LMFDB - Embedded newform 234.2.t.a.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(25,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("234.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.2
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.987257 - 1.42314i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.56656 + 0.738845i) q^{6} +(-1.90832 + 1.10177i) q^{7} +1.00000i q^{8} +(-1.05065 + 2.81001i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.987257 - 1.42314i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.56656 + 0.738845i) q^{6} +(-1.90832 + 1.10177i) q^{7} +1.00000i q^{8} +(-1.05065 + 2.81001i) q^{9} -2.93284 q^{10} +(4.47678 - 2.58467i) q^{11} +(-1.72610 + 0.143421i) q^{12} +(2.72585 - 2.36003i) q^{13} +(1.10177 - 1.90832i) q^{14} +(-0.420631 - 5.06239i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.31124 q^{17} +(-0.495118 - 2.95886i) q^{18} +5.16934i q^{19} +(2.53992 - 1.46642i) q^{20} +(3.45197 + 1.62807i) q^{21} +(-2.58467 + 4.47678i) q^{22} +(4.19626 - 7.26814i) q^{23} +(1.42314 - 0.987257i) q^{24} +(1.80079 + 3.11906i) q^{25} +(-1.18064 + 3.40677i) q^{26} +(5.03629 - 1.27899i) q^{27} +2.20354i q^{28} +(4.72655 + 8.18662i) q^{29} +(2.89547 + 4.17384i) q^{30} +(-5.38944 - 3.11159i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-8.09808 - 3.81934i) q^{33} +(-2.00159 + 1.15562i) q^{34} -6.46263 q^{35} +(1.90822 + 2.31489i) q^{36} -0.646136i q^{37} +(-2.58467 - 4.47678i) q^{38} +(-6.04977 - 1.54930i) q^{39} +(-1.46642 + 2.53992i) q^{40} +(-0.674934 - 0.389673i) q^{41} +(-3.80353 + 0.316033i) q^{42} +(-1.74579 - 3.02379i) q^{43} -5.16934i q^{44} +(-6.78921 + 5.59650i) q^{45} +8.39252i q^{46} +(-4.79295 + 2.76721i) q^{47} +(-0.738845 + 1.56656i) q^{48} +(-1.07221 + 1.85713i) q^{49} +(-3.11906 - 1.80079i) q^{50} +(-2.28179 - 3.28921i) q^{51} +(-0.680923 - 3.54067i) q^{52} -8.68475 q^{53} +(-3.72206 + 3.62578i) q^{54} +15.1609 q^{55} +(-1.10177 - 1.90832i) q^{56} +(7.35669 - 5.10347i) q^{57} +(-8.18662 - 4.72655i) q^{58} +(2.59002 + 1.49535i) q^{59} +(-4.59448 - 2.16692i) q^{60} +(0.432428 + 0.748988i) q^{61} +6.22318 q^{62} +(-1.09101 - 6.51996i) q^{63} -1.00000 q^{64} +(10.3842 - 1.99704i) q^{65} +(8.92281 - 0.741391i) q^{66} +(-9.68023 - 5.58888i) q^{67} +(1.15562 - 2.00159i) q^{68} +(-14.4864 + 1.20366i) q^{69} +(5.59680 - 3.23131i) q^{70} +12.9489i q^{71} +(-2.81001 - 1.05065i) q^{72} -4.27533i q^{73} +(0.323068 + 0.559571i) q^{74} +(2.66101 - 5.64209i) q^{75} +(4.47678 + 2.58467i) q^{76} +(-5.69541 + 9.86475i) q^{77} +(6.01390 - 1.68315i) q^{78} +(1.52175 + 2.63575i) q^{79} -2.93284i q^{80} +(-6.79229 - 5.90464i) q^{81} +0.779346 q^{82} +(-3.19308 + 1.84352i) q^{83} +(3.13594 - 2.17546i) q^{84} +(5.87036 + 3.38925i) q^{85} +(3.02379 + 1.74579i) q^{86} +(6.98438 - 14.8088i) q^{87} +(2.58467 + 4.47678i) q^{88} -3.34650i q^{89} +(3.08138 - 8.24132i) q^{90} +(-2.60158 + 7.50694i) q^{91} +(-4.19626 - 7.26814i) q^{92} +(0.892535 + 10.7419i) q^{93} +(2.76721 - 4.79295i) q^{94} +(-7.58044 + 13.1297i) q^{95} +(-0.143421 - 1.72610i) q^{96} +(-1.29119 + 0.745470i) q^{97} -2.14443i q^{98} +(2.55943 + 15.2954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 - 16 * q^9	$ 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.987257	−	1.42314i	−0.569993	−	0.821649i
$3$	−0.987257	−	1.42314i	−0.569993	−	0.821649i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.53992	+	1.46642i	1.13589	+	0.655804i	0.945409	−	0.325888i	$-0.105663\pi$
$5$	2.53992	+	1.46642i	1.13589	+	0.655804i	0.190477	+	0.981692i	$0.438996\pi$
$6$	1.56656	+	0.738845i	0.639545	+	0.301632i
$7$	−1.90832	+	1.10177i	−0.721276	+	0.416429i	−0.815222	−	0.579148i	$-0.803385\pi$
$7$	−1.90832	+	1.10177i	−0.721276	+	0.416429i	0.0939459	+	0.995577i	$0.470052\pi$
$8$			1.00000i			0.353553i
$9$	−1.05065	+	2.81001i	−0.350215	+	0.936669i
$10$	−2.93284			−0.927447
$11$	4.47678	−	2.58467i	1.34980	−	0.779307i	0.361579	−	0.932341i	$-0.382238\pi$
$11$	4.47678	−	2.58467i	1.34980	−	0.779307i	0.988221	+	0.153034i	$0.0489044\pi$
$12$	−1.72610	+	0.143421i	−0.498283	+	0.0414020i
$13$	2.72585	−	2.36003i	0.756014	−	0.654555i
$13$	2.72585	−	2.36003i	0.756014	−	0.654555i
$14$	1.10177	−	1.90832i	0.294460	−	0.510019i
$15$	−0.420631	−	5.06239i	−0.108606	−	1.30710i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.31124			0.560558			0.280279	−	0.959919i	$-0.409573\pi$
$17$	2.31124			0.560558			0.280279	+	0.959919i	$0.409573\pi$
$18$	−0.495118	−	2.95886i	−0.116701	−	0.697410i
$19$			5.16934i			1.18593i	0.805229	+	0.592964i	$0.202042\pi$
$19$			5.16934i			1.18593i	−0.805229	+	0.592964i	$0.797958\pi$
$20$	2.53992	−	1.46642i	0.567943	−	0.327902i
$21$	3.45197	+	1.62807i	0.753281	+	0.355274i
$22$	−2.58467	+	4.47678i	−0.551054	+	0.954453i
$23$	4.19626	−	7.26814i	0.874981	−	1.51551i	0.0181984	−	0.999834i	$-0.494207\pi$
$23$	4.19626	−	7.26814i	0.874981	−	1.51551i	0.856783	−	0.515677i	$-0.172460\pi$
$24$	1.42314	−	0.987257i	0.290497	−	0.201523i
$25$	1.80079	+	3.11906i	0.360158	+	0.623812i
$26$	−1.18064	+	3.40677i	−0.231542	+	0.668123i
$27$	5.03629	−	1.27899i	0.969234	−	0.246141i
$28$			2.20354i			0.416429i
$29$	4.72655	+	8.18662i	0.877698	+	1.52022i	0.853860	+	0.520502i	$0.174255\pi$
$29$	4.72655	+	8.18662i	0.877698	+	1.52022i	0.0238379	+	0.999716i	$0.492411\pi$
$30$	2.89547	+	4.17384i	0.528639	+	0.762036i
$31$	−5.38944	−	3.11159i	−0.967971	−	0.558858i	−0.0693541	−	0.997592i	$-0.522094\pi$
$31$	−5.38944	−	3.11159i	−0.967971	−	0.558858i	−0.898617	+	0.438734i	$0.855427\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−8.09808	−	3.81934i	−1.40969	−	0.664862i
$34$	−2.00159	+	1.15562i	−0.343270	+	0.198187i
$35$	−6.46263			−1.09238
$36$	1.90822	+	2.31489i	0.318036	+	0.385815i
$37$		−	0.646136i		−	0.106224i	−0.998589	−	0.0531121i	$-0.983086\pi$
$37$		−	0.646136i		−	0.106224i	0.998589	−	0.0531121i	$-0.0169141\pi$
$38$	−2.58467	−	4.47678i	−0.419289	−	0.726230i
$39$	−6.04977	−	1.54930i	−0.968738	−	0.248087i
$40$	−1.46642	+	2.53992i	−0.231862	+	0.401596i
$41$	−0.674934	−	0.389673i	−0.105407	−	0.0608567i	0.446370	−	0.894849i	$-0.352717\pi$
$41$	−0.674934	−	0.389673i	−0.105407	−	0.0608567i	−0.551777	+	0.833992i	$0.686050\pi$
$42$	−3.80353	+	0.316033i	−0.586897	+	0.0487650i
$43$	−1.74579	−	3.02379i	−0.266230	−	0.461124i	0.701655	−	0.712517i	$-0.252445\pi$
$43$	−1.74579	−	3.02379i	−0.266230	−	0.461124i	−0.967885	+	0.251393i	$0.919111\pi$
$44$		−	5.16934i		−	0.779307i
$45$	−6.78921	+	5.59650i	−1.01208	+	0.834277i
$46$			8.39252i			1.23741i
$47$	−4.79295	+	2.76721i	−0.699124	+	0.403639i	−0.807021	−	0.590523i	$-0.798922\pi$
$47$	−4.79295	+	2.76721i	−0.699124	+	0.403639i	0.107897	+	0.994162i	$0.465588\pi$
$48$	−0.738845	+	1.56656i	−0.106643	+	0.226113i
$49$	−1.07221	+	1.85713i	−0.153174	+	0.265304i
$50$	−3.11906	−	1.80079i	−0.441102	−	0.254670i
$51$	−2.28179	−	3.28921i	−0.319514	−	0.460582i
$52$	−0.680923	−	3.54067i	−0.0944270	−	0.491003i
