LMFDB - Embedded newform 252.2.bj.b.115.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(103,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

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

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

chi := DirichletCharacter("252.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.21
Character	$\chi$	$=$	252.115
Dual form			252.2.bj.b.103.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0863867 - 1.41157i) q^{2} +(-0.595168 + 1.62658i) q^{3} +(-1.98507 - 0.243882i) q^{4} +(-1.73413 - 1.00120i) q^{5} +(2.24463 + 0.980638i) q^{6} +(1.27710 + 2.31711i) q^{7} +(-0.515742 + 2.78101i) q^{8} +(-2.29155 - 1.93618i) q^{9} +O(q^{10})$	\(q+(0.0863867 - 1.41157i) q^{2} +(-0.595168 + 1.62658i) q^{3} +(-1.98507 - 0.243882i) q^{4} +(-1.73413 - 1.00120i) q^{5} +(2.24463 + 0.980638i) q^{6} +(1.27710 + 2.31711i) q^{7} +(-0.515742 + 2.78101i) q^{8} +(-2.29155 - 1.93618i) q^{9} +(-1.56307 + 2.36135i) q^{10} +(-4.35761 + 2.51587i) q^{11} +(1.57815 - 3.08374i) q^{12} +(-3.29495 + 1.90234i) q^{13} +(3.38110 - 1.60256i) q^{14} +(2.66063 - 2.22482i) q^{15} +(3.88104 + 0.968249i) q^{16} +(1.61527 + 0.932579i) q^{17} +(-2.93102 + 3.06743i) q^{18} +(3.12744 + 5.41689i) q^{19} +(3.19819 + 2.41038i) q^{20} +(-4.52907 + 0.698243i) q^{21} +(3.17489 + 6.36842i) q^{22} +(-5.43501 - 3.13791i) q^{23} +(-4.21659 - 2.49407i) q^{24} +(-0.495206 - 0.857721i) q^{25} +(2.40065 + 4.81540i) q^{26} +(4.51322 - 2.57504i) q^{27} +(-1.97004 - 4.91110i) q^{28} +(-1.23970 + 2.14722i) q^{29} +(-2.91065 - 3.94787i) q^{30} +1.11523 q^{31} +(1.70202 - 5.39473i) q^{32} +(-1.49876 - 8.58538i) q^{33} +(1.45594 - 2.19952i) q^{34} +(0.105232 - 5.29680i) q^{35} +(4.07670 + 4.40233i) q^{36} +(0.559132 + 0.968445i) q^{37} +(7.91650 - 3.94667i) q^{38} +(-1.13327 - 6.49172i) q^{39} +(3.67870 - 4.30626i) q^{40} +(6.39139 - 3.69007i) q^{41} +(0.594369 + 6.45343i) q^{42} +(-6.79358 - 3.92228i) q^{43} +(9.26376 - 3.93144i) q^{44} +(2.03533 + 5.65188i) q^{45} +(-4.89889 + 7.40084i) q^{46} -3.90038 q^{47} +(-3.88481 + 5.73657i) q^{48} +(-3.73802 + 5.91838i) q^{49} +(-1.25351 + 0.624923i) q^{50} +(-2.47828 + 2.07234i) q^{51} +(7.00467 - 2.97271i) q^{52} +(2.80349 - 4.85579i) q^{53} +(-3.24498 - 6.59319i) q^{54} +10.0755 q^{55} +(-7.10256 + 2.35660i) q^{56} +(-10.6724 + 1.86309i) q^{57} +(2.92386 + 1.93541i) q^{58} +8.70605 q^{59} +(-5.82414 + 3.76755i) q^{60} +2.11799i q^{61} +(0.0963407 - 1.57422i) q^{62} +(1.55981 - 7.78248i) q^{63} +(-7.46802 - 2.86856i) q^{64} +7.61847 q^{65} +(-12.2484 + 1.37394i) q^{66} +12.0225i q^{67} +(-2.97900 - 2.24518i) q^{68} +(8.33881 - 6.97292i) q^{69} +(-7.46772 - 0.606115i) q^{70} +3.84867i q^{71} +(6.56639 - 5.37425i) q^{72} +(-0.499355 - 0.288303i) q^{73} +(1.41533 - 0.705595i) q^{74} +(1.68989 - 0.295005i) q^{75} +(-4.88713 - 11.5157i) q^{76} +(-11.3947 - 6.88405i) q^{77} +(-9.26144 + 1.03889i) q^{78} -3.95949i q^{79} +(-5.76081 - 5.56476i) q^{80} +(1.50240 + 8.87371i) q^{81} +(-4.65667 - 9.34068i) q^{82} +(-5.34720 + 9.26162i) q^{83} +(9.16083 - 0.281504i) q^{84} +(-1.86739 - 3.23442i) q^{85} +(-6.12345 + 9.25080i) q^{86} +(-2.75480 - 3.29442i) q^{87} +(-4.74925 - 13.4161i) q^{88} +(-5.13938 + 2.96722i) q^{89} +(8.15386 - 2.38477i) q^{90} +(-8.61592 - 5.20528i) q^{91} +(10.0236 + 7.55448i) q^{92} +(-0.663747 + 1.81401i) q^{93} +(-0.336941 + 5.50567i) q^{94} -12.5248i q^{95} +(7.76199 + 5.97926i) q^{96} +(14.0382 + 8.10496i) q^{97} +(8.03131 + 5.78775i) q^{98} +(14.8569 + 2.67189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.0863867	−	1.41157i	0.0610846	−	0.998133i
$2$	0.0863867	−	1.41157i	0.0610846	−	0.998133i
$3$	−0.595168	+	1.62658i	−0.343621	+	0.939109i
$3$	−0.595168	+	1.62658i	−0.343621	+	0.939109i
$4$	−1.98507	−	0.243882i	−0.992537	−	0.121941i
$5$	−1.73413	−	1.00120i	−0.775525	−	0.447749i	0.0593173	−	0.998239i	$-0.481108\pi$
$5$	−1.73413	−	1.00120i	−0.775525	−	0.447749i	−0.834842	+	0.550490i	$0.814441\pi$
$6$	2.24463	+	0.980638i	0.916365	+	0.400344i
$7$	1.27710	+	2.31711i	0.482699	+	0.875786i
$7$	1.27710	+	2.31711i	0.482699	+	0.875786i
$8$	−0.515742	+	2.78101i	−0.182342	+	0.983235i
$9$	−2.29155	−	1.93618i	−0.763850	−	0.645394i
$10$	−1.56307	+	2.36135i	−0.494286	+	0.746726i
$11$	−4.35761	+	2.51587i	−1.31387	+	0.758563i	−0.982735	−	0.185021i	$-0.940765\pi$
$11$	−4.35761	+	2.51587i	−1.31387	+	0.758563i	−0.331135	+	0.943584i	$0.607431\pi$
$12$	1.57815	−	3.08374i	0.455572	−	0.890199i
$13$	−3.29495	+	1.90234i	−0.913854	+	0.527614i	−0.881669	−	0.471868i	$-0.843580\pi$
$13$	−3.29495	+	1.90234i	−0.913854	+	0.527614i	−0.0321850	+	0.999482i	$0.510247\pi$
$14$	3.38110	−	1.60256i	0.903636	−	0.428301i
$15$	2.66063	−	2.22482i	0.686971	−	0.574446i
$16$	3.88104	+	0.968249i	0.970261	+	0.242062i
$17$	1.61527	+	0.932579i	0.391762	+	0.226184i	0.682923	−	0.730490i	$-0.260708\pi$
$17$	1.61527	+	0.932579i	0.391762	+	0.226184i	−0.291161	+	0.956674i	$0.594042\pi$
$18$	−2.93102	+	3.06743i	−0.690848	+	0.723000i
$19$	3.12744	+	5.41689i	0.717485	+	1.24272i	0.961993	+	0.273073i	$0.0880400\pi$
$19$	3.12744	+	5.41689i	0.717485	+	1.24272i	−0.244509	+	0.969647i	$0.578627\pi$
$20$	3.19819	+	2.41038i	0.715138	+	0.538976i
$21$	−4.52907	+	0.698243i	−0.988324	+	0.152369i
$22$	3.17489	+	6.36842i	0.676889	+	1.35775i
$23$	−5.43501	−	3.13791i	−1.13328	−	0.654299i	−0.188521	−	0.982069i	$-0.560369\pi$
$23$	−5.43501	−	3.13791i	−1.13328	−	0.654299i	−0.944757	+	0.327771i	$0.893703\pi$
$24$	−4.21659	−	2.49407i	−0.860708	−	0.509099i
$25$	−0.495206	−	0.857721i	−0.0990411	−	0.171544i
$26$	2.40065	+	4.81540i	0.470806	+	0.944377i
$27$	4.51322	−	2.57504i	0.868570	−	0.495567i
$28$	−1.97004	−	4.91110i	−0.372303	−	0.928111i
$29$	−1.23970	+	2.14722i	−0.230206	+	0.398728i	−0.957869	−	0.287207i	$-0.907273\pi$
$29$	−1.23970	+	2.14722i	−0.230206	+	0.398728i	0.727663	+	0.685935i	$0.240607\pi$
$30$	−2.91065	−	3.94787i	−0.531410	−	0.720778i
$31$	1.11523			0.200301			0.100150	−	0.994972i	$-0.468068\pi$
$31$	1.11523			0.200301			0.100150	+	0.994972i	$0.468068\pi$
$32$	1.70202	−	5.39473i	0.300878	−	0.953663i
$33$	−1.49876	−	8.58538i	−0.260900	−	1.49452i
$34$	1.45594	−	2.19952i	0.249692	−	0.377214i
$35$	0.105232	−	5.29680i	0.0177874	−	0.895322i
$36$	4.07670	+	4.40233i	0.679449	+	0.733722i
$37$	0.559132	+	0.968445i	0.0919207	+	0.159211i	0.908319	−	0.418277i	$-0.137366\pi$
$37$	0.559132	+	0.968445i	0.0919207	+	0.159211i	−0.816399	+	0.577489i	$0.804033\pi$
$38$	7.91650	−	3.94667i	1.28423	−	0.640234i
$39$	−1.13327	−	6.49172i	−0.181468	−	1.03951i
$40$	3.67870	−	4.30626i	0.581654	−	0.680879i
$41$	6.39139	−	3.69007i	0.998167	−	0.576292i	0.0904619	−	0.995900i	$-0.471166\pi$
$41$	6.39139	−	3.69007i	0.998167	−	0.576292i	0.907706	+	0.419608i	$0.137832\pi$
$42$	0.594369	+	6.45343i	0.0917131	+	0.995785i
$43$	−6.79358	−	3.92228i	−1.03601	−	0.598141i	−0.117310	−	0.993095i	$-0.537427\pi$
$43$	−6.79358	−	3.92228i	−1.03601	−	0.598141i	−0.918701	+	0.394954i	$0.870761\pi$
$44$	9.26376	−	3.93144i	1.39656	−	0.592687i
$45$	2.03533	+	5.65188i	0.303410	+	0.842532i
$46$	−4.89889	+	7.40084i	−0.722303	+	1.09119i
$47$	−3.90038			−0.568929			−0.284464	−	0.958687i	$-0.591816\pi$
$47$	−3.90038			−0.568929			−0.284464	+	0.958687i	$0.591816\pi$
$48$	−3.88481	+	5.73657i	−0.560724	+	0.828003i
$49$	−3.73802	+	5.91838i	−0.534003	+	0.845483i
$50$	−1.25351	+	0.624923i	−0.177274	+	0.0883774i
$51$	−2.47828	+	2.07234i	−0.347028	+	0.290185i
$52$	7.00467	−	2.97271i	0.971372	−	0.412240i
$53$	2.80349	−	4.85579i	0.385089	−	0.666994i	−0.606692	−	0.794937i	$-0.707504\pi$
$53$	2.80349	−	4.85579i	0.385089	−	0.666994i	0.991782	+	0.127942i	$0.0408373\pi$
$54$	−3.24498	−	6.59319i	−0.441586	−	0.897219i
$55$	10.0755			1.35858
$56$	−7.10256	+	2.35660i	−0.949120	+	0.314914i
$57$	−10.6724	+	1.86309i	−1.41359	+	0.246772i
$58$	2.92386	+	1.93541i	0.383921	+	0.254132i
$59$	8.70605			1.13343			0.566715	−	0.823914i	$-0.308214\pi$
$59$	8.70605			1.13343			0.566715	+	0.823914i	$0.308214\pi$
$60$	−5.82414	+	3.76755i	−0.751893	+	0.486389i
$61$			2.11799i			0.271181i	0.990765	+	0.135590i	$0.0432931\pi$
$61$			2.11799i			0.271181i	−0.990765	+	0.135590i	$0.956707\pi$
$62$	0.0963407	−	1.57422i	0.0122353	−	0.199927i
$63$	1.55981	−	7.78248i	0.196517	−	0.980500i
$64$	−7.46802	−	2.86856i	−0.933503	−	0.358570i
$65$	7.61847			0.944955
$66$	−12.2484	+	1.37394i	−1.50767	+	0.169121i
$67$			12.0225i			1.46879i	0.678723	+	0.734394i	$0.262534\pi$
$67$			12.0225i			1.46879i	−0.678723	+	0.734394i	$0.737466\pi$
$68$	−2.97900	−	2.24518i	−0.361257	−	0.272268i
$69$	8.33881	−	6.97292i	1.00388	−	0.839441i
$70$	−7.46772	−	0.606115i	−0.892563	−	0.0724446i
$71$			3.84867i			0.456753i	0.973573	+	0.228377i	$0.0733417\pi$
$71$			3.84867i			0.456753i	−0.973573	+	0.228377i	$0.926658\pi$
$72$	6.56639	−	5.37425i	0.773856	−	0.633361i
$73$	−0.499355	−	0.288303i	−0.0584450	−	0.0337433i	0.470493	−	0.882404i	$-0.344076\pi$
$73$	−0.499355	−	0.288303i	−0.0584450	−	0.0337433i	−0.528938	+	0.848661i	$0.677410\pi$
$74$	1.41533	−	0.705595i	0.164529	−	0.0820237i
$75$	1.68989	−	0.295005i	0.195131	−	0.0340642i
$76$	−4.88713	−	11.5157i	−0.560592	−	1.32094i
