LMFDB - Embedded newform 418.2.q.a.21.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, 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("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.10
Character	$\chi$	$=$	418.21
Dual form			418.2.q.a.219.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(2.03306 - 2.42290i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.703704 + 0.256127i) q^{5} +(2.03306 + 2.42290i) q^{6} +(-0.970561 + 0.560354i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.21619 - 6.89736i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(2.03306 - 2.42290i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.703704 + 0.256127i) q^{5} +(2.03306 + 2.42290i) q^{6} +(-0.970561 + 0.560354i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.21619 - 6.89736i) q^{9} +(-0.130039 - 0.737489i) q^{10} +(-0.612660 - 3.25955i) q^{11} +(-2.73913 + 1.58144i) q^{12} +(4.43177 - 3.71870i) q^{13} +(-0.383305 - 1.05312i) q^{14} +(-0.810098 + 2.22573i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.24933 + 0.220291i) q^{17} +7.00376 q^{18} +(-2.69634 + 3.42487i) q^{19} +0.748866 q^{20} +(-0.615523 + 3.49080i) q^{21} +(3.31641 - 0.0373376i) q^{22} +(2.59125 + 0.943139i) q^{23} +(-1.08177 - 2.97213i) q^{24} +(-3.40062 + 2.85346i) q^{25} +(2.89263 + 5.01019i) q^{26} +(-10.9668 - 6.33170i) q^{27} +(1.10368 - 0.194609i) q^{28} +(-0.934634 - 5.30057i) q^{29} +(-2.05124 - 1.18428i) q^{30} +(7.73703 - 4.46698i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-9.14313 - 5.14243i) q^{33} +(-0.433888 + 1.19210i) q^{34} +(0.539466 - 0.642911i) q^{35} +(-1.21619 + 6.89736i) q^{36} +4.82219i q^{37} +(-2.90463 - 3.25010i) q^{38} -18.2981i q^{39} +(-0.130039 + 0.737489i) q^{40} +(-0.305487 - 0.256334i) q^{41} +(-3.33089 - 1.21234i) q^{42} +(1.00105 + 2.75038i) q^{43} +(-0.539119 + 3.27251i) q^{44} +(2.62244 + 4.54220i) q^{45} +(-1.37878 + 2.38811i) q^{46} +(1.65688 + 9.39664i) q^{47} +(3.11482 - 0.549227i) q^{48} +(-2.87201 + 4.97446i) q^{49} +(-2.21960 - 3.84446i) q^{50} +(3.07370 - 2.57914i) q^{51} +(-5.43637 + 1.97868i) q^{52} +(0.632679 - 1.73827i) q^{53} +(8.13987 - 9.70072i) q^{54} +(1.26599 + 2.13684i) q^{55} +1.12071i q^{56} +(2.81632 + 13.4959i) q^{57} +5.38234 q^{58} +(1.60668 + 0.283301i) q^{59} +(1.52249 - 1.81443i) q^{60} +(-3.64562 + 10.0163i) q^{61} +(3.05559 + 8.39517i) q^{62} +(5.04535 + 6.01281i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.16620 + 3.75196i) q^{65} +(6.65199 - 8.11125i) q^{66} +(10.7841 - 1.90153i) q^{67} +(-1.09864 - 0.634302i) q^{68} +(7.55329 - 4.36090i) q^{69} +(0.539466 + 0.642911i) q^{70} +(-1.89854 - 5.21619i) q^{71} +(-6.58139 - 2.39543i) q^{72} +(-5.72403 + 6.82163i) q^{73} +(-4.74893 - 0.837364i) q^{74} +14.0406i q^{75} +(3.70511 - 2.29613i) q^{76} +(2.42112 + 2.82028i) q^{77} +(18.0201 + 3.17743i) q^{78} +(7.62542 + 6.39848i) q^{79} +(-0.703704 - 0.256127i) q^{80} +(-17.8931 + 6.51255i) q^{81} +(0.305487 - 0.256334i) q^{82} +(11.0979 - 6.40739i) q^{83} +(1.77233 - 3.06976i) q^{84} +(-0.935582 + 0.164968i) q^{85} +(-2.88242 + 0.508249i) q^{86} +(-14.7429 - 8.51183i) q^{87} +(-3.12918 - 1.09919i) q^{88} +(1.44105 + 1.71738i) q^{89} +(-4.92858 + 1.79386i) q^{90} +(-2.21752 + 6.09259i) q^{91} +(-2.11241 - 1.77252i) q^{92} +(4.90677 - 27.8277i) q^{93} -9.54160 q^{94} +(1.02022 - 3.10070i) q^{95} +3.16287i q^{96} +(-9.60677 - 1.69393i) q^{97} +(-4.40017 - 3.69218i) q^{98} +(-21.7372 + 8.18997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	2.03306	−	2.42290i	1.17379	−	1.39886i	0.274451	−	0.961601i	$-0.411504\pi$
$3$	2.03306	−	2.42290i	1.17379	−	1.39886i	0.899334	−	0.437261i	$-0.144052\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.703704	+	0.256127i	−0.314706	+	0.114544i	−0.494544	−	0.869153i	$-0.664665\pi$
$5$	−0.703704	+	0.256127i	−0.314706	+	0.114544i	0.179838	+	0.983696i	$0.442443\pi$
$6$	2.03306	+	2.42290i	0.829991	+	0.989145i
$7$	−0.970561	+	0.560354i	−0.366838	+	0.211794i	−0.672076	−	0.740482i	$-0.734597\pi$
$7$	−0.970561	+	0.560354i	−0.366838	+	0.211794i	0.305238	+	0.952276i	$0.401264\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.21619	−	6.89736i	−0.405397	−	2.29912i
$10$	−0.130039	−	0.737489i	−0.0411220	−	0.233215i
$11$	−0.612660	−	3.25955i	−0.184724	−	0.982790i
$11$	−0.612660	−	3.25955i	−0.184724	−	0.982790i
$12$	−2.73913	+	1.58144i	−0.790718	+	0.456521i
$13$	4.43177	−	3.71870i	1.22915	−	1.03138i	0.230859	−	0.972987i	$-0.425846\pi$
$13$	4.43177	−	3.71870i	1.22915	−	1.03138i	0.998294	−	0.0583944i	$-0.0185981\pi$
$14$	−0.383305	−	1.05312i	−0.102442	−	0.281458i
$15$	−0.810098	+	2.22573i	−0.209166	+	0.574680i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.24933	+	0.220291i	0.303007	+	0.0534284i	0.323085	−	0.946370i	$-0.395280\pi$
$17$	1.24933	+	0.220291i	0.303007	+	0.0534284i	−0.0200773	+	0.999798i	$0.506391\pi$
$18$	7.00376			1.65080
$19$	−2.69634	+	3.42487i	−0.618583	+	0.785720i
$19$	−2.69634	+	3.42487i	−0.618583	+	0.785720i
$20$	0.748866			0.167452
$21$	−0.615523	+	3.49080i	−0.134318	+	0.761756i
$22$	3.31641	−	0.0373376i	0.707062	−	0.00796041i
$23$	2.59125	+	0.943139i	0.540314	+	0.196658i	0.597738	−	0.801692i	$-0.296066\pi$
$23$	2.59125	+	0.943139i	0.540314	+	0.196658i	−0.0574239	+	0.998350i	$0.518289\pi$
$24$	−1.08177	−	2.97213i	−0.220815	−	0.606683i
$25$	−3.40062	+	2.85346i	−0.680125	+	0.570692i
$26$	2.89263	+	5.01019i	0.567292	+	0.982579i
$27$	−10.9668	−	6.33170i	−2.11057	−	1.21854i
$28$	1.10368	−	0.194609i	0.208576	−	0.0367776i
$29$	−0.934634	−	5.30057i	−0.173557	−	0.984291i	−0.939796	−	0.341736i	$-0.888985\pi$
$29$	−0.934634	−	5.30057i	−0.173557	−	0.984291i	0.766239	−	0.642556i	$-0.222126\pi$
$30$	−2.05124	−	1.18428i	−0.374504	−	0.216220i
$31$	7.73703	−	4.46698i	1.38961	−	0.802292i	0.396340	−	0.918104i	$-0.370280\pi$
$31$	7.73703	−	4.46698i	1.38961	−	0.802292i	0.993271	+	0.115811i	$0.0369468\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−9.14313	−	5.14243i	−1.59161	−	0.895181i
$34$	−0.433888	+	1.19210i	−0.0744112	+	0.204443i
$35$	0.539466	−	0.642911i	0.0911864	−	0.108672i
$36$	−1.21619	+	6.89736i	−0.202698	+	1.14956i
$37$			4.82219i			0.792763i	0.918086	+	0.396381i	$0.129734\pi$
$37$			4.82219i			0.792763i	−0.918086	+	0.396381i	$0.870266\pi$
$38$	−2.90463	−	3.25010i	−0.471193	−	0.527236i
$39$		−	18.2981i		−	2.93004i
$40$	−0.130039	+	0.737489i	−0.0205610	+	0.116607i
$41$	−0.305487	−	0.256334i	−0.0477091	−	0.0400327i	0.618621	−	0.785689i	$-0.287692\pi$
$41$	−0.305487	−	0.256334i	−0.0477091	−	0.0400327i	−0.666330	+	0.745657i	$0.732136\pi$
$42$	−3.33089	−	1.21234i	−0.513967	−	0.187069i
$43$	1.00105	+	2.75038i	0.152659	+	0.419428i	0.992322	−	0.123680i	$-0.0394696\pi$
$43$	1.00105	+	2.75038i	0.152659	+	0.419428i	−0.839663	+	0.543108i	$0.817247\pi$
$44$	−0.539119	+	3.27251i	−0.0812752	+	0.493350i
$45$	2.62244	+	4.54220i	0.390930	+	0.677111i
$46$	−1.37878	+	2.38811i	−0.203290	+	0.352108i
$47$	1.65688	+	9.39664i	0.241681	+	1.37064i	0.828076	+	0.560616i	$0.189436\pi$
$47$	1.65688	+	9.39664i	0.241681	+	1.37064i	−0.586395	+	0.810025i	$0.699453\pi$
$48$	3.11482	−	0.549227i	0.449586	−	0.0792741i
$49$	−2.87201	+	4.97446i	−0.410287	+	0.710638i
$50$	−2.21960	−	3.84446i	−0.313899	−	0.543689i
$51$	3.07370	−	2.57914i	0.430405	−	0.361152i
$52$	−5.43637	+	1.97868i	−0.753890	+	0.274393i
$53$	0.632679	−	1.73827i	0.0869052	−	0.238770i	−0.888625	−	0.458634i	$-0.848339\pi$
$53$	0.632679	−	1.73827i	0.0869052	−	0.238770i	0.975531	+	0.219864i	$0.0705612\pi$
$54$	8.13987	−	9.70072i	1.10770	−	1.32010i
$55$	1.26599	+	2.13684i	0.170706	+	0.288131i
$56$			1.12071i			0.149761i
$57$	2.81632	+	13.4959i	0.373031	+	1.78758i
$58$	5.38234			0.706736
$59$	1.60668	+	0.283301i	0.209172	+	0.0368827i	0.277252	−	0.960797i	$-0.410576\pi$
$59$	1.60668	+	0.283301i	0.209172	+	0.0368827i	−0.0680801	+	0.997680i	$0.521687\pi$
$60$	1.52249	−	1.81443i	0.196552	−	0.234242i
$61$	−3.64562	+	10.0163i	−0.466773	+	1.28245i	0.453529	+	0.891242i	$0.350165\pi$
$61$	−3.64562	+	10.0163i	−0.466773	+	1.28245i	−0.920302	+	0.391208i	$0.872057\pi$
$62$	3.05559	+	8.39517i	0.388060	+	1.06619i
$63$	5.04535	+	6.01281i	0.635654	+	0.757543i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.16620	+	3.75196i	−0.268684	+	0.465374i
$66$	6.65199	−	8.11125i	0.818803	−	0.998426i
$67$	10.7841	−	1.90153i	1.31749	−	0.232308i	0.529662	−	0.848209i	$-0.322319\pi$
$67$	10.7841	−	1.90153i	1.31749	−	0.232308i	0.787824	+	0.615900i	$0.211208\pi$
$68$	−1.09864	−	0.634302i	−0.133230	−	0.0769205i
$69$	7.55329	−	4.36090i	0.909310	−	0.524990i
$70$	0.539466	+	0.642911i	0.0644785	+	0.0768425i
$71$	−1.89854	−	5.21619i	−0.225315	−	0.619048i	0.774595	−	0.632458i	$-0.217954\pi$
$71$	−1.89854	−	5.21619i	−0.225315	−	0.619048i	−0.999910	+	0.0134094i	$0.995732\pi$
$72$	−6.58139	−	2.39543i	−0.775624	−	0.282304i
$73$	−5.72403	+	6.82163i	−0.669947	+	0.798412i	−0.988777	−	0.149400i	$-0.952266\pi$
$73$	−5.72403	+	6.82163i	−0.669947	+	0.798412i	0.318830	+	0.947812i	$0.396710\pi$
$74$	−4.74893	−	0.837364i	−0.552051	−	0.0973416i
$75$			14.0406i			1.62127i
$76$	3.70511	−	2.29613i	0.425005	−	0.263384i
$77$	2.42112	+	2.82028i	0.275913	+	0.321401i
