LMFDB - Embedded newform 57.2.j.b.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (of order $18$, 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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	57.53
Dual form			57.2.j.b.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.886259 + 0.322572i) q^{2} +(-0.292097 + 1.70724i) q^{3} +(-0.850687 - 0.713811i) q^{4} +(0.485824 + 0.578982i) q^{5} +(-0.809582 + 1.41884i) q^{6} +(1.38278 - 2.39504i) q^{7} +(-1.46681 - 2.54059i) q^{8} +(-2.82936 - 0.997362i) q^{9} +O(q^{10})$	\(q+(0.886259 + 0.322572i) q^{2} +(-0.292097 + 1.70724i) q^{3} +(-0.850687 - 0.713811i) q^{4} +(0.485824 + 0.578982i) q^{5} +(-0.809582 + 1.41884i) q^{6} +(1.38278 - 2.39504i) q^{7} +(-1.46681 - 2.54059i) q^{8} +(-2.82936 - 0.997362i) q^{9} +(0.243802 + 0.669841i) q^{10} +(-2.28018 + 1.31646i) q^{11} +(1.46713 - 1.24383i) q^{12} +(1.90254 + 0.335470i) q^{13} +(1.99807 - 1.67658i) q^{14} +(-1.13037 + 0.660300i) q^{15} +(-0.0947805 - 0.537527i) q^{16} +(0.220652 - 0.606237i) q^{17} +(-2.18582 - 1.79659i) q^{18} +(-1.94082 + 3.90298i) q^{19} -0.839319i q^{20} +(3.68501 + 3.06032i) q^{21} +(-2.44549 + 0.431205i) q^{22} +(-5.61638 + 6.69334i) q^{23} +(4.76586 - 1.76210i) q^{24} +(0.769045 - 4.36147i) q^{25} +(1.57793 + 0.911019i) q^{26} +(2.52919 - 4.53908i) q^{27} +(-2.88591 + 1.05039i) q^{28} +(8.33804 - 3.03480i) q^{29} +(-1.21480 + 0.220571i) q^{30} +(2.10245 + 1.21385i) q^{31} +(-0.929445 + 5.27114i) q^{32} +(-1.58149 - 4.27736i) q^{33} +(0.391110 - 0.466106i) q^{34} +(2.05847 - 0.362964i) q^{35} +(1.69497 + 2.86807i) q^{36} +6.09943i q^{37} +(-2.97906 + 2.83300i) q^{38} +(-1.12846 + 3.15011i) q^{39} +(0.758345 - 2.08354i) q^{40} +(-0.930968 - 5.27978i) q^{41} +(2.27870 + 3.90091i) q^{42} +(-1.12968 + 0.947914i) q^{43} +(2.87943 + 0.507721i) q^{44} +(-0.797115 - 2.12269i) q^{45} +(-7.13664 + 4.12034i) q^{46} +(-3.48030 - 9.56204i) q^{47} +(0.945374 - 0.00480320i) q^{48} +(-0.324139 - 0.561425i) q^{49} +(2.08846 - 3.61732i) q^{50} +(0.970541 + 0.553787i) q^{51} +(-1.37901 - 1.64344i) q^{52} +(-4.16382 - 3.49386i) q^{53} +(3.70569 - 3.20695i) q^{54} +(-1.86998 - 0.680616i) q^{55} -8.11308 q^{56} +(-6.09642 - 4.45349i) q^{57} +8.36860 q^{58} +(7.06560 + 2.57167i) q^{59} +(1.43292 + 0.245163i) q^{60} +(-1.37444 - 1.15329i) q^{61} +(1.47176 + 1.75398i) q^{62} +(-6.30109 + 5.39729i) q^{63} +(-3.06987 + 5.31717i) q^{64} +(0.730070 + 1.26452i) q^{65} +(-0.0218522 - 4.30099i) q^{66} +(-3.35090 - 9.20653i) q^{67} +(-0.620444 + 0.358214i) q^{68} +(-9.78662 - 11.5436i) q^{69} +(1.94142 + 0.342325i) q^{70} +(-2.08521 + 1.74970i) q^{71} +(1.61624 + 8.65118i) q^{72} +(0.952144 + 5.39988i) q^{73} +(-1.96750 + 5.40567i) q^{74} +(7.22146 + 2.58692i) q^{75} +(4.43702 - 1.93484i) q^{76} +7.28150i q^{77} +(-2.01624 + 2.42781i) q^{78} +(9.22088 - 1.62589i) q^{79} +(0.265172 - 0.316020i) q^{80} +(7.01054 + 5.64379i) q^{81} +(0.878031 - 4.97956i) q^{82} +(7.02840 + 4.05785i) q^{83} +(-0.950298 - 5.23377i) q^{84} +(0.458198 - 0.166771i) q^{85} +(-1.30696 + 0.475694i) q^{86} +(2.74562 + 15.1215i) q^{87} +(6.68919 + 3.86200i) q^{88} +(0.233188 - 1.32248i) q^{89} +(-0.0217297 - 2.13838i) q^{90} +(3.43425 - 4.09278i) q^{91} +(9.55556 - 1.68490i) q^{92} +(-2.68646 + 3.23483i) q^{93} -9.59708i q^{94} +(-3.20265 + 0.772462i) q^{95} +(-8.72763 - 3.12647i) q^{96} +(4.64863 - 12.7720i) q^{97} +(-0.106171 - 0.602125i) q^{98} +(7.76444 - 1.45058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.886259	+	0.322572i	0.626679	+	0.228093i	0.635785	−	0.771866i	$-0.280676\pi$
$2$	0.886259	+	0.322572i	0.626679	+	0.228093i	−0.00910593	+	0.999959i	$0.502899\pi$
$3$	−0.292097	+	1.70724i	−0.168642	+	0.985677i
$3$	−0.292097	+	1.70724i	−0.168642	+	0.985677i
$4$	−0.850687	−	0.713811i	−0.425344	−	0.356906i
$5$	0.485824	+	0.578982i	0.217267	+	0.258929i	0.863659	−	0.504077i	$-0.168167\pi$
$5$	0.485824	+	0.578982i	0.217267	+	0.258929i	−0.646392	+	0.763006i	$0.723723\pi$
$6$	−0.809582	+	1.41884i	−0.330511	+	0.579238i
$7$	1.38278	−	2.39504i	0.522640	−	0.905239i	−0.477013	−	0.878896i	$-0.658280\pi$
$7$	1.38278	−	2.39504i	0.522640	−	0.905239i	0.999653	−	0.0263430i	$-0.00838621\pi$
$8$	−1.46681	−	2.54059i	−0.518596	−	0.898234i
$9$	−2.82936	−	0.997362i	−0.943119	−	0.332454i
$10$	0.243802	+	0.669841i	0.0770971	+	0.211822i
$11$	−2.28018	+	1.31646i	−0.687501	+	0.396929i	−0.802675	−	0.596417i	$-0.796591\pi$
$11$	−2.28018	+	1.31646i	−0.687501	+	0.396929i	0.115174	+	0.993345i	$0.463257\pi$
$12$	1.46713	−	1.24383i	0.423525	−	0.359062i
$13$	1.90254	+	0.335470i	0.527670	+	0.0930425i	0.431136	−	0.902287i	$-0.358113\pi$
$13$	1.90254	+	0.335470i	0.527670	+	0.0930425i	0.0965347	+	0.995330i	$0.469224\pi$
$14$	1.99807	−	1.67658i	0.534006	−	0.448085i
$15$	−1.13037	+	0.660300i	−0.291861	+	0.170489i
$16$	−0.0947805	−	0.537527i	−0.0236951	−	0.134382i
$17$	0.220652	−	0.606237i	0.0535160	−	0.147034i	−0.910054	−	0.414489i	$-0.863960\pi$
$17$	0.220652	−	0.606237i	0.0535160	−	0.147034i	0.963570	+	0.267455i	$0.0861826\pi$
$18$	−2.18582	−	1.79659i	−0.515203	−	0.423461i
$19$	−1.94082	+	3.90298i	−0.445254	+	0.895404i
$19$	−1.94082	+	3.90298i	−0.445254	+	0.895404i
$20$		−	0.839319i		−	0.187678i
$21$	3.68501	+	3.06032i	0.804135	+	0.667816i
$22$	−2.44549	+	0.431205i	−0.521379	+	0.0919332i
$23$	−5.61638	+	6.69334i	−1.17110	+	1.39566i	−0.269542	+	0.962989i	$0.586872\pi$
$23$	−5.61638	+	6.69334i	−1.17110	+	1.39566i	−0.901553	+	0.432668i	$0.857572\pi$
$24$	4.76586	−	1.76210i	0.972826	−	0.359688i
$25$	0.769045	−	4.36147i	0.153809	−	0.872294i
$26$	1.57793	+	0.911019i	0.309458	+	0.178666i
$27$	2.52919	−	4.53908i	0.486742	−	0.873546i
$28$	−2.88591	+	1.05039i	−0.545387	+	0.198504i
$29$	8.33804	−	3.03480i	1.54834	−	0.563548i	0.580309	−	0.814397i	$-0.302932\pi$
$29$	8.33804	−	3.03480i	1.54834	−	0.563548i	0.968026	+	0.250849i	$0.0807096\pi$
$30$	−1.21480	+	0.220571i	−0.221790	+	0.0402706i
$31$	2.10245	+	1.21385i	0.377611	+	0.218014i	0.676778	−	0.736187i	$-0.263375\pi$
$31$	2.10245	+	1.21385i	0.377611	+	0.218014i	−0.299167	+	0.954201i	$0.596709\pi$
$32$	−0.929445	+	5.27114i	−0.164304	+	0.931815i
$33$	−1.58149	−	4.27736i	−0.275302	−	0.744593i
$34$	0.391110	−	0.466106i	0.0670747	−	0.0799366i
$35$	2.05847	−	0.362964i	0.347945	−	0.0613521i
$36$	1.69497	+	2.86807i	0.282495	+	0.478012i
$37$			6.09943i			1.00274i	0.865233	+	0.501370i	$0.167171\pi$
$37$			6.09943i			1.00274i	−0.865233	+	0.501370i	$0.832829\pi$
$38$	−2.97906	+	2.83300i	−0.483267	+	0.459573i
$39$	−1.12846	+	3.15011i	−0.180698	+	0.504422i
$40$	0.758345	−	2.08354i	0.119905	−	0.329436i
$41$	−0.930968	−	5.27978i	−0.145393	−	0.824564i	−0.967051	−	0.254583i	$-0.918062\pi$
$41$	−0.930968	−	5.27978i	−0.145393	−	0.824564i	0.821658	−	0.569981i	$-0.193049\pi$
$42$	2.27870	+	3.90091i	0.351611	+	0.601924i
$43$	−1.12968	+	0.947914i	−0.172275	+	0.144556i	−0.724848	−	0.688908i	$-0.758090\pi$
$43$	−1.12968	+	0.947914i	−0.172275	+	0.144556i	0.552574	+	0.833464i	$0.313646\pi$
$44$	2.87943	+	0.507721i	0.434090	+	0.0765418i
$45$	−0.797115	−	2.12269i	−0.118827	−	0.316432i
$46$	−7.13664	+	4.12034i	−1.05224	+	0.607511i
$47$	−3.48030	−	9.56204i	−0.507653	−	1.39477i	−0.883651	−	0.468146i	$-0.844922\pi$
$47$	−3.48030	−	9.56204i	−0.507653	−	1.39477i	0.375998	−	0.926621i	$-0.377300\pi$
$48$	0.945374	−	0.00480320i	0.136453	−	0.000693282i
$49$	−0.324139	−	0.561425i	−0.0463055	−	0.0802035i
$50$	2.08846	−	3.61732i	0.295353	−	0.511566i
$51$	0.970541	+	0.553787i	0.135903	+	0.0775457i
$52$	−1.37901	−	1.64344i	−0.191234	−	0.227904i
$53$	−4.16382	−	3.49386i	−0.571945	−	0.479919i	0.310346	−	0.950624i	$-0.399555\pi$
$53$	−4.16382	−	3.49386i	−0.571945	−	0.479919i	−0.882291	+	0.470705i	$0.844000\pi$
$54$	3.70569	−	3.20695i	0.504281	−	0.436411i
$55$	−1.86998	−	0.680616i	−0.252148	−	0.0917742i
$56$	−8.11308			−1.08416
$57$	−6.09642	−	4.45349i	−0.807491	−	0.589880i
$58$	8.36860			1.09885
$59$	7.06560	+	2.57167i	0.919863	+	0.334803i	0.758184	−	0.652041i	$-0.226087\pi$
$59$	7.06560	+	2.57167i	0.919863	+	0.334803i	0.161679	+	0.986843i	$0.448309\pi$
$60$	1.43292	+	0.245163i	0.184989	+	0.0316504i
$61$	−1.37444	−	1.15329i	−0.175979	−	0.147664i	0.550544	−	0.834806i	$-0.314420\pi$
$61$	−1.37444	−	1.15329i	−0.175979	−	0.147664i	−0.726523	+	0.687142i	$0.758865\pi$
$62$	1.47176	+	1.75398i	0.186914	+	0.222755i
$63$	−6.30109	+	5.39729i	−0.793863	+	0.679995i
$64$	−3.06987	+	5.31717i	−0.383734	+	0.664646i
$65$	0.730070	+	1.26452i	0.0905540	+	0.156844i
$66$	−0.0218522	−	4.30099i	−0.00268982	−	0.529415i
$67$	−3.35090	−	9.20653i	−0.409378	−	1.12476i	−0.957519	−	0.288371i	$-0.906886\pi$
$67$	−3.35090	−	9.20653i	−0.409378	−	1.12476i	0.548141	−	0.836386i	$-0.315336\pi$
$68$	−0.620444	+	0.358214i	−0.0752399	+	0.0434398i
$69$	−9.78662	−	11.5436i	−1.17817	−	1.38969i
$70$	1.94142	+	0.342325i	0.232044	+	0.0409156i
$71$	−2.08521	+	1.74970i	−0.247469	+	0.207651i	−0.758082	−	0.652160i	$-0.773863\pi$
$71$	−2.08521	+	1.74970i	−0.247469	+	0.207651i	0.510613	+	0.859811i	$0.329419\pi$
$72$	1.61624	+	8.65118i	0.190476	+	1.01955i
$73$	0.952144	+	5.39988i	0.111440	+	0.632008i	0.988451	+	0.151538i	$0.0484226\pi$
$73$	0.952144	+	5.39988i	0.111440	+	0.632008i	−0.877011	+	0.480470i	$0.840466\pi$
$74$	−1.96750	+	5.40567i	−0.228718	+	0.628397i
$75$	7.22146	+	2.58692i	0.833862	+	0.298712i
$76$	4.43702	−	1.93484i	0.508961	−	0.221941i
