LMFDB - Embedded newform 483.2.q.f.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	483.85
Dual form			483.2.q.f.358.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24645 + 1.43848i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.230954 - 1.60632i) q^{4} +(0.274912 + 0.601974i) q^{5} +(-0.270879 + 1.88400i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-0.603914 - 0.388112i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.24645 + 1.43848i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.230954 - 1.60632i) q^{4} +(0.274912 + 0.601974i) q^{5} +(-0.270879 + 1.88400i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-0.603914 - 0.388112i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-1.20859 - 0.354874i) q^{10} +(1.84851 + 2.13329i) q^{11} +(-1.06274 - 1.22646i) q^{12} +(0.944710 + 0.277392i) q^{13} +(-0.790691 + 1.73137i) q^{14} +(0.556723 + 0.357784i) q^{15} +(4.42525 - 1.29937i) q^{16} +(-0.769121 + 5.34936i) q^{17} +(0.790691 + 1.73137i) q^{18} +(0.164929 + 1.14711i) q^{19} +(0.903473 - 0.580627i) q^{20} +(0.654861 - 0.755750i) q^{21} -5.37276 q^{22} +(2.85316 - 3.85480i) q^{23} -0.717874 q^{24} +(2.98751 - 3.44777i) q^{25} +(-1.57655 + 1.01319i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-0.674153 - 1.47619i) q^{28} +(-1.43610 + 9.98827i) q^{29} +(-1.20859 + 0.354874i) q^{30} +(5.82310 + 3.74228i) q^{31} +(-3.05029 + 6.67920i) q^{32} +(2.70841 + 0.795261i) q^{33} +(-6.73625 - 7.77405i) q^{34} +(0.433372 + 0.500138i) q^{35} +(-1.55711 - 0.457207i) q^{36} +(1.98313 - 4.34245i) q^{37} +(-1.85566 - 1.19256i) q^{38} +(0.944710 - 0.277392i) q^{39} +(0.0676099 - 0.470237i) q^{40} +(1.03105 + 2.25768i) q^{41} +(0.270879 + 1.88400i) q^{42} +(-8.69148 + 5.58567i) q^{43} +(2.99984 - 3.46200i) q^{44} +0.661778 q^{45} +(1.98873 + 8.90900i) q^{46} +9.23599 q^{47} +(3.02026 - 3.48557i) q^{48} +(0.841254 - 0.540641i) q^{49} +(1.23576 + 8.59492i) q^{50} +(2.24505 + 4.91598i) q^{51} +(0.227396 - 1.58157i) q^{52} +(-5.29835 + 1.55574i) q^{53} +(1.60122 + 1.02904i) q^{54} +(-0.776009 + 1.69922i) q^{55} +(-0.688795 - 0.202249i) q^{56} +(0.758921 + 0.875841i) q^{57} +(-12.5779 - 14.5156i) q^{58} +(-12.7678 - 3.74895i) q^{59} +(0.446139 - 0.976909i) q^{60} +(-4.55712 - 2.92868i) q^{61} +(-12.6414 + 3.71184i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-1.97401 - 4.32247i) q^{64} +(0.0927297 + 0.644949i) q^{65} +(-4.51985 + 2.90473i) q^{66} +(3.58274 - 4.13470i) q^{67} +8.77043 q^{68} +(0.316169 - 4.78540i) q^{69} -1.25961 q^{70} +(-5.87692 + 6.78233i) q^{71} +(-0.603914 + 0.388112i) q^{72} +(0.212771 + 1.47986i) q^{73} +(3.77464 + 8.26532i) q^{74} +(0.649247 - 4.51562i) q^{75} +(1.80454 - 0.529859i) q^{76} +(2.37465 + 1.52609i) q^{77} +(-0.778509 + 1.70470i) q^{78} +(0.245273 + 0.0720186i) q^{79} +(1.99874 + 2.30667i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-4.53277 - 1.33094i) q^{82} +(5.74475 - 12.5792i) q^{83} +(-1.36522 - 0.877374i) q^{84} +(-3.43161 + 1.00761i) q^{85} +(2.79861 - 19.4647i) q^{86} +(4.19194 + 9.17908i) q^{87} +(-0.288384 - 2.00575i) q^{88} +(5.53639 - 3.55802i) q^{89} +(-0.824870 + 0.951951i) q^{90} +0.984593 q^{91} +(-6.85101 - 3.69281i) q^{92} +6.92193 q^{93} +(-11.5122 + 13.2857i) q^{94} +(-0.645188 + 0.414637i) q^{95} +(1.04498 + 7.26801i) q^{96} +(-0.522077 - 1.14319i) q^{97} +(-0.270879 + 1.88400i) q^{98} +(2.70841 - 0.795261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−1.24645	+	1.43848i	−0.881371	+	1.01716i	0.118337	+	0.992974i	$0.462244\pi$
$2$	−1.24645	+	1.43848i	−0.881371	+	1.01716i	−0.999708	+	0.0241826i	$0.992302\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.230954	−	1.60632i	−0.115477	−	0.803162i
$5$	0.274912	+	0.601974i	0.122945	+	0.269211i	0.961090	−	0.276236i	$-0.0890872\pi$
$5$	0.274912	+	0.601974i	0.122945	+	0.269211i	−0.838145	+	0.545447i	$0.816360\pi$
$6$	−0.270879	+	1.88400i	−0.110586	+	0.769141i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	−0.603914	−	0.388112i	−0.213516	−	0.137218i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−1.20859	−	0.354874i	−0.382189	−	0.112221i
$11$	1.84851	+	2.13329i	0.557346	+	0.643212i	0.962579	−	0.271002i	$-0.0873549\pi$
$11$	1.84851	+	2.13329i	0.557346	+	0.643212i	−0.405233	+	0.914214i	$0.632809\pi$
$12$	−1.06274	−	1.22646i	−0.306785	−	0.354049i
$13$	0.944710	+	0.277392i	0.262015	+	0.0769346i	0.410102	−	0.912040i	$-0.365493\pi$
$13$	0.944710	+	0.277392i	0.262015	+	0.0769346i	−0.148086	+	0.988974i	$0.547311\pi$
$14$	−0.790691	+	1.73137i	−0.211321	+	0.462729i
$15$	0.556723	+	0.357784i	0.143745	+	0.0923794i
$16$	4.42525	−	1.29937i	1.10631	−	0.324842i
$17$	−0.769121	+	5.34936i	−0.186539	+	1.29741i	0.654346	+	0.756195i	$0.272944\pi$
$17$	−0.769121	+	5.34936i	−0.186539	+	1.29741i	−0.840885	+	0.541214i	$0.817965\pi$
$18$	0.790691	+	1.73137i	0.186368	+	0.408088i
$19$	0.164929	+	1.14711i	0.0378374	+	0.263165i	0.999955	−	0.00946946i	$-0.00301427\pi$
$19$	0.164929	+	1.14711i	0.0378374	+	0.263165i	−0.962118	+	0.272634i	$0.912105\pi$
$20$	0.903473	−	0.580627i	0.202023	−	0.129832i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	−5.37276			−1.14548
$23$	2.85316	−	3.85480i	0.594925	−	0.803781i
$23$	2.85316	−	3.85480i	0.594925	−	0.803781i
$24$	−0.717874			−0.146535
$25$	2.98751	−	3.44777i	0.597502	−	0.689554i
$26$	−1.57655	+	1.01319i	−0.309187	+	0.198703i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	−0.674153	−	1.47619i	−0.127403	−	0.278973i
$29$	−1.43610	+	9.98827i	−0.266676	+	1.85477i	0.212637	+	0.977131i	$0.431795\pi$
$29$	−1.43610	+	9.98827i	−0.266676	+	1.85477i	−0.479314	+	0.877644i	$0.659114\pi$
$30$	−1.20859	+	0.354874i	−0.220657	+	0.0647908i
$31$	5.82310	+	3.74228i	1.04586	+	0.672133i	0.946429	−	0.322912i	$-0.104662\pi$
$31$	5.82310	+	3.74228i	1.04586	+	0.672133i	0.0994299	+	0.995045i	$0.468298\pi$
$32$	−3.05029	+	6.67920i	−0.539220	+	1.18073i
$33$	2.70841	+	0.795261i	0.471474	+	0.138437i
$34$	−6.73625	−	7.77405i	−1.15526	−	1.33324i
$35$	0.433372	+	0.500138i	0.0732533	+	0.0845388i
$36$	−1.55711	−	0.457207i	−0.259518	−	0.0762012i
$37$	1.98313	−	4.34245i	0.326025	−	0.713894i	−0.673659	−	0.739042i	$-0.735278\pi$
$37$	1.98313	−	4.34245i	0.326025	−	0.713894i	0.999684	+	0.0251479i	$0.00800566\pi$
$38$	−1.85566	−	1.19256i	−0.301028	−	0.193459i
$39$	0.944710	−	0.277392i	0.151275	−	0.0444182i
$40$	0.0676099	−	0.470237i	0.0106901	−	0.0743511i
$41$	1.03105	+	2.25768i	0.161023	+	0.352591i	0.972896	−	0.231243i	$-0.0742793\pi$
$41$	1.03105	+	2.25768i	0.161023	+	0.352591i	−0.811873	+	0.583834i	$0.801552\pi$
$42$	0.270879	+	1.88400i	0.0417975	+	0.290708i
$43$	−8.69148	+	5.58567i	−1.32544	+	0.851807i	−0.995733	−	0.0922767i	$-0.970586\pi$
$43$	−8.69148	+	5.58567i	−1.32544	+	0.851807i	−0.329705	+	0.944084i	$0.606949\pi$
$44$	2.99984	−	3.46200i	0.452242	−	0.521916i
$45$	0.661778			0.0986520
$46$	1.98873	+	8.90900i	0.293222	+	1.31356i
$47$	9.23599			1.34721			0.673604	−	0.739093i	$-0.264745\pi$
$47$	9.23599			1.34721			0.673604	+	0.739093i	$0.264745\pi$
$48$	3.02026	−	3.48557i	0.435937	−	0.503098i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	1.23576	+	8.59492i	0.174763	+	1.21550i
$51$	2.24505	+	4.91598i	0.314370	+	0.688375i
$52$	0.227396	−	1.58157i	0.0315342	−	0.219325i
$53$	−5.29835	+	1.55574i	−0.727784	+	0.213697i	−0.624577	−	0.780963i	$-0.714729\pi$
$53$	−5.29835	+	1.55574i	−0.727784	+	0.213697i	−0.103207	+	0.994660i	$0.532910\pi$
$54$	1.60122	+	1.02904i	0.217899	+	0.140035i
$55$	−0.776009	+	1.69922i	−0.104637	+	0.229123i
$56$	−0.688795	−	0.202249i	−0.0920441	−	0.0270266i
$57$	0.758921	+	0.875841i	0.100521	+	0.116008i
$58$	−12.5779	−	14.5156i	−1.65155	−	1.90600i
$59$	−12.7678	−	3.74895i	−1.66222	−	0.488072i	−0.690329	−	0.723496i	$-0.742534\pi$
$59$	−12.7678	−	3.74895i	−1.66222	−	0.488072i	−0.971893	+	0.235424i	$0.924352\pi$
$60$	0.446139	−	0.976909i	0.0575963	−	0.126118i
$61$	−4.55712	−	2.92868i	−0.583480	−	0.374980i	0.215350	−	0.976537i	$-0.430911\pi$
$61$	−4.55712	−	2.92868i	−0.583480	−	0.374980i	−0.798830	+	0.601557i	$0.794547\pi$
$62$	−12.6414	+	3.71184i	−1.60545	+	0.471404i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	−1.97401	−	4.32247i	−0.246751	−	0.540309i
$65$	0.0927297	+	0.644949i	0.0115017	+	0.0799961i
$66$	−4.51985	+	2.90473i	−0.556355	+	0.357548i
$67$	3.58274	−	4.13470i	0.437701	−	0.505134i	−0.493447	−	0.869776i	$-0.664263\pi$
$67$	3.58274	−	4.13470i	0.437701	−	0.505134i	0.931148	+	0.364642i	$0.118809\pi$
$68$	8.77043			1.06357
$69$	0.316169	−	4.78540i	0.0380622	−	0.576094i
$70$	−1.25961			−0.150552
$71$	−5.87692	+	6.78233i	−0.697462	+	0.804914i	−0.988407	−	0.151826i	$-0.951485\pi$
$71$	−5.87692	+	6.78233i	−0.697462	+	0.804914i	0.290945	+	0.956740i	$0.406030\pi$
$72$	−0.603914	+	0.388112i	−0.0711720	+	0.0457394i
$73$	0.212771	+	1.47986i	0.0249030	+	0.173204i	0.998477	−	0.0551671i	$-0.0175691\pi$
$73$	0.212771	+	1.47986i	0.0249030	+	0.173204i	−0.973574	+	0.228371i	$0.926660\pi$
$74$	3.77464	+	8.26532i	0.438793	+	0.960823i
$75$	0.649247	−	4.51562i	0.0749686	−	0.521418i
$76$	1.80454	−	0.529859i	0.206994	−	0.0607790i
$77$	2.37465	+	1.52609i	0.270616	+	0.173915i
$78$	−0.778509	+	1.70470i	−0.0881487	+	0.193019i
