - 11.9709i) q^{95} +(-4.73581 - 3.09387i) q^{96} +(1.57589 + 1.57589i) q^{97} +(-7.11882 - 1.54646i) q^{98} +(-0.650315 - 0.533699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.39167	+	0.251498i	−0.984060	+	0.177836i
$2$	−1.39167	+	0.251498i	−0.984060	+	0.177836i
$3$	0.0980171	+	0.995185i	0.0565902	+	0.574570i
$3$	0.0980171	+	0.995185i	0.0565902	+	0.574570i
$4$	1.87350	−	0.700005i	0.936749	−	0.350003i
$5$	−2.59468	−	1.38689i	−1.16038	−	0.620235i	−0.225165	−	0.974321i	$-0.572292\pi$
$5$	−2.59468	−	1.38689i	−1.16038	−	0.620235i	−0.935213	+	0.354086i	$0.884792\pi$
$6$	−0.386695	−	1.36032i	−0.157867	−	0.555348i
$7$	0.265268	−	1.33359i	0.100262	−	0.504050i	−0.897721	−	0.440564i	$-0.854778\pi$
$7$	0.265268	−	1.33359i	0.100262	−	0.504050i	0.997983	−	0.0634854i	$-0.0202216\pi$
$8$	−2.43124	+	1.44536i	−0.859574	+	0.511011i
$9$	−0.980785	+	0.195090i	−0.326928	+	0.0650301i
$10$	3.95975	+	1.27753i	1.25218	+	0.403991i
$11$	0.533699	+	0.650315i	0.160916	+	0.196077i	0.847227	−	0.531232i	$-0.178271\pi$
$11$	0.533699	+	0.650315i	0.160916	+	0.196077i	−0.686310	+	0.727309i	$0.740771\pi$
$12$	0.880269	+	1.79586i	0.254112	+	0.518421i
$13$	3.22942	+	6.04181i	0.895679	+	1.67570i	0.723148	+	0.690693i	$0.242695\pi$
$13$	3.22942	+	6.04181i	0.895679	+	1.67570i	0.172531	+	0.985004i	$0.444805\pi$
$14$	−0.0337699	+	1.92263i	−0.00902537	+	0.513845i
$15$	1.12589	−	2.71813i	0.290702	−	0.701818i
$16$	3.01999	−	2.62292i	0.754996	−	0.655729i
$17$	0.823388	+	1.98783i	0.199701	+	0.482120i	0.991727	−	0.128367i	$-0.0409736\pi$
$17$	0.823388	+	1.98783i	0.199701	+	0.482120i	−0.792026	+	0.610487i	$0.790974\pi$
$18$	1.31587	−	0.518167i	0.310153	−	0.122133i
$19$	−1.67036	+	5.50644i	−0.383207	+	1.26327i	0.527267	+	0.849700i	$0.323217\pi$
$19$	−1.67036	+	5.50644i	−0.383207	+	1.26327i	−0.910474	+	0.413565i	$0.864283\pi$
$20$	−5.83196	−	0.782037i	−1.30407	−	0.174869i
$21$	1.35317	+	0.133276i	0.295286	+	0.0290831i
$22$	−0.906287	−	0.770800i	−0.193221	−	0.164335i
$23$	4.34114	+	2.90066i	0.905191	+	0.604829i	0.918647	−	0.395080i	$-0.129283\pi$
$23$	4.34114	+	2.90066i	0.905191	+	0.604829i	−0.0134558	+	0.999909i	$0.504283\pi$
$24$	−1.67670	−	2.27787i	−0.342255	−	0.464967i
$25$	2.03108	+	3.03972i	0.406215	+	0.607944i
$26$	−6.01379	−	7.59602i	−1.17940	−	1.48970i
$27$	−0.290285	−	0.956940i	−0.0558653	−	0.184163i
$28$	−0.436542	−	2.68417i	−0.0824987	−	0.507260i
$29$	2.85483	+	2.34289i	0.530128	+	0.435065i	0.860996	−	0.508613i	$-0.169841\pi$
$29$	2.85483	+	2.34289i	0.530128	+	0.435065i	−0.330868	+	0.943677i	$0.607341\pi$
$30$	−0.883259	+	4.06590i	−0.161260	+	0.742328i
$31$	−6.18979	−	6.18979i	−1.11172	−	1.11172i	−0.992918	−	0.118800i	$-0.962095\pi$
$31$	−6.18979	−	6.18979i	−1.11172	−	1.11172i	−0.118800	−	0.992918i	$-0.537905\pi$
$32$	−3.54317	+	4.40976i	−0.626349	+	0.779542i
$33$	−0.594872	+	0.594872i	−0.103554	+	0.103554i
$34$	−1.64582	−	2.55933i	−0.282256	−	0.438922i
$35$	−2.53783	+	3.09235i	−0.428971	+	0.522702i
$36$	−1.70093	+	1.05206i	−0.283489	+	0.175343i
$37$	2.51667	−	0.763422i	0.413737	−	0.125506i	−0.0765520	−	0.997066i	$-0.524391\pi$
$37$	2.51667	−	0.763422i	0.413737	−	0.125506i	0.490289	+	0.871560i	$0.336891\pi$
$38$	0.939734	−	8.08325i	0.152445	−	1.31128i
$39$	−5.69618	+	3.80607i	−0.912119	+	0.609458i
$40$	8.31285	−	0.378388i	1.31438	−	0.0598285i
$41$	−6.09075	+	9.11546i	−0.951216	+	1.42360i	−0.0458568	+	0.998948i	$0.514602\pi$
$41$	−6.09075	+	9.11546i	−0.951216	+	1.42360i	−0.905359	+	0.424647i	$0.860398\pi$
$42$	−1.91669	+	0.154844i	−0.295751	+	0.0238929i
$43$	−0.874026	+	8.87413i	−0.133288	+	1.35329i	0.663111	+	0.748521i	$0.269236\pi$
$43$	−0.874026	+	8.87413i	−0.133288	+	1.35329i	−0.796399	+	0.604772i	$0.793264\pi$
$44$	1.45511	+	0.844770i	0.219366	+	0.127354i
$45$	2.81540	+	0.854041i	0.419694	+	0.127313i
$46$	−6.77095	−	2.94497i	−0.998323	−	0.434213i
$47$	0.833630	−	0.345301i	0.121597	−	0.0503673i	−0.321055	−	0.947060i	$-0.604038\pi$
$47$	0.833630	−	0.345301i	0.121597	−	0.0503673i	0.442653	+	0.896693i	$0.354038\pi$
$48$	2.90630	+	2.74835i	0.419488	+	0.396690i
$49$	4.75906	+	1.97127i	0.679866	+	0.281610i
$50$	−3.59107	−	3.71948i	−0.507855	−	0.526014i
$51$	−1.89756	+	1.01426i	−0.265711	+	0.142025i
$52$	10.2796	+	9.05871i	1.42552	+	1.25622i
$53$	10.5951	−	8.69519i	1.45535	−	1.19438i	0.513616	−	0.858020i	$-0.328306\pi$
$53$	10.5951	−	8.69519i	1.45535	−	1.19438i	0.941735	−	0.336355i	$-0.109194\pi$
$54$	0.644650	+	1.25874i	0.0877257	+	0.171293i
$55$	−0.482868	−	2.42754i	−0.0651099	−	0.327330i
$56$	1.28259	+	3.62569i	0.171393	+	0.484503i
$57$	−5.64365	−	1.12259i	−0.747520	−	0.148691i
$58$	−4.56221	−	2.54256i	−0.599048	−	0.333854i
$59$	−4.50037	+	8.41960i	−0.585898	+	1.09614i	0.397996	+	0.917387i	$0.369706\pi$
$59$	−4.50037	+	8.41960i	−0.585898	+	1.09614i	−0.983894	+	0.178751i	$0.942794\pi$
$60$	0.206639	−	5.88053i	0.0266770	−	0.759174i
$61$	3.34094	−	0.329054i	0.427763	−	0.0421310i	0.118155	−	0.992995i	$-0.462302\pi$
$61$	3.34094	−	0.329054i	0.427763	−	0.0421310i	0.309608	+	0.950864i	$0.399802\pi$
$62$	10.1709	+	7.05743i	1.29170	+	0.896294i
$63$			1.35972i			0.171308i
$64$	3.82188	−	7.02803i	0.477735	−	0.878504i
$65$		−	20.1554i		−	2.49997i
$66$	0.678257	−	0.977475i	0.0834876	−	0.120319i
$67$	−3.83692	+	0.377904i	−0.468754	+	0.0461683i	−0.329637	−	0.944108i	$-0.606926\pi$
$67$	−3.83692	+	0.377904i	−0.468754	+	0.0461683i	−0.139117	+	0.990276i	$0.544426\pi$
$68$	2.93411	+	3.14783i	0.355813	+	0.381730i
$69$	−2.46118	+	4.60455i	−0.296292	+	0.554323i
$70$	2.75410	−	4.94179i	0.329178	−	0.590657i
$71$	−4.72390	−	0.939642i	−0.560624	−	0.111515i	−0.0933591	−	0.995632i	$-0.529760\pi$
$71$	−4.72390	−	0.939642i	−0.560624	−	0.111515i	−0.467265	+	0.884117i	$0.654760\pi$
$72$	2.10255	−	1.89190i	0.247788	−	0.222962i
$73$	−0.914367	−	4.59683i	−0.107019	−	0.538018i	−0.996681	−	0.0814006i	$-0.974061\pi$
$73$	−0.914367	−	4.59683i	−0.107019	−	0.538018i	0.889663	−	0.456618i	$-0.150939\pi$
$74$	−3.31037	+	1.69537i	−0.384823	+	0.197083i
$75$	−2.82600	+	2.31924i	−0.326319	+	0.267803i
$76$	0.725122	+	11.4856i	0.0831772	+	1.31749i
$77$	1.00883	−	0.539229i	0.114966	−	0.0614509i
$78$	6.96999	−	6.72937i	0.789196	−	0.761951i
$79$	−5.80215	−	2.40333i	−0.652793	−	0.270396i	0.0316093	−	0.999500i	$-0.489937\pi$
$79$	−5.80215	−	2.40333i	−0.652793	−	0.270396i	−0.684402	+	0.729105i	$0.739937\pi$
$80$	−11.4736	+	2.61726i	−1.28279	+	0.292619i
$81$	0.923880	−	0.382683i	0.102653	−	0.0425204i
$82$	6.18381	−	14.2175i	0.682887	−	1.57006i
$83$	1.84959	+	0.561066i	0.203019	+	0.0615850i	0.390156	−	0.920749i	$-0.372421\pi$
$83$	1.84959	+	0.561066i	0.203019	+	0.0615850i	−0.187138	+	0.982334i	$0.559921\pi$
$84$	2.62845	−	0.697535i	0.286788	−	0.0761073i
$85$	0.620471	−	6.29975i	0.0672995	−	0.683303i
$86$	−1.01547	−	12.5697i	−0.109501	−	1.35542i
$87$	−2.05179	+	3.07072i	−0.219975	+	0.329216i
$88$	−2.23749	−	0.809686i	−0.238517	−	0.0863128i
$89$	8.85921	−	5.91954i	0.939075	−	0.627470i	0.0110301	−	0.999939i	$-0.496489\pi$
$89$	8.85921	−	5.91954i	0.939075	−	0.627470i	0.928044	+	0.372470i	$0.121489\pi$
$90$	−4.13290	−	0.480478i	−0.435645	−	0.0506468i
$91$	8.91396	−	2.70402i	0.934437	−	0.283458i
$92$	10.1636	+	2.39555i	1.05963	+	0.249754i
$93$	5.55328	−	6.76669i	0.575848	−	0.701673i
$94$	−1.07330	+	0.690201i	−0.110702	+	0.0711888i
$95$	11.9709	−	11.9709i	1.22819	−	1.22819i
$96$	−4.73581	−	3.09387i	−0.483347	−	0.315767i
$97$	1.57589	+	1.57589i	0.160007	+	0.160007i	0.782570	−	0.622563i	$-0.213908\pi$
$97$	1.57589	+	1.57589i	0.160007	+	0.160007i	−0.622563	+	0.782570i	$0.713908\pi$
$98$	−7.11882	−	1.54646i	−0.719109	−	0.156216i
$99$	−0.650315	−	0.533699i	−0.0653591	−	0.0536388i
$100$	5.93304	+	4.27314i	0.593304	+	0.427314i
$101$	−1.47613	−	4.86614i	−0.146880	−	0.484199i	0.852369	−	0.522941i	$-0.175165\pi$
$101$	−1.47613	−	4.86614i	−0.146880	−	0.484199i	−0.999249	+	0.0387415i	$0.987665\pi$
$102$	2.38569	−	1.88875i	0.236218	−	0.187015i
$103$	−5.91273	−	8.84903i	−0.582599	−	0.871921i	0.416712	−	0.909039i	$-0.363182\pi$
$103$	−5.91273	−	8.84903i	−0.582599	−	0.871921i	−0.999311	+	0.0371176i	$0.988182\pi$
$104$	−16.5841	−	10.0214i	−1.62620	−	0.982684i
$105$	−3.32621	−	2.22250i	−0.324605	−	0.216894i
$106$	−12.5581	+	14.7655i	−1.21975	+	1.43415i
$107$	−2.47512	−	0.243778i	−0.239279	−	0.0235669i	−0.0223333	−	0.999751i	$-0.507109\pi$
$107$	−2.47512	−	0.243778i	−0.239279	−	0.0235669i	−0.216946	+	0.976184i	$0.569609\pi$
$108$	−1.21371	−	1.58962i	−0.116789	−	0.152962i
$109$	−3.32587	+	10.9639i	−0.318560	+	1.05015i	0.640739	+	0.767759i	$0.278628\pi$
$109$	−3.32587	+	10.9639i	−0.318560	+	1.05015i	−0.959299	+	0.282393i	$0.908872\pi$
$110$	1.28252	+	3.25690i	0.122283	+	0.310533i
$111$	1.00642	+	2.42972i	0.0955254	+	0.230619i
$112$	−2.69679	−	4.72320i	−0.254823	−	0.446300i
$113$	−3.11210	+	7.51328i	−0.292762	+	0.706790i	−1.00000		0.000185328i	$-0.999941\pi$
$113$	−3.11210	+	7.51328i	−0.292762	+	0.706790i	0.707238	+	0.706976i	$0.249941\pi$