$77$			7.28150i			0.829804i
$78$	−2.01624	+	2.42781i	−0.228294	+	0.274895i
$79$	9.22088	−	1.62589i	1.03743	−	0.182927i	0.371107	−	0.928590i	$-0.378978\pi$
$79$	9.22088	−	1.62589i	1.03743	−	0.182927i	0.666323	+	0.745663i	$0.267867\pi$
$80$	0.265172	−	0.316020i	0.0296471	−	0.0353321i
$81$	7.01054	+	5.64379i	0.778949	+	0.627088i
$82$	0.878031	−	4.97956i	0.0969622	−	0.549900i
$83$	7.02840	+	4.05785i	0.771467	+	0.445406i	0.833398	−	0.552674i	$-0.186393\pi$
$83$	7.02840	+	4.05785i	0.771467	+	0.445406i	−0.0619310	+	0.998080i	$0.519726\pi$
$84$	−0.950298	−	5.23377i	−0.103686	−	0.571051i
$85$	0.458198	−	0.166771i	0.0496986	−	0.0180888i
$86$	−1.30696	+	0.475694i	−0.140933	+	0.0512954i
$87$	2.74562	+	15.1215i	0.294361	+	1.62120i
$88$	6.68919	+	3.86200i	0.713070	+	0.411691i
$89$	0.233188	−	1.32248i	0.0247179	−	0.140182i	−0.969951	−	0.243299i	$-0.921770\pi$
$89$	0.233188	−	1.32248i	0.0247179	−	0.140182i	0.994669	+	0.103117i	$0.0328815\pi$
$90$	−0.0217297	−	2.13838i	−0.00229051	−	0.225405i
$91$	3.43425	−	4.09278i	0.360008	−	0.429040i
$92$	9.55556	−	1.68490i	0.996236	−	0.175663i
$93$	−2.68646	+	3.23483i	−0.278573	+	0.335436i
$94$		−	9.59708i		−	0.989863i
$95$	−3.20265	+	0.772462i	−0.328585	+	0.0792529i
$96$	−8.72763	−	3.12647i	−0.890760	−	0.319094i
$97$	4.64863	−	12.7720i	0.471997	−	1.29680i	−0.444148	−	0.895953i	$-0.646494\pi$
$97$	4.64863	−	12.7720i	0.471997	−	1.29680i	0.916145	−	0.400847i	$-0.131284\pi$
$98$	−0.106171	−	0.602125i	−0.0107249	−	0.0608239i
$99$	7.76444	−	1.45058i	0.780356	−	0.145789i
$100$	−3.76748	+	3.16129i	−0.376748	+	0.316129i
$101$	−2.06421	−	0.363975i	−0.205396	−	0.0362169i	0.0700033	−	0.997547i	$-0.477699\pi$
$101$	−2.06421	−	0.363975i	−0.205396	−	0.0362169i	−0.275400	+	0.961330i	$0.588810\pi$
$102$	0.681515	+	0.803868i	0.0674800	+	0.0795948i
$103$	−10.4189	+	6.01535i	−1.02660	+	0.592710i	−0.916010	−	0.401155i	$-0.868609\pi$
$103$	−10.4189	+	6.01535i	−1.02660	+	0.592710i	−0.110594	+	0.993866i	$0.535275\pi$
$104$	−1.93838	−	5.32565i	−0.190074	−	0.522223i
$105$	0.0183940	+	3.62033i	0.00179507	+	0.353308i
$106$	−2.56320	−	4.43960i	−0.248960	−	0.431212i
$107$	−3.41283	+	5.91119i	−0.329930	+	0.571456i	−0.982498	−	0.186275i	$-0.940359\pi$
$107$	−3.41283	+	5.91119i	−0.329930	+	0.571456i	0.652567	+	0.757731i	$0.273692\pi$
$108$	−5.39159	+	2.05597i	−0.518806	+	0.197836i
$109$	7.55399	+	9.00250i	0.723541	+	0.862283i	0.994970	−	0.100176i	$-0.0319405\pi$
$109$	7.55399	+	9.00250i	0.723541	+	0.862283i	−0.271429	+	0.962459i	$0.587496\pi$
$110$	−1.43774	−	1.20640i	−0.137083	−	0.115026i
$111$	−10.4132	−	1.78163i	−0.988379	−	0.169105i
$112$	−1.41846	−	0.516276i	−0.134032	−	0.0487835i
$113$	1.98486			0.186720			0.0933599	−	0.995632i	$-0.470239\pi$
$113$	1.98486			0.186720			0.0933599	+	0.995632i	$0.470239\pi$
$114$	−3.96644	−	5.91348i	−0.371491	−	0.553848i
$115$	−6.60389			−0.615816
$116$	−9.25934	−	3.37012i	−0.859708	−	0.312908i
$117$	−5.04839	−	2.84669i	−0.466724	−	0.263176i
$118$	5.43240	+	4.55833i	0.500093	+	0.419628i
$119$	−1.14685	−	1.36676i	−0.105131	−	0.125291i
$120$	3.33559	+	1.90328i	0.304497	+	0.173744i
$121$	−2.03385	+	3.52273i	−0.184895	+	0.320248i
$122$	−0.846091	−	1.46547i	−0.0766015	−	0.132678i
$123$	9.28581	−	0.0471788i	0.837273	−	0.00425397i
$124$	−0.922067	−	2.53336i	−0.0828041	−	0.227502i
$125$	6.17158	−	3.56316i	0.552003	−	0.318699i
$126$	−7.32541	+	2.75084i	−0.652599	+	0.245065i
$127$	−11.1687	−	1.96935i	−0.991065	−	0.174751i	−0.345468	−	0.938430i	$-0.612280\pi$
$127$	−11.1687	−	1.96935i	−0.991065	−	0.174751i	−0.645596	+	0.763679i	$0.723391\pi$
$128$	3.76458	−	3.15885i	0.332745	−	0.279206i
$129$	−1.28834	−	2.20552i	−0.113432	−	0.194185i
$130$	0.239133	+	1.35619i	0.0209733	+	0.118946i
$131$	6.23539	−	17.1316i	0.544789	−	1.49679i	−0.295869	−	0.955228i	$-0.595609\pi$
$131$	6.23539	−	17.1316i	0.544789	−	1.49679i	0.840658	−	0.541566i	$-0.182168\pi$
$132$	−1.70788	+	4.76758i	−0.148652	+	0.414965i
$133$	6.66407	+	10.0453i	0.577848	+	0.871035i
$134$		−	9.24028i		−	0.798238i
$135$	3.85679	−	0.740837i	0.331939	−	0.0637611i
$136$	−1.86385	+	0.328648i	−0.159824	+	0.0281813i
$137$	−5.03788	+	6.00391i	−0.430415	+	0.512949i	−0.937042	−	0.349217i	$-0.886448\pi$
$137$	−5.03788	+	6.00391i	−0.430415	+	0.512949i	0.506627	+	0.862165i	$0.330892\pi$
$138$	−4.94983	−	13.3875i	−0.421358	−	1.13962i
$139$	−0.0146771	+	0.0832380i	−0.00124490	+	0.00706015i	−0.985424	−	0.170117i	$-0.945585\pi$
$139$	−0.0146771	+	0.0832380i	−0.00124490	+	0.00706015i	0.984179	+	0.177177i	$0.0566966\pi$
$140$	−2.01020	−	1.16059i	−0.169893	−	0.0980878i
$141$	17.3413	−	3.14867i	1.46040	−	0.265166i
$142$	−2.41244	+	0.878056i	−0.202447	+	0.0736849i
$143$	−4.77978	+	1.73970i	−0.399705	+	0.145481i
$144$	−0.267941	+	1.61539i	−0.0223284	+	0.134615i
$145$	5.80791	+	3.35320i	0.482321	+	0.278468i
$146$	−0.898002	+	5.09282i	−0.0743192	+	0.421485i
$147$	1.05317	−	0.389393i	0.0868639	−	0.0321166i
$148$	4.35384	−	5.18871i	0.357884	−	0.426509i
$149$	−11.7508	+	2.07199i	−0.962664	+	0.169744i	−0.632826	−	0.774294i	$-0.718105\pi$
$149$	−11.7508	+	2.07199i	−0.962664	+	0.169744i	−0.329838	+	0.944038i	$0.606994\pi$
$150$	5.56561	+	4.62212i	0.454430	+	0.377394i
$151$			2.63924i			0.214778i	0.994217	+	0.107389i	$0.0342491\pi$
$151$			2.63924i			0.214778i	−0.994217	+	0.107389i	$0.965751\pi$
$152$	12.7627	−	0.794111i	1.03519	−	0.0644109i
$153$	−1.22894	+	1.49519i	−0.0993540	+	0.120879i
$154$	−2.34881	+	6.45329i	−0.189272	+	0.520021i
$155$	0.318623	+	1.80700i	0.0255924	+	0.145142i
$156$	3.20855	−	1.87426i	0.256890	−	0.150061i
$157$	−10.0279	+	8.41440i	−0.800313	+	0.671543i	−0.948275	−	0.317451i	$-0.897173\pi$
$157$	−10.0279	+	8.41440i	−0.800313	+	0.671543i	0.147962	+	0.988993i	$0.452729\pi$
$158$	8.69655	+	1.53344i	0.691861	+	0.121994i
$159$	7.18111	−	6.08811i	0.569499	−	0.482818i
$160$	−3.50345	+	2.02272i	−0.276972	+	0.159910i
$161$	8.26461	+	22.7068i	0.651342	+	1.78955i
$162$	4.39262	+	7.26326i	0.345117	+	0.570656i
$163$	−10.9580	−	18.9799i	−0.858299	−	1.48662i	−0.873550	−	0.486734i	$-0.838188\pi$
$163$	−10.9580	−	18.9799i	−0.858299	−	1.48662i	0.0152513	−	0.999884i	$-0.495145\pi$
$164$	−2.97681	+	5.15598i	−0.232450	+	0.402614i
$165$	1.70819	−	2.99370i	0.132983	−	0.233059i
$166$	4.92003	+	5.86346i	0.381868	+	0.455093i
$167$	−0.977437	−	0.820167i	−0.0756363	−	0.0634664i	0.604186	−	0.796844i	$-0.293499\pi$
$167$	−0.977437	−	0.820167i	−0.0756363	−	0.0634664i	−0.679822	+	0.733377i	$0.737943\pi$
$168$	2.36981	−	13.8510i	0.182835	−	1.06863i
$169$	−8.70887	−	3.16977i	−0.669913	−	0.243829i
$170$	0.459878			0.0352710
$171$	9.38395	−	9.10723i	0.717608	−	0.696447i
$172$	1.63764			0.124869
$173$	−2.84010	−	1.03371i	−0.215929	−	0.0785917i	0.231791	−	0.972766i	$-0.425542\pi$
$173$	−2.84010	−	1.03371i	−0.215929	−	0.0785917i	−0.447720	+	0.894174i	$0.647764\pi$
$174$	−2.44445	+	14.2872i	−0.185313	+	1.08311i
$175$	−9.38247	−	7.87283i	−0.709248	−	0.595130i
$176$	0.923751	+	1.10088i	0.0696304	+	0.0829822i
$177$	−6.45431	+	11.3115i	−0.485135	+	0.850226i
$178$	0.633259	−	1.09684i	0.0474647	−	0.0822113i
$179$	6.00020	+	10.3927i	0.448476	+	0.776784i	0.998287	−	0.0585055i	$-0.0186335\pi$
$179$	6.00020	+	10.3927i	0.448476	+	0.776784i	−0.549811	+	0.835289i	$0.685300\pi$
$180$	−0.837106	+	2.37474i	−0.0623942	+	0.177002i
$181$	2.65765	+	7.30183i	0.197542	+	0.542741i	0.998426	−	0.0560773i	$-0.0178593\pi$
$181$	2.65765	+	7.30183i	0.197542	+	0.542741i	−0.800885	+	0.598818i	$0.795637\pi$
$182$	4.36385	−	2.51947i	0.323470	−	0.186756i
$183$	2.37042	−	2.00963i	0.175227	−	0.148556i
$184$	25.2432	+	4.45105i	1.86095	+	0.328136i
$185$	−3.53146	+	2.96325i	−0.259638	+	0.217863i
$186$	−3.42436	+	2.00032i	−0.251086	+	0.146671i
$187$	0.294962	+	1.67281i	0.0215697	+	0.122328i
$188$	−3.86485	+	10.6186i	−0.281873	+	0.774439i
$189$	−7.37396	−	12.3340i	−0.536377	−	0.897168i
$190$	−3.08755	−	0.348484i	−0.223994	−	0.0252817i
$191$		−	1.07540i		−	0.0778132i	−0.999243	−	0.0389066i	$-0.987613\pi$
$191$		−	1.07540i		−	0.0778132i	0.999243	−	0.0389066i	$-0.0123875\pi$
$192$	−8.18100	−	6.79414i	−0.590413	−	0.490325i
$193$	−1.90955	+	0.336705i	−0.137452	+	0.0242366i	−0.241951	−	0.970288i	$-0.577787\pi$
$193$	−1.90955	+	0.336705i	−0.137452	+	0.0242366i	0.104499	+	0.994525i	$0.466676\pi$
$194$	8.23978	−	9.81978i	0.591581	−	0.705019i
$195$	−2.37209	+	0.877045i	−0.169869	+	0.0628065i
$196$	−0.125011	+	0.708971i	−0.00892933	+	0.0506408i
$197$	−13.7608	−	7.94478i	−0.980414	−	0.566042i	−0.0780187	−	0.996952i	$-0.524859\pi$
$197$	−13.7608	−	7.94478i	−0.980414	−	0.566042i	−0.902395	+	0.430910i	$0.858193\pi$
$198$	7.34922	+	1.21900i	0.522286	+	0.0866306i
$199$	−2.60596	+	0.948493i	−0.184732	+	0.0672369i	−0.432730	−	0.901524i	$-0.642450\pi$
$199$	−2.60596	+	0.948493i	−0.184732	+	0.0672369i	0.247998	+	0.968761i	$0.420227\pi$
$200$	−12.2088	+	4.44362i	−0.863289	+	0.314212i
$201$	16.6966	−	3.03161i	1.17769	−	0.213833i
$202$	−1.71201	−	0.988431i	−0.120457	−	0.0695458i
$203$	4.26118	−	24.1664i	0.299076	−	1.69615i
$204$	−0.430328	−	1.16388i	−0.0301290	−	0.0814881i
$205$	2.60462	−	3.10406i	0.181914	−	0.216797i
$206$	−11.1742	+	1.97032i	−0.778545	+	0.137278i
$207$	22.5664	−	13.3363i	1.56847	−	0.926936i
$208$		−	1.05446i		−	0.0731139i
$209$	−0.712715	−	11.4545i	−0.0492996	−	0.792325i
$210$	−1.15151	+	3.21448i	−0.0794621	+	0.221820i
