LMFDB - Embedded newform 75.2.l.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(2,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("75.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, degree $8$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	75.17
Dual form			75.2.l.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.685506 - 0.349283i) q^{2} +(1.03848 - 1.38621i) q^{3} +(-0.827650 - 1.13916i) q^{4} +(-2.01837 - 0.962386i) q^{5} +(-1.19606 + 0.587530i) q^{6} +(1.53819 + 1.53819i) q^{7} +(0.410179 + 2.58977i) q^{8} +(-0.843130 - 2.87909i) q^{9} +O(q^{10})$	\(q+(-0.685506 - 0.349283i) q^{2} +(1.03848 - 1.38621i) q^{3} +(-0.827650 - 1.13916i) q^{4} +(-2.01837 - 0.962386i) q^{5} +(-1.19606 + 0.587530i) q^{6} +(1.53819 + 1.53819i) q^{7} +(0.410179 + 2.58977i) q^{8} +(-0.843130 - 2.87909i) q^{9} +(1.04746 + 1.36470i) q^{10} +(4.90058 - 1.59230i) q^{11} +(-2.43861 - 0.0357015i) q^{12} +(1.29863 + 2.54870i) q^{13} +(-0.517176 - 1.59170i) q^{14} +(-3.43009 + 1.79846i) q^{15} +(-0.246862 + 0.759765i) q^{16} +(-0.429678 + 0.0680543i) q^{17} +(-0.427644 + 2.26812i) q^{18} +(-0.215974 + 0.297262i) q^{19} +(0.574189 + 3.09577i) q^{20} +(3.72962 - 0.534872i) q^{21} +(-3.91554 - 0.620161i) q^{22} +(-2.51281 + 4.93166i) q^{23} +(4.01591 + 2.12082i) q^{24} +(3.14763 + 3.88490i) q^{25} -2.20074i q^{26} +(-4.86657 - 1.82111i) q^{27} +(0.479166 - 3.02533i) q^{28} +(-0.866605 + 0.629625i) q^{29} +(2.97952 - 0.0347805i) q^{30} +(-7.68489 - 5.58340i) q^{31} +(4.14273 - 4.14273i) q^{32} +(2.88189 - 8.44678i) q^{33} +(0.318317 + 0.103427i) q^{34} +(-1.62430 - 4.58497i) q^{35} +(-2.58193 + 3.34334i) q^{36} +(2.68497 - 1.36806i) q^{37} +(0.251880 - 0.128339i) q^{38} +(4.88162 + 0.846603i) q^{39} +(1.66446 - 5.62185i) q^{40} +(3.75980 + 1.22163i) q^{41} +(-2.74350 - 0.936035i) q^{42} +(-1.30753 + 1.30753i) q^{43} +(-5.86985 - 4.26470i) q^{44} +(-1.06904 + 6.62247i) q^{45} +(3.44509 - 2.50300i) q^{46} +(-1.03262 + 6.51970i) q^{47} +(0.796829 + 1.13120i) q^{48} -2.26794i q^{49} +(-0.800788 - 3.76253i) q^{50} +(-0.351873 + 0.666294i) q^{51} +(1.82858 - 3.58878i) q^{52} +(1.97500 + 0.312809i) q^{53} +(2.69998 + 2.94819i) q^{54} +(-11.4236 - 1.50241i) q^{55} +(-3.35262 + 4.61449i) q^{56} +(0.187783 + 0.608084i) q^{57} +(0.813980 - 0.128922i) q^{58} +(-1.69584 + 5.21927i) q^{59} +(4.88766 + 2.41894i) q^{60} +(3.56751 + 10.9797i) q^{61} +(3.31785 + 6.51165i) q^{62} +(3.13169 - 5.72548i) q^{63} +(-2.76733 + 0.899158i) q^{64} +(-0.168276 - 6.39400i) q^{65} +(-4.92587 + 4.78372i) q^{66} +(0.319489 + 2.01717i) q^{67} +(0.433148 + 0.433148i) q^{68} +(4.22680 + 8.60469i) q^{69} +(-0.487982 + 3.71037i) q^{70} +(-6.93698 - 9.54793i) q^{71} +(7.11032 - 3.36445i) q^{72} +(-11.0907 - 5.65098i) q^{73} -2.31840 q^{74} +(8.65401 - 0.328875i) q^{75} +0.517381 q^{76} +(9.98729 + 5.08878i) q^{77} +(-3.05068 - 2.28542i) q^{78} +(0.932978 + 1.28413i) q^{79} +(1.22945 - 1.29591i) q^{80} +(-7.57826 + 4.85489i) q^{81} +(-2.15067 - 2.15067i) q^{82} +(-1.52390 - 9.62155i) q^{83} +(-3.69613 - 3.80596i) q^{84} +(0.932743 + 0.276157i) q^{85} +(1.35302 - 0.439623i) q^{86} +(-0.0271595 + 1.85514i) q^{87} +(6.13379 + 12.0382i) q^{88} +(2.35501 + 7.24797i) q^{89} +(3.04595 - 4.16635i) q^{90} +(-1.92285 + 5.91793i) q^{91} +(7.69770 - 1.21920i) q^{92} +(-15.7203 + 4.85460i) q^{93} +(2.98509 - 4.10862i) q^{94} +(0.721996 - 0.392135i) q^{95} +(-1.44054 - 10.0448i) q^{96} +(2.72539 + 0.431660i) q^{97} +(-0.792151 + 1.55468i) q^{98} +(-8.71618 - 12.7667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	−0.685506	−	0.349283i	−0.484726	−	0.246980i	0.194509	−	0.980901i	$-0.437688\pi$
$2$	−0.685506	−	0.349283i	−0.484726	−	0.246980i	−0.679235	+	0.733920i	$0.737688\pi$
$3$	1.03848	−	1.38621i	0.599565	−	0.800326i
$3$	1.03848	−	1.38621i	0.599565	−	0.800326i
$4$	−0.827650	−	1.13916i	−0.413825	−	0.569582i
$5$	−2.01837	−	0.962386i	−0.902642	−	0.430392i
$5$	−2.01837	−	0.962386i	−0.902642	−	0.430392i
$6$	−1.19606	+	0.587530i	−0.488289	+	0.239858i
$7$	1.53819	+	1.53819i	0.581382	+	0.581382i	0.935283	−	0.353901i	$-0.115145\pi$
$7$	1.53819	+	1.53819i	0.581382	+	0.581382i	−0.353901	+	0.935283i	$0.615145\pi$
$8$	0.410179	+	2.58977i	0.145020	+	0.915620i
$9$	−0.843130	−	2.87909i	−0.281043	−	0.959695i
$10$	1.04746	+	1.36470i	0.331236	+	0.431557i
$11$	4.90058	−	1.59230i	1.47758	−	0.480095i	0.544192	−	0.838961i	$-0.316836\pi$
$11$	4.90058	−	1.59230i	1.47758	−	0.480095i	0.933389	+	0.358866i	$0.116836\pi$
$12$	−2.43861	−	0.0357015i	−0.703966	−	0.0103061i
$13$	1.29863	+	2.54870i	0.360175	+	0.706883i	0.997994	−	0.0633031i	$-0.0201635\pi$
$13$	1.29863	+	2.54870i	0.360175	+	0.706883i	−0.637820	+	0.770186i	$0.720163\pi$
$14$	−0.517176	−	1.59170i	−0.138221	−	0.425400i
$15$	−3.43009	+	1.79846i	−0.885647	+	0.464360i
$16$	−0.246862	+	0.759765i	−0.0617156	+	0.189941i
$17$	−0.429678	+	0.0680543i	−0.104212	+	0.0165056i	−0.208323	−	0.978060i	$-0.566800\pi$
$17$	−0.429678	+	0.0680543i	−0.104212	+	0.0165056i	0.104111	+	0.994566i	$0.466800\pi$
$18$	−0.427644	+	2.26812i	−0.100797	+	0.534601i
$19$	−0.215974	+	0.297262i	−0.0495478	+	0.0681967i	−0.833072	−	0.553165i	$-0.813420\pi$
$19$	−0.215974	+	0.297262i	−0.0495478	+	0.0681967i	0.783524	+	0.621361i	$0.213420\pi$
$20$	0.574189	+	3.09577i	0.128393	+	0.692235i
$21$	3.72962	−	0.534872i	0.813871	−	0.116719i
$22$	−3.91554	−	0.620161i	−0.834796	−	0.132219i
$23$	−2.51281	+	4.93166i	−0.523957	+	1.02832i	0.465710	+	0.884937i	$0.345799\pi$
$23$	−2.51281	+	4.93166i	−0.523957	+	1.02832i	−0.989667	+	0.143386i	$0.954201\pi$
$24$	4.01591	+	2.12082i	0.819744	+	0.432911i
$25$	3.14763	+	3.88490i	0.629525	+	0.776980i
$26$		−	2.20074i		−	0.431600i
$27$	−4.86657	−	1.82111i	−0.936573	−	0.350473i
$28$	0.479166	−	3.02533i	0.0905539	−	0.571735i
$29$	−0.866605	+	0.629625i	−0.160924	+	0.116918i	−0.665333	−	0.746547i	$-0.731711\pi$
$29$	−0.866605	+	0.629625i	−0.160924	+	0.116918i	0.504409	+	0.863465i	$0.331711\pi$
$30$	2.97952	−	0.0347805i	0.543984	−	0.00635002i
$31$	−7.68489	−	5.58340i	−1.38025	−	1.00281i	−0.996857	−	0.0792213i	$-0.974757\pi$
$31$	−7.68489	−	5.58340i	−1.38025	−	1.00281i	−0.383390	−	0.923587i	$-0.625243\pi$
$32$	4.14273	−	4.14273i	0.732339	−	0.732339i
$33$	2.88189	−	8.44678i	0.501673	−	1.47039i
$34$	0.318317	+	0.103427i	0.0545909	+	0.0177377i
$35$	−1.62430	−	4.58497i	−0.274557	−	0.775001i
$36$	−2.58193	+	3.34334i	−0.430322	+	0.557223i
$37$	2.68497	−	1.36806i	0.441406	−	0.224908i	−0.219140	−	0.975694i	$-0.570325\pi$
$37$	2.68497	−	1.36806i	0.441406	−	0.224908i	0.660546	+	0.750786i	$0.270325\pi$
$38$	0.251880	−	0.128339i	0.0408603	−	0.0208194i
$39$	4.88162	+	0.846603i	0.781685	+	0.135565i
$40$	1.66446	−	5.62185i	0.263175	−	0.888893i
$41$	3.75980	+	1.22163i	0.587183	+	0.190787i	0.587516	−	0.809213i	$-0.300106\pi$
$41$	3.75980	+	1.22163i	0.587183	+	0.190787i	−0.000332972		1.00000i	$0.500106\pi$
$42$	−2.74350	−	0.936035i	−0.423332	−	0.144433i
$43$	−1.30753	+	1.30753i	−0.199397	+	0.199397i	−0.799742	−	0.600344i	$-0.795030\pi$
$43$	−1.30753	+	1.30753i	−0.199397	+	0.199397i	0.600344	+	0.799742i	$0.295030\pi$
$44$	−5.86985	−	4.26470i	−0.884914	−	0.642927i
$45$	−1.06904	+	6.62247i	−0.159364	+	0.987220i
$46$	3.44509	−	2.50300i	0.507951	−	0.369048i
$47$	−1.03262	+	6.51970i	−0.150623	+	0.950997i	0.790384	+	0.612611i	$0.209881\pi$
$47$	−1.03262	+	6.51970i	−0.150623	+	0.950997i	−0.941008	+	0.338386i	$0.890119\pi$
$48$	0.796829	+	1.13120i	0.115012	+	0.163275i
$49$		−	2.26794i		−	0.323991i
$50$	−0.800788	−	3.76253i	−0.113248	−	0.532103i
$51$	−0.351873	+	0.666294i	−0.0492721	+	0.0932999i
$52$	1.82858	−	3.58878i	0.253578	−	0.497675i
$53$	1.97500	+	0.312809i	0.271287	+	0.0429676i	0.290596	−	0.956846i	$-0.406147\pi$
$53$	1.97500	+	0.312809i	0.271287	+	0.0429676i	−0.0193089	+	0.999814i	$0.506147\pi$
$54$	2.69998	+	2.94819i	0.367421	+	0.401198i
$55$	−11.4236	−	1.50241i	−1.54036	−	0.202585i
$56$	−3.35262	+	4.61449i	−0.448013	+	0.616637i
$57$	0.187783	+	0.608084i	0.0248724	+	0.0805427i
$58$	0.813980	−	0.128922i	0.106881	−	0.0169283i
$59$	−1.69584	+	5.21927i	−0.220780	+	0.679491i	0.777912	+	0.628373i	$0.216279\pi$
$59$	−1.69584	+	5.21927i	−0.220780	+	0.679491i	−0.998693	+	0.0511187i	$0.983721\pi$
$60$	4.88766	+	2.41894i	0.630994	+	0.312284i
$61$	3.56751	+	10.9797i	0.456773	+	1.40580i	0.869041	+	0.494740i	$0.164737\pi$
$61$	3.56751	+	10.9797i	0.456773	+	1.40580i	−0.412268	+	0.911063i	$0.635263\pi$
$62$	3.31785	+	6.51165i	0.421368	+	0.826981i
$63$	3.13169	−	5.72548i	0.394556	−	0.721342i
$64$	−2.76733	+	0.899158i	−0.345916	+	0.112395i
$65$	−0.168276	−	6.39400i	−0.0208720	−	0.793078i
$66$	−4.92587	+	4.78372i	−0.606333	+	0.588835i
$67$	0.319489	+	2.01717i	0.0390318	+	0.246437i	0.999488	−	0.0319938i	$-0.0101857\pi$
$67$	0.319489	+	2.01717i	0.0390318	+	0.246437i	−0.960456	+	0.278431i	$0.910186\pi$
$68$	0.433148	+	0.433148i	0.0525269	+	0.0525269i
$69$	4.22680	+	8.60469i	0.508847	+	1.03588i
$70$	−0.487982	+	3.71037i	−0.0583250	+	0.443474i
$71$	−6.93698	−	9.54793i	−0.823268	−	1.13313i	−0.989139	−	0.146983i	$-0.953044\pi$
$71$	−6.93698	−	9.54793i	−0.823268	−	1.13313i	0.165871	−	0.986147i	$-0.446956\pi$
$72$	7.11032	−	3.36445i	0.837960	−	0.396504i
$73$	−11.0907	−	5.65098i	−1.29806	−	0.661397i	−0.337992	−	0.941149i	$-0.609748\pi$
$73$	−11.0907	−	5.65098i	−1.29806	−	0.661397i	−0.960072	+	0.279752i	$0.909748\pi$
$74$	−2.31840			−0.269509
$75$	8.65401	−	0.328875i	0.999279	−	0.0379752i