$79$	0.245273	+	0.0720186i	0.0275953	+	0.00810272i	0.295501	−	0.955342i	$-0.404513\pi$
$79$	0.245273	+	0.0720186i	0.0275953	+	0.00810272i	−0.267906	+	0.963445i	$0.586332\pi$
$80$	1.99874	+	2.30667i	0.223466	+	0.257894i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−4.53277	−	1.33094i	−0.500560	−	0.146978i
$83$	5.74475	−	12.5792i	0.630568	−	1.38075i	−0.277010	−	0.960867i	$-0.589344\pi$
$83$	5.74475	−	12.5792i	0.630568	−	1.38075i	0.907578	−	0.419884i	$-0.137929\pi$
$84$	−1.36522	−	0.877374i	−0.148958	−	0.0957294i
$85$	−3.43161	+	1.00761i	−0.372211	+	0.109291i
$86$	2.79861	−	19.4647i	0.301781	−	2.09894i
$87$	4.19194	+	9.17908i	0.449424	+	0.984100i
$88$	−0.288384	−	2.00575i	−0.0307418	−	0.213814i
$89$	5.53639	−	3.55802i	0.586856	−	0.377150i	−0.213259	−	0.976996i	$-0.568408\pi$
$89$	5.53639	−	3.55802i	0.586856	−	0.377150i	0.800115	+	0.599846i	$0.204772\pi$
$90$	−0.824870	+	0.951951i	−0.0869490	+	0.100344i
$91$	0.984593			0.103213
$92$	−6.85101	−	3.69281i	−0.714267	−	0.385003i
$93$	6.92193			0.717770
$94$	−11.5122	+	13.2857i	−1.18739	+	1.37032i
$95$	−0.645188	+	0.414637i	−0.0661949	+	0.0425409i
$96$	1.04498	+	7.26801i	0.106653	+	0.741789i
$97$	−0.522077	−	1.14319i	−0.0530089	−	0.116073i	0.881274	−	0.472605i	$-0.156686\pi$
$97$	−0.522077	−	1.14319i	−0.0530089	−	0.116073i	−0.934283	+	0.356532i	$0.883959\pi$
$98$	−0.270879	+	1.88400i	−0.0273629	+	0.190313i
$99$	2.70841	−	0.795261i	0.272205	−	0.0799267i
$100$	−6.22821	−	4.00263i	−0.622821	−	0.400263i
$101$	7.26581	−	15.9099i	0.722975	−	1.58309i	−0.0867131	−	0.996233i	$-0.527636\pi$
$101$	7.26581	−	15.9099i	0.722975	−	1.58309i	0.809688	−	0.586861i	$-0.199636\pi$
$102$	−9.86986	−	2.89805i	−0.977262	−	0.286950i
$103$	1.06204	+	1.22566i	0.104646	+	0.120768i	0.805656	−	0.592383i	$-0.201813\pi$
$103$	1.06204	+	1.22566i	0.104646	+	0.120768i	−0.701011	+	0.713151i	$0.747267\pi$
$104$	−0.462864	−	0.534174i	−0.0453876	−	0.0523801i
$105$	0.634971	+	0.186444i	0.0619668	+	0.0181951i
$106$	4.36622	−	9.56069i	0.424085	−	0.928616i
$107$	4.23884	+	2.72414i	0.409784	+	0.263352i	0.729252	−	0.684245i	$-0.239868\pi$
$107$	4.23884	+	2.72414i	0.409784	+	0.263352i	−0.319468	+	0.947597i	$0.603504\pi$
$108$	−1.55711	+	0.457207i	−0.149833	+	0.0439948i
$109$	−0.907844	+	6.31419i	−0.0869556	+	0.604790i	0.899021	+	0.437906i	$0.144280\pi$
$109$	−0.907844	+	6.31419i	−0.0869556	+	0.604790i	−0.985977	+	0.166884i	$0.946629\pi$
$110$	−1.47704	−	3.23426i	−0.140830	−	0.308375i
$111$	−0.679390	−	4.72526i	−0.0644849	−	0.448502i
$112$	3.87992	−	2.49347i	0.366618	−	0.235611i
$113$	10.4702	−	12.0832i	0.984952	−	1.13670i	−0.00565846	−	0.999984i	$-0.501801\pi$
$113$	10.4702	−	12.0832i	0.984952	−	1.13670i	0.990611	−	0.136712i	$-0.0436534\pi$
$114$	−2.20583			−0.206595
$115$	3.10486	+	0.657796i	0.289529	+	0.0613398i
$116$	16.3761			1.52048
$117$	0.644771	−	0.744105i	0.0596091	−	0.0687926i
$118$	21.3071	−	13.6933i	1.96148	−	1.26057i
$119$	0.769121	+	5.34936i	0.0705052	+	0.490375i
$120$	−0.197352	−	0.432142i	−0.0180157	−	0.0394490i
$121$	0.431510	−	3.00122i	0.0392282	−	0.272838i
$122$	9.89305	−	2.90486i	0.895674	−	0.262994i
$123$	2.08797	+	1.34186i	0.188266	+	0.120991i
$124$	4.66644	−	10.2181i	0.419058	−	0.917610i
$125$	6.07162	+	1.78279i	0.543063	+	0.159458i
$126$	1.24645	+	1.43848i	0.111042	+	0.128150i
$127$	−1.45507	−	1.67924i	−0.129116	−	0.149008i	0.687510	−	0.726175i	$-0.258704\pi$
$127$	−1.45507	−	1.67924i	−0.129116	−	0.149008i	−0.816626	+	0.577167i	$0.804158\pi$
$128$	−5.41238	−	1.58922i	−0.478391	−	0.140468i
$129$	−4.29189	+	9.39794i	−0.377880	+	0.827442i
$130$	−1.04333	−	0.670505i	−0.0915058	−	0.0588072i
$131$	8.73128	−	2.56374i	0.762856	−	0.223995i	0.122913	−	0.992417i	$-0.460776\pi$
$131$	8.73128	−	2.56374i	0.762856	−	0.223995i	0.639943	+	0.768423i	$0.278958\pi$
$132$	0.651927	−	4.53425i	0.0567429	−	0.394656i
$133$	0.481426	+	1.05418i	0.0417449	+	0.0914086i
$134$	1.48198	+	10.3074i	0.128023	+	0.890421i
$135$	0.556723	−	0.357784i	0.0479151	−	0.0307931i
$136$	2.54063	−	2.93205i	0.217857	−	0.251421i
$137$	−18.3118			−1.56448			−0.782242	−	0.622975i	$-0.785924\pi$
$137$	−18.3118			−1.56448			−0.782242	+	0.622975i	$0.785924\pi$
$138$	6.48959	+	6.41954i	0.552431	+	0.546468i
$139$	20.5395			1.74214			0.871070	−	0.491159i	$-0.163427\pi$
$139$	20.5395			1.74214			0.871070	+	0.491159i	$0.163427\pi$
$140$	0.703294	−	0.811645i	0.0594392	−	0.0685965i
$141$	7.76981	−	4.99335i	0.654336	−	0.420516i
$142$	−2.43095	−	16.9076i	−0.204001	−	1.41886i
$143$	1.15455	+	2.52810i	0.0965480	+	0.211411i
$144$	0.656366	−	4.56512i	0.0546971	−	0.380427i
$145$	−6.40748	+	1.88141i	−0.532112	+	0.156242i
$146$	−2.39394	−	1.53849i	−0.198124	−	0.127327i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	−7.43339	−	2.18264i	−0.611021	−	0.179412i
$149$	−10.8960	−	12.5746i	−0.892631	−	1.03015i	−0.999357	−	0.0358627i	$-0.988582\pi$
$149$	−10.8960	−	12.5746i	−0.892631	−	1.03015i	0.106726	−	0.994289i	$-0.465963\pi$
$150$	5.68635	+	6.56240i	0.464289	+	0.535818i
$151$	−12.6452	−	3.71297i	−1.02905	−	0.302157i	−0.276728	−	0.960948i	$-0.589250\pi$
$151$	−12.6452	−	3.71297i	−1.02905	−	0.302157i	−0.752326	+	0.658791i	$0.771068\pi$
$152$	0.345603	−	0.756766i	0.0280321	−	0.0613818i
$153$	4.54644	+	2.92182i	0.367558	+	0.236215i
$154$	−5.15512	+	1.51368i	−0.415412	+	0.121976i
$155$	−0.651912	+	4.53415i	−0.0523629	+	0.364192i
$156$	−0.663766	−	1.45344i	−0.0531438	−	0.116369i
$157$	1.09762	+	7.63412i	0.0875997	+	0.609269i	0.985577	+	0.169228i	$0.0541273\pi$
$157$	1.09762	+	7.63412i	0.0875997	+	0.609269i	−0.897977	+	0.440042i	$0.854964\pi$
$158$	−0.409316	+	0.263052i	−0.0325635	+	0.0209273i
$159$	−3.61616	+	4.17327i	−0.286780	+	0.330962i
$160$	−4.85927			−0.384159
$161$	1.65156	−	4.50248i	0.130161	−	0.354845i
$162$	1.90338			0.149543
$163$	10.6651	−	12.3081i	0.835351	−	0.964047i	−0.164399	−	0.986394i	$-0.552568\pi$
$163$	10.6651	−	12.3081i	0.835351	−	0.964047i	0.999750	+	0.0223469i	$0.00711384\pi$
$164$	3.38844	−	2.17762i	0.264593	−	0.170043i
$165$	0.265849	+	1.84902i	0.0206963	+	0.143946i
$166$	10.9344	+	23.9430i	0.848675	+	1.85834i
$167$	1.74679	−	12.1492i	0.135171	−	0.940132i	−0.803497	−	0.595309i	$-0.797030\pi$
$167$	1.74679	−	12.1492i	0.135171	−	0.940132i	0.938668	−	0.344823i	$-0.112061\pi$
$168$	−0.688795	+	0.202249i	−0.0531417	+	0.0156038i
$169$	−10.1208	−	6.50422i	−0.778520	−	0.500325i
$170$	2.82790	−	6.19223i	0.216890	−	0.474922i
$171$	1.11196	+	0.326501i	0.0850337	+	0.0249681i
$172$	10.9797	+	12.6713i	0.837197	+	0.966177i
$173$	−13.9634	−	16.1146i	−1.06162	−	1.22517i	−0.973409	−	0.229072i	$-0.926431\pi$
$173$	−13.9634	−	16.1146i	−1.06162	−	1.22517i	−0.0882098	−	0.996102i	$-0.528115\pi$
$174$	−18.4289	−	5.41122i	−1.39709	−	0.410223i
$175$	1.89514	−	4.14979i	0.143259	−	0.313694i
$176$	10.9520	+	7.03845i	0.825541	+	0.530543i
$177$	−12.7678	+	3.74895i	−0.959684	+	0.281789i
$178$	−1.78269	+	12.3988i	−0.133618	+	0.929333i
$179$	−1.78191	−	3.90185i	−0.133187	−	0.291638i	0.831275	−	0.555862i	$-0.187612\pi$
$179$	−1.78191	−	3.90185i	−0.133187	−	0.291638i	−0.964461	+	0.264224i	$0.914884\pi$
$180$	−0.152840	−	1.06303i	−0.0113921	−	0.0792335i
$181$	−9.84321	+	6.32585i	−0.731640	+	0.470196i	−0.852668	−	0.522453i	$-0.825017\pi$
$181$	−9.84321	+	6.32585i	−0.731640	+	0.470196i	0.121028	+	0.992649i	$0.461381\pi$
$182$	−1.22724	+	1.41631i	−0.0909692	+	0.104984i
$183$	−5.41706			−0.400441
$184$	−3.21916	+	1.22062i	−0.237319	+	0.0899855i
$185$	3.15923			0.232271
$186$	−8.62781	+	9.95703i	−0.632622	+	0.730085i
$187$	−12.8335	+	8.24757i	−0.938476	+	0.603122i
$188$	−2.13309	−	14.8360i	−0.155572	−	1.08203i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	0.207747	−	1.44491i	0.0150715	−	0.104825i
$191$	−20.9754	+	6.15894i	−1.51773	+	0.445645i	−0.931269	−	0.364334i	$-0.881297\pi$
$191$	−20.9754	+	6.15894i	−1.51773	+	0.445645i	−0.586459	+	0.809979i	$0.699479\pi$
$192$	−3.99754	−	2.56906i	−0.288498	−	0.185406i
$193$	2.17169	−	4.75533i	0.156321	−	0.342296i	−0.815225	−	0.579144i	$-0.803387\pi$
$193$	2.17169	−	4.75533i	0.156321	−	0.342296i	0.971547	+	0.236848i	$0.0761143\pi$
$194$	2.29519	+	0.673929i	0.164785	+	0.0483853i
$195$	0.426695	+	0.492432i	0.0305563	+	0.0352638i
$196$	−1.06274	−	1.22646i	−0.0759097	−	0.0876044i
$197$	−8.05447	−	2.36500i	−0.573857	−	0.168500i	−0.0180880	−	0.999836i	$-0.505758\pi$
$197$	−8.05447	−	2.36500i	−0.573857	−	0.168500i	−0.555769	+	0.831337i	$0.687576\pi$
$198$	−2.23192	+	4.88723i	−0.158616	+	0.347320i
$199$	14.8683	+	9.55528i	1.05399	+	0.677356i	0.948407	−	0.317055i	$-0.102694\pi$
$199$	14.8683	+	9.55528i	1.05399	+	0.677356i	0.105579	+	0.994411i	$0.466330\pi$
$200$	−3.14232	+	0.922668i	−0.222195	+	0.0652425i
$201$	0.778604	−	5.41531i	0.0549185	−	0.381966i
$202$	13.8296	+	30.2825i	0.973045	+	2.13067i
$203$	1.43610	+	9.98827i	0.100794	+	0.701039i
$204$	7.37815	−	4.74165i	0.516574	−	0.331982i
$205$	−1.07562	+	1.24133i	−0.0751244	+	0.0866982i
$206$	−3.08685			−0.215071
$207$	−2.32120	−	4.19667i	−0.161335	−	0.291689i
$208$	4.54101			0.314862
$209$	−2.14224	+	2.47228i	−0.148182	+	0.171011i
$210$	−1.05965	+	0.680998i	−0.0731230	+	0.0469933i