$114$	8.13644	+	0.142911i	0.762047	+	0.0133849i
$115$	−7.24101	−	13.5470i	−0.675227	−	1.26326i
$116$	6.98855	+	2.39101i	0.648870	+	0.222000i
$117$	−4.34606	−	5.29569i	−0.401794	−	0.489587i
$118$	4.14552	−	12.8492i	0.381626	−	1.18286i
$119$	2.86937	−	0.570754i	0.263035	−	0.0523209i
$120$	1.19137	+	8.23574i	0.108757	+	0.751817i
$121$	2.00792	−	10.0945i	0.182538	−	0.917681i
$122$	−4.56673	+	1.29817i	−0.413452	+	0.117531i
$123$	−9.66856	−	5.16795i	−0.871785	−	0.465979i
$124$	−15.9294	−	7.26366i	−1.43051	−	0.652296i
$125$	0.387621	+	3.93558i	0.0346699	+	0.352009i
$126$	−0.341966	−	1.89228i	−0.0304648	−	0.168578i
$127$	15.1530			1.34461			0.672304	−	0.740275i	$-0.265305\pi$
$127$	15.1530			1.34461			0.672304	+	0.740275i	$0.265305\pi$
$128$	−3.55126	+	10.7419i	−0.313890	+	0.949459i
$129$	−8.91707			−0.785104
$130$	5.06905	+	28.0497i	0.444585	+	2.46012i
$131$	−0.246518	−	2.50294i	−0.0215384	−	0.218683i	−0.999929	−	0.0119176i	$-0.996206\pi$
$131$	−0.246518	−	2.50294i	−0.0215384	−	0.218683i	0.978391	−	0.206765i	$-0.0662936\pi$
$132$	−0.698077	+	1.53090i	−0.0607598	+	0.133248i
$133$	6.90025	+	3.68826i	0.598327	+	0.319813i
$134$	5.24469	−	1.49090i	0.453072	−	0.128794i
$135$	−0.573972	+	2.88555i	−0.0493996	+	0.248349i
$136$	−4.87499	−	3.64282i	−0.418027	−	0.312369i
$137$	19.6175	−	3.90216i	1.67604	−	0.333384i	0.736657	−	0.676267i	$-0.236403\pi$
$137$	19.6175	−	3.90216i	1.67604	−	0.333384i	0.939378	+	0.342883i	$0.111403\pi$
$138$	2.26712	−	7.02701i	0.192990	−	0.598179i
$139$	−6.56190	−	7.99570i	−0.556573	−	0.678187i	0.416379	−	0.909191i	$-0.363299\pi$
$139$	−6.56190	−	7.99570i	−0.556573	−	0.678187i	−0.972953	+	0.231004i	$0.925799\pi$
$140$	−2.58995	+	7.57000i	−0.218891	+	0.639782i
$141$	0.425348	+	0.795770i	0.0358208	+	0.0670159i
$142$	6.81043	+	0.119621i	0.571519	+	0.0100384i
$143$	−2.20554	+	5.32465i	−0.184437	+	0.445270i
$144$	−2.45025	+	3.16169i	−0.204188	+	0.263474i
$145$	−4.15804	−	10.0384i	−0.345306	−	0.833643i
$146$	2.42859	+	6.16732i	0.200992	+	0.510411i
$147$	−1.49531	+	4.92936i	−0.123331	+	0.406567i
$148$	4.18057	−	3.19195i	0.343641	−	0.262377i
$149$	−9.42292	−	0.928077i	−0.771956	−	0.0760310i	−0.295633	−	0.955302i	$-0.595531\pi$
$149$	−9.42292	−	0.928077i	−0.771956	−	0.0760310i	−0.476323	+	0.879270i	$0.658031\pi$
$150$	3.34958	−	3.93836i	0.273492	−	0.321565i
$151$	9.52394	+	6.36369i	0.775047	+	0.517870i	0.879063	−	0.476706i	$-0.158169\pi$
$151$	9.52394	+	6.36369i	0.775047	+	0.517870i	−0.104016	+	0.994576i	$0.533169\pi$
$152$	−3.89773	−	15.8018i	−0.316148	−	1.28169i
$153$	−1.19537	−	1.78900i	−0.0966402	−	0.144632i
$154$	−1.26834	+	1.00415i	−0.102206	+	0.0809165i
$155$	7.47600	+	24.6451i	0.600487	+	1.97954i
$156$	−8.00751	+	11.1180i	−0.641114	+	0.890154i
$157$	−0.895514	−	0.734929i	−0.0714698	−	0.0586537i	0.597980	−	0.801511i	$-0.295970\pi$
$157$	−0.895514	−	0.734929i	−0.0714698	−	0.0586537i	−0.669450	+	0.742857i	$0.733470\pi$
$158$	8.67912	+	1.88541i	0.690474	+	0.149996i
$159$	9.69182	+	9.69182i	0.768611	+	0.768611i
$160$	15.3092	−	6.52795i	1.21030	−	0.516080i
$161$	5.01986	−	5.01986i	0.395620	−	0.395620i
$162$	−1.18949	+	0.764923i	−0.0934553	+	0.0600981i
$163$	−2.69591	+	3.28498i	−0.211160	+	0.257299i	−0.867810	−	0.496896i	$-0.834473\pi$
$163$	−2.69591	+	3.28498i	−0.211160	+	0.257299i	0.656650	+	0.754196i	$0.271973\pi$
$164$	−5.03014	+	21.3413i	−0.392788	+	1.66648i
$165$	2.36852	−	0.718484i	0.184389	−	0.0559339i
$166$	−2.71512	−	0.315652i	−0.210734	−	0.0244993i
$167$	−13.6467	+	9.11844i	−1.05601	+	0.705606i	−0.957179	−	0.289498i	$-0.906512\pi$
$167$	−13.6467	+	9.11844i	−1.05601	+	0.705606i	−0.0988350	+	0.995104i	$0.531512\pi$
$168$	−3.48251	+	1.63179i	−0.268682	+	0.125895i
$169$	−18.8520	+	28.2140i	−1.45015	+	2.17030i
$170$	0.720883	+	8.92322i	0.0552892	+	0.684380i
$171$	0.564012	−	5.72651i	0.0431311	−	0.437917i
$172$	4.57446	+	17.2375i	0.348799	+	1.31435i
$173$	17.8301	+	5.40870i	1.35560	+	0.411216i	0.882715	−	0.469909i	$-0.155713\pi$
$173$	17.8301	+	5.40870i	1.35560	+	0.411216i	0.472883	+	0.881125i	$0.343213\pi$
$174$	2.08314	−	4.78946i	0.157922	−	0.363088i
$175$	4.59252	−	1.90228i	0.347162	−	0.143799i
$176$	3.31749	+	0.564092i	0.250065	+	0.0425200i
$177$	−8.82017	−	3.65343i	−0.662965	−	0.274609i
$178$	−10.8404	+	10.4661i	−0.812519	+	0.784469i
$179$	12.3003	−	6.57465i	0.919368	−	0.491413i	0.0573866	−	0.998352i	$-0.481723\pi$
$179$	12.3003	−	6.57465i	0.919368	−	0.491413i	0.861982	+	0.506939i	$0.169223\pi$
$180$	5.87247	−	0.370749i	0.437708	−	0.0276340i
$181$	−12.9654	+	10.6404i	−0.963708	+	0.790895i	−0.977915	−	0.209004i	$-0.932978\pi$
$181$	−12.9654	+	10.6404i	−0.963708	+	0.790895i	0.0142065	+	0.999899i	$0.495478\pi$
$182$	−11.7252	+	6.00495i	−0.869133	+	0.445117i
$183$	0.654938	+	3.29260i	0.0484144	+	0.243396i
$184$	−14.7469	−	0.777698i	−1.08715	−	0.0573326i
$185$	−7.58873	−	1.50949i	−0.557935	−	0.110980i
$186$	−6.02652	+	10.8136i	−0.441886	+	0.792895i
$187$	−0.853276	+	1.59637i	−0.0623977	+	0.116738i
$188$	1.32009	−	1.23047i	0.0962775	−	0.0897409i
$189$	−1.35317	+	0.133276i	−0.0984286	+	0.00969437i
$190$	−13.6489	+	19.6702i	−0.990193	+	1.42702i
$191$		−	14.1967i		−	1.02724i	−0.858018	−	0.513619i	$-0.828305\pi$
$191$		−	14.1967i		−	1.02724i	0.858018	−	0.513619i	$-0.171695\pi$
$192$	7.36880	+	3.11461i	0.531797	+	0.224777i
$193$			1.29660i			0.0933316i	0.998911	+	0.0466658i	$0.0148596\pi$
$193$			1.29660i			0.0933316i	−0.998911	+	0.0466658i	$0.985140\pi$
$194$	−2.58945	−	1.79679i	−0.185912	−	0.129002i
$195$	20.0584	−	1.97558i	1.43641	−	0.141474i
$196$	10.2960	+	0.361797i	0.735427	+	0.0258426i
$197$	−2.63192	+	4.92398i	−0.187517	+	0.350819i	−0.958060	−	0.286569i	$-0.907485\pi$
$197$	−2.63192	+	4.92398i	−0.187517	+	0.350819i	0.770543	+	0.637388i	$0.219985\pi$
$198$	1.03925	+	0.579181i	0.0738562	+	0.0411606i
$199$	−23.6161	−	4.69753i	−1.67410	−	0.332999i	−0.735373	−	0.677663i	$-0.762993\pi$
$199$	−23.6161	−	4.69753i	−1.67410	−	0.332999i	−0.938726	+	0.344664i	$0.887993\pi$
$200$	−9.33153	−	4.45466i	−0.659838	−	0.314992i
$201$	−0.752168	−	3.78140i	−0.0530538	−	0.266720i
$202$	3.27811	+	6.40083i	0.230647	+	0.450361i
$203$	3.88175	−	3.18567i	0.272446	−	0.223590i
$204$	−2.84507	+	3.22852i	−0.199195	+	0.226042i
$205$	28.4457	−	15.2045i	1.98673	−	1.06193i
$206$	10.4541	+	10.8279i	0.728371	+	0.754416i
$207$	−4.82362	−	1.99801i	−0.335265	−	0.138871i
$208$	25.6000	+	9.77570i	1.77504	+	0.677823i
$209$	−4.47239	+	1.85253i	−0.309362	+	0.128142i
$210$	5.18794	+	2.25646i	0.358002	+	0.155710i
$211$	−18.6627	−	5.66128i	−1.28480	−	0.389738i	−0.427244	−	0.904137i	$-0.640515\pi$
$211$	−18.6627	−	5.66128i	−1.28480	−	0.389738i	−0.857551	+	0.514398i	$0.828015\pi$
$212$	13.7632	−	23.7070i	0.945263	−	1.62821i
$213$	0.472094	−	4.79325i	0.0323474	−	0.328428i
$214$	3.50587	−	0.283229i	0.239656	−	0.0193612i
$215$	14.5752	−	21.8134i	0.994024	−	1.48766i
$216$	2.08887	+	1.90699i	0.142130	+	0.129754i
$217$	−9.89659	+	6.61269i	−0.671824	+	0.448899i
$218$	1.87111	−	16.0946i	0.126727	−	1.09006i
$219$	4.48507	−	1.36053i	0.303073	−	0.0919362i
$220$	−2.60394	−	4.20998i	−0.175558	−	0.283837i
$221$	−9.35106	+	11.3943i	−0.629020	+	0.766463i
$222$	−2.01168	−	3.12826i	−0.135015	−	0.209955i
$223$	10.2371	−	10.2371i	0.685525	−	0.685525i	−0.275714	−	0.961240i	$-0.588914\pi$
$223$	10.2371	−	10.2371i	0.685525	−	0.685525i	0.961240	+	0.275714i	$0.0889144\pi$
$224$	4.94092	+	5.89490i	0.330129	+	0.393870i
$225$	−2.58507	−	2.58507i	−0.172338	−	0.172338i
$226$	2.44145	−	11.2387i	0.162403	−	0.747588i
$227$	1.56139	+	1.28140i	0.103633	+	0.0850496i	0.684783	−	0.728747i	$-0.259897\pi$
$227$	1.56139	+	1.28140i	0.103633	+	0.0850496i	−0.581150	+	0.813797i	$0.697397\pi$
$228$	−11.3592	+	1.84741i	−0.752281	+	0.122348i
$229$	5.38454	+	17.7504i	0.355820	+	1.17298i	0.934060	+	0.357115i	$0.116240\pi$
$229$	5.38454	+	17.7504i	0.355820	+	1.17298i	−0.578240	+	0.815867i	$0.696260\pi$
$230$	13.4841	+	17.0318i	0.889118	+	1.12305i
$231$	0.635515	+	0.951115i	0.0418138	+	0.0625788i
$232$	−10.3271	−	1.56990i	−0.678007	−	0.103069i
$233$	1.98110	+	1.32373i	0.129786	+	0.0867204i	0.618769	−	0.785573i	$-0.287632\pi$
$233$	1.98110	+	1.32373i	0.129786	+	0.0867204i	−0.488982	+	0.872294i	$0.662632\pi$
$234$	7.38015	+	6.27684i	0.482455	+	0.410330i
$235$	−2.64190	−	0.260204i	−0.172338	−	0.0169739i
$236$	−2.53767	+	18.9244i	−0.165188	+	1.23187i
$237$	1.82305	−	6.00978i	0.118420	−	0.390377i
$238$	−3.84968	+	1.51594i	−0.249538	+	0.0982641i
$239$	−6.96415	−	16.8129i	−0.450473	−	1.08754i	−0.972142	−	0.234391i	$-0.924690\pi$
$239$	−6.96415	−	16.8129i	−0.450473	−	1.08754i	0.521669	−	0.853148i	$-0.325310\pi$
$240$	−3.72927	−	11.1618i	−0.240723	−	0.720492i
$241$	2.97020	−	7.17069i	0.191327	−	0.461905i	−0.798883	−	0.601486i	$-0.794576\pi$
$241$	2.97020	−	7.17069i	0.191327	−	0.461905i	0.990211	+	0.139581i	$0.0445756\pi$
$242$	−0.255618	+	14.5532i	−0.0164317	+	0.935515i
