LMFDB - Embedded newform 187.2.g.c.137.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
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			137.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	187.137
Dual form			187.2.g.c.86.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690983 + 2.12663i) q^{2} +(0.309017 + 0.224514i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(-0.263932 + 0.812299i) q^{6} +(-0.500000 + 0.363271i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.881966 - 2.71441i) q^{9} +O(q^{10})$	\(q+(0.690983 + 2.12663i) q^{2} +(0.309017 + 0.224514i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(-0.263932 + 0.812299i) q^{6} +(-0.500000 + 0.363271i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.881966 - 2.71441i) q^{9} -4.47214 q^{10} +(3.23607 + 0.726543i) q^{11} -1.14590 q^{12} +(-0.500000 - 1.53884i) q^{13} +(-1.11803 - 0.812299i) q^{14} +(-0.618034 + 0.449028i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(5.16312 - 3.75123i) q^{18} +(0.618034 + 0.449028i) q^{19} +(-1.85410 - 5.70634i) q^{20} -0.236068 q^{21} +(0.690983 + 7.38394i) q^{22} +2.85410 q^{23} +(-0.263932 - 0.812299i) q^{24} +(0.809017 + 0.587785i) q^{25} +(2.92705 - 2.12663i) q^{26} +(0.690983 - 2.12663i) q^{27} +(0.572949 - 1.76336i) q^{28} +(6.23607 - 4.53077i) q^{29} +(-1.38197 - 1.00406i) q^{30} +(-2.00000 - 6.15537i) q^{31} -6.70820 q^{32} +(0.836881 + 0.951057i) q^{33} -2.23607 q^{34} +(-0.381966 - 1.17557i) q^{35} +(6.92705 + 5.03280i) q^{36} +(-2.00000 + 1.45309i) q^{37} +(-0.527864 + 1.62460i) q^{38} +(0.190983 - 0.587785i) q^{39} +(3.61803 - 2.62866i) q^{40} +(5.61803 + 4.08174i) q^{41} +(-0.163119 - 0.502029i) q^{42} +2.76393 q^{43} +(-9.13525 + 3.94298i) q^{44} +5.70820 q^{45} +(1.97214 + 6.06961i) q^{46} +(-7.23607 - 5.25731i) q^{47} +(-0.309017 + 0.224514i) q^{48} +(-2.04508 + 6.29412i) q^{49} +(-0.690983 + 2.12663i) q^{50} +(-0.309017 + 0.224514i) q^{51} +(3.92705 + 2.85317i) q^{52} +(-1.33688 - 4.11450i) q^{53} +5.00000 q^{54} +(-3.38197 + 5.70634i) q^{55} +1.38197 q^{56} +(0.0901699 + 0.277515i) q^{57} +(13.9443 + 10.1311i) q^{58} +(-0.236068 + 0.171513i) q^{59} +(0.708204 - 2.17963i) q^{60} +(0.236068 - 0.726543i) q^{61} +(11.7082 - 8.50651i) q^{62} +(1.42705 + 1.03681i) q^{63} +(-4.01722 - 12.3637i) q^{64} +3.23607 q^{65} +(-1.44427 + 2.43690i) q^{66} -12.0000 q^{67} +(-0.927051 - 2.85317i) q^{68} +(0.881966 + 0.640786i) q^{69} +(2.23607 - 1.62460i) q^{70} +(3.23607 - 9.95959i) q^{71} +(-1.97214 + 6.06961i) q^{72} +(-3.85410 + 2.80017i) q^{73} +(-4.47214 - 3.24920i) q^{74} +(0.118034 + 0.363271i) q^{75} -2.29180 q^{76} +(-1.88197 + 0.812299i) q^{77} +1.38197 q^{78} +(-2.95492 - 9.09429i) q^{79} +(-1.61803 - 1.17557i) q^{80} +(-6.23607 + 4.53077i) q^{81} +(-4.79837 + 14.7679i) q^{82} +(2.38197 - 7.33094i) q^{83} +(0.572949 - 0.416272i) q^{84} +(-1.61803 - 1.17557i) q^{85} +(1.90983 + 5.87785i) q^{86} +2.94427 q^{87} +(-4.89919 - 5.56758i) q^{88} -9.79837 q^{89} +(3.94427 + 12.1392i) q^{90} +(0.809017 + 0.587785i) q^{91} +(-6.92705 + 5.03280i) q^{92} +(0.763932 - 2.35114i) q^{93} +(6.18034 - 19.0211i) q^{94} +(-1.23607 + 0.898056i) q^{95} +(-2.07295 - 1.50609i) q^{96} +(1.85410 + 5.70634i) q^{97} -14.7984 q^{98} +(-0.881966 - 9.42481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9} + 4 q^{11} - 18 q^{12} - 2 q^{13} + 2 q^{15} + q^{16} + q^{17} + 5 q^{18} - 2 q^{19} + 6 q^{20} + 8 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{24} + q^{25} + 5 q^{26} + 5 q^{27} + 9 q^{28} + 16 q^{29} - 10 q^{30} - 8 q^{31} + 19 q^{33} - 6 q^{35} + 21 q^{36} - 8 q^{37} - 20 q^{38} + 3 q^{39} + 10 q^{40} + 18 q^{41} + 15 q^{42} + 20 q^{43} - 3 q^{44} - 4 q^{45} - 10 q^{46} - 20 q^{47} + q^{48} + 3 q^{49} - 5 q^{50} + q^{51} + 9 q^{52} - 21 q^{53} + 20 q^{54} - 18 q^{55} + 10 q^{56} - 22 q^{57} + 20 q^{58} + 8 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} - q^{63} + 13 q^{64} + 4 q^{65} + 30 q^{66} - 48 q^{67} + 3 q^{68} + 8 q^{69} + 4 q^{71} + 10 q^{72} - 2 q^{73} - 4 q^{75} - 36 q^{76} - 12 q^{77} + 10 q^{78} - 23 q^{79} - 2 q^{80} - 16 q^{81} + 30 q^{82} + 14 q^{83} + 9 q^{84} - 2 q^{85} + 30 q^{86} - 24 q^{87} + 5 q^{88} + 10 q^{89} - 20 q^{90} + q^{91} - 21 q^{92} + 12 q^{93} - 20 q^{94} + 4 q^{95} - 15 q^{96} - 6 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9 + 4 * q^11 - 18 * q^12 - 2 * q^13 + 2 * q^15 + q^16 + q^17 + 5 * q^18 - 2 * q^19 + 6 * q^20 + 8 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^24 + q^25 + 5 * q^26 + 5 * q^27 + 9 * q^28 + 16 * q^29 - 10 * q^30 - 8 * q^31 + 19 * q^33 - 6 * q^35 + 21 * q^36 - 8 * q^37 - 20 * q^38 + 3 * q^39 + 10 * q^40 + 18 * q^41 + 15 * q^42 + 20 * q^43 - 3 * q^44 - 4 * q^45 - 10 * q^46 - 20 * q^47 + q^48 + 3 * q^49 - 5 * q^50 + q^51 + 9 * q^52 - 21 * q^53 + 20 * q^54 - 18 * q^55 + 10 * q^56 - 22 * q^57 + 20 * q^58 + 8 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 - q^63 + 13 * q^64 + 4 * q^65 + 30 * q^66 - 48 * q^67 + 3 * q^68 + 8 * q^69 + 4 * q^71 + 10 * q^72 - 2 * q^73 - 4 * q^75 - 36 * q^76 - 12 * q^77 + 10 * q^78 - 23 * q^79 - 2 * q^80 - 16 * q^81 + 30 * q^82 + 14 * q^83 + 9 * q^84 - 2 * q^85 + 30 * q^86 - 24 * q^87 + 5 * q^88 + 10 * q^89 - 20 * q^90 + q^91 - 21 * q^92 + 12 * q^93 - 20 * q^94 + 4 * q^95 - 15 * q^96 - 6 * q^97 - 10 * q^98 - 8 * 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 $

$2$	0.690983	+	2.12663i	0.488599	+	1.50375i	0.826700	+	0.562643i	$0.190215\pi$
$2$	0.690983	+	2.12663i	0.488599	+	1.50375i	−0.338101	+	0.941110i	$0.609785\pi$
$3$	0.309017	+	0.224514i	0.178411	+	0.129623i	0.673407	−	0.739272i	$-0.264830\pi$
$3$	0.309017	+	0.224514i	0.178411	+	0.129623i	−0.494996	+	0.868895i	$0.664830\pi$
$4$	−2.42705	+	1.76336i	−1.21353	+	0.881678i
$5$	−0.618034	+	1.90211i	−0.276393	+	0.850651i	0.712454	+	0.701719i	$0.247584\pi$
$5$	−0.618034	+	1.90211i	−0.276393	+	0.850651i	−0.988847	+	0.148932i	$0.952416\pi$
$6$	−0.263932	+	0.812299i	−0.107750	+	0.331620i
$7$	−0.500000	+	0.363271i	−0.188982	+	0.137304i	−0.678253	−	0.734828i	$-0.737263\pi$
$7$	−0.500000	+	0.363271i	−0.188982	+	0.137304i	0.489271	+	0.872132i	$0.337263\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	−0.881966	−	2.71441i	−0.293989	−	0.904804i
$10$	−4.47214			−1.41421
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$	−1.14590			−0.330792
$13$	−0.500000	−	1.53884i	−0.138675	−	0.426798i	0.857468	−	0.514536i	$-0.172036\pi$
$13$	−0.500000	−	1.53884i	−0.138675	−	0.426798i	−0.996144	+	0.0877386i	$0.972036\pi$
$14$	−1.11803	−	0.812299i	−0.298807	−	0.217096i
$15$	−0.618034	+	0.449028i	−0.159576	+	0.115939i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$18$	5.16312	−	3.75123i	1.21696	−	0.884172i
$19$	0.618034	+	0.449028i	0.141787	+	0.103014i	0.656418	−	0.754398i	$-0.272071\pi$
$19$	0.618034	+	0.449028i	0.141787	+	0.103014i	−0.514631	+	0.857412i	$0.672071\pi$
$20$	−1.85410	−	5.70634i	−0.414590	−	1.27598i
$21$	−0.236068			−0.0515143
$22$	0.690983	+	7.38394i	0.147318	+	1.57426i
$23$	2.85410			0.595121			0.297561	−	0.954703i	$-0.403827\pi$
$23$	2.85410			0.595121			0.297561	+	0.954703i	$0.403827\pi$
$24$	−0.263932	−	0.812299i	−0.0538749	−	0.165810i
$25$	0.809017	+	0.587785i	0.161803	+	0.117557i
$26$	2.92705	−	2.12663i	0.574042	−	0.417066i
$27$	0.690983	−	2.12663i	0.132980	−	0.409270i
$28$	0.572949	−	1.76336i	0.108277	−	0.333243i
$29$	6.23607	−	4.53077i	1.15801	−	0.841343i	0.168484	−	0.985704i	$-0.446113\pi$
$29$	6.23607	−	4.53077i	1.15801	−	0.841343i	0.989525	+	0.144362i	$0.0461129\pi$
$30$	−1.38197	−	1.00406i	−0.252311	−	0.183315i
$31$	−2.00000	−	6.15537i	−0.359211	−	1.10554i	−0.953528	−	0.301306i	$-0.902578\pi$
$31$	−2.00000	−	6.15537i	−0.359211	−	1.10554i	0.594317	−	0.804231i	$-0.297422\pi$
$32$	−6.70820			−1.18585
$33$	0.836881	+	0.951057i	0.145682	+	0.165558i
$34$	−2.23607			−0.383482
$35$	−0.381966	−	1.17557i	−0.0645640	−	0.198708i
$36$	6.92705	+	5.03280i	1.15451	+	0.838800i
$37$	−2.00000	+	1.45309i	−0.328798	+	0.238886i	−0.739920	−	0.672694i	$-0.765137\pi$
$37$	−2.00000	+	1.45309i	−0.328798	+	0.238886i	0.411122	+	0.911580i	$0.365137\pi$
$38$	−0.527864	+	1.62460i	−0.0856309	+	0.263545i
$39$	0.190983	−	0.587785i	0.0305818	−	0.0941210i
$40$	3.61803	−	2.62866i	0.572061	−	0.415627i
$41$	5.61803	+	4.08174i	0.877390	+	0.637461i	0.932560	−	0.361016i	$-0.117570\pi$
$41$	5.61803	+	4.08174i	0.877390	+	0.637461i	−0.0551700	+	0.998477i	$0.517570\pi$
$42$	−0.163119	−	0.502029i	−0.0251698	−	0.0774647i
$43$	2.76393			0.421496			0.210748	−	0.977540i	$-0.432410\pi$
$43$	2.76393			0.421496			0.210748	+	0.977540i	$0.432410\pi$
$44$	−9.13525	+	3.94298i	−1.37719	+	0.594427i
$45$	5.70820			0.850929
$46$	1.97214	+	6.06961i	0.290776	+	0.894915i
$47$	−7.23607	−	5.25731i	−1.05549	−	0.766858i	−0.0822405	−	0.996613i	$-0.526208\pi$
$47$	−7.23607	−	5.25731i	−1.05549	−	0.766858i	−0.973249	+	0.229755i	$0.926208\pi$
$48$	−0.309017	+	0.224514i	−0.0446028	+	0.0324058i
$49$	−2.04508	+	6.29412i	−0.292155	+	0.899161i
$50$	−0.690983	+	2.12663i	−0.0977198	+	0.300750i
$51$	−0.309017	+	0.224514i	−0.0432710	+	0.0314382i
$52$	3.92705	+	2.85317i	0.544584	+	0.395663i
$53$	−1.33688	−	4.11450i	−0.183635	−	0.565170i	0.816287	−	0.577646i	$-0.196029\pi$
$53$	−1.33688	−	4.11450i	−0.183635	−	0.565170i	−0.999922	+	0.0124763i	$0.996029\pi$
$54$	5.00000			0.680414