$77$	−11.3947	−	6.88405i	−1.29854	−	0.784511i
$78$	−9.26144	+	1.03889i	−1.04865	+	0.117631i
$79$		−	3.95949i		−	0.445477i	−0.974878	−	0.222739i	$-0.928500\pi$
$79$		−	3.95949i		−	0.445477i	0.974878	−	0.222739i	$-0.0714996\pi$
$80$	−5.76081	−	5.56476i	−0.644078	−	0.622159i
$81$	1.50240	+	8.87371i	0.166933	+	0.985968i
$82$	−4.65667	−	9.34068i	−0.514243	−	1.03151i
$83$	−5.34720	+	9.26162i	−0.586931	+	1.01660i	0.407700	+	0.913116i	$0.366331\pi$
$83$	−5.34720	+	9.26162i	−0.586931	+	1.01660i	−0.994632	+	0.103479i	$0.967002\pi$
$84$	9.16083	−	0.281504i	0.999528	−	0.0307146i
$85$	−1.86739	−	3.23442i	−0.202547	−	0.350822i
$86$	−6.12345	+	9.25080i	−0.660309	+	0.997539i
$87$	−2.75480	−	3.29442i	−0.295345	−	0.353199i
$88$	−4.74925	−	13.4161i	−0.506272	−	1.43016i
$89$	−5.13938	+	2.96722i	−0.544773	+	0.314525i	−0.747011	−	0.664811i	$-0.768512\pi$
$89$	−5.13938	+	2.96722i	−0.544773	+	0.314525i	0.202238	+	0.979336i	$0.435179\pi$
$90$	8.15386	−	2.38477i	0.859492	−	0.251377i
$91$	−8.61592	−	5.20528i	−0.903194	−	0.545662i
$92$	10.0236	+	7.55448i	1.04504	+	0.787609i
$93$	−0.663747	+	1.81401i	−0.0688274	+	0.188104i
$94$	−0.336941	+	5.50567i	−0.0347528	+	0.567866i
$95$		−	12.5248i		−	1.28501i
$96$	7.76199	+	5.97926i	0.792205	+	0.610255i
$97$	14.0382	+	8.10496i	1.42536	+	0.822934i	0.996750	−	0.0805547i	$-0.0256692\pi$
$97$	14.0382	+	8.10496i	1.42536	+	0.822934i	0.428613	+	0.903488i	$0.359003\pi$
$98$	8.03131	+	5.78775i	0.811285	+	0.584651i
$99$	14.8569	+	2.67189i	1.49317	+	0.268535i
$100$	0.773837	+	1.82341i	0.0773837	+	0.182341i
$101$	−3.28562	+	1.89695i	−0.326931	+	0.188754i	−0.654478	−	0.756081i	$-0.727112\pi$
$101$	−3.28562	+	1.89695i	−0.326931	+	0.188754i	0.327546	+	0.944835i	$0.393778\pi$
$102$	2.71117	+	3.67729i	0.268445	+	0.364106i
$103$	−4.63360	+	8.02563i	−0.456562	+	0.790789i	−0.998777	−	0.0494511i	$-0.984253\pi$
$103$	−4.63360	+	8.02563i	−0.456562	+	0.790789i	0.542214	+	0.840240i	$0.317586\pi$
$104$	−3.59108	−	10.1444i	−0.352134	−	0.994740i
$105$	8.55305	+	3.32365i	0.834692	+	0.324355i
$106$	−6.61212	−	4.37681i	−0.642226	−	0.425113i
$107$	−6.79221	+	3.92148i	−0.656628	+	0.379104i	−0.790991	−	0.611828i	$-0.790434\pi$
$107$	−6.79221	+	3.92148i	−0.656628	+	0.379104i	0.134363	+	0.990932i	$0.457101\pi$
$108$	−9.58709	+	4.01096i	−0.922518	+	0.385955i
$109$	8.27240	−	14.3282i	0.792353	−	1.37239i	−0.132154	−	0.991229i	$-0.542189\pi$
$109$	8.27240	−	14.3282i	0.792353	−	1.37239i	0.924507	−	0.381166i	$-0.124477\pi$
$110$	0.870392	−	14.2223i	0.0829886	−	1.35605i
$111$	−1.90803	+	0.333087i	−0.181103	+	0.0316153i
$112$	2.71295	+	10.2294i	0.256350	+	0.966584i
$113$	9.70786	+	16.8145i	0.913238	+	1.58178i	0.809460	+	0.587175i	$0.199760\pi$
$113$	9.70786	+	16.8145i	0.913238	+	1.58178i	0.103778	+	0.994600i	$0.466907\pi$
$114$	1.70793	+	15.2258i	0.159962	+	1.42603i
$115$	6.28333	+	10.8830i	0.585923	+	1.01485i
$116$	2.98456	−	3.96004i	0.277109	−	0.367681i
$117$	11.2338	+	2.02031i	1.03857	+	0.186778i
$118$	0.752087	−	12.2892i	0.0692352	−	1.13131i
$119$	−0.0980195	+	4.93377i	−0.00898544	+	0.452278i
$120$	4.81505	+	8.54666i	0.439552	+	0.780200i
$121$	7.15918	−	12.4001i	0.650835	−	1.12728i
$122$	2.98969	+	0.182966i	0.270674	+	0.0165650i
$123$	2.19826	+	12.5923i	0.198210	+	1.13541i
$124$	−2.21381	−	0.271984i	−0.198806	−	0.0244249i
$125$			11.9952i			1.07288i
$126$	−10.8508	−	2.87408i	−0.966665	−	0.256044i
$127$			2.21609i			0.196646i	0.995155	+	0.0983232i	$0.0313479\pi$
$127$			2.21609i			0.196646i	−0.995155	+	0.0983232i	$0.968652\pi$
$128$	−4.69432	+	10.2938i	−0.414924	+	0.909856i
$129$	10.4232	−	8.71591i	0.917715	−	0.767393i
$130$	0.658135	−	10.7540i	0.0577222	−	0.943191i
$131$	−7.95137	+	13.7722i	−0.694714	+	1.20328i	0.275563	+	0.961283i	$0.411136\pi$
$131$	−7.95137	+	13.7722i	−0.694714	+	1.20328i	−0.970277	+	0.241997i	$0.922198\pi$
$132$	0.881324	+	17.4082i	0.0767094	+	1.51519i
$133$	−8.55748	+	14.1646i	−0.742028	+	1.22822i
$134$	16.9707	+	1.03859i	1.46605	+	0.0897204i
$135$	−10.4046	−	0.0531777i	−0.895487	−	0.00457681i
$136$	−3.42658	+	4.01112i	−0.293826	+	0.343951i
$137$	2.15086	+	3.72539i	0.183760	+	0.318282i	0.943158	−	0.332345i	$-0.107840\pi$
$137$	2.15086	+	3.72539i	0.183760	+	0.318282i	−0.759398	+	0.650626i	$0.774506\pi$
$138$	−9.12242	−	12.3732i	−0.776552	−	1.05328i
$139$	−2.19727	−	3.80579i	−0.186370	−	0.322803i	0.757667	−	0.652641i	$-0.226339\pi$
$139$	−2.19727	−	3.80579i	−0.186370	−	0.322803i	−0.944037	+	0.329838i	$0.893006\pi$
$140$	−1.50069	+	10.4889i	−0.126831	+	0.886471i
$141$	2.32138	−	6.34429i	0.195496	−	0.534286i
$142$	5.43268	+	0.332474i	0.455900	+	0.0279006i
$143$	9.57207	−	16.5793i	0.800457	−	1.38643i
$144$	−7.01890	−	9.73320i	−0.584908	−	0.811100i
$145$	4.29958	−	2.48236i	0.357060	−	0.206149i
$146$	−0.450098	+	0.679970i	−0.0372503	+	0.0562747i
$147$	−7.40199	−	9.60263i	−0.610506	−	0.792012i
$148$	−0.873732	−	2.05880i	−0.0718204	−	0.169232i
$149$	−2.29237	+	3.97051i	−0.187799	+	0.325277i	−0.944516	−	0.328465i	$-0.893469\pi$
$149$	−2.29237	+	3.97051i	−0.187799	+	0.325277i	0.756717	+	0.653742i	$0.226802\pi$
$150$	−0.270437	−	2.41088i	−0.0220811	−	0.196848i
$151$	20.3466	−	11.7471i	1.65578	−	0.955967i	0.681154	−	0.732140i	$-0.261478\pi$
$151$	20.3466	−	11.7471i	1.65578	−	0.955967i	0.974629	−	0.223827i	$-0.0718550\pi$
$152$	−16.6774	+	5.90373i	−1.35271	+	0.478856i
$153$	−1.89584	−	5.26452i	−0.153269	−	0.425611i
$154$	−10.7017	+	15.4897i	−0.862367	+	1.24820i
$155$	−1.93394	−	1.11656i	−0.155338	−	0.0896844i
$156$	0.666401	+	13.1629i	0.0533548	+	1.05388i
$157$		−	16.3940i		−	1.30838i	−0.756330	−	0.654191i	$-0.773009\pi$
$157$		−	16.3940i		−	1.30838i	0.756330	−	0.654191i	$-0.226991\pi$
$158$	−5.58910	−	0.342047i	−0.444645	−	0.0272118i
$159$	6.22980	+	7.45013i	0.494056	+	0.590834i
$160$	−8.35272	+	7.65108i	−0.660340	+	0.604871i
$161$	0.329812	−	16.6010i	0.0259928	−	1.30834i
$162$	12.6557	−	1.35417i	0.994324	−	0.106394i
$163$	−4.37894	+	2.52818i	−0.342985	+	0.198022i	−0.661591	−	0.749865i	$-0.730119\pi$
$163$	−4.37894	+	2.52818i	−0.342985	+	0.198022i	0.318606	+	0.947887i	$0.396785\pi$
$164$	−13.5873	+	5.76632i	−1.06099	+	0.450274i
$165$	−5.99663	+	16.3887i	−0.466837	+	1.27586i
$166$	12.6115	+	8.34804i	0.978844	+	0.647934i
$167$	−4.45705	−	7.71983i	−0.344897	−	0.597378i	0.640438	−	0.768010i	$-0.278753\pi$
$167$	−4.45705	−	7.71983i	−0.344897	−	0.597378i	−0.985335	+	0.170631i	$0.945419\pi$
$168$	0.394010	−	12.9555i	0.0303985	−	0.999538i
$169$	0.737790	−	1.27789i	0.0567530	−	0.0982992i
$170$	−4.72694	+	2.35655i	−0.362539	+	0.180739i
$171$	3.32140	−	18.4684i	0.253993	−	1.41231i
$172$	12.5292	+	9.44284i	0.955342	+	0.720010i
$173$		−	3.03710i		−	0.230907i	−0.993313	−	0.115453i	$-0.963168\pi$
$173$		−	3.03710i		−	0.230907i	0.993313	−	0.115453i	$-0.0368321\pi$
$174$	−4.88830	+	3.60400i	−0.370581	+	0.273219i
$175$	1.35501	−	2.24284i	0.102429	−	0.169543i
$176$	−19.3481	+	5.54494i	−1.45842	+	0.417966i
$177$	−5.18156	+	14.1611i	−0.389470	+	1.06441i
$178$	3.74448	+	7.51094i	0.280660	+	0.562968i
$179$	−4.01804	−	2.31982i	−0.300323	−	0.173391i	0.342265	−	0.939603i	$-0.388806\pi$
$179$	−4.01804	−	2.31982i	−0.300323	−	0.173391i	−0.642588	+	0.766212i	$0.722139\pi$
$180$	−2.66190	−	11.7158i	−0.198406	−	0.873243i
$181$			3.81679i			0.283700i	0.989888	+	0.141850i	$0.0453050\pi$
$181$			3.81679i			0.283700i	−0.989888	+	0.141850i	$0.954695\pi$
$182$	−8.09194	+	11.7123i	−0.599814	+	0.868176i
$183$	−3.44509	−	1.26056i	−0.254668	−	0.0931832i
$184$	11.5296	−	13.4965i	0.849974	−	0.994973i
$185$		−	2.23921i		−	0.164630i
$186$	2.50327	+	1.09363i	0.183548	+	0.0801891i
$187$	−9.38499			−0.686298
$188$	7.74254	+	0.951233i	0.564683	+	0.0693758i
$189$	11.7305	+	7.16904i	0.853269	+	0.521471i
$190$	−17.6796	−	1.08197i	−1.28261	−	0.0784946i
$191$		−	3.77400i		−	0.273077i	−0.990635	−	0.136539i	$-0.956402\pi$
$191$		−	3.77400i		−	0.273077i	0.990635	−	0.136539i	$-0.0435978\pi$
$192$	9.11069	−	10.4401i	0.657507	−	0.753448i
$193$	−12.1379			−0.873707			−0.436853	−	0.899533i	$-0.643907\pi$
$193$	−12.1379			−0.873707			−0.436853	+	0.899533i	$0.643907\pi$
$194$	12.6534	−	19.1158i	0.908465	−	1.37243i
$195$	−4.53427	+	12.3921i	−0.324706	+	0.887416i
$196$	8.86363	−	10.8368i	0.633117	−	0.774056i
$197$	−6.35688			−0.452909			−0.226455	−	0.974022i	$-0.572713\pi$
$197$	−6.35688			−0.452909			−0.226455	+	0.974022i	$0.572713\pi$
$198$	5.05501	−	20.7407i	0.359244	−	1.47398i
$199$	−1.00759	+	1.74520i	−0.0714262	+	0.123714i	−0.899527	−	0.436866i	$-0.856088\pi$
$199$	−1.00759	+	1.74520i	−0.0714262	+	0.123714i	0.828100	+	0.560580i	$0.189422\pi$
$200$	2.64073	−	0.934809i	0.186728	−	0.0661009i
$201$	−19.5557	−	7.15544i	−1.37935	−	0.504706i
$202$	2.39385	+	4.80176i	0.168431	+	0.337851i
$203$	−6.55856	−	0.130299i	−0.460321	−	0.00914521i
$204$	5.42497	−	3.50934i	0.379824	−	0.245703i
$205$	−14.7780			−1.03214
$206$	10.9285	+	7.23397i	0.761424	+	0.504015i
$207$	6.37904	+	17.7138i	0.443374	+	1.23120i
$208$	−14.6298	+	4.19273i	−1.01439	+	0.290714i
$209$	−27.2564	−	15.7365i	−1.88536	−	1.08851i
$210$	5.43045	−	11.7861i	0.374737	−	0.813321i
$211$	15.8266	−	9.13752i	1.08955	−	0.629053i	0.156094	−	0.987742i	$-0.450110\pi$
