LMFDB - Embedded newform 588.2.ba.a.103.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(103,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 29]))

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

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

chi := DirichletCharacter("588.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.ba (of order $42$, degree $12$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.13
Character	$\chi$	$=$	588.103
Dual form			588.2.ba.a.451.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.194188 - 1.40082i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.92458 + 0.544043i) q^{4} +(1.91992 + 0.143878i) q^{5} +(-0.628664 + 1.26680i) q^{6} +(-0.854457 + 2.50398i) q^{7} +(1.13584 + 2.59034i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.194188 - 1.40082i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.92458 + 0.544043i) q^{4} +(1.91992 + 0.143878i) q^{5} +(-0.628664 + 1.26680i) q^{6} +(-0.854457 + 2.50398i) q^{7} +(1.13584 + 2.59034i) q^{8} +(0.365341 + 0.930874i) q^{9} +(-0.171278 - 2.71740i) q^{10} +(-3.77175 - 1.48030i) q^{11} +(1.89663 + 0.634646i) q^{12} +(5.43869 - 4.33721i) q^{13} +(3.67354 + 0.710697i) q^{14} +(-1.50527 - 1.20041i) q^{15} +(3.40803 - 2.09411i) q^{16} +(0.310536 + 0.334678i) q^{17} +(1.23304 - 0.692540i) q^{18} +(3.78849 - 6.56186i) q^{19} +(-3.77333 + 0.767615i) q^{20} +(2.11653 - 1.58755i) q^{21} +(-1.34121 + 5.57099i) q^{22} +(4.33999 - 4.67739i) q^{23} +(0.520721 - 2.78008i) q^{24} +(-1.27875 - 0.192740i) q^{25} +(-7.13177 - 6.77639i) q^{26} +(0.222521 - 0.974928i) q^{27} +(0.282201 - 5.28397i) q^{28} +(0.102108 + 0.447366i) q^{29} +(-1.38925 + 2.34171i) q^{30} +(5.15269 + 8.92472i) q^{31} +(-3.59527 - 4.36739i) q^{32} +(2.28248 + 3.34779i) q^{33} +(0.408521 - 0.499994i) q^{34} +(-2.00076 + 4.68451i) q^{35} +(-1.20956 - 1.59278i) q^{36} +(2.69306 + 0.830700i) q^{37} +(-9.92766 - 4.03276i) q^{38} +(-6.93690 + 0.519849i) q^{39} +(1.80802 + 5.13668i) q^{40} +(-2.54184 - 5.27819i) q^{41} +(-2.63487 - 2.65659i) q^{42} +(1.90435 - 3.95443i) q^{43} +(8.06439 + 0.796970i) q^{44} +(0.567494 + 1.83977i) q^{45} +(-7.39495 - 5.17124i) q^{46} +(-3.29060 + 0.495978i) q^{47} +(-3.99550 - 0.189578i) q^{48} +(-5.53981 - 4.27908i) q^{49} +(-0.0216770 + 1.82872i) q^{50} +(-0.0680459 - 0.451455i) q^{51} +(-8.10758 + 11.3062i) q^{52} +(4.44105 - 1.36988i) q^{53} +(-1.40891 - 0.122392i) q^{54} +(-7.02849 - 3.38474i) q^{55} +(-7.45668 + 0.630770i) q^{56} +(-6.82663 + 3.28753i) q^{57} +(0.606851 - 0.229908i) q^{58} +(-0.637984 - 8.51330i) q^{59} +(3.55008 + 1.49136i) q^{60} +(-0.699329 + 2.26717i) q^{61} +(11.5013 - 8.95105i) q^{62} +(-2.64306 + 0.119414i) q^{63} +(-5.41976 + 5.88441i) q^{64} +(11.0659 - 7.54461i) q^{65} +(4.24641 - 3.84744i) q^{66} +(6.48431 - 3.74372i) q^{67} +(-0.779731 - 0.475170i) q^{68} +(-6.22073 + 1.41984i) q^{69} +(6.95067 + 1.89303i) q^{70} +(7.39410 + 1.68766i) q^{71} +(-1.99632 + 2.00368i) q^{72} +(-1.51250 + 10.0348i) q^{73} +(0.640700 - 3.93380i) q^{74} +(0.947977 + 0.879594i) q^{75} +(-3.72133 + 14.6900i) q^{76} +(6.92944 - 8.17952i) q^{77} +(2.07527 + 9.61638i) q^{78} +(3.90374 + 2.25383i) q^{79} +(6.84446 - 3.53019i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-6.90019 + 4.58562i) q^{82} +(-8.34666 + 10.4664i) q^{83} +(-3.20973 + 4.20685i) q^{84} +(0.548052 + 0.687236i) q^{85} +(-5.90923 - 1.89975i) q^{86} +(0.167644 - 0.427151i) q^{87} +(-0.449594 - 11.4515i) q^{88} +(2.88164 - 1.13096i) q^{89} +(2.46698 - 1.15222i) q^{90} +(6.21316 + 17.3243i) q^{91} +(-5.80796 + 11.3632i) q^{92} +(0.770122 - 10.2766i) q^{93} +(1.33377 + 4.51322i) q^{94} +(8.21773 - 12.0532i) q^{95} +(0.510313 + 5.63379i) q^{96} +6.46599i q^{97} +(-4.91845 + 8.59121i) q^{98} -4.05184i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9	$ 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9} + 41 q^{10} + 6 q^{11} + 52 q^{14} + 20 q^{16} - 6 q^{19} - 25 q^{20} + 4 q^{21} + 6 q^{22} + 9 q^{24} - 26 q^{25} - 18 q^{26} + 56 q^{27} + 5 q^{30} + 2 q^{31} + 15 q^{32} + 6 q^{33} + 44 q^{34} - 12 q^{35} + 16 q^{37} - 100 q^{38} + 8 q^{39} - 7 q^{40} - 7 q^{42} - 53 q^{44} - 10 q^{46} + 4 q^{47} + 8 q^{48} - 4 q^{49} - 114 q^{50} - 28 q^{52} - 4 q^{53} + q^{56} - 12 q^{57} + 27 q^{58} - 10 q^{59} - 7 q^{60} + 2 q^{61} - 16 q^{62} - 12 q^{63} - 84 q^{64} - 4 q^{65} + 21 q^{66} + 42 q^{67} + 26 q^{68} - 70 q^{70} + 28 q^{71} + 15 q^{72} + 18 q^{73} + 20 q^{74} + 54 q^{75} + 49 q^{76} - 8 q^{77} - 6 q^{78} - 6 q^{79} - 40 q^{80} + 28 q^{81} - 99 q^{82} + 10 q^{83} + 54 q^{84} + 24 q^{85} - 314 q^{86} - 40 q^{88} + 20 q^{90} - 34 q^{91} + 14 q^{92} - 2 q^{93} - 152 q^{94} - 24 q^{95} - 10 q^{96} - 156 q^{98}+O(q^{100}) $ 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9 + 41 * q^10 + 6 * q^11 + 52 * q^14 + 20 * q^16 - 6 * q^19 - 25 * q^20 + 4 * q^21 + 6 * q^22 + 9 * q^24 - 26 * q^25 - 18 * q^26 + 56 * q^27 + 5 * q^30 + 2 * q^31 + 15 * q^32 + 6 * q^33 + 44 * q^34 - 12 * q^35 + 16 * q^37 - 100 * q^38 + 8 * q^39 - 7 * q^40 - 7 * q^42 - 53 * q^44 - 10 * q^46 + 4 * q^47 + 8 * q^48 - 4 * q^49 - 114 * q^50 - 28 * q^52 - 4 * q^53 + q^56 - 12 * q^57 + 27 * q^58 - 10 * q^59 - 7 * q^60 + 2 * q^61 - 16 * q^62 - 12 * q^63 - 84 * q^64 - 4 * q^65 + 21 * q^66 + 42 * q^67 + 26 * q^68 - 70 * q^70 + 28 * q^71 + 15 * q^72 + 18 * q^73 + 20 * q^74 + 54 * q^75 + 49 * q^76 - 8 * q^77 - 6 * q^78 - 6 * q^79 - 40 * q^80 + 28 * q^81 - 99 * q^82 + 10 * q^83 + 54 * q^84 + 24 * q^85 - 314 * q^86 - 40 * q^88 + 20 * q^90 - 34 * q^91 + 14 * q^92 - 2 * q^93 - 152 * q^94 - 24 * q^95 - 10 * q^96 - 156 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−0.194188	−	1.40082i	−0.137311	−	0.990528i
$2$	−0.194188	−	1.40082i	−0.137311	−	0.990528i
$3$	−0.826239	−	0.563320i	−0.477029	−	0.325233i
$3$	−0.826239	−	0.563320i	−0.477029	−	0.325233i
$4$	−1.92458	+	0.544043i	−0.962291	+	0.272021i
$5$	1.91992	+	0.143878i	0.858616	+	0.0643444i	0.496758	−	0.867889i	$-0.334524\pi$
$5$	1.91992	+	0.143878i	0.858616	+	0.0643444i	0.361858	+	0.932233i	$0.382143\pi$
$6$	−0.628664	+	1.26680i	−0.256651	+	0.517169i
$7$	−0.854457	+	2.50398i	−0.322954	+	0.946415i
$7$	−0.854457	+	2.50398i	−0.322954	+	0.946415i
$8$	1.13584	+	2.59034i	0.401578	+	0.915825i
$9$	0.365341	+	0.930874i	0.121780	+	0.310291i
$10$	−0.171278	−	2.71740i	−0.0541628	−	0.859318i
$11$	−3.77175	−	1.48030i	−1.13723	−	0.446328i	−0.279352	−	0.960189i	$-0.590120\pi$
$11$	−3.77175	−	1.48030i	−1.13723	−	0.446328i	−0.857874	+	0.513861i	$0.828215\pi$
$12$	1.89663	+	0.634646i	0.547511	+	0.183207i
$13$	5.43869	−	4.33721i	1.50842	−	1.20293i	0.589951	−	0.807439i	$-0.299147\pi$
$13$	5.43869	−	4.33721i	1.50842	−	1.20293i	0.918471	−	0.395487i	$-0.129424\pi$
$14$	3.67354	+	0.710697i	0.981795	+	0.189942i
$15$	−1.50527	−	1.20041i	−0.388658	−	0.309944i
$16$	3.40803	−	2.09411i	0.852009	−	0.523528i
$17$	0.310536	+	0.334678i	0.0753160	+	0.0811713i	0.769585	−	0.638544i	$-0.220463\pi$
$17$	0.310536	+	0.334678i	0.0753160	+	0.0811713i	−0.694269	+	0.719715i	$0.744272\pi$
$18$	1.23304	−	0.692540i	0.290630	−	0.163233i
$19$	3.78849	−	6.56186i	0.869140	−	1.50539i	0.00626350	−	0.999980i	$-0.498006\pi$
$19$	3.78849	−	6.56186i	0.869140	−	1.50539i	0.862877	−	0.505415i	$-0.168660\pi$
$20$	−3.77333	+	0.767615i	−0.843742	+	0.171644i
$21$	2.11653	−	1.58755i	0.461864	−	0.346432i
$22$	−1.34121	+	5.57099i	−0.285946	+	1.18774i
$23$	4.33999	−	4.67739i	0.904950	−	0.975304i	−0.0948465	−	0.995492i	$-0.530236\pi$
$23$	4.33999	−	4.67739i	0.904950	−	0.975304i	0.999796	+	0.0201881i	$0.00642651\pi$
$24$	0.520721	−	2.78008i	0.106292	−	0.567482i
$25$	−1.27875	−	0.192740i	−0.255750	−	0.0385481i
$26$	−7.13177	−	6.77639i	−1.39866	−	1.32896i
$27$	0.222521	−	0.974928i	0.0428242	−	0.187625i
$28$	0.282201	−	5.28397i	0.0533309	−	0.998577i
$29$	0.102108	+	0.447366i	0.0189611	+	0.0830738i	0.983523	−	0.180782i	$-0.0578628\pi$
$29$	0.102108	+	0.447366i	0.0189611	+	0.0830738i	−0.964562	+	0.263856i	$0.915006\pi$
$30$	−1.38925	+	2.34171i	−0.253641	+	0.427535i
$31$	5.15269	+	8.92472i	0.925450	+	1.60293i	0.790835	+	0.612029i	$0.209646\pi$
$31$	5.15269	+	8.92472i	0.925450	+	1.60293i	0.134615	+	0.990898i	$0.457020\pi$
$32$	−3.59527	−	4.36739i	−0.635559	−	0.772052i
$33$	2.28248	+	3.34779i	0.397329	+	0.582775i
$34$	0.408521	−	0.499994i	0.0700607	−	0.0857483i
$35$	−2.00076	+	4.68451i	−0.338190	+	0.791826i
$36$	−1.20956	−	1.59278i	−0.201594	−	0.265464i
$37$	2.69306	+	0.830700i	0.442737	+	0.136566i	0.508105	−	0.861295i	$-0.330346\pi$
$37$	2.69306	+	0.830700i	0.442737	+	0.136566i	−0.0653684	+	0.997861i	$0.520822\pi$
$38$	−9.92766	−	4.03276i	−1.61048	−	0.654200i
$39$	−6.93690	+	0.519849i	−1.11079	+	0.0832424i
$40$	1.80802	+	5.13668i	0.285873	+	0.812181i
$41$	−2.54184	−	5.27819i	−0.396969	−	0.824315i	−0.999653	−	0.0263349i	$-0.991616\pi$
$41$	−2.54184	−	5.27819i	−0.396969	−	0.824315i	0.602684	−	0.797980i	$-0.294098\pi$
$42$	−2.63487	−	2.65659i	−0.406570	−	0.409920i
$43$	1.90435	−	3.95443i	0.290411	−	0.603044i	−0.703811	−	0.710387i	$-0.748520\pi$
$43$	1.90435	−	3.95443i	0.290411	−	0.603044i	0.994222	+	0.107343i	$0.0342342\pi$
$44$	8.06439	+	0.796970i	1.21575	+	0.120148i
$45$	0.567494	+	1.83977i	0.0845971	+	0.274257i
$46$	−7.39495	−	5.17124i	−1.09033	−	0.762458i
$47$	−3.29060	+	0.495978i	−0.479983	+	0.0723458i	−0.384578	−	0.923093i	$-0.625653\pi$
$47$	−3.29060	+	0.495978i	−0.479983	+	0.0723458i	−0.0954055	+	0.995438i	$0.530415\pi$
$48$	−3.99550	−	0.189578i	−0.576701	−	0.0273633i
$49$	−5.53981	−	4.27908i	−0.791401	−	0.611297i
$50$	−0.0216770	+	1.82872i	−0.00306559	+	0.258620i
$51$	−0.0680459	−	0.451455i	−0.00952833	−	0.0632163i
$52$	−8.10758	+	11.3062i	−1.12432	+	1.56789i
$53$	4.44105	−	1.36988i	0.610025	−	0.188168i	0.0256759	−	0.999670i	$-0.491826\pi$
$53$	4.44105	−	1.36988i	0.610025	−	0.188168i	0.584349	+	0.811503i	$0.301350\pi$
$54$	−1.40891	−	0.122392i	−0.191728	−	0.0166555i