$243$	0.471397	+	0.881921i	0.0302401	+	0.0565753i
$244$	6.02890	−	2.95516i	0.385961	−	0.189184i
$245$	−9.61433	−	11.7151i	−0.614237	−	0.748450i
$246$	14.7552	+	4.76047i	0.940756	+	0.303516i
$247$	−38.6632	+	7.69059i	−2.46008	+	0.489340i
$248$	23.9953	+	6.10241i	1.52370	+	0.387504i
$249$	−0.377073	+	1.89567i	−0.0238960	+	0.120133i
$250$	−1.52923	−	5.37955i	−0.0967171	−	0.340233i
$251$	−2.55536	−	1.36587i	−0.161293	−	0.0862127i	0.388775	−	0.921333i	$-0.372898\pi$
$251$	−2.55536	−	1.36587i	−0.161293	−	0.0862127i	−0.550068	+	0.835120i	$0.685398\pi$
$252$	0.951809	+	2.54743i	0.0599583	+	0.160473i
$253$	0.430525	+	4.37119i	0.0270668	+	0.274814i
$254$	−21.0880	+	3.81094i	−1.32318	+	0.239120i
$255$	6.33023			0.396414
$256$	2.24062	−	15.8423i	0.140039	−	0.990146i
$257$	3.26443			0.203630			0.101815	−	0.994803i	$-0.467535\pi$
$257$	3.26443			0.203630			0.101815	+	0.994803i	$0.467535\pi$
$258$	12.4096	−	2.24263i	0.772590	−	0.139620i
$259$	−0.350503	−	3.55871i	−0.0217792	−	0.221128i
$260$	−14.1089	−	37.7611i	−0.874997	−	2.34185i
$261$	−3.25705	−	1.74093i	−0.201606	−	0.107761i
$262$	0.972556	+	3.42127i	0.0600847	+	0.211367i
$263$	5.15697	−	25.9258i	0.317992	−	1.59865i	−0.409349	−	0.912378i	$-0.634244\pi$
$263$	5.15697	−	25.9258i	0.317992	−	1.59865i	0.727341	−	0.686276i	$-0.240756\pi$
$264$	0.586474	−	2.30608i	0.0360950	−	0.141929i
$265$	−39.5502	+	7.86703i	−2.42955	+	0.483268i
$266$	−10.5305	−	3.39745i	−0.645664	−	0.208311i
$267$	6.75939	+	8.23634i	0.413668	+	0.504056i
$268$	−6.92393	+	3.39387i	−0.422946	+	0.207313i
$269$	−7.56996	−	14.1624i	−0.461549	−	0.863497i	−0.999786	−	0.0207033i	$-0.993409\pi$
$269$	−7.56996	−	14.1624i	−0.461549	−	0.863497i	0.538237	−	0.842794i	$-0.319091\pi$
$270$	0.0730694	−	4.16009i	0.00444686	−	0.253175i
$271$	−3.72532	+	8.99371i	−0.226297	+	0.546329i	−0.995721	−	0.0924090i	$-0.970543\pi$
$271$	−3.72532	+	8.99371i	−0.226297	+	0.546329i	0.769424	+	0.638738i	$0.220543\pi$
$272$	7.70054	+	3.84355i	0.466914	+	0.233050i
$273$	3.56472	+	8.60600i	0.215747	+	0.520859i
$274$	−26.3197	+	10.3643i	−1.59003	+	0.626129i
$275$	−0.892791	+	2.94314i	−0.0538373	+	0.177478i
$276$	−1.38781	+	10.3495i	−0.0835364	+	0.622964i
$277$	−14.8875	−	1.46629i	−0.894505	−	0.0881010i	−0.359692	−	0.933071i	$-0.617118\pi$
$277$	−14.8875	−	1.46629i	−0.894505	−	0.0881010i	−0.534813	+	0.844970i	$0.679618\pi$
$278$	11.1429	+	9.47708i	0.668308	+	0.568398i
$279$	7.27842	+	4.86328i	0.435748	+	0.291157i
$280$	1.70052	−	11.1863i	0.101625	−	0.668510i
$281$	6.46525	+	9.67593i	0.385684	+	0.577217i	0.972616	−	0.232419i	$-0.0746642\pi$
$281$	6.46525	+	9.67593i	0.385684	+	0.577217i	−0.586931	+	0.809637i	$0.699664\pi$
$282$	−0.792079	−	1.00048i	−0.0471676	−	0.0595775i
$283$	3.90035	+	12.8577i	0.231852	+	0.764313i	0.993246	+	0.116024i	$0.0370151\pi$
$283$	3.90035	+	12.8577i	0.231852	+	0.764313i	−0.761395	+	0.648289i	$0.775485\pi$
$284$	−9.50797	+	1.54634i	−0.564194	+	0.0917583i
$285$	13.0866	+	10.7399i	0.775183	+	0.636176i
$286$	1.73025	−	7.96485i	0.102312	−	0.470971i
$287$	10.5406	+	10.5406i	0.622192	+	0.622192i
$288$	2.61479	−	5.01626i	0.154078	−	0.295586i
$289$	8.74730	−	8.74730i	0.514547	−	0.514547i
$290$	8.31126	+	12.9244i	0.488054	+	0.758947i
$291$	−1.41384	+	1.72276i	−0.0828805	+	0.100990i
$292$	−4.93087	−	7.97209i	−0.288557	−	0.466531i
$293$	12.3215	−	3.73768i	0.719828	−	0.218357i	0.0909432	−	0.995856i	$-0.471012\pi$
$293$	12.3215	−	3.73768i	0.719828	−	0.218357i	0.628885	+	0.777499i	$0.283512\pi$
$294$	0.841249	−	7.23612i	0.0490626	−	0.422019i
$295$	23.3541	−	15.6047i	1.35973	−	0.908540i
$296$	−5.01521	+	5.49355i	−0.291503	+	0.319306i
$297$	0.467388	−	0.699495i	0.0271206	−	0.0405888i
$298$	13.3470	−	1.07827i	0.773172	−	0.0624625i
$299$	−3.50588	+	35.5958i	−0.202750	+	2.05856i
$300$	−3.67103	+	6.32331i	−0.211947	+	0.365076i
$301$	11.6026	+	3.51961i	0.668763	+	0.202867i
$302$	−14.8547	−	6.46092i	−0.854789	−	0.371784i
$303$	4.69803	−	1.94599i	0.269894	−	0.111794i
$304$	9.39848	+	21.0106i	0.539040	+	1.20504i
$305$	−9.12504	−	3.77971i	−0.522498	−	0.216426i
$306$	2.11350	+	2.18907i	0.120821	+	0.125141i
$307$	12.7131	−	6.79531i	0.725576	−	0.387829i	−0.0668770	−	0.997761i	$-0.521304\pi$
$307$	12.7131	−	6.79531i	0.725576	−	0.387829i	0.792453	+	0.609933i	$0.208804\pi$
$308$	1.51257	−	1.71643i	0.0861867	−	0.0978026i
$309$	8.22687	−	6.75162i	0.468010	−	0.384086i
$310$	−16.6023	−	32.4176i	−0.942949	−	1.84120i
$311$	3.97507	+	19.9840i	0.225406	+	1.13319i	0.913271	+	0.407353i	$0.133548\pi$
$311$	3.97507	+	19.9840i	0.225406	+	1.13319i	−0.687865	+	0.725839i	$0.741452\pi$
$312$	8.34767	−	17.4865i	0.472594	−	0.989978i
$313$	4.25386	+	0.846145i	0.240442	+	0.0478269i	0.313840	−	0.949476i	$-0.398384\pi$
$313$	4.25386	+	0.846145i	0.240442	+	0.0478269i	−0.0733981	+	0.997303i	$0.523384\pi$
$314$	1.43109	+	0.797560i	0.0807613	+	0.0450089i
$315$	1.88577	−	3.52804i	0.106251	−	0.198782i
$316$	−12.5527	−	0.441095i	−0.706142	−	0.0248135i
$317$	−11.3136	+	1.11429i	−0.635435	+	0.0625849i	−0.410605	−	0.911813i	$-0.634683\pi$
$317$	−11.3136	+	1.11429i	−0.635435	+	0.0625849i	−0.224830	+	0.974398i	$0.572183\pi$
$318$	−15.9253	−	11.0504i	−0.893046	−	0.619673i
$319$			3.10694i			0.173955i
$320$	−19.6637	+	12.9350i	−1.09923	+	0.723089i
$321$		−	2.48710i		−	0.138816i
$322$	−5.72350	+	8.24847i	−0.318958	+	0.459669i
$323$	−12.3213	+	1.21354i	−0.685573	+	0.0675230i
$324$	1.46301	−	1.36368i	0.0812781	−	0.0757598i
$325$	−11.8062	+	22.0879i	−0.654892	+	1.22522i
$326$	2.92566	−	5.24963i	0.162037	−	0.290750i
$327$	−11.2371	−	2.23520i	−0.621413	−	0.123607i
$328$	1.63300	−	30.9652i	0.0901672	−	1.70977i
$329$	−0.239355	−	1.20332i	−0.0131961	−	0.0663410i
$330$	−3.11551	+	1.59557i	−0.171503	+	0.0878334i
$331$	21.0287	−	17.2578i	1.15584	−	0.948576i	0.156607	−	0.987661i	$-0.449944\pi$
$331$	21.0287	−	17.2578i	1.15584	−	0.948576i	0.999236	+	0.0390850i	$0.0124443\pi$
$332$	3.85795	−	0.243565i	0.211732	−	0.0133674i
$333$	−2.31937	+	1.23973i	−0.127101	+	0.0679368i
$334$	16.6985	−	16.1220i	0.913699	−	0.882156i
$335$	10.4797	+	4.34084i	0.572567	+	0.237165i
$336$	4.43612	−	3.14676i	0.242010	−	0.171670i
$337$	−5.96780	+	2.47195i	−0.325087	+	0.134655i	−0.539258	−	0.842141i	$-0.681295\pi$
$337$	−5.96780	+	2.47195i	−0.325087	+	0.134655i	0.214171	+	0.976796i	$0.431295\pi$
$338$	19.1400	−	44.0058i	1.04108	−	2.39360i
$339$	−7.78215	−	2.36069i	−0.422668	−	0.128215i
$340$	−3.24741	−	12.2369i	−0.176115	−	0.663639i
$341$	0.721823	−	7.32879i	0.0390889	−	0.396876i
$342$	0.655287	+	8.11127i	0.0354339	+	0.438607i
$343$	9.17922	−	13.7377i	0.495631	−	0.741764i
$344$	−10.7013	−	22.8385i	−0.576977	−	1.23137i
$345$	12.7720	−	8.53397i	0.687621	−	0.459454i
$346$	−26.1739	−	3.04290i	−1.40712	−	0.163587i
$347$	−17.2415	+	5.23015i	−0.925573	+	0.280769i	−0.716868	−	0.697209i	$-0.754425\pi$
$347$	−17.2415	+	5.23015i	−0.925573	+	0.280769i	−0.208705	+	0.977979i	$0.566925\pi$
$348$	−1.69450	+	7.18925i	−0.0908349	+	0.385385i
$349$	14.6248	−	17.8204i	0.782847	−	0.953902i	−0.216904	−	0.976193i	$-0.569596\pi$
$349$	14.6248	−	17.8204i	0.782847	−	0.953902i	0.999752	+	0.0222909i	$0.00709599\pi$
$350$	−5.91286	+	3.80237i	−0.316056	+	0.203245i
$351$	4.84420	−	4.84420i	0.258564	−	0.258564i
$352$	−4.75872	+	0.0493113i	−0.253640	+	0.00262830i
$353$	−20.1780	−	20.1780i	−1.07396	−	1.07396i	−0.997037	−	0.0769283i	$-0.975489\pi$
$353$	−20.1780	−	20.1780i	−1.07396	−	1.07396i	−0.0769283	−	0.997037i	$-0.524511\pi$
$354$	13.1936	+	2.86612i	0.701232	+	0.152333i
$355$	10.9538	+	8.98959i	0.581370	+	0.477118i
$356$	12.4540	−	17.2917i	0.660061	−	0.916460i
$357$	0.849253	+	2.79961i	0.0449473	+	0.148171i
$358$	−15.4645	+	12.2433i	−0.817323	+	0.647076i
$359$	1.29323	+	1.93545i	0.0682540	+	0.102149i	0.864026	−	0.503446i	$-0.167935\pi$
$359$	1.29323	+	1.93545i	0.0682540	+	0.102149i	−0.795772	+	0.605596i	$0.792935\pi$
$360$	−8.07931	+	1.99288i	−0.425817	+	0.105034i
$361$	−11.7329	−	7.83967i	−0.617521	−	0.412614i
$362$	15.3675	−	18.0687i	0.807697	−	0.949670i
$363$	10.2427	+	1.00882i	0.537602	+	0.0529492i
$364$	14.8075	−	11.3058i	0.776122	−	0.592585i
$365$	−4.00280	+	13.1954i	−0.209516	+	0.690681i
$366$	−1.73954	−	4.41750i	−0.0909273	−	0.230906i
$367$	12.9140	+	31.1772i	0.674107	+	1.62744i	0.774564	+	0.632496i	$0.217969\pi$
$367$	12.9140	+	31.1772i	0.674107	+	1.62744i	−0.100457	+	0.994941i	$0.532031\pi$
$368$	20.7184	−	2.62651i	1.08002	−	0.136916i
$369$	4.19538	−	10.1286i	0.218403	−	0.527271i
$370$	10.9407	+	0.192166i	0.568778	+	0.00999022i
$371$	−8.78528	−	16.4361i	−0.456109	−	0.853320i
$372$	5.66733	−	16.5647i	0.293837	−	0.858839i
$373$	13.9564	+	17.0059i	0.722633	+	0.880531i	0.996699	−	0.0811799i	$-0.0258688\pi$
$373$	13.9564	+	17.0059i	0.722633	+	0.880531i	−0.274066	+	0.961711i	$0.588369\pi$
$374$	0.785996	−	2.43622i	0.0406429	−	0.125974i
$375$	−3.87864	+	0.771509i	−0.200292	+	0.0398405i
$376$	−1.52767	+	2.04440i	−0.0787837	+	0.105432i