$55$	−3.38197	+	5.70634i	−0.456024	+	0.769443i
$56$	1.38197			0.184673
$57$	0.0901699	+	0.277515i	0.0119433	+	0.0367577i
$58$	13.9443	+	10.1311i	1.83097	+	1.33028i
$59$	−0.236068	+	0.171513i	−0.0307334	+	0.0223291i	−0.603046	−	0.797706i	$-0.706046\pi$
$59$	−0.236068	+	0.171513i	−0.0307334	+	0.0223291i	0.572312	+	0.820036i	$0.306046\pi$
$60$	0.708204	−	2.17963i	0.0914287	−	0.281389i
$61$	0.236068	−	0.726543i	0.0302254	−	0.0930242i	−0.934806	−	0.355159i	$-0.884427\pi$
$61$	0.236068	−	0.726543i	0.0302254	−	0.0930242i	0.965031	+	0.262135i	$0.0844266\pi$
$62$	11.7082	−	8.50651i	1.48694	−	1.08033i
$63$	1.42705	+	1.03681i	0.179792	+	0.130626i
$64$	−4.01722	−	12.3637i	−0.502153	−	1.54547i
$65$	3.23607			0.401385
$66$	−1.44427	+	2.43690i	−0.177778	+	0.299961i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−0.927051	−	2.85317i	−0.112421	−	0.345998i
$69$	0.881966	+	0.640786i	0.106176	+	0.0771415i
$70$	2.23607	−	1.62460i	0.267261	−	0.194177i
$71$	3.23607	−	9.95959i	0.384051	−	1.18199i	−0.553116	−	0.833104i	$-0.686561\pi$
$71$	3.23607	−	9.95959i	0.384051	−	1.18199i	0.937167	−	0.348882i	$-0.113439\pi$
$72$	−1.97214	+	6.06961i	−0.232418	+	0.715310i
$73$	−3.85410	+	2.80017i	−0.451089	+	0.327735i	−0.790025	−	0.613074i	$-0.789933\pi$
$73$	−3.85410	+	2.80017i	−0.451089	+	0.327735i	0.338937	+	0.940809i	$0.389933\pi$
$74$	−4.47214	−	3.24920i	−0.519875	−	0.377711i
$75$	0.118034	+	0.363271i	0.0136294	+	0.0419470i
$76$	−2.29180			−0.262887
$77$	−1.88197	+	0.812299i	−0.214470	+	0.0925701i
$78$	1.38197			0.156477
$79$	−2.95492	−	9.09429i	−0.332454	−	1.02319i	−0.967963	−	0.251094i	$-0.919210\pi$
$79$	−2.95492	−	9.09429i	−0.332454	−	1.02319i	0.635509	−	0.772094i	$-0.280790\pi$
$80$	−1.61803	−	1.17557i	−0.180902	−	0.131433i
$81$	−6.23607	+	4.53077i	−0.692896	+	0.503419i
$82$	−4.79837	+	14.7679i	−0.529892	+	1.63084i
$83$	2.38197	−	7.33094i	0.261455	−	0.804675i	−0.731034	−	0.682341i	$-0.760962\pi$
$83$	2.38197	−	7.33094i	0.261455	−	0.804675i	0.992489	−	0.122334i	$-0.0390380\pi$
$84$	0.572949	−	0.416272i	0.0625139	−	0.0454190i
$85$	−1.61803	−	1.17557i	−0.175500	−	0.127509i
$86$	1.90983	+	5.87785i	0.205942	+	0.633825i
$87$	2.94427			0.315659
$88$	−4.89919	−	5.56758i	−0.522255	−	0.593506i
$89$	−9.79837			−1.03863			−0.519313	−	0.854584i	$-0.673812\pi$
$89$	−9.79837			−1.03863			−0.519313	+	0.854584i	$0.673812\pi$
$90$	3.94427	+	12.1392i	0.415763	+	1.27959i
$91$	0.809017	+	0.587785i	0.0848080	+	0.0616166i
$92$	−6.92705	+	5.03280i	−0.722195	+	0.524705i
$93$	0.763932	−	2.35114i	0.0792161	−	0.243802i
$94$	6.18034	−	19.0211i	0.637453	−	1.96188i
$95$	−1.23607	+	0.898056i	−0.126818	+	0.0921386i
$96$	−2.07295	−	1.50609i	−0.211569	−	0.153714i
$97$	1.85410	+	5.70634i	0.188256	+	0.579391i	0.999989	−	0.00463676i	$-0.00147593\pi$
$97$	1.85410	+	5.70634i	0.188256	+	0.579391i	−0.811734	+	0.584028i	$0.801476\pi$
$98$	−14.7984			−1.49486
$99$	−0.881966	−	9.42481i	−0.0886409	−	0.947229i
$100$	−3.00000			−0.300000
$101$	−4.28115	−	13.1760i	−0.425991	−	1.31106i	−0.902043	−	0.431647i	$-0.857933\pi$
$101$	−4.28115	−	13.1760i	−0.425991	−	1.31106i	0.476052	−	0.879417i	$-0.342067\pi$
$102$	−0.690983	−	0.502029i	−0.0684175	−	0.0497082i
$103$	−11.4721	+	8.33499i	−1.13038	+	0.821271i	−0.985751	−	0.168214i	$-0.946200\pi$
$103$	−11.4721	+	8.33499i	−1.13038	+	0.821271i	−0.144633	+	0.989485i	$0.546200\pi$
$104$	−1.11803	+	3.44095i	−0.109632	+	0.337413i
$105$	0.145898	−	0.449028i	0.0142382	−	0.0438206i
$106$	7.82624	−	5.68609i	0.760151	−	0.552282i
$107$	−2.73607	−	1.98787i	−0.264506	−	0.192175i	0.447625	−	0.894221i	$-0.352270\pi$
$107$	−2.73607	−	1.98787i	−0.264506	−	0.192175i	−0.712131	+	0.702047i	$0.752270\pi$
$108$	2.07295	+	6.37988i	0.199470	+	0.613904i
$109$	8.47214			0.811483			0.405742	−	0.913988i	$-0.367013\pi$
$109$	8.47214			0.811483			0.405742	+	0.913988i	$0.367013\pi$
$110$	−14.4721	−	3.24920i	−1.37986	−	0.309799i
$111$	−0.944272			−0.0896263
$112$	−0.190983	−	0.587785i	−0.0180462	−	0.0555405i
$113$	3.23607	+	2.35114i	0.304424	+	0.221177i	0.729500	−	0.683981i	$-0.239753\pi$
$113$	3.23607	+	2.35114i	0.304424	+	0.221177i	−0.425076	+	0.905157i	$0.639753\pi$
$114$	−0.527864	+	0.383516i	−0.0494390	+	0.0359195i
$115$	−1.76393	+	5.42882i	−0.164488	+	0.506240i
$116$	−7.14590	+	21.9928i	−0.663480	+	2.04198i
$117$	−3.73607	+	2.71441i	−0.345400	+	0.250948i
$118$	−0.527864	−	0.383516i	−0.0485938	−	0.0353055i
$119$	−0.190983	−	0.587785i	−0.0175074	−	0.0538822i
$120$	1.70820			0.155937
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$	1.70820			0.154654
$123$	0.819660	+	2.52265i	0.0739063	+	0.227460i
$124$	15.7082	+	11.4127i	1.41064	+	1.02489i
$125$	−9.70820	+	7.05342i	−0.868328	+	0.630877i
$126$	−1.21885	+	3.75123i	−0.108584	+	0.334186i
$127$	3.23607	−	9.95959i	0.287155	−	0.883771i	−0.698590	−	0.715522i	$-0.746189\pi$
$127$	3.23607	−	9.95959i	0.287155	−	0.883771i	0.985745	−	0.168249i	$-0.0538112\pi$
$128$	12.6631	−	9.20029i	1.11927	−	0.813199i
$129$	0.854102	+	0.620541i	0.0751995	+	0.0546356i
$130$	2.23607	+	6.88191i	0.196116	+	0.603583i
$131$	19.6180			1.71404			0.857018	−	0.515287i	$-0.172315\pi$
$131$	19.6180			1.71404			0.857018	+	0.515287i	$0.172315\pi$
$132$	−3.70820	−	0.832544i	−0.322758	−	0.0724636i
$133$	−0.472136			−0.0409394
$134$	−8.29180	−	25.5195i	−0.716302	−	2.20455i
$135$	3.61803	+	2.62866i	0.311391	+	0.226239i
$136$	1.80902	−	1.31433i	0.155122	−	0.112703i
$137$	−6.61803	+	20.3682i	−0.565417	+	1.74017i	0.101293	+	0.994857i	$0.467702\pi$
$137$	−6.61803	+	20.3682i	−0.565417	+	1.74017i	−0.666710	+	0.745317i	$0.732298\pi$
$138$	−0.753289	+	2.31838i	−0.0641242	+	0.197354i
$139$	−3.23607	+	2.35114i	−0.274480	+	0.199421i	−0.716506	−	0.697581i	$-0.754260\pi$
$139$	−3.23607	+	2.35114i	−0.274480	+	0.199421i	0.442026	+	0.897002i	$0.354260\pi$
$140$	3.00000	+	2.17963i	0.253546	+	0.184212i
$141$	−1.05573	−	3.24920i	−0.0889083	−	0.273632i
$142$	23.4164			1.96506
$143$	−0.500000	−	5.34307i	−0.0418121	−	0.446810i
$144$	2.85410			0.237842
$145$	4.76393	+	14.6619i	0.395623	+	1.21760i
$146$	−8.61803	−	6.26137i	−0.713234	−	0.518195i
$147$	−2.04508	+	1.48584i	−0.168676	+	0.122550i
$148$	2.29180	−	7.05342i	0.188384	−	0.579788i
$149$	−4.37132	+	13.4535i	−0.358113	+	1.10216i	0.596070	+	0.802933i	$0.296728\pi$
$149$	−4.37132	+	13.4535i	−0.358113	+	1.10216i	−0.954183	+	0.299225i	$0.903272\pi$
$150$	−0.690983	+	0.502029i	−0.0564185	+	0.0409905i
$151$	2.61803	+	1.90211i	0.213053	+	0.154792i	0.689194	−	0.724577i	$-0.257965\pi$
$151$	2.61803	+	1.90211i	0.213053	+	0.154792i	−0.476141	+	0.879369i	$0.657965\pi$
$152$	−0.527864	−	1.62460i	−0.0428154	−	0.131772i
$153$	2.85410			0.230740
$154$	−3.02786	−	3.44095i	−0.243992	−	0.277280i
$155$	12.9443			1.03971
$156$	0.572949	+	1.76336i	0.0458726	+	0.141181i
$157$	−0.0729490	−	0.0530006i	−0.00582197	−	0.00422991i	0.584870	−	0.811127i	$-0.301145\pi$
$157$	−0.0729490	−	0.0530006i	−0.00582197	−	0.00422991i	−0.590692	+	0.806897i	$0.701145\pi$
$158$	17.2984	−	12.5680i	1.37618	−	0.999857i
$159$	0.510643	−	1.57160i	0.0404966	−	0.124636i
$160$	4.14590	−	12.7598i	0.327762	−	1.00875i
$161$	−1.42705	+	1.03681i	−0.112467	+	0.0817123i
$162$	−13.9443	−	10.1311i	−1.09557	−	0.795975i
$163$	2.19098	+	6.74315i	0.171611	+	0.528164i	0.999462	−	0.0327829i	$-0.0104370\pi$
$163$	2.19098	+	6.74315i	0.171611	+	0.528164i	−0.827851	+	0.560947i	$0.810437\pi$
$164$	−20.8328			−1.62677
$165$	−2.32624	+	1.00406i	−0.181097	+	0.0781657i
$166$	17.2361			1.33778
$167$	4.11803	+	12.6740i	0.318663	+	0.980744i	0.974220	+	0.225599i	$0.0724338\pi$
$167$	4.11803	+	12.6740i	0.318663	+	0.980744i	−0.655557	+	0.755145i	$0.727566\pi$
$168$	0.427051	+	0.310271i	0.0329477	+	0.0239379i
$169$	8.39919	−	6.10237i	0.646091	−	0.469413i
$170$	1.38197	−	4.25325i	0.105992	−	0.326210i
$171$	0.673762	−	2.07363i	0.0515239	−	0.158574i
$172$	−6.70820	+	4.87380i	−0.511496	+	0.371623i
$173$	−7.61803	−	5.53483i	−0.579188	−	0.420805i	0.259243	−	0.965812i	$-0.416527\pi$
$173$	−7.61803	−	5.53483i	−0.579188	−	0.420805i	−0.838431	+	0.545007i	$0.816527\pi$
$174$	2.03444	+	6.26137i	0.154231	+	0.474673i
$175$	−0.618034			−0.0467190
$176$	−1.69098	+	2.85317i	−0.127463	+	0.215066i
$177$	−0.111456			−0.00837756
$178$	−6.77051	−	20.8375i	−0.507471	−	1.56184i
$179$	−9.09017	−	6.60440i	−0.679431	−	0.493636i	0.193738	−	0.981053i	$-0.437939\pi$
$179$	−9.09017	−	6.60440i	−0.679431	−	0.493636i	−0.873169	+	0.487418i	$0.837939\pi$
$180$	−13.8541	+	10.0656i	−1.03262	+	0.750245i
$181$	−1.61803	+	4.97980i	−0.120268	+	0.370145i	−0.993009	−	0.118037i	$-0.962340\pi$
$181$	−1.61803	+	4.97980i	−0.120268	+	0.370145i	0.872742	+	0.488182i	$0.162340\pi$
$182$	−0.690983	+	2.12663i	−0.0512191	+	0.157636i
$183$	0.236068	−	0.171513i	0.0174506	−	0.0126786i
$184$	−5.16312	−	3.75123i	−0.380630	−	0.276544i
$185$	−1.52786	−	4.70228i	−0.112331	−	0.345719i
$186$	5.52786			0.405323
$187$	−1.69098	+	2.85317i	−0.123657	+	0.208644i
$188$	26.8328			1.95698
$189$	0.427051	+	1.31433i	0.0310634	+	0.0956033i
$190$	−2.76393	−	2.00811i	−0.200517	−	0.145684i
$191$	14.5623	−	10.5801i	1.05369	−	0.765552i	0.0807805	−	0.996732i	$-0.474259\pi$
$191$	14.5623	−	10.5801i	1.05369	−	0.765552i	0.972911	+	0.231180i	$0.0742587\pi$
$192$	1.53444	−	4.72253i	0.110739	−	0.340819i
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	0.790047	+	0.613046i	$0.210056\pi$
