LMFDB - Embedded newform 312.2.bt.d.19.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	312.19
Dual form			312.2.bt.d.115.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.764112 - 1.19001i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.832266 - 1.81861i) q^{4} +(-0.513065 - 0.513065i) q^{5} +(-0.648526 - 1.25675i) q^{6} +(-1.43100 - 0.383434i) q^{7} +(-2.80011 - 0.399211i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00259 + 0.218515i) q^{10} +(1.43129 - 0.383513i) q^{11} +(-1.99109 - 0.188540i) q^{12} +(-0.967164 - 3.47341i) q^{13} +(-1.54973 + 1.40992i) q^{14} +(-0.700859 + 0.187795i) q^{15} +(-2.61467 + 3.02713i) q^{16} +(1.08804 - 0.628178i) q^{17} +(-1.41264 - 0.0667332i) q^{18} +(6.19113 + 1.65891i) q^{19} +(-0.506057 + 1.36007i) q^{20} +(-1.04756 + 1.04756i) q^{21} +(0.637280 - 1.99630i) q^{22} +(-1.68941 + 2.92615i) q^{23} +(-1.74578 + 2.22536i) q^{24} -4.47353i q^{25} +(-4.87243 - 1.50314i) q^{26} -1.00000 q^{27} +(0.493654 + 2.92154i) q^{28} +(5.98829 + 3.45734i) q^{29} +(-0.312057 + 0.977529i) q^{30} +(1.65000 + 1.65000i) q^{31} +(1.60443 + 5.42455i) q^{32} +(0.383513 - 1.43129i) q^{33} +(0.0838407 - 1.77478i) q^{34} +(0.537467 + 0.930920i) q^{35} +(-1.15883 + 1.63007i) q^{36} +(-0.944898 - 3.52641i) q^{37} +(6.70484 - 6.09994i) q^{38} +(-3.49165 - 0.899118i) q^{39} +(1.23182 + 1.64146i) q^{40} +(0.503062 + 1.87745i) q^{41} +(0.446159 + 2.04707i) q^{42} +(7.93214 - 4.57963i) q^{43} +(-1.88867 - 2.28377i) q^{44} +(-0.187795 + 0.700859i) q^{45} +(2.19126 + 4.24633i) q^{46} +(-2.96711 + 2.96711i) q^{47} +(1.31424 + 3.77793i) q^{48} +(-4.16145 - 2.40261i) q^{49} +(-5.32356 - 3.41828i) q^{50} -1.25636i q^{51} +(-5.51184 + 4.64970i) q^{52} -0.513310i q^{53} +(-0.764112 + 1.19001i) q^{54} +(-0.931112 - 0.537578i) q^{55} +(3.85388 + 1.64493i) q^{56} +(4.53222 - 4.53222i) q^{57} +(8.69000 - 4.48435i) q^{58} +(-3.60773 + 13.4642i) q^{59} +(0.924827 + 1.11829i) q^{60} +(12.2267 - 7.05906i) q^{61} +(3.22431 - 0.702740i) q^{62} +(0.383434 + 1.43100i) q^{63} +(7.68126 + 2.23567i) q^{64} +(-1.28587 + 2.27830i) q^{65} +(-1.41021 - 1.55005i) q^{66} +(1.88176 + 7.02284i) q^{67} +(-2.04795 - 1.45590i) q^{68} +(1.68941 + 2.92615i) q^{69} +(1.51849 + 0.0717338i) q^{70} +(0.979852 - 3.65686i) q^{71} +(1.05433 + 2.62457i) q^{72} +(-4.42114 - 4.42114i) q^{73} +(-4.91848 - 1.57013i) q^{74} +(-3.87419 - 2.23676i) q^{75} +(-2.13577 - 12.6399i) q^{76} -2.19522 q^{77} +(-3.73797 + 3.46808i) q^{78} +3.24902i q^{79} +(2.89461 - 0.211622i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.61859 + 0.835933i) q^{82} +(-2.89926 + 2.89926i) q^{83} +(2.77695 + 1.03325i) q^{84} +(-0.880529 - 0.235937i) q^{85} +(0.611226 - 12.9387i) q^{86} +(5.98829 - 3.45734i) q^{87} +(-4.16088 + 0.502494i) q^{88} +(-2.05252 + 0.549972i) q^{89} +(0.690536 + 0.759013i) q^{90} +(0.0521823 + 5.34128i) q^{91} +(6.72756 + 0.637043i) q^{92} +(2.25395 - 0.603943i) q^{93} +(1.26370 + 5.79811i) q^{94} +(-2.32532 - 4.02758i) q^{95} +(5.50002 + 1.32280i) q^{96} +(1.09430 + 0.293217i) q^{97} +(-6.03896 + 3.11632i) q^{98} +(-1.04778 - 1.04778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) $ 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.764112	−	1.19001i	0.540309	−	0.841467i
$2$	0.764112	−	1.19001i	0.540309	−	0.841467i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.832266	−	1.81861i	−0.416133	−	0.909304i
$5$	−0.513065	−	0.513065i	−0.229449	−	0.229449i	0.583013	−	0.812463i	$-0.301874\pi$
$5$	−0.513065	−	0.513065i	−0.229449	−	0.229449i	−0.812463	+	0.583013i	$0.801874\pi$
$6$	−0.648526	−	1.25675i	−0.264760	−	0.513065i
$7$	−1.43100	−	0.383434i	−0.540866	−	0.144925i	−0.0219645	−	0.999759i	$-0.506992\pi$
$7$	−1.43100	−	0.383434i	−0.540866	−	0.144925i	−0.518901	+	0.854834i	$0.673659\pi$
$8$	−2.80011	−	0.399211i	−0.989989	−	0.141142i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00259	+	0.218515i	−0.317048	+	0.0691006i
$11$	1.43129	−	0.383513i	0.431550	−	0.115634i	−0.0365035	−	0.999334i	$-0.511622\pi$
$11$	1.43129	−	0.383513i	0.431550	−	0.115634i	0.468054	+	0.883700i	$0.344955\pi$
$12$	−1.99109	−	0.188540i	−0.574779	−	0.0544268i
$13$	−0.967164	−	3.47341i	−0.268243	−	0.963351i
$13$	−0.967164	−	3.47341i	−0.268243	−	0.963351i
$14$	−1.54973	+	1.40992i	−0.414184	+	0.376817i
$15$	−0.700859	+	0.187795i	−0.180961	+	0.0484884i
$16$	−2.61467	+	3.02713i	−0.653666	+	0.756783i
$17$	1.08804	−	0.628178i	0.263888	−	0.152356i	−0.362219	−	0.932093i	$-0.617981\pi$
$17$	1.08804	−	0.628178i	0.263888	−	0.152356i	0.626107	+	0.779737i	$0.284647\pi$
$18$	−1.41264	−	0.0667332i	−0.332962	−	0.0157292i
$19$	6.19113	+	1.65891i	1.42034	+	0.380580i	0.885605	−	0.464439i	$-0.153744\pi$
$19$	6.19113	+	1.65891i	1.42034	+	0.380580i	0.534737	+	0.845018i	$0.320411\pi$
$20$	−0.506057	+	1.36007i	−0.113158	+	0.304121i
$21$	−1.04756	+	1.04756i	−0.228597	+	0.228597i
$22$	0.637280	−	1.99630i	0.135869	−	0.425613i
$23$	−1.68941	+	2.92615i	−0.352267	+	0.610144i	−0.986646	−	0.162878i	$-0.947922\pi$
$23$	−1.68941	+	2.92615i	−0.352267	+	0.610144i	0.634379	+	0.773022i	$0.281256\pi$
$24$	−1.74578	+	2.22536i	−0.356356	+	0.454250i
$25$		−	4.47353i		−	0.894706i
$26$	−4.87243	−	1.50314i	−0.955562	−	0.294789i
$27$	−1.00000			−0.192450
$28$	0.493654	+	2.92154i	0.0932918	+	0.552119i
$29$	5.98829	+	3.45734i	1.11200	+	0.642012i	0.939346	−	0.342971i	$-0.111433\pi$
$29$	5.98829	+	3.45734i	1.11200	+	0.642012i	0.172651	+	0.984983i	$0.444767\pi$
$30$	−0.312057	+	0.977529i	−0.0569735	+	0.178471i
$31$	1.65000	+	1.65000i	0.296349	+	0.296349i	0.839582	−	0.543233i	$-0.182800\pi$
$31$	1.65000	+	1.65000i	0.296349	+	0.296349i	−0.543233	+	0.839582i	$0.682800\pi$
$32$	1.60443	+	5.42455i	0.283626	+	0.958935i
$33$	0.383513	−	1.43129i	0.0667611	−	0.249156i
$34$	0.0838407	−	1.77478i	0.0143786	−	0.304372i
$35$	0.537467	+	0.930920i	0.0908485	+	0.157354i
$36$	−1.15883	+	1.63007i	−0.193138	+	0.271678i
$37$	−0.944898	−	3.52641i	−0.155340	−	0.579738i	−0.999076	−	0.0429788i	$-0.986315\pi$
$37$	−0.944898	−	3.52641i	−0.155340	−	0.579738i	0.843736	−	0.536759i	$-0.180351\pi$
$38$	6.70484	−	6.09994i	1.08767	−	0.989541i
$39$	−3.49165	−	0.899118i	−0.559111	−	0.143974i
$40$	1.23182	+	1.64146i	0.194768	+	0.259538i
$41$	0.503062	+	1.87745i	0.0785651	+	0.293209i	0.994018	−	0.109216i	$-0.0348341\pi$
$41$	0.503062	+	1.87745i	0.0785651	+	0.293209i	−0.915453	+	0.402425i	$0.868167\pi$
$42$	0.446159	+	2.04707i	0.0688438	+	0.315869i
$43$	7.93214	−	4.57963i	1.20964	−	0.698386i	0.246960	−	0.969026i	$-0.420568\pi$
$43$	7.93214	−	4.57963i	1.20964	−	0.698386i	0.962681	+	0.270639i	$0.0872351\pi$
$44$	−1.88867	−	2.28377i	−0.284728	−	0.344291i
$45$	−0.187795	+	0.700859i	−0.0279948	+	0.104478i
$46$	2.19126	+	4.24633i	0.323083	+	0.626087i
$47$	−2.96711	+	2.96711i	−0.432797	+	0.432797i	−0.889579	−	0.456781i	$-0.849002\pi$
$47$	−2.96711	+	2.96711i	−0.432797	+	0.432797i	0.456781	+	0.889579i	$0.349002\pi$
$48$	1.31424	+	3.77793i	0.189694	+	0.545298i
$49$	−4.16145	−	2.40261i	−0.594493	−	0.343231i
$50$	−5.32356	−	3.41828i	−0.752865	−	0.483417i
$51$		−	1.25636i		−	0.175925i
$52$	−5.51184	+	4.64970i	−0.764354	+	0.644797i
$53$		−	0.513310i		−	0.0705086i	−0.999378	−	0.0352543i	$-0.988776\pi$
$53$		−	0.513310i		−	0.0705086i	0.999378	−	0.0352543i	$-0.0112241\pi$
$54$	−0.764112	+	1.19001i	−0.103982	+	0.161940i
$55$	−0.931112	−	0.537578i	−0.125551	−	0.0724869i
$56$	3.85388	+	1.64493i	0.514996	+	0.219813i
$57$	4.53222	−	4.53222i	0.600307	−	0.600307i
$58$	8.69000	−	4.48435i	1.14105	−	0.588824i
$59$	−3.60773	+	13.4642i	−0.469687	+	1.75290i	0.171176	+	0.985241i	$0.445243\pi$
$59$	−3.60773	+	13.4642i	−0.469687	+	1.75290i	−0.640863	+	0.767655i	$0.721423\pi$
$60$	0.924827	+	1.11829i	0.119395	+	0.144371i
$61$	12.2267	−	7.05906i	1.56546	−	0.903820i	0.568775	−	0.822493i	$-0.307417\pi$
$61$	12.2267	−	7.05906i	1.56546	−	0.903820i	0.996687	−	0.0813276i	$-0.0259160\pi$
$62$	3.22431	−	0.702740i	0.409488	−	0.0892481i
$63$	0.383434	+	1.43100i	0.0483082	+	0.180289i
$64$	7.68126	+	2.23567i	0.960158	+	0.279459i
$65$	−1.28587	+	2.27830i	−0.159492	+	0.282589i
$66$	−1.41021	−	1.55005i	−0.173585	−	0.190798i
$67$	1.88176	+	7.02284i	0.229894	+	0.857977i	0.980384	+	0.197095i	$0.0631507\pi$
$67$	1.88176	+	7.02284i	0.229894	+	0.857977i	−0.750490	+	0.660881i	$0.770183\pi$
$68$	−2.04795	−	1.45590i	−0.248350	−	0.176554i
$69$	1.68941	+	2.92615i	0.203381	+	0.352267i
$70$	1.51849	+	0.0717338i	0.181495	+	0.00857383i
$71$	0.979852	−	3.65686i	0.116287	−	0.433989i	−0.883093	−	0.469198i	$-0.844543\pi$
$71$	0.979852	−	3.65686i	0.116287	−	0.433989i	0.999380	+	0.0352090i	$0.0112097\pi$
$72$	1.05433	+	2.62457i	0.124254	+	0.309309i
$73$	−4.42114	−	4.42114i	−0.517455	−	0.517455i	0.399345	−	0.916801i	$-0.369237\pi$
$73$	−4.42114	−	4.42114i	−0.517455	−	0.517455i	−0.916801	+	0.399345i	$0.869237\pi$
$74$	−4.91848	−	1.57013i	−0.571762	−	0.182524i
$75$	−3.87419	−	2.23676i	−0.447353	−	0.258279i
$76$	−2.13577	−	12.6399i	−0.244989	−	1.44989i
$77$	−2.19522			−0.250169
$78$	−3.73797	+	3.46808i	−0.423242	+	0.392683i
$79$			3.24902i			0.365543i	0.983155	+	0.182771i	$0.0585068\pi$
$79$			3.24902i			0.365543i	−0.983155	+	0.182771i	$0.941493\pi$