$377$	−4.93591	+	24.8145i	−0.254212	+	1.27801i
$378$	1.84965	−	0.525795i	0.0951357	−	0.0270440i
$379$	2.86341	+	1.53052i	0.147083	+	0.0786176i	0.543297	−	0.839541i	$-0.317176\pi$
$379$	2.86341	+	1.53052i	0.147083	+	0.0786176i	−0.396213	+	0.918158i	$0.629676\pi$
$380$	14.0477	−	30.8071i	0.720633	−	1.58037i
$381$	1.48525	+	15.0800i	0.0760917	+	0.772572i
$382$	3.57045	+	19.7571i	0.182680	+	1.01086i
$383$	−15.8843			−0.811652			−0.405826	−	0.913950i	$-0.633016\pi$
$383$	−15.8843			−0.811652			−0.405826	+	0.913950i	$0.633016\pi$
$384$	−11.0383	−	2.48127i	−0.563294	−	0.126622i
$385$	−3.36544			−0.171519
$386$	−0.326094	−	1.80445i	−0.0165977	−	0.0918439i
$387$	−0.874026	−	8.87413i	−0.0444292	−	0.451098i
$388$	4.05555	+	1.84929i	0.205890	+	0.0938836i
$389$	−23.1522	−	12.3751i	−1.17386	−	0.627443i	−0.235088	−	0.971974i	$-0.575538\pi$
$389$	−23.1522	−	12.3751i	−1.17386	−	0.627443i	−0.938775	+	0.344531i	$0.888038\pi$
$390$	−27.4178	+	7.79400i	−1.38835	+	0.394664i
$391$	−2.19158	+	11.0178i	−0.110833	+	0.557196i
$392$	−14.4196	+	2.08592i	−0.728301	+	0.105355i
$393$	2.46672	−	0.490661i	0.124430	−	0.0247506i
$394$	2.42440	−	7.51449i	0.122140	−	0.378574i
$395$	11.7216	+	14.2828i	0.589778	+	0.718646i
$396$	−1.59196	−	0.544661i	−0.0799988	−	0.0273702i
$397$	−9.80205	−	18.3383i	−0.491951	−	0.920375i	−0.998313	−	0.0580545i	$-0.981510\pi$
$397$	−9.80205	−	18.3383i	−0.491951	−	0.920375i	0.506363	−	0.862321i	$-0.330990\pi$
$398$	34.0472	+	0.598018i	1.70663	+	0.0299759i
$399$	−2.99416	+	7.22854i	−0.149895	+	0.361879i
$400$	14.1068	+	3.85257i	0.705338	+	0.192628i
$401$	6.71056	+	16.2007i	0.335109	+	0.809026i	0.998171	+	0.0604606i	$0.0192569\pi$
$401$	6.71056	+	16.2007i	0.335109	+	0.809026i	−0.663061	+	0.748565i	$0.730743\pi$
$402$	1.99779	+	5.07330i	0.0996405	+	0.253033i
$403$	17.4081	−	57.3869i	0.867161	−	2.85865i
$404$	−6.17185	−	8.08341i	−0.307061	−	0.402165i
$405$	−2.92791	−	0.288374i	−0.145489	−	0.0143294i
$406$	−4.60094	+	5.40966i	−0.228341	+	0.268477i
$407$	1.83961	+	1.22919i	0.0911860	+	0.0609285i
$408$	3.14744	−	5.20857i	0.155822	−	0.257863i
$409$	14.7448	+	22.0671i	0.729082	+	1.09115i	0.991989	+	0.126327i	$0.0403189\pi$
$409$	14.7448	+	22.0671i	0.729082	+	1.09115i	−0.262907	+	0.964821i	$0.584681\pi$
$410$	−35.7631	+	28.3138i	−1.76622	+	1.39832i
$411$	5.80622	+	19.1405i	0.286400	+	0.944134i
$412$	−17.2719	−	12.4397i	−0.850924	−	0.612860i
$413$	10.0345	+	8.23510i	0.493765	+	0.405223i
$414$	7.21539	+	1.56744i	0.354617	+	0.0770355i
$415$	−4.02096	−	4.02096i	−0.197381	−	0.197381i
$416$	−38.0853	−	7.16621i	−1.86729	−	0.351353i
$417$	7.31402	−	7.31402i	0.358169	−	0.358169i
$418$	5.75819	−	3.70291i	0.281642	−	0.181115i
$419$	−3.18330	+	3.87886i	−0.155514	+	0.189495i	−0.844939	−	0.534863i	$-0.820363\pi$
$419$	−3.18330	+	3.87886i	−0.155514	+	0.189495i	0.689425	+	0.724357i	$0.257863\pi$
$420$	−7.78741	−	1.83549i	−0.379987	−	0.0895626i
$421$	36.8978	−	11.1928i	1.79829	−	0.545505i	0.799790	−	0.600280i	$-0.204944\pi$
$421$	36.8978	−	11.1928i	1.79829	−	0.545505i	0.998499	+	0.0547754i	$0.0174443\pi$
$422$	27.3962	+	3.18499i	1.33363	+	0.155043i
$423$	−0.750247	+	0.501299i	−0.0364782	+	0.0243740i
$424$	−13.1916	+	36.4538i	−0.640642	+	1.77035i
$425$	−4.37010	+	6.54031i	−0.211981	+	0.317252i
$426$	0.548494	+	6.78936i	0.0265746	+	0.328946i
$427$	0.447420	−	4.54273i	0.0216522	−	0.219838i
$428$	−4.80778	+	1.27588i	−0.232393	+	0.0616720i
$429$	−5.51519	−	1.67301i	−0.266276	−	0.0807739i
$430$	−14.7979	+	34.0227i	−0.713619	+	1.64072i
$431$	21.5903	−	8.94298i	1.03997	−	0.430768i	0.203667	−	0.979040i	$-0.434714\pi$
$431$	21.5903	−	8.94298i	1.03997	−	0.430768i	0.836300	+	0.548272i	$0.184714\pi$
$432$	−3.38663	−	2.12855i	−0.162939	−	0.102410i
$433$	22.1582	+	9.17822i	1.06485	+	0.441077i	0.845172	−	0.534495i	$-0.179498\pi$
$433$	22.1582	+	9.17822i	1.06485	+	0.441077i	0.219682	+	0.975572i	$0.429498\pi$
$434$	12.1097	−	11.6917i	0.581285	−	0.561218i
$435$	9.58250	−	5.12195i	0.459445	−	0.245579i
$436$	1.44379	+	22.8690i	0.0691452	+	1.09523i
$437$	−23.2236	+	19.0591i	−1.11094	+	0.911721i
$438$	−5.89958	+	3.02140i	−0.281893	+	0.144368i
$439$	−0.602497	−	3.02896i	−0.0287556	−	0.144564i	0.963740	−	0.266842i	$-0.0859802\pi$
$439$	−0.602497	−	3.02896i	−0.0287556	−	0.144564i	−0.992496	+	0.122278i	$0.960980\pi$
$440$	4.68264	+	5.20403i	0.223236	+	0.248092i
$441$	−5.05219	−	1.00494i	−0.240581	−	0.0478544i
$442$	10.1480	−	18.2089i	0.482689	−	0.866108i
$443$	−1.64697	+	3.08126i	−0.0782499	+	0.146395i	−0.918003	−	0.396573i	$-0.870199\pi$
$443$	−1.64697	+	3.08126i	−0.0782499	+	0.146395i	0.839753	+	0.542968i	$0.182699\pi$
$444$	3.58635	+	3.84757i	0.170200	+	0.182598i
$445$	−31.1966	+	3.07260i	−1.47886	+	0.145655i
$446$	−11.6720	+	16.8212i	−0.552687	+	0.796509i
$447$		−	9.46852i		−	0.447846i
$448$	−8.35870	−	6.96113i	−0.394911	−	0.328883i
$449$			8.19634i			0.386809i	0.981119	+	0.193404i	$0.0619530\pi$
$449$			8.19634i			0.386809i	−0.981119	+	0.193404i	$0.938047\pi$
$450$	4.24771	+	2.94743i	0.200239	+	0.138943i
$451$	−9.17855	+	0.904008i	−0.432201	+	0.0425681i
$452$	−0.571180	+	16.2546i	−0.0268661	+	0.764553i
$453$	−5.39954	+	10.1018i	−0.253693	+	0.474626i
$454$	−2.49521	−	1.39060i	−0.117106	−	0.0652642i
$455$	−26.8791	−	5.34658i	−1.26011	−	0.250652i
$456$	15.3436	−	5.42781i	0.718532	−	0.254180i
$457$	−2.68458	−	13.4963i	−0.125579	−	0.631329i	−0.991388	−	0.130955i	$-0.958196\pi$
$457$	−2.68458	−	13.4963i	−0.125579	−	0.631329i	0.865809	−	0.500374i	$-0.166804\pi$
$458$	−11.9577	−	23.3486i	−0.558747	−	1.09101i
$459$	1.66322	−	1.36497i	0.0776325	−	0.0637114i
$460$	−23.0490	−	20.3115i	−1.07466	−	0.947027i
$461$	−16.4657	+	8.80109i	−0.766883	+	0.409908i	−0.807952	−	0.589249i	$-0.799424\pi$
$461$	−16.4657	+	8.80109i	−0.766883	+	0.409908i	0.0410686	+	0.999156i	$0.486924\pi$
$462$	−1.12363	−	1.16381i	−0.0522761	−	0.0541453i
$463$	27.6072	+	11.4353i	1.28302	+	0.531443i	0.916897	−	0.399125i	$-0.130686\pi$
$463$	27.6072	+	11.4353i	1.28302	+	0.531443i	0.366120	+	0.930568i	$0.380686\pi$
$464$	14.7667	−	0.412461i	0.685529	−	0.0191480i
$465$	−23.7936	+	9.85564i	−1.10340	+	0.457044i
$466$	−3.08996	−	1.34395i	−0.143139	−	0.0622574i
$467$	27.7806	+	8.42716i	1.28553	+	0.389963i	0.857820	−	0.513951i	$-0.171819\pi$
$467$	27.7806	+	8.42716i	1.28553	+	0.389963i	0.427715	+	0.903914i	$0.359319\pi$
$468$	−11.8494	−	6.87920i	−0.547736	−	0.317991i
$469$	−0.513842	+	5.21713i	−0.0237270	+	0.240904i
$470$	3.74209	−	0.302314i	0.172610	−	0.0139447i
$471$	0.643615	−	0.963237i	0.0296562	−	0.0443836i
$472$	−1.22785	−	26.9747i	−0.0565163	−	1.24161i
$473$	−6.23745	+	4.16773i	−0.286798	+	0.191632i
$474$	−1.02563	+	8.82213i	−0.0471089	+	0.405214i
$475$	−20.1307	+	6.10658i	−0.923659	+	0.280189i
$476$	4.97623	−	3.07788i	0.228085	−	0.141075i
$477$	−8.69519	+	10.5951i	−0.398125	+	0.485117i
$478$	13.9202	+	21.6466i	0.636697	+	0.990094i
$479$	6.45555	−	6.45555i	0.294962	−	0.294962i	−0.544075	−	0.839037i	$-0.683119\pi$
$479$	6.45555	−	6.45555i	0.294962	−	0.294962i	0.839037	+	0.544075i	$0.183119\pi$
$480$	7.99709	+	14.5957i	0.365015	+	0.666198i
$481$	12.7398	+	12.7398i	0.580886	+	0.580886i
$482$	−2.33012	+	10.7262i	−0.106134	+	0.488567i
$483$	5.48772	+	4.50365i	0.249700	+	0.204923i
$484$	−3.30437	−	20.3176i	−0.150198	−	0.923525i
$485$	−1.90335	−	6.27451i	−0.0864268	−	0.284911i
$486$	−0.877831	−	1.10879i	−0.0398192	−	0.0502957i
$487$	14.3468	+	21.4715i	0.650115	+	0.972966i	0.999354	+	0.0359325i	$0.0114401\pi$
$487$	14.3468	+	21.4715i	0.650115	+	0.972966i	−0.349239	+	0.937034i	$0.613560\pi$
$488$	−7.64703	+	5.62886i	−0.346165	+	0.254807i
$489$	−3.53341	−	2.36095i	−0.159786	−	0.106766i
$490$	16.3263	+	13.8856i	0.737548	+	0.627286i
$491$	11.3071	+	1.11365i	0.510282	+	0.0502584i	0.349882	−	0.936794i	$-0.386222\pi$
$491$	11.3071	+	1.11365i	0.510282	+	0.0502584i	0.160400	+	0.987052i	$0.448722\pi$
$492$	−21.7316	−	2.91410i	−0.979737	−	0.131378i
$493$	−2.30666	+	7.60403i	−0.103887	+	0.342468i
$494$	51.8723	−	20.4265i	2.33384	−	0.919031i
$495$	0.947180	+	2.28669i	0.0425726	+	0.102779i
$496$	−34.9284	−	2.45777i	−1.56833	−	0.110357i
$497$	−2.50620	+	6.05049i	−0.112418	+	0.271402i
$498$	0.0480032	−	2.73299i	0.00215108	−	0.122468i
$499$	−19.5564	−	36.5874i	−0.875463	−	1.63788i	−0.765032	−	0.643993i	$-0.777277\pi$
$499$	−19.5564	−	36.5874i	−0.875463	−	1.63788i	−0.110432	−	0.993884i	$-0.535223\pi$
$500$	3.48114	+	7.10197i	0.155681	+	0.317610i
$501$	−10.4121	−	12.6872i	−0.465180	−	0.566824i
$502$	3.89973	+	1.25817i	0.174053	+	0.0561549i
$503$	5.30122	−	1.05448i	0.236370	−	0.0470169i	−0.0754838	−	0.997147i	$-0.524050\pi$
$503$	5.30122	−	1.05448i	0.236370	−	0.0470169i	0.311854	+	0.950130i	$0.399050\pi$
$504$	−1.96528	−	3.30580i	−0.0875405	−	0.147252i
$505$	−2.91871	+	14.6733i	−0.129881	+	0.652954i
$506$	−1.69849	−	5.97498i	−0.0755073	−	0.265620i
$507$	−29.9259	−	15.9957i	−1.32906	−	0.710395i
$508$	28.3891	−	10.6072i	1.25956	−	0.470617i
