LMFDB - Embedded newform 187.2.g.d.137.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			137.2
Root			$1.40126 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	187.137
Dual form			187.2.g.d.86.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 1.53884i) q^{2} +(2.71028 + 1.96913i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(1.03523 - 3.18612i) q^{5} +(1.67504 - 5.15525i) q^{6} +(-1.71028 + 1.24259i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(2.54107 + 7.82060i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 1.53884i) q^{2} +(2.71028 + 1.96913i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(1.03523 - 3.18612i) q^{5} +(1.67504 - 5.15525i) q^{6} +(-1.71028 + 1.24259i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(2.54107 + 7.82060i) q^{9} -5.42055 q^{10} +(-2.74551 - 1.86069i) q^{11} -2.07047 q^{12} +(0.690983 + 2.12663i) q^{13} +(2.76728 + 2.01055i) q^{14} +(9.07965 - 6.59675i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(10.7641 - 7.82060i) q^{18} +(2.30252 + 1.67288i) q^{19} +(0.639809 + 1.96913i) q^{20} -7.08214 q^{21} +(-1.49056 + 5.15525i) q^{22} -3.42055 q^{23} +(-2.31485 - 7.12438i) q^{24} +(-5.03457 - 3.65783i) q^{25} +(2.92705 - 2.12663i) q^{26} +(-5.40709 + 16.6413i) q^{27} +(0.403741 - 1.24259i) q^{28} +(1.65327 - 1.20117i) q^{29} +(-14.6912 - 10.6738i) q^{30} +(-1.11402 - 3.42859i) q^{31} +3.38197 q^{32} +(-3.77714 - 10.4493i) q^{33} +1.61803 q^{34} +(2.18850 + 6.73551i) q^{35} +(-4.11153 - 2.98720i) q^{36} +(3.76186 - 2.73315i) q^{37} +(1.42303 - 4.37965i) q^{38} +(-2.31485 + 7.12438i) q^{39} +(-6.06036 + 4.40311i) q^{40} +(3.59158 + 2.60943i) q^{41} +(3.54107 + 10.8983i) q^{42} -5.74597 q^{43} +(2.04869 - 0.0670174i) q^{44} +27.5480 q^{45} +(1.71028 + 5.26369i) q^{46} +(2.36060 + 1.71508i) q^{47} +(-13.1560 + 9.55836i) q^{48} +(-0.782101 + 2.40706i) q^{49} +(-3.11153 + 9.57632i) q^{50} +(-2.71028 + 1.96913i) q^{51} +(-1.11803 - 0.812299i) q^{52} +(-1.27962 - 3.93826i) q^{53} +28.3119 q^{54} +(-8.77064 + 6.82127i) q^{55} +4.72709 q^{56} +(2.94634 + 9.06791i) q^{57} +(-2.67504 - 1.94353i) q^{58} +(2.42705 - 1.76336i) q^{59} +(-2.14342 + 6.59675i) q^{60} +(4.04066 - 12.4359i) q^{61} +(-4.71905 + 3.42859i) q^{62} +(-14.0637 - 10.2179i) q^{63} +(1.30902 + 4.02874i) q^{64} +7.49102 q^{65} +(-14.1912 + 11.0370i) q^{66} -12.6872 q^{67} +(-0.190983 - 0.587785i) q^{68} +(-9.27064 - 6.73551i) q^{69} +(9.27064 - 6.73551i) q^{70} +(-2.35523 + 7.24864i) q^{71} +(5.68200 - 17.4874i) q^{72} +(2.89476 - 2.10317i) q^{73} +(-6.08682 - 4.42233i) q^{74} +(-6.44233 - 19.8274i) q^{75} -1.75897 q^{76} +(7.00765 - 0.229236i) q^{77} +12.1207 q^{78} +(1.43719 + 4.42320i) q^{79} +(13.1560 + 9.55836i) q^{80} +(-27.4658 + 19.9551i) q^{81} +(2.21972 - 6.83158i) q^{82} +(0.397653 - 1.22385i) q^{83} +(3.54107 - 2.57274i) q^{84} +(2.71028 + 1.96913i) q^{85} +(2.87298 + 8.84213i) q^{86} +6.84607 q^{87} +(2.52111 + 6.97453i) q^{88} -9.65437 q^{89} +(-13.7740 - 42.3920i) q^{90} +(-3.82429 - 2.77851i) q^{91} +(1.71028 - 1.24259i) q^{92} +(3.73205 - 11.4861i) q^{93} +(1.45893 - 4.49013i) q^{94} +(7.71363 - 5.60428i) q^{95} +(9.16606 + 6.65953i) q^{96} +(-2.92457 - 9.00090i) q^{97} +4.09514 q^{98} +(7.57522 - 26.1997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9} - 12 q^{10} - 2 q^{11} - 8 q^{12} + 10 q^{13} + 4 q^{14} + 14 q^{15} - 12 q^{16} + 2 q^{17} + 14 q^{18} - 4 q^{19} - 2 q^{20} - 20 q^{21} - 14 q^{22} + 4 q^{23} - 4 q^{25} + 10 q^{26} - 18 q^{27} + 14 q^{28} - 32 q^{30} - 4 q^{31} + 36 q^{32} + 6 q^{33} + 4 q^{34} - 6 q^{36} + 10 q^{37} + 2 q^{38} - 10 q^{40} - 10 q^{41} + 10 q^{42} + 16 q^{43} + 6 q^{44} + 40 q^{45} - 2 q^{46} + 10 q^{47} - 24 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} + 4 q^{53} + 64 q^{54} - 16 q^{55} - 20 q^{56} - 10 q^{57} - 10 q^{58} + 6 q^{59} - 22 q^{60} + 30 q^{61} + 12 q^{62} - 38 q^{63} + 6 q^{64} + 20 q^{65} - 28 q^{66} - 20 q^{67} - 6 q^{68} - 20 q^{69} + 20 q^{70} + 18 q^{71} + 10 q^{72} - 6 q^{73} - 40 q^{74} - 22 q^{75} + 12 q^{76} + 32 q^{77} + 20 q^{78} - 4 q^{79} + 24 q^{80} - 76 q^{81} - 20 q^{83} + 10 q^{84} + 6 q^{85} - 8 q^{86} + 36 q^{87} - 10 q^{88} - 48 q^{89} - 20 q^{90} - 10 q^{91} - 2 q^{92} + 16 q^{93} + 30 q^{94} + 10 q^{95} + 22 q^{96} + 12 q^{97} + 32 q^{98} + 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9 - 12 * q^10 - 2 * q^11 - 8 * q^12 + 10 * q^13 + 4 * q^14 + 14 * q^15 - 12 * q^16 + 2 * q^17 + 14 * q^18 - 4 * q^19 - 2 * q^20 - 20 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^25 + 10 * q^26 - 18 * q^27 + 14 * q^28 - 32 * q^30 - 4 * q^31 + 36 * q^32 + 6 * q^33 + 4 * q^34 - 6 * q^36 + 10 * q^37 + 2 * q^38 - 10 * q^40 - 10 * q^41 + 10 * q^42 + 16 * q^43 + 6 * q^44 + 40 * q^45 - 2 * q^46 + 10 * q^47 - 24 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 + 4 * q^53 + 64 * q^54 - 16 * q^55 - 20 * q^56 - 10 * q^57 - 10 * q^58 + 6 * q^59 - 22 * q^60 + 30 * q^61 + 12 * q^62 - 38 * q^63 + 6 * q^64 + 20 * q^65 - 28 * q^66 - 20 * q^67 - 6 * q^68 - 20 * q^69 + 20 * q^70 + 18 * q^71 + 10 * q^72 - 6 * q^73 - 40 * q^74 - 22 * q^75 + 12 * q^76 + 32 * q^77 + 20 * q^78 - 4 * q^79 + 24 * q^80 - 76 * q^81 - 20 * q^83 + 10 * q^84 + 6 * q^85 - 8 * q^86 + 36 * q^87 - 10 * q^88 - 48 * q^89 - 20 * q^90 - 10 * q^91 - 2 * q^92 + 16 * q^93 + 30 * q^94 + 10 * q^95 + 22 * q^96 + 12 * q^97 + 32 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	−0.956844	−	0.290604i	$-0.906144\pi$
$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	0.603290	−	0.797522i	$-0.293856\pi$
$3$	2.71028	+	1.96913i	1.56478	+	1.13688i	0.931951	+	0.362585i	$0.118106\pi$
$3$	2.71028	+	1.96913i	1.56478	+	1.13688i	0.632828	+	0.774293i	$0.281894\pi$
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	1.03523	−	3.18612i	0.462970	−	1.42488i	−0.398547	−	0.917148i	$-0.630485\pi$
$5$	1.03523	−	3.18612i	0.462970	−	1.42488i	0.861517	−	0.507728i	$-0.169515\pi$
$6$	1.67504	−	5.15525i	0.683833	−	2.10462i
$7$	−1.71028	+	1.24259i	−0.646423	+	0.469654i	−0.862051	−	0.506822i	$-0.830820\pi$
$7$	−1.71028	+	1.24259i	−0.646423	+	0.469654i	0.215628	+	0.976476i	$0.430820\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	2.54107	+	7.82060i	0.847023	+	2.60687i
$10$	−5.42055			−1.71413
$11$	−2.74551	−	1.86069i	−0.827802	−	0.561020i
$11$	−2.74551	−	1.86069i	−0.827802	−	0.561020i
$12$	−2.07047			−0.597692
$13$	0.690983	+	2.12663i	0.191644	+	0.589820i	0.999999	+	0.00112510i	$0.000358132\pi$
$13$	0.690983	+	2.12663i	0.191644	+	0.589820i	−0.808355	+	0.588695i	$0.799642\pi$
$14$	2.76728	+	2.01055i	0.739588	+	0.537342i
$15$	9.07965	−	6.59675i	2.34436	−	1.70327i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$18$	10.7641	−	7.82060i	2.53713	−	1.84333i
$19$	2.30252	+	1.67288i	0.528234	+	0.383784i	0.819697	−	0.572798i	$-0.194142\pi$
$19$	2.30252	+	1.67288i	0.528234	+	0.383784i	−0.291463	+	0.956582i	$0.594142\pi$
$20$	0.639809	+	1.96913i	0.143066	+	0.440311i
$21$	−7.08214			−1.54545
$22$	−1.49056	+	5.15525i	−0.317788	+	1.09910i
$23$	−3.42055			−0.713234			−0.356617	−	0.934251i	$-0.616070\pi$
$23$	−3.42055			−0.713234			−0.356617	+	0.934251i	$0.616070\pi$
$24$	−2.31485	−	7.12438i	−0.472517	−	1.45426i
$25$	−5.03457	−	3.65783i	−1.00691	−	0.731566i
$26$	2.92705	−	2.12663i	0.574042	−	0.417066i
$27$	−5.40709	+	16.6413i	−1.04060	+	3.20262i
$28$	0.403741	−	1.24259i	0.0762999	−	0.234827i
$29$	1.65327	−	1.20117i	0.307004	−	0.223051i	−0.423606	−	0.905847i	$-0.639236\pi$
$29$	1.65327	−	1.20117i	0.307004	−	0.223051i	0.730610	+	0.682795i	$0.239236\pi$
$30$	−14.6912	−	10.6738i	−2.68223	−	1.94876i
$31$	−1.11402	−	3.42859i	−0.200083	−	0.615793i	−0.999880	−	0.0155215i	$-0.995059\pi$
$31$	−1.11402	−	3.42859i	−0.200083	−	0.615793i	0.799796	−	0.600272i	$-0.204941\pi$
$32$	3.38197			0.597853
$33$	−3.77714	−	10.4493i	−0.657515	−	1.81898i
$34$	1.61803			0.277491
$35$	2.18850	+	6.73551i	0.369924	+	1.13851i
$36$	−4.11153	−	2.98720i	−0.685256	−	0.497867i
$37$	3.76186	−	2.73315i	0.618446	−	0.449327i	−0.233932	−	0.972253i	$-0.575159\pi$
$37$	3.76186	−	2.73315i	0.618446	−	0.449327i	0.852378	+	0.522926i	$0.175159\pi$
$38$	1.42303	−	4.37965i	0.230847	−	0.710473i
$39$	−2.31485	+	7.12438i	−0.370673	+	1.14081i
$40$	−6.06036	+	4.40311i	−0.958227	+	0.696193i
$41$	3.59158	+	2.60943i	0.560910	+	0.407525i	0.831792	−	0.555088i	$-0.187315\pi$
$41$	3.59158	+	2.60943i	0.560910	+	0.407525i	−0.270882	+	0.962613i	$0.587315\pi$
$42$	3.54107	+	10.8983i	0.546399	+	1.68164i
$43$	−5.74597			−0.876252			−0.438126	−	0.898914i	$-0.644358\pi$
$43$	−5.74597			−0.876252			−0.438126	+	0.898914i	$0.644358\pi$
$44$	2.04869	−	0.0670174i	0.308852	−	0.0101033i
$45$	27.5480			4.10661
$46$	1.71028	+	5.26369i	0.252166	+	0.776088i
$47$	2.36060	+	1.71508i	0.344329	+	0.250170i	0.746486	−	0.665401i	$-0.231739\pi$
$47$	2.36060	+	1.71508i	0.344329	+	0.250170i	−0.402157	+	0.915571i	$0.631739\pi$
$48$	−13.1560	+	9.55836i	−1.89890	+	1.37963i
$49$	−0.782101	+	2.40706i	−0.111729	+	0.343866i
$50$	−3.11153	+	9.57632i	−0.440037	+	1.35430i
$51$	−2.71028	+	1.96913i	−0.379514	+	0.275733i
$52$	−1.11803	−	0.812299i	−0.155043	−	0.112646i
$53$	−1.27962	−	3.93826i	−0.175769	−	0.540962i	0.823899	−	0.566737i	$-0.191795\pi$
$53$	−1.27962	−	3.93826i	−0.175769	−	0.540962i	−0.999668	+	0.0257755i	$0.991795\pi$