$80$	2.89461	−	0.211622i	0.323627	−	0.0236600i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.61859	+	0.835933i	0.289175	+	0.0923134i
$83$	−2.89926	+	2.89926i	−0.318235	+	0.318235i	−0.848089	−	0.529854i	$-0.822247\pi$
$83$	−2.89926	+	2.89926i	−0.318235	+	0.318235i	0.529854	+	0.848089i	$0.322247\pi$
$84$	2.77695	+	1.03325i	0.302991	+	0.112737i
$85$	−0.880529	−	0.235937i	−0.0955068	−	0.0255910i
$86$	0.611226	−	12.9387i	0.0659102	−	1.39522i
$87$	5.98829	−	3.45734i	0.642012	−	0.370666i
$88$	−4.16088	+	0.502494i	−0.443551	+	0.0535660i
$89$	−2.05252	+	0.549972i	−0.217567	+	0.0582969i	−0.365956	−	0.930632i	$-0.619258\pi$
$89$	−2.05252	+	0.549972i	−0.217567	+	0.0582969i	0.148389	+	0.988929i	$0.452591\pi$
$90$	0.690536	+	0.759013i	0.0727889	+	0.0800070i
$91$	0.0521823	+	5.34128i	0.00547019	+	0.559919i
$92$	6.72756	+	0.637043i	0.701396	+	0.0664163i
$93$	2.25395	−	0.603943i	0.233723	−	0.0626260i
$94$	1.26370	+	5.79811i	0.130341	+	0.598029i
$95$	−2.32532	−	4.02758i	−0.238573	−	0.413221i
$96$	5.50002	+	1.32280i	0.561343	+	0.135008i
$97$	1.09430	+	0.293217i	0.111109	+	0.0297716i	0.313945	−	0.949441i	$-0.398349\pi$
$97$	1.09430	+	0.293217i	0.111109	+	0.0297716i	−0.202836	+	0.979213i	$0.565016\pi$
$98$	−6.03896	+	3.11632i	−0.610027	+	0.314796i
$99$	−1.04778	−	1.04778i	−0.105306	−	0.105306i
$100$	−8.13559	+	3.72317i	−0.813559	+	0.372317i
$101$	5.72724	−	9.91986i	0.569881	−	0.987063i	−0.426696	−	0.904395i	$-0.640323\pi$
$101$	5.72724	−	9.91986i	0.569881	−	0.987063i	0.996577	−	0.0826680i	$-0.0263441\pi$
$102$	−1.49508	−	0.959997i	−0.148035	−	0.0950538i
$103$	2.48901			0.245249			0.122625	−	0.992453i	$-0.460869\pi$
$103$	2.48901			0.245249			0.122625	+	0.992453i	$0.460869\pi$
$104$	1.32154	+	10.1120i	0.129588	+	0.991568i
$105$	1.07493			0.104903
$106$	−0.610846	−	0.392226i	−0.0593307	−	0.0380964i
$107$	−5.13018	+	8.88572i	−0.495953	+	0.859015i	−0.999989	−	0.00466706i	$-0.998514\pi$
$107$	−5.13018	+	8.88572i	−0.495953	+	0.859015i	0.504036	+	0.863682i	$0.331848\pi$
$108$	0.832266	+	1.81861i	0.0800849	+	0.174996i
$109$	7.21056	+	7.21056i	0.690646	+	0.690646i	0.962374	−	0.271728i	$-0.0875951\pi$
$109$	7.21056	+	7.21056i	0.690646	+	0.690646i	−0.271728	+	0.962374i	$0.587595\pi$
$110$	−1.35120	+	0.697266i	−0.128832	+	0.0664817i
$111$	−3.52641	−	0.944898i	−0.334712	−	0.0896857i
$112$	4.90228	−	3.32926i	0.463222	−	0.314586i
$113$	−2.37145	−	4.10748i	−0.223088	−	0.386399i	0.732656	−	0.680599i	$-0.238280\pi$
$113$	−2.37145	−	4.10748i	−0.223088	−	0.386399i	−0.955744	+	0.294200i	$0.904947\pi$
$114$	−1.93028	−	8.85653i	−0.180788	−	0.829490i
$115$	2.36808	−	0.634526i	0.220825	−	0.0591698i
$116$	1.30369	−	13.7678i	0.121045	−	1.27831i
$117$	−2.52448	+	2.57429i	−0.233388	+	0.237994i
$118$	13.2659	+	14.5814i	1.22123	+	1.34233i
$119$	−1.79784	+	0.481730i	−0.164808	+	0.0441601i
$120$	2.03745	−	0.246056i	0.185993	−	0.0224617i
$121$	−7.62477	+	4.40216i	−0.693161	+	0.400197i
$122$	0.942148	−	19.9438i	0.0852981	−	1.80563i
$123$	1.87745	+	0.503062i	0.169284	+	0.0453596i
$124$	1.62747	−	4.37395i	0.146151	−	0.392792i
$125$	−4.86053	+	4.86053i	−0.434739	+	0.434739i
$126$	1.99589	+	0.637149i	0.177808	+	0.0567617i
$127$	−9.40686	+	16.2932i	−0.834724	+	1.44578i	0.0595311	+	0.998226i	$0.481039\pi$
$127$	−9.40686	+	16.2932i	−0.834724	+	1.44578i	−0.894255	+	0.447558i	$0.852294\pi$
$128$	8.52982	−	7.43251i	0.753937	−	0.656947i
$129$		−	9.15925i		−	0.806427i
$130$	1.72867	+	3.27108i	0.151614	+	0.286893i
$131$	−1.40105			−0.122410			−0.0612050	−	0.998125i	$-0.519494\pi$
$131$	−1.40105			−0.122410			−0.0612050	+	0.998125i	$0.519494\pi$
$132$	−2.92214	+	0.493755i	−0.254340	+	0.0429759i
$133$	−8.22340	−	4.74778i	−0.713059	−	0.411685i
$134$	9.79516	+	3.12691i	0.846173	+	0.270124i
$135$	0.513065	+	0.513065i	0.0441576	+	0.0441576i
$136$	−3.29740	+	1.32461i	−0.282750	+	0.113585i
$137$	−4.33906	+	16.1936i	−0.370711	+	1.38351i	0.488800	+	0.872396i	$0.337435\pi$
$137$	−4.33906	+	16.1936i	−0.370711	+	1.38351i	−0.859511	+	0.511117i	$0.829232\pi$
$138$	4.77306	+	0.225480i	0.406310	+	0.0191941i
$139$	−7.57593	−	13.1219i	−0.642582	−	1.11298i	−0.984854	−	0.173384i	$-0.944530\pi$
$139$	−7.57593	−	13.1219i	−0.642582	−	1.11298i	0.342273	−	0.939601i	$-0.388803\pi$
$140$	1.24566	−	1.75221i	0.105278	−	0.148089i
$141$	1.08604	+	4.05315i	0.0914609	+	0.341337i
$142$	−3.60299	−	3.96028i	−0.302357	−	0.332340i
$143$	−2.71639	−	4.60054i	−0.227156	−	0.384717i
$144$	3.92891	+	0.750801i	0.327409	+	0.0625667i
$145$	−1.29854	−	4.84622i	−0.107838	−	0.402456i
$146$	−8.63946	+	1.88297i	−0.715007	+	0.155836i
$147$	−4.16145	+	2.40261i	−0.343231	+	0.198164i
$148$	−5.62674	+	4.65331i	−0.462515	+	0.382499i
$149$	−2.01396	+	7.51621i	−0.164990	+	0.615752i	0.833051	+	0.553196i	$0.186592\pi$
$149$	−2.01396	+	7.51621i	−0.164990	+	0.615752i	−0.998041	+	0.0625561i	$0.980075\pi$
$150$	−5.62210	+	2.90120i	−0.459042	+	0.236882i
$151$	−6.96070	+	6.96070i	−0.566453	+	0.566453i	−0.931133	−	0.364680i	$-0.881178\pi$
$151$	−6.96070	+	6.96070i	−0.566453	+	0.566453i	0.364680	+	0.931133i	$0.381178\pi$
$152$	−16.6736	−	7.11669i	−1.35241	−	0.577240i
$153$	−1.08804	−	0.628178i	−0.0879625	−	0.0507852i
$154$	−1.67740	+	2.61235i	−0.135168	+	0.210509i
$155$		−	1.69312i		−	0.135994i
$156$	1.27084	+	7.09824i	0.101748	+	0.568314i
$157$		−	10.6185i		−	0.847450i	−0.905791	−	0.423725i	$-0.860722\pi$
$157$		−	10.6185i		−	0.847450i	0.905791	−	0.423725i	$-0.139278\pi$
$158$	3.86637	+	2.48261i	0.307592	+	0.197506i
$159$	−0.444540	−	0.256655i	−0.0352543	−	0.0203541i
$160$	1.95997	−	3.60632i	0.154949	−	0.285105i
$161$	3.53953	−	3.53953i	0.278954	−	0.278954i
$162$	0.648526	+	1.25675i	0.0509530	+	0.0987394i
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	−0.743197	−	0.669073i	$-0.766692\pi$
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	0.978164	−	0.207835i	$-0.0666418\pi$
$164$	2.99567	−	2.47741i	0.233922	−	0.193453i
$165$	−0.931112	+	0.537578i	−0.0724869	+	0.0418504i
$166$	1.23480	+	5.66552i	0.0958391	+	0.439729i
$167$	−2.32855	−	8.69026i	−0.180189	−	0.672473i	−0.995609	−	0.0936043i	$-0.970161\pi$
$167$	−2.32855	−	8.69026i	−0.180189	−	0.672473i	0.815421	−	0.578868i	$-0.196506\pi$
$168$	3.35149	−	2.51509i	0.258573	−	0.194044i
$169$	−11.1292	+	6.71872i	−0.856091	+	0.516824i
$170$	−0.953591	+	0.867560i	−0.0731371	+	0.0665388i
$171$	−1.65891	−	6.19113i	−0.126860	−	0.473447i
$172$	−14.9302	−	10.6140i	−1.13842	−	0.809309i
$173$	6.97351	+	12.0785i	0.530186	+	0.918309i	0.999380	+	0.0352137i	$0.0112112\pi$
$173$	6.97351	+	12.0785i	0.530186	+	0.918309i	−0.469194	+	0.883095i	$0.655455\pi$
$174$	0.461439	−	9.76794i	0.0349816	−	0.740505i
$175$	−1.71530	+	6.40160i	−0.129665	+	0.483916i
$176$	−2.58140	+	5.33546i	−0.194580	+	0.402176i
$177$	9.85651	+	9.85651i	0.740861	+	0.740861i
$178$	−0.913883	+	2.86277i	−0.0684984	+	0.214574i
$179$	−8.03592	−	4.63954i	−0.600633	−	0.346776i	0.168658	−	0.985675i	$-0.446057\pi$
$179$	−8.03592	−	4.63954i	−0.600633	−	0.346776i	−0.769291	+	0.638899i	$0.779390\pi$
$180$	1.43088	−	0.241777i	0.106652	−	0.0180210i
$181$	−20.7868			−1.54507			−0.772535	−	0.634973i	$-0.781011\pi$
$181$	−20.7868			−1.54507			−0.772535	+	0.634973i	$0.781011\pi$
$182$	6.39607	+	4.01924i	0.474109	+	0.297926i
$183$		−	14.1181i		−	1.04364i
$184$	5.89870	−	7.51912i	0.434858	−	0.554317i
$185$	−1.32448	+	2.29407i	−0.0973778	+	0.168663i
$186$	1.00357	−	3.14371i	0.0735851	−	0.230508i
$187$	1.31638	−	1.31638i	0.0962634	−	0.0962634i
$188$	7.86543	+	2.92658i	0.573646	+	0.213443i
$189$	1.43100	+	0.383434i	0.104090	+	0.0278907i
$190$	−6.56968	−	0.310353i	−0.476615	−	0.0225153i
$191$	22.5621	−	13.0262i	1.63254	−	0.942545i	0.649228	−	0.760593i	$-0.275092\pi$
$191$	22.5621	−	13.0262i	1.63254	−	0.942545i	0.983307	−	0.181952i	$-0.0582414\pi$
$192$	5.77678	−	5.53433i	0.416903	−	0.399406i
$193$	−14.5165	+	3.88969i	−1.04492	+	0.279986i	−0.740152	−	0.672439i	$-0.765247\pi$
$193$	−14.5165	+	3.88969i	−1.04492	+	0.279986i	−0.304771	+	0.952426i	$0.598580\pi$
$194$	1.18510	−	1.07818i	0.0850851	−	0.0774089i
$195$	1.33013	+	2.25275i	0.0952529	+	0.161322i
$196$	−0.905977	+	9.56766i	−0.0647126	+	0.683404i
$197$	−19.2785	+	5.16566i	−1.37354	+	0.368038i	−0.868769	−	0.495217i	$-0.835088\pi$
$197$	−19.2785	+	5.16566i	−1.37354	+	0.368038i	−0.504767	+	0.863255i	$0.668422\pi$
$198$	−2.04749	+	0.446251i	−0.145509	+	0.0317137i
$199$	5.62998	+	9.75141i	0.399098	+	0.691259i	0.993615	−	0.112825i	$-0.0359898\pi$
$199$	5.62998	+	9.75141i	0.399098	+	0.691259i	−0.594516	+	0.804083i	$0.702656\pi$
$200$	−1.78588	+	12.5264i	−0.126281	+	0.885749i
$201$	7.02284	+	1.88176i	0.495353	+	0.132729i
$202$	−7.42853	−	14.3954i	−0.522669	−	1.01285i
$203$	−7.24355	−	7.24355i	−0.508398	−	0.508398i
$204$	−2.28482	+	1.04562i	−0.159969	+	0.0732083i
$205$	0.705151	−	1.22136i	0.0492499	−	0.0853033i
$206$	1.90188	−	2.96196i	0.132510	−	0.206369i
$207$	3.37883			0.234845
$208$	13.0433	+	6.15408i	0.904389	+	0.426709i
$209$	9.49752			0.656957
$210$	0.821370	−	1.27919i	0.0566799	−	0.0882722i
$211$	0.571787	−	0.990365i	0.0393635	−	0.0681795i	−0.845672	−	0.533702i	$-0.820800\pi$
$211$	0.571787	−	0.990365i	0.0393635	−	0.0681795i	0.885036	+	0.465523i	$0.154134\pi$
$212$	−0.933510	+	0.427211i	−0.0641137	+	0.0293410i