$78$	18.0201	+	3.17743i	2.04037	+	0.359773i
$79$	7.62542	+	6.39848i	0.857926	+	0.719886i	0.961520	−	0.274734i	$-0.0885898\pi$
$79$	7.62542	+	6.39848i	0.857926	+	0.719886i	−0.103594	+	0.994620i	$0.533034\pi$
$80$	−0.703704	−	0.256127i	−0.0786765	−	0.0286359i
$81$	−17.8931	+	6.51255i	−1.98812	+	0.723617i
$82$	0.305487	−	0.256334i	0.0337354	−	0.0283074i
$83$	11.0979	−	6.40739i	1.21816	−	0.703303i	0.253633	−	0.967301i	$-0.418375\pi$
$83$	11.0979	−	6.40739i	1.21816	−	0.703303i	0.964523	+	0.263998i	$0.0850413\pi$
$84$	1.77233	−	3.06976i	0.193377	−	0.334938i
$85$	−0.935582	+	0.164968i	−0.101478	+	0.0178933i
$86$	−2.88242	+	0.508249i	−0.310820	+	0.0548059i
$87$	−14.7429	−	8.51183i	−1.58061	−	0.912564i
$88$	−3.12918	−	1.09919i	−0.333572	−	0.117175i
$89$	1.44105	+	1.71738i	0.152752	+	0.182042i	0.836993	−	0.547213i	$-0.184311\pi$
$89$	1.44105	+	1.71738i	0.152752	+	0.182042i	−0.684242	+	0.729255i	$0.739867\pi$
$90$	−4.92858	+	1.79386i	−0.519518	+	0.189089i
$91$	−2.21752	+	6.09259i	−0.232459	+	0.638677i
$92$	−2.11241	−	1.77252i	−0.220234	−	0.184798i
$93$	4.90677	−	27.8277i	0.508808	−	2.88559i
$94$	−9.54160			−0.984141
$95$	1.02022	−	3.10070i	0.104672	−	0.318125i
$96$			3.16287i			0.322809i
$97$	−9.60677	−	1.69393i	−0.975420	−	0.171993i	−0.336851	−	0.941558i	$-0.609362\pi$
$97$	−9.60677	−	1.69393i	−0.975420	−	0.171993i	−0.638568	+	0.769565i	$0.720473\pi$
$98$	−4.40017	−	3.69218i	−0.444484	−	0.372967i
$99$	−21.7372	+	8.18997i	−2.18467	+	0.823123i
$100$	4.17148	−	1.51830i	0.417148	−	0.151830i
$101$	−7.72962	−	9.21181i	−0.769126	−	0.916609i	0.229262	−	0.973365i	$-0.426369\pi$
$101$	−7.72962	−	9.21181i	−0.769126	−	0.916609i	−0.998388	+	0.0567558i	$0.981924\pi$
$102$	2.00622	+	3.47487i	0.198645	+	0.344064i
$103$	5.68723	+	3.28353i	0.560380	+	0.323535i	0.753298	−	0.657679i	$-0.228462\pi$
$103$	5.68723	+	3.28353i	0.560380	+	0.323535i	−0.192918	+	0.981215i	$0.561795\pi$
$104$	−1.00460	−	5.69738i	−0.0985093	−	0.558674i
$105$	−0.460944	−	2.61415i	−0.0449836	−	0.255114i
$106$	1.60200	+	0.924915i	0.155600	+	0.0898357i
$107$	0.269354	+	0.466534i	0.0260394	+	0.0451015i	0.878751	−	0.477280i	$-0.158377\pi$
$107$	0.269354	+	0.466534i	0.0260394	+	0.0451015i	−0.852712	+	0.522381i	$0.825044\pi$
$108$	8.13987	+	9.70072i	0.783260	+	0.933453i
$109$	8.27816	−	3.01300i	0.792904	−	0.288593i	0.0863613	−	0.996264i	$-0.472476\pi$
$109$	8.27816	−	3.01300i	0.792904	−	0.288593i	0.706543	+	0.707670i	$0.250254\pi$
$110$	−2.32421	+	0.875699i	−0.221605	+	0.0834946i
$111$	11.6837	+	9.80377i	1.10897	+	0.930533i
$112$	−1.10368	−	0.194609i	−0.104288	−	0.0183888i
$113$			18.6070i			1.75040i	0.483762	+	0.875200i	$0.339270\pi$
$113$			18.6070i			1.75040i	−0.483762	+	0.875200i	$0.660730\pi$
$114$	−13.7799	+	0.429994i	−1.29061	+	0.0402726i
$115$	−2.06504			−0.192566
$116$	−0.934634	+	5.30057i	−0.0867786	+	0.492146i
$117$	−31.0391	−	26.0449i	−2.86957	−	2.40785i
$118$	−0.557995	+	1.53308i	−0.0513676	+	0.141131i
$119$	−1.33599	+	0.486262i	−0.122470	+	0.0445756i
$120$	1.52249	+	1.81443i	0.138983	+	0.165634i
$121$	−10.2493	+	3.99399i	−0.931754	+	0.363090i
$122$	−9.23103	−	5.32954i	−0.835738	−	0.482513i
$123$	−1.24214	+	0.219024i	−0.112000	+	0.0197487i
$124$	−8.79822	+	1.55136i	−0.790104	+	0.139317i
$125$	3.53435	−	6.12167i	0.316122	−	0.547539i
$126$	−6.79758	+	3.92459i	−0.605577	+	0.349630i
$127$	0.519507	−	0.435918i	0.0460988	−	0.0386815i	−0.619447	−	0.785038i	$-0.712643\pi$
$127$	0.519507	−	0.435918i	0.0460988	−	0.0386815i	0.665546	+	0.746357i	$0.268199\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	8.69909	+	3.16621i	0.765912	+	0.278769i
$130$	−3.31881	−	2.78481i	−0.291078	−	0.244244i
$131$	−19.1685	−	3.37992i	−1.67476	−	0.295305i	−0.745988	−	0.665959i	$-0.768023\pi$
$131$	−19.1685	−	3.37992i	−1.67476	−	0.295305i	−0.928771	+	0.370654i	$0.879134\pi$
$132$	6.83292	+	7.95944i	0.594729	+	0.692780i
$133$	0.697821	−	4.83495i	0.0605088	−	0.419244i
$134$			10.9505i			0.945975i
$135$	9.33912	+	1.64674i	0.803783	+	0.141729i
$136$	0.815443	−	0.971808i	0.0699237	−	0.0833318i
$137$	0.744439	+	0.270953i	0.0636017	+	0.0231491i	0.373625	−	0.927580i	$-0.378115\pi$
$137$	0.744439	+	0.270953i	0.0636017	+	0.0231491i	−0.310023	+	0.950729i	$0.600337\pi$
$138$	2.98303	+	8.19580i	0.253932	+	0.697673i
$139$	12.9942	+	15.4859i	1.10215	+	1.31350i	0.945420	+	0.325855i	$0.105652\pi$
$139$	12.9942	+	15.4859i	1.10215	+	1.31350i	0.156735	+	0.987641i	$0.449903\pi$
$140$	−0.726821	+	0.419630i	−0.0614275	+	0.0354652i
$141$	26.1357	+	15.0894i	2.20102	+	1.27076i
$142$	5.46663	−	0.963914i	0.458749	−	0.0808898i
$143$	−14.8364	−	12.1673i	−1.24069	−	1.01748i
$144$	3.50188	−	6.06544i	0.291824	−	0.505453i
$145$	2.01533	+	3.49065i	0.167364	+	0.289883i
$146$	−5.72403	−	6.82163i	−0.473724	−	0.564562i
$147$	6.21368	+	17.0719i	0.512496	+	1.40807i
$148$	1.64928	−	4.53137i	0.135570	−	0.372477i
$149$	5.62123	−	6.69912i	0.460509	−	0.548813i	−0.484956	−	0.874539i	$-0.661164\pi$
$149$	5.62123	−	6.69912i	0.460509	−	0.548813i	0.945464	+	0.325726i	$0.105609\pi$
$150$	−13.8273	−	2.43813i	−1.12900	−	0.199072i
$151$	19.9954			1.62721			0.813603	−	0.581420i	$-0.197503\pi$
$151$	19.9954			1.62721			0.813603	+	0.581420i	$0.197503\pi$
$152$	1.61786	+	4.04753i	0.131226	+	0.328298i
$153$		−	8.88501i		−	0.718310i
$154$	−3.19786	+	1.89460i	−0.257691	+	0.152672i
$155$	−4.30046	+	5.12509i	−0.345422	+	0.411657i
$156$	−6.25831	+	17.1946i	−0.501066	+	1.37667i
$157$	−9.85125	+	3.58556i	−0.786215	+	0.286159i	−0.703762	−	0.710436i	$-0.748498\pi$
$157$	−9.85125	+	3.58556i	−0.786215	+	0.286159i	−0.0824535	+	0.996595i	$0.526276\pi$
$158$	−7.62542	+	6.39848i	−0.606646	+	0.509036i
$159$	−2.92539	−	5.06692i	−0.231998	−	0.401833i
$160$	0.374433	−	0.648537i	0.0296015	−	0.0512714i
$161$	−3.04346	+	0.536644i	−0.239858	+	0.0422935i
$162$	−3.30651	−	18.7521i	−0.259784	−	1.47331i
$163$	−2.88002	+	4.98833i	−0.225580	+	0.390717i	−0.956493	−	0.291754i	$-0.905761\pi$
$163$	−2.88002	+	4.98833i	−0.225580	+	0.390717i	0.730913	+	0.682471i	$0.239094\pi$
$164$	0.199393	+	0.345358i	0.0155699	+	0.0269679i
$165$	7.75118	+	1.27694i	0.603428	+	0.0994097i
$166$	4.38291	+	12.0420i	0.340180	+	0.934637i
$167$	−22.4396	−	8.16734i	−1.73643	−	0.632007i	−0.737372	−	0.675487i	$-0.763933\pi$
$167$	−22.4396	−	8.16734i	−1.73643	−	0.632007i	−0.999054	+	0.0434794i	$0.986156\pi$
$168$	2.71536	+	2.27846i	0.209495	+	0.175787i
$169$	3.55446	−	20.1584i	0.273420	−	1.55064i
$170$		−	0.950015i		−	0.0728628i
$171$	26.9019	+	14.4323i	2.05724	+	1.10367i
$172$		−	2.92689i		−	0.223173i
$173$	3.09831	−	17.5714i	0.235560	−	1.33593i	−0.605870	−	0.795563i	$-0.707175\pi$
$173$	3.09831	−	17.5714i	0.235560	−	1.33593i	0.841431	−	0.540365i	$-0.181714\pi$
$174$	10.9426	−	13.0409i	0.829556	−	0.988627i
$175$	1.70157	−	4.67501i	0.128626	−	0.353398i
$176$	1.62587	−	2.89077i	0.122555	−	0.217900i
$177$	3.95288	−	3.31686i	0.297117	−	0.249311i
$178$	−1.94153	+	1.12094i	−0.145524	+	0.0840181i
$179$	−14.2508	−	8.22773i	−1.06516	−	0.614969i	−0.138304	−	0.990390i	$-0.544165\pi$
$179$	−14.2508	−	8.22773i	−1.06516	−	0.614969i	−0.926855	+	0.375420i	$0.877498\pi$
$180$	−0.910764	−	5.16520i	−0.0678844	−	0.384991i
$181$	−5.10690	+	0.900484i	−0.379593	+	0.0669325i	−0.360189	−	0.932879i	$-0.617288\pi$
$181$	−5.10690	+	0.900484i	−0.379593	+	0.0669325i	−0.0194036	+	0.999812i	$0.506177\pi$
$182$	−5.61496	−	3.24180i	−0.416208	−	0.240298i
$183$	16.8566	+	29.1966i	1.24608	+	2.15827i
$184$	2.11241	−	1.77252i	0.155729	−	0.130672i
$185$	−1.23509	−	3.39339i	−0.0908059	−	0.249487i
$186$	26.5528	+	9.66445i	1.94695	+	0.708632i
$187$	−0.0473667	−	4.20722i	−0.00346380	−	0.307662i
$188$	1.65688	−	9.39664i	0.120841	−	0.685321i
$189$	14.1920			1.03231
$190$	2.87644	+	1.54315i	0.208679	+	0.111952i
$191$	−12.3364			−0.892632			−0.446316	−	0.894875i	$-0.647264\pi$
$191$	−12.3364			−0.892632			−0.446316	+	0.894875i	$0.647264\pi$
$192$	−3.11482	−	0.549227i	−0.224793	−	0.0396371i
$193$	−3.26924	−	2.74322i	−0.235325	−	0.197461i	0.517498	−	0.855685i	$-0.326864\pi$
$193$	−3.26924	−	2.74322i	−0.235325	−	0.197461i	−0.752822	+	0.658224i	$0.771308\pi$
$194$	3.33640	−	9.16667i	0.239539	−	0.658129i
$195$	4.68664	+	12.8764i	0.335617	+	0.922100i
$196$	4.40017	−	3.69218i	0.314298	−	0.263727i
$197$	5.77939	−	3.33673i	0.411764	−	0.237732i	−0.279783	−	0.960063i	$-0.590263\pi$
$197$	5.77939	−	3.33673i	0.411764	−	0.237732i	0.691548	+	0.722331i	$0.256929\pi$
$198$	−4.29092	−	22.8291i	−0.304943	−	1.62239i
$199$	0.00928201	+	0.0526409i	0.000657984	+	0.00373161i	0.985135	−	0.171782i	$-0.0549525\pi$
$199$	0.00928201	+	0.0526409i	0.000657984	+	0.00373161i	−0.984477	+	0.175514i	$0.943841\pi$
$200$	0.770859	+	4.37176i	0.0545080	+	0.309130i
$201$	17.3174	−	29.9947i	1.22148	−	2.11566i
$202$	10.4141	−	6.01258i	0.732733	−	0.423044i
$203$	3.87731	+	4.62080i	0.272134	+	0.324317i
$204$	−3.77046	+	1.37233i	−0.263985	+	0.0960826i
$205$	0.280627	+	0.102140i	0.0195998	+	0.00713375i
$206$	−4.22122	+	5.03065i	−0.294106	+	0.350502i
$207$	3.35371	−	19.0198i	0.233099	−	1.32197i
$208$	5.78527			0.401136
$209$	12.8155	+	6.69056i	0.886465	+	0.462796i
$210$	2.65447			0.183176