$53$	−8.68475			−1.19294			−0.596471	−	0.802635i	$-0.703431\pi$
$53$	−8.68475			−1.19294			−0.596471	+	0.802635i	$0.703431\pi$
$54$	−3.72206	+	3.62578i	−0.506508	+	0.493406i
$55$	15.1609			2.04429
$56$	−1.10177	−	1.90832i	−0.147230	−	0.255010i
$57$	7.35669	−	5.10347i	0.974417	−	0.675971i
$58$	−8.18662	−	4.72655i	−1.07496	−	0.620626i
$59$	2.59002	+	1.49535i	0.337192	+	0.194678i	0.659030	−	0.752117i	$-0.270967\pi$
$59$	2.59002	+	1.49535i	0.337192	+	0.194678i	−0.321838	+	0.946795i	$0.604300\pi$
$60$	−4.59448	−	2.16692i	−0.593144	−	0.279748i
$61$	0.432428	+	0.748988i	0.0553668	+	0.0958981i	0.892380	−	0.451284i	$-0.149034\pi$
$61$	0.432428	+	0.748988i	0.0553668	+	0.0958981i	−0.837014	+	0.547182i	$0.815701\pi$
$62$	6.22318			0.790345
$63$	−1.09101	−	6.51996i	−0.137454	−	0.821437i
$64$	−1.00000			−0.125000
$65$	10.3842	−	1.99704i	1.28801	−	0.247703i
$66$	8.92281	−	0.741391i	1.09832	−	0.0912590i
$67$	−9.68023	−	5.58888i	−1.18263	−	0.682791i	−0.226007	−	0.974126i	$-0.572567\pi$
$67$	−9.68023	−	5.58888i	−1.18263	−	0.682791i	−0.956621	+	0.291335i	$0.905901\pi$
$68$	1.15562	−	2.00159i	0.140139	−	0.242729i
$69$	−14.4864	+	1.20366i	−1.74395	+	0.144904i
$70$	5.59680	−	3.23131i	0.668946	−	0.386216i
$71$			12.9489i			1.53675i	0.639998	+	0.768376i	$0.278935\pi$
$71$			12.9489i			1.53675i	−0.639998	+	0.768376i	$0.721065\pi$
$72$	−2.81001	−	1.05065i	−0.331163	−	0.123820i
$73$		−	4.27533i		−	0.500390i	−0.968196	−	0.250195i	$-0.919505\pi$
$73$		−	4.27533i		−	0.500390i	0.968196	−	0.250195i	$-0.0804947\pi$
$74$	0.323068	+	0.559571i	0.0375559	+	0.0650488i
$75$	2.66101	−	5.64209i	0.307267	−	0.651492i
$76$	4.47678	+	2.58467i	0.513522	+	0.296482i
$77$	−5.69541	+	9.86475i	−0.649053	+	1.12419i
$78$	6.01390	−	1.68315i	0.680940	−	0.190579i
$79$	1.52175	+	2.63575i	0.171210	+	0.296545i	0.938843	−	0.344345i	$-0.111899\pi$
$79$	1.52175	+	2.63575i	0.171210	+	0.296545i	−0.767633	+	0.640890i	$0.778566\pi$
$80$		−	2.93284i		−	0.327902i
$81$	−6.79229	−	5.90464i	−0.754699	−	0.656072i
$82$	0.779346			0.0860644
$83$	−3.19308	+	1.84352i	−0.350486	+	0.202353i	−0.664899	−	0.746933i	$-0.731526\pi$
$83$	−3.19308	+	1.84352i	−0.350486	+	0.202353i	0.314413	+	0.949286i	$0.398192\pi$
$84$	3.13594	−	2.17546i	0.342159	−	0.237362i
$85$	5.87036	+	3.38925i	0.636730	+	0.367616i
$86$	3.02379	+	1.74579i	0.326064	+	0.188253i
$87$	6.98438	−	14.8088i	0.748804	−	1.58767i
$88$	2.58467	+	4.47678i	0.275527	+	0.477226i
$89$		−	3.34650i		−	0.354728i	−0.984145	−	0.177364i	$-0.943243\pi$
$89$		−	3.34650i		−	0.354728i	0.984145	−	0.177364i	$-0.0567570\pi$
$90$	3.08138	−	8.24132i	0.324806	−	0.868711i
$91$	−2.60158	+	7.50694i	−0.272720	+	0.786942i
$92$	−4.19626	−	7.26814i	−0.437491	−	0.757756i
$93$	0.892535	+	10.7419i	0.0925515	+	1.11388i
$94$	2.76721	−	4.79295i	0.285416	−	0.494355i
$95$	−7.58044	+	13.1297i	−0.777736	+	1.34708i
$96$	−0.143421	−	1.72610i	−0.0146378	−	0.176170i
$97$	−1.29119	+	0.745470i	−0.131101	+	0.0756910i	−0.564116	−	0.825696i	$-0.690783\pi$
$97$	−1.29119	+	0.745470i	−0.131101	+	0.0756910i	0.433015	+	0.901387i	$0.357450\pi$
$98$		−	2.14443i		−	0.216620i
$99$	2.55943	+	15.2954i	0.257233	+	1.53724i
$100$	3.60158			0.360158
$101$	−0.203346	−	0.352206i	−0.0202337	−	0.0350458i	0.855731	−	0.517421i	$-0.173108\pi$
$101$	−0.203346	−	0.352206i	−0.0202337	−	0.0350458i	−0.875965	+	0.482375i	$0.839774\pi$
$102$	3.62069	+	1.70765i	0.358502	+	0.169082i
$103$	−8.58044	+	14.8618i	−0.845456	+	1.46437i	0.0397695	+	0.999209i	$0.487338\pi$
$103$	−8.58044	+	14.8618i	−0.845456	+	1.46437i	−0.885225	+	0.465163i	$0.845996\pi$
$104$	2.36003	+	2.72585i	0.231420	+	0.267291i
$105$	6.38028	+	9.19721i	0.622651	+	0.897556i
$106$	7.52122	−	4.34238i	0.730525	−	0.421769i
$107$	−0.329555			−0.0318592			−0.0159296	−	0.999873i	$-0.505071\pi$
$107$	−0.329555			−0.0318592			−0.0159296	+	0.999873i	$0.505071\pi$
$108$	1.41051	−	5.00105i	0.135726	−	0.481226i
$109$		−	9.64927i		−	0.924232i	−0.886819	−	0.462116i	$-0.847090\pi$
$109$		−	9.64927i		−	0.924232i	0.886819	−	0.462116i	$-0.152910\pi$
$110$	−13.1297	+	7.58044i	−1.25187	+	0.722766i
$111$	−0.919542	+	0.637903i	−0.0872790	+	0.0605471i
$112$	1.90832	+	1.10177i	0.180319	+	0.104107i
$113$	1.51605	−	2.62588i	0.142618	−	0.247022i	−0.785864	−	0.618400i	$-0.787781\pi$
$113$	1.51605	−	2.62588i	0.142618	−	0.247022i	0.928482	+	0.371378i	$0.121115\pi$
$114$	−3.81934	+	8.09808i	−0.357714	+	0.758454i
$115$	21.3163	−	12.3070i	1.98776	−	1.14763i
$116$	9.45310			0.877698
$117$	3.76781	+	10.1392i	0.348334	+	0.937371i
$118$	−2.99070			−0.275316
$119$	−4.41058	+	2.54645i	−0.404317	+	0.233433i
$120$	5.06239	−	0.420631i	0.462131	−	0.0383982i
$121$	7.86104	−	13.6157i	0.714640	−	1.23779i
$122$	−0.748988	−	0.432428i	−0.0678102	−	0.0391502i
$123$	0.111775	+	1.34523i	0.0100784	+	0.121295i
$124$	−5.38944	+	3.11159i	−0.483986	+	0.279429i
$125$		−	4.10135i		−	0.366836i
$126$	4.20482	+	5.10094i	0.374595	+	0.454428i
$127$	−9.03355			−0.801598			−0.400799	−	0.916166i	$-0.631267\pi$
$127$	−9.03355			−0.801598			−0.400799	+	0.916166i	$0.631267\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.57974	+	5.46976i	−0.227133	+	0.481586i
$130$	−7.99449	+	6.92161i	−0.701163	+	0.607065i
$131$	8.70860	−	15.0837i	0.760874	−	1.31787i	−0.181527	−	0.983386i	$-0.558104\pi$
$131$	8.70860	−	15.0837i	0.760874	−	1.31787i	0.942401	−	0.334486i	$-0.108563\pi$
$132$	−7.35669	+	5.10347i	−0.640317	+	0.444200i
$133$	−5.69541	−	9.86475i	−0.493855	−	0.855382i
$134$	11.1778			0.965612
$135$	14.6673	+	4.13680i	1.26236	+	0.356039i
$136$			2.31124i			0.198187i
$137$	4.20543	−	2.42800i	0.359294	−	0.207438i	−0.309477	−	0.950907i	$-0.600154\pi$
$137$	4.20543	−	2.42800i	0.359294	−	0.207438i	0.668771	+	0.743468i	$0.266821\pi$
$138$	11.9437	−	8.28558i	1.01672	−	0.705316i
$139$	5.82263	−	10.0851i	0.493869	−	0.855406i	−0.506106	−	0.862471i	$-0.668916\pi$
$139$	5.82263	−	10.0851i	0.493869	−	0.855406i	0.999975	+	0.00706513i	$0.00224892\pi$
$140$	−3.23131	+	5.59680i	−0.273096	+	0.473016i
$141$	8.67000	+	4.08908i	0.730146	+	0.344363i
$142$	−6.47445	−	11.2141i	−0.543324	−	0.941065i
$143$	6.10312	−	17.6108i	0.510369	−	1.47269i
$144$	2.95886	−	0.495118i	0.246572	−	0.0412599i
$145$			27.7245i			2.30239i
$146$	2.13767	+	3.70254i	0.176914	+	0.306425i
$147$	3.70151	−	0.307556i	0.305295	−	0.0253668i
$148$	−0.559571	−	0.323068i	−0.0459964	−	0.0265560i
$149$	−18.8841	−	10.9027i	−1.54704	−	0.893186i	−0.998365	−	0.0571529i	$-0.981798\pi$
$149$	−18.8841	−	10.9027i	−1.54704	−	0.893186i	−0.548679	−	0.836033i	$-0.684869\pi$
$150$	0.516542	+	6.21669i	0.0421754	+	0.507591i
$151$	12.6987	−	7.33161i	1.03341	−	0.596638i	0.115448	−	0.993313i	$-0.463170\pi$
$151$	12.6987	−	7.33161i	1.03341	−	0.596638i	0.917959	+	0.396676i	$0.129836\pi$
$152$	−5.16934			−0.419289
$153$	−2.42829	+	6.49460i	−0.196316	+	0.525057i
$154$		−	11.3908i		−	0.917899i
$155$	−9.12582	−	15.8064i	−0.733003	−	1.26960i
$156$	−4.36662	+	4.46460i	−0.349609	+	0.357454i
