LMFDB - Embedded newform 605.2.k.a.56.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(56,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.56");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.k (of order $11$, degree $10$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			56.18
Character	$\chi$	$=$	605.56
Dual form			605.2.k.a.551.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63524 + 0.480149i) q^{2} -0.780476 q^{3} +(0.760954 + 0.489036i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.27626 - 0.374745i) q^{6} +(-1.25961 + 2.75817i) q^{7} +(-1.22259 - 1.41095i) q^{8} -2.39086 q^{9} +O(q^{10})$	\(q+(1.63524 + 0.480149i) q^{2} -0.780476 q^{3} +(0.760954 + 0.489036i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.27626 - 0.374745i) q^{6} +(-1.25961 + 2.75817i) q^{7} +(-1.22259 - 1.41095i) q^{8} -2.39086 q^{9} +(-1.43373 + 0.921400i) q^{10} +(-3.28383 + 0.465272i) q^{11} +(-0.593906 - 0.381680i) q^{12} +(-1.33468 - 0.857746i) q^{13} +(-3.38410 + 3.90546i) q^{14} +(0.511103 - 0.589844i) q^{15} +(-2.07329 - 4.53987i) q^{16} +(0.538241 + 3.74355i) q^{17} +(-3.90962 - 1.14797i) q^{18} +(0.356483 - 2.47940i) q^{19} +(-0.867907 + 0.254841i) q^{20} +(0.983098 - 2.15268i) q^{21} +(-5.59324 - 0.815896i) q^{22} +(1.58339 + 3.46715i) q^{23} +(0.954203 + 1.10121i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(-1.77067 - 2.04346i) q^{26} +4.20743 q^{27} +(-2.30735 + 1.48284i) q^{28} +(-0.636484 + 4.42684i) q^{29} +(1.11899 - 0.719130i) q^{30} +(-0.0314286 + 0.0201979i) q^{31} +(-0.679118 - 4.72337i) q^{32} +(2.56295 - 0.363134i) q^{33} +(-0.917310 + 6.38003i) q^{34} +(-1.25961 - 2.75817i) q^{35} +(-1.81933 - 1.16921i) q^{36} +(-6.04414 + 3.88433i) q^{37} +(1.77342 - 3.88324i) q^{38} +(1.04168 + 0.669450i) q^{39} +1.86695 q^{40} +(3.16252 + 0.928600i) q^{41} +(2.64121 - 3.04812i) q^{42} +(-2.29903 - 2.65322i) q^{43} +(-2.72638 - 1.25186i) q^{44} +(1.56568 - 1.80689i) q^{45} +(0.924477 + 6.42988i) q^{46} +(0.995228 - 0.292225i) q^{47} +(1.61815 + 3.54326i) q^{48} +(-1.43685 - 1.65821i) q^{49} +(0.242543 - 1.68693i) q^{50} +(-0.420084 - 2.92175i) q^{51} +(-0.596161 - 1.30541i) q^{52} +(1.64401 - 3.59989i) q^{53} +(6.88016 + 2.02020i) q^{54} +(1.79882 - 2.78644i) q^{55} +(5.43162 - 1.59487i) q^{56} +(-0.278227 + 1.93511i) q^{57} +(-3.16635 + 6.93334i) q^{58} +(-13.2238 + 3.88286i) q^{59} +(0.677381 - 0.198897i) q^{60} +(-2.55140 + 0.749159i) q^{61} +(-0.0610912 + 0.0179380i) q^{62} +(3.01156 - 6.59439i) q^{63} +(-0.263153 + 1.83027i) q^{64} +(1.52227 - 0.446979i) q^{65} +(4.36539 + 0.636787i) q^{66} +(8.51594 + 2.50051i) q^{67} +(-1.42115 + 3.11189i) q^{68} +(-1.23580 - 2.70603i) q^{69} +(-0.735436 - 5.11507i) q^{70} +(0.954723 - 6.64025i) q^{71} +(2.92304 + 3.37337i) q^{72} +(5.10658 + 11.1819i) q^{73} +(-11.7487 + 3.44972i) q^{74} +(0.111073 + 0.772532i) q^{75} +(1.48378 - 1.71237i) q^{76} +(2.85305 - 9.64341i) q^{77} +(1.38197 + 1.59487i) q^{78} +(-3.80352 + 4.38950i) q^{79} +(4.78872 + 1.40610i) q^{80} +3.88877 q^{81} +(4.72561 + 3.03696i) q^{82} +(6.12416 - 13.4100i) q^{83} +(1.80083 - 1.15732i) q^{84} +(-3.18166 - 2.04473i) q^{85} +(-2.48552 - 5.44253i) q^{86} +(0.496760 - 3.45504i) q^{87} +(4.67126 + 4.06447i) q^{88} +(1.09105 + 7.58845i) q^{89} +(3.42783 - 2.20294i) q^{90} +(4.04699 - 2.60084i) q^{91} +(-0.490669 + 3.41268i) q^{92} +(0.0245292 - 0.0157640i) q^{93} +1.76775 q^{94} +(1.64036 + 1.89307i) q^{95} +(0.530035 + 3.68647i) q^{96} +(-7.13939 - 8.23930i) q^{97} +(-1.55340 - 3.40146i) q^{98} +(7.85116 - 1.11240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 4 q^{2} - 4 q^{3} - 24 q^{4} - 22 q^{5} - 12 q^{6} - 8 q^{7} - 12 q^{8} + 212 q^{9}+O(q^{10}) $ 220 * q - 4 * q^2 - 4 * q^3 - 24 * q^4 - 22 * q^5 - 12 * q^6 - 8 * q^7 - 12 * q^8 + 212 * q^9	\( 220 q - 4 q^{2} - 4 q^{3} - 24 q^{4} - 22 q^{5} - 12 q^{6} - 8 q^{7} - 12 q^{8} + 212 q^{9} - 4 q^{10} - 10 q^{11} + 5 q^{12} + 6 q^{13} + 68 q^{14} + 7 q^{15} - 44 q^{16} - 24 q^{17} - 36 q^{18} - 16 q^{19} - 24 q^{20} - 10 q^{21} + 45 q^{22} + 51 q^{23} + 72 q^{24} - 22 q^{25} - 30 q^{26} - 34 q^{27} - 56 q^{28} - 36 q^{29} - q^{30} + 4 q^{31} + 42 q^{32} - 44 q^{33} - 52 q^{34} - 8 q^{35} - 94 q^{36} + 69 q^{37} - 40 q^{38} - 56 q^{39} + 54 q^{40} - 44 q^{41} - 76 q^{42} + 7 q^{43} - 67 q^{44} - 30 q^{45} + 56 q^{46} + 14 q^{47} + 54 q^{48} + 10 q^{49} - 4 q^{50} + 27 q^{51} + 58 q^{52} + 86 q^{53} - 43 q^{54} - 10 q^{55} - 79 q^{56} + 129 q^{57} + 100 q^{58} - 54 q^{59} - 28 q^{60} - 52 q^{61} + 55 q^{62} - 104 q^{63} + 36 q^{64} - 16 q^{65} - 33 q^{66} + 13 q^{67} - 120 q^{68} - 22 q^{69} - 9 q^{70} - 70 q^{71} + 60 q^{72} - 66 q^{73} + 20 q^{74} - 4 q^{75} - 12 q^{76} + 44 q^{77} + 187 q^{78} - 22 q^{79} - 44 q^{80} + 108 q^{81} - 76 q^{82} + 96 q^{83} - 224 q^{84} + 9 q^{85} - 66 q^{86} - 76 q^{87} - 47 q^{88} + 52 q^{89} + 8 q^{90} + 88 q^{91} + 8 q^{92} + 38 q^{93} + 22 q^{94} + 28 q^{95} - 120 q^{96} + 37 q^{97} + 12 q^{98} + 118 q^{99}+O(q^{100}) \) 220 * q - 4 * q^2 - 4 * q^3 - 24 * q^4 - 22 * q^5 - 12 * q^6 - 8 * q^7 - 12 * q^8 + 212 * q^9 - 4 * q^10 - 10 * q^11 + 5 * q^12 + 6 * q^13 + 68 * q^14 + 7 * q^15 - 44 * q^16 - 24 * q^17 - 36 * q^18 - 16 * q^19 - 24 * q^20 - 10 * q^21 + 45 * q^22 + 51 * q^23 + 72 * q^24 - 22 * q^25 - 30 * q^26 - 34 * q^27 - 56 * q^28 - 36 * q^29 - q^30 + 4 * q^31 + 42 * q^32 - 44 * q^33 - 52 * q^34 - 8 * q^35 - 94 * q^36 + 69 * q^37 - 40 * q^38 - 56 * q^39 + 54 * q^40 - 44 * q^41 - 76 * q^42 + 7 * q^43 - 67 * q^44 - 30 * q^45 + 56 * q^46 + 14 * q^47 + 54 * q^48 + 10 * q^49 - 4 * q^50 + 27 * q^51 + 58 * q^52 + 86 * q^53 - 43 * q^54 - 10 * q^55 - 79 * q^56 + 129 * q^57 + 100 * q^58 - 54 * q^59 - 28 * q^60 - 52 * q^61 + 55 * q^62 - 104 * q^63 + 36 * q^64 - 16 * q^65 - 33 * q^66 + 13 * q^67 - 120 * q^68 - 22 * q^69 - 9 * q^70 - 70 * q^71 + 60 * q^72 - 66 * q^73 + 20 * q^74 - 4 * q^75 - 12 * q^76 + 44 * q^77 + 187 * q^78 - 22 * q^79 - 44 * q^80 + 108 * q^81 - 76 * q^82 + 96 * q^83 - 224 * q^84 + 9 * q^85 - 66 * q^86 - 76 * q^87 - 47 * q^88 + 52 * q^89 + 8 * q^90 + 88 * q^91 + 8 * q^92 + 38 * q^93 + 22 * q^94 + 28 * q^95 - 120 * q^96 + 37 * q^97 + 12 * q^98 + 118 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	1.63524	+	0.480149i	1.15629	+	0.339517i	0.802989	−	0.595994i	$-0.203242\pi$
$2$	1.63524	+	0.480149i	1.15629	+	0.339517i	0.353299	+	0.935510i	$0.385060\pi$
$3$	−0.780476			−0.450608			−0.225304	−	0.974289i	$-0.572338\pi$
$3$	−0.780476			−0.450608			−0.225304	+	0.974289i	$0.572338\pi$
$4$	0.760954	+	0.489036i	0.380477	+	0.244518i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−1.27626	−	0.374745i	−0.521033	−	0.152989i
$7$	−1.25961	+	2.75817i	−0.476089	+	1.04249i	0.507431	+	0.861692i	$0.330595\pi$
$7$	−1.25961	+	2.75817i	−0.476089	+	1.04249i	−0.983520	+	0.180798i	$0.942132\pi$
$8$	−1.22259	−	1.41095i	−0.432252	−	0.498845i
$9$	−2.39086			−0.796953
$10$	−1.43373	+	0.921400i	−0.453384	+	0.291372i
$11$	−3.28383	+	0.465272i	−0.990111	+	0.140285i
$11$	−3.28383	+	0.465272i	−0.990111	+	0.140285i
$12$	−0.593906	−	0.381680i	−0.171446	−	0.110182i
$13$	−1.33468	−	0.857746i	−0.370173	−	0.237896i	0.342307	−	0.939588i	$-0.388792\pi$
$13$	−1.33468	−	0.857746i	−0.370173	−	0.237896i	−0.712480	+	0.701692i	$0.752428\pi$
$14$	−3.38410	+	3.90546i	−0.904439	+	1.04378i
$15$	0.511103	−	0.589844i	0.131966	−	0.152297i
$16$	−2.07329	−	4.53987i	−0.518323	−	1.13497i
$17$	0.538241	+	3.74355i	0.130543	+	0.907944i	0.944848	+	0.327508i	$0.106209\pi$
$17$	0.538241	+	3.74355i	0.130543	+	0.907944i	−0.814306	+	0.580436i	$0.802882\pi$
$18$	−3.90962	−	1.14797i	−0.921507	−	0.270579i
$19$	0.356483	−	2.47940i	0.0817829	−	0.568813i	−0.907191	−	0.420720i	$-0.861777\pi$
$19$	0.356483	−	2.47940i	0.0817829	−	0.568813i	0.988973	−	0.148093i	$-0.0473134\pi$
$20$	−0.867907	+	0.254841i	−0.194070	+	0.0569841i
$21$	0.983098	−	2.15268i	0.214530	−	0.469754i
$22$	−5.59324	−	0.815896i	−1.19248	−	0.173950i
$23$	1.58339	+	3.46715i	0.330160	+	0.722951i	0.999805	−	0.0197309i	$-0.00628093\pi$
$23$	1.58339	+	3.46715i	0.330160	+	0.722951i	−0.669645	+	0.742681i	$0.733554\pi$
$24$	0.954203	+	1.10121i	0.194776	+	0.224783i
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−1.77067	−	2.04346i	−0.347257	−	0.400756i
$27$	4.20743			0.809721
$28$	−2.30735	+	1.48284i	−0.436048	+	0.280231i
$29$	−0.636484	+	4.42684i	−0.118192	+	0.822044i	0.841352	+	0.540487i	$0.181760\pi$
$29$	−0.636484	+	4.42684i	−0.118192	+	0.822044i	−0.959544	+	0.281557i	$0.909149\pi$
$30$	1.11899	−	0.719130i	0.204298	−	0.131295i
$31$	−0.0314286	+	0.0201979i	−0.00564474	+	0.00362765i	−0.543460	−	0.839435i	$-0.682886\pi$
$31$	−0.0314286	+	0.0201979i	−0.00564474	+	0.00362765i	0.537815	+	0.843063i	$0.319250\pi$
$32$	−0.679118	−	4.72337i	−0.120052	−	0.834981i
$33$	2.56295	−	0.363134i	0.446152	−	0.0632135i
$34$	−0.917310	+	6.38003i	−0.157317	+	1.09417i
$35$	−1.25961	−	2.75817i	−0.212914	−	0.466216i
$36$	−1.81933	−	1.16921i	−0.303222	−	0.194869i
$37$	−6.04414	+	3.88433i	−0.993651	+	0.638581i	−0.933112	−	0.359585i	$-0.882918\pi$
$37$	−6.04414	+	3.88433i	−0.993651	+	0.638581i	−0.0605386	+	0.998166i	$0.519282\pi$
$38$	1.77342	−	3.88324i	0.287686	−	0.629945i
$39$	1.04168	+	0.669450i	0.166803	+	0.107198i
$40$	1.86695			0.295191
$41$	3.16252	+	0.928600i	0.493903	+	0.145023i	0.519193	−	0.854657i	$-0.326233\pi$
$41$	3.16252	+	0.928600i	0.493903	+	0.145023i	−0.0252900	+	0.999680i	$0.508051\pi$
$42$	2.64121	−	3.04812i	0.407547	−	0.470335i
$43$	−2.29903	−	2.65322i	−0.350599	−	0.404612i	0.552869	−	0.833268i	$-0.313533\pi$
$43$	−2.29903	−	2.65322i	−0.350599	−	0.404612i	−0.903468	+	0.428655i	$0.858987\pi$
$44$	−2.72638	−	1.25186i	−0.411017	−	0.188725i
$45$	1.56568	−	1.80689i	0.233398	−	0.269355i
$46$	0.924477	+	6.42988i	0.136307	+	0.948034i
$47$	0.995228	−	0.292225i	0.145169	−	0.0426254i	−0.208341	−	0.978056i	$-0.566806\pi$