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	−0.999501	+	0.0315871i	$0.989944\pi$
$194$	−10.8541	+	7.88597i	−0.779279	+	0.566179i
$195$	1.00000	+	0.726543i	0.0716115	+	0.0520288i
$196$	−6.13525	−	18.8824i	−0.438232	−	1.34874i
$197$	23.7082			1.68914			0.844570	−	0.535445i	$-0.179856\pi$
$197$	23.7082			1.68914			0.844570	+	0.535445i	$0.179856\pi$
$198$	19.4336	−	8.38800i	1.38109	−	0.596109i
$199$	−21.8541			−1.54920			−0.774598	−	0.632454i	$-0.782048\pi$
$199$	−21.8541			−1.54920			−0.774598	+	0.632454i	$0.782048\pi$
$200$	−0.690983	−	2.12663i	−0.0488599	−	0.150375i
$201$	−3.70820	−	2.69417i	−0.261557	−	0.190032i
$202$	25.0623	−	18.2088i	1.76338	−	1.28117i
$203$	−1.47214	+	4.53077i	−0.103324	+	0.317998i
$204$	0.354102	−	1.08981i	0.0247921	−	0.0763022i
$205$	−11.2361	+	8.16348i	−0.784761	+	0.570162i
$206$	−25.6525	−	18.6376i	−1.78729	−	1.29854i
$207$	−2.51722	−	7.74721i	−0.174959	−	0.538468i
$208$	1.61803			0.112190
$209$	1.67376	+	1.90211i	0.115777	+	0.131572i
$210$	1.05573			0.0728522
$211$	−7.41641	−	22.8254i	−0.510567	−	1.57136i	−0.791206	−	0.611549i	$-0.790547\pi$
$211$	−7.41641	−	22.8254i	−0.510567	−	1.57136i	0.280640	−	0.959813i	$-0.409453\pi$
$212$	10.5000	+	7.62870i	0.721143	+	0.523941i
$213$	3.23607	−	2.35114i	0.221732	−	0.161098i
$214$	2.33688	−	7.19218i	0.159746	−	0.491647i
$215$	−1.70820	+	5.25731i	−0.116499	+	0.358546i
$216$	−4.04508	+	2.93893i	−0.275233	+	0.199969i
$217$	3.23607	+	2.35114i	0.219679	+	0.159606i
$218$	5.85410	+	18.0171i	0.396490	+	1.22027i
$219$	−1.81966			−0.122961
$220$	−1.85410	−	19.8132i	−0.125004	−	1.33580i
$221$	1.61803			0.108841
$222$	−0.652476	−	2.00811i	−0.0437913	−	0.134776i
$223$	10.7082	+	7.77997i	0.717074	+	0.520985i	0.885448	−	0.464738i	$-0.153852\pi$
$223$	10.7082	+	7.77997i	0.717074	+	0.520985i	−0.168374	+	0.985723i	$0.553852\pi$
$224$	3.35410	−	2.43690i	0.224105	−	0.162822i
$225$	0.881966	−	2.71441i	0.0587977	−	0.180961i
$226$	−2.76393	+	8.50651i	−0.183854	+	0.565845i
$227$	−10.9721	+	7.97172i	−0.728246	+	0.529102i	−0.889008	−	0.457891i	$-0.848605\pi$
$227$	−10.9721	+	7.97172i	−0.728246	+	0.529102i	0.160762	+	0.986993i	$0.448605\pi$
$228$	−0.708204	−	0.514540i	−0.0469020	−	0.0340763i
$229$	−1.71885	−	5.29007i	−0.113585	−	0.349577i	0.878065	−	0.478542i	$-0.158835\pi$
$229$	−1.71885	−	5.29007i	−0.113585	−	0.349577i	−0.991649	+	0.128965i	$0.958835\pi$
$230$	−12.7639			−0.841629
$231$	−0.763932	−	0.171513i	−0.0502630	−	0.0112848i
$232$	−17.2361			−1.13160
$233$	7.67376	+	23.6174i	0.502725	+	1.54723i	0.804562	+	0.593869i	$0.202400\pi$
$233$	7.67376	+	23.6174i	0.502725	+	1.54723i	−0.301837	+	0.953359i	$0.597600\pi$
$234$	−8.35410	−	6.06961i	−0.546125	−	0.396783i
$235$	14.4721	−	10.5146i	0.944058	−	0.685898i
$236$	0.270510	−	0.832544i	0.0176087	−	0.0541940i
$237$	1.12868	−	3.47371i	0.0733155	−	0.225642i
$238$	1.11803	−	0.812299i	0.0724714	−	0.0526535i
$239$	17.9443	+	13.0373i	1.16072	+	0.843311i	0.989869	−	0.141986i	$-0.0453487\pi$
$239$	17.9443	+	13.0373i	1.16072	+	0.843311i	0.170850	+	0.985297i	$0.445349\pi$
$240$	−0.236068	−	0.726543i	−0.0152381	−	0.0468981i
$241$	9.70820			0.625360			0.312680	−	0.949858i	$-0.398773\pi$
$241$	9.70820			0.625360			0.312680	+	0.949858i	$0.398773\pi$
$242$	−3.12868	+	24.3970i	−0.201119	+	1.56830i
$243$	−9.65248			−0.619207
$244$	0.708204	+	2.17963i	0.0453381	+	0.139536i
$245$	−10.7082	−	7.77997i	−0.684122	−	0.497044i
$246$	−4.79837	+	3.48622i	−0.305933	+	0.222273i
$247$	0.381966	−	1.17557i	0.0243039	−	0.0747998i
$248$	−4.47214	+	13.7638i	−0.283981	+	0.874003i
$249$	2.38197	−	1.73060i	0.150951	−	0.109672i
$250$	−21.7082	−	15.7719i	−1.37295	−	0.997505i
$251$	−1.47214	−	4.53077i	−0.0929204	−	0.285980i	0.893786	−	0.448494i	$-0.148040\pi$
$251$	−1.47214	−	4.53077i	−0.0929204	−	0.285980i	−0.986706	+	0.162515i	$0.948040\pi$
$252$	−5.29180			−0.333352
$253$	9.23607	+	2.07363i	0.580667	+	0.130368i
$254$	23.4164			1.46928
$255$	−0.236068	−	0.726543i	−0.0147832	−	0.0454979i
$256$	7.28115	+	5.29007i	0.455072	+	0.330629i
$257$	15.2082	−	11.0494i	0.948662	−	0.689243i	−0.00182827	−	0.999998i	$-0.500582\pi$
$257$	15.2082	−	11.0494i	0.948662	−	0.689243i	0.950490	+	0.310755i	$0.100582\pi$
$258$	−0.729490	+	2.24514i	−0.0454161	+	0.139776i
$259$	0.472136	−	1.45309i	0.0293371	−	0.0902903i
$260$	−7.85410	+	5.70634i	−0.487091	+	0.353892i
$261$	−17.7984	−	12.9313i	−1.10169	−	0.800426i
$262$	13.5557	+	41.7202i	0.837476	+	2.57749i
$263$	17.1246			1.05595			0.527974	−	0.849260i	$-0.322952\pi$
$263$	17.1246			1.05595			0.527974	+	0.849260i	$0.322952\pi$
$264$	−0.263932	−	2.82041i	−0.0162439	−	0.173584i
$265$	8.65248			0.531517
$266$	−0.326238	−	1.00406i	−0.0200029	−	0.0615627i
$267$	−3.02786	−	2.19987i	−0.185302	−	0.134630i
$268$	29.1246	−	21.1603i	1.77907	−	1.29257i
$269$	−7.52786	+	23.1684i	−0.458982	+	1.41260i	0.407414	+	0.913244i	$0.366431\pi$
$269$	−7.52786	+	23.1684i	−0.458982	+	1.41260i	−0.866396	+	0.499358i	$0.833569\pi$
$270$	−3.09017	+	9.51057i	−0.188062	+	0.578795i
$271$	−24.5623	+	17.8456i	−1.49205	+	1.08404i	−0.518638	+	0.854994i	$0.673561\pi$
$271$	−24.5623	+	17.8456i	−1.49205	+	1.08404i	−0.973415	+	0.229047i	$0.926439\pi$
$272$	−0.809017	−	0.587785i	−0.0490539	−	0.0356397i
$273$	0.118034	+	0.363271i	0.00714374	+	0.0219862i
$274$	−47.8885			−2.89305
$275$	2.19098	+	2.48990i	0.132121	+	0.150147i
$276$	−3.27051			−0.196862
$277$	7.85410	+	24.1724i	0.471907	+	1.45238i	0.850084	+	0.526648i	$0.176551\pi$
$277$	7.85410	+	24.1724i	0.471907	+	1.45238i	−0.378176	+	0.925734i	$0.623449\pi$
$278$	−7.23607	−	5.25731i	−0.433991	−	0.315313i
$279$	−14.9443	+	10.8576i	−0.894690	+	0.650030i
$280$	−0.854102	+	2.62866i	−0.0510424	+	0.157092i
$281$	−4.26393	+	13.1230i	−0.254365	+	0.782855i	0.739589	+	0.673058i	$0.235020\pi$
$281$	−4.26393	+	13.1230i	−0.254365	+	0.782855i	−0.993954	+	0.109796i	$0.964980\pi$
$282$	6.18034	−	4.49028i	0.368034	−	0.267392i
$283$	−15.4443	−	11.2209i	−0.918067	−	0.667014i	0.0249754	−	0.999688i	$-0.492049\pi$
$283$	−15.4443	−	11.2209i	−0.918067	−	0.667014i	−0.943042	+	0.332674i	$0.892049\pi$
$284$	9.70820	+	29.8788i	0.576076	+	1.77298i
$285$	−0.583592			−0.0345690
$286$	11.0172	−	4.75528i	0.651462	−	0.281186i
$287$	−4.29180			−0.253337
$288$	5.91641	+	18.2088i	0.348628	+	1.07297i
$289$	−0.809017	−	0.587785i	−0.0475892	−	0.0345756i
$290$	−27.8885	+	20.2622i	−1.63767	+	1.18984i
$291$	−0.708204	+	2.17963i	−0.0415156	+	0.127772i
$292$	4.41641	−	13.5923i	0.258451	−	0.795430i
$293$	7.92705	−	5.75934i	0.463103	−	0.336464i	−0.331644	−	0.943405i	$-0.607603\pi$
$293$	7.92705	−	5.75934i	0.463103	−	0.336464i	0.794747	+	0.606940i	$0.207603\pi$
$294$	−4.57295	−	3.32244i	−0.266700	−	0.193769i
$295$	−0.180340	−	0.555029i	−0.0104998	−	0.0323150i
$296$	5.52786			0.321301
$297$	3.78115	−	6.37988i	0.219405	−	0.370198i
$298$	−31.6312			−1.83235
$299$	−1.42705	−	4.39201i	−0.0825285	−	0.253997i
$300$	−0.927051	−	0.673542i	−0.0535233	−	0.0388870i
$301$	−1.38197	+	1.00406i	−0.0796552	+	0.0578729i
$302$	−2.23607	+	6.88191i	−0.128671	+	0.396009i
$303$	1.63525	−	5.03280i	0.0939429	−	0.289127i
$304$	−0.618034	+	0.449028i	−0.0354467	+	0.0257535i
$305$	1.23607	+	0.898056i	0.0707770	+	0.0514225i
$306$	1.97214	+	6.06961i	0.112740	+	0.346977i
$307$	−25.7082			−1.46724			−0.733622	−	0.679557i	$-0.762172\pi$
$307$	−25.7082			−1.46724			−0.733622	+	0.679557i	$0.762172\pi$
$308$	3.13525	−	5.29007i	0.178648	−	0.301430i
$309$	−5.41641			−0.308129
$310$	8.94427	+	27.5276i	0.508001	+	1.56346i
$311$	−20.9164	−	15.1967i	−1.18606	−	0.861724i	−0.193218	−	0.981156i	$-0.561893\pi$
$311$	−20.9164	−	15.1967i	−1.18606	−	0.861724i	−0.992842	+	0.119432i	$0.961893\pi$
$312$	−1.11803	+	0.812299i	−0.0632962	+	0.0459874i
$313$	−3.76393	+	11.5842i	−0.212750	+	0.654777i	0.786556	+	0.617519i	$0.211862\pi$
$313$	−3.76393	+	11.5842i	−0.212750	+	0.654777i	−0.999306	+	0.0372578i	$0.988138\pi$
$314$	0.0623059	−	0.191758i	0.00351613	−	0.0108215i
$315$	−2.85410	+	2.07363i	−0.160810	+	0.116836i
$316$	23.2082	+	16.8617i	1.30556	+	0.948547i
$317$	−10.2361	−	31.5034i	−0.574915	−	1.76941i	−0.636469	−	0.771302i	$-0.719606\pi$
$317$	−10.2361	−	31.5034i	−0.574915	−	1.76941i	0.0615542	−	0.998104i	$-0.480394\pi$
$318$	3.69505			0.207208
$319$	23.4721	−	10.1311i	1.31419	−	0.567233i
$320$	26.0000			1.45344
$321$	−0.399187	−	1.22857i	−0.0222804	−	0.0685722i
$322$	−3.19098	−	2.31838i	−0.177827	−	0.129199i
$323$	−0.618034	+	0.449028i	−0.0343883	+	0.0249846i
$324$	7.14590	−	21.9928i	0.396994	−	1.22182i
$325$	0.500000	−	1.53884i	0.0277350	−	0.0853596i
$326$	−12.8262	+	9.31881i	−0.710380	+	0.516121i
$327$	2.61803	+	1.90211i	0.144778	+	0.105187i
$328$	−4.79837	−	14.7679i	−0.264946	−	0.815420i
$329$	5.52786			0.304761
$330$	−3.74265	−	4.25325i	−0.206026	−	0.234134i
$331$	0.763932			0.0419895			0.0209948	−	0.999780i	$-0.493317\pi$
$331$	0.763932			0.0419895			0.0209948	+	0.999780i	$0.493317\pi$
$332$	7.14590	+	21.9928i	0.392182	+	1.20701i
$333$	5.70820	+	4.14725i	0.312808	+	0.227268i
$334$	−24.1074	+	17.5150i	−1.31910	+	0.958381i
$335$	7.41641	−	22.8254i	0.405202	−	1.24708i
$336$	0.0729490	−	0.224514i	0.00397970	−	0.0122482i
$337$	20.0344	−	14.5559i	1.09135	−	0.792909i	0.111720	−	0.993740i	$-0.464364\pi$
$337$	20.0344	−	14.5559i	1.09135	−	0.792909i	0.979626	+	0.200831i	$0.0643641\pi$