$211$	3.80710	−	21.5911i	0.262091	−	1.48639i	−0.515100	−	0.857130i	$-0.672245\pi$
$211$	3.80710	−	21.5911i	0.262091	−	1.48639i	0.777191	−	0.629264i	$-0.216644\pi$
$212$	−1.18905	+	1.41705i	−0.0816642	+	0.0973236i
$213$	−16.4982	−	6.00484i	−1.13044	−	0.411445i
$214$	−0.506219	+	0.184249i	−0.0346044	+	0.0125950i
$215$	−1.40889	−	1.67905i	−0.0960857	−	0.114510i
$216$	−10.9668	+	6.33170i	−0.746198	+	0.430818i
$217$	−5.00617	+	8.67095i	−0.339841	+	0.588622i
$218$	1.52974	+	8.67560i	0.103607	+	0.587586i
$219$	4.89087	+	27.7375i	0.330495	+	1.87433i
$220$	−0.458800	−	2.44096i	−0.0309323	−	0.164570i
$221$	6.35595	−	3.66961i	0.427548	−	0.246845i
$222$	−11.6837	+	9.80377i	−0.784157	+	0.657986i
$223$	−1.94815	−	5.35250i	−0.130458	−	0.358430i	0.857216	−	0.514957i	$-0.172192\pi$
$223$	−1.94815	−	5.35250i	−0.130458	−	0.358430i	−0.987674	+	0.156527i	$0.949970\pi$
$224$	0.383305	−	1.05312i	0.0256106	−	0.0703646i
$225$	23.8172	+	19.9850i	1.58781	+	1.33233i
$226$	−18.3243	−	3.23107i	−1.21892	−	0.214928i
$227$	21.7462			1.44335			0.721673	−	0.692234i	$-0.243373\pi$
$227$	21.7462			1.44335			0.721673	+	0.692234i	$0.243373\pi$
$228$	1.96940	−	13.6453i	0.130427	−	0.903679i
$229$	10.9723			0.725068			0.362534	−	0.931971i	$-0.381912\pi$
$229$	10.9723			0.725068			0.362534	+	0.931971i	$0.381912\pi$
$230$	0.358590	−	2.03367i	0.0236447	−	0.134096i
$231$	11.7555	−	0.132349i	0.773458	−	0.00870793i
$232$	−5.05775	−	1.84087i	−0.332057	−	0.120859i
$233$	−1.01801	−	2.79697i	−0.0666922	−	0.183235i	0.901870	−	0.432008i	$-0.142195\pi$
$233$	−1.01801	−	2.79697i	−0.0666922	−	0.183235i	−0.968562	+	0.248773i	$0.919973\pi$
$234$	31.0391	−	26.0449i	2.02909	−	1.70261i
$235$	−3.57269	−	6.18808i	−0.233057	−	0.403666i
$236$	−1.41289	−	0.815733i	−0.0919714	−	0.0530997i
$237$	31.0058	−	5.46716i	2.01404	−	0.355130i
$238$	−0.246882	−	1.40014i	−0.0160030	−	0.0907573i
$239$	20.3670	+	11.7589i	1.31743	+	0.760618i	0.983314	−	0.181915i	$-0.0582295\pi$
$239$	20.3670	+	11.7589i	1.31743	+	0.760618i	0.334114	+	0.942533i	$0.391563\pi$
$240$	−2.05124	+	1.18428i	−0.132407	+	0.0764452i
$241$	0.365712	−	0.306869i	0.0235576	−	0.0197672i	−0.630933	−	0.775837i	$-0.717328\pi$
$241$	0.365712	−	0.306869i	0.0235576	−	0.0197672i	0.654490	+	0.756070i	$0.272883\pi$
$242$	−2.15354	−	10.7871i	−0.138435	−	0.693423i
$243$	−7.60495	+	20.8944i	−0.487858	+	1.34038i
$244$	6.85152	−	8.16532i	0.438624	−	0.522731i
$245$	0.746947	−	4.23615i	0.0477207	−	0.270638i
$246$		−	1.26131i		−	0.0804180i
$247$	0.786510	+	25.2051i	0.0500444	+	1.60376i
$248$		−	8.93395i		−	0.567306i
$249$	7.03823	−	39.9158i	0.446029	−	2.52956i
$250$	5.41494	+	4.54367i	0.342471	+	0.287367i
$251$	−10.2201	−	3.71980i	−0.645085	−	0.234792i	−0.00130121	−	0.999999i	$-0.500414\pi$
$251$	−10.2201	−	3.71980i	−0.645085	−	0.234792i	−0.643784	+	0.765207i	$0.722636\pi$
$252$	−2.68457	−	7.37581i	−0.169112	−	0.464632i
$253$	1.48665	−	9.02414i	0.0934649	−	0.567343i
$254$	0.339084	+	0.587311i	0.0212760	+	0.0368512i
$255$	−1.50239	+	2.60221i	−0.0940832	+	0.162957i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−11.2440	+	1.98263i	−0.701383	+	0.123673i	−0.512957	−	0.858415i	$-0.671450\pi$
$257$	−11.2440	+	1.98263i	−0.701383	+	0.123673i	−0.188426	+	0.982087i	$0.560339\pi$
$258$	−4.62869	+	8.01712i	−0.288169	+	0.499124i
$259$	−2.70213	−	4.68023i	−0.167902	−	0.290815i
$260$	3.31881	−	2.78481i	0.205824	−	0.172706i
$261$	−35.4233	+	12.8930i	−2.19264	+	0.798057i
$262$	6.65715	−	18.2904i	0.411280	−	1.12998i
$263$	−4.98609	+	5.94219i	−0.307455	+	0.366411i	−0.897542	−	0.440929i	$-0.854649\pi$
$263$	−4.98609	+	5.94219i	−0.307455	+	0.366411i	0.590087	+	0.807340i	$0.299094\pi$
$264$	−9.02504	+	5.34697i	−0.555453	+	0.329083i
$265$			1.38528i			0.0850968i
$266$	4.64032	+	1.52680i	0.284516	+	0.0936142i
$267$	7.09079			0.433949
$268$	−10.7841	−	1.90153i	−0.658743	−	0.116154i
$269$	−17.1089	+	20.3896i	−1.04315	+	1.24317i	−0.0738517	+	0.997269i	$0.523529\pi$
$269$	−17.1089	+	20.3896i	−1.04315	+	1.24317i	−0.969294	+	0.245904i	$0.920915\pi$
$270$	−3.24344	+	8.91128i	−0.197390	+	0.542323i
$271$	6.73391	+	18.5013i	0.409056	+	1.12387i	0.957688	+	0.287808i	$0.0929266\pi$
$271$	6.73391	+	18.5013i	0.409056	+	1.12387i	−0.548632	+	0.836064i	$0.684851\pi$
$272$	0.815443	+	0.971808i	0.0494435	+	0.0589245i
$273$	10.2534	+	17.7594i	0.620564	+	1.07485i
$274$	−0.396108	+	0.686078i	−0.0239297	+	0.0414475i
$275$	11.3844	+	9.33629i	0.686506	+	0.563000i
$276$	−8.58929	+	1.51452i	−0.517014	+	0.0911636i
$277$	−0.874135	−	0.504682i	−0.0525217	−	0.0303234i	0.473509	−	0.880789i	$-0.342987\pi$
$277$	−0.874135	−	0.504682i	−0.0525217	−	0.0303234i	−0.526031	+	0.850465i	$0.676320\pi$
$278$	−17.5070	+	10.1077i	−1.05000	+	0.606219i
$279$	−40.2200	−	47.9324i	−2.40791	−	2.86964i
$280$	−0.287044	−	0.788647i	−0.0171542	−	0.0471306i
$281$	−13.4639	−	4.90046i	−0.803189	−	0.292337i	−0.0923817	−	0.995724i	$-0.529448\pi$
$281$	−13.4639	−	4.90046i	−0.803189	−	0.292337i	−0.710807	+	0.703387i	$0.751670\pi$
$282$	−19.3986	+	23.1184i	−1.15517	+	1.37668i
$283$	−9.78915	−	1.72609i	−0.581905	−	0.102606i	−0.125056	−	0.992150i	$-0.539911\pi$
$283$	−9.78915	−	1.72609i	−0.581905	−	0.102606i	−0.456849	+	0.889544i	$0.651022\pi$
$284$			5.55096i			0.329389i
$285$	−5.43853	−	8.77580i	−0.322151	−	0.519833i
$286$	14.5587	−	12.4982i	0.860877	−	0.739035i
$287$	0.440132	+	0.0776071i	0.0259802	+	0.00458100i
$288$	5.36519	+	4.50193i	0.316147	+	0.265279i
$289$	−14.4625	−	5.26391i	−0.850734	−	0.309642i
$290$	−3.78758	+	1.37856i	−0.222414	+	0.0809521i
$291$	−23.6353	+	19.8324i	−1.38553	+	1.16260i
$292$	7.71197	−	4.45251i	0.451309	−	0.260563i
$293$	4.27187	−	7.39910i	0.249565	−	0.432260i	−0.713840	−	0.700309i	$-0.753046\pi$
$293$	4.27187	−	7.39910i	0.249565	−	0.432260i	0.963405	+	0.268049i	$0.0863789\pi$
$294$	−17.8916	+	3.15477i	−1.04346	+	0.183990i
$295$	−1.20319	+	0.212155i	−0.0700524	+	0.0123521i
$296$	4.17614	+	2.41109i	0.242733	+	0.140142i
$297$	−13.9195	+	39.6261i	−0.807694	+	2.29934i
$298$	5.62123	+	6.69912i	0.325629	+	0.388069i
$299$	14.9911	−	5.45631i	0.866958	−	0.315547i
$300$	4.80218	−	13.1939i	0.277254	−	0.761748i
$301$	−2.51277	−	2.10846i	−0.144834	−	0.121530i
$302$	−3.47217	+	19.6917i	−0.199801	+	1.13313i
$303$	−38.0341			−2.18500
$304$	−4.26698	+	0.890432i	−0.244728	+	0.0510698i
$305$		−	7.98222i		−	0.457061i
$306$	8.75003	+	1.54287i	0.500206	+	0.0881998i
$307$	2.01973	+	1.69475i	0.115272	+	0.0967246i	0.698602	−	0.715511i	$-0.253806\pi$
$307$	2.01973	+	1.69475i	0.115272	+	0.0967246i	−0.583330	+	0.812235i	$0.698250\pi$
$308$	−1.31052	−	3.47827i	−0.0746737	−	0.198193i
$309$	19.5181	−	7.10401i	1.11035	−	0.404133i
$310$	−4.30046	−	5.12509i	−0.244250	−	0.291086i
$311$	2.33526	+	4.04479i	0.132420	+	0.229359i	0.924609	−	0.380917i	$-0.124392\pi$
$311$	2.33526	+	4.04479i	0.132420	+	0.229359i	−0.792189	+	0.610276i	$0.791058\pi$
$312$	−15.8466	−	9.14903i	−0.897137	−	0.517962i
$313$	−4.42754	−	25.1098i	−0.250259	−	1.41929i	−0.807955	−	0.589245i	$-0.799425\pi$
$313$	−4.42754	−	25.1098i	−0.250259	−	1.41929i	0.557695	−	0.830046i	$-0.311686\pi$
$314$	−1.82044	−	10.3242i	−0.102733	−	0.582629i
$315$	−5.09048	−	2.93899i	−0.286816	−	0.165593i
$316$	−4.97714	−	8.62065i	−0.279986	−	0.484950i
$317$	6.80518	+	8.11009i	0.382217	+	0.455508i	0.922513	−	0.385967i	$-0.126132\pi$
$317$	6.80518	+	8.11009i	0.382217	+	0.455508i	−0.540296	+	0.841475i	$0.681688\pi$
$318$	5.49793	−	2.00108i	0.308309	−	0.112215i
$319$	−16.7049	+	6.29393i	−0.935292	+	0.352392i
$320$	0.573665	+	0.481362i	0.0320688	+	0.0269090i
$321$	1.67798	+	0.295873i	0.0936555	+	0.0165140i
$322$		−	3.09041i		−	0.172222i
$323$	−4.12309	+	3.68482i	−0.229415	+	0.205029i
$324$	19.0414			1.05786
$325$	−4.45963	+	25.2918i	−0.247376	+	1.40294i
$326$	−4.41244	−	3.70248i	−0.244383	−	0.205061i
$327$	9.52975	−	26.1828i	0.526996	−	1.44791i
$328$	−0.374735	+	0.136393i	−0.0206913	+	0.00753102i
$329$	−6.87355	−	8.19158i	−0.378951	−	0.451616i
$330$	−2.60352	+	7.41168i	−0.143319	+	0.408000i
$331$	9.86413	+	5.69506i	0.542182	+	0.313029i	0.745963	−	0.665988i	$-0.231990\pi$
$331$	9.86413	+	5.69506i	0.542182	+	0.313029i	−0.203781	+	0.979017i	$0.565323\pi$
$332$	−12.6201	+	2.22526i	−0.692618	+	0.122127i
$333$	33.2604	−	5.86470i	1.82266	−	0.321384i
$334$	11.9398	−	20.6804i	0.653319	−	1.13158i
$335$	−7.10178	+	4.10021i	−0.388012	+	0.224019i
$336$	−2.71536	+	2.27846i	−0.148135	+	0.124300i
$337$	−30.9792	+	11.2755i	−1.68754	+	0.614215i	−0.994313	−	0.106501i	$-0.966035\pi$
$337$	−30.9792	+	11.2755i	−1.68754	+	0.614215i	−0.693230	+	0.720716i	$0.743813\pi$
$338$	19.2349	+	7.00093i	1.04624	+	0.380800i
$339$	45.0829	+	37.8291i	2.44857	+	2.05459i
$340$	0.935582	+	0.164968i	0.0507391	+	0.00894667i
$341$	−19.3005	−	22.4825i	−1.04518	−	1.21749i
$342$	−18.8845	+	23.9870i	−1.02116	+	1.29707i
$343$		−	14.2823i		−	0.771172i
$344$	2.88242	+	0.508249i	0.155410	+	0.0274029i
$345$	−4.19834	+	5.00339i	−0.226031	+	0.269373i
$346$	16.7664	+	6.10248i	0.901369	+	0.328071i
$347$	−1.57201	−	4.31906i	−0.0843900	−	0.231859i	0.890319	−	0.455337i	$-0.150481\pi$
$347$	−1.57201	−	4.31906i	−0.0843900	−	0.231859i	−0.974709	+	0.223478i	$0.928259\pi$
$348$	10.9426	+	13.0409i	0.586585	+	0.699065i