$213$	−2.67700	−	2.67700i	−0.183425	−	0.183425i
$214$	6.65411	+	12.8947i	0.454865	+	0.881461i
$215$	−6.41935	−	1.72006i	−0.437796	−	0.117307i
$216$	2.80011	+	0.399211i	0.190524	+	0.0271628i
$217$	−1.72848	−	2.99382i	−0.117337	−	0.203233i
$218$	14.0903	−	3.07099i	0.954318	−	0.207994i
$219$	−6.03939	+	1.61825i	−0.408104	+	0.109351i
$220$	−0.202710	+	2.14073i	−0.0136667	+	0.144328i
$221$	−3.23423	−	3.17165i	−0.217558	−	0.213348i
$222$	−3.81901	+	3.47447i	−0.256315	+	0.233191i
$223$	14.1824	−	3.80017i	0.949726	−	0.254478i	0.249480	−	0.968380i	$-0.419740\pi$
$223$	14.1824	−	3.80017i	0.949726	−	0.254478i	0.700246	+	0.713902i	$0.253074\pi$
$224$	−0.215976	−	8.37771i	−0.0144305	−	0.559759i
$225$	−3.87419	+	2.23676i	−0.258279	+	0.149118i
$226$	−6.70001	−	0.316509i	−0.445678	−	0.0210539i
$227$	−8.65489	−	2.31907i	−0.574445	−	0.153922i	−0.0401107	−	0.999195i	$-0.512771\pi$
$227$	−8.65489	−	2.31907i	−0.574445	−	0.153922i	−0.534334	+	0.845273i	$0.679438\pi$
$228$	−12.0143	−	4.47032i	−0.795670	−	0.296054i
$229$	1.63656	−	1.63656i	0.108147	−	0.108147i	−0.650963	−	0.759110i	$-0.725635\pi$
$229$	1.63656	−	1.63656i	0.108147	−	0.108147i	0.759110	+	0.650963i	$0.225635\pi$
$230$	1.05438	−	3.30290i	0.0695241	−	0.217787i
$231$	−1.09761	+	1.90112i	−0.0722175	+	0.125084i
$232$	−15.3877	−	12.0715i	−1.01025	−	0.792534i
$233$		−	15.2245i		−	0.997391i	−0.866777	−	0.498695i	$-0.833813\pi$
$233$		−	15.2245i		−	0.997391i	0.866777	−	0.498695i	$-0.166187\pi$
$234$	1.13446	+	4.97122i	0.0741620	+	0.324979i
$235$	3.04464			0.198610
$236$	27.4888	−	4.64479i	1.78937	−	0.302350i
$237$	2.81373	+	1.62451i	0.182771	+	0.105523i
$238$	−0.800486	+	2.50755i	−0.0518878	+	0.162540i
$239$	20.1260	+	20.1260i	1.30184	+	1.30184i	0.927149	+	0.374693i	$0.122252\pi$
$239$	20.1260	+	20.1260i	1.30184	+	1.30184i	0.374693	+	0.927149i	$0.377748\pi$
$240$	1.26403	−	2.61261i	0.0815930	−	0.168643i
$241$	0.968043	−	3.61278i	0.0623571	−	0.232720i	−0.927713	−	0.373294i	$-0.878228\pi$
$241$	0.968043	−	3.61278i	0.0623571	−	0.232720i	0.990070	+	0.140574i	$0.0448949\pi$
$242$	−0.587541	+	12.4373i	−0.0377686	+	0.799502i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−23.0135	−	16.3605i	−1.47329	−	1.04737i
$245$	0.902396	+	3.36779i	0.0576520	+	0.215160i
$246$	2.03323	−	1.84980i	0.129634	−	0.117939i
$247$	−0.225764	−	23.1088i	−0.0143650	−	1.47038i
$248$	−3.96150	−	5.27889i	−0.251555	−	0.335210i
$249$	1.06120	+	3.96046i	0.0672510	+	0.250984i
$250$	2.07011	+	9.49809i	0.130925	+	0.600712i
$251$	19.4389	−	11.2231i	1.22697	−	0.708393i	0.260577	−	0.965453i	$-0.416087\pi$
$251$	19.4389	−	11.2231i	1.22697	−	0.708393i	0.966395	+	0.257060i	$0.0827538\pi$
$252$	2.28330	−	1.88829i	0.143834	−	0.118951i
$253$	−1.29582	+	4.83608i	−0.0814678	+	0.304042i
$254$	12.2012	+	23.6441i	0.765571	+	1.48356i
$255$	−0.644592	+	0.644592i	−0.0403659	+	0.0403659i
$256$	−2.32705	−	15.8299i	−0.145441	−	0.989367i
$257$	25.8091	+	14.9009i	1.60993	+	0.929494i	0.989384	+	0.145324i	$0.0464223\pi$
$257$	25.8091	+	14.9009i	1.60993	+	0.929494i	0.620546	+	0.784170i	$0.286911\pi$
$258$	−10.8996	−	6.99869i	−0.678582	−	0.435719i
$259$			5.40858i			0.336073i
$260$	5.21352	+	0.442333i	0.323329	+	0.0274324i
$261$		−	6.91468i		−	0.428008i
$262$	−1.07056	+	1.66727i	−0.0661392	+	0.103004i
$263$	−2.11644	−	1.22193i	−0.130506	−	0.0753474i	0.433326	−	0.901237i	$-0.357340\pi$
$263$	−2.11644	−	1.22193i	−0.130506	−	0.0753474i	−0.563831	+	0.825890i	$0.690673\pi$
$264$	−1.64527	+	3.85467i	−0.101259	+	0.237239i
$265$	−0.263361	+	0.263361i	−0.0161782	+	0.0161782i
$266$	−11.9335	+	6.15812i	−0.731691	+	0.377579i
$267$	−0.549972	+	2.05252i	−0.0336577	+	0.125612i
$268$	11.2057	−	9.26706i	0.684495	−	0.566076i
$269$	22.9614	−	13.2568i	1.39998	−	0.808280i	0.405592	−	0.914054i	$-0.367065\pi$
$269$	22.9614	−	13.2568i	1.39998	−	0.808280i	0.994390	+	0.105774i	$0.0337320\pi$
$270$	1.00259	−	0.218515i	0.0610159	−	0.0132984i
$271$	1.72024	+	6.42004i	0.104497	+	0.389990i	0.998288	−	0.0584956i	$-0.0186304\pi$
$271$	1.72024	+	6.42004i	0.104497	+	0.389990i	−0.893790	+	0.448485i	$0.851964\pi$
$272$	−0.943273	+	4.93610i	−0.0571943	+	0.299295i
$273$	4.65178	+	2.62545i	0.281538	+	0.158899i
$274$	15.9551	+	17.5373i	0.963882	+	1.05946i
$275$	−1.71566	−	6.40292i	−0.103458	−	0.386111i
$276$	3.91547	−	5.50771i	0.235684	−	0.331525i
$277$	−0.878646	−	1.52186i	−0.0527927	−	0.0914397i	0.838421	−	0.545023i	$-0.183479\pi$
$277$	−0.878646	−	1.52186i	−0.0527927	−	0.0914397i	−0.891214	+	0.453583i	$0.850146\pi$
$278$	−21.4041	−	1.01113i	−1.28373	−	0.0606437i
$279$	0.603943	−	2.25395i	0.0361571	−	0.134940i
$280$	−1.13333	−	2.82124i	−0.0677297	−	0.168602i
$281$	17.3570	+	17.3570i	1.03543	+	1.03543i	0.999349	+	0.0360826i	$0.0114879\pi$
$281$	17.3570	+	17.3570i	1.03543	+	1.03543i	0.0360826	+	0.999349i	$0.488512\pi$
$282$	5.65316	+	1.80466i	0.336641	+	0.107466i
$283$	−3.46233	−	1.99897i	−0.205814	−	0.118827i	0.393551	−	0.919303i	$-0.371247\pi$
$283$	−3.46233	−	1.99897i	−0.205814	−	0.118827i	−0.599364	+	0.800476i	$0.704580\pi$
$284$	−7.46588	+	1.26151i	−0.443019	+	0.0748570i
$285$	−4.65064			−0.275480
$286$	−7.55034	−	0.282785i	−0.446461	−	0.0167214i
$287$		−	2.87952i		−	0.169973i
$288$	3.89559	−	4.10176i	0.229550	−	0.241698i
$289$	−7.71078	+	13.3555i	−0.453576	+	0.785616i
$290$	−6.75929	−	2.15777i	−0.396919	−	0.126709i
$291$	0.801083	−	0.801083i	0.0469603	−	0.0469603i
$292$	−4.36075	+	11.7199i	−0.255194	+	0.685854i
$293$	−20.3123	−	5.44266i	−1.18666	−	0.317963i	−0.389093	−	0.921199i	$-0.627211\pi$
$293$	−20.3123	−	5.44266i	−1.18666	−	0.317963i	−0.797563	+	0.603235i	$0.793878\pi$
$294$	−0.320668	+	6.78805i	−0.0187018	+	0.395887i
$295$	8.75903	−	5.05703i	0.509971	−	0.294432i
$296$	1.23804	+	10.2515i	0.0719597	+	0.595859i
$297$	−1.43129	+	0.383513i	−0.0830519	+	0.0222537i
$298$	7.40550	+	8.13987i	0.428989	+	0.471530i
$299$	11.7977	+	3.03796i	0.682276	+	0.175690i
$300$	−0.843438	+	8.90721i	−0.0486959	+	0.514258i
$301$	−13.1069	+	3.51197i	−0.755466	+	0.202427i
$302$	2.96458	+	13.6021i	0.170592	+	0.782711i
$303$	−5.72724	−	9.91986i	−0.329021	−	0.569881i
$304$	−21.2095	+	14.4039i	−1.21645	+	0.826119i
$305$	−9.89482	−	2.65131i	−0.566576	−	0.151814i
$306$	−1.57892	+	0.814780i	−0.0902610	+	0.0465779i
$307$	−1.73231	−	1.73231i	−0.0988683	−	0.0988683i	0.655943	−	0.754811i	$-0.272271\pi$
$307$	−1.73231	−	1.73231i	−0.0988683	−	0.0988683i	−0.754811	+	0.655943i	$0.772271\pi$
$308$	1.82701	+	3.99225i	0.104104	+	0.227479i
$309$	1.24450	−	2.15555i	0.0707974	−	0.122625i
$310$	−2.01483	−	1.29373i	−0.114435	−	0.0734790i
$311$	2.28061			0.129321			0.0646606	−	0.997907i	$-0.479404\pi$
$311$	2.28061			0.129321			0.0646606	+	0.997907i	$0.479404\pi$
$312$	9.41806	+	3.91153i	0.533193	+	0.221447i
$313$	32.2565			1.82325			0.911623	−	0.411028i	$-0.134830\pi$
$313$	32.2565			1.82325			0.911623	+	0.411028i	$0.134830\pi$
$314$	−12.6362	−	8.11373i	−0.713101	−	0.457884i
$315$	0.537467	−	0.930920i	0.0302828	−	0.0524514i
$316$	5.90868	−	2.70405i	0.332389	−	0.152115i
$317$	17.9781	+	17.9781i	1.00975	+	1.00975i	0.999952	+	0.00979695i	$0.00311852\pi$
$317$	17.9781	+	17.9781i	1.00975	+	1.00975i	0.00979695	+	0.999952i	$0.496881\pi$
$318$	−0.645101	+	0.332895i	−0.0361755	+	0.0186678i
$319$	9.89691	+	2.65187i	0.554121	+	0.148476i
$320$	−2.79394	−	5.08803i	−0.156186	−	0.284429i
$321$	5.13018	+	8.88572i	0.286338	+	0.495953i
$322$	−1.50749	−	6.91668i	−0.0840093	−	0.385452i
$323$	7.77826	−	2.08418i	0.432794	−	0.115967i
$324$	1.99109	+	0.188540i	0.110616	+	0.0104744i
$325$	−15.5384	+	4.32664i	−0.861916	+	0.239999i
$326$	−11.0307	−	12.1246i	−0.610934	−	0.671518i
$327$	9.84980	−	2.63925i	0.544695	−	0.145951i
$328$	−0.659131	−	5.45791i	−0.0363944	−	0.301362i
$329$	5.38361	−	3.10823i	0.296808	−	0.171362i
$330$	−0.0717486	+	1.51881i	−0.00394963	+	0.0836075i
$331$	28.0985	+	7.52896i	1.54443	+	0.413829i	0.927694	−	0.373341i	$-0.121788\pi$
$331$	28.0985	+	7.52896i	1.54443	+	0.413829i	0.616736	+	0.787170i	$0.288454\pi$
$332$	7.68557	+	2.85966i	0.421800	+	0.156944i
$333$	−2.58151	+	2.58151i	−0.141466	+	0.141466i
$334$	−12.1208	−	3.86933i	−0.663221	−	0.211720i
$335$	2.63770	−	4.56864i	0.144113	−	0.249611i
$336$	−0.432084	−	5.91013i	−0.0235721	−	0.322424i
$337$			13.9376i			0.759229i	0.925145	+	0.379615i	$0.123943\pi$
$337$			13.9376i			0.759229i	−0.925145	+	0.379615i	$0.876057\pi$
$338$	−0.508576	+	18.3777i	−0.0276629	+	0.999617i
$339$	−4.74291			−0.257599
$340$	0.303758	+	1.79770i	0.0164736	+	0.0974939i
$341$	2.99443	+	1.72884i	0.162158	+	0.0936217i
$342$	−8.63512	−	2.75659i	−0.466934	−	0.149059i
$343$	12.3667	+	12.3667i	0.667739	+	0.667739i
$344$	−24.0391	+	9.65687i	−1.29610	+	0.520664i
$345$	0.634526	−	2.36808i	0.0341617	−	0.127493i
$346$	19.7021	+	0.930729i	1.05919	+	0.0500363i
$347$	−14.4501	−	25.0283i	−0.775720	−	1.34359i	−0.934389	−	0.356255i	$-0.884053\pi$
$347$	−14.4501	−	25.0283i	−0.775720	−	1.34359i	0.158668	−	0.987332i	$-0.449280\pi$
$348$	−11.2714	−	8.01291i	−0.604210	−	0.429537i
$349$	5.08095	+	18.9624i	0.271977	+	1.01503i	0.957840	+	0.287302i	$0.0927583\pi$
$349$	5.08095	+	18.9624i	0.271977	+	1.01503i	−0.685863	+	0.727731i	$0.740575\pi$
$350$	6.30731	+	6.93278i	0.337140	+	0.370572i