$55$	−7.02849	−	3.38474i	−0.947721	−	0.456398i
$56$	−7.45668	+	0.630770i	−0.996441	+	0.0842902i
$57$	−6.82663	+	3.28753i	−0.904209	+	0.435444i
$58$	0.606851	−	0.229908i	0.0796834	−	0.0301884i
$59$	−0.637984	−	8.51330i	−0.0830584	−	1.10834i	−0.870572	−	0.492040i	$-0.836251\pi$
$59$	−0.637984	−	8.51330i	−0.0830584	−	1.10834i	0.787514	−	0.616297i	$-0.211368\pi$
$60$	3.55008	+	1.49136i	0.458314	+	0.192533i
$61$	−0.699329	+	2.26717i	−0.0895399	+	0.290281i	−0.989256	−	0.146195i	$-0.953297\pi$
$61$	−0.699329	+	2.26717i	−0.0895399	+	0.290281i	0.899716	+	0.436476i	$0.143774\pi$
$62$	11.5013	−	8.95105i	1.46067	−	1.13678i
$63$	−2.64306	+	0.119414i	−0.332994	+	0.0150448i
$64$	−5.41976	+	5.88441i	−0.677470	+	0.735551i
$65$	11.0659	−	7.54461i	1.37256	−	0.935794i
$66$	4.24641	−	3.84744i	0.522697	−	0.473587i
$67$	6.48431	−	3.74372i	0.792185	−	0.457368i	−0.0485462	−	0.998821i	$-0.515459\pi$
$67$	6.48431	−	3.74372i	0.792185	−	0.457368i	0.840731	+	0.541453i	$0.182125\pi$
$68$	−0.779731	−	0.475170i	−0.0945563	−	0.0576229i
$69$	−6.22073	+	1.41984i	−0.748888	+	0.170929i
$70$	6.95067	+	1.89303i	0.830764	+	0.226260i
$71$	7.39410	+	1.68766i	0.877518	+	0.200288i	0.637472	−	0.770474i	$-0.279980\pi$
$71$	7.39410	+	1.68766i	0.877518	+	0.200288i	0.240046	+	0.970761i	$0.422837\pi$
$72$	−1.99632	+	2.00368i	−0.235268	+	0.236136i
$73$	−1.51250	+	10.0348i	−0.177024	+	1.17448i	0.707060	+	0.707153i	$0.250021\pi$
$73$	−1.51250	+	10.0348i	−0.177024	+	1.17448i	−0.884085	+	0.467327i	$0.845217\pi$
$74$	0.640700	−	3.93380i	0.0744799	−	0.457295i
$75$	0.947977	+	0.879594i	0.109463	+	0.101567i
$76$	−3.72133	+	14.6900i	−0.426866	+	1.68505i
$77$	6.92944	−	8.17952i	0.789683	−	0.932143i
$78$	2.07527	+	9.61638i	0.234978	+	1.08884i
$79$	3.90374	+	2.25383i	0.439205	+	0.253575i	0.703261	−	0.710932i	$-0.251727\pi$
$79$	3.90374	+	2.25383i	0.439205	+	0.253575i	−0.264055	+	0.964508i	$0.585060\pi$
$80$	6.84446	−	3.53019i	0.765234	−	0.394687i
$81$	−0.733052	+	0.680173i	−0.0814502	+	0.0755747i
$82$	−6.90019	+	4.58562i	−0.761998	+	0.506397i
$83$	−8.34666	+	10.4664i	−0.916165	+	1.14883i	0.0722995	+	0.997383i	$0.476966\pi$
$83$	−8.34666	+	10.4664i	−0.916165	+	1.14883i	−0.988465	+	0.151452i	$0.951605\pi$
$84$	−3.20973	+	4.20685i	−0.350211	+	0.459005i
$85$	0.548052	+	0.687236i	0.0594446	+	0.0745412i
$86$	−5.90923	−	1.89975i	−0.637209	−	0.204855i
$87$	0.167644	−	0.427151i	0.0179734	−	0.0457954i
$88$	−0.449594	−	11.4515i	−0.0479269	−	1.22073i
$89$	2.88164	−	1.13096i	0.305453	−	0.119881i	−0.207664	−	0.978200i	$-0.566586\pi$
$89$	2.88164	−	1.13096i	0.305453	−	0.119881i	0.513117	+	0.858319i	$0.328491\pi$
$90$	2.46698	−	1.15222i	0.260043	−	0.121454i
$91$	6.21316	+	17.3243i	0.651316	+	1.81608i
$92$	−5.80796	+	11.3632i	−0.605521	+	1.18469i
$93$	0.770122	−	10.2766i	0.0798579	−	1.06563i
$94$	1.33377	+	4.51322i	0.137568	+	0.465503i
$95$	8.21773	−	12.0532i	0.843121	−	1.23663i
$96$	0.510313	+	5.63379i	0.0520836	+	0.574996i
$97$			6.46599i			0.656522i	0.944587	+	0.328261i	$0.106463\pi$
$97$			6.46599i			0.656522i	−0.944587	+	0.328261i	$0.893537\pi$
$98$	−4.91845	+	8.59121i	−0.496839	+	0.867843i
$99$		−	4.05184i		−	0.407225i
$100$	2.56591	−	0.324749i	0.256591	−	0.0324749i
$101$	4.59534	−	6.74012i	0.457253	−	0.670667i	−0.526504	−	0.850173i	$-0.676497\pi$
$101$	4.59534	−	6.74012i	0.457253	−	0.670667i	0.983757	+	0.179506i	$0.0574498\pi$
$102$	−0.619193	+	0.182987i	−0.0613092	+	0.0181184i
$103$	0.0198069	−	0.264305i	0.00195163	−	0.0260427i	−0.996143	−	0.0877451i	$-0.972034\pi$
$103$	0.0198069	−	0.264305i	0.00195163	−	0.0260427i	0.998095	+	0.0617023i	$0.0196530\pi$
$104$	17.4123	+	9.16172i	1.70742	+	0.898381i
$105$	4.29198	−	2.74345i	0.418855	−	0.267734i
$106$	−2.78135	−	5.95508i	−0.270149	−	0.578409i
$107$	−12.2316	+	4.80055i	−1.18247	+	0.464087i	−0.873425	−	0.486959i	$-0.838106\pi$
$107$	−12.2316	+	4.80055i	−1.18247	+	0.464087i	−0.309049	+	0.951046i	$0.600011\pi$
$108$	0.102143	+	1.99739i	0.00982870	+	0.192199i
$109$	−1.74405	+	4.44377i	−0.167050	+	0.425636i	−0.989745	−	0.142847i	$-0.954374\pi$
$109$	−1.74405	+	4.44377i	−0.167050	+	0.425636i	0.822695	+	0.568483i	$0.192470\pi$
$110$	−3.37656	+	10.5029i	−0.321942	+	1.00141i
$111$	−1.75716	−	2.20341i	−0.166783	−	0.209139i
$112$	2.33159	+	10.3230i	0.220314	+	0.975429i
$113$	−2.37040	+	2.97239i	−0.222989	+	0.279619i	−0.880724	−	0.473630i	$-0.842943\pi$
$113$	−2.37040	+	2.97239i	−0.222989	+	0.279619i	0.657735	+	0.753250i	$0.271515\pi$
$114$	5.93088	+	8.92447i	0.555478	+	0.835853i
$115$	9.00542	−	8.35581i	0.839760	−	0.779183i
$116$	−0.439903	−	0.805442i	−0.0408439	−	0.0747834i
$117$	6.02438	+	3.47818i	0.556954	+	0.321557i
$118$	−11.8017	+	2.54688i	−1.08643	+	0.234459i
$119$	−1.10337	+	0.491607i	−0.101145	+	0.0450655i
$120$	1.39974	−	5.26262i	0.127778	−	0.480410i
$121$	3.97123	+	3.68476i	0.361021	+	0.334978i
$122$	3.31169	+	0.539376i	0.299826	+	0.0488328i
$123$	−0.873142	+	5.79292i	−0.0787285	+	0.522330i
$124$	−14.7722	−	14.3731i	−1.32658	−	1.29074i
$125$	−11.8125	−	2.69614i	−1.05655	−	0.241150i
$126$	0.680526	+	3.67925i	0.0606261	+	0.327774i
$127$	14.4339	−	3.29445i	1.28080	−	0.292335i	0.472620	−	0.881267i	$-0.343308\pi$
$127$	14.4339	−	3.29445i	1.28080	−	0.292335i	0.808183	+	0.588932i	$0.200451\pi$
$128$	9.29543	+	6.44941i	0.821608	+	0.570053i
$129$	−3.80106	+	2.19454i	−0.334664	+	0.193219i
$130$	−12.7175	−	14.0363i	−1.11540	−	1.23106i
$131$	2.86733	−	1.95491i	0.250520	−	0.170801i	−0.431549	−	0.902089i	$-0.642033\pi$
$131$	2.86733	−	1.95491i	0.250520	−	0.170801i	0.682069	+	0.731288i	$0.261080\pi$
$132$	−6.21416	−	5.20132i	−0.540873	−	0.452717i
$133$	13.1937	+	15.0931i	1.14404	+	1.30874i
$134$	−6.50344	−	8.35636i	−0.561812	−	0.721880i
$135$	0.567494	−	1.83977i	0.0488421	−	0.158342i
$136$	−0.514213	+	1.18453i	−0.0440934	+	0.101573i
$137$	−1.32540	−	17.6863i	−0.113237	−	1.51104i	−0.707468	−	0.706745i	$-0.750163\pi$
$137$	−1.32540	−	17.6863i	−0.113237	−	1.51104i	0.594232	−	0.804294i	$-0.297456\pi$
$138$	3.19693	+	8.43840i	0.272141	+	0.718324i
$139$	−4.40942	+	2.12347i	−0.374002	+	0.180110i	−0.611436	−	0.791294i	$-0.709408\pi$
$139$	−4.40942	+	2.12347i	−0.374002	+	0.180110i	0.237434	+	0.971404i	$0.423694\pi$
$140$	1.30205	−	10.1042i	0.110044	−	0.853963i
$141$	2.99821	+	1.44386i	0.252495	+	0.121595i
$142$	0.928255	−	10.6855i	0.0778974	−	0.896708i
$143$	−26.9338	+	8.30797i	−2.25232	+	0.694747i
$144$	3.19445	+	2.40739i	0.266204	+	0.200615i
$145$	0.131674	+	0.873600i	0.0109349	+	0.0725486i
$146$	14.3506	+	0.170107i	1.18766	+	0.0140781i
$147$	2.16671	+	6.65623i	0.178707	+	0.548996i
$148$	−5.63496	−	0.133608i	−0.463191	−	0.0109825i
$149$	9.58466	−	1.44466i	0.785206	−	0.118351i	0.255812	−	0.966727i	$-0.417657\pi$
$149$	9.58466	−	1.44466i	0.785206	−	0.118351i	0.529394	+	0.848376i	$0.322419\pi$
$150$	1.04807	−	1.49875i	0.0855742	−	0.122372i
$151$	5.02896	+	16.3035i	0.409251	+	1.32676i	0.892410	+	0.451226i	$0.149013\pi$
$151$	5.02896	+	16.3035i	0.409251	+	1.32676i	−0.483159	+	0.875533i	$0.660511\pi$
$152$	21.3006	+	2.36030i	1.72771	+	0.191446i
$153$	−0.198091	+	0.411341i	−0.0160147	+	0.0332550i
$154$	−12.8036	−	8.11852i	−1.03175	−	0.654209i
$155$	8.60870	+	17.8761i	0.691467	+	1.43585i
$156$	13.0678	−	4.77446i	1.04626	−	0.382263i
$157$	5.45515	−	0.408807i	0.435369	−	0.0326264i	0.144756	−	0.989467i	$-0.453760\pi$
$157$	5.45515	−	0.408807i	0.435369	−	0.0326264i	0.290612	+	0.956841i	$0.406141\pi$
$158$	2.39914	−	5.90610i	0.190866	−	0.469864i
$159$	−4.44105	−	1.36988i	−0.352198	−	0.108639i
$160$	−6.27427	−	8.90233i	−0.496024	−	0.703791i
$161$	8.00376	+	14.8639i	0.630784	+	1.17144i
$162$	1.09515	+	0.894791i	0.0860429	+	0.0703014i
$163$	5.41135	+	7.93700i	0.423850	+	0.621674i	0.977465	−	0.211099i	$-0.0677043\pi$
$163$	5.41135	+	7.93700i	0.423850	+	0.621674i	−0.553615	+	0.832773i	$0.686752\pi$
$164$	7.76355	+	8.77544i	0.606231	+	0.685247i
$165$	3.90052	+	6.75589i	0.303655	+	0.525946i
$166$	16.2823	+	9.65971i	1.26375	+	0.749739i
$167$	−5.19744	−	22.7715i	−0.402190	−	1.76211i	−0.618501	−	0.785784i	$-0.712260\pi$
$167$	−5.19744	−	22.7715i	−0.402190	−	1.76211i	0.216312	−	0.976324i	$-0.430597\pi$
$168$	6.51633	+	3.67933i	0.502745	+	0.283867i
$169$	7.87520	−	34.5035i	0.605784	−	2.65411i
$170$	0.856267	−	0.901174i	0.0656727	−	0.0691169i
$171$	7.49236	+	1.12929i	0.572955	+	0.0863591i
$172$	−1.51370	+	8.64667i	−0.115419	+	0.659302i
$173$	−13.3303	+	14.3667i	−1.01349	+	1.09228i	−0.0177674	+	0.999842i	$0.505656\pi$
$173$	−13.3303	+	14.3667i	−1.01349	+	1.09228i	−0.995719	+	0.0924360i	$0.970535\pi$
$174$	−0.630915	−	0.151892i	−0.0478296	−	0.0115149i
$175$	1.57525	−	3.03727i	0.119078	−	0.229596i
$176$	−15.9542	+	2.85354i	−1.20259	+	0.215094i
$177$	−4.26859	+	7.39341i	−0.320847	+	0.555723i
$178$	−2.14385	−	3.81703i	−0.160688	−	0.286098i
$179$	8.63626	+	9.30768i	0.645505	+	0.695689i	0.968019	−	0.250876i	$-0.0807186\pi$
$179$	8.63626	+	9.30768i	0.645505	+	0.695689i	−0.322515	+	0.946564i	$0.604528\pi$
$180$	−2.09310	−	3.23205i	−0.156011	−	0.240903i
$181$	−11.1129	−	8.86223i	−0.826014	−	0.658724i	0.116389	−	0.993204i	$-0.462868\pi$
$181$	−11.1129	−	8.86223i	−0.826014	−	0.658724i	−0.942403	+	0.334479i	$0.891440\pi$
$182$	23.0617	−	12.0677i	1.70945	−	0.894515i
$183$	1.85495	−	1.47928i	0.137122	−	0.109351i
$184$	17.0456	+	5.92931i	1.25662	+	0.437114i
$185$	5.05096	+	1.98235i	0.371354	+	0.145746i
$186$	−14.5451	+	0.916780i	−1.06650	+	0.0672216i
$187$	−0.675838	−	1.72201i	−0.0494222	−	0.125926i
$188$	6.06319	−	2.74478i	0.442204	−	0.200183i
$189$	2.25106	+	1.39022i	0.163741	+	0.101124i
$190$	−18.4801	−	9.17096i	−1.34069	−	0.665332i
$191$	−14.7908	−	1.10842i	−1.07022	−	0.0802022i	−0.472053	−	0.881570i	$-0.656487\pi$
$191$	−14.7908	−	1.10842i	−1.07022	−	0.0802022i	−0.598172	+	0.801368i	$0.704106\pi$
$192$	7.79282	−	1.80887i	0.562398	−	0.130544i
$193$	−13.6279	−	9.29136i	−0.980959	−	0.668806i	−0.0371540	−	0.999310i	$-0.511829\pi$