$211$	−4.07334	+	11.1914i	−0.280420	+	0.770449i	0.716892	+	0.697184i	$0.245564\pi$
$211$	−4.07334	+	11.1914i	−0.280420	+	0.770449i	−0.997313	+	0.0732647i	$0.976658\pi$
$212$	1.04815	+	5.94436i	0.0719874	+	0.408261i
$213$	−2.37808	−	4.07105i	−0.162943	−	0.278943i
$214$	−4.93143	+	4.13796i	−0.337105	+	0.282865i
$215$	−1.09765	−	0.193546i	−0.0748592	−	0.0131997i
$216$	−15.2418	+	0.232334i	−1.03707	+	0.0158083i
$217$	5.81444	−	3.35697i	0.394710	−	0.227886i
$218$	3.79084	+	10.4152i	0.256748	+	0.705409i
$219$	−9.49702	+	0.0482519i	−0.641749	+	0.00326056i
$220$	1.10493	+	1.91380i	0.0744946	+	0.129028i
$221$	0.623174	−	1.07937i	0.0419192	−	0.0726062i
$222$	−8.65410	−	4.93799i	−0.580825	−	0.331416i
$223$	4.22862	+	5.03948i	0.283170	+	0.337468i	0.888815	−	0.458266i	$-0.151529\pi$
$223$	4.22862	+	5.03948i	0.283170	+	0.337468i	−0.605645	+	0.795735i	$0.707085\pi$
$224$	11.3394	+	9.51487i	0.757644	+	0.635739i
$225$	−6.52587	+	11.5731i	−0.435058	+	0.771543i
$226$	1.75910	+	0.640260i	0.117013	+	0.0425894i
$227$	18.9131			1.25531			0.627655	−	0.778492i	$-0.284015\pi$
$227$	18.9131			1.25531			0.627655	+	0.778492i	$0.284015\pi$
$228$	2.00720	+	8.14023i	0.132930	+	0.539100i
$229$	9.56916			0.632348			0.316174	−	0.948701i	$-0.397602\pi$
$229$	9.56916			0.632348			0.316174	+	0.948701i	$0.397602\pi$
$230$	−5.85276	−	2.13023i	−0.385919	−	0.140463i
$231$	−12.4313	−	2.12691i	−0.817919	−	0.139940i
$232$	−19.9405	−	16.7321i	−1.30916	−	1.09851i
$233$	−10.9126	−	13.0052i	−0.714910	−	0.851997i	0.279216	−	0.960228i	$-0.409926\pi$
$233$	−10.9126	−	13.0052i	−0.714910	−	0.851997i	−0.994126	+	0.108232i	$0.965481\pi$
$234$	−3.55592	−	4.15137i	−0.232458	−	0.271384i
$235$	3.84544	−	6.66050i	0.250849	−	0.434483i
$236$	−4.17493	−	7.23119i	−0.271765	−	0.470710i
$237$	0.0823954	+	16.2172i	0.00535215	+	1.05342i
$238$	−0.575525	−	1.58124i	−0.0373058	−	0.102497i
$239$	−15.3984	+	8.89028i	−0.996041	+	0.575064i	−0.907074	−	0.420970i	$-0.861690\pi$
$239$	−15.3984	+	8.89028i	−0.996041	+	0.575064i	−0.0889661	+	0.996035i	$0.528356\pi$
$240$	0.462066	+	0.545021i	0.0298262	+	0.0351810i
$241$	−6.54342	−	1.15378i	−0.421499	−	0.0743216i	−0.0411240	−	0.999154i	$-0.513094\pi$
$241$	−6.54342	−	1.15378i	−0.421499	−	0.0743216i	−0.380375	+	0.924832i	$0.624205\pi$
$242$	−2.93885	+	2.46598i	−0.188916	+	0.158519i
$243$	−11.6831	+	10.3202i	−0.749470	+	0.662038i
$244$	0.345986	+	1.96218i	0.0221495	+	0.125616i
$245$	0.167581	−	0.460424i	0.0107063	−	0.0294154i
$246$	8.24485	+	2.95353i	0.525672	+	0.188310i
$247$	−5.00182	+	6.77450i	−0.318258	+	0.431051i
$248$		−	7.12195i		−	0.452244i
$249$	−8.98070	+	10.8139i	−0.569129	+	0.685303i
$250$	6.61899	−	1.16711i	0.418622	−	0.0738143i
$251$	18.5555	−	22.1135i	1.17121	−	1.39579i	0.269751	−	0.962930i	$-0.413059\pi$
$251$	18.5555	−	22.1135i	1.17121	−	1.39579i	0.901459	−	0.432864i	$-0.142497\pi$
$252$	9.21290	−	0.0936191i	0.580358	−	0.00589745i
$253$	3.99483	−	22.6558i	0.251153	−	1.42436i
$254$	−9.26313	−	5.34807i	−0.581220	−	0.335568i
$255$	0.150879	+	0.830969i	0.00944844	+	0.0520373i
$256$	15.8943	−	5.78504i	0.993392	−	0.361565i
$257$	6.67388	−	2.42909i	0.416305	−	0.151523i	−0.125371	−	0.992110i	$-0.540012\pi$
$257$	6.67388	−	2.42909i	0.416305	−	0.151523i	0.541676	+	0.840587i	$0.317790\pi$
$258$	−0.430366	−	2.37025i	−0.0267934	−	0.147565i
$259$	14.6084	+	8.43415i	0.907720	+	0.524073i
$260$	0.281566	−	1.59684i	0.0174620	−	0.0990319i
$261$	−26.6181	+	0.270486i	−1.64762	+	0.0167427i
$262$	11.0523	−	13.1717i	0.682816	−	0.813748i
$263$	1.50286	−	0.264995i	0.0926703	−	0.0163403i	−0.127121	−	0.991887i	$-0.540574\pi$
$263$	1.50286	−	0.264995i	0.0926703	−	0.0163403i	0.219791	+	0.975547i	$0.429462\pi$
$264$	−8.54727	+	10.2920i	−0.526048	+	0.633428i
$265$		−	4.10818i		−	0.252364i
$266$	2.66577	+	11.0523i	0.163449	+	0.677663i
$267$	2.18967	+	0.784401i	0.134006	+	0.0480045i
$268$	−3.72116	+	10.2238i	−0.227306	+	0.624518i
$269$	2.20000	+	12.4768i	0.134136	+	0.760726i	0.975457	+	0.220189i	$0.0706675\pi$
$269$	2.20000	+	12.4768i	0.134136	+	0.760726i	−0.841321	+	0.540536i	$0.818221\pi$
$270$	3.65708	+	0.587517i	0.222563	+	0.0357552i
$271$	17.4285	−	14.6242i	1.05871	−	0.888359i	0.0647232	−	0.997903i	$-0.479384\pi$
$271$	17.4285	−	14.6242i	1.05871	−	0.888359i	0.993982	+	0.109544i	$0.0349391\pi$
$272$	−0.346782	−	0.0611470i	−0.0210267	−	0.00370758i
$273$	5.98424	+	7.05860i	0.362183	+	0.427206i
$274$	−6.40155	+	3.69594i	−0.386732	+	0.223280i
$275$	3.98816	+	10.9574i	0.240495	+	0.660754i
$276$	0.0853859	+	16.8058i	0.00513963	+	1.01159i
$277$	1.84387	+	3.19367i	0.110787	+	0.191889i	0.916088	−	0.400978i	$-0.131329\pi$
$277$	1.84387	+	3.19367i	0.110787	+	0.191889i	−0.805301	+	0.592867i	$0.797996\pi$
$278$	−0.0398579	+	0.0690360i	−0.00239052	+	0.00414050i
$279$	−4.73794	−	5.53132i	−0.283653	−	0.331152i
$280$	−3.94153	−	4.69733i	−0.235551	−	0.280719i
$281$	7.23561	+	6.07140i	0.431640	+	0.362189i	0.832570	−	0.553919i	$-0.186868\pi$
$281$	7.23561	+	6.07140i	0.431640	+	0.362189i	−0.400930	+	0.916109i	$0.631313\pi$
$282$	16.3846	+	2.80328i	0.975686	+	0.166933i
$283$	−15.5216	−	5.64941i	−0.922665	−	0.335823i	−0.163367	−	0.986565i	$-0.552235\pi$
$283$	−15.5216	−	5.64941i	−0.922665	−	0.335823i	−0.759298	+	0.650743i	$0.774458\pi$
$284$	3.02282			0.179371
$285$	−0.383295	−	5.69334i	−0.0227044	−	0.337244i
$286$	−4.79730			−0.283670
$287$	−13.9326	−	5.07105i	−0.822416	−	0.299335i
$288$	7.88697	−	13.9870i	0.464744	−	0.824189i
$289$	12.7039	+	10.6599i	0.747289	+	0.627050i
$290$	4.06567	+	4.84527i	0.238744	+	0.284524i
$291$	20.4471	+	11.6670i	1.19863	+	0.683932i
$292$	3.04452	−	5.27326i	0.178167	−	0.308594i
$293$	12.9655	+	22.4569i	0.757453	+	1.31195i	0.944145	+	0.329529i	$0.106890\pi$
$293$	12.9655	+	22.4569i	0.757453	+	1.31195i	−0.186692	+	0.982418i	$0.559777\pi$
$294$	1.05899	−	0.00538043i	0.0617614	−	0.000313793i
$295$	1.94369	+	5.34024i	0.113166	+	0.310921i
$296$	15.4962	−	8.94671i	0.900696	−	0.520017i
$297$	0.208520	+	13.6795i	0.0120996	+	0.793765i
$298$	−11.0826	−	1.95417i	−0.641999	−	0.113202i
$299$	−12.9308	+	10.8502i	−0.747808	+	0.627485i
$300$	−4.29663	−	7.35542i	−0.248066	−	0.424665i
$301$	0.708196	+	4.01638i	0.0408197	+	0.231500i
$302$	−0.851345	+	2.33905i	−0.0489894	+	0.134597i
$303$	1.22434	−	3.41779i	0.0703367	−	0.196347i
$304$	2.28191	+	0.673314i	0.130876	+	0.0386172i
$305$		−	1.35608i		−	0.0776487i
$306$	−1.57147	+	0.928704i	−0.0898347	+	0.0530905i
$307$	11.7253	−	2.06749i	0.669199	−	0.117998i	0.171281	−	0.985222i	$-0.445209\pi$
$307$	11.7253	−	2.06749i	0.669199	−	0.117998i	0.497917	+	0.867224i	$0.334098\pi$
$308$	5.19761	−	6.19428i	0.296162	−	0.352952i
$309$	−7.22634	−	19.5447i	−0.411092	−	1.11186i
$310$	−0.300505	+	1.70425i	−0.0170675	+	0.0967948i
$311$	11.8340	+	6.83236i	0.671045	+	0.387428i	0.796472	−	0.604675i	$-0.206697\pi$
$311$	11.8340	+	6.83236i	0.671045	+	0.387428i	−0.125428	+	0.992103i	$0.540030\pi$
$312$	9.65838	−	1.75368i	0.546798	−	0.0992823i
$313$	−0.501783	+	0.182634i	−0.0283624	+	0.0103231i	−0.356162	−	0.934424i	$-0.615915\pi$
$313$	−0.501783	+	0.182634i	−0.0283624	+	0.0103231i	0.327800	+	0.944747i	$0.393693\pi$
$314$	−11.6016	+	4.22262i	−0.654714	+	0.238296i
$315$	−6.18616	−	1.02609i	−0.348551	−	0.0578134i
$316$	−9.00467	−	5.19885i	−0.506552	−	0.292458i
$317$	−1.24799	+	7.07772i	−0.0700943	+	0.397525i	0.929494	+	0.368837i	$0.120244\pi$
$317$	−1.24799	+	7.07772i	−0.0700943	+	0.397525i	−0.999588	+	0.0286876i	$0.990867\pi$
$318$	8.32817	−	3.07921i	0.467021	−	0.172674i
$319$	−15.0170	+	17.8966i	−0.840793	+	1.00202i
$320$	−4.56996	+	0.805808i	−0.255469	+	0.0450460i
$321$	−9.09496	−	7.55316i	−0.507631	−	0.421577i
$322$			22.7900i			1.27004i
$323$	1.93788	+	2.03779i	0.107827	+	0.113386i
$324$	−1.93517	−	9.80530i	−0.107510	−	0.544739i
$325$	2.92628	−	8.03990i	0.162321	−	0.445973i
$326$	−3.58928	−	20.3558i	−0.198792	−	1.12740i
$327$	−17.5759	+	10.2669i	−0.971952	+	0.567761i
$328$	−12.0482	+	10.1096i	−0.665251	+	0.558212i
$329$	−27.7139	−	4.88671i	−1.52792	−	0.269413i
$330$	2.47958	−	2.10218i	0.136497	−	0.115721i
$331$	10.8346	−	6.25537i	0.595524	−	0.343826i	−0.171755	−	0.985140i	$-0.554944\pi$
$331$	10.8346	−	6.25537i	0.595524	−	0.343826i	0.767279	+	0.641314i	$0.221610\pi$
$332$	−3.08243	−	8.46890i	−0.169170	−	0.464791i
$333$	6.08334	−	17.2575i	0.333365	−	0.945704i
$334$	−0.601699	−	1.04217i	−0.0329235	−	0.0570252i
$335$	3.70247	−	6.41287i	0.202288	−	0.350373i
$336$	1.29574	−	2.27085i	0.0706882	−	0.123885i
$337$	−10.1355	−	12.0790i	−0.552114	−	0.657984i	0.415744	−	0.909482i	$-0.363521\pi$
$337$	−10.1355	−	12.0790i	−0.552114	−	0.657984i	−0.967858	+	0.251498i	$0.919077\pi$
$338$	−6.69584	−	5.61847i	−0.364205	−	0.305605i
$339$	−0.579772	+	3.38864i	−0.0314889	+	0.184046i
$340$	−0.508826	−	0.185198i	−0.0275950	−	0.0100437i
$341$	−6.39196			−0.346144
$342$	11.2543	−	5.04436i	0.608565	−	0.272768i
$343$	17.5660			0.948476
$344$	4.06529	+	1.47964i	0.219186	+	0.0797770i
$345$	1.92898	−	11.2745i	0.103853	−	0.606996i
$346$	−2.18362	−	1.83227i	−0.117392	−	0.0985036i
$347$	−6.99541	−	8.33680i	−0.375533	−	0.447543i	0.544866	−	0.838523i	$-0.316581\pi$
$347$	−6.99541	−	8.33680i	−0.375533	−	0.447543i	−0.920399	+	0.390980i	$0.872136\pi$
$348$	8.45825	−	14.8235i	0.453410	−	0.794625i
$349$	−15.3337	+	26.5588i	−0.820796	+	1.42166i	0.0842943	+	0.996441i	$0.473136\pi$
$349$	−15.3337	+	26.5588i	−0.820796	+	1.42166i	−0.905090	+	0.425219i	$0.860197\pi$