$338$	18.7812	+	13.6453i	1.02156	+	0.742207i
$339$	0.472136	+	1.45309i	0.0256429	+	0.0789207i
$340$	6.00000			0.325396
$341$	−2.00000	−	21.3723i	−0.108306	−	1.15737i
$342$	4.87539			0.263631
$343$	−2.60081	−	8.00448i	−0.140431	−	0.432201i
$344$	−5.00000	−	3.63271i	−0.269582	−	0.195863i
$345$	−1.76393	+	1.28157i	−0.0949669	+	0.0689975i
$346$	6.50658	−	20.0252i	0.349796	−	1.07656i
$347$	3.11803	−	9.59632i	0.167385	−	0.515158i	−0.831819	−	0.555047i	$-0.812700\pi$
$347$	3.11803	−	9.59632i	0.167385	−	0.515158i	0.999204	+	0.0398890i	$0.0127004\pi$
$348$	−7.14590	+	5.19180i	−0.383060	+	0.278310i
$349$	−6.97214	−	5.06555i	−0.373210	−	0.271153i	0.385331	−	0.922778i	$-0.374087\pi$
$349$	−6.97214	−	5.06555i	−0.373210	−	0.271153i	−0.758541	+	0.651626i	$0.774087\pi$
$350$	−0.427051	−	1.31433i	−0.0228268	−	0.0702538i
$351$	−3.61803			−0.193116
$352$	−21.7082	−	4.87380i	−1.15705	−	0.259774i
$353$	32.9787			1.75528			0.877640	−	0.479321i	$-0.159117\pi$
$353$	32.9787			1.75528			0.877640	+	0.479321i	$0.159117\pi$
$354$	−0.0770143	−	0.237026i	−0.00409327	−	0.0125978i
$355$	16.9443	+	12.3107i	0.899309	+	0.653386i
$356$	23.7812	−	17.2780i	1.26040	−	0.915733i
$357$	0.0729490	−	0.224514i	0.00386087	−	0.0118825i
$358$	7.76393	−	23.8949i	0.410337	−	1.26289i
$359$	−8.94427	+	6.49839i	−0.472061	+	0.342972i	−0.798244	−	0.602334i	$-0.794237\pi$
$359$	−8.94427	+	6.49839i	−0.472061	+	0.342972i	0.326183	+	0.945307i	$0.394237\pi$
$360$	−10.3262	−	7.50245i	−0.544241	−	0.395414i
$361$	−5.69098	−	17.5150i	−0.299525	−	0.921844i
$362$	−11.7082			−0.615370
$363$	2.01722	+	3.68571i	0.105877	+	0.193450i
$364$	−3.00000			−0.157243
$365$	−2.94427	−	9.06154i	−0.154110	−	0.474303i
$366$	0.527864	+	0.383516i	0.0275919	+	0.0200467i
$367$	18.9164	−	13.7436i	0.987428	−	0.717409i	0.0280720	−	0.999606i	$-0.491063\pi$
$367$	18.9164	−	13.7436i	0.987428	−	0.717409i	0.959356	+	0.282197i	$0.0910632\pi$
$368$	−0.881966	+	2.71441i	−0.0459757	+	0.141499i
$369$	6.12461	−	18.8496i	0.318835	−	0.981272i
$370$	8.94427	−	6.49839i	0.464991	−	0.337835i
$371$	2.16312	+	1.57160i	0.112304	+	0.0815933i
$372$	2.29180	+	7.05342i	0.118824	+	0.365703i
$373$	−26.2148			−1.35735			−0.678675	−	0.734439i	$-0.737445\pi$
$373$	−26.2148			−1.35735			−0.678675	+	0.734439i	$0.737445\pi$
$374$	−7.23607	−	1.62460i	−0.374168	−	0.0840060i
$375$	−4.58359			−0.236696
$376$	6.18034	+	19.0211i	0.318727	+	0.980940i
$377$	−10.0902	−	7.33094i	−0.519670	−	0.377562i
$378$	−2.50000	+	1.81636i	−0.128586	+	0.0934233i
$379$	−4.37132	+	13.4535i	−0.224540	+	0.691062i	0.773798	+	0.633432i	$0.218354\pi$
$379$	−4.37132	+	13.4535i	−0.224540	+	0.691062i	−0.998338	+	0.0576302i	$0.981646\pi$
$380$	1.41641	−	4.35926i	0.0726602	−	0.223625i
$381$	3.23607	−	2.35114i	0.165789	−	0.120453i
$382$	32.5623	+	23.6579i	1.66603	+	1.21044i
$383$	−1.94427	−	5.98385i	−0.0993477	−	0.305761i	0.889015	−	0.457879i	$-0.151391\pi$
$383$	−1.94427	−	5.98385i	−0.0993477	−	0.305761i	−0.988362	+	0.152118i	$0.951391\pi$
$384$	5.97871			0.305100
$385$	−0.381966	−	4.08174i	−0.0194668	−	0.208025i
$386$	−21.0557			−1.07171
$387$	−2.43769	−	7.50245i	−0.123915	−	0.381371i
$388$	−14.5623	−	10.5801i	−0.739289	−	0.537125i
$389$	−9.50000	+	6.90215i	−0.481669	+	0.349953i	−0.801972	−	0.597362i	$-0.796215\pi$
$389$	−9.50000	+	6.90215i	−0.481669	+	0.349953i	0.320302	+	0.947315i	$0.396215\pi$
$390$	−0.854102	+	2.62866i	−0.0432491	+	0.133107i
$391$	−0.881966	+	2.71441i	−0.0446029	+	0.137274i
$392$	11.9721	−	8.69827i	0.604684	−	0.439329i
$393$	6.06231	+	4.40452i	0.305803	+	0.222179i
$394$	16.3820	+	50.4185i	0.825312	+	2.54005i
$395$	19.1246			0.962264
$396$	18.7599	+	21.3193i	0.942719	+	1.07133i
$397$	−27.5967			−1.38504			−0.692521	−	0.721398i	$-0.743500\pi$
$397$	−27.5967			−1.38504			−0.692521	+	0.721398i	$0.743500\pi$
$398$	−15.1008	−	46.4755i	−0.756935	−	2.32961i
$399$	−0.145898	−	0.106001i	−0.00730404	−	0.00530669i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	9.03444	−	27.8052i	0.451158	−	1.38852i	−0.424428	−	0.905462i	$-0.639525\pi$
$401$	9.03444	−	27.8052i	0.451158	−	1.38852i	0.875586	−	0.483061i	$-0.160475\pi$
$402$	3.16718	−	9.74759i	0.157965	−	0.486166i
$403$	−8.47214	+	6.15537i	−0.422027	+	0.306621i
$404$	33.6246	+	24.4297i	1.67289	+	1.21542i
$405$	−4.76393	−	14.6619i	−0.236722	−	0.728554i
$406$	−10.6525			−0.528673
$407$	−7.52786	+	3.24920i	−0.373142	+	0.161057i
$408$	0.854102			0.0422843
$409$	−10.9721	−	33.7688i	−0.542537	−	1.66976i	−0.726775	−	0.686876i	$-0.758982\pi$
$409$	−10.9721	−	33.7688i	−0.542537	−	1.66976i	0.184237	−	0.982882i	$-0.441018\pi$
$410$	−25.1246	−	18.2541i	−1.24082	−	0.901506i
$411$	−6.61803	+	4.80828i	−0.326444	+	0.237175i
$412$	13.1459	−	40.4589i	0.647652	−	1.99327i
$413$	0.0557281	−	0.171513i	0.00274220	−	0.00843962i
$414$	14.7361	−	10.7064i	0.724238	−	0.526190i
$415$	12.4721	+	9.06154i	0.612233	+	0.444813i
$416$	3.35410	+	10.3229i	0.164448	+	0.506120i
$417$	−1.52786			−0.0748198
$418$	−2.88854	+	4.87380i	−0.141283	+	0.238385i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$	0.437694	+	1.34708i	0.0213573	+	0.0657310i
$421$	5.30902	+	3.85723i	0.258746	+	0.187990i	0.709594	−	0.704611i	$-0.248878\pi$
$421$	5.30902	+	3.85723i	0.258746	+	0.187990i	−0.450848	+	0.892601i	$0.648878\pi$
$422$	43.4164	−	31.5439i	2.11348	−	1.53553i
$423$	−7.88854	+	24.2784i	−0.383554	+	1.18046i
$424$	−2.98936	+	9.20029i	−0.145176	+	0.446806i
$425$	−0.809017	+	0.587785i	−0.0392431	+	0.0285118i
$426$	7.23607	+	5.25731i	0.350589	+	0.254718i
$427$	0.145898	+	0.449028i	0.00706050	+	0.0217300i
$428$	10.1459			0.490420
$429$	1.04508	−	1.76336i	0.0504572	−	0.0851356i
$430$	−12.3607			−0.596085
$431$	−0.0623059	−	0.191758i	−0.00300117	−	0.00923665i	0.949545	−	0.313632i	$-0.101546\pi$
$431$	−0.0623059	−	0.191758i	−0.00300117	−	0.00923665i	−0.952546	+	0.304395i	$0.901546\pi$
$432$	1.80902	+	1.31433i	0.0870364	+	0.0632356i
$433$	−30.1074	+	21.8743i	−1.44687	+	1.05121i	−0.460319	+	0.887754i	$0.652265\pi$
$433$	−30.1074	+	21.8743i	−1.44687	+	1.05121i	−0.986550	+	0.163458i	$0.947735\pi$
$434$	−2.76393	+	8.50651i	−0.132673	+	0.408325i
$435$	−1.81966	+	5.60034i	−0.0872460	+	0.268516i
$436$	−20.5623	+	14.9394i	−0.984756	+	0.715467i
$437$	1.76393	+	1.28157i	0.0843803	+	0.0613059i
$438$	−1.25735	−	3.86974i	−0.0600787	−	0.184903i
$439$	−5.14590			−0.245600			−0.122800	−	0.992431i	$-0.539187\pi$
$439$	−5.14590			−0.245600			−0.122800	+	0.992431i	$0.539187\pi$
$440$	13.6180	−	5.87785i	0.649214	−	0.280216i
$441$	18.8885			0.899454
$442$	1.11803	+	3.44095i	0.0531795	+	0.163670i
$443$	21.3262	+	15.4944i	1.01324	+	0.736162i	0.964886	−	0.262668i	$-0.0846025\pi$
$443$	21.3262	+	15.4944i	1.01324	+	0.736162i	0.0483539	+	0.998830i	$0.484602\pi$
$444$	2.29180	−	1.66509i	0.108764	−	0.0790215i
$445$	6.05573	−	18.6376i	0.287069	−	0.883508i
$446$	−9.14590	+	28.1482i	−0.433071	+	1.33285i
$447$	−4.37132	+	3.17595i	−0.206756	+	0.150217i
$448$	6.50000	+	4.72253i	0.307096	+	0.223118i
$449$	8.05573	+	24.7930i	0.380173	+	1.17005i	0.939922	+	0.341390i	$0.110898\pi$
$449$	8.05573	+	24.7930i	0.380173	+	1.17005i	−0.559748	+	0.828663i	$0.689102\pi$
$450$	6.38197			0.300849
$451$	15.2148	+	17.2905i	0.716436	+	0.814179i
$452$	−12.0000			−0.564433
$453$	0.381966	+	1.17557i	0.0179463	+	0.0552331i
$454$	−24.5344	−	17.8253i	−1.15146	−	0.836584i
$455$	−1.61803	+	1.17557i	−0.0758546	+	0.0551116i
$456$	0.201626	−	0.620541i	0.00944201	−	0.0290595i
$457$	−1.80902	+	5.56758i	−0.0846222	+	0.260440i	−0.984410	−	0.175886i	$-0.943721\pi$
$457$	−1.80902	+	5.56758i	−0.0846222	+	0.260440i	0.899788	+	0.436327i	$0.143721\pi$
$458$	10.0623	−	7.31069i	0.470181	−	0.341606i
$459$	1.80902	+	1.31433i	0.0844377	+	0.0613476i
$460$	−5.29180	−	16.2865i	−0.246731	−	0.759361i
$461$	−6.79837			−0.316632			−0.158316	−	0.987389i	$-0.550606\pi$
$461$	−6.79837			−0.316632			−0.158316	+	0.987389i	$0.550606\pi$
$462$	−0.163119	−	1.74311i	−0.00758898	−	0.0810969i
$463$	−31.1246			−1.44648			−0.723242	−	0.690595i	$-0.757349\pi$
$463$	−31.1246			−1.44648			−0.723242	+	0.690595i	$0.757349\pi$
$464$	2.38197	+	7.33094i	0.110580	+	0.340330i
$465$	4.00000	+	2.90617i	0.185496	+	0.134770i
$466$	−44.9230	+	32.6385i	−2.08102	+	1.51195i
$467$	10.6180	−	32.6789i	0.491344	−	1.51220i	−0.331234	−	0.943549i	$-0.607465\pi$
$467$	10.6180	−	32.6789i	0.491344	−	1.51220i	0.822578	−	0.568653i	$-0.192535\pi$
$468$	4.28115	−	13.1760i	0.197896	−	0.609062i
$469$	6.00000	−	4.35926i	0.277054	−	0.201292i
$470$	32.3607	+	23.5114i	1.49269	+	1.08450i
$471$	−0.0106431	−	0.0327561i	−0.000490409	−	0.00150932i
$472$	0.652476			0.0300326
$473$	8.94427	+	2.00811i	0.411258	+	0.0923332i
$474$	8.16718			0.375131
$475$	0.236068	+	0.726543i	0.0108315	+	0.0333361i
$476$	1.50000	+	1.08981i	0.0687524	+	0.0499515i
$477$	−9.98936	+	7.25769i	−0.457381	+	0.332307i
$478$	−15.3262	+	47.1693i	−0.701006	+	2.15747i
$479$	−3.42705	+	10.5474i	−0.156586	+	0.481922i	−0.998318	−	0.0579733i	$-0.981536\pi$
$479$	−3.42705	+	10.5474i	−0.156586	+	0.481922i	0.841732	+	0.539895i	$0.181536\pi$
$480$	4.14590	−	3.01217i	0.189233	−	0.137486i
$481$	3.23607	+	2.35114i	0.147552	+	0.107203i
$482$	6.70820	+	20.6457i	0.305550	+	0.940387i
$483$	−0.673762			−0.0306572
$484$	−32.4271	+	6.12261i	−1.47396	+	0.278300i
$485$	−12.0000			−0.544892
$486$	−6.66970	−	20.5272i	−0.302544	−	0.931133i
