LMFDB - Embedded newform 950.2.r.a.311.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(11,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("950.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.r (of order $15$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$25$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			311.18
Character	$\chi$	$=$	950.311
Dual form			950.2.r.a.391.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(1.39673 - 0.296884i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.51731 + 1.64249i) q^{5} +(-1.39673 - 0.296884i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.877927 + 0.390878i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(1.39673 - 0.296884i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.51731 + 1.64249i) q^{5} +(-1.39673 - 0.296884i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.877927 + 0.390878i) q^{9} +(-0.718069 - 2.11763i) q^{10} +(-2.40985 + 1.75086i) q^{11} +(1.15522 + 0.839317i) q^{12} +(-2.73730 + 1.21872i) q^{13} +(1.11852 + 0.497998i) q^{14} +(2.60690 + 1.84365i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-0.342831 + 0.380752i) q^{17} +0.961011 q^{18} +(2.55818 + 3.52926i) q^{19} +(-0.205331 + 2.22662i) q^{20} +(-1.71012 + 0.363497i) q^{21} +(2.91365 - 0.619315i) q^{22} +(0.0323273 + 0.307574i) q^{23} +(-0.713966 - 1.23663i) q^{24} +(-0.395549 + 4.98433i) q^{25} +2.99635 q^{26} +(-4.57584 + 3.32454i) q^{27} +(-0.819266 - 0.909887i) q^{28} +(4.98343 + 5.53466i) q^{29} +(-1.63164 - 2.74458i) q^{30} +(-0.0174028 - 0.0535604i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.84611 + 3.16092i) q^{33} +(0.468057 - 0.208393i) q^{34} +(-1.85775 - 2.01102i) q^{35} +(-0.877927 - 0.390878i) q^{36} +(1.46749 + 1.06620i) q^{37} +(-0.901535 - 4.26465i) q^{38} +(-3.46144 + 2.51489i) q^{39} +(1.09323 - 1.95060i) q^{40} +(0.285756 - 2.71878i) q^{41} +(1.71012 + 0.363497i) q^{42} +(-0.211978 - 0.367157i) q^{43} +(-2.91365 - 0.619315i) q^{44} +(-1.97410 - 0.848904i) q^{45} +(0.0955690 - 0.294131i) q^{46} +(3.24282 + 3.60152i) q^{47} +(0.149260 + 1.42011i) q^{48} -5.50091 q^{49} +(2.38866 - 4.39253i) q^{50} +(-0.365802 + 0.633588i) q^{51} +(-2.73730 - 1.21872i) q^{52} +(-5.07067 - 5.63155i) q^{53} +(5.53245 - 1.17596i) q^{54} +(-6.53226 - 1.30156i) q^{55} +(0.378352 + 1.16445i) q^{56} +(4.62087 + 4.16994i) q^{57} +(-2.30144 - 7.08311i) q^{58} +(0.588310 - 5.59740i) q^{59} +(0.374257 + 3.17094i) q^{60} +(0.783155 + 7.45122i) q^{61} +(-0.00588670 + 0.0560082i) q^{62} +(1.07491 - 0.478581i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-6.15507 - 2.64681i) q^{65} +(3.88571 - 1.73003i) q^{66} +(4.82766 + 1.02615i) q^{67} -0.512352 q^{68} +(0.136466 + 0.419999i) q^{69} +(0.879185 + 2.59278i) q^{70} +(-9.24291 + 1.96464i) q^{71} +(0.643042 + 0.714170i) q^{72} +(-0.565179 - 0.251634i) q^{73} +(-0.906960 - 1.57090i) q^{74} +(0.927292 + 7.07919i) q^{75} +(-0.910996 + 4.26264i) q^{76} +(2.95056 - 2.14371i) q^{77} +(4.18508 - 0.889567i) q^{78} +(11.5183 - 2.44830i) q^{79} +(-1.79209 + 1.33731i) q^{80} +(-3.47508 + 3.85947i) q^{81} +(-1.36688 + 2.36751i) q^{82} +(-4.64032 - 14.2814i) q^{83} +(-1.41442 - 1.02764i) q^{84} +(-1.14556 + 0.0146223i) q^{85} +(0.0443155 + 0.421634i) q^{86} +(8.60365 + 6.25091i) q^{87} +(2.40985 + 1.75086i) q^{88} +(1.73500 + 16.5074i) q^{89} +(1.45815 + 1.57845i) q^{90} +(3.35148 - 1.49217i) q^{91} +(-0.206941 + 0.229831i) q^{92} +(-0.0402082 - 0.0696427i) q^{93} +(-1.49760 - 4.60913i) q^{94} +(-1.91523 + 9.55677i) q^{95} +(0.441255 - 1.35804i) q^{96} +(9.34485 - 1.98631i) q^{97} +(5.02533 + 2.23742i) q^{98} +(1.43130 - 2.47909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9}+O(q^{10}) $ 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9	\( 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9} + 4 q^{10} - 2 q^{11} + 8 q^{13} + 7 q^{14} + 10 q^{15} + 25 q^{16} - 13 q^{17} - 216 q^{18} - 36 q^{19} - 2 q^{20} + 4 q^{22} - 13 q^{23} + 33 q^{25} - 64 q^{26} - 2 q^{28} + 12 q^{29} - 20 q^{30} + 12 q^{31} + 100 q^{32} - 12 q^{33} + 8 q^{34} - 22 q^{35} + 37 q^{36} + 8 q^{37} + 18 q^{38} + 28 q^{39} - q^{40} + 2 q^{41} + 70 q^{43} - 4 q^{44} + 60 q^{45} + 24 q^{46} - 22 q^{47} + 156 q^{49} + 26 q^{50} - 42 q^{51} + 8 q^{52} - 18 q^{53} - 10 q^{55} - 4 q^{56} + 74 q^{57} + 24 q^{58} + 50 q^{59} + 12 q^{61} - 4 q^{62} - 45 q^{63} - 50 q^{64} + 120 q^{65} + 2 q^{66} - 18 q^{67} - 84 q^{68} + 4 q^{69} - 13 q^{70} + 19 q^{71} - 17 q^{72} - 24 q^{73} + 4 q^{74} - 136 q^{75} - 6 q^{76} - 12 q^{77} - 26 q^{78} - 8 q^{79} + q^{80} - 63 q^{81} + 28 q^{82} + 16 q^{83} - 20 q^{84} - 5 q^{85} + 20 q^{86} - 64 q^{87} + 2 q^{88} + 16 q^{89} - 65 q^{90} + 72 q^{91} + 12 q^{92} - 8 q^{93} - 44 q^{94} - 73 q^{95} - 11 q^{97} - 27 q^{98} + 16 q^{99}+O(q^{100}) \) 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9 + 4 * q^10 - 2 * q^11 + 8 * q^13 + 7 * q^14 + 10 * q^15 + 25 * q^16 - 13 * q^17 - 216 * q^18 - 36 * q^19 - 2 * q^20 + 4 * q^22 - 13 * q^23 + 33 * q^25 - 64 * q^26 - 2 * q^28 + 12 * q^29 - 20 * q^30 + 12 * q^31 + 100 * q^32 - 12 * q^33 + 8 * q^34 - 22 * q^35 + 37 * q^36 + 8 * q^37 + 18 * q^38 + 28 * q^39 - q^40 + 2 * q^41 + 70 * q^43 - 4 * q^44 + 60 * q^45 + 24 * q^46 - 22 * q^47 + 156 * q^49 + 26 * q^50 - 42 * q^51 + 8 * q^52 - 18 * q^53 - 10 * q^55 - 4 * q^56 + 74 * q^57 + 24 * q^58 + 50 * q^59 + 12 * q^61 - 4 * q^62 - 45 * q^63 - 50 * q^64 + 120 * q^65 + 2 * q^66 - 18 * q^67 - 84 * q^68 + 4 * q^69 - 13 * q^70 + 19 * q^71 - 17 * q^72 - 24 * q^73 + 4 * q^74 - 136 * q^75 - 6 * q^76 - 12 * q^77 - 26 * q^78 - 8 * q^79 + q^80 - 63 * q^81 + 28 * q^82 + 16 * q^83 - 20 * q^84 - 5 * q^85 + 20 * q^86 - 64 * q^87 + 2 * q^88 + 16 * q^89 - 65 * q^90 + 72 * q^91 + 12 * q^92 - 8 * q^93 - 44 * q^94 - 73 * q^95 - 11 * q^97 - 27 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	1.39673	−	0.296884i	0.806401	−	0.171406i	0.213774	−	0.976883i	$-0.431424\pi$
$3$	1.39673	−	0.296884i	0.806401	−	0.171406i	0.592627	+	0.805477i	$0.298091\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	1.51731	+	1.64249i	0.678561	+	0.734544i
$5$	1.51731	+	1.64249i	0.678561	+	0.734544i
$6$	−1.39673	−	0.296884i	−0.570212	−	0.121202i
$7$	−1.22437			−0.462770			−0.231385	−	0.972862i	$-0.574326\pi$
$7$	−1.22437			−0.462770			−0.231385	+	0.972862i	$0.574326\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.877927	+	0.390878i	−0.292642	+	0.130293i
$10$	−0.718069	−	2.11763i	−0.227073	−	0.669655i
$11$	−2.40985	+	1.75086i	−0.726598	+	0.527904i	−0.888485	−	0.458905i	$-0.848242\pi$
$11$	−2.40985	+	1.75086i	−0.726598	+	0.527904i	0.161888	+	0.986809i	$0.448242\pi$
$12$	1.15522	+	0.839317i	0.333484	+	0.242290i
$13$	−2.73730	+	1.21872i	−0.759190	+	0.338013i	−0.749557	−	0.661940i	$-0.769733\pi$
$13$	−2.73730	+	1.21872i	−0.759190	+	0.338013i	−0.00963382	+	0.999954i	$0.503067\pi$
$14$	1.11852	+	0.497998i	0.298937	+	0.133095i
$15$	2.60690	+	1.84365i	0.673098	+	0.476028i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	−0.342831	+	0.380752i	−0.0831487	+	0.0923459i	−0.783283	−	0.621665i	$-0.786457\pi$
$17$	−0.342831	+	0.380752i	−0.0831487	+	0.0923459i	0.700135	+	0.714011i	$0.253123\pi$
$18$	0.961011			0.226512
$19$	2.55818	+	3.52926i	0.586887	+	0.809669i
$19$	2.55818	+	3.52926i	0.586887	+	0.809669i
$20$	−0.205331	+	2.22662i	−0.0459133	+	0.497888i
$21$	−1.71012	+	0.363497i	−0.373178	+	0.0793214i
$22$	2.91365	−	0.619315i	0.621192	−	0.132038i
$23$	0.0323273	+	0.307574i	0.00674071	+	0.0641335i	0.997375	−	0.0724073i	$-0.0230682\pi$
$23$	0.0323273	+	0.307574i	0.00674071	+	0.0641335i	−0.990634	+	0.136541i	$0.956401\pi$
$24$	−0.713966	−	1.23663i	−0.145738	−	0.252425i
$25$	−0.395549	+	4.98433i	−0.0791098	+	0.996866i
$26$	2.99635			0.587632
$27$	−4.57584	+	3.32454i	−0.880621	+	0.639809i
$28$	−0.819266	−	0.909887i	−0.154827	−	0.171952i
$29$	4.98343	+	5.53466i	0.925400	+	1.02776i	0.999534	+	0.0305122i	$0.00971383\pi$
$29$	4.98343	+	5.53466i	0.925400	+	1.02776i	−0.0741348	+	0.997248i	$0.523619\pi$
$30$	−1.63164	−	2.74458i	−0.297895	−	0.501089i
$31$	−0.0174028	−	0.0535604i	−0.00312564	−	0.00961973i	0.949482	−	0.313823i	$-0.101610\pi$
$31$	−0.0174028	−	0.0535604i	−0.00312564	−	0.00961973i	−0.952607	+	0.304203i	$0.901610\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.84611	+	3.16092i	−0.495443	+	0.550246i
$34$	0.468057	−	0.208393i	0.0802712	−	0.0357390i
$35$	−1.85775	−	2.01102i	−0.314017	−	0.339925i
$36$	−0.877927	−	0.390878i	−0.146321	−	0.0651464i
$37$	1.46749	+	1.06620i	0.241254	+	0.175281i	0.701842	−	0.712333i	$-0.252361\pi$
$37$	1.46749	+	1.06620i	0.241254	+	0.175281i	−0.460588	+	0.887614i	$0.652361\pi$
$38$	−0.901535	−	4.26465i	−0.146248	−	0.691817i
$39$	−3.46144	+	2.51489i	−0.554275	+	0.402704i
$40$	1.09323	−	1.95060i	0.172854	−	0.308418i
$41$	0.285756	−	2.71878i	0.0446276	−	0.424603i	−0.949284	−	0.314420i	$-0.898190\pi$
$41$	0.285756	−	2.71878i	0.0446276	−	0.424603i	0.993911	−	0.110182i	$-0.0351435\pi$
$42$	1.71012	+	0.363497i	0.263877	+	0.0560887i
$43$	−0.211978	−	0.367157i	−0.0323263	−	0.0559909i	0.849410	−	0.527734i	$-0.176958\pi$
$43$	−0.211978	−	0.367157i	−0.0323263	−	0.0559909i	−0.881736	+	0.471743i	$0.843625\pi$
$44$	−2.91365	−	0.619315i	−0.439249	−	0.0933652i
$45$	−1.97410	−	0.848904i	−0.294281	−	0.126547i
$46$	0.0955690	−	0.294131i	0.0140909	−	0.0433673i
$47$	3.24282	+	3.60152i	0.473015	+	0.525336i	0.931683	−	0.363271i	$-0.118340\pi$
$47$	3.24282	+	3.60152i	0.473015	+	0.525336i	−0.458669	+	0.888607i	$0.651674\pi$
$48$	0.149260	+	1.42011i	0.0215438	+	0.204975i
$49$	−5.50091			−0.785844
$50$	2.38866	−	4.39253i	0.337808	−	0.621197i
$51$	−0.365802	+	0.633588i	−0.0512225	+	0.0887201i
$52$	−2.73730	−	1.21872i	−0.379595	−	0.169007i
$53$	−5.07067	−	5.63155i	−0.696510	−	0.773552i	0.286307	−	0.958138i	$-0.407572\pi$
$53$	−5.07067	−	5.63155i	−0.696510	−	0.773552i	−0.982816	+	0.184586i	$0.940906\pi$
$54$	5.53245	−	1.17596i	0.752872	−	0.160028i