$350$	−5.77575	−	10.0039i	−0.308727	−	0.534730i
$351$	6.33461	−	7.78732i	0.338116	−	0.415656i
$352$	−4.81997	−	13.2427i	−0.256905	−	0.705841i
$353$	9.45086	−	5.45646i	0.503018	−	0.290418i	−0.226941	−	0.973909i	$-0.572872\pi$
$353$	9.45086	−	5.45646i	0.503018	−	0.290418i	0.729959	+	0.683491i	$0.239539\pi$
$354$	−9.36896	+	7.94296i	−0.497955	+	0.422163i
$355$	−2.02609	−	0.357255i	−0.107534	−	0.0189611i
$356$	−1.14237	+	0.958561i	−0.0605454	+	0.0508036i
$357$	2.66838	−	1.55872i	0.141226	−	0.0824962i
$358$	1.96535	+	11.1461i	0.103872	+	0.589089i
$359$	−0.231280	+	0.635437i	−0.0122065	+	0.0335371i	−0.945646	−	0.325197i	$-0.894569\pi$
$359$	−0.231280	+	0.635437i	−0.0122065	+	0.0335371i	0.933440	+	0.358734i	$0.116792\pi$
$360$	−4.22367	+	5.13873i	−0.222607	+	0.270835i
$361$	−11.4665	−	15.1499i	−0.603498	−	0.797364i
$362$			7.32860i			0.385183i
$363$	−5.42007	−	4.50125i	−0.284480	−	0.236254i
$364$	−5.84295	+	1.03027i	−0.306254	+	0.0540008i
$365$	−2.66386	+	3.17466i	−0.139433	+	0.166170i
$366$	2.74906	−	1.01642i	0.143696	−	0.0531293i
$367$	−0.213597	+	1.21137i	−0.0111497	+	0.0632330i	−0.989875	−	0.141942i	$-0.954665\pi$
$367$	−0.213597	+	1.21137i	−0.0111497	+	0.0632330i	0.978725	+	0.205175i	$0.0657764\pi$
$368$	4.13017	+	2.38455i	0.215300	+	0.124303i
$369$	−2.63181	+	15.8669i	−0.137007	+	0.825999i
$370$	−4.08565	+	1.48706i	−0.212403	+	0.0773083i
$371$	−14.1256	+	5.14128i	−0.733363	+	0.266922i
$372$	4.59439	−	0.834206i	0.238208	−	0.0432516i
$373$	5.13058	+	2.96214i	0.265652	+	0.153374i	0.626910	−	0.779092i	$-0.284319\pi$
$373$	5.13058	+	2.96214i	0.265652	+	0.153374i	−0.361258	+	0.932466i	$0.617653\pi$
$374$	−0.278189	+	1.57769i	−0.0143848	+	0.0815803i
$375$	4.28048	+	11.5772i	0.221043	+	0.597843i
$376$	−19.1883	+	22.8677i	−0.989560	+	1.17931i
$377$	16.8816	−	2.97667i	0.869445	−	0.153307i
$378$	−2.55663	−	13.3098i	−0.131499	−	0.684581i
$379$		−	10.4298i		−	0.535745i	−0.963454	−	0.267872i	$-0.913679\pi$
$379$		−	10.4298i		−	0.535745i	0.963454	−	0.267872i	$-0.0863205\pi$
$380$	3.27585	+	1.62896i	0.168047	+	0.0835641i
$381$	6.62451	−	18.4925i	0.339384	−	0.947399i
$382$	0.346894	−	0.953083i	0.0177486	−	0.0487640i
$383$	2.22181	+	12.6005i	0.113529	+	0.643855i	0.987468	+	0.157820i	$0.0504464\pi$
$383$	2.22181	+	12.6005i	0.113529	+	0.643855i	−0.873939	+	0.486036i	$0.838442\pi$
$384$	4.29331	+	7.34974i	0.219092	+	0.375065i
$385$	−4.21586	+	3.53753i	−0.214860	+	0.180289i
$386$	−1.80097	−	0.317559i	−0.0916668	−	0.0161633i
$387$	4.14168	−	1.55529i	0.210534	−	0.0790598i
$388$	−13.0713	+	7.54673i	−0.663596	+	0.383127i
$389$	−5.42537	−	14.9061i	−0.275077	−	0.755768i	−0.997902	−	0.0647371i	$-0.979379\pi$
$389$	−5.42537	−	14.9061i	−0.275077	−	0.755768i	0.722825	−	0.691031i	$-0.242843\pi$
$390$	−2.38520	+	0.0121186i	−0.120779	+	0.000613647i
$391$	2.81848	+	4.88175i	0.142537	+	0.246881i
$392$	−0.950900	+	1.64701i	−0.0480277	+	0.0831864i
$393$	27.4265	+	15.6494i	1.38348	+	0.789409i
$394$	−9.63283	−	11.4800i	−0.485295	−	0.578352i
$395$	5.42109	+	4.54883i	0.272765	+	0.228877i
$396$	−7.64055	−	4.30836i	−0.383952	−	0.216503i
$397$	17.4496	+	6.35113i	0.875770	+	0.318754i	0.740501	−	0.672055i	$-0.234588\pi$
$397$	17.4496	+	6.35113i	0.875770	+	0.318754i	0.135269	+	0.990809i	$0.456810\pi$
$398$	−2.61552			−0.131104
$399$	−19.0963	+	8.44299i	−0.956010	+	0.422678i
$400$	−2.41730			−0.120865
$401$	30.7150	+	11.1794i	1.53384	+	0.558271i	0.964557	−	0.263874i	$-0.0850002\pi$
$401$	30.7150	+	11.1794i	1.53384	+	0.558271i	0.569279	+	0.822144i	$0.307222\pi$
$402$	15.7754	+	2.69906i	0.786806	+	0.134617i
$403$	3.59279	+	3.01471i	0.178970	+	0.150173i
$404$	1.49618	+	1.78308i	0.0744379	+	0.0887117i
$405$	0.138232	+	6.80087i	0.00686878	+	0.337938i
$406$	11.5719	−	20.0431i	0.574304	−	0.994723i
$407$	−8.02968	−	13.9078i	−0.398017	−	0.689385i
$408$	−0.0166549	−	3.27805i	−0.000824540	−	0.162288i
$409$	6.25333	+	17.1809i	0.309207	+	0.849540i	0.992812	+	0.119687i	$0.0381891\pi$
$409$	6.25333	+	17.1809i	0.309207	+	0.849540i	−0.683605	+	0.729853i	$0.739589\pi$
$410$	3.30965	−	1.91082i	0.163452	−	0.0943689i
$411$	−8.77858	−	10.3546i	−0.433016	−	0.510755i
$412$	13.1570	+	2.31994i	0.648201	+	0.114295i
$413$	15.9294	−	13.3663i	0.783834	−	0.657715i
$414$	24.3016	−	4.54011i	1.19436	−	0.223134i
$415$	1.06514	+	6.04072i	0.0522857	+	0.296527i
$416$	−3.53662	+	9.71678i	−0.173397	+	0.476404i
$417$	−0.137820	−	0.0493710i	−0.00674909	−	0.00241771i
$418$	3.06325	−	10.3816i	0.149829	−	0.507779i
$419$			23.0832i			1.12769i	0.825882	+	0.563843i	$0.190678\pi$
$419$			23.0832i			1.12769i	−0.825882	+	0.563843i	$0.809322\pi$
$420$	2.56859	−	3.09290i	0.125334	−	0.150918i
$421$	−11.4247	+	2.01448i	−0.556804	+	0.0981796i	−0.444967	−	0.895547i	$-0.646785\pi$
$421$	−11.4247	+	2.01448i	−0.556804	+	0.0981796i	−0.111837	+	0.993727i	$0.535674\pi$
$422$	−7.22007	+	8.60454i	−0.351467	+	0.418863i
$423$	0.310193	+	30.5255i	0.0150821	+	1.48420i
$424$	−2.76893	+	15.7034i	−0.134471	+	0.762624i
$425$	−2.47439	−	1.42859i	−0.120026	−	0.0692968i
$426$	−0.794389	−	4.37510i	−0.0384883	−	0.211974i
$427$	−4.66273	+	1.69709i	−0.225645	+	0.0821282i
$428$	7.12272	−	2.59246i	0.344290	−	0.125311i
$429$	−1.57393	−	8.66840i	−0.0759898	−	0.418514i
$430$	−0.910371	−	0.525603i	−0.0439020	−	0.0253468i
$431$	−1.52061	+	8.62379i	−0.0732450	+	0.415393i	0.926034	+	0.377439i	$0.123195\pi$
$431$	−1.52061	+	8.62379i	−0.0732450	+	0.415393i	−0.999279	+	0.0379542i	$0.987916\pi$
$432$	−2.67959	−	0.929290i	−0.128922	−	0.0447105i
$433$	22.4687	−	26.7771i	1.07977	−	1.28683i	0.124142	−	0.992264i	$-0.460382\pi$
$433$	22.4687	−	26.7771i	1.07977	−	1.28683i	0.955633	−	0.294561i	$-0.0951734\pi$
$434$	6.23596	−	1.09957i	0.299335	−	0.0527809i
$435$	−7.42121	+	8.93606i	−0.355820	+	0.428451i
$436$		−	13.0504i		−	0.625002i
$437$	−15.2236	−	34.9111i	−0.728243	−	1.67003i
$438$	−8.43238	−	3.02071i	−0.402915	−	0.144335i
$439$	7.13625	−	19.6067i	0.340595	−	0.935777i	−0.644628	−	0.764497i	$-0.722988\pi$
$439$	7.13625	−	19.6067i	0.340595	−	0.935777i	0.985222	−	0.171280i	$-0.0547902\pi$
$440$	1.01374	+	5.74918i	0.0483279	+	0.274081i
$441$	0.357161	+	1.91176i	0.0170077	+	0.0910360i
$442$	0.900467	−	0.755582i	0.0428309	−	0.0359394i
$443$	3.66884	+	0.646915i	0.174312	+	0.0307359i	0.260123	−	0.965576i	$-0.416237\pi$
$443$	3.66884	+	0.646915i	0.174312	+	0.0307359i	−0.0858110	+	0.996311i	$0.527348\pi$
$444$	7.58664	+	8.94868i	0.360046	+	0.424685i
$445$	0.878979	−	0.507479i	0.0416676	−	0.0240568i
$446$	2.12206	+	5.83032i	0.100483	+	0.276073i
$447$	−0.105002	−	20.6667i	−0.00496643	−	0.977502i
$448$	8.48988	+	14.7049i	0.401109	+	0.694742i
$449$	3.50765	−	6.07543i	0.165536	−	0.286717i	−0.771309	−	0.636461i	$-0.780398\pi$
$449$	3.50765	−	6.07543i	0.165536	−	0.286717i	0.936846	+	0.349743i	$0.113731\pi$
$450$	−9.51678	+	8.15174i	−0.448625	+	0.384277i
$451$	9.07342	+	10.8133i	0.427251	+	0.509178i
$452$	−1.68849	−	1.41681i	−0.0794201	−	0.0666414i
$453$	−4.50583	−	0.770915i	−0.211702	−	0.0362208i
$454$	16.7619	+	6.10085i	0.786677	+	0.286327i
$455$	4.03809			0.189309
$456$	−2.37220	+	22.0209i	−0.111089	+	1.03123i
$457$	−30.3503			−1.41973			−0.709864	−	0.704339i	$-0.751243\pi$
$457$	−30.3503			−1.41973			−0.709864	+	0.704339i	$0.751243\pi$
$458$	8.48075	+	3.08674i	0.396280	+	0.144234i
$459$	−2.19368	−	2.53484i	−0.102392	−	0.118316i
$460$	5.61785	+	4.71393i	0.261933	+	0.219788i
$461$	12.4414	+	14.8271i	0.579453	+	0.690565i	0.973542	−	0.228507i	$-0.0733843\pi$
$461$	12.4414	+	14.8271i	0.579453	+	0.690565i	−0.394089	+	0.919072i	$0.628940\pi$
$462$	−10.3313	−	5.89497i	−0.480654	−	0.274259i
$463$	−6.55643	+	11.3561i	−0.304703	+	0.527761i	−0.977195	−	0.212343i	$-0.931891\pi$
$463$	−6.55643	+	11.3561i	−0.304703	+	0.527761i	0.672492	+	0.740104i	$0.265224\pi$
$464$	−2.42157	−	4.19428i	−0.112418	−	0.194715i
$465$	−3.17806	+	0.0161469i	−0.147379	+	0.000748793i
$466$	−5.47631	−	15.0460i	−0.253685	−	0.696995i
$467$	−31.3996	+	18.1286i	−1.45300	+	0.838891i	−0.998651	−	0.0519317i	$-0.983462\pi$
$467$	−31.3996	+	18.1286i	−1.45300	+	0.838891i	−0.454351	+	0.890823i	$0.650129\pi$
$468$	2.26260	+	6.02524i	0.104589	+	0.278517i
$469$	−26.6836	−	4.70503i	−1.23213	−	0.217258i
$470$	5.55654	−	4.66249i	0.256304	−	0.215065i
$471$	−11.4363	−	19.5779i	−0.526957	−	0.902101i
$472$	−3.83034	−	21.7229i	−0.176306	−	0.999880i
$473$	1.32798	−	3.64860i	0.0610607	−	0.167763i
$474$	−5.15819	+	14.3992i	−0.236924	+	0.661378i
$475$	15.5302	+	11.4664i	0.712572	+	0.526114i
$476$			1.98132i			0.0908135i
$477$	8.29630	+	14.0382i	0.379861	+	0.642766i
$478$	−16.5147	+	2.91199i	−0.755366	+	0.133191i
$479$	7.11537	−	8.47977i	0.325110	−	0.387451i	−0.578589	−	0.815619i	$-0.696397\pi$
$479$	7.11537	−	8.47977i	0.325110	−	0.387451i	0.903699	+	0.428169i	$0.140841\pi$
$480$	−2.42992	−	6.57206i	−0.110910	−	0.299972i
$481$	−2.04617	+	11.6044i	−0.0932975	+	0.529117i
$482$	−5.42698	−	3.13327i	−0.247192	−	0.142717i
$483$	−41.1801	+	7.47709i	−1.87376	+	0.340219i
$484$	4.24473	−	1.54495i	0.192942	−	0.0702252i
$485$	9.65318	−	3.51347i	0.438328	−	0.159538i
$486$	−13.6832	+	5.37770i	−0.620684	+	0.243937i
$487$	−16.7012	−	9.64242i	−0.756802	−	0.436940i	0.0713444	−	0.997452i	$-0.477271\pi$
$487$	−16.7012	−	9.64242i	−0.756802	−	0.436940i	−0.828146	+	0.560512i	$0.810604\pi$
$488$	−0.914001	+	5.18356i	−0.0413749	+	0.234649i