$509$	−3.73561	−	37.9283i	−0.165578	−	1.68114i	−0.615548	−	0.788100i	$-0.711065\pi$
$509$	−3.73561	−	37.9283i	−0.165578	−	1.68114i	0.449970	−	0.893044i	$-0.351435\pi$
$510$	−8.80960	+	1.59204i	−0.390095	+	0.0704967i
$511$	−6.37284			−0.281918
$512$	0.866112	+	22.6108i	0.0382771	+	0.999267i
$513$	5.75422			0.254055
$514$	−4.54302	+	0.820999i	−0.200384	+	0.0362127i
$515$	3.06906	+	31.1607i	0.135239	+	1.37311i
$516$	−16.7061	+	6.24200i	−0.735446	+	0.274789i
$517$	0.669462	+	0.357835i	0.0294429	+	0.0157376i
$518$	1.38279	+	4.86441i	0.0607565	+	0.213730i
$519$	−3.63500	+	18.2744i	−0.159559	+	0.802157i
$520$	29.1318	+	49.0027i	1.27751	+	2.14891i
$521$	21.2766	−	4.23219i	0.932147	−	0.185416i	0.294418	−	0.955677i	$-0.404874\pi$
$521$	21.2766	−	4.23219i	0.932147	−	0.185416i	0.637729	+	0.770261i	$0.279874\pi$
$522$	4.97058	+	1.60366i	0.217556	+	0.0701902i
$523$	21.7044	+	26.4469i	0.949068	+	1.15644i	0.987569	+	0.157184i	$0.0502415\pi$
$523$	21.7044	+	26.4469i	0.949068	+	1.15644i	−0.0385016	+	0.999259i	$0.512258\pi$
$524$	−2.21392	−	4.51668i	−0.0967155	−	0.197312i
$525$	2.34327	+	4.38395i	0.102269	+	0.191331i
$526$	−0.656507	+	37.3772i	−0.0286251	+	1.62972i
$527$	7.20767	−	17.4009i	0.313971	−	0.757993i
$528$	−0.236205	+	3.35680i	−0.0102795	+	0.146086i
$529$	1.62998	+	3.93511i	0.0708686	+	0.171092i
$530$	53.0624	−	20.8951i	2.30488	−	0.907626i
$531$	2.77131	−	9.13580i	0.120265	−	0.396460i
$532$	15.5094	+	2.07973i	0.672418	+	0.0901679i
$533$	−74.7435	−	7.36159i	−3.23750	−	0.318866i
$534$	−11.4783	−	9.76230i	−0.496713	−	0.422456i
$535$	6.08407	+	4.06524i	0.263037	+	0.175756i
$536$	8.78228	−	6.46450i	0.379337	−	0.279224i
$537$	7.74863	+	11.5967i	0.334378	+	0.500432i
$538$	14.0967	+	17.8056i	0.607752	+	0.767653i
$539$	1.25796	+	4.14695i	0.0541843	+	0.178622i
$540$	0.944566	+	5.80785i	0.0406477	+	0.249930i
$541$	−11.3917	−	9.34891i	−0.489767	−	0.401941i	0.356836	−	0.934167i	$-0.383856\pi$
$541$	−11.3917	−	9.34891i	−0.489767	−	0.401941i	−0.846602	+	0.532226i	$0.821356\pi$
$542$	2.92252	−	13.4532i	0.125533	−	0.577865i
$543$	−11.8600	−	11.8600i	−0.508961	−	0.508961i
$544$	−11.6833	−	3.41229i	−0.500916	−	0.146301i
$545$	23.8353	−	23.8353i	1.02099	−	1.02099i
$546$	−7.12531	−	11.0802i	−0.304935	−	0.474189i
$547$	−17.1044	+	20.8418i	−0.731332	+	0.891131i	−0.997344	−	0.0728390i	$-0.976794\pi$
$547$	−17.1044	+	20.8418i	−0.731332	+	0.891131i	0.266012	+	0.963970i	$0.414294\pi$
$548$	34.0218	−	21.0430i	1.45334	−	0.898914i
$549$	−3.21255	+	0.974516i	−0.137108	+	0.0415913i
$550$	0.502278	−	4.32041i	0.0214172	−	0.184223i
$551$	−17.6696	+	11.8065i	−0.752751	+	0.502972i
$552$	−0.671492	−	14.7521i	−0.0285806	−	0.627890i
$553$	−4.74418	+	7.10017i	−0.201743	+	0.301930i
$554$	21.0873	−	1.70359i	0.895914	−	0.0723785i
$555$	0.758398	−	7.70015i	0.0321922	−	0.326853i
$556$	−17.8907	−	10.3866i	−0.758737	−	0.440488i
$557$	−8.53201	−	2.58816i	−0.361513	−	0.109664i	0.104303	−	0.994546i	$-0.466739\pi$
$557$	−8.53201	−	2.58816i	−0.361513	−	0.109664i	−0.465816	+	0.884882i	$0.654239\pi$
$558$	−11.3523	−	4.93758i	−0.480580	−	0.209025i
$559$	−56.4384	+	23.3776i	−2.38709	+	0.988766i
$560$	0.446778	+	15.9954i	0.0188798	+	0.675927i
$561$	−1.67232	−	0.692696i	−0.0706052	−	0.0292456i
$562$	−11.4310	−	11.8397i	−0.482187	−	0.499428i
$563$	−18.3161	+	9.79016i	−0.771932	+	0.412606i	−0.809822	−	0.586676i	$-0.800436\pi$
$563$	−18.3161	+	9.79016i	−0.771932	+	0.412606i	0.0378901	+	0.999282i	$0.487936\pi$
$564$	1.35393	+	1.19313i	0.0570108	+	0.0502397i
$565$	18.4950	−	15.1785i	0.778091	−	0.638563i
$566$	−8.66170	−	16.9128i	−0.364079	−	0.710898i
$567$	−0.265268	−	1.33359i	−0.0111402	−	0.0560055i
$568$	12.8431	−	4.54323i	0.538883	−	0.190630i
$569$	41.0779	+	8.17090i	1.72208	+	0.342542i	0.954453	−	0.298360i	$-0.0964397\pi$
$569$	41.0779	+	8.17090i	1.72208	+	0.342542i	0.767622	+	0.640903i	$0.221440\pi$
$570$	−20.9133	−	11.6551i	−0.875961	−	0.488180i
$571$	19.5971	−	36.6636i	0.820113	−	1.53432i	−0.0249693	−	0.999688i	$-0.507949\pi$
$571$	19.5971	−	36.6636i	0.820113	−	1.53432i	0.845083	−	0.534636i	$-0.179551\pi$
$572$	−0.404794	+	11.5196i	−0.0169253	+	0.481659i
$573$	14.1283	−	1.39152i	0.590220	−	0.0581316i
$574$	−17.3200	−	12.0181i	−0.722923	−	0.501626i
$575$			19.0873i			0.795996i
$576$	−2.37734	+	7.63860i	−0.0990559	+	0.318275i
$577$		−	2.64771i		−	0.110226i	−0.998480	−	0.0551128i	$-0.982448\pi$
$577$		−	2.64771i		−	0.110226i	0.998480	−	0.0551128i	$-0.0175518\pi$
$578$	−9.97344	+	14.3733i	−0.414840	+	0.597850i
$579$	−1.29036	+	0.127089i	−0.0536256	+	0.00528166i
$580$	−14.8170	−	15.8963i	−0.615242	−	0.660056i
$581$	1.23887	−	2.31776i	0.0513969	−	0.0961568i
$582$	1.53432	−	2.75310i	0.0635997	−	0.114120i
$583$	11.3092	+	2.24954i	0.468380	+	0.0931665i
$584$	8.86712	+	9.85442i	0.366924	+	0.407779i
$585$	3.93213	+	19.7681i	0.162574	+	0.817312i
$586$	−16.2074	+	8.30044i	−0.669522	+	0.342888i
$587$	28.3833	−	23.2935i	1.17150	−	0.961428i	0.171784	−	0.985135i	$-0.445047\pi$
$587$	28.3833	−	23.2935i	1.17150	−	0.961428i	0.999719	+	0.0237071i	$0.00754692\pi$
$588$	0.649128	+	10.2819i	0.0267696	+	0.424017i
$589$	44.4229	−	23.7445i	1.83041	−	0.978376i
$590$	−28.5766	+	27.5901i	−1.17648	+	1.13587i
$591$	−5.15825	−	2.13662i	−0.212182	−	0.0878886i
$592$	5.59790	−	8.90653i	0.230072	−	0.366056i
$593$	2.95804	−	1.22526i	0.121472	−	0.0503155i	−0.321119	−	0.947039i	$-0.604059\pi$
$593$	2.95804	−	1.22526i	0.121472	−	0.0503155i	0.442592	+	0.896723i	$0.354059\pi$
$594$	−0.474528	+	1.09101i	−0.0194701	+	0.0447649i
$595$	−8.23669	−	2.49857i	−0.337671	−	0.102431i
$596$	−18.3035	+	4.85735i	−0.749740	+	0.198965i
$597$	2.36013	−	23.9628i	0.0965936	−	0.980732i
$598$	−4.07324	−	50.4194i	−0.166567	−	2.06180i
$599$	−10.3893	+	15.5486i	−0.424494	+	0.635300i	−0.980648	−	0.195779i	$-0.937276\pi$
$599$	−10.3893	+	15.5486i	−0.424494	+	0.635300i	0.556154	+	0.831079i	$0.312276\pi$
$600$	3.51856	−	9.72322i	0.143645	−	0.396949i
$601$	22.0844	−	14.7563i	0.900842	−	0.601923i	−0.0165698	−	0.999863i	$-0.505275\pi$
$601$	22.0844	−	14.7563i	0.900842	−	0.601923i	0.917412	+	0.397939i	$0.130275\pi$
$602$	−17.0322	−	1.98011i	−0.694180	−	0.0807033i
$603$	3.68947	−	1.11919i	0.150247	−	0.0455769i
$604$	22.2977	+	5.25556i	0.907281	+	0.213846i
$605$	−19.2098	+	23.4073i	−0.780991	+	0.951640i
$606$	−6.04869	+	3.88972i	−0.245711	+	0.158009i
$607$	−6.31599	+	6.31599i	−0.256358	+	0.256358i	−0.823571	−	0.567213i	$-0.808022\pi$
$607$	−6.31599	+	6.31599i	−0.256358	+	0.256358i	0.567213	+	0.823571i	$0.308022\pi$
$608$	−18.3637	−	26.8761i	−0.744747	−	1.08997i
$609$	3.55081	+	3.55081i	0.143886	+	0.143886i
$610$	13.6496	+	2.96519i	0.552658	+	0.120057i
$611$	4.77838	+	3.92151i	0.193313	+	0.158647i
$612$	−3.49184	−	2.51492i	−0.141149	−	0.101660i
$613$	−2.05732	−	6.78206i	−0.0830942	−	0.273925i	0.905541	−	0.424258i	$-0.139465\pi$
$613$	−2.05732	−	6.78206i	−0.0830942	−	0.273925i	−0.988635	+	0.150334i	$0.951965\pi$
$614$	−15.9835	+	12.6542i	−0.645041	+	0.510680i
$615$	17.9195	+	26.8184i	0.722584	+	1.08142i
$616$	−1.67332	+	2.76911i	−0.0674201	+	0.111571i
$617$	−22.5948	−	15.0973i	−0.909631	−	0.607796i	0.0102697	−	0.999947i	$-0.496731\pi$
$617$	−22.5948	−	15.0973i	−0.909631	−	0.607796i	−0.919901	+	0.392151i	$0.871731\pi$
$618$	−9.75108	+	11.4651i	−0.392246	+	0.461193i
$619$	15.4761	+	1.52427i	0.622039	+	0.0612655i	0.404127	−	0.914703i	$-0.367575\pi$
$619$	15.4761	+	1.52427i	0.622039	+	0.0612655i	0.217912	+	0.975968i	$0.430075\pi$
$620$	31.2580	+	40.9392i	1.25535	+	1.64416i
$621$	1.51559	−	4.99623i	0.0608185	−	0.200492i
$622$	−10.5579	−	26.8115i	−0.423335	−	1.07504i
$623$	−5.54417	−	13.3848i	−0.222123	−	0.536252i
$624$	−7.21939	+	26.4349i	−0.289007	+	1.05824i
$625$	11.4476	−	27.6370i	0.457904	−	1.10548i
$626$	−6.13277	−	0.107718i	−0.245115	−	0.00430529i
$627$	−2.28198	−	4.26928i	−0.0911334	−	0.170499i
$628$	−2.19220	−	0.750024i	−0.0874782	−	0.0299292i
$629$	3.58975	+	4.37412i	0.143133	+	0.174408i
$630$	−1.73708	+	5.38413i	−0.0692071	+	0.214509i
$631$	12.2544	−	2.43754i	0.487838	−	0.0970371i	0.0549584	−	0.998489i	$-0.482497\pi$
$631$	12.2544	−	2.43754i	0.487838	−	0.0970371i	0.432880	+	0.901452i	$0.357497\pi$
$632$	17.5801	−	2.54311i	0.699299	−	0.101159i
$633$	3.80475	−	19.1278i	0.151225	−	0.760260i
$634$	15.4646	−	4.39608i	0.614176	−	0.174591i
$635$	−39.3172	−	21.0155i	−1.56025	−	0.833973i
$636$	24.9419	+	11.3733i	0.989012	+	0.450980i
$637$	3.45896	+	35.1194i	0.137049	+	1.39148i
$638$	−0.781389	−	4.32383i	−0.0309355	−	0.171182i
$639$	4.81645			0.190536
$640$	24.1122	−	22.9466i	0.953119	−	0.907046i
$641$	36.1648			1.42842			0.714211	−	0.699930i	$-0.246786\pi$
$641$	36.1648			1.42842			0.714211	+	0.699930i	$0.246786\pi$
$642$	0.625500	+	3.46122i	0.0246865	+	0.136604i
$643$	−1.38797	−	14.0923i	−0.0547362	−	0.555746i	−0.982972	−	0.183754i	$-0.941175\pi$
$643$	−1.38797	−	14.0923i	−0.0547362	−	0.555746i	0.928236	−	0.371992i	$-0.121325\pi$
