LMFDB - Embedded newform 110.2.k.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	110.7
Dual form			110.2.k.a.63.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(-0.757609 - 1.48689i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.65111 - 1.50793i) q^{5} +(-0.980883 - 1.35007i) q^{6} +(2.92930 + 1.49255i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.126480 - 0.174085i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(-0.757609 - 1.48689i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.65111 - 1.50793i) q^{5} +(-0.980883 - 1.35007i) q^{6} +(2.92930 + 1.49255i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.126480 - 0.174085i) q^{9} +(-1.86667 - 1.23107i) q^{10} +(-3.16916 - 0.977970i) q^{11} +(-1.18000 - 1.18000i) q^{12} +(0.966831 + 6.10433i) q^{13} +(3.12672 + 1.01593i) q^{14} +(-0.991229 + 3.59744i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.839551 + 5.30072i) q^{17} +(0.0976902 - 0.191728i) q^{18} +(0.213692 - 0.657676i) q^{19} +(-2.03627 - 0.923903i) q^{20} -5.48632i q^{21} +(-3.28313 - 0.470163i) q^{22} +(3.92788 - 3.92788i) q^{23} +(-1.35007 - 0.980883i) q^{24} +(0.452316 + 4.97950i) q^{25} +(1.90986 + 5.87793i) q^{26} +(-5.29937 - 0.839337i) q^{27} +(3.24715 + 0.514298i) q^{28} +(0.689338 + 2.12156i) q^{29} +(-0.416262 + 3.70821i) q^{30} +(-4.63905 - 3.37046i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.946850 + 5.45312i) q^{33} +5.36679i q^{34} +(-2.58593 - 6.88153i) q^{35} +(0.0664946 - 0.204649i) q^{36} +(1.48742 - 2.91923i) q^{37} +(0.108178 - 0.683008i) q^{38} +(8.34400 - 6.06227i) q^{39} +(-2.15573 - 0.593985i) q^{40} +(1.24362 + 0.404076i) q^{41} +(-0.858249 - 5.41877i) q^{42} +(-4.38796 - 4.38796i) q^{43} +(-3.31626 + 0.0492198i) q^{44} +(-0.471340 + 0.0967105i) q^{45} +(3.26507 - 4.49398i) q^{46} +(-1.57073 + 0.800329i) q^{47} +(-1.48689 - 0.757609i) q^{48} +(2.23857 + 3.08113i) q^{49} +(1.22571 + 4.84744i) q^{50} +(8.51765 - 2.76755i) q^{51} +(2.80585 + 5.50680i) q^{52} +(-3.09304 + 0.489889i) q^{53} -5.36542 q^{54} +(3.75792 + 6.39359i) q^{55} +3.28763 q^{56} +(-1.13979 + 0.180525i) q^{57} +(1.01274 + 1.98761i) q^{58} +(0.820602 - 0.266630i) q^{59} +(0.168955 + 3.72767i) q^{60} +(-5.96441 - 8.20931i) q^{61} +(-5.10919 - 2.60326i) q^{62} +(0.630329 - 0.321169i) q^{63} +(0.587785 - 0.809017i) q^{64} +(7.60854 - 11.5368i) q^{65} +(1.78825 + 5.23786i) q^{66} +(9.05603 + 9.05603i) q^{67} +(0.839551 + 5.30072i) q^{68} +(-8.81614 - 2.86454i) q^{69} +(-3.63060 - 6.39227i) q^{70} +(1.58734 - 1.15327i) q^{71} +(0.0336617 - 0.212532i) q^{72} +(-1.52454 + 2.99208i) q^{73} +(1.01244 - 3.11597i) q^{74} +(7.06130 - 4.44506i) q^{75} -0.691521i q^{76} +(-7.82374 - 7.59490i) q^{77} +(7.29292 - 7.29292i) q^{78} +(-3.40098 - 2.47096i) q^{79} +(-2.22211 - 0.249441i) q^{80} +(2.56736 + 7.90152i) q^{81} +(1.29152 + 0.204556i) q^{82} +(-5.96478 - 0.944728i) q^{83} +(-1.69537 - 5.21780i) q^{84} +(9.37928 - 7.48608i) q^{85} +(-5.02037 - 3.64751i) q^{86} +(2.63229 - 2.63229i) q^{87} +(-3.26773 + 0.567391i) q^{88} -4.90528i q^{89} +(-0.450408 + 0.169254i) q^{90} +(-6.27889 + 19.3244i) q^{91} +(2.52186 - 4.94942i) q^{92} +(-1.49693 + 9.45125i) q^{93} +(-1.42620 + 1.03619i) q^{94} +(-1.34456 + 0.763663i) q^{95} +(-1.58710 - 0.515681i) q^{96} +(2.36159 + 14.9105i) q^{97} +(2.69301 + 2.69301i) q^{98} +(-0.571086 + 0.428010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$	−0.757609	−	1.48689i	−0.437406	−	0.858457i	−0.999507	−	0.0313890i	$-0.990007\pi$
$3$	−0.757609	−	1.48689i	−0.437406	−	0.858457i	0.562101	−	0.827068i	$-0.309993\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−1.65111	−	1.50793i	−0.738398	−	0.674365i
$5$	−1.65111	−	1.50793i	−0.738398	−	0.674365i
$6$	−0.980883	−	1.35007i	−0.400444	−	0.551164i
$7$	2.92930	+	1.49255i	1.10717	+	0.564131i	0.909319	−	0.416101i	$-0.136604\pi$
$7$	2.92930	+	1.49255i	1.10717	+	0.564131i	0.197851	+	0.980232i	$0.436604\pi$
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	0.126480	−	0.174085i	0.0421601	−	0.0580284i
$10$	−1.86667	−	1.23107i	−0.590293	−	0.389299i
$11$	−3.16916	−	0.977970i	−0.955538	−	0.294869i
$11$	−3.16916	−	0.977970i	−0.955538	−	0.294869i
$12$	−1.18000	−	1.18000i	−0.340638	−	0.340638i
$13$	0.966831	+	6.10433i	0.268151	+	1.69304i	0.642931	+	0.765924i	$0.277718\pi$
$13$	0.966831	+	6.10433i	0.268151	+	1.69304i	−0.374781	+	0.927114i	$0.622282\pi$
$14$	3.12672	+	1.01593i	0.835651	+	0.271519i
$15$	−0.991229	+	3.59744i	−0.255934	+	0.928855i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.839551	+	5.30072i	−0.203621	+	1.28561i	0.648075	+	0.761577i	$0.275574\pi$
$17$	−0.839551	+	5.30072i	−0.203621	+	1.28561i	−0.851696	+	0.524036i	$0.824426\pi$
$18$	0.0976902	−	0.191728i	0.0230258	−	0.0451907i
$19$	0.213692	−	0.657676i	0.0490243	−	0.150881i	−0.923548	−	0.383484i	$-0.874724\pi$
$19$	0.213692	−	0.657676i	0.0490243	−	0.150881i	0.972572	+	0.232603i	$0.0747242\pi$
$20$	−2.03627	−	0.923903i	−0.455324	−	0.206591i
$21$		−	5.48632i		−	1.19721i
$22$	−3.28313	−	0.470163i	−0.699966	−	0.100239i
$23$	3.92788	−	3.92788i	0.819020	−	0.819020i	−0.166946	−	0.985966i	$-0.553391\pi$
$23$	3.92788	−	3.92788i	0.819020	−	0.819020i	0.985966	+	0.166946i	$0.0533905\pi$
$24$	−1.35007	−	0.980883i	−0.275582	−	0.200222i
$25$	0.452316	+	4.97950i	0.0904633	+	0.995900i
$26$	1.90986	+	5.87793i	0.374554	+	1.15276i
$27$	−5.29937	−	0.839337i	−1.01986	−	0.161530i
$28$	3.24715	+	0.514298i	0.613654	+	0.0971932i
$29$	0.689338	+	2.12156i	0.128007	+	0.393965i	0.994437	−	0.105334i	$-0.0335911\pi$
$29$	0.689338	+	2.12156i	0.128007	+	0.393965i	−0.866430	+	0.499298i	$0.833591\pi$
$30$	−0.416262	+	3.70821i	−0.0759986	+	0.677023i
$31$	−4.63905	−	3.37046i	−0.833197	−	0.605353i	0.0872648	−	0.996185i	$-0.472187\pi$
$31$	−4.63905	−	3.37046i	−0.833197	−	0.605353i	−0.920462	+	0.390832i	$0.872187\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.946850	+	5.45312i	0.164825	+	0.949266i
$34$			5.36679i			0.920397i
$35$	−2.58593	−	6.88153i	−0.437102	−	1.16319i
$36$	0.0664946	−	0.204649i	0.0110824	−	0.0341082i
$37$	1.48742	−	2.91923i	0.244530	−	0.479918i	−0.735821	−	0.677176i	$-0.763204\pi$
$37$	1.48742	−	2.91923i	0.244530	−	0.479918i	0.980352	+	0.197258i	$0.0632036\pi$
$38$	0.108178	−	0.683008i	0.0175488	−	0.110798i
$39$	8.34400	−	6.06227i	1.33611	−	0.970740i
$40$	−2.15573	−	0.593985i	−0.340851	−	0.0939172i
$41$	1.24362	+	0.404076i	0.194220	+	0.0631060i	0.404512	−	0.914533i	$-0.367441\pi$
$41$	1.24362	+	0.404076i	0.194220	+	0.0631060i	−0.210292	+	0.977639i	$0.567441\pi$
$42$	−0.858249	−	5.41877i	−0.132431	−	0.836135i
$43$	−4.38796	−	4.38796i	−0.669158	−	0.669158i	0.288363	−	0.957521i	$-0.406889\pi$
$43$	−4.38796	−	4.38796i	−0.669158	−	0.669158i	−0.957521	+	0.288363i	$0.906889\pi$
$44$	−3.31626	+	0.0492198i	−0.499945	+	0.00742017i
$45$	−0.471340	+	0.0967105i	−0.0702633	+	0.0144168i
$46$	3.26507	−	4.49398i	0.481408	−	0.662601i
$47$	−1.57073	+	0.800329i	−0.229115	+	0.116740i	−0.564780	−	0.825241i	$-0.691039\pi$
$47$	−1.57073	+	0.800329i	−0.229115	+	0.116740i	0.335665	+	0.941981i	$0.391039\pi$
$48$	−1.48689	−	0.757609i	−0.214614	−	0.109351i
$49$	2.23857	+	3.08113i	0.319796	+	0.440161i
$50$	1.22571	+	4.84744i	0.173342	+	0.685531i
$51$	8.51765	−	2.76755i	1.19271	−	0.387535i
$52$	2.80585	+	5.50680i	0.389102	+	0.763655i
$53$	−3.09304	+	0.489889i	−0.424862	+	0.0672915i	−0.365204	−	0.930927i	$-0.619001\pi$
$53$	−3.09304	+	0.489889i	−0.424862	+	0.0672915i	−0.0596574	+	0.998219i	$0.519001\pi$
$54$	−5.36542			−0.730142
$55$	3.75792	+	6.39359i	0.506718	+	0.862112i
$56$	3.28763			0.439328
$57$	−1.13979	+	0.180525i	−0.150969	+	0.0239111i
$58$	1.01274	+	1.98761i	0.132979	+	0.260986i
$59$	0.820602	−	0.266630i	0.106833	−	0.0347122i	−0.255113	−	0.966911i	$-0.582113\pi$
$59$	0.820602	−	0.266630i	0.106833	−	0.0347122i	0.361946	+	0.932199i	$0.382113\pi$
$60$	0.168955	+	3.72767i	0.0218120	+	0.481241i
$61$	−5.96441	−	8.20931i	−0.763665	−	1.05109i	−0.996900	−	0.0786740i	$-0.974931\pi$
$61$	−5.96441	−	8.20931i	−0.763665	−	1.05109i	0.233236	−	0.972420i	$-0.425069\pi$
$62$	−5.10919	−	2.60326i	−0.648868	−	0.330615i
$63$	0.630329	−	0.321169i	0.0794140	−	0.0404635i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	7.60854	−	11.5368i	0.943723	−	1.43097i
$66$	1.78825	+	5.23786i	0.220118	+	0.644736i
$67$	9.05603	+	9.05603i	1.10637	+	1.10637i	0.993624	+	0.112746i	$0.0359646\pi$
$67$	9.05603	+	9.05603i	1.10637	+	1.10637i	0.112746	+	0.993624i	$0.464035\pi$
$68$	0.839551	+	5.30072i	0.101811	+	0.642807i
$69$	−8.81614	−	2.86454i	−1.06134	−	0.344850i
$70$	−3.63060	−	6.39227i	−0.433940	−	0.764023i
$71$	1.58734	−	1.15327i	0.188383	−	0.136868i	−0.489596	−	0.871949i	$-0.662856\pi$
$71$	1.58734	−	1.15327i	0.188383	−	0.136868i	0.677979	+	0.735081i	$0.262856\pi$
$72$	0.0336617	−	0.212532i	0.00396707	−	0.0250471i
$73$	−1.52454	+	2.99208i	−0.178434	+	0.350196i	−0.962849	−	0.270040i	$-0.912963\pi$
$73$	−1.52454	+	2.99208i	−0.178434	+	0.350196i	0.784415	+	0.620236i	$0.212963\pi$
$74$	1.01244	−	3.11597i	0.117694	−	0.362224i
$75$	7.06130	−	4.44506i	0.815368	−	0.513271i
$76$		−	0.691521i		−	0.0793229i
$77$	−7.82374	−	7.59490i	−0.891598	−	0.865519i
$78$	7.29292	−	7.29292i	0.825761	−	0.825761i
$79$	−3.40098	−	2.47096i	−0.382640	−	0.278004i	0.379793	−	0.925072i	$-0.375995\pi$
