LMFDB - Embedded newform 187.2.h.a.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.3
Character	$\chi$	$=$	187.111
Dual form			187.2.h.a.155.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63835 + 1.63835i) q^{2} +(0.151924 + 0.0629292i) q^{3} -3.36837i q^{4} +(0.00973985 - 0.0235141i) q^{5} +(-0.352005 + 0.145805i) q^{6} +(-1.50462 - 3.63248i) q^{7} +(2.24186 + 2.24186i) q^{8} +(-2.10220 - 2.10220i) q^{9} +O(q^{10})$	\(q+(-1.63835 + 1.63835i) q^{2} +(0.151924 + 0.0629292i) q^{3} -3.36837i q^{4} +(0.00973985 - 0.0235141i) q^{5} +(-0.352005 + 0.145805i) q^{6} +(-1.50462 - 3.63248i) q^{7} +(2.24186 + 2.24186i) q^{8} +(-2.10220 - 2.10220i) q^{9} +(0.0225670 + 0.0544815i) q^{10} +(-0.923880 + 0.382683i) q^{11} +(0.211969 - 0.511737i) q^{12} -3.84725i q^{13} +(8.41635 + 3.48617i) q^{14} +(0.00295944 - 0.00295944i) q^{15} -0.609168 q^{16} +(-3.94778 + 1.18954i) q^{17} +6.88827 q^{18} +(-0.979730 + 0.979730i) q^{19} +(-0.0792041 - 0.0328074i) q^{20} -0.646546i q^{21} +(0.886668 - 2.14060i) q^{22} +(7.98135 - 3.30598i) q^{23} +(0.199515 + 0.481672i) q^{24} +(3.53508 + 3.53508i) q^{25} +(6.30314 + 6.30314i) q^{26} +(-0.375873 - 0.907438i) q^{27} +(-12.2355 + 5.06812i) q^{28} +(-0.720217 + 1.73876i) q^{29} +0.00969719i q^{30} +(-4.62393 - 1.91529i) q^{31} +(-3.48570 + 3.48570i) q^{32} -0.164442 q^{33} +(4.51897 - 8.41672i) q^{34} -0.100069 q^{35} +(-7.08098 + 7.08098i) q^{36} +(-3.46367 - 1.43470i) q^{37} -3.21028i q^{38} +(0.242104 - 0.584492i) q^{39} +(0.0745507 - 0.0308799i) q^{40} +(-0.0559742 - 0.135134i) q^{41} +(1.05927 + 1.05927i) q^{42} +(-5.86507 - 5.86507i) q^{43} +(1.28902 + 3.11197i) q^{44} +(-0.0699064 + 0.0289562i) q^{45} +(-7.65988 + 18.4926i) q^{46} -10.8866i q^{47} +(-0.0925476 - 0.0383345i) q^{48} +(-5.98125 + 5.98125i) q^{49} -11.5834 q^{50} +(-0.674622 - 0.0677109i) q^{51} -12.9590 q^{52} +(-2.40462 + 2.40462i) q^{53} +(2.10251 + 0.870889i) q^{54} +0.0254514i q^{55} +(4.77036 - 11.5167i) q^{56} +(-0.210499 + 0.0871914i) q^{57} +(-1.66872 - 4.02866i) q^{58} +(5.88683 + 5.88683i) q^{59} +(-0.00996849 - 0.00996849i) q^{60} +(2.47157 + 5.96691i) q^{61} +(10.7135 - 4.43769i) q^{62} +(-4.47318 + 10.7992i) q^{63} -12.6399i q^{64} +(-0.0904646 - 0.0374717i) q^{65} +(0.269413 - 0.269413i) q^{66} +2.04855 q^{67} +(4.00680 + 13.2976i) q^{68} +1.42061 q^{69} +(0.163948 - 0.163948i) q^{70} +(4.30237 + 1.78210i) q^{71} -9.42569i q^{72} +(3.59323 - 8.67481i) q^{73} +(8.02522 - 3.32416i) q^{74} +(0.314605 + 0.759524i) q^{75} +(3.30009 + 3.30009i) q^{76} +(2.78018 + 2.78018i) q^{77} +(0.560950 + 1.35425i) q^{78} +(14.9418 - 6.18912i) q^{79} +(-0.00593321 + 0.0143240i) q^{80} +8.75736i q^{81} +(0.313101 + 0.129691i) q^{82} +(-0.885057 + 0.885057i) q^{83} -2.17781 q^{84} +(-0.0104799 + 0.104414i) q^{85} +19.2181 q^{86} +(-0.218837 + 0.218837i) q^{87} +(-2.92914 - 1.21329i) q^{88} +3.74866i q^{89} +(0.0670907 - 0.161971i) q^{90} +(-13.9751 + 5.78866i) q^{91} +(-11.1358 - 26.8841i) q^{92} +(-0.581960 - 0.581960i) q^{93} +(17.8361 + 17.8361i) q^{94} +(0.0134950 + 0.0325799i) q^{95} +(-0.748915 + 0.310211i) q^{96} +(2.88662 - 6.96892i) q^{97} -19.5987i q^{98} +(2.74666 + 1.13770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−1.63835	+	1.63835i	−1.15849	+	1.15849i	−0.173686	+	0.984801i	$0.555568\pi$
$2$	−1.63835	+	1.63835i	−1.15849	+	1.15849i	−0.984801	+	0.173686i	$0.944432\pi$
$3$	0.151924	+	0.0629292i	0.0877136	+	0.0363322i	0.426109	−	0.904672i	$-0.359884\pi$
$3$	0.151924	+	0.0629292i	0.0877136	+	0.0363322i	−0.338395	+	0.941004i	$0.609884\pi$
$4$		−	3.36837i		−	1.68418i
$5$	0.00973985	−	0.0235141i	0.00435579	−	0.0105158i	−0.921687	−	0.387935i	$-0.873188\pi$
$5$	0.00973985	−	0.0235141i	0.00435579	−	0.0105158i	0.926042	+	0.377419i	$0.123188\pi$
$6$	−0.352005	+	0.145805i	−0.143705	+	0.0595247i
$7$	−1.50462	−	3.63248i	−0.568693	−	1.37295i	−0.902657	−	0.430361i	$-0.858386\pi$
$7$	−1.50462	−	3.63248i	−0.568693	−	1.37295i	0.333964	−	0.942586i	$-0.391614\pi$
$8$	2.24186	+	2.24186i	0.792618	+	0.792618i
$9$	−2.10220	−	2.10220i	−0.700733	−	0.700733i
$10$	0.0225670	+	0.0544815i	0.00713630	+	0.0172286i
$11$	−0.923880	+	0.382683i	−0.278560	+	0.115383i
$11$	−0.923880	+	0.382683i	−0.278560	+	0.115383i
$12$	0.211969	−	0.511737i	0.0611901	−	0.147726i
$13$		−	3.84725i		−	1.06704i	−0.845789	−	0.533518i	$-0.820870\pi$
$13$		−	3.84725i		−	1.06704i	0.845789	−	0.533518i	$-0.179130\pi$
$14$	8.41635	+	3.48617i	2.24936	+	0.931717i
$15$	0.00295944	−	0.00295944i	0.000764125	−	0.000764125i
$16$	−0.609168			−0.152292
$17$	−3.94778	+	1.18954i	−0.957478	+	0.288505i
$17$	−3.94778	+	1.18954i	−0.957478	+	0.288505i
$18$	6.88827			1.62358
$19$	−0.979730	+	0.979730i	−0.224766	+	0.224766i	−0.810502	−	0.585736i	$-0.800805\pi$
$19$	−0.979730	+	0.979730i	−0.224766	+	0.224766i	0.585736	+	0.810502i	$0.300805\pi$
$20$	−0.0792041	−	0.0328074i	−0.0177106	−	0.00733596i
$21$		−	0.646546i		−	0.141088i
$22$	0.886668	−	2.14060i	0.189038	−	0.456378i
$23$	7.98135	−	3.30598i	1.66423	−	0.689346i	0.665839	−	0.746096i	$-0.268074\pi$
$23$	7.98135	−	3.30598i	1.66423	−	0.689346i	0.998388	+	0.0567500i	$0.0180738\pi$
$24$	0.199515	+	0.481672i	0.0407259	+	0.0983210i
$25$	3.53508	+	3.53508i	0.707015	+	0.707015i
$26$	6.30314	+	6.30314i	1.23615	+	1.23615i
$27$	−0.375873	−	0.907438i	−0.0723369	−	0.174637i
$28$	−12.2355	+	5.06812i	−2.31230	+	0.957784i
$29$	−0.720217	+	1.73876i	−0.133741	+	0.322879i	−0.976536	−	0.215356i	$-0.930909\pi$
$29$	−0.720217	+	1.73876i	−0.133741	+	0.322879i	0.842795	+	0.538235i	$0.180909\pi$
$30$			0.00969719i			0.00177046i
$31$	−4.62393	−	1.91529i	−0.830482	−	0.343997i	−0.0733887	−	0.997303i	$-0.523381\pi$
$31$	−4.62393	−	1.91529i	−0.830482	−	0.343997i	−0.757094	+	0.653306i	$0.773381\pi$
$32$	−3.48570	+	3.48570i	−0.616190	+	0.616190i
$33$	−0.164442			−0.0286256
$34$	4.51897	−	8.41672i	0.774997	−	1.44346i
$35$	−0.100069			−0.0169148
$36$	−7.08098	+	7.08098i	−1.18016	+	1.18016i
$37$	−3.46367	−	1.43470i	−0.569423	−	0.235863i	0.0793472	−	0.996847i	$-0.474716\pi$
$37$	−3.46367	−	1.43470i	−0.569423	−	0.235863i	−0.648770	+	0.760984i	$0.724716\pi$
$38$		−	3.21028i		−	0.520776i
$39$	0.242104	−	0.584492i	0.0387677	−	0.0935936i
$40$	0.0745507	−	0.0308799i	0.0117875	−	0.00488255i
$41$	−0.0559742	−	0.135134i	−0.00874170	−	0.0211043i	0.919448	−	0.393211i	$-0.128636\pi$
$41$	−0.0559742	−	0.135134i	−0.00874170	−	0.0211043i	−0.928190	+	0.372106i	$0.878636\pi$
$42$	1.05927	+	1.05927i	0.163449	+	0.163449i
$43$	−5.86507	−	5.86507i	−0.894415	−	0.894415i	0.100520	−	0.994935i	$-0.467949\pi$
$43$	−5.86507	−	5.86507i	−0.894415	−	0.894415i	−0.994935	+	0.100520i	$0.967949\pi$
$44$	1.28902	+	3.11197i	0.194327	+	0.469147i
$45$	−0.0699064	+	0.0289562i	−0.0104210	+	0.00431653i
$46$	−7.65988	+	18.4926i	−1.12939	+	2.72658i
$47$		−	10.8866i		−	1.58798i	−0.607932	−	0.793989i	$-0.708001\pi$
$47$		−	10.8866i		−	1.58798i	0.607932	−	0.793989i	$-0.291999\pi$
$48$	−0.0925476	−	0.0383345i	−0.0133581	−	0.00553310i
$49$	−5.98125	+	5.98125i	−0.854465	+	0.854465i
$50$	−11.5834			−1.63814
$51$	−0.674622	−	0.0677109i	−0.0944659	−	0.00948143i
$52$	−12.9590			−1.79709
$53$	−2.40462	+	2.40462i	−0.330300	+	0.330300i	−0.852700	−	0.522400i	$-0.825037\pi$
$53$	−2.40462	+	2.40462i	−0.330300	+	0.330300i	0.522400	+	0.852700i	$0.325037\pi$
$54$	2.10251	+	0.870889i	0.286116	+	0.118513i
$55$			0.0254514i			0.00343187i
$56$	4.77036	−	11.5167i	0.637466	−	1.53898i
$57$	−0.210499	+	0.0871914i	−0.0278812	+	0.0115488i
$58$	−1.66872	−	4.02866i	−0.219114	−	0.528989i
$59$	5.88683	+	5.88683i	0.766400	+	0.766400i	0.977471	−	0.211071i	$-0.0676951\pi$
$59$	5.88683	+	5.88683i	0.766400	+	0.766400i	−0.211071	+	0.977471i	$0.567695\pi$
$60$	−0.00996849	−	0.00996849i	−0.00128693	−	0.00128693i
$61$	2.47157	+	5.96691i	0.316453	+	0.763984i	0.999437	+	0.0335512i	$0.0106817\pi$
$61$	2.47157	+	5.96691i	0.316453	+	0.763984i	−0.682984	+	0.730433i	$0.739318\pi$
$62$	10.7135	−	4.43769i	1.36062	−	0.563587i
$63$	−4.47318	+	10.7992i	−0.563567	+	1.36057i
$64$		−	12.6399i		−	1.57999i
$65$	−0.0904646	−	0.0374717i	−0.0112208	−	0.00464779i
$66$	0.269413	−	0.269413i	0.0331624	−	0.0331624i
$67$	2.04855			0.250270			0.125135	−	0.992140i	$-0.460064\pi$
$67$	2.04855			0.250270			0.125135	+	0.992140i	$0.460064\pi$
$68$	4.00680	+	13.2976i	0.485896	+	1.61257i
$69$	1.42061			0.171021
$70$	0.163948	−	0.163948i	0.0195955	−	0.0195955i
$71$	4.30237	+	1.78210i	0.510597	+	0.211496i	0.623081	−	0.782157i	$-0.285881\pi$
$71$	4.30237	+	1.78210i	0.510597	+	0.211496i	−0.112484	+	0.993654i	$0.535881\pi$
$72$		−	9.42569i		−	1.11083i
$73$	3.59323	−	8.67481i	0.420555	−	1.01531i	−0.561629	−	0.827389i	$-0.689825\pi$
$73$	3.59323	−	8.67481i	0.420555	−	1.01531i	0.982184	−	0.187921i	$-0.0601748\pi$
$74$	8.02522	−	3.32416i	0.932913	−	0.386425i
$75$	0.314605	+	0.759524i	0.0363275	+	0.0877023i