$157$	−3.97434	+	6.88376i	−0.317187	+	0.549384i	−0.979900	−	0.199489i	$-0.936072\pi$
$157$	−3.97434	+	6.88376i	−0.317187	+	0.549384i	0.662713	+	0.748874i	$0.269405\pi$
$158$	−2.63575	−	1.52175i	−0.209689	−	0.121064i
$159$	8.57409	+	12.3596i	0.679969	+	0.980180i
$160$	1.46642	+	2.53992i	0.115931	+	0.200798i
$161$			18.4932i			1.45747i
$162$	8.83462	+	1.71743i	0.694113	+	0.134934i
$163$			0.222533i			0.0174302i	0.999962	+	0.00871508i	$0.00277413\pi$
$163$			0.222533i			0.0174302i	−0.999962	+	0.00871508i	$0.997226\pi$
$164$	−0.674934	+	0.389673i	−0.0527035	+	0.0304284i
$165$	−14.9677	−	21.5760i	−1.16523	−	1.67969i
$166$	1.84352	−	3.19308i	0.143085	−	0.247831i
$167$	3.26552	+	1.88535i	0.252693	+	0.145893i	0.620997	−	0.783813i	$-0.286728\pi$
$167$	3.26552	+	1.88535i	0.252693	+	0.145893i	−0.368303	+	0.929706i	$0.620061\pi$
$168$	−1.62807	+	3.45197i	−0.125608	+	0.266325i
$169$	1.86050	−	12.8662i	0.143115	−	0.989706i
$170$	−6.77851			−0.519888
$171$	−14.5259	−	5.43114i	−1.11082	−	0.415330i
$172$	−3.49158			−0.266230
$173$	5.42672	+	9.39936i	0.412586	+	0.714620i	0.995172	−	0.0981495i	$-0.0312923\pi$
$173$	5.42672	+	9.39936i	0.412586	+	0.714620i	−0.582586	+	0.812769i	$0.697959\pi$
$174$	1.35577	+	16.3170i	0.102781	+	1.23699i
$175$	−6.87296	−	3.96810i	−0.519547	−	0.299960i
$176$	−4.47678	−	2.58467i	−0.337450	−	0.194827i
$177$	−0.428929	−	5.16226i	−0.0322403	−	0.388019i
$178$	1.67325	+	2.89815i	0.125415	+	0.217226i
$179$	−14.6400			−1.09425			−0.547123	−	0.837052i	$-0.684277\pi$
$179$	−14.6400			−1.09425			−0.547123	+	0.837052i	$0.684277\pi$
$180$	1.45211	+	8.67788i	0.108234	+	0.646811i
$181$	−2.81354			−0.209129			−0.104565	−	0.994518i	$-0.533345\pi$
$181$	−2.81354			−0.209129			−0.104565	+	0.994518i	$0.533345\pi$
$182$	−1.50044	−	7.80199i	−0.111220	−	0.578322i
$183$	0.638995	−	1.35485i	0.0472359	−	0.100153i
$184$	7.26814	+	4.19626i	0.535814	+	0.309353i
$185$	0.947509	−	1.64113i	0.0696622	−	0.120659i
$186$	−6.14389	−	8.85645i	−0.450492	−	0.649387i
$187$	10.3469	−	5.97379i	0.756641	−	0.436847i
$188$			5.53442i			0.403639i
$189$	−8.20169	+	7.98953i	−0.596585	+	0.581153i
$190$		−	15.1609i		−	1.09989i
$191$	4.38820	+	7.60058i	0.317519	+	0.549959i	0.979970	−	0.199147i	$-0.0638170\pi$
$191$	4.38820	+	7.60058i	0.317519	+	0.549959i	−0.662451	+	0.749105i	$0.730484\pi$
$192$	0.987257	+	1.42314i	0.0712492	+	0.102706i
$193$	−13.7032	−	7.91153i	−0.986376	−	0.569485i	−0.0821872	−	0.996617i	$-0.526191\pi$
$193$	−13.7032	−	7.91153i	−0.986376	−	0.569485i	−0.904189	+	0.427132i	$0.859524\pi$
$194$	0.745470	−	1.29119i	0.0535216	−	0.0927022i
$195$	−13.0940	−	12.8066i	−0.937679	−	0.917100i
$196$	1.07221	+	1.85713i	0.0765868	+	0.132652i
$197$			0.395717i			0.0281936i	0.999901	+	0.0140968i	$0.00448731\pi$
$197$			0.395717i			0.0281936i	−0.999901	+	0.0140968i	$0.995513\pi$
$198$	−9.86422	−	11.9665i	−0.701019	−	0.850419i
$199$	3.20316			0.227066			0.113533	−	0.993534i	$-0.463783\pi$
$199$	3.20316			0.227066			0.113533	+	0.993534i	$0.463783\pi$
$200$	−3.11906	+	1.80079i	−0.220551	+	0.127335i
$201$	1.60313	+	19.2940i	0.113076	+	1.36089i
$202$	0.352206	+	0.203346i	0.0247811	+	0.0143074i
$203$	−18.0395	−	10.4151i	−1.26613	−	0.730998i
$204$	−3.98944	+	0.331480i	−0.279316	+	0.0232082i
$205$	−1.14285	−	1.97948i	−0.0798202	−	0.138253i
$206$		−	17.1609i		−	1.19565i
$207$	16.0147	+	19.4278i	1.11310	+	1.35032i
$208$	−3.40677	−	1.18064i	−0.236217	−	0.0818625i
$209$	13.3610	+	23.1420i	0.924202	+	1.60077i
$210$	−10.1241	−	4.77488i	−0.698629	−	0.329498i
$211$	−4.13986	+	7.17045i	−0.285000	+	0.493634i	−0.972609	−	0.232447i	$-0.925327\pi$
$211$	−4.13986	+	7.17045i	−0.285000	+	0.493634i	0.687609	+	0.726081i	$0.258660\pi$
$212$	−4.34238	+	7.52122i	−0.298236	+	0.516559i
$213$	18.4281	−	12.7839i	1.26267	−	0.875939i
$214$	0.285403	−	0.164777i	0.0195097	−	0.0112639i
$215$		−	10.2403i		−	0.698380i
$216$	1.27899	+	5.03629i	0.0870241	+	0.342676i
$217$	13.7130			0.930900
$218$	4.82463	+	8.35651i	0.326765	+	0.565974i
$219$	−6.08439	+	4.22085i	−0.411145	+	0.285219i
$220$	7.58044	−	13.1297i	0.511073	−	0.885204i
$221$	6.30009	−	5.45460i	0.423790	−	0.366916i
$222$	0.477395	−	1.01221i	0.0320406	−	0.0679352i
$223$	−12.4014	+	7.15993i	−0.830456	+	0.479464i	−0.854009	−	0.520258i	$-0.825836\pi$
$223$	−12.4014	+	7.15993i	−0.830456	+	0.479464i	0.0235526	+	0.999723i	$0.492502\pi$
$224$	−2.20354			−0.147230
$225$	−10.6566	+	1.78321i	−0.710438	+	0.118881i
$226$			3.03210i			0.201692i
$227$	−17.3351	+	10.0084i	−1.15057	+	0.664284i	−0.949027	−	0.315195i	$-0.897930\pi$
$227$	−17.3351	+	10.0084i	−1.15057	+	0.664284i	−0.201546	+	0.979479i	$0.564597\pi$
$228$	−0.741391	−	8.92281i	−0.0490998	−	0.590928i
$229$	2.23215	+	1.28873i	0.147505	+	0.0851619i	0.571936	−	0.820298i	$-0.306193\pi$
$229$	2.23215	+	1.28873i	0.147505	+	0.0851619i	−0.424431	+	0.905460i	$0.639526\pi$
$230$	−12.3070	+	21.3163i	−0.811499	+	1.40556i
$231$	19.6617	−	1.63368i	1.29365	−	0.107488i
$232$	−8.18662	+	4.72655i	−0.537478	+	0.310313i
$233$	14.0412			0.919866			0.459933	−	0.887954i	$-0.347873\pi$
$233$	14.0412			0.919866			0.459933	+	0.887954i	$0.347873\pi$
$234$	−8.33262	−	6.89691i	−0.544721	−	0.450865i
$235$	−16.2316			−1.05883
$236$	2.59002	−	1.49535i	0.168596	−	0.0973390i
$237$	2.24867	−	4.76782i	0.146067	−	0.309703i
$238$	2.54645	−	4.41058i	0.165062	−	0.285895i
$239$	−4.07262	−	2.35133i	−0.263436	−	0.152095i	0.362465	−	0.931997i	$-0.381935\pi$
$239$	−4.07262	−	2.35133i	−0.263436	−	0.152095i	−0.625901	+	0.779903i	$0.715269\pi$
$240$	−4.17384	+	2.89547i	−0.269420	+	0.186902i
$241$	−19.5733	+	11.3007i	−1.26083	+	0.727939i	−0.973235	−	0.229814i	$-0.926188\pi$
$241$	−19.5733	+	11.3007i	−1.26083	+	0.727939i	−0.287593	+	0.957753i	$0.592855\pi$
$242$			15.7221i			1.01065i
$243$	−1.69739	+	15.4958i	−0.108887	+	0.994054i
$244$	0.864857			0.0553668
$245$	−5.44668	+	3.14464i	−0.347975	+	0.200904i
$246$	−0.769415	−	1.10912i	−0.0490561	−	0.0707147i
$247$	12.1998	+	14.0908i	0.776255	+	0.896579i
$248$	3.11159	−	5.38944i	0.197586	−	0.342230i
$249$	5.77598	+	2.72416i	0.366038	+	0.172637i
$250$	2.05068	+	3.55188i	0.129696	+	0.224640i
$251$	3.40669			0.215028			0.107514	−	0.994204i	$-0.465711\pi$
$251$	3.40669			0.215028			0.107514	+	0.994204i	$0.465711\pi$
$252$	−6.19195	−	2.31513i	−0.390056	−	0.145840i
$253$		−	43.3838i		−	2.72752i
$254$	7.82328	−	4.51677i	0.490876	−	0.283408i
$255$	−0.972179	−	11.7004i	−0.0608802	−	0.732707i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.9148	−	18.9049i	0.680844	−	1.17926i	−0.293880	−	0.955842i	$-0.594947\pi$
$257$	10.9148	−	18.9049i	0.680844	−	1.17926i	0.974724	−	0.223414i	$-0.0717201\pi$
$258$	−0.500765	−	6.02682i	−0.0311763	−	0.375213i
$259$	0.711892	+	1.23303i	0.0442348	+	0.0766170i
$260$	3.46263	−	9.99153i	0.214743	−	0.619649i
$261$	−27.9704	+	4.68040i	−1.73132	+	0.289710i
$262$			17.4172i			1.07604i
$263$	−2.95513	−	5.11843i	−0.182221	−	0.315616i	0.760416	−	0.649437i	$-0.224995\pi$
$263$	−2.95513	−	5.11843i	−0.182221	−	0.315616i	−0.942637	+	0.333821i	$0.891662\pi$