$76$	0.517381			0.0593477
$77$	9.98729	+	5.08878i	1.13816	+	0.579920i
$78$	−3.05068	−	2.28542i	−0.345421	−	0.258773i
$79$	0.932978	+	1.28413i	0.104968	+	0.144476i	0.858270	−	0.513199i	$-0.171540\pi$
$79$	0.932978	+	1.28413i	0.104968	+	0.144476i	−0.753301	+	0.657676i	$0.771540\pi$
$80$	1.22945	−	1.29591i	0.137456	−	0.144887i
$81$	−7.57826	+	4.85489i	−0.842029	+	0.539432i
$82$	−2.15067	−	2.15067i	−0.237502	−	0.237502i
$83$	−1.52390	−	9.62155i	−0.167270	−	1.05610i	−0.918315	−	0.395851i	$-0.870450\pi$
$83$	−1.52390	−	9.62155i	−0.167270	−	1.05610i	0.751045	−	0.660251i	$-0.229550\pi$
$84$	−3.69613	−	3.80596i	−0.403281	−	0.415265i
$85$	0.932743	+	0.276157i	0.101170	+	0.0299535i
$86$	1.35302	−	0.439623i	0.145900	−	0.0474058i
$87$	−0.0271595	+	1.85514i	−0.00291180	+	0.198892i
$88$	6.13379	+	12.0382i	0.653864	+	1.28328i
$89$	2.35501	+	7.24797i	0.249630	+	0.768283i	0.994840	+	0.101453i	$0.0323492\pi$
$89$	2.35501	+	7.24797i	0.249630	+	0.768283i	−0.745210	+	0.666830i	$0.767651\pi$
$90$	3.04595	−	4.16635i	0.321071	−	0.439171i
$91$	−1.92285	+	5.91793i	−0.201570	+	0.620367i
$92$	7.69770	−	1.21920i	0.802540	−	0.127110i
$93$	−15.7203	+	4.85460i	−1.63012	+	0.503399i
$94$	2.98509	−	4.10862i	0.307888	−	0.423772i
$95$	0.721996	−	0.392135i	0.0740752	−	0.0402322i
$96$	−1.44054	−	10.0448i	−0.147025	−	1.02519i
$97$	2.72539	+	0.431660i	0.276722	+	0.0438284i	0.293253	−	0.956035i	$-0.405262\pi$
$97$	2.72539	+	0.431660i	0.276722	+	0.0438284i	−0.0165311	+	0.999863i	$0.505262\pi$
$98$	−0.792151	+	1.55468i	−0.0800194	+	0.157047i
$99$	−8.71618	−	12.7667i	−0.876009	−	1.28310i
$100$	1.82040	−	6.80100i	0.182040	−	0.680100i
$101$			0.133742i			0.0133078i	0.999978	+	0.00665389i	$0.00211802\pi$
$101$			0.133742i			0.0133078i	−0.999978	+	0.00665389i	$0.997882\pi$
$102$	0.473937	−	0.333846i	0.0469267	−	0.0330556i
$103$	0.887243	−	5.60183i	0.0874227	−	0.551965i	−0.904636	−	0.426186i	$-0.859857\pi$
$103$	0.887243	−	5.60183i	0.0874227	−	0.551965i	0.992058	−	0.125779i	$-0.0401431\pi$
$104$	−6.06787	+	4.40857i	−0.595004	+	0.432295i
$105$	−8.04251	−	2.50977i	−0.784869	−	0.244928i
$106$	−1.24461	−	0.904265i	−0.120888	−	0.0878300i
$107$	−7.64218	+	7.64218i	−0.738797	+	0.738797i	−0.972345	−	0.233548i	$-0.924966\pi$
$107$	−7.64218	+	7.64218i	−0.738797	+	0.738797i	0.233548	+	0.972345i	$0.424966\pi$
$108$	1.95328	+	7.05107i	0.187954	+	0.678489i
$109$	13.8598	+	4.50331i	1.32752	+	0.431339i	0.885072	−	0.465453i	$-0.154109\pi$
$109$	13.8598	+	4.50331i	1.32752	+	0.431339i	0.442452	+	0.896792i	$0.354109\pi$
$110$	7.30617	+	5.01997i	0.696616	+	0.478636i
$111$	0.891866	−	5.14261i	0.0846522	−	0.488115i
$112$	−1.54838	+	0.788941i	−0.146309	+	0.0745480i
$113$	−2.09081	+	1.06532i	−0.196687	+	0.100217i	−0.549560	−	0.835454i	$-0.685205\pi$
$113$	−2.09081	+	1.06532i	−0.196687	+	0.100217i	0.352873	+	0.935671i	$0.385205\pi$
$114$	0.0836670	−	0.482435i	0.00783614	−	0.0451841i
$115$	9.81794	−	7.53562i	0.915527	−	0.702701i
$116$	1.43449	+	0.466095i	0.133189	+	0.0432758i
$117$	6.24302	−	5.88775i	0.577167	−	0.544323i
$118$	2.98551	−	2.98551i	0.274839	−	0.274839i
$119$	−0.765607	−	0.556246i	−0.0701831	−	0.0509910i
$120$	−6.06454	−	8.14545i	−0.553614	−	0.743575i
$121$	12.5811	−	9.14071i	1.14374	−	0.830974i
$122$	1.38946	−	8.77270i	0.125796	−	0.794243i
$123$	5.59791	−	3.94322i	0.504746	−	0.355548i
$124$			13.3754i			1.20115i
$125$	−2.61430	−	10.8704i	−0.233830	−	0.972278i
$126$	−4.14660	+	2.83101i	−0.369409	+	0.252206i
$127$	−2.73210	+	5.36205i	−0.242435	+	0.475805i	−0.979876	−	0.199606i	$-0.936034\pi$
$127$	−2.73210	+	5.36205i	−0.242435	+	0.475805i	0.737441	+	0.675411i	$0.236034\pi$
$128$	−9.36208	−	1.48281i	−0.827499	−	0.131063i
$129$	0.454666	+	3.17036i	0.0400311	+	0.279134i
$130$	−2.11796	+	4.44190i	−0.185757	+	0.389581i
$131$	4.56799	−	6.28730i	0.399107	−	0.549324i	−0.561412	−	0.827536i	$-0.689742\pi$
$131$	4.56799	−	6.28730i	0.399107	−	0.549324i	0.960520	+	0.278212i	$0.0897419\pi$
$132$	−12.0075	+	3.70803i	−1.04511	+	0.322743i
$133$	−0.789455	+	0.125037i	−0.0684544	+	0.0108421i
$134$	0.485553	−	1.49438i	0.0419454	−	0.129095i
$135$	8.06993	+	8.35920i	0.694549	+	0.719445i
$136$	−0.352489	−	1.08485i	−0.0302257	−	0.0930252i
$137$	−8.58851	−	16.8559i	−0.733766	−	1.44010i	−0.891691	−	0.452645i	$-0.850480\pi$
$137$	−8.58851	−	16.8559i	−0.733766	−	1.44010i	0.157925	−	0.987451i	$-0.449520\pi$
$138$	0.107969	−	7.37491i	0.00919096	−	0.627794i
$139$	−9.60888	+	3.12212i	−0.815015	+	0.264814i	−0.686720	−	0.726922i	$-0.740950\pi$
$139$	−9.60888	+	3.12212i	−0.815015	+	0.264814i	−0.128295	+	0.991736i	$0.540950\pi$
$140$	−3.87867	+	5.64510i	−0.327808	+	0.477098i
$141$	7.96530	+	8.20199i	0.670799	+	0.690732i
$142$	1.42041	+	8.96813i	0.119198	+	0.752589i
$143$	10.4223	+	10.4223i	0.871558	+	0.871558i
$144$	2.39556	+	0.0701576i	0.199630	+	0.00584646i
$145$	2.35507	−	0.436808i	0.195578	−	0.0362749i
$146$	5.62893	+	7.74756i	0.465854	+	0.641192i
$147$	−3.14383	−	2.35520i	−0.259298	−	0.194254i
$148$	−3.78066	−	1.92634i	−0.310768	−	0.158344i
$149$	7.03411			0.576257			0.288128	−	0.957592i	$-0.406967\pi$
$149$	7.03411			0.576257			0.288128	+	0.957592i	$0.406967\pi$
$150$	−6.04724	−	2.79725i	−0.493755	−	0.228394i
$151$	−0.575132			−0.0468035			−0.0234018	−	0.999726i	$-0.507450\pi$
$151$	−0.575132			−0.0468035			−0.0234018	+	0.999726i	$0.507450\pi$
$152$	−0.858428	−	0.437391i	−0.0696277	−	0.0354771i
$153$	0.558208	+	1.17970i	0.0451285	+	0.0953731i
$154$	−5.06892	−	6.97677i	−0.408465	−	0.562204i
$155$	10.1376	+	18.6652i	0.814268	+	1.49922i
$156$	−3.07586	−	6.26165i	−0.246266	−	0.501333i
$157$	−4.06173	−	4.06173i	−0.324161	−	0.324161i	0.526200	−	0.850361i	$-0.323616\pi$
$157$	−4.06173	−	4.06173i	−0.324161	−	0.324161i	−0.850361	+	0.526200i	$0.823616\pi$
$158$	−0.191036	−	1.20615i	−0.0151980	−	0.0959565i
$159$	2.48461	−	2.41291i	0.197042	−	0.191356i
$160$	−12.3485	+	4.37466i	−0.976233	+	0.345847i
$161$	−11.4510	+	3.72066i	−0.902467	+	0.293229i
$162$	6.89067	−	0.681098i	0.541382	−	0.0535121i
$163$	5.33700	+	10.4744i	0.418026	+	0.820422i	0.999974	+	0.00719617i	$0.00229063\pi$
$163$	5.33700	+	10.4744i	0.418026	+	0.820422i	−0.581948	+	0.813226i	$0.697709\pi$
$164$	−1.72016	−	5.29412i	−0.134322	−	0.413401i
$165$	−13.9458	+	14.2752i	−1.08568	+	1.11132i
$166$	−2.31600	+	7.12790i	−0.179756	+	0.553232i
$167$	−17.9975	+	2.85052i	−1.39269	+	0.220580i	−0.807285	−	0.590162i	$-0.799064\pi$
$167$	−17.9975	+	2.85052i	−1.39269	+	0.220580i	−0.585404	+	0.810742i	$0.699064\pi$
$168$	2.91501	+	9.43946i	0.224898	+	0.728270i
$169$	2.83176	−	3.89759i	0.217828	−	0.299815i
$170$	−0.542944	−	0.515099i	−0.0416419	−	0.0395063i
$171$	1.03794	+	0.371176i	0.0793731	+	0.0283845i
$172$	2.57168	+	0.407313i	0.196088	+	0.0310574i
$173$	−0.0137306	+	0.0269478i	−0.00104392	+	0.00204880i	−0.891528	−	0.452966i	$-0.850366\pi$
$173$	−0.0137306	+	0.0269478i	−0.00104392	+	0.00204880i	0.890484	+	0.455015i	$0.150366\pi$
$174$	0.666588	−	1.26223i	0.0505339	−	0.0956891i
$175$	−1.13407	+	10.8174i	−0.0857276	+	0.817716i
$176$			4.11637i			0.310283i
$177$	5.47389	+	7.77088i	0.411443	+	0.584095i
$178$	0.917218	−	5.79109i	0.0687484	−	0.434060i
$179$	21.2464	−	15.4364i	1.58803	−	1.15377i	0.681353	−	0.731955i	$-0.261392\pi$
$179$	21.2464	−	15.4364i	1.58803	−	1.15377i	0.906680	−	0.421818i	$-0.138608\pi$
$180$	8.42887	−	4.26328i	0.628251	−	0.317766i
$181$	−5.90612	−	4.29105i	−0.438998	−	0.318951i	0.346238	−	0.938147i	$-0.387459\pi$
$181$	−5.90612	−	4.29105i	−0.438998	−	0.318951i	−0.785237	+	0.619196i	$0.787459\pi$
$182$	3.38516	−	3.38516i	0.250924	−	0.250924i
$183$	18.9249	+	6.45683i	1.39897	+	0.477303i
$184$	−13.8026	−	4.48472i	−1.01754	−	0.330618i
$185$	−6.73586	+	0.177273i	−0.495230	+	0.0130333i
$186$	12.4720	+	2.16298i	0.914492	+	0.158597i
$187$	−1.99731	+	1.01768i	−0.146058	+	0.0744201i
$188$	8.28165	−	4.21971i	0.604002	−	0.307754i
$189$	−4.68450	−	10.2869i	−0.340747	−	0.748265i
$190$	−0.631898	+	0.0166302i	−0.0458427	+	0.00120648i
$191$	3.21712	+	1.04530i	0.232782	+	0.0756356i	0.423085	−	0.906090i	$-0.360947\pi$
$191$	3.21712	+	1.04530i	0.232782	+	0.0756356i	−0.190303	+	0.981725i	$0.560947\pi$
$192$	−1.62739	+	4.76984i	−0.117446	+	0.344233i
$193$	16.9891	−	16.9891i	1.22291	−	1.22291i	0.256311	−	0.966594i	$-0.417493\pi$
$193$	16.9891	−	16.9891i	1.22291	−	1.22291i	0.966594	−	0.256311i	$-0.0825071\pi$
$194$	−1.71750	−	1.24784i	−0.123309	−	0.0895895i
$195$	−9.03815	−	6.40676i	−0.647235	−	0.458798i
$196$	−2.58355	+	1.87706i	−0.184539	+	0.134076i
$197$	−0.406658	+	2.56754i	−0.0289732	+	0.182929i	−0.997931	−	0.0642975i	$-0.979519\pi$
$197$	−0.406658	+	2.56754i	−0.0289732	+	0.182929i	0.968958	+	0.247227i	$0.0795193\pi$
$198$	1.51582	+	11.7960i	0.107724	+	0.838309i
$199$			5.01969i			0.355836i	0.984045	+	0.177918i	$0.0569362\pi$
$199$			5.01969i			0.355836i	−0.984045	+	0.177918i	$0.943064\pi$
$200$	−8.76989	+	9.74512i	−0.620125	+	0.689084i
$201$	3.12800	+	1.65191i	0.220632	+	0.116517i
$202$	0.0467136	−	0.0916807i	0.00328676	−	0.00645063i
$203$	−2.30149	−	0.364520i	−0.161533	−	0.0255843i
$204$	1.05025	−	0.150618i	0.0735319	−	0.0105454i
$205$	−6.41299	−	6.08409i	−0.447903	−	0.424932i
$206$	−2.56483	+	3.53019i	−0.178700	+	0.245960i
$207$	16.3173	+	3.07655i	1.13413	+	0.213835i
$208$	−2.25700	+	0.357473i	−0.156494	+	0.0247863i
$209$	−0.585067	+	1.80065i	−0.0404700	+	0.124554i
$210$	4.63657	+	4.52957i	0.319954	+	0.312570i
$211$	−3.44922	−	10.6156i	−0.237454	−	0.730808i	−0.996786	−	0.0801050i	$-0.974474\pi$