$55$	−6.53226	−	1.30156i	−0.880810	−	0.175503i
$56$	0.378352	+	1.16445i	0.0505594	+	0.155606i
$57$	4.62087	+	4.16994i	0.612049	+	0.552322i
$58$	−2.30144	−	7.08311i	−0.302194	−	0.930057i
$59$	0.588310	−	5.59740i	0.0765915	−	0.728719i	−0.887078	−	0.461620i	$-0.847268\pi$
$59$	0.588310	−	5.59740i	0.0765915	−	0.728719i	0.963669	−	0.267099i	$-0.0860650\pi$
$60$	0.374257	+	3.17094i	0.0483163	+	0.409367i
$61$	0.783155	+	7.45122i	0.100273	+	0.954031i	0.922793	+	0.385295i	$0.125900\pi$
$61$	0.783155	+	7.45122i	0.100273	+	0.954031i	−0.822521	+	0.568735i	$0.807433\pi$
$62$	−0.00588670	+	0.0560082i	−0.000747611	+	0.00711305i
$63$	1.07491	−	0.478581i	0.135426	−	0.0602955i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.15507	−	2.64681i	−0.763443	−	0.328296i
$66$	3.88571	−	1.73003i	0.478298	−	0.212952i
$67$	4.82766	+	1.02615i	0.589792	+	0.125364i	0.493134	−	0.869953i	$-0.335851\pi$
$67$	4.82766	+	1.02615i	0.589792	+	0.125364i	0.0966584	+	0.995318i	$0.469185\pi$
$68$	−0.512352			−0.0621319
$69$	0.136466	+	0.419999i	0.0164286	+	0.0505620i
$70$	0.879185	+	2.59278i	0.105083	+	0.309896i
$71$	−9.24291	+	1.96464i	−1.09693	+	0.233160i	−0.720618	−	0.693332i	$-0.756142\pi$
$71$	−9.24291	+	1.96464i	−1.09693	+	0.233160i	−0.376314	+	0.926492i	$0.622809\pi$
$72$	0.643042	+	0.714170i	0.0757832	+	0.0841658i
$73$	−0.565179	−	0.251634i	−0.0661492	−	0.0294515i	0.373395	−	0.927672i	$-0.378193\pi$
$73$	−0.565179	−	0.251634i	−0.0661492	−	0.0294515i	−0.439545	+	0.898221i	$0.644860\pi$
$74$	−0.906960	−	1.57090i	−0.105432	−	0.182613i
$75$	0.927292	+	7.07919i	0.107074	+	0.817434i
$76$	−0.910996	+	4.26264i	−0.104498	+	0.488958i
$77$	2.95056	−	2.14371i	0.336247	−	0.244298i
$78$	4.18508	−	0.889567i	0.473867	−	0.100724i
$79$	11.5183	−	2.44830i	1.29591	−	0.275455i	0.492206	−	0.870479i	$-0.336191\pi$
$79$	11.5183	−	2.44830i	1.29591	−	0.275455i	0.803708	+	0.595023i	$0.202857\pi$
$80$	−1.79209	+	1.33731i	−0.200362	+	0.149516i
$81$	−3.47508	+	3.85947i	−0.386120	+	0.428830i
$82$	−1.36688	+	2.36751i	−0.150947	+	0.261447i
$83$	−4.64032	−	14.2814i	−0.509341	−	1.56759i	−0.793349	−	0.608768i	$-0.791664\pi$
$83$	−4.64032	−	14.2814i	−0.509341	−	1.56759i	0.284008	−	0.958822i	$-0.408336\pi$
$84$	−1.41442	−	1.02764i	−0.154326	−	0.112124i
$85$	−1.14556	+	0.0146223i	−0.124254	+	0.00158601i
$86$	0.0443155	+	0.421634i	0.00477866	+	0.0454659i
$87$	8.60365	+	6.25091i	0.922408	+	0.670168i
$88$	2.40985	+	1.75086i	0.256891	+	0.186642i
$89$	1.73500	+	16.5074i	0.183909	+	1.74978i	0.564863	+	0.825185i	$0.308929\pi$
$89$	1.73500	+	16.5074i	0.183909	+	1.74978i	−0.380954	+	0.924594i	$0.624404\pi$
$90$	1.45815	+	1.57845i	0.153702	+	0.166383i
$91$	3.35148	−	1.49217i	0.351330	−	0.156422i
$92$	−0.206941	+	0.229831i	−0.0215750	+	0.0239615i
$93$	−0.0402082	−	0.0696427i	−0.00416940	−	0.00722161i
$94$	−1.49760	−	4.60913i	−0.154465	−	0.475395i
$95$	−1.91523	+	9.55677i	−0.196498	+	0.980504i
$96$	0.441255	−	1.35804i	0.0450354	−	0.138605i
$97$	9.34485	−	1.98631i	0.948826	−	0.201679i	0.292593	−	0.956237i	$-0.405482\pi$
$97$	9.34485	−	1.98631i	0.948826	−	0.201679i	0.656233	+	0.754558i	$0.272149\pi$
$98$	5.02533	+	2.23742i	0.507635	+	0.226014i
$99$	1.43130	−	2.47909i	0.143851	−	0.249157i
$100$	−3.96875	+	3.04122i	−0.396875	+	0.304122i
$101$	2.57371	−	4.45780i	0.256094	−	0.443568i	−0.709098	−	0.705110i	$-0.750898\pi$
$101$	2.57371	−	4.45780i	0.256094	−	0.443568i	0.965192	+	0.261542i	$0.0842309\pi$
$102$	0.591880	−	0.430026i	0.0586049	−	0.0425789i
$103$	3.15958	−	9.72417i	0.311322	−	0.958151i	−0.665920	−	0.746023i	$-0.731961\pi$
$103$	3.15958	−	9.72417i	0.311322	−	0.958151i	0.977242	−	0.212128i	$-0.0680393\pi$
$104$	2.00495	+	2.22672i	0.196601	+	0.218348i
$105$	−3.19181	−	2.25731i	−0.311489	−	0.220291i
$106$	2.34173	+	7.20710i	0.227449	+	0.700016i
$107$	16.3035			1.57611			0.788057	−	0.615602i	$-0.211087\pi$
$107$	16.3035			1.57611			0.788057	+	0.615602i	$0.211087\pi$
$108$	−5.53245	−	1.17596i	−0.532361	−	0.113157i
$109$	−1.35292	+	12.8722i	−0.129587	+	1.23293i	0.715618	+	0.698492i	$0.246145\pi$
$109$	−1.35292	+	12.8722i	−0.129587	+	1.23293i	−0.845205	+	0.534443i	$0.820522\pi$
$110$	5.43812	+	3.84595i	0.518505	+	0.366697i
$111$	2.36622	+	1.05351i	0.224592	+	0.0999948i
$112$	0.127982	−	1.21767i	0.0120932	−	0.115059i
$113$	1.49272	+	1.08452i	0.140423	+	0.102023i	0.655779	−	0.754953i	$-0.272340\pi$
$113$	1.49272	+	1.08452i	0.140423	+	0.102023i	−0.515356	+	0.856976i	$0.672340\pi$
$114$	−2.52530	−	5.68890i	−0.236516	−	0.532815i
$115$	−0.456136	+	0.519781i	−0.0425349	+	0.0484699i
$116$	−0.778488	+	7.40682i	−0.0722808	+	0.687706i
$117$	1.92678	−	2.13990i	0.178131	−	0.197834i
$118$	−2.81411	+	4.87419i	−0.259060	+	0.448706i
$119$	0.419753	−	0.466183i	0.0384787	−	0.0427349i
$120$	0.947838	−	3.04902i	0.0865254	−	0.278337i
$121$	−0.657312	+	2.02300i	−0.0597556	+	0.183909i
$122$	2.31524	−	7.12556i	0.209612	−	0.645118i
$123$	−0.408040	−	3.88224i	−0.0367917	−	0.350050i
$124$	0.0281583	−	0.0487717i	0.00252869	−	0.00437983i
$125$	−8.78688	+	6.91308i	−0.785923	+	0.618325i
$126$	−1.17664			−0.104823
$127$	0.165969	+	1.57909i	0.0147274	+	0.140122i	0.999415	−	0.0342078i	$-0.0108908\pi$
$127$	0.165969	+	1.57909i	0.0147274	+	0.140122i	−0.984687	+	0.174330i	$0.944224\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	−0.405079	−	0.449885i	−0.0356652	−	0.0396102i
$130$	4.54638	+	4.92147i	0.398744	+	0.431642i
$131$	1.80268	−	2.00207i	0.157500	−	0.174922i	−0.659230	−	0.751941i	$-0.729118\pi$
$131$	1.80268	−	2.00207i	0.157500	−	0.174922i	0.816730	+	0.577019i	$0.195784\pi$
$132$	−4.25344			−0.370214
$133$	−3.13217	−	4.32114i	−0.271594	−	0.374690i
$134$	−3.99291	−	2.90102i	−0.344935	−	0.250610i
$135$	−12.4035	−	2.47142i	−1.06752	−	0.212706i
$136$	0.468057	+	0.208393i	0.0401356	+	0.0178695i
$137$	−0.211684	+	0.0942476i	−0.0180853	+	0.00805212i	−0.415759	−	0.909475i	$-0.636484\pi$
$137$	−0.211684	+	0.0942476i	−0.0180853	+	0.00805212i	0.397674	+	0.917527i	$0.369817\pi$
$138$	0.0461612	−	0.439194i	0.00392950	−	0.0373867i
$139$	−0.291062	−	2.76927i	−0.0246876	−	0.234887i	−0.999907	−	0.0136463i	$-0.995656\pi$
$139$	−0.291062	−	2.76927i	−0.0246876	−	0.234887i	0.975219	−	0.221240i	$-0.0710106\pi$
$140$	0.251401	−	2.72622i	0.0212473	−	0.230407i
$141$	5.59858	+	4.06760i	0.471485	+	0.342554i
$142$	9.24291	+	1.96464i	0.775648	+	0.164869i
$143$	4.46267	−	7.72957i	0.373187	−	0.646379i
$144$	−0.296969	−	0.913975i	−0.0247474	−	0.0761646i
$145$	−1.52922	+	16.5830i	−0.126995	+	1.37714i
$146$	0.413968	+	0.459758i	0.0342602	+	0.0380499i
$147$	−7.68328	+	1.63313i	−0.633706	+	0.134698i
$148$	0.189606	+	1.80398i	0.0155855	+	0.148286i
$149$	−4.59550	−	7.95964i	−0.376478	−	0.652079i	0.614069	−	0.789252i	$-0.289532\pi$
$149$	−4.59550	−	7.95964i	−0.376478	−	0.652079i	−0.990547	+	0.137173i	$0.956198\pi$
$150$	2.03224	−	6.84432i	0.165932	−	0.558836i
$151$	11.5284			0.938170			0.469085	−	0.883153i	$-0.344584\pi$
$151$	11.5284			0.938170			0.469085	+	0.883153i	$0.344584\pi$
$152$	2.56601	−	3.52358i	0.208131	−	0.285800i
$153$	0.152153	−	0.468278i	0.0123008	−	0.0378580i
$154$	−3.56739	+	0.758273i	−0.287469	+	0.0611034i
$155$	0.0615669	−	0.109852i	0.00494518	−	0.00882349i
$156$	−4.18508	−	0.889567i	−0.335075	−	0.0712224i
$157$	4.64225	+	8.04061i	0.370492	+	0.641711i	0.989641	−	0.143563i	$-0.0458558\pi$
$157$	4.64225	+	8.04061i	0.370492	+	0.641711i	−0.619149	+	0.785273i	$0.712522\pi$
$158$	−11.5183	−	2.44830i	−0.916350	−	0.194776i
$159$	−8.75426	−	6.36034i	−0.694258	−	0.504408i
$160$	2.18109	−	0.492783i	0.172431	−	0.0389579i
$161$	−0.0395807	−	0.376585i	−0.00311939	−	0.0296791i
$162$	4.74443	−	2.11236i	0.372758	−	0.165962i
$163$	9.73797	+	7.07505i	0.762737	+	0.554161i	0.899749	−	0.436409i	$-0.143750\pi$
$163$	9.73797	+	7.07505i	0.762737	+	0.554161i	−0.137012	+	0.990569i	$0.543750\pi$
$164$	2.21166	−	1.60686i	0.172702	−	0.125475i
$165$	−9.51020	+	0.121391i	−0.740368	+	0.00945029i
$166$	−1.56964	+	14.9341i	−0.121828	+	1.15911i
$167$	−4.30790	−	0.915672i	−0.333355	−	0.0708568i	0.0381933	−	0.999270i	$-0.487840\pi$
$167$	−4.30790	−	0.915672i	−0.333355	−	0.0708568i	−0.371549	+	0.928414i	$0.621173\pi$
$168$	0.874161	+	1.51409i	0.0674430	+	0.116815i
$169$	−2.69118	+	2.98885i	−0.207014	+	0.229912i
$170$	1.05247	+	0.452584i	0.0807208	+	0.0347116i
$171$	−3.62541	−	2.09850i	−0.277242	−	0.160476i
$172$	0.131010	−	0.403206i	0.00998939	−	0.0307442i
$173$	−14.4053	−	6.41366i	−1.09522	−	0.487622i	−0.222046	−	0.975036i	$-0.571273\pi$
$173$	−14.4053	−	6.41366i	−1.09522	−	0.487622i	−0.873171	+	0.487415i	$0.837940\pi$
$174$	−5.31735	−	9.20991i	−0.403107	−	0.698202i
$175$	0.484300	−	6.10268i	0.0366096	−	0.461319i
$176$	−1.48937	−	2.57966i	−0.112265	−	0.194450i
$177$	−0.840067	−	7.99270i	−0.0631433	−	0.600768i
$178$	5.12916	−	15.7859i	0.384447	−	1.18321i
$179$	−2.86979	+	8.83230i	−0.214498	+	0.660157i	0.784691	+	0.619887i	$0.212822\pi$
$179$	−2.86979	+	8.83230i	−0.214498	+	0.660157i	−0.999189	+	0.0402698i	$0.987178\pi$
$180$	−0.690072	−	2.03507i	−0.0514350	−	0.151685i
$181$	5.52190	+	1.17372i	0.410440	+	0.0872417i	0.408504	−	0.912756i	$-0.366051\pi$
$181$	5.52190	+	1.17372i	0.410440	+	0.0872417i	0.00193571	+	0.999998i	$0.499384\pi$
$182$	−3.66865			−0.271938
$183$	3.30600	+	10.1748i	0.244386	+	0.752144i
$184$	0.282530	−	0.125791i	0.0208284	−	0.00927340i
$185$	0.475423	+	4.02809i	0.0349538	+	0.296151i
$186$	0.00840580	+	0.0799759i	0.000616343	+	0.00586412i
$187$	0.159528	−	1.51780i	0.0116658	−	0.110993i
$188$	−0.506579	+	4.81978i	−0.0369461	+	0.351518i
$189$	5.60254	−	4.07048i	0.407525	−	0.296084i
$190$	5.63674	−	7.95155i	0.408932	−	0.576866i
$191$	−14.4004	−	10.4625i	−1.04198	−	0.757040i	−0.0713063	−	0.997454i	$-0.522717\pi$
$191$	−14.4004	−	10.4625i	−1.04198	−	0.757040i	−0.970670	+	0.240414i	$0.922717\pi$
$192$	−0.955473	+	1.06116i	−0.0689553	+	0.0765826i
$193$	−0.767746	−	1.32977i	−0.0552636	−	0.0957193i	0.837070	−	0.547096i	$-0.184267\pi$