$489$	35.6041	−	13.1641i	1.61007	−	0.595299i
$490$	0.297040	−	0.353998i	0.0134189	−	0.0159920i
$491$	−20.1391	+	3.55106i	−0.908864	+	0.160257i	−0.608488	−	0.793563i	$-0.708224\pi$
$491$	−20.1391	+	3.55106i	−0.908864	+	0.160257i	−0.300377	+	0.953821i	$0.597112\pi$
$492$	−7.93299	−	6.58818i	−0.357647	−	0.297018i
$493$		−	5.72446i		−	0.257817i
$494$	−6.61816	+	4.39051i	−0.297765	+	0.197538i
$495$	4.61201	+	3.79075i	0.207295	+	0.170382i
$496$	0.453206	−	1.24517i	0.0203495	−	0.0559099i
$497$	1.30722	+	7.41360i	0.0586368	+	0.332546i
$498$	−11.4475	+	6.68698i	−0.512974	+	0.299651i
$499$	26.4116	−	22.1619i	1.18234	−	0.992104i	0.182383	−	0.983227i	$-0.441619\pi$
$499$	26.4116	−	22.1619i	1.18234	−	0.992104i	0.999961	−	0.00887695i	$-0.00282566\pi$
$500$	−7.79351	−	1.37421i	−0.348536	−	0.0614564i
$501$	1.68573	−	1.42915i	0.0753129	−	0.0638499i
$502$	23.5781	−	13.6128i	1.05234	−	0.607571i
$503$	−14.2850	−	39.2477i	−0.636936	−	1.74997i	−0.661141	−	0.750262i	$-0.729928\pi$
$503$	−14.2850	−	39.2477i	−0.636936	−	1.74997i	0.0242047	−	0.999707i	$-0.492295\pi$
$504$	22.9548	+	8.09168i	1.02249	+	0.360432i
$505$	−0.792106	−	1.37197i	−0.0352482	−	0.0610517i
$506$	10.8486	−	18.7903i	0.482277	−	0.835329i
$507$	7.95541	−	13.9423i	0.353312	−	0.619199i
$508$	8.09535	+	9.64767i	0.359173	+	0.428046i
$509$	−2.29929	−	1.92934i	−0.101914	−	0.0855163i	0.590407	−	0.807106i	$-0.298967\pi$
$509$	−2.29929	−	1.92934i	−0.101914	−	0.0855163i	−0.692321	+	0.721590i	$0.743412\pi$
$510$	−0.134329	+	0.785123i	−0.00594819	+	0.0347658i
$511$	14.2495	+	5.18640i	0.630361	+	0.229433i
$512$	6.12392			0.270642
$513$	12.8072	+	18.6809i	0.565453	+	0.824781i
$514$	6.69834			0.295451
$515$	−8.54453	−	3.10996i	−0.376517	−	0.137041i
$516$	−0.478349	+	2.79584i	−0.0210581	+	0.123080i
$517$	20.5238	+	17.2215i	0.902635	+	0.757401i
$518$	10.2262	+	12.1871i	0.449313	+	0.535470i
$519$	2.59438	−	4.54680i	0.113881	−	0.199582i
$520$	2.14175	−	3.70962i	0.0939219	−	0.162677i
$521$	−15.2958	−	26.4931i	−0.670121	−	1.16068i	−0.977869	−	0.209216i	$-0.932909\pi$
$521$	−15.2958	−	26.4931i	−0.670121	−	1.16068i	0.307748	−	0.951468i	$-0.400425\pi$
$522$	−23.6778	−	8.34653i	−1.03635	−	0.365317i
$523$	6.27523	+	17.2410i	0.274397	+	0.753898i	0.997972	+	0.0636530i	$0.0202751\pi$
$523$	6.27523	+	17.2410i	0.274397	+	0.753898i	−0.723576	+	0.690245i	$0.757503\pi$
$524$	−17.5331	+	10.1227i	−0.765937	+	0.442214i
$525$	16.1814	−	13.7185i	0.706216	−	0.598726i
$526$	1.41740	+	0.249926i	0.0618016	+	0.0108973i
$527$	1.19979	−	1.00674i	0.0522637	−	0.0438545i
$528$	−2.14930	+	1.25550i	−0.0935363	+	0.0546387i
$529$	−9.26316	−	52.5340i	−0.402746	−	2.28409i
$530$	1.32518	−	3.64091i	0.0575623	−	0.158151i
$531$	−17.4262	−	14.3231i	−0.756234	−	0.621571i
$532$	1.50139	−	13.3023i	0.0650936	−	0.576726i
$533$		−	10.3573i		−	0.448626i
$534$	1.68759	+	1.40151i	0.0730293	+	0.0606492i
$535$	−5.08051	+	0.895830i	−0.219649	+	0.0387301i
$536$	−18.4749	+	22.0175i	−0.797994	+	0.951012i
$537$	−19.4954	+	7.20814i	−0.841290	+	0.311054i
$538$	−2.07490	+	11.7674i	−0.0894554	+	0.507327i
$539$	1.47819	+	0.853434i	0.0636702	+	0.0367600i
$540$	−3.80973	−	2.12280i	−0.163945	−	0.0913506i
$541$	−11.3765	+	4.14071i	−0.489114	+	0.178023i	−0.574791	−	0.818300i	$-0.694917\pi$
$541$	−11.3765	+	4.14071i	−0.489114	+	0.178023i	0.0856773	+	0.996323i	$0.472695\pi$
$542$	20.1635	−	7.33892i	0.866097	−	0.315234i
$543$	−13.2423	+	2.40441i	−0.568281	+	0.103183i
$544$	2.99048	+	1.72655i	0.128216	+	0.0740253i
$545$	−1.54238	+	8.74726i	−0.0660682	+	0.374691i
$546$	3.02668	+	8.18609i	0.129530	+	0.350332i
$547$	−14.0778	+	16.7773i	−0.601923	+	0.717344i	−0.977850	−	0.209305i	$-0.932880\pi$
$547$	−14.0778	+	16.7773i	−0.601923	+	0.717344i	0.375927	+	0.926649i	$0.377324\pi$
$548$	8.57132	−	1.51135i	0.366148	−	0.0645618i
$549$	2.73854	+	4.63390i	0.116878	+	0.197770i
$550$			10.9975i			0.468936i
$551$	−4.33785	+	38.4332i	−0.184799	+	1.63731i
$552$	−14.9725	+	41.7961i	−0.637272	+	1.77896i
$553$	8.85635	−	24.3326i	0.376610	−	1.03473i
$554$	0.603955	+	3.42520i	0.0256596	+	0.145523i
$555$	−4.02746	−	6.89463i	−0.170956	−	0.292661i
$556$	0.0719018	−	0.0603328i	0.00304932	−	0.00255868i
$557$	26.7456	+	4.71596i	1.13325	+	0.199822i	0.708649	−	0.705561i	$-0.249305\pi$
$557$	26.7456	+	4.71596i	1.13325	+	0.199822i	0.424596	+	0.905383i	$0.360416\pi$
$558$	−2.41479	−	6.43051i	−0.102226	−	0.272225i
$559$	−2.46726	+	1.42447i	−0.104354	+	0.0602488i
$560$	−0.390206	−	1.07208i	−0.0164892	−	0.0453037i
$561$	−2.94205	+	0.0149478i	−0.124214	+	0.000631096i
$562$	4.45416	+	7.71484i	0.187887	+	0.325431i
$563$	−0.218964	+	0.379256i	−0.00922822	+	0.0159837i	−0.870603	−	0.491987i	$-0.836271\pi$
$563$	−0.218964	+	0.379256i	−0.00922822	+	0.0159837i	0.861374	+	0.507971i	$0.169604\pi$
$564$	−16.9996	−	9.69989i	−0.715811	−	0.408439i
$565$	0.964292	+	1.14920i	0.0405681	+	0.0483472i
$566$	−11.9338	−	10.0137i	−0.501617	−	0.420906i
$567$	23.2111	−	8.98641i	0.974774	−	0.377394i
$568$	7.50388	+	2.73119i	0.314856	+	0.114598i
$569$	−32.6261			−1.36776			−0.683878	−	0.729596i	$-0.739708\pi$
$569$	−32.6261			−1.36776			−0.683878	+	0.729596i	$0.739708\pi$
$570$	1.49681	−	5.16941i	0.0626945	−	0.216523i
$571$	−22.3986			−0.937353			−0.468676	−	0.883370i	$-0.655269\pi$
$571$	−22.3986			−0.937353			−0.468676	+	0.883370i	$0.655269\pi$
$572$	5.30791	+	1.93192i	0.221935	+	0.0807777i
$573$	1.83597	+	0.314122i	0.0766988	+	0.0131226i
$574$	−10.7121	−	8.98853i	−0.447115	−	0.375174i
$575$	24.8735	+	29.6431i	1.03730	+	1.23620i
$576$	13.9889	−	11.9824i	0.582871	−	0.499267i
$577$	11.7982	−	20.4351i	0.491165	−	0.850723i	−0.508783	−	0.860895i	$-0.669904\pi$
$577$	11.7982	−	20.4351i	0.491165	−	0.850723i	0.999948	+	0.0101715i	$0.00323775\pi$
$578$	7.82039	+	13.5453i	0.325285	+	0.563411i
$579$	−0.0170632	−	3.35842i	−0.000709124	−	0.139571i
$580$	−2.54717	−	6.99828i	−0.105765	−	0.290588i
$581$	19.4374	−	11.2222i	0.806399	−	0.465575i
$582$	14.3579	+	16.9356i	0.595156	+	0.702005i
$583$	14.0938	+	2.48512i	0.583706	+	0.102923i
$584$	12.3223	−	10.3396i	0.509899	−	0.427856i
$585$	−0.804447	−	4.30592i	−0.0332598	−	0.178028i
$586$	4.24683	+	24.0849i	0.175435	+	0.994940i
$587$	−5.00085	+	13.7397i	−0.206407	+	0.567099i	−0.999095	−	0.0425285i	$-0.986459\pi$
$587$	−5.00085	+	13.7397i	−0.206407	+	0.567099i	0.792688	+	0.609627i	$0.208681\pi$
$588$	−1.17387	−	0.420512i	−0.0484096	−	0.0173416i
$589$	−8.81810	+	5.84996i	−0.363343	+	0.241043i
$590$			5.35981i			0.220660i
$591$	17.5832	−	21.1723i	0.723274	−	0.870913i
$592$	3.27861	−	0.578107i	0.134750	−	0.0237601i
$593$	−25.5787	+	30.4835i	−1.05039	+	1.25181i	−0.0835298	+	0.996505i	$0.526619\pi$
$593$	−25.5787	+	30.4835i	−1.05039	+	1.25181i	−0.966861	+	0.255302i	$0.917825\pi$
$594$	−4.22782	+	12.1908i	−0.173469	+	0.500196i
$595$	0.234164	−	1.32801i	0.00959978	−	0.0544431i
$596$	11.4753	+	6.62525i	0.470045	+	0.271381i
$597$	−0.858114	−	4.72607i	−0.0351203	−	0.193425i
$598$	−14.9600	+	5.44500i	−0.611761	+	0.222663i
$599$	38.7502	−	14.1039i	1.58329	−	0.576270i	0.607374	−	0.794416i	$-0.292223\pi$
$599$	38.7502	−	14.1039i	1.58329	−	0.576270i	0.975916	+	0.218146i	$0.0700008\pi$
$600$	−4.02020	−	22.1413i	−0.164124	−	0.903914i
$601$	−33.4472	−	19.3108i	−1.36434	−	0.787703i	−0.374143	−	0.927371i	$-0.622063\pi$
$601$	−33.4472	−	19.3108i	−1.36434	−	0.787703i	−0.990198	+	0.139669i	$0.955396\pi$
$602$	−0.667926	+	3.78800i	−0.0272226	+	0.154387i
$603$	0.298660	+	29.3907i	0.0121624	+	1.19688i
$604$	1.88392	−	2.24517i	0.0766556	−	0.0913546i
$605$	−3.02769	+	0.533863i	−0.123093	+	0.0217046i
$606$	2.18757	−	2.63410i	0.0888638	−	0.107003i
$607$			14.1262i			0.573366i	0.958026	+	0.286683i	$0.0925526\pi$
$607$			14.1262i			0.573366i	−0.958026	+	0.286683i	$0.907447\pi$
$608$	−18.7693	−	13.8579i	−0.761194	−	0.562013i
$609$	40.0132	+	14.3338i	1.62142	+	0.580835i
$610$	0.437432	−	1.20183i	0.0177111	−	0.0486608i
$611$	−3.41364	−	19.3597i	−0.138101	−	0.783210i
$612$	2.11273	−	0.394707i	0.0854020	−	0.0159551i
$613$	−3.94393	+	3.30935i	−0.159294	+	0.133663i	−0.718951	−	0.695061i	$-0.755377\pi$
$613$	−3.94393	+	3.30935i	−0.159294	+	0.133663i	0.559657	+	0.828724i	$0.310933\pi$
$614$	11.0586	+	1.94992i	0.446287	+	0.0786925i
$615$	4.53858	+	5.35340i	0.183013	+	0.215870i
$616$	18.4993	−	10.6806i	0.745358	−	0.430333i
$617$	0.607820	+	1.66997i	0.0244699	+	0.0672305i	0.951326	−	0.308186i	$-0.0997219\pi$
$617$	0.607820	+	1.66997i	0.0244699	+	0.0672305i	−0.926856	+	0.375416i	$0.877500\pi$
$618$	−0.0998499	−	19.6526i	−0.00401655	−	0.790545i
$619$	11.8880	+	20.5906i	0.477819	+	0.827606i	0.999677	−	0.0254261i	$-0.00809425\pi$
$619$	11.8880	+	20.5906i	0.477819	+	0.827606i	−0.521858	+	0.853032i	$0.674761\pi$
$620$	1.01881	−	1.76463i	0.0409163	−	0.0708692i
$621$	16.1767	+	42.4219i	0.649148	+	1.70233i
$622$	8.28406	+	9.87256i	0.332161	+	0.395853i
$623$	−2.84493	−	2.38718i	−0.113980	−	0.0956405i
$624$	1.80023	+	0.308006i	0.0720667	+	0.0123301i
$625$	−15.7470	−	5.73145i	−0.629881	−	0.229258i
$626$	−0.503622			−0.0201288
$627$	19.7638	+	2.12905i	0.789291	+	0.0850262i
$628$	14.5369			0.580085
$629$	3.69770	+	1.34585i	0.147437	+	0.0536627i
$630$	−5.15155	−	2.90486i	−0.205243	−	0.115732i
$631$	21.9849	+	18.4475i	0.875205	+	0.734385i	0.965188	−	0.261559i	$-0.0842365\pi$
$631$	21.9849	+	18.4475i	0.875205	+	0.734385i	−0.0899821	+	0.995943i	$0.528681\pi$