$211$	15.8266	−	9.13752i	1.08955	−	0.629053i	0.933457	+	0.358690i	$0.116776\pi$
$212$	−6.74939	+	8.95539i	−0.463550	+	0.615059i
$213$	−6.26018	−	2.29061i	−0.428941	−	0.156950i
$214$	4.94870	+	9.92646i	0.338286	+	0.678559i
$215$	7.85395	+	13.6034i	0.535635	+	0.927747i
$216$	4.83356	+	13.8794i	0.328882	+	0.944371i
$217$	1.42426	+	2.58410i	0.0966850	+	0.175420i
$218$	−19.5107	−	12.9149i	−1.32143	−	0.874705i
$219$	0.766148	−	0.640654i	0.0517715	−	0.0432914i
$220$	−20.0007	−	2.45724i	−1.34845	−	0.165667i
$221$	−7.09633			−0.477351
$222$	0.305348	+	2.72210i	0.0204936	+	0.182696i
$223$	−8.23280	+	14.2596i	−0.551309	+	0.954896i	0.446871	+	0.894598i	$0.352538\pi$
$223$	−8.23280	+	14.2596i	−0.551309	+	0.954896i	−0.998180	+	0.0602974i	$0.980795\pi$
$224$	14.6739	−	2.94584i	0.980438	−	0.196827i
$225$	−0.525916	+	2.92432i	−0.0350611	+	0.194955i
$226$	24.5735	−	12.2508i	1.63461	−	0.814911i
$227$	−0.220711	−	0.382282i	−0.0146491	−	0.0253729i	0.858608	−	0.512633i	$-0.171330\pi$
$227$	−0.220711	−	0.382282i	−0.0146491	−	0.0253729i	−0.873257	+	0.487260i	$0.837996\pi$
$228$	21.6398	−	1.09556i	1.43313	−	0.0725554i
$229$	−4.65451	−	2.68728i	−0.307579	−	0.177581i	0.338264	−	0.941051i	$-0.390160\pi$
$229$	−4.65451	−	2.68728i	−0.307579	−	0.177581i	−0.645843	+	0.763471i	$0.723494\pi$
$230$	15.9050	−	7.92922i	1.04874	−	0.522838i
$231$	17.9792	−	14.4372i	1.18295	−	0.949899i
$232$	−5.33206	−	4.55501i	−0.350067	−	0.299051i
$233$	3.38198	+	5.85776i	0.221561	+	0.383754i	0.955282	−	0.295696i	$-0.0955516\pi$
$233$	3.38198	+	5.85776i	0.221561	+	0.383754i	−0.733721	+	0.679450i	$0.762218\pi$
$234$	3.82227	−	15.6828i	0.249870	−	1.02522i
$235$	6.76375	+	3.90505i	0.441218	+	0.254737i
$236$	−17.2822	−	2.12325i	−1.12497	−	0.138212i
$237$	6.44044	+	2.35656i	0.418351	+	0.153075i
$238$	6.95591	+	0.564574i	0.450885	+	0.0365959i
$239$	−0.169520	+	0.0978724i	−0.0109653	+	0.00633084i	−0.505473	−	0.862843i	$-0.668682\pi$
$239$	−0.169520	+	0.0978724i	−0.0109653	+	0.00633084i	0.494507	+	0.869173i	$0.335349\pi$
$240$	12.4802	−	6.05847i	0.805593	−	0.391072i
$241$	−11.1305	+	6.42621i	−0.716980	+	0.413948i	−0.813640	−	0.581369i	$-0.802517\pi$
$241$	−11.1305	+	6.42621i	−0.716980	+	0.413948i	0.0966603	+	0.995317i	$0.469184\pi$
$242$	−16.8851	−	11.1769i	−1.08542	−	0.718479i
$243$	−15.3280	−	2.83758i	−0.983293	−	0.182031i
$244$	0.516540	−	4.20437i	0.0330681	−	0.269157i
$245$	12.4077	−	6.52072i	0.792697	−	0.416593i
$246$	17.9649	−	2.01519i	1.14540	−	0.128484i
$247$	−20.6095	−	11.8989i	−1.31135	−	0.757110i
$248$	−0.575169	+	3.10145i	−0.0365232	+	0.196943i
$249$	−11.8823	−	14.2099i	−0.753011	−	0.900515i
$250$	16.9321	+	1.03622i	1.07088	+	0.0655365i
$251$	13.7723			0.869299			0.434650	−	0.900600i	$-0.356872\pi$
$251$	13.7723			0.869299			0.434650	+	0.900600i	$0.356872\pi$
$252$	−4.99434	+	15.0684i	−0.314614	+	0.949220i
$253$	31.5782			1.98531
$254$	3.12817	+	0.191441i	0.196279	+	0.0120121i
$255$	6.37247	−	1.11245i	0.399059	−	0.0696641i
$256$	14.1250	+	7.51563i	0.882812	+	0.469727i
$257$	11.9977	+	6.92685i	0.748393	+	0.432085i	0.825113	−	0.564968i	$-0.191111\pi$
$257$	11.9977	+	6.92685i	0.748393	+	0.432085i	−0.0767200	+	0.997053i	$0.524445\pi$
$258$	−11.4027	−	15.4661i	−0.709902	−	0.962877i
$259$	−1.52993	+	2.53238i	−0.0950650	+	0.157354i
$260$	−15.1232	−	1.85801i	−0.937903	−	0.115229i
$261$	6.99822	−	2.52017i	0.433179	−	0.155995i
$262$	18.7535	+	12.4137i	1.15860	+	0.766919i
$263$	1.40157	−	0.809197i	0.0864246	−	0.0498972i	−0.456165	−	0.889895i	$-0.650777\pi$
$263$	1.40157	−	0.809197i	0.0864246	−	0.0498972i	0.542589	+	0.839998i	$0.317444\pi$
$264$	24.6490	+	0.259780i	1.51704	+	0.0159883i
$265$	−9.72322	+	5.61370i	−0.597293	+	0.344847i
$266$	19.2551	+	13.3031i	1.18060	+	0.815667i
$267$	−1.76764	−	10.1256i	−0.108178	−	0.619678i
$268$	2.93209	−	23.8657i	0.179106	−	1.45783i
$269$	−3.95786	−	2.28507i	−0.241315	−	0.139323i	0.374466	−	0.927241i	$-0.377826\pi$
$269$	−3.95786	−	2.28507i	−0.241315	−	0.139323i	−0.615781	+	0.787917i	$0.711159\pi$
$270$	−0.973885	+	14.6823i	−0.0592688	+	0.893535i
$271$	−11.9451	−	20.6896i	−0.725615	−	1.25680i	−0.958720	−	0.284351i	$-0.908222\pi$
$271$	−11.9451	−	20.6896i	−0.725615	−	1.25680i	0.233105	−	0.972452i	$-0.425111\pi$
$272$	5.36598	+	5.18337i	0.325360	+	0.314288i
$273$	13.5948	−	10.9165i	0.822792	−	0.660696i
$274$	5.44447	−	2.71426i	0.328912	−	0.163975i
$275$	4.31583	+	2.49174i	0.260254	+	0.150258i
$276$	−18.2537	+	11.8081i	−1.09875	+	0.710763i
$277$	−6.15272	−	10.6568i	−0.369681	−	0.640307i	0.619834	−	0.784733i	$-0.287200\pi$
$277$	−6.15272	−	10.6568i	−0.369681	−	0.640307i	−0.989516	+	0.144426i	$0.953866\pi$
$278$	−5.56196	+	2.77284i	−0.333584	+	0.166304i
$279$	−2.55560	−	2.15928i	−0.153000	−	0.129273i
$280$	14.6762	+	3.02443i	0.877069	+	0.180744i
$281$	−6.68674	+	11.5818i	−0.398897	+	0.690910i	−0.993590	−	0.113043i	$-0.963940\pi$
$281$	−6.68674	+	11.5818i	−0.398897	+	0.690910i	0.594693	+	0.803953i	$0.297274\pi$
$282$	−8.75489	−	3.82486i	−0.521346	−	0.227767i
$283$	6.45065			0.383451			0.191726	−	0.981449i	$-0.438592\pi$
$283$	6.45065			0.383451			0.191726	+	0.981449i	$0.438592\pi$
$284$	0.938622	−	7.63990i	0.0556970	−	0.453345i
$285$	20.3726	+	7.45434i	1.20677	+	0.441557i
$286$	−22.5760	−	14.9439i	−1.33495	−	0.883652i
$287$	16.7128	+	10.0970i	0.986524	+	0.596005i
$288$	−14.3455	+	9.06686i	−0.845314	+	0.534270i
$289$	−6.76059	−	11.7097i	−0.397682	−	0.688805i
$290$	−3.13261	−	6.28361i	−0.183953	−	0.368986i
$291$	−21.5385	+	18.0105i	−1.26261	+	1.05579i
$292$	0.920944	+	0.694086i	0.0538942	+	0.0406183i
$293$	−18.9236	+	10.9255i	−1.10553	+	0.638277i	−0.937668	−	0.347534i	$-0.887019\pi$
$293$	−18.9236	+	10.9255i	−1.10553	+	0.638277i	−0.167861	+	0.985811i	$0.553686\pi$
$294$	−14.1942	+	9.61891i	−0.827825	+	0.560986i
$295$	−15.0974	−	8.71648i	−0.879003	−	0.507493i
$296$	−2.98162	+	1.05548i	−0.173303	+	0.0613487i
$297$	−13.1884	+	22.5757i	−0.765268	+	1.30998i
$298$	5.40663	+	3.57885i	0.313198	+	0.207317i
$299$	23.8774			1.38087
$300$	−3.42650	+	0.173474i	−0.197829	+	0.0100155i
$301$	0.412254	−	20.7506i	0.0237619	−	1.19605i
$302$	−14.8242	−	29.7355i	−0.853039	−	1.71109i
$303$	−1.13006	−	6.47334i	−0.0649201	−	0.371884i
$304$	6.89284	+	24.0513i	0.395332	+	1.37944i
$305$	2.12053	−	3.67286i	0.121421	−	0.210307i
$306$	−7.59502	+	2.22133i	−0.434179	+	0.126985i
$307$	5.00234			0.285499			0.142749	−	0.989759i	$-0.454406\pi$
$307$	5.00234			0.285499			0.142749	+	0.989759i	$0.454406\pi$
$308$	20.9404	+	16.4443i	1.19319	+	0.937002i
$309$	−10.2966	−	12.3135i	−0.585753	−	0.700493i
$310$	−1.74318	+	2.63344i	−0.0990057	+	0.149570i
$311$	20.3936			1.15641			0.578206	−	0.815891i	$-0.303753\pi$
$311$	20.3936			1.15641			0.578206	+	0.815891i	$0.303753\pi$
$312$	18.6380	+	0.196429i	1.05517	+	0.0111206i
$313$			21.0715i			1.19103i	0.803344	+	0.595515i	$0.203052\pi$
$313$			21.0715i			1.19103i	−0.803344	+	0.595515i	$0.796948\pi$
$314$	−23.1413	−	1.41622i	−1.30594	−	0.0799220i
$315$	−10.4967	+	11.9341i	−0.591422	+	0.672412i
$316$	−0.965649	+	7.85988i	−0.0543220	+	0.442153i
$317$	12.0763			0.678271			0.339136	−	0.940737i	$-0.389865\pi$
$317$	12.0763			0.678271			0.339136	+	0.940737i	$0.389865\pi$
$318$	11.0546	−	8.15023i	0.619910	−	0.457042i
$319$		−	12.4756i		−	0.698502i
$320$	10.0785	+	12.4514i	0.563405	+	0.696055i
$321$	−2.33611	−	13.3820i	−0.130389	−	0.746913i
$322$	−23.4050	−	1.89966i	−1.30431	−	0.105864i
$323$			11.6664i			0.649133i
$324$	−0.818232	−	17.9814i	−0.0454573	−	0.998966i
$325$	3.26335	+	1.88410i	0.181018	+	0.104511i
$326$	3.19043	+	6.39959i	0.176701	+	0.354440i
$327$	18.3826	+	21.9835i	1.01656	+	1.21569i
$328$	6.96581	+	19.6776i	0.384623	+	1.08652i
$329$	−4.98118	−	9.03762i	−0.274622	−	0.498260i
$330$	22.6158	+	9.88045i	1.24496	+	0.543901i
$331$		−	1.27458i		−	0.0700570i	−0.999386	−	0.0350285i	$-0.988848\pi$
$331$		−	1.27458i		−	0.0700570i	0.999386	−	0.0350285i	$-0.0111522\pi$
$332$	12.8733	−	17.0809i	0.706516	−	0.937437i
$333$	0.593807	−	3.30182i	0.0325404	−	0.180939i
$334$	−11.2821	+	5.62455i	−0.617331	+	0.307762i
$335$	12.0370	−	20.8486i	0.657649	−	1.13908i
$336$	−18.2536	−	1.67536i	−0.995814	−	0.0913982i
$337$	−6.12539	−	10.6095i	−0.333671	−	0.577935i	0.649558	−	0.760312i	$-0.274954\pi$
$337$	−6.12539	−	10.6095i	−0.333671	−	0.577935i	−0.983229	+	0.182377i	$0.941621\pi$
$338$	−1.74010	−	1.15184i	−0.0946489	−	0.0626516i
$339$	−33.1280	+	5.78319i	−1.79927	+	0.314100i
$340$	2.91810	+	6.87599i	0.158256	+	0.372903i
$341$	−4.85972	+	2.80576i	−0.263169	+	0.151941i
$342$	−25.7825	−	6.28381i	−1.39416	−	0.339790i
$343$	−18.4874	−	1.10303i	−0.998225	−	0.0595581i
$344$	14.4116	−	16.8701i	0.777022	−	0.909576i
$345$	−21.4418	+	3.74312i	−1.15439	+	0.201523i
$346$	−4.28709	−	0.262365i	−0.230476	−	0.0141049i
$347$		−	8.63583i		−	0.463596i	−0.972764	−	0.231798i	$-0.925539\pi$
$347$		−	8.63583i		−	0.463596i	0.972764	−	0.231798i	$-0.0744608\pi$
$348$	4.66503	+	7.21152i	0.250072	+	0.386578i
$349$	6.91380	+	3.99168i	0.370087	+	0.213670i	0.673497	−	0.739190i	$-0.264792\pi$
$349$	6.91380	+	3.99168i	0.370087	+	0.213670i	−0.303409	+	0.952860i	$0.598125\pi$