$349$	11.9980	−	6.92706i	0.642239	−	0.370797i	−0.143238	−	0.989688i	$-0.545751\pi$
$349$	11.9980	−	6.92706i	0.642239	−	0.370797i	0.785476	+	0.618892i	$0.212418\pi$
$350$	4.30851	+	2.48752i	0.230300	+	0.132964i
$351$	−72.1482	+	12.7217i	−3.85098	+	0.679032i
$352$	2.56452	+	2.10315i	0.136689	+	0.112098i
$353$	6.39611	−	11.0784i	0.340431	−	0.589643i	−0.644082	−	0.764956i	$-0.722760\pi$
$353$	6.39611	−	11.0784i	0.340431	−	0.589643i	0.984513	+	0.175313i	$0.0560938\pi$
$354$	2.58006	+	4.46880i	0.137129	+	0.237514i
$355$	2.67202	+	3.18439i	0.141816	+	0.169010i
$356$	−0.766769	−	2.10668i	−0.0406387	−	0.111654i
$357$	−1.53798	+	4.22558i	−0.0813988	+	0.223641i
$358$	10.5774	−	12.6056i	0.559031	−	0.666227i
$359$	13.9064	+	2.45207i	0.733952	+	0.129415i	0.528117	−	0.849171i	$-0.322898\pi$
$359$	13.9064	+	2.45207i	0.733952	+	0.129415i	0.205834	+	0.978587i	$0.434009\pi$
$360$	5.24488			0.276430
$361$	−4.45951	−	18.4692i	−0.234711	−	0.972065i
$362$		−	5.18568i		−	0.272553i
$363$	−11.1604	+	32.9530i	−0.585767	+	1.72959i
$364$	4.16757	−	4.96672i	0.218440	−	0.260327i
$365$	2.28082	−	6.26649i	0.119383	−	0.328003i
$366$	−31.6801	+	11.5306i	−1.65595	+	0.602715i
$367$	23.0906	−	19.3753i	1.20532	−	1.01138i	0.205855	−	0.978582i	$-0.434002\pi$
$367$	23.0906	−	19.3753i	1.20532	−	1.01138i	0.999462	−	0.0327986i	$-0.0104420\pi$
$368$	1.37878	+	2.38811i	0.0718737	+	0.124489i
$369$	−1.39650	+	2.41881i	−0.0726988	+	0.125918i
$370$	3.55631	−	0.627074i	0.184884	−	0.0326000i
$371$	0.359993	+	2.04162i	0.0186899	+	0.105996i
$372$	−14.1285	+	24.4712i	−0.732527	+	1.26877i
$373$	0.918775	+	1.59137i	0.0475724	+	0.0823978i	0.888831	−	0.458235i	$-0.151518\pi$
$373$	0.918775	+	1.59137i	0.0475724	+	0.0823978i	−0.841259	+	0.540633i	$0.818185\pi$
$374$	4.15153	+	0.683929i	0.214670	+	0.0353651i
$375$	−7.64668	−	21.0091i	−0.394873	−	1.08490i
$376$	8.96617	+	3.26342i	0.462395	+	0.168298i
$377$	−23.8533	−	20.0153i	−1.22851	−	1.03084i
$378$	−2.46441	+	13.9764i	−0.126756	+	0.718866i
$379$			21.7404i			1.11673i	0.829596	+	0.558364i	$0.188571\pi$
$379$			21.7404i			1.11673i	−0.829596	+	0.558364i	$0.811429\pi$
$380$	−2.01920	+	2.56477i	−0.103583	+	0.131570i
$381$		−	2.14496i		−	0.109890i
$382$	2.14220	−	12.1490i	0.109604	−	0.621597i
$383$	1.32311	−	1.57682i	0.0676079	−	0.0805720i	−0.731180	−	0.682184i	$-0.761030\pi$
$383$	1.32311	−	1.57682i	0.0676079	−	0.0805720i	0.798788	+	0.601612i	$0.205475\pi$
$384$	1.08177	−	2.97213i	0.0552037	−	0.151671i
$385$	−2.42611	−	1.36453i	−0.123646	−	0.0695429i
$386$	3.26924	−	2.74322i	0.166400	−	0.139626i
$387$	17.7529	−	10.2496i	0.902428	−	0.521017i
$388$	8.44805	+	4.87749i	0.428885	+	0.247617i
$389$	−3.74440	−	21.2356i	−0.189849	−	1.07669i	−0.919566	−	0.392936i	$-0.871459\pi$
$389$	−3.74440	−	21.2356i	−0.189849	−	1.07669i	0.729717	−	0.683749i	$-0.239652\pi$
$390$	−13.4946	+	2.37947i	−0.683327	+	0.120489i
$391$	3.02957	+	1.74912i	0.153212	+	0.0884570i
$392$	2.87201	+	4.97446i	0.145058	+	0.251248i
$393$	−47.1598	+	39.5718i	−2.37890	+	1.99613i
$394$	2.28246	+	6.27100i	0.114989	+	0.315929i
$395$	−7.00486	−	2.54956i	−0.352453	−	0.128282i
$396$	23.2274	−	0.261504i	1.16722	−	0.0131411i
$397$	−6.19612	+	35.1399i	−0.310974	+	1.76362i	0.282981	+	0.959126i	$0.408677\pi$
$397$	−6.19612	+	35.1399i	−0.310974	+	1.76362i	−0.593955	+	0.804498i	$0.702434\pi$
$398$	−0.0534529			−0.00267935
$399$	−10.2959	−	11.5205i	−0.515440	−	0.576745i
$400$	−4.43920			−0.221960
$401$	−4.69787	−	0.828361i	−0.234600	−	0.0413664i	0.0551118	−	0.998480i	$-0.482448\pi$
$401$	−4.69787	−	0.828361i	−0.234600	−	0.0413664i	−0.289712	+	0.957114i	$0.593560\pi$
$402$	26.5319	+	22.2629i	1.32329	+	1.11037i
$403$	17.6774	−	48.5683i	0.880575	−	2.41936i
$404$	4.11285	+	11.3000i	0.204622	+	0.562194i
$405$	10.9234	−	9.16582i	0.542788	−	0.455453i
$406$	−5.22389	+	3.01602i	−0.259257	+	0.149682i
$407$	15.7181	−	2.95436i	0.779119	−	0.146442i
$408$	−0.696752	−	3.95148i	−0.0344944	−	0.195627i
$409$	4.92492	+	27.9306i	0.243522	+	1.38108i	0.823901	+	0.566734i	$0.191793\pi$
$409$	4.92492	+	27.9306i	0.243522	+	1.38108i	−0.580379	+	0.814346i	$0.697096\pi$
$410$	−0.149318	+	0.258627i	−0.00737431	+	0.0127727i
$411$	2.16998	−	1.25284i	0.107037	−	0.0617979i
$412$	−4.22122	−	5.03065i	−0.207965	−	0.247842i
$413$	−1.71813	+	0.625349i	−0.0845437	+	0.0307714i
$414$	18.1485	+	6.60552i	0.891951	+	0.324644i
$415$	−6.16855	+	7.35139i	−0.302802	+	0.360866i
$416$	−1.00460	+	5.69738i	−0.0492546	+	0.279337i
$417$	63.9387			3.13109
$418$	−8.81430	+	11.4590i	−0.431122	+	0.560477i
$419$	28.4437			1.38957			0.694783	−	0.719220i	$-0.255501\pi$
$419$	28.4437			1.38957			0.694783	+	0.719220i	$0.255501\pi$
$420$	−0.460944	+	2.61415i	−0.0224918	+	0.127557i
$421$	−11.1660	+	13.3072i	−0.544200	+	0.648552i	−0.966124	−	0.258079i	$-0.916911\pi$
$421$	−11.1660	+	13.3072i	−0.544200	+	0.648552i	0.421924	+	0.906631i	$0.361355\pi$
$422$	20.6020	+	7.49852i	1.00289	+	0.365022i
$423$	62.7970	−	22.8562i	3.05329	−	1.11131i
$424$	−1.18905	−	1.41705i	−0.0577453	−	0.0688181i
$425$	−4.87710	+	2.81579i	−0.236574	+	0.136586i
$426$	8.77849	−	15.2048i	0.425319	−	0.736674i
$427$	−2.07435	−	11.7642i	−0.100385	−	0.569310i
$428$	−0.0935455	−	0.530523i	−0.00452169	−	0.0256438i
$429$	−59.6434	+	11.2105i	−2.87961	+	0.541248i
$430$	1.89820	−	1.09592i	0.0915391	−	0.0528501i
$431$	−3.16429	+	2.65515i	−0.152418	+	0.127894i	−0.715808	−	0.698297i	$-0.753941\pi$
$431$	−3.16429	+	2.65515i	−0.152418	+	0.127894i	0.563390	+	0.826191i	$0.309497\pi$
$432$	−4.33114	−	11.8997i	−0.208382	−	0.572525i
$433$	−0.747657	+	2.05417i	−0.0359301	+	0.0987171i	−0.956360	−	0.292189i	$-0.905616\pi$
$433$	−0.747657	+	2.05417i	−0.0359301	+	0.0987171i	0.920430	+	0.390907i	$0.127838\pi$
$434$	−7.66990	−	6.43581i	−0.368167	−	0.308929i
$435$	12.5548	+	2.21374i	0.601955	+	0.106141i
$436$	−8.80943			−0.421895
$437$	−10.2170	+	6.33169i	−0.488747	+	0.302886i
$438$	−28.1654			−1.34580
$439$	−2.49443	+	14.1466i	−0.119053	+	0.675182i	0.865611	+	0.500718i	$0.166930\pi$
$439$	−2.49443	+	14.1466i	−0.119053	+	0.675182i	−0.984663	+	0.174464i	$0.944181\pi$
$440$	2.48355	−	0.0279609i	0.118399	−	0.00133298i
$441$	37.8036	+	13.7594i	1.80017	+	0.655208i
$442$	2.51016	+	6.89661i	0.119396	+	0.328038i
$443$	−3.76601	+	3.16005i	−0.178928	+	0.150139i	−0.727853	−	0.685733i	$-0.759482\pi$
$443$	−3.76601	+	3.16005i	−0.178928	+	0.150139i	0.548925	+	0.835872i	$0.315037\pi$
$444$	−7.62598	−	13.2086i	−0.361913	−	0.626852i
$445$	−1.45394	−	0.839435i	−0.0689236	−	0.0397931i
$446$	5.60948	−	0.989102i	0.265616	−	0.0468354i
$447$	−4.80303	−	27.2393i	−0.227176	−	1.28838i
$448$	0.970561	+	0.560354i	0.0458547	+	0.0264742i
$449$	−23.0156	+	13.2881i	−1.08617	+	0.627103i	−0.932555	−	0.361027i	$-0.882426\pi$
$449$	−23.0156	+	13.2881i	−1.08617	+	0.627103i	−0.153619	+	0.988130i	$0.549093\pi$
$450$	−23.8172	+	19.9850i	−1.12275	+	0.942101i
$451$	−0.648373	+	1.15280i	−0.0305307	+	0.0542830i
$452$	6.36397	−	17.4849i	0.299336	−	0.822419i
$453$	40.6519	−	48.4470i	1.90999	−	2.27624i
$454$	−3.77619	+	21.4158i	−0.177225	+	1.00509i
$455$		−	4.85535i		−	0.227622i
$456$	13.0960	+	4.30895i	0.613275	+	0.201785i
$457$		−	19.6467i		−	0.919034i	−0.888169	−	0.459517i	$-0.848023\pi$
$457$		−	19.6467i		−	0.919034i	0.888169	−	0.459517i	$-0.151977\pi$
$458$	−1.90531	+	10.8056i	−0.0890295	+	0.504911i
$459$	−12.3064	−	10.3263i	−0.574413	−	0.481990i
$460$	1.94050	+	0.706285i	0.0904764	+	0.0329307i
$461$	6.81212	+	18.7161i	0.317272	+	0.871698i	0.991137	+	0.132843i	$0.0424107\pi$
$461$	6.81212	+	18.7161i	0.317272	+	0.871698i	−0.673865	+	0.738854i	$0.735367\pi$
$462$	−1.91099	+	11.5999i	−0.0889073	+	0.539678i
$463$	−12.1729	−	21.0840i	−0.565722	−	0.979859i	−0.996982	−	0.0776311i	$-0.975264\pi$
$463$	−12.1729	−	21.0840i	−0.565722	−	0.979859i	0.431261	−	0.902227i	$-0.358069\pi$
$464$	2.69117	−	4.66124i	0.124934	−	0.216393i
$465$	3.67451	+	20.8392i	0.170401	+	0.966395i
$466$	2.93125	−	0.516859i	0.135788	−	0.0239430i
$467$	19.4275	−	33.6494i	0.898997	−	1.55711i	0.0702195	−	0.997532i	$-0.477630\pi$
$467$	19.4275	−	33.6494i	0.898997	−	1.55711i	0.828778	−	0.559578i	$-0.189037\pi$
$468$	20.2593	+	35.0902i	0.936488	+	1.62204i
$469$	−9.40109	+	7.88845i	−0.434102	+	0.364255i
$470$	6.71447	−	2.44387i	0.309715	−	0.112727i
$471$	−11.3407	+	31.1583i	−0.522551	+	1.43570i
$472$	1.04869	−	1.24978i	0.0482697	−	0.0575256i
$473$	8.35167	−	4.94803i	0.384010	−	0.227511i
$474$			31.4841i			1.44611i
$475$	−0.603511	−	19.3406i	−0.0276910	−	0.887408i
$476$	1.42173			0.0651651
$477$	−12.7589	−	2.24975i	−0.584192	−	0.103009i
$478$	−15.1169	+	18.0156i	−0.691431	+	0.824016i
$479$	−3.22073	+	8.84889i	−0.147159	+	0.404316i	−0.991269	−	0.131854i	$-0.957907\pi$
$479$	−3.22073	+	8.84889i	−0.147159	+	0.404316i	0.844110	+	0.536170i	$0.180129\pi$
$480$	−0.810098	−	2.22573i	−0.0369758	−	0.101590i
$481$	17.9323	+	21.3708i	0.817641	+	0.974426i
$482$	0.238702	+	0.413443i	0.0108726	+	0.0188318i
$483$	−4.88729	+	8.46503i	−0.222379	+	0.385172i
$484$	10.9972	−	0.247654i	0.499873	−	0.0112570i
$485$	7.19419	−	1.26853i	0.326671	−	0.0576009i
$486$	−19.2564	−	11.1177i	−0.873489	−	0.504309i