$193$	−13.6279	−	9.29136i	−0.980959	−	0.668806i	−0.943805	+	0.330503i	$0.892782\pi$
$194$	9.05768	−	1.25562i	0.650303	−	0.0901479i
$195$	−13.3931			−0.959101
$196$	12.9898	+	5.22155i	0.927844	+	0.372968i
$197$	−16.5196			−1.17697			−0.588485	−	0.808508i	$-0.700275\pi$
$197$	−16.5196			−1.17697			−0.588485	+	0.808508i	$0.700275\pi$
$198$	−5.67589	+	0.786817i	−0.403368	+	0.0559166i
$199$	−0.636496	−	0.433956i	−0.0451200	−	0.0307623i	0.540550	−	0.841312i	$-0.318216\pi$
$199$	−0.636496	−	0.433956i	−0.0451200	−	0.0307623i	−0.585670	+	0.810550i	$0.699169\pi$
$200$	−0.953184	−	3.53132i	−0.0674003	−	0.249702i
$201$	−7.46650	−	0.559537i	−0.526647	−	0.0394667i
$202$	−10.3340	−	5.12838i	−0.727101	−	0.360832i
$203$	−1.20744	−	0.126578i	−0.0847458	−	0.00888403i
$204$	0.376571	+	0.831842i	0.0263652	+	0.0582406i
$205$	−4.12073	−	10.4994i	−0.287804	−	0.733313i
$206$	−0.374090	+	0.0235789i	−0.0260641	+	0.00164282i
$207$	5.93964	+	2.33114i	0.412833	+	0.162025i
$208$	9.45265	−	26.1706i	0.655423	−	1.81460i
$209$	−24.0028	+	19.1416i	−1.66031	+	1.32405i
$210$	−4.67653	−	5.47954i	−0.322711	−	0.378124i
$211$	3.65311	+	2.91326i	0.251491	+	0.200557i	0.741118	−	0.671375i	$-0.234296\pi$
$211$	3.65311	+	2.91326i	0.251491	+	0.200557i	−0.489628	+	0.871932i	$0.662867\pi$
$212$	−7.80189	+	5.05257i	−0.535836	+	0.347012i
$213$	−5.15860	−	5.55965i	−0.353462	−	0.380941i
$214$	9.09992	+	16.2020i	0.622058	+	1.10755i
$215$	4.22516	−	7.31820i	0.288154	−	0.499097i
$216$	2.77815	−	0.530952i	0.189029	−	0.0361267i
$217$	−26.7500	+	5.27643i	−1.81591	+	0.358188i
$218$	6.56359	+	1.58017i	0.444542	+	0.107023i
$219$	6.90247	−	7.43909i	0.466426	−	0.502687i
$220$	15.3683	+	2.69041i	1.03613	+	0.181388i
$221$	3.14048	+	0.473351i	0.211251	+	0.0318410i
$222$	−2.74536	+	2.88934i	−0.184257	+	0.193920i
$223$	−3.34709	+	14.6646i	−0.224138	+	0.982011i	0.730189	+	0.683245i	$0.239432\pi$
$223$	−3.34709	+	14.6646i	−0.224138	+	0.982011i	−0.954327	+	0.298766i	$0.903425\pi$
$224$	14.0078	−	5.27073i	0.935938	−	0.352165i
$225$	−0.287762	−	1.26077i	−0.0191842	−	0.0840513i
$226$	4.62408	+	2.74330i	0.307590	+	0.182482i
$227$	1.82325	+	3.15795i	0.121013	+	0.209601i	0.920167	−	0.391525i	$-0.128052\pi$
$227$	1.82325	+	3.15795i	0.121013	+	0.209601i	−0.799154	+	0.601126i	$0.794719\pi$
$228$	11.3499	−	10.0411i	0.751662	−	0.664989i
$229$	5.98786	+	8.78258i	0.395689	+	0.580369i	0.971449	−	0.237250i	$-0.0762460\pi$
$229$	5.98786	+	8.78258i	0.395689	+	0.580369i	−0.575760	+	0.817619i	$0.695294\pi$
$230$	−13.4537	−	10.9924i	−0.887111	−	0.724815i
$231$	−10.3331	+	2.85474i	−0.679866	+	0.187828i
$232$	−1.04285	+	0.772630i	−0.0684667	+	0.0507257i
$233$	−10.9664	−	3.38270i	−0.718435	−	0.221608i	−0.0860820	−	0.996288i	$-0.527435\pi$
$233$	−10.9664	−	3.38270i	−0.718435	−	0.221608i	−0.632353	+	0.774680i	$0.717911\pi$
$234$	3.70243	−	9.11447i	0.242036	−	0.595832i
$235$	−6.38906	+	0.478794i	−0.416776	+	0.0312331i
$236$	5.85945	+	16.0375i	0.381418	+	1.04395i
$237$	−1.95580	−	4.06126i	−0.127043	−	0.263807i
$238$	0.902912	+	1.45015i	0.0585271	+	0.0939993i
$239$	−2.17937	+	4.52551i	−0.140972	+	0.292731i	−0.959486	−	0.281755i	$-0.909084\pi$
$239$	−2.17937	+	4.52551i	−0.140972	+	0.292731i	0.818515	+	0.574485i	$0.194798\pi$
$240$	−7.64379	−	0.938843i	−0.493404	−	0.0606020i
$241$	5.61228	+	18.1946i	0.361519	+	1.17202i	0.935554	+	0.353185i	$0.114901\pi$
$241$	5.61228	+	18.1946i	0.361519	+	1.17202i	−0.574035	+	0.818831i	$0.694622\pi$
$242$	4.39052	−	6.27850i	0.282233	−	0.403597i
$243$	0.988831	−	0.149042i	0.0634335	−	0.00956107i
$244$	0.112479	−	4.74382i	0.00720072	−	0.303692i
$245$	−10.0203	−	9.01257i	−0.640176	−	0.575792i
$246$	8.28437	+	0.0982000i	0.528192	+	0.00626100i
$247$	−7.85575	−	52.1195i	−0.499849	−	3.31628i
$248$	−17.2655	+	23.4842i	−1.09636	+	1.49125i
$249$	12.7923	−	3.94589i	0.810676	−	0.250061i
$250$	−1.48295	+	17.0708i	−0.0937898	+	1.07965i
$251$	12.6582	+	6.09586i	0.798978	+	0.384767i	0.788389	−	0.615176i	$-0.210915\pi$
$251$	12.6582	+	6.09586i	0.798978	+	0.384767i	0.0105884	+	0.999944i	$0.496630\pi$
$252$	5.02181	−	1.66776i	0.316344	−	0.105059i
$253$	−23.2933	+	11.2175i	−1.46444	+	0.705236i
$254$	−7.41780	−	19.5795i	−0.465434	−	1.22853i
$255$	−0.0656883	−	0.876549i	−0.00411356	−	0.0548916i
$256$	7.22940	−	14.2736i	0.451837	−	0.892100i
$257$	−4.12799	+	13.3826i	−0.257497	+	0.834785i	0.730846	+	0.682542i	$0.239126\pi$
$257$	−4.12799	+	13.3826i	−0.257497	+	0.834785i	−0.988343	+	0.152243i	$0.951351\pi$
$258$	3.81227	+	4.89843i	0.237342	+	0.304963i
$259$	−4.38116	+	6.03357i	−0.272232	+	0.374908i
$260$	−17.1927	+	20.5406i	−1.06624	+	1.27387i
$261$	−0.379137	+	0.258491i	−0.0234680	+	0.0160002i
$262$	−3.29528	−	3.63699i	−0.203583	−	0.224694i
$263$	−0.756986	+	0.437046i	−0.0466778	+	0.0269494i	−0.523157	−	0.852236i	$-0.675246\pi$
$263$	−0.756986	+	0.437046i	−0.0466778	+	0.0269494i	0.476480	+	0.879186i	$0.341913\pi$
$264$	−6.07939	+	9.71494i	−0.374161	+	0.597913i
$265$	8.72357	−	1.99110i	0.535885	−	0.122312i
$266$	18.5807	−	21.4128i	1.13926	−	1.31290i
$267$	−3.01801	−	0.688841i	−0.184699	−	0.0421564i
$268$	−10.4429	+	10.7328i	−0.637899	+	0.655613i
$269$	−3.88825	+	25.7968i	−0.237070	+	1.57286i	0.480893	+	0.876779i	$0.340313\pi$
$269$	−3.88825	+	25.7968i	−0.237070	+	1.57286i	−0.717964	+	0.696081i	$0.754926\pi$
$270$	−2.68739	−	0.437695i	−0.163549	−	0.0266373i
$271$	0.510787	+	0.473941i	0.0310281	+	0.0287899i	0.695534	−	0.718493i	$-0.255168\pi$
$271$	0.510787	+	0.473941i	0.0310281	+	0.0287899i	−0.664506	+	0.747283i	$0.731358\pi$
$272$	1.75917	+	0.490298i	0.106665	+	0.0297287i
$273$	4.62559	−	17.8140i	0.279953	−	1.07815i
$274$	−24.5179	+	5.29110i	−1.48118	+	0.319647i
$275$	4.53780	+	2.61990i	0.273640	+	0.157986i
$276$	11.1999	−	6.11695i	0.674152	−	0.368197i
$277$	−3.92116	+	3.63831i	−0.235600	+	0.218605i	−0.789133	−	0.614223i	$-0.789470\pi$
$277$	−3.92116	+	3.63831i	−0.235600	+	0.218605i	0.553533	+	0.832827i	$0.313279\pi$
$278$	3.83085	+	5.76445i	0.229759	+	0.345729i
$279$	−6.42530	+	8.05707i	−0.384673	+	0.482364i
$280$	−14.4070	+	0.138175i	−0.860984	+	0.00825751i
$281$	19.1610	+	24.0272i	1.14305	+	1.43334i	0.884006	+	0.467476i	$0.154837\pi$
$281$	19.1610	+	24.0272i	1.14305	+	1.43334i	0.259046	+	0.965865i	$0.416592\pi$
$282$	1.44037	−	4.48033i	0.0857731	−	0.266800i
$283$	−5.34334	+	13.6146i	−0.317628	+	0.809304i	0.679507	+	0.733669i	$0.262194\pi$
$283$	−5.34334	+	13.6146i	−0.317628	+	0.809304i	−0.997136	+	0.0756352i	$0.975902\pi$
$284$	−15.1487	+	0.774677i	−0.898911	+	0.0459686i
$285$	−13.5796	+	5.32961i	−0.804387	+	0.315699i
$286$	16.8682	+	36.1160i	0.997435	+	2.13558i
$287$	15.3884	−	1.85473i	0.908346	−	0.109481i
$288$	2.75199	−	4.94232i	0.162162	−	0.291229i
$289$	1.25483	−	16.7446i	0.0738138	−	0.984977i
$290$	1.19819	−	0.354094i	0.0703599	−	0.0207931i
$291$	3.64242	−	5.34245i	0.213523	−	0.313180i
$292$	−2.54842	−	20.1356i	−0.149135	−	1.17835i
$293$		−	9.92035i		−	0.579553i	−0.957094	−	0.289777i	$-0.906419\pi$
$293$		−	9.92035i		−	0.579553i	0.957094	−	0.289777i	$-0.0935810\pi$
$294$	8.90341	−	4.32773i	0.519258	−	0.252398i
$295$		−	16.4367i		−	0.956981i
$296$	0.907078	+	7.91950i	0.0527229	+	0.460311i
$297$	−2.28248	+	3.34779i	−0.132443	+	0.194258i
$298$	−3.88492	−	13.1458i	−0.225048	−	0.761518i
$299$	3.31700	−	44.2624i	0.191827	−	2.55976i
$300$	−2.30300	−	1.17711i	−0.132964	−	0.0679605i
$301$	8.27461	+	8.14734i	0.476940	+	0.469605i
$302$	21.8617	−	10.2106i	1.25800	−	0.587554i
$303$	−7.59369	+	2.98030i	−0.436246	+	0.171214i
$304$	−0.829954	−	30.2966i	−0.0476011	−	1.73763i
$305$	−1.66885	+	4.25217i	−0.0955583	+	0.243479i
$306$	0.614681	+	0.197613i	0.0351390	+	0.0112968i
$307$	−8.15293	−	10.2234i	−0.465312	−	0.583483i	0.492704	−	0.870197i	$-0.336008\pi$
$307$	−8.15293	−	10.2234i	−0.465312	−	0.583483i	−0.958016	+	0.286714i	$0.907437\pi$
$308$	−8.88627	+	19.5121i	−0.506342	+	1.11180i
$309$	−0.165254	+	0.207221i	−0.00940095	+	0.0117884i
$310$	23.3695	−	15.5305i	1.32730	−	0.882075i
$311$	−25.0629	+	23.2550i	−1.42119	+	1.31867i	−0.543522	+	0.839395i	$0.682909\pi$
$311$	−25.0629	+	23.2550i	−1.42119	+	1.31867i	−0.877665	+	0.479274i	$0.840900\pi$
$312$	−9.22576	−	17.3785i	−0.522306	−	0.983863i
$313$	16.2769	+	9.39745i	0.920023	+	0.531176i	0.883642	−	0.468162i	$-0.155084\pi$
$313$	16.2769	+	9.39745i	0.920023	+	0.531176i	0.0363806	+	0.999338i	$0.488417\pi$
$314$	−1.63199	−	7.56229i	−0.0920984	−	0.426765i
$315$	−5.09165	−	0.151012i	−0.286882	−	0.00850856i
$316$	−8.73925	−	2.21387i	−0.491621	−	0.124540i
$317$	−3.81335	−	3.53827i	−0.214179	−	0.198729i	0.565786	−	0.824552i	$-0.308573\pi$
$317$	−3.81335	−	3.53827i	−0.214179	−	0.198729i	−0.779965	+	0.625823i	$0.784763\pi$
$318$	−1.05656	+	6.48711i	−0.0592489	+	0.363779i
$319$	0.277110	−	1.83850i	0.0155152	−	0.102937i
$320$	−11.2522	+	10.5178i	−0.629015	+	0.587964i
$321$	12.8105	+	2.92391i	0.715011	+	0.163197i
$322$	19.2673	−	14.0982i	1.07373	−	0.785661i
$323$	3.37257	−	0.769768i	0.187655	−	0.0428310i
$324$	1.04078	−	1.70786i	0.0578209	−	0.0948811i
$325$	−7.79067	+	4.49795i	−0.432149	+	0.249501i
$326$	10.0675	−	9.12159i	0.557586	−	0.505198i
$327$	3.94427	−	2.68916i	0.218119	−	0.148711i
$328$	10.7852	−	12.5794i	0.595514	−	0.694581i
$329$	1.56976	−	8.66338i	0.0865435	−	0.477627i
$330$	8.70634	−	6.77582i	0.479268	−	0.372997i
$331$	0.460436	−	1.49270i	0.0253079	−	0.0820461i	−0.942038	−	0.335506i	$-0.891093\pi$
$331$	0.460436	−	1.49270i	0.0253079	−	0.0820461i	0.967346	+	0.253460i	$0.0815687\pi$
$332$	10.3697	−	24.6844i	0.569110	−	1.35473i
$333$	0.210610	+	2.81039i	0.0115413	+	0.154008i
$334$	−30.8894	+	11.7026i	−1.69019	+	0.640338i
$335$	12.9880	−	6.25470i	0.709612	−	0.341731i
$336$	3.88869	−	9.84267i	0.212145	−	0.536962i
$337$	−24.0262	−	11.5704i	−1.30879	−	0.630279i	−0.356163	−	0.934424i	$-0.615915\pi$
$337$	−24.0262	−	11.5704i	−1.30879	−	0.630279i	−0.952626	+	0.304144i	$0.901629\pi$
$338$	−49.8624	−	4.33157i	−2.71216	−	0.235606i