$211$	2.43615	+	16.9438i	0.167711	+	1.16646i	0.883599	+	0.468244i	$0.155113\pi$
$211$	2.43615	+	16.9438i	0.167711	+	1.16646i	−0.715888	+	0.698215i	$0.753978\pi$
$212$	3.72269	+	8.15156i	0.255675	+	0.559851i
$213$	−1.27718	+	8.88296i	−0.0875107	+	0.608650i
$214$	−9.20209	+	2.70198i	−0.629042	+	0.184703i
$215$	−5.75183	−	3.69647i	−0.392271	−	0.252097i
$216$	−0.298216	+	0.653001i	−0.0202910	+	0.0444311i
$217$	6.64154	+	1.95013i	0.450857	+	0.132384i
$218$	−7.95123	−	9.17621i	−0.538525	−	0.621491i
$219$	0.979065	+	1.12990i	0.0661591	+	0.0763516i
$220$	2.90872	+	0.854078i	0.196106	+	0.0575820i
$221$	−2.21046	+	4.84024i	−0.148692	+	0.325590i
$222$	7.64400	+	4.91250i	0.513032	+	0.329705i
$223$	−4.31741	+	1.26771i	−0.289115	+	0.0848918i	−0.423074	−	0.906095i	$-0.639049\pi$
$223$	−4.31741	+	1.26771i	−0.289115	+	0.0848918i	0.133959	+	0.990987i	$0.457231\pi$
$224$	−1.04498	+	7.26801i	−0.0698208	+	0.485615i
$225$	−1.89514	−	4.14979i	−0.126343	−	0.276652i
$226$	4.33092	+	30.1222i	0.288089	+	2.00370i
$227$	−3.22833	+	2.07472i	−0.214272	+	0.137704i	−0.643375	−	0.765552i	$-0.722466\pi$
$227$	−3.22833	+	2.07472i	−0.214272	+	0.137704i	0.429103	+	0.903256i	$0.358830\pi$
$228$	1.23161	−	1.42135i	0.0815652	−	0.0941313i
$229$	−24.5084			−1.61956			−0.809779	−	0.586734i	$-0.800413\pi$
$229$	−24.5084			−1.61956			−0.809779	+	0.586734i	$0.800413\pi$
$230$	−4.81626	+	3.64636i	−0.317575	+	0.240434i
$231$	2.82275			0.185723
$232$	4.74385	−	5.47469i	0.311449	−	0.359431i
$233$	14.3223	−	9.20437i	0.938284	−	0.602999i	0.0203764	−	0.999792i	$-0.493514\pi$
$233$	14.3223	−	9.20437i	0.938284	−	0.602999i	0.917908	+	0.396794i	$0.129877\pi$
$234$	0.266705	+	1.85498i	0.0174351	+	0.121264i
$235$	2.53909	+	5.55983i	0.165632	+	0.362683i
$236$	−3.07326	+	21.3750i	−0.200052	+	1.39139i
$237$	0.245273	−	0.0720186i	0.0159322	−	0.00467811i
$238$	−8.65359	−	5.56132i	−0.560929	−	0.360487i
$239$	−2.15492	+	4.71862i	−0.139390	+	0.305222i	−0.966434	−	0.256916i	$-0.917294\pi$
$239$	−2.15492	+	4.71862i	−0.139390	+	0.305222i	0.827044	+	0.562138i	$0.190021\pi$
$240$	2.92853	+	0.859894i	0.189036	+	0.0555059i
$241$	1.94005	+	2.23894i	0.124970	+	0.144223i	0.814786	−	0.579762i	$-0.196854\pi$
$241$	1.94005	+	2.23894i	0.124970	+	0.144223i	−0.689817	+	0.723984i	$0.742309\pi$
$242$	3.77932	+	4.36157i	0.242944	+	0.280372i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−3.65193	+	7.99660i	−0.233791	+	0.511930i
$245$	0.556723	+	0.357784i	0.0355677	+	0.0228580i
$246$	−4.53277	+	1.33094i	−0.288999	+	0.0848577i
$247$	−0.162388	+	1.12943i	−0.0103325	+	0.0718642i
$248$	−2.06423	−	4.52003i	−0.131079	−	0.287022i
$249$	−1.96806	−	13.6882i	−0.124721	−	0.867453i
$250$	−10.1325	+	6.51173i	−0.640833	+	0.411838i
$251$	−7.14810	+	8.24935i	−0.451184	+	0.520694i	−0.935083	−	0.354430i	$-0.884675\pi$
$251$	−7.14810	+	8.24935i	−0.451184	+	0.520694i	0.483898	+	0.875124i	$0.339220\pi$
$252$	−1.62284			−0.102229
$253$	13.4975	−	1.03901i	0.848581	−	0.0653217i
$254$	4.22921			0.265364
$255$	−2.34210	+	2.70293i	−0.146668	+	0.169264i
$256$	17.0274	−	10.9428i	1.06421	−	0.683927i
$257$	1.43262	+	9.96412i	0.0893647	+	0.621545i	0.984452	+	0.175654i	$0.0562040\pi$
$257$	1.43262	+	9.96412i	0.0893647	+	0.621545i	−0.895087	+	0.445891i	$0.852887\pi$
$258$	−8.16909	−	17.8878i	−0.508585	−	1.11365i
$259$	0.679390	−	4.72526i	0.0422152	−	0.293614i
$260$	1.01458	−	0.297908i	0.0629216	−	0.0184755i
$261$	8.48907	+	5.45560i	0.525460	+	0.337693i
$262$	−7.19521	+	15.7553i	−0.444521	+	0.973366i
$263$	−8.68941	−	2.55144i	−0.535812	−	0.157329i	0.00262166	−	0.999997i	$-0.499165\pi$
$263$	−8.68941	−	2.55144i	−0.535812	−	0.157329i	−0.538433	+	0.842668i	$0.680984\pi$
$264$	−1.32700	−	1.53144i	−0.0816710	−	0.0942534i
$265$	−2.39309	−	2.76178i	−0.147007	−	0.169655i
$266$	−2.11648	−	0.621454i	−0.129770	−	0.0381038i
$267$	2.73390	−	5.98640i	0.167312	−	0.366362i
$268$	−7.46912	−	4.80011i	−0.456249	−	0.293213i
$269$	7.08619	−	2.08069i	0.432053	−	0.126862i	−0.0584728	−	0.998289i	$-0.518623\pi$
$269$	7.08619	−	2.08069i	0.432053	−	0.126862i	0.490525	+	0.871427i	$0.336805\pi$
$270$	−0.179261	+	1.24679i	−0.0109095	+	0.0758773i
$271$	10.0933	+	22.1013i	0.613125	+	1.34256i	0.920416	+	0.390941i	$0.127850\pi$
$271$	10.0933	+	22.1013i	0.613125	+	1.34256i	−0.307291	+	0.951616i	$0.599423\pi$
$272$	3.54724	+	24.6716i	0.215083	+	1.49593i
$273$	0.828292	−	0.532311i	0.0501305	−	0.0322169i
$274$	22.8247	−	26.3411i	1.37889	−	1.59132i
$275$	12.8775			0.776544
$276$	−7.75992	+	0.597340i	−0.467092	+	0.0359556i
$277$	−5.31170			−0.319149			−0.159574	−	0.987186i	$-0.551012\pi$
$277$	−5.31170			−0.319149			−0.159574	+	0.987186i	$0.551012\pi$
$278$	−25.6014	+	29.5456i	−1.53547	+	1.77203i
$279$	5.82310	−	3.74228i	0.348620	−	0.224044i
$280$	−0.0676099	−	0.470237i	−0.00404047	−	0.0281021i
$281$	4.42427	+	9.68780i	0.263930	+	0.577926i	0.994479	−	0.104934i	$-0.0334632\pi$
$281$	4.42427	+	9.68780i	0.263930	+	0.577926i	−0.730549	+	0.682860i	$0.760736\pi$
$282$	−2.50183	+	17.4006i	−0.148982	+	1.03619i
$283$	−16.7492	+	4.91801i	−0.995636	+	0.292345i	−0.738664	−	0.674074i	$-0.764543\pi$
$283$	−16.7492	+	4.91801i	−0.995636	+	0.292345i	−0.256972	+	0.966419i	$0.582725\pi$
$284$	12.2519	+	7.87382i	0.727017	+	0.467225i
$285$	−0.318597	+	0.697630i	−0.0188721	+	0.0413240i
$286$	−5.07570	−	1.49036i	−0.300132	−	0.0881268i
$287$	1.62535	+	1.87575i	0.0959411	+	0.110722i
$288$	4.80848	+	5.54928i	0.283342	+	0.326995i
$289$	−11.7127	−	3.43915i	−0.688981	−	0.202303i
$290$	5.28022	−	11.5621i	0.310065	−	0.678948i
$291$	−1.05725	−	0.679455i	−0.0619773	−	0.0398304i
$292$	2.32799	−	0.683559i	0.136235	−	0.0400022i
$293$	1.57001	−	10.9196i	0.0917207	−	0.637931i	−0.891160	−	0.453689i	$-0.850108\pi$
$293$	1.57001	−	10.9196i	0.0917207	−	0.637931i	0.982881	−	0.184242i	$-0.0589832\pi$
$294$	0.790691	+	1.73137i	0.0461140	+	0.100976i
$295$	−1.25324	−	8.71650i	−0.0729666	−	0.507494i
$296$	−2.88300	+	1.85279i	−0.167571	+	0.107691i
$297$	1.84851	−	2.13329i	0.107261	−	0.123786i
$298$	31.6695			1.83456
$299$	3.76470	−	2.85022i	0.217718	−	0.164833i
$300$	−7.40349			−0.427440
$301$	−6.76575	+	7.80809i	−0.389971	+	0.450051i
$302$	21.1026	−	13.5618i	1.21432	−	0.780396i
$303$	−2.48915	−	17.3124i	−0.142998	−	0.994574i
$304$	2.22037	+	4.86193i	0.127347	+	0.278851i
$305$	0.510183	−	3.54840i	0.0292130	−	0.203181i
$306$	−9.86986	+	2.89805i	−0.564222	+	0.165671i
$307$	8.03363	+	5.16290i	0.458503	+	0.294662i	0.749431	−	0.662083i	$-0.230327\pi$
$307$	8.03363	+	5.16290i	0.458503	+	0.294662i	−0.290927	+	0.956745i	$0.593964\pi$
$308$	1.90297	−	4.16691i	0.108432	−	0.237432i
$309$	1.55608	+	0.456907i	0.0885225	+	0.0259926i
$310$	−5.70969	−	6.58934i	−0.324289	−	0.374249i
$311$	0.427128	+	0.492932i	0.0242202	+	0.0279516i	0.767730	−	0.640773i	$-0.221386\pi$
$311$	0.427128	+	0.492932i	0.0242202	+	0.0279516i	−0.743510	+	0.668725i	$0.766841\pi$
$312$	−0.678183	−	0.199132i	−0.0383945	−	0.0112737i
$313$	7.66005	−	16.7732i	0.432972	−	0.948075i	−0.559864	−	0.828585i	$-0.689147\pi$
$313$	7.66005	−	16.7732i	0.432972	−	0.948075i	0.992835	−	0.119491i	$-0.0381262\pi$
$314$	−12.3496	−	7.93662i	−0.696930	−	0.447890i
$315$	0.634971	−	0.186444i	0.0357766	−	0.0105049i
$316$	0.0590383	−	0.410620i	0.00332116	−	0.0230992i
$317$	−12.9802	−	28.4228i	−0.729043	−	1.59638i	−0.800781	−	0.598958i	$-0.795582\pi$
$317$	−12.9802	−	28.4228i	−0.729043	−	1.59638i	0.0717378	−	0.997424i	$-0.477146\pi$
$318$	−1.49580	−	10.4035i	−0.0838803	−	0.583400i
$319$	−23.9625	+	15.3998i	−1.34164	+	0.862222i
$320$	2.05934	−	2.37660i	0.115120	−	0.132856i
$321$	5.03872			0.281234
$322$	4.41812	+	7.98784i	0.246212	+	0.445145i
$323$	−6.26314			−0.348490
$324$	−1.06274	+	1.22646i	−0.0590409	+	0.0681368i
$325$	3.77871	−	2.42843i	0.209605	−	0.134705i
$326$	4.41153	+	30.6828i	0.244332	+	1.69937i
$327$	2.64998	+	5.80265i	0.146544	+	0.320887i
$328$	0.253569	−	1.76361i	0.0140010	−	0.0973790i
$329$	8.86187	−	2.60208i	0.488571	−	0.143457i
$330$	−2.99114	−	1.92229i	−0.164657	−	0.105818i
$331$	−11.4427	+	25.0561i	−0.628950	+	1.37721i	0.279878	+	0.960036i	$0.409706\pi$
$331$	−11.4427	+	25.0561i	−0.628950	+	1.37721i	−0.908827	+	0.417172i	$0.863021\pi$
$332$	−21.5331	−	6.32269i	−1.18178	−	0.347003i
$333$	−3.12621	−	3.60784i	−0.171315	−	0.197708i
$334$	15.2990	+	17.6560i	0.837125	+	0.966094i
$335$	3.47392	+	1.02004i	0.189801	+	0.0557305i
$336$	1.91592	−	4.19528i	0.104522	−	0.228872i
$337$	−24.5396	−	15.7706i	−1.33676	−	0.859081i	−0.340068	−	0.940401i	$-0.610450\pi$
$337$	−24.5396	−	15.7706i	−1.33676	−	0.859081i	−0.996688	+	0.0813196i	$0.974087\pi$
$338$	21.9712	−	6.45131i	1.19507	−	0.350905i
$339$	2.27539	−	15.8257i	0.123582	−	0.859533i
$340$	2.41110	+	5.27957i	0.130760	+	0.286325i
$341$	2.78067	+	19.3400i	0.150582	+	1.04732i
$342$	−1.85566	+	1.19256i	−0.100343	+	0.0644864i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	7.41678			0.399886
$345$	2.96760	−	1.12524i	0.159770	−	0.0605809i
$346$	40.5852			2.18187
$347$	2.24509	−	2.59097i	0.120523	−	0.139090i	−0.692282	−	0.721627i	$-0.743394\pi$
$347$	2.24509	−	2.59097i	0.120523	−	0.139090i	0.812804	+	0.582537i	$0.197940\pi$
$348$	13.7764	−	8.85357i	0.738494	−	0.474601i