$76$	3.30009	+	3.30009i	0.378547	+	0.378547i
$77$	2.78018	+	2.78018i	0.316831	+	0.316831i
$78$	0.560950	+	1.35425i	0.0635151	+	0.153339i
$79$	14.9418	−	6.18912i	1.68109	−	0.696330i	0.681712	−	0.731621i	$-0.261236\pi$
$79$	14.9418	−	6.18912i	1.68109	−	0.696330i	0.999377	+	0.0352908i	$0.0112357\pi$
$80$	−0.00593321	+	0.0143240i	−0.000663353	+	0.00160148i
$81$			8.75736i			0.973040i
$82$	0.313101	+	0.129691i	0.0345762	+	0.0143219i
$83$	−0.885057	+	0.885057i	−0.0971477	+	0.0971477i	−0.754010	−	0.656863i	$-0.771883\pi$
$83$	−0.885057	+	0.885057i	−0.0971477	+	0.0971477i	0.656863	+	0.754010i	$0.271883\pi$
$84$	−2.17781			−0.237618
$85$	−0.0104799	+	0.104414i	−0.00113671	+	0.0113253i
$86$	19.2181			2.07234
$87$	−0.218837	+	0.218837i	−0.0234618	+	0.0234618i
$88$	−2.92914	−	1.21329i	−0.312247	−	0.129337i
$89$			3.74866i			0.397357i	0.980065	+	0.198679i	$0.0636650\pi$
$89$			3.74866i			0.397357i	−0.980065	+	0.198679i	$0.936335\pi$
$90$	0.0670907	−	0.161971i	0.00707198	−	0.0170733i
$91$	−13.9751	+	5.78866i	−1.46498	+	0.606816i
$92$	−11.1358	−	26.8841i	−1.16098	−	2.80287i
$93$	−0.581960	−	0.581960i	−0.0603465	−	0.0603465i
$94$	17.8361	+	17.8361i	1.83965	+	1.83965i
$95$	0.0134950	+	0.0325799i	0.00138456	+	0.00334262i
$96$	−0.748915	+	0.310211i	−0.0764358	+	0.0316607i
$97$	2.88662	−	6.96892i	0.293092	−	0.707586i	−0.706908	−	0.707305i	$-0.749911\pi$
$97$	2.88662	−	6.96892i	0.293092	−	0.707586i	1.00000		0.000280991i	$-8.94423e-5\pi$
$98$		−	19.5987i		−	1.97977i
$99$	2.74666	+	1.13770i	0.276049	+	0.114343i
$100$	11.9074	−	11.9074i	1.19074	−	1.19074i
$101$	−16.8094			−1.67260			−0.836299	−	0.548274i	$-0.815285\pi$
$101$	−16.8094			−1.67260			−0.836299	+	0.548274i	$0.815285\pi$
$102$	1.21620	−	0.994331i	0.120422	−	0.0984534i
$103$	3.10598			0.306042			0.153021	−	0.988223i	$-0.451100\pi$
$103$	3.10598			0.306042			0.153021	+	0.988223i	$0.451100\pi$
$104$	8.62502	−	8.62502i	0.845753	−	0.845753i
$105$	−0.0152029	−	0.00629726i	−0.00148365	−	0.000614550i
$106$		−	7.87921i		−	0.765296i
$107$	3.24075	−	7.82387i	0.313295	−	0.756362i	−0.686283	−	0.727334i	$-0.740759\pi$
$107$	3.24075	−	7.82387i	0.313295	−	0.756362i	0.999579	−	0.0290277i	$-0.00924109\pi$
$108$	−3.05659	+	1.26608i	−0.294120	+	0.121829i
$109$	0.684030	+	1.65139i	0.0655182	+	0.158175i	0.953247	−	0.302191i	$-0.0977181\pi$
$109$	0.684030	+	1.65139i	0.0655182	+	0.158175i	−0.887729	+	0.460366i	$0.847718\pi$
$110$	−0.0416983	−	0.0416983i	−0.00397578	−	0.00397578i
$111$	−0.435931	−	0.435931i	−0.0413768	−	0.0413768i
$112$	0.916568	+	2.21279i	0.0866075	+	0.209089i
$113$	−3.81663	+	1.58090i	−0.359039	+	0.148719i	−0.554909	−	0.831911i	$-0.687247\pi$
$113$	−3.81663	+	1.58090i	−0.359039	+	0.148719i	0.195870	+	0.980630i	$0.437247\pi$
$114$	0.202020	−	0.487720i	0.0189209	−	0.0456791i
$115$		−	0.219874i		−	0.0205033i
$116$	5.85678	+	2.42596i	0.543788	+	0.225244i
$117$	−8.08769	+	8.08769i	−0.747708	+	0.747708i
$118$	−19.2893			−1.77573
$119$	10.2609	+	12.5504i	0.940614	+	1.15050i
$120$	0.0132693			0.00121132
$121$	0.707107	−	0.707107i	0.0642824	−	0.0642824i
$122$	−13.8252	−	5.72657i	−1.25167	−	0.518459i
$123$		−	0.0240525i		−	0.00216874i
$124$	−6.45142	+	15.5751i	−0.579354	+	1.39869i
$125$	0.235125	−	0.0973922i	0.0210303	−	0.00871102i
$126$	−10.3642	−	25.0215i	−0.923319	−	2.22909i
$127$	8.92910	+	8.92910i	0.792329	+	0.792329i	0.981872	−	0.189543i	$-0.0607007\pi$
$127$	8.92910	+	8.92910i	0.792329	+	0.792329i	−0.189543	+	0.981872i	$0.560701\pi$
$128$	13.7372	+	13.7372i	1.21421	+	1.21421i
$129$	−0.521963	−	1.26013i	−0.0459563	−	0.110948i
$130$	0.209604	−	0.0868209i	0.0183835	−	0.00761469i
$131$	2.95451	−	7.13283i	0.258137	−	0.623198i	−0.740678	−	0.671860i	$-0.765496\pi$
$131$	2.95451	−	7.13283i	0.258137	−	0.623198i	0.998815	+	0.0486619i	$0.0154957\pi$
$132$			0.553901i			0.0482109i
$133$	5.03297	+	2.08472i	0.436414	+	0.180769i
$134$	−3.35623	+	3.35623i	−0.289934	+	0.289934i
$135$	−0.0249985			−0.00215153
$136$	−11.5172	−	6.18361i	−0.987590	−	0.530240i
$137$	−13.3509			−1.14065			−0.570323	−	0.821421i	$-0.693182\pi$
$137$	−13.3509			−1.14065			−0.570323	+	0.821421i	$0.693182\pi$
$138$	−2.32745	+	2.32745i	−0.198125	+	0.198125i
$139$	13.7822	+	5.70876i	1.16899	+	0.484211i	0.880858	−	0.473380i	$-0.156966\pi$
$139$	13.7822	+	5.70876i	1.16899	+	0.484211i	0.288130	+	0.957591i	$0.406966\pi$
$140$			0.337070i			0.0284876i
$141$	0.685086	−	1.65394i	0.0576947	−	0.139287i
$142$	−9.96847	+	4.12908i	−0.836536	+	0.346504i
$143$	1.47228	+	3.55440i	0.123118	+	0.297234i
$144$	1.28059	+	1.28059i	0.106716	+	0.106716i
$145$	0.0338705	+	0.0338705i	0.00281279	+	0.00281279i
$146$	8.32541	+	20.0993i	0.689016	+	1.66343i
$147$	−1.28509	+	0.532303i	−0.105993	+	0.0439036i
$148$	−4.83259	+	11.6669i	−0.397236	+	0.959014i
$149$			2.41277i			0.197662i	0.995104	+	0.0988309i	$0.0315103\pi$
$149$			2.41277i			0.197662i	−0.995104	+	0.0988309i	$0.968490\pi$
$150$	−1.75980	−	0.728932i	−0.143687	−	0.0595170i
$151$	10.9867	−	10.9867i	0.894084	−	0.894084i	−0.100821	−	0.994905i	$-0.532147\pi$
$151$	10.9867	−	10.9867i	0.894084	−	0.894084i	0.994905	+	0.100821i	$0.0321469\pi$
$152$	−4.39284			−0.356307
$153$	10.7997	+	5.79838i	0.873102	+	0.468772i
$154$	−9.10980			−0.734088
$155$	−0.0900727	+	0.0900727i	−0.00723482	+	0.00723482i
$156$	−1.96878	−	0.815497i	−0.157629	−	0.0652920i
$157$			14.2759i			1.13934i	0.821874	+	0.569669i	$0.192929\pi$
$157$			14.2759i			1.13934i	−0.821874	+	0.569669i	$0.807071\pi$
$158$	−14.3400	+	34.6199i	−1.14083	+	2.75421i
$159$	−0.516641	+	0.214000i	−0.0409723	+	0.0169713i
$160$	0.0480128	+	0.115913i	0.00379574	+	0.00916373i
$161$	−24.0178	−	24.0178i	−1.89287	−	1.89287i
$162$	−14.3476	−	14.3476i	−1.12725	−	1.12725i
$163$	−3.84586	−	9.28472i	−0.301231	−	0.727236i	−0.999930	−	0.0118202i	$-0.996237\pi$
$163$	−3.84586	−	9.28472i	−0.301231	−	0.727236i	0.698699	−	0.715416i	$-0.253763\pi$
$164$	−0.455180	+	0.188542i	−0.0355436	+	0.0147226i
$165$	−0.00160164	+	0.00386670i	−0.000124687	+	0.000301022i
$166$		−	2.90006i		−	0.225089i
$167$	−10.9859	−	4.55049i	−0.850111	−	0.352127i	−0.0852788	−	0.996357i	$-0.527178\pi$
$167$	−10.9859	−	4.55049i	−0.850111	−	0.352127i	−0.764832	+	0.644230i	$0.777178\pi$
$168$	1.44947	−	1.44947i	0.111829	−	0.111829i
$169$	−1.80136			−0.138566
$170$	−0.153897	−	0.188237i	−0.0118034	−	0.0144371i
$171$	4.11918			0.315001
$172$	−19.7557	+	19.7557i	−1.50636	+	1.50636i
$173$	20.0555	+	8.30726i	1.52479	+	0.631589i	0.978545	−	0.206035i	$-0.0660560\pi$
$173$	20.0555	+	8.30726i	1.52479	+	0.631589i	0.546247	+	0.837624i	$0.316056\pi$
$174$		−	0.717063i		−	0.0543604i
$175$	7.52213	−	18.1600i	0.568620	−	1.37277i
$176$	0.562798	−	0.233119i	0.0424225	−	0.0175720i
$177$	0.523900	+	1.26481i	0.0393787	+	0.0950687i
$178$	−6.14161	−	6.14161i	−0.460333	−	0.460333i
$179$	−17.7072	−	17.7072i	−1.32350	−	1.32350i	−0.910922	−	0.412578i	$-0.864629\pi$
$179$	−17.7072	−	17.7072i	−1.32350	−	1.32350i	−0.412578	−	0.910922i	$-0.635371\pi$
$180$	0.0975350	+	0.235470i	0.00726983	+	0.0175509i
$181$	16.2762	−	6.74182i	1.20980	−	0.501116i	0.315647	−	0.948877i	$-0.397779\pi$
$181$	16.2762	−	6.74182i	1.20980	−	0.501116i	0.894153	+	0.447761i	$0.147779\pi$
$182$	13.4122	−	32.3798i	0.994176	−	2.40015i
$183$			1.06205i			0.0785092i
$184$	25.3047	+	10.4815i	1.86549	+	0.772709i
$185$	−0.0674712	+	0.0674712i	−0.00496058	+	0.00496058i
$186$	1.90691			0.139821
$187$	3.19206	−	2.60974i	0.233427	−	0.190843i
$188$	−36.6702			−2.67445
$189$	−2.73070	+	2.73070i	−0.198629	+	0.198629i
$190$	−0.0754867	−	0.0312676i	−0.00547638	−	0.00226839i
$191$		−	6.82008i		−	0.493484i	−0.969081	−	0.246742i	$-0.920640\pi$
$191$		−	6.82008i		−	0.493484i	0.969081	−	0.246742i	$-0.0793600\pi$
$192$	0.795419	−	1.92031i	0.0574044	−	0.138586i
$193$	3.55891	−	1.47415i	0.256176	−	0.106112i	−0.250900	−	0.968013i	$-0.580726\pi$
$193$	3.55891	−	1.47415i	0.256176	−	0.106112i	0.507076	+	0.861902i	$0.330726\pi$
$194$	6.68822	+	16.1468i	0.480187	+	1.15927i
$195$	−0.0113857	−	0.0113857i	−0.000815349	−	0.000815349i
$196$	20.1471	+	20.1471i	1.43908	+	1.43908i
$197$	7.43235	+	17.9433i	0.529533	+	1.27841i	0.931829	+	0.362896i	$0.118212\pi$
$197$	7.43235	+	17.9433i	0.529533	+	1.27841i	−0.402296	+	0.915509i	$0.631788\pi$
$198$	−6.36393	+	2.63603i	−0.452265	+	0.187334i
$199$	−6.39472	+	15.4382i	−0.453310	+	1.09439i	0.517746	+	0.855534i	$0.326771\pi$
$199$	−6.39472	+	15.4382i	−0.453310	+	1.09439i	−0.971056	+	0.238852i	$0.923229\pi$
$200$			15.8503i			1.12079i
$201$	0.311224	+	0.128913i	0.0219521	+	0.00909284i
$202$	27.5396	−	27.5396i	1.93768	−	1.93768i
$203$	7.39965			0.519354
$204$	−0.228075	+	2.27237i	−0.0159685	+	0.159098i
$205$	−0.00372272			−0.000260006
$206$	−5.08868	+	5.08868i	−0.354545	+	0.354545i
$207$	−23.7282	−	9.82856i	−1.64923	−	0.683132i
$208$			2.34363i			0.162501i
$209$	0.530226	−	1.28008i	0.0366765	−	0.0885449i