$339$	3.63293	−	1.12061i	0.197314	−	0.0608632i
$340$	−1.42866	−	1.02448i	−0.0774798	−	0.0555601i
$341$	−6.22337	−	41.2893i	−0.337014	−	2.23594i
$342$	0.127009	−	10.7147i	0.00686784	−	0.579386i
$343$	15.4482	−	10.2153i	0.834127	−	0.551572i
$344$	12.4063	+	0.441347i	0.668905	+	0.0237958i
$345$	−12.1476	+	1.83096i	−0.654006	+	0.0985755i
$346$	22.7137	+	15.8835i	1.22110	+	0.853904i
$347$	−0.788483	−	2.55620i	−0.0423280	−	0.137224i	0.931942	−	0.362606i	$-0.118113\pi$
$347$	−0.788483	−	2.55620i	−0.0423280	−	0.137224i	−0.974270	+	0.225382i	$0.927637\pi$
$348$	−0.0902570	+	0.913293i	−0.00483828	+	0.0489577i
$349$	−1.44990	+	3.01075i	−0.0776114	+	0.161162i	−0.936164	−	0.351564i	$-0.885650\pi$
$349$	−1.44990	+	3.01075i	−0.0776114	+	0.161162i	0.858552	+	0.512726i	$0.171364\pi$
$350$	−4.56055	−	1.61684i	−0.243772	−	0.0864238i
$351$	−3.01825	−	6.26745i	−0.161102	−	0.334532i
$352$	7.09539	+	21.7948i	0.378186	+	1.16166i
$353$	−19.4434	+	1.45708i	−1.03487	+	0.0775525i	−0.581316	−	0.813678i	$-0.697462\pi$
$353$	−19.4434	+	1.45708i	−1.03487	+	0.0775525i	−0.453551	+	0.891230i	$0.649843\pi$
$354$	11.1857	+	4.54380i	0.594515	+	0.241500i
$355$	13.9533	+	4.30402i	0.740564	+	0.228434i
$356$	−4.93066	+	3.74436i	−0.261324	+	0.198451i
$357$	1.18858	+	0.215363i	0.0629061	+	0.0113982i
$358$	11.3613	−	13.9053i	0.600464	−	0.734916i
$359$	−9.94867	−	14.5920i	−0.525071	−	0.770137i	0.468486	−	0.883471i	$-0.344800\pi$
$359$	−9.94867	−	14.5920i	−0.525071	−	0.770137i	−0.993557	+	0.113334i	$0.963847\pi$
$360$	−4.12106	+	3.55968i	−0.217199	+	0.187612i
$361$	−19.2054	−	33.2647i	−1.01081	−	1.75077i
$362$	−10.2564	+	17.2881i	−0.539064	+	0.908640i
$363$	−1.20548	−	5.28156i	−0.0632714	−	0.277210i
$364$	−21.3829	−	29.9619i	−1.12077	−	1.57043i
$365$	−4.34767	+	19.0484i	−0.227567	+	0.997037i
$366$	−2.43241	−	2.31120i	−0.127144	−	0.120808i
$367$	−24.3882	−	3.67593i	−1.27306	−	0.191882i	−0.522471	−	0.852657i	$-0.674990\pi$
$367$	−24.3882	−	3.67593i	−1.27306	−	0.191882i	−0.750584	+	0.660775i	$0.770228\pi$
$368$	4.99584	−	25.0291i	0.260426	−	1.30473i
$369$	3.98469	−	4.29447i	0.207435	−	0.223561i
$370$	1.79608	−	7.46042i	0.0933740	−	0.387849i
$371$	−0.364530	+	12.2908i	−0.0189254	+	0.638106i
$372$	4.10873	+	20.1971i	0.213028	+	1.04717i
$373$	−0.0176725	+	0.0306096i	−0.000915045	+	0.00158490i	−0.866483	−	0.499207i	$-0.833625\pi$
$373$	−0.0176725	+	0.0306096i	−0.000915045	+	0.00158490i	0.865568	+	0.500792i	$0.166958\pi$
$374$	−2.28098	+	1.28112i	−0.117947	+	0.0662451i
$375$	8.24120	+	8.88190i	0.425574	+	0.458659i
$376$	−5.02233	−	7.96043i	−0.259007	−	0.410528i
$377$	2.49566	+	1.99022i	0.128533	+	0.102502i
$378$	1.51032	−	3.42329i	0.0776824	−	0.176075i
$379$	10.7868	−	8.60220i	0.554082	−	0.441865i	−0.305993	−	0.952034i	$-0.598988\pi$
$379$	10.7868	−	8.60220i	0.554082	−	0.441865i	0.860074	+	0.510168i	$0.170417\pi$
$380$	−9.25824	+	27.6682i	−0.474938	+	1.41935i
$381$	−13.7817	−	5.40891i	−0.706057	−	0.277107i
$382$	1.31950	+	20.9345i	0.0675114	+	1.07110i
$383$	−5.72809	−	14.5949i	−0.292692	−	0.745767i	−0.999273	−	0.0381342i	$-0.987859\pi$
$383$	−5.72809	−	14.5949i	−0.292692	−	0.745767i	0.706581	−	0.707632i	$-0.250237\pi$
$384$	−4.04716	−	10.5651i	−0.206531	−	0.539146i
$385$	14.4809	−	14.7071i	0.738013	−	0.749541i
$386$	−10.3691	+	20.8945i	−0.527775	+	1.06350i
$387$	4.37681	+	0.327996i	0.222486	+	0.0166730i
$388$	−3.51778	−	12.4443i	−0.178588	−	0.631765i
$389$	16.9526	+	11.5581i	0.859529	+	0.586017i	0.910884	−	0.412663i	$-0.135401\pi$
$389$	16.9526	+	11.5581i	0.859529	+	0.586017i	−0.0513543	+	0.998680i	$0.516354\pi$
$390$	2.60078	+	18.7613i	0.131695	+	0.950016i
$391$	2.91314			0.147324
$392$	4.79198	−	19.2103i	0.242032	−	0.970268i
$393$	−3.47034			−0.175056
$394$	3.20789	+	23.1409i	0.161611	+	1.16582i
$395$	7.17061	+	4.88884i	0.360793	+	0.245984i
$396$	2.20437	+	7.79810i	0.110774	+	0.391869i
$397$	16.7709	+	1.25681i	0.841708	+	0.0630773i	0.488603	−	0.872506i	$-0.337507\pi$
$397$	16.7709	+	1.25681i	0.841708	+	0.0630773i	0.353105	+	0.935584i	$0.385126\pi$
$398$	−0.484293	+	0.975884i	−0.0242754	+	0.0489167i
$399$	−2.39885	−	19.9028i	−0.120093	−	0.996385i
$400$	−4.76164	+	2.02097i	−0.238082	+	0.101049i
$401$	12.6088	+	32.1267i	0.629653	+	1.60433i	0.787117	+	0.616804i	$0.211573\pi$
$401$	12.6088	+	32.1267i	0.629653	+	1.60433i	−0.157464	+	0.987525i	$0.550332\pi$
$402$	0.666093	+	10.5679i	0.0332217	+	0.527077i
$403$	66.7323	+	26.1905i	3.32417	+	1.30464i
$404$	−5.17719	+	15.4720i	−0.257575	+	0.769760i
$405$	−1.50527	+	1.20041i	−0.0747973	+	0.0596488i
$406$	0.0571578	+	1.71599i	0.00283669	+	0.0851630i
$407$	−8.92787	−	7.11974i	−0.442538	−	0.352913i
$408$	1.09213	−	0.689041i	0.0540687	−	0.0341126i
$409$	18.0112	+	19.4115i	0.890596	+	0.959835i	0.999414	−	0.0342272i	$-0.0108970\pi$
$409$	18.0112	+	19.4115i	0.890596	+	0.959835i	−0.108818	+	0.994062i	$0.534707\pi$
$410$	−13.9076	+	7.81125i	−0.686848	+	0.385770i
$411$	−8.86793	+	15.3597i	−0.437423	+	0.757638i
$412$	0.105673	+	0.519453i	0.00520615	+	0.0255916i
$413$	21.8622	+	5.67675i	1.07577	+	0.279335i
$414$	2.11209	−	8.77303i	0.103804	−	0.431171i
$415$	−17.5308	+	18.8938i	−0.860555	+	0.927458i
$416$	−38.4958	−	8.15943i	−1.88741	−	0.400049i
$417$	4.83943	+	0.729426i	0.236988	+	0.0357202i
$418$	31.4749	+	29.9065i	1.53949	+	1.46277i
$419$	−1.06481	+	4.66522i	−0.0520192	+	0.227911i	−0.994255	−	0.107040i	$-0.965863\pi$
$419$	−1.06481	+	4.66522i	−0.0520192	+	0.227911i	0.942235	+	0.334951i	$0.108720\pi$
$420$	−6.76772	+	7.61503i	−0.330231	+	0.371575i
$421$	3.86079	+	16.9152i	0.188163	+	0.824398i	0.977584	+	0.210545i	$0.0675240\pi$
$421$	3.86079	+	16.9152i	0.188163	+	0.824398i	−0.789421	+	0.613853i	$0.789619\pi$
$422$	3.37156	−	5.68306i	0.164125	−	0.276647i
$423$	−1.66388	−	2.88193i	−0.0809008	−	0.140124i
$424$	8.59276	+	9.94788i	0.417301	+	0.483112i
$425$	−0.332591	−	0.487822i	−0.0161330	−	0.0236628i
$426$	−6.78632	+	8.30588i	−0.328798	+	0.402421i
$427$	−5.07939	−	3.68830i	−0.245809	−	0.178489i
$428$	20.9290	−	15.8936i	1.01164	−	0.768245i
$429$	26.9338	+	8.30797i	1.30038	+	0.401113i
$430$	−11.0719	−	4.49758i	−0.533936	−	0.216893i
$431$	−2.65775	+	0.199171i	−0.128019	+	0.00959371i	−0.138586	−	0.990350i	$-0.544256\pi$
$431$	−2.65775	+	0.199171i	−0.128019	+	0.00959371i	0.0105664	+	0.999944i	$0.496637\pi$
$432$	−1.28325	−	3.78857i	−0.0617403	−	0.182278i
$433$	−7.63976	−	15.8641i	−0.367144	−	0.762382i	0.632785	−	0.774327i	$-0.281912\pi$
$433$	−7.63976	−	15.8641i	−0.367144	−	0.762382i	−0.999929	+	0.0119460i	$0.996197\pi$
$434$	12.5858	+	36.4473i	0.604140	+	1.74953i
$435$	0.383322	−	0.795977i	0.0183789	−	0.0381642i
$436$	0.938968	−	9.50124i	0.0449684	−	0.455027i
$437$	−14.2504	−	46.1987i	−0.681689	−	2.20998i
$438$	−11.7612	−	8.22452i	−0.561971	−	0.392983i
$439$	−3.46253	+	0.521892i	−0.165257	+	0.0249085i	−0.231150	−	0.972918i	$-0.574249\pi$
$439$	−3.46253	+	0.521892i	−0.165257	+	0.0249085i	0.0658923	+	0.997827i	$0.479011\pi$
$440$	0.784438	−	22.0507i	0.0373966	−	1.05123i
$441$	1.95937	−	6.72019i	0.0933031	−	0.320009i
$442$	0.0532366	−	4.49116i	0.00253221	−	0.213623i
$443$	−3.12491	−	20.7324i	−0.148469	−	0.985026i	−0.931683	−	0.363274i	$-0.881659\pi$
$443$	−3.12491	−	20.7324i	−0.148469	−	0.985026i	0.783214	−	0.621753i	$-0.213579\pi$
$444$	4.58056	+	3.28468i	0.217384	+	0.155884i
$445$	5.69524	−	1.75675i	0.269980	−	0.0832779i
$446$	21.1923	+	1.84099i	1.00349	+	0.0871733i
$447$	−8.73302	−	4.20560i	−0.413058	−	0.198918i
$448$	−10.1035	−	18.5989i	−0.477344	−	0.878716i
$449$	9.85630	−	4.74654i	0.465147	−	0.224003i	−0.186605	−	0.982435i	$-0.559748\pi$
$449$	9.85630	−	4.74654i	0.465147	−	0.224003i	0.651752	+	0.758432i	$0.274034\pi$
$450$	−1.71023	+	0.647928i	−0.0806209	+	0.0305436i
$451$	1.77387	+	23.6707i	0.0835285	+	1.11461i
$452$	2.94493	−	7.01022i	0.138518	−	0.329733i
$453$	5.02896	−	16.3035i	0.236281	−	0.766005i
$454$	4.06967	−	3.16727i	0.190999	−	0.148647i
$455$	9.43619	+	34.1553i	0.442375	+	1.60123i
$456$	−16.2698	−	13.9492i	−0.761902	−	0.653232i
$457$	−9.05378	+	6.17276i	−0.423518	+	0.288750i	−0.756264	−	0.654267i	$-0.772977\pi$
$457$	−9.05378	+	6.17276i	−0.423518	+	0.288750i	0.332746	+	0.943017i	$0.392025\pi$
$458$	11.1400	−	10.0934i	0.520539	−	0.471632i
$459$	0.395388	−	0.228277i	0.0184551	−	0.0106551i
$460$	−12.7858	+	20.9808i	−0.596139	+	0.978234i
$461$	23.7438	−	5.41937i	1.10586	−	0.252405i	0.369658	−	0.929168i	$-0.379475\pi$
$461$	23.7438	−	5.41937i	1.10586	−	0.252405i	0.736201	+	0.676763i	$0.236618\pi$
$462$	6.00553	+	13.9204i	0.279403	+	0.647635i
$463$	0.423199	+	0.0965923i	0.0196677	+	0.00448903i	0.232343	−	0.972634i	$-0.425361\pi$
$463$	0.423199	+	0.0965923i	0.0196677	+	0.00448903i	−0.212676	+	0.977123i	$0.568218\pi$
$464$	1.28482	+	1.31081i	0.0596464	+	0.0608530i
$465$	2.95715	−	19.6194i	0.137135	−	0.909828i
$466$	−2.60900	+	16.0189i	−0.120860	+	0.742060i
$467$	14.5236	+	13.4759i	0.672070	+	0.623590i	0.940534	−	0.339700i	$-0.110326\pi$
$467$	14.5236	+	13.4759i	0.672070	+	0.623590i	−0.268464	+	0.963290i	$0.586516\pi$
$468$	−13.4867	−	3.41651i	−0.623422	−	0.157928i
$469$	3.83363	+	19.4354i	0.177020	+	0.897444i
$470$	1.91138	+	8.85693i	0.0881653	+	0.408540i
$471$	−4.73755	−	2.73522i	−0.218295	−	0.126032i
$472$	21.3277	−	11.3223i	0.981688	−	0.521151i
$473$	−13.0365	+	12.0961i	−0.599418	+	0.556179i
$474$	−5.30929	+	3.52836i	−0.243864	+	0.162063i
$475$	−6.10926	+	7.66078i	−0.280312	+	0.351500i
$476$	1.85606	−	1.54642i	0.0850725	−	0.0708799i
$477$	2.89768	+	3.63358i	0.132676	+	0.166370i
$478$	6.76262	+	2.17410i	0.309315	+	0.0994411i
$479$	6.29022	−	16.0272i	0.287407	−	0.732302i	−0.712135	−	0.702043i	$-0.752272\pi$
$479$	6.29022	−	16.0272i	0.287407	−	0.732302i	0.999542	−	0.0302592i	$-0.00963326\pi$
$480$	0.169181	+	10.8899i	0.00772202	+	0.497052i
$481$	18.2497	−	7.16247i	0.832113	−	0.326580i
$482$	24.3975	−	11.3950i	1.11127	−	0.519026i
$483$	1.76010	−	16.7898i	0.0800871	−	0.763961i