$264$	3.81934	−	8.09808i	0.235064	−	0.498402i
$265$	−22.0586	−	12.7355i	−1.35505	−	0.782336i
$266$	9.86475	+	5.69541i	0.604846	+	0.349208i
$267$	−4.76253	+	3.30385i	−0.291462	+	0.202193i
$268$	−9.68023	+	5.58888i	−0.591314	+	0.341395i
$269$	1.05911			0.0645751			0.0322875	−	0.999479i	$-0.489721\pi$
$269$	1.05911			0.0645751			0.0322875	+	0.999479i	$0.489721\pi$
$270$	−14.7706	+	3.75107i	−0.898913	+	0.228283i
$271$			21.8135i			1.32508i	0.749027	+	0.662539i	$0.230521\pi$
$271$			21.8135i			1.32508i	−0.749027	+	0.662539i	$0.769479\pi$
$272$	−1.15562	−	2.00159i	−0.0700697	−	0.121364i
$273$	13.2518	−	3.70888i	0.802038	−	0.224472i
$274$	−2.42800	+	4.20543i	−0.146681	+	0.254059i
$275$	16.1235	+	9.30889i	0.972282	+	0.561347i
$276$	−6.20078	+	13.1474i	−0.373243	+	0.791380i
$277$	8.83826	+	15.3083i	0.531040	+	0.919788i	0.999344	+	0.0362206i	$0.0115319\pi$
$277$	8.83826	+	15.3083i	0.531040	+	0.919788i	−0.468304	+	0.883567i	$0.655135\pi$
$278$			11.6453i			0.698436i
$279$	14.4060	−	11.8752i	0.862464	−	0.710948i
$280$		−	6.46263i		−	0.386216i
$281$	11.5370	−	6.66092i	0.688243	−	0.397357i	−0.114711	−	0.993399i	$-0.536594\pi$
$281$	11.5370	−	6.66092i	0.688243	−	0.397357i	0.802953	+	0.596042i	$0.203261\pi$
$282$	−9.55298	+	0.793752i	−0.568872	+	0.0472672i
$283$	−2.64908	+	4.58833i	−0.157471	+	0.272748i	−0.933956	−	0.357388i	$-0.883667\pi$
$283$	−2.64908	+	4.58833i	−0.157471	+	0.272748i	0.776485	+	0.630136i	$0.217001\pi$
$284$	11.2141	+	6.47445i	0.665433	+	0.384188i
$285$	26.1692	−	2.17439i	1.55013	−	0.128799i
$286$	3.51992	+	18.3029i	0.208137	+	1.08227i
$287$	1.71732			0.101370
$288$	−2.31489	+	1.90822i	−0.136406	+	0.112443i
$289$	−11.6582			−0.685775
$290$	−13.8622	−	24.0101i	−0.814019	−	1.40992i
$291$	2.33565	+	1.10157i	0.136918	+	0.0645754i
$292$	−3.70254	−	2.13767i	−0.216675	−	0.125097i
$293$	12.7124	+	7.33950i	0.742666	+	0.428778i	0.823038	−	0.567987i	$-0.192278\pi$
$293$	12.7124	+	7.33950i	0.742666	+	0.428778i	−0.0803721	+	0.996765i	$0.525611\pi$
$294$	−3.05182	+	2.11710i	−0.177986	+	0.123472i
$295$	4.38563	+	7.59613i	0.255341	+	0.442264i
$296$	0.646136			0.0375559
$297$	19.2406	−	18.7429i	1.11645	−	1.08757i
$298$	21.8055			1.26316
$299$	−5.71466	−	29.7152i	−0.330488	−	1.71847i
$300$	−3.55569	−	5.12554i	−0.205288	−	0.295923i
$301$	6.66304	+	3.84691i	0.384051	+	0.221732i
$302$	−7.33161	+	12.6987i	−0.421887	+	0.730729i
$303$	−0.300482	+	0.637107i	−0.0172623	+	0.0366008i
$304$	4.47678	−	2.58467i	0.256761	−	0.148241i
$305$			2.53649i			0.145239i
$306$	−1.14434	−	6.83864i	−0.0654174	−	0.390939i
$307$		−	3.41724i		−	0.195032i	−0.995234	−	0.0975160i	$-0.968910\pi$
$307$		−	3.41724i		−	0.195032i	0.995234	−	0.0975160i	$-0.0310897\pi$
$308$	5.69541	+	9.86475i	0.324526	+	0.562096i
$309$	29.6214	−	2.46123i	1.68510	−	0.140014i
$310$	15.8064	+	9.12582i	0.897742	+	0.518312i
$311$	−5.41458	+	9.37832i	−0.307033	+	0.531796i	−0.977712	−	0.209952i	$-0.932669\pi$
$311$	−5.41458	+	9.37832i	−0.307033	+	0.531796i	0.670679	+	0.741747i	$0.266003\pi$
$312$	1.54930	−	6.04977i	0.0877119	−	0.342501i
$313$	−9.67596	−	16.7593i	−0.546918	−	0.947289i	−0.998484	−	0.0550515i	$-0.982468\pi$
$313$	−9.67596	−	16.7593i	−0.546918	−	0.947289i	0.451566	−	0.892238i	$-0.350866\pi$
$314$		−	7.94869i		−	0.448570i
$315$	6.78993	−	18.1600i	0.382569	−	1.02320i
$316$	3.04350			0.171210
$317$	−13.7615	+	7.94519i	−0.772922	+	0.446247i	−0.833916	−	0.551892i	$-0.813906\pi$
$317$	−13.7615	+	7.94519i	−0.772922	+	0.446247i	0.0609942	+	0.998138i	$0.480573\pi$
$318$	−13.6052	−	6.41669i	−0.762940	−	0.359830i
$319$	42.3194	+	24.4331i	2.36943	+	1.36799i
$320$	−2.53992	−	1.46642i	−0.141986	−	0.0819755i
$321$	0.325355	+	0.469002i	0.0181596	+	0.0261771i
$322$	−9.24661	−	16.0156i	−0.515294	−	0.892515i
$323$			11.9476i			0.664781i
$324$	−8.50972	+	2.92997i	−0.472762	+	0.162776i
$325$	12.2698	+	4.25216i	0.680604	+	0.235867i
$326$	−0.111267	−	0.192720i	−0.00616249	−	0.0106737i
$327$	−13.7322	+	9.52631i	−0.759395	+	0.526806i
$328$	0.389673	−	0.674934i	0.0215161	−	0.0372670i
$329$	6.09765	−	10.5614i	0.336174	−	0.582271i
$330$	23.7504	+	11.2015i	1.30742	+	0.616624i
$331$	−24.7786	+	14.3059i	−1.36195	+	0.786325i	−0.989884	−	0.141880i	$-0.954685\pi$
$331$	−24.7786	+	14.3059i	−1.36195	+	0.786325i	−0.372070	+	0.928204i	$0.621352\pi$
$332$			3.68705i			0.202353i
$333$	1.81565	+	0.678860i	0.0994969	+	0.0372013i
$334$	−3.77070			−0.206323
$335$	−16.3913	−	28.3906i	−0.895554	−	1.55115i
$336$	−0.316033	−	3.80353i	−0.0172410	−	0.207500i
$337$	2.75329	−	4.76884i	0.149981	−	0.259775i	−0.781239	−	0.624232i	$-0.785412\pi$
$337$	2.75329	−	4.76884i	0.149981	−	0.259775i	0.931220	+	0.364457i	$0.118745\pi$
$338$	4.82185	+	12.0727i	0.262274	+	0.656668i
$339$	−5.23372	+	0.434867i	−0.284257	+	0.0236187i
$340$	5.87036	−	3.38925i	0.318365	−	0.183808i
$341$	−32.1698			−1.74209
$342$	15.2954	−	2.55943i	0.827078	−	0.138398i
$343$		−	20.1501i		−	1.08800i
$344$	3.02379	−	1.74579i	0.163032	−	0.0941266i
$345$	−38.5592	−	18.1859i	−2.07596	−	0.979097i
$346$	−9.39936	−	5.42672i	−0.505312	−	0.291742i
$347$	1.32309	−	2.29165i	0.0710271	−	0.123022i	−0.828325	−	0.560248i	$-0.810706\pi$
$347$	1.32309	−	2.29165i	0.0710271	−	0.123022i	0.899352	+	0.437226i	$0.144039\pi$
$348$	−9.33264	−	13.4531i	−0.500282	−	0.721160i
$349$	−4.83660	+	2.79241i	−0.258897	+	0.149474i	−0.623831	−	0.781559i	$-0.714425\pi$
$349$	−4.83660	+	2.79241i	−0.258897	+	0.149474i	0.364934	+	0.931033i	$0.381092\pi$
$350$	7.93621			0.424208
$351$	10.7097	−	15.3721i	0.571642	−	0.820503i
$352$	5.16934			0.275527
$353$	22.2107	−	12.8233i	1.18216	−	0.682518i	0.225643	−	0.974210i	$-0.427552\pi$
$353$	22.2107	−	12.8233i	1.18216	−	0.682518i	0.956512	+	0.291692i	$0.0942183\pi$
$354$	2.95259	+	4.25618i	0.156928	+	0.226213i
$355$	−18.9886	+	32.8892i	−1.00781	+	1.74558i
$356$	−2.89815	−	1.67325i	−0.153602	−	0.0886820i
$357$	7.97833	+	3.76286i	0.422258	+	0.199152i
$358$	12.6786	−	7.32001i	0.670086	−	0.386874i
$359$		−	5.78875i		−	0.305519i	−0.988263	−	0.152759i	$-0.951184\pi$
$359$		−	5.78875i		−	0.305519i	0.988263	−	0.152759i	$-0.0488160\pi$
$360$	−5.59650	−	6.78921i	−0.294961	−	0.357823i
$361$	−7.72208			−0.406425
$362$	2.43660	−	1.40677i	0.128065	−	0.0739383i
$363$	−27.1379	+	2.25487i	−1.42437	+	0.118350i
$364$	5.20041	+	6.00651i	0.272576	+	0.314826i
$365$	6.26944	−	10.8590i	0.328158	−	0.568386i
$366$	0.124039	+	1.49283i	0.00648360	+	0.0780316i
$367$	15.3992	+	26.6722i	0.803831	+	1.39228i	0.917078	+	0.398708i	$0.130541\pi$
$367$	15.3992	+	26.6722i	0.803831	+	1.39228i	−0.113247	+	0.993567i	$0.536125\pi$
$368$	−8.39252			−0.437491
$369$	1.80410	−	1.48716i	0.0939177	−	0.0774185i
$370$			1.89502i			0.0985173i
$371$	16.5733	−	9.56858i	0.860441	−	0.496776i
$372$	9.74899	+	4.59797i	0.505461	+	0.238394i
$373$	15.6441	−	27.0964i	0.810021	−	1.40300i	−0.102828	−	0.994699i	$-0.532789\pi$
$373$	15.6441	−	27.0964i	0.810021	−	1.40300i	0.912849	−	0.408298i	$-0.133878\pi$