$211$	−3.44922	−	10.6156i	−0.237454	−	0.730808i	0.759333	−	0.650703i	$-0.225526\pi$
$212$	−1.27827	−	2.50874i	−0.0877917	−	0.172301i
$213$	−20.4393	−	0.299233i	−1.40048	−	0.0205031i
$214$	7.90804	−	2.56948i	0.540582	−	0.175646i
$215$	3.89744	−	1.38073i	0.265803	−	0.0941653i
$216$	2.72009	−	13.3503i	0.185079	−	0.908371i
$217$	−3.23249	−	20.4092i	−0.219436	−	1.38546i
$218$	−7.92802	−	7.92802i	−0.536953	−	0.536953i
$219$	−19.3508	+	9.50553i	−1.30761	+	0.642324i
$220$	7.74324	+	14.2568i	0.522049	+	0.961193i
$221$	−0.731442	−	1.00674i	−0.0492021	−	0.0677209i
$222$	−2.40761	+	3.21378i	−0.161588	+	0.215695i
$223$	−8.26413	−	4.21078i	−0.553407	−	0.281975i	0.154840	−	0.987940i	$-0.450514\pi$
$223$	−8.26413	−	4.21078i	−0.553407	−	0.281975i	−0.708247	+	0.705965i	$0.750514\pi$
$224$	12.7446			0.851536
$225$	8.53110	−	12.3378i	0.568740	−	0.822517i
$226$	1.80536			0.120091
$227$	−15.5033	−	7.89935i	−1.02899	−	0.524298i	−0.143841	−	0.989601i	$-0.545945\pi$
$227$	−15.5033	−	7.89935i	−1.02899	−	0.524298i	−0.885152	+	0.465303i	$0.845945\pi$
$228$	0.537288	−	0.717196i	0.0355828	−	0.0474975i
$229$	−8.56577	−	11.7898i	−0.566042	−	0.779090i	0.426037	−	0.904706i	$-0.359909\pi$
$229$	−8.56577	−	11.7898i	−0.566042	−	0.779090i	−0.992079	+	0.125616i	$0.959909\pi$
$230$	−9.36232	+	1.73648i	−0.617333	+	0.114500i
$231$	17.4257	−	8.55985i	1.14652	−	0.563197i
$232$	−1.98604	−	1.98604i	−0.130390	−	0.130390i
$233$	3.03073	+	19.1353i	0.198550	+	1.25359i	0.862592	+	0.505900i	$0.168839\pi$
$233$	3.03073	+	19.1353i	0.198550	+	1.25359i	−0.664043	+	0.747695i	$0.731161\pi$
$234$	−6.33611	+	1.85551i	−0.414205	+	0.121298i
$235$	8.35868	−	12.1654i	0.545260	−	0.793583i
$236$	7.34917	−	2.38789i	0.478390	−	0.155438i
$237$	2.74895	+	0.0402449i	0.178563	+	0.00261418i
$238$	0.330541	+	0.648723i	0.0214258	+	0.0420505i
$239$	−4.75062	−	14.6209i	−0.307292	−	0.945747i	−0.978812	−	0.204761i	$-0.934358\pi$
$239$	−4.75062	−	14.6209i	−0.307292	−	0.945747i	0.671520	−	0.740986i	$-0.265642\pi$
$240$	−0.519643	−	3.05004i	−0.0335428	−	0.196879i
$241$	4.57932	−	14.0937i	0.294980	−	0.907854i	−0.688249	−	0.725475i	$-0.741620\pi$
$241$	4.57932	−	14.0937i	0.294980	−	0.907854i	0.983228	−	0.182379i	$-0.0583799\pi$
$242$	−11.8171	+	1.87165i	−0.759633	+	0.120314i
$243$	−1.13998	+	15.5467i	−0.0731299	+	0.997322i
$244$	9.55498	−	13.1513i	0.611695	−	0.841926i
$245$	−2.18263	+	4.57753i	−0.139443	+	0.292448i
$246$	−5.21470	+	0.747849i	−0.332477	+	0.0476811i
$247$	−1.03810	−	0.164419i	−0.0660529	−	0.0104617i
$248$	11.3075	−	22.1923i	0.718028	−	1.40921i
$249$	−14.9200	−	7.87931i	−0.945515	−	0.499331i
$250$	−2.00473	+	8.36485i	−0.126790	+	0.529039i
$251$			5.20939i			0.328814i	0.986393	+	0.164407i	$0.0525710\pi$
$251$			5.20939i			0.328814i	−0.986393	+	0.164407i	$0.947429\pi$
$252$	−9.11420	+	1.17119i	−0.574140	+	0.0737781i
$253$	−4.46156	+	28.1692i	−0.280496	+	1.77098i
$254$	3.74574	−	2.72144i	0.235029	−	0.170758i
$255$	1.35144	−	1.00619i	0.0846306	−	0.0630101i
$256$	10.6079	+	7.70709i	0.662994	+	0.481693i
$257$	9.15234	−	9.15234i	0.570907	−	0.570907i	−0.361475	−	0.932382i	$-0.617727\pi$
$257$	9.15234	−	9.15234i	0.570907	−	0.570907i	0.932382	+	0.361475i	$0.117727\pi$
$258$	0.795674	−	2.33211i	0.0495365	−	0.145191i
$259$	6.23433	+	2.02566i	0.387382	+	0.125868i
$260$	−7.14454	+	5.48369i	−0.443085	+	0.340084i
$261$	2.54341	+	1.96417i	0.157433	+	0.121579i
$262$	−5.32743	+	2.71446i	−0.329130	+	0.167700i
$263$	6.15633	−	3.13681i	0.379616	−	0.193424i	−0.253762	−	0.967267i	$-0.581668\pi$
$263$	6.15633	−	3.13681i	0.379616	−	0.193424i	0.633378	+	0.773843i	$0.281668\pi$
$264$	23.0573	+	3.99874i	1.41908	+	0.246106i
$265$	−3.68523	−	2.53207i	−0.226382	−	0.155544i
$266$	0.584850	+	0.190029i	0.0358594	+	0.0116514i
$267$	12.4928	+	4.26233i	0.764547	+	0.260850i
$268$	2.03347	−	2.03347i	0.124214	−	0.124214i
$269$	19.7082	+	14.3188i	1.20163	+	0.873033i	0.994444	−	0.105269i	$-0.0335703\pi$
$269$	19.7082	+	14.3188i	1.20163	+	0.873033i	0.207184	+	0.978302i	$0.433570\pi$
$270$	−2.61226	−	8.54897i	−0.158977	−	0.520274i
$271$	−19.5798	+	14.2255i	−1.18939	+	0.864140i	−0.993199	−	0.116426i	$-0.962856\pi$
$271$	−19.5798	+	14.2255i	−1.18939	+	0.864140i	−0.196188	+	0.980566i	$0.562856\pi$
$272$	0.0543661	−	0.343254i	0.00329643	−	0.0208128i
$273$	6.20663	+	8.81110i	0.375642	+	0.533272i
$274$			14.5546i			0.879278i
$275$	21.6111	+	14.0263i	1.30320	+	0.845819i
$276$	6.30383	−	11.9367i	0.379446	−	0.718504i
$277$	−3.45182	+	6.77458i	−0.207400	+	0.407045i	−0.971151	−	0.238466i	$-0.923356\pi$
$277$	−3.45182	+	6.77458i	−0.207400	+	0.407045i	0.763751	+	0.645511i	$0.223356\pi$
$278$	7.67745	+	1.21599i	0.460463	+	0.0729301i
$279$	−9.59572	+	26.8330i	−0.574481	+	1.60645i
$280$	11.2077	−	6.08722i	0.669791	−	0.363781i
$281$	−11.1107	+	15.2925i	−0.662807	+	0.912275i	−0.999570	−	0.0293143i	$-0.990668\pi$
$281$	−11.1107	+	15.2925i	−0.662807	+	0.912275i	0.336764	+	0.941589i	$0.390668\pi$
$282$	−2.59545	−	8.40465i	−0.154557	−	0.500490i
$283$	−16.8479	+	2.66845i	−1.00151	+	0.158623i	−0.635591	−	0.772026i	$-0.719244\pi$
$283$	−16.8479	+	2.66845i	−1.00151	+	0.158623i	−0.365914	+	0.930649i	$0.619244\pi$
$284$	−5.13526	+	15.8047i	−0.304721	+	0.937836i
$285$	0.206197	−	1.40806i	0.0122140	−	0.0834061i
$286$	−3.50423	−	10.7849i	−0.207209	−	0.637725i
$287$	3.90419	+	7.66241i	0.230457	+	0.452297i
$288$	−15.4201	−	8.43442i	−0.908641	−	0.497003i
$289$	−15.9880	+	5.19481i	−0.940469	+	0.305577i
$290$	−1.76698	−	0.523152i	−0.103761	−	0.0307205i
$291$	3.42863	−	3.32968i	0.200990	−	0.195190i
$292$	2.74181	+	17.3111i	0.160452	+	1.01306i
$293$	−9.45804	−	9.45804i	−0.552544	−	0.552544i	0.374630	−	0.927174i	$-0.377770\pi$
$293$	−9.45804	−	9.45804i	−0.552544	−	0.552544i	−0.927174	+	0.374630i	$0.877770\pi$
$294$	1.33248	+	2.71259i	0.0777119	+	0.158201i
$295$	8.44579	−	8.90236i	0.491733	−	0.518315i
$296$	4.64427	+	6.39229i	0.269943	+	0.371544i
$297$	−26.7488	−	1.17549i	−1.55212	−	0.0682086i
$298$	−4.82192	−	2.45689i	−0.279326	−	0.142324i
$299$	−15.8325			−0.915619
$300$	−7.53714	−	9.58613i	−0.435157	−	0.553456i
$301$	−4.02247			−0.231852
$302$	0.394256	+	0.200884i	0.0226869	+	0.0115595i
$303$	0.185393	+	0.138888i	0.0106506	+	0.00797889i
$304$	−0.172534	−	0.237472i	−0.00989548	−	0.0136200i
$305$	3.36613	−	25.5943i	0.192744	−	1.46553i
$306$	0.0293938	−	1.00366i	0.00168033	−	0.0573757i
$307$	18.7048	+	18.7048i	1.06754	+	1.06754i	0.997548	+	0.0699905i	$0.0222969\pi$
$307$	18.7048	+	18.7048i	1.06754	+	1.06754i	0.0699905	+	0.997548i	$0.477703\pi$
$308$	−2.46904	−	15.5889i	−0.140686	−	0.888259i
$309$	−6.84391	−	7.04728i	−0.389336	−	0.400906i
$310$	−0.429926	−	16.3360i	−0.0244182	−	0.927821i
$311$	−10.1953	+	3.31267i	−0.578124	+	0.187844i	−0.583460	−	0.812142i	$-0.698302\pi$
$311$	−10.1953	+	3.31267i	−0.578124	+	0.187844i	0.00533576	+	0.999986i	$0.498302\pi$
$312$	−0.190168	+	12.9895i	−0.0107661	+	0.735386i
$313$	1.89796	+	3.72496i	0.107279	+	0.210547i	0.938405	−	0.345537i	$-0.112303\pi$
$313$	1.89796	+	3.72496i	0.107279	+	0.210547i	−0.831126	+	0.556084i	$0.812303\pi$
$314$	1.36565	+	4.20303i	0.0770680	+	0.237191i
$315$	−11.8310	+	8.54223i	−0.666603	+	0.481300i
$316$	0.690659	−	2.12563i	0.0388526	−	0.119576i
$317$	22.8273	−	3.61549i	1.28211	−	0.203066i	0.522048	−	0.852916i	$-0.325168\pi$
$317$	22.8273	−	3.61549i	1.28211	−	0.203066i	0.760063	+	0.649850i	$0.225168\pi$
$318$	−2.54600	+	0.786232i	−0.142773	+	0.0440897i
$319$	−3.24432	+	4.46542i	−0.181647	+	0.250016i
$320$	6.45082	+	0.848402i	0.360612	+	0.0474271i
$321$	2.65740	+	18.5299i	0.148322	+	1.03424i
$322$	9.14930	+	1.44911i	0.509871	+	0.0807556i
$323$	0.0725691	−	0.142425i	0.00403786	−	0.00792474i
$324$	11.8027	+	4.61473i	0.655703	+	0.256374i
$325$	−5.81386	+	13.0674i	−0.322495	+	0.724849i
$326$		−	9.04442i		−	0.500924i
$327$	20.6356	−	14.5359i	1.14115	−	0.803836i
$328$	−1.62156	+	10.2381i	−0.0895355	+	0.565305i
$329$	−11.6169	+	8.44018i	−0.640461	+	0.465322i
$330$	14.5460	−	4.91472i	0.800731	−	0.270547i
$331$	21.9739	+	15.9650i	1.20779	+	0.877514i	0.995029	−	0.0995896i	$-0.0317530\pi$
$331$	21.9739	+	15.9650i	1.20779	+	0.877514i	0.212765	+	0.977103i	$0.431753\pi$
$332$	−9.69925	+	9.69925i	−0.532316	+	0.532316i
$333$	−6.20254	−	6.57680i	−0.339897	−	0.360406i
$334$	13.3330	+	4.33217i	0.729551	+	0.237046i
$335$	1.29645	−	4.37887i	0.0708328	−	0.239243i
$336$	−0.514327	+	2.96568i	−0.0280589	+	0.161791i
$337$	9.28843	−	4.73269i	0.505973	−	0.257806i	−0.182319	−	0.983239i	$-0.558361\pi$
$337$	9.28843	−	4.73269i	0.505973	−	0.257806i	0.688293	+	0.725433i	$0.258361\pi$
$338$	−3.30255	+	1.68273i	−0.179635	+	0.0915287i
$339$	−0.694505	+	4.00460i	−0.0377203	+	0.217500i
$340$	−0.457397	−	1.29111i	−0.0248058	−	0.0700202i
$341$	−46.5508	−	15.1253i	−2.52087	−	0.819080i
$342$	−0.581867	−	0.616977i	−0.0314638	−	0.0333623i
$343$	14.2559	−	14.2559i	0.769744	−	0.769744i
$344$	−3.92253	−	2.84989i	−0.211489	−	0.153656i
$345$	−0.250218	−	21.4353i	−0.0134713	−	1.15404i
$346$	0.0188248	−	0.0136770i	0.00101203	−	0.000735281i
$347$	−1.46440	+	9.24588i	−0.0786133	+	0.496345i	0.916695	+	0.399588i	$0.130847\pi$
$347$	−1.46440	+	9.24588i	−0.0786133	+	0.496345i	−0.995308	+	0.0967566i	$0.969153\pi$
$348$	2.13579	−	1.50447i	0.114490	−	0.0806481i
$349$		−	16.4074i		−	0.878268i	−0.898422	−	0.439134i	$-0.855285\pi$
$349$		−	16.4074i		−	0.878268i	0.898422	−	0.439134i	$-0.144715\pi$