$644$	5.89076	−	12.9186i	0.232128	−	0.509065i
$645$	23.1370	+	12.3670i	0.911018	+	0.486949i
$646$	16.8419	−	4.78762i	0.662637	−	0.188366i
$647$	−2.24615	+	11.2921i	−0.0883052	+	0.443940i	0.911185	+	0.411998i	$0.135169\pi$
$647$	−2.24615	+	11.2921i	−0.0883052	+	0.443940i	−0.999490	+	0.0319417i	$0.989831\pi$
$648$	−1.69306	+	2.26573i	−0.0665097	+	0.0890064i
$649$	−7.87724	+	1.56688i	−0.309209	+	0.0615054i
$650$	10.8753	−	33.7083i	0.426565	−	1.32215i
$651$	−7.55088	−	9.20078i	−0.295942	−	0.360607i
$652$	−2.75128	+	8.04155i	−0.107749	+	0.314932i
$653$	4.76743	+	8.91923i	0.186564	+	0.349036i	0.957764	−	0.287557i	$-0.0928430\pi$
$653$	4.76743	+	8.91923i	0.186564	+	0.349036i	−0.771200	+	0.636593i	$0.780343\pi$
$654$	16.2005	+	0.284552i	0.633490	+	0.0111269i
$655$	−2.83166	+	6.83622i	−0.110642	+	0.267113i
$656$	5.51510	+	43.5041i	0.215328	+	1.69855i
$657$	1.79359	+	4.33012i	0.0699748	+	0.168934i
$658$	0.635735	+	1.61443i	0.0247835	+	0.0629368i
$659$	−8.68982	+	28.6465i	−0.338507	+	1.11591i	0.608192	+	0.793790i	$0.291895\pi$
$659$	−8.68982	+	28.6465i	−0.338507	+	1.11591i	−0.946699	+	0.322119i	$0.895605\pi$
$660$	3.93448	−	3.00406i	0.153149	−	0.116933i
$661$	−5.84686	−	0.575865i	−0.227416	−	0.0223986i	−0.0163330	−	0.999867i	$-0.505199\pi$
$661$	−5.84686	−	0.575865i	−0.227416	−	0.0223986i	−0.211083	+	0.977468i	$0.567699\pi$
$662$	−24.9248	+	29.3059i	−0.968728	+	1.13901i
$663$	−12.2560	−	8.18919i	−0.475983	−	0.318042i
$664$	−5.30774	+	1.30923i	−0.205980	+	0.0508079i
$665$	−12.7888	−	19.1397i	−0.495927	−	0.742207i
$666$	2.91601	−	2.30862i	0.112993	−	0.0894570i
$667$	5.59727	+	18.4517i	0.216727	+	0.714453i
$668$	−19.1841	+	26.6361i	−0.742256	+	1.03058i
$669$	11.1912	+	9.18437i	0.432676	+	0.355088i
$670$	−15.6760	−	3.40539i	−0.605617	−	0.131562i
$671$	1.99705	+	1.99705i	0.0770951	+	0.0770951i
$672$	−5.38222	+	5.49493i	−0.207624	+	0.211972i
$673$	27.9171	−	27.9171i	1.07613	−	1.07613i	0.0792737	−	0.996853i	$-0.474740\pi$
$673$	27.9171	−	27.9171i	1.07613	−	1.07613i	0.996853	−	0.0792737i	$-0.0252601\pi$
$674$	7.68353	−	4.94103i	0.295959	−	0.190321i
$675$	2.31924	−	2.82600i	0.0892676	−	0.108773i
$676$	−15.5692	+	66.0552i	−0.598815	+	2.54059i
$677$	−5.57494	+	1.69114i	−0.214262	+	0.0649957i	−0.395591	−	0.918427i	$-0.629460\pi$
$677$	−5.57494	+	1.69114i	−0.214262	+	0.0649957i	0.181329	+	0.983423i	$0.441960\pi$
$678$	11.4239	+	1.32811i	0.438732	+	0.0510056i
$679$	2.51962	−	1.68356i	0.0966942	−	0.0646090i
$680$	7.59687	+	16.2130i	0.291327	+	0.621741i
$681$	−1.12219	+	1.67947i	−0.0430023	+	0.0643575i
$682$	0.838637	+	10.3808i	0.0321131	+	0.397502i
$683$	4.36116	−	44.2796i	0.166875	−	1.69431i	−0.438788	−	0.898591i	$-0.644592\pi$
$683$	4.36116	−	44.2796i	0.166875	−	1.69431i	0.605663	−	0.795721i	$-0.292908\pi$
$684$	−2.95191	−	11.1234i	−0.112869	−	0.425314i
$685$	−56.3130	−	17.0824i	−2.15161	−	0.652684i
$686$	−9.31945	+	21.4269i	−0.355818	+	0.818082i
$687$	−17.1372	+	7.09846i	−0.653825	+	0.270823i
$688$	20.6366	+	29.0922i	0.786762	+	1.10913i
$689$	86.7507	+	35.9333i	3.30494	+	1.36895i
$690$	−15.6281	+	15.0886i	−0.594953	+	0.574414i
$691$	−40.2580	+	21.5184i	−1.53149	+	0.818597i	−0.999602	−	0.0282193i	$-0.991016\pi$
$691$	−40.2580	+	21.5184i	−1.53149	+	0.818597i	−0.531885	+	0.846816i	$0.678516\pi$
$692$	37.1908	−	2.34798i	1.41378	−	0.0892567i
$693$	−0.884244	+	0.725680i	−0.0335897	+	0.0275663i
$694$	22.6791	−	11.6149i	0.860888	−	0.440894i
$695$	5.93693	+	29.8469i	0.225200	+	1.13216i
$696$	0.550107	−	10.4312i	0.0208518	−	0.395395i
$697$	−23.1351	−	4.60185i	−0.876303	−	0.174307i
$698$	−15.8711	+	28.4782i	−0.600731	+	1.07792i
$699$	−1.12317	+	2.10131i	−0.0424823	+	0.0794788i
$700$	7.27247	−	6.77872i	0.274873	−	0.256211i
$701$	−30.4933	+	3.00333i	−1.15172	+	0.113434i	−0.655799	−	0.754935i	$-0.727668\pi$
$701$	−30.4933	+	3.00333i	−1.15172	+	0.113434i	−0.495918	+	0.868370i	$0.665168\pi$
$702$	−5.52323	+	7.95985i	−0.208461	+	0.300425i
$703$			15.1331i			0.570755i
$704$	6.61017	−	1.26543i	0.249130	−	0.0476928i
$705$		−	2.65468i		−	0.0999811i
$706$	33.1558	+	23.0064i	1.24784	+	0.865856i
$707$	−6.88101	+	0.677720i	−0.258787	+	0.0254883i
$708$	−19.0820	−	0.670533i	−0.717145	−	0.0252002i
$709$	3.17698	−	5.94370i	0.119314	−	0.223221i	−0.815173	−	0.579217i	$-0.803358\pi$
$709$	3.17698	−	5.94370i	0.119314	−	0.223221i	0.934487	+	0.355996i	$0.115858\pi$
$710$	−17.5050	−	9.75568i	−0.656952	−	0.366124i
$711$	6.15953	+	1.22521i	0.231000	+	0.0459488i
$712$	−12.9830	+	27.1966i	−0.486560	+	1.01923i
$713$	−8.91629	−	44.8252i	−0.333918	−	1.67872i
$714$	−1.88598	−	3.68256i	−0.0705810	−	0.137816i
$715$	13.1074	−	10.7569i	0.490188	−	0.402287i
$716$	18.4423	−	20.9279i	0.689221	−	0.782111i
$717$	16.0494	−	8.57857i	0.599375	−	0.320373i
$718$	−2.28651	−	2.36827i	−0.0853318	−	0.0883830i
$719$	−15.9699	−	6.61496i	−0.595578	−	0.246696i	0.0644705	−	0.997920i	$-0.479464\pi$
$719$	−15.9699	−	6.61496i	−0.595578	−	0.246696i	−0.660048	+	0.751223i	$0.729464\pi$
$720$	10.7425	−	4.80536i	0.400351	−	0.179085i
$721$	−13.3694	+	5.53780i	−0.497904	+	0.206239i
$722$	18.3000	+	7.95945i	0.681056	+	0.296220i
$723$	7.42729	+	2.25304i	0.276224	+	0.0837916i
$724$	−16.8422	+	29.0106i	−0.625937	+	1.07817i
$725$	−1.32338	+	13.4365i	−0.0491490	+	0.499018i
$726$	−14.5082	+	1.17208i	−0.538449	+	0.0434998i
$727$	22.0145	−	32.9470i	0.816472	−	1.22194i	−0.155731	−	0.987799i	$-0.549773\pi$
$727$	22.0145	−	32.9470i	0.816472	−	1.22194i	0.972203	−	0.234138i	$-0.0752266\pi$
$728$	−17.7637	+	19.4580i	−0.658367	+	0.721162i
$729$	−0.831470	+	0.555570i	−0.0307952	+	0.0205767i
$730$	2.25195	−	19.3704i	0.0833482	−	0.716931i
$731$	−18.3600	+	5.56943i	−0.679068	+	0.205993i
$732$	3.53186	+	5.71021i	0.130541	+	0.211056i
$733$	−7.67889	+	9.35675i	−0.283626	+	0.345600i	−0.895262	−	0.445540i	$-0.853012\pi$
$733$	−7.67889	+	9.35675i	−0.283626	+	0.345600i	0.611636	+	0.791139i	$0.290512\pi$
$734$	−25.8131	−	40.1406i	−0.952778	−	1.48162i
$735$	10.7163	−	10.7163i	0.395277	−	0.395277i
$736$	−28.1726	+	8.86587i	−1.03846	+	0.326800i
$737$	−2.29352	−	2.29352i	−0.0844828	−	0.0844828i
$738$	−3.29128	+	15.1507i	−0.121154	+	0.557707i
$739$	−9.79998	−	8.04263i	−0.360498	−	0.295853i	0.436657	−	0.899628i	$-0.356162\pi$
$739$	−9.79998	−	8.04263i	−0.360498	−	0.295853i	−0.797155	+	0.603775i	$0.793662\pi$
$740$	−15.2741	+	2.48412i	−0.561488	+	0.0913182i
$741$	−11.4432	−	37.7232i	−0.420377	−	1.38580i
$742$	16.3599	+	20.6642i	0.600589	+	0.758605i
$743$	−17.6397	−	26.3996i	−0.647136	−	0.968508i	−0.999467	−	0.0326326i	$-0.989611\pi$
$743$	−17.6397	−	26.3996i	−0.647136	−	0.968508i	0.352331	−	0.935875i	$-0.385389\pi$
$744$	−3.72107	+	24.4779i	−0.136421	+	0.897404i
$745$	23.1624	+	15.4766i	0.848604	+	0.567019i
$746$	−23.6996	−	20.1566i	−0.867704	−	0.737985i
$747$	−1.92351	−	0.189449i	−0.0703774	−	0.00693157i
$748$	−0.481145	+	3.58809i	−0.0175924	+	0.131193i
$749$	−0.981670	+	3.23613i	−0.0358694	+	0.118246i
$750$	5.20375	−	2.04916i	0.190014	−	0.0748246i
$751$	15.6515	+	37.7860i	0.571130	+	1.37883i	0.900594	+	0.434662i	$0.143132\pi$
$751$	15.6515	+	37.7860i	0.571130	+	1.37883i	−0.329463	+	0.944168i	$0.606868\pi$
$752$	1.61185	−	3.22934i	0.0587783	−	0.117762i
$753$	1.10882	−	2.67693i	0.0404077	−	0.0975527i
$754$	0.628365	−	35.7750i	0.0228837	−	1.30285i
$755$	−15.8859	−	29.7204i	−0.578147	−	1.08164i
$756$	−2.44187	+	1.19692i	−0.0888098	+	0.0435315i
$757$	−24.9562	−	30.4093i	−0.907050	−	1.10524i	−0.994038	−	0.109034i	$-0.965224\pi$
$757$	−24.9562	−	30.4093i	−0.907050	−	1.10524i	0.0869884	−	0.996209i	$-0.472276\pi$
$758$	−4.36984	−	1.40984i	−0.158720	−	0.0512078i
$759$	−4.30794	+	0.856903i	−0.156368	+	0.0311036i
$760$	−11.8019	+	46.4063i	−0.428100	+	1.68333i
$761$	−4.31904	+	21.7133i	−0.156565	+	0.787106i	0.820080	+	0.572248i	$0.193929\pi$
$761$	−4.31904	+	21.7133i	−0.156565	+	0.787106i	−0.976645	+	0.214857i	$0.931071\pi$
$762$	−5.85957	−	20.6129i	−0.212270	−	0.746726i
$763$	13.7391	+	7.34371i	0.497390	+	0.265860i
$764$	−9.93777	−	26.5975i	−0.359536	−	0.962264i
$765$	0.620471	+	6.29975i	0.0224332	+	0.227768i
$766$	22.1058	−	3.99488i	0.798714	−	0.144341i
$767$	−65.4032			−2.36157
$768$	15.9857	+	0.677010i	0.576833	+	0.0244295i
$769$	44.7569			1.61398			0.806988	−	0.590568i	$-0.201096\pi$
$769$	44.7569			1.61398			0.806988	+	0.590568i	$0.201096\pi$
$770$	4.68358	−	0.846401i	0.168785	−	0.0305022i
$771$	0.319971	+	3.24872i	0.0115235	+	0.117000i
$772$	0.907630	+	2.42919i	0.0326663	+	0.0874283i
$773$	16.6543	+	8.90193i	0.599015	+	0.320180i	0.742888	−	0.669416i	$-0.233456\pi$
$773$	16.6543	+	8.90193i	0.599015	+	0.320180i	−0.143873	+	0.989596i	$0.545956\pi$
$774$	3.44818	+	12.1301i	0.123942	+	0.436006i
$775$	6.24329	−	31.3872i	0.224266	−	1.12746i
$776$	−6.10909	−	1.55364i	−0.219304	−	0.0557726i
$777$	3.50722	−	0.697630i	0.125821	−	0.0250273i
$778$	35.3326	+	11.3993i	1.26673	+	0.408686i
$779$	−40.0200	−	48.7645i	−1.43387	−	1.74717i
$780$	36.1964	−	17.7422i	1.29604	−	0.635273i