$79$	−3.40098	−	2.47096i	−0.382640	−	0.278004i	−0.762433	+	0.647067i	$0.775995\pi$
$80$	−2.22211	−	0.249441i	−0.248440	−	0.0278884i
$81$	2.56736	+	7.90152i	0.285262	+	0.877947i
$82$	1.29152	+	0.204556i	0.142624	+	0.0225895i
$83$	−5.96478	−	0.944728i	−0.654720	−	0.103697i	−0.179768	−	0.983709i	$-0.557535\pi$
$83$	−5.96478	−	0.944728i	−0.654720	−	0.103697i	−0.474952	+	0.880012i	$0.657535\pi$
$84$	−1.69537	−	5.21780i	−0.184980	−	0.569308i
$85$	9.37928	−	7.48608i	1.01733	−	0.811979i
$86$	−5.02037	−	3.64751i	−0.541360	−	0.393321i
$87$	2.63229	−	2.63229i	0.282211	−	0.282211i
$88$	−3.26773	+	0.567391i	−0.348341	+	0.0604841i
$89$		−	4.90528i		−	0.519959i	−0.965614	−	0.259979i	$-0.916284\pi$
$89$		−	4.90528i		−	0.519959i	0.965614	−	0.259979i	$-0.0837158\pi$
$90$	−0.450408	+	0.169254i	−0.0474772	+	0.0178409i
$91$	−6.27889	+	19.3244i	−0.658207	+	2.02575i
$92$	2.52186	−	4.94942i	0.262922	−	0.516013i
$93$	−1.49693	+	9.45125i	−0.155225	+	0.980049i
$94$	−1.42620	+	1.03619i	−0.147101	+	0.106875i
$95$	−1.34456	+	0.763663i	−0.137948	+	0.0783501i
$96$	−1.58710	−	0.515681i	−0.161983	−	0.0526314i
$97$	2.36159	+	14.9105i	0.239783	+	1.51393i	0.754346	+	0.656477i	$0.227954\pi$
$97$	2.36159	+	14.9105i	0.239783	+	1.51393i	−0.514563	+	0.857453i	$0.672046\pi$
$98$	2.69301	+	2.69301i	0.272035	+	0.272035i
$99$	−0.571086	+	0.428010i	−0.0573963	+	0.0430166i
$100$	1.96893	+	4.59601i	0.196893	+	0.459601i
$101$	−7.97621	+	10.9783i	−0.793663	+	1.09238i	0.199979	+	0.979800i	$0.435913\pi$
$101$	−7.97621	+	10.9783i	−0.793663	+	1.09238i	−0.993642	+	0.112583i	$0.964087\pi$
$102$	7.97984	−	4.06593i	0.790122	−	0.402587i
$103$	0.154442	+	0.0786923i	0.0152176	+	0.00775378i	0.461583	−	0.887097i	$-0.347282\pi$
$103$	0.154442	+	0.0786923i	0.0152176	+	0.00775378i	−0.446365	+	0.894851i	$0.647282\pi$
$104$	3.63276	+	5.00007i	0.356222	+	0.490297i
$105$	−8.27296	+	9.05850i	−0.807358	+	0.884019i
$106$	−2.97832	+	0.967716i	−0.289280	+	0.0939929i
$107$	2.38621	+	4.68320i	0.230684	+	0.452742i	0.977113	−	0.212723i	$-0.0682332\pi$
$107$	2.38621	+	4.68320i	0.230684	+	0.452742i	−0.746429	+	0.665465i	$0.768233\pi$
$108$	−5.29937	+	0.839337i	−0.509932	+	0.0807652i
$109$	6.31752			0.605109			0.302554	−	0.953132i	$-0.402161\pi$
$109$	6.31752			0.605109			0.302554	+	0.953132i	$0.402161\pi$
$110$	4.71183	+	5.72701i	0.449256	+	0.546049i
$111$	−5.46746			−0.518948
$112$	3.24715	−	0.514298i	0.306827	−	0.0485966i
$113$	−6.94709	−	13.6344i	−0.653527	−	1.28262i	−0.945322	−	0.326139i	$-0.894252\pi$
$113$	−6.94709	−	13.6344i	−0.653527	−	1.28262i	0.291794	−	0.956481i	$-0.405748\pi$
$114$	−1.09751	+	0.356604i	−0.102792	+	0.0333990i
$115$	−12.4083	+	0.562402i	−1.15708	+	0.0524442i
$116$	1.31120	+	1.80471i	0.121742	+	0.167563i
$117$	1.18496	+	0.603767i	0.109549	+	0.0558183i
$118$	0.768789	−	0.391717i	0.0707727	−	0.0360605i
$119$	−10.3709	+	14.2743i	−0.950698	+	1.30852i
$120$	0.750012	+	3.65535i	0.0684664	+	0.333686i
$121$	9.08715	+	6.19869i	0.826105	+	0.563517i
$122$	−7.17520	−	7.17520i	−0.649612	−	0.649612i
$123$	−0.341359	−	2.15526i	−0.0307793	−	0.194333i
$124$	−5.45353	−	1.77196i	−0.489741	−	0.159127i
$125$	6.76189	−	8.90375i	0.604802	−	0.796376i
$126$	0.572327	−	0.415820i	0.0509869	−	0.0370442i
$127$	2.04599	−	12.9179i	0.181552	−	1.14628i	−0.713613	−	0.700540i	$-0.752942\pi$
$127$	2.04599	−	12.9179i	0.181552	−	1.14628i	0.895165	−	0.445735i	$-0.147058\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$	−3.20006	+	9.84878i	−0.281750	+	0.867137i
$130$	5.71011	−	12.5850i	0.500810	−	1.10378i
$131$			3.15120i			0.275322i	0.990479	+	0.137661i	$0.0439584\pi$
$131$			3.15120i			0.275322i	−0.990479	+	0.137661i	$0.956042\pi$
$132$	2.58561	+	4.89363i	0.225049	+	0.425936i
$133$	1.60758	−	1.60758i	0.139395	−	0.139395i
$134$	10.3612	+	7.52786i	0.895072	+	0.650308i
$135$	7.48417	+	9.37689i	0.644135	+	0.807034i
$136$	1.65843	+	5.10412i	0.142209	+	0.437675i
$137$	−11.7822	−	1.86611i	−1.00662	−	0.159432i	−0.368709	−	0.929545i	$-0.620200\pi$
$137$	−11.7822	−	1.86611i	−1.00662	−	0.159432i	−0.637908	+	0.770112i	$0.720200\pi$
$138$	−9.15571	−	1.45012i	−0.779386	−	0.123443i
$139$	−2.70056	−	8.31147i	−0.229059	−	0.704970i	−0.997854	−	0.0654751i	$-0.979144\pi$
$139$	−2.70056	−	8.31147i	−0.229059	−	0.704970i	0.768796	−	0.639494i	$-0.220856\pi$
$140$	−4.58587	−	5.74562i	−0.387577	−	0.485594i
$141$	2.38001	+	1.72918i	0.200433	+	0.145623i
$142$	1.38739	−	1.38739i	0.116427	−	0.116427i
$143$	2.90581	−	20.2911i	0.242996	−	1.69683i
$144$		−	0.215181i		−	0.0179318i
$145$	2.06099	−	4.54240i	0.171156	−	0.377226i
$146$	−1.03771	+	3.19373i	−0.0858812	+	0.264315i
$147$	2.88534	−	5.66281i	0.237979	−	0.467060i
$148$	0.512530	−	3.23599i	0.0421297	−	0.265997i
$149$	5.78912	−	4.20604i	0.474263	−	0.344572i	−0.324837	−	0.945770i	$-0.605310\pi$
$149$	5.78912	−	4.20604i	0.474263	−	0.344572i	0.799100	+	0.601198i	$0.205310\pi$
$150$	6.27900	−	5.49496i	0.512678	−	0.448662i
$151$	−9.35240	−	3.03878i	−0.761087	−	0.247292i	−0.0973420	−	0.995251i	$-0.531034\pi$
$151$	−9.35240	−	3.03878i	−0.761087	−	0.247292i	−0.663745	+	0.747959i	$0.731034\pi$
$152$	−0.108178	−	0.683008i	−0.00877438	−	0.0553992i
$153$	0.816590	+	0.816590i	0.0660174	+	0.0660174i
$154$	−8.91552	−	6.27749i	−0.718433	−	0.505854i
$155$	2.57715	+	12.5603i	0.207002	+	1.00887i
$156$	6.06227	−	8.34400i	0.485370	−	0.668055i
$157$	8.82771	−	4.49794i	0.704528	−	0.358975i	−0.0647390	−	0.997902i	$-0.520621\pi$
$157$	8.82771	−	4.49794i	0.704528	−	0.358975i	0.769267	+	0.638927i	$0.220621\pi$
$158$	−3.74565	−	1.90850i	−0.297988	−	0.151832i
$159$	3.07173	+	4.22787i	0.243604	+	0.335292i
$160$	−2.23377	+	0.101245i	−0.176595	+	0.00800411i
$161$	17.3685	−	5.64337i	1.36883	−	0.444760i
$162$	3.77182	+	7.40262i	0.296342	+	0.581605i
$163$	−4.04749	+	0.641060i	−0.317024	+	0.0502117i	−0.312919	−	0.949780i	$-0.601307\pi$
$163$	−4.04749	+	0.641060i	−0.317024	+	0.0502117i	−0.00410528	+	0.999992i	$0.501307\pi$
$164$	1.30762			0.102108
$165$	6.65955	−	10.4315i	0.518445	−	0.812088i
$166$	−6.03913			−0.468728
$167$	6.15330	−	0.974586i	0.476156	−	0.0754158i	0.0862564	−	0.996273i	$-0.472510\pi$
$167$	6.15330	−	0.974586i	0.476156	−	0.0754158i	0.389900	+	0.920857i	$0.372510\pi$
$168$	−2.49074	−	4.88834i	−0.192164	−	0.377144i
$169$	−23.9644	+	7.78650i	−1.84341	+	0.598961i
$170$	8.09273	−	8.86116i	0.620684	−	0.679620i
$171$	−0.0874638	−	0.120384i	−0.00668853	−	0.00920597i
$172$	−5.52915	−	2.81724i	−0.421594	−	0.214813i
$173$	18.9975	−	9.67972i	1.44436	−	0.735936i	0.456270	−	0.889842i	$-0.349185\pi$
$173$	18.9975	−	9.67972i	1.44436	−	0.735936i	0.988085	+	0.153906i	$0.0491853\pi$
$174$	2.18810	−	3.01166i	0.165879	−	0.228313i
$175$	−6.10719	+	15.2615i	−0.461660	+	1.15366i
$176$	−3.13874	+	1.07159i	−0.236591	+	0.0807742i
$177$	−1.01815	−	1.01815i	−0.0765285	−	0.0765285i
$178$	−0.767355	−	4.84489i	−0.0575157	−	0.363140i
$179$	24.3710	+	7.91861i	1.82157	+	0.591864i	0.999756	+	0.0221110i	$0.00703873\pi$
$179$	24.3710	+	7.91861i	1.82157	+	0.591864i	0.821816	+	0.569753i	$0.192961\pi$
$180$	−0.418386	+	0.237629i	−0.0311847	+	0.0177118i
$181$	16.4629	−	11.9610i	1.22368	−	0.889056i	0.227281	−	0.973829i	$-0.427016\pi$
$181$	16.4629	−	11.9610i	1.22368	−	0.889056i	0.996400	+	0.0847729i	$0.0270165\pi$
$182$	−3.17858	+	20.0688i	−0.235612	+	1.48760i
$183$	−7.68766	+	15.0879i	−0.568288	+	1.11533i
$184$	1.71655	−	5.28299i	0.126546	−	0.389467i
$185$	−6.85787	+	2.57704i	−0.504201	+	0.189468i
$186$			9.56906i			0.701638i
$187$	7.84461	−	15.9778i	0.573655	−	1.16841i
$188$	−1.24654	+	1.24654i	−0.0909134	+	0.0909134i
$189$	−14.2707	−	10.3682i	−1.03804	−	0.754178i
$190$	−1.20854	+	0.964595i	−0.0876766	+	0.0699791i
$191$	−0.225845	−	0.695079i	−0.0163416	−	0.0502942i	0.942553	−	0.334056i	$-0.108417\pi$
$191$	−0.225845	−	0.695079i	−0.0163416	−	0.0502942i	−0.958895	+	0.283762i	$0.908417\pi$
$192$	−1.64823	−	0.261054i	−0.118951	−	0.0188400i
$193$	16.2563	+	2.57474i	1.17015	+	0.185334i	0.711111	−	0.703080i	$-0.248192\pi$
$193$	16.2563	+	2.57474i	1.17015	+	0.185334i	0.459043	+	0.888414i	$0.348192\pi$
$194$	4.66503	+	14.3575i	0.334929	+	1.03081i
$195$	−22.9183	−	2.57267i	−1.64121	−	0.184233i
$196$	3.08113	+	2.23857i	0.220081	+	0.159898i
$197$	−8.59023	+	8.59023i	−0.612028	+	0.612028i	−0.943474	−	0.331446i	$-0.892464\pi$
$197$	−8.59023	+	8.59023i	−0.612028	+	0.612028i	0.331446	+	0.943474i	$0.392464\pi$
$198$	−0.497100	+	0.512078i	−0.0353273	+	0.0363918i
$199$		−	13.9785i		−	0.990907i	−0.868634	−	0.495453i	$-0.835002\pi$
$199$		−	13.9785i		−	0.990907i	0.868634	−	0.495453i	$-0.164998\pi$
$200$	2.66366	+	4.23142i	0.188349	+	0.299206i
$201$	6.60440	−	20.3263i	0.465839	−	1.43370i
$202$	−6.16063	+	12.0909i	−0.433460	+	0.850714i
$203$	−1.14727	+	7.24356i	−0.0805224	+	0.508398i
$204$	7.24554	−	5.26420i	0.507289	−	0.368567i
$205$	−1.44403	−	2.54246i	−0.100855	−	0.177573i
$206$	0.164851	+	0.0535633i	0.0114857	+	0.00373193i
$207$	−0.186986	−	1.18059i	−0.0129965	−	0.0820564i
$208$	4.37022	+	4.37022i	0.303020	+	0.303020i
$209$	−1.32041	+	1.87530i	−0.0913347	+	0.129717i
$210$	−6.75405	+	10.2412i	−0.466073	+	0.706707i
$211$	3.00713	−	4.13896i	0.207019	−	0.284938i	−0.692864	−	0.721068i	$-0.743651\pi$
$211$	3.00713	−	4.13896i	0.207019	−	0.284938i	0.899883	+	0.436131i	$0.143651\pi$
$212$	−2.79027	+	1.42171i	−0.191637	+	0.0976437i
$213$	−2.91737	−	1.48648i	−0.199895	−	0.101852i