$54$	28.3119			3.85276
$55$	−8.77064	+	6.82127i	−1.18263	+	0.919780i
$56$	4.72709			0.631683
$57$	2.94634	+	9.06791i	0.390253	+	1.20107i
$58$	−2.67504	−	1.94353i	−0.351250	−	0.255198i
$59$	2.42705	−	1.76336i	0.315975	−	0.229569i	−0.418481	−	0.908226i	$-0.637437\pi$
$59$	2.42705	−	1.76336i	0.315975	−	0.229569i	0.734456	+	0.678656i	$0.237437\pi$
$60$	−2.14342	+	6.59675i	−0.276714	+	0.851637i
$61$	4.04066	−	12.4359i	0.517353	−	1.59225i	−0.261606	−	0.965175i	$-0.584252\pi$
$61$	4.04066	−	12.4359i	0.517353	−	1.59225i	0.778959	−	0.627074i	$-0.215748\pi$
$62$	−4.71905	+	3.42859i	−0.599320	+	0.435432i
$63$	−14.0637	−	10.2179i	−1.77186	−	1.28733i
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	7.49102			0.929146
$66$	−14.1912	+	11.0370i	−1.74681	+	1.35857i
$67$	−12.6872			−1.54998			−0.774992	−	0.631971i	$-0.782246\pi$
$67$	−12.6872			−1.54998			−0.774992	+	0.631971i	$0.782246\pi$
$68$	−0.190983	−	0.587785i	−0.0231601	−	0.0712794i
$69$	−9.27064	−	6.73551i	−1.11605	−	0.810860i
$70$	9.27064	−	6.73551i	1.10805	−	0.805048i
$71$	−2.35523	+	7.24864i	−0.279514	+	0.860255i	0.708476	+	0.705735i	$0.249383\pi$
$71$	−2.35523	+	7.24864i	−0.279514	+	0.860255i	−0.987990	+	0.154520i	$0.950617\pi$
$72$	5.68200	−	17.4874i	0.669630	−	2.06091i
$73$	2.89476	−	2.10317i	0.338806	−	0.246157i	−0.405352	−	0.914161i	$-0.632851\pi$
$73$	2.89476	−	2.10317i	0.338806	−	0.246157i	0.744158	+	0.668004i	$0.232851\pi$
$74$	−6.08682	−	4.42233i	−0.707578	−	0.514086i
$75$	−6.44233	−	19.8274i	−0.743896	−	2.28948i
$76$	−1.75897			−0.201767
$77$	7.00765	−	0.229236i	0.798596	−	0.0261239i
$78$	12.1207			1.37240
$79$	1.43719	+	4.42320i	0.161696	+	0.497649i	0.998778	−	0.0494288i	$-0.0157401\pi$
$79$	1.43719	+	4.42320i	0.161696	+	0.497649i	−0.837082	+	0.547078i	$0.815740\pi$
$80$	13.1560	+	9.55836i	1.47088	+	1.06866i
$81$	−27.4658	+	19.9551i	−3.05176	+	2.21723i
$82$	2.21972	−	6.83158i	0.245127	−	0.754422i
$83$	0.397653	−	1.22385i	0.0436480	−	0.134335i	−0.926858	−	0.375413i	$-0.877501\pi$
$83$	0.397653	−	1.22385i	0.0436480	−	0.134335i	0.970506	+	0.241078i	$0.0775010\pi$
$84$	3.54107	−	2.57274i	0.386362	−	0.280709i
$85$	2.71028	+	1.96913i	0.293971	+	0.213582i
$86$	2.87298	+	8.84213i	0.309802	+	0.953472i
$87$	6.84607			0.733975
$88$	2.52111	+	6.97453i	0.268751	+	0.743487i
$89$	−9.65437			−1.02336			−0.511681	−	0.859176i	$-0.670977\pi$
$89$	−9.65437			−1.02336			−0.511681	+	0.859176i	$0.670977\pi$
$90$	−13.7740	−	42.3920i	−1.45191	−	4.46851i
$91$	−3.82429	−	2.77851i	−0.400895	−	0.291267i
$92$	1.71028	−	1.24259i	0.178309	−	0.129549i
$93$	3.73205	−	11.4861i	0.386996	−	1.19105i
$94$	1.45893	−	4.49013i	0.150477	−	0.463122i
$95$	7.71363	−	5.60428i	0.791401	−	0.574987i
$96$	9.16606	+	6.65953i	0.935507	+	0.679686i
$97$	−2.92457	−	9.00090i	−0.296945	−	0.913902i	−0.982561	−	0.185939i	$-0.940467\pi$
$97$	−2.92457	−	9.00090i	−0.296945	−	0.913902i	0.685616	−	0.727963i	$-0.259533\pi$
$98$	4.09514			0.413671
$99$	7.57522	−	26.1997i	0.761339	−	2.63317i
$100$	3.84607			0.384607
$101$	−4.28435	−	13.1859i	−0.426309	−	1.31204i	−0.901736	−	0.432288i	$-0.857706\pi$
$101$	−4.28435	−	13.1859i	−0.426309	−	1.31204i	0.475427	−	0.879755i	$-0.342294\pi$
$102$	4.38532	+	3.18612i	0.434211	+	0.315473i
$103$	7.57965	−	5.50694i	0.746845	−	0.542615i	−0.148002	−	0.988987i	$-0.547284\pi$
$103$	7.57965	−	5.50694i	0.746845	−	0.542615i	0.894847	+	0.446372i	$0.147284\pi$
$104$	1.54508	−	4.75528i	0.151508	−	0.466294i
$105$	−7.33166	+	22.5645i	−0.715497	+	2.20207i
$106$	−5.42055	+	3.93826i	−0.526490	+	0.382518i
$107$	−6.07382	−	4.41289i	−0.587178	−	0.426610i	0.254127	−	0.967171i	$-0.418212\pi$
$107$	−6.07382	−	4.41289i	−0.587178	−	0.426610i	−0.841305	+	0.540561i	$0.818212\pi$
$108$	−3.34177	−	10.2849i	−0.321562	−	0.989665i
$109$	7.81643			0.748678			0.374339	−	0.927292i	$-0.377870\pi$
$109$	7.81643			0.748678			0.374339	+	0.927292i	$0.377870\pi$
$110$	14.8822	+	10.0860i	1.41896	+	0.961661i
$111$	15.5776			1.47856
$112$	−3.17103	−	9.75941i	−0.299634	−	0.922178i
$113$	11.0067	+	7.99684i	1.03542	+	0.752279i	0.969387	−	0.245538i	$-0.0789646\pi$
$113$	11.0067	+	7.99684i	1.03542	+	0.752279i	0.0660366	+	0.997817i	$0.478965\pi$
$114$	12.4809	−	9.06791i	1.16894	−	0.849288i
$115$	−3.54107	+	10.8983i	−0.330206	+	1.01627i
$116$	−0.390283	+	1.20117i	−0.0362369	+	0.111526i
$117$	−14.8757	+	10.8078i	−1.37526	+	0.999182i
$118$	−3.92705	−	2.85317i	−0.361514	−	0.262656i
$119$	−0.653267	−	2.01055i	−0.0598849	−	0.184307i
$120$	−25.0955			−2.29090
$121$	4.07564	+	10.2171i	0.370512	+	0.928828i
$122$	−21.1572			−1.91548
$123$	4.59585	+	14.1446i	0.414394	+	1.27537i
$124$	1.80252	+	1.30961i	0.161871	+	0.117606i
$125$	−3.31485	+	2.40838i	−0.296489	+	0.215412i
$126$	−8.69185	+	26.7508i	−0.774332	+	2.38315i
$127$	−3.62276	+	11.1497i	−0.321468	+	0.989378i	0.651541	+	0.758613i	$0.274123\pi$
$127$	−3.62276	+	11.1497i	−0.321468	+	0.989378i	−0.973010	+	0.230764i	$0.925877\pi$
$128$	11.0172	−	8.00448i	0.973794	−	0.707503i
$129$	−15.5732	−	11.3146i	−1.37114	−	0.996191i
$130$	−3.74551	−	11.5275i	−0.328503	−	1.01103i
$131$	12.3254			1.07688			0.538438	−	0.842665i	$-0.319015\pi$
$131$	12.3254			1.07688			0.538438	+	0.842665i	$0.319015\pi$
$132$	5.68448	+	3.85250i	0.494771	+	0.335317i
$133$	−6.01663			−0.521708
$134$	6.34358	+	19.5235i	0.548002	+	1.68658i
$135$	47.4236	+	34.4553i	4.08158	+	2.96544i
$136$	1.80902	−	1.31433i	0.155122	−	0.112703i
$137$	1.58367	−	4.87404i	0.135302	−	0.416417i	−0.860335	−	0.509729i	$-0.829746\pi$
$137$	1.58367	−	4.87404i	0.135302	−	0.416417i	0.995637	+	0.0933124i	$0.0297455\pi$
$138$	−5.72957	+	17.6338i	−0.487733	+	1.50109i
$139$	15.3534	−	11.1549i	1.30226	−	0.946148i	0.302286	−	0.953217i	$-0.402250\pi$
$139$	15.3534	−	11.1549i	1.30226	−	0.946148i	0.999975	+	0.00706875i	$0.00225007\pi$
$140$	−3.54107	−	2.57274i	−0.299275	−	0.217436i
$141$	3.02067	+	9.29667i	0.254386	+	0.782921i
$142$	12.3321			1.03489
$143$	2.05990	−	7.12438i	0.172258	−	0.595771i
$144$	−39.9156			−3.32630
$145$	−2.11555	−	6.51100i	−0.175687	−	0.540709i
$146$	−4.68382	−	3.40299i	−0.387636	−	0.281634i
$147$	−6.85953	+	4.98374i	−0.565764	+	0.411052i
$148$	−0.888055	+	2.73315i	−0.0729977	+	0.224664i
$149$	3.80653	−	11.7153i	0.311843	−	0.959755i	−0.665191	−	0.746673i	$-0.731650\pi$
$149$	3.80653	−	11.7153i	0.311843	−	0.959755i	0.977034	−	0.213082i	$-0.0683502\pi$
$150$	−27.2901	+	19.8274i	−2.22823	+	1.61890i
$151$	−4.36247	−	3.16952i	−0.355012	−	0.257932i	0.395956	−	0.918269i	$-0.370413\pi$
$151$	−4.36247	−	3.16952i	−0.355012	−	0.257932i	−0.750969	+	0.660338i	$0.770413\pi$
$152$	−1.96658	−	6.05252i	−0.159511	−	0.490925i
$153$	−8.22307			−0.664796
$154$	−3.85658	−	10.6690i	−0.310772	−	0.859737i
$155$	−12.0772			−0.970062
$156$	−1.43066	−	4.40311i	−0.114544	−	0.352531i
$157$	3.89765	+	2.83181i	0.311067	+	0.226003i	0.732354	−	0.680924i	$-0.238422\pi$
$157$	3.89765	+	2.83181i	0.311067	+	0.226003i	−0.421287	+	0.906927i	$0.638422\pi$
$158$	6.08802	−	4.42320i	0.484337	−	0.351891i
$159$	4.28683	−	13.1935i	0.339968	−	1.04631i
$160$	3.50112	−	10.7753i	0.276788	−	0.851866i
$161$	5.85008	−	4.25034i	0.461051	−	0.334973i
$162$	44.4407	+	32.2880i	3.49159	+	2.53679i
$163$	−0.433551	−	1.33433i	−0.0339583	−	0.104513i	0.932641	−	0.360807i	$-0.117499\pi$
$163$	−0.433551	−	1.33433i	−0.0339583	−	0.104513i	−0.966599	+	0.256294i	$0.917499\pi$
$164$	−2.74372			−0.214249
$165$	−37.2028	+	1.21699i	−2.89623	+	0.0947425i
$166$	−2.08214			−0.161605
$167$	5.54803	+	17.0751i	0.429319	+	1.32131i	0.898797	+	0.438364i	$0.144442\pi$
$167$	5.54803	+	17.0751i	0.429319	+	1.32131i	−0.469478	+	0.882944i	$0.655558\pi$
$168$	12.8117	+	9.30825i	0.988444	+	0.718147i
$169$	6.47214	−	4.70228i	0.497857	−	0.361714i
$170$	1.67504	−	5.15525i	0.128470	−	0.395390i
$171$	−7.23205	+	22.2580i	−0.553049	+	1.70211i
$172$	2.87298	−	2.08734i	0.219063	−	0.159159i
$173$	1.42887	+	1.03813i	0.108635	+	0.0789278i	0.640776	−	0.767728i	$-0.278613\pi$
$173$	1.42887	+	1.03813i	0.108635	+	0.0789278i	−0.532142	+	0.846655i	$0.678613\pi$
$174$	−3.42303	−	10.5350i	−0.259500	−	0.798657i
$175$	13.1557			0.994475
$176$	12.7082	−	9.88367i	0.957917	−	0.745010i
$177$	10.0503			0.755423
$178$	4.82719	+	14.8566i	0.361813	+	1.11355i
$179$	−10.5373	−	7.65576i	−0.787591	−	0.572219i	0.119656	−	0.992815i	$-0.461821\pi$
$179$	−10.5373	−	7.65576i	−0.787591	−	0.572219i	−0.907248	+	0.420597i	$0.861821\pi$
$180$	−13.7740	+	10.0074i	−1.02665	+	0.745907i
$181$	3.85728	−	11.8715i	0.286709	−	0.882400i	−0.699172	−	0.714954i	$-0.746448\pi$
$181$	3.85728	−	11.8715i	0.286709	−	0.882400i	0.985881	−	0.167447i	$-0.0535522\pi$
$182$	−2.36354	+	7.27424i	−0.175197	+	0.539202i
$183$	35.4391	−	25.7480i	2.61974	−	1.90335i
$184$	6.18784	+	4.49573i	0.456173	+	0.331429i
$185$	−4.81375	−	14.8152i	−0.353914	−	1.08923i
$186$	−19.5413			−1.43284
$187$	2.61803	−	2.03615i	0.191450	−	0.148898i
$188$	−1.80334			−0.131522
$189$	−11.4307	−	35.1800i	−0.831460	−	2.55897i
$190$	−12.4809	−	9.06791i	−0.905460	−	0.657856i
$191$	−0.322017	+	0.233959i	−0.0233003	+	0.0169287i	−0.599374	−	0.800469i	$-0.704584\pi$
$191$	−0.322017	+	0.233959i	−0.0233003	+	0.0169287i	0.576074	+	0.817397i	$0.304584\pi$
$192$	−4.38532	+	13.4966i	−0.316483	+	0.974035i
$193$	−4.60586	+	14.1754i	−0.331537	+	1.02037i	0.636866	+	0.770974i	$0.280230\pi$