$193$	−0.767746	−	1.32977i	−0.0552636	−	0.0957193i	−0.892334	+	0.451376i	$0.850933\pi$
$194$	−9.34485	−	1.98631i	−0.670921	−	0.142609i
$195$	−9.38276	−	1.86953i	−0.671913	−	0.133880i
$196$	−3.68083	−	4.08797i	−0.262916	−	0.291998i
$197$	7.73512	−	23.8063i	0.551105	−	1.69613i	−0.154910	−	0.987929i	$-0.549509\pi$
$197$	7.73512	−	23.8063i	0.551105	−	1.69613i	0.706015	−	0.708197i	$-0.250491\pi$
$198$	−2.31589	+	1.68259i	−0.164583	+	0.119577i
$199$	2.58383	−	4.47533i	0.183163	−	0.317248i	−0.759793	−	0.650165i	$-0.774700\pi$
$199$	2.58383	−	4.47533i	0.183163	−	0.317248i	0.942956	+	0.332917i	$0.108033\pi$
$200$	4.86261	−	1.16405i	0.343838	−	0.0823110i
$201$	7.04757			0.497098
$202$	−4.16436	+	3.02558i	−0.293003	+	0.212879i
$203$	−6.10158	−	6.77649i	−0.428247	−	0.475616i
$204$	−0.715617	+	0.152109i	−0.0501032	+	0.0106498i
$205$	4.89916	−	3.65588i	0.342172	−	0.255338i
$206$	−6.84159	+	7.59836i	−0.476676	+	0.529403i
$207$	−0.148605	−	0.257391i	−0.0103288	−	0.0178899i
$208$	−0.925922	−	2.84970i	−0.0642012	−	0.197591i
$209$	−12.3441	−	4.02598i	−0.853858	−	0.278483i
$210$	1.99774	+	3.36039i	0.137857	+	0.231889i
$211$	13.5236	+	6.02110i	0.931005	+	0.414510i	0.815474	−	0.578794i	$-0.196476\pi$
$211$	13.5236	+	6.02110i	0.931005	+	0.414510i	0.115531	+	0.993304i	$0.463143\pi$
$212$	0.792116	−	7.53648i	0.0544028	−	0.517608i
$213$	−12.3266	+	5.48814i	−0.844603	+	0.376041i
$214$	−14.8939	−	6.63121i	−1.01813	−	0.453300i
$215$	0.281415	−	0.905262i	0.0191924	−	0.0617383i
$216$	4.57584	+	3.32454i	0.311347	+	0.226207i
$217$	0.0213075	+	0.0655779i	0.00144645	+	0.00445172i
$218$	6.47156	−	11.2091i	0.438309	−	0.759174i
$219$	−0.864108	−	0.183672i	−0.0583910	−	0.0124114i
$220$	−3.40368	−	5.72533i	−0.229476	−	0.386002i
$221$	0.474399	−	1.46005i	0.0319115	−	0.0982135i
$222$	−1.73315	−	1.92486i	−0.116321	−	0.129188i
$223$	2.09937	+	0.934699i	0.140584	+	0.0625921i	0.475823	−	0.879541i	$-0.342150\pi$
$223$	2.09937	+	0.934699i	0.140584	+	0.0625921i	−0.335239	+	0.942133i	$0.608817\pi$
$224$	−0.612187	+	1.06034i	−0.0409034	+	0.0708468i
$225$	−1.60100	−	4.53049i	−0.106734	−	0.302033i
$226$	−0.922551	−	1.59791i	−0.0613672	−	0.106291i
$227$	6.34168	−	4.60750i	0.420912	−	0.305811i	−0.357092	−	0.934069i	$-0.616232\pi$
$227$	6.34168	−	4.60750i	0.420912	−	0.305811i	0.778005	+	0.628258i	$0.216232\pi$
$228$	−0.00690553	+	6.22421i	−0.000457330	+	0.412208i
$229$	4.40665	−	13.5623i	0.291199	−	0.896220i	−0.693272	−	0.720676i	$-0.743832\pi$
$229$	4.40665	−	13.5623i	0.291199	−	0.896220i	0.984472	−	0.175544i	$-0.0561684\pi$
$230$	0.628115	−	0.289317i	0.0414167	−	0.0190770i
$231$	3.48470	−	3.87015i	0.229276	−	0.254637i
$232$	3.72381	−	6.44983i	0.244480	−	0.423452i
$233$	16.6211	−	18.4596i	1.08888	−	1.20933i	0.112416	−	0.993661i	$-0.464141\pi$
$233$	16.6211	−	18.4596i	1.08888	−	1.20933i	0.976467	−	0.215666i	$-0.0691923\pi$
$234$	−2.63057	+	1.17121i	−0.171966	+	0.0765642i
$235$	−0.995098	+	10.7909i	−0.0649131	+	0.703922i
$236$	4.55333	−	3.30819i	0.296397	−	0.215345i
$237$	15.3611	−	6.83922i	0.997813	−	0.444255i
$238$	−0.573077	+	0.255150i	−0.0371471	+	0.0165389i
$239$	−15.5276	+	11.2814i	−1.00439	+	0.729735i	−0.963026	−	0.269409i	$-0.913172\pi$
$239$	−15.5276	+	11.2814i	−1.00439	+	0.729735i	−0.0413679	+	0.999144i	$0.513172\pi$
$240$	−2.10604	+	2.39990i	−0.135945	+	0.154913i
$241$	0.505159	−	0.224911i	0.0325401	−	0.0144878i	−0.390402	−	0.920644i	$-0.627664\pi$
$241$	0.505159	−	0.224911i	0.0325401	−	0.0144878i	0.422942	+	0.906157i	$0.360997\pi$
$242$	1.42331	−	1.58075i	0.0914940	−	0.101614i
$243$	4.77615	−	8.27254i	0.306390	−	0.530683i
$244$	−5.01330	+	5.56783i	−0.320944	+	0.356444i
$245$	−8.34658	−	9.03519i	−0.533243	−	0.577237i
$246$	−1.20629	+	3.71257i	−0.0769100	+	0.236705i
$247$	−11.3037	−	6.54293i	−0.719238	−	0.416317i
$248$	−0.0455612	+	0.0331021i	−0.00289314	+	0.00210199i
$249$	−10.7212	−	18.5696i	−0.679427	−	1.17680i
$250$	10.8390	−	2.74147i	0.685520	−	0.173386i
$251$	−0.891763	+	1.54458i	−0.0562876	+	0.0974929i	−0.892796	−	0.450461i	$-0.851260\pi$
$251$	−0.891763	+	1.54458i	−0.0562876	+	0.0974929i	0.836509	+	0.547954i	$0.184593\pi$
$252$	1.07491	+	0.478581i	0.0677130	+	0.0301478i
$253$	−0.616422	−	0.684606i	−0.0387541	−	0.0430408i
$254$	0.490655	−	1.51008i	0.0307864	−	0.0947508i
$255$	−1.59570	+	0.360522i	−0.0999264	+	0.0225768i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−0.0269474	+	0.0466742i	−0.00168093	+	0.00291146i	−0.866865	−	0.498544i	$-0.833868\pi$
$257$	−0.0269474	+	0.0466742i	−0.00168093	+	0.00291146i	0.865184	+	0.501455i	$0.167202\pi$
$258$	0.187073	+	0.575751i	0.0116466	+	0.0358447i
$259$	−1.79676	−	1.30542i	−0.111645	−	0.0811149i
$260$	−2.15159	−	6.34517i	−0.133436	−	0.393511i
$261$	−6.53847	−	2.91111i	−0.404721	−	0.180193i
$262$	−2.46114	+	1.09577i	−0.152050	+	0.0676970i
$263$	2.37923	−	22.6369i	0.146710	−	1.39585i	−0.635148	−	0.772391i	$-0.719061\pi$
$263$	2.37923	−	22.6369i	0.146710	−	1.39585i	0.781857	−	0.623458i	$-0.214273\pi$
$264$	3.88571	+	1.73003i	0.239149	+	0.106476i
$265$	1.55599	−	16.8733i	0.0955839	−	1.03652i
$266$	1.10382	+	5.22152i	0.0676793	+	0.320152i
$267$	7.32409	+	22.5412i	0.448227	+	1.37950i
$268$	2.46776	+	4.27428i	0.150742	+	0.261093i
$269$	−4.20785	+	4.67329i	−0.256557	+	0.284936i	−0.857639	−	0.514252i	$-0.828070\pi$
$269$	−4.20785	+	4.67329i	−0.256557	+	0.284936i	0.601082	+	0.799187i	$0.294736\pi$
$270$	10.3259	+	7.30271i	0.628417	+	0.444429i
$271$	9.22994	−	1.96188i	0.560679	−	0.119176i	0.0811497	−	0.996702i	$-0.474141\pi$
$271$	9.22994	−	1.96188i	0.560679	−	0.119176i	0.479529	+	0.877526i	$0.340807\pi$
$272$	−0.342831	−	0.380752i	−0.0207872	−	0.0230865i
$273$	4.23810	−	3.07916i	0.256502	−	0.186359i
$274$	0.231717			0.0139985
$275$	−7.77365	−	12.7040i	−0.468769	−	0.766083i
$276$	−0.220807	+	0.382448i	−0.0132910	+	0.0230207i
$277$	11.3498	−	8.24609i	0.681942	−	0.495460i	−0.192059	−	0.981383i	$-0.561517\pi$
$277$	11.3498	−	8.24609i	0.681942	−	0.495460i	0.874001	+	0.485923i	$0.161517\pi$
$278$	−0.860466	+	2.64824i	−0.0516073	+	0.158831i
$279$	0.0362140	+	0.0402197i	0.00216807	+	0.00240789i
$280$	−1.33852	+	2.38827i	−0.0799918	+	0.142726i
$281$	2.88185	+	0.612556i	0.171917	+	0.0365421i	0.293066	−	0.956092i	$-0.405325\pi$
$281$	2.88185	+	0.612556i	0.171917	+	0.0365421i	−0.121149	+	0.992634i	$0.538658\pi$
$282$	−3.46011	−	5.99309i	−0.206047	−	0.356883i
$283$	3.35793	−	3.72936i	0.199608	−	0.221687i	−0.635028	−	0.772489i	$-0.719011\pi$
$283$	3.35793	−	3.72936i	0.199608	−	0.221687i	0.834636	+	0.550802i	$0.185678\pi$
$284$	−7.64473	−	5.55422i	−0.453631	−	0.329582i
$285$	0.162196	+	13.9168i	0.00960766	+	0.824361i
$286$	−7.22075	+	5.24618i	−0.426972	+	0.310213i
$287$	−0.349872	+	3.32881i	−0.0206523	+	0.196493i
$288$	−0.100453	+	0.955746i	−0.00591925	+	0.0563179i
$289$	1.74954	+	16.6458i	0.102914	+	0.979165i
$290$	8.14194	−	14.5274i	0.478111	−	0.853075i
$291$	12.4625	−	5.54867i	0.730566	−	0.325269i
$292$	−0.191178	−	0.588386i	−0.0111879	−	0.0344327i
$293$	−5.62169			−0.328423			−0.164211	−	0.986425i	$-0.552508\pi$
$293$	−5.62169			−0.328423			−0.164211	+	0.986425i	$0.552508\pi$
$294$	7.68328	+	1.63313i	0.448098	+	0.0952461i
$295$	10.0863	−	7.52669i	0.587248	−	0.438221i
$296$	0.560532	−	1.72514i	0.0325803	−	0.100272i
$297$	5.20629	−	16.0233i	0.302100	−	0.929767i
$298$	0.960721	+	9.14065i	0.0556531	+	0.529504i
$299$	−0.463337	−	0.802523i	−0.0267955	−	0.0464111i
$300$	−4.64038	+	5.42601i	−0.267912	+	0.313271i
$301$	0.259540	+	0.449537i	0.0149597	+	0.0259109i
$302$	−10.5317	−	4.68903i	−0.606033	−	0.269823i
$303$	2.27133	−	6.99043i	0.130484	−	0.401590i
$304$	−3.77733	+	2.17526i	−0.216645	+	0.124760i
$305$	−11.0503	+	12.5921i	−0.632736	+	0.721023i
$306$	−0.329464	+	0.365907i	−0.0188342	+	0.0209175i
$307$	12.5946	+	21.8145i	0.718812	+	1.24502i	0.961471	+	0.274908i	$0.0886473\pi$
$307$	12.5946	+	21.8145i	0.718812	+	1.24502i	−0.242658	+	0.970112i	$0.578019\pi$
$308$	3.56739	+	0.758273i	0.203271	+	0.0432066i
$309$	1.52612	−	14.5201i	0.0868179	−	0.826017i
$310$	−0.100925	+	0.0753129i	−0.00573215	+	0.00427748i
$311$	−14.8661	+	10.8008i	−0.842977	+	0.612459i	−0.923201	−	0.384318i	$-0.874437\pi$
$311$	−14.8661	+	10.8008i	−0.842977	+	0.612459i	0.0802236	+	0.996777i	$0.474437\pi$
$312$	3.46144	+	2.51489i	0.195966	+	0.142377i
$313$	−24.2137	+	10.7807i	−1.36864	+	0.609358i	−0.953774	−	0.300524i	$-0.902839\pi$
$313$	−24.2137	+	10.7807i	−1.36864	+	0.609358i	−0.414867	+	0.909882i	$0.636172\pi$
$314$	−0.970494	−	9.23364i	−0.0547682	−	0.521084i
$315$	2.41704	+	1.03937i	0.136185	+	0.0585621i
$316$	9.52672	+	6.92156i	0.535920	+	0.389368i
$317$	−31.5762	−	6.71172i	−1.77349	−	0.376968i	−0.798992	−	0.601342i	$-0.794633\pi$
$317$	−31.5762	−	6.71172i	−1.77349	−	0.376968i	−0.974503	+	0.224374i	$0.927966\pi$
$318$	5.41043	+	9.37114i	0.303402	+	0.525507i
$319$	−21.6997	−	4.61242i	−1.21495	−	0.258246i
$320$	−2.19296	−	0.436951i	−0.122590	−	0.0244263i
$321$	22.7715	−	4.84023i	1.27098	−	0.270155i
$322$	−0.117012	+	0.360126i	−0.00652083	+	0.0200691i
$323$	−2.22080	−	0.235907i	−0.123569	−	0.0131262i
$324$	−5.19343			−0.288524
$325$	−4.99179	−	14.1257i	−0.276895	−	0.783551i
$326$	−6.01840	−	10.4242i	−0.333328	−	0.577342i
$327$	1.93188	+	18.3806i	0.106833	+	1.01645i
$328$	−2.67402	+	0.568381i	−0.147648	+	0.0313836i
$329$	−3.97043	−	4.40961i	−0.218897	−	0.243110i
$330$	8.73738	+	3.75725i	0.480977	+	0.206830i
$331$	4.31229	+	13.2719i	0.237025	+	0.729488i	0.996846	+	0.0793560i	$0.0252864\pi$
$331$	4.31229	+	13.2719i	0.237025	+	0.729488i	−0.759821	+	0.650132i	$0.774714\pi$
$332$	7.50819	−	13.0046i	0.412065	−	0.713718i
$333$	−1.70510	−	0.362431i	−0.0934391	−	0.0198611i
$334$	3.56302	+	2.58869i	0.194960	+	0.141647i
$335$	5.63961	+	9.48637i	0.308125	+	0.518296i
$336$	−0.182749	−	1.73874i	−0.00996980	−	0.0948563i
$337$	−3.35208	+	31.8929i	−0.182599	+	1.73732i	0.392958	+	0.919556i	$0.371452\pi$
$337$	−3.35208	+	31.8929i	−0.182599	+	1.73732i	−0.575557	+	0.817761i	$0.695215\pi$
