LMFDB - Embedded newform 19.2.e.a.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,2,Mod(4,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("19.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	19.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.151715763840$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			6.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	19.6
Dual form			19.2.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93969 + 1.62760i) q^{2} +(0.613341 + 0.223238i) q^{3} +(0.766044 - 4.34445i) q^{4} +(-0.233956 - 1.32683i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-1.97178 - 1.65452i) q^{9} +O(q^{10})$	\(q+(-1.93969 + 1.62760i) q^{2} +(0.613341 + 0.223238i) q^{3} +(0.766044 - 4.34445i) q^{4} +(-0.233956 - 1.32683i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-1.97178 - 1.65452i) q^{9} +(2.61334 + 2.19285i) q^{10} +(0.592396 + 1.02606i) q^{11} +(1.43969 - 2.49362i) q^{12} +(-2.55303 + 0.929228i) q^{13} +(-0.673648 - 3.82045i) q^{14} +(0.152704 - 0.866025i) q^{15} +(-6.23783 - 2.27038i) q^{16} +(2.97178 - 2.49362i) q^{17} +6.51754 q^{18} +(0.819078 + 4.28125i) q^{19} -5.94356 q^{20} +(-0.766044 + 0.642788i) q^{21} +(-2.81908 - 1.02606i) q^{22} +(-0.879385 + 4.98724i) q^{23} +(0.692066 + 3.92490i) q^{24} +(2.99273 - 1.08926i) q^{25} +(3.43969 - 5.95772i) q^{26} +(-1.81908 - 3.15074i) q^{27} +(5.17752 + 4.34445i) q^{28} +(-3.56418 - 2.99070i) q^{29} +(1.11334 + 1.92836i) q^{30} +(1.91875 - 3.32337i) q^{31} +(4.31908 - 1.57202i) q^{32} +(0.134285 + 0.761570i) q^{33} +(-1.70574 + 9.67372i) q^{34} +(1.93969 + 0.705990i) q^{35} +(-8.69846 + 7.29888i) q^{36} -4.10607 q^{37} +(-8.55690 - 6.97118i) q^{38} -1.77332 q^{39} +(6.30200 - 5.28801i) q^{40} +(9.38326 + 3.41523i) q^{41} +(0.439693 - 2.49362i) q^{42} +(-1.51114 - 8.57013i) q^{43} +(4.91147 - 1.78763i) q^{44} +(-1.73396 + 3.00330i) q^{45} +(-6.41147 - 11.1050i) q^{46} +(0.439693 + 0.368946i) q^{47} +(-3.31908 - 2.78504i) q^{48} +(2.32635 + 4.02936i) q^{49} +(-4.03209 + 6.98378i) q^{50} +(2.37939 - 0.866025i) q^{51} +(2.08125 + 11.8034i) q^{52} +(0.511144 - 2.89884i) q^{53} +(8.65657 + 3.15074i) q^{54} +(1.22281 - 1.02606i) q^{55} -9.35504 q^{56} +(-0.453363 + 2.80872i) q^{57} +11.7811 q^{58} +(-3.01501 + 2.52990i) q^{59} +(-3.64543 - 1.32683i) q^{60} +(-0.784463 + 4.44891i) q^{61} +(1.68732 + 9.56926i) q^{62} +(3.70574 - 1.34878i) q^{63} +(0.819078 - 1.41868i) q^{64} +(1.83022 + 3.17004i) q^{65} +(-1.50000 - 1.25865i) q^{66} +(-2.97771 - 2.49860i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(-1.65270 + 2.86257i) q^{69} +(-4.91147 + 1.78763i) q^{70} +(-1.20439 - 6.83045i) q^{71} +(2.72921 - 15.4781i) q^{72} +(-5.75877 - 2.09602i) q^{73} +(7.96451 - 6.68302i) q^{74} +2.07873 q^{75} +(19.2271 - 0.278817i) q^{76} -1.81521 q^{77} +(3.43969 - 2.88624i) q^{78} +(-9.21688 - 3.35467i) q^{79} +(-1.55303 + 8.80769i) q^{80} +(0.928548 + 5.26606i) q^{81} +(-23.7592 + 8.64766i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(2.20574 + 3.82045i) q^{84} +(-4.00387 - 3.35965i) q^{85} +(16.8799 + 14.1639i) q^{86} +(-1.51842 - 2.62998i) q^{87} +(-3.61721 + 6.26519i) q^{88} +(2.27972 - 0.829748i) q^{89} +(-1.52481 - 8.64766i) q^{90} +(0.722811 - 4.09927i) q^{91} +(20.9932 + 7.64090i) q^{92} +(1.91875 - 1.61002i) q^{93} -1.45336 q^{94} +(5.48886 - 2.08840i) q^{95} +3.00000 q^{96} +(5.64543 - 4.73708i) q^{97} +(-11.0706 - 4.02936i) q^{98} +(0.529563 - 3.00330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9	$ 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.93969	+	1.62760i	−1.37157	+	1.15088i	−0.399354	+	0.916797i	$0.630766\pi$
$2$	−1.93969	+	1.62760i	−1.37157	+	1.15088i	−0.972216	+	0.234087i	$0.924790\pi$
$3$	0.613341	+	0.223238i	0.354112	+	0.128886i	0.512950	−	0.858418i	$-0.328552\pi$
$3$	0.613341	+	0.223238i	0.354112	+	0.128886i	−0.158838	+	0.987305i	$0.550775\pi$
$4$	0.766044	−	4.34445i	0.383022	−	2.17223i
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	−0.991368	−	0.131107i	$-0.958147\pi$
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	0.886740	−	0.462268i	$-0.152964\pi$
$6$	−1.55303	+	0.565258i	−0.634023	+	0.230766i
$7$	−0.766044	+	1.32683i	−0.289538	+	0.501494i	−0.973699	−	0.227836i	$-0.926835\pi$
$7$	−0.766044	+	1.32683i	−0.289538	+	0.501494i	0.684162	+	0.729330i	$0.260168\pi$
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$	−1.97178	−	1.65452i	−0.657261	−	0.551507i
$10$	2.61334	+	2.19285i	0.826411	+	0.693441i
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	0.941406	−	0.337275i	$-0.109505\pi$
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	−0.762792	+	0.646644i	$0.776172\pi$
$12$	1.43969	−	2.49362i	0.415603	−	0.719846i
$13$	−2.55303	+	0.929228i	−0.708084	+	0.257722i	−0.670859	−	0.741585i	$-0.734074\pi$
$13$	−2.55303	+	0.929228i	−0.708084	+	0.257722i	−0.0372256	+	0.999307i	$0.511852\pi$
$14$	−0.673648	−	3.82045i	−0.180040	−	1.02106i
$15$	0.152704	−	0.866025i	0.0394279	−	0.223607i
$16$	−6.23783	−	2.27038i	−1.55946	−	0.567596i
$17$	2.97178	−	2.49362i	0.720763	−	0.604792i	−0.206833	−	0.978376i	$-0.566316\pi$
$17$	2.97178	−	2.49362i	0.720763	−	0.604792i	0.927596	+	0.373584i	$0.121871\pi$
$18$	6.51754			1.53620
$19$	0.819078	+	4.28125i	0.187909	+	0.982186i
$19$	0.819078	+	4.28125i	0.187909	+	0.982186i
$20$	−5.94356			−1.32902
$21$	−0.766044	+	0.642788i	−0.167165	+	0.140268i
$22$	−2.81908	−	1.02606i	−0.601029	−	0.218757i
$23$	−0.879385	+	4.98724i	−0.183364	+	1.03991i	0.744674	+	0.667428i	$0.232605\pi$
$23$	−0.879385	+	4.98724i	−0.183364	+	1.03991i	−0.928039	+	0.372484i	$0.878506\pi$
$24$	0.692066	+	3.92490i	0.141267	+	0.801168i
$25$	2.99273	−	1.08926i	0.598545	−	0.217853i
$26$	3.43969	−	5.95772i	0.674579	−	1.16841i
$27$	−1.81908	−	3.15074i	−0.350082	−	0.606359i
$28$	5.17752	+	4.34445i	0.978459	+	0.821025i
$29$	−3.56418	−	2.99070i	−0.661851	−	0.555359i	0.248790	−	0.968557i	$-0.419967\pi$
$29$	−3.56418	−	2.99070i	−0.661851	−	0.555359i	−0.910641	+	0.413198i	$0.864412\pi$
$30$	1.11334	+	1.92836i	0.203267	+	0.352069i
$31$	1.91875	−	3.32337i	0.344617	−	0.596895i	−0.640667	−	0.767819i	$-0.721342\pi$
$31$	1.91875	−	3.32337i	0.344617	−	0.596895i	0.985284	+	0.170924i	$0.0546753\pi$
$32$	4.31908	−	1.57202i	0.763512	−	0.277896i
$33$	0.134285	+	0.761570i	0.0233761	+	0.132572i
$34$	−1.70574	+	9.67372i	−0.292531	+	1.65903i
$35$	1.93969	+	0.705990i	0.327868	+	0.119334i
$36$	−8.69846	+	7.29888i	−1.44974	+	1.21648i
$37$	−4.10607			−0.675033			−0.337517	−	0.941320i	$-0.609587\pi$
$37$	−4.10607			−0.675033			−0.337517	+	0.941320i	$0.609587\pi$
$38$	−8.55690	−	6.97118i	−1.38811	−	1.13088i
$39$	−1.77332			−0.283958
$40$	6.30200	−	5.28801i	0.996434	−	0.836108i
$41$	9.38326	+	3.41523i	1.46542	+	0.533369i	0.946852	−	0.321669i	$-0.104244\pi$
$41$	9.38326	+	3.41523i	1.46542	+	0.533369i	0.518566	+	0.855038i	$0.326466\pi$
$42$	0.439693	−	2.49362i	0.0678460	−	0.384774i
$43$	−1.51114	−	8.57013i	−0.230447	−	1.30693i	−0.851993	−	0.523554i	$-0.824606\pi$
$43$	−1.51114	−	8.57013i	−0.230447	−	1.30693i	0.621545	−	0.783378i	$-0.286505\pi$
$44$	4.91147	−	1.78763i	0.740433	−	0.269495i
$45$	−1.73396	+	3.00330i	−0.258483	+	0.447705i
$46$	−6.41147	−	11.1050i	−0.945320	−	1.63734i
$47$	0.439693	+	0.368946i	0.0641358	+	0.0538163i	0.674292	−	0.738465i	$-0.264449\pi$
$47$	0.439693	+	0.368946i	0.0641358	+	0.0538163i	−0.610156	+	0.792281i	$0.708893\pi$
$48$	−3.31908	−	2.78504i	−0.479068	−	0.401985i
$49$	2.32635	+	4.02936i	0.332336	+	0.575623i
$50$	−4.03209	+	6.98378i	−0.570223	+	0.987656i
$51$	2.37939	−	0.866025i	0.333181	−	0.121268i
$52$	2.08125	+	11.8034i	0.288618	+	1.63683i
$53$	0.511144	−	2.89884i	0.0702111	−	0.398187i	−0.929367	−	0.369156i	$-0.879647\pi$
$53$	0.511144	−	2.89884i	0.0702111	−	0.398187i	0.999579	−	0.0290308i	$-0.00924209\pi$
$54$	8.65657	+	3.15074i	1.17801	+	0.428761i
$55$	1.22281	−	1.02606i	0.164884	−	0.138354i
$56$	−9.35504			−1.25012
$57$	−0.453363	+	2.80872i	−0.0600494	+	0.372023i
$58$	11.7811			1.54693
$59$	−3.01501	+	2.52990i	−0.392521	+	0.329365i	−0.817595	−	0.575794i	$-0.804693\pi$
$59$	−3.01501	+	2.52990i	−0.392521	+	0.329365i	0.425073	+	0.905159i	$0.360248\pi$
$60$	−3.64543	−	1.32683i	−0.470623	−	0.171293i
$61$	−0.784463	+	4.44891i	−0.100440	+	0.569624i	0.892504	+	0.451040i	$0.148947\pi$
$61$	−0.784463	+	4.44891i	−0.100440	+	0.569624i	−0.992944	+	0.118585i	$0.962164\pi$
$62$	1.68732	+	9.56926i	0.214290	+	1.21530i
$63$	3.70574	−	1.34878i	0.466879	−	0.169930i
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	1.83022	+	3.17004i	0.227011	+	0.393195i
$66$	−1.50000	−	1.25865i	−0.184637	−	0.154929i
$67$	−2.97771	−	2.49860i	−0.363785	−	0.305252i	0.442512	−	0.896763i	$-0.354087\pi$
$67$	−2.97771	−	2.49860i	−0.363785	−	0.305252i	−0.806297	+	0.591510i	$0.798532\pi$
$68$	−8.55690	−	14.8210i	−1.03768	−	1.79731i
$69$	−1.65270	+	2.86257i	−0.198962	+	0.344613i
$70$	−4.91147	+	1.78763i	−0.587033	+	0.213663i
$71$	−1.20439	−	6.83045i	−0.142935	−	0.810625i	−0.969002	−	0.247053i	$-0.920538\pi$
$71$	−1.20439	−	6.83045i	−0.142935	−	0.810625i	0.826067	−	0.563572i	$-0.190573\pi$
$72$	2.72921	−	15.4781i	0.321640	−	1.82411i
$73$	−5.75877	−	2.09602i	−0.674013	−	0.245321i	−0.0177383	−	0.999843i	$-0.505647\pi$
$73$	−5.75877	−	2.09602i	−0.674013	−	0.245321i	−0.656275	+	0.754522i	$0.727869\pi$
$74$	7.96451	−	6.68302i	0.925855	−	0.776885i