$374$	−5.97379	+	10.3469i	−0.308897	+	0.535026i
$375$	−5.83679	+	4.04909i	−0.301411	+	0.209094i
$376$	−2.76721	−	4.79295i	−0.142708	−	0.247178i
$377$	32.2046	+	11.1607i	1.65862	+	0.574805i
$378$	3.10811	−	11.0200i	0.159864	−	0.566807i
$379$			5.29769i			0.272124i	0.990700	+	0.136062i	$0.0434447\pi$
$379$			5.29769i			0.272124i	−0.990700	+	0.136062i	$0.956555\pi$
$380$	7.58044	+	13.1297i	0.388868	+	0.673539i
$381$	8.91844	+	12.8560i	0.456905	+	0.658632i
$382$	−7.60058	−	4.38820i	−0.388880	−	0.224520i
$383$	19.2301	+	11.1025i	0.982611	+	0.567311i	0.903057	−	0.429520i	$-0.141317\pi$
$383$	19.2301	+	11.1025i	0.982611	+	0.567311i	0.0795536	+	0.996831i	$0.474651\pi$
$384$	−1.56656	−	0.738845i	−0.0799431	−	0.0377040i
$385$	−28.9318	+	16.7038i	−1.47450	+	0.851303i
$386$	15.8231			0.805373
$387$	10.3311	−	1.72874i	0.525159	−	0.0878770i
$388$			1.49094i			0.0756910i
$389$	4.38589	+	7.59658i	0.222373	+	0.385162i	0.955528	−	0.294900i	$-0.0952863\pi$
$389$	4.38589	+	7.59658i	0.222373	+	0.385162i	−0.733155	+	0.680062i	$0.761953\pi$
$390$	17.7430	+	4.54386i	0.898453	+	0.230087i
$391$	9.69857	−	16.7984i	0.490478	−	0.849532i
$392$	−1.85713	−	1.07221i	−0.0937993	−	0.0541550i
$393$	−30.0639	+	2.49799i	−1.51652	+	0.126007i
$394$	−0.197858	−	0.342701i	−0.00996796	−	0.0172650i
$395$			8.92611i			0.449121i
$396$	14.5259	+	5.43114i	0.729953	+	0.272925i
$397$			33.5447i			1.68356i	0.539819	+	0.841781i	$0.318492\pi$
$397$			33.5447i			1.68356i	−0.539819	+	0.841781i	$0.681508\pi$
$398$	−2.77402	+	1.60158i	−0.139049	+	0.0802799i
$399$	−8.41606	+	17.8444i	−0.421330	+	0.893338i
$400$	1.80079	−	3.11906i	0.0900395	−	0.155953i
$401$	−1.76682	−	1.02008i	−0.0882309	−	0.0509401i	0.455235	−	0.890371i	$-0.349555\pi$
$401$	−1.76682	−	1.02008i	−0.0882309	−	0.0509401i	−0.543466	+	0.839431i	$0.682888\pi$
$402$	−11.0353	−	15.9075i	−0.550393	−	0.793395i
$403$	−22.0342	+	4.23751i	−1.09760	+	0.211085i
$404$	−0.406692			−0.0202337
$405$	−8.59315	−	24.9577i	−0.426997	−	1.24016i
$406$	20.8302			1.03379
$407$	−1.67005	−	2.89261i	−0.0827813	−	0.143381i
$408$	3.28921	−	2.28179i	0.162840	−	0.112965i
$409$	28.2129	+	16.2887i	1.39504	+	0.805424i	0.993867	−	0.110580i	$-0.0352707\pi$
$409$	28.2129	+	16.2887i	1.39504	+	0.805424i	0.401169	+	0.916004i	$0.368604\pi$
$410$	1.97948	+	1.14285i	0.0977593	+	0.0564414i
$411$	−7.60723	−	3.58784i	−0.375237	−	0.176975i
$412$	8.58044	+	14.8618i	0.422728	+	0.732186i
$413$	−6.59011			−0.324278
$414$	−23.5831	−	8.81757i	−1.15904	−	0.433360i
$415$	−10.8135			−0.530816
$416$	3.54067	−	0.680923i	0.173596	−	0.0333850i
$417$	−20.1009	+	1.67017i	−0.984346	+	0.0817887i
$418$	−23.1420	−	13.3610i	−1.13191	−	0.653510i
$419$	−5.83046	+	10.0986i	−0.284837	+	0.493351i	−0.972570	−	0.232612i	$-0.925273\pi$
$419$	−5.83046	+	10.0986i	−0.284837	+	0.493351i	0.687733	+	0.725964i	$0.258606\pi$
$420$	11.1552	−	0.926876i	0.544316	−	0.0452269i
$421$	1.41549	−	0.817233i	0.0689867	−	0.0398295i	−0.465110	−	0.885253i	$-0.653985\pi$
$421$	1.41549	−	0.817233i	0.0689867	−	0.0398295i	0.534097	+	0.845423i	$0.320652\pi$
$422$		−	8.27972i		−	0.403051i
$423$	−2.74019	−	16.3756i	−0.133233	−	0.796208i
$424$		−	8.68475i		−	0.421769i
$425$	4.16206	+	7.20889i	0.201889	+	0.349683i
$426$	−9.56724	+	20.2852i	−0.463534	+	0.982823i
$427$	−1.65042	−	0.952872i	−0.0798695	−	0.0461127i
$428$	−0.164777	+	0.285403i	−0.00796481	+	0.0137955i
$429$	−31.0879	+	8.70077i	−1.50094	+	0.420077i
$430$	5.12013	+	8.86832i	0.246914	+	0.427668i
$431$			2.92645i			0.140962i	0.997513	+	0.0704810i	$0.0224534\pi$
$431$			2.92645i			0.140962i	−0.997513	+	0.0704810i	$0.977547\pi$
$432$	−3.62578	−	3.72206i	−0.174445	−	0.179078i
$433$	−33.9770			−1.63283			−0.816414	−	0.577467i	$-0.804041\pi$
$433$	−33.9770			−1.63283			−0.816414	+	0.577467i	$0.804041\pi$
$434$	−11.8758	+	6.85651i	−0.570057	+	0.329123i
$435$	39.4558	−	27.3712i	1.89176	−	1.31235i
$436$	−8.35651	−	4.82463i	−0.400204	−	0.231058i
$437$	37.5715	+	21.6919i	1.79729	+	1.03766i
$438$	3.15881	−	6.69756i	0.150934	−	0.320022i
$439$	8.24661	+	14.2836i	0.393589	+	0.681717i	0.992920	−	0.118785i	$-0.0378998\pi$
$439$	8.24661	+	14.2836i	0.393589	+	0.681717i	−0.599331	+	0.800502i	$0.704566\pi$
$440$			15.1609i			0.722766i
$441$	−4.09203	−	4.96412i	−0.194859	−	0.236387i
$442$	−2.72874	+	7.87386i	−0.129793	+	0.374522i
$443$	14.4784	+	25.0774i	0.687891	+	1.19146i	0.972519	+	0.232824i	$0.0747967\pi$
$443$	14.4784	+	25.0774i	0.687891	+	1.19146i	−0.284628	+	0.958638i	$0.591870\pi$
$444$	0.0926695	+	1.11530i	0.00439790	+	0.0529297i
$445$	4.90738	−	8.49983i	0.232632	−	0.402930i
$446$	7.15993	−	12.4014i	0.339032	−	0.587221i
$447$	3.12736	+	37.6385i	0.147919	+	1.78024i
$448$	1.90832	−	1.10177i	0.0901596	−	0.0520536i
$449$		−	38.1292i		−	1.79943i	−0.436478	−	0.899715i	$-0.643774\pi$
$449$		−	38.1292i		−	1.79943i	0.436478	−	0.899715i	$-0.356226\pi$
$450$	8.33726	−	6.87259i	0.393022	−	0.323977i
$451$	−4.02871			−0.189704
$452$	−1.51605	−	2.62588i	−0.0713090	−	0.123511i
$453$	−22.9708	−	10.8338i	−1.07926	−	0.509019i
$454$	10.0084	−	17.3351i	0.469719	−	0.813578i
$455$	−17.6161	+	15.2520i	−0.825858	+	0.715025i
$456$	5.10347	+	7.35669i	0.238992	+	0.344508i
$457$	27.1535	−	15.6771i	1.27019	−	0.733343i	0.295164	−	0.955447i	$-0.404626\pi$
$457$	27.1535	−	15.6771i	1.27019	−	0.733343i	0.975023	+	0.222104i	$0.0712924\pi$
$458$	−2.57747			−0.120437
$459$	11.6401	−	2.95605i	0.543312	−	0.137976i
$460$		−	24.6140i		−	1.14763i
$461$	−20.5156	+	11.8447i	−0.955507	+	0.551662i	−0.894787	−	0.446493i	$-0.852673\pi$
$461$	−20.5156	+	11.8447i	−0.955507	+	0.551662i	−0.0607196	+	0.998155i	$0.519340\pi$
$462$	−16.2107	+	11.2457i	−0.754191	+	0.523196i
$463$	5.85941	+	3.38293i	0.272310	+	0.157218i	0.629937	−	0.776646i	$-0.283081\pi$
$463$	5.85941	+	3.38293i	0.272310	+	0.157218i	−0.357627	+	0.933865i	$0.616414\pi$
$464$	4.72655	−	8.18662i	0.219425	−	0.380054i
$465$	−13.4851	+	28.5923i	−0.625358	+	1.32593i
$466$	−12.1600	+	7.02058i	−0.563301	+	0.325222i
$467$	−28.8066			−1.33301			−0.666505	−	0.745500i	$-0.732211\pi$
$467$	−28.8066			−1.33301			−0.666505	+	0.745500i	$0.732211\pi$
$468$	10.6647	+	1.80659i	0.492977	+	0.0835096i
$469$	24.6306			1.13734
$470$	14.0570	−	8.11580i	0.648400	−	0.374354i
$471$	13.7202	−	1.14001i	0.632196	−	0.0525288i
$472$	−1.49535	+	2.59002i	−0.0688291	+	0.119215i
$473$	−15.6310	−	9.02458i	−0.718715	−	0.414950i
$474$	0.436501	+	5.25339i	0.0200492	+	0.241296i
$475$	−16.1235	+	9.30889i	−0.739796	+	0.427121i
$476$			5.09290i			0.233433i
$477$	9.12459	−	24.4042i	0.417786	−	1.11739i
$478$	4.70266			0.215095
$479$	34.9597	−	20.1840i	1.59735	−	0.922230i	0.605354	−	0.795957i	$-0.293032\pi$
$479$	34.9597	−	20.1840i	1.59735	−	0.922230i	0.991996	−	0.126273i	$-0.0403016\pi$
$480$	2.16692	−	4.59448i	0.0989058	−	0.209708i
$481$	−1.52490	−	1.76127i	−0.0695296	−	0.0803070i
$482$	11.3007	−	19.5733i	0.514731	−	0.891540i
$483$	26.3184	−	18.2576i	1.19753	−	0.830749i