$210$	0.0352248	−	0.0145906i	0.00243074	−	0.00100685i
$211$	8.02909	+	19.3839i	0.552745	+	1.33444i	0.915409	+	0.402525i	$0.131867\pi$
$211$	8.02909	+	19.3839i	0.552745	+	1.33444i	−0.362664	+	0.931920i	$0.618133\pi$
$212$	8.09964	+	8.09964i	0.556286	+	0.556286i
$213$	0.541489	+	0.541489i	0.0371022	+	0.0371022i
$214$	7.50874	+	18.1277i	0.513287	+	1.23918i
$215$	−0.195037	+	0.0807868i	−0.0133014	+	0.00550961i
$216$	1.19170	−	2.87701i	0.0810847	−	0.195756i
$217$			19.6781i			1.33584i
$218$	−3.82624	−	1.58488i	−0.259145	−	0.107342i
$219$	1.09180	−	1.09180i	0.0737768	−	0.0737768i
$220$	0.0857298			0.00577991
$221$	4.57645	+	15.1881i	0.307846	+	1.02166i
$222$	1.42841			0.0958689
$223$	11.5494	−	11.5494i	0.773406	−	0.773406i	−0.205294	−	0.978700i	$-0.565815\pi$
$223$	11.5494	−	11.5494i	0.773406	−	0.773406i	0.978700	+	0.205294i	$0.0658151\pi$
$224$	17.9064	+	7.41706i	1.19642	+	0.495573i
$225$		−	14.8629i		−	0.990858i
$226$	3.66291	−	8.84304i	0.243653	−	0.588230i
$227$	3.37979	−	1.39995i	0.224324	−	0.0929182i	−0.267691	−	0.963505i	$-0.586260\pi$
$227$	3.37979	−	1.39995i	0.224324	−	0.0929182i	0.492015	+	0.870587i	$0.336260\pi$
$228$	0.293693	+	0.709037i	0.0194503	+	0.0469571i
$229$	−10.9101	−	10.9101i	−0.720963	−	0.720963i	0.247839	−	0.968801i	$-0.420280\pi$
$229$	−10.9101	−	10.9101i	−0.720963	−	0.720963i	−0.968801	+	0.247839i	$0.920280\pi$
$230$	0.360230	+	0.360230i	0.0237529	+	0.0237529i
$231$	0.247423	+	0.597331i	0.0162792	+	0.0393015i
$232$	−5.51269	+	2.28343i	−0.361926	+	0.149915i
$233$	5.76628	−	13.9210i	0.377762	−	0.911997i	−0.614623	−	0.788821i	$-0.710692\pi$
$233$	5.76628	−	13.9210i	0.377762	−	0.911997i	0.992385	−	0.123176i	$-0.0393081\pi$
$234$		−	26.5009i		−	1.73242i
$235$	−0.255989	−	0.106034i	−0.0166989	−	0.00691690i
$236$	19.8290	−	19.8290i	1.29076	−	1.29076i
$237$	2.65951			0.172754
$238$	−37.3729	−	3.75107i	−2.42252	−	0.243146i
$239$	12.1343			0.784901			0.392451	−	0.919773i	$-0.371627\pi$
$239$	12.1343			0.784901			0.392451	+	0.919773i	$0.371627\pi$
$240$	−0.00180280	+	0.00180280i	−0.000116370	+	0.000116370i
$241$	−14.7877	−	6.12528i	−0.952562	−	0.394564i	−0.148369	−	0.988932i	$-0.547402\pi$
$241$	−14.7877	−	6.12528i	−0.952562	−	0.394564i	−0.804193	+	0.594368i	$0.797402\pi$
$242$			2.31697i			0.148941i
$243$	−1.67871	+	4.05277i	−0.107690	+	0.259985i
$244$	20.0987	−	8.32517i	1.28669	−	0.532964i
$245$	0.0823871	+	0.198900i	0.00526352	+	0.0127073i
$246$	0.0394064	+	0.0394064i	0.00251246	+	0.00251246i
$247$	3.76927	+	3.76927i	0.239833	+	0.239833i
$248$	−6.07239	−	14.6600i	−0.385597	−	0.930914i
$249$	−0.190158	+	0.0787659i	−0.0120508	+	0.00499159i
$250$	−0.225655	+	0.544780i	−0.0142717	+	0.0344549i
$251$		−	23.7946i		−	1.50190i	−0.660360	−	0.750950i	$-0.729596\pi$
$251$		−	23.7946i		−	1.50190i	0.660360	−	0.750950i	$-0.270404\pi$
$252$	36.3757	+	15.0673i	2.29145	+	0.949151i
$253$	−6.10866	+	6.10866i	−0.384048	+	0.384048i
$254$	−29.2579			−1.83581
$255$	−0.00816287	+	0.0152036i	−0.000511179	+	0.000952087i
$256$	−19.7327			−1.23330
$257$	−16.9695	+	16.9695i	−1.05853	+	1.05853i	−0.0603488	+	0.998177i	$0.519221\pi$
$257$	−16.9695	+	16.9695i	−1.05853	+	1.05853i	−0.998177	+	0.0603488i	$0.980779\pi$
$258$	2.91969	+	1.20938i	0.181772	+	0.0752925i
$259$			14.7404i			0.915921i
$260$	−0.126218	+	0.304718i	−0.00782773	+	0.0188978i
$261$	5.16926	−	2.14118i	0.319969	−	0.132535i
$262$	6.84553	+	16.5266i	0.422918	+	1.02102i
$263$	−9.50136	−	9.50136i	−0.585879	−	0.585879i	0.350634	−	0.936513i	$-0.385966\pi$
$263$	−9.50136	−	9.50136i	−0.585879	−	0.585879i	−0.936513	+	0.350634i	$0.885966\pi$
$264$	−0.368656	−	0.368656i	−0.0226892	−	0.0226892i
$265$	0.0331218	+	0.0799630i	0.00203465	+	0.00491209i
$266$	−11.6613	+	4.83025i	−0.714998	+	0.296162i
$267$	−0.235900	+	0.569513i	−0.0144368	+	0.0348536i
$268$		−	6.90025i		−	0.421500i
$269$	22.9228	+	9.49495i	1.39763	+	0.578917i	0.949135	−	0.314868i	$-0.101960\pi$
$269$	22.9228	+	9.49495i	1.39763	+	0.578917i	0.448495	+	0.893786i	$0.351960\pi$
$270$	0.0409563	−	0.0409563i	0.00249252	−	0.00249252i
$271$	−27.3656			−1.66234			−0.831171	−	0.556017i	$-0.812329\pi$
$271$	−27.3656			−1.66234			−0.831171	+	0.556017i	$0.812329\pi$
$272$	2.40487	−	0.724629i	0.145816	−	0.0439371i
$273$	−2.48743			−0.150546
$274$	21.8734	−	21.8734i	1.32142	−	1.32142i
$275$	−4.61880	−	1.91317i	−0.278524	−	0.115368i
$276$		−	4.78512i		−	0.288031i
$277$	2.87657	−	6.94465i	0.172836	−	0.417264i	−0.813596	−	0.581430i	$-0.802493\pi$
$277$	2.87657	−	6.94465i	0.172836	−	0.417264i	0.986433	+	0.164166i	$0.0524934\pi$
$278$	−31.9329	+	13.2271i	−1.91521	+	0.793306i
$279$	5.69409	+	13.7468i	0.340896	+	0.822997i
$280$	−0.224341	−	0.224341i	−0.0134070	−	0.0134070i
$281$	−6.53280	−	6.53280i	−0.389714	−	0.389714i	0.484871	−	0.874585i	$-0.338866\pi$
$281$	−6.53280	−	6.53280i	−0.389714	−	0.389714i	−0.874585	+	0.484871i	$0.838866\pi$
$282$	1.58733	+	3.83215i	0.0945240	+	0.228201i
$283$	14.8937	−	6.16916i	0.885337	−	0.366719i	0.106773	−	0.994283i	$-0.465948\pi$
$283$	14.8937	−	6.16916i	0.885337	−	0.366719i	0.778564	+	0.627565i	$0.215948\pi$
$284$	6.00277	−	14.4920i	0.356199	−	0.859940i
$285$			0.00579891i			0.000343498i
$286$	−8.23545	−	3.41124i	−0.486972	−	0.201711i
$287$	−0.406650	+	0.406650i	−0.0240038	+	0.0240038i
$288$	14.6553			0.863570
$289$	14.1700	−	9.39208i	0.833529	−	0.552475i
$290$	−0.110983			−0.00651716
$291$	0.877096	−	0.877096i	0.0514163	−	0.0514163i
$292$	−29.2200	−	12.1033i	−1.70997	−	0.708292i
$293$		−	5.01974i		−	0.293256i	−0.989192	−	0.146628i	$-0.953158\pi$
$293$		−	5.01974i		−	0.293256i	0.989192	−	0.146628i	$-0.0468421\pi$
$294$	1.23333	−	2.97753i	0.0719294	−	0.173653i
$295$	0.195760	−	0.0810865i	0.0113976	−	0.00472104i
$296$	−4.54867	−	10.9815i	−0.264386	−	0.638285i
$297$	0.694523	+	0.694523i	0.0403003	+	0.0403003i
$298$	−3.95296	−	3.95296i	−0.228989	−	0.228989i
$299$	−12.7190	−	30.7063i	−0.735557	−	1.77579i
$300$	2.55836	−	1.05971i	0.147707	−	0.0611821i
$301$	−12.4800	+	30.1294i	−0.719336	+	1.73663i
$302$			36.0000i			2.07157i
$303$	−2.55376	−	1.05780i	−0.146710	−	0.0607691i
$304$	0.596821	−	0.596821i	0.0342300	−	0.0342300i
$305$	0.164379			0.00941232
$306$	−27.1934	+	8.19385i	−1.55454	+	0.468411i
$307$	5.03332			0.287267			0.143633	−	0.989631i	$-0.454121\pi$
$307$	5.03332			0.287267			0.143633	+	0.989631i	$0.454121\pi$
$308$	9.36466	−	9.36466i	0.533601	−	0.533601i
$309$	0.471875	+	0.195457i	0.0268440	+	0.0111192i
$310$		−	0.295141i		−	0.0167629i
$311$	−6.97511	+	16.8394i	−0.395522	+	0.954875i	0.593192	+	0.805061i	$0.297867\pi$
$311$	−6.97511	+	16.8394i	−0.395522	+	0.954875i	−0.988714	+	0.149814i	$0.952133\pi$
$312$	1.85312	−	0.767586i	0.104912	−	0.0434560i
$313$	1.06810	+	2.57863i	0.0603727	+	0.145753i	0.951187	−	0.308615i	$-0.0998654\pi$
$313$	1.06810	+	2.57863i	0.0603727	+	0.145753i	−0.890814	+	0.454367i	$0.849865\pi$
$314$	−23.3889	−	23.3889i	−1.31991	−	1.31991i
$315$	0.210365	+	0.210365i	0.0118527	+	0.0118527i
$316$	−20.8472	−	50.3296i	−1.17275	−	2.83126i
$317$	−2.88508	+	1.19504i	−0.162042	+	0.0671200i	−0.462230	−	0.886760i	$-0.652951\pi$
$317$	−2.88508	+	1.19504i	−0.162042	+	0.0671200i	0.300188	+	0.953880i	$0.402951\pi$
$318$	0.495832	−	1.19704i	0.0278049	−	0.0671269i
$319$		−	1.88202i		−	0.105373i
$320$	−0.297216	−	0.123111i	−0.0166149	−	0.00688210i
$321$	0.984699	−	0.984699i	0.0549606	−	0.0549606i
$322$	78.6991			4.38573
$323$	2.70234	−	5.03319i	0.150362	−	0.280054i
$324$	29.4980			1.63878
$325$	13.6003	−	13.6003i	0.754411	−	0.754411i
$326$	21.5125	+	8.91075i	1.19147	+	0.493521i
$327$			0.293933i			0.0162545i
$328$	0.177465	−	0.428437i	0.00979884	−	0.0236565i
$329$	−39.5454	+	16.3802i	−2.18021	+	0.903072i
$330$	−0.00371095	−	0.00895904i	−0.000204281	−	0.000493179i
$331$	10.3179	+	10.3179i	0.567124	+	0.567124i	0.931322	−	0.364197i	$-0.118657\pi$
$331$	10.3179	+	10.3179i	0.567124	+	0.567124i	−0.364197	+	0.931322i	$0.618657\pi$
$332$	2.98120	+	2.98120i	0.163615	+	0.163615i
$333$	4.26530	+	10.2973i	0.233737	+	0.564291i
$334$	25.4539	−	10.5434i	1.39278	−	0.576907i
$335$	0.0199525	−	0.0481696i	0.00109012	−	0.00263179i
$336$			0.393856i			0.0214866i
$337$	−1.13612	−	0.470595i	−0.0618882	−	0.0256349i	0.351525	−	0.936179i	$-0.385663\pi$
$337$	−1.13612	−	0.470595i	−0.0618882	−	0.0256349i	−0.413413	+	0.910544i	$0.635663\pi$
$338$	2.95126	−	2.95126i	0.160527	−	0.160527i
$339$	−0.679325			−0.0368959
$340$	0.351706	+	0.0353003i	0.0190739	+	0.00191443i
$341$	5.00491			0.271031
$342$	−6.74865	+	6.74865i	−0.364925	+	0.364925i
$343$	5.29894	+	2.19489i	0.286116	+	0.118513i
$344$		−	26.2974i		−	1.41786i
$345$	0.0138365	−	0.0334042i	0.000744931	−	0.00179842i
$346$	−46.4681	+	19.2477i	−2.49814	+	1.03476i
$347$	8.89196	+	21.4671i	0.477346	+	1.15241i	0.960849	+	0.277072i	$0.0893640\pi$
$347$	8.89196	+	21.4671i	0.477346	+	1.15241i	−0.483504	+	0.875342i	$0.660636\pi$