$75$	2.07873			0.240031
$76$	19.2271	−	0.278817i	2.20551	−	0.0319825i
$77$	−1.81521			−0.206862
$78$	3.43969	−	2.88624i	0.389468	−	0.326803i
$79$	−9.21688	−	3.35467i	−1.03698	−	0.377430i	−0.233246	−	0.972418i	$-0.574935\pi$
$79$	−9.21688	−	3.35467i	−1.03698	−	0.377430i	−0.803735	+	0.594988i	$0.797157\pi$
$80$	−1.55303	+	8.80769i	−0.173634	+	0.984730i
$81$	0.928548	+	5.26606i	0.103172	+	0.585118i
$82$	−23.7592	+	8.64766i	−2.62377	+	0.954974i
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	0.300112	+	0.953904i	$0.402976\pi$
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	−0.976161	+	0.217047i	$0.930357\pi$
$84$	2.20574	+	3.82045i	0.240666	+	0.416845i
$85$	−4.00387	−	3.35965i	−0.434281	−	0.364405i
$86$	16.8799	+	14.1639i	1.82020	+	1.52733i
$87$	−1.51842	−	2.62998i	−0.162792	−	0.281963i
$88$	−3.61721	+	6.26519i	−0.385596	+	0.667872i
$89$	2.27972	−	0.829748i	0.241649	−	0.0879532i	−0.218356	−	0.975869i	$-0.570070\pi$
$89$	2.27972	−	0.829748i	0.241649	−	0.0879532i	0.460006	+	0.887916i	$0.347847\pi$
$90$	−1.52481	−	8.64766i	−0.160730	−	0.911543i
$91$	0.722811	−	4.09927i	0.0757712	−	0.429720i
$92$	20.9932	+	7.64090i	2.18869	+	0.796619i
$93$	1.91875	−	1.61002i	0.198965	−	0.166951i
$94$	−1.45336			−0.149903
$95$	5.48886	−	2.08840i	0.563145	−	0.214265i
$96$	3.00000			0.306186
$97$	5.64543	−	4.73708i	0.573207	−	0.480977i	−0.309502	−	0.950899i	$-0.600162\pi$
$97$	5.64543	−	4.73708i	0.573207	−	0.480977i	0.882708	+	0.469922i	$0.155718\pi$
$98$	−11.0706	−	4.02936i	−1.11830	−	0.407027i
$99$	0.529563	−	3.00330i	0.0532231	−	0.301843i
$100$	−2.43969	−	13.8362i	−0.243969	−	1.38362i
$101$	−2.03936	+	0.742267i	−0.202924	+	0.0738584i	−0.441483	−	0.897270i	$-0.645547\pi$
$101$	−2.03936	+	0.742267i	−0.202924	+	0.0738584i	0.238559	+	0.971128i	$0.423325\pi$
$102$	−3.20574	+	5.55250i	−0.317415	+	0.549779i
$103$	6.23783	+	10.8042i	0.614631	+	1.06457i	0.990449	+	0.137879i	$0.0440285\pi$
$103$	6.23783	+	10.8042i	0.614631	+	1.06457i	−0.375818	+	0.926694i	$0.622638\pi$
$104$	−12.7083	−	10.6635i	−1.24615	−	1.04564i
$105$	1.03209	+	0.866025i	0.100722	+	0.0845154i
$106$	3.72668	+	6.45480i	0.361967	+	0.626946i
$107$	3.34002	−	5.78509i	0.322892	−	0.559266i	−0.658191	−	0.752851i	$-0.728678\pi$
$107$	3.34002	−	5.78509i	0.322892	−	0.559266i	0.981083	+	0.193585i	$0.0620116\pi$
$108$	−15.0817	+	5.48930i	−1.45124	+	0.528208i
$109$	1.64156	+	9.30975i	0.157233	+	0.891712i	0.956716	+	0.291023i	$0.0939957\pi$
$109$	1.64156	+	9.30975i	0.157233	+	0.891712i	−0.799483	+	0.600689i	$0.794893\pi$
$110$	−0.701867	+	3.98048i	−0.0669204	+	0.379524i
$111$	−2.51842	−	0.916629i	−0.239038	−	0.0870026i
$112$	7.79086	−	6.53731i	0.736167	−	0.617717i
$113$	1.31046			0.123278			0.0616388	−	0.998099i	$-0.480367\pi$
$113$	1.31046			0.123278			0.0616388	+	0.998099i	$0.480367\pi$
$114$	−3.69207	−	6.18594i	−0.345794	−	0.579366i
$115$	6.82295			0.636243
$116$	−15.7233	+	13.1934i	−1.45987	+	1.22498i
$117$	6.57145	+	2.39181i	0.607531	+	0.221123i
$118$	1.73055	−	9.81445i	0.159310	−	0.903493i
$119$	1.03209	+	5.85327i	0.0946114	+	0.536568i
$120$	5.04576	−	1.83651i	0.460613	−	0.167649i
$121$	4.79813	−	8.31061i	0.436194	−	0.755510i
$122$	−5.71941	−	9.90630i	−0.517811	−	0.896875i
$123$	4.99273	+	4.18939i	0.450179	+	0.377745i
$124$	−12.9684	−	10.8818i	−1.16459	−	0.977211i
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$	−4.99273	+	8.64766i	−0.444787	+	0.770394i
$127$	13.6284	−	4.96032i	1.20932	−	0.440157i	0.342853	−	0.939389i	$-0.388607\pi$
$127$	13.6284	−	4.96032i	1.20932	−	0.440157i	0.866468	+	0.499232i	$0.166385\pi$
$128$	2.31655	+	13.1378i	0.204756	+	1.16123i
$129$	0.986329	−	5.59375i	0.0868415	−	0.492502i
$130$	−8.70961	−	3.17004i	−0.763883	−	0.278031i
$131$	−15.1741	+	12.7326i	−1.32577	+	1.11245i	−0.340722	+	0.940164i	$0.610671\pi$
$131$	−15.1741	+	12.7326i	−1.32577	+	1.11245i	−0.985047	+	0.172288i	$0.944884\pi$
$132$	3.41147			0.296931
$133$	−6.30793	−	2.19285i	−0.546967	−	0.190144i
$134$	9.84255			0.850267
$135$	−3.75490	+	3.15074i	−0.323170	+	0.271172i
$136$	22.2592	+	8.10170i	1.90871	+	0.694715i
$137$	1.77197	−	10.0494i	0.151390	−	0.858575i	−0.810622	−	0.585569i	$-0.800871\pi$
$137$	1.77197	−	10.0494i	0.151390	−	0.858575i	0.962012	−	0.273006i	$-0.0880179\pi$
$138$	−1.45336	−	8.24243i	−0.123718	−	0.701642i
$139$	1.56031	−	0.567905i	0.132344	−	0.0481691i	−0.274999	−	0.961444i	$-0.588678\pi$
$139$	1.56031	−	0.567905i	0.132344	−	0.0481691i	0.407343	+	0.913275i	$0.366455\pi$
$140$	4.55303	−	7.88609i	0.384802	−	0.666496i
$141$	0.187319	+	0.324446i	0.0157751	+	0.0273232i
$142$	13.4534	+	11.2887i	1.12898	+	0.947328i
$143$	−2.46585	−	2.06910i	−0.206205	−	0.173026i
$144$	8.54323	+	14.7973i	0.711936	+	1.23311i
$145$	−3.13429	+	5.42874i	−0.260288	+	0.450832i
$146$	14.5817	−	5.30731i	1.20679	−	0.439236i
$147$	0.527341	+	2.99070i	0.0434944	+	0.246669i
$148$	−3.14543	+	17.8386i	−0.258553	+	1.46633i
$149$	−10.5312	−	3.83305i	−0.862750	−	0.314015i	−0.127523	−	0.991836i	$-0.540703\pi$
$149$	−10.5312	−	3.83305i	−0.862750	−	0.314015i	−0.735228	+	0.677820i	$0.762925\pi$
$150$	−4.03209	+	3.38332i	−0.329219	+	0.276247i
$151$	−11.0419			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$152$	−20.1386	+	17.4021i	−1.63346	+	1.41150i
$153$	−9.98545			−0.807276
$154$	3.52094	−	2.95442i	0.283726	−	0.238074i
$155$	−4.85844	−	1.76833i	−0.390239	−	0.142036i
$156$	−1.35844	+	7.70410i	−0.108762	+	0.616822i
$157$	1.90895	+	10.8262i	0.152351	+	0.864023i	0.961168	+	0.275964i	$0.0889969\pi$
$157$	1.90895	+	10.8262i	0.152351	+	0.864023i	−0.808817	+	0.588060i	$0.799892\pi$
$158$	23.3380	−	8.49432i	1.85667	−	0.675772i
$159$	0.960637	−	1.66387i	0.0761835	−	0.131954i
$160$	−3.09627	−	5.36289i	−0.244781	−	0.423974i
$161$	−5.94356	−	4.98724i	−0.468418	−	0.393050i
$162$	−10.3721	−	8.70323i	−0.814910	−	0.683791i
$163$	3.16637	+	5.48432i	0.248010	+	0.429565i	0.962973	−	0.269596i	$-0.0868902\pi$
$163$	3.16637	+	5.48432i	0.248010	+	0.429565i	−0.714964	+	0.699161i	$0.753557\pi$
$164$	22.0253	−	38.1489i	1.71989	−	2.97893i
$165$	0.979055	−	0.356347i	0.0762194	−	0.0277416i
$166$	−5.41622	−	30.7169i	−0.420380	−	2.38410i
$167$	−2.39259	+	13.5690i	−0.185144	+	1.05000i	0.740626	+	0.671917i	$0.234529\pi$
$167$	−2.39259	+	13.5690i	−0.185144	+	1.05000i	−0.925770	+	0.378087i	$0.876582\pi$
$168$	−5.73783	−	2.08840i	−0.442683	−	0.161123i
$169$	−4.30406	+	3.61154i	−0.331082	+	0.277811i
$170$	13.2344			1.01503
$171$	5.46838	−	9.79687i	0.418177	−	0.749186i
$172$	−38.3901			−2.92722
$173$	19.3405	−	16.2286i	1.47043	−	1.23384i	0.554696	−	0.832053i	$-0.312835\pi$
$173$	19.3405	−	16.2286i	1.47043	−	1.23384i	0.915734	−	0.401784i	$-0.131610\pi$
$174$	7.22580	+	2.62998i	0.547787	+	0.199378i
$175$	−0.847296	+	4.80526i	−0.0640496	+	0.363243i
$176$	−1.36571	−	7.74535i	−0.102945	−	0.583828i
$177$	−2.41400	+	0.878624i	−0.181447	+	0.0660414i
$178$	−3.07145	+	5.31991i	−0.230215	+	0.398744i
$179$	−2.91534	−	5.04952i	−0.217903	−	0.377419i	0.736264	−	0.676695i	$-0.236588\pi$
$179$	−2.91534	−	5.04952i	−0.217903	−	0.377419i	−0.954167	+	0.299276i	$0.903255\pi$
$180$	11.7194	+	9.83375i	0.873513	+	0.732964i
$181$	10.3892	+	8.71756i	0.772222	+	0.647971i	0.941277	−	0.337635i	$-0.109627\pi$
$181$	10.3892	+	8.71756i	0.772222	+	0.647971i	−0.169055	+	0.985607i	$0.554072\pi$
$182$	5.26991	+	9.12776i	0.390632	+	0.676595i
$183$	−1.47431	+	2.55358i	−0.108984	+	0.188766i
$184$	−29.0574	+	10.5760i	−2.14214	+	0.779674i
$185$	0.960637	+	5.44804i	0.0706274	+	0.400548i
$186$	−1.10132	+	6.24589i	−0.0807526	+	0.457971i
$187$	4.31908	+	1.57202i	0.315842	+	0.114957i
$188$	1.93969	−	1.62760i	0.141467	−	0.118705i
$189$	5.57398			0.405447
$190$	−7.24763	+	12.9845i	−0.525798	+	0.941994i
$191$	−10.2841			−0.744128			−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841			−0.744128			−0.372064	+	0.928207i	$0.621350\pi$
$192$	0.819078	−	0.687288i	0.0591119	−	0.0496007i
$193$	−12.9684	−	4.72010i	−0.933484	−	0.339760i	−0.169895	−	0.985462i	$-0.554343\pi$
$193$	−12.9684	−	4.72010i	−0.933484	−	0.339760i	−0.763590	+	0.645702i	$0.776565\pi$
$194$	−3.24035	+	18.3770i	−0.232644	+	1.31939i
$195$	0.414878	+	2.35289i	0.0297100	+	0.168494i
$196$	19.2875	−	7.02006i	1.37768	−	0.501433i
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	−0.689211	−	0.724560i	$-0.742043\pi$
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	0.972093	+	0.234594i	$0.0753762\pi$
$198$	3.86097	+	6.68739i	0.274387	+	0.475252i
$199$	20.7101	+	17.3778i	1.46810	+	1.23188i	0.917879	+	0.396861i	$0.129900\pi$
$199$	20.7101	+	17.3778i	1.46810	+	1.23188i	0.550219	+	0.835020i	$0.314544\pi$
$200$	14.8969	+	12.5000i	1.05337	+	0.883884i
$201$	−1.26857	−	2.19723i	−0.0894781	−	0.154981i
$202$	2.74763	−	4.75903i	0.193322	−	0.334844i
$203$	6.69846	−	2.43804i	0.470140	−	0.171117i
$204$	−1.93969	−	11.0005i	−0.135806	−	0.770192i
$205$	2.33615	−	13.2490i	0.163164	−	0.925349i
$206$	−29.6844	−	10.8042i	−2.06821	−	0.752766i
$207$	9.98545	−	8.37879i	0.694037	−	0.582366i
$208$	18.0351			1.25051
$209$	−3.90760	+	3.37662i	−0.270295	+	0.233566i
$210$	−3.41147			−0.235414
$211$	−6.18345	+	5.18853i	−0.425686	+	0.357193i	−0.830321	−	0.557285i	$-0.811843\pi$
$211$	−6.18345	+	5.18853i	−0.425686	+	0.357193i	0.404635	+	0.914478i	$0.367399\pi$
$212$	−12.2023	−	4.44129i	−0.838060	−	0.305029i
$213$	0.786112	−	4.45826i	0.0538635	−	0.305475i
$214$	2.93717	+	16.6575i	0.200781	+	1.13868i