$351$	0.967164	+	3.47341i	0.0516234	+	0.185397i
$352$	4.37680	+	7.14879i	0.233284	+	0.381032i
$353$	−4.83344	−	18.0387i	−0.257258	−	0.960101i	−0.966820	−	0.255458i	$-0.917774\pi$
$353$	−4.83344	−	18.0387i	−0.257258	−	0.960101i	0.709562	−	0.704643i	$-0.248893\pi$
$354$	19.2609	−	4.19791i	1.02370	−	0.223116i
$355$	−2.37893	+	1.37348i	−0.126261	+	0.0728966i
$356$	2.70843	+	3.27501i	0.143546	+	0.173575i
$357$	−0.481730	+	1.79784i	−0.0254959	+	0.0951518i
$358$	−11.6615	+	6.01773i	−0.616327	+	0.318047i
$359$	−16.3844	+	16.3844i	−0.864734	+	0.864734i	−0.991884	−	0.127149i	$-0.959417\pi$
$359$	−16.3844	+	16.3844i	−0.864734	+	0.864734i	0.127149	+	0.991884i	$0.459417\pi$
$360$	0.805637	−	1.88752i	0.0424608	−	0.0994808i
$361$	19.1236	+	11.0410i	1.00651	+	0.581107i
$362$	−15.8834	+	24.7366i	−0.834814	+	1.30012i
$363$			8.80433i			0.462107i
$364$	9.67027	−	4.54027i	0.506860	−	0.237975i
$365$			4.53666i			0.237460i
$366$	−16.8008	−	10.7878i	−0.878190	−	0.563889i
$367$	−25.4992	−	14.7220i	−1.33105	−	0.768480i	−0.345587	−	0.938387i	$-0.612320\pi$
$367$	−25.4992	−	14.7220i	−1.33105	−	0.768480i	−0.985460	+	0.169907i	$0.945653\pi$
$368$	−4.44059	−	12.7650i	−0.231482	−	0.665420i
$369$	1.37439	−	1.37439i	0.0715479	−	0.0715479i
$370$	1.71792	+	3.32907i	0.0893105	+	0.173070i
$371$	−0.196821	+	0.734545i	−0.0102184	+	0.0381357i
$372$	−2.97422	−	3.59640i	−0.154206	−	0.186465i
$373$	20.6658	−	11.9314i	1.07003	−	0.617785i	0.141844	−	0.989889i	$-0.454697\pi$
$373$	20.6658	−	11.9314i	1.07003	−	0.617785i	0.928191	+	0.372104i	$0.121364\pi$
$374$	−0.560650	−	2.57238i	−0.0289905	−	0.133014i
$375$	1.77908	+	6.63961i	0.0918712	+	0.342868i
$376$	9.49274	−	7.12374i	0.489551	−	0.367379i
$377$	6.21711	−	24.1436i	0.320197	−	1.24346i
$378$	1.54973	−	1.40992i	0.0797097	−	0.0725184i
$379$	3.24058	+	12.0940i	0.166457	+	0.621227i	0.997850	+	0.0655416i	$0.0208775\pi$
$379$	3.24058	+	12.0940i	0.166457	+	0.621227i	−0.831393	+	0.555686i	$0.812456\pi$
$380$	−5.38929	+	7.58087i	−0.276465	+	0.388890i
$381$	9.40686	+	16.2932i	0.481928	+	0.834724i
$382$	1.73856	−	36.8027i	0.0889527	−	1.88299i
$383$	8.74431	−	32.6342i	0.446814	−	1.66753i	−0.264290	−	0.964443i	$-0.585138\pi$
$383$	8.74431	−	32.6342i	0.446814	−	1.66753i	0.711103	−	0.703088i	$-0.248196\pi$
$384$	−2.17183	−	11.1033i	−0.110831	−	0.566613i
$385$	1.12629	+	1.12629i	0.0574011	+	0.0574011i
$386$	−6.46347	+	20.2470i	−0.328982	+	1.03055i
$387$	−7.93214	−	4.57963i	−0.403214	−	0.232795i
$388$	−0.377503	−	2.23414i	−0.0191648	−	0.113421i
$389$	−29.5448			−1.49798			−0.748990	−	0.662581i	$-0.769461\pi$
$389$	−29.5448			−1.49798			−0.748990	+	0.662581i	$0.769461\pi$
$390$	3.69717	+	0.138471i	0.187213	+	0.00701175i
$391$			4.24501i			0.214679i
$392$	10.6934	+	8.38889i	0.540097	+	0.423703i
$393$	−0.700524	+	1.21334i	−0.0353367	+	0.0612050i
$394$	−8.58372	+	26.8888i	−0.432442	+	1.35464i
$395$	1.66696	−	1.66696i	0.0838736	−	0.0838736i
$396$	−1.03347	+	2.77753i	−0.0519336	+	0.139576i
$397$	28.0508	+	7.51619i	1.40783	+	0.377227i	0.881150	−	0.472838i	$-0.156770\pi$
$397$	28.0508	+	7.51619i	1.40783	+	0.377227i	0.526679	+	0.850064i	$0.323437\pi$
$398$	15.9062	+	0.751413i	0.797308	+	0.0376649i
$399$	−8.22340	+	4.74778i	−0.411685	+	0.237686i
$400$	13.5420	+	11.6968i	0.677098	+	0.584839i
$401$	−5.34143	+	1.43123i	−0.266738	+	0.0714723i	−0.389709	−	0.920938i	$-0.627424\pi$
$401$	−5.34143	+	1.43123i	−0.266738	+	0.0714723i	0.122971	+	0.992410i	$0.460758\pi$
$402$	7.60556	−	6.91940i	0.379331	−	0.345108i
$403$	4.13532	−	7.32697i	0.205995	−	0.364982i
$404$	−22.8069	−	2.15962i	−1.13469	−	0.107445i
$405$	0.700859	−	0.187795i	0.0348260	−	0.00933159i
$406$	−14.1548	+	3.08504i	−0.702491	+	0.153108i
$407$	−2.70485	−	4.68493i	−0.134074	−	0.232223i
$408$	−0.501551	+	3.51794i	−0.0248305	+	0.174164i
$409$	−17.8385	−	4.77981i	−0.882056	−	0.236346i	−0.210762	−	0.977537i	$-0.567595\pi$
$409$	−17.8385	−	4.77981i	−0.882056	−	0.236346i	−0.671294	+	0.741191i	$0.734261\pi$
$410$	−0.914619	−	1.77239i	−0.0451698	−	0.0875323i
$411$	11.8545	+	11.8545i	0.584741	+	0.584741i
$412$	−2.07152	−	4.52653i	−0.102056	−	0.223006i
$413$	10.3253	−	17.8840i	0.508075	−	0.880012i
$414$	2.58180	−	4.02085i	0.126889	−	0.197614i
$415$	2.97501			0.146038
$416$	17.2900	−	10.8193i	0.847710	−	0.530459i
$417$	−15.1519			−0.741990
$418$	7.25716	−	11.3022i	0.354960	−	0.552808i
$419$	14.1415	−	24.4939i	0.690859	−	1.19660i	−0.280698	−	0.959796i	$-0.590566\pi$
$419$	14.1415	−	24.4939i	0.690859	−	1.19660i	0.971557	−	0.236807i	$-0.0761009\pi$
$420$	−0.894631	−	1.95488i	−0.0436535	−	0.0953885i
$421$	−19.6915	−	19.6915i	−0.959704	−	0.959704i	0.0395149	−	0.999219i	$-0.487419\pi$
$421$	−19.6915	−	19.6915i	−0.959704	−	0.959704i	−0.999219	+	0.0395149i	$0.987419\pi$
$422$	−0.741639	−	1.43718i	−0.0361024	−	0.0699611i
$423$	4.05315	+	1.08604i	0.197071	+	0.0528050i
$424$	−0.204919	+	1.43733i	−0.00995174	+	0.0698028i
$425$	−2.81017	−	4.86736i	−0.136313	−	0.236102i
$426$	−5.23120	+	1.14014i	−0.253453	+	0.0552401i
$427$	−20.2030	+	5.41337i	−0.977691	+	0.261971i
$428$	20.4293	+	1.93448i	0.987488	+	0.0935068i
$429$	−5.34238	+	0.0521930i	−0.257933	+	0.00251990i
$430$	−6.95199	+	6.32479i	−0.335255	+	0.305009i
$431$	−30.7854	+	8.24891i	−1.48288	+	0.397336i	−0.907326	−	0.420428i	$-0.861880\pi$
$431$	−30.7854	+	8.24891i	−1.48288	+	0.397336i	−0.575553	+	0.817764i	$0.695213\pi$
$432$	2.61467	−	3.02713i	0.125798	−	0.145643i
$433$	13.1701	−	7.60376i	0.632915	−	0.365414i	−0.148965	−	0.988842i	$-0.547594\pi$
$433$	13.1701	−	7.60376i	0.632915	−	0.365414i	0.781880	+	0.623429i	$0.214261\pi$
$434$	−4.88344	−	0.230694i	−0.234412	−	0.0110737i
$435$	−4.84622	−	1.29854i	−0.232358	−	0.0622602i
$436$	7.11207	−	19.1143i	0.340606	−	0.915408i
$437$	−15.3136	+	15.3136i	−0.732548	+	0.732548i
$438$	−2.68903	+	8.42348i	−0.128487	+	0.402489i
$439$	−1.65131	+	2.86016i	−0.0788129	+	0.136508i	−0.902738	−	0.430191i	$-0.858446\pi$
$439$	−1.65131	+	2.86016i	−0.0788129	+	0.136508i	0.823925	+	0.566699i	$0.191780\pi$
$440$	2.39261	+	1.87699i	0.114063	+	0.0894819i
$441$			4.80523i			0.228820i
$442$	−6.24562	+	1.42529i	−0.297074	+	0.0677940i
$443$	−12.1161			−0.575654			−0.287827	−	0.957682i	$-0.592933\pi$
$443$	−12.1161			−0.575654			−0.287827	+	0.957682i	$0.592933\pi$
$444$	1.21651	+	7.19955i	0.0577331	+	0.341676i
$445$	1.33525	+	0.770906i	0.0632968	+	0.0365444i
$446$	6.31471	−	19.7810i	0.299010	−	0.936660i
$447$	5.50225	+	5.50225i	0.260247	+	0.260247i
$448$	−10.1346	−	6.14449i	−0.478816	−	0.290300i
$449$	2.46287	−	9.19155i	0.116230	−	0.433776i	−0.883146	−	0.469098i	$-0.844579\pi$
$449$	2.46287	−	9.19155i	0.116230	−	0.433776i	0.999376	+	0.0353221i	$0.0112457\pi$
$450$	−0.298533	+	6.31948i	−0.0140730	+	0.297903i
$451$	1.44006	+	2.49425i	0.0678096	+	0.117450i
$452$	−5.49621	+	7.73126i	−0.258520	+	0.363648i
$453$	2.54779	+	9.50849i	0.119706	+	0.446748i
$454$	−9.37303	+	8.52741i	−0.439898	+	0.400211i
$455$	2.71365	−	2.76720i	0.127218	−	0.129728i
$456$	−14.5000	+	10.8814i	−0.679027	+	0.509569i
$457$	−3.13824	−	11.7121i	−0.146800	−	0.547867i	−0.999669	−	0.0257405i	$-0.991806\pi$
$457$	−3.13824	−	11.7121i	−0.146800	−	0.547867i	0.852868	−	0.522126i	$-0.174861\pi$
$458$	−0.697013	−	3.19804i	−0.0325693	−	0.149434i
$459$	−1.08804	+	0.628178i	−0.0507852	+	0.0293208i
$460$	−3.12483	−	3.77852i	−0.145696	−	0.176174i
$461$	6.26259	−	23.3723i	0.291678	−	1.08856i	−0.652142	−	0.758097i	$-0.726129\pi$
$461$	6.26259	−	23.3723i	0.291678	−	1.08856i	0.943820	−	0.330460i	$-0.107204\pi$
$462$	1.42366	+	2.75884i	0.0662347	+	0.128353i
$463$	−12.7547	+	12.7547i	−0.592763	+	0.592763i	−0.938377	−	0.345614i	$-0.887671\pi$
$463$	−12.7547	+	12.7547i	−0.592763	+	0.592763i	0.345614	+	0.938377i	$0.387671\pi$
$464$	−26.1232	+	9.08755i	−1.21274	+	0.421879i
$465$	−1.46628	−	0.846559i	−0.0679972	−	0.0392582i
$466$	−18.1174	−	11.6332i	−0.839271	−	0.538899i
$467$			18.1587i			0.840286i	0.907458	+	0.420143i	$0.138020\pi$
$467$			18.1587i			0.840286i	−0.907458	+	0.420143i	$0.861980\pi$
$468$	6.78267	+	2.44854i	0.313529	+	0.113184i
$469$		−	10.7712i		−	0.497367i
$470$	2.32644	−	3.62316i	0.107311	−	0.167124i
$471$	−9.19590	−	5.30926i	−0.423725	−	0.244638i
$472$	15.4771	−	36.2612i	0.712393	−	1.66906i
$473$	9.59686	−	9.59686i	0.441264	−	0.441264i
$474$	4.08319	−	2.10707i	0.187547	−	0.0967811i
$475$	7.42117	−	27.6962i	0.340507	−	1.27079i
$476$	2.37236	+	2.86864i	0.108737	+	0.131484i
$477$	−0.444540	+	0.256655i	−0.0203541	+	0.0117514i
$478$	39.3287	−	8.57170i	1.79885	−	0.392061i
$479$	−4.24253	−	15.8334i	−0.193846	−	0.723444i	−0.992562	−	0.121736i	$-0.961154\pi$
$479$	−4.24253	−	15.8334i	−0.193846	−	0.723444i	0.798716	−	0.601708i	$-0.205513\pi$
$480$	−2.14318	−	3.50055i	−0.0978225	−	0.159777i
$481$	−11.3348	+	6.69263i	−0.516822	+	0.305158i
$482$	−3.55957	−	3.91256i	−0.162134	−	0.178212i
$483$	−1.29556	−	4.83509i	−0.0589499	−	0.220004i
$484$	14.3516	+	10.2027i	0.652347	+	0.463759i
$485$	−0.411007	−	0.711885i	−0.0186629	−	0.0323251i
$486$	1.41264	+	0.0667332i	0.0640786	+	0.00302708i
$487$	9.33917	−	34.8542i	0.423198	−	1.57940i	−0.344629	−	0.938739i	$-0.611995\pi$
$487$	9.33917	−	34.8542i	0.423198	−	1.57940i	0.767827	−	0.640658i	$-0.221338\pi$