$47$	0.995228	−	0.292225i	0.145169	−	0.0426254i	0.353510	+	0.935431i	$0.384988\pi$
$48$	1.61815	+	3.54326i	0.233560	+	0.511426i
$49$	−1.43685	−	1.65821i	−0.205264	−	0.236887i
$50$	0.242543	−	1.68693i	0.0343008	−	0.238567i
$51$	−0.420084	−	2.92175i	−0.0588235	−	0.409127i
$52$	−0.596161	−	1.30541i	−0.0826727	−	0.181028i
$53$	1.64401	−	3.59989i	0.225823	−	0.494483i	−0.762475	−	0.647017i	$-0.776016\pi$
$53$	1.64401	−	3.59989i	0.225823	−	0.494483i	0.988298	+	0.152534i	$0.0487434\pi$
$54$	6.88016	+	2.02020i	0.936271	+	0.274914i
$55$	1.79882	−	2.78644i	0.242553	−	0.375723i
$56$	5.43162	−	1.59487i	0.725831	−	0.213123i
$57$	−0.278227	+	1.93511i	−0.0368520	+	0.256311i
$58$	−3.16635	+	6.93334i	−0.415762	+	0.910392i
$59$	−13.2238	+	3.88286i	−1.72159	+	0.505505i	−0.985252	−	0.171107i	$-0.945266\pi$
$59$	−13.2238	+	3.88286i	−1.72159	+	0.505505i	−0.736340	+	0.676612i	$0.763447\pi$
$60$	0.677381	−	0.198897i	0.0874495	−	0.0256775i
$61$	−2.55140	+	0.749159i	−0.326673	+	0.0959199i	−0.440957	−	0.897528i	$-0.645361\pi$
$61$	−2.55140	+	0.749159i	−0.326673	+	0.0959199i	0.114284	+	0.993448i	$0.463543\pi$
$62$	−0.0610912	+	0.0179380i	−0.00775859	+	0.00227813i
$63$	3.01156	−	6.59439i	0.379421	−	0.830815i
$64$	−0.263153	+	1.83027i	−0.0328941	+	0.228783i
$65$	1.52227	−	0.446979i	0.188814	−	0.0554409i
$66$	4.36539	+	0.636787i	0.537342	+	0.0783831i
$67$	8.51594	+	2.50051i	1.04039	+	0.305485i	0.756928	−	0.653499i	$-0.226700\pi$
$67$	8.51594	+	2.50051i	1.04039	+	0.305485i	0.283460	+	0.958984i	$0.408518\pi$
$68$	−1.42115	+	3.11189i	−0.172340	+	0.377372i
$69$	−1.23580	−	2.70603i	−0.148773	−	0.325767i
$70$	−0.735436	−	5.11507i	−0.0879014	−	0.611367i
$71$	0.954723	−	6.64025i	0.113305	−	0.788052i	−0.851362	−	0.524579i	$-0.824223\pi$
$71$	0.954723	−	6.64025i	0.113305	−	0.788052i	0.964667	−	0.263473i	$-0.0848681\pi$
$72$	2.92304	+	3.37337i	0.344484	+	0.397556i
$73$	5.10658	+	11.1819i	0.597680	+	1.30874i	0.930688	+	0.365813i	$0.119209\pi$
$73$	5.10658	+	11.1819i	0.597680	+	1.30874i	−0.333008	+	0.942924i	$0.608064\pi$
$74$	−11.7487	+	3.44972i	−1.36576	+	0.401022i
$75$	0.111073	+	0.772532i	0.0128256	+	0.0892043i
$76$	1.48378	−	1.71237i	0.170201	−	0.196423i
$77$	2.85305	−	9.64341i	0.325136	−	1.09897i
$78$	1.38197	+	1.59487i	0.156477	+	0.180584i
$79$	−3.80352	+	4.38950i	−0.427929	+	0.493857i	−0.928236	−	0.371991i	$-0.878675\pi$
$79$	−3.80352	+	4.38950i	−0.427929	+	0.493857i	0.500307	+	0.865848i	$0.333221\pi$
$80$	4.78872	+	1.40610i	0.535395	+	0.157206i
$81$	3.88877			0.432086
$82$	4.72561	+	3.03696i	0.521856	+	0.335376i
$83$	6.12416	−	13.4100i	0.672214	−	1.47194i	−0.198473	−	0.980106i	$-0.563598\pi$
$83$	6.12416	−	13.4100i	0.672214	−	1.47194i	0.870687	−	0.491838i	$-0.163675\pi$
$84$	1.80083	−	1.15732i	0.196487	−	0.126274i
$85$	−3.18166	−	2.04473i	−0.345099	−	0.221782i
$86$	−2.48552	−	5.44253i	−0.268020	−	0.586883i
$87$	0.496760	−	3.45504i	0.0532583	−	0.370420i
$88$	4.67126	+	4.06447i	0.497958	+	0.433274i
$89$	1.09105	+	7.58845i	0.115652	+	0.804374i	0.962255	+	0.272150i	$0.0877347\pi$
$89$	1.09105	+	7.58845i	0.115652	+	0.804374i	−0.846603	+	0.532224i	$0.821356\pi$
$90$	3.42783	−	2.20294i	0.361326	−	0.232210i
$91$	4.04699	−	2.60084i	0.424240	−	0.272642i
$92$	−0.490669	+	3.41268i	−0.0511558	+	0.355796i
$93$	0.0245292	−	0.0157640i	0.00254356	−	0.00163465i
$94$	1.76775			0.182329
$95$	1.64036	+	1.89307i	0.168297	+	0.194225i
$96$	0.530035	+	3.68647i	0.0540965	+	0.376249i
$97$	−7.13939	−	8.23930i	−0.724896	−	0.836574i	0.266991	−	0.963699i	$-0.413971\pi$
$97$	−7.13939	−	8.23930i	−0.724896	−	0.836574i	−0.991887	+	0.127125i	$0.959425\pi$
$98$	−1.55340	−	3.40146i	−0.156917	−	0.343600i
$99$	7.85116	−	1.11240i	0.789072	−	0.111800i
$100$	0.375763	−	0.822806i	0.0375763	−	0.0822806i
$101$	−6.57533	+	1.93069i	−0.654270	+	0.192111i	−0.591987	−	0.805948i	$-0.701656\pi$
$101$	−6.57533	+	1.93069i	−0.654270	+	0.192111i	−0.0622830	+	0.998059i	$0.519838\pi$
$102$	0.715938	−	4.97946i	0.0708884	−	0.493040i
$103$	−9.11004	−	2.67495i	−0.897639	−	0.263571i	−0.199810	−	0.979835i	$-0.564032\pi$
$103$	−9.11004	−	2.67495i	−0.897639	−	0.263571i	−0.697829	+	0.716264i	$0.745851\pi$
$104$	0.421534	+	2.93183i	0.0413348	+	0.287490i
$105$	0.983098	+	2.15268i	0.0959405	+	0.210080i
$106$	4.41684	−	5.09731i	0.429002	−	0.495094i
$107$	0.796173	−	0.918833i	0.0769689	−	0.0888269i	−0.715959	−	0.698142i	$-0.754010\pi$
$107$	0.796173	−	0.918833i	0.0769689	−	0.0888269i	0.792928	+	0.609315i	$0.208556\pi$
$108$	3.20166	+	2.05758i	0.308080	+	0.197991i
$109$	4.89614	+	3.14656i	0.468965	+	0.301386i	0.753698	−	0.657221i	$-0.228268\pi$
$109$	4.89614	+	3.14656i	0.468965	+	0.301386i	−0.284732	+	0.958607i	$0.591905\pi$
$110$	4.27941	−	3.69279i	0.408025	−	0.352094i
$111$	4.71731	−	3.03163i	0.447747	−	0.287749i
$112$	15.1333			1.42996
$113$	9.59101	+	11.0686i	0.902246	+	1.04125i	0.998944	+	0.0459338i	$0.0146263\pi$
$113$	9.59101	+	11.0686i	0.902246	+	1.04125i	−0.0966984	+	0.995314i	$0.530828\pi$
$114$	−1.38411	+	3.03077i	−0.129634	+	0.283858i
$115$	−3.65720	−	1.07385i	−0.341036	−	0.100137i
$116$	−2.64922	+	3.05736i	−0.245974	+	0.283869i
$117$	3.19103	+	2.05075i	0.295011	+	0.189592i
$118$	−23.4884			−2.16228
$119$	−11.0033	−	3.23086i	−1.00867	−	0.296173i
$120$	−1.45711			−0.133015
$121$	10.5670	−	3.05575i	0.960640	−	0.277795i
$122$	−4.53186			−0.410295
$123$	−2.46827	−	0.724749i	−0.222556	−	0.0653484i
$124$	−0.0337932			−0.00303472
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	8.09091	−	9.33740i	0.720795	−	0.831842i
$127$	−3.24798	−	0.953694i	−0.288212	−	0.0846267i	0.134431	−	0.990923i	$-0.457079\pi$
$127$	−3.24798	−	0.953694i	−0.288212	−	0.0846267i	−0.422643	+	0.906296i	$0.638898\pi$
$128$	−5.27379	+	11.5480i	−0.466142	+	1.02071i
$129$	1.79434	+	2.07077i	0.157983	+	0.182322i
$130$	2.70389			0.237147
$131$	6.13454	−	3.94243i	0.535977	−	0.344452i	−0.244487	−	0.969653i	$-0.578619\pi$
$131$	6.13454	−	3.94243i	0.535977	−	0.344452i	0.780464	+	0.625201i	$0.214983\pi$
$132$	2.12787	+	0.977044i	0.185207	+	0.0850408i
$133$	6.38957	+	4.10632i	0.554046	+	0.356063i
$134$	12.7250	+	8.17784i	1.09927	+	0.706458i
$135$	−2.75528	+	3.17977i	−0.237137	+	0.273671i
$136$	4.62390	−	5.33626i	0.396496	−	0.457581i
$137$	1.92658	+	4.21862i	0.164599	+	0.360421i	0.973902	−	0.226970i	$-0.0728821\pi$
$137$	1.92658	+	4.21862i	0.164599	+	0.360421i	−0.809303	+	0.587392i	$0.800155\pi$
$138$	−0.721532	−	5.01837i	−0.0614209	−	0.427192i
$139$	−10.2772	−	3.01765i	−0.871697	−	0.255953i	−0.184860	−	0.982765i	$-0.559183\pi$
$139$	−10.2772	−	3.01765i	−0.871697	−	0.255953i	−0.686837	+	0.726811i	$0.741001\pi$
$140$	0.390334	−	2.71484i	0.0329893	−	0.229446i
$141$	−0.776751	+	0.228075i	−0.0654143	+	0.0192074i
$142$	4.74951	−	10.4000i	0.398570	−	0.872747i
$143$	4.78194	+	2.19570i	0.399886	+	0.183614i
$144$	4.95694	+	10.8542i	0.413078	+	0.904516i
$145$	−2.92878	−	3.37999i	−0.243222	−	0.280693i
$146$	2.98152	+	20.7369i	0.246752	+	1.71620i
$147$	1.12142	+	1.29419i	0.0924934	+	0.106743i
$148$	−6.49889			−0.534206
$149$	−1.35406	+	0.870199i	−0.110929	+	0.0712894i	−0.594929	−	0.803778i	$-0.702820\pi$
$149$	−1.35406	+	0.870199i	−0.110929	+	0.0712894i	0.484000	+	0.875068i	$0.339183\pi$
$150$	−0.189299	+	1.31661i	−0.0154562	+	0.107500i
$151$	−8.58565	+	5.51766i	−0.698690	+	0.449021i	−0.841166	−	0.540777i	$-0.818130\pi$
$151$	−8.58565	+	5.51766i	−0.698690	+	0.449021i	0.142476	+	0.989798i	$0.454494\pi$
$152$	−3.93413	+	2.52831i	−0.319100	+	0.205073i
$153$	−1.28686	−	8.95029i	−0.104036	−	0.723588i
$154$	9.29570	−	14.3994i	0.749069	−	1.16034i
$155$	0.00531677	−	0.0369790i	0.000427053	−	0.00297022i
$156$	0.465289	+	1.01884i	0.0372530	+	0.0815726i
$157$	−16.4038	−	10.5421i	−1.30917	−	0.841351i	−0.314989	−	0.949095i	$-0.602001\pi$
$157$	−16.4038	−	10.5421i	−1.30917	−	0.841351i	−0.994179	+	0.107745i	$0.965637\pi$
$158$	−8.32728	+	5.35161i	−0.662482	+	0.425752i
$159$	−1.28311	+	2.80963i	−0.101758	+	0.222818i
$160$	4.01441	+	2.57991i	0.317367	+	0.203959i
$161$	−11.5574			−0.910855
$162$	6.35907	+	1.86719i	0.499616	+	0.146700i
$163$	2.45263	−	2.83048i	0.192105	−	0.221701i	−0.651523	−	0.758628i	$-0.725870\pi$
$163$	2.45263	−	2.83048i	0.192105	−	0.221701i	0.843628	+	0.536928i	$0.180415\pi$
$164$	1.95241	+	2.25321i	0.152458	+	0.175946i
$165$	−1.40394	+	2.17475i	−0.109296	+	0.169304i
$166$	16.4533	−	18.9881i	1.27702	−	1.47376i
$167$	−0.00118787	−	0.00826181i	−9.19201e−5	−	0.000639318i	0.989775	−	0.142634i	$-0.0455573\pi$
$167$	−0.00118787	−	0.00826181i	−9.19201e−5	−	0.000639318i	−0.989867	+	0.141995i	$0.954648\pi$
$168$	−4.23925	+	1.24476i	−0.327065	+	0.0960350i
$169$	−4.35476	−	9.53558i	−0.334981	−	0.733507i
$170$	−4.22100	−	4.87129i	−0.323736	−	0.373611i
$171$	−0.852301	+	5.92789i	−0.0651771	+	0.453317i
$172$	−0.451936	−	3.14329i	−0.0344598	−	0.239673i
$173$	4.79125	+	10.4914i	0.364272	+	0.797645i	0.999676	+	0.0254645i	$0.00810648\pi$
$173$	4.79125	+	10.4914i	0.364272	+	0.797645i	−0.635404	+	0.772180i	$0.719166\pi$
$174$	2.47126	−	5.41130i	0.187346	−	0.410230i
$175$	2.90936	+	0.854264i	0.219927	+	0.0645763i
$176$	8.92060	+	13.9435i	0.672416	+	1.05103i
$177$	10.3209	−	3.03048i	0.775763	−	0.227785i
$178$	−1.85946	+	12.9328i	−0.139372	+	0.969354i
$179$	−10.8572	+	23.7740i	−0.811508	+	1.77695i	−0.210718	+	0.977547i	$0.567580\pi$
$179$	−10.8572	+	23.7740i	−0.811508	+	1.77695i	−0.600789	+	0.799407i	$0.705147\pi$
$180$	2.07504	−	0.609288i	0.154665	−	0.0454136i
$181$	−22.6549	+	6.65209i	−1.68393	+	0.494446i	−0.977071	−	0.212912i	$-0.931705\pi$
$181$	−22.6549	+	6.65209i	−1.68393	+	0.494446i	−0.706856	+	0.707357i	$0.749887\pi$
$182$	7.86658	−	2.30984i	0.583110	−	0.171217i
$183$	1.99131	−	0.584700i	0.147202	−	0.0432223i
$184$	2.95612	−	6.47299i	0.217928	−	0.477195i
$185$	1.02249	−	7.11156i	0.0751748	−	0.522852i
$186$	0.0476802	−	0.0140002i	0.00349608	−	0.00102654i
$187$	−3.50926	−	12.0427i	−0.256623	−	0.880652i