$350$	4.55573	−	7.01926i	0.243514	−	0.375195i
$351$	−1.67840	−	14.7684i	−0.0895863	−	0.788279i
$352$	13.7053	−	26.8983i	0.730498	−	1.43368i
$353$	−6.13612	−	0.971866i	−0.326593	−	0.0517272i	−0.00901471	−	0.999959i	$-0.502870\pi$
$353$	−6.13612	−	0.971866i	−0.326593	−	0.0517272i	−0.317578	+	0.948232i	$0.602870\pi$
$354$	−1.03815	−	7.23892i	−0.0551769	−	0.384744i
$355$	4.81258	+	25.9473i	0.255425	+	1.37714i
$356$	6.30749	−	8.68152i	0.334297	−	0.460120i
$357$	−1.56614	+	0.483640i	−0.0828887	+	0.0255969i
$358$	−19.9562	+	3.16076i	−1.05472	+	0.167051i
$359$	8.66840	−	26.6786i	0.457501	−	1.40804i	−0.410673	−	0.911783i	$-0.634706\pi$
$359$	8.66840	−	26.6786i	0.457501	−	1.40804i	0.868174	−	0.496260i	$-0.165294\pi$
$360$	−17.5892	−	0.0521763i	−0.927030	−	0.00274993i
$361$	5.82960	+	17.9417i	0.306821	+	0.944299i
$362$	2.54989	+	5.00444i	0.134019	+	0.263028i
$363$	0.394293	−	26.9324i	0.0206950	−	1.41359i
$364$	8.33293	−	2.70753i	0.436764	−	0.141913i
$365$	16.9466	+	22.0793i	0.887027	+	1.15568i
$366$	−10.7178	−	11.0363i	−0.560230	−	0.576878i
$367$	−5.21510	−	32.9269i	−0.272226	−	1.71877i	−0.622926	−	0.782280i	$-0.714056\pi$
$367$	−5.21510	−	32.9269i	−0.272226	−	1.71877i	0.350700	−	0.936488i	$-0.385944\pi$
$368$	−3.12659	−	3.12659i	−0.162985	−	0.162985i
$369$	0.347185	−	11.8548i	0.0180737	−	0.617136i
$370$	4.67939	+	2.23120i	0.243270	+	0.115994i
$371$	2.55676	+	3.51908i	0.132741	+	0.182702i
$372$	18.5411	+	13.8901i	0.961312	+	0.720168i
$373$	24.2984	+	12.3806i	1.25812	+	0.641045i	0.950577	−	0.310488i	$-0.100493\pi$
$373$	24.2984	+	12.3806i	1.25812	+	0.641045i	0.307545	+	0.951534i	$0.400493\pi$
$374$	1.72463			0.0891783
$375$	−17.7835	−	7.66471i	−0.918335	−	0.395804i
$376$	−17.3081			−0.892595
$377$	−2.73012	−	1.39107i	−0.140609	−	0.0716436i
$378$	−0.381796	+	8.68798i	−0.0196375	+	0.446861i
$379$	−0.900980	−	1.24009i	−0.0462803	−	0.0636993i	0.785250	−	0.619179i	$-0.212535\pi$
$379$	−0.900980	−	1.24009i	−0.0462803	−	0.0636993i	−0.831530	+	0.555480i	$0.812535\pi$
$380$	−1.04427	−	0.497920i	−0.0535697	−	0.0255428i
$381$	4.59568	+	9.35562i	0.235444	+	0.479303i
$382$	−1.84025	−	1.84025i	−0.0941551	−	0.0941551i
$383$	−0.580663	−	3.66616i	−0.0296705	−	0.187332i	0.968402	−	0.249395i	$-0.0802319\pi$
$383$	−0.580663	−	3.66616i	−0.0296705	−	0.187332i	−0.998072	+	0.0620634i	$0.980232\pi$
$384$	−11.7778	+	11.4379i	−0.601032	+	0.583688i
$385$	−15.2607	−	19.8827i	−0.777755	−	1.01331i
$386$	−17.5802	+	5.71215i	−0.894807	+	0.290741i
$387$	4.86692	+	2.66208i	0.247400	+	0.135321i
$388$	−1.76394	−	3.46193i	−0.0895505	−	0.175753i
$389$	9.31206	+	28.6596i	0.472140	+	1.45310i	0.849776	+	0.527144i	$0.176737\pi$
$389$	9.31206	+	28.6596i	0.472140	+	1.45310i	−0.377636	+	0.925954i	$0.623263\pi$
$390$	3.95794	+	7.54874i	0.200418	+	0.382245i
$391$	0.744077	−	2.29003i	0.0376296	−	0.115812i
$392$	5.87343	−	0.930259i	0.296653	−	0.0469852i
$393$	−3.97173	−	12.8614i	−0.200347	−	0.648771i
$394$	1.17556	−	1.61802i	0.0592240	−	0.0815148i
$395$	−0.647261	−	3.48974i	−0.0325672	−	0.175588i
$396$	−7.32938	+	20.4955i	−0.368315	+	1.02994i
$397$	1.69684	+	0.268753i	0.0851618	+	0.0134883i	0.198870	−	0.980026i	$-0.436273\pi$
$397$	1.69684	+	0.268753i	0.0851618	+	0.0134883i	−0.113708	+	0.993514i	$0.536273\pi$
$398$	1.75329	−	3.44102i	0.0878845	−	0.172483i
$399$	−0.646504	+	1.22420i	−0.0323657	+	0.0612864i
$400$	−3.72864	+	1.43242i	−0.186432	+	0.0716209i
$401$			5.32499i			0.265917i	0.991122	+	0.132959i	$0.0424478\pi$
$401$			5.32499i			0.265917i	−0.991122	+	0.132959i	$0.957552\pi$
$402$	−1.56728	−	2.22495i	−0.0781687	−	0.110971i
$403$	4.25060	−	26.8372i	0.211738	−	1.33686i
$404$	0.152354	−	0.110691i	0.00757987	−	0.00550710i
$405$	19.9680	−	2.50574i	0.992218	−	0.124511i
$406$	1.45036	+	1.05375i	0.0719803	+	0.0522968i
$407$	10.9795	−	10.9795i	0.544236	−	0.544236i
$408$	−1.86988	−	0.637970i	−0.0925727	−	0.0315842i
$409$	27.8795	+	9.05860i	1.37855	+	0.447919i	0.902193	−	0.431332i	$-0.141956\pi$
$409$	27.8795	+	9.05860i	1.37855	+	0.447919i	0.476359	+	0.879251i	$0.341956\pi$
$410$	2.27107	+	6.41063i	0.112160	+	0.316598i
$411$	−32.2847	−	5.59903i	−1.59249	−	0.276180i
$412$	−7.11573	+	3.62564i	−0.350567	+	0.178623i
$413$	−10.6368	+	5.41970i	−0.523401	+	0.266686i
$414$	−10.1110	−	7.80835i	−0.496930	−	0.383759i
$415$	−6.18384	+	20.8864i	−0.303553	+	1.02527i
$416$	15.9385	+	5.17872i	0.781447	+	0.253908i
$417$	−5.65071	+	16.5621i	−0.276717	+	0.811051i
$418$	1.03000	−	1.03000i	0.0503792	−	0.0503792i
$419$	−10.5144	−	7.63915i	−0.513661	−	0.373197i	0.300549	−	0.953766i	$-0.402830\pi$
$419$	−10.5144	−	7.63915i	−0.513661	−	0.373197i	−0.814211	+	0.580569i	$0.802830\pi$
$420$	3.79735	+	11.2389i	0.185292	+	0.548404i
$421$	−21.9342	+	15.9361i	−1.06901	+	0.776678i	−0.975733	−	0.218963i	$-0.929733\pi$
$421$	−21.9342	+	15.9361i	−1.06901	+	0.776678i	−0.0932723	+	0.995641i	$0.529733\pi$
$422$	−1.34339	+	8.48181i	−0.0653950	+	0.412888i
$423$	19.6414	−	2.52396i	0.954998	−	0.122719i
$424$			5.24309i			0.254627i
$425$	−1.61685	−	1.45505i	−0.0784287	−	0.0705801i
$426$	13.9067	+	7.34421i	0.673783	+	0.355828i
$427$	−11.4013	+	22.3763i	−0.551748	+	1.08287i
$428$	15.0307	+	2.38063i	0.726538	+	0.115072i
$429$	25.2708	−	3.62413i	1.22009	−	0.174975i
$430$	−3.15398	−	0.414807i	−0.152099	−	0.0200038i
$431$	8.08512	−	11.1282i	0.389446	−	0.536027i	−0.568610	−	0.822607i	$-0.692519\pi$
$431$	8.08512	−	11.1282i	0.389446	−	0.536027i	0.958056	+	0.286580i	$0.0925185\pi$
$432$	2.58499	−	3.24789i	0.124370	−	0.156264i
$433$	−13.6439	+	2.16098i	−0.655683	+	0.103850i	−0.475407	−	0.879766i	$-0.657699\pi$
$433$	−13.6439	+	2.16098i	−0.655683	+	0.103850i	−0.180276	+	0.983616i	$0.557699\pi$
$434$	−4.91267	+	15.1197i	−0.235816	+	0.725767i
$435$	1.84018	−	3.71823i	0.0882300	−	0.178275i
$436$	−6.34103	−	19.5157i	−0.303680	−	0.934632i
$437$	−0.923297	−	1.81207i	−0.0441673	−	0.0866832i
$438$	16.5852	+	0.242809i	0.792472	+	0.0116019i
$439$	−18.1510	+	5.89762i	−0.866300	+	0.281478i	−0.708257	−	0.705954i	$-0.750518\pi$
$439$	−18.1510	+	5.89762i	−0.866300	+	0.281478i	−0.158043	+	0.987432i	$0.550518\pi$
$440$	−0.794814	−	30.2007i	−0.0378913	−	1.43976i
$441$	−6.52958	+	1.91217i	−0.310933	+	0.0910555i
$442$	0.149770	+	0.945609i	0.00712382	+	0.0449780i
$443$	−5.14976	−	5.14976i	−0.244672	−	0.244672i	0.574107	−	0.818780i	$-0.305349\pi$
$443$	−5.14976	−	5.14976i	−0.244672	−	0.244672i	−0.818780	+	0.574107i	$0.805349\pi$
$444$	−6.59643	+	3.24031i	−0.313053	+	0.153778i
$445$	2.22207	−	16.8955i	0.105336	−	0.800923i
$446$	4.19435	+	5.77303i	0.198608	+	0.273361i
$447$	7.30476	−	9.75072i	0.345503	−	0.461193i
$448$	−5.63975	−	2.87360i	−0.266453	−	0.135765i
$449$	8.73298			0.412135			0.206067	−	0.978538i	$-0.433933\pi$
$449$	8.73298			0.412135			0.206067	+	0.978538i	$0.433933\pi$
$450$	−10.1575	+	5.47784i	−0.478829	+	0.258228i
$451$	20.3704			0.959206
$452$	2.94403	+	1.50006i	0.138476	+	0.0705569i
$453$	−0.597261	+	0.797250i	−0.0280618	+	0.0374581i
$454$	7.86853	+	10.8301i	0.369288	+	0.508282i
$455$	9.57635	−	10.0940i	0.448946	−	0.473216i
$456$	−1.49777	+	0.735737i	−0.0701395	+	0.0344540i
$457$	−11.9057	−	11.9057i	−0.556924	−	0.556924i	0.371507	−	0.928430i	$-0.378841\pi$
$457$	−11.9057	−	11.9057i	−0.556924	−	0.556924i	−0.928430	+	0.371507i	$0.878841\pi$
$458$	1.75392	+	11.0738i	0.0819555	+	0.517446i
$459$	2.21499	+	0.451300i	0.103387	+	0.0210649i
$460$	−16.7101	−	4.94737i	−0.779114	−	0.230672i
$461$	39.9116	−	12.9681i	1.85887	−	0.603983i	0.863917	−	0.503634i	$-0.168004\pi$
$461$	39.9116	−	12.9681i	1.85887	−	0.603983i	0.994952	−	0.100350i	$-0.0319961\pi$
$462$	−14.9352	−	0.218653i	−0.694848	−	0.0101726i
$463$	6.40275	+	12.5661i	0.297561	+	0.583997i	0.990582	−	0.136921i	$-0.0437206\pi$
$463$	6.40275	+	12.5661i	0.297561	+	0.583997i	−0.693021	+	0.720918i	$0.743721\pi$
$464$	−0.264435	−	0.813847i	−0.0122761	−	0.0377819i
$465$	36.4014	+	5.33064i	1.68807	+	0.247203i
$466$	4.60604	−	14.1759i	0.213371	−	0.656688i
$467$	−16.7035	+	2.64558i	−0.772948	+	0.122423i	−0.530435	−	0.847725i	$-0.677972\pi$
$467$	−16.7035	+	2.64558i	−0.772948	+	0.122423i	−0.242513	+	0.970148i	$0.577972\pi$
$468$	−11.8741	−	2.23882i	−0.548882	−	0.103489i
$469$	−2.61136	+	3.59423i	−0.120582	+	0.165966i
$470$	−9.97909	+	5.41990i	−0.460301	+	0.250002i
$471$	−9.84840	+	1.41238i	−0.453790	+	0.0650789i
$472$	−14.2123	−	2.25101i	−0.654174	−	0.103611i
$473$	−4.32570	+	8.48966i	−0.198896	+	0.390355i
$474$	−1.87037	−	0.987749i	−0.0859087	−	0.0453688i
$475$	−1.83464	+	0.0966341i	−0.0841790	+	0.00443388i
$476$			1.33253i			0.0610763i
$477$	−0.764577	−	5.94992i	−0.0350076	−	0.272428i
$478$	−1.85025	+	11.6820i	−0.0846285	+	0.534323i
$479$	−23.4758	+	17.0561i	−1.07264	+	0.779315i	−0.976384	−	0.216042i	$-0.930685\pi$
$479$	−23.4758	+	17.0561i	−1.07264	+	0.779315i	−0.0962511	+	0.995357i	$0.530685\pi$
$480$	−6.75944	+	21.6605i	−0.308525	+	0.988662i
$481$	6.97355	+	5.06658i	0.317966	+	0.231016i
$482$	−8.06183	+	8.06183i	−0.367206	+	0.367206i
$483$	−6.73402	+	19.7373i	−0.306409	+	0.898078i
$484$	−20.8255	−	6.76662i	−0.946615	−	0.307574i
$485$	−5.08542	−	3.49413i	−0.230917	−	0.158660i
$486$	6.21167	−	10.2592i	0.281767	−	0.465366i
$487$	−8.83779	+	4.50308i	−0.400479	+	0.204054i	−0.642617	−	0.766188i	$-0.722151\pi$
$487$	−8.83779	+	4.50308i	−0.400479	+	0.204054i	0.242138	+	0.970242i	$0.422151\pi$
$488$	−26.9715	+	13.7426i	−1.22094	+	0.622100i
$489$	20.0621	+	3.47930i	0.907239	+	0.157339i
$490$	3.09506	−	2.37557i	0.139821	−	0.107317i