$214$	3.08945	+	4.25226i	0.211190	+	0.290678i
$215$	0.628276	+	13.8617i	0.0428481	+	0.945361i
$216$	−5.10282	+	1.65801i	−0.347203	+	0.112813i
$217$	−8.55855	−	16.7971i	−0.580992	−	1.14026i
$218$	6.23974	−	0.988278i	0.422609	−	0.0669346i
$219$	5.60390			0.378677
$220$	5.54972	+	4.91941i	0.374162	+	0.331666i
$221$	−33.1691			−2.23119
$222$	−5.40015	+	0.855299i	−0.362434	+	0.0574039i
$223$	−5.31616	−	10.4336i	−0.355996	−	0.698682i	0.641668	−	0.766982i	$-0.278243\pi$
$223$	−5.31616	−	10.4336i	−0.355996	−	0.698682i	−0.997665	+	0.0682998i	$0.978243\pi$
$224$	3.12672	−	1.01593i	0.208913	−	0.0678798i
$225$	0.924066	+	0.551067i	0.0616044	+	0.0367378i
$226$	−8.99446	−	12.3798i	−0.598302	−	0.823493i
$227$	−6.88595	−	3.50856i	−0.457036	−	0.232872i	0.210287	−	0.977640i	$-0.432560\pi$
$227$	−6.88595	−	3.50856i	−0.457036	−	0.232872i	−0.667323	+	0.744768i	$0.732560\pi$
$228$	−1.02822	+	0.523903i	−0.0680954	+	0.0346963i
$229$	11.1724	−	15.3775i	0.738292	−	1.01617i	−0.260423	−	0.965495i	$-0.583862\pi$
$229$	11.1724	−	15.3775i	0.738292	−	1.01617i	0.998715	−	0.0506768i	$-0.0161378\pi$
$230$	−12.1676	+	2.49657i	−0.802306	+	0.164619i
$231$	−5.36545	+	17.3870i	−0.353021	+	1.14398i
$232$	1.57737	+	1.57737i	0.103560	+	0.103560i
$233$	3.30566	+	20.8711i	0.216561	+	1.36731i	0.821122	+	0.570753i	$0.193349\pi$
$233$	3.30566	+	20.8711i	0.216561	+	1.36731i	−0.604561	+	0.796559i	$0.706651\pi$
$234$	1.26482	+	0.410965i	0.0826839	+	0.0268656i
$235$	3.80029	+	1.04712i	0.247904	+	0.0683067i
$236$	0.698046	−	0.507160i	0.0454389	−	0.0330133i
$237$	−1.09743	+	6.92891i	−0.0712858	+	0.450081i
$238$	−8.01021	+	15.7209i	−0.519225	+	1.01904i
$239$	−6.55831	+	20.1844i	−0.424222	+	1.30562i	0.479515	+	0.877534i	$0.340813\pi$
$239$	−6.55831	+	20.1844i	−0.424222	+	1.30562i	−0.903737	+	0.428088i	$0.859187\pi$
$240$	1.31260	+	3.49302i	0.0847280	+	0.225473i
$241$			12.6447i			0.814517i	0.913313	+	0.407259i	$0.133515\pi$
$241$			12.6447i			0.814517i	−0.913313	+	0.407259i	$0.866485\pi$
$242$	9.94496	+	4.70083i	0.639286	+	0.302181i
$243$	−1.57813	+	1.57813i	−0.101237	+	0.101237i
$244$	−8.20931	−	5.96441i	−0.525547	−	0.381832i
$245$	0.949992	−	8.46288i	0.0606928	−	0.540674i
$246$	−0.674313	−	2.07532i	−0.0429926	−	0.132318i
$247$	4.22128	+	0.668585i	0.268593	+	0.0425410i
$248$	−5.66358	−	0.897023i	−0.359638	−	0.0569610i
$249$	3.11426	+	9.58472i	0.197358	+	0.607407i
$250$	5.28579	−	9.85192i	0.334303	−	0.623090i
$251$	20.8486	+	15.1474i	1.31595	+	0.956094i	0.999973	+	0.00732735i	$0.00233239\pi$
$251$	20.8486	+	15.1474i	1.31595	+	0.956094i	0.315977	+	0.948767i	$0.397668\pi$
$252$	0.500232	−	0.500232i	0.0315117	−	0.0315117i
$253$	−16.2894	+	8.60674i	−1.02411	+	0.541101i
$254$		−	13.0789i		−	0.820643i
$255$	−18.2368	−	8.27446i	−1.14203	−	0.518167i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.88116	−	3.69199i	0.117344	−	0.230300i	−0.824863	−	0.565333i	$-0.808748\pi$
$257$	1.88116	−	3.69199i	0.117344	−	0.230300i	0.942206	+	0.335033i	$0.108748\pi$
$258$	−1.61998	+	10.2281i	−0.100855	+	0.636775i
$259$	8.71419	−	6.33123i	0.541474	−	0.393404i
$260$	3.67108	−	13.3233i	0.227671	−	0.826278i
$261$	0.456520	+	0.148332i	0.0282579	+	0.00918155i
$262$	0.492957	+	3.11241i	0.0304550	+	0.192285i
$263$	9.62879	+	9.62879i	0.593736	+	0.593736i	0.938639	−	0.344902i	$-0.112088\pi$
$263$	9.62879	+	9.62879i	0.593736	+	0.593736i	−0.344902	+	0.938639i	$0.612088\pi$
$264$	3.31931	+	4.42890i	0.204290	+	0.272580i
$265$	5.84566	+	3.85522i	0.359096	+	0.236824i
$266$	1.33631	−	1.83927i	0.0819343	−	0.112773i
$267$	−7.29362	+	3.71629i	−0.446363	+	0.227433i
$268$	11.4113	+	5.81433i	0.697054	+	0.355167i
$269$	−9.43066	−	12.9802i	−0.574997	−	0.791416i	0.418138	−	0.908383i	$-0.362683\pi$
$269$	−9.43066	−	12.9802i	−0.574997	−	0.791416i	−0.993136	+	0.116967i	$0.962683\pi$
$270$	8.85889	+	8.09066i	0.539135	+	0.492382i
$271$	11.0157	−	3.57921i	0.669155	−	0.217422i	0.0453136	−	0.998973i	$-0.485571\pi$
$271$	11.0157	−	3.57921i	0.669155	−	0.217422i	0.623841	+	0.781551i	$0.285571\pi$
$272$	2.43647	+	4.78185i	0.147733	+	0.289942i
$273$	33.4903	−	5.30434i	2.02693	−	0.321033i
$274$	−11.9290			−0.720658
$275$	3.43634	−	16.2232i	0.207219	−	0.978295i
$276$	−9.26983			−0.557978
$277$	−8.27557	+	1.31072i	−0.497231	+	0.0787537i	−0.400013	−	0.916509i	$-0.630994\pi$
$277$	−8.27557	+	1.31072i	−0.497231	+	0.0787537i	−0.0972180	+	0.995263i	$0.530994\pi$
$278$	−3.96751	−	7.78668i	−0.237956	−	0.467014i
$279$	−1.17350	+	0.381292i	−0.0702554	+	0.0228273i
$280$	−5.42823	−	4.95750i	−0.324399	−	0.296267i
$281$	−15.2667	−	21.0128i	−0.910736	−	1.25352i	−0.966915	−	0.255100i	$-0.917892\pi$
$281$	−15.2667	−	21.0128i	−0.910736	−	1.25352i	0.0561786	−	0.998421i	$-0.482108\pi$
$282$	2.62121	+	1.33557i	0.156091	+	0.0795321i
$283$	−11.5828	+	5.90173i	−0.688526	+	0.350822i	−0.762997	−	0.646402i	$-0.776273\pi$
$283$	−11.5828	+	5.90173i	−0.688526	+	0.350822i	0.0744712	+	0.997223i	$0.476273\pi$
$284$	1.15327	−	1.58734i	0.0684341	−	0.0941914i
$285$	2.15413	+	1.42065i	0.127600	+	0.0841521i
$286$	−0.304199	−	20.4959i	−0.0179877	−	1.21195i
$287$	3.03982	+	3.03982i	0.179435	+	0.179435i
$288$	−0.0336617	−	0.212532i	−0.00198354	−	0.0125236i
$289$	−11.2248	−	3.64716i	−0.660283	−	0.214539i
$290$	1.32503	−	4.80889i	0.0778083	−	0.282388i
$291$	20.3811	−	14.8077i	1.19476	−	0.868045i
$292$	−0.525321	+	3.31675i	−0.0307421	+	0.194098i
$293$	−7.04473	+	13.8261i	−0.411557	+	0.807727i	−1.00000		0.000812545i	$-0.999741\pi$
$293$	−7.04473	+	13.8261i	−0.411557	+	0.807727i	0.588442	+	0.808539i	$0.299741\pi$
$294$	1.96396	−	6.04445i	0.114541	−	0.352520i
$295$	−1.75696	−	0.797173i	−0.102294	−	0.0464132i
$296$		−	3.27633i		−	0.190433i
$297$	15.9737	+	7.84261i	0.926888	+	0.455075i
$298$	5.05988	−	5.05988i	0.293111	−	0.293111i
$299$	27.7747	+	20.1795i	1.60625	+	1.16701i
$300$	5.34209	−	6.40956i	0.308426	−	0.370056i
$301$	−6.30438	−	19.4029i	−0.363379	−	1.11836i
$302$	−9.71262	−	1.53833i	−0.558899	−	0.0885208i
$303$	22.3664	+	3.54249i	1.28492	+	0.203511i
$304$	−0.213692	−	0.657676i	−0.0122561	−	0.0377203i
$305$	−2.53114	+	22.5484i	−0.144933	+	1.29111i
$306$	0.934279	+	0.678794i	0.0534092	+	0.0388040i
$307$	−16.0844	+	16.0844i	−0.917983	+	0.917983i	−0.996883	−	0.0788993i	$-0.974859\pi$
$307$	−16.0844	+	16.0844i	−0.917983	+	0.917983i	0.0788993	+	0.996883i	$0.474859\pi$
$308$	−9.78777	−	4.80551i	−0.557710	−	0.273819i
$309$		−	0.289257i		−	0.0164552i
$310$	4.51030	+	12.0025i	0.256168	+	0.681699i
$311$	−1.79145	+	5.51353i	−0.101584	+	0.312643i	−0.988914	−	0.148492i	$-0.952558\pi$
$311$	−1.79145	+	5.51353i	−0.101584	+	0.312643i	0.887330	+	0.461136i	$0.152558\pi$
$312$	4.68235	−	9.18962i	0.265086	−	0.520260i
$313$	0.803412	−	5.07254i	0.0454115	−	0.286717i	−0.954523	−	0.298136i	$-0.903635\pi$
$313$	0.803412	−	5.07254i	0.0454115	−	0.286717i	0.999935	+	0.0114194i	$0.00363499\pi$
$314$	8.01540	−	5.82353i	0.452335	−	0.328641i
$315$	−1.52504	−	0.420206i	−0.0859263	−	0.0236759i
$316$	−3.99809	−	1.29906i	−0.224910	−	0.0730777i
$317$	−0.285296	−	1.80129i	−0.0160238	−	0.101171i	0.978380	−	0.206814i	$-0.0663096\pi$
$317$	−0.285296	−	1.80129i	−0.0160238	−	0.101171i	−0.994404	+	0.105644i	$0.966310\pi$
$318$	3.69529	+	3.69529i	0.207222	+	0.207222i
$319$	−0.109797	−	7.39773i	−0.00614744	−	0.414193i
$320$	−2.19044	+	0.449438i	−0.122449	+	0.0251243i
$321$	5.15560	−	7.09607i	0.287757	−	0.396064i
$322$	16.2718	−	8.29092i	0.906795	−	0.462035i
$323$	3.30675	+	1.68487i	0.183992	+	0.0937489i
$324$	4.88341	+	6.72144i	0.271301	+	0.373413i
$325$	−29.9592	+	7.57543i	−1.66184	+	0.420209i
$326$	−3.89738	+	1.26633i	−0.215856	+	0.0701358i
$327$	−4.78621	−	9.39347i	−0.264678	−	0.519460i
$328$	1.29152	−	0.204556i	0.0713121	−	0.0112947i
$329$	−5.79568			−0.319526
$330$	4.94572	−	11.3448i	0.272253	−	0.624512i
$331$	−20.3356			−1.11775			−0.558873	−	0.829254i	$-0.688766\pi$
$331$	−20.3356			−1.11775			−0.558873	+	0.829254i	$0.688766\pi$
$332$	−5.96478	+	0.944728i	−0.327360	+	0.0518487i
$333$	−0.320065	−	0.628163i	−0.0175394	−	0.0344231i
$334$	5.92508	−	1.92518i	0.324206	−	0.105341i
$335$	−1.29666	−	28.6083i	−0.0708440	−	1.56304i
$336$	−3.22478	−	4.43852i	−0.175926	−	0.242141i
$337$	−22.5356	−	11.4824i	−1.22759	−	0.625488i	−0.284708	−	0.958614i	$-0.591897\pi$
$337$	−22.5356	−	11.4824i	−1.22759	−	0.625488i	−0.942882	+	0.333126i	$0.891897\pi$
$338$	−22.4513	+	11.4395i	−1.22119	+	0.622226i
$339$	−15.0097	+	20.6591i	−0.815218	+	1.12205i
$340$	6.60690	−	10.0180i	0.358310	−	0.543305i
$341$	11.4057	+	15.2184i	0.617651	+	0.824122i
$342$	−0.105219	−	0.105219i	−0.00568960	−	0.00568960i
$343$	−1.64139	−	10.3633i	−0.0886267	−	0.559567i
$344$	−5.90179	−	1.91761i	−0.318203	−	0.103391i
$345$	10.2369	+	18.0237i	0.551135	+	0.970366i
$346$	17.2494	−	12.5324i	0.927333	−	0.673747i
$347$	−0.0587704	+	0.371062i	−0.00315496	+	0.0199196i	−0.989216	−	0.146467i	$-0.953210\pi$
$347$	−0.0587704	+	0.371062i	−0.00315496	+	0.0199196i	0.986061	+	0.166386i	$0.0532099\pi$
$348$	1.69003	−	3.31688i	0.0905952	−	0.177803i
$349$	4.40564	−	13.5592i	0.235828	−	0.725805i	−0.761182	−	0.648538i	$-0.775381\pi$
$349$	4.40564	−	13.5592i	0.235828	−	0.725805i	0.997010	−	0.0772669i	$-0.0246194\pi$
$350$	−3.64457	+	16.0290i	−0.194810	+	0.856787i
$351$		−	33.1606i		−	1.76998i
$352$	−2.93246	+	1.54941i	−0.156301	+	0.0825836i
$353$	8.09648	−	8.09648i	0.430932	−	0.430932i	−0.458013	−	0.888945i	$-0.651439\pi$