$188$	0.900231	+	0.264332i	0.0656561	+	0.0192784i
$189$	−5.29974	+	11.6048i	−0.385499	+	0.844126i
$190$	1.77342	+	3.88324i	0.128657	+	0.281720i
$191$	−1.56407	−	10.8783i	−0.113172	−	0.787129i	−0.964800	−	0.262983i	$-0.915294\pi$
$191$	−1.56407	−	10.8783i	−0.113172	−	0.787129i	0.851628	−	0.524146i	$-0.175615\pi$
$192$	0.205384	−	1.42848i	0.0148223	−	0.103092i
$193$	7.15897	+	8.26190i	0.515314	+	0.594704i	0.952451	−	0.304690i	$-0.0985530\pi$
$193$	7.15897	+	8.26190i	0.515314	+	0.594704i	−0.437137	+	0.899395i	$0.644008\pi$
$194$	−7.71852	−	16.9012i	−0.554157	−	1.21344i
$195$	−1.18809	+	0.348856i	−0.0850812	+	0.0249821i
$196$	−0.282451	−	1.96449i	−0.0201751	−	0.140321i
$197$	0.0184429	−	0.0212842i	0.00131400	−	0.00151644i	−0.755092	−	0.655619i	$-0.772408\pi$
$197$	0.0184429	−	0.0212842i	0.00131400	−	0.00151644i	0.756406	+	0.654102i	$0.226953\pi$
$198$	13.3726	+	1.95069i	0.950352	+	0.138630i
$199$	0.0496586	+	0.0573091i	0.00352021	+	0.00406254i	0.757507	−	0.652827i	$-0.226417\pi$
$199$	0.0496586	+	0.0573091i	0.00352021	+	0.00406254i	−0.753987	+	0.656890i	$0.771872\pi$
$200$	−1.22259	+	1.41095i	−0.0864503	+	0.0997690i
$201$	−6.64648	−	1.95158i	−0.468807	−	0.137654i
$202$	−11.6793			−0.821750
$203$	−11.4083	−	7.33164i	−0.800703	−	0.514580i
$204$	1.10917	−	2.42875i	0.0776577	−	0.170047i
$205$	−2.77280	+	1.78197i	−0.193661	+	0.124458i
$206$	−13.6127	−	8.74836i	−0.948443	−	0.609527i
$207$	−3.78567	−	8.28946i	−0.263122	−	0.576157i
$208$	−1.12688	+	7.83763i	−0.0781351	+	0.543442i
$209$	−0.0170351	+	8.30777i	−0.00117834	+	0.574661i
$210$	0.573990	+	3.99219i	0.0396090	+	0.275487i
$211$	−20.5298	+	13.1937i	−1.41333	+	0.908292i	−0.999997	−	0.00228876i	$-0.999271\pi$
$211$	−20.5298	+	13.1937i	−1.41333	+	0.908292i	−0.413332	+	0.910580i	$0.635635\pi$
$212$	3.01149	−	1.93537i	0.206830	−	0.132922i
$213$	−0.745138	+	5.18255i	−0.0510560	+	0.355103i
$214$	1.74311	−	1.12023i	0.119157	−	0.0765772i
$215$	3.51072			0.239429
$216$	−5.14398	−	5.93646i	−0.350003	−	0.403925i
$217$	−0.0161214	−	0.112127i	−0.00109439	−	0.00761167i
$218$	6.49554	+	7.49626i	0.439934	+	0.507710i
$219$	−3.98556	−	8.72716i	−0.269319	−	0.589727i
$220$	2.73149	−	1.24067i	0.184157	−	0.0836457i
$221$	2.49264	−	5.45811i	0.167673	−	0.367152i
$222$	9.16955	−	2.69242i	0.615420	−	0.180704i
$223$	1.10191	−	7.66397i	0.0737895	−	0.513217i	−0.919086	−	0.394058i	$-0.871071\pi$
$223$	1.10191	−	7.66397i	0.0737895	−	0.513217i	0.992875	−	0.119159i	$-0.0380199\pi$
$224$	13.8833	+	4.07650i	0.927615	+	0.272372i
$225$	0.340255	+	2.36652i	0.0226836	+	0.157768i
$226$	10.3690	+	22.7049i	0.689735	+	1.51031i
$227$	3.69171	−	4.26047i	0.245028	−	0.282777i	−0.619892	−	0.784687i	$-0.712824\pi$
$227$	3.69171	−	4.26047i	0.245028	−	0.282777i	0.864920	+	0.501910i	$0.167369\pi$
$228$	−1.15805	+	1.33647i	−0.0766941	+	0.0885097i
$229$	7.00734	+	4.50334i	0.463058	+	0.297589i	0.751291	−	0.659971i	$-0.229431\pi$
$229$	7.00734	+	4.50334i	0.463058	+	0.297589i	−0.288233	+	0.957560i	$0.593068\pi$
$230$	−5.46478	−	3.51200i	−0.360337	−	0.231575i
$231$	−2.22674	+	7.52645i	−0.146509	+	0.495204i
$232$	7.02420	−	4.51418i	0.461161	−	0.296370i
$233$	19.8204			1.29848			0.649238	−	0.760585i	$-0.275088\pi$
$233$	19.8204			1.29848			0.649238	+	0.760585i	$0.275088\pi$
$234$	4.23342	+	4.88563i	0.276748	+	0.319384i
$235$	−0.430887	+	0.943510i	−0.0281079	+	0.0615478i
$236$	−11.9616	−	3.51223i	−0.778631	−	0.228627i
$237$	2.96855	−	3.42589i	0.192828	−	0.222536i
$238$	−16.4417	−	10.5665i	−1.06576	−	0.684922i
$239$	−6.53327			−0.422602			−0.211301	−	0.977421i	$-0.567770\pi$
$239$	−6.53327			−0.422602			−0.211301	+	0.977421i	$0.567770\pi$
$240$	−3.73748	−	1.09742i	−0.241253	−	0.0708384i
$241$	−19.0095			−1.22451			−0.612256	−	0.790660i	$-0.709738\pi$
$241$	−19.0095			−1.22451			−0.612256	+	0.790660i	$0.709738\pi$
$242$	18.7469	+	0.0768811i	1.20509	+	0.00494211i
$243$	−15.6574			−1.00442
$244$	−2.30786	−	0.677650i	−0.147746	−	0.0433821i
$245$	2.19412			0.140177
$246$	−3.68822	−	2.37028i	−0.235152	−	0.151123i
$247$	−2.60248	+	3.00343i	−0.165592	+	0.191103i
$248$	0.0669225	+	0.0196502i	0.00424958	+	0.00124779i
$249$	−4.77976	+	10.4662i	−0.302905	+	0.663270i
$250$	1.11606	+	1.28800i	0.0705859	+	0.0814605i
$251$	−12.4953			−0.788698			−0.394349	−	0.918961i	$-0.629030\pi$
$251$	−12.4953			−0.788698			−0.394349	+	0.918961i	$0.629030\pi$
$252$	5.51655	−	3.54527i	0.347510	−	0.223331i
$253$	−6.81276	−	10.6488i	−0.428315	−	0.669485i
$254$	−4.85331	−	3.11904i	−0.304524	−	0.195706i
$255$	2.48321	+	1.59586i	0.155504	+	0.0999366i
$256$	−11.7469	+	13.5566i	−0.734179	+	0.847288i
$257$	−2.65126	+	3.05972i	−0.165381	+	0.190860i	−0.832391	−	0.554189i	$-0.813028\pi$
$257$	−2.65126	+	3.05972i	−0.165381	+	0.190860i	0.667010	+	0.745049i	$0.267574\pi$
$258$	1.93989	+	4.24776i	0.120772	+	0.264454i
$259$	−3.10037	−	21.5635i	−0.192647	−	1.33989i
$260$	1.37697	+	0.404314i	0.0853958	+	0.0250745i
$261$	1.52174	−	10.5840i	0.0941935	−	0.655130i
$262$	11.9244	−	3.50132i	0.736691	−	0.216312i
$263$	5.27574	−	11.5523i	0.325316	−	0.712343i	−0.674344	−	0.738418i	$-0.735573\pi$
$263$	5.27574	−	11.5523i	0.325316	−	0.712343i	0.999660	+	0.0260744i	$0.00830068\pi$
$264$	−3.64580	−	3.17222i	−0.224384	−	0.195236i
$265$	1.64401	+	3.59989i	0.100991	+	0.221140i
$266$	8.47681	+	9.78276i	0.519747	+	0.599820i
$267$	−0.851542	−	5.92260i	−0.0521135	−	0.362457i
$268$	5.25740	+	6.06737i	0.321147	+	0.370623i
$269$	20.4470			1.24668			0.623338	−	0.781952i	$-0.285776\pi$
$269$	20.4470			1.24668			0.623338	+	0.781952i	$0.285776\pi$
$270$	−6.03231	+	3.87673i	−0.367114	+	0.235930i
$271$	−0.100807	+	0.701127i	−0.00612358	+	0.0425904i	−0.992654	−	0.120987i	$-0.961394\pi$
$271$	−0.100807	+	0.701127i	−0.00612358	+	0.0425904i	0.986531	+	0.163577i	$0.0523033\pi$
$272$	15.8793	−	10.2050i	0.962824	−	0.618769i
$273$	−3.15858	+	2.02989i	−0.191166	+	0.122855i
$274$	1.12485	+	7.82350i	0.0679547	+	0.472635i
$275$	0.927874	+	3.18419i	0.0559529	+	0.192014i
$276$	0.382955	−	2.66351i	0.0230512	−	0.160325i
$277$	7.41909	+	16.2455i	0.445770	+	0.976100i	0.990503	+	0.137491i	$0.0439037\pi$
$277$	7.41909	+	16.2455i	0.445770	+	0.976100i	−0.544733	+	0.838609i	$0.683369\pi$
$278$	−15.3567	−	9.86914i	−0.921033	−	0.591912i
$279$	0.0751412	−	0.0482903i	0.00449859	−	0.00289107i
$280$	−2.35164	+	5.14936i	−0.140537	+	0.307733i
$281$	4.99609	+	3.21079i	0.298042	+	0.191540i	0.681112	−	0.732180i	$-0.261497\pi$
$281$	4.99609	+	3.21079i	0.298042	+	0.191540i	−0.383070	+	0.923719i	$0.625133\pi$
$282$	−1.37968			−0.0821589
$283$	−1.31682	−	0.386653i	−0.0782767	−	0.0229841i	0.242360	−	0.970186i	$-0.422079\pi$
$283$	−1.31682	−	0.386653i	−0.0782767	−	0.0229841i	−0.320636	+	0.947202i	$0.603897\pi$
$284$	3.97382	−	4.58603i	0.235803	−	0.272131i
$285$	−1.28026	−	1.47750i	−0.0758360	−	0.0875194i
$286$	6.76535	+	5.88654i	0.400043	+	0.348078i
$287$	−6.54479	+	7.55309i	−0.386327	+	0.445845i
$288$	1.62367	+	11.2929i	0.0956759	+	0.665441i
$289$	2.58693	−	0.759591i	0.152172	−	0.0446818i
$290$	−3.16635	−	6.93334i	−0.185934	−	0.407140i
$291$	5.57212	+	6.43057i	0.326644	+	0.376967i
$292$	−1.58245	+	11.0062i	−0.0926058	+	0.644088i
$293$	−2.17890	−	15.1546i	−0.127293	−	0.885342i	−0.948965	−	0.315381i	$-0.897868\pi$
$293$	−2.17890	−	15.1546i	−0.127293	−	0.885342i	0.821672	−	0.569961i	$-0.193042\pi$
$294$	1.21239	+	2.65476i	0.0707079	+	0.154829i
$295$	5.72528	−	12.5366i	0.333339	−	0.729910i
$296$	12.8701	+	3.77901i	0.748060	+	0.219650i
$297$	−13.8165	+	1.95760i	−0.801714	+	0.113592i
$298$	−2.63203	+	0.772833i	−0.152469	+	0.0447690i
$299$	0.860611	−	5.98568i	0.0497704	−	0.346161i
$300$	−0.293274	+	0.642180i	−0.0169322	+	0.0370763i
$301$	10.2139	−	2.99908i	0.588721	−	0.172864i
$302$	−16.6889	+	4.90030i	−0.960337	+	0.281980i
$303$	5.13189	−	1.50686i	0.294819	−	0.0865667i
$304$	−11.9952	+	3.52212i	−0.687974	+	0.202007i
$305$	1.10464	−	2.41881i	0.0632512	−	0.138501i
$306$	2.19316	−	15.2537i	0.125374	−	0.871999i
$307$	24.6902	−	7.24971i	1.40915	−	0.413763i	0.513332	−	0.858190i	$-0.328411\pi$
$307$	24.6902	−	7.24971i	1.40915	−	0.413763i	0.895815	+	0.444428i	$0.146593\pi$
$308$	6.88702	−	5.94295i	0.392424	−	0.338631i
$309$	7.11017	+	2.08773i	0.404483	+	0.118767i
$310$	0.0264496	−	0.0579166i	0.00150224	−	0.00328944i
$311$	12.0095	+	26.2971i	0.680996	+	1.49117i	0.861584	+	0.507615i	$0.169473\pi$
$311$	12.0095	+	26.2971i	0.680996	+	1.49117i	−0.180588	+	0.983559i	$0.557800\pi$
$312$	−0.328997	−	2.28823i	−0.0186258	−	0.129545i
$313$	−0.655750	+	4.56084i	−0.0370652	+	0.257794i	−0.999926	−	0.0122060i	$-0.996115\pi$
$313$	−0.655750	+	4.56084i	−0.0370652	+	0.257794i	0.962860	+	0.270000i	$0.0870237\pi$
$314$	−21.7624	−	25.1151i	−1.22812	−	1.41733i
$315$	3.01156	+	6.59439i	0.169682	+	0.371552i
$316$	−5.04092	+	1.48015i	−0.283574	+	0.0832649i
$317$	−1.56448	−	10.8812i	−0.0878700	−	0.611149i	−0.985408	−	0.170211i	$-0.945555\pi$
$317$	−1.56448	−	10.8812i	−0.0878700	−	0.611149i	0.897538	−	0.440938i	$-0.145354\pi$
$318$	−3.44724	+	3.97832i	−0.193311	+	0.223093i
$319$	0.0304153	−	14.8331i	0.00170293	−	0.830496i
$320$	−1.21090	−	1.39745i	−0.0676911	−	0.0781197i
$321$	−0.621394	+	0.717126i	−0.0346828	+	0.0400261i
$322$	−18.8992	−	5.54930i	−1.05321	−	0.309250i
$323$	9.47362			0.527126
$324$	2.95918	+	1.90175i	0.164399	+	0.105653i
$325$	−0.659071	+	1.44316i	−0.0365587	+	0.0800523i
$326$	5.36969	−	3.45089i	0.297399	−	0.191127i
$327$	−3.82132	−	2.45581i	−0.211320	−	0.135807i
$328$	−2.55627	−	5.59744i	−0.141146	−	0.309067i
$329$	−0.447596	+	3.11310i	−0.0246768	+	0.171631i
$330$	−3.33997	+	2.88213i	−0.183859	+	0.158656i
$331$	−1.23994	−	8.62398i	−0.0681533	−	0.474017i	−0.995104	−	0.0988335i	$-0.968489\pi$
$331$	−1.23994	−	8.62398i	−0.0681533	−	0.474017i	0.926951	−	0.375183i	$-0.122420\pi$
$332$	11.2182	−	7.20950i	0.615679	−	0.395673i
$333$	14.4507	−	9.28689i	0.791893	−	0.508918i