$193$	−4.60586	+	14.1754i	−0.331537	+	1.02037i	−0.968403	+	0.249391i	$0.919770\pi$
$194$	−12.3887	+	9.00090i	−0.889455	+	0.646227i
$195$	20.3027	+	14.7508i	1.45391	+	1.05633i
$196$	−0.483365	−	1.48765i	−0.0345261	−	0.106260i
$197$	−17.0147			−1.21225			−0.606125	−	0.795369i	$-0.707277\pi$
$197$	−17.0147			−1.21225			−0.606125	+	0.795369i	$0.707277\pi$
$198$	−44.1048	+	1.44277i	−3.13439	+	0.102533i
$199$	7.50857			0.532268			0.266134	−	0.963936i	$-0.414254\pi$
$199$	7.50857			0.532268			0.266134	+	0.963936i	$0.414254\pi$
$200$	4.30003	+	13.2341i	0.304058	+	0.935795i
$201$	−34.3857	−	24.9827i	−2.42538	−	1.76214i
$202$	−18.1488	+	13.1859i	−1.27694	+	0.927754i
$203$	−1.33498	+	4.10866i	−0.0936975	+	0.288371i
$204$	0.639809	−	1.96913i	0.0447956	−	0.137867i
$205$	12.0321	−	8.74182i	0.840357	−	0.610555i
$206$	−12.2641	−	8.91042i	−0.854483	−	0.620818i
$207$	−8.69185	−	26.7508i	−0.604125	−	1.85931i
$208$	−10.8541			−0.752597
$209$	−3.20887	−	8.87718i	−0.221962	−	0.614047i
$210$	38.3891			2.64910
$211$	2.29822	+	7.07318i	0.158216	+	0.486938i	0.998473	−	0.0552506i	$-0.0175958\pi$
$211$	2.29822	+	7.07318i	0.158216	+	0.486938i	−0.840257	+	0.542189i	$0.817596\pi$
$212$	2.07047	+	1.50428i	0.142200	+	0.103314i
$213$	−20.6568	+	15.0081i	−1.41538	+	1.02834i
$214$	−3.75383	+	11.5531i	−0.256606	+	0.789753i
$215$	−5.94842	+	18.3073i	−0.405679	+	1.24855i
$216$	31.6537	−	22.9977i	2.15376	−	1.56480i
$217$	6.16560	+	4.47957i	0.418548	+	0.304093i
$218$	−3.90822	−	12.0283i	−0.264698	−	0.814656i
$219$	11.9870			0.810006
$220$	1.90735	−	6.59675i	0.128593	−	0.444753i
$221$	−2.23607			−0.150414
$222$	−7.78881	−	23.9715i	−0.522750	−	1.60886i
$223$	−2.96008	−	2.15063i	−0.198222	−	0.144017i	0.484247	−	0.874931i	$-0.339094\pi$
$223$	−2.96008	−	2.15063i	−0.198222	−	0.144017i	−0.682469	+	0.730915i	$0.739094\pi$
$224$	−5.78409	+	4.20239i	−0.386466	+	0.280784i
$225$	15.8132	−	48.6681i	1.05422	−	3.24454i
$226$	6.80252	−	20.9360i	0.452497	−	1.39264i
$227$	−16.6117	+	12.0691i	−1.10256	+	0.801057i	−0.981476	−	0.191586i	$-0.938637\pi$
$227$	−16.6117	+	12.0691i	−1.10256	+	0.801057i	−0.121084	+	0.992642i	$0.538637\pi$
$228$	−4.76728	−	3.46363i	−0.315721	−	0.229385i
$229$	8.90660	+	27.4117i	0.588565	+	1.81142i	0.584457	+	0.811425i	$0.301308\pi$
$229$	8.90660	+	27.4117i	0.588565	+	1.81142i	0.00410819	+	0.999992i	$0.498692\pi$
$230$	18.5413			1.22258
$231$	19.4441	+	13.1777i	1.27933	+	0.867028i
$232$	−4.56952			−0.300004
$233$	4.86035	+	14.9586i	0.318412	+	0.979971i	0.974327	+	0.225137i	$0.0722829\pi$
$233$	4.86035	+	14.9586i	0.318412	+	0.979971i	−0.655915	+	0.754835i	$0.727717\pi$
$234$	24.0693	+	17.4874i	1.57346	+	1.14319i
$235$	7.90822	−	5.74566i	0.515875	−	0.374805i
$236$	−0.572949	+	1.76336i	−0.0372958	+	0.114785i
$237$	−4.81469	+	14.8181i	−0.312748	+	0.962539i
$238$	−2.76728	+	2.01055i	−0.179376	+	0.130325i
$239$	−0.0330335	−	0.0240002i	−0.00213676	−	0.00155244i	0.586716	−	0.809793i	$-0.300420\pi$
$239$	−0.0330335	−	0.0240002i	−0.00213676	−	0.00155244i	−0.588853	+	0.808240i	$0.700420\pi$
$240$	16.8346	+	51.8116i	1.08667	+	3.34442i
$241$	−9.06243			−0.583763			−0.291881	−	0.956455i	$-0.594281\pi$
$241$	−9.06243			−0.583763			−0.291881	+	0.956455i	$0.594281\pi$
$242$	13.6847	−	11.3803i	0.879685	−	0.731554i
$243$	−61.2410			−3.92861
$244$	2.49726	+	7.68579i	0.159871	+	0.492032i
$245$	6.85953	+	4.98374i	0.438239	+	0.318399i
$246$	19.4683	−	14.1446i	1.24125	−	0.901824i
$247$	−1.96658	+	6.05252i	−0.125131	+	0.385113i
$248$	−2.49102	+	7.66656i	−0.158180	+	0.486827i
$249$	3.48767	−	2.53394i	0.221022	−	0.160582i
$250$	5.36354	+	3.89684i	0.339220	+	0.246458i
$251$	2.95536	+	9.09565i	0.186540	+	0.574112i	0.999972	−	0.00754902i	$-0.00240295\pi$
$251$	2.95536	+	9.09565i	0.186540	+	0.574112i	−0.813431	+	0.581661i	$0.802403\pi$
$252$	10.7437			0.676791
$253$	9.39115	+	6.36460i	0.590417	+	0.400139i
$254$	18.9690			1.19022
$255$	3.46812	+	10.6738i	0.217182	+	0.668418i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	−12.6752	+	9.20905i	−0.790655	+	0.574445i	−0.908158	−	0.418628i	$-0.862511\pi$
$257$	−12.6752	+	9.20905i	−0.790655	+	0.574445i	0.117502	+	0.993073i	$0.462511\pi$
$258$	−9.62474	+	29.6219i	−0.599210	+	1.84418i
$259$	−3.03764	+	9.34888i	−0.188750	+	0.580911i
$260$	−3.74551	+	2.72127i	−0.232287	+	0.168766i
$261$	13.5949	+	9.87729i	0.841505	+	0.611389i
$262$	−6.16271	−	18.9669i	−0.380733	−	1.17178i
$263$	−18.0538			−1.11325			−0.556623	−	0.830765i	$-0.687903\pi$
$263$	−18.0538			−1.11325			−0.556623	+	0.830765i	$0.687903\pi$
$264$	−6.90085	+	23.8673i	−0.424718	+	1.46893i
$265$	−13.8725			−0.852179
$266$	3.00832	+	9.25865i	0.184452	+	0.567684i
$267$	−26.1660	−	19.0107i	−1.60133	−	1.16344i
$268$	6.34358	−	4.60888i	0.387496	−	0.281532i
$269$	0.0989956	−	0.304677i	0.00603587	−	0.0185765i	−0.947993	−	0.318290i	$-0.896891\pi$
$269$	0.0989956	−	0.304677i	0.00603587	−	0.0185765i	0.954029	+	0.299714i	$0.0968913\pi$
$270$	29.3094	−	90.2051i	1.78371	−	5.48971i
$271$	18.0002	−	13.0779i	1.09343	−	0.794427i	0.113459	−	0.993543i	$-0.463807\pi$
$271$	18.0002	−	13.0779i	1.09343	−	0.794427i	0.979976	+	0.199116i	$0.0638071\pi$
$272$	−3.92705	−	2.85317i	−0.238112	−	0.172999i
$273$	−4.89364	−	15.0611i	−0.296176	−	0.911537i
$274$	−8.29220			−0.500950
$275$	7.01635	+	19.4104i	0.423102	+	1.17049i
$276$	7.08214			0.426294
$277$	6.68561	+	20.5762i	0.401699	+	1.23630i	0.923620	+	0.383309i	$0.125216\pi$
$277$	6.68561	+	20.5762i	0.401699	+	1.23630i	−0.521921	+	0.852994i	$0.674784\pi$
$278$	−24.8424	−	18.0490i	−1.48995	−	1.08251i
$279$	23.9829	−	17.4246i	1.43582	−	1.04318i
$280$	4.89364	−	15.0611i	0.292451	−	0.900071i
$281$	−0.783636	+	2.41178i	−0.0467478	+	0.143875i	−0.971706	−	0.236194i	$-0.924100\pi$
$281$	−0.783636	+	2.41178i	−0.0467478	+	0.143875i	0.924958	+	0.380069i	$0.124100\pi$
$282$	12.7958	−	9.29667i	0.761977	−	0.553608i
$283$	22.6734	+	16.4732i	1.34780	+	0.979231i	0.999118	+	0.0419879i	$0.0133691\pi$
$283$	22.6734	+	16.4732i	1.34780	+	0.979231i	0.348677	+	0.937243i	$0.386631\pi$
$284$	−1.45561	−	4.47990i	−0.0863745	−	0.265833i
$285$	31.9416			1.89206
$286$	−11.9932	+	0.392327i	−0.709176	+	0.0231988i
$287$	−9.38503			−0.553981
$288$	8.59380	+	26.4490i	0.506395	+	1.55852i
$289$	−0.809017	−	0.587785i	−0.0475892	−	0.0345756i
$290$	−8.96162	+	6.51100i	−0.526244	+	0.382339i
$291$	9.79755	−	30.1538i	0.574343	−	1.76764i
$292$	−0.683360	+	2.10317i	−0.0399906	+	0.123078i
$293$	−5.35195	+	3.88842i	−0.312664	+	0.227164i	−0.733039	−	0.680187i	$-0.761899\pi$
$293$	−5.35195	+	3.88842i	−0.312664	+	0.227164i	0.420375	+	0.907351i	$0.361899\pi$
$294$	11.0989	+	8.06386i	0.647304	+	0.470294i
$295$	−3.10570	−	9.55836i	−0.180821	−	0.556509i
$296$	−10.3975			−0.604344
$297$	45.8096	−	35.6279i	2.65814	−	2.06734i
$298$	−19.9313			−1.15459
$299$	−2.36354	−	7.27424i	−0.136687	−	0.420680i
$300$	10.4239	+	7.57341i	0.601824	+	0.437251i
$301$	9.82719	−	7.13987i	0.566430	−	0.411535i
$302$	−2.69615	+	8.29790i	−0.155146	+	0.477491i
$303$	14.3529	−	44.1738i	0.824554	−	2.53772i
$304$	−11.1767	+	8.12031i	−0.641025	+	0.465732i
$305$	−35.4391	−	25.7480i	−2.02924	−	1.47433i
$306$	4.11153	+	12.6540i	0.235041	+	0.723381i
$307$	−23.7701			−1.35663			−0.678315	−	0.734771i	$-0.737289\pi$
$307$	−23.7701			−1.35663			−0.678315	+	0.734771i	$0.737289\pi$
$308$	−3.42055	+	2.66030i	−0.194904	+	0.151584i
$309$	31.3868			1.78553
$310$	6.03859	+	18.5849i	0.342969	+	1.05555i
$311$	0.411776	+	0.299173i	0.0233497	+	0.0169645i	0.599399	−	0.800450i	$-0.295406\pi$
$311$	0.411776	+	0.299173i	0.0233497	+	0.0169645i	−0.576049	+	0.817415i	$0.695406\pi$
$312$	13.5514	−	9.84565i	0.767196	−	0.557400i
$313$	−7.12651	+	21.9331i	−0.402814	+	1.23973i	0.519893	+	0.854232i	$0.325972\pi$
$313$	−7.12651	+	21.9331i	−0.402814	+	1.23973i	−0.922707	+	0.385503i	$0.874028\pi$
$314$	2.40888	−	7.41378i	0.135941	−	0.418384i
$315$	−47.1146	+	34.2308i	−2.65461	+	1.92869i
$316$	−2.32542	−	1.68951i	−0.130815	−	0.0950426i
$317$	−10.0267	−	30.8590i	−0.563155	−	1.73321i	−0.673370	−	0.739305i	$-0.735154\pi$
$317$	−10.0267	−	30.8590i	−0.563155	−	1.73321i	0.110215	−	0.993908i	$-0.464846\pi$
$318$	−22.4461			−1.25872
$319$	−6.77407	+	0.221595i	−0.379275	+	0.0124070i
$320$	14.1912			0.793311
$321$	−7.77217	−	23.9203i	−0.433800	−	1.33510i
$322$	−9.46564	−	6.87719i	−0.527499	−	0.383251i
$323$	−2.30252	+	1.67288i	−0.128115	+	0.0930813i
$324$	6.48381	−	19.9551i	0.360211	−	1.10862i
$325$	4.30003	−	13.2341i	0.238523	−	0.734098i
$326$	−1.83655	+	1.33433i	−0.101717	+	0.0739018i
$327$	21.1847	+	15.3916i	1.17152	+	0.851156i
$328$	−3.06757	−	9.44102i	−0.169378	−	0.521293i
$329$	−6.16841			−0.340076
$330$	20.4742	+	56.6407i	1.12707	+	3.11797i
$331$	18.5019			1.01695			0.508477	−	0.861075i	$-0.330209\pi$
$331$	18.5019			1.01695			0.508477	+	0.861075i	$0.330209\pi$
$332$	0.245763	+	0.756380i	0.0134880	+	0.0415117i
$333$	30.9340	+	22.4749i	1.69517	+	1.23162i
$334$	23.5018	−	17.0751i	1.28596	−	0.934306i
$335$	−13.1342	+	40.4228i	−0.717597	+	2.20854i
$336$	10.6232	−	32.6949i	0.579543	−	1.78365i
$337$	−2.44159	+	1.77392i	−0.133002	+	0.0966313i	−0.652297	−	0.757964i	$-0.726194\pi$
$337$	−2.44159	+	1.77392i	−0.133002	+	0.0966313i	0.519295	+	0.854595i	$0.326194\pi$