$348$	0.737124	+	0.737124i	0.0395140	+	0.0395140i
$349$	−21.6904	−	21.6904i	−1.16106	−	1.16106i	−0.984244	−	0.176815i	$-0.943420\pi$
$349$	−21.6904	−	21.6904i	−1.16106	−	1.16106i	−0.176815	−	0.984244i	$-0.556580\pi$
$350$	17.4286	+	42.0763i	0.931597	+	2.24907i
$351$	−3.49115	+	1.44608i	−0.186344	+	0.0771860i
$352$	1.88645	−	4.55428i	0.100548	−	0.242744i
$353$		−	12.1905i		−	0.648837i	−0.945914	−	0.324418i	$-0.894831\pi$
$353$		−	12.1905i		−	0.648837i	0.945914	−	0.324418i	$-0.105169\pi$
$354$	−2.93052	−	1.21386i	−0.155756	−	0.0645161i
$355$	0.0838088	−	0.0838088i	0.00444811	−	0.00444811i
$356$	12.6269			0.669222
$357$	0.769091	+	2.55243i	0.0407046	+	0.135089i
$358$	58.0212			3.06652
$359$	7.17403	−	7.17403i	0.378631	−	0.378631i	−0.491977	−	0.870608i	$-0.663726\pi$
$359$	7.17403	−	7.17403i	0.378631	−	0.378631i	0.870608	+	0.491977i	$0.163726\pi$
$360$	−0.221636	−	0.0918048i	−0.0116813	−	0.00483854i
$361$			17.0803i			0.898961i
$362$	−15.6206	+	37.7115i	−0.821002	+	1.98207i
$363$	0.151924	−	0.0629292i	0.00797397	−	0.00330292i
$364$	19.4983	+	47.0731i	1.02199	+	2.46730i
$365$	−0.168983	−	0.168983i	−0.00884496	−	0.00884496i
$366$	−1.74001	−	1.74001i	−0.0909519	−	0.0909519i
$367$	−11.5202	−	27.8123i	−0.601350	−	1.45179i	−0.872192	−	0.489164i	$-0.837302\pi$
$367$	−11.5202	−	27.8123i	−0.601350	−	1.45179i	0.270842	−	0.962624i	$-0.412698\pi$
$368$	−4.86199	+	2.01390i	−0.253449	+	0.104982i
$369$	−0.166409	+	0.401747i	−0.00866290	+	0.0209141i
$370$		−	0.221082i		−	0.0114935i
$371$	12.3528	+	5.11668i	0.641324	+	0.265645i
$372$	−1.96026	+	1.96026i	−0.101635	+	0.101635i
$373$	26.4785			1.37101			0.685503	−	0.728070i	$-0.259582\pi$
$373$	26.4785			1.37101			0.685503	+	0.728070i	$0.259582\pi$
$374$	−0.954042	+	9.50537i	−0.0493324	+	0.491511i
$375$	0.0418501			0.00216113
$376$	24.4063	−	24.4063i	1.25866	−	1.25866i
$377$	6.68944	+	2.77086i	0.344524	+	0.142706i
$378$		−	8.94768i		−	0.460219i
$379$	−4.44316	+	10.7267i	−0.228230	+	0.550995i	−0.995962	−	0.0897754i	$-0.971385\pi$
$379$	−4.44316	+	10.7267i	−0.228230	+	0.550995i	0.767732	+	0.640771i	$0.221385\pi$
$380$	0.109741	−	0.0454562i	0.00562959	−	0.00233185i
$381$	0.794647	+	1.91845i	0.0407110	+	0.0982851i
$382$	11.1737	+	11.1737i	0.571695	+	0.571695i
$383$	11.6876	+	11.6876i	0.597207	+	0.597207i	0.939568	−	0.342362i	$-0.111227\pi$
$383$	11.6876	+	11.6876i	0.597207	+	0.597207i	−0.342362	+	0.939568i	$0.611227\pi$
$384$	1.22254	+	2.95148i	0.0623877	+	0.150617i
$385$	0.0924518	−	0.0382948i	0.00471178	−	0.00195168i
$386$	−3.41556	+	8.24590i	−0.173848	+	0.419705i
$387$			24.6591i			1.25349i
$388$	−23.4739	−	9.72320i	−1.19171	−	0.493621i
$389$	−1.16201	+	1.16201i	−0.0589162	+	0.0589162i	−0.735951	−	0.677035i	$-0.763265\pi$
$389$	−1.16201	+	1.16201i	−0.0589162	+	0.0589162i	0.677035	+	0.735951i	$0.263265\pi$
$390$	0.0373076			0.00188914
$391$	−27.5761	+	22.5454i	−1.39458	+	1.14017i
$392$	−26.8183			−1.35453
$393$	0.897726	−	0.897726i	0.0452843	−	0.0452843i
$394$	−41.5741	−	17.2206i	−2.09447	−	0.867559i
$395$		−	0.411625i		−	0.0207111i
$396$	3.83220	−	9.25175i	0.192575	−	0.464918i
$397$	0.739425	−	0.306280i	0.0371107	−	0.0153718i	−0.364051	−	0.931379i	$-0.618607\pi$
$397$	0.739425	−	0.306280i	0.0371107	−	0.0153718i	0.401162	+	0.916007i	$0.368607\pi$
$398$	−14.8164	−	35.7700i	−0.742679	−	1.79299i
$399$	0.633441	+	0.633441i	0.0317117	+	0.0317117i
$400$	−2.15346	−	2.15346i	−0.107673	−	0.107673i
$401$	−13.8564	−	33.4524i	−0.691957	−	1.67053i	−0.740799	−	0.671727i	$-0.765553\pi$
$401$	−13.8564	−	33.4524i	−0.691957	−	1.67053i	0.0488418	−	0.998807i	$-0.484447\pi$
$402$	−0.721098	+	0.298689i	−0.0359651	+	0.0148972i
$403$	−7.36862	+	17.7894i	−0.367057	+	0.886155i
$404$			56.6202i			2.81696i
$405$	0.205921	+	0.0852954i	0.0102323	+	0.00423836i
$406$	−12.1232	+	12.1232i	−0.601665	+	0.601665i
$407$	3.74905			0.185833
$408$	−1.36061	−	1.66421i	−0.0673603	−	0.0823906i
$409$	−8.13631			−0.402314			−0.201157	−	0.979559i	$-0.564470\pi$
$409$	−8.13631			−0.402314			−0.201157	+	0.979559i	$0.564470\pi$
$410$	0.00609911	−	0.00609911i	0.000301214	−	0.000301214i
$411$	−2.02833	−	0.840162i	−0.100050	−	0.0414421i
$412$		−	10.4621i		−	0.515431i
$413$	12.5263	−	30.2412i	0.616380	−	1.48807i
$414$	54.9777	−	22.7725i	2.70201	−	1.11921i
$415$	0.0121910	+	0.0294316i	0.000598432	+	0.00144474i
$416$	13.4104	+	13.4104i	0.657497	+	0.657497i
$417$	1.73460	+	1.73460i	0.0849438	+	0.0849438i
$418$	1.22852	+	2.96591i	0.0600889	+	0.145067i
$419$	0.547321	−	0.226708i	0.0267384	−	0.0110754i	−0.369274	−	0.929320i	$-0.620394\pi$
$419$	0.547321	−	0.226708i	0.0267384	−	0.0110754i	0.396013	+	0.918245i	$0.370394\pi$
$420$	−0.0212115	+	0.0512091i	−0.00103502	+	0.00249875i
$421$		−	25.5233i		−	1.24393i	−0.783044	−	0.621966i	$-0.786334\pi$
$421$		−	25.5233i		−	1.24393i	0.783044	−	0.621966i	$-0.213666\pi$
$422$	−44.9121	−	18.6032i	−2.18629	−	0.905589i
$423$	−22.8859	+	22.8859i	−1.11275	+	1.11275i
$424$	−10.7817			−0.523604
$425$	−18.1608	−	9.75061i	−0.880929	−	0.472974i
$426$	−1.77429			−0.0859648
$427$	17.9559	−	17.9559i	0.868945	−	0.868945i
$428$	−26.3537	−	10.9161i	−1.27385	−	0.527647i
$429$			0.632649i			0.0305446i
$430$	0.187181	−	0.451895i	0.00902666	−	0.0217923i
$431$	18.6940	−	7.74331i	0.900458	−	0.372982i	0.116062	−	0.993242i	$-0.462973\pi$
$431$	18.6940	−	7.74331i	0.900458	−	0.372982i	0.784396	+	0.620260i	$0.212973\pi$
$432$	0.228970	+	0.552783i	0.0110163	+	0.0265958i
$433$	−25.1047	−	25.1047i	−1.20645	−	1.20645i	−0.972168	−	0.234286i	$-0.924725\pi$
$433$	−25.1047	−	25.1047i	−1.20645	−	1.20645i	−0.234286	−	0.972168i	$-0.575275\pi$
$434$	−32.2396	−	32.2396i	−1.54755	−	1.54755i
$435$	0.00301431	+	0.00727719i	0.000144525	+	0.000348915i
$436$	5.56250	−	2.30406i	0.266396	−	0.110345i
$437$	−4.58060	+	11.0585i	−0.219120	+	0.529002i
$438$			3.57749i			0.170939i
$439$	−13.8933	−	5.75479i	−0.663090	−	0.274661i	0.0256479	−	0.999671i	$-0.491835\pi$
$439$	−13.8933	−	5.75479i	−0.663090	−	0.274661i	−0.688738	+	0.725010i	$0.741835\pi$
$440$	−0.0570587	+	0.0570587i	−0.00272017	+	0.00272017i
$441$	25.1476			1.19750
$442$	−32.3813	−	17.3856i	−1.54022	−	0.826949i
$443$	−29.0738			−1.38134			−0.690669	−	0.723171i	$-0.742684\pi$
$443$	−29.0738			−1.38134			−0.690669	+	0.723171i	$0.742684\pi$
$444$	−1.46838	+	1.46838i	−0.0696861	+	0.0696861i
$445$	0.0881462	+	0.0365114i	0.00417853	+	0.00173080i
$446$			37.8439i			1.79196i
$447$	−0.151834	+	0.366559i	−0.00718148	+	0.0173376i
$448$	−45.9142	+	19.0183i	−2.16924	+	0.898529i
$449$	2.41583	+	5.83233i	0.114010	+	0.275245i	0.970577	−	0.240792i	$-0.0774070\pi$
$449$	2.41583	+	5.83233i	0.114010	+	0.275245i	−0.856567	+	0.516036i	$0.827407\pi$
$450$	24.3506	+	24.3506i	1.14790	+	1.14790i
$451$	0.103427	+	0.103427i	0.00487018	+	0.00487018i
$452$	5.32506	+	12.8558i	0.250470	+	0.604687i
$453$	2.36053	−	0.977763i	0.110907	−	0.0459393i
$454$	−3.24366	+	7.83088i	−0.152232	+	0.367522i
$455$			0.384991i			0.0180487i
$456$	−0.667380	−	0.276438i	−0.0312529	−	0.0129454i
$457$	−21.8069	+	21.8069i	−1.02009	+	1.02009i	−0.0202911	+	0.999794i	$0.506459\pi$
$457$	−21.8069	+	21.8069i	−1.02009	+	1.02009i	−0.999794	+	0.0202911i	$0.993541\pi$
$458$	35.7492			1.67045
$459$	2.56330	+	3.13526i	0.119645	+	0.146341i
$460$	−0.740616			−0.0345314
$461$	−4.62623	+	4.62623i	−0.215465	+	0.215465i	−0.806584	−	0.591119i	$-0.798686\pi$
$461$	−4.62623	+	4.62623i	−0.215465	+	0.215465i	0.591119	+	0.806584i	$0.298686\pi$
$462$	−1.38400	−	0.573272i	−0.0643895	−	0.0266710i
$463$			12.7055i			0.590473i	0.955424	+	0.295236i	$0.0953984\pi$
$463$			12.7055i			0.590473i	−0.955424	+	0.295236i	$0.904602\pi$
$464$	0.438734	−	1.05920i	0.0203677	−	0.0491720i
$465$	−0.0193525	+	0.00801605i	−0.000897449	+	0.000371735i
$466$	13.3603	+	32.2547i	0.618905	+	1.49417i
$467$	7.60796	+	7.60796i	0.352055	+	0.352055i	0.860874	−	0.508819i	$-0.169918\pi$
$467$	7.60796	+	7.60796i	0.352055	+	0.352055i	−0.508819	+	0.860874i	$0.669918\pi$
$468$	27.2423	+	27.2423i	1.25928	+	1.25928i
$469$	−3.08228	−	7.44129i	−0.142327	−	0.343607i
$470$	0.593120	−	0.245678i	0.0273586	−	0.0113323i
$471$	−0.898369	+	2.16885i	−0.0413947	+	0.0999355i
$472$			26.3949i			1.21493i
$473$	7.66308	+	3.17415i	0.352349	+	0.145948i
$474$	−4.35720	+	4.35720i	−0.200133	+	0.200133i
$475$	−6.92684			−0.317825
$476$	42.2745	−	34.5624i	1.93765	−	1.58417i
$477$	10.1100			0.462904
$478$	−19.8802	+	19.8802i	−0.909298	+	0.909298i
$479$	−11.4961	−	4.76186i	−0.525272	−	0.217575i	0.104259	−	0.994550i	$-0.466753\pi$
$479$	−11.4961	−	4.76186i	−0.525272	−	0.217575i	−0.629531	+	0.776975i	$0.716753\pi$
$480$			0.0206314i			0.000941692i
$481$	−5.51965	+	13.3256i	−0.251674	+	0.607595i
$482$	34.2628	−	14.1921i	1.56063	−	0.646434i
$483$	−2.13747	−	5.16032i	−0.0972584	−	0.234803i
$484$	−2.38180	−	2.38180i	−0.108263	−	0.108263i
$485$	−0.135752	−	0.135752i	−0.00616420	−	0.00616420i