$781$	−1.91008	−	3.57351i	−0.0683480	−	0.127870i
$782$	0.278999	−	15.8844i	0.00997699	−	0.568024i
$783$	1.41330	−	3.41200i	0.0505072	−	0.121935i
$784$	19.5428	−	6.52942i	0.697956	−	0.233194i
$785$	1.30431	+	3.14889i	0.0465529	+	0.112389i
$786$	−3.30947	+	1.30322i	−0.118045	+	0.0464841i
$787$	1.43354	−	4.72574i	0.0511000	−	0.168454i	−0.927676	−	0.373385i	$-0.878197\pi$
$787$	1.43354	−	4.72574i	0.0511000	−	0.168454i	0.978776	+	0.204931i	$0.0656970\pi$
$788$	−1.48409	+	11.0674i	−0.0528684	+	0.394261i
$789$	26.3064	+	2.59096i	0.936534	+	0.0922406i
$790$	−19.9047	−	16.9290i	−0.708178	−	0.602307i
$791$	9.19410	+	6.14330i	0.326905	+	0.218431i
$792$	2.35246	+	0.357615i	0.0835910	+	0.0127073i
$793$	12.7774	+	19.1227i	0.453737	+	0.679066i
$794$	18.2533	+	23.0557i	0.647785	+	0.818218i
$795$	−11.7057	−	38.5887i	−0.415160	−	1.36860i
$796$	−47.5329	+	7.73057i	−1.68476	+	0.274003i
$797$	−11.5400	−	9.47065i	−0.408769	−	0.335468i	0.407433	−	0.913235i	$-0.366424\pi$
$797$	−11.5400	−	9.47065i	−0.408769	−	0.335468i	−0.816201	+	0.577767i	$0.803924\pi$
$798$	2.34892	−	10.8128i	0.0831509	−	0.382768i
$799$	1.37280	+	1.37280i	0.0485662	+	0.0485662i
$800$	−20.6009	−	1.81369i	−0.728351	−	0.0641235i
$801$	−7.53414	+	7.53414i	−0.266206	+	0.266206i
$802$	−13.4133	−	20.8584i	−0.473642	−	0.736536i
$803$	2.50139	−	3.04795i	0.0882721	−	0.107560i
$804$	−4.05619	−	6.55793i	−0.143051	−	0.231280i
$805$	−19.9869	+	6.06296i	−0.704446	+	0.213691i
$806$	−9.79369	+	84.2418i	−0.344968	+	2.96729i
$807$	13.3522	−	8.92167i	0.470020	−	0.314058i
$808$	10.6221	+	9.69724i	0.373686	+	0.341148i
$809$	−0.447241	+	0.669343i	−0.0157242	+	0.0235329i	−0.839248	−	0.543748i	$-0.817005\pi$
$809$	−0.447241	+	0.669343i	−0.0157242	+	0.0235329i	0.823524	+	0.567281i	$0.192005\pi$
$810$	4.14722	−	0.335043i	0.145718	−	0.0117722i
$811$	0.411045	−	4.17341i	0.0144337	−	0.146548i	−0.985267	−	0.171025i	$-0.945292\pi$
$811$	0.411045	−	4.17341i	0.0144337	−	0.146548i	0.999700	+	0.0244770i	$0.00779204\pi$
$812$	5.04247	−	8.68560i	0.176956	−	0.304805i
$813$	−9.31555	−	2.82584i	−0.326711	−	0.0991066i
$814$	−2.86927	−	1.24797i	−0.100568	−	0.0437412i
$815$	11.5509	−	4.78456i	0.404612	−	0.167596i
$816$	−3.07026	+	8.04019i	−0.107481	+	0.281463i
$817$	−47.4050	−	19.6358i	−1.65849	−	0.686969i
$818$	−26.0697	−	27.0019i	−0.911506	−	0.944099i
$819$	−8.21516	+	4.39109i	−0.287061	+	0.153437i
$820$	42.6497	−	48.3978i	1.48939	−	1.69012i
$821$	34.7776	−	28.5413i	1.21375	−	0.996097i	0.213933	−	0.976848i	$-0.431373\pi$
$821$	34.7776	−	28.5413i	1.21375	−	0.996097i	0.999815	−	0.0192488i	$-0.00612745\pi$
$822$	−12.8942	−	25.1771i	−0.449736	−	0.878152i
$823$	5.87976	+	29.5595i	0.204955	+	1.03038i	0.937055	+	0.349183i	$0.113541\pi$
$823$	5.87976	+	29.5595i	0.204955	+	1.03038i	−0.732099	+	0.681198i	$0.761459\pi$
$824$	27.1653	+	12.9681i	0.946348	+	0.451766i
$825$	−3.01647	−	0.600014i	−0.105020	−	0.0208898i
$826$	−16.0358	−	8.93689i	−0.557958	−	0.310954i
$827$	−7.53606	+	14.0990i	−0.262055	+	0.490270i	−0.978196	−	0.207686i	$-0.933407\pi$
$827$	−7.53606	+	14.0990i	−0.262055	+	0.490270i	0.716141	+	0.697956i	$0.245907\pi$
$828$	−10.4357	−	0.366705i	−0.362664	−	0.0127439i
$829$	10.7061	−	1.05446i	0.371837	−	0.0366228i	0.0896270	−	0.995975i	$-0.471433\pi$
$829$	10.7061	−	1.05446i	0.371837	−	0.0366228i	0.282210	+	0.959353i	$0.408933\pi$
$830$	6.60711	+	4.58459i	0.229336	+	0.159133i
$831$		−	14.9596i		−	0.518941i
$832$	54.8045	+	0.394633i	1.90000	+	0.0136814i
$833$			11.0833i			0.384015i
$834$	−8.33925	+	12.0182i	−0.288765	+	0.416155i
$835$	48.0551	−	4.73302i	1.66302	−	0.163793i
$836$	−7.08224	+	6.60140i	−0.244944	+	0.228314i
$837$	−4.12646	+	7.72006i	−0.142631	+	0.266844i
$838$	3.45458	−	6.19869i	0.119336	−	0.214130i
$839$	−42.5583	−	8.46537i	−1.46928	−	0.292257i	−0.605383	−	0.795934i	$-0.706980\pi$
$839$	−42.5583	−	8.46537i	−1.46928	−	0.292257i	−0.863892	+	0.503677i	$0.831980\pi$
$840$	11.2991	+	0.595877i	0.389857	+	0.0205597i
$841$	−2.99675	−	15.0657i	−0.103336	−	0.519506i
$842$	−48.5346	+	24.8565i	−1.67261	+	0.856610i
$843$	−8.99563	+	7.38252i	−0.309826	+	0.254268i
$844$	−38.9275	+	2.45762i	−1.33994	+	0.0845948i
$845$	88.0444	−	47.0607i	3.02882	−	1.61894i
$846$	0.918021	−	0.886329i	0.0315622	−	0.0304726i
$847$	−12.9293	−	5.35548i	−0.444255	−	0.184017i
$848$	9.19034	−	54.0494i	0.315598	−	1.85606i
$849$	−12.4135	+	5.14185i	−0.426031	+	0.176468i
$850$	4.43686	−	10.2010i	0.152183	−	0.349893i
$851$	13.1396	+	3.98586i	0.450421	+	0.136634i
$852$	−2.47084	−	9.31062i	−0.0846494	−	0.318977i
$853$	−0.774471	+	7.86334i	−0.0265174	+	0.269236i	0.972779	+	0.231734i	$0.0744399\pi$
$853$	−0.774471	+	7.86334i	−0.0265174	+	0.269236i	−0.999297	+	0.0375016i	$0.988060\pi$
$854$	0.519827	+	6.43451i	0.0177881	+	0.220184i
$855$	−9.40546	+	14.0763i	−0.321660	+	0.481398i
$856$	6.36997	−	2.98475i	0.217721	−	0.102017i
$857$	15.1040	−	10.0922i	0.515943	−	0.344742i	−0.270182	−	0.962809i	$-0.587084\pi$
$857$	15.1040	−	10.0922i	0.515943	−	0.344742i	0.786125	+	0.618067i	$0.212084\pi$
$858$	8.09609	+	0.941226i	0.276396	+	0.0321329i
$859$	4.93372	−	1.49663i	0.168336	−	0.0510643i	−0.204991	−	0.978764i	$-0.565717\pi$
$859$	4.93372	−	1.49663i	0.168336	−	0.0510643i	0.373328	+	0.927699i	$0.378217\pi$
$860$	12.0372	−	51.0701i	0.410465	−	1.74148i
$861$	−9.45669	+	11.5230i	−0.322283	+	0.392703i
$862$	−27.7974	+	17.8756i	−0.946784	+	0.608846i
$863$	27.9056	−	27.9056i	0.949918	−	0.949918i	−0.0488859	−	0.998804i	$-0.515567\pi$
$863$	27.9056	−	27.9056i	0.949918	−	0.949918i	0.998804	+	0.0488859i	$0.0155671\pi$
$864$	5.24840	+	2.11052i	0.178554	+	0.0718012i
$865$	−38.7622	−	38.7622i	−1.31796	−	1.31796i
$866$	−33.1452	−	7.20032i	−1.12632	−	0.244677i
$867$	9.56256	+	7.84779i	0.324762	+	0.266525i
$868$	−13.9123	+	19.3165i	−0.472215	+	0.655646i
$869$	−1.53368	−	5.05588i	−0.0520267	−	0.171509i
$870$	−12.0475	+	9.53805i	−0.408449	+	0.323370i
$871$	−14.6742	−	21.9615i	−0.497217	−	0.744139i
$872$	−7.76079	−	31.4630i	−0.262814	−	1.06547i
$873$	−1.85305	−	1.23817i	−0.0627162	−	0.0419056i
$874$	27.5263	−	32.3647i	0.931090	−	1.09475i
$875$	5.35128	+	0.527055i	0.180906	+	0.0178177i
$876$	7.45039	−	5.68853i	0.251725	−	0.192198i
$877$	11.1124	−	36.6327i	0.375240	−	1.23700i	−0.542581	−	0.840004i	$-0.682553\pi$
$877$	11.1124	−	36.6327i	0.375240	−	1.23700i	0.917820	−	0.396996i	$-0.129947\pi$
$878$	1.60026	+	4.06379i	0.0540060	+	0.137146i
$879$	4.92739	+	11.8958i	0.166197	+	0.401235i
$880$	−7.82549	−	6.06462i	−0.263797	−	0.204438i
$881$	−11.1548	+	26.9302i	−0.375816	+	0.907300i	0.616924	+	0.787022i	$0.288378\pi$
$881$	−11.1548	+	26.9302i	−0.375816	+	0.907300i	−0.992740	+	0.120278i	$0.961622\pi$
$882$	7.28373	+	0.127934i	0.245256	+	0.00430777i
$883$	15.8475	+	29.6487i	0.533312	+	0.997757i	0.993915	+	0.110151i	$0.0351333\pi$
$883$	15.8475	+	29.6487i	0.533312	+	0.997757i	−0.460603	+	0.887606i	$0.652367\pi$
$884$	−9.54311	+	27.8930i	−0.320970	+	0.938142i
$885$	17.8187	+	21.7121i	0.598968	+	0.729844i
$886$	1.51711	−	4.70231i	0.0509682	−	0.157977i
$887$	0.700910	−	0.139420i	0.0235343	−	0.00468126i	−0.183309	−	0.983055i	$-0.558681\pi$
$887$	0.700910	−	0.139420i	0.0235343	−	0.00468126i	0.206843	+	0.978374i	$0.433681\pi$
$888$	−5.95867	−	4.45259i	−0.199960	−	0.149419i
$889$	4.01959	−	20.2079i	0.134813	−	0.677750i
$890$	42.6426	−	12.1219i	1.42938	−	0.406328i
$891$	0.741939	+	0.396575i	0.0248559	+	0.0132857i
$892$	12.0131	−	26.3451i	0.402229	−	0.882101i
$893$	0.508916	+	5.16711i	0.0170302	+	0.172911i
$894$	2.38131	+	13.1771i	0.0796431	+	0.440707i
$895$	−41.0337			−1.37161
$896$	13.3833	+	7.58541i	0.447104	+	0.253411i
$897$	−35.7680			−1.19426
$898$	−2.06136	−	11.4066i	−0.0687886	−	0.380643i
$899$	−3.16874	−	32.1728i	−0.105683	−	1.07302i
$900$	−6.65268	−	3.03356i	−0.221756	−	0.101119i
$901$	26.0085	+	13.9018i	0.866468	+	0.463137i
$902$	12.5462	−	3.56647i	0.417742	−	0.118750i
$903$	−2.36541	+	11.8917i	−0.0787159	+	0.395732i
$904$	−3.29311	−	22.7647i	−0.109527	−	0.757143i
$905$	48.3981	−	9.62698i	1.60881	−	0.320011i
$906$	4.97380	−	15.4164i	0.165243	−	0.512176i
$907$	29.4076	+	35.8333i	0.976464	+	1.18982i	0.981815	+	0.189839i	$0.0607965\pi$
$907$	29.4076	+	35.8333i	0.976464	+	1.18982i	−0.00535170	+	0.999986i	$0.501704\pi$
$908$	3.82225	+	1.30772i	0.126846	+	0.0433982i
$909$	2.39710	+	4.48466i	0.0795069	+	0.148747i
$910$	38.7515	+	0.680646i	1.28460	+	0.0225632i
$911$	15.4885	−	37.3926i	0.513157	−	1.23887i	−0.428879	−	0.903362i	$-0.641091\pi$
$911$	15.4885	−	37.3926i	0.513157	−	1.23887i	0.942037	−	0.335510i	$-0.108909\pi$
$912$	−19.9882	+	11.4126i	−0.661876	+	0.377910i
$913$	0.622254	+	1.50225i	0.0205936	+	0.0497174i
$914$	7.13033	+	18.1072i	0.235850	+	0.598933i
$915$	2.86710	−	9.45157i	0.0947835	−	0.312459i
$916$	22.5133	+	29.4862i	0.743861	+	0.974251i
$917$	−3.40329	−	0.335194i	−0.112386	−	0.0110691i
$918$	−1.97137	+	2.31789i	−0.0650649	+	0.0765017i