$487$	13.8147	−	7.97591i	0.626003	−	0.361423i	−0.153200	−	0.988195i	$-0.548958\pi$
$487$	13.8147	−	7.97591i	0.626003	−	0.361423i	0.779202	+	0.626772i	$0.215624\pi$
$488$	6.85152	+	8.16532i	0.310154	+	0.369627i
$489$	6.23101	+	17.1196i	0.281776	+	0.774173i
$490$	4.04209	+	1.47120i	0.182603	+	0.0664620i
$491$	−26.1204	+	31.1290i	−1.17880	+	1.40483i	−0.283727	+	0.958905i	$0.591571\pi$
$491$	−26.1204	+	31.1290i	−1.17880	+	1.40483i	−0.895069	+	0.445929i	$0.852874\pi$
$492$	1.24214	+	0.219024i	0.0560002	+	0.00987434i
$493$		−	6.82806i		−	0.307521i
$494$	−24.9588	−	3.60226i	−1.12295	−	0.162074i
$495$	13.1989	−	11.3308i	0.593244	−	0.509281i
$496$	8.79822	+	1.55136i	0.395052	+	0.0696583i
$497$	4.76556	+	3.99878i	0.213765	+	0.179370i
$498$	38.0872	+	13.8626i	1.70673	+	0.621198i
$499$	−26.5748	+	9.67244i	−1.18965	+	0.432998i	−0.859601	−	0.510965i	$-0.829288\pi$
$499$	−26.5748	+	9.67244i	−1.18965	+	0.432998i	−0.330051	+	0.943963i	$0.607066\pi$
$500$	−5.41494	+	4.54367i	−0.242163	+	0.203199i
$501$	−65.4095	+	37.7642i	−2.92228	+	1.68718i
$502$	5.43799	−	9.41887i	0.242709	−	0.420385i
$503$	−38.8719	+	6.85416i	−1.73321	+	0.305612i	−0.949093	−	0.314997i	$-0.897996\pi$
$503$	−38.8719	+	6.85416i	−1.73321	+	0.305612i	−0.784120	+	0.620609i	$0.786885\pi$
$504$	7.72992	−	1.36299i	0.344318	−	0.0607126i
$505$	7.79876	+	4.50262i	0.347040	+	0.200364i
$506$	8.62889	+	3.03109i	0.383601	+	0.134748i
$507$	−41.6153	−	49.5952i	−1.84820	−	2.20260i
$508$	−0.637270	+	0.231947i	−0.0282743	+	0.0102910i
$509$	3.17090	−	8.71199i	0.140548	−	0.386152i	−0.849369	−	0.527799i	$-0.823017\pi$
$509$	3.17090	−	8.71199i	0.140548	−	0.386152i	0.989917	+	0.141647i	$0.0452397\pi$
$510$	−2.30179	−	1.93143i	−0.101925	−	0.0855253i
$511$	1.73299	−	9.82830i	0.0766631	−	0.434778i
$512$	−1.00000			−0.0441942
$513$	51.2555	−	20.4876i	2.26299	−	0.904548i
$514$		−	11.4175i		−	0.503604i
$515$	−4.84313	−	0.853974i	−0.213414	−	0.0376306i
$516$	−7.09156	−	5.95053i	−0.312189	−	0.261957i
$517$	29.6137	−	11.1576i	1.30241	−	0.490712i
$518$	5.07834	−	1.84837i	0.223130	−	0.0812125i
$519$	−36.2747	−	43.2305i	−1.59228	−	1.89761i
$520$	2.16620	+	3.75196i	0.0949940	+	0.164534i
$521$	26.6338	+	15.3770i	1.16685	+	0.673680i	0.952936	−	0.303173i	$-0.0980460\pi$
$521$	26.6338	+	15.3770i	1.16685	+	0.673680i	0.213912	+	0.976853i	$0.431379\pi$
$522$	−6.54595	−	37.1240i	−0.286509	−	1.62487i
$523$	−1.38505	−	7.85501i	−0.0605640	−	0.343476i	−1.00000		0.000750489i	$-0.999761\pi$
$523$	−1.38505	−	7.85501i	−0.0605640	−	0.343476i	0.939436	−	0.342725i	$-0.111350\pi$
$524$	16.8565	+	9.73210i	0.736379	+	0.425149i
$525$	−7.86772	−	13.6273i	−0.343375	−	0.594743i
$526$	−4.98609	−	5.94219i	−0.217404	−	0.259092i
$527$	10.6501	−	3.87634i	0.463928	−	0.168856i
$528$	−3.69856	−	9.81642i	−0.160959	−	0.427205i
$529$	−11.7939	−	9.89629i	−0.512780	−	0.430273i
$530$	−1.36423	−	0.240551i	−0.0592584	−	0.0104489i
$531$		−	11.4264i		−	0.495864i
$532$	−2.30939	+	4.30470i	−0.100125	+	0.186632i
$533$	−2.30708			−0.0999307
$534$	−1.23130	+	6.98307i	−0.0532837	+	0.302187i
$535$	−0.309037	−	0.259313i	−0.0133608	−	0.0112111i
$536$	3.74528	−	10.2901i	0.161771	−	0.444463i
$537$	−48.9077	+	17.8010i	−2.11052	+	0.768168i
$538$	−17.1089	−	20.3896i	−0.737616	−	0.879056i
$539$	17.9741	+	6.31379i	0.774198	+	0.271954i
$540$	−8.21268	−	4.74160i	−0.353418	−	0.204046i
$541$	−9.30970	+	1.64155i	−0.400255	+	0.0705758i	−0.370153	−	0.928971i	$-0.620695\pi$
$541$	−9.30970	+	1.64155i	−0.400255	+	0.0705758i	−0.0301028	+	0.999547i	$0.509583\pi$
$542$	−19.3895	+	3.41890i	−0.832852	+	0.146854i
$543$	−8.20083	+	14.2042i	−0.351931	+	0.609563i
$544$	−1.09864	+	0.634302i	−0.0471040	+	0.0271955i
$545$	−5.05366	+	4.24053i	−0.216475	+	0.181644i
$546$	−19.2701	+	7.01373i	−0.824683	+	0.300160i
$547$	−11.0915	−	4.03696i	−0.474237	−	0.172608i	0.0938339	−	0.995588i	$-0.470088\pi$
$547$	−11.0915	−	4.03696i	−0.474237	−	0.172608i	−0.568071	+	0.822980i	$0.692310\pi$
$548$	−0.606872	−	0.509226i	−0.0259243	−	0.0217531i
$549$	73.5195	+	12.9635i	3.13773	+	0.553267i
$550$	−11.1713	+	9.59024i	−0.476347	+	0.408929i
$551$	20.6739	+	11.0911i	0.880737	+	0.472498i
$552$		−	8.72179i		−	0.371224i
$553$	−10.9863	−	1.93719i	−0.467187	−	0.0823777i
$554$	0.648807	−	0.773218i	0.0275652	−	0.0328509i
$555$	−10.7329	−	3.90644i	−0.455585	−	0.165819i
$556$	−6.91407	−	18.9963i	−0.293222	−	0.805621i
$557$	12.4846	+	14.8785i	0.528989	+	0.630424i	0.962682	−	0.270637i	$-0.0872342\pi$
$557$	12.4846	+	14.8785i	0.528989	+	0.630424i	−0.433693	+	0.901061i	$0.642790\pi$
$558$	54.1883	−	31.2856i	2.29397	−	1.32443i
$559$	14.6643	+	8.46642i	0.620232	+	0.358091i
$560$	0.826510	−	0.145736i	0.0349264	−	0.00615847i
$561$	−10.2900	−	8.43875i	−0.434443	−	0.356284i
$562$	7.16399	−	12.4084i	0.302195	−	0.523417i
$563$	−1.17982	−	2.04351i	−0.0497236	−	0.0861238i	0.840092	−	0.542443i	$-0.182501\pi$
$563$	−1.17982	−	2.04351i	−0.0497236	−	0.0861238i	−0.889816	+	0.456320i	$0.849167\pi$
$564$	−19.3986	−	23.1184i	−0.816829	−	0.973459i
$565$	−4.76576	−	13.0938i	−0.200497	−	0.550861i
$566$	3.39974	−	9.34070i	0.142902	−	0.392619i
$567$	13.7170	−	16.3473i	0.576060	−	0.686521i
$568$	−5.46663	−	0.963914i	−0.229375	−	0.0404449i
$569$	−24.2850			−1.01808			−0.509041	−	0.860742i	$-0.670000\pi$
$569$	−24.2850			−1.01808			−0.509041	+	0.860742i	$0.670000\pi$
$570$	9.58686	−	3.83201i	0.401550	−	0.160505i
$571$			29.8373i			1.24865i	0.781164	+	0.624326i	$0.214626\pi$
$571$			29.8373i			1.24865i	−0.781164	+	0.624326i	$0.785374\pi$
$572$	9.78024	+	16.5079i	0.408933	+	0.690228i
$573$	−25.0806	+	29.8899i	−1.04776	+	1.24867i
$574$	−0.152856	+	0.419969i	−0.00638009	+	0.0175292i
$575$	−11.5031	+	4.18678i	−0.479712	+	0.174601i
$576$	−5.36519	+	4.50193i	−0.223550	+	0.187581i
$577$	1.90813	+	3.30498i	0.0794366	+	0.137588i	0.903007	−	0.429626i	$-0.141355\pi$
$577$	1.90813	+	3.30498i	0.0794366	+	0.137588i	−0.823570	+	0.567214i	$0.808021\pi$
$578$	7.69532	−	13.3287i	0.320083	−	0.554400i
$579$	−13.2931	+	2.34393i	−0.552442	+	0.0974104i
$580$	−0.699916	−	3.96942i	−0.0290624	−	0.164821i
$581$	−7.18081	+	12.4375i	−0.297910	+	0.515996i
$582$	−15.4269	−	26.7201i	−0.639464	−	1.10758i
$583$	−6.05360	−	0.997279i	−0.250714	−	0.0413031i
$584$	3.04569	+	8.36797i	0.126032	+	0.346269i
$585$	28.5131	+	10.3779i	1.17887	+	0.429075i
$586$	6.54489	+	5.49181i	0.270367	+	0.226865i
$587$	−1.29139	+	7.32381i	−0.0533012	+	0.302286i	−0.999791	−	0.0204479i	$-0.993491\pi$
$587$	−1.29139	+	7.32381i	−0.0533012	+	0.302286i	0.946490	+	0.322734i	$0.104602\pi$
$588$		−	18.1676i		−	0.749219i
$589$	−5.56283	+	38.5428i	−0.229212	+	1.58813i
$590$		−	1.22175i		−	0.0502987i
$591$	3.66525	−	20.7866i	0.150768	−	0.855048i
$592$	−3.09964	+	3.69401i	−0.127394	+	0.151823i
$593$	−5.36420	+	14.7380i	−0.220281	+	0.605217i	−0.999775	−	0.0211919i	$-0.993254\pi$
$593$	−5.36420	+	14.7380i	−0.220281	+	0.605217i	0.779494	+	0.626409i	$0.215476\pi$
$594$	−36.6069	−	20.5891i	−1.50200	−	0.844779i
$595$	0.815599	−	0.684369i	0.0334363	−	0.0280564i
$596$	−7.57346	+	4.37254i	−0.310221	+	0.179106i
$597$	0.146414	+	0.0845324i	0.00599235	+	0.00345968i
$598$	2.77024	+	15.7108i	0.113284	+	0.642464i
$599$	−21.9820	+	3.87601i	−0.898159	+	0.158370i	−0.603622	−	0.797271i	$-0.706276\pi$
$599$	−21.9820	+	3.87601i	−0.898159	+	0.158370i	−0.294537	+	0.955640i	$0.595165\pi$
$600$	12.1595	+	7.02031i	0.496411	+	0.286603i
$601$	−1.80494	−	3.12625i	−0.0736250	−	0.127522i	0.826862	−	0.562404i	$-0.190123\pi$
$601$	−1.80494	−	3.12625i	−0.0736250	−	0.127522i	−0.900488	+	0.434882i	$0.856790\pi$
$602$	2.51277	−	2.10846i	0.102413	−	0.0859345i
$603$	−26.2310	−	72.0692i	−1.06821	−	2.93488i
$604$	−18.7896	−	6.83885i	−0.764537	−	0.278269i
$605$	6.18950	−	5.43571i	0.251639	−	0.220993i
$606$	6.60454	−	37.4562i	0.268291	−	1.52156i
$607$	−31.0567			−1.26055			−0.630277	−	0.776370i	$-0.717059\pi$
$607$	−31.0567			−1.26055			−0.630277	+	0.776370i	$0.717059\pi$
$608$	−0.135950	−	4.35678i	−0.00551352	−	0.176691i
$609$	19.0785			0.773102
$610$	7.86095	+	1.38610i	0.318281	+	0.0561215i
$611$	42.2862	+	35.4824i	1.71072	+	1.43546i
$612$	−3.03885	+	8.34918i	−0.122838	+	0.337495i
$613$	1.45814	+	4.00620i	0.0588936	+	0.161809i	0.965650	−	0.259846i	$-0.0836717\pi$
$613$	1.45814	+	4.00620i	0.0588936	+	0.161809i	−0.906757	+	0.421655i	$0.861450\pi$
$614$	−2.01973	+	1.69475i	−0.0815095	+	0.0683946i
$615$	0.818004	−	0.472275i	0.0329851	−	0.0190440i
$616$	3.65300	−	0.686612i	0.147184	−	0.0276644i
$617$	−6.03157	−	34.2067i	−0.242822	−	1.37711i	−0.825497	−	0.564406i	$-0.809105\pi$
$617$	−6.03157	−	34.2067i	−0.242822	−	1.37711i	0.582675	−	0.812705i	$-0.302006\pi$
$618$	3.60680	+	20.4552i	0.145087	+	0.822828i
$619$	−19.5881	+	33.9276i	−0.787311	+	1.36366i	0.140297	+	0.990109i	$0.455194\pi$
$619$	−19.5881	+	33.9276i	−0.787311	+	1.36366i	−0.927608	+	0.373554i	$0.878139\pi$
$620$	5.79400	−	3.34517i	0.232693	−	0.134345i
$621$	−22.4461	−	26.7503i	−0.900733	−	1.07345i
$622$	−4.38885	+	1.59741i	−0.175977	+	0.0640504i
$623$	−2.36097	−	0.859324i	−0.0945904	−	0.0344281i
$624$	11.7618	−	14.0171i	0.470848	−	0.561134i
$625$	2.93509	−	16.6457i	0.117403	−	0.665828i
$626$	25.4972			1.01907
$627$	42.2651	−	17.4483i	1.68791	−	0.696820i