$353$	8.09648	−	8.09648i	0.430932	−	0.430932i	0.888945	+	0.458013i	$0.151439\pi$
$354$	−1.16488	−	0.846337i	−0.0619128	−	0.0449823i
$355$	−4.35992	−	0.489419i	−0.231401	−	0.0259757i
$356$	−1.51582	−	4.66520i	−0.0803381	−	0.247255i
$357$	29.0814	+	4.60604i	1.53915	+	0.243778i
$358$	25.3097	+	4.00866i	1.33766	+	0.211864i
$359$	0.556243	+	1.71194i	0.0293574	+	0.0903528i	0.964662	−	0.263492i	$-0.0848742\pi$
$359$	0.556243	+	1.71194i	0.0293574	+	0.0903528i	−0.935304	+	0.353845i	$0.884874\pi$
$360$	−0.376062	+	0.300154i	−0.0198202	+	0.0158195i
$361$	14.9844	+	10.8868i	0.788655	+	0.572992i
$362$	14.3891	−	14.3891i	0.756277	−	0.756277i
$363$	2.33227	−	18.2078i	0.122412	−	0.955661i
$364$			20.3189i			1.06500i
$365$	7.02902	−	2.64135i	0.367916	−	0.138255i
$366$	−5.23275	+	16.1047i	−0.273520	+	0.841808i
$367$	−1.92399	+	3.77605i	−0.100432	+	0.197108i	−0.935755	−	0.352651i	$-0.885280\pi$
$367$	−1.92399	+	3.77605i	−0.100432	+	0.197108i	0.835323	+	0.549759i	$0.185280\pi$
$368$	0.868972	−	5.48648i	0.0452983	−	0.286002i
$369$	0.227637	−	0.165388i	0.0118503	−	0.00860974i
$370$	−6.37030	+	3.61812i	−0.331176	+	0.188097i
$371$	−9.79161	−	3.18149i	−0.508355	−	0.165175i
$372$	1.49693	+	9.45125i	0.0776123	+	0.490025i
$373$	−0.763112	−	0.763112i	−0.0395124	−	0.0395124i	0.687075	−	0.726587i	$-0.258895\pi$
$373$	−0.763112	−	0.763112i	−0.0395124	−	0.0395124i	−0.726587	+	0.687075i	$0.758895\pi$
$374$	5.24856	−	17.0082i	0.271397	−	0.879474i
$375$	−18.3618	−	3.30864i	−0.948199	−	0.170857i
$376$	−1.03619	+	1.42620i	−0.0534376	+	0.0735505i
$377$	−12.2843	+	6.25914i	−0.632671	+	0.322362i
$378$	−15.7169	−	8.00817i	−0.808391	−	0.411896i
$379$	9.39910	+	12.9368i	0.482799	+	0.664516i	0.979040	−	0.203669i	$-0.0652866\pi$
$379$	9.39910	+	12.9368i	0.482799	+	0.664516i	−0.496240	+	0.868185i	$0.665287\pi$
$380$	−1.04276	+	1.14178i	−0.0534926	+	0.0585719i
$381$	−20.7575	+	6.74453i	−1.06344	+	0.345533i
$382$	−0.331799	−	0.651192i	−0.0169763	−	0.0333179i
$383$	−29.8986	+	4.73547i	−1.52775	+	0.241971i	−0.863041	−	0.505133i	$-0.831443\pi$
$383$	−29.8986	+	4.73547i	−1.52775	+	0.241971i	−0.664706	+	0.747105i	$0.731443\pi$
$384$	−1.66878			−0.0851595
$385$	1.46530	+	24.3376i	0.0746784	+	1.24036i
$386$	16.4589			0.837738
$387$	−1.31887	+	0.208888i	−0.0670419	+	0.0106184i
$388$	6.85359	+	13.4509i	0.347939	+	0.682868i
$389$	31.4274	−	10.2114i	1.59343	−	0.517737i	0.627960	−	0.778246i	$-0.283890\pi$
$389$	31.4274	−	10.2114i	1.59343	−	0.517737i	0.965472	+	0.260508i	$0.0838902\pi$
$390$	−23.0386	+	1.04421i	−1.16660	+	0.0528759i
$391$	17.5229	+	24.1183i	0.886173	+	1.21971i
$392$	3.39339	+	1.72902i	0.171392	+	0.0873285i
$393$	4.68550	−	2.38738i	0.236352	−	0.120427i
$394$	−7.14066	+	9.82828i	−0.359741	+	0.495141i
$395$	1.88936	+	9.20824i	0.0950642	+	0.463317i
$396$	−0.410873	+	0.583537i	−0.0206471	+	0.0293238i
$397$	24.0891	+	24.0891i	1.20900	+	1.20900i	0.971352	+	0.237647i	$0.0763760\pi$
$397$	24.0891	+	24.0891i	1.20900	+	1.20900i	0.237647	+	0.971352i	$0.423624\pi$
$398$	−2.18671	−	13.8064i	−0.109610	−	0.692051i
$399$	−3.60822	−	1.17238i	−0.180637	−	0.0586925i
$400$	3.29281	+	3.76263i	0.164640	+	0.188132i
$401$	−18.1981	+	13.2217i	−0.908772	+	0.660262i	−0.940704	−	0.339228i	$-0.889834\pi$
$401$	−18.1981	+	13.2217i	−0.908772	+	0.660262i	0.0319319	+	0.999490i	$0.489834\pi$
$402$	3.34336	−	21.1092i	0.166752	−	1.05283i
$403$	16.0893	−	31.5769i	0.801463	−	1.57296i
$404$	−4.19334	+	12.9058i	−0.208627	+	0.642087i
$405$	7.67593	−	16.9177i	0.381420	−	0.840645i
$406$			7.33385i			0.363973i
$407$	−7.56879	+	7.79685i	−0.375171	+	0.386475i
$408$	6.33284	−	6.33284i	0.313522	−	0.313522i
$409$	20.4850	+	14.8832i	1.01292	+	0.735928i	0.964819	−	0.262915i	$-0.0846838\pi$
$409$	20.4850	+	14.8832i	1.01292	+	0.735928i	0.0480988	+	0.998843i	$0.484684\pi$
$410$	−1.82398	−	2.28526i	−0.0900799	−	0.112861i
$411$	6.15156	+	18.9326i	0.303434	+	0.933875i
$412$	0.171201	+	0.0271155i	0.00843445	+	0.00133588i
$413$	2.80174	+	0.443753i	0.137865	+	0.0218356i
$414$	−0.369369	−	1.13680i	−0.0181535	−	0.0558707i
$415$	8.42392	+	10.5543i	0.413514	+	0.518090i
$416$	5.00007	+	3.63276i	0.245149	+	0.178111i
$417$	−10.3123	+	10.3123i	−0.504995	+	0.504995i
$418$	−1.01079	+	2.05877i	−0.0494395	+	0.100698i
$419$		−	31.5445i		−	1.54105i	−0.637409	−	0.770526i	$-0.719994\pi$
$419$		−	31.5445i		−	1.54105i	0.637409	−	0.770526i	$-0.280006\pi$
$420$	−5.06882	+	11.1716i	−0.247333	+	0.545120i
$421$	−3.43588	+	10.5745i	−0.167454	+	0.515372i	−0.999209	−	0.0397722i	$-0.987337\pi$
$421$	−3.43588	+	10.5745i	−0.167454	+	0.515372i	0.831754	+	0.555144i	$0.187337\pi$
$422$	2.32263	−	4.55842i	0.113064	−	0.221900i
$423$	−0.0593415	+	0.374667i	−0.00288528	+	0.0182170i
$424$	−2.53351	+	1.84071i	−0.123038	+	0.0893925i
$425$	−26.7747	−	1.78294i	−1.29876	−	0.0864854i
$426$	−3.11399	−	1.01180i	−0.150873	−	0.0490218i
$427$	−5.21872	−	32.9497i	−0.252551	−	1.59455i
$428$	3.71661	+	3.71661i	0.179649	+	0.179649i
$429$	−32.3722	+	11.0521i	−1.56294	+	0.533602i
$430$	2.78899	+	13.5928i	0.134497	+	0.655502i
$431$	12.2800	−	16.9020i	0.591508	−	0.814141i	−0.403389	−	0.915028i	$-0.632168\pi$
$431$	12.2800	−	16.9020i	0.591508	−	0.814141i	0.994898	+	0.100887i	$0.0321680\pi$
$432$	−4.78063	+	2.43585i	−0.230008	+	0.117195i
$433$	−31.5249	−	16.0627i	−1.51499	−	0.771925i	−0.518454	−	0.855106i	$-0.673492\pi$
$433$	−31.5249	−	16.0627i	−1.51499	−	0.771925i	−0.996534	+	0.0831808i	$0.973492\pi$
$434$	−11.0808	−	15.2514i	−0.531897	−	0.732093i
$435$	−8.31549	+	0.376896i	−0.398697	+	0.0180708i
$436$	6.00832	−	1.95222i	0.287746	−	0.0934945i
$437$	−1.74392	−	3.42263i	−0.0834229	−	0.163727i
$438$	5.53491	−	0.876644i	0.264468	−	0.0418877i
$439$	9.73788			0.464764			0.232382	−	0.972625i	$-0.425348\pi$
$439$	9.73788			0.464764			0.232382	+	0.972625i	$0.425348\pi$
$440$	6.25096	+	3.99067i	0.298003	+	0.190248i
$441$	0.819514			0.0390245
$442$	−32.7607	+	5.18878i	−1.55827	+	0.246805i
$443$	3.39795	+	6.66885i	0.161442	+	0.316847i	0.957530	−	0.288333i	$-0.0931011\pi$
$443$	3.39795	+	6.66885i	0.161442	+	0.316847i	−0.796089	+	0.605180i	$0.793101\pi$
$444$	−5.19986	+	1.68954i	−0.246775	+	0.0801819i
$445$	−7.39680	+	8.09915i	−0.350642	+	0.383937i
$446$	−6.88288	−	9.47347i	−0.325914	−	0.448582i
$447$	−10.6398	−	5.42126i	−0.503246	−	0.256417i
$448$	2.92930	−	1.49255i	0.138396	−	0.0705164i
$449$	3.57047	−	4.91433i	0.168501	−	0.231921i	−0.716413	−	0.697677i	$-0.754217\pi$
$449$	3.57047	−	4.91433i	0.168501	−	0.231921i	0.884914	+	0.465755i	$0.154217\pi$
$450$	0.998895	+	0.399727i	0.0470884	+	0.0188433i
$451$	−3.54605	−	2.49680i	−0.166977	−	0.117570i
$452$	−10.8203	−	10.8203i	−0.508946	−	0.508946i
$453$	2.56713	+	16.2082i	0.120614	+	0.761528i
$454$	−7.35003	−	2.38817i	−0.344954	−	0.112082i
$455$	39.5070	−	22.4386i	1.85212	−	1.05194i
$456$	−0.933602	+	0.678302i	−0.0437199	+	0.0317644i
$457$	1.78273	−	11.2557i	0.0833926	−	0.526520i	−0.910261	−	0.414035i	$-0.864119\pi$
$457$	1.78273	−	11.2557i	0.0833926	−	0.526520i	0.993653	−	0.112485i	$-0.0358810\pi$
$458$	8.62926	−	16.9359i	0.403219	−	0.791362i
$459$	8.89818	−	27.3858i	0.415331	−	1.27826i
$460$	−11.6272	+	4.36926i	−0.542122	+	0.203718i
$461$			16.0054i			0.745447i	0.927943	+	0.372723i	$0.121576\pi$
$461$			16.0054i			0.745447i	−0.927943	+	0.372723i	$0.878424\pi$
$462$	−2.57947	+	18.0123i	−0.120008	+	0.838008i
$463$	−25.6272	+	25.6272i	−1.19100	+	1.19100i	−0.214208	+	0.976788i	$0.568717\pi$
$463$	−25.6272	+	25.6272i	−1.19100	+	1.19100i	−0.976788	+	0.214208i	$0.931283\pi$
$464$	1.80471	+	1.31120i	0.0837816	+	0.0608709i
$465$	16.7234	−	13.3478i	0.775529	−	0.618988i
$466$	6.52992	+	20.0970i	0.302493	+	0.930977i
$467$	−1.53364	−	0.242904i	−0.0709682	−	0.0112403i	0.120849	−	0.992671i	$-0.461438\pi$
$467$	−1.53364	−	0.242904i	−0.0709682	−	0.0112403i	−0.191818	+	0.981431i	$0.561438\pi$
$468$	1.31354	+	0.208044i	0.0607183	+	0.00961683i
$469$	13.0112	+	40.0444i	0.600802	+	1.84908i
$470$	3.91731	+	0.439734i	0.180692	+	0.0202834i
$471$	−13.3759	−	9.71817i	−0.616330	−	0.447790i
$472$	0.610114	−	0.610114i	0.0280828	−	0.0280828i
$473$	9.61486	+	18.1974i	0.442092	+	0.836719i
$474$			7.01528i			0.322222i
$475$	3.37155	+	0.766601i	0.154697	+	0.0351741i
$476$	−5.45230	+	16.7804i	−0.249906	+	0.769131i
$477$	−0.305926	+	0.600414i	−0.0140074	+	0.0274911i
$478$	−3.32003	+	20.9619i	−0.151855	+	0.958773i
$479$	−28.0212	+	20.3586i	−1.28032	+	0.930209i	−0.999563	−	0.0295692i	$-0.990586\pi$
$479$	−28.0212	+	20.3586i	−1.28032	+	0.930209i	−0.280760	+	0.959778i	$0.590586\pi$
$480$	1.84287	+	3.24468i	0.0841151	+	0.148099i
$481$	19.2580	+	6.25731i	0.878090	+	0.285309i
$482$	1.97807	+	12.4890i	0.0900985	+	0.568860i
$483$	−21.5496	−	21.5496i	−0.980541	−	0.980541i
$484$	10.5579	+	3.08722i	0.479904	+	0.140328i
$485$	18.5847	−	28.1799i	0.843886	−	1.27958i
$486$	−1.31182	+	1.80557i	−0.0595055	+	0.0819023i
$487$	28.3070	−	14.4231i	1.28271	−	0.653575i	0.326210	−	0.945297i	$-0.394228\pi$
$487$	28.3070	−	14.4231i	1.28271	−	0.653575i	0.956503	+	0.291723i	$0.0942284\pi$
$488$	−9.04128	−	4.60676i	−0.409279	−	0.208538i
$489$	4.01960	+	5.53251i	0.181773	+	0.250189i
$490$	−0.385590	−	8.50730i	−0.0174192	−	0.384321i
$491$	−8.90838	+	2.89451i	−0.402030	+	0.130627i	−0.503051	−	0.864257i	$-0.667789\pi$
$491$	−8.90838	+	2.89451i	−0.402030	+	0.130627i	0.101021	+	0.994884i	$0.467789\pi$