$491$	16.1224	+	5.23847i	0.727591	+	0.236409i	0.649311	−	0.760523i	$-0.275057\pi$
$491$	16.1224	+	5.23847i	0.727591	+	0.236409i	0.0782800	+	0.996931i	$0.475057\pi$
$492$	−9.12508	−	3.11332i	−0.411391	−	0.140359i
$493$	0.329512	−	0.329512i	0.0148405	−	0.0148405i
$494$	0.654197	+	0.475302i	0.0294337	+	0.0213848i
$495$	5.30600	+	34.1562i	0.238487	+	1.53521i
$496$	6.13918	−	4.46037i	0.275657	−	0.200277i
$497$	4.01614	−	25.3569i	0.180149	−	1.13741i
$498$	7.47563	+	10.6126i	0.334991	+	0.475562i
$499$		−	14.4839i		−	0.648389i	−0.945990	−	0.324195i	$-0.894907\pi$
$499$		−	14.4839i		−	0.648389i	0.945990	−	0.324195i	$-0.105093\pi$
$500$	−10.2194	+	11.9750i	−0.457027	+	0.535538i
$501$	−14.7386	+	27.9084i	−0.658471	+	1.24686i
$502$	1.81955	−	3.57107i	0.0812106	−	0.159385i
$503$	29.3507	+	4.64869i	1.30868	+	0.207275i	0.771521	−	0.636204i	$-0.219496\pi$
$503$	29.3507	+	4.64869i	1.30868	+	0.207275i	0.537162	+	0.843479i	$0.319496\pi$
$504$	16.1122	+	5.76187i	0.717694	+	0.256654i
$505$	0.128711	−	0.269940i	0.00572757	−	0.0120122i
$506$	12.8974	−	17.7518i	0.573360	−	0.789163i
$507$	−2.46214	−	7.97297i	−0.109347	−	0.354092i
$508$	8.36948	−	1.32559i	0.371335	−	0.0588138i
$509$	5.89618	−	18.1466i	0.261344	−	0.804333i	−0.731169	−	0.682196i	$-0.761025\pi$
$509$	5.89618	−	18.1466i	0.261344	−	0.804333i	0.992513	−	0.122137i	$-0.0389749\pi$
$510$	−1.27787	+	0.217714i	−0.0565849	+	0.00964052i
$511$	−8.36728	−	25.7518i	−0.370147	−	1.13919i
$512$	4.02673	+	7.90290i	0.177958	+	0.349262i
$513$	1.59240	−	1.05334i	0.0703062	−	0.0465060i
$514$	−9.47074	+	3.07723i	−0.417736	+	0.135731i
$515$	−7.18191	+	10.4527i	−0.316473	+	0.460601i
$516$	3.23525	−	3.14189i	0.142424	−	0.138314i
$517$	5.32086	+	33.5946i	0.234011	+	1.47749i
$518$	−3.56614	−	3.56614i	−0.156687	−	0.156687i
$519$	0.0230963	+	0.0470181i	0.00101381	+	0.00206386i
$520$	16.4899	−	3.05848i	0.723132	−	0.134123i
$521$	−5.73574	−	7.89456i	−0.251287	−	0.345867i	0.664674	−	0.747133i	$-0.268570\pi$
$521$	−5.73574	−	7.89456i	−0.251287	−	0.345867i	−0.915962	+	0.401266i	$0.868570\pi$
$522$	−1.05747	−	2.23482i	−0.0462841	−	0.0978154i
$523$	−9.85940	−	5.02361i	−0.431121	−	0.219667i	0.224943	−	0.974372i	$-0.427780\pi$
$523$	−9.85940	−	5.02361i	−0.431121	−	0.219667i	−0.656065	+	0.754704i	$0.727780\pi$
$524$	−10.9430			−0.478045
$525$	13.8174	+	12.8056i	0.603040	+	0.558884i
$526$	−5.31584			−0.231781
$527$	3.68200	+	1.87607i	0.160390	+	0.0817230i
$528$	5.70613	+	4.27475i	0.248327	+	0.186035i
$529$	−4.48804	−	6.17725i	−0.195132	−	0.268576i
$530$	1.64184	+	3.02294i	0.0713169	+	0.131308i
$531$	16.4565	+	0.481954i	0.714153	+	0.0209150i
$532$	0.795831	+	0.795831i	0.0345036	+	0.0345036i
$533$	1.76901	+	11.1691i	0.0766242	+	0.483786i
$534$	−7.07513	−	7.28537i	−0.306171	−	0.315269i
$535$	22.7795	−	8.07001i	0.984842	−	0.348897i
$536$	−5.09296	+	1.65480i	−0.219982	+	0.0714766i
$537$	0.665865	−	45.4823i	0.0287342	−	1.96271i
$538$	−8.50874	−	16.6994i	−0.366838	−	0.719960i
$539$	−3.61123	−	11.1142i	−0.155547	−	0.478723i
$540$	2.84341	−	16.1115i	0.122361	−	0.693327i
$541$	5.43050	−	16.7134i	0.233476	−	0.718564i	−0.763844	−	0.645400i	$-0.776691\pi$
$541$	5.43050	−	16.7134i	0.233476	−	0.718564i	0.997320	−	0.0731634i	$-0.0233095\pi$
$542$	18.3908	−	2.91282i	0.789952	−	0.125116i
$543$	−12.0816	+	3.73094i	−0.518473	+	0.160110i
$544$	−1.49811	+	2.06197i	−0.0642309	+	0.0884063i
$545$	−23.6402	−	22.4278i	−1.01263	−	0.960701i
$546$	−1.17711	−	8.20793i	−0.0503758	−	0.351267i
$547$	0.690451	+	0.109357i	0.0295215	+	0.00467575i	0.171178	−	0.985240i	$-0.445243\pi$
$547$	0.690451	+	0.109357i	0.0295215	+	0.00467575i	−0.141656	+	0.989916i	$0.545243\pi$
$548$	−12.0933	+	23.7345i	−0.516602	+	1.01389i
$549$	28.6035	−	19.5285i	1.22077	−	0.833454i
$550$	−9.91539	−	17.1635i	−0.422794	−	0.731855i
$551$		−	0.393592i		−	0.0167676i
$552$	−20.5504	+	14.4759i	−0.874682	+	0.616135i
$553$	−0.540145	+	3.41034i	−0.0229693	+	0.145022i
$554$	4.73249	−	3.43836i	0.201064	−	0.146082i
$555$	−6.74930	+	9.52137i	−0.286492	+	0.404160i
$556$	11.5094	+	8.36206i	0.488107	+	0.354631i
$557$	−13.3952	+	13.3952i	−0.567574	+	0.567574i	−0.931448	−	0.363874i	$-0.881454\pi$
$557$	−13.3952	+	13.3952i	−0.567574	+	0.567574i	0.363874	+	0.931448i	$0.381454\pi$
$558$	15.9502	−	15.0426i	0.675227	−	0.636802i
$559$	−5.03052	−	1.63451i	−0.212768	−	0.0691326i
$560$	3.88448	−	0.102231i	0.164149	−	0.00432004i
$561$	−0.663447	+	3.82552i	−0.0280107	+	0.161513i
$562$	12.9578	−	6.60235i	0.546593	−	0.278503i
$563$	−7.43106	+	3.78631i	−0.313182	+	0.159574i	−0.603515	−	0.797351i	$-0.706234\pi$
$563$	−7.43106	+	3.78631i	−0.313182	+	0.159574i	0.290334	+	0.956926i	$0.406234\pi$
$564$	2.75092	−	15.8622i	0.115835	−	0.667917i
$565$	5.24527	−	0.138044i	0.220670	−	0.00580755i
$566$	12.4814	+	4.05545i	0.524633	+	0.170463i
$567$	−19.1246	−	4.18907i	−0.803156	−	0.175924i
$568$	21.8815	−	21.8815i	0.918127	−	0.918127i
$569$	−16.4674	−	11.9642i	−0.690347	−	0.501567i	0.186427	−	0.982469i	$-0.440309\pi$
$569$	−16.4674	−	11.9642i	−0.690347	−	0.501567i	−0.876774	+	0.480902i	$0.840309\pi$
$570$	−0.633159	+	0.893211i	−0.0265201	+	0.0374125i
$571$	−0.152544	+	0.110830i	−0.00638378	+	0.00463809i	−0.590973	−	0.806692i	$-0.701256\pi$
$571$	−0.152544	+	0.110830i	−0.00638378	+	0.00463809i	0.584589	+	0.811330i	$0.301256\pi$
$572$	3.24668	−	20.4988i	0.135751	−	0.857096i
$573$	4.78991	−	3.37406i	0.200101	−	0.140953i
$574$		−	6.61629i		−	0.276159i
$575$	−27.0684	+	5.76102i	−1.12883	+	0.240251i
$576$	4.92197	+	7.20926i	0.205082	+	0.300386i
$577$	−14.7750	+	28.9976i	−0.615093	+	1.20719i	0.347867	+	0.937544i	$0.386906\pi$
$577$	−14.7750	+	28.9976i	−0.615093	+	1.20719i	−0.962960	+	0.269644i	$0.913094\pi$
$578$	12.7743	+	2.02325i	0.531341	+	0.0841562i
$579$	−5.90760	−	41.1933i	−0.245512	−	1.71193i
$580$	−2.44677	−	2.32129i	−0.101597	−	0.0963862i
$581$	12.4557	−	17.1438i	0.516750	−	0.711246i
$582$	−3.51335	+	1.08496i	−0.145633	+	0.0449730i
$583$	10.1767	−	1.61183i	0.421477	−	0.0667553i
$584$	10.0856	−	31.0401i	0.417343	−	1.28445i
$585$	−18.2670	+	5.87546i	−0.755247	+	0.242920i
$586$	3.18001	+	9.78707i	0.131365	+	0.404300i
$587$	6.67560	+	13.1016i	0.275532	+	0.540761i	0.986758	−	0.162202i	$-0.0518597\pi$
$587$	6.67560	+	13.1016i	0.275532	+	0.540761i	−0.711226	+	0.702963i	$0.751860\pi$
$588$	−0.0809687	+	5.53061i	−0.00333909	+	0.228079i
$589$	3.31947	−	1.07856i	0.136776	−	0.0444413i
$590$	−8.89908	+	3.15265i	−0.366369	+	0.129793i
$591$	3.13683	+	3.23004i	0.129032	+	0.132866i
$592$	0.376585	+	2.37767i	0.0154776	+	0.0977215i
$593$	26.9790	+	26.9790i	1.10790	+	1.10790i	0.993427	+	0.114469i	$0.0365167\pi$
$593$	26.9790	+	26.9790i	1.10790	+	1.10790i	0.114469	+	0.993427i	$0.463483\pi$
$594$	17.9259	+	10.1487i	0.735508	+	0.416406i
$595$	1.00995	+	1.85952i	0.0414041	+	0.0762329i
$596$	−5.82178	−	8.01300i	−0.238469	−	0.328225i
$597$	6.95831	+	5.21283i	0.284785	+	0.213347i
$598$	10.8533	+	5.53003i	0.443825	+	0.226140i
$599$	−13.6870			−0.559237			−0.279618	−	0.960111i	$-0.590208\pi$
$599$	−13.6870			−0.559237			−0.279618	+	0.960111i	$0.590208\pi$
$600$	4.40140	+	22.2770i	0.179686	+	0.909453i
$601$	11.1180			0.453512			0.226756	−	0.973952i	$-0.427188\pi$
$601$	11.1180			0.453512			0.226756	+	0.973952i	$0.427188\pi$
$602$	2.75743	+	1.40498i	0.112384	+	0.0572628i
$603$	5.53825	−	2.62058i	0.225535	−	0.106718i
$604$	0.476008	+	0.655169i	0.0193685	+	0.0266584i
$605$	−34.1902	+	6.34144i	−1.39003	+	0.257816i
$606$	−0.0785772	−	0.159963i	−0.00319198	−	0.00649805i
$607$	−18.6302	−	18.6302i	−0.756175	−	0.756175i	0.219449	−	0.975624i	$-0.429574\pi$
$607$	−18.6302	−	18.6302i	−0.756175	−	0.756175i	−0.975624	+	0.219449i	$0.929574\pi$
$608$	0.336757	+	2.12620i	0.0136573	+	0.0862288i
$609$	−2.89534	+	2.81179i	−0.117325	+	0.113939i
$610$	−11.2472	+	16.3693i	−0.455384	+	0.662775i
$611$	−17.9578	+	5.83483i	−0.726494	+	0.236052i
$612$	0.881870	−	1.61227i	0.0356475	−	0.0651722i
$613$	−9.47824	−	18.6021i	−0.382823	−	0.751332i	0.616529	−	0.787332i	$-0.288538\pi$
$613$	−9.47824	−	18.6021i	−0.382823	−	0.751332i	−0.999352	+	0.0360003i	$0.988538\pi$
$614$	−6.28898	−	19.3555i	−0.253803	−	0.781124i
$615$	−15.0935	+	2.57153i	−0.608630	+	0.103694i
$616$	−9.08217	+	27.9520i	−0.365931	+	1.12622i
$617$	13.4535	−	2.13083i	0.541619	−	0.0857840i	0.120370	−	0.992729i	$-0.461592\pi$
$617$	13.4535	−	2.13083i	0.541619	−	0.0857840i	0.421249	+	0.906945i	$0.361592\pi$
$618$	2.23005	+	7.22141i	0.0897057	+	0.290488i
$619$	−4.53363	+	6.24000i	−0.182222	+	0.250807i	−0.890350	−	0.455277i	$-0.849540\pi$
$619$	−4.53363	+	6.24000i	−0.182222	+	0.250807i	0.708128	+	0.706084i	$0.249540\pi$
$620$	12.8723	−	26.9966i	0.516966	−	1.08421i
$621$	21.2099	−	19.4242i	0.851123	−	0.779466i
$622$	8.14602	+	1.29020i	0.326626	+	0.0517324i
$623$	−7.52631	+	14.7712i	−0.301535	+	0.591796i
$624$	−1.84831	+	3.49989i	−0.0739915	+	0.140108i
$625$	−5.18490	+	24.4564i	−0.207396	+	0.978257i
$626$		−	3.21641i		−	0.128553i
$627$	1.88849	+	2.68096i	0.0754192	+	0.107067i
$628$	−1.26528	+	7.98866i	−0.0504902	+	0.318782i
$629$	−1.06057	+	0.770548i	−0.0422876	+	0.0307238i
$630$	11.0939	−	1.72338i	0.441991	−	0.0686612i
$631$	−2.74981	−	1.99785i	−0.109468	−	0.0795333i	0.531704	−	0.846930i	$-0.321552\pi$
$631$	−2.74981	−	1.99785i	−0.109468	−	0.0795333i	−0.641173	+	0.767397i	$0.721552\pi$
$632$	−2.94292	+	2.94292i	−0.117063	+	0.117063i
$633$	−18.2973	−	6.24273i	−0.727253	−	0.248126i