$349$	−1.67906	−	11.6781i	−0.0898781	−	0.625116i	−0.984116	−	0.177524i	$-0.943191\pi$
$349$	−1.67906	−	11.6781i	−0.0898781	−	0.625116i	0.894238	−	0.447591i	$-0.147718\pi$
$350$	3.60717	+	7.89861i	0.192811	+	0.422198i
$351$	0.140122	−	0.974571i	0.00747917	−	0.0520187i
$352$	−19.8872	+	5.83940i	−1.05999	+	0.311241i
$353$	−12.4842	−	8.02312i	−0.664468	−	0.427028i	0.164459	−	0.986384i	$-0.447412\pi$
$353$	−12.4842	−	8.02312i	−0.664468	−	0.427028i	−0.828927	+	0.559356i	$0.811048\pi$
$354$	10.5216	−	23.0390i	0.559214	−	1.22451i
$355$	−5.69842	−	1.67321i	−0.302441	−	0.0888046i
$356$	−6.99399	−	8.07149i	−0.370681	−	0.427788i
$357$	3.53911	+	4.08435i	0.187309	+	0.216167i
$358$	7.83378	+	2.30020i	0.414028	+	0.121570i
$359$	−5.30076	+	11.6070i	−0.279763	+	0.612596i	−0.996393	−	0.0848575i	$-0.972957\pi$
$359$	−5.30076	+	11.6070i	−0.279763	+	0.612596i	0.716630	+	0.697454i	$0.245684\pi$
$360$	−0.399657	−	0.256844i	−0.0210638	−	0.0135369i
$361$	16.9417	−	4.97454i	0.891669	−	0.261818i
$362$	3.16946	−	22.0440i	0.166583	−	1.15861i
$363$	−1.25957	−	2.75808i	−0.0661103	−	0.144761i
$364$	−0.227396	−	1.58157i	−0.0119188	−	0.0828970i
$365$	−0.832341	+	0.534913i	−0.0435667	+	0.0279986i
$366$	6.75208	−	7.79231i	0.352937	−	0.407311i
$367$	2.05489			0.107265			0.0536323	−	0.998561i	$-0.482920\pi$
$367$	2.05489			0.107265			0.0536323	+	0.998561i	$0.482920\pi$
$368$	7.61713	−	20.7657i	0.397070	−	1.08249i
$369$	2.48197			0.129206
$370$	−3.93781	+	4.54447i	−0.204717	+	0.236256i
$371$	−4.64543	+	2.98543i	−0.241178	+	0.154996i
$372$	−1.59865	−	11.1189i	−0.0828861	−	0.576486i
$373$	1.66467	+	3.64512i	0.0861934	+	0.188737i	0.947820	−	0.318805i	$-0.103281\pi$
$373$	1.66467	+	3.64512i	0.0861934	+	0.188737i	−0.861627	+	0.507542i	$0.830554\pi$
$374$	4.13230	−	28.7408i	0.213676	−	1.48615i
$375$	6.07162	−	1.78279i	0.313537	−	0.0920629i
$376$	−5.57774	−	3.58460i	−0.287650	−	0.184862i
$377$	−4.12736	+	9.03765i	−0.212570	+	0.465463i
$378$	1.82628	+	0.536243i	0.0939335	+	0.0275814i
$379$	−15.0898	−	17.4146i	−0.775113	−	0.894528i	0.221633	−	0.975130i	$-0.428861\pi$
$379$	−15.0898	−	17.4146i	−0.775113	−	0.894528i	−0.996746	+	0.0806018i	$0.974316\pi$
$380$	0.815050	+	0.940618i	0.0418112	+	0.0482527i
$381$	−2.13195	−	0.625996i	−0.109223	−	0.0320707i
$382$	17.2853	−	37.8494i	0.884390	−	1.93654i
$383$	−2.32130	−	1.49181i	−0.118613	−	0.0762280i	0.479989	−	0.877274i	$-0.340641\pi$
$383$	−2.32130	−	1.49181i	−0.118613	−	0.0762280i	−0.598602	+	0.801046i	$0.704277\pi$
$384$	−5.41238	+	1.58922i	−0.276199	+	0.0810995i
$385$	−0.265849	+	1.84902i	−0.0135489	+	0.0942347i
$386$	4.13354	+	9.05118i	0.210391	+	0.460693i
$387$	1.47034	+	10.2264i	0.0747414	+	0.519838i
$388$	−1.71575	+	1.10265i	−0.0871043	+	0.0559785i
$389$	−1.94224	+	2.24147i	−0.0984757	+	0.113647i	−0.802848	−	0.596184i	$-0.796683\pi$
$389$	−1.94224	+	2.24147i	−0.0984757	+	0.113647i	0.704372	+	0.709831i	$0.251229\pi$
$390$	−1.24020			−0.0628002
$391$	18.4263	+	18.2274i	0.931856	+	0.921798i
$392$	−0.717874			−0.0362581
$393$	5.95916	−	6.87724i	0.300600	−	0.346911i
$394$	13.4415	−	8.63830i	0.677171	−	0.435191i
$395$	0.0240752	+	0.167447i	0.00121135	+	0.00842515i
$396$	−1.90297	−	4.16691i	−0.0956276	−	0.209395i
$397$	5.10998	−	35.5407i	0.256462	−	1.78374i	−0.301092	−	0.953595i	$-0.597351\pi$
$397$	5.10998	−	35.5407i	0.256462	−	1.78374i	0.557555	−	0.830140i	$-0.311740\pi$
$398$	−32.2776	+	9.47756i	−1.61793	+	0.475067i
$399$	0.974932	+	0.626551i	0.0488076	+	0.0313668i
$400$	8.74053	−	19.1391i	0.437027	−	0.956955i
$401$	19.2901	+	5.66408i	0.963300	+	0.282850i	0.725314	−	0.688418i	$-0.241695\pi$
$401$	19.2901	+	5.66408i	0.963300	+	0.282850i	0.237986	+	0.971269i	$0.423513\pi$
$402$	6.81930	+	7.86989i	0.340116	+	0.392515i
$403$	4.46306	+	5.15064i	0.222321	+	0.256572i
$404$	−27.2345	−	7.99677i	−1.35497	−	0.397854i
$405$	0.274912	−	0.601974i	0.0136605	−	0.0299123i
$406$	−16.1579	−	10.3841i	−0.801903	−	0.515352i
$407$	12.9295	−	3.79646i	0.640894	−	0.188183i
$408$	0.552132	−	3.84016i	0.0273346	−	0.190116i
$409$	7.13761	+	15.6292i	0.352932	+	0.772814i	0.999947	+	0.0103359i	$0.00329007\pi$
$409$	7.13761	+	15.6292i	0.352932	+	0.772814i	−0.647014	+	0.762478i	$0.723983\pi$
$410$	−0.444922	−	3.09450i	−0.0219731	−	0.152826i
$411$	−15.4049	+	9.90012i	−0.759867	+	0.488337i
$412$	1.72352	−	1.98905i	0.0849117	−	0.0979933i
$413$	−13.3068			−0.654784
$414$	8.93006	+	1.89193i	0.438889	+	0.0929830i
$415$	9.15168			0.449238
$416$	−4.73439	+	5.46378i	−0.232123	+	0.267884i
$417$	17.2789	−	11.1045i	0.846154	−	0.543790i
$418$	−0.886125	−	6.16313i	−0.0433418	−	0.301449i
$419$	8.21229	+	17.9824i	0.401197	+	0.878498i	0.997148	+	0.0754770i	$0.0240480\pi$
$419$	8.21229	+	17.9824i	0.401197	+	0.878498i	−0.595951	+	0.803021i	$0.703225\pi$
$420$	0.152840	−	1.06303i	0.00745785	−	0.0518705i
$421$	−8.00014	+	2.34905i	−0.389903	+	0.114486i	−0.470807	−	0.882236i	$-0.656037\pi$
$421$	−8.00014	+	2.34905i	−0.389903	+	0.114486i	0.0809045	+	0.996722i	$0.474219\pi$
$422$	−27.4098	−	17.6152i	−1.33429	−	0.857494i
$423$	3.83677	−	8.40135i	0.186550	−	0.408488i
$424$	3.80355	+	1.11682i	0.184717	+	0.0542377i
$425$	16.1456	+	18.6330i	0.783176	+	0.903833i
$426$	−11.1860	−	12.9093i	−0.541963	−	0.625458i
$427$	−5.19763	−	1.52616i	−0.251531	−	0.0738562i
$428$	3.39687	−	7.43810i	0.164194	−	0.359534i
$429$	2.33806	+	1.50258i	0.112883	+	0.0725453i
$430$	12.4866	−	3.66641i	0.602159	−	0.176810i
$431$	−1.24469	+	8.65703i	−0.0599548	+	0.416994i	0.937636	+	0.347619i	$0.113010\pi$
$431$	−1.24469	+	8.65703i	−0.0599548	+	0.416994i	−0.997591	+	0.0693754i	$0.977899\pi$
$432$	−1.91592	−	4.19528i	−0.0921799	−	0.201846i
$433$	4.31116	+	29.9848i	0.207181	+	1.44098i	0.782298	+	0.622905i	$0.214048\pi$
$433$	4.31116	+	29.9848i	0.207181	+	1.44098i	−0.575117	+	0.818071i	$0.695043\pi$
$434$	−11.0835	+	7.12296i	−0.532027	+	0.341913i
$435$	−4.37315	+	5.04688i	−0.209676	+	0.241980i
$436$	10.3523			0.495785
$437$	4.89244	+	2.63711i	0.234037	+	0.126150i
$438$	−2.84569			−0.135972
$439$	−4.33169	+	4.99904i	−0.206740	+	0.238591i	−0.849645	−	0.527355i	$-0.823184\pi$
$439$	−4.33169	+	4.99904i	−0.206740	+	0.238591i	0.642905	+	0.765946i	$0.277729\pi$
$440$	1.12813	−	0.725006i	0.0537816	−	0.0345633i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−4.20734	−	9.21280i	−0.200123	−	0.438208i
$443$	0.993335	−	6.90880i	0.0471948	−	0.328247i	−0.952522	−	0.304468i	$-0.901521\pi$
$443$	0.993335	−	6.90880i	0.0471948	−	0.328247i	0.999717	−	0.0237786i	$-0.00756968\pi$
$444$	−7.43339	+	2.18264i	−0.352773	+	0.103584i
$445$	3.66386	+	2.35462i	0.173684	+	0.111620i
$446$	3.55785	−	7.79061i	0.168469	−	0.368896i
$447$	−15.9646	−	4.68763i	−0.755100	−	0.221717i
$448$	−3.11182	−	3.59124i	−0.147020	−	0.169670i
$449$	5.99609	+	6.91986i	0.282973	+	0.326568i	0.879386	−	0.476110i	$-0.157953\pi$
$449$	5.99609	+	6.91986i	0.282973	+	0.326568i	−0.596413	+	0.802678i	$0.703408\pi$
$450$	8.33156	+	2.44637i	0.392754	+	0.115323i
$451$	−2.91039	+	6.37287i	−0.137045	+	0.300087i
$452$	−21.8277	−	14.0278i	−1.02669	−	0.659814i
$453$	−12.6452	+	3.71297i	−0.594124	+	0.174451i
$454$	1.03950	−	7.22991i	0.0487863	−	0.339316i
$455$	0.270677	+	0.592699i	0.0126895	+	0.0277862i
$456$	−0.118398	−	0.823479i	−0.00554451	−	0.0385629i
$457$	14.1965	−	9.12357i	0.664087	−	0.426782i	−0.164703	−	0.986343i	$-0.552667\pi$
$457$	14.1965	−	9.12357i	0.664087	−	0.426782i	0.828789	+	0.559561i	$0.189030\pi$
$458$	30.5484	−	35.2547i	1.42743	−	1.64734i
$459$	5.40436			0.252254
$460$	0.339553	−	5.13933i	0.0158317	−	0.239622i
$461$	−11.4136			−0.531584			−0.265792	−	0.964030i	$-0.585633\pi$
$461$	−11.4136			−0.531584			−0.265792	+	0.964030i	$0.585633\pi$
$462$	−3.51841	+	4.06046i	−0.163691	+	0.188910i
$463$	0.671972	−	0.431850i	0.0312292	−	0.0200698i	−0.524933	−	0.851143i	$-0.675910\pi$
$463$	0.671972	−	0.431850i	0.0312292	−	0.0200698i	0.556162	+	0.831074i	$0.312273\pi$
$464$	6.62337	+	46.0666i	0.307482	+	2.13859i
$465$	1.90292	+	4.16682i	0.0882460	+	0.193232i
$466$	−4.61169	+	32.0750i	−0.213633	+	1.48585i
$467$	26.0910	−	7.66100i	1.20735	−	0.354509i	0.384689	−	0.923046i	$-0.374309\pi$
$467$	26.0910	−	7.66100i	1.20735	−	0.354509i	0.822657	+	0.568538i	$0.192491\pi$
$468$	−1.34419	−	0.863856i	−0.0621351	−	0.0399318i
$469$	2.27273	−	4.97659i	0.104945	−	0.229798i
$470$	−11.1625	−	3.27761i	−0.514888	−	0.151185i
$471$	5.05070	+	5.82881i	0.232724	+	0.268578i
$472$	6.25562	+	7.21937i	0.287938	+	0.332298i
$473$	−27.9822	−	8.21630i	−1.28662	−	0.377786i
$474$	−0.202122	+	0.442586i	−0.00928379	+	0.0203287i
$475$	4.44769	+	2.85836i	0.204074	+	0.131150i
$476$	8.41516	−	2.47091i	0.385708	−	0.113254i
$477$	−0.785867	+	5.46582i	−0.0359824	+	0.250263i
$478$	−4.10163	−	8.98131i	−0.187604	−	0.410795i
$479$	−2.29677	−	15.9744i	−0.104942	−	0.729890i	−0.972559	−	0.232656i	$-0.925258\pi$
$479$	−2.29677	−	15.9744i	−0.104942	−	0.729890i	0.867617	−	0.497234i	$-0.165651\pi$
$480$	−4.08788	+	2.62712i	−0.186585	+	0.119911i
$481$	3.07804	−	3.55225i	0.140347	−	0.161969i
$482$	−5.63883			−0.256842
$483$	−1.04484	−	4.68063i	−0.0475419	−	0.212976i
$484$	−4.92058			−0.223663
$485$	0.544645	−	0.628553i	0.0247310	−	0.0285411i
$486$	1.60122	−	1.02904i	0.0726329	−	0.0466783i