$492$	−0.990662	−	1.94428i	−0.0446625	−	0.0876551i
$493$	−11.8245	+	1.87282i	−0.532551	+	0.0843478i
$494$	4.27390			0.192292
$495$	1.58833	+	0.154465i	0.0713902	+	0.00694270i
$496$	−5.73418			−0.257472
$497$	6.37111	−	1.00908i	0.285783	−	0.0452636i
$498$	4.57530	+	8.97953i	0.205024	+	0.402383i
$499$	−35.8360	+	11.6438i	−1.60424	+	0.521249i	−0.968151	−	0.250366i	$-0.919449\pi$
$499$	−35.8360	+	11.6438i	−1.60424	+	0.521249i	−0.636090	+	0.771615i	$0.719449\pi$
$500$	3.67953	−	10.5575i	0.164554	−	0.472146i
$501$	−6.11090	−	8.41093i	−0.273015	−	0.375773i
$502$	22.9615	+	11.6995i	1.02482	+	0.522172i
$503$	17.7555	−	9.04689i	0.791679	−	0.403381i	−0.0108892	−	0.999941i	$-0.503466\pi$
$503$	17.7555	−	9.04689i	0.791679	−	0.403381i	0.802569	+	0.596560i	$0.203466\pi$
$504$	0.415820	−	0.572327i	0.0185221	−	0.0254935i
$505$	29.7241	−	6.09885i	1.32270	−	0.271395i
$506$	−14.7425	+	11.0490i	−0.655384	+	0.491188i
$507$	29.7333	+	29.7333i	1.32050	+	1.32050i
$508$	−2.04599	−	12.9179i	−0.0907761	−	0.573138i
$509$	−22.4047	−	7.27974i	−0.993072	−	0.322669i	−0.232978	−	0.972482i	$-0.574847\pi$
$509$	−22.4047	−	7.27974i	−0.993072	−	0.322669i	−0.760094	+	0.649813i	$0.774847\pi$
$510$	−19.3067	−	5.31972i	−0.854915	−	0.235561i
$511$	−8.93166	+	6.48923i	−0.395113	+	0.287067i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	−1.68444	+	3.30591i	−0.0743700	+	0.145959i
$514$	1.28045	−	3.94081i	0.0564781	−	0.173822i
$515$	−0.136339	−	0.362817i	−0.00600780	−	0.0159876i
$516$			10.3556i			0.455881i
$517$	5.76061	−	1.00024i	0.253351	−	0.0439905i
$518$	7.61648	−	7.61648i	0.334649	−	0.334649i
$519$	−28.7854	−	20.9138i	−1.26354	−	0.918015i
$520$	1.54165	−	13.7336i	0.0676059	−	0.602258i
$521$	1.58405	+	4.87520i	0.0693984	+	0.213586i	0.979741	−	0.200270i	$-0.0641818\pi$
$521$	1.58405	+	4.87520i	0.0693984	+	0.213586i	−0.910342	+	0.413856i	$0.864182\pi$
$522$	0.474104	+	0.0750907i	0.0207510	+	0.00328663i
$523$	19.0660	+	3.01976i	0.833698	+	0.132045i	0.558669	−	0.829391i	$-0.311312\pi$
$523$	19.0660	+	3.01976i	0.833698	+	0.132045i	0.275030	+	0.961436i	$0.411312\pi$
$524$	0.973775	+	2.99697i	0.0425396	+	0.130923i
$525$	27.3191	−	2.48155i	1.19230	−	0.108304i
$526$	11.0165	+	8.00397i	0.480343	+	0.348989i
$527$	21.7606	−	21.7606i	0.947907	−	0.947907i
$528$	3.97128	+	3.85512i	0.172828	+	0.167773i
$529$		−	7.85653i		−	0.341588i
$530$	6.37678	+	2.89329i	0.276990	+	0.125676i
$531$	0.0573737	−	0.176578i	0.00248981	−	0.00766283i
$532$	1.03213	−	2.02567i	0.0447486	−	0.0878240i
$533$	−1.26424	+	7.98213i	−0.0547605	+	0.345744i
$534$	−6.62247	+	4.81151i	−0.286582	+	0.208214i
$535$	3.12203	−	11.3307i	0.134977	−	0.489869i
$536$	12.1803	+	3.95763i	0.526110	+	0.170944i
$537$	−6.68956	−	42.2362i	−0.288676	−	1.82263i
$538$	−11.3451	−	11.3451i	−0.489122	−	0.489122i
$539$	−4.08114	−	11.9538i	−0.175787	−	0.514889i
$540$	10.0155	+	6.60522i	0.430998	+	0.284243i
$541$	8.73481	−	12.0224i	0.375539	−	0.516885i	−0.578857	−	0.815429i	$-0.696501\pi$
$541$	8.73481	−	12.0224i	0.375539	−	0.516885i	0.954396	+	0.298544i	$0.0965011\pi$
$542$	10.3201	−	5.25838i	0.443288	−	0.225867i
$543$	−30.2572	−	15.4168i	−1.29846	−	0.661600i
$544$	3.15452	+	4.34183i	0.135249	+	0.186154i
$545$	−10.4309	−	9.52636i	−0.446811	−	0.408064i
$546$	32.2482	−	10.4781i	1.38010	−	0.448420i
$547$	6.94045	+	13.6214i	0.296752	+	0.582409i	0.990452	−	0.137855i	$-0.0440207\pi$
$547$	6.94045	+	13.6214i	0.296752	+	0.582409i	−0.693700	+	0.720264i	$0.744021\pi$
$548$	−11.7822	+	1.86611i	−0.503309	+	0.0797162i
$549$	−2.18350			−0.0931895
$550$	0.856165	−	16.5610i	0.0365070	−	0.706164i
$551$	1.54261			0.0657173
$552$	−9.15571	+	1.45012i	−0.389693	+	0.0617213i
$553$	−6.27445	−	12.3143i	−0.266817	−	0.523657i
$554$	−7.96865	+	2.58917i	−0.338555	+	0.110003i
$555$	9.02737	+	8.24453i	0.383190	+	0.349961i
$556$	−5.13677	−	7.07016i	−0.217848	−	0.299841i
$557$	23.4008	+	11.9233i	0.991523	+	0.505206i	0.872987	−	0.487744i	$-0.162180\pi$
$557$	23.4008	+	11.9233i	0.991523	+	0.505206i	0.118536	+	0.992950i	$0.462180\pi$
$558$	−1.09940	+	0.560173i	−0.0465414	+	0.0237140i
$559$	22.5432	−	31.0280i	0.953474	−	1.31234i
$560$	−6.13692	−	4.04730i	−0.259332	−	0.171030i
$561$	−29.7004	+	0.440812i	−1.25395	+	0.0186111i
$562$	−18.3659	−	18.3659i	−0.774718	−	0.774718i
$563$	−1.33794	−	8.44742i	−0.0563874	−	0.356016i	−0.999709	−	0.0241352i	$-0.992317\pi$
$563$	−1.33794	−	8.44742i	−0.0563874	−	0.356016i	0.943321	−	0.331881i	$-0.107683\pi$
$564$	2.79786	+	0.909081i	0.117811	+	0.0382792i
$565$	−9.08932	+	32.9876i	−0.382391	+	1.38780i
$566$	−10.5170	+	7.64102i	−0.442061	+	0.321176i
$567$	−4.27287	+	26.9778i	−0.179444	+	1.13296i
$568$	0.890758	−	1.74821i	0.0373754	−	0.0733533i
$569$	3.86425	−	11.8929i	0.161998	−	0.498578i	−0.836805	−	0.547501i	$-0.815579\pi$
$569$	3.86425	−	11.8929i	0.161998	−	0.498578i	0.998803	+	0.0489236i	$0.0155791\pi$
$570$	2.34985	+	1.06618i	0.0984243	+	0.0446573i
$571$		−	12.4922i		−	0.522784i	−0.965233	−	0.261392i	$-0.915818\pi$
$571$		−	12.4922i		−	0.522784i	0.965233	−	0.261392i	$-0.0841815\pi$
$572$	−3.50672	−	20.1960i	−0.146623	−	0.844436i
$573$	−0.862406	+	0.862406i	−0.0360275	+	0.0360275i
$574$	3.47793	+	2.52686i	0.145166	+	0.105469i
$575$	21.3355	+	17.7822i	0.889753	+	0.741571i
$576$	−0.0664946	−	0.204649i	−0.00277061	−	0.00852706i
$577$	−7.33080	−	1.16108i	−0.305185	−	0.0483366i	0.00196373	−	0.999998i	$-0.499375\pi$
$577$	−7.33080	−	1.16108i	−0.305185	−	0.0483366i	−0.307149	+	0.951662i	$0.599375\pi$
$578$	−11.6572	−	1.84631i	−0.484874	−	0.0767965i
$579$	−8.48755	−	26.1220i	−0.352731	−	1.08559i
$580$	0.556439	−	4.95696i	0.0231049	−	0.205827i
$581$	−16.0626	−	11.6701i	−0.666387	−	0.484158i
$582$	17.8137	−	17.8137i	0.738403	−	0.738403i
$583$	10.2814	+	1.47236i	0.425813	+	0.0609790i
$584$			3.35809i			0.138959i
$585$	−1.04606	−	2.78372i	−0.0432492	−	0.115092i
$586$	−4.79512	+	14.7579i	−0.198085	+	0.609642i
$587$	−14.5824	+	28.6196i	−0.601881	+	1.18126i	0.366180	+	0.930544i	$0.380665\pi$
$587$	−14.5824	+	28.6196i	−0.601881	+	1.18126i	−0.968061	+	0.250714i	$0.919335\pi$
$588$	0.994222	−	6.27727i	0.0410010	−	0.258870i
$589$	−3.20800	+	2.33075i	−0.132183	+	0.0960368i
$590$	−1.86003	−	0.512509i	−0.0765764	−	0.0210997i
$591$	19.2808	+	6.26470i	0.793105	+	0.257695i
$592$	−0.512530	−	3.23599i	−0.0210649	−	0.132998i
$593$	−10.2796	−	10.2796i	−0.422131	−	0.422131i	0.463806	−	0.885937i	$-0.346483\pi$
$593$	−10.2796	−	10.2796i	−0.422131	−	0.422131i	−0.885937	+	0.463806i	$0.846483\pi$
$594$	17.0039	+	5.24722i	0.697678	+	0.215296i
$595$	38.6481	−	7.92988i	1.58442	−	0.325093i
$596$	4.20604	−	5.78912i	0.172286	−	0.237132i
$597$	−20.7845	+	10.5902i	−0.850651	+	0.433429i
$598$	30.5895	+	15.5861i	1.25090	+	0.637365i
$599$	13.2708	+	18.2657i	0.542232	+	0.746318i	0.988933	−	0.148365i	$-0.0474011\pi$
$599$	13.2708	+	18.2657i	0.542232	+	0.746318i	−0.446701	+	0.894683i	$0.647401\pi$
$600$	4.27365	−	7.16634i	0.174471	−	0.292565i
$601$	14.7655	−	4.79760i	0.602298	−	0.195698i	0.00803271	−	0.999968i	$-0.497443\pi$
$601$	14.7655	−	4.79760i	0.602298	−	0.195698i	0.594265	+	0.804269i	$0.297443\pi$
$602$	−9.26205	−	18.1778i	−0.377493	−	0.740871i
$603$	2.72193	−	0.431111i	0.110846	−	0.0175562i
$604$	−9.83369			−0.400127
$605$	−5.65671	−	23.9375i	−0.229978	−	0.973196i
$606$	22.6452			0.919899
$607$	12.6602	−	2.00517i	0.513861	−	0.0813875i	0.105881	−	0.994379i	$-0.466234\pi$
$607$	12.6602	−	2.00517i	0.513861	−	0.0813875i	0.407979	+	0.912991i	$0.366234\pi$
$608$	−0.313944	−	0.616150i	−0.0127321	−	0.0249882i
$609$	11.6396	−	3.78193i	0.471659	−	0.153251i
$610$	1.02736	+	22.6667i	0.0415965	+	0.917748i
$611$	−6.40411	−	8.81450i	−0.259083	−	0.356597i
$612$	1.02896	+	0.524283i	0.0415934	+	0.0211929i
$613$	−30.1068	+	15.3402i	−1.21600	+	0.619584i	−0.939869	−	0.341535i	$-0.889053\pi$
$613$	−30.1068	+	15.3402i	−1.21600	+	0.619584i	−0.276134	+	0.961119i	$0.589053\pi$
$614$	−13.3702	+	18.4025i	−0.539577	+	0.742664i
$615$	−2.68635	+	4.07330i	−0.108324	+	0.164251i
$616$	−10.4190	−	3.21520i	−0.419794	−	0.129544i
$617$	−4.79584	−	4.79584i	−0.193073	−	0.193073i	0.603949	−	0.797023i	$-0.293593\pi$
$617$	−4.79584	−	4.79584i	−0.193073	−	0.193073i	−0.797023	+	0.603949i	$0.793593\pi$
$618$	−0.0452497	−	0.285696i	−0.00182021	−	0.0114924i
$619$	1.03088	+	0.334954i	0.0414346	+	0.0134629i	0.329661	−	0.944099i	$-0.393066\pi$
$619$	1.03088	+	0.334954i	0.0414346	+	0.0134629i	−0.288226	+	0.957562i	$0.593066\pi$
$620$	6.33238	+	11.1492i	0.254314	+	0.447763i
$621$	−24.1121	+	17.5185i	−0.967585	+	0.702992i
$622$	−0.906892	+	5.72589i	−0.0363631	+	0.229587i
$623$	7.32138	−	14.3690i	0.293325	−	0.575683i
$624$	3.18713	−	9.80896i	0.127587	−	0.392673i
$625$	−24.5908	+	4.50462i	−0.983633	+	0.180185i
$626$		−	5.13577i		−	0.205267i
$627$	3.78872	+	0.542567i	0.151307	+	0.0216680i
$628$	7.00571	−	7.00571i	0.279558	−	0.279558i
$629$	14.2252	+	10.3352i	0.567197	+	0.412093i
$630$	−1.57200	−	0.176463i	−0.0626300	−	0.00703047i
$631$	0.413885	+	1.27381i	0.0164765	+	0.0507094i	0.958957	−	0.283552i	$-0.0915130\pi$
$631$	0.413885	+	1.27381i	0.0164765	+	0.0507094i	−0.942480	+	0.334262i	$0.891513\pi$
$632$	−4.15208	−	0.657626i	−0.165161	−	0.0261589i
$633$	−8.43241	−	1.33556i	−0.335158	−	0.0530839i
$634$	−0.563568	−	1.73448i	−0.0223821	−	0.0688851i
$635$	−22.8573	+	18.2436i	−0.907066	+	0.723975i