$215$	−11.0175	+	4.01006i	−0.751390	+	0.273484i
$216$	11.1074	−	19.2386i	0.755764	−	1.30902i
$217$	2.93969	+	5.09170i	0.199559	+	0.345647i
$218$	−18.3366	−	15.3863i	−1.24191	−	1.04209i
$219$	−3.06418	−	2.57115i	−0.207058	−	0.173742i
$220$	−3.52094	−	6.09845i	−0.237382	−	0.411158i
$221$	−5.26991	+	9.12776i	−0.354493	+	0.614000i
$222$	6.37686	−	2.32099i	0.427987	−	0.155774i
$223$	−2.68732	−	15.2405i	−0.179956	−	1.02058i	−0.932266	−	0.361773i	$-0.882172\pi$
$223$	−2.68732	−	15.2405i	−0.179956	−	1.02058i	0.752310	−	0.658809i	$-0.228940\pi$
$224$	−1.22281	+	6.93491i	−0.0817025	+	0.463358i
$225$	−7.70321	−	2.80374i	−0.513547	−	0.186916i
$226$	−2.54189	+	2.13290i	−0.169084	+	0.141878i
$227$	9.87258			0.655266			0.327633	−	0.944805i	$-0.393749\pi$
$227$	9.87258			0.655266			0.327633	+	0.944805i	$0.393749\pi$
$228$	11.8550	+	4.12122i	0.785119	+	0.272934i
$229$	20.1189			1.32949			0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189			1.32949			0.664746	+	0.747070i	$0.268540\pi$
$230$	−13.2344	+	11.1050i	−0.872652	+	0.732242i
$231$	−1.11334	−	0.405223i	−0.0732524	−	0.0266617i
$232$	4.93330	−	27.9781i	0.323887	−	1.83685i
$233$	0.613808	+	3.48108i	0.0402119	+	0.228053i	0.998290	−	0.0584538i	$-0.0186170\pi$
$233$	0.613808	+	3.48108i	0.0402119	+	0.228053i	−0.958078	+	0.286507i	$0.907506\pi$
$234$	−16.6395	+	6.05628i	−1.08776	+	0.395912i
$235$	0.386659	−	0.669713i	0.0252229	−	0.0436873i
$236$	8.68139	+	15.0366i	0.565110	+	0.978800i
$237$	−4.90420	−	4.11511i	−0.318562	−	0.267305i
$238$	−11.5287	−	9.67372i	−0.747294	−	0.627054i
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	0.604825	−	0.796358i	$-0.293243\pi$
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	−0.992079	+	0.125615i	$0.959910\pi$
$240$	−2.91875	+	5.05542i	−0.188404	+	0.326326i
$241$	−12.1236	+	4.41263i	−0.780950	+	0.284243i	−0.701569	−	0.712602i	$-0.747517\pi$
$241$	−12.1236	+	4.41263i	−0.780950	+	0.284243i	−0.0793814	+	0.996844i	$0.525294\pi$
$242$	4.21941	+	23.9294i	0.271234	+	1.53824i
$243$	−2.50134	+	14.1858i	−0.160461	+	0.910021i
$244$	18.7271	+	6.81612i	1.19888	+	0.436358i
$245$	4.80200	−	4.02936i	0.306789	−	0.257426i
$246$	−16.5030			−1.05219
$247$	−6.06939	−	10.1691i	−0.386186	−	0.647042i
$248$	23.4320			1.48793
$249$	−6.15910	+	5.16810i	−0.390317	+	0.327515i
$250$	26.2383	+	9.54996i	1.65946	+	0.603992i
$251$	2.49407	−	14.1446i	0.157424	−	0.892798i	−0.799112	−	0.601183i	$-0.794696\pi$
$251$	2.49407	−	14.1446i	0.157424	−	0.892798i	0.956536	−	0.291615i	$-0.0941925\pi$
$252$	−3.02094	−	17.1326i	−0.190302	−	1.07925i
$253$	−5.63816	+	2.05212i	−0.354468	+	0.129016i
$254$	−18.3614	+	31.8029i	−1.15210	+	1.99549i
$255$	−1.70574	−	2.95442i	−0.106817	−	0.185013i
$256$	−23.3666	−	19.6069i	−1.46042	−	1.22543i
$257$	3.81315	+	3.19961i	0.237858	+	0.199586i	0.753923	−	0.656963i	$-0.228159\pi$
$257$	3.81315	+	3.19961i	0.237858	+	0.199586i	−0.516065	+	0.856549i	$0.672604\pi$
$258$	7.19119	+	12.4555i	0.447704	+	0.775446i
$259$	3.14543	−	5.44804i	0.195447	−	0.338525i
$260$	15.1741	−	5.52293i	0.941059	−	0.342517i
$261$	2.07960	+	11.7940i	0.128724	+	0.730031i
$262$	8.70961	−	49.3946i	0.538081	−	3.05161i
$263$	22.5929	+	8.22313i	1.39314	+	0.507060i	0.926133	−	0.377196i	$-0.123112\pi$
$263$	22.5929	+	8.22313i	1.39314	+	0.507060i	0.467002	+	0.884256i	$0.345334\pi$
$264$	−3.61721	+	3.03520i	−0.222624	+	0.186804i
$265$	−3.96585			−0.243620
$266$	15.8045	−	6.01330i	0.969038	−	0.368699i
$267$	1.58347			0.0969070
$268$	−13.1361	+	11.0225i	−0.802415	+	0.673306i
$269$	12.3204	+	4.48427i	0.751189	+	0.273411i	0.689106	−	0.724660i	$-0.258003\pi$
$269$	12.3204	+	4.48427i	0.751189	+	0.273411i	0.0620832	+	0.998071i	$0.480226\pi$
$270$	2.15523	−	12.2229i	0.131163	−	0.743863i
$271$	−4.61381	−	26.1662i	−0.280269	−	1.58948i	−0.721711	−	0.692194i	$-0.756644\pi$
$271$	−4.61381	−	26.1662i	−0.280269	−	1.58948i	0.441443	−	0.897290i	$-0.354467\pi$
$272$	−24.1989	+	8.80769i	−1.46728	+	0.534045i
$273$	1.35844	−	2.35289i	0.0822166	−	0.142403i
$274$	12.9192	+	22.3767i	0.780478	+	1.35183i
$275$	2.89053	+	2.42544i	0.174305	+	0.146260i
$276$	11.1702	+	9.37295i	0.672370	+	0.564185i
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	0.999989	−	0.00459317i	$-0.00146206\pi$
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	−0.503973	+	0.863720i	$0.668129\pi$
$278$	−2.10220	+	3.64111i	−0.126081	+	0.218379i
$279$	−9.28194	+	3.37835i	−0.555695	+	0.202256i
$280$	2.18866	+	12.4125i	0.130798	+	0.741790i
$281$	−3.36706	+	19.0955i	−0.200862	+	1.13914i	0.702958	+	0.711231i	$0.251862\pi$
$281$	−3.36706	+	19.0955i	−0.200862	+	1.13914i	−0.903820	+	0.427913i	$0.859249\pi$
$282$	−0.891407	−	0.324446i	−0.0530825	−	0.0193205i
$283$	−8.66431	+	7.27022i	−0.515040	+	0.432170i	−0.862899	−	0.505377i	$-0.831353\pi$
$283$	−8.66431	+	7.27022i	−0.515040	+	0.432170i	0.347859	+	0.937547i	$0.386909\pi$
$284$	−30.5972			−1.81561
$285$	3.83275	−	0.0555796i	0.227032	−	0.00329225i
$286$	8.15064			0.481958
$287$	−11.7194	+	9.83375i	−0.691775	+	0.580468i
$288$	−11.1172	−	4.04633i	−0.655088	−	0.238433i
$289$	−0.338678	+	1.92074i	−0.0199222	+	0.112985i
$290$	−2.75624	−	15.6314i	−0.161852	−	0.917910i
$291$	4.52007	−	1.64517i	0.264971	−	0.0964416i
$292$	−13.5175	+	23.4131i	−0.791054	+	1.37015i
$293$	−1.94949	−	3.37662i	−0.113891	−	0.197264i	0.803445	−	0.595379i	$-0.202998\pi$
$293$	−1.94949	−	3.37662i	−0.113891	−	0.197264i	−0.917336	+	0.398115i	$0.869665\pi$
$294$	−5.89053	−	4.94274i	−0.343543	−	0.288267i
$295$	4.06212	+	3.40852i	0.236506	+	0.198452i
$296$	−12.5360	−	21.7129i	−0.728638	−	1.26204i
$297$	2.15523	−	3.73297i	0.125059	−	0.216609i
$298$	26.6660	−	9.70562i	1.54472	−	0.562231i
$299$	−2.38919	−	13.5497i	−0.138170	−	0.783602i
$300$	1.59240	−	9.03093i	0.0919370	−	0.521401i
$301$	12.5287	+	4.56007i	0.722141	+	0.262838i
$302$	21.4179	−	17.9717i	1.23246	−	1.03416i
$303$	−1.41653			−0.0813773
$304$	4.61081	−	28.5653i	0.264448	−	1.63833i
$305$	6.08647			0.348510
$306$	19.3687	−	16.2523i	1.10724	−	0.929081i
$307$	−21.7777	−	7.92642i	−1.24292	−	0.452385i	−0.364914	−	0.931041i	$-0.618902\pi$
$307$	−21.7777	−	7.92642i	−1.24292	−	0.452385i	−0.878002	+	0.478657i	$0.841124\pi$
$308$	−1.39053	+	7.88609i	−0.0792328	+	0.449351i
$309$	1.41400	+	8.01919i	0.0804397	+	0.456196i
$310$	12.3020	−	4.47756i	0.698707	−	0.254308i
$311$	1.73055	−	2.99740i	0.0981306	−	0.169967i	−0.812780	−	0.582570i	$-0.802047\pi$
$311$	1.73055	−	2.99740i	0.0981306	−	0.169967i	0.910911	+	0.412603i	$0.135380\pi$
$312$	−5.41400	−	9.37732i	−0.306507	−	0.530886i
$313$	−17.5346	−	14.7133i	−0.991115	−	0.831644i	−0.00538626	−	0.999985i	$-0.501715\pi$
$313$	−17.5346	−	14.7133i	−0.991115	−	0.831644i	−0.985729	+	0.168341i	$0.946159\pi$
$314$	−21.3234	−	17.8925i	−1.20335	−	1.00973i
$315$	−2.65657	−	4.60132i	−0.149681	−	0.259255i
$316$	−21.6348	+	37.4725i	−1.21705	+	2.10799i
$317$	−24.5453	+	8.93378i	−1.37860	+	0.501771i	−0.921755	−	0.387773i	$-0.873244\pi$
$317$	−24.5453	+	8.93378i	−1.37860	+	0.501771i	−0.456849	+	0.889544i	$0.651022\pi$
$318$	0.844770	+	4.79093i	0.0473724	+	0.268662i
$319$	0.957234	−	5.42874i	0.0535948	−	0.303951i
$320$	−2.07398	−	0.754866i	−0.115939	−	0.0421983i
$321$	3.34002	−	2.80261i	0.186422	−	0.156427i
$322$	19.6459			1.09482
$323$	13.1099	+	10.6805i	0.729456	+	0.594277i
$324$	23.5895			1.31053
$325$	−6.62836	+	5.56185i	−0.367675	+	0.308516i
$326$	−15.0680	−	5.48432i	−0.834542	−	0.303748i
$327$	−1.07145	+	6.07650i	−0.0592514	+	0.336031i
$328$	10.5876	+	60.0455i	0.584605	+	3.31546i
$329$	−0.826352	+	0.300767i	−0.0455583	+	0.0165818i
$330$	−1.31908	+	2.28471i	−0.0726128	+	0.125769i
$331$	−9.52229	−	16.4931i	−0.523392	−	0.906542i	−0.999629	−	0.0272251i	$-0.991333\pi$
$331$	−9.52229	−	16.4931i	−0.523392	−	0.906542i	0.476237	−	0.879317i	$-0.342000\pi$
$332$	41.6279	+	34.9300i	2.28463	+	1.91703i
$333$	8.09627	+	6.79357i	0.443673	+	0.372286i
$334$	−17.4440	−	30.2139i	−0.954495	−	1.65323i
$335$	−2.61856	+	4.53547i	−0.143067	+	0.247799i
$336$	6.23783	−	2.27038i	0.340301	−	0.123860i
$337$	0.295445	+	1.67555i	0.0160939	+	0.0912731i	0.991797	−	0.127825i	$-0.0407996\pi$
$337$	0.295445	+	1.67555i	0.0160939	+	0.0912731i	−0.975703	+	0.219098i	$0.929688\pi$
$338$	2.47044	−	14.0105i	0.134374	−	0.762073i
$339$	0.803758	+	0.292544i	0.0436542	+	0.0158888i
$340$	−17.6630	+	14.8210i	−0.957909	+	0.803781i
$341$	4.54664			0.246214
$342$	5.33837	+	27.9032i	0.288666	+	1.50883i
$343$	−17.8530			−0.963970
$344$	40.7053	−	34.1558i	2.19468	−	1.84156i
$345$	4.18479	+	1.52314i	0.225302	+	0.0820031i
$346$	−11.1010	+	62.9570i	−0.596794	+	3.38459i
$347$	−0.851167	−	4.82721i	−0.0456930	−	0.259138i	0.953400	−	0.301708i	$-0.0975567\pi$
$347$	−0.851167	−	4.82721i	−0.0456930	−	0.259138i	−0.999094	+	0.0425697i	$0.986446\pi$
$348$	−12.5890	+	4.58202i	−0.674841	+	0.245622i
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	−0.193566	−	0.981087i	$-0.562006\pi$
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	0.946430	−	0.322910i	$-0.104661\pi$
$350$	−6.17752	−	10.6998i	−0.330202	−	0.571927i
$351$	7.57192	+	6.35359i	0.404159	+	0.339130i
$352$	4.17159	+	3.50038i	0.222346	+	0.186571i
$353$	4.15998	+	7.20529i	0.221413	+	0.383499i	0.955237	−	0.295841i	$-0.0955997\pi$
$353$	4.15998	+	7.20529i	0.221413	+	0.383499i	−0.733824	+	0.679340i	$0.762266\pi$
$354$	3.25237	−	5.63328i	0.172862	−	0.299405i