$338$	3.67419	−	1.63585i	0.199849	−	0.0889787i
$339$	2.40690	+	1.07162i	0.130725	+	0.0582025i
$340$	−0.777397	−	0.841534i	−0.0421603	−	0.0456386i
$341$	0.135715	+	0.0986026i	0.00734937	+	0.00533963i
$342$	2.45844	+	3.39166i	0.132937	+	0.183400i
$343$	15.3058			0.826435
$344$	−0.283682	+	0.315061i	−0.0152951	+	0.0169869i
$345$	−0.482784	+	0.861413i	−0.0259922	+	0.0463769i
$346$	10.5512	+	11.7183i	0.567238	+	0.629982i
$347$	30.3515	−	6.45140i	1.62935	−	0.346330i	0.699606	−	0.714529i	$-0.253359\pi$
$347$	30.3515	−	6.45140i	1.62935	−	0.346330i	0.929747	+	0.368200i	$0.120026\pi$
$348$	1.11163	+	10.5764i	0.0595895	+	0.566956i
$349$	31.6070			1.69188			0.845942	−	0.533275i	$-0.179039\pi$
$349$	31.6070			1.69188			0.845942	+	0.533275i	$0.179039\pi$
$350$	−2.92461	+	5.37809i	−0.156327	+	0.287471i
$351$	8.47375	−	14.6770i	0.452295	−	0.783399i
$352$	0.311363	+	2.96242i	0.0165957	+	0.157898i
$353$	−3.62978	+	11.1713i	−0.193194	+	0.594589i	0.806799	+	0.590826i	$0.201198\pi$
$353$	−3.62978	+	11.1713i	−0.193194	+	0.594589i	−0.999993	+	0.00376312i	$0.998802\pi$
$354$	−2.48349	+	7.64338i	−0.131996	+	0.406241i
$355$	−17.2513	−	12.2004i	−0.915602	−	0.647532i
$356$	−11.1064	+	12.3349i	−0.588640	+	0.653751i
$357$	0.447878	−	0.775748i	0.0237042	−	0.0410570i
$358$	6.21410	−	6.90146i	0.328426	−	0.364754i
$359$	2.33078	−	22.1759i	0.123014	−	1.17040i	−0.742618	−	0.669715i	$-0.766416\pi$
$359$	2.33078	−	22.1759i	0.123014	−	1.17040i	0.865632	−	0.500681i	$-0.166917\pi$
$360$	−0.197325	+	2.13981i	−0.0103999	+	0.112778i
$361$	−5.91140	+	18.0570i	−0.311127	+	0.950368i
$362$	−4.56712	−	3.31820i	−0.240042	−	0.174401i
$363$	−0.317491	+	3.02072i	−0.0166639	+	0.158547i
$364$	3.35148	+	1.49217i	0.175665	+	0.0782112i
$365$	−0.444245	−	1.31011i	−0.0232528	−	0.0685742i
$366$	1.11829	−	10.6398i	0.0584540	−	0.556153i
$367$	−10.1002	−	2.14687i	−0.527229	−	0.112066i	−0.0633955	−	0.997988i	$-0.520193\pi$
$367$	−10.1002	−	2.14687i	−0.527229	−	0.112066i	−0.463833	+	0.885923i	$0.653526\pi$
$368$	−0.309268			−0.0161217
$369$	0.811841	+	2.49859i	0.0422628	+	0.130071i
$370$	1.20405	−	3.87321i	0.0625956	−	0.201359i
$371$	6.20839	+	6.89512i	0.322324	+	0.357977i
$372$	0.0248500	−	0.0764805i	0.00128841	−	0.00396533i
$373$	−3.17971	+	2.31019i	−0.164639	+	0.119617i	−0.667054	−	0.745009i	$-0.732445\pi$
$373$	−3.17971	+	2.31019i	−0.164639	+	0.119617i	0.502415	+	0.864627i	$0.332445\pi$
$374$	−0.763082	+	1.32170i	−0.0394581	+	0.0683434i
$375$	−10.2205	+	12.2644i	−0.527785	+	0.633330i
$376$	2.42316	−	4.19704i	0.124965	−	0.216446i
$377$	−20.3864	−	9.07660i	−1.04995	−	0.467468i
$378$	−6.77379	+	1.43981i	−0.348406	+	0.0740560i
$379$	10.2568	−	31.5672i	0.526857	−	1.62150i	−0.233757	−	0.972295i	$-0.575102\pi$
$379$	10.2568	−	31.5672i	0.526857	−	1.62150i	0.760614	−	0.649204i	$-0.224898\pi$
$380$	−8.38360	+	4.97144i	−0.430070	+	0.255029i
$381$	0.700621	+	2.15629i	0.0358939	+	0.110470i
$382$	8.89994	+	15.4151i	0.455361	+	0.788708i
$383$	21.4969	−	23.8747i	1.09844	−	1.21994i	0.124719	−	0.992192i	$-0.460197\pi$
$383$	21.4969	−	23.8747i	1.09844	−	1.21994i	0.973720	−	0.227748i	$-0.0731361\pi$
$384$	1.30448	−	0.580792i	0.0665690	−	0.0296384i
$385$	7.99792	+	1.59360i	0.407612	+	0.0812174i
$386$	0.160503	+	1.52708i	0.00816937	+	0.0777263i
$387$	0.329615	+	0.239479i	0.0167553	+	0.0121734i
$388$	7.72904	+	5.61548i	0.392383	+	0.285083i
$389$	2.16322	+	20.5817i	0.109680	+	1.04353i	0.901500	+	0.432780i	$0.142467\pi$
$389$	2.16322	+	20.5817i	0.109680	+	1.04353i	−0.791820	+	0.610755i	$0.790866\pi$
$390$	7.81117	+	5.52421i	0.395534	+	0.279729i
$391$	−0.128192	−	0.0931370i	−0.00648295	−	0.00471014i
$392$	1.69987	+	5.23168i	0.0858566	+	0.264240i
$393$	1.92346	−	3.33154i	0.0970259	−	0.168054i
$394$	−16.7493	+	18.6019i	−0.843816	+	0.937152i
$395$	21.4982	+	15.2039i	1.08169	+	0.764993i
$396$	2.80005	−	0.595168i	0.140708	−	0.0299083i
$397$	3.15194	−	0.669965i	0.158191	−	0.0336246i	−0.128135	−	0.991757i	$-0.540899\pi$
$397$	3.15194	−	0.669965i	0.158191	−	0.0336246i	0.286326	+	0.958132i	$0.407566\pi$
$398$	−4.18073	+	3.03748i	−0.209561	+	0.152255i
$399$	−5.65767	−	5.10556i	−0.283238	−	0.255598i
$400$	−4.91568	−	0.914386i	−0.245784	−	0.0457193i
$401$	0.895123	+	1.55040i	0.0447003	+	0.0774232i	0.887510	−	0.460789i	$-0.152433\pi$
$401$	0.895123	+	1.55040i	0.0447003	+	0.0774232i	−0.842810	+	0.538212i	$0.819100\pi$
$402$	−6.43828	−	2.86651i	−0.321112	−	0.142968i
$403$	0.112912	+	0.125402i	0.00562455	+	0.00624670i
$404$	5.03495	−	1.07021i	0.250498	−	0.0532450i
$405$	−11.6119	+	0.148218i	−0.577000	+	0.00736501i
$406$	2.81782	+	8.67237i	0.139846	+	0.430402i
$407$	−5.40320			−0.267826
$408$	0.715617	+	0.152109i	0.0354283	+	0.00753052i
$409$	−35.5950	+	15.8479i	−1.76006	+	0.783630i	−0.770871	+	0.636991i	$0.780179\pi$
$409$	−35.5950	+	15.8479i	−1.76006	+	0.783630i	−0.989190	+	0.146638i	$0.953155\pi$
$410$	−5.96258	+	1.34715i	−0.294471	+	0.0665310i
$411$	−0.267684	+	0.194484i	−0.0132039	+	0.00959317i
$412$	9.34064	−	4.15872i	0.460180	−	0.204885i
$413$	−0.720311	+	6.85330i	−0.0354442	+	0.337229i
$414$	0.0310669	+	0.295582i	0.00152685	+	0.0145270i
$415$	16.4163	−	29.2910i	0.805845	−	1.43784i
$416$	−0.313204	+	2.97993i	−0.0153561	+	0.146103i
$417$	−1.22869	−	3.78151i	−0.0601691	−	0.185181i
$418$	9.63937	+	8.69871i	0.471477	+	0.425468i
$419$	5.97871	+	18.4006i	0.292079	+	0.898928i	0.984187	+	0.177133i	$0.0566823\pi$
$419$	5.97871	+	18.4006i	0.292079	+	0.898928i	−0.692108	+	0.721794i	$0.743318\pi$
$420$	−0.458230	−	3.88242i	−0.0223593	−	0.189443i
$421$	−28.9405	+	6.15149i	−1.41047	+	0.299805i	−0.849308	−	0.527898i	$-0.822980\pi$
$421$	−28.9405	+	6.15149i	−1.41047	+	0.299805i	−0.561166	+	0.827703i	$0.689647\pi$
$422$	−9.90544	−	11.0011i	−0.482189	−	0.535525i
$423$	−4.25472	−	1.89432i	−0.206872	−	0.0921051i
$424$	−3.78900	+	6.56274i	−0.184010	+	0.318715i
$425$	−1.76219	−	1.85939i	−0.0854786	−	0.0901935i
$426$	13.4931			0.653743
$427$	−0.958874	−	9.12307i	−0.0464031	−	0.441496i
$428$	10.9091	+	12.1158i	0.527313	+	0.585641i
$429$	3.93835	−	12.1210i	0.190146	−	0.585208i
$430$	−0.625289	+	0.712536i	−0.0301541	+	0.0343615i
$431$	−18.7112	−	3.97719i	−0.901288	−	0.191575i	−0.266112	−	0.963942i	$-0.585739\pi$
$431$	−18.7112	−	3.97719i	−0.901288	−	0.191575i	−0.635176	+	0.772368i	$0.719072\pi$
$432$	−2.82803	−	4.89829i	−0.136063	−	0.235669i
$433$	−1.24386	−	0.264392i	−0.0597763	−	0.0127059i	0.177926	−	0.984044i	$-0.443061\pi$
$433$	−1.24386	−	0.264392i	−0.0597763	−	0.0127059i	−0.237703	+	0.971338i	$0.576394\pi$
$434$	0.00720752	−	0.0685749i	0.000345972	−	0.00329170i
$435$	2.78732	+	23.6160i	0.133642	+	1.13230i
$436$	−10.4712	+	7.60777i	−0.501480	+	0.364346i
$437$	−1.00281	+	0.900921i	−0.0479709	+	0.0430969i
$438$	0.714696	+	0.519257i	0.0341495	+	0.0248110i
$439$	27.9007	+	12.4222i	1.33163	+	0.592878i	0.944306	−	0.329067i	$-0.106734\pi$
$439$	27.9007	+	12.4222i	1.33163	+	0.592878i	0.387320	+	0.921945i	$0.373401\pi$
$440$	0.780719	+	6.61475i	0.0372193	+	0.315346i
$441$	4.82940	−	2.15019i	0.229971	−	0.102390i
$442$	−1.02724	+	1.14087i	−0.0488608	+	0.0542654i
$443$	−0.872437	+	1.51111i	−0.0414507	+	0.0717948i	−0.886006	−	0.463673i	$-0.846531\pi$
$443$	−0.872437	+	1.51111i	−0.0414507	+	0.0717948i	0.844556	+	0.535468i	$0.179865\pi$
$444$	0.800401	+	2.46338i	0.0379854	+	0.116907i
$445$	−24.4807	+	27.8965i	−1.16050	+	1.32242i
$446$	−1.53769	−	1.70778i	−0.0728118	−	0.0808657i
$447$	−8.78175	−	9.75312i	−0.415363	−	0.461307i
$448$	0.990539	−	0.719669i	0.0467986	−	0.0340011i
$449$	5.74838			0.271283			0.135641	−	0.990758i	$-0.456691\pi$
$449$	5.74838			0.271283			0.135641	+	0.990758i	$0.456691\pi$
$450$	−0.380127	+	4.78999i	−0.0179193	+	0.225802i
$451$	4.07158	+	7.05219i	0.191723	+	0.332074i
$452$	0.192866	+	1.83499i	0.00907164	+	0.0863109i
$453$	16.1021	−	3.42260i	0.756541	−	0.160808i
$454$	−7.66746	+	1.62977i	−0.359852	+	0.0764888i
$455$	7.53611	+	3.24068i	0.353298	+	0.151925i
$456$	2.53792	−	5.68329i	0.118849	−	0.266144i
$457$	−7.24468			−0.338892			−0.169446	−	0.985539i	$-0.554198\pi$
$457$	−7.24468			−0.338892			−0.169446	+	0.985539i	$0.554198\pi$
$458$	−9.54194	+	10.5974i	−0.445866	+	0.495184i
$459$	0.302912	−	2.88202i	0.0141387	−	0.134521i
$460$	−0.691488	+	0.00882636i	−0.0322408	+	0.000411531i
$461$	2.48443	+	1.10614i	0.115711	+	0.0515180i	0.463776	−	0.885953i	$-0.346494\pi$
$461$	2.48443	+	1.10614i	0.115711	+	0.0515180i	−0.348064	+	0.937471i	$0.613161\pi$
$462$	−4.75756	+	2.11820i	−0.221342	+	0.0985477i
$463$	−1.65967	−	1.20582i	−0.0771315	−	0.0560393i	0.548551	−	0.836117i	$-0.315180\pi$
$463$	−1.65967	−	1.20582i	−0.0771315	−	0.0560393i	−0.625683	+	0.780078i	$0.715180\pi$
$464$	−6.02525	+	4.37760i	−0.279715	+	0.203225i
$465$	0.0533791	−	0.171711i	0.00247540	−	0.00796291i
$466$	−22.6923	+	10.1033i	−1.05120	+	0.468025i
$467$	5.29749	+	16.3040i	0.245139	+	0.754459i	0.995614	+	0.0935602i	$0.0298248\pi$
$467$	5.29749	+	16.3040i	0.245139	+	0.754459i	−0.750475	+	0.660899i	$0.770175\pi$
$468$	2.87952			0.133106
$469$	−5.91086	−	1.25639i	−0.272938	−	0.0580148i
$470$	5.29813	−	9.45326i	0.244385	−	0.436046i
$471$	8.87109	+	9.85234i	0.408758	+	0.453972i
$472$	−5.50524	+	1.17017i	−0.253399	+	0.0538617i
$473$	1.15368	+	0.513649i	0.0530461	+	0.0236176i
$474$	−16.8149			−0.772332
$475$	−18.6029	+	11.3548i	−0.853560	+	0.520995i
$476$	0.627311			0.0287527
$477$	6.65293	+	2.96207i	0.304617	+	0.135624i
$478$	18.7737	−	3.99047i	0.858689	−	0.182520i
$479$	6.82008	+	7.57447i	0.311617	+	0.346086i	0.878526	−	0.477694i	$-0.158527\pi$
$479$	6.82008	+	7.57447i	0.311617	+	0.346086i	−0.566909	+	0.823781i	$0.691861\pi$
$480$	2.90009	−	1.33581i	0.132371	−	0.0609713i
$481$	−5.31636	−	1.13003i	−0.242405	−	0.0515248i
$482$	−0.552965			−0.0251869
$483$	−0.167085	−	0.514236i	−0.00760265	−	0.0233985i
$484$	−1.94321	+	0.865172i	−0.0883276	+	0.0393260i
$485$	17.4415	+	12.3350i	0.791979	+	0.560103i