$484$	−9.64762	−	4.93111i	−0.438528	−	0.224141i
$485$	−0.930316	+	12.4142i	−0.0422435	+	0.563700i
$486$	−0.400800	−	1.35623i	−0.0181806	−	0.0615198i
$487$	−20.4416	+	29.9823i	−0.926298	+	1.35863i	0.00717259	+	0.999974i	$0.497717\pi$
$487$	−20.4416	+	29.9823i	−0.926298	+	1.35863i	−0.933470	+	0.358655i	$0.883236\pi$
$488$	−6.66706	+	0.763628i	−0.301804	+	0.0345678i
$489$		−	9.60618i		−	0.434406i
$490$	−10.6791	+	15.7868i	−0.482434	+	0.713175i
$491$			0.0420575i			0.00189803i	1.00000		0.000949013i	$0.000302080\pi$
$491$			0.0420575i			0.00189803i	−1.00000		0.000949013i	$0.999698\pi$
$492$	−1.47116	−	11.6240i	−0.0663251	−	0.524049i
$493$	−0.118015	+	0.173097i	−0.00531514	+	0.00779588i
$494$	−71.4844	+	21.1254i	−3.21624	+	0.950478i
$495$	0.582972	−	7.77922i	0.0262026	−	0.349650i
$496$	36.2499	+	19.6254i	1.62767	+	0.881209i
$497$	−10.5438	+	17.0726i	−0.472954	+	0.765812i
$498$	−8.01157	−	17.1534i	−0.359007	−	0.768662i
$499$	22.1073	−	8.67649i	0.989661	−	0.388413i	0.185383	−	0.982666i	$-0.440648\pi$
$499$	22.1073	−	8.67649i	0.989661	−	0.388413i	0.804278	+	0.594253i	$0.202552\pi$
$500$	24.2010	−	1.23760i	1.08230	−	0.0553470i
$501$	−8.53329	+	21.7425i	−0.381239	+	0.971382i
$502$	6.08113	−	18.9156i	0.271414	−	0.844243i
$503$	−0.385610	−	0.483540i	−0.0171935	−	0.0215600i	0.773160	−	0.634211i	$-0.218675\pi$
$503$	−0.385610	−	0.483540i	−0.0171935	−	0.0215600i	−0.790354	+	0.612651i	$0.790103\pi$
$504$	−3.31140	−	6.71078i	−0.147501	−	0.298922i
$505$	9.79246	−	12.2794i	0.435759	−	0.546424i
$506$	20.2369	+	30.4514i	0.899640	+	1.35373i
$507$	−25.9433	+	24.0719i	−1.15218	+	1.06907i
$508$	−25.9869	+	14.1931i	−1.15298	+	0.629717i
$509$	8.60168	+	4.96618i	0.381263	+	0.220122i	0.678368	−	0.734723i	$-0.262688\pi$
$509$	8.60168	+	4.96618i	0.381263	+	0.220122i	−0.297105	+	0.954845i	$0.596021\pi$
$510$	−1.21513	+	0.262232i	−0.0538069	+	0.0116118i
$511$	−23.8345	−	12.3615i	−1.05437	−	0.546842i
$512$	−21.3986	−	7.35531i	−0.945693	−	0.325062i
$513$	−5.55433	−	5.15366i	−0.245229	−	0.227540i
$514$	19.5482	+	3.18383i	0.862235	+	0.140433i
$515$	0.0760556	−	0.504596i	0.00335141	−	0.0222351i
$516$	6.12152	−	6.29151i	0.269485	−	0.276968i
$517$	13.1455	+	3.00038i	0.578139	+	0.131956i
$518$	9.30271	+	4.96556i	0.408737	+	0.218174i
$519$	19.1071	−	4.36106i	0.838707	−	0.191429i
$520$	32.1122	+	20.0951i	1.40821	+	0.881227i
$521$	4.67483	−	2.69901i	0.204808	−	0.118246i	−0.394088	−	0.919073i	$-0.628940\pi$
$521$	4.67483	−	2.69901i	0.204808	−	0.118246i	0.598896	+	0.800827i	$0.295606\pi$
$522$	0.435723	+	0.480906i	0.0190711	+	0.0210487i
$523$	−8.89706	+	6.06591i	−0.389041	+	0.265244i	−0.742007	−	0.670393i	$-0.766126\pi$
$523$	−8.89706	+	6.06591i	−0.389041	+	0.265244i	0.352965	+	0.935636i	$0.385173\pi$
$524$	−4.45486	+	5.32234i	−0.194611	+	0.232508i
$525$	−3.01249	+	1.62214i	−0.131476	+	0.0707959i
$526$	0.759220	+	0.975531i	0.0331036	+	0.0425352i
$527$	−1.38681	+	4.49594i	−0.0604105	+	0.195846i
$528$	14.7894	+	6.62960i	0.643626	+	0.288516i
$529$	−1.32373	−	17.6640i	−0.0575535	−	0.767998i
$530$	−4.48317	−	11.8335i	−0.194737	−	0.514014i
$531$	7.69173	−	3.70414i	0.333792	−	0.160746i
$532$	−33.6036	−	21.8701i	−1.45690	−	0.948187i
$533$	−36.7169	−	17.6819i	−1.59039	−	0.765890i
$534$	−0.378881	+	4.36145i	−0.0163958	+	0.188738i
$535$	−24.1744	+	7.45683i	−1.04515	+	0.322387i
$536$	17.0626	+	12.5443i	0.736994	+	0.541833i
$537$	−1.89241	−	12.5553i	−0.0816637	−	0.541803i
$538$	36.8917	+	0.437301i	1.59051	+	0.0188534i
$539$	14.5604	+	24.3402i	0.627162	+	1.04841i
$540$	−0.0912748	+	3.84953i	−0.00392784	+	0.165658i
$541$	−10.2107	+	1.53901i	−0.438991	+	0.0661672i	−0.364820	−	0.931078i	$-0.618869\pi$
$541$	−10.2107	+	1.53901i	−0.438991	+	0.0661672i	−0.0741715	+	0.997246i	$0.523631\pi$
$542$	0.564717	−	0.807554i	0.0242567	−	0.0346874i
$543$	4.18962	+	13.5824i	0.179794	+	0.582878i
$544$	0.345209	−	2.55949i	0.0148007	−	0.109737i
$545$	−3.98781	+	8.28077i	−0.170819	+	0.354709i
$546$	−25.8524	−	3.02035i	−1.10638	−	0.129259i
$547$	11.1198	+	23.0904i	0.475447	+	0.987275i	0.991425	+	0.130674i	$0.0417141\pi$
$547$	11.1198	+	23.0904i	0.475447	+	0.987275i	−0.515979	+	0.856601i	$0.672572\pi$
$548$	12.1729	+	33.3176i	0.520002	+	1.42326i
$549$	−2.36594	+	0.177303i	−0.100976	+	0.00756710i
$550$	2.78882	−	6.86539i	0.118916	−	0.292741i
$551$	3.32239	+	1.02482i	0.141539	+	0.0436589i
$552$	−10.7436	−	14.5011i	−0.457278	−	0.617209i
$553$	−8.97911	+	7.84909i	−0.381831	+	0.333777i
$554$	5.85805	+	4.78632i	0.248885	+	0.203351i
$555$	−3.05660	−	4.48320i	−0.129745	−	0.190301i
$556$	7.33104	−	6.48570i	0.310905	−	0.275055i
$557$	3.42918	+	5.93952i	0.145299	+	0.251665i	0.929484	−	0.368861i	$-0.120252\pi$
$557$	3.42918	+	5.93952i	0.145299	+	0.251665i	−0.784185	+	0.620527i	$0.786919\pi$
$558$	12.5342	+	7.43609i	0.530615	+	0.314795i
$559$	−6.79401	−	29.7665i	−0.287356	−	1.25899i
$560$	2.99122	+	20.1548i	0.126402	+	0.851695i
$561$	−0.411638	+	1.80350i	−0.0173794	+	0.0761440i
$562$	29.9369	−	31.5069i	1.26281	−	1.32904i
$563$	−27.7019	−	4.17540i	−1.16750	−	0.175972i	−0.463449	−	0.886124i	$-0.653388\pi$
$563$	−27.7019	−	4.17540i	−1.16750	−	0.175972i	−0.704049	+	0.710152i	$0.748626\pi$
$564$	−6.55583	−	1.14768i	−0.276050	−	0.0483259i
$565$	−4.97866	+	5.36572i	−0.209454	+	0.225737i
$566$	20.1092	+	4.84126i	0.845252	+	0.203493i
$567$	−1.07678	−	2.41672i	−0.0452204	−	0.101493i
$568$	4.02687	+	21.0702i	0.168964	+	0.884084i
$569$	2.61672	−	4.53230i	0.109699	−	0.190004i	−0.805949	−	0.591984i	$-0.798345\pi$
$569$	2.61672	−	4.53230i	0.109699	−	0.190004i	0.915648	+	0.401981i	$0.131678\pi$
$570$	10.1028	+	17.9876i	0.423160	+	0.753419i
$571$	−16.0635	−	17.3124i	−0.672237	−	0.724499i	0.301173	−	0.953570i	$-0.402622\pi$
$571$	−16.0635	−	17.3124i	−0.672237	−	0.724499i	−0.973410	+	0.229070i	$0.926431\pi$
$572$	47.3164	−	30.6425i	1.97840	−	1.28123i
$573$	11.5963	+	9.24777i	0.484444	+	0.386331i
$574$	−5.58637	−	21.1961i	−0.233171	−	0.884709i
$575$	−6.45127	+	5.14472i	−0.269037	+	0.214550i
$576$	−7.45770	−	2.89529i	−0.310737	−	0.120637i
$577$	16.3274	+	6.40803i	0.679719	+	0.266770i	0.679981	−	0.733230i	$-0.261988\pi$
$577$	16.3274	+	6.40803i	0.679719	+	0.266770i	−0.000261983		1.00000i	$0.500083\pi$
$578$	−23.6998	+	1.49380i	−0.985783	+	0.0621339i
$579$	6.02591	+	15.3538i	0.250428	+	0.638080i
$580$	−0.728694	−	1.60968i	−0.0302574	−	0.0668383i
$581$	−19.0757	−	29.8429i	−0.791394	−	1.23809i
$582$	−8.19112	−	4.06493i	−0.339533	−	0.168497i
$583$	−18.7784	−	1.40724i	−0.777720	−	0.0582821i
$584$	−27.7114	+	7.47995i	−1.14671	+	0.309523i
$585$	11.0659	+	7.54461i	0.457519	+	0.311931i
$586$	−13.8966	+	1.92641i	−0.574063	+	0.0795792i
$587$	−1.09947			−0.0453801			−0.0226900	−	0.999743i	$-0.507223\pi$
$587$	−1.09947			−0.0453801			−0.0226900	+	0.999743i	$0.507223\pi$
$588$	−7.79129	−	11.6317i	−0.321307	−	0.479682i
$589$	78.0837			3.21738
$590$	−23.0248	+	3.19180i	−0.947916	+	0.131404i
$591$	13.6491	+	9.30580i	0.561449	+	0.382789i
$592$	10.9176	−	2.80852i	0.448712	−	0.115429i
$593$	−12.1872	−	0.913303i	−0.500468	−	0.0375049i	−0.177895	−	0.984050i	$-0.556929\pi$
$593$	−12.1872	−	0.913303i	−0.500468	−	0.0375049i	−0.322573	+	0.946545i	$0.604548\pi$
$594$	5.13287	+	2.54724i	0.210604	+	0.104515i
$595$	−2.18911	+	0.785097i	−0.0897447	+	0.0321858i
$596$	−17.6605	+	7.99483i	−0.723403	+	0.327481i
$597$	0.281442	+	0.717102i	0.0115187	+	0.0293490i
$598$	−62.6476	+	3.94868i	−2.56185	+	0.161474i
$599$	18.0842	+	7.09751i	0.738899	+	0.289997i	0.704785	−	0.709421i	$-0.251044\pi$
$599$	18.0842	+	7.09751i	0.738899	+	0.289997i	0.0341145	+	0.999418i	$0.489139\pi$
$600$	−1.20170	+	3.45466i	−0.0490594	+	0.141036i
$601$	25.9568	−	20.6998i	1.05880	−	0.844364i	0.0705946	−	0.997505i	$-0.477510\pi$
$601$	25.9568	−	20.6998i	1.05880	−	0.844364i	0.988204	+	0.153141i	$0.0489389\pi$
$602$	9.80611	−	13.1733i	0.399667	−	0.536905i
$603$	5.85392	+	4.66834i	0.238390	+	0.190110i
$604$	−18.5484	−	28.6414i	−0.754726	−	1.16540i
$605$	7.09430	+	7.64583i	0.288424	+	0.310847i
$606$	5.64947	+	10.0586i	0.229494	+	0.408604i
$607$	15.7920	−	27.3525i	0.640976	−	1.11020i	−0.344240	−	0.938882i	$-0.611863\pi$
$607$	15.7920	−	27.3525i	0.640976	−	1.11020i	0.985215	−	0.171320i	$-0.0548033\pi$
$608$	−42.2788	+	7.04584i	−1.71463	+	0.285746i
$609$	0.926332	+	0.784760i	0.0375369	+	0.0318001i
$610$	6.28059	+	1.51204i	0.254294	+	0.0612208i
$611$	−15.7454	+	16.9695i	−0.636990	+	0.686512i
$612$	0.157456	−	0.899430i	0.00636478	−	0.0363573i
$613$	−17.3802	−	2.61964i	−0.701980	−	0.105806i	−0.211653	−	0.977345i	$-0.567885\pi$
$613$	−17.3802	−	2.61964i	−0.701980	−	0.105806i	−0.490327	+	0.871538i	$0.663123\pi$
$614$	−12.7380	+	13.4060i	−0.514063	+	0.541023i
$615$	−2.50984	+	10.9963i	−0.101207	+	0.443415i
$616$	29.0585	+	8.65904i	1.17080	+	0.348883i
$617$	4.55707	+	19.9658i	0.183461	+	0.803793i	0.979966	+	0.199162i	$0.0638222\pi$
$617$	4.55707	+	19.9658i	0.183461	+	0.803793i	−0.796506	+	0.604631i	$0.793321\pi$
$618$	0.322370	+	0.191250i	0.0129676	+	0.00769322i
$619$	−3.44189	−	5.96152i	−0.138341	−	0.239614i	0.788528	−	0.614999i	$-0.210844\pi$
$619$	−3.44189	−	5.96152i	−0.138341	−	0.239614i	−0.926869	+	0.375385i	$0.877510\pi$
$620$	−26.2935	−	29.7206i	−1.05597	−	1.19361i
$621$	−3.59438	−	5.27199i	−0.144238	−	0.211558i
$622$	37.4429	+	30.5927i	1.50132	+	1.22666i
$623$	0.369662	+	8.18191i	0.0148102	+	0.327801i
$624$	−22.5526	+	16.2983i	−0.902825	+	0.652454i
$625$	−16.1126	−	4.97007i	−0.644503	−	0.198803i
$626$	10.0034	−	24.6258i	0.399815	−	0.984245i
$627$	30.6149	−	2.29427i	1.22264	−	0.0916242i
$628$	−10.2765	+	3.75462i	−0.410076	+	0.149826i
$629$	0.558276	+	1.15927i	0.0222599	+	0.0462232i
$630$	0.777194	+	7.16179i	0.0309642	+	0.285333i
$631$	4.73681	−	9.83609i	0.188570	−	0.391569i	−0.785154	−	0.619300i	$-0.787416\pi$
$631$	4.73681	−	9.83609i	0.188570	−	0.391569i	0.973724	+	0.227731i	$0.0731308\pi$
$632$	−1.40418	+	12.6720i	−0.0558551	+	0.504065i