$487$	−0.267494	−	1.86046i	−0.0121213	−	0.0843055i	0.982863	−	0.184338i	$-0.0590143\pi$
$487$	−0.267494	−	1.86046i	−0.0121213	−	0.0843055i	−0.994984	+	0.100033i	$0.968105\pi$
$488$	1.61545	+	3.53735i	0.0731281	+	0.160128i
$489$	2.31774	−	16.1202i	0.104812	−	0.728982i
$490$	−1.20859	+	0.354874i	−0.0545985	+	0.0160316i
$491$	3.70921	+	2.38376i	0.167394	+	0.107578i	0.621656	−	0.783291i	$-0.286460\pi$
$491$	3.70921	+	2.38376i	0.167394	+	0.107578i	−0.454261	+	0.890868i	$0.650097\pi$
$492$	1.67323	−	3.66386i	0.0754350	−	0.165180i
$493$	−52.3263	−	15.3644i	−2.35666	−	0.691977i
$494$	−1.42226	−	1.64137i	−0.0639903	−	0.0738487i
$495$	1.22330	+	1.41177i	0.0549833	+	0.0634541i
$496$	30.6312	+	8.99414i	1.37538	+	0.403849i
$497$	−3.72806	+	8.16331i	−0.167226	+	0.366175i
$498$	22.1432	+	14.2306i	0.992260	+	0.637687i
$499$	−26.8209	+	7.87531i	−1.20067	+	0.352547i	−0.820108	−	0.572209i	$-0.806087\pi$
$499$	−26.8209	+	7.87531i	−1.20067	+	0.352547i	−0.380559	+	0.924757i	$0.624268\pi$
$500$	1.46147	−	10.1647i	0.0653588	−	0.454581i
$501$	−5.09885	−	11.1649i	−0.227800	−	0.498812i
$502$	−2.95676	−	20.5647i	−0.131967	−	0.917850i
$503$	7.31551	−	4.70139i	0.326182	−	0.209625i	−0.367293	−	0.930105i	$-0.619715\pi$
$503$	7.31551	−	4.70139i	0.326182	−	0.209625i	0.693475	+	0.720481i	$0.256079\pi$
$504$	−0.470108	+	0.542533i	−0.0209403	+	0.0241663i
$505$	11.5748			0.515072
$506$	−15.3293	+	20.7109i	−0.681472	+	0.920712i
$507$	−12.0306			−0.534297
$508$	−2.36135	+	2.72514i	−0.104768	+	0.120908i
$509$	11.0840	−	7.12327i	0.491291	−	0.315734i	−0.271433	−	0.962457i	$-0.587498\pi$
$509$	11.0840	−	7.12327i	0.491291	−	0.315734i	0.762724	+	0.646724i	$0.223861\pi$
$510$	−0.968794	−	6.73811i	−0.0428989	−	0.298369i
$511$	0.621076	+	1.35997i	0.0274748	+	0.0601614i
$512$	−3.87716	+	26.9662i	−0.171348	+	1.19175i
$513$	1.11196	−	0.326501i	0.0490942	−	0.0144154i
$514$	−16.1188	−	10.3590i	−0.710972	−	0.456914i
$515$	−0.445846	+	0.976268i	−0.0196463	+	0.0430195i
$516$	16.0874	+	4.72367i	0.708206	+	0.207948i
$517$	17.0728	+	19.7031i	0.750861	+	0.866540i
$518$	5.95035	+	6.86707i	0.261443	+	0.301722i
$519$	−20.4590	−	6.00731i	−0.898051	−	0.263692i
$520$	0.194312	−	0.425483i	0.00852113	−	0.0186587i
$521$	16.6050	+	10.6714i	0.727479	+	0.467522i	0.851231	−	0.524791i	$-0.175856\pi$
$521$	16.6050	+	10.6714i	0.727479	+	0.467522i	−0.123752	+	0.992313i	$0.539493\pi$
$522$	−18.4289	+	5.41122i	−0.806612	+	0.236843i
$523$	−3.83542	+	26.6759i	−0.167711	+	1.16646i	0.715888	+	0.698215i	$0.246022\pi$
$523$	−3.83542	+	26.6759i	−0.167711	+	1.16646i	−0.883600	+	0.468243i	$0.844887\pi$
$524$	−6.13472	−	13.4332i	−0.267996	−	0.586830i
$525$	−0.649247	−	4.51562i	−0.0283355	−	0.197078i
$526$	14.5011	−	9.31927i	0.632277	−	0.406339i
$527$	−24.4974	+	28.2715i	−1.06713	+	1.23153i
$528$	13.0187			0.566567
$529$	−6.71896	−	21.9967i	−0.292129	−	0.956379i
$530$	6.95561			0.302132
$531$	−8.71409	+	10.0566i	−0.378159	+	0.436419i
$532$	1.58216	−	1.01679i	0.0685953	−	0.0440835i
$533$	0.347779	+	2.41886i	0.0150640	+	0.104772i
$534$	5.20363	+	11.3944i	0.225183	+	0.493083i
$535$	−0.474550	+	3.30057i	−0.0205166	+	0.142696i
$536$	−3.76839	+	1.10650i	−0.162770	+	0.0477935i
$537$	−3.60854	−	2.31907i	−0.155720	−	0.100075i
$538$	−5.83953	+	12.7868i	−0.251760	+	0.551277i
$539$	2.70841	+	0.795261i	0.116659	+	0.0342543i
$540$	−0.703294	−	0.811645i	−0.0302650	−	0.0349276i
$541$	−12.3155	−	14.2128i	−0.529485	−	0.611058i	0.426495	−	0.904490i	$-0.359748\pi$
$541$	−12.3155	−	14.2128i	−0.529485	−	0.611058i	−0.955980	+	0.293432i	$0.905203\pi$
$542$	−44.3729	−	13.0291i	−1.90598	−	0.559646i
$543$	−4.86062	+	10.6433i	−0.208589	+	0.456747i
$544$	−33.3834	−	21.4542i	−1.43130	−	0.919841i
$545$	−4.05056	+	1.18935i	−0.173507	+	0.0509462i
$546$	−0.266705	+	1.85498i	−0.0114139	+	0.0793856i
$547$	5.61605	+	12.2974i	0.240125	+	0.525800i	0.990875	−	0.134787i	$-0.0430349\pi$
$547$	5.61605	+	12.2974i	0.240125	+	0.525800i	−0.750750	+	0.660587i	$0.770308\pi$
$548$	4.22920	+	29.4147i	0.180662	+	1.25653i
$549$	−4.55712	+	2.92868i	−0.194493	+	0.124993i
$550$	−16.0512	+	18.5240i	−0.684423	+	0.789867i
$551$	−11.6945			−0.498201
$552$	−2.04821	+	2.76726i	−0.0871776	+	0.117782i
$553$	0.255627			0.0108704
$554$	6.62074	−	7.64075i	0.281288	−	0.324624i
$555$	2.65771	−	1.70801i	0.112814	−	0.0725009i
$556$	−4.74370	−	32.9931i	−0.201177	−	1.39922i
$557$	−5.45573	−	11.9464i	−0.231167	−	0.506184i	0.758130	−	0.652104i	$-0.226113\pi$
$557$	−5.45573	−	11.9464i	−0.231167	−	0.506184i	−0.989296	+	0.145919i	$0.953386\pi$
$558$	−1.87500	+	13.0409i	−0.0793752	+	0.552067i
$559$	−9.76034	+	2.86590i	−0.412819	+	0.121214i
$560$	2.56764	+	1.65012i	0.108503	+	0.0697305i
$561$	−6.33723	+	13.8766i	−0.267558	+	0.585870i
$562$	−19.4503	−	5.71112i	−0.820461	−	0.240909i
$563$	11.3323	+	13.0782i	0.477600	+	0.551180i	0.942510	−	0.334178i	$-0.108459\pi$
$563$	11.3323	+	13.0782i	0.477600	+	0.551180i	−0.464910	+	0.885358i	$0.653913\pi$
$564$	−9.81541	−	11.3276i	−0.413303	−	0.476978i
$565$	10.1522	+	2.98095i	0.427105	+	0.125409i
$566$	13.8025	−	30.2233i	0.580164	−	1.27038i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	6.18146	−	1.81504i	0.259368	−	0.0761574i
$569$	2.03684	−	14.1665i	0.0853887	−	0.593892i	−0.901535	−	0.432706i	$-0.857559\pi$
$569$	2.03684	−	14.1665i	0.0853887	−	0.593892i	0.986924	−	0.161186i	$-0.0515319\pi$
$570$	−0.606410	−	1.32785i	−0.0253997	−	0.0556176i
$571$	6.26959	+	43.6060i	0.262374	+	1.82485i	0.514885	+	0.857259i	$0.327835\pi$
$571$	6.26959	+	43.6060i	0.262374	+	1.82485i	−0.252511	+	0.967594i	$0.581256\pi$
$572$	3.79430	−	2.43845i	0.158648	−	0.101957i
$573$	−14.3159	+	16.5214i	−0.598054	+	0.690191i
$574$	−4.72413			−0.197181
$575$	−4.76662	−	21.3533i	−0.198782	−	0.890493i
$576$	−4.75189			−0.197995
$577$	14.3249	−	16.5318i	0.596352	−	0.688227i	−0.374686	−	0.927152i	$-0.622249\pi$
$577$	14.3249	−	16.5318i	0.596352	−	0.688227i	0.971038	+	0.238925i	$0.0767949\pi$
$578$	19.5464	−	12.5617i	0.813021	−	0.522497i
$579$	−0.743986	−	5.17454i	−0.0309190	−	0.215047i
$580$	4.50198	+	9.85796i	0.186935	+	0.409330i
$581$	1.96806	−	13.6882i	0.0816490	−	0.567881i
$582$	2.29519	−	0.673929i	0.0951387	−	0.0279352i
$583$	−13.1129	−	8.42714i	−0.543080	−	0.349016i
$584$	0.445854	−	0.976285i	0.0184496	−	0.0403990i
$585$	0.625188	+	0.183572i	0.0258483	+	0.00758975i
$586$	13.7507	+	15.8691i	0.568036	+	0.655548i
$587$	6.63755	+	7.66014i	0.273961	+	0.316168i	0.876012	−	0.482290i	$-0.160195\pi$
$587$	6.63755	+	7.66014i	0.273961	+	0.316168i	−0.602051	+	0.798458i	$0.705649\pi$
$588$	−1.55711	−	0.457207i	−0.0642139	−	0.0188549i
$589$	−3.33240	+	7.29693i	−0.137309	+	0.300665i
$590$	14.1006	+	9.06189i	0.580511	+	0.373072i
$591$	−8.05447	+	2.36500i	−0.331316	+	0.0972833i
$592$	3.13339	−	21.7932i	0.128782	−	0.895696i
$593$	−11.7298	−	25.6846i	−0.481683	−	1.05474i	−0.981997	−	0.188895i	$-0.939509\pi$
$593$	−11.7298	−	25.6846i	−0.481683	−	1.05474i	0.500314	−	0.865844i	$-0.333218\pi$
$594$	0.764623	+	5.31807i	0.0313729	+	0.218203i
$595$	−3.00873	+	1.93359i	−0.123346	+	0.0792697i
$596$	−17.6824	+	20.4066i	−0.724299	+	0.835886i
$597$	17.6740			0.723348
$598$	−0.592516	+	8.96808i	−0.0242298	+	0.366732i
$599$	21.3613			0.872800			0.436400	−	0.899753i	$-0.356253\pi$
$599$	21.3613			0.872800			0.436400	+	0.899753i	$0.356253\pi$
$600$	−2.14465	+	2.47506i	−0.0875552	+	0.101044i
$601$	−4.19924	+	2.69868i	−0.171290	+	0.110082i	−0.623477	−	0.781842i	$-0.714280\pi$
$601$	−4.19924	+	2.69868i	−0.171290	+	0.110082i	0.452187	+	0.891923i	$0.350644\pi$
$602$	−2.79861	−	19.4647i	−0.114063	−	0.793323i
$603$	−2.27273	−	4.97659i	−0.0925528	−	0.202662i
$604$	−3.04376	+	21.1698i	−0.123849	+	0.861389i
$605$	1.92528	−	0.565314i	0.0782738	−	0.0229833i
$606$	28.0061	+	17.9985i	1.13767	+	0.731137i
$607$	18.2665	−	39.9980i	0.741414	−	1.62347i	−0.0398016	−	0.999208i	$-0.512673\pi$
$607$	18.2665	−	39.9980i	0.741414	−	1.62347i	0.781215	−	0.624262i	$-0.214600\pi$
$608$	−8.16485	−	2.39742i	−0.331128	−	0.0972280i
$609$	6.60819	+	7.62625i	0.267777	+	0.309031i
$610$	4.46837	+	5.15678i	0.180919	+	0.208792i
$611$	8.72533	+	2.56199i	0.352989	+	0.103647i
$612$	3.64337	−	7.97786i	0.147274	−	0.322486i
$613$	−37.2544	−	23.9419i	−1.50469	−	0.967005i	−0.994249	−	0.107092i	$-0.965846\pi$
$613$	−37.2544	−	23.9419i	−1.50469	−	0.967005i	−0.510440	−	0.859913i	$-0.670518\pi$
$614$	−17.4402	+	5.12090i	−0.703829	+	0.206663i
$615$	−0.233754	+	1.62579i	−0.00942587	+	0.0655584i
$616$	−0.841789	−	1.84326i	−0.0339166	−	0.0742671i
$617$	5.27903	+	36.7164i	0.212526	+	1.47815i	0.764682	+	0.644408i	$0.222896\pi$
$617$	5.27903	+	36.7164i	0.212526	+	1.47815i	−0.552157	+	0.833740i	$0.686195\pi$
$618$	−2.59683	+	1.66888i	−0.104460	+	0.0671321i
$619$	24.0831	−	27.7934i	0.967983	−	1.11711i	−0.0250986	−	0.999685i	$-0.507990\pi$
$619$	24.0831	−	27.7934i	0.967983	−	1.11711i	0.993082	−	0.117427i	$-0.0374646\pi$
$620$	7.43388			0.298552
$621$	−4.22161	−	2.27552i	−0.169407	−	0.0913136i
$622$	−1.24146			−0.0497782
$623$	4.30972	−	4.97368i	0.172665	−	0.199266i
$624$	3.82014	−	2.45505i	0.152928	−	0.0982808i
$625$	−2.65027	−	18.4330i	−0.106011	−	0.737320i
$626$	14.5800	+	31.9257i	0.582732	+	1.27601i