$487$	6.20820	+	4.51052i	0.281321	+	0.204391i	0.719493	−	0.694499i	$-0.244374\pi$
$487$	6.20820	+	4.51052i	0.281321	+	0.204391i	−0.438173	+	0.898891i	$0.644374\pi$
$488$	−1.38197	+	1.00406i	−0.0625587	+	0.0454515i
$489$	−0.836881	+	2.57565i	−0.0378451	+	0.116475i
$490$	9.14590	−	28.1482i	0.413170	−	1.27161i
$491$	14.1803	−	10.3026i	0.639950	−	0.464951i	−0.219883	−	0.975526i	$-0.570568\pi$
$491$	14.1803	−	10.3026i	0.639950	−	0.464951i	0.859833	+	0.510575i	$0.170568\pi$
$492$	−6.43769	−	4.67726i	−0.290234	−	0.210867i
$493$	2.38197	+	7.33094i	0.107278	+	0.330169i
$494$	2.76393			0.124355
$495$	18.4721	+	4.14725i	0.830261	+	0.186405i
$496$	6.47214			0.290607
$497$	2.00000	+	6.15537i	0.0897123	+	0.276106i
$498$	5.32624	+	3.86974i	0.238674	+	0.173407i
$499$	−2.92705	+	2.12663i	−0.131033	+	0.0952009i	−0.651371	−	0.758759i	$-0.725806\pi$
$499$	−2.92705	+	2.12663i	−0.131033	+	0.0952009i	0.520338	+	0.853960i	$0.325806\pi$
$500$	11.1246	−	34.2380i	0.497508	−	1.53117i
$501$	−1.57295	+	4.84104i	−0.0702742	+	0.216282i
$502$	8.61803	−	6.26137i	0.384642	−	0.279459i
$503$	27.8713	+	20.2497i	1.24272	+	0.902890i	0.997777	−	0.0666476i	$-0.0212303\pi$
$503$	27.8713	+	20.2497i	1.24272	+	0.902890i	0.244944	+	0.969537i	$0.421230\pi$
$504$	−1.21885	−	3.75123i	−0.0542918	−	0.167093i
$505$	27.7082			1.23300
$506$	1.97214	+	21.0745i	0.0876721	+	0.936876i
$507$	3.96556			0.176117
$508$	9.70820	+	29.8788i	0.430732	+	1.32566i
$509$	−1.97214	−	1.43284i	−0.0874134	−	0.0635095i	0.543220	−	0.839590i	$-0.317205\pi$
$509$	−1.97214	−	1.43284i	−0.0874134	−	0.0635095i	−0.630634	+	0.776081i	$0.717205\pi$
$510$	1.38197	−	1.00406i	0.0611945	−	0.0444604i
$511$	0.909830	−	2.80017i	0.0402485	−	0.123872i
$512$	3.45492	−	10.6331i	0.152687	−	0.469923i
$513$	1.38197	−	1.00406i	0.0610153	−	0.0443302i
$514$	34.0066	+	24.7072i	1.49997	+	1.08979i
$515$	−8.76393	−	26.9726i	−0.386185	−	1.18856i
$516$	−3.16718			−0.139428
$517$	−19.5967	−	22.2703i	−0.861864	−	0.979448i
$518$	3.41641			0.150108
$519$	−1.11146	−	3.42071i	−0.0487875	−	0.150153i
$520$	−5.85410	−	4.25325i	−0.256719	−	0.186518i
$521$	−4.94427	+	3.59222i	−0.216612	+	0.157378i	−0.690800	−	0.723045i	$-0.742742\pi$
$521$	−4.94427	+	3.59222i	−0.216612	+	0.157378i	0.474188	+	0.880424i	$0.342742\pi$
$522$	15.2016	−	46.7858i	0.665357	−	2.04776i
$523$	−0.326238	+	1.00406i	−0.0142654	+	0.0439044i	−0.957936	−	0.286982i	$-0.907348\pi$
$523$	−0.326238	+	1.00406i	−0.0142654	+	0.0439044i	0.943670	+	0.330887i	$0.107348\pi$
$524$	−47.6140	+	34.5936i	−2.08003	+	1.51123i
$525$	−0.190983	−	0.138757i	−0.00833518	−	0.00605586i
$526$	11.8328	+	36.4177i	0.515935	+	1.58789i
$527$	6.47214			0.281931
$528$	−1.16312	+	0.502029i	−0.0506183	+	0.0218480i
$529$	−14.8541			−0.645831
$530$	5.97871	+	18.4006i	0.259699	+	0.799271i
$531$	0.673762	+	0.489517i	0.0292388	+	0.0212432i
$532$	1.14590	−	0.832544i	0.0496810	−	0.0360953i
$533$	3.47214	−	10.6861i	0.150395	−	0.462868i
$534$	2.58610	−	7.95921i	0.111912	−	0.344429i
$535$	5.47214	−	3.97574i	0.236581	−	0.171886i
$536$	21.7082	+	15.7719i	0.937652	+	0.681244i
$537$	−1.32624	−	4.08174i	−0.0572314	−	0.176140i
$538$	−54.4721			−2.34846
$539$	−11.1910	+	18.8824i	−0.482030	+	0.813321i
$540$	−13.4164			−0.577350
$541$	−4.85410	−	14.9394i	−0.208694	−	0.642295i	−0.999541	−	0.0302810i	$-0.990360\pi$
$541$	−4.85410	−	14.9394i	−0.208694	−	0.642295i	0.790847	−	0.612014i	$-0.209640\pi$
$542$	−54.9230	−	39.9039i	−2.35914	−	1.71402i
$543$	−1.61803	+	1.17557i	−0.0694365	+	0.0504486i
$544$	2.07295	−	6.37988i	0.0888770	−	0.273535i
$545$	−5.23607	+	16.1150i	−0.224289	+	0.690289i
$546$	−0.690983	+	0.502029i	−0.0295713	+	0.0214848i
$547$	−15.2533	−	11.0822i	−0.652184	−	0.473839i	0.211831	−	0.977306i	$-0.432057\pi$
$547$	−15.2533	−	11.0822i	−0.652184	−	0.473839i	−0.864014	+	0.503467i	$0.832057\pi$
$548$	−19.8541	−	61.1046i	−0.848125	−	2.61026i
$549$	−2.18034			−0.0930546
$550$	−3.78115	+	6.37988i	−0.161229	+	0.272039i
$551$	5.88854			0.250860
$552$	−0.753289	−	2.31838i	−0.0320621	−	0.0986770i
$553$	4.78115	+	3.47371i	0.203315	+	0.147717i
$554$	−45.9787	+	33.4055i	−1.95345	+	1.41926i
$555$	0.583592	−	1.79611i	0.0247721	−	0.0762407i
$556$	3.70820	−	11.4127i	0.157263	−	0.484005i
$557$	−16.1074	+	11.7027i	−0.682492	+	0.495860i	−0.874183	−	0.485596i	$-0.838603\pi$
$557$	−16.1074	+	11.7027i	−0.682492	+	0.495860i	0.191691	+	0.981455i	$0.438603\pi$
$558$	−33.4164	−	24.2784i	−1.41463	−	1.02779i
$559$	−1.38197	−	4.25325i	−0.0584509	−	0.179893i
$560$	1.23607			0.0522334
$561$	−1.16312	+	0.502029i	−0.0491069	+	0.0211957i
$562$	−30.8541			−1.30150
$563$	11.3607	+	34.9646i	0.478796	+	1.47358i	0.840770	+	0.541393i	$0.182103\pi$
$563$	11.3607	+	34.9646i	0.478796	+	1.47358i	−0.361974	+	0.932188i	$0.617897\pi$
$564$	8.29180	+	6.02434i	0.349148	+	0.253671i
$565$	−6.47214	+	4.70228i	−0.272285	+	0.197826i
$566$	13.1910	−	40.5977i	0.554458	−	1.70645i
$567$	1.47214	−	4.53077i	0.0618239	−	0.190274i
$568$	−18.9443	+	13.7638i	−0.794884	+	0.577517i
$569$	6.69098	+	4.86128i	0.280501	+	0.203796i	0.719136	−	0.694870i	$-0.244538\pi$
$569$	6.69098	+	4.86128i	0.280501	+	0.203796i	−0.438635	+	0.898665i	$0.644538\pi$
$570$	−0.403252	−	1.24108i	−0.0168904	−	0.0519832i
$571$	10.0902			0.422260			0.211130	−	0.977458i	$-0.432286\pi$
$571$	10.0902			0.422260			0.211130	+	0.977458i	$0.432286\pi$
$572$	10.6353	+	12.0862i	0.444682	+	0.505350i
$573$	6.87539			0.287223
$574$	−2.96556	−	9.12705i	−0.123780	−	0.380956i
$575$	2.30902	+	1.67760i	0.0962927	+	0.0699607i
$576$	−30.0172	+	21.8088i	−1.25072	+	0.908699i
$577$	2.39261	−	7.36369i	0.0996056	−	0.306555i	−0.888821	−	0.458255i	$-0.848475\pi$
$577$	2.39261	−	7.36369i	0.0996056	−	0.306555i	0.988427	+	0.151700i	$0.0484748\pi$
$578$	0.690983	−	2.12663i	0.0287411	−	0.0884560i
$579$	−2.90983	+	2.11412i	−0.120928	+	0.0878596i
$580$	−37.4164	−	27.1846i	−1.55363	−	1.12878i
$581$	1.47214	+	4.53077i	0.0610745	+	0.187968i
$582$	−5.12461			−0.212422
$583$	−1.33688	−	14.2861i	−0.0553680	−	0.591669i
$584$	10.6525			0.440803
$585$	−2.85410	−	8.78402i	−0.118003	−	0.363175i
$586$	17.7254	+	12.8783i	0.732231	+	0.531997i
$587$	10.9443	−	7.95148i	0.451718	−	0.328193i	−0.338555	−	0.940946i	$-0.609938\pi$
$587$	10.9443	−	7.95148i	0.451718	−	0.328193i	0.790274	+	0.612754i	$0.209938\pi$
$588$	2.34346	−	7.21242i	0.0966426	−	0.297435i
$589$	1.52786	−	4.70228i	0.0629545	−	0.193754i
$590$	1.05573	−	0.767031i	0.0434636	−	0.0315782i
$591$	7.32624	+	5.32282i	0.301361	+	0.218952i
$592$	−0.763932	−	2.35114i	−0.0313974	−	0.0966313i
$593$	−14.9656			−0.614562			−0.307281	−	0.951619i	$-0.599419\pi$
$593$	−14.9656			−0.614562			−0.307281	+	0.951619i	$0.599419\pi$
$594$	16.1803	+	3.63271i	0.663887	+	0.149052i
$595$	1.23607			0.0506738
$596$	−13.1140	−	40.3606i	−0.537169	−	1.65324i
$597$	−6.75329	−	4.90655i	−0.276394	−	0.200812i
$598$	8.35410	−	6.06961i	0.341625	−	0.248205i
$599$	2.34752	−	7.22494i	0.0959172	−	0.295203i	−0.891574	−	0.452874i	$-0.850399\pi$
$599$	2.34752	−	7.22494i	0.0959172	−	0.295203i	0.987492	+	0.157671i	$0.0503987\pi$
$600$	0.263932	−	0.812299i	0.0107750	−	0.0331620i
$601$	12.4164	−	9.02105i	0.506476	−	0.367976i	−0.305009	−	0.952349i	$-0.598660\pi$
$601$	12.4164	−	9.02105i	0.506476	−	0.367976i	0.811485	+	0.584373i	$0.198660\pi$
$602$	−3.09017	−	2.24514i	−0.125946	−	0.0915051i
$603$	10.5836	+	32.5729i	0.430997	+	1.32647i
$604$	−9.70820			−0.395021
$605$	−15.0902	+	16.0090i	−0.613503	+	0.650857i
$606$	11.8328			0.480675
$607$	6.00658	+	18.4863i	0.243799	+	0.750338i	0.995832	+	0.0912111i	$0.0290738\pi$
$607$	6.00658	+	18.4863i	0.243799	+	0.750338i	−0.752032	+	0.659126i	$0.770926\pi$
$608$	−4.14590	−	3.01217i	−0.168138	−	0.122160i
$609$	−1.47214	+	1.06957i	−0.0596540	+	0.0433411i
$610$	−1.05573	+	3.24920i	−0.0427452	+	0.131556i
$611$	−4.47214	+	13.7638i	−0.180923	+	0.556825i
$612$	−6.92705	+	5.03280i	−0.280009	+	0.203439i
$613$	26.1074	+	18.9681i	1.05447	+	0.766116i	0.973057	−	0.230565i	$-0.0740575\pi$
$613$	26.1074	+	18.9681i	1.05447	+	0.766116i	0.0814107	+	0.996681i	$0.474057\pi$
$614$	−17.7639	−	54.6718i	−0.716894	−	2.20637i
$615$	−5.30495			−0.213916
$616$	4.47214	+	1.00406i	0.180187	+	0.0404546i
$617$	−16.0000			−0.644136			−0.322068	−	0.946717i	$-0.604378\pi$
$617$	−16.0000			−0.644136			−0.322068	+	0.946717i	$0.604378\pi$
$618$	−3.74265	−	11.5187i	−0.150551	−	0.463349i
$619$	19.4164	+	14.1068i	0.780411	+	0.567002i	0.905102	−	0.425194i	$-0.139794\pi$
$619$	19.4164	+	14.1068i	0.780411	+	0.567002i	−0.124691	+	0.992196i	$0.539794\pi$
$620$	−31.4164	+	22.8254i	−1.26171	+	0.916688i
$621$	1.97214	−	6.06961i	0.0791391	−	0.243565i
$622$	17.8647	−	54.9820i	0.716311	−	2.20458i
$623$	4.89919	−	3.55947i	0.196282	−	0.142607i
$624$	0.500000	+	0.363271i	0.0200160	+	0.0145425i
$625$	−5.87132	−	18.0701i	−0.234853	−	0.722803i
$626$	−27.2361			−1.08857
$627$	0.0901699	+	0.963568i	0.00360104	+	0.0384812i
$628$	0.270510			0.0107945
$629$	−0.763932	−	2.35114i	−0.0304600	−	0.0937461i
$630$	−6.38197	−	4.63677i	−0.254264	−	0.184733i
$631$	30.8885	−	22.4418i	1.22965	−	0.893396i	0.232789	−	0.972527i	$-0.425215\pi$
$631$	30.8885	−	22.4418i	1.22965	−	0.893396i	0.996864	+	0.0791316i	$0.0252147\pi$
$632$	−6.60739	+	20.3355i	−0.262828	+	0.808901i
$633$	2.83282	−	8.71851i	0.112594	−	0.346530i
$634$	59.9230	−	43.5366i	2.37985	−	1.72906i