$350$	−3.04888	−	2.10644i	−0.162970	−	0.112594i
$351$	−9.97222	+	17.0703i	−0.532278	+	0.911146i
$352$	6.15567	+	27.7902i	0.328098	+	1.48122i
$353$	16.3881	−	9.46167i	0.872250	−	0.503594i	0.00415479	−	0.999991i	$-0.498677\pi$
$353$	16.3881	−	9.46167i	0.872250	−	0.503594i	0.868095	+	0.496398i	$0.165344\pi$
$354$	19.5418	+	8.53748i	1.03864	+	0.453762i
$355$	3.85328	−	6.67408i	0.204511	−	0.354223i
$356$	10.9257	−	4.63675i	0.579061	−	0.245747i
$357$	−7.96686	−	3.09586i	−0.421651	−	0.163850i
$358$	−3.62170	+	5.47136i	−0.191413	+	0.289170i
$359$	−22.7971	+	13.1619i	−1.20319	+	0.694659i	−0.961262	−	0.275636i	$-0.911111\pi$
$359$	−22.7971	+	13.1619i	−1.20319	+	0.694659i	−0.241923	+	0.970295i	$0.577778\pi$
$360$	−16.7676	+	2.74537i	−0.883732	+	0.144694i
$361$	−10.0618	+	17.4276i	−0.529569	+	0.917240i
$362$	5.38768	+	0.329720i	0.283170	+	0.0173297i
$363$	15.9088	+	19.0251i	0.834997	+	0.998561i
$364$	15.8338	+	12.4341i	0.829915	+	0.651726i
$365$	0.577296	+	0.999906i	0.0302170	+	0.0523375i
$366$	−2.07698	+	4.75409i	−0.108566	+	0.248500i
$367$	0.779957	+	1.35093i	0.0407134	+	0.0705178i	0.885664	−	0.464327i	$-0.153704\pi$
$367$	0.779957	+	1.35093i	0.0407134	+	0.0705178i	−0.844951	+	0.534844i	$0.820370\pi$
$368$	−18.0552	−	17.4408i	−0.941194	−	0.909164i
$369$	−21.7908	−	3.91891i	−1.13439	−	0.204011i
$370$	−3.16080	−	0.193438i	−0.164322	−	0.0100564i
$371$	14.8318	+	0.294664i	0.770027	+	0.0152982i
$372$	1.75999	−	3.43907i	0.0912514	−	0.178307i
$373$	−17.9989	+	31.1751i	−0.931950	+	1.61418i	−0.151964	+	0.988386i	$0.548560\pi$
$373$	−17.9989	+	31.1751i	−0.931950	+	1.61418i	−0.779985	+	0.625798i	$0.784773\pi$
$374$	−0.810738	+	13.2476i	−0.0419223	+	0.685017i
$375$	−19.5112	−	7.13915i	−1.00755	−	0.368664i
$376$	2.01159	−	10.8470i	0.103740	−	0.559391i
$377$		−	9.43329i		−	0.485839i
$378$	11.1330	−	15.9392i	0.572619	−	0.819822i
$379$		−	19.4764i		−	1.00044i	−0.865899	−	0.500219i	$-0.833253\pi$
$379$		−	19.4764i		−	1.00044i	0.865899	−	0.500219i	$-0.166747\pi$
$380$	−3.05457	+	24.8626i	−0.156696	+	1.27542i
$381$	−3.60466	−	1.31895i	−0.184672	−	0.0675717i
$382$	−5.32728	−	0.326024i	−0.272567	−	0.0166808i
$383$	0.0495758	−	0.0858679i	0.00253321	−	0.00438764i	−0.864756	−	0.502192i	$-0.832527\pi$
$383$	0.0495758	−	0.0858679i	0.00253321	−	0.00438764i	0.867289	+	0.497805i	$0.165860\pi$
$384$	−13.9499	−	13.7623i	−0.711878	−	0.702304i
$385$	12.8675	+	23.3461i	0.655788	+	1.18983i
$386$	−1.04855	+	17.1336i	−0.0533700	+	0.872075i
$387$	7.97359	+	22.1417i	0.405320	+	1.12553i
$388$	−25.8902	−	19.5126i	−1.31438	−	0.990603i
$389$	13.2831	+	23.0070i	0.673481	+	1.16650i	0.976910	+	0.213650i	$0.0685351\pi$
$389$	13.2831	+	23.0070i	0.673481	+	1.16650i	−0.303429	+	0.952854i	$0.598132\pi$
$390$	17.1006	+	7.47097i	0.865924	+	0.378307i
$391$	−5.85269	−	10.1372i	−0.295983	−	0.512658i
$392$	−14.5312	−	13.4478i	−0.733937	−	0.679217i
$393$	−17.6692	−	21.1303i	−0.891293	−	1.06588i
$394$	−0.549150	+	8.97320i	−0.0276658	+	0.452063i
$395$	−3.96423	+	6.86625i	−0.199462	+	0.345478i
$396$	−28.8404	−	8.92723i	−1.44928	−	0.448610i
$397$	23.4405	−	13.5334i	1.17645	−	0.679221i	0.221256	−	0.975216i	$-0.428984\pi$
$397$	23.4405	−	13.5334i	1.17645	−	0.679221i	0.955190	+	0.295995i	$0.0956511\pi$
$398$	2.37643	+	1.57305i	0.119120	+	0.0788499i
$399$	−17.9467	−	22.3498i	−0.898459	−	1.11889i
$400$	−1.09143	−	3.80833i	−0.0545713	−	0.190417i
$401$	15.9990	−	27.7112i	0.798954	−	1.38383i	−0.121344	−	0.992611i	$-0.538720\pi$
$401$	15.9990	−	27.7112i	0.798954	−	1.38383i	0.920298	−	0.391219i	$-0.127946\pi$
$402$	−11.7898	+	26.9861i	−0.588020	+	1.34595i
$403$	−3.67461	+	2.12154i	−0.183046	+	0.105681i
$404$	6.98484	−	2.96429i	0.347509	−	0.147479i
$405$	6.27900	−	16.8923i	0.312006	−	0.839387i
$406$	−0.750499	+	9.24662i	−0.0372466	+	0.458902i
$407$	−4.87296	−	2.81340i	−0.241544	−	0.139455i
$408$	−4.48504	−	7.96091i	−0.222043	−	0.394124i
$409$			21.8701i			1.08141i	0.841213	+	0.540704i	$0.181842\pi$
$409$			21.8701i			1.08141i	−0.841213	+	0.540704i	$0.818158\pi$
$410$	−1.27662	+	20.8602i	−0.0630478	+	1.03021i
$411$	−7.33978	+	1.28131i	−0.362045	+	0.0632025i
$412$	11.1554	−	14.8014i	0.549585	−	0.729214i
$413$	11.1185	+	20.1729i	0.547106	+	0.992643i
$414$	25.5554	−	7.47424i	1.25598	−	0.367339i
$415$	18.5454	−	10.7072i	0.910359	−	0.525596i
$416$	4.65453	+	21.0132i	0.228207	+	1.03026i
$417$	7.49818	−	1.30896i	0.367188	−	0.0641003i
$418$	−24.5678	+	37.1149i	−1.20165	+	1.81535i
$419$	9.62802	+	16.6762i	0.470360	+	0.814687i	0.999425	−	0.0338939i	$-0.0107908\pi$
$419$	9.62802	+	16.6762i	0.470360	+	0.814687i	−0.529066	+	0.848581i	$0.677458\pi$
$420$	−16.1679	−	8.68364i	−0.788911	−	0.423718i
$421$	16.8866	−	29.2484i	0.823002	−	1.42548i	−0.0804343	−	0.996760i	$-0.525631\pi$
$421$	16.8866	−	29.2484i	0.823002	−	1.42548i	0.903437	−	0.428722i	$-0.141036\pi$
$422$	−11.5311	−	23.1298i	−0.561323	−	1.12594i
$423$	8.93791	+	7.55184i	0.434576	+	0.367183i
$424$	12.0581	+	10.3009i	0.585594	+	0.500255i
$425$		−	1.84727i		−	0.0896059i
$426$	−3.77415	+	8.63883i	−0.182858	+	0.418553i
$427$	−4.90762	+	2.70489i	−0.237496	+	0.130899i
$428$	14.4394	−	6.12794i	0.697956	−	0.296205i
$429$	21.2706	+	25.4373i	1.02696	+	1.22812i
$430$	19.8807	−	9.91126i	0.958733	−	0.477964i
$431$	−2.57782	−	1.48830i	−0.124169	−	0.0716890i	0.436629	−	0.899642i	$-0.356172\pi$
$431$	−2.57782	−	1.48830i	−0.124169	−	0.0716890i	−0.560798	+	0.827953i	$0.689506\pi$
$432$	20.0093	−	5.62393i	0.962697	−	0.270582i
$433$			25.5918i			1.22986i	0.788580	+	0.614932i	$0.210817\pi$
$433$			25.5918i			1.22986i	−0.788580	+	0.614932i	$0.789183\pi$
$434$	3.77069	−	1.78721i	0.180999	−	0.0857889i
$435$	1.47880	+	8.47104i	0.0709029	+	0.406155i
$436$	−19.9157	+	26.4251i	−0.953791	+	1.26553i
$437$		−	39.2545i		−	1.87780i
$438$	−0.838144	−	1.13682i	−0.0400481	−	0.0543193i
$439$	29.1310			1.39035			0.695174	−	0.718841i	$-0.255327\pi$
$439$	29.1310			1.39035			0.695174	+	0.718841i	$0.255327\pi$
$440$	−5.19637	+	28.0201i	−0.247727	+	1.33581i
$441$	20.0249	−	6.32478i	0.953567	−	0.301180i
$442$	−0.613029	+	10.0170i	−0.0291588	+	0.476459i
$443$		−	25.3941i		−	1.20651i	−0.797549	−	0.603254i	$-0.793870\pi$
$443$		−	25.3941i		−	1.20651i	0.797549	−	0.603254i	$-0.206130\pi$
$444$	3.86883	−	0.195867i	0.183606	−	0.00929546i
$445$	11.8831			0.563313
$446$	19.4173	+	12.8530i	0.919436	+	0.608609i
$447$	−5.09401	−	6.09186i	−0.240939	−	0.288135i
$448$	−2.89064	−	20.9677i	−0.136570	−	0.990630i
$449$	30.7532			1.45133			0.725667	−	0.688046i	$-0.241531\pi$
$449$	30.7532			1.45133			0.725667	+	0.688046i	$0.241531\pi$
$450$	4.08246	+	0.994991i	0.192449	+	0.0469043i
$451$	−18.5675	+	32.1598i	−0.874308	+	1.51435i
$452$	−15.1701	−	35.7456i	−0.713540	−	1.68133i
$453$	6.99802	+	40.0870i	0.328796	+	1.88345i
$454$	−0.558685	+	0.278525i	−0.0262204	+	0.0130718i
$455$	9.72957	+	17.6529i	0.456129	+	0.827579i
$456$	0.322929	−	30.6409i	0.0151225	−	1.43489i
$457$	−10.9861			−0.513907			−0.256954	−	0.966424i	$-0.582719\pi$
$457$	−10.9861			−0.513907			−0.256954	+	0.966424i	$0.582719\pi$
$458$	−4.19538	+	6.33804i	−0.196037	+	0.296157i
$459$	9.69152	+	0.0495331i	0.452361	+	0.00231201i
$460$	−9.81870	−	23.1360i	−0.457799	−	1.07872i
$461$	−14.3875	−	8.30665i	−0.670095	−	0.386879i	0.126018	−	0.992028i	$-0.459780\pi$
$461$	−14.3875	−	8.30665i	−0.670095	−	0.386879i	−0.796113	+	0.605149i	$0.793114\pi$
$462$	−18.8260	−	26.6262i	−0.875865	−	1.23876i
$463$	6.92387	−	3.99750i	0.321779	−	0.185779i	−0.330406	−	0.943839i	$-0.607186\pi$
$463$	6.92387	−	3.99750i	0.321779	−	0.185779i	0.652185	+	0.758059i	$0.273852\pi$
$464$	−6.89035	+	7.13310i	−0.319876	+	0.331146i
$465$	2.96720	−	2.48118i	0.137601	−	0.115062i
$466$	8.56081	−	4.26787i	0.396572	−	0.197705i
$467$	−12.6639	−	21.9346i	−0.586017	−	1.01501i	−0.994748	−	0.102356i	$-0.967362\pi$
$467$	−12.6639	−	21.9346i	−0.586017	−	1.01501i	0.408731	−	0.912655i	$-0.365971\pi$
$468$	−21.8072	−	6.75020i	−1.00804	−	0.312028i
$469$	−27.8576	+	15.3540i	−1.28634	+	0.708983i
$470$	6.09656	−	9.21018i	0.281213	−	0.424834i
$471$	26.6662	+	9.75717i	1.22871	+	0.449587i
$472$	−4.49007	+	24.2116i	−0.206672	+	1.11443i
$473$	39.4717			1.81491
$474$	3.88283	−	8.88757i	0.178344	−	0.408220i
$475$	3.09745	−	5.36495i	0.142121	−	0.246161i
$476$	1.39784	−	9.77000i	0.0640697	−	0.447807i
$477$	−15.8260	+	5.69922i	−0.724625	+	0.260949i
$478$	0.123510	+	0.247745i	0.00564920	+	0.0113316i
$479$	2.09384	+	3.62664i	0.0956701	+	0.165705i	0.909888	−	0.414854i	$-0.136167\pi$
$479$	2.09384	+	3.62664i	0.0956701	+	0.165705i	−0.814218	+	0.580559i	$0.802834\pi$
$480$	−7.47385	−	18.1401i	−0.341133	−	0.827977i
$481$	−3.68462	−	2.12732i	−0.168004	−	0.0969973i
$482$	8.10953	+	16.2667i	0.369379	+	0.740927i
$483$	26.8066	+	10.4168i	1.21974	+	0.473982i
$484$	−17.2357	+	22.8691i	−0.783440	+	1.03950i
$485$	−16.2293	−	28.1100i	−0.736936	−	1.27641i
$486$	−5.32958	+	21.3915i	−0.241755	+	0.970337i
$487$	−29.8039	−	17.2073i	−1.35054	−	0.779737i	−0.362219	−	0.932093i	$-0.617981\pi$
$487$	−29.8039	−	17.2073i	−1.35054	−	0.779737i	−0.988326	+	0.152356i	$0.951314\pi$
$488$	−5.89015	−	1.09233i	−0.266634	−	0.0494477i
$489$	−1.50609	−	8.62740i	−0.0681079	−	0.390144i