$484$	−7.86104	−	13.6157i	−0.357320	−	0.618896i
$485$	−4.37270			−0.198554
$486$	−6.27790	−	14.2684i	−0.284772	−	0.647229i
$487$		−	40.9866i		−	1.85728i	−0.370982	−	0.928640i	$-0.620979\pi$
$487$		−	40.9866i		−	1.85728i	0.370982	−	0.928640i	$-0.379021\pi$
$488$	−0.748988	+	0.432428i	−0.0339051	+	0.0195751i
$489$	0.316696	−	0.219698i	0.0143215	−	0.00993507i
$490$	3.14464	−	5.44668i	0.142060	−	0.246056i
$491$	4.25969	−	7.37800i	0.192237	−	0.332965i	−0.753754	−	0.657157i	$-0.771759\pi$
$491$	4.25969	−	7.37800i	0.192237	−	0.332965i	0.945991	+	0.324192i	$0.105092\pi$
$492$	1.22089	+	0.575816i	0.0550421	+	0.0259598i
$493$	10.9242	+	18.9212i	0.492001	+	0.852170i
$494$	−17.6108	−	6.10312i	−0.792346	−	0.274592i
$495$	−15.9287	+	42.6022i	−0.715942	+	1.91483i
$496$			6.22318i			0.279429i
$497$	−14.2667	−	24.7106i	−0.639949	−	1.10842i
$498$	−6.36423	+	0.528800i	−0.285188	+	0.0236961i
$499$	−18.9967	−	10.9677i	−0.850408	−	0.490983i	0.0103807	−	0.999946i	$-0.496696\pi$
$499$	−18.9967	−	10.9677i	−0.850408	−	0.490983i	−0.860788	+	0.508963i	$0.830029\pi$
$500$	−3.55188	−	2.05068i	−0.158845	−	0.0917090i
$501$	−0.540797	−	6.50861i	−0.0241610	−	0.290783i
$502$	−2.95028	+	1.70335i	−0.131678	+	0.0760241i
$503$	31.5620			1.40728			0.703641	−	0.710556i	$-0.251556\pi$
$503$	31.5620			1.40728			0.703641	+	0.710556i	$0.251556\pi$
$504$	6.51996	−	1.09101i	0.290422	−	0.0485975i
$505$		−	1.19276i		−	0.0530773i
$506$	21.6919	+	37.5715i	0.964323	+	1.67026i
$507$	−20.1471	+	10.0545i	−0.894766	+	0.446535i
$508$	−4.51677	+	7.82328i	−0.200399	+	0.347102i
$509$	−32.3673	−	18.6873i	−1.43466	−	0.828299i	−0.437184	−	0.899372i	$-0.644024\pi$
$509$	−32.3673	−	18.6873i	−1.43466	−	0.828299i	−0.997471	+	0.0710731i	$0.977358\pi$
$510$	6.69213	+	9.64675i	0.296333	+	0.427165i
$511$	4.71042	+	8.15869i	0.208377	+	0.360919i
$512$		−	1.00000i		−	0.0441942i
$513$	6.61152	+	26.0343i	0.291906	+	1.14944i
$514$			21.8295i			0.962858i
$515$	−43.5872	+	25.1651i	−1.92068	+	1.10891i
$516$	3.44709	+	4.96900i	0.151749	+	0.218748i
$517$	−14.3047	+	24.7764i	−0.629118	+	1.08966i
$518$	−1.23303	−	0.711892i	−0.0541764	−	0.0312788i
$519$	8.01901	−	17.0026i	0.351996	−	0.746329i
$520$	1.99704	+	10.3842i	0.0875761	+	0.455379i
$521$	−17.2949			−0.757705			−0.378853	−	0.925457i	$-0.623681\pi$
$521$	−17.2949			−0.757705			−0.378853	+	0.925457i	$0.623681\pi$
$522$	21.8829	−	18.0386i	0.957788	−	0.789526i
$523$	−10.5189			−0.459960			−0.229980	−	0.973195i	$-0.573866\pi$
$523$	−10.5189			−0.459960			−0.229980	+	0.973195i	$0.573866\pi$
$524$	−8.70860	−	15.0837i	−0.380437	−	0.658936i
$525$	1.13822	+	13.6987i	0.0496759	+	0.597861i
$526$	5.11843	+	2.95513i	0.223174	+	0.128850i
$527$	−12.4563	−	7.19163i	−0.542604	−	0.313273i
$528$	0.741391	+	8.92281i	0.0322649	+	0.388316i
$529$	−23.7172	−	41.0795i	−1.03118	−	1.78606i
$530$	25.4710			1.10639
$531$	−6.92314	+	5.70690i	−0.300439	+	0.247658i
$532$	−11.3908			−0.493855
$533$	−2.75941	+	0.530675i	−0.119523	+	0.0229861i
$534$	2.47254	−	5.24249i	0.106997	−	0.226865i
$535$	−0.837042	−	0.483266i	−0.0361885	−	0.0208934i
$536$	5.58888	−	9.68023i	0.241403	−	0.418122i
$537$	14.4535	+	20.8348i	0.623713	+	0.899086i
$538$	−0.917216	+	0.529555i	−0.0395440	+	0.0228307i
$539$			11.0853i			0.477477i
$540$	10.9162	−	10.6338i	0.469759	−	0.457608i
$541$		−	21.7436i		−	0.934832i	−0.884038	−	0.467416i	$-0.845185\pi$
$541$		−	21.7436i		−	0.934832i	0.884038	−	0.467416i	$-0.154815\pi$
$542$	−10.9068	−	18.8911i	−0.468486	−	0.811441i
$543$	2.77769	+	4.00406i	0.119202	+	0.171831i
$544$	2.00159	+	1.15562i	0.0858175	+	0.0495468i
$545$	14.1499	−	24.5084i	0.606115	−	1.04982i
$546$	−9.62200	+	9.83791i	−0.411783	+	0.421024i
$547$	−13.9964	−	24.2425i	−0.598444	−	1.03654i	−0.993051	−	0.117685i	$-0.962453\pi$
$547$	−13.9964	−	24.2425i	−0.598444	−	1.03654i	0.394607	−	0.918850i	$-0.370881\pi$
$548$		−	4.85601i		−	0.207438i
$549$	−2.55899	+	0.428206i	−0.109215	+	0.0182754i
$550$	−18.6178			−0.793865
$551$	−42.3194	+	24.4331i	−1.80287	+	1.04089i
$552$	−1.20366	−	14.4864i	−0.0512313	−	0.616580i
$553$	−5.80796	−	3.35323i	−0.246980	−	0.142594i
$554$	−15.3083	−	8.83826i	−0.650388	−	0.375502i
$555$	−3.27100	+	0.271785i	−0.138846	+	0.0115366i
$556$	−5.82263	−	10.0851i	−0.246934	−	0.427703i
$557$		−	8.27318i		−	0.350546i	−0.984520	−	0.175273i	$-0.943919\pi$
$557$		−	8.27318i		−	0.350546i	0.984520	−	0.175273i	$-0.0560808\pi$
$558$	−6.53836	+	17.4872i	−0.276791	+	0.740292i
$559$	−11.8950	−	4.12229i	−0.503105	−	0.174354i
$560$	3.23131	+	5.59680i	0.136548	+	0.236508i
$561$	−18.7166	−	8.82741i	−0.790215	−	0.372694i
$562$	−6.66092	+	11.5370i	−0.280974	+	0.486661i
$563$	−5.05976	+	8.76376i	−0.213243	+	0.369349i	−0.952728	−	0.303825i	$-0.901736\pi$
$563$	−5.05976	+	8.76376i	−0.213243	+	0.369349i	0.739484	+	0.673174i	$0.235069\pi$
$564$	7.87625	−	5.46390i	0.331650	−	0.230072i
$565$	7.70129	−	4.44634i	0.323996	−	0.187059i
$566$		−	5.29815i		−	0.222698i
$567$	19.4674	+	3.78441i	0.817554	+	0.158930i
$568$	−12.9489			−0.543324
$569$	10.6762	+	18.4917i	0.447568	+	0.775211i	0.998227	−	0.0595196i	$-0.0189569\pi$
$569$	10.6762	+	18.4917i	0.447568	+	0.775211i	−0.550659	+	0.834730i	$0.685624\pi$
$570$	−21.5760	+	14.9677i	−0.903720	+	0.626927i
$571$	−5.62132	+	9.73641i	−0.235245	+	0.407456i	−0.959344	−	0.282240i	$-0.908923\pi$
$571$	−5.62132	+	9.73641i	−0.235245	+	0.407456i	0.724099	+	0.689696i	$0.242256\pi$
$572$	−12.1998	−	14.0908i	−0.510100	−	0.589168i
$573$	6.48440	−	13.7487i	0.270890	−	0.574362i
$574$	−1.48724	+	0.858659i	−0.0620762	+	0.0358397i
$575$	30.2263			1.26053
$576$	1.05065	−	2.81001i	0.0437769	−	0.117084i
$577$			13.4761i			0.561018i	0.959851	+	0.280509i	$0.0905032\pi$
$577$			13.4761i			0.561018i	−0.959851	+	0.280509i	$0.909497\pi$
$578$	10.0963	−	5.82909i	0.419950	−	0.242458i
$579$	2.26936	+	27.3122i	0.0943113	+	1.13506i
$580$	24.0101	+	13.8622i	0.996965	+	0.575598i
$581$	4.06227	−	7.03606i	0.168531	−	0.291905i
$582$	−2.57352	+	0.213832i	−0.106676	+	0.00886362i
$583$	−38.8797	+	22.4472i	−1.61023	+	0.929669i
$584$	4.27533			0.176914
$585$	−5.29845	+	31.2780i	−0.219064	+	1.29318i
$586$	−14.6790			−0.606384
$587$	24.4663	−	14.1256i	1.00983	−	0.583027i	0.0986903	−	0.995118i	$-0.468535\pi$
$587$	24.4663	−	14.1256i	1.00983	−	0.583027i	0.911143	+	0.412091i	$0.135201\pi$
$588$	1.58440	−	3.35938i	0.0653396	−	0.138538i
$589$	16.0849	−	27.8598i	0.662766	−	1.14794i
$590$	−7.59613	−	4.38563i	−0.312728	−	0.180554i
$591$	0.563159	−	0.390674i	0.0231653	−	0.0160702i
$592$	−0.559571	+	0.323068i	−0.0229982	+	0.0132780i
$593$			33.3901i			1.37117i	0.727993	+	0.685585i	$0.240453\pi$
$593$			33.3901i			1.37117i	−0.727993	+	0.685585i	$0.759547\pi$
$594$	−7.29140	+	25.8521i	−0.299170	+	1.06072i
$595$	−14.9367			−0.612344
$596$	−18.8841	+	10.9027i	−0.773522	+	0.446593i
$597$	−3.16234	−	4.55854i	−0.129426	−	0.186568i
$598$	19.8066	+	22.8768i	0.809953	+	0.935500i
$599$	−10.0405	+	17.3907i	−0.410245	+	0.710564i	−0.994916	−	0.100706i	$-0.967890\pi$