$488$	−37.0541	+	14.8852i	−1.67736	+	0.673820i
$489$	−8.19576	−	8.19576i	−0.370625	−	0.370625i
$490$	4.69725	+	1.49950i	0.212200	+	0.0677406i
$491$	−12.9846	−	7.49664i	−0.585985	−	0.338319i	0.177523	−	0.984117i	$-0.443192\pi$
$491$	−12.9846	−	7.49664i	−0.585985	−	0.338319i	−0.763508	+	0.645798i	$0.776525\pi$
$492$	−0.647669	−	3.83303i	−0.0291992	−	0.172806i
$493$	8.68730			0.391256
$494$	−27.6723	−	17.3890i	−1.24503	−	0.782369i
$495$			1.07516i			0.0483246i
$496$	−9.30899	+	0.680571i	−0.417986	+	0.0305585i
$497$	−2.80433	+	4.85724i	−0.125791	+	0.217877i
$498$	5.52388	+	1.76339i	0.247531	+	0.0790194i
$499$	−30.5157	+	30.5157i	−1.36607	+	1.36607i	−0.500105	+	0.865965i	$0.666705\pi$
$499$	−30.5157	+	30.5157i	−1.36607	+	1.36607i	−0.865965	+	0.500105i	$0.833295\pi$
$500$	12.8847	+	4.79414i	0.576219	+	0.214401i
$501$	−8.69026	−	2.32855i	−0.388252	−	0.104032i
$502$	1.49790	−	31.7082i	0.0668546	−	1.41521i
$503$	−30.7732	+	17.7669i	−1.37211	+	0.792187i	−0.991193	−	0.132424i	$-0.957724\pi$
$503$	−30.7732	+	17.7669i	−1.37211	+	0.792187i	−0.380914	+	0.924610i	$0.624391\pi$
$504$	−0.502390	−	4.16002i	−0.0223782	−	0.185302i
$505$	−8.02797	+	2.15109i	−0.357240	+	0.0957222i
$506$	4.76485	+	5.23736i	0.211823	+	0.232829i
$507$	0.253986	+	12.9975i	0.0112799	+	0.577240i
$508$	37.4599	+	3.54714i	1.66201	+	0.157379i
$509$	−17.3479	+	4.64835i	−0.768931	+	0.206034i	−0.621899	−	0.783097i	$-0.713639\pi$
$509$	−17.3479	+	4.64835i	−0.768931	+	0.206034i	−0.147032	+	0.989132i	$0.546972\pi$
$510$	0.274533	+	1.25961i	0.0121565	+	0.0557766i
$511$	4.63141	+	8.02185i	0.204882	+	0.354866i
$512$	−20.6159	−	9.32657i	−0.911102	−	0.412180i
$513$	−6.19113	−	1.65891i	−0.273345	−	0.0732426i
$514$	37.4534	−	19.3273i	1.65200	−	0.852490i
$515$	−1.27702	−	1.27702i	−0.0562724	−	0.0562724i
$516$	−16.6571	+	7.62294i	−0.733287	+	0.335581i
$517$	−3.10887	+	5.38472i	−0.136728	+	0.236820i
$518$	6.43628	+	4.13276i	0.282794	+	0.181583i
$519$	13.9470			0.612206
$520$	4.51010	−	5.86617i	0.197781	−	0.257249i
$521$	−33.0188			−1.44658			−0.723289	−	0.690545i	$-0.757371\pi$
$521$	−33.0188			−1.44658			−0.723289	+	0.690545i	$0.757371\pi$
$522$	−8.22856	−	5.28359i	−0.360154	−	0.231256i
$523$	0.905353	−	1.56812i	0.0395883	−	0.0685690i	−0.845552	−	0.533893i	$-0.820729\pi$
$523$	0.905353	−	1.56812i	0.0395883	−	0.0685690i	0.885141	+	0.465324i	$0.154062\pi$
$524$	1.16604	+	2.54796i	0.0509389	+	0.111308i
$525$	4.68630	+	4.68630i	0.204527	+	0.204527i
$526$	−3.07131	+	1.58491i	−0.133916	+	0.0691053i
$527$	2.83176	+	0.758768i	0.123353	+	0.0330524i
$528$	3.32995	+	4.90329i	0.144917	+	0.213388i
$529$	5.79177	+	10.0316i	0.251816	+	0.436158i
$530$	0.112166	+	0.514641i	0.00487219	+	0.0223546i
$531$	13.4642	−	3.60773i	0.584299	−	0.156562i
$532$	−1.79029	+	18.9066i	−0.0776190	+	0.819703i
$533$	6.03462	−	3.56315i	0.261389	−	0.154337i
$534$	2.02229	+	2.22283i	0.0875131	+	0.0961913i
$535$	7.19106	−	1.92684i	0.310897	−	0.0833045i
$536$	−2.46556	−	20.4160i	−0.106496	−	0.881835i
$537$	−8.03592	+	4.63954i	−0.346776	+	0.200211i
$538$	1.76934	−	37.4541i	0.0762815	−	1.61476i
$539$	−6.87768	−	1.84287i	−0.296243	−	0.0793780i
$540$	0.506057	−	1.36007i	0.0217772	−	0.0585281i
$541$	27.7884	−	27.7884i	1.19472	−	1.19472i	0.218990	−	0.975727i	$-0.429724\pi$
$541$	27.7884	−	27.7884i	1.19472	−	1.19472i	0.975727	−	0.218990i	$-0.0702761\pi$
$542$	8.95439	+	2.85851i	0.384624	+	0.122784i
$543$	−10.3934	+	18.0019i	−0.446023	+	0.772535i
$544$	5.15327	+	4.89424i	0.220945	+	0.209839i
$545$		−	7.39896i		−	0.316937i
$546$	6.67880	−	3.52954i	0.285826	−	0.151050i
$547$	6.37762			0.272687			0.136344	−	0.990662i	$-0.456465\pi$
$547$	6.37762			0.272687			0.136344	+	0.990662i	$0.456465\pi$
$548$	33.0611	−	5.58634i	1.41230	−	0.238637i
$549$	−12.2267	−	7.05906i	−0.521821	−	0.301273i
$550$	−8.93052	−	2.85089i	−0.380799	−	0.121562i
$551$	31.3388	+	31.3388i	1.33508	+	1.33508i
$552$	−3.56240	−	8.86798i	−0.151626	−	0.377446i
$553$	1.24578	−	4.64933i	0.0529761	−	0.197710i
$554$	−2.48242	−	0.117270i	−0.105468	−	0.00498231i
$555$	1.32448	+	2.29407i	0.0562211	+	0.0973778i
$556$	−17.5584	+	24.6985i	−0.744641	+	1.04745i
$557$	1.53541	+	5.73023i	0.0650574	+	0.242798i	0.990795	−	0.135368i	$-0.0432217\pi$
$557$	1.53541	+	5.73023i	0.0650574	+	0.242798i	−0.925738	+	0.378166i	$0.876555\pi$
$558$	−2.22075	−	2.44097i	−0.0940118	−	0.103334i
$559$	−23.5786	−	23.1224i	−0.997269	−	0.977972i
$560$	−4.22331	−	0.807061i	−0.178468	−	0.0341046i
$561$	−0.481829	−	1.79821i	−0.0203428	−	0.0759205i
$562$	33.9177	−	7.39238i	1.43073	−	0.311829i
$563$	5.39506	−	3.11484i	0.227375	−	0.131275i	−0.381986	−	0.924168i	$-0.624760\pi$
$563$	5.39506	−	3.11484i	0.227375	−	0.131275i	0.609360	+	0.792893i	$0.291426\pi$
$564$	6.46721	−	5.34837i	0.272319	−	0.225207i
$565$	−0.890693	+	3.32411i	−0.0374717	+	0.139846i
$566$	−5.02441	+	2.59278i	−0.211192	+	0.108982i
$567$	1.04756	−	1.04756i	0.0439935	−	0.0439935i
$568$	−4.20355	+	9.84844i	−0.176377	+	0.413232i
$569$	−1.68213	−	0.971181i	−0.0705187	−	0.0407140i	0.464326	−	0.885664i	$-0.346297\pi$
$569$	−1.68213	−	0.971181i	−0.0705187	−	0.0407140i	−0.534845	+	0.844950i	$0.679630\pi$
$570$	−3.55361	+	5.53433i	−0.148844	+	0.231808i
$571$			31.5350i			1.31970i	0.751398	+	0.659850i	$0.229380\pi$
$571$			31.5350i			1.31970i	−0.751398	+	0.659850i	$0.770620\pi$
$572$	−6.10582	+	8.76893i	−0.255297	+	0.366647i
$573$		−	26.0525i		−	1.08836i
$574$	−3.42667	−	2.20027i	−0.143026	−	0.0918377i
$575$	13.0902	+	7.55764i	0.545900	+	0.315175i
$576$	−1.90448	−	7.77000i	−0.0793535	−	0.323750i
$577$	17.6927	−	17.6927i	0.736558	−	0.736558i	−0.235352	−	0.971910i	$-0.575624\pi$
$577$	17.6927	−	17.6927i	0.736558	−	0.736558i	0.971910	+	0.235352i	$0.0756242\pi$
$578$	10.0013	+	19.3810i	0.415999	+	0.806144i
$579$	−3.88969	+	14.5165i	−0.161650	+	0.603287i
$580$	−7.73263	+	6.39488i	−0.321080	+	0.265533i
$581$	5.26050	−	3.03715i	0.218242	−	0.126002i
$582$	−0.341183	−	1.56542i	−0.0141425	−	0.0648886i
$583$	−0.196861	−	0.734696i	−0.00815316	−	0.0304280i
$584$	10.6147	+	14.1446i	0.439240	+	0.585310i
$585$	2.61600	−	0.0255573i	0.108158	−	0.00105667i
$586$	−21.9977	+	20.0131i	−0.908716	+	0.826733i
$587$	7.64218	+	28.5210i	0.315427	+	1.17719i	0.923592	+	0.383377i	$0.125239\pi$
$587$	7.64218	+	28.5210i	0.315427	+	1.17719i	−0.608165	+	0.793810i	$0.708094\pi$
$588$	7.83285	+	5.56843i	0.323021	+	0.229638i
$589$	7.47818	+	12.9526i	0.308133	+	0.533702i
$590$	0.674944	−	14.2875i	0.0277870	−	0.588207i
$591$	−5.16566	+	19.2785i	−0.212487	+	0.793012i
$592$	13.1455	+	6.36004i	0.540276	+	0.261396i
$593$	−20.5469	−	20.5469i	−0.843759	−	0.843759i	0.145586	−	0.989346i	$-0.453493\pi$
$593$	−20.5469	−	20.5469i	−0.843759	−	0.843759i	−0.989346	+	0.145586i	$0.953493\pi$
$594$	−0.637280	+	1.99630i	−0.0261479	+	0.0819093i
$595$	1.16957	+	0.675250i	0.0479476	+	0.0276825i
$596$	15.3452	−	2.59288i	0.628563	−	0.106209i
$597$	11.2600			0.460839
$598$	12.6300	−	11.7180i	0.516477	−	0.479186i
$599$			28.2451i			1.15407i	0.816721	+	0.577033i	$0.195789\pi$
$599$			28.2451i			1.15407i	−0.816721	+	0.577033i	$0.804211\pi$
$600$	9.95523	+	7.80981i	0.406420	+	0.318834i
$601$	−2.74994	+	4.76304i	−0.112172	+	0.194288i	−0.916646	−	0.399700i	$-0.869114\pi$
$601$	−2.74994	+	4.76304i	−0.112172	+	0.194288i	0.804473	+	0.593989i	$0.202448\pi$
$602$	−5.83581	+	18.2809i	−0.237850	+	0.745073i
$603$	5.14108	−	5.14108i	0.209361	−	0.209361i
$604$	18.4519	+	6.86562i	0.750798	+	0.279358i
$605$	6.17059	+	1.65341i	0.250870	+	0.0672205i
$606$	−16.1810	−	0.764394i	−0.657309	−	0.0310514i
$607$	1.25794	−	0.726274i	0.0510584	−	0.0294786i	−0.474254	−	0.880388i	$-0.657282\pi$
$607$	1.25794	−	0.726274i	0.0510584	−	0.0294786i	0.525312	+	0.850910i	$0.323949\pi$
$608$	0.934410	+	36.2457i	0.0378953	+	1.46996i
$609$	−9.89488	+	2.65132i	−0.400961	+	0.107437i
$610$	−10.7158	+	9.74908i	−0.433872	+	0.394729i
$611$	13.1757	+	7.43632i	0.533031	+	0.300841i
$612$	−0.236873	+	2.50152i	−0.00957503	+	0.101118i
$613$	−30.9474	+	8.29232i	−1.24995	+	0.334924i	−0.822318	−	0.569028i	$-0.807319\pi$
$613$	−30.9474	+	8.29232i	−1.24995	+	0.334924i	−0.427634	+	0.903952i	$0.640653\pi$
$614$	−3.38516	+	0.737796i	−0.136614	+	0.0297750i
$615$	−0.705151	−	1.22136i	−0.0284344	−	0.0492499i
$616$	6.14687	+	0.876356i	0.247665	+	0.0353094i
$617$	−4.26824	−	1.14367i	−0.171833	−	0.0460425i	0.171877	−	0.985118i	$-0.445017\pi$
$617$	−4.26824	−	1.14367i	−0.171833	−	0.0460425i	−0.343710	+	0.939076i	$0.611684\pi$
$618$	−1.61419	−	3.12806i	−0.0649322	−	0.125829i
$619$	−8.69550	−	8.69550i	−0.349502	−	0.349502i	0.510422	−	0.859924i	$-0.329489\pi$
$619$	−8.69550	−	8.69550i	−0.349502	−	0.349502i	−0.859924	+	0.510422i	$0.829489\pi$
$620$	−3.07912	+	1.40912i	−0.123660	+	0.0565918i
$621$	1.68941	−	2.92615i	0.0677938	−	0.117422i
$622$	1.74264	−	2.71395i	0.0698734	−	0.108820i
$623$	3.14803			0.126123
$624$	11.8512	−	8.21878i	0.474429	−	0.329014i
$625$	−17.3801			−0.695204
$626$	24.6476	−	38.3857i	0.985115	−	1.53420i
$627$	4.74876	−	8.22509i	0.189647	−	0.328479i
$628$	−19.3109	+	8.83743i	−0.770589	+	0.352652i
$629$	−3.24329	−	3.24329i	−0.129319	−	0.129319i
$630$	−0.697123	−	1.35092i	−0.0277740	−	0.0538219i