$334$	0.00202445	−	0.0140804i	0.000110773	−	0.000770445i
$335$	−7.46651	+	4.79843i	−0.407939	+	0.262167i
$336$	−11.8112			−0.644351
$337$	11.8813	+	13.7117i	0.647214	+	0.746925i	0.980633	−	0.195854i	$-0.0627478\pi$
$337$	11.8813	+	13.7117i	0.647214	+	0.746925i	−0.333419	+	0.942779i	$0.608202\pi$
$338$	−2.54256	−	17.6839i	−0.138297	−	0.961877i
$339$	−7.48555	−	8.63878i	−0.406559	−	0.469194i
$340$	−1.42115	−	3.11189i	−0.0770728	−	0.168766i
$341$	0.0938085	−	0.0809493i	0.00508001	−	0.00438365i
$342$	−4.23999	+	9.28427i	−0.229272	+	0.502036i
$343$	−13.9820	+	4.10549i	−0.754958	+	0.221676i
$344$	−0.932778	+	6.48762i	−0.0502920	+	0.349789i
$345$	2.85436	+	0.838114i	0.153673	+	0.0451226i
$346$	2.79741	+	19.4564i	0.150390	+	1.04598i
$347$	−9.85461	−	21.5786i	−0.529023	−	1.15840i	−0.965909	−	0.258882i	$-0.916646\pi$
$347$	−9.85461	−	21.5786i	−0.529023	−	1.15840i	0.436885	−	0.899517i	$-0.356082\pi$
$348$	2.06765	−	2.38620i	0.110838	−	0.127914i
$349$	−7.36039	+	8.49435i	−0.393993	+	0.454692i	−0.917740	−	0.397182i	$-0.869988\pi$
$349$	−7.36039	+	8.49435i	−0.393993	+	0.454692i	0.523747	+	0.851874i	$0.324534\pi$
$350$	4.34732	+	2.79385i	0.232374	+	0.149338i
$351$	−5.61557	−	3.60891i	−0.299737	−	0.192629i
$352$	4.42776	+	15.1948i	0.236000	+	0.809883i
$353$	14.2850	−	9.18039i	0.760312	−	0.488623i	−0.102135	−	0.994771i	$-0.532567\pi$
$353$	14.2850	−	9.18039i	0.760312	−	0.488623i	0.862447	+	0.506148i	$0.168931\pi$
$354$	18.3321			0.974342
$355$	4.39315	+	5.06997i	0.233164	+	0.269086i
$356$	−2.88078	+	6.30803i	−0.152681	+	0.334325i
$357$	8.58782	+	2.52161i	0.454516	+	0.133458i
$358$	−29.1692	+	33.6631i	−1.54164	+	1.77915i
$359$	11.4452	+	7.35537i	0.604054	+	0.388202i	0.806623	−	0.591066i	$-0.201293\pi$
$359$	11.4452	+	7.35537i	0.604054	+	0.388202i	−0.202569	+	0.979268i	$0.564929\pi$
$360$	−4.46361			−0.235253
$361$	12.2100	+	3.58519i	0.642634	+	0.188694i
$362$	−40.2402			−2.11498
$363$	−8.24732	+	2.38494i	−0.432872	+	0.125177i
$364$	4.35148			0.228079
$365$	−11.7948	−	3.46326i	−0.617367	−	0.181275i
$366$	3.53700			0.184882
$367$	−27.3058	−	17.5484i	−1.42535	−	0.916017i	−0.999939	−	0.0110170i	$-0.996493\pi$
$367$	−27.3058	−	17.5484i	−1.42535	−	0.916017i	−0.425411	−	0.905000i	$-0.639871\pi$
$368$	12.4576	−	14.3768i	0.649396	−	0.749443i
$369$	−7.56113	−	2.22015i	−0.393617	−	0.115576i
$370$	5.08662	−	11.1381i	0.264441	−	0.579044i
$371$	7.85828	+	9.06894i	0.407982	+	0.470836i
$372$	0.0263748			0.00136747
$373$	23.3651	−	15.0159i	1.20980	−	0.777491i	0.229175	−	0.973385i	$-0.426397\pi$
$373$	23.3651	−	15.0159i	1.20980	−	0.777491i	0.980625	+	0.195894i	$0.0627609\pi$
$374$	0.0438350	−	21.3777i	0.00226665	−	1.10542i
$375$	−0.656578	−	0.421957i	−0.0339055	−	0.0217898i
$376$	−1.62907	−	1.04694i	−0.0840130	−	0.0539919i
$377$	4.64661	−	5.36247i	0.239313	−	0.276181i
$378$	−14.2384	+	16.4320i	−0.732343	+	0.845169i
$379$	−4.95782	−	10.8561i	−0.254666	−	0.557641i	0.738513	−	0.674239i	$-0.235528\pi$
$379$	−4.95782	−	10.8561i	−0.254666	−	0.557641i	−0.993179	+	0.116598i	$0.962801\pi$
$380$	0.322456	+	2.24273i	0.0165417	+	0.115050i
$381$	2.53497	+	0.744335i	0.129871	+	0.0381335i
$382$	2.66560	−	18.5397i	0.136384	−	0.948572i
$383$	−18.7718	+	5.51191i	−0.959196	+	0.281645i	−0.723611	−	0.690208i	$-0.757519\pi$
$383$	−18.7718	+	5.51191i	−0.959196	+	0.281645i	−0.235585	+	0.971854i	$0.575701\pi$
$384$	4.11606	−	9.01292i	0.210047	−	0.459939i
$385$	5.41965	+	8.47129i	0.276211	+	0.431737i
$386$	7.73969	+	16.9475i	0.393940	+	0.862608i
$387$	5.49665	+	6.34348i	0.279411	+	0.322457i
$388$	−1.40344	−	9.76115i	−0.0712489	−	0.495547i
$389$	13.9262	+	16.0717i	0.706089	+	0.814870i	0.989562	−	0.144110i	$-0.0460320\pi$
$389$	13.9262	+	16.0717i	0.706089	+	0.814870i	−0.283473	+	0.958980i	$0.591487\pi$
$390$	−2.11032			−0.106860
$391$	−12.1272	+	7.79367i	−0.613299	+	0.394143i
$392$	−0.582967	+	4.05462i	−0.0294443	+	0.204789i
$393$	−4.78786	+	3.07697i	−0.241515	+	0.155213i
$394$	0.0403782	−	0.0259495i	0.00203422	−	0.00130732i
$395$	−0.826584	−	5.74902i	−0.0415899	−	0.289264i
$396$	6.51838	+	2.99301i	0.327561	+	0.150405i
$397$	−4.40660	+	30.6486i	−0.221161	+	1.53821i	0.512497	+	0.858689i	$0.328721\pi$
$397$	−4.40660	+	30.6486i	−0.221161	+	1.53821i	−0.733658	+	0.679519i	$0.762189\pi$
$398$	0.0536868	+	0.117558i	0.00269107	+	0.00589263i
$399$	−4.98690	−	3.20489i	−0.249657	−	0.160445i
$400$	−4.19860	+	2.69828i	−0.209930	+	0.134914i
$401$	−14.2524	+	31.2084i	−0.711731	+	1.55847i	0.113410	+	0.993548i	$0.463823\pi$
$401$	−14.2524	+	31.2084i	−0.711731	+	1.55847i	−0.825141	+	0.564926i	$0.808905\pi$
$402$	−9.93153	−	6.38261i	−0.495340	−	0.318336i
$403$	0.0592717			0.00295254
$404$	−5.94770	−	1.74640i	−0.295909	−	0.0868868i
$405$	−2.54661	+	2.93894i	−0.126542	+	0.146037i
$406$	−15.1349	−	17.4667i	−0.751134	−	0.866855i
$407$	18.0406	−	15.5677i	0.894242	−	0.771660i
$408$	−3.60884	+	4.16482i	−0.178664	+	0.206189i
$409$	−2.99147	−	20.8061i	−0.147919	−	1.02880i	−0.919619	−	0.392811i	$-0.871503\pi$
$409$	−2.99147	−	20.8061i	−0.147919	−	1.02880i	0.771701	−	0.635986i	$-0.219406\pi$
$410$	−5.38980	+	1.58259i	−0.266183	+	0.0781584i
$411$	−1.50365	−	3.29253i	−0.0741696	−	0.162409i
$412$	−5.62418	−	6.49065i	−0.277083	−	0.319771i
$413$	5.94730	−	41.3644i	0.292647	−	2.03541i
$414$	−2.21029	−	15.3729i	−0.108630	−	0.755538i
$415$	6.12416	+	13.4100i	0.300623	+	0.658273i
$416$	−3.14505	+	6.88669i	−0.154199	+	0.337648i
$417$	8.02107	+	2.35520i	0.392794	+	0.115335i
$418$	−4.01683	+	13.5770i	−0.196469	+	0.664073i
$419$	−29.9012	+	8.77979i	−1.46077	+	0.428921i	−0.913087	−	0.407765i	$-0.866308\pi$
$419$	−29.9012	+	8.77979i	−1.46077	+	0.428921i	−0.547683	+	0.836686i	$0.684490\pi$
$420$	−0.304647	+	2.11886i	−0.0148652	+	0.103390i
$421$	−15.9730	+	34.9760i	−0.778476	+	1.70462i	−0.0714422	+	0.997445i	$0.522760\pi$
$421$	−15.9730	+	34.9760i	−0.778476	+	1.70462i	−0.707034	+	0.707180i	$0.749967\pi$
$422$	−39.9061	+	11.7175i	−1.94260	+	0.570398i
$423$	−2.37945	+	0.698669i	−0.115693	+	0.0339705i
$424$	−7.08921	+	2.08158i	−0.344283	+	0.101090i
$425$	3.62884	−	1.06553i	0.176025	−	0.0516856i
$426$	−3.70688	+	8.11693i	−0.179599	+	0.393266i
$427$	1.14747	−	7.98084i	0.0555301	−	0.386220i
$428$	1.05519	−	0.309833i	0.0510047	−	0.0149763i
$429$	−3.73219	−	1.71369i	−0.180192	−	0.0827378i
$430$	5.74086	+	1.68567i	0.276849	+	0.0812901i
$431$	−9.96446	+	21.8191i	−0.479971	+	1.05099i	0.502500	+	0.864577i	$0.332414\pi$
$431$	−9.96446	+	21.8191i	−0.479971	+	1.05099i	−0.982471	+	0.186413i	$0.940314\pi$
$432$	−8.72323	−	19.1012i	−0.419697	−	0.919007i
$433$	4.62977	+	32.2007i	0.222492	+	1.54747i	0.728564	+	0.684977i	$0.240188\pi$
$433$	4.62977	+	32.2007i	0.222492	+	1.54747i	−0.506072	+	0.862491i	$0.668903\pi$
$434$	0.0274753	−	0.191095i	0.00131886	−	0.00917285i
$435$	2.28584	+	2.63800i	0.109598	+	0.126482i
$436$	2.18696	+	4.78878i	0.104736	+	0.229341i
$437$	9.16089	−	2.68988i	0.438225	−	0.128674i
$438$	−2.32700	−	16.1847i	−0.111188	−	0.773333i
$439$	3.20935	−	3.70378i	0.153174	−	0.176772i	−0.673976	−	0.738753i	$-0.735415\pi$
$439$	3.20935	−	3.70378i	0.153174	−	0.176772i	0.827150	+	0.561981i	$0.189961\pi$
$440$	−6.13074	+	0.868640i	−0.292272	+	0.0414108i
$441$	3.43529	+	3.96454i	0.163585	+	0.188788i
$442$	6.69676	−	7.72847i	0.318532	−	0.367606i
$443$	33.5645	+	9.85544i	1.59470	+	0.468246i	0.954065	−	0.299600i	$-0.0968534\pi$
$443$	33.5645	+	9.85544i	1.59470	+	0.468246i	0.640634	+	0.767846i	$0.278672\pi$
$444$	5.07223			0.240717
$445$	−6.44946	−	4.14482i	−0.305734	−	0.196483i
$446$	5.48174	−	12.0033i	0.259568	−	0.568374i
$447$	1.05681	−	0.679169i	0.0499853	−	0.0321236i
$448$	−4.71672	−	3.03125i	−0.222844	−	0.143213i
$449$	6.92038	+	15.1535i	0.326593	+	0.715139i	0.999702	−	0.0244042i	$-0.00776887\pi$
$449$	6.92038	+	15.1535i	0.326593	+	0.715139i	−0.673109	+	0.739543i	$0.735042\pi$
$450$	−0.579887	+	4.03320i	−0.0273361	+	0.190127i
$451$	−10.8172	−	1.57793i	−0.509363	−	0.0743017i
$452$	1.88537	+	13.1130i	0.0886804	+	0.616786i
$453$	6.70089	−	4.30640i	0.314835	−	0.202332i
$454$	8.08249	−	5.19430i	0.379330	−	0.243781i
$455$	−0.684629	+	4.76170i	−0.0320959	+	0.223232i
$456$	3.07049	−	1.97329i	0.143789	−	0.0924076i
$457$	−42.3668			−1.98184			−0.990918	−	0.134466i	$-0.957068\pi$
$457$	−42.3668			−1.98184			−0.990918	+	0.134466i	$0.957068\pi$
$458$	9.29639	+	10.7286i	0.434392	+	0.501315i
$459$	2.26461	+	15.7507i	0.105703	+	0.735181i
$460$	−2.25781	−	2.60565i	−0.105271	−	0.121489i
$461$	−8.29186	−	18.1566i	−0.386190	−	0.845639i	−0.998486	−	0.0550100i	$-0.982481\pi$
$461$	−8.29186	−	18.1566i	−0.386190	−	0.845639i	0.612295	−	0.790629i	$-0.290246\pi$
$462$	−7.25507	+	11.2384i	−0.337536	+	0.522856i
$463$	0.472759	−	1.03520i	0.0219710	−	0.0481097i	−0.898328	−	0.439325i	$-0.855218\pi$
$463$	0.472759	−	1.03520i	0.0219710	−	0.0481097i	0.920299	+	0.391215i	$0.127945\pi$
$464$	21.4169	−	6.28857i	0.994255	−	0.291940i
$465$	−0.00414961	+	0.0288612i	−0.000192434	+	0.00133840i
$466$	32.4110	+	9.51674i	1.50141	+	0.440854i
$467$	3.07099	+	21.3592i	0.142109	+	0.988387i	0.928678	+	0.370886i	$0.120946\pi$
$467$	3.07099	+	21.3592i	0.142109	+	0.988387i	−0.786570	+	0.617501i	$0.788145\pi$
$468$	1.42534	+	3.12105i	0.0658862	+	0.144271i
$469$	−17.6236	+	20.3387i	−0.813783	+	0.939155i
$470$	−1.15763	+	1.33597i	−0.0533974	+	0.0616239i
$471$	12.8028	+	8.22785i	0.589921	+	0.379119i
$472$	21.6458	+	13.9109i	0.996330	+	0.640302i
$473$	8.78409	+	7.64305i	0.403893	+	0.351428i
$474$	6.49924	−	4.17681i	0.298520	−	0.191847i
$475$	−2.50489			−0.114932
$476$	−6.79301	−	7.83955i	−0.311357	−	0.359325i
$477$	−3.93061	+	8.60683i	−0.179970	+	0.394079i
$478$	−10.6835	−	3.13694i	−0.488650	−	0.143481i
$479$	−9.51715	+	10.9834i	−0.434850	+	0.501843i	−0.930303	−	0.366791i	$-0.880456\pi$
$479$	−9.51715	+	10.9834i	−0.434850	+	0.501843i	0.495454	+	0.868634i	$0.335002\pi$
$480$	−3.13315	−	2.01355i	−0.143008	−	0.0919057i