$632$	−17.6560	−	21.0416i	−0.702318	−	0.836990i
$633$	−17.9167	−	10.2232i	−0.712123	−	0.406334i
$634$	−3.38912	+	5.87013i	−0.134599	+	0.233132i
$635$	−4.28582	−	7.42326i	−0.170078	−	0.294583i
$636$	−10.4546	+	0.0531173i	−0.414553	+	0.00210624i
$637$	−0.428347	−	1.17687i	−0.0169717	−	0.0466294i
$638$	−19.0819	+	11.0170i	−0.755461	+	0.436166i
$639$	7.64489	−	2.87082i	0.302427	−	0.113568i
$640$	3.65784	+	0.644976i	0.144589	+	0.0254949i
$641$	23.9818	−	20.1231i	0.947225	−	0.794816i	−0.0316033	−	0.999500i	$-0.510061\pi$
$641$	23.9818	−	20.1231i	0.947225	−	0.794816i	0.978828	+	0.204685i	$0.0656169\pi$
$642$	−5.62405	−	9.62783i	−0.221963	−	0.379980i
$643$	−2.95925	−	16.7827i	−0.116701	−	0.661846i	−0.985894	−	0.167372i	$-0.946472\pi$
$643$	−2.95925	−	16.7827i	−0.116701	−	0.661846i	0.869192	−	0.494474i	$-0.164639\pi$
$644$	9.17779	−	25.2158i	0.361656	−	0.993640i
$645$	0.651050	−	1.81742i	0.0256351	−	0.0715610i
$646$	1.06013	+	2.43112i	0.0417103	+	0.0956511i
$647$		−	3.40639i		−	0.133919i	−0.997756	−	0.0669596i	$-0.978670\pi$
$647$		−	3.40639i		−	0.133919i	0.997756	−	0.0669596i	$-0.0213299\pi$
$648$	4.05543	−	26.0893i	0.159312	−	1.02488i
$649$	−19.4964	+	3.43774i	−0.765299	+	0.134943i
$650$	5.18689	−	6.18149i	0.203446	−	0.242458i
$651$	4.03278	+	10.9072i	0.158057	+	0.427488i
$652$	−4.22619	+	23.9679i	−0.165510	+	0.938655i
$653$	−4.29421	−	2.47926i	−0.168045	−	0.0970211i	0.413618	−	0.910450i	$-0.364265\pi$
$653$	−4.29421	−	2.47926i	−0.168045	−	0.0970211i	−0.581664	+	0.813429i	$0.697598\pi$
$654$	−18.8886	+	3.42962i	−0.738605	+	0.134109i
$655$	12.9482	−	4.71276i	0.505928	−	0.184143i
$656$	−2.74979	+	1.00084i	−0.107361	+	0.0390763i
$657$	2.69168	−	16.2278i	0.105012	−	0.633107i
$658$	−22.9854	−	13.2706i	−0.896063	−	0.517342i
$659$	2.99511	−	16.9861i	0.116673	−	0.661686i	−0.869235	−	0.494399i	$-0.835388\pi$
$659$	2.99511	−	16.9861i	0.116673	−	0.661686i	0.985908	−	0.167287i	$-0.0535007\pi$
$660$	−3.59007	+	1.32737i	−0.139743	+	0.0516680i
$661$	−15.2930	+	18.2255i	−0.594830	+	0.708891i	−0.976527	−	0.215397i	$-0.930896\pi$
$661$	−15.2930	+	18.2255i	−0.594830	+	0.708891i	0.381696	+	0.924288i	$0.375340\pi$
$662$	11.6201	−	2.04893i	0.451627	−	0.0796340i
$663$	1.66072	+	1.37919i	0.0644969	+	0.0535633i
$664$		−	23.8084i		−	0.923943i
$665$	−2.57847	+	8.73861i	−0.0999889	+	0.338869i
$666$	10.9582	−	13.3323i	0.424621	−	0.516615i
$667$	−26.5166	+	72.8539i	−1.02673	+	2.82091i
$668$	0.246049	+	1.39541i	0.00951991	+	0.0539901i
$669$	−9.83878	+	5.74727i	−0.380389	+	0.222202i
$670$	5.34996	−	4.48915i	0.206687	−	0.173431i
$671$	4.65225	+	0.820317i	0.179598	+	0.0316680i
$672$	−19.5564	+	16.5798i	−0.754404	+	0.639580i
$673$	9.66092	−	5.57774i	0.372401	−	0.215006i	−0.302106	−	0.953274i	$-0.597690\pi$
$673$	9.66092	−	5.57774i	0.372401	−	0.215006i	0.674507	+	0.738268i	$0.264356\pi$
$674$	−5.08631	−	13.9745i	−0.195917	−	0.538278i
$675$	−17.8520	−	14.5217i	−0.687123	−	0.558942i
$676$	5.14591	+	8.91298i	0.197920	+	0.342807i
$677$	−12.7624	+	22.1050i	−0.490497	+	0.849566i	−0.999940	−	0.0109384i	$-0.996518\pi$
$677$	−12.7624	+	22.1050i	−0.490497	+	0.849566i	0.509443	+	0.860504i	$0.329851\pi$
$678$	−1.60691	+	2.81619i	−0.0617129	+	0.108155i
$679$	−24.1614	−	28.7945i	−0.927230	−	1.10503i
$680$	−1.09579	−	0.919473i	−0.0420215	−	0.0352602i
$681$	−5.52448	+	32.2893i	−0.211698	+	1.23733i
$682$	−5.66493	−	2.06187i	−0.216921	−	0.0789529i
$683$	−19.7577			−0.756007			−0.378004	−	0.925804i	$-0.623389\pi$
$683$	−19.7577			−0.756007			−0.378004	+	0.925804i	$0.623389\pi$
$684$	−14.4836	+	1.04903i	−0.553796	+	0.0401108i
$685$	−5.92368			−0.226332
$686$	15.5680	+	5.66630i	0.594390	+	0.216340i
$687$	−2.79513	+	16.3369i	−0.106641	+	0.623291i
$688$	0.616601	+	0.517389i	0.0235077	+	0.0197253i
$689$	−6.74976	−	8.04406i	−0.257146	−	0.306454i
$690$	5.34639	−	9.36985i	0.203534	−	0.356704i
$691$	6.70762	−	11.6179i	0.255170	−	0.441967i	−0.709772	−	0.704432i	$-0.751202\pi$
$691$	6.70762	−	11.6179i	0.255170	−	0.441967i	0.964942	+	0.262465i	$0.0845353\pi$
$692$	1.67816	+	2.90666i	0.0637941	+	0.110495i
$693$	7.26229	−	20.6020i	0.275872	−	0.782604i
$694$	−3.51052	−	9.64508i	−0.133258	−	0.366122i
$695$	−0.0553238	+	0.0319412i	−0.00209855	+	0.00121160i
$696$	34.3903	−	29.1559i	1.30356	−	1.10515i
$697$	−3.40622	−	0.600608i	−0.129020	−	0.0227497i
$698$	−22.1568	+	18.5917i	−0.838646	+	0.703708i
$699$	25.3905	−	14.8317i	0.960358	−	0.560988i
$700$	2.36183	+	13.3946i	0.0892690	+	0.506269i
$701$	−14.9221	+	40.9982i	−0.563601	+	1.54848i	0.250717	+	0.968060i	$0.419334\pi$
$701$	−14.9221	+	40.9982i	−0.563601	+	1.54848i	−0.814318	+	0.580420i	$0.802889\pi$
$702$	8.12607	−	4.85821i	0.306699	−	0.183361i
$703$	−23.8059	−	11.8379i	−0.897858	−	0.446474i
$704$		−	16.1655i		−	0.609260i
$705$	10.2478	+	8.51061i	0.385956	+	0.320528i
$706$	10.1360	−	1.78725i	0.381474	−	0.0672641i
$707$	−3.72607	+	4.44056i	−0.140133	+	0.167004i
$708$	13.5649	−	5.01541i	0.509800	−	0.188491i
$709$	−2.60312	+	14.7630i	−0.0977623	+	0.554438i	0.896104	+	0.443845i	$0.146386\pi$
$709$	−2.60312	+	14.7630i	−0.0977623	+	0.554438i	−0.993866	+	0.110593i	$0.964725\pi$
$710$	−1.68040	−	0.970180i	−0.0630643	−	0.0364102i
$711$	−27.7108	−	4.59633i	−1.03924	−	0.172376i
$712$	−3.70191	+	1.34739i	−0.138735	+	0.0504954i
$713$	−19.9329	+	7.25497i	−0.746491	+	0.271701i
$714$	2.86768	−	0.520685i	0.107320	−	0.0194861i
$715$	−3.32938	−	1.92222i	−0.124512	−	0.0718870i
$716$	2.31410	−	13.1239i	0.0864820	−	0.490464i
$717$	−10.6800	−	28.8857i	−0.398853	−	1.07875i
$718$	−0.409948	+	0.488557i	−0.0152991	+	0.0182328i
$719$	41.3087	−	7.28384i	1.54056	−	0.271642i	0.662082	−	0.749432i	$-0.269673\pi$
$719$	41.3087	−	7.28384i	1.54056	−	0.271642i	0.878474	+	0.477790i	$0.158562\pi$
$720$	−1.06545	+	0.629660i	−0.0397071	+	0.0234660i
$721$			33.2715i			1.23910i
$722$	−5.27532	−	17.1255i	−0.196327	−	0.637345i
$723$	3.88110	−	10.8342i	0.144340	−	0.402928i
$724$	2.95130	−	8.10864i	0.109684	−	0.301355i
$725$	−6.82386	−	38.7000i	−0.253432	−	1.43728i
$726$	−3.35161	−	5.73763i	−0.124390	−	0.212943i
$727$	11.3609	−	9.53290i	0.421351	−	0.353556i	−0.407326	−	0.913283i	$-0.633539\pi$
$727$	11.3609	−	9.53290i	0.421351	−	0.353556i	0.828677	+	0.559727i	$0.189094\pi$
$728$	−15.4355	−	2.72169i	−0.572077	−	0.100873i
$729$	−14.2064	−	22.9603i	−0.526164	−	0.850383i
$730$	−3.38493	+	1.95429i	−0.125282	+	0.0723314i
$731$	0.325394	+	0.894013i	0.0120351	+	0.0330663i
$732$	−3.45099	+	0.0175336i	−0.127552	+	0.000648059i
$733$	−0.804203	−	1.39292i	−0.0297039	−	0.0514487i	0.850791	−	0.525504i	$-0.176123\pi$
$733$	−0.804203	−	1.39292i	−0.0297039	−	0.0514487i	−0.880495	+	0.474055i	$0.842790\pi$
$734$	−0.580056	+	1.00469i	−0.0214103	+	0.0370836i
$735$	0.737106	+	0.420590i	0.0271886	+	0.0155137i
$736$	−30.0614	−	35.8258i	−1.10808	−	1.32056i
$737$	19.7607	+	16.5812i	0.727896	+	0.610778i
$738$	−7.45069	+	13.2132i	−0.274264	+	0.486386i
$739$	1.21979	+	0.443965i	0.0448705	+	0.0163315i	0.364358	−	0.931259i	$-0.381288\pi$
$739$	1.21979	+	0.443965i	0.0448705	+	0.0163315i	−0.319487	+	0.947591i	$0.603511\pi$
$740$	5.11937			0.188192
$741$	−10.1047	−	10.5181i	−0.371205	−	0.386393i
$742$	−14.1773			−0.520466
$743$	−8.68786	−	3.16212i	−0.318727	−	0.116007i	0.177703	−	0.984084i	$-0.443134\pi$
$743$	−8.68786	−	3.16212i	−0.318727	−	0.116007i	−0.496429	+	0.868077i	$0.665356\pi$
$744$	12.1589	+	2.08030i	0.445767	+	0.0762676i
$745$	−6.90847	−	5.79689i	−0.253107	−	0.212382i
$746$	3.59152	+	4.28021i	0.131495	+	0.156710i
$747$	−15.8387	−	18.4910i	−0.579508	−	0.676549i
$748$	0.943151	−	1.63358i	0.0344850	−	0.0597298i
$749$	9.43835	+	16.3477i	0.344870	+	0.597332i
$750$	0.0591456	+	11.6411i	0.00215969	+	0.425074i
$751$	9.38727	+	25.7913i	0.342546	+	0.941138i	0.984653	+	0.174523i	$0.0558383\pi$
$751$	9.38727	+	25.7913i	0.342546	+	0.941138i	−0.642107	+	0.766615i	$0.721939\pi$
$752$	−4.80999	+	2.77705i	−0.175402	+	0.101268i
$753$	32.3332	+	38.1380i	1.17829	+	1.38983i
$754$	15.9216	+	2.80741i	0.579831	+	0.102240i
$755$	−1.52807	+	1.28221i	−0.0556123	+	0.0466643i
$756$	−2.53123	+	15.7560i	−0.0920601	+	0.573041i
$757$	3.02250	+	17.1414i	0.109855	+	0.623016i	0.989170	+	0.146776i	$0.0468897\pi$
$757$	3.02250	+	17.1414i	0.109855	+	0.623016i	−0.879315	+	0.476240i	$0.841999\pi$
$758$	3.36437	−	9.24353i	0.122199	−	0.335740i
$759$	37.5120	+	13.4378i	1.36160	+	0.487762i
$760$	6.66019	+	7.00357i	0.241590	+	0.254046i
$761$		−	8.35519i		−	0.302875i	−0.988467	−	0.151438i	$-0.951610\pi$
$761$		−	8.35519i		−	0.302875i	0.988467	−	0.151438i	$-0.0483903\pi$
$762$	11.8362	−	14.2523i	0.428780	−	0.516305i
$763$	32.0068	−	5.64366i	1.15872	−	0.204314i
$764$	−0.767633	+	0.914829i	−0.0277720	+	0.0330974i
$765$	−1.46274	+	0.0148640i	−0.0528854	+	0.000537408i
$766$	−2.09547	+	11.8840i	−0.0757124	+	0.429386i
$767$	12.5799	+	7.26301i	0.454234	+	0.262252i
$768$	5.23380	+	28.8252i	0.188859	+	1.04014i
$769$	31.8082	−	11.5772i	1.14703	−	0.417486i	0.302585	−	0.953122i	$-0.402150\pi$
$769$	31.8082	−	11.5772i	1.14703	−	0.417486i	0.844449	+	0.535636i	$0.179928\pi$
$770$	−4.87745	+	1.77525i	−0.175771	+	0.0639754i
$771$	2.19763	+	12.1035i	0.0791457	+	0.435896i
$772$	1.86477	+	1.07663i	0.0671146	+	0.0387487i
$773$	−7.25002	+	41.1169i	−0.260765	+	1.47887i	0.520064	+	0.854127i	$0.325908\pi$
$773$	−7.25002	+	41.1169i	−0.260765	+	1.47887i	−0.780829	+	0.624744i	$0.785203\pi$