$338$	−10.4721	−	7.60845i	−0.569609	−	0.413845i
$339$	14.0844	+	43.3473i	0.764959	+	2.35430i
$340$	−2.07047			−0.112287
$341$	−3.32102	+	11.4861i	−0.179843	+	0.622006i
$342$	37.8675			2.04764
$343$	−6.22625	−	19.1624i	−0.336186	−	1.03467i
$344$	10.3946	+	7.55208i	0.560437	+	0.407181i
$345$	−31.0574	+	22.5645i	−1.67208	+	1.21483i
$346$	0.883089	−	2.71787i	0.0474752	−	0.146114i
$347$	9.70370	−	29.8649i	0.520922	−	1.60323i	−0.251320	−	0.967904i	$-0.580865\pi$
$347$	9.70370	−	29.8649i	0.520922	−	1.60323i	0.772242	−	0.635328i	$-0.219135\pi$
$348$	−3.42303	+	2.48698i	−0.183494	+	0.133316i
$349$	−14.6012	−	10.6084i	−0.781585	−	0.567855i	0.123869	−	0.992299i	$-0.460470\pi$
$349$	−14.6012	−	10.6084i	−0.781585	−	0.567855i	−0.905454	+	0.424444i	$0.860470\pi$
$350$	−6.57784	−	20.2445i	−0.351600	−	1.08211i
$351$	−39.1261			−2.08840
$352$	−9.28522	−	6.29280i	−0.494904	−	0.335408i
$353$	21.1643			1.12646			0.563230	−	0.826300i	$-0.309558\pi$
$353$	21.1643			1.12646			0.563230	+	0.826300i	$0.309558\pi$
$354$	−5.02513	−	15.4658i	−0.267082	−	0.821995i
$355$	20.6568	+	15.0081i	1.09635	+	0.796545i
$356$	4.82719	−	3.50716i	0.255840	−	0.185879i
$357$	2.18850	−	6.73551i	0.115828	−	0.356481i
$358$	−6.51238	+	20.0430i	−0.344190	+	1.05931i
$359$	−6.23420	+	4.52941i	−0.329029	+	0.239053i	−0.740018	−	0.672587i	$-0.765183\pi$
$359$	−6.23420	+	4.52941i	−0.329029	+	0.239053i	0.410990	+	0.911640i	$0.365183\pi$
$360$	−49.8348	−	36.2071i	−2.62652	−	1.90828i
$361$	−3.36825	−	10.3664i	−0.177277	−	0.545601i
$362$	−20.1970			−1.06153
$363$	−9.07271	+	35.7166i	−0.476194	+	1.87464i
$364$	2.92150			0.153128
$365$	−3.70419	−	11.4003i	−0.193886	−	0.596720i
$366$	−57.3417	−	41.6612i	−2.99730	−	2.17767i
$367$	−10.9388	+	7.94748i	−0.570999	+	0.414855i	−0.835468	−	0.549539i	$-0.814803\pi$
$367$	−10.9388	+	7.94748i	−0.570999	+	0.414855i	0.264469	+	0.964394i	$0.414803\pi$
$368$	5.13083	−	15.7911i	0.267463	−	0.823166i
$369$	−11.2809	+	34.7190i	−0.587260	+	1.80740i
$370$	−20.3914	+	14.8152i	−1.06010	+	0.770205i
$371$	7.08214	+	5.14547i	0.367686	+	0.267140i
$372$	2.30653	+	7.09878i	0.119588	+	0.368055i
$373$	1.05737			0.0547487			0.0273743	−	0.999625i	$-0.491285\pi$
$373$	1.05737			0.0547487			0.0273743	+	0.999625i	$0.491285\pi$
$374$	−4.44233	−	3.01067i	−0.229707	−	0.155678i
$375$	−13.7266			−0.708837
$376$	−2.01619	−	6.20521i	−0.103977	−	0.320009i
$377$	3.69682	+	2.68590i	0.190396	+	0.138331i
$378$	−48.4212	+	35.1800i	−2.49052	+	1.80947i
$379$	2.40039	−	7.38764i	0.123300	−	0.379478i	−0.870288	−	0.492544i	$-0.836067\pi$
$379$	2.40039	−	7.38764i	0.123300	−	0.379478i	0.993587	+	0.113066i	$0.0360672\pi$
$380$	−1.82094	+	5.60428i	−0.0934123	+	0.287493i
$381$	−31.7739	+	23.0851i	−1.62783	+	1.18269i
$382$	0.521034	+	0.378553i	0.0266584	+	0.0193685i
$383$	6.66465	+	20.5117i	0.340548	+	1.04810i	0.963924	+	0.266177i	$0.0857605\pi$
$383$	6.66465	+	20.5117i	0.340548	+	1.04810i	−0.623376	+	0.781922i	$0.714240\pi$
$384$	45.6216			2.32812
$385$	6.52418	−	22.5645i	0.332503	−	1.15000i
$386$	24.1166			1.22750
$387$	−14.6009	−	44.9369i	−0.742205	−	2.28427i
$388$	4.73205	+	3.43804i	0.240233	+	0.174540i
$389$	−11.3022	+	8.21152i	−0.573044	+	0.416341i	−0.836210	−	0.548410i	$-0.815233\pi$
$389$	−11.3022	+	8.21152i	−0.573044	+	0.416341i	0.263166	+	0.964751i	$0.415233\pi$
$390$	12.5478	−	38.6181i	0.635381	−	1.95550i
$391$	1.05701	−	3.25314i	0.0534552	−	0.164518i
$392$	4.57850	−	3.32648i	0.231249	−	0.168012i
$393$	33.4053	+	24.2704i	1.68507	+	1.22428i
$394$	8.50737	+	26.1830i	0.428595	+	1.31908i
$395$	15.5807			0.783949
$396$	5.72998	+	15.8517i	0.287942	+	0.796578i
$397$	−8.14093			−0.408582			−0.204291	−	0.978910i	$-0.565489\pi$
$397$	−8.14093			−0.408582			−0.204291	+	0.978910i	$0.565489\pi$
$398$	−3.75428	−	11.5545i	−0.188185	−	0.579175i
$399$	−16.3067	−	11.8475i	−0.816358	−	0.593119i
$400$	24.4383	−	17.7555i	1.22192	−	0.887773i
$401$	10.9766	−	33.7825i	0.548146	−	1.68702i	−0.165245	−	0.986253i	$-0.552841\pi$
$401$	10.9766	−	33.7825i	0.548146	−	1.68702i	0.713391	−	0.700767i	$-0.247159\pi$
$402$	−21.2515	+	65.4055i	−1.05993	+	3.26213i
$403$	6.52157	−	4.73820i	0.324862	−	0.236026i
$404$	6.93222	+	5.03655i	0.344891	+	0.250578i
$405$	35.1458	+	108.168i	1.74641	+	5.37489i
$406$	6.99007			0.346911
$407$	−15.4138	+	0.504220i	−0.764033	+	0.0249933i
$408$	7.49102			0.370861
$409$	7.19639	+	22.1482i	0.355839	+	1.09516i	0.955522	+	0.294921i	$0.0952933\pi$
$409$	7.19639	+	22.1482i	0.355839	+	1.09516i	−0.599683	+	0.800238i	$0.704707\pi$
$410$	−19.4683	−	14.1446i	−0.961472	−	0.698550i
$411$	13.8898	−	10.0915i	0.685133	−	0.497778i
$412$	−1.78931	+	5.50694i	−0.0881531	+	0.271307i
$413$	−1.95980	+	6.03165i	−0.0964355	+	0.296798i
$414$	−36.8193	+	26.7508i	−1.80957	+	1.31473i
$415$	−3.48767	−	2.53394i	−0.171203	−	0.124386i
$416$	2.33688	+	7.19218i	0.114575	+	0.352626i
$417$	63.5775			3.11341
$418$	−12.0561	+	9.37653i	−0.589685	+	0.458621i
$419$	−5.41697			−0.264636			−0.132318	−	0.991207i	$-0.542242\pi$
$419$	−5.41697			−0.264636			−0.132318	+	0.991207i	$0.542242\pi$
$420$	−4.53122	−	13.9456i	−0.221101	−	0.680478i
$421$	0.0181693	+	0.0132007i	0.000885515	+	0.000643364i	0.588228	−	0.808695i	$-0.299826\pi$
$421$	0.0181693	+	0.0132007i	0.000885515	+	0.000643364i	−0.587342	+	0.809339i	$0.699826\pi$
$422$	9.73540	−	7.07318i	0.473912	−	0.344317i
$423$	−7.41449	+	22.8195i	−0.360505	+	1.10952i
$424$	−2.86131	+	8.80622i	−0.138958	+	0.427668i
$425$	5.03457	−	3.65783i	0.244212	−	0.177431i
$426$	33.4234	+	24.2836i	1.61937	+	1.17654i
$427$	8.54202	+	26.2896i	0.413377	+	1.27224i
$428$	4.63998			0.224282
$429$	19.6117	−	15.2528i	0.946864	−	0.736413i
$430$	31.1463			1.50201
$431$	4.18292	+	12.8737i	0.201484	+	0.620104i	0.999839	+	0.0179178i	$0.00570371\pi$
$431$	4.18292	+	12.8737i	0.201484	+	0.620104i	−0.798355	+	0.602187i	$0.794296\pi$
$432$	−68.7144	−	49.9240i	−3.30603	−	2.40197i
$433$	3.17497	−	2.30675i	0.152579	−	0.110855i	−0.508876	−	0.860840i	$-0.669939\pi$
$433$	3.17497	−	2.30675i	0.152579	−	0.110855i	0.661456	+	0.749984i	$0.269939\pi$
$434$	3.81055	−	11.7277i	0.182912	−	0.562946i
$435$	7.08728	−	21.8124i	0.339809	−	1.04582i
$436$	−3.90822	+	2.83949i	−0.187170	+	0.135987i
$437$	−7.87588	−	5.72216i	−0.376754	−	0.273728i
$438$	−5.99350	−	18.4461i	−0.286381	−	0.881389i
$439$	−19.4557			−0.928568			−0.464284	−	0.885686i	$-0.653688\pi$
$439$	−19.4557			−0.928568			−0.464284	+	0.885686i	$0.653688\pi$
$440$	24.8316	−	0.812299i	1.18380	−	0.0387248i
$441$	−20.8120			−0.991049
$442$	1.11803	+	3.44095i	0.0531795	+	0.163670i
$443$	15.7252	+	11.4250i	0.747128	+	0.542820i	0.894935	−	0.446196i	$-0.147222\pi$
$443$	15.7252	+	11.4250i	0.747128	+	0.542820i	−0.147807	+	0.989016i	$0.547222\pi$
$444$	−7.78881	+	5.65890i	−0.369640	+	0.268559i
$445$	−9.99453	+	30.7600i	−0.473786	+	1.45816i
$446$	−1.82943	+	5.63042i	−0.0866262	+	0.266608i
$447$	33.3857	−	24.2561i	1.57909	−	1.14728i
$448$	−7.24484	−	5.26369i	−0.342287	−	0.248686i
$449$	−4.05255	−	12.4725i	−0.191252	−	0.588612i	−1.00000		0.000457184i	$-0.999854\pi$
$449$	−4.05255	−	12.4725i	−0.191252	−	0.588612i	0.808748	−	0.588155i	$-0.200146\pi$
$450$	−82.7992			−3.90319
$451$	−5.00535	−	13.8470i	−0.235693	−	0.652032i
$452$	−8.40837			−0.395497
$453$	−5.58229	−	17.1805i	−0.262279	−	0.807212i
$454$	26.8784	+	19.5283i	1.26146	+	0.916507i
$455$	−12.8117	+	9.30825i	−0.600622	+	0.436377i
$456$	6.58822	−	20.2765i	0.308522	−	0.949533i
$457$	−11.4605	+	35.2719i	−0.536101	+	1.64995i	0.205158	+	0.978729i	$0.434229\pi$
$457$	−11.4605	+	35.2719i	−0.536101	+	1.64995i	−0.741259	+	0.671219i	$0.765771\pi$
$458$	37.7290	−	27.4117i	1.76296	−	1.28086i
$459$	−14.1560	−	10.2849i	−0.660743	−	0.480058i
$460$	−2.18850	−	6.73551i	−0.102039	−	0.314045i
$461$	−38.2452			−1.78126			−0.890628	−	0.454733i	$-0.849735\pi$
$461$	−38.2452			−1.78126			−0.890628	+	0.454733i	$0.849735\pi$
$462$	10.5563	−	36.5102i	0.491126	−	1.69861i
$463$	−37.6104			−1.74790			−0.873952	−	0.486012i	$-0.838451\pi$
$463$	−37.6104			−1.74790			−0.873952	+	0.486012i	$0.838451\pi$
$464$	3.06533	+	9.43410i	0.142304	+	0.437967i
$465$	−32.7325	−	23.7815i	−1.51793	−	1.10284i
$466$	20.5888	−	14.9586i	0.953756	−	0.692944i
$467$	−0.493296	+	1.51821i	−0.0228270	+	0.0702544i	−0.961821	−	0.273679i	$-0.911759\pi$
$467$	−0.493296	+	1.51821i	−0.0228270	+	0.0702544i	0.938994	+	0.343933i	$0.111759\pi$
$468$	3.51167	−	10.8078i	0.162327	−	0.499591i
$469$	21.6986	−	15.7649i	1.00195	−	0.727957i
$470$	−12.7958	−	9.29667i	−0.590225	−	0.428823i
$471$	4.98751	+	15.3500i	0.229812	+	0.707289i
$472$	−6.70820			−0.308770
$473$	15.7756	+	10.6915i	0.725363	+	0.491595i
$474$	25.2101			1.15794
$475$	−5.47308	−	16.8444i	−0.251122	−	0.772875i
$476$	1.05701	+	0.767962i	0.0484479	+	0.0351995i
$477$	27.5480	−	20.0148i	1.26134	−	0.916414i
$478$	−0.0204158	+	0.0628334i	−0.000933797	+	0.00287393i
$479$	10.9061	−	33.5657i	0.498314	−	1.53365i	−0.313412	−	0.949617i	$-0.601472\pi$
$479$	10.9061	−	33.5657i	0.498314	−	1.53365i	0.811727	−	0.584037i	$-0.198528\pi$
$480$	30.7071	−	22.3100i	1.40158	−	1.01831i
$481$	8.41178	+	6.11151i	0.383544	+	0.278661i
$482$	4.53122	+	13.9456i	0.206391	+	0.635207i
$483$	24.2248			1.10227
$484$	−5.74940	−	3.62799i	−0.261336	−	0.164909i
$485$	−31.7055			−1.43967
$486$	30.6205	+	94.2403i	1.38897	+	4.27482i