$486$	−3.88954	−	9.39017i	−0.176433	−	0.425947i
$487$	−22.4086	+	9.28193i	−1.01543	+	0.420605i	−0.827433	−	0.561565i	$-0.810199\pi$
$487$	−22.4086	+	9.28193i	−1.01543	+	0.420605i	−0.187997	+	0.982170i	$0.560199\pi$
$488$	−7.83606	+	18.9179i	−0.354722	+	0.856374i
$489$		−	1.65259i		−	0.0747328i
$490$	−0.460846	−	0.190889i	−0.0208189	−	0.00862348i
$491$	22.2826	−	22.2826i	1.00560	−	1.00560i	0.00561526	−	0.999984i	$-0.498213\pi$
$491$	22.2826	−	22.2826i	1.00560	−	1.00560i	0.999984	−	0.00561526i	$-0.00178740\pi$
$492$	−0.0810177			−0.00365256
$493$	0.774944	−	7.72097i	0.0349017	−	0.347735i
$494$	−12.3508			−0.555687
$495$	0.0535040	−	0.0535040i	0.00240483	−	0.00240483i
$496$	2.81675	+	1.16674i	0.126476	+	0.0523880i
$497$		−	18.3096i		−	0.821299i
$498$	0.182499	−	0.440591i	0.00817796	−	0.0197433i
$499$	−4.09464	+	1.69606i	−0.183301	+	0.0759259i	−0.472446	−	0.881359i	$-0.656629\pi$
$499$	−4.09464	+	1.69606i	−0.183301	+	0.0759259i	0.289145	+	0.957285i	$0.406629\pi$
$500$	−0.328053	−	0.791989i	−0.0146710	−	0.0354188i
$501$	−1.38266	−	1.38266i	−0.0617727	−	0.0617727i
$502$	38.9838	+	38.9838i	1.73993	+	1.73993i
$503$	5.48565	+	13.2435i	0.244593	+	0.590500i	0.997728	−	0.0673660i	$-0.0214595\pi$
$503$	5.48565	+	13.2435i	0.244593	+	0.590500i	−0.753135	+	0.657866i	$0.771460\pi$
$504$	−34.2386	+	14.1821i	−1.52511	+	0.631720i
$505$	−0.163721	+	0.395257i	−0.00728549	+	0.0175887i
$506$		−	20.0162i		−	0.889830i
$507$	−0.273671	−	0.113358i	−0.0121542	−	0.00503442i
$508$	30.0765	−	30.0765i	1.33443	−	1.33443i
$509$	−10.2968			−0.456398			−0.228199	−	0.973614i	$-0.573284\pi$
$509$	−10.2968			−0.456398			−0.228199	+	0.973614i	$0.573284\pi$
$510$	−0.0115352	−	0.0382824i	−0.000510786	−	0.00169517i
$511$	−36.9175			−1.63313
$512$	4.85472	−	4.85472i	0.214550	−	0.214550i
$513$	1.25730	+	0.520790i	0.0555111	+	0.0229935i
$514$		−	55.6038i		−	2.45258i
$515$	0.0302518	−	0.0730343i	0.00133305	−	0.00321828i
$516$	−4.24459	+	1.75817i	−0.186858	+	0.0773989i
$517$	4.16613	+	10.0579i	0.183226	+	0.442347i
$518$	−24.1498	−	24.1498i	−1.06108	−	1.06108i
$519$	2.52415	+	2.52415i	0.110798	+	0.110798i
$520$	−0.118803	−	0.286816i	−0.00520985	−	0.0125777i
$521$	35.7664	−	14.8149i	1.56695	−	0.649054i	0.580675	−	0.814135i	$-0.302789\pi$
$521$	35.7664	−	14.8149i	1.56695	−	0.649054i	0.986280	+	0.165081i	$0.0527887\pi$
$522$	−4.96105	+	11.9770i	−0.217139	+	0.524220i
$523$		−	25.0197i		−	1.09404i	−0.837121	−	0.547018i	$-0.815763\pi$
$523$		−	25.0197i		−	1.09404i	0.837121	−	0.547018i	$-0.184237\pi$
$524$	−24.0260	−	9.95189i	−1.04958	−	0.434750i
$525$	2.28559	−	2.28559i	0.0997514	−	0.0997514i
$526$	31.1331			1.35747
$527$	20.5326	+	2.06083i	0.894414	+	0.0897712i
$528$	0.100173			0.00435946
$529$	36.5090	−	36.5090i	1.58735	−	1.58735i
$530$	−0.185272	−	0.0767423i	−0.00804771	−	0.00333347i
$531$		−	24.7506i		−	1.07408i
$532$	7.02212	−	16.9529i	0.304447	−	0.735001i
$533$	−0.519893	+	0.215347i	−0.0225191	+	0.00932771i
$534$	−0.546574	−	1.31955i	−0.0236526	−	0.0571024i
$535$	−0.152407	−	0.152407i	−0.00658911	−	0.00658911i
$536$	4.59256	+	4.59256i	0.198368	+	0.198368i
$537$	−1.57586	−	3.80446i	−0.0680033	−	0.164175i
$538$	−53.1116	+	21.9996i	−2.28980	+	0.948468i
$539$	3.23703	−	7.81488i	0.139429	−	0.336611i
$540$			0.0842042i			0.00362357i
$541$	42.1295	+	17.4506i	1.81129	+	0.750261i	0.981301	+	0.192481i	$0.0616533\pi$
$541$	42.1295	+	17.4506i	1.81129	+	0.750261i	0.829989	+	0.557780i	$0.188347\pi$
$542$	44.8344	−	44.8344i	1.92580	−	1.92580i
$543$	2.89701			0.124323
$544$	9.61441	−	17.9071i	0.412215	−	0.767763i
$545$	0.0454933			0.00194872
$546$	4.07527	−	4.07527i	0.174406	−	0.174406i
$547$	3.50743	+	1.45282i	0.149967	+	0.0621183i	0.456404	−	0.889772i	$-0.349137\pi$
$547$	3.50743	+	1.45282i	0.149967	+	0.0621183i	−0.306438	+	0.951891i	$0.599137\pi$
$548$			44.9708i			1.92106i
$549$	7.34789	−	17.7394i	0.313600	−	0.757098i
$550$	10.7016	−	4.43276i	0.456319	−	0.189014i
$551$	−0.997895	−	2.40913i	−0.0425118	−	0.102633i
$552$	3.18480	+	3.18480i	0.135554	+	0.135554i
$553$	−44.9636	−	44.9636i	−1.91205	−	1.91205i
$554$	6.66493	+	16.0906i	0.283166	+	0.683623i
$555$	−0.0144964	+	0.00600461i	−0.000615339	+	0.000254882i
$556$	19.2292	−	46.4234i	0.815500	−	1.96879i
$557$			40.4256i			1.71289i	0.516240	+	0.856444i	$0.327331\pi$
$557$			40.4256i			1.71289i	−0.516240	+	0.856444i	$0.672669\pi$
$558$	−31.8509	−	13.1931i	−1.34835	−	0.558507i
$559$	−22.5644	+	22.5644i	−0.954373	+	0.954373i
$560$	0.0609589			0.00257598
$561$	0.649181	−	0.195610i	0.0274084	−	0.00825865i
$562$	21.4060			0.902957
$563$	−21.8717	+	21.8717i	−0.921783	+	0.921783i	−0.997155	−	0.0753724i	$-0.975985\pi$
$563$	−21.8717	+	21.8717i	−0.921783	+	0.921783i	0.0753724	+	0.997155i	$0.475985\pi$
$564$	−5.57109	−	2.30762i	−0.234585	−	0.0971685i
$565$			0.105142i			0.00442337i
$566$	−14.2938	+	34.5082i	−0.600813	+	1.45049i
$567$	31.8109	−	13.1765i	1.33593	−	0.553361i
$568$	5.65010	+	13.6405i	0.237073	+	0.572345i
$569$	−6.03128	−	6.03128i	−0.252844	−	0.252844i	0.569291	−	0.822136i	$-0.307218\pi$
$569$	−6.03128	−	6.03128i	−0.252844	−	0.252844i	−0.822136	+	0.569291i	$0.807218\pi$
$570$	−0.00950063	−	0.00950063i	−0.000397938	−	0.000397938i
$571$	1.35493	+	3.27108i	0.0567019	+	0.136890i	0.949692	−	0.313187i	$-0.101397\pi$
$571$	1.35493	+	3.27108i	0.0567019	+	0.136890i	−0.892990	+	0.450077i	$0.851397\pi$
$572$	11.9725	−	4.95918i	0.500596	−	0.207354i
$573$	0.429182	−	1.03614i	0.0179293	−	0.0432853i
$574$		−	1.33247i		−	0.0556161i
$575$	39.9016	+	16.5278i	1.66401	+	0.689256i
$576$	−26.5716	+	26.5716i	−1.10715	+	1.10715i
$577$	8.52437			0.354874			0.177437	−	0.984132i	$-0.443219\pi$
$577$	8.52437			0.354874			0.177437	+	0.984132i	$0.443219\pi$
$578$	−7.82790	+	38.6029i	−0.325598	+	1.60567i
$579$	0.633452			0.0263254
$580$	0.114088	−	0.114088i	0.00473726	−	0.00473726i
$581$	4.54663	+	1.88327i	0.188626	+	0.0781314i
$582$			2.87398i			0.119130i
$583$	1.30137	−	3.14179i	0.0538973	−	0.130120i
$584$	27.5033	−	11.3922i	1.13809	−	0.471414i
$585$	0.111402	+	0.268948i	0.00460589	+	0.0111196i
$586$	8.22408	+	8.22408i	0.339734	+	0.339734i
$587$	−23.0019	−	23.0019i	−0.949390	−	0.949390i	0.0493894	−	0.998780i	$-0.484272\pi$
$587$	−23.0019	−	23.0019i	−0.949390	−	0.949390i	−0.998780	+	0.0493894i	$0.984272\pi$
$588$	1.79299	+	4.32867i	0.0739418	+	0.178511i
$589$	6.40668	−	2.65373i	0.263983	−	0.109345i
$590$	−0.187875	+	0.453571i	−0.00773470	+	0.0186732i
$591$			3.19373i			0.131373i
$592$	2.10996	+	0.873972i	0.0867187	+	0.0359200i
$593$	4.96885	−	4.96885i	0.204046	−	0.204046i	−0.597685	−	0.801731i	$-0.703913\pi$
$593$	4.96885	−	4.96885i	0.204046	−	0.204046i	0.801731	+	0.597685i	$0.203913\pi$
$594$	−2.27574			−0.0933748
$595$	0.395051	−	0.119036i	0.0161955	−	0.00488000i
$596$	8.12710			0.332899
$597$	−1.94303	+	1.94303i	−0.0795229	+	0.0795229i
$598$	71.1457	+	29.4695i	2.90936	+	1.20510i
$599$			20.5237i			0.838577i	0.907853	+	0.419289i	$0.137720\pi$
$599$			20.5237i			0.838577i	−0.907853	+	0.419289i	$0.862280\pi$
$600$	−0.997447	+	2.40805i	−0.0407206	+	0.0983082i
$601$	27.5304	−	11.4034i	1.12299	−	0.465156i	0.257595	−	0.966253i	$-0.417070\pi$
$601$	27.5304	−	11.4034i	1.12299	−	0.465156i	0.865391	+	0.501096i	$0.167070\pi$
$602$	−28.9159	−	69.8091i	−1.17852	−	2.84521i
$603$	−4.30645	−	4.30645i	−0.175372	−	0.175372i
$604$	−37.0072	−	37.0072i	−1.50580	−	1.50580i
$605$	−0.00973985	−	0.0235141i	−0.000395981	−	0.000955983i
$606$	5.91699	−	2.45090i	0.240361	−	0.0995609i
$607$	7.15320	−	17.2693i	0.290339	−	0.700941i	−0.709654	−	0.704550i	$-0.751149\pi$
$607$	7.15320	−	17.2693i	0.290339	−	0.700941i	0.999993	+	0.00360903i	$0.00114879\pi$
$608$		−	6.83009i		−	0.276997i
$609$	1.12419	+	0.465654i	0.0455544	+	0.0188692i
$610$	−0.269310	+	0.269310i	−0.0109040	+	0.0109040i
$611$	−41.8836			−1.69443
$612$	19.5311	−	36.3773i	0.789498	−	1.47046i
$613$	41.3796			1.67131			0.835653	−	0.549258i	$-0.185090\pi$
$613$	41.3796			1.67131			0.835653	+	0.549258i	$0.185090\pi$
$614$	−8.24633	+	8.24633i	−0.332795	+	0.332795i
$615$	−0.000565572	0	0.000234268i	−2.28061e−5	0	9.44658e-6i
$616$			12.4656i			0.502252i
$617$	9.02392	−	21.7857i	0.363289	−	0.877058i	−0.631525	−	0.775355i	$-0.717571\pi$
$617$	9.02392	−	21.7857i	0.363289	−	0.877058i	0.994815	−	0.101703i	$-0.0324292\pi$
$618$	−1.09332	+	0.452869i	−0.0439799	+	0.0182171i
$619$	4.70294	+	11.3539i	0.189027	+	0.456352i	0.989773	−	0.142653i	$-0.0455631\pi$
$619$	4.70294	+	11.3539i	0.189027	+	0.456352i	−0.800746	+	0.599005i	$0.795563\pi$
$620$	0.303398	+	0.303398i	0.0121848	+	0.0121848i
$621$	−5.99996	−	5.99996i	−0.240770	−	0.240770i
$622$	−16.1611	−	39.0165i	−0.648003	−	1.56442i
$623$	13.6169	−	5.64031i	0.545550	−	0.225974i
$624$	−0.147482	+	0.356054i	−0.00590402	+	0.0142536i
$625$			24.9903i			0.999611i
$626$	−5.97461	−	2.47477i	−0.238794	−	0.0989116i