$627$	−0.465554	+	3.23800i	−0.0185924	+	0.129313i
$628$	12.0094	−	3.52627i	0.479226	−	0.140713i
$629$	21.7040	+	13.9483i	0.865397	+	0.556157i
$630$	−0.523262	+	1.14578i	−0.0208472	+	0.0456491i
$631$	−16.6899	−	4.90061i	−0.664416	−	0.195090i	−0.0679011	−	0.997692i	$-0.521630\pi$
$631$	−16.6899	−	4.90061i	−0.664416	−	0.195090i	−0.596515	+	0.802602i	$0.703448\pi$
$632$	−0.120172	−	0.138686i	−0.00478020	−	0.00551665i
$633$	11.2099	+	12.9369i	0.445554	+	0.514197i
$634$	57.0646	+	16.7557i	2.26633	+	0.665453i
$635$	0.610842	−	1.33756i	0.0242405	−	0.0530793i
$636$	7.53879	+	4.84489i	0.298932	+	0.192112i
$637$	0.944710	−	0.277392i	0.0374308	−	0.0109907i
$638$	7.71580	−	53.6645i	0.305471	−	2.12460i
$639$	3.72806	+	8.16331i	0.147480	+	0.322936i
$640$	−0.531262	−	3.69501i	−0.0210000	−	0.146058i
$641$	8.64338	−	5.55476i	0.341393	−	0.219400i	−0.358698	−	0.933454i	$-0.616779\pi$
$641$	8.64338	−	5.55476i	0.341393	−	0.219400i	0.700091	+	0.714054i	$0.253143\pi$
$642$	−6.28049	+	7.24807i	−0.247871	+	0.286059i
$643$	−13.6236			−0.537263			−0.268632	−	0.963243i	$-0.586571\pi$
$643$	−13.6236			−0.537263			−0.268632	+	0.963243i	$0.586571\pi$
$644$	−7.61388	−	1.61308i	−0.300029	−	0.0635642i
$645$	−6.83721			−0.269215
$646$	7.80667	−	9.00937i	0.307149	−	0.354469i
$647$	−16.6846	+	10.7226i	−0.655941	+	0.421548i	−0.825833	−	0.563915i	$-0.809295\pi$
$647$	−16.6846	+	10.7226i	−0.655941	+	0.421548i	0.169892	+	0.985463i	$0.445658\pi$
$648$	0.102164	+	0.710567i	0.00401339	+	0.0279137i
$649$	−15.6037	−	34.1674i	−0.612499	−	1.34119i
$650$	−1.21672	+	8.46249i	−0.0477238	+	0.331926i
$651$	6.64154	−	1.95013i	0.260303	−	0.0764317i
$652$	−22.2340	−	14.2889i	−0.870750	−	0.559597i
$653$	−6.52923	+	14.2970i	−0.255508	+	0.559486i	−0.993303	−	0.115540i	$-0.963140\pi$
$653$	−6.52923	+	14.2970i	−0.255508	+	0.559486i	0.737794	+	0.675026i	$0.235867\pi$
$654$	−11.6500	−	3.42076i	−0.455552	−	0.133762i
$655$	3.94364	+	4.55120i	0.154091	+	0.177830i
$656$	7.49621	+	8.65108i	0.292678	+	0.337768i
$657$	1.43451	+	0.421211i	0.0559657	+	0.0164330i
$658$	−7.30281	+	15.9909i	−0.284693	+	0.623391i
$659$	27.9735	+	17.9775i	1.08969	+	0.700303i	0.956777	−	0.290824i	$-0.0939293\pi$
$659$	27.9735	+	17.9775i	1.08969	+	0.700303i	0.132917	+	0.991127i	$0.457566\pi$
$660$	2.90872	−	0.854078i	0.113222	−	0.0332450i
$661$	0.686517	−	4.77483i	0.0267024	−	0.185719i	−0.972105	−	0.234547i	$-0.924639\pi$
$661$	0.686517	−	4.77483i	0.0267024	−	0.185719i	0.998807	+	0.0488275i	$0.0155485\pi$
$662$	−21.7798	−	47.6912i	−0.846497	−	1.85357i
$663$	0.757271	+	5.26694i	0.0294100	+	0.204551i
$664$	−8.35149	+	5.36718i	−0.324101	+	0.208287i
$665$	−0.502237	+	0.579612i	−0.0194759	+	0.0224764i
$666$	9.08644			0.352092
$667$	34.4054	+	34.0340i	1.33218	+	1.31780i
$668$	−19.9189			−0.770687
$669$	−2.94666	+	3.40063i	−0.113924	+	0.131476i
$670$	−5.79735	+	3.72573i	−0.223971	+	0.143938i
$671$	−2.17614	−	15.1354i	−0.0840089	−	0.584294i
$672$	3.05029	+	6.67920i	0.117667	+	0.257656i
$673$	−3.54088	+	24.6274i	−0.136491	+	0.949316i	0.800343	+	0.599542i	$0.204651\pi$
$673$	−3.54088	+	24.6274i	−0.136491	+	0.949316i	−0.936834	+	0.349774i	$0.886258\pi$
$674$	53.2730	−	15.6424i	2.05200	−	0.602521i
$675$	−3.83784	−	2.46643i	−0.147719	−	0.0949330i
$676$	−8.11045	+	17.7594i	−0.311940	+	0.683054i
$677$	5.84013	+	1.71482i	0.224454	+	0.0659057i	0.392026	−	0.919954i	$-0.371774\pi$
$677$	5.84013	+	1.71482i	0.224454	+	0.0659057i	−0.167572	+	0.985860i	$0.553593\pi$
$678$	19.9287	+	22.9990i	0.765357	+	0.883270i
$679$	−0.823002	−	0.949795i	−0.0315839	−	0.0364498i
$680$	2.46347	+	0.723339i	0.0944696	+	0.0277388i
$681$	−1.59417	+	3.49074i	−0.0610885	+	0.133765i
$682$	−31.2861	−	20.1063i	−1.19801	−	0.769912i
$683$	−13.9742	+	4.10320i	−0.534709	+	0.157005i	−0.537929	−	0.842990i	$-0.680793\pi$
$683$	−13.9742	+	4.10320i	−0.534709	+	0.157005i	0.00322015	+	0.999995i	$0.498975\pi$
$684$	0.267654	−	1.86157i	0.0102340	−	0.0711791i
$685$	−5.03414	−	11.0232i	−0.192345	−	0.421176i
$686$	0.270879	+	1.88400i	0.0103422	+	0.0719316i
$687$	−20.6178	+	13.2502i	−0.786616	+	0.505528i
$688$	−31.2041	+	36.0114i	−1.18964	+	1.37292i
$689$	−5.43695			−0.207131
$690$	−2.08033	+	5.67138i	−0.0791968	+	0.215906i
$691$	47.7010			1.81463			0.907317	−	0.420448i	$-0.138127\pi$
$691$	47.7010			1.81463			0.907317	+	0.420448i	$0.138127\pi$
$692$	−22.6604	+	26.1515i	−0.861420	+	0.994132i
$693$	2.37465	−	1.52609i	0.0902055	−	0.0579715i
$694$	0.928665	+	6.45901i	0.0352516	+	0.245181i
$695$	5.64657	+	12.3643i	0.214187	+	0.469003i
$696$	1.03094	−	7.17032i	0.0390775	−	0.271790i
$697$	−12.8701	+	3.77901i	−0.487491	+	0.143140i
$698$	18.8916	+	12.1409i	0.715056	+	0.459539i
$699$	7.07241	−	15.4864i	0.267503	−	0.585750i
$700$	−7.10359	−	2.08580i	−0.268491	−	0.0788359i
$701$	−32.8548	−	37.9164i	−1.24091	−	1.43208i	−0.862201	−	0.506567i	$-0.830914\pi$
$701$	−32.8548	−	37.9164i	−1.24091	−	1.43208i	−0.378707	−	0.925517i	$-0.623631\pi$
$702$	1.22724	+	1.41631i	0.0463193	+	0.0534553i
$703$	5.30833	+	1.55867i	0.200208	+	0.0587863i
$704$	5.57212	−	12.2013i	0.210007	−	0.459852i
$705$	5.14188	+	3.30449i	0.193655	+	0.124454i
$706$	27.1020	−	7.95786i	1.02000	−	0.299498i
$707$	2.48915	−	17.3124i	0.0936143	−	0.651102i
$708$	8.97081	+	19.6433i	0.337144	+	0.738241i
$709$	−3.46839	−	24.1232i	−0.130258	−	0.905965i	−0.945216	−	0.326445i	$-0.894149\pi$
$709$	−3.46839	−	24.1232i	−0.130258	−	0.905965i	0.814958	−	0.579520i	$-0.196760\pi$
$710$	9.50964	−	6.11148i	0.356891	−	0.229360i
$711$	0.167400	−	0.193190i	0.00627800	−	0.00724520i
$712$	−4.72442			−0.177055
$713$	31.0400	−	11.7696i	1.16246	−	0.440773i
$714$	−10.2865			−0.384964
$715$	−1.20445	+	1.39001i	−0.0450440	+	0.0519836i
$716$	−5.85609	+	3.76348i	−0.218852	+	0.140648i
$717$	0.738243	+	5.13459i	0.0275702	+	0.191755i
$718$	−10.0893	−	22.0926i	−0.376531	−	0.824488i
$719$	0.171912	−	1.19568i	0.00641125	−	0.0445912i	−0.986365	−	0.164574i	$-0.947375\pi$
$719$	0.171912	−	1.19568i	0.00641125	−	0.0445912i	0.992776	+	0.119983i	$0.0382840\pi$
$720$	2.92853	−	0.859894i	0.109140	−	0.0320463i
$721$	1.36433	+	0.876799i	0.0508101	+	0.0326537i
$722$	−13.9612	+	30.5707i	−0.519582	+	1.13772i
$723$	2.84254	+	0.834644i	0.105715	+	0.0310407i
$724$	12.4347	+	14.3504i	0.462132	+	0.533328i
$725$	30.1469	+	34.7914i	1.11963	+	1.29212i
$726$	5.53741	+	1.62593i	0.205513	+	0.0603440i
$727$	−0.449546	+	0.984370i	−0.0166728	+	0.0365082i	−0.917785	−	0.397077i	$-0.870025\pi$
$727$	−0.449546	+	0.984370i	−0.0166728	+	0.0365082i	0.901112	+	0.433585i	$0.142752\pi$
$728$	−0.594609	−	0.382132i	−0.0220377	−	0.0141628i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.268009	−	1.86404i	0.00991946	−	0.0689913i
$731$	−23.1950	−	50.7899i	−0.857896	−	1.87853i
$732$	1.25109	+	8.70155i	0.0462418	+	0.321619i
$733$	−42.1962	+	27.1179i	−1.55855	+	1.00162i	−0.575608	+	0.817726i	$0.695234\pi$
$733$	−42.1962	+	27.1179i	−1.55855	+	1.00162i	−0.982946	+	0.183896i	$0.941129\pi$
$734$	−2.56131	+	2.95591i	−0.0945399	+	0.109105i
$735$	0.661778			0.0244100
$736$	17.0440	+	30.8151i	0.628251	+	1.13586i
$737$	15.4433			0.568860
$738$	−3.09365	+	3.57026i	−0.113879	+	0.131423i
$739$	−11.1374	+	7.15760i	−0.409697	+	0.263297i	−0.729216	−	0.684283i	$-0.760115\pi$
$739$	−11.1374	+	7.15760i	−0.409697	+	0.263297i	0.319519	+	0.947580i	$0.396479\pi$
$740$	−0.729638	−	5.07474i	−0.0268220	−	0.186551i
$741$	0.474009	+	1.03793i	0.0174131	+	0.0381295i
$742$	1.49580	−	10.4035i	0.0549125	−	0.381925i
$743$	17.7834	−	5.22168i	0.652410	−	0.191565i	0.0612539	−	0.998122i	$-0.480490\pi$
$743$	17.7834	−	5.22168i	0.652410	−	0.191565i	0.591156	+	0.806557i	$0.298672\pi$
$744$	−4.18025	−	2.68648i	−0.153255	−	0.0984913i
$745$	4.57415	−	10.0160i	0.167584	−	0.366958i
$746$	−7.31834	−	2.14886i	−0.267943	−	0.0786753i
$747$	−9.05602	−	10.4512i	−0.331343	−	0.382390i
$748$	16.2122	+	18.7099i	0.592777	+	0.684101i
$749$	4.83461	+	1.41957i	0.176653	+	0.0518700i
$750$	−5.00345	+	10.9560i	−0.182700	+	0.400058i
$751$	12.0709	+	7.75750i	0.440474	+	0.283075i	0.742022	−	0.670376i	$-0.233867\pi$
$751$	12.0709	+	7.75750i	0.440474	+	0.283075i	−0.301548	+	0.953451i	$0.597503\pi$
$752$	40.8715	−	12.0010i	1.49043	−	0.437630i
$753$	−1.55343	+	10.8044i	−0.0566102	+	0.393732i
$754$	−7.85591	−	17.2021i	−0.286096	−	0.626462i
$755$	−1.24121	−	8.63284i	−0.0451724	−	0.314181i
$756$	−1.36522	+	0.877374i	−0.0496526	+	0.0319098i
$757$	−15.6119	+	18.0171i	−0.567425	+	0.654844i	−0.964853	−	0.262790i	$-0.915357\pi$
$757$	−15.6119	+	18.0171i	−0.567425	+	0.654844i	0.397428	+	0.917633i	$0.369903\pi$
$758$	43.8592			1.59304
$759$	10.7931	−	8.17137i	0.391765	−	0.296602i
$760$	0.550564			0.0199711
$761$	18.3309	−	21.1550i	0.664494	−	0.766867i	−0.319010	−	0.947751i	$-0.603351\pi$
$761$	18.3309	−	21.1550i	0.664494	−	0.766867i	0.983504	+	0.180884i	$0.0578960\pi$
$762$	3.55784	−	2.28648i	0.128887	−	0.0828305i
$763$	0.907844	+	6.31419i	0.0328661	+	0.228589i
$764$	14.7376	+	32.2709i	0.533188	+	1.16752i
$765$	−0.508987	+	3.54008i	−0.0184025	+	0.127992i
$766$	5.03932	−	1.47968i	0.182078	−	0.0534629i
$767$	−11.0219	−	7.08335i	−0.397978	−	0.255765i
$768$	8.40820	−	18.4114i	0.303405	−	0.664364i