$487$	15.3979	+	11.1872i	0.697746	+	0.506942i	0.879197	−	0.476458i	$-0.158080\pi$
$487$	15.3979	+	11.1872i	0.697746	+	0.506942i	−0.181452	+	0.983400i	$0.558080\pi$
$488$	−23.6544	+	17.1859i	−1.07079	+	0.777971i
$489$	1.45243	−	4.47013i	0.0656813	−	0.202146i
$490$	4.23942	−	13.0476i	0.191517	−	0.589430i
$491$	−6.17497	+	4.48638i	−0.278672	+	0.202467i	−0.718338	−	0.695694i	$-0.755097\pi$
$491$	−6.17497	+	4.48638i	−0.278672	+	0.202467i	0.439666	+	0.898161i	$0.355097\pi$
$492$	−7.43624	−	5.40274i	−0.335251	−	0.243574i
$493$	0.631492	+	1.94353i	0.0284410	+	0.0875323i
$494$	10.2972			0.463292
$495$	−75.6332	−	51.2584i	−3.39946	−	2.30389i
$496$	17.4992			0.785737
$497$	−4.97899	−	15.3237i	−0.223338	−	0.687364i
$498$	−5.64316	−	4.10000i	−0.252876	−	0.183725i
$499$	1.06123	−	0.771031i	0.0475073	−	0.0345161i	−0.563778	−	0.825926i	$-0.690653\pi$
$499$	1.06123	−	0.771031i	0.0475073	−	0.0345161i	0.611285	+	0.791410i	$0.290653\pi$
$500$	0.782530	−	2.40838i	0.0349958	−	0.107706i
$501$	−18.5864	+	57.2029i	−0.830377	+	2.55564i
$502$	12.5191	−	9.09565i	0.558754	−	0.405959i
$503$	−25.3987	−	18.4533i	−1.13247	−	0.822790i	−0.146420	−	0.989222i	$-0.546775\pi$
$503$	−25.3987	−	18.4533i	−1.13247	−	0.822790i	−0.986053	+	0.166433i	$0.946775\pi$
$504$	12.0118	+	36.9687i	0.535050	+	1.64671i
$505$	−46.4471			−2.06687
$506$	5.09853	−	17.6338i	0.226657	−	0.783918i
$507$	26.8007			1.19026
$508$	−2.23899	−	6.89091i	−0.0993392	−	0.305734i
$509$	23.2668	+	16.9043i	1.03128	+	0.749272i	0.968565	−	0.248760i	$-0.0800230\pi$
$509$	23.2668	+	16.9043i	1.03128	+	0.749272i	0.0627186	+	0.998031i	$0.480023\pi$
$510$	14.6912	−	10.6738i	0.650537	−	0.472643i
$511$	−2.33747	+	7.19398i	−0.103403	+	0.318243i
$512$	1.63525	−	5.03280i	0.0722687	−	0.222420i
$513$	−40.2888	+	29.2715i	−1.77879	+	1.29237i
$514$	20.5089	+	14.9006i	0.904607	+	0.657235i
$515$	−9.69906	−	29.8507i	−0.427392	−	1.31538i
$516$	11.8968			0.523729
$517$	−3.28982	−	9.10112i	−0.144686	−	0.400267i
$518$	15.9053			0.698838
$519$	1.82841	+	5.62726i	0.0802581	+	0.247009i
$520$	−13.5514	−	9.84565i	−0.594267	−	0.431760i
$521$	−6.82020	+	4.95516i	−0.298798	+	0.217090i	−0.727075	−	0.686558i	$-0.759121\pi$
$521$	−6.82020	+	4.95516i	−0.298798	+	0.217090i	0.428277	+	0.903648i	$0.359121\pi$
$522$	8.40213	−	25.8591i	0.367751	−	1.13182i
$523$	−5.38043	+	16.5593i	−0.235270	+	0.724086i	0.761816	+	0.647794i	$0.224308\pi$
$523$	−5.38043	+	16.5593i	−0.235270	+	0.724086i	−0.997085	+	0.0762923i	$0.975692\pi$
$524$	−6.16271	+	4.47747i	−0.269219	+	0.195599i
$525$	35.6555	+	25.9052i	1.55613	+	1.13060i
$526$	9.02692	+	27.7820i	0.393592	+	1.21135i
$527$	3.60503			0.157038
$528$	53.9050	−	1.76336i	2.34591	−	0.0767402i
$529$	−11.2998			−0.491297
$530$	6.93624	+	21.3475i	0.301291	+	0.927278i
$531$	19.9578	+	14.5002i	0.866095	+	0.629255i
$532$	3.00832	−	2.18567i	0.130427	−	0.0947608i
$533$	−3.06757	+	9.44102i	−0.132871	+	0.408936i
$534$	−16.1715	+	49.7707i	−0.699809	+	2.15379i
$535$	−20.3478	+	14.7835i	−0.879712	+	0.639148i
$536$	22.9513	+	16.6751i	0.991345	+	0.720255i
$537$	−13.4837	−	41.4985i	−0.581863	−	1.79079i
$538$	−0.518348			−0.0223475
$539$	6.62607	−	5.15335i	0.285405	−	0.221971i
$540$	−36.2284			−1.55902
$541$	2.56901	+	7.90660i	0.110450	+	0.339931i	0.990971	−	0.134077i	$-0.0428068\pi$
$541$	2.56901	+	7.90660i	0.110450	+	0.339931i	−0.880521	+	0.474008i	$0.842807\pi$
$542$	−29.1249	−	21.1605i	−1.25102	−	0.908922i
$543$	33.8308	−	24.5795i	1.45182	−	1.05481i
$544$	−1.04508	+	3.21644i	−0.0448076	+	0.137904i
$545$	8.09183	−	24.9041i	0.346616	−	1.06677i
$546$	−20.7298	+	15.0611i	−0.887152	+	0.644554i
$547$	31.8640	+	23.1506i	1.36241	+	0.989847i	0.998288	+	0.0584947i	$0.0186301\pi$
$547$	31.8640	+	23.1506i	1.36241	+	0.989847i	0.364120	+	0.931352i	$0.381370\pi$
$548$	0.978762	+	3.01232i	0.0418106	+	0.128680i
$549$	107.524			4.58899
$550$	26.3613	−	20.5022i	1.12405	−	0.874219i
$551$	5.81608			0.247773
$552$	7.91807	+	24.3693i	0.337015	+	1.03723i
$553$	−7.95420	−	5.77907i	−0.338247	−	0.245751i
$554$	28.3207	−	20.5762i	1.20323	−	0.874198i
$555$	16.1265	−	49.6321i	0.684530	−	2.10677i
$556$	−3.62445	+	11.1549i	−0.153711	+	0.473074i
$557$	−17.6992	+	12.8592i	−0.749940	+	0.544863i	−0.895808	−	0.444441i	$-0.853402\pi$
$557$	−17.6992	+	12.8592i	−0.749940	+	0.544863i	0.145868	+	0.989304i	$0.453402\pi$
$558$	−38.8051	−	28.1935i	−1.64275	−	1.19353i
$559$	−3.97037	−	12.2195i	−0.167929	−	0.516831i
$560$	−34.3774			−1.45271
$561$	11.1050	−	0.363271i	0.468855	−	0.0153373i
$562$	4.10317			0.173082
$563$	−1.79072	−	5.51127i	−0.0754699	−	0.232273i	0.906204	−	0.422841i	$-0.138967\pi$
$563$	−1.79072	−	5.51127i	−0.0754699	−	0.232273i	−0.981674	+	0.190568i	$0.938967\pi$
$564$	−4.88755	−	3.55101i	−0.205803	−	0.149525i
$565$	36.8734	−	26.7901i	1.55128	−	1.12707i
$566$	14.0129	−	43.1274i	0.589008	−	1.81278i
$567$	22.1782	−	68.2574i	0.931396	−	2.86654i
$568$	13.7877	−	10.0174i	0.578520	−	0.420320i
$569$	−18.0024	−	13.0795i	−0.754698	−	0.548320i	0.142581	−	0.989783i	$-0.454460\pi$
$569$	−18.0024	−	13.0795i	−0.754698	−	0.548320i	−0.897280	+	0.441463i	$0.854460\pi$
$570$	−15.9708	−	49.1531i	−0.668943	−	2.05880i
$571$	−2.88016			−0.120531			−0.0602655	−	0.998182i	$-0.519195\pi$
$571$	−2.88016			−0.120531			−0.0602655	+	0.998182i	$0.519195\pi$
$572$	1.55813	+	4.31049i	0.0651488	+	0.180231i
$573$	−1.33345			−0.0557057
$574$	4.69252	+	14.4421i	0.195862	+	0.602801i
$575$	17.2210	+	12.5118i	0.718165	+	0.521778i
$576$	−28.1809	+	20.4746i	−1.17420	+	0.853108i
$577$	0.676685	−	2.08262i	0.0281708	−	0.0867007i	−0.935983	−	0.352046i	$-0.885486\pi$
$577$	0.676685	−	2.08262i	0.0281708	−	0.0867007i	0.964153	+	0.265345i	$0.0854860\pi$
$578$	−0.500000	+	1.53884i	−0.0207973	+	0.0640074i
$579$	−40.3963	+	29.3496i	−1.67881	+	1.21973i
$580$	3.42303	+	2.48698i	0.142134	+	0.103266i
$581$	0.840644	+	2.58724i	0.0348758	+	0.107337i
$582$	−51.3006			−2.12648
$583$	−3.81469	+	13.1935i	−0.157989	+	0.546419i
$584$	−8.00092			−0.331080
$585$	19.0352	+	58.5843i	0.787008	+	2.42216i
$586$	8.65964	+	6.29159i	0.357726	+	0.259903i
$587$	−20.5765	+	14.9497i	−0.849281	+	0.617039i	−0.924948	−	0.380094i	$-0.875892\pi$
$587$	−20.5765	+	14.9497i	−0.849281	+	0.617039i	0.0756665	+	0.997133i	$0.475892\pi$
$588$	1.61931	−	4.98374i	0.0667794	−	0.205526i
$589$	3.17057	−	9.75800i	0.130641	−	0.402071i
$590$	−13.1560	+	9.55836i	−0.541622	+	0.393511i
$591$	−46.1146	−	33.5042i	−1.89690	−	1.37818i
$592$	6.97487	+	21.4665i	0.286666	+	0.882266i
$593$	18.3255			0.752537			0.376269	−	0.926511i	$-0.377207\pi$
$593$	18.3255			0.752537			0.376269	+	0.926511i	$0.377207\pi$
$594$	−77.7306	−	52.6798i	−3.18932	−	2.16148i
$595$	−7.08214			−0.290339
$596$	2.35257	+	7.24046i	0.0963649	+	0.296581i
$597$	20.3503	+	14.7854i	0.832882	+	0.605124i
$598$	−10.0121	+	7.27424i	−0.409426	+	0.297466i
$599$	−10.1214	+	31.1506i	−0.413551	+	1.27278i	0.499990	+	0.866031i	$0.333337\pi$
$599$	−10.1214	+	31.1506i	−0.413551	+	1.27278i	−0.913541	+	0.406747i	$0.866663\pi$
$600$	−14.4055	+	44.3355i	−0.588101	+	1.80999i
$601$	23.4612	−	17.0455i	0.957001	−	0.695302i	0.00454837	−	0.999990i	$-0.498552\pi$
$601$	23.4612	−	17.0455i	0.957001	−	0.695302i	0.952452	+	0.304688i	$0.0985522\pi$
$602$	−15.9007	−	11.5526i	−0.648065	−	0.470847i
$603$	−32.2390	−	99.2213i	−1.31287	−	4.04060i
$604$	3.33263			0.135603
$605$	36.7721	−	2.40838i	1.49500	−	0.0979146i
$606$	−75.1529			−3.05288
$607$	−7.95563	−	24.4849i	−0.322909	−	0.993812i	−0.972376	−	0.233422i	$-0.925008\pi$
$607$	−7.95563	−	24.4849i	−0.322909	−	0.993812i	0.649467	−	0.760390i	$-0.274992\pi$
$608$	7.78703	+	5.65761i	0.315806	+	0.229446i
$609$	−11.7087	+	8.50684i	−0.474459	+	0.344715i
$610$	−21.9026	+	67.4092i	−0.886810	+	2.72932i
$611$	−2.01619	+	6.20521i	−0.0815665	+	0.251036i
$612$	4.11153	−	2.98720i	0.166199	−	0.120751i
$613$	2.90486	+	2.11051i	0.117326	+	0.0852426i	0.644901	−	0.764266i	$-0.276899\pi$
$613$	2.90486	+	2.11051i	0.117326	+	0.0852426i	−0.527575	+	0.849509i	$0.676899\pi$
$614$	11.8850	+	36.5784i	0.479641	+	1.47618i
$615$	49.8241			2.00910
$616$	−12.9783	−	8.79566i	−0.522909	−	0.354387i
$617$	46.2052			1.86015			0.930075	−	0.367370i	$-0.119742\pi$
$617$	46.2052			1.86015			0.930075	+	0.367370i	$0.119742\pi$
$618$	−15.6934	−	48.2994i	−0.631282	−	1.94289i
$619$	−28.5338	−	20.7310i	−1.14687	−	0.833249i	−0.158808	−	0.987310i	$-0.550765\pi$
$619$	−28.5338	−	20.7310i	−1.14687	−	0.833249i	−0.988061	+	0.154060i	$0.950765\pi$
$620$	6.03859	−	4.38729i	0.242515	−	0.176198i
$621$	18.4952	−	56.9225i	0.742188	−	2.28422i
$622$	0.254491	−	0.783244i	0.0102042	−	0.0314052i
$623$	16.5116	−	11.9964i	0.661525	−	0.480626i
$624$	−29.4176	−	21.3731i	−1.17765	−	0.855610i
$625$	−5.37342	−	16.5377i	−0.214937	−	0.661508i
$626$	37.3149			1.49140
$627$	8.78340	−	30.3783i	0.350775	−	1.21319i
$628$	−2.97754			−0.118817
$629$	1.43690	+	4.42233i	0.0572931	+	0.176330i
$630$	76.2331	+	55.3866i	3.03720	+	2.20665i
$631$	23.8039	−	17.2945i	0.947617	−	0.688484i	−0.00262488	−	0.999997i	$-0.500836\pi$
$631$	23.8039	−	17.2945i	0.947617	−	0.688484i	0.950242	+	0.311512i	$0.100836\pi$
$632$	3.21365	−	9.89058i	0.127832	−	0.393426i
$633$	−7.69922	+	23.6958i	−0.306017	+	0.941822i
$634$	−42.4737	+	30.8590i	−1.68685	+	1.22557i
$635$	31.7739	+	23.0851i	1.26091	+	0.916105i