$631$	9.04870	+	2.42459i	0.360223	+	0.0965215i	0.434391	−	0.900724i	$-0.356963\pi$
$631$	9.04870	+	2.42459i	0.360223	+	0.0965215i	−0.0741682	+	0.997246i	$0.523630\pi$
$632$	1.29704	−	9.09761i	0.0515935	−	0.361884i
$633$	−0.571787	−	0.990365i	−0.0227265	−	0.0393635i
$634$	35.1314	−	7.65690i	1.39525	−	0.304094i
$635$	13.1858	−	3.53312i	0.523261	−	0.140207i
$636$	−0.0967794	+	1.02205i	−0.00383755	+	0.0405269i
$637$	−4.32047	+	16.7782i	−0.171183	+	0.664775i
$638$	10.7181	−	9.75114i	0.424334	−	0.386051i
$639$	−3.65686	+	0.979852i	−0.144663	+	0.0387623i
$640$	−8.18971	−	0.562992i	−0.323727	−	0.0222542i
$641$	−31.6965	+	18.3000i	−1.25194	+	0.722805i	−0.971494	−	0.237066i	$-0.923814\pi$
$641$	−31.6965	+	18.3000i	−1.25194	+	0.722805i	−0.280442	+	0.959871i	$0.590481\pi$
$642$	14.4942	+	0.684706i	0.572039	+	0.0270232i
$643$	−13.8446	−	3.70965i	−0.545977	−	0.146294i	−0.0247210	−	0.999694i	$-0.507870\pi$
$643$	−13.8446	−	3.70965i	−0.545977	−	0.146294i	−0.521256	+	0.853400i	$0.674536\pi$
$644$	−9.38284	−	3.49118i	−0.369736	−	0.137572i
$645$	−4.69929	+	4.69929i	−0.185034	+	0.185034i
$646$	3.46326	−	10.8488i	0.136260	−	0.426840i
$647$	−16.5697	+	28.6996i	−0.651422	+	1.12830i	0.331356	+	0.943506i	$0.392494\pi$
$647$	−16.5697	+	28.6996i	−0.651422	+	1.12830i	−0.982778	+	0.184790i	$0.940839\pi$
$648$	1.74578	−	2.22536i	0.0685808	−	0.0874205i
$649$			20.6549i			0.810774i
$650$	−6.72433	+	21.7970i	−0.263750	+	0.854947i
$651$	−3.45696			−0.135489
$652$	−22.8571	+	3.86217i	−0.895153	+	0.151254i
$653$	35.8657	+	20.7071i	1.40353	+	0.810330i	0.994753	−	0.102303i	$-0.0326210\pi$
$653$	35.8657	+	20.7071i	1.40353	+	0.810330i	0.408780	+	0.912633i	$0.365954\pi$
$654$	4.38561	−	13.7381i	0.171491	−	0.537202i
$655$	0.718828	+	0.718828i	0.0280869	+	0.0280869i
$656$	−6.99864	−	3.38608i	−0.273251	−	0.132204i
$657$	−1.61825	+	6.03939i	−0.0631339	+	0.235619i
$658$	0.414845	−	8.78161i	0.0161723	−	0.342343i
$659$	14.1419	+	24.4945i	0.550889	+	0.954168i	0.998211	+	0.0597950i	$0.0190447\pi$
$659$	14.1419	+	24.4945i	0.550889	+	0.954168i	−0.447321	+	0.894373i	$0.647622\pi$
$660$	1.75258	+	1.24592i	0.0682189	+	0.0484973i
$661$	6.42654	+	23.9842i	0.249963	+	0.932876i	0.970823	+	0.239796i	$0.0770804\pi$
$661$	6.42654	+	23.9842i	0.249963	+	0.932876i	−0.720860	+	0.693081i	$0.756253\pi$
$662$	30.4299	−	27.6846i	1.18269	−	1.07599i
$663$	−4.36384	+	1.21510i	−0.169478	+	0.0471907i
$664$	9.27567	−	6.96084i	0.359966	−	0.270133i
$665$	1.78322	+	6.65505i	0.0691502	+	0.258072i
$666$	1.09947	+	5.04459i	0.0426036	+	0.195474i
$667$	−20.2334	+	11.6817i	−0.783440	+	0.452319i
$668$	−13.8662	+	11.4673i	−0.536500	+	0.443684i
$669$	3.80017	−	14.1824i	0.146923	−	0.548324i
$670$	−3.42124	−	6.62985i	−0.132174	−	0.256134i
$671$	14.7927	−	14.7927i	0.571064	−	0.571064i
$672$	−7.36330	−	4.00181i	−0.284045	−	0.154373i
$673$	19.3181	+	11.1533i	0.744658	+	0.429929i	0.823761	−	0.566938i	$-0.191872\pi$
$673$	19.3181	+	11.1533i	0.744658	+	0.429929i	−0.0791022	+	0.996867i	$0.525205\pi$
$674$	16.5859	+	10.6499i	0.638866	+	0.410218i
$675$			4.47353i			0.172186i
$676$	21.4812	+	14.6479i	0.826198	+	0.563379i
$677$		−	7.36423i		−	0.283030i	−0.989936	−	0.141515i	$-0.954803\pi$
$677$		−	7.36423i		−	0.283030i	0.989936	−	0.141515i	$-0.0451974\pi$
$678$	−3.62411	+	5.64412i	−0.139183	+	0.216761i
$679$	−1.45351	−	0.839184i	−0.0557805	−	0.0322049i
$680$	2.37139	+	1.01217i	0.0909387	+	0.0388148i
$681$	−6.33582	+	6.33582i	−0.242789	+	0.242789i
$682$	4.34542	−	2.24239i	0.166395	−	0.0858656i
$683$	1.34151	−	5.00660i	0.0513316	−	0.191572i	−0.935499	−	0.353329i	$-0.885049\pi$
$683$	1.34151	−	5.00660i	0.0513316	−	0.191572i	0.986831	+	0.161757i	$0.0517162\pi$
$684$	−9.87858	+	8.16957i	−0.377717	+	0.312371i
$685$	10.5346	−	6.08214i	0.402506	−	0.232387i
$686$	24.1661	−	5.26701i	0.922666	−	0.201095i
$687$	−0.599021	−	2.23558i	−0.0228541	−	0.0852926i
$688$	−6.87677	+	35.9858i	−0.262174	+	1.37195i
$689$	−1.78294	+	0.496455i	−0.0679245	+	0.0189134i
$690$	−2.33320	−	2.56457i	−0.0888235	−	0.0976316i
$691$	6.75090	+	25.1947i	0.256816	+	0.958451i	0.967071	+	0.254506i	$0.0819130\pi$
$691$	6.75090	+	25.1947i	0.256816	+	0.958451i	−0.710255	+	0.703945i	$0.751420\pi$
$692$	16.1622	−	22.7346i	0.614394	−	0.864239i
$693$	1.09761	+	1.90112i	0.0416948	+	0.0722175i
$694$	−40.8254	−	1.92860i	−1.54971	−	0.0732086i
$695$	−2.84544	+	10.6193i	−0.107934	+	0.402814i
$696$	−18.1481	+	7.29035i	−0.687901	+	0.276340i
$697$	1.72672	+	1.72672i	0.0654044	+	0.0654044i
$698$	26.4479	+	8.44297i	1.00107	+	0.319571i
$699$	−13.1848	−	7.61226i	−0.498695	−	0.287922i
$700$	13.0696	−	2.20837i	0.493984	−	0.0834687i
$701$	2.13901			0.0807892			0.0403946	−	0.999184i	$-0.487138\pi$
$701$	2.13901			0.0807892			0.0403946	+	0.999184i	$0.487138\pi$
$702$	4.87243	+	1.50314i	0.183898	+	0.0567322i
$703$		−	23.3999i		−	0.882545i
$704$	11.8515	+	0.254028i	0.446671	+	0.00957402i
$705$	1.52232	−	2.63673i	0.0573339	−	0.0993052i
$706$	−25.1596	−	8.03169i	−0.946892	−	0.302277i
$707$	−11.9993	+	11.9993i	−0.451279	+	0.451279i
$708$	9.72188	−	26.1284i	0.365371	−	0.981965i
$709$	31.8967	+	8.54671i	1.19791	+	0.320978i	0.802007	−	0.597315i	$-0.203766\pi$
$709$	31.8967	+	8.54671i	1.19791	+	0.320978i	0.395901	+	0.918293i	$0.370433\pi$
$710$	−0.183313	+	3.88045i	−0.00687962	+	0.145631i
$711$	2.81373	−	1.62451i	0.105523	−	0.0609238i
$712$	5.96685	−	0.720594i	0.223617	−	0.0270054i
$713$	−7.61569	+	2.04062i	−0.285210	+	0.0764218i
$714$	1.77136	+	1.94702i	0.0662915	+	0.0728653i
$715$	−0.966691	+	3.75406i	−0.0361522	+	0.140394i
$716$	−1.74948	+	18.4755i	−0.0653810	+	0.690462i
$717$	27.4926	−	7.36662i	1.02673	−	0.275112i
$718$	6.97814	+	32.0171i	0.260422	+	1.19487i
$719$	−24.1212	−	41.7791i	−0.899568	−	1.55810i	−0.828047	−	0.560659i	$-0.810548\pi$
$719$	−24.1212	−	41.7791i	−0.899568	−	1.55810i	−0.0715216	−	0.997439i	$-0.522785\pi$
$720$	−1.63057	−	2.40099i	−0.0607679	−	0.0894797i
$721$	−3.56176	−	0.954371i	−0.132647	−	0.0355426i
$722$	27.7516	−	14.3208i	1.03281	−	0.532965i
$723$	−2.64474	−	2.64474i	−0.0983590	−	0.0983590i
$724$	17.3001	+	37.8030i	0.642955	+	1.40494i
$725$	15.4665	−	26.7888i	0.574412	−	0.994910i
$726$	10.4773	+	6.72749i	0.388848	+	0.249681i
$727$	−35.9735			−1.33418			−0.667092	−	0.744976i	$-0.732461\pi$
$727$	−35.9735			−1.33418			−0.667092	+	0.744976i	$0.732461\pi$
$728$	1.98618	−	14.9770i	0.0736127	−	0.555085i
$729$	1.00000			0.0370370
$730$	5.39869	+	3.46651i	0.199814	+	0.128301i
$731$	5.75364	−	9.96560i	0.212806	−	0.368591i
$732$	−25.6753	+	11.7500i	−0.948987	+	0.434294i
$733$	−7.99326	−	7.99326i	−0.295238	−	0.295238i	0.543907	−	0.839145i	$-0.316944\pi$
$733$	−7.99326	−	7.99326i	−0.295238	−	0.295238i	−0.839145	+	0.543907i	$0.816944\pi$
$734$	−37.0036	+	19.0952i	−1.36583	+	0.704815i
$735$	3.36779	+	0.902396i	0.124223	+	0.0332854i
$736$	−18.5836	−	4.46951i	−0.685001	−	0.164748i
$737$	5.38670	+	9.33004i	0.198422	+	0.343677i
$738$	−0.585356	−	2.68573i	−0.0215473	−	0.0988632i
$739$	10.6104	−	2.84304i	0.390308	−	0.104583i	−0.0583274	−	0.998298i	$-0.518577\pi$
$739$	10.6104	−	2.84304i	0.390308	−	0.104583i	0.448636	+	0.893715i	$0.351910\pi$
$740$	5.27433	+	0.499435i	0.193888	+	0.0183596i
$741$	−20.1257	−	11.3589i	−0.739335	−	0.417279i
$742$	0.723726	+	0.795494i	0.0265688	+	0.0292035i
$743$	−9.10445	+	2.43953i	−0.334010	+	0.0894977i	−0.421926	−	0.906630i	$-0.638646\pi$
$743$	−9.10445	+	2.43953i	−0.334010	+	0.0894977i	0.0879163	+	0.996128i	$0.471979\pi$
$744$	−6.55241	+	0.791310i	−0.240223	+	0.0290108i
$745$	4.88959	−	2.82301i	0.179141	−	0.103427i
$746$	1.59244	−	33.7095i	0.0583035	−	1.23419i
$747$	3.96046	+	1.06120i	0.144906	+	0.0388274i
$748$	−3.48956	−	1.29840i	−0.127591	−	0.0474742i
$749$	10.7484	−	10.7484i	0.392736	−	0.392736i
$750$	9.26065	+	2.95628i	0.338151	+	0.107948i
$751$	−11.9625	+	20.7197i	−0.436519	+	0.756073i	−0.997418	−	0.0718109i	$-0.977122\pi$
$751$	−11.9625	+	20.7197i	−0.436519	+	0.756073i	0.560899	+	0.827884i	$0.310456\pi$
$752$	−1.22383	−	16.7398i	−0.0446286	−	0.610439i
$753$		−	22.4461i		−	0.817982i
$754$	−23.9807	−	25.8469i	−0.873324	−	0.941287i
$755$	7.14257			0.259945
$756$	−0.493654	−	2.92154i	−0.0179540	−	0.106255i
$757$	−4.03960	−	2.33226i	−0.146822	−	0.0847676i	0.424789	−	0.905292i	$-0.360348\pi$
$757$	−4.03960	−	2.33226i	−0.146822	−	0.0847676i	−0.571611	+	0.820525i	$0.693681\pi$
$758$	16.8682	+	5.38484i	0.612680	+	0.195586i
$759$	3.54026	+	3.54026i	0.128503	+	0.128503i
$760$	4.90331	+	12.2060i	0.177862	+	0.442757i
$761$	−5.39526	+	20.1354i	−0.195578	+	0.729907i	0.796538	+	0.604588i	$0.206662\pi$
$761$	−5.39526	+	20.1354i	−0.195578	+	0.729907i	−0.992116	+	0.125319i	$0.960004\pi$
$762$	26.5770	+	1.25550i	0.962782	+	0.0454820i
$763$	−7.55350	−	13.0831i	−0.273455	−	0.473638i
$764$	−42.4673	−	30.1903i	−1.53641	−	1.09225i
$765$	0.235937	+	0.880529i	0.00853032	+	0.0318356i
$766$	−32.1535	−	35.3420i	−1.16175	−	1.27696i
$767$	50.2562	−	0.490983i	1.81464	−	0.0177284i
$768$	−14.8726	−	5.89965i	−0.536669	−	0.212885i
$769$	−10.2054	−	38.0871i	−0.368016	−	1.37346i	−0.863285	−	0.504716i	$-0.831597\pi$
$769$	−10.2054	−	38.0871i	−0.368016	−	1.37346i	0.495269	−	0.868740i	$-0.335070\pi$
$770$	2.20091	−	0.479690i	0.0793155	−	0.0172868i
$771$	25.8091	−	14.9009i	0.929494	−	0.536643i