$627$	0.161109	−	0.161109i	0.00643406	−	0.00643406i
$628$	48.0864			1.91886
$629$	15.3804	+	1.54372i	0.613258	+	0.0615520i
$630$	−0.689303			−0.0274625
$631$	−9.22242	+	9.22242i	−0.367139	+	0.367139i	−0.866433	−	0.499294i	$-0.833593\pi$
$631$	−9.22242	+	9.22242i	−0.367139	+	0.367139i	0.499294	+	0.866433i	$0.333593\pi$
$632$	47.3727	+	19.6224i	1.88439	+	0.780538i
$633$			3.45016i			0.137131i
$634$	2.76887	−	6.68465i	0.109966	−	0.265481i
$635$	0.296927	−	0.122991i	0.0117832	−	0.00488076i
$636$	0.720830	+	1.74024i	0.0285828	+	0.0690049i
$637$	23.0114	+	23.0114i	0.911745	+	0.911745i
$638$	3.08340	+	3.08340i	0.122073	+	0.122073i
$639$	−5.29811	−	12.7908i	−0.209590	−	0.505995i
$640$	0.456815	−	0.189219i	0.0180572	−	0.00747953i
$641$	1.11828	−	2.69977i	0.0441695	−	0.106635i	−0.900255	−	0.435363i	$-0.856620\pi$
$641$	1.11828	−	2.69977i	0.0441695	−	0.106635i	0.944425	+	0.328728i	$0.106620\pi$
$642$			3.22656i			0.127342i
$643$	−26.6192	−	11.0260i	−1.04976	−	0.434825i	−0.209954	−	0.977711i	$-0.567331\pi$
$643$	−26.6192	−	11.0260i	−1.04976	−	0.434825i	−0.839806	+	0.542887i	$0.817331\pi$
$644$	−80.9009	+	80.9009i	−3.18794	+	3.18794i
$645$	−0.0347147			−0.00136689
$646$	3.81875	+	12.6735i	0.150247	+	0.498632i
$647$	−3.87325			−0.152273			−0.0761366	−	0.997097i	$-0.524258\pi$
$647$	−3.87325			−0.152273			−0.0761366	+	0.997097i	$0.524258\pi$
$648$	−19.6328	+	19.6328i	−0.771250	+	0.771250i
$649$	−7.69151	−	3.18593i	−0.301918	−	0.125059i
$650$			44.5642i			1.74795i
$651$	−1.23833	+	2.98959i	−0.0485339	+	0.117171i
$652$	−31.2744	+	12.9543i	−1.22480	+	0.507328i
$653$	−11.3516	−	27.4051i	−0.444221	−	1.07244i	−0.974453	−	0.224592i	$-0.927895\pi$
$653$	−11.3516	−	27.4051i	−0.444221	−	1.07244i	0.530232	−	0.847853i	$-0.322105\pi$
$654$	−0.481564	−	0.481564i	−0.0188306	−	0.0188306i
$655$	−0.138945	−	0.138945i	−0.00542904	−	0.00542904i
$656$	0.0340977	+	0.0823191i	0.00133129	+	0.00321402i
$657$	−25.7899	+	10.6825i	−1.00616	+	0.416764i
$658$	37.9526	−	91.6257i	1.47955	−	3.57194i
$659$			10.7826i			0.420030i	0.977698	+	0.210015i	$0.0673513\pi$
$659$			10.7826i			0.420030i	−0.977698	+	0.210015i	$0.932649\pi$
$660$	0.0130245	+	0.00539491i	0.000506976	+	0.000209996i
$661$	−14.3421	+	14.3421i	−0.557843	+	0.557843i	−0.928693	−	0.370850i	$-0.879066\pi$
$661$	−14.3421	+	14.3421i	−0.557843	+	0.557843i	0.370850	+	0.928693i	$0.379066\pi$
$662$	−33.8087			−1.31401
$663$	−0.260501	+	2.59544i	−0.0101170	+	0.100799i
$664$	−3.96836			−0.154002
$665$	0.0980407	−	0.0980407i	0.00380186	−	0.00380186i
$666$	−23.8587	−	9.88258i	−0.924504	−	0.382942i
$667$			16.2587i			0.629538i
$668$	−15.3277	+	37.0044i	−0.593047	+	1.43174i
$669$	2.48143	−	1.02784i	0.0959378	−	0.0397387i
$670$	0.0462295	+	0.111608i	0.00178600	+	0.00431178i
$671$	−4.56687	−	4.56687i	−0.176302	−	0.176302i
$672$	2.25367	+	2.25367i	0.0869370	+	0.0869370i
$673$	13.2364	+	31.9554i	0.510225	+	1.23179i	0.943753	+	0.330652i	$0.107268\pi$
$673$	13.2364	+	31.9554i	0.510225	+	1.23179i	−0.433528	+	0.901140i	$0.642732\pi$
$674$	2.63235	−	1.09036i	0.101394	−	0.0419989i
$675$	1.87912	−	4.53660i	0.0723275	−	0.174614i
$676$			6.06765i			0.233371i
$677$	−2.84174	−	1.17709i	−0.109217	−	0.0452391i	0.327406	−	0.944884i	$-0.393826\pi$
$677$	−2.84174	−	1.17709i	−0.109217	−	0.0452391i	−0.436623	+	0.899645i	$0.643826\pi$
$678$	1.11297	−	1.11297i	0.0427434	−	0.0427434i
$679$	−29.6577			−1.13816
$680$	−0.257577	+	0.210588i	−0.00987764	+	0.00807569i
$681$	0.601571			0.0230522
$682$	−8.19978	+	8.19978i	−0.313986	+	0.313986i
$683$	26.8786	+	11.1335i	1.02848	+	0.426010i	0.832164	−	0.554530i	$-0.187102\pi$
$683$	26.8786	+	11.1335i	1.02848	+	0.426010i	0.196316	+	0.980541i	$0.437102\pi$
$684$		−	13.8749i		−	0.530520i
$685$	−0.130036	+	0.313934i	−0.00496841	+	0.0119948i
$686$	−12.2775	+	5.08551i	−0.468758	+	0.194166i
$687$	−0.970951	−	2.34408i	−0.0370441	−	0.0894324i
$688$	3.57282	+	3.57282i	0.136212	+	0.136212i
$689$	9.25118	+	9.25118i	0.352442	+	0.352442i
$690$	0.0320588	+	0.0773967i	0.00122046	+	0.00294644i
$691$	−32.8729	+	13.6164i	−1.25054	+	0.517993i	−0.906995	−	0.421142i	$-0.861629\pi$
$691$	−32.8729	+	13.6164i	−1.25054	+	0.517993i	−0.343550	+	0.939134i	$0.611629\pi$
$692$	27.9819	−	67.5543i	1.06371	−	2.56803i
$693$		−	11.6890i		−	0.444027i
$694$	−49.7387	−	20.6024i	−1.88806	−	0.782058i
$695$	0.268473	−	0.268473i	0.0101837	−	0.0101837i
$696$	−0.981206			−0.0371925
$697$	0.381720	+	0.466895i	0.0144587	+	0.0176849i
$698$	71.0728			2.69014
$699$	1.75208	−	1.75208i	0.0662697	−	0.0662697i
$700$	−61.1697	−	25.3373i	−2.31200	−	0.957660i
$701$			15.9959i			0.604156i	0.953283	+	0.302078i	$0.0976802\pi$
$701$			15.9959i			0.604156i	−0.953283	+	0.302078i	$0.902320\pi$
$702$	3.35053	−	8.08889i	0.126458	−	0.305296i
$703$	4.79908	−	1.98784i	0.181001	−	0.0749729i
$704$	4.83708	+	11.6778i	0.182304	+	0.440122i
$705$	−0.0322183	−	0.0322183i	−0.00121341	−	0.00121341i
$706$	19.9723	+	19.9723i	0.751669	+	0.751669i
$707$	25.2918	+	61.0597i	0.951195	+	2.29639i
$708$	4.26033	−	1.76469i	0.160113	−	0.0663210i
$709$	−7.98015	+	19.2658i	−0.299701	+	0.723542i	0.700252	+	0.713895i	$0.253071\pi$
$709$	−7.98015	+	19.2658i	−0.299701	+	0.723542i	−0.999953	+	0.00964689i	$0.996929\pi$
$710$			0.274616i			0.0103062i
$711$	−44.4215	−	18.4000i	−1.66594	−	0.690053i
$712$	−8.40398	+	8.40398i	−0.314953	+	0.314953i
$713$	−43.2372			−1.61924
$714$	−5.44180	−	2.92172i	−0.203654	−	0.109343i
$715$	0.0979182			0.00366193
$716$	−59.6445	+	59.6445i	−2.22902	+	2.22902i
$717$	1.84349	+	0.763600i	0.0688465	+	0.0285172i
$718$			23.5071i			0.877277i
$719$	9.06157	−	21.8766i	0.337940	−	0.815858i	−0.659974	−	0.751289i	$-0.729433\pi$
$719$	9.06157	−	21.8766i	0.337940	−	0.815858i	0.997913	−	0.0645696i	$-0.0205674\pi$
$720$	0.0425847	−	0.0176392i	0.00158704	−	0.000657373i
$721$	−4.67333	−	11.2824i	−0.174044	−	0.420179i
$722$	−27.9834	−	27.9834i	−1.04143	−	1.04143i
$723$	−1.86116	−	1.86116i	−0.0692173	−	0.0692173i
$724$	−22.7089	−	54.8242i	−0.843971	−	2.03753i
$725$	−8.69266	+	3.60062i	−0.322837	+	0.133724i
$726$	−0.145805	+	0.352005i	−0.00541134	+	0.0130641i
$727$			8.83544i			0.327688i	0.986486	+	0.163844i	$0.0523894\pi$
$727$			8.83544i			0.327688i	−0.986486	+	0.163844i	$0.947611\pi$
$728$	−44.3076	−	18.3528i	−1.64215	−	0.680200i
$729$	18.0671	−	18.0671i	0.669152	−	0.669152i
$730$	0.553705			0.0204935
$731$	30.1308	+	16.1773i	1.11443	+	0.598339i
$732$	3.57739			0.132224
$733$	−13.4417	+	13.4417i	−0.496481	+	0.496481i	−0.910341	−	0.413860i	$-0.864180\pi$
$733$	−13.4417	+	13.4417i	−0.496481	+	0.496481i	0.413860	+	0.910341i	$0.364180\pi$
$734$	64.4403	+	26.6920i	2.37853	+	0.985221i
$735$			0.0354023i			0.00130583i
$736$	−16.2969	+	39.3442i	−0.600712	+	1.45025i
$737$	−1.89261	+	0.783944i	−0.0697151	+	0.0288770i
$738$	−0.385565	−	0.930836i	−0.0141928	−	0.0342646i
$739$	9.81389	+	9.81389i	0.361010	+	0.361010i	0.864185	−	0.503175i	$-0.167835\pi$
$739$	9.81389	+	9.81389i	0.361010	+	0.361010i	−0.503175	+	0.864185i	$0.667835\pi$
$740$	0.227268	+	0.227268i	0.00835453	+	0.00835453i
$741$	0.335447	+	0.809842i	0.0123230	+	0.0297503i
$742$	−28.6210	+	11.8552i	−1.05071	+	0.435219i
$743$	14.9689	−	36.1381i	0.549155	−	1.32578i	−0.368953	−	0.929448i	$-0.620284\pi$
$743$	14.9689	−	36.1381i	0.549155	−	1.32578i	0.918108	−	0.396330i	$-0.129716\pi$
$744$		−	2.60935i		−	0.0956634i
$745$	0.0567340	+	0.0235000i	0.00207857	+	0.000860974i
$746$	−43.3811	+	43.3811i	−1.58829	+	1.58829i
$747$	3.72113			0.136149
$748$	−8.79057	−	10.7520i	−0.321415	−	0.393133i
$749$	−33.2961			−1.21661
$750$	−0.0685650	+	0.0685650i	−0.00250364	+	0.00250364i
$751$	27.9777	+	11.5887i	1.02092	+	0.422879i	0.829427	−	0.558615i	$-0.188667\pi$
$751$	27.9777	+	11.5887i	1.02092	+	0.422879i	0.191493	+	0.981494i	$0.438667\pi$
$752$			6.63179i			0.241836i
$753$	1.49737	−	3.61497i	0.0545673	−	0.131737i
$754$	−15.4993	+	6.42001i	−0.564450	+	0.233803i
$755$	−0.151333	−	0.365350i	−0.00550757	−	0.0132965i
$756$	9.19801	+	9.19801i	0.334528	+	0.334528i
$757$	37.1514	+	37.1514i	1.35029	+	1.35029i	0.885333	+	0.464958i	$0.153930\pi$
$757$	37.1514	+	37.1514i	1.35029	+	1.35029i	0.464958	+	0.885333i	$0.346070\pi$
$758$	−10.2947	−	24.8536i	−0.373920	−	0.902722i
$759$	−1.31247	+	0.543642i	−0.0476396	+	0.0197330i
$760$	−0.0427856	+	0.103294i	−0.00155200	+	0.00374685i
$761$		−	6.23194i		−	0.225907i	−0.993600	−	0.112954i	$-0.963969\pi$
$761$		−	6.23194i		−	0.225907i	0.993600	−	0.112954i	$-0.0360312\pi$
$762$	−4.44499	−	1.84118i	−0.161025	−	0.0666988i
$763$	4.96944	−	4.96944i	0.179906	−	0.179906i
$764$	−22.9726			−0.831118
$765$	0.241531	−	0.197469i	0.00873256	−	0.00713950i
$766$	−38.2966			−1.38371
$767$	22.6481	−	22.6481i	0.817776	−	0.817776i
$768$	−2.99788	−	1.24176i	−0.108177	−	0.0448083i
$769$			34.4552i			1.24249i	0.783618	+	0.621243i	$0.213372\pi$