$633$	−1.37724	−	4.46492i	−0.0547406	−	0.177465i
$634$	−4.21597	+	6.02889i	−0.167437	+	0.239438i
$635$	28.1860	−	4.24836i	1.11853	−	0.168591i
$636$	9.29244	+	0.220329i	0.368469	+	0.00873663i
$637$	−48.6886	+	0.754718i	−1.92911	+	0.0299030i
$638$	−2.62922	−	0.0311659i	−0.104092	−	0.00123387i
$639$	1.13037	+	7.49954i	0.0447169	+	0.296677i
$640$	16.9186	+	13.7198i	0.668766	+	0.542322i
$641$	19.7756	−	6.09997i	0.781090	−	0.240934i	0.121531	−	0.992588i	$-0.461220\pi$
$641$	19.7756	−	6.09997i	0.781090	−	0.240934i	0.659558	+	0.751653i	$0.270743\pi$
$642$	1.60823	−	18.5129i	0.0634716	−	0.730647i
$643$	−14.8619	−	7.15711i	−0.586095	−	0.282249i	0.117244	−	0.993103i	$-0.462594\pi$
$643$	−14.8619	−	7.15711i	−0.586095	−	0.282249i	−0.703339	+	0.710854i	$0.748308\pi$
$644$	−23.4905	−	24.2523i	−0.925654	−	0.955676i
$645$	−7.61348	+	3.66646i	−0.299781	+	0.144367i
$646$	−1.73322	−	4.57488i	−0.0681925	−	0.179996i
$647$	0.00999027	+	0.133311i	0.000392758	+	0.00524099i	0.997397	−	0.0721093i	$-0.0229731\pi$
$647$	0.00999027	+	0.133311i	0.000392758	+	0.00524099i	−0.997004	+	0.0773503i	$0.975354\pi$
$648$	−2.59451	−	1.12629i	−0.101922	−	0.0442449i
$649$	−10.1959	+	33.0544i	−0.400226	+	1.29750i
$650$	7.81366	+	10.0399i	0.306477	+	0.393796i
$651$	25.0742	+	10.7092i	0.982737	+	0.419728i
$652$	−14.7327	−	12.3314i	−0.576976	−	0.482935i
$653$	19.6912	−	13.4252i	0.770576	−	0.525370i	−0.113035	−	0.993591i	$-0.536057\pi$
$653$	19.6912	−	13.4252i	0.770576	−	0.525370i	0.883611	+	0.468221i	$0.155105\pi$
$654$	−4.53295	−	5.00300i	−0.177252	−	0.195633i
$655$	5.78632	−	3.34074i	0.226090	−	0.130533i
$656$	−19.7158	−	12.6654i	−0.769773	−	0.494499i
$657$	−9.89368	+	2.25817i	−0.385989	+	0.0880995i
$658$	−12.4406	−	0.516623i	−0.484987	−	0.0201400i
$659$	37.3473	+	8.52428i	1.45484	+	0.332059i	0.875577	−	0.483078i	$-0.160481\pi$
$659$	37.3473	+	8.52428i	1.45484	+	0.332059i	0.579268	+	0.815137i	$0.303339\pi$
$660$	−11.1824	−	10.8802i	−0.435273	−	0.423512i
$661$	3.26771	−	21.6799i	0.127099	−	0.843249i	−0.830888	−	0.556439i	$-0.812167\pi$
$661$	3.26771	−	21.6799i	0.127099	−	0.843249i	0.957988	−	0.286810i	$-0.0925947\pi$
$662$	−2.18041	−	0.355124i	−0.0847440	−	0.0138023i
$663$	−2.32814	−	2.16020i	−0.0904174	−	0.0838950i
$664$	−36.5920	−	9.73263i	−1.42004	−	0.377699i
$665$	23.1592	+	30.8759i	0.898077	+	1.19732i
$666$	3.89595	−	0.840769i	0.150965	−	0.0325791i
$667$	2.53566	+	1.46396i	0.0981810	+	0.0566848i
$668$	22.3915	+	40.9979i	0.866355	+	1.58626i
$669$	11.0263	−	10.2309i	0.426303	−	0.395551i
$670$	−11.2838	−	16.9793i	−0.435932	−	0.655967i
$671$	5.99379	−	7.51597i	0.231388	−	0.290151i
$672$	−14.5429	−	3.53602i	−0.561005	−	0.136405i
$673$	5.63571	+	7.06695i	0.217241	+	0.272411i	0.878496	−	0.477750i	$-0.158547\pi$
$673$	5.63571	+	7.06695i	0.217241	+	0.272411i	−0.661255	+	0.750161i	$0.729976\pi$
$674$	−11.5424	+	35.9031i	−0.444598	+	1.38294i
$675$	−0.472456	+	1.20380i	−0.0181848	+	0.0463342i
$676$	3.61492	+	70.6892i	0.139035	+	2.71882i
$677$	17.3444	−	6.80718i	0.666600	−	0.261621i	−0.00781956	−	0.999969i	$-0.502489\pi$
$677$	17.3444	−	6.80718i	0.666600	−	0.261621i	0.674420	+	0.738348i	$0.264394\pi$
$678$	−2.27524	−	4.87146i	−0.0873801	−	0.187087i
$679$	−16.1907	−	5.52491i	−0.621342	−	0.212027i
$680$	−1.15768	+	2.20023i	−0.0443950	+	0.0843749i
$681$	0.272503	−	3.63629i	0.0104423	−	0.139343i
$682$	−56.6304	+	16.7357i	−2.16849	+	0.640842i
$683$	−15.9192	+	23.3492i	−0.609132	+	0.893432i	−0.999631	−	0.0271713i	$-0.991350\pi$
$683$	−15.9192	+	23.3492i	−0.609132	+	0.893432i	0.390499	+	0.920603i	$0.372302\pi$
$684$	−15.0340	+	1.90275i	−0.574841	+	0.0727535i
$685$		−	34.1470i		−	1.30469i
$686$	−17.3096	−	19.6565i	−0.660883	−	0.750489i
$687$		−	10.6296i		−	0.405544i
$688$	−1.79091	−	17.4647i	−0.0682779	−	0.665837i
$689$	18.2120	−	26.7121i	0.693823	−	1.01765i
$690$	4.92376	+	16.6611i	0.187444	+	0.634276i
$691$	−3.30151	+	44.0556i	−0.125595	+	1.67595i	0.477767	+	0.878486i	$0.341446\pi$
$691$	−3.30151	+	44.0556i	−0.125595	+	1.67595i	−0.603363	+	0.797467i	$0.706173\pi$
$692$	17.8392	−	34.9021i	0.678146	−	1.32678i
$693$	10.1457	+	3.46212i	0.385404	+	0.131515i
$694$	−3.42766	+	1.60090i	−0.130112	+	0.0607695i
$695$	−8.77128	+	3.44247i	−0.332714	+	0.130580i
$696$	1.29688	−	0.0509166i	0.0491583	−	0.00192999i
$697$	0.977161	−	2.48977i	0.0370126	−	0.0943066i
$698$	4.49907	+	1.44640i	0.170292	+	0.0547469i
$699$	7.15536	+	8.97253i	0.270640	+	0.339372i
$700$	−1.37930	+	6.70248i	−0.0521326	+	0.253330i
$701$	21.2201	−	26.6092i	0.801472	−	1.00501i	−0.198219	−	0.980158i	$-0.563516\pi$
$701$	21.2201	−	26.6092i	0.801472	−	1.00501i	0.999691	−	0.0248568i	$-0.00791297\pi$
$702$	−8.19346	+	5.44508i	−0.309242	+	0.205511i
$703$	15.6536	−	14.5244i	0.590387	−	0.547799i
$704$	29.1527	−	14.1716i	1.09873	−	0.534113i
$705$	5.54860	+	3.20349i	0.208972	+	0.120650i
$706$	5.81677	+	26.9537i	0.218917	+	1.01442i
$707$	12.9506	+	17.2658i	0.487057	+	0.649346i
$708$	4.19291	−	16.5515i	0.157579	−	0.622044i
$709$	−17.4944	−	16.2324i	−0.657016	−	0.609622i	0.279542	−	0.960133i	$-0.409817\pi$
$709$	−17.4944	−	16.2324i	−0.657016	−	0.609622i	−0.936558	+	0.350511i	$0.886008\pi$
$710$	3.31959	−	20.3818i	0.124582	−	0.764916i
$711$	−0.671831	+	4.45731i	−0.0251956	+	0.167162i
$712$	6.20264	+	6.17984i	0.232454	+	0.231599i
$713$	64.1070	+	14.6320i	2.40083	+	0.547973i
$714$	0.0708782	−	1.70680i	0.00265255	−	0.0638753i
$715$	−52.9061	+	12.0755i	−1.97858	+	0.451597i
$716$	−21.6850	−	13.2149i	−0.810406	−	0.493864i
$717$	4.34999	−	2.51147i	0.162453	−	0.0937924i
$718$	−18.5089	+	16.7699i	−0.690744	+	0.625846i
$719$	7.90163	−	5.38724i	0.294681	−	0.200910i	−0.406950	−	0.913450i	$-0.633408\pi$
$719$	7.90163	−	5.38724i	0.294681	−	0.200910i	0.701631	+	0.712540i	$0.252455\pi$
$720$	5.78673	+	5.08161i	0.215659	+	0.189380i
$721$	0.644890	+	0.275433i	0.0240169	+	0.0102577i
$722$	−42.8683	+	33.3628i	−1.59539	+	1.24164i
$723$	5.61228	−	18.1946i	0.208723	−	0.676664i
$724$	26.2091	+	11.0102i	0.974053	+	0.409191i
$725$	−0.0443455	−	0.591749i	−0.00164695	−	0.0219770i
$726$	−7.16442	+	2.71428i	−0.265897	+	0.100736i
$727$	−27.8675	+	13.4203i	−1.03355	+	0.497731i	−0.872191	−	0.489165i	$-0.837301\pi$
$727$	−27.8675	+	13.4203i	−1.03355	+	0.497731i	−0.161357	+	0.986896i	$0.551587\pi$
$728$	−37.8188	+	35.7718i	−1.40166	+	1.32579i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	27.5276	+	2.39133i	1.01884	+	0.0885072i
$731$	1.91483	−	0.590646i	0.0708225	−	0.0218458i
$732$	−2.76522	+	3.85616i	−0.102206	+	0.142528i
$733$	−0.535587	−	3.55339i	−0.0197824	−	0.131247i	0.976760	−	0.214337i	$-0.0687592\pi$
$733$	−0.535587	−	3.55339i	−0.0197824	−	0.131247i	−0.996542	+	0.0830900i	$0.973521\pi$
$734$	−0.413423	+	34.8773i	−0.0152597	+	1.28734i
$735$	3.20223	+	13.0912i	0.118116	+	0.482876i
$736$	−36.0314	−	2.13792i	−1.32813	−	0.0788048i
$737$	−29.9990	+	4.52163i	−1.10503	+	0.166556i
$738$	−6.78955	−	4.74789i	−0.249927	−	0.174772i
$739$	−2.64386	−	8.57118i	−0.0972559	−	0.315296i	0.893851	−	0.448364i	$-0.147993\pi$
$739$	−2.64386	−	8.57118i	−0.0972559	−	0.315296i	−0.991107	+	0.133068i	$0.957517\pi$
$740$	−10.7995	−	1.06727i	−0.396996	−	0.0392335i
$741$	−22.8692	+	47.4884i	−0.840122	+	1.74453i
$742$	17.2879	−	1.87608i	0.634660	−	0.0688730i
$743$	−16.7871	−	34.8588i	−0.615860	−	1.27885i	−0.942661	−	0.333753i	$-0.891685\pi$
$743$	−16.7871	−	34.8588i	−0.615860	−	1.27885i	0.326801	−	0.945093i	$-0.394029\pi$
$744$	27.4946	−	9.67760i	1.00800	−	0.354798i
$745$	18.6097	−	1.39460i	0.681806	−	0.0510943i
$746$	0.0463103	+	0.0188119i	0.00169554	+	0.000688752i
$747$	−12.7923	−	3.94589i	−0.468044	−	0.144373i
$748$	2.23755	+	2.94646i	0.0818130	+	0.107733i
$749$	−1.56910	−	34.7295i	−0.0573335	−	1.26899i
$750$	10.8416	−	13.2692i	0.395879	−	0.484522i
$751$	15.8120	+	23.1920i	0.576989	+	0.846288i	0.998156	−	0.0606952i	$-0.0193318\pi$
$751$	15.8120	+	23.1920i	0.576989	+	0.846288i	−0.421167	+	0.906983i	$0.638379\pi$
$752$	−10.1758	+	8.58119i	−0.371075	+	0.312924i
$753$	−7.02477	−	12.1673i	−0.255997	−	0.443399i
$754$	2.30331	−	3.88244i	0.0838817	−	0.141390i
$755$	7.30950	+	32.0250i	0.266020	+	1.16551i
$756$	−5.08870	−	1.45092i	−0.185074	−	0.0527694i
$757$	−2.36758	+	10.3730i	−0.0860510	+	0.377014i	−0.999555	−	0.0298147i	$-0.990508\pi$
$757$	−2.36758	+	10.3730i	−0.0860510	+	0.377014i	0.913504	+	0.406829i	$0.133365\pi$
$758$	−14.1448	−	13.4399i	−0.513762	−	0.488160i
$759$	25.5648	+	3.85328i	0.927945	+	0.139865i
$760$	40.5559	+	7.59630i	1.47112	+	0.275547i
$761$	−21.6186	+	23.2993i	−0.783672	+	0.844598i	−0.991026	−	0.133668i	$-0.957324\pi$
$761$	−21.6186	+	23.2993i	−0.783672	+	0.844598i	0.207354	+	0.978266i	$0.433515\pi$
$762$	−4.90067	+	20.3560i	−0.177533	+	0.737419i
$763$	−9.63688	−	8.16407i	−0.348879	−	0.295559i
$764$	29.0691	−	5.91359i	1.05168	−	0.213946i
$765$	−0.439504	+	0.761243i	−0.0158903	+	0.0275228i
$766$	−19.3325	+	10.8582i	−0.698513	+	0.392322i
$767$	−40.3938	−	43.5342i	−1.45854	−	1.57193i
$768$	−14.0138	+	7.72094i	−0.505680	+	0.278605i
$769$	14.0288	+	11.1876i	0.505893	+	0.403436i	0.842904	−	0.538065i	$-0.180844\pi$
$769$	14.0288	+	11.1876i	0.505893	+	0.403436i	−0.337011	+	0.941501i	$0.609416\pi$
$770$	−23.4139	−	17.4291i	−0.843779	−	0.628102i
$771$	10.9494	−	8.73186i	0.394333	−	0.314470i
$772$	31.2829	+	10.4678i	1.12590	+	0.376745i
$773$	−35.9170	−	14.0964i	−1.29184	−	0.507011i	−0.382846	−	0.923812i	$-0.625056\pi$
$773$	−35.9170	−	14.0964i	−1.29184	−	0.507011i	−0.908998	+	0.416801i	$0.863151\pi$
$774$	−0.390459	−	6.19481i	−0.0140347	−	0.222668i
$775$	−4.86884	−	12.4056i	−0.174894	−	0.445622i
$776$	−16.7491	+	7.34430i	−0.601259	+	0.263645i
$777$	7.01872	−	2.51718i	0.251795	−	0.0903032i
$778$	12.8988	−	25.9919i	0.462443	−	0.931855i
$779$	−44.2645	−	3.31717i	−1.58594	−	0.118850i
$780$	25.7761	−	7.28643i	0.922934	−	0.260896i
$781$	−25.3905	−	17.3109i	−0.908542	−	0.619433i
$782$	−0.565696	−	4.08078i	−0.0202292	−	0.145928i
$783$	0.458871			0.0163987