$772$	19.1555	+	23.1626i	0.689420	+	0.833641i
$773$	12.6898	−	47.3590i	0.456421	−	1.70339i	−0.227456	−	0.973788i	$-0.573041\pi$
$773$	12.6898	−	47.3590i	0.456421	−	1.70339i	0.683877	−	0.729597i	$-0.260293\pi$
$774$	−11.5109	+	5.94002i	−0.413749	+	0.213509i
$775$	7.38134	−	7.38134i	0.265146	−	0.265146i
$776$	−2.94711	−	1.25790i	−0.105795	−	0.0451558i
$777$	4.68397	+	2.70429i	0.168036	+	0.0970158i
$778$	−22.5755	+	35.1587i	−0.809372	+	1.26050i
$779$			12.4581i			0.446357i
$780$	2.98983	−	4.29388i	0.107053	−	0.153745i
$781$		−	5.60981i		−	0.200735i
$782$	5.05162	+	3.24366i	0.180646	+	0.115993i
$783$	−5.98829	−	3.45734i	−0.214004	−	0.123555i
$784$	18.1538	−	6.31523i	0.648351	−	0.225544i
$785$	−5.44798	+	5.44798i	−0.194447	+	0.194447i
$786$	0.908616	+	1.76076i	0.0324093	+	0.0628043i
$787$	4.46886	−	16.6780i	0.159298	−	0.594507i	−0.839401	−	0.543512i	$-0.817094\pi$
$787$	4.46886	−	16.6780i	0.159298	−	0.594507i	0.998699	−	0.0509947i	$-0.0162392\pi$
$788$	25.4392	+	30.7608i	0.906232	+	1.09581i
$789$	−2.11644	+	1.22193i	−0.0753474	+	0.0435019i
$790$	−0.709960	−	3.25744i	−0.0252592	−	0.115895i
$791$	1.81859	+	6.78708i	0.0646617	+	0.241321i
$792$	2.51561	+	3.35218i	0.0893883	+	0.119114i
$793$	−36.3442	−	35.6409i	−1.29062	−	1.26565i
$794$	30.3783	−	27.6376i	1.07809	−	0.980823i
$795$	0.0963970	+	0.359758i	0.00341885	+	0.0127593i
$796$	13.0483	−	18.3545i	0.462486	−	0.650557i
$797$	7.88369	+	13.6550i	0.279255	+	0.483683i	0.971200	−	0.238267i	$-0.0765793\pi$
$797$	7.88369	+	13.6550i	0.279255	+	0.483683i	−0.691945	+	0.721950i	$0.743246\pi$
$798$	−0.633670	+	13.4138i	−0.0224317	+	0.474843i
$799$	−1.36445	+	5.09220i	−0.0482708	+	0.180149i
$800$	24.2669	−	7.17748i	0.857965	−	0.253762i
$801$	1.50255	+	1.50255i	0.0530900	+	0.0530900i
$802$	−2.37826	+	7.45000i	−0.0839794	+	0.263069i
$803$	−8.02350	−	4.63237i	−0.283143	−	0.163473i
$804$	−2.42268	−	14.3379i	−0.0854415	−	0.505659i
$805$	−3.63201			−0.128012
$806$	−5.55935	−	10.5197i	−0.195820	−	0.370541i
$807$		−	26.5136i		−	0.933322i
$808$	−19.9970	+	25.4904i	−0.703493	+	0.896748i
$809$	16.1331	−	27.9433i	0.567210	−	0.982436i	−0.429631	−	0.903005i	$-0.641356\pi$
$809$	16.1331	−	27.9433i	0.567210	−	0.982436i	0.996840	−	0.0794311i	$-0.0253104\pi$
$810$	0.312057	−	0.977529i	0.0109645	−	0.0343469i
$811$	−2.82597	+	2.82597i	−0.0992332	+	0.0992332i	−0.754980	−	0.655747i	$-0.772354\pi$
$811$	−2.82597	+	2.82597i	−0.0992332	+	0.0992332i	0.655747	+	0.754980i	$0.272354\pi$
$812$	−7.14461	+	19.2017i	−0.250727	+	0.673849i
$813$	6.42004	+	1.72024i	0.225161	+	0.0603316i
$814$	−7.64194	−	0.361006i	−0.267850	−	0.0126533i
$815$	−7.28319	+	4.20495i	−0.255119	+	0.147293i
$816$	3.80316	+	3.28495i	0.133137	+	0.114996i
$817$	56.7061	−	15.1944i	1.98390	−	0.531583i
$818$	−19.3186	+	17.5757i	−0.675460	+	0.614521i
$819$	4.59960	−	2.71583i	0.160723	−	0.0948989i
$820$	−2.80804	−	0.265898i	−0.0980612	−	0.00928557i
$821$	−25.7200	+	6.89166i	−0.897635	+	0.240521i	−0.678000	−	0.735062i	$-0.737153\pi$
$821$	−25.7200	+	6.89166i	−0.897635	+	0.240521i	−0.219635	+	0.975582i	$0.570487\pi$
$822$	23.1653	−	5.04887i	0.807981	−	0.176100i
$823$	1.80298	+	3.12285i	0.0628478	+	0.108856i	0.895737	−	0.444584i	$-0.146648\pi$
$823$	1.80298	+	3.12285i	0.0628478	+	0.108856i	−0.832889	+	0.553439i	$0.813315\pi$
$824$	−6.96951	−	0.993639i	−0.242794	−	0.0346151i
$825$	−6.40292	−	1.71566i	−0.222921	−	0.0597315i
$826$	−13.3925	−	25.9526i	−0.465984	−	0.903007i
$827$	18.5758	+	18.5758i	0.645943	+	0.645943i	0.952010	−	0.306067i	$-0.0990132\pi$
$827$	18.5758	+	18.5758i	0.645943	+	0.645943i	−0.306067	+	0.952010i	$0.599013\pi$
$828$	−2.81208	−	6.14476i	−0.0977267	−	0.213545i
$829$	−0.283646	+	0.491289i	−0.00985143	+	0.0170632i	−0.870909	−	0.491444i	$-0.836469\pi$
$829$	−0.283646	+	0.491289i	−0.00985143	+	0.0170632i	0.861058	+	0.508507i	$0.169803\pi$
$830$	2.27324	−	3.54031i	0.0789054	−	0.122886i
$831$	−1.75729			−0.0609598
$832$	0.336364	−	28.8424i	0.0116613	−	0.999932i
$833$	−6.03708			−0.209172
$834$	−11.5777	+	18.0309i	−0.400903	+	0.624360i
$835$	−3.26397	+	5.65336i	−0.112954	+	0.195643i
$836$	−7.90446	−	17.2723i	−0.273382	−	0.597373i
$837$	−1.65000	−	1.65000i	−0.0570325	−	0.0570325i
$838$	−18.3423	−	35.5447i	−0.633625	−	1.22787i
$839$	−32.7243	−	8.76844i	−1.12977	−	0.302720i	−0.354937	−	0.934890i	$-0.615498\pi$
$839$	−32.7243	−	8.76844i	−1.12977	−	0.302720i	−0.774830	+	0.632170i	$0.782164\pi$
$840$	−3.00994	−	0.429125i	−0.103853	−	0.0148062i
$841$	9.40638	+	16.2923i	0.324358	+	0.561805i
$842$	−38.4796	+	8.38665i	−1.32610	+	0.289023i
$843$	23.7101	−	6.35310i	0.816619	−	0.218812i
$844$	−2.27696	−	0.215609i	−0.0783764	−	0.00742158i
$845$	9.15713	+	2.26286i	0.315015	+	0.0778446i
$846$	4.38946	−	3.99345i	0.150913	−	0.137298i
$847$	12.5990	−	3.37588i	0.432905	−	0.115997i
$848$	1.55386	+	1.34213i	0.0533597	+	0.0460891i
$849$	−3.46233	+	1.99897i	−0.118827	+	0.0686046i
$850$	−7.93952	−	0.375064i	−0.272323	−	0.0128646i
$851$	11.9151	+	3.19264i	0.408445	+	0.109442i
$852$	−2.64044	+	7.09640i	−0.0904600	+	0.243119i
$853$	−15.4913	+	15.4913i	−0.530411	+	0.530411i	−0.920695	−	0.390283i	$-0.872377\pi$
$853$	−15.4913	+	15.4913i	−0.530411	+	0.530411i	0.390283	+	0.920695i	$0.372377\pi$
$854$	−8.99535	+	28.1783i	−0.307814	+	0.964240i
$855$	−2.32532	+	4.02758i	−0.0795244	+	0.137740i
$856$	17.9123	−	22.8330i	0.612231	−	0.780416i
$857$		−	17.3171i		−	0.591540i	−0.955259	−	0.295770i	$-0.904424\pi$
$857$		−	17.3171i		−	0.591540i	0.955259	−	0.295770i	$-0.0955762\pi$
$858$	−4.02007	+	6.39739i	−0.137243	+	0.218403i
$859$	−22.9629			−0.783484			−0.391742	−	0.920075i	$-0.628127\pi$
$859$	−22.9629			−0.783484			−0.391742	+	0.920075i	$0.628127\pi$
$860$	2.21450	+	13.1058i	0.0755137	+	0.446905i
$861$	−2.49374	−	1.43976i	−0.0849863	−	0.0490669i
$862$	−13.7071	+	42.9381i	−0.466867	+	1.46248i
$863$	18.9344	+	18.9344i	0.644536	+	0.644536i	0.951667	−	0.307131i	$-0.0993691\pi$
$863$	18.9344	+	18.9344i	0.644536	+	0.644536i	−0.307131	+	0.951667i	$0.599369\pi$
$864$	−1.60443	−	5.42455i	−0.0545839	−	0.184547i
$865$	2.61917	−	9.77489i	0.0890546	−	0.332356i
$866$	1.01485	−	21.4827i	0.0344859	−	0.730013i
$867$	7.71078	+	13.3555i	0.261872	+	0.453576i
$868$	−4.00602	+	5.63508i	−0.135973	+	0.191267i
$869$	1.24604	+	4.65029i	0.0422690	+	0.157750i
$870$	−5.24833	+	4.77484i	−0.177935	+	0.161882i
$871$	22.5732	−	13.3284i	0.764865	−	0.451615i
$872$	−17.3118	−	23.0689i	−0.586253	−	0.781212i
$873$	−0.293217	−	1.09430i	−0.00992388	−	0.0370364i
$874$	6.52209	+	29.9247i	0.220613	+	1.01222i
$875$	8.81910	−	5.09171i	0.298140	−	0.172131i
$876$	7.96934	+	9.63646i	0.269259	+	0.325586i
$877$	−11.6288	+	43.3992i	−0.392676	+	1.46549i	0.433027	+	0.901381i	$0.357446\pi$
$877$	−11.6288	+	43.3992i	−0.392676	+	1.46549i	−0.825703	+	0.564106i	$0.809221\pi$
$878$	2.14184	+	4.15057i	0.0722837	+	0.140075i
$879$	−14.8696	+	14.8696i	−0.501540	+	0.501540i
$880$	4.06186	−	1.41301i	0.136925	−	0.0476326i
$881$	2.13057	+	1.23009i	0.0717808	+	0.0414427i	0.535461	−	0.844560i	$-0.320138\pi$
$881$	2.13057	+	1.23009i	0.0717808	+	0.0414427i	−0.463680	+	0.886003i	$0.653471\pi$
$882$	5.71829	+	3.67173i	0.192545	+	0.123634i
$883$		−	39.7470i		−	1.33759i	−0.743446	−	0.668796i	$-0.766810\pi$
$883$		−	39.7470i		−	1.33759i	0.743446	−	0.668796i	$-0.233190\pi$
$884$	−3.07624	+	8.52145i	−0.103465	+	0.286607i
$885$		−	10.1141i		−	0.339980i
$886$	−9.25807	+	14.4184i	−0.311031	+	0.484394i
$887$	−17.1497	−	9.90141i	−0.575832	−	0.332457i	0.183643	−	0.982993i	$-0.441211\pi$
$887$	−17.1497	−	9.90141i	−0.575832	−	0.332457i	−0.759475	+	0.650536i	$0.774544\pi$
$888$	9.49712	+	4.05360i	0.318703	+	0.136030i
$889$	19.7085	−	19.7085i	0.661003	−	0.661003i
$890$	1.93767	−	0.999906i	0.0649508	−	0.0335169i
$891$	−0.383513	+	1.43129i	−0.0128482	+	0.0479500i
$892$	−18.7146	−	22.6295i	−0.626610	−	0.757692i
$893$	−23.2919	+	13.4476i	−0.779435	+	0.450007i
$894$	10.7521	−	2.34342i	0.359603	−	0.0783757i
$895$	1.74256	+	6.50333i	0.0582474	+	0.217382i
$896$	−15.0560	+	7.36526i	−0.502986	+	0.246056i
$897$	8.52978	−	8.69809i	0.284801	−	0.290421i
$898$	−9.05616	−	9.95422i	−0.302208	−	0.332177i
$899$	4.17607	+	15.5853i	0.139280	+	0.519799i
$900$	7.29215	+	5.18405i	0.243072	+	0.172802i
$901$	−0.322450	−	0.558500i	−0.0107424	−	0.0186063i
$902$	4.06855	+	0.192199i	0.135468	+	0.00639953i
$903$	−3.51197	+	13.1069i	−0.116871	+	0.436169i
$904$	5.00059	+	12.4481i	0.166317	+	0.414018i
$905$	10.6650	+	10.6650i	0.354515	+	0.354515i
$906$	13.2620	+	4.23364i	0.440601	+	0.140653i
$907$	−16.4874	−	9.51900i	−0.547455	−	0.316073i	0.200640	−	0.979665i	$-0.435698\pi$
$907$	−16.4874	−	9.51900i	−0.547455	−	0.316073i	−0.748095	+	0.663592i	$0.769031\pi$
$908$	2.98569	+	17.6699i	0.0990838	+	0.586397i
$909$	−11.4545			−0.379921
$910$	−1.21947	−	5.34373i	−0.0404250	−	0.177143i
$911$		−	1.28948i		−	0.0427225i	−0.999772	−	0.0213612i	$-0.993200\pi$
$911$		−	1.28948i		−	0.0427225i	0.999772	−	0.0213612i	$-0.00680001\pi$
$912$	1.86939	+	25.5699i	0.0619017	+	0.846703i
$913$	−3.03778	+	5.26159i	−0.100536	+	0.174133i
$914$	−16.3355	−	5.21477i	−0.540329	−	0.172489i
$915$	−7.24351	+	7.24351i	−0.239463	+	0.239463i
$916$	−4.33830	−	1.61420i	−0.143342	−	0.0533347i