$628$	10.4835			0.418336
$629$	−1.06228	+	6.02451i	−0.0423560	+	0.240213i
$630$	3.77829	−	4.50279i	0.150531	−	0.179396i
$631$	32.3566	+	11.7769i	1.28810	+	0.468829i	0.893102	−	0.449854i	$-0.148524\pi$
$631$	32.3566	+	11.7769i	1.28810	+	0.468829i	0.394995	+	0.918683i	$0.370746\pi$
$632$	9.35396	−	3.40456i	0.372080	−	0.135426i
$633$	−44.5731	−	53.1202i	−1.77162	−	2.11134i
$634$	−9.16859	+	5.29349i	−0.364131	+	0.210231i
$635$	−0.253929	+	0.439817i	−0.0100769	+	0.0174536i
$636$	1.01598	+	5.76189i	0.0402861	+	0.228474i
$637$	5.77045	+	32.7258i	0.228633	+	1.29664i
$638$	−3.29754	−	17.5440i	−0.130551	−	0.694573i
$639$	−33.6690	+	19.4388i	−1.33192	+	0.768987i
$640$	−0.573665	+	0.481362i	−0.0226761	+	0.0190275i
$641$	9.75064	+	26.7897i	0.385127	+	1.05813i	0.969167	+	0.246403i	$0.0792488\pi$
$641$	9.75064	+	26.7897i	0.385127	+	1.05813i	−0.584040	+	0.811725i	$0.698529\pi$
$642$	−0.582755	+	1.60111i	−0.0229995	+	0.0631906i
$643$	−23.2541	−	19.5125i	−0.917051	−	0.769497i	0.0563965	−	0.998408i	$-0.482039\pi$
$643$	−23.2541	−	19.5125i	−0.917051	−	0.769497i	−0.973447	+	0.228911i	$0.926483\pi$
$644$	3.04346	+	0.536644i	0.119929	+	0.0211468i
$645$	−6.93254			−0.272968
$646$	−2.91288	−	4.70031i	−0.114606	−	0.184931i
$647$	34.8954			1.37188			0.685940	−	0.727658i	$-0.259391\pi$
$647$	34.8954			1.37188			0.685940	+	0.727658i	$0.259391\pi$
$648$	−3.30651	+	18.7521i	−0.129892	+	0.736654i
$649$	−0.0609151	−	5.41062i	−0.00239113	−	0.212385i
$650$	−24.1332	−	8.78375i	−0.946580	−	0.344527i
$651$	10.8310	+	29.7580i	0.424501	+	1.16631i
$652$	4.41244	−	3.70248i	0.172805	−	0.145000i
$653$	8.96459	+	15.5271i	0.350812	+	0.607624i	0.986392	−	0.164411i	$-0.0525724\pi$
$653$	8.96459	+	15.5271i	0.350812	+	0.607624i	−0.635580	+	0.772035i	$0.719239\pi$
$654$	24.1302	+	13.9316i	0.943564	+	0.544767i
$655$	14.3546	−	2.53111i	0.560882	−	0.0988987i
$656$	−0.0692483	−	0.392727i	−0.00270369	−	0.0153334i
$657$	54.0128	+	31.1843i	2.10724	+	1.21662i
$658$	9.26071	−	5.34667i	0.361020	−	0.208435i
$659$	2.22425	−	1.86637i	0.0866445	−	0.0727034i	−0.598437	−	0.801170i	$-0.704211\pi$
$659$	2.22425	−	1.86637i	0.0866445	−	0.0727034i	0.685081	+	0.728467i	$0.259767\pi$
$660$	−6.84698	−	3.85099i	−0.266518	−	0.149900i
$661$	5.96913	−	16.4000i	0.232172	−	0.637888i	−0.767824	−	0.640661i	$-0.778660\pi$
$661$	5.96913	−	16.4000i	0.232172	−	0.637888i	0.999996	+	0.00277300i	$0.000882673\pi$
$662$	−7.32143	+	8.72534i	−0.284555	+	0.339120i
$663$	4.03090	−	22.8604i	0.156547	−	0.887823i
$664$		−	12.8148i		−	0.497310i
$665$	0.747304	+	3.58111i	0.0289792	+	0.138869i
$666$			33.7735i			1.30869i
$667$	2.57730	−	14.6166i	0.0997936	−	0.565958i
$668$	18.2929	+	15.3496i	0.707774	+	0.593893i
$669$	−16.9293	−	6.16175i	−0.654524	−	0.238227i
$670$	−2.80471	−	7.70588i	−0.108355	−	0.297704i
$671$	34.8820	+	5.74651i	1.34660	+	0.221841i
$672$	−1.77233	−	3.06976i	−0.0683690	−	0.118419i
$673$	−8.09700	+	14.0244i	−0.312116	+	0.540602i	−0.978820	−	0.204721i	$-0.934371\pi$
$673$	−8.09700	+	14.0244i	−0.312116	+	0.540602i	0.666704	+	0.745323i	$0.267705\pi$
$674$	−5.72472	−	32.4665i	−0.220508	−	1.25056i
$675$	55.3613	−	9.76169i	2.13086	−	0.375728i
$676$	−10.2347	+	17.7270i	−0.393641	+	0.681806i
$677$	23.6747	+	41.0058i	0.909894	+	1.57598i	0.814210	+	0.580570i	$0.197170\pi$
$677$	23.6747	+	41.0058i	0.909894	+	1.57598i	0.0956831	+	0.995412i	$0.469496\pi$
$678$	−45.0829	+	37.8291i	−1.73140	+	1.45282i
$679$	10.2732	−	3.73912i	0.394248	−	0.143494i
$680$	−0.324924	+	0.892722i	−0.0124603	+	0.0342343i
$681$	44.2112	−	52.6889i	1.69418	−	2.01904i
$682$	25.4924	−	15.1032i	0.976155	−	0.578332i
$683$			14.5734i			0.557637i	0.960344	+	0.278818i	$0.0899427\pi$
$683$			14.5734i			0.557637i	−0.960344	+	0.278818i	$0.910057\pi$
$684$	−20.3433	−	22.7629i	−0.777846	−	0.870362i
$685$	−0.593263			−0.0226674
$686$	14.0653	+	2.48010i	0.537017	+	0.0946906i
$687$	22.3072	−	26.5847i	0.851073	−	1.01427i
$688$	−1.00105	+	2.75038i	−0.0381649	+	0.104857i
$689$	−3.66022	−	10.0564i	−0.139443	−	0.383117i
$690$	−4.19834	−	5.00339i	−0.159828	−	0.190476i
$691$	−13.8351	−	23.9631i	−0.526311	−	0.911597i	−0.999530	−	0.0306526i	$-0.990241\pi$
$691$	−13.8351	−	23.9631i	−0.526311	−	0.911597i	0.473219	−	0.880945i	$-0.343092\pi$
$692$	−8.92123	+	15.4520i	−0.339134	+	0.587398i
$693$	16.5080	−	20.1294i	0.627086	−	0.764651i
$694$	4.52642	−	0.798131i	0.171821	−	0.0302966i
$695$	−13.1104	−	7.56931i	−0.497307	−	0.287120i
$696$	−14.7429	+	8.51183i	−0.558829	+	0.322640i
$697$	−0.325187	−	0.387542i	−0.0123173	−	0.0146792i
$698$	4.73839	+	13.0186i	0.179351	+	0.492762i
$699$	−8.84645	−	3.21984i	−0.334603	−	0.121786i
$700$	−3.19790	+	3.81110i	−0.120869	+	0.144046i
$701$	−8.86596	−	1.56331i	−0.334863	−	0.0590453i	0.00368886	−	0.999993i	$-0.498826\pi$
$701$	−8.86596	−	1.56331i	−0.334863	−	0.0590453i	−0.338551	+	0.940948i	$0.609937\pi$
$702$		−	73.2612i		−	2.76506i
$703$	−16.5154	−	13.0022i	−0.622889	−	0.490389i
$704$	−2.51652	+	2.16035i	−0.0948449	+	0.0814213i
$705$	−22.2566	−	3.92444i	−0.838232	−	0.147803i
$706$	9.79941	+	8.22268i	0.368806	+	0.309465i
$707$	12.6639	+	4.60930i	0.476277	+	0.173351i
$708$	−4.84893	+	1.76487i	−0.182234	+	0.0663277i
$709$	−22.9147	+	19.2277i	−0.860579	+	0.722112i	−0.962093	−	0.272722i	$-0.912076\pi$
$709$	−22.9147	+	19.2277i	−0.860579	+	0.722112i	0.101514	+	0.994834i	$0.467631\pi$
$710$	−3.60000	+	2.07846i	−0.135106	+	0.0780033i
$711$	34.8587	−	60.3770i	1.30730	−	2.26432i
$712$	2.20782	−	0.389299i	0.0827417	−	0.0145896i
$713$	24.2616	−	4.27797i	0.908603	−	0.160211i
$714$	−3.89431	−	2.24838i	−0.145741	−	0.0841436i
$715$	13.5568	+	4.76214i	0.506997	+	0.178094i
$716$	10.5774	+	12.6056i	0.395295	+	0.471094i
$717$	69.8977	−	25.4407i	2.61038	−	0.950100i
$718$	−4.82964	+	13.2693i	−0.180241	+	0.495207i
$719$	2.78310	+	2.33530i	0.103792	+	0.0870921i	0.693207	−	0.720739i	$-0.256197\pi$
$719$	2.78310	+	2.33530i	0.103792	+	0.0870921i	−0.589415	+	0.807831i	$0.700642\pi$
$720$	−0.910764	+	5.16520i	−0.0339422	+	0.192496i
$721$	−7.35974			−0.274091
$722$	18.9630	−	1.18461i	0.705731	−	0.0440867i
$723$		−	1.50997i		−	0.0561562i
$724$	5.10690	+	0.900484i	0.189796	+	0.0334662i
$725$	18.3033	+	15.3583i	0.679768	+	0.570393i
$726$	−30.5144	−	16.7130i	−1.13250	−	0.620279i
$727$	15.7697	−	5.73972i	0.584868	−	0.212874i	−0.0326030	−	0.999468i	$-0.510380\pi$
$727$	15.7697	−	5.73972i	0.584868	−	0.212874i	0.617471	+	0.786594i	$0.288157\pi$
$728$	4.16757	+	4.96672i	0.154461	+	0.184079i
$729$	6.60174	+	11.4345i	0.244509	+	0.423502i
$730$	5.77523	+	3.33433i	0.213751	+	0.123409i
$731$	0.644767	+	3.65665i	0.0238476	+	0.135246i
$732$	−5.85425	−	33.2011i	−0.216379	−	1.22715i
$733$	28.5285	+	16.4709i	1.05372	+	0.608368i	0.923690	−	0.383141i	$-0.125158\pi$
$733$	28.5285	+	16.4709i	1.05372	+	0.608368i	0.130035	+	0.991509i	$0.458491\pi$
$734$	15.0713	+	26.1042i	0.556291	+	0.963525i
$735$	−8.74519	−	10.4221i	−0.322571	−	0.384425i
$736$	−2.59125	+	0.943139i	−0.0955149	+	0.0347646i
$737$	−12.8051	−	33.9863i	−0.471682	−	1.25190i
$738$	−2.13956	−	1.79530i	−0.0787583	−	0.0660860i
$739$	−29.0512	−	5.12252i	−1.06867	−	0.188435i	−0.388468	−	0.921462i	$-0.626996\pi$
$739$	−29.0512	−	5.12252i	−1.06867	−	0.188435i	−0.680199	+	0.733027i	$0.738107\pi$
$740$			3.61117i			0.132749i
$741$	62.6686	+	49.3378i	2.30219	+	1.81247i
$742$	−2.07312			−0.0761066
$743$	2.10519	−	11.9391i	0.0772318	−	0.438004i	−0.921532	−	0.388302i	$-0.873062\pi$
$743$	2.10519	−	11.9391i	0.0772318	−	0.438004i	0.998764	−	0.0497018i	$-0.0158271\pi$
$744$	−21.6461	−	18.1632i	−0.793584	−	0.665896i
$745$	−2.23985	+	6.15394i	−0.0820619	+	0.225463i
$746$	−1.72673	+	0.628479i	−0.0632202	+	0.0230103i
$747$	−57.6913	−	68.7538i	−2.11081	−	2.51557i
$748$	−1.39444	+	3.96969i	−0.0509859	+	0.145146i
$749$	−0.522848	−	0.301867i	−0.0191045	−	0.0110300i
$750$	22.0177	−	3.88232i	0.803974	−	0.141762i
$751$	−24.6662	+	4.34932i	−0.900084	+	0.158709i	−0.604498	−	0.796607i	$-0.706626\pi$
$751$	−24.6662	+	4.34932i	−0.900084	+	0.158709i	−0.295586	+	0.955316i	$0.595515\pi$
$752$	−4.77080	+	8.26327i	−0.173973	+	0.301330i
$753$	−29.7907	+	17.1997i	−1.08563	+	0.626790i
$754$	23.8533	−	20.0153i	0.868687	−	0.728915i
$755$	−14.0709	+	5.12138i	−0.512092	+	0.186386i
$756$	−13.3361	−	4.85394i	−0.485029	−	0.176536i
$757$	−34.4167	−	28.8790i	−1.25089	−	1.04963i	−0.996591	−	0.0825008i	$-0.973709\pi$
$757$	−34.4167	−	28.8790i	−1.25089	−	1.04963i	−0.254304	−	0.967124i	$-0.581846\pi$
$758$	−21.4101	−	3.77518i	−0.777650	−	0.137121i
$759$	−18.8421	−	21.9486i	−0.683927	−	0.796683i
$760$	−2.17518	−	2.43389i	−0.0789020	−	0.0882864i
$761$		−	17.5983i		−	0.637936i	−0.947765	−	0.318968i	$-0.896664\pi$
$761$		−	17.5983i		−	0.637936i	0.947765	−	0.318968i	$-0.103336\pi$
$762$	2.11237	+	0.372468i	0.0765232	+	0.0134931i
$763$	−6.34611	+	7.56300i	−0.229745	+	0.273799i
$764$	11.5924	+	4.21931i	0.419400	+	0.152649i
$765$	2.27569	+	6.25242i	0.0822779	+	0.226057i
$766$	1.32311	+	1.57682i	0.0478060	+	0.0569730i
$767$	8.17396	−	4.71924i	0.295145	−	0.170402i
$768$	2.73913	+	1.58144i	0.0988398	+	0.0570652i
$769$	−39.5633	+	6.97608i	−1.42669	+	0.251564i	−0.833064	−	0.553177i	$-0.813415\pi$