$486$	−7.72797	+	5.61470i	−0.350548	+	0.254688i
$487$	11.0300	+	8.01378i	0.499818	+	0.363139i	0.808947	−	0.587881i	$-0.200038\pi$
$487$	11.0300	+	8.01378i	0.499818	+	0.363139i	−0.309130	+	0.951020i	$0.600038\pi$
$488$	6.84452	−	3.04738i	0.309837	−	0.137948i
$489$	15.7018	+	6.99088i	0.710059	+	0.316138i
$490$	3.95004	+	11.6489i	0.178444	+	0.526244i
$491$	1.49564	−	14.2301i	0.0674975	−	0.642196i	−0.907511	−	0.420028i	$-0.862020\pi$
$491$	1.49564	−	14.2301i	0.0674975	−	0.642196i	0.975009	−	0.222168i	$-0.0713132\pi$
$492$	2.61203	−	2.90096i	0.117760	−	0.130785i
$493$	−3.81581			−0.171855
$494$	7.66520	+	10.5749i	0.344874	+	0.475787i
$495$	6.24360	−	1.41064i	0.280629	−	0.0634036i
$496$	0.0550860	−	0.0117089i	0.00247344	−	0.000525745i
$497$	11.3168	−	2.40546i	0.507627	−	0.107899i
$498$	2.24134	+	21.3249i	0.100437	+	0.955591i
$499$	−10.7335	−	18.5910i	−0.480499	−	0.832249i	0.519251	−	0.854622i	$-0.326211\pi$
$499$	−10.7335	−	18.5910i	−0.480499	−	0.832249i	−0.999750	+	0.0223731i	$0.992878\pi$
$500$	−11.0170	−	1.90417i	−0.492695	−	0.0851572i
$501$	−6.28881			−0.280963
$502$	1.44290	−	1.04833i	0.0643999	−	0.0467892i
$503$	8.36633	+	9.29176i	0.373036	+	0.414299i	0.900208	−	0.435460i	$-0.143414\pi$
$503$	8.36633	+	9.29176i	0.373036	+	0.414299i	−0.527172	+	0.849759i	$0.676748\pi$
$504$	−0.787323	−	0.874411i	−0.0350702	−	0.0389494i
$505$	11.2270	−	2.53656i	0.499596	−	0.112876i
$506$	0.284675	+	0.876141i	0.0126554	+	0.0389492i
$507$	−2.87150	+	4.97358i	−0.127528	+	0.220885i
$508$	−1.06244	+	1.17996i	−0.0471382	+	0.0523522i
$509$	−8.90679	+	3.96556i	−0.394786	+	0.175770i	−0.594522	−	0.804080i	$-0.702659\pi$
$509$	−8.90679	+	3.96556i	−0.394786	+	0.175770i	0.199735	+	0.979850i	$0.435992\pi$
$510$	1.60438	+	0.319675i	0.0710431	+	0.0141555i
$511$	0.691990	+	0.308094i	0.0306118	+	0.0136293i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−23.4390	−	7.64457i	−1.03486	−	0.337516i
$514$	0.0436018	−	0.0316785i	0.00192319	−	0.00139728i
$515$	20.7659	−	9.56500i	0.915055	−	0.421484i
$516$	0.0632795	−	0.602064i	0.00278572	−	0.0265044i
$517$	−14.1205	−	3.00140i	−0.621018	−	0.132001i
$518$	1.11046	+	1.92337i	0.0487907	+	0.0845080i
$519$	−22.0244	−	4.68144i	−0.966765	−	0.205492i
$520$	−0.615242	+	6.67173i	−0.0269801	+	0.292575i
$521$	2.51977	−	7.75506i	0.110393	−	0.339755i	−0.880565	−	0.473925i	$-0.842837\pi$
$521$	2.51977	−	7.75506i	0.110393	−	0.339755i	0.990958	+	0.134170i	$0.0428367\pi$
$522$	4.78913	+	5.31887i	0.209614	+	0.232800i
$523$	3.64333	+	34.6640i	0.159312	+	1.51575i	0.723627	+	0.690191i	$0.242474\pi$
$523$	3.64333	+	34.6640i	0.159312	+	1.51575i	−0.564315	+	0.825560i	$0.690860\pi$
$524$	2.69406			0.117690
$525$	−1.13535	−	8.66757i	−0.0495508	−	0.378284i
$526$	−11.3808	+	19.7121i	−0.496225	+	0.859488i
$527$	0.0263594	+	0.0117360i	0.00114824	+	0.000511227i
$528$	−2.84611	−	3.16092i	−0.123861	−	0.137561i
$529$	22.4038	−	4.76208i	0.974080	−	0.207047i
$530$	−8.28447	+	14.7817i	−0.359854	+	0.642074i
$531$	1.67141	+	5.14406i	0.0725329	+	0.223233i
$532$	1.11540	−	5.21906i	0.0483587	−	0.226275i
$533$	2.53125	+	7.79039i	0.109641	+	0.337439i
$534$	2.47746	−	23.5714i	0.107210	−	1.02003i
$535$	24.7374	+	26.7783i	1.06949	+	1.15773i
$536$	−0.515901	−	4.90847i	−0.0222836	−	0.212014i
$537$	−1.38615	+	13.1883i	−0.0598167	+	0.569118i
$538$	5.74486	−	2.55778i	0.247679	−	0.110274i
$539$	13.2564	−	9.63132i	0.570993	−	0.414850i
$540$	−6.46294	−	10.8713i	−0.278121	−	0.467826i
$541$	24.6951	−	10.9949i	1.06172	−	0.472710i	0.199846	−	0.979827i	$-0.435956\pi$
$541$	24.6951	−	10.9949i	1.06172	−	0.472710i	0.861877	+	0.507118i	$0.169289\pi$
$542$	−9.22994	−	1.96188i	−0.396460	−	0.0842701i
$543$	8.06106			0.345933
$544$	0.158326	+	0.487276i	0.00678815	+	0.0208918i
$545$	−23.1953	+	17.3090i	−0.993577	+	0.741434i
$546$	−5.12410	+	1.08916i	−0.219291	+	0.0466118i
$547$	11.1239	+	12.3544i	0.475624	+	0.528234i	0.932439	−	0.361328i	$-0.117676\pi$
$547$	11.1239	+	12.3544i	0.475624	+	0.528234i	−0.456815	+	0.889562i	$0.651010\pi$
$548$	−0.211684	−	0.0942476i	−0.00904267	−	0.00402606i
$549$	−3.60007	−	6.23551i	−0.153647	−	0.266125i
$550$	1.93438	+	14.7675i	0.0824822	+	0.629690i
$551$	−6.78475	+	31.7465i	−0.289040	+	1.35245i
$552$	0.357273	−	0.259574i	0.0152065	−	0.0110482i
$553$	−14.1028	+	2.99763i	−0.599710	+	0.127472i
$554$	−13.7225	+	2.91681i	−0.583014	+	0.123923i
$555$	1.85991	+	5.48500i	0.0789488	+	0.232825i
$556$	1.86321	−	2.06931i	0.0790178	−	0.0877582i
$557$	−13.0204	+	22.5520i	−0.551691	+	0.955558i	0.446461	+	0.894803i	$0.352684\pi$
$557$	−13.0204	+	22.5520i	−0.551691	+	0.955558i	−0.998153	+	0.0607547i	$0.980649\pi$
$558$	−0.0167243	−	0.0514721i	−0.000707996	−	0.00217899i
$559$	1.02771	+	0.746675i	0.0434675	+	0.0315810i
$560$	2.19419	−	1.63737i	0.0927216	−	0.0691914i
$561$	−0.227795	−	2.16732i	−0.00961750	−	0.0915044i
$562$	−2.38355	−	1.73175i	−0.100544	−	0.0730496i
$563$	29.0049	+	21.0733i	1.22241	+	0.888134i	0.996298	−	0.0859665i	$-0.0273978\pi$
$563$	29.0049	+	21.0733i	1.22241	+	0.888134i	0.226114	+	0.974101i	$0.427398\pi$
$564$	0.723360	+	6.88231i	0.0304590	+	0.289798i
$565$	0.483596	+	4.09733i	0.0203450	+	0.172376i
$566$	−4.58449	+	2.04115i	−0.192700	+	0.0857957i
$567$	4.25480	−	4.72543i	0.178685	−	0.198449i
$568$	4.72470	+	8.18343i	0.198244	+	0.343369i
$569$	0.782955	+	2.40969i	0.0328232	+	0.101019i	0.966126	−	0.258071i	$-0.0830869\pi$
$569$	0.782955	+	2.40969i	0.0328232	+	0.101019i	−0.933303	+	0.359091i	$0.883087\pi$
$570$	5.51230	−	12.7796i	0.230885	−	0.535279i
$571$	10.0746	−	31.0063i	0.421607	−	1.29757i	−0.484599	−	0.874736i	$-0.661034\pi$
$571$	10.0746	−	31.0063i	0.421607	−	1.29757i	0.906206	−	0.422836i	$-0.138966\pi$
$572$	8.73030	−	1.85568i	0.365032	−	0.0775900i
$573$	−23.2196	−	10.3380i	−0.970013	−	0.431877i
$574$	1.67357	−	2.89871i	0.0698535	−	0.120990i
$575$	−1.54584	+	0.0394695i	−0.0644658	+	0.00164599i
$576$	0.480505	−	0.832260i	0.0200211	−	0.0346775i
$577$	−16.9760	+	12.3338i	−0.706722	+	0.513463i	−0.882114	−	0.471035i	$-0.843880\pi$
$577$	−16.9760	+	12.3338i	−0.706722	+	0.513463i	0.175393	+	0.984499i	$0.443880\pi$
$578$	5.17217	−	15.9183i	0.215134	−	0.662114i
$579$	−1.46712	−	1.62940i	−0.0609715	−	0.0677157i
$580$	−13.3468	+	9.95977i	−0.554197	+	0.413557i
$581$	5.68148	+	17.4858i	0.235707	+	0.725433i
$582$	−13.6419			−0.565476
$583$	22.0796	+	4.69316i	0.914444	+	0.194371i
$584$	−0.0646682	+	0.615276i	−0.00267599	+	0.0254603i
$585$	6.43828	−	0.0821803i	0.266190	−	0.00339774i
$586$	5.13567	+	2.28655i	0.212153	+	0.0944564i
$587$	2.43802	−	23.1962i	0.100628	−	0.957409i	−0.821417	−	0.570327i	$-0.806816\pi$
$587$	2.43802	−	23.1962i	0.100628	−	0.957409i	0.922045	−	0.387082i	$-0.126517\pi$
$588$	−6.35477	−	4.61701i	−0.262066	−	0.190402i
$589$	0.144509	−	0.198436i	0.00595439	−	0.00817643i
$590$	−12.2757	+	2.77349i	−0.505382	+	0.114183i
$591$	3.73617	−	35.5473i	0.153686	−	1.46222i
$592$	−1.21375	+	1.34800i	−0.0498848	+	0.0554027i
$593$	−2.58058	+	4.46970i	−0.105972	+	0.183549i	−0.914135	−	0.405410i	$-0.867129\pi$
$593$	−2.58058	+	4.46970i	−0.105972	+	0.183549i	0.808163	+	0.588959i	$0.200462\pi$
$594$	−11.2735	+	12.5204i	−0.462555	+	0.513720i
$595$	1.40260	−	0.0179032i	0.0575008	−	0.000733958i
$596$	2.84018	−	8.74116i	0.116338	−	0.358052i
$597$	2.28026	−	7.01792i	0.0933248	−	0.287224i
$598$	0.0968638	+	0.921598i	0.00396106	+	0.0376869i
$599$	−6.22300	+	10.7786i	−0.254265	+	0.440400i	−0.964696	−	0.263367i	$-0.915167\pi$
$599$	−6.22300	+	10.7786i	−0.254265	+	0.440400i	0.710431	+	0.703767i	$0.248500\pi$
$600$	6.44616	−	3.06950i	0.263163	−	0.125312i
$601$	42.5401			1.73525			0.867623	−	0.497223i	$-0.165647\pi$
$601$	42.5401			1.73525			0.867623	+	0.497223i	$0.165647\pi$
$602$	−0.0542587	−	0.516237i	−0.00221142	−	0.0210402i
$603$	−4.63943	+	0.986142i	−0.188932	+	0.0401588i
$604$	7.71402	+	8.56729i	0.313879	+	0.348598i
$605$	−4.32010	+	1.98988i	−0.175637	+	0.0809003i
$606$	−4.91823	+	5.46225i	−0.199789	+	0.221889i
$607$	−39.4762			−1.60229			−0.801145	−	0.598471i	$-0.795775\pi$
$607$	−39.4762			−1.60229			−0.801145	+	0.598471i	$0.795775\pi$
$608$	4.33552	−	0.450819i	0.175829	−	0.0182831i
$609$	−10.5341	−	7.65345i	−0.426862	−	0.310134i
$610$	15.2166	−	7.00893i	0.616102	−	0.283783i
$611$	−13.2658	−	5.90634i	−0.536679	−	0.238945i
$612$	0.449808	−	0.200267i	0.0181824	−	0.00809533i
$613$	0.143078	−	1.36130i	0.00577889	−	0.0549824i	−0.991252	−	0.131980i	$-0.957867\pi$
$613$	0.143078	−	1.36130i	0.00577889	−	0.0549824i	0.997031	+	0.0769973i	$0.0245333\pi$
$614$	−2.63299	−	25.0512i	−0.106259	−	1.01099i
$615$	5.75742	−	6.56076i	0.232161	−	0.264555i
$616$	−2.95056	−	2.14371i	−0.118881	−	0.0863724i
$617$	−11.5086	−	2.44623i	−0.463319	−	0.0984816i	−0.0296631	−	0.999560i	$-0.509443\pi$
$617$	−11.5086	−	2.44623i	−0.463319	−	0.0984816i	−0.433656	+	0.901078i	$0.642777\pi$
$618$	−7.30002	+	12.6440i	−0.293650	+	0.508616i
$619$	9.10140	+	28.0112i	0.365816	+	1.12587i	0.949468	+	0.313863i	$0.101623\pi$
$619$	9.10140	+	28.0112i	0.365816	+	1.12587i	−0.583652	+	0.812004i	$0.698377\pi$
$620$	0.122832	−	0.0277519i	0.00493305	−	0.00111454i
$621$	−1.17047	−	1.29994i	−0.0469692	−	0.0521646i
$622$	17.9739	−	3.82047i	0.720688	−	0.153187i
$623$	−2.12428	−	20.2112i	−0.0851076	−	0.809745i
$624$	−2.13929	−	3.70536i	−0.0856402	−	0.148333i
$625$	−24.6871	−	3.94309i	−0.987483	−	0.157724i
$626$	26.5052			1.05936
$627$	−18.4366	−	1.95845i	−0.736286	−	0.0782128i
$628$	−2.86907	+	8.83008i	−0.114488	+	0.352359i
$629$	−0.909057	+	0.193226i	−0.0362465	+	0.00770443i
$630$	−1.78532	−	1.93261i	−0.0711289	−	0.0769972i
$631$	15.3248	+	3.25740i	0.610072	+	0.129675i	0.502580	−	0.864531i	$-0.332384\pi$
$631$	15.3248	+	3.25740i	0.610072	+	0.129675i	0.107493	+	0.994206i	$0.465718\pi$
$632$	−5.88783	−	10.1980i	−0.234205	−	0.405656i
$633$	20.6764	+	4.39490i	0.821813	+	0.174682i
$634$	26.1164	+	18.9747i	1.03721	+	0.753580i
$635$	−2.34182	+	2.66858i	−0.0929323	+	0.105899i
$636$	−1.13109	−	10.7616i	−0.0448505	−	0.426724i