$919$	−1.89259	−	1.26459i	−0.0624307	−	0.0417148i	0.523963	−	0.851741i	$-0.324453\pi$
$919$	−1.89259	−	1.26459i	−0.0624307	−	0.0417148i	−0.586394	+	0.810026i	$0.699453\pi$
$920$	37.1849	+	22.4701i	1.22595	+	0.740818i
$921$	8.00869	+	11.9858i	0.263895	+	0.394947i
$922$	20.7014	−	16.3893i	0.681763	−	0.539753i
$923$	−9.57830	−	31.5754i	−0.315274	−	1.03932i
$924$	1.85642	+	1.33705i	0.0610718	+	0.0439857i
$925$	7.43213	+	6.09939i	0.244367	+	0.200547i
$926$	−41.2961	−	8.97100i	−1.35708	−	0.294805i
$927$	7.52548	+	7.52548i	0.247169	+	0.247169i
$928$	−20.4467	+	4.28782i	−0.671197	+	0.140755i
$929$	−40.4098	+	40.4098i	−1.32580	+	1.32580i	−0.416808	+	0.908995i	$0.636851\pi$
$929$	−40.4098	+	40.4098i	−1.32580	+	1.32580i	−0.908995	+	0.416808i	$0.863149\pi$
$930$	30.6342	−	19.6999i	1.00454	−	0.645984i
$931$	−18.8040	+	22.9128i	−0.616277	+	0.750936i
$932$	4.63821	+	1.09322i	0.151929	+	0.0358097i
$933$	−19.4982	+	5.91471i	−0.638342	+	0.193639i
$934$	−40.7809	−	4.74106i	−1.33439	−	0.155132i
$935$	4.42796	−	2.95867i	0.144810	−	0.0967588i
$936$	18.2205	+	6.59350i	0.595556	+	0.215515i
$937$	8.29709	−	12.4175i	0.271054	−	0.405661i	−0.670824	−	0.741617i	$-0.734059\pi$
$937$	8.29709	−	12.4175i	0.271054	−	0.405661i	0.941878	+	0.335956i	$0.109059\pi$
$938$	−0.596998	−	7.38975i	−0.0194927	−	0.241284i
$939$	−0.425119	+	4.31631i	−0.0138732	+	0.140857i
$940$	−5.13173	+	1.36185i	−0.167379	+	0.0444187i
$941$	26.8137	+	8.13384i	0.874101	+	0.265156i	0.695291	−	0.718728i	$-0.255275\pi$
$941$	26.8137	+	8.13384i	0.874101	+	0.265156i	0.178810	+	0.983884i	$0.442775\pi$
$942$	−0.653448	+	1.50238i	−0.0212905	+	0.0489501i
$943$	−52.8817	+	21.9043i	−1.72206	+	0.713302i
$944$	8.49286	+	37.2312i	0.276419	+	1.21177i
$945$	3.69589	+	1.53089i	0.120227	+	0.0497997i
$946$	7.63230	−	7.36881i	0.248147	−	0.239581i
$947$	16.6011	−	8.87345i	0.539462	−	0.288349i	−0.179077	−	0.983835i	$-0.557311\pi$
$947$	16.6011	−	8.87345i	0.539462	−	0.288349i	0.718539	+	0.695487i	$0.244811\pi$
$948$	−0.791405	−	12.5354i	−0.0257036	−	0.407132i
$949$	24.8203	−	20.3695i	0.805702	−	0.661222i
$950$	26.4795	−	13.5612i	0.859109	−	0.439983i
$951$	−2.21785	−	11.1499i	−0.0719188	−	0.361560i
$952$	−6.15120	+	5.53491i	−0.199362	+	0.179388i
$953$	−32.1822	−	6.40144i	−1.04248	−	0.207363i	−0.355984	−	0.934492i	$-0.615854\pi$
$953$	−32.1822	−	6.40144i	−1.04248	−	0.207363i	−0.686501	+	0.727129i	$0.740854\pi$
$954$	9.43619	−	16.9317i	0.305508	−	0.548185i
$955$	−19.6892	+	36.8360i	−0.637129	+	1.19198i
$956$	−24.8165	−	26.6241i	−0.802622	−	0.861084i
$957$	−3.09198	+	0.304533i	−0.0999494	+	0.00984415i
$958$	−7.36044	+	10.6076i	−0.237805	+	0.342715i
$959$		−	27.1968i		−	0.878231i
$960$	−14.8001	−	18.3011i	−0.477671	−	0.590666i
$961$			45.6269i			1.47184i
$962$	−20.9337	−	14.5256i	−0.674929	−	0.468324i
$963$	2.47512	−	0.243778i	0.0797597	−	0.00785564i
$964$	0.545135	−	15.5134i	0.0175576	−	0.499654i
$965$	1.79824	−	3.36428i	0.0578875	−	0.108300i
$966$	−8.76975	−	4.88745i	−0.282162	−	0.157251i
$967$	17.1836	+	3.41803i	0.552587	+	0.109916i	0.463483	−	0.886106i	$-0.346600\pi$
$967$	17.1836	+	3.41803i	0.552587	+	0.109916i	0.0891040	+	0.996022i	$0.471600\pi$
$968$	9.70842	+	27.4443i	0.312040	+	0.882094i
$969$	−2.41539	−	12.1430i	−0.0775934	−	0.390088i
$970$	4.22687	+	8.25337i	0.135717	+	0.265000i
$971$	13.2725	−	10.8924i	0.425934	−	0.349555i	−0.396875	−	0.917873i	$-0.629905\pi$
$971$	13.2725	−	10.8924i	0.425934	−	0.349555i	0.822809	+	0.568318i	$0.192405\pi$
$972$	1.50051	+	1.32230i	0.0481289	+	0.0424127i
$973$	−12.4037	+	6.62989i	−0.397643	+	0.212545i
$974$	−25.3661	−	26.2731i	−0.812781	−	0.841843i
$975$	−23.1388	−	9.58439i	−0.741033	−	0.306946i
$976$	9.22650	−	9.75674i	0.295333	−	0.312306i
$977$	−36.4903	+	15.1148i	−1.16743	+	0.483565i	−0.880342	−	0.474339i	$-0.842687\pi$
$977$	−36.4903	+	15.1148i	−1.16743	+	0.483565i	−0.287087	+	0.957904i	$0.592687\pi$
$978$	5.51111	+	2.39702i	0.176226	+	0.0766481i
$979$	8.57772	+	2.60202i	0.274145	+	0.0831610i
$980$	−26.2131	−	15.2181i	−0.837345	−	0.486125i
$981$	1.12301	−	11.4021i	0.0358549	−	0.364041i
$982$	−16.0158	+	1.29388i	−0.511086	+	0.0412892i
$983$	−25.6501	+	38.3881i	−0.818112	+	1.22439i	0.153579	+	0.988136i	$0.450920\pi$
$983$	−25.6501	+	38.3881i	−0.818112	+	1.22439i	−0.971691	+	0.236255i	$0.924080\pi$
$984$	30.9762	−	1.40999i	0.987484	−	0.0449488i
$985$	13.6580	−	9.12600i	0.435181	−	0.290778i
$986$	1.29771	−	11.1624i	0.0413275	−	0.355484i
$987$	1.17406	−	0.356148i	0.0373708	−	0.0113363i
$988$	−67.0520	+	41.4727i	−2.13321	+	1.31942i
$989$	−29.5351	+	35.9886i	−0.939162	+	1.14437i
$990$	−1.89326	−	2.94411i	−0.0601718	−	0.0935701i
$991$	35.2216	−	35.2216i	1.11885	−	1.11885i	0.126942	−	0.991910i	$-0.459484\pi$
$991$	35.2216	−	35.2216i	1.11885	−	1.11885i	0.991910	−	0.126942i	$-0.0405161\pi$
$992$	49.2269	−	5.36401i	1.56296	−	0.170307i
$993$	19.2359	+	19.2359i	0.610433	+	0.610433i
$994$	1.96611	−	9.05060i	0.0623613	−	0.287068i
$995$	54.7613	+	44.9414i	1.73605	+	1.42474i
$996$	0.620537	+	3.81549i	0.0196625	+	0.120899i
$997$	1.92824	+	6.35657i	0.0610681	+	0.201314i	0.982166	−	0.188017i	$-0.0602060\pi$
$997$	1.92824	+	6.35657i	0.0610681	+	0.201314i	−0.921098	+	0.389332i	$0.872706\pi$
$998$	36.4177	+	45.9992i	1.15278	+	1.45608i
$999$	−1.46110	−	2.18669i	−0.0462271	−	0.0691838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.181.2	yes	512
128.29	even	32	inner	384.2.v.a.157.2	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.2	✓	512	128.29	even	32	inner
384.2.v.a.181.2	yes	512	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39167 + 0.251498i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(1.87350 - 0.700005i) q^{4} +(-2.59468 - 1.38689i) q^{5} +(-0.386695 - 1.36032i) q^{6} +(0.265268 - 1.33359i) q^{7} +(-2.43124 + 1.44536i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(-1.39167 + 0.251498i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(1.87350 - 0.700005i) q^{4} +(-2.59468 - 1.38689i) q^{5} +(-0.386695 - 1.36032i) q^{6} +(0.265268 - 1.33359i) q^{7} +(-2.43124 + 1.44536i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(3.95975 + 1.27753i) q^{10} +(0.533699 + 0.650315i) q^{11} +(0.880269 + 1.79586i) q^{12} +(3.22942 + 6.04181i) q^{13} +(-0.0337699 + 1.92263i) q^{14} +(1.12589 - 2.71813i) q^{15} +(3.01999 - 2.62292i) q^{16} +(0.823388 + 1.98783i) q^{17} +(1.31587 - 0.518167i) q^{18} +(-1.67036 + 5.50644i) q^{19} +(-5.83196 - 0.782037i) q^{20} +(1.35317 + 0.133276i) q^{21} +(-0.906287 - 0.770800i) q^{22} +(4.34114 + 2.90066i) q^{23} +(-1.67670 - 2.27787i) q^{24} +(2.03108 + 3.03972i) q^{25} +(-6.01379 - 7.59602i) q^{26} +(-0.290285 - 0.956940i) q^{27} +(-0.436542 - 2.68417i) q^{28} +(2.85483 + 2.34289i) q^{29} +(-0.883259 + 4.06590i) q^{30} +(-6.18979 - 6.18979i) q^{31} +(-3.54317 + 4.40976i) q^{32} +(-0.594872 + 0.594872i) q^{33} +(-1.64582 - 2.55933i) q^{34} +(-2.53783 + 3.09235i) q^{35} +(-1.70093 + 1.05206i) q^{36} +(2.51667 - 0.763422i) q^{37} +(0.939734 - 8.08325i) q^{38} +(-5.69618 + 3.80607i) q^{39} +(8.31285 - 0.378388i) q^{40} +(-6.09075 + 9.11546i) q^{41} +(-1.91669 + 0.154844i) q^{42} +(-0.874026 + 8.87413i) q^{43} +(1.45511 + 0.844770i) q^{44} +(2.81540 + 0.854041i) q^{45} +(-6.77095 - 2.94497i) q^{46} +(0.833630 - 0.345301i) q^{47} +(2.90630 + 2.74835i) q^{48} +(4.75906 + 1.97127i) q^{49} +(-3.59107 - 3.71948i) q^{50} +(-1.89756 + 1.01426i) q^{51} +(10.2796 + 9.05871i) q^{52} +(10.5951 - 8.69519i) q^{53} +(0.644650 + 1.25874i) q^{54} +(-0.482868 - 2.42754i) q^{55} +(1.28259 + 3.62569i) q^{56} +(-5.64365 - 1.12259i) q^{57} +(-4.56221 - 2.54256i) q^{58} +(-4.50037 + 8.41960i) q^{59} +(0.206639 - 5.88053i) q^{60} +(3.34094 - 0.329054i) q^{61} +(10.1709 + 7.05743i) q^{62} +1.35972i q^{63} +(3.82188 - 7.02803i) q^{64} -20.1554i q^{65} +(0.678257 - 0.977475i) q^{66} +(-3.83692 + 0.377904i) q^{67} +(2.93411 + 3.14783i) q^{68} +(-2.46118 + 4.60455i) q^{69} +(2.75410 - 4.94179i) q^{70} +(-4.72390 - 0.939642i) q^{71} +(2.10255 - 1.89190i) q^{72} +(-0.914367 - 4.59683i) q^{73} +(-3.31037 + 1.69537i) q^{74} +(-2.82600 + 2.31924i) q^{75} +(0.725122 + 11.4856i) q^{76} +(1.00883 - 0.539229i) q^{77} +(6.96999 - 6.72937i) q^{78} +(-5.80215 - 2.40333i) q^{79} +(-11.4736 + 2.61726i) q^{80} +(0.923880 - 0.382683i) q^{81} +(6.18381 - 14.2175i) q^{82} +(1.84959 + 0.561066i) q^{83} +(2.62845 - 0.697535i) q^{84} +(0.620471 - 6.29975i) q^{85} +(-1.01547 - 12.5697i) q^{86} +(-2.05179 + 3.07072i) q^{87} +(-2.23749 - 0.809686i) q^{88} +(8.85921 - 5.91954i) q^{89} +(-4.13290 - 0.480478i) q^{90} +(8.91396 - 2.70402i) q^{91} +(10.1636 + 2.39555i) q^{92} +(5.55328 - 6.76669i) q^{93} +(-1.07330 + 0.690201i) q^{94} +(11.9709 - 11.9709i) q^{95} +(-4.73581 - 3.09387i) q^{96} +(1.57589 + 1.57589i) q^{97} +(-7.11882 - 1.54646i) q^{98} +(-0.650315 - 0.533699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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