$634$	−16.9111	−	5.49475i	−0.671626	−	0.218224i
$635$	10.6748	−	8.19326i	0.423615	−	0.325140i
$636$	−4.80508	−	0.833329i	−0.190534	−	0.0330436i
$637$	5.78029	−	2.94521i	0.229024	−	0.116693i
$638$	3.78370	−	1.92789i	0.149798	−	0.0763259i
$639$	−21.6405	+	28.0223i	−0.856086	+	1.10854i
$640$	17.4691	+	12.0028i	0.690527	+	0.474452i
$641$	23.7267	+	7.70928i	0.937149	+	0.304498i	0.737483	−	0.675366i	$-0.236014\pi$
$641$	23.7267	+	7.70928i	0.937149	+	0.304498i	0.199666	+	0.979864i	$0.436014\pi$
$642$	4.65049	−	13.6305i	0.183540	−	0.537953i
$643$	−10.0033	+	10.0033i	−0.394493	+	0.394493i	−0.876286	−	0.481792i	$-0.839986\pi$
$643$	−10.0033	+	10.0033i	−0.394493	+	0.394493i	0.481792	+	0.876286i	$0.339986\pi$
$644$	13.7159	+	9.96517i	0.540481	+	0.392683i
$645$	2.13342	−	6.83651i	0.0840034	−	0.269187i
$646$	−0.0994932	+	0.0722860i	−0.00391451	+	0.00284406i
$647$	−3.74242	+	23.6287i	−0.147130	+	0.928939i	0.798098	+	0.602527i	$0.205840\pi$
$647$	−3.74242	+	23.6287i	−0.147130	+	0.928939i	−0.945228	+	0.326412i	$0.894160\pi$
$648$	−15.6815	−	17.6346i	−0.616026	−	0.692751i
$649$			28.2778i			1.11000i
$650$	8.54965	−	6.92710i	0.335345	−	0.271703i
$651$	−31.6482	−	16.7135i	−1.24039	−	0.655056i
$652$	7.51494	−	14.7489i	0.294308	−	0.577611i
$653$	−30.4899	−	4.82912i	−1.19316	−	0.188978i	−0.471907	−	0.881648i	$-0.656434\pi$
$653$	−30.4899	−	4.82912i	−1.19316	−	0.188978i	−0.721254	+	0.692670i	$0.756434\pi$
$654$	−19.2229	+	2.75680i	−0.751676	+	0.107799i
$655$	−15.2707	+	8.29392i	−0.596676	+	0.324070i
$656$	−1.85631	+	2.55499i	−0.0724767	+	0.0997556i
$657$	−6.91877	+	36.6955i	−0.269927	+	1.43163i
$658$	10.9115	−	1.72821i	0.425374	−	0.0673726i
$659$	0.365005	−	1.12337i	0.0142186	−	0.0437603i	−0.943696	−	0.330815i	$-0.892676\pi$
$659$	0.365005	−	1.12337i	0.0142186	−	0.0437603i	0.957914	+	0.287055i	$0.0926763\pi$
$660$	27.8040	+	4.07164i	1.08227	+	0.158488i
$661$	1.44634	+	4.45139i	0.0562563	+	0.173139i	0.975236	−	0.221165i	$-0.0709858\pi$
$661$	1.44634	+	4.45139i	0.0562563	+	0.173139i	−0.918980	+	0.394304i	$0.870986\pi$
$662$	−9.48695	−	18.6192i	−0.368721	−	0.723655i
$663$	−2.15514	−	0.0315514i	−0.0836986	−	0.00122536i
$664$	24.2925	−	7.89310i	0.942731	−	0.306312i
$665$	1.71375	+	0.507389i	0.0664562	+	0.0196757i
$666$	1.95471	+	6.67487i	0.0757436	+	0.258646i
$667$	−0.927488	−	5.85593i	−0.0359125	−	0.226743i
$668$	18.1429	+	18.1429i	0.701968	+	0.701968i
$669$	−14.4191	+	7.08297i	−0.557475	+	0.273844i
$670$	−2.41819	+	2.54892i	−0.0934229	+	0.0984732i
$671$	34.9658	+	48.1262i	1.34984	+	1.85789i
$672$	13.2350	−	17.6667i	0.510552	−	0.681507i
$673$	25.7906	+	13.1410i	0.994155	+	0.506547i	0.873853	−	0.486190i	$-0.161614\pi$
$673$	25.7906	+	13.1410i	0.994155	+	0.506547i	0.120302	+	0.992737i	$0.461614\pi$
$674$	−8.02032			−0.308931
$675$	−8.24331	−	24.6383i	−0.317285	−	0.948330i
$676$	−6.78370			−0.260912
$677$	33.5456	+	17.0923i	1.28926	+	0.656911i	0.958038	−	0.286641i	$-0.0925387\pi$
$677$	33.5456	+	17.0923i	1.28926	+	0.656911i	0.331223	+	0.943552i	$0.392539\pi$
$678$	1.87483	−	2.50260i	0.0720022	−	0.0961118i
$679$	3.52820	+	4.85615i	0.135400	+	0.186362i
$680$	−0.332592	+	2.52886i	−0.0127543	+	0.0969773i
$681$	−27.0500	+	13.2875i	−1.03656	+	0.509179i
$682$	26.6279	+	26.6279i	1.01963	+	1.01963i
$683$	−0.899485	−	5.67912i	−0.0344178	−	0.217306i	0.964485	−	0.264138i	$-0.0850874\pi$
$683$	−0.899485	−	5.67912i	−0.0344178	−	0.217306i	−0.998903	+	0.0468323i	$0.985087\pi$
$684$	−0.436220	−	1.48958i	−0.0166793	−	0.0569557i
$685$	1.11290	+	42.2869i	0.0425216	+	1.61570i
$686$	−14.7518	+	4.79315i	−0.563226	+	0.183003i
$687$	−25.2384	−	0.369492i	−0.962905	−	0.0140970i
$688$	−0.670637	−	1.31620i	−0.0255678	−	0.0501796i
$689$	1.76753	+	5.43990i	0.0673376	+	0.207244i
$690$	−7.31544	+	14.7814i	−0.278494	+	0.562718i
$691$	4.08516	−	12.5728i	0.155407	−	0.478293i	−0.842795	−	0.538234i	$-0.819092\pi$
$691$	4.08516	−	12.5728i	0.155407	−	0.478293i	0.998202	+	0.0599418i	$0.0190915\pi$
$692$	0.0420621	−	0.00666197i	0.00159896	−	0.000253250i
$693$	6.23044	−	33.0447i	0.236675	−	1.25527i
$694$	4.23328	−	5.82661i	0.160693	−	0.221175i
$695$	22.3990	+	2.94588i	0.849641	+	0.111743i
$696$	−4.81553	+	0.690604i	−0.182532	+	0.0261773i
$697$	−1.69864	−	0.269038i	−0.0643407	−	0.0101906i
$698$	−5.73082	+	11.2474i	−0.216915	+	0.425719i
$699$	29.6728	+	15.6703i	1.12233	+	0.592707i
$700$	13.2614	−	7.66111i	0.501232	−	0.289563i
$701$		−	27.2123i		−	1.02780i	−0.857851	−	0.513898i	$-0.828201\pi$
$701$		−	27.2123i		−	1.02780i	0.857851	−	0.513898i	$-0.171799\pi$
$702$	−4.00779	+	10.7101i	−0.151264	+	0.404225i
$703$	−0.173210	+	1.09360i	−0.00653274	+	0.0412461i
$704$	−12.1298	+	8.81280i	−0.457158	+	0.332145i
$705$	−8.18343	−	24.2203i	−0.308206	−	0.912190i
$706$	3.86689	+	2.80946i	0.145532	+	0.105735i
$707$	−0.205720	+	0.205720i	−0.00773690	+	0.00773690i
$708$	4.32184	−	12.6672i	0.162425	−	0.476063i
$709$	3.74942	+	1.21826i	0.140813	+	0.0457528i	0.378575	−	0.925570i	$-0.376414\pi$
$709$	3.74942	+	1.21826i	0.140813	+	0.0457528i	−0.237763	+	0.971323i	$0.576414\pi$
$710$	5.76389	−	19.4680i	0.216315	−	0.730620i
$711$	2.91051	−	3.76882i	0.109153	−	0.141342i
$712$	−17.8046	+	9.07188i	−0.667254	+	0.339983i
$713$	46.8461	−	23.8693i	1.75440	−	0.893911i
$714$	1.24252	+	0.215487i	0.0465003	+	0.00806438i
$715$	−11.0058	−	31.0664i	−0.411593	−	1.16182i
$716$	−35.1692	−	11.4272i	−1.31434	−	0.427054i
$717$	−25.2010	−	8.59814i	−0.941148	−	0.321103i
$718$	−15.2606	+	15.2606i	−0.569521	+	0.569521i
$719$	20.8362	+	15.1384i	0.777058	+	0.564566i	0.904095	−	0.427332i	$-0.140547\pi$
$719$	20.8362	+	15.1384i	0.777058	+	0.564566i	−0.127037	+	0.991898i	$0.540547\pi$
$720$	−4.76761	−	2.44706i	−0.177678	−	0.0911966i
$721$	9.98144	−	7.25194i	0.371728	−	0.270076i
$722$	2.27049	−	14.3353i	0.0844989	−	0.533505i
$723$	−14.7812	−	20.9838i	−0.549720	−	0.780398i
$724$			10.2795i			0.382035i
$725$	−5.17378	−	1.38485i	−0.192149	−	0.0514320i
$726$	−9.67732	+	18.3246i	−0.359159	+	0.680090i
$727$	8.01791	−	15.7360i	0.297368	−	0.583617i	−0.693183	−	0.720761i	$-0.743792\pi$
$727$	8.01791	−	15.7360i	0.297368	−	0.583617i	0.990551	+	0.137144i	$0.0437924\pi$
$728$	−16.1148	−	2.55233i	−0.597253	−	0.0945955i
$729$	20.3671	+	17.7252i	0.754337	+	0.656487i
$730$	−3.90511	−	21.0546i	−0.144535	−	0.779267i
$731$	0.472835	−	0.650802i	0.0174884	−	0.0240708i
$732$	−8.30778	−	26.9025i	−0.307064	−	0.994345i
$733$	−17.3916	+	2.75455i	−0.642372	+	0.101742i	−0.469118	−	0.883135i	$-0.655428\pi$
$733$	−17.3916	+	2.75455i	−0.642372	+	0.101742i	−0.173254	+	0.984877i	$0.555428\pi$
$734$	−7.92580	+	24.3931i	−0.292547	+	0.900366i
$735$	4.07879	+	7.77924i	0.150448	+	0.286942i
$736$	10.0207	+	30.8405i	0.369367	+	1.13679i
$737$	4.77762	+	9.37661i	0.175986	+	0.345392i
$738$	−4.37867	+	8.00527i	−0.161181	+	0.294678i
$739$	36.9276	−	11.9985i	1.35841	−	0.441373i	0.462895	−	0.886413i	$-0.346811\pi$
$739$	36.9276	−	11.9985i	1.35841	−	0.441373i	0.895510	+	0.445040i	$0.146811\pi$
$740$	5.77688	+	7.52652i	0.212362	+	0.276680i
$741$	−1.30596	+	1.26828i	−0.0479758	+	0.0465913i
$742$	−0.523522	−	3.30539i	−0.0192191	−	0.121345i
$743$	−26.2844	−	26.2844i	−0.964280	−	0.964280i	0.0351039	−	0.999384i	$-0.488824\pi$
$743$	−26.2844	−	26.2844i	−0.964280	−	0.964280i	−0.999384	+	0.0351039i	$0.988824\pi$
$744$	−19.0204	−	38.7207i	−0.697322	−	1.41957i
$745$	−14.1974	−	6.76953i	−0.520153	−	0.248016i
$746$	−12.3323	−	16.9740i	−0.451519	−	0.621462i
$747$	−26.4164	+	12.4997i	−0.966526	+	0.457339i
$748$	2.81238	+	1.43298i	0.102831	+	0.0523948i
$749$	−23.5103			−0.859046
$750$	9.51354	+	11.4657i	0.347385	+	0.418667i
$751$	−3.19837			−0.116710			−0.0583551	−	0.998296i	$-0.518586\pi$
$751$	−3.19837			−0.116710			−0.0583551	+	0.998296i	$0.518586\pi$
$752$	−4.69853	−	2.39402i	−0.171338	−	0.0873009i
$753$	7.22129	+	5.40984i	0.263158	+	0.197145i
$754$	1.38564	+	1.90717i	0.0504621	+	0.0694551i
$755$	1.16083	+	0.553499i	0.0422468	+	0.0201439i
$756$	−7.84137	+	13.8504i	−0.285188	+	0.503734i
$757$	−8.49050	−	8.49050i	−0.308593	−	0.308593i	0.535771	−	0.844363i	$-0.320021\pi$
$757$	−8.49050	−	8.49050i	−0.308593	−	0.308593i	−0.844363	+	0.535771i	$0.820021\pi$
$758$	0.184484	+	1.16479i	0.00670077	+	0.0423070i
$759$	34.4150	+	35.4377i	1.24919	+	1.28631i
$760$	1.31168	+	1.70895i	0.0475798	+	0.0619903i
$761$	27.9703	−	9.08810i	1.01392	−	0.329443i	0.245507	−	0.969395i	$-0.421046\pi$
$761$	27.9703	−	9.08810i	1.01392	−	0.329443i	0.768415	+	0.639951i	$0.221046\pi$
$762$	0.117392	−	8.01853i	0.00425266	−	0.290481i
$763$	14.3920	+	28.2459i	0.521026	+	1.02257i
$764$	−1.47188	−	4.52997i	−0.0532506	−	0.163888i
$765$	0.00865677	−	2.91828i	0.000312986	−	0.105511i
$766$	−0.882479	+	2.71599i	−0.0318853	+	0.0981328i
$767$	−15.5046	+	2.45569i	−0.559840	+	0.0886699i
$768$	21.6997	−	6.70109i	0.783019	−	0.241805i
$769$	3.26861	−	4.49885i	0.117869	−	0.162233i	−0.746006	−	0.665940i	$-0.768031\pi$
$769$	3.26861	−	4.49885i	0.117869	−	0.162233i	0.863875	+	0.503707i	$0.168031\pi$
$770$	3.51661	+	18.9600i	0.126730	+	0.683270i
$771$	−3.18253	−	22.1915i	−0.114616	−	0.799208i
$772$	−33.4145	−	5.29233i	−1.20261	−	0.190475i
$773$	18.7998	−	36.8966i	0.676181	−	1.32708i	−0.256559	−	0.966529i	$-0.582589\pi$
$773$	18.7998	−	36.8966i	0.676181	−	1.32708i	0.932740	−	0.360551i	$-0.117411\pi$
$774$	−2.40649	−	3.52481i	−0.0864994	−	0.126697i
$775$	−2.49821	−	47.4295i	−0.0897382	−	1.70372i
$776$			7.23519i			0.259728i
$777$	9.28218	−	6.53846i	0.332996	−	0.234566i