$635$	16.9443	+	12.3107i	0.672413	+	0.488537i
$636$	1.53193	+	4.71479i	0.0607450	+	0.186954i
$637$	10.7082			0.424274
$638$	37.7639	+	42.9161i	1.49509	+	1.69906i
$639$	−29.8885			−1.18237
$640$	9.67376	+	29.7728i	0.382389	+	1.17687i
$641$	31.8885	+	23.1684i	1.25952	+	0.915096i	0.998734	−	0.0503001i	$-0.0160178\pi$
$641$	31.8885	+	23.1684i	1.25952	+	0.915096i	0.260788	+	0.965396i	$0.416018\pi$
$642$	2.33688	−	1.69784i	0.0922293	−	0.0670085i
$643$	−3.70163	+	11.3924i	−0.145978	+	0.449274i	−0.997135	−	0.0756365i	$-0.975901\pi$
$643$	−3.70163	+	11.3924i	−0.145978	+	0.449274i	0.851158	+	0.524910i	$0.175901\pi$
$644$	1.63525	−	5.03280i	0.0644381	−	0.198320i
$645$	−1.70820	+	1.24108i	−0.0672605	+	0.0488676i
$646$	−1.38197	−	1.00406i	−0.0543727	−	0.0395041i
$647$	7.67376	+	23.6174i	0.301687	+	0.928496i	0.980893	+	0.194549i	$0.0623242\pi$
$647$	7.67376	+	23.6174i	0.301687	+	0.928496i	−0.679206	+	0.733948i	$0.737676\pi$
$648$	17.2361			0.677097
$649$	−0.888544	+	0.383516i	−0.0348784	+	0.0150543i
$650$	3.61803			0.141911
$651$	0.472136	+	1.45309i	0.0185045	+	0.0569509i
$652$	−17.2082	−	12.5025i	−0.673925	−	0.489635i
$653$	−8.85410	+	6.43288i	−0.346488	+	0.251738i	−0.747394	−	0.664381i	$-0.768695\pi$
$653$	−8.85410	+	6.43288i	−0.346488	+	0.251738i	0.400906	+	0.916119i	$0.368695\pi$
$654$	−2.23607	+	6.88191i	−0.0874372	+	0.269104i
$655$	−12.1246	+	37.3157i	−0.473748	+	1.45805i
$656$	−5.61803	+	4.08174i	−0.219347	+	0.159365i
$657$	11.0000	+	7.99197i	0.429151	+	0.311796i
$658$	3.81966	+	11.7557i	0.148906	+	0.458285i
$659$	−41.1246			−1.60199			−0.800994	−	0.598673i	$-0.795695\pi$
$659$	−41.1246			−1.60199			−0.800994	+	0.598673i	$0.795695\pi$
$660$	3.87539	−	6.53888i	0.150849	−	0.254526i
$661$	46.7426			1.81808			0.909039	−	0.416711i	$-0.136817\pi$
$661$	46.7426			1.81808			0.909039	+	0.416711i	$0.136817\pi$
$662$	0.527864	+	1.62460i	0.0205160	+	0.0631418i
$663$	0.500000	+	0.363271i	0.0194184	+	0.0141083i
$664$	−13.9443	+	10.1311i	−0.541143	+	0.393163i
$665$	0.291796	−	0.898056i	0.0113154	−	0.0348251i
$666$	−4.87539	+	15.0049i	−0.188917	+	0.581428i
$667$	17.7984	−	12.9313i	0.689156	−	0.500701i
$668$	−32.3435	−	23.4989i	−1.25141	−	0.909200i
$669$	1.56231	+	4.80828i	0.0604022	+	0.185899i
$670$	53.6656			2.07328
$671$	1.29180	−	2.17963i	0.0498692	−	0.0841436i
$672$	1.58359			0.0610884
$673$	−0.326238	−	1.00406i	−0.0125755	−	0.0387036i	0.944572	−	0.328305i	$-0.106477\pi$
$673$	−0.326238	−	1.00406i	−0.0125755	−	0.0387036i	−0.957147	+	0.289601i	$0.906477\pi$
$674$	44.7984	+	32.5479i	1.72557	+	1.25370i
$675$	1.80902	−	1.31433i	0.0696291	−	0.0505885i
$676$	−9.62461	+	29.6215i	−0.370177	+	1.13929i
$677$	−10.9443	+	33.6830i	−0.420623	+	1.29454i	0.486502	+	0.873680i	$0.338273\pi$
$677$	−10.9443	+	33.6830i	−0.420623	+	1.29454i	−0.907124	+	0.420863i	$0.861727\pi$
$678$	−2.76393	+	2.00811i	−0.106148	+	0.0771212i
$679$	−3.00000	−	2.17963i	−0.115129	−	0.0836464i
$680$	1.38197	+	4.25325i	0.0529960	+	0.163105i
$681$	−5.18034			−0.198511
$682$	44.0689	−	19.0211i	1.68748	−	0.728357i
$683$	−17.8541			−0.683168			−0.341584	−	0.939851i	$-0.610963\pi$
$683$	−17.8541			−0.683168			−0.341584	+	0.939851i	$0.610963\pi$
$684$	2.02129	+	6.22088i	0.0772858	+	0.237861i
$685$	−34.6525	−	25.1765i	−1.32400	−	0.961945i
$686$	15.2254	−	11.0619i	0.581309	−	0.422346i
$687$	0.656541	−	2.02063i	0.0250486	−	0.0770917i
$688$	−0.854102	+	2.62866i	−0.0325623	+	0.100217i
$689$	−5.66312	+	4.11450i	−0.215748	+	0.156750i
$690$	−3.94427	−	2.86568i	−0.150156	−	0.109095i
$691$	−2.35410	−	7.24518i	−0.0895543	−	0.275620i	0.896242	−	0.443565i	$-0.146287\pi$
$691$	−2.35410	−	7.24518i	−0.0895543	−	0.275620i	−0.985796	+	0.167946i	$0.946287\pi$
$692$	28.2492			1.07387
$693$	3.86475	+	4.39201i	0.146810	+	0.166839i
$694$	22.5623			0.856453
$695$	−2.47214	−	7.60845i	−0.0937735	−	0.288605i
$696$	−5.32624	−	3.86974i	−0.201891	−	0.146682i
$697$	−5.61803	+	4.08174i	−0.212798	+	0.154607i
$698$	5.95492	−	18.3273i	0.225397	−	0.693700i
$699$	−2.93112	+	9.02105i	−0.110865	+	0.341207i
$700$	1.50000	−	1.08981i	0.0566947	−	0.0411911i
$701$	−39.3435	−	28.5847i	−1.48598	−	1.07963i	−0.975567	−	0.219701i	$-0.929492\pi$
$701$	−39.3435	−	28.5847i	−1.48598	−	1.07963i	−0.510415	−	0.859928i	$-0.670508\pi$
$702$	−2.50000	−	7.69421i	−0.0943564	−	0.290399i
$703$	−1.88854			−0.0712278
$704$	−4.01722	−	42.9286i	−0.151405	−	1.61793i
$705$	6.83282			0.257339
$706$	22.7877	+	70.1334i	0.857628	+	2.63951i
$707$	6.92705	+	5.03280i	0.260519	+	0.189278i
$708$	0.270510	−	0.196537i	0.0101664	−	0.00738631i
$709$	−1.20163	+	3.69822i	−0.0451280	+	0.138890i	−0.971082	−	0.238747i	$-0.923263\pi$
$709$	−1.20163	+	3.69822i	−0.0451280	+	0.138890i	0.925954	+	0.377637i	$0.123263\pi$
$710$	−14.4721	+	44.5407i	−0.543130	+	1.67158i
$711$	−22.0795	+	16.0417i	−0.828047	+	0.601611i
$712$	17.7254	+	12.8783i	0.664288	+	0.482634i
$713$	−5.70820	−	17.5680i	−0.213774	−	0.657928i
$714$	0.527864			0.0197548
$715$	10.4721	+	2.35114i	0.391636	+	0.0879277i
$716$	33.7082			1.25973
$717$	2.61803	+	8.05748i	0.0977723	+	0.300912i
$718$	−20.0000	−	14.5309i	−0.746393	−	0.542287i
$719$	24.8156	−	18.0296i	0.925466	−	0.672390i	−0.0194129	−	0.999812i	$-0.506180\pi$
$719$	24.8156	−	18.0296i	0.925466	−	0.672390i	0.944878	+	0.327421i	$0.106180\pi$
$720$	−1.76393	+	5.42882i	−0.0657379	+	0.202320i
$721$	2.70820	−	8.33499i	0.100859	−	0.310411i
$722$	33.3156	−	24.2052i	1.23988	−	0.900824i
$723$	3.00000	+	2.17963i	0.111571	+	0.0810612i
$724$	−4.85410	−	14.9394i	−0.180401	−	0.555218i
$725$	7.70820			0.286276
$726$	−6.44427	+	6.83664i	−0.239169	+	0.253732i
$727$	−39.4853			−1.46443			−0.732214	−	0.681074i	$-0.761513\pi$
$727$	−39.4853			−1.46443			−0.732214	+	0.681074i	$0.761513\pi$
$728$	−0.690983	−	2.12663i	−0.0256095	−	0.0788180i
$729$	15.7254	+	11.4252i	0.582423	+	0.423155i
$730$	17.2361	−	12.5227i	0.637935	−	0.463487i
$731$	−0.854102	+	2.62866i	−0.0315901	+	0.0972243i
$732$	−0.270510	+	0.832544i	−0.00999833	+	0.0307717i
$733$	16.8541	−	12.2452i	0.622520	−	0.452288i	−0.231281	−	0.972887i	$-0.574292\pi$
$733$	16.8541	−	12.2452i	0.622520	−	0.452288i	0.853801	+	0.520600i	$0.174292\pi$
$734$	42.2984	+	30.7316i	1.56126	+	1.13432i
$735$	−1.56231	−	4.80828i	−0.0576265	−	0.177356i
$736$	−19.1459			−0.705727
$737$	−38.8328	−	8.71851i	−1.43043	−	0.321150i
$738$	44.3181			1.63137
$739$	−1.41641	−	4.35926i	−0.0521034	−	0.160358i	0.921619	−	0.388096i	$-0.126867\pi$
$739$	−1.41641	−	4.35926i	−0.0521034	−	0.160358i	−0.973722	+	0.227738i	$0.926867\pi$
$740$	12.0000	+	8.71851i	0.441129	+	0.320499i
$741$	0.381966	−	0.277515i	0.0140319	−	0.0101948i
$742$	−1.84752	+	5.68609i	−0.0678247	+	0.208743i
$743$	−7.82624	+	24.0867i	−0.287117	+	0.883655i	0.698639	+	0.715474i	$0.253789\pi$
$743$	−7.82624	+	24.0867i	−0.287117	+	0.883655i	−0.985756	+	0.168181i	$0.946211\pi$
$744$	−4.47214	+	3.24920i	−0.163956	+	0.119121i
$745$	−22.8885	−	16.6295i	−0.838571	−	0.609258i
$746$	−18.1140	−	55.7491i	−0.663200	−	2.04112i
$747$	−22.0000			−0.804938
$748$	−0.927051	−	9.90659i	−0.0338963	−	0.362221i
$749$	2.09017			0.0763731
$750$	−3.16718	−	9.74759i	−0.115649	−	0.355932i
$751$	0.635255	+	0.461540i	0.0231808	+	0.0168418i	0.599315	−	0.800513i	$-0.295440\pi$
$751$	0.635255	+	0.461540i	0.0231808	+	0.0168418i	−0.576135	+	0.817355i	$0.695440\pi$
$752$	7.23607	−	5.25731i	0.263872	−	0.191714i
$753$	0.562306	−	1.73060i	0.0204916	−	0.0630666i
$754$	8.61803	−	26.5236i	0.313850	−	0.965932i
$755$	−5.23607	+	3.80423i	−0.190560	+	0.138450i
$756$	−3.35410	−	2.43690i	−0.121988	−	0.0886291i
$757$	−6.14590	−	18.9151i	−0.223376	−	0.687482i	−0.998452	−	0.0556139i	$-0.982288\pi$
$757$	−6.14590	−	18.9151i	−0.223376	−	0.687482i	0.775076	−	0.631868i	$-0.217712\pi$
$758$	−31.6312			−1.14890
$759$	2.38854	+	2.71441i	0.0866986	+	0.0985269i
$760$	3.41641			0.123926
$761$	7.98936	+	24.5887i	0.289614	+	0.891340i	0.984978	+	0.172682i	$0.0552433\pi$
$761$	7.98936	+	24.5887i	0.289614	+	0.891340i	−0.695364	+	0.718658i	$0.744757\pi$
$762$	7.23607	+	5.25731i	0.262135	+	0.190452i
$763$	−4.23607	+	3.07768i	−0.153356	+	0.111420i
$764$	−16.6869	+	51.3571i	−0.603711	+	1.85803i
$765$	−1.76393	+	5.42882i	−0.0637751	+	0.196280i
$766$	11.3820	−	8.26948i	0.411247	−	0.298789i
$767$	0.381966	+	0.277515i	0.0137920	+	0.0100205i
$768$	1.06231	+	3.26944i	0.0383327	+	0.117976i
$769$	−23.0902			−0.832653			−0.416326	−	0.909215i	$-0.636683\pi$
$769$	−23.0902			−0.832653			−0.416326	+	0.909215i	$0.636683\pi$
$770$	8.41641	−	3.63271i	0.303306	−	0.130914i
$771$	7.18034			0.258594
$772$	−8.72949	−	26.8666i	−0.314181	−	0.966950i
$773$	−42.1525	−	30.6256i	−1.51612	−	1.10153i	−0.963369	−	0.268178i	$-0.913579\pi$
$773$	−42.1525	−	30.6256i	−1.51612	−	1.10153i	−0.552750	−	0.833347i	$-0.686421\pi$
$774$	14.2705	−	10.3681i	0.512943	−	0.372675i
$775$	2.00000	−	6.15537i	0.0718421	−	0.221107i
$776$	4.14590	−	12.7598i	0.148829	−	0.458049i
$777$	0.472136	−	0.343027i	0.0169378	−	0.0123060i
$778$	−21.2426	−	15.4337i	−0.761586	−	0.553324i
$779$	1.63932	+	5.04531i	0.0587347	+	0.180767i
$780$	−3.70820			−0.132775
$781$	17.7082	−	29.8788i	0.633649	−	1.06915i
$782$	−6.38197			−0.228219
$783$	−5.32624	−	16.3925i	−0.190344	−	0.585819i
$784$	−5.35410	−	3.88998i	−0.191218	−	0.138928i
$785$	0.145898	−	0.106001i	0.00520732	−	0.00378334i
$786$	−5.17783	+	15.9357i	−0.184687	+	0.568408i