$481$	11.3988			0.519739
$482$	−31.0851	−	9.12741i	−1.41589	−	0.415742i
$483$	9.02031			0.410438
$484$	9.53540	+	2.84237i	0.433427	+	0.129199i
$485$	10.9022			0.495041
$486$	−25.6036	−	7.51789i	−1.16140	−	0.341018i
$487$	7.55291			0.342255			0.171127	−	0.985249i	$-0.445259\pi$
$487$	7.55291			0.342255			0.171127	+	0.985249i	$0.445259\pi$
$488$	4.17634	+	2.68397i	0.189054	+	0.121498i
$489$	−1.91422	+	2.20912i	−0.0865639	+	0.0999000i
$490$	3.58791	+	1.05351i	0.162085	+	0.0475926i
$491$	17.7650	−	38.9000i	0.801725	−	1.75553i	0.162205	−	0.986757i	$-0.448139\pi$
$491$	17.7650	−	38.9000i	0.801725	−	1.75553i	0.639520	−	0.768775i	$-0.279133\pi$
$492$	−1.52381	−	1.75857i	−0.0686987	−	0.0792826i
$493$	−16.9147			−0.761799
$494$	−5.69778	+	3.66174i	−0.256355	+	0.164749i
$495$	−4.30072	+	6.66198i	−0.193303	+	0.299434i
$496$	0.156857	+	0.100806i	0.00704307	+	0.00452630i
$497$	17.1123	+	10.9974i	0.767593	+	0.493302i
$498$	−12.8414	+	14.8198i	−0.575437	+	0.664089i
$499$	10.6686	−	12.3122i	0.477593	−	0.551171i	−0.464915	−	0.885355i	$-0.653915\pi$
$499$	10.6686	−	12.3122i	0.477593	−	0.551171i	0.942508	+	0.334184i	$0.108461\pi$
$500$	0.375763	+	0.822806i	0.0168046	+	0.0367970i
$501$	0.000927103		0.00644815i	4.14199e−5		0.000288082i
$502$	−20.4328	−	5.99962i	−0.911962	−	0.267776i
$503$	2.77377	−	19.2920i	0.123676	−	0.860189i	−0.829658	−	0.558272i	$-0.811465\pi$
$503$	2.77377	−	19.2920i	0.123676	−	0.860189i	0.953334	−	0.301917i	$-0.0976264\pi$
$504$	−12.9862	+	3.81310i	−0.578453	+	0.169849i
$505$	2.84681	−	6.23364i	0.126681	−	0.277393i
$506$	−6.02747	−	20.6845i	−0.267954	−	0.919538i
$507$	3.39878	+	7.44229i	0.150945	+	0.330524i
$508$	−2.00518	−	2.31410i	−0.0889653	−	0.102671i
$509$	1.27314	+	8.85485i	0.0564307	+	0.392484i	0.998388	+	0.0567524i	$0.0180746\pi$
$509$	1.27314	+	8.85485i	0.0564307	+	0.392484i	−0.941958	+	0.335732i	$0.891016\pi$
$510$	3.29438	+	3.80192i	0.145878	+	0.168352i
$511$	−37.2738			−1.64889
$512$	−4.35832	+	2.80092i	−0.192612	+	0.123784i
$513$	1.49988	−	10.4319i	0.0662213	−	0.460580i
$514$	−5.80456	+	3.73037i	−0.256028	+	0.164539i
$515$	7.98740	−	5.13319i	0.351967	−	0.226195i
$516$	0.352725	+	2.45326i	0.0155279	+	0.107999i
$517$	−3.13219	+	1.42267i	−0.137754	+	0.0625689i
$518$	5.28387	−	36.7501i	0.232160	−	1.61471i
$519$	−3.73946	−	8.18827i	−0.164144	−	0.359425i
$520$	−2.49178	−	1.60137i	−0.109272	−	0.0702247i
$521$	25.6617	−	16.4918i	1.12426	−	0.722518i	0.159905	−	0.987132i	$-0.448881\pi$
$521$	25.6617	−	16.4918i	1.12426	−	0.722518i	0.964354	+	0.264615i	$0.0852448\pi$
$522$	7.57029	−	16.5766i	0.331343	−	0.725539i
$523$	−3.08449	−	1.98228i	−0.134875	−	0.0866791i	0.471463	−	0.881886i	$-0.343726\pi$
$523$	−3.08449	−	1.98228i	−0.134875	−	0.0866791i	−0.606339	+	0.795207i	$0.707362\pi$
$524$	6.59609			0.288152
$525$	−2.27068	−	0.666732i	−0.0991007	−	0.0290986i
$526$	14.1739	−	16.3576i	0.618012	−	0.713224i
$527$	−0.0925280	−	0.106783i	−0.00403058	−	0.00465154i
$528$	−6.96231	−	10.8826i	−0.302996	−	0.473603i
$529$	5.54781	−	6.40251i	0.241209	−	0.278370i
$530$	0.959871	+	6.67605i	0.0416941	+	0.289989i
$531$	31.6162	−	9.28336i	1.37203	−	0.402864i
$532$	2.85403	+	6.24945i	0.123738	+	0.270948i
$533$	−3.42445	−	3.95202i	−0.148329	−	0.171181i
$534$	1.45126	−	10.0937i	0.0628022	−	0.436799i
$535$	0.173025	+	1.20341i	0.00748052	+	0.0520282i
$536$	−6.88344	−	15.0726i	−0.297319	−	0.651039i
$537$	8.47381	−	18.5550i	0.365672	−	0.800709i
$538$	33.4357	+	9.81762i	1.44152	+	0.423268i
$539$	5.48987	+	4.77674i	0.236465	+	0.205749i
$540$	−3.65166	+	1.07222i	−0.157143	+	0.0461412i
$541$	5.75206	−	40.0065i	0.247300	−	1.72001i	−0.366386	−	0.930463i	$-0.619405\pi$
$541$	5.75206	−	40.0065i	0.247300	−	1.72001i	0.613687	−	0.789550i	$-0.289686\pi$
$542$	−0.501489	+	1.09811i	−0.0215408	+	0.0471678i
$543$	17.6816	−	5.19179i	0.758791	−	0.222801i
$544$	17.3166	−	5.08462i	0.742444	−	0.218001i
$545$	−5.58430	+	1.63970i	−0.239205	+	0.0702370i
$546$	−6.13968	+	1.80277i	−0.262754	+	0.0771515i
$547$	14.2461	−	31.1946i	0.609118	−	1.33378i	−0.314057	−	0.949404i	$-0.601688\pi$
$547$	14.2461	−	31.1946i	0.609118	−	1.33378i	0.923175	−	0.384379i	$-0.125584\pi$
$548$	−0.597017	+	4.15235i	−0.0255033	+	0.177379i
$549$	6.10003	−	1.79113i	0.260343	−	0.0764436i
$550$	−0.0115903	+	5.65242i	−0.000494212	+	0.241020i
$551$	10.7490	+	3.15619i	0.457923	+	0.134458i
$552$	−2.30718	+	5.05201i	−0.0982000	+	0.215028i
$553$	−7.31601	−	16.0198i	−0.311108	−	0.681232i
$554$	4.33170	+	30.1276i	0.184036	+	1.28000i
$555$	−0.798027	+	5.55040i	−0.0338743	+	0.235601i
$556$	−6.34471	−	7.32219i	−0.269076	−	0.310530i
$557$	16.4720	+	36.0686i	0.697941	+	1.52828i	0.842451	+	0.538774i	$0.181112\pi$
$557$	16.4720	+	36.0686i	0.697941	+	1.52828i	−0.144510	+	0.989503i	$0.546161\pi$
$558$	0.146060	−	0.0428872i	0.00618323	−	0.00181556i
$559$	0.792676	+	5.51318i	0.0335266	+	0.233183i
$560$	−9.91019	+	11.4370i	−0.418782	+	0.483300i
$561$	2.73889	+	9.39906i	0.115636	+	0.396829i
$562$	6.62813	+	7.64927i	0.279591	+	0.322665i
$563$	16.2090	−	18.7061i	0.683126	−	0.788370i	−0.303244	−	0.952913i	$-0.598070\pi$
$563$	16.2090	−	18.7061i	0.683126	−	0.788370i	0.986370	+	0.164543i	$0.0526150\pi$
$564$	−0.702609	−	0.206305i	−0.0295852	−	0.00868699i
$565$	−14.6459			−0.616157
$566$	−1.96766	−	1.26454i	−0.0827069	−	0.0531525i
$567$	−4.89835	+	10.7259i	−0.205711	+	0.450445i
$568$	−10.5363	+	6.77125i	−0.442092	+	0.284115i
$569$	−1.75141	−	1.12556i	−0.0734230	−	0.0471861i	0.503414	−	0.864045i	$-0.332077\pi$
$569$	−1.75141	−	1.12556i	−0.0734230	−	0.0471861i	−0.576837	+	0.816859i	$0.695713\pi$
$570$	−1.38411	−	3.03077i	−0.0579739	−	0.126945i
$571$	3.09673	−	21.5383i	0.129594	−	0.901348i	−0.816474	−	0.577382i	$-0.804074\pi$
$571$	3.09673	−	21.5383i	0.129594	−	0.901348i	0.946069	−	0.323966i	$-0.105016\pi$
$572$	2.56506	+	4.00937i	0.107251	+	0.167640i
$573$	1.22072	+	8.49028i	0.0509962	+	0.354687i
$574$	−14.3289	+	9.20862i	−0.598077	+	0.384360i
$575$	3.20652	−	2.06070i	0.133721	−	0.0859373i
$576$	0.629161	−	4.37591i	0.0262150	−	0.182329i
$577$	−31.2158	+	20.0612i	−1.29953	+	0.835159i	−0.993161	−	0.116753i	$-0.962751\pi$
$577$	−31.2158	+	20.0612i	−1.29953	+	0.835159i	−0.306372	+	0.951912i	$0.599115\pi$
$578$	4.59496			0.191125
$579$	−5.58741	−	6.44821i	−0.232205	−	0.267978i
$580$	−0.575730	−	4.00429i	−0.0239059	−	0.166269i
$581$	29.2731	+	33.7830i	1.21445	+	1.40155i
$582$	6.02411	+	13.1910i	0.249708	+	0.546783i
$583$	−3.72373	+	12.5863i	−0.154221	+	0.521273i
$584$	9.53373	−	20.8760i	0.394509	−	0.863853i
$585$	−3.63953	+	1.06866i	−0.150476	+	0.0441838i
$586$	3.71345	−	25.8276i	0.153401	−	1.06693i
$587$	43.8404	+	12.8727i	1.80949	+	0.531313i	0.998551	−	0.0538209i	$-0.0171400\pi$
$587$	43.8404	+	12.8727i	1.80949	+	0.531313i	0.810936	+	0.585134i	$0.198958\pi$
$588$	0.220446	+	1.53324i	0.00909104	+	0.0632296i
$589$	0.0388749	+	0.0851241i	0.00160181	+	0.00350748i
$590$	15.3816	−	17.7514i	0.633252	−	0.730812i
$591$	−0.0143942	+	0.0166118i	−0.000592100	+	0.000683320i
$592$	30.1656	+	19.3863i	1.23980	+	0.796771i
$593$	28.2825	+	18.1761i	1.16142	+	0.746401i	0.971881	−	0.235471i	$-0.0756634\pi$
$593$	28.2825	+	18.1761i	1.16142	+	0.746401i	0.189542	+	0.981873i	$0.439300\pi$
$594$	−23.5332	−	3.43283i	−0.965578	−	0.140851i
$595$	9.64736	−	6.19998i	0.395503	−	0.254175i
$596$	−1.45593			−0.0596373
$597$	−0.0387574	−	0.0447284i	−0.00158623	−	0.00183061i
$598$	4.28132	−	9.37479i	0.175076	−	0.383364i
$599$	45.5245	+	13.3672i	1.86008	+	0.546169i	0.999309	+	0.0371812i	$0.0118379\pi$
$599$	45.5245	+	13.3672i	1.86008	+	0.546169i	0.860774	+	0.508988i	$0.169980\pi$
$600$	0.954203	−	1.10121i	0.0389552	−	0.0449567i
$601$	−16.7419	−	10.7594i	−0.682915	−	0.438883i	0.152645	−	0.988281i	$-0.451221\pi$
$601$	−16.7419	−	10.7594i	−0.682915	−	0.438883i	−0.835561	+	0.549398i	$0.814857\pi$
$602$	18.1422			0.739421
$603$	−20.3604	−	5.97835i	−0.829140	−	0.243457i
$604$	−9.23162			−0.375629
$605$	−4.61056	+	9.98713i	−0.187446	+	0.406034i
$606$	9.11538			0.370287
$607$	18.1899	+	5.34103i	0.738305	+	0.216786i	0.629199	−	0.777244i	$-0.283383\pi$
$607$	18.1899	+	5.34103i	0.738305	+	0.216786i	0.109106	+	0.994030i	$0.465201\pi$
$608$	−11.9532			−0.484766
$609$	8.90387	+	5.72217i	0.360803	+	0.231874i
$610$	2.96773	−	3.42495i	0.120160	−	0.138672i
$611$	−1.57896	−	0.463626i	−0.0638781	−	0.0187563i
$612$	3.39777	−	7.44008i	0.137347	−	0.300747i
$613$	26.2082	+	30.2459i	1.05854	+	1.22162i	0.974318	+	0.225175i	$0.0722953\pi$
$613$	26.2082	+	30.2459i	1.05854	+	1.22162i	0.0842227	+	0.996447i	$0.473159\pi$
$614$	43.8554			1.76986
$615$	2.16410	−	1.39078i	0.0872650	−	0.0560818i
$616$	−17.0945	+	7.76446i	−0.688756	+	0.312839i
$617$	19.4538	+	12.5022i	0.783179	+	0.503318i	0.870087	−	0.492898i	$-0.164062\pi$
$617$	19.4538	+	12.5022i	0.783179	+	0.503318i	−0.0869083	+	0.996216i	$0.527699\pi$
$618$	10.6244	+	6.82788i	0.427376	+	0.274658i
$619$	24.0930	−	27.8049i	0.968381	−	1.11757i	−0.0246473	−	0.999696i	$-0.507846\pi$
$619$	24.0930	−	27.8049i	0.968381	−	1.11757i	0.993028	−	0.117875i	$-0.0376083\pi$
$620$	0.0221298	−	0.0255392i	0.000888756	−	0.00102568i
$621$	6.66203	+	14.5878i	0.267338	+	0.585388i
$622$	7.01184	+	48.7684i	0.281149	+	1.95544i
$623$	−22.3045	−	6.54921i	−0.893613	−	0.262388i
$624$	0.879503	−	6.11708i	0.0352083	−	0.244879i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−3.26219	+	7.14321i	−0.130383	+	0.285500i
$627$	0.0132955	−	6.48402i	0.000530970	−	0.258947i
$628$	−7.32710	−	16.0441i	−0.292383	−	0.640229i
$629$	−17.7944	−	20.5358i	−0.709509	−	0.818817i
$630$	1.75832	+	12.2294i	0.0700532	+	0.487231i
$631$	−7.51004	−	8.66705i	−0.298970	−	0.345030i	0.586311	−	0.810086i	$-0.300580\pi$
$631$	−7.51004	−	8.66705i	−0.298970	−	0.345030i	−0.885281	+	0.465056i	$0.846034\pi$
$632$	10.8435			0.431331
$633$	16.0230	−	10.2974i	0.636857	−	0.409283i
$634$	2.66630	−	18.5445i	0.105892	−	0.736498i