$355$	−8.78106	+	3.19604i	−0.466050	+	0.169628i
$356$	−1.85844	−	10.5397i	−0.0984972	−	0.558605i
$357$	−0.673648	+	3.82045i	−0.0356532	+	0.202200i
$358$	13.8735	+	5.04952i	0.733235	+	0.266876i
$359$	19.0967	−	16.0241i	1.00789	−	0.845718i	0.0198296	−	0.999803i	$-0.493688\pi$
$359$	19.0967	−	16.0241i	1.00789	−	0.845718i	0.988057	+	0.154086i	$0.0492432\pi$
$360$	−21.1753			−1.11604
$361$	−17.6582	+	7.01336i	−0.929380	+	0.369124i
$362$	−34.3405			−1.80490
$363$	4.79813	−	4.02611i	0.251837	−	0.211316i
$364$	−17.2554	−	6.28044i	−0.904427	−	0.329184i
$365$	−1.43376	+	8.13127i	−0.0750466	+	0.425610i
$366$	−1.29648	−	7.35273i	−0.0677683	−	0.384333i
$367$	2.42989	−	0.884409i	0.126839	−	0.0461657i	−0.277821	−	0.960633i	$-0.589612\pi$
$367$	2.42989	−	0.884409i	0.126839	−	0.0461657i	0.404660	+	0.914467i	$0.367390\pi$
$368$	16.8084	−	29.1130i	0.876198	−	1.51762i
$369$	−12.8512	−	22.2589i	−0.669005	−	1.15875i
$370$	−10.7306	−	9.00400i	−0.557855	−	0.468096i
$371$	3.45471	+	2.89884i	0.179359	+	0.150500i
$372$	−5.52481	−	9.56926i	−0.286448	−	0.496143i
$373$	11.6917	−	20.2505i	0.605371	−	1.04853i	−0.386622	−	0.922238i	$-0.626358\pi$
$373$	11.6917	−	20.2505i	0.605371	−	1.04853i	0.991993	−	0.126295i	$-0.0403086\pi$
$374$	−10.9363	+	3.98048i	−0.565502	+	0.205826i
$375$	−1.24985	−	7.08824i	−0.0645419	−	0.366035i
$376$	−0.608593	+	3.45150i	−0.0313858	+	0.177998i
$377$	11.8785	+	4.32342i	0.611774	+	0.222668i
$378$	−10.8118	+	9.07218i	−0.556099	+	0.466623i
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$	−4.86824	−	25.4459i	−0.249735	−	1.30535i
$381$	9.46616			0.484966
$382$	19.9479	−	16.7383i	1.02062	−	0.856405i
$383$	25.8234	+	9.39895i	1.31951	+	0.480264i	0.903303	−	0.429003i	$-0.141135\pi$
$383$	25.8234	+	9.39895i	1.31951	+	0.480264i	0.416212	+	0.909268i	$0.363357\pi$
$384$	−1.51202	+	8.57510i	−0.0771600	+	0.437596i
$385$	0.424678	+	2.40847i	0.0216436	+	0.122747i
$386$	32.8371	−	11.9517i	1.67136	−	0.608327i
$387$	−11.1998	+	19.3986i	−0.569318	+	0.986088i
$388$	−16.2554	−	28.1551i	−0.825241	−	1.42936i
$389$	−2.56031	−	2.14835i	−0.129813	−	0.108926i	0.575570	−	0.817753i	$-0.304780\pi$
$389$	−2.56031	−	2.14835i	−0.129813	−	0.108926i	−0.705383	+	0.708827i	$0.749225\pi$
$390$	−4.63429	−	3.88863i	−0.234666	−	0.196908i
$391$	9.82295	+	17.0138i	0.496768	+	0.860427i
$392$	−14.2049	+	24.6035i	−0.717454	+	1.24267i
$393$	−12.1493	+	4.42198i	−0.612851	+	0.223060i
$394$	3.49154	+	19.8015i	0.175901	+	0.997587i
$395$	−2.29473	+	13.0141i	−0.115460	+	0.654808i
$396$	−12.6420	−	4.60132i	−0.635286	−	0.231225i
$397$	−10.0530	+	8.43550i	−0.504547	+	0.423365i	−0.859206	−	0.511631i	$-0.829042\pi$
$397$	−10.0530	+	8.43550i	−0.504547	+	0.423365i	0.354658	+	0.934996i	$0.384597\pi$
$398$	−68.4552			−3.43135
$399$	−3.37939	−	2.75314i	−0.169181	−	0.137829i
$400$	−21.1411			−1.05706
$401$	13.1099	−	11.0005i	0.654679	−	0.549341i	−0.253808	−	0.967255i	$-0.581683\pi$
$401$	13.1099	−	11.0005i	0.654679	−	0.549341i	0.908487	+	0.417914i	$0.137239\pi$
$402$	6.03684	+	2.19723i	0.301090	+	0.109588i
$403$	−1.81046	+	10.2676i	−0.0901854	+	0.511467i
$404$	1.66250	+	9.42853i	0.0827127	+	0.469087i
$405$	6.76991	−	2.46405i	0.336400	−	0.122440i
$406$	−9.02481	+	15.6314i	−0.447894	+	0.775775i
$407$	−2.43242	−	4.21307i	−0.120571	−	0.208834i
$408$	11.8439	+	9.93821i	0.586360	+	0.492015i
$409$	−6.73964	−	5.65523i	−0.333254	−	0.279633i	0.460770	−	0.887519i	$-0.347573\pi$
$409$	−6.73964	−	5.65523i	−0.333254	−	0.279633i	−0.794024	+	0.607886i	$0.792018\pi$
$410$	17.0326	+	29.5013i	0.841178	+	1.45696i
$411$	3.33022	−	5.76811i	0.164268	−	0.284520i
$412$	51.7169	−	18.8234i	2.54791	−	0.927364i
$413$	−1.04710	−	5.93842i	−0.0515246	−	0.292211i
$414$	−5.73143	+	32.5046i	−0.281684	+	1.59751i
$415$	15.5954	+	5.67626i	0.765548	+	0.278637i
$416$	−9.56599	+	8.02682i	−0.469011	+	0.393547i
$417$	1.08378			0.0530728
$418$	2.08378	−	12.9096i	0.101921	−	0.631429i
$419$	6.84018			0.334165			0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018			0.334165			0.167082	+	0.985943i	$0.446565\pi$
$420$	4.55303	−	3.82045i	0.222165	−	0.186419i
$421$	4.53209	+	1.64955i	0.220880	+	0.0803939i	0.450090	−	0.892983i	$-0.351392\pi$
$421$	4.53209	+	1.64955i	0.220880	+	0.0803939i	−0.229210	+	0.973377i	$0.573614\pi$
$422$	3.54916	−	20.1283i	0.172771	−	0.979830i
$423$	−0.256549	−	1.45496i	−0.0124738	−	0.0707426i
$424$	16.8897	−	6.14733i	0.820234	−	0.298541i
$425$	6.17752	−	10.6998i	0.299654	−	0.519015i
$426$	5.73143	+	9.92713i	0.277689	+	0.480971i
$427$	−5.30200	−	4.44891i	−0.256582	−	0.215298i
$428$	−22.5744	−	18.9422i	−1.09118	−	0.915606i
$429$	−1.05051	−	1.81953i	−0.0507190	−	0.0878478i
$430$	14.8439	−	25.7104i	0.715836	−	1.23986i
$431$	−1.22503	+	0.445875i	−0.0590077	+	0.0214771i	−0.371355	−	0.928491i	$-0.621107\pi$
$431$	−1.22503	+	0.445875i	−0.0590077	+	0.0214771i	0.312348	+	0.949968i	$0.398885\pi$
$432$	4.19372	+	23.7837i	0.201770	+	1.14430i
$433$	3.44238	−	19.5227i	0.165430	−	0.938202i	−0.783189	−	0.621783i	$-0.786409\pi$
$433$	3.44238	−	19.5227i	0.165430	−	0.938202i	0.948620	−	0.316419i	$-0.102480\pi$
$434$	−13.9893	−	5.09170i	−0.671509	−	0.244409i
$435$	−3.13429	+	2.62998i	−0.150277	+	0.126098i
$436$	41.7033			1.99722
$437$	−22.0719	+	0.320070i	−1.05584	+	0.0153110i
$438$	10.1284			0.483952
$439$	−26.4800	+	22.2193i	−1.26382	+	1.06047i	−0.268557	+	0.963264i	$0.586547\pi$
$439$	−26.4800	+	22.2193i	−1.26382	+	1.06047i	−0.995264	+	0.0972078i	$0.969009\pi$
$440$	9.15910	+	3.33364i	0.436643	+	0.158925i
$441$	2.07960	−	11.7940i	0.0990287	−	0.561620i
$442$	−4.63429	−	26.2823i	−0.220430	−	1.25012i
$443$	−15.9843	+	5.81780i	−0.759436	+	0.276412i	−0.692571	−	0.721350i	$-0.743522\pi$
$443$	−15.9843	+	5.81780i	−0.759436	+	0.276412i	−0.0668650	+	0.997762i	$0.521300\pi$
$444$	−5.91147	+	10.2390i	−0.280546	+	0.485920i
$445$	−1.63429	−	2.83067i	−0.0774726	−	0.134186i
$446$	30.0180	+	25.1881i	1.42139	+	1.19269i
$447$	−5.60354	−	4.70193i	−0.265038	−	0.222394i
$448$	1.25490	+	2.17355i	0.0592885	+	0.102691i
$449$	−18.7049	+	32.3978i	−0.882737	+	1.52895i	−0.0344512	+	0.999406i	$0.510968\pi$
$449$	−18.7049	+	32.3978i	−0.882737	+	1.52895i	−0.848286	+	0.529539i	$0.822365\pi$
$450$	19.5052	−	7.09932i	0.919485	−	0.334665i
$451$	2.05438	+	11.6510i	0.0967369	+	0.548622i
$452$	1.00387	−	5.69323i	0.0472181	−	0.267787i
$453$	−6.77244	−	2.46497i	−0.318197	−	0.115814i
$454$	−19.1498	+	16.0686i	−0.898743	+	0.754135i
$455$	−5.60813			−0.262913
$456$	−16.2366	+	6.17771i	−0.760351	+	0.289298i
$457$	9.11112			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$457$	9.11112			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$458$	−39.0244	+	32.7454i	−1.82349	+	1.53009i
$459$	−13.2626	−	4.82721i	−0.619047	−	0.225315i
$460$	5.22668	−	29.6420i	0.243695	−	1.38206i
$461$	−4.24540	−	24.0769i	−0.197728	−	1.12137i	−0.908480	−	0.417929i	$-0.862756\pi$
$461$	−4.24540	−	24.0769i	−0.197728	−	1.12137i	0.710751	−	0.703443i	$-0.248355\pi$
$462$	2.81908	−	1.02606i	0.131155	−	0.0477367i
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	−0.863098	−	0.505037i	$-0.831479\pi$
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	0.868924	+	0.494946i	$0.164812\pi$
$464$	15.4427	+	26.7475i	0.716909	+	1.24172i
$465$	−2.58512	−	2.16918i	−0.119882	−	0.100593i
$466$	−6.85638	−	5.75319i	−0.317616	−	0.266511i
$467$	−7.68092	−	13.3037i	−0.355431	−	0.615624i	0.631761	−	0.775163i	$-0.282332\pi$
$467$	−7.68092	−	13.3037i	−0.355431	−	0.615624i	−0.987192	+	0.159539i	$0.948999\pi$
$468$	15.4251	−	26.7171i	0.713028	−	1.23500i
$469$	5.59627	−	2.03687i	0.258412	−	0.0940541i
$470$	0.340022	+	1.92836i	0.0156841	+	0.0889487i
$471$	−1.24598	+	7.06629i	−0.0574116	+	0.325597i
$472$	−22.5831	−	8.21956i	−1.03947	−	0.378336i
$473$	7.89827	−	6.62744i	0.363163	−	0.304730i
$474$	16.2104			0.744567
$475$	7.11468	+	11.9204i	0.326444	+	0.546946i
$476$	26.2199			1.20179
$477$	−5.80406	+	4.87019i	−0.265750	+	0.222991i
$478$	28.4898	+	10.3694i	1.30309	+	0.474287i
$479$	−0.124896	+	0.708319i	−0.00570663	+	0.0323639i	−0.987528	−	0.157443i	$-0.949675\pi$
$479$	−0.124896	+	0.708319i	−0.00570663	+	0.0323639i	0.981821	+	0.189807i	$0.0607861\pi$
$480$	−0.701867	−	3.98048i	−0.0320357	−	0.181683i
$481$	10.4829	−	3.81547i	0.477980	−	0.173971i
$482$	16.3341	−	28.2915i	0.743998	−	1.28864i
$483$	−2.53209	−	4.38571i	−0.115214	−	0.199557i
$484$	−32.4295	−	27.2116i	−1.47407	−	1.23689i
$485$	−7.60607	−	6.38225i	−0.345374	−	0.289803i
$486$	−18.2369	−	31.5873i	−0.827245	−	1.43283i
$487$	−5.87346	+	10.1731i	−0.266152	+	0.460988i	−0.967865	−	0.251471i	$-0.919086\pi$
$487$	−5.87346	+	10.1731i	−0.266152	+	0.460988i	0.701713	+	0.712460i	$0.252419\pi$
$488$	−25.9209	+	9.43442i	−1.17338	+	0.427076i
$489$	0.717759	+	4.07061i	0.0324582	+	0.184079i
$490$	−2.75624	+	15.6314i	−0.124514	+	0.706156i
$491$	−0.0834734	−	0.0303818i	−0.00376710	−	0.00137111i	0.340136	−	0.940376i	$-0.389527\pi$
$491$	−0.0834734	−	0.0303818i	−0.00376710	−	0.00137111i	−0.343903	+	0.939005i	$0.611749\pi$
$492$	22.0253	−	18.4814i	0.992976	−	0.833206i
$493$	−18.0496			−0.812914
$494$	28.3239	+	9.84635i	1.27435	+	0.443008i
$495$	−4.10876			−0.184675
$496$	−19.5141	+	16.3743i	−0.876211	+	0.735228i
$497$	9.98545	+	3.63441i	0.447909	+	0.163025i
$498$	3.53519	−	20.0490i	0.158416	−	0.898419i
$499$	2.55097	+	14.4673i	0.114197	+	0.647645i	0.987145	+	0.159830i	$0.0510947\pi$