$490$	−8.13261	−	18.0776i	−0.367394	−	0.816664i
$491$	−12.1909	+	7.03839i	−0.550166	+	0.317638i	−0.749189	−	0.662357i	$-0.769556\pi$
$491$	−12.1909	+	7.03839i	−0.550166	+	0.317638i	0.199023	+	0.979995i	$0.436223\pi$
$492$	−1.29265	−	25.5329i	−0.0582774	−	1.15111i
$493$	−4.00490	+	2.31223i	−0.180372	+	0.104138i
$494$	−18.5766	+	28.0639i	−0.835800	+	1.26266i
$495$	−23.0886	−	19.5081i	−1.03775	−	0.876822i
$496$	4.32824	+	1.07982i	0.194344	+	0.0484852i
$497$	−8.91780	+	4.91515i	−0.400018	+	0.220474i
$498$	−21.0848	+	15.5452i	−0.944831	+	0.696598i
$499$	13.5870	+	7.84445i	0.608237	+	0.351166i	0.772275	−	0.635288i	$-0.219119\pi$
$499$	13.5870	+	7.84445i	0.608237	+	0.351166i	−0.164038	+	0.986454i	$0.552452\pi$
$500$	2.92541	−	23.8113i	0.130828	−	1.06487i
$501$	15.2096	−	2.65516i	0.679517	−	0.118624i
$502$	1.18974	−	19.4406i	0.0531008	−	0.867676i
$503$	−9.76063			−0.435205			−0.217603	−	0.976037i	$-0.569824\pi$
$503$	−9.76063			−0.435205			−0.217603	+	0.976037i	$0.569824\pi$
$504$	20.8387	+	8.35159i	0.928229	+	0.372009i
$505$	7.59691			0.338058
$506$	2.72794	−	44.5750i	0.121272	−	1.98160i
$507$	1.63948	+	1.96064i	0.0728121	+	0.0870749i
$508$	0.540465	−	4.39911i	0.0239793	−	0.195179i
$509$	28.6835	+	16.5604i	1.27137	+	0.734028i	0.975246	−	0.221121i	$-0.0709716\pi$
$509$	28.6835	+	16.5604i	1.27137	+	0.734028i	0.296127	+	0.955149i	$0.404305\pi$
$510$	−1.01980	−	9.09130i	−0.0451577	−	0.402570i
$511$	0.0303023	−	1.52525i	0.00134049	−	0.0674732i
$512$	11.8291	−	19.2892i	0.522776	−	0.852470i
$513$	28.0636	+	16.3943i	1.23904	+	0.723827i
$514$	10.8142	−	16.3372i	0.476993	−	0.720602i
$515$	16.0705	−	9.27831i	0.708151	−	0.408851i
$516$	−22.8166	+	14.7597i	−1.00444	+	0.649760i
$517$	16.9963	−	9.81284i	0.747498	−	0.431568i
$518$	3.44247	+	2.37837i	0.151253	+	0.104499i
$519$	4.94010	+	1.80759i	0.216846	+	0.0793443i
$520$	−3.92916	+	21.1870i	−0.172305	+	0.929113i
$521$	12.6595	+	7.30899i	0.554624	+	0.320213i	0.750985	−	0.660319i	$-0.229579\pi$
$521$	12.6595	+	7.30899i	0.554624	+	0.320213i	−0.196361	+	0.980532i	$0.562912\pi$
$522$	−2.95286	−	10.0962i	−0.129243	−	0.441899i
$523$	6.22510	+	10.7822i	0.272205	+	0.471472i	0.969426	−	0.245383i	$-0.0789139\pi$
$523$	6.22510	+	10.7822i	0.272205	+	0.471472i	−0.697221	+	0.716856i	$0.745581\pi$
$524$	19.1428	−	25.3996i	0.836259	−	1.10959i
$525$	2.84172	+	3.53890i	0.124023	+	0.154450i
$526$	−1.02116	−	2.04832i	−0.0445248	−	0.0893111i
$527$	1.80140	+	1.04004i	0.0784701	+	0.0453047i
$528$	2.49604	−	34.7714i	0.108626	−	1.51323i
$529$	8.19290	+	14.1905i	0.356213	+	0.616979i
$530$	7.08419	+	14.2100i	0.307718	+	0.617242i
$531$	−19.9503	−	16.8565i	−0.865771	−	0.731509i
$532$	20.4417	−	26.0307i	0.886261	−	1.12857i
$533$	−14.0395	+	24.3172i	−0.608120	+	1.05329i
$534$	−14.4458	+	1.62043i	−0.625129	+	0.0701230i
$535$	15.7047			0.678974
$536$	−33.4348	−	6.20053i	−1.44416	−	0.267822i
$537$	6.16479	−	5.15500i	0.266030	−	0.222455i
$538$	−3.56745	+	5.38940i	−0.153804	+	0.232354i
$539$	1.39897	−	35.1944i	0.0602579	−	1.51593i
$540$	20.6410	+	2.64306i	0.888246	+	0.113739i
$541$	−18.8784	−	32.6984i	−0.811647	−	1.40581i	−0.911711	−	0.410832i	$-0.865238\pi$
$541$	−18.8784	−	32.6984i	−0.811647	−	1.40581i	0.100064	−	0.994981i	$-0.468095\pi$
$542$	−30.2368	+	15.0741i	−1.29878	+	0.647489i
$543$	−6.20833	−	2.27163i	−0.266425	−	0.0974851i
$544$	7.78025	−	7.12670i	0.333575	−	0.305555i
$545$	−28.6908	+	16.5646i	−1.22898	+	0.709551i
$546$	−14.2350	−	20.1330i	−0.609203	−	0.861614i
$547$	−4.46357	−	2.57704i	−0.190848	−	0.110186i	0.401531	−	0.915845i	$-0.368478\pi$
$547$	−4.46357	−	2.57704i	−0.190848	−	0.110186i	−0.592380	+	0.805659i	$0.701811\pi$
$548$	−3.36105	−	7.91973i	−0.143577	−	0.338314i
$549$	4.10081	−	4.85348i	0.175018	−	0.207141i
$550$	3.89011	−	5.87685i	0.165875	−	0.250590i
$551$	−15.5083			−0.660676
$552$	15.0911	+	26.7865i	0.642319	+	1.14011i
$553$	9.17458	−	5.05667i	0.390143	−	0.215032i
$554$	−15.5744	+	7.76441i	−0.661693	+	0.329878i
$555$	3.64226	+	1.33271i	0.154605	+	0.0565702i
$556$	3.43359	+	8.09065i	0.145617	+	0.343120i
$557$	−21.0386	+	36.4399i	−0.891434	+	1.54401i	−0.0532780	+	0.998580i	$0.516967\pi$
$557$	−21.0386	+	36.4399i	−0.891434	+	1.54401i	−0.838156	+	0.545430i	$0.816366\pi$
$558$	−3.26875	+	3.42088i	−0.138377	+	0.144817i
$559$	29.8460			1.26235
$560$	5.53703	−	20.4552i	0.233982	−	0.864390i
$561$	5.58565	−	15.2655i	0.235826	−	0.644508i
$562$	15.7709	+	10.4393i	0.665254	+	0.440356i
$563$	−32.5793			−1.37305			−0.686526	−	0.727105i	$-0.740865\pi$
$563$	−32.5793			−1.37305			−0.686526	+	0.727105i	$0.740865\pi$
$564$	−6.15538	+	12.0278i	−0.259188	+	0.506460i
$565$		−	38.8779i		−	1.63561i
$566$	0.557251	−	9.10556i	0.0234230	−	0.382735i
$567$	−18.6427	+	14.8139i	−0.782919	+	0.622124i
$568$	−10.7032	−	1.98492i	−0.449096	−	0.0832854i
$569$	40.7388			1.70786			0.853930	−	0.520389i	$-0.174213\pi$
$569$	40.7388			1.70786			0.853930	+	0.520389i	$0.174213\pi$
$570$	12.2823	−	28.1134i	0.514447	−	1.17754i
$571$			26.7644i			1.12006i	0.828473	+	0.560029i	$0.189210\pi$
$571$			26.7644i			1.12006i	−0.828473	+	0.560029i	$0.810790\pi$
$572$	−23.0447	+	30.5767i	−0.963546	+	1.27848i
$573$	6.13873	+	2.24617i	0.256449	+	0.0938350i
$574$	15.6964	−	22.7190i	0.655154	−	0.948275i
$575$			6.21563i			0.259210i
$576$	11.5593	+	21.0329i	0.481637	+	0.876371i
$577$	4.34065	+	2.50607i	0.180704	+	0.104329i	0.587623	−	0.809135i	$-0.300064\pi$
$577$	4.34065	+	2.50607i	0.180704	+	0.104329i	−0.406920	+	0.913464i	$0.633397\pi$
$578$	−17.1131	+	8.53150i	−0.711811	+	0.354864i
$579$	7.22410	−	19.7433i	0.300224	−	0.820505i
$580$	−9.14038	+	3.87908i	−0.379534	+	0.161070i
$581$	−28.2891	−	0.562022i	−1.17363	−	0.0233166i
$582$	23.5625	+	31.9590i	0.976696	+	1.32474i
$583$			28.2129i			1.16846i
$584$	1.05931	−	1.24002i	0.0438346	−	0.0513124i
$585$	−17.4581	−	14.7507i	−0.721804	−	0.609868i
$586$	13.7875	+	27.6559i	0.569554	+	1.14245i
$587$	−10.2852	+	17.8145i	−0.424517	+	0.735285i	−0.996375	−	0.0850676i	$-0.972889\pi$
$587$	−10.2852	+	17.8145i	−0.424517	+	0.735285i	0.571858	+	0.820352i	$0.306223\pi$
$588$	12.3516	+	20.8672i	0.509371	+	0.860547i
$589$	3.48781	+	6.04106i	0.143713	+	0.248918i
$590$	−13.6082	+	20.5581i	−0.560239	+	0.846362i
$591$	3.78341	−	10.3400i	0.155629	−	0.425331i
$592$	1.23232	+	4.29996i	0.0506480	+	0.176727i
$593$	−15.5093	+	8.95431i	−0.636891	+	0.367709i	−0.783416	−	0.621498i	$-0.786525\pi$
$593$	−15.5093	+	8.95431i	−0.636891	+	0.367709i	0.146525	+	0.989207i	$0.453191\pi$
$594$	30.7279	+	20.5666i	1.26078	+	0.843858i
$595$	5.10966	−	8.45764i	0.209476	−	0.346730i
$596$	5.51887	−	7.32268i	0.226062	−	0.299949i
$597$	−2.23903	−	2.67762i	−0.0916372	−	0.109588i
$598$	2.06269	−	33.7047i	0.0843498	−	1.37829i
$599$			21.0167i			0.858719i	0.903134	+	0.429360i	$0.141261\pi$
$599$			21.0167i			0.858719i	−0.903134	+	0.429360i	$0.858739\pi$
$600$	−0.0511332	+	4.85173i	−0.00208750	+	0.198071i
$601$	17.3571	+	10.0211i	0.708012	+	0.408771i	0.810325	−	0.585981i	$-0.199291\pi$
$601$	17.3571	+	10.0211i	0.708012	+	0.408771i	−0.102312	+	0.994752i	$0.532624\pi$
$602$	−29.2554	−	2.37451i	−1.19236	−	0.0967776i
$603$	23.2778	−	27.5503i	0.947947	−	1.12193i
$604$	−43.2544	+	18.3567i	−1.76000	+	0.746925i
$605$	−24.8299	+	14.3355i	−1.00948	+	0.582822i
$606$	−9.23522	+	1.03595i	−0.375155	+	0.0420825i
$607$	−9.29855	+	16.1056i	−0.377417	+	0.653705i	−0.990686	−	0.136169i	$-0.956521\pi$
$607$	−9.29855	+	16.1056i	−0.377417	+	0.653705i	0.613269	+	0.789874i	$0.289854\pi$
$608$	34.5457	−	7.65203i	1.40101	−	0.310331i
$609$	4.11539	−	10.5905i	0.166764	−	0.429148i
$610$	−5.00132	−	3.31056i	−0.202498	−	0.134041i
$611$	12.8515	−	7.41984i	0.519918	−	0.300175i
$612$	2.47946	+	10.9128i	0.100226	+	0.441125i
$613$	16.7357	−	28.9871i	0.675949	−	1.17078i	−0.300242	−	0.953863i	$-0.597067\pi$
$613$	16.7357	−	28.9871i	0.675949	−	1.17078i	0.976191	−	0.216915i	$-0.0695993\pi$
$614$	0.432136	−	7.06117i	0.0174396	−	0.284966i
$615$	8.79538	−	24.0376i	0.354664	−	0.969289i
$616$	25.0213	−	28.1383i	1.00814	−	1.13372i
$617$	−12.3643	−	21.4156i	−0.497769	−	0.862161i	0.502228	−	0.864735i	$-0.332514\pi$
$617$	−12.3643	−	21.4156i	−0.497769	−	0.862161i	−0.999997	+	0.00257408i	$0.999181\pi$
$618$	−18.2710	+	13.4707i	−0.734965	+	0.541870i
$619$	−21.3150	−	36.9187i	−0.856723	−	1.48389i	−0.875038	−	0.484055i	$-0.839163\pi$
$619$	−21.3150	−	36.9187i	−0.856723	−	1.48389i	0.0183147	−	0.999832i	$-0.494170\pi$
$620$	3.56671	+	2.68811i	0.143243	+	0.107957i
$621$	−32.6096	−	0.166667i	−1.30858	−	0.00668812i
$622$	1.76173	−	28.7870i	0.0706391	−	1.15425i
$623$	−13.4389	−	8.11907i	−0.538418	−	0.325284i
$624$	1.88735	−	26.2919i	0.0755545	−	1.05252i
$625$	9.53352	−	16.5125i	0.381341	−	0.660501i
$626$	29.7439	+	1.82029i	1.18881	+	0.0727536i
$627$	41.8188	−	34.9689i	1.67008	−	1.39652i
$628$	−3.99820	+	32.5433i	−0.159545	+	1.29862i
$629$			2.08574i			0.0831639i
$630$	15.9391	+	15.8478i	0.635029	+	0.631392i
$631$			43.8344i			1.74502i	0.488596	+	0.872510i	$0.337509\pi$
$631$			43.8344i			1.74502i	−0.488596	+	0.872510i	$0.662491\pi$
$632$	11.0114	+	2.04207i	0.438009	+	0.0812293i
$633$	5.44342	+	31.1817i	0.216357	+	1.23936i