$774$	4.17229	−	0.0423978i	0.149970	−	0.00152396i
$775$	6.91105	−	8.23627i	0.248252	−	0.295856i
$776$	−39.2671	+	6.92385i	−1.40961	+	0.248552i
$777$	−18.6662	+	22.4765i	−0.669647	+	0.806338i
$778$		−	14.9607i		−	0.536367i
$779$	22.4137	+	6.61354i	0.803055	+	0.236955i
$780$	2.64395	+	0.947135i	0.0946687	+	0.0339129i
$781$	2.45124	−	6.73474i	0.0877124	−	0.240988i
$782$	0.923187	+	5.23566i	0.0330131	+	0.187227i
$783$	7.31329	−	45.5226i	0.261356	−	1.62684i
$784$	−0.271059	+	0.227445i	−0.00968067	+	0.00812305i
$785$	−9.74359	−	1.71806i	−0.347763	−	0.0613201i
$786$	19.2589	+	22.7164i	0.686941	+	0.810269i
$787$	26.7581	−	15.4488i	0.953822	−	0.550689i	0.0595556	−	0.998225i	$-0.481032\pi$
$787$	26.7581	−	15.4488i	0.953822	−	0.550689i	0.894266	+	0.447536i	$0.147698\pi$
$788$	6.03503	+	16.5811i	0.214989	+	0.590678i
$789$	0.0134292	+	2.64315i	0.000478090	+	0.0940986i
$790$	3.33716	+	5.78013i	0.118731	+	0.205648i
$791$	2.74462	−	4.75381i	0.0975873	−	0.169026i
$792$	−15.0743	−	17.5985i	−0.535642	−	0.625337i
$793$	−2.22804	−	2.65528i	−0.0791200	−	0.0942916i
$794$	13.4162	+	11.2575i	0.476122	+	0.399513i
$795$	7.01366	+	1.19999i	0.248749	+	0.0425592i
$796$	2.89391	+	1.05330i	0.102572	+	0.0373331i
$797$	24.5528			0.869703			0.434852	−	0.900502i	$-0.356801\pi$
$797$	24.5528			0.869703			0.434852	+	0.900502i	$0.356801\pi$
$798$	−19.6477	+	1.32275i	−0.695521	+	0.0468249i
$799$	−6.56479			−0.232246
$800$	22.2752	+	8.10749i	0.787546	+	0.286643i
$801$	−1.97876	+	3.50919i	−0.0699161	+	0.123991i
$802$	23.6153	+	19.8156i	0.833886	+	0.699714i
$803$	−9.27980	−	11.0592i	−0.327477	−	0.390272i
$804$	−16.3676	−	9.33926i	−0.577239	−	0.329370i
$805$	−9.13171	+	15.8166i	−0.321850	+	0.557461i
$806$	2.21168	+	3.83075i	0.0779032	+	0.134932i
$807$	−21.9436	+	0.111490i	−0.772451	+	0.00392462i
$808$	2.10309	+	5.77818i	0.0739863	+	0.203276i
$809$	34.4237	−	19.8745i	1.21027	−	0.698751i	0.247454	−	0.968900i	$-0.420406\pi$
$809$	34.4237	−	19.8745i	1.21027	−	0.698751i	0.962819	+	0.270148i	$0.0870728\pi$
$810$	−2.07126	+	6.07192i	−0.0727766	+	0.213345i
$811$	−24.3550	−	4.29445i	−0.855221	−	0.150799i	−0.271186	−	0.962527i	$-0.587416\pi$
$811$	−24.3550	−	4.29445i	−0.855221	−	0.150799i	−0.584035	+	0.811728i	$0.698527\pi$
$812$	−20.8752	+	17.5163i	−0.732574	+	0.614703i
$813$	19.8763	+	34.0264i	0.697093	+	1.19336i
$814$	−2.63011	−	14.9161i	−0.0921852	−	0.522808i
$815$	5.66533	−	15.5654i	0.198448	−	0.545231i
$816$	0.205687	−	0.574180i	0.00720048	−	0.0201003i
$817$	−1.50719	−	6.24884i	−0.0527298	−	0.218619i
$818$			17.2438i			0.602917i
$819$	−13.7987	+	8.15476i	−0.482166	+	0.284950i
$820$	−4.43143	+	0.781380i	−0.154752	+	0.0272870i
$821$	0.437587	−	0.521496i	0.0152719	−	0.0182003i	−0.758354	−	0.651842i	$-0.773996\pi$
$821$	0.437587	−	0.521496i	0.0152719	−	0.0182003i	0.773626	+	0.633642i	$0.218441\pi$
$822$	−4.43999	−	12.0086i	−0.154862	−	0.418847i
$823$	8.74011	−	49.5676i	0.304661	−	1.72782i	−0.320435	−	0.947270i	$-0.603829\pi$
$823$	8.74011	−	49.5676i	0.304661	−	1.72782i	0.625096	−	0.780548i	$-0.285060\pi$
$824$	30.5651	+	17.6468i	1.06479	+	0.614754i
$825$	−19.8718	+	3.60813i	−0.691848	+	0.125619i
$826$	18.4292	−	6.70767i	0.641233	−	0.233390i
$827$	−10.4120	+	3.78966i	−0.362061	+	0.131779i	−0.516644	−	0.856201i	$-0.672819\pi$
$827$	−10.4120	+	3.78966i	−0.362061	+	0.131779i	0.154583	+	0.987980i	$0.450597\pi$
$828$	−28.7166	−	4.76316i	−0.997969	−	0.165531i
$829$	−15.6901	−	9.05871i	−0.544941	−	0.314622i	0.202138	−	0.979357i	$-0.435211\pi$
$829$	−15.6901	−	9.05871i	−0.544941	−	0.314622i	−0.747079	+	0.664735i	$0.768544\pi$
$830$	−1.00457	+	5.69722i	−0.0348693	+	0.197753i
$831$	−5.99096	+	2.21507i	−0.207824	+	0.0768398i
$832$	−7.62431	+	9.08629i	−0.264325	+	0.315011i
$833$	−0.411878	+	0.0726252i	−0.0142707	+	0.00251631i
$834$	−0.106219	−	0.0882124i	−0.00367806	−	0.00305455i
$835$		−	0.964376i		−	0.0333736i
$836$	−7.57006	+	10.2530i	−0.261816	+	0.354606i
$837$	10.8273	−	6.47313i	0.374245	−	0.223744i
$838$	−7.44597	+	20.4576i	−0.257217	+	0.706698i
$839$	4.98678	+	28.2814i	0.172163	+	0.976384i	0.941368	+	0.337382i	$0.109541\pi$
$839$	4.98678	+	28.2814i	0.172163	+	0.976384i	−0.769205	+	0.639002i	$0.779348\pi$
$840$	9.17080	−	5.35707i	0.316422	−	0.184836i
$841$	38.0976	−	31.9677i	1.31371	−	1.10233i
$842$	−10.7750	−	1.89993i	−0.371332	−	0.0654758i
$843$	−12.4789	+	10.5795i	−0.429795	+	0.364378i
$844$	11.4537	−	6.61279i	0.394253	−	0.227622i
$845$	−2.39574	−	6.58224i	−0.0824159	−	0.226436i
$846$	−9.57177	+	27.1536i	−0.329084	+	0.933560i
$847$	5.62471	+	9.74228i	0.193267	+	0.334749i
$848$	−1.48339	+	2.56931i	−0.0509400	+	0.0882306i
$849$	14.1787	−	24.8490i	0.486613	−	0.852816i
$850$	−1.73213	−	2.06427i	−0.0594115	−	0.0708039i
$851$	−40.8256	−	34.2567i	−1.39948	−	1.17430i
$852$	−0.882957	+	5.16068i	−0.0302496	+	0.176802i
$853$	−4.18389	−	1.52281i	−0.143254	−	0.0521401i	0.269398	−	0.963029i	$-0.413175\pi$
$853$	−4.18389	−	1.52281i	−0.143254	−	0.0521401i	−0.412652	+	0.910889i	$0.635397\pi$
$854$	−4.67982			−0.160140
$855$	9.83187	+	1.00863i	0.336243	+	0.0344945i
$856$	20.0239			0.684402
$857$	−39.7782	−	14.4781i	−1.35880	−	0.494562i	−0.443116	−	0.896464i	$-0.646127\pi$
$857$	−39.7782	−	14.4781i	−1.35880	−	0.494562i	−0.915683	+	0.401902i	$0.868349\pi$
$858$	1.40128	−	8.19015i	0.0478388	−	0.279607i
$859$	−16.2198	−	13.6100i	−0.553411	−	0.464367i	0.322683	−	0.946507i	$-0.395415\pi$
$859$	−16.2198	−	13.6100i	−0.553411	−	0.464367i	−0.876094	+	0.482140i	$0.839860\pi$
$860$	0.795603	+	0.948162i	0.0271298	+	0.0323321i
$861$	12.7272	−	22.3051i	0.433742	−	0.760156i
$862$	−4.12944	+	7.15240i	−0.140649	+	0.243612i
$863$	−12.2868	−	21.2813i	−0.418246	−	0.724424i	0.577517	−	0.816379i	$-0.304022\pi$
$863$	−12.2868	−	21.2813i	−0.418246	−	0.724424i	−0.995763	+	0.0919547i	$0.970688\pi$
$864$	21.5754	+	17.5505i	0.734009	+	0.597081i
$865$	−0.781288	−	2.14657i	−0.0265646	−	0.0729856i
$866$	28.5506	−	16.4837i	0.970188	−	0.560138i
$867$	−21.9097	+	18.5750i	−0.744094	+	0.630839i
$868$	−7.34251	−	1.29468i	−0.249221	−	0.0439444i
$869$	−18.8849	+	15.8463i	−0.640625	+	0.537548i
$870$	−9.45963	+	5.52579i	−0.320711	+	0.187342i
$871$	−3.28673	−	18.6400i	−0.111366	−	0.631591i
$872$	11.7914	−	32.3965i	0.399306	−	1.09709i
$873$	−25.8910	+	31.5002i	−0.876276	+	1.06612i
$874$	−2.23070	−	35.8510i	−0.0754545	−	1.21268i
$875$		−	19.7082i		−	0.666260i
$876$	8.11344	+	6.73803i	0.274128	+	0.227657i
$877$	51.5733	−	9.09377i	1.74151	−	0.307075i	0.789637	−	0.613574i	$-0.210269\pi$
$877$	51.5733	−	9.09377i	1.74151	−	0.307075i	0.951871	+	0.306499i	$0.0991577\pi$
$878$	12.6491	−	15.0747i	0.426888	−	0.508745i
$879$	−42.1266	+	15.5757i	−1.42090	+	0.525354i
$880$	−0.188612	+	1.06967i	−0.00635811	+	0.0360586i
$881$	−11.8654	−	6.85051i	−0.399756	−	0.230799i	0.286623	−	0.958044i	$-0.407467\pi$
$881$	−11.8654	−	6.85051i	−0.399756	−	0.230799i	−0.686379	+	0.727244i	$0.740801\pi$
$882$	−0.300141	+	1.80952i	−0.0101063	+	0.0609297i
$883$	−50.1392	+	18.2492i	−1.68732	+	0.614134i	−0.994284	−	0.106769i	$-0.965950\pi$
$883$	−50.1392	+	18.2492i	−1.68732	+	0.614134i	−0.693036	+	0.720903i	$0.743727\pi$
$884$	−1.30059	+	0.473377i	−0.0437436	+	0.0159214i
$885$	−9.68483	+	1.75848i	−0.325552	+	0.0591106i
$886$	3.04286	+	1.75680i	0.102227	+	0.0590208i
$887$	5.01003	−	28.4133i	0.168220	−	0.954025i	−0.777461	−	0.628931i	$-0.783493\pi$
$887$	5.01003	−	28.4133i	0.168220	−	0.954025i	0.945682	−	0.325094i	$-0.105396\pi$
$888$	10.7478	+	29.0690i	0.360673	+	0.975492i
$889$	−20.1605	+	24.0264i	−0.676162	+	0.805819i
$890$	0.942701	−	0.166224i	0.0315994	−	0.00557183i
$891$	−23.4151	−	3.63975i	−0.784437	−	0.121936i
$892$		−	7.30546i		−	0.244605i
$893$	44.0750	+	4.97463i	1.47491	+	0.166470i
$894$	6.57344	−	18.3499i	0.219849	−	0.613713i
$895$	−3.10212	+	8.52301i	−0.103693	+	0.284893i
$896$	−2.36001	−	13.3843i	−0.0788425	−	0.447138i
$897$	−14.7469	−	25.2454i	−0.492386	−	0.842918i
$898$	5.06845	−	4.25293i	0.169136	−	0.141922i
$899$	21.2141	+	3.74062i	0.707530	+	0.124757i
$900$	13.8125	−	5.18689i	0.460417	−	0.172896i
$901$	−3.03686	+	1.75333i	−0.101173	+	0.0584120i
$902$	4.55334	+	12.5102i	0.151610	+	0.416544i
$903$	−7.06380	+	0.0358893i	−0.235069	+	0.00119432i
$904$	−2.91141	−	5.04271i	−0.0968321	−	0.167718i
$905$	−2.93648	+	5.08614i	−0.0976120	+	0.169069i
$906$	−3.74465	−	2.13668i	−0.124408	−	0.0709865i
$907$	−4.09841	−	4.88429i	−0.136085	−	0.162180i	0.693698	−	0.720266i	$-0.255980\pi$
$907$	−4.09841	−	4.88429i	−0.136085	−	0.162180i	−0.829783	+	0.558086i	$0.811536\pi$
$908$	−16.0892	−	13.5004i	−0.533938	−	0.448027i
$909$	5.47736	+	3.08858i	0.181673	+	0.102442i
$910$	3.57879	+	1.30257i	0.118636	+	0.0431799i
$911$	20.6085			0.682792			0.341396	−	0.939920i	$-0.389100\pi$
$911$	20.6085			0.682792			0.341396	+	0.939920i	$0.389100\pi$
$912$	−1.81605	+	3.69909i	−0.0601354	+	0.122489i
$913$	−21.3680			−0.707178
$914$	−26.8982	−	9.79015i	−0.889714	−	0.323829i
$915$	2.31515	+	0.396106i	0.0765365	+	0.0130949i
$916$	−8.14036	−	6.83058i	−0.268965	−	0.225689i
$917$	−32.4087	−	38.6232i	−1.07023	−	1.27545i
$918$	−1.12650	−	2.95415i	−0.0371801	−	0.0975014i
$919$	19.9111	−	34.4870i	0.656806	−	1.13762i	−0.324631	−	0.945841i	$-0.605240\pi$
$919$	19.9111	−	34.4870i	0.656806	−	1.13762i	0.981438	−	0.191781i	$-0.0614264\pi$
$920$	9.68666	+	16.7778i	0.319360	+	0.553147i
$921$	0.104774	+	20.6219i	0.00345243	+	0.679513i