$499$	2.55097	+	14.4673i	0.114197	+	0.647645i	−0.872947	+	0.487815i	$0.837794\pi$
$500$	−45.7131	+	16.6382i	−2.04435	+	0.744083i
$501$	−4.49660	+	7.78833i	−0.200893	+	0.347957i
$502$	18.1839	+	31.4955i	0.811588	+	1.40571i
$503$	−3.75671	−	3.15225i	−0.167503	−	0.140552i	0.555183	−	0.831728i	$-0.312648\pi$
$503$	−3.75671	−	3.15225i	−0.167503	−	0.140552i	−0.722686	+	0.691176i	$0.757093\pi$
$504$	18.4461	+	15.4781i	0.821654	+	0.689450i
$505$	1.46198	+	2.53223i	0.0650573	+	0.112683i
$506$	7.59627	−	13.1571i	0.337695	−	0.584905i
$507$	−3.44609	+	1.25427i	−0.153046	+	0.0557043i
$508$	−11.1099	−	63.0076i	−0.492924	−	2.79551i
$509$	1.11375	−	6.31640i	0.0493662	−	0.279969i	−0.950125	−	0.311870i	$-0.899045\pi$
$509$	1.11375	−	6.31640i	0.0493662	−	0.279969i	0.999491	+	0.0319002i	$0.0101559\pi$
$510$	8.11721	+	2.95442i	0.359436	+	0.130824i
$511$	7.19253	−	6.03525i	0.318179	−	0.266984i
$512$	50.5553			2.23425
$513$	11.9991	−	10.3686i	0.529774	−	0.457786i
$514$	−12.6040			−0.555939
$515$	12.8760	−	10.8042i	0.567384	−	0.476091i
$516$	−23.5462	−	8.57013i	−1.03656	−	0.377279i
$517$	−0.118089	+	0.669713i	−0.00519353	+	0.0294540i
$518$	2.76604	+	15.6870i	0.121533	+	0.689248i
$519$	15.4851	−	5.63613i	0.679723	−	0.247399i
$520$	−11.1755	+	19.3565i	−0.490076	+	0.848837i
$521$	17.9067	+	31.0154i	0.784508	+	1.35881i	0.929293	+	0.369344i	$0.120418\pi$
$521$	17.9067	+	31.0154i	0.784508	+	1.35881i	−0.144785	+	0.989463i	$0.546249\pi$
$522$	−23.2297	−	19.4920i	−1.01674	−	0.853142i
$523$	29.7015	+	24.9225i	1.29875	+	1.08978i	0.990359	+	0.138526i	$0.0442363\pi$
$523$	29.7015	+	24.9225i	1.29875	+	1.08978i	0.308395	+	0.951258i	$0.400208\pi$
$524$	43.6921	+	75.6770i	1.90870	+	3.30596i
$525$	−1.59240	+	2.75811i	−0.0694979	+	0.120374i
$526$	−57.2071	+	20.8217i	−2.49435	+	0.907869i
$527$	−2.58512	−	14.6610i	−0.112610	−	0.638641i
$528$	0.891407	−	5.05542i	0.0387935	−	0.220009i
$529$	−2.48633	−	0.904950i	−0.108101	−	0.0393456i
$530$	7.69253	−	6.45480i	0.334142	−	0.280379i
$531$	10.1307			0.439636
$532$	−14.3589	+	25.7247i	−0.622538	+	1.11531i
$533$	−27.1293			−1.17510
$534$	−3.07145	+	2.57725i	−0.132915	+	0.111529i
$535$	−8.45723	−	3.07818i	−0.365638	−	0.133081i
$536$	4.12155	−	23.3745i	0.178024	−	1.00962i
$537$	−0.660855	−	3.74789i	−0.0285180	−	0.161734i
$538$	−31.1964	+	11.3546i	−1.34497	+	0.489530i
$539$	−2.75624	+	4.77396i	−0.118720	+	0.205629i
$540$	10.8118	+	18.7266i	0.465266	+	0.805864i
$541$	7.26991	+	6.10018i	0.312558	+	0.262267i	0.785548	−	0.618800i	$-0.212381\pi$
$541$	7.26991	+	6.10018i	0.312558	+	0.262267i	−0.472990	+	0.881068i	$0.656825\pi$
$542$	51.5374	+	43.2450i	2.21372	+	1.85753i
$543$	4.42602	+	7.66610i	0.189939	+	0.328984i
$544$	8.91534	−	15.4418i	0.382242	−	0.662063i
$545$	11.9684	−	4.35613i	0.512669	−	0.186596i
$546$	1.19459	+	6.77487i	0.0511238	+	0.289938i
$547$	2.46791	−	13.9962i	0.105520	−	0.598435i	−0.885491	−	0.464657i	$-0.846178\pi$
$547$	2.46791	−	13.9962i	0.105520	−	0.598435i	0.991011	−	0.133779i	$-0.0427111\pi$
$548$	−42.3016	−	15.3965i	−1.80703	−	0.657707i
$549$	8.90760	−	7.47437i	0.380167	−	0.318998i
$550$	−9.55438			−0.407400
$551$	9.88460	−	17.7088i	0.421098	−	0.754418i
$552$	−20.1830			−0.859047
$553$	11.5116	−	9.65939i	0.489524	−	0.410759i
$554$	−39.2854	−	14.2987i	−1.66908	−	0.607494i
$555$	−0.627011	+	3.55596i	−0.0266152	+	0.150942i
$556$	−1.27197	−	7.21372i	−0.0539437	−	0.305930i
$557$	−21.1805	+	7.70908i	−0.897447	+	0.326644i	−0.749229	−	0.662311i	$-0.769576\pi$
$557$	−21.1805	+	7.70908i	−0.897447	+	0.326644i	−0.148218	+	0.988955i	$0.547354\pi$
$558$	12.5055	−	21.6602i	0.529401	−	0.916949i
$559$	11.8216	+	20.4756i	0.500001	+	0.866026i
$560$	−10.4966	−	8.80769i	−0.443562	−	0.372193i
$561$	2.29813	+	1.92836i	0.0970273	+	0.0814155i
$562$	−24.5488	−	42.5197i	−1.03553	−	1.79358i
$563$	21.4859	−	37.2147i	0.905524	−	1.56841i	0.0853106	−	0.996354i	$-0.472812\pi$
$563$	21.4859	−	37.2147i	0.905524	−	1.56841i	0.820213	−	0.572058i	$-0.193855\pi$
$564$	1.55303	−	0.565258i	0.0653945	−	0.0238017i
$565$	−0.306589	−	1.73875i	−0.0128983	−	0.0731500i
$566$	4.97313	−	28.2040i	0.209036	−	1.18550i
$567$	−7.69846	−	2.80201i	−0.323305	−	0.117673i
$568$	32.4424	−	27.2224i	1.36125	−	1.14223i
$569$	7.42696			0.311354			0.155677	−	0.987808i	$-0.450244\pi$
$569$	7.42696			0.311354			0.155677	+	0.987808i	$0.450244\pi$
$570$	−7.34389	+	6.34597i	−0.307602	+	0.265803i
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	−10.8780	+	9.12776i	−0.454834	+	0.381651i
$573$	−6.30763	−	2.29579i	−0.263505	−	0.0959080i
$574$	6.72668	−	38.1489i	0.280766	−	1.59230i
$575$	2.80066	+	15.8833i	0.116796	+	0.662381i
$576$	−3.96229	+	1.44215i	−0.165095	+	0.0600898i
$577$	−1.61721	+	2.80109i	−0.0673254	+	0.116611i	−0.897723	−	0.440560i	$-0.854780\pi$
$577$	−1.61721	+	2.80109i	−0.0673254	+	0.116611i	0.830398	+	0.557171i	$0.188113\pi$
$578$	−2.46926	−	4.27688i	−0.102707	−	0.177895i
$579$	−6.90033	−	5.79006i	−0.286768	−	0.240627i
$580$	21.1839	+	17.7754i	0.879614	+	0.738084i
$581$	−9.43629	−	16.3441i	−0.391483	−	0.678069i
$582$	−6.08987	+	10.5480i	−0.252433	+	0.437227i
$583$	3.27719	−	1.19280i	0.135727	−	0.0494007i
$584$	−6.49794	−	36.8517i	−0.268887	−	1.52493i
$585$	1.63610	−	9.27876i	0.0676443	−	0.383630i
$586$	9.27719	+	3.37662i	0.383237	+	0.139487i
$587$	−31.2610	+	26.2311i	−1.29028	+	1.08267i	−0.298543	+	0.954396i	$0.596501\pi$
$587$	−31.2610	+	26.2311i	−1.29028	+	1.08267i	−0.991738	+	0.128279i	$0.959055\pi$
$588$	13.3969			0.552480
$589$	15.7998	+	5.49254i	0.651019	+	0.226316i
$590$	−13.4270			−0.552779
$591$	3.97044	−	3.33159i	0.163322	−	0.137043i
$592$	25.6129	+	9.32234i	1.05268	+	0.383146i
$593$	−1.92127	+	10.8961i	−0.0788973	+	0.447449i	0.919610	+	0.392832i	$0.128505\pi$
$593$	−1.92127	+	10.8961i	−0.0788973	+	0.447449i	−0.998507	+	0.0546164i	$0.982606\pi$
$594$	1.89528	+	10.7487i	0.0777642	+	0.441023i
$595$	7.52481	−	2.73881i	0.308487	−	0.112280i
$596$	−24.7199	+	42.8161i	−1.01257	+	1.75381i
$597$	8.82295	+	15.2818i	0.361099	+	0.625442i
$598$	26.6878	+	22.3937i	1.09134	+	0.915747i
$599$	−34.1332	−	28.6411i	−1.39464	−	1.17024i	−0.963419	−	0.268000i	$-0.913637\pi$
$599$	−34.1332	−	28.6411i	−1.39464	−	1.17024i	−0.431224	−	0.902245i	$-0.641918\pi$
$600$	6.34642	+	10.9923i	0.259091	+	0.448760i
$601$	2.49953	−	4.32932i	0.101958	−	0.176597i	−0.810533	−	0.585693i	$-0.800823\pi$
$601$	2.49953	−	4.32932i	0.101958	−	0.176597i	0.912491	+	0.409096i	$0.134156\pi$
$602$	−31.7237	+	11.5465i	−1.29296	+	0.470600i
$603$	1.73742	+	9.85337i	0.0707530	+	0.401260i
$604$	−8.45858	+	47.9710i	−0.344175	+	1.95191i
$605$	−12.1493	−	4.42198i	−0.493939	−	0.179779i
$606$	2.74763	−	2.30553i	0.111615	−	0.0936558i
$607$	−31.1881			−1.26589			−0.632943	−	0.774199i	$-0.718153\pi$
$607$	−31.1881			−1.26589			−0.632943	+	0.774199i	$0.718153\pi$
$608$	10.2679	+	17.2035i	0.416417	+	0.697692i
$609$	4.65270			0.188537
$610$	−11.8059	+	9.90630i	−0.478006	+	0.401095i
$611$	−1.46538	−	0.533356i	−0.0592831	−	0.0215773i
$612$	−7.64930	+	43.3813i	−0.309205	+	1.75359i
$613$	2.84255	+	16.1209i	0.114809	+	0.651117i	0.986844	+	0.161673i	$0.0516890\pi$
$613$	2.84255	+	16.1209i	0.114809	+	0.651117i	−0.872035	+	0.489444i	$0.837200\pi$
$614$	55.1430	−	20.0704i	2.22539	−	0.809975i
$615$	4.39053	−	7.60462i	0.177043	−	0.306648i
$616$	−5.54189	−	9.59883i	−0.223289	−	0.386748i
$617$	12.3014	+	10.3221i	0.495235	+	0.415551i	0.855898	−	0.517145i	$-0.173005\pi$
$617$	12.3014	+	10.3221i	0.495235	+	0.415551i	−0.360663	+	0.932696i	$0.617450\pi$
$618$	−15.7947	−	13.2534i	−0.635357	−	0.533128i
$619$	−11.9213	−	20.6483i	−0.479156	−	0.829923i	0.520558	−	0.853826i	$-0.325724\pi$
$619$	−11.9213	−	20.6483i	−0.479156	−	0.829923i	−0.999714	+	0.0239031i	$0.992391\pi$
$620$	−11.4042	+	19.7527i	−0.458004	+	0.793286i
$621$	17.3131	−	6.30147i	0.694753	−	0.252869i
$622$	1.52182	+	8.63068i	0.0610195	+	0.346059i
$623$	−0.645430	+	3.66041i	−0.0258586	+	0.146651i
$624$	11.0617	+	4.02611i	0.442820	+	0.161173i
$625$	0.817267	−	0.685768i	0.0326907	−	0.0274307i
$626$	57.9590			2.31651
$627$	−3.15048	+	1.19869i	−0.125818	+	0.0478712i
$628$	48.4962			1.93521
$629$	−12.2023	+	10.2390i	−0.486539	+	0.408255i
$630$	12.6420	+	4.60132i	0.503670	+	0.183321i
$631$	3.72874	−	21.1467i	0.148439	−	0.841838i	−0.816103	−	0.577907i	$-0.803870\pi$
$631$	3.72874	−	21.1467i	0.148439	−	0.841838i	0.964541	−	0.263931i	$-0.0850193\pi$
$632$	−10.3999	−	58.9809i	−0.413687	−	2.34613i
$633$	−4.95084	+	1.80196i	−0.196778	+	0.0716214i
$634$	33.0699	−	57.2787i	1.31337	−	2.27483i
$635$	−9.76991	−	16.9220i	−0.387707	−	0.671529i
$636$	−6.49273	−	5.44804i	−0.257453	−	0.216029i
$637$	−9.68345	−	8.12538i	−0.383672	−	0.321939i
$638$	6.97906	+	12.0881i	0.276303	+	0.478572i
$639$	−8.92633	+	15.4609i	−0.353120	+	0.611622i
$640$	16.8897	−	6.14733i	0.667622	−	0.242995i
$641$	2.21466	+	12.5600i	0.0874738	+	0.496089i	0.996795	+	0.0799944i	$0.0254902\pi$
$641$	2.21466	+	12.5600i	0.0874738	+	0.496089i	−0.909322	+	0.416094i	$0.863399\pi$
$642$	−1.91710	+	10.8724i	−0.0756619	+	0.429100i
$643$	−26.8828	−	9.78456i	−1.06016	−	0.385865i	−0.247669	−	0.968845i	$-0.579665\pi$
$643$	−26.8828	−	9.78456i	−1.06016	−	0.385865i	−0.812487	+	0.582979i	$0.801887\pi$
$644$	−26.2199	+	22.0011i	−1.03321	+	0.866964i
$645$	−7.65270			−0.301325
$646$	−42.8127	+	0.620838i	−1.68444	+	0.0244265i
$647$	16.7128			0.657046			0.328523	−	0.944496i	$-0.393449\pi$