$634$	1.04323	−	17.0465i	0.0414319	−	0.677005i
$635$	2.21875	−	3.84298i	0.0880483	−	0.152504i
$636$	−10.5497	−	16.3084i	−0.418322	−	0.646670i
$637$	1.05781	−	26.6117i	0.0419120	−	1.05440i
$638$	−17.6103	−	1.07773i	−0.697197	−	0.0426677i
$639$	7.45173	−	8.81942i	0.294786	−	0.348891i
$640$	18.4467	−	13.1509i	0.729171	−	0.519834i
$641$	−13.1042	−	22.6971i	−0.517584	−	0.896482i	−0.999791	−	0.0204246i	$-0.993498\pi$
$641$	−13.1042	−	22.6971i	−0.517584	−	0.896482i	0.482208	−	0.876057i	$-0.339835\pi$
$642$	−19.0915	+	2.14156i	−0.753483	+	0.0845208i
$643$	−24.8988	−	43.1259i	−0.981911	−	1.70072i	−0.654930	−	0.755690i	$-0.727302\pi$
$643$	−24.8988	−	43.1259i	−0.981911	−	1.70072i	−0.326981	−	0.945031i	$-0.606031\pi$
$644$	−4.70338	+	32.8737i	−0.185339	+	1.29541i
$645$	−26.8016	+	4.67877i	−1.05531	+	0.184226i
$646$	16.4679	+	1.00782i	0.647921	+	0.0396521i
$647$	−7.44967	+	12.9032i	−0.292877	+	0.507277i	−0.974489	−	0.224436i	$-0.927946\pi$
$647$	−7.44967	+	12.9032i	−0.292877	+	0.507277i	0.681612	+	0.731714i	$0.261279\pi$
$648$	−25.4527	−	0.398360i	−0.999878	−	0.0156491i
$649$	−37.9376	+	21.9033i	−1.48918	+	0.859778i
$650$	2.94145	−	4.44370i	0.115373	−	0.174296i
$651$	−5.05094	+	0.778699i	−0.197962	+	0.0305196i
$652$	9.30909	−	3.95068i	0.364572	−	0.154721i
$653$	−21.6074	+	37.4251i	−0.845563	+	1.46456i	0.0395692	+	0.999217i	$0.487401\pi$
$653$	−21.6074	+	37.4251i	−0.845563	+	1.46456i	−0.885132	+	0.465341i	$0.845932\pi$
$654$	32.6193	−	24.0493i	1.27551	−	0.940401i
$655$	27.5773	−	15.9218i	1.07754	−	0.622116i
$656$	28.3782	−	8.13287i	1.10798	−	0.317535i
$657$	0.586090	+	1.62750i	0.0228655	+	0.0634949i
$658$	−13.1876	+	6.25057i	−0.514105	+	0.243673i
$659$	28.1704	+	16.2642i	1.09736	+	0.633562i	0.935527	−	0.353256i	$-0.114925\pi$
$659$	28.1704	+	16.2642i	1.09736	+	0.633562i	0.161835	+	0.986818i	$0.448259\pi$
$660$	15.9007	−	31.0703i	0.618933	−	1.20941i
$661$			30.2157i			1.17525i	0.809132	+	0.587627i	$0.199938\pi$
$661$			30.2157i			1.17525i	−0.809132	+	0.587627i	$0.800062\pi$
$662$	−1.79916	−	0.110106i	−0.0699262	−	0.00427941i
$663$	4.22351	−	11.5428i	0.164028	−	0.448284i
$664$	−22.9989	−	19.6472i	−0.892530	−	0.762460i
$665$	29.0213	−	15.9954i	1.12540	−	0.620275i
$666$	−4.60946	−	1.12344i	−0.178613	−	0.0435322i
$667$	13.4755	−	7.78009i	0.521774	−	0.301246i
$668$	6.96484	+	16.4114i	0.269478	+	0.634977i
$669$	−18.2946	−	21.8782i	−0.707310	−	0.845861i
$670$	−28.3895	−	18.7921i	−1.09678	−	0.726001i
$671$	−5.32858	−	9.22937i	−0.205708	−	0.356296i
$672$	−3.94175	+	25.6215i	−0.152056	+	0.988372i
$673$	−7.60245	+	13.1678i	−0.293053	+	0.507582i	−0.974530	−	0.224257i	$-0.928005\pi$
$673$	−7.60245	+	13.1678i	−0.293053	+	0.507582i	0.681477	+	0.731839i	$0.261338\pi$
$674$	−15.5052	+	7.72991i	−0.597238	+	0.297745i
$675$	−4.44364	−	2.59591i	−0.171036	−	0.0999166i
$676$	−1.77622	+	2.35677i	−0.0683162	+	0.0906451i
$677$		−	40.7536i		−	1.56629i	−0.621841	−	0.783143i	$-0.713615\pi$
$677$		−	40.7536i		−	1.56629i	0.621841	−	0.783143i	$-0.286385\pi$
$678$	5.30157	+	47.2622i	0.203605	+	1.81509i
$679$	−0.851878	+	42.8789i	−0.0326921	+	1.64554i
$680$	9.95804	−	3.52511i	0.381873	−	0.135182i
$681$	0.753174	−	0.131482i	0.0288617	−	0.00503841i
$682$	3.54072	+	7.10223i	0.135581	+	0.271959i
$683$	−1.67736	−	0.968424i	−0.0641824	−	0.0370557i	0.467565	−	0.883958i	$-0.345131\pi$
$683$	−1.67736	−	0.968424i	−0.0641824	−	0.0370557i	−0.531748	+	0.846903i	$0.678465\pi$
$684$	−11.0973	+	35.8511i	−0.424317	+	1.37080i
$685$		−	8.61373i		−	0.329114i
$686$	−3.15407	+	26.0010i	−0.120423	+	0.992723i
$687$	7.14131	−	5.97157i	0.272458	−	0.227830i
$688$	−22.5684	−	21.8004i	−0.860414	−	0.831132i
$689$			21.3328i			0.812714i
$690$	3.43139	+	30.5900i	0.130631	+	1.16454i
$691$	−16.0475			−0.610476			−0.305238	−	0.952276i	$-0.598736\pi$
$691$	−16.0475			−0.610476			−0.305238	+	0.952276i	$0.598736\pi$
$692$	−0.740696	+	6.02888i	−0.0281570	+	0.229184i
$693$	12.7827	+	37.8373i	0.485573	+	1.43732i
$694$	−12.1901	−	0.746021i	−0.462730	−	0.0283186i
$695$			8.79962i			0.333789i
$696$	10.5826	−	5.96205i	0.401132	−	0.225991i
$697$	13.7651			0.521392
$698$	6.23181	−	9.41450i	0.235878	−	0.356344i
$699$	−11.5410	+	2.01472i	−0.436520	+	0.0762036i
$700$	−3.23678	+	4.12175i	−0.122339	+	0.155788i
$701$	−15.9608			−0.602830			−0.301415	−	0.953493i	$-0.597459\pi$
$701$	−15.9608			−0.602830			−0.301415	+	0.953493i	$0.597459\pi$
$702$	23.2345	+	15.5512i	0.876930	+	0.586941i
$703$	−3.49731	+	6.05751i	−0.131903	+	0.228463i
$704$	39.7597	−	6.28847i	1.49850	−	0.237006i
$705$	−10.3775	+	8.67764i	−0.390838	+	0.326819i
$706$	−11.9401	−	23.9503i	−0.449372	−	0.901383i
$707$	−8.59153	−	5.19055i	−0.323118	−	0.195211i
$708$	13.7394	−	26.8472i	0.516360	−	1.00898i
$709$	−3.09287			−0.116155			−0.0580776	−	0.998312i	$-0.518497\pi$
$709$	−3.09287			−0.116155			−0.0580776	+	0.998312i	$0.518497\pi$
$710$	−9.08807	−	6.01574i	−0.341069	−	0.225767i
$711$	−7.66629	+	9.07336i	−0.287508	+	0.340278i
$712$	−5.60128	−	15.8230i	−0.209917	−	0.592991i
$713$	−6.06127	−	3.49947i	−0.226996	−	0.131056i
$714$	−5.05826	+	10.9784i	−0.189301	+	0.410855i
$715$	−33.1983	+	19.1671i	−1.24155	+	0.716808i
$716$	7.41035	+	5.58494i	0.276938	+	0.208719i
$717$	−0.0583048	−	0.333989i	−0.00217743	−	0.0124730i
$718$	16.6096	+	33.3168i	0.619866	+	1.24337i
$719$	−12.5658	−	21.7645i	−0.468624	−	0.811680i	0.530733	−	0.847539i	$-0.321917\pi$
$719$	−12.5658	−	21.7645i	−0.468624	−	0.811680i	−0.999357	+	0.0358588i	$0.988583\pi$
$720$	2.42679	+	23.9059i	0.0904412	+	0.890920i
$721$	−24.5139	−	0.487019i	−0.912945	−	0.0181375i
$722$	23.7311	+	15.7085i	0.883179	+	0.584609i
$723$	−3.82823	−	21.9294i	−0.142374	−	0.815563i
$724$	0.930848	−	7.57662i	0.0345947	−	0.281583i
$725$	2.45562			0.0911993
$726$	28.2297	−	20.8130i	1.04770	−	0.772441i
$727$	−26.4226	+	45.7653i	−0.979960	+	1.69734i	−0.317474	+	0.948267i	$0.602835\pi$
$727$	−26.4226	+	45.7653i	−0.979960	+	1.69734i	−0.662486	+	0.749074i	$0.730499\pi$
$728$	18.9195	−	21.2764i	0.701204	−	0.788555i
$729$	13.7383	−	23.2435i	0.508826	−	0.860869i
$730$	1.46131	−	0.728516i	0.0540855	−	0.0269636i
$731$	−7.31567	−	12.6711i	−0.270580	−	0.468658i
$732$	6.53132	+	3.34250i	0.241405	+	0.123542i
$733$	3.33874	+	1.92762i	0.123319	+	0.0711983i	0.560391	−	0.828228i	$-0.310651\pi$
$733$	3.33874	+	1.92762i	0.123319	+	0.0711983i	−0.437072	+	0.899427i	$0.643984\pi$
$734$	1.97431	−	0.984264i	0.0728730	−	0.0363299i
$735$	3.22185	+	24.0630i	0.118840	+	0.887578i
$736$	−26.1787	+	23.9796i	−0.964959	+	0.883901i
$737$	−30.2471	−	52.3896i	−1.11417	−	1.92980i
$738$	−7.41427	+	30.4208i	−0.272923	+	1.11981i
$739$	−3.15539	−	1.82177i	−0.116073	−	0.0670148i	0.440840	−	0.897586i	$-0.354681\pi$
$739$	−3.15539	−	1.82177i	−0.116073	−	0.0670148i	−0.556912	+	0.830571i	$0.688014\pi$
$740$	−0.546103	+	4.44499i	−0.0200751	+	0.163401i
$741$	31.6207	−	26.4413i	1.16162	−	0.971344i
$742$	1.69721	−	20.9107i	0.0623064	−	0.767654i
$743$	10.9054	−	6.29626i	0.400082	−	0.230987i	−0.286437	−	0.958099i	$-0.592471\pi$
$743$	10.9054	−	6.29626i	0.400082	−	0.230987i	0.686519	+	0.727112i	$0.259138\pi$
$744$	−4.70245	−	2.78145i	−0.172400	−	0.101973i
$745$	7.95053	−	4.59024i	0.291285	−	0.168173i
$746$	42.4510	+	28.0999i	1.55424	+	1.02881i
$747$	30.1856	−	10.8703i	1.10443	−	0.397724i
$748$	18.6299	+	2.28883i	0.681177	+	0.0836880i
$749$	−17.7609	−	10.7302i	−0.648968	−	0.392072i
$750$	−11.7629	+	26.9247i	−0.429521	+	0.983151i
$751$	11.5923	+	6.69279i	0.423007	+	0.244223i	0.696363	−	0.717690i	$-0.254800\pi$
$751$	11.5923	+	6.69279i	0.423007	+	0.244223i	−0.273356	+	0.961913i	$0.588134\pi$
$752$	−15.1375	−	3.77654i	−0.552009	−	0.137716i
$753$	−8.19683	+	22.4018i	−0.298709	+	0.816367i
$754$	−13.3158	−	0.814911i	−0.484932	−	0.0296773i
$755$	−47.0448			−1.71213
$756$	−21.5375	−	17.0919i	−0.783312	−	0.621628i
$757$	1.72257			0.0626080			0.0313040	−	0.999510i	$-0.490034\pi$
$757$	1.72257			0.0626080			0.0313040	+	0.999510i	$0.490034\pi$
$758$	−27.4924	−	1.68250i	−0.998569	−	0.0611113i
$759$	−18.7944	+	51.3646i	−0.682192	+	1.86442i
$760$	34.8315	+	6.45954i	1.26347	+	0.234312i
$761$	17.9347	+	10.3546i	0.650134	+	0.375355i	0.788507	−	0.615025i	$-0.210854\pi$
$761$	17.9347	+	10.3546i	0.650134	+	0.375355i	−0.138374	+	0.990380i	$0.544188\pi$
$762$	−2.17319	+	4.97430i	−0.0787262	+	0.180200i
$763$	43.7648	+	0.869478i	1.58439	+	0.0314772i
$764$	−0.920413	+	7.49168i	−0.0332994	+	0.271040i
$765$	−1.98320	+	11.0274i	−0.0717028	+	0.398698i
$766$	−0.116926	−	0.0773977i	−0.00422471	−	0.00279649i
$767$	−28.6860	+	16.5619i	−1.03579	+	0.598014i
$768$	−20.6315	+	18.5024i	−0.744477	+	0.667648i
$769$	6.19700	−	3.57784i	0.223470	−	0.129020i	−0.384086	−	0.923297i	$-0.625483\pi$
$769$	6.19700	−	3.57784i	0.223470	−	0.129020i	0.607556	+	0.794277i	$0.292150\pi$
$770$	34.0663	−	16.1466i	1.22767	−	0.581883i
$771$	−18.4077	+	15.3925i	−0.662938	+	0.554349i
$772$	24.0947	+	2.96022i	0.867186	+	0.106541i
$773$	28.6131	+	16.5198i	1.02914	+	0.594176i	0.916739	−	0.399487i	$-0.130812\pi$
$773$	28.6131	+	16.5198i	1.02914	+	0.594176i	0.112404	+	0.993663i	$0.464145\pi$
$774$	31.9434	−	9.34255i	1.14818	−	0.335811i