$787$	4.06231	−	12.5025i	0.144806	−	0.445666i	−0.852180	−	0.523248i	$-0.824720\pi$
$787$	4.06231	−	12.5025i	0.144806	−	0.445666i	0.996986	+	0.0775824i	$0.0247201\pi$
$788$	−57.5410	+	41.8060i	−2.04981	+	1.48928i
$789$	5.29180	+	3.84471i	0.188393	+	0.136875i
$790$	13.2148	+	40.6709i	0.470161	+	1.44701i
$791$	−2.47214			−0.0878990
$792$	−10.7918	+	18.2088i	−0.383470	+	0.647023i
$793$	−1.23607			−0.0438941
$794$	−19.0689	−	58.6880i	−0.676729	−	2.08276i
$795$	2.67376	+	1.94260i	0.0948286	+	0.0688970i
$796$	53.0410	−	38.5366i	1.87999	−	1.36589i
$797$	4.73607	−	14.5761i	0.167760	−	0.516313i	−0.831469	−	0.555571i	$-0.812500\pi$
$797$	4.73607	−	14.5761i	0.167760	−	0.516313i	0.999229	+	0.0392586i	$0.0124996\pi$
$798$	0.124612	−	0.383516i	0.00441121	−	0.0135763i
$799$	7.23607	−	5.25731i	0.255994	−	0.185990i
$800$	−5.42705	−	3.94298i	−0.191875	−	0.139406i
$801$	8.64183	+	26.5968i	0.305344	+	0.939753i
$802$	65.3738			2.30843
$803$	−14.5066	+	6.26137i	−0.511926	+	0.220959i
$804$	13.7508			0.484952
$805$	−1.09017	−	3.35520i	−0.0384234	−	0.118255i
$806$	−18.9443	−	13.7638i	−0.667284	−	0.484810i
$807$	−7.52786	+	5.46931i	−0.264993	+	0.192529i
$808$	−9.57295	+	29.4625i	−0.336775	+	1.03649i
$809$	−4.79837	+	14.7679i	−0.168702	+	0.519211i	−0.999290	−	0.0376763i	$-0.988004\pi$
$809$	−4.79837	+	14.7679i	−0.168702	+	0.519211i	0.830588	+	0.556887i	$0.188004\pi$
$810$	27.8885	−	20.2622i	0.979904	−	0.711942i
$811$	−12.7812	−	9.28605i	−0.448807	−	0.326077i	0.340318	−	0.940311i	$-0.389465\pi$
$811$	−12.7812	−	9.28605i	−0.448807	−	0.326077i	−0.789125	+	0.614233i	$0.789465\pi$
$812$	−4.41641	−	13.5923i	−0.154986	−	0.476996i
$813$	−11.5967			−0.406716
$814$	−12.1115	−	13.7638i	−0.424506	−	0.482422i
$815$	−14.1803			−0.496716
$816$	−0.118034	−	0.363271i	−0.00413202	−	0.0127170i
$817$	1.70820	+	1.24108i	0.0597625	+	0.0434200i
$818$	64.2320	−	46.6673i	2.24582	−	1.63168i
$819$	0.881966	−	2.71441i	0.0308184	−	0.0948492i
$820$	12.8754	−	39.6264i	0.449628	−	1.38381i
$821$	20.6525	−	15.0049i	0.720776	−	0.523675i	−0.165856	−	0.986150i	$-0.553039\pi$
$821$	20.6525	−	15.0049i	0.720776	−	0.523675i	0.886632	+	0.462475i	$0.153039\pi$
$822$	−14.7984	−	10.7516i	−0.516153	−	0.375007i
$823$	−1.80902	−	5.56758i	−0.0630584	−	0.194074i	0.914564	−	0.404441i	$-0.132534\pi$
$823$	−1.80902	−	5.56758i	−0.0630584	−	0.194074i	−0.977622	+	0.210367i	$0.932534\pi$
$824$	31.7082			1.10461
$825$	0.118034	+	1.26133i	0.00410942	+	0.0439138i
$826$	0.403252			0.0140309
$827$	−1.52786	−	4.70228i	−0.0531290	−	0.163514i	0.920971	−	0.389630i	$-0.127397\pi$
$827$	−1.52786	−	4.70228i	−0.0531290	−	0.163514i	−0.974100	+	0.226116i	$0.927397\pi$
$828$	19.7705	+	14.3641i	0.687073	+	0.499188i
$829$	17.7361	−	12.8860i	0.615999	−	0.447550i	−0.235523	−	0.971869i	$-0.575680\pi$
$829$	17.7361	−	12.8860i	0.615999	−	0.447550i	0.851522	+	0.524319i	$0.175680\pi$
$830$	−10.6525	+	32.7849i	−0.369753	+	1.13798i
$831$	−3.00000	+	9.23305i	−0.104069	+	0.320291i
$832$	−17.0172	+	12.3637i	−0.589966	+	0.428635i
$833$	−5.35410	−	3.88998i	−0.185509	−	0.134780i
$834$	−1.05573	−	3.24920i	−0.0365569	−	0.112510i
$835$	−26.6525			−0.922347
$836$	−7.41641	−	1.66509i	−0.256502	−	0.0575882i
$837$	−14.4721			−0.500230
$838$	8.29180	+	25.5195i	0.286435	+	0.881557i
$839$	41.2877	+	29.9973i	1.42541	+	1.03562i	0.990848	+	0.134980i	$0.0430970\pi$
$839$	41.2877	+	29.9973i	1.42541	+	1.03562i	0.434562	+	0.900642i	$0.356903\pi$
$840$	−0.854102	+	0.620541i	−0.0294693	+	0.0214107i
$841$	9.39919	−	28.9277i	0.324110	−	0.997508i
$842$	−4.53444	+	13.9556i	−0.156267	+	0.480941i
$843$	−4.26393	+	3.09793i	−0.146858	+	0.106698i
$844$	58.2492	+	42.3205i	2.00502	+	1.45673i
$845$	6.41641	+	19.7477i	0.220731	+	0.679341i
$846$	−57.0820			−1.96252
$847$	−6.68034	+	1.26133i	−0.229539	+	0.0433397i
$848$	4.32624			0.148564
$849$	−2.25329	−	6.93491i	−0.0773327	−	0.238006i
$850$	−1.80902	−	1.31433i	−0.0620488	−	0.0450811i
$851$	−5.70820	+	4.14725i	−0.195675	+	0.142166i
$852$	−3.70820	+	11.4127i	−0.127041	+	0.390992i
$853$	3.56231	−	10.9637i	0.121971	−	0.375388i	−0.871366	−	0.490633i	$-0.836765\pi$
$853$	3.56231	−	10.9637i	0.121971	−	0.375388i	0.993337	+	0.115245i	$0.0367654\pi$
$854$	−0.854102	+	0.620541i	−0.0292268	+	0.0212345i
$855$	3.52786	+	2.56314i	0.120650	+	0.0876576i
$856$	2.33688	+	7.19218i	0.0798729	+	0.245824i
$857$	52.1803			1.78245			0.891223	−	0.453565i	$-0.149848\pi$
$857$	52.1803			1.78245			0.891223	+	0.453565i	$0.149848\pi$
$858$	4.47214	+	1.00406i	0.152676	+	0.0342779i
$859$	53.8885			1.83865			0.919327	−	0.393495i	$-0.128734\pi$
$859$	53.8885			1.83865			0.919327	+	0.393495i	$0.128734\pi$
$860$	−5.12461	−	15.7719i	−0.174748	−	0.537818i
$861$	−1.32624	−	0.963568i	−0.0451981	−	0.0328383i
$862$	0.364745	−	0.265003i	0.0124233	−	0.00902603i
$863$	−5.72949	+	17.6336i	−0.195034	+	0.600253i	0.804942	+	0.593353i	$0.202196\pi$
$863$	−5.72949	+	17.6336i	−0.195034	+	0.600253i	−0.999976	+	0.00689989i	$0.997804\pi$
$864$	−4.63525	+	14.2658i	−0.157695	+	0.485334i
$865$	15.2361	−	11.0697i	0.518042	−	0.376379i
$866$	−67.3222	−	48.9124i	−2.28770	−	1.66211i
$867$	−0.118034	−	0.363271i	−0.00400864	−	0.0123373i
$868$	−12.0000			−0.407307
$869$	−2.95492	−	31.5766i	−0.100239	−	1.07116i
$870$	−13.1672			−0.446409
$871$	6.00000	+	18.4661i	0.203302	+	0.625700i
$872$	−15.3262	−	11.1352i	−0.519012	−	0.377084i
$873$	13.8541	−	10.0656i	0.468890	−	0.340669i
$874$	−1.50658	+	4.63677i	−0.0509608	+	0.156841i
$875$	2.29180	−	7.05342i	0.0774768	−	0.238449i
$876$	4.41641	−	3.20871i	0.149217	−	0.108412i
$877$	−1.00000	−	0.726543i	−0.0337676	−	0.0245336i	0.570773	−	0.821108i	$-0.306643\pi$
$877$	−1.00000	−	0.726543i	−0.0337676	−	0.0245336i	−0.604541	+	0.796574i	$0.706643\pi$
$878$	−3.55573	−	10.9434i	−0.120000	−	0.369322i
$879$	3.74265			0.126236
$880$	−4.38197	−	4.97980i	−0.147716	−	0.167869i
$881$	−31.5967			−1.06452			−0.532261	−	0.846580i	$-0.678657\pi$
$881$	−31.5967			−1.06452			−0.532261	+	0.846580i	$0.678657\pi$
$882$	13.0517	+	40.1689i	0.439472	+	1.35256i
$883$	−12.3262	−	8.95554i	−0.414811	−	0.301378i	0.360736	−	0.932668i	$-0.382526\pi$
$883$	−12.3262	−	8.95554i	−0.414811	−	0.301378i	−0.775547	+	0.631290i	$0.782526\pi$
$884$	−3.92705	+	2.85317i	−0.132081	+	0.0959625i
$885$	0.0688837	−	0.212002i	0.00231550	−	0.00712638i
$886$	−18.2148	+	56.0593i	−0.611938	+	1.88335i
$887$	−34.1803	+	24.8335i	−1.14766	+	0.833826i	−0.988168	−	0.153372i	$-0.950987\pi$
$887$	−34.1803	+	24.8335i	−1.14766	+	0.833826i	−0.159495	+	0.987199i	$0.550987\pi$
$888$	1.70820	+	1.24108i	0.0573236	+	0.0416480i
$889$	2.00000	+	6.15537i	0.0670778	+	0.206444i
$890$	43.8197			1.46884
$891$	−23.4721	+	10.1311i	−0.786346	+	0.339405i
$892$	−39.7082			−1.32953
$893$	−2.11146	−	6.49839i	−0.0706572	−	0.217460i
$894$	−9.77458	−	7.10164i	−0.326911	−	0.237515i
$895$	18.1803	−	13.2088i	0.607702	−	0.441521i
$896$	−2.98936	+	9.20029i	−0.0998674	+	0.307360i
$897$	0.545085	−	1.67760i	0.0181999	−	0.0560134i
$898$	−47.1591	+	34.2631i	−1.57372	+	1.14337i
$899$	−40.3607	−	29.3238i	−1.34610	−	0.978002i
$900$	2.64590	+	8.14324i	0.0881966	+	0.271441i
$901$	4.32624			0.144128
$902$	−26.2574	+	44.3036i	−0.874274	+	1.47515i
$903$	−0.652476			−0.0217130
$904$	−2.76393	−	8.50651i	−0.0919270	−	0.282922i
$905$	−8.47214	−	6.15537i	−0.281623	−	0.204611i
$906$	−2.23607	+	1.62460i	−0.0742884	+	0.0539737i
$907$	−11.8197	+	36.3772i	−0.392465	+	1.20788i	0.538453	+	0.842656i	$0.319009\pi$
$907$	−11.8197	+	36.3772i	−0.392465	+	1.20788i	−0.930918	+	0.365228i	$0.880991\pi$
$908$	12.5729	−	38.6956i	0.417248	−	1.28416i
$909$	−31.9894	+	23.2416i	−1.06102	+	0.770876i
$910$	−3.61803	−	2.62866i	−0.119937	−	0.0871391i
$911$	4.82624	+	14.8536i	0.159900	+	0.492123i	0.998624	−	0.0524339i	$-0.0166979\pi$
$911$	4.82624	+	14.8536i	0.159900	+	0.492123i	−0.838724	+	0.544557i	$0.816698\pi$
$912$	−0.291796			−0.00966233
$913$	13.0344	−	21.9928i	0.431377	−	0.727856i
$914$	−13.0902			−0.432984
$915$	0.180340	+	0.555029i	0.00596185	+	0.0183487i
$916$	13.5000	+	9.80832i	0.446053	+	0.324076i
$917$	−9.80902	+	7.12667i	−0.323922	+	0.235343i
$918$	−1.54508	+	4.75528i	−0.0509954	+	0.156948i
$919$	14.4377	−	44.4347i	0.476256	−	1.46576i	−0.368001	−	0.929825i	$-0.619958\pi$
$919$	14.4377	−	44.4347i	0.476256	−	1.46576i	0.844257	−	0.535939i	$-0.180042\pi$
$920$	10.3262	−	7.50245i	0.340446	−	0.247348i
$921$	−7.94427	−	5.77185i	−0.261773	−	0.190189i
$922$	−4.69756	−	14.4576i	−0.154706	−	0.476136i
$923$	−16.9443			−0.557728
$924$	2.15654	−	0.930812i	0.0709450	−	0.0306215i
$925$	−2.47214			−0.0812833
$926$	−21.5066	−	66.1904i	−0.706750	−	2.17515i
$927$	32.7426	+	23.7889i	1.07541	+	0.781331i
$928$	−41.8328	+	30.3933i	−1.37323	+	0.997710i
$929$	−12.8197	+	39.4549i	−0.420599	+	1.29447i	0.486546	+	0.873655i	$0.338257\pi$
$929$	−12.8197	+	39.4549i	−0.420599	+	1.29447i	−0.907146	+	0.420817i	$0.861743\pi$
$930$	−3.41641	+	10.5146i	−0.112028	+	0.344788i
$931$	−4.09017	+	2.97168i	−0.134050	+	0.0973930i
$932$	−60.2705	−	43.7891i	−1.97423	−	1.43436i
$933$	−3.05166	−	9.39205i	−0.0999070	−	0.307482i
$934$	76.8328			2.51405
$935$	−4.38197	−	4.97980i	−0.143306	−	0.162857i
$936$	10.3262			0.337524
$937$	17.4443	+	53.6879i	0.569880	+	1.75391i	0.652988	+	0.757368i	$0.273515\pi$
$937$	17.4443	+	53.6879i	0.569880	+	1.75391i	−0.0831084	+	0.996541i	$0.526485\pi$