$647$	16.7128			0.657046			0.328523	+	0.944496i	$0.393449\pi$
$648$	−25.0121	+	20.9876i	−0.982567	+	0.824472i
$649$	−4.38191	−	1.59489i	−0.172005	−	0.0626047i
$650$	3.80453	−	21.5766i	0.149226	−	0.846302i
$651$	0.666374	+	3.77920i	0.0261173	+	0.148118i
$652$	26.2520	−	9.55493i	1.02811	−	0.374200i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	−7.81180	−	13.5304i	−0.305466	−	0.529082i
$655$	20.4440	+	17.1546i	0.798814	+	0.670285i
$656$	−50.7772	−	42.6072i	−1.98252	−	1.66353i
$657$	7.88713	+	13.6609i	0.307706	+	0.532963i
$658$	1.11334	−	1.92836i	0.0434025	−	0.0751754i
$659$	41.2533	−	15.0150i	1.60700	−	0.584900i	0.626157	−	0.779697i	$-0.284627\pi$
$659$	41.2533	−	15.0150i	1.60700	−	0.584900i	0.980844	+	0.194797i	$0.0624047\pi$
$660$	−0.798133	−	4.52644i	−0.0310673	−	0.176191i
$661$	−1.86777	+	10.5927i	−0.0726480	+	0.412007i	0.926697	+	0.375810i	$0.122636\pi$
$661$	−1.86777	+	10.5927i	−0.0726480	+	0.412007i	−0.999345	+	0.0361971i	$0.988476\pi$
$662$	45.3144	+	16.4931i	1.76119	+	0.641022i
$663$	−5.26991	+	4.42198i	−0.204667	+	0.171736i
$664$	−75.2158			−2.91894
$665$	−1.43376	+	8.88257i	−0.0555989	+	0.344451i
$666$	−26.7615			−1.03699
$667$	18.0496	−	15.1454i	0.698884	−	0.586434i
$668$	57.1173	+	20.7890i	2.20993	+	0.804350i
$669$	1.75402	−	9.94756i	0.0678144	−	0.384595i
$670$	−2.30272	−	13.0594i	−0.0889618	−	0.504527i
$671$	−5.02956	+	1.83061i	−0.194164	+	0.0706700i
$672$	−2.29813	+	3.98048i	−0.0886524	+	0.153550i
$673$	−2.32888	−	4.03374i	−0.0897717	−	0.155489i	0.817643	−	0.575726i	$-0.195280\pi$
$673$	−2.32888	−	4.03374i	−0.0897717	−	0.155489i	−0.907415	+	0.420237i	$0.861947\pi$
$674$	−3.30019	−	2.76919i	−0.127119	−	0.106665i
$675$	−8.87598	−	7.44783i	−0.341637	−	0.286667i
$676$	12.3931	+	21.4654i	0.476656	+	0.825592i
$677$	−1.63429	+	2.83067i	−0.0628107	+	0.108791i	−0.895721	−	0.444617i	$-0.853340\pi$
$677$	−1.63429	+	2.83067i	−0.0628107	+	0.108791i	0.832910	+	0.553408i	$0.186673\pi$
$678$	−2.03519	+	0.740748i	−0.0781609	+	0.0284482i
$679$	1.96064	+	11.1193i	0.0752423	+	0.426721i
$680$	5.54189	−	31.4296i	0.212522	−	1.20527i
$681$	6.05525	+	2.20393i	0.232038	+	0.0844549i
$682$	−8.81908	+	7.40008i	−0.337700	+	0.283364i
$683$	6.21894			0.237961			0.118981	−	0.992897i	$-0.462037\pi$
$683$	6.21894			0.237961			0.118981	+	0.992897i	$0.462037\pi$
$684$	−38.3730	−	31.2620i	−1.46723	−	1.19533i
$685$	−13.7483			−0.525297
$686$	34.6293	−	29.0574i	1.32215	−	1.10942i
$687$	12.3397	+	4.49129i	0.470790	+	0.171353i
$688$	−10.0312	+	56.8898i	−0.382436	+	2.16890i
$689$	1.38872	+	7.87581i	0.0529060	+	0.300045i
$690$	−10.5963	+	3.85673i	−0.403393	+	0.146823i
$691$	−11.1088	+	19.2409i	−0.422597	+	0.731959i	−0.996193	−	0.0871792i	$-0.972215\pi$
$691$	−11.1088	+	19.2409i	−0.422597	+	0.731959i	0.573596	+	0.819139i	$0.305548\pi$
$692$	−55.6887	−	96.4557i	−2.11697	−	3.66670i
$693$	3.57919	+	3.00330i	0.135962	+	0.114086i
$694$	9.50774	+	7.97794i	0.360909	+	0.302839i
$695$	−1.11856	−	1.93739i	−0.0424292	−	0.0734896i
$696$	9.27156	−	16.0588i	0.351438	−	0.608708i
$697$	36.4013	−	13.2490i	1.37880	−	0.501841i
$698$	12.3682	+	70.1438i	0.468145	+	2.65498i
$699$	−0.400634	+	2.27211i	−0.0151534	+	0.0859391i
$700$	20.2271	+	7.36208i	0.764514	+	0.278260i
$701$	−21.2750	+	17.8518i	−0.803544	+	0.674254i	−0.949058	−	0.315102i	$-0.897961\pi$
$701$	−21.2750	+	17.8518i	−0.803544	+	0.674254i	0.145513	+	0.989356i	$0.453517\pi$
$702$	−25.0283			−0.944631
$703$	−3.36319	−	17.5791i	−0.126845	−	0.663008i
$704$	1.94087			0.0731495
$705$	0.386659	−	0.324446i	0.0145624	−	0.0122193i
$706$	−19.7964	−	7.20529i	−0.745047	−	0.271175i
$707$	0.577382	−	3.27449i	0.0217147	−	0.123150i
$708$	1.96791	+	11.1606i	0.0739586	+	0.419440i
$709$	5.73947	−	2.08900i	0.215551	−	0.0784540i	−0.231988	−	0.972719i	$-0.574523\pi$
$709$	5.73947	−	2.08900i	0.215551	−	0.0784540i	0.447538	+	0.894265i	$0.352301\pi$
$710$	11.8307	−	20.4914i	0.443998	−	0.769027i
$711$	12.6233	+	21.8642i	0.473411	+	0.819972i
$712$	11.3478	+	9.52190i	0.425275	+	0.356848i
$713$	14.8871	+	12.4918i	0.557527	+	0.467821i
$714$	−4.91147	−	8.50692i	−0.183807	−	0.318364i
$715$	−2.16843	+	3.75584i	−0.0810948	+	0.140460i
$716$	−24.1707	+	8.79742i	−0.903302	+	0.328775i
$717$	−1.35710	−	7.69648i	−0.0506817	−	0.287430i
$718$	−10.9611	+	62.1635i	−0.409065	+	2.31992i
$719$	−36.3885	−	13.2443i	−1.35706	−	0.493930i	−0.441917	−	0.897056i	$-0.645701\pi$
$719$	−36.3885	−	13.2443i	−1.35706	−	0.493930i	−0.915144	+	0.403126i	$0.867924\pi$
$720$	17.6348	−	14.7973i	0.657208	−	0.551463i
$721$	−19.1138			−0.711835
$722$	22.8366	−	42.3442i	0.849891	−	1.57589i
$723$	−8.42097			−0.313179
$724$	45.8316	−	38.4573i	1.70332	−	1.42925i
$725$	−13.9243	−	5.06802i	−0.517134	−	0.188221i
$726$	−2.75402	+	15.6188i	−0.102211	+	0.579669i
$727$	−1.92366	−	10.9096i	−0.0713445	−	0.404615i	−0.999476	−	0.0323628i	$-0.989697\pi$
$727$	−1.92366	−	10.9096i	−0.0713445	−	0.404615i	0.928132	−	0.372252i	$-0.121414\pi$
$728$	23.8837	−	8.69296i	0.885190	−	0.322183i
$729$	3.31996	−	5.75033i	0.122961	−	0.212975i
$730$	−10.4534	−	18.1058i	−0.386896	−	0.670124i
$731$	−25.8614	−	21.7003i	−0.956520	−	0.802615i
$732$	9.96451	+	8.36121i	0.368299	+	0.309039i
$733$	7.90373	+	13.6897i	0.291931	+	0.505639i	0.974266	−	0.225400i	$-0.0723689\pi$
$733$	7.90373	+	13.6897i	0.291931	+	0.505639i	−0.682335	+	0.731039i	$0.739036\pi$
$734$	−3.27379	+	5.67036i	−0.120838	+	0.209297i
$735$	3.84477	−	1.39938i	0.141816	−	0.0516170i
$736$	4.04189	+	22.9227i	0.148986	+	0.844942i
$737$	0.799726	−	4.53547i	0.0294583	−	0.167066i
$738$	61.1558	+	22.2589i	2.25117	+	0.819360i
$739$	1.18685	−	0.995887i	0.0436591	−	0.0366343i	−0.620697	−	0.784050i	$-0.713150\pi$
$739$	1.18685	−	0.995887i	0.0436591	−	0.0366343i	0.664356	+	0.747416i	$0.268706\pi$
$740$	24.4047			0.897133
$741$	−1.45249	−	7.59202i	−0.0533584	−	0.278900i
$742$	−11.4192			−0.419213
$743$	29.2349	−	24.5310i	1.07252	−	0.899955i	0.0772453	−	0.997012i	$-0.475388\pi$
$743$	29.2349	−	24.5310i	1.07252	−	0.899955i	0.995279	+	0.0970576i	$0.0309431\pi$
$744$	14.3718	+	5.23091i	0.526896	+	0.191774i
$745$	−2.62196	+	14.8699i	−0.0960611	+	0.544790i
$746$	10.2815	+	58.3091i	0.376431	+	2.13485i
$747$	29.7946	−	10.8444i	1.09013	−	0.396774i
$748$	10.1382	−	17.5598i	0.370688	−	0.642050i
$749$	5.11721	+	8.86327i	0.186979	+	0.323857i
$750$	13.9611	+	11.7148i	0.509787	+	0.427762i
$751$	−19.4179	−	16.2935i	−0.708568	−	0.594559i	0.215629	−	0.976475i	$-0.430820\pi$
$751$	−19.4179	−	16.2935i	−0.708568	−	0.594559i	−0.924197	+	0.381916i	$0.875264\pi$
$752$	−1.90508	−	3.29969i	−0.0694710	−	0.120327i
$753$	4.68732	−	8.11867i	0.170815	−	0.295861i
$754$	−30.0774	+	10.9473i	−1.09536	+	0.398677i
$755$	2.58331	+	14.6507i	0.0940163	+	0.533193i
$756$	4.26991	−	24.2159i	0.155295	−	0.880723i
$757$	−39.8153	−	14.4916i	−1.44711	−	0.526705i	−0.505328	−	0.862927i	$-0.668628\pi$
$757$	−39.8153	−	14.4916i	−1.44711	−	0.526705i	−0.941783	+	0.336222i	$0.890851\pi$
$758$	−49.3435	+	41.4041i	−1.79224	+	1.50386i
$759$	−3.91622			−0.142150
$760$	27.8011	+	22.6492i	1.00845	+	0.821572i
$761$	−2.85710			−0.103570			−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710			−0.103570			−0.0517848	+	0.998658i	$0.516491\pi$
$762$	−18.3614	+	15.4071i	−0.665165	+	0.558139i
$763$	−13.6099	−	4.95361i	−0.492713	−	0.179333i
$764$	−7.87804	+	44.6786i	−0.285018	+	1.61641i
$765$	2.33615	+	13.2490i	0.0844638	+	0.479018i
$766$	−65.3872	+	23.7990i	−2.36253	+	0.859892i
$767$	5.34658	−	9.26055i	0.193054	−	0.334379i
$768$	−9.95471	−	17.2421i	−0.359210	−	0.622169i
$769$	14.6472	+	12.2905i	0.528193	+	0.443207i	0.867477	−	0.497477i	$-0.165740\pi$
$769$	14.6472	+	12.2905i	0.528193	+	0.443207i	−0.339284	+	0.940684i	$0.610185\pi$
$770$	−4.74376	−	3.98048i	−0.170953	−	0.143447i
$771$	1.62449	+	2.81369i	0.0585044	+	0.101333i
$772$	−30.4406	+	52.7247i	−1.09558	+	1.89760i
$773$	−2.36319	+	0.860130i	−0.0849980	+	0.0309367i	−0.384169	−	0.923263i	$-0.625512\pi$
$773$	−2.36319	+	0.860130i	−0.0849980	+	0.0309367i	0.299171	+	0.954199i	$0.403290\pi$
$774$	−9.84895	−	55.8561i	−0.354013	−	2.00771i
$775$	2.12226	−	12.0360i	0.0762340	−	0.432344i
$776$	42.2854	+	15.3906i	1.51796	+	0.552491i
$777$	3.14543	−	2.63933i	0.112842	−	0.0946854i
$778$	8.46286			0.303408
$779$	−6.93582	+	42.9694i	−0.248502	+	1.53954i
$780$	10.5398			0.377386
$781$	6.29498	−	5.28211i	0.225252	−	0.189009i
$782$	−46.7452	−	17.0138i	−1.67160	−	0.608414i
$783$	−2.93939	+	16.6701i	−0.105045	+	0.595741i
$784$	−5.36319	−	30.4162i	−0.191542	−	1.08629i
$785$	13.9179	−	5.06569i	0.496750	−	0.180802i
$786$	16.3687	−	28.3514i	0.583852	−	1.01126i
$787$	−1.36303	−	2.36083i	−0.0485866	−	0.0841545i	0.840709	−	0.541487i	$-0.182138\pi$
$787$	−1.36303	−	2.36083i	−0.0485866	−	0.0841545i	−0.889296	+	0.457332i	$0.848805\pi$
$788$	−26.8353	−	22.5175i	−0.955967	−	0.802152i
$789$	12.0214	+	10.0872i	0.427974	+	0.359112i
$790$	−16.7306	−	28.9782i	−0.595246	−	1.03100i
$791$	−1.00387	+	1.73875i	−0.0356935	+	0.0618230i
$792$	17.4982	−	6.36884i	0.621773	−	0.226307i
$793$	−2.13129	−	12.0872i	−0.0756844	−	0.429228i
$794$	5.77022	−	32.7245i	0.204777	−	1.16135i
$795$	−2.43242	−	0.885328i	−0.0862690	−	0.0313993i
$796$	91.3620	−	76.6618i	3.23824	−	2.71720i
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$	11.0360	−	0.160035i	0.390669	−	0.00566518i
$799$	2.22668			0.0787743
$800$	11.2135	−	9.40923i	0.396456	−	0.332666i