$778$	3.62682	−	22.8988i	0.130028	−	0.820963i
$779$	−1.17517	+	0.853807i	−0.0421047	+	0.0305908i
$780$	0.182084	+	15.5985i	0.00651965	+	0.558515i
$781$	−49.1983	−	35.7447i	−1.76046	−	1.27905i
$782$	−1.30994	+	1.30994i	−0.0468433	+	0.0468433i
$783$	5.36402	−	1.48593i	0.191694	−	0.0531029i
$784$	1.72310	+	0.559869i	0.0615392	+	0.0199953i
$785$	4.28912	+	12.1070i	0.153085	+	0.432118i
$786$	−1.76961	+	10.2038i	−0.0631200	+	0.363958i
$787$	47.5326	−	24.2191i	1.69435	−	0.863317i	0.706542	−	0.707671i	$-0.250254\pi$
$787$	47.5326	−	24.2191i	1.69435	−	0.863317i	0.987813	−	0.155646i	$-0.0497458\pi$
$788$	3.26141	−	1.66177i	0.116183	−	0.0591982i
$789$	2.04495	−	11.7914i	0.0728022	−	0.419787i
$790$	−0.775205	+	2.61832i	−0.0275806	+	0.0931555i
$791$	−4.85473	−	1.57740i	−0.172614	−	0.0560858i
$792$	29.4875	−	27.8095i	1.04779	−	0.988167i
$793$	−23.3510	+	23.3510i	−0.829219	+	0.829219i
$794$	−1.06932	−	0.776907i	−0.0379488	−	0.0275714i
$795$	−7.33700	+	2.47898i	−0.260217	+	0.0879205i
$796$	5.71824	−	4.15454i	0.202678	−	0.147254i
$797$	−1.83018	+	11.5553i	−0.0648283	+	0.409310i	0.933839	+	0.357694i	$0.116437\pi$
$797$	−1.83018	+	11.5553i	−0.0648283	+	0.409310i	−0.998667	+	0.0516156i	$0.983563\pi$
$798$	0.870772	−	0.613381i	0.0308250	−	0.0217134i
$799$		−	2.87165i		−	0.101592i
$800$	29.1339	+	3.05433i	1.03004	+	0.107987i
$801$	18.8819	−	12.8912i	0.667160	−	0.455490i
$802$	1.85993	−	3.65032i	0.0656764	−	0.128897i
$803$	−63.3487	−	10.0335i	−2.23553	−	0.354073i
$804$	−0.707093	−	4.93051i	−0.0249372	−	0.173886i
$805$	26.6931	+	3.51063i	0.940808	+	0.123734i
$806$	−12.2876	+	16.9124i	−0.432812	+	0.595715i
$807$	40.3153	−	12.4498i	1.41917	−	0.438253i
$808$	−0.346360	+	0.0548580i	−0.0121849	+	0.00192990i
$809$	−15.6932	+	48.2988i	−0.551744	+	1.69809i	0.152646	+	0.988281i	$0.451220\pi$
$809$	−15.6932	+	48.2988i	−0.551744	+	1.69809i	−0.704390	+	0.709813i	$0.748780\pi$
$810$	−14.5634	−	5.25678i	−0.511706	−	0.184704i
$811$	−1.92758	−	5.93247i	−0.0676863	−	0.208317i	0.911492	−	0.411317i	$-0.134931\pi$
$811$	−1.92758	−	5.93247i	−0.0676863	−	0.208317i	−0.979179	+	0.203000i	$0.934931\pi$
$812$	1.48958	+	2.92347i	0.0522740	+	0.102594i
$813$	−0.613632	+	41.9145i	−0.0215210	+	1.47001i
$814$	−11.3615	+	3.69158i	−0.398221	+	0.129390i
$815$	−0.691566	−	26.2776i	−0.0242245	−	0.920462i
$816$	−0.419363	−	0.431824i	−0.0146806	−	0.0151169i
$817$	−0.106288	−	0.671074i	−0.00371853	−	0.0234779i
$818$	−15.9476	−	15.9476i	−0.557593	−	0.557593i
$819$	18.6594	+	0.546468i	0.652013	+	0.0190952i
$820$	−1.62306	+	12.3409i	−0.0566798	+	0.430964i
$821$	−32.5850	−	44.8494i	−1.13723	−	1.56526i	−0.773556	−	0.633728i	$-0.781524\pi$
$821$	−32.5850	−	44.8494i	−1.13723	−	1.56526i	−0.363669	−	0.931528i	$-0.618476\pi$
$822$	20.1757	+	15.1147i	0.703709	+	0.527184i
$823$	−45.8805	−	23.3773i	−1.59929	−	0.814881i	−0.999896	−	0.0144301i	$-0.995407\pi$
$823$	−45.8805	−	23.3773i	−1.59929	−	0.814881i	−0.599398	−	0.800451i	$-0.704593\pi$
$824$	14.8714			0.518068
$825$	41.8860	−	15.3914i	1.45828	−	0.535860i
$826$	9.18458			0.319572
$827$	−17.0452	−	8.68498i	−0.592721	−	0.302006i	0.131781	−	0.991279i	$-0.457930\pi$
$827$	−17.0452	−	8.68498i	−0.592721	−	0.302006i	−0.724502	+	0.689272i	$0.757930\pi$
$828$	−10.0003	−	21.1344i	−0.347535	−	0.734470i
$829$	−8.34732	−	11.4891i	−0.289914	−	0.399033i	0.639072	−	0.769147i	$-0.279319\pi$
$829$	−8.34732	−	11.4891i	−0.289914	−	0.399033i	−0.928986	+	0.370114i	$0.879319\pi$
$830$	11.5343	−	12.1579i	0.400362	−	0.422005i
$831$	5.80632	+	11.8202i	0.201419	+	0.410038i
$832$	−5.88541	−	5.88541i	−0.204040	−	0.204040i
$833$	0.154343	+	0.974482i	0.00534766	+	0.0337638i
$834$	9.65846	−	9.37974i	0.334445	−	0.324794i
$835$	39.0689	+	11.5671i	1.35204	+	0.400297i
$836$	2.53547	−	0.823824i	0.0876910	−	0.0284925i
$837$	27.2311	+	41.1671i	0.941244	+	1.42294i
$838$	4.53945	+	8.90918i	0.156813	+	0.307762i
$839$	2.18200	+	6.71550i	0.0753310	+	0.231845i	0.981631	−	0.190791i	$-0.0611051\pi$
$839$	2.18200	+	6.71550i	0.0753310	+	0.231845i	−0.906300	+	0.422635i	$0.861105\pi$
$840$	3.20085	−	21.8577i	0.110440	−	0.754161i
$841$	−8.60692	+	26.4894i	−0.296790	+	0.913426i
$842$	20.6022	−	3.26307i	0.709999	−	0.112453i
$843$	9.66040	+	31.2826i	0.332722	+	1.07743i
$844$	−9.23815	+	12.7152i	−0.317990	+	0.437676i
$845$	−9.46653	+	5.14152i	−0.325659	+	0.176874i
$846$	−14.3459	−	5.13022i	−0.493222	−	0.176381i
$847$	33.4123	+	5.29199i	1.14806	+	0.181835i
$848$	−0.725214	+	1.42331i	−0.0249039	+	0.0488767i
$849$	−13.7972	+	26.1258i	−0.473518	+	0.896636i
$850$	0.600137	+	1.56218i	0.0205845	+	0.0535823i
$851$			16.6790i			0.571750i
$852$	16.5757	+	23.5313i	0.567874	+	0.806170i
$853$	1.68663	−	10.6490i	0.0577492	−	0.364614i	−0.941843	−	0.336054i	$-0.890908\pi$
$853$	1.68663	−	10.6490i	0.0577492	−	0.364614i	0.999592	−	0.0285606i	$-0.00909235\pi$
$854$	15.6313	−	11.3568i	0.534893	−	0.388623i
$855$	−1.73773	−	1.74807i	−0.0594290	−	0.0597826i
$856$	−22.9261	−	16.6568i	−0.783598	−	0.569317i
$857$	11.3374	−	11.3374i	0.387279	−	0.387279i	−0.486437	−	0.873716i	$-0.661704\pi$
$857$	11.3374	−	11.3374i	0.387279	−	0.387279i	0.873716	+	0.486437i	$0.161704\pi$
$858$	−18.5891	−	6.34230i	−0.634623	−	0.216522i
$859$	−18.9377	−	6.15322i	−0.646145	−	0.209945i	−0.0324314	−	0.999474i	$-0.510325\pi$
$859$	−18.9377	−	6.15322i	−0.646145	−	0.209945i	−0.613714	+	0.789529i	$0.710325\pi$
$860$	−4.79860	−	3.29705i	−0.163631	−	0.112429i
$861$	14.6761	+	2.54522i	0.500159	+	0.0867410i
$862$	−9.42929	+	4.80446i	−0.321163	+	0.163641i
$863$	−4.68315	+	2.38619i	−0.159416	+	0.0812267i	−0.531878	−	0.846821i	$-0.678514\pi$
$863$	−4.68315	+	2.38619i	−0.159416	+	0.0812267i	0.372462	+	0.928047i	$0.378514\pi$
$864$	−27.7053	+	12.6165i	−0.942554	+	0.429223i
$865$	0.0536476	−	0.0411765i	0.00182407	−	0.00140004i
$866$	10.1077	+	3.28421i	0.343475	+	0.111602i
$867$	−9.40207	+	27.5573i	−0.319311	+	0.935895i
$868$	−20.5740	+	20.5740i	−0.698327	+	0.698327i
$869$	6.61686	+	4.80743i	0.224461	+	0.163081i
$870$	−2.56017	+	1.90612i	−0.0867979	+	0.0646236i
$871$	−4.72628	+	3.43384i	−0.160144	+	0.116351i
$872$	−5.97754	+	37.7407i	−0.202425	+	1.27806i
$873$	−1.05508	−	8.21058i	−0.0357089	−	0.277886i
$874$			1.56468i			0.0529260i
$875$	12.6995	−	20.7420i	0.429320	−	0.701208i
$876$	26.8441	+	14.1765i	0.906977	+	0.478979i
$877$	14.8586	−	29.1616i	0.501738	−	0.984717i	−0.491745	−	0.870739i	$-0.663641\pi$
$877$	14.8586	−	29.1616i	0.501738	−	0.984717i	0.993483	−	0.113978i	$-0.0363592\pi$
$878$	14.5026	+	2.29698i	0.489438	+	0.0775193i
$879$	−22.9327	+	3.28883i	−0.773502	+	0.110929i
$880$	3.96153	−	8.30835i	0.133543	−	0.280074i
$881$	−21.5438	+	29.6526i	−0.725831	+	0.999020i	0.273479	+	0.961878i	$0.411825\pi$
$881$	−21.5438	+	29.6526i	−0.725831	+	0.999020i	−0.999310	+	0.0371423i	$0.988175\pi$
$882$	5.14396	+	0.969870i	0.173206	+	0.0326572i
$883$	51.6801	−	8.18533i	1.73917	−	0.275458i	0.795409	−	0.606073i	$-0.207256\pi$
$883$	51.6801	−	8.18533i	1.73917	−	0.275458i	0.943766	+	0.330615i	$0.107256\pi$
$884$	−0.541467	+	1.66646i	−0.0182115	+	0.0560492i
$885$	−3.56973	−	20.9525i	−0.119995	−	0.704311i
$886$	1.73147	+	5.32891i	0.0581698	+	0.179028i
$887$	10.5412	+	20.6882i	0.353938	+	0.694643i	0.997494	−	0.0707566i	$-0.0225413\pi$
$887$	10.5412	+	20.6882i	0.353938	+	0.694643i	−0.643555	+	0.765400i	$0.722541\pi$
$888$	13.6840	+	0.200335i	0.459205	+	0.00672280i
$889$	−12.4504	+	4.04536i	−0.417571	+	0.135677i
$890$	−7.42455	+	10.8058i	−0.248871	+	0.362212i
$891$	−29.4075	+	35.8586i	−0.985188	+	1.20131i
$892$	2.04304	+	12.8992i	0.0684060	+	0.431899i
$893$	−1.71504	−	1.71504i	−0.0573918	−	0.0573918i
$894$	−8.41321	+	4.13275i	−0.281380	+	0.138220i
$895$	−57.7390	+	10.7092i	−1.93000	+	0.357967i
$896$	−12.1198	−	16.6815i	−0.404895	−	0.557290i
$897$	−16.4417	+	21.9472i	−0.548973	+	0.732794i
$898$	−5.98651	−	3.05028i	−0.199772	−	0.101789i
$899$	10.1752			0.339362
$900$	−21.1155	+	0.493037i	−0.703850	+	0.0164346i
$901$	−0.869900			−0.0289806
$902$	−13.9641	−	7.11504i	−0.464952	−	0.236905i
$903$	−4.17725	+	5.57598i	−0.139010	+	0.185557i
$904$	−3.61654	−	4.97773i	−0.120284	−	0.165557i
$905$	7.79108	+	14.3449i	0.258984	+	0.476840i
$906$	0.687892	−	0.337907i	0.0228537	−	0.0112262i
$907$	13.9913	+	13.9913i	0.464574	+	0.464574i	0.900151	−	0.435577i	$-0.143456\pi$
$907$	13.9913	+	13.9913i	0.464574	+	0.464574i	−0.435577	+	0.900151i	$0.643456\pi$
$908$	3.83270	+	24.1987i	0.127193	+	0.803063i
$909$	0.385054	−	0.112762i	0.0127714	−	0.00374007i
$910$	−10.0903	+	3.57467i	−0.334491	+	0.118499i
$911$	−5.51604	+	1.79227i	−0.182754	+	0.0593805i	−0.398965	−	0.916966i	$-0.630630\pi$
$911$	−5.51604	+	1.79227i	−0.182754	+	0.0593805i	0.216210	+	0.976347i	$0.430630\pi$
$912$	−0.508357	−	0.00744239i	−0.0168334	−	0.000246442i
$913$	−22.7884	−	44.7247i	−0.754185	−	1.48017i
$914$	4.00296	+	12.3199i	0.132406	+	0.407505i
$915$	−31.9834	−	31.2453i	−1.05734	−	1.03294i
$916$	−6.34101	+	19.5156i	−0.209513	+	0.644814i
$917$	16.6975	−	2.64463i	0.551400	−	0.0873332i
$918$	−1.36076	−	1.08303i	−0.0449118	−	0.0357453i
$919$	20.0148	−	27.5480i	0.660228	−	0.908726i	−0.339261	−	0.940692i	$-0.610177\pi$
$919$	20.0148	−	27.5480i	0.660228	−	0.908726i	0.999489	+	0.0319665i	$0.0101770\pi$
$920$	23.5426	+	22.3352i	0.776177	+	0.736370i
$921$	45.3531	−	6.50418i	1.49444	−	0.214320i
$922$	−31.8892	−	5.05075i	−1.05021	−	0.166338i
$923$	15.3263	−	30.0795i	0.504470	−	0.990078i
$924$	−24.1734	−	12.7661i	−0.795247	−	0.419974i