$635$	2.84773	−	1.83013i	0.113009	−	0.0726263i
$636$	−2.35040	+	1.51051i	−0.0931993	+	0.0598956i
$637$	0.495406	+	3.44562i	0.0196287	+	0.136521i
$638$	7.17185	−	24.2411i	0.283936	−	0.959714i
$639$	−2.28261	+	15.8759i	−0.0902986	+	0.628040i
$640$	−5.27379	−	11.5480i	−0.208465	−	0.456474i
$641$	14.4379	+	9.27865i	0.570262	+	0.366485i	0.793771	−	0.608217i	$-0.208115\pi$
$641$	14.4379	+	9.27865i	0.570262	+	0.366485i	−0.223509	+	0.974702i	$0.571751\pi$
$642$	−1.36045	+	0.874311i	−0.0536929	+	0.0345063i
$643$	10.4141	−	22.8037i	0.410691	−	0.899289i	−0.585382	−	0.810758i	$-0.699055\pi$
$643$	10.4141	−	22.8037i	0.410691	−	0.899289i	0.996073	−	0.0885312i	$-0.0282173\pi$
$644$	−8.79469	−	5.65200i	−0.346559	−	0.222720i
$645$	−2.74003			−0.107888
$646$	15.4916	+	4.54875i	0.609510	+	0.178968i
$647$	−25.9696	+	29.9705i	−1.02097	+	1.17826i	−0.0371136	+	0.999311i	$0.511816\pi$
$647$	−25.9696	+	29.9705i	−1.02097	+	1.17826i	−0.983858	+	0.178953i	$0.942729\pi$
$648$	−4.75438	−	5.48685i	−0.186770	−	0.215544i
$649$	41.6181	−	18.9033i	1.63365	−	0.742020i
$650$	−1.77067	+	2.04346i	−0.0694515	+	0.0801513i
$651$	0.0125824	+	0.0875123i	0.000493142	+	0.00342988i
$652$	3.25054	−	0.954446i	0.127301	−	0.0373790i
$653$	6.81081	+	14.9136i	0.266528	+	0.583614i	0.994820	−	0.101653i	$-0.0324130\pi$
$653$	6.81081	+	14.9136i	0.266528	+	0.583614i	−0.728292	+	0.685267i	$0.759686\pi$
$654$	−5.06961	−	5.85065i	−0.198238	−	0.228778i
$655$	−1.03778	+	7.21792i	−0.0405494	+	0.282027i
$656$	−2.34110	−	16.2827i	−0.0914045	−	0.635732i
$657$	−12.2091	−	26.7342i	−0.476323	−	1.04300i
$658$	−2.22668	+	4.87574i	−0.0868049	+	0.190076i
$659$	40.1285	+	11.7828i	1.56319	+	0.458993i	0.945008	−	0.327046i	$-0.106053\pi$
$659$	40.1285	+	11.7828i	1.56319	+	0.458993i	0.618177	+	0.786039i	$0.287871\pi$
$660$	−2.13186	+	0.968310i	−0.0829825	+	0.0376914i
$661$	−7.72735	+	2.26895i	−0.300559	+	0.0882521i	−0.428535	−	0.903525i	$-0.640970\pi$
$661$	−7.72735	+	2.26895i	−0.300559	+	0.0882521i	0.127976	+	0.991777i	$0.459152\pi$
$662$	2.11320	−	14.6976i	0.0821318	−	0.571239i
$663$	−1.94544	+	4.25992i	−0.0755547	+	0.165442i
$664$	−26.4082	+	7.75415i	−1.02484	+	0.300919i
$665$	−7.28763	+	2.13984i	−0.282602	+	0.0829795i
$666$	28.0894	−	8.24779i	1.08844	−	0.319596i
$667$	−16.3563	+	4.80265i	−0.633320	+	0.185959i
$668$	0.00313641	−	0.00686777i	0.000121351	−	0.000265722i
$669$	−0.860015	+	5.98154i	−0.0332501	+	0.231260i
$670$	−14.5135	+	4.26154i	−0.560705	+	0.164638i
$671$	8.02979	−	3.64720i	0.309987	−	0.140799i
$672$	−10.8356	−	3.18161i	−0.417991	−	0.122733i
$673$	−3.97591	+	8.70603i	−0.153260	+	0.335593i	−0.970652	−	0.240490i	$-0.922692\pi$
$673$	−3.97591	+	8.70603i	−0.153260	+	0.335593i	0.817392	+	0.576082i	$0.195419\pi$
$674$	12.8450	+	28.1267i	0.494772	+	1.08340i
$675$	−0.598780	−	4.16461i	−0.0230471	−	0.160296i
$676$	1.34947	−	9.38577i	0.0519027	−	0.360991i
$677$	−24.1074	−	27.8214i	−0.926523	−	1.06926i	−0.997420	−	0.0717808i	$-0.977132\pi$
$677$	−24.1074	−	27.8214i	−0.926523	−	1.06926i	0.0708975	−	0.997484i	$-0.477414\pi$
$678$	−8.09275	−	17.7207i	−0.310800	−	0.680557i
$679$	31.7183	−	9.31332i	1.21724	−	0.357412i
$680$	1.00487	+	6.98902i	0.0385350	+	0.268017i
$681$	−2.88129	+	3.32519i	−0.110411	+	0.127422i
$682$	0.192267	−	0.0873294i	0.00736228	−	0.00334401i
$683$	−3.58695	−	4.13956i	−0.137251	−	0.158396i	0.682963	−	0.730453i	$-0.260691\pi$
$683$	−3.58695	−	4.13956i	−0.137251	−	0.158396i	−0.820214	+	0.572057i	$0.806146\pi$
$684$	−3.54751	+	4.09404i	−0.135642	+	0.156540i
$685$	−4.44986	−	1.30660i	−0.170021	−	0.0499226i
$686$	−24.8352			−0.948211
$687$	−5.46905	−	3.51475i	−0.208657	−	0.134096i
$688$	−7.27873	+	15.9382i	−0.277499	+	0.607638i
$689$	−5.28202	+	3.39455i	−0.201229	+	0.129322i
$690$	4.26513	+	2.74103i	0.162371	+	0.104349i
$691$	17.2150	+	37.6955i	0.654888	+	1.43400i	0.887210	+	0.461366i	$0.152640\pi$
$691$	17.2150	+	37.6955i	0.654888	+	1.43400i	−0.232322	+	0.972639i	$0.574632\pi$
$692$	−1.48473	+	10.3265i	−0.0564411	+	0.392557i
$693$	−6.82124	+	23.0560i	−0.259118	+	0.875826i
$694$	−5.75370	−	40.0178i	−0.218407	−	1.51906i
$695$	9.01070	−	5.79082i	0.341795	−	0.219658i
$696$	−5.48222	+	3.52321i	−0.207803	+	0.133547i
$697$	−1.77406	+	12.3389i	−0.0671973	+	0.467367i
$698$	−16.1146	+	10.3562i	−0.609945	+	0.391988i
$699$	−15.4693			−0.585103
$700$	1.79612	+	2.07283i	0.0678870	+	0.0783458i
$701$	−3.35084	−	23.3056i	−0.126560	−	0.880241i	−0.949869	−	0.312648i	$-0.898784\pi$
$701$	−3.35084	−	23.3056i	−0.126560	−	0.880241i	0.823310	−	0.567593i	$-0.192125\pi$
$702$	−7.44998	−	8.59774i	−0.281182	−	0.324501i
$703$	7.47617	+	16.3705i	0.281969	+	0.617426i
$704$	0.0125751	−	6.13272i	0.000473943	−	0.231136i
$705$	0.336296	−	0.736387i	0.0126657	−	0.0277339i
$706$	27.7673	−	8.15321i	1.04504	−	0.306850i
$707$	2.95720	−	20.5678i	0.111217	−	0.773532i
$708$	9.33571	+	2.74121i	0.350857	+	0.103021i
$709$	2.36635	+	16.4583i	0.0888702	+	0.618106i	0.984772	+	0.173853i	$0.0556218\pi$
$709$	2.36635	+	16.4583i	0.0888702	+	0.618106i	−0.895901	+	0.444253i	$0.853469\pi$
$710$	4.74951	+	10.4000i	0.178246	+	0.390304i
$711$	9.09368	−	10.4947i	0.341039	−	0.393581i
$712$	9.37299	−	10.8170i	0.351268	−	0.405384i
$713$	−0.119793	−	0.0769863i	−0.00448628	−	0.00288316i
$714$	12.8324	+	8.24687i	0.480240	+	0.308631i
$715$	−4.79090	+	2.17607i	−0.179170	+	0.0813805i
$716$	−19.8882	+	12.7814i	−0.743257	+	0.477662i
$717$	5.09906			0.190428
$718$	15.1839	+	17.5232i	0.566659	+	0.653959i
$719$	5.99492	−	13.1270i	0.223573	−	0.489556i	−0.764292	−	0.644870i	$-0.776912\pi$
$719$	5.99492	−	13.1270i	0.223573	−	0.489556i	0.987865	+	0.155314i	$0.0496389\pi$
$720$	−11.4492	−	3.36178i	−0.426685	−	0.125286i
$721$	18.8531	−	21.7576i	0.702126	−	0.810297i
$722$	18.2449	+	11.7253i	0.679005	+	0.436370i
$723$	14.8365			0.551774
$724$	−20.4925	−	6.01713i	−0.761597	−	0.223625i
$725$	4.47237			0.166099
$726$	−14.6315	−	0.0600038i	−0.543024	−	0.00222695i
$727$	−29.8151			−1.10578			−0.552890	−	0.833254i	$-0.686475\pi$
$727$	−29.8151			−1.10578			−0.552890	+	0.833254i	$0.686475\pi$
$728$	−8.61746	−	2.53032i	−0.319384	−	0.0937797i
$729$	0.553894			0.0205146
$730$	−17.6244	−	11.3265i	−0.652308	−	0.419213i
$731$	8.69503	−	10.0346i	0.321597	−	0.371143i
$732$	1.80123	+	0.528889i	0.0665754	+	0.0195483i
$733$	12.8067	−	28.0427i	0.473024	−	1.03578i	−0.511298	−	0.859403i	$-0.670835\pi$
$733$	12.8067	−	28.0427i	0.473024	−	1.03578i	0.984323	−	0.176376i	$-0.0564374\pi$
$734$	−36.2256	−	41.8066i	−1.33711	−	1.54311i
$735$	−1.71246			−0.0631650
$736$	15.3013	−	9.83356i	0.564014	−	0.362470i
$737$	−29.1283	−	4.24900i	−1.07295	−	0.156514i
$738$	−11.2983	−	7.26095i	−0.415894	−	0.267279i
$739$	−12.9661	−	8.33283i	−0.476967	−	0.306528i	0.279978	−	0.960006i	$-0.409673\pi$
$739$	−12.9661	−	8.33283i	−0.476967	−	0.306528i	−0.756945	+	0.653478i	$0.773309\pi$
$740$	4.25587	−	4.91154i	0.156449	−	0.180552i
$741$	2.03118	−	2.34410i	0.0746171	−	0.0861127i
$742$	8.49572	+	18.6030i	0.311888	+	0.682939i
$743$	−1.33296	−	9.27097i	−0.0489017	−	0.340119i	−0.999554	−	0.0298608i	$-0.990494\pi$
$743$	−1.33296	−	9.27097i	−0.0489017	−	0.340119i	0.950652	−	0.310258i	$-0.100415\pi$
$744$	−0.0522314	−	0.0153365i	−0.00191490	−	0.000562264i
$745$	0.229066	−	1.59319i	0.00839231	−	0.0583698i
$746$	45.4174	−	13.3357i	1.66285	−	0.488256i
$747$	−14.6420	+	32.0615i	−0.535723	+	1.17307i
$748$	3.21894	−	10.8801i	0.117696	−	0.397817i
$749$	1.53143	+	3.35335i	0.0559571	+	0.122529i
$750$	−0.871059	−	1.00526i	−0.0318066	−	0.0367067i
$751$	−0.550639	−	3.82978i	−0.0200931	−	0.139751i	0.977305	−	0.211835i	$-0.0679440\pi$
$751$	−0.550639	−	3.82978i	−0.0200931	−	0.139751i	−0.997399	+	0.0720845i	$0.977035\pi$
$752$	−3.39006	−	3.91234i	−0.123623	−	0.142668i
$753$	9.75230			0.355394
$754$	10.1731	−	6.53785i	0.370482	−	0.238095i
$755$	1.45243	−	10.1019i	0.0528595	−	0.367646i
$756$	−9.70802	+	6.23897i	−0.353077	+	0.226909i
$757$	−34.5116	+	22.1792i	−1.25434	+	0.806118i	−0.987500	−	0.157622i	$-0.949617\pi$
$757$	−34.5116	+	22.1792i	−1.25434	+	0.806118i	−0.266844	+	0.963740i	$0.585981\pi$
$758$	−2.89466	−	20.1328i	−0.105139	−	0.731257i
$759$	5.31719	+	8.31114i	0.193002	+	0.301675i
$760$	0.665537	−	4.62891i	0.0241416	−	0.167908i
$761$	−16.1745	−	35.4172i	−0.586325	−	1.28387i	−0.937638	−	0.347614i	$-0.886992\pi$
$761$	−16.1745	−	35.4172i	−0.586325	−	1.28387i	0.351313	−	0.936258i	$-0.385735\pi$
$762$	3.78789	+	2.43433i	0.137221	+	0.0881865i
$763$	−14.8460	+	9.54094i	−0.537461	+	0.345405i
$764$	4.12971	−	9.04280i	0.149408	−	0.327157i
$765$	7.60689	+	4.88865i	0.275028	+	0.176750i
$766$	−33.3430			−1.20473
$767$	20.9800	+	6.16029i	0.757545	+	0.222435i
$768$	9.16815	−	10.5806i	0.330827	−	0.381795i
$769$	−5.63376	−	6.50170i	−0.203158	−	0.234457i	0.645023	−	0.764163i	$-0.276848\pi$
$769$	−5.63376	−	6.50170i	−0.203158	−	0.234457i	−0.848181	+	0.529706i	$0.822302\pi$
$770$	4.79494	+	16.4548i	0.172798	+	0.592990i
$771$	2.06924	−	2.38803i	0.0745220	−	0.0860030i
$772$	1.40729	+	9.78792i	0.0506495	+	0.352275i
$773$	31.4894	−	9.24612i	1.13259	−	0.332560i	0.338867	−	0.940834i	$-0.389956\pi$
$773$	31.4894	−	9.24612i	1.13259	−	0.332560i	0.793727	+	0.608274i	$0.208138\pi$
$774$	5.94252	+	13.0123i	0.213600	+	0.467718i
$775$	0.0244651	+	0.0282342i	0.000878812	+	0.00101420i
$776$	−2.89664	+	20.1466i	−0.103983	+	0.723221i
$777$	2.41976	+	16.8298i	0.0868084	+	0.603766i
$778$	15.0559	+	32.9678i	0.539780	+	1.18195i
$779$	3.42975	−	7.51011i	0.122884	−	0.269078i
$780$	−1.07469	−	0.315557i	−0.0384800	−	0.0112988i
$781$	−0.0456228	+	22.2496i	−0.00163251	+	0.796154i
$782$	−23.5730	+	6.92165i	−0.842968	+	0.247518i
$783$	−2.67796	+	18.6256i	−0.0957026	+	0.665626i
$784$	−4.54905	+	9.96104i	−0.162466	+	0.355751i
$785$	18.7094	−	5.49358i	0.667767	−	0.196074i
$786$	−9.30669	+	2.73269i	−0.331959	+	0.0974719i