$801$	−5.86794	−	2.13575i	−0.207333	−	0.0754632i
$802$	−7.52481	+	42.6753i	−0.265710	+	1.50692i
$803$	−1.26083	−	7.15052i	−0.0444937	−	0.252336i
$804$	−10.5175	+	3.82807i	−0.370925	+	0.135006i
$805$	−5.22668	+	9.05288i	−0.184216	+	0.319072i
$806$	−13.1998	−	22.8627i	−0.464943	−	0.805306i
$807$	6.55556	+	5.50077i	0.230767	+	0.193636i
$808$	−10.1514	−	8.51800i	−0.357124	−	0.299662i
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.717633	−	0.696422i	$-0.754774\pi$
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.244302	−	0.969699i	$-0.578559\pi$
$810$	−9.12108	+	15.7982i	−0.320482	+	0.555091i
$811$	2.17112	−	0.790224i	0.0762384	−	0.0277485i	−0.303619	−	0.952793i	$-0.598195\pi$
$811$	2.17112	−	0.790224i	0.0762384	−	0.0277485i	0.379858	+	0.925045i	$0.375973\pi$
$812$	−5.46064	−	30.9688i	−0.191631	−	1.08679i
$813$	3.01145	−	17.0788i	0.105616	−	0.598979i
$814$	11.5753	+	4.21307i	0.405715	+	0.147668i
$815$	6.53596	−	5.48432i	0.228945	−	0.192107i
$816$	−16.8084			−0.588412
$817$	35.4531	−	13.4892i	1.24035	−	0.471927i
$818$	22.2772			0.778906
$819$	−8.20755	+	6.88695i	−0.286795	+	0.240650i
$820$	−55.7700	−	20.2986i	−1.94757	−	0.708858i
$821$	0.192944	−	1.09424i	0.00673379	−	0.0381892i	−0.981256	−	0.192710i	$-0.938272\pi$
$821$	0.192944	−	1.09424i	0.00673379	−	0.0381892i	0.987990	+	0.154521i	$0.0493834\pi$
$822$	2.92855	+	16.6086i	0.102145	+	0.579292i
$823$	−19.4024	+	7.06191i	−0.676327	+	0.246163i	−0.657270	−	0.753656i	$-0.728289\pi$
$823$	−19.4024	+	7.06191i	−0.676327	+	0.246163i	−0.0190572	+	0.999818i	$0.506066\pi$
$824$	−38.0886	+	65.9714i	−1.32688	+	2.29822i
$825$	1.23143	+	2.13290i	0.0428729	+	0.0742580i
$826$	11.6964	+	9.81445i	0.406970	+	0.341488i
$827$	27.8116	+	23.3367i	0.967103	+	0.811495i	0.982094	−	0.188392i	$-0.0603276\pi$
$827$	27.8116	+	23.3367i	0.967103	+	0.811495i	−0.0149913	+	0.999888i	$0.504772\pi$
$828$	−28.7520	−	49.7999i	−0.999200	−	1.73066i
$829$	3.57486	−	6.19183i	0.124160	−	0.215051i	−0.797244	−	0.603657i	$-0.793710\pi$
$829$	3.57486	−	6.19183i	0.124160	−	0.215051i	0.921404	+	0.388606i	$0.127043\pi$
$830$	−39.4889	+	14.3728i	−1.37068	+	0.498887i
$831$	1.87134	+	10.6129i	0.0649161	+	0.368157i
$832$	−0.772852	+	4.38306i	−0.0267938	+	0.151955i
$833$	16.9611	+	6.17334i	0.587667	+	0.213893i
$834$	−2.10220	+	1.76395i	−0.0727931	+	0.0610807i
$835$	18.5635			0.642418
$836$	11.6762	+	19.5630i	0.403829	+	0.676602i
$837$	−13.9614			−0.482577
$838$	−13.2679	+	11.1331i	−0.458330	+	0.384585i
$839$	32.5197	+	11.8362i	1.12270	+	0.408631i	0.835638	−	0.549280i	$-0.185098\pi$
$839$	32.5197	+	11.8362i	1.12270	+	0.408631i	0.287065	+	0.957911i	$0.407320\pi$
$840$	−1.42855	+	8.10170i	−0.0492896	+	0.279535i
$841$	−1.27672	−	7.24065i	−0.0440249	−	0.249678i
$842$	−11.4757	+	4.17680i	−0.395477	+	0.143942i
$843$	−6.32800	+	10.9604i	−0.217948	+	0.377497i
$844$	17.8045	+	30.8384i	0.612857	+	1.06150i
$845$	5.79885	+	4.86581i	0.199486	+	0.167389i
$846$	2.86571	+	2.40462i	0.0985253	+	0.0826725i
$847$	7.35117	+	12.7326i	0.252589	+	0.437497i
$848$	−9.76991	+	16.9220i	−0.335500	+	0.581103i
$849$	−6.93717	+	2.52492i	−0.238083	+	0.0866551i
$850$	5.43242	+	30.8088i	0.186330	+	1.05673i
$851$	3.61081	−	20.4779i	0.123777	−	0.701975i
$852$	−18.7665	−	6.83045i	−0.642930	−	0.234007i
$853$	25.4716	−	21.3732i	0.872132	−	0.731805i	−0.0924142	−	0.995721i	$-0.529458\pi$
$853$	25.4716	−	21.3732i	0.872132	−	0.731805i	0.964546	+	0.263915i	$0.0850139\pi$
$854$	17.5253			0.599703
$855$	−14.2781	−	4.96356i	−0.488301	−	0.169750i
$856$	40.7888			1.39413
$857$	−2.97700	+	2.49800i	−0.101692	+	0.0853299i	−0.692216	−	0.721690i	$-0.743366\pi$
$857$	−2.97700	+	2.49800i	−0.101692	+	0.0853299i	0.590524	+	0.807020i	$0.298921\pi$
$858$	4.99912	+	1.81953i	0.170667	+	0.0621178i
$859$	0.287866	−	1.63257i	0.00982187	−	0.0557026i	−0.979503	−	0.201430i	$-0.935441\pi$
$859$	0.287866	−	1.63257i	0.00982187	−	0.0557026i	0.989325	+	0.145727i	$0.0465522\pi$
$860$	8.98158	+	50.9371i	0.306269	+	1.73694i
$861$	−9.38326	+	3.41523i	−0.319780	+	0.116391i
$862$	1.65048	−	2.85872i	0.0562156	−	0.0973684i
$863$	26.3594	+	45.6558i	0.897284	+	1.55414i	0.830953	+	0.556343i	$0.187796\pi$
$863$	26.3594	+	45.6558i	0.897284	+	1.55414i	0.0663308	+	0.997798i	$0.478871\pi$
$864$	−12.8097	−	10.7487i	−0.435796	−	0.365677i
$865$	−26.0574	−	21.8647i	−0.885977	−	0.743423i
$866$	25.0979	+	43.4709i	0.852862	+	1.47720i
$867$	−0.636507	+	1.10246i	−0.0216169	+	0.0374416i
$868$	24.3726	−	8.87089i	0.827259	−	0.301098i
$869$	−2.01795	−	11.4444i	−0.0684543	−	0.388224i
$870$	1.79901	−	10.2027i	0.0609922	−	0.345904i
$871$	9.92396	+	3.61203i	0.336261	+	0.122389i
$872$	−44.2183	+	37.1035i	−1.49742	+	1.25648i
$873$	−18.9691			−0.642008
$874$	42.2918	−	36.5450i	1.43054	−	1.23615i
$875$	16.8949			0.571151
$876$	−13.5175	+	11.3426i	−0.456715	+	0.383230i
$877$	19.9119	+	7.24735i	0.672378	+	0.244726i	0.655572	−	0.755133i	$-0.272428\pi$
$877$	19.9119	+	7.24735i	0.672378	+	0.244726i	0.0168069	+	0.999859i	$0.494650\pi$
$878$	15.1989	−	86.1974i	0.512939	−	2.90902i
$879$	−0.441914	−	2.50622i	−0.0149054	−	0.0845327i
$880$	−9.95723	+	3.62414i	−0.335658	+	0.122170i
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	0.458106	+	0.888898i	$0.348528\pi$
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	−0.998861	+	0.0477179i	$0.984805\pi$
$882$	15.1621	+	26.2615i	0.510534	+	0.884271i
$883$	−36.2315	−	30.4018i	−1.21929	−	1.02310i	−0.998862	−	0.0476989i	$-0.984811\pi$
$883$	−36.2315	−	30.4018i	−1.21929	−	1.02310i	−0.220425	−	0.975404i	$-0.570744\pi$
$884$	35.6181	+	29.8872i	1.19797	+	1.00521i
$885$	1.73055	+	2.99740i	0.0581719	+	0.100757i
$886$	21.5355	−	37.3007i	0.723501	−	1.25314i
$887$	−9.92602	+	3.61278i	−0.333283	+	0.121305i	−0.503241	−	0.864146i	$-0.667859\pi$
$887$	−9.92602	+	3.61278i	−0.333283	+	0.121305i	0.169958	+	0.985451i	$0.445637\pi$
$888$	−2.84167	−	16.1159i	−0.0953602	−	0.540815i
$889$	−3.85844	+	21.8823i	−0.129408	+	0.733909i
$890$	7.77719	+	2.83067i	0.260692	+	0.0948841i
$891$	−4.85323	+	4.07234i	−0.162589	+	0.136429i
$892$	−68.2704			−2.28586
$893$	−1.21941	+	2.18463i	−0.0408059	+	0.0731059i
$894$	18.5220			0.619468
$895$	−6.01779	+	5.04952i	−0.201153	+	0.168787i
$896$	−19.2062	−	6.99049i	−0.641634	−	0.233536i
$897$	1.55943	−	8.84397i	0.0520679	−	0.295291i
$898$	−16.4488	−	93.2857i	−0.548903	−	3.11298i
$899$	−16.7780	+	6.10668i	−0.559576	+	0.203669i
$900$	−18.0817	+	31.3185i	−0.602724	+	1.04395i
$901$	−5.70961	−	9.88933i	−0.190215	−	0.329461i
$902$	−22.9479	−	19.2556i	−0.764081	−	0.641141i
$903$	6.66637	+	5.59375i	0.221843	+	0.186148i
$904$	4.00088	+	6.92972i	0.133067	+	0.230479i
$905$	9.13610	−	15.8242i	0.303694	−	0.526014i
$906$	17.1484	−	6.24152i	0.569718	−	0.207360i
$907$	7.45306	+	42.2684i	0.247475	+	1.40350i	0.814674	+	0.579919i	$0.196916\pi$
$907$	7.45306	+	42.2684i	0.247475	+	1.40350i	−0.567200	+	0.823580i	$0.691973\pi$
$908$	7.56283	−	42.8910i	0.250981	−	1.42339i
$909$	5.24928	+	1.91058i	0.174107	+	0.0633699i
$910$	10.8780	−	9.12776i	0.360604	−	0.302582i
$911$	−55.1411			−1.82691			−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411			−1.82691			−0.913454	+	0.406942i	$0.866595\pi$
$912$	9.20486	−	16.4910i	0.304803	−	0.546071i
$913$	−14.5945			−0.483008
$914$	−17.6728	+	14.8292i	−0.584563	+	0.490507i
$915$	3.73308	+	1.35873i	0.123412	+	0.0449182i
$916$	15.4119	−	87.4055i	0.509225	−	2.88796i
$917$	−5.26991	−	29.8872i	−0.174028	−	0.986961i
$918$	33.5822	−	12.2229i	1.10838	−	0.403416i
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	−0.589285	−	0.807925i	$-0.700590\pi$
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	0.994326	+	0.106373i	$0.0339237\pi$
$920$	20.8307	+	36.0798i	0.686767	+	1.18952i
$921$	−11.5876	−	9.72319i	−0.381826	−	0.320390i
$922$	47.4222	+	39.7920i	1.56177	+	1.31048i
$923$	9.42190	+	16.3192i	0.310126	+	0.537154i
$924$	−2.61334	+	4.52644i	−0.0859726	+	0.148909i
$925$	−12.2883	+	4.47259i	−0.404038	+	0.147058i
$926$	0.110242	+	0.625213i	0.00362277	+	0.0205458i
$927$	5.57620	−	31.6242i	0.183146	−	1.03867i
$928$	−20.0954	−	7.31412i	−0.659663	−	0.240098i
$929$	−17.0654	+	14.3195i	−0.559896	+	0.469809i	−0.878276	−	0.478155i	$-0.841306\pi$
$929$	−17.0654	+	14.3195i	−0.559896	+	0.469809i	0.318379	+	0.947963i	$0.396861\pi$
$930$	8.54488			0.280198
$931$	−15.3452	+	13.2601i	−0.502920	+	0.434581i
$932$	15.5936			0.510785
$933$	1.73055	−	1.45211i	0.0566557	−	0.0475398i
$934$	36.5517	+	13.3037i	1.19601	+	0.435312i
$935$	1.07532	−	6.09845i	0.0351668	−	0.199441i
$936$	7.41493	+	42.0522i	0.242365	+	1.37452i
$937$	8.97565	−	3.26687i	0.293222	−	0.106724i	−0.191221	−	0.981547i	$-0.561245\pi$
$937$	8.97565	−	3.26687i	0.293222	−	0.106724i	0.484443	+	0.874823i	$0.339022\pi$
$938$	−7.53983	+	13.0594i	−0.246184	+	0.426403i
$939$	−7.47013	−	12.9386i	−0.243779	−	0.422237i
$940$	−2.61334	−	2.19285i	−0.0852378	−	0.0715230i
$941$	−42.6883	−	35.8197i	−1.39160	−	1.16769i	−0.964688	−	0.263394i	$-0.915158\pi$
$941$	−42.6883	−	35.8197i	−1.39160	−	1.16769i	−0.426909	−	0.904295i	$-0.640398\pi$
$942$	−9.08424	−	15.7344i	−0.295981	−	0.512654i
$943$	−25.2841	+	43.7933i	−0.823362	+	1.42610i
$944$	24.5510	−	8.93582i	0.799066	−	0.290836i
$945$	−1.30406	−	7.39571i	−0.0424212	−	0.240582i
$946$	−4.53343	+	25.7104i	−0.147395	+	0.835916i
$947$	25.4119	+	9.24919i	0.825777	+	0.300558i	0.720125	−	0.693845i	$-0.244085\pi$