$636$	2.64941	+	8.15404i	0.105056	+	0.323329i
$637$	−5.65934			−0.224231
$638$	3.72803	+	10.3134i	0.147594	+	0.408312i
$639$	−62.6735			−2.47933
$640$	−14.0978	−	43.3887i	−0.557266	−	1.71509i
$641$	31.4482	+	22.8484i	1.24213	+	0.902458i	0.997738	−	0.0672187i	$-0.0214125\pi$
$641$	31.4482	+	22.8484i	1.24213	+	0.902458i	0.244389	+	0.969677i	$0.421413\pi$
$642$	−32.9234	+	23.9203i	−1.29938	+	0.944058i
$643$	−0.662582	+	2.03922i	−0.0261297	+	0.0804189i	−0.963271	−	0.268531i	$-0.913462\pi$
$643$	−0.662582	+	2.03922i	−0.0261297	+	0.0804189i	0.937141	+	0.348950i	$0.113462\pi$
$644$	−1.38102	+	4.25034i	−0.0544197	+	0.167487i
$645$	−52.1714	+	37.9047i	−2.05425	+	1.49250i
$646$	3.72555	+	2.70677i	0.146580	+	0.106496i
$647$	9.06724	+	27.9061i	0.356470	+	1.09710i	0.955152	+	0.296115i	$0.0956912\pi$
$647$	9.06724	+	27.9061i	0.356470	+	1.09710i	−0.598682	+	0.800987i	$0.704309\pi$
$648$	75.9137			2.98217
$649$	−9.94455	+	0.325309i	−0.390358	+	0.0127695i
$650$	−22.5153			−0.883122
$651$	7.88962	+	24.2817i	0.309219	+	0.951677i
$652$	0.701500	+	0.509670i	0.0274729	+	0.0199602i
$653$	5.99384	−	4.35478i	0.234557	−	0.170416i	−0.464298	−	0.885679i	$-0.653693\pi$
$653$	5.99384	−	4.35478i	0.234557	−	0.170416i	0.698855	+	0.715263i	$0.253693\pi$
$654$	13.0929	−	40.2957i	0.511971	−	1.57569i
$655$	12.7597	−	39.2703i	0.498562	−	1.53442i
$656$	−17.4339	+	12.6665i	−0.680679	+	0.494542i
$657$	23.8038	+	17.2945i	0.928675	+	0.674722i
$658$	3.08421	+	9.49221i	0.120235	+	0.370045i
$659$	−23.8797			−0.930223			−0.465111	−	0.885252i	$-0.653986\pi$
$659$	−23.8797			−0.930223			−0.465111	+	0.885252i	$0.653986\pi$
$660$	18.1593	−	14.1232i	0.706850	−	0.549745i
$661$	−1.12180			−0.0436328			−0.0218164	−	0.999762i	$-0.506945\pi$
$661$	−1.12180			−0.0436328			−0.0218164	+	0.999762i	$0.506945\pi$
$662$	−9.25093	−	28.4714i	−0.359548	−	1.10657i
$663$	−6.06036	−	4.40311i	−0.235365	−	0.171003i
$664$	−2.32790	+	1.69132i	−0.0903400	+	0.0656358i
$665$	−6.22862	+	19.1697i	−0.241536	+	0.743370i
$666$	19.1183	−	58.8400i	0.740818	−	2.28000i
$667$	−5.65508	+	4.10866i	−0.218966	+	0.159088i
$668$	−8.97689	−	6.52210i	−0.347326	−	0.252347i
$669$	−3.78778	−	11.6576i	−0.146444	−	0.450708i
$670$	68.7715			2.65687
$671$	−34.2330	+	26.6243i	−1.32155	+	1.02782i
$672$	−23.9515			−0.923951
$673$	4.97873	+	15.3230i	0.191916	+	0.590657i	0.999999	+	0.00158780i	$0.000505413\pi$
$673$	4.97873	+	15.3230i	0.191916	+	0.590657i	−0.808083	+	0.589069i	$0.799495\pi$
$674$	3.95057	+	2.87026i	0.152170	+	0.110558i
$675$	88.0935	−	64.0036i	3.39072	−	2.46350i
$676$	−1.52786	+	4.70228i	−0.0587640	+	0.180857i
$677$	2.24745	−	6.91695i	0.0863767	−	0.265840i	−0.898534	−	0.438904i	$-0.855367\pi$
$677$	2.24745	−	6.91695i	0.0863767	−	0.265840i	0.984911	+	0.173064i	$0.0553668\pi$
$678$	59.6624	−	43.3473i	2.29132	−	1.66474i
$679$	16.1862	+	11.7600i	0.621170	+	0.451307i
$680$	−2.31485	−	7.12438i	−0.0887705	−	0.273208i
$681$	−68.7881			−2.63597
$682$	19.3358	−	0.632517i	0.740404	−	0.0242203i
$683$	10.1848			0.389712			0.194856	−	0.980832i	$-0.437576\pi$
$683$	10.1848			0.389712			0.194856	+	0.980832i	$0.437576\pi$
$684$	−4.46965	−	13.7562i	−0.170901	−	0.525981i
$685$	−13.8898	−	10.0915i	−0.530702	−	0.385577i
$686$	−26.3748	+	19.1624i	−1.00699	+	0.731624i
$687$	−29.8379	+	91.8315i	−1.13839	+	3.50359i
$688$	8.61895	−	26.5264i	0.328594	−	1.01131i
$689$	7.49102	−	5.44254i	0.285385	−	0.207344i
$690$	50.2520	+	36.5102i	1.91306	+	1.38992i
$691$	0.603929	+	1.85870i	0.0229745	+	0.0707083i	0.961886	−	0.273449i	$-0.0881646\pi$
$691$	0.603929	+	1.85870i	0.0229745	+	0.0707083i	−0.938912	+	0.344158i	$0.888165\pi$
$692$	−1.09156			−0.0414948
$693$	19.5997	+	54.2216i	0.744531	+	2.05971i
$694$	−50.8092			−1.92869
$695$	−19.6465	−	60.4658i	−0.745236	−	2.29360i
$696$	−12.3847	−	8.99798i	−0.469439	−	0.341067i
$697$	−3.59158	+	2.60943i	−0.136041	+	0.0988393i
$698$	−9.02405	+	27.7732i	−0.341565	+	1.05123i
$699$	−16.2826	+	50.1126i	−0.615864	+	1.89543i
$700$	−6.57784	+	4.77908i	−0.248619	+	0.180632i
$701$	21.8314	+	15.8614i	0.824561	+	0.599079i	0.918015	−	0.396545i	$-0.129791\pi$
$701$	21.8314	+	15.8614i	0.824561	+	0.599079i	−0.0934544	+	0.995624i	$0.529791\pi$
$702$	19.5630	+	60.2089i	0.738360	+	2.27244i
$703$	13.2340			0.499129
$704$	3.90233	−	13.4966i	0.147075	−	0.508673i
$705$	32.7474			1.23334
$706$	−10.5821	−	32.5685i	−0.398264	−	1.22573i
$707$	23.7120	+	17.2278i	0.891782	+	0.647918i
$708$	−5.02513	+	3.65097i	−0.188856	+	0.137212i
$709$	12.6634	−	38.9740i	0.475585	−	1.46370i	−0.369582	−	0.929198i	$-0.620499\pi$
$709$	12.6634	−	38.9740i	0.475585	−	1.46370i	0.845167	−	0.534502i	$-0.179501\pi$
$710$	12.7666	−	39.2916i	0.479123	−	1.47459i
$711$	−30.9401	+	22.4793i	−1.16035	+	0.843040i
$712$	17.4649	+	12.6890i	0.654526	+	0.475541i
$713$	3.81055	+	11.7277i	0.142706	+	0.439205i
$714$	−11.4591			−0.428847
$715$	−20.5667	−	13.9385i	−0.769149	−	0.521270i
$716$	8.04975			0.300833
$717$	−0.0422702	−	0.130094i	−0.00157861	−	0.00485846i
$718$	10.0872	+	7.32875i	0.376449	+	0.273506i
$719$	−14.4239	+	10.4796i	−0.537921	+	0.390822i	−0.823312	−	0.567589i	$-0.807876\pi$
$719$	−14.4239	+	10.4796i	−0.537921	+	0.390822i	0.285391	+	0.958411i	$0.407876\pi$
$720$	−41.3220	+	127.176i	−1.53998	+	4.73957i
$721$	−6.12044	+	18.8368i	−0.227937	+	0.701518i
$722$	−14.2682	+	10.3664i	−0.531006	+	0.385798i
$723$	−24.5617	−	17.8451i	−0.913459	−	0.663667i
$724$	2.38393	+	7.33698i	0.0885980	+	0.272677i
$725$	−12.7172			−0.472303
$726$	59.4986	−	3.89684i	2.20820	−	0.144625i
$727$	−28.2450			−1.04755			−0.523774	−	0.851857i	$-0.675476\pi$
$727$	−28.2450			−1.04755			−0.523774	+	0.851857i	$0.675476\pi$
$728$	3.26634	+	10.0527i	0.121058	+	0.372580i
$729$	−83.5825	−	60.7263i	−3.09565	−	2.24912i
$730$	−15.6912	+	11.4003i	−0.580757	+	0.421945i
$731$	1.77560	−	5.46474i	0.0656730	−	0.202121i
$732$	−8.36604	+	25.7480i	−0.309218	+	0.951675i
$733$	−4.72245	+	3.43106i	−0.174428	+	0.126729i	−0.671574	−	0.740938i	$-0.734381\pi$
$733$	−4.72245	+	3.43106i	−0.174428	+	0.126729i	0.497146	+	0.867667i	$0.334381\pi$
$734$	17.6993	+	12.8593i	0.653293	+	0.474645i
$735$	8.77758	+	27.0146i	0.323766	+	0.996449i
$736$	−11.5682			−0.426409
$737$	34.8327	+	23.6069i	1.28308	+	0.869573i
$738$	59.0676			2.17431
$739$	6.84499	+	21.0667i	0.251797	+	0.774952i	0.994444	+	0.105269i	$0.0335702\pi$
$739$	6.84499	+	21.0667i	0.251797	+	0.774952i	−0.742647	+	0.669683i	$0.766430\pi$
$740$	7.78881	+	5.65890i	0.286322	+	0.208025i
$741$	−17.2482	+	12.5315i	−0.633628	+	0.460358i
$742$	4.37700	−	13.4710i	0.160685	−	0.494537i
$743$	3.49987	−	10.7715i	0.128398	−	0.395168i	−0.866107	−	0.499859i	$-0.833385\pi$
$743$	3.49987	−	10.7715i	0.128398	−	0.395168i	0.994505	+	0.104691i	$0.0333852\pi$
$744$	−21.8478	+	15.8734i	−0.800979	+	0.581946i
$745$	−33.3857	−	24.2561i	−1.22316	−	0.888677i
$746$	−0.528686	−	1.62713i	−0.0193566	−	0.0595734i
$747$	10.5817			0.387164
$748$	−0.569343	+	1.96913i	−0.0208172	+	0.0719985i
$749$	15.8713			0.579925
$750$	6.86329	+	21.1230i	0.250612	+	0.771304i
$751$	2.01709	+	1.46550i	0.0736048	+	0.0534770i	0.623979	−	0.781441i	$-0.285515\pi$
$751$	2.01709	+	1.46550i	0.0736048	+	0.0534770i	−0.550374	+	0.834918i	$0.685515\pi$
$752$	−11.4586	+	8.32516i	−0.417852	+	0.303587i
$753$	−9.90069	+	30.4712i	−0.360801	+	1.11043i
$754$	2.28476	−	7.03177i	0.0832060	−	0.256082i
$755$	−14.6146	+	10.6182i	−0.531881	+	0.386434i
$756$	18.4952	+	13.4376i	0.672665	+	0.488720i
$757$	−15.7625	−	48.5119i	−0.572897	−	1.76320i	−0.643231	−	0.765672i	$-0.722407\pi$
$757$	−15.7625	−	48.5119i	−0.572897	−	1.76320i	0.0703344	−	0.997523i	$-0.477593\pi$
$758$	−12.5686			−0.456512
$759$	12.9199	+	35.7422i	0.468962	+	1.29736i
$760$	−21.3199			−0.773356
$761$	−9.03362	−	27.8026i	−0.327468	−	1.00784i	−0.970314	−	0.241848i	$-0.922246\pi$
$761$	−9.03362	−	27.8026i	−0.327468	−	1.00784i	0.642846	−	0.765996i	$-0.277754\pi$
$762$	51.4113	+	37.3525i	1.86244	+	1.35314i
$763$	−13.3683	+	9.71261i	−0.483963	+	0.351620i
$764$	0.0760179	−	0.233959i	0.00275023	−	0.00846434i
$765$	−8.51279	+	26.1997i	−0.307781	+	0.947251i
$766$	28.2319	−	20.5117i	1.02006	−	0.741118i
$767$	5.42705	+	3.94298i	0.195959	+	0.142373i
$768$	−14.0401	−	43.2111i	−0.506630	−	1.55925i
$769$	28.2037			1.01705			0.508525	−	0.861047i	$-0.330191\pi$
$769$	28.2037			1.01705			0.508525	+	0.861047i	$0.330191\pi$
$770$	−37.9853	+	1.24259i	−1.36890	+	0.0447798i
$771$	−52.4870			−1.89027
$772$	−2.84658	−	8.76086i	−0.102451	−	0.315310i
$773$	25.3595	+	18.4247i	0.912117	+	0.662692i	0.941549	−	0.336875i	$-0.109370\pi$
$773$	25.3595	+	18.4247i	0.912117	+	0.662692i	−0.0294324	+	0.999567i	$0.509370\pi$
$774$	−61.8504	+	44.9369i	−2.22317	+	1.61522i
$775$	−6.93260	+	21.3364i	−0.249026	+	0.766425i
$776$	−6.53953	+	20.1266i	−0.234756	+	0.722503i
$777$	−26.6420	+	19.3566i	−0.955777	+	0.694412i
$778$	18.2873	+	13.2865i	0.655632	+	0.476345i
$779$	3.90441	+	12.0165i	0.139890	+	0.430537i
$780$	−15.5099			−0.555343
$781$	19.9538	−	15.5188i	0.714003	−	0.555308i
$782$	−5.53457			−0.197916
$783$	11.0497	+	34.0074i	0.394883	+	1.21532i
$784$	−9.93910	−	7.22118i	−0.354968	−	0.257899i
$785$	13.0575	−	9.48680i	0.466041	−	0.338599i
$786$	20.6456	−	63.5406i	0.736404	−	2.26642i
$787$	14.2982	−	44.0054i	0.509676	−	1.56862i	−0.283088	−	0.959094i	$-0.591359\pi$