$787$	7.33905	−	2.15494i	0.261609	−	0.0768153i	−0.148298	−	0.988943i	$-0.547379\pi$
$787$	7.33905	−	2.15494i	0.261609	−	0.0768153i	0.409907	+	0.912127i	$0.365561\pi$
$788$	0.0244430	−	0.00717710i	0.000870744	−	0.000255674i
$789$	−4.11759	+	9.01626i	−0.146590	+	0.320987i
$790$	1.40872	−	9.79790i	0.0501202	−	0.348594i
$791$	−42.6101	+	12.5114i	−1.51504	+	0.444856i
$792$	−11.1683	−	9.71756i	−0.396849	−	0.345298i
$793$	4.04789	+	1.18857i	0.143745	+	0.0422073i
$794$	−21.9217	+	48.0019i	−0.777973	+	1.70352i
$795$	−1.28311	−	2.80963i	−0.0455073	−	0.0996472i
$796$	0.00976175	+	0.0678944i	0.000345996	+	0.00240645i
$797$	−2.80897	+	19.5368i	−0.0994987	+	0.692029i	0.877624	+	0.479350i	$0.159128\pi$
$797$	−2.80897	+	19.5368i	−0.0994987	+	0.692029i	−0.977122	+	0.212678i	$0.931781\pi$
$798$	−6.61595	−	7.63521i	−0.234202	−	0.270283i
$799$	1.62963	+	3.56840i	0.0576522	+	0.126241i
$800$	−4.57864	+	1.34441i	−0.161879	+	0.0475321i
$801$	−2.60856	−	18.1429i	−0.0921688	−	0.641048i
$802$	−38.2908	+	44.1899i	−1.35209	+	1.56040i
$803$	−21.9717	−	34.3433i	−0.775366	−	1.21195i
$804$	−4.10328	−	4.73543i	−0.144711	−	0.167006i
$805$	7.56852	−	8.73454i	0.266755	−	0.307852i
$806$	0.0969234	+	0.0284593i	0.00341398	+	0.00100244i
$807$	−15.9584			−0.561762
$808$	10.7631	+	6.91699i	0.378643	+	0.243339i
$809$	−1.70026	+	3.72305i	−0.0597780	+	0.130896i	−0.937163	−	0.348891i	$-0.886558\pi$
$809$	−1.70026	+	3.72305i	−0.0597780	+	0.130896i	0.877385	+	0.479786i	$0.159286\pi$
$810$	−5.57544	+	3.58312i	−0.195901	+	0.125898i
$811$	−35.0569	−	22.5297i	−1.23102	−	0.791126i	−0.246967	−	0.969024i	$-0.579434\pi$
$811$	−35.0569	−	22.5297i	−1.23102	−	0.791126i	−0.984049	+	0.177898i	$0.943070\pi$
$812$	−5.09573	−	11.1581i	−0.178825	−	0.391572i
$813$	0.0786773	−	0.547213i	0.00275933	−	0.0191916i
$814$	36.9756	−	16.7946i	1.29599	−	0.588651i
$815$	0.533007	+	3.70715i	0.0186704	+	0.129856i
$816$	−12.3934	+	7.96476i	−0.433856	+	0.278822i
$817$	−7.39796	+	4.75438i	−0.258822	+	0.166335i
$818$	5.09828	−	35.4593i	0.178257	−	1.23981i
$819$	−9.67577	+	6.21824i	−0.338099	+	0.217283i
$820$	−2.98142			−0.104116
$821$	−20.3318	−	23.4641i	−0.709584	−	0.818903i	0.280430	−	0.959875i	$-0.409523\pi$
$821$	−20.3318	−	23.4641i	−0.709584	−	0.818903i	−0.990014	+	0.140971i	$0.954978\pi$
$822$	−0.877918	−	6.10605i	−0.0306209	−	0.212973i
$823$	30.6218	+	35.3395i	1.06741	+	1.23186i	0.971643	+	0.236453i	$0.0759850\pi$
$823$	30.6218	+	35.3395i	1.06741	+	1.23186i	0.0957674	+	0.995404i	$0.469469\pi$
$824$	7.36366	+	16.1242i	0.256525	+	0.561712i
$825$	−0.724183	−	2.48518i	−0.0252128	−	0.0865229i
$826$	29.5863	−	64.7850i	1.02944	−	2.25416i
$827$	−12.9615	+	3.80585i	−0.450717	+	0.132342i	−0.499210	−	0.866481i	$-0.666376\pi$
$827$	−12.9615	+	3.80585i	−0.450717	+	0.132342i	0.0484930	+	0.998824i	$0.484558\pi$
$828$	1.17312	−	8.15923i	0.0407687	−	0.283553i
$829$	−19.5321	−	5.73515i	−0.678379	−	0.199190i	−0.0756483	−	0.997135i	$-0.524103\pi$
$829$	−19.5321	−	5.73515i	−0.678379	−	0.199190i	−0.602731	+	0.797944i	$0.705921\pi$
$830$	3.57564	+	24.8691i	0.124112	+	0.863220i
$831$	−5.79042	−	12.6793i	−0.200867	−	0.439838i
$832$	1.92113	−	2.21710i	0.0666031	−	0.0768641i
$833$	5.43421	−	6.27141i	0.188284	−	0.217292i
$834$	11.9855	+	7.70263i	0.415025	+	0.266720i
$835$	0.00702175	+	0.00451261i	0.000242998	+	0.000156165i
$836$	−4.07576	+	6.31350i	−0.140963	+	0.218357i
$837$	−0.132234	+	0.0849814i	−0.00457066	+	0.00293739i
$838$	−53.1112			−1.83470
$839$	−4.63524	−	5.34935i	−0.160026	−	0.184680i	0.670074	−	0.742294i	$-0.266262\pi$
$839$	−4.63524	−	5.34935i	−0.160026	−	0.184680i	−0.830100	+	0.557614i	$0.811717\pi$
$840$	1.83539	−	4.01895i	0.0633271	−	0.138667i
$841$	8.63347	+	2.53501i	0.297706	+	0.0874143i
$842$	−42.9133	+	49.5246i	−1.47889	+	1.70673i
$843$	−3.89932	−	2.50594i	−0.134300	−	0.0863093i
$844$	−22.0744			−0.759833
$845$	10.0583	+	2.95338i	0.346015	+	0.101599i
$846$	−4.22643			−0.145308
$847$	−4.88212	+	32.9948i	−0.167752	+	1.13371i
$848$	−19.7516			−0.678271
$849$	1.02774	+	0.301773i	0.0352721	+	0.0103568i
$850$	6.44564			0.221084
$851$	−23.0378	−	14.8055i	−0.789727	−	0.507526i
$852$	−3.10147	+	3.57928i	−0.106255	+	0.122624i
$853$	−31.6834	−	9.30308i	−1.08482	−	0.318531i	−0.310013	−	0.950732i	$-0.600334\pi$
$853$	−31.6834	−	9.30308i	−1.08482	−	0.318531i	−0.774805	+	0.632201i	$0.782152\pi$
$854$	5.70839	−	12.4996i	0.195337	−	0.427728i
$855$	−3.92186	−	4.52607i	−0.134125	−	0.154788i
$856$	−2.26982			−0.0775808
$857$	−33.1616	+	21.3117i	−1.13278	+	0.727993i	−0.966138	−	0.258025i	$-0.916928\pi$
$857$	−33.1616	+	21.3117i	−1.13278	+	0.727993i	−0.166641	+	0.986018i	$0.553292\pi$
$858$	−5.28019	−	4.59430i	−0.180263	−	0.156847i
$859$	−23.0131	−	14.7896i	−0.785196	−	0.504615i	0.0855584	−	0.996333i	$-0.472733\pi$
$859$	−23.0131	−	14.7896i	−0.785196	−	0.504615i	−0.870754	+	0.491718i	$0.836369\pi$
$860$	2.67149	+	1.71686i	0.0910972	+	0.0585446i
$861$	5.10805	−	5.89500i	0.174082	−	0.200901i
$862$	−26.7707	+	30.8950i	−0.911814	+	1.05229i
$863$	7.18496	+	15.7329i	0.244579	+	0.535553i	0.991615	−	0.129231i	$-0.0412509\pi$
$863$	7.18496	+	15.7329i	0.244579	+	0.535553i	−0.747036	+	0.664784i	$0.768524\pi$
$864$	−2.85734	−	19.8733i	−0.0972088	−	0.676102i
$865$	−11.0665	−	3.24940i	−0.376271	−	0.110483i
$866$	−7.89039	+	54.8789i	−0.268126	+	1.86486i
$867$	−2.01903	+	0.592842i	−0.0685700	+	0.0201340i
$868$	0.0425664	−	0.0932074i	0.00144480	−	0.00316366i
$869$	10.4478	−	16.1840i	0.354417	−	0.549005i
$870$	2.47126	+	5.41130i	0.0837835	+	0.183460i
$871$	−9.22125	−	10.6419i	−0.312450	−	0.360587i
$872$	−1.54636	−	10.7552i	−0.0523663	−	0.364216i
$873$	17.0693	+	19.6990i	0.577707	+	0.666710i
$874$	16.2718			0.550402
$875$	−2.55083	+	1.63932i	−0.0862339	+	0.0554192i
$876$	1.23506	−	8.59005i	0.0417289	−	0.290231i
$877$	2.32305	−	1.49293i	0.0784439	−	0.0504128i	−0.500831	−	0.865545i	$-0.666972\pi$
$877$	2.32305	−	1.49293i	0.0784439	−	0.0504128i	0.579275	+	0.815132i	$0.303336\pi$
$878$	7.02642	−	4.51560i	0.237130	−	0.152394i
$879$	1.70058	+	11.8278i	0.0573592	+	0.398942i
$880$	−16.3796	−	2.38932i	−0.552155	−	0.0805438i
$881$	0.953033	−	6.62849i	0.0321085	−	0.223319i	−0.967449	−	0.253066i	$-0.918561\pi$
$881$	0.953033	−	6.62849i	0.0321085	−	0.223319i	0.999557	+	0.0297467i	$0.00947007\pi$
$882$	3.71395	+	8.13242i	0.125055	+	0.273833i
$883$	12.4088	+	7.97463i	0.417588	+	0.268368i	0.732518	−	0.680747i	$-0.238345\pi$
$883$	12.4088	+	7.97463i	0.417588	+	0.268368i	−0.314930	+	0.949115i	$0.601981\pi$
$884$	4.56599	−	2.93438i	0.153571	−	0.0986940i
$885$	−4.46844	+	9.78452i	−0.150205	+	0.328903i
$886$	50.1539	+	32.2320i	1.68495	+	1.08285i
$887$	15.2638			0.512510			0.256255	−	0.966609i	$-0.417511\pi$
$887$	15.2638			0.512510			0.256255	+	0.966609i	$0.417511\pi$
$888$	−10.0448	−	2.94942i	−0.337082	−	0.0989761i
$889$	6.72166	−	7.75721i	0.225437	−	0.260168i
$890$	−8.55627	−	9.87447i	−0.286807	−	0.330993i
$891$	−12.7701	+	1.80934i	−0.427813	+	0.0606151i
$892$	4.58646	−	5.29305i	0.153566	−	0.177225i
$893$	−0.369760	−	2.57174i	−0.0123736	−	0.0860600i
$894$	2.05423	−	0.603178i	0.0687039	−	0.0201733i
$895$	−10.8572	−	23.7740i	−0.362917	−	0.794678i
$896$	−25.2084	−	29.0920i	−0.842152	−	0.971896i
$897$	−0.671686	+	4.67168i	−0.0224269	+	0.155983i
$898$	4.04052	+	28.1024i	0.134834	+	0.937791i
$899$	−0.0694092	−	0.151985i	−0.00231493	−	0.00506898i
$900$	−0.898395	+	1.96721i	−0.0299465	+	0.0655737i
$901$	14.3612	+	4.21684i	0.478442	+	0.140483i
$902$	−16.9311	−	7.77417i	−0.563744	−	0.258851i
$903$	−7.97172	+	2.34071i	−0.265282	+	0.0778939i
$904$	3.89133	−	27.0648i	0.129424	−	0.900162i
$905$	9.80851	−	21.4776i	0.326046	−	0.713941i
$906$	13.0253	−	3.82456i	0.432736	−	0.127063i
$907$	−39.6810	+	11.6514i	−1.31759	+	0.386878i	−0.863622	−	0.504141i	$-0.831809\pi$
$907$	−39.6810	+	11.6514i	−1.31759	+	0.386878i	−0.453966	+	0.891019i	$0.649991\pi$
$908$	4.89274	−	1.43664i	0.162371	−	0.0476766i
$909$	15.7207	−	4.61601i	0.521422	−	0.153103i
$910$	−3.40586	+	7.45779i	−0.112903	+	0.247223i
$911$	2.09155	−	14.5471i	0.0692962	−	0.481966i	−0.925390	−	0.379016i	$-0.876263\pi$
$911$	2.09155	−	14.5471i	0.0692962	−	0.481966i	0.994687	−	0.102950i	$-0.0328282\pi$
$912$	9.36199	−	2.74893i	0.310007	−	0.0910261i
$913$	−13.8714	+	46.8857i	−0.459075	+	1.55169i
$914$	−69.2799	−	20.3424i	−2.29157	−	0.672867i
$915$	−0.862141	+	1.88783i	−0.0285015	+	0.0624096i
$916$	3.12997	+	6.85367i	0.103417	+	0.226452i
$917$	3.14674	+	21.8860i	0.103914	+	0.722740i
$918$	−3.85952	+	26.8436i	−0.127383	+	0.885969i
$919$	−25.6701	−	29.6249i	−0.846778	−	0.977234i	0.153162	−	0.988201i	$-0.451055\pi$
$919$	−25.6701	−	29.6249i	−0.846778	−	0.977234i	−0.999940	+	0.0109669i	$0.996509\pi$
$920$	2.95612	+	6.47299i	0.0974603	+	0.213408i
$921$	−19.2701	+	5.65822i	−0.634972	+	0.186445i
$922$	−4.84127	−	33.6718i	−0.159439	−	1.10892i
$923$	−6.96989	+	8.04369i	−0.229417	+	0.264761i
$924$	−5.37515	+	4.63833i	−0.176829	+	0.152590i
$925$	4.70497	+	5.42982i	0.154698	+	0.178531i
$926$	1.27012	−	1.46580i	0.0417388	−	0.0481692i
$927$	21.7808	+	6.39542i	0.715376	+	0.210053i
$928$	21.3419			0.700581
$929$	−25.2201	−	16.2079i	−0.827443	−	0.531766i	0.0570212	−	0.998373i	$-0.481840\pi$
$929$	−25.2201	−	16.2079i	−0.827443	−	0.531766i	−0.884465	+	0.466607i	$0.845476\pi$
$930$	−0.0206433	+	0.0452025i	−0.000676920	+	0.00148225i
$931$	−4.62357	+	2.97139i	−0.151531	+	0.0973832i
$932$	15.0824	+	9.69287i	0.494040	+	0.317500i
$933$	−9.37312	−	20.5243i	−0.306862	−	0.671934i
$934$	−5.23381	+	36.4020i	−0.171256	+	1.19111i
$935$	11.3994	+	5.23419i	0.372799	+	0.171176i
$936$	−1.00783	−	7.00960i	−0.0329419	−	0.229116i
$937$	26.0786	−	16.7597i	0.851951	−	0.547516i	−0.0402318	−	0.999190i	$-0.512810\pi$
$937$	26.0786	−	16.7597i	0.851951	−	0.547516i	0.892183	+	0.451675i	$0.149173\pi$
$938$	−38.5844	+	24.7967i	−1.25983	+	0.809641i
$939$	0.511797	−	3.55963i	0.0167019	−	0.116164i
$940$	−0.789295	+	0.507249i	−0.0257440	+	0.0165446i