$769$	−39.5633	+	6.97608i	−1.42669	+	0.251564i	−0.593626	+	0.804741i	$0.702304\pi$
$770$	1.76509	−	2.15230i	0.0636094	−	0.0775635i
$771$	−18.0560	+	31.2740i	−0.650272	+	1.12630i
$772$	2.13384	+	3.69592i	0.0767987	+	0.133019i
$773$	21.0763	+	25.1178i	0.758062	+	0.903423i	0.997724	−	0.0674336i	$-0.0214811\pi$
$773$	21.0763	+	25.1178i	0.758062	+	0.903423i	−0.239662	+	0.970856i	$0.577037\pi$
$774$	7.01115	+	19.2630i	0.252011	+	0.692393i
$775$	−13.5644	+	37.2678i	−0.487247	+	1.33870i
$776$	−6.27037	+	7.47274i	−0.225093	+	0.268256i
$777$	−16.8333	−	2.96817i	−0.603892	−	0.106482i
$778$	21.5631			0.773076
$779$	1.70161	−	0.355091i	0.0609665	−	0.0127225i
$780$		−	13.7028i		−	0.490639i
$781$	−15.8393	+	9.38413i	−0.566774	+	0.335791i
$782$	−2.24863	+	2.67981i	−0.0804108	+	0.0958299i
$783$	−23.3117	+	64.0482i	−0.833091	+	2.28890i
$784$	−5.39761	+	1.96457i	−0.192772	+	0.0701632i
$785$	6.01401	−	5.04635i	0.214649	−	0.180112i
$786$	−30.7814	−	53.3149i	−1.09794	−	1.90168i
$787$	9.30137	−	16.1104i	0.331558	−	0.574276i	−0.651259	−	0.758855i	$-0.725759\pi$
$787$	9.30137	−	16.1104i	0.331558	−	0.574276i	0.982818	+	0.184580i	$0.0590924\pi$
$788$	−6.57208	+	1.15883i	−0.234121	+	0.0412818i
$789$	4.26034	+	24.1616i	0.151672	+	0.860176i
$790$	3.72721	−	6.45572i	0.132608	−	0.229684i
$791$	−10.4265	−	18.0592i	−0.370724	−	0.642112i
$792$	−3.77586	+	22.9199i	−0.134169	+	0.814424i
$793$	21.0909	+	57.9467i	0.748959	+	2.05775i
$794$	−33.5301	−	12.2040i	−1.18994	−	0.433103i
$795$	3.35639	+	2.81634i	0.119039	+	0.0998854i
$796$	0.00928201	−	0.0526409i	0.000328992	−	0.00186581i
$797$		−	15.7493i		−	0.557867i	−0.960310	−	0.278934i	$-0.910019\pi$
$797$		−	15.7493i		−	0.557867i	0.960310	−	0.278934i	$-0.0899809\pi$
$798$	13.1333	−	8.13897i	0.464915	−	0.288117i
$799$			12.1045i			0.428227i
$800$	0.770859	−	4.37176i	0.0272540	−	0.154565i
$801$	10.0928	−	12.0281i	0.356612	−	0.424993i
$802$	1.63155	−	4.48265i	0.0576121	−	0.158288i
$803$	25.7423	+	14.4784i	0.908427	+	0.510932i
$804$	−26.5319	+	22.2629i	−0.935707	+	0.785151i
$805$	2.00425	−	1.15715i	0.0706404	−	0.0407843i
$806$	44.7608	+	25.8427i	1.57663	+	0.910269i
$807$	14.6186	+	82.9062i	0.514599	+	2.91844i
$808$	−11.8425	+	2.08815i	−0.416617	+	0.0734608i
$809$	−12.2225	−	7.05664i	−0.429719	−	0.248098i	0.269508	−	0.962998i	$-0.413139\pi$
$809$	−12.2225	−	7.05664i	−0.429719	−	0.248098i	−0.699227	+	0.714900i	$0.746472\pi$
$810$	7.12974	+	12.3491i	0.250513	+	0.433902i
$811$	11.2691	−	9.45588i	0.395711	−	0.332041i	−0.423122	−	0.906073i	$-0.639066\pi$
$811$	11.2691	−	9.45588i	0.395711	−	0.332041i	0.818833	+	0.574032i	$0.194621\pi$
$812$	−2.06308	−	5.66825i	−0.0723998	−	0.198917i
$813$	58.5172	+	21.2985i	2.05229	+	0.746971i
$814$	0.180049	+	15.9924i	0.00631071	+	0.560532i
$815$	0.749030	−	4.24796i	0.0262374	−	0.148800i
$816$	4.01244			0.140463
$817$	−12.1189	−	3.98746i	−0.423986	−	0.139504i
$818$	−28.3615			−0.991636
$819$	44.7197	+	7.88529i	1.56263	+	0.275534i
$820$	−0.228769	−	0.191960i	−0.00798896	−	0.00670353i
$821$	−1.60498	+	4.40966i	−0.0560143	+	0.153898i	−0.964544	−	0.263922i	$-0.914984\pi$
$821$	−1.60498	+	4.40966i	−0.0560143	+	0.153898i	0.908530	+	0.417821i	$0.137206\pi$
$822$	0.856991	+	2.35456i	0.0298910	+	0.0821249i
$823$	11.3010	−	9.48267i	0.393928	−	0.330545i	−0.424213	−	0.905563i	$-0.639449\pi$
$823$	11.3010	−	9.48267i	0.393928	−	0.330545i	0.818141	+	0.575017i	$0.195005\pi$
$824$	5.68723	−	3.28353i	0.198124	−	0.114387i
$825$	45.7661	−	8.60212i	1.59337	−	0.299488i
$826$	−0.317498	−	1.80062i	−0.0110472	−	0.0626516i
$827$	9.24267	+	52.4178i	0.321399	+	1.82275i	0.533856	+	0.845575i	$0.320742\pi$
$827$	9.24267	+	52.4178i	0.321399	+	1.82275i	−0.212457	+	0.977170i	$0.568147\pi$
$828$	−9.65663	+	16.7258i	−0.335591	+	0.581261i
$829$	−14.4291	+	8.33066i	−0.501144	+	0.289336i	−0.729186	−	0.684315i	$-0.760101\pi$
$829$	−14.4291	+	8.33066i	−0.501144	+	0.289336i	0.228042	+	0.973651i	$0.426768\pi$
$830$	−6.16855	−	7.35139i	−0.214113	−	0.255170i
$831$	−2.99996	+	1.09190i	−0.104067	+	0.0378775i
$832$	−5.43637	−	1.97868i	−0.188472	−	0.0685983i
$833$	−4.68392	+	5.58208i	−0.162288	+	0.193408i
$834$	−11.1028	+	62.9674i	−0.384460	+	2.18038i
$835$	17.8827			0.618856
$836$	−9.75430	−	10.6702i	−0.337359	−	0.369037i
$837$	−113.134			−3.91049
$838$	−4.93919	+	28.0116i	−0.170622	+	0.967644i
$839$	26.9664	−	32.1374i	0.930985	−	1.10950i	−0.0627819	−	0.998027i	$-0.519997\pi$
$839$	26.9664	−	32.1374i	0.930985	−	1.10950i	0.993767	−	0.111477i	$-0.0355583\pi$
$840$	−2.49439	−	0.907883i	−0.0860646	−	0.0313249i
$841$	0.0285682	−	0.0103980i	0.000985110	−	0.000358551i
$842$	−11.1660	−	13.3072i	−0.384807	−	0.458596i
$843$	−39.2462	+	22.6588i	−1.35171	+	0.780410i
$844$	−10.9621	+	18.9869i	−0.377331	+	0.653557i
$845$	2.66182	+	15.0959i	0.0915693	+	0.519315i
$846$	11.6044	+	65.8119i	0.398968	+	2.26266i
$847$	7.70952	−	9.61964i	0.264902	−	0.330535i
$848$	1.60200	−	0.924915i	0.0550129	−	0.0317617i
$849$	−24.0840	+	20.2089i	−0.826562	+	0.693568i
$850$	−1.92612	−	5.29196i	−0.0660653	−	0.181513i
$851$	−4.54799	+	12.4955i	−0.155903	+	0.428340i
$852$	13.4494	+	11.2854i	0.460770	+	0.386632i
$853$	−50.3868	−	8.88456i	−1.72521	−	0.304201i	−0.778826	−	0.627240i	$-0.784185\pi$
$853$	−50.3868	−	8.88456i	−1.72521	−	0.304201i	−0.946386	+	0.323038i	$0.895296\pi$
$854$	11.9457			0.408773
$855$	−22.6275	−	3.26579i	−0.773843	−	0.111688i
$856$	0.538707			0.0184126
$857$	2.37075	−	13.4452i	0.0809834	−	0.459279i	−0.917168	−	0.398501i	$-0.869531\pi$
$857$	2.37075	−	13.4452i	0.0809834	−	0.459279i	0.998151	−	0.0607785i	$-0.0193583\pi$
$858$	−0.683207	−	60.6840i	−0.0233243	−	2.07172i
$859$	36.1978	+	13.1749i	1.23505	+	0.449522i	0.875325	−	0.483535i	$-0.160647\pi$
$859$	36.1978	+	13.1749i	1.23505	+	0.449522i	0.359728	+	0.933057i	$0.382870\pi$
$860$	0.749656	+	2.05966i	0.0255631	+	0.0702339i
$861$	1.08285	−	0.908616i	0.0369033	−	0.0309656i
$862$	−2.06534	−	3.57728i	−0.0703459	−	0.121843i
$863$	−15.7787	−	9.10981i	−0.537112	−	0.310102i	0.206796	−	0.978384i	$-0.433696\pi$
$863$	−15.7787	−	9.10981i	−0.537112	−	0.310102i	−0.743908	+	0.668283i	$0.767030\pi$
$864$	12.4710	−	2.19898i	0.424272	−	0.0748107i
$865$	2.32022	+	13.1586i	0.0788899	+	0.447407i
$866$	−1.89313	−	1.09300i	−0.0643313	−	0.0371417i
$867$	−42.1569	+	24.3393i	−1.43172	+	0.826607i
$868$	7.66990	−	6.43581i	0.260333	−	0.218446i
$869$	16.1844	−	28.7755i	0.549017	−	0.976142i
$870$	−4.36023	+	11.9796i	−0.147825	+	0.406147i
$871$	40.7214	−	48.5299i	1.37979	−	1.64437i
$872$	1.52974	−	8.67560i	0.0518036	−	0.293793i
$873$			68.3215i			2.31233i
$874$	−4.46133	−	11.1613i	−0.150907	−	0.377536i
$875$			7.92194i			0.267811i
$876$	4.89087	−	27.7375i	0.165247	−	0.937164i
$877$	−20.0748	−	16.8448i	−0.677878	−	0.568807i	0.237508	−	0.971386i	$-0.423670\pi$
$877$	−20.0748	−	16.8448i	−0.677878	−	0.568807i	−0.915385	+	0.402579i	$0.868114\pi$
$878$	−13.4986	−	4.91307i	−0.455554	−	0.165808i
$879$	−9.24233	−	25.3931i	−0.311736	−	0.856488i
$880$	−0.403728	+	2.45068i	−0.0136097	+	0.0826123i
$881$	−7.93864	−	13.7501i	−0.267459	−	0.463253i	0.700746	−	0.713411i	$-0.252851\pi$
$881$	−7.93864	−	13.7501i	−0.267459	−	0.463253i	−0.968205	+	0.250158i	$0.919517\pi$
$882$	−20.1149	+	34.8400i	−0.677303	+	1.17312i
$883$	9.58488	+	54.3585i	0.322557	+	1.82931i	0.526315	+	0.850290i	$0.323573\pi$
$883$	9.58488	+	54.3585i	0.322557	+	1.82931i	−0.203758	+	0.979021i	$0.565316\pi$
$884$	−7.22772	+	1.27444i	−0.243095	+	0.0428641i
$885$	−1.93212	+	3.34653i	−0.0649475	+	0.112492i
$886$	−2.45809	−	4.25753i	−0.0825810	−	0.143035i
$887$	36.2003	−	30.3756i	1.21549	−	1.01991i	0.216438	−	0.976296i	$-0.430556\pi$
$887$	36.2003	−	30.3756i	1.21549	−	1.01991i	0.999048	−	0.0436173i	$-0.0138882\pi$
$888$	14.3322	−	5.21648i	0.480956	−	0.175054i
$889$	−0.259945	+	0.714193i	−0.00871828	+	0.0239533i
$890$	1.07916	−	1.28609i	0.0361734	−	0.0431098i
$891$	32.1903	+	54.3334i	1.07842	+	1.82024i
$892$			5.69601i			0.190717i
$893$	−36.6498	−	19.6619i	−1.22644	−	0.657961i
$894$	27.6596			0.925074
$895$	12.1357	+	2.13986i	0.405653	+	0.0715275i
$896$	−0.720377	+	0.858512i	−0.0240661	+	0.0286809i
$897$	17.2576	−	47.4149i	0.576215	−	1.58314i
$898$	−9.08958	−	24.9734i	−0.303323	−	0.833374i
$899$	−30.9088	−	36.8357i	−1.03087	−	1.22854i
$900$	−15.5456	−	26.9257i	−0.518185	−	0.897523i
$901$	1.17335	−	2.03231i	0.0390900	−	0.0677059i
$902$	−1.02269	−	0.838704i	−0.0340519	−	0.0279258i
$903$	−10.2172	+	1.80157i	−0.340007	+	0.0599524i
$904$	16.1141	+	9.30350i	0.535948	+	0.309430i
$905$	3.36311	−	1.94169i	0.111793	−	0.0645440i
$906$	40.6519	+	48.4470i	1.35057	+	1.60954i
$907$	2.06048	+	5.66113i	0.0684172	+	0.187975i	0.969189	−	0.246318i	$-0.0792207\pi$
$907$	2.06048	+	5.66113i	0.0684172	+	0.187975i	−0.900772	+	0.434292i	$0.856998\pi$
$908$	−20.4347	−	7.43764i	−0.678151	−	0.246827i
$909$	−54.1365	+	64.5173i	−1.79559	+	2.13990i
$910$	4.78158	+	0.843122i	0.158508	+	0.0279492i
$911$			46.7608i			1.54925i	0.632418	+	0.774627i	$0.282062\pi$
$911$			46.7608i			1.54925i	−0.632418	+	0.774627i	$0.717938\pi$
$912$	−6.51758	+	12.1488i	−0.215819	+	0.402286i
$913$	−27.6844	−	32.2487i	−0.916221	−	1.06728i
$914$	19.3482	+	3.41161i	0.639982	+	0.112846i