$938$	13.4164	+	9.74759i	0.438061	+	0.318270i
$939$	−3.76393	+	2.73466i	−0.122831	+	0.0892421i
$940$	−16.5836	+	51.0390i	−0.540897	+	1.66471i
$941$	11.3820	−	35.0301i	0.371041	−	1.14195i	−0.575069	−	0.818105i	$-0.695025\pi$
$941$	11.3820	−	35.0301i	0.371041	−	1.14195i	0.946111	−	0.323843i	$-0.104975\pi$
$942$	0.0623059	−	0.0452679i	0.00203004	−	0.00147491i
$943$	16.0344	+	11.6497i	0.522153	+	0.379367i
$944$	−0.0901699	−	0.277515i	−0.00293478	−	0.00903233i
$945$	−2.76393			−0.0899107
$946$	1.90983	+	20.4087i	0.0620939	+	0.663544i
$947$	−15.7984			−0.513378			−0.256689	−	0.966494i	$-0.582632\pi$
$947$	−15.7984			−0.513378			−0.256689	+	0.966494i	$0.582632\pi$
$948$	3.38603	+	10.4211i	0.109973	+	0.338463i
$949$	6.23607	+	4.53077i	0.202431	+	0.147075i
$950$	−1.38197	+	1.00406i	−0.0448369	+	0.0325759i
$951$	3.90983	−	12.0332i	0.126785	−	0.390204i
$952$	−0.427051	+	1.31433i	−0.0138408	+	0.0425976i
$953$	28.3885	−	20.6255i	0.919595	−	0.668125i	−0.0238281	−	0.999716i	$-0.507585\pi$
$953$	28.3885	−	20.6255i	0.919595	−	0.668125i	0.943423	+	0.331591i	$0.107585\pi$
$954$	−22.3369	−	16.2287i	−0.723183	−	0.525423i
$955$	11.1246	+	34.2380i	0.359984	+	1.10792i
$956$	−66.5410			−2.15209
$957$	9.52786	+	2.13914i	0.307992	+	0.0691485i
$958$	−24.7984			−0.801199
$959$	−4.09017	−	12.5882i	−0.132078	−	0.406496i
$960$	8.03444	+	5.83736i	0.259310	+	0.188400i
$961$	−8.80902	+	6.40013i	−0.284162	+	0.206456i
$962$	−2.76393	+	8.50651i	−0.0891127	+	0.274261i
$963$	−2.98278	+	9.18005i	−0.0961187	+	0.295823i
$964$	−23.5623	+	17.1190i	−0.758891	+	0.551366i
$965$	−15.2361	−	11.0697i	−0.490466	−	0.356345i
$966$	−0.465558	−	1.43284i	−0.0149791	−	0.0461009i
$967$	−11.0557			−0.355528			−0.177764	−	0.984073i	$-0.556886\pi$
$967$	−11.0557			−0.355528			−0.177764	+	0.984073i	$0.556886\pi$
$968$	−11.8090	−	21.5765i	−0.379556	−	0.693496i
$969$	−0.291796			−0.00937384
$970$	−8.29180	−	25.5195i	−0.266234	−	0.819383i
$971$	14.5623	+	10.5801i	0.467327	+	0.339533i	0.796399	−	0.604772i	$-0.206736\pi$
$971$	14.5623	+	10.5801i	0.467327	+	0.339533i	−0.329072	+	0.944305i	$0.606736\pi$
$972$	23.4271	−	17.0207i	0.751423	−	0.545941i
$973$	0.763932	−	2.35114i	0.0244905	−	0.0753741i
$974$	−5.30244	+	16.3192i	−0.169901	+	0.522902i
$975$	0.500000	−	0.363271i	0.0160128	−	0.0116340i
$976$	0.618034	+	0.449028i	0.0197828	+	0.0143730i
$977$	8.50000	+	26.1603i	0.271939	+	0.836942i	0.990013	+	0.140976i	$0.0450239\pi$
$977$	8.50000	+	26.1603i	0.271939	+	0.836942i	−0.718074	+	0.695967i	$0.754976\pi$
$978$	−6.05573			−0.193641
$979$	−31.7082	−	7.11894i	−1.01340	−	0.227522i
$980$	39.7082			1.26843
$981$	−7.47214	−	22.9969i	−0.238567	−	0.734234i
$982$	31.7082	+	23.0374i	1.01185	+	0.735152i
$983$	26.1976	−	19.0336i	0.835572	−	0.607079i	−0.0855579	−	0.996333i	$-0.527267\pi$
$983$	26.1976	−	19.0336i	0.835572	−	0.607079i	0.921130	+	0.389254i	$0.127267\pi$
$984$	1.83282	−	5.64083i	0.0584280	−	0.179823i
$985$	−14.6525	+	45.0957i	−0.466867	+	1.43687i
$986$	−13.9443	+	10.1311i	−0.444076	+	0.322640i
$987$	1.70820	+	1.24108i	0.0543727	+	0.0395041i
$988$	1.14590	+	3.52671i	0.0364559	+	0.112200i
$989$	7.88854			0.250841
$990$	3.94427	+	42.1490i	0.125357	+	1.33958i
$991$	14.4508			0.459046			0.229523	−	0.973303i	$-0.426283\pi$
$991$	14.4508			0.459046			0.229523	+	0.973303i	$0.426283\pi$
$992$	13.4164	+	41.2915i	0.425971	+	1.31101i
$993$	0.236068	+	0.171513i	0.00749139	+	0.00544281i
$994$	−11.7082	+	8.50651i	−0.371362	+	0.269810i
$995$	13.5066	−	41.5690i	0.428187	−	1.31783i
$996$	−2.72949	+	8.40051i	−0.0864872	+	0.266180i
$997$	23.1803	−	16.8415i	0.734129	−	0.533376i	−0.156738	−	0.987640i	$-0.550098\pi$
$997$	23.1803	−	16.8415i	0.734129	−	0.533376i	0.890867	+	0.454264i	$0.150098\pi$
$998$	−6.54508	−	4.75528i	−0.207181	−	0.150526i
$999$	1.70820	+	5.25731i	0.0540452	+	0.166334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.c.137.1	yes	4
11.3	even	5		2057.2.a.k.1.2		2
11.8	odd	10		2057.2.a.j.1.1		2
11.9	even	5	inner	187.2.g.c.86.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.c.86.1	✓	4	11.9	even	5	inner
187.2.g.c.137.1	yes	4	1.1	even	1	trivial
2057.2.a.j.1.1		2	11.8	odd	10
2057.2.a.k.1.2		2	11.3	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.690983 + 2.12663i) q^{2} +(0.309017 + 0.224514i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(-0.263932 + 0.812299i) q^{6} +(-0.500000 + 0.363271i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.881966 - 2.71441i) q^{9} +O(q^{10})\)	\(q+(0.690983 + 2.12663i) q^{2} +(0.309017 + 0.224514i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(-0.263932 + 0.812299i) q^{6} +(-0.500000 + 0.363271i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.881966 - 2.71441i) q^{9} -4.47214 q^{10} +(3.23607 + 0.726543i) q^{11} -1.14590 q^{12} +(-0.500000 - 1.53884i) q^{13} +(-1.11803 - 0.812299i) q^{14} +(-0.618034 + 0.449028i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(5.16312 - 3.75123i) q^{18} +(0.618034 + 0.449028i) q^{19} +(-1.85410 - 5.70634i) q^{20} -0.236068 q^{21} +(0.690983 + 7.38394i) q^{22} +2.85410 q^{23} +(-0.263932 - 0.812299i) q^{24} +(0.809017 + 0.587785i) q^{25} +(2.92705 - 2.12663i) q^{26} +(0.690983 - 2.12663i) q^{27} +(0.572949 - 1.76336i) q^{28} +(6.23607 - 4.53077i) q^{29} +(-1.38197 - 1.00406i) q^{30} +(-2.00000 - 6.15537i) q^{31} -6.70820 q^{32} +(0.836881 + 0.951057i) q^{33} -2.23607 q^{34} +(-0.381966 - 1.17557i) q^{35} +(6.92705 + 5.03280i) q^{36} +(-2.00000 + 1.45309i) q^{37} +(-0.527864 + 1.62460i) q^{38} +(0.190983 - 0.587785i) q^{39} +(3.61803 - 2.62866i) q^{40} +(5.61803 + 4.08174i) q^{41} +(-0.163119 - 0.502029i) q^{42} +2.76393 q^{43} +(-9.13525 + 3.94298i) q^{44} +5.70820 q^{45} +(1.97214 + 6.06961i) q^{46} +(-7.23607 - 5.25731i) q^{47} +(-0.309017 + 0.224514i) q^{48} +(-2.04508 + 6.29412i) q^{49} +(-0.690983 + 2.12663i) q^{50} +(-0.309017 + 0.224514i) q^{51} +(3.92705 + 2.85317i) q^{52} +(-1.33688 - 4.11450i) q^{53} +5.00000 q^{54} +(-3.38197 + 5.70634i) q^{55} +1.38197 q^{56} +(0.0901699 + 0.277515i) q^{57} +(13.9443 + 10.1311i) q^{58} +(-0.236068 + 0.171513i) q^{59} +(0.708204 - 2.17963i) q^{60} +(0.236068 - 0.726543i) q^{61} +(11.7082 - 8.50651i) q^{62} +(1.42705 + 1.03681i) q^{63} +(-4.01722 - 12.3637i) q^{64} +3.23607 q^{65} +(-1.44427 + 2.43690i) q^{66} -12.0000 q^{67} +(-0.927051 - 2.85317i) q^{68} +(0.881966 + 0.640786i) q^{69} +(2.23607 - 1.62460i) q^{70} +(3.23607 - 9.95959i) q^{71} +(-1.97214 + 6.06961i) q^{72} +(-3.85410 + 2.80017i) q^{73} +(-4.47214 - 3.24920i) q^{74} +(0.118034 + 0.363271i) q^{75} -2.29180 q^{76} +(-1.88197 + 0.812299i) q^{77} +1.38197 q^{78} +(-2.95492 - 9.09429i) q^{79} +(-1.61803 - 1.17557i) q^{80} +(-6.23607 + 4.53077i) q^{81} +(-4.79837 + 14.7679i) q^{82} +(2.38197 - 7.33094i) q^{83} +(0.572949 - 0.416272i) q^{84} +(-1.61803 - 1.17557i) q^{85} +(1.90983 + 5.87785i) q^{86} +2.94427 q^{87} +(-4.89919 - 5.56758i) q^{88} -9.79837 q^{89} +(3.94427 + 12.1392i) q^{90} +(0.809017 + 0.587785i) q^{91} +(-6.92705 + 5.03280i) q^{92} +(0.763932 - 2.35114i) q^{93} +(6.18034 - 19.0211i) q^{94} +(-1.23607 + 0.898056i) q^{95} +(-2.07295 - 1.50609i) q^{96} +(1.85410 + 5.70634i) q^{97} -14.7984 q^{98} +(-0.881966 - 9.42481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9} + 4 q^{11} - 18 q^{12} - 2 q^{13} + 2 q^{15} + q^{16} + q^{17} + 5 q^{18} - 2 q^{19} + 6 q^{20} + 8 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{24} + q^{25} + 5 q^{26} + 5 q^{27} + 9 q^{28} + 16 q^{29} - 10 q^{30} - 8 q^{31} + 19 q^{33} - 6 q^{35} + 21 q^{36} - 8 q^{37} - 20 q^{38} + 3 q^{39} + 10 q^{40} + 18 q^{41} + 15 q^{42} + 20 q^{43} - 3 q^{44} - 4 q^{45} - 10 q^{46} - 20 q^{47} + q^{48} + 3 q^{49} - 5 q^{50} + q^{51} + 9 q^{52} - 21 q^{53} + 20 q^{54} - 18 q^{55} + 10 q^{56} - 22 q^{57} + 20 q^{58} + 8 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} - q^{63} + 13 q^{64} + 4 q^{65} + 30 q^{66} - 48 q^{67} + 3 q^{68} + 8 q^{69} + 4 q^{71} + 10 q^{72} - 2 q^{73} - 4 q^{75} - 36 q^{76} - 12 q^{77} + 10 q^{78} - 23 q^{79} - 2 q^{80} - 16 q^{81} + 30 q^{82} + 14 q^{83} + 9 q^{84} - 2 q^{85} + 30 q^{86} - 24 q^{87} + 5 q^{88} + 10 q^{89} - 20 q^{90} + q^{91} - 21 q^{92} + 12 q^{93} - 20 q^{94} + 4 q^{95} - 15 q^{96} - 6 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9 + 4 * q^11 - 18 * q^12 - 2 * q^13 + 2 * q^15 + q^16 + q^17 + 5 * q^18 - 2 * q^19 + 6 * q^20 + 8 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^24 + q^25 + 5 * q^26 + 5 * q^27 + 9 * q^28 + 16 * q^29 - 10 * q^30 - 8 * q^31 + 19 * q^33 - 6 * q^35 + 21 * q^36 - 8 * q^37 - 20 * q^38 + 3 * q^39 + 10 * q^40 + 18 * q^41 + 15 * q^42 + 20 * q^43 - 3 * q^44 - 4 * q^45 - 10 * q^46 - 20 * q^47 + q^48 + 3 * q^49 - 5 * q^50 + q^51 + 9 * q^52 - 21 * q^53 + 20 * q^54 - 18 * q^55 + 10 * q^56 - 22 * q^57 + 20 * q^58 + 8 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 - q^63 + 13 * q^64 + 4 * q^65 + 30 * q^66 - 48 * q^67 + 3 * q^68 + 8 * q^69 + 4 * q^71 + 10 * q^72 - 2 * q^73 - 4 * q^75 - 36 * q^76 - 12 * q^77 + 10 * q^78 - 23 * q^79 - 2 * q^80 - 16 * q^81 + 30 * q^82 + 14 * q^83 + 9 * q^84 - 2 * q^85 + 30 * q^86 - 24 * q^87 + 5 * q^88 + 10 * q^89 - 20 * q^90 + q^91 - 21 * q^92 + 12 * q^93 - 20 * q^94 + 4 * q^95 - 15 * q^96 - 6 * q^97 - 10 * q^98 - 8 * q^99

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