$775$	−0.552266	−	0.956553i	−0.0198380	−	0.0343604i
$776$	−29.7800	+	34.8603i	−1.06904	+	1.25141i
$777$	−3.20856	−	3.99574i	−0.115106	−	0.143347i
$778$	33.6236	−	16.7626i	1.20546	−	0.600968i
$779$	39.9774	+	23.0810i	1.43234	+	0.826962i
$780$	12.0231	−	23.4934i	0.430495	−	0.841198i
$781$	−9.68275	−	16.7710i	−0.346476	−	0.600114i
$782$	−14.8149	+	7.38578i	−0.529781	+	0.264115i
$783$	−0.0658453	+	12.8831i	−0.00235312	+	0.460405i
$784$	−20.2379	+	19.3502i	−0.722781	+	0.691077i
$785$	−16.4136	+	28.4292i	−0.585827	+	1.01468i
$786$	−31.3534	+	23.1160i	−1.11834	+	0.824519i
$787$	23.4826			0.837066			0.418533	−	0.908202i	$-0.362544\pi$
$787$	23.4826			0.837066			0.418533	+	0.908202i	$0.362544\pi$
$788$	12.6189	+	1.55033i	0.449529	+	0.0552282i
$789$	0.482057	+	2.76138i	0.0171617	+	0.0983078i
$790$	9.34975	+	6.18895i	0.332649	+	0.220193i
$791$	−26.5632	+	43.9680i	−0.944477	+	1.56332i
$792$	−15.0929	+	39.9391i	−0.536301	+	1.41917i
$793$	−4.02913	−	6.97866i	−0.143079	−	0.247820i
$794$	−17.0784	−	34.2571i	−0.606090	−	1.21574i
$795$	−3.34421	−	19.1567i	−0.118607	−	0.679419i
$796$	2.42577	−	3.21862i	0.0859790	−	0.114081i
$797$	−15.6061	+	9.01016i	−0.552795	+	0.319156i	−0.750248	−	0.661156i	$-0.770066\pi$
$797$	−15.6061	+	9.01016i	−0.552795	+	0.319156i	0.197454	+	0.980312i	$0.436733\pi$
$798$	−33.0987	+	23.4024i	−1.17168	+	0.828435i
$799$	−6.30018	−	3.63741i	−0.222884	−	0.128682i
$800$	−5.47003	+	1.21164i	−0.193395	+	0.0428379i
$801$	17.5222	+	3.15124i	0.619117	+	0.111344i
$802$	−37.7342	−	24.9777i	−1.33244	−	0.881993i
$803$	2.90132			0.102386
$804$	37.0744	+	18.9734i	1.30751	+	0.669139i
$805$	−17.1928	+	28.4579i	−0.605966	+	1.00301i
$806$	2.67727	+	5.37026i	0.0943028	+	0.189159i
$807$	6.07245	−	5.07779i	0.213760	−	0.178747i
$808$	−3.58091	−	10.1157i	−0.125976	−	0.355868i
$809$	6.22093	−	10.7750i	0.218716	−	0.378828i	−0.735699	−	0.677308i	$-0.763146\pi$
$809$	6.22093	−	10.7750i	0.218716	−	0.378828i	0.954416	+	0.298480i	$0.0964797\pi$
$810$	−23.3023	−	10.3225i	−0.818761	−	0.362697i
$811$	11.5370			0.405118			0.202559	−	0.979270i	$-0.435074\pi$
$811$	11.5370			0.405118			0.202559	+	0.979270i	$0.435074\pi$
$812$	12.9874	+	1.85817i	0.455770	+	0.0652090i
$813$	40.7627	−	7.11598i	1.42961	−	0.249568i
$814$	−4.39228	+	6.63550i	−0.153949	+	0.232574i
$815$	10.1248			0.354657
$816$	−11.6248	+	5.64324i	−0.406951	+	0.197553i
$817$		−	49.0668i		−	1.71663i
$818$	30.8713	+	1.88929i	1.07939	+	0.0660574i
$819$	9.66543	+	28.6102i	0.337738	+	0.999720i
$820$	29.3354	+	3.60408i	1.02444	+	0.125860i
$821$	30.6967			1.07132			0.535661	−	0.844433i	$-0.320062\pi$
$821$	30.6967			1.07132			0.535661	+	0.844433i	$0.320062\pi$
$822$	1.17461	+	10.4713i	0.0409691	+	0.365229i
$823$			43.1892i			1.50548i	0.658317	+	0.752740i	$0.271268\pi$
$823$			43.1892i			1.50548i	−0.658317	+	0.752740i	$0.728732\pi$
$824$	−19.9296	−	17.0252i	−0.694281	−	0.593102i
$825$	−6.62167	+	5.53705i	−0.230537	+	0.192775i
$826$	29.4360	−	13.9519i	1.02421	−	0.485449i
$827$		−	24.5381i		−	0.853273i	−0.904423	−	0.426637i	$-0.859698\pi$
$827$		−	24.5381i		−	0.853273i	0.904423	−	0.426637i	$-0.140302\pi$
$828$	−8.34278	−	36.7190i	−0.289932	−	1.27607i
$829$	−44.2845	−	25.5676i	−1.53806	−	0.888001i	−0.998952	−	0.0457657i	$-0.985427\pi$
$829$	−44.2845	−	25.5676i	−1.53806	−	0.888001i	−0.539110	−	0.842235i	$-0.681239\pi$
$830$	−13.5119	−	27.1032i	−0.469006	−	0.940765i
$831$	20.9961	−	3.66531i	0.728348	−	0.127148i
$832$	30.0637	−	4.75494i	1.04227	−	0.164848i
$833$	−11.5573	+	6.07381i	−0.400436	+	0.210445i
$834$	−1.19995	−	10.6973i	−0.0415510	−	0.370417i
$835$			17.8495i			0.617709i
$836$	50.2681	+	37.8854i	1.73856	+	1.31029i
$837$	5.03326	−	2.87176i	0.173975	−	0.0992624i
$838$	24.3714	−	12.1500i	0.841897	−	0.419717i
$839$	−14.4267	+	24.9878i	−0.498066	+	0.862675i	−0.999998	−	0.00223194i	$-0.999290\pi$
$839$	−14.4267	+	24.9878i	−0.498066	+	0.862675i	0.501932	+	0.864907i	$0.332623\pi$
$840$	−13.6543	+	22.0720i	−0.471117	+	0.761555i
$841$	11.4263	+	19.7909i	0.394011	+	0.682447i
$842$	−39.8275	−	26.3633i	−1.37255	−	0.908540i
$843$	−14.8590	−	17.7696i	−0.511770	−	0.612019i
$844$	−33.6455	+	14.2788i	−1.15813	+	0.491497i
$845$	−2.55884	+	1.47735i	−0.0880268	+	0.0508223i
$846$	11.4321	−	11.9641i	0.393043	−	0.411335i
$847$	37.8754	+	0.752472i	1.30141	+	0.0258552i
$848$	15.5821	−	16.1311i	0.535091	−	0.553943i
$849$	−3.83922	+	10.4925i	−0.131762	+	0.360103i
$850$	−2.60756	−	0.159580i	−0.0894386	−	0.00547355i
$851$		−	7.01801i		−	0.240574i
$852$	11.8683	+	6.07377i	0.406601	+	0.208084i
$853$	2.27160	+	1.31151i	0.0777781	+	0.0449052i	0.538385	−	0.842699i	$-0.319035\pi$
$853$	2.27160	+	1.31151i	0.0777781	+	0.0449052i	−0.460607	+	0.887604i	$0.652368\pi$
$854$	3.39419	+	7.16113i	0.116147	+	0.245049i
$855$	−24.2502	+	28.7011i	−0.829340	+	0.981557i
$856$	−7.40266	−	20.9117i	−0.253018	−	0.714746i
$857$	−17.9320	+	10.3531i	−0.612546	+	0.353654i	−0.773961	−	0.633233i	$-0.781728\pi$
$857$	−17.9320	+	10.3531i	−0.612546	+	0.353654i	0.161415	+	0.986887i	$0.448394\pi$
$858$	37.7440	−	27.8276i	1.28856	−	0.950019i
$859$	27.2547	−	47.2066i	0.929920	−	1.61067i	0.146468	−	0.989215i	$-0.453210\pi$
$859$	27.2547	−	47.2066i	0.929920	−	1.61067i	0.783452	−	0.621453i	$-0.213457\pi$
$860$	−12.2730	−	28.9193i	−0.418507	−	0.986139i
$861$	−26.3705	+	21.1753i	−0.898703	+	0.721653i
$862$	−2.32354	+	3.51021i	−0.0791400	+	0.119558i
$863$	27.4054	−	15.8225i	0.932891	−	0.538605i	0.0451662	−	0.998979i	$-0.485618\pi$
$863$	27.4054	−	15.8225i	0.932891	−	0.538605i	0.887725	+	0.460375i	$0.152285\pi$
$864$	−6.21005	−	28.7304i	−0.211270	−	0.977428i
$865$	−3.04074	+	5.26672i	−0.103388	+	0.179074i
$866$	36.1247	+	2.21079i	1.22757	+	0.0751258i
$867$	23.0705	−	4.02743i	0.783515	−	0.136779i
$868$	−2.19704	−	5.47699i	−0.0745725	−	0.185901i
$869$	9.96155	+	17.2539i	0.337922	+	0.585299i
$870$	12.0852	−	1.35564i	0.409728	−	0.0459607i
$871$	−22.8710	−	39.6137i	−0.774953	−	1.34226i
$872$	35.5805	+	30.3953i	1.20491	+	1.02931i
$873$	−16.4766	−	45.7534i	−0.557647	−	1.54852i
$874$	−55.4106	−	3.39107i	−1.87429	−	0.114705i
$875$	−27.7942	+	15.3191i	−0.939614	+	0.517879i
$876$	−1.67711	+	1.08490i	−0.0566641	+	0.0366552i
$877$	−3.95510	+	6.85043i	−0.133554	+	0.231322i	−0.925044	−	0.379860i	$-0.875972\pi$
$877$	−3.95510	+	6.85043i	−0.133554	+	0.231322i	0.791490	+	0.611182i	$0.209306\pi$
$878$	2.51654	−	41.1206i	0.0849289	−	1.38775i
$879$	−6.50859	−	37.2834i	−0.219529	−	1.25754i
$880$	39.1036	+	9.75562i	1.31818	+	0.328862i
$881$			22.7935i			0.767932i	0.923347	+	0.383966i	$0.125442\pi$
$881$			22.7935i			0.767932i	−0.923347	+	0.383966i	$0.874558\pi$
$882$	−7.19799	−	28.8130i	−0.242369	−	0.970184i
$883$			13.4192i			0.451591i	0.974175	+	0.225795i	$0.0724981\pi$
$883$			13.4192i			0.451591i	−0.974175	+	0.225795i	$0.927502\pi$
$884$	14.0867	+	1.73067i	0.473788	+	0.0582087i
$885$	23.1636	−	19.3694i	0.778635	−	0.651095i
$886$	−35.8456	−	2.19371i	−1.20426	−	0.0736991i
$887$	29.1587	−	50.5043i	0.979053	−	1.69577i	0.313199	−	0.949687i	$-0.398599\pi$
$887$	29.1587	−	50.5043i	0.979053	−	1.69577i	0.665854	−	0.746082i	$-0.268067\pi$
$888$	0.0577340	−	5.47805i	0.00193743	−	0.183831i
$889$	−5.13493	+	2.83018i	−0.172220	+	0.0949211i
$890$	1.02654	−	16.7739i	0.0344098	−	0.562261i
$891$	−28.8720	−	34.8884i	−0.967247	−	1.16880i
$892$	19.8204	−	26.2986i	0.663636	−	0.880542i
$893$	−12.1982	−	21.1279i	−0.408198	−	0.707019i
$894$	−9.03915	+	6.66432i	−0.302315	+	0.222888i
$895$	4.64519	+	8.04571i	0.155272	+	0.268938i
$896$	−29.8471	+	2.26902i	−0.997123	+	0.0758028i
$897$	−14.2111	+	38.8387i	−0.474495	+	1.29679i
$898$	2.65667	−	43.4104i	0.0886542	−	1.44862i
$899$	−1.38254	+	2.39463i	−0.0461103	+	0.0798654i
$900$	1.75717	−	5.67673i	0.0585724	−	0.189224i
$901$	9.05682	−	5.22896i	0.301727	−	0.174202i
$902$	43.7919	+	28.9875i	1.45811	+	0.965178i
$903$	33.5073	+	13.0207i	1.11505	+	0.433301i
$904$	−51.7680	+	18.3257i	−1.72178	+	0.609504i
$905$	3.82136	−	6.61880i	0.127026	−	0.220016i
$906$	57.1902	−	6.41523i	1.90002	−	0.213132i
$907$	1.79909	−	1.03871i	0.0597379	−	0.0344897i	−0.469834	−	0.882755i	$-0.655686\pi$
$907$	1.79909	−	1.03871i	0.0597379	−	0.0344897i	0.529571	+	0.848265i	$0.322353\pi$
$908$	0.344895	+	0.812686i	0.0114457	+	0.0269699i
$909$	11.2020	+	2.01460i	0.371547	+	0.0668199i
$910$	25.7588	−	12.2090i	0.853896	−	0.404725i
$911$	−39.6927	−	22.9166i	−1.31508	−	0.759261i	−0.332147	−	0.943228i	$-0.607773\pi$
$911$	−39.6927	−	22.9166i	−1.31508	−	0.759261i	−0.982933	+	0.183966i	$0.941106\pi$
$912$	−43.2239	−	3.10280i	−1.43129	−	0.102744i
$913$		−	53.8114i		−	1.78090i
$914$	−0.949052	+	15.5077i	−0.0313918	+	0.512948i
$915$	4.71214	+	5.63518i	0.155779	+	0.186293i
$916$	8.58417	+	6.46961i	0.283629	+	0.213762i
$917$	−42.0664	−	0.835735i	−1.38915	−	0.0275984i
$918$	0.907138	−	13.6760i	0.0299400	−	0.451376i
$919$	3.35149	−	1.93498i	0.110555	−	0.0638292i	−0.443703	−	0.896174i	$-0.646335\pi$
$919$	3.35149	−	1.93498i	0.110555	−	0.0638292i	0.554258	+	0.832345i	$0.313002\pi$
$920$	−33.5064	+	11.8612i	−1.10467	+	0.391051i
$921$	−2.97724	+	8.13673i	−0.0981032	+	0.268114i
$922$	−12.9683	+	19.5915i	−0.427089	+	0.645211i