$917$	2.00489	+	0.537210i	0.0662074	+	0.0177402i
$918$	−0.0838407	+	1.77478i	−0.00276716	+	0.0585764i
$919$	−23.2515	+	13.4243i	−0.766997	+	0.442826i	−0.831802	−	0.555072i	$-0.812691\pi$
$919$	−23.2515	+	13.4243i	−0.766997	+	0.442826i	0.0648055	+	0.997898i	$0.479357\pi$
$920$	−6.88421	+	0.831380i	−0.226966	+	0.0274098i
$921$	−2.36638	+	0.634071i	−0.0779750	+	0.0208933i
$922$	−23.0281	−	25.3116i	−0.758389	−	0.833595i
$923$	−13.6494	+	0.133350i	−0.449277	+	0.00438926i
$924$	4.37089	+	0.413887i	0.143792	+	0.0136159i
$925$	−15.7755	+	4.22703i	−0.518695	+	0.138984i
$926$	5.43227	+	24.9244i	0.178516	+	0.819066i
$927$	−1.24450	−	2.15555i	−0.0408749	−	0.0707974i
$928$	−9.14672	+	38.0309i	−0.300256	+	1.24842i
$929$	37.8024	+	10.1291i	1.24026	+	0.332326i	0.818566	−	0.574413i	$-0.194770\pi$
$929$	37.8024	+	10.1291i	1.24026	+	0.332326i	0.421692	+	0.906739i	$0.361436\pi$
$930$	−2.12782	+	1.09803i	−0.0697740	+	0.0360059i
$931$	−21.7784	−	21.7784i	−0.713757	−	0.713757i
$932$	−27.6874	+	12.6708i	−0.906931	+	0.415047i
$933$	1.14030	−	1.97506i	0.0373318	−	0.0646606i
$934$	21.6091	+	13.8753i	0.707073	+	0.454014i
$935$	−1.35078			−0.0441752
$936$	8.09652	−	6.20052i	0.264643	−	0.202670i
$937$	46.1571			1.50789			0.753943	−	0.656939i	$-0.228149\pi$
$937$	46.1571			1.50789			0.753943	+	0.656939i	$0.228149\pi$
$938$	−12.8179	−	8.23039i	−0.418518	−	0.268732i
$939$	16.1283	−	27.9350i	0.526326	−	0.911623i
$940$	−2.53395	−	5.53700i	−0.0826484	−	0.180597i
$941$	−35.7367	−	35.7367i	−1.16498	−	1.16498i	−0.983370	−	0.181611i	$-0.941869\pi$
$941$	−35.7367	−	35.7367i	−1.16498	−	1.16498i	−0.181611	−	0.983370i	$-0.558131\pi$
$942$	−13.3448	+	6.88639i	−0.434797	+	0.224371i
$943$	−6.34359	−	1.69976i	−0.206576	−	0.0553518i
$944$	−31.3250	−	46.1256i	−1.01954	−	1.50126i
$945$	−0.537467	−	0.930920i	−0.0174838	−	0.0302828i
$946$	−4.08732	−	18.7535i	−0.132890	−	0.609728i
$947$	0.723796	−	0.193941i	0.0235202	−	0.00630222i	−0.247040	−	0.969005i	$-0.579458\pi$
$947$	0.723796	−	0.193941i	0.0235202	−	0.00630222i	0.270560	+	0.962703i	$0.412791\pi$
$948$	0.612569	−	6.46909i	0.0198953	−	0.210106i
$949$	−11.0805	+	19.6324i	−0.359687	+	0.637295i
$950$	−27.2883	−	29.9943i	−0.885348	−	0.973143i
$951$	24.5585	−	6.58043i	0.796364	−	0.213385i
$952$	5.22647	−	0.631181i	0.169391	−	0.0204567i
$953$	−41.5062	+	23.9636i	−1.34452	+	0.776257i	−0.987467	−	0.157828i	$-0.949551\pi$
$953$	−41.5062	+	23.9636i	−1.34452	+	0.776257i	−0.357050	+	0.934085i	$0.616217\pi$
$954$	−0.0342549	+	0.725122i	−0.00110904	+	0.0234767i
$955$	−18.2591	−	4.89251i	−0.590851	−	0.158318i
$956$	19.8511	−	53.3514i	0.642030	−	1.72551i
$957$	7.24504	−	7.24504i	0.234199	−	0.234199i
$958$	−22.0837	−	7.04978i	−0.713491	−	0.227768i
$959$	12.4184	−	21.5092i	0.401010	−	0.694569i
$960$	−5.80333	−	0.124390i	−0.187302	−	0.00401466i
$961$		−	25.5550i		−	0.824354i
$962$	−0.696723	+	18.6025i	−0.0224633	+	0.599768i
$963$	10.2604			0.330635
$964$	−7.37591	+	1.24631i	−0.237562	+	0.0401409i
$965$	9.44359	+	5.45226i	0.304000	+	0.175514i
$966$	−6.74377	−	2.15281i	−0.216977	−	0.0692657i
$967$	−8.44481	−	8.44481i	−0.271567	−	0.271567i	0.558164	−	0.829731i	$-0.311506\pi$
$967$	−8.44481	−	8.44481i	−0.271567	−	0.271567i	−0.829731	+	0.558164i	$0.811506\pi$
$968$	23.1076	−	9.28266i	0.742706	−	0.298356i
$969$	2.08418	−	7.77826i	0.0669535	−	0.249874i
$970$	−1.16121	−	0.0548557i	−0.0372842	−	0.00176131i
$971$	24.1539	+	41.8358i	0.775136	+	1.34257i	0.934718	+	0.355390i	$0.115652\pi$
$971$	24.1539	+	41.8358i	0.775136	+	1.34257i	−0.159582	+	0.987185i	$0.551015\pi$
$972$	1.15883	−	1.63007i	0.0371694	−	0.0522844i
$973$	5.80974	+	21.6822i	0.186252	+	0.695101i
$974$	−34.3409	−	37.7463i	−1.10035	−	1.20947i
$975$	−4.02223	+	15.6200i	−0.128814	+	0.500240i
$976$	−10.5999	+	55.4688i	−0.339295	+	1.77551i
$977$	8.21436	+	30.6564i	0.262801	+	0.980786i	0.963583	+	0.267410i	$0.0861679\pi$
$977$	8.21436	+	30.6564i	0.262801	+	0.980786i	−0.700782	+	0.713376i	$0.747165\pi$
$978$	−16.0155	+	3.49059i	−0.512120	+	0.111617i
$979$	−2.72683	+	1.57434i	−0.0871500	+	0.0503161i
$980$	5.37365	−	4.44400i	0.171655	−	0.141958i
$981$	2.63925	−	9.84980i	0.0842647	−	0.314480i
$982$	−18.8428	+	9.72354i	−0.601297	+	0.310291i
$983$	−18.1345	+	18.1345i	−0.578400	+	0.578400i	−0.934462	−	0.356062i	$-0.884119\pi$
$983$	−18.1345	+	18.1345i	−0.578400	+	0.578400i	0.356062	+	0.934462i	$0.384119\pi$
$984$	−5.05625	−	2.15813i	−0.161187	−	0.0687986i
$985$	12.5414	+	7.24080i	0.399603	+	0.230711i
$986$	6.63807	−	10.3380i	0.211399	−	0.329229i
$987$		−	6.21646i		−	0.197872i
$988$	−41.8379	+	19.6432i	−1.33104	+	0.624935i
$989$			30.9475i			0.984074i
$990$	1.27945	+	0.821539i	0.0406636	+	0.0261102i
$991$	−15.3411	−	8.85718i	−0.487326	−	0.281358i	0.236139	−	0.971719i	$-0.424118\pi$
$991$	−15.3411	−	8.85718i	−0.487326	−	0.281358i	−0.723464	+	0.690362i	$0.757451\pi$
$992$	−6.30322	+	11.5979i	−0.200127	+	0.368232i
$993$	20.5695	−	20.5695i	0.652753	−	0.652753i
$994$	3.63736	+	7.04866i	0.115370	+	0.223570i
$995$	2.11456	−	7.89164i	0.0670360	−	0.250182i
$996$	6.31932	−	5.22607i	0.200235	−	0.165594i
$997$	−4.27051	+	2.46558i	−0.135249	+	0.0780858i	−0.566098	−	0.824338i	$-0.691547\pi$
$997$	−4.27051	+	2.46558i	−0.135249	+	0.0780858i	0.430849	+	0.902424i	$0.358214\pi$
$998$	12.9967	+	59.6315i	0.411403	+	1.88760i
$999$	0.944898	+	3.52641i	0.0298952	+	0.111571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.d.19.10	yes	56
3.2	odd	2		936.2.ed.e.19.5		56
8.3	odd	2	inner	312.2.bt.d.19.3	✓	56
13.11	odd	12	inner	312.2.bt.d.115.3	yes	56
24.11	even	2		936.2.ed.e.19.12		56
39.11	even	12		936.2.ed.e.739.12		56
104.11	even	12	inner	312.2.bt.d.115.10	yes	56
312.11	odd	12		936.2.ed.e.739.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.3	✓	56	8.3	odd	2	inner
312.2.bt.d.19.10	yes	56	1.1	even	1	trivial
312.2.bt.d.115.3	yes	56	13.11	odd	12	inner
312.2.bt.d.115.10	yes	56	104.11	even	12	inner
936.2.ed.e.19.5		56	3.2	odd	2
936.2.ed.e.19.12		56	24.11	even	2
936.2.ed.e.739.5		56	312.11	odd	12
936.2.ed.e.739.12		56	39.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764112 - 1.19001i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.832266 - 1.81861i) q^{4} +(-0.513065 - 0.513065i) q^{5} +(-0.648526 - 1.25675i) q^{6} +(-1.43100 - 0.383434i) q^{7} +(-2.80011 - 0.399211i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00259 + 0.218515i) q^{10} +(1.43129 - 0.383513i) q^{11} +(-1.99109 - 0.188540i) q^{12} +(-0.967164 - 3.47341i) q^{13} +(-1.54973 + 1.40992i) q^{14} +(-0.700859 + 0.187795i) q^{15} +(-2.61467 + 3.02713i) q^{16} +(1.08804 - 0.628178i) q^{17} +(-1.41264 - 0.0667332i) q^{18} +(6.19113 + 1.65891i) q^{19} +(-0.506057 + 1.36007i) q^{20} +(-1.04756 + 1.04756i) q^{21} +(0.637280 - 1.99630i) q^{22} +(-1.68941 + 2.92615i) q^{23} +(-1.74578 + 2.22536i) q^{24} -4.47353i q^{25} +(-4.87243 - 1.50314i) q^{26} -1.00000 q^{27} +(0.493654 + 2.92154i) q^{28} +(5.98829 + 3.45734i) q^{29} +(-0.312057 + 0.977529i) q^{30} +(1.65000 + 1.65000i) q^{31} +(1.60443 + 5.42455i) q^{32} +(0.383513 - 1.43129i) q^{33} +(0.0838407 - 1.77478i) q^{34} +(0.537467 + 0.930920i) q^{35} +(-1.15883 + 1.63007i) q^{36} +(-0.944898 - 3.52641i) q^{37} +(6.70484 - 6.09994i) q^{38} +(-3.49165 - 0.899118i) q^{39} +(1.23182 + 1.64146i) q^{40} +(0.503062 + 1.87745i) q^{41} +(0.446159 + 2.04707i) q^{42} +(7.93214 - 4.57963i) q^{43} +(-1.88867 - 2.28377i) q^{44} +(-0.187795 + 0.700859i) q^{45} +(2.19126 + 4.24633i) q^{46} +(-2.96711 + 2.96711i) q^{47} +(1.31424 + 3.77793i) q^{48} +(-4.16145 - 2.40261i) q^{49} +(-5.32356 - 3.41828i) q^{50} -1.25636i q^{51} +(-5.51184 + 4.64970i) q^{52} -0.513310i q^{53} +(-0.764112 + 1.19001i) q^{54} +(-0.931112 - 0.537578i) q^{55} +(3.85388 + 1.64493i) q^{56} +(4.53222 - 4.53222i) q^{57} +(8.69000 - 4.48435i) q^{58} +(-3.60773 + 13.4642i) q^{59} +(0.924827 + 1.11829i) q^{60} +(12.2267 - 7.05906i) q^{61} +(3.22431 - 0.702740i) q^{62} +(0.383434 + 1.43100i) q^{63} +(7.68126 + 2.23567i) q^{64} +(-1.28587 + 2.27830i) q^{65} +(-1.41021 - 1.55005i) q^{66} +(1.88176 + 7.02284i) q^{67} +(-2.04795 - 1.45590i) q^{68} +(1.68941 + 2.92615i) q^{69} +(1.51849 + 0.0717338i) q^{70} +(0.979852 - 3.65686i) q^{71} +(1.05433 + 2.62457i) q^{72} +(-4.42114 - 4.42114i) q^{73} +(-4.91848 - 1.57013i) q^{74} +(-3.87419 - 2.23676i) q^{75} +(-2.13577 - 12.6399i) q^{76} -2.19522 q^{77} +(-3.73797 + 3.46808i) q^{78} +3.24902i q^{79} +(2.89461 - 0.211622i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.61859 + 0.835933i) q^{82} +(-2.89926 + 2.89926i) q^{83} +(2.77695 + 1.03325i) q^{84} +(-0.880529 - 0.235937i) q^{85} +(0.611226 - 12.9387i) q^{86} +(5.98829 - 3.45734i) q^{87} +(-4.16088 + 0.502494i) q^{88} +(-2.05252 + 0.549972i) q^{89} +(0.690536 + 0.759013i) q^{90} +(0.0521823 + 5.34128i) q^{91} +(6.72756 + 0.637043i) q^{92} +(2.25395 - 0.603943i) q^{93} +(1.26370 + 5.79811i) q^{94} +(-2.32532 - 4.02758i) q^{95} +(5.50002 + 1.32280i) q^{96} +(1.09430 + 0.293217i) q^{97} +(-6.03896 + 3.11632i) q^{98} +(-1.04778 - 1.04778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) \) 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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