$636$	4.22787	+	3.07173i	0.167646	+	0.121802i
$637$	−16.6439	+	16.6439i	−0.659456	+	0.659456i
$638$	−1.26570	−	7.28947i	−0.0501097	−	0.288593i
$639$		−	0.422199i		−	0.0167019i
$640$	−2.09316	+	0.786564i	−0.0827394	+	0.0310917i
$641$	4.00585	−	12.3287i	0.158222	−	0.486956i	−0.840252	−	0.542197i	$-0.817593\pi$
$641$	4.00585	−	12.3287i	0.158222	−	0.486956i	0.998473	+	0.0552410i	$0.0175927\pi$
$642$	3.98205	−	7.81522i	0.157159	−	0.308442i
$643$	−6.44700	+	40.7047i	−0.254245	+	1.60524i	0.448491	+	0.893787i	$0.351962\pi$
$643$	−6.44700	+	40.7047i	−0.254245	+	1.60524i	−0.702736	+	0.711451i	$0.748038\pi$
$644$	14.7745	−	10.7343i	0.582198	−	0.422992i
$645$	20.1349	−	11.4359i	0.792811	−	0.450290i
$646$	3.52961	+	1.14684i	0.138871	+	0.0451218i
$647$	1.18678	+	7.49301i	0.0466570	+	0.294581i	0.999973	−	0.00739486i	$-0.00235388\pi$
$647$	1.18678	+	7.49301i	0.0466570	+	0.294581i	−0.953316	+	0.301976i	$0.902354\pi$
$648$	5.87475	+	5.87475i	0.230782	+	0.230782i
$649$	−2.86137	+	0.0424684i	−0.112319	+	0.00166703i
$650$	−28.4053	+	12.1688i	−1.11415	+	0.477300i
$651$	−18.4914	+	25.4513i	−0.724736	+	0.997514i
$652$	−3.65130	+	1.86043i	−0.142996	+	0.0728600i
$653$	25.5769	+	13.0321i	1.00090	+	0.509984i	0.876065	−	0.482193i	$-0.160160\pi$
$653$	25.5769	+	13.0321i	1.00090	+	0.509984i	0.124836	+	0.992177i	$0.460160\pi$
$654$	−6.19675	−	8.52909i	−0.242312	−	0.333514i
$655$	4.75178	−	5.20298i	0.185668	−	0.203297i
$656$	1.24362	−	0.404076i	0.0485551	−	0.0157765i
$657$	0.328052	+	0.643839i	0.0127985	+	0.0251186i
$658$	−5.72432	+	0.906644i	−0.223157	+	0.0353447i
$659$	−32.7832			−1.27705			−0.638526	−	0.769600i	$-0.720456\pi$
$659$	−32.7832			−1.27705			−0.638526	+	0.769600i	$0.720456\pi$
$660$	3.11011	−	11.9788i	0.121061	−	0.466275i
$661$	19.2907			0.750323			0.375162	−	0.926959i	$-0.377587\pi$
$661$	19.2907			0.750323			0.375162	+	0.926959i	$0.377587\pi$
$662$	−20.0852	+	3.18119i	−0.780634	+	0.123640i
$663$	25.1292	+	49.3188i	0.975936	+	1.91538i
$664$	−5.74356	+	1.86619i	−0.222893	+	0.0724224i
$665$	−5.07841	+	0.230177i	−0.196932	+	0.00892586i
$666$	−0.414391	−	0.570360i	−0.0160573	−	0.0221010i
$667$	11.0409	+	5.62562i	0.427505	+	0.217825i
$668$	5.55097	−	2.82836i	0.214773	−	0.109433i
$669$	−11.4860	+	15.8091i	−0.444074	+	0.611216i
$670$	−5.75602	−	28.0532i	−0.222374	−	1.08379i
$671$	10.8737	+	31.8496i	0.419775	+	1.22954i
$672$	−3.87941	−	3.87941i	−0.149652	−	0.149652i
$673$	−0.859942	−	5.42946i	−0.0331483	−	0.209290i	0.965555	−	0.260199i	$-0.0837882\pi$
$673$	−0.859942	−	5.42946i	−0.0331483	−	0.209290i	−0.998703	+	0.0509088i	$0.983788\pi$
$674$	−24.0544	−	7.81573i	−0.926539	−	0.301051i
$675$	1.78249	−	26.7678i	0.0686080	−	1.03029i
$676$	−20.3853	+	14.8108i	−0.784051	+	0.569646i
$677$	−4.79944	+	30.3025i	−0.184457	+	1.16462i	0.705546	+	0.708664i	$0.250702\pi$
$677$	−4.79944	+	30.3025i	−0.184457	+	1.16462i	−0.890003	+	0.455954i	$0.849298\pi$
$678$	−11.5932	+	22.7528i	−0.445232	+	0.873818i
$679$	−15.3369	+	47.2020i	−0.588575	+	1.81145i
$680$	4.95839	−	10.9282i	0.190146	−	0.419079i
$681$			12.8968i			0.494206i
$682$	13.6459	+	13.2468i	0.522529	+	0.507246i
$683$	−12.8058	+	12.8058i	−0.489999	+	0.489999i	−0.908306	−	0.418307i	$-0.862624\pi$
$683$	−12.8058	+	12.8058i	−0.489999	+	0.489999i	0.418307	+	0.908306i	$0.362624\pi$
$684$	−0.120384	−	0.0874638i	−0.00460298	−	0.00334426i
$685$	16.6397	+	20.8478i	0.635768	+	0.796552i
$686$	−3.24236	−	9.97897i	−0.123794	−	0.380999i
$687$	−31.3289	−	4.96201i	−1.19527	−	0.189313i
$688$	−6.12911	−	0.970756i	−0.233670	−	0.0370097i
$689$	−5.98089	−	18.4073i	−0.227854	−	0.701262i
$690$	12.9304	+	16.2004i	0.492251	+	0.616740i
$691$	−28.6104	−	20.7867i	−1.08839	−	0.790763i	−0.109265	−	0.994013i	$-0.534850\pi$
$691$	−28.6104	−	20.7867i	−1.08839	−	0.790763i	−0.979127	+	0.203249i	$0.934850\pi$
$692$	15.0765	−	15.0765i	0.573123	−	0.573123i
$693$	−2.31171	+	0.401392i	−0.0878145	+	0.0152476i
$694$			0.375687i			0.0142609i
$695$	−8.07417	+	17.7954i	−0.306271	+	0.675017i
$696$	1.15035	−	3.54042i	0.0436040	−	0.134199i
$697$	−3.18597	+	6.25282i	−0.120677	+	0.236843i
$698$	2.23028	−	14.0814i	0.0844172	−	0.532990i
$699$	28.5287	−	20.7273i	1.07905	−	0.783979i
$700$	−1.09221	+	16.4018i	−0.0412816	+	0.619930i
$701$	37.5754	+	12.2090i	1.41920	+	0.461127i	0.915349	−	0.402661i	$-0.131915\pi$
$701$	37.5754	+	12.2090i	1.41920	+	0.461127i	0.503855	+	0.863788i	$0.331915\pi$
$702$	−5.18746	−	32.7523i	−0.195788	−	1.23616i
$703$	−1.60206	−	1.60206i	−0.0604227	−	0.0604227i
$704$	−2.65398	+	1.98907i	−0.100026	+	0.0749658i
$705$	−1.32218	−	6.44393i	−0.0497961	−	0.242692i
$706$	6.73023	−	9.26336i	0.253295	−	0.348631i
$707$	−39.7504	+	20.2538i	−1.49497	+	0.761724i
$708$	−1.28294	−	0.653689i	−0.0482157	−	0.0245672i
$709$	−8.24861	−	11.3532i	−0.309783	−	0.426380i	0.625531	−	0.780200i	$-0.284883\pi$
$709$	−8.24861	−	11.3532i	−0.309783	−	0.426380i	−0.935314	+	0.353820i	$0.884883\pi$
$710$	−4.38281	+	0.198649i	−0.164484	+	0.00745515i
$711$	−0.860314	+	0.279533i	−0.0322643	+	0.0104833i
$712$	−2.22695	−	4.37064i	−0.0834585	−	0.163797i
$713$	−31.4604	+	4.98284i	−1.17820	+	0.186609i
$714$	29.4439			1.10191
$715$	−35.3953	+	29.1211i	−1.32371	+	1.08907i
$716$	25.6251			0.957657
$717$	34.9807	−	5.54039i	1.30638	−	0.206910i
$718$	0.817202	+	1.60385i	0.0304977	+	0.0598551i
$719$	17.2499	−	5.60484i	0.643314	−	0.209025i	0.0308501	−	0.999524i	$-0.490179\pi$
$719$	17.2499	−	5.60484i	0.643314	−	0.209025i	0.612464	+	0.790499i	$0.290179\pi$
$720$	−0.324477	+	0.355287i	−0.0120926	+	0.0132408i
$721$	0.334955	+	0.461026i	0.0124744	+	0.0171695i
$722$	16.5030	+	8.40872i	0.614180	+	0.312940i
$723$	18.8013	−	9.57975i	0.699228	−	0.356275i
$724$	11.9610	−	16.4629i	0.444528	−	0.611841i
$725$	−10.2525	+	4.39218i	−0.380769	+	0.163121i
$726$	−0.544775	−	18.3485i	−0.0202185	−	0.680976i
$727$	−33.9484	−	33.9484i	−1.25908	−	1.25908i	−0.951534	−	0.307543i	$-0.900493\pi$
$727$	−33.9484	−	33.9484i	−1.25908	−	1.25908i	−0.307543	−	0.951534i	$-0.599507\pi$
$728$	3.17858	+	20.0688i	0.117806	+	0.743798i
$729$	27.2467	+	8.85298i	1.00914	+	0.327888i
$730$	6.52928	−	3.70841i	0.241659	−	0.137255i
$731$	26.9433	−	19.5754i	0.996533	−	0.724023i
$732$	−2.64899	+	16.7250i	−0.0979094	+	0.618176i
$733$	10.0298	−	19.6845i	0.370458	−	0.727064i	−0.628244	−	0.778017i	$-0.716226\pi$
$733$	10.0298	−	19.6845i	0.370458	−	0.727064i	0.998701	+	0.0509529i	$0.0162259\pi$
$734$	−1.30960	+	4.03054i	−0.0483383	+	0.148770i
$735$	−13.3031	+	4.99902i	−0.490693	+	0.184392i
$736$		−	5.55487i		−	0.204755i
$737$	−19.8435	−	37.5565i	−0.730944	−	1.38341i
$738$	0.198962	−	0.198962i	0.00732388	−	0.00732388i
$739$	−16.6360	−	12.0867i	−0.611963	−	0.444617i	0.238142	−	0.971230i	$-0.423462\pi$
$739$	−16.6360	−	12.0867i	−0.611963	−	0.444617i	−0.850105	+	0.526613i	$0.823462\pi$
$740$	−5.72588	+	4.57011i	−0.210487	+	0.168001i
$741$	−2.20397	−	6.78311i	−0.0809647	−	0.249184i
$742$	−10.1688	−	1.61057i	−0.373307	−	0.0591260i
$743$	13.7599	+	2.17935i	0.504800	+	0.0799525i	0.403640	−	0.914918i	$-0.367745\pi$
$743$	13.7599	+	2.17935i	0.504800	+	0.0799525i	0.101160	+	0.994870i	$0.467745\pi$
$744$	2.95700	+	9.10072i	0.108409	+	0.333649i
$745$	−15.9009	−	1.78494i	−0.582563	−	0.0653950i
$746$	−0.873094	−	0.634340i	−0.0319662	−	0.0232248i
$747$	−0.918890	+	0.918890i	−0.0336204	+	0.0336204i
$748$	2.52327	−	17.6199i	0.0922599	−	0.644247i
$749$			17.2800i			0.631398i
$750$	−18.6533	−	0.395490i	−0.681123	−	0.0144412i
$751$	10.2437	−	31.5269i	0.373798	−	1.15043i	−0.570487	−	0.821306i	$-0.693246\pi$
$751$	10.2437	−	31.5269i	0.373798	−	1.15043i	0.944286	−	0.329127i	$-0.106754\pi$
$752$	−0.800329	+	1.57073i	−0.0291850	+	0.0572788i
$753$	6.72744	−	42.4754i	0.245161	−	1.54789i
$754$	−11.1539	+	8.10376i	−0.406200	+	0.295122i
$755$	10.8596	+	19.1201i	0.395220	+	0.695851i
$756$	−16.7762	−	5.45091i	−0.610143	−	0.198248i
$757$	2.28724	+	14.4411i	0.0831311	+	0.524869i	0.993751	+	0.111623i	$0.0356050\pi$
$757$	2.28724	+	14.4411i	0.0831311	+	0.524869i	−0.910620	+	0.413246i	$0.864395\pi$
$758$	11.3071	+	11.3071i	0.410694	+	0.410694i
$759$	25.1383	+	17.7001i	0.912463	+	0.642473i
$760$	−0.851312	+	1.29084i	−0.0308803	+	0.0468238i
$761$	6.58319	−	9.06098i	0.238640	−	0.328460i	−0.672852	−	0.739777i	$-0.734931\pi$
$761$	6.58319	−	9.06098i	0.238640	−	0.328460i	0.911493	+	0.411317i	$0.134931\pi$
$762$	−19.4469	+	9.90869i	−0.704487	+	0.358954i
$763$	18.5059	+	9.42922i	0.669958	+	0.341361i
$764$	−0.429583	−	0.591270i	−0.0155418	−	0.0213914i
$765$	−0.116921	−	2.57964i	−0.00422728	−	0.0932669i
$766$	−28.7897	+	9.35435i	−1.04021	+	0.337986i
$767$	2.42098	+	4.75144i	0.0874165	+	0.171565i
$768$	−1.64823	+	0.261054i	−0.0594755	+	0.00941999i
$769$	37.2217			1.34225			0.671125	−	0.741345i	$-0.265812\pi$
$769$	37.2217			1.34225			0.671125	+	0.741345i	$0.265812\pi$
$770$	5.25450	+	23.8088i	0.189359	+	0.858008i
$771$	−6.91477			−0.249029
$772$	16.2563	−	2.57474i	0.585077	−	0.0926671i
$773$	−11.9548	−	23.4625i	−0.429983	−	0.843889i	−0.999756	−	0.0220869i	$-0.992969\pi$
$773$	−11.9548	−	23.4625i	−0.429983	−	0.843889i	0.569773	−	0.821802i	$-0.307031\pi$
$774$	−1.26995	+	0.412633i	−0.0456476	+	0.0148318i
$775$	14.6849	−	24.6246i	0.527497	−	0.884543i
$776$	8.87341	+	12.2132i	0.318537	+	0.438428i
$777$	−16.0158	−	8.16046i	−0.574564	−	0.292755i