$925$	13.7660	+	6.12469i	0.452625	+	0.201379i
$926$		−	10.8505i		−	0.356570i
$927$	−16.8762	+	2.16863i	−0.554288	+	0.0712270i
$928$	−0.981743	+	6.19848i	−0.0322273	+	0.203475i
$929$	1.63342	−	1.18675i	0.0535908	−	0.0389360i	−0.560667	−	0.828041i	$-0.689455\pi$
$929$	1.63342	−	1.18675i	0.0535908	−	0.0389360i	0.614258	+	0.789105i	$0.289455\pi$
$930$	−23.0915	−	16.3686i	−0.757199	−	0.536747i
$931$	0.674172	+	0.489815i	0.0220951	+	0.0160530i
$932$	19.2898	−	19.2898i	0.631859	−	0.631859i
$933$	−5.99559	+	17.5730i	−0.196287	+	0.575313i
$934$	12.3744	+	4.02070i	0.404904	+	0.131561i
$935$	5.01071	−	0.131871i	0.163868	−	0.00431263i
$936$	17.8086	+	13.7529i	0.582094	+	0.449528i
$937$	−36.9326	+	18.8181i	−1.20654	+	0.614760i	−0.937371	−	0.348334i	$-0.886748\pi$
$937$	−36.9326	+	18.8181i	−1.20654	+	0.614760i	−0.269165	+	0.963094i	$0.586748\pi$
$938$	3.04551	−	1.55176i	0.0994394	−	0.0506669i
$939$	7.13455	+	1.23732i	0.232827	+	0.0403784i
$940$	−20.7764	+	0.546789i	−0.677652	+	0.0178343i
$941$	4.14679	+	1.34737i	0.135181	+	0.0439231i	0.375826	−	0.926690i	$-0.377359\pi$
$941$	4.14679	+	1.34737i	0.135181	+	0.0439231i	−0.240645	+	0.970613i	$0.577359\pi$
$942$	7.24446	+	2.47168i	0.236037	+	0.0805318i
$943$	−15.4724	+	15.4724i	−0.503849	+	0.503849i
$944$	−3.54678	−	2.57688i	−0.115438	−	0.0838705i
$945$	−0.444955	+	25.2711i	−0.0144744	+	0.822070i
$946$	5.93058	−	4.30882i	0.192820	−	0.140092i
$947$	6.24562	−	39.4333i	0.202955	−	1.28141i	−0.650204	−	0.759760i	$-0.725317\pi$
$947$	6.24562	−	39.4333i	0.202955	−	1.28141i	0.853159	−	0.521650i	$-0.174683\pi$
$948$	−2.22932	−	3.16481i	−0.0724051	−	0.102788i
$949$		−	35.6053i		−	1.15580i
$950$	1.29141	+	0.574565i	0.0418988	+	0.0186413i
$951$	18.6938	−	35.3980i	0.606189	−	1.14786i
$952$	1.12651	−	2.21090i	0.0365104	−	0.0716558i
$953$	47.6668	+	7.54968i	1.54408	+	0.244558i	0.869608	−	0.493743i	$-0.164372\pi$
$953$	47.6668	+	7.54968i	1.54408	+	0.244558i	0.674471	+	0.738301i	$0.264372\pi$
$954$	−1.55408	+	4.34576i	−0.0503153	+	0.140699i
$955$	−5.48734	−	5.20592i	−0.177566	−	0.168460i
$956$	−12.7237	+	17.5127i	−0.411515	+	0.566402i
$957$	2.82084	+	9.13453i	0.0911848	+	0.295277i
$958$	22.0502	−	3.49241i	0.712409	−	0.112835i
$959$	12.7168	−	39.1384i	0.410648	−	1.26384i
$960$	7.87509	−	8.06112i	0.254167	−	0.260171i
$961$	18.3036	+	56.3328i	0.590440	+	1.81719i
$962$	−3.01074	−	5.90891i	−0.0970702	−	0.190511i
$963$	28.4458	+	15.5591i	0.916654	+	0.501386i
$964$	−19.8451	+	6.44806i	−0.639167	+	0.207678i
$965$	−50.6405	+	17.9402i	−1.63017	+	0.577517i
$966$	11.5101	−	11.1779i	0.370332	−	0.359645i
$967$	2.71356	+	17.1327i	0.0872622	+	0.550952i	0.992125	+	0.125249i	$0.0399730\pi$
$967$	2.71356	+	17.1327i	0.0872622	+	0.550952i	−0.904863	+	0.425703i	$0.860027\pi$
$968$	28.8328	+	28.8328i	0.926722	+	0.926722i
$969$	−0.122069	−	0.248501i	−0.00392142	−	0.00798300i
$970$	2.26565	+	4.17150i	0.0727456	+	0.133939i
$971$	8.44377	+	11.6218i	0.270973	+	0.372963i	0.922718	−	0.385476i	$-0.125963\pi$
$971$	8.44377	+	11.6218i	0.270973	+	0.372963i	−0.651745	+	0.758438i	$0.725963\pi$
$972$	18.6538	−	11.5686i	0.598319	−	0.371064i
$973$	−19.5827	−	9.97789i	−0.627793	−	0.319876i
$974$	7.63121			0.244520
$975$	12.0765	+	21.6294i	0.386759	+	0.692695i
$976$	−9.22265			−0.295210
$977$	−46.3358	−	23.6093i	−1.48241	−	0.755328i	−0.489260	−	0.872138i	$-0.662733\pi$
$977$	−46.3358	−	23.6093i	−1.48241	−	0.755328i	−0.993154	+	0.116810i	$0.962733\pi$
$978$	−12.5374	−	9.39242i	−0.400902	−	0.300337i
$979$	23.0818	+	31.7694i	0.737698	+	1.01535i
$980$	7.02101	−	1.30222i	0.224278	−	0.0415980i
$981$	1.27983	−	43.7003i	0.0408617	−	1.39524i
$982$	−9.22226	−	9.22226i	−0.294294	−	0.294294i
$983$	−8.98995	−	56.7603i	−0.286735	−	1.81037i	−0.538546	−	0.842596i	$-0.681026\pi$
$983$	−8.98995	−	56.7603i	−0.286735	−	1.81037i	0.251812	−	0.967776i	$-0.418974\pi$
$984$	12.5082	+	12.8798i	0.398746	+	0.410594i
$985$	3.29175	−	4.79087i	0.104884	−	0.152650i
$986$	−0.340976	+	0.110790i	−0.0108589	+	0.00352826i
$987$	−0.364075	+	24.8684i	−0.0115886	+	0.791569i
$988$	0.671886	+	1.31865i	0.0213755	+	0.0419518i
$989$	−3.16274	−	9.73390i	−0.100569	−	0.309520i
$990$	8.29288	−	25.2676i	0.263565	−	0.803056i
$991$	5.55191	−	17.0870i	0.176362	−	0.542787i	−0.823331	−	0.567562i	$-0.807887\pi$
$991$	5.55191	−	17.0870i	0.176362	−	0.542787i	0.999693	+	0.0247748i	$0.00788689\pi$
$992$	−54.9670	+	8.70591i	−1.74520	+	0.276413i
$993$	44.9501	−	13.8811i	1.42645	−	0.440502i
$994$	−11.6098	+	15.9796i	−0.368241	+	0.506841i
$995$	4.83088	−	10.1316i	0.153149	−	0.321193i
$996$	3.37270	+	23.5176i	0.106868	+	0.745184i
$997$	32.2352	+	5.10555i	1.02090	+	0.161694i	0.644372	−	0.764712i	$-0.277119\pi$
$997$	32.2352	+	5.10555i	1.02090	+	0.161694i	0.376526	+	0.926406i	$0.377119\pi$
$998$	−5.05898	+	9.92881i	−0.160139	+	0.314291i
$999$	−15.5580	+	1.76813i	−0.492233	+	0.0559413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.17.4	✓	64
3.2	odd	2	inner	75.2.l.a.17.5	yes	64
5.2	odd	4		375.2.l.b.143.5		64
5.3	odd	4		375.2.l.a.143.4		64
5.4	even	2		375.2.l.c.107.5		64
15.2	even	4		375.2.l.b.143.4		64
15.8	even	4		375.2.l.a.143.5		64
15.14	odd	2		375.2.l.c.107.4		64
25.3	odd	20	inner	75.2.l.a.53.5	yes	64
25.4	even	10		375.2.l.b.257.4		64
25.21	even	5		375.2.l.a.257.5		64
25.22	odd	20		375.2.l.c.368.4		64
75.29	odd	10		375.2.l.b.257.5		64
75.47	even	20		375.2.l.c.368.5		64
75.53	even	20	inner	75.2.l.a.53.4	yes	64
75.71	odd	10		375.2.l.a.257.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.17.4	✓	64	1.1	even	1	trivial
75.2.l.a.17.5	yes	64	3.2	odd	2	inner
75.2.l.a.53.4	yes	64	75.53	even	20	inner
75.2.l.a.53.5	yes	64	25.3	odd	20	inner
375.2.l.a.143.4		64	5.3	odd	4
375.2.l.a.143.5		64	15.8	even	4
375.2.l.a.257.4		64	75.71	odd	10
375.2.l.a.257.5		64	25.21	even	5
375.2.l.b.143.4		64	15.2	even	4
375.2.l.b.143.5		64	5.2	odd	4
375.2.l.b.257.4		64	25.4	even	10
375.2.l.b.257.5		64	75.29	odd	10
375.2.l.c.107.4		64	15.14	odd	2
375.2.l.c.107.5		64	5.4	even	2
375.2.l.c.368.4		64	25.22	odd	20
375.2.l.c.368.5		64	75.47	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.685506 - 0.349283i) q^{2} +(1.03848 - 1.38621i) q^{3} +(-0.827650 - 1.13916i) q^{4} +(-2.01837 - 0.962386i) q^{5} +(-1.19606 + 0.587530i) q^{6} +(1.53819 + 1.53819i) q^{7} +(0.410179 + 2.58977i) q^{8} +(-0.843130 - 2.87909i) q^{9} +O(q^{10})\)	\(q+(-0.685506 - 0.349283i) q^{2} +(1.03848 - 1.38621i) q^{3} +(-0.827650 - 1.13916i) q^{4} +(-2.01837 - 0.962386i) q^{5} +(-1.19606 + 0.587530i) q^{6} +(1.53819 + 1.53819i) q^{7} +(0.410179 + 2.58977i) q^{8} +(-0.843130 - 2.87909i) q^{9} +(1.04746 + 1.36470i) q^{10} +(4.90058 - 1.59230i) q^{11} +(-2.43861 - 0.0357015i) q^{12} +(1.29863 + 2.54870i) q^{13} +(-0.517176 - 1.59170i) q^{14} +(-3.43009 + 1.79846i) q^{15} +(-0.246862 + 0.759765i) q^{16} +(-0.429678 + 0.0680543i) q^{17} +(-0.427644 + 2.26812i) q^{18} +(-0.215974 + 0.297262i) q^{19} +(0.574189 + 3.09577i) q^{20} +(3.72962 - 0.534872i) q^{21} +(-3.91554 - 0.620161i) q^{22} +(-2.51281 + 4.93166i) q^{23} +(4.01591 + 2.12082i) q^{24} +(3.14763 + 3.88490i) q^{25} -2.20074i q^{26} +(-4.86657 - 1.82111i) q^{27} +(0.479166 - 3.02533i) q^{28} +(-0.866605 + 0.629625i) q^{29} +(2.97952 - 0.0347805i) q^{30} +(-7.68489 - 5.58340i) q^{31} +(4.14273 - 4.14273i) q^{32} +(2.88189 - 8.44678i) q^{33} +(0.318317 + 0.103427i) q^{34} +(-1.62430 - 4.58497i) q^{35} +(-2.58193 + 3.34334i) q^{36} +(2.68497 - 1.36806i) q^{37} +(0.251880 - 0.128339i) q^{38} +(4.88162 + 0.846603i) q^{39} +(1.66446 - 5.62185i) q^{40} +(3.75980 + 1.22163i) q^{41} +(-2.74350 - 0.936035i) q^{42} +(-1.30753 + 1.30753i) q^{43} +(-5.86985 - 4.26470i) q^{44} +(-1.06904 + 6.62247i) q^{45} +(3.44509 - 2.50300i) q^{46} +(-1.03262 + 6.51970i) q^{47} +(0.796829 + 1.13120i) q^{48} -2.26794i q^{49} +(-0.800788 - 3.76253i) q^{50} +(-0.351873 + 0.666294i) q^{51} +(1.82858 - 3.58878i) q^{52} +(1.97500 + 0.312809i) q^{53} +(2.69998 + 2.94819i) q^{54} +(-11.4236 - 1.50241i) q^{55} +(-3.35262 + 4.61449i) q^{56} +(0.187783 + 0.608084i) q^{57} +(0.813980 - 0.128922i) q^{58} +(-1.69584 + 5.21927i) q^{59} +(4.88766 + 2.41894i) q^{60} +(3.56751 + 10.9797i) q^{61} +(3.31785 + 6.51165i) q^{62} +(3.13169 - 5.72548i) q^{63} +(-2.76733 + 0.899158i) q^{64} +(-0.168276 - 6.39400i) q^{65} +(-4.92587 + 4.78372i) q^{66} +(0.319489 + 2.01717i) q^{67} +(0.433148 + 0.433148i) q^{68} +(4.22680 + 8.60469i) q^{69} +(-0.487982 + 3.71037i) q^{70} +(-6.93698 - 9.54793i) q^{71} +(7.11032 - 3.36445i) q^{72} +(-11.0907 - 5.65098i) q^{73} -2.31840 q^{74} +(8.65401 - 0.328875i) q^{75} +0.517381 q^{76} +(9.98729 + 5.08878i) q^{77} +(-3.05068 - 2.28542i) q^{78} +(0.932978 + 1.28413i) q^{79} +(1.22945 - 1.29591i) q^{80} +(-7.57826 + 4.85489i) q^{81} +(-2.15067 - 2.15067i) q^{82} +(-1.52390 - 9.62155i) q^{83} +(-3.69613 - 3.80596i) q^{84} +(0.932743 + 0.276157i) q^{85} +(1.35302 - 0.439623i) q^{86} +(-0.0271595 + 1.85514i) q^{87} +(6.13379 + 12.0382i) q^{88} +(2.35501 + 7.24797i) q^{89} +(3.04595 - 4.16635i) q^{90} +(-1.92285 + 5.91793i) q^{91} +(7.69770 - 1.21920i) q^{92} +(-15.7203 + 4.85460i) q^{93} +(2.98509 - 4.10862i) q^{94} +(0.721996 - 0.392135i) q^{95} +(-1.44054 - 10.0448i) q^{96} +(2.72539 + 0.431660i) q^{97} +(-0.792151 + 1.55468i) q^{98} +(-8.71618 - 12.7667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Introduction

L-functions

Modular forms

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