$915$	−19.3401	−	16.2283i	−0.639365	−	0.536491i
$916$	−10.3106	−	3.75274i	−0.340670	−	0.123994i
$917$	20.4982	−	7.46072i	0.676909	−	0.246375i
$918$	12.3064	−	10.3263i	0.406171	−	0.340818i
$919$	1.03263	−	0.596188i	0.0340633	−	0.0196664i	−0.482872	−	0.875691i	$-0.660406\pi$
$919$	1.03263	−	0.596188i	0.0340633	−	0.0196664i	0.516935	+	0.856025i	$0.327073\pi$
$920$	−1.03252	+	1.78838i	−0.0340412	+	0.0589610i
$921$	8.21243	−	1.44807i	0.270609	−	0.0477156i
$922$	−19.6147	+	3.45860i	−0.645976	+	0.113903i
$923$	−27.8114	−	16.0569i	−0.915422	−	0.528519i
$924$	−11.0919	−	3.89627i	−0.364896	−	0.128178i
$925$	−13.7599	−	16.3984i	−0.452424	−	0.539177i
$926$	22.8775	−	8.32674i	0.751802	−	0.273634i
$927$	15.7309	−	43.2203i	0.516671	−	1.41954i
$928$	4.12311	+	3.45970i	0.135348	+	0.113570i
$929$	6.81465	−	38.6478i	0.223581	−	1.26799i	−0.641797	−	0.766874i	$-0.721811\pi$
$929$	6.81465	−	38.6478i	0.223581	−	1.26799i	0.865379	−	0.501118i	$-0.167078\pi$
$930$	−21.1607			−0.693886
$931$	−9.29300	−	23.2491i	−0.304566	−	0.761958i
$932$			2.97647i			0.0974975i
$933$	14.5478	+	2.56518i	0.476275	+	0.0839801i
$934$	29.7647	+	24.9755i	0.973929	+	0.817224i
$935$	1.11092	+	2.94851i	0.0363308	+	0.0964264i
$936$	−38.0751	+	13.8582i	−1.24452	+	0.452969i
$937$	6.53290	+	7.78561i	0.213420	+	0.254345i	0.862125	−	0.506696i	$-0.169133\pi$
$937$	6.53290	+	7.78561i	0.213420	+	0.254345i	−0.648704	+	0.761040i	$0.724689\pi$
$938$	−6.13613	−	10.6281i	−0.200352	−	0.347019i
$939$	−69.8400	−	40.3222i	−2.27914	−	1.31586i
$940$	1.24078	+	7.03683i	0.0404699	+	0.229516i
$941$	−1.56388	−	8.86918i	−0.0509809	−	0.289127i	0.948649	−	0.316331i	$-0.102451\pi$
$941$	−1.56388	−	8.86918i	−0.0509809	−	0.289127i	−0.999630	+	0.0272035i	$0.991340\pi$
$942$	−28.7156	−	16.5790i	−0.935605	−	0.540172i
$943$	−0.549836	−	0.952343i	−0.0179051	−	0.0310126i
$944$	1.04869	+	1.24978i	0.0341318	+	0.0406767i
$945$	−9.98694	+	3.63495i	−0.324875	+	0.118245i
$946$	3.42260	+	9.08401i	0.111278	+	0.295347i
$947$	−11.8750	−	9.96433i	−0.385887	−	0.323797i	0.429122	−	0.903247i	$-0.358823\pi$
$947$	−11.8750	−	9.96433i	−0.385887	−	0.323797i	−0.815008	+	0.579449i	$0.803268\pi$
$948$	−31.0058	−	5.46716i	−1.00702	−	0.177565i
$949$			51.5179i			1.67234i
$950$	19.1516	+	2.76412i	0.621359	+	0.0896798i
$951$	33.4853			1.08583
$952$	−0.246882	+	1.40014i	−0.00800148	+	0.0453787i
$953$	23.3692	+	19.6091i	0.757002	+	0.635200i	0.937344	−	0.348404i	$-0.113276\pi$
$953$	23.3692	+	19.6091i	0.757002	+	0.635200i	−0.180343	+	0.983604i	$0.557721\pi$
$954$	4.43114	−	12.1744i	0.143463	−	0.394162i
$955$	8.68119	−	3.15970i	0.280917	−	0.102245i
$956$	−15.1169	−	18.0156i	−0.488916	−	0.582667i
$957$	−18.7123	+	53.2701i	−0.604883	+	1.72198i
$958$	−8.15518	−	4.70839i	−0.263482	−	0.152121i
$959$	−0.874353	+	0.154172i	−0.0282343	+	0.00497847i
$960$	2.33258	−	0.411298i	0.0752839	−	0.0132746i
$961$	24.4077	−	42.2754i	0.787346	−	1.36372i
$962$	−24.1601	+	13.9488i	−0.778952	+	0.449728i
$963$	2.89027	−	2.42522i	0.0931376	−	0.0781517i
$964$	−0.448612	+	0.163282i	−0.0144488	+	0.00525894i
$965$	3.00319	+	1.09307i	0.0966761	+	0.0351872i
$966$	−7.48776	−	6.28298i	−0.240915	−	0.202152i
$967$	2.49861	+	0.440572i	0.0803498	+	0.0141678i	0.213679	−	0.976904i	$-0.431455\pi$
$967$	2.49861	+	0.440572i	0.0803498	+	0.0141678i	−0.133329	+	0.991072i	$0.542567\pi$
$968$	−1.66575	+	10.8731i	−0.0535394	+	0.349476i
$969$	0.545493	+	17.4813i	0.0175237	+	0.561580i
$970$			7.30517i			0.234555i
$971$	−50.8749	−	8.97062i	−1.63265	−	0.287881i	−0.719194	−	0.694810i	$-0.755489\pi$
$971$	−50.8749	−	8.97062i	−1.63265	−	0.287881i	−0.913460	+	0.406929i	$0.866600\pi$
$972$	14.2926	−	17.0333i	0.458437	−	0.546343i
$973$	−21.2893	−	7.74865i	−0.682502	−	0.248410i
$974$	5.45584	+	14.9898i	0.174816	+	0.480304i
$975$	52.2129	+	62.2249i	1.67215	+	1.99279i
$976$	−9.23103	+	5.32954i	−0.295478	+	0.170594i
$977$	−3.48092	−	2.00971i	−0.111365	−	0.0642963i	0.443283	−	0.896382i	$-0.353814\pi$
$977$	−3.48092	−	2.00971i	−0.111365	−	0.0642963i	−0.554648	+	0.832085i	$0.687147\pi$
$978$	−17.9415	+	3.16357i	−0.573705	+	0.101160i
$979$	4.71501	−	5.74936i	0.150692	−	0.183750i
$980$	−2.15075	+	3.72521i	−0.0687032	+	0.118997i
$981$	−30.8496	−	53.4331i	−0.984952	−	1.70599i
$982$	−26.1204	−	31.1290i	−0.833534	−	0.993367i
$983$	−1.18396	−	3.25289i	−0.0377623	−	0.103751i	0.919378	−	0.393374i	$-0.128692\pi$
$983$	−1.18396	−	3.25289i	−0.0377623	−	0.103751i	−0.957141	+	0.289623i	$0.906470\pi$
$984$	−0.431392	+	1.18524i	−0.0137523	+	0.0377841i
$985$	−3.21235	+	3.82833i	−0.102354	+	0.121981i
$986$	6.72433	+	1.18568i	0.214146	+	0.0377598i
$987$	−33.8217			−1.07656
$988$	7.88159	−	23.9541i	0.250747	−	0.762081i
$989$			8.07105i			0.256645i
$990$	8.86670	+	14.9659i	0.281802	+	0.475648i
$991$	2.42945	−	2.89531i	0.0771741	−	0.0919725i	−0.726076	−	0.687615i	$-0.758658\pi$
$991$	2.42945	−	2.89531i	0.0771741	−	0.0919725i	0.803250	+	0.595642i	$0.203102\pi$
$992$	−3.05559	+	8.39517i	−0.0970151	+	0.266547i
$993$	33.8529	−	12.3214i	1.07429	−	0.391009i
$994$	−4.76556	+	3.99878i	−0.151154	+	0.126834i
$995$	−0.0200146	−	0.0346662i	−0.000634504	−	0.00109899i
$996$	−20.2658	+	35.1013i	−0.642145	+	1.11223i
$997$	52.3920	−	9.23813i	1.65927	−	0.292574i	0.736074	−	0.676901i	$-0.236677\pi$
$997$	52.3920	−	9.23813i	1.65927	−	0.292574i	0.923197	+	0.384326i	$0.125566\pi$
$998$	−4.91083	−	27.8507i	−0.155450	−	0.881598i
$999$	30.5326	−	52.8841i	0.966010	−	1.67318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.a.21.10	✓	60
11.10	odd	2		418.2.q.b.21.10	yes	60
19.10	odd	18		418.2.q.b.219.10	yes	60
209.10	even	18	inner	418.2.q.a.219.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.21.10	✓	60	1.1	even	1	trivial
418.2.q.a.219.10	yes	60	209.10	even	18	inner
418.2.q.b.21.10	yes	60	11.10	odd	2
418.2.q.b.219.10	yes	60	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(2.03306 - 2.42290i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.703704 + 0.256127i) q^{5} +(2.03306 + 2.42290i) q^{6} +(-0.970561 + 0.560354i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.21619 - 6.89736i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(2.03306 - 2.42290i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.703704 + 0.256127i) q^{5} +(2.03306 + 2.42290i) q^{6} +(-0.970561 + 0.560354i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.21619 - 6.89736i) q^{9} +(-0.130039 - 0.737489i) q^{10} +(-0.612660 - 3.25955i) q^{11} +(-2.73913 + 1.58144i) q^{12} +(4.43177 - 3.71870i) q^{13} +(-0.383305 - 1.05312i) q^{14} +(-0.810098 + 2.22573i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.24933 + 0.220291i) q^{17} +7.00376 q^{18} +(-2.69634 + 3.42487i) q^{19} +0.748866 q^{20} +(-0.615523 + 3.49080i) q^{21} +(3.31641 - 0.0373376i) q^{22} +(2.59125 + 0.943139i) q^{23} +(-1.08177 - 2.97213i) q^{24} +(-3.40062 + 2.85346i) q^{25} +(2.89263 + 5.01019i) q^{26} +(-10.9668 - 6.33170i) q^{27} +(1.10368 - 0.194609i) q^{28} +(-0.934634 - 5.30057i) q^{29} +(-2.05124 - 1.18428i) q^{30} +(7.73703 - 4.46698i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-9.14313 - 5.14243i) q^{33} +(-0.433888 + 1.19210i) q^{34} +(0.539466 - 0.642911i) q^{35} +(-1.21619 + 6.89736i) q^{36} +4.82219i q^{37} +(-2.90463 - 3.25010i) q^{38} -18.2981i q^{39} +(-0.130039 + 0.737489i) q^{40} +(-0.305487 - 0.256334i) q^{41} +(-3.33089 - 1.21234i) q^{42} +(1.00105 + 2.75038i) q^{43} +(-0.539119 + 3.27251i) q^{44} +(2.62244 + 4.54220i) q^{45} +(-1.37878 + 2.38811i) q^{46} +(1.65688 + 9.39664i) q^{47} +(3.11482 - 0.549227i) q^{48} +(-2.87201 + 4.97446i) q^{49} +(-2.21960 - 3.84446i) q^{50} +(3.07370 - 2.57914i) q^{51} +(-5.43637 + 1.97868i) q^{52} +(0.632679 - 1.73827i) q^{53} +(8.13987 - 9.70072i) q^{54} +(1.26599 + 2.13684i) q^{55} +1.12071i q^{56} +(2.81632 + 13.4959i) q^{57} +5.38234 q^{58} +(1.60668 + 0.283301i) q^{59} +(1.52249 - 1.81443i) q^{60} +(-3.64562 + 10.0163i) q^{61} +(3.05559 + 8.39517i) q^{62} +(5.04535 + 6.01281i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.16620 + 3.75196i) q^{65} +(6.65199 - 8.11125i) q^{66} +(10.7841 - 1.90153i) q^{67} +(-1.09864 - 0.634302i) q^{68} +(7.55329 - 4.36090i) q^{69} +(0.539466 + 0.642911i) q^{70} +(-1.89854 - 5.21619i) q^{71} +(-6.58139 - 2.39543i) q^{72} +(-5.72403 + 6.82163i) q^{73} +(-4.74893 - 0.837364i) q^{74} +14.0406i q^{75} +(3.70511 - 2.29613i) q^{76} +(2.42112 + 2.82028i) q^{77} +(18.0201 + 3.17743i) q^{78} +(7.62542 + 6.39848i) q^{79} +(-0.703704 - 0.256127i) q^{80} +(-17.8931 + 6.51255i) q^{81} +(0.305487 - 0.256334i) q^{82} +(11.0979 - 6.40739i) q^{83} +(1.77233 - 3.06976i) q^{84} +(-0.935582 + 0.164968i) q^{85} +(-2.88242 + 0.508249i) q^{86} +(-14.7429 - 8.51183i) q^{87} +(-3.12918 - 1.09919i) q^{88} +(1.44105 + 1.71738i) q^{89} +(-4.92858 + 1.79386i) q^{90} +(-2.21752 + 6.09259i) q^{91} +(-2.11241 - 1.77252i) q^{92} +(4.90677 - 27.8277i) q^{93} -9.54160 q^{94} +(1.02022 - 3.10070i) q^{95} +3.16287i q^{96} +(-9.60677 - 1.69393i) q^{97} +(-4.40017 - 3.69218i) q^{98} +(-21.7372 + 8.18997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Introduction

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