$922$	6.24349	+	17.1539i	0.205618	+	0.564932i
$923$	−4.55417	+	2.62935i	−0.149902	+	0.0865462i
$924$	9.05693	+	10.6829i	0.297951	+	0.351442i
$925$	26.6025	+	4.69074i	0.874685	+	0.154231i
$926$	−9.47384	+	7.94949i	−0.311330	+	0.261237i
$927$	35.4783	−	6.62817i	1.16526	−	0.217698i
$928$	8.24711	+	46.7717i	0.270725	+	1.53536i
$929$	3.83622	−	10.5399i	0.125862	−	0.345804i	−0.860718	−	0.509083i	$-0.829985\pi$
$929$	3.83622	−	10.5399i	0.125862	−	0.345804i	0.986580	+	0.163279i	$0.0522070\pi$
$930$	−2.82179	−	1.01084i	−0.0925301	−	0.0331468i
$931$	2.82032	−	0.175484i	0.0924323	−	0.00575126i
$932$			18.8529i			0.617547i
$933$	−15.1212	+	18.2078i	−0.495045	+	0.596097i
$934$	−33.6760	+	5.93798i	−1.10191	+	0.194297i
$935$	−0.825228	+	0.983469i	−0.0269879	+	0.0321629i
$936$	0.172764	+	17.0014i	0.00564697	+	0.555709i
$937$	−7.56135	+	42.8826i	−0.247019	+	1.40091i	0.568739	+	0.822518i	$0.307432\pi$
$937$	−7.56135	+	42.8826i	−0.247019	+	1.40091i	−0.815757	+	0.578394i	$0.803680\pi$
$938$	−22.1308	−	12.7772i	−0.722597	−	0.417191i
$939$	−0.165231	−	0.910012i	−0.00539212	−	0.0296971i
$940$	−8.02560	+	2.92108i	−0.261766	+	0.0952751i
$941$	−36.3696	+	13.2374i	−1.18561	+	0.431529i	−0.858182	−	0.513346i	$-0.828406\pi$
$941$	−36.3696	+	13.2374i	−1.18561	+	0.431529i	−0.327433	+	0.944874i	$0.606184\pi$
$942$	−3.82026	−	21.0401i	−0.124471	−	0.685523i
$943$	40.5680	+	23.4220i	1.32108	+	0.762724i
$944$	0.712660	−	4.04169i	0.0231951	−	0.131546i
$945$	3.55874	−	10.2616i	0.115766	−	0.333809i
$946$	2.35387	−	2.80523i	0.0765309	−	0.0912060i
$947$	39.6810	−	6.99682i	1.28946	−	0.227366i	0.513466	−	0.858110i	$-0.328361\pi$
$947$	39.6810	−	6.99682i	1.28946	−	0.227366i	0.775991	+	0.630743i	$0.217250\pi$
$948$	11.5059	−	13.8546i	0.373695	−	0.449976i
$949$			10.5929i			0.343860i
$950$	10.0650	+	15.1718i	0.326552	+	0.492237i
$951$	−11.7189	−	4.19801i	−0.380010	−	0.136130i
$952$	−1.79017	+	4.91845i	−0.0580197	+	0.159408i
$953$	−2.40512	−	13.6401i	−0.0779096	−	0.441847i	−0.998663	−	0.0517013i	$-0.983536\pi$
$953$	−2.40512	−	13.6401i	−0.0779096	−	0.441847i	0.920753	−	0.390146i	$-0.127575\pi$
$954$	2.82433	+	15.1176i	0.0914411	+	0.489452i
$955$	0.622638	−	0.522455i	0.0201481	−	0.0169063i
$956$	19.4452	+	3.42872i	0.628903	+	0.110893i
$957$	−26.1674	−	30.8653i	−0.845873	−	0.997734i
$958$	9.04139	−	5.22005i	0.292114	−	0.168652i
$959$	7.41334	+	20.3680i	0.239389	+	0.657716i
$960$	−0.0408360	−	8.03741i	−0.00131798	−	0.259406i
$961$	−12.5531	−	21.7427i	−0.404940	−	0.701376i
$962$	−5.55670	+	9.62449i	−0.179155	+	0.310306i
$963$	15.5517	−	13.3210i	0.501147	−	0.429265i
$964$	4.74282	+	5.65227i	0.152756	+	0.182047i
$965$	−1.12265	−	0.942016i	−0.0361394	−	0.0303246i
$966$	−38.9081	−	6.65691i	−1.25185	−	0.214183i
$967$	7.29648	+	2.65570i	0.234639	+	0.0854016i	0.456664	−	0.889639i	$-0.349044\pi$
$967$	7.29648	+	2.65570i	0.234639	+	0.0854016i	−0.222025	+	0.975041i	$0.571267\pi$
$968$	11.9331			0.383543
$969$	−4.04506	+	2.71320i	−0.129946	+	0.0871606i
$970$	9.68856			0.311081
$971$	−19.9285	−	7.25337i	−0.639535	−	0.232772i	0.00184129	−	0.999998i	$-0.499414\pi$
$971$	−19.9285	−	7.25337i	−0.639535	−	0.232772i	−0.641376	+	0.767227i	$0.721636\pi$
$972$	17.3053	−	0.439709i	0.555067	−	0.0141037i
$973$	0.179063	+	0.150252i	0.00574050	+	0.00481685i
$974$	−11.6912	−	13.9330i	−0.374609	−	0.446442i
$975$	12.8713	+	7.34431i	0.412211	+	0.235206i
$976$	−0.489656	+	0.848109i	−0.0156735	+	0.0271473i
$977$	29.9393	+	51.8564i	0.957844	+	1.65903i	0.727722	+	0.685872i	$0.240579\pi$
$977$	29.9393	+	51.8564i	0.957844	+	1.65903i	0.230121	+	0.973162i	$0.426088\pi$
$978$	35.8007	−	0.181894i	1.14478	−	0.00581634i
$979$	1.20928	+	3.32247i	0.0386488	+	0.106187i
$980$	−0.471215	+	0.272056i	−0.0150524	+	0.00869051i
$981$	−12.3942	−	33.0054i	−0.395716	−	1.05378i
$982$	−18.9939	−	3.34914i	−0.606120	−	0.106875i
$983$	−1.76552	+	1.48145i	−0.0563114	+	0.0472509i	−0.670509	−	0.741901i	$-0.733924\pi$
$983$	−1.76552	+	1.48145i	−0.0563114	+	0.0472509i	0.614198	+	0.789152i	$0.289480\pi$
$984$	−13.7404	−	23.5222i	−0.438027	−	0.749861i
$985$	−2.08542	−	11.8270i	−0.0664470	−	0.376840i
$986$	1.84655	−	5.07335i	0.0588061	−	0.161568i
$987$	16.4380	−	45.8870i	0.523226	−	1.46060i
$988$	9.09069	−	2.19263i	0.289213	−	0.0697567i
$989$		−	12.8852i		−	0.409725i
$990$	2.86465	+	4.84729i	0.0910445	+	0.154057i
$991$	−47.0657	+	8.29896i	−1.49509	+	0.263625i	−0.860591	−	0.509297i	$-0.829906\pi$
$991$	−47.0657	+	8.29896i	−1.49509	+	0.263625i	−0.634501	+	0.772922i	$0.718795\pi$
$992$	−8.35249	+	9.95411i	−0.265192	+	0.316043i
$993$	7.51467	+	20.3245i	0.238471	+	0.644978i
$994$	−1.23289	+	6.99204i	−0.0391048	+	0.221774i
$995$	−1.81520	−	1.04801i	−0.0575457	−	0.0332240i
$996$	15.3588	−	2.78871i	0.486664	−	0.0883637i
$997$	32.6262	−	11.8750i	1.03328	−	0.376084i	0.230952	−	0.972965i	$-0.425816\pi$
$997$	32.6262	−	11.8750i	1.03328	−	0.376084i	0.802329	+	0.596882i	$0.203594\pi$
$998$	30.5563	−	11.1216i	0.967243	−	0.352047i
$999$	27.6858	+	15.4266i	0.875940	+	0.488076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.53.3	yes	24
3.2	odd	2	inner	57.2.j.b.53.2	yes	24
4.3	odd	2		912.2.cc.e.737.1		24
12.11	even	2		912.2.cc.e.737.2		24
19.9	even	9		1083.2.d.d.1082.12		24
19.10	odd	18		1083.2.d.d.1082.14		24
19.14	odd	18	inner	57.2.j.b.14.2	✓	24
57.14	even	18	inner	57.2.j.b.14.3	yes	24
57.29	even	18		1083.2.d.d.1082.11		24
57.47	odd	18		1083.2.d.d.1082.13		24
76.71	even	18		912.2.cc.e.641.2		24
228.71	odd	18		912.2.cc.e.641.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.14.2	✓	24	19.14	odd	18	inner
57.2.j.b.14.3	yes	24	57.14	even	18	inner
57.2.j.b.53.2	yes	24	3.2	odd	2	inner
57.2.j.b.53.3	yes	24	1.1	even	1	trivial
912.2.cc.e.641.1		24	228.71	odd	18
912.2.cc.e.641.2		24	76.71	even	18
912.2.cc.e.737.1		24	4.3	odd	2
912.2.cc.e.737.2		24	12.11	even	2
1083.2.d.d.1082.11		24	57.29	even	18
1083.2.d.d.1082.12		24	19.9	even	9
1083.2.d.d.1082.13		24	57.47	odd	18
1083.2.d.d.1082.14		24	19.10	odd	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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.886259 + 0.322572i) q^{2} +(-0.292097 + 1.70724i) q^{3} +(-0.850687 - 0.713811i) q^{4} +(0.485824 + 0.578982i) q^{5} +(-0.809582 + 1.41884i) q^{6} +(1.38278 - 2.39504i) q^{7} +(-1.46681 - 2.54059i) q^{8} +(-2.82936 - 0.997362i) q^{9} +O(q^{10})\)	\(q+(0.886259 + 0.322572i) q^{2} +(-0.292097 + 1.70724i) q^{3} +(-0.850687 - 0.713811i) q^{4} +(0.485824 + 0.578982i) q^{5} +(-0.809582 + 1.41884i) q^{6} +(1.38278 - 2.39504i) q^{7} +(-1.46681 - 2.54059i) q^{8} +(-2.82936 - 0.997362i) q^{9} +(0.243802 + 0.669841i) q^{10} +(-2.28018 + 1.31646i) q^{11} +(1.46713 - 1.24383i) q^{12} +(1.90254 + 0.335470i) q^{13} +(1.99807 - 1.67658i) q^{14} +(-1.13037 + 0.660300i) q^{15} +(-0.0947805 - 0.537527i) q^{16} +(0.220652 - 0.606237i) q^{17} +(-2.18582 - 1.79659i) q^{18} +(-1.94082 + 3.90298i) q^{19} -0.839319i q^{20} +(3.68501 + 3.06032i) q^{21} +(-2.44549 + 0.431205i) q^{22} +(-5.61638 + 6.69334i) q^{23} +(4.76586 - 1.76210i) q^{24} +(0.769045 - 4.36147i) q^{25} +(1.57793 + 0.911019i) q^{26} +(2.52919 - 4.53908i) q^{27} +(-2.88591 + 1.05039i) q^{28} +(8.33804 - 3.03480i) q^{29} +(-1.21480 + 0.220571i) q^{30} +(2.10245 + 1.21385i) q^{31} +(-0.929445 + 5.27114i) q^{32} +(-1.58149 - 4.27736i) q^{33} +(0.391110 - 0.466106i) q^{34} +(2.05847 - 0.362964i) q^{35} +(1.69497 + 2.86807i) q^{36} +6.09943i q^{37} +(-2.97906 + 2.83300i) q^{38} +(-1.12846 + 3.15011i) q^{39} +(0.758345 - 2.08354i) q^{40} +(-0.930968 - 5.27978i) q^{41} +(2.27870 + 3.90091i) q^{42} +(-1.12968 + 0.947914i) q^{43} +(2.87943 + 0.507721i) q^{44} +(-0.797115 - 2.12269i) q^{45} +(-7.13664 + 4.12034i) q^{46} +(-3.48030 - 9.56204i) q^{47} +(0.945374 - 0.00480320i) q^{48} +(-0.324139 - 0.561425i) q^{49} +(2.08846 - 3.61732i) q^{50} +(0.970541 + 0.553787i) q^{51} +(-1.37901 - 1.64344i) q^{52} +(-4.16382 - 3.49386i) q^{53} +(3.70569 - 3.20695i) q^{54} +(-1.86998 - 0.680616i) q^{55} -8.11308 q^{56} +(-6.09642 - 4.45349i) q^{57} +8.36860 q^{58} +(7.06560 + 2.57167i) q^{59} +(1.43292 + 0.245163i) q^{60} +(-1.37444 - 1.15329i) q^{61} +(1.47176 + 1.75398i) q^{62} +(-6.30109 + 5.39729i) q^{63} +(-3.06987 + 5.31717i) q^{64} +(0.730070 + 1.26452i) q^{65} +(-0.0218522 - 4.30099i) q^{66} +(-3.35090 - 9.20653i) q^{67} +(-0.620444 + 0.358214i) q^{68} +(-9.78662 - 11.5436i) q^{69} +(1.94142 + 0.342325i) q^{70} +(-2.08521 + 1.74970i) q^{71} +(1.61624 + 8.65118i) q^{72} +(0.952144 + 5.39988i) q^{73} +(-1.96750 + 5.40567i) q^{74} +(7.22146 + 2.58692i) q^{75} +(4.43702 - 1.93484i) q^{76} +7.28150i q^{77} +(-2.01624 + 2.42781i) q^{78} +(9.22088 - 1.62589i) q^{79} +(0.265172 - 0.316020i) q^{80} +(7.01054 + 5.64379i) q^{81} +(0.878031 - 4.97956i) q^{82} +(7.02840 + 4.05785i) q^{83} +(-0.950298 - 5.23377i) q^{84} +(0.458198 - 0.166771i) q^{85} +(-1.30696 + 0.475694i) q^{86} +(2.74562 + 15.1215i) q^{87} +(6.68919 + 3.86200i) q^{88} +(0.233188 - 1.32248i) q^{89} +(-0.0217297 - 2.13838i) q^{90} +(3.43425 - 4.09278i) q^{91} +(9.55556 - 1.68490i) q^{92} +(-2.68646 + 3.23483i) q^{93} -9.59708i q^{94} +(-3.20265 + 0.772462i) q^{95} +(-8.72763 - 3.12647i) q^{96} +(4.64863 - 12.7720i) q^{97} +(-0.106171 - 0.602125i) q^{98} +(7.76444 - 1.45058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

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