$947$	25.4119	+	9.24919i	0.825777	+	0.300558i	0.105653	+	0.994403i	$0.466307\pi$
$948$	−21.6348	+	18.1537i	−0.702664	+	0.589605i
$949$	16.6500			0.540482
$950$	−33.2019	−	11.5421i	−1.07721	−	0.374476i
$951$	−17.0490			−0.552852
$952$	−27.8011	+	23.3279i	−0.901040	+	0.756062i
$953$	−21.7361	−	7.91128i	−0.704100	−	0.256272i	−0.0349398	−	0.999389i	$-0.511124\pi$
$953$	−21.7361	−	7.91128i	−0.704100	−	0.256272i	−0.669161	+	0.743118i	$0.733346\pi$
$954$	3.33140	−	18.8933i	0.107858	−	0.611694i
$955$	2.40601	+	13.6452i	0.0778567	+	0.441547i
$956$	−49.6357	+	18.0659i	−1.60533	+	0.584293i
$957$	1.79901	−	3.11598i	0.0581538	−	0.100725i
$958$	−0.910597	−	1.57720i	−0.0294200	−	0.0509570i
$959$	11.9764	+	10.0494i	0.386737	+	0.324511i
$960$	−1.10354	−	0.925981i	−0.0356166	−	0.0298859i
$961$	8.13681	+	14.0934i	0.262478	+	0.454625i
$962$	−14.1236	+	24.4628i	−0.455363	+	0.788713i
$963$	−16.1573	+	5.88079i	−0.520663	+	0.189506i
$964$	9.88326	+	56.0507i	0.318318	+	1.80527i
$965$	−3.22874	+	18.3111i	−0.103937	+	0.589455i
$966$	12.0496	+	4.38571i	0.387690	+	0.141108i
$967$	29.9026	−	25.0913i	0.961603	−	0.806881i	−0.0196101	−	0.999808i	$-0.506242\pi$
$967$	29.9026	−	25.0913i	0.961603	−	0.806881i	0.981213	+	0.192927i	$0.0617980\pi$
$968$	58.5954			1.88333
$969$	5.65657	+	9.47740i	0.181715	+	0.304458i
$970$	25.1411			0.807234
$971$	−31.5631	+	26.4845i	−1.01291	+	0.849930i	−0.988720	−	0.149778i	$-0.952144\pi$
$971$	−31.5631	+	26.4845i	−1.01291	+	0.849930i	−0.0241869	+	0.999707i	$0.507700\pi$
$972$	59.7135	+	21.7339i	1.91531	+	0.697117i
$973$	−0.441752	+	2.50530i	−0.0141619	+	0.0803162i
$974$	−5.16503	−	29.2923i	−0.165498	−	0.938587i
$975$	−5.30706	+	1.93161i	−0.169962	+	0.0618610i
$976$	14.9941	−	25.9705i	0.479948	−	0.831295i
$977$	−11.2469	−	19.4802i	−0.359821	−	0.623227i	0.628110	−	0.778125i	$-0.283829\pi$
$977$	−11.2469	−	19.4802i	−0.359821	−	0.623227i	−0.987931	+	0.154897i	$0.950495\pi$
$978$	−8.01754	−	6.72752i	−0.256373	−	0.215122i
$979$	2.20187	+	1.84759i	0.0703720	+	0.0590491i
$980$	−13.8268	−	23.9488i	−0.441682	−	0.765015i
$981$	12.1664	−	21.0728i	0.388442	−	0.672802i
$982$	0.211362	−	0.0769295i	0.00674484	−	0.00245492i
$983$	−7.73536	−	43.8694i	−0.246720	−	1.39922i	−0.816465	−	0.577395i	$-0.804069\pi$
$983$	−7.73536	−	43.8694i	−0.246720	−	1.39922i	0.569746	−	0.821821i	$-0.307042\pi$
$984$	−6.91060	+	39.1919i	−0.220302	+	1.24939i
$985$	−10.0535	−	3.65917i	−0.320331	−	0.116591i
$986$	35.0107	−	29.3775i	1.11497	−	0.935570i
$987$	−0.573978			−0.0182699
$988$	−48.8285	+	18.5782i	−1.55344	+	0.591052i
$989$	44.0702			1.40135
$990$	7.96972	−	6.68739i	0.253294	−	0.212539i
$991$	42.5959	+	15.5036i	1.35310	+	0.492489i	0.913915	−	0.405907i	$-0.133044\pi$
$991$	42.5959	+	15.5036i	1.35310	+	0.492489i	0.439187	+	0.898395i	$0.355266\pi$
$992$	3.06283	−	17.3702i	0.0972451	−	0.551504i
$993$	−2.15853	−	12.2416i	−0.0684988	−	0.388476i
$994$	−25.2841	+	9.20264i	−0.801961	+	0.291890i
$995$	18.2121	−	31.5443i	0.577363	−	1.00002i
$996$	17.7344	+	30.7169i	0.561937	+	0.973303i
$997$	−8.03667	−	6.74357i	−0.254524	−	0.213571i	0.506593	−	0.862185i	$-0.330905\pi$
$997$	−8.03667	−	6.74357i	−0.254524	−	0.213571i	−0.761117	+	0.648614i	$0.775349\pi$
$998$	−28.4950	−	23.9101i	−0.901994	−	0.756862i
$999$	7.46926	+	12.9371i	0.236317	+	0.409313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.2.e.a.6.1	✓	6
3.2	odd	2		171.2.u.c.82.1		6
4.3	odd	2		304.2.u.b.177.1		6
5.2	odd	4		475.2.u.a.424.1		12
5.3	odd	4		475.2.u.a.424.2		12
5.4	even	2		475.2.l.a.101.1		6
7.2	even	3		931.2.x.a.557.1		6
7.3	odd	6		931.2.v.a.177.1		6
7.4	even	3		931.2.v.b.177.1		6
7.5	odd	6		931.2.x.b.557.1		6
7.6	odd	2		931.2.w.a.785.1		6
19.2	odd	18		361.2.e.a.62.1		6
19.3	odd	18		361.2.e.h.54.1		6
19.4	even	9		361.2.a.g.1.1		3
19.5	even	9		361.2.e.f.245.1		6
19.6	even	9		361.2.c.i.292.3		6
19.7	even	3		361.2.e.f.28.1		6
19.8	odd	6		361.2.e.a.99.1		6
19.9	even	9		361.2.c.i.68.3		6
19.10	odd	18		361.2.c.h.68.1		6
19.11	even	3		361.2.e.g.99.1		6
19.12	odd	6		361.2.e.b.28.1		6
19.13	odd	18		361.2.c.h.292.1		6
19.14	odd	18		361.2.e.b.245.1		6
19.15	odd	18		361.2.a.h.1.3		3
19.16	even	9	inner	19.2.e.a.16.1	yes	6
19.17	even	9		361.2.e.g.62.1		6
19.18	odd	2		361.2.e.h.234.1		6
57.23	odd	18		3249.2.a.z.1.3		3
57.35	odd	18		171.2.u.c.73.1		6
57.53	even	18		3249.2.a.s.1.1		3
76.15	even	18		5776.2.a.bi.1.2		3
76.23	odd	18		5776.2.a.br.1.2		3
76.35	odd	18		304.2.u.b.225.1		6
95.4	even	18		9025.2.a.bd.1.3		3
95.34	odd	18		9025.2.a.x.1.1		3
95.54	even	18		475.2.l.a.301.1		6
95.73	odd	36		475.2.u.a.149.1		12
95.92	odd	36		475.2.u.a.149.2		12
133.16	even	9		931.2.v.b.263.1		6
133.54	odd	18		931.2.v.a.263.1		6
133.73	odd	18		931.2.x.b.814.1		6
133.111	odd	18		931.2.w.a.491.1		6
133.130	even	9		931.2.x.a.814.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	1.1	even	1	trivial
19.2.e.a.16.1	yes	6	19.16	even	9	inner
171.2.u.c.73.1		6	57.35	odd	18
171.2.u.c.82.1		6	3.2	odd	2
304.2.u.b.177.1		6	4.3	odd	2
304.2.u.b.225.1		6	76.35	odd	18
361.2.a.g.1.1		3	19.4	even	9
361.2.a.h.1.3		3	19.15	odd	18
361.2.c.h.68.1		6	19.10	odd	18
361.2.c.h.292.1		6	19.13	odd	18
361.2.c.i.68.3		6	19.9	even	9
361.2.c.i.292.3		6	19.6	even	9
361.2.e.a.62.1		6	19.2	odd	18
361.2.e.a.99.1		6	19.8	odd	6
361.2.e.b.28.1		6	19.12	odd	6
361.2.e.b.245.1		6	19.14	odd	18
361.2.e.f.28.1		6	19.7	even	3
361.2.e.f.245.1		6	19.5	even	9
361.2.e.g.62.1		6	19.17	even	9
361.2.e.g.99.1		6	19.11	even	3
361.2.e.h.54.1		6	19.3	odd	18
361.2.e.h.234.1		6	19.18	odd	2
475.2.l.a.101.1		6	5.4	even	2
475.2.l.a.301.1		6	95.54	even	18
475.2.u.a.149.1		12	95.73	odd	36
475.2.u.a.149.2		12	95.92	odd	36
475.2.u.a.424.1		12	5.2	odd	4
475.2.u.a.424.2		12	5.3	odd	4
931.2.v.a.177.1		6	7.3	odd	6
931.2.v.a.263.1		6	133.54	odd	18
931.2.v.b.177.1		6	7.4	even	3
931.2.v.b.263.1		6	133.16	even	9
931.2.w.a.491.1		6	133.111	odd	18
931.2.w.a.785.1		6	7.6	odd	2
931.2.x.a.557.1		6	7.2	even	3
931.2.x.a.814.1		6	133.130	even	9
931.2.x.b.557.1		6	7.5	odd	6
931.2.x.b.814.1		6	133.73	odd	18
3249.2.a.s.1.1		3	57.53	even	18
3249.2.a.z.1.3		3	57.23	odd	18
5776.2.a.bi.1.2		3	76.15	even	18
5776.2.a.br.1.2		3	76.23	odd	18
9025.2.a.x.1.1		3	95.34	odd	18
9025.2.a.bd.1.3		3	95.4	even	18

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93969 + 1.62760i) q^{2} +(0.613341 + 0.223238i) q^{3} +(0.766044 - 4.34445i) q^{4} +(-0.233956 - 1.32683i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-1.97178 - 1.65452i) q^{9} +O(q^{10})\)	\(q+(-1.93969 + 1.62760i) q^{2} +(0.613341 + 0.223238i) q^{3} +(0.766044 - 4.34445i) q^{4} +(-0.233956 - 1.32683i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-1.97178 - 1.65452i) q^{9} +(2.61334 + 2.19285i) q^{10} +(0.592396 + 1.02606i) q^{11} +(1.43969 - 2.49362i) q^{12} +(-2.55303 + 0.929228i) q^{13} +(-0.673648 - 3.82045i) q^{14} +(0.152704 - 0.866025i) q^{15} +(-6.23783 - 2.27038i) q^{16} +(2.97178 - 2.49362i) q^{17} +6.51754 q^{18} +(0.819078 + 4.28125i) q^{19} -5.94356 q^{20} +(-0.766044 + 0.642788i) q^{21} +(-2.81908 - 1.02606i) q^{22} +(-0.879385 + 4.98724i) q^{23} +(0.692066 + 3.92490i) q^{24} +(2.99273 - 1.08926i) q^{25} +(3.43969 - 5.95772i) q^{26} +(-1.81908 - 3.15074i) q^{27} +(5.17752 + 4.34445i) q^{28} +(-3.56418 - 2.99070i) q^{29} +(1.11334 + 1.92836i) q^{30} +(1.91875 - 3.32337i) q^{31} +(4.31908 - 1.57202i) q^{32} +(0.134285 + 0.761570i) q^{33} +(-1.70574 + 9.67372i) q^{34} +(1.93969 + 0.705990i) q^{35} +(-8.69846 + 7.29888i) q^{36} -4.10607 q^{37} +(-8.55690 - 6.97118i) q^{38} -1.77332 q^{39} +(6.30200 - 5.28801i) q^{40} +(9.38326 + 3.41523i) q^{41} +(0.439693 - 2.49362i) q^{42} +(-1.51114 - 8.57013i) q^{43} +(4.91147 - 1.78763i) q^{44} +(-1.73396 + 3.00330i) q^{45} +(-6.41147 - 11.1050i) q^{46} +(0.439693 + 0.368946i) q^{47} +(-3.31908 - 2.78504i) q^{48} +(2.32635 + 4.02936i) q^{49} +(-4.03209 + 6.98378i) q^{50} +(2.37939 - 0.866025i) q^{51} +(2.08125 + 11.8034i) q^{52} +(0.511144 - 2.89884i) q^{53} +(8.65657 + 3.15074i) q^{54} +(1.22281 - 1.02606i) q^{55} -9.35504 q^{56} +(-0.453363 + 2.80872i) q^{57} +11.7811 q^{58} +(-3.01501 + 2.52990i) q^{59} +(-3.64543 - 1.32683i) q^{60} +(-0.784463 + 4.44891i) q^{61} +(1.68732 + 9.56926i) q^{62} +(3.70574 - 1.34878i) q^{63} +(0.819078 - 1.41868i) q^{64} +(1.83022 + 3.17004i) q^{65} +(-1.50000 - 1.25865i) q^{66} +(-2.97771 - 2.49860i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(-1.65270 + 2.86257i) q^{69} +(-4.91147 + 1.78763i) q^{70} +(-1.20439 - 6.83045i) q^{71} +(2.72921 - 15.4781i) q^{72} +(-5.75877 - 2.09602i) q^{73} +(7.96451 - 6.68302i) q^{74} +2.07873 q^{75} +(19.2271 - 0.278817i) q^{76} -1.81521 q^{77} +(3.43969 - 2.88624i) q^{78} +(-9.21688 - 3.35467i) q^{79} +(-1.55303 + 8.80769i) q^{80} +(0.928548 + 5.26606i) q^{81} +(-23.7592 + 8.64766i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(2.20574 + 3.82045i) q^{84} +(-4.00387 - 3.35965i) q^{85} +(16.8799 + 14.1639i) q^{86} +(-1.51842 - 2.62998i) q^{87} +(-3.61721 + 6.26519i) q^{88} +(2.27972 - 0.829748i) q^{89} +(-1.52481 - 8.64766i) q^{90} +(0.722811 - 4.09927i) q^{91} +(20.9932 + 7.64090i) q^{92} +(1.91875 - 1.61002i) q^{93} -1.45336 q^{94} +(5.48886 - 2.08840i) q^{95} +3.00000 q^{96} +(5.64543 - 4.73708i) q^{97} +(-11.0706 - 4.02936i) q^{98} +(0.529563 - 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9	\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more