$599$	−10.0405	+	17.3907i	−0.410245	+	0.710564i	0.584672	+	0.811270i	$0.301223\pi$
$600$	5.64209	+	2.66101i	0.230337	+	0.108635i
$601$	−5.78337	−	10.0171i	−0.235909	−	0.408606i	0.723628	−	0.690191i	$-0.242473\pi$
$601$	−5.78337	−	10.0171i	−0.235909	−	0.408606i	−0.959536	+	0.281585i	$0.909140\pi$
$602$	−7.69382			−0.313577
$603$	25.8753	−	21.3296i	1.05372	−	0.868608i
$604$		−	14.6632i		−	0.596638i
$605$	39.9328	−	23.0552i	1.62350	−	0.937328i
$606$	−0.0583281	−	0.701992i	−0.00236942	−	0.0285165i
$607$	−12.0487	+	20.8689i	−0.489040	+	0.847042i	−0.999920	−	0.0126098i	$-0.995986\pi$
$607$	−12.0487	+	20.8689i	−0.489040	+	0.847042i	0.510881	+	0.859652i	$0.329319\pi$
$608$	−2.58467	+	4.47678i	−0.104822	+	0.181557i
$609$	2.98749	+	35.9551i	0.121059	+	1.45698i
$610$	−1.26825	−	2.19667i	−0.0513498	−	0.0889404i
$611$	−6.53415	+	18.8545i	−0.264344	+	0.762772i
$612$	4.41034	+	5.35026i	0.178278	+	0.216272i
$613$		−	3.75444i		−	0.151641i	−0.997122	−	0.0758203i	$-0.975842\pi$
$613$		−	3.75444i		−	0.151641i	0.997122	−	0.0758203i	$-0.0241575\pi$
$614$	1.70862	+	2.95941i	0.0689542	+	0.119432i
$615$	−1.68878	+	3.58069i	−0.0680982	+	0.144387i
$616$	−9.86475	−	5.69541i	−0.397462	−	0.229475i
$617$	−12.4831	−	7.20712i	−0.502551	−	0.290148i	0.227216	−	0.973844i	$-0.427038\pi$
$617$	−12.4831	−	7.20712i	−0.502551	−	0.290148i	−0.729766	+	0.683697i	$0.760371\pi$
$618$	−24.4223	+	16.9422i	−0.982409	+	0.681515i
$619$	7.94447	−	4.58674i	0.319315	−	0.184357i	−0.331772	−	0.943360i	$-0.607647\pi$
$619$	7.94447	−	4.58674i	0.319315	−	0.184357i	0.651087	+	0.759003i	$0.274313\pi$
$620$	−18.2516			−0.733003
$621$	11.8377	−	41.9714i	0.475032	−	1.68425i
$622$		−	10.8292i		−	0.434210i
$623$	3.68706	+	6.38618i	0.147719	+	0.255857i
$624$	1.68315	+	6.01390i	0.0673799	+	0.240749i
$625$	15.0183	−	26.0124i	0.600730	−	1.04050i
$626$	16.7593	+	9.67596i	0.669835	+	0.386729i
$627$	19.7435	−	41.8617i	0.788479	−	1.67180i
$628$	3.97434	+	6.88376i	0.158594	+	0.274692i
$629$		−	1.49338i		−	0.0595448i
$630$	3.19977	+	19.1220i	0.127482	+	0.761840i
$631$		−	32.8572i		−	1.30803i	−0.756483	−	0.654013i	$-0.773084\pi$
$631$		−	32.8572i		−	1.30803i	0.756483	−	0.654013i	$-0.226916\pi$
$632$	−2.63575	+	1.52175i	−0.104844	+	0.0605319i
$633$	14.2916	−	1.18748i	0.568042	−	0.0471983i
$634$	7.94519	−	13.7615i	0.315544	−	0.546538i
$635$	−22.9445	−	13.2470i	−0.910523	−	0.525691i
$636$	14.9908	−	1.24557i	0.594423	−	0.0493902i
$637$	1.46019	+	7.59272i	0.0578549	+	0.300834i
$638$	−48.8663			−1.93463
$639$	−36.3865	−	13.6047i	−1.43943	−	0.538194i
$640$	2.93284			0.115931
$641$	10.6942	+	18.5230i	0.422397	+	0.731613i	0.996173	−	0.0873990i	$-0.0278555\pi$
$641$	10.6942	+	18.5230i	0.422397	+	0.731613i	−0.573776	+	0.819012i	$0.694522\pi$
$642$	−0.516267	−	0.243490i	−0.0203754	−	0.00960978i
$643$	4.58280	+	2.64588i	0.180728	+	0.104343i	0.587635	−	0.809126i	$-0.300059\pi$
$643$	4.58280	+	2.64588i	0.180728	+	0.104343i	−0.406907	+	0.913470i	$0.633393\pi$
$644$	16.0156	+	9.24661i	0.631103	+	0.364368i
$645$	−14.5733	+	10.1098i	−0.573823	+	0.398072i
$646$	−5.97379	−	10.3469i	−0.235036	−	0.407094i
$647$	0.564603			0.0221968			0.0110984	−	0.999938i	$-0.496467\pi$
$647$	0.564603			0.0221968			0.0110984	+	0.999938i	$0.496467\pi$
$648$	5.90464	−	6.79229i	0.231956	−	0.266826i
$649$	15.4599			0.606856
$650$	−12.7520	+	2.45240i	−0.500175	+	0.0961910i
$651$	−13.5383	−	19.5155i	−0.530607	−	0.764873i
$652$	0.192720	+	0.111267i	0.00754748	+	0.00435754i
$653$	8.01118	−	13.8758i	0.313502	−	0.543001i	−0.665616	−	0.746294i	$-0.731831\pi$
$653$	8.01118	−	13.8758i	0.313502	−	0.543001i	0.979118	+	0.203293i	$0.0651645\pi$
$654$	7.12932	−	15.1162i	0.278778	−	0.591088i
$655$	44.2382	−	25.5410i	1.72853	−	0.997968i
$656$			0.779346i			0.0304284i
$657$	12.0137	+	4.49186i	0.468700	+	0.175244i
$658$			12.1953i			0.475422i
$659$	3.71611	+	6.43648i	0.144759	+	0.250730i	0.929283	−	0.369369i	$-0.120426\pi$
$659$	3.71611	+	6.43648i	0.144759	+	0.250730i	−0.784524	+	0.620098i	$0.787093\pi$
$660$	−26.1692	+	2.17439i	−1.01864	+	0.0846378i
$661$	13.6161	+	7.86129i	0.529607	+	0.305769i	0.740856	−	0.671664i	$-0.234420\pi$
$661$	13.6161	+	7.86129i	0.529607	+	0.305769i	−0.211250	+	0.977432i	$0.567753\pi$
$662$	14.3059	−	24.7786i	0.556016	−	0.963047i
$663$	−13.9825	−	3.58080i	−0.543034	−	0.139067i
$664$	−1.84352	−	3.19308i	−0.0715426	−	0.123915i
$665$		−	33.4075i		−	1.29549i
$666$	−1.91183	+	0.319914i	−0.0740818	+	0.0123964i
$667$	79.3354			3.07188
$668$	3.26552	−	1.88535i	0.126347	−	0.0729463i
$669$	22.4329	+	10.5802i	0.867306	+	0.409052i
$670$	28.3906	+	16.3913i	1.09683	+	0.633252i
$671$	3.87177	+	2.23537i	0.149468	+	0.0862955i
$672$	2.17546	+	3.13594i	0.0839201	+	0.120971i
$673$	19.8291	+	34.3450i	0.764356	+	1.32390i	0.940586	+	0.339554i	$0.110276\pi$
$673$	19.8291	+	34.3450i	0.764356	+	1.32390i	−0.176231	+	0.984349i	$0.556390\pi$
$674$			5.50659i			0.212106i
$675$	13.0585	+	13.4053i	0.502623	+	0.515970i
$676$	−10.2122	−	8.04433i	−0.392776	−	0.309397i
$677$	18.2613	+	31.6296i	0.701840	+	1.21562i	0.967820	+	0.251644i	$0.0809712\pi$
$677$	18.2613	+	31.6296i	0.701840	+	1.21562i	−0.265980	+	0.963979i	$0.585695\pi$
$678$	4.31510	−	2.99347i	0.165720	−	0.114963i
$679$	1.64267	−	2.84519i	0.0630399	−	0.109188i
$680$	−3.38925	+	5.87036i	−0.129972	+	0.225118i
$681$	31.3576	+	14.7894i	1.20163	+	0.566730i
$682$	27.8598	−	16.0849i	1.06681	−	0.615922i
$683$		−	8.46240i		−	0.323805i	−0.986807	−	0.161902i	$-0.948237\pi$
$683$		−	8.46240i		−	0.323805i	0.986807	−	0.161902i	$-0.0517630\pi$
$684$	−11.9665	+	9.86422i	−0.457549	+	0.377168i
$685$	14.2419			0.544156
$686$	10.0750	+	17.4505i	0.384667	+	0.666262i
$687$	−0.369662	−	4.44897i	−0.0141035	−	0.169739i
$688$	−1.74579	+	3.02379i	−0.0665576	+	0.115281i
$689$	−23.6733	+	20.4963i	−0.901882	+	0.780846i
$690$	42.4862	−	3.53016i	1.61742	−	0.134391i
$691$	42.2875	−	24.4147i	1.60869	−	0.928779i	0.619028	−	0.785369i	$-0.287527\pi$
$691$	42.2875	−	24.4147i	1.60869	−	0.928779i	0.989663	−	0.143410i	$-0.0458067\pi$
$692$	10.8534			0.412586
$693$	−21.7362	−	26.3685i	−0.825688	−	1.00166i
$694$			2.64618i			0.100447i
$695$	29.5780	−	17.0769i	1.12196	−	0.647762i
$696$	14.8088	+	6.98438i	0.561328	+	0.264742i
$697$	−1.55993	−	0.900628i	−0.0590867	−	0.0341137i
$698$	2.79241	−	4.83660i	0.105694	−	0.183068i
$699$	−13.8622	−	19.9825i	−0.524318	−	0.755808i
$700$	−6.87296	+	3.96810i	−0.259773	+	0.149980i
$701$	−40.2942			−1.52189			−0.760946	−	0.648816i	$-0.775265\pi$
$701$	−40.2942			−1.52189			−0.760946	+	0.648816i	$0.775265\pi$
$702$	−1.58882	+	18.6675i	−0.0599660	+	0.704559i
$703$	3.34010			0.125974
$704$	−4.47678	+	2.58467i	−0.168725	+	0.0974134i
$705$	16.0248	+	23.0998i	0.603528	+	0.869990i
$706$	−12.8233	+	22.2107i	−0.482613	+	0.835910i
$707$	0.776098	+	0.448080i	0.0291882	+	0.0168518i
$708$	−4.68511	−	2.20966i	−0.176077	−	0.0830443i
$709$	33.3511	−	19.2553i	1.25253	−	0.723146i	0.280916	−	0.959732i	$-0.409362\pi$