$941$	60.7973			1.98193			0.990967	−	0.134103i	$-0.0428152\pi$
$941$	60.7973			1.98193			0.990967	+	0.134103i	$0.0428152\pi$
$942$	16.9850	+	19.6017i	0.553401	+	0.638659i
$943$	1.78792	+	12.4353i	0.0582227	+	0.404948i
$944$	45.0445	+	51.9841i	1.46607	+	1.69194i
$945$	−5.29974	−	11.6048i	−0.172401	−	0.377505i
$946$	10.6943	+	16.7159i	0.347701	+	0.543480i
$947$	−12.0627	+	26.4137i	−0.391986	+	0.858329i	0.606035	+	0.795438i	$0.292759\pi$
$947$	−12.0627	+	26.4137i	−0.391986	+	0.858329i	−0.998020	+	0.0628907i	$0.979968\pi$
$948$	3.93432	−	1.15522i	0.127781	−	0.0375198i
$949$	2.77554	−	19.3043i	0.0900980	−	0.626645i
$950$	−4.09610	−	1.20272i	−0.132895	−	0.0390215i
$951$	1.22104	+	8.49251i	0.0395949	+	0.275389i
$952$	8.89399	+	19.4751i	0.288256	+	0.631192i
$953$	−17.9370	+	20.7004i	−0.581036	+	0.670551i	−0.967827	−	0.251616i	$-0.919038\pi$
$953$	−17.9370	+	20.7004i	−0.581036	+	0.670551i	0.386791	+	0.922167i	$0.373583\pi$
$954$	−10.5600	+	12.1869i	−0.341894	+	0.394567i
$955$	9.24555	+	5.94175i	0.299179	+	0.192271i
$956$	−4.97152	−	3.19500i	−0.160790	−	0.103334i
$957$	−0.0237384	+	11.5769i	−0.000767354	+	0.374228i
$958$	−20.8365	+	13.3908i	−0.673196	+	0.432637i
$959$	−14.0624			−0.454099
$960$	0.945074	+	1.09067i	0.0305021	+	0.0352013i
$961$	−12.8773	+	28.1973i	−0.415396	+	0.909591i
$962$	18.6397	+	5.47311i	0.600968	+	0.176460i
$963$	−1.90354	+	2.19680i	−0.0613406	+	0.0707908i
$964$	−14.4654	−	9.29633i	−0.465898	−	0.299415i
$965$	−10.9321			−0.351915
$966$	14.7504	+	4.33109i	0.474585	+	0.139351i
$967$	−18.3247			−0.589283			−0.294641	−	0.955608i	$-0.595200\pi$
$967$	−18.3247			−0.589283			−0.294641	+	0.955608i	$0.595200\pi$
$968$	−17.2307	−	11.1736i	−0.553815	−	0.359133i
$969$	−7.39393			−0.237527
$970$	17.8276	+	5.23466i	0.572411	+	0.168075i
$971$	32.5445			1.04440			0.522202	−	0.852822i	$-0.325111\pi$
$971$	32.5445			1.04440			0.522202	+	0.852822i	$0.325111\pi$
$972$	−11.9146	−	7.65702i	−0.382160	−	0.245599i
$973$	21.2684	−	24.5451i	0.681835	−	0.786879i
$974$	12.3508	+	3.62652i	0.395745	+	0.116201i
$975$	0.514389	−	1.12635i	0.0164736	−	0.0360722i
$976$	8.69088	+	10.0298i	0.278188	+	0.321046i
$977$	−45.7938			−1.46507			−0.732537	−	0.680728i	$-0.761664\pi$
$977$	−45.7938			−1.46507			−0.732537	+	0.680728i	$0.761664\pi$
$978$	−4.19091	+	2.69333i	−0.134011	+	0.0861233i
$979$	−7.11353	−	24.4115i	−0.227350	−	0.780196i
$980$	1.66963	+	1.07300i	0.0533343	+	0.0342759i
$981$	−11.7060	−	7.52298i	−0.373743	−	0.240190i
$982$	47.7279	−	55.0809i	1.52306	−	1.75770i
$983$	12.4187	−	14.3319i	0.396094	−	0.457117i	−0.522313	−	0.852754i	$-0.674931\pi$
$983$	12.4187	−	14.3319i	0.396094	−	0.457117i	0.918407	+	0.395637i	$0.129476\pi$
$984$	1.99510	+	4.36867i	0.0636016	+	0.139268i
$985$	0.00400803	+	0.0278764i	0.000127706	+	0.000888217i
$986$	−27.6595	−	8.12157i	−0.880859	−	0.258644i
$987$	0.349338	−	2.42970i	0.0111195	−	0.0773381i
$988$	−3.44915	+	1.01276i	−0.109732	+	0.0322203i
$989$	5.55885	−	12.1722i	0.176761	−	0.387053i
$990$	−10.2315	+	8.82894i	−0.325177	+	0.280602i
$991$	19.7803	+	43.3128i	0.628342	+	1.37588i	0.909293	+	0.416156i	$0.136623\pi$
$991$	19.7803	+	43.3128i	0.628342	+	1.37588i	−0.280951	+	0.959722i	$0.590650\pi$
$992$	0.116746	+	0.134732i	0.00370669	+	0.00427774i
$993$	0.967744	+	6.73081i	0.0307104	+	0.213596i
$994$	22.7023	+	26.1999i	0.720075	+	0.831010i
$995$	−0.0758308			−0.00240400
$996$	−8.75553	+	5.62684i	−0.277430	+	0.178293i
$997$	0.923318	−	6.42182i	0.0292418	−	0.203381i	−0.969963	−	0.243252i	$-0.921786\pi$
$997$	0.923318	−	6.42182i	0.0292418	−	0.203381i	0.999205	+	0.0398713i	$0.0126948\pi$
$998$	23.3574	−	15.0109i	0.739367	−	0.475162i
$999$	−25.4303	+	16.3431i	−0.804580	+	0.517072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.k.a.56.18	✓	220
121.67	even	11	inner	605.2.k.a.551.18	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.k.a.56.18	✓	220	1.1	even	1	trivial
605.2.k.a.551.18	yes	220	121.67	even	11	inner

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63524 + 0.480149i) q^{2} -0.780476 q^{3} +(0.760954 + 0.489036i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.27626 - 0.374745i) q^{6} +(-1.25961 + 2.75817i) q^{7} +(-1.22259 - 1.41095i) q^{8} -2.39086 q^{9} +O(q^{10})\)	\(q+(1.63524 + 0.480149i) q^{2} -0.780476 q^{3} +(0.760954 + 0.489036i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.27626 - 0.374745i) q^{6} +(-1.25961 + 2.75817i) q^{7} +(-1.22259 - 1.41095i) q^{8} -2.39086 q^{9} +(-1.43373 + 0.921400i) q^{10} +(-3.28383 + 0.465272i) q^{11} +(-0.593906 - 0.381680i) q^{12} +(-1.33468 - 0.857746i) q^{13} +(-3.38410 + 3.90546i) q^{14} +(0.511103 - 0.589844i) q^{15} +(-2.07329 - 4.53987i) q^{16} +(0.538241 + 3.74355i) q^{17} +(-3.90962 - 1.14797i) q^{18} +(0.356483 - 2.47940i) q^{19} +(-0.867907 + 0.254841i) q^{20} +(0.983098 - 2.15268i) q^{21} +(-5.59324 - 0.815896i) q^{22} +(1.58339 + 3.46715i) q^{23} +(0.954203 + 1.10121i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(-1.77067 - 2.04346i) q^{26} +4.20743 q^{27} +(-2.30735 + 1.48284i) q^{28} +(-0.636484 + 4.42684i) q^{29} +(1.11899 - 0.719130i) q^{30} +(-0.0314286 + 0.0201979i) q^{31} +(-0.679118 - 4.72337i) q^{32} +(2.56295 - 0.363134i) q^{33} +(-0.917310 + 6.38003i) q^{34} +(-1.25961 - 2.75817i) q^{35} +(-1.81933 - 1.16921i) q^{36} +(-6.04414 + 3.88433i) q^{37} +(1.77342 - 3.88324i) q^{38} +(1.04168 + 0.669450i) q^{39} +1.86695 q^{40} +(3.16252 + 0.928600i) q^{41} +(2.64121 - 3.04812i) q^{42} +(-2.29903 - 2.65322i) q^{43} +(-2.72638 - 1.25186i) q^{44} +(1.56568 - 1.80689i) q^{45} +(0.924477 + 6.42988i) q^{46} +(0.995228 - 0.292225i) q^{47} +(1.61815 + 3.54326i) q^{48} +(-1.43685 - 1.65821i) q^{49} +(0.242543 - 1.68693i) q^{50} +(-0.420084 - 2.92175i) q^{51} +(-0.596161 - 1.30541i) q^{52} +(1.64401 - 3.59989i) q^{53} +(6.88016 + 2.02020i) q^{54} +(1.79882 - 2.78644i) q^{55} +(5.43162 - 1.59487i) q^{56} +(-0.278227 + 1.93511i) q^{57} +(-3.16635 + 6.93334i) q^{58} +(-13.2238 + 3.88286i) q^{59} +(0.677381 - 0.198897i) q^{60} +(-2.55140 + 0.749159i) q^{61} +(-0.0610912 + 0.0179380i) q^{62} +(3.01156 - 6.59439i) q^{63} +(-0.263153 + 1.83027i) q^{64} +(1.52227 - 0.446979i) q^{65} +(4.36539 + 0.636787i) q^{66} +(8.51594 + 2.50051i) q^{67} +(-1.42115 + 3.11189i) q^{68} +(-1.23580 - 2.70603i) q^{69} +(-0.735436 - 5.11507i) q^{70} +(0.954723 - 6.64025i) q^{71} +(2.92304 + 3.37337i) q^{72} +(5.10658 + 11.1819i) q^{73} +(-11.7487 + 3.44972i) q^{74} +(0.111073 + 0.772532i) q^{75} +(1.48378 - 1.71237i) q^{76} +(2.85305 - 9.64341i) q^{77} +(1.38197 + 1.59487i) q^{78} +(-3.80352 + 4.38950i) q^{79} +(4.78872 + 1.40610i) q^{80} +3.88877 q^{81} +(4.72561 + 3.03696i) q^{82} +(6.12416 - 13.4100i) q^{83} +(1.80083 - 1.15732i) q^{84} +(-3.18166 - 2.04473i) q^{85} +(-2.48552 - 5.44253i) q^{86} +(0.496760 - 3.45504i) q^{87} +(4.67126 + 4.06447i) q^{88} +(1.09105 + 7.58845i) q^{89} +(3.42783 - 2.20294i) q^{90} +(4.04699 - 2.60084i) q^{91} +(-0.490669 + 3.41268i) q^{92} +(0.0245292 - 0.0157640i) q^{93} +1.76775 q^{94} +(1.64036 + 1.89307i) q^{95} +(0.530035 + 3.68647i) q^{96} +(-7.13939 - 8.23930i) q^{97} +(-1.55340 - 3.40146i) q^{98} +(7.85116 - 1.11240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 4 q^{2} - 4 q^{3} - 24 q^{4} - 22 q^{5} - 12 q^{6} - 8 q^{7} - 12 q^{8} + 212 q^{9}+O(q^{10}) \) 220 * q - 4 * q^2 - 4 * q^3 - 24 * q^4 - 22 * q^5 - 12 * q^6 - 8 * q^7 - 12 * q^8 + 212 * q^9	\( 220 q - 4 q^{2} - 4 q^{3} - 24 q^{4} - 22 q^{5} - 12 q^{6} - 8 q^{7} - 12 q^{8} + 212 q^{9} - 4 q^{10} - 10 q^{11} + 5 q^{12} + 6 q^{13} + 68 q^{14} + 7 q^{15} - 44 q^{16} - 24 q^{17} - 36 q^{18} - 16 q^{19} - 24 q^{20} - 10 q^{21} + 45 q^{22} + 51 q^{23} + 72 q^{24} - 22 q^{25} - 30 q^{26} - 34 q^{27} - 56 q^{28} - 36 q^{29} - q^{30} + 4 q^{31} + 42 q^{32} - 44 q^{33} - 52 q^{34} - 8 q^{35} - 94 q^{36} + 69 q^{37} - 40 q^{38} - 56 q^{39} + 54 q^{40} - 44 q^{41} - 76 q^{42} + 7 q^{43} - 67 q^{44} - 30 q^{45} + 56 q^{46} + 14 q^{47} + 54 q^{48} + 10 q^{49} - 4 q^{50} + 27 q^{51} + 58 q^{52} + 86 q^{53} - 43 q^{54} - 10 q^{55} - 79 q^{56} + 129 q^{57} + 100 q^{58} - 54 q^{59} - 28 q^{60} - 52 q^{61} + 55 q^{62} - 104 q^{63} + 36 q^{64} - 16 q^{65} - 33 q^{66} + 13 q^{67} - 120 q^{68} - 22 q^{69} - 9 q^{70} - 70 q^{71} + 60 q^{72} - 66 q^{73} + 20 q^{74} - 4 q^{75} - 12 q^{76} + 44 q^{77} + 187 q^{78} - 22 q^{79} - 44 q^{80} + 108 q^{81} - 76 q^{82} + 96 q^{83} - 224 q^{84} + 9 q^{85} - 66 q^{86} - 76 q^{87} - 47 q^{88} + 52 q^{89} + 8 q^{90} + 88 q^{91} + 8 q^{92} + 38 q^{93} + 22 q^{94} + 28 q^{95} - 120 q^{96} + 37 q^{97} + 12 q^{98} + 118 q^{99}+O(q^{100}) \) 220 * q - 4 * q^2 - 4 * q^3 - 24 * q^4 - 22 * q^5 - 12 * q^6 - 8 * q^7 - 12 * q^8 + 212 * q^9 - 4 * q^10 - 10 * q^11 + 5 * q^12 + 6 * q^13 + 68 * q^14 + 7 * q^15 - 44 * q^16 - 24 * q^17 - 36 * q^18 - 16 * q^19 - 24 * q^20 - 10 * q^21 + 45 * q^22 + 51 * q^23 + 72 * q^24 - 22 * q^25 - 30 * q^26 - 34 * q^27 - 56 * q^28 - 36 * q^29 - q^30 + 4 * q^31 + 42 * q^32 - 44 * q^33 - 52 * q^34 - 8 * q^35 - 94 * q^36 + 69 * q^37 - 40 * q^38 - 56 * q^39 + 54 * q^40 - 44 * q^41 - 76 * q^42 + 7 * q^43 - 67 * q^44 - 30 * q^45 + 56 * q^46 + 14 * q^47 + 54 * q^48 + 10 * q^49 - 4 * q^50 + 27 * q^51 + 58 * q^52 + 86 * q^53 - 43 * q^54 - 10 * q^55 - 79 * q^56 + 129 * q^57 + 100 * q^58 - 54 * q^59 - 28 * q^60 - 52 * q^61 + 55 * q^62 - 104 * q^63 + 36 * q^64 - 16 * q^65 - 33 * q^66 + 13 * q^67 - 120 * q^68 - 22 * q^69 - 9 * q^70 - 70 * q^71 + 60 * q^72 - 66 * q^73 + 20 * q^74 - 4 * q^75 - 12 * q^76 + 44 * q^77 + 187 * q^78 - 22 * q^79 - 44 * q^80 + 108 * q^81 - 76 * q^82 + 96 * q^83 - 224 * q^84 + 9 * q^85 - 66 * q^86 - 76 * q^87 - 47 * q^88 + 52 * q^89 + 8 * q^90 + 88 * q^91 + 8 * q^92 + 38 * q^93 + 22 * q^94 + 28 * q^95 - 120 * q^96 + 37 * q^97 + 12 * q^98 + 118 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more