$923$	−7.32148	−	12.6812i	−0.240989	−	0.417406i
$924$	−39.2111	+	24.2741i	−1.28995	+	0.798560i
$925$	0.553771	−	0.959159i	0.0182079	−	0.0315369i
$926$	−5.04463	−	10.1189i	−0.165777	−	0.332527i
$927$	26.1572	−	9.41964i	0.859116	−	0.309382i
$928$	9.47366	+	10.3424i	0.310988	+	0.339507i
$929$		−	8.04071i		−	0.263807i	−0.991263	−	0.131904i	$-0.957891\pi$
$929$		−	8.04071i		−	0.263807i	0.991263	−	0.131904i	$-0.0421089\pi$
$930$	−3.24604	−	4.40276i	−0.106442	−	0.144372i
$931$	−43.7497	−	1.73904i	−1.43384	−	0.0569947i
$932$	−5.28487	−	12.4529i	−0.173112	−	0.407908i
$933$	−12.1376	+	33.1718i	−0.397367	+	1.08600i
$934$	−32.0562	+	15.9812i	−1.04891	+	0.522921i
$935$	16.2747	+	9.39623i	0.532241	+	0.307290i
$936$	−11.4123	+	30.1994i	−0.373021	+	0.987097i
$937$			51.2010i			1.67267i	0.548222	+	0.836333i	$0.315305\pi$
$937$			51.2010i			1.67267i	−0.548222	+	0.836333i	$0.684695\pi$
$938$	19.2668	+	40.6494i	0.629083	+	1.32725i
$939$	−34.2745	−	12.5411i	−1.11851	−	0.409262i
$940$	−12.4742	−	9.40138i	−0.406863	−	0.306639i
$941$		−	56.1237i		−	1.82958i	−0.403929	−	0.914790i	$-0.632356\pi$
$941$		−	56.1237i		−	1.82958i	0.403929	−	0.914790i	$-0.367644\pi$
$942$	16.0766	−	36.7983i	0.523803	−	1.19895i
$943$	−46.3164			−1.50827
$944$	33.7885	+	8.42962i	1.09972	+	0.274361i
$945$	−13.1645	−	24.1766i	−0.428243	−	0.786464i
$946$	3.40983	−	55.7172i	0.110863	−	1.81152i
$947$			8.74354i			0.284127i	0.989858	+	0.142063i	$0.0453737\pi$
$947$			8.74354i			0.284127i	−0.989858	+	0.142063i	$0.954626\pi$
$948$	−12.2100	−	6.24866i	−0.396563	−	0.202947i
$949$	2.19380			0.0712137
$950$	−7.30544	−	4.83574i	−0.237020	−	0.156892i
$951$	−7.18742	+	19.6431i	−0.233068	+	0.636970i
$952$	−13.6703	−	2.81714i	−0.443057	−	0.0913042i
$953$	−0.861914			−0.0279201			−0.0139601	−	0.999903i	$-0.504444\pi$
$953$	−0.861914			−0.0279201			−0.0139601	+	0.999903i	$0.504444\pi$
$954$	6.67770	+	22.8319i	0.216198	+	0.739212i
$955$	−3.77853	+	6.54460i	−0.122270	+	0.211778i
$956$	0.360379	−	0.152941i	0.0116555	−	0.00494647i
$957$	20.2927	+	7.42511i	0.655969	+	0.240020i
$958$	5.30015	−	2.64232i	0.171240	−	0.0853694i
$959$	−5.88529	+	9.74148i	−0.190046	+	0.314569i
$960$	−26.2517	+	8.98282i	−0.847269	+	0.289919i
$961$	−29.7563			−0.959880
$962$	−3.32117	+	5.01734i	−0.107079	+	0.161766i
$963$	23.1574	+	4.16468i	0.746236	+	0.134205i
$964$	23.6622	−	10.0420i	0.762107	−	0.323430i
$965$	21.0487	+	12.1525i	0.677581	+	0.391201i
$966$	17.0198	−	36.9395i	0.547604	−	1.18851i
$967$	34.3142	−	19.8113i	1.10347	−	0.637090i	0.166341	−	0.986068i	$-0.446805\pi$
$967$	34.3142	−	19.8113i	1.10347	−	0.637090i	0.937131	+	0.348979i	$0.113471\pi$
$968$	30.7924	+	26.3050i	0.989706	+	0.845474i
$969$	−18.9763	−	6.94344i	−0.609607	−	0.223056i
$970$	−41.0813	+	20.4805i	−1.31904	+	0.657591i
$971$	5.76791	+	9.99031i	0.185101	+	0.320604i	0.943611	−	0.331058i	$-0.107405\pi$
$971$	5.76791	+	9.99031i	0.185101	+	0.320604i	−0.758510	+	0.651662i	$0.774072\pi$
$972$	29.7352	+	9.37103i	0.953758	+	0.300576i
$973$	6.01230	−	9.95171i	0.192745	−	0.319037i
$974$	−26.8640	+	40.5839i	−0.860779	+	1.30039i
$975$	−5.00689	+	4.18676i	−0.160349	+	0.134084i
$976$	−2.05074	+	8.22000i	−0.0656426	+	0.263116i
$977$	−4.92945			−0.157707			−0.0788536	−	0.996886i	$-0.525126\pi$
$977$	−4.92945			−0.157707			−0.0788536	+	0.996886i	$0.525126\pi$
$978$	−12.3083	+	1.38067i	−0.393576	+	0.0441489i
$979$	14.9303	−	25.8600i	0.477174	−	0.826489i
$980$	−26.2204	+	9.91810i	−0.837581	+	0.316822i
$981$	−46.6987	+	16.8170i	−1.49097	+	0.536924i
$982$	8.88207	+	17.8163i	0.283438	+	0.568541i
$983$	−3.26743	−	5.65936i	−0.104215	−	0.180506i	0.809202	−	0.587530i	$-0.199900\pi$
$983$	−3.26743	−	5.65936i	−0.104215	−	0.180506i	−0.913417	+	0.407025i	$0.866566\pi$
$984$	−36.1532	−	0.381024i	−1.15252	−	0.0121466i
$985$	11.0236	+	6.36450i	0.351242	+	0.202790i
$986$	2.91791	+	5.85295i	0.0929251	+	0.186396i
$987$	17.6651	−	2.72341i	0.562286	−	0.0866871i
$988$	38.0095	+	28.6465i	1.20924	+	0.911368i
$989$	24.6155	+	42.6352i	0.782726	+	1.35572i
$990$	−29.5316	+	30.9060i	−0.938575	+	0.982256i
$991$	−9.59915	−	5.54207i	−0.304927	−	0.176050i	0.339727	−	0.940524i	$-0.389665\pi$
$991$	−9.59915	−	5.54207i	−0.304927	−	0.176050i	−0.644654	+	0.764474i	$0.722999\pi$
$992$	1.89814	−	6.01635i	0.0602661	−	0.191019i
$993$	2.07320	+	0.758587i	0.0657912	+	0.0240730i
$994$	6.16771	+	13.0127i	0.195628	+	0.412739i
$995$	3.49458	−	2.01760i	0.110786	−	0.0639621i
$996$	20.1218	+	31.1056i	0.637582	+	0.985618i
$997$	10.9455	−	6.31941i	0.346649	−	0.200138i	−0.316560	−	0.948573i	$-0.602528\pi$
$997$	10.9455	−	6.31941i	0.346649	−	0.200138i	0.663208	+	0.748435i	$0.269194\pi$
$998$	12.2467	−	18.5014i	0.387664	−	0.585650i
$999$	5.01727	+	2.93102i	0.158740	+	0.0927333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.115.21	yes	84
3.2	odd	2		756.2.bj.b.451.22		84
4.3	odd	2	inner	252.2.bj.b.115.22	yes	84
7.5	odd	6		252.2.n.b.187.7	yes	84
9.4	even	3		252.2.n.b.31.35	yes	84
9.5	odd	6		756.2.n.b.199.8		84
12.11	even	2		756.2.bj.b.451.21		84
21.5	even	6		756.2.n.b.19.36		84
28.19	even	6		252.2.n.b.187.35	yes	84
36.23	even	6		756.2.n.b.199.36		84
36.31	odd	6		252.2.n.b.31.7	✓	84
63.5	even	6		756.2.bj.b.523.22		84
63.40	odd	6	inner	252.2.bj.b.103.21	yes	84
84.47	odd	6		756.2.n.b.19.8		84
252.103	even	6	inner	252.2.bj.b.103.22	yes	84
252.131	odd	6		756.2.bj.b.523.21		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.7	✓	84	36.31	odd	6
252.2.n.b.31.35	yes	84	9.4	even	3
252.2.n.b.187.7	yes	84	7.5	odd	6
252.2.n.b.187.35	yes	84	28.19	even	6
252.2.bj.b.103.21	yes	84	63.40	odd	6	inner
252.2.bj.b.103.22	yes	84	252.103	even	6	inner
252.2.bj.b.115.21	yes	84	1.1	even	1	trivial
252.2.bj.b.115.22	yes	84	4.3	odd	2	inner
756.2.n.b.19.8		84	84.47	odd	6
756.2.n.b.19.36		84	21.5	even	6
756.2.n.b.199.8		84	9.5	odd	6
756.2.n.b.199.36		84	36.23	even	6
756.2.bj.b.451.21		84	12.11	even	2
756.2.bj.b.451.22		84	3.2	odd	2
756.2.bj.b.523.21		84	252.131	odd	6
756.2.bj.b.523.22		84	63.5	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0863867 - 1.41157i) q^{2} +(-0.595168 + 1.62658i) q^{3} +(-1.98507 - 0.243882i) q^{4} +(-1.73413 - 1.00120i) q^{5} +(2.24463 + 0.980638i) q^{6} +(1.27710 + 2.31711i) q^{7} +(-0.515742 + 2.78101i) q^{8} +(-2.29155 - 1.93618i) q^{9} +O(q^{10})\)	\(q+(0.0863867 - 1.41157i) q^{2} +(-0.595168 + 1.62658i) q^{3} +(-1.98507 - 0.243882i) q^{4} +(-1.73413 - 1.00120i) q^{5} +(2.24463 + 0.980638i) q^{6} +(1.27710 + 2.31711i) q^{7} +(-0.515742 + 2.78101i) q^{8} +(-2.29155 - 1.93618i) q^{9} +(-1.56307 + 2.36135i) q^{10} +(-4.35761 + 2.51587i) q^{11} +(1.57815 - 3.08374i) q^{12} +(-3.29495 + 1.90234i) q^{13} +(3.38110 - 1.60256i) q^{14} +(2.66063 - 2.22482i) q^{15} +(3.88104 + 0.968249i) q^{16} +(1.61527 + 0.932579i) q^{17} +(-2.93102 + 3.06743i) q^{18} +(3.12744 + 5.41689i) q^{19} +(3.19819 + 2.41038i) q^{20} +(-4.52907 + 0.698243i) q^{21} +(3.17489 + 6.36842i) q^{22} +(-5.43501 - 3.13791i) q^{23} +(-4.21659 - 2.49407i) q^{24} +(-0.495206 - 0.857721i) q^{25} +(2.40065 + 4.81540i) q^{26} +(4.51322 - 2.57504i) q^{27} +(-1.97004 - 4.91110i) q^{28} +(-1.23970 + 2.14722i) q^{29} +(-2.91065 - 3.94787i) q^{30} +1.11523 q^{31} +(1.70202 - 5.39473i) q^{32} +(-1.49876 - 8.58538i) q^{33} +(1.45594 - 2.19952i) q^{34} +(0.105232 - 5.29680i) q^{35} +(4.07670 + 4.40233i) q^{36} +(0.559132 + 0.968445i) q^{37} +(7.91650 - 3.94667i) q^{38} +(-1.13327 - 6.49172i) q^{39} +(3.67870 - 4.30626i) q^{40} +(6.39139 - 3.69007i) q^{41} +(0.594369 + 6.45343i) q^{42} +(-6.79358 - 3.92228i) q^{43} +(9.26376 - 3.93144i) q^{44} +(2.03533 + 5.65188i) q^{45} +(-4.89889 + 7.40084i) q^{46} -3.90038 q^{47} +(-3.88481 + 5.73657i) q^{48} +(-3.73802 + 5.91838i) q^{49} +(-1.25351 + 0.624923i) q^{50} +(-2.47828 + 2.07234i) q^{51} +(7.00467 - 2.97271i) q^{52} +(2.80349 - 4.85579i) q^{53} +(-3.24498 - 6.59319i) q^{54} +10.0755 q^{55} +(-7.10256 + 2.35660i) q^{56} +(-10.6724 + 1.86309i) q^{57} +(2.92386 + 1.93541i) q^{58} +8.70605 q^{59} +(-5.82414 + 3.76755i) q^{60} +2.11799i q^{61} +(0.0963407 - 1.57422i) q^{62} +(1.55981 - 7.78248i) q^{63} +(-7.46802 - 2.86856i) q^{64} +7.61847 q^{65} +(-12.2484 + 1.37394i) q^{66} +12.0225i q^{67} +(-2.97900 - 2.24518i) q^{68} +(8.33881 - 6.97292i) q^{69} +(-7.46772 - 0.606115i) q^{70} +3.84867i q^{71} +(6.56639 - 5.37425i) q^{72} +(-0.499355 - 0.288303i) q^{73} +(1.41533 - 0.705595i) q^{74} +(1.68989 - 0.295005i) q^{75} +(-4.88713 - 11.5157i) q^{76} +(-11.3947 - 6.88405i) q^{77} +(-9.26144 + 1.03889i) q^{78} -3.95949i q^{79} +(-5.76081 - 5.56476i) q^{80} +(1.50240 + 8.87371i) q^{81} +(-4.65667 - 9.34068i) q^{82} +(-5.34720 + 9.26162i) q^{83} +(9.16083 - 0.281504i) q^{84} +(-1.86739 - 3.23442i) q^{85} +(-6.12345 + 9.25080i) q^{86} +(-2.75480 - 3.29442i) q^{87} +(-4.74925 - 13.4161i) q^{88} +(-5.13938 + 2.96722i) q^{89} +(8.15386 - 2.38477i) q^{90} +(-8.61592 - 5.20528i) q^{91} +(10.0236 + 7.55448i) q^{92} +(-0.663747 + 1.81401i) q^{93} +(-0.336941 + 5.50567i) q^{94} -12.5248i q^{95} +(7.76199 + 5.97926i) q^{96} +(14.0382 + 8.10496i) q^{97} +(8.03131 + 5.78775i) q^{98} +(14.8569 + 2.67189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more