$769$			34.4552i			1.24249i	−0.783618	+	0.621243i	$0.786628\pi$
$770$	−0.0887280	+	0.214208i	−0.00319754	+	0.00771953i
$771$	−3.64595	+	1.51020i	−0.131306	+	0.0543886i
$772$	−4.96547	−	11.9877i	−0.178711	−	0.431447i
$773$	14.5627	+	14.5627i	0.523785	+	0.523785i	0.918712	−	0.394927i	$-0.129230\pi$
$773$	14.5627	+	14.5627i	0.523785	+	0.523785i	−0.394927	+	0.918712i	$0.629230\pi$
$774$	−40.4002	−	40.4002i	−1.45215	−	1.45215i
$775$	−9.57523	−	23.1167i	−0.343952	−	0.830375i
$776$	22.0948	−	9.15195i	0.793156	−	0.328536i
$777$	−0.927599	+	2.23942i	−0.0332774	+	0.0803388i
$778$		−	3.80755i		−	0.136507i
$779$	0.187234	+	0.0775549i	0.00670836	+	0.00277869i
$780$	−0.0383513	+	0.0383513i	−0.00137320	+	0.00137320i
$781$	−4.65685			−0.166635
$782$	8.24193	−	82.1165i	0.294731	−	2.93648i
$783$	1.84853			0.0660609
$784$	3.64359	−	3.64359i	0.130128	−	0.130128i
$785$	0.335684	+	0.139045i	0.0119811	+	0.00496272i
$786$			2.94157i			0.104922i
$787$	−6.05148	+	14.6096i	−0.215712	+	0.520775i	−0.994282	−	0.106782i	$-0.965945\pi$
$787$	−6.05148	+	14.6096i	−0.215712	+	0.520775i	0.778570	+	0.627557i	$0.215945\pi$
$788$	60.4396	−	25.0349i	2.15307	−	0.891831i
$789$	−0.845576	−	2.04140i	−0.0301033	−	0.0726758i
$790$	0.674384	+	0.674384i	0.0239935	+	0.0239935i
$791$	11.4852	+	11.4852i	0.408366	+	0.408366i
$792$	3.60705	+	8.70820i	0.128171	+	0.309432i
$793$	22.9562	−	9.50877i	0.815199	−	0.337666i
$794$	−0.709643	+	1.71323i	−0.0251843	+	0.0608002i
$795$			0.0142327i			0.000504780i
$796$	52.0016	+	21.5398i	1.84315	+	0.763457i
$797$	39.5674	−	39.5674i	1.40155	−	1.40155i	0.606349	−	0.795199i	$-0.292634\pi$
$797$	39.5674	−	39.5674i	1.40155	−	1.40155i	0.795199	−	0.606349i	$-0.207366\pi$
$798$	−2.07559			−0.0734752
$799$	12.9501	+	42.9781i	0.458140	+	1.52045i
$800$	−24.6444			−0.871311
$801$	7.88043	−	7.88043i	0.278441	−	0.278441i
$802$	77.5083	+	32.1050i	2.73691	+	1.13367i
$803$			9.38955i			0.331350i
$804$	0.434227	−	1.04832i	0.0153140	−	0.0369713i
$805$	−0.798687	+	0.330827i	−0.0281500	+	0.0116601i
$806$	−17.0729	−	41.2177i	−0.601368	−	1.45183i
$807$	2.88503	+	2.88503i	0.101558	+	0.101558i
$808$	−37.6844	−	37.6844i	−1.32573	−	1.32573i
$809$	−2.96546	−	7.15926i	−0.104260	−	0.251706i	0.863137	−	0.504969i	$-0.168496\pi$
$809$	−2.96546	−	7.15926i	−0.104260	−	0.251706i	−0.967397	+	0.253263i	$0.918496\pi$
$810$	−0.477114	+	0.197627i	−0.0167641	+	0.00694391i
$811$	−11.5690	+	27.9301i	−0.406244	+	0.980759i	0.579873	+	0.814707i	$0.303102\pi$
$811$	−11.5690	+	27.9301i	−0.406244	+	0.980759i	−0.986117	+	0.166052i	$0.946898\pi$
$812$		−	24.9248i		−	0.874687i
$813$	−4.15750	−	1.72209i	−0.145810	−	0.0603965i
$814$	−6.14224	+	6.14224i	−0.215285	+	0.215285i
$815$	−0.255780			−0.00895957
$816$	0.410958	+	0.0412474i	0.0143864	+	0.00144395i
$817$	11.4924			0.402067
$818$	13.3301	−	13.3301i	0.466076	−	0.466076i
$819$	41.5473	+	17.2094i	1.45178	+	0.601347i
$820$			0.0125395i			0.000437898i
$821$	9.07769	−	21.9155i	0.316814	−	0.764856i	−0.682606	−	0.730787i	$-0.739153\pi$
$821$	9.07769	−	21.9155i	0.316814	−	0.764856i	0.999419	−	0.0340690i	$-0.0108466\pi$
$822$	4.69959	−	1.94663i	0.163917	−	0.0678966i
$823$	4.04002	+	9.75346i	0.140826	+	0.339984i	0.978519	−	0.206158i	$-0.0660959\pi$
$823$	4.04002	+	9.75346i	0.140826	+	0.339984i	−0.837693	+	0.546142i	$0.816096\pi$
$824$	6.96319	+	6.96319i	0.242574	+	0.242574i
$825$	−0.581314	−	0.581314i	−0.0202388	−	0.0202388i
$826$	29.0232	+	70.0681i	1.00984	+	2.43798i
$827$	−24.6479	+	10.2095i	−0.857091	+	0.355019i	−0.767569	−	0.640966i	$-0.778534\pi$
$827$	−24.6479	+	10.2095i	−0.857091	+	0.355019i	−0.0895220	+	0.995985i	$0.528534\pi$
$828$	−33.1062	+	79.9254i	−1.15052	+	2.77760i
$829$			38.7531i			1.34595i	0.739665	+	0.672975i	$0.234984\pi$
$829$			38.7531i			1.34595i	−0.739665	+	0.672975i	$0.765016\pi$
$830$	−0.0681923	−	0.0282462i	−0.00236699	−	0.000980439i
$831$	0.874042	−	0.874042i	0.0303202	−	0.0303202i
$832$	−48.6289			−1.68590
$833$	16.4978	−	30.7276i	0.571614	−	1.06465i
$834$	−5.68376			−0.196813
$835$	−0.214001	+	0.214001i	−0.00740581	+	0.00740581i
$836$	−4.31178	−	1.78600i	−0.149126	−	0.0617700i
$837$			4.91584i			0.169916i
$838$	−0.525276	+	1.26813i	−0.0181454	+	0.0438068i
$839$	−11.6420	+	4.82227i	−0.401926	+	0.166483i	−0.574483	−	0.818516i	$-0.694797\pi$
$839$	−11.6420	+	4.82227i	−0.401926	+	0.166483i	0.172557	+	0.984999i	$0.444797\pi$
$840$	−0.0199653	−	0.0482005i	−0.000688869	−	0.00166308i
$841$	18.0015	+	18.0015i	0.620742	+	0.620742i
$842$	41.8161	+	41.8161i	1.44108	+	1.44108i
$843$	−0.581388	−	1.40360i	−0.0200241	−	0.0483424i
$844$	65.2922	−	27.0449i	2.24745	−	0.930925i
$845$	−0.0175450	+	0.0423574i	−0.000603566	+	0.00145714i
$846$		−	74.9900i		−	2.57821i
$847$	−3.63248	−	1.50462i	−0.124813	−	0.0516994i
$848$	1.46482	−	1.46482i	0.0503021	−	0.0503021i
$849$	2.65093			0.0909798
$850$	45.7286	−	13.7789i	1.56848	−	0.472611i
$851$	−32.3878			−1.11024
$852$	1.82393	−	1.82393i	0.0624869	−	0.0624869i
$853$	−5.97312	−	2.47415i	−0.204516	−	0.0847131i	0.278074	−	0.960560i	$-0.410304\pi$
$853$	−5.97312	−	2.47415i	−0.204516	−	0.0847131i	−0.482590	+	0.875846i	$0.660304\pi$
$854$			58.8359i			2.01332i
$855$	0.0401202	−	0.0968586i	0.00137208	−	0.00331249i
$856$	24.8054	−	10.2747i	0.847830	−	0.351183i
$857$	−2.08284	−	5.02843i	−0.0711486	−	0.171768i	0.884305	−	0.466910i	$-0.154633\pi$
$857$	−2.08284	−	5.02843i	−0.0711486	−	0.171768i	−0.955453	+	0.295142i	$0.904633\pi$
$858$	−1.03650	−	1.03650i	−0.0353855	−	0.0353855i
$859$	−1.68711	−	1.68711i	−0.0575633	−	0.0575633i	0.677739	−	0.735302i	$-0.262960\pi$
$859$	−1.68711	−	1.68711i	−0.0575633	−	0.0575633i	−0.735302	+	0.677739i	$0.762960\pi$
$860$	0.272120	+	0.656955i	0.00927920	+	0.0224020i
$861$	−0.0873701	+	0.0361899i	−0.00297757	+	0.00123335i
$862$	−17.9410	+	43.3135i	−0.611074	+	1.47526i
$863$			8.43916i			0.287272i	0.989631	+	0.143636i	$0.0458795\pi$
$863$			8.43916i			0.287272i	−0.989631	+	0.143636i	$0.954120\pi$
$864$	4.47324	+	1.85288i	0.152183	+	0.0630361i
$865$	0.390675	−	0.390675i	0.0132833	−	0.0132833i
$866$	82.2604			2.79532
$867$	2.74380	−	0.535179i	0.0931845	−	0.0181756i
$868$	66.2831			2.24980
$869$	−11.4360	+	11.4360i	−0.387940	+	0.387940i
$870$	−0.0168611	−	0.00698408i	−0.000571644	−	0.000236783i
$871$		−	7.88127i		−	0.267047i
$872$	−2.16870	+	5.23570i	−0.0734414	+	0.177303i
$873$	−20.7183	+	8.58180i	−0.701208	+	0.290450i
$874$	−10.6131	−	25.6224i	−0.358995	−	0.866689i
$875$	−0.707549	−	0.707549i	−0.0239195	−	0.0239195i
$876$	−3.67758	−	3.67758i	−0.124254	−	0.124254i
$877$	5.16828	+	12.4773i	0.174521	+	0.421330i	0.986801	−	0.161937i	$-0.0517742\pi$
$877$	5.16828	+	12.4773i	0.174521	+	0.421330i	−0.812281	+	0.583267i	$0.801774\pi$
$878$	32.1904	−	13.3337i	1.08637	−	0.449990i
$879$	0.315888	−	0.762621i	0.0106546	−	0.0257226i
$880$		−	0.0155042i		−	0.000522647i
$881$	−39.5695	−	16.3902i	−1.33313	−	0.552200i	−0.401582	−	0.915823i	$-0.631540\pi$
$881$	−39.5695	−	16.3902i	−1.33313	−	0.552200i	−0.931546	+	0.363623i	$0.881540\pi$
$882$	−41.2005	+	41.2005i	−1.38729	+	1.38729i
$883$	10.6020			0.356784			0.178392	−	0.983959i	$-0.442910\pi$
$883$	10.6020			0.356784			0.178392	+	0.983959i	$0.442910\pi$
$884$	51.1592	−	15.4152i	1.72067	−	0.518469i
$885$	0.0348434			0.00117125
$886$	47.6330	−	47.6330i	1.60026	−	1.60026i
$887$	−35.0985	−	14.5383i	−1.17849	−	0.488148i	−0.294502	−	0.955651i	$-0.595154\pi$
$887$	−35.0985	−	14.5383i	−1.17849	−	0.488148i	−0.883991	+	0.467503i	$0.845154\pi$
$888$		−	1.95460i		−	0.0655920i
$889$	18.9998	−	45.8696i	0.637234	−	1.53842i
$890$	−0.204233	+	0.0845959i	−0.00684589	+	0.00283566i
$891$	−3.35130	−	8.09075i	−0.112273	−	0.271050i
$892$	−38.9027	−	38.9027i	−1.30256	−	1.30256i
$893$	10.6660	+	10.6660i	0.356923	+	0.356923i
$894$	−0.351795	−	0.849307i	−0.0117658	−	0.0284051i
$895$	−0.588835	+	0.243903i	−0.0196826	+	0.00815279i
$896$	29.2307	−	70.5692i	0.976530	−	2.35755i
$897$		−	5.46543i		−	0.182485i
$898$	−13.5134	−	5.59741i	−0.450946	−	0.186788i
$899$	6.66047	−	6.66047i	0.222139	−	0.222139i
$900$	−50.0636			−1.66879
$901$	6.63253	−	12.3533i	0.220962	−	0.411548i
$902$	−0.338898			−0.0112841
$903$	−3.79204	+	3.79204i	−0.126191	+	0.126191i
$904$	−12.1005	−	5.01221i	−0.402458	−	0.166704i
$905$		−	0.448384i		−	0.0149048i
$906$	−2.26545	+	5.46928i	−0.0752646	+	0.181705i
$907$	−4.11165	+	1.70310i	−0.136525	+	0.0565505i	−0.449900	−	0.893079i	$-0.648540\pi$
$907$	−4.11165	+	1.70310i	−0.136525	+	0.0565505i	0.313375	+	0.949629i	$0.398540\pi$
$908$	−4.71556	−	11.3844i	−0.156491	−	0.377804i
$909$	35.3367	+	35.3367i	1.17204	+	1.17204i
$910$	−0.630750	−	0.630750i	−0.0209091	−	0.0209091i
$911$	10.1839	+	24.5860i	0.337406	+	0.814570i	0.997963	+	0.0637944i	$0.0203202\pi$
$911$	10.1839	+	24.5860i	0.337406	+	0.814570i	−0.660557	+	0.750776i	$0.729680\pi$
$912$	0.128229	−	0.0531142i	0.00424609	−	0.00175879i