$784$	−27.8407	−	2.98228i	−0.994312	−	0.106510i
$785$	10.5323			0.375914
$786$	0.673897	+	4.86132i	0.0240371	+	0.173397i
$787$	36.0161	+	24.5554i	1.28384	+	0.875304i	0.996587	−	0.0825518i	$-0.0263070\pi$
$787$	36.0161	+	24.5554i	1.28384	+	0.875304i	0.287249	+	0.957856i	$0.407259\pi$
$788$	31.7932	−	8.98735i	1.13259	−	0.320161i
$789$	0.871648	+	0.0653210i	0.0310315	+	0.00232549i
$790$	5.45593	−	10.9941i	0.194113	−	0.391152i
$791$	−5.41740	−	8.47522i	−0.192620	−	0.301344i
$792$	10.4957	−	4.60222i	0.372947	−	0.163533i
$793$	6.02976	+	15.3636i	0.214123	+	0.545576i
$794$	−1.49615	−	23.7371i	−0.0530963	−	0.842397i
$795$	−8.32938	−	3.26904i	−0.295412	−	0.115941i
$796$	1.46108	+	0.488902i	0.0517866	+	0.0173287i
$797$	−23.1661	+	18.4744i	−0.820586	+	0.654396i	−0.941030	−	0.338324i	$-0.890140\pi$
$797$	−23.1661	+	18.4744i	−0.820586	+	0.654396i	0.120443	+	0.992720i	$0.461568\pi$
$798$	−27.4144	+	7.22522i	−0.970458	+	0.255770i
$799$	−1.18784	−	0.947272i	−0.0420228	−	0.0335121i
$800$	3.75567	+	6.27774i	0.132783	+	0.221952i
$801$	2.10556	+	2.26925i	0.0743963	+	0.0801801i
$802$	42.5551	−	23.9012i	1.50267	−	0.843981i
$803$	20.5593	−	35.6097i	0.725520	−	1.25664i
$804$	14.6743	−	2.98522i	0.517523	−	0.105281i
$805$	13.2280	+	29.6890i	0.466226	+	1.04640i
$806$	23.7295	−	98.5657i	0.835837	−	3.47183i
$807$	17.7445	−	19.1240i	0.624635	−	0.673197i
$808$	22.6788	+	4.24783i	0.797837	+	0.149438i
$809$	2.48918	+	0.375184i	0.0875150	+	0.0131908i	0.192654	−	0.981267i	$-0.438291\pi$
$809$	2.48918	+	0.375184i	0.0875150	+	0.0131908i	−0.105139	+	0.994458i	$0.533529\pi$
$810$	1.97386	+	1.87550i	0.0693543	+	0.0658983i
$811$	4.94215	−	21.6530i	0.173542	−	0.760338i	−0.810979	−	0.585075i	$-0.801065\pi$
$811$	4.94215	−	21.6530i	0.173542	−	0.760338i	0.984522	−	0.175263i	$-0.0560777\pi$
$812$	2.39269	−	0.413291i	0.0839668	−	0.0145037i
$813$	−0.155052	−	0.679325i	−0.00543790	−	0.0238250i
$814$	−8.23978	+	13.8889i	−0.288804	+	0.486805i
$815$	9.24742	+	16.0170i	0.323923	+	0.561051i
$816$	−1.17730	−	1.39608i	−0.0412137	−	0.0488725i
$817$	−18.7338	−	27.4774i	−0.655412	−	0.961313i
$818$	23.6944	−	28.9999i	0.828454	−	1.01396i
$819$	−13.8568	+	12.1130i	−0.484197	+	0.423261i
$820$	13.6428	+	17.9652i	0.476428	+	0.627371i
$821$	18.8526	+	5.81525i	0.657959	+	0.202954i	0.605716	−	0.795681i	$-0.292887\pi$
$821$	18.8526	+	5.81525i	0.657959	+	0.202954i	0.0522431	+	0.998634i	$0.483363\pi$
$822$	23.2382	+	9.43969i	0.810525	+	0.329247i
$823$	−30.4743	+	2.28373i	−1.06227	+	0.0796060i	−0.594382	−	0.804183i	$-0.702603\pi$
$823$	−30.4743	+	2.28373i	−1.06227	+	0.0796060i	−0.467886	+	0.883789i	$0.654984\pi$
$824$	0.707138	−	0.248900i	0.0246343	−	0.00867085i
$825$	−2.27347	−	4.72090i	−0.0791519	−	0.164361i
$826$	3.70672	−	31.7274i	0.128973	−	1.10394i
$827$	7.05959	−	14.6594i	0.245486	−	0.509757i	−0.741423	−	0.671038i	$-0.765849\pi$
$827$	7.05959	−	14.6594i	0.245486	−	0.509757i	0.986908	+	0.161282i	$0.0515628\pi$
$828$	−12.6996	−	1.25504i	−0.441340	−	0.0436158i
$829$	−8.87101	−	28.7591i	−0.308103	−	0.998845i	−0.968727	−	0.248128i	$-0.920184\pi$
$829$	−8.87101	−	28.7591i	−0.308103	−	0.998845i	0.660624	−	0.750717i	$-0.270292\pi$
$830$	29.8710	+	20.8886i	1.03684	+	0.725053i
$831$	5.28935	−	0.797241i	0.183485	−	0.0276560i
$832$	−3.95447	+	55.5101i	−0.137097	+	1.92447i
$833$	−0.288194	−	3.18286i	−0.00998534	−	0.110280i
$834$	0.0820367	−	6.92080i	0.00284070	−	0.239648i
$835$	−6.70236	−	44.4673i	−0.231945	−	1.53885i
$836$	35.7815	−	49.8981i	1.23753	−	1.72576i
$837$	9.84754	−	3.03756i	0.340381	−	0.104994i
$838$	6.74190	+	0.585672i	0.232895	+	0.0202317i
$839$	−43.2551	−	20.8306i	−1.49333	−	0.719151i	−0.503849	−	0.863792i	$-0.668083\pi$
$839$	−43.2551	−	20.8306i	−1.49333	−	0.719151i	−0.989484	+	0.144640i	$0.953798\pi$
$840$	11.9815	+	8.00160i	0.413400	+	0.276081i
$841$	25.9384	−	12.4913i	0.894427	−	0.430733i
$842$	22.9454	−	8.69300i	0.790752	−	0.299580i
$843$	−2.29660	−	30.6460i	−0.0790991	−	1.05550i
$844$	−8.61565	−	3.61936i	−0.296563	−	0.124583i
$845$	20.0841	−	65.1110i	0.690913	−	2.23989i
$846$	−3.71395	+	2.89043i	−0.127688	+	0.0993751i
$847$	−12.6198	+	6.79540i	−0.433621	+	0.233493i
$848$	12.2666	−	13.9686i	0.421235	−	0.479685i
$849$	12.0843	−	8.23890i	0.414730	−	0.282758i
$850$	−0.618764	+	0.560628i	−0.0212234	+	0.0192294i
$851$	15.5734	−	8.99129i	0.533848	−	0.308217i
$852$	12.9528	+	7.89351i	0.443757	+	0.270427i
$853$	−4.12019	+	0.940407i	−0.141073	+	0.0321989i	−0.292474	−	0.956273i	$-0.594479\pi$
$853$	−4.12019	+	0.940407i	−0.141073	+	0.0321989i	0.151401	+	0.988472i	$0.451621\pi$
$854$	−4.18028	+	7.83153i	−0.143046	+	0.267989i
$855$	14.2223	+	3.24614i	0.486392	+	0.111016i
$856$	−26.3282	−	26.2314i	−0.899878	−	0.896571i
$857$	−1.31088	+	8.69709i	−0.0447786	+	0.297087i	0.955221	+	0.295894i	$0.0956177\pi$
$857$	−1.31088	+	8.69709i	−0.0447786	+	0.297087i	−0.999999	+	0.00119244i	$0.999620\pi$
$858$	6.40775	−	39.3426i	0.218757	−	1.34314i
$859$	−28.0752	−	26.0499i	−0.957912	−	0.888813i	0.0359595	−	0.999353i	$-0.488551\pi$
$859$	−28.0752	−	26.0499i	−0.957912	−	0.888813i	−0.993872	+	0.110541i	$0.964742\pi$
$860$	−4.15026	+	16.3832i	−0.141523	+	0.558661i
$861$	−13.7593	−	7.13612i	−0.468915	−	0.243198i
$862$	0.795103	+	3.68434i	0.0270813	+	0.125489i
$863$	45.9187	+	26.5112i	1.56309	+	0.902450i	0.996942	+	0.0781463i	$0.0249001\pi$
$863$	45.9187	+	26.5112i	1.56309	+	0.902450i	0.566148	+	0.824304i	$0.308433\pi$
$864$	−5.05791	+	2.53329i	−0.172074	+	0.0861843i
$865$	−27.6603	+	25.6650i	−0.940477	+	0.872635i
$866$	−20.7392	+	13.7825i	−0.704747	+	0.468350i
$867$	−10.4694	+	13.1282i	−0.355558	+	0.445856i
$868$	48.6121	−	24.7081i	1.65000	−	0.838648i
$869$	−11.3876	−	14.2796i	−0.386298	−	0.484402i
$870$	−1.18946	−	0.382396i	−0.0403263	−	0.0129644i
$871$	19.0289	−	48.4848i	0.644769	−	1.64284i
$872$	−13.4918	+	0.529699i	−0.456892	+	0.0179379i
$873$	−6.01902	+	2.36229i	−0.203713	+	0.0799515i
$874$	−61.9487	+	28.9334i	−2.09545	+	0.978688i
$875$	16.8444	−	27.2746i	0.569444	−	0.922050i
$876$	−9.23718	+	18.0724i	−0.312096	+	0.610609i
$877$	−2.25243	+	30.0566i	−0.0760591	+	1.01494i	0.820394	+	0.571799i	$0.193754\pi$
$877$	−2.25243	+	30.0566i	−0.0760591	+	1.01494i	−0.896453	+	0.443139i	$0.853865\pi$
$878$	1.40346	+	4.74903i	0.0473643	+	0.160272i
$879$	−5.58833	+	8.19658i	−0.188490	+	0.276464i
$880$	−31.0414	+	3.18312i	−1.04640	+	0.107303i
$881$			32.7319i			1.10277i	0.834252	+	0.551383i	$0.185900\pi$
$881$			32.7319i			1.10277i	−0.834252	+	0.551383i	$0.814100\pi$
$882$	−9.79424	−	1.43974i	−0.329789	−	0.0484785i
$883$		−	12.8044i		−	0.430903i	−0.976515	−	0.215452i	$-0.930878\pi$
$883$		−	12.8044i		−	0.430903i	0.976515	−	0.215452i	$-0.0691223\pi$
$884$	−6.30163	+	0.797552i	−0.211947	+	0.0268246i
$885$	−9.25911	+	13.5806i	−0.311242	+	0.456508i
$886$	−28.4355	+	8.40340i	−0.955309	+	0.282318i
$887$	−0.962598	+	12.8450i	−0.0323209	+	0.431292i	0.957447	+	0.288608i	$0.0931924\pi$
$887$	−0.962598	+	12.8450i	−0.0323209	+	0.431292i	−0.989768	+	0.142684i	$0.954427\pi$
$888$	3.71175	−	7.05437i	0.124558	−	0.236729i
$889$	−4.08393	+	38.9571i	−0.136971	+	1.30658i
$890$	−3.56683	−	7.63686i	−0.119560	−	0.255988i
$891$	3.77175	−	1.48030i	0.126358	−	0.0495920i
$892$	−1.53640	−	30.0441i	−0.0514425	−	1.00595i
$893$	−9.21187	+	23.4715i	−0.308264	+	0.785443i
$894$	−4.19544	+	13.0501i	−0.140316	+	0.436459i
$895$	15.2418	+	19.1126i	0.509477	+	0.638864i
$896$	−24.0917	+	17.7648i	−0.804848	+	0.593481i
$897$	−27.6745	+	34.7027i	−0.924025	+	1.15869i
$898$	−8.56301	−	12.8852i	−0.285751	−	0.429983i
$899$	−3.46649	+	3.21643i	−0.115614	+	0.107274i
$900$	1.23973	+	2.26990i	0.0413245	+	0.0756633i
$901$	1.83757	+	1.06092i	0.0612184	+	0.0353445i
$902$	32.8139	−	7.08143i	1.09258	−	0.235786i
$903$	−2.24724	−	11.3929i	−0.0747836	−	0.379132i
$904$	−10.3919	−	2.76401i	−0.345630	−	0.0919297i
$905$	−20.0608	−	18.6137i	−0.666844	−	0.618741i
$906$	−23.8148	−	3.87872i	−0.791193	−	0.128862i
$907$	4.21037	−	27.9340i	0.139803	−	0.927532i	−0.803430	−	0.595400i	$-0.796994\pi$
$907$	4.21037	−	27.9340i	0.139803	−	0.927532i	0.943233	−	0.332133i	$-0.107768\pi$
$908$	−5.22705	−	5.08582i	−0.173466	−	0.168779i
$909$	7.95307	+	1.81524i	0.263787	+	0.0602076i
$910$	46.0130	−	19.8509i	1.52532	−	0.658052i
$911$	25.0444	−	5.71622i	0.829758	−	0.189387i	0.213512	−	0.976941i	$-0.431510\pi$
$911$	25.0444	−	5.71622i	0.829758	−	0.189387i	0.616246	+	0.787554i	$0.288653\pi$
$912$	−16.3809	+	25.4997i	−0.542427	+	0.844381i
$913$	46.9749	−	27.1210i	1.55464	−	0.897574i
$914$	10.4050	+	11.4840i	0.344168	+	0.379858i
$915$	3.77421	−	2.57321i	0.124771	−	0.0850677i
$916$	−16.3022	−	13.6451i	−0.538641	−	0.450848i
$917$	2.44505	+	8.85012i	0.0807426	+	0.292257i
$918$	−0.396554	−	0.509537i	−0.0130882	−	0.0168172i
$919$	−4.10311	+	13.3020i	−0.135349	+	0.438791i	−0.997720	−	0.0674856i	$-0.978502\pi$
$919$	−4.10311	+	13.3020i	−0.135349	+	0.438791i	0.862371	+	0.506277i	$0.168979\pi$
$920$	31.8731	+	13.8363i	1.05082	+	0.456169i
$921$	0.977191	+	13.0397i	0.0321996	+	0.429673i
$922$	−12.2023	−	32.2084i	−0.401861	−	1.06073i
$923$	47.5340	−	22.8912i	1.56460	−	0.753472i
$924$	18.3337	−	11.1158i	0.603135	−	0.365684i
$925$	−3.28364	−	1.58132i	−0.107965	−	0.0519934i
$926$	0.0531284	−	0.611581i	0.00174591	−	0.0200978i
$927$	0.253271	−	0.0781237i	0.00831851	−	0.00256592i
$928$	1.58671	−	2.05435i	0.0520864	−	0.0674373i
$929$	−6.30916	−	41.8585i	−0.206997	−	1.37333i	−0.815029	−	0.579421i	$-0.803279\pi$
$929$	−6.30916	−	41.8585i	−0.206997	−	1.37333i	0.608032	−	0.793913i	$-0.291959\pi$
$930$	−28.0575	−	0.332583i	−0.920041	−	0.0109058i
$931$	−49.0663	+	20.1402i	−1.60808	+	0.660068i
$932$	22.9461	+	0.544067i	0.751626	+	0.0178215i
$933$	33.8079	−	5.09573i	1.10682	−	0.166827i
$934$	16.0570	−	22.9617i	0.525400	−	0.751330i
$935$	−1.04980	−	3.40336i	−0.0343321	−	0.111302i
$936$	−2.16697	+	19.5558i	−0.0708296	+	0.639202i