$778$	29.4430	−	15.0020i	1.05558	−	0.537847i
$779$	0.531502	−	0.731549i	0.0190430	−	0.0262105i
$780$	−22.5916	+	4.63539i	−0.808909	+	0.165974i
$781$	−6.15840	+	2.10253i	−0.220365	+	0.0752344i
$782$	21.0801	+	21.0801i	0.753824	+	0.753824i
$783$	−1.87235	−	11.8215i	−0.0669122	−	0.422467i
$784$	3.62208	+	1.17689i	0.129360	+	0.0420317i
$785$	−21.3581	−	5.88495i	−0.762303	−	0.210043i
$786$	4.25434	−	3.09096i	0.151747	−	0.110251i
$787$	6.07686	−	38.3678i	0.216617	−	1.36766i	−0.604364	−	0.796709i	$-0.706573\pi$
$787$	6.07686	−	38.3678i	0.216617	−	1.36766i	0.820981	−	0.570956i	$-0.193427\pi$
$788$	−5.51527	+	10.8243i	−0.196473	+	0.385600i
$789$	7.02211	−	21.6118i	0.249994	−	0.769401i
$790$	3.30659	+	8.79931i	0.117643	+	0.313065i
$791$		−	50.3082i		−	1.78875i
$792$	−0.314529	+	0.640627i	−0.0111763	+	0.0227637i
$793$	44.3458	−	44.3458i	1.57476	−	1.57476i
$794$	27.5609	+	20.0242i	0.978100	+	0.710631i
$795$	1.30356	−	11.6126i	0.0462326	−	0.411857i
$796$	−4.31958	−	13.2943i	−0.153104	−	0.471204i
$797$	40.1968	+	6.36654i	1.42384	+	0.225515i	0.820354	−	0.571856i	$-0.193777\pi$
$797$	40.1968	+	6.36654i	1.42384	+	0.225515i	0.603489	+	0.797371i	$0.293777\pi$
$798$	−3.74720	−	0.593498i	−0.132649	−	0.0210096i
$799$	−2.92361	−	8.99794i	−0.103430	−	0.318324i
$800$	3.84087	+	3.20120i	0.135795	+	0.113180i
$801$	−0.853937	−	0.620422i	−0.0301724	−	0.0219215i
$802$	−15.9058	+	15.9058i	−0.561652	+	0.561652i
$803$	7.75768	−	7.99142i	0.273762	−	0.282011i
$804$		−	21.3723i		−	0.753743i
$805$	−37.1871	−	16.8726i	−1.31067	−	0.594681i
$806$	10.9515	−	33.7051i	0.385748	−	1.18721i
$807$	−12.1554	+	23.8563i	−0.427890	+	0.839781i
$808$	−2.12281	+	13.4029i	−0.0746801	+	0.471512i
$809$	−39.9952	+	29.0582i	−1.40615	+	1.02163i	−0.412287	+	0.911054i	$0.635270\pi$
$809$	−39.9952	+	29.0582i	−1.40615	+	1.02163i	−0.993868	+	0.110577i	$0.964730\pi$
$810$	4.93492	−	17.9102i	0.173395	−	0.629299i
$811$	−33.0590	−	10.7415i	−1.16086	−	0.377186i	−0.335636	−	0.941992i	$-0.608951\pi$
$811$	−33.0590	−	10.7415i	−1.16086	−	0.377186i	−0.825224	+	0.564805i	$0.808951\pi$
$812$	1.14727	+	7.24356i	0.0402612	+	0.254199i
$813$	−13.6675	−	13.6675i	−0.479339	−	0.479339i
$814$	−6.25591	+	8.88487i	−0.219270	+	0.311415i
$815$	7.64952	+	5.04486i	0.267951	+	0.176714i
$816$	5.26420	−	7.24554i	0.184284	−	0.253645i
$817$	−3.82353	+	1.94818i	−0.133768	+	0.0681584i
$818$	22.5610	+	11.4954i	0.788828	+	0.401928i
$819$	2.56994	+	3.53722i	0.0898011	+	0.123601i
$820$	−2.15902	−	1.97179i	−0.0753961	−	0.0688579i
$821$	−13.1314	+	4.26664i	−0.458288	+	0.148907i	−0.529058	−	0.848586i	$-0.677454\pi$
$821$	−13.1314	+	4.26664i	−0.458288	+	0.148907i	0.0707697	+	0.997493i	$0.477454\pi$
$822$	9.03753	+	17.7372i	0.315220	+	0.618654i
$823$	15.2526	−	2.41578i	0.531673	−	0.0842087i	0.115175	−	0.993345i	$-0.463257\pi$
$823$	15.2526	−	2.41578i	0.531673	−	0.0842087i	0.416498	+	0.909137i	$0.363257\pi$
$824$	0.173335			0.00603840
$825$	−26.7255	+	7.18137i	−0.930463	+	0.250023i
$826$	2.83667			0.0987003
$827$	47.3254	−	7.49561i	1.64567	−	0.260648i	0.736303	−	0.676652i	$-0.236570\pi$
$827$	47.3254	−	7.49561i	1.64567	−	0.260648i	0.909363	+	0.416004i	$0.136570\pi$
$828$	−0.542656	−	1.06502i	−0.0188586	−	0.0370121i
$829$	42.1108	−	13.6826i	1.46257	−	0.475218i	0.533716	−	0.845664i	$-0.320795\pi$
$829$	42.1108	−	13.6826i	1.46257	−	0.475218i	0.928854	+	0.370446i	$0.120795\pi$
$830$	9.97126	+	9.10657i	0.346107	+	0.316093i
$831$	8.21855	+	11.3119i	0.285098	+	0.392404i
$832$	5.50680	+	2.80585i	0.190914	+	0.0972755i
$833$	−18.2116	+	9.27927i	−0.630994	+	0.321508i
$834$	−8.57213	+	11.7985i	−0.296829	+	0.408549i
$835$	−11.6294	−	7.66957i	−0.402451	−	0.265416i
$836$	−0.676287	+	2.19154i	−0.0233899	+	0.0757961i
$837$	21.7550	+	21.7550i	0.751964	+	0.751964i
$838$	−4.93465	−	31.1562i	−0.170465	−	1.07627i
$839$	6.92949	+	2.25153i	0.239233	+	0.0777314i	0.426179	−	0.904639i	$-0.359859\pi$
$839$	6.92949	+	2.25153i	0.239233	+	0.0777314i	−0.186947	+	0.982370i	$0.559859\pi$
$840$	−3.25879	+	11.8270i	−0.112439	+	0.408071i
$841$	19.4356	−	14.1208i	0.670195	−	0.486925i
$842$	−1.73935	+	10.9818i	−0.0599420	+	0.378459i
$843$	−19.6776	+	38.6195i	−0.677733	+	1.33013i
$844$	1.58094	−	4.86564i	0.0544182	−	0.167482i
$845$	51.3092	+	23.2802i	1.76509	+	0.800862i
$846$			0.379338i			0.0130419i
$847$	17.3671	+	31.7208i	0.596741	+	1.08994i
$848$	−2.21437	+	2.21437i	−0.0760418	+	0.0760418i
$849$	17.5505	+	12.7512i	0.602331	+	0.437619i
$850$	−26.7239	+	2.42749i	−0.916624	+	0.0832622i
$851$	−5.62397	−	17.3088i	−0.192787	−	0.593338i
$852$	−3.23393	−	0.512205i	−0.110793	−	0.0175479i
$853$	−6.88475	−	1.09044i	−0.235729	−	0.0373358i	0.0374520	−	0.999298i	$-0.488076\pi$
$853$	−6.88475	−	1.09044i	−0.235729	−	0.0373358i	−0.273181	+	0.961963i	$0.588076\pi$
$854$	−10.3089	−	31.7276i	−0.352764	−	1.08570i
$855$	−0.0371174	+	0.330655i	−0.00126939	+	0.0113082i
$856$	4.25226	+	3.08945i	0.145339	+	0.105595i
$857$	22.8797	−	22.8797i	0.781554	−	0.781554i	−0.198539	−	0.980093i	$-0.563620\pi$
$857$	22.8797	−	22.8797i	0.781554	−	0.781554i	0.980093	+	0.198539i	$0.0636196\pi$
$858$	−30.2447	+	15.9802i	−1.03254	+	0.545555i
$859$			53.1298i			1.81276i	0.422459	+	0.906382i	$0.361167\pi$
$859$			53.1298i			1.81276i	−0.422459	+	0.906382i	$0.638833\pi$
$860$	4.88103	+	12.9891i	0.166442	+	0.442926i
$861$	2.21689	−	6.82288i	0.0755513	−	0.232523i
$862$	9.48479	−	18.6149i	0.323053	−	0.634028i
$863$	−3.08038	+	19.4487i	−0.104857	+	0.662042i	0.878138	+	0.478408i	$0.158786\pi$
$863$	−3.08038	+	19.4487i	−0.104857	+	0.662042i	−0.982995	+	0.183634i	$0.941214\pi$
$864$	−4.34072	+	3.15372i	−0.147674	+	0.107292i
$865$	−45.9633	−	12.6646i	−1.56280	−	0.430609i
$866$	−33.6495	−	10.9334i	−1.14346	−	0.371532i
$867$	3.08108	+	19.4532i	0.104639	+	0.660665i
$868$	−13.3303	−	13.3303i	−0.452458	−	0.452458i
$869$	8.36173	+	11.1569i	0.283652	+	0.378472i
$870$	−8.15415	+	1.67308i	−0.276452	+	0.0567229i
$871$	−46.5254	+	64.0367i	−1.57645	+	2.16980i
$872$	5.62895	−	2.86809i	0.190620	−	0.0971259i
$873$	2.89439	+	1.47476i	0.0979602	+	0.0499132i
$874$	−2.25786	−	3.10768i	−0.0763734	−	0.105119i
$875$	33.0969	−	15.9893i	1.11888	−	0.540535i
$876$	5.32963	−	1.73170i	0.180072	−	0.0585088i
$877$	−8.36653	−	16.4202i	−0.282518	−	0.554472i	0.705519	−	0.708691i	$-0.250714\pi$
$877$	−8.36653	−	16.4202i	−0.282518	−	0.554472i	−0.988037	+	0.154219i	$0.950714\pi$
$878$	9.61799	−	1.52334i	0.324592	−	0.0514103i
$879$	25.8950			0.873416
$880$	6.79828	+	2.96368i	0.229170	+	0.0999055i
$881$	−8.88945			−0.299493			−0.149747	−	0.988724i	$-0.547846\pi$
$881$	−8.88945			−0.299493			−0.149747	+	0.988724i	$0.547846\pi$
$882$	0.809425	−	0.128200i	0.0272547	−	0.00431673i
$883$	9.55336	+	18.7495i	0.321496	+	0.630972i	0.994032	−	0.109093i	$-0.0347947\pi$
$883$	9.55336	+	18.7495i	0.321496	+	0.630972i	−0.672535	+	0.740065i	$0.734795\pi$
$884$	−31.5456	+	10.2498i	−1.06099	+	0.344738i
$885$	0.145780	+	3.21636i	0.00490034	+	0.108117i
$886$	4.39936	+	6.05519i	0.147799	+	0.203428i
$887$	−16.2354	−	8.27236i	−0.545132	−	0.277759i	0.159661	−	0.987172i	$-0.448960\pi$
$887$	−16.2354	−	8.27236i	−0.545132	−	0.277759i	−0.704793	+	0.709413i	$0.748960\pi$
$888$	−4.87154	+	2.48217i	−0.163478	+	0.0832963i
$889$	25.2739	−	34.7865i	0.847659	−	1.16670i
$890$	−6.03875	+	9.15655i	−0.202419	+	0.306928i
$891$	−0.408926	−	27.5520i	−0.0136995	−	0.923027i
$892$	−8.28012	−	8.28012i	−0.277239	−	0.277239i
$893$	0.190704	+	1.20406i	0.00638167	+	0.0402923i
$894$	−11.3569	−	3.69008i	−0.379831	−	0.123415i
$895$	−28.2984	−	49.8241i	−0.945912	−	1.66544i
$896$	2.65975	−	1.93242i	0.0888559	−	0.0645576i
$897$	8.96237	−	56.5862i	0.299245	−	1.88936i
$898$	2.75774	−	5.41237i	0.0920269	−	0.180613i
$899$	3.95278	−	12.1654i	0.131833	−	0.405739i
$900$	1.04913	+	0.238544i	0.0349709	+	0.00795145i
$901$		−	16.8066i		−	0.559910i
$902$	−3.89298	−	1.91134i	−0.129622	−	0.0636406i
$903$	−24.0737	+	24.0737i	−0.801124	+	0.801124i
$904$	−12.3798	−	8.99446i	−0.411746	−	0.299151i
$905$	−45.2185	−	5.07595i	−1.50311	−	0.168730i
$906$	5.07104	+	15.6071i	0.168474	+	0.518510i
$907$	−32.3651	−	5.12613i	−1.07467	−	0.170211i	−0.406075	−	0.913840i	$-0.633103\pi$
$907$	−32.3651	−	5.12613i	−1.07467	−	0.170211i	−0.668592	+	0.743629i	$0.733103\pi$
$908$	−7.63313	−	1.20897i	−0.253314	−	0.0401210i
$909$	0.902328	+	2.77708i	0.0299283	+	0.0921100i
$910$	35.5104	−	28.3426i	1.17716	−	0.939549i
$911$	−6.48533	−	4.71187i	−0.214869	−	0.156111i	0.475145	−	0.879907i	$-0.342396\pi$
$911$	−6.48533	−	4.71187i	−0.214869	−	0.156111i	−0.690014	+	0.723796i	$0.742396\pi$
$912$	−0.815998	+	0.815998i	−0.0270204	+	0.0270204i
$913$	17.9794	+	8.82737i	0.595032	+	0.292143i
$914$		−	11.3960i		−	0.376947i
$915$	35.4446	−	13.3193i	1.17176	−	0.440323i
$916$	5.87367	−	18.0773i	0.194071	−	0.597291i
$917$	−4.70333	+	9.23081i	−0.155318	+	0.304828i
$918$	4.50455	−	28.4406i	0.148672	−	0.938679i
$919$	12.3712	−	8.98820i	0.408088	−	0.296493i	−0.364739	−	0.931110i	$-0.618842\pi$
$919$	12.3712	−	8.98820i	0.408088	−	0.296493i	0.772827	+	0.634616i	$0.218842\pi$
$920$	−10.8006	+	6.13436i	−0.356084	+	0.202244i
$921$	36.1014	+	11.7300i	1.18958	+	0.386518i
$922$	2.50380	+	15.8084i	0.0824582	+	0.520621i
$923$	8.57464	+	8.57464i	0.282238	+	0.282238i
$924$	0.270036	+	18.1941i	0.00888352	+	0.598540i
$925$	15.2091	+	6.08620i	0.500071	+	0.200113i