$769$	30.7925	+	9.04150i	1.11041	+	0.326045i	0.784979	−	0.619522i	$-0.212674\pi$
$769$	30.7925	+	9.04150i	1.11041	+	0.326045i	0.325428	+	0.945567i	$0.394492\pi$
$770$	−2.32840	−	2.68712i	−0.0839098	−	0.0968371i
$771$	6.59221	+	7.60782i	0.237413	+	0.273989i
$772$	−8.14016	−	2.39017i	−0.292971	−	0.0860239i
$773$	−12.7231	+	27.8597i	−0.457619	+	1.00205i	0.530405	+	0.847744i	$0.322040\pi$
$773$	−12.7231	+	27.8597i	−0.457619	+	1.00205i	−0.988024	+	0.154301i	$0.950687\pi$
$774$	−16.5432	−	10.6316i	−0.594631	−	0.382146i
$775$	30.2990	−	8.89660i	1.08837	−	0.319575i
$776$	−0.128396	+	0.893012i	−0.00460914	+	0.0320573i
$777$	−1.98313	−	4.34245i	−0.0711444	−	0.155785i
$778$	−0.803396	−	5.58774i	−0.0288032	−	0.200330i
$779$	−2.41975	+	1.55508i	−0.0866967	+	0.0557166i
$780$	0.692458	−	0.799140i	0.0247940	−	0.0286138i
$781$	−25.3322			−0.906458
$782$	−49.1870	+	3.78630i	−1.75892	+	0.135398i
$783$	10.0910			0.360622
$784$	3.02026	−	3.48557i	0.107867	−	0.124485i
$785$	−4.29379	+	2.75945i	−0.153252	+	0.0984891i
$786$	2.46497	+	17.1442i	0.0879225	+	0.611514i
$787$	−5.49247	−	12.0268i	−0.195785	−	0.428710i	0.786122	−	0.618071i	$-0.212086\pi$
$787$	−5.49247	−	12.0268i	−0.195785	−	0.428710i	−0.981908	+	0.189361i	$0.939358\pi$
$788$	−1.93875	+	13.4843i	−0.0690650	+	0.480358i
$789$	−8.68941	+	2.55144i	−0.309351	+	0.0908337i
$790$	−0.270876	−	0.174082i	−0.00963735	−	0.00619355i
$791$	6.64183	−	14.5436i	0.236156	−	0.517110i
$792$	−1.94430	−	0.570897i	−0.0690876	−	0.0202859i
$793$	−3.49276	−	4.03086i	−0.124032	−	0.143140i
$794$	44.7551	+	51.6501i	1.58830	+	1.83299i
$795$	−3.50633	−	1.02955i	−0.124357	−	0.0365144i
$796$	11.9150	−	26.0901i	0.422315	−	0.924741i
$797$	38.7585	+	24.9086i	1.37290	+	0.882307i	0.998980	−	0.0451550i	$-0.0143782\pi$
$797$	38.7585	+	24.9086i	1.37290	+	0.882307i	0.373917	+	0.927462i	$0.378015\pi$
$798$	−2.11648	+	0.621454i	−0.0749225	+	0.0219992i
$799$	−7.10359	+	49.4066i	−0.251307	+	1.74788i
$800$	13.9156	+	30.4709i	0.491990	+	1.07731i
$801$	−0.936591	−	6.51413i	−0.0330928	−	0.230166i
$802$	−32.1917	+	20.6883i	−1.13673	+	0.730531i
$803$	−2.76366	+	3.18943i	−0.0975273	+	0.112553i
$804$	−8.87856			−0.313123
$805$	3.16441	−	0.243589i	0.111531	−	0.00858538i
$806$	−12.9720			−0.456921
$807$	4.83637	−	5.58147i	0.170248	−	0.196477i
$808$	−10.5627	+	6.78827i	−0.371596	+	0.238810i
$809$	−0.829461	−	5.76903i	−0.0291623	−	0.202828i	0.970031	−	0.242980i	$-0.0781249\pi$
$809$	−0.829461	−	5.76903i	−0.0291623	−	0.202828i	−0.999194	+	0.0401518i	$0.987216\pi$
$810$	0.523262	+	1.14578i	0.0183855	+	0.0402587i
$811$	2.48582	−	17.2893i	0.0872889	−	0.607108i	−0.898482	−	0.439011i	$-0.855329\pi$
$811$	2.48582	−	17.2893i	0.0872889	−	0.607108i	0.985771	−	0.168097i	$-0.0537621\pi$
$812$	15.7127	−	4.61367i	0.551408	−	0.161908i
$813$	20.4399	+	13.1359i	0.716858	+	0.460697i
$814$	−10.6549	+	23.3309i	−0.373453	+	0.817749i
$815$	10.3411	+	3.03643i	0.362234	+	0.106361i
$816$	16.3226	+	18.8373i	0.571405	+	0.659437i
$817$	−7.84085	−	9.04882i	−0.274317	−	0.316578i
$818$	−31.3789	−	9.21367i	−1.09714	−	0.322148i
$819$	0.409015	−	0.895617i	0.0142921	−	0.0312954i
$820$	2.24239	+	1.44110i	0.0783078	+	0.0503254i
$821$	−26.8191	+	7.87481i	−0.935994	+	0.274833i	−0.713944	−	0.700203i	$-0.753093\pi$
$821$	−26.8191	+	7.87481i	−0.935994	+	0.274833i	−0.222050	+	0.975035i	$0.571275\pi$
$822$	4.96028	−	34.4995i	0.173010	−	1.20331i
$823$	2.15759	+	4.72447i	0.0752090	+	0.164685i	0.943502	−	0.331367i	$-0.107510\pi$
$823$	2.15759	+	4.72447i	0.0752090	+	0.164685i	−0.868293	+	0.496052i	$0.834783\pi$
$824$	−0.165687	−	1.15238i	−0.00577200	−	0.0401451i
$825$	10.8333	−	6.96212i	0.377166	−	0.242390i
$826$	16.5862	−	19.1415i	0.577107	−	0.666018i
$827$	26.7190			0.929110			0.464555	−	0.885544i	$-0.346214\pi$
$827$	26.7190			0.929110			0.464555	+	0.885544i	$0.346214\pi$
$828$	−6.20511	+	4.69784i	−0.215643	+	0.163261i
$829$	2.51276			0.0872718			0.0436359	−	0.999047i	$-0.486106\pi$
$829$	2.51276			0.0872718			0.0436359	+	0.999047i	$0.486106\pi$
$830$	−11.4071	+	13.1645i	−0.395945	+	0.456945i
$831$	−4.46848	+	2.87172i	−0.155010	+	0.0996188i
$832$	−0.665845	−	4.63105i	−0.0230840	−	0.160553i
$833$	2.24505	+	4.91598i	0.0777865	+	0.170329i
$834$	−5.56372	+	38.6965i	−0.192656	+	1.33995i
$835$	7.79370	−	2.28844i	0.269712	−	0.0791946i
$836$	4.46604	+	2.87015i	0.154461	+	0.0992663i
$837$	2.87547	−	6.29641i	0.0993909	−	0.217636i
$838$	−36.1034	−	10.6009i	−1.24717	−	0.366203i
$839$	−21.0274	−	24.2669i	−0.725947	−	0.837787i	0.266062	−	0.963956i	$-0.414277\pi$
$839$	−21.0274	−	24.2669i	−0.725947	−	0.837787i	−0.992009	+	0.126169i	$0.959732\pi$
$840$	−0.311107	−	0.359036i	−0.0107342	−	0.0123879i
$841$	−69.8778	−	20.5180i	−2.40958	−	0.707517i
$842$	6.59269	−	14.4360i	0.227199	−	0.497496i
$843$	8.95955	+	5.75795i	0.308583	+	0.198314i
$844$	26.6546	−	7.82649i	0.917488	−	0.269399i
$845$	1.13305	−	7.88053i	0.0389781	−	0.271098i
$846$	7.30281	+	15.9909i	0.251076	+	0.549780i
$847$	−0.431510	−	3.00122i	−0.0148268	−	0.103123i
$848$	−21.4250	+	13.7690i	−0.735738	+	0.472830i
$849$	−11.4314	+	13.1926i	−0.392326	+	0.452768i
$850$	−46.9277			−1.60961
$851$	−11.0811	−	20.0343i	−0.379855	−	0.686766i
$852$	14.5639			0.498950
$853$	19.9822	−	23.0607i	0.684177	−	0.789582i	−0.302347	−	0.953198i	$-0.597770\pi$
$853$	19.9822	−	23.0607i	0.684177	−	0.789582i	0.986524	+	0.163616i	$0.0523157\pi$
$854$	8.67392	−	5.57439i	0.296815	−	0.190752i
$855$	0.109146	+	0.759130i	0.00373273	+	0.0259617i
$856$	−1.50262	−	3.29029i	−0.0513587	−	0.112460i
$857$	−0.345551	+	2.40336i	−0.0118038	+	0.0820972i	−0.994872	−	0.101144i	$-0.967750\pi$
$857$	−0.345551	+	2.40336i	−0.0118038	+	0.0820972i	0.983068	+	0.183241i	$0.0586589\pi$
$858$	−5.07570	+	1.49036i	−0.173281	+	0.0508800i
$859$	−31.1248	−	20.0027i	−1.06197	−	0.682484i	−0.111642	−	0.993748i	$-0.535611\pi$
$859$	−31.1248	−	20.0027i	−1.06197	−	0.682484i	−0.950323	+	0.311265i	$0.899247\pi$
$860$	−4.60932	+	10.0930i	−0.157177	+	0.344169i
$861$	2.38143	+	0.699252i	0.0811591	+	0.0238305i
$862$	−10.9015	−	12.5810i	−0.371306	−	0.428510i
$863$	−14.4967	−	16.7301i	−0.493474	−	0.569499i	0.453317	−	0.891349i	$-0.350241\pi$
$863$	−14.4967	−	16.7301i	−0.493474	−	0.569499i	−0.946791	+	0.321850i	$0.895695\pi$
$864$	7.04532	+	2.06869i	0.239687	+	0.0703784i
$865$	5.86188	−	12.8357i	0.199310	−	0.436428i
$866$	−48.5060	−	31.1729i	−1.64830	−	1.05930i
$867$	−11.7127	+	3.43915i	−0.397783	+	0.116800i
$868$	1.59865	−	11.1189i	0.0542617	−	0.377399i
$869$	0.299752	+	0.656365i	0.0101684	+	0.0222657i
$870$	−1.80892	−	12.5813i	−0.0613282	−	0.426547i
$871$	4.53158	−	2.91227i	0.153547	−	0.0986785i
$872$	2.99887	−	3.46088i	0.101555	−	0.117200i
$873$	−1.25676			−0.0425349
$874$	−9.89159	+	3.75064i	−0.334588	+	0.126867i
$875$	6.32795			0.213924
$876$	1.58887	−	1.83365i	0.0536828	−	0.0619533i
$877$	−14.4893	+	9.31169i	−0.489268	+	0.314433i	−0.761911	−	0.647682i	$-0.775739\pi$
$877$	−14.4893	+	9.31169i	−0.489268	+	0.314433i	0.272643	+	0.962115i	$0.412102\pi$
$878$	−1.79177	−	12.4621i	−0.0604695	−	0.420574i
$879$	−4.58282	−	10.0350i	−0.154575	−	0.338472i
$880$	−1.22611	+	8.52780i	−0.0413323	+	0.287472i
$881$	40.9552	−	12.0255i	1.37982	−	0.405151i	0.494112	−	0.869399i	$-0.335493\pi$
$881$	40.9552	−	12.0255i	1.37982	−	0.405151i	0.885705	+	0.464248i	$0.153675\pi$
$882$	1.60122	+	1.02904i	0.0539160	+	0.0346497i
$883$	−17.8109	+	39.0005i	−0.599386	+	1.31247i	0.330216	+	0.943906i	$0.392879\pi$
$883$	−17.8109	+	39.0005i	−0.599386	+	1.31247i	−0.929601	+	0.368566i	$0.879849\pi$
$884$	8.28551	+	2.43284i	0.278672	+	0.0818254i
$885$	−5.76679	−	6.65523i	−0.193848	−	0.223713i
$886$	8.70000	+	10.0403i	0.292282	+	0.337312i
$887$	43.5559	+	12.7892i	1.46246	+	0.429418i	0.913641	−	0.406522i	$-0.133258\pi$
$887$	43.5559	+	12.7892i	1.46246	+	0.429418i	0.548822	+	0.835939i	$0.315077\pi$
$888$	−1.42364	+	3.11733i	−0.0477742	+	0.104611i
$889$	−1.86922	−	1.20128i	−0.0626918	−	0.0402895i
$890$	−7.95387	+	2.33547i	−0.266614	+	0.0782850i
$891$	0.401719	−	2.79402i	0.0134581	−	0.0936032i
$892$	3.03347	+	6.64237i	0.101568	+	0.222403i
$893$	1.52328	+	10.5947i	0.0509748	+	0.354537i
$894$	26.6421	−	17.1218i	0.891044	−	0.572639i
$895$	1.85894	−	2.14533i	0.0621376	−	0.0717106i
$896$	−5.64088			−0.188448
$897$	1.62612	−	4.43311i	0.0542945	−	0.148017i
$898$	−17.4278			−0.581575
$899$	−45.7414	+	52.7884i	−1.52556	+	1.76059i
$900$	−6.22821	+	4.00263i	−0.207607	+	0.133421i
$901$	−4.24711	−	29.5393i	−0.141492	−	0.984096i
$902$	−5.53957	−	12.1300i	−0.184448	−	0.403884i
$903$	−1.47034	+	10.2264i	−0.0489298	+	0.340314i
$904$	−11.0127	+	3.23363i	−0.366279	+	0.107549i
$905$	−6.51401	−	4.18630i	−0.216533	−	0.139157i
$906$	10.4206	−	22.8179i	0.346200	−	0.758073i
$907$	16.9926	+	4.98947i	0.564229	+	0.165673i	0.551394	−	0.834245i	$-0.314096\pi$
$907$	16.9926	+	4.98947i	0.564229	+	0.165673i	0.0128353	+	0.999918i	$0.495914\pi$
$908$	4.07827	+	4.70658i	0.135342	+	0.156193i
$909$	−11.4538	−	13.2184i	−0.379899	−	0.438427i
$910$	−1.18997	−	0.349406i	−0.0394470	−	0.0115827i
$911$	−17.2027	+	37.6687i	−0.569951	+	1.24802i	0.376872	+	0.926265i	$0.377000\pi$
$911$	−17.2027	+	37.6687i	−0.569951	+	1.24802i	−0.946823	+	0.321754i	$0.895728\pi$