$637$	15.0576	−	6.70409i	0.596605	−	0.265626i
$638$	17.9477	+	13.0397i	0.710554	+	0.516248i
$639$	7.34667	−	5.33767i	0.290630	−	0.211155i
$640$	1.82564	+	1.29113i	0.0721649	+	0.0510365i
$641$	1.33862	−	12.7361i	0.0528722	−	0.503045i	−0.935754	−	0.352653i	$-0.885280\pi$
$641$	1.33862	−	12.7361i	0.0528722	−	0.503045i	0.988626	−	0.150392i	$-0.0480537\pi$
$642$	−22.7715	−	4.84023i	−0.898719	−	0.191029i
$643$	−8.63120	−	14.9497i	−0.340381	−	0.589558i	0.644122	−	0.764923i	$-0.277223\pi$
$643$	−8.63120	−	14.9497i	−0.340381	−	0.589558i	−0.984504	+	0.175365i	$0.943890\pi$
$644$	0.253373	−	0.281399i	0.00998428	−	0.0110887i
$645$	0.124303	−	1.34795i	0.00489443	−	0.0530756i
$646$	1.93285	+	1.11879i	0.0760469	+	0.0440183i
$647$	−2.70137	+	8.31397i	−0.106202	+	0.326856i	−0.990011	−	0.140992i	$-0.954971\pi$
$647$	−2.70137	+	8.31397i	−0.106202	+	0.326856i	0.883809	+	0.467848i	$0.154971\pi$
$648$	4.74443	+	2.11236i	0.186379	+	0.0829812i
$649$	8.38252	+	14.5189i	0.329043	+	0.569918i
$650$	−1.18520	+	14.9348i	−0.0464874	+	0.585790i
$651$	0.0492299	+	0.0852686i	0.00192947	+	0.00334194i
$652$	1.25819	+	11.9709i	0.0492744	+	0.468815i
$653$	−12.8453	+	39.5337i	−0.502674	+	1.54707i	0.301971	+	0.953317i	$0.402355\pi$
$653$	−12.8453	+	39.5337i	−0.502674	+	1.54707i	−0.804645	+	0.593756i	$0.797645\pi$
$654$	5.71122	−	17.5773i	0.223326	−	0.687328i
$655$	6.02360	−	0.0768871i	0.235362	−	0.00300423i
$656$	2.67402	+	0.568381i	0.104403	+	0.0221915i
$657$	0.594544			0.0231954
$658$	1.83362	+	5.64330i	0.0714819	+	0.219999i
$659$	40.2997	−	17.9426i	1.56985	−	0.698944i	0.576830	−	0.816864i	$-0.304289\pi$
$659$	40.2997	−	17.9426i	1.56985	−	0.698944i	0.993023	+	0.117920i	$0.0376227\pi$
$660$	−6.45378	−	6.98623i	−0.251213	−	0.271939i
$661$	−2.39946	−	22.8294i	−0.0933283	−	0.887960i	−0.936583	−	0.350446i	$-0.886030\pi$
$661$	−2.39946	−	22.8294i	−0.0933283	−	0.887960i	0.843255	−	0.537514i	$-0.180637\pi$
$662$	1.45868	−	13.8784i	0.0566932	−	0.539400i
$663$	0.229141	−	2.18013i	0.00889910	−	0.0846693i
$664$	−12.1485	+	8.82640i	−0.471453	+	0.342531i
$665$	2.34496	−	11.7011i	0.0909335	−	0.453748i
$666$	1.41028	+	1.02462i	0.0546471	+	0.0397034i
$667$	−1.54121	+	1.71169i	−0.0596761	+	0.0662770i
$668$	−2.20207	−	3.81410i	−0.0852006	−	0.147572i
$669$	3.20974	+	0.682252i	0.124096	+	0.0263774i
$670$	−1.29358	−	10.9601i	−0.0499754	−	0.423424i
$671$	−14.9333	−	16.5851i	−0.576494	−	0.640262i
$672$	−0.540261	+	1.66275i	−0.0208410	+	0.0641421i
$673$	−10.3466	+	7.51724i	−0.398832	+	0.289768i	−0.769065	−	0.639171i	$-0.779278\pi$
$673$	−10.3466	+	7.51724i	−0.398832	+	0.289768i	0.370233	+	0.928939i	$0.379278\pi$
$674$	16.0343	−	27.7722i	0.617618	−	1.06975i
$675$	−14.7607	−	24.1225i	−0.568138	−	0.928477i
$676$	−4.02190			−0.154688
$677$	3.20007	−	2.32499i	0.122989	−	0.0893565i	−0.524590	−	0.851355i	$-0.675782\pi$
$677$	3.20007	−	2.32499i	0.122989	−	0.0893565i	0.647579	+	0.761998i	$0.275782\pi$
$678$	−1.76295	−	1.95795i	−0.0677055	−	0.0751946i
$679$	−11.4416	+	2.43199i	−0.439088	+	0.0933310i
$680$	0.367905	+	1.08498i	0.0141085	+	0.0416069i
$681$	7.48972	−	8.31817i	0.287007	−	0.318753i
$682$	−0.0838764	−	0.145278i	−0.00321179	−	0.00556299i
$683$	3.59192	+	11.0548i	0.137441	+	0.423000i	0.995962	−	0.0897791i	$-0.0286161\pi$
$683$	3.59192	+	11.0548i	0.137441	+	0.423000i	−0.858521	+	0.512779i	$0.828616\pi$
$684$	−0.866385	−	4.09837i	−0.0331271	−	0.156705i
$685$	−0.475990	−	0.204686i	−0.0181866	−	0.00782063i
$686$	−13.9825	−	6.22542i	−0.533855	−	0.237688i
$687$	2.12847	−	20.2511i	0.0812063	−	0.772626i
$688$	0.387303	−	0.172438i	0.0147658	−	0.00657415i
$689$	20.7432	+	9.23549i	0.790255	+	0.351844i
$690$	0.791413	−	0.590574i	0.0301286	−	0.0224828i
$691$	−17.3424	−	12.6000i	−0.659738	−	0.479328i	0.206837	−	0.978376i	$-0.433683\pi$
$691$	−17.3424	−	12.6000i	−0.659738	−	0.479328i	−0.866574	+	0.499048i	$0.833683\pi$
$692$	−4.87276	−	14.9968i	−0.185235	−	0.570093i
$693$	−1.75245	+	3.03533i	−0.0665699	+	0.115303i
$694$	−30.3515	−	6.45140i	−1.15213	−	0.244892i
$695$	4.10687	−	4.67991i	0.155783	−	0.177519i
$696$	3.28630	−	10.1142i	0.124567	−	0.383377i
$697$	0.937217	+	1.04088i	0.0354996	+	0.0394263i
$698$	−28.8744	−	12.8557i	−1.09291	−	0.486596i
$699$	17.7348	−	30.7175i	0.670791	−	1.16184i
$700$	4.85924	−	3.72359i	0.183662	−	0.140738i
$701$	−6.63575	−	11.4935i	−0.250629	−	0.434102i	0.713070	−	0.701092i	$-0.247304\pi$
$701$	−6.63575	−	11.4935i	−0.250629	−	0.434102i	−0.963699	+	0.266991i	$0.913971\pi$
$702$	−13.7108	+	9.96149i	−0.517481	+	0.375972i
$703$	−0.00877218	+	7.90669i	−0.000330849	+	0.298206i
$704$	0.920481	−	2.83295i	0.0346919	−	0.106771i
$705$	1.81377	+	15.3674i	0.0683105	+	0.578771i
$706$	7.85975	−	8.72913i	0.295805	−	0.328525i
$707$	−3.15119	+	5.45802i	−0.118513	+	0.205270i
$708$	5.37762	−	5.97245i	0.202103	−	0.224459i
$709$	14.4385	−	6.42844i	0.542249	−	0.241425i	−0.117286	−	0.993098i	$-0.537420\pi$
$709$	14.4385	−	6.42844i	0.542249	−	0.241425i	0.659536	+	0.751673i	$0.270753\pi$
$710$	10.7974	+	18.1624i	0.405221	+	0.681621i
$711$	−9.15528	+	6.65170i	−0.343350	+	0.249458i
$712$	15.1633	−	6.75114i	0.568269	−	0.253010i
$713$	0.0159112	−	0.00708411i	0.000595878	−	0.000265302i
$714$	−0.724683	+	0.526513i	−0.0271206	+	0.0197042i
$715$	19.4670	−	4.39825i	0.728024	−	0.164485i
$716$	−8.48394	+	3.77729i	−0.317060	+	0.141164i
$717$	−18.3385	+	20.3670i	−0.684864	+	0.760618i
$718$	−11.1490	+	19.3106i	−0.416077	+	0.720667i
$719$	3.50189	−	3.88924i	0.130598	−	0.145044i	−0.674299	−	0.738459i	$-0.735554\pi$
$719$	3.50189	−	3.88924i	0.130598	−	0.145044i	0.804897	+	0.593415i	$0.202221\pi$
$720$	1.05060	−	1.87455i	0.0391537	−	0.0698604i
$721$	−3.86850	+	11.9060i	−0.144070	+	0.443403i
$722$	12.7448	−	14.0915i	0.474312	−	0.524432i
$723$	0.638797	−	0.464113i	0.0237571	−	0.0172605i
$724$	2.82263	+	4.88894i	0.104902	+	0.181696i
$725$	−29.5578	+	22.6498i	−1.09775	+	0.841193i
$726$	1.51868	−	2.63043i	0.0563635	−	0.0976245i
$727$	−20.4073	−	9.08592i	−0.756865	−	0.336978i	−0.00823515	−	0.999966i	$-0.502621\pi$
$727$	−20.4073	−	9.08592i	−0.756865	−	0.336978i	−0.748630	+	0.662988i	$0.769288\pi$
$728$	−2.45481	−	2.72634i	−0.0909811	−	0.101045i
$729$	9.02957	−	27.7902i	0.334429	−	1.02927i
$730$	−0.127031	+	1.37753i	−0.00470163	+	0.0509848i
$731$	0.212468	+	0.0451615i	0.00785842	+	0.00167036i
$732$	−5.34922	+	9.26512i	−0.197713	+	0.342449i
$733$	−10.5976	−	32.6162i	−0.391433	−	1.20471i	−0.931705	−	0.363216i	$-0.881679\pi$
$733$	−10.5976	−	32.6162i	−0.391433	−	1.20471i	0.540272	−	0.841491i	$-0.318321\pi$
$734$	8.35382	+	6.06941i	0.308345	+	0.224026i
$735$	−14.3403	−	10.1417i	−0.528950	−	0.374084i
$736$	0.282530	+	0.125791i	0.0104142	+	0.00463670i
$737$	−13.4306	+	5.97968i	−0.494722	+	0.220264i
$738$	0.274614	−	2.61278i	0.0101087	−	0.0961778i
$739$	−1.29895	−	0.578328i	−0.0477825	−	0.0212741i	0.382706	−	0.923870i	$-0.374992\pi$
$739$	−1.29895	−	0.578328i	−0.0477825	−	0.0212741i	−0.430489	+	0.902596i	$0.641659\pi$
$740$	−2.67533	+	3.04863i	−0.0983472	+	0.112070i
$741$	−17.7307	−	5.78281i	−0.651354	−	0.212437i
$742$	−2.86715	−	8.82418i	−0.105256	−	0.323946i
$743$	−21.7657	−	37.6993i	−0.798506	−	1.38305i	−0.920589	−	0.390533i	$-0.872291\pi$
$743$	−21.7657	−	37.6993i	−0.798506	−	1.38305i	0.122083	−	0.992520i	$-0.461042\pi$
$744$	−0.0538091	+	0.0597610i	−0.00197274	+	0.00219095i
$745$	6.10084	−	19.6253i	0.223517	−	0.719015i
$746$	3.84445	−	0.817162i	0.140755	−	0.0299184i
$747$	9.65616	+	10.7242i	0.353300	+	0.392380i
$748$	1.23469	−	0.897057i	0.0451449	−	0.0327997i
$749$	−19.9615			−0.729378
$750$	14.3253	−	7.04701i	0.523085	−	0.257321i
$751$	2.24922	−	3.89577i	0.0820753	−	0.142159i	−0.822066	−	0.569392i	$-0.807179\pi$
$751$	2.24922	−	3.89577i	0.0820753	−	0.142159i	0.904141	+	0.427234i	$0.140512\pi$
$752$	−3.92076	+	2.84860i	−0.142975	+	0.103878i
$753$	−0.786990	+	2.42211i	−0.0286795	+	0.0882664i
$754$	14.9321	+	16.5838i	0.543795	+	0.603945i
$755$	17.4922	+	18.9353i	0.636605	+	0.689127i
$756$	6.77379	+	1.43981i	0.246360	+	0.0523655i
$757$	−19.5187	−	33.8073i	−0.709418	−	1.22875i	−0.965073	−	0.261980i	$-0.915625\pi$
$757$	−19.5187	−	33.8073i	−0.709418	−	1.22875i	0.255656	−	0.966768i	$-0.417709\pi$
$758$	−22.2096	+	24.6663i	−0.806689	+	0.895919i
$759$	−1.06422	−	0.773203i	−0.0386288	−	0.0280655i
$760$	9.68087	−	1.13171i	0.351162	−	0.0410516i
$761$	23.6498	−	17.1826i	0.857304	−	0.622868i	−0.0698459	−	0.997558i	$-0.522251\pi$
$761$	23.6498	−	17.1826i	0.857304	−	0.622868i	0.927150	+	0.374690i	$0.122251\pi$
$762$	0.236993	−	2.25484i	0.00858535	−	0.0816842i
$763$	1.65648	−	15.7604i	0.0599688	−	0.570565i
$764$	−1.86059	−	17.7024i	−0.0673139	−	0.640449i
$765$	1.00000	−	0.460612i	0.0361552	−	0.0166535i
$766$	−29.3491	+	13.0671i	−1.06043	+	0.472132i
$767$	5.21130	+	16.0387i	0.188169	+	0.579125i
$768$	−1.42793			−0.0515261
$769$	9.87665	+	2.09935i	0.356161	+	0.0757044i	0.382518	−	0.923948i	$-0.375057\pi$
$769$	9.87665	+	2.09935i	0.356161	+	0.0757044i	−0.0263565	+	0.999653i	$0.508390\pi$
$770$	−6.65829	−	4.70887i	−0.239948	−	0.169696i
$771$	−0.0237813	+	0.0731915i	−0.000856464	+	0.00263593i
$772$	0.474493	−	1.46034i	0.0170774	−	0.0525588i
$773$	−2.37323	−	22.5798i	−0.0853591	−	0.812138i	−0.950524	−	0.310650i	$-0.899453\pi$
$773$	−2.37323	−	22.5798i	−0.0853591	−	0.812138i	0.865165	−	0.501487i	$-0.167214\pi$
$774$	−0.203713	−	0.352842i	−0.00732232	−	0.0126826i
$775$	0.273846	−	0.0655556i	0.00983684	−	0.00235483i
$776$	−4.77681	−	8.27368i	−0.171478	−	0.297008i
$777$	−2.89714	−	1.28989i	−0.103934	−	0.0462745i
$778$	6.39513	−	19.6822i	0.229277	−	0.705641i
$779$	10.3263	−	5.94664i	0.369979	−	0.213060i
$780$	−4.88896	−	8.22371i	−0.175053	−	0.294456i
$781$	18.8342	−	20.9175i	0.673942	−	0.748488i
$782$	0.0792271	+	0.137225i	0.00283315	+	0.00490717i
$783$	−41.2036	−	8.75810i	−1.47250	−	0.312989i
$784$	0.575002	−	5.47078i	0.0205358	−	0.195385i
$785$	−6.16290	+	19.8249i	−0.219963	+	0.707582i