$937$	−8.71657	+	18.1001i	−0.284758	+	0.591306i	−0.993457	−	0.114205i	$-0.963568\pi$
$937$	−8.71657	+	18.1001i	−0.284758	+	0.591306i	0.708699	+	0.705511i	$0.249282\pi$
$938$	26.4810	−	9.14433i	0.864637	−	0.298573i
$939$	−8.15481	−	16.9336i	−0.266122	−	0.552608i
$940$	12.0358	−	4.39740i	0.392564	−	0.143427i
$941$	1.00555	−	0.0753554i	0.0327799	−	0.00245652i	−0.0583300	−	0.998297i	$-0.518578\pi$
$941$	1.00555	−	0.0753554i	0.0327799	−	0.00245652i	0.0911100	+	0.995841i	$0.470959\pi$
$942$	−2.91158	+	7.16759i	−0.0948644	+	0.233533i
$943$	−35.7197	−	11.0181i	−1.16319	−	0.358798i
$944$	−20.0021	−	27.6776i	−0.651012	−	0.900830i
$945$	4.12185	+	2.99300i	0.134084	+	0.0973622i
$946$	19.4759	+	15.9128i	0.633217	+	0.517371i
$947$	−0.322416	−	0.472897i	−0.0104771	−	0.0153671i	0.820964	−	0.570979i	$-0.193436\pi$
$947$	−0.322416	−	0.472897i	−0.0104771	−	0.0153671i	−0.831442	+	0.555612i	$0.812484\pi$
$948$	5.97359	+	6.75218i	0.194013	+	0.219301i
$949$	35.2969	+	61.1360i	1.14579	+	1.98456i
$950$	11.9177	+	7.07034i	0.386661	+	0.229392i
$951$	1.15756	+	5.07159i	0.0375364	+	0.164458i
$952$	−2.52667	−	2.29971i	−0.0818899	−	0.0745341i
$953$	1.56287	−	6.84738i	0.0506263	−	0.221808i	−0.943286	−	0.331981i	$-0.892283\pi$
$953$	1.56287	−	6.84738i	0.0506263	−	0.221808i	0.993912	+	0.110172i	$0.0351403\pi$
$954$	4.52729	−	4.76472i	0.146576	−	0.154264i
$955$	−28.2377	−	4.25615i	−0.913751	−	0.137726i
$956$	1.73231	−	9.89538i	0.0560267	−	0.320039i
$957$	−1.26463	+	1.36294i	−0.0408795	+	0.0440577i
$958$	−23.6727	−	5.69916i	−0.764830	−	0.184132i
$959$	45.4185	+	11.7934i	1.46664	+	0.380828i
$960$	15.2219	−	2.35167i	0.491284	−	0.0758998i
$961$	−37.6004	+	65.1258i	−1.21292	+	2.10083i
$962$	−13.5772	−	24.1736i	−0.437746	−	0.779388i
$963$	−8.93741	−	9.63224i	−0.288004	−	0.310395i
$964$	−20.6999	−	31.9636i	−0.666700	−	1.02948i
$965$	−24.8277	−	19.7995i	−0.799233	−	0.637367i
$966$	−23.8612	+	0.794792i	−0.767722	+	0.0255720i
$967$	37.2134	−	29.6767i	1.19670	−	0.954338i	0.197041	−	0.980395i	$-0.436867\pi$
$967$	37.2134	−	29.6767i	1.19670	−	0.954338i	0.999660	+	0.0260574i	$0.00829527\pi$
$968$	−5.03413	+	14.4721i	−0.161803	+	0.465152i
$969$	−3.22018	−	1.26383i	−0.103447	−	0.0406000i
$970$	17.5707	−	1.10748i	0.564161	−	0.0355591i
$971$	−1.00962	−	2.57248i	−0.0324004	−	0.0825548i	0.913758	−	0.406259i	$-0.133167\pi$
$971$	−1.00962	−	2.57248i	−0.0324004	−	0.0825548i	−0.946158	+	0.323704i	$0.895072\pi$
$972$	−1.82200	+	0.824811i	−0.0584407	+	0.0264558i
$973$	−1.54945	−	12.8555i	−0.0496731	−	0.412129i
$974$	45.9693	+	22.8128i	1.47295	+	0.730968i
$975$	8.97074	+	0.672264i	0.287294	+	0.0215297i
$976$	2.36437	+	9.19106i	0.0756815	+	0.294199i
$977$	38.3673	+	26.1584i	1.22748	+	0.836881i	0.990883	−	0.134728i	$-0.0430160\pi$
$977$	38.3673	+	26.1584i	1.22748	+	0.836881i	0.236596	+	0.971608i	$0.423968\pi$
$978$	−13.4565	+	1.86540i	−0.430292	+	0.0596489i
$979$	−12.5430			−0.400875
$980$	24.1882	+	11.8939i	0.772664	+	0.379938i
$981$	−4.77376			−0.152415
$982$	0.0589148	−	0.00816704i	0.00188005	−	0.000260621i
$983$	−5.02350	−	3.42497i	−0.160225	−	0.109239i	0.480553	−	0.876965i	$-0.340436\pi$
$983$	−5.02350	−	3.42497i	−0.160225	−	0.109239i	−0.640778	+	0.767726i	$0.721388\pi$
$984$	−15.9974	+	4.31806i	−0.509978	+	0.137655i
$985$	−31.7163	−	2.37681i	−1.01056	−	0.0757314i
$986$	0.265394	+	0.131705i	0.00845187	+	0.00419433i
$987$	−6.17725	+	6.27374i	−0.196624	+	0.199695i
$988$	43.4743	+	96.0344i	1.38310	+	3.05526i
$989$	−10.2315	−	26.0695i	−0.325344	−	0.828963i
$990$	−11.0105	+	0.693990i	−0.349936	+	0.0220565i
$991$	−32.7185	−	12.8411i	−1.03934	−	0.407910i	−0.216557	−	0.976270i	$-0.569483\pi$
$991$	−32.7185	−	12.8411i	−1.03934	−	0.407910i	−0.822780	+	0.568360i	$0.807578\pi$
$992$	20.4524	−	54.5905i	0.649364	−	1.73325i
$993$	−1.22130	+	0.973952i	−0.0387567	+	0.0309074i
$994$	25.9631	+	11.4546i	0.823500	+	0.363319i
$995$	−1.15959	−	0.924740i	−0.0367614	−	0.0293162i
$996$	−22.4730	+	14.5537i	−0.712085	+	0.461153i
$997$	6.91891	+	7.45682i	0.219124	+	0.236160i	0.833041	−	0.553211i	$-0.186598\pi$
$997$	6.91891	+	7.45682i	0.219124	+	0.236160i	−0.613917	+	0.789370i	$0.710407\pi$
$998$	−16.4472	−	29.2835i	−0.520626	−	0.926953i
$999$	1.40914	−	2.44069i	0.0445831	−	0.0772202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.ba.a.103.13	✓	336
4.3	odd	2		588.2.ba.b.103.15	yes	336
49.10	odd	42		588.2.ba.b.451.15	yes	336
196.59	even	42	inner	588.2.ba.a.451.13	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.ba.a.103.13	✓	336	1.1	even	1	trivial
588.2.ba.a.451.13	yes	336	196.59	even	42	inner
588.2.ba.b.103.15	yes	336	4.3	odd	2
588.2.ba.b.451.15	yes	336	49.10	odd	42

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.ba (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.194188 - 1.40082i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.92458 + 0.544043i) q^{4} +(1.91992 + 0.143878i) q^{5} +(-0.628664 + 1.26680i) q^{6} +(-0.854457 + 2.50398i) q^{7} +(1.13584 + 2.59034i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.194188 - 1.40082i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.92458 + 0.544043i) q^{4} +(1.91992 + 0.143878i) q^{5} +(-0.628664 + 1.26680i) q^{6} +(-0.854457 + 2.50398i) q^{7} +(1.13584 + 2.59034i) q^{8} +(0.365341 + 0.930874i) q^{9} +(-0.171278 - 2.71740i) q^{10} +(-3.77175 - 1.48030i) q^{11} +(1.89663 + 0.634646i) q^{12} +(5.43869 - 4.33721i) q^{13} +(3.67354 + 0.710697i) q^{14} +(-1.50527 - 1.20041i) q^{15} +(3.40803 - 2.09411i) q^{16} +(0.310536 + 0.334678i) q^{17} +(1.23304 - 0.692540i) q^{18} +(3.78849 - 6.56186i) q^{19} +(-3.77333 + 0.767615i) q^{20} +(2.11653 - 1.58755i) q^{21} +(-1.34121 + 5.57099i) q^{22} +(4.33999 - 4.67739i) q^{23} +(0.520721 - 2.78008i) q^{24} +(-1.27875 - 0.192740i) q^{25} +(-7.13177 - 6.77639i) q^{26} +(0.222521 - 0.974928i) q^{27} +(0.282201 - 5.28397i) q^{28} +(0.102108 + 0.447366i) q^{29} +(-1.38925 + 2.34171i) q^{30} +(5.15269 + 8.92472i) q^{31} +(-3.59527 - 4.36739i) q^{32} +(2.28248 + 3.34779i) q^{33} +(0.408521 - 0.499994i) q^{34} +(-2.00076 + 4.68451i) q^{35} +(-1.20956 - 1.59278i) q^{36} +(2.69306 + 0.830700i) q^{37} +(-9.92766 - 4.03276i) q^{38} +(-6.93690 + 0.519849i) q^{39} +(1.80802 + 5.13668i) q^{40} +(-2.54184 - 5.27819i) q^{41} +(-2.63487 - 2.65659i) q^{42} +(1.90435 - 3.95443i) q^{43} +(8.06439 + 0.796970i) q^{44} +(0.567494 + 1.83977i) q^{45} +(-7.39495 - 5.17124i) q^{46} +(-3.29060 + 0.495978i) q^{47} +(-3.99550 - 0.189578i) q^{48} +(-5.53981 - 4.27908i) q^{49} +(-0.0216770 + 1.82872i) q^{50} +(-0.0680459 - 0.451455i) q^{51} +(-8.10758 + 11.3062i) q^{52} +(4.44105 - 1.36988i) q^{53} +(-1.40891 - 0.122392i) q^{54} +(-7.02849 - 3.38474i) q^{55} +(-7.45668 + 0.630770i) q^{56} +(-6.82663 + 3.28753i) q^{57} +(0.606851 - 0.229908i) q^{58} +(-0.637984 - 8.51330i) q^{59} +(3.55008 + 1.49136i) q^{60} +(-0.699329 + 2.26717i) q^{61} +(11.5013 - 8.95105i) q^{62} +(-2.64306 + 0.119414i) q^{63} +(-5.41976 + 5.88441i) q^{64} +(11.0659 - 7.54461i) q^{65} +(4.24641 - 3.84744i) q^{66} +(6.48431 - 3.74372i) q^{67} +(-0.779731 - 0.475170i) q^{68} +(-6.22073 + 1.41984i) q^{69} +(6.95067 + 1.89303i) q^{70} +(7.39410 + 1.68766i) q^{71} +(-1.99632 + 2.00368i) q^{72} +(-1.51250 + 10.0348i) q^{73} +(0.640700 - 3.93380i) q^{74} +(0.947977 + 0.879594i) q^{75} +(-3.72133 + 14.6900i) q^{76} +(6.92944 - 8.17952i) q^{77} +(2.07527 + 9.61638i) q^{78} +(3.90374 + 2.25383i) q^{79} +(6.84446 - 3.53019i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-6.90019 + 4.58562i) q^{82} +(-8.34666 + 10.4664i) q^{83} +(-3.20973 + 4.20685i) q^{84} +(0.548052 + 0.687236i) q^{85} +(-5.90923 - 1.89975i) q^{86} +(0.167644 - 0.427151i) q^{87} +(-0.449594 - 11.4515i) q^{88} +(2.88164 - 1.13096i) q^{89} +(2.46698 - 1.15222i) q^{90} +(6.21316 + 17.3243i) q^{91} +(-5.80796 + 11.3632i) q^{92} +(0.770122 - 10.2766i) q^{93} +(1.33377 + 4.51322i) q^{94} +(8.21773 - 12.0532i) q^{95} +(0.510313 + 5.63379i) q^{96} +6.46599i q^{97} +(-4.91845 + 8.59121i) q^{98} -4.05184i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9	\( 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9} + 41 q^{10} + 6 q^{11} + 52 q^{14} + 20 q^{16} - 6 q^{19} - 25 q^{20} + 4 q^{21} + 6 q^{22} + 9 q^{24} - 26 q^{25} - 18 q^{26} + 56 q^{27} + 5 q^{30} + 2 q^{31} + 15 q^{32} + 6 q^{33} + 44 q^{34} - 12 q^{35} + 16 q^{37} - 100 q^{38} + 8 q^{39} - 7 q^{40} - 7 q^{42} - 53 q^{44} - 10 q^{46} + 4 q^{47} + 8 q^{48} - 4 q^{49} - 114 q^{50} - 28 q^{52} - 4 q^{53} + q^{56} - 12 q^{57} + 27 q^{58} - 10 q^{59} - 7 q^{60} + 2 q^{61} - 16 q^{62} - 12 q^{63} - 84 q^{64} - 4 q^{65} + 21 q^{66} + 42 q^{67} + 26 q^{68} - 70 q^{70} + 28 q^{71} + 15 q^{72} + 18 q^{73} + 20 q^{74} + 54 q^{75} + 49 q^{76} - 8 q^{77} - 6 q^{78} - 6 q^{79} - 40 q^{80} + 28 q^{81} - 99 q^{82} + 10 q^{83} + 54 q^{84} + 24 q^{85} - 314 q^{86} - 40 q^{88} + 20 q^{90} - 34 q^{91} + 14 q^{92} - 2 q^{93} - 152 q^{94} - 24 q^{95} - 10 q^{96} - 156 q^{98}+O(q^{100}) \) 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9 + 41 * q^10 + 6 * q^11 + 52 * q^14 + 20 * q^16 - 6 * q^19 - 25 * q^20 + 4 * q^21 + 6 * q^22 + 9 * q^24 - 26 * q^25 - 18 * q^26 + 56 * q^27 + 5 * q^30 + 2 * q^31 + 15 * q^32 + 6 * q^33 + 44 * q^34 - 12 * q^35 + 16 * q^37 - 100 * q^38 + 8 * q^39 - 7 * q^40 - 7 * q^42 - 53 * q^44 - 10 * q^46 + 4 * q^47 + 8 * q^48 - 4 * q^49 - 114 * q^50 - 28 * q^52 - 4 * q^53 + q^56 - 12 * q^57 + 27 * q^58 - 10 * q^59 - 7 * q^60 + 2 * q^61 - 16 * q^62 - 12 * q^63 - 84 * q^64 - 4 * q^65 + 21 * q^66 + 42 * q^67 + 26 * q^68 - 70 * q^70 + 28 * q^71 + 15 * q^72 + 18 * q^73 + 20 * q^74 + 54 * q^75 + 49 * q^76 - 8 * q^77 - 6 * q^78 - 6 * q^79 - 40 * q^80 + 28 * q^81 - 99 * q^82 + 10 * q^83 + 54 * q^84 + 24 * q^85 - 314 * q^86 - 40 * q^88 + 20 * q^90 - 34 * q^91 + 14 * q^92 - 2 * q^93 - 152 * q^94 - 24 * q^95 - 10 * q^96 - 156 * q^98

Introduction

L-functions

Modular forms

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