$913$	0.478990	−	1.15638i	0.0158522	−	0.0382707i
$914$		−	71.4547i		−	2.36351i
$915$	0.0249732	+	0.0103442i	0.000825588	+	0.000341970i
$916$	−36.7494	+	36.7494i	−1.21423	+	1.21423i
$917$	−30.3552			−1.00242
$918$	−9.33622	−	0.937064i	−0.308141	−	0.0309277i
$919$	−3.28226			−0.108272			−0.0541359	−	0.998534i	$-0.517240\pi$
$919$	−3.28226			−0.108272			−0.0541359	+	0.998534i	$0.517240\pi$
$920$	0.492927	−	0.492927i	0.0162513	−	0.0162513i
$921$	0.764684	+	0.316743i	0.0251972	+	0.0104370i
$922$		−	15.1587i		−	0.499226i
$923$	6.85619	−	16.5523i	0.225674	−	0.544826i
$924$	2.01203	−	0.833411i	0.0661910	−	0.0274172i
$925$	−7.17256	−	17.3161i	−0.235832	−	0.569349i
$926$	−20.8160	−	20.8160i	−0.684055	−	0.684055i
$927$	−6.52940	−	6.52940i	−0.214454	−	0.214454i
$928$	−3.55033	−	8.57124i	−0.116545	−	0.281365i
$929$	4.38833	−	1.81771i	0.143976	−	0.0596370i	−0.309532	−	0.950889i	$-0.600172\pi$
$929$	4.38833	−	1.81771i	0.143976	−	0.0596370i	0.453508	+	0.891252i	$0.350172\pi$
$930$	0.0185730	−	0.0448391i	0.000609032	−	0.00147033i
$931$		−	11.7200i		−	0.384108i
$932$	−46.8912	−	19.4230i	−1.53597	−	0.636220i
$933$	−2.11938	+	2.11938i	−0.0693854	+	0.0693854i
$934$	−24.9290			−0.815701
$935$	−0.0302755	−	0.100477i	−0.000990113	−	0.00328594i
$936$	−36.2630			−1.18529
$937$	−25.9089	+	25.9089i	−0.846408	+	0.846408i	−0.989683	−	0.143275i	$-0.954237\pi$
$937$	−25.9089	+	25.9089i	−0.846408	+	0.846408i	0.143275	+	0.989683i	$0.454237\pi$
$938$	17.2413	+	7.14157i	0.562948	+	0.233181i
$939$			0.458971i			0.0149780i
$940$	−0.357162	+	0.862265i	−0.0116493	+	0.0281240i
$941$	27.0066	−	11.1865i	0.880389	−	0.364669i	0.103741	−	0.994604i	$-0.466919\pi$
$941$	27.0066	−	11.1865i	0.880389	−	0.364669i	0.776648	+	0.629935i	$0.216919\pi$
$942$	−2.08150	−	5.02518i	−0.0678188	−	0.163729i
$943$	−0.893499	−	0.893499i	−0.0290963	−	0.0290963i
$944$	−3.58607	−	3.58607i	−0.116717	−	0.116717i
$945$	0.0376133	+	0.0908065i	0.00122356	+	0.00295394i
$946$	−17.7552	+	7.35443i	−0.577270	+	0.239113i
$947$	−10.9195	+	26.3619i	−0.354835	+	0.856647i	0.641174	+	0.767395i	$0.278448\pi$
$947$	−10.9195	+	26.3619i	−0.354835	+	0.856647i	−0.996009	+	0.0892518i	$0.971552\pi$
$948$		−	8.95820i		−	0.290949i
$949$	−33.3742	−	13.8240i	−1.08337	−	0.448748i
$950$	11.3486	−	11.3486i	0.368196	−	0.368196i
$951$	−0.513516			−0.0166519
$952$	−5.13284	+	51.1399i	−0.166356	+	1.65745i
$953$	39.7328			1.28707			0.643537	−	0.765415i	$-0.277466\pi$
$953$	39.7328			1.28707			0.643537	+	0.765415i	$0.277466\pi$
$954$	−16.5637	+	16.5637i	−0.536268	+	0.536268i
$955$	−0.160368	−	0.0664266i	−0.00518939	−	0.00214951i
$956$		−	40.8727i		−	1.32192i
$957$	0.118434	−	0.285925i	0.00382842	−	0.00924263i
$958$	26.6363	−	11.0331i	0.860579	−	0.356463i
$959$	20.0881	+	48.4969i	0.648677	+	1.56605i
$960$	−0.0374071	−	0.0374071i	−0.00120731	−	0.00120731i
$961$	−4.20793	−	4.20793i	−0.135740	−	0.135740i
$962$	−12.7889	−	30.8751i	−0.412330	−	0.995452i
$963$	−23.2600	+	9.63463i	−0.749544	+	0.310471i
$964$	−20.6322	+	49.8106i	−0.664519	+	1.60429i
$965$		−	0.0980424i		−	0.00315610i
$966$	11.9563	+	4.95247i	0.384688	+	0.159343i
$967$	2.31440	−	2.31440i	0.0744260	−	0.0744260i	−0.668914	−	0.743340i	$-0.733241\pi$
$967$	2.31440	−	2.31440i	0.0744260	−	0.0744260i	0.743340	+	0.668914i	$0.233241\pi$
$968$	3.17047			0.101903
$969$	0.727286	−	0.594609i	0.0233638	−	0.0191016i
$970$	0.444819			0.0142823
$971$	−26.4435	+	26.4435i	−0.848613	+	0.848613i	−0.989960	−	0.141347i	$-0.954857\pi$
$971$	−26.4435	+	26.4435i	−0.848613	+	0.848613i	0.141347	+	0.989960i	$0.454857\pi$
$972$	13.6512	+	5.65452i	0.437863	+	0.181369i
$973$		−	58.6529i		−	1.88033i
$974$	21.5060	−	51.9201i	0.689097	−	1.66363i
$975$	2.92208	−	1.21037i	0.0935815	−	0.0387627i
$976$	−1.50560	−	3.63485i	−0.0481932	−	0.116349i
$977$	−18.8582	−	18.8582i	−0.603327	−	0.603327i	0.337867	−	0.941194i	$-0.390295\pi$
$977$	−18.8582	−	18.8582i	−0.603327	−	0.603327i	−0.941194	+	0.337867i	$0.890295\pi$
$978$	2.70752	+	2.70752i	0.0865770	+	0.0865770i
$979$	−1.43455	−	3.46331i	−0.0458484	−	0.110688i
$980$	0.669969	−	0.277510i	0.0214014	−	0.00886474i
$981$	2.03359	−	4.90953i	0.0649276	−	0.156749i
$982$			73.0133i			2.32995i
$983$	11.5459	+	4.78247i	0.368257	+	0.152537i	0.559135	−	0.829077i	$-0.311133\pi$
$983$	11.5459	+	4.78247i	0.368257	+	0.152537i	−0.190878	+	0.981614i	$0.561133\pi$
$984$	0.0539224	−	0.0539224i	0.00171898	−	0.00171898i
$985$	0.494310			0.0157500
$986$	11.3800	+	13.9193i	0.362413	+	0.443280i
$987$	−7.03871			−0.224045
$988$	12.6963	−	12.6963i	0.403923	−	0.403923i
$989$	−66.2010	−	27.4214i	−2.10507	−	0.871949i
$990$			0.175316i			0.00557192i
$991$	−0.688441	+	1.66204i	−0.0218691	+	0.0527966i	−0.934437	−	0.356129i	$-0.884096\pi$
$991$	−0.688441	+	1.66204i	−0.0218691	+	0.0527966i	0.912568	+	0.408925i	$0.134096\pi$
$992$	22.7938	−	9.44148i	0.723702	−	0.299767i
$993$	0.918247	+	2.21684i	0.0291397	+	0.0703494i
$994$	29.9976	+	29.9976i	0.951465	+	0.951465i
$995$	0.300732	+	0.300732i	0.00953384	+	0.00953384i
$996$	0.265313	+	0.640521i	0.00840675	+	0.0202957i
$997$	−29.4194	+	12.1859i	−0.931720	+	0.385931i	−0.796331	−	0.604861i	$-0.793229\pi$
$997$	−29.4194	+	12.1859i	−0.931720	+	0.385931i	−0.135390	+	0.990792i	$0.543229\pi$
$998$	3.92972	−	9.48717i	0.124393	−	0.300311i
$999$			3.68233i			0.116504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.111.3	✓	56
17.2	even	8	inner	187.2.h.a.155.3	yes	56
17.6	odd	16		3179.2.a.bh.1.4		28
17.11	odd	16		3179.2.a.bi.1.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.3	✓	56	1.1	even	1	trivial
187.2.h.a.155.3	yes	56	17.2	even	8	inner
3179.2.a.bh.1.4		28	17.6	odd	16
3179.2.a.bi.1.4		28	17.11	odd	16

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.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63835 + 1.63835i) q^{2} +(0.151924 + 0.0629292i) q^{3} -3.36837i q^{4} +(0.00973985 - 0.0235141i) q^{5} +(-0.352005 + 0.145805i) q^{6} +(-1.50462 - 3.63248i) q^{7} +(2.24186 + 2.24186i) q^{8} +(-2.10220 - 2.10220i) q^{9} +O(q^{10})\)	\(q+(-1.63835 + 1.63835i) q^{2} +(0.151924 + 0.0629292i) q^{3} -3.36837i q^{4} +(0.00973985 - 0.0235141i) q^{5} +(-0.352005 + 0.145805i) q^{6} +(-1.50462 - 3.63248i) q^{7} +(2.24186 + 2.24186i) q^{8} +(-2.10220 - 2.10220i) q^{9} +(0.0225670 + 0.0544815i) q^{10} +(-0.923880 + 0.382683i) q^{11} +(0.211969 - 0.511737i) q^{12} -3.84725i q^{13} +(8.41635 + 3.48617i) q^{14} +(0.00295944 - 0.00295944i) q^{15} -0.609168 q^{16} +(-3.94778 + 1.18954i) q^{17} +6.88827 q^{18} +(-0.979730 + 0.979730i) q^{19} +(-0.0792041 - 0.0328074i) q^{20} -0.646546i q^{21} +(0.886668 - 2.14060i) q^{22} +(7.98135 - 3.30598i) q^{23} +(0.199515 + 0.481672i) q^{24} +(3.53508 + 3.53508i) q^{25} +(6.30314 + 6.30314i) q^{26} +(-0.375873 - 0.907438i) q^{27} +(-12.2355 + 5.06812i) q^{28} +(-0.720217 + 1.73876i) q^{29} +0.00969719i q^{30} +(-4.62393 - 1.91529i) q^{31} +(-3.48570 + 3.48570i) q^{32} -0.164442 q^{33} +(4.51897 - 8.41672i) q^{34} -0.100069 q^{35} +(-7.08098 + 7.08098i) q^{36} +(-3.46367 - 1.43470i) q^{37} -3.21028i q^{38} +(0.242104 - 0.584492i) q^{39} +(0.0745507 - 0.0308799i) q^{40} +(-0.0559742 - 0.135134i) q^{41} +(1.05927 + 1.05927i) q^{42} +(-5.86507 - 5.86507i) q^{43} +(1.28902 + 3.11197i) q^{44} +(-0.0699064 + 0.0289562i) q^{45} +(-7.65988 + 18.4926i) q^{46} -10.8866i q^{47} +(-0.0925476 - 0.0383345i) q^{48} +(-5.98125 + 5.98125i) q^{49} -11.5834 q^{50} +(-0.674622 - 0.0677109i) q^{51} -12.9590 q^{52} +(-2.40462 + 2.40462i) q^{53} +(2.10251 + 0.870889i) q^{54} +0.0254514i q^{55} +(4.77036 - 11.5167i) q^{56} +(-0.210499 + 0.0871914i) q^{57} +(-1.66872 - 4.02866i) q^{58} +(5.88683 + 5.88683i) q^{59} +(-0.00996849 - 0.00996849i) q^{60} +(2.47157 + 5.96691i) q^{61} +(10.7135 - 4.43769i) q^{62} +(-4.47318 + 10.7992i) q^{63} -12.6399i q^{64} +(-0.0904646 - 0.0374717i) q^{65} +(0.269413 - 0.269413i) q^{66} +2.04855 q^{67} +(4.00680 + 13.2976i) q^{68} +1.42061 q^{69} +(0.163948 - 0.163948i) q^{70} +(4.30237 + 1.78210i) q^{71} -9.42569i q^{72} +(3.59323 - 8.67481i) q^{73} +(8.02522 - 3.32416i) q^{74} +(0.314605 + 0.759524i) q^{75} +(3.30009 + 3.30009i) q^{76} +(2.78018 + 2.78018i) q^{77} +(0.560950 + 1.35425i) q^{78} +(14.9418 - 6.18912i) q^{79} +(-0.00593321 + 0.0143240i) q^{80} +8.75736i q^{81} +(0.313101 + 0.129691i) q^{82} +(-0.885057 + 0.885057i) q^{83} -2.17781 q^{84} +(-0.0104799 + 0.104414i) q^{85} +19.2181 q^{86} +(-0.218837 + 0.218837i) q^{87} +(-2.92914 - 1.21329i) q^{88} +3.74866i q^{89} +(0.0670907 - 0.161971i) q^{90} +(-13.9751 + 5.78866i) q^{91} +(-11.1358 - 26.8841i) q^{92} +(-0.581960 - 0.581960i) q^{93} +(17.8361 + 17.8361i) q^{94} +(0.0134950 + 0.0325799i) q^{95} +(-0.748915 + 0.310211i) q^{96} +(2.88662 - 6.96892i) q^{97} -19.5987i q^{98} +(2.74666 + 1.13770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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