$786$	−3.11223	+	2.26117i	−0.111010	+	0.0806532i
$787$	−16.6122	−	12.0695i	−0.592160	−	0.430230i	0.250927	−	0.968006i	$-0.419265\pi$
$787$	−16.6122	−	12.0695i	−0.592160	−	0.430230i	−0.843088	+	0.537776i	$0.819265\pi$
$788$	22.8673	−	10.1812i	0.814614	−	0.362689i
$789$	−3.39738	−	32.3239i	−0.120950	−	1.15076i
$790$	−13.4556	−	22.6336i	−0.478728	−	0.805267i
$791$	−1.82765	−	1.32786i	−0.0649836	−	0.0472134i
$792$	−2.80005	−	0.595168i	−0.0994953	−	0.0211484i
$793$	−11.2247	−	19.4418i	−0.398601	−	0.690397i
$794$	−3.15194	−	0.669965i	−0.111858	−	0.0237762i
$795$	−2.83611	−	24.0294i	−0.100587	−	0.852235i
$796$	5.05474	−	1.07442i	0.179160	−	0.0380817i
$797$	−2.37631	+	7.31353i	−0.0841732	+	0.259058i	−0.984281	−	0.176608i	$-0.943487\pi$
$797$	−2.37631	+	7.31353i	−0.0841732	+	0.259058i	0.900108	+	0.435667i	$0.143487\pi$
$798$	3.09192	+	6.96534i	0.109453	+	0.246570i
$799$	−2.48303			−0.0878432
$800$	4.11878	+	2.83472i	0.145621	+	0.100222i
$801$	−7.97558	−	13.8141i	−0.281803	−	0.488097i
$802$	−0.187132	−	1.78044i	−0.00660785	−	0.0628695i
$803$	1.80257	−	0.383149i	0.0636114	−	0.0135210i
$804$	4.71575	+	5.23737i	0.166312	+	0.184708i
$805$	0.558481	−	0.636407i	0.0196839	−	0.0224304i
$806$	−0.0521449	−	0.160485i	−0.00183673	−	0.00565286i
$807$	−4.48980	+	7.77656i	−0.158048	+	0.273748i
$808$	−5.03495	−	1.07021i	−0.177129	−	0.0376499i
$809$	43.3169	+	31.4716i	1.52294	+	1.10648i	0.960006	+	0.279979i	$0.0903276\pi$
$809$	43.3169	+	31.4716i	1.52294	+	1.10648i	0.562934	+	0.826502i	$0.309672\pi$
$810$	10.6683	+	4.58758i	0.374846	+	0.161191i
$811$	−1.72748	−	16.4359i	−0.0606601	−	0.577142i	−0.982066	−	0.188540i	$-0.939625\pi$
$811$	−1.72748	−	16.4359i	−0.0606601	−	0.577142i	0.921405	−	0.388603i	$-0.127042\pi$
$812$	0.953160	−	9.06871i	0.0334494	−	0.318249i
$813$	12.3093	−	5.48044i	0.431705	−	0.192207i
$814$	4.93606	+	2.19768i	0.173009	+	0.0770286i
$815$	3.15481	+	26.7296i	0.110508	+	0.936296i
$816$	−0.591880	−	0.430026i	−0.0207200	−	0.0150539i
$817$	0.753514	−	1.68738i	0.0263621	−	0.0590340i
$818$	38.9636			1.36233
$819$	−2.35909	+	2.62004i	−0.0824334	+	0.0915516i
$820$	5.99503	+	1.19452i	0.209355	+	0.0417144i
$821$	−20.2984	−	22.5436i	−0.708419	−	0.786779i	0.276274	−	0.961079i	$-0.410900\pi$
$821$	−20.2984	−	22.5436i	−0.708419	−	0.786779i	−0.984693	+	0.174300i	$0.944234\pi$
$822$	0.323645	−	0.0687929i	0.0112884	−	0.00239943i
$823$	−1.01046	−	9.61391i	−0.0352225	−	0.335120i	−0.997916	−	0.0645257i	$-0.979447\pi$
$823$	−1.01046	−	9.61391i	−0.0352225	−	0.335120i	0.962694	−	0.270594i	$-0.0872201\pi$
$824$	−10.2246			−0.356191
$825$	−14.6293	−	15.4362i	−0.509327	−	0.537420i
$826$	3.44553	−	5.96783i	0.119885	−	0.207647i
$827$	2.92810	+	27.8590i	0.101820	+	0.968753i	0.919503	+	0.393084i	$0.128592\pi$
$827$	2.92810	+	27.8590i	0.101820	+	0.968753i	−0.817683	+	0.575669i	$0.804742\pi$
$828$	0.0918429	−	0.282663i	0.00319176	−	0.00982323i
$829$	−5.91878	+	18.2161i	−0.205568	+	0.632673i	0.794122	+	0.607759i	$0.207931\pi$
$829$	−5.91878	+	18.2161i	−0.205568	+	0.632673i	−0.999690	+	0.0249139i	$0.992069\pi$
$830$	−26.9108	+	20.0815i	−0.934086	+	0.697041i
$831$	13.4044	−	14.8871i	0.464994	−	0.516428i
$832$	1.49817	−	2.59491i	0.0519398	−	0.0899624i
$833$	1.88588	−	2.09448i	0.0653419	−	0.0725695i
$834$	−0.415617	+	3.95433i	−0.0143916	+	0.136927i
$835$	−5.03243	−	8.46504i	−0.174154	−	0.292945i
$836$	−5.26792	−	11.8674i	−0.182195	−	0.410441i
$837$	0.257696	+	0.187227i	0.00890729	+	0.00647153i
$838$	2.02237	−	19.2415i	0.0698615	−	0.664688i
$839$	38.1713	+	16.9949i	1.31782	+	0.586731i	0.940639	−	0.339409i	$-0.110227\pi$
$839$	38.1713	+	16.9949i	1.31782	+	0.586731i	0.377180	+	0.926140i	$0.376894\pi$
$840$	−1.16051	+	3.73314i	−0.0400413	+	0.128806i
$841$	−2.76656	+	26.3220i	−0.0953985	+	0.907656i
$842$	28.9405	+	6.15149i	0.997355	+	0.211994i
$843$	4.20702			0.144897
$844$	4.57452	+	14.0789i	0.157461	+	0.484616i
$845$	−8.99251	+	0.114783i	−0.309352	+	0.00394866i
$846$	3.11639	+	3.46110i	0.107144	+	0.118995i
$847$	0.804795	−	2.47691i	0.0276531	−	0.0851075i
$848$	6.13073	−	4.45423i	0.210530	−	0.152959i
$849$	3.58293	−	6.20581i	0.122966	−	0.212983i
$850$	0.853557	+	2.41538i	0.0292768	+	0.0828469i
$851$	−0.280494	+	0.485829i	−0.00961519	+	0.0166540i
$852$	−12.3266	−	5.48814i	−0.422301	−	0.188021i
$853$	−6.26406	+	1.33147i	−0.214477	+	0.0455886i	−0.313897	−	0.949457i	$-0.601635\pi$
$853$	−6.26406	+	1.33147i	−0.214477	+	0.0455886i	0.0994197	+	0.995046i	$0.468301\pi$
$854$	−2.83471	+	8.72435i	−0.0970019	+	0.298541i
$855$	−2.05410	−	9.13877i	−0.0702489	−	0.312539i
$856$	−5.03805	−	15.5055i	−0.172197	−	0.529967i
$857$	23.3278	+	40.4049i	0.796862	+	1.38021i	0.921650	+	0.388022i	$0.126842\pi$
$857$	23.3278	+	40.4049i	0.796862	+	1.38021i	−0.124788	+	0.992183i	$0.539825\pi$
$858$	−8.52792	+	9.47122i	−0.291138	+	0.323342i
$859$	−8.86438	+	3.94667i	−0.302449	+	0.134659i	−0.552350	−	0.833613i	$-0.686269\pi$
$859$	−8.86438	+	3.94667i	−0.302449	+	0.134659i	0.249901	+	0.968271i	$0.419602\pi$
$860$	0.861044	−	0.396606i	0.0293614	−	0.0135242i
$861$	0.499593	+	4.75331i	0.0170261	+	0.161992i
$862$	15.4759	+	11.2439i	0.527110	+	0.382968i
$863$	−18.1917	−	13.2171i	−0.619254	−	0.449915i	0.233407	−	0.972379i	$-0.425013\pi$
$863$	−18.1917	−	13.2171i	−0.619254	−	0.449915i	−0.852661	+	0.522465i	$0.825013\pi$
$864$	0.591219	+	5.62507i	0.0201137	+	0.191369i
$865$	−11.3229	−	33.3921i	−0.384992	−	1.13537i
$866$	1.02879	+	0.747459i	0.0349597	+	0.0253997i
$867$	7.38551	+	22.7303i	0.250825	+	0.771960i
$868$	−0.0344763	+	0.0597148i	−0.00117020	+	0.00202685i
$869$	−23.4709	+	26.0670i	−0.796195	+	0.884264i
$870$	7.05914	−	22.7080i	0.239327	−	0.769872i
$871$	−14.4653	+	3.07470i	−0.490140	+	0.104182i
$872$	12.6603	−	2.69103i	0.428731	−	0.0911296i
$873$	−7.42769	+	5.39653i	−0.251389	+	0.182645i
$874$	1.28255	−	0.415153i	0.0433829	−	0.0140428i
$875$	10.7584	−	8.46419i	0.363701	−	0.286142i
$876$	−0.441706	−	0.765057i	−0.0149239	−	0.0258489i
$877$	−36.2987	−	16.1612i	−1.22572	−	0.545726i	−0.311231	−	0.950334i	$-0.600741\pi$
$877$	−36.2987	−	16.1612i	−1.22572	−	0.545726i	−0.914490	+	0.404608i	$0.867408\pi$
$878$	−20.4360	−	22.6964i	−0.689681	−	0.765968i
$879$	−7.85198	+	1.66899i	−0.264841	+	0.0562936i
$880$	1.97724	−	6.36042i	0.0666528	−	0.214410i
$881$	15.9626	+	49.1278i	0.537794	+	1.65516i	0.737534	+	0.675310i	$0.235990\pi$
$881$	15.9626	+	49.1278i	0.537794	+	1.65516i	−0.199740	+	0.979849i	$0.564010\pi$
$882$	−5.28643			−0.178003
$883$	−21.0504	−	4.47441i	−0.708404	−	0.150576i	−0.160400	−	0.987052i	$-0.551279\pi$
$883$	−21.0504	−	4.47441i	−0.708404	−	0.150576i	−0.548003	+	0.836476i	$0.684612\pi$
$884$	1.40246	−	0.624416i	0.0471699	−	0.0210014i
$885$	11.8533	−	13.5072i	0.398444	−	0.454039i
$886$	1.41163	−	1.02561i	0.0474247	−	0.0344561i
$887$	30.7090	−	13.6725i	1.03111	−	0.459078i	0.179776	−	0.983708i	$-0.442463\pi$
$887$	30.7090	−	13.6725i	1.03111	−	0.459078i	0.851331	+	0.524629i	$0.175796\pi$
$888$	0.270745	−	2.57596i	0.00908560	−	0.0864437i
$889$	−0.203209	−	1.93340i	−0.00681540	−	0.0648442i
$890$	33.7108	−	15.5275i	1.12999	−	0.520484i
$891$	1.61704	−	15.3851i	0.0541729	−	0.515421i
$892$	0.710135	+	2.18557i	0.0237771	+	0.0731783i
$893$	−4.41498	+	20.6581i	−0.147742	+	0.691298i
$894$	4.05558	+	12.4818i	0.135639	+	0.417453i
$895$	−18.8613	+	8.68773i	−0.630465	+	0.290399i
$896$	−1.19762	+	0.254562i	−0.0400096	+	0.00850430i
$897$	−0.885412	−	0.983350i	−0.0295630	−	0.0328331i
$898$	−5.25140	−	2.33808i	−0.175242	−	0.0780226i
$899$	0.209713	−	0.363233i	0.00699431	−	0.0121145i
$900$	2.29553	−	4.22127i	0.0765176	−	0.140709i
$901$	3.88260			0.129348
$902$	−0.851192	−	8.09855i	−0.0283416	−	0.269652i
$903$	0.495967	+	0.550828i	0.0165048	+	0.0183304i
$904$	0.570168	−	1.75480i	0.0189635	−	0.0583637i
$905$	6.45061	+	10.8506i	0.214426	+	0.360685i
$906$	−16.1021	−	3.42260i	−0.534955	−	0.113708i
$907$	29.6839	+	51.4141i	0.985638	+	1.70718i	0.639064	+	0.769153i	$0.279322\pi$
$907$	29.6839	+	51.4141i	0.985638	+	1.70718i	0.346574	+	0.938023i	$0.387345\pi$
$908$	7.66746	+	1.62977i	0.254454	+	0.0540858i
$909$	−0.517075	+	4.91964i	−0.0171503	+	0.163174i
$910$	−5.56647	−	6.02572i	−0.184527	−	0.199751i
$911$	22.8828	−	16.6253i	0.758141	−	0.550821i	−0.140199	−	0.990123i	$-0.544774\pi$
$911$	22.8828	−	16.6253i	0.758141	−	0.550821i	0.898339	+	0.439302i	$0.144774\pi$
$912$	−4.63011	+	4.15968i	−0.153318	+	0.137741i
$913$	36.1872	+	26.2916i	1.19762	+	0.870124i
$914$	6.61835	+	2.94668i	0.218915	+	0.0974675i
$915$	−11.6958	+	20.8684i	−0.386652	+	0.689888i
$916$	13.0274	−	5.80015i	0.430436	−	0.191642i
$917$	−2.20715	+	2.45129i	−0.0728864	+	0.0809486i
$918$	−1.44895	+	2.50965i	−0.0478224	+	0.0828307i
$919$	9.23146	+	28.4115i	0.304518	+	0.937209i	0.979857	+	0.199702i	$0.0639974\pi$
$919$	9.23146	+	28.4115i	0.304518	+	0.937209i	−0.675339	+	0.737508i	$0.736003\pi$
$920$	0.635295	+	0.273190i	0.0209451	+	0.00900681i
$921$	24.0676	+	26.7298i	0.793055	+	0.880777i
$922$	−1.81973	−	2.02102i	−0.0599296	−	0.0665586i
$923$	22.9063	−	16.6424i	0.753969	−	0.547791i
$924$	5.20780			0.171324
$925$	−5.89473	+	6.89273i	−0.193818	+	0.226632i
$926$	1.02573	+	1.77662i	0.0337077	+	0.0583834i
$927$	1.02709	+	9.77212i	0.0337341	+	0.320959i
$928$	7.28487	−	1.54845i	0.239138	−	0.0508303i
$929$	50.2283	−	10.6764i	1.64794	−	0.350280i	0.711927	−	0.702253i	$-0.247823\pi$
$929$	50.2283	−	10.6764i	1.64794	−	0.350280i	0.936010	+	0.351974i	$0.114489\pi$
$930$	−0.118605	+	0.135155i	−0.00388922	+	0.00443189i
$931$	−14.0723	−	19.4142i	−0.461202	−	0.636273i
$932$	24.8398			0.813655
$933$	−17.5573	+	19.4993i	−0.574799	+	0.638379i
$934$	1.79194	−	17.0491i	0.0586339	−	0.557864i
$935$	2.73503	−	2.04096i	0.0894451	−	0.0667464i
$936$	−2.63057	−	1.17121i	−0.0859830	−	0.0382821i
$937$	−13.6220	+	6.06489i	−0.445010	+	0.198131i	−0.616993	−	0.786969i	$-0.711649\pi$
$937$	−13.6220	+	6.06489i	−0.445010	+	0.198131i	0.171983	+	0.985100i	$0.444983\pi$