$787$	14.2982	−	44.0054i	0.509676	−	1.56862i	0.792764	−	0.609529i	$-0.208641\pi$
$788$	8.50737	−	6.18097i	0.303062	−	0.220188i
$789$	−48.9309	−	35.5503i	−1.74198	−	1.26563i
$790$	−7.79034	−	23.9762i	−0.277168	−	0.853035i
$791$	−28.7613			−1.02263
$792$	−48.1387	+	37.4393i	−1.71053	+	1.33035i
$793$	29.2385			1.03829
$794$	4.07047	+	12.5276i	0.144455	+	0.444588i
$795$	−37.5982	−	27.3167i	−1.33347	−	0.968824i
$796$	−3.75428	+	2.72765i	−0.133067	+	0.0966789i
$797$	15.6331	−	48.1137i	0.553753	−	1.70428i	−0.145461	−	0.989364i	$-0.546467\pi$
$797$	15.6331	−	48.1137i	0.553753	−	1.70428i	0.699214	−	0.714912i	$-0.253533\pi$
$798$	−10.0781	+	31.0173i	−0.356762	+	1.09800i
$799$	−2.36060	+	1.71508i	−0.0835121	+	0.0606751i
$800$	−17.0267	−	12.3706i	−0.601986	−	0.437368i
$801$	−24.5324	−	75.5030i	−0.866810	−	2.66777i
$802$	−57.4743			−2.02949
$803$	−11.8609	+	0.387998i	−0.418563	+	0.0136922i
$804$	26.2684			0.926414
$805$	−7.48588	−	23.0392i	−0.263842	−	0.812024i
$806$	−10.5521	−	7.66656i	−0.371683	−	0.270043i
$807$	0.868254	−	0.630823i	0.0305640	−	0.0222060i
$808$	−9.58009	+	29.4845i	−0.337026	+	1.03726i
$809$	4.24177	−	13.0548i	0.149133	−	0.458984i	−0.848386	−	0.529377i	$-0.822426\pi$
$809$	4.24177	−	13.0548i	0.149133	−	0.458984i	0.997519	+	0.0703937i	$0.0224256\pi$
$810$	148.880	−	108.168i	5.23111	−	3.80062i
$811$	2.67803	+	1.94570i	0.0940384	+	0.0683229i	0.633811	−	0.773488i	$-0.281490\pi$
$811$	2.67803	+	1.94570i	0.0940384	+	0.0683229i	−0.539773	+	0.841811i	$0.681490\pi$
$812$	−0.825066	−	2.53929i	−0.0289541	−	0.0891117i
$813$	74.5376			2.61415
$814$	8.48280	+	23.4673i	0.297322	+	0.822527i
$815$	−4.70017			−0.164640
$816$	−5.02513	−	15.4658i	−0.175915	−	0.541410i
$817$	−13.2302	−	9.61229i	−0.462866	−	0.336292i
$818$	30.4844	−	22.1482i	1.06586	−	0.774394i
$819$	12.0118	−	36.9687i	0.419728	−	1.29179i
$820$	−2.84039	+	8.74182i	−0.0991907	+	0.305278i
$821$	−37.2296	+	27.0489i	−1.29932	+	0.944014i	−0.999949	−	0.0101219i	$-0.996778\pi$
$821$	−37.2296	+	27.0489i	−1.29932	+	0.944014i	−0.299375	+	0.954136i	$0.596778\pi$
$822$	−22.4742	−	16.3284i	−0.783876	−	0.569519i
$823$	−14.9608	−	46.0446i	−0.521501	−	1.60501i	−0.771134	−	0.636673i	$-0.780310\pi$
$823$	−14.9608	−	46.0446i	−0.521501	−	1.60501i	0.249633	−	0.968341i	$-0.419690\pi$
$824$	−20.9496			−0.729815
$825$	−19.2053	+	66.4236i	−0.668644	+	2.31257i
$826$	10.2617			0.357049
$827$	2.86546	+	8.81897i	0.0996417	+	0.306666i	0.988436	−	0.151642i	$-0.0484559\pi$
$827$	2.86546	+	8.81897i	0.0996417	+	0.306666i	−0.888794	+	0.458307i	$0.848456\pi$
$828$	14.0637	+	10.2179i	0.488748	+	0.355096i
$829$	−13.9990	+	10.1708i	−0.486204	+	0.353248i	−0.803723	−	0.595004i	$-0.797150\pi$
$829$	−13.9990	+	10.1708i	−0.486204	+	0.353248i	0.317519	+	0.948252i	$0.397150\pi$
$830$	−2.15550	+	6.63393i	−0.0748184	+	0.230267i
$831$	−22.3973	+	68.9319i	−0.776955	+	2.39122i
$832$	−7.66312	+	5.56758i	−0.265671	+	0.193021i
$833$	−2.04757	−	1.48765i	−0.0709440	−	0.0515438i
$834$	−31.7888	−	97.8358i	−1.10076	−	3.38778i
$835$	60.1467			2.08146
$836$	4.82926	+	3.27290i	0.167023	+	0.113196i
$837$	63.0799			2.18036
$838$	2.70849	+	8.33587i	0.0935631	+	0.287958i
$839$	7.28637	+	5.29386i	0.251554	+	0.182764i	0.706415	−	0.707798i	$-0.250311\pi$
$839$	7.28637	+	5.29386i	0.251554	+	0.182764i	−0.454862	+	0.890562i	$0.650311\pi$
$840$	42.9203	−	31.1834i	1.48089	−	1.07593i
$841$	−7.67101	+	23.6089i	−0.264517	+	0.814101i
$842$	0.0112292	−	0.0345600i	0.000386984	−	0.00119102i
$843$	−6.87298	+	4.99351i	−0.236718	+	0.171986i
$844$	−3.71859	−	2.70172i	−0.127999	−	0.0929969i
$845$	−8.28187	−	25.4890i	−0.284905	−	0.876847i
$846$	38.8228			1.33475
$847$	−19.6661	−	12.4097i	−0.675735	−	0.426403i
$848$	20.1005			0.690254
$849$	29.0133	+	89.2939i	0.995735	+	3.06456i
$850$	−8.14610	−	5.91849i	−0.279409	−	0.203003i
$851$	−12.8676	+	9.34888i	−0.441097	+	0.320476i
$852$	4.87641	−	15.0081i	0.167063	−	0.514168i
$853$	5.96136	−	18.3472i	0.204113	−	0.628196i	−0.795635	−	0.605776i	$-0.792863\pi$
$853$	5.96136	−	18.3472i	0.204113	−	0.628196i	0.999749	−	0.0224202i	$-0.00713716\pi$
$854$	36.1846	−	26.2896i	1.23821	−	0.899612i
$855$	63.4297	+	46.0844i	2.16925	+	1.57605i
$856$	5.18766	+	15.9660i	0.177311	+	0.545706i
$857$	−46.2512			−1.57991			−0.789955	−	0.613165i	$-0.789896\pi$
$857$	−46.2512			−1.57991			−0.789955	+	0.613165i	$0.789896\pi$
$858$	−33.2775	−	22.5530i	−1.13608	−	0.769945i
$859$	57.0054			1.94500			0.972500	−	0.232903i	$-0.0748224\pi$
$859$	57.0054			1.94500			0.972500	+	0.232903i	$0.0748224\pi$
$860$	−3.67632	−	11.3146i	−0.125362	−	0.385823i
$861$	−25.4360	−	18.4804i	−0.866858	−	0.629809i
$862$	17.7191	−	12.8737i	0.603516	−	0.438480i
$863$	−0.413575	+	1.27285i	−0.0140783	+	0.0433284i	−0.957849	−	0.287273i	$-0.907251\pi$
$863$	−0.413575	+	1.27285i	−0.0140783	+	0.0433284i	0.943771	+	0.330601i	$0.107251\pi$
$864$	−18.2866	+	56.2804i	−0.622123	+	1.91470i
$865$	4.78683	−	3.47784i	0.162757	−	0.118250i
$866$	−5.13720	−	3.73240i	−0.174569	−	0.126832i
$867$	−1.03523	−	3.18612i	−0.0351584	−	0.108206i
$868$	−4.71010			−0.159871
$869$	4.28442	−	14.8181i	0.145339	−	0.502670i
$870$	−37.1095			−1.25813
$871$	−8.76662	−	26.9809i	−0.297046	−	0.914212i
$872$	−14.1401	−	10.2734i	−0.478843	−	0.347900i
$873$	62.9609	−	45.7438i	2.13090	−	1.54819i
$874$	−4.86756	+	14.9808i	−0.164648	+	0.506733i
$875$	2.67668	−	8.23799i	0.0904885	−	0.278495i
$876$	−5.99350	+	4.35453i	−0.202502	+	0.147126i
$877$	−5.57128	−	4.04777i	−0.188129	−	0.136684i	0.489734	−	0.871872i	$-0.337094\pi$
$877$	−5.57128	−	4.04777i	−0.188129	−	0.136684i	−0.677863	+	0.735188i	$0.737094\pi$
$878$	9.72783	+	29.9392i	0.328298	+	1.01040i
$879$	−22.1621			−0.747508
$880$	−18.3346	−	50.7218i	−0.618059	−	1.70983i
$881$	−21.5904			−0.727401			−0.363700	−	0.931516i	$-0.618487\pi$
$881$	−21.5904			−0.727401			−0.363700	+	0.931516i	$0.618487\pi$
$882$	10.4060	+	32.0264i	0.350389	+	1.07839i
$883$	−6.98452	−	5.07455i	−0.235048	−	0.170772i	0.464026	−	0.885821i	$-0.346404\pi$
$883$	−6.98452	−	5.07455i	−0.235048	−	0.170772i	−0.699074	+	0.715049i	$0.746404\pi$
$884$	1.11803	−	0.812299i	0.0376036	−	0.0273206i
$885$	10.4044	−	32.0213i	0.349739	−	1.07638i
$886$	9.71872	−	29.9111i	0.326507	−	1.00488i
$887$	−37.5596	+	27.2887i	−1.26113	+	0.916264i	−0.998813	−	0.0487176i	$-0.984487\pi$
$887$	−37.5596	+	27.2887i	−1.26113	+	0.916264i	−0.262317	+	0.964982i	$0.584487\pi$
$888$	−28.1802	−	20.4741i	−0.945664	−	0.687065i
$889$	−7.65858	−	23.5707i	−0.256861	−	0.790536i
$890$	52.3320			1.75417
$891$	112.538	−	3.68138i	3.77017	−	0.123331i
$892$	2.26130			0.0757140
$893$	2.56621	+	7.89799i	0.0858750	+	0.264296i
$894$	−54.0192	−	39.2473i	−1.80667	−	1.31263i
$895$	−35.3007	+	25.6475i	−1.17997	+	0.857300i
$896$	−8.89621	+	27.3797i	−0.297202	+	0.914693i
$897$	7.91807	−	24.3693i	0.264377	−	0.813668i
$898$	−17.1669	+	12.4725i	−0.572866	+	0.416212i
$899$	−5.96008	−	4.33025i	−0.198780	−	0.144422i
$900$	9.77312	+	30.0786i	0.325771	+	1.00262i
$901$	4.14093			0.137954
$902$	−18.8057	+	14.6260i	−0.626163	+	0.486991i
$903$	40.6937			1.35420
$904$	−9.40085	−	28.9328i	−0.312668	−	0.962292i
$905$	−33.8308	−	24.5795i	−1.12457	−	0.817050i
$906$	−23.6470	+	17.1805i	−0.785618	+	0.570785i
$907$	8.38688	−	25.8122i	0.278482	−	0.857079i	−0.709795	−	0.704408i	$-0.751213\pi$
$907$	8.38688	−	25.8122i	0.278482	−	0.857079i	0.988277	−	0.152671i	$-0.0487874\pi$
$908$	3.92150	−	12.0691i	0.130140	−	0.400528i
$909$	92.2346	−	67.0124i	3.05923	−	2.22266i
$910$	20.7298	+	15.0611i	0.687185	+	0.499269i
$911$	16.5084	+	50.8076i	0.546947	+	1.68333i	0.716314	+	0.697778i	$0.245828\pi$
$911$	16.5084	+	50.8076i	0.546947	+	1.68333i	−0.169367	+	0.985553i	$0.554172\pi$
$912$	−46.2818			−1.53254
$913$	−3.36897	+	2.62018i	−0.111497	+	0.0867152i
$914$	60.0081			1.98489
$915$	−45.3486	−	139.569i	−1.49918	−	4.61399i
$916$	−14.4112	−	10.4703i	−0.476159	−	0.345950i
$917$	−21.0799	+	15.3154i	−0.696118	+	0.505759i
$918$	−8.74886	+	26.9262i	−0.288755	+	0.888698i
$919$	12.9521	−	39.8623i	0.427249	−	1.31494i	−0.473576	−	0.880753i	$-0.657037\pi$
$919$	12.9521	−	39.8623i	0.427249	−	1.31494i	0.900825	−	0.434183i	$-0.142963\pi$
$920$	20.7298	−	15.0611i	0.683440	−	0.496548i
$921$	−64.4234	−	46.8064i	−2.12282	−	1.54232i
$922$	19.1226	+	58.8533i	0.629769	+	1.93823i
$923$	−17.0426			−0.560963
$924$	−14.5091	+	0.474626i	−0.477315	+	0.0156141i
$925$	−28.9367			−0.951434
$926$	18.8052	+	57.8765i	0.617977	+	1.90194i
$927$	62.3280	+	45.2839i	2.04712	+	1.48732i
$928$	5.59129	−	4.06231i	0.183543	−	0.133352i
$929$	−11.5776	+	35.6321i	−0.379848	+	1.16905i	0.560301	+	0.828289i	$0.310685\pi$
$929$	−11.5776	+	35.6321i	−0.379848	+	1.16905i	−0.940149	+	0.340763i	$0.889315\pi$
$930$	−20.2298	+	62.2608i	−0.663360	+	2.04161i
$931$	−5.82752	+	4.23394i	−0.190989	+	0.138762i
$932$	−7.86421	−	5.71368i	−0.257601	−	0.187158i
$933$	0.526916	+	1.62168i	0.0172504	+	0.0530914i
$934$	2.58293			0.0845161
$935$	−3.77714	−	10.4493i	−0.123526	−	0.341727i
$936$	41.1153			1.34390
$937$	7.06535	+	21.7449i	0.230815	+	0.710376i	0.997649	+	0.0685302i	$0.0218310\pi$
$937$	7.06535	+	21.7449i	0.230815	+	0.710376i	−0.766834	+	0.641846i	$0.778169\pi$
$938$	−35.1090	−	25.5082i	−1.14635	−	0.832872i
$939$	−62.5040	+	45.4118i	−2.03974	+	1.48196i