$912$	4.49645	+	2.88969i	0.148892	+	0.0956873i
$913$	37.4544	−	10.9976i	1.23956	−	0.363968i
$914$	−4.57121	+	31.7934i	−0.151202	+	1.05163i
$915$	−1.48922	−	3.26093i	−0.0492320	−	0.107803i
$916$	5.66032	+	39.3684i	0.187022	+	1.30077i
$917$	7.65532	−	4.91977i	0.252801	−	0.162465i
$918$	−6.73625	+	7.77405i	−0.222329	+	0.256582i
$919$	49.4621			1.63161			0.815803	−	0.578330i	$-0.196296\pi$
$919$	49.4621			1.63161			0.815803	+	0.578330i	$0.196296\pi$
$920$	−1.61977	−	1.60229i	−0.0534022	−	0.0528258i
$921$	9.54959			0.314670
$922$	14.2264	−	16.4182i	0.468522	−	0.540704i
$923$	−7.43334	+	4.77712i	−0.244671	+	0.157241i
$924$	−0.651927	−	4.53425i	−0.0214468	−	0.149166i
$925$	−9.04714	−	19.8105i	−0.297468	−	0.651364i
$926$	−0.216371	+	1.50489i	−0.00711039	+	0.0494538i
$927$	1.55608	−	0.456907i	0.0511085	−	0.0150068i
$928$	−62.3332	−	40.0591i	−2.04619	−	1.31500i
$929$	8.57665	−	18.7803i	0.281391	−	0.616160i	−0.715177	−	0.698944i	$-0.753654\pi$
$929$	8.57665	−	18.7803i	0.281391	−	0.616160i	0.996568	+	0.0827836i	$0.0263810\pi$
$930$	−8.36576	−	2.45641i	−0.274324	−	0.0805488i
$931$	0.758921	+	0.875841i	0.0248726	+	0.0287045i
$932$	−18.0930	−	20.8804i	−0.592656	−	0.683961i
$933$	0.625823	+	0.183758i	0.0204885	+	0.00601597i
$934$	−21.5008	+	47.0803i	−0.703529	+	1.54051i
$935$	−8.49290	−	5.45806i	−0.277748	−	0.178498i
$936$	−0.678183	+	0.199132i	−0.0221671	+	0.00650885i
$937$	1.46739	−	10.2060i	0.0479377	−	0.333414i	−0.951713	−	0.306989i	$-0.900679\pi$
$937$	1.46739	−	10.2060i	0.0479377	−	0.333414i	0.999651	−	0.0264251i	$-0.00841236\pi$
$938$	4.32587	+	9.47233i	0.141245	+	0.309282i
$939$	−2.62422	−	18.2518i	−0.0856380	−	0.595626i
$940$	8.34446	−	5.36266i	0.272166	−	0.174911i
$941$	−37.7958	+	43.6187i	−1.23211	+	1.42193i	−0.359761	+	0.933045i	$0.617142\pi$
$941$	−37.7958	+	43.6187i	−1.23211	+	1.42193i	−0.872348	+	0.488885i	$0.837404\pi$
$942$	−14.6800			−0.478301
$943$	11.6447	+	2.46704i	0.379202	+	0.0803379i
$944$	−61.3718			−1.99748
$945$	0.433372	−	0.500138i	0.0140976	−	0.0162695i
$946$	46.6972	−	30.0105i	1.51826	−	0.975725i
$947$	−7.01561	−	48.7946i	−0.227977	−	1.58561i	−0.706614	−	0.707599i	$-0.749778\pi$
$947$	−7.01561	−	48.7946i	−0.227977	−	1.58561i	0.478637	−	0.878013i	$-0.341131\pi$
$948$	−0.172332	−	0.377354i	−0.00559708	−	0.0122559i
$949$	−0.209493	+	1.45705i	−0.00680043	+	0.0472980i
$950$	−9.65548	+	2.83511i	−0.313265	+	0.0919830i
$951$	−26.2862	−	16.8931i	−0.852388	−	0.547796i
$952$	1.61167	−	3.52906i	0.0522344	−	0.114377i
$953$	−19.0595	−	5.59637i	−0.617397	−	0.181284i	−0.0419454	−	0.999120i	$-0.513356\pi$
$953$	−19.0595	−	5.59637i	−0.617397	−	0.181284i	−0.575452	+	0.817836i	$0.695174\pi$
$954$	−6.88291	−	7.94330i	−0.222843	−	0.257174i
$955$	−9.47392	−	10.9335i	−0.306569	−	0.353799i
$956$	8.07732	+	2.37171i	0.261239	+	0.0767067i
$957$	−11.8328	+	25.9102i	−0.382501	+	0.837559i
$958$	25.8416	+	16.6074i	0.834905	+	0.536561i
$959$	−17.5701	+	5.15903i	−0.567367	+	0.166594i
$960$	0.447536	−	3.11268i	0.0144442	−	0.100461i
$961$	7.02595	+	15.3847i	0.226644	+	0.496280i
$962$	1.27321	+	8.85538i	0.0410500	+	0.285509i
$963$	4.23884	−	2.72414i	0.136595	−	0.0877841i
$964$	3.14840	−	3.63344i	0.101403	−	0.117025i
$965$	3.45961			0.111369
$966$	8.03531	+	4.33118i	0.258532	+	0.139353i
$967$	−31.0496			−0.998488			−0.499244	−	0.866461i	$-0.666389\pi$
$967$	−31.0496			−0.998488			−0.499244	+	0.866461i	$0.666389\pi$
$968$	−1.42540	+	1.64500i	−0.0458142	+	0.0528724i
$969$	−5.26889	+	3.38611i	−0.169261	+	0.108777i
$970$	0.225289	+	1.56692i	0.00723358	+	0.0503106i
$971$	12.0438	+	26.3723i	0.386504	+	0.846326i	0.998462	+	0.0554361i	$0.0176549\pi$
$971$	12.0438	+	26.3723i	0.386504	+	0.846326i	−0.611958	+	0.790890i	$0.709618\pi$
$972$	−0.230954	+	1.60632i	−0.00740787	+	0.0515229i
$973$	19.7075	−	5.78665i	0.631794	−	0.185512i
$974$	3.00964	+	1.93418i	0.0964352	+	0.0619751i
$975$	1.86595	−	4.08585i	0.0597581	−	0.130852i
$976$	−23.9718	−	7.03876i	−0.767320	−	0.225305i
$977$	−37.4285	−	43.1947i	−1.19744	−	1.38192i	−0.904875	−	0.425677i	$-0.860036\pi$
$977$	−37.4285	−	43.1947i	−1.19744	−	1.38192i	−0.292567	−	0.956245i	$-0.594510\pi$
$978$	20.2996	+	23.4270i	0.649110	+	0.749113i
$979$	17.8244	+	5.23371i	0.569669	+	0.167270i
$980$	0.446139	−	0.976909i	0.0142514	−	0.0312062i
$981$	5.36646	+	3.44881i	0.171338	+	0.110112i
$982$	−8.05232	+	2.36437i	−0.256960	+	0.0754502i
$983$	−7.55378	+	52.5377i	−0.240928	+	1.67569i	0.406566	+	0.913621i	$0.366726\pi$
$983$	−7.55378	+	52.5377i	−0.240928	+	1.67569i	−0.647494	+	0.762070i	$0.724183\pi$
$984$	−0.740163	−	1.62073i	−0.0235955	−	0.0516670i
$985$	−0.790601	−	5.49875i	−0.0251906	−	0.175205i
$986$	87.3232	−	56.1192i	2.78094	−	1.78720i
$987$	6.04829	−	6.98009i	0.192519	−	0.222179i
$988$	1.85174			0.0589117
$989$	−3.26652	+	49.4407i	−0.103869	+	1.57212i
$990$	−3.55557			−0.113003
$991$	9.46610	−	10.9245i	0.300700	−	0.347027i	−0.585211	−	0.810881i	$-0.698988\pi$
$991$	9.46610	−	10.9245i	0.300700	−	0.347027i	0.885912	+	0.463854i	$0.153534\pi$
$992$	−42.7576	+	27.4786i	−1.35755	+	0.872447i
$993$	3.92011	+	27.2649i	0.124401	+	0.865227i
$994$	−7.09590	−	15.5379i	−0.225068	−	0.492831i
$995$	−1.66455	+	11.5772i	−0.0527698	+	0.367022i
$996$	−21.5331	+	6.32269i	−0.682302	+	0.200342i
$997$	30.9728	+	19.9050i	0.980917	+	0.630397i	0.929711	−	0.368291i	$-0.120057\pi$
$997$	30.9728	+	19.9050i	0.980917	+	0.630397i	0.0512066	+	0.998688i	$0.483693\pi$
$998$	22.1023	−	48.3973i	0.699636	−	1.53199i
$999$	−4.58048	−	1.34495i	−0.144920	−	0.0425523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.85.2	✓	80
23.13	even	11	inner	483.2.q.f.358.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.85.2	✓	80	1.1	even	1	trivial
483.2.q.f.358.2	yes	80	23.13	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24645 + 1.43848i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.230954 - 1.60632i) q^{4} +(0.274912 + 0.601974i) q^{5} +(-0.270879 + 1.88400i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-0.603914 - 0.388112i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.24645 + 1.43848i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.230954 - 1.60632i) q^{4} +(0.274912 + 0.601974i) q^{5} +(-0.270879 + 1.88400i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-0.603914 - 0.388112i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-1.20859 - 0.354874i) q^{10} +(1.84851 + 2.13329i) q^{11} +(-1.06274 - 1.22646i) q^{12} +(0.944710 + 0.277392i) q^{13} +(-0.790691 + 1.73137i) q^{14} +(0.556723 + 0.357784i) q^{15} +(4.42525 - 1.29937i) q^{16} +(-0.769121 + 5.34936i) q^{17} +(0.790691 + 1.73137i) q^{18} +(0.164929 + 1.14711i) q^{19} +(0.903473 - 0.580627i) q^{20} +(0.654861 - 0.755750i) q^{21} -5.37276 q^{22} +(2.85316 - 3.85480i) q^{23} -0.717874 q^{24} +(2.98751 - 3.44777i) q^{25} +(-1.57655 + 1.01319i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-0.674153 - 1.47619i) q^{28} +(-1.43610 + 9.98827i) q^{29} +(-1.20859 + 0.354874i) q^{30} +(5.82310 + 3.74228i) q^{31} +(-3.05029 + 6.67920i) q^{32} +(2.70841 + 0.795261i) q^{33} +(-6.73625 - 7.77405i) q^{34} +(0.433372 + 0.500138i) q^{35} +(-1.55711 - 0.457207i) q^{36} +(1.98313 - 4.34245i) q^{37} +(-1.85566 - 1.19256i) q^{38} +(0.944710 - 0.277392i) q^{39} +(0.0676099 - 0.470237i) q^{40} +(1.03105 + 2.25768i) q^{41} +(0.270879 + 1.88400i) q^{42} +(-8.69148 + 5.58567i) q^{43} +(2.99984 - 3.46200i) q^{44} +0.661778 q^{45} +(1.98873 + 8.90900i) q^{46} +9.23599 q^{47} +(3.02026 - 3.48557i) q^{48} +(0.841254 - 0.540641i) q^{49} +(1.23576 + 8.59492i) q^{50} +(2.24505 + 4.91598i) q^{51} +(0.227396 - 1.58157i) q^{52} +(-5.29835 + 1.55574i) q^{53} +(1.60122 + 1.02904i) q^{54} +(-0.776009 + 1.69922i) q^{55} +(-0.688795 - 0.202249i) q^{56} +(0.758921 + 0.875841i) q^{57} +(-12.5779 - 14.5156i) q^{58} +(-12.7678 - 3.74895i) q^{59} +(0.446139 - 0.976909i) q^{60} +(-4.55712 - 2.92868i) q^{61} +(-12.6414 + 3.71184i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-1.97401 - 4.32247i) q^{64} +(0.0927297 + 0.644949i) q^{65} +(-4.51985 + 2.90473i) q^{66} +(3.58274 - 4.13470i) q^{67} +8.77043 q^{68} +(0.316169 - 4.78540i) q^{69} -1.25961 q^{70} +(-5.87692 + 6.78233i) q^{71} +(-0.603914 + 0.388112i) q^{72} +(0.212771 + 1.47986i) q^{73} +(3.77464 + 8.26532i) q^{74} +(0.649247 - 4.51562i) q^{75} +(1.80454 - 0.529859i) q^{76} +(2.37465 + 1.52609i) q^{77} +(-0.778509 + 1.70470i) q^{78} +(0.245273 + 0.0720186i) q^{79} +(1.99874 + 2.30667i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-4.53277 - 1.33094i) q^{82} +(5.74475 - 12.5792i) q^{83} +(-1.36522 - 0.877374i) q^{84} +(-3.43161 + 1.00761i) q^{85} +(2.79861 - 19.4647i) q^{86} +(4.19194 + 9.17908i) q^{87} +(-0.288384 - 2.00575i) q^{88} +(5.53639 - 3.55802i) q^{89} +(-0.824870 + 0.951951i) q^{90} +0.984593 q^{91} +(-6.85101 - 3.69281i) q^{92} +6.92193 q^{93} +(-11.5122 + 13.2857i) q^{94} +(-0.645188 + 0.414637i) q^{95} +(1.04498 + 7.26801i) q^{96} +(-0.522077 - 1.14319i) q^{97} +(-0.270879 + 1.88400i) q^{98} +(2.70841 - 0.795261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

L-functions

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