$938$	4.88882	+	3.55193i	0.159626	+	0.115975i
$939$	−30.6194	+	22.2463i	−0.999227	+	0.725981i
$940$	−8.68507	+	6.48104i	−0.283276	+	0.211388i
$941$	−30.0801	+	13.3925i	−0.980582	+	0.436583i	−0.833487	−	0.552539i	$-0.813659\pi$
$941$	−30.0801	+	13.3925i	−0.980582	+	0.436583i	−0.147095	+	0.989122i	$0.546992\pi$
$942$	−4.09683	−	12.6088i	−0.133482	−	0.410815i
$943$	0.845464			0.0275321
$944$	5.50524	+	1.17017i	0.179180	+	0.0380859i
$945$	15.1865	+	3.02594i	0.494017	+	0.0984338i
$946$	−0.845015	−	0.938484i	−0.0274738	−	0.0305128i
$947$	−32.6538	+	6.94077i	−1.06111	+	0.225545i	−0.705223	−	0.708986i	$-0.749153\pi$
$947$	−32.6538	+	6.94077i	−1.06111	+	0.225545i	−0.355882	+	0.934531i	$0.615820\pi$
$948$	15.3611	+	6.83922i	0.498906	+	0.222127i
$949$	1.85374			0.0601749
$950$	21.6130	−	2.80667i	0.701219	−	0.0910604i
$951$	−46.0959			−1.49476
$952$	−0.573077	−	0.255150i	−0.0185735	−	0.00826947i
$953$	−48.5450	+	10.3186i	−1.57253	+	0.334251i	−0.909942	−	0.414735i	$-0.863874\pi$
$953$	−48.5450	+	10.3186i	−1.57253	+	0.334251i	−0.662585	+	0.748986i	$0.730541\pi$
$954$	−4.87297	−	5.41198i	−0.157768	−	0.175219i
$955$	−4.66529	−	39.5274i	−0.150965	−	1.27908i
$956$	−18.7737	−	3.99047i	−0.607185	−	0.129061i
$957$	−31.6780			−1.02400
$958$	−3.14964	−	9.69360i	−0.101760	−	0.313186i
$959$	0.259180	−	0.115394i	0.00836935	−	0.00372627i
$960$	−3.19269	+	0.0407525i	−0.103044	+	0.00131528i
$961$	25.0770	−	18.2195i	0.808934	−	0.587725i
$962$	4.39712	+	3.19469i	0.141769	+	0.103001i
$963$	−14.3132	+	6.37267i	−0.461238	+	0.205356i
$964$	0.505159	+	0.224911i	0.0162701	+	0.00724390i
$965$	1.01923	−	3.27869i	0.0328103	−	0.105545i
$966$	−0.0565185	+	0.537738i	−0.00181845	+	0.0173014i
$967$	−17.3681	+	19.2893i	−0.558521	+	0.620301i	−0.954591	−	0.297920i	$-0.903707\pi$
$967$	−17.3681	+	19.2893i	−0.558521	+	0.620301i	0.396070	+	0.918220i	$0.370374\pi$
$968$	2.12711			0.0683678
$969$	−3.17189	+	0.329821i	−0.101896	+	0.0105954i
$970$	−10.9165	−	18.3627i	−0.350509	−	0.589590i
$971$	8.77110	−	1.86435i	0.281478	−	0.0598300i	−0.0650094	−	0.997885i	$-0.520708\pi$
$971$	8.77110	−	1.86435i	0.281478	−	0.0598300i	0.346487	+	0.938055i	$0.387374\pi$
$972$	9.34356	−	1.98604i	0.299695	−	0.0637021i
$973$	0.356369	+	3.39063i	0.0114247	+	0.108698i
$974$	−6.81693	−	11.8073i	−0.218428	−	0.378329i
$975$	−11.1659	−	18.2477i	−0.357593	−	0.584395i
$976$	−7.49226			−0.239821
$977$	18.9353	−	13.7573i	0.605792	−	0.440134i	−0.242138	−	0.970242i	$-0.577849\pi$
$977$	18.9353	−	13.7573i	0.605792	−	0.440134i	0.847930	+	0.530108i	$0.177849\pi$
$978$	−11.5008	−	12.7730i	−0.367756	−	0.408435i
$979$	−33.0832	−	36.7426i	−1.05734	−	1.17430i
$980$	1.12950	−	12.2484i	0.0360807	−	0.391262i
$981$	−3.84370	−	11.8297i	−0.122720	−	0.377693i
$982$	−7.15425	+	12.3915i	−0.228301	+	0.395429i
$983$	2.91311	−	3.23534i	0.0929138	−	0.103191i	−0.694895	−	0.719112i	$-0.744549\pi$
$983$	2.91311	−	3.23534i	0.0929138	−	0.103191i	0.787808	+	0.615920i	$0.211216\pi$
$984$	−3.56614	+	1.58775i	−0.113684	+	0.0506155i
$985$	50.8381	−	23.4166i	1.61984	−	0.746114i
$986$	3.48591	+	1.55203i	0.111014	+	0.0494266i
$987$	−6.85475	−	4.98027i	−0.218189	−	0.158524i
$988$	−2.70131	−	12.7784i	−0.0859402	−	0.406534i
$989$	0.106075	−	0.0770680i	0.00337299	−	0.00245062i
$990$	−6.27757	−	1.25082i	−0.199514	−	0.0397536i
$991$	−3.47070	+	33.0215i	−0.110251	+	1.04896i	0.789856	+	0.613293i	$0.210155\pi$
$991$	−3.47070	+	33.0215i	−0.110251	+	1.04896i	−0.900106	+	0.435671i	$0.856511\pi$
$992$	−0.0550860	−	0.0117089i	−0.00174898	−	0.000371758i
$993$	9.96330	+	17.2569i	0.316176	+	0.547633i
$994$	−11.3168	−	2.40546i	−0.358946	−	0.0762964i
$995$	11.2712	−	2.54654i	0.357320	−	0.0807306i
$996$	6.62605	−	20.3929i	0.209955	−	0.646174i
$997$	29.0664	+	32.2815i	0.920542	+	1.02237i	0.999675	+	0.0255016i	$0.00811829\pi$
$997$	29.0664	+	32.2815i	0.920542	+	1.02237i	−0.0791326	+	0.996864i	$0.525215\pi$
$998$	2.24392	+	21.3495i	0.0710301	+	0.675806i
$999$	−10.2596			−0.324600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.r.a.311.18	yes	200
19.11	even	3	inner	950.2.r.a.11.8	✓	200
25.16	even	5	inner	950.2.r.a.691.8	yes	200
475.391	even	15	inner	950.2.r.a.391.18	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.r.a.11.8	✓	200	19.11	even	3	inner
950.2.r.a.311.18	yes	200	1.1	even	1	trivial
950.2.r.a.391.18	yes	200	475.391	even	15	inner
950.2.r.a.691.8	yes	200	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.r (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(1.39673 - 0.296884i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.51731 + 1.64249i) q^{5} +(-1.39673 - 0.296884i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.877927 + 0.390878i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(1.39673 - 0.296884i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.51731 + 1.64249i) q^{5} +(-1.39673 - 0.296884i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.877927 + 0.390878i) q^{9} +(-0.718069 - 2.11763i) q^{10} +(-2.40985 + 1.75086i) q^{11} +(1.15522 + 0.839317i) q^{12} +(-2.73730 + 1.21872i) q^{13} +(1.11852 + 0.497998i) q^{14} +(2.60690 + 1.84365i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-0.342831 + 0.380752i) q^{17} +0.961011 q^{18} +(2.55818 + 3.52926i) q^{19} +(-0.205331 + 2.22662i) q^{20} +(-1.71012 + 0.363497i) q^{21} +(2.91365 - 0.619315i) q^{22} +(0.0323273 + 0.307574i) q^{23} +(-0.713966 - 1.23663i) q^{24} +(-0.395549 + 4.98433i) q^{25} +2.99635 q^{26} +(-4.57584 + 3.32454i) q^{27} +(-0.819266 - 0.909887i) q^{28} +(4.98343 + 5.53466i) q^{29} +(-1.63164 - 2.74458i) q^{30} +(-0.0174028 - 0.0535604i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.84611 + 3.16092i) q^{33} +(0.468057 - 0.208393i) q^{34} +(-1.85775 - 2.01102i) q^{35} +(-0.877927 - 0.390878i) q^{36} +(1.46749 + 1.06620i) q^{37} +(-0.901535 - 4.26465i) q^{38} +(-3.46144 + 2.51489i) q^{39} +(1.09323 - 1.95060i) q^{40} +(0.285756 - 2.71878i) q^{41} +(1.71012 + 0.363497i) q^{42} +(-0.211978 - 0.367157i) q^{43} +(-2.91365 - 0.619315i) q^{44} +(-1.97410 - 0.848904i) q^{45} +(0.0955690 - 0.294131i) q^{46} +(3.24282 + 3.60152i) q^{47} +(0.149260 + 1.42011i) q^{48} -5.50091 q^{49} +(2.38866 - 4.39253i) q^{50} +(-0.365802 + 0.633588i) q^{51} +(-2.73730 - 1.21872i) q^{52} +(-5.07067 - 5.63155i) q^{53} +(5.53245 - 1.17596i) q^{54} +(-6.53226 - 1.30156i) q^{55} +(0.378352 + 1.16445i) q^{56} +(4.62087 + 4.16994i) q^{57} +(-2.30144 - 7.08311i) q^{58} +(0.588310 - 5.59740i) q^{59} +(0.374257 + 3.17094i) q^{60} +(0.783155 + 7.45122i) q^{61} +(-0.00588670 + 0.0560082i) q^{62} +(1.07491 - 0.478581i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-6.15507 - 2.64681i) q^{65} +(3.88571 - 1.73003i) q^{66} +(4.82766 + 1.02615i) q^{67} -0.512352 q^{68} +(0.136466 + 0.419999i) q^{69} +(0.879185 + 2.59278i) q^{70} +(-9.24291 + 1.96464i) q^{71} +(0.643042 + 0.714170i) q^{72} +(-0.565179 - 0.251634i) q^{73} +(-0.906960 - 1.57090i) q^{74} +(0.927292 + 7.07919i) q^{75} +(-0.910996 + 4.26264i) q^{76} +(2.95056 - 2.14371i) q^{77} +(4.18508 - 0.889567i) q^{78} +(11.5183 - 2.44830i) q^{79} +(-1.79209 + 1.33731i) q^{80} +(-3.47508 + 3.85947i) q^{81} +(-1.36688 + 2.36751i) q^{82} +(-4.64032 - 14.2814i) q^{83} +(-1.41442 - 1.02764i) q^{84} +(-1.14556 + 0.0146223i) q^{85} +(0.0443155 + 0.421634i) q^{86} +(8.60365 + 6.25091i) q^{87} +(2.40985 + 1.75086i) q^{88} +(1.73500 + 16.5074i) q^{89} +(1.45815 + 1.57845i) q^{90} +(3.35148 - 1.49217i) q^{91} +(-0.206941 + 0.229831i) q^{92} +(-0.0402082 - 0.0696427i) q^{93} +(-1.49760 - 4.60913i) q^{94} +(-1.91523 + 9.55677i) q^{95} +(0.441255 - 1.35804i) q^{96} +(9.34485 - 1.98631i) q^{97} +(5.02533 + 2.23742i) q^{98} +(1.43130 - 2.47909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9}+O(q^{10}) \) 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9	\( 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9} + 4 q^{10} - 2 q^{11} + 8 q^{13} + 7 q^{14} + 10 q^{15} + 25 q^{16} - 13 q^{17} - 216 q^{18} - 36 q^{19} - 2 q^{20} + 4 q^{22} - 13 q^{23} + 33 q^{25} - 64 q^{26} - 2 q^{28} + 12 q^{29} - 20 q^{30} + 12 q^{31} + 100 q^{32} - 12 q^{33} + 8 q^{34} - 22 q^{35} + 37 q^{36} + 8 q^{37} + 18 q^{38} + 28 q^{39} - q^{40} + 2 q^{41} + 70 q^{43} - 4 q^{44} + 60 q^{45} + 24 q^{46} - 22 q^{47} + 156 q^{49} + 26 q^{50} - 42 q^{51} + 8 q^{52} - 18 q^{53} - 10 q^{55} - 4 q^{56} + 74 q^{57} + 24 q^{58} + 50 q^{59} + 12 q^{61} - 4 q^{62} - 45 q^{63} - 50 q^{64} + 120 q^{65} + 2 q^{66} - 18 q^{67} - 84 q^{68} + 4 q^{69} - 13 q^{70} + 19 q^{71} - 17 q^{72} - 24 q^{73} + 4 q^{74} - 136 q^{75} - 6 q^{76} - 12 q^{77} - 26 q^{78} - 8 q^{79} + q^{80} - 63 q^{81} + 28 q^{82} + 16 q^{83} - 20 q^{84} - 5 q^{85} + 20 q^{86} - 64 q^{87} + 2 q^{88} + 16 q^{89} - 65 q^{90} + 72 q^{91} + 12 q^{92} - 8 q^{93} - 44 q^{94} - 73 q^{95} - 11 q^{97} - 27 q^{98} + 16 q^{99}+O(q^{100}) \) 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9 + 4 * q^10 - 2 * q^11 + 8 * q^13 + 7 * q^14 + 10 * q^15 + 25 * q^16 - 13 * q^17 - 216 * q^18 - 36 * q^19 - 2 * q^20 + 4 * q^22 - 13 * q^23 + 33 * q^25 - 64 * q^26 - 2 * q^28 + 12 * q^29 - 20 * q^30 + 12 * q^31 + 100 * q^32 - 12 * q^33 + 8 * q^34 - 22 * q^35 + 37 * q^36 + 8 * q^37 + 18 * q^38 + 28 * q^39 - q^40 + 2 * q^41 + 70 * q^43 - 4 * q^44 + 60 * q^45 + 24 * q^46 - 22 * q^47 + 156 * q^49 + 26 * q^50 - 42 * q^51 + 8 * q^52 - 18 * q^53 - 10 * q^55 - 4 * q^56 + 74 * q^57 + 24 * q^58 + 50 * q^59 + 12 * q^61 - 4 * q^62 - 45 * q^63 - 50 * q^64 + 120 * q^65 + 2 * q^66 - 18 * q^67 - 84 * q^68 + 4 * q^69 - 13 * q^70 + 19 * q^71 - 17 * q^72 - 24 * q^73 + 4 * q^74 - 136 * q^75 - 6 * q^76 - 12 * q^77 - 26 * q^78 - 8 * q^79 + q^80 - 63 * q^81 + 28 * q^82 + 16 * q^83 - 20 * q^84 - 5 * q^85 + 20 * q^86 - 64 * q^87 + 2 * q^88 + 16 * q^89 - 65 * q^90 + 72 * q^91 + 12 * q^92 - 8 * q^93 - 44 * q^94 - 73 * q^95 - 11 * q^97 - 27 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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