$940$	−1.86688	+	5.74566i	−0.0608908	+	0.187403i
$941$	−13.3099	+	40.9638i	−0.433892	+	1.33538i	0.460326	+	0.887750i	$0.347732\pi$
$941$	−13.3099	+	40.9638i	−0.433892	+	1.33538i	−0.894218	+	0.447632i	$0.852268\pi$
$942$	21.1274	−	15.3500i	0.688369	−	0.500129i
$943$	−12.2852	−	8.92570i	−0.400060	−	0.290661i
$944$	4.50000	+	13.8496i	0.146463	+	0.450765i
$945$	−123.921			−4.03116
$946$	8.56470	−	29.6219i	0.278463	−	0.963091i
$947$	22.1196			0.718790			0.359395	−	0.933186i	$-0.382983\pi$
$947$	22.1196			0.718790			0.359395	+	0.933186i	$0.382983\pi$
$948$	−2.97564	−	9.15809i	−0.0966445	−	0.297441i
$949$	6.47288	+	4.70282i	0.210118	+	0.152660i
$950$	−23.1844	+	16.8444i	−0.752200	+	0.546505i
$951$	33.5903	−	103.380i	1.08924	−	3.35233i
$952$	−1.46075	+	4.49573i	−0.0473432	+	0.145707i
$953$	46.7905	−	33.9953i	1.51569	−	1.10122i	0.552124	−	0.833762i	$-0.313818\pi$
$953$	46.7905	−	33.9953i	1.51569	−	1.10122i	0.963571	−	0.267454i	$-0.0861824\pi$
$954$	−44.5736	−	32.3846i	−1.44312	−	1.04849i
$955$	0.412059	+	1.26819i	0.0133339	+	0.0410375i
$956$	0.0252353			0.000816169
$957$	−18.7959	−	12.7384i	−0.607586	−	0.411775i
$958$	−57.1053			−1.84499
$959$	3.34791	+	10.3038i	0.108109	+	0.332727i
$960$	38.4620	+	27.9443i	1.24136	+	0.901898i
$961$	14.5653	−	10.5823i	0.469849	−	0.341365i
$962$	5.19876	−	16.0001i	0.167615	−	0.515865i
$963$	19.0775	−	58.7144i	0.614762	−	1.89204i
$964$	4.53122	−	3.29212i	0.145941	−	0.106032i
$965$	40.3963	+	29.3496i	1.30040	+	0.944798i
$966$	−12.1124	−	37.2781i	−0.389710	−	1.19940i
$967$	36.0493			1.15927			0.579633	−	0.814877i	$-0.303196\pi$
$967$	36.0493			1.15927			0.579633	+	0.814877i	$0.303196\pi$
$968$	6.05573	−	23.8396i	0.194638	−	0.766235i
$969$	−9.53457			−0.306294
$970$	15.8528	+	48.7898i	0.509002	+	1.56655i
$971$	44.1341	+	32.0653i	1.41633	+	1.02903i	0.992363	+	0.123348i	$0.0393631\pi$
$971$	44.1341	+	32.0653i	1.41633	+	1.02903i	0.423968	+	0.905677i	$0.360637\pi$
$972$	30.6205	−	22.2471i	0.982153	−	0.713576i
$973$	−12.3976	+	38.1560i	−0.397450	+	1.22322i
$974$	9.51643	−	29.2886i	0.304926	−	0.938466i
$975$	37.7140	−	27.4009i	1.20782	−	0.877530i
$976$	51.3495	+	37.3076i	1.64366	+	1.19419i
$977$	−11.4656	−	35.2874i	−0.366816	−	1.12894i	−0.948836	−	0.315769i	$-0.897738\pi$
$977$	−11.4656	−	35.2874i	−0.366816	−	1.12894i	0.582021	−	0.813174i	$-0.302262\pi$
$978$	−7.60503			−0.243182
$979$	26.5062	+	17.9638i	0.847141	+	0.574127i
$980$	−5.24021			−0.167392
$981$	19.8621	+	61.1292i	0.634148	+	1.95171i
$982$	9.99131	+	7.25911i	0.318835	+	0.231647i
$983$	−1.37567	+	0.999483i	−0.0438771	+	0.0318785i	−0.609508	−	0.792780i	$-0.708633\pi$
$983$	−1.37567	+	0.999483i	−0.0438771	+	0.0318785i	0.565631	+	0.824659i	$0.308633\pi$
$984$	10.2766	−	31.6282i	0.327607	−	1.00827i
$985$	−17.6142	+	54.2110i	−0.561236	+	1.72731i
$986$	2.67504	−	1.94353i	0.0851907	−	0.0618947i
$987$	−16.7181	−	12.1464i	−0.532143	−	0.386625i
$988$	−1.21542	−	3.74067i	−0.0386675	−	0.119006i
$989$	19.6544			0.624973
$990$	−41.0619	+	142.017i	−1.30503	+	4.51359i
$991$	−1.54137			−0.0489633			−0.0244816	−	0.999700i	$-0.507794\pi$
$991$	−1.54137			−0.0489633			−0.0244816	+	0.999700i	$0.507794\pi$
$992$	−3.76757	−	11.5954i	−0.119620	−	0.368154i
$993$	50.1452	+	36.4326i	1.59131	+	1.15615i
$994$	−21.0913	+	15.3237i	−0.668976	+	0.486040i
$995$	7.77312	−	23.9232i	0.246424	−	0.758416i
$996$	−0.823326	+	2.53394i	−0.0260881	+	0.0802909i
$997$	−8.81643	+	6.40551i	−0.279219	+	0.202865i	−0.718577	−	0.695448i	$-0.755206\pi$
$997$	−8.81643	+	6.40551i	−0.279219	+	0.202865i	0.439358	+	0.898312i	$0.355206\pi$
$998$	−1.71711	−	1.24755i	−0.0543542	−	0.0394906i
$999$	25.1425	+	77.3807i	0.795474	+	2.44822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.d.137.2	yes	8
11.3	even	5		2057.2.a.q.1.1		4
11.8	odd	10		2057.2.a.t.1.3		4
11.9	even	5	inner	187.2.g.d.86.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.d.86.2	✓	8	11.9	even	5	inner
187.2.g.d.137.2	yes	8	1.1	even	1	trivial
2057.2.a.q.1.1		4	11.3	even	5
2057.2.a.t.1.3		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{2} +(2.71028 + 1.96913i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(1.03523 - 3.18612i) q^{5} +(1.67504 - 5.15525i) q^{6} +(-1.71028 + 1.24259i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(2.54107 + 7.82060i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 1.53884i) q^{2} +(2.71028 + 1.96913i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(1.03523 - 3.18612i) q^{5} +(1.67504 - 5.15525i) q^{6} +(-1.71028 + 1.24259i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(2.54107 + 7.82060i) q^{9} -5.42055 q^{10} +(-2.74551 - 1.86069i) q^{11} -2.07047 q^{12} +(0.690983 + 2.12663i) q^{13} +(2.76728 + 2.01055i) q^{14} +(9.07965 - 6.59675i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(10.7641 - 7.82060i) q^{18} +(2.30252 + 1.67288i) q^{19} +(0.639809 + 1.96913i) q^{20} -7.08214 q^{21} +(-1.49056 + 5.15525i) q^{22} -3.42055 q^{23} +(-2.31485 - 7.12438i) q^{24} +(-5.03457 - 3.65783i) q^{25} +(2.92705 - 2.12663i) q^{26} +(-5.40709 + 16.6413i) q^{27} +(0.403741 - 1.24259i) q^{28} +(1.65327 - 1.20117i) q^{29} +(-14.6912 - 10.6738i) q^{30} +(-1.11402 - 3.42859i) q^{31} +3.38197 q^{32} +(-3.77714 - 10.4493i) q^{33} +1.61803 q^{34} +(2.18850 + 6.73551i) q^{35} +(-4.11153 - 2.98720i) q^{36} +(3.76186 - 2.73315i) q^{37} +(1.42303 - 4.37965i) q^{38} +(-2.31485 + 7.12438i) q^{39} +(-6.06036 + 4.40311i) q^{40} +(3.59158 + 2.60943i) q^{41} +(3.54107 + 10.8983i) q^{42} -5.74597 q^{43} +(2.04869 - 0.0670174i) q^{44} +27.5480 q^{45} +(1.71028 + 5.26369i) q^{46} +(2.36060 + 1.71508i) q^{47} +(-13.1560 + 9.55836i) q^{48} +(-0.782101 + 2.40706i) q^{49} +(-3.11153 + 9.57632i) q^{50} +(-2.71028 + 1.96913i) q^{51} +(-1.11803 - 0.812299i) q^{52} +(-1.27962 - 3.93826i) q^{53} +28.3119 q^{54} +(-8.77064 + 6.82127i) q^{55} +4.72709 q^{56} +(2.94634 + 9.06791i) q^{57} +(-2.67504 - 1.94353i) q^{58} +(2.42705 - 1.76336i) q^{59} +(-2.14342 + 6.59675i) q^{60} +(4.04066 - 12.4359i) q^{61} +(-4.71905 + 3.42859i) q^{62} +(-14.0637 - 10.2179i) q^{63} +(1.30902 + 4.02874i) q^{64} +7.49102 q^{65} +(-14.1912 + 11.0370i) q^{66} -12.6872 q^{67} +(-0.190983 - 0.587785i) q^{68} +(-9.27064 - 6.73551i) q^{69} +(9.27064 - 6.73551i) q^{70} +(-2.35523 + 7.24864i) q^{71} +(5.68200 - 17.4874i) q^{72} +(2.89476 - 2.10317i) q^{73} +(-6.08682 - 4.42233i) q^{74} +(-6.44233 - 19.8274i) q^{75} -1.75897 q^{76} +(7.00765 - 0.229236i) q^{77} +12.1207 q^{78} +(1.43719 + 4.42320i) q^{79} +(13.1560 + 9.55836i) q^{80} +(-27.4658 + 19.9551i) q^{81} +(2.21972 - 6.83158i) q^{82} +(0.397653 - 1.22385i) q^{83} +(3.54107 - 2.57274i) q^{84} +(2.71028 + 1.96913i) q^{85} +(2.87298 + 8.84213i) q^{86} +6.84607 q^{87} +(2.52111 + 6.97453i) q^{88} -9.65437 q^{89} +(-13.7740 - 42.3920i) q^{90} +(-3.82429 - 2.77851i) q^{91} +(1.71028 - 1.24259i) q^{92} +(3.73205 - 11.4861i) q^{93} +(1.45893 - 4.49013i) q^{94} +(7.71363 - 5.60428i) q^{95} +(9.16606 + 6.65953i) q^{96} +(-2.92457 - 9.00090i) q^{97} +4.09514 q^{98} +(7.57522 - 26.1997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9} - 12 q^{10} - 2 q^{11} - 8 q^{12} + 10 q^{13} + 4 q^{14} + 14 q^{15} - 12 q^{16} + 2 q^{17} + 14 q^{18} - 4 q^{19} - 2 q^{20} - 20 q^{21} - 14 q^{22} + 4 q^{23} - 4 q^{25} + 10 q^{26} - 18 q^{27} + 14 q^{28} - 32 q^{30} - 4 q^{31} + 36 q^{32} + 6 q^{33} + 4 q^{34} - 6 q^{36} + 10 q^{37} + 2 q^{38} - 10 q^{40} - 10 q^{41} + 10 q^{42} + 16 q^{43} + 6 q^{44} + 40 q^{45} - 2 q^{46} + 10 q^{47} - 24 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} + 4 q^{53} + 64 q^{54} - 16 q^{55} - 20 q^{56} - 10 q^{57} - 10 q^{58} + 6 q^{59} - 22 q^{60} + 30 q^{61} + 12 q^{62} - 38 q^{63} + 6 q^{64} + 20 q^{65} - 28 q^{66} - 20 q^{67} - 6 q^{68} - 20 q^{69} + 20 q^{70} + 18 q^{71} + 10 q^{72} - 6 q^{73} - 40 q^{74} - 22 q^{75} + 12 q^{76} + 32 q^{77} + 20 q^{78} - 4 q^{79} + 24 q^{80} - 76 q^{81} - 20 q^{83} + 10 q^{84} + 6 q^{85} - 8 q^{86} + 36 q^{87} - 10 q^{88} - 48 q^{89} - 20 q^{90} - 10 q^{91} - 2 q^{92} + 16 q^{93} + 30 q^{94} + 10 q^{95} + 22 q^{96} + 12 q^{97} + 32 q^{98} + 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9 - 12 * q^10 - 2 * q^11 - 8 * q^12 + 10 * q^13 + 4 * q^14 + 14 * q^15 - 12 * q^16 + 2 * q^17 + 14 * q^18 - 4 * q^19 - 2 * q^20 - 20 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^25 + 10 * q^26 - 18 * q^27 + 14 * q^28 - 32 * q^30 - 4 * q^31 + 36 * q^32 + 6 * q^33 + 4 * q^34 - 6 * q^36 + 10 * q^37 + 2 * q^38 - 10 * q^40 - 10 * q^41 + 10 * q^42 + 16 * q^43 + 6 * q^44 + 40 * q^45 - 2 * q^46 + 10 * q^47 - 24 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 + 4 * q^53 + 64 * q^54 - 16 * q^55 - 20 * q^56 - 10 * q^57 - 10 * q^58 + 6 * q^59 - 22 * q^60 + 30 * q^61 + 12 * q^62 - 38 * q^63 + 6 * q^64 + 20 * q^65 - 28 * q^66 - 20 * q^67 - 6 * q^68 - 20 * q^69 + 20 * q^70 + 18 * q^71 + 10 * q^72 - 6 * q^73 - 40 * q^74 - 22 * q^75 + 12 * q^76 + 32 * q^77 + 20 * q^78 - 4 * q^79 + 24 * q^80 - 76 * q^81 - 20 * q^83 + 10 * q^84 + 6 * q^85 - 8 * q^86 + 36 * q^87 - 10 * q^88 - 48 * q^89 - 20 * q^90 - 10 * q^91 - 2 * q^92 + 16 * q^93 + 30 * q^94 + 10 * q^95 + 22 * q^96 + 12 * q^97 + 32 * q^98 + 22 * q^99

Introduction

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