$709$	33.3511	−	19.2553i	1.25253	−	0.723146i	0.971611	+	0.236586i	$0.0760286\pi$
$710$		−	37.9771i		−	1.42526i
$711$	−9.00529	+	1.50689i	−0.337725	+	0.0565128i
$712$	3.34650			0.125415
$713$	−45.2310	+	26.1141i	−1.69391	+	0.977981i
$714$	−8.79087	+	0.730428i	−0.328990	+	0.0273356i
$715$	41.3262	−	35.7801i	1.54551	−	1.33810i
$716$	−7.32001	+	12.6786i	−0.273561	+	0.473822i
$717$	0.674460	+	8.11727i	0.0251882	+	0.303145i
$718$	2.89438	+	5.01321i	0.108017	+	0.187091i
$719$	−0.951205			−0.0354740			−0.0177370	−	0.999843i	$-0.505646\pi$
$719$	−0.951205			−0.0354740			−0.0177370	+	0.999843i	$0.505646\pi$
$720$	8.24132	+	3.08138i	0.307136	+	0.114836i
$721$		−	37.8146i		−	1.40829i
$722$	6.68752	−	3.86104i	0.248884	−	0.143693i
$723$	35.4063	+	16.6989i	1.31677	+	0.621038i
$724$	−1.40677	+	2.43660i	−0.0522823	+	0.0905555i
$725$	−17.0230	+	29.4848i	−0.632220	+	1.09504i
$726$	22.3747	−	15.5217i	0.830403	−	0.576066i
$727$	−0.999064	−	1.73043i	−0.0370532	−	0.0641781i	0.846904	−	0.531746i	$-0.178464\pi$
$727$	−0.999064	−	1.73043i	−0.0370532	−	0.0641781i	−0.883957	+	0.467568i	$0.845130\pi$
$728$	−7.50694	−	2.60158i	−0.278226	−	0.0964209i
$729$	23.7284	−	12.8827i	0.878829	−	0.477137i
$730$			12.5389i			0.464085i
$731$	−4.03494	−	6.98871i	−0.149237	−	0.258487i
$732$	−0.853836	−	1.23081i	−0.0315587	−	0.0454921i
$733$	−13.5363	−	7.81519i	−0.499975	−	0.288661i	0.228728	−	0.973490i	$-0.426543\pi$
$733$	−13.5363	−	7.81519i	−0.499975	−	0.288661i	−0.728703	+	0.684830i	$0.759877\pi$
$734$	−26.6722	−	15.3992i	−0.984487	−	0.568394i
$735$	9.85253	+	4.64680i	0.363416	+	0.171400i
$736$	7.26814	−	4.19626i	0.267907	−	0.154676i
$737$	−57.7817			−2.12842
$738$	−0.818817	+	2.18997i	−0.0301411	+	0.0806139i
$739$			20.0122i			0.736162i	0.929794	+	0.368081i	$0.119985\pi$
$739$			20.0122i			0.736162i	−0.929794	+	0.368081i	$0.880015\pi$
$740$	−0.947509	−	1.64113i	−0.0348311	−	0.0603293i
$741$	8.00886	−	31.2733i	0.294213	−	1.14885i
$742$	−9.56858	+	16.5733i	−0.351274	+	0.608424i
$743$	33.5922	+	19.3945i	1.23238	+	0.711515i	0.967526	−	0.252773i	$-0.0813427\pi$
$743$	33.5922	+	19.3945i	1.23238	+	0.711515i	0.264855	+	0.964288i	$0.414676\pi$
$744$	−10.7419	+	0.892535i	−0.393816	+	0.0327219i
$745$	−31.9760	−	55.3841i	−1.17151	−	2.02912i
$746$			31.2882i			1.14554i
$747$	−1.82553	−	10.9095i	−0.0667925	−	0.399156i
$748$		−	11.9476i		−	0.436847i
$749$	0.628895	−	0.363093i	0.0229793	−	0.0132671i
$750$	3.03026	−	6.42501i	0.110650	−	0.234608i
$751$	7.46950	−	12.9376i	0.272566	−	0.472098i	−0.696952	−	0.717118i	$-0.745461\pi$
$751$	7.46950	−	12.9376i	0.272566	−	0.472098i	0.969518	+	0.245020i	$0.0787944\pi$
$752$	4.79295	+	2.76721i	0.174781	+	0.100910i
$753$	−3.36328	−	4.84819i	−0.122565	−	0.176678i
$754$	−33.4703	+	6.43683i	−1.21892	+	0.234416i
$755$	43.0049			1.56511
$756$	2.81829	+	11.0976i	0.102500	+	0.403617i
$757$	−26.1383			−0.950011			−0.475006	−	0.879983i	$-0.657554\pi$
$757$	−26.1383			−0.950011			−0.475006	+	0.879983i	$0.657554\pi$
$758$	−2.64885	−	4.58794i	−0.0962105	−	0.166641i
$759$	−61.7412	+	42.8310i	−2.24106	+	1.55467i
$760$	−13.1297	−	7.58044i	−0.476264	−	0.274971i
$761$	2.64121	+	1.52490i	0.0957437	+	0.0552776i	0.547107	−	0.837062i	$-0.315729\pi$
$761$	2.64121	+	1.52490i	0.0957437	+	0.0552776i	−0.451364	+	0.892340i	$0.649062\pi$
$762$	−14.1516	−	6.67439i	−0.512658	−	0.241788i
$763$	10.6313	+	18.4139i	0.384877	+	0.666627i
$764$	8.77640			0.317519
$765$	−15.6915	+	12.9349i	−0.567327	+	0.467661i
$766$	−22.2050			−0.802299
$767$	10.5891	−	2.03644i	0.382350	−	0.0735315i
$768$	1.72610	−	0.143421i	0.0622854	−	0.00517525i
$769$	5.95518	+	3.43822i	0.214749	+	0.123985i	0.603517	−	0.797350i	$-0.293766\pi$
$769$	5.95518	+	3.43822i	0.214749	+	0.123985i	−0.388767	+	0.921336i	$0.627099\pi$
$770$	16.7038	−	28.9318i	0.601962	−	1.04263i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.987257 - 1.42314i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.56656 + 0.738845i) q^{6} +(-1.90832 + 1.10177i) q^{7} +1.00000i q^{8} +(-1.05065 + 2.81001i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.987257 - 1.42314i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.56656 + 0.738845i) q^{6} +(-1.90832 + 1.10177i) q^{7} +1.00000i q^{8} +(-1.05065 + 2.81001i) q^{9} -2.93284 q^{10} +(4.47678 - 2.58467i) q^{11} +(-1.72610 + 0.143421i) q^{12} +(2.72585 - 2.36003i) q^{13} +(1.10177 - 1.90832i) q^{14} +(-0.420631 - 5.06239i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.31124 q^{17} +(-0.495118 - 2.95886i) q^{18} +5.16934i q^{19} +(2.53992 - 1.46642i) q^{20} +(3.45197 + 1.62807i) q^{21} +(-2.58467 + 4.47678i) q^{22} +(4.19626 - 7.26814i) q^{23} +(1.42314 - 0.987257i) q^{24} +(1.80079 + 3.11906i) q^{25} +(-1.18064 + 3.40677i) q^{26} +(5.03629 - 1.27899i) q^{27} +2.20354i q^{28} +(4.72655 + 8.18662i) q^{29} +(2.89547 + 4.17384i) q^{30} +(-5.38944 - 3.11159i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-8.09808 - 3.81934i) q^{33} +(-2.00159 + 1.15562i) q^{34} -6.46263 q^{35} +(1.90822 + 2.31489i) q^{36} -0.646136i q^{37} +(-2.58467 - 4.47678i) q^{38} +(-6.04977 - 1.54930i) q^{39} +(-1.46642 + 2.53992i) q^{40} +(-0.674934 - 0.389673i) q^{41} +(-3.80353 + 0.316033i) q^{42} +(-1.74579 - 3.02379i) q^{43} -5.16934i q^{44} +(-6.78921 + 5.59650i) q^{45} +8.39252i q^{46} +(-4.79295 + 2.76721i) q^{47} +(-0.738845 + 1.56656i) q^{48} +(-1.07221 + 1.85713i) q^{49} +(-3.11906 - 1.80079i) q^{50} +(-2.28179 - 3.28921i) q^{51} +(-0.680923 - 3.54067i) q^{52} -8.68475 q^{53} +(-3.72206 + 3.62578i) q^{54} +15.1609 q^{55} +(-1.10177 - 1.90832i) q^{56} +(7.35669 - 5.10347i) q^{57} +(-8.18662 - 4.72655i) q^{58} +(2.59002 + 1.49535i) q^{59} +(-4.59448 - 2.16692i) q^{60} +(0.432428 + 0.748988i) q^{61} +6.22318 q^{62} +(-1.09101 - 6.51996i) q^{63} -1.00000 q^{64} +(10.3842 - 1.99704i) q^{65} +(8.92281 - 0.741391i) q^{66} +(-9.68023 - 5.58888i) q^{67} +(1.15562 - 2.00159i) q^{68} +(-14.4864 + 1.20366i) q^{69} +(5.59680 - 3.23131i) q^{70} +12.9489i q^{71} +(-2.81001 - 1.05065i) q^{72} -4.27533i q^{73} +(0.323068 + 0.559571i) q^{74} +(2.66101 - 5.64209i) q^{75} +(4.47678 + 2.58467i) q^{76} +(-5.69541 + 9.86475i) q^{77} +(6.01390 - 1.68315i) q^{78} +(1.52175 + 2.63575i) q^{79} -2.93284i q^{80} +(-6.79229 - 5.90464i) q^{81} +0.779346 q^{82} +(-3.19308 + 1.84352i) q^{83} +(3.13594 - 2.17546i) q^{84} +(5.87036 + 3.38925i) q^{85} +(3.02379 + 1.74579i) q^{86} +(6.98438 - 14.8088i) q^{87} +(2.58467 + 4.47678i) q^{88} -3.34650i q^{89} +(3.08138 - 8.24132i) q^{90} +(-2.60158 + 7.50694i) q^{91} +(-4.19626 - 7.26814i) q^{92} +(0.892535 + 10.7419i) q^{93} +(2.76721 - 4.79295i) q^{94} +(-7.58044 + 13.1297i) q^{95} +(-0.143421 - 1.72610i) q^{96} +(-1.29119 + 0.745470i) q^{97} -2.14443i q^{98} +(2.55943 + 15.2954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 - 16 * q^9	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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