$926$	−21.3027	+	29.3206i	−0.700050	+	0.963536i
$927$	0.0332331	−	0.0169331i	0.00109152	−	0.000556156i
$928$	1.98761	+	1.01274i	0.0652464	+	0.0332447i
$929$	−9.74393	−	13.4114i	−0.319688	−	0.440013i	0.618684	−	0.785640i	$-0.287666\pi$
$929$	−9.74393	−	13.4114i	−0.319688	−	0.440013i	−0.938372	+	0.345627i	$0.887666\pi$
$930$	14.4294	−	15.7996i	0.473160	−	0.518088i
$931$	2.50475	−	0.813842i	0.0820898	−	0.0266726i
$932$	9.59340	+	18.8281i	0.314242	+	0.616735i
$933$	9.55524	−	1.51340i	0.312825	−	0.0495465i
$934$	−1.55275			−0.0508076
$935$	−37.0456	+	14.5519i	−1.21152	+	0.475899i
$936$	1.32991			0.0434695
$937$	−17.9644	+	2.84529i	−0.586872	+	0.0929514i	−0.442807	−	0.896617i	$-0.646017\pi$
$937$	−17.9644	+	2.84529i	−0.586872	+	0.0929514i	−0.144065	+	0.989568i	$0.546017\pi$
$938$	19.1153	+	37.5160i	0.624138	+	1.22494i
$939$	−8.15099	+	2.64842i	−0.265998	+	0.0864278i
$940$	3.93787	−	0.178482i	0.128439	−	0.00582145i
$941$	1.89175	+	2.60377i	0.0616692	+	0.0848804i	0.838738	−	0.544536i	$-0.183294\pi$
$941$	1.89175	+	2.60377i	0.0616692	+	0.0848804i	−0.777068	+	0.629416i	$0.783294\pi$
$942$	−14.7315	−	7.50607i	−0.479978	−	0.244561i
$943$	6.47194	−	3.29762i	0.210756	−	0.107385i
$944$	0.507160	−	0.698046i	0.0165066	−	0.0227195i
$945$	7.92786	+	38.6382i	0.257893	+	1.25690i
$946$	12.3432	+	16.4693i	0.401312	+	0.535463i
$947$	−11.9236	−	11.9236i	−0.387464	−	0.387464i	0.486318	−	0.873782i	$-0.338340\pi$
$947$	−11.9236	−	11.9236i	−0.387464	−	0.387464i	−0.873782	+	0.486318i	$0.838340\pi$
$948$	1.09743	+	6.92891i	0.0356429	+	0.225040i
$949$	−19.7386	−	6.41347i	−0.640743	−	0.208190i
$950$	3.44997	+	0.229736i	0.111932	+	0.00745361i
$951$	−2.46218	+	1.78888i	−0.0798417	+	0.0580084i
$952$	−2.76013	+	17.4268i	−0.0894564	+	0.564805i
$953$	4.71508	−	9.25387i	0.152736	−	0.299762i	−0.801942	−	0.597402i	$-0.796200\pi$
$953$	4.71508	−	9.25387i	0.152736	−	0.299762i	0.954678	+	0.297640i	$0.0961996\pi$
$954$	−0.208234	+	0.640879i	−0.00674183	+	0.0207492i
$955$	−0.675234	+	1.48821i	−0.0218501	+	0.0481573i
$956$			21.2231i			0.686406i
$957$	−10.9164	+	5.76784i	−0.352878	+	0.186448i
$958$	−24.4915	+	24.4915i	−0.791283	+	0.791283i
$959$	−31.7281	−	23.0518i	−1.02456	−	0.744383i
$960$	2.32776	+	2.91644i	0.0751281	+	0.0941278i
$961$	0.581191	+	1.78872i	0.0187481	+	0.0577007i
$962$	19.9998	+	3.16765i	0.644819	+	0.102129i
$963$	1.11708	+	0.176929i	0.0359975	+	0.00570145i
$964$	3.90743	+	12.0258i	0.125850	+	0.387326i
$965$	−22.9584	−	28.7645i	−0.739056	−	0.925961i
$966$	−24.6554	−	17.9132i	−0.793275	−	0.576348i
$967$	−20.8838	+	20.8838i	−0.671577	+	0.671577i	−0.958080	−	0.286502i	$-0.907507\pi$
$967$	−20.8838	+	20.8838i	−0.671577	+	0.671577i	0.286502	+	0.958080i	$0.407507\pi$
$968$	10.9109	+	1.39759i	0.350688	+	0.0449202i
$969$		−	6.19325i		−	0.198956i
$970$	13.9475	−	30.7403i	0.447829	−	0.987010i
$971$	−4.09100	+	12.5908i	−0.131286	+	0.404058i	−0.994994	−	0.0999353i	$-0.968136\pi$
$971$	−4.09100	+	12.5908i	−0.131286	+	0.404058i	0.863708	+	0.503993i	$0.168136\pi$
$972$	−1.01322	+	1.98855i	−0.0324990	+	0.0637829i
$973$	4.49455	−	28.3775i	0.144089	−	0.909740i
$974$	25.7022	−	18.6738i	0.823552	−	0.598346i
$975$	33.9612	+	38.8069i	1.08763	+	1.24281i
$976$	−9.65062	−	3.13568i	−0.308909	−	0.100371i
$977$	4.12077	+	26.0175i	0.131835	+	0.832374i	0.961639	+	0.274319i	$0.0884523\pi$
$977$	4.12077	+	26.0175i	0.131835	+	0.832374i	−0.829804	+	0.558055i	$0.811548\pi$
$978$	4.83559	+	4.83559i	0.154625	+	0.154625i
$979$	−4.79722	+	15.5456i	−0.153320	+	0.496840i
$980$	−1.71168	−	8.34224i	−0.0546775	−	0.266483i
$981$	0.799042	−	1.09979i	0.0255114	−	0.0351135i
$982$	−8.34590	+	4.25245i	−0.266328	+	0.135701i
$983$	50.7333	+	25.8499i	1.61814	+	0.824483i	0.999239	+	0.0390141i	$0.0124217\pi$
$983$	50.7333	+	25.8499i	1.61814	+	0.824483i	0.618901	+	0.785469i	$0.287578\pi$
$984$	−1.28262	−	1.76537i	−0.0408884	−	0.0562780i
$985$	27.1368	−	1.22996i	0.864651	−	0.0391899i
$986$	−11.3860	+	3.69953i	−0.362604	+	0.117817i
$987$	4.39086	+	8.61755i	0.139763	+	0.274300i
$988$	4.22128	−	0.668585i	0.134297	−	0.0212705i
$989$	−34.4708			−1.09611
$990$	1.59294	−	0.0959063i	0.0506270	−	0.00304810i
$991$	−15.2937			−0.485820			−0.242910	−	0.970049i	$-0.578102\pi$
$991$	−15.2937			−0.485820			−0.242910	+	0.970049i	$0.578102\pi$
$992$	−5.66358	+	0.897023i	−0.179819	+	0.0284805i
$993$	15.4064	+	30.2368i	0.488908	+	0.959536i
$994$	6.13482	−	1.99332i	0.194585	−	0.0632244i
$995$	−21.0785	+	23.0800i	−0.668233	+	0.731684i
$996$	5.92368	+	8.15325i	0.187699	+	0.258346i
$997$	−5.57042	−	2.83827i	−0.176417	−	0.0898889i	0.363552	−	0.931574i	$-0.381564\pi$
$997$	−5.57042	−	2.83827i	−0.176417	−	0.0898889i	−0.539969	+	0.841685i	$0.681564\pi$
$998$	−33.5733	+	17.1065i	−1.06275	+	0.541496i
$999$	−10.3326	+	14.2216i	−0.326909	+	0.449952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.7.5	✓	48
3.2	odd	2		990.2.bh.c.667.3		48
4.3	odd	2		880.2.cm.c.337.4		48
5.2	odd	4		550.2.bh.b.293.5		48
5.3	odd	4	inner	110.2.k.a.73.2	yes	48
5.4	even	2		550.2.bh.b.7.2		48
11.8	odd	10	inner	110.2.k.a.107.2	yes	48
15.8	even	4		990.2.bh.c.73.5		48
20.3	even	4		880.2.cm.c.513.3		48
33.8	even	10		990.2.bh.c.217.5		48
44.19	even	10		880.2.cm.c.657.3		48
55.8	even	20	inner	110.2.k.a.63.5	yes	48
55.19	odd	10		550.2.bh.b.107.5		48
55.52	even	20		550.2.bh.b.393.2		48
165.8	odd	20		990.2.bh.c.613.3		48
220.63	odd	20		880.2.cm.c.833.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.5	✓	48	1.1	even	1	trivial
110.2.k.a.63.5	yes	48	55.8	even	20	inner
110.2.k.a.73.2	yes	48	5.3	odd	4	inner
110.2.k.a.107.2	yes	48	11.8	odd	10	inner
550.2.bh.b.7.2		48	5.4	even	2
550.2.bh.b.107.5		48	55.19	odd	10
550.2.bh.b.293.5		48	5.2	odd	4
550.2.bh.b.393.2		48	55.52	even	20
880.2.cm.c.337.4		48	4.3	odd	2
880.2.cm.c.513.3		48	20.3	even	4
880.2.cm.c.657.3		48	44.19	even	10
880.2.cm.c.833.4		48	220.63	odd	20
990.2.bh.c.73.5		48	15.8	even	4
990.2.bh.c.217.5		48	33.8	even	10
990.2.bh.c.613.3		48	165.8	odd	20
990.2.bh.c.667.3		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(-0.757609 - 1.48689i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.65111 - 1.50793i) q^{5} +(-0.980883 - 1.35007i) q^{6} +(2.92930 + 1.49255i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.126480 - 0.174085i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(-0.757609 - 1.48689i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.65111 - 1.50793i) q^{5} +(-0.980883 - 1.35007i) q^{6} +(2.92930 + 1.49255i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.126480 - 0.174085i) q^{9} +(-1.86667 - 1.23107i) q^{10} +(-3.16916 - 0.977970i) q^{11} +(-1.18000 - 1.18000i) q^{12} +(0.966831 + 6.10433i) q^{13} +(3.12672 + 1.01593i) q^{14} +(-0.991229 + 3.59744i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.839551 + 5.30072i) q^{17} +(0.0976902 - 0.191728i) q^{18} +(0.213692 - 0.657676i) q^{19} +(-2.03627 - 0.923903i) q^{20} -5.48632i q^{21} +(-3.28313 - 0.470163i) q^{22} +(3.92788 - 3.92788i) q^{23} +(-1.35007 - 0.980883i) q^{24} +(0.452316 + 4.97950i) q^{25} +(1.90986 + 5.87793i) q^{26} +(-5.29937 - 0.839337i) q^{27} +(3.24715 + 0.514298i) q^{28} +(0.689338 + 2.12156i) q^{29} +(-0.416262 + 3.70821i) q^{30} +(-4.63905 - 3.37046i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.946850 + 5.45312i) q^{33} +5.36679i q^{34} +(-2.58593 - 6.88153i) q^{35} +(0.0664946 - 0.204649i) q^{36} +(1.48742 - 2.91923i) q^{37} +(0.108178 - 0.683008i) q^{38} +(8.34400 - 6.06227i) q^{39} +(-2.15573 - 0.593985i) q^{40} +(1.24362 + 0.404076i) q^{41} +(-0.858249 - 5.41877i) q^{42} +(-4.38796 - 4.38796i) q^{43} +(-3.31626 + 0.0492198i) q^{44} +(-0.471340 + 0.0967105i) q^{45} +(3.26507 - 4.49398i) q^{46} +(-1.57073 + 0.800329i) q^{47} +(-1.48689 - 0.757609i) q^{48} +(2.23857 + 3.08113i) q^{49} +(1.22571 + 4.84744i) q^{50} +(8.51765 - 2.76755i) q^{51} +(2.80585 + 5.50680i) q^{52} +(-3.09304 + 0.489889i) q^{53} -5.36542 q^{54} +(3.75792 + 6.39359i) q^{55} +3.28763 q^{56} +(-1.13979 + 0.180525i) q^{57} +(1.01274 + 1.98761i) q^{58} +(0.820602 - 0.266630i) q^{59} +(0.168955 + 3.72767i) q^{60} +(-5.96441 - 8.20931i) q^{61} +(-5.10919 - 2.60326i) q^{62} +(0.630329 - 0.321169i) q^{63} +(0.587785 - 0.809017i) q^{64} +(7.60854 - 11.5368i) q^{65} +(1.78825 + 5.23786i) q^{66} +(9.05603 + 9.05603i) q^{67} +(0.839551 + 5.30072i) q^{68} +(-8.81614 - 2.86454i) q^{69} +(-3.63060 - 6.39227i) q^{70} +(1.58734 - 1.15327i) q^{71} +(0.0336617 - 0.212532i) q^{72} +(-1.52454 + 2.99208i) q^{73} +(1.01244 - 3.11597i) q^{74} +(7.06130 - 4.44506i) q^{75} -0.691521i q^{76} +(-7.82374 - 7.59490i) q^{77} +(7.29292 - 7.29292i) q^{78} +(-3.40098 - 2.47096i) q^{79} +(-2.22211 - 0.249441i) q^{80} +(2.56736 + 7.90152i) q^{81} +(1.29152 + 0.204556i) q^{82} +(-5.96478 - 0.944728i) q^{83} +(-1.69537 - 5.21780i) q^{84} +(9.37928 - 7.48608i) q^{85} +(-5.02037 - 3.64751i) q^{86} +(2.63229 - 2.63229i) q^{87} +(-3.26773 + 0.567391i) q^{88} -4.90528i q^{89} +(-0.450408 + 0.169254i) q^{90} +(-6.27889 + 19.3244i) q^{91} +(2.52186 - 4.94942i) q^{92} +(-1.49693 + 9.45125i) q^{93} +(-1.42620 + 1.03619i) q^{94} +(-1.34456 + 0.763663i) q^{95} +(-1.58710 - 0.515681i) q^{96} +(2.36159 + 14.9105i) q^{97} +(2.69301 + 2.69301i) q^{98} +(